id	sid	tid	token	lemma	pos
10_1101-2021_01_08_425885	1	1	Computing	compute	VBG
10_1101-2021_01_08_425885	1	2	the	the	DT
10_1101-2021_01_08_425885	1	3	Riemannian	riemannian	JJ
10_1101-2021_01_08_425885	1	4	curvature	curvature	NN
10_1101-2021_01_08_425885	1	5	of	of	IN
10_1101-2021_01_08_425885	1	6	image	image	NN
10_1101-2021_01_08_425885	1	7	patch	patch	NN
10_1101-2021_01_08_425885	1	8	and	and	CC
10_1101-2021_01_08_425885	1	9	single	single	JJ
10_1101-2021_01_08_425885	1	10	-	-	HYPH
10_1101-2021_01_08_425885	1	11	cell	cell	NN
10_1101-2021_01_08_425885	1	12	RNA	RNA	NNP
10_1101-2021_01_08_425885	1	13	sequencing	sequence	VBG
10_1101-2021_01_08_425885	1	14	data	data	NN
10_1101-2021_01_08_425885	1	15	manifolds	manifold	NNS
10_1101-2021_01_08_425885	1	16	using	use	VBG
10_1101-2021_01_08_425885	1	17	extrinsic	extrinsic	JJ
10_1101-2021_01_08_425885	1	18	differential	differential	NN
10_1101-2021_01_08_425885	1	19	geometry	geometry	NN
10_1101-2021_01_08_425885	1	20	Computing	compute	VBG
10_1101-2021_01_08_425885	1	21	the	the	DT
10_1101-2021_01_08_425885	1	22	Riemannian	riemannian	JJ
10_1101-2021_01_08_425885	1	23	curvature	curvature	NN
10_1101-2021_01_08_425885	1	24	of	of	IN
10_1101-2021_01_08_425885	1	25	image	image	NN
10_1101-2021_01_08_425885	1	26	patch	patch	NN
10_1101-2021_01_08_425885	1	27	and	and	CC
10_1101-2021_01_08_425885	1	28	single	single	JJ
10_1101-2021_01_08_425885	1	29	-	-	HYPH
10_1101-2021_01_08_425885	1	30	cell	cell	NN
10_1101-2021_01_08_425885	1	31	RNA	RNA	NNP
10_1101-2021_01_08_425885	1	32	sequencing	sequence	VBG
10_1101-2021_01_08_425885	1	33	data	data	NN
10_1101-2021_01_08_425885	1	34	manifolds	manifold	NNS
10_1101-2021_01_08_425885	1	35	using	use	VBG
10_1101-2021_01_08_425885	1	36	extrinsic	extrinsic	JJ
10_1101-2021_01_08_425885	1	37	differential	differential	NN
10_1101-2021_01_08_425885	1	38	geometry	geometry	NN
10_1101-2021_01_08_425885	1	39	Duluxan	Duluxan	NNP
10_1101-2021_01_08_425885	1	40	Sritharan∗1,2	Sritharan∗1,2	NNP
10_1101-2021_01_08_425885	1	41	,	,	,
10_1101-2021_01_08_425885	1	42	Shu	Shu	NNP
10_1101-2021_01_08_425885	1	43	Wang∗1,3	Wang∗1,3	NNP
10_1101-2021_01_08_425885	1	44	,	,	,
10_1101-2021_01_08_425885	1	45	and	and	CC
10_1101-2021_01_08_425885	1	46	Sahand	Sahand	NNP
10_1101-2021_01_08_425885	1	47	Hormoz†2,4,5	Hormoz†2,4,5	NNP
10_1101-2021_01_08_425885	1	48	1Harvard	1Harvard	NNP
10_1101-2021_01_08_425885	1	49	Graduate	Graduate	NNP
10_1101-2021_01_08_425885	1	50	Program	Program	NNP
10_1101-2021_01_08_425885	1	51	in	in	IN
10_1101-2021_01_08_425885	1	52	Biophysics	Biophysics	NNP
10_1101-2021_01_08_425885	1	53	,	,	,
10_1101-2021_01_08_425885	1	54	Harvard	Harvard	NNP
10_1101-2021_01_08_425885	1	55	University	University	NNP
10_1101-2021_01_08_425885	1	56	,	,	,
10_1101-2021_01_08_425885	1	57	Cambridge	Cambridge	NNP
10_1101-2021_01_08_425885	1	58	,	,	,
10_1101-2021_01_08_425885	1	59	MA	MA	NNP
10_1101-2021_01_08_425885	1	60	,	,	,
10_1101-2021_01_08_425885	1	61	USA	USA	NNP
10_1101-2021_01_08_425885	1	62	2Department	2department	CD
10_1101-2021_01_08_425885	1	63	of	of	IN
10_1101-2021_01_08_425885	1	64	Data	Data	NNP
10_1101-2021_01_08_425885	1	65	Sciences	Sciences	NNPS
10_1101-2021_01_08_425885	1	66	,	,	,
10_1101-2021_01_08_425885	1	67	Dana	Dana	NNP
10_1101-2021_01_08_425885	1	68	-	-	HYPH
10_1101-2021_01_08_425885	1	69	Farber	Farber	NNP
10_1101-2021_01_08_425885	1	70	Cancer	Cancer	NNP
10_1101-2021_01_08_425885	1	71	Institute	Institute	NNP
10_1101-2021_01_08_425885	1	72	,	,	,
10_1101-2021_01_08_425885	1	73	Boston	Boston	NNP
10_1101-2021_01_08_425885	1	74	,	,	,
10_1101-2021_01_08_425885	1	75	MA	MA	NNP
10_1101-2021_01_08_425885	1	76	,	,	,
10_1101-2021_01_08_425885	1	77	USA	USA	NNP
10_1101-2021_01_08_425885	1	78	3Laboratory	3laboratory	CD
10_1101-2021_01_08_425885	1	79	of	of	IN
10_1101-2021_01_08_425885	1	80	Systems	Systems	NNP
10_1101-2021_01_08_425885	1	81	Pharmacology	Pharmacology	NNP
10_1101-2021_01_08_425885	1	82	,	,	,
10_1101-2021_01_08_425885	1	83	Harvard	Harvard	NNP
10_1101-2021_01_08_425885	1	84	Medical	Medical	NNP
10_1101-2021_01_08_425885	1	85	School	School	NNP
10_1101-2021_01_08_425885	1	86	,	,	,
10_1101-2021_01_08_425885	1	87	Boston	Boston	NNP
10_1101-2021_01_08_425885	1	88	,	,	,
10_1101-2021_01_08_425885	1	89	MA	MA	NNP
10_1101-2021_01_08_425885	1	90	,	,	,
10_1101-2021_01_08_425885	1	91	USA	USA	NNP
10_1101-2021_01_08_425885	1	92	4Department	4department	CD
10_1101-2021_01_08_425885	1	93	of	of	IN
10_1101-2021_01_08_425885	1	94	Systems	Systems	NNP
10_1101-2021_01_08_425885	1	95	Biology	Biology	NNP
10_1101-2021_01_08_425885	1	96	,	,	,
10_1101-2021_01_08_425885	1	97	Harvard	Harvard	NNP
10_1101-2021_01_08_425885	1	98	Medical	Medical	NNP
10_1101-2021_01_08_425885	1	99	School	School	NNP
10_1101-2021_01_08_425885	1	100	,	,	,
10_1101-2021_01_08_425885	1	101	Boston	Boston	NNP
10_1101-2021_01_08_425885	1	102	,	,	,
10_1101-2021_01_08_425885	1	103	MA	MA	NNP
10_1101-2021_01_08_425885	1	104	,	,	,
10_1101-2021_01_08_425885	1	105	USA	USA	NNP
10_1101-2021_01_08_425885	1	106	5Broad	5Broad	NNP
10_1101-2021_01_08_425885	1	107	Institute	Institute	NNP
10_1101-2021_01_08_425885	1	108	of	of	IN
10_1101-2021_01_08_425885	1	109	MIT	MIT	NNP
10_1101-2021_01_08_425885	1	110	and	and	CC
10_1101-2021_01_08_425885	1	111	Harvard	Harvard	NNP
10_1101-2021_01_08_425885	1	112	,	,	,
10_1101-2021_01_08_425885	1	113	Cambridge	Cambridge	NNP
10_1101-2021_01_08_425885	1	114	,	,	,
10_1101-2021_01_08_425885	1	115	MA	MA	NNP
10_1101-2021_01_08_425885	1	116	,	,	,
10_1101-2021_01_08_425885	1	117	USA	USA	NNP
10_1101-2021_01_08_425885	1	118	Abstract	Abstract	NNP
10_1101-2021_01_08_425885	1	119	Most	Most	NNP
10_1101-2021_01_08_425885	1	120	high	high	JJ
10_1101-2021_01_08_425885	1	121	-	-	HYPH
10_1101-2021_01_08_425885	1	122	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	1	123	datasets	dataset	NNS
10_1101-2021_01_08_425885	1	124	are	be	VBP
10_1101-2021_01_08_425885	1	125	thought	think	VBN
10_1101-2021_01_08_425885	1	126	to	to	TO
10_1101-2021_01_08_425885	1	127	be	be	VB
10_1101-2021_01_08_425885	1	128	inherently	inherently	RB
10_1101-2021_01_08_425885	1	129	low	low	JJ
10_1101-2021_01_08_425885	1	130	-	-	HYPH
10_1101-2021_01_08_425885	1	131	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	1	132	,	,	,
10_1101-2021_01_08_425885	1	133	that	that	RB
10_1101-2021_01_08_425885	1	134	is	is	RB
10_1101-2021_01_08_425885	1	135	,	,	,
10_1101-2021_01_08_425885	1	136	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	1	137	are	be	VBP
10_1101-2021_01_08_425885	1	138	constrained	constrain	VBN
10_1101-2021_01_08_425885	1	139	to	to	TO
10_1101-2021_01_08_425885	1	140	lie	lie	VB
10_1101-2021_01_08_425885	1	141	on	on	IN
10_1101-2021_01_08_425885	1	142	a	a	DT
10_1101-2021_01_08_425885	1	143	low	low	JJ
10_1101-2021_01_08_425885	1	144	-	-	HYPH
10_1101-2021_01_08_425885	1	145	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	1	146	manifold	manifold	NN
10_1101-2021_01_08_425885	1	147	embedded	embed	VBN
10_1101-2021_01_08_425885	1	148	in	in	IN
10_1101-2021_01_08_425885	1	149	a	a	DT
10_1101-2021_01_08_425885	1	150	high	high	JJ
10_1101-2021_01_08_425885	1	151	-	-	HYPH
10_1101-2021_01_08_425885	1	152	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	1	153	ambient	ambient	JJ
10_1101-2021_01_08_425885	1	154	space	space	NN
10_1101-2021_01_08_425885	1	155	.	.	.
10_1101-2021_01_08_425885	2	1	Here	here	RB
10_1101-2021_01_08_425885	2	2	we	-PRON-	PRP
10_1101-2021_01_08_425885	2	3	study	study	VBP
10_1101-2021_01_08_425885	2	4	the	the	DT
10_1101-2021_01_08_425885	2	5	viability	viability	NN
10_1101-2021_01_08_425885	2	6	of	of	IN
10_1101-2021_01_08_425885	2	7	two	two	CD
10_1101-2021_01_08_425885	2	8	approaches	approach	NNS
10_1101-2021_01_08_425885	2	9	from	from	IN
10_1101-2021_01_08_425885	2	10	differential	differential	NN
10_1101-2021_01_08_425885	2	11	geometry	geometry	NN
10_1101-2021_01_08_425885	2	12	to	to	TO
10_1101-2021_01_08_425885	2	13	estimate	estimate	VB
10_1101-2021_01_08_425885	2	14	the	the	DT
10_1101-2021_01_08_425885	2	15	Riemannian	riemannian	JJ
10_1101-2021_01_08_425885	2	16	curvature	curvature	NN
10_1101-2021_01_08_425885	2	17	of	of	IN
10_1101-2021_01_08_425885	2	18	these	these	DT
10_1101-2021_01_08_425885	2	19	low	low	JJ
10_1101-2021_01_08_425885	2	20	-	-	HYPH
10_1101-2021_01_08_425885	2	21	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	2	22	manifolds	manifold	NNS
10_1101-2021_01_08_425885	2	23	.	.	.
10_1101-2021_01_08_425885	3	1	The	the	DT
10_1101-2021_01_08_425885	3	2	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	3	3	approach	approach	NN
10_1101-2021_01_08_425885	3	4	relates	relate	VBZ
10_1101-2021_01_08_425885	3	5	curvature	curvature	JJ
10_1101-2021_01_08_425885	3	6	to	to	IN
10_1101-2021_01_08_425885	3	7	the	the	DT
10_1101-2021_01_08_425885	3	8	Laplace	Laplace	NNP
10_1101-2021_01_08_425885	3	9	-	-	HYPH
10_1101-2021_01_08_425885	3	10	Beltrami	Beltrami	NNP
10_1101-2021_01_08_425885	3	11	operator	operator	NN
10_1101-2021_01_08_425885	3	12	using	use	VBG
10_1101-2021_01_08_425885	3	13	the	the	DT
10_1101-2021_01_08_425885	3	14	heat	heat	NN
10_1101-2021_01_08_425885	3	15	-	-	HYPH
10_1101-2021_01_08_425885	3	16	trace	trace	NN
10_1101-2021_01_08_425885	3	17	expansion	expansion	NN
10_1101-2021_01_08_425885	3	18	,	,	,
10_1101-2021_01_08_425885	3	19	and	and	CC
10_1101-2021_01_08_425885	3	20	is	be	VBZ
10_1101-2021_01_08_425885	3	21	agnostic	agnostic	JJ
10_1101-2021_01_08_425885	3	22	to	to	IN
10_1101-2021_01_08_425885	3	23	how	how	WRB
10_1101-2021_01_08_425885	3	24	a	a	DT
10_1101-2021_01_08_425885	3	25	manifold	manifold	NN
10_1101-2021_01_08_425885	3	26	is	be	VBZ
10_1101-2021_01_08_425885	3	27	embedded	embed	VBN
10_1101-2021_01_08_425885	3	28	in	in	IN
10_1101-2021_01_08_425885	3	29	a	a	DT
10_1101-2021_01_08_425885	3	30	high-	high-	JJ
10_1101-2021_01_08_425885	3	31	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	3	32	space	space	NN
10_1101-2021_01_08_425885	3	33	.	.	.
10_1101-2021_01_08_425885	4	1	The	the	DT
10_1101-2021_01_08_425885	4	2	extrinsic	extrinsic	NN
10_1101-2021_01_08_425885	4	3	approach	approach	NN
10_1101-2021_01_08_425885	4	4	relates	relate	VBZ
10_1101-2021_01_08_425885	4	5	the	the	DT
10_1101-2021_01_08_425885	4	6	ambient	ambient	JJ
10_1101-2021_01_08_425885	4	7	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	4	8	of	of	IN
10_1101-2021_01_08_425885	4	9	a	a	DT
10_1101-2021_01_08_425885	4	10	manifold	manifold	NN
10_1101-2021_01_08_425885	4	11	’s	’s	,
10_1101-2021_01_08_425885	4	12	embedding	embedding	NN
10_1101-2021_01_08_425885	4	13	to	to	IN
10_1101-2021_01_08_425885	4	14	its	-PRON-	PRP$
10_1101-2021_01_08_425885	4	15	curvature	curvature	NN
10_1101-2021_01_08_425885	4	16	using	use	VBG
10_1101-2021_01_08_425885	4	17	the	the	DT
10_1101-2021_01_08_425885	4	18	Second	Second	NNP
10_1101-2021_01_08_425885	4	19	Fundamental	Fundamental	NNP
10_1101-2021_01_08_425885	4	20	Form	Form	NNP
10_1101-2021_01_08_425885	4	21	and	and	CC
10_1101-2021_01_08_425885	4	22	the	the	DT
10_1101-2021_01_08_425885	4	23	Gauss	Gauss	NNP
10_1101-2021_01_08_425885	4	24	-	-	HYPH
10_1101-2021_01_08_425885	4	25	Codazzi	Codazzi	NNP
10_1101-2021_01_08_425885	4	26	equation	equation	NN
10_1101-2021_01_08_425885	4	27	.	.	.
10_1101-2021_01_08_425885	5	1	Keeping	keep	VBG
10_1101-2021_01_08_425885	5	2	in	in	IN
10_1101-2021_01_08_425885	5	3	mind	mind	NN
10_1101-2021_01_08_425885	5	4	practical	practical	JJ
10_1101-2021_01_08_425885	5	5	constraints	constraint	NNS
10_1101-2021_01_08_425885	5	6	of	of	IN
10_1101-2021_01_08_425885	5	7	real	real	JJ
10_1101-2021_01_08_425885	5	8	-	-	HYPH
10_1101-2021_01_08_425885	5	9	world	world	NN
10_1101-2021_01_08_425885	5	10	datasets	dataset	NNS
10_1101-2021_01_08_425885	5	11	,	,	,
10_1101-2021_01_08_425885	5	12	like	like	IN
10_1101-2021_01_08_425885	5	13	small	small	JJ
10_1101-2021_01_08_425885	5	14	sample	sample	NN
10_1101-2021_01_08_425885	5	15	sizes	size	NNS
10_1101-2021_01_08_425885	5	16	and	and	CC
10_1101-2021_01_08_425885	5	17	measurement	measurement	NN
10_1101-2021_01_08_425885	5	18	noise	noise	NN
10_1101-2021_01_08_425885	5	19	,	,	,
10_1101-2021_01_08_425885	5	20	we	-PRON-	PRP
10_1101-2021_01_08_425885	5	21	found	find	VBD
10_1101-2021_01_08_425885	5	22	that	that	IN
10_1101-2021_01_08_425885	5	23	estimating	estimate	VBG
10_1101-2021_01_08_425885	5	24	curvature	curvature	NN
10_1101-2021_01_08_425885	5	25	is	be	VBZ
10_1101-2021_01_08_425885	5	26	only	only	RB
10_1101-2021_01_08_425885	5	27	feasible	feasible	JJ
10_1101-2021_01_08_425885	5	28	for	for	IN
10_1101-2021_01_08_425885	5	29	even	even	RB
10_1101-2021_01_08_425885	5	30	simple	simple	JJ
10_1101-2021_01_08_425885	5	31	,	,	,
10_1101-2021_01_08_425885	5	32	low	low	JJ
10_1101-2021_01_08_425885	5	33	-	-	HYPH
10_1101-2021_01_08_425885	5	34	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	5	35	toy	toy	NN
10_1101-2021_01_08_425885	5	36	manifolds	manifold	NNS
10_1101-2021_01_08_425885	5	37	,	,	,
10_1101-2021_01_08_425885	5	38	when	when	WRB
10_1101-2021_01_08_425885	5	39	the	the	DT
10_1101-2021_01_08_425885	5	40	extrinsic	extrinsic	NN
10_1101-2021_01_08_425885	5	41	approach	approach	NN
10_1101-2021_01_08_425885	5	42	is	be	VBZ
10_1101-2021_01_08_425885	5	43	used	use	VBN
10_1101-2021_01_08_425885	5	44	.	.	.
10_1101-2021_01_08_425885	6	1	To	to	TO
10_1101-2021_01_08_425885	6	2	test	test	VB
10_1101-2021_01_08_425885	6	3	the	the	DT
10_1101-2021_01_08_425885	6	4	applicability	applicability	NN
10_1101-2021_01_08_425885	6	5	of	of	IN
10_1101-2021_01_08_425885	6	6	the	the	DT
10_1101-2021_01_08_425885	6	7	extrinsic	extrinsic	JJ
10_1101-2021_01_08_425885	6	8	approach	approach	NN
10_1101-2021_01_08_425885	6	9	to	to	IN
10_1101-2021_01_08_425885	6	10	real	real	JJ
10_1101-2021_01_08_425885	6	11	-	-	HYPH
10_1101-2021_01_08_425885	6	12	world	world	NN
10_1101-2021_01_08_425885	6	13	data	datum	NNS
10_1101-2021_01_08_425885	6	14	,	,	,
10_1101-2021_01_08_425885	6	15	we	-PRON-	PRP
10_1101-2021_01_08_425885	6	16	computed	compute	VBD
10_1101-2021_01_08_425885	6	17	the	the	DT
10_1101-2021_01_08_425885	6	18	curvature	curvature	NN
10_1101-2021_01_08_425885	6	19	of	of	IN
10_1101-2021_01_08_425885	6	20	a	a	DT
10_1101-2021_01_08_425885	6	21	well	well	RB
10_1101-2021_01_08_425885	6	22	-	-	HYPH
10_1101-2021_01_08_425885	6	23	studied	study	VBN
10_1101-2021_01_08_425885	6	24	manifold	manifold	NN
10_1101-2021_01_08_425885	6	25	of	of	IN
10_1101-2021_01_08_425885	6	26	image	image	NN
10_1101-2021_01_08_425885	6	27	patches	patch	NNS
10_1101-2021_01_08_425885	6	28	,	,	,
10_1101-2021_01_08_425885	6	29	and	and	CC
10_1101-2021_01_08_425885	6	30	recapitulated	recapitulate	VBN
10_1101-2021_01_08_425885	6	31	its	-PRON-	PRP$
10_1101-2021_01_08_425885	6	32	topological	topological	JJ
10_1101-2021_01_08_425885	6	33	classification	classification	NN
10_1101-2021_01_08_425885	6	34	as	as	IN
10_1101-2021_01_08_425885	6	35	a	a	DT
10_1101-2021_01_08_425885	6	36	Klein	Klein	NNP
10_1101-2021_01_08_425885	6	37	bottle	bottle	NN
10_1101-2021_01_08_425885	6	38	.	.	.
10_1101-2021_01_08_425885	7	1	Lastly	lastly	RB
10_1101-2021_01_08_425885	7	2	,	,	,
10_1101-2021_01_08_425885	7	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	7	4	applied	apply	VBD
10_1101-2021_01_08_425885	7	5	the	the	DT
10_1101-2021_01_08_425885	7	6	approach	approach	NN
10_1101-2021_01_08_425885	7	7	to	to	TO
10_1101-2021_01_08_425885	7	8	study	study	VB
10_1101-2021_01_08_425885	7	9	single	single	JJ
10_1101-2021_01_08_425885	7	10	-	-	HYPH
10_1101-2021_01_08_425885	7	11	cell	cell	NN
10_1101-2021_01_08_425885	7	12	transcriptomic	transcriptomic	JJ
10_1101-2021_01_08_425885	7	13	sequencing	sequencing	NN
10_1101-2021_01_08_425885	7	14	(	(	-LRB-
10_1101-2021_01_08_425885	7	15	scRNAseq	scrnaseq	NN
10_1101-2021_01_08_425885	7	16	)	)	-RRB-
10_1101-2021_01_08_425885	7	17	datasets	dataset	NNS
10_1101-2021_01_08_425885	7	18	of	of	IN
10_1101-2021_01_08_425885	7	19	blood	blood	NN
10_1101-2021_01_08_425885	7	20	,	,	,
10_1101-2021_01_08_425885	7	21	gastrulation	gastrulation	NN
10_1101-2021_01_08_425885	7	22	,	,	,
10_1101-2021_01_08_425885	7	23	and	and	CC
10_1101-2021_01_08_425885	7	24	brain	brain	NN
10_1101-2021_01_08_425885	7	25	cells	cell	NNS
10_1101-2021_01_08_425885	7	26	,	,	,
10_1101-2021_01_08_425885	7	27	revealing	reveal	VBG
10_1101-2021_01_08_425885	7	28	for	for	IN
10_1101-2021_01_08_425885	7	29	the	the	DT
10_1101-2021_01_08_425885	7	30	first	first	JJ
10_1101-2021_01_08_425885	7	31	time	time	NN
10_1101-2021_01_08_425885	7	32	the	the	DT
10_1101-2021_01_08_425885	7	33	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	7	34	curvature	curvature	NN
10_1101-2021_01_08_425885	7	35	of	of	IN
10_1101-2021_01_08_425885	7	36	scRNAseq	scrnaseq	JJ
10_1101-2021_01_08_425885	7	37	manifolds	manifold	NNS
10_1101-2021_01_08_425885	7	38	.	.	.
10_1101-2021_01_08_425885	8	1	∗Equal	∗Equal	:
10_1101-2021_01_08_425885	8	2	contribution	contribution	NN
10_1101-2021_01_08_425885	8	3	†To	†To	NNP
10_1101-2021_01_08_425885	8	4	whom	whom	WP
10_1101-2021_01_08_425885	8	5	correspondence	correspondence	NN
10_1101-2021_01_08_425885	8	6	should	should	MD
10_1101-2021_01_08_425885	8	7	be	be	VB
10_1101-2021_01_08_425885	8	8	addressed	address	VBN
10_1101-2021_01_08_425885	8	9	(	(	-LRB-
10_1101-2021_01_08_425885	8	10	Sahand	Sahand	NNP
10_1101-2021_01_08_425885	8	11	Hormoz@hms.harvard.edu	Hormoz@hms.harvard.edu	NNP
10_1101-2021_01_08_425885	8	12	)	)	-RRB-
10_1101-2021_01_08_425885	8	13	1	1	CD
10_1101-2021_01_08_425885	8	14	.CC	.CC	NFP
10_1101-2021_01_08_425885	8	15	-	-	HYPH
10_1101-2021_01_08_425885	8	16	BY	by	IN
10_1101-2021_01_08_425885	8	17	-	-	HYPH
10_1101-2021_01_08_425885	8	18	NC	NC	NNP
10_1101-2021_01_08_425885	8	19	-	-	HYPH
10_1101-2021_01_08_425885	8	20	ND	ND	NNP
10_1101-2021_01_08_425885	8	21	4.0	4.0	CD
10_1101-2021_01_08_425885	8	22	International	International	NNP
10_1101-2021_01_08_425885	8	23	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	8	24	under	under	IN
10_1101-2021_01_08_425885	8	25	a	a	DT
10_1101-2021_01_08_425885	8	26	(	(	-LRB-
10_1101-2021_01_08_425885	8	27	which	which	WDT
10_1101-2021_01_08_425885	8	28	was	be	VBD
10_1101-2021_01_08_425885	8	29	not	not	RB
10_1101-2021_01_08_425885	8	30	certified	certify	VBN
10_1101-2021_01_08_425885	8	31	by	by	IN
10_1101-2021_01_08_425885	8	32	peer	peer	NN
10_1101-2021_01_08_425885	8	33	review	review	NN
10_1101-2021_01_08_425885	8	34	)	)	-RRB-
10_1101-2021_01_08_425885	8	35	is	be	VBZ
10_1101-2021_01_08_425885	8	36	the	the	DT
10_1101-2021_01_08_425885	8	37	author	author	NN
10_1101-2021_01_08_425885	8	38	/	/	SYM
10_1101-2021_01_08_425885	8	39	funder	funder	NN
10_1101-2021_01_08_425885	8	40	,	,	,
10_1101-2021_01_08_425885	8	41	who	who	WP
10_1101-2021_01_08_425885	8	42	has	have	VBZ
10_1101-2021_01_08_425885	8	43	granted	grant	VBN
10_1101-2021_01_08_425885	8	44	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	8	45	a	a	DT
10_1101-2021_01_08_425885	8	46	license	license	NN
10_1101-2021_01_08_425885	8	47	to	to	TO
10_1101-2021_01_08_425885	8	48	display	display	VB
10_1101-2021_01_08_425885	8	49	the	the	DT
10_1101-2021_01_08_425885	8	50	preprint	preprint	NN
10_1101-2021_01_08_425885	8	51	in	in	IN
10_1101-2021_01_08_425885	8	52	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	8	53	.	.	.
10_1101-2021_01_08_425885	9	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	9	2	is	be	VBZ
10_1101-2021_01_08_425885	9	3	made	make	VBN
10_1101-2021_01_08_425885	9	4	The	the	DT
10_1101-2021_01_08_425885	9	5	copyright	copyright	NN
10_1101-2021_01_08_425885	9	6	holder	holder	NN
10_1101-2021_01_08_425885	9	7	for	for	IN
10_1101-2021_01_08_425885	9	8	this	this	DT
10_1101-2021_01_08_425885	9	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	9	10	version	version	NN
10_1101-2021_01_08_425885	9	11	posted	post	VBD
10_1101-2021_01_08_425885	9	12	January	January	NNP
10_1101-2021_01_08_425885	9	13	8	8	CD
10_1101-2021_01_08_425885	9	14	,	,	,
10_1101-2021_01_08_425885	9	15	2021	2021	CD
10_1101-2021_01_08_425885	9	16	.	.	.
10_1101-2021_01_08_425885	9	17	;	;	:
10_1101-2021_01_08_425885	9	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	9	19	:	:	:
10_1101-2021_01_08_425885	9	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	9	21	preprint	preprint	NN
10_1101-2021_01_08_425885	9	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	9	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NN
10_1101-2021_01_08_425885	9	24	1	1	CD
10_1101-2021_01_08_425885	9	25	Introduction	Introduction	NNP
10_1101-2021_01_08_425885	9	26	High	high	JJ
10_1101-2021_01_08_425885	9	27	-	-	HYPH
10_1101-2021_01_08_425885	9	28	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	9	29	biological	biological	JJ
10_1101-2021_01_08_425885	9	30	datasets	dataset	NNS
10_1101-2021_01_08_425885	9	31	have	have	VBP
10_1101-2021_01_08_425885	9	32	become	become	VBN
10_1101-2021_01_08_425885	9	33	prevalent	prevalent	JJ
10_1101-2021_01_08_425885	9	34	in	in	IN
10_1101-2021_01_08_425885	9	35	recent	recent	JJ
10_1101-2021_01_08_425885	9	36	decades	decade	NNS
10_1101-2021_01_08_425885	9	37	because	because	IN
10_1101-2021_01_08_425885	9	38	of	of	IN
10_1101-2021_01_08_425885	9	39	new	new	JJ
10_1101-2021_01_08_425885	9	40	technologies	technology	NNS
10_1101-2021_01_08_425885	9	41	such	such	JJ
10_1101-2021_01_08_425885	9	42	as	as	IN
10_1101-2021_01_08_425885	9	43	high	high	JJ
10_1101-2021_01_08_425885	9	44	-	-	HYPH
10_1101-2021_01_08_425885	9	45	throughput	throughput	NN
10_1101-2021_01_08_425885	9	46	scRNAseq	scrnaseq	NN
10_1101-2021_01_08_425885	9	47	[	[	-LRB-
10_1101-2021_01_08_425885	9	48	1	1	CD
10_1101-2021_01_08_425885	9	49	,	,	,
10_1101-2021_01_08_425885	9	50	2	2	CD
10_1101-2021_01_08_425885	9	51	,	,	,
10_1101-2021_01_08_425885	9	52	3	3	CD
10_1101-2021_01_08_425885	9	53	]	]	-RRB-
10_1101-2021_01_08_425885	9	54	,	,	,
10_1101-2021_01_08_425885	9	55	mass	mass	NN
10_1101-2021_01_08_425885	9	56	cytometry	cytometry	NN
10_1101-2021_01_08_425885	9	57	[	[	-LRB-
10_1101-2021_01_08_425885	9	58	4	4	CD
10_1101-2021_01_08_425885	9	59	,	,	,
10_1101-2021_01_08_425885	9	60	5	5	CD
10_1101-2021_01_08_425885	9	61	]	]	-RRB-
10_1101-2021_01_08_425885	9	62	and	and	CC
10_1101-2021_01_08_425885	9	63	multiplex	multiplex	NNP
10_1101-2021_01_08_425885	9	64	imaging	image	VBG
10_1101-2021_01_08_425885	9	65	[	[	-LRB-
10_1101-2021_01_08_425885	9	66	6	6	CD
10_1101-2021_01_08_425885	9	67	,	,	,
10_1101-2021_01_08_425885	9	68	7	7	CD
10_1101-2021_01_08_425885	9	69	]	]	-RRB-
10_1101-2021_01_08_425885	9	70	.	.	.
10_1101-2021_01_08_425885	10	1	Interpre-	interpre-	NN
10_1101-2021_01_08_425885	10	2	tation	tation	NN
10_1101-2021_01_08_425885	10	3	and	and	CC
10_1101-2021_01_08_425885	10	4	visualization	visualization	NN
10_1101-2021_01_08_425885	10	5	of	of	IN
10_1101-2021_01_08_425885	10	6	such	such	JJ
10_1101-2021_01_08_425885	10	7	high	high	JJ
10_1101-2021_01_08_425885	10	8	-	-	HYPH
10_1101-2021_01_08_425885	10	9	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	10	10	datasets	dataset	NNS
10_1101-2021_01_08_425885	10	11	have	have	VBP
10_1101-2021_01_08_425885	10	12	been	be	VBN
10_1101-2021_01_08_425885	10	13	challenging	challenge	VBG
10_1101-2021_01_08_425885	10	14	however	however	RB
10_1101-2021_01_08_425885	10	15	,	,	,
10_1101-2021_01_08_425885	10	16	prompting	prompt	VBG
10_1101-2021_01_08_425885	10	17	the	the	DT
10_1101-2021_01_08_425885	10	18	development	development	NN
10_1101-2021_01_08_425885	10	19	of	of	IN
10_1101-2021_01_08_425885	10	20	tools	tool	NNS
10_1101-2021_01_08_425885	10	21	for	for	IN
10_1101-2021_01_08_425885	10	22	non	non	JJ
10_1101-2021_01_08_425885	10	23	-	-	JJ
10_1101-2021_01_08_425885	10	24	linear	linear	JJ
10_1101-2021_01_08_425885	10	25	projection	projection	NN
10_1101-2021_01_08_425885	10	26	of	of	IN
10_1101-2021_01_08_425885	10	27	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	10	28	onto	onto	IN
10_1101-2021_01_08_425885	10	29	2	2	CD
10_1101-2021_01_08_425885	10	30	or	or	CC
10_1101-2021_01_08_425885	10	31	3	3	CD
10_1101-2021_01_08_425885	10	32	dimensions	dimension	NNS
10_1101-2021_01_08_425885	10	33	[	[	-LRB-
10_1101-2021_01_08_425885	10	34	8	8	CD
10_1101-2021_01_08_425885	10	35	]	]	-RRB-
10_1101-2021_01_08_425885	10	36	.	.	.
10_1101-2021_01_08_425885	11	1	These	these	DT
10_1101-2021_01_08_425885	11	2	tools	tool	NNS
10_1101-2021_01_08_425885	11	3	,	,	,
10_1101-2021_01_08_425885	11	4	such	such	JJ
10_1101-2021_01_08_425885	11	5	as	as	IN
10_1101-2021_01_08_425885	11	6	IsoMAP	IsoMAP	NNP
10_1101-2021_01_08_425885	11	7	[	[	-LRB-
10_1101-2021_01_08_425885	11	8	9	9	CD
10_1101-2021_01_08_425885	11	9	]	]	-RRB-
10_1101-2021_01_08_425885	11	10	,	,	,
10_1101-2021_01_08_425885	11	11	t	t	NNP
10_1101-2021_01_08_425885	11	12	-	-	HYPH
10_1101-2021_01_08_425885	11	13	SNE	SNE	NNP
10_1101-2021_01_08_425885	11	14	[	[	-LRB-
10_1101-2021_01_08_425885	11	15	10	10	CD
10_1101-2021_01_08_425885	11	16	]	]	-RRB-
10_1101-2021_01_08_425885	11	17	and	and	CC
10_1101-2021_01_08_425885	11	18	UMAP	UMAP	NNP
10_1101-2021_01_08_425885	11	19	[	[	-LRB-
10_1101-2021_01_08_425885	11	20	11	11	CD
10_1101-2021_01_08_425885	11	21	]	]	-RRB-
10_1101-2021_01_08_425885	11	22	,	,	,
10_1101-2021_01_08_425885	11	23	appeal	appeal	VBP
10_1101-2021_01_08_425885	11	24	to	to	IN
10_1101-2021_01_08_425885	11	25	the	the	DT
10_1101-2021_01_08_425885	11	26	ansatz	ansatz	NN
10_1101-2021_01_08_425885	11	27	that	that	IN
10_1101-2021_01_08_425885	11	28	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	11	29	in	in	IN
10_1101-2021_01_08_425885	11	30	a	a	DT
10_1101-2021_01_08_425885	11	31	high	high	JJ
10_1101-2021_01_08_425885	11	32	-	-	HYPH
10_1101-2021_01_08_425885	11	33	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	11	34	ambient	ambient	JJ
10_1101-2021_01_08_425885	11	35	space	space	NN
10_1101-2021_01_08_425885	11	36	are	be	VBP
10_1101-2021_01_08_425885	11	37	constrained	constrain	VBN
10_1101-2021_01_08_425885	11	38	to	to	TO
10_1101-2021_01_08_425885	11	39	lie	lie	VB
10_1101-2021_01_08_425885	11	40	on	on	IN
10_1101-2021_01_08_425885	11	41	a	a	DT
10_1101-2021_01_08_425885	11	42	low	low	JJ
10_1101-2021_01_08_425885	11	43	-	-	HYPH
10_1101-2021_01_08_425885	11	44	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	11	45	manifold	manifold	NN
10_1101-2021_01_08_425885	11	46	.	.	.
10_1101-2021_01_08_425885	12	1	Unfortunately	unfortunately	RB
10_1101-2021_01_08_425885	12	2	,	,	,
10_1101-2021_01_08_425885	12	3	determining	determine	VBG
10_1101-2021_01_08_425885	12	4	the	the	DT
10_1101-2021_01_08_425885	12	5	geometry	geometry	NN
10_1101-2021_01_08_425885	12	6	of	of	IN
10_1101-2021_01_08_425885	12	7	a	a	DT
10_1101-2021_01_08_425885	12	8	low	low	JJ
10_1101-2021_01_08_425885	12	9	-	-	HYPH
10_1101-2021_01_08_425885	12	10	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	12	11	manifold	manifold	NN
10_1101-2021_01_08_425885	12	12	from	from	IN
10_1101-2021_01_08_425885	12	13	these	these	DT
10_1101-2021_01_08_425885	12	14	visualizations	visualization	NNS
10_1101-2021_01_08_425885	12	15	is	be	VBZ
10_1101-2021_01_08_425885	12	16	difficult	difficult	JJ
10_1101-2021_01_08_425885	12	17	,	,	,
10_1101-2021_01_08_425885	12	18	since	since	IN
10_1101-2021_01_08_425885	12	19	many	many	JJ
10_1101-2021_01_08_425885	12	20	geometric	geometric	JJ
10_1101-2021_01_08_425885	12	21	properties	property	NNS
10_1101-2021_01_08_425885	12	22	are	be	VBP
10_1101-2021_01_08_425885	12	23	lost	lose	VBN
10_1101-2021_01_08_425885	12	24	after	after	IN
10_1101-2021_01_08_425885	12	25	projecting	project	VBG
10_1101-2021_01_08_425885	12	26	onto	onto	IN
10_1101-2021_01_08_425885	12	27	2	2	CD
10_1101-2021_01_08_425885	12	28	or	or	CC
10_1101-2021_01_08_425885	12	29	3	3	CD
10_1101-2021_01_08_425885	12	30	dimensions	dimension	NNS
10_1101-2021_01_08_425885	12	31	.	.	.
10_1101-2021_01_08_425885	13	1	For	for	IN
10_1101-2021_01_08_425885	13	2	example	example	NN
10_1101-2021_01_08_425885	13	3	,	,	,
10_1101-2021_01_08_425885	13	4	the	the	DT
10_1101-2021_01_08_425885	13	5	cartographic	cartographic	JJ
10_1101-2021_01_08_425885	13	6	projections	projection	NNS
10_1101-2021_01_08_425885	13	7	used	use	VBN
10_1101-2021_01_08_425885	13	8	in	in	IN
10_1101-2021_01_08_425885	13	9	an	an	DT
10_1101-2021_01_08_425885	13	10	atlas	atlas	NN
10_1101-2021_01_08_425885	13	11	to	to	TO
10_1101-2021_01_08_425885	13	12	flatten	flatten	VB
10_1101-2021_01_08_425885	13	13	Earth	Earth	NNP
10_1101-2021_01_08_425885	13	14	’s	’s	POS
10_1101-2021_01_08_425885	13	15	curved	curved	JJ
10_1101-2021_01_08_425885	13	16	surface	surface	NN
10_1101-2021_01_08_425885	13	17	tear	tear	NN
10_1101-2021_01_08_425885	13	18	apart	apart	RB
10_1101-2021_01_08_425885	13	19	continuous	continuous	JJ
10_1101-2021_01_08_425885	13	20	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	13	21	and	and	CC
10_1101-2021_01_08_425885	13	22	non	non	JJ
10_1101-2021_01_08_425885	13	23	-	-	JJ
10_1101-2021_01_08_425885	13	24	uniformly	uniformly	JJ
10_1101-2021_01_08_425885	13	25	stretch	stretch	NN
10_1101-2021_01_08_425885	13	26	distances	distance	NNS
10_1101-2021_01_08_425885	13	27	.	.	.
10_1101-2021_01_08_425885	14	1	Fortunately	fortunately	RB
10_1101-2021_01_08_425885	14	2	,	,	,
10_1101-2021_01_08_425885	14	3	topology	topology	NN
10_1101-2021_01_08_425885	14	4	and	and	CC
10_1101-2021_01_08_425885	14	5	differential	differential	NN
10_1101-2021_01_08_425885	14	6	geometry	geometry	NN
10_1101-2021_01_08_425885	14	7	provide	provide	VBP
10_1101-2021_01_08_425885	14	8	a	a	DT
10_1101-2021_01_08_425885	14	9	wealth	wealth	NN
10_1101-2021_01_08_425885	14	10	of	of	IN
10_1101-2021_01_08_425885	14	11	concepts	concept	NNS
10_1101-2021_01_08_425885	14	12	to	to	TO
10_1101-2021_01_08_425885	14	13	characterize	characterize	VB
10_1101-2021_01_08_425885	14	14	a	a	DT
10_1101-2021_01_08_425885	14	15	manifold	manifold	NN
10_1101-2021_01_08_425885	14	16	’s	’s	POS
10_1101-2021_01_08_425885	14	17	shape	shape	NN
10_1101-2021_01_08_425885	14	18	directly	directly	RB
10_1101-2021_01_08_425885	14	19	without	without	IN
10_1101-2021_01_08_425885	14	20	confounding	confound	VBG
10_1101-2021_01_08_425885	14	21	projections	projection	NNS
10_1101-2021_01_08_425885	14	22	.	.	.
10_1101-2021_01_08_425885	15	1	In	in	IN
10_1101-2021_01_08_425885	15	2	particular	particular	JJ
10_1101-2021_01_08_425885	15	3	,	,	,
10_1101-2021_01_08_425885	15	4	homology	homology	NN
10_1101-2021_01_08_425885	15	5	[	[	-LRB-
10_1101-2021_01_08_425885	15	6	12	12	CD
10_1101-2021_01_08_425885	15	7	,	,	,
10_1101-2021_01_08_425885	15	8	13	13	CD
10_1101-2021_01_08_425885	15	9	]	]	-RRB-
10_1101-2021_01_08_425885	15	10	categorizes	categorize	VBZ
10_1101-2021_01_08_425885	15	11	a	a	DT
10_1101-2021_01_08_425885	15	12	manifold	manifold	NN
10_1101-2021_01_08_425885	15	13	according	accord	VBG
10_1101-2021_01_08_425885	15	14	to	to	IN
10_1101-2021_01_08_425885	15	15	the	the	DT
10_1101-2021_01_08_425885	15	16	number	number	NN
10_1101-2021_01_08_425885	15	17	of	of	IN
10_1101-2021_01_08_425885	15	18	holes	hole	NNS
10_1101-2021_01_08_425885	15	19	it	-PRON-	PRP
10_1101-2021_01_08_425885	15	20	contains	contain	VBZ
10_1101-2021_01_08_425885	15	21	,	,	,
10_1101-2021_01_08_425885	15	22	and	and	CC
10_1101-2021_01_08_425885	15	23	the	the	DT
10_1101-2021_01_08_425885	15	24	dimensionality	dimensionality	NN
10_1101-2021_01_08_425885	15	25	of	of	IN
10_1101-2021_01_08_425885	15	26	each	each	DT
10_1101-2021_01_08_425885	15	27	hole	hole	NN
10_1101-2021_01_08_425885	15	28	(	(	-LRB-
10_1101-2021_01_08_425885	15	29	whereas	whereas	IN
10_1101-2021_01_08_425885	15	30	for	for	IN
10_1101-2021_01_08_425885	15	31	example	example	NN
10_1101-2021_01_08_425885	15	32	,	,	,
10_1101-2021_01_08_425885	15	33	the	the	DT
10_1101-2021_01_08_425885	15	34	hole	hole	NN
10_1101-2021_01_08_425885	15	35	in	in	IN
10_1101-2021_01_08_425885	15	36	a	a	DT
10_1101-2021_01_08_425885	15	37	hollow	hollow	JJ
10_1101-2021_01_08_425885	15	38	sphere	sphere	NN
10_1101-2021_01_08_425885	15	39	does	do	VBZ
10_1101-2021_01_08_425885	15	40	not	not	RB
10_1101-2021_01_08_425885	15	41	survive	survive	VB
10_1101-2021_01_08_425885	15	42	projection	projection	NN
10_1101-2021_01_08_425885	15	43	onto	onto	IN
10_1101-2021_01_08_425885	15	44	a	a	DT
10_1101-2021_01_08_425885	15	45	2-dimensional	2-dimensional	CD
10_1101-2021_01_08_425885	15	46	plane	plane	NN
10_1101-2021_01_08_425885	15	47	)	)	-RRB-
10_1101-2021_01_08_425885	15	48	.	.	.
10_1101-2021_01_08_425885	16	1	Similarly	similarly	RB
10_1101-2021_01_08_425885	16	2	,	,	,
10_1101-2021_01_08_425885	16	3	metrics	metric	NNS
10_1101-2021_01_08_425885	16	4	[	[	-LRB-
10_1101-2021_01_08_425885	16	5	14	14	CD
10_1101-2021_01_08_425885	16	6	]	]	-RRB-
10_1101-2021_01_08_425885	16	7	and	and	CC
10_1101-2021_01_08_425885	16	8	geodesics	geodesic	NNS
10_1101-2021_01_08_425885	16	9	[	[	-LRB-
10_1101-2021_01_08_425885	16	10	9	9	CD
10_1101-2021_01_08_425885	16	11	]	]	-RRB-
10_1101-2021_01_08_425885	16	12	determine	determine	VB
10_1101-2021_01_08_425885	16	13	shortest	short	JJS
10_1101-2021_01_08_425885	16	14	-	-	HYPH
10_1101-2021_01_08_425885	16	15	distance	distance	NN
10_1101-2021_01_08_425885	16	16	paths	path	NNS
10_1101-2021_01_08_425885	16	17	between	between	IN
10_1101-2021_01_08_425885	16	18	pairs	pair	NNS
10_1101-2021_01_08_425885	16	19	of	of	IN
10_1101-2021_01_08_425885	16	20	points	point	NNS
10_1101-2021_01_08_425885	16	21	on	on	IN
10_1101-2021_01_08_425885	16	22	a	a	DT
10_1101-2021_01_08_425885	16	23	manifold	manifold	NN
10_1101-2021_01_08_425885	16	24	without	without	IN
10_1101-2021_01_08_425885	16	25	any	any	DT
10_1101-2021_01_08_425885	16	26	distortion	distortion	NN
10_1101-2021_01_08_425885	16	27	from	from	IN
10_1101-2021_01_08_425885	16	28	a	a	DT
10_1101-2021_01_08_425885	16	29	projection	projection	NN
10_1101-2021_01_08_425885	16	30	(	(	-LRB-
10_1101-2021_01_08_425885	16	31	whereas	whereas	IN
10_1101-2021_01_08_425885	16	32	for	for	IN
10_1101-2021_01_08_425885	16	33	example	example	NN
10_1101-2021_01_08_425885	16	34	,	,	,
10_1101-2021_01_08_425885	16	35	most	most	JJS
10_1101-2021_01_08_425885	16	36	atlases	atlas	NNS
10_1101-2021_01_08_425885	16	37	exaggerate	exaggerate	VBP
10_1101-2021_01_08_425885	16	38	distances	distance	NNS
10_1101-2021_01_08_425885	16	39	at	at	IN
10_1101-2021_01_08_425885	16	40	the	the	DT
10_1101-2021_01_08_425885	16	41	poles	pole	NNS
10_1101-2021_01_08_425885	16	42	)	)	-RRB-
10_1101-2021_01_08_425885	16	43	.	.	.
10_1101-2021_01_08_425885	17	1	Curvature	curvature	NN
10_1101-2021_01_08_425885	17	2	[	[	-LRB-
10_1101-2021_01_08_425885	17	3	15	15	CD
10_1101-2021_01_08_425885	17	4	]	]	-RRB-
10_1101-2021_01_08_425885	17	5	is	be	VBZ
10_1101-2021_01_08_425885	17	6	a	a	DT
10_1101-2021_01_08_425885	17	7	local	local	JJ
10_1101-2021_01_08_425885	17	8	manifold	manifold	JJ
10_1101-2021_01_08_425885	17	9	property	property	NN
10_1101-2021_01_08_425885	17	10	that	that	WDT
10_1101-2021_01_08_425885	17	11	quantifies	quantify	VBZ
10_1101-2021_01_08_425885	17	12	the	the	DT
10_1101-2021_01_08_425885	17	13	extent	extent	NN
10_1101-2021_01_08_425885	17	14	to	to	TO
10_1101-2021_01_08_425885	17	15	which	which	WDT
10_1101-2021_01_08_425885	17	16	a	a	DT
10_1101-2021_01_08_425885	17	17	manifold	manifold	JJ
10_1101-2021_01_08_425885	17	18	deviates	deviate	NNS
10_1101-2021_01_08_425885	17	19	from	from	IN
10_1101-2021_01_08_425885	17	20	the	the	DT
10_1101-2021_01_08_425885	17	21	tangent	tangent	JJ
10_1101-2021_01_08_425885	17	22	plane	plane	NN
10_1101-2021_01_08_425885	17	23	at	at	IN
10_1101-2021_01_08_425885	17	24	each	each	DT
10_1101-2021_01_08_425885	17	25	point	point	NN
10_1101-2021_01_08_425885	17	26	p.	p.	NN
10_1101-2021_01_08_425885	17	27	Projecting	project	VBG
10_1101-2021_01_08_425885	17	28	a	a	DT
10_1101-2021_01_08_425885	17	29	manifold	manifold	NN
10_1101-2021_01_08_425885	17	30	onto	onto	IN
10_1101-2021_01_08_425885	17	31	a	a	DT
10_1101-2021_01_08_425885	17	32	plane	plane	NN
10_1101-2021_01_08_425885	17	33	for	for	IN
10_1101-2021_01_08_425885	17	34	visualization	visualization	NN
10_1101-2021_01_08_425885	17	35	destroys	destroy	NNS
10_1101-2021_01_08_425885	17	36	this	this	DT
10_1101-2021_01_08_425885	17	37	property	property	NN
10_1101-2021_01_08_425885	17	38	by	by	IN
10_1101-2021_01_08_425885	17	39	definition	definition	NN
10_1101-2021_01_08_425885	17	40	.	.	.
10_1101-2021_01_08_425885	18	1	Recent	recent	JJ
10_1101-2021_01_08_425885	18	2	methods	method	NNS
10_1101-2021_01_08_425885	18	3	have	have	VBP
10_1101-2021_01_08_425885	18	4	emerged	emerge	VBN
10_1101-2021_01_08_425885	18	5	for	for	IN
10_1101-2021_01_08_425885	18	6	estimating	estimate	VBG
10_1101-2021_01_08_425885	18	7	homology	homology	NN
10_1101-2021_01_08_425885	18	8	[	[	-LRB-
10_1101-2021_01_08_425885	18	9	16	16	CD
10_1101-2021_01_08_425885	18	10	,	,	,
10_1101-2021_01_08_425885	18	11	17	17	CD
10_1101-2021_01_08_425885	18	12	]	]	-RRB-
10_1101-2021_01_08_425885	18	13	,	,	,
10_1101-2021_01_08_425885	18	14	metrics	metric	NNS
10_1101-2021_01_08_425885	18	15	[	[	-LRB-
10_1101-2021_01_08_425885	18	16	14	14	CD
10_1101-2021_01_08_425885	18	17	]	]	-RRB-
10_1101-2021_01_08_425885	18	18	and	and	CC
10_1101-2021_01_08_425885	18	19	geodesics	geodesic	NNS
10_1101-2021_01_08_425885	18	20	[	[	-LRB-
10_1101-2021_01_08_425885	18	21	18	18	CD
10_1101-2021_01_08_425885	18	22	]	]	-RRB-
10_1101-2021_01_08_425885	18	23	from	from	IN
10_1101-2021_01_08_425885	18	24	noisy	noisy	NNP
10_1101-2021_01_08_425885	18	25	,	,	,
10_1101-2021_01_08_425885	18	26	sampled	sample	VBN
10_1101-2021_01_08_425885	18	27	data	datum	NNS
10_1101-2021_01_08_425885	18	28	,	,	,
10_1101-2021_01_08_425885	18	29	with	with	IN
10_1101-2021_01_08_425885	18	30	accompanying	accompany	VBG
10_1101-2021_01_08_425885	18	31	statistical	statistical	JJ
10_1101-2021_01_08_425885	18	32	guarantees	guarantee	NNS
10_1101-2021_01_08_425885	18	33	[	[	-LRB-
10_1101-2021_01_08_425885	18	34	18	18	CD
10_1101-2021_01_08_425885	18	35	,	,	,
10_1101-2021_01_08_425885	18	36	19	19	CD
10_1101-2021_01_08_425885	18	37	,	,	,
10_1101-2021_01_08_425885	18	38	20	20	CD
10_1101-2021_01_08_425885	18	39	]	]	-RRB-
10_1101-2021_01_08_425885	18	40	.	.	.
10_1101-2021_01_08_425885	19	1	These	these	DT
10_1101-2021_01_08_425885	19	2	methods	method	NNS
10_1101-2021_01_08_425885	19	3	have	have	VBP
10_1101-2021_01_08_425885	19	4	been	be	VBN
10_1101-2021_01_08_425885	19	5	applied	apply	VBN
10_1101-2021_01_08_425885	19	6	to	to	TO
10_1101-2021_01_08_425885	19	7	analyze	analyze	VB
10_1101-2021_01_08_425885	19	8	images	image	NNS
10_1101-2021_01_08_425885	19	9	[	[	-LRB-
10_1101-2021_01_08_425885	19	10	21	21	CD
10_1101-2021_01_08_425885	19	11	,	,	,
10_1101-2021_01_08_425885	19	12	22	22	CD
10_1101-2021_01_08_425885	19	13	]	]	-RRB-
10_1101-2021_01_08_425885	19	14	and	and	CC
10_1101-2021_01_08_425885	19	15	biological	biological	JJ
10_1101-2021_01_08_425885	19	16	datasets	dataset	NNS
10_1101-2021_01_08_425885	19	17	[	[	-LRB-
10_1101-2021_01_08_425885	19	18	23	23	CD
10_1101-2021_01_08_425885	19	19	,	,	,
10_1101-2021_01_08_425885	19	20	24	24	CD
10_1101-2021_01_08_425885	19	21	]	]	-RRB-
10_1101-2021_01_08_425885	19	22	.	.	.
10_1101-2021_01_08_425885	20	1	However	however	RB
10_1101-2021_01_08_425885	20	2	,	,	,
10_1101-2021_01_08_425885	20	3	estimating	estimate	VBG
10_1101-2021_01_08_425885	20	4	curvature	curvature	NN
10_1101-2021_01_08_425885	20	5	has	have	VBZ
10_1101-2021_01_08_425885	20	6	received	receive	VBN
10_1101-2021_01_08_425885	20	7	less	less	JJR
10_1101-2021_01_08_425885	20	8	attention	attention	NN
10_1101-2021_01_08_425885	20	9	although	although	IN
10_1101-2021_01_08_425885	20	10	it	-PRON-	PRP
10_1101-2021_01_08_425885	20	11	is	be	VBZ
10_1101-2021_01_08_425885	20	12	fundamental	fundamental	JJ
10_1101-2021_01_08_425885	20	13	to	to	IN
10_1101-2021_01_08_425885	20	14	quantifying	quantify	VBG
10_1101-2021_01_08_425885	20	15	geometry	geometry	NN
10_1101-2021_01_08_425885	20	16	.	.	.
10_1101-2021_01_08_425885	21	1	Curvature	curvature	NN
10_1101-2021_01_08_425885	21	2	arises	arise	VBZ
10_1101-2021_01_08_425885	21	3	from	from	IN
10_1101-2021_01_08_425885	21	4	two	two	CD
10_1101-2021_01_08_425885	21	5	sources	source	NNS
10_1101-2021_01_08_425885	21	6	.	.	.
10_1101-2021_01_08_425885	22	1	On	on	IN
10_1101-2021_01_08_425885	22	2	the	the	DT
10_1101-2021_01_08_425885	22	3	one	one	CD
10_1101-2021_01_08_425885	22	4	hand	hand	NN
10_1101-2021_01_08_425885	22	5	,	,	,
10_1101-2021_01_08_425885	22	6	a	a	DT
10_1101-2021_01_08_425885	22	7	manifold	manifold	NN
10_1101-2021_01_08_425885	22	8	itself	-PRON-	PRP
10_1101-2021_01_08_425885	22	9	can	can	MD
10_1101-2021_01_08_425885	22	10	be	be	VB
10_1101-2021_01_08_425885	22	11	curved	curve	VBN
10_1101-2021_01_08_425885	22	12	,	,	,
10_1101-2021_01_08_425885	22	13	resulting	result	VBG
10_1101-2021_01_08_425885	22	14	in	in	IN
10_1101-2021_01_08_425885	22	15	Riemannian	riemannian	JJ
10_1101-2021_01_08_425885	22	16	or	or	CC
10_1101-2021_01_08_425885	22	17	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	22	18	curvature	curvature	NN
10_1101-2021_01_08_425885	22	19	.	.	.
10_1101-2021_01_08_425885	23	1	A	a	DT
10_1101-2021_01_08_425885	23	2	sphere	sphere	NN
10_1101-2021_01_08_425885	23	3	has	have	VBZ
10_1101-2021_01_08_425885	23	4	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	23	5	curvature	curvature	NN
10_1101-2021_01_08_425885	23	6	because	because	IN
10_1101-2021_01_08_425885	23	7	it	-PRON-	PRP
10_1101-2021_01_08_425885	23	8	can	can	MD
10_1101-2021_01_08_425885	23	9	not	not	RB
10_1101-2021_01_08_425885	23	10	be	be	VB
10_1101-2021_01_08_425885	23	11	flattened	flatten	VBN
10_1101-2021_01_08_425885	23	12	so	so	IN
10_1101-2021_01_08_425885	23	13	that	that	IN
10_1101-2021_01_08_425885	23	14	all	all	DT
10_1101-2021_01_08_425885	23	15	geodesics	geodesic	NNS
10_1101-2021_01_08_425885	23	16	on	on	IN
10_1101-2021_01_08_425885	23	17	its	-PRON-	PRP$
10_1101-2021_01_08_425885	23	18	surface	surface	NN
10_1101-2021_01_08_425885	23	19	correspond	correspond	NN
10_1101-2021_01_08_425885	23	20	to	to	IN
10_1101-2021_01_08_425885	23	21	straight	straight	JJ
10_1101-2021_01_08_425885	23	22	lines	line	NNS
10_1101-2021_01_08_425885	23	23	on	on	IN
10_1101-2021_01_08_425885	23	24	a	a	DT
10_1101-2021_01_08_425885	23	25	Euclidean	euclidean	JJ
10_1101-2021_01_08_425885	23	26	plane	plane	NN
10_1101-2021_01_08_425885	23	27	(	(	-LRB-
10_1101-2021_01_08_425885	23	28	see	see	VB
10_1101-2021_01_08_425885	23	29	Figure	Figure	NNP
10_1101-2021_01_08_425885	23	30	1A	1a	NN
10_1101-2021_01_08_425885	23	31	)	)	-RRB-
10_1101-2021_01_08_425885	23	32	.	.	.
10_1101-2021_01_08_425885	24	1	On	on	IN
10_1101-2021_01_08_425885	24	2	the	the	DT
10_1101-2021_01_08_425885	24	3	other	other	JJ
10_1101-2021_01_08_425885	24	4	hand	hand	NN
10_1101-2021_01_08_425885	24	5	,	,	,
10_1101-2021_01_08_425885	24	6	the	the	DT
10_1101-2021_01_08_425885	24	7	embedding	embedding	NN
10_1101-2021_01_08_425885	24	8	of	of	IN
10_1101-2021_01_08_425885	24	9	a	a	DT
10_1101-2021_01_08_425885	24	10	manifold	manifold	NN
10_1101-2021_01_08_425885	24	11	in	in	IN
10_1101-2021_01_08_425885	24	12	an	an	DT
10_1101-2021_01_08_425885	24	13	ambient	ambient	JJ
10_1101-2021_01_08_425885	24	14	space	space	NN
10_1101-2021_01_08_425885	24	15	can	can	MD
10_1101-2021_01_08_425885	24	16	give	give	VB
10_1101-2021_01_08_425885	24	17	rise	rise	NN
10_1101-2021_01_08_425885	24	18	to	to	IN
10_1101-2021_01_08_425885	24	19	extrinsic	extrinsic	NN
10_1101-2021_01_08_425885	24	20	curvature	curvature	NN
10_1101-2021_01_08_425885	24	21	,	,	,
10_1101-2021_01_08_425885	24	22	a	a	DT
10_1101-2021_01_08_425885	24	23	property	property	NN
10_1101-2021_01_08_425885	24	24	that	that	WDT
10_1101-2021_01_08_425885	24	25	is	be	VBZ
10_1101-2021_01_08_425885	24	26	not	not	RB
10_1101-2021_01_08_425885	24	27	inherent	inherent	JJ
10_1101-2021_01_08_425885	24	28	to	to	IN
10_1101-2021_01_08_425885	24	29	the	the	DT
10_1101-2021_01_08_425885	24	30	manifold	manifold	NN
10_1101-2021_01_08_425885	24	31	itself	-PRON-	PRP
10_1101-2021_01_08_425885	24	32	.	.	.
10_1101-2021_01_08_425885	25	1	For	for	IN
10_1101-2021_01_08_425885	25	2	example	example	NN
10_1101-2021_01_08_425885	25	3	,	,	,
10_1101-2021_01_08_425885	25	4	a	a	DT
10_1101-2021_01_08_425885	25	5	scroll	scroll	NN
10_1101-2021_01_08_425885	25	6	has	have	VBZ
10_1101-2021_01_08_425885	25	7	extrinsic	extrinsic	NN
10_1101-2021_01_08_425885	25	8	curvature	curvature	JJ
10_1101-2021_01_08_425885	25	9	because	because	IN
10_1101-2021_01_08_425885	25	10	it	-PRON-	PRP
10_1101-2021_01_08_425885	25	11	is	be	VBZ
10_1101-2021_01_08_425885	25	12	formed	form	VBN
10_1101-2021_01_08_425885	25	13	by	by	IN
10_1101-2021_01_08_425885	25	14	rolling	roll	VBG
10_1101-2021_01_08_425885	25	15	a	a	DT
10_1101-2021_01_08_425885	25	16	piece	piece	NN
10_1101-2021_01_08_425885	25	17	of	of	IN
10_1101-2021_01_08_425885	25	18	parchment	parchment	NN
10_1101-2021_01_08_425885	25	19	,	,	,
10_1101-2021_01_08_425885	25	20	but	but	CC
10_1101-2021_01_08_425885	25	21	the	the	DT
10_1101-2021_01_08_425885	25	22	parchment	parchment	NN
10_1101-2021_01_08_425885	25	23	itself	-PRON-	PRP
10_1101-2021_01_08_425885	25	24	is	be	VBZ
10_1101-2021_01_08_425885	25	25	not	not	RB
10_1101-2021_01_08_425885	25	26	inherently	inherently	RB
10_1101-2021_01_08_425885	25	27	curved	curve	VBN
10_1101-2021_01_08_425885	25	28	(	(	-LRB-
10_1101-2021_01_08_425885	25	29	see	see	VB
10_1101-2021_01_08_425885	25	30	Figure	Figure	NNP
10_1101-2021_01_08_425885	25	31	1B	1b	NN
10_1101-2021_01_08_425885	25	32	)	)	-RRB-
10_1101-2021_01_08_425885	25	33	.	.	.
10_1101-2021_01_08_425885	26	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	26	2	is	be	VBZ
10_1101-2021_01_08_425885	26	3	important	important	JJ
10_1101-2021_01_08_425885	26	4	to	to	TO
10_1101-2021_01_08_425885	26	5	note	note	VB
10_1101-2021_01_08_425885	26	6	that	that	IN
10_1101-2021_01_08_425885	26	7	both	both	DT
10_1101-2021_01_08_425885	26	8	types	type	NNS
10_1101-2021_01_08_425885	26	9	of	of	IN
10_1101-2021_01_08_425885	26	10	curvature	curvature	JJ
10_1101-2021_01_08_425885	26	11	scale	scale	NN
10_1101-2021_01_08_425885	26	12	inversely	inversely	RB
10_1101-2021_01_08_425885	26	13	with	with	IN
10_1101-2021_01_08_425885	26	14	the	the	DT
10_1101-2021_01_08_425885	26	15	global	global	JJ
10_1101-2021_01_08_425885	26	16	length	length	NN
10_1101-2021_01_08_425885	26	17	scale	scale	NN
10_1101-2021_01_08_425885	26	18	(	(	-LRB-
10_1101-2021_01_08_425885	26	19	L	l	NN
10_1101-2021_01_08_425885	26	20	)	)	-RRB-
10_1101-2021_01_08_425885	26	21	associated	associate	VBD
10_1101-2021_01_08_425885	26	22	with	with	IN
10_1101-2021_01_08_425885	26	23	a	a	DT
10_1101-2021_01_08_425885	26	24	manifold	manifold	NN
10_1101-2021_01_08_425885	26	25	.	.	.
10_1101-2021_01_08_425885	27	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	27	2	is	be	VBZ
10_1101-2021_01_08_425885	27	3	for	for	IN
10_1101-2021_01_08_425885	27	4	this	this	DT
10_1101-2021_01_08_425885	27	5	reason	reason	NN
10_1101-2021_01_08_425885	27	6	that	that	IN
10_1101-2021_01_08_425885	27	7	a	a	DT
10_1101-2021_01_08_425885	27	8	marble	marble	NN
10_1101-2021_01_08_425885	27	9	(	(	-LRB-
10_1101-2021_01_08_425885	27	10	L	L	NNP
10_1101-2021_01_08_425885	27	11	≈	≈	NNP
10_1101-2021_01_08_425885	27	12	1	1	CD
10_1101-2021_01_08_425885	27	13	cm	cm	NNS
10_1101-2021_01_08_425885	27	14	)	)	-RRB-
10_1101-2021_01_08_425885	27	15	is	be	VBZ
10_1101-2021_01_08_425885	27	16	visibly	visibly	RB
10_1101-2021_01_08_425885	27	17	round	round	JJ
10_1101-2021_01_08_425885	27	18	,	,	,
10_1101-2021_01_08_425885	27	19	but	but	CC
10_1101-2021_01_08_425885	27	20	the	the	DT
10_1101-2021_01_08_425885	27	21	Earth	Earth	NNP
10_1101-2021_01_08_425885	27	22	(	(	-LRB-
10_1101-2021_01_08_425885	27	23	L	L	NNP
10_1101-2021_01_08_425885	27	24	≈	≈	NNP
10_1101-2021_01_08_425885	27	25	10	10	CD
10_1101-2021_01_08_425885	27	26	,	,	,
10_1101-2021_01_08_425885	27	27	000	000	CD
10_1101-2021_01_08_425885	27	28	km	km	NNS
10_1101-2021_01_08_425885	27	29	)	)	-RRB-
10_1101-2021_01_08_425885	27	30	is	be	VBZ
10_1101-2021_01_08_425885	27	31	still	still	RB
10_1101-2021_01_08_425885	27	32	mistaken	mistake	VBN
10_1101-2021_01_08_425885	27	33	by	by	IN
10_1101-2021_01_08_425885	27	34	some	some	DT
10_1101-2021_01_08_425885	27	35	to	to	TO
10_1101-2021_01_08_425885	27	36	be	be	VB
10_1101-2021_01_08_425885	27	37	flat	flat	JJ
10_1101-2021_01_08_425885	27	38	.	.	.
10_1101-2021_01_08_425885	28	1	Since	since	IN
10_1101-2021_01_08_425885	28	2	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	28	3	curvature	curvature	NN
10_1101-2021_01_08_425885	28	4	is	be	VBZ
10_1101-2021_01_08_425885	28	5	an	an	DT
10_1101-2021_01_08_425885	28	6	inherent	inherent	JJ
10_1101-2021_01_08_425885	28	7	property	property	NN
10_1101-2021_01_08_425885	28	8	of	of	IN
10_1101-2021_01_08_425885	28	9	a	a	DT
10_1101-2021_01_08_425885	28	10	manifold	manifold	NN
10_1101-2021_01_08_425885	28	11	,	,	,
10_1101-2021_01_08_425885	28	12	while	while	IN
10_1101-2021_01_08_425885	28	13	2	2	CD
10_1101-2021_01_08_425885	28	14	.CC	.CC	:
10_1101-2021_01_08_425885	28	15	-	-	HYPH
10_1101-2021_01_08_425885	28	16	BY	by	IN
10_1101-2021_01_08_425885	28	17	-	-	HYPH
10_1101-2021_01_08_425885	28	18	NC	NC	NNP
10_1101-2021_01_08_425885	28	19	-	-	HYPH
10_1101-2021_01_08_425885	28	20	ND	ND	NNP
10_1101-2021_01_08_425885	28	21	4.0	4.0	CD
10_1101-2021_01_08_425885	28	22	International	International	NNP
10_1101-2021_01_08_425885	28	23	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	28	24	under	under	IN
10_1101-2021_01_08_425885	28	25	a	a	DT
10_1101-2021_01_08_425885	28	26	(	(	-LRB-
10_1101-2021_01_08_425885	28	27	which	which	WDT
10_1101-2021_01_08_425885	28	28	was	be	VBD
10_1101-2021_01_08_425885	28	29	not	not	RB
10_1101-2021_01_08_425885	28	30	certified	certify	VBN
10_1101-2021_01_08_425885	28	31	by	by	IN
10_1101-2021_01_08_425885	28	32	peer	peer	NN
10_1101-2021_01_08_425885	28	33	review	review	NN
10_1101-2021_01_08_425885	28	34	)	)	-RRB-
10_1101-2021_01_08_425885	28	35	is	be	VBZ
10_1101-2021_01_08_425885	28	36	the	the	DT
10_1101-2021_01_08_425885	28	37	author	author	NN
10_1101-2021_01_08_425885	28	38	/	/	SYM
10_1101-2021_01_08_425885	28	39	funder	funder	NN
10_1101-2021_01_08_425885	28	40	,	,	,
10_1101-2021_01_08_425885	28	41	who	who	WP
10_1101-2021_01_08_425885	28	42	has	have	VBZ
10_1101-2021_01_08_425885	28	43	granted	grant	VBN
10_1101-2021_01_08_425885	28	44	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	28	45	a	a	DT
10_1101-2021_01_08_425885	28	46	license	license	NN
10_1101-2021_01_08_425885	28	47	to	to	TO
10_1101-2021_01_08_425885	28	48	display	display	VB
10_1101-2021_01_08_425885	28	49	the	the	DT
10_1101-2021_01_08_425885	28	50	preprint	preprint	NN
10_1101-2021_01_08_425885	28	51	in	in	IN
10_1101-2021_01_08_425885	28	52	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	28	53	.	.	.
10_1101-2021_01_08_425885	29	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	29	2	is	be	VBZ
10_1101-2021_01_08_425885	29	3	made	make	VBN
10_1101-2021_01_08_425885	29	4	The	the	DT
10_1101-2021_01_08_425885	29	5	copyright	copyright	NN
10_1101-2021_01_08_425885	29	6	holder	holder	NN
10_1101-2021_01_08_425885	29	7	for	for	IN
10_1101-2021_01_08_425885	29	8	this	this	DT
10_1101-2021_01_08_425885	29	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	29	10	version	version	NN
10_1101-2021_01_08_425885	29	11	posted	post	VBD
10_1101-2021_01_08_425885	29	12	January	January	NNP
10_1101-2021_01_08_425885	29	13	8	8	CD
10_1101-2021_01_08_425885	29	14	,	,	,
10_1101-2021_01_08_425885	29	15	2021	2021	CD
10_1101-2021_01_08_425885	29	16	.	.	.
10_1101-2021_01_08_425885	29	17	;	;	:
10_1101-2021_01_08_425885	29	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	29	19	:	:	:
10_1101-2021_01_08_425885	29	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	29	21	preprint	preprint	NN
10_1101-2021_01_08_425885	29	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	29	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NN
10_1101-2021_01_08_425885	29	24	A	A	NNP
10_1101-2021_01_08_425885	29	25	B	b	NN
10_1101-2021_01_08_425885	29	26	C	c	NN
10_1101-2021_01_08_425885	29	27	D	d	NN
10_1101-2021_01_08_425885	29	28	Intrinsic	Intrinsic	NNP
10_1101-2021_01_08_425885	29	29	(	(	-LRB-
10_1101-2021_01_08_425885	29	30	Riemannian	Riemannian	NNP
10_1101-2021_01_08_425885	29	31	)	)	-RRB-
10_1101-2021_01_08_425885	29	32	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	29	33	Extrinsic	Extrinsic	NNP
10_1101-2021_01_08_425885	29	34	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	29	35	Intrinsic	Intrinsic	NNP
10_1101-2021_01_08_425885	29	36	Differen	Differen	NNP
10_1101-2021_01_08_425885	29	37	�	�	,
10_1101-2021_01_08_425885	29	38	al	al	NNP
10_1101-2021_01_08_425885	29	39	Geometry	Geometry	NNP
10_1101-2021_01_08_425885	29	40	Extrinsic	Extrinsic	NNP
10_1101-2021_01_08_425885	29	41	Differen	Differen	NNP
10_1101-2021_01_08_425885	29	42	�	�	NNP
10_1101-2021_01_08_425885	29	43	al	al	NNP
10_1101-2021_01_08_425885	29	44	Geometry	Geometry	NNP
10_1101-2021_01_08_425885	29	45	z	z	NNP
10_1101-2021_01_08_425885	29	46	=	=	SYM
10_1101-2021_01_08_425885	29	47	±	±	CD
10_1101-2021_01_08_425885	29	48	1	1	CD
10_1101-2021_01_08_425885	29	49	−	−	NNP
10_1101-2021_01_08_425885	29	50	x	x	SYM
10_1101-2021_01_08_425885	29	51	2	2	CD
10_1101-2021_01_08_425885	29	52	−	−	NNP
10_1101-2021_01_08_425885	29	53	y2	y2	NN
10_1101-2021_01_08_425885	29	54	Figure	figure	NN
10_1101-2021_01_08_425885	29	55	1	1	CD
10_1101-2021_01_08_425885	29	56	:	:	:
10_1101-2021_01_08_425885	29	57	Riemannian	riemannian	JJ
10_1101-2021_01_08_425885	29	58	curvature	curvature	NN
10_1101-2021_01_08_425885	29	59	is	be	VBZ
10_1101-2021_01_08_425885	29	60	an	an	DT
10_1101-2021_01_08_425885	29	61	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	29	62	property	property	NN
10_1101-2021_01_08_425885	29	63	of	of	IN
10_1101-2021_01_08_425885	29	64	a	a	DT
10_1101-2021_01_08_425885	29	65	manifold	manifold	NN
10_1101-2021_01_08_425885	29	66	while	while	IN
10_1101-2021_01_08_425885	29	67	extrinsic	extrinsic	NN
10_1101-2021_01_08_425885	29	68	curvature	curvature	NN
10_1101-2021_01_08_425885	29	69	depends	depend	VBZ
10_1101-2021_01_08_425885	29	70	on	on	IN
10_1101-2021_01_08_425885	29	71	the	the	DT
10_1101-2021_01_08_425885	29	72	embedding	embedding	NN
10_1101-2021_01_08_425885	29	73	.	.	.
10_1101-2021_01_08_425885	30	1	(	(	-LRB-
10_1101-2021_01_08_425885	30	2	A	a	NN
10_1101-2021_01_08_425885	30	3	)	)	-RRB-
10_1101-2021_01_08_425885	30	4	(	(	-LRB-
10_1101-2021_01_08_425885	30	5	Left	left	NN
10_1101-2021_01_08_425885	30	6	)	)	-RRB-
10_1101-2021_01_08_425885	30	7	N	n	NN
10_1101-2021_01_08_425885	30	8	=	=	SYM
10_1101-2021_01_08_425885	30	9	104	104	CD
10_1101-2021_01_08_425885	30	10	points	point	NNS
10_1101-2021_01_08_425885	30	11	uniformly	uniformly	RB
10_1101-2021_01_08_425885	30	12	sampled	sample	VBN
10_1101-2021_01_08_425885	30	13	from	from	IN
10_1101-2021_01_08_425885	30	14	the	the	DT
10_1101-2021_01_08_425885	30	15	2-dimensional	2-dimensional	CD
10_1101-2021_01_08_425885	30	16	hollow	hollow	JJ
10_1101-2021_01_08_425885	30	17	unit	unit	NN
10_1101-2021_01_08_425885	30	18	sphere	sphere	VBD
10_1101-2021_01_08_425885	30	19	,	,	,
10_1101-2021_01_08_425885	30	20	S2	S2	NNP
10_1101-2021_01_08_425885	30	21	,	,	,
10_1101-2021_01_08_425885	30	22	embedded	embed	VBN
10_1101-2021_01_08_425885	30	23	in	in	IN
10_1101-2021_01_08_425885	30	24	the	the	DT
10_1101-2021_01_08_425885	30	25	3-dimensional	3-dimensional	CD
10_1101-2021_01_08_425885	30	26	ambient	ambient	JJ
10_1101-2021_01_08_425885	30	27	space	space	NN
10_1101-2021_01_08_425885	30	28	R3	r3	NN
10_1101-2021_01_08_425885	30	29	,	,	,
10_1101-2021_01_08_425885	30	30	colored	color	VBN
10_1101-2021_01_08_425885	30	31	according	accord	VBG
10_1101-2021_01_08_425885	30	32	to	to	IN
10_1101-2021_01_08_425885	30	33	the	the	DT
10_1101-2021_01_08_425885	30	34	z	z	NN
10_1101-2021_01_08_425885	30	35	-	-	HYPH
10_1101-2021_01_08_425885	30	36	coordinate	coordinate	JJ
10_1101-2021_01_08_425885	30	37	.	.	.
10_1101-2021_01_08_425885	31	1	S2	s2	NN
10_1101-2021_01_08_425885	31	2	has	have	VBZ
10_1101-2021_01_08_425885	31	3	Riemannian	riemannian	JJ
10_1101-2021_01_08_425885	31	4	or	or	CC
10_1101-2021_01_08_425885	31	5	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	31	6	curvature	curvature	NN
10_1101-2021_01_08_425885	31	7	because	because	IN
10_1101-2021_01_08_425885	31	8	there	there	EX
10_1101-2021_01_08_425885	31	9	is	be	VBZ
10_1101-2021_01_08_425885	31	10	no	no	DT
10_1101-2021_01_08_425885	31	11	projection	projection	NN
10_1101-2021_01_08_425885	31	12	onto	onto	IN
10_1101-2021_01_08_425885	31	13	2-dimensional	2-dimensional	CD
10_1101-2021_01_08_425885	31	14	Euclidean	euclidean	JJ
10_1101-2021_01_08_425885	31	15	space	space	NN
10_1101-2021_01_08_425885	31	16	that	that	WDT
10_1101-2021_01_08_425885	31	17	preserves	preserve	VBZ
10_1101-2021_01_08_425885	31	18	geodesic	geodesic	NN
10_1101-2021_01_08_425885	31	19	(	(	-LRB-
10_1101-2021_01_08_425885	31	20	shortest	shortest	NN
10_1101-2021_01_08_425885	31	21	-	-	HYPH
10_1101-2021_01_08_425885	31	22	path	path	NN
10_1101-2021_01_08_425885	31	23	)	)	-RRB-
10_1101-2021_01_08_425885	31	24	distances	distance	NNS
10_1101-2021_01_08_425885	31	25	.	.	.
10_1101-2021_01_08_425885	32	1	(	(	-LRB-
10_1101-2021_01_08_425885	32	2	Right	right	UH
10_1101-2021_01_08_425885	32	3	)	)	-RRB-
10_1101-2021_01_08_425885	32	4	For	for	IN
10_1101-2021_01_08_425885	32	5	example	example	NN
10_1101-2021_01_08_425885	32	6	,	,	,
10_1101-2021_01_08_425885	32	7	a	a	DT
10_1101-2021_01_08_425885	32	8	stereographic	stereographic	JJ
10_1101-2021_01_08_425885	32	9	projection	projection	NN
10_1101-2021_01_08_425885	32	10	using	use	VBG
10_1101-2021_01_08_425885	32	11	the	the	DT
10_1101-2021_01_08_425885	32	12	point	point	NN
10_1101-2021_01_08_425885	32	13	z	z	NN
10_1101-2021_01_08_425885	32	14	=	=	SYM
10_1101-2021_01_08_425885	32	15	(	(	-LRB-
10_1101-2021_01_08_425885	32	16	0	0	CD
10_1101-2021_01_08_425885	32	17	,	,	,
10_1101-2021_01_08_425885	32	18	0	0	CD
10_1101-2021_01_08_425885	32	19	,	,	,
10_1101-2021_01_08_425885	32	20	1	1	CD
10_1101-2021_01_08_425885	32	21	)	)	-RRB-
10_1101-2021_01_08_425885	32	22	and	and	CC
10_1101-2021_01_08_425885	32	23	the	the	DT
10_1101-2021_01_08_425885	32	24	plane	plane	NN
10_1101-2021_01_08_425885	32	25	z	z	NN
10_1101-2021_01_08_425885	32	26	=	=	SYM
10_1101-2021_01_08_425885	32	27	0	0	CD
10_1101-2021_01_08_425885	32	28	introduces	introduce	NNS
10_1101-2021_01_08_425885	32	29	distortions	distortion	NNS
10_1101-2021_01_08_425885	32	30	since	since	IN
10_1101-2021_01_08_425885	32	31	the	the	DT
10_1101-2021_01_08_425885	32	32	geodesic	geodesic	NN
10_1101-2021_01_08_425885	32	33	distance	distance	NN
10_1101-2021_01_08_425885	32	34	between	between	IN
10_1101-2021_01_08_425885	32	35	any	any	DT
10_1101-2021_01_08_425885	32	36	pair	pair	NN
10_1101-2021_01_08_425885	32	37	of	of	IN
10_1101-2021_01_08_425885	32	38	points	point	NNS
10_1101-2021_01_08_425885	32	39	in	in	IN
10_1101-2021_01_08_425885	32	40	the	the	DT
10_1101-2021_01_08_425885	32	41	lower	low	JJR
10_1101-2021_01_08_425885	32	42	hemisphere	hemisphere	NN
10_1101-2021_01_08_425885	32	43	is	be	VBZ
10_1101-2021_01_08_425885	32	44	(	(	-LRB-
10_1101-2021_01_08_425885	32	45	non	non	JJ
10_1101-2021_01_08_425885	32	46	-	-	JJ
10_1101-2021_01_08_425885	32	47	uniformly	uniformly	JJ
10_1101-2021_01_08_425885	32	48	)	)	-RRB-
10_1101-2021_01_08_425885	32	49	larger	large	JJR
10_1101-2021_01_08_425885	32	50	than	than	IN
10_1101-2021_01_08_425885	32	51	the	the	DT
10_1101-2021_01_08_425885	32	52	Euclidean	euclidean	JJ
10_1101-2021_01_08_425885	32	53	distance	distance	NN
10_1101-2021_01_08_425885	32	54	in	in	IN
10_1101-2021_01_08_425885	32	55	this	this	DT
10_1101-2021_01_08_425885	32	56	projection	projection	NN
10_1101-2021_01_08_425885	32	57	.	.	.
10_1101-2021_01_08_425885	33	1	(	(	-LRB-
10_1101-2021_01_08_425885	33	2	B	b	NN
10_1101-2021_01_08_425885	33	3	)	)	-RRB-
10_1101-2021_01_08_425885	33	4	(	(	-LRB-
10_1101-2021_01_08_425885	33	5	Left	left	NN
10_1101-2021_01_08_425885	33	6	)	)	-RRB-
10_1101-2021_01_08_425885	33	7	N	n	NN
10_1101-2021_01_08_425885	33	8	=	=	SYM
10_1101-2021_01_08_425885	33	9	104	104	CD
10_1101-2021_01_08_425885	33	10	points	point	NNS
10_1101-2021_01_08_425885	33	11	uniformly	uniformly	RB
10_1101-2021_01_08_425885	33	12	sampled	sample	VBN
10_1101-2021_01_08_425885	33	13	from	from	IN
10_1101-2021_01_08_425885	33	14	a	a	DT
10_1101-2021_01_08_425885	33	15	scroll	scroll	NN
10_1101-2021_01_08_425885	33	16	,	,	,
10_1101-2021_01_08_425885	33	17	which	which	WDT
10_1101-2021_01_08_425885	33	18	is	be	VBZ
10_1101-2021_01_08_425885	33	19	also	also	RB
10_1101-2021_01_08_425885	33	20	a	a	DT
10_1101-2021_01_08_425885	33	21	2-dimensional	2-dimensional	CD
10_1101-2021_01_08_425885	33	22	manifold	manifold	NN
10_1101-2021_01_08_425885	33	23	embedded	embed	VBN
10_1101-2021_01_08_425885	33	24	in	in	IN
10_1101-2021_01_08_425885	33	25	R3	r3	NN
10_1101-2021_01_08_425885	33	26	.	.	.
10_1101-2021_01_08_425885	34	1	The	the	DT
10_1101-2021_01_08_425885	34	2	scroll	scroll	NN
10_1101-2021_01_08_425885	34	3	has	have	VBZ
10_1101-2021_01_08_425885	34	4	extrinsic	extrinsic	NN
10_1101-2021_01_08_425885	34	5	curvature	curvature	JJ
10_1101-2021_01_08_425885	34	6	because	because	IN
10_1101-2021_01_08_425885	34	7	it	-PRON-	PRP
10_1101-2021_01_08_425885	34	8	curls	curl	VBZ
10_1101-2021_01_08_425885	34	9	away	away	RB
10_1101-2021_01_08_425885	34	10	from	from	IN
10_1101-2021_01_08_425885	34	11	the	the	DT
10_1101-2021_01_08_425885	34	12	tangent	tangent	JJ
10_1101-2021_01_08_425885	34	13	plane	plane	NN
10_1101-2021_01_08_425885	34	14	at	at	IN
10_1101-2021_01_08_425885	34	15	any	any	DT
10_1101-2021_01_08_425885	34	16	point	point	NN
10_1101-2021_01_08_425885	34	17	.	.	.
10_1101-2021_01_08_425885	35	1	(	(	-LRB-
10_1101-2021_01_08_425885	35	2	Right	right	UH
10_1101-2021_01_08_425885	35	3	)	)	-RRB-
10_1101-2021_01_08_425885	35	4	However	however	RB
10_1101-2021_01_08_425885	35	5	,	,	,
10_1101-2021_01_08_425885	35	6	it	-PRON-	PRP
10_1101-2021_01_08_425885	35	7	does	do	VBZ
10_1101-2021_01_08_425885	35	8	not	not	RB
10_1101-2021_01_08_425885	35	9	have	have	VB
10_1101-2021_01_08_425885	35	10	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	35	11	curvature	curvature	NN
10_1101-2021_01_08_425885	35	12	,	,	,
10_1101-2021_01_08_425885	35	13	because	because	IN
10_1101-2021_01_08_425885	35	14	it	-PRON-	PRP
10_1101-2021_01_08_425885	35	15	can	can	MD
10_1101-2021_01_08_425885	35	16	be	be	VB
10_1101-2021_01_08_425885	35	17	projected	project	VBN
10_1101-2021_01_08_425885	35	18	onto	onto	IN
10_1101-2021_01_08_425885	35	19	2-dimensional	2-dimensional	CD
10_1101-2021_01_08_425885	35	20	Euclidean	Euclidean	NNP
10_1101-2021_01_08_425885	35	21	space	space	NN
10_1101-2021_01_08_425885	35	22	in	in	IN
10_1101-2021_01_08_425885	35	23	a	a	DT
10_1101-2021_01_08_425885	35	24	way	way	NN
10_1101-2021_01_08_425885	35	25	that	that	WDT
10_1101-2021_01_08_425885	35	26	preserves	preserve	VBZ
10_1101-2021_01_08_425885	35	27	geodesic	geodesic	NN
10_1101-2021_01_08_425885	35	28	distances	distance	NNS
10_1101-2021_01_08_425885	35	29	,	,	,
10_1101-2021_01_08_425885	35	30	by	by	IN
10_1101-2021_01_08_425885	35	31	unfurling	unfurl	VBG
10_1101-2021_01_08_425885	35	32	.	.	.
10_1101-2021_01_08_425885	36	1	(	(	-LRB-
10_1101-2021_01_08_425885	36	2	C	C	NNP
10_1101-2021_01_08_425885	36	3	)	)	-RRB-
10_1101-2021_01_08_425885	36	4	Intrinsic	Intrinsic	NNP
10_1101-2021_01_08_425885	36	5	differential	differential	NN
10_1101-2021_01_08_425885	36	6	geometry	geometry	NN
10_1101-2021_01_08_425885	36	7	treats	treat	VBZ
10_1101-2021_01_08_425885	36	8	manifolds	manifold	NNS
10_1101-2021_01_08_425885	36	9	as	as	IN
10_1101-2021_01_08_425885	36	10	self	self	NN
10_1101-2021_01_08_425885	36	11	-	-	HYPH
10_1101-2021_01_08_425885	36	12	contained	contain	VBN
10_1101-2021_01_08_425885	36	13	objects	object	NNS
10_1101-2021_01_08_425885	36	14	that	that	WDT
10_1101-2021_01_08_425885	36	15	can	can	MD
10_1101-2021_01_08_425885	36	16	be	be	VB
10_1101-2021_01_08_425885	36	17	described	describe	VBN
10_1101-2021_01_08_425885	36	18	using	use	VBG
10_1101-2021_01_08_425885	36	19	only	only	RB
10_1101-2021_01_08_425885	36	20	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	36	21	coor-	coor-	NN
10_1101-2021_01_08_425885	36	22	dinates	dinate	NNS
10_1101-2021_01_08_425885	36	23	,	,	,
10_1101-2021_01_08_425885	36	24	which	which	WDT
10_1101-2021_01_08_425885	36	25	do	do	VBP
10_1101-2021_01_08_425885	36	26	not	not	RB
10_1101-2021_01_08_425885	36	27	depend	depend	VB
10_1101-2021_01_08_425885	36	28	on	on	IN
10_1101-2021_01_08_425885	36	29	any	any	DT
10_1101-2021_01_08_425885	36	30	embedding	embedding	NN
10_1101-2021_01_08_425885	36	31	or	or	CC
10_1101-2021_01_08_425885	36	32	ambient	ambient	JJ
10_1101-2021_01_08_425885	36	33	space	space	NN
10_1101-2021_01_08_425885	36	34	.	.	.
10_1101-2021_01_08_425885	37	1	One	one	CD
10_1101-2021_01_08_425885	37	2	possible	possible	JJ
10_1101-2021_01_08_425885	37	3	set	set	NN
10_1101-2021_01_08_425885	37	4	of	of	IN
10_1101-2021_01_08_425885	37	5	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	37	6	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	37	7	for	for	IN
10_1101-2021_01_08_425885	37	8	S2	s2	NN
10_1101-2021_01_08_425885	37	9	are	be	VBP
10_1101-2021_01_08_425885	37	10	polar	polar	JJ
10_1101-2021_01_08_425885	37	11	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	37	12	,	,	,
10_1101-2021_01_08_425885	37	13	where	where	WRB
10_1101-2021_01_08_425885	37	14	θ1	θ1	NN
10_1101-2021_01_08_425885	37	15	and	and	CC
10_1101-2021_01_08_425885	37	16	θ2	θ2	NNP
10_1101-2021_01_08_425885	37	17	are	be	VBP
10_1101-2021_01_08_425885	37	18	the	the	DT
10_1101-2021_01_08_425885	37	19	azimuthal	azimuthal	NN
10_1101-2021_01_08_425885	37	20	and	and	CC
10_1101-2021_01_08_425885	37	21	elevation	elevation	NN
10_1101-2021_01_08_425885	37	22	angles	angle	NNS
10_1101-2021_01_08_425885	37	23	respectively	respectively	RB
10_1101-2021_01_08_425885	37	24	.	.	.
10_1101-2021_01_08_425885	38	1	While	while	IN
10_1101-2021_01_08_425885	38	2	this	this	DT
10_1101-2021_01_08_425885	38	3	representation	representation	NN
10_1101-2021_01_08_425885	38	4	superficially	superficially	RB
10_1101-2021_01_08_425885	38	5	resem-	resem-	FW
10_1101-2021_01_08_425885	38	6	bles	ble	VBZ
10_1101-2021_01_08_425885	38	7	the	the	DT
10_1101-2021_01_08_425885	38	8	unfurled	unfurled	JJ
10_1101-2021_01_08_425885	38	9	scroll	scroll	NN
10_1101-2021_01_08_425885	38	10	in	in	IN
10_1101-2021_01_08_425885	38	11	(	(	-LRB-
10_1101-2021_01_08_425885	38	12	B	b	NN
10_1101-2021_01_08_425885	38	13	)	)	-RRB-
10_1101-2021_01_08_425885	38	14	,	,	,
10_1101-2021_01_08_425885	38	15	distances	distance	NNS
10_1101-2021_01_08_425885	38	16	in	in	IN
10_1101-2021_01_08_425885	38	17	this	this	DT
10_1101-2021_01_08_425885	38	18	plane	plane	NN
10_1101-2021_01_08_425885	38	19	are	be	VBP
10_1101-2021_01_08_425885	38	20	non	non	JJ
10_1101-2021_01_08_425885	38	21	-	-	JJ
10_1101-2021_01_08_425885	38	22	Euclidean	euclidean	JJ
10_1101-2021_01_08_425885	38	23	.	.	.
10_1101-2021_01_08_425885	39	1	Any	any	DT
10_1101-2021_01_08_425885	39	2	line	line	NN
10_1101-2021_01_08_425885	39	3	segment	segment	NN
10_1101-2021_01_08_425885	39	4	along	along	IN
10_1101-2021_01_08_425885	39	5	θ2	θ2	NNP
10_1101-2021_01_08_425885	39	6	=	=	SYM
10_1101-2021_01_08_425885	39	7	±π2	±π2	NNP
10_1101-2021_01_08_425885	39	8	has	have	VBZ
10_1101-2021_01_08_425885	39	9	zero	zero	CD
10_1101-2021_01_08_425885	39	10	length	length	NN
10_1101-2021_01_08_425885	39	11	for	for	IN
10_1101-2021_01_08_425885	39	12	example	example	NN
10_1101-2021_01_08_425885	39	13	.	.	.
10_1101-2021_01_08_425885	40	1	(	(	-LRB-
10_1101-2021_01_08_425885	40	2	D	d	NN
10_1101-2021_01_08_425885	40	3	)	)	-RRB-
10_1101-2021_01_08_425885	40	4	Extrinsic	Extrinsic	NNP
10_1101-2021_01_08_425885	40	5	differential	differential	NN
10_1101-2021_01_08_425885	40	6	geometry	geometry	NN
10_1101-2021_01_08_425885	40	7	defines	define	VBZ
10_1101-2021_01_08_425885	40	8	manifolds	manifold	NNS
10_1101-2021_01_08_425885	40	9	in	in	IN
10_1101-2021_01_08_425885	40	10	the	the	DT
10_1101-2021_01_08_425885	40	11	coordinate	coordinate	JJ
10_1101-2021_01_08_425885	40	12	system	system	NN
10_1101-2021_01_08_425885	40	13	of	of	IN
10_1101-2021_01_08_425885	40	14	the	the	DT
10_1101-2021_01_08_425885	40	15	ambient	ambient	JJ
10_1101-2021_01_08_425885	40	16	space	space	NN
10_1101-2021_01_08_425885	40	17	,	,	,
10_1101-2021_01_08_425885	40	18	which	which	WDT
10_1101-2021_01_08_425885	40	19	requires	require	VBZ
10_1101-2021_01_08_425885	40	20	a	a	DT
10_1101-2021_01_08_425885	40	21	privileged	privileged	JJ
10_1101-2021_01_08_425885	40	22	vantage	vantage	NN
10_1101-2021_01_08_425885	40	23	point	point	NN
10_1101-2021_01_08_425885	40	24	off	off	IN
10_1101-2021_01_08_425885	40	25	the	the	DT
10_1101-2021_01_08_425885	40	26	manifold	manifold	NN
10_1101-2021_01_08_425885	40	27	itself	-PRON-	PRP
10_1101-2021_01_08_425885	40	28	.	.	.
10_1101-2021_01_08_425885	41	1	Both	both	DT
10_1101-2021_01_08_425885	41	2	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	41	3	and	and	CC
10_1101-2021_01_08_425885	41	4	extrinsic	extrinsic	JJ
10_1101-2021_01_08_425885	41	5	differential	differential	NN
10_1101-2021_01_08_425885	41	6	geometry	geometry	NN
10_1101-2021_01_08_425885	41	7	can	can	MD
10_1101-2021_01_08_425885	41	8	be	be	VB
10_1101-2021_01_08_425885	41	9	used	use	VBN
10_1101-2021_01_08_425885	41	10	to	to	TO
10_1101-2021_01_08_425885	41	11	compute	compute	VB
10_1101-2021_01_08_425885	41	12	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	41	13	curvature	curvature	NN
10_1101-2021_01_08_425885	41	14	,	,	,
10_1101-2021_01_08_425885	41	15	whereas	whereas	IN
10_1101-2021_01_08_425885	41	16	only	only	JJ
10_1101-2021_01_08_425885	41	17	extrinsic	extrinsic	NN
10_1101-2021_01_08_425885	41	18	differential	differential	NN
10_1101-2021_01_08_425885	41	19	geometry	geometry	NN
10_1101-2021_01_08_425885	41	20	can	can	MD
10_1101-2021_01_08_425885	41	21	be	be	VB
10_1101-2021_01_08_425885	41	22	used	use	VBN
10_1101-2021_01_08_425885	41	23	to	to	TO
10_1101-2021_01_08_425885	41	24	compute	compute	VB
10_1101-2021_01_08_425885	41	25	extrinsic	extrinsic	NN
10_1101-2021_01_08_425885	41	26	curvature	curvature	NN
10_1101-2021_01_08_425885	41	27	(	(	-LRB-
10_1101-2021_01_08_425885	41	28	as	as	IN
10_1101-2021_01_08_425885	41	29	indicated	indicate	VBN
10_1101-2021_01_08_425885	41	30	by	by	IN
10_1101-2021_01_08_425885	41	31	the	the	DT
10_1101-2021_01_08_425885	41	32	black	black	JJ
10_1101-2021_01_08_425885	41	33	arrows	arrow	NNS
10_1101-2021_01_08_425885	41	34	)	)	-RRB-
10_1101-2021_01_08_425885	41	35	.	.	.
10_1101-2021_01_08_425885	42	1	3	3	LS
10_1101-2021_01_08_425885	42	2	.CC	.CC	:
10_1101-2021_01_08_425885	42	3	-	-	HYPH
10_1101-2021_01_08_425885	42	4	BY	by	IN
10_1101-2021_01_08_425885	42	5	-	-	HYPH
10_1101-2021_01_08_425885	42	6	NC	NC	NNP
10_1101-2021_01_08_425885	42	7	-	-	HYPH
10_1101-2021_01_08_425885	42	8	ND	ND	NNP
10_1101-2021_01_08_425885	42	9	4.0	4.0	CD
10_1101-2021_01_08_425885	42	10	International	International	NNP
10_1101-2021_01_08_425885	42	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	42	12	under	under	IN
10_1101-2021_01_08_425885	42	13	a	a	DT
10_1101-2021_01_08_425885	42	14	(	(	-LRB-
10_1101-2021_01_08_425885	42	15	which	which	WDT
10_1101-2021_01_08_425885	42	16	was	be	VBD
10_1101-2021_01_08_425885	42	17	not	not	RB
10_1101-2021_01_08_425885	42	18	certified	certify	VBN
10_1101-2021_01_08_425885	42	19	by	by	IN
10_1101-2021_01_08_425885	42	20	peer	peer	NN
10_1101-2021_01_08_425885	42	21	review	review	NN
10_1101-2021_01_08_425885	42	22	)	)	-RRB-
10_1101-2021_01_08_425885	42	23	is	be	VBZ
10_1101-2021_01_08_425885	42	24	the	the	DT
10_1101-2021_01_08_425885	42	25	author	author	NN
10_1101-2021_01_08_425885	42	26	/	/	SYM
10_1101-2021_01_08_425885	42	27	funder	funder	NN
10_1101-2021_01_08_425885	42	28	,	,	,
10_1101-2021_01_08_425885	42	29	who	who	WP
10_1101-2021_01_08_425885	42	30	has	have	VBZ
10_1101-2021_01_08_425885	42	31	granted	grant	VBN
10_1101-2021_01_08_425885	42	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	42	33	a	a	DT
10_1101-2021_01_08_425885	42	34	license	license	NN
10_1101-2021_01_08_425885	42	35	to	to	TO
10_1101-2021_01_08_425885	42	36	display	display	VB
10_1101-2021_01_08_425885	42	37	the	the	DT
10_1101-2021_01_08_425885	42	38	preprint	preprint	NN
10_1101-2021_01_08_425885	42	39	in	in	IN
10_1101-2021_01_08_425885	42	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	42	41	.	.	.
10_1101-2021_01_08_425885	43	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	43	2	is	be	VBZ
10_1101-2021_01_08_425885	43	3	made	make	VBN
10_1101-2021_01_08_425885	43	4	The	the	DT
10_1101-2021_01_08_425885	43	5	copyright	copyright	NN
10_1101-2021_01_08_425885	43	6	holder	holder	NN
10_1101-2021_01_08_425885	43	7	for	for	IN
10_1101-2021_01_08_425885	43	8	this	this	DT
10_1101-2021_01_08_425885	43	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	43	10	version	version	NN
10_1101-2021_01_08_425885	43	11	posted	post	VBD
10_1101-2021_01_08_425885	43	12	January	January	NNP
10_1101-2021_01_08_425885	43	13	8	8	CD
10_1101-2021_01_08_425885	43	14	,	,	,
10_1101-2021_01_08_425885	43	15	2021	2021	CD
10_1101-2021_01_08_425885	43	16	.	.	.
10_1101-2021_01_08_425885	43	17	;	;	:
10_1101-2021_01_08_425885	43	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	43	19	:	:	:
10_1101-2021_01_08_425885	43	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	43	21	preprint	preprint	NN
10_1101-2021_01_08_425885	43	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	NNP
10_1101-2021_01_08_425885	43	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NN
10_1101-2021_01_08_425885	43	24	extrinsic	extrinsic	NN
10_1101-2021_01_08_425885	43	25	curvature	curvature	NN
10_1101-2021_01_08_425885	43	26	is	be	VBZ
10_1101-2021_01_08_425885	43	27	incidental	incidental	JJ
10_1101-2021_01_08_425885	43	28	to	to	IN
10_1101-2021_01_08_425885	43	29	an	an	DT
10_1101-2021_01_08_425885	43	30	embedding	embedding	NN
10_1101-2021_01_08_425885	43	31	,	,	,
10_1101-2021_01_08_425885	43	32	we	-PRON-	PRP
10_1101-2021_01_08_425885	43	33	will	will	MD
10_1101-2021_01_08_425885	43	34	restrict	restrict	VB
10_1101-2021_01_08_425885	43	35	our	-PRON-	PRP$
10_1101-2021_01_08_425885	43	36	attention	attention	NN
10_1101-2021_01_08_425885	43	37	to	to	IN
10_1101-2021_01_08_425885	43	38	the	the	DT
10_1101-2021_01_08_425885	43	39	former	former	JJ
10_1101-2021_01_08_425885	43	40	.	.	.
10_1101-2021_01_08_425885	44	1	A	a	DT
10_1101-2021_01_08_425885	44	2	precise	precise	JJ
10_1101-2021_01_08_425885	44	3	description	description	NN
10_1101-2021_01_08_425885	44	4	of	of	IN
10_1101-2021_01_08_425885	44	5	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	44	6	curvature	curvature	NN
10_1101-2021_01_08_425885	44	7	is	be	VBZ
10_1101-2021_01_08_425885	44	8	provided	provide	VBN
10_1101-2021_01_08_425885	44	9	by	by	IN
10_1101-2021_01_08_425885	44	10	the	the	DT
10_1101-2021_01_08_425885	44	11	Riemannian	riemannian	JJ
10_1101-2021_01_08_425885	44	12	curvature	curvature	NN
10_1101-2021_01_08_425885	44	13	tensor	tensor	NN
10_1101-2021_01_08_425885	44	14	,	,	,
10_1101-2021_01_08_425885	44	15	Rlkij(p	rlkij(p	NN
10_1101-2021_01_08_425885	44	16	)	)	-RRB-
10_1101-2021_01_08_425885	44	17	.	.	.
10_1101-2021_01_08_425885	45	1	For	for	IN
10_1101-2021_01_08_425885	45	2	a	a	DT
10_1101-2021_01_08_425885	45	3	given	give	VBN
10_1101-2021_01_08_425885	45	4	basis	basis	NN
10_1101-2021_01_08_425885	45	5	{	{	-LRB-
10_1101-2021_01_08_425885	45	6	v	v	NN
10_1101-2021_01_08_425885	45	7	}	}	-RRB-
10_1101-2021_01_08_425885	45	8	,	,	,
10_1101-2021_01_08_425885	45	9	this	this	DT
10_1101-2021_01_08_425885	45	10	tensor	tensor	NN
10_1101-2021_01_08_425885	45	11	quantifies	quantify	VBZ
10_1101-2021_01_08_425885	45	12	how	how	WRB
10_1101-2021_01_08_425885	45	13	much	much	JJ
10_1101-2021_01_08_425885	45	14	a	a	DT
10_1101-2021_01_08_425885	45	15	vector	vector	NN
10_1101-2021_01_08_425885	45	16	initially	initially	RB
10_1101-2021_01_08_425885	45	17	pointing	point	VBG
10_1101-2021_01_08_425885	45	18	in	in	IN
10_1101-2021_01_08_425885	45	19	direction	direction	NN
10_1101-2021_01_08_425885	45	20	vk	vk	NNP
10_1101-2021_01_08_425885	45	21	is	be	VBZ
10_1101-2021_01_08_425885	45	22	displaced	displace	VBN
10_1101-2021_01_08_425885	45	23	in	in	IN
10_1101-2021_01_08_425885	45	24	direction	direction	NN
10_1101-2021_01_08_425885	45	25	vl	vl	NN
10_1101-2021_01_08_425885	45	26	after	after	IN
10_1101-2021_01_08_425885	45	27	parallel	parallel	JJ
10_1101-2021_01_08_425885	45	28	transport	transport	NN
10_1101-2021_01_08_425885	45	29	around	around	IN
10_1101-2021_01_08_425885	45	30	an	an	DT
10_1101-2021_01_08_425885	45	31	infinitesimal	infinitesimal	JJ
10_1101-2021_01_08_425885	45	32	parallelogram	parallelogram	NN
10_1101-2021_01_08_425885	45	33	defined	define	VBN
10_1101-2021_01_08_425885	45	34	by	by	IN
10_1101-2021_01_08_425885	45	35	directions	direction	NNS
10_1101-2021_01_08_425885	45	36	vi	vi	NNP
10_1101-2021_01_08_425885	45	37	and	and	CC
10_1101-2021_01_08_425885	45	38	vj	vj	NNP
10_1101-2021_01_08_425885	45	39	.	.	.
10_1101-2021_01_08_425885	46	1	The	the	DT
10_1101-2021_01_08_425885	46	2	simplest	simple	JJS
10_1101-2021_01_08_425885	46	3	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	46	4	curvature	curvature	NN
10_1101-2021_01_08_425885	46	5	descriptor	descriptor	NN
10_1101-2021_01_08_425885	46	6	is	be	VBZ
10_1101-2021_01_08_425885	46	7	scalar	scalar	JJ
10_1101-2021_01_08_425885	46	8	curvature	curvature	NN
10_1101-2021_01_08_425885	46	9	,	,	,
10_1101-2021_01_08_425885	46	10	S(p	s(p	JJ
10_1101-2021_01_08_425885	46	11	)	)	-RRB-
10_1101-2021_01_08_425885	46	12	,	,	,
10_1101-2021_01_08_425885	46	13	which	which	WDT
10_1101-2021_01_08_425885	46	14	is	be	VBZ
10_1101-2021_01_08_425885	46	15	formed	form	VBN
10_1101-2021_01_08_425885	46	16	by	by	IN
10_1101-2021_01_08_425885	46	17	contracting	contract	VBG
10_1101-2021_01_08_425885	46	18	Rlkij(p	rlkij(p	NN
10_1101-2021_01_08_425885	46	19	)	)	-RRB-
10_1101-2021_01_08_425885	46	20	to	to	IN
10_1101-2021_01_08_425885	46	21	a	a	DT
10_1101-2021_01_08_425885	46	22	scalar	scalar	JJ
10_1101-2021_01_08_425885	46	23	quantity	quantity	NN
10_1101-2021_01_08_425885	46	24	,	,	,
10_1101-2021_01_08_425885	46	25	as	as	IN
10_1101-2021_01_08_425885	46	26	its	-PRON-	PRP$
10_1101-2021_01_08_425885	46	27	name	name	NN
10_1101-2021_01_08_425885	46	28	suggests	suggest	VBZ
10_1101-2021_01_08_425885	46	29	.	.	.
10_1101-2021_01_08_425885	47	1	When	when	WRB
10_1101-2021_01_08_425885	47	2	S(p	S(p	VBN
10_1101-2021_01_08_425885	47	3	)	)	-RRB-
10_1101-2021_01_08_425885	47	4	is	be	VBZ
10_1101-2021_01_08_425885	47	5	greater	great	JJR
10_1101-2021_01_08_425885	47	6	(	(	-LRB-
10_1101-2021_01_08_425885	47	7	less	less	JJR
10_1101-2021_01_08_425885	47	8	)	)	-RRB-
10_1101-2021_01_08_425885	47	9	than	than	IN
10_1101-2021_01_08_425885	47	10	0	0	CD
10_1101-2021_01_08_425885	47	11	,	,	,
10_1101-2021_01_08_425885	47	12	the	the	DT
10_1101-2021_01_08_425885	47	13	sum	sum	NN
10_1101-2021_01_08_425885	47	14	of	of	IN
10_1101-2021_01_08_425885	47	15	the	the	DT
10_1101-2021_01_08_425885	47	16	angles	angle	NNS
10_1101-2021_01_08_425885	47	17	of	of	IN
10_1101-2021_01_08_425885	47	18	a	a	DT
10_1101-2021_01_08_425885	47	19	triangle	triangle	NN
10_1101-2021_01_08_425885	47	20	formed	form	VBN
10_1101-2021_01_08_425885	47	21	by	by	IN
10_1101-2021_01_08_425885	47	22	connecting	connect	VBG
10_1101-2021_01_08_425885	47	23	three	three	CD
10_1101-2021_01_08_425885	47	24	points	point	NNS
10_1101-2021_01_08_425885	47	25	near	near	IN
10_1101-2021_01_08_425885	47	26	p	p	NN
10_1101-2021_01_08_425885	47	27	by	by	IN
10_1101-2021_01_08_425885	47	28	geodesics	geodesic	NNS
10_1101-2021_01_08_425885	47	29	is	be	VBZ
10_1101-2021_01_08_425885	47	30	greater	great	JJR
10_1101-2021_01_08_425885	47	31	(	(	-LRB-
10_1101-2021_01_08_425885	47	32	less	less	RBR
10_1101-2021_01_08_425885	47	33	)	)	-RRB-
10_1101-2021_01_08_425885	47	34	than	than	IN
10_1101-2021_01_08_425885	47	35	π	π	NN
10_1101-2021_01_08_425885	47	36	.	.	.
10_1101-2021_01_08_425885	48	1	Likewise	likewise	RB
10_1101-2021_01_08_425885	48	2	,	,	,
10_1101-2021_01_08_425885	48	3	when	when	WRB
10_1101-2021_01_08_425885	48	4	S(p	s(p	NN
10_1101-2021_01_08_425885	48	5	)	)	-RRB-
10_1101-2021_01_08_425885	48	6	is	be	VBZ
10_1101-2021_01_08_425885	48	7	greater	great	JJR
10_1101-2021_01_08_425885	48	8	(	(	-LRB-
10_1101-2021_01_08_425885	48	9	less	less	JJR
10_1101-2021_01_08_425885	48	10	)	)	-RRB-
10_1101-2021_01_08_425885	48	11	than	than	IN
10_1101-2021_01_08_425885	48	12	0	0	CD
10_1101-2021_01_08_425885	48	13	,	,	,
10_1101-2021_01_08_425885	48	14	a	a	DT
10_1101-2021_01_08_425885	48	15	small	small	JJ
10_1101-2021_01_08_425885	48	16	ball	ball	NN
10_1101-2021_01_08_425885	48	17	centred	centre	VBN
10_1101-2021_01_08_425885	48	18	at	at	IN
10_1101-2021_01_08_425885	48	19	p	p	NN
10_1101-2021_01_08_425885	48	20	has	have	VBZ
10_1101-2021_01_08_425885	48	21	a	a	DT
10_1101-2021_01_08_425885	48	22	smaller	small	JJR
10_1101-2021_01_08_425885	48	23	(	(	-LRB-
10_1101-2021_01_08_425885	48	24	larger	large	JJR
10_1101-2021_01_08_425885	48	25	)	)	-RRB-
10_1101-2021_01_08_425885	48	26	volume	volume	NN
10_1101-2021_01_08_425885	48	27	than	than	IN
10_1101-2021_01_08_425885	48	28	a	a	DT
10_1101-2021_01_08_425885	48	29	ball	ball	NN
10_1101-2021_01_08_425885	48	30	of	of	IN
10_1101-2021_01_08_425885	48	31	the	the	DT
10_1101-2021_01_08_425885	48	32	same	same	JJ
10_1101-2021_01_08_425885	48	33	radius	radius	NN
10_1101-2021_01_08_425885	48	34	in	in	IN
10_1101-2021_01_08_425885	48	35	Euclidean	euclidean	JJ
10_1101-2021_01_08_425885	48	36	space	space	NN
10_1101-2021_01_08_425885	48	37	.	.	.
10_1101-2021_01_08_425885	49	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	49	2	furnish	furnish	VBP
10_1101-2021_01_08_425885	49	3	toy	toy	NN
10_1101-2021_01_08_425885	49	4	examples	example	NNS
10_1101-2021_01_08_425885	49	5	in	in	IN
10_1101-2021_01_08_425885	49	6	the	the	DT
10_1101-2021_01_08_425885	49	7	main	main	JJ
10_1101-2021_01_08_425885	49	8	text	text	NN
10_1101-2021_01_08_425885	49	9	to	to	TO
10_1101-2021_01_08_425885	49	10	provide	provide	VB
10_1101-2021_01_08_425885	49	11	stronger	strong	JJR
10_1101-2021_01_08_425885	49	12	intuition	intuition	NN
10_1101-2021_01_08_425885	49	13	for	for	IN
10_1101-2021_01_08_425885	49	14	this	this	DT
10_1101-2021_01_08_425885	49	15	quantity	quantity	NN
10_1101-2021_01_08_425885	49	16	.	.	.
10_1101-2021_01_08_425885	50	1	In	in	IN
10_1101-2021_01_08_425885	50	2	theory	theory	NN
10_1101-2021_01_08_425885	50	3	,	,	,
10_1101-2021_01_08_425885	50	4	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	50	5	curvature	curvature	NN
10_1101-2021_01_08_425885	50	6	can	can	MD
10_1101-2021_01_08_425885	50	7	be	be	VB
10_1101-2021_01_08_425885	50	8	equivalently	equivalently	RB
10_1101-2021_01_08_425885	50	9	computed	compute	VBN
10_1101-2021_01_08_425885	50	10	using	use	VBG
10_1101-2021_01_08_425885	50	11	tools	tool	NNS
10_1101-2021_01_08_425885	50	12	from	from	IN
10_1101-2021_01_08_425885	50	13	either	either	DT
10_1101-2021_01_08_425885	50	14	one	one	CD
10_1101-2021_01_08_425885	50	15	of	of	IN
10_1101-2021_01_08_425885	50	16	the	the	DT
10_1101-2021_01_08_425885	50	17	two	two	CD
10_1101-2021_01_08_425885	50	18	branches	branch	NNS
10_1101-2021_01_08_425885	50	19	of	of	IN
10_1101-2021_01_08_425885	50	20	differential	differential	NN
10_1101-2021_01_08_425885	50	21	geometry	geometry	NN
10_1101-2021_01_08_425885	50	22	.	.	.
10_1101-2021_01_08_425885	51	1	Intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	51	2	differential	differential	NN
10_1101-2021_01_08_425885	51	3	geometry	geometry	NN
10_1101-2021_01_08_425885	51	4	makes	make	VBZ
10_1101-2021_01_08_425885	51	5	no	no	DT
10_1101-2021_01_08_425885	51	6	recourse	recourse	NN
10_1101-2021_01_08_425885	51	7	to	to	IN
10_1101-2021_01_08_425885	51	8	an	an	DT
10_1101-2021_01_08_425885	51	9	external	external	JJ
10_1101-2021_01_08_425885	51	10	vantage	vantage	NN
10_1101-2021_01_08_425885	51	11	point	point	NN
10_1101-2021_01_08_425885	51	12	off	off	IN
10_1101-2021_01_08_425885	51	13	a	a	DT
10_1101-2021_01_08_425885	51	14	manifold	manifold	NN
10_1101-2021_01_08_425885	51	15	,	,	,
10_1101-2021_01_08_425885	51	16	just	just	RB
10_1101-2021_01_08_425885	51	17	as	as	IN
10_1101-2021_01_08_425885	51	18	the	the	DT
10_1101-2021_01_08_425885	51	19	polygonal	polygonal	JJ
10_1101-2021_01_08_425885	51	20	characters	character	NNS
10_1101-2021_01_08_425885	51	21	in	in	IN
10_1101-2021_01_08_425885	51	22	Edwin	Edwin	NNP
10_1101-2021_01_08_425885	51	23	Abbot	Abbot	NNP
10_1101-2021_01_08_425885	51	24	’s	’s	POS
10_1101-2021_01_08_425885	51	25	classic	classic	JJ
10_1101-2021_01_08_425885	51	26	Flatland	Flatland	NNP
10_1101-2021_01_08_425885	51	27	[	[	-LRB-
10_1101-2021_01_08_425885	51	28	25	25	CD
10_1101-2021_01_08_425885	51	29	]	]	-RRB-
10_1101-2021_01_08_425885	51	30	were	be	VBD
10_1101-2021_01_08_425885	51	31	confined	confine	VBN
10_1101-2021_01_08_425885	51	32	to	to	IN
10_1101-2021_01_08_425885	51	33	traversing	traverse	VBG
10_1101-2021_01_08_425885	51	34	in	in	IN
10_1101-2021_01_08_425885	51	35	R2	R2	NNP
10_1101-2021_01_08_425885	51	36	,	,	,
10_1101-2021_01_08_425885	51	37	and	and	CC
10_1101-2021_01_08_425885	51	38	found	find	VBD
10_1101-2021_01_08_425885	51	39	the	the	DT
10_1101-2021_01_08_425885	51	40	notion	notion	NN
10_1101-2021_01_08_425885	51	41	of	of	IN
10_1101-2021_01_08_425885	51	42	R3	r3	NN
10_1101-2021_01_08_425885	51	43	unfathomable	unfathomable	JJ
10_1101-2021_01_08_425885	51	44	.	.	.
10_1101-2021_01_08_425885	52	1	In	in	IN
10_1101-2021_01_08_425885	52	2	this	this	DT
10_1101-2021_01_08_425885	52	3	branch	branch	NN
10_1101-2021_01_08_425885	52	4	,	,	,
10_1101-2021_01_08_425885	52	5	a	a	DT
10_1101-2021_01_08_425885	52	6	manifold	manifold	NN
10_1101-2021_01_08_425885	52	7	is	be	VBZ
10_1101-2021_01_08_425885	52	8	therefore	therefore	RB
10_1101-2021_01_08_425885	52	9	represented	represent	VBN
10_1101-2021_01_08_425885	52	10	in	in	IN
10_1101-2021_01_08_425885	52	11	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	52	12	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	52	13	,	,	,
10_1101-2021_01_08_425885	52	14	which	which	WDT
10_1101-2021_01_08_425885	52	15	are	be	VBP
10_1101-2021_01_08_425885	52	16	agnostic	agnostic	JJ
10_1101-2021_01_08_425885	52	17	to	to	IN
10_1101-2021_01_08_425885	52	18	any	any	DT
10_1101-2021_01_08_425885	52	19	ambient	ambient	JJ
10_1101-2021_01_08_425885	52	20	space	space	NN
10_1101-2021_01_08_425885	52	21	or	or	CC
10_1101-2021_01_08_425885	52	22	embedding	embedding	NN
10_1101-2021_01_08_425885	52	23	.	.	.
10_1101-2021_01_08_425885	53	1	A	a	DT
10_1101-2021_01_08_425885	53	2	hollow	hollow	JJ
10_1101-2021_01_08_425885	53	3	sphere	sphere	NN
10_1101-2021_01_08_425885	53	4	represented	represent	VBN
10_1101-2021_01_08_425885	53	5	in	in	IN
10_1101-2021_01_08_425885	53	6	polar	polar	JJ
10_1101-2021_01_08_425885	53	7	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	53	8	and	and	CC
10_1101-2021_01_08_425885	53	9	k	k	NN
10_1101-2021_01_08_425885	53	10	-	-	HYPH
10_1101-2021_01_08_425885	53	11	nearest	nearest	NNP
10_1101-2021_01_08_425885	53	12	neighbor	neighbor	NN
10_1101-2021_01_08_425885	53	13	(	(	-LRB-
10_1101-2021_01_08_425885	53	14	kNN	kNN	NNP
10_1101-2021_01_08_425885	53	15	)	)	-RRB-
10_1101-2021_01_08_425885	53	16	graph	graph	NN
10_1101-2021_01_08_425885	53	17	representations	representation	NNS
10_1101-2021_01_08_425885	53	18	of	of	IN
10_1101-2021_01_08_425885	53	19	a	a	DT
10_1101-2021_01_08_425885	53	20	dataset	dataset	NN
10_1101-2021_01_08_425885	53	21	,	,	,
10_1101-2021_01_08_425885	53	22	for	for	IN
10_1101-2021_01_08_425885	53	23	instance	instance	NN
10_1101-2021_01_08_425885	53	24	,	,	,
10_1101-2021_01_08_425885	53	25	are	be	VBP
10_1101-2021_01_08_425885	53	26	in	in	IN
10_1101-2021_01_08_425885	53	27	this	this	DT
10_1101-2021_01_08_425885	53	28	spirit	spirit	NN
10_1101-2021_01_08_425885	53	29	(	(	-LRB-
10_1101-2021_01_08_425885	53	30	see	see	VB
10_1101-2021_01_08_425885	53	31	Figure	Figure	NNP
10_1101-2021_01_08_425885	53	32	1C	1c	NN
10_1101-2021_01_08_425885	53	33	)	)	-RRB-
10_1101-2021_01_08_425885	53	34	.	.	.
10_1101-2021_01_08_425885	54	1	Conversely	conversely	RB
10_1101-2021_01_08_425885	54	2	,	,	,
10_1101-2021_01_08_425885	54	3	in	in	IN
10_1101-2021_01_08_425885	54	4	extrinsic	extrinsic	JJ
10_1101-2021_01_08_425885	54	5	differential	differential	NN
10_1101-2021_01_08_425885	54	6	geometry	geometry	NN
10_1101-2021_01_08_425885	54	7	,	,	,
10_1101-2021_01_08_425885	54	8	a	a	DT
10_1101-2021_01_08_425885	54	9	manifold	manifold	NN
10_1101-2021_01_08_425885	54	10	is	be	VBZ
10_1101-2021_01_08_425885	54	11	treated	treat	VBN
10_1101-2021_01_08_425885	54	12	as	as	IN
10_1101-2021_01_08_425885	54	13	a	a	DT
10_1101-2021_01_08_425885	54	14	surface	surface	NN
10_1101-2021_01_08_425885	54	15	embedded	embed	VBN
10_1101-2021_01_08_425885	54	16	in	in	IN
10_1101-2021_01_08_425885	54	17	an	an	DT
10_1101-2021_01_08_425885	54	18	ambient	ambient	JJ
10_1101-2021_01_08_425885	54	19	space	space	NN
10_1101-2021_01_08_425885	54	20	,	,	,
10_1101-2021_01_08_425885	54	21	and	and	CC
10_1101-2021_01_08_425885	54	22	is	be	VBZ
10_1101-2021_01_08_425885	54	23	represented	represent	VBN
10_1101-2021_01_08_425885	54	24	in	in	IN
10_1101-2021_01_08_425885	54	25	ambient	ambient	JJ
10_1101-2021_01_08_425885	54	26	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	54	27	(	(	-LRB-
10_1101-2021_01_08_425885	54	28	see	see	VB
10_1101-2021_01_08_425885	54	29	Figure	Figure	NNP
10_1101-2021_01_08_425885	54	30	1D	1D	NNP
10_1101-2021_01_08_425885	54	31	)	)	-RRB-
10_1101-2021_01_08_425885	54	32	.	.	.
10_1101-2021_01_08_425885	55	1	The	the	DT
10_1101-2021_01_08_425885	55	2	surface	surface	NN
10_1101-2021_01_08_425885	55	3	of	of	IN
10_1101-2021_01_08_425885	55	4	an	an	DT
10_1101-2021_01_08_425885	55	5	organ	organ	NN
10_1101-2021_01_08_425885	55	6	is	be	VBZ
10_1101-2021_01_08_425885	55	7	parameterized	parameterize	VBN
10_1101-2021_01_08_425885	55	8	this	this	DT
10_1101-2021_01_08_425885	55	9	way	way	NN
10_1101-2021_01_08_425885	55	10	,	,	,
10_1101-2021_01_08_425885	55	11	for	for	IN
10_1101-2021_01_08_425885	55	12	example	example	NN
10_1101-2021_01_08_425885	55	13	,	,	,
10_1101-2021_01_08_425885	55	14	in	in	IN
10_1101-2021_01_08_425885	55	15	a	a	DT
10_1101-2021_01_08_425885	55	16	surgical	surgical	JJ
10_1101-2021_01_08_425885	55	17	robot	robot	NN
10_1101-2021_01_08_425885	55	18	suturing	suture	VBG
10_1101-2021_01_08_425885	55	19	an	an	DT
10_1101-2021_01_08_425885	55	20	incision	incision	NN
10_1101-2021_01_08_425885	55	21	.	.	.
10_1101-2021_01_08_425885	56	1	In	in	IN
10_1101-2021_01_08_425885	56	2	this	this	DT
10_1101-2021_01_08_425885	56	3	work	work	NN
10_1101-2021_01_08_425885	56	4	,	,	,
10_1101-2021_01_08_425885	56	5	we	-PRON-	PRP
10_1101-2021_01_08_425885	56	6	explore	explore	VBP
10_1101-2021_01_08_425885	56	7	two	two	CD
10_1101-2021_01_08_425885	56	8	approaches	approach	NNS
10_1101-2021_01_08_425885	56	9	for	for	IN
10_1101-2021_01_08_425885	56	10	estimating	estimate	VBG
10_1101-2021_01_08_425885	56	11	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	56	12	curvature	curvature	NN
10_1101-2021_01_08_425885	56	13	based	base	VBN
10_1101-2021_01_08_425885	56	14	on	on	IN
10_1101-2021_01_08_425885	56	15	these	these	DT
10_1101-2021_01_08_425885	56	16	twin	twin	JJ
10_1101-2021_01_08_425885	56	17	views	view	NNS
10_1101-2021_01_08_425885	56	18	,	,	,
10_1101-2021_01_08_425885	56	19	keeping	keep	VBG
10_1101-2021_01_08_425885	56	20	in	in	IN
10_1101-2021_01_08_425885	56	21	mind	mind	NN
10_1101-2021_01_08_425885	56	22	practical	practical	JJ
10_1101-2021_01_08_425885	56	23	limitations	limitation	NNS
10_1101-2021_01_08_425885	56	24	of	of	IN
10_1101-2021_01_08_425885	56	25	real	real	JJ
10_1101-2021_01_08_425885	56	26	-	-	HYPH
10_1101-2021_01_08_425885	56	27	world	world	NN
10_1101-2021_01_08_425885	56	28	datasets	dataset	NNS
10_1101-2021_01_08_425885	56	29	,	,	,
10_1101-2021_01_08_425885	56	30	which	which	WDT
10_1101-2021_01_08_425885	56	31	may	may	MD
10_1101-2021_01_08_425885	56	32	be	be	VB
10_1101-2021_01_08_425885	56	33	comprised	comprise	VBN
10_1101-2021_01_08_425885	56	34	of	of	IN
10_1101-2021_01_08_425885	56	35	a	a	DT
10_1101-2021_01_08_425885	56	36	relatively	relatively	RB
10_1101-2021_01_08_425885	56	37	small	small	JJ
10_1101-2021_01_08_425885	56	38	number	number	NN
10_1101-2021_01_08_425885	56	39	of	of	IN
10_1101-2021_01_08_425885	56	40	noisy	noisy	JJ
10_1101-2021_01_08_425885	56	41	measurements	measurement	NNS
10_1101-2021_01_08_425885	56	42	.	.	.
10_1101-2021_01_08_425885	57	1	The	the	DT
10_1101-2021_01_08_425885	57	2	first	first	JJ
10_1101-2021_01_08_425885	57	3	approach	approach	NN
10_1101-2021_01_08_425885	57	4	uses	use	VBZ
10_1101-2021_01_08_425885	57	5	the	the	DT
10_1101-2021_01_08_425885	57	6	Laplace	Laplace	NNP
10_1101-2021_01_08_425885	57	7	-	-	HYPH
10_1101-2021_01_08_425885	57	8	Beltrami	Beltrami	NNP
10_1101-2021_01_08_425885	57	9	operator	operator	NN
10_1101-2021_01_08_425885	57	10	,	,	,
10_1101-2021_01_08_425885	57	11	which	which	WDT
10_1101-2021_01_08_425885	57	12	is	be	VBZ
10_1101-2021_01_08_425885	57	13	well	well	RB
10_1101-2021_01_08_425885	57	14	-	-	HYPH
10_1101-2021_01_08_425885	57	15	studied	study	VBN
10_1101-2021_01_08_425885	57	16	in	in	IN
10_1101-2021_01_08_425885	57	17	previous	previous	JJ
10_1101-2021_01_08_425885	57	18	applications	application	NNS
10_1101-2021_01_08_425885	57	19	of	of	IN
10_1101-2021_01_08_425885	57	20	differential	differential	NN
10_1101-2021_01_08_425885	57	21	geometry	geometry	NN
10_1101-2021_01_08_425885	57	22	to	to	IN
10_1101-2021_01_08_425885	57	23	data	data	NN
10_1101-2021_01_08_425885	57	24	analysis	analysis	NN
10_1101-2021_01_08_425885	57	25	[	[	-LRB-
10_1101-2021_01_08_425885	57	26	14	14	CD
10_1101-2021_01_08_425885	57	27	,	,	,
10_1101-2021_01_08_425885	57	28	26	26	CD
10_1101-2021_01_08_425885	57	29	,	,	,
10_1101-2021_01_08_425885	57	30	27	27	CD
10_1101-2021_01_08_425885	57	31	,	,	,
10_1101-2021_01_08_425885	57	32	28	28	CD
10_1101-2021_01_08_425885	57	33	,	,	,
10_1101-2021_01_08_425885	57	34	29	29	CD
10_1101-2021_01_08_425885	57	35	]	]	-RRB-
10_1101-2021_01_08_425885	57	36	,	,	,
10_1101-2021_01_08_425885	57	37	and	and	CC
10_1101-2021_01_08_425885	57	38	is	be	VBZ
10_1101-2021_01_08_425885	57	39	theoretically	theoretically	RB
10_1101-2021_01_08_425885	57	40	appealing	appealing	JJ
10_1101-2021_01_08_425885	57	41	as	as	IN
10_1101-2021_01_08_425885	57	42	an	an	DT
10_1101-2021_01_08_425885	57	43	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	57	44	quantity	quantity	NN
10_1101-2021_01_08_425885	57	45	that	that	WDT
10_1101-2021_01_08_425885	57	46	is	be	VBZ
10_1101-2021_01_08_425885	57	47	embedding	embed	VBG
10_1101-2021_01_08_425885	57	48	-	-	HYPH
10_1101-2021_01_08_425885	57	49	invariant	invariant	JJ
10_1101-2021_01_08_425885	57	50	.	.	.
10_1101-2021_01_08_425885	58	1	However	however	RB
10_1101-2021_01_08_425885	58	2	,	,	,
10_1101-2021_01_08_425885	58	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	58	4	find	find	VBP
10_1101-2021_01_08_425885	58	5	that	that	IN
10_1101-2021_01_08_425885	58	6	this	this	DT
10_1101-2021_01_08_425885	58	7	approach	approach	NN
10_1101-2021_01_08_425885	58	8	can	can	MD
10_1101-2021_01_08_425885	58	9	not	not	RB
10_1101-2021_01_08_425885	58	10	accurately	accurately	RB
10_1101-2021_01_08_425885	58	11	estimate	estimate	VB
10_1101-2021_01_08_425885	58	12	even	even	RB
10_1101-2021_01_08_425885	58	13	average	average	JJ
10_1101-2021_01_08_425885	58	14	scalar	scalar	JJ
10_1101-2021_01_08_425885	58	15	curvature	curvature	NN
10_1101-2021_01_08_425885	58	16	on	on	IN
10_1101-2021_01_08_425885	58	17	the	the	DT
10_1101-2021_01_08_425885	58	18	simplest	simple	JJS
10_1101-2021_01_08_425885	58	19	of	of	IN
10_1101-2021_01_08_425885	58	20	low	low	JJ
10_1101-2021_01_08_425885	58	21	-	-	HYPH
10_1101-2021_01_08_425885	58	22	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	58	23	toy	toy	NN
10_1101-2021_01_08_425885	58	24	manifolds	manifold	NNS
10_1101-2021_01_08_425885	58	25	for	for	IN
10_1101-2021_01_08_425885	58	26	small	small	JJ
10_1101-2021_01_08_425885	58	27	sample	sample	NN
10_1101-2021_01_08_425885	58	28	sizes	size	NNS
10_1101-2021_01_08_425885	58	29	,	,	,
10_1101-2021_01_08_425885	58	30	despite	despite	IN
10_1101-2021_01_08_425885	58	31	the	the	DT
10_1101-2021_01_08_425885	58	32	history	history	NN
10_1101-2021_01_08_425885	58	33	and	and	CC
10_1101-2021_01_08_425885	58	34	ubiquity	ubiquity	NN
10_1101-2021_01_08_425885	58	35	of	of	IN
10_1101-2021_01_08_425885	58	36	the	the	DT
10_1101-2021_01_08_425885	58	37	Laplace	Laplace	NNP
10_1101-2021_01_08_425885	58	38	-	-	HYPH
10_1101-2021_01_08_425885	58	39	Beltrami	Beltrami	NNP
10_1101-2021_01_08_425885	58	40	operator	operator	NN
10_1101-2021_01_08_425885	58	41	in	in	IN
10_1101-2021_01_08_425885	58	42	geometric	geometric	JJ
10_1101-2021_01_08_425885	58	43	data	datum	NNS
10_1101-2021_01_08_425885	58	44	analysis	analysis	NN
10_1101-2021_01_08_425885	58	45	.	.	.
10_1101-2021_01_08_425885	59	1	Meanwhile	meanwhile	RB
10_1101-2021_01_08_425885	59	2	,	,	,
10_1101-2021_01_08_425885	59	3	the	the	DT
10_1101-2021_01_08_425885	59	4	second	second	JJ
10_1101-2021_01_08_425885	59	5	approach	approach	NN
10_1101-2021_01_08_425885	59	6	uses	use	VBZ
10_1101-2021_01_08_425885	59	7	the	the	DT
10_1101-2021_01_08_425885	59	8	Second	Second	NNP
10_1101-2021_01_08_425885	59	9	Fundamental	Fundamental	NNP
10_1101-2021_01_08_425885	59	10	Form	Form	NNP
10_1101-2021_01_08_425885	59	11	and	and	CC
10_1101-2021_01_08_425885	59	12	the	the	DT
10_1101-2021_01_08_425885	59	13	Gauss	Gauss	NNP
10_1101-2021_01_08_425885	59	14	-	-	HYPH
10_1101-2021_01_08_425885	59	15	Codazzi	Codazzi	NNP
10_1101-2021_01_08_425885	59	16	equation	equation	NN
10_1101-2021_01_08_425885	59	17	[	[	-LRB-
10_1101-2021_01_08_425885	59	18	15	15	CD
10_1101-2021_01_08_425885	59	19	]	]	-RRB-
10_1101-2021_01_08_425885	59	20	,	,	,
10_1101-2021_01_08_425885	59	21	identities	identity	NNS
10_1101-2021_01_08_425885	59	22	that	that	WDT
10_1101-2021_01_08_425885	59	23	rely	rely	VBP
10_1101-2021_01_08_425885	59	24	on	on	IN
10_1101-2021_01_08_425885	59	25	information	information	NN
10_1101-2021_01_08_425885	59	26	from	from	IN
10_1101-2021_01_08_425885	59	27	the	the	DT
10_1101-2021_01_08_425885	59	28	ambient	ambient	JJ
10_1101-2021_01_08_425885	59	29	space	space	NN
10_1101-2021_01_08_425885	59	30	.	.	.
10_1101-2021_01_08_425885	60	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	60	2	find	find	VBP
10_1101-2021_01_08_425885	60	3	that	that	IN
10_1101-2021_01_08_425885	60	4	this	this	DT
10_1101-2021_01_08_425885	60	5	extrinsic	extrinsic	JJ
10_1101-2021_01_08_425885	60	6	approach	approach	NN
10_1101-2021_01_08_425885	60	7	is	be	VBZ
10_1101-2021_01_08_425885	60	8	not	not	RB
10_1101-2021_01_08_425885	60	9	only	only	RB
10_1101-2021_01_08_425885	60	10	more	more	RBR
10_1101-2021_01_08_425885	60	11	robust	robust	JJ
10_1101-2021_01_08_425885	60	12	to	to	IN
10_1101-2021_01_08_425885	60	13	small	small	JJ
10_1101-2021_01_08_425885	60	14	sample	sample	NN
10_1101-2021_01_08_425885	60	15	sizes	size	NNS
10_1101-2021_01_08_425885	60	16	and	and	CC
10_1101-2021_01_08_425885	60	17	noise	noise	NN
10_1101-2021_01_08_425885	60	18	,	,	,
10_1101-2021_01_08_425885	60	19	but	but	CC
10_1101-2021_01_08_425885	60	20	permits	permit	VBZ
10_1101-2021_01_08_425885	60	21	computation	computation	NN
10_1101-2021_01_08_425885	60	22	of	of	IN
10_1101-2021_01_08_425885	60	23	the	the	DT
10_1101-2021_01_08_425885	60	24	full	full	JJ
10_1101-2021_01_08_425885	60	25	Riemannian	riemannian	JJ
10_1101-2021_01_08_425885	60	26	curvature	curvature	JJ
10_1101-2021_01_08_425885	60	27	tensor	tensor	NN
10_1101-2021_01_08_425885	60	28	,	,	,
10_1101-2021_01_08_425885	60	29	though	though	IN
10_1101-2021_01_08_425885	60	30	we	-PRON-	PRP
10_1101-2021_01_08_425885	60	31	focus	focus	VBP
10_1101-2021_01_08_425885	60	32	on	on	IN
10_1101-2021_01_08_425885	60	33	the	the	DT
10_1101-2021_01_08_425885	60	34	scalar	scalar	JJ
10_1101-2021_01_08_425885	60	35	curvature	curvature	NN
10_1101-2021_01_08_425885	60	36	for	for	IN
10_1101-2021_01_08_425885	60	37	simplicity	simplicity	NN
10_1101-2021_01_08_425885	60	38	.	.	.
10_1101-2021_01_08_425885	61	1	Using	use	VBG
10_1101-2021_01_08_425885	61	2	these	these	DT
10_1101-2021_01_08_425885	61	3	insights	insight	NNS
10_1101-2021_01_08_425885	61	4	,	,	,
10_1101-2021_01_08_425885	61	5	we	-PRON-	PRP
10_1101-2021_01_08_425885	61	6	developed	develop	VBD
10_1101-2021_01_08_425885	61	7	a	a	DT
10_1101-2021_01_08_425885	61	8	software	software	NN
10_1101-2021_01_08_425885	61	9	package	package	NN
10_1101-2021_01_08_425885	61	10	to	to	TO
10_1101-2021_01_08_425885	61	11	compute	compute	VB
10_1101-2021_01_08_425885	61	12	the	the	DT
10_1101-2021_01_08_425885	61	13	scalar	scalar	JJ
10_1101-2021_01_08_425885	61	14	curvature	curvature	NN
10_1101-2021_01_08_425885	61	15	(	(	-LRB-
10_1101-2021_01_08_425885	61	16	and	and	CC
10_1101-2021_01_08_425885	61	17	associated	associate	VBN
10_1101-2021_01_08_425885	61	18	uncertainty	uncertainty	NN
10_1101-2021_01_08_425885	61	19	)	)	-RRB-
10_1101-2021_01_08_425885	61	20	at	at	IN
10_1101-2021_01_08_425885	61	21	each	each	DT
10_1101-2021_01_08_425885	61	22	sampled	sample	VBN
10_1101-2021_01_08_425885	61	23	point	point	NN
10_1101-2021_01_08_425885	61	24	on	on	IN
10_1101-2021_01_08_425885	61	25	a	a	DT
10_1101-2021_01_08_425885	61	26	manifold	manifold	NN
10_1101-2021_01_08_425885	61	27	,	,	,
10_1101-2021_01_08_425885	61	28	and	and	CC
10_1101-2021_01_08_425885	61	29	applied	apply	VBD
10_1101-2021_01_08_425885	61	30	this	this	DT
10_1101-2021_01_08_425885	61	31	tool	tool	NN
10_1101-2021_01_08_425885	61	32	to	to	TO
10_1101-2021_01_08_425885	61	33	investigate	investigate	VB
10_1101-2021_01_08_425885	61	34	the	the	DT
10_1101-2021_01_08_425885	61	35	curvature	curvature	NN
10_1101-2021_01_08_425885	61	36	of	of	IN
10_1101-2021_01_08_425885	61	37	image	image	NN
10_1101-2021_01_08_425885	61	38	and	and	CC
10_1101-2021_01_08_425885	61	39	scRNAseq	scrnaseq	NN
10_1101-2021_01_08_425885	61	40	datasets	dataset	NNS
10_1101-2021_01_08_425885	61	41	.	.	.
10_1101-2021_01_08_425885	62	1	4	4	LS
10_1101-2021_01_08_425885	62	2	.CC	.CC	:
10_1101-2021_01_08_425885	62	3	-	-	HYPH
10_1101-2021_01_08_425885	62	4	BY	by	IN
10_1101-2021_01_08_425885	62	5	-	-	HYPH
10_1101-2021_01_08_425885	62	6	NC	NC	NNP
10_1101-2021_01_08_425885	62	7	-	-	HYPH
10_1101-2021_01_08_425885	62	8	ND	ND	NNP
10_1101-2021_01_08_425885	62	9	4.0	4.0	CD
10_1101-2021_01_08_425885	62	10	International	International	NNP
10_1101-2021_01_08_425885	62	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	62	12	under	under	IN
10_1101-2021_01_08_425885	62	13	a	a	DT
10_1101-2021_01_08_425885	62	14	(	(	-LRB-
10_1101-2021_01_08_425885	62	15	which	which	WDT
10_1101-2021_01_08_425885	62	16	was	be	VBD
10_1101-2021_01_08_425885	62	17	not	not	RB
10_1101-2021_01_08_425885	62	18	certified	certify	VBN
10_1101-2021_01_08_425885	62	19	by	by	IN
10_1101-2021_01_08_425885	62	20	peer	peer	NN
10_1101-2021_01_08_425885	62	21	review	review	NN
10_1101-2021_01_08_425885	62	22	)	)	-RRB-
10_1101-2021_01_08_425885	62	23	is	be	VBZ
10_1101-2021_01_08_425885	62	24	the	the	DT
10_1101-2021_01_08_425885	62	25	author	author	NN
10_1101-2021_01_08_425885	62	26	/	/	SYM
10_1101-2021_01_08_425885	62	27	funder	funder	NN
10_1101-2021_01_08_425885	62	28	,	,	,
10_1101-2021_01_08_425885	62	29	who	who	WP
10_1101-2021_01_08_425885	62	30	has	have	VBZ
10_1101-2021_01_08_425885	62	31	granted	grant	VBN
10_1101-2021_01_08_425885	62	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	62	33	a	a	DT
10_1101-2021_01_08_425885	62	34	license	license	NN
10_1101-2021_01_08_425885	62	35	to	to	TO
10_1101-2021_01_08_425885	62	36	display	display	VB
10_1101-2021_01_08_425885	62	37	the	the	DT
10_1101-2021_01_08_425885	62	38	preprint	preprint	NN
10_1101-2021_01_08_425885	62	39	in	in	IN
10_1101-2021_01_08_425885	62	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	62	41	.	.	.
10_1101-2021_01_08_425885	63	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	63	2	is	be	VBZ
10_1101-2021_01_08_425885	63	3	made	make	VBN
10_1101-2021_01_08_425885	63	4	The	the	DT
10_1101-2021_01_08_425885	63	5	copyright	copyright	NN
10_1101-2021_01_08_425885	63	6	holder	holder	NN
10_1101-2021_01_08_425885	63	7	for	for	IN
10_1101-2021_01_08_425885	63	8	this	this	DT
10_1101-2021_01_08_425885	63	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	63	10	version	version	NN
10_1101-2021_01_08_425885	63	11	posted	post	VBD
10_1101-2021_01_08_425885	63	12	January	January	NNP
10_1101-2021_01_08_425885	63	13	8	8	CD
10_1101-2021_01_08_425885	63	14	,	,	,
10_1101-2021_01_08_425885	63	15	2021	2021	CD
10_1101-2021_01_08_425885	63	16	.	.	.
10_1101-2021_01_08_425885	63	17	;	;	:
10_1101-2021_01_08_425885	63	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	63	19	:	:	:
10_1101-2021_01_08_425885	63	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	63	21	preprint	preprint	NN
10_1101-2021_01_08_425885	63	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	63	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	RB
10_1101-2021_01_08_425885	63	24	2	2	CD
10_1101-2021_01_08_425885	63	25	Results	Results	NNPS
10_1101-2021_01_08_425885	63	26	2.1	2.1	CD
10_1101-2021_01_08_425885	63	27	Estimators	Estimators	NNPS
10_1101-2021_01_08_425885	63	28	of	of	IN
10_1101-2021_01_08_425885	63	29	the	the	DT
10_1101-2021_01_08_425885	63	30	Laplace	Laplace	NNP
10_1101-2021_01_08_425885	63	31	-	-	HYPH
10_1101-2021_01_08_425885	63	32	Beltrami	Beltrami	NNP
10_1101-2021_01_08_425885	63	33	Operator	Operator	NNP
10_1101-2021_01_08_425885	63	34	Yield	Yield	NNP
10_1101-2021_01_08_425885	63	35	Inaccurate	Inaccurate	NNP
10_1101-2021_01_08_425885	63	36	Scalar	Scalar	NNP
10_1101-2021_01_08_425885	63	37	Cur-	Cur-	NNP
10_1101-2021_01_08_425885	63	38	vatures	vature	VBZ
10_1101-2021_01_08_425885	63	39	Intrinsic	Intrinsic	NNP
10_1101-2021_01_08_425885	63	40	differential	differential	NN
10_1101-2021_01_08_425885	63	41	geometry	geometry	NN
10_1101-2021_01_08_425885	63	42	treats	treat	VBZ
10_1101-2021_01_08_425885	63	43	a	a	DT
10_1101-2021_01_08_425885	63	44	d	d	NN
10_1101-2021_01_08_425885	63	45	-	-	HYPH
10_1101-2021_01_08_425885	63	46	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	63	47	manifold	manifold	NN
10_1101-2021_01_08_425885	63	48	,	,	,
10_1101-2021_01_08_425885	63	49	M	M	NNP
10_1101-2021_01_08_425885	63	50	,	,	,
10_1101-2021_01_08_425885	63	51	as	as	IN
10_1101-2021_01_08_425885	63	52	a	a	DT
10_1101-2021_01_08_425885	63	53	self	self	NN
10_1101-2021_01_08_425885	63	54	-	-	HYPH
10_1101-2021_01_08_425885	63	55	contained	contain	VBN
10_1101-2021_01_08_425885	63	56	object	object	NN
10_1101-2021_01_08_425885	63	57	and	and	CC
10_1101-2021_01_08_425885	63	58	is	be	VBZ
10_1101-2021_01_08_425885	63	59	agnostic	agnostic	JJ
10_1101-2021_01_08_425885	63	60	to	to	IN
10_1101-2021_01_08_425885	63	61	how	how	WRB
10_1101-2021_01_08_425885	63	62	M	M	NNP
10_1101-2021_01_08_425885	63	63	may	may	MD
10_1101-2021_01_08_425885	63	64	be	be	VB
10_1101-2021_01_08_425885	63	65	represented	represent	VBN
10_1101-2021_01_08_425885	63	66	in	in	IN
10_1101-2021_01_08_425885	63	67	ambient	ambient	JJ
10_1101-2021_01_08_425885	63	68	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	63	69	due	due	JJ
10_1101-2021_01_08_425885	63	70	to	to	IN
10_1101-2021_01_08_425885	63	71	any	any	DT
10_1101-2021_01_08_425885	63	72	particular	particular	JJ
10_1101-2021_01_08_425885	63	73	embedding	embedding	NN
10_1101-2021_01_08_425885	63	74	(	(	-LRB-
10_1101-2021_01_08_425885	63	75	see	see	VB
10_1101-2021_01_08_425885	63	76	Figure	Figure	NNP
10_1101-2021_01_08_425885	63	77	1C	1c	NN
10_1101-2021_01_08_425885	63	78	)	)	-RRB-
10_1101-2021_01_08_425885	63	79	.	.	.
10_1101-2021_01_08_425885	64	1	Conceptually	conceptually	RB
10_1101-2021_01_08_425885	64	2	,	,	,
10_1101-2021_01_08_425885	64	3	this	this	DT
10_1101-2021_01_08_425885	64	4	is	be	VBZ
10_1101-2021_01_08_425885	64	5	accomplished	accomplish	VBN
10_1101-2021_01_08_425885	64	6	by	by	IN
10_1101-2021_01_08_425885	64	7	only	only	RB
10_1101-2021_01_08_425885	64	8	considering	consider	VBG
10_1101-2021_01_08_425885	64	9	M	M	NNP
10_1101-2021_01_08_425885	64	10	as	as	IN
10_1101-2021_01_08_425885	64	11	a	a	DT
10_1101-2021_01_08_425885	64	12	collection	collection	NN
10_1101-2021_01_08_425885	64	13	of	of	IN
10_1101-2021_01_08_425885	64	14	local	local	JJ
10_1101-2021_01_08_425885	64	15	,	,	,
10_1101-2021_01_08_425885	64	16	overlapping	overlap	VBG
10_1101-2021_01_08_425885	64	17	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	64	18	.	.	.
10_1101-2021_01_08_425885	65	1	The	the	DT
10_1101-2021_01_08_425885	65	2	geometry	geometry	NN
10_1101-2021_01_08_425885	65	3	of	of	IN
10_1101-2021_01_08_425885	65	4	these	these	DT
10_1101-2021_01_08_425885	65	5	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	65	6	is	be	VBZ
10_1101-2021_01_08_425885	65	7	encoded	encode	VBN
10_1101-2021_01_08_425885	65	8	using	use	VBG
10_1101-2021_01_08_425885	65	9	tools	tool	NNS
10_1101-2021_01_08_425885	65	10	such	such	JJ
10_1101-2021_01_08_425885	65	11	as	as	IN
10_1101-2021_01_08_425885	65	12	the	the	DT
10_1101-2021_01_08_425885	65	13	Laplace	Laplace	NNP
10_1101-2021_01_08_425885	65	14	-	-	HYPH
10_1101-2021_01_08_425885	65	15	Beltrami	Beltrami	NNP
10_1101-2021_01_08_425885	65	16	operator	operator	NN
10_1101-2021_01_08_425885	65	17	,	,	,
10_1101-2021_01_08_425885	65	18	∆M	∆M	NNP
10_1101-2021_01_08_425885	65	19	,	,	,
10_1101-2021_01_08_425885	65	20	which	which	WDT
10_1101-2021_01_08_425885	65	21	captures	capture	VBZ
10_1101-2021_01_08_425885	65	22	diffusion	diffusion	NN
10_1101-2021_01_08_425885	65	23	dynamics	dynamic	NNS
10_1101-2021_01_08_425885	65	24	across	across	IN
10_1101-2021_01_08_425885	65	25	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	65	26	.	.	.
10_1101-2021_01_08_425885	66	1	For	for	IN
10_1101-2021_01_08_425885	66	2	most	most	JJS
10_1101-2021_01_08_425885	66	3	practical	practical	JJ
10_1101-2021_01_08_425885	66	4	applications	application	NNS
10_1101-2021_01_08_425885	66	5	,	,	,
10_1101-2021_01_08_425885	66	6	we	-PRON-	PRP
10_1101-2021_01_08_425885	66	7	do	do	VBP
10_1101-2021_01_08_425885	66	8	not	not	RB
10_1101-2021_01_08_425885	66	9	have	have	VB
10_1101-2021_01_08_425885	66	10	direct	direct	JJ
10_1101-2021_01_08_425885	66	11	access	access	NN
10_1101-2021_01_08_425885	66	12	to	to	IN
10_1101-2021_01_08_425885	66	13	M	M	NNP
10_1101-2021_01_08_425885	66	14	but	but	CC
10_1101-2021_01_08_425885	66	15	instead	instead	RB
10_1101-2021_01_08_425885	66	16	to	to	IN
10_1101-2021_01_08_425885	66	17	a	a	DT
10_1101-2021_01_08_425885	66	18	finite	finite	JJ
10_1101-2021_01_08_425885	66	19	number	number	NN
10_1101-2021_01_08_425885	66	20	(	(	-LRB-
10_1101-2021_01_08_425885	66	21	N	n	NN
10_1101-2021_01_08_425885	66	22	)	)	-RRB-
10_1101-2021_01_08_425885	66	23	of	of	IN
10_1101-2021_01_08_425885	66	24	points	point	NNS
10_1101-2021_01_08_425885	66	25	sampled	sample	VBN
10_1101-2021_01_08_425885	66	26	from	from	IN
10_1101-2021_01_08_425885	66	27	M.	M.	NNP
10_1101-2021_01_08_425885	66	28	For	for	IN
10_1101-2021_01_08_425885	66	29	these	these	DT
10_1101-2021_01_08_425885	66	30	cases	case	NNS
10_1101-2021_01_08_425885	66	31	,	,	,
10_1101-2021_01_08_425885	66	32	estimators	estimator	NNS
10_1101-2021_01_08_425885	66	33	of	of	IN
10_1101-2021_01_08_425885	66	34	∆M	∆M	NNP
10_1101-2021_01_08_425885	66	35	are	be	VBP
10_1101-2021_01_08_425885	66	36	used	use	VBN
10_1101-2021_01_08_425885	66	37	instead	instead	RB
10_1101-2021_01_08_425885	66	38	.	.	.
10_1101-2021_01_08_425885	67	1	These	these	DT
10_1101-2021_01_08_425885	67	2	estimators	estimator	NNS
10_1101-2021_01_08_425885	67	3	are	be	VBP
10_1101-2021_01_08_425885	67	4	well	well	RB
10_1101-2021_01_08_425885	67	5	-	-	HYPH
10_1101-2021_01_08_425885	67	6	studied	study	VBN
10_1101-2021_01_08_425885	67	7	[	[	-LRB-
10_1101-2021_01_08_425885	67	8	14	14	CD
10_1101-2021_01_08_425885	67	9	,	,	,
10_1101-2021_01_08_425885	67	10	26	26	CD
10_1101-2021_01_08_425885	67	11	,	,	,
10_1101-2021_01_08_425885	67	12	27	27	CD
10_1101-2021_01_08_425885	67	13	,	,	,
10_1101-2021_01_08_425885	67	14	28	28	CD
10_1101-2021_01_08_425885	67	15	,	,	,
10_1101-2021_01_08_425885	67	16	29	29	CD
10_1101-2021_01_08_425885	67	17	]	]	-RRB-
10_1101-2021_01_08_425885	67	18	,	,	,
10_1101-2021_01_08_425885	67	19	and	and	CC
10_1101-2021_01_08_425885	67	20	the	the	DT
10_1101-2021_01_08_425885	67	21	convergence	convergence	NN
10_1101-2021_01_08_425885	67	22	rates	rate	NNS
10_1101-2021_01_08_425885	67	23	of	of	IN
10_1101-2021_01_08_425885	67	24	some	some	DT
10_1101-2021_01_08_425885	67	25	have	have	VBP
10_1101-2021_01_08_425885	67	26	been	be	VBN
10_1101-2021_01_08_425885	67	27	characterized	characterize	VBN
10_1101-2021_01_08_425885	67	28	[	[	-LRB-
10_1101-2021_01_08_425885	67	29	30	30	CD
10_1101-2021_01_08_425885	67	30	]	]	-RRB-
10_1101-2021_01_08_425885	67	31	.	.	.
10_1101-2021_01_08_425885	68	1	The	the	DT
10_1101-2021_01_08_425885	68	2	scalar	scalar	JJ
10_1101-2021_01_08_425885	68	3	curvature	curvature	NN
10_1101-2021_01_08_425885	68	4	averaged	average	VBD
10_1101-2021_01_08_425885	68	5	across	across	IN
10_1101-2021_01_08_425885	68	6	M	M	NNP
10_1101-2021_01_08_425885	68	7	,	,	,
10_1101-2021_01_08_425885	68	8	has	have	VBZ
10_1101-2021_01_08_425885	68	9	a	a	DT
10_1101-2021_01_08_425885	68	10	well	well	RB
10_1101-2021_01_08_425885	68	11	-	-	HYPH
10_1101-2021_01_08_425885	68	12	known	know	VBN
10_1101-2021_01_08_425885	68	13	connection	connection	NN
10_1101-2021_01_08_425885	68	14	to	to	IN
10_1101-2021_01_08_425885	68	15	∆M	∆M	NNP
10_1101-2021_01_08_425885	68	16	via	via	IN
10_1101-2021_01_08_425885	68	17	the	the	DT
10_1101-2021_01_08_425885	68	18	heat	heat	NN
10_1101-2021_01_08_425885	68	19	-	-	HYPH
10_1101-2021_01_08_425885	68	20	trace	trace	NN
10_1101-2021_01_08_425885	68	21	expan-	expan-	JJ
10_1101-2021_01_08_425885	68	22	sion	sion	NN
10_1101-2021_01_08_425885	68	23	[	[	-LRB-
10_1101-2021_01_08_425885	68	24	27	27	CD
10_1101-2021_01_08_425885	68	25	,	,	,
10_1101-2021_01_08_425885	68	26	31	31	CD
10_1101-2021_01_08_425885	68	27	]	]	-RRB-
10_1101-2021_01_08_425885	68	28	,	,	,
10_1101-2021_01_08_425885	68	29	which	which	WDT
10_1101-2021_01_08_425885	68	30	relates	relate	VBZ
10_1101-2021_01_08_425885	68	31	the	the	DT
10_1101-2021_01_08_425885	68	32	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	68	33	,	,	,
10_1101-2021_01_08_425885	68	34	λk	λk	NNP
10_1101-2021_01_08_425885	68	35	,	,	,
10_1101-2021_01_08_425885	68	36	of	of	IN
10_1101-2021_01_08_425885	68	37	∆M	∆M	NNP
10_1101-2021_01_08_425885	68	38	to	to	IN
10_1101-2021_01_08_425885	68	39	the	the	DT
10_1101-2021_01_08_425885	68	40	geometry	geometry	NN
10_1101-2021_01_08_425885	68	41	of	of	IN
10_1101-2021_01_08_425885	68	42	M	M	NNP
10_1101-2021_01_08_425885	68	43	:	:	:
10_1101-2021_01_08_425885	68	44	Z(t	Z(t	NNP
10_1101-2021_01_08_425885	68	45	)	)	-RRB-
10_1101-2021_01_08_425885	68	46	≡	≡	ADD
10_1101-2021_01_08_425885	68	47	∞∑	∞∑	NNS
10_1101-2021_01_08_425885	68	48	k=1	k=1	JJ
10_1101-2021_01_08_425885	68	49	e−λkt	e−λkt	NN
10_1101-2021_01_08_425885	68	50	=	=	FW
10_1101-2021_01_08_425885	68	51	(	(	-LRB-
10_1101-2021_01_08_425885	68	52	4πt)−	4πt)−	CD
10_1101-2021_01_08_425885	68	53	d	d	SYM
10_1101-2021_01_08_425885	68	54	2	2	CD
10_1101-2021_01_08_425885	68	55	(	(	-LRB-
10_1101-2021_01_08_425885	68	56	n∑	n∑	NN
10_1101-2021_01_08_425885	68	57	i=0	i=0	JJ
10_1101-2021_01_08_425885	68	58	cit	cit	RB
10_1101-2021_01_08_425885	68	59	i	i	PRP
10_1101-2021_01_08_425885	68	60	2	2	CD
10_1101-2021_01_08_425885	68	61	+	+	SYM
10_1101-2021_01_08_425885	68	62	o(t	o(t	NNP
10_1101-2021_01_08_425885	68	63	n+1	n+1	NN
10_1101-2021_01_08_425885	68	64	2	2	CD
10_1101-2021_01_08_425885	68	65	)	)	-RRB-
10_1101-2021_01_08_425885	68	66	)	)	-RRB-
10_1101-2021_01_08_425885	68	67	,	,	,
10_1101-2021_01_08_425885	68	68	λk	λk	NNP
10_1101-2021_01_08_425885	68	69	≤	≤	NNP
10_1101-2021_01_08_425885	68	70	λk+1	λk+1	NNP
10_1101-2021_01_08_425885	68	71	(	(	-LRB-
10_1101-2021_01_08_425885	68	72	1	1	LS
10_1101-2021_01_08_425885	68	73	)	)	-RRB-
10_1101-2021_01_08_425885	68	74	The	the	DT
10_1101-2021_01_08_425885	68	75	first	first	JJ
10_1101-2021_01_08_425885	68	76	few	few	JJ
10_1101-2021_01_08_425885	68	77	coefficients	coefficient	NNS
10_1101-2021_01_08_425885	68	78	,	,	,
10_1101-2021_01_08_425885	68	79	ci	ci	NNP
10_1101-2021_01_08_425885	68	80	,	,	,
10_1101-2021_01_08_425885	68	81	are	be	VBP
10_1101-2021_01_08_425885	68	82	given	give	VBN
10_1101-2021_01_08_425885	68	83	by	by	IN
10_1101-2021_01_08_425885	68	84	[	[	-LRB-
10_1101-2021_01_08_425885	68	85	27	27	CD
10_1101-2021_01_08_425885	68	86	]	]	-RRB-
10_1101-2021_01_08_425885	68	87	:	:	:
10_1101-2021_01_08_425885	68	88	c0	c0	NNP
10_1101-2021_01_08_425885	68	89	=	=	SYM
10_1101-2021_01_08_425885	68	90	∫	∫	:
10_1101-2021_01_08_425885	68	91	M	M	NNP
10_1101-2021_01_08_425885	68	92	dM	dM	NNP
10_1101-2021_01_08_425885	68	93	,	,	,
10_1101-2021_01_08_425885	68	94	c1	c1	NN
10_1101-2021_01_08_425885	68	95	=	=	SYM
10_1101-2021_01_08_425885	68	96	−	−	NNP
10_1101-2021_01_08_425885	68	97	√	√	NNP
10_1101-2021_01_08_425885	68	98	π	π	NN
10_1101-2021_01_08_425885	68	99	2	2	CD
10_1101-2021_01_08_425885	68	100	∫	∫	CD
10_1101-2021_01_08_425885	68	101	∂M	∂M	.
10_1101-2021_01_08_425885	68	102	d(∂M	d(∂M	NNP
10_1101-2021_01_08_425885	68	103	)	)	-RRB-
10_1101-2021_01_08_425885	68	104	,	,	,
10_1101-2021_01_08_425885	68	105	c2	c2	NNP
10_1101-2021_01_08_425885	68	106	=	=	SYM
10_1101-2021_01_08_425885	68	107	1	1	CD
10_1101-2021_01_08_425885	68	108	6	6	CD
10_1101-2021_01_08_425885	68	109	∫	∫	.
10_1101-2021_01_08_425885	68	110	M	M	NNP
10_1101-2021_01_08_425885	68	111	S	S	NNP
10_1101-2021_01_08_425885	68	112	dM	dM	NNP
10_1101-2021_01_08_425885	68	113	−	−	NNP
10_1101-2021_01_08_425885	68	114	1	1	CD
10_1101-2021_01_08_425885	68	115	6	6	CD
10_1101-2021_01_08_425885	68	116	∫	∫	CD
10_1101-2021_01_08_425885	68	117	∂M	∂M	.
10_1101-2021_01_08_425885	68	118	J	J	NNP
10_1101-2021_01_08_425885	68	119	d(∂M	d(∂M	NNP
10_1101-2021_01_08_425885	68	120	)	)	-RRB-
10_1101-2021_01_08_425885	68	121	(	(	-LRB-
10_1101-2021_01_08_425885	68	122	2	2	LS
10_1101-2021_01_08_425885	68	123	)	)	-RRB-
10_1101-2021_01_08_425885	68	124	where	where	WRB
10_1101-2021_01_08_425885	68	125	∂M	∂M	.
10_1101-2021_01_08_425885	68	126	is	be	VBZ
10_1101-2021_01_08_425885	68	127	the	the	DT
10_1101-2021_01_08_425885	68	128	boundary	boundary	JJ
10_1101-2021_01_08_425885	68	129	of	of	IN
10_1101-2021_01_08_425885	68	130	the	the	DT
10_1101-2021_01_08_425885	68	131	manifold	manifold	NN
10_1101-2021_01_08_425885	68	132	and	and	CC
10_1101-2021_01_08_425885	68	133	J	J	NNP
10_1101-2021_01_08_425885	68	134	is	be	VBZ
10_1101-2021_01_08_425885	68	135	the	the	DT
10_1101-2021_01_08_425885	68	136	mean	mean	JJ
10_1101-2021_01_08_425885	68	137	curvature	curvature	NN
10_1101-2021_01_08_425885	68	138	on	on	RB
10_1101-2021_01_08_425885	68	139	∂M.	∂M.	.
10_1101-2021_01_08_425885	69	1	Recall	recall	VB
10_1101-2021_01_08_425885	69	2	that	that	IN
10_1101-2021_01_08_425885	69	3	S	s	NN
10_1101-2021_01_08_425885	69	4	is	be	VBZ
10_1101-2021_01_08_425885	69	5	the	the	DT
10_1101-2021_01_08_425885	69	6	point	point	NN
10_1101-2021_01_08_425885	69	7	-	-	HYPH
10_1101-2021_01_08_425885	69	8	wise	wise	JJ
10_1101-2021_01_08_425885	69	9	scalar	scalar	JJ
10_1101-2021_01_08_425885	69	10	curvature	curvature	NN
10_1101-2021_01_08_425885	69	11	.	.	.
10_1101-2021_01_08_425885	70	1	By	by	IN
10_1101-2021_01_08_425885	70	2	inspection	inspection	NN
10_1101-2021_01_08_425885	70	3	,	,	,
10_1101-2021_01_08_425885	70	4	c0	c0	NNP
10_1101-2021_01_08_425885	70	5	is	be	VBZ
10_1101-2021_01_08_425885	70	6	the	the	DT
10_1101-2021_01_08_425885	70	7	volume	volume	NN
10_1101-2021_01_08_425885	70	8	,	,	,
10_1101-2021_01_08_425885	70	9	c1	c1	NN
10_1101-2021_01_08_425885	70	10	is	be	VBZ
10_1101-2021_01_08_425885	70	11	proportional	proportional	JJ
10_1101-2021_01_08_425885	70	12	to	to	IN
10_1101-2021_01_08_425885	70	13	the	the	DT
10_1101-2021_01_08_425885	70	14	area	area	NN
10_1101-2021_01_08_425885	70	15	,	,	,
10_1101-2021_01_08_425885	70	16	and	and	CC
10_1101-2021_01_08_425885	70	17	c2	c2	NN
10_1101-2021_01_08_425885	70	18	is	be	VBZ
10_1101-2021_01_08_425885	70	19	directly	directly	RB
10_1101-2021_01_08_425885	70	20	related	relate	VBN
10_1101-2021_01_08_425885	70	21	to	to	IN
10_1101-2021_01_08_425885	70	22	the	the	DT
10_1101-2021_01_08_425885	70	23	average	average	JJ
10_1101-2021_01_08_425885	70	24	scalar	scalar	JJ
10_1101-2021_01_08_425885	70	25	curvature	curvature	NN
10_1101-2021_01_08_425885	70	26	.	.	.
10_1101-2021_01_08_425885	71	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	71	2	reasoned	reason	VBD
10_1101-2021_01_08_425885	71	3	that	that	IN
10_1101-2021_01_08_425885	71	4	if	if	IN
10_1101-2021_01_08_425885	71	5	the	the	DT
10_1101-2021_01_08_425885	71	6	average	average	JJ
10_1101-2021_01_08_425885	71	7	scalar	scalar	JJ
10_1101-2021_01_08_425885	71	8	curvature	curvature	NN
10_1101-2021_01_08_425885	71	9	can	can	MD
10_1101-2021_01_08_425885	71	10	not	not	RB
10_1101-2021_01_08_425885	71	11	be	be	VB
10_1101-2021_01_08_425885	71	12	accurately	accurately	RB
10_1101-2021_01_08_425885	71	13	computed	compute	VBN
10_1101-2021_01_08_425885	71	14	for	for	IN
10_1101-2021_01_08_425885	71	15	a	a	DT
10_1101-2021_01_08_425885	71	16	manifold	manifold	NN
10_1101-2021_01_08_425885	71	17	with	with	IN
10_1101-2021_01_08_425885	71	18	constant	constant	JJ
10_1101-2021_01_08_425885	71	19	scalar	scalar	JJ
10_1101-2021_01_08_425885	71	20	curvature	curvature	NN
10_1101-2021_01_08_425885	71	21	using	use	VBG
10_1101-2021_01_08_425885	71	22	these	these	DT
10_1101-2021_01_08_425885	71	23	relations	relation	NNS
10_1101-2021_01_08_425885	71	24	,	,	,
10_1101-2021_01_08_425885	71	25	then	then	RB
10_1101-2021_01_08_425885	71	26	computing	compute	VBG
10_1101-2021_01_08_425885	71	27	the	the	DT
10_1101-2021_01_08_425885	71	28	point	point	NN
10_1101-2021_01_08_425885	71	29	-	-	HYPH
10_1101-2021_01_08_425885	71	30	wise	wise	JJ
10_1101-2021_01_08_425885	71	31	scalar	scalar	JJ
10_1101-2021_01_08_425885	71	32	curvature	curvature	NN
10_1101-2021_01_08_425885	71	33	for	for	IN
10_1101-2021_01_08_425885	71	34	more	more	RBR
10_1101-2021_01_08_425885	71	35	complex	complex	JJ
10_1101-2021_01_08_425885	71	36	manifolds	manifold	NNS
10_1101-2021_01_08_425885	71	37	is	be	VBZ
10_1101-2021_01_08_425885	71	38	intractable	intractable	JJ
10_1101-2021_01_08_425885	71	39	.	.	.
10_1101-2021_01_08_425885	72	1	To	to	TO
10_1101-2021_01_08_425885	72	2	investigate	investigate	VB
10_1101-2021_01_08_425885	72	3	this	this	DT
10_1101-2021_01_08_425885	72	4	,	,	,
10_1101-2021_01_08_425885	72	5	we	-PRON-	PRP
10_1101-2021_01_08_425885	72	6	considered	consider	VBD
10_1101-2021_01_08_425885	72	7	the	the	DT
10_1101-2021_01_08_425885	72	8	2-dimensional	2-dimensional	CD
10_1101-2021_01_08_425885	72	9	hollow	hollow	JJ
10_1101-2021_01_08_425885	72	10	unit	unit	NN
10_1101-2021_01_08_425885	72	11	sphere	sphere	VBD
10_1101-2021_01_08_425885	72	12	,	,	,
10_1101-2021_01_08_425885	72	13	S2	S2	NNP
10_1101-2021_01_08_425885	72	14	,	,	,
10_1101-2021_01_08_425885	72	15	for	for	IN
10_1101-2021_01_08_425885	72	16	which	which	WDT
10_1101-2021_01_08_425885	72	17	the	the	DT
10_1101-2021_01_08_425885	72	18	true	true	JJ
10_1101-2021_01_08_425885	72	19	scalar	scalar	JJ
10_1101-2021_01_08_425885	72	20	curvature	curvature	NN
10_1101-2021_01_08_425885	72	21	is	be	VBZ
10_1101-2021_01_08_425885	72	22	S(p	s(p	XX
10_1101-2021_01_08_425885	72	23	)	)	-RRB-
10_1101-2021_01_08_425885	72	24	=	=	NFP
10_1101-2021_01_08_425885	72	25	2	2	CD
10_1101-2021_01_08_425885	72	26	∀p	∀p	NNP
10_1101-2021_01_08_425885	72	27	∈	∈	NNP
10_1101-2021_01_08_425885	72	28	M	M	NNP
10_1101-2021_01_08_425885	72	29	,	,	,
10_1101-2021_01_08_425885	72	30	and	and	CC
10_1101-2021_01_08_425885	72	31	uniformly	uniformly	RB
10_1101-2021_01_08_425885	72	32	sampled	sample	VBD
10_1101-2021_01_08_425885	72	33	N	n	NN
10_1101-2021_01_08_425885	72	34	=	=	SYM
10_1101-2021_01_08_425885	72	35	104	104	CD
10_1101-2021_01_08_425885	72	36	points	point	NNS
10_1101-2021_01_08_425885	72	37	to	to	TO
10_1101-2021_01_08_425885	72	38	mirror	mirror	VB
10_1101-2021_01_08_425885	72	39	the	the	DT
10_1101-2021_01_08_425885	72	40	typical	typical	JJ
10_1101-2021_01_08_425885	72	41	size	size	NN
10_1101-2021_01_08_425885	72	42	of	of	IN
10_1101-2021_01_08_425885	72	43	current	current	JJ
10_1101-2021_01_08_425885	72	44	scRNAseq	scrnaseq	JJ
10_1101-2021_01_08_425885	72	45	datasets	dataset	NNS
10_1101-2021_01_08_425885	72	46	(	(	-LRB-
10_1101-2021_01_08_425885	72	47	see	see	VB
10_1101-2021_01_08_425885	72	48	Figure	figure	NN
10_1101-2021_01_08_425885	72	49	1A	1a	NN
10_1101-2021_01_08_425885	72	50	;	;	:
10_1101-2021_01_08_425885	72	51	Methods	Methods	NNP
10_1101-2021_01_08_425885	72	52	Section	Section	NNP
10_1101-2021_01_08_425885	72	53	4.4.1.1	4.4.1.1	CD
10_1101-2021_01_08_425885	72	54	)	)	-RRB-
10_1101-2021_01_08_425885	72	55	.	.	.
10_1101-2021_01_08_425885	73	1	Since	since	IN
10_1101-2021_01_08_425885	73	2	common	common	JJ
10_1101-2021_01_08_425885	73	3	estimators	estimator	NNS
10_1101-2021_01_08_425885	73	4	of	of	IN
10_1101-2021_01_08_425885	73	5	∆M	∆M	NNP
10_1101-2021_01_08_425885	73	6	only	only	RB
10_1101-2021_01_08_425885	73	7	yield	yield	VBP
10_1101-2021_01_08_425885	73	8	as	as	RB
10_1101-2021_01_08_425885	73	9	many	many	JJ
10_1101-2021_01_08_425885	73	10	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	73	11	as	as	IN
10_1101-2021_01_08_425885	73	12	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	73	13	(	(	-LRB-
10_1101-2021_01_08_425885	73	14	N	n	NN
10_1101-2021_01_08_425885	73	15	)	)	-RRB-
10_1101-2021_01_08_425885	73	16	,	,	,
10_1101-2021_01_08_425885	73	17	we	-PRON-	PRP
10_1101-2021_01_08_425885	73	18	can	can	MD
10_1101-2021_01_08_425885	73	19	not	not	RB
10_1101-2021_01_08_425885	73	20	compute	compute	VB
10_1101-2021_01_08_425885	73	21	5	5	CD
10_1101-2021_01_08_425885	73	22	.CC	.CC	,
10_1101-2021_01_08_425885	73	23	-	-	HYPH
10_1101-2021_01_08_425885	73	24	BY	by	IN
10_1101-2021_01_08_425885	73	25	-	-	HYPH
10_1101-2021_01_08_425885	73	26	NC	NC	NNP
10_1101-2021_01_08_425885	73	27	-	-	HYPH
10_1101-2021_01_08_425885	73	28	ND	ND	NNP
10_1101-2021_01_08_425885	73	29	4.0	4.0	CD
10_1101-2021_01_08_425885	73	30	International	International	NNP
10_1101-2021_01_08_425885	73	31	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	73	32	under	under	IN
10_1101-2021_01_08_425885	73	33	a	a	DT
10_1101-2021_01_08_425885	73	34	(	(	-LRB-
10_1101-2021_01_08_425885	73	35	which	which	WDT
10_1101-2021_01_08_425885	73	36	was	be	VBD
10_1101-2021_01_08_425885	73	37	not	not	RB
10_1101-2021_01_08_425885	73	38	certified	certify	VBN
10_1101-2021_01_08_425885	73	39	by	by	IN
10_1101-2021_01_08_425885	73	40	peer	peer	NN
10_1101-2021_01_08_425885	73	41	review	review	NN
10_1101-2021_01_08_425885	73	42	)	)	-RRB-
10_1101-2021_01_08_425885	73	43	is	be	VBZ
10_1101-2021_01_08_425885	73	44	the	the	DT
10_1101-2021_01_08_425885	73	45	author	author	NN
10_1101-2021_01_08_425885	73	46	/	/	SYM
10_1101-2021_01_08_425885	73	47	funder	funder	NN
10_1101-2021_01_08_425885	73	48	,	,	,
10_1101-2021_01_08_425885	73	49	who	who	WP
10_1101-2021_01_08_425885	73	50	has	have	VBZ
10_1101-2021_01_08_425885	73	51	granted	grant	VBN
10_1101-2021_01_08_425885	73	52	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	73	53	a	a	DT
10_1101-2021_01_08_425885	73	54	license	license	NN
10_1101-2021_01_08_425885	73	55	to	to	TO
10_1101-2021_01_08_425885	73	56	display	display	VB
10_1101-2021_01_08_425885	73	57	the	the	DT
10_1101-2021_01_08_425885	73	58	preprint	preprint	NN
10_1101-2021_01_08_425885	73	59	in	in	IN
10_1101-2021_01_08_425885	73	60	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	73	61	.	.	.
10_1101-2021_01_08_425885	74	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	74	2	is	be	VBZ
10_1101-2021_01_08_425885	74	3	made	make	VBN
10_1101-2021_01_08_425885	74	4	The	the	DT
10_1101-2021_01_08_425885	74	5	copyright	copyright	NN
10_1101-2021_01_08_425885	74	6	holder	holder	NN
10_1101-2021_01_08_425885	74	7	for	for	IN
10_1101-2021_01_08_425885	74	8	this	this	DT
10_1101-2021_01_08_425885	74	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	74	10	version	version	NN
10_1101-2021_01_08_425885	74	11	posted	post	VBD
10_1101-2021_01_08_425885	74	12	January	January	NNP
10_1101-2021_01_08_425885	74	13	8	8	CD
10_1101-2021_01_08_425885	74	14	,	,	,
10_1101-2021_01_08_425885	74	15	2021	2021	CD
10_1101-2021_01_08_425885	74	16	.	.	.
10_1101-2021_01_08_425885	74	17	;	;	:
10_1101-2021_01_08_425885	74	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	74	19	:	:	:
10_1101-2021_01_08_425885	74	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	74	21	preprint	preprint	NN
10_1101-2021_01_08_425885	74	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	74	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	VB
10_1101-2021_01_08_425885	74	24	the	the	DT
10_1101-2021_01_08_425885	74	25	infinite	infinite	JJ
10_1101-2021_01_08_425885	74	26	set	set	NN
10_1101-2021_01_08_425885	74	27	of	of	IN
10_1101-2021_01_08_425885	74	28	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	74	29	needed	need	VBN
10_1101-2021_01_08_425885	74	30	in	in	IN
10_1101-2021_01_08_425885	74	31	Equation	Equation	NNP
10_1101-2021_01_08_425885	74	32	1	1	CD
10_1101-2021_01_08_425885	74	33	.	.	.
10_1101-2021_01_08_425885	75	1	Therefore	therefore	RB
10_1101-2021_01_08_425885	75	2	,	,	,
10_1101-2021_01_08_425885	75	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	75	4	introduced	introduce	VBD
10_1101-2021_01_08_425885	75	5	a	a	DT
10_1101-2021_01_08_425885	75	6	truncated	truncate	VBN
10_1101-2021_01_08_425885	75	7	series	series	NN
10_1101-2021_01_08_425885	75	8	with	with	IN
10_1101-2021_01_08_425885	75	9	m	m	NNP
10_1101-2021_01_08_425885	75	10	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	75	11	,	,	,
10_1101-2021_01_08_425885	75	12	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	75	13	)	)	-RRB-
10_1101-2021_01_08_425885	75	14	,	,	,
10_1101-2021_01_08_425885	75	15	where	where	WRB
10_1101-2021_01_08_425885	75	16	we	-PRON-	PRP
10_1101-2021_01_08_425885	75	17	have	have	VBP
10_1101-2021_01_08_425885	75	18	substituted	substitute	VBN
10_1101-2021_01_08_425885	75	19	x	x	SYM
10_1101-2021_01_08_425885	75	20	=	=	SYM
10_1101-2021_01_08_425885	75	21	√	√	NNP
10_1101-2021_01_08_425885	75	22	t	t	NN
10_1101-2021_01_08_425885	75	23	and	and	CC
10_1101-2021_01_08_425885	75	24	divided	divide	VBN
10_1101-2021_01_08_425885	75	25	through	through	IN
10_1101-2021_01_08_425885	75	26	by	by	IN
10_1101-2021_01_08_425885	75	27	the	the	DT
10_1101-2021_01_08_425885	75	28	prefactor	prefactor	NN
10_1101-2021_01_08_425885	75	29	in	in	IN
10_1101-2021_01_08_425885	75	30	the	the	DT
10_1101-2021_01_08_425885	75	31	RHS	RHS	NNP
10_1101-2021_01_08_425885	75	32	of	of	IN
10_1101-2021_01_08_425885	75	33	Equation	Equation	NNP
10_1101-2021_01_08_425885	75	34	1	1	CD
10_1101-2021_01_08_425885	75	35	to	to	TO
10_1101-2021_01_08_425885	75	36	isolate	isolate	VB
10_1101-2021_01_08_425885	75	37	for	for	IN
10_1101-2021_01_08_425885	75	38	ci	ci	NNP
10_1101-2021_01_08_425885	75	39	,	,	,
10_1101-2021_01_08_425885	75	40	following	follow	VBG
10_1101-2021_01_08_425885	75	41	the	the	DT
10_1101-2021_01_08_425885	75	42	approach	approach	NN
10_1101-2021_01_08_425885	75	43	in	in	IN
10_1101-2021_01_08_425885	75	44	[	[	-LRB-
10_1101-2021_01_08_425885	75	45	27	27	CD
10_1101-2021_01_08_425885	75	46	]	]	-RRB-
10_1101-2021_01_08_425885	75	47	:	:	:
10_1101-2021_01_08_425885	75	48	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	75	49	)	)	-RRB-
10_1101-2021_01_08_425885	75	50	=	=	NFP
10_1101-2021_01_08_425885	75	51	(	(	-LRB-
10_1101-2021_01_08_425885	75	52	4π	4π	LS
10_1101-2021_01_08_425885	75	53	)	)	-RRB-
10_1101-2021_01_08_425885	75	54	d/2xd	d/2xd	NNP
10_1101-2021_01_08_425885	75	55	m∑	m∑	JJ
10_1101-2021_01_08_425885	75	56	k=1	k=1	JJ
10_1101-2021_01_08_425885	75	57	e−λkx	e−λkx	NNP
10_1101-2021_01_08_425885	75	58	2	2	CD
10_1101-2021_01_08_425885	75	59	(	(	-LRB-
10_1101-2021_01_08_425885	75	60	3	3	LS
10_1101-2021_01_08_425885	75	61	)	)	-RRB-
10_1101-2021_01_08_425885	75	62	The	the	DT
10_1101-2021_01_08_425885	75	63	scalar	scalar	JJ
10_1101-2021_01_08_425885	75	64	curvature	curvature	NN
10_1101-2021_01_08_425885	75	65	can	can	MD
10_1101-2021_01_08_425885	75	66	then	then	RB
10_1101-2021_01_08_425885	75	67	be	be	VB
10_1101-2021_01_08_425885	75	68	approximated	approximate	VBN
10_1101-2021_01_08_425885	75	69	by	by	IN
10_1101-2021_01_08_425885	75	70	fitting	fit	VBG
10_1101-2021_01_08_425885	75	71	the	the	DT
10_1101-2021_01_08_425885	75	72	truncated	truncate	VBN
10_1101-2021_01_08_425885	75	73	series	series	NN
10_1101-2021_01_08_425885	75	74	,	,	,
10_1101-2021_01_08_425885	75	75	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	75	76	)	)	-RRB-
10_1101-2021_01_08_425885	75	77	,	,	,
10_1101-2021_01_08_425885	75	78	to	to	IN
10_1101-2021_01_08_425885	75	79	a	a	DT
10_1101-2021_01_08_425885	75	80	second	second	JJ
10_1101-2021_01_08_425885	75	81	-	-	HYPH
10_1101-2021_01_08_425885	75	82	order	order	NN
10_1101-2021_01_08_425885	75	83	polynomial	polynomial	JJ
10_1101-2021_01_08_425885	75	84	,	,	,
10_1101-2021_01_08_425885	75	85	p2(x	p2(x	JJ
10_1101-2021_01_08_425885	75	86	)	)	-RRB-
10_1101-2021_01_08_425885	75	87	,	,	,
10_1101-2021_01_08_425885	75	88	over	over	IN
10_1101-2021_01_08_425885	75	89	intervals	interval	NNS
10_1101-2021_01_08_425885	75	90	of	of	IN
10_1101-2021_01_08_425885	75	91	small	small	JJ
10_1101-2021_01_08_425885	75	92	x	x	SYM
10_1101-2021_01_08_425885	75	93	:	:	:
10_1101-2021_01_08_425885	75	94	zm(x	zm(x	.
10_1101-2021_01_08_425885	75	95	)	)	-RRB-
10_1101-2021_01_08_425885	75	96	≈	≈	IN
10_1101-2021_01_08_425885	75	97	p2(x	p2(x	ADD
10_1101-2021_01_08_425885	75	98	)	)	-RRB-
10_1101-2021_01_08_425885	75	99	,	,	,
10_1101-2021_01_08_425885	75	100	where	where	WRB
10_1101-2021_01_08_425885	75	101	p2(x	p2(x	NN
10_1101-2021_01_08_425885	75	102	)	)	-RRB-
10_1101-2021_01_08_425885	75	103	=	=	NFP
10_1101-2021_01_08_425885	75	104	c0	c0	NNP
10_1101-2021_01_08_425885	75	105	+	+	CC
10_1101-2021_01_08_425885	75	106	c1x	c1x	NNP
10_1101-2021_01_08_425885	75	107	+	+	CD
10_1101-2021_01_08_425885	75	108	c2x	c2x	CD
10_1101-2021_01_08_425885	75	109	2	2	CD
10_1101-2021_01_08_425885	75	110	(	(	-LRB-
10_1101-2021_01_08_425885	75	111	4	4	CD
10_1101-2021_01_08_425885	75	112	)	)	-RRB-
10_1101-2021_01_08_425885	75	113	We	-PRON-	PRP
10_1101-2021_01_08_425885	75	114	estimated	estimate	VBD
10_1101-2021_01_08_425885	75	115	∆M	∆M	NNP
10_1101-2021_01_08_425885	75	116	using	use	VBG
10_1101-2021_01_08_425885	75	117	the	the	DT
10_1101-2021_01_08_425885	75	118	N	N	NNP
10_1101-2021_01_08_425885	75	119	sampled	sample	VBN
10_1101-2021_01_08_425885	75	120	points	point	NNS
10_1101-2021_01_08_425885	75	121	(	(	-LRB-
10_1101-2021_01_08_425885	75	122	see	see	VB
10_1101-2021_01_08_425885	75	123	Methods	Methods	NNP
10_1101-2021_01_08_425885	75	124	Section	Section	NNP
10_1101-2021_01_08_425885	75	125	4.2.5	4.2.5	CD
10_1101-2021_01_08_425885	75	126	)	)	-RRB-
10_1101-2021_01_08_425885	75	127	,	,	,
10_1101-2021_01_08_425885	75	128	substituted	substitute	VBD
10_1101-2021_01_08_425885	75	129	the	the	DT
10_1101-2021_01_08_425885	75	130	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	75	131	of	of	IN
10_1101-2021_01_08_425885	75	132	the	the	DT
10_1101-2021_01_08_425885	75	133	estimate	estimate	NN
10_1101-2021_01_08_425885	75	134	into	into	IN
10_1101-2021_01_08_425885	75	135	Equation	Equation	NNP
10_1101-2021_01_08_425885	75	136	3	3	CD
10_1101-2021_01_08_425885	75	137	,	,	,
10_1101-2021_01_08_425885	75	138	and	and	CC
10_1101-2021_01_08_425885	75	139	numerically	numerically	RB
10_1101-2021_01_08_425885	75	140	fit	fit	JJ
10_1101-2021_01_08_425885	75	141	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	75	142	)	)	-RRB-
10_1101-2021_01_08_425885	75	143	to	to	IN
10_1101-2021_01_08_425885	75	144	p2(x	p2(x	ADD
10_1101-2021_01_08_425885	75	145	)	)	-RRB-
10_1101-2021_01_08_425885	75	146	(	(	-LRB-
10_1101-2021_01_08_425885	75	147	see	see	VB
10_1101-2021_01_08_425885	75	148	Figure	Figure	NNP
10_1101-2021_01_08_425885	75	149	S1A	s1a	NN
10_1101-2021_01_08_425885	75	150	-	-	HYPH
10_1101-2021_01_08_425885	75	151	G	g	NN
10_1101-2021_01_08_425885	75	152	;	;	:
10_1101-2021_01_08_425885	75	153	Methods	Methods	NNP
10_1101-2021_01_08_425885	75	154	Section	Section	NNP
10_1101-2021_01_08_425885	75	155	4.2.1	4.2.1	CD
10_1101-2021_01_08_425885	75	156	)	)	-RRB-
10_1101-2021_01_08_425885	75	157	.	.	.
10_1101-2021_01_08_425885	76	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	76	2	obtained	obtain	VBD
10_1101-2021_01_08_425885	76	3	the	the	DT
10_1101-2021_01_08_425885	76	4	scalar	scalar	JJ
10_1101-2021_01_08_425885	76	5	curvature	curvature	NN
10_1101-2021_01_08_425885	76	6	by	by	IN
10_1101-2021_01_08_425885	76	7	inspecting	inspect	VBG
10_1101-2021_01_08_425885	76	8	the	the	DT
10_1101-2021_01_08_425885	76	9	resulting	result	VBG
10_1101-2021_01_08_425885	76	10	c2	c2	NN
10_1101-2021_01_08_425885	76	11	coefficient	coefficient	NN
10_1101-2021_01_08_425885	76	12	,	,	,
10_1101-2021_01_08_425885	76	13	and	and	CC
10_1101-2021_01_08_425885	76	14	compared	compare	VBD
10_1101-2021_01_08_425885	76	15	the	the	DT
10_1101-2021_01_08_425885	76	16	result	result	NN
10_1101-2021_01_08_425885	76	17	to	to	IN
10_1101-2021_01_08_425885	76	18	the	the	DT
10_1101-2021_01_08_425885	76	19	true	true	JJ
10_1101-2021_01_08_425885	76	20	value	value	NN
10_1101-2021_01_08_425885	76	21	of	of	IN
10_1101-2021_01_08_425885	76	22	2	2	CD
10_1101-2021_01_08_425885	76	23	.	.	.
10_1101-2021_01_08_425885	77	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	77	2	found	find	VBD
10_1101-2021_01_08_425885	77	3	that	that	IN
10_1101-2021_01_08_425885	77	4	the	the	DT
10_1101-2021_01_08_425885	77	5	scalar	scalar	JJ
10_1101-2021_01_08_425885	77	6	curvature	curvature	NN
10_1101-2021_01_08_425885	77	7	was	be	VBD
10_1101-2021_01_08_425885	77	8	always	always	RB
10_1101-2021_01_08_425885	77	9	over	over	RB
10_1101-2021_01_08_425885	77	10	-	-	HYPH
10_1101-2021_01_08_425885	77	11	estimated	estimate	VBN
10_1101-2021_01_08_425885	77	12	(	(	-LRB-
10_1101-2021_01_08_425885	77	13	S	S	NNP
10_1101-2021_01_08_425885	77	14	>	>	XX
10_1101-2021_01_08_425885	77	15	3	3	LS
10_1101-2021_01_08_425885	77	16	)	)	-RRB-
10_1101-2021_01_08_425885	77	17	regardless	regardless	RB
10_1101-2021_01_08_425885	77	18	of	of	IN
10_1101-2021_01_08_425885	77	19	m	m	NNP
10_1101-2021_01_08_425885	77	20	,	,	,
10_1101-2021_01_08_425885	77	21	the	the	DT
10_1101-2021_01_08_425885	77	22	number	number	NN
10_1101-2021_01_08_425885	77	23	of	of	IN
10_1101-2021_01_08_425885	77	24	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	77	25	used	use	VBN
10_1101-2021_01_08_425885	77	26	in	in	IN
10_1101-2021_01_08_425885	77	27	the	the	DT
10_1101-2021_01_08_425885	77	28	truncated	truncate	VBN
10_1101-2021_01_08_425885	77	29	series	series	NN
10_1101-2021_01_08_425885	77	30	(	(	-LRB-
10_1101-2021_01_08_425885	77	31	see	see	VB
10_1101-2021_01_08_425885	77	32	Methods	Methods	NNP
10_1101-2021_01_08_425885	77	33	Section	Section	NNP
10_1101-2021_01_08_425885	77	34	4.2.3	4.2.3	CD
10_1101-2021_01_08_425885	77	35	)	)	-RRB-
10_1101-2021_01_08_425885	77	36	,	,	,
10_1101-2021_01_08_425885	77	37	or	or	CC
10_1101-2021_01_08_425885	77	38	the	the	DT
10_1101-2021_01_08_425885	77	39	choice	choice	NN
10_1101-2021_01_08_425885	77	40	of	of	IN
10_1101-2021_01_08_425885	77	41	estimator	estimator	NN
10_1101-2021_01_08_425885	77	42	for	for	IN
10_1101-2021_01_08_425885	77	43	∆M	∆M	NNP
10_1101-2021_01_08_425885	77	44	(	(	-LRB-
10_1101-2021_01_08_425885	77	45	see	see	VB
10_1101-2021_01_08_425885	77	46	Methods	Methods	NNP
10_1101-2021_01_08_425885	77	47	Section	Section	NNP
10_1101-2021_01_08_425885	77	48	4.2.5	4.2.5	CD
10_1101-2021_01_08_425885	77	49	)	)	-RRB-
10_1101-2021_01_08_425885	77	50	.	.	.
10_1101-2021_01_08_425885	78	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	78	2	identified	identify	VBD
10_1101-2021_01_08_425885	78	3	the	the	DT
10_1101-2021_01_08_425885	78	4	poor	poor	JJ
10_1101-2021_01_08_425885	78	5	convergence	convergence	NN
10_1101-2021_01_08_425885	78	6	of	of	IN
10_1101-2021_01_08_425885	78	7	the	the	DT
10_1101-2021_01_08_425885	78	8	estimated	estimate	VBN
10_1101-2021_01_08_425885	78	9	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	78	10	of	of	IN
10_1101-2021_01_08_425885	78	11	∆M	∆M	NNP
10_1101-2021_01_08_425885	78	12	as	as	IN
10_1101-2021_01_08_425885	78	13	the	the	DT
10_1101-2021_01_08_425885	78	14	source	source	NN
10_1101-2021_01_08_425885	78	15	of	of	IN
10_1101-2021_01_08_425885	78	16	error	error	NN
10_1101-2021_01_08_425885	78	17	(	(	-LRB-
10_1101-2021_01_08_425885	78	18	see	see	VB
10_1101-2021_01_08_425885	78	19	Methods	Methods	NNP
10_1101-2021_01_08_425885	78	20	Section	Section	NNP
10_1101-2021_01_08_425885	78	21	4.2.4	4.2.4	NN
10_1101-2021_01_08_425885	78	22	)	)	-RRB-
10_1101-2021_01_08_425885	78	23	and	and	CC
10_1101-2021_01_08_425885	78	24	found	find	VBD
10_1101-2021_01_08_425885	78	25	that	that	IN
10_1101-2021_01_08_425885	78	26	at	at	IN
10_1101-2021_01_08_425885	78	27	least	least	JJS
10_1101-2021_01_08_425885	78	28	N	n	CD
10_1101-2021_01_08_425885	78	29	≈	≈	NNP
10_1101-2021_01_08_425885	78	30	107	107	CD
10_1101-2021_01_08_425885	78	31	points	point	NNS
10_1101-2021_01_08_425885	78	32	are	be	VBP
10_1101-2021_01_08_425885	78	33	required	require	VBN
10_1101-2021_01_08_425885	78	34	to	to	TO
10_1101-2021_01_08_425885	78	35	reduce	reduce	VB
10_1101-2021_01_08_425885	78	36	the	the	DT
10_1101-2021_01_08_425885	78	37	error	error	NN
10_1101-2021_01_08_425885	78	38	to	to	TO
10_1101-2021_01_08_425885	78	39	±0.5	±0.5	NNP
10_1101-2021_01_08_425885	78	40	,	,	,
10_1101-2021_01_08_425885	78	41	so	so	IN
10_1101-2021_01_08_425885	78	42	that	that	IN
10_1101-2021_01_08_425885	78	43	S	S	NNP
10_1101-2021_01_08_425885	78	44	≈	≈	NNP
10_1101-2021_01_08_425885	78	45	2.5	2.5	CD
10_1101-2021_01_08_425885	78	46	(	(	-LRB-
10_1101-2021_01_08_425885	78	47	see	see	VB
10_1101-2021_01_08_425885	78	48	Figure	Figure	NNP
10_1101-2021_01_08_425885	78	49	S1H	s1h	NN
10_1101-2021_01_08_425885	78	50	)	)	-RRB-
10_1101-2021_01_08_425885	78	51	.	.	.
10_1101-2021_01_08_425885	79	1	Therefore	therefore	RB
10_1101-2021_01_08_425885	79	2	,	,	,
10_1101-2021_01_08_425885	79	3	despite	despite	IN
10_1101-2021_01_08_425885	79	4	the	the	DT
10_1101-2021_01_08_425885	79	5	prevalence	prevalence	NN
10_1101-2021_01_08_425885	79	6	of	of	IN
10_1101-2021_01_08_425885	79	7	the	the	DT
10_1101-2021_01_08_425885	79	8	Laplace	Laplace	NNP
10_1101-2021_01_08_425885	79	9	-	-	HYPH
10_1101-2021_01_08_425885	79	10	Beltrami	Beltrami	NNP
10_1101-2021_01_08_425885	79	11	operator	operator	NN
10_1101-2021_01_08_425885	79	12	in	in	IN
10_1101-2021_01_08_425885	79	13	geometric	geometric	JJ
10_1101-2021_01_08_425885	79	14	data	datum	NNS
10_1101-2021_01_08_425885	79	15	analysis	analysis	NN
10_1101-2021_01_08_425885	79	16	,	,	,
10_1101-2021_01_08_425885	79	17	our	-PRON-	PRP$
10_1101-2021_01_08_425885	79	18	exam-	exam-	FW
10_1101-2021_01_08_425885	79	19	ple	ple	NN
10_1101-2021_01_08_425885	79	20	shows	show	VBZ
10_1101-2021_01_08_425885	79	21	that	that	IN
10_1101-2021_01_08_425885	79	22	an	an	DT
10_1101-2021_01_08_425885	79	23	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	79	24	approach	approach	NN
10_1101-2021_01_08_425885	79	25	relying	rely	VBG
10_1101-2021_01_08_425885	79	26	on	on	IN
10_1101-2021_01_08_425885	79	27	the	the	DT
10_1101-2021_01_08_425885	79	28	operator	operator	NN
10_1101-2021_01_08_425885	79	29	is	be	VBZ
10_1101-2021_01_08_425885	79	30	not	not	RB
10_1101-2021_01_08_425885	79	31	practical	practical	JJ
10_1101-2021_01_08_425885	79	32	for	for	IN
10_1101-2021_01_08_425885	79	33	computing	compute	VBG
10_1101-2021_01_08_425885	79	34	scalar	scalar	JJ
10_1101-2021_01_08_425885	79	35	curvatures	curvature	NNS
10_1101-2021_01_08_425885	79	36	.	.	.
10_1101-2021_01_08_425885	80	1	Even	even	RB
10_1101-2021_01_08_425885	80	2	for	for	IN
10_1101-2021_01_08_425885	80	3	noise	noise	NN
10_1101-2021_01_08_425885	80	4	-	-	HYPH
10_1101-2021_01_08_425885	80	5	free	free	JJ
10_1101-2021_01_08_425885	80	6	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	80	7	uniformly	uniformly	RB
10_1101-2021_01_08_425885	80	8	sampled	sample	VBN
10_1101-2021_01_08_425885	80	9	from	from	IN
10_1101-2021_01_08_425885	80	10	S2	s2	NN
10_1101-2021_01_08_425885	80	11	,	,	,
10_1101-2021_01_08_425885	80	12	the	the	DT
10_1101-2021_01_08_425885	80	13	sample	sample	NN
10_1101-2021_01_08_425885	80	14	size	size	NN
10_1101-2021_01_08_425885	80	15	needed	need	VBN
10_1101-2021_01_08_425885	80	16	to	to	TO
10_1101-2021_01_08_425885	80	17	compute	compute	VB
10_1101-2021_01_08_425885	80	18	average	average	JJ
10_1101-2021_01_08_425885	80	19	scalar	scalar	JJ
10_1101-2021_01_08_425885	80	20	curvature	curvature	NN
10_1101-2021_01_08_425885	80	21	accurate	accurate	JJ
10_1101-2021_01_08_425885	80	22	to	to	IN
10_1101-2021_01_08_425885	80	23	±0.5	±0.5	NNP
10_1101-2021_01_08_425885	80	24	is	be	VBZ
10_1101-2021_01_08_425885	80	25	several	several	JJ
10_1101-2021_01_08_425885	80	26	orders	order	NNS
10_1101-2021_01_08_425885	80	27	of	of	IN
10_1101-2021_01_08_425885	80	28	magnitude	magnitude	NN
10_1101-2021_01_08_425885	80	29	greater	great	JJR
10_1101-2021_01_08_425885	80	30	than	than	IN
10_1101-2021_01_08_425885	80	31	what	what	WP
10_1101-2021_01_08_425885	80	32	is	be	VBZ
10_1101-2021_01_08_425885	80	33	typically	typically	RB
10_1101-2021_01_08_425885	80	34	feasible	feasible	JJ
10_1101-2021_01_08_425885	80	35	in	in	IN
10_1101-2021_01_08_425885	80	36	current	current	JJ
10_1101-2021_01_08_425885	80	37	scRNAseq	scrnaseq	JJ
10_1101-2021_01_08_425885	80	38	experiments	experiment	NNS
10_1101-2021_01_08_425885	80	39	.	.	.
10_1101-2021_01_08_425885	81	1	Noise	Noise	NNP
10_1101-2021_01_08_425885	81	2	and	and	CC
10_1101-2021_01_08_425885	81	3	non	non	JJ
10_1101-2021_01_08_425885	81	4	-	-	JJ
10_1101-2021_01_08_425885	81	5	uniform	uniform	JJ
10_1101-2021_01_08_425885	81	6	sampling	sampling	NN
10_1101-2021_01_08_425885	81	7	would	would	MD
10_1101-2021_01_08_425885	81	8	confound	confound	VB
10_1101-2021_01_08_425885	81	9	the	the	DT
10_1101-2021_01_08_425885	81	10	issue	issue	NN
10_1101-2021_01_08_425885	81	11	further	further	RB
10_1101-2021_01_08_425885	81	12	.	.	.
10_1101-2021_01_08_425885	82	1	Most	Most	JJS
10_1101-2021_01_08_425885	82	2	impor-	impor-	RB
10_1101-2021_01_08_425885	82	3	tantly	tantly	RB
10_1101-2021_01_08_425885	82	4	,	,	,
10_1101-2021_01_08_425885	82	5	we	-PRON-	PRP
10_1101-2021_01_08_425885	82	6	would	would	MD
10_1101-2021_01_08_425885	82	7	eventually	eventually	RB
10_1101-2021_01_08_425885	82	8	like	like	VB
10_1101-2021_01_08_425885	82	9	to	to	TO
10_1101-2021_01_08_425885	82	10	compute	compute	VB
10_1101-2021_01_08_425885	82	11	local	local	JJ
10_1101-2021_01_08_425885	82	12	values	value	NNS
10_1101-2021_01_08_425885	82	13	of	of	IN
10_1101-2021_01_08_425885	82	14	S(p	S(p	NNP
10_1101-2021_01_08_425885	82	15	)	)	-RRB-
10_1101-2021_01_08_425885	82	16	∀p	∀p	NFP
10_1101-2021_01_08_425885	82	17	∈	∈	NNP
10_1101-2021_01_08_425885	82	18	M	M	NNP
10_1101-2021_01_08_425885	82	19	,	,	,
10_1101-2021_01_08_425885	82	20	but	but	CC
10_1101-2021_01_08_425885	82	21	this	this	DT
10_1101-2021_01_08_425885	82	22	approach	approach	NN
10_1101-2021_01_08_425885	82	23	failed	fail	VBD
10_1101-2021_01_08_425885	82	24	to	to	TO
10_1101-2021_01_08_425885	82	25	correctly	correctly	RB
10_1101-2021_01_08_425885	82	26	recover	recover	VB
10_1101-2021_01_08_425885	82	27	even	even	RB
10_1101-2021_01_08_425885	82	28	average	average	JJ
10_1101-2021_01_08_425885	82	29	scalar	scalar	JJ
10_1101-2021_01_08_425885	82	30	curvature	curvature	NN
10_1101-2021_01_08_425885	82	31	,	,	,
10_1101-2021_01_08_425885	82	32	which	which	WDT
10_1101-2021_01_08_425885	82	33	one	one	PRP
10_1101-2021_01_08_425885	82	34	might	may	MD
10_1101-2021_01_08_425885	82	35	have	have	VB
10_1101-2021_01_08_425885	82	36	expected	expect	VBN
10_1101-2021_01_08_425885	82	37	to	to	TO
10_1101-2021_01_08_425885	82	38	be	be	VB
10_1101-2021_01_08_425885	82	39	feasible	feasible	JJ
10_1101-2021_01_08_425885	82	40	.	.	.
10_1101-2021_01_08_425885	83	1	To	to	TO
10_1101-2021_01_08_425885	83	2	find	find	VB
10_1101-2021_01_08_425885	83	3	an	an	DT
10_1101-2021_01_08_425885	83	4	alternative	alternative	JJ
10_1101-2021_01_08_425885	83	5	approach	approach	NN
10_1101-2021_01_08_425885	83	6	,	,	,
10_1101-2021_01_08_425885	83	7	we	-PRON-	PRP
10_1101-2021_01_08_425885	83	8	next	next	RB
10_1101-2021_01_08_425885	83	9	considered	consider	VBN
10_1101-2021_01_08_425885	83	10	tools	tool	NNS
10_1101-2021_01_08_425885	83	11	from	from	IN
10_1101-2021_01_08_425885	83	12	extrinsic	extrinsic	JJ
10_1101-2021_01_08_425885	83	13	differential	differential	NN
10_1101-2021_01_08_425885	83	14	geometry	geometry	NN
10_1101-2021_01_08_425885	83	15	.	.	.
10_1101-2021_01_08_425885	84	1	2.2	2.2	CD
10_1101-2021_01_08_425885	84	2	Curvature	curvature	NN
10_1101-2021_01_08_425885	84	3	Can	Can	MD
10_1101-2021_01_08_425885	84	4	Be	be	VB
10_1101-2021_01_08_425885	84	5	Computed	compute	VBN
10_1101-2021_01_08_425885	84	6	Accurately	accurately	RB
10_1101-2021_01_08_425885	84	7	Using	use	VBG
10_1101-2021_01_08_425885	84	8	the	the	DT
10_1101-2021_01_08_425885	84	9	Second	Second	NNP
10_1101-2021_01_08_425885	84	10	Fundamental	Fundamental	NNP
10_1101-2021_01_08_425885	84	11	Form	Form	NNP
10_1101-2021_01_08_425885	84	12	In	in	IN
10_1101-2021_01_08_425885	84	13	extrinsic	extrinsic	NN
10_1101-2021_01_08_425885	84	14	differential	differential	NN
10_1101-2021_01_08_425885	84	15	geometry	geometry	NN
10_1101-2021_01_08_425885	84	16	,	,	,
10_1101-2021_01_08_425885	84	17	a	a	DT
10_1101-2021_01_08_425885	84	18	manifold	manifold	NN
10_1101-2021_01_08_425885	84	19	is	be	VBZ
10_1101-2021_01_08_425885	84	20	described	describe	VBN
10_1101-2021_01_08_425885	84	21	in	in	IN
10_1101-2021_01_08_425885	84	22	the	the	DT
10_1101-2021_01_08_425885	84	23	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	84	24	of	of	IN
10_1101-2021_01_08_425885	84	25	the	the	DT
10_1101-2021_01_08_425885	84	26	ambient	ambient	JJ
10_1101-2021_01_08_425885	84	27	space	space	NN
10_1101-2021_01_08_425885	84	28	in	in	IN
10_1101-2021_01_08_425885	84	29	which	which	WDT
10_1101-2021_01_08_425885	84	30	it	-PRON-	PRP
10_1101-2021_01_08_425885	84	31	is	be	VBZ
10_1101-2021_01_08_425885	84	32	embedded	embed	VBN
10_1101-2021_01_08_425885	84	33	,	,	,
10_1101-2021_01_08_425885	84	34	usually	usually	RB
10_1101-2021_01_08_425885	84	35	Rn	Rn	VBZ
10_1101-2021_01_08_425885	84	36	(	(	-LRB-
10_1101-2021_01_08_425885	84	37	see	see	VB
10_1101-2021_01_08_425885	84	38	Figure	Figure	NNP
10_1101-2021_01_08_425885	84	39	1D	1d	NN
10_1101-2021_01_08_425885	84	40	)	)	-RRB-
10_1101-2021_01_08_425885	84	41	.	.	.
10_1101-2021_01_08_425885	85	1	Since	since	IN
10_1101-2021_01_08_425885	85	2	the	the	DT
10_1101-2021_01_08_425885	85	3	shape	shape	NN
10_1101-2021_01_08_425885	85	4	of	of	IN
10_1101-2021_01_08_425885	85	5	the	the	DT
10_1101-2021_01_08_425885	85	6	sphere	sphere	NN
10_1101-2021_01_08_425885	85	7	in	in	IN
10_1101-2021_01_08_425885	85	8	Figure	figure	NN
10_1101-2021_01_08_425885	85	9	1A	1a	NN
10_1101-2021_01_08_425885	85	10	is	be	VBZ
10_1101-2021_01_08_425885	85	11	visually	visually	RB
10_1101-2021_01_08_425885	85	12	unambiguous	unambiguous	JJ
10_1101-2021_01_08_425885	85	13	6	6	CD
10_1101-2021_01_08_425885	85	14	.CC	.CC	,
10_1101-2021_01_08_425885	85	15	-	-	HYPH
10_1101-2021_01_08_425885	85	16	BY	by	IN
10_1101-2021_01_08_425885	85	17	-	-	HYPH
10_1101-2021_01_08_425885	85	18	NC	NC	NNP
10_1101-2021_01_08_425885	85	19	-	-	HYPH
10_1101-2021_01_08_425885	85	20	ND	ND	NNP
10_1101-2021_01_08_425885	85	21	4.0	4.0	CD
10_1101-2021_01_08_425885	85	22	International	International	NNP
10_1101-2021_01_08_425885	85	23	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	85	24	under	under	IN
10_1101-2021_01_08_425885	85	25	a	a	DT
10_1101-2021_01_08_425885	85	26	(	(	-LRB-
10_1101-2021_01_08_425885	85	27	which	which	WDT
10_1101-2021_01_08_425885	85	28	was	be	VBD
10_1101-2021_01_08_425885	85	29	not	not	RB
10_1101-2021_01_08_425885	85	30	certified	certify	VBN
10_1101-2021_01_08_425885	85	31	by	by	IN
10_1101-2021_01_08_425885	85	32	peer	peer	NN
10_1101-2021_01_08_425885	85	33	review	review	NN
10_1101-2021_01_08_425885	85	34	)	)	-RRB-
10_1101-2021_01_08_425885	85	35	is	be	VBZ
10_1101-2021_01_08_425885	85	36	the	the	DT
10_1101-2021_01_08_425885	85	37	author	author	NN
10_1101-2021_01_08_425885	85	38	/	/	SYM
10_1101-2021_01_08_425885	85	39	funder	funder	NN
10_1101-2021_01_08_425885	85	40	,	,	,
10_1101-2021_01_08_425885	85	41	who	who	WP
10_1101-2021_01_08_425885	85	42	has	have	VBZ
10_1101-2021_01_08_425885	85	43	granted	grant	VBN
10_1101-2021_01_08_425885	85	44	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	85	45	a	a	DT
10_1101-2021_01_08_425885	85	46	license	license	NN
10_1101-2021_01_08_425885	85	47	to	to	TO
10_1101-2021_01_08_425885	85	48	display	display	VB
10_1101-2021_01_08_425885	85	49	the	the	DT
10_1101-2021_01_08_425885	85	50	preprint	preprint	NN
10_1101-2021_01_08_425885	85	51	in	in	IN
10_1101-2021_01_08_425885	85	52	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	85	53	.	.	.
10_1101-2021_01_08_425885	86	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	86	2	is	be	VBZ
10_1101-2021_01_08_425885	86	3	made	make	VBN
10_1101-2021_01_08_425885	86	4	The	the	DT
10_1101-2021_01_08_425885	86	5	copyright	copyright	NN
10_1101-2021_01_08_425885	86	6	holder	holder	NN
10_1101-2021_01_08_425885	86	7	for	for	IN
10_1101-2021_01_08_425885	86	8	this	this	DT
10_1101-2021_01_08_425885	86	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	86	10	version	version	NN
10_1101-2021_01_08_425885	86	11	posted	post	VBD
10_1101-2021_01_08_425885	86	12	January	January	NNP
10_1101-2021_01_08_425885	86	13	8	8	CD
10_1101-2021_01_08_425885	86	14	,	,	,
10_1101-2021_01_08_425885	86	15	2021	2021	CD
10_1101-2021_01_08_425885	86	16	.	.	.
10_1101-2021_01_08_425885	86	17	;	;	:
10_1101-2021_01_08_425885	86	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	86	19	:	:	:
10_1101-2021_01_08_425885	86	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	86	21	preprint	preprint	NN
10_1101-2021_01_08_425885	86	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	86	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	RB
10_1101-2021_01_08_425885	86	24	to	to	IN
10_1101-2021_01_08_425885	86	25	the	the	DT
10_1101-2021_01_08_425885	86	26	eye	eye	NN
10_1101-2021_01_08_425885	86	27	(	(	-LRB-
10_1101-2021_01_08_425885	86	28	thanks	thank	NNS
10_1101-2021_01_08_425885	86	29	to	to	IN
10_1101-2021_01_08_425885	86	30	its	-PRON-	PRP$
10_1101-2021_01_08_425885	86	31	extrinsic	extrinsic	JJ
10_1101-2021_01_08_425885	86	32	view	view	NN
10_1101-2021_01_08_425885	86	33	from	from	IN
10_1101-2021_01_08_425885	86	34	a	a	DT
10_1101-2021_01_08_425885	86	35	vantage	vantage	NN
10_1101-2021_01_08_425885	86	36	point	point	NN
10_1101-2021_01_08_425885	86	37	off	off	IN
10_1101-2021_01_08_425885	86	38	the	the	DT
10_1101-2021_01_08_425885	86	39	manifold	manifold	NN
10_1101-2021_01_08_425885	86	40	)	)	-RRB-
10_1101-2021_01_08_425885	86	41	,	,	,
10_1101-2021_01_08_425885	86	42	we	-PRON-	PRP
10_1101-2021_01_08_425885	86	43	reasoned	reason	VBD
10_1101-2021_01_08_425885	86	44	that	that	IN
10_1101-2021_01_08_425885	86	45	an	an	DT
10_1101-2021_01_08_425885	86	46	extrinsic	extrinsic	JJ
10_1101-2021_01_08_425885	86	47	approach	approach	NN
10_1101-2021_01_08_425885	86	48	would	would	MD
10_1101-2021_01_08_425885	86	49	be	be	VB
10_1101-2021_01_08_425885	86	50	more	more	RBR
10_1101-2021_01_08_425885	86	51	fruitful	fruitful	JJ
10_1101-2021_01_08_425885	86	52	.	.	.
10_1101-2021_01_08_425885	87	1	A	a	DT
10_1101-2021_01_08_425885	87	2	d	d	NNP
10_1101-2021_01_08_425885	87	3	-	-	HYPH
10_1101-2021_01_08_425885	87	4	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	87	5	manifold	manifold	NN
10_1101-2021_01_08_425885	87	6	,	,	,
10_1101-2021_01_08_425885	87	7	M	M	NNP
10_1101-2021_01_08_425885	87	8	,	,	,
10_1101-2021_01_08_425885	87	9	embedded	embed	VBN
10_1101-2021_01_08_425885	87	10	in	in	IN
10_1101-2021_01_08_425885	87	11	Rn	Rn	NNS
10_1101-2021_01_08_425885	87	12	can	can	MD
10_1101-2021_01_08_425885	87	13	be	be	VB
10_1101-2021_01_08_425885	87	14	described	describe	VBN
10_1101-2021_01_08_425885	87	15	at	at	IN
10_1101-2021_01_08_425885	87	16	each	each	DT
10_1101-2021_01_08_425885	87	17	point	point	NN
10_1101-2021_01_08_425885	87	18	p	p	NN
10_1101-2021_01_08_425885	87	19	in	in	IN
10_1101-2021_01_08_425885	87	20	terms	term	NNS
10_1101-2021_01_08_425885	87	21	of	of	IN
10_1101-2021_01_08_425885	87	22	a	a	DT
10_1101-2021_01_08_425885	87	23	d-	d-	JJ
10_1101-2021_01_08_425885	87	24	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	87	25	tangent	tangent	NN
10_1101-2021_01_08_425885	87	26	space	space	NN
10_1101-2021_01_08_425885	87	27	,	,	,
10_1101-2021_01_08_425885	87	28	TM	TM	NNP
10_1101-2021_01_08_425885	87	29	(	(	-LRB-
10_1101-2021_01_08_425885	87	30	p	p	NNP
10_1101-2021_01_08_425885	87	31	)	)	-RRB-
10_1101-2021_01_08_425885	87	32	,	,	,
10_1101-2021_01_08_425885	87	33	and	and	CC
10_1101-2021_01_08_425885	87	34	an	an	DT
10_1101-2021_01_08_425885	87	35	(	(	-LRB-
10_1101-2021_01_08_425885	87	36	n	n	IN
10_1101-2021_01_08_425885	87	37	−	−	NNP
10_1101-2021_01_08_425885	87	38	d)-dimensional	d)-dimensional	CD
10_1101-2021_01_08_425885	87	39	normal	normal	JJ
10_1101-2021_01_08_425885	87	40	space	space	NN
10_1101-2021_01_08_425885	87	41	,	,	,
10_1101-2021_01_08_425885	87	42	NM	NM	NNP
10_1101-2021_01_08_425885	87	43	(	(	-LRB-
10_1101-2021_01_08_425885	87	44	p	p	NNP
10_1101-2021_01_08_425885	87	45	)	)	-RRB-
10_1101-2021_01_08_425885	87	46	,	,	,
10_1101-2021_01_08_425885	87	47	as	as	IN
10_1101-2021_01_08_425885	87	48	shown	show	VBN
10_1101-2021_01_08_425885	87	49	in	in	IN
10_1101-2021_01_08_425885	87	50	Fig-	Fig-	NNP
10_1101-2021_01_08_425885	87	51	ure	ure	NN
10_1101-2021_01_08_425885	87	52	2A.	2a.	CD
10_1101-2021_01_08_425885	88	1	Given	give	VBN
10_1101-2021_01_08_425885	88	2	orthonormal	orthonormal	JJ
10_1101-2021_01_08_425885	88	3	bases	basis	NNS
10_1101-2021_01_08_425885	88	4	for	for	IN
10_1101-2021_01_08_425885	88	5	TM	TM	NNP
10_1101-2021_01_08_425885	88	6	(	(	-LRB-
10_1101-2021_01_08_425885	88	7	p	p	NNP
10_1101-2021_01_08_425885	88	8	)	)	-RRB-
10_1101-2021_01_08_425885	88	9	and	and	CC
10_1101-2021_01_08_425885	88	10	NM	NM	NNP
10_1101-2021_01_08_425885	88	11	(	(	-LRB-
10_1101-2021_01_08_425885	88	12	p	p	NNP
10_1101-2021_01_08_425885	88	13	)	)	-RRB-
10_1101-2021_01_08_425885	88	14	,	,	,
10_1101-2021_01_08_425885	88	15	points	point	NNS
10_1101-2021_01_08_425885	88	16	in	in	IN
10_1101-2021_01_08_425885	88	17	the	the	DT
10_1101-2021_01_08_425885	88	18	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	88	19	of	of	IN
10_1101-2021_01_08_425885	88	20	p	p	NN
10_1101-2021_01_08_425885	88	21	can	can	MD
10_1101-2021_01_08_425885	88	22	be	be	VB
10_1101-2021_01_08_425885	88	23	expressed	express	VBN
10_1101-2021_01_08_425885	88	24	as	as	IN
10_1101-2021_01_08_425885	88	25	Y	y	NN
10_1101-2021_01_08_425885	88	26	=	=	NFP
10_1101-2021_01_08_425885	88	27	[	[	-LRB-
10_1101-2021_01_08_425885	88	28	t1	t1	NNP
10_1101-2021_01_08_425885	88	29	,	,	,
10_1101-2021_01_08_425885	88	30	...	...	.
10_1101-2021_01_08_425885	88	31	,	,	,
10_1101-2021_01_08_425885	88	32	td	td	NNP
10_1101-2021_01_08_425885	88	33	,	,	,
10_1101-2021_01_08_425885	88	34	n1	n1	NNP
10_1101-2021_01_08_425885	88	35	,	,	,
10_1101-2021_01_08_425885	88	36	...	...	:
10_1101-2021_01_08_425885	88	37	,	,	,
10_1101-2021_01_08_425885	88	38	nn−d	nn−d	NNP
10_1101-2021_01_08_425885	88	39	]	]	-RRB-
10_1101-2021_01_08_425885	88	40	where	where	WRB
10_1101-2021_01_08_425885	88	41	ti	ti	PRP
10_1101-2021_01_08_425885	88	42	is	be	VBZ
10_1101-2021_01_08_425885	88	43	Y	Y	NNP
10_1101-2021_01_08_425885	88	44	’s	's	NN
10_1101-2021_01_08_425885	88	45	coordinate	coordinate	JJ
10_1101-2021_01_08_425885	88	46	along	along	IN
10_1101-2021_01_08_425885	88	47	the	the	DT
10_1101-2021_01_08_425885	88	48	i	i	NNP
10_1101-2021_01_08_425885	88	49	th	th	XX
10_1101-2021_01_08_425885	88	50	basis	basis	NN
10_1101-2021_01_08_425885	88	51	vector	vector	NN
10_1101-2021_01_08_425885	88	52	of	of	IN
10_1101-2021_01_08_425885	88	53	TM	TM	NNP
10_1101-2021_01_08_425885	88	54	(	(	-LRB-
10_1101-2021_01_08_425885	88	55	p	p	NNP
10_1101-2021_01_08_425885	88	56	)	)	-RRB-
10_1101-2021_01_08_425885	88	57	and	and	CC
10_1101-2021_01_08_425885	88	58	nk	nk	NN
10_1101-2021_01_08_425885	88	59	is	be	VBZ
10_1101-2021_01_08_425885	88	60	Y	Y	NNP
10_1101-2021_01_08_425885	88	61	’s	's	NNP
10_1101-2021_01_08_425885	88	62	coordinate	coordinate	VB
10_1101-2021_01_08_425885	88	63	along	along	IN
10_1101-2021_01_08_425885	88	64	the	the	DT
10_1101-2021_01_08_425885	88	65	kth	kth	NNP
10_1101-2021_01_08_425885	88	66	basis	basis	NN
10_1101-2021_01_08_425885	88	67	vector	vector	NN
10_1101-2021_01_08_425885	88	68	of	of	IN
10_1101-2021_01_08_425885	88	69	NM	NM	NNP
10_1101-2021_01_08_425885	88	70	(	(	-LRB-
10_1101-2021_01_08_425885	88	71	p	p	NNP
10_1101-2021_01_08_425885	88	72	)	)	-RRB-
10_1101-2021_01_08_425885	88	73	.	.	.
10_1101-2021_01_08_425885	89	1	The	the	DT
10_1101-2021_01_08_425885	89	2	nks	nks	NN
10_1101-2021_01_08_425885	89	3	can	can	MD
10_1101-2021_01_08_425885	89	4	then	then	RB
10_1101-2021_01_08_425885	89	5	be	be	VB
10_1101-2021_01_08_425885	89	6	locally	locally	RB
10_1101-2021_01_08_425885	89	7	approximated	approximate	VBN
10_1101-2021_01_08_425885	89	8	as	as	IN
10_1101-2021_01_08_425885	89	9	functions	function	NNS
10_1101-2021_01_08_425885	89	10	of	of	IN
10_1101-2021_01_08_425885	89	11	the	the	DT
10_1101-2021_01_08_425885	89	12	tis	tis	NNP
10_1101-2021_01_08_425885	89	13	i.e.	i.e.	FW
10_1101-2021_01_08_425885	90	1	nk	nk	NNP
10_1101-2021_01_08_425885	90	2	≈	≈	NNP
10_1101-2021_01_08_425885	90	3	fk(t1	fk(t1	CD
10_1101-2021_01_08_425885	90	4	,	,	,
10_1101-2021_01_08_425885	90	5	...	...	NFP
10_1101-2021_01_08_425885	90	6	,	,	,
10_1101-2021_01_08_425885	90	7	td	td	NNP
10_1101-2021_01_08_425885	90	8	)	)	-RRB-
10_1101-2021_01_08_425885	90	9	as	as	IN
10_1101-2021_01_08_425885	90	10	shown	show	VBN
10_1101-2021_01_08_425885	90	11	in	in	IN
10_1101-2021_01_08_425885	90	12	Figure	Figure	NNP
10_1101-2021_01_08_425885	90	13	2B.	2b.	CD
10_1101-2021_01_08_425885	91	1	The	the	DT
10_1101-2021_01_08_425885	91	2	Riemannian	riemannian	JJ
10_1101-2021_01_08_425885	91	3	curvature	curvature	NN
10_1101-2021_01_08_425885	91	4	of	of	IN
10_1101-2021_01_08_425885	91	5	M	M	NNP
10_1101-2021_01_08_425885	91	6	is	be	VBZ
10_1101-2021_01_08_425885	91	7	related	relate	VBN
10_1101-2021_01_08_425885	91	8	to	to	IN
10_1101-2021_01_08_425885	91	9	the	the	DT
10_1101-2021_01_08_425885	91	10	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	91	11	terms	term	NNS
10_1101-2021_01_08_425885	91	12	in	in	IN
10_1101-2021_01_08_425885	91	13	the	the	DT
10_1101-2021_01_08_425885	91	14	Taylor	Taylor	NNP
10_1101-2021_01_08_425885	91	15	expansion	expansion	NN
10_1101-2021_01_08_425885	91	16	of	of	IN
10_1101-2021_01_08_425885	91	17	each	each	DT
10_1101-2021_01_08_425885	91	18	fk	fk	UH
10_1101-2021_01_08_425885	91	19	with	with	IN
10_1101-2021_01_08_425885	91	20	respect	respect	NN
10_1101-2021_01_08_425885	91	21	to	to	IN
10_1101-2021_01_08_425885	91	22	the	the	DT
10_1101-2021_01_08_425885	91	23	tis	tis	NN
10_1101-2021_01_08_425885	91	24	.	.	.
10_1101-2021_01_08_425885	92	1	Specifically	specifically	RB
10_1101-2021_01_08_425885	92	2	,	,	,
10_1101-2021_01_08_425885	92	3	the	the	DT
10_1101-2021_01_08_425885	92	4	Second	Second	NNP
10_1101-2021_01_08_425885	92	5	Fundamental	Fundamental	NNP
10_1101-2021_01_08_425885	92	6	Form	Form	NNP
10_1101-2021_01_08_425885	92	7	of	of	IN
10_1101-2021_01_08_425885	92	8	M	M	NNP
10_1101-2021_01_08_425885	92	9	,	,	,
10_1101-2021_01_08_425885	92	10	h	h	NNP
10_1101-2021_01_08_425885	92	11	k	k	NNP
10_1101-2021_01_08_425885	92	12	ij	ij	NNP
10_1101-2021_01_08_425885	92	13	,	,	,
10_1101-2021_01_08_425885	92	14	gives	give	VBZ
10_1101-2021_01_08_425885	92	15	the	the	DT
10_1101-2021_01_08_425885	92	16	second	second	JJ
10_1101-2021_01_08_425885	92	17	-	-	HYPH
10_1101-2021_01_08_425885	92	18	order	order	NN
10_1101-2021_01_08_425885	92	19	coefficient	coefficient	NN
10_1101-2021_01_08_425885	92	20	relating	relate	VBG
10_1101-2021_01_08_425885	92	21	each	each	DT
10_1101-2021_01_08_425885	92	22	fk	fk	UH
10_1101-2021_01_08_425885	92	23	to	to	IN
10_1101-2021_01_08_425885	92	24	the	the	DT
10_1101-2021_01_08_425885	92	25	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	92	26	term	term	NN
10_1101-2021_01_08_425885	92	27	titj	titj	NN
10_1101-2021_01_08_425885	92	28	[	[	-LRB-
10_1101-2021_01_08_425885	92	29	32	32	CD
10_1101-2021_01_08_425885	92	30	]	]	-RRB-
10_1101-2021_01_08_425885	92	31	:	:	:
10_1101-2021_01_08_425885	92	32	hkij(p	hkij(p	ADD
10_1101-2021_01_08_425885	92	33	)	)	-RRB-
10_1101-2021_01_08_425885	92	34	=	=	NFP
10_1101-2021_01_08_425885	92	35	∂2fk	∂2fk	.
10_1101-2021_01_08_425885	92	36	∂ti∂tj	∂ti∂tj	NFP
10_1101-2021_01_08_425885	92	37	∣∣∣∣	∣∣∣∣	NNP
10_1101-2021_01_08_425885	92	38	p	p	NN
10_1101-2021_01_08_425885	92	39	(	(	-LRB-
10_1101-2021_01_08_425885	92	40	5	5	CD
10_1101-2021_01_08_425885	92	41	)	)	-RRB-
10_1101-2021_01_08_425885	92	42	The	the	DT
10_1101-2021_01_08_425885	92	43	Riemannian	riemannian	JJ
10_1101-2021_01_08_425885	92	44	curvature	curvature	NN
10_1101-2021_01_08_425885	92	45	tensor	tensor	NN
10_1101-2021_01_08_425885	92	46	is	be	VBZ
10_1101-2021_01_08_425885	92	47	related	relate	VBN
10_1101-2021_01_08_425885	92	48	to	to	IN
10_1101-2021_01_08_425885	92	49	the	the	DT
10_1101-2021_01_08_425885	92	50	Second	Second	NNP
10_1101-2021_01_08_425885	92	51	Fundamental	Fundamental	NNP
10_1101-2021_01_08_425885	92	52	Form	Form	NNP
10_1101-2021_01_08_425885	92	53	according	accord	VBG
10_1101-2021_01_08_425885	92	54	to	to	IN
10_1101-2021_01_08_425885	92	55	the	the	DT
10_1101-2021_01_08_425885	92	56	Gauss	Gauss	NNP
10_1101-2021_01_08_425885	92	57	-	-	HYPH
10_1101-2021_01_08_425885	92	58	Codazzi	Codazzi	NNP
10_1101-2021_01_08_425885	92	59	equation	equation	NN
10_1101-2021_01_08_425885	92	60	[	[	-LRB-
10_1101-2021_01_08_425885	92	61	15	15	CD
10_1101-2021_01_08_425885	92	62	]	]	-RRB-
10_1101-2021_01_08_425885	92	63	:	:	:
10_1101-2021_01_08_425885	92	64	Rijkl	Rijkl	NNP
10_1101-2021_01_08_425885	92	65	=	=	NFP
10_1101-2021_01_08_425885	92	66	(	(	-LRB-
10_1101-2021_01_08_425885	92	67	h	h	NNP
10_1101-2021_01_08_425885	92	68	α	α	IN
10_1101-2021_01_08_425885	92	69	jkh	jkh	NNP
10_1101-2021_01_08_425885	92	70	β	β	NNP
10_1101-2021_01_08_425885	92	71	il	il	NNP
10_1101-2021_01_08_425885	92	72	−h	−h	NNP
10_1101-2021_01_08_425885	92	73	β	β	NNP
10_1101-2021_01_08_425885	92	74	jih	jih	NNP
10_1101-2021_01_08_425885	92	75	α	α	NNP
10_1101-2021_01_08_425885	92	76	kl)gαβ	kl)gαβ	NNP
10_1101-2021_01_08_425885	92	77	(	(	-LRB-
10_1101-2021_01_08_425885	92	78	6	6	CD
10_1101-2021_01_08_425885	92	79	)	)	-RRB-
10_1101-2021_01_08_425885	92	80	where	where	WRB
10_1101-2021_01_08_425885	92	81	gαβ	gαβ	NNP
10_1101-2021_01_08_425885	92	82	is	be	VBZ
10_1101-2021_01_08_425885	92	83	the	the	DT
10_1101-2021_01_08_425885	92	84	metric	metric	NN
10_1101-2021_01_08_425885	92	85	of	of	IN
10_1101-2021_01_08_425885	92	86	the	the	DT
10_1101-2021_01_08_425885	92	87	ambient	ambient	JJ
10_1101-2021_01_08_425885	92	88	space	space	NN
10_1101-2021_01_08_425885	92	89	,	,	,
10_1101-2021_01_08_425885	92	90	which	which	WDT
10_1101-2021_01_08_425885	92	91	we	-PRON-	PRP
10_1101-2021_01_08_425885	92	92	take	take	VBP
10_1101-2021_01_08_425885	92	93	to	to	TO
10_1101-2021_01_08_425885	92	94	be	be	VB
10_1101-2021_01_08_425885	92	95	the	the	DT
10_1101-2021_01_08_425885	92	96	usual	usual	JJ
10_1101-2021_01_08_425885	92	97	Euclidean	Euclidean	NNP
10_1101-2021_01_08_425885	92	98	metric	metric	NN
10_1101-2021_01_08_425885	92	99	δα	δα	XX
10_1101-2021_01_08_425885	92	100	,	,	,
10_1101-2021_01_08_425885	92	101	β	β	NNP
10_1101-2021_01_08_425885	92	102	going	go	VBG
10_1101-2021_01_08_425885	92	103	forward	forward	RB
10_1101-2021_01_08_425885	92	104	.	.	.
10_1101-2021_01_08_425885	93	1	The	the	DT
10_1101-2021_01_08_425885	93	2	scalar	scalar	JJ
10_1101-2021_01_08_425885	93	3	curvature	curvature	NN
10_1101-2021_01_08_425885	93	4	can	can	MD
10_1101-2021_01_08_425885	93	5	be	be	VB
10_1101-2021_01_08_425885	93	6	obtained	obtain	VBN
10_1101-2021_01_08_425885	93	7	by	by	IN
10_1101-2021_01_08_425885	93	8	contracting	contract	VBG
10_1101-2021_01_08_425885	93	9	the	the	DT
10_1101-2021_01_08_425885	93	10	Riemannian	riemannian	JJ
10_1101-2021_01_08_425885	93	11	curvature	curvature	NN
10_1101-2021_01_08_425885	93	12	tensor	tensor	NN
10_1101-2021_01_08_425885	93	13	:	:	:
10_1101-2021_01_08_425885	93	14	S	S	NNP
10_1101-2021_01_08_425885	93	15	=	=	NFP
10_1101-2021_01_08_425885	93	16	∑	∑	.
10_1101-2021_01_08_425885	93	17	i	i	PRP
10_1101-2021_01_08_425885	93	18	,	,	,
10_1101-2021_01_08_425885	93	19	j	j	NNP
10_1101-2021_01_08_425885	93	20	Rijij	Rijij	NNP
10_1101-2021_01_08_425885	93	21	(	(	-LRB-
10_1101-2021_01_08_425885	93	22	7	7	LS
10_1101-2021_01_08_425885	93	23	)	)	-RRB-
10_1101-2021_01_08_425885	93	24	This	this	DT
10_1101-2021_01_08_425885	93	25	suggests	suggest	VBZ
10_1101-2021_01_08_425885	93	26	a	a	DT
10_1101-2021_01_08_425885	93	27	conceptually	conceptually	RB
10_1101-2021_01_08_425885	93	28	simple	simple	JJ
10_1101-2021_01_08_425885	93	29	procedure	procedure	NN
10_1101-2021_01_08_425885	93	30	to	to	TO
10_1101-2021_01_08_425885	93	31	estimate	estimate	VB
10_1101-2021_01_08_425885	93	32	the	the	DT
10_1101-2021_01_08_425885	93	33	scalar	scalar	JJ
10_1101-2021_01_08_425885	93	34	curvature	curvature	NN
10_1101-2021_01_08_425885	93	35	of	of	IN
10_1101-2021_01_08_425885	93	36	a	a	DT
10_1101-2021_01_08_425885	93	37	data	data	NN
10_1101-2021_01_08_425885	93	38	manifold	manifold	NN
10_1101-2021_01_08_425885	93	39	at	at	IN
10_1101-2021_01_08_425885	93	40	each	each	DT
10_1101-2021_01_08_425885	93	41	point	point	NN
10_1101-2021_01_08_425885	93	42	p	p	NN
10_1101-2021_01_08_425885	93	43	:	:	:
10_1101-2021_01_08_425885	93	44	(	(	-LRB-
10_1101-2021_01_08_425885	93	45	i	i	NN
10_1101-2021_01_08_425885	93	46	)	)	-RRB-
10_1101-2021_01_08_425885	93	47	estimate	estimate	VBP
10_1101-2021_01_08_425885	93	48	TM	TM	NNP
10_1101-2021_01_08_425885	93	49	(	(	-LRB-
10_1101-2021_01_08_425885	93	50	p	p	NNP
10_1101-2021_01_08_425885	93	51	)	)	-RRB-
10_1101-2021_01_08_425885	93	52	and	and	CC
10_1101-2021_01_08_425885	93	53	NM	NM	NNP
10_1101-2021_01_08_425885	93	54	(	(	-LRB-
10_1101-2021_01_08_425885	93	55	p	p	NNP
10_1101-2021_01_08_425885	93	56	)	)	-RRB-
10_1101-2021_01_08_425885	93	57	,	,	,
10_1101-2021_01_08_425885	93	58	(	(	-LRB-
10_1101-2021_01_08_425885	93	59	ii	ii	NNP
10_1101-2021_01_08_425885	93	60	)	)	-RRB-
10_1101-2021_01_08_425885	93	61	determine	determine	VB
10_1101-2021_01_08_425885	93	62	h	h	NNP
10_1101-2021_01_08_425885	93	63	k	k	NNP
10_1101-2021_01_08_425885	93	64	ij(p	ij(p	NNP
10_1101-2021_01_08_425885	93	65	)	)	-RRB-
10_1101-2021_01_08_425885	93	66	in	in	IN
10_1101-2021_01_08_425885	93	67	local	local	JJ
10_1101-2021_01_08_425885	93	68	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	93	69	,	,	,
10_1101-2021_01_08_425885	93	70	(	(	-LRB-
10_1101-2021_01_08_425885	93	71	iii	iii	NN
10_1101-2021_01_08_425885	93	72	)	)	-RRB-
10_1101-2021_01_08_425885	93	73	compute	compute	NN
10_1101-2021_01_08_425885	93	74	S	S	NNP
10_1101-2021_01_08_425885	93	75	using	use	VBG
10_1101-2021_01_08_425885	93	76	Equations	Equations	NNP
10_1101-2021_01_08_425885	93	77	6	6	CD
10_1101-2021_01_08_425885	93	78	and	and	CC
10_1101-2021_01_08_425885	93	79	7	7	CD
10_1101-2021_01_08_425885	93	80	.	.	.
10_1101-2021_01_08_425885	94	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	94	2	developed	develop	VBD
10_1101-2021_01_08_425885	94	3	a	a	DT
10_1101-2021_01_08_425885	94	4	computational	computational	JJ
10_1101-2021_01_08_425885	94	5	tool	tool	NN
10_1101-2021_01_08_425885	94	6	that	that	WDT
10_1101-2021_01_08_425885	94	7	provides	provide	VBZ
10_1101-2021_01_08_425885	94	8	an	an	DT
10_1101-2021_01_08_425885	94	9	implementation	implementation	NN
10_1101-2021_01_08_425885	94	10	of	of	IN
10_1101-2021_01_08_425885	94	11	this	this	DT
10_1101-2021_01_08_425885	94	12	procedure	procedure	NN
10_1101-2021_01_08_425885	94	13	.	.	.
10_1101-2021_01_08_425885	95	1	Briefly	briefly	RB
10_1101-2021_01_08_425885	95	2	,	,	,
10_1101-2021_01_08_425885	95	3	given	give	VBN
10_1101-2021_01_08_425885	95	4	a	a	DT
10_1101-2021_01_08_425885	95	5	set	set	NN
10_1101-2021_01_08_425885	95	6	of	of	IN
10_1101-2021_01_08_425885	95	7	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	95	8	{	{	-LRB-
10_1101-2021_01_08_425885	95	9	X	x	NN
10_1101-2021_01_08_425885	95	10	}	}	-RRB-
10_1101-2021_01_08_425885	95	11	∈	∈	JJ
10_1101-2021_01_08_425885	95	12	Rn	Rn	NNS
10_1101-2021_01_08_425885	95	13	and	and	CC
10_1101-2021_01_08_425885	95	14	manifold	manifold	JJ
10_1101-2021_01_08_425885	95	15	dimension	dimension	NN
10_1101-2021_01_08_425885	95	16	d	d	NNP
10_1101-2021_01_08_425885	95	17	,	,	,
10_1101-2021_01_08_425885	95	18	a	a	DT
10_1101-2021_01_08_425885	95	19	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	95	20	around	around	IN
10_1101-2021_01_08_425885	95	21	each	each	DT
10_1101-2021_01_08_425885	95	22	point	point	NN
10_1101-2021_01_08_425885	95	23	p	p	NN
10_1101-2021_01_08_425885	95	24	is	be	VBZ
10_1101-2021_01_08_425885	95	25	selected	select	VBN
10_1101-2021_01_08_425885	95	26	to	to	TO
10_1101-2021_01_08_425885	95	27	be	be	VB
10_1101-2021_01_08_425885	95	28	the	the	DT
10_1101-2021_01_08_425885	95	29	n	n	JJ
10_1101-2021_01_08_425885	95	30	-	-	HYPH
10_1101-2021_01_08_425885	95	31	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	95	32	ball	ball	NN
10_1101-2021_01_08_425885	95	33	centred	centre	VBN
10_1101-2021_01_08_425885	95	34	on	on	IN
10_1101-2021_01_08_425885	95	35	p	p	NN
10_1101-2021_01_08_425885	95	36	of	of	IN
10_1101-2021_01_08_425885	95	37	radius	radius	NN
10_1101-2021_01_08_425885	95	38	r	r	NN
10_1101-2021_01_08_425885	95	39	encompassing	encompass	VBG
10_1101-2021_01_08_425885	95	40	Np(r	Np(r	NNP
10_1101-2021_01_08_425885	95	41	)	)	-RRB-
10_1101-2021_01_08_425885	95	42	points	point	NNS
10_1101-2021_01_08_425885	95	43	(	(	-LRB-
10_1101-2021_01_08_425885	95	44	see	see	VB
10_1101-2021_01_08_425885	95	45	Methods	Methods	NNP
10_1101-2021_01_08_425885	95	46	Section	Section	NNP
10_1101-2021_01_08_425885	95	47	4.3.2	4.3.2	CD
10_1101-2021_01_08_425885	95	48	)	)	-RRB-
10_1101-2021_01_08_425885	95	49	.	.	.
10_1101-2021_01_08_425885	96	1	For	for	IN
10_1101-2021_01_08_425885	96	2	each	each	DT
10_1101-2021_01_08_425885	96	3	point	point	NN
10_1101-2021_01_08_425885	96	4	p	p	NN
10_1101-2021_01_08_425885	96	5	,	,	,
10_1101-2021_01_08_425885	96	6	Principal	Principal	NNP
10_1101-2021_01_08_425885	96	7	Component	Component	NNP
10_1101-2021_01_08_425885	96	8	Analysis	Analysis	NNP
10_1101-2021_01_08_425885	96	9	(	(	-LRB-
10_1101-2021_01_08_425885	96	10	PCA	PCA	NNP
10_1101-2021_01_08_425885	96	11	)	)	-RRB-
10_1101-2021_01_08_425885	96	12	[	[	-LRB-
10_1101-2021_01_08_425885	96	13	33	33	CD
10_1101-2021_01_08_425885	96	14	]	]	-RRB-
10_1101-2021_01_08_425885	96	15	is	be	VBZ
10_1101-2021_01_08_425885	96	16	performed	perform	VBN
10_1101-2021_01_08_425885	96	17	on	on	IN
10_1101-2021_01_08_425885	96	18	the	the	DT
10_1101-2021_01_08_425885	96	19	Np(r	Np(r	NNP
10_1101-2021_01_08_425885	96	20	)	)	-RRB-
10_1101-2021_01_08_425885	96	21	points	point	VBZ
10_1101-2021_01_08_425885	96	22	in	in	IN
10_1101-2021_01_08_425885	96	23	its	-PRON-	PRP$
10_1101-2021_01_08_425885	96	24	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	96	25	,	,	,
10_1101-2021_01_08_425885	96	26	and	and	CC
10_1101-2021_01_08_425885	96	27	the	the	DT
10_1101-2021_01_08_425885	96	28	first	first	JJ
10_1101-2021_01_08_425885	96	29	d	d	NN
10_1101-2021_01_08_425885	96	30	(	(	-LRB-
10_1101-2021_01_08_425885	96	31	last	last	JJ
10_1101-2021_01_08_425885	96	32	n−d	n−d	NNP
10_1101-2021_01_08_425885	96	33	)	)	-RRB-
10_1101-2021_01_08_425885	96	34	Principal	Principal	NNP
10_1101-2021_01_08_425885	96	35	Components	component	NNS
10_1101-2021_01_08_425885	96	36	(	(	-LRB-
10_1101-2021_01_08_425885	96	37	PCs	pc	NNS
10_1101-2021_01_08_425885	96	38	)	)	-RRB-
10_1101-2021_01_08_425885	96	39	accounting	account	VBG
10_1101-2021_01_08_425885	96	40	for	for	IN
10_1101-2021_01_08_425885	96	41	the	the	DT
10_1101-2021_01_08_425885	96	42	most	most	JJS
10_1101-2021_01_08_425885	96	43	(	(	-LRB-
10_1101-2021_01_08_425885	96	44	least	least	JJS
10_1101-2021_01_08_425885	96	45	)	)	-RRB-
10_1101-2021_01_08_425885	96	46	variance	variance	NN
10_1101-2021_01_08_425885	96	47	are	be	VBP
10_1101-2021_01_08_425885	96	48	taken	take	VBN
10_1101-2021_01_08_425885	96	49	as	as	IN
10_1101-2021_01_08_425885	96	50	an	an	DT
10_1101-2021_01_08_425885	96	51	orthonormal	orthonormal	JJ
10_1101-2021_01_08_425885	96	52	basis	basis	NN
10_1101-2021_01_08_425885	96	53	for	for	IN
10_1101-2021_01_08_425885	96	54	TM	TM	NNP
10_1101-2021_01_08_425885	96	55	(	(	-LRB-
10_1101-2021_01_08_425885	96	56	p	p	NNP
10_1101-2021_01_08_425885	96	57	)	)	-RRB-
10_1101-2021_01_08_425885	96	58	(	(	-LRB-
10_1101-2021_01_08_425885	96	59	NM	NM	NNP
10_1101-2021_01_08_425885	96	60	(	(	-LRB-
10_1101-2021_01_08_425885	96	61	p	p	NNP
10_1101-2021_01_08_425885	96	62	)	)	-RRB-
10_1101-2021_01_08_425885	96	63	)	)	-RRB-
10_1101-2021_01_08_425885	96	64	.	.	.
10_1101-2021_01_08_425885	97	1	The	the	DT
10_1101-2021_01_08_425885	97	2	normal	normal	JJ
10_1101-2021_01_08_425885	97	3	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	97	4	,	,	,
10_1101-2021_01_08_425885	97	5	nk	nk	NNP
10_1101-2021_01_08_425885	97	6	,	,	,
10_1101-2021_01_08_425885	97	7	of	of	IN
10_1101-2021_01_08_425885	97	8	the	the	DT
10_1101-2021_01_08_425885	97	9	Np(r	Np(r	NNP
10_1101-2021_01_08_425885	97	10	)	)	-RRB-
10_1101-2021_01_08_425885	97	11	points	point	VBZ
10_1101-2021_01_08_425885	97	12	in	in	IN
10_1101-2021_01_08_425885	97	13	each	each	DT
10_1101-2021_01_08_425885	97	14	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	97	15	are	be	VBP
10_1101-2021_01_08_425885	97	16	fit	fit	JJ
10_1101-2021_01_08_425885	97	17	by	by	IN
10_1101-2021_01_08_425885	97	18	regression	regression	NN
10_1101-2021_01_08_425885	97	19	to	to	IN
10_1101-2021_01_08_425885	97	20	a	a	DT
10_1101-2021_01_08_425885	97	21	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	97	22	model	model	NN
10_1101-2021_01_08_425885	97	23	in	in	IN
10_1101-2021_01_08_425885	97	24	terms	term	NNS
10_1101-2021_01_08_425885	97	25	of	of	IN
10_1101-2021_01_08_425885	97	26	the	the	DT
10_1101-2021_01_08_425885	97	27	tangent	tangent	NN
10_1101-2021_01_08_425885	97	28	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	97	29	,	,	,
10_1101-2021_01_08_425885	97	30	ti	ti	NN
10_1101-2021_01_08_425885	97	31	,	,	,
10_1101-2021_01_08_425885	97	32	to	to	TO
10_1101-2021_01_08_425885	97	33	obtain	obtain	VB
10_1101-2021_01_08_425885	97	34	h	h	NN
10_1101-2021_01_08_425885	97	35	k	k	NNP
10_1101-2021_01_08_425885	97	36	ij(p	ij(p	NNP
10_1101-2021_01_08_425885	97	37	)	)	-RRB-
10_1101-2021_01_08_425885	97	38	with	with	IN
10_1101-2021_01_08_425885	97	39	associated	associated	JJ
10_1101-2021_01_08_425885	97	40	uncertainties	uncertainty	NNS
10_1101-2021_01_08_425885	97	41	(	(	-LRB-
10_1101-2021_01_08_425885	97	42	see	see	VB
10_1101-2021_01_08_425885	97	43	Figure	figure	NN
10_1101-2021_01_08_425885	97	44	2B	2B	NNS
10_1101-2021_01_08_425885	97	45	;	;	:
10_1101-2021_01_08_425885	97	46	Methods	Methods	NNP
10_1101-2021_01_08_425885	97	47	Section	Section	NNP
10_1101-2021_01_08_425885	97	48	4.3.1	4.3.1	CD
10_1101-2021_01_08_425885	97	49	)	)	-RRB-
10_1101-2021_01_08_425885	97	50	.	.	.
10_1101-2021_01_08_425885	98	1	7	7	LS
10_1101-2021_01_08_425885	98	2	.CC	.CC	:
10_1101-2021_01_08_425885	98	3	-	-	HYPH
10_1101-2021_01_08_425885	98	4	BY	by	IN
10_1101-2021_01_08_425885	98	5	-	-	HYPH
10_1101-2021_01_08_425885	98	6	NC	NC	NNP
10_1101-2021_01_08_425885	98	7	-	-	HYPH
10_1101-2021_01_08_425885	98	8	ND	ND	NNP
10_1101-2021_01_08_425885	98	9	4.0	4.0	CD
10_1101-2021_01_08_425885	98	10	International	International	NNP
10_1101-2021_01_08_425885	98	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	98	12	under	under	IN
10_1101-2021_01_08_425885	98	13	a	a	DT
10_1101-2021_01_08_425885	98	14	(	(	-LRB-
10_1101-2021_01_08_425885	98	15	which	which	WDT
10_1101-2021_01_08_425885	98	16	was	be	VBD
10_1101-2021_01_08_425885	98	17	not	not	RB
10_1101-2021_01_08_425885	98	18	certified	certify	VBN
10_1101-2021_01_08_425885	98	19	by	by	IN
10_1101-2021_01_08_425885	98	20	peer	peer	NN
10_1101-2021_01_08_425885	98	21	review	review	NN
10_1101-2021_01_08_425885	98	22	)	)	-RRB-
10_1101-2021_01_08_425885	98	23	is	be	VBZ
10_1101-2021_01_08_425885	98	24	the	the	DT
10_1101-2021_01_08_425885	98	25	author	author	NN
10_1101-2021_01_08_425885	98	26	/	/	SYM
10_1101-2021_01_08_425885	98	27	funder	funder	NN
10_1101-2021_01_08_425885	98	28	,	,	,
10_1101-2021_01_08_425885	98	29	who	who	WP
10_1101-2021_01_08_425885	98	30	has	have	VBZ
10_1101-2021_01_08_425885	98	31	granted	grant	VBN
10_1101-2021_01_08_425885	98	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	98	33	a	a	DT
10_1101-2021_01_08_425885	98	34	license	license	NN
10_1101-2021_01_08_425885	98	35	to	to	TO
10_1101-2021_01_08_425885	98	36	display	display	VB
10_1101-2021_01_08_425885	98	37	the	the	DT
10_1101-2021_01_08_425885	98	38	preprint	preprint	NN
10_1101-2021_01_08_425885	98	39	in	in	IN
10_1101-2021_01_08_425885	98	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	98	41	.	.	.
10_1101-2021_01_08_425885	99	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	99	2	is	be	VBZ
10_1101-2021_01_08_425885	99	3	made	make	VBN
10_1101-2021_01_08_425885	99	4	The	the	DT
10_1101-2021_01_08_425885	99	5	copyright	copyright	NN
10_1101-2021_01_08_425885	99	6	holder	holder	NN
10_1101-2021_01_08_425885	99	7	for	for	IN
10_1101-2021_01_08_425885	99	8	this	this	DT
10_1101-2021_01_08_425885	99	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	99	10	version	version	NN
10_1101-2021_01_08_425885	99	11	posted	post	VBD
10_1101-2021_01_08_425885	99	12	January	January	NNP
10_1101-2021_01_08_425885	99	13	8	8	CD
10_1101-2021_01_08_425885	99	14	,	,	,
10_1101-2021_01_08_425885	99	15	2021	2021	CD
10_1101-2021_01_08_425885	99	16	.	.	.
10_1101-2021_01_08_425885	99	17	;	;	:
10_1101-2021_01_08_425885	99	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	99	19	:	:	:
10_1101-2021_01_08_425885	99	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	99	21	preprint	preprint	NN
10_1101-2021_01_08_425885	99	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	99	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NN
10_1101-2021_01_08_425885	99	24	The	the	DT
10_1101-2021_01_08_425885	99	25	choice	choice	NN
10_1101-2021_01_08_425885	99	26	of	of	IN
10_1101-2021_01_08_425885	99	27	r(p	r(p	NNP
10_1101-2021_01_08_425885	99	28	)	)	-RRB-
10_1101-2021_01_08_425885	99	29	is	be	VBZ
10_1101-2021_01_08_425885	99	30	an	an	DT
10_1101-2021_01_08_425885	99	31	important	important	JJ
10_1101-2021_01_08_425885	99	32	one	one	NN
10_1101-2021_01_08_425885	99	33	since	since	IN
10_1101-2021_01_08_425885	99	34	it	-PRON-	PRP
10_1101-2021_01_08_425885	99	35	sets	set	VBZ
10_1101-2021_01_08_425885	99	36	the	the	DT
10_1101-2021_01_08_425885	99	37	length	length	NN
10_1101-2021_01_08_425885	99	38	scale	scale	NN
10_1101-2021_01_08_425885	99	39	at	at	IN
10_1101-2021_01_08_425885	99	40	which	which	WDT
10_1101-2021_01_08_425885	99	41	curvature	curvature	NN
10_1101-2021_01_08_425885	99	42	is	be	VBZ
10_1101-2021_01_08_425885	99	43	computed	compute	VBN
10_1101-2021_01_08_425885	99	44	for	for	IN
10_1101-2021_01_08_425885	99	45	point	point	NN
10_1101-2021_01_08_425885	99	46	p	p	NN
10_1101-2021_01_08_425885	99	47	(	(	-LRB-
10_1101-2021_01_08_425885	99	48	see	see	VB
10_1101-2021_01_08_425885	99	49	Methods	Methods	NNP
10_1101-2021_01_08_425885	99	50	Section	Section	NNP
10_1101-2021_01_08_425885	99	51	4.3.5	4.3.5	CD
10_1101-2021_01_08_425885	99	52	)	)	-RRB-
10_1101-2021_01_08_425885	99	53	.	.	.
10_1101-2021_01_08_425885	100	1	Our	-PRON-	PRP$
10_1101-2021_01_08_425885	100	2	tool	tool	NN
10_1101-2021_01_08_425885	100	3	allows	allow	VBZ
10_1101-2021_01_08_425885	100	4	interrogation	interrogation	NN
10_1101-2021_01_08_425885	100	5	of	of	IN
10_1101-2021_01_08_425885	100	6	curvature	curvature	NN
10_1101-2021_01_08_425885	100	7	at	at	IN
10_1101-2021_01_08_425885	100	8	any	any	DT
10_1101-2021_01_08_425885	100	9	length	length	NN
10_1101-2021_01_08_425885	100	10	scale	scale	NN
10_1101-2021_01_08_425885	100	11	of	of	IN
10_1101-2021_01_08_425885	100	12	interest	interest	NN
10_1101-2021_01_08_425885	100	13	by	by	IN
10_1101-2021_01_08_425885	100	14	allowing	allow	VBG
10_1101-2021_01_08_425885	100	15	the	the	DT
10_1101-2021_01_08_425885	100	16	user	user	NN
10_1101-2021_01_08_425885	100	17	to	to	TO
10_1101-2021_01_08_425885	100	18	manually	manually	RB
10_1101-2021_01_08_425885	100	19	set	set	VB
10_1101-2021_01_08_425885	100	20	r(p	r(p	NNP
10_1101-2021_01_08_425885	100	21	)	)	-RRB-
10_1101-2021_01_08_425885	100	22	,	,	,
10_1101-2021_01_08_425885	100	23	a	a	DT
10_1101-2021_01_08_425885	100	24	feature	feature	NN
10_1101-2021_01_08_425885	100	25	we	-PRON-	PRP
10_1101-2021_01_08_425885	100	26	use	use	VBP
10_1101-2021_01_08_425885	100	27	to	to	TO
10_1101-2021_01_08_425885	100	28	inspect	inspect	VB
10_1101-2021_01_08_425885	100	29	real	real	JJ
10_1101-2021_01_08_425885	100	30	-	-	HYPH
10_1101-2021_01_08_425885	100	31	world	world	NN
10_1101-2021_01_08_425885	100	32	datasets	dataset	NNS
10_1101-2021_01_08_425885	100	33	later	later	RB
10_1101-2021_01_08_425885	100	34	in	in	IN
10_1101-2021_01_08_425885	100	35	the	the	DT
10_1101-2021_01_08_425885	100	36	paper	paper	NN
10_1101-2021_01_08_425885	100	37	.	.	.
10_1101-2021_01_08_425885	101	1	However	however	RB
10_1101-2021_01_08_425885	101	2	,	,	,
10_1101-2021_01_08_425885	101	3	since	since	IN
10_1101-2021_01_08_425885	101	4	the	the	DT
10_1101-2021_01_08_425885	101	5	local	local	JJ
10_1101-2021_01_08_425885	101	6	geometry	geometry	NN
10_1101-2021_01_08_425885	101	7	of	of	IN
10_1101-2021_01_08_425885	101	8	the	the	DT
10_1101-2021_01_08_425885	101	9	manifold	manifold	NN
10_1101-2021_01_08_425885	101	10	may	may	MD
10_1101-2021_01_08_425885	101	11	be	be	VB
10_1101-2021_01_08_425885	101	12	non	non	JJ
10_1101-2021_01_08_425885	101	13	-	-	JJ
10_1101-2021_01_08_425885	101	14	trivial	trivial	JJ
10_1101-2021_01_08_425885	101	15	and	and	CC
10_1101-2021_01_08_425885	101	16	unknown	unknown	JJ
10_1101-2021_01_08_425885	101	17	a	a	DT
10_1101-2021_01_08_425885	101	18	priori	priori	FW
10_1101-2021_01_08_425885	101	19	,	,	,
10_1101-2021_01_08_425885	101	20	we	-PRON-	PRP
10_1101-2021_01_08_425885	101	21	also	also	RB
10_1101-2021_01_08_425885	101	22	provide	provide	VBP
10_1101-2021_01_08_425885	101	23	the	the	DT
10_1101-2021_01_08_425885	101	24	ability	ability	NN
10_1101-2021_01_08_425885	101	25	to	to	TO
10_1101-2021_01_08_425885	101	26	set	set	VB
10_1101-2021_01_08_425885	101	27	r(p	r(p	NNP
10_1101-2021_01_08_425885	101	28	)	)	-RRB-
10_1101-2021_01_08_425885	101	29	according	accord	VBG
10_1101-2021_01_08_425885	101	30	to	to	IN
10_1101-2021_01_08_425885	101	31	statistical	statistical	JJ
10_1101-2021_01_08_425885	101	32	rather	rather	RB
10_1101-2021_01_08_425885	101	33	than	than	IN
10_1101-2021_01_08_425885	101	34	geometric	geometric	JJ
10_1101-2021_01_08_425885	101	35	principles	principle	NNS
10_1101-2021_01_08_425885	101	36	.	.	.
10_1101-2021_01_08_425885	102	1	Specifically	specifically	RB
10_1101-2021_01_08_425885	102	2	,	,	,
10_1101-2021_01_08_425885	102	3	our	-PRON-	PRP$
10_1101-2021_01_08_425885	102	4	tool	tool	NN
10_1101-2021_01_08_425885	102	5	algorithmically	algorithmically	RB
10_1101-2021_01_08_425885	102	6	chooses	choose	VBZ
10_1101-2021_01_08_425885	102	7	r	r	NN
10_1101-2021_01_08_425885	102	8	at	at	IN
10_1101-2021_01_08_425885	102	9	each	each	DT
10_1101-2021_01_08_425885	102	10	p	p	NN
10_1101-2021_01_08_425885	102	11	so	so	IN
10_1101-2021_01_08_425885	102	12	that	that	IN
10_1101-2021_01_08_425885	102	13	the	the	DT
10_1101-2021_01_08_425885	102	14	uncertainty	uncertainty	NN
10_1101-2021_01_08_425885	102	15	in	in	IN
10_1101-2021_01_08_425885	102	16	hkij(p	hkij(p	NNP
10_1101-2021_01_08_425885	102	17	)	)	-RRB-
10_1101-2021_01_08_425885	102	18	from	from	IN
10_1101-2021_01_08_425885	102	19	regression	regression	NN
10_1101-2021_01_08_425885	102	20	is	be	VBZ
10_1101-2021_01_08_425885	102	21	less	less	JJR
10_1101-2021_01_08_425885	102	22	than	than	IN
10_1101-2021_01_08_425885	102	23	a	a	DT
10_1101-2021_01_08_425885	102	24	user	user	NN
10_1101-2021_01_08_425885	102	25	-	-	HYPH
10_1101-2021_01_08_425885	102	26	specified	specify	VBN
10_1101-2021_01_08_425885	102	27	global	global	JJ
10_1101-2021_01_08_425885	102	28	parameter	parameter	NN
10_1101-2021_01_08_425885	102	29	,	,	,
10_1101-2021_01_08_425885	102	30	σh	σh	NNP
10_1101-2021_01_08_425885	102	31	(	(	-LRB-
10_1101-2021_01_08_425885	102	32	see	see	VB
10_1101-2021_01_08_425885	102	33	Methods	Methods	NNP
10_1101-2021_01_08_425885	102	34	Section	Section	NNP
10_1101-2021_01_08_425885	102	35	4.3.2	4.3.2	CD
10_1101-2021_01_08_425885	102	36	)	)	-RRB-
10_1101-2021_01_08_425885	102	37	.	.	.
10_1101-2021_01_08_425885	103	1	Since	since	IN
10_1101-2021_01_08_425885	103	2	a	a	DT
10_1101-2021_01_08_425885	103	3	larger	large	JJR
10_1101-2021_01_08_425885	103	4	number	number	NN
10_1101-2021_01_08_425885	103	5	of	of	IN
10_1101-2021_01_08_425885	103	6	points	point	NNS
10_1101-2021_01_08_425885	103	7	reduces	reduce	VBZ
10_1101-2021_01_08_425885	103	8	the	the	DT
10_1101-2021_01_08_425885	103	9	uncertainty	uncertainty	NN
10_1101-2021_01_08_425885	103	10	in	in	IN
10_1101-2021_01_08_425885	103	11	regression	regression	NN
10_1101-2021_01_08_425885	103	12	,	,	,
10_1101-2021_01_08_425885	103	13	a	a	DT
10_1101-2021_01_08_425885	103	14	smaller	small	JJR
10_1101-2021_01_08_425885	103	15	σh	σh	NNP
10_1101-2021_01_08_425885	103	16	requires	require	VBZ
10_1101-2021_01_08_425885	103	17	a	a	DT
10_1101-2021_01_08_425885	103	18	larger	large	JJR
10_1101-2021_01_08_425885	103	19	r(p	r(p	NN
10_1101-2021_01_08_425885	103	20	)	)	-RRB-
10_1101-2021_01_08_425885	103	21	∀p	∀p	.
10_1101-2021_01_08_425885	103	22	∈	∈	NNP
10_1101-2021_01_08_425885	103	23	M.	M.	NNP
10_1101-2021_01_08_425885	103	24	This	this	DT
10_1101-2021_01_08_425885	103	25	strategy	strategy	NN
10_1101-2021_01_08_425885	103	26	of	of	IN
10_1101-2021_01_08_425885	103	27	setting	set	VBG
10_1101-2021_01_08_425885	103	28	σh	σh	NNP
10_1101-2021_01_08_425885	103	29	therefore	therefore	RB
10_1101-2021_01_08_425885	103	30	allows	allow	VBZ
10_1101-2021_01_08_425885	103	31	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	103	32	sizes	size	NNS
10_1101-2021_01_08_425885	103	33	to	to	TO
10_1101-2021_01_08_425885	103	34	dynamically	dynamically	RB
10_1101-2021_01_08_425885	103	35	vary	vary	VB
10_1101-2021_01_08_425885	103	36	over	over	IN
10_1101-2021_01_08_425885	103	37	the	the	DT
10_1101-2021_01_08_425885	103	38	manifold	manifold	NN
10_1101-2021_01_08_425885	103	39	based	base	VBN
10_1101-2021_01_08_425885	103	40	on	on	IN
10_1101-2021_01_08_425885	103	41	the	the	DT
10_1101-2021_01_08_425885	103	42	local	local	JJ
10_1101-2021_01_08_425885	103	43	density	density	NN
10_1101-2021_01_08_425885	103	44	of	of	IN
10_1101-2021_01_08_425885	103	45	the	the	DT
10_1101-2021_01_08_425885	103	46	data	datum	NNS
10_1101-2021_01_08_425885	103	47	,	,	,
10_1101-2021_01_08_425885	103	48	which	which	WDT
10_1101-2021_01_08_425885	103	49	means	mean	VBZ
10_1101-2021_01_08_425885	103	50	the	the	DT
10_1101-2021_01_08_425885	103	51	algorithm	algorithm	NN
10_1101-2021_01_08_425885	103	52	can	can	MD
10_1101-2021_01_08_425885	103	53	gracefully	gracefully	RB
10_1101-2021_01_08_425885	103	54	handle	handle	VB
10_1101-2021_01_08_425885	103	55	non	non	JJ
10_1101-2021_01_08_425885	103	56	-	-	JJ
10_1101-2021_01_08_425885	103	57	uniform	uniform	JJ
10_1101-2021_01_08_425885	103	58	sampling	sampling	NN
10_1101-2021_01_08_425885	103	59	of	of	IN
10_1101-2021_01_08_425885	103	60	the	the	DT
10_1101-2021_01_08_425885	103	61	manifold	manifold	NN
10_1101-2021_01_08_425885	103	62	.	.	.
10_1101-2021_01_08_425885	104	1	The	the	DT
10_1101-2021_01_08_425885	104	2	choice	choice	NN
10_1101-2021_01_08_425885	104	3	of	of	IN
10_1101-2021_01_08_425885	104	4	σh	σh	NNP
10_1101-2021_01_08_425885	104	5	will	will	MD
10_1101-2021_01_08_425885	104	6	depend	depend	VB
10_1101-2021_01_08_425885	104	7	on	on	IN
10_1101-2021_01_08_425885	104	8	the	the	DT
10_1101-2021_01_08_425885	104	9	global	global	JJ
10_1101-2021_01_08_425885	104	10	length	length	NN
10_1101-2021_01_08_425885	104	11	scale	scale	NN
10_1101-2021_01_08_425885	104	12	,	,	,
10_1101-2021_01_08_425885	104	13	L	l	NN
10_1101-2021_01_08_425885	104	14	,	,	,
10_1101-2021_01_08_425885	104	15	of	of	IN
10_1101-2021_01_08_425885	104	16	the	the	DT
10_1101-2021_01_08_425885	104	17	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	104	18	(	(	-LRB-
10_1101-2021_01_08_425885	104	19	see	see	VB
10_1101-2021_01_08_425885	104	20	Methods	Methods	NNP
10_1101-2021_01_08_425885	104	21	Section	Section	NNP
10_1101-2021_01_08_425885	104	22	4.3.5	4.3.5	CD
10_1101-2021_01_08_425885	104	23	)	)	-RRB-
10_1101-2021_01_08_425885	104	24	,	,	,
10_1101-2021_01_08_425885	104	25	the	the	DT
10_1101-2021_01_08_425885	104	26	average	average	JJ
10_1101-2021_01_08_425885	104	27	density	density	NN
10_1101-2021_01_08_425885	104	28	of	of	IN
10_1101-2021_01_08_425885	104	29	sampled	sample	VBN
10_1101-2021_01_08_425885	104	30	points	point	NNS
10_1101-2021_01_08_425885	104	31	,	,	,
10_1101-2021_01_08_425885	104	32	and	and	CC
10_1101-2021_01_08_425885	104	33	of	of	IN
10_1101-2021_01_08_425885	104	34	course	course	NN
10_1101-2021_01_08_425885	104	35	,	,	,
10_1101-2021_01_08_425885	104	36	the	the	DT
10_1101-2021_01_08_425885	104	37	desired	desire	VBN
10_1101-2021_01_08_425885	104	38	uncertainty	uncertainty	NN
10_1101-2021_01_08_425885	104	39	in	in	IN
10_1101-2021_01_08_425885	104	40	the	the	DT
10_1101-2021_01_08_425885	104	41	estimates	estimate	NNS
10_1101-2021_01_08_425885	104	42	of	of	IN
10_1101-2021_01_08_425885	104	43	hkij	hkij	NNP
10_1101-2021_01_08_425885	104	44	.	.	.
10_1101-2021_01_08_425885	105	1	These	these	DT
10_1101-2021_01_08_425885	105	2	uncertainties	uncertainty	NNS
10_1101-2021_01_08_425885	105	3	are	be	VBP
10_1101-2021_01_08_425885	105	4	in	in	IN
10_1101-2021_01_08_425885	105	5	turn	turn	NN
10_1101-2021_01_08_425885	105	6	used	use	VBN
10_1101-2021_01_08_425885	105	7	to	to	TO
10_1101-2021_01_08_425885	105	8	compute	compute	VB
10_1101-2021_01_08_425885	105	9	a	a	DT
10_1101-2021_01_08_425885	105	10	standard	standard	JJ
10_1101-2021_01_08_425885	105	11	error	error	NN
10_1101-2021_01_08_425885	105	12	,	,	,
10_1101-2021_01_08_425885	105	13	σS	σS	NNP
10_1101-2021_01_08_425885	105	14	,	,	,
10_1101-2021_01_08_425885	105	15	accompanying	accompany	VBG
10_1101-2021_01_08_425885	105	16	the	the	DT
10_1101-2021_01_08_425885	105	17	scalar	scalar	JJ
10_1101-2021_01_08_425885	105	18	curvature	curvature	JJ
10_1101-2021_01_08_425885	105	19	estimate	estimate	NN
10_1101-2021_01_08_425885	105	20	at	at	IN
10_1101-2021_01_08_425885	105	21	each	each	DT
10_1101-2021_01_08_425885	105	22	point	point	NN
10_1101-2021_01_08_425885	105	23	,	,	,
10_1101-2021_01_08_425885	105	24	using	use	VBG
10_1101-2021_01_08_425885	105	25	standard	standard	JJ
10_1101-2021_01_08_425885	105	26	error	error	NN
10_1101-2021_01_08_425885	105	27	propagation	propagation	NN
10_1101-2021_01_08_425885	105	28	formulas	formula	NNS
10_1101-2021_01_08_425885	105	29	(	(	-LRB-
10_1101-2021_01_08_425885	105	30	see	see	VB
10_1101-2021_01_08_425885	105	31	Methods	Methods	NNP
10_1101-2021_01_08_425885	105	32	Section	Section	NNP
10_1101-2021_01_08_425885	105	33	4.3.4	4.3.4	CD
10_1101-2021_01_08_425885	105	34	)	)	-RRB-
10_1101-2021_01_08_425885	105	35	.	.	.
10_1101-2021_01_08_425885	106	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	106	2	specify	specify	VBP
10_1101-2021_01_08_425885	106	3	σh	σh	NNP
10_1101-2021_01_08_425885	106	4	instead	instead	RB
10_1101-2021_01_08_425885	106	5	of	of	IN
10_1101-2021_01_08_425885	106	6	σS	σS	NNP
10_1101-2021_01_08_425885	106	7	as	as	IN
10_1101-2021_01_08_425885	106	8	the	the	DT
10_1101-2021_01_08_425885	106	9	global	global	JJ
10_1101-2021_01_08_425885	106	10	parameter	parameter	NN
10_1101-2021_01_08_425885	106	11	for	for	IN
10_1101-2021_01_08_425885	106	12	choosing	choose	VBG
10_1101-2021_01_08_425885	106	13	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	106	14	sizes	size	NNS
10_1101-2021_01_08_425885	106	15	,	,	,
10_1101-2021_01_08_425885	106	16	since	since	IN
10_1101-2021_01_08_425885	106	17	the	the	DT
10_1101-2021_01_08_425885	106	18	latter	latter	NN
10_1101-2021_01_08_425885	106	19	depends	depend	VBZ
10_1101-2021_01_08_425885	106	20	non	non	JJ
10_1101-2021_01_08_425885	106	21	-	-	JJ
10_1101-2021_01_08_425885	106	22	linearly	linearly	JJ
10_1101-2021_01_08_425885	106	23	on	on	IN
10_1101-2021_01_08_425885	106	24	the	the	DT
10_1101-2021_01_08_425885	106	25	values	value	NNS
10_1101-2021_01_08_425885	106	26	of	of	IN
10_1101-2021_01_08_425885	106	27	hkij(p	hkij(p	NNP
10_1101-2021_01_08_425885	106	28	)	)	-RRB-
10_1101-2021_01_08_425885	106	29	,	,	,
10_1101-2021_01_08_425885	106	30	which	which	WDT
10_1101-2021_01_08_425885	106	31	makes	make	VBZ
10_1101-2021_01_08_425885	106	32	determining	determine	VBG
10_1101-2021_01_08_425885	106	33	r(p	r(p	NNP
10_1101-2021_01_08_425885	106	34	)	)	-RRB-
10_1101-2021_01_08_425885	106	35	more	more	RBR
10_1101-2021_01_08_425885	106	36	difficult	difficult	JJ
10_1101-2021_01_08_425885	106	37	.	.	.
10_1101-2021_01_08_425885	107	1	Our	-PRON-	PRP$
10_1101-2021_01_08_425885	107	2	algorithm	algorithm	NN
10_1101-2021_01_08_425885	107	3	also	also	RB
10_1101-2021_01_08_425885	107	4	computes	compute	VBZ
10_1101-2021_01_08_425885	107	5	a	a	DT
10_1101-2021_01_08_425885	107	6	goodness	goodness	NN
10_1101-2021_01_08_425885	107	7	-	-	HYPH
10_1101-2021_01_08_425885	107	8	of	of	IN
10_1101-2021_01_08_425885	107	9	-	-	HYPH
10_1101-2021_01_08_425885	107	10	fit	fit	NN
10_1101-2021_01_08_425885	107	11	(	(	-LRB-
10_1101-2021_01_08_425885	107	12	GOF	GOF	NNP
10_1101-2021_01_08_425885	107	13	)	)	-RRB-
10_1101-2021_01_08_425885	107	14	p	p	NN
10_1101-2021_01_08_425885	107	15	-	-	HYPH
10_1101-2021_01_08_425885	107	16	value	value	NN
10_1101-2021_01_08_425885	107	17	at	at	IN
10_1101-2021_01_08_425885	107	18	each	each	DT
10_1101-2021_01_08_425885	107	19	p	p	NN
10_1101-2021_01_08_425885	107	20	by	by	IN
10_1101-2021_01_08_425885	107	21	comparing	compare	VBG
10_1101-2021_01_08_425885	107	22	residuals	residual	NNS
10_1101-2021_01_08_425885	107	23	from	from	IN
10_1101-2021_01_08_425885	107	24	regression	regression	NN
10_1101-2021_01_08_425885	107	25	against	against	IN
10_1101-2021_01_08_425885	107	26	a	a	DT
10_1101-2021_01_08_425885	107	27	normal	normal	JJ
10_1101-2021_01_08_425885	107	28	distribution	distribution	NN
10_1101-2021_01_08_425885	107	29	to	to	TO
10_1101-2021_01_08_425885	107	30	quantify	quantify	VB
10_1101-2021_01_08_425885	107	31	how	how	WRB
10_1101-2021_01_08_425885	107	32	well	well	RB
10_1101-2021_01_08_425885	107	33	the	the	DT
10_1101-2021_01_08_425885	107	34	normal	normal	JJ
10_1101-2021_01_08_425885	107	35	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	107	36	are	be	VBP
10_1101-2021_01_08_425885	107	37	fit	fit	JJ
10_1101-2021_01_08_425885	107	38	by	by	IN
10_1101-2021_01_08_425885	107	39	a	a	DT
10_1101-2021_01_08_425885	107	40	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	107	41	function	function	NN
10_1101-2021_01_08_425885	107	42	(	(	-LRB-
10_1101-2021_01_08_425885	107	43	see	see	VB
10_1101-2021_01_08_425885	107	44	Methods	Methods	NNP
10_1101-2021_01_08_425885	107	45	Section	Section	NNP
10_1101-2021_01_08_425885	107	46	4.3.3	4.3.3	CD
10_1101-2021_01_08_425885	107	47	)	)	-RRB-
10_1101-2021_01_08_425885	107	48	.	.	.
10_1101-2021_01_08_425885	108	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	108	2	tested	test	VBD
10_1101-2021_01_08_425885	108	3	this	this	DT
10_1101-2021_01_08_425885	108	4	p	p	NN
10_1101-2021_01_08_425885	108	5	-	-	HYPH
10_1101-2021_01_08_425885	108	6	value	value	NN
10_1101-2021_01_08_425885	108	7	at	at	IN
10_1101-2021_01_08_425885	108	8	significance	significance	NN
10_1101-2021_01_08_425885	108	9	level	level	NN
10_1101-2021_01_08_425885	108	10	α	α	NN
10_1101-2021_01_08_425885	108	11	=	=	SYM
10_1101-2021_01_08_425885	108	12	0.05	0.05	CD
10_1101-2021_01_08_425885	108	13	,	,	,
10_1101-2021_01_08_425885	108	14	declaring	declare	VBG
10_1101-2021_01_08_425885	108	15	fits	fit	NNS
10_1101-2021_01_08_425885	108	16	to	to	TO
10_1101-2021_01_08_425885	108	17	be	be	VB
10_1101-2021_01_08_425885	108	18	poor	poor	JJ
10_1101-2021_01_08_425885	108	19	when	when	WRB
10_1101-2021_01_08_425885	108	20	the	the	DT
10_1101-2021_01_08_425885	108	21	residuals	residual	NNS
10_1101-2021_01_08_425885	108	22	are	be	VBP
10_1101-2021_01_08_425885	108	23	significantly	significantly	RB
10_1101-2021_01_08_425885	108	24	non	non	JJ
10_1101-2021_01_08_425885	108	25	-	-	JJ
10_1101-2021_01_08_425885	108	26	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	108	27	.	.	.
10_1101-2021_01_08_425885	109	1	The	the	DT
10_1101-2021_01_08_425885	109	2	p	p	NN
10_1101-2021_01_08_425885	109	3	-	-	HYPH
10_1101-2021_01_08_425885	109	4	value	value	NN
10_1101-2021_01_08_425885	109	5	can	can	MD
10_1101-2021_01_08_425885	109	6	be	be	VB
10_1101-2021_01_08_425885	109	7	disregarded	disregard	VBN
10_1101-2021_01_08_425885	109	8	if	if	IN
10_1101-2021_01_08_425885	109	9	the	the	DT
10_1101-2021_01_08_425885	109	10	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	109	11	size	size	NN
10_1101-2021_01_08_425885	109	12	is	be	VBZ
10_1101-2021_01_08_425885	109	13	manually	manually	RB
10_1101-2021_01_08_425885	109	14	specified	specify	VBN
10_1101-2021_01_08_425885	109	15	to	to	TO
10_1101-2021_01_08_425885	109	16	be	be	VB
10_1101-2021_01_08_425885	109	17	larger	large	JJR
10_1101-2021_01_08_425885	109	18	than	than	IN
10_1101-2021_01_08_425885	109	19	a	a	DT
10_1101-2021_01_08_425885	109	20	length	length	NN
10_1101-2021_01_08_425885	109	21	scale	scale	NN
10_1101-2021_01_08_425885	109	22	for	for	IN
10_1101-2021_01_08_425885	109	23	which	which	WDT
10_1101-2021_01_08_425885	109	24	a	a	DT
10_1101-2021_01_08_425885	109	25	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	109	26	fit	fit	NN
10_1101-2021_01_08_425885	109	27	is	be	VBZ
10_1101-2021_01_08_425885	109	28	appropriate	appropriate	JJ
10_1101-2021_01_08_425885	109	29	.	.	.
10_1101-2021_01_08_425885	110	1	However	however	RB
10_1101-2021_01_08_425885	110	2	,	,	,
10_1101-2021_01_08_425885	110	3	when	when	WRB
10_1101-2021_01_08_425885	110	4	σh	σh	NNP
10_1101-2021_01_08_425885	110	5	is	be	VBZ
10_1101-2021_01_08_425885	110	6	specified	specify	VBN
10_1101-2021_01_08_425885	110	7	instead	instead	RB
10_1101-2021_01_08_425885	110	8	,	,	,
10_1101-2021_01_08_425885	110	9	a	a	DT
10_1101-2021_01_08_425885	110	10	uniform	uniform	JJ
10_1101-2021_01_08_425885	110	11	distribution	distribution	NN
10_1101-2021_01_08_425885	110	12	of	of	IN
10_1101-2021_01_08_425885	110	13	these	these	DT
10_1101-2021_01_08_425885	110	14	p	p	NN
10_1101-2021_01_08_425885	110	15	-	-	HYPH
10_1101-2021_01_08_425885	110	16	values	value	NNS
10_1101-2021_01_08_425885	110	17	over	over	IN
10_1101-2021_01_08_425885	110	18	M	M	NNP
10_1101-2021_01_08_425885	110	19	indicates	indicate	VBZ
10_1101-2021_01_08_425885	110	20	that	that	IN
10_1101-2021_01_08_425885	110	21	the	the	DT
10_1101-2021_01_08_425885	110	22	desired	desire	VBN
10_1101-2021_01_08_425885	110	23	uncertainty	uncertainty	NN
10_1101-2021_01_08_425885	110	24	results	result	NNS
10_1101-2021_01_08_425885	110	25	in	in	IN
10_1101-2021_01_08_425885	110	26	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	110	27	that	that	WDT
10_1101-2021_01_08_425885	110	28	are	be	VBP
10_1101-2021_01_08_425885	110	29	well	well	RB
10_1101-2021_01_08_425885	110	30	-	-	HYPH
10_1101-2021_01_08_425885	110	31	approximated	approximate	VBN
10_1101-2021_01_08_425885	110	32	using	use	VBG
10_1101-2021_01_08_425885	110	33	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	110	34	regression	regression	NN
10_1101-2021_01_08_425885	110	35	.	.	.
10_1101-2021_01_08_425885	111	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	111	2	adopted	adopt	VBD
10_1101-2021_01_08_425885	111	3	this	this	DT
10_1101-2021_01_08_425885	111	4	heuristic	heuristic	JJ
10_1101-2021_01_08_425885	111	5	when	when	WRB
10_1101-2021_01_08_425885	111	6	choosing	choose	VBG
10_1101-2021_01_08_425885	111	7	σh	σh	NNP
10_1101-2021_01_08_425885	111	8	for	for	IN
10_1101-2021_01_08_425885	111	9	the	the	DT
10_1101-2021_01_08_425885	111	10	datasets	dataset	NNS
10_1101-2021_01_08_425885	111	11	studied	study	VBN
10_1101-2021_01_08_425885	111	12	in	in	IN
10_1101-2021_01_08_425885	111	13	this	this	DT
10_1101-2021_01_08_425885	111	14	paper	paper	NN
10_1101-2021_01_08_425885	111	15	(	(	-LRB-
10_1101-2021_01_08_425885	111	16	see	see	VB
10_1101-2021_01_08_425885	111	17	Methods	Methods	NNP
10_1101-2021_01_08_425885	111	18	Section	Section	NNP
10_1101-2021_01_08_425885	111	19	4.4.3	4.4.3	NNS
10_1101-2021_01_08_425885	111	20	,	,	,
10_1101-2021_01_08_425885	111	21	4.5.7	4.5.7	CD
10_1101-2021_01_08_425885	111	22	and	and	CC
10_1101-2021_01_08_425885	111	23	4.6.4	4.6.4	CD
10_1101-2021_01_08_425885	111	24	)	)	-RRB-
10_1101-2021_01_08_425885	111	25	.	.	.
10_1101-2021_01_08_425885	112	1	The	the	DT
10_1101-2021_01_08_425885	112	2	software	software	NN
10_1101-2021_01_08_425885	112	3	is	be	VBZ
10_1101-2021_01_08_425885	112	4	available	available	JJ
10_1101-2021_01_08_425885	112	5	at	at	IN
10_1101-2021_01_08_425885	112	6	https://gitlab.com/hormozlab/ManifoldCurvature	https://gitlab.com/hormozlab/manifoldcurvature	NN
10_1101-2021_01_08_425885	112	7	.	.	.
10_1101-2021_01_08_425885	113	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	113	2	first	first	RB
10_1101-2021_01_08_425885	113	3	applied	apply	VBD
10_1101-2021_01_08_425885	113	4	our	-PRON-	PRP$
10_1101-2021_01_08_425885	113	5	algorithm	algorithm	NN
10_1101-2021_01_08_425885	113	6	to	to	TO
10_1101-2021_01_08_425885	113	7	compute	compute	VB
10_1101-2021_01_08_425885	113	8	scalar	scalar	JJ
10_1101-2021_01_08_425885	113	9	curvatures	curvature	NNS
10_1101-2021_01_08_425885	113	10	for	for	IN
10_1101-2021_01_08_425885	113	11	the	the	DT
10_1101-2021_01_08_425885	113	12	same	same	JJ
10_1101-2021_01_08_425885	113	13	N	n	NN
10_1101-2021_01_08_425885	113	14	=	=	SYM
10_1101-2021_01_08_425885	113	15	104	104	CD
10_1101-2021_01_08_425885	113	16	points	point	NNS
10_1101-2021_01_08_425885	113	17	uniformly	uniformly	RB
10_1101-2021_01_08_425885	113	18	sampled	sample	VBN
10_1101-2021_01_08_425885	113	19	from	from	IN
10_1101-2021_01_08_425885	113	20	S2	s2	NN
10_1101-2021_01_08_425885	113	21	for	for	IN
10_1101-2021_01_08_425885	113	22	which	which	WDT
10_1101-2021_01_08_425885	113	23	the	the	DT
10_1101-2021_01_08_425885	113	24	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	113	25	approach	approach	NN
10_1101-2021_01_08_425885	113	26	failed	fail	VBD
10_1101-2021_01_08_425885	113	27	(	(	-LRB-
10_1101-2021_01_08_425885	113	28	see	see	VB
10_1101-2021_01_08_425885	113	29	Figure	figure	NN
10_1101-2021_01_08_425885	113	30	2C	2c	NN
10_1101-2021_01_08_425885	113	31	;	;	:
10_1101-2021_01_08_425885	113	32	Methods	Methods	NNP
10_1101-2021_01_08_425885	113	33	Section	Section	NNP
10_1101-2021_01_08_425885	113	34	4.4.1.1	4.4.1.1	CD
10_1101-2021_01_08_425885	113	35	)	)	-RRB-
10_1101-2021_01_08_425885	113	36	.	.	.
10_1101-2021_01_08_425885	114	1	The	the	DT
10_1101-2021_01_08_425885	114	2	algorithm	algorithm	NN
10_1101-2021_01_08_425885	114	3	yielded	yield	VBD
10_1101-2021_01_08_425885	114	4	scalar	scalar	JJ
10_1101-2021_01_08_425885	114	5	curvature	curvature	NN
10_1101-2021_01_08_425885	114	6	estimates	estimate	NNS
10_1101-2021_01_08_425885	114	7	at	at	IN
10_1101-2021_01_08_425885	114	8	each	each	DT
10_1101-2021_01_08_425885	114	9	point	point	NN
10_1101-2021_01_08_425885	114	10	with	with	IN
10_1101-2021_01_08_425885	114	11	mean	mean	JJ
10_1101-2021_01_08_425885	114	12	error	error	NN
10_1101-2021_01_08_425885	114	13	−0.17	−0.17	NNP
10_1101-2021_01_08_425885	114	14	(	(	-LRB-
10_1101-2021_01_08_425885	114	15	computed	compute	VBN
10_1101-2021_01_08_425885	114	16	by	by	IN
10_1101-2021_01_08_425885	114	17	averaging	average	VBG
10_1101-2021_01_08_425885	114	18	the	the	DT
10_1101-2021_01_08_425885	114	19	difference	difference	NN
10_1101-2021_01_08_425885	114	20	between	between	IN
10_1101-2021_01_08_425885	114	21	the	the	DT
10_1101-2021_01_08_425885	114	22	point	point	NN
10_1101-2021_01_08_425885	114	23	-	-	HYPH
10_1101-2021_01_08_425885	114	24	wise	wise	JJ
10_1101-2021_01_08_425885	114	25	scalar	scalar	JJ
10_1101-2021_01_08_425885	114	26	curvature	curvature	NN
10_1101-2021_01_08_425885	114	27	estimates	estimate	NNS
10_1101-2021_01_08_425885	114	28	and	and	CC
10_1101-2021_01_08_425885	114	29	the	the	DT
10_1101-2021_01_08_425885	114	30	ground	ground	NN
10_1101-2021_01_08_425885	114	31	truth	truth	NN
10_1101-2021_01_08_425885	114	32	value	value	NN
10_1101-2021_01_08_425885	114	33	of	of	IN
10_1101-2021_01_08_425885	114	34	2	2	CD
10_1101-2021_01_08_425885	114	35	across	across	IN
10_1101-2021_01_08_425885	114	36	all	all	DT
10_1101-2021_01_08_425885	114	37	points	point	NNS
10_1101-2021_01_08_425885	114	38	)	)	-RRB-
10_1101-2021_01_08_425885	114	39	using	use	VBG
10_1101-2021_01_08_425885	114	40	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	114	41	that	that	WDT
10_1101-2021_01_08_425885	114	42	only	only	RB
10_1101-2021_01_08_425885	114	43	contained	contain	VBD
10_1101-2021_01_08_425885	114	44	Np(r	Np(r	NNP
10_1101-2021_01_08_425885	114	45	)	)	-RRB-
10_1101-2021_01_08_425885	114	46	≈	≈	NNP
10_1101-2021_01_08_425885	114	47	102	102	CD
10_1101-2021_01_08_425885	114	48	points	point	NNS
10_1101-2021_01_08_425885	114	49	.	.	.
10_1101-2021_01_08_425885	115	1	This	this	DT
10_1101-2021_01_08_425885	115	2	is	be	VBZ
10_1101-2021_01_08_425885	115	3	already	already	RB
10_1101-2021_01_08_425885	115	4	superior	superior	JJ
10_1101-2021_01_08_425885	115	5	to	to	IN
10_1101-2021_01_08_425885	115	6	the	the	DT
10_1101-2021_01_08_425885	115	7	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	115	8	approach	approach	NN
10_1101-2021_01_08_425885	115	9	,	,	,
10_1101-2021_01_08_425885	115	10	which	which	WDT
10_1101-2021_01_08_425885	115	11	failed	fail	VBD
10_1101-2021_01_08_425885	115	12	to	to	TO
10_1101-2021_01_08_425885	115	13	compute	compute	VB
10_1101-2021_01_08_425885	115	14	even	even	RB
10_1101-2021_01_08_425885	115	15	average	average	JJ
10_1101-2021_01_08_425885	115	16	scalar	scalar	JJ
10_1101-2021_01_08_425885	115	17	accurate	accurate	JJ
10_1101-2021_01_08_425885	115	18	to	to	IN
10_1101-2021_01_08_425885	115	19	±1	±1	ADD
10_1101-2021_01_08_425885	115	20	for	for	IN
10_1101-2021_01_08_425885	115	21	the	the	DT
10_1101-2021_01_08_425885	115	22	same	same	JJ
10_1101-2021_01_08_425885	115	23	sample	sample	NN
10_1101-2021_01_08_425885	115	24	size	size	NN
10_1101-2021_01_08_425885	115	25	.	.	.
10_1101-2021_01_08_425885	116	1	The	the	DT
10_1101-2021_01_08_425885	116	2	non	non	JJ
10_1101-2021_01_08_425885	116	3	-	-	JJ
10_1101-2021_01_08_425885	116	4	zero	zero	JJ
10_1101-2021_01_08_425885	116	5	value	value	NN
10_1101-2021_01_08_425885	116	6	of	of	IN
10_1101-2021_01_08_425885	116	7	the	the	DT
10_1101-2021_01_08_425885	116	8	mean	mean	NNP
10_1101-2021_01_08_425885	116	9	error	error	NN
10_1101-2021_01_08_425885	116	10	indicates	indicate	VBZ
10_1101-2021_01_08_425885	116	11	that	that	IN
10_1101-2021_01_08_425885	116	12	our	-PRON-	PRP$
10_1101-2021_01_08_425885	116	13	estimator	estimator	NN
10_1101-2021_01_08_425885	116	14	is	be	VBZ
10_1101-2021_01_08_425885	116	15	biased	bias	VBN
10_1101-2021_01_08_425885	116	16	.	.	.
10_1101-2021_01_08_425885	117	1	The	the	DT
10_1101-2021_01_08_425885	117	2	values	value	NNS
10_1101-2021_01_08_425885	117	3	of	of	IN
10_1101-2021_01_08_425885	117	4	hkij	hkij	NNP
10_1101-2021_01_08_425885	117	5	are	be	VBP
10_1101-2021_01_08_425885	117	6	not	not	RB
10_1101-2021_01_08_425885	117	7	biased	biased	JJ
10_1101-2021_01_08_425885	117	8	because	because	IN
10_1101-2021_01_08_425885	117	9	they	-PRON-	PRP
10_1101-2021_01_08_425885	117	10	8	8	CD
10_1101-2021_01_08_425885	117	11	.CC	.CC	:
10_1101-2021_01_08_425885	117	12	-	-	HYPH
10_1101-2021_01_08_425885	117	13	BY	by	IN
10_1101-2021_01_08_425885	117	14	-	-	HYPH
10_1101-2021_01_08_425885	117	15	NC	NC	NNP
10_1101-2021_01_08_425885	117	16	-	-	HYPH
10_1101-2021_01_08_425885	117	17	ND	ND	NNP
10_1101-2021_01_08_425885	117	18	4.0	4.0	CD
10_1101-2021_01_08_425885	117	19	International	International	NNP
10_1101-2021_01_08_425885	117	20	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	117	21	under	under	IN
10_1101-2021_01_08_425885	117	22	a	a	DT
10_1101-2021_01_08_425885	117	23	(	(	-LRB-
10_1101-2021_01_08_425885	117	24	which	which	WDT
10_1101-2021_01_08_425885	117	25	was	be	VBD
10_1101-2021_01_08_425885	117	26	not	not	RB
10_1101-2021_01_08_425885	117	27	certified	certify	VBN
10_1101-2021_01_08_425885	117	28	by	by	IN
10_1101-2021_01_08_425885	117	29	peer	peer	NN
10_1101-2021_01_08_425885	117	30	review	review	NN
10_1101-2021_01_08_425885	117	31	)	)	-RRB-
10_1101-2021_01_08_425885	117	32	is	be	VBZ
10_1101-2021_01_08_425885	117	33	the	the	DT
10_1101-2021_01_08_425885	117	34	author	author	NN
10_1101-2021_01_08_425885	117	35	/	/	SYM
10_1101-2021_01_08_425885	117	36	funder	funder	NN
10_1101-2021_01_08_425885	117	37	,	,	,
10_1101-2021_01_08_425885	117	38	who	who	WP
10_1101-2021_01_08_425885	117	39	has	have	VBZ
10_1101-2021_01_08_425885	117	40	granted	grant	VBN
10_1101-2021_01_08_425885	117	41	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	117	42	a	a	DT
10_1101-2021_01_08_425885	117	43	license	license	NN
10_1101-2021_01_08_425885	117	44	to	to	TO
10_1101-2021_01_08_425885	117	45	display	display	VB
10_1101-2021_01_08_425885	117	46	the	the	DT
10_1101-2021_01_08_425885	117	47	preprint	preprint	NN
10_1101-2021_01_08_425885	117	48	in	in	IN
10_1101-2021_01_08_425885	117	49	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	117	50	.	.	.
10_1101-2021_01_08_425885	118	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	118	2	is	be	VBZ
10_1101-2021_01_08_425885	118	3	made	make	VBN
10_1101-2021_01_08_425885	118	4	The	the	DT
10_1101-2021_01_08_425885	118	5	copyright	copyright	NN
10_1101-2021_01_08_425885	118	6	holder	holder	NN
10_1101-2021_01_08_425885	118	7	for	for	IN
10_1101-2021_01_08_425885	118	8	this	this	DT
10_1101-2021_01_08_425885	118	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	118	10	version	version	NN
10_1101-2021_01_08_425885	118	11	posted	post	VBD
10_1101-2021_01_08_425885	118	12	January	January	NNP
10_1101-2021_01_08_425885	118	13	8	8	CD
10_1101-2021_01_08_425885	118	14	,	,	,
10_1101-2021_01_08_425885	118	15	2021	2021	CD
10_1101-2021_01_08_425885	118	16	.	.	.
10_1101-2021_01_08_425885	118	17	;	;	:
10_1101-2021_01_08_425885	118	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	118	19	:	:	:
10_1101-2021_01_08_425885	118	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	118	21	preprint	preprint	NN
10_1101-2021_01_08_425885	118	22	https://gitlab.com/hormozlab/ManifoldCurvature	https://gitlab.com/hormozlab/manifoldcurvature	NN
10_1101-2021_01_08_425885	118	23	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	118	24	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	JJ
10_1101-2021_01_08_425885	118	25	C	c	NN
10_1101-2021_01_08_425885	118	26	D	d	NN
10_1101-2021_01_08_425885	118	27	B	b	NN
10_1101-2021_01_08_425885	118	28	E	e	NN
10_1101-2021_01_08_425885	118	29	F	f	NN
10_1101-2021_01_08_425885	118	30	I	i	NN
10_1101-2021_01_08_425885	118	31	G	g	NN
10_1101-2021_01_08_425885	118	32	H	h	NN
10_1101-2021_01_08_425885	118	33	Figure	figure	NN
10_1101-2021_01_08_425885	118	34	2	2	CD
10_1101-2021_01_08_425885	118	35	:	:	:
10_1101-2021_01_08_425885	118	36	Scalar	scalar	JJ
10_1101-2021_01_08_425885	118	37	curvature	curvature	NN
10_1101-2021_01_08_425885	118	38	is	be	VBZ
10_1101-2021_01_08_425885	118	39	accurately	accurately	RB
10_1101-2021_01_08_425885	118	40	estimated	estimate	VBN
10_1101-2021_01_08_425885	118	41	using	use	VBG
10_1101-2021_01_08_425885	118	42	the	the	DT
10_1101-2021_01_08_425885	118	43	Second	Second	NNP
10_1101-2021_01_08_425885	118	44	Fundamental	Fundamental	NNP
10_1101-2021_01_08_425885	118	45	Form	Form	NNP
10_1101-2021_01_08_425885	118	46	and	and	CC
10_1101-2021_01_08_425885	118	47	the	the	DT
10_1101-2021_01_08_425885	118	48	Gauss	Gauss	NNP
10_1101-2021_01_08_425885	118	49	-	-	HYPH
10_1101-2021_01_08_425885	118	50	Codazzi	Codazzi	NNP
10_1101-2021_01_08_425885	118	51	equation	equation	NN
10_1101-2021_01_08_425885	118	52	.	.	.
10_1101-2021_01_08_425885	119	1	(	(	-LRB-
10_1101-2021_01_08_425885	119	2	A	a	NN
10_1101-2021_01_08_425885	119	3	)	)	-RRB-
10_1101-2021_01_08_425885	119	4	A	a	DT
10_1101-2021_01_08_425885	119	5	hypothetical	hypothetical	JJ
10_1101-2021_01_08_425885	119	6	manifold	manifold	NN
10_1101-2021_01_08_425885	119	7	(	(	-LRB-
10_1101-2021_01_08_425885	119	8	shown	show	VBN
10_1101-2021_01_08_425885	119	9	in	in	IN
10_1101-2021_01_08_425885	119	10	grey	grey	NNP
10_1101-2021_01_08_425885	119	11	)	)	-RRB-
10_1101-2021_01_08_425885	119	12	from	from	IN
10_1101-2021_01_08_425885	119	13	which	which	WDT
10_1101-2021_01_08_425885	119	14	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	119	15	are	be	VBP
10_1101-2021_01_08_425885	119	16	sampled	sample	VBN
10_1101-2021_01_08_425885	119	17	(	(	-LRB-
10_1101-2021_01_08_425885	119	18	shown	show	VBN
10_1101-2021_01_08_425885	119	19	as	as	IN
10_1101-2021_01_08_425885	119	20	colored	colored	JJ
10_1101-2021_01_08_425885	119	21	dots	dot	NNS
10_1101-2021_01_08_425885	119	22	)	)	-RRB-
10_1101-2021_01_08_425885	119	23	.	.	.
10_1101-2021_01_08_425885	120	1	The	the	DT
10_1101-2021_01_08_425885	120	2	manifold	manifold	NN
10_1101-2021_01_08_425885	120	3	at	at	IN
10_1101-2021_01_08_425885	120	4	any	any	DT
10_1101-2021_01_08_425885	120	5	given	give	VBN
10_1101-2021_01_08_425885	120	6	point	point	NN
10_1101-2021_01_08_425885	120	7	p	p	NNP
10_1101-2021_01_08_425885	120	8	(	(	-LRB-
10_1101-2021_01_08_425885	120	9	shown	show	VBN
10_1101-2021_01_08_425885	120	10	in	in	IN
10_1101-2021_01_08_425885	120	11	red	red	NN
10_1101-2021_01_08_425885	120	12	)	)	-RRB-
10_1101-2021_01_08_425885	120	13	can	can	MD
10_1101-2021_01_08_425885	120	14	be	be	VB
10_1101-2021_01_08_425885	120	15	decomposed	decompose	VBN
10_1101-2021_01_08_425885	120	16	into	into	IN
10_1101-2021_01_08_425885	120	17	a	a	DT
10_1101-2021_01_08_425885	120	18	tangent	tangent	NN
10_1101-2021_01_08_425885	120	19	space	space	NN
10_1101-2021_01_08_425885	120	20	TM	TM	NNP
10_1101-2021_01_08_425885	120	21	(	(	-LRB-
10_1101-2021_01_08_425885	120	22	p	p	NNP
10_1101-2021_01_08_425885	120	23	)	)	-RRB-
10_1101-2021_01_08_425885	120	24	(	(	-LRB-
10_1101-2021_01_08_425885	120	25	the	the	DT
10_1101-2021_01_08_425885	120	26	cyan	cyan	NNP
10_1101-2021_01_08_425885	120	27	plane	plane	NN
10_1101-2021_01_08_425885	120	28	)	)	-RRB-
10_1101-2021_01_08_425885	120	29	and	and	CC
10_1101-2021_01_08_425885	120	30	a	a	DT
10_1101-2021_01_08_425885	120	31	normal	normal	JJ
10_1101-2021_01_08_425885	120	32	space	space	NN
10_1101-2021_01_08_425885	120	33	NM	NM	NNP
10_1101-2021_01_08_425885	120	34	(	(	-LRB-
10_1101-2021_01_08_425885	120	35	p	p	NN
10_1101-2021_01_08_425885	120	36	)	)	-RRB-
10_1101-2021_01_08_425885	120	37	(	(	-LRB-
10_1101-2021_01_08_425885	120	38	the	the	DT
10_1101-2021_01_08_425885	120	39	cyan	cyan	NN
10_1101-2021_01_08_425885	120	40	line	line	NN
10_1101-2021_01_08_425885	120	41	)	)	-RRB-
10_1101-2021_01_08_425885	120	42	.	.	.
10_1101-2021_01_08_425885	121	1	Points	point	NNS
10_1101-2021_01_08_425885	121	2	in	in	IN
10_1101-2021_01_08_425885	121	3	the	the	DT
10_1101-2021_01_08_425885	121	4	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	121	5	around	around	RB
10_1101-2021_01_08_425885	121	6	p	p	NN
10_1101-2021_01_08_425885	121	7	(	(	-LRB-
10_1101-2021_01_08_425885	121	8	shown	show	VBN
10_1101-2021_01_08_425885	121	9	in	in	IN
10_1101-2021_01_08_425885	121	10	green	green	NN
10_1101-2021_01_08_425885	121	11	)	)	-RRB-
10_1101-2021_01_08_425885	121	12	can	can	MD
10_1101-2021_01_08_425885	121	13	be	be	VB
10_1101-2021_01_08_425885	121	14	expressed	express	VBN
10_1101-2021_01_08_425885	121	15	in	in	IN
10_1101-2021_01_08_425885	121	16	terms	term	NNS
10_1101-2021_01_08_425885	121	17	of	of	IN
10_1101-2021_01_08_425885	121	18	orthonormal	orthonormal	JJ
10_1101-2021_01_08_425885	121	19	bases	basis	NNS
10_1101-2021_01_08_425885	121	20	for	for	IN
10_1101-2021_01_08_425885	121	21	TM	TM	NNP
10_1101-2021_01_08_425885	121	22	(	(	-LRB-
10_1101-2021_01_08_425885	121	23	p	p	NNP
10_1101-2021_01_08_425885	121	24	)	)	-RRB-
10_1101-2021_01_08_425885	121	25	and	and	CC
10_1101-2021_01_08_425885	121	26	NM	NM	NNP
10_1101-2021_01_08_425885	121	27	(	(	-LRB-
10_1101-2021_01_08_425885	121	28	p	p	NN
10_1101-2021_01_08_425885	121	29	)	)	-RRB-
10_1101-2021_01_08_425885	121	30	(	(	-LRB-
10_1101-2021_01_08_425885	121	31	see	see	VB
10_1101-2021_01_08_425885	121	32	(	(	-LRB-
10_1101-2021_01_08_425885	121	33	B	b	NN
10_1101-2021_01_08_425885	121	34	)	)	-RRB-
10_1101-2021_01_08_425885	121	35	below	below	RB
10_1101-2021_01_08_425885	121	36	)	)	-RRB-
10_1101-2021_01_08_425885	121	37	.	.	.
10_1101-2021_01_08_425885	122	1	(	(	-LRB-
10_1101-2021_01_08_425885	122	2	B	b	NN
10_1101-2021_01_08_425885	122	3	)	)	-RRB-
10_1101-2021_01_08_425885	122	4	The	the	DT
10_1101-2021_01_08_425885	122	5	set	set	NN
10_1101-2021_01_08_425885	122	6	of	of	IN
10_1101-2021_01_08_425885	122	7	points	point	NNS
10_1101-2021_01_08_425885	122	8	in	in	IN
10_1101-2021_01_08_425885	122	9	the	the	DT
10_1101-2021_01_08_425885	122	10	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	122	11	of	of	IN
10_1101-2021_01_08_425885	122	12	p	p	NN
10_1101-2021_01_08_425885	122	13	(	(	-LRB-
10_1101-2021_01_08_425885	122	14	shown	show	VBN
10_1101-2021_01_08_425885	122	15	as	as	IN
10_1101-2021_01_08_425885	122	16	green	green	JJ
10_1101-2021_01_08_425885	122	17	dots	dot	NNS
10_1101-2021_01_08_425885	122	18	in	in	IN
10_1101-2021_01_08_425885	122	19	(	(	-LRB-
10_1101-2021_01_08_425885	122	20	A	a	NN
10_1101-2021_01_08_425885	122	21	)	)	-RRB-
10_1101-2021_01_08_425885	122	22	)	)	-RRB-
10_1101-2021_01_08_425885	122	23	are	be	VBP
10_1101-2021_01_08_425885	122	24	represented	represent	VBN
10_1101-2021_01_08_425885	122	25	here	here	RB
10_1101-2021_01_08_425885	122	26	in	in	IN
10_1101-2021_01_08_425885	122	27	local	local	JJ
10_1101-2021_01_08_425885	122	28	tangent	tangent	NN
10_1101-2021_01_08_425885	122	29	(	(	-LRB-
10_1101-2021_01_08_425885	122	30	t1	t1	NNP
10_1101-2021_01_08_425885	122	31	,	,	,
10_1101-2021_01_08_425885	122	32	t2	t2	NN
10_1101-2021_01_08_425885	122	33	)	)	-RRB-
10_1101-2021_01_08_425885	122	34	and	and	CC
10_1101-2021_01_08_425885	122	35	normal	normal	JJ
10_1101-2021_01_08_425885	122	36	(	(	-LRB-
10_1101-2021_01_08_425885	122	37	n1	n1	NNP
10_1101-2021_01_08_425885	122	38	)	)	-RRB-
10_1101-2021_01_08_425885	122	39	coordinates	coordinate	VBZ
10_1101-2021_01_08_425885	122	40	,	,	,
10_1101-2021_01_08_425885	122	41	corresponding	correspond	VBG
10_1101-2021_01_08_425885	122	42	to	to	IN
10_1101-2021_01_08_425885	122	43	orthonormal	orthonormal	JJ
10_1101-2021_01_08_425885	122	44	bases	basis	NNS
10_1101-2021_01_08_425885	122	45	for	for	IN
10_1101-2021_01_08_425885	122	46	TM	TM	NNP
10_1101-2021_01_08_425885	122	47	(	(	-LRB-
10_1101-2021_01_08_425885	122	48	p	p	NNP
10_1101-2021_01_08_425885	122	49	)	)	-RRB-
10_1101-2021_01_08_425885	122	50	and	and	CC
10_1101-2021_01_08_425885	122	51	NM	NM	NNP
10_1101-2021_01_08_425885	122	52	(	(	-LRB-
10_1101-2021_01_08_425885	122	53	p	p	NNP
10_1101-2021_01_08_425885	122	54	)	)	-RRB-
10_1101-2021_01_08_425885	122	55	respectively	respectively	RB
10_1101-2021_01_08_425885	122	56	.	.	.
10_1101-2021_01_08_425885	123	1	Coloring	color	VBG
10_1101-2021_01_08_425885	123	2	corresponds	correspond	NNS
10_1101-2021_01_08_425885	123	3	to	to	TO
10_1101-2021_01_08_425885	123	4	magnitude	magnitude	VB
10_1101-2021_01_08_425885	123	5	in	in	IN
10_1101-2021_01_08_425885	123	6	the	the	DT
10_1101-2021_01_08_425885	123	7	normal	normal	JJ
10_1101-2021_01_08_425885	123	8	direction	direction	NN
10_1101-2021_01_08_425885	123	9	.	.	.
10_1101-2021_01_08_425885	124	1	The	the	DT
10_1101-2021_01_08_425885	124	2	normal	normal	JJ
10_1101-2021_01_08_425885	124	3	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	124	4	(	(	-LRB-
10_1101-2021_01_08_425885	124	5	n1	n1	NNP
10_1101-2021_01_08_425885	124	6	)	)	-RRB-
10_1101-2021_01_08_425885	124	7	can	can	MD
10_1101-2021_01_08_425885	124	8	be	be	VB
10_1101-2021_01_08_425885	124	9	locally	locally	RB
10_1101-2021_01_08_425885	124	10	approximated	approximate	VBN
10_1101-2021_01_08_425885	124	11	as	as	IN
10_1101-2021_01_08_425885	124	12	a	a	DT
10_1101-2021_01_08_425885	124	13	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	124	14	function	function	NN
10_1101-2021_01_08_425885	124	15	(	(	-LRB-
10_1101-2021_01_08_425885	124	16	the	the	DT
10_1101-2021_01_08_425885	124	17	translucent	translucent	NNP
10_1101-2021_01_08_425885	124	18	surface	surface	NN
10_1101-2021_01_08_425885	124	19	)	)	-RRB-
10_1101-2021_01_08_425885	124	20	of	of	IN
10_1101-2021_01_08_425885	124	21	the	the	DT
10_1101-2021_01_08_425885	124	22	tangent	tangent	NN
10_1101-2021_01_08_425885	124	23	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	124	24	(	(	-LRB-
10_1101-2021_01_08_425885	124	25	t1	t1	NNP
10_1101-2021_01_08_425885	124	26	,	,	,
10_1101-2021_01_08_425885	124	27	t2	t2	NN
10_1101-2021_01_08_425885	124	28	)	)	-RRB-
10_1101-2021_01_08_425885	124	29	,	,	,
10_1101-2021_01_08_425885	124	30	according	accord	VBG
10_1101-2021_01_08_425885	124	31	to	to	IN
10_1101-2021_01_08_425885	124	32	the	the	DT
10_1101-2021_01_08_425885	124	33	Second	Second	NNP
10_1101-2021_01_08_425885	124	34	Fundamental	Fundamental	NNP
10_1101-2021_01_08_425885	124	35	Form	Form	NNP
10_1101-2021_01_08_425885	124	36	,	,	,
10_1101-2021_01_08_425885	124	37	h	h	NNP
10_1101-2021_01_08_425885	124	38	k	k	NNP
10_1101-2021_01_08_425885	124	39	ij	ij	NNP
10_1101-2021_01_08_425885	124	40	.	.	.
10_1101-2021_01_08_425885	125	1	(	(	-LRB-
10_1101-2021_01_08_425885	125	2	C	C	NNP
10_1101-2021_01_08_425885	125	3	)	)	-RRB-
10_1101-2021_01_08_425885	125	4	Scalar	Scalar	NNP
10_1101-2021_01_08_425885	125	5	curvatures	curvature	NNS
10_1101-2021_01_08_425885	125	6	computed	compute	VBD
10_1101-2021_01_08_425885	125	7	using	use	VBG
10_1101-2021_01_08_425885	125	8	the	the	DT
10_1101-2021_01_08_425885	125	9	extrinsic	extrinsic	JJ
10_1101-2021_01_08_425885	125	10	approach	approach	NN
10_1101-2021_01_08_425885	125	11	for	for	IN
10_1101-2021_01_08_425885	125	12	N	n	NN
10_1101-2021_01_08_425885	125	13	=	=	SYM
10_1101-2021_01_08_425885	125	14	104	104	CD
10_1101-2021_01_08_425885	125	15	points	point	NNS
10_1101-2021_01_08_425885	125	16	uniformly	uniformly	RB
10_1101-2021_01_08_425885	125	17	sampled	sample	VBN
10_1101-2021_01_08_425885	125	18	from	from	IN
10_1101-2021_01_08_425885	125	19	the	the	DT
10_1101-2021_01_08_425885	125	20	2-dimensional	2-dimensional	CD
10_1101-2021_01_08_425885	125	21	hollow	hollow	JJ
10_1101-2021_01_08_425885	125	22	unit	unit	NN
10_1101-2021_01_08_425885	125	23	sphere	sphere	VBD
10_1101-2021_01_08_425885	125	24	,	,	,
10_1101-2021_01_08_425885	125	25	S2	S2	NNP
10_1101-2021_01_08_425885	125	26	.	.	.
10_1101-2021_01_08_425885	126	1	The	the	DT
10_1101-2021_01_08_425885	126	2	true	true	JJ
10_1101-2021_01_08_425885	126	3	value	value	NN
10_1101-2021_01_08_425885	126	4	is	be	VBZ
10_1101-2021_01_08_425885	126	5	2	2	CD
10_1101-2021_01_08_425885	126	6	at	at	IN
10_1101-2021_01_08_425885	126	7	all	all	DT
10_1101-2021_01_08_425885	126	8	points	point	NNS
10_1101-2021_01_08_425885	126	9	on	on	IN
10_1101-2021_01_08_425885	126	10	the	the	DT
10_1101-2021_01_08_425885	126	11	manifold	manifold	NN
10_1101-2021_01_08_425885	126	12	.	.	.
10_1101-2021_01_08_425885	127	1	See	see	VB
10_1101-2021_01_08_425885	127	2	Methods	Methods	NNP
10_1101-2021_01_08_425885	127	3	Section	Section	NNP
10_1101-2021_01_08_425885	127	4	4.4.1.1	4.4.1.1	CD
10_1101-2021_01_08_425885	127	5	.	.	.
10_1101-2021_01_08_425885	128	1	(	(	-LRB-
10_1101-2021_01_08_425885	128	2	D	D	NNP
10_1101-2021_01_08_425885	128	3	)	)	-RRB-
10_1101-2021_01_08_425885	128	4	Scalar	scalar	JJ
10_1101-2021_01_08_425885	128	5	curvatures	curvature	NNS
10_1101-2021_01_08_425885	128	6	(	(	-LRB-
10_1101-2021_01_08_425885	128	7	S	S	NNP
10_1101-2021_01_08_425885	128	8	)	)	-RRB-
10_1101-2021_01_08_425885	128	9	computed	compute	VBD
10_1101-2021_01_08_425885	128	10	in	in	IN
10_1101-2021_01_08_425885	128	11	(	(	-LRB-
10_1101-2021_01_08_425885	128	12	C	C	NNP
10_1101-2021_01_08_425885	128	13	)	)	-RRB-
10_1101-2021_01_08_425885	128	14	are	be	VBP
10_1101-2021_01_08_425885	128	15	plotted	plot	VBN
10_1101-2021_01_08_425885	128	16	against	against	IN
10_1101-2021_01_08_425885	128	17	their	-PRON-	PRP$
10_1101-2021_01_08_425885	128	18	associated	associate	VBN
10_1101-2021_01_08_425885	128	19	standard	standard	JJ
10_1101-2021_01_08_425885	128	20	errors	error	NNS
10_1101-2021_01_08_425885	128	21	(	(	-LRB-
10_1101-2021_01_08_425885	128	22	σS	σs	NN
10_1101-2021_01_08_425885	128	23	)	)	-RRB-
10_1101-2021_01_08_425885	128	24	.	.	.
10_1101-2021_01_08_425885	129	1	Points	point	NNS
10_1101-2021_01_08_425885	129	2	enclosed	enclose	VBN
10_1101-2021_01_08_425885	129	3	by	by	IN
10_1101-2021_01_08_425885	129	4	the	the	DT
10_1101-2021_01_08_425885	129	5	red	red	JJ
10_1101-2021_01_08_425885	129	6	lines	line	NNS
10_1101-2021_01_08_425885	129	7	have	have	VBP
10_1101-2021_01_08_425885	129	8	a	a	DT
10_1101-2021_01_08_425885	129	9	95	95	CD
10_1101-2021_01_08_425885	129	10	%	%	NN
10_1101-2021_01_08_425885	129	11	confidence	confidence	NN
10_1101-2021_01_08_425885	129	12	interval	interval	NN
10_1101-2021_01_08_425885	129	13	(	(	-LRB-
10_1101-2021_01_08_425885	129	14	CI	CI	NNP
10_1101-2021_01_08_425885	129	15	)	)	-RRB-
10_1101-2021_01_08_425885	129	16	,	,	,
10_1101-2021_01_08_425885	129	17	computed	compute	VBD
10_1101-2021_01_08_425885	129	18	as	as	IN
10_1101-2021_01_08_425885	129	19	S	S	NNP
10_1101-2021_01_08_425885	129	20	±	±	NNP
10_1101-2021_01_08_425885	129	21	2σS	2σs	CD
10_1101-2021_01_08_425885	129	22	,	,	,
10_1101-2021_01_08_425885	129	23	containing	contain	VBG
10_1101-2021_01_08_425885	129	24	the	the	DT
10_1101-2021_01_08_425885	129	25	true	true	JJ
10_1101-2021_01_08_425885	129	26	value	value	NN
10_1101-2021_01_08_425885	129	27	of	of	IN
10_1101-2021_01_08_425885	129	28	2	2	CD
10_1101-2021_01_08_425885	129	29	.	.	.
10_1101-2021_01_08_425885	130	1	(	(	-LRB-
10_1101-2021_01_08_425885	130	2	E	e	NN
10_1101-2021_01_08_425885	130	3	)	)	-RRB-
10_1101-2021_01_08_425885	130	4	As	as	IN
10_1101-2021_01_08_425885	130	5	in	in	IN
10_1101-2021_01_08_425885	130	6	(	(	-LRB-
10_1101-2021_01_08_425885	130	7	C	c	NN
10_1101-2021_01_08_425885	130	8	)	)	-RRB-
10_1101-2021_01_08_425885	130	9	but	but	CC
10_1101-2021_01_08_425885	130	10	for	for	IN
10_1101-2021_01_08_425885	130	11	N	n	NN
10_1101-2021_01_08_425885	130	12	=	=	SYM
10_1101-2021_01_08_425885	130	13	104	104	CD
10_1101-2021_01_08_425885	130	14	points	point	NNS
10_1101-2021_01_08_425885	130	15	uniformly	uniformly	RB
10_1101-2021_01_08_425885	130	16	sampled	sample	VBN
10_1101-2021_01_08_425885	130	17	from	from	IN
10_1101-2021_01_08_425885	130	18	a	a	DT
10_1101-2021_01_08_425885	130	19	one	one	CD
10_1101-2021_01_08_425885	130	20	-	-	HYPH
10_1101-2021_01_08_425885	130	21	sheet	sheet	NN
10_1101-2021_01_08_425885	130	22	hyperboloid	hyperboloid	NN
10_1101-2021_01_08_425885	130	23	,	,	,
10_1101-2021_01_08_425885	130	24	H22	H22	NNP
10_1101-2021_01_08_425885	130	25	,	,	,
10_1101-2021_01_08_425885	130	26	which	which	WDT
10_1101-2021_01_08_425885	130	27	is	be	VBZ
10_1101-2021_01_08_425885	130	28	also	also	RB
10_1101-2021_01_08_425885	130	29	a	a	DT
10_1101-2021_01_08_425885	130	30	2-dimensional	2-dimensional	CD
10_1101-2021_01_08_425885	130	31	manifold	manifold	NN
10_1101-2021_01_08_425885	130	32	.	.	.
10_1101-2021_01_08_425885	131	1	Due	due	IN
10_1101-2021_01_08_425885	131	2	to	to	IN
10_1101-2021_01_08_425885	131	3	the	the	DT
10_1101-2021_01_08_425885	131	4	radial	radial	JJ
10_1101-2021_01_08_425885	131	5	symmetry	symmetry	NN
10_1101-2021_01_08_425885	131	6	of	of	IN
10_1101-2021_01_08_425885	131	7	the	the	DT
10_1101-2021_01_08_425885	131	8	manifold	manifold	JJ
10_1101-2021_01_08_425885	131	9	,	,	,
10_1101-2021_01_08_425885	131	10	scalar	scalar	JJ
10_1101-2021_01_08_425885	131	11	curvature	curvature	NN
10_1101-2021_01_08_425885	131	12	only	only	RB
10_1101-2021_01_08_425885	131	13	varies	vary	VBZ
10_1101-2021_01_08_425885	131	14	only	only	RB
10_1101-2021_01_08_425885	131	15	along	along	IN
10_1101-2021_01_08_425885	131	16	the	the	DT
10_1101-2021_01_08_425885	131	17	z	z	NN
10_1101-2021_01_08_425885	131	18	-	-	HYPH
10_1101-2021_01_08_425885	131	19	direction	direction	NN
10_1101-2021_01_08_425885	131	20	.	.	.
10_1101-2021_01_08_425885	132	1	See	see	VB
10_1101-2021_01_08_425885	132	2	Methods	Methods	NNP
10_1101-2021_01_08_425885	132	3	Section	Section	NNP
10_1101-2021_01_08_425885	132	4	4.4.1.2	4.4.1.2	CD
10_1101-2021_01_08_425885	132	5	.	.	.
10_1101-2021_01_08_425885	133	1	(	(	-LRB-
10_1101-2021_01_08_425885	133	2	F	F	NNP
10_1101-2021_01_08_425885	133	3	)	)	-RRB-
10_1101-2021_01_08_425885	133	4	Scalar	Scalar	NNP
10_1101-2021_01_08_425885	133	5	curvatures	curvature	NNS
10_1101-2021_01_08_425885	133	6	(	(	-LRB-
10_1101-2021_01_08_425885	133	7	black	black	JJ
10_1101-2021_01_08_425885	133	8	)	)	-RRB-
10_1101-2021_01_08_425885	133	9	computed	compute	VBD
10_1101-2021_01_08_425885	133	10	in	in	IN
10_1101-2021_01_08_425885	133	11	(	(	-LRB-
10_1101-2021_01_08_425885	133	12	E	e	NN
10_1101-2021_01_08_425885	133	13	)	)	-RRB-
10_1101-2021_01_08_425885	133	14	with	with	IN
10_1101-2021_01_08_425885	133	15	their	-PRON-	PRP$
10_1101-2021_01_08_425885	133	16	associated	associate	VBN
10_1101-2021_01_08_425885	133	17	95	95	CD
10_1101-2021_01_08_425885	133	18	%	%	NN
10_1101-2021_01_08_425885	133	19	CIs	ci	NNS
10_1101-2021_01_08_425885	133	20	(	(	-LRB-
10_1101-2021_01_08_425885	133	21	shown	show	VBN
10_1101-2021_01_08_425885	133	22	in	in	IN
10_1101-2021_01_08_425885	133	23	grey	grey	NNP
10_1101-2021_01_08_425885	133	24	)	)	-RRB-
10_1101-2021_01_08_425885	133	25	plotted	plot	VBD
10_1101-2021_01_08_425885	133	26	as	as	IN
10_1101-2021_01_08_425885	133	27	a	a	DT
10_1101-2021_01_08_425885	133	28	function	function	NN
10_1101-2021_01_08_425885	133	29	of	of	IN
10_1101-2021_01_08_425885	133	30	the	the	DT
10_1101-2021_01_08_425885	133	31	z	z	NN
10_1101-2021_01_08_425885	133	32	-	-	HYPH
10_1101-2021_01_08_425885	133	33	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	133	34	of	of	IN
10_1101-2021_01_08_425885	133	35	the	the	DT
10_1101-2021_01_08_425885	133	36	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	133	37	.	.	.
10_1101-2021_01_08_425885	134	1	The	the	DT
10_1101-2021_01_08_425885	134	2	true	true	JJ
10_1101-2021_01_08_425885	134	3	value	value	NN
10_1101-2021_01_08_425885	134	4	is	be	VBZ
10_1101-2021_01_08_425885	134	5	shown	show	VBN
10_1101-2021_01_08_425885	134	6	as	as	IN
10_1101-2021_01_08_425885	134	7	a	a	DT
10_1101-2021_01_08_425885	134	8	dashed	dash	VBN
10_1101-2021_01_08_425885	134	9	red	red	JJ
10_1101-2021_01_08_425885	134	10	line	line	NN
10_1101-2021_01_08_425885	134	11	.	.	.
10_1101-2021_01_08_425885	135	1	(	(	-LRB-
10_1101-2021_01_08_425885	135	2	G	g	NN
10_1101-2021_01_08_425885	135	3	)	)	-RRB-
10_1101-2021_01_08_425885	135	4	As	as	IN
10_1101-2021_01_08_425885	135	5	in	in	IN
10_1101-2021_01_08_425885	135	6	(	(	-LRB-
10_1101-2021_01_08_425885	135	7	C	c	NN
10_1101-2021_01_08_425885	135	8	)	)	-RRB-
10_1101-2021_01_08_425885	135	9	but	but	CC
10_1101-2021_01_08_425885	135	10	for	for	IN
10_1101-2021_01_08_425885	135	11	N	n	NN
10_1101-2021_01_08_425885	135	12	=	=	SYM
10_1101-2021_01_08_425885	135	13	104	104	CD
10_1101-2021_01_08_425885	135	14	points	point	NNS
10_1101-2021_01_08_425885	135	15	uniformly	uniformly	RB
10_1101-2021_01_08_425885	135	16	sampled	sample	VBN
10_1101-2021_01_08_425885	135	17	from	from	IN
10_1101-2021_01_08_425885	135	18	a	a	DT
10_1101-2021_01_08_425885	135	19	2-dimensional	2-dimensional	CD
10_1101-2021_01_08_425885	135	20	ring	ring	NN
10_1101-2021_01_08_425885	135	21	torus	torus	NN
10_1101-2021_01_08_425885	135	22	,	,	,
10_1101-2021_01_08_425885	135	23	T2	T2	NNP
10_1101-2021_01_08_425885	135	24	.	.	.
10_1101-2021_01_08_425885	136	1	T2	t2	NN
10_1101-2021_01_08_425885	136	2	is	be	VBZ
10_1101-2021_01_08_425885	136	3	constructed	construct	VBN
10_1101-2021_01_08_425885	136	4	by	by	IN
10_1101-2021_01_08_425885	136	5	revolving	revolve	VBG
10_1101-2021_01_08_425885	136	6	a	a	DT
10_1101-2021_01_08_425885	136	7	circle	circle	NN
10_1101-2021_01_08_425885	136	8	parameterized	parameterize	VBN
10_1101-2021_01_08_425885	136	9	by	by	IN
10_1101-2021_01_08_425885	136	10	θ	θ	NNP
10_1101-2021_01_08_425885	136	11	,	,	,
10_1101-2021_01_08_425885	136	12	oriented	orient	VBN
10_1101-2021_01_08_425885	136	13	perpendicular	perpendicular	IN
10_1101-2021_01_08_425885	136	14	to	to	IN
10_1101-2021_01_08_425885	136	15	the	the	DT
10_1101-2021_01_08_425885	136	16	xy	xy	NNP
10_1101-2021_01_08_425885	136	17	-	-	HYPH
10_1101-2021_01_08_425885	136	18	plane	plane	NN
10_1101-2021_01_08_425885	136	19	,	,	,
10_1101-2021_01_08_425885	136	20	through	through	IN
10_1101-2021_01_08_425885	136	21	an	an	DT
10_1101-2021_01_08_425885	136	22	angle	angle	NN
10_1101-2021_01_08_425885	136	23	φ	φ	NN
10_1101-2021_01_08_425885	136	24	around	around	IN
10_1101-2021_01_08_425885	136	25	the	the	DT
10_1101-2021_01_08_425885	136	26	z	z	NN
10_1101-2021_01_08_425885	136	27	-	-	HYPH
10_1101-2021_01_08_425885	136	28	axis	axis	NN
10_1101-2021_01_08_425885	136	29	.	.	.
10_1101-2021_01_08_425885	137	1	The	the	DT
10_1101-2021_01_08_425885	137	2	scalar	scalar	JJ
10_1101-2021_01_08_425885	137	3	curvature	curvature	NN
10_1101-2021_01_08_425885	137	4	only	only	RB
10_1101-2021_01_08_425885	137	5	depends	depend	VBZ
10_1101-2021_01_08_425885	137	6	on	on	IN
10_1101-2021_01_08_425885	137	7	the	the	DT
10_1101-2021_01_08_425885	137	8	value	value	NN
10_1101-2021_01_08_425885	137	9	of	of	IN
10_1101-2021_01_08_425885	137	10	θ	θ	NNP
10_1101-2021_01_08_425885	137	11	.	.	.
10_1101-2021_01_08_425885	138	1	See	see	VB
10_1101-2021_01_08_425885	138	2	Methods	Methods	NNP
10_1101-2021_01_08_425885	138	3	Section	Section	NNP
10_1101-2021_01_08_425885	138	4	4.4.1.3	4.4.1.3	CD
10_1101-2021_01_08_425885	138	5	.	.	.
10_1101-2021_01_08_425885	139	1	(	(	-LRB-
10_1101-2021_01_08_425885	139	2	H	h	NN
10_1101-2021_01_08_425885	139	3	)	)	-RRB-
10_1101-2021_01_08_425885	139	4	Scalar	Scalar	NNP
10_1101-2021_01_08_425885	139	5	curvatures	curvature	NNS
10_1101-2021_01_08_425885	139	6	computed	compute	VBD
10_1101-2021_01_08_425885	139	7	in	in	IN
10_1101-2021_01_08_425885	139	8	(	(	-LRB-
10_1101-2021_01_08_425885	139	9	G	g	NN
10_1101-2021_01_08_425885	139	10	)	)	-RRB-
10_1101-2021_01_08_425885	139	11	with	with	IN
10_1101-2021_01_08_425885	139	12	their	-PRON-	PRP$
10_1101-2021_01_08_425885	139	13	associated	associate	VBN
10_1101-2021_01_08_425885	139	14	95	95	CD
10_1101-2021_01_08_425885	139	15	%	%	NN
10_1101-2021_01_08_425885	139	16	CIs	ci	NNS
10_1101-2021_01_08_425885	139	17	plotted	plot	VBD
10_1101-2021_01_08_425885	139	18	as	as	IN
10_1101-2021_01_08_425885	139	19	a	a	DT
10_1101-2021_01_08_425885	139	20	function	function	NN
10_1101-2021_01_08_425885	139	21	of	of	IN
10_1101-2021_01_08_425885	139	22	the	the	DT
10_1101-2021_01_08_425885	139	23	θ	θ	NNP
10_1101-2021_01_08_425885	139	24	values	value	NNS
10_1101-2021_01_08_425885	139	25	of	of	IN
10_1101-2021_01_08_425885	139	26	the	the	DT
10_1101-2021_01_08_425885	139	27	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	139	28	.	.	.
10_1101-2021_01_08_425885	140	1	Colors	color	NNS
10_1101-2021_01_08_425885	140	2	as	as	IN
10_1101-2021_01_08_425885	140	3	in	in	IN
10_1101-2021_01_08_425885	140	4	(	(	-LRB-
10_1101-2021_01_08_425885	140	5	F	f	NN
10_1101-2021_01_08_425885	140	6	)	)	-RRB-
10_1101-2021_01_08_425885	140	7	.	.	.
10_1101-2021_01_08_425885	141	1	(	(	-LRB-
10_1101-2021_01_08_425885	141	2	I	i	NN
10_1101-2021_01_08_425885	141	3	)	)	-RRB-
10_1101-2021_01_08_425885	141	4	Distribution	distribution	NN
10_1101-2021_01_08_425885	141	5	of	of	IN
10_1101-2021_01_08_425885	141	6	computed	computed	JJ
10_1101-2021_01_08_425885	141	7	scalar	scalar	JJ
10_1101-2021_01_08_425885	141	8	curvatures	curvature	NNS
10_1101-2021_01_08_425885	141	9	for	for	IN
10_1101-2021_01_08_425885	141	10	N	n	NN
10_1101-2021_01_08_425885	141	11	=	=	SYM
10_1101-2021_01_08_425885	141	12	104	104	CD
10_1101-2021_01_08_425885	141	13	points	point	NNS
10_1101-2021_01_08_425885	141	14	uniformly	uniformly	RB
10_1101-2021_01_08_425885	141	15	sampled	sample	VBN
10_1101-2021_01_08_425885	141	16	from	from	IN
10_1101-2021_01_08_425885	141	17	the	the	DT
10_1101-2021_01_08_425885	141	18	d	d	NNP
10_1101-2021_01_08_425885	141	19	-	-	HYPH
10_1101-2021_01_08_425885	141	20	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	141	21	unit	unit	NN
10_1101-2021_01_08_425885	141	22	hypersphere	hypersphere	RB
10_1101-2021_01_08_425885	141	23	,	,	,
10_1101-2021_01_08_425885	141	24	Sd	Sd	NNP
10_1101-2021_01_08_425885	141	25	,	,	,
10_1101-2021_01_08_425885	141	26	for	for	IN
10_1101-2021_01_08_425885	141	27	d	d	NN
10_1101-2021_01_08_425885	141	28	=	=	SYM
10_1101-2021_01_08_425885	141	29	2	2	CD
10_1101-2021_01_08_425885	141	30	,	,	,
10_1101-2021_01_08_425885	141	31	3	3	CD
10_1101-2021_01_08_425885	141	32	,	,	,
10_1101-2021_01_08_425885	141	33	5	5	CD
10_1101-2021_01_08_425885	141	34	,	,	,
10_1101-2021_01_08_425885	141	35	7	7	CD
10_1101-2021_01_08_425885	141	36	.	.	.
10_1101-2021_01_08_425885	142	1	As	as	IN
10_1101-2021_01_08_425885	142	2	with	with	IN
10_1101-2021_01_08_425885	142	3	S2	s2	NN
10_1101-2021_01_08_425885	142	4	,	,	,
10_1101-2021_01_08_425885	142	5	these	these	DT
10_1101-2021_01_08_425885	142	6	manifolds	manifold	NNS
10_1101-2021_01_08_425885	142	7	are	be	VBP
10_1101-2021_01_08_425885	142	8	isotropic	isotropic	JJ
10_1101-2021_01_08_425885	142	9	and	and	CC
10_1101-2021_01_08_425885	142	10	have	have	VBP
10_1101-2021_01_08_425885	142	11	constant	constant	JJ
10_1101-2021_01_08_425885	142	12	scalar	scalar	JJ
10_1101-2021_01_08_425885	142	13	curvature	curvature	NN
10_1101-2021_01_08_425885	142	14	.	.	.
10_1101-2021_01_08_425885	143	1	The	the	DT
10_1101-2021_01_08_425885	143	2	true	true	JJ
10_1101-2021_01_08_425885	143	3	values	value	NNS
10_1101-2021_01_08_425885	143	4	are	be	VBP
10_1101-2021_01_08_425885	143	5	shown	show	VBN
10_1101-2021_01_08_425885	143	6	as	as	IN
10_1101-2021_01_08_425885	143	7	dashed	dash	VBN
10_1101-2021_01_08_425885	143	8	red	red	JJ
10_1101-2021_01_08_425885	143	9	lines	line	NNS
10_1101-2021_01_08_425885	143	10	.	.	.
10_1101-2021_01_08_425885	144	1	See	see	VB
10_1101-2021_01_08_425885	144	2	Methods	Methods	NNP
10_1101-2021_01_08_425885	144	3	Section	Section	NNP
10_1101-2021_01_08_425885	144	4	4.4.1.1	4.4.1.1	CD
10_1101-2021_01_08_425885	144	5	.	.	.
10_1101-2021_01_08_425885	145	1	9	9	CD
10_1101-2021_01_08_425885	145	2	.CC	.CC	:
10_1101-2021_01_08_425885	145	3	-	-	HYPH
10_1101-2021_01_08_425885	145	4	BY	by	IN
10_1101-2021_01_08_425885	145	5	-	-	HYPH
10_1101-2021_01_08_425885	145	6	NC	NC	NNP
10_1101-2021_01_08_425885	145	7	-	-	HYPH
10_1101-2021_01_08_425885	145	8	ND	ND	NNP
10_1101-2021_01_08_425885	145	9	4.0	4.0	CD
10_1101-2021_01_08_425885	145	10	International	International	NNP
10_1101-2021_01_08_425885	145	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	145	12	under	under	IN
10_1101-2021_01_08_425885	145	13	a	a	DT
10_1101-2021_01_08_425885	145	14	(	(	-LRB-
10_1101-2021_01_08_425885	145	15	which	which	WDT
10_1101-2021_01_08_425885	145	16	was	be	VBD
10_1101-2021_01_08_425885	145	17	not	not	RB
10_1101-2021_01_08_425885	145	18	certified	certify	VBN
10_1101-2021_01_08_425885	145	19	by	by	IN
10_1101-2021_01_08_425885	145	20	peer	peer	NN
10_1101-2021_01_08_425885	145	21	review	review	NN
10_1101-2021_01_08_425885	145	22	)	)	-RRB-
10_1101-2021_01_08_425885	145	23	is	be	VBZ
10_1101-2021_01_08_425885	145	24	the	the	DT
10_1101-2021_01_08_425885	145	25	author	author	NN
10_1101-2021_01_08_425885	145	26	/	/	SYM
10_1101-2021_01_08_425885	145	27	funder	funder	NN
10_1101-2021_01_08_425885	145	28	,	,	,
10_1101-2021_01_08_425885	145	29	who	who	WP
10_1101-2021_01_08_425885	145	30	has	have	VBZ
10_1101-2021_01_08_425885	145	31	granted	grant	VBN
10_1101-2021_01_08_425885	145	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	145	33	a	a	DT
10_1101-2021_01_08_425885	145	34	license	license	NN
10_1101-2021_01_08_425885	145	35	to	to	TO
10_1101-2021_01_08_425885	145	36	display	display	VB
10_1101-2021_01_08_425885	145	37	the	the	DT
10_1101-2021_01_08_425885	145	38	preprint	preprint	NN
10_1101-2021_01_08_425885	145	39	in	in	IN
10_1101-2021_01_08_425885	145	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	145	41	.	.	.
10_1101-2021_01_08_425885	146	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	146	2	is	be	VBZ
10_1101-2021_01_08_425885	146	3	made	make	VBN
10_1101-2021_01_08_425885	146	4	The	the	DT
10_1101-2021_01_08_425885	146	5	copyright	copyright	NN
10_1101-2021_01_08_425885	146	6	holder	holder	NN
10_1101-2021_01_08_425885	146	7	for	for	IN
10_1101-2021_01_08_425885	146	8	this	this	DT
10_1101-2021_01_08_425885	146	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	146	10	version	version	NN
10_1101-2021_01_08_425885	146	11	posted	post	VBD
10_1101-2021_01_08_425885	146	12	January	January	NNP
10_1101-2021_01_08_425885	146	13	8	8	CD
10_1101-2021_01_08_425885	146	14	,	,	,
10_1101-2021_01_08_425885	146	15	2021	2021	CD
10_1101-2021_01_08_425885	146	16	.	.	.
10_1101-2021_01_08_425885	146	17	;	;	:
10_1101-2021_01_08_425885	146	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	146	19	:	:	:
10_1101-2021_01_08_425885	146	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	146	21	preprint	preprint	NN
10_1101-2021_01_08_425885	146	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	NNP
10_1101-2021_01_08_425885	146	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	CD
10_1101-2021_01_08_425885	146	24	are	be	VBP
10_1101-2021_01_08_425885	146	25	obtained	obtain	VBN
10_1101-2021_01_08_425885	146	26	using	use	VBG
10_1101-2021_01_08_425885	146	27	regression	regression	NN
10_1101-2021_01_08_425885	146	28	.	.	.
10_1101-2021_01_08_425885	147	1	Even	even	RB
10_1101-2021_01_08_425885	147	2	so	so	RB
10_1101-2021_01_08_425885	147	3	,	,	,
10_1101-2021_01_08_425885	147	4	the	the	DT
10_1101-2021_01_08_425885	147	5	components	component	NNS
10_1101-2021_01_08_425885	147	6	of	of	IN
10_1101-2021_01_08_425885	147	7	the	the	DT
10_1101-2021_01_08_425885	147	8	Riemannian	riemannian	JJ
10_1101-2021_01_08_425885	147	9	curvature	curvature	NN
10_1101-2021_01_08_425885	147	10	tensor	tensor	NN
10_1101-2021_01_08_425885	147	11	,	,	,
10_1101-2021_01_08_425885	147	12	Rijkl	Rijkl	NNP
10_1101-2021_01_08_425885	147	13	,	,	,
10_1101-2021_01_08_425885	147	14	may	may	MD
10_1101-2021_01_08_425885	147	15	still	still	RB
10_1101-2021_01_08_425885	147	16	be	be	VB
10_1101-2021_01_08_425885	147	17	biased	biased	JJ
10_1101-2021_01_08_425885	147	18	because	because	IN
10_1101-2021_01_08_425885	147	19	they	-PRON-	PRP
10_1101-2021_01_08_425885	147	20	are	be	VBP
10_1101-2021_01_08_425885	147	21	non	non	JJ
10_1101-2021_01_08_425885	147	22	-	-	JJ
10_1101-2021_01_08_425885	147	23	linear	linear	JJ
10_1101-2021_01_08_425885	147	24	functions	function	NNS
10_1101-2021_01_08_425885	147	25	of	of	IN
10_1101-2021_01_08_425885	147	26	hkij	hkij	NNP
10_1101-2021_01_08_425885	147	27	.	.	.
10_1101-2021_01_08_425885	148	1	Note	note	VB
10_1101-2021_01_08_425885	148	2	that	that	IN
10_1101-2021_01_08_425885	148	3	for	for	IN
10_1101-2021_01_08_425885	148	4	S	S	NNP
10_1101-2021_01_08_425885	148	5	2	2	CD
10_1101-2021_01_08_425885	148	6	,	,	,
10_1101-2021_01_08_425885	148	7	this	this	DT
10_1101-2021_01_08_425885	148	8	bias	bias	NN
10_1101-2021_01_08_425885	148	9	is	be	VBZ
10_1101-2021_01_08_425885	148	10	the	the	DT
10_1101-2021_01_08_425885	148	11	same	same	JJ
10_1101-2021_01_08_425885	148	12	across	across	IN
10_1101-2021_01_08_425885	148	13	all	all	DT
10_1101-2021_01_08_425885	148	14	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	148	15	(	(	-LRB-
10_1101-2021_01_08_425885	148	16	because	because	IN
10_1101-2021_01_08_425885	148	17	of	of	IN
10_1101-2021_01_08_425885	148	18	the	the	DT
10_1101-2021_01_08_425885	148	19	isotropic	isotropic	JJ
10_1101-2021_01_08_425885	148	20	nature	nature	NN
10_1101-2021_01_08_425885	148	21	of	of	IN
10_1101-2021_01_08_425885	148	22	the	the	DT
10_1101-2021_01_08_425885	148	23	manifold	manifold	NN
10_1101-2021_01_08_425885	148	24	)	)	-RRB-
10_1101-2021_01_08_425885	148	25	and	and	CC
10_1101-2021_01_08_425885	148	26	therefore	therefore	RB
10_1101-2021_01_08_425885	148	27	results	result	VBZ
10_1101-2021_01_08_425885	148	28	in	in	IN
10_1101-2021_01_08_425885	148	29	a	a	DT
10_1101-2021_01_08_425885	148	30	systematic	systematic	JJ
10_1101-2021_01_08_425885	148	31	under-	under-	JJ
10_1101-2021_01_08_425885	148	32	estimation	estimation	NN
10_1101-2021_01_08_425885	148	33	of	of	IN
10_1101-2021_01_08_425885	148	34	scalar	scalar	JJ
10_1101-2021_01_08_425885	148	35	curvature	curvature	NN
10_1101-2021_01_08_425885	148	36	(	(	-LRB-
10_1101-2021_01_08_425885	148	37	see	see	VB
10_1101-2021_01_08_425885	148	38	Figure	figure	NN
10_1101-2021_01_08_425885	148	39	2C	2c	NN
10_1101-2021_01_08_425885	148	40	;	;	:
10_1101-2021_01_08_425885	148	41	Methods	Methods	NNP
10_1101-2021_01_08_425885	148	42	Sections	Sections	NNPS
10_1101-2021_01_08_425885	148	43	4.3.4	4.3.4	CD
10_1101-2021_01_08_425885	148	44	)	)	-RRB-
10_1101-2021_01_08_425885	148	45	.	.	.
10_1101-2021_01_08_425885	149	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	149	2	also	also	RB
10_1101-2021_01_08_425885	149	3	computed	compute	VBD
10_1101-2021_01_08_425885	149	4	95	95	CD
10_1101-2021_01_08_425885	149	5	%	%	NN
10_1101-2021_01_08_425885	149	6	confidence	confidence	NN
10_1101-2021_01_08_425885	149	7	intervals	interval	NNS
10_1101-2021_01_08_425885	149	8	(	(	-LRB-
10_1101-2021_01_08_425885	149	9	CI	CI	NNP
10_1101-2021_01_08_425885	149	10	)	)	-RRB-
10_1101-2021_01_08_425885	149	11	for	for	IN
10_1101-2021_01_08_425885	149	12	our	-PRON-	PRP$
10_1101-2021_01_08_425885	149	13	estimates	estimate	NNS
10_1101-2021_01_08_425885	149	14	as	as	IN
10_1101-2021_01_08_425885	149	15	S	S	NNP
10_1101-2021_01_08_425885	149	16	±	±	NNP
10_1101-2021_01_08_425885	149	17	2σS	2σs	CD
10_1101-2021_01_08_425885	149	18	,	,	,
10_1101-2021_01_08_425885	149	19	and	and	CC
10_1101-2021_01_08_425885	149	20	despite	despite	IN
10_1101-2021_01_08_425885	149	21	the	the	DT
10_1101-2021_01_08_425885	149	22	mean	mean	JJ
10_1101-2021_01_08_425885	149	23	error	error	NN
10_1101-2021_01_08_425885	149	24	,	,	,
10_1101-2021_01_08_425885	149	25	73	73	CD
10_1101-2021_01_08_425885	149	26	%	%	NN
10_1101-2021_01_08_425885	149	27	of	of	IN
10_1101-2021_01_08_425885	149	28	points	point	NNS
10_1101-2021_01_08_425885	149	29	still	still	RB
10_1101-2021_01_08_425885	149	30	reported	report	VBD
10_1101-2021_01_08_425885	149	31	a	a	DT
10_1101-2021_01_08_425885	149	32	95	95	CD
10_1101-2021_01_08_425885	149	33	%	%	NN
10_1101-2021_01_08_425885	149	34	CI	ci	NN
10_1101-2021_01_08_425885	149	35	containing	contain	VBG
10_1101-2021_01_08_425885	149	36	the	the	DT
10_1101-2021_01_08_425885	149	37	true	true	JJ
10_1101-2021_01_08_425885	149	38	value	value	NN
10_1101-2021_01_08_425885	149	39	of	of	IN
10_1101-2021_01_08_425885	149	40	2	2	CD
10_1101-2021_01_08_425885	149	41	(	(	-LRB-
10_1101-2021_01_08_425885	149	42	see	see	VB
10_1101-2021_01_08_425885	149	43	Figure	Figure	NNP
10_1101-2021_01_08_425885	149	44	2D	2d	NN
10_1101-2021_01_08_425885	149	45	)	)	-RRB-
10_1101-2021_01_08_425885	149	46	.	.	.
10_1101-2021_01_08_425885	150	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	150	2	next	next	RB
10_1101-2021_01_08_425885	150	3	tested	test	VBD
10_1101-2021_01_08_425885	150	4	our	-PRON-	PRP$
10_1101-2021_01_08_425885	150	5	algorithm	algorithm	NN
10_1101-2021_01_08_425885	150	6	on	on	IN
10_1101-2021_01_08_425885	150	7	a	a	DT
10_1101-2021_01_08_425885	150	8	2-dimensional	2-dimensional	CD
10_1101-2021_01_08_425885	150	9	manifold	manifold	NN
10_1101-2021_01_08_425885	150	10	with	with	IN
10_1101-2021_01_08_425885	150	11	negative	negative	JJ
10_1101-2021_01_08_425885	150	12	scalar	scalar	JJ
10_1101-2021_01_08_425885	150	13	curvature	curvature	NN
10_1101-2021_01_08_425885	150	14	,	,	,
10_1101-2021_01_08_425885	150	15	by	by	IN
10_1101-2021_01_08_425885	150	16	uniformly	uniformly	RB
10_1101-2021_01_08_425885	150	17	sampling	sample	VBG
10_1101-2021_01_08_425885	150	18	N	n	NN
10_1101-2021_01_08_425885	150	19	=	=	SYM
10_1101-2021_01_08_425885	150	20	104	104	CD
10_1101-2021_01_08_425885	150	21	points	point	NNS
10_1101-2021_01_08_425885	150	22	from	from	IN
10_1101-2021_01_08_425885	150	23	the	the	DT
10_1101-2021_01_08_425885	150	24	one	one	CD
10_1101-2021_01_08_425885	150	25	-	-	HYPH
10_1101-2021_01_08_425885	150	26	sheet	sheet	NN
10_1101-2021_01_08_425885	150	27	hyperboloid	hyperboloid	NN
10_1101-2021_01_08_425885	150	28	,	,	,
10_1101-2021_01_08_425885	150	29	H22	H22	NNP
10_1101-2021_01_08_425885	150	30	(	(	-LRB-
10_1101-2021_01_08_425885	150	31	see	see	VB
10_1101-2021_01_08_425885	150	32	Figure	figure	NN
10_1101-2021_01_08_425885	150	33	2E	2e	NN
10_1101-2021_01_08_425885	150	34	;	;	:
10_1101-2021_01_08_425885	150	35	Methods	Methods	NNP
10_1101-2021_01_08_425885	150	36	Section	Section	NNP
10_1101-2021_01_08_425885	150	37	4.4.1.2	4.4.1.2	CD
10_1101-2021_01_08_425885	150	38	)	)	-RRB-
10_1101-2021_01_08_425885	150	39	.	.	.
10_1101-2021_01_08_425885	151	1	Here	here	RB
10_1101-2021_01_08_425885	151	2	,	,	,
10_1101-2021_01_08_425885	151	3	71	71	CD
10_1101-2021_01_08_425885	151	4	%	%	NN
10_1101-2021_01_08_425885	151	5	of	of	IN
10_1101-2021_01_08_425885	151	6	points	point	NNS
10_1101-2021_01_08_425885	151	7	reported	report	VBD
10_1101-2021_01_08_425885	151	8	a	a	DT
10_1101-2021_01_08_425885	151	9	95	95	CD
10_1101-2021_01_08_425885	151	10	%	%	NN
10_1101-2021_01_08_425885	151	11	CI	ci	NN
10_1101-2021_01_08_425885	151	12	containing	contain	VBG
10_1101-2021_01_08_425885	151	13	the	the	DT
10_1101-2021_01_08_425885	151	14	true	true	JJ
10_1101-2021_01_08_425885	151	15	scalar	scalar	JJ
10_1101-2021_01_08_425885	151	16	curvature	curvature	NN
10_1101-2021_01_08_425885	151	17	(	(	-LRB-
10_1101-2021_01_08_425885	151	18	see	see	VB
10_1101-2021_01_08_425885	151	19	Figure	Figure	NNP
10_1101-2021_01_08_425885	151	20	2F	2f	NN
10_1101-2021_01_08_425885	151	21	)	)	-RRB-
10_1101-2021_01_08_425885	151	22	.	.	.
10_1101-2021_01_08_425885	152	1	Lastly	lastly	RB
10_1101-2021_01_08_425885	152	2	,	,	,
10_1101-2021_01_08_425885	152	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	152	4	considered	consider	VBD
10_1101-2021_01_08_425885	152	5	the	the	DT
10_1101-2021_01_08_425885	152	6	2-dimensional	2-dimensional	CD
10_1101-2021_01_08_425885	152	7	ring	ring	NN
10_1101-2021_01_08_425885	152	8	torus	torus	NN
10_1101-2021_01_08_425885	152	9	,	,	,
10_1101-2021_01_08_425885	152	10	T	T	NNP
10_1101-2021_01_08_425885	152	11	2	2	CD
10_1101-2021_01_08_425885	152	12	(	(	-LRB-
10_1101-2021_01_08_425885	152	13	see	see	VB
10_1101-2021_01_08_425885	152	14	Figure	figure	NN
10_1101-2021_01_08_425885	152	15	2	2	CD
10_1101-2021_01_08_425885	152	16	G	g	NN
10_1101-2021_01_08_425885	152	17	;	;	:
10_1101-2021_01_08_425885	152	18	Methods	Methods	NNP
10_1101-2021_01_08_425885	152	19	Section	Section	NNP
10_1101-2021_01_08_425885	152	20	4.4.1.3	4.4.1.3	CD
10_1101-2021_01_08_425885	152	21	)	)	-RRB-
10_1101-2021_01_08_425885	152	22	.	.	.
10_1101-2021_01_08_425885	153	1	As	as	IN
10_1101-2021_01_08_425885	153	2	a	a	DT
10_1101-2021_01_08_425885	153	3	manifold	manifold	NN
10_1101-2021_01_08_425885	153	4	with	with	IN
10_1101-2021_01_08_425885	153	5	regions	region	NNS
10_1101-2021_01_08_425885	153	6	of	of	IN
10_1101-2021_01_08_425885	153	7	positive	positive	JJ
10_1101-2021_01_08_425885	153	8	,	,	,
10_1101-2021_01_08_425885	153	9	zero	zero	CD
10_1101-2021_01_08_425885	153	10	,	,	,
10_1101-2021_01_08_425885	153	11	and	and	CC
10_1101-2021_01_08_425885	153	12	negative	negative	JJ
10_1101-2021_01_08_425885	153	13	scalar	scalar	JJ
10_1101-2021_01_08_425885	153	14	curvature	curvature	NN
10_1101-2021_01_08_425885	153	15	,	,	,
10_1101-2021_01_08_425885	153	16	T	T	NNP
10_1101-2021_01_08_425885	153	17	2	2	CD
10_1101-2021_01_08_425885	153	18	is	be	VBZ
10_1101-2021_01_08_425885	153	19	a	a	DT
10_1101-2021_01_08_425885	153	20	useful	useful	JJ
10_1101-2021_01_08_425885	153	21	toy	toy	NN
10_1101-2021_01_08_425885	153	22	model	model	NN
10_1101-2021_01_08_425885	153	23	for	for	IN
10_1101-2021_01_08_425885	153	24	understanding	understand	VBG
10_1101-2021_01_08_425885	153	25	more	more	RBR
10_1101-2021_01_08_425885	153	26	complex	complex	JJ
10_1101-2021_01_08_425885	153	27	2-dimensional	2-dimensional	CD
10_1101-2021_01_08_425885	153	28	manifolds	manifold	NNS
10_1101-2021_01_08_425885	153	29	and	and	CC
10_1101-2021_01_08_425885	153	30	gaining	gain	VBG
10_1101-2021_01_08_425885	153	31	intuition	intuition	NN
10_1101-2021_01_08_425885	153	32	for	for	IN
10_1101-2021_01_08_425885	153	33	higher	high	JJR
10_1101-2021_01_08_425885	153	34	-	-	HYPH
10_1101-2021_01_08_425885	153	35	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	153	36	manifolds	manifold	NNS
10_1101-2021_01_08_425885	153	37	.	.	.
10_1101-2021_01_08_425885	154	1	In	in	IN
10_1101-2021_01_08_425885	154	2	2	2	CD
10_1101-2021_01_08_425885	154	3	dimensions	dimension	NNS
10_1101-2021_01_08_425885	154	4	,	,	,
10_1101-2021_01_08_425885	154	5	regions	region	NNS
10_1101-2021_01_08_425885	154	6	of	of	IN
10_1101-2021_01_08_425885	154	7	a	a	DT
10_1101-2021_01_08_425885	154	8	manifold	manifold	NN
10_1101-2021_01_08_425885	154	9	with	with	IN
10_1101-2021_01_08_425885	154	10	positive	positive	JJ
10_1101-2021_01_08_425885	154	11	scalar	scalar	JJ
10_1101-2021_01_08_425885	154	12	curvature	curvature	NN
10_1101-2021_01_08_425885	154	13	(	(	-LRB-
10_1101-2021_01_08_425885	154	14	θ	θ	NNP
10_1101-2021_01_08_425885	154	15	=	=	SYM
10_1101-2021_01_08_425885	154	16	0	0	CD
10_1101-2021_01_08_425885	154	17	,	,	,
10_1101-2021_01_08_425885	154	18	2π	2π	CD
10_1101-2021_01_08_425885	154	19	in	in	IN
10_1101-2021_01_08_425885	154	20	Figure	Figure	NNP
10_1101-2021_01_08_425885	154	21	2H	2h	NN
10_1101-2021_01_08_425885	154	22	)	)	-RRB-
10_1101-2021_01_08_425885	154	23	are	be	VBP
10_1101-2021_01_08_425885	154	24	dome	dome	NN
10_1101-2021_01_08_425885	154	25	-	-	HYPH
10_1101-2021_01_08_425885	154	26	shaped	shaped	JJ
10_1101-2021_01_08_425885	154	27	,	,	,
10_1101-2021_01_08_425885	154	28	regions	region	NNS
10_1101-2021_01_08_425885	154	29	with	with	IN
10_1101-2021_01_08_425885	154	30	zero	zero	CD
10_1101-2021_01_08_425885	154	31	scalar	scalar	JJ
10_1101-2021_01_08_425885	154	32	curvature	curvature	NN
10_1101-2021_01_08_425885	154	33	(	(	-LRB-
10_1101-2021_01_08_425885	154	34	θ	θ	NNP
10_1101-2021_01_08_425885	154	35	=	=	SYM
10_1101-2021_01_08_425885	154	36	π	π	NN
10_1101-2021_01_08_425885	154	37	2	2	CD
10_1101-2021_01_08_425885	154	38	,	,	,
10_1101-2021_01_08_425885	154	39	3π	3π	CD
10_1101-2021_01_08_425885	154	40	2	2	CD
10_1101-2021_01_08_425885	154	41	in	in	IN
10_1101-2021_01_08_425885	154	42	Figure	Figure	NNP
10_1101-2021_01_08_425885	154	43	2H	2h	NN
10_1101-2021_01_08_425885	154	44	)	)	-RRB-
10_1101-2021_01_08_425885	154	45	are	be	VBP
10_1101-2021_01_08_425885	154	46	planar	planar	JJ
10_1101-2021_01_08_425885	154	47	,	,	,
10_1101-2021_01_08_425885	154	48	and	and	CC
10_1101-2021_01_08_425885	154	49	regions	region	NNS
10_1101-2021_01_08_425885	154	50	with	with	IN
10_1101-2021_01_08_425885	154	51	negative	negative	JJ
10_1101-2021_01_08_425885	154	52	scalar	scalar	JJ
10_1101-2021_01_08_425885	154	53	curvature	curvature	NN
10_1101-2021_01_08_425885	154	54	(	(	-LRB-
10_1101-2021_01_08_425885	154	55	θ	θ	NNP
10_1101-2021_01_08_425885	154	56	=	=	SYM
10_1101-2021_01_08_425885	154	57	π	π	NN
10_1101-2021_01_08_425885	154	58	in	in	IN
10_1101-2021_01_08_425885	154	59	Figure	Figure	NNP
10_1101-2021_01_08_425885	154	60	2H	2h	NN
10_1101-2021_01_08_425885	154	61	)	)	-RRB-
10_1101-2021_01_08_425885	154	62	are	be	VBP
10_1101-2021_01_08_425885	154	63	saddle	saddle	NN
10_1101-2021_01_08_425885	154	64	-	-	HYPH
10_1101-2021_01_08_425885	154	65	shaped	shaped	JJ
10_1101-2021_01_08_425885	154	66	.	.	.
10_1101-2021_01_08_425885	155	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	155	2	applied	apply	VBD
10_1101-2021_01_08_425885	155	3	our	-PRON-	PRP$
10_1101-2021_01_08_425885	155	4	tool	tool	NN
10_1101-2021_01_08_425885	155	5	to	to	IN
10_1101-2021_01_08_425885	155	6	N	n	NN
10_1101-2021_01_08_425885	155	7	=	=	SYM
10_1101-2021_01_08_425885	155	8	104	104	CD
10_1101-2021_01_08_425885	155	9	points	point	NNS
10_1101-2021_01_08_425885	155	10	uniformly	uniformly	RB
10_1101-2021_01_08_425885	155	11	sampled	sample	VBN
10_1101-2021_01_08_425885	155	12	from	from	IN
10_1101-2021_01_08_425885	155	13	T	T	NNP
10_1101-2021_01_08_425885	155	14	2	2	CD
10_1101-2021_01_08_425885	155	15	and	and	CC
10_1101-2021_01_08_425885	155	16	found	find	VBD
10_1101-2021_01_08_425885	155	17	that	that	IN
10_1101-2021_01_08_425885	155	18	88	88	CD
10_1101-2021_01_08_425885	155	19	%	%	NN
10_1101-2021_01_08_425885	155	20	of	of	IN
10_1101-2021_01_08_425885	155	21	points	point	NNS
10_1101-2021_01_08_425885	155	22	reported	report	VBD
10_1101-2021_01_08_425885	155	23	a	a	DT
10_1101-2021_01_08_425885	155	24	95	95	CD
10_1101-2021_01_08_425885	155	25	%	%	NN
10_1101-2021_01_08_425885	155	26	CI	ci	NN
10_1101-2021_01_08_425885	155	27	containing	contain	VBG
10_1101-2021_01_08_425885	155	28	the	the	DT
10_1101-2021_01_08_425885	155	29	true	true	JJ
10_1101-2021_01_08_425885	155	30	scalar	scalar	JJ
10_1101-2021_01_08_425885	155	31	curvature	curvature	NN
10_1101-2021_01_08_425885	155	32	(	(	-LRB-
10_1101-2021_01_08_425885	155	33	see	see	VB
10_1101-2021_01_08_425885	155	34	Figure	Figure	NNP
10_1101-2021_01_08_425885	155	35	2H	2h	NN
10_1101-2021_01_08_425885	155	36	)	)	-RRB-
10_1101-2021_01_08_425885	155	37	.	.	.
10_1101-2021_01_08_425885	156	1	To	to	TO
10_1101-2021_01_08_425885	156	2	test	test	VB
10_1101-2021_01_08_425885	156	3	the	the	DT
10_1101-2021_01_08_425885	156	4	applicability	applicability	NN
10_1101-2021_01_08_425885	156	5	of	of	IN
10_1101-2021_01_08_425885	156	6	our	-PRON-	PRP$
10_1101-2021_01_08_425885	156	7	algorithm	algorithm	NN
10_1101-2021_01_08_425885	156	8	to	to	IN
10_1101-2021_01_08_425885	156	9	higher	higher	RBR
10_1101-2021_01_08_425885	156	10	-	-	HYPH
10_1101-2021_01_08_425885	156	11	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	156	12	manifolds	manifold	NNS
10_1101-2021_01_08_425885	156	13	,	,	,
10_1101-2021_01_08_425885	156	14	we	-PRON-	PRP
10_1101-2021_01_08_425885	156	15	uniformly	uniformly	RB
10_1101-2021_01_08_425885	156	16	sampled	sample	VBD
10_1101-2021_01_08_425885	156	17	N	n	NN
10_1101-2021_01_08_425885	156	18	=	=	SYM
10_1101-2021_01_08_425885	156	19	104	104	CD
10_1101-2021_01_08_425885	156	20	points	point	NNS
10_1101-2021_01_08_425885	156	21	from	from	IN
10_1101-2021_01_08_425885	156	22	unit	unit	NN
10_1101-2021_01_08_425885	156	23	hyperspheres	hypersphere	NNS
10_1101-2021_01_08_425885	156	24	,	,	,
10_1101-2021_01_08_425885	156	25	Sd	Sd	NNP
10_1101-2021_01_08_425885	156	26	,	,	,
10_1101-2021_01_08_425885	156	27	and	and	CC
10_1101-2021_01_08_425885	156	28	found	find	VBD
10_1101-2021_01_08_425885	156	29	that	that	IN
10_1101-2021_01_08_425885	156	30	90	90	CD
10_1101-2021_01_08_425885	156	31	%	%	NN
10_1101-2021_01_08_425885	156	32	,	,	,
10_1101-2021_01_08_425885	156	33	84	84	CD
10_1101-2021_01_08_425885	156	34	%	%	NN
10_1101-2021_01_08_425885	156	35	and	and	CC
10_1101-2021_01_08_425885	156	36	78	78	CD
10_1101-2021_01_08_425885	156	37	%	%	NN
10_1101-2021_01_08_425885	156	38	of	of	IN
10_1101-2021_01_08_425885	156	39	points	point	NNS
10_1101-2021_01_08_425885	156	40	reported	report	VBD
10_1101-2021_01_08_425885	156	41	a	a	DT
10_1101-2021_01_08_425885	156	42	95	95	CD
10_1101-2021_01_08_425885	156	43	%	%	NN
10_1101-2021_01_08_425885	156	44	CI	ci	NN
10_1101-2021_01_08_425885	156	45	containing	contain	VBG
10_1101-2021_01_08_425885	156	46	the	the	DT
10_1101-2021_01_08_425885	156	47	true	true	JJ
10_1101-2021_01_08_425885	156	48	scalar	scalar	JJ
10_1101-2021_01_08_425885	156	49	curvature	curvature	NN
10_1101-2021_01_08_425885	156	50	for	for	IN
10_1101-2021_01_08_425885	156	51	d	d	NN
10_1101-2021_01_08_425885	156	52	=	=	SYM
10_1101-2021_01_08_425885	156	53	3	3	CD
10_1101-2021_01_08_425885	156	54	,	,	,
10_1101-2021_01_08_425885	156	55	5	5	CD
10_1101-2021_01_08_425885	156	56	and	and	CC
10_1101-2021_01_08_425885	156	57	7	7	CD
10_1101-2021_01_08_425885	156	58	respectively	respectively	RB
10_1101-2021_01_08_425885	156	59	(	(	-LRB-
10_1101-2021_01_08_425885	156	60	see	see	VB
10_1101-2021_01_08_425885	156	61	Figure	figure	NN
10_1101-2021_01_08_425885	156	62	2I	2i	NN
10_1101-2021_01_08_425885	156	63	;	;	:
10_1101-2021_01_08_425885	156	64	Methods	Methods	NNP
10_1101-2021_01_08_425885	156	65	Section	Section	NNP
10_1101-2021_01_08_425885	156	66	4.4.1.1	4.4.1.1	CD
10_1101-2021_01_08_425885	156	67	)	)	-RRB-
10_1101-2021_01_08_425885	156	68	.	.	.
10_1101-2021_01_08_425885	157	1	The	the	DT
10_1101-2021_01_08_425885	157	2	number	number	NN
10_1101-2021_01_08_425885	157	3	of	of	IN
10_1101-2021_01_08_425885	157	4	terms	term	NNS
10_1101-2021_01_08_425885	157	5	,	,	,
10_1101-2021_01_08_425885	157	6	hkij	hkij	NNP
10_1101-2021_01_08_425885	157	7	,	,	,
10_1101-2021_01_08_425885	157	8	in	in	IN
10_1101-2021_01_08_425885	157	9	the	the	DT
10_1101-2021_01_08_425885	157	10	Second	Second	NNP
10_1101-2021_01_08_425885	157	11	Fundamental	Fundamental	NNP
10_1101-2021_01_08_425885	157	12	Form	Form	NNP
10_1101-2021_01_08_425885	157	13	grows	grow	VBZ
10_1101-2021_01_08_425885	157	14	as	as	IN
10_1101-2021_01_08_425885	157	15	d	d	NN
10_1101-2021_01_08_425885	157	16	2	2	CD
10_1101-2021_01_08_425885	157	17	.	.	.
10_1101-2021_01_08_425885	158	1	For	for	IN
10_1101-2021_01_08_425885	158	2	larger	large	JJR
10_1101-2021_01_08_425885	158	3	d	d	NN
10_1101-2021_01_08_425885	158	4	,	,	,
10_1101-2021_01_08_425885	158	5	a	a	DT
10_1101-2021_01_08_425885	158	6	greater	great	JJR
10_1101-2021_01_08_425885	158	7	number	number	NN
10_1101-2021_01_08_425885	158	8	of	of	IN
10_1101-2021_01_08_425885	158	9	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	158	10	and	and	CC
10_1101-2021_01_08_425885	158	11	hence	hence	RB
10_1101-2021_01_08_425885	158	12	larger	large	JJR
10_1101-2021_01_08_425885	158	13	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	158	14	are	be	VBP
10_1101-2021_01_08_425885	158	15	needed	need	VBN
10_1101-2021_01_08_425885	158	16	for	for	IN
10_1101-2021_01_08_425885	158	17	regression	regression	NN
10_1101-2021_01_08_425885	158	18	,	,	,
10_1101-2021_01_08_425885	158	19	but	but	CC
10_1101-2021_01_08_425885	158	20	these	these	DT
10_1101-2021_01_08_425885	158	21	are	be	VBP
10_1101-2021_01_08_425885	158	22	no	no	RB
10_1101-2021_01_08_425885	158	23	longer	long	RBR
10_1101-2021_01_08_425885	158	24	well	well	RB
10_1101-2021_01_08_425885	158	25	-	-	HYPH
10_1101-2021_01_08_425885	158	26	approximated	approximate	VBN
10_1101-2021_01_08_425885	158	27	by	by	IN
10_1101-2021_01_08_425885	158	28	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	158	29	fits	fit	NNS
10_1101-2021_01_08_425885	158	30	according	accord	VBG
10_1101-2021_01_08_425885	158	31	to	to	IN
10_1101-2021_01_08_425885	158	32	our	-PRON-	PRP$
10_1101-2021_01_08_425885	158	33	GOF	GOF	NNP
10_1101-2021_01_08_425885	158	34	measure	measure	NN
10_1101-2021_01_08_425885	158	35	.	.	.
10_1101-2021_01_08_425885	159	1	More	more	RBR
10_1101-2021_01_08_425885	159	2	generally	generally	RB
10_1101-2021_01_08_425885	159	3	,	,	,
10_1101-2021_01_08_425885	159	4	higher	high	JJR
10_1101-2021_01_08_425885	159	5	-	-	HYPH
10_1101-2021_01_08_425885	159	6	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	159	7	manifolds	manifold	NNS
10_1101-2021_01_08_425885	159	8	require	require	VBP
10_1101-2021_01_08_425885	159	9	a	a	DT
10_1101-2021_01_08_425885	159	10	higher	high	JJR
10_1101-2021_01_08_425885	159	11	density	density	NN
10_1101-2021_01_08_425885	159	12	of	of	IN
10_1101-2021_01_08_425885	159	13	data	datum	NNS
10_1101-2021_01_08_425885	159	14	to	to	TO
10_1101-2021_01_08_425885	159	15	estimate	estimate	VB
10_1101-2021_01_08_425885	159	16	scalar	scalar	JJ
10_1101-2021_01_08_425885	159	17	curvatures	curvature	NNS
10_1101-2021_01_08_425885	159	18	accurately	accurately	RB
10_1101-2021_01_08_425885	159	19	.	.	.
10_1101-2021_01_08_425885	160	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	160	2	additionally	additionally	RB
10_1101-2021_01_08_425885	160	3	characterized	characterize	VBD
10_1101-2021_01_08_425885	160	4	how	how	WRB
10_1101-2021_01_08_425885	160	5	our	-PRON-	PRP$
10_1101-2021_01_08_425885	160	6	algorithm	algorithm	NN
10_1101-2021_01_08_425885	160	7	performed	perform	VBD
10_1101-2021_01_08_425885	160	8	when	when	WRB
10_1101-2021_01_08_425885	160	9	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	160	10	were	be	VBD
10_1101-2021_01_08_425885	160	11	non	non	JJ
10_1101-2021_01_08_425885	160	12	-	-	JJ
10_1101-2021_01_08_425885	160	13	uniformly	uniformly	RB
10_1101-2021_01_08_425885	160	14	sampled	sample	VBN
10_1101-2021_01_08_425885	160	15	(	(	-LRB-
10_1101-2021_01_08_425885	160	16	see	see	VB
10_1101-2021_01_08_425885	160	17	Figure	figure	NN
10_1101-2021_01_08_425885	160	18	S2A	s2a	NN
10_1101-2021_01_08_425885	160	19	;	;	:
10_1101-2021_01_08_425885	160	20	Methods	Methods	NNP
10_1101-2021_01_08_425885	160	21	Section	Section	NNP
10_1101-2021_01_08_425885	160	22	4.4.2.1	4.4.2.1	CD
10_1101-2021_01_08_425885	160	23	)	)	-RRB-
10_1101-2021_01_08_425885	160	24	or	or	CC
10_1101-2021_01_08_425885	160	25	convoluted	convolute	VBN
10_1101-2021_01_08_425885	160	26	by	by	IN
10_1101-2021_01_08_425885	160	27	observational	observational	JJ
10_1101-2021_01_08_425885	160	28	noise	noise	NN
10_1101-2021_01_08_425885	160	29	(	(	-LRB-
10_1101-2021_01_08_425885	160	30	see	see	VB
10_1101-2021_01_08_425885	160	31	Figure	figure	NN
10_1101-2021_01_08_425885	160	32	S2B	s2b	NN
10_1101-2021_01_08_425885	160	33	;	;	:
10_1101-2021_01_08_425885	160	34	Methods	Methods	NNP
10_1101-2021_01_08_425885	160	35	Sec-	Sec-	NNP
10_1101-2021_01_08_425885	160	36	tion	tion	NN
10_1101-2021_01_08_425885	160	37	4.4.2.2	4.4.2.2	CD
10_1101-2021_01_08_425885	160	38	)	)	-RRB-
10_1101-2021_01_08_425885	160	39	,	,	,
10_1101-2021_01_08_425885	160	40	when	when	WRB
10_1101-2021_01_08_425885	160	41	the	the	DT
10_1101-2021_01_08_425885	160	42	dimension	dimension	NN
10_1101-2021_01_08_425885	160	43	of	of	IN
10_1101-2021_01_08_425885	160	44	the	the	DT
10_1101-2021_01_08_425885	160	45	ambient	ambient	JJ
10_1101-2021_01_08_425885	160	46	space	space	NN
10_1101-2021_01_08_425885	160	47	was	be	VBD
10_1101-2021_01_08_425885	160	48	large	large	JJ
10_1101-2021_01_08_425885	160	49	(	(	-LRB-
10_1101-2021_01_08_425885	160	50	see	see	VB
10_1101-2021_01_08_425885	160	51	Figure	figure	NN
10_1101-2021_01_08_425885	160	52	S2C	s2c	NN
10_1101-2021_01_08_425885	160	53	;	;	:
10_1101-2021_01_08_425885	160	54	Methods	Methods	NNP
10_1101-2021_01_08_425885	160	55	Section	Section	NNP
10_1101-2021_01_08_425885	160	56	4.4.2.3	4.4.2.3	CD
10_1101-2021_01_08_425885	160	57	)	)	-RRB-
10_1101-2021_01_08_425885	160	58	,	,	,
10_1101-2021_01_08_425885	160	59	and	and	CC
10_1101-2021_01_08_425885	160	60	when	when	WRB
10_1101-2021_01_08_425885	160	61	the	the	DT
10_1101-2021_01_08_425885	160	62	specified	specify	VBN
10_1101-2021_01_08_425885	160	63	manifold	manifold	JJ
10_1101-2021_01_08_425885	160	64	dimension	dimension	NN
10_1101-2021_01_08_425885	160	65	differed	differ	VBN
10_1101-2021_01_08_425885	160	66	from	from	IN
10_1101-2021_01_08_425885	160	67	the	the	DT
10_1101-2021_01_08_425885	160	68	ground	ground	NN
10_1101-2021_01_08_425885	160	69	truth	truth	NN
10_1101-2021_01_08_425885	160	70	(	(	-LRB-
10_1101-2021_01_08_425885	160	71	see	see	VB
10_1101-2021_01_08_425885	160	72	Figure	figure	NN
10_1101-2021_01_08_425885	160	73	S2D	s2d	NN
10_1101-2021_01_08_425885	160	74	;	;	:
10_1101-2021_01_08_425885	160	75	Methods	Methods	NNP
10_1101-2021_01_08_425885	160	76	Sec-	Sec-	NNP
10_1101-2021_01_08_425885	160	77	tion	tion	NN
10_1101-2021_01_08_425885	160	78	4.4.2.4	4.4.2.4	CD
10_1101-2021_01_08_425885	160	79	)	)	-RRB-
10_1101-2021_01_08_425885	160	80	.	.	.
10_1101-2021_01_08_425885	161	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	161	2	found	find	VBD
10_1101-2021_01_08_425885	161	3	that	that	IN
10_1101-2021_01_08_425885	161	4	the	the	DT
10_1101-2021_01_08_425885	161	5	algorithm	algorithm	NN
10_1101-2021_01_08_425885	161	6	is	be	VBZ
10_1101-2021_01_08_425885	161	7	robust	robust	JJ
10_1101-2021_01_08_425885	161	8	to	to	IN
10_1101-2021_01_08_425885	161	9	non	non	JJ
10_1101-2021_01_08_425885	161	10	-	-	JJ
10_1101-2021_01_08_425885	161	11	uniform	uniform	JJ
10_1101-2021_01_08_425885	161	12	sampling	sampling	NN
10_1101-2021_01_08_425885	161	13	,	,	,
10_1101-2021_01_08_425885	161	14	large	large	JJ
10_1101-2021_01_08_425885	161	15	ambient	ambient	JJ
10_1101-2021_01_08_425885	161	16	dimension	dimension	NN
10_1101-2021_01_08_425885	161	17	and	and	CC
10_1101-2021_01_08_425885	161	18	small	small	JJ
10_1101-2021_01_08_425885	161	19	observational	observational	JJ
10_1101-2021_01_08_425885	161	20	noise	noise	NN
10_1101-2021_01_08_425885	161	21	,	,	,
10_1101-2021_01_08_425885	161	22	and	and	CC
10_1101-2021_01_08_425885	161	23	provides	provide	VBZ
10_1101-2021_01_08_425885	161	24	signatures	signature	NNS
10_1101-2021_01_08_425885	161	25	indicating	indicate	VBG
10_1101-2021_01_08_425885	161	26	when	when	WRB
10_1101-2021_01_08_425885	161	27	the	the	DT
10_1101-2021_01_08_425885	161	28	manifold	manifold	JJ
10_1101-2021_01_08_425885	161	29	dimension	dimension	NN
10_1101-2021_01_08_425885	161	30	may	may	MD
10_1101-2021_01_08_425885	161	31	be	be	VB
10_1101-2021_01_08_425885	161	32	mis-	mis-	RB
10_1101-2021_01_08_425885	161	33	specified	specify	VBN
10_1101-2021_01_08_425885	161	34	.	.	.
10_1101-2021_01_08_425885	162	1	However	however	RB
10_1101-2021_01_08_425885	162	2	,	,	,
10_1101-2021_01_08_425885	162	3	when	when	WRB
10_1101-2021_01_08_425885	162	4	the	the	DT
10_1101-2021_01_08_425885	162	5	noise	noise	NN
10_1101-2021_01_08_425885	162	6	scale	scale	NN
10_1101-2021_01_08_425885	162	7	is	be	VBZ
10_1101-2021_01_08_425885	162	8	large	large	JJ
10_1101-2021_01_08_425885	162	9	,	,	,
10_1101-2021_01_08_425885	162	10	the	the	DT
10_1101-2021_01_08_425885	162	11	resulting	result	VBG
10_1101-2021_01_08_425885	162	12	manifold	manifold	NN
10_1101-2021_01_08_425885	162	13	is	be	VBZ
10_1101-2021_01_08_425885	162	14	no	no	DT
10_1101-2021_01_08_425885	162	15	longer	long	RBR
10_1101-2021_01_08_425885	162	16	trivially	trivially	RB
10_1101-2021_01_08_425885	162	17	related	related	JJ
10_1101-2021_01_08_425885	162	18	to	to	IN
10_1101-2021_01_08_425885	162	19	the	the	DT
10_1101-2021_01_08_425885	162	20	noise	noise	NN
10_1101-2021_01_08_425885	162	21	-	-	HYPH
10_1101-2021_01_08_425885	162	22	free	free	JJ
10_1101-2021_01_08_425885	162	23	manifold	manifold	NN
10_1101-2021_01_08_425885	162	24	,	,	,
10_1101-2021_01_08_425885	162	25	consistent	consistent	JJ
10_1101-2021_01_08_425885	162	26	with	with	IN
10_1101-2021_01_08_425885	162	27	existing	exist	VBG
10_1101-2021_01_08_425885	162	28	literature	literature	NN
10_1101-2021_01_08_425885	162	29	[	[	-LRB-
10_1101-2021_01_08_425885	162	30	34	34	CD
10_1101-2021_01_08_425885	162	31	,	,	,
10_1101-2021_01_08_425885	162	32	35	35	CD
10_1101-2021_01_08_425885	162	33	,	,	,
10_1101-2021_01_08_425885	162	34	36	36	CD
10_1101-2021_01_08_425885	162	35	,	,	,
10_1101-2021_01_08_425885	162	36	37	37	CD
10_1101-2021_01_08_425885	162	37	]	]	-RRB-
10_1101-2021_01_08_425885	162	38	,	,	,
10_1101-2021_01_08_425885	162	39	so	so	IN
10_1101-2021_01_08_425885	162	40	that	that	IN
10_1101-2021_01_08_425885	162	41	scalar	scalar	JJ
10_1101-2021_01_08_425885	162	42	curvature	curvature	NN
10_1101-2021_01_08_425885	162	43	can	can	MD
10_1101-2021_01_08_425885	162	44	not	not	RB
10_1101-2021_01_08_425885	162	45	be	be	VB
10_1101-2021_01_08_425885	162	46	accurately	accurately	RB
10_1101-2021_01_08_425885	162	47	computed	compute	VBN
10_1101-2021_01_08_425885	162	48	.	.	.
10_1101-2021_01_08_425885	163	1	Lastly	lastly	RB
10_1101-2021_01_08_425885	163	2	,	,	,
10_1101-2021_01_08_425885	163	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	163	4	note	note	VBP
10_1101-2021_01_08_425885	163	5	that	that	IN
10_1101-2021_01_08_425885	163	6	since	since	IN
10_1101-2021_01_08_425885	163	7	the	the	DT
10_1101-2021_01_08_425885	163	8	full	full	JJ
10_1101-2021_01_08_425885	163	9	Riemannian	riemannian	JJ
10_1101-2021_01_08_425885	163	10	curvature	curvature	JJ
10_1101-2021_01_08_425885	163	11	tensor	tensor	NN
10_1101-2021_01_08_425885	163	12	is	be	VBZ
10_1101-2021_01_08_425885	163	13	computed	compute	VBN
10_1101-2021_01_08_425885	163	14	as	as	IN
10_1101-2021_01_08_425885	163	15	an	an	DT
10_1101-2021_01_08_425885	163	16	10	10	CD
10_1101-2021_01_08_425885	163	17	.CC	.cc	CD
10_1101-2021_01_08_425885	163	18	-	-	HYPH
10_1101-2021_01_08_425885	163	19	BY	by	IN
10_1101-2021_01_08_425885	163	20	-	-	HYPH
10_1101-2021_01_08_425885	163	21	NC	NC	NNP
10_1101-2021_01_08_425885	163	22	-	-	HYPH
10_1101-2021_01_08_425885	163	23	ND	ND	NNP
10_1101-2021_01_08_425885	163	24	4.0	4.0	CD
10_1101-2021_01_08_425885	163	25	International	International	NNP
10_1101-2021_01_08_425885	163	26	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	163	27	under	under	IN
10_1101-2021_01_08_425885	163	28	a	a	DT
10_1101-2021_01_08_425885	163	29	(	(	-LRB-
10_1101-2021_01_08_425885	163	30	which	which	WDT
10_1101-2021_01_08_425885	163	31	was	be	VBD
10_1101-2021_01_08_425885	163	32	not	not	RB
10_1101-2021_01_08_425885	163	33	certified	certify	VBN
10_1101-2021_01_08_425885	163	34	by	by	IN
10_1101-2021_01_08_425885	163	35	peer	peer	NN
10_1101-2021_01_08_425885	163	36	review	review	NN
10_1101-2021_01_08_425885	163	37	)	)	-RRB-
10_1101-2021_01_08_425885	163	38	is	be	VBZ
10_1101-2021_01_08_425885	163	39	the	the	DT
10_1101-2021_01_08_425885	163	40	author	author	NN
10_1101-2021_01_08_425885	163	41	/	/	SYM
10_1101-2021_01_08_425885	163	42	funder	funder	NN
10_1101-2021_01_08_425885	163	43	,	,	,
10_1101-2021_01_08_425885	163	44	who	who	WP
10_1101-2021_01_08_425885	163	45	has	have	VBZ
10_1101-2021_01_08_425885	163	46	granted	grant	VBN
10_1101-2021_01_08_425885	163	47	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	163	48	a	a	DT
10_1101-2021_01_08_425885	163	49	license	license	NN
10_1101-2021_01_08_425885	163	50	to	to	TO
10_1101-2021_01_08_425885	163	51	display	display	VB
10_1101-2021_01_08_425885	163	52	the	the	DT
10_1101-2021_01_08_425885	163	53	preprint	preprint	NN
10_1101-2021_01_08_425885	163	54	in	in	IN
10_1101-2021_01_08_425885	163	55	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	163	56	.	.	.
10_1101-2021_01_08_425885	164	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	164	2	is	be	VBZ
10_1101-2021_01_08_425885	164	3	made	make	VBN
10_1101-2021_01_08_425885	164	4	The	the	DT
10_1101-2021_01_08_425885	164	5	copyright	copyright	NN
10_1101-2021_01_08_425885	164	6	holder	holder	NN
10_1101-2021_01_08_425885	164	7	for	for	IN
10_1101-2021_01_08_425885	164	8	this	this	DT
10_1101-2021_01_08_425885	164	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	164	10	version	version	NN
10_1101-2021_01_08_425885	164	11	posted	post	VBD
10_1101-2021_01_08_425885	164	12	January	January	NNP
10_1101-2021_01_08_425885	164	13	8	8	CD
10_1101-2021_01_08_425885	164	14	,	,	,
10_1101-2021_01_08_425885	164	15	2021	2021	CD
10_1101-2021_01_08_425885	164	16	.	.	.
10_1101-2021_01_08_425885	164	17	;	;	:
10_1101-2021_01_08_425885	164	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	164	19	:	:	:
10_1101-2021_01_08_425885	164	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	164	21	preprint	preprint	NN
10_1101-2021_01_08_425885	164	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	NNP
10_1101-2021_01_08_425885	164	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	CD
10_1101-2021_01_08_425885	164	24	intermediate	intermediate	JJ
10_1101-2021_01_08_425885	164	25	step	step	NN
10_1101-2021_01_08_425885	164	26	in	in	IN
10_1101-2021_01_08_425885	164	27	our	-PRON-	PRP$
10_1101-2021_01_08_425885	164	28	algorithm	algorithm	NN
10_1101-2021_01_08_425885	164	29	,	,	,
10_1101-2021_01_08_425885	164	30	more	more	RBR
10_1101-2021_01_08_425885	164	31	intricate	intricate	JJ
10_1101-2021_01_08_425885	164	32	geometric	geometric	JJ
10_1101-2021_01_08_425885	164	33	features	feature	NNS
10_1101-2021_01_08_425885	164	34	in	in	IN
10_1101-2021_01_08_425885	164	35	the	the	DT
10_1101-2021_01_08_425885	164	36	data	datum	NNS
10_1101-2021_01_08_425885	164	37	can	can	MD
10_1101-2021_01_08_425885	164	38	also	also	RB
10_1101-2021_01_08_425885	164	39	be	be	VB
10_1101-2021_01_08_425885	164	40	analyzed	analyze	VBN
10_1101-2021_01_08_425885	164	41	using	use	VBG
10_1101-2021_01_08_425885	164	42	our	-PRON-	PRP$
10_1101-2021_01_08_425885	164	43	tool	tool	NN
10_1101-2021_01_08_425885	164	44	,	,	,
10_1101-2021_01_08_425885	164	45	though	though	IN
10_1101-2021_01_08_425885	164	46	we	-PRON-	PRP
10_1101-2021_01_08_425885	164	47	defer	defer	VBP
10_1101-2021_01_08_425885	164	48	such	such	JJ
10_1101-2021_01_08_425885	164	49	investigation	investigation	NN
10_1101-2021_01_08_425885	164	50	to	to	IN
10_1101-2021_01_08_425885	164	51	future	future	JJ
10_1101-2021_01_08_425885	164	52	studies	study	NNS
10_1101-2021_01_08_425885	164	53	.	.	.
10_1101-2021_01_08_425885	165	1	Taken	take	VBN
10_1101-2021_01_08_425885	165	2	together	together	RB
10_1101-2021_01_08_425885	165	3	,	,	,
10_1101-2021_01_08_425885	165	4	these	these	DT
10_1101-2021_01_08_425885	165	5	examples	example	NNS
10_1101-2021_01_08_425885	165	6	demonstrate	demonstrate	VBP
10_1101-2021_01_08_425885	165	7	the	the	DT
10_1101-2021_01_08_425885	165	8	utility	utility	NN
10_1101-2021_01_08_425885	165	9	of	of	IN
10_1101-2021_01_08_425885	165	10	the	the	DT
10_1101-2021_01_08_425885	165	11	algorithm	algorithm	NN
10_1101-2021_01_08_425885	165	12	in	in	IN
10_1101-2021_01_08_425885	165	13	recovering	recover	VBG
10_1101-2021_01_08_425885	165	14	curvature	curvature	JJ
10_1101-2021_01_08_425885	165	15	with	with	IN
10_1101-2021_01_08_425885	165	16	specified	specified	JJ
10_1101-2021_01_08_425885	165	17	uncertainties	uncertainty	NNS
10_1101-2021_01_08_425885	165	18	for	for	IN
10_1101-2021_01_08_425885	165	19	manifolds	manifold	NNS
10_1101-2021_01_08_425885	165	20	with	with	IN
10_1101-2021_01_08_425885	165	21	positive	positive	JJ
10_1101-2021_01_08_425885	165	22	and/or	and/or	CC
10_1101-2021_01_08_425885	165	23	negative	negative	JJ
10_1101-2021_01_08_425885	165	24	scalar	scalar	JJ
10_1101-2021_01_08_425885	165	25	curvature	curvature	NN
10_1101-2021_01_08_425885	165	26	.	.	.
10_1101-2021_01_08_425885	166	1	Next	next	RB
10_1101-2021_01_08_425885	166	2	,	,	,
10_1101-2021_01_08_425885	166	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	166	4	tested	test	VBD
10_1101-2021_01_08_425885	166	5	our	-PRON-	PRP$
10_1101-2021_01_08_425885	166	6	algorithm	algorithm	NN
10_1101-2021_01_08_425885	166	7	on	on	IN
10_1101-2021_01_08_425885	166	8	real	real	JJ
10_1101-2021_01_08_425885	166	9	-	-	HYPH
10_1101-2021_01_08_425885	166	10	world	world	NN
10_1101-2021_01_08_425885	166	11	data	datum	NNS
10_1101-2021_01_08_425885	166	12	.	.	.
10_1101-2021_01_08_425885	167	1	2.3	2.3	CD
10_1101-2021_01_08_425885	167	2	Curvature	curvature	DT
10_1101-2021_01_08_425885	167	3	of	of	IN
10_1101-2021_01_08_425885	167	4	Image	Image	NNP
10_1101-2021_01_08_425885	167	5	Patch	Patch	NNP
10_1101-2021_01_08_425885	167	6	Manifold	Manifold	NNP
10_1101-2021_01_08_425885	167	7	is	be	VBZ
10_1101-2021_01_08_425885	167	8	Consistent	consistent	JJ
10_1101-2021_01_08_425885	167	9	with	with	IN
10_1101-2021_01_08_425885	167	10	a	a	DT
10_1101-2021_01_08_425885	167	11	Noisy	Noisy	NNP
10_1101-2021_01_08_425885	167	12	Klein	Klein	NNP
10_1101-2021_01_08_425885	167	13	Bottle	Bottle	NNP
10_1101-2021_01_08_425885	167	14	Pixel	Pixel	NNP
10_1101-2021_01_08_425885	167	15	intensity	intensity	NN
10_1101-2021_01_08_425885	167	16	values	value	NNS
10_1101-2021_01_08_425885	167	17	in	in	IN
10_1101-2021_01_08_425885	167	18	images	image	NNS
10_1101-2021_01_08_425885	167	19	of	of	IN
10_1101-2021_01_08_425885	167	20	natural	natural	JJ
10_1101-2021_01_08_425885	167	21	scenes	scene	NNS
10_1101-2021_01_08_425885	167	22	are	be	VBP
10_1101-2021_01_08_425885	167	23	not	not	RB
10_1101-2021_01_08_425885	167	24	independently	independently	RB
10_1101-2021_01_08_425885	167	25	or	or	CC
10_1101-2021_01_08_425885	167	26	uniformly	uniformly	RB
10_1101-2021_01_08_425885	167	27	distributed	distribute	VBN
10_1101-2021_01_08_425885	167	28	.	.	.
10_1101-2021_01_08_425885	168	1	Understand-	Understand-	NNP
10_1101-2021_01_08_425885	168	2	ing	e	VBG
10_1101-2021_01_08_425885	168	3	the	the	DT
10_1101-2021_01_08_425885	168	4	statistics	statistic	NNS
10_1101-2021_01_08_425885	168	5	of	of	IN
10_1101-2021_01_08_425885	168	6	such	such	JJ
10_1101-2021_01_08_425885	168	7	images	image	NNS
10_1101-2021_01_08_425885	168	8	is	be	VBZ
10_1101-2021_01_08_425885	168	9	important	important	JJ
10_1101-2021_01_08_425885	168	10	for	for	IN
10_1101-2021_01_08_425885	168	11	designing	design	VBG
10_1101-2021_01_08_425885	168	12	compression	compression	NN
10_1101-2021_01_08_425885	168	13	algorithms	algorithm	NNS
10_1101-2021_01_08_425885	168	14	[	[	-LRB-
10_1101-2021_01_08_425885	168	15	38	38	CD
10_1101-2021_01_08_425885	168	16	]	]	-RRB-
10_1101-2021_01_08_425885	168	17	and	and	CC
10_1101-2021_01_08_425885	168	18	for	for	IN
10_1101-2021_01_08_425885	168	19	addressing	address	VBG
10_1101-2021_01_08_425885	168	20	challenges	challenge	NNS
10_1101-2021_01_08_425885	168	21	in	in	IN
10_1101-2021_01_08_425885	168	22	the	the	DT
10_1101-2021_01_08_425885	168	23	field	field	NN
10_1101-2021_01_08_425885	168	24	of	of	IN
10_1101-2021_01_08_425885	168	25	computer	computer	NN
10_1101-2021_01_08_425885	168	26	vision	vision	NN
10_1101-2021_01_08_425885	168	27	such	such	JJ
10_1101-2021_01_08_425885	168	28	as	as	IN
10_1101-2021_01_08_425885	168	29	segmentation	segmentation	NN
10_1101-2021_01_08_425885	168	30	[	[	-LRB-
10_1101-2021_01_08_425885	168	31	39	39	CD
10_1101-2021_01_08_425885	168	32	]	]	-RRB-
10_1101-2021_01_08_425885	168	33	.	.	.
10_1101-2021_01_08_425885	169	1	Lee	Lee	NNP
10_1101-2021_01_08_425885	169	2	et	et	NNP
10_1101-2021_01_08_425885	169	3	al	al	NNP
10_1101-2021_01_08_425885	169	4	.	.	.
10_1101-2021_01_08_425885	170	1	discovered	discover	VBD
10_1101-2021_01_08_425885	170	2	that	that	IN
10_1101-2021_01_08_425885	170	3	3x3-pixel	3x3-pixel	CD
10_1101-2021_01_08_425885	170	4	patches	patch	NNS
10_1101-2021_01_08_425885	170	5	extracted	extract	VBN
10_1101-2021_01_08_425885	170	6	from	from	IN
10_1101-2021_01_08_425885	170	7	greyscale	greyscale	JJ
10_1101-2021_01_08_425885	170	8	images	image	NNS
10_1101-2021_01_08_425885	170	9	of	of	IN
10_1101-2021_01_08_425885	170	10	natural	natural	JJ
10_1101-2021_01_08_425885	170	11	scenes	scene	NNS
10_1101-2021_01_08_425885	170	12	,	,	,
10_1101-2021_01_08_425885	170	13	whose	whose	WP$
10_1101-2021_01_08_425885	170	14	pixels	pixel	NNS
10_1101-2021_01_08_425885	170	15	have	have	VBP
10_1101-2021_01_08_425885	170	16	high	high	JJ
10_1101-2021_01_08_425885	170	17	-	-	HYPH
10_1101-2021_01_08_425885	170	18	contrast	contrast	NN
10_1101-2021_01_08_425885	170	19	(	(	-LRB-
10_1101-2021_01_08_425885	170	20	i.e.	i.e.	FW
10_1101-2021_01_08_425885	171	1	the	the	DT
10_1101-2021_01_08_425885	171	2	differ-	differ-	NN
10_1101-2021_01_08_425885	171	3	ences	ence	NNS
10_1101-2021_01_08_425885	171	4	between	between	IN
10_1101-2021_01_08_425885	171	5	the	the	DT
10_1101-2021_01_08_425885	171	6	intensity	intensity	NN
10_1101-2021_01_08_425885	171	7	values	value	NNS
10_1101-2021_01_08_425885	171	8	of	of	IN
10_1101-2021_01_08_425885	171	9	adjacent	adjacent	JJ
10_1101-2021_01_08_425885	171	10	pixels	pixel	NNS
10_1101-2021_01_08_425885	171	11	in	in	IN
10_1101-2021_01_08_425885	171	12	a	a	DT
10_1101-2021_01_08_425885	171	13	patch	patch	NN
10_1101-2021_01_08_425885	171	14	are	be	VBP
10_1101-2021_01_08_425885	171	15	large	large	JJ
10_1101-2021_01_08_425885	171	16	)	)	-RRB-
10_1101-2021_01_08_425885	171	17	,	,	,
10_1101-2021_01_08_425885	171	18	are	be	VBP
10_1101-2021_01_08_425885	171	19	not	not	RB
10_1101-2021_01_08_425885	171	20	uniformly	uniformly	RB
10_1101-2021_01_08_425885	171	21	distributed	distribute	VBN
10_1101-2021_01_08_425885	171	22	in	in	IN
10_1101-2021_01_08_425885	171	23	R9	R9	NNP
10_1101-2021_01_08_425885	171	24	,	,	,
10_1101-2021_01_08_425885	171	25	but	but	CC
10_1101-2021_01_08_425885	171	26	are	be	VBP
10_1101-2021_01_08_425885	171	27	instead	instead	RB
10_1101-2021_01_08_425885	171	28	concentrated	concentrated	JJ
10_1101-2021_01_08_425885	171	29	on	on	IN
10_1101-2021_01_08_425885	171	30	a	a	DT
10_1101-2021_01_08_425885	171	31	low	low	JJ
10_1101-2021_01_08_425885	171	32	-	-	HYPH
10_1101-2021_01_08_425885	171	33	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	171	34	manifold	manifold	NN
10_1101-2021_01_08_425885	171	35	[	[	-LRB-
10_1101-2021_01_08_425885	171	36	40	40	CD
10_1101-2021_01_08_425885	171	37	]	]	-RRB-
10_1101-2021_01_08_425885	171	38	.	.	.
10_1101-2021_01_08_425885	172	1	This	this	DT
10_1101-2021_01_08_425885	172	2	is	be	VBZ
10_1101-2021_01_08_425885	172	3	because	because	IN
10_1101-2021_01_08_425885	172	4	high	high	JJ
10_1101-2021_01_08_425885	172	5	-	-	HYPH
10_1101-2021_01_08_425885	172	6	contrast	contrast	NN
10_1101-2021_01_08_425885	172	7	regions	region	NNS
10_1101-2021_01_08_425885	172	8	in	in	IN
10_1101-2021_01_08_425885	172	9	a	a	DT
10_1101-2021_01_08_425885	172	10	natural	natural	JJ
10_1101-2021_01_08_425885	172	11	scene	scene	NN
10_1101-2021_01_08_425885	172	12	usually	usually	RB
10_1101-2021_01_08_425885	172	13	correspond	correspond	VBP
10_1101-2021_01_08_425885	172	14	to	to	IN
10_1101-2021_01_08_425885	172	15	the	the	DT
10_1101-2021_01_08_425885	172	16	edges	edge	NNS
10_1101-2021_01_08_425885	172	17	of	of	IN
10_1101-2021_01_08_425885	172	18	objects	object	NNS
10_1101-2021_01_08_425885	172	19	in	in	IN
10_1101-2021_01_08_425885	172	20	the	the	DT
10_1101-2021_01_08_425885	172	21	scene	scene	NN
10_1101-2021_01_08_425885	172	22	.	.	.
10_1101-2021_01_08_425885	173	1	High	high	JJ
10_1101-2021_01_08_425885	173	2	-	-	HYPH
10_1101-2021_01_08_425885	173	3	contrast	contrast	NN
10_1101-2021_01_08_425885	173	4	image	image	NN
10_1101-2021_01_08_425885	173	5	patches	patch	NNS
10_1101-2021_01_08_425885	173	6	consequently	consequently	RB
10_1101-2021_01_08_425885	173	7	tend	tend	VBP
10_1101-2021_01_08_425885	173	8	to	to	TO
10_1101-2021_01_08_425885	173	9	be	be	VB
10_1101-2021_01_08_425885	173	10	comprised	comprise	VBN
10_1101-2021_01_08_425885	173	11	of	of	IN
10_1101-2021_01_08_425885	173	12	gradients	gradient	NNS
10_1101-2021_01_08_425885	173	13	and	and	CC
10_1101-2021_01_08_425885	173	14	not	not	RB
10_1101-2021_01_08_425885	173	15	simply	simply	RB
10_1101-2021_01_08_425885	173	16	random	random	JJ
10_1101-2021_01_08_425885	173	17	speckle	speckle	NNP
10_1101-2021_01_08_425885	173	18	.	.	.
10_1101-2021_01_08_425885	174	1	Subsequent	subsequent	JJ
10_1101-2021_01_08_425885	174	2	work	work	NN
10_1101-2021_01_08_425885	174	3	using	use	VBG
10_1101-2021_01_08_425885	174	4	topological	topological	JJ
10_1101-2021_01_08_425885	174	5	data	datum	NNS
10_1101-2021_01_08_425885	174	6	analysis	analysis	NN
10_1101-2021_01_08_425885	174	7	revealed	reveal	VBD
10_1101-2021_01_08_425885	174	8	that	that	IN
10_1101-2021_01_08_425885	174	9	after	after	IN
10_1101-2021_01_08_425885	174	10	appropriate	appropriate	JJ
10_1101-2021_01_08_425885	174	11	normalization	normalization	NN
10_1101-2021_01_08_425885	174	12	(	(	-LRB-
10_1101-2021_01_08_425885	174	13	which	which	WDT
10_1101-2021_01_08_425885	174	14	takes	take	VBZ
10_1101-2021_01_08_425885	174	15	image	image	NN
10_1101-2021_01_08_425885	174	16	patches	patch	NNS
10_1101-2021_01_08_425885	174	17	from	from	IN
10_1101-2021_01_08_425885	174	18	R9	r9	VB
10_1101-2021_01_08_425885	174	19	to	to	IN
10_1101-2021_01_08_425885	174	20	S7	S7	NNP
10_1101-2021_01_08_425885	174	21	∈	∈	NNP
10_1101-2021_01_08_425885	174	22	R8	R8	NNP
10_1101-2021_01_08_425885	174	23	,	,	,
10_1101-2021_01_08_425885	174	24	so	so	IN
10_1101-2021_01_08_425885	174	25	that	that	IN
10_1101-2021_01_08_425885	174	26	the	the	DT
10_1101-2021_01_08_425885	174	27	global	global	JJ
10_1101-2021_01_08_425885	174	28	length	length	NN
10_1101-2021_01_08_425885	174	29	scale	scale	NN
10_1101-2021_01_08_425885	174	30	is	be	VBZ
10_1101-2021_01_08_425885	174	31	L	l	NN
10_1101-2021_01_08_425885	174	32	=	=	SYM
10_1101-2021_01_08_425885	174	33	1	1	CD
10_1101-2021_01_08_425885	174	34	;	;	:
10_1101-2021_01_08_425885	174	35	see	see	VB
10_1101-2021_01_08_425885	174	36	Methods	Methods	NNP
10_1101-2021_01_08_425885	174	37	Section	Section	NNP
10_1101-2021_01_08_425885	174	38	4.5.2	4.5.2	CD
10_1101-2021_01_08_425885	174	39	)	)	-RRB-
10_1101-2021_01_08_425885	174	40	,	,	,
10_1101-2021_01_08_425885	174	41	dense	dense	JJ
10_1101-2021_01_08_425885	174	42	regions	region	NNS
10_1101-2021_01_08_425885	174	43	of	of	IN
10_1101-2021_01_08_425885	174	44	high	high	JJ
10_1101-2021_01_08_425885	174	45	-	-	HYPH
10_1101-2021_01_08_425885	174	46	contrast	contrast	NN
10_1101-2021_01_08_425885	174	47	image	image	NN
10_1101-2021_01_08_425885	174	48	patches	patch	NNS
10_1101-2021_01_08_425885	174	49	have	have	VBP
10_1101-2021_01_08_425885	174	50	the	the	DT
10_1101-2021_01_08_425885	174	51	same	same	JJ
10_1101-2021_01_08_425885	174	52	homology	homology	NN
10_1101-2021_01_08_425885	174	53	as	as	IN
10_1101-2021_01_08_425885	174	54	a	a	DT
10_1101-2021_01_08_425885	174	55	2-dimensional	2-dimensional	CD
10_1101-2021_01_08_425885	174	56	manifold	manifold	NN
10_1101-2021_01_08_425885	174	57	called	call	VBN
10_1101-2021_01_08_425885	174	58	a	a	DT
10_1101-2021_01_08_425885	174	59	Klein	Klein	NNP
10_1101-2021_01_08_425885	174	60	bottle	bottle	NN
10_1101-2021_01_08_425885	174	61	[	[	-LRB-
10_1101-2021_01_08_425885	174	62	21	21	CD
10_1101-2021_01_08_425885	174	63	]	]	-RRB-
10_1101-2021_01_08_425885	174	64	.	.	.
10_1101-2021_01_08_425885	175	1	A	a	DT
10_1101-2021_01_08_425885	175	2	Klein	Klein	NNP
10_1101-2021_01_08_425885	175	3	bottle	bottle	NN
10_1101-2021_01_08_425885	175	4	,	,	,
10_1101-2021_01_08_425885	175	5	K2	K2	NNP
10_1101-2021_01_08_425885	175	6	,	,	,
10_1101-2021_01_08_425885	175	7	is	be	VBZ
10_1101-2021_01_08_425885	175	8	a	a	DT
10_1101-2021_01_08_425885	175	9	canonical	canonical	JJ
10_1101-2021_01_08_425885	175	10	manifold	manifold	NN
10_1101-2021_01_08_425885	175	11	typically	typically	RB
10_1101-2021_01_08_425885	175	12	introduced	introduce	VBN
10_1101-2021_01_08_425885	175	13	in	in	IN
10_1101-2021_01_08_425885	175	14	the	the	DT
10_1101-2021_01_08_425885	175	15	context	context	NN
10_1101-2021_01_08_425885	175	16	of	of	IN
10_1101-2021_01_08_425885	175	17	orientability	orientability	NN
10_1101-2021_01_08_425885	175	18	,	,	,
10_1101-2021_01_08_425885	175	19	where	where	WRB
10_1101-2021_01_08_425885	175	20	it	-PRON-	PRP
10_1101-2021_01_08_425885	175	21	is	be	VBZ
10_1101-2021_01_08_425885	175	22	often	often	RB
10_1101-2021_01_08_425885	175	23	visualized	visualize	VBN
10_1101-2021_01_08_425885	175	24	in	in	IN
10_1101-2021_01_08_425885	175	25	R3	r3	NN
10_1101-2021_01_08_425885	175	26	(	(	-LRB-
10_1101-2021_01_08_425885	175	27	as	as	IN
10_1101-2021_01_08_425885	175	28	shown	show	VBN
10_1101-2021_01_08_425885	175	29	in	in	IN
10_1101-2021_01_08_425885	175	30	Figure	Figure	NNP
10_1101-2021_01_08_425885	175	31	3A	3a	NN
10_1101-2021_01_08_425885	175	32	)	)	-RRB-
10_1101-2021_01_08_425885	175	33	to	to	TO
10_1101-2021_01_08_425885	175	34	highlight	highlight	VB
10_1101-2021_01_08_425885	175	35	that	that	IN
10_1101-2021_01_08_425885	175	36	it	-PRON-	PRP
10_1101-2021_01_08_425885	175	37	is	be	VBZ
10_1101-2021_01_08_425885	175	38	non	non	JJ
10_1101-2021_01_08_425885	175	39	-	-	JJ
10_1101-2021_01_08_425885	175	40	orientable	orientable	JJ
10_1101-2021_01_08_425885	175	41	.	.	.
10_1101-2021_01_08_425885	176	1	From	from	IN
10_1101-2021_01_08_425885	176	2	a	a	DT
10_1101-2021_01_08_425885	176	3	topological	topological	JJ
10_1101-2021_01_08_425885	176	4	perspective	perspective	NN
10_1101-2021_01_08_425885	176	5	,	,	,
10_1101-2021_01_08_425885	176	6	K2	K2	NNP
10_1101-2021_01_08_425885	176	7	is	be	VBZ
10_1101-2021_01_08_425885	176	8	a	a	DT
10_1101-2021_01_08_425885	176	9	manifold	manifold	NN
10_1101-2021_01_08_425885	176	10	parameterized	parameterize	VBN
10_1101-2021_01_08_425885	176	11	by	by	IN
10_1101-2021_01_08_425885	176	12	θ	θ	NNP
10_1101-2021_01_08_425885	176	13	,	,	,
10_1101-2021_01_08_425885	176	14	φ	φ	NNP
10_1101-2021_01_08_425885	176	15	∈	∈	NNP
10_1101-2021_01_08_425885	176	16	[	[	-LRB-
10_1101-2021_01_08_425885	176	17	0	0	CD
10_1101-2021_01_08_425885	176	18	,	,	,
10_1101-2021_01_08_425885	176	19	2π	2π	LS
10_1101-2021_01_08_425885	176	20	]	]	-RRB-
10_1101-2021_01_08_425885	176	21	as	as	IN
10_1101-2021_01_08_425885	176	22	shown	show	VBN
10_1101-2021_01_08_425885	176	23	in	in	IN
10_1101-2021_01_08_425885	176	24	Figure	Figure	NNP
10_1101-2021_01_08_425885	176	25	3B	3b	NN
10_1101-2021_01_08_425885	176	26	in	in	IN
10_1101-2021_01_08_425885	176	27	which	which	WDT
10_1101-2021_01_08_425885	176	28	vertical	vertical	JJ
10_1101-2021_01_08_425885	176	29	edges	edge	NNS
10_1101-2021_01_08_425885	176	30	are	be	VBP
10_1101-2021_01_08_425885	176	31	defined	define	VBN
10_1101-2021_01_08_425885	176	32	to	to	TO
10_1101-2021_01_08_425885	176	33	be	be	VB
10_1101-2021_01_08_425885	176	34	θ	θ	NNP
10_1101-2021_01_08_425885	176	35	=	=	SYM
10_1101-2021_01_08_425885	176	36	0	0	CD
10_1101-2021_01_08_425885	176	37	and	and	CC
10_1101-2021_01_08_425885	176	38	θ	θ	NNP
10_1101-2021_01_08_425885	176	39	=	=	SYM
10_1101-2021_01_08_425885	176	40	π	π	NN
10_1101-2021_01_08_425885	176	41	,	,	,
10_1101-2021_01_08_425885	176	42	and	and	CC
10_1101-2021_01_08_425885	176	43	horizontal	horizontal	JJ
10_1101-2021_01_08_425885	176	44	edges	edge	NNS
10_1101-2021_01_08_425885	176	45	are	be	VBP
10_1101-2021_01_08_425885	176	46	defined	define	VBN
10_1101-2021_01_08_425885	176	47	to	to	TO
10_1101-2021_01_08_425885	176	48	be	be	VB
10_1101-2021_01_08_425885	176	49	φ	φ	NN
10_1101-2021_01_08_425885	176	50	=	=	SYM
10_1101-2021_01_08_425885	176	51	0	0	CD
10_1101-2021_01_08_425885	176	52	and	and	CC
10_1101-2021_01_08_425885	176	53	φ	φ	NN
10_1101-2021_01_08_425885	176	54	=	=	SYM
10_1101-2021_01_08_425885	176	55	2π	2π	CD
10_1101-2021_01_08_425885	176	56	.	.	.
10_1101-2021_01_08_425885	177	1	To	to	TO
10_1101-2021_01_08_425885	177	2	make	make	VB
10_1101-2021_01_08_425885	177	3	a	a	DT
10_1101-2021_01_08_425885	177	4	closed	close	VBN
10_1101-2021_01_08_425885	177	5	surface	surface	NN
10_1101-2021_01_08_425885	177	6	,	,	,
10_1101-2021_01_08_425885	177	7	the	the	DT
10_1101-2021_01_08_425885	177	8	vertical	vertical	JJ
10_1101-2021_01_08_425885	177	9	(	(	-LRB-
10_1101-2021_01_08_425885	177	10	horizontal	horizontal	JJ
10_1101-2021_01_08_425885	177	11	)	)	-RRB-
10_1101-2021_01_08_425885	177	12	edges	edge	NNS
10_1101-2021_01_08_425885	177	13	are	be	VBP
10_1101-2021_01_08_425885	177	14	glued	glue	VBN
10_1101-2021_01_08_425885	177	15	together	together	RB
10_1101-2021_01_08_425885	177	16	according	accord	VBG
10_1101-2021_01_08_425885	177	17	to	to	IN
10_1101-2021_01_08_425885	177	18	the	the	DT
10_1101-2021_01_08_425885	177	19	red	red	JJ
10_1101-2021_01_08_425885	177	20	(	(	-LRB-
10_1101-2021_01_08_425885	177	21	blue	blue	NNP
10_1101-2021_01_08_425885	177	22	)	)	-RRB-
10_1101-2021_01_08_425885	177	23	arrows	arrow	NNS
10_1101-2021_01_08_425885	177	24	in	in	IN
10_1101-2021_01_08_425885	177	25	Figure	figure	NN
10_1101-2021_01_08_425885	177	26	3B.	3b.	CD
10_1101-2021_01_08_425885	178	1	K2	K2	NNP
10_1101-2021_01_08_425885	178	2	is	be	VBZ
10_1101-2021_01_08_425885	178	3	therefore	therefore	RB
10_1101-2021_01_08_425885	178	4	2π	2π	CD
10_1101-2021_01_08_425885	178	5	-	-	HYPH
10_1101-2021_01_08_425885	178	6	periodic	periodic	JJ
10_1101-2021_01_08_425885	178	7	in	in	IN
10_1101-2021_01_08_425885	178	8	φ	φ	NNP
10_1101-2021_01_08_425885	178	9	,	,	,
10_1101-2021_01_08_425885	178	10	since	since	IN
10_1101-2021_01_08_425885	178	11	a	a	DT
10_1101-2021_01_08_425885	178	12	point	point	NN
10_1101-2021_01_08_425885	178	13	corresponding	correspond	VBG
10_1101-2021_01_08_425885	178	14	to	to	IN
10_1101-2021_01_08_425885	178	15	θ	θ	NNP
10_1101-2021_01_08_425885	178	16	on	on	IN
10_1101-2021_01_08_425885	178	17	the	the	DT
10_1101-2021_01_08_425885	178	18	bottom	bottom	JJ
10_1101-2021_01_08_425885	178	19	horizontal	horizontal	JJ
10_1101-2021_01_08_425885	178	20	edge	edge	NN
10_1101-2021_01_08_425885	178	21	(	(	-LRB-
10_1101-2021_01_08_425885	178	22	φ	φ	NN
10_1101-2021_01_08_425885	178	23	=	=	SYM
10_1101-2021_01_08_425885	178	24	0	0	NFP
10_1101-2021_01_08_425885	178	25	)	)	-RRB-
10_1101-2021_01_08_425885	178	26	is	be	VBZ
10_1101-2021_01_08_425885	178	27	the	the	DT
10_1101-2021_01_08_425885	178	28	same	same	JJ
10_1101-2021_01_08_425885	178	29	as	as	IN
10_1101-2021_01_08_425885	178	30	the	the	DT
10_1101-2021_01_08_425885	178	31	point	point	NN
10_1101-2021_01_08_425885	178	32	corresponding	correspond	VBG
10_1101-2021_01_08_425885	178	33	to	to	IN
10_1101-2021_01_08_425885	178	34	θ	θ	NNP
10_1101-2021_01_08_425885	178	35	on	on	IN
10_1101-2021_01_08_425885	178	36	the	the	DT
10_1101-2021_01_08_425885	178	37	top	top	JJ
10_1101-2021_01_08_425885	178	38	horizontal	horizontal	JJ
10_1101-2021_01_08_425885	178	39	edge	edge	NN
10_1101-2021_01_08_425885	178	40	(	(	-LRB-
10_1101-2021_01_08_425885	178	41	φ	φ	NN
10_1101-2021_01_08_425885	178	42	=	=	SYM
10_1101-2021_01_08_425885	178	43	2π	2π	NN
10_1101-2021_01_08_425885	178	44	)	)	-RRB-
10_1101-2021_01_08_425885	178	45	.	.	.
10_1101-2021_01_08_425885	179	1	Similarly	similarly	RB
10_1101-2021_01_08_425885	179	2	,	,	,
10_1101-2021_01_08_425885	179	3	a	a	DT
10_1101-2021_01_08_425885	179	4	point	point	NN
10_1101-2021_01_08_425885	179	5	corresponding	correspond	VBG
10_1101-2021_01_08_425885	179	6	to	to	IN
10_1101-2021_01_08_425885	179	7	φ	φ	NNP
10_1101-2021_01_08_425885	179	8	on	on	IN
10_1101-2021_01_08_425885	179	9	the	the	DT
10_1101-2021_01_08_425885	179	10	left	left	JJ
10_1101-2021_01_08_425885	179	11	vertical	vertical	JJ
10_1101-2021_01_08_425885	179	12	edge	edge	NN
10_1101-2021_01_08_425885	179	13	(	(	-LRB-
10_1101-2021_01_08_425885	179	14	θ	θ	NNP
10_1101-2021_01_08_425885	179	15	=	=	SYM
10_1101-2021_01_08_425885	179	16	0	0	CD
10_1101-2021_01_08_425885	179	17	)	)	-RRB-
10_1101-2021_01_08_425885	179	18	is	be	VBZ
10_1101-2021_01_08_425885	179	19	the	the	DT
10_1101-2021_01_08_425885	179	20	same	same	JJ
10_1101-2021_01_08_425885	179	21	as	as	IN
10_1101-2021_01_08_425885	179	22	the	the	DT
10_1101-2021_01_08_425885	179	23	point	point	NN
10_1101-2021_01_08_425885	179	24	corresponding	correspond	VBG
10_1101-2021_01_08_425885	179	25	to	to	IN
10_1101-2021_01_08_425885	179	26	2π	2π	CD
10_1101-2021_01_08_425885	179	27	−φ	−φ	ADD
10_1101-2021_01_08_425885	179	28	on	on	IN
10_1101-2021_01_08_425885	179	29	the	the	DT
10_1101-2021_01_08_425885	179	30	right	right	JJ
10_1101-2021_01_08_425885	179	31	vertical	vertical	JJ
10_1101-2021_01_08_425885	179	32	edges	edge	NNS
10_1101-2021_01_08_425885	179	33	(	(	-LRB-
10_1101-2021_01_08_425885	179	34	θ	θ	NNP
10_1101-2021_01_08_425885	179	35	=	=	SYM
10_1101-2021_01_08_425885	179	36	π	π	NN
10_1101-2021_01_08_425885	179	37	)	)	-RRB-
10_1101-2021_01_08_425885	179	38	.	.	.
10_1101-2021_01_08_425885	180	1	In	in	IN
10_1101-2021_01_08_425885	180	2	short	short	JJ
10_1101-2021_01_08_425885	180	3	,	,	,
10_1101-2021_01_08_425885	180	4	points	point	NNS
10_1101-2021_01_08_425885	180	5	on	on	IN
10_1101-2021_01_08_425885	180	6	K2	K2	NNP
10_1101-2021_01_08_425885	180	7	obey	obey	VBP
10_1101-2021_01_08_425885	180	8	the	the	DT
10_1101-2021_01_08_425885	180	9	similarity	similarity	NN
10_1101-2021_01_08_425885	180	10	relation	relation	NN
10_1101-2021_01_08_425885	180	11	(	(	-LRB-
10_1101-2021_01_08_425885	180	12	θ	θ	NNP
10_1101-2021_01_08_425885	180	13	,	,	,
10_1101-2021_01_08_425885	180	14	φ	φ	NNP
10_1101-2021_01_08_425885	180	15	)	)	-RRB-
10_1101-2021_01_08_425885	180	16	∼	∼	NNP
10_1101-2021_01_08_425885	180	17	(	(	-LRB-
10_1101-2021_01_08_425885	180	18	θ	θ	NNP
10_1101-2021_01_08_425885	180	19	+	+	SYM
10_1101-2021_01_08_425885	180	20	π	π	NN
10_1101-2021_01_08_425885	180	21	,	,	,
10_1101-2021_01_08_425885	180	22	2π	2π	CD
10_1101-2021_01_08_425885	180	23	−	−	NNP
10_1101-2021_01_08_425885	180	24	φ	φ	NNP
10_1101-2021_01_08_425885	180	25	)	)	-RRB-
10_1101-2021_01_08_425885	180	26	.	.	.
10_1101-2021_01_08_425885	181	1	K2	K2	NNP
10_1101-2021_01_08_425885	181	2	captures	capture	VBZ
10_1101-2021_01_08_425885	181	3	the	the	DT
10_1101-2021_01_08_425885	181	4	dominant	dominant	JJ
10_1101-2021_01_08_425885	181	5	features	feature	NNS
10_1101-2021_01_08_425885	181	6	in	in	IN
10_1101-2021_01_08_425885	181	7	high	high	JJ
10_1101-2021_01_08_425885	181	8	-	-	HYPH
10_1101-2021_01_08_425885	181	9	contrast	contrast	NN
10_1101-2021_01_08_425885	181	10	image	image	NN
10_1101-2021_01_08_425885	181	11	patches	patch	NNS
10_1101-2021_01_08_425885	181	12	because	because	IN
10_1101-2021_01_08_425885	181	13	θ	θ	NNP
10_1101-2021_01_08_425885	181	14	can	can	MD
10_1101-2021_01_08_425885	181	15	be	be	VB
10_1101-2021_01_08_425885	181	16	treated	treat	VBN
10_1101-2021_01_08_425885	181	17	as	as	IN
10_1101-2021_01_08_425885	181	18	a	a	DT
10_1101-2021_01_08_425885	181	19	parameter	parameter	NN
10_1101-2021_01_08_425885	181	20	controlling	control	VBG
10_1101-2021_01_08_425885	181	21	rotation	rotation	NN
10_1101-2021_01_08_425885	181	22	and	and	CC
10_1101-2021_01_08_425885	181	23	φ	φ	NN
10_1101-2021_01_08_425885	181	24	as	as	IN
10_1101-2021_01_08_425885	181	25	a	a	DT
10_1101-2021_01_08_425885	181	26	parameter	parameter	NN
10_1101-2021_01_08_425885	181	27	controlling	control	VBG
10_1101-2021_01_08_425885	181	28	the	the	DT
10_1101-2021_01_08_425885	181	29	relative	relative	JJ
10_1101-2021_01_08_425885	181	30	contribution	contribution	NN
10_1101-2021_01_08_425885	181	31	of	of	IN
10_1101-2021_01_08_425885	181	32	linear	linear	NNP
10_1101-2021_01_08_425885	181	33	vs.	vs.	IN
10_1101-2021_01_08_425885	181	34	quadratic	quadratic	NNP
10_1101-2021_01_08_425885	181	35	gradients	gradient	NNS
10_1101-2021_01_08_425885	181	36	(	(	-LRB-
10_1101-2021_01_08_425885	181	37	see	see	VB
10_1101-2021_01_08_425885	181	38	Figure	Figure	NNP
10_1101-2021_01_08_425885	181	39	3B	3b	NN
10_1101-2021_01_08_425885	181	40	)	)	-RRB-
10_1101-2021_01_08_425885	181	41	.	.	.
10_1101-2021_01_08_425885	182	1	An	an	DT
10_1101-2021_01_08_425885	182	2	embedding	embedding	NN
10_1101-2021_01_08_425885	182	3	of	of	IN
10_1101-2021_01_08_425885	182	4	K2	K2	NNP
10_1101-2021_01_08_425885	182	5	into	into	IN
10_1101-2021_01_08_425885	182	6	R9	R9	NNP
10_1101-2021_01_08_425885	182	7	with	with	IN
10_1101-2021_01_08_425885	182	8	an	an	DT
10_1101-2021_01_08_425885	182	9	analytical	analytical	JJ
10_1101-2021_01_08_425885	182	10	form	form	NN
10_1101-2021_01_08_425885	182	11	,	,	,
10_1101-2021_01_08_425885	182	12	k0	k0	NNP
10_1101-2021_01_08_425885	182	13	,	,	,
10_1101-2021_01_08_425885	182	14	was	be	VBD
10_1101-2021_01_08_425885	182	15	proposed	propose	VBN
10_1101-2021_01_08_425885	182	16	by	by	IN
10_1101-2021_01_08_425885	182	17	Carlsson	Carlsson	NNP
10_1101-2021_01_08_425885	182	18	et	et	FW
10_1101-2021_01_08_425885	182	19	al	al	NNP
10_1101-2021_01_08_425885	182	20	.	.	.
10_1101-2021_01_08_425885	183	1	in	in	IN
10_1101-2021_01_08_425885	183	2	[	[	-LRB-
10_1101-2021_01_08_425885	183	3	21	21	CD
10_1101-2021_01_08_425885	183	4	]	]	-RRB-
10_1101-2021_01_08_425885	183	5	to	to	TO
10_1101-2021_01_08_425885	183	6	model	model	VB
10_1101-2021_01_08_425885	183	7	image	image	NN
10_1101-2021_01_08_425885	183	8	patches	patch	NNS
10_1101-2021_01_08_425885	183	9	(	(	-LRB-
10_1101-2021_01_08_425885	183	10	see	see	VB
10_1101-2021_01_08_425885	183	11	Equation	Equation	NNP
10_1101-2021_01_08_425885	183	12	31	31	CD
10_1101-2021_01_08_425885	183	13	in	in	IN
10_1101-2021_01_08_425885	183	14	Methods	Methods	NNP
10_1101-2021_01_08_425885	183	15	Section	Section	NNP
10_1101-2021_01_08_425885	183	16	4.5.3	4.5.3	CD
10_1101-2021_01_08_425885	183	17	)	)	-RRB-
10_1101-2021_01_08_425885	183	18	.	.	.
10_1101-2021_01_08_425885	184	1	This	this	DT
10_1101-2021_01_08_425885	184	2	embedding	embedding	NN
10_1101-2021_01_08_425885	184	3	takes	take	VBZ
10_1101-2021_01_08_425885	184	4	points	point	NNS
10_1101-2021_01_08_425885	184	5	from	from	IN
10_1101-2021_01_08_425885	184	6	(	(	-LRB-
10_1101-2021_01_08_425885	184	7	θ	θ	NNP
10_1101-2021_01_08_425885	184	8	,	,	,
10_1101-2021_01_08_425885	184	9	φ	φ	NNP
10_1101-2021_01_08_425885	184	10	)	)	-RRB-
10_1101-2021_01_08_425885	184	11	into	into	IN
10_1101-2021_01_08_425885	184	12	11	11	CD
10_1101-2021_01_08_425885	184	13	.CC	.CC	,
10_1101-2021_01_08_425885	184	14	-	-	HYPH
10_1101-2021_01_08_425885	184	15	BY	by	IN
10_1101-2021_01_08_425885	184	16	-	-	HYPH
10_1101-2021_01_08_425885	184	17	NC	NC	NNP
10_1101-2021_01_08_425885	184	18	-	-	HYPH
10_1101-2021_01_08_425885	184	19	ND	ND	NNP
10_1101-2021_01_08_425885	184	20	4.0	4.0	CD
10_1101-2021_01_08_425885	184	21	International	International	NNP
10_1101-2021_01_08_425885	184	22	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	184	23	under	under	IN
10_1101-2021_01_08_425885	184	24	a	a	DT
10_1101-2021_01_08_425885	184	25	(	(	-LRB-
10_1101-2021_01_08_425885	184	26	which	which	WDT
10_1101-2021_01_08_425885	184	27	was	be	VBD
10_1101-2021_01_08_425885	184	28	not	not	RB
10_1101-2021_01_08_425885	184	29	certified	certify	VBN
10_1101-2021_01_08_425885	184	30	by	by	IN
10_1101-2021_01_08_425885	184	31	peer	peer	NN
10_1101-2021_01_08_425885	184	32	review	review	NN
10_1101-2021_01_08_425885	184	33	)	)	-RRB-
10_1101-2021_01_08_425885	184	34	is	be	VBZ
10_1101-2021_01_08_425885	184	35	the	the	DT
10_1101-2021_01_08_425885	184	36	author	author	NN
10_1101-2021_01_08_425885	184	37	/	/	SYM
10_1101-2021_01_08_425885	184	38	funder	funder	NN
10_1101-2021_01_08_425885	184	39	,	,	,
10_1101-2021_01_08_425885	184	40	who	who	WP
10_1101-2021_01_08_425885	184	41	has	have	VBZ
10_1101-2021_01_08_425885	184	42	granted	grant	VBN
10_1101-2021_01_08_425885	184	43	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	184	44	a	a	DT
10_1101-2021_01_08_425885	184	45	license	license	NN
10_1101-2021_01_08_425885	184	46	to	to	TO
10_1101-2021_01_08_425885	184	47	display	display	VB
10_1101-2021_01_08_425885	184	48	the	the	DT
10_1101-2021_01_08_425885	184	49	preprint	preprint	NN
10_1101-2021_01_08_425885	184	50	in	in	IN
10_1101-2021_01_08_425885	184	51	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	184	52	.	.	.
10_1101-2021_01_08_425885	185	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	185	2	is	be	VBZ
10_1101-2021_01_08_425885	185	3	made	make	VBN
10_1101-2021_01_08_425885	185	4	The	the	DT
10_1101-2021_01_08_425885	185	5	copyright	copyright	NN
10_1101-2021_01_08_425885	185	6	holder	holder	NN
10_1101-2021_01_08_425885	185	7	for	for	IN
10_1101-2021_01_08_425885	185	8	this	this	DT
10_1101-2021_01_08_425885	185	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	185	10	version	version	NN
10_1101-2021_01_08_425885	185	11	posted	post	VBD
10_1101-2021_01_08_425885	185	12	January	January	NNP
10_1101-2021_01_08_425885	185	13	8	8	CD
10_1101-2021_01_08_425885	185	14	,	,	,
10_1101-2021_01_08_425885	185	15	2021	2021	CD
10_1101-2021_01_08_425885	185	16	.	.	.
10_1101-2021_01_08_425885	185	17	;	;	:
10_1101-2021_01_08_425885	185	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	185	19	:	:	:
10_1101-2021_01_08_425885	185	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	185	21	preprint	preprint	NN
10_1101-2021_01_08_425885	185	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	NNP
10_1101-2021_01_08_425885	185	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	JJ
10_1101-2021_01_08_425885	185	24	image	image	NN
10_1101-2021_01_08_425885	185	25	patches	patch	NNS
10_1101-2021_01_08_425885	185	26	in	in	IN
10_1101-2021_01_08_425885	185	27	R9	R9	NNP
10_1101-2021_01_08_425885	185	28	as	as	IN
10_1101-2021_01_08_425885	185	29	shown	show	VBN
10_1101-2021_01_08_425885	185	30	in	in	IN
10_1101-2021_01_08_425885	185	31	Figure	figure	NN
10_1101-2021_01_08_425885	185	32	3B.	3b.	CD
10_1101-2021_01_08_425885	186	1	For	for	IN
10_1101-2021_01_08_425885	186	2	example	example	NN
10_1101-2021_01_08_425885	186	3	,	,	,
10_1101-2021_01_08_425885	186	4	θ	θ	NNP
10_1101-2021_01_08_425885	186	5	=	=	SYM
10_1101-2021_01_08_425885	186	6	0	0	NFP
10_1101-2021_01_08_425885	186	7	(	(	-LRB-
10_1101-2021_01_08_425885	186	8	θ	θ	NNP
10_1101-2021_01_08_425885	186	9	=	=	SYM
10_1101-2021_01_08_425885	186	10	π	π	NN
10_1101-2021_01_08_425885	186	11	2	2	CD
10_1101-2021_01_08_425885	186	12	)	)	-RRB-
10_1101-2021_01_08_425885	186	13	corresponds	correspond	VBZ
10_1101-2021_01_08_425885	186	14	to	to	IN
10_1101-2021_01_08_425885	186	15	patches	patch	NNS
10_1101-2021_01_08_425885	186	16	with	with	IN
10_1101-2021_01_08_425885	186	17	vertical	vertical	JJ
10_1101-2021_01_08_425885	186	18	(	(	-LRB-
10_1101-2021_01_08_425885	186	19	horizontal	horizontal	JJ
10_1101-2021_01_08_425885	186	20	)	)	-RRB-
10_1101-2021_01_08_425885	186	21	stripes	stripe	NNS
10_1101-2021_01_08_425885	186	22	and	and	CC
10_1101-2021_01_08_425885	186	23	φ	φ	NNP
10_1101-2021_01_08_425885	186	24	=	=	SYM
10_1101-2021_01_08_425885	186	25	π	π	NN
10_1101-2021_01_08_425885	186	26	2	2	CD
10_1101-2021_01_08_425885	186	27	,	,	,
10_1101-2021_01_08_425885	186	28	3π	3π	CD
10_1101-2021_01_08_425885	186	29	2	2	CD
10_1101-2021_01_08_425885	186	30	(	(	-LRB-
10_1101-2021_01_08_425885	186	31	φ	φ	NNP
10_1101-2021_01_08_425885	186	32	=	=	SYM
10_1101-2021_01_08_425885	186	33	0,π	0,π	CD
10_1101-2021_01_08_425885	186	34	)	)	-RRB-
10_1101-2021_01_08_425885	186	35	corresponds	correspond	NNS
10_1101-2021_01_08_425885	186	36	to	to	IN
10_1101-2021_01_08_425885	186	37	patches	patch	NNS
10_1101-2021_01_08_425885	186	38	with	with	IN
10_1101-2021_01_08_425885	186	39	linear	linear	NNP
10_1101-2021_01_08_425885	186	40	(	(	-LRB-
10_1101-2021_01_08_425885	186	41	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	186	42	)	)	-RRB-
10_1101-2021_01_08_425885	186	43	gradients	gradient	NNS
10_1101-2021_01_08_425885	186	44	.	.	.
10_1101-2021_01_08_425885	187	1	As	as	IN
10_1101-2021_01_08_425885	187	2	θ	θ	NN
10_1101-2021_01_08_425885	187	3	increases	increase	VBZ
10_1101-2021_01_08_425885	187	4	,	,	,
10_1101-2021_01_08_425885	187	5	stripes	stripe	NNS
10_1101-2021_01_08_425885	187	6	in	in	IN
10_1101-2021_01_08_425885	187	7	the	the	DT
10_1101-2021_01_08_425885	187	8	image	image	NN
10_1101-2021_01_08_425885	187	9	patches	patch	NNS
10_1101-2021_01_08_425885	187	10	are	be	VBP
10_1101-2021_01_08_425885	187	11	rotated	rotate	VBN
10_1101-2021_01_08_425885	187	12	clockwise	clockwise	RB
10_1101-2021_01_08_425885	187	13	.	.	.
10_1101-2021_01_08_425885	188	1	As	as	IN
10_1101-2021_01_08_425885	188	2	φ	φ	NN
10_1101-2021_01_08_425885	188	3	increases	increase	NNS
10_1101-2021_01_08_425885	188	4	,	,	,
10_1101-2021_01_08_425885	188	5	image	image	NN
10_1101-2021_01_08_425885	188	6	patches	patch	NNS
10_1101-2021_01_08_425885	188	7	oscillate	oscillate	VBP
10_1101-2021_01_08_425885	188	8	between	between	IN
10_1101-2021_01_08_425885	188	9	having	have	VBG
10_1101-2021_01_08_425885	188	10	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	188	11	and	and	CC
10_1101-2021_01_08_425885	188	12	linear	linear	JJ
10_1101-2021_01_08_425885	188	13	gradients	gradient	NNS
10_1101-2021_01_08_425885	188	14	.	.	.
10_1101-2021_01_08_425885	189	1	Importantly	importantly	RB
10_1101-2021_01_08_425885	189	2	,	,	,
10_1101-2021_01_08_425885	189	3	the	the	DT
10_1101-2021_01_08_425885	189	4	image	image	NN
10_1101-2021_01_08_425885	189	5	patches	patch	NNS
10_1101-2021_01_08_425885	189	6	constructed	construct	VBN
10_1101-2021_01_08_425885	189	7	by	by	IN
10_1101-2021_01_08_425885	189	8	this	this	DT
10_1101-2021_01_08_425885	189	9	embedding	embedding	NN
10_1101-2021_01_08_425885	189	10	obey	obey	NN
10_1101-2021_01_08_425885	189	11	the	the	DT
10_1101-2021_01_08_425885	189	12	same	same	JJ
10_1101-2021_01_08_425885	189	13	similarity	similarity	NN
10_1101-2021_01_08_425885	189	14	relation	relation	NN
10_1101-2021_01_08_425885	189	15	(	(	-LRB-
10_1101-2021_01_08_425885	189	16	θ	θ	NNP
10_1101-2021_01_08_425885	189	17	,	,	,
10_1101-2021_01_08_425885	189	18	φ	φ	NNP
10_1101-2021_01_08_425885	189	19	)	)	-RRB-
10_1101-2021_01_08_425885	189	20	∼	∼	NNP
10_1101-2021_01_08_425885	189	21	(	(	-LRB-
10_1101-2021_01_08_425885	189	22	θ+π	θ+π	UH
10_1101-2021_01_08_425885	189	23	,	,	,
10_1101-2021_01_08_425885	189	24	2π−φ	2π−φ	JJ
10_1101-2021_01_08_425885	189	25	)	)	-RRB-
10_1101-2021_01_08_425885	189	26	topologically	topologically	RB
10_1101-2021_01_08_425885	189	27	required	require	VBN
10_1101-2021_01_08_425885	189	28	of	of	IN
10_1101-2021_01_08_425885	189	29	a	a	DT
10_1101-2021_01_08_425885	189	30	Klein	Klein	NNP
10_1101-2021_01_08_425885	189	31	bottle	bottle	NN
10_1101-2021_01_08_425885	189	32	.	.	.
10_1101-2021_01_08_425885	190	1	Whereas	whereas	IN
10_1101-2021_01_08_425885	190	2	Carlsson	Carlsson	NNP
10_1101-2021_01_08_425885	190	3	et	et	FW
10_1101-2021_01_08_425885	190	4	al	al	NNP
10_1101-2021_01_08_425885	190	5	.	.	.
10_1101-2021_01_08_425885	191	1	studied	study	VBD
10_1101-2021_01_08_425885	191	2	the	the	DT
10_1101-2021_01_08_425885	191	3	global	global	JJ
10_1101-2021_01_08_425885	191	4	topology	topology	NN
10_1101-2021_01_08_425885	191	5	of	of	IN
10_1101-2021_01_08_425885	191	6	image	image	NN
10_1101-2021_01_08_425885	191	7	patches	patch	NNS
10_1101-2021_01_08_425885	191	8	using	use	VBG
10_1101-2021_01_08_425885	191	9	this	this	DT
10_1101-2021_01_08_425885	191	10	embedding	embedding	NN
10_1101-2021_01_08_425885	191	11	,	,	,
10_1101-2021_01_08_425885	191	12	here	here	RB
10_1101-2021_01_08_425885	191	13	we	-PRON-	PRP
10_1101-2021_01_08_425885	191	14	study	study	VBP
10_1101-2021_01_08_425885	191	15	their	-PRON-	PRP$
10_1101-2021_01_08_425885	191	16	local	local	JJ
10_1101-2021_01_08_425885	191	17	geometry	geometry	NN
10_1101-2021_01_08_425885	191	18	instead	instead	RB
10_1101-2021_01_08_425885	191	19	.	.	.
10_1101-2021_01_08_425885	192	1	First	first	RB
10_1101-2021_01_08_425885	192	2	,	,	,
10_1101-2021_01_08_425885	192	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	192	4	analytically	analytically	RB
10_1101-2021_01_08_425885	192	5	calculated	calculate	VBD
10_1101-2021_01_08_425885	192	6	the	the	DT
10_1101-2021_01_08_425885	192	7	scalar	scalar	JJ
10_1101-2021_01_08_425885	192	8	curvature	curvature	NN
10_1101-2021_01_08_425885	192	9	of	of	IN
10_1101-2021_01_08_425885	192	10	k0	k0	NNP
10_1101-2021_01_08_425885	192	11	as	as	IN
10_1101-2021_01_08_425885	192	12	a	a	DT
10_1101-2021_01_08_425885	192	13	function	function	NN
10_1101-2021_01_08_425885	192	14	of	of	IN
10_1101-2021_01_08_425885	192	15	(	(	-LRB-
10_1101-2021_01_08_425885	192	16	θ	θ	NNP
10_1101-2021_01_08_425885	192	17	,	,	,
10_1101-2021_01_08_425885	192	18	φ	φ	NNP
10_1101-2021_01_08_425885	192	19	)	)	-RRB-
10_1101-2021_01_08_425885	192	20	as	as	IN
10_1101-2021_01_08_425885	192	21	shown	show	VBN
10_1101-2021_01_08_425885	192	22	in	in	IN
10_1101-2021_01_08_425885	192	23	Figure	figure	NN
10_1101-2021_01_08_425885	192	24	3C	3c	NN
10_1101-2021_01_08_425885	192	25	(	(	-LRB-
10_1101-2021_01_08_425885	192	26	see	see	VB
10_1101-2021_01_08_425885	192	27	Methods	Methods	NNP
10_1101-2021_01_08_425885	192	28	Section	Section	NNP
10_1101-2021_01_08_425885	192	29	4.1	4.1	CD
10_1101-2021_01_08_425885	192	30	)	)	-RRB-
10_1101-2021_01_08_425885	192	31	.	.	.
10_1101-2021_01_08_425885	193	1	Next	next	RB
10_1101-2021_01_08_425885	193	2	,	,	,
10_1101-2021_01_08_425885	193	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	193	4	used	use	VBD
10_1101-2021_01_08_425885	193	5	our	-PRON-	PRP$
10_1101-2021_01_08_425885	193	6	algorithm	algorithm	NN
10_1101-2021_01_08_425885	193	7	to	to	TO
10_1101-2021_01_08_425885	193	8	compute	compute	VB
10_1101-2021_01_08_425885	193	9	the	the	DT
10_1101-2021_01_08_425885	193	10	scalar	scalar	JJ
10_1101-2021_01_08_425885	193	11	curvature	curvature	NN
10_1101-2021_01_08_425885	193	12	on	on	IN
10_1101-2021_01_08_425885	193	13	a	a	DT
10_1101-2021_01_08_425885	193	14	data	data	NN
10_1101-2021_01_08_425885	193	15	manifold	manifold	NN
10_1101-2021_01_08_425885	193	16	of	of	IN
10_1101-2021_01_08_425885	193	17	N	N	NNP
10_1101-2021_01_08_425885	193	18	≈	≈	NNP
10_1101-2021_01_08_425885	193	19	4.2×105	4.2×105	CD
10_1101-2021_01_08_425885	193	20	high	high	JJ
10_1101-2021_01_08_425885	193	21	-	-	HYPH
10_1101-2021_01_08_425885	193	22	contrast	contrast	NN
10_1101-2021_01_08_425885	193	23	3x3-pixel	3x3-pixel	CD
10_1101-2021_01_08_425885	193	24	image	image	NN
10_1101-2021_01_08_425885	193	25	patches	patch	NNS
10_1101-2021_01_08_425885	193	26	randomly	randomly	RB
10_1101-2021_01_08_425885	193	27	sampled	sample	VBN
10_1101-2021_01_08_425885	193	28	from	from	IN
10_1101-2021_01_08_425885	193	29	the	the	DT
10_1101-2021_01_08_425885	193	30	same	same	JJ
10_1101-2021_01_08_425885	193	31	van	van	NNP
10_1101-2021_01_08_425885	193	32	Hateren	Hateren	NNP
10_1101-2021_01_08_425885	193	33	dataset	dataset	NN
10_1101-2021_01_08_425885	193	34	used	use	VBD
10_1101-2021_01_08_425885	193	35	to	to	TO
10_1101-2021_01_08_425885	193	36	propose	propose	VB
10_1101-2021_01_08_425885	193	37	k0	k0	NNP
10_1101-2021_01_08_425885	193	38	(	(	-LRB-
10_1101-2021_01_08_425885	193	39	see	see	VB
10_1101-2021_01_08_425885	193	40	Methods	Methods	NNP
10_1101-2021_01_08_425885	193	41	Section	Section	NNP
10_1101-2021_01_08_425885	193	42	4.5.2	4.5.2	CD
10_1101-2021_01_08_425885	193	43	)	)	-RRB-
10_1101-2021_01_08_425885	193	44	.	.	.
10_1101-2021_01_08_425885	194	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	194	2	picked	pick	VBD
10_1101-2021_01_08_425885	194	3	σh	σh	NNP
10_1101-2021_01_08_425885	194	4	so	so	IN
10_1101-2021_01_08_425885	194	5	that	that	IN
10_1101-2021_01_08_425885	194	6	the	the	DT
10_1101-2021_01_08_425885	194	7	distribution	distribution	NN
10_1101-2021_01_08_425885	194	8	of	of	IN
10_1101-2021_01_08_425885	194	9	GOF	GOF	NNP
10_1101-2021_01_08_425885	194	10	p	p	NN
10_1101-2021_01_08_425885	194	11	-	-	HYPH
10_1101-2021_01_08_425885	194	12	values	value	NNS
10_1101-2021_01_08_425885	194	13	was	be	VBD
10_1101-2021_01_08_425885	194	14	flat	flat	JJ
10_1101-2021_01_08_425885	194	15	,	,	,
10_1101-2021_01_08_425885	194	16	and	and	CC
10_1101-2021_01_08_425885	194	17	fixed	fix	VBD
10_1101-2021_01_08_425885	194	18	this	this	DT
10_1101-2021_01_08_425885	194	19	value	value	NN
10_1101-2021_01_08_425885	194	20	for	for	IN
10_1101-2021_01_08_425885	194	21	all	all	DT
10_1101-2021_01_08_425885	194	22	subsequent	subsequent	JJ
10_1101-2021_01_08_425885	194	23	simulations	simulation	NNS
10_1101-2021_01_08_425885	194	24	(	(	-LRB-
10_1101-2021_01_08_425885	194	25	see	see	VB
10_1101-2021_01_08_425885	194	26	Methods	Methods	NNP
10_1101-2021_01_08_425885	194	27	Section	Section	NNP
10_1101-2021_01_08_425885	194	28	4.5.7	4.5.7	CD
10_1101-2021_01_08_425885	194	29	)	)	-RRB-
10_1101-2021_01_08_425885	194	30	.	.	.
10_1101-2021_01_08_425885	195	1	To	to	TO
10_1101-2021_01_08_425885	195	2	visualize	visualize	VB
10_1101-2021_01_08_425885	195	3	the	the	DT
10_1101-2021_01_08_425885	195	4	results	result	NNS
10_1101-2021_01_08_425885	195	5	,	,	,
10_1101-2021_01_08_425885	195	6	we	-PRON-	PRP
10_1101-2021_01_08_425885	195	7	associated	associate	VBD
10_1101-2021_01_08_425885	195	8	each	each	DT
10_1101-2021_01_08_425885	195	9	image	image	NN
10_1101-2021_01_08_425885	195	10	patch	patch	NN
10_1101-2021_01_08_425885	195	11	to	to	IN
10_1101-2021_01_08_425885	195	12	its	-PRON-	PRP$
10_1101-2021_01_08_425885	195	13	closest	close	JJS
10_1101-2021_01_08_425885	195	14	point	point	NN
10_1101-2021_01_08_425885	195	15	on	on	IN
10_1101-2021_01_08_425885	195	16	k0	k0	NNP
10_1101-2021_01_08_425885	195	17	(	(	-LRB-
10_1101-2021_01_08_425885	195	18	see	see	VB
10_1101-2021_01_08_425885	195	19	Methods	Methods	NNP
10_1101-2021_01_08_425885	195	20	Section	Section	NNP
10_1101-2021_01_08_425885	195	21	4.5.4	4.5.4	CD
10_1101-2021_01_08_425885	195	22	)	)	-RRB-
10_1101-2021_01_08_425885	195	23	,	,	,
10_1101-2021_01_08_425885	195	24	and	and	CC
10_1101-2021_01_08_425885	195	25	plotted	plot	VBD
10_1101-2021_01_08_425885	195	26	the	the	DT
10_1101-2021_01_08_425885	195	27	scalar	scalar	JJ
10_1101-2021_01_08_425885	195	28	curvatures	curvature	NNS
10_1101-2021_01_08_425885	195	29	on	on	IN
10_1101-2021_01_08_425885	195	30	the	the	DT
10_1101-2021_01_08_425885	195	31	resulting	result	VBG
10_1101-2021_01_08_425885	195	32	(	(	-LRB-
10_1101-2021_01_08_425885	195	33	θ0,φ0	θ0,φ0	NN
10_1101-2021_01_08_425885	195	34	)	)	-RRB-
10_1101-2021_01_08_425885	195	35	coordinates	coordinate	VBZ
10_1101-2021_01_08_425885	195	36	(	(	-LRB-
10_1101-2021_01_08_425885	195	37	see	see	VB
10_1101-2021_01_08_425885	195	38	Figure	Figure	NNP
10_1101-2021_01_08_425885	195	39	3D	3d	NN
10_1101-2021_01_08_425885	195	40	)	)	-RRB-
10_1101-2021_01_08_425885	195	41	.	.	.
10_1101-2021_01_08_425885	196	1	Most	Most	JJS
10_1101-2021_01_08_425885	196	2	image	image	NN
10_1101-2021_01_08_425885	196	3	patches	patch	NNS
10_1101-2021_01_08_425885	196	4	map	map	VBP
10_1101-2021_01_08_425885	196	5	to	to	IN
10_1101-2021_01_08_425885	196	6	φ	φ	NN
10_1101-2021_01_08_425885	196	7	=	=	SYM
10_1101-2021_01_08_425885	196	8	π	π	NN
10_1101-2021_01_08_425885	196	9	2	2	CD
10_1101-2021_01_08_425885	196	10	,	,	,
10_1101-2021_01_08_425885	196	11	3π	3π	CD
10_1101-2021_01_08_425885	196	12	2	2	CD
10_1101-2021_01_08_425885	196	13	or	or	CC
10_1101-2021_01_08_425885	196	14	θ	θ	NNP
10_1101-2021_01_08_425885	196	15	=	=	SYM
10_1101-2021_01_08_425885	196	16	0	0	CD
10_1101-2021_01_08_425885	196	17	,	,	,
10_1101-2021_01_08_425885	196	18	π	π	NN
10_1101-2021_01_08_425885	196	19	2	2	CD
10_1101-2021_01_08_425885	196	20	because	because	IN
10_1101-2021_01_08_425885	196	21	linear	linear	JJ
10_1101-2021_01_08_425885	196	22	gradients	gradient	NNS
10_1101-2021_01_08_425885	196	23	(	(	-LRB-
10_1101-2021_01_08_425885	196	24	of	of	IN
10_1101-2021_01_08_425885	196	25	any	any	DT
10_1101-2021_01_08_425885	196	26	orientation	orientation	NN
10_1101-2021_01_08_425885	196	27	)	)	-RRB-
10_1101-2021_01_08_425885	196	28	and	and	CC
10_1101-2021_01_08_425885	196	29	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	196	30	gradients	gradient	NNS
10_1101-2021_01_08_425885	196	31	that	that	WDT
10_1101-2021_01_08_425885	196	32	are	be	VBP
10_1101-2021_01_08_425885	196	33	vertically	vertically	RB
10_1101-2021_01_08_425885	196	34	or	or	CC
10_1101-2021_01_08_425885	196	35	horizontally	horizontally	RB
10_1101-2021_01_08_425885	196	36	oriented	orient	VBN
10_1101-2021_01_08_425885	196	37	are	be	VBP
10_1101-2021_01_08_425885	196	38	the	the	DT
10_1101-2021_01_08_425885	196	39	dominant	dominant	JJ
10_1101-2021_01_08_425885	196	40	features	feature	NNS
10_1101-2021_01_08_425885	196	41	in	in	IN
10_1101-2021_01_08_425885	196	42	the	the	DT
10_1101-2021_01_08_425885	196	43	data	datum	NNS
10_1101-2021_01_08_425885	196	44	as	as	IN
10_1101-2021_01_08_425885	196	45	previously	previously	RB
10_1101-2021_01_08_425885	196	46	reported	report	VBN
10_1101-2021_01_08_425885	196	47	[	[	-LRB-
10_1101-2021_01_08_425885	196	48	21	21	CD
10_1101-2021_01_08_425885	196	49	,	,	,
10_1101-2021_01_08_425885	196	50	40	40	CD
10_1101-2021_01_08_425885	196	51	]	]	-RRB-
10_1101-2021_01_08_425885	196	52	.	.	.
10_1101-2021_01_08_425885	197	1	The	the	DT
10_1101-2021_01_08_425885	197	2	scalar	scalar	JJ
10_1101-2021_01_08_425885	197	3	curvatures	curvature	NNS
10_1101-2021_01_08_425885	197	4	computed	compute	VBD
10_1101-2021_01_08_425885	197	5	for	for	IN
10_1101-2021_01_08_425885	197	6	the	the	DT
10_1101-2021_01_08_425885	197	7	image	image	NN
10_1101-2021_01_08_425885	197	8	patches	patch	NNS
10_1101-2021_01_08_425885	197	9	did	do	VBD
10_1101-2021_01_08_425885	197	10	not	not	RB
10_1101-2021_01_08_425885	197	11	match	match	VB
10_1101-2021_01_08_425885	197	12	the	the	DT
10_1101-2021_01_08_425885	197	13	analytical	analytical	JJ
10_1101-2021_01_08_425885	197	14	scalar	scalar	JJ
10_1101-2021_01_08_425885	197	15	curvature	curvature	NN
10_1101-2021_01_08_425885	197	16	of	of	IN
10_1101-2021_01_08_425885	197	17	k0	k0	NNP
10_1101-2021_01_08_425885	197	18	(	(	-LRB-
10_1101-2021_01_08_425885	197	19	cf	cf	NN
10_1101-2021_01_08_425885	197	20	.	.	.
10_1101-2021_01_08_425885	198	1	Figures	figure	NNS
10_1101-2021_01_08_425885	198	2	3C	3c	NN
10_1101-2021_01_08_425885	198	3	and	and	CC
10_1101-2021_01_08_425885	198	4	3D	3d	NN
10_1101-2021_01_08_425885	198	5	)	)	-RRB-
10_1101-2021_01_08_425885	198	6	.	.	.
10_1101-2021_01_08_425885	199	1	To	to	TO
10_1101-2021_01_08_425885	199	2	identify	identify	VB
10_1101-2021_01_08_425885	199	3	the	the	DT
10_1101-2021_01_08_425885	199	4	cause	cause	NN
10_1101-2021_01_08_425885	199	5	of	of	IN
10_1101-2021_01_08_425885	199	6	this	this	DT
10_1101-2021_01_08_425885	199	7	discrepancy	discrepancy	NN
10_1101-2021_01_08_425885	199	8	,	,	,
10_1101-2021_01_08_425885	199	9	we	-PRON-	PRP
10_1101-2021_01_08_425885	199	10	first	first	RB
10_1101-2021_01_08_425885	199	11	validated	validate	VBD
10_1101-2021_01_08_425885	199	12	our	-PRON-	PRP$
10_1101-2021_01_08_425885	199	13	algorithm	algorithm	NN
10_1101-2021_01_08_425885	199	14	by	by	IN
10_1101-2021_01_08_425885	199	15	computing	compute	VBG
10_1101-2021_01_08_425885	199	16	scalar	scalar	JJ
10_1101-2021_01_08_425885	199	17	curvatures	curvature	NNS
10_1101-2021_01_08_425885	199	18	on	on	IN
10_1101-2021_01_08_425885	199	19	the	the	DT
10_1101-2021_01_08_425885	199	20	set	set	NN
10_1101-2021_01_08_425885	199	21	of	of	IN
10_1101-2021_01_08_425885	199	22	N	N	NNP
10_1101-2021_01_08_425885	199	23	≈	≈	NNP
10_1101-2021_01_08_425885	199	24	4.2	4.2	CD
10_1101-2021_01_08_425885	199	25	×	×	CD
10_1101-2021_01_08_425885	199	26	105	105	CD
10_1101-2021_01_08_425885	199	27	(	(	-LRB-
10_1101-2021_01_08_425885	199	28	θ0,φ0	θ0,φ0	NN
10_1101-2021_01_08_425885	199	29	)	)	-RRB-
10_1101-2021_01_08_425885	199	30	points	point	NNS
10_1101-2021_01_08_425885	199	31	on	on	IN
10_1101-2021_01_08_425885	199	32	k0	k0	NNP
10_1101-2021_01_08_425885	199	33	associated	associate	VBN
10_1101-2021_01_08_425885	199	34	with	with	IN
10_1101-2021_01_08_425885	199	35	the	the	DT
10_1101-2021_01_08_425885	199	36	image	image	NN
10_1101-2021_01_08_425885	199	37	patches	patch	NNS
10_1101-2021_01_08_425885	199	38	(	(	-LRB-
10_1101-2021_01_08_425885	199	39	see	see	VB
10_1101-2021_01_08_425885	199	40	Figure	Figure	NNP
10_1101-2021_01_08_425885	199	41	3E	3e	NN
10_1101-2021_01_08_425885	199	42	)	)	-RRB-
10_1101-2021_01_08_425885	199	43	;	;	:
10_1101-2021_01_08_425885	199	44	we	-PRON-	PRP
10_1101-2021_01_08_425885	199	45	found	find	VBD
10_1101-2021_01_08_425885	199	46	close	close	JJ
10_1101-2021_01_08_425885	199	47	agreement	agreement	NN
10_1101-2021_01_08_425885	199	48	with	with	IN
10_1101-2021_01_08_425885	199	49	the	the	DT
10_1101-2021_01_08_425885	199	50	analytical	analytical	JJ
10_1101-2021_01_08_425885	199	51	calculation	calculation	NN
10_1101-2021_01_08_425885	199	52	(	(	-LRB-
10_1101-2021_01_08_425885	199	53	75	75	CD
10_1101-2021_01_08_425885	199	54	%	%	NN
10_1101-2021_01_08_425885	199	55	of	of	IN
10_1101-2021_01_08_425885	199	56	points	point	NNS
10_1101-2021_01_08_425885	199	57	reported	report	VBD
10_1101-2021_01_08_425885	199	58	a	a	DT
10_1101-2021_01_08_425885	199	59	95	95	CD
10_1101-2021_01_08_425885	199	60	%	%	NN
10_1101-2021_01_08_425885	199	61	CI	ci	NN
10_1101-2021_01_08_425885	199	62	containing	contain	VBG
10_1101-2021_01_08_425885	199	63	the	the	DT
10_1101-2021_01_08_425885	199	64	true	true	JJ
10_1101-2021_01_08_425885	199	65	scalar	scalar	JJ
10_1101-2021_01_08_425885	199	66	curvature	curvature	NN
10_1101-2021_01_08_425885	199	67	)	)	-RRB-
10_1101-2021_01_08_425885	199	68	.	.	.
10_1101-2021_01_08_425885	200	1	Next	next	RB
10_1101-2021_01_08_425885	200	2	,	,	,
10_1101-2021_01_08_425885	200	3	observing	observe	VBG
10_1101-2021_01_08_425885	200	4	that	that	IN
10_1101-2021_01_08_425885	200	5	the	the	DT
10_1101-2021_01_08_425885	200	6	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	200	7	sizes	size	NNS
10_1101-2021_01_08_425885	200	8	used	use	VBN
10_1101-2021_01_08_425885	200	9	for	for	IN
10_1101-2021_01_08_425885	200	10	computing	compute	VBG
10_1101-2021_01_08_425885	200	11	the	the	DT
10_1101-2021_01_08_425885	200	12	scalar	scalar	JJ
10_1101-2021_01_08_425885	200	13	curvature	curvature	NN
10_1101-2021_01_08_425885	200	14	of	of	IN
10_1101-2021_01_08_425885	200	15	image	image	NN
10_1101-2021_01_08_425885	200	16	patches	patch	NNS
10_1101-2021_01_08_425885	200	17	were	be	VBD
10_1101-2021_01_08_425885	200	18	larger	large	JJR
10_1101-2021_01_08_425885	200	19	than	than	IN
10_1101-2021_01_08_425885	200	20	those	those	DT
10_1101-2021_01_08_425885	200	21	used	use	VBN
10_1101-2021_01_08_425885	200	22	for	for	IN
10_1101-2021_01_08_425885	200	23	computing	compute	VBG
10_1101-2021_01_08_425885	200	24	the	the	DT
10_1101-2021_01_08_425885	200	25	scalar	scalar	JJ
10_1101-2021_01_08_425885	200	26	curvature	curvature	NN
10_1101-2021_01_08_425885	200	27	of	of	IN
10_1101-2021_01_08_425885	200	28	the	the	DT
10_1101-2021_01_08_425885	200	29	associated	associated	JJ
10_1101-2021_01_08_425885	200	30	(	(	-LRB-
10_1101-2021_01_08_425885	200	31	θ0,φ0	θ0,φ0	NNP
10_1101-2021_01_08_425885	200	32	)	)	-RRB-
10_1101-2021_01_08_425885	200	33	points	point	NNS
10_1101-2021_01_08_425885	200	34	(	(	-LRB-
10_1101-2021_01_08_425885	200	35	cf	cf	NN
10_1101-2021_01_08_425885	200	36	.	.	.
10_1101-2021_01_08_425885	201	1	Figures	figure	NNS
10_1101-2021_01_08_425885	201	2	S3A	s3a	NN
10_1101-2021_01_08_425885	201	3	and	and	CC
10_1101-2021_01_08_425885	201	4	S3B	s3b	NN
10_1101-2021_01_08_425885	201	5	)	)	-RRB-
10_1101-2021_01_08_425885	201	6	,	,	,
10_1101-2021_01_08_425885	201	7	we	-PRON-	PRP
10_1101-2021_01_08_425885	201	8	recomputed	recompute	VBD
10_1101-2021_01_08_425885	201	9	the	the	DT
10_1101-2021_01_08_425885	201	10	scalar	scalar	JJ
10_1101-2021_01_08_425885	201	11	curvatures	curvature	NNS
10_1101-2021_01_08_425885	201	12	of	of	IN
10_1101-2021_01_08_425885	201	13	these	these	DT
10_1101-2021_01_08_425885	201	14	(	(	-LRB-
10_1101-2021_01_08_425885	201	15	θ0,φ0	θ0,φ0	NN
10_1101-2021_01_08_425885	201	16	)	)	-RRB-
10_1101-2021_01_08_425885	201	17	points	point	NNS
10_1101-2021_01_08_425885	201	18	,	,	,
10_1101-2021_01_08_425885	201	19	but	but	CC
10_1101-2021_01_08_425885	201	20	now	now	RB
10_1101-2021_01_08_425885	201	21	with	with	IN
10_1101-2021_01_08_425885	201	22	the	the	DT
10_1101-2021_01_08_425885	201	23	same	same	JJ
10_1101-2021_01_08_425885	201	24	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	201	25	sizes	size	NNS
10_1101-2021_01_08_425885	201	26	used	use	VBN
10_1101-2021_01_08_425885	201	27	for	for	IN
10_1101-2021_01_08_425885	201	28	the	the	DT
10_1101-2021_01_08_425885	201	29	image	image	NN
10_1101-2021_01_08_425885	201	30	patches	patch	NNS
10_1101-2021_01_08_425885	201	31	.	.	.
10_1101-2021_01_08_425885	202	1	The	the	DT
10_1101-2021_01_08_425885	202	2	results	result	NNS
10_1101-2021_01_08_425885	202	3	agreed	agree	VBD
10_1101-2021_01_08_425885	202	4	with	with	IN
10_1101-2021_01_08_425885	202	5	the	the	DT
10_1101-2021_01_08_425885	202	6	analytical	analytical	JJ
10_1101-2021_01_08_425885	202	7	calculation	calculation	NN
10_1101-2021_01_08_425885	202	8	,	,	,
10_1101-2021_01_08_425885	202	9	but	but	CC
10_1101-2021_01_08_425885	202	10	still	still	RB
10_1101-2021_01_08_425885	202	11	did	do	VBD
10_1101-2021_01_08_425885	202	12	not	not	RB
10_1101-2021_01_08_425885	202	13	match	match	VB
10_1101-2021_01_08_425885	202	14	the	the	DT
10_1101-2021_01_08_425885	202	15	scalar	scalar	JJ
10_1101-2021_01_08_425885	202	16	curvatures	curvature	NNS
10_1101-2021_01_08_425885	202	17	computed	compute	VBD
10_1101-2021_01_08_425885	202	18	for	for	IN
10_1101-2021_01_08_425885	202	19	the	the	DT
10_1101-2021_01_08_425885	202	20	image	image	NN
10_1101-2021_01_08_425885	202	21	patches	patch	NNS
10_1101-2021_01_08_425885	202	22	(	(	-LRB-
10_1101-2021_01_08_425885	202	23	see	see	VB
10_1101-2021_01_08_425885	202	24	Figure	Figure	NNP
10_1101-2021_01_08_425885	202	25	S3C	S3C	NNS
10_1101-2021_01_08_425885	202	26	)	)	-RRB-
10_1101-2021_01_08_425885	202	27	.	.	.
10_1101-2021_01_08_425885	203	1	Having	have	VBG
10_1101-2021_01_08_425885	203	2	ruled	rule	VBN
10_1101-2021_01_08_425885	203	3	out	out	RP
10_1101-2021_01_08_425885	203	4	these	these	DT
10_1101-2021_01_08_425885	203	5	two	two	CD
10_1101-2021_01_08_425885	203	6	possibilities	possibility	NNS
10_1101-2021_01_08_425885	203	7	,	,	,
10_1101-2021_01_08_425885	203	8	we	-PRON-	PRP
10_1101-2021_01_08_425885	203	9	hypothesized	hypothesize	VBD
10_1101-2021_01_08_425885	203	10	that	that	IN
10_1101-2021_01_08_425885	203	11	the	the	DT
10_1101-2021_01_08_425885	203	12	discrepancy	discrepancy	NN
10_1101-2021_01_08_425885	203	13	was	be	VBD
10_1101-2021_01_08_425885	203	14	caused	cause	VBN
10_1101-2021_01_08_425885	203	15	by	by	IN
10_1101-2021_01_08_425885	203	16	fluctuations	fluctuation	NNS
10_1101-2021_01_08_425885	203	17	in	in	IN
10_1101-2021_01_08_425885	203	18	the	the	DT
10_1101-2021_01_08_425885	203	19	positions	position	NNS
10_1101-2021_01_08_425885	203	20	of	of	IN
10_1101-2021_01_08_425885	203	21	the	the	DT
10_1101-2021_01_08_425885	203	22	image	image	NN
10_1101-2021_01_08_425885	203	23	patches	patch	NNS
10_1101-2021_01_08_425885	203	24	with	with	IN
10_1101-2021_01_08_425885	203	25	respect	respect	NN
10_1101-2021_01_08_425885	203	26	to	to	IN
10_1101-2021_01_08_425885	203	27	the	the	DT
10_1101-2021_01_08_425885	203	28	(	(	-LRB-
10_1101-2021_01_08_425885	203	29	θ0,φ0	θ0,φ0	NN
10_1101-2021_01_08_425885	203	30	)	)	-RRB-
10_1101-2021_01_08_425885	203	31	points	point	VBZ
10_1101-2021_01_08_425885	203	32	on	on	IN
10_1101-2021_01_08_425885	203	33	the	the	DT
10_1101-2021_01_08_425885	203	34	k	k	NNP
10_1101-2021_01_08_425885	203	35	0	0	CD
10_1101-2021_01_08_425885	203	36	manifold	manifold	NN
10_1101-2021_01_08_425885	203	37	(	(	-LRB-
10_1101-2021_01_08_425885	203	38	real	real	JJ
10_1101-2021_01_08_425885	203	39	image	image	NN
10_1101-2021_01_08_425885	203	40	patches	patch	NNS
10_1101-2021_01_08_425885	203	41	are	be	VBP
10_1101-2021_01_08_425885	203	42	noisy	noisy	JJ
10_1101-2021_01_08_425885	203	43	and	and	CC
10_1101-2021_01_08_425885	203	44	the	the	DT
10_1101-2021_01_08_425885	203	45	Klein	Klein	NNP
10_1101-2021_01_08_425885	203	46	bottle	bottle	NN
10_1101-2021_01_08_425885	203	47	embedding	embedding	NN
10_1101-2021_01_08_425885	203	48	is	be	VBZ
10_1101-2021_01_08_425885	203	49	only	only	RB
10_1101-2021_01_08_425885	203	50	an	an	DT
10_1101-2021_01_08_425885	203	51	idealization	idealization	NN
10_1101-2021_01_08_425885	203	52	)	)	-RRB-
10_1101-2021_01_08_425885	203	53	.	.	.
10_1101-2021_01_08_425885	204	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	204	2	found	find	VBD
10_1101-2021_01_08_425885	204	3	that	that	IN
10_1101-2021_01_08_425885	204	4	adding	add	VBG
10_1101-2021_01_08_425885	204	5	isotropic	isotropic	JJ
10_1101-2021_01_08_425885	204	6	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	204	7	noise	noise	NN
10_1101-2021_01_08_425885	204	8	of	of	IN
10_1101-2021_01_08_425885	204	9	increasing	increase	VBG
10_1101-2021_01_08_425885	204	10	magnitude	magnitude	NN
10_1101-2021_01_08_425885	204	11	in	in	IN
10_1101-2021_01_08_425885	204	12	R9	R9	NNP
10_1101-2021_01_08_425885	204	13	to	to	IN
10_1101-2021_01_08_425885	204	14	the	the	DT
10_1101-2021_01_08_425885	204	15	set	set	NN
10_1101-2021_01_08_425885	204	16	of	of	IN
10_1101-2021_01_08_425885	204	17	(	(	-LRB-
10_1101-2021_01_08_425885	204	18	θ0,φ0	θ0,φ0	NN
10_1101-2021_01_08_425885	204	19	)	)	-RRB-
10_1101-2021_01_08_425885	204	20	points	point	NNS
10_1101-2021_01_08_425885	204	21	on	on	IN
10_1101-2021_01_08_425885	204	22	k0	k0	NNP
10_1101-2021_01_08_425885	204	23	indeed	indeed	RB
10_1101-2021_01_08_425885	204	24	resulted	result	VBD
10_1101-2021_01_08_425885	204	25	in	in	IN
10_1101-2021_01_08_425885	204	26	scalar	scalar	JJ
10_1101-2021_01_08_425885	204	27	curvatures	curvature	NNS
10_1101-2021_01_08_425885	204	28	that	that	WDT
10_1101-2021_01_08_425885	204	29	resemble	resemble	VBP
10_1101-2021_01_08_425885	204	30	the	the	DT
10_1101-2021_01_08_425885	204	31	data	datum	NNS
10_1101-2021_01_08_425885	204	32	(	(	-LRB-
10_1101-2021_01_08_425885	204	33	see	see	VB
10_1101-2021_01_08_425885	204	34	Figure	figure	NN
10_1101-2021_01_08_425885	204	35	3F	3f	NN
10_1101-2021_01_08_425885	204	36	;	;	:
10_1101-2021_01_08_425885	204	37	Methods	Methods	NNP
10_1101-2021_01_08_425885	204	38	Section	Section	NNP
10_1101-2021_01_08_425885	204	39	4.5.6	4.5.6	CD
10_1101-2021_01_08_425885	204	40	)	)	-RRB-
10_1101-2021_01_08_425885	204	41	.	.	.
10_1101-2021_01_08_425885	205	1	The	the	DT
10_1101-2021_01_08_425885	205	2	best	good	JJS
10_1101-2021_01_08_425885	205	3	agreement	agreement	NN
10_1101-2021_01_08_425885	205	4	between	between	IN
10_1101-2021_01_08_425885	205	5	the	the	DT
10_1101-2021_01_08_425885	205	6	scalar	scalar	JJ
10_1101-2021_01_08_425885	205	7	curvatures	curvature	NNS
10_1101-2021_01_08_425885	205	8	of	of	IN
10_1101-2021_01_08_425885	205	9	the	the	DT
10_1101-2021_01_08_425885	205	10	image	image	NN
10_1101-2021_01_08_425885	205	11	patches	patch	NNS
10_1101-2021_01_08_425885	205	12	and	and	CC
10_1101-2021_01_08_425885	205	13	the	the	DT
10_1101-2021_01_08_425885	205	14	noisy	noisy	JJ
10_1101-2021_01_08_425885	205	15	(	(	-LRB-
10_1101-2021_01_08_425885	205	16	θ0,φ0	θ0,φ0	NNP
10_1101-2021_01_08_425885	205	17	)	)	-RRB-
10_1101-2021_01_08_425885	205	18	points	point	NNS
10_1101-2021_01_08_425885	205	19	was	be	VBD
10_1101-2021_01_08_425885	205	20	achieved	achieve	VBN
10_1101-2021_01_08_425885	205	21	when	when	WRB
10_1101-2021_01_08_425885	205	22	the	the	DT
10_1101-2021_01_08_425885	205	23	magnitude	magnitude	NN
10_1101-2021_01_08_425885	205	24	of	of	IN
10_1101-2021_01_08_425885	205	25	noise	noise	NN
10_1101-2021_01_08_425885	205	26	was	be	VBD
10_1101-2021_01_08_425885	205	27	12	12	CD
10_1101-2021_01_08_425885	205	28	.CC	.CC	,
10_1101-2021_01_08_425885	205	29	-	-	HYPH
10_1101-2021_01_08_425885	205	30	BY	by	IN
10_1101-2021_01_08_425885	205	31	-	-	HYPH
10_1101-2021_01_08_425885	205	32	NC	NC	NNP
10_1101-2021_01_08_425885	205	33	-	-	HYPH
10_1101-2021_01_08_425885	205	34	ND	ND	NNP
10_1101-2021_01_08_425885	205	35	4.0	4.0	CD
10_1101-2021_01_08_425885	205	36	International	International	NNP
10_1101-2021_01_08_425885	205	37	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	205	38	under	under	IN
10_1101-2021_01_08_425885	205	39	a	a	DT
10_1101-2021_01_08_425885	205	40	(	(	-LRB-
10_1101-2021_01_08_425885	205	41	which	which	WDT
10_1101-2021_01_08_425885	205	42	was	be	VBD
10_1101-2021_01_08_425885	205	43	not	not	RB
10_1101-2021_01_08_425885	205	44	certified	certify	VBN
10_1101-2021_01_08_425885	205	45	by	by	IN
10_1101-2021_01_08_425885	205	46	peer	peer	NN
10_1101-2021_01_08_425885	205	47	review	review	NN
10_1101-2021_01_08_425885	205	48	)	)	-RRB-
10_1101-2021_01_08_425885	205	49	is	be	VBZ
10_1101-2021_01_08_425885	205	50	the	the	DT
10_1101-2021_01_08_425885	205	51	author	author	NN
10_1101-2021_01_08_425885	205	52	/	/	SYM
10_1101-2021_01_08_425885	205	53	funder	funder	NN
10_1101-2021_01_08_425885	205	54	,	,	,
10_1101-2021_01_08_425885	205	55	who	who	WP
10_1101-2021_01_08_425885	205	56	has	have	VBZ
10_1101-2021_01_08_425885	205	57	granted	grant	VBN
10_1101-2021_01_08_425885	205	58	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	205	59	a	a	DT
10_1101-2021_01_08_425885	205	60	license	license	NN
10_1101-2021_01_08_425885	205	61	to	to	TO
10_1101-2021_01_08_425885	205	62	display	display	VB
10_1101-2021_01_08_425885	205	63	the	the	DT
10_1101-2021_01_08_425885	205	64	preprint	preprint	NN
10_1101-2021_01_08_425885	205	65	in	in	IN
10_1101-2021_01_08_425885	205	66	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	205	67	.	.	.
10_1101-2021_01_08_425885	206	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	206	2	is	be	VBZ
10_1101-2021_01_08_425885	206	3	made	make	VBN
10_1101-2021_01_08_425885	206	4	The	the	DT
10_1101-2021_01_08_425885	206	5	copyright	copyright	NN
10_1101-2021_01_08_425885	206	6	holder	holder	NN
10_1101-2021_01_08_425885	206	7	for	for	IN
10_1101-2021_01_08_425885	206	8	this	this	DT
10_1101-2021_01_08_425885	206	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	206	10	version	version	NN
10_1101-2021_01_08_425885	206	11	posted	post	VBD
10_1101-2021_01_08_425885	206	12	January	January	NNP
10_1101-2021_01_08_425885	206	13	8	8	CD
10_1101-2021_01_08_425885	206	14	,	,	,
10_1101-2021_01_08_425885	206	15	2021	2021	CD
10_1101-2021_01_08_425885	206	16	.	.	.
10_1101-2021_01_08_425885	206	17	;	;	:
10_1101-2021_01_08_425885	206	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	206	19	:	:	:
10_1101-2021_01_08_425885	206	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	206	21	preprint	preprint	NN
10_1101-2021_01_08_425885	206	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	206	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NN
10_1101-2021_01_08_425885	206	24	A	A	NNP
10_1101-2021_01_08_425885	206	25	B	b	NN
10_1101-2021_01_08_425885	206	26	C	c	NN
10_1101-2021_01_08_425885	206	27	D	d	NN
10_1101-2021_01_08_425885	206	28	E	e	NN
10_1101-2021_01_08_425885	206	29	F	f	NN
10_1101-2021_01_08_425885	206	30	G	g	NN
10_1101-2021_01_08_425885	206	31	H	h	NN
10_1101-2021_01_08_425885	206	32	I	-PRON-	PRP
10_1101-2021_01_08_425885	206	33	J	J	NNP
10_1101-2021_01_08_425885	206	34	Figure	figure	NN
10_1101-2021_01_08_425885	206	35	3	3	CD
10_1101-2021_01_08_425885	206	36	:	:	:
10_1101-2021_01_08_425885	206	37	Scalar	scalar	JJ
10_1101-2021_01_08_425885	206	38	curvature	curvature	NN
10_1101-2021_01_08_425885	206	39	computed	compute	VBD
10_1101-2021_01_08_425885	206	40	for	for	IN
10_1101-2021_01_08_425885	206	41	image	image	NN
10_1101-2021_01_08_425885	206	42	patches	patch	NNS
10_1101-2021_01_08_425885	206	43	is	be	VBZ
10_1101-2021_01_08_425885	206	44	consistent	consistent	JJ
10_1101-2021_01_08_425885	206	45	with	with	IN
10_1101-2021_01_08_425885	206	46	that	that	DT
10_1101-2021_01_08_425885	206	47	of	of	IN
10_1101-2021_01_08_425885	206	48	a	a	DT
10_1101-2021_01_08_425885	206	49	Klein	Klein	NNP
10_1101-2021_01_08_425885	206	50	bottle	bottle	NN
10_1101-2021_01_08_425885	206	51	with	with	IN
10_1101-2021_01_08_425885	206	52	added	add	VBN
10_1101-2021_01_08_425885	206	53	isotropic	isotropic	JJ
10_1101-2021_01_08_425885	206	54	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	206	55	noise	noise	NN
10_1101-2021_01_08_425885	206	56	.	.	.
10_1101-2021_01_08_425885	207	1	(	(	-LRB-
10_1101-2021_01_08_425885	207	2	A	a	NN
10_1101-2021_01_08_425885	207	3	)	)	-RRB-
10_1101-2021_01_08_425885	207	4	The	the	DT
10_1101-2021_01_08_425885	207	5	Klein	Klein	NNP
10_1101-2021_01_08_425885	207	6	bottle	bottle	NN
10_1101-2021_01_08_425885	207	7	,	,	,
10_1101-2021_01_08_425885	207	8	K2	K2	NNP
10_1101-2021_01_08_425885	207	9	,	,	,
10_1101-2021_01_08_425885	207	10	is	be	VBZ
10_1101-2021_01_08_425885	207	11	a	a	DT
10_1101-2021_01_08_425885	207	12	2-dimensional	2-dimensional	CD
10_1101-2021_01_08_425885	207	13	manifold	manifold	NN
10_1101-2021_01_08_425885	207	14	shown	show	VBN
10_1101-2021_01_08_425885	207	15	here	here	RB
10_1101-2021_01_08_425885	207	16	in	in	IN
10_1101-2021_01_08_425885	207	17	R3	r3	NN
10_1101-2021_01_08_425885	207	18	.	.	.
10_1101-2021_01_08_425885	208	1	(	(	-LRB-
10_1101-2021_01_08_425885	208	2	B	b	NN
10_1101-2021_01_08_425885	208	3	)	)	-RRB-
10_1101-2021_01_08_425885	208	4	k0	k0	NNP
10_1101-2021_01_08_425885	208	5	is	be	VBZ
10_1101-2021_01_08_425885	208	6	an	an	DT
10_1101-2021_01_08_425885	208	7	analytical	analytical	JJ
10_1101-2021_01_08_425885	208	8	embedding	embedding	NN
10_1101-2021_01_08_425885	208	9	given	give	VBN
10_1101-2021_01_08_425885	208	10	by	by	IN
10_1101-2021_01_08_425885	208	11	Carlsson	Carlsson	NNP
10_1101-2021_01_08_425885	208	12	et	et	FW
10_1101-2021_01_08_425885	208	13	al	al	NNP
10_1101-2021_01_08_425885	208	14	.	.	.
10_1101-2021_01_08_425885	209	1	in	in	IN
10_1101-2021_01_08_425885	209	2	[	[	-LRB-
10_1101-2021_01_08_425885	209	3	21	21	CD
10_1101-2021_01_08_425885	209	4	]	]	-RRB-
10_1101-2021_01_08_425885	209	5	relating	relate	VBG
10_1101-2021_01_08_425885	209	6	parameter	parameter	NN
10_1101-2021_01_08_425885	209	7	values	value	NNS
10_1101-2021_01_08_425885	209	8	θ	θ	NNP
10_1101-2021_01_08_425885	209	9	,	,	,
10_1101-2021_01_08_425885	209	10	φ	φ	NNP
10_1101-2021_01_08_425885	209	11	∈	∈	NNP
10_1101-2021_01_08_425885	209	12	[	[	-LRB-
10_1101-2021_01_08_425885	209	13	0	0	CD
10_1101-2021_01_08_425885	209	14	,	,	,
10_1101-2021_01_08_425885	209	15	2π	2π	LS
10_1101-2021_01_08_425885	209	16	]	]	-RRB-
10_1101-2021_01_08_425885	209	17	to	to	IN
10_1101-2021_01_08_425885	209	18	3x3-pixel	3x3-pixel	CD
10_1101-2021_01_08_425885	209	19	patches	patch	NNS
10_1101-2021_01_08_425885	209	20	of	of	IN
10_1101-2021_01_08_425885	209	21	greyscale	greyscale	JJ
10_1101-2021_01_08_425885	209	22	images	image	NNS
10_1101-2021_01_08_425885	209	23	(	(	-LRB-
10_1101-2021_01_08_425885	209	24	see	see	VB
10_1101-2021_01_08_425885	209	25	Equation	Equation	NNP
10_1101-2021_01_08_425885	209	26	31	31	CD
10_1101-2021_01_08_425885	209	27	in	in	IN
10_1101-2021_01_08_425885	209	28	Methods	Methods	NNP
10_1101-2021_01_08_425885	209	29	Section	Section	NNP
10_1101-2021_01_08_425885	209	30	4.5.3	4.5.3	CD
10_1101-2021_01_08_425885	209	31	)	)	-RRB-
10_1101-2021_01_08_425885	209	32	.	.	.
10_1101-2021_01_08_425885	210	1	θ	θ	NNP
10_1101-2021_01_08_425885	210	2	controls	control	VBZ
10_1101-2021_01_08_425885	210	3	the	the	DT
10_1101-2021_01_08_425885	210	4	rotation	rotation	NN
10_1101-2021_01_08_425885	210	5	of	of	IN
10_1101-2021_01_08_425885	210	6	stripes	stripe	NNS
10_1101-2021_01_08_425885	210	7	in	in	IN
10_1101-2021_01_08_425885	210	8	the	the	DT
10_1101-2021_01_08_425885	210	9	image	image	NN
10_1101-2021_01_08_425885	210	10	patches	patch	NNS
10_1101-2021_01_08_425885	210	11	and	and	CC
10_1101-2021_01_08_425885	210	12	φ	φ	NN
10_1101-2021_01_08_425885	210	13	determines	determine	VBZ
10_1101-2021_01_08_425885	210	14	the	the	DT
10_1101-2021_01_08_425885	210	15	relative	relative	JJ
10_1101-2021_01_08_425885	210	16	contribution	contribution	NN
10_1101-2021_01_08_425885	210	17	of	of	IN
10_1101-2021_01_08_425885	210	18	linear	linear	NNP
10_1101-2021_01_08_425885	210	19	vs.	vs.	IN
10_1101-2021_01_08_425885	210	20	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	210	21	gradients	gradient	NNS
10_1101-2021_01_08_425885	210	22	.	.	.
10_1101-2021_01_08_425885	211	1	Importantly	importantly	RB
10_1101-2021_01_08_425885	211	2	,	,	,
10_1101-2021_01_08_425885	211	3	as	as	IN
10_1101-2021_01_08_425885	211	4	shown	show	VBN
10_1101-2021_01_08_425885	211	5	in	in	IN
10_1101-2021_01_08_425885	211	6	the	the	DT
10_1101-2021_01_08_425885	211	7	figure	figure	NN
10_1101-2021_01_08_425885	211	8	,	,	,
10_1101-2021_01_08_425885	211	9	this	this	DT
10_1101-2021_01_08_425885	211	10	embedding	embedding	NN
10_1101-2021_01_08_425885	211	11	has	have	VBZ
10_1101-2021_01_08_425885	211	12	boundary	boundary	JJ
10_1101-2021_01_08_425885	211	13	conditions	condition	NNS
10_1101-2021_01_08_425885	211	14	consistent	consistent	JJ
10_1101-2021_01_08_425885	211	15	with	with	IN
10_1101-2021_01_08_425885	211	16	the	the	DT
10_1101-2021_01_08_425885	211	17	topology	topology	NN
10_1101-2021_01_08_425885	211	18	of	of	IN
10_1101-2021_01_08_425885	211	19	a	a	DT
10_1101-2021_01_08_425885	211	20	Klein	Klein	NNP
10_1101-2021_01_08_425885	211	21	bottle	bottle	NN
10_1101-2021_01_08_425885	211	22	(	(	-LRB-
10_1101-2021_01_08_425885	211	23	depicted	depict	VBN
10_1101-2021_01_08_425885	211	24	by	by	IN
10_1101-2021_01_08_425885	211	25	the	the	DT
10_1101-2021_01_08_425885	211	26	blue	blue	JJ
10_1101-2021_01_08_425885	211	27	/	/	SYM
10_1101-2021_01_08_425885	211	28	red	red	JJ
10_1101-2021_01_08_425885	211	29	arrows	arrow	NNS
10_1101-2021_01_08_425885	211	30	)	)	-RRB-
10_1101-2021_01_08_425885	211	31	.	.	.
10_1101-2021_01_08_425885	212	1	In	in	IN
10_1101-2021_01_08_425885	212	2	particular	particular	JJ
10_1101-2021_01_08_425885	212	3	,	,	,
10_1101-2021_01_08_425885	212	4	the	the	DT
10_1101-2021_01_08_425885	212	5	embedding	embedding	NN
10_1101-2021_01_08_425885	212	6	produces	produce	VBZ
10_1101-2021_01_08_425885	212	7	image	image	NN
10_1101-2021_01_08_425885	212	8	patches	patch	NNS
10_1101-2021_01_08_425885	212	9	that	that	WDT
10_1101-2021_01_08_425885	212	10	obey	obey	VBP
10_1101-2021_01_08_425885	212	11	the	the	DT
10_1101-2021_01_08_425885	212	12	similarity	similarity	NN
10_1101-2021_01_08_425885	212	13	relation	relation	NN
10_1101-2021_01_08_425885	212	14	(	(	-LRB-
10_1101-2021_01_08_425885	212	15	θ	θ	NNP
10_1101-2021_01_08_425885	212	16	,	,	,
10_1101-2021_01_08_425885	212	17	φ	φ	NNP
10_1101-2021_01_08_425885	212	18	)	)	-RRB-
10_1101-2021_01_08_425885	212	19	∼	∼	NNP
10_1101-2021_01_08_425885	212	20	(	(	-LRB-
10_1101-2021_01_08_425885	212	21	θ	θ	NNP
10_1101-2021_01_08_425885	212	22	+	+	SYM
10_1101-2021_01_08_425885	212	23	π	π	NN
10_1101-2021_01_08_425885	212	24	,	,	,
10_1101-2021_01_08_425885	212	25	2π	2π	CD
10_1101-2021_01_08_425885	212	26	−φ	−φ	CD
10_1101-2021_01_08_425885	212	27	)	)	-RRB-
10_1101-2021_01_08_425885	212	28	.	.	.
10_1101-2021_01_08_425885	213	1	Adapted	adapt	VBN
10_1101-2021_01_08_425885	213	2	from	from	IN
10_1101-2021_01_08_425885	213	3	Figure	figure	NN
10_1101-2021_01_08_425885	213	4	6	6	CD
10_1101-2021_01_08_425885	213	5	of	of	IN
10_1101-2021_01_08_425885	213	6	[	[	-LRB-
10_1101-2021_01_08_425885	213	7	21	21	CD
10_1101-2021_01_08_425885	213	8	]	]	-RRB-
10_1101-2021_01_08_425885	213	9	.	.	.
10_1101-2021_01_08_425885	214	1	(	(	-LRB-
10_1101-2021_01_08_425885	214	2	C	C	NNP
10_1101-2021_01_08_425885	214	3	)	)	-RRB-
10_1101-2021_01_08_425885	214	4	The	the	DT
10_1101-2021_01_08_425885	214	5	analytical	analytical	JJ
10_1101-2021_01_08_425885	214	6	scalar	scalar	JJ
10_1101-2021_01_08_425885	214	7	curvature	curvature	NN
10_1101-2021_01_08_425885	214	8	of	of	IN
10_1101-2021_01_08_425885	214	9	k0	k0	NNP
10_1101-2021_01_08_425885	214	10	(	(	-LRB-
10_1101-2021_01_08_425885	214	11	derived	derive	VBN
10_1101-2021_01_08_425885	214	12	as	as	IN
10_1101-2021_01_08_425885	214	13	described	describe	VBN
10_1101-2021_01_08_425885	214	14	in	in	IN
10_1101-2021_01_08_425885	214	15	Methods	Methods	NNP
10_1101-2021_01_08_425885	214	16	Section	Section	NNP
10_1101-2021_01_08_425885	214	17	4.1	4.1	CD
10_1101-2021_01_08_425885	214	18	)	)	-RRB-
10_1101-2021_01_08_425885	214	19	.	.	.
10_1101-2021_01_08_425885	215	1	(	(	-LRB-
10_1101-2021_01_08_425885	215	2	D	D	NNP
10_1101-2021_01_08_425885	215	3	)	)	-RRB-
10_1101-2021_01_08_425885	215	4	Scalar	scalar	JJ
10_1101-2021_01_08_425885	215	5	curvatures	curvature	NNS
10_1101-2021_01_08_425885	215	6	computed	compute	VBD
10_1101-2021_01_08_425885	215	7	for	for	IN
10_1101-2021_01_08_425885	215	8	N	N	NNP
10_1101-2021_01_08_425885	215	9	≈	≈	NNP
10_1101-2021_01_08_425885	215	10	4.2	4.2	CD
10_1101-2021_01_08_425885	215	11	×	×	CD
10_1101-2021_01_08_425885	215	12	105	105	CD
10_1101-2021_01_08_425885	215	13	high	high	JJ
10_1101-2021_01_08_425885	215	14	-	-	HYPH
10_1101-2021_01_08_425885	215	15	contrast	contrast	NN
10_1101-2021_01_08_425885	215	16	3x3-pixel	3x3-pixel	CD
10_1101-2021_01_08_425885	215	17	patches	patch	NNS
10_1101-2021_01_08_425885	215	18	sampled	sample	VBN
10_1101-2021_01_08_425885	215	19	from	from	IN
10_1101-2021_01_08_425885	215	20	the	the	DT
10_1101-2021_01_08_425885	215	21	greyscale	greyscale	JJ
10_1101-2021_01_08_425885	215	22	images	image	NNS
10_1101-2021_01_08_425885	215	23	in	in	IN
10_1101-2021_01_08_425885	215	24	the	the	DT
10_1101-2021_01_08_425885	215	25	van	van	NNP
10_1101-2021_01_08_425885	215	26	Hateren	Hateren	NNP
10_1101-2021_01_08_425885	215	27	dataset	dataset	NN
10_1101-2021_01_08_425885	215	28	[	[	-LRB-
10_1101-2021_01_08_425885	215	29	41	41	CD
10_1101-2021_01_08_425885	215	30	]	]	-RRB-
10_1101-2021_01_08_425885	215	31	are	be	VBP
10_1101-2021_01_08_425885	215	32	plotted	plot	VBN
10_1101-2021_01_08_425885	215	33	here	here	RB
10_1101-2021_01_08_425885	215	34	as	as	IN
10_1101-2021_01_08_425885	215	35	a	a	DT
10_1101-2021_01_08_425885	215	36	function	function	NN
10_1101-2021_01_08_425885	215	37	of	of	IN
10_1101-2021_01_08_425885	215	38	(	(	-LRB-
10_1101-2021_01_08_425885	215	39	θ0,φ0	θ0,φ0	NN
10_1101-2021_01_08_425885	215	40	)	)	-RRB-
10_1101-2021_01_08_425885	215	41	,	,	,
10_1101-2021_01_08_425885	215	42	the	the	DT
10_1101-2021_01_08_425885	215	43	parameter	parameter	NN
10_1101-2021_01_08_425885	215	44	values	value	NNS
10_1101-2021_01_08_425885	215	45	of	of	IN
10_1101-2021_01_08_425885	215	46	the	the	DT
10_1101-2021_01_08_425885	215	47	closest	close	JJS
10_1101-2021_01_08_425885	215	48	point	point	NN
10_1101-2021_01_08_425885	215	49	on	on	IN
10_1101-2021_01_08_425885	215	50	k	k	NNP
10_1101-2021_01_08_425885	215	51	0	0	CD
10_1101-2021_01_08_425885	215	52	associated	associate	VBN
10_1101-2021_01_08_425885	215	53	with	with	IN
10_1101-2021_01_08_425885	215	54	each	each	DT
10_1101-2021_01_08_425885	215	55	image	image	NN
10_1101-2021_01_08_425885	215	56	patch	patch	NN
10_1101-2021_01_08_425885	215	57	(	(	-LRB-
10_1101-2021_01_08_425885	215	58	see	see	VB
10_1101-2021_01_08_425885	215	59	Methods	Methods	NNP
10_1101-2021_01_08_425885	215	60	Section	Section	NNP
10_1101-2021_01_08_425885	215	61	4.5.4	4.5.4	CD
10_1101-2021_01_08_425885	215	62	)	)	-RRB-
10_1101-2021_01_08_425885	215	63	.	.	.
10_1101-2021_01_08_425885	216	1	(	(	-LRB-
10_1101-2021_01_08_425885	216	2	E	e	NN
10_1101-2021_01_08_425885	216	3	)	)	-RRB-
10_1101-2021_01_08_425885	216	4	Scalar	scalar	JJ
10_1101-2021_01_08_425885	216	5	curvatures	curvature	NNS
10_1101-2021_01_08_425885	216	6	computed	compute	VBD
10_1101-2021_01_08_425885	216	7	for	for	IN
10_1101-2021_01_08_425885	216	8	the	the	DT
10_1101-2021_01_08_425885	216	9	set	set	NN
10_1101-2021_01_08_425885	216	10	of	of	IN
10_1101-2021_01_08_425885	216	11	N	N	NNP
10_1101-2021_01_08_425885	216	12	≈	≈	NNP
10_1101-2021_01_08_425885	216	13	4.2	4.2	CD
10_1101-2021_01_08_425885	216	14	×	×	CD
10_1101-2021_01_08_425885	216	15	105	105	CD
10_1101-2021_01_08_425885	216	16	closest	close	JJS
10_1101-2021_01_08_425885	216	17	points	point	NNS
10_1101-2021_01_08_425885	216	18	on	on	IN
10_1101-2021_01_08_425885	216	19	k0	k0	NNP
10_1101-2021_01_08_425885	216	20	associated	associate	VBN
10_1101-2021_01_08_425885	216	21	with	with	IN
10_1101-2021_01_08_425885	216	22	the	the	DT
10_1101-2021_01_08_425885	216	23	image	image	NN
10_1101-2021_01_08_425885	216	24	patches	patch	NNS
10_1101-2021_01_08_425885	216	25	.	.	.
10_1101-2021_01_08_425885	217	1	Note	note	VB
10_1101-2021_01_08_425885	217	2	the	the	DT
10_1101-2021_01_08_425885	217	3	close	close	JJ
10_1101-2021_01_08_425885	217	4	correspondence	correspondence	NN
10_1101-2021_01_08_425885	217	5	with	with	IN
10_1101-2021_01_08_425885	217	6	Figure	figure	NN
10_1101-2021_01_08_425885	217	7	3C	3c	NN
10_1101-2021_01_08_425885	217	8	,	,	,
10_1101-2021_01_08_425885	217	9	indicating	indicate	VBG
10_1101-2021_01_08_425885	217	10	that	that	IN
10_1101-2021_01_08_425885	217	11	our	-PRON-	PRP$
10_1101-2021_01_08_425885	217	12	algorithm	algorithm	NN
10_1101-2021_01_08_425885	217	13	correctly	correctly	RB
10_1101-2021_01_08_425885	217	14	recapitulates	recapitulate	VBZ
10_1101-2021_01_08_425885	217	15	the	the	DT
10_1101-2021_01_08_425885	217	16	analytical	analytical	JJ
10_1101-2021_01_08_425885	217	17	scalar	scalar	JJ
10_1101-2021_01_08_425885	217	18	curvature	curvature	NN
10_1101-2021_01_08_425885	217	19	.	.	.
10_1101-2021_01_08_425885	218	1	(	(	-LRB-
10_1101-2021_01_08_425885	218	2	F	f	NN
10_1101-2021_01_08_425885	218	3	)	)	-RRB-
10_1101-2021_01_08_425885	218	4	As	as	IN
10_1101-2021_01_08_425885	218	5	in	in	IN
10_1101-2021_01_08_425885	218	6	(	(	-LRB-
10_1101-2021_01_08_425885	218	7	E	e	NN
10_1101-2021_01_08_425885	218	8	)	)	-RRB-
10_1101-2021_01_08_425885	218	9	,	,	,
10_1101-2021_01_08_425885	218	10	but	but	CC
10_1101-2021_01_08_425885	218	11	after	after	IN
10_1101-2021_01_08_425885	218	12	adding	add	VBG
10_1101-2021_01_08_425885	218	13	isotropic	isotropic	JJ
10_1101-2021_01_08_425885	218	14	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	218	15	noise	noise	NN
10_1101-2021_01_08_425885	218	16	in	in	IN
10_1101-2021_01_08_425885	218	17	R9	R9	NNP
10_1101-2021_01_08_425885	218	18	to	to	IN
10_1101-2021_01_08_425885	218	19	the	the	DT
10_1101-2021_01_08_425885	218	20	set	set	NN
10_1101-2021_01_08_425885	218	21	of	of	IN
10_1101-2021_01_08_425885	218	22	closest	close	JJS
10_1101-2021_01_08_425885	218	23	points	point	NNS
10_1101-2021_01_08_425885	218	24	on	on	IN
10_1101-2021_01_08_425885	218	25	k0	k0	NNP
10_1101-2021_01_08_425885	218	26	(	(	-LRB-
10_1101-2021_01_08_425885	218	27	see	see	VB
10_1101-2021_01_08_425885	218	28	Methods	Methods	NNP
10_1101-2021_01_08_425885	218	29	Section	Section	NNP
10_1101-2021_01_08_425885	218	30	4.5.6	4.5.6	CD
10_1101-2021_01_08_425885	218	31	)	)	-RRB-
10_1101-2021_01_08_425885	218	32	.	.	.
10_1101-2021_01_08_425885	219	1	Left	leave	VBN
10_1101-2021_01_08_425885	219	2	to	to	IN
10_1101-2021_01_08_425885	219	3	right	right	JJ
10_1101-2021_01_08_425885	219	4	corresponds	correspond	NNS
10_1101-2021_01_08_425885	219	5	to	to	IN
10_1101-2021_01_08_425885	219	6	increasing	increase	VBG
10_1101-2021_01_08_425885	219	7	levels	level	NNS
10_1101-2021_01_08_425885	219	8	of	of	IN
10_1101-2021_01_08_425885	219	9	noise	noise	NN
10_1101-2021_01_08_425885	219	10	,	,	,
10_1101-2021_01_08_425885	219	11	σ	σ	NNP
10_1101-2021_01_08_425885	219	12	=	=	SYM
10_1101-2021_01_08_425885	219	13	0.007	0.007	CD
10_1101-2021_01_08_425885	219	14	,	,	,
10_1101-2021_01_08_425885	219	15	0.01	0.01	CD
10_1101-2021_01_08_425885	219	16	,	,	,
10_1101-2021_01_08_425885	219	17	0.03	0.03	CD
10_1101-2021_01_08_425885	219	18	.	.	.
10_1101-2021_01_08_425885	220	1	(	(	-LRB-
10_1101-2021_01_08_425885	220	2	G	g	NN
10_1101-2021_01_08_425885	220	3	)	)	-RRB-
10_1101-2021_01_08_425885	220	4	The	the	DT
10_1101-2021_01_08_425885	220	5	distribution	distribution	NN
10_1101-2021_01_08_425885	220	6	of	of	IN
10_1101-2021_01_08_425885	220	7	Euclidean	euclidean	JJ
10_1101-2021_01_08_425885	220	8	distances	distance	NNS
10_1101-2021_01_08_425885	220	9	in	in	IN
10_1101-2021_01_08_425885	220	10	R8	R8	NNS
10_1101-2021_01_08_425885	220	11	between	between	IN
10_1101-2021_01_08_425885	220	12	each	each	DT
10_1101-2021_01_08_425885	220	13	image	image	NN
10_1101-2021_01_08_425885	220	14	patch	patch	NN
10_1101-2021_01_08_425885	220	15	and	and	CC
10_1101-2021_01_08_425885	220	16	its	-PRON-	PRP$
10_1101-2021_01_08_425885	220	17	closest	close	JJS
10_1101-2021_01_08_425885	220	18	point	point	NN
10_1101-2021_01_08_425885	220	19	on	on	IN
10_1101-2021_01_08_425885	220	20	k0	k0	NNP
10_1101-2021_01_08_425885	220	21	is	be	VBZ
10_1101-2021_01_08_425885	220	22	shown	show	VBN
10_1101-2021_01_08_425885	220	23	in	in	IN
10_1101-2021_01_08_425885	220	24	blue	blue	NNP
10_1101-2021_01_08_425885	220	25	.	.	.
10_1101-2021_01_08_425885	221	1	The	the	DT
10_1101-2021_01_08_425885	221	2	distribution	distribution	NN
10_1101-2021_01_08_425885	221	3	of	of	IN
10_1101-2021_01_08_425885	221	4	distances	distance	NNS
10_1101-2021_01_08_425885	221	5	to	to	IN
10_1101-2021_01_08_425885	221	6	k0	k0	NNP
10_1101-2021_01_08_425885	221	7	after	after	IN
10_1101-2021_01_08_425885	221	8	adding	add	VBG
10_1101-2021_01_08_425885	221	9	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	221	10	noise	noise	NN
10_1101-2021_01_08_425885	221	11	to	to	IN
10_1101-2021_01_08_425885	221	12	these	these	DT
10_1101-2021_01_08_425885	221	13	closest	close	JJS
10_1101-2021_01_08_425885	221	14	points	point	NNS
10_1101-2021_01_08_425885	221	15	on	on	IN
10_1101-2021_01_08_425885	221	16	k0	k0	NNP
10_1101-2021_01_08_425885	221	17	is	be	VBZ
10_1101-2021_01_08_425885	221	18	also	also	RB
10_1101-2021_01_08_425885	221	19	shown	show	VBN
10_1101-2021_01_08_425885	221	20	.	.	.
10_1101-2021_01_08_425885	222	1	(	(	-LRB-
10_1101-2021_01_08_425885	222	2	H	h	NN
10_1101-2021_01_08_425885	222	3	)	)	-RRB-
10_1101-2021_01_08_425885	222	4	k1	k1	NNP
10_1101-2021_01_08_425885	222	5	is	be	VBZ
10_1101-2021_01_08_425885	222	6	the	the	DT
10_1101-2021_01_08_425885	222	7	analytical	analytical	JJ
10_1101-2021_01_08_425885	222	8	embedding	embedding	NN
10_1101-2021_01_08_425885	222	9	from	from	IN
10_1101-2021_01_08_425885	222	10	θ	θ	NNP
10_1101-2021_01_08_425885	222	11	,	,	,
10_1101-2021_01_08_425885	222	12	φ	φ	NNP
10_1101-2021_01_08_425885	222	13	∈	∈	NNP
10_1101-2021_01_08_425885	222	14	[	[	-LRB-
10_1101-2021_01_08_425885	222	15	0	0	CD
10_1101-2021_01_08_425885	222	16	,	,	,
10_1101-2021_01_08_425885	222	17	2π	2π	LS
10_1101-2021_01_08_425885	222	18	]	]	-RRB-
10_1101-2021_01_08_425885	222	19	to	to	TO
10_1101-2021_01_08_425885	222	20	R9	r9	VB
10_1101-2021_01_08_425885	222	21	that	that	DT
10_1101-2021_01_08_425885	222	22	minimizes	minimize	VBZ
10_1101-2021_01_08_425885	222	23	the	the	DT
10_1101-2021_01_08_425885	222	24	sum	sum	NN
10_1101-2021_01_08_425885	222	25	of	of	IN
10_1101-2021_01_08_425885	222	26	Euclidean	euclidean	JJ
10_1101-2021_01_08_425885	222	27	distances	distance	NNS
10_1101-2021_01_08_425885	222	28	from	from	IN
10_1101-2021_01_08_425885	222	29	the	the	DT
10_1101-2021_01_08_425885	222	30	image	image	NN
10_1101-2021_01_08_425885	222	31	patches	patch	NNS
10_1101-2021_01_08_425885	222	32	to	to	IN
10_1101-2021_01_08_425885	222	33	the	the	DT
10_1101-2021_01_08_425885	222	34	closest	close	JJS
10_1101-2021_01_08_425885	222	35	point	point	NN
10_1101-2021_01_08_425885	222	36	on	on	IN
10_1101-2021_01_08_425885	222	37	the	the	DT
10_1101-2021_01_08_425885	222	38	embedding	embedding	NN
10_1101-2021_01_08_425885	222	39	(	(	-LRB-
10_1101-2021_01_08_425885	222	40	see	see	VB
10_1101-2021_01_08_425885	222	41	Methods	Methods	NNP
10_1101-2021_01_08_425885	222	42	Section	Section	NNP
10_1101-2021_01_08_425885	222	43	4.5.5	4.5.5	CD
10_1101-2021_01_08_425885	222	44	)	)	-RRB-
10_1101-2021_01_08_425885	222	45	.	.	.
10_1101-2021_01_08_425885	223	1	Each	each	DT
10_1101-2021_01_08_425885	223	2	of	of	IN
10_1101-2021_01_08_425885	223	3	the	the	DT
10_1101-2021_01_08_425885	223	4	N	N	NNP
10_1101-2021_01_08_425885	223	5	≈	≈	NNP
10_1101-2021_01_08_425885	223	6	4.2	4.2	CD
10_1101-2021_01_08_425885	223	7	×	×	CD
10_1101-2021_01_08_425885	223	8	105	105	CD
10_1101-2021_01_08_425885	223	9	image	image	NN
10_1101-2021_01_08_425885	223	10	patches	patch	NNS
10_1101-2021_01_08_425885	223	11	was	be	VBD
10_1101-2021_01_08_425885	223	12	associated	associate	VBN
10_1101-2021_01_08_425885	223	13	to	to	IN
10_1101-2021_01_08_425885	223	14	its	-PRON-	PRP$
10_1101-2021_01_08_425885	223	15	closest	close	JJS
10_1101-2021_01_08_425885	223	16	point	point	NN
10_1101-2021_01_08_425885	223	17	on	on	IN
10_1101-2021_01_08_425885	223	18	k1	k1	NNP
10_1101-2021_01_08_425885	223	19	,	,	,
10_1101-2021_01_08_425885	223	20	given	give	VBN
10_1101-2021_01_08_425885	223	21	by	by	IN
10_1101-2021_01_08_425885	223	22	parameter	parameter	NN
10_1101-2021_01_08_425885	223	23	values	value	NNS
10_1101-2021_01_08_425885	223	24	(	(	-LRB-
10_1101-2021_01_08_425885	223	25	θ1,φ1	θ1,φ1	NNP
10_1101-2021_01_08_425885	223	26	)	)	-RRB-
10_1101-2021_01_08_425885	223	27	(	(	-LRB-
10_1101-2021_01_08_425885	223	28	see	see	VB
10_1101-2021_01_08_425885	223	29	Methods	Methods	NNP
10_1101-2021_01_08_425885	223	30	Section	Section	NNP
10_1101-2021_01_08_425885	223	31	4.5.4	4.5.4	CD
10_1101-2021_01_08_425885	223	32	)	)	-RRB-
10_1101-2021_01_08_425885	223	33	.	.	.
10_1101-2021_01_08_425885	224	1	Scalar	scalar	JJ
10_1101-2021_01_08_425885	224	2	curvatures	curvature	NNS
10_1101-2021_01_08_425885	224	3	computed	compute	VBD
10_1101-2021_01_08_425885	224	4	on	on	IN
10_1101-2021_01_08_425885	224	5	this	this	DT
10_1101-2021_01_08_425885	224	6	set	set	NN
10_1101-2021_01_08_425885	224	7	of	of	IN
10_1101-2021_01_08_425885	224	8	N	N	NNP
10_1101-2021_01_08_425885	224	9	≈	≈	NNP
10_1101-2021_01_08_425885	224	10	4.2	4.2	CD
10_1101-2021_01_08_425885	224	11	×	×	CD
10_1101-2021_01_08_425885	224	12	105	105	CD
10_1101-2021_01_08_425885	224	13	points	point	NNS
10_1101-2021_01_08_425885	224	14	on	on	IN
10_1101-2021_01_08_425885	224	15	k1	k1	NNP
10_1101-2021_01_08_425885	224	16	are	be	VBP
10_1101-2021_01_08_425885	224	17	shown	show	VBN
10_1101-2021_01_08_425885	224	18	.	.	.
10_1101-2021_01_08_425885	225	1	(	(	-LRB-
10_1101-2021_01_08_425885	225	2	I	i	NN
10_1101-2021_01_08_425885	225	3	)	)	-RRB-
10_1101-2021_01_08_425885	225	4	The	the	DT
10_1101-2021_01_08_425885	225	5	same	same	JJ
10_1101-2021_01_08_425885	225	6	scalar	scalar	JJ
10_1101-2021_01_08_425885	225	7	curvatures	curvature	NNS
10_1101-2021_01_08_425885	225	8	computed	compute	VBN
10_1101-2021_01_08_425885	225	9	for	for	IN
10_1101-2021_01_08_425885	225	10	the	the	DT
10_1101-2021_01_08_425885	225	11	image	image	NN
10_1101-2021_01_08_425885	225	12	patches	patch	NNS
10_1101-2021_01_08_425885	225	13	and	and	CC
10_1101-2021_01_08_425885	225	14	visualized	visualize	VBN
10_1101-2021_01_08_425885	225	15	on	on	IN
10_1101-2021_01_08_425885	225	16	(	(	-LRB-
10_1101-2021_01_08_425885	225	17	θ0,φ0	θ0,φ0	NN
10_1101-2021_01_08_425885	225	18	)	)	-RRB-
10_1101-2021_01_08_425885	225	19	coordinates	coordinate	VBZ
10_1101-2021_01_08_425885	225	20	in	in	IN
10_1101-2021_01_08_425885	225	21	(	(	-LRB-
10_1101-2021_01_08_425885	225	22	D	D	NNP
10_1101-2021_01_08_425885	225	23	)	)	-RRB-
10_1101-2021_01_08_425885	225	24	,	,	,
10_1101-2021_01_08_425885	225	25	are	be	VBP
10_1101-2021_01_08_425885	225	26	shown	show	VBN
10_1101-2021_01_08_425885	225	27	here	here	RB
10_1101-2021_01_08_425885	225	28	plotted	plot	VBN
10_1101-2021_01_08_425885	225	29	on	on	IN
10_1101-2021_01_08_425885	225	30	(	(	-LRB-
10_1101-2021_01_08_425885	225	31	θ1,φ1	θ1,φ1	NN
10_1101-2021_01_08_425885	225	32	)	)	-RRB-
10_1101-2021_01_08_425885	225	33	coordinates	coordinate	VBZ
10_1101-2021_01_08_425885	225	34	.	.	.
10_1101-2021_01_08_425885	226	1	(	(	-LRB-
10_1101-2021_01_08_425885	226	2	J	J	NNP
10_1101-2021_01_08_425885	226	3	)	)	-RRB-
10_1101-2021_01_08_425885	226	4	Scalar	Scalar	NNP
10_1101-2021_01_08_425885	226	5	curvatures	curvature	NNS
10_1101-2021_01_08_425885	226	6	computed	compute	VBD
10_1101-2021_01_08_425885	226	7	for	for	IN
10_1101-2021_01_08_425885	226	8	a	a	DT
10_1101-2021_01_08_425885	226	9	densely	densely	RB
10_1101-2021_01_08_425885	226	10	sampled	sample	VBN
10_1101-2021_01_08_425885	226	11	manifold	manifold	NN
10_1101-2021_01_08_425885	226	12	comprised	comprise	VBN
10_1101-2021_01_08_425885	226	13	of	of	IN
10_1101-2021_01_08_425885	226	14	the	the	DT
10_1101-2021_01_08_425885	226	15	full	full	JJ
10_1101-2021_01_08_425885	226	16	set	set	NN
10_1101-2021_01_08_425885	226	17	of	of	IN
10_1101-2021_01_08_425885	226	18	N	N	NNP
10_1101-2021_01_08_425885	226	19	≈	≈	NNP
10_1101-2021_01_08_425885	226	20	1.3×108	1.3×108	CD
10_1101-2021_01_08_425885	226	21	high	high	JJ
10_1101-2021_01_08_425885	226	22	-	-	HYPH
10_1101-2021_01_08_425885	226	23	contrast	contrast	NN
10_1101-2021_01_08_425885	226	24	3x3-pixel	3x3-pixel	CD
10_1101-2021_01_08_425885	226	25	image	image	NN
10_1101-2021_01_08_425885	226	26	patches	patch	NNS
10_1101-2021_01_08_425885	226	27	in	in	IN
10_1101-2021_01_08_425885	226	28	the	the	DT
10_1101-2021_01_08_425885	226	29	van	van	NNP
10_1101-2021_01_08_425885	226	30	Hateren	Hateren	NNP
10_1101-2021_01_08_425885	226	31	image	image	NN
10_1101-2021_01_08_425885	226	32	dataset	dataset	NN
10_1101-2021_01_08_425885	226	33	(	(	-LRB-
10_1101-2021_01_08_425885	226	34	see	see	VB
10_1101-2021_01_08_425885	226	35	Methods	Methods	NNP
10_1101-2021_01_08_425885	226	36	Section	Section	NNP
10_1101-2021_01_08_425885	226	37	4.5.2	4.5.2	CD
10_1101-2021_01_08_425885	226	38	)	)	-RRB-
10_1101-2021_01_08_425885	226	39	,	,	,
10_1101-2021_01_08_425885	226	40	visualized	visualize	VBN
10_1101-2021_01_08_425885	226	41	on	on	IN
10_1101-2021_01_08_425885	226	42	(	(	-LRB-
10_1101-2021_01_08_425885	226	43	θ1,φ1	θ1,φ1	NN
10_1101-2021_01_08_425885	226	44	)	)	-RRB-
10_1101-2021_01_08_425885	226	45	coordinates	coordinate	VBZ
10_1101-2021_01_08_425885	226	46	.	.	.
10_1101-2021_01_08_425885	227	1	13	13	CD
10_1101-2021_01_08_425885	227	2	.CC	.CC	:
10_1101-2021_01_08_425885	227	3	-	-	HYPH
10_1101-2021_01_08_425885	227	4	BY	by	IN
10_1101-2021_01_08_425885	227	5	-	-	HYPH
10_1101-2021_01_08_425885	227	6	NC	NC	NNP
10_1101-2021_01_08_425885	227	7	-	-	HYPH
10_1101-2021_01_08_425885	227	8	ND	ND	NNP
10_1101-2021_01_08_425885	227	9	4.0	4.0	CD
10_1101-2021_01_08_425885	227	10	International	International	NNP
10_1101-2021_01_08_425885	227	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	227	12	under	under	IN
10_1101-2021_01_08_425885	227	13	a	a	DT
10_1101-2021_01_08_425885	227	14	(	(	-LRB-
10_1101-2021_01_08_425885	227	15	which	which	WDT
10_1101-2021_01_08_425885	227	16	was	be	VBD
10_1101-2021_01_08_425885	227	17	not	not	RB
10_1101-2021_01_08_425885	227	18	certified	certify	VBN
10_1101-2021_01_08_425885	227	19	by	by	IN
10_1101-2021_01_08_425885	227	20	peer	peer	NN
10_1101-2021_01_08_425885	227	21	review	review	NN
10_1101-2021_01_08_425885	227	22	)	)	-RRB-
10_1101-2021_01_08_425885	227	23	is	be	VBZ
10_1101-2021_01_08_425885	227	24	the	the	DT
10_1101-2021_01_08_425885	227	25	author	author	NN
10_1101-2021_01_08_425885	227	26	/	/	SYM
10_1101-2021_01_08_425885	227	27	funder	funder	NN
10_1101-2021_01_08_425885	227	28	,	,	,
10_1101-2021_01_08_425885	227	29	who	who	WP
10_1101-2021_01_08_425885	227	30	has	have	VBZ
10_1101-2021_01_08_425885	227	31	granted	grant	VBN
10_1101-2021_01_08_425885	227	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	227	33	a	a	DT
10_1101-2021_01_08_425885	227	34	license	license	NN
10_1101-2021_01_08_425885	227	35	to	to	TO
10_1101-2021_01_08_425885	227	36	display	display	VB
10_1101-2021_01_08_425885	227	37	the	the	DT
10_1101-2021_01_08_425885	227	38	preprint	preprint	NN
10_1101-2021_01_08_425885	227	39	in	in	IN
10_1101-2021_01_08_425885	227	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	227	41	.	.	.
10_1101-2021_01_08_425885	228	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	228	2	is	be	VBZ
10_1101-2021_01_08_425885	228	3	made	make	VBN
10_1101-2021_01_08_425885	228	4	The	the	DT
10_1101-2021_01_08_425885	228	5	copyright	copyright	NN
10_1101-2021_01_08_425885	228	6	holder	holder	NN
10_1101-2021_01_08_425885	228	7	for	for	IN
10_1101-2021_01_08_425885	228	8	this	this	DT
10_1101-2021_01_08_425885	228	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	228	10	version	version	NN
10_1101-2021_01_08_425885	228	11	posted	post	VBD
10_1101-2021_01_08_425885	228	12	January	January	NNP
10_1101-2021_01_08_425885	228	13	8	8	CD
10_1101-2021_01_08_425885	228	14	,	,	,
10_1101-2021_01_08_425885	228	15	2021	2021	CD
10_1101-2021_01_08_425885	228	16	.	.	.
10_1101-2021_01_08_425885	228	17	;	;	:
10_1101-2021_01_08_425885	228	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	228	19	:	:	:
10_1101-2021_01_08_425885	228	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	228	21	preprint	preprint	NN
10_1101-2021_01_08_425885	228	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	NNP
10_1101-2021_01_08_425885	228	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NNP
10_1101-2021_01_08_425885	228	24	σ	σ	NNP
10_1101-2021_01_08_425885	228	25	=	=	SYM
10_1101-2021_01_08_425885	228	26	0.03	0.03	CD
10_1101-2021_01_08_425885	228	27	.	.	.
10_1101-2021_01_08_425885	229	1	Notably	notably	RB
10_1101-2021_01_08_425885	229	2	,	,	,
10_1101-2021_01_08_425885	229	3	in	in	IN
10_1101-2021_01_08_425885	229	4	this	this	DT
10_1101-2021_01_08_425885	229	5	case	case	NN
10_1101-2021_01_08_425885	229	6	,	,	,
10_1101-2021_01_08_425885	229	7	the	the	DT
10_1101-2021_01_08_425885	229	8	median	median	JJ
10_1101-2021_01_08_425885	229	9	Euclidean	euclidean	JJ
10_1101-2021_01_08_425885	229	10	distance	distance	NN
10_1101-2021_01_08_425885	229	11	of	of	IN
10_1101-2021_01_08_425885	229	12	the	the	DT
10_1101-2021_01_08_425885	229	13	noisy	noisy	JJ
10_1101-2021_01_08_425885	229	14	(	(	-LRB-
10_1101-2021_01_08_425885	229	15	θ0,φ0	θ0,φ0	NN
10_1101-2021_01_08_425885	229	16	)	)	-RRB-
10_1101-2021_01_08_425885	229	17	points	point	VBZ
10_1101-2021_01_08_425885	229	18	to	to	IN
10_1101-2021_01_08_425885	229	19	k	k	NNP
10_1101-2021_01_08_425885	229	20	0	0	CD
10_1101-2021_01_08_425885	229	21	was	be	VBD
10_1101-2021_01_08_425885	229	22	0.132	0.132	CD
10_1101-2021_01_08_425885	229	23	,	,	,
10_1101-2021_01_08_425885	229	24	which	which	WDT
10_1101-2021_01_08_425885	229	25	is	be	VBZ
10_1101-2021_01_08_425885	229	26	comparable	comparable	JJ
10_1101-2021_01_08_425885	229	27	to	to	IN
10_1101-2021_01_08_425885	229	28	0.148	0.148	CD
10_1101-2021_01_08_425885	229	29	,	,	,
10_1101-2021_01_08_425885	229	30	the	the	DT
10_1101-2021_01_08_425885	229	31	median	median	JJ
10_1101-2021_01_08_425885	229	32	Euclidean	euclidean	JJ
10_1101-2021_01_08_425885	229	33	distance	distance	NN
10_1101-2021_01_08_425885	229	34	of	of	IN
10_1101-2021_01_08_425885	229	35	the	the	DT
10_1101-2021_01_08_425885	229	36	image	image	NN
10_1101-2021_01_08_425885	229	37	patches	patch	NNS
10_1101-2021_01_08_425885	229	38	to	to	IN
10_1101-2021_01_08_425885	229	39	k0	k0	NNP
10_1101-2021_01_08_425885	229	40	(	(	-LRB-
10_1101-2021_01_08_425885	229	41	see	see	VB
10_1101-2021_01_08_425885	229	42	Figure	figure	NN
10_1101-2021_01_08_425885	229	43	3	3	CD
10_1101-2021_01_08_425885	229	44	G	g	NN
10_1101-2021_01_08_425885	229	45	)	)	-RRB-
10_1101-2021_01_08_425885	229	46	.	.	.
10_1101-2021_01_08_425885	230	1	Furthermore	furthermore	RB
10_1101-2021_01_08_425885	230	2	,	,	,
10_1101-2021_01_08_425885	230	3	the	the	DT
10_1101-2021_01_08_425885	230	4	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	230	5	sizes	size	NNS
10_1101-2021_01_08_425885	230	6	chosen	choose	VBN
10_1101-2021_01_08_425885	230	7	by	by	IN
10_1101-2021_01_08_425885	230	8	our	-PRON-	PRP$
10_1101-2021_01_08_425885	230	9	algorithm	algorithm	NN
10_1101-2021_01_08_425885	230	10	when	when	WRB
10_1101-2021_01_08_425885	230	11	σ	σ	NN
10_1101-2021_01_08_425885	230	12	=	=	SYM
10_1101-2021_01_08_425885	230	13	0.03	0.03	CD
10_1101-2021_01_08_425885	230	14	(	(	-LRB-
10_1101-2021_01_08_425885	230	15	see	see	VB
10_1101-2021_01_08_425885	230	16	Figure	Figure	NNP
10_1101-2021_01_08_425885	230	17	S3A	s3a	NN
10_1101-2021_01_08_425885	230	18	)	)	-RRB-
10_1101-2021_01_08_425885	230	19	matched	match	VBD
10_1101-2021_01_08_425885	230	20	those	those	DT
10_1101-2021_01_08_425885	230	21	chosen	choose	VBN
10_1101-2021_01_08_425885	230	22	for	for	IN
10_1101-2021_01_08_425885	230	23	the	the	DT
10_1101-2021_01_08_425885	230	24	image	image	NN
10_1101-2021_01_08_425885	230	25	patches	patch	NNS
10_1101-2021_01_08_425885	230	26	(	(	-LRB-
10_1101-2021_01_08_425885	230	27	see	see	VB
10_1101-2021_01_08_425885	230	28	Figure	Figure	NNP
10_1101-2021_01_08_425885	230	29	S3B	s3b	NN
10_1101-2021_01_08_425885	230	30	)	)	-RRB-
10_1101-2021_01_08_425885	230	31	.	.	.
10_1101-2021_01_08_425885	231	1	To	to	TO
10_1101-2021_01_08_425885	231	2	find	find	VB
10_1101-2021_01_08_425885	231	3	an	an	DT
10_1101-2021_01_08_425885	231	4	embedding	embedding	NN
10_1101-2021_01_08_425885	231	5	of	of	IN
10_1101-2021_01_08_425885	231	6	the	the	DT
10_1101-2021_01_08_425885	231	7	Klein	Klein	NNP
10_1101-2021_01_08_425885	231	8	bottle	bottle	NN
10_1101-2021_01_08_425885	231	9	that	that	WDT
10_1101-2021_01_08_425885	231	10	might	may	MD
10_1101-2021_01_08_425885	231	11	better	well	RBR
10_1101-2021_01_08_425885	231	12	explain	explain	VB
10_1101-2021_01_08_425885	231	13	the	the	DT
10_1101-2021_01_08_425885	231	14	scalar	scalar	JJ
10_1101-2021_01_08_425885	231	15	curvature	curvature	NN
10_1101-2021_01_08_425885	231	16	of	of	IN
10_1101-2021_01_08_425885	231	17	the	the	DT
10_1101-2021_01_08_425885	231	18	image	image	NN
10_1101-2021_01_08_425885	231	19	patches	patch	NNS
10_1101-2021_01_08_425885	231	20	without	without	IN
10_1101-2021_01_08_425885	231	21	needing	need	VBG
10_1101-2021_01_08_425885	231	22	to	to	TO
10_1101-2021_01_08_425885	231	23	add	add	VB
10_1101-2021_01_08_425885	231	24	noise	noise	NN
10_1101-2021_01_08_425885	231	25	,	,	,
10_1101-2021_01_08_425885	231	26	we	-PRON-	PRP
10_1101-2021_01_08_425885	231	27	incorporated	incorporate	VBD
10_1101-2021_01_08_425885	231	28	higher	high	JJR
10_1101-2021_01_08_425885	231	29	-	-	HYPH
10_1101-2021_01_08_425885	231	30	order	order	NN
10_1101-2021_01_08_425885	231	31	terms	term	NNS
10_1101-2021_01_08_425885	231	32	to	to	IN
10_1101-2021_01_08_425885	231	33	k0	k0	NNP
10_1101-2021_01_08_425885	231	34	(	(	-LRB-
10_1101-2021_01_08_425885	231	35	see	see	VB
10_1101-2021_01_08_425885	231	36	Methods	Methods	NNP
10_1101-2021_01_08_425885	231	37	Section	Section	NNP
10_1101-2021_01_08_425885	231	38	4.5.3	4.5.3	CD
10_1101-2021_01_08_425885	231	39	)	)	-RRB-
10_1101-2021_01_08_425885	231	40	.	.	.
10_1101-2021_01_08_425885	232	1	The	the	DT
10_1101-2021_01_08_425885	232	2	coefficients	coefficient	NNS
10_1101-2021_01_08_425885	232	3	for	for	IN
10_1101-2021_01_08_425885	232	4	the	the	DT
10_1101-2021_01_08_425885	232	5	higher	high	JJR
10_1101-2021_01_08_425885	232	6	-	-	HYPH
10_1101-2021_01_08_425885	232	7	order	order	NN
10_1101-2021_01_08_425885	232	8	terms	term	NNS
10_1101-2021_01_08_425885	232	9	were	be	VBD
10_1101-2021_01_08_425885	232	10	determined	determine	VBN
10_1101-2021_01_08_425885	232	11	by	by	IN
10_1101-2021_01_08_425885	232	12	fitting	fit	VBG
10_1101-2021_01_08_425885	232	13	the	the	DT
10_1101-2021_01_08_425885	232	14	data	datum	NNS
10_1101-2021_01_08_425885	232	15	,	,	,
10_1101-2021_01_08_425885	232	16	resulting	result	VBG
10_1101-2021_01_08_425885	232	17	in	in	IN
10_1101-2021_01_08_425885	232	18	a	a	DT
10_1101-2021_01_08_425885	232	19	new	new	JJ
10_1101-2021_01_08_425885	232	20	embedding	embedding	NN
10_1101-2021_01_08_425885	232	21	,	,	,
10_1101-2021_01_08_425885	232	22	which	which	WDT
10_1101-2021_01_08_425885	232	23	we	-PRON-	PRP
10_1101-2021_01_08_425885	232	24	refer	refer	VBP
10_1101-2021_01_08_425885	232	25	to	to	IN
10_1101-2021_01_08_425885	232	26	as	as	IN
10_1101-2021_01_08_425885	232	27	k1	k1	NNP
10_1101-2021_01_08_425885	232	28	(	(	-LRB-
10_1101-2021_01_08_425885	232	29	see	see	VB
10_1101-2021_01_08_425885	232	30	Methods	Methods	NNP
10_1101-2021_01_08_425885	232	31	Section	Section	NNP
10_1101-2021_01_08_425885	232	32	4.5.5	4.5.5	CD
10_1101-2021_01_08_425885	232	33	)	)	-RRB-
10_1101-2021_01_08_425885	232	34	.	.	.
10_1101-2021_01_08_425885	233	1	The	the	DT
10_1101-2021_01_08_425885	233	2	median	median	JJ
10_1101-2021_01_08_425885	233	3	Euclidean	euclidean	JJ
10_1101-2021_01_08_425885	233	4	distance	distance	NN
10_1101-2021_01_08_425885	233	5	of	of	IN
10_1101-2021_01_08_425885	233	6	the	the	DT
10_1101-2021_01_08_425885	233	7	image	image	NN
10_1101-2021_01_08_425885	233	8	patches	patch	NNS
10_1101-2021_01_08_425885	233	9	to	to	IN
10_1101-2021_01_08_425885	233	10	k1	k1	NNP
10_1101-2021_01_08_425885	233	11	was	be	VBD
10_1101-2021_01_08_425885	233	12	0.115	0.115	CD
10_1101-2021_01_08_425885	233	13	versus	versus	IN
10_1101-2021_01_08_425885	233	14	0.148	0.148	CD
10_1101-2021_01_08_425885	233	15	to	to	IN
10_1101-2021_01_08_425885	233	16	k0	k0	NNP
10_1101-2021_01_08_425885	233	17	.	.	.
10_1101-2021_01_08_425885	234	1	As	as	IN
10_1101-2021_01_08_425885	234	2	was	be	VBD
10_1101-2021_01_08_425885	234	3	done	do	VBN
10_1101-2021_01_08_425885	234	4	for	for	IN
10_1101-2021_01_08_425885	234	5	k0	k0	NNP
10_1101-2021_01_08_425885	234	6	,	,	,
10_1101-2021_01_08_425885	234	7	we	-PRON-	PRP
10_1101-2021_01_08_425885	234	8	associated	associate	VBD
10_1101-2021_01_08_425885	234	9	each	each	DT
10_1101-2021_01_08_425885	234	10	image	image	NN
10_1101-2021_01_08_425885	234	11	patch	patch	NN
10_1101-2021_01_08_425885	234	12	to	to	IN
10_1101-2021_01_08_425885	234	13	its	-PRON-	PRP$
10_1101-2021_01_08_425885	234	14	closest	close	JJS
10_1101-2021_01_08_425885	234	15	point	point	NN
10_1101-2021_01_08_425885	234	16	(	(	-LRB-
10_1101-2021_01_08_425885	234	17	θ1,φ1	θ1,φ1	NN
10_1101-2021_01_08_425885	234	18	)	)	-RRB-
10_1101-2021_01_08_425885	234	19	on	on	IN
10_1101-2021_01_08_425885	234	20	k	k	NNP
10_1101-2021_01_08_425885	234	21	1	1	CD
10_1101-2021_01_08_425885	234	22	,	,	,
10_1101-2021_01_08_425885	234	23	and	and	CC
10_1101-2021_01_08_425885	234	24	used	use	VBD
10_1101-2021_01_08_425885	234	25	our	-PRON-	PRP$
10_1101-2021_01_08_425885	234	26	algorithm	algorithm	NN
10_1101-2021_01_08_425885	234	27	to	to	TO
10_1101-2021_01_08_425885	234	28	compute	compute	VB
10_1101-2021_01_08_425885	234	29	the	the	DT
10_1101-2021_01_08_425885	234	30	scalar	scalar	JJ
10_1101-2021_01_08_425885	234	31	curvature	curvature	NN
10_1101-2021_01_08_425885	234	32	of	of	IN
10_1101-2021_01_08_425885	234	33	these	these	DT
10_1101-2021_01_08_425885	234	34	(	(	-LRB-
10_1101-2021_01_08_425885	234	35	θ1,φ1	θ1,φ1	NN
10_1101-2021_01_08_425885	234	36	)	)	-RRB-
10_1101-2021_01_08_425885	234	37	points	point	NNS
10_1101-2021_01_08_425885	234	38	(	(	-LRB-
10_1101-2021_01_08_425885	234	39	see	see	VB
10_1101-2021_01_08_425885	234	40	Figure	Figure	NNP
10_1101-2021_01_08_425885	234	41	3H	3h	NN
10_1101-2021_01_08_425885	234	42	)	)	-RRB-
10_1101-2021_01_08_425885	234	43	.	.	.
10_1101-2021_01_08_425885	235	1	Despite	despite	IN
10_1101-2021_01_08_425885	235	2	the	the	DT
10_1101-2021_01_08_425885	235	3	reduction	reduction	NN
10_1101-2021_01_08_425885	235	4	in	in	IN
10_1101-2021_01_08_425885	235	5	the	the	DT
10_1101-2021_01_08_425885	235	6	median	median	JJ
10_1101-2021_01_08_425885	235	7	Euclidean	euclidean	JJ
10_1101-2021_01_08_425885	235	8	distance	distance	NN
10_1101-2021_01_08_425885	235	9	of	of	IN
10_1101-2021_01_08_425885	235	10	images	image	NNS
10_1101-2021_01_08_425885	235	11	patches	patch	NNS
10_1101-2021_01_08_425885	235	12	to	to	IN
10_1101-2021_01_08_425885	235	13	the	the	DT
10_1101-2021_01_08_425885	235	14	embedding	embedding	NN
10_1101-2021_01_08_425885	235	15	,	,	,
10_1101-2021_01_08_425885	235	16	the	the	DT
10_1101-2021_01_08_425885	235	17	scalar	scalar	JJ
10_1101-2021_01_08_425885	235	18	curvature	curvature	NN
10_1101-2021_01_08_425885	235	19	of	of	IN
10_1101-2021_01_08_425885	235	20	k1	k1	NN
10_1101-2021_01_08_425885	235	21	was	be	VBD
10_1101-2021_01_08_425885	235	22	even	even	RB
10_1101-2021_01_08_425885	235	23	less	less	RBR
10_1101-2021_01_08_425885	235	24	similar	similar	JJ
10_1101-2021_01_08_425885	235	25	to	to	IN
10_1101-2021_01_08_425885	235	26	that	that	DT
10_1101-2021_01_08_425885	235	27	of	of	IN
10_1101-2021_01_08_425885	235	28	the	the	DT
10_1101-2021_01_08_425885	235	29	image	image	NN
10_1101-2021_01_08_425885	235	30	patches	patch	NNS
10_1101-2021_01_08_425885	235	31	(	(	-LRB-
10_1101-2021_01_08_425885	235	32	visualized	visualize	VBN
10_1101-2021_01_08_425885	235	33	in	in	IN
10_1101-2021_01_08_425885	235	34	Figure	Figure	NNP
10_1101-2021_01_08_425885	235	35	3I	3i	NN
10_1101-2021_01_08_425885	235	36	on	on	IN
10_1101-2021_01_08_425885	235	37	these	these	DT
10_1101-2021_01_08_425885	235	38	new	new	JJ
10_1101-2021_01_08_425885	235	39	(	(	-LRB-
10_1101-2021_01_08_425885	235	40	θ1,φ1	θ1,φ1	NN
10_1101-2021_01_08_425885	235	41	)	)	-RRB-
10_1101-2021_01_08_425885	235	42	coordinates	coordinate	VBZ
10_1101-2021_01_08_425885	235	43	for	for	IN
10_1101-2021_01_08_425885	235	44	k	k	NNP
10_1101-2021_01_08_425885	235	45	1	1	CD
10_1101-2021_01_08_425885	235	46	)	)	-RRB-
10_1101-2021_01_08_425885	235	47	than	than	IN
10_1101-2021_01_08_425885	235	48	was	be	VBD
10_1101-2021_01_08_425885	235	49	the	the	DT
10_1101-2021_01_08_425885	235	50	scalar	scalar	JJ
10_1101-2021_01_08_425885	235	51	curvature	curvature	NN
10_1101-2021_01_08_425885	235	52	of	of	IN
10_1101-2021_01_08_425885	235	53	k0	k0	NNP
10_1101-2021_01_08_425885	235	54	;	;	:
10_1101-2021_01_08_425885	235	55	the	the	DT
10_1101-2021_01_08_425885	235	56	range	range	NN
10_1101-2021_01_08_425885	235	57	of	of	IN
10_1101-2021_01_08_425885	235	58	scalar	scalar	JJ
10_1101-2021_01_08_425885	235	59	curvature	curvature	JJ
10_1101-2021_01_08_425885	235	60	values	value	NNS
10_1101-2021_01_08_425885	235	61	for	for	IN
10_1101-2021_01_08_425885	235	62	k1	k1	NNP
10_1101-2021_01_08_425885	235	63	was	be	VBD
10_1101-2021_01_08_425885	235	64	much	much	RB
10_1101-2021_01_08_425885	235	65	larger	large	JJR
10_1101-2021_01_08_425885	235	66	than	than	IN
10_1101-2021_01_08_425885	235	67	for	for	IN
10_1101-2021_01_08_425885	235	68	either	either	CC
10_1101-2021_01_08_425885	235	69	the	the	DT
10_1101-2021_01_08_425885	235	70	image	image	NN
10_1101-2021_01_08_425885	235	71	patches	patch	NNS
10_1101-2021_01_08_425885	235	72	or	or	CC
10_1101-2021_01_08_425885	235	73	k0	k0	NNP
10_1101-2021_01_08_425885	235	74	,	,	,
10_1101-2021_01_08_425885	235	75	and	and	CC
10_1101-2021_01_08_425885	235	76	the	the	DT
10_1101-2021_01_08_425885	235	77	scalar	scalar	JJ
10_1101-2021_01_08_425885	235	78	curvature	curvature	NN
10_1101-2021_01_08_425885	235	79	fluctuates	fluctuate	NNS
10_1101-2021_01_08_425885	235	80	on	on	IN
10_1101-2021_01_08_425885	235	81	smaller	small	JJR
10_1101-2021_01_08_425885	235	82	length	length	NN
10_1101-2021_01_08_425885	235	83	scales	scale	NNS
10_1101-2021_01_08_425885	235	84	.	.	.
10_1101-2021_01_08_425885	236	1	Lastly	lastly	RB
10_1101-2021_01_08_425885	236	2	,	,	,
10_1101-2021_01_08_425885	236	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	236	4	reasoned	reason	VBD
10_1101-2021_01_08_425885	236	5	that	that	IN
10_1101-2021_01_08_425885	236	6	there	there	EX
10_1101-2021_01_08_425885	236	7	might	may	MD
10_1101-2021_01_08_425885	236	8	be	be	VB
10_1101-2021_01_08_425885	236	9	fine	fine	JJ
10_1101-2021_01_08_425885	236	10	-	-	HYPH
10_1101-2021_01_08_425885	236	11	scale	scale	NN
10_1101-2021_01_08_425885	236	12	scalar	scalar	JJ
10_1101-2021_01_08_425885	236	13	curvature	curvature	NN
10_1101-2021_01_08_425885	236	14	fluctuations	fluctuation	NNS
10_1101-2021_01_08_425885	236	15	in	in	IN
10_1101-2021_01_08_425885	236	16	the	the	DT
10_1101-2021_01_08_425885	236	17	image	image	NN
10_1101-2021_01_08_425885	236	18	patches	patch	NNS
10_1101-2021_01_08_425885	236	19	that	that	WDT
10_1101-2021_01_08_425885	236	20	are	be	VBP
10_1101-2021_01_08_425885	236	21	masked	mask	VBN
10_1101-2021_01_08_425885	236	22	by	by	IN
10_1101-2021_01_08_425885	236	23	the	the	DT
10_1101-2021_01_08_425885	236	24	larger	large	JJR
10_1101-2021_01_08_425885	236	25	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	236	26	sizes	size	NNS
10_1101-2021_01_08_425885	236	27	used	use	VBN
10_1101-2021_01_08_425885	236	28	to	to	TO
10_1101-2021_01_08_425885	236	29	compute	compute	VB
10_1101-2021_01_08_425885	236	30	scalar	scalar	JJ
10_1101-2021_01_08_425885	236	31	curvature	curvature	NN
10_1101-2021_01_08_425885	236	32	for	for	IN
10_1101-2021_01_08_425885	236	33	the	the	DT
10_1101-2021_01_08_425885	236	34	image	image	NN
10_1101-2021_01_08_425885	236	35	patches	patch	NNS
10_1101-2021_01_08_425885	236	36	(	(	-LRB-
10_1101-2021_01_08_425885	236	37	see	see	VB
10_1101-2021_01_08_425885	236	38	Figure	figure	NN
10_1101-2021_01_08_425885	236	39	S3B	s3b	RP
10_1101-2021_01_08_425885	236	40	)	)	-RRB-
10_1101-2021_01_08_425885	236	41	relative	relative	JJ
10_1101-2021_01_08_425885	236	42	to	to	IN
10_1101-2021_01_08_425885	236	43	k1	k1	NNP
10_1101-2021_01_08_425885	236	44	(	(	-LRB-
10_1101-2021_01_08_425885	236	45	see	see	VB
10_1101-2021_01_08_425885	236	46	Figure	Figure	NNP
10_1101-2021_01_08_425885	236	47	S3D	s3d	NN
10_1101-2021_01_08_425885	236	48	)	)	-RRB-
10_1101-2021_01_08_425885	236	49	.	.	.
10_1101-2021_01_08_425885	237	1	To	to	TO
10_1101-2021_01_08_425885	237	2	decrease	decrease	VB
10_1101-2021_01_08_425885	237	3	the	the	DT
10_1101-2021_01_08_425885	237	4	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	237	5	sizes	size	NNS
10_1101-2021_01_08_425885	237	6	chosen	choose	VBN
10_1101-2021_01_08_425885	237	7	by	by	IN
10_1101-2021_01_08_425885	237	8	the	the	DT
10_1101-2021_01_08_425885	237	9	algorithm	algorithm	NN
10_1101-2021_01_08_425885	237	10	for	for	IN
10_1101-2021_01_08_425885	237	11	the	the	DT
10_1101-2021_01_08_425885	237	12	same	same	JJ
10_1101-2021_01_08_425885	237	13	σh	σh	NNP
10_1101-2021_01_08_425885	237	14	,	,	,
10_1101-2021_01_08_425885	237	15	we	-PRON-	PRP
10_1101-2021_01_08_425885	237	16	augmented	augment	VBD
10_1101-2021_01_08_425885	237	17	the	the	DT
10_1101-2021_01_08_425885	237	18	image	image	NN
10_1101-2021_01_08_425885	237	19	patch	patch	NN
10_1101-2021_01_08_425885	237	20	dataset	dataset	NN
10_1101-2021_01_08_425885	237	21	using	use	VBG
10_1101-2021_01_08_425885	237	22	the	the	DT
10_1101-2021_01_08_425885	237	23	full	full	JJ
10_1101-2021_01_08_425885	237	24	set	set	NN
10_1101-2021_01_08_425885	237	25	of	of	IN
10_1101-2021_01_08_425885	237	26	N	N	NNP
10_1101-2021_01_08_425885	237	27	≈	≈	NNP
10_1101-2021_01_08_425885	237	28	1.3	1.3	CD
10_1101-2021_01_08_425885	237	29	×	×	CD
10_1101-2021_01_08_425885	237	30	108	108	CD
10_1101-2021_01_08_425885	237	31	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	237	32	from	from	IN
10_1101-2021_01_08_425885	237	33	the	the	DT
10_1101-2021_01_08_425885	237	34	van	van	NNP
10_1101-2021_01_08_425885	237	35	Hateren	Hateren	NNP
10_1101-2021_01_08_425885	237	36	dataset	dataset	NN
10_1101-2021_01_08_425885	237	37	(	(	-LRB-
10_1101-2021_01_08_425885	237	38	see	see	VB
10_1101-2021_01_08_425885	237	39	Methods	Methods	NNP
10_1101-2021_01_08_425885	237	40	Section	Section	NNP
10_1101-2021_01_08_425885	237	41	4.5.2	4.5.2	CD
10_1101-2021_01_08_425885	237	42	)	)	-RRB-
10_1101-2021_01_08_425885	237	43	.	.	.
10_1101-2021_01_08_425885	238	1	This	this	DT
10_1101-2021_01_08_425885	238	2	resulted	result	VBD
10_1101-2021_01_08_425885	238	3	in	in	IN
10_1101-2021_01_08_425885	238	4	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	238	5	sizes	size	VBZ
10_1101-2021_01_08_425885	238	6	comparable	comparable	JJ
10_1101-2021_01_08_425885	238	7	to	to	IN
10_1101-2021_01_08_425885	238	8	those	those	DT
10_1101-2021_01_08_425885	238	9	determined	determined	JJ
10_1101-2021_01_08_425885	238	10	for	for	IN
10_1101-2021_01_08_425885	238	11	k1	k1	NNP
10_1101-2021_01_08_425885	238	12	(	(	-LRB-
10_1101-2021_01_08_425885	238	13	cf	cf	NNP
10_1101-2021_01_08_425885	238	14	.	.	.
10_1101-2021_01_08_425885	239	1	Figures	figure	NNS
10_1101-2021_01_08_425885	239	2	S3D	s3d	VBP
10_1101-2021_01_08_425885	239	3	and	and	CC
10_1101-2021_01_08_425885	239	4	S3E	S3E	NNP
10_1101-2021_01_08_425885	239	5	)	)	-RRB-
10_1101-2021_01_08_425885	239	6	,	,	,
10_1101-2021_01_08_425885	239	7	but	but	CC
10_1101-2021_01_08_425885	239	8	failed	fail	VBD
10_1101-2021_01_08_425885	239	9	to	to	TO
10_1101-2021_01_08_425885	239	10	recapitulate	recapitulate	VB
10_1101-2021_01_08_425885	239	11	the	the	DT
10_1101-2021_01_08_425885	239	12	fine	fine	JJ
10_1101-2021_01_08_425885	239	13	-	-	HYPH
10_1101-2021_01_08_425885	239	14	scale	scale	NN
10_1101-2021_01_08_425885	239	15	scalar	scalar	JJ
10_1101-2021_01_08_425885	239	16	curvature	curvature	NN
10_1101-2021_01_08_425885	239	17	fluctuations	fluctuation	NNS
10_1101-2021_01_08_425885	239	18	observed	observe	VBN
10_1101-2021_01_08_425885	239	19	in	in	IN
10_1101-2021_01_08_425885	239	20	k1	k1	NNP
10_1101-2021_01_08_425885	239	21	(	(	-LRB-
10_1101-2021_01_08_425885	239	22	see	see	VB
10_1101-2021_01_08_425885	239	23	Figure	Figure	NNP
10_1101-2021_01_08_425885	239	24	3J	3j	NN
10_1101-2021_01_08_425885	239	25	)	)	-RRB-
10_1101-2021_01_08_425885	239	26	.	.	.
10_1101-2021_01_08_425885	240	1	As	as	IN
10_1101-2021_01_08_425885	240	2	a	a	DT
10_1101-2021_01_08_425885	240	3	sanity	sanity	NN
10_1101-2021_01_08_425885	240	4	check	check	NN
10_1101-2021_01_08_425885	240	5	,	,	,
10_1101-2021_01_08_425885	240	6	we	-PRON-	PRP
10_1101-2021_01_08_425885	240	7	confirmed	confirm	VBD
10_1101-2021_01_08_425885	240	8	that	that	IN
10_1101-2021_01_08_425885	240	9	the	the	DT
10_1101-2021_01_08_425885	240	10	scalar	scalar	JJ
10_1101-2021_01_08_425885	240	11	curvature	curvature	NN
10_1101-2021_01_08_425885	240	12	of	of	IN
10_1101-2021_01_08_425885	240	13	the	the	DT
10_1101-2021_01_08_425885	240	14	augmented	augment	VBN
10_1101-2021_01_08_425885	240	15	image	image	NN
10_1101-2021_01_08_425885	240	16	patch	patch	NN
10_1101-2021_01_08_425885	240	17	dataset	dataset	NNP
10_1101-2021_01_08_425885	240	18	matched	match	VBD
10_1101-2021_01_08_425885	240	19	that	that	DT
10_1101-2021_01_08_425885	240	20	of	of	IN
10_1101-2021_01_08_425885	240	21	the	the	DT
10_1101-2021_01_08_425885	240	22	original	original	JJ
10_1101-2021_01_08_425885	240	23	image	image	NN
10_1101-2021_01_08_425885	240	24	patch	patch	NN
10_1101-2021_01_08_425885	240	25	dataset	dataset	NNP
10_1101-2021_01_08_425885	240	26	,	,	,
10_1101-2021_01_08_425885	240	27	when	when	WRB
10_1101-2021_01_08_425885	240	28	computed	compute	VBN
10_1101-2021_01_08_425885	240	29	using	use	VBG
10_1101-2021_01_08_425885	240	30	the	the	DT
10_1101-2021_01_08_425885	240	31	same	same	JJ
10_1101-2021_01_08_425885	240	32	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	240	33	sizes	size	VBZ
10_1101-2021_01_08_425885	240	34	as	as	IN
10_1101-2021_01_08_425885	240	35	the	the	DT
10_1101-2021_01_08_425885	240	36	latter	latter	JJ
10_1101-2021_01_08_425885	240	37	(	(	-LRB-
10_1101-2021_01_08_425885	240	38	see	see	VB
10_1101-2021_01_08_425885	240	39	Figure	Figure	NNP
10_1101-2021_01_08_425885	240	40	S3F	S3F	NNP
10_1101-2021_01_08_425885	240	41	)	)	-RRB-
10_1101-2021_01_08_425885	240	42	.	.	.
10_1101-2021_01_08_425885	241	1	Therefore	therefore	RB
10_1101-2021_01_08_425885	241	2	,	,	,
10_1101-2021_01_08_425885	241	3	including	include	VBG
10_1101-2021_01_08_425885	241	4	higher	high	JJR
10_1101-2021_01_08_425885	241	5	-	-	HYPH
10_1101-2021_01_08_425885	241	6	order	order	NN
10_1101-2021_01_08_425885	241	7	terms	term	NNS
10_1101-2021_01_08_425885	241	8	in	in	IN
10_1101-2021_01_08_425885	241	9	the	the	DT
10_1101-2021_01_08_425885	241	10	embedding	embedding	NN
10_1101-2021_01_08_425885	241	11	does	do	VBZ
10_1101-2021_01_08_425885	241	12	not	not	RB
10_1101-2021_01_08_425885	241	13	yield	yield	VB
10_1101-2021_01_08_425885	241	14	scalar	scalar	JJ
10_1101-2021_01_08_425885	241	15	curvatures	curvature	NNS
10_1101-2021_01_08_425885	241	16	that	that	WDT
10_1101-2021_01_08_425885	241	17	better	better	RB
10_1101-2021_01_08_425885	241	18	agree	agree	VBP
10_1101-2021_01_08_425885	241	19	with	with	IN
10_1101-2021_01_08_425885	241	20	the	the	DT
10_1101-2021_01_08_425885	241	21	data	datum	NNS
10_1101-2021_01_08_425885	241	22	.	.	.
10_1101-2021_01_08_425885	242	1	Taken	take	VBN
10_1101-2021_01_08_425885	242	2	together	together	RB
10_1101-2021_01_08_425885	242	3	,	,	,
10_1101-2021_01_08_425885	242	4	our	-PRON-	PRP$
10_1101-2021_01_08_425885	242	5	analysis	analysis	NN
10_1101-2021_01_08_425885	242	6	of	of	IN
10_1101-2021_01_08_425885	242	7	curvature	curvature	JJ
10_1101-2021_01_08_425885	242	8	suggests	suggest	VBZ
10_1101-2021_01_08_425885	242	9	that	that	IN
10_1101-2021_01_08_425885	242	10	the	the	DT
10_1101-2021_01_08_425885	242	11	image	image	NN
10_1101-2021_01_08_425885	242	12	patch	patch	NN
10_1101-2021_01_08_425885	242	13	dataset	dataset	NN
10_1101-2021_01_08_425885	242	14	can	can	MD
10_1101-2021_01_08_425885	242	15	be	be	VB
10_1101-2021_01_08_425885	242	16	best	well	RBS
10_1101-2021_01_08_425885	242	17	modelled	model	VBN
10_1101-2021_01_08_425885	242	18	by	by	IN
10_1101-2021_01_08_425885	242	19	adding	add	VBG
10_1101-2021_01_08_425885	242	20	noise	noise	NN
10_1101-2021_01_08_425885	242	21	to	to	IN
10_1101-2021_01_08_425885	242	22	the	the	DT
10_1101-2021_01_08_425885	242	23	simplest	simple	JJS
10_1101-2021_01_08_425885	242	24	embedding	embedding	NN
10_1101-2021_01_08_425885	242	25	,	,	,
10_1101-2021_01_08_425885	242	26	k0	k0	NNP
10_1101-2021_01_08_425885	242	27	.	.	.
10_1101-2021_01_08_425885	243	1	Having	have	VBG
10_1101-2021_01_08_425885	243	2	applied	apply	VBN
10_1101-2021_01_08_425885	243	3	our	-PRON-	PRP$
10_1101-2021_01_08_425885	243	4	algorithm	algorithm	NN
10_1101-2021_01_08_425885	243	5	on	on	IN
10_1101-2021_01_08_425885	243	6	real	real	JJ
10_1101-2021_01_08_425885	243	7	-	-	HYPH
10_1101-2021_01_08_425885	243	8	world	world	NN
10_1101-2021_01_08_425885	243	9	manifold	manifold	NN
10_1101-2021_01_08_425885	243	10	-	-	HYPH
10_1101-2021_01_08_425885	243	11	valued	value	VBN
10_1101-2021_01_08_425885	243	12	data	datum	NNS
10_1101-2021_01_08_425885	243	13	that	that	WDT
10_1101-2021_01_08_425885	243	14	is	be	VBZ
10_1101-2021_01_08_425885	243	15	well	well	RB
10_1101-2021_01_08_425885	243	16	-	-	HYPH
10_1101-2021_01_08_425885	243	17	modelled	model	VBN
10_1101-2021_01_08_425885	243	18	by	by	IN
10_1101-2021_01_08_425885	243	19	an	an	DT
10_1101-2021_01_08_425885	243	20	analyti-	analyti-	NN
10_1101-2021_01_08_425885	243	21	cal	cal	NN
10_1101-2021_01_08_425885	243	22	embedding	embedding	NN
10_1101-2021_01_08_425885	243	23	,	,	,
10_1101-2021_01_08_425885	243	24	we	-PRON-	PRP
10_1101-2021_01_08_425885	243	25	next	next	RB
10_1101-2021_01_08_425885	243	26	turned	turn	VBD
10_1101-2021_01_08_425885	243	27	our	-PRON-	PRP$
10_1101-2021_01_08_425885	243	28	attention	attention	NN
10_1101-2021_01_08_425885	243	29	to	to	IN
10_1101-2021_01_08_425885	243	30	scRNAseq	scrnaseq	NN
10_1101-2021_01_08_425885	243	31	datasets	dataset	NNS
10_1101-2021_01_08_425885	243	32	,	,	,
10_1101-2021_01_08_425885	243	33	which	which	WDT
10_1101-2021_01_08_425885	243	34	are	be	VBP
10_1101-2021_01_08_425885	243	35	generally	generally	RB
10_1101-2021_01_08_425885	243	36	regarded	regard	VBN
10_1101-2021_01_08_425885	243	37	as	as	IN
10_1101-2021_01_08_425885	243	38	low-	low-	NN
10_1101-2021_01_08_425885	243	39	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	243	40	manifolds	manifold	NNS
10_1101-2021_01_08_425885	243	41	and	and	CC
10_1101-2021_01_08_425885	243	42	have	have	VBP
10_1101-2021_01_08_425885	243	43	no	no	DT
10_1101-2021_01_08_425885	243	44	known	know	VBN
10_1101-2021_01_08_425885	243	45	analytical	analytical	JJ
10_1101-2021_01_08_425885	243	46	form	form	NN
10_1101-2021_01_08_425885	243	47	.	.	.
10_1101-2021_01_08_425885	244	1	14	14	CD
10_1101-2021_01_08_425885	244	2	.CC	.CC	:
10_1101-2021_01_08_425885	244	3	-	-	HYPH
10_1101-2021_01_08_425885	244	4	BY	by	IN
10_1101-2021_01_08_425885	244	5	-	-	HYPH
10_1101-2021_01_08_425885	244	6	NC	NC	NNP
10_1101-2021_01_08_425885	244	7	-	-	HYPH
10_1101-2021_01_08_425885	244	8	ND	ND	NNP
10_1101-2021_01_08_425885	244	9	4.0	4.0	CD
10_1101-2021_01_08_425885	244	10	International	International	NNP
10_1101-2021_01_08_425885	244	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	244	12	under	under	IN
10_1101-2021_01_08_425885	244	13	a	a	DT
10_1101-2021_01_08_425885	244	14	(	(	-LRB-
10_1101-2021_01_08_425885	244	15	which	which	WDT
10_1101-2021_01_08_425885	244	16	was	be	VBD
10_1101-2021_01_08_425885	244	17	not	not	RB
10_1101-2021_01_08_425885	244	18	certified	certify	VBN
10_1101-2021_01_08_425885	244	19	by	by	IN
10_1101-2021_01_08_425885	244	20	peer	peer	NN
10_1101-2021_01_08_425885	244	21	review	review	NN
10_1101-2021_01_08_425885	244	22	)	)	-RRB-
10_1101-2021_01_08_425885	244	23	is	be	VBZ
10_1101-2021_01_08_425885	244	24	the	the	DT
10_1101-2021_01_08_425885	244	25	author	author	NN
10_1101-2021_01_08_425885	244	26	/	/	SYM
10_1101-2021_01_08_425885	244	27	funder	funder	NN
10_1101-2021_01_08_425885	244	28	,	,	,
10_1101-2021_01_08_425885	244	29	who	who	WP
10_1101-2021_01_08_425885	244	30	has	have	VBZ
10_1101-2021_01_08_425885	244	31	granted	grant	VBN
10_1101-2021_01_08_425885	244	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	244	33	a	a	DT
10_1101-2021_01_08_425885	244	34	license	license	NN
10_1101-2021_01_08_425885	244	35	to	to	TO
10_1101-2021_01_08_425885	244	36	display	display	VB
10_1101-2021_01_08_425885	244	37	the	the	DT
10_1101-2021_01_08_425885	244	38	preprint	preprint	NN
10_1101-2021_01_08_425885	244	39	in	in	IN
10_1101-2021_01_08_425885	244	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	244	41	.	.	.
10_1101-2021_01_08_425885	245	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	245	2	is	be	VBZ
10_1101-2021_01_08_425885	245	3	made	make	VBN
10_1101-2021_01_08_425885	245	4	The	the	DT
10_1101-2021_01_08_425885	245	5	copyright	copyright	NN
10_1101-2021_01_08_425885	245	6	holder	holder	NN
10_1101-2021_01_08_425885	245	7	for	for	IN
10_1101-2021_01_08_425885	245	8	this	this	DT
10_1101-2021_01_08_425885	245	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	245	10	version	version	NN
10_1101-2021_01_08_425885	245	11	posted	post	VBD
10_1101-2021_01_08_425885	245	12	January	January	NNP
10_1101-2021_01_08_425885	245	13	8	8	CD
10_1101-2021_01_08_425885	245	14	,	,	,
10_1101-2021_01_08_425885	245	15	2021	2021	CD
10_1101-2021_01_08_425885	245	16	.	.	.
10_1101-2021_01_08_425885	245	17	;	;	:
10_1101-2021_01_08_425885	245	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	245	19	:	:	:
10_1101-2021_01_08_425885	245	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	245	21	preprint	preprint	NN
10_1101-2021_01_08_425885	245	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	245	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NN
10_1101-2021_01_08_425885	245	24	2.4	2.4	CD
10_1101-2021_01_08_425885	245	25	scRNAseq	scRNAseq	NNS
10_1101-2021_01_08_425885	245	26	Datasets	dataset	NNS
10_1101-2021_01_08_425885	245	27	have	have	VBP
10_1101-2021_01_08_425885	245	28	Non	non	JJ
10_1101-2021_01_08_425885	245	29	-	-	JJ
10_1101-2021_01_08_425885	245	30	Trivial	trivial	JJ
10_1101-2021_01_08_425885	245	31	Intrinsic	intrinsic	NN
10_1101-2021_01_08_425885	245	32	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	245	33	In	in	IN
10_1101-2021_01_08_425885	245	34	scRNAseq	scrnaseq	NN
10_1101-2021_01_08_425885	245	35	datasets	dataset	NNS
10_1101-2021_01_08_425885	245	36	,	,	,
10_1101-2021_01_08_425885	245	37	each	each	DT
10_1101-2021_01_08_425885	245	38	datapoint	datapoint	JJ
10_1101-2021_01_08_425885	245	39	corresponds	correspond	VBZ
10_1101-2021_01_08_425885	245	40	to	to	IN
10_1101-2021_01_08_425885	245	41	a	a	DT
10_1101-2021_01_08_425885	245	42	cell	cell	NN
10_1101-2021_01_08_425885	245	43	,	,	,
10_1101-2021_01_08_425885	245	44	and	and	CC
10_1101-2021_01_08_425885	245	45	each	each	DT
10_1101-2021_01_08_425885	245	46	coordinate	coordinate	VB
10_1101-2021_01_08_425885	245	47	to	to	IN
10_1101-2021_01_08_425885	245	48	the	the	DT
10_1101-2021_01_08_425885	245	49	abundance	abundance	NN
10_1101-2021_01_08_425885	245	50	of	of	IN
10_1101-2021_01_08_425885	245	51	a	a	DT
10_1101-2021_01_08_425885	245	52	different	different	JJ
10_1101-2021_01_08_425885	245	53	gene	gene	NN
10_1101-2021_01_08_425885	245	54	.	.	.
10_1101-2021_01_08_425885	246	1	Here	here	RB
10_1101-2021_01_08_425885	246	2	we	-PRON-	PRP
10_1101-2021_01_08_425885	246	3	consider	consider	VBP
10_1101-2021_01_08_425885	246	4	the	the	DT
10_1101-2021_01_08_425885	246	5	data	datum	NNS
10_1101-2021_01_08_425885	246	6	manifold	manifold	NN
10_1101-2021_01_08_425885	246	7	after	after	IN
10_1101-2021_01_08_425885	246	8	basic	basic	JJ
10_1101-2021_01_08_425885	246	9	preprocessing	preprocessing	NN
10_1101-2021_01_08_425885	246	10	and	and	CC
10_1101-2021_01_08_425885	246	11	linear	linear	JJ
10_1101-2021_01_08_425885	246	12	dimensionality	dimensionality	NN
10_1101-2021_01_08_425885	246	13	reduction	reduction	NN
10_1101-2021_01_08_425885	246	14	using	use	VBG
10_1101-2021_01_08_425885	246	15	PCA	PCA	NNP
10_1101-2021_01_08_425885	246	16	(	(	-LRB-
10_1101-2021_01_08_425885	246	17	see	see	VB
10_1101-2021_01_08_425885	246	18	Methods	Methods	NNP
10_1101-2021_01_08_425885	246	19	Section	Section	NNP
10_1101-2021_01_08_425885	246	20	4.6.1	4.6.1	CD
10_1101-2021_01_08_425885	246	21	)	)	-RRB-
10_1101-2021_01_08_425885	246	22	.	.	.
10_1101-2021_01_08_425885	247	1	Since	since	IN
10_1101-2021_01_08_425885	247	2	many	many	JJ
10_1101-2021_01_08_425885	247	3	common	common	JJ
10_1101-2021_01_08_425885	247	4	analyses	analysis	NNS
10_1101-2021_01_08_425885	247	5	in	in	IN
10_1101-2021_01_08_425885	247	6	the	the	DT
10_1101-2021_01_08_425885	247	7	field	field	NN
10_1101-2021_01_08_425885	247	8	such	such	JJ
10_1101-2021_01_08_425885	247	9	as	as	IN
10_1101-2021_01_08_425885	247	10	clustering	clustering	NN
10_1101-2021_01_08_425885	247	11	,	,	,
10_1101-2021_01_08_425885	247	12	visualization	visualization	NN
10_1101-2021_01_08_425885	247	13	,	,	,
10_1101-2021_01_08_425885	247	14	and	and	CC
10_1101-2021_01_08_425885	247	15	inference	inference	NN
10_1101-2021_01_08_425885	247	16	of	of	IN
10_1101-2021_01_08_425885	247	17	cell	cell	NN
10_1101-2021_01_08_425885	247	18	differentiation	differentiation	NN
10_1101-2021_01_08_425885	247	19	trajectories	trajectory	NNS
10_1101-2021_01_08_425885	247	20	are	be	VBP
10_1101-2021_01_08_425885	247	21	performed	perform	VBN
10_1101-2021_01_08_425885	247	22	in	in	IN
10_1101-2021_01_08_425885	247	23	this	this	DT
10_1101-2021_01_08_425885	247	24	reduced	reduce	VBN
10_1101-2021_01_08_425885	247	25	space	space	NN
10_1101-2021_01_08_425885	247	26	,	,	,
10_1101-2021_01_08_425885	247	27	it	-PRON-	PRP
10_1101-2021_01_08_425885	247	28	is	be	VBZ
10_1101-2021_01_08_425885	247	29	natural	natural	JJ
10_1101-2021_01_08_425885	247	30	to	to	TO
10_1101-2021_01_08_425885	247	31	compute	compute	VB
10_1101-2021_01_08_425885	247	32	curvature	curvature	NN
10_1101-2021_01_08_425885	247	33	in	in	IN
10_1101-2021_01_08_425885	247	34	this	this	DT
10_1101-2021_01_08_425885	247	35	space	space	NN
10_1101-2021_01_08_425885	247	36	as	as	RB
10_1101-2021_01_08_425885	247	37	well	well	RB
10_1101-2021_01_08_425885	247	38	.	.	.
10_1101-2021_01_08_425885	248	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	248	2	set	set	VBD
10_1101-2021_01_08_425885	248	3	the	the	DT
10_1101-2021_01_08_425885	248	4	ambient	ambient	JJ
10_1101-2021_01_08_425885	248	5	dimension	dimension	NN
10_1101-2021_01_08_425885	248	6	,	,	,
10_1101-2021_01_08_425885	248	7	n	n	NNP
10_1101-2021_01_08_425885	248	8	,	,	,
10_1101-2021_01_08_425885	248	9	to	to	TO
10_1101-2021_01_08_425885	248	10	be	be	VB
10_1101-2021_01_08_425885	248	11	the	the	DT
10_1101-2021_01_08_425885	248	12	number	number	NN
10_1101-2021_01_08_425885	248	13	of	of	IN
10_1101-2021_01_08_425885	248	14	PCs	pc	NNS
10_1101-2021_01_08_425885	248	15	needed	need	VBN
10_1101-2021_01_08_425885	248	16	to	to	TO
10_1101-2021_01_08_425885	248	17	explain	explain	VB
10_1101-2021_01_08_425885	248	18	80	80	CD
10_1101-2021_01_08_425885	248	19	%	%	NN
10_1101-2021_01_08_425885	248	20	of	of	IN
10_1101-2021_01_08_425885	248	21	the	the	DT
10_1101-2021_01_08_425885	248	22	variance	variance	NN
10_1101-2021_01_08_425885	248	23	.	.	.
10_1101-2021_01_08_425885	249	1	The	the	DT
10_1101-2021_01_08_425885	249	2	manifold	manifold	JJ
10_1101-2021_01_08_425885	249	3	dimension	dimension	NN
10_1101-2021_01_08_425885	249	4	,	,	,
10_1101-2021_01_08_425885	249	5	d	d	NN
10_1101-2021_01_08_425885	249	6	,	,	,
10_1101-2021_01_08_425885	249	7	for	for	IN
10_1101-2021_01_08_425885	249	8	scRNAseq	scrnaseq	JJ
10_1101-2021_01_08_425885	249	9	datasets	dataset	NNS
10_1101-2021_01_08_425885	249	10	is	be	VBZ
10_1101-2021_01_08_425885	249	11	not	not	RB
10_1101-2021_01_08_425885	249	12	well	well	RB
10_1101-2021_01_08_425885	249	13	-	-	HYPH
10_1101-2021_01_08_425885	249	14	defined	define	VBN
10_1101-2021_01_08_425885	249	15	and	and	CC
10_1101-2021_01_08_425885	249	16	needs	need	VBZ
10_1101-2021_01_08_425885	249	17	to	to	TO
10_1101-2021_01_08_425885	249	18	be	be	VB
10_1101-2021_01_08_425885	249	19	chosen	choose	VBN
10_1101-2021_01_08_425885	249	20	heuristically	heuristically	RB
10_1101-2021_01_08_425885	249	21	.	.	.
10_1101-2021_01_08_425885	250	1	As	as	IN
10_1101-2021_01_08_425885	250	2	a	a	DT
10_1101-2021_01_08_425885	250	3	simple	simple	JJ
10_1101-2021_01_08_425885	250	4	heuristic	heuristic	NN
10_1101-2021_01_08_425885	250	5	,	,	,
10_1101-2021_01_08_425885	250	6	we	-PRON-	PRP
10_1101-2021_01_08_425885	250	7	specified	specify	VBD
10_1101-2021_01_08_425885	250	8	d	d	XX
10_1101-2021_01_08_425885	250	9	as	as	IN
10_1101-2021_01_08_425885	250	10	the	the	DT
10_1101-2021_01_08_425885	250	11	number	number	NN
10_1101-2021_01_08_425885	250	12	of	of	IN
10_1101-2021_01_08_425885	250	13	PCs	pc	NNS
10_1101-2021_01_08_425885	250	14	needed	need	VBN
10_1101-2021_01_08_425885	250	15	to	to	TO
10_1101-2021_01_08_425885	250	16	explain	explain	VB
10_1101-2021_01_08_425885	250	17	80	80	CD
10_1101-2021_01_08_425885	250	18	%	%	NN
10_1101-2021_01_08_425885	250	19	of	of	IN
10_1101-2021_01_08_425885	250	20	the	the	DT
10_1101-2021_01_08_425885	250	21	variance	variance	NN
10_1101-2021_01_08_425885	250	22	in	in	IN
10_1101-2021_01_08_425885	250	23	the	the	DT
10_1101-2021_01_08_425885	250	24	ambient	ambient	JJ
10_1101-2021_01_08_425885	250	25	space	space	NN
10_1101-2021_01_08_425885	250	26	i.e.	i.e.	FW
10_1101-2021_01_08_425885	251	1	64	64	CD
10_1101-2021_01_08_425885	251	2	%	%	NN
10_1101-2021_01_08_425885	251	3	of	of	IN
10_1101-2021_01_08_425885	251	4	the	the	DT
10_1101-2021_01_08_425885	251	5	original	original	JJ
10_1101-2021_01_08_425885	251	6	variance	variance	NN
10_1101-2021_01_08_425885	251	7	(	(	-LRB-
10_1101-2021_01_08_425885	251	8	we	-PRON-	PRP
10_1101-2021_01_08_425885	251	9	show	show	VBP
10_1101-2021_01_08_425885	251	10	later	later	RB
10_1101-2021_01_08_425885	251	11	that	that	IN
10_1101-2021_01_08_425885	251	12	our	-PRON-	PRP$
10_1101-2021_01_08_425885	251	13	computations	computation	NNS
10_1101-2021_01_08_425885	251	14	are	be	VBP
10_1101-2021_01_08_425885	251	15	relatively	relatively	RB
10_1101-2021_01_08_425885	251	16	insensitive	insensitive	JJ
10_1101-2021_01_08_425885	251	17	to	to	IN
10_1101-2021_01_08_425885	251	18	the	the	DT
10_1101-2021_01_08_425885	251	19	choice	choice	NN
10_1101-2021_01_08_425885	251	20	of	of	IN
10_1101-2021_01_08_425885	251	21	d	d	NN
10_1101-2021_01_08_425885	251	22	)	)	-RRB-
10_1101-2021_01_08_425885	251	23	.	.	.
10_1101-2021_01_08_425885	252	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	252	2	considered	consider	VBD
10_1101-2021_01_08_425885	252	3	three	three	CD
10_1101-2021_01_08_425885	252	4	datasets	dataset	NNS
10_1101-2021_01_08_425885	252	5	.	.	.
10_1101-2021_01_08_425885	253	1	The	the	DT
10_1101-2021_01_08_425885	253	2	first	first	JJ
10_1101-2021_01_08_425885	253	3	consists	consist	VBZ
10_1101-2021_01_08_425885	253	4	of	of	IN
10_1101-2021_01_08_425885	253	5	N	N	NNP
10_1101-2021_01_08_425885	253	6	≈	≈	NNP
10_1101-2021_01_08_425885	253	7	104	104	CD
10_1101-2021_01_08_425885	253	8	peripheral	peripheral	JJ
10_1101-2021_01_08_425885	253	9	blood	blood	NN
10_1101-2021_01_08_425885	253	10	mononuclear	mononuclear	NN
10_1101-2021_01_08_425885	253	11	cells	cell	NNS
10_1101-2021_01_08_425885	253	12	(	(	-LRB-
10_1101-2021_01_08_425885	253	13	PBMCs	PBMCs	NNP
10_1101-2021_01_08_425885	253	14	)	)	-RRB-
10_1101-2021_01_08_425885	253	15	collected	collect	VBD
10_1101-2021_01_08_425885	253	16	from	from	IN
10_1101-2021_01_08_425885	253	17	a	a	DT
10_1101-2021_01_08_425885	253	18	healthy	healthy	JJ
10_1101-2021_01_08_425885	253	19	human	human	JJ
10_1101-2021_01_08_425885	253	20	donor	donor	NN
10_1101-2021_01_08_425885	253	21	[	[	-LRB-
10_1101-2021_01_08_425885	253	22	42	42	CD
10_1101-2021_01_08_425885	253	23	]	]	-RRB-
10_1101-2021_01_08_425885	253	24	.	.	.
10_1101-2021_01_08_425885	254	1	The	the	DT
10_1101-2021_01_08_425885	254	2	second	second	JJ
10_1101-2021_01_08_425885	254	3	is	be	VBZ
10_1101-2021_01_08_425885	254	4	a	a	DT
10_1101-2021_01_08_425885	254	5	gastrulation	gastrulation	NN
10_1101-2021_01_08_425885	254	6	dataset	dataset	NN
10_1101-2021_01_08_425885	254	7	comprised	comprise	VBN
10_1101-2021_01_08_425885	254	8	of	of	IN
10_1101-2021_01_08_425885	254	9	N	N	NNP
10_1101-2021_01_08_425885	254	10	≈	≈	NNP
10_1101-2021_01_08_425885	254	11	1.2×105	1.2×105	CD
10_1101-2021_01_08_425885	254	12	cells	cell	NNS
10_1101-2021_01_08_425885	254	13	pooled	pool	VBN
10_1101-2021_01_08_425885	254	14	from	from	IN
10_1101-2021_01_08_425885	254	15	9	9	CD
10_1101-2021_01_08_425885	254	16	embryonic	embryonic	JJ
10_1101-2021_01_08_425885	254	17	mice	mouse	NNS
10_1101-2021_01_08_425885	254	18	sacked	sack	VBN
10_1101-2021_01_08_425885	254	19	at	at	IN
10_1101-2021_01_08_425885	254	20	6-hour	6-hour	CD
10_1101-2021_01_08_425885	254	21	intervals	interval	NNS
10_1101-2021_01_08_425885	254	22	from	from	IN
10_1101-2021_01_08_425885	254	23	embryonic	embryonic	JJ
10_1101-2021_01_08_425885	254	24	day	day	NN
10_1101-2021_01_08_425885	254	25	6.5	6.5	CD
10_1101-2021_01_08_425885	254	26	to	to	TO
10_1101-2021_01_08_425885	254	27	8.5	8.5	CD
10_1101-2021_01_08_425885	254	28	[	[	-LRB-
10_1101-2021_01_08_425885	254	29	43	43	CD
10_1101-2021_01_08_425885	254	30	]	]	-RRB-
10_1101-2021_01_08_425885	254	31	.	.	.
10_1101-2021_01_08_425885	255	1	The	the	DT
10_1101-2021_01_08_425885	255	2	final	final	JJ
10_1101-2021_01_08_425885	255	3	dataset	dataset	NN
10_1101-2021_01_08_425885	255	4	is	be	VBZ
10_1101-2021_01_08_425885	255	5	a	a	DT
10_1101-2021_01_08_425885	255	6	benchmark	benchmark	NN
10_1101-2021_01_08_425885	255	7	in	in	IN
10_1101-2021_01_08_425885	255	8	the	the	DT
10_1101-2021_01_08_425885	255	9	field	field	NN
10_1101-2021_01_08_425885	255	10	consisting	consist	VBG
10_1101-2021_01_08_425885	255	11	of	of	IN
10_1101-2021_01_08_425885	255	12	N	N	NNP
10_1101-2021_01_08_425885	255	13	≈	≈	NNP
10_1101-2021_01_08_425885	255	14	1.3	1.3	CD
10_1101-2021_01_08_425885	255	15	×	×	CD
10_1101-2021_01_08_425885	255	16	106	106	CD
10_1101-2021_01_08_425885	255	17	brain	brain	NN
10_1101-2021_01_08_425885	255	18	cells	cell	NNS
10_1101-2021_01_08_425885	255	19	pooled	pool	VBN
10_1101-2021_01_08_425885	255	20	from	from	IN
10_1101-2021_01_08_425885	255	21	2	2	CD
10_1101-2021_01_08_425885	255	22	embryonic	embryonic	JJ
10_1101-2021_01_08_425885	255	23	mice	mouse	NNS
10_1101-2021_01_08_425885	255	24	sacked	sack	VBN
10_1101-2021_01_08_425885	255	25	at	at	IN
10_1101-2021_01_08_425885	255	26	embryonic	embryonic	NNP
10_1101-2021_01_08_425885	255	27	day	day	NN
10_1101-2021_01_08_425885	255	28	18	18	CD
10_1101-2021_01_08_425885	255	29	[	[	-LRB-
10_1101-2021_01_08_425885	255	30	44	44	CD
10_1101-2021_01_08_425885	255	31	]	]	-RRB-
10_1101-2021_01_08_425885	255	32	.	.	.
10_1101-2021_01_08_425885	256	1	Refer	refer	VB
10_1101-2021_01_08_425885	256	2	to	to	IN
10_1101-2021_01_08_425885	256	3	Figures	figure	NNS
10_1101-2021_01_08_425885	256	4	S4A	s4a	NN
10_1101-2021_01_08_425885	256	5	,	,	,
10_1101-2021_01_08_425885	256	6	S5A	s5a	JJ
10_1101-2021_01_08_425885	256	7	and	and	CC
10_1101-2021_01_08_425885	256	8	S6A	s6a	NN
10_1101-2021_01_08_425885	256	9	for	for	IN
10_1101-2021_01_08_425885	256	10	cell	cell	NN
10_1101-2021_01_08_425885	256	11	type	type	NN
10_1101-2021_01_08_425885	256	12	annotations	annotation	NNS
10_1101-2021_01_08_425885	256	13	for	for	IN
10_1101-2021_01_08_425885	256	14	the	the	DT
10_1101-2021_01_08_425885	256	15	three	three	CD
10_1101-2021_01_08_425885	256	16	datasets	dataset	NNS
10_1101-2021_01_08_425885	256	17	.	.	.
10_1101-2021_01_08_425885	257	1	The	the	DT
10_1101-2021_01_08_425885	257	2	PBMC	PBMC	NNP
10_1101-2021_01_08_425885	257	3	dataset	dataset	NN
10_1101-2021_01_08_425885	257	4	is	be	VBZ
10_1101-2021_01_08_425885	257	5	characteristic	characteristic	JJ
10_1101-2021_01_08_425885	257	6	of	of	IN
10_1101-2021_01_08_425885	257	7	the	the	DT
10_1101-2021_01_08_425885	257	8	sample	sample	NN
10_1101-2021_01_08_425885	257	9	size	size	NN
10_1101-2021_01_08_425885	257	10	of	of	IN
10_1101-2021_01_08_425885	257	11	current	current	JJ
10_1101-2021_01_08_425885	257	12	scRNAseq	scrnaseq	JJ
10_1101-2021_01_08_425885	257	13	data	datum	NNS
10_1101-2021_01_08_425885	257	14	.	.	.
10_1101-2021_01_08_425885	258	1	The	the	DT
10_1101-2021_01_08_425885	258	2	other	other	JJ
10_1101-2021_01_08_425885	258	3	two	two	CD
10_1101-2021_01_08_425885	258	4	are	be	VBP
10_1101-2021_01_08_425885	258	5	larger	large	JJR
10_1101-2021_01_08_425885	258	6	than	than	IN
10_1101-2021_01_08_425885	258	7	most	most	JJS
10_1101-2021_01_08_425885	258	8	scRNAseq	scrnaseq	NN
10_1101-2021_01_08_425885	258	9	datasets	dataset	NNS
10_1101-2021_01_08_425885	258	10	,	,	,
10_1101-2021_01_08_425885	258	11	and	and	CC
10_1101-2021_01_08_425885	258	12	we	-PRON-	PRP
10_1101-2021_01_08_425885	258	13	included	include	VBD
10_1101-2021_01_08_425885	258	14	these	these	DT
10_1101-2021_01_08_425885	258	15	to	to	TO
10_1101-2021_01_08_425885	258	16	verify	verify	VB
10_1101-2021_01_08_425885	258	17	if	if	IN
10_1101-2021_01_08_425885	258	18	geometric	geometric	JJ
10_1101-2021_01_08_425885	258	19	features	feature	NNS
10_1101-2021_01_08_425885	258	20	seen	see	VBN
10_1101-2021_01_08_425885	258	21	in	in	IN
10_1101-2021_01_08_425885	258	22	the	the	DT
10_1101-2021_01_08_425885	258	23	first	first	JJ
10_1101-2021_01_08_425885	258	24	dataset	dataset	NN
10_1101-2021_01_08_425885	258	25	can	can	MD
10_1101-2021_01_08_425885	258	26	be	be	VB
10_1101-2021_01_08_425885	258	27	reproduced	reproduce	VBN
10_1101-2021_01_08_425885	258	28	for	for	IN
10_1101-2021_01_08_425885	258	29	more	more	RBR
10_1101-2021_01_08_425885	258	30	densely	densely	RB
10_1101-2021_01_08_425885	258	31	sampled	sample	VBN
10_1101-2021_01_08_425885	258	32	manifolds	manifold	NNS
10_1101-2021_01_08_425885	258	33	.	.	.
10_1101-2021_01_08_425885	259	1	For	for	IN
10_1101-2021_01_08_425885	259	2	the	the	DT
10_1101-2021_01_08_425885	259	3	PBMC	PBMC	NNS
10_1101-2021_01_08_425885	259	4	,	,	,
10_1101-2021_01_08_425885	259	5	gastrulation	gastrulation	NN
10_1101-2021_01_08_425885	259	6	and	and	CC
10_1101-2021_01_08_425885	259	7	brain	brain	NN
10_1101-2021_01_08_425885	259	8	datasets	dataset	NNS
10_1101-2021_01_08_425885	259	9	,	,	,
10_1101-2021_01_08_425885	259	10	the	the	DT
10_1101-2021_01_08_425885	259	11	ambient	ambient	JJ
10_1101-2021_01_08_425885	259	12	(	(	-LRB-
10_1101-2021_01_08_425885	259	13	manifold	manifold	NN
10_1101-2021_01_08_425885	259	14	)	)	-RRB-
10_1101-2021_01_08_425885	259	15	dimensions	dimension	NNS
10_1101-2021_01_08_425885	259	16	were	be	VBD
10_1101-2021_01_08_425885	259	17	determined	determine	VBN
10_1101-2021_01_08_425885	259	18	to	to	TO
10_1101-2021_01_08_425885	259	19	be	be	VB
10_1101-2021_01_08_425885	259	20	8	8	CD
10_1101-2021_01_08_425885	259	21	,	,	,
10_1101-2021_01_08_425885	259	22	11	11	CD
10_1101-2021_01_08_425885	259	23	and	and	CC
10_1101-2021_01_08_425885	259	24	9	9	CD
10_1101-2021_01_08_425885	259	25	(	(	-LRB-
10_1101-2021_01_08_425885	259	26	3	3	CD
10_1101-2021_01_08_425885	259	27	,	,	,
10_1101-2021_01_08_425885	259	28	3	3	CD
10_1101-2021_01_08_425885	259	29	and	and	CC
10_1101-2021_01_08_425885	259	30	5	5	CD
10_1101-2021_01_08_425885	259	31	)	)	-RRB-
10_1101-2021_01_08_425885	259	32	respectively	respectively	RB
10_1101-2021_01_08_425885	259	33	,	,	,
10_1101-2021_01_08_425885	259	34	according	accord	VBG
10_1101-2021_01_08_425885	259	35	to	to	IN
10_1101-2021_01_08_425885	259	36	the	the	DT
10_1101-2021_01_08_425885	259	37	aforementioned	aforementioned	JJ
10_1101-2021_01_08_425885	259	38	heuristic	heuristic	NN
10_1101-2021_01_08_425885	259	39	(	(	-LRB-
10_1101-2021_01_08_425885	259	40	see	see	VB
10_1101-2021_01_08_425885	259	41	Methods	Methods	NNP
10_1101-2021_01_08_425885	259	42	Section	Section	NNP
10_1101-2021_01_08_425885	259	43	4.6.4	4.6.4	CD
10_1101-2021_01_08_425885	259	44	)	)	-RRB-
10_1101-2021_01_08_425885	259	45	.	.	.
10_1101-2021_01_08_425885	260	1	For	for	IN
10_1101-2021_01_08_425885	260	2	all	all	DT
10_1101-2021_01_08_425885	260	3	three	three	CD
10_1101-2021_01_08_425885	260	4	datasets	dataset	NNS
10_1101-2021_01_08_425885	260	5	,	,	,
10_1101-2021_01_08_425885	260	6	the	the	DT
10_1101-2021_01_08_425885	260	7	global	global	JJ
10_1101-2021_01_08_425885	260	8	length	length	NN
10_1101-2021_01_08_425885	260	9	scale	scale	NN
10_1101-2021_01_08_425885	260	10	happened	happen	VBD
10_1101-2021_01_08_425885	260	11	to	to	TO
10_1101-2021_01_08_425885	260	12	be	be	VB
10_1101-2021_01_08_425885	260	13	L	L	NNP
10_1101-2021_01_08_425885	260	14	≈	≈	NNP
10_1101-2021_01_08_425885	260	15	20	20	CD
10_1101-2021_01_08_425885	260	16	(	(	-LRB-
10_1101-2021_01_08_425885	260	17	see	see	VB
10_1101-2021_01_08_425885	260	18	Methods	Methods	NNP
10_1101-2021_01_08_425885	260	19	Sections	Sections	NNPS
10_1101-2021_01_08_425885	260	20	4.3.5	4.3.5	CD
10_1101-2021_01_08_425885	260	21	)	)	-RRB-
10_1101-2021_01_08_425885	260	22	.	.	.
10_1101-2021_01_08_425885	261	1	As	as	IN
10_1101-2021_01_08_425885	261	2	before	before	RB
10_1101-2021_01_08_425885	261	3	,	,	,
10_1101-2021_01_08_425885	261	4	we	-PRON-	PRP
10_1101-2021_01_08_425885	261	5	picked	pick	VBD
10_1101-2021_01_08_425885	261	6	σh	σh	NNP
10_1101-2021_01_08_425885	261	7	for	for	IN
10_1101-2021_01_08_425885	261	8	each	each	DT
10_1101-2021_01_08_425885	261	9	dataset	dataset	NN
10_1101-2021_01_08_425885	261	10	according	accord	VBG
10_1101-2021_01_08_425885	261	11	to	to	IN
10_1101-2021_01_08_425885	261	12	the	the	DT
10_1101-2021_01_08_425885	261	13	distribution	distribution	NN
10_1101-2021_01_08_425885	261	14	of	of	IN
10_1101-2021_01_08_425885	261	15	GOF	GOF	NNP
10_1101-2021_01_08_425885	261	16	p	p	NN
10_1101-2021_01_08_425885	261	17	-	-	HYPH
10_1101-2021_01_08_425885	261	18	values	value	NNS
10_1101-2021_01_08_425885	261	19	(	(	-LRB-
10_1101-2021_01_08_425885	261	20	see	see	VB
10_1101-2021_01_08_425885	261	21	Figures	Figures	NNP
10_1101-2021_01_08_425885	261	22	S4B	S4B	NNP
10_1101-2021_01_08_425885	261	23	,	,	,
10_1101-2021_01_08_425885	261	24	S5B	S5B	NNP
10_1101-2021_01_08_425885	261	25	and	and	CC
10_1101-2021_01_08_425885	261	26	S6B	S6B	NNP
10_1101-2021_01_08_425885	261	27	;	;	:
10_1101-2021_01_08_425885	261	28	Methods	Methods	NNP
10_1101-2021_01_08_425885	261	29	Section	Section	NNP
10_1101-2021_01_08_425885	261	30	4.6.4	4.6.4	CD
10_1101-2021_01_08_425885	261	31	)	)	-RRB-
10_1101-2021_01_08_425885	261	32	.	.	.
10_1101-2021_01_08_425885	262	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	262	2	visualized	visualize	VBD
10_1101-2021_01_08_425885	262	3	the	the	DT
10_1101-2021_01_08_425885	262	4	computed	compute	VBN
10_1101-2021_01_08_425885	262	5	scalar	scalar	JJ
10_1101-2021_01_08_425885	262	6	curvatures	curvature	NNS
10_1101-2021_01_08_425885	262	7	on	on	IN
10_1101-2021_01_08_425885	262	8	standard	standard	JJ
10_1101-2021_01_08_425885	262	9	plots	plot	NNS
10_1101-2021_01_08_425885	262	10	employed	employ	VBN
10_1101-2021_01_08_425885	262	11	in	in	IN
10_1101-2021_01_08_425885	262	12	the	the	DT
10_1101-2021_01_08_425885	262	13	field	field	NN
10_1101-2021_01_08_425885	262	14	(	(	-LRB-
10_1101-2021_01_08_425885	262	15	UMAP	UMAP	NNP
10_1101-2021_01_08_425885	262	16	and	and	CC
10_1101-2021_01_08_425885	262	17	t-	t-	XX
10_1101-2021_01_08_425885	262	18	SNE	SNE	NNP
10_1101-2021_01_08_425885	262	19	;	;	:
10_1101-2021_01_08_425885	262	20	shown	show	VBN
10_1101-2021_01_08_425885	262	21	in	in	IN
10_1101-2021_01_08_425885	262	22	Figure	Figure	NNP
10_1101-2021_01_08_425885	262	23	4A	4a	NN
10_1101-2021_01_08_425885	262	24	,	,	,
10_1101-2021_01_08_425885	262	25	D	d	NN
10_1101-2021_01_08_425885	262	26	,	,	,
10_1101-2021_01_08_425885	262	27	G	g	NN
10_1101-2021_01_08_425885	262	28	)	)	-RRB-
10_1101-2021_01_08_425885	262	29	and	and	CC
10_1101-2021_01_08_425885	262	30	observed	observe	VBD
10_1101-2021_01_08_425885	262	31	non	non	JJ
10_1101-2021_01_08_425885	262	32	-	-	JJ
10_1101-2021_01_08_425885	262	33	trivial	trivial	JJ
10_1101-2021_01_08_425885	262	34	scalar	scalar	JJ
10_1101-2021_01_08_425885	262	35	curvature	curvature	NN
10_1101-2021_01_08_425885	262	36	for	for	IN
10_1101-2021_01_08_425885	262	37	all	all	DT
10_1101-2021_01_08_425885	262	38	three	three	CD
10_1101-2021_01_08_425885	262	39	datasets	dataset	NNS
10_1101-2021_01_08_425885	262	40	.	.	.
10_1101-2021_01_08_425885	263	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	263	2	found	find	VBD
10_1101-2021_01_08_425885	263	3	statistically	statistically	RB
10_1101-2021_01_08_425885	263	4	significant	significant	JJ
10_1101-2021_01_08_425885	263	5	correlations	correlation	NNS
10_1101-2021_01_08_425885	263	6	between	between	IN
10_1101-2021_01_08_425885	263	7	the	the	DT
10_1101-2021_01_08_425885	263	8	scalar	scalar	JJ
10_1101-2021_01_08_425885	263	9	curvature	curvature	NN
10_1101-2021_01_08_425885	263	10	reported	report	VBN
10_1101-2021_01_08_425885	263	11	by	by	IN
10_1101-2021_01_08_425885	263	12	each	each	DT
10_1101-2021_01_08_425885	263	13	point	point	NN
10_1101-2021_01_08_425885	263	14	and	and	CC
10_1101-2021_01_08_425885	263	15	its	-PRON-	PRP$
10_1101-2021_01_08_425885	263	16	kNN	knn	NN
10_1101-2021_01_08_425885	263	17	for	for	IN
10_1101-2021_01_08_425885	263	18	k	k	NNP
10_1101-2021_01_08_425885	263	19	≤	≤	NNP
10_1101-2021_01_08_425885	263	20	250	250	CD
10_1101-2021_01_08_425885	263	21	(	(	-LRB-
10_1101-2021_01_08_425885	263	22	ρPearson	ρPearson	NNP
10_1101-2021_01_08_425885	263	23	=	=	SYM
10_1101-2021_01_08_425885	263	24	0.58	0.58	CD
10_1101-2021_01_08_425885	263	25	,	,	,
10_1101-2021_01_08_425885	263	26	0.18	0.18	CD
10_1101-2021_01_08_425885	263	27	and	and	CC
10_1101-2021_01_08_425885	263	28	0.38	0.38	CD
10_1101-2021_01_08_425885	263	29	for	for	IN
10_1101-2021_01_08_425885	263	30	the	the	DT
10_1101-2021_01_08_425885	263	31	PBMC	PBMC	NNS
10_1101-2021_01_08_425885	263	32	,	,	,
10_1101-2021_01_08_425885	263	33	gastrulation	gastrulation	NN
10_1101-2021_01_08_425885	263	34	and	and	CC
10_1101-2021_01_08_425885	263	35	brain	brain	NN
10_1101-2021_01_08_425885	263	36	datasets	dataset	NNS
10_1101-2021_01_08_425885	263	37	respectively	respectively	RB
10_1101-2021_01_08_425885	263	38	at	at	IN
10_1101-2021_01_08_425885	263	39	k	k	NN
10_1101-2021_01_08_425885	263	40	=	=	SYM
10_1101-2021_01_08_425885	263	41	250	250	CD
10_1101-2021_01_08_425885	263	42	,	,	,
10_1101-2021_01_08_425885	263	43	p	p	NN
10_1101-2021_01_08_425885	263	44	<	<	XX
10_1101-2021_01_08_425885	263	45	10−6	10−6	CD
10_1101-2021_01_08_425885	263	46	;	;	:
10_1101-2021_01_08_425885	263	47	see	see	VB
10_1101-2021_01_08_425885	263	48	Figures	Figures	NNP
10_1101-2021_01_08_425885	263	49	S4C	s4c	NN
10_1101-2021_01_08_425885	263	50	,	,	,
10_1101-2021_01_08_425885	263	51	S5C	s5c	JJ
10_1101-2021_01_08_425885	263	52	and	and	CC
10_1101-2021_01_08_425885	263	53	S6C	S6C	NNP
10_1101-2021_01_08_425885	263	54	)	)	-RRB-
10_1101-2021_01_08_425885	263	55	,	,	,
10_1101-2021_01_08_425885	263	56	indicating	indicate	VBG
10_1101-2021_01_08_425885	263	57	that	that	IN
10_1101-2021_01_08_425885	263	58	our	-PRON-	PRP$
10_1101-2021_01_08_425885	263	59	algorithm	algorithm	NNP
10_1101-2021_01_08_425885	263	60	yields	yield	VBZ
10_1101-2021_01_08_425885	263	61	scalar	scalar	JJ
10_1101-2021_01_08_425885	263	62	curvatures	curvature	NNS
10_1101-2021_01_08_425885	263	63	that	that	WDT
10_1101-2021_01_08_425885	263	64	vary	vary	VBP
10_1101-2021_01_08_425885	263	65	continuously	continuously	RB
10_1101-2021_01_08_425885	263	66	over	over	IN
10_1101-2021_01_08_425885	263	67	the	the	DT
10_1101-2021_01_08_425885	263	68	data	data	NN
10_1101-2021_01_08_425885	263	69	manifolds	manifold	NNS
10_1101-2021_01_08_425885	263	70	.	.	.
10_1101-2021_01_08_425885	264	1	By	by	IN
10_1101-2021_01_08_425885	264	2	plotting	plot	VBG
10_1101-2021_01_08_425885	264	3	scalar	scalar	JJ
10_1101-2021_01_08_425885	264	4	curvatures	curvature	NNS
10_1101-2021_01_08_425885	264	5	against	against	IN
10_1101-2021_01_08_425885	264	6	their	-PRON-	PRP$
10_1101-2021_01_08_425885	264	7	standard	standard	JJ
10_1101-2021_01_08_425885	264	8	errors	error	NNS
10_1101-2021_01_08_425885	264	9	,	,	,
10_1101-2021_01_08_425885	264	10	σS	σS	NNP
10_1101-2021_01_08_425885	264	11	,	,	,
10_1101-2021_01_08_425885	264	12	we	-PRON-	PRP
10_1101-2021_01_08_425885	264	13	verified	verify	VBD
10_1101-2021_01_08_425885	264	14	that	that	IN
10_1101-2021_01_08_425885	264	15	regions	region	NNS
10_1101-2021_01_08_425885	264	16	with	with	IN
10_1101-2021_01_08_425885	264	17	non	non	JJ
10_1101-2021_01_08_425885	264	18	-	-	JJ
10_1101-2021_01_08_425885	264	19	zero	zero	JJ
10_1101-2021_01_08_425885	264	20	scalar	scalar	JJ
10_1101-2021_01_08_425885	264	21	curvature	curvature	NN
10_1101-2021_01_08_425885	264	22	are	be	VBP
10_1101-2021_01_08_425885	264	23	statistically	statistically	RB
10_1101-2021_01_08_425885	264	24	significant	significant	JJ
10_1101-2021_01_08_425885	264	25	(	(	-LRB-
10_1101-2021_01_08_425885	264	26	see	see	VB
10_1101-2021_01_08_425885	264	27	Figure	Figure	NNP
10_1101-2021_01_08_425885	264	28	4B	4b	NN
10_1101-2021_01_08_425885	264	29	,	,	,
10_1101-2021_01_08_425885	264	30	E	e	NN
10_1101-2021_01_08_425885	264	31	,	,	,
10_1101-2021_01_08_425885	264	32	H	h	NN
10_1101-2021_01_08_425885	264	33	)	)	-RRB-
10_1101-2021_01_08_425885	264	34	.	.	.
10_1101-2021_01_08_425885	265	1	As	as	IN
10_1101-2021_01_08_425885	265	2	a	a	DT
10_1101-2021_01_08_425885	265	3	consistency	consistency	NN
10_1101-2021_01_08_425885	265	4	check	check	NN
10_1101-2021_01_08_425885	265	5	,	,	,
10_1101-2021_01_08_425885	265	6	we	-PRON-	PRP
10_1101-2021_01_08_425885	265	7	confirmed	confirm	VBD
10_1101-2021_01_08_425885	265	8	that	that	IN
10_1101-2021_01_08_425885	265	9	the	the	DT
10_1101-2021_01_08_425885	265	10	percentage	percentage	NN
10_1101-2021_01_08_425885	265	11	of	of	IN
10_1101-2021_01_08_425885	265	12	points	point	NNS
10_1101-2021_01_08_425885	265	13	with	with	IN
10_1101-2021_01_08_425885	265	14	95	95	CD
10_1101-2021_01_08_425885	265	15	%	%	NN
10_1101-2021_01_08_425885	265	16	CIs	ci	NNS
10_1101-2021_01_08_425885	265	17	containing	contain	VBG
10_1101-2021_01_08_425885	265	18	the	the	DT
10_1101-2021_01_08_425885	265	19	scalar	scalar	JJ
10_1101-2021_01_08_425885	265	20	curvatures	curvature	NNS
10_1101-2021_01_08_425885	265	21	reported	report	VBN
10_1101-2021_01_08_425885	265	22	by	by	IN
10_1101-2021_01_08_425885	265	23	their	-PRON-	PRP$
10_1101-2021_01_08_425885	265	24	respective	respective	JJ
10_1101-2021_01_08_425885	265	25	kNNs	knns	NN
10_1101-2021_01_08_425885	265	26	(	(	-LRB-
10_1101-2021_01_08_425885	265	27	i	i	NN
10_1101-2021_01_08_425885	265	28	)	)	-RRB-
10_1101-2021_01_08_425885	265	29	decayed	decay	VBD
10_1101-2021_01_08_425885	265	30	with	with	IN
10_1101-2021_01_08_425885	265	31	increasing	increase	VBG
10_1101-2021_01_08_425885	265	32	k	k	NNP
10_1101-2021_01_08_425885	265	33	for	for	IN
10_1101-2021_01_08_425885	265	34	k	k	NNP
10_1101-2021_01_08_425885	265	35	≤	≤	NNP
10_1101-2021_01_08_425885	265	36	250	250	CD
10_1101-2021_01_08_425885	265	37	,	,	,
10_1101-2021_01_08_425885	265	38	and	and	CC
10_1101-2021_01_08_425885	265	39	(	(	-LRB-
10_1101-2021_01_08_425885	265	40	ii	ii	NNP
10_1101-2021_01_08_425885	265	41	)	)	-RRB-
10_1101-2021_01_08_425885	265	42	was	be	VBD
10_1101-2021_01_08_425885	265	43	significantly	significantly	RB
10_1101-2021_01_08_425885	265	44	larger	large	JJR
10_1101-2021_01_08_425885	265	45	15	15	CD
10_1101-2021_01_08_425885	265	46	.CC	.CC	:
10_1101-2021_01_08_425885	265	47	-	-	HYPH
10_1101-2021_01_08_425885	265	48	BY	by	IN
10_1101-2021_01_08_425885	265	49	-	-	HYPH
10_1101-2021_01_08_425885	265	50	NC	NC	NNP
10_1101-2021_01_08_425885	265	51	-	-	HYPH
10_1101-2021_01_08_425885	265	52	ND	ND	NNP
10_1101-2021_01_08_425885	265	53	4.0	4.0	CD
10_1101-2021_01_08_425885	265	54	International	International	NNP
10_1101-2021_01_08_425885	265	55	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	265	56	under	under	IN
10_1101-2021_01_08_425885	265	57	a	a	DT
10_1101-2021_01_08_425885	265	58	(	(	-LRB-
10_1101-2021_01_08_425885	265	59	which	which	WDT
10_1101-2021_01_08_425885	265	60	was	be	VBD
10_1101-2021_01_08_425885	265	61	not	not	RB
10_1101-2021_01_08_425885	265	62	certified	certify	VBN
10_1101-2021_01_08_425885	265	63	by	by	IN
10_1101-2021_01_08_425885	265	64	peer	peer	NN
10_1101-2021_01_08_425885	265	65	review	review	NN
10_1101-2021_01_08_425885	265	66	)	)	-RRB-
10_1101-2021_01_08_425885	265	67	is	be	VBZ
10_1101-2021_01_08_425885	265	68	the	the	DT
10_1101-2021_01_08_425885	265	69	author	author	NN
10_1101-2021_01_08_425885	265	70	/	/	SYM
10_1101-2021_01_08_425885	265	71	funder	funder	NN
10_1101-2021_01_08_425885	265	72	,	,	,
10_1101-2021_01_08_425885	265	73	who	who	WP
10_1101-2021_01_08_425885	265	74	has	have	VBZ
10_1101-2021_01_08_425885	265	75	granted	grant	VBN
10_1101-2021_01_08_425885	265	76	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	265	77	a	a	DT
10_1101-2021_01_08_425885	265	78	license	license	NN
10_1101-2021_01_08_425885	265	79	to	to	TO
10_1101-2021_01_08_425885	265	80	display	display	VB
10_1101-2021_01_08_425885	265	81	the	the	DT
10_1101-2021_01_08_425885	265	82	preprint	preprint	NN
10_1101-2021_01_08_425885	265	83	in	in	IN
10_1101-2021_01_08_425885	265	84	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	265	85	.	.	.
10_1101-2021_01_08_425885	266	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	266	2	is	be	VBZ
10_1101-2021_01_08_425885	266	3	made	make	VBN
10_1101-2021_01_08_425885	266	4	The	the	DT
10_1101-2021_01_08_425885	266	5	copyright	copyright	NN
10_1101-2021_01_08_425885	266	6	holder	holder	NN
10_1101-2021_01_08_425885	266	7	for	for	IN
10_1101-2021_01_08_425885	266	8	this	this	DT
10_1101-2021_01_08_425885	266	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	266	10	version	version	NN
10_1101-2021_01_08_425885	266	11	posted	post	VBD
10_1101-2021_01_08_425885	266	12	January	January	NNP
10_1101-2021_01_08_425885	266	13	8	8	CD
10_1101-2021_01_08_425885	266	14	,	,	,
10_1101-2021_01_08_425885	266	15	2021	2021	CD
10_1101-2021_01_08_425885	266	16	.	.	.
10_1101-2021_01_08_425885	266	17	;	;	:
10_1101-2021_01_08_425885	266	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	266	19	:	:	:
10_1101-2021_01_08_425885	266	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	266	21	preprint	preprint	NN
10_1101-2021_01_08_425885	266	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	266	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	RB
10_1101-2021_01_08_425885	266	24	than	than	IN
10_1101-2021_01_08_425885	266	25	expected	expect	VBN
10_1101-2021_01_08_425885	266	26	by	by	IN
10_1101-2021_01_08_425885	266	27	chance	chance	NN
10_1101-2021_01_08_425885	266	28	(	(	-LRB-
10_1101-2021_01_08_425885	266	29	67	67	CD
10_1101-2021_01_08_425885	266	30	%	%	NN
10_1101-2021_01_08_425885	266	31	,	,	,
10_1101-2021_01_08_425885	266	32	72	72	CD
10_1101-2021_01_08_425885	266	33	%	%	NN
10_1101-2021_01_08_425885	266	34	and	and	CC
10_1101-2021_01_08_425885	266	35	61	61	CD
10_1101-2021_01_08_425885	266	36	%	%	NN
10_1101-2021_01_08_425885	266	37	for	for	IN
10_1101-2021_01_08_425885	266	38	the	the	DT
10_1101-2021_01_08_425885	266	39	PBMC	PBMC	NNS
10_1101-2021_01_08_425885	266	40	,	,	,
10_1101-2021_01_08_425885	266	41	gastrulation	gastrulation	NN
10_1101-2021_01_08_425885	266	42	and	and	CC
10_1101-2021_01_08_425885	266	43	brain	brain	NN
10_1101-2021_01_08_425885	266	44	datasets	dataset	NNS
10_1101-2021_01_08_425885	266	45	respectively	respectively	RB
10_1101-2021_01_08_425885	266	46	at	at	IN
10_1101-2021_01_08_425885	266	47	k	k	NN
10_1101-2021_01_08_425885	266	48	=	=	SYM
10_1101-2021_01_08_425885	266	49	250	250	CD
10_1101-2021_01_08_425885	266	50	,	,	,
10_1101-2021_01_08_425885	266	51	p	p	NN
10_1101-2021_01_08_425885	266	52	<	<	XX
10_1101-2021_01_08_425885	266	53	0.001	0.001	CD
10_1101-2021_01_08_425885	266	54	;	;	:
10_1101-2021_01_08_425885	266	55	see	see	VB
10_1101-2021_01_08_425885	266	56	Figures	Figures	NNP
10_1101-2021_01_08_425885	266	57	S4D	s4d	NN
10_1101-2021_01_08_425885	266	58	,	,	,
10_1101-2021_01_08_425885	266	59	S5D	S5D	NNP
10_1101-2021_01_08_425885	266	60	and	and	CC
10_1101-2021_01_08_425885	266	61	S6D	s6d	JJ
10_1101-2021_01_08_425885	266	62	;	;	:
10_1101-2021_01_08_425885	266	63	Methods	Methods	NNP
10_1101-2021_01_08_425885	266	64	Section	Section	NNP
10_1101-2021_01_08_425885	266	65	4.6.3.1	4.6.3.1	CD
10_1101-2021_01_08_425885	266	66	)	)	-RRB-
10_1101-2021_01_08_425885	266	67	.	.	.
10_1101-2021_01_08_425885	267	1	To	to	TO
10_1101-2021_01_08_425885	267	2	rule	rule	VB
10_1101-2021_01_08_425885	267	3	out	out	RP
10_1101-2021_01_08_425885	267	4	the	the	DT
10_1101-2021_01_08_425885	267	5	possibility	possibility	NN
10_1101-2021_01_08_425885	267	6	that	that	IN
10_1101-2021_01_08_425885	267	7	localization	localization	NN
10_1101-2021_01_08_425885	267	8	of	of	IN
10_1101-2021_01_08_425885	267	9	non	non	JJ
10_1101-2021_01_08_425885	267	10	-	-	JJ
10_1101-2021_01_08_425885	267	11	zero	zero	JJ
10_1101-2021_01_08_425885	267	12	scalar	scalar	JJ
10_1101-2021_01_08_425885	267	13	curvature	curvature	NN
10_1101-2021_01_08_425885	267	14	in	in	IN
10_1101-2021_01_08_425885	267	15	certain	certain	JJ
10_1101-2021_01_08_425885	267	16	regions	region	NNS
10_1101-2021_01_08_425885	267	17	of	of	IN
10_1101-2021_01_08_425885	267	18	the	the	DT
10_1101-2021_01_08_425885	267	19	UMAP	UMAP	NNP
10_1101-2021_01_08_425885	267	20	/	/	SYM
10_1101-2021_01_08_425885	267	21	t-	t-	NN
10_1101-2021_01_08_425885	267	22	SNE	SNE	NNP
10_1101-2021_01_08_425885	267	23	plots	plot	NNS
10_1101-2021_01_08_425885	267	24	is	be	VBZ
10_1101-2021_01_08_425885	267	25	an	an	DT
10_1101-2021_01_08_425885	267	26	artifact	artifact	NN
10_1101-2021_01_08_425885	267	27	caused	cause	VBN
10_1101-2021_01_08_425885	267	28	by	by	IN
10_1101-2021_01_08_425885	267	29	other	other	JJ
10_1101-2021_01_08_425885	267	30	features	feature	NNS
10_1101-2021_01_08_425885	267	31	of	of	IN
10_1101-2021_01_08_425885	267	32	the	the	DT
10_1101-2021_01_08_425885	267	33	data	datum	NNS
10_1101-2021_01_08_425885	267	34	that	that	WDT
10_1101-2021_01_08_425885	267	35	are	be	VBP
10_1101-2021_01_08_425885	267	36	also	also	RB
10_1101-2021_01_08_425885	267	37	localized	localize	VBN
10_1101-2021_01_08_425885	267	38	,	,	,
10_1101-2021_01_08_425885	267	39	we	-PRON-	PRP
10_1101-2021_01_08_425885	267	40	considered	consider	VBD
10_1101-2021_01_08_425885	267	41	several	several	JJ
10_1101-2021_01_08_425885	267	42	factors	factor	NNS
10_1101-2021_01_08_425885	267	43	.	.	.
10_1101-2021_01_08_425885	268	1	First	first	RB
10_1101-2021_01_08_425885	268	2	,	,	,
10_1101-2021_01_08_425885	268	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	268	4	plotted	plot	VBD
10_1101-2021_01_08_425885	268	5	the	the	DT
10_1101-2021_01_08_425885	268	6	GOF	GOF	NNP
10_1101-2021_01_08_425885	268	7	p	p	NN
10_1101-2021_01_08_425885	268	8	-	-	HYPH
10_1101-2021_01_08_425885	268	9	value	value	NN
10_1101-2021_01_08_425885	268	10	at	at	IN
10_1101-2021_01_08_425885	268	11	each	each	DT
10_1101-2021_01_08_425885	268	12	point	point	NN
10_1101-2021_01_08_425885	268	13	on	on	IN
10_1101-2021_01_08_425885	268	14	UMAP	UMAP	NNP
10_1101-2021_01_08_425885	268	15	/	/	SYM
10_1101-2021_01_08_425885	268	16	t	t	NNP
10_1101-2021_01_08_425885	268	17	-	-	HYPH
10_1101-2021_01_08_425885	268	18	SNE	SNE	NNP
10_1101-2021_01_08_425885	268	19	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	268	20	and	and	CC
10_1101-2021_01_08_425885	268	21	noted	note	VBD
10_1101-2021_01_08_425885	268	22	that	that	IN
10_1101-2021_01_08_425885	268	23	poor	poor	JJ
10_1101-2021_01_08_425885	268	24	GOFs	gof	NNS
10_1101-2021_01_08_425885	268	25	were	be	VBD
10_1101-2021_01_08_425885	268	26	not	not	RB
10_1101-2021_01_08_425885	268	27	localized	localize	VBN
10_1101-2021_01_08_425885	268	28	on	on	IN
10_1101-2021_01_08_425885	268	29	the	the	DT
10_1101-2021_01_08_425885	268	30	data	data	NN
10_1101-2021_01_08_425885	268	31	manifolds	manifold	NNS
10_1101-2021_01_08_425885	268	32	,	,	,
10_1101-2021_01_08_425885	268	33	let	let	VB
10_1101-2021_01_08_425885	268	34	alone	alone	RB
10_1101-2021_01_08_425885	268	35	to	to	IN
10_1101-2021_01_08_425885	268	36	regions	region	NNS
10_1101-2021_01_08_425885	268	37	of	of	IN
10_1101-2021_01_08_425885	268	38	non	non	JJ
10_1101-2021_01_08_425885	268	39	-	-	JJ
10_1101-2021_01_08_425885	268	40	zero	zero	JJ
10_1101-2021_01_08_425885	268	41	scalar	scalar	JJ
10_1101-2021_01_08_425885	268	42	curvature	curvature	NN
10_1101-2021_01_08_425885	268	43	(	(	-LRB-
10_1101-2021_01_08_425885	268	44	see	see	VB
10_1101-2021_01_08_425885	268	45	Figures	Figures	NNP
10_1101-2021_01_08_425885	268	46	S4B	S4B	NNP
10_1101-2021_01_08_425885	268	47	,	,	,
10_1101-2021_01_08_425885	268	48	S5B	S5B	NNP
10_1101-2021_01_08_425885	268	49	and	and	CC
10_1101-2021_01_08_425885	268	50	S6B	S6B	NNP
10_1101-2021_01_08_425885	268	51	)	)	-RRB-
10_1101-2021_01_08_425885	268	52	.	.	.
10_1101-2021_01_08_425885	269	1	Therefore	therefore	RB
10_1101-2021_01_08_425885	269	2	,	,	,
10_1101-2021_01_08_425885	269	3	the	the	DT
10_1101-2021_01_08_425885	269	4	computed	compute	VBN
10_1101-2021_01_08_425885	269	5	scalar	scalar	JJ
10_1101-2021_01_08_425885	269	6	curvatures	curvature	NNS
10_1101-2021_01_08_425885	269	7	are	be	VBP
10_1101-2021_01_08_425885	269	8	not	not	RB
10_1101-2021_01_08_425885	269	9	due	due	JJ
10_1101-2021_01_08_425885	269	10	to	to	IN
10_1101-2021_01_08_425885	269	11	poor	poor	JJ
10_1101-2021_01_08_425885	269	12	fits	fit	NNS
10_1101-2021_01_08_425885	269	13	.	.	.
10_1101-2021_01_08_425885	270	1	Next	next	RB
10_1101-2021_01_08_425885	270	2	,	,	,
10_1101-2021_01_08_425885	270	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	270	4	plotted	plot	VBD
10_1101-2021_01_08_425885	270	5	the	the	DT
10_1101-2021_01_08_425885	270	6	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	270	7	size	size	NN
10_1101-2021_01_08_425885	270	8	,	,	,
10_1101-2021_01_08_425885	270	9	r(p	r(p	NNP
10_1101-2021_01_08_425885	270	10	)	)	-RRB-
10_1101-2021_01_08_425885	270	11	,	,	,
10_1101-2021_01_08_425885	270	12	used	use	VBN
10_1101-2021_01_08_425885	270	13	for	for	IN
10_1101-2021_01_08_425885	270	14	fitting	fitting	NN
10_1101-2021_01_08_425885	270	15	and	and	CC
10_1101-2021_01_08_425885	270	16	observed	observe	VBD
10_1101-2021_01_08_425885	270	17	that	that	IN
10_1101-2021_01_08_425885	270	18	in	in	IN
10_1101-2021_01_08_425885	270	19	some	some	DT
10_1101-2021_01_08_425885	270	20	regions	region	NNS
10_1101-2021_01_08_425885	270	21	,	,	,
10_1101-2021_01_08_425885	270	22	non	non	JJ
10_1101-2021_01_08_425885	270	23	-	-	JJ
10_1101-2021_01_08_425885	270	24	zero	zero	CD
10_1101-2021_01_08_425885	270	25	scalar	scalar	JJ
10_1101-2021_01_08_425885	270	26	curvatures	curvature	NNS
10_1101-2021_01_08_425885	270	27	seemed	seem	VBD
10_1101-2021_01_08_425885	270	28	to	to	TO
10_1101-2021_01_08_425885	270	29	correspond	correspond	VB
10_1101-2021_01_08_425885	270	30	to	to	IN
10_1101-2021_01_08_425885	270	31	small	small	JJ
10_1101-2021_01_08_425885	270	32	r	r	NN
10_1101-2021_01_08_425885	270	33	(	(	-LRB-
10_1101-2021_01_08_425885	270	34	see	see	VB
10_1101-2021_01_08_425885	270	35	Figures	Figures	NNP
10_1101-2021_01_08_425885	270	36	S4E	s4e	NN
10_1101-2021_01_08_425885	270	37	,	,	,
10_1101-2021_01_08_425885	270	38	S5E	s5e	NN
10_1101-2021_01_08_425885	270	39	and	and	CC
10_1101-2021_01_08_425885	270	40	S6E	S6E	NNP
10_1101-2021_01_08_425885	270	41	)	)	-RRB-
10_1101-2021_01_08_425885	270	42	.	.	.
10_1101-2021_01_08_425885	271	1	Since	since	IN
10_1101-2021_01_08_425885	271	2	σh	σh	NNP
10_1101-2021_01_08_425885	271	3	is	be	VBZ
10_1101-2021_01_08_425885	271	4	fixed	fix	VBN
10_1101-2021_01_08_425885	271	5	,	,	,
10_1101-2021_01_08_425885	271	6	these	these	DT
10_1101-2021_01_08_425885	271	7	regions	region	NNS
10_1101-2021_01_08_425885	271	8	necessarily	necessarily	RB
10_1101-2021_01_08_425885	271	9	have	have	VBP
10_1101-2021_01_08_425885	271	10	a	a	DT
10_1101-2021_01_08_425885	271	11	larger	large	JJR
10_1101-2021_01_08_425885	271	12	number	number	NN
10_1101-2021_01_08_425885	271	13	of	of	IN
10_1101-2021_01_08_425885	271	14	neighbors	neighbor	NNS
10_1101-2021_01_08_425885	271	15	Np(r	Np(r	NNP
10_1101-2021_01_08_425885	271	16	)	)	-RRB-
10_1101-2021_01_08_425885	271	17	and	and	CC
10_1101-2021_01_08_425885	271	18	are	be	VBP
10_1101-2021_01_08_425885	271	19	hence	hence	RB
10_1101-2021_01_08_425885	271	20	more	more	RBR
10_1101-2021_01_08_425885	271	21	dense	dense	JJ
10_1101-2021_01_08_425885	271	22	(	(	-LRB-
10_1101-2021_01_08_425885	271	23	see	see	VB
10_1101-2021_01_08_425885	271	24	Figures	Figures	NNP
10_1101-2021_01_08_425885	271	25	S4F	s4f	NN
10_1101-2021_01_08_425885	271	26	,	,	,
10_1101-2021_01_08_425885	271	27	S5F	S5F	NNP
10_1101-2021_01_08_425885	271	28	and	and	CC
10_1101-2021_01_08_425885	271	29	S6F	S6F	NNP
10_1101-2021_01_08_425885	271	30	)	)	-RRB-
10_1101-2021_01_08_425885	271	31	.	.	.
10_1101-2021_01_08_425885	272	1	To	to	TO
10_1101-2021_01_08_425885	272	2	rule	rule	VB
10_1101-2021_01_08_425885	272	3	out	out	RP
10_1101-2021_01_08_425885	272	4	the	the	DT
10_1101-2021_01_08_425885	272	5	possibility	possibility	NN
10_1101-2021_01_08_425885	272	6	that	that	IN
10_1101-2021_01_08_425885	272	7	the	the	DT
10_1101-2021_01_08_425885	272	8	non	non	JJ
10_1101-2021_01_08_425885	272	9	-	-	JJ
10_1101-2021_01_08_425885	272	10	zero	zero	CD
10_1101-2021_01_08_425885	272	11	scalar	scalar	JJ
10_1101-2021_01_08_425885	272	12	curvatures	curvature	NNS
10_1101-2021_01_08_425885	272	13	were	be	VBD
10_1101-2021_01_08_425885	272	14	an	an	DT
10_1101-2021_01_08_425885	272	15	artifact	artifact	NN
10_1101-2021_01_08_425885	272	16	of	of	IN
10_1101-2021_01_08_425885	272	17	smaller	small	JJR
10_1101-2021_01_08_425885	272	18	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	272	19	size	size	NN
10_1101-2021_01_08_425885	272	20	,	,	,
10_1101-2021_01_08_425885	272	21	we	-PRON-	PRP
10_1101-2021_01_08_425885	272	22	recomputed	recompute	VBD
10_1101-2021_01_08_425885	272	23	the	the	DT
10_1101-2021_01_08_425885	272	24	scalar	scalar	JJ
10_1101-2021_01_08_425885	272	25	curvature	curvature	NN
10_1101-2021_01_08_425885	272	26	at	at	IN
10_1101-2021_01_08_425885	272	27	three	three	CD
10_1101-2021_01_08_425885	272	28	fixed	fix	VBN
10_1101-2021_01_08_425885	272	29	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	272	30	sizes	size	NNS
10_1101-2021_01_08_425885	272	31	(	(	-LRB-
10_1101-2021_01_08_425885	272	32	see	see	VB
10_1101-2021_01_08_425885	272	33	Figure	Figure	NNP
10_1101-2021_01_08_425885	272	34	4C	4c	NN
10_1101-2021_01_08_425885	272	35	,	,	,
10_1101-2021_01_08_425885	272	36	F	F	NNP
10_1101-2021_01_08_425885	272	37	,	,	,
10_1101-2021_01_08_425885	272	38	I	-PRON-	PRP
10_1101-2021_01_08_425885	272	39	)	)	-RRB-
10_1101-2021_01_08_425885	272	40	,	,	,
10_1101-2021_01_08_425885	272	41	corresponding	correspond	VBG
10_1101-2021_01_08_425885	272	42	to	to	IN
10_1101-2021_01_08_425885	272	43	the	the	DT
10_1101-2021_01_08_425885	272	44	25	25	CD
10_1101-2021_01_08_425885	272	45	,	,	,
10_1101-2021_01_08_425885	272	46	50	50	CD
10_1101-2021_01_08_425885	272	47	,	,	,
10_1101-2021_01_08_425885	272	48	and	and	CC
10_1101-2021_01_08_425885	272	49	75%-ile	75%-ile	CD
10_1101-2021_01_08_425885	272	50	values	value	NNS
10_1101-2021_01_08_425885	272	51	of	of	IN
10_1101-2021_01_08_425885	272	52	r(p	r(p	NNP
10_1101-2021_01_08_425885	272	53	)	)	-RRB-
10_1101-2021_01_08_425885	272	54	which	which	WDT
10_1101-2021_01_08_425885	272	55	arose	arise	VBD
10_1101-2021_01_08_425885	272	56	from	from	IN
10_1101-2021_01_08_425885	272	57	setting	set	VBG
10_1101-2021_01_08_425885	272	58	σh	σh	NNP
10_1101-2021_01_08_425885	272	59	(	(	-LRB-
10_1101-2021_01_08_425885	272	60	see	see	VB
10_1101-2021_01_08_425885	272	61	Figures	Figures	NNP
10_1101-2021_01_08_425885	272	62	S4E	s4e	NN
10_1101-2021_01_08_425885	272	63	,	,	,
10_1101-2021_01_08_425885	272	64	S5E	s5e	NN
10_1101-2021_01_08_425885	272	65	and	and	CC
10_1101-2021_01_08_425885	272	66	S6E	S6E	NNP
10_1101-2021_01_08_425885	272	67	)	)	-RRB-
10_1101-2021_01_08_425885	272	68	.	.	.
10_1101-2021_01_08_425885	273	1	In	in	IN
10_1101-2021_01_08_425885	273	2	general	general	JJ
10_1101-2021_01_08_425885	273	3	,	,	,
10_1101-2021_01_08_425885	273	4	the	the	DT
10_1101-2021_01_08_425885	273	5	scalar	scalar	JJ
10_1101-2021_01_08_425885	273	6	curvatures	curvature	NNS
10_1101-2021_01_08_425885	273	7	decreased	decrease	VBD
10_1101-2021_01_08_425885	273	8	in	in	IN
10_1101-2021_01_08_425885	273	9	magnitude	magnitude	NN
10_1101-2021_01_08_425885	273	10	when	when	WRB
10_1101-2021_01_08_425885	273	11	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	273	12	sizes	size	NNS
10_1101-2021_01_08_425885	273	13	increased	increase	VBD
10_1101-2021_01_08_425885	273	14	.	.	.
10_1101-2021_01_08_425885	274	1	However	however	RB
10_1101-2021_01_08_425885	274	2	,	,	,
10_1101-2021_01_08_425885	274	3	regions	region	NNS
10_1101-2021_01_08_425885	274	4	which	which	WDT
10_1101-2021_01_08_425885	274	5	had	have	VBD
10_1101-2021_01_08_425885	274	6	statistically	statistically	RB
10_1101-2021_01_08_425885	274	7	significant	significant	JJ
10_1101-2021_01_08_425885	274	8	non	non	JJ
10_1101-2021_01_08_425885	274	9	-	-	JJ
10_1101-2021_01_08_425885	274	10	zero	zero	CD
10_1101-2021_01_08_425885	274	11	scalar	scalar	JJ
10_1101-2021_01_08_425885	274	12	curvatures	curvature	NNS
10_1101-2021_01_08_425885	274	13	(	(	-LRB-
10_1101-2021_01_08_425885	274	14	zero	zero	CD
10_1101-2021_01_08_425885	274	15	falls	fall	VBZ
10_1101-2021_01_08_425885	274	16	outside	outside	RB
10_1101-2021_01_08_425885	274	17	of	of	IN
10_1101-2021_01_08_425885	274	18	the	the	DT
10_1101-2021_01_08_425885	274	19	95	95	CD
10_1101-2021_01_08_425885	274	20	%	%	NN
10_1101-2021_01_08_425885	274	21	CI	CI	NNP
10_1101-2021_01_08_425885	274	22	)	)	-RRB-
10_1101-2021_01_08_425885	274	23	using	use	VBG
10_1101-2021_01_08_425885	274	24	variable	variable	JJ
10_1101-2021_01_08_425885	274	25	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	274	26	sizes	size	NNS
10_1101-2021_01_08_425885	274	27	also	also	RB
10_1101-2021_01_08_425885	274	28	had	have	VBD
10_1101-2021_01_08_425885	274	29	non	non	JJ
10_1101-2021_01_08_425885	274	30	-	-	JJ
10_1101-2021_01_08_425885	274	31	zero	zero	CD
10_1101-2021_01_08_425885	274	32	scalar	scalar	JJ
10_1101-2021_01_08_425885	274	33	curvatures	curvature	NNS
10_1101-2021_01_08_425885	274	34	for	for	IN
10_1101-2021_01_08_425885	274	35	all	all	DT
10_1101-2021_01_08_425885	274	36	three	three	CD
10_1101-2021_01_08_425885	274	37	fixed	fix	VBN
10_1101-2021_01_08_425885	274	38	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	274	39	sizes	size	NNS
10_1101-2021_01_08_425885	274	40	.	.	.
10_1101-2021_01_08_425885	275	1	Additionally	additionally	RB
10_1101-2021_01_08_425885	275	2	,	,	,
10_1101-2021_01_08_425885	275	3	statistically	statistically	RB
10_1101-2021_01_08_425885	275	4	significant	significant	JJ
10_1101-2021_01_08_425885	275	5	non	non	JJ
10_1101-2021_01_08_425885	275	6	-	-	JJ
10_1101-2021_01_08_425885	275	7	zero	zero	JJ
10_1101-2021_01_08_425885	275	8	scalar	scalar	JJ
10_1101-2021_01_08_425885	275	9	curvature	curvature	NN
10_1101-2021_01_08_425885	275	10	also	also	RB
10_1101-2021_01_08_425885	275	11	emerged	emerge	VBD
10_1101-2021_01_08_425885	275	12	on	on	IN
10_1101-2021_01_08_425885	275	13	other	other	JJ
10_1101-2021_01_08_425885	275	14	parts	part	NNS
10_1101-2021_01_08_425885	275	15	of	of	IN
10_1101-2021_01_08_425885	275	16	the	the	DT
10_1101-2021_01_08_425885	275	17	manifolds	manifold	NNS
10_1101-2021_01_08_425885	275	18	when	when	WRB
10_1101-2021_01_08_425885	275	19	using	use	VBG
10_1101-2021_01_08_425885	275	20	small	small	JJ
10_1101-2021_01_08_425885	275	21	fixed	fix	VBN
10_1101-2021_01_08_425885	275	22	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	275	23	sizes	size	NNS
10_1101-2021_01_08_425885	275	24	.	.	.
10_1101-2021_01_08_425885	276	1	These	these	DT
10_1101-2021_01_08_425885	276	2	regions	region	NNS
10_1101-2021_01_08_425885	276	3	are	be	VBP
10_1101-2021_01_08_425885	276	4	therefore	therefore	RB
10_1101-2021_01_08_425885	276	5	curved	curved	JJ
10_1101-2021_01_08_425885	276	6	at	at	IN
10_1101-2021_01_08_425885	276	7	small	small	JJ
10_1101-2021_01_08_425885	276	8	length	length	NN
10_1101-2021_01_08_425885	276	9	scales	scale	NNS
10_1101-2021_01_08_425885	276	10	but	but	CC
10_1101-2021_01_08_425885	276	11	do	do	VBP
10_1101-2021_01_08_425885	276	12	not	not	RB
10_1101-2021_01_08_425885	276	13	have	have	VB
10_1101-2021_01_08_425885	276	14	a	a	DT
10_1101-2021_01_08_425885	276	15	sufficient	sufficient	JJ
10_1101-2021_01_08_425885	276	16	density	density	NN
10_1101-2021_01_08_425885	276	17	of	of	IN
10_1101-2021_01_08_425885	276	18	points	point	NNS
10_1101-2021_01_08_425885	276	19	to	to	TO
10_1101-2021_01_08_425885	276	20	resolve	resolve	VB
10_1101-2021_01_08_425885	276	21	curvature	curvature	JJ
10_1101-2021_01_08_425885	276	22	to	to	IN
10_1101-2021_01_08_425885	276	23	the	the	DT
10_1101-2021_01_08_425885	276	24	desired	desire	VBN
10_1101-2021_01_08_425885	276	25	uncertainty	uncertainty	NN
10_1101-2021_01_08_425885	276	26	σh	σh	NN
10_1101-2021_01_08_425885	276	27	(	(	-LRB-
10_1101-2021_01_08_425885	276	28	see	see	VB
10_1101-2021_01_08_425885	276	29	Method	Method	NNP
10_1101-2021_01_08_425885	276	30	Section	Section	NNP
10_1101-2021_01_08_425885	276	31	4.3.5	4.3.5	NNP
10_1101-2021_01_08_425885	276	32	)	)	-RRB-
10_1101-2021_01_08_425885	276	33	.	.	.
10_1101-2021_01_08_425885	277	1	This	this	DT
10_1101-2021_01_08_425885	277	2	is	be	VBZ
10_1101-2021_01_08_425885	277	3	analogous	analogous	JJ
10_1101-2021_01_08_425885	277	4	to	to	IN
10_1101-2021_01_08_425885	277	5	the	the	DT
10_1101-2021_01_08_425885	277	6	image	image	NN
10_1101-2021_01_08_425885	277	7	patch	patch	NN
10_1101-2021_01_08_425885	277	8	dataset	dataset	NN
10_1101-2021_01_08_425885	277	9	for	for	IN
10_1101-2021_01_08_425885	277	10	which	which	WDT
10_1101-2021_01_08_425885	277	11	we	-PRON-	PRP
10_1101-2021_01_08_425885	277	12	could	could	MD
10_1101-2021_01_08_425885	277	13	resolve	resolve	VB
10_1101-2021_01_08_425885	277	14	scalar	scalar	JJ
10_1101-2021_01_08_425885	277	15	curvatures	curvature	NNS
10_1101-2021_01_08_425885	277	16	of	of	IN
10_1101-2021_01_08_425885	277	17	larger	large	JJR
10_1101-2021_01_08_425885	277	18	magnitude	magnitude	NN
10_1101-2021_01_08_425885	277	19	at	at	IN
10_1101-2021_01_08_425885	277	20	a	a	DT
10_1101-2021_01_08_425885	277	21	smaller	small	JJR
10_1101-2021_01_08_425885	277	22	length	length	NN
10_1101-2021_01_08_425885	277	23	scale	scale	NN
10_1101-2021_01_08_425885	277	24	when	when	WRB
10_1101-2021_01_08_425885	277	25	the	the	DT
10_1101-2021_01_08_425885	277	26	dataset	dataset	NN
10_1101-2021_01_08_425885	277	27	was	be	VBD
10_1101-2021_01_08_425885	277	28	augmented	augment	VBN
10_1101-2021_01_08_425885	277	29	with	with	IN
10_1101-2021_01_08_425885	277	30	enough	enough	JJ
10_1101-2021_01_08_425885	277	31	points	point	NNS
10_1101-2021_01_08_425885	277	32	to	to	TO
10_1101-2021_01_08_425885	277	33	attain	attain	VB
10_1101-2021_01_08_425885	277	34	smaller	small	JJR
10_1101-2021_01_08_425885	277	35	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	277	36	sizes	size	NNS
10_1101-2021_01_08_425885	277	37	for	for	IN
10_1101-2021_01_08_425885	277	38	a	a	DT
10_1101-2021_01_08_425885	277	39	fixed	fix	VBN
10_1101-2021_01_08_425885	277	40	σh	σh	NN
10_1101-2021_01_08_425885	277	41	.	.	.
10_1101-2021_01_08_425885	278	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	278	2	also	also	RB
10_1101-2021_01_08_425885	278	3	checked	check	VBD
10_1101-2021_01_08_425885	278	4	how	how	WRB
10_1101-2021_01_08_425885	278	5	computed	compute	VBN
10_1101-2021_01_08_425885	278	6	scalar	scalar	JJ
10_1101-2021_01_08_425885	278	7	curvatures	curvature	NNS
10_1101-2021_01_08_425885	278	8	changed	change	VBN
10_1101-2021_01_08_425885	278	9	with	with	IN
10_1101-2021_01_08_425885	278	10	density	density	NN
10_1101-2021_01_08_425885	278	11	in	in	IN
10_1101-2021_01_08_425885	278	12	a	a	DT
10_1101-2021_01_08_425885	278	13	toy	toy	NN
10_1101-2021_01_08_425885	278	14	model	model	NN
10_1101-2021_01_08_425885	278	15	with	with	IN
10_1101-2021_01_08_425885	278	16	zero	zero	CD
10_1101-2021_01_08_425885	278	17	scalar	scalar	JJ
10_1101-2021_01_08_425885	278	18	curvature	curvature	NN
10_1101-2021_01_08_425885	278	19	.	.	.
10_1101-2021_01_08_425885	279	1	Importantly	importantly	RB
10_1101-2021_01_08_425885	279	2	,	,	,
10_1101-2021_01_08_425885	279	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	279	4	did	do	VBD
10_1101-2021_01_08_425885	279	5	not	not	RB
10_1101-2021_01_08_425885	279	6	observe	observe	VB
10_1101-2021_01_08_425885	279	7	the	the	DT
10_1101-2021_01_08_425885	279	8	artifactual	artifactual	JJ
10_1101-2021_01_08_425885	279	9	appearance	appearance	NN
10_1101-2021_01_08_425885	279	10	of	of	IN
10_1101-2021_01_08_425885	279	11	statistically	statistically	RB
10_1101-2021_01_08_425885	279	12	significant	significant	JJ
10_1101-2021_01_08_425885	279	13	non	non	JJ
10_1101-2021_01_08_425885	279	14	-	-	JJ
10_1101-2021_01_08_425885	279	15	zero	zero	JJ
10_1101-2021_01_08_425885	279	16	scalar	scalar	JJ
10_1101-2021_01_08_425885	279	17	curvature	curvature	NN
10_1101-2021_01_08_425885	279	18	,	,	,
10_1101-2021_01_08_425885	279	19	for	for	IN
10_1101-2021_01_08_425885	279	20	either	either	DT
10_1101-2021_01_08_425885	279	21	variable	variable	JJ
10_1101-2021_01_08_425885	279	22	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	279	23	sizes	size	NNS
10_1101-2021_01_08_425885	279	24	chosen	choose	VBN
10_1101-2021_01_08_425885	279	25	by	by	IN
10_1101-2021_01_08_425885	279	26	the	the	DT
10_1101-2021_01_08_425885	279	27	algorithm	algorithm	NN
10_1101-2021_01_08_425885	279	28	to	to	TO
10_1101-2021_01_08_425885	279	29	achieve	achieve	VB
10_1101-2021_01_08_425885	279	30	σh	σh	NNP
10_1101-2021_01_08_425885	279	31	,	,	,
10_1101-2021_01_08_425885	279	32	or	or	CC
10_1101-2021_01_08_425885	279	33	for	for	IN
10_1101-2021_01_08_425885	279	34	fixed	fix	VBN
10_1101-2021_01_08_425885	279	35	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	279	36	sizes	size	NNS
10_1101-2021_01_08_425885	279	37	(	(	-LRB-
10_1101-2021_01_08_425885	279	38	see	see	VB
10_1101-2021_01_08_425885	279	39	Figure	figure	NN
10_1101-2021_01_08_425885	279	40	S2A	s2a	NN
10_1101-2021_01_08_425885	279	41	;	;	:
10_1101-2021_01_08_425885	279	42	Methods	Methods	NNP
10_1101-2021_01_08_425885	279	43	Section	Section	NNP
10_1101-2021_01_08_425885	279	44	4.4.2.1	4.4.2.1	CD
10_1101-2021_01_08_425885	279	45	)	)	-RRB-
10_1101-2021_01_08_425885	279	46	.	.	.
10_1101-2021_01_08_425885	280	1	Taken	take	VBN
10_1101-2021_01_08_425885	280	2	together	together	RB
10_1101-2021_01_08_425885	280	3	,	,	,
10_1101-2021_01_08_425885	280	4	although	although	IN
10_1101-2021_01_08_425885	280	5	higher	high	JJR
10_1101-2021_01_08_425885	280	6	density	density	NN
10_1101-2021_01_08_425885	280	7	allows	allow	VBZ
10_1101-2021_01_08_425885	280	8	us	-PRON-	PRP
10_1101-2021_01_08_425885	280	9	to	to	TO
10_1101-2021_01_08_425885	280	10	resolve	resolve	VB
10_1101-2021_01_08_425885	280	11	statistically	statistically	RB
10_1101-2021_01_08_425885	280	12	significant	significant	JJ
10_1101-2021_01_08_425885	280	13	non	non	JJ
10_1101-2021_01_08_425885	280	14	-	-	JJ
10_1101-2021_01_08_425885	280	15	zero	zero	CD
10_1101-2021_01_08_425885	280	16	scalar	scalar	JJ
10_1101-2021_01_08_425885	280	17	curvatures	curvature	NNS
10_1101-2021_01_08_425885	280	18	in	in	IN
10_1101-2021_01_08_425885	280	19	scRNAseq	scrnaseq	JJ
10_1101-2021_01_08_425885	280	20	data	datum	NNS
10_1101-2021_01_08_425885	280	21	,	,	,
10_1101-2021_01_08_425885	280	22	these	these	DT
10_1101-2021_01_08_425885	280	23	computed	compute	VBN
10_1101-2021_01_08_425885	280	24	scalar	scalar	JJ
10_1101-2021_01_08_425885	280	25	curvatures	curvature	NNS
10_1101-2021_01_08_425885	280	26	are	be	VBP
10_1101-2021_01_08_425885	280	27	not	not	RB
10_1101-2021_01_08_425885	280	28	an	an	DT
10_1101-2021_01_08_425885	280	29	artifact	artifact	NN
10_1101-2021_01_08_425885	280	30	of	of	IN
10_1101-2021_01_08_425885	280	31	the	the	DT
10_1101-2021_01_08_425885	280	32	smaller	small	JJR
10_1101-2021_01_08_425885	280	33	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	280	34	sizes	size	NNS
10_1101-2021_01_08_425885	280	35	used	use	VBN
10_1101-2021_01_08_425885	280	36	in	in	IN
10_1101-2021_01_08_425885	280	37	regions	region	NNS
10_1101-2021_01_08_425885	280	38	with	with	IN
10_1101-2021_01_08_425885	280	39	higher	high	JJR
10_1101-2021_01_08_425885	280	40	density	density	NN
10_1101-2021_01_08_425885	280	41	.	.	.
10_1101-2021_01_08_425885	281	1	To	to	TO
10_1101-2021_01_08_425885	281	2	ensure	ensure	VB
10_1101-2021_01_08_425885	281	3	that	that	IN
10_1101-2021_01_08_425885	281	4	the	the	DT
10_1101-2021_01_08_425885	281	5	computed	compute	VBN
10_1101-2021_01_08_425885	281	6	scalar	scalar	JJ
10_1101-2021_01_08_425885	281	7	curvatures	curvature	NNS
10_1101-2021_01_08_425885	281	8	were	be	VBD
10_1101-2021_01_08_425885	281	9	not	not	RB
10_1101-2021_01_08_425885	281	10	sensitively	sensitively	RB
10_1101-2021_01_08_425885	281	11	dependent	dependent	JJ
10_1101-2021_01_08_425885	281	12	on	on	IN
10_1101-2021_01_08_425885	281	13	the	the	DT
10_1101-2021_01_08_425885	281	14	heuristically	heuristically	RB
10_1101-2021_01_08_425885	281	15	chosen	choose	VBN
10_1101-2021_01_08_425885	281	16	manifold	manifold	JJ
10_1101-2021_01_08_425885	281	17	dimension	dimension	NN
10_1101-2021_01_08_425885	281	18	,	,	,
10_1101-2021_01_08_425885	281	19	d	d	NNP
10_1101-2021_01_08_425885	281	20	,	,	,
10_1101-2021_01_08_425885	281	21	we	-PRON-	PRP
10_1101-2021_01_08_425885	281	22	also	also	RB
10_1101-2021_01_08_425885	281	23	recomputed	recompute	VBD
10_1101-2021_01_08_425885	281	24	scalar	scalar	JJ
10_1101-2021_01_08_425885	281	25	curvatures	curvature	NNS
10_1101-2021_01_08_425885	281	26	for	for	IN
10_1101-2021_01_08_425885	281	27	d	d	NN
10_1101-2021_01_08_425885	281	28	−	−	NNP
10_1101-2021_01_08_425885	281	29	1	1	CD
10_1101-2021_01_08_425885	281	30	and	and	CC
10_1101-2021_01_08_425885	281	31	d	d	NN
10_1101-2021_01_08_425885	281	32	+	+	SYM
10_1101-2021_01_08_425885	281	33	1	1	CD
10_1101-2021_01_08_425885	281	34	and	and	CC
10_1101-2021_01_08_425885	281	35	observed	observe	VBD
10_1101-2021_01_08_425885	281	36	similar	similar	JJ
10_1101-2021_01_08_425885	281	37	qualitative	qualitative	JJ
10_1101-2021_01_08_425885	281	38	results	result	NNS
10_1101-2021_01_08_425885	281	39	(	(	-LRB-
10_1101-2021_01_08_425885	281	40	see	see	VB
10_1101-2021_01_08_425885	281	41	Figures	Figures	NNP
10_1101-2021_01_08_425885	281	42	S4	S4	NNP
10_1101-2021_01_08_425885	281	43	G	g	NN
10_1101-2021_01_08_425885	281	44	,	,	,
10_1101-2021_01_08_425885	281	45	S5	s5	NN
10_1101-2021_01_08_425885	281	46	G	g	NN
10_1101-2021_01_08_425885	281	47	and	and	CC
10_1101-2021_01_08_425885	281	48	S6	S6	NNP
10_1101-2021_01_08_425885	281	49	G	G	NNP
10_1101-2021_01_08_425885	281	50	)	)	-RRB-
10_1101-2021_01_08_425885	281	51	.	.	.
10_1101-2021_01_08_425885	282	1	Lastly	lastly	RB
10_1101-2021_01_08_425885	282	2	,	,	,
10_1101-2021_01_08_425885	282	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	282	4	verified	verify	VBD
10_1101-2021_01_08_425885	282	5	that	that	IN
10_1101-2021_01_08_425885	282	6	the	the	DT
10_1101-2021_01_08_425885	282	7	computed	compute	VBN
10_1101-2021_01_08_425885	282	8	scalar	scalar	JJ
10_1101-2021_01_08_425885	282	9	curvatures	curvature	NNS
10_1101-2021_01_08_425885	282	10	were	be	VBD
10_1101-2021_01_08_425885	282	11	not	not	RB
10_1101-2021_01_08_425885	282	12	correlated	correlate	VBN
10_1101-2021_01_08_425885	282	13	with	with	IN
10_1101-2021_01_08_425885	282	14	the	the	DT
10_1101-2021_01_08_425885	282	15	number	number	NN
10_1101-2021_01_08_425885	282	16	of	of	IN
10_1101-2021_01_08_425885	282	17	transcripts	transcript	NNS
10_1101-2021_01_08_425885	282	18	in	in	IN
10_1101-2021_01_08_425885	282	19	each	each	DT
10_1101-2021_01_08_425885	282	20	cell	cell	NN
10_1101-2021_01_08_425885	282	21	(	(	-LRB-
10_1101-2021_01_08_425885	282	22	see	see	VB
10_1101-2021_01_08_425885	282	23	Figures	Figures	NNP
10_1101-2021_01_08_425885	282	24	S4H	s4h	NN
10_1101-2021_01_08_425885	282	25	,	,	,
10_1101-2021_01_08_425885	282	26	S5H	s5h	NN
10_1101-2021_01_08_425885	282	27	and	and	CC
10_1101-2021_01_08_425885	282	28	S6H	s6h	NN
10_1101-2021_01_08_425885	282	29	)	)	-RRB-
10_1101-2021_01_08_425885	282	30	.	.	.
10_1101-2021_01_08_425885	283	1	16	16	CD
10_1101-2021_01_08_425885	283	2	.CC	.CC	:
10_1101-2021_01_08_425885	283	3	-	-	HYPH
10_1101-2021_01_08_425885	283	4	BY	by	IN
10_1101-2021_01_08_425885	283	5	-	-	HYPH
10_1101-2021_01_08_425885	283	6	NC	NC	NNP
10_1101-2021_01_08_425885	283	7	-	-	HYPH
10_1101-2021_01_08_425885	283	8	ND	ND	NNP
10_1101-2021_01_08_425885	283	9	4.0	4.0	CD
10_1101-2021_01_08_425885	283	10	International	International	NNP
10_1101-2021_01_08_425885	283	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	283	12	under	under	IN
10_1101-2021_01_08_425885	283	13	a	a	DT
10_1101-2021_01_08_425885	283	14	(	(	-LRB-
10_1101-2021_01_08_425885	283	15	which	which	WDT
10_1101-2021_01_08_425885	283	16	was	be	VBD
10_1101-2021_01_08_425885	283	17	not	not	RB
10_1101-2021_01_08_425885	283	18	certified	certify	VBN
10_1101-2021_01_08_425885	283	19	by	by	IN
10_1101-2021_01_08_425885	283	20	peer	peer	NN
10_1101-2021_01_08_425885	283	21	review	review	NN
10_1101-2021_01_08_425885	283	22	)	)	-RRB-
10_1101-2021_01_08_425885	283	23	is	be	VBZ
10_1101-2021_01_08_425885	283	24	the	the	DT
10_1101-2021_01_08_425885	283	25	author	author	NN
10_1101-2021_01_08_425885	283	26	/	/	SYM
10_1101-2021_01_08_425885	283	27	funder	funder	NN
10_1101-2021_01_08_425885	283	28	,	,	,
10_1101-2021_01_08_425885	283	29	who	who	WP
10_1101-2021_01_08_425885	283	30	has	have	VBZ
10_1101-2021_01_08_425885	283	31	granted	grant	VBN
10_1101-2021_01_08_425885	283	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	283	33	a	a	DT
10_1101-2021_01_08_425885	283	34	license	license	NN
10_1101-2021_01_08_425885	283	35	to	to	TO
10_1101-2021_01_08_425885	283	36	display	display	VB
10_1101-2021_01_08_425885	283	37	the	the	DT
10_1101-2021_01_08_425885	283	38	preprint	preprint	NN
10_1101-2021_01_08_425885	283	39	in	in	IN
10_1101-2021_01_08_425885	283	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	283	41	.	.	.
10_1101-2021_01_08_425885	284	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	284	2	is	be	VBZ
10_1101-2021_01_08_425885	284	3	made	make	VBN
10_1101-2021_01_08_425885	284	4	The	the	DT
10_1101-2021_01_08_425885	284	5	copyright	copyright	NN
10_1101-2021_01_08_425885	284	6	holder	holder	NN
10_1101-2021_01_08_425885	284	7	for	for	IN
10_1101-2021_01_08_425885	284	8	this	this	DT
10_1101-2021_01_08_425885	284	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	284	10	version	version	NN
10_1101-2021_01_08_425885	284	11	posted	post	VBD
10_1101-2021_01_08_425885	284	12	January	January	NNP
10_1101-2021_01_08_425885	284	13	8	8	CD
10_1101-2021_01_08_425885	284	14	,	,	,
10_1101-2021_01_08_425885	284	15	2021	2021	CD
10_1101-2021_01_08_425885	284	16	.	.	.
10_1101-2021_01_08_425885	284	17	;	;	:
10_1101-2021_01_08_425885	284	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	284	19	:	:	:
10_1101-2021_01_08_425885	284	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	284	21	preprint	preprint	NN
10_1101-2021_01_08_425885	284	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	284	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NN
10_1101-2021_01_08_425885	284	24	A	A	NNP
10_1101-2021_01_08_425885	284	25	B	b	NN
10_1101-2021_01_08_425885	284	26	C	c	NN
10_1101-2021_01_08_425885	284	27	D	d	NN
10_1101-2021_01_08_425885	284	28	E	e	NN
10_1101-2021_01_08_425885	284	29	F	f	NN
10_1101-2021_01_08_425885	284	30	H	h	NN
10_1101-2021_01_08_425885	284	31	IG	IG	NNP
10_1101-2021_01_08_425885	284	32	Figure	figure	NN
10_1101-2021_01_08_425885	284	33	4	4	CD
10_1101-2021_01_08_425885	284	34	:	:	:
10_1101-2021_01_08_425885	284	35	scRNAseq	scrnaseq	NN
10_1101-2021_01_08_425885	284	36	datasets	dataset	NNS
10_1101-2021_01_08_425885	284	37	have	have	VBP
10_1101-2021_01_08_425885	284	38	localized	localize	VBN
10_1101-2021_01_08_425885	284	39	regions	region	NNS
10_1101-2021_01_08_425885	284	40	of	of	IN
10_1101-2021_01_08_425885	284	41	non	non	JJ
10_1101-2021_01_08_425885	284	42	-	-	JJ
10_1101-2021_01_08_425885	284	43	zero	zero	JJ
10_1101-2021_01_08_425885	284	44	scalar	scalar	JJ
10_1101-2021_01_08_425885	284	45	curvature	curvature	NN
10_1101-2021_01_08_425885	284	46	.	.	.
10_1101-2021_01_08_425885	285	1	(	(	-LRB-
10_1101-2021_01_08_425885	285	2	A	a	DT
10_1101-2021_01_08_425885	285	3	)	)	-RRB-
10_1101-2021_01_08_425885	285	4	Scalar	scalar	JJ
10_1101-2021_01_08_425885	285	5	curvatures	curvature	NNS
10_1101-2021_01_08_425885	285	6	were	be	VBD
10_1101-2021_01_08_425885	285	7	computed	compute	VBN
10_1101-2021_01_08_425885	285	8	for	for	IN
10_1101-2021_01_08_425885	285	9	a	a	DT
10_1101-2021_01_08_425885	285	10	scRNAseq	scrnaseq	JJ
10_1101-2021_01_08_425885	285	11	dataset	dataset	NN
10_1101-2021_01_08_425885	285	12	with	with	IN
10_1101-2021_01_08_425885	285	13	N	N	NNP
10_1101-2021_01_08_425885	285	14	≈	≈	NNP
10_1101-2021_01_08_425885	285	15	104	104	CD
10_1101-2021_01_08_425885	285	16	peripheral	peripheral	JJ
10_1101-2021_01_08_425885	285	17	blood	blood	NN
10_1101-2021_01_08_425885	285	18	mononuclear	mononuclear	NN
10_1101-2021_01_08_425885	285	19	cells	cell	NNS
10_1101-2021_01_08_425885	285	20	(	(	-LRB-
10_1101-2021_01_08_425885	285	21	PBMCs	PBMCs	NNP
10_1101-2021_01_08_425885	285	22	)	)	-RRB-
10_1101-2021_01_08_425885	285	23	collected	collect	VBD
10_1101-2021_01_08_425885	285	24	from	from	IN
10_1101-2021_01_08_425885	285	25	a	a	DT
10_1101-2021_01_08_425885	285	26	healthy	healthy	JJ
10_1101-2021_01_08_425885	285	27	human	human	JJ
10_1101-2021_01_08_425885	285	28	donor	donor	NN
10_1101-2021_01_08_425885	285	29	.	.	.
10_1101-2021_01_08_425885	286	1	The	the	DT
10_1101-2021_01_08_425885	286	2	ambient	ambient	JJ
10_1101-2021_01_08_425885	286	3	(	(	-LRB-
10_1101-2021_01_08_425885	286	4	n	n	NN
10_1101-2021_01_08_425885	286	5	)	)	-RRB-
10_1101-2021_01_08_425885	286	6	and	and	CC
10_1101-2021_01_08_425885	286	7	manifold	manifold	NNP
10_1101-2021_01_08_425885	286	8	(	(	-LRB-
10_1101-2021_01_08_425885	286	9	d	d	NN
10_1101-2021_01_08_425885	286	10	)	)	-RRB-
10_1101-2021_01_08_425885	286	11	dimensions	dimension	NNS
10_1101-2021_01_08_425885	286	12	were	be	VBD
10_1101-2021_01_08_425885	286	13	specified	specify	VBN
10_1101-2021_01_08_425885	286	14	to	to	TO
10_1101-2021_01_08_425885	286	15	be	be	VB
10_1101-2021_01_08_425885	286	16	8	8	CD
10_1101-2021_01_08_425885	286	17	and	and	CC
10_1101-2021_01_08_425885	286	18	3	3	CD
10_1101-2021_01_08_425885	286	19	respectively	respectively	RB
10_1101-2021_01_08_425885	286	20	and	and	CC
10_1101-2021_01_08_425885	286	21	variable	variable	JJ
10_1101-2021_01_08_425885	286	22	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	286	23	sizes	size	NNS
10_1101-2021_01_08_425885	286	24	were	be	VBD
10_1101-2021_01_08_425885	286	25	chosen	choose	VBN
10_1101-2021_01_08_425885	286	26	by	by	IN
10_1101-2021_01_08_425885	286	27	setting	set	VBG
10_1101-2021_01_08_425885	286	28	σh	σh	NNP
10_1101-2021_01_08_425885	286	29	(	(	-LRB-
10_1101-2021_01_08_425885	286	30	see	see	VB
10_1101-2021_01_08_425885	286	31	Methods	Methods	NNP
10_1101-2021_01_08_425885	286	32	Section	Section	NNP
10_1101-2021_01_08_425885	286	33	4.6.4	4.6.4	CD
10_1101-2021_01_08_425885	286	34	)	)	-RRB-
10_1101-2021_01_08_425885	286	35	.	.	.
10_1101-2021_01_08_425885	287	1	The	the	DT
10_1101-2021_01_08_425885	287	2	scalar	scalar	JJ
10_1101-2021_01_08_425885	287	3	curvatures	curvature	NNS
10_1101-2021_01_08_425885	287	4	are	be	VBP
10_1101-2021_01_08_425885	287	5	shown	show	VBN
10_1101-2021_01_08_425885	287	6	here	here	RB
10_1101-2021_01_08_425885	287	7	overlaid	overlay	VBN
10_1101-2021_01_08_425885	287	8	onto	onto	IN
10_1101-2021_01_08_425885	287	9	UMAP	UMAP	NNP
10_1101-2021_01_08_425885	287	10	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	287	11	,	,	,
10_1101-2021_01_08_425885	287	12	after	after	IN
10_1101-2021_01_08_425885	287	13	smoothing	smooth	VBG
10_1101-2021_01_08_425885	287	14	the	the	DT
10_1101-2021_01_08_425885	287	15	values	value	NNS
10_1101-2021_01_08_425885	287	16	over	over	IN
10_1101-2021_01_08_425885	287	17	k	k	NN
10_1101-2021_01_08_425885	287	18	=	=	SYM
10_1101-2021_01_08_425885	287	19	250	250	CD
10_1101-2021_01_08_425885	287	20	nearest	near	JJS
10_1101-2021_01_08_425885	287	21	neighbors	neighbor	NNS
10_1101-2021_01_08_425885	287	22	in	in	IN
10_1101-2021_01_08_425885	287	23	the	the	DT
10_1101-2021_01_08_425885	287	24	ambient	ambient	JJ
10_1101-2021_01_08_425885	287	25	space	space	NN
10_1101-2021_01_08_425885	287	26	.	.	.
10_1101-2021_01_08_425885	288	1	(	(	-LRB-
10_1101-2021_01_08_425885	288	2	B	b	NN
10_1101-2021_01_08_425885	288	3	)	)	-RRB-
10_1101-2021_01_08_425885	288	4	Scatter	scatter	NN
10_1101-2021_01_08_425885	288	5	plot	plot	NN
10_1101-2021_01_08_425885	288	6	of	of	IN
10_1101-2021_01_08_425885	288	7	(	(	-LRB-
10_1101-2021_01_08_425885	288	8	unsmoothed	unsmoothed	JJ
10_1101-2021_01_08_425885	288	9	)	)	-RRB-
10_1101-2021_01_08_425885	288	10	scalar	scalar	JJ
10_1101-2021_01_08_425885	288	11	curvatures	curvature	NNS
10_1101-2021_01_08_425885	288	12	,	,	,
10_1101-2021_01_08_425885	288	13	S	S	NNP
10_1101-2021_01_08_425885	288	14	,	,	,
10_1101-2021_01_08_425885	288	15	and	and	CC
10_1101-2021_01_08_425885	288	16	associated	associate	VBD
10_1101-2021_01_08_425885	288	17	standard	standard	JJ
10_1101-2021_01_08_425885	288	18	errors	error	NNS
10_1101-2021_01_08_425885	288	19	,	,	,
10_1101-2021_01_08_425885	288	20	σS	σS	NNP
10_1101-2021_01_08_425885	288	21	,	,	,
10_1101-2021_01_08_425885	288	22	for	for	IN
10_1101-2021_01_08_425885	288	23	each	each	DT
10_1101-2021_01_08_425885	288	24	datapoint	datapoint	NN
10_1101-2021_01_08_425885	288	25	in	in	IN
10_1101-2021_01_08_425885	288	26	the	the	DT
10_1101-2021_01_08_425885	288	27	PBMC	PBMC	NNP
10_1101-2021_01_08_425885	288	28	dataset	dataset	NN
10_1101-2021_01_08_425885	288	29	.	.	.
10_1101-2021_01_08_425885	289	1	Points	point	NNS
10_1101-2021_01_08_425885	289	2	enclosed	enclose	VBN
10_1101-2021_01_08_425885	289	3	by	by	IN
10_1101-2021_01_08_425885	289	4	the	the	DT
10_1101-2021_01_08_425885	289	5	red	red	JJ
10_1101-2021_01_08_425885	289	6	lines	line	NNS
10_1101-2021_01_08_425885	289	7	reported	report	VBD
10_1101-2021_01_08_425885	289	8	a	a	DT
10_1101-2021_01_08_425885	289	9	95	95	CD
10_1101-2021_01_08_425885	289	10	%	%	NN
10_1101-2021_01_08_425885	289	11	CI	ci	NN
10_1101-2021_01_08_425885	289	12	(	(	-LRB-
10_1101-2021_01_08_425885	289	13	S	S	NNP
10_1101-2021_01_08_425885	289	14	±	±	NNP
10_1101-2021_01_08_425885	289	15	2σS	2σs	CD
10_1101-2021_01_08_425885	289	16	)	)	-RRB-
10_1101-2021_01_08_425885	289	17	including	include	VBG
10_1101-2021_01_08_425885	289	18	0	0	CD
10_1101-2021_01_08_425885	289	19	.	.	.
10_1101-2021_01_08_425885	290	1	(	(	-LRB-
10_1101-2021_01_08_425885	290	2	C	C	NNP
10_1101-2021_01_08_425885	290	3	)	)	-RRB-
10_1101-2021_01_08_425885	290	4	As	as	IN
10_1101-2021_01_08_425885	290	5	in	in	IN
10_1101-2021_01_08_425885	290	6	(	(	-LRB-
10_1101-2021_01_08_425885	290	7	A	a	NN
10_1101-2021_01_08_425885	290	8	)	)	-RRB-
10_1101-2021_01_08_425885	290	9	but	but	CC
10_1101-2021_01_08_425885	290	10	with	with	IN
10_1101-2021_01_08_425885	290	11	scalar	scalar	JJ
10_1101-2021_01_08_425885	290	12	curvatures	curvature	NNS
10_1101-2021_01_08_425885	290	13	computed	compute	VBD
10_1101-2021_01_08_425885	290	14	using	use	VBG
10_1101-2021_01_08_425885	290	15	a	a	DT
10_1101-2021_01_08_425885	290	16	fixed	fix	VBN
10_1101-2021_01_08_425885	290	17	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	290	18	size	size	NN
10_1101-2021_01_08_425885	290	19	,	,	,
10_1101-2021_01_08_425885	290	20	r	r	NNP
10_1101-2021_01_08_425885	290	21	,	,	,
10_1101-2021_01_08_425885	290	22	for	for	IN
10_1101-2021_01_08_425885	290	23	all	all	DT
10_1101-2021_01_08_425885	290	24	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	290	25	.	.	.
10_1101-2021_01_08_425885	291	1	The	the	DT
10_1101-2021_01_08_425885	291	2	value	value	NN
10_1101-2021_01_08_425885	291	3	of	of	IN
10_1101-2021_01_08_425885	291	4	r	r	NN
10_1101-2021_01_08_425885	291	5	was	be	VBD
10_1101-2021_01_08_425885	291	6	set	set	VBN
10_1101-2021_01_08_425885	291	7	to	to	TO
10_1101-2021_01_08_425885	291	8	be	be	VB
10_1101-2021_01_08_425885	291	9	the	the	DT
10_1101-2021_01_08_425885	291	10	25	25	CD
10_1101-2021_01_08_425885	291	11	,	,	,
10_1101-2021_01_08_425885	291	12	50	50	CD
10_1101-2021_01_08_425885	291	13	,	,	,
10_1101-2021_01_08_425885	291	14	and	and	CC
10_1101-2021_01_08_425885	291	15	75-%ile	75-%ile	CD
10_1101-2021_01_08_425885	291	16	values	value	NNS
10_1101-2021_01_08_425885	291	17	(	(	-LRB-
10_1101-2021_01_08_425885	291	18	left	leave	VBN
10_1101-2021_01_08_425885	291	19	to	to	IN
10_1101-2021_01_08_425885	291	20	right	right	NN
10_1101-2021_01_08_425885	291	21	)	)	-RRB-
10_1101-2021_01_08_425885	291	22	of	of	IN
10_1101-2021_01_08_425885	291	23	the	the	DT
10_1101-2021_01_08_425885	291	24	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	291	25	sizes	size	NNS
10_1101-2021_01_08_425885	291	26	used	use	VBN
10_1101-2021_01_08_425885	291	27	in	in	IN
10_1101-2021_01_08_425885	291	28	(	(	-LRB-
10_1101-2021_01_08_425885	291	29	A	a	NN
10_1101-2021_01_08_425885	291	30	)	)	-RRB-
10_1101-2021_01_08_425885	291	31	(	(	-LRB-
10_1101-2021_01_08_425885	291	32	see	see	VB
10_1101-2021_01_08_425885	291	33	Figure	figure	NN
10_1101-2021_01_08_425885	291	34	S4E	s4e	NN
10_1101-2021_01_08_425885	291	35	)	)	-RRB-
10_1101-2021_01_08_425885	291	36	.	.	.
10_1101-2021_01_08_425885	292	1	Points	point	NNS
10_1101-2021_01_08_425885	292	2	for	for	IN
10_1101-2021_01_08_425885	292	3	which	which	WDT
10_1101-2021_01_08_425885	292	4	a	a	DT
10_1101-2021_01_08_425885	292	5	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	292	6	of	of	IN
10_1101-2021_01_08_425885	292	7	size	size	NN
10_1101-2021_01_08_425885	292	8	r	r	NN
10_1101-2021_01_08_425885	292	9	does	do	VBZ
10_1101-2021_01_08_425885	292	10	not	not	RB
10_1101-2021_01_08_425885	292	11	include	include	VB
10_1101-2021_01_08_425885	292	12	enough	enough	JJ
10_1101-2021_01_08_425885	292	13	neighbors	neighbor	NNS
10_1101-2021_01_08_425885	292	14	for	for	IN
10_1101-2021_01_08_425885	292	15	regression	regression	NN
10_1101-2021_01_08_425885	292	16	are	be	VBP
10_1101-2021_01_08_425885	292	17	not	not	RB
10_1101-2021_01_08_425885	292	18	shown	show	VBN
10_1101-2021_01_08_425885	292	19	.	.	.
10_1101-2021_01_08_425885	293	1	(	(	-LRB-
10_1101-2021_01_08_425885	293	2	D	D	NNP
10_1101-2021_01_08_425885	293	3	-	-	HYPH
10_1101-2021_01_08_425885	293	4	F	f	NN
10_1101-2021_01_08_425885	293	5	)	)	-RRB-
10_1101-2021_01_08_425885	293	6	As	as	IN
10_1101-2021_01_08_425885	293	7	in	in	IN
10_1101-2021_01_08_425885	293	8	(	(	-LRB-
10_1101-2021_01_08_425885	293	9	A	A	NNP
10_1101-2021_01_08_425885	293	10	-	-	HYPH
10_1101-2021_01_08_425885	293	11	C	C	NNP
10_1101-2021_01_08_425885	293	12	)	)	-RRB-
10_1101-2021_01_08_425885	293	13	for	for	IN
10_1101-2021_01_08_425885	293	14	a	a	DT
10_1101-2021_01_08_425885	293	15	mouse	mouse	NN
10_1101-2021_01_08_425885	293	16	gastrulation	gastrulation	NN
10_1101-2021_01_08_425885	293	17	dataset	dataset	NN
10_1101-2021_01_08_425885	293	18	with	with	IN
10_1101-2021_01_08_425885	293	19	N	N	NNP
10_1101-2021_01_08_425885	293	20	≈	≈	NNP
10_1101-2021_01_08_425885	293	21	1.2	1.2	CD
10_1101-2021_01_08_425885	293	22	×	×	CD
10_1101-2021_01_08_425885	293	23	105	105	CD
10_1101-2021_01_08_425885	293	24	,	,	,
10_1101-2021_01_08_425885	293	25	d	d	NN
10_1101-2021_01_08_425885	293	26	=	=	SYM
10_1101-2021_01_08_425885	293	27	3	3	CD
10_1101-2021_01_08_425885	293	28	and	and	CC
10_1101-2021_01_08_425885	293	29	n	n	CD
10_1101-2021_01_08_425885	293	30	=	=	SYM
10_1101-2021_01_08_425885	293	31	11	11	CD
10_1101-2021_01_08_425885	293	32	.	.	.
10_1101-2021_01_08_425885	294	1	(	(	-LRB-
10_1101-2021_01_08_425885	294	2	G	g	NN
10_1101-2021_01_08_425885	294	3	-	-	:
10_1101-2021_01_08_425885	294	4	I	i	NN
10_1101-2021_01_08_425885	294	5	)	)	-RRB-
10_1101-2021_01_08_425885	294	6	As	as	IN
10_1101-2021_01_08_425885	294	7	in	in	IN
10_1101-2021_01_08_425885	294	8	(	(	-LRB-
10_1101-2021_01_08_425885	294	9	A	A	NNP
10_1101-2021_01_08_425885	294	10	-	-	HYPH
10_1101-2021_01_08_425885	294	11	C	C	NNP
10_1101-2021_01_08_425885	294	12	)	)	-RRB-
10_1101-2021_01_08_425885	294	13	for	for	IN
10_1101-2021_01_08_425885	294	14	a	a	DT
10_1101-2021_01_08_425885	294	15	mouse	mouse	NN
10_1101-2021_01_08_425885	294	16	brain	brain	NN
10_1101-2021_01_08_425885	294	17	dataset	dataset	NN
10_1101-2021_01_08_425885	294	18	with	with	IN
10_1101-2021_01_08_425885	294	19	N	N	NNP
10_1101-2021_01_08_425885	294	20	≈	≈	NNP
10_1101-2021_01_08_425885	294	21	1.3	1.3	CD
10_1101-2021_01_08_425885	294	22	×	×	CD
10_1101-2021_01_08_425885	294	23	106	106	CD
10_1101-2021_01_08_425885	294	24	,	,	,
10_1101-2021_01_08_425885	294	25	d	d	NN
10_1101-2021_01_08_425885	294	26	=	=	SYM
10_1101-2021_01_08_425885	294	27	5	5	CD
10_1101-2021_01_08_425885	294	28	and	and	CC
10_1101-2021_01_08_425885	294	29	n	n	CD
10_1101-2021_01_08_425885	294	30	=	=	SYM
10_1101-2021_01_08_425885	294	31	9	9	CD
10_1101-2021_01_08_425885	294	32	,	,	,
10_1101-2021_01_08_425885	294	33	plotted	plot	VBN
10_1101-2021_01_08_425885	294	34	on	on	IN
10_1101-2021_01_08_425885	294	35	t	t	NNP
10_1101-2021_01_08_425885	294	36	-	-	HYPH
10_1101-2021_01_08_425885	294	37	SNE	SNE	NNP
10_1101-2021_01_08_425885	294	38	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	294	39	.	.	.
10_1101-2021_01_08_425885	295	1	17	17	CD
10_1101-2021_01_08_425885	295	2	.CC	.CC	:
10_1101-2021_01_08_425885	295	3	-	-	HYPH
10_1101-2021_01_08_425885	295	4	BY	by	IN
10_1101-2021_01_08_425885	295	5	-	-	HYPH
10_1101-2021_01_08_425885	295	6	NC	NC	NNP
10_1101-2021_01_08_425885	295	7	-	-	HYPH
10_1101-2021_01_08_425885	295	8	ND	ND	NNP
10_1101-2021_01_08_425885	295	9	4.0	4.0	CD
10_1101-2021_01_08_425885	295	10	International	International	NNP
10_1101-2021_01_08_425885	295	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	295	12	under	under	IN
10_1101-2021_01_08_425885	295	13	a	a	DT
10_1101-2021_01_08_425885	295	14	(	(	-LRB-
10_1101-2021_01_08_425885	295	15	which	which	WDT
10_1101-2021_01_08_425885	295	16	was	be	VBD
10_1101-2021_01_08_425885	295	17	not	not	RB
10_1101-2021_01_08_425885	295	18	certified	certify	VBN
10_1101-2021_01_08_425885	295	19	by	by	IN
10_1101-2021_01_08_425885	295	20	peer	peer	NN
10_1101-2021_01_08_425885	295	21	review	review	NN
10_1101-2021_01_08_425885	295	22	)	)	-RRB-
10_1101-2021_01_08_425885	295	23	is	be	VBZ
10_1101-2021_01_08_425885	295	24	the	the	DT
10_1101-2021_01_08_425885	295	25	author	author	NN
10_1101-2021_01_08_425885	295	26	/	/	SYM
10_1101-2021_01_08_425885	295	27	funder	funder	NN
10_1101-2021_01_08_425885	295	28	,	,	,
10_1101-2021_01_08_425885	295	29	who	who	WP
10_1101-2021_01_08_425885	295	30	has	have	VBZ
10_1101-2021_01_08_425885	295	31	granted	grant	VBN
10_1101-2021_01_08_425885	295	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	295	33	a	a	DT
10_1101-2021_01_08_425885	295	34	license	license	NN
10_1101-2021_01_08_425885	295	35	to	to	TO
10_1101-2021_01_08_425885	295	36	display	display	VB
10_1101-2021_01_08_425885	295	37	the	the	DT
10_1101-2021_01_08_425885	295	38	preprint	preprint	NN
10_1101-2021_01_08_425885	295	39	in	in	IN
10_1101-2021_01_08_425885	295	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	295	41	.	.	.
10_1101-2021_01_08_425885	296	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	296	2	is	be	VBZ
10_1101-2021_01_08_425885	296	3	made	make	VBN
10_1101-2021_01_08_425885	296	4	The	the	DT
10_1101-2021_01_08_425885	296	5	copyright	copyright	NN
10_1101-2021_01_08_425885	296	6	holder	holder	NN
10_1101-2021_01_08_425885	296	7	for	for	IN
10_1101-2021_01_08_425885	296	8	this	this	DT
10_1101-2021_01_08_425885	296	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	296	10	version	version	NN
10_1101-2021_01_08_425885	296	11	posted	post	VBD
10_1101-2021_01_08_425885	296	12	January	January	NNP
10_1101-2021_01_08_425885	296	13	8	8	CD
10_1101-2021_01_08_425885	296	14	,	,	,
10_1101-2021_01_08_425885	296	15	2021	2021	CD
10_1101-2021_01_08_425885	296	16	.	.	.
10_1101-2021_01_08_425885	296	17	;	;	:
10_1101-2021_01_08_425885	296	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	296	19	:	:	:
10_1101-2021_01_08_425885	296	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	296	21	preprint	preprint	NN
10_1101-2021_01_08_425885	296	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	296	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	RB
10_1101-2021_01_08_425885	296	24	To	to	TO
10_1101-2021_01_08_425885	296	25	confirm	confirm	VB
10_1101-2021_01_08_425885	296	26	the	the	DT
10_1101-2021_01_08_425885	296	27	robustness	robustness	NN
10_1101-2021_01_08_425885	296	28	of	of	IN
10_1101-2021_01_08_425885	296	29	our	-PRON-	PRP$
10_1101-2021_01_08_425885	296	30	results	result	NNS
10_1101-2021_01_08_425885	296	31	to	to	IN
10_1101-2021_01_08_425885	296	32	sampling	sampling	NN
10_1101-2021_01_08_425885	296	33	,	,	,
10_1101-2021_01_08_425885	296	34	we	-PRON-	PRP
10_1101-2021_01_08_425885	296	35	randomly	randomly	RB
10_1101-2021_01_08_425885	296	36	discarded	discard	VBD
10_1101-2021_01_08_425885	296	37	f%	f%	NNP
10_1101-2021_01_08_425885	296	38	of	of	IN
10_1101-2021_01_08_425885	296	39	points	point	NNS
10_1101-2021_01_08_425885	296	40	in	in	IN
10_1101-2021_01_08_425885	296	41	the	the	DT
10_1101-2021_01_08_425885	296	42	ambient	ambient	JJ
10_1101-2021_01_08_425885	296	43	space	space	NN
10_1101-2021_01_08_425885	296	44	determined	determine	VBN
10_1101-2021_01_08_425885	296	45	for	for	IN
10_1101-2021_01_08_425885	296	46	each	each	DT
10_1101-2021_01_08_425885	296	47	dataset	dataset	NN
10_1101-2021_01_08_425885	296	48	,	,	,
10_1101-2021_01_08_425885	296	49	and	and	CC
10_1101-2021_01_08_425885	296	50	recomputed	recompute	VBN
10_1101-2021_01_08_425885	296	51	scalar	scalar	JJ
10_1101-2021_01_08_425885	296	52	curvatures	curvature	NNS
10_1101-2021_01_08_425885	296	53	using	use	VBG
10_1101-2021_01_08_425885	296	54	the	the	DT
10_1101-2021_01_08_425885	296	55	same	same	JJ
10_1101-2021_01_08_425885	296	56	values	value	NNS
10_1101-2021_01_08_425885	296	57	of	of	IN
10_1101-2021_01_08_425885	296	58	n	n	NN
10_1101-2021_01_08_425885	296	59	,	,	,
10_1101-2021_01_08_425885	296	60	d	d	NN
10_1101-2021_01_08_425885	296	61	and	and	CC
10_1101-2021_01_08_425885	296	62	r(p	r(p	NNP
10_1101-2021_01_08_425885	296	63	)	)	-RRB-
10_1101-2021_01_08_425885	296	64	used	use	VBN
10_1101-2021_01_08_425885	296	65	for	for	IN
10_1101-2021_01_08_425885	296	66	the	the	DT
10_1101-2021_01_08_425885	296	67	original	original	JJ
10_1101-2021_01_08_425885	296	68	dataset	dataset	NN
10_1101-2021_01_08_425885	296	69	.	.	.
10_1101-2021_01_08_425885	297	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	297	2	found	find	VBD
10_1101-2021_01_08_425885	297	3	that	that	IN
10_1101-2021_01_08_425885	297	4	a	a	DT
10_1101-2021_01_08_425885	297	5	statistically	statistically	RB
10_1101-2021_01_08_425885	297	6	significant	significant	JJ
10_1101-2021_01_08_425885	297	7	percentage	percentage	NN
10_1101-2021_01_08_425885	297	8	of	of	IN
10_1101-2021_01_08_425885	297	9	downsampled	downsampled	JJ
10_1101-2021_01_08_425885	297	10	points	point	NNS
10_1101-2021_01_08_425885	297	11	(	(	-LRB-
10_1101-2021_01_08_425885	297	12	82	82	CD
10_1101-2021_01_08_425885	297	13	%	%	NN
10_1101-2021_01_08_425885	297	14	for	for	IN
10_1101-2021_01_08_425885	297	15	the	the	DT
10_1101-2021_01_08_425885	297	16	PBMC	PBMC	NNP
10_1101-2021_01_08_425885	297	17	dataset	dataset	NN
10_1101-2021_01_08_425885	297	18	with	with	IN
10_1101-2021_01_08_425885	297	19	f	f	NNP
10_1101-2021_01_08_425885	297	20	=	=	SYM
10_1101-2021_01_08_425885	297	21	75	75	CD
10_1101-2021_01_08_425885	297	22	,	,	,
10_1101-2021_01_08_425885	297	23	78	78	CD
10_1101-2021_01_08_425885	297	24	%	%	NN
10_1101-2021_01_08_425885	297	25	for	for	IN
10_1101-2021_01_08_425885	297	26	the	the	DT
10_1101-2021_01_08_425885	297	27	gastrulation	gastrulation	NN
10_1101-2021_01_08_425885	297	28	dataset	dataset	NN
10_1101-2021_01_08_425885	297	29	with	with	IN
10_1101-2021_01_08_425885	297	30	f	f	NNP
10_1101-2021_01_08_425885	297	31	=	=	SYM
10_1101-2021_01_08_425885	297	32	75	75	CD
10_1101-2021_01_08_425885	297	33	,	,	,
10_1101-2021_01_08_425885	297	34	and	and	CC
10_1101-2021_01_08_425885	297	35	76	76	CD
10_1101-2021_01_08_425885	297	36	%	%	NN
10_1101-2021_01_08_425885	297	37	for	for	IN
10_1101-2021_01_08_425885	297	38	the	the	DT
10_1101-2021_01_08_425885	297	39	brain	brain	NN
10_1101-2021_01_08_425885	297	40	dataset	dataset	NN
10_1101-2021_01_08_425885	297	41	with	with	IN
10_1101-2021_01_08_425885	297	42	f	f	NNP
10_1101-2021_01_08_425885	297	43	=	=	SYM
10_1101-2021_01_08_425885	297	44	50	50	CD
10_1101-2021_01_08_425885	297	45	;	;	:
10_1101-2021_01_08_425885	297	46	p	p	NN
10_1101-2021_01_08_425885	297	47	<	<	XX
10_1101-2021_01_08_425885	297	48	0.001	0.001	CD
10_1101-2021_01_08_425885	297	49	)	)	-RRB-
10_1101-2021_01_08_425885	297	50	had	have	VBD
10_1101-2021_01_08_425885	297	51	a	a	DT
10_1101-2021_01_08_425885	297	52	95	95	CD
10_1101-2021_01_08_425885	297	53	%	%	NN
10_1101-2021_01_08_425885	297	54	CI	ci	NN
10_1101-2021_01_08_425885	297	55	containing	contain	VBG
10_1101-2021_01_08_425885	297	56	the	the	DT
10_1101-2021_01_08_425885	297	57	scalar	scalar	JJ
10_1101-2021_01_08_425885	297	58	curvature	curvature	NN
10_1101-2021_01_08_425885	297	59	reported	report	VBN
10_1101-2021_01_08_425885	297	60	by	by	IN
10_1101-2021_01_08_425885	297	61	the	the	DT
10_1101-2021_01_08_425885	297	62	same	same	JJ
10_1101-2021_01_08_425885	297	63	point	point	NN
10_1101-2021_01_08_425885	297	64	for	for	IN
10_1101-2021_01_08_425885	297	65	the	the	DT
10_1101-2021_01_08_425885	297	66	original	original	JJ
10_1101-2021_01_08_425885	297	67	dataset	dataset	NN
10_1101-2021_01_08_425885	297	68	(	(	-LRB-
10_1101-2021_01_08_425885	297	69	see	see	VB
10_1101-2021_01_08_425885	297	70	Figures	Figures	NNP
10_1101-2021_01_08_425885	297	71	S4I	s4i	NN
10_1101-2021_01_08_425885	297	72	,	,	,
10_1101-2021_01_08_425885	297	73	S5I	S5I	NNS
10_1101-2021_01_08_425885	297	74	and	and	CC
10_1101-2021_01_08_425885	297	75	S6I	S6I	NNS
10_1101-2021_01_08_425885	297	76	;	;	:
10_1101-2021_01_08_425885	297	77	Methods	Methods	NNP
10_1101-2021_01_08_425885	297	78	Section	Section	NNP
10_1101-2021_01_08_425885	297	79	4.6.3.2	4.6.3.2	CD
10_1101-2021_01_08_425885	297	80	)	)	-RRB-
10_1101-2021_01_08_425885	297	81	.	.	.
10_1101-2021_01_08_425885	298	1	This	this	DT
10_1101-2021_01_08_425885	298	2	suggests	suggest	VBZ
10_1101-2021_01_08_425885	298	3	that	that	IN
10_1101-2021_01_08_425885	298	4	if	if	IN
10_1101-2021_01_08_425885	298	5	the	the	DT
10_1101-2021_01_08_425885	298	6	datasets	dataset	NNS
10_1101-2021_01_08_425885	298	7	were	be	VBD
10_1101-2021_01_08_425885	298	8	more	more	RBR
10_1101-2021_01_08_425885	298	9	highly	highly	RB
10_1101-2021_01_08_425885	298	10	sampled	sample	VBN
10_1101-2021_01_08_425885	298	11	,	,	,
10_1101-2021_01_08_425885	298	12	and	and	CC
10_1101-2021_01_08_425885	298	13	scalar	scalar	JJ
10_1101-2021_01_08_425885	298	14	curvatures	curvature	NNS
10_1101-2021_01_08_425885	298	15	were	be	VBD
10_1101-2021_01_08_425885	298	16	recomputed	recompute	VBN
10_1101-2021_01_08_425885	298	17	using	use	VBG
10_1101-2021_01_08_425885	298	18	the	the	DT
10_1101-2021_01_08_425885	298	19	same	same	JJ
10_1101-2021_01_08_425885	298	20	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	298	21	sizes	size	NNS
10_1101-2021_01_08_425885	298	22	,	,	,
10_1101-2021_01_08_425885	298	23	they	-PRON-	PRP
10_1101-2021_01_08_425885	298	24	would	would	MD
10_1101-2021_01_08_425885	298	25	be	be	VB
10_1101-2021_01_08_425885	298	26	reliably	reliably	RB
10_1101-2021_01_08_425885	298	27	contained	contain	VBN
10_1101-2021_01_08_425885	298	28	within	within	IN
10_1101-2021_01_08_425885	298	29	the	the	DT
10_1101-2021_01_08_425885	298	30	currently	currently	RB
10_1101-2021_01_08_425885	298	31	reported	report	VBN
10_1101-2021_01_08_425885	298	32	95	95	CD
10_1101-2021_01_08_425885	298	33	%	%	NN
10_1101-2021_01_08_425885	298	34	CIs	ci	NNS
10_1101-2021_01_08_425885	298	35	.	.	.
10_1101-2021_01_08_425885	299	1	Unlike	unlike	IN
10_1101-2021_01_08_425885	299	2	the	the	DT
10_1101-2021_01_08_425885	299	3	two	two	CD
10_1101-2021_01_08_425885	299	4	other	other	JJ
10_1101-2021_01_08_425885	299	5	datasets	dataset	NNS
10_1101-2021_01_08_425885	299	6	,	,	,
10_1101-2021_01_08_425885	299	7	the	the	DT
10_1101-2021_01_08_425885	299	8	brain	brain	NN
10_1101-2021_01_08_425885	299	9	dataset	dataset	NN
10_1101-2021_01_08_425885	299	10	could	could	MD
10_1101-2021_01_08_425885	299	11	not	not	RB
10_1101-2021_01_08_425885	299	12	be	be	VB
10_1101-2021_01_08_425885	299	13	downsampled	downsample	VBN
10_1101-2021_01_08_425885	299	14	to	to	IN
10_1101-2021_01_08_425885	299	15	f	f	NNP
10_1101-2021_01_08_425885	299	16	=	=	SYM
10_1101-2021_01_08_425885	299	17	75	75	CD
10_1101-2021_01_08_425885	299	18	while	while	IN
10_1101-2021_01_08_425885	299	19	still	still	RB
10_1101-2021_01_08_425885	299	20	having	have	VBG
10_1101-2021_01_08_425885	299	21	at	at	RB
10_1101-2021_01_08_425885	299	22	least	least	RBS
10_1101-2021_01_08_425885	299	23	75	75	CD
10_1101-2021_01_08_425885	299	24	%	%	NN
10_1101-2021_01_08_425885	299	25	of	of	IN
10_1101-2021_01_08_425885	299	26	points	point	NNS
10_1101-2021_01_08_425885	299	27	report	report	VBP
10_1101-2021_01_08_425885	299	28	95	95	CD
10_1101-2021_01_08_425885	299	29	%	%	NN
10_1101-2021_01_08_425885	299	30	CIs	ci	NNS
10_1101-2021_01_08_425885	299	31	containing	contain	VBG
10_1101-2021_01_08_425885	299	32	the	the	DT
10_1101-2021_01_08_425885	299	33	originally	originally	RB
10_1101-2021_01_08_425885	299	34	reported	report	VBN
10_1101-2021_01_08_425885	299	35	scalar	scalar	JJ
10_1101-2021_01_08_425885	299	36	curvatures	curvature	NNS
10_1101-2021_01_08_425885	299	37	,	,	,
10_1101-2021_01_08_425885	299	38	despite	despite	IN
10_1101-2021_01_08_425885	299	39	having	have	VBG
10_1101-2021_01_08_425885	299	40	the	the	DT
10_1101-2021_01_08_425885	299	41	most	most	JJS
10_1101-2021_01_08_425885	299	42	points	point	NNS
10_1101-2021_01_08_425885	299	43	.	.	.
10_1101-2021_01_08_425885	300	1	This	this	DT
10_1101-2021_01_08_425885	300	2	might	may	MD
10_1101-2021_01_08_425885	300	3	be	be	VB
10_1101-2021_01_08_425885	300	4	because	because	IN
10_1101-2021_01_08_425885	300	5	the	the	DT
10_1101-2021_01_08_425885	300	6	brain	brain	NN
10_1101-2021_01_08_425885	300	7	dataset	dataset	NN
10_1101-2021_01_08_425885	300	8	has	have	VBZ
10_1101-2021_01_08_425885	300	9	a	a	DT
10_1101-2021_01_08_425885	300	10	larger	large	JJR
10_1101-2021_01_08_425885	300	11	manifold	manifold	JJ
10_1101-2021_01_08_425885	300	12	dimension	dimension	NN
10_1101-2021_01_08_425885	300	13	according	accord	VBG
10_1101-2021_01_08_425885	300	14	to	to	IN
10_1101-2021_01_08_425885	300	15	our	-PRON-	PRP$
10_1101-2021_01_08_425885	300	16	heuristic	heuristic	JJ
10_1101-2021_01_08_425885	300	17	and	and	CC
10_1101-2021_01_08_425885	300	18	therefore	therefore	RB
10_1101-2021_01_08_425885	300	19	requires	require	VBZ
10_1101-2021_01_08_425885	300	20	a	a	DT
10_1101-2021_01_08_425885	300	21	greater	great	JJR
10_1101-2021_01_08_425885	300	22	number	number	NN
10_1101-2021_01_08_425885	300	23	of	of	IN
10_1101-2021_01_08_425885	300	24	terms	term	NNS
10_1101-2021_01_08_425885	300	25	,	,	,
10_1101-2021_01_08_425885	300	26	hkij	hkij	NNP
10_1101-2021_01_08_425885	300	27	,	,	,
10_1101-2021_01_08_425885	300	28	to	to	TO
10_1101-2021_01_08_425885	300	29	be	be	VB
10_1101-2021_01_08_425885	300	30	estimated	estimate	VBN
10_1101-2021_01_08_425885	300	31	in	in	IN
10_1101-2021_01_08_425885	300	32	the	the	DT
10_1101-2021_01_08_425885	300	33	Second	Second	NNP
10_1101-2021_01_08_425885	300	34	Fundamental	Fundamental	NNP
10_1101-2021_01_08_425885	300	35	Form	Form	NNP
10_1101-2021_01_08_425885	300	36	.	.	.
10_1101-2021_01_08_425885	301	1	For	for	IN
10_1101-2021_01_08_425885	301	2	the	the	DT
10_1101-2021_01_08_425885	301	3	PBMC	PBMC	NNP
10_1101-2021_01_08_425885	301	4	dataset	dataset	NN
10_1101-2021_01_08_425885	301	5	,	,	,
10_1101-2021_01_08_425885	301	6	we	-PRON-	PRP
10_1101-2021_01_08_425885	301	7	additionally	additionally	RB
10_1101-2021_01_08_425885	301	8	downsampled	downsample	VBD
10_1101-2021_01_08_425885	301	9	the	the	DT
10_1101-2021_01_08_425885	301	10	single	single	JJ
10_1101-2021_01_08_425885	301	11	-	-	HYPH
10_1101-2021_01_08_425885	301	12	cell	cell	NN
10_1101-2021_01_08_425885	301	13	count	count	NN
10_1101-2021_01_08_425885	301	14	matrix	matrix	NN
10_1101-2021_01_08_425885	301	15	by	by	IN
10_1101-2021_01_08_425885	301	16	discarding	discard	VBG
10_1101-2021_01_08_425885	301	17	f%	f%	NN
10_1101-2021_01_08_425885	301	18	of	of	IN
10_1101-2021_01_08_425885	301	19	transcripts	transcript	NNS
10_1101-2021_01_08_425885	301	20	at	at	IN
10_1101-2021_01_08_425885	301	21	random	random	JJ
10_1101-2021_01_08_425885	301	22	and	and	CC
10_1101-2021_01_08_425885	301	23	preprocessing	preprocesse	VBG
10_1101-2021_01_08_425885	301	24	the	the	DT
10_1101-2021_01_08_425885	301	25	same	same	JJ
10_1101-2021_01_08_425885	301	26	way	way	NN
10_1101-2021_01_08_425885	301	27	.	.	.
10_1101-2021_01_08_425885	302	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	302	2	recomputed	recompute	VBD
10_1101-2021_01_08_425885	302	3	scalar	scalar	JJ
10_1101-2021_01_08_425885	302	4	curvatures	curvature	NNS
10_1101-2021_01_08_425885	302	5	for	for	IN
10_1101-2021_01_08_425885	302	6	this	this	DT
10_1101-2021_01_08_425885	302	7	downsam-	downsam-	NN
10_1101-2021_01_08_425885	302	8	pled	plead	VBN
10_1101-2021_01_08_425885	302	9	dataset	dataset	NNP
10_1101-2021_01_08_425885	302	10	with	with	IN
10_1101-2021_01_08_425885	302	11	the	the	DT
10_1101-2021_01_08_425885	302	12	same	same	JJ
10_1101-2021_01_08_425885	302	13	n	n	NN
10_1101-2021_01_08_425885	302	14	,	,	,
10_1101-2021_01_08_425885	302	15	d	d	NN
10_1101-2021_01_08_425885	302	16	and	and	CC
10_1101-2021_01_08_425885	302	17	r(p	r(p	NNP
10_1101-2021_01_08_425885	302	18	)	)	-RRB-
10_1101-2021_01_08_425885	302	19	values	value	NNS
10_1101-2021_01_08_425885	302	20	used	use	VBN
10_1101-2021_01_08_425885	302	21	for	for	IN
10_1101-2021_01_08_425885	302	22	the	the	DT
10_1101-2021_01_08_425885	302	23	original	original	JJ
10_1101-2021_01_08_425885	302	24	dataset	dataset	NN
10_1101-2021_01_08_425885	302	25	.	.	.
10_1101-2021_01_08_425885	303	1	Here	here	RB
10_1101-2021_01_08_425885	303	2	too	too	RB
10_1101-2021_01_08_425885	303	3	,	,	,
10_1101-2021_01_08_425885	303	4	we	-PRON-	PRP
10_1101-2021_01_08_425885	303	5	found	find	VBD
10_1101-2021_01_08_425885	303	6	that	that	IN
10_1101-2021_01_08_425885	303	7	when	when	WRB
10_1101-2021_01_08_425885	303	8	f	f	NNP
10_1101-2021_01_08_425885	303	9	=	=	SYM
10_1101-2021_01_08_425885	303	10	50	50	CD
10_1101-2021_01_08_425885	303	11	(	(	-LRB-
10_1101-2021_01_08_425885	303	12	f	f	NNP
10_1101-2021_01_08_425885	303	13	=	=	SYM
10_1101-2021_01_08_425885	303	14	75	75	CD
10_1101-2021_01_08_425885	303	15	)	)	-RRB-
10_1101-2021_01_08_425885	303	16	,	,	,
10_1101-2021_01_08_425885	303	17	70	70	CD
10_1101-2021_01_08_425885	303	18	%	%	NN
10_1101-2021_01_08_425885	303	19	(	(	-LRB-
10_1101-2021_01_08_425885	303	20	65	65	CD
10_1101-2021_01_08_425885	303	21	%	%	NN
10_1101-2021_01_08_425885	303	22	)	)	-RRB-
10_1101-2021_01_08_425885	303	23	of	of	IN
10_1101-2021_01_08_425885	303	24	the	the	DT
10_1101-2021_01_08_425885	303	25	downsampled	downsampled	JJ
10_1101-2021_01_08_425885	303	26	points	point	NNS
10_1101-2021_01_08_425885	303	27	had	have	VBD
10_1101-2021_01_08_425885	303	28	a	a	DT
10_1101-2021_01_08_425885	303	29	95	95	CD
10_1101-2021_01_08_425885	303	30	%	%	NN
10_1101-2021_01_08_425885	303	31	CI	ci	NN
10_1101-2021_01_08_425885	303	32	containing	contain	VBG
10_1101-2021_01_08_425885	303	33	the	the	DT
10_1101-2021_01_08_425885	303	34	originally	originally	RB
10_1101-2021_01_08_425885	303	35	reported	report	VBN
10_1101-2021_01_08_425885	303	36	scalar	scalar	JJ
10_1101-2021_01_08_425885	303	37	curvature	curvature	NN
10_1101-2021_01_08_425885	303	38	(	(	-LRB-
10_1101-2021_01_08_425885	303	39	p	p	NN
10_1101-2021_01_08_425885	303	40	<	<	XX
10_1101-2021_01_08_425885	303	41	0.001	0.001	CD
10_1101-2021_01_08_425885	303	42	,	,	,
10_1101-2021_01_08_425885	303	43	see	see	VB
10_1101-2021_01_08_425885	303	44	Figure	figure	NN
10_1101-2021_01_08_425885	303	45	S4J	s4j	NN
10_1101-2021_01_08_425885	303	46	;	;	:
10_1101-2021_01_08_425885	303	47	Methods	Methods	NNP
10_1101-2021_01_08_425885	303	48	Section	Section	NNP
10_1101-2021_01_08_425885	303	49	4.6.3.3	4.6.3.3	CD
10_1101-2021_01_08_425885	303	50	)	)	-RRB-
10_1101-2021_01_08_425885	303	51	.	.	.
10_1101-2021_01_08_425885	304	1	Therefore	therefore	RB
10_1101-2021_01_08_425885	304	2	,	,	,
10_1101-2021_01_08_425885	304	3	the	the	DT
10_1101-2021_01_08_425885	304	4	computed	compute	VBN
10_1101-2021_01_08_425885	304	5	scalar	scalar	JJ
10_1101-2021_01_08_425885	304	6	cur-	cur-	NN
10_1101-2021_01_08_425885	304	7	vature	vature	NN
10_1101-2021_01_08_425885	304	8	is	be	VBZ
10_1101-2021_01_08_425885	304	9	robust	robust	JJ
10_1101-2021_01_08_425885	304	10	to	to	IN
10_1101-2021_01_08_425885	304	11	changes	change	NNS
10_1101-2021_01_08_425885	304	12	in	in	IN
10_1101-2021_01_08_425885	304	13	capture	capture	NN
10_1101-2021_01_08_425885	304	14	efficiency	efficiency	NN
10_1101-2021_01_08_425885	304	15	and	and	CC
10_1101-2021_01_08_425885	304	16	sequencing	sequence	VBG
10_1101-2021_01_08_425885	304	17	depth	depth	NN
10_1101-2021_01_08_425885	304	18	.	.	.
10_1101-2021_01_08_425885	305	1	Taken	take	VBN
10_1101-2021_01_08_425885	305	2	together	together	RB
10_1101-2021_01_08_425885	305	3	,	,	,
10_1101-2021_01_08_425885	305	4	our	-PRON-	PRP$
10_1101-2021_01_08_425885	305	5	computational	computational	JJ
10_1101-2021_01_08_425885	305	6	analysis	analysis	NN
10_1101-2021_01_08_425885	305	7	reveals	reveal	VBZ
10_1101-2021_01_08_425885	305	8	non	non	JJ
10_1101-2021_01_08_425885	305	9	-	-	JJ
10_1101-2021_01_08_425885	305	10	trivial	trivial	JJ
10_1101-2021_01_08_425885	305	11	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	305	12	geometry	geometry	NN
10_1101-2021_01_08_425885	305	13	in	in	IN
10_1101-2021_01_08_425885	305	14	scRNAseq	scrnaseq	JJ
10_1101-2021_01_08_425885	305	15	data	datum	NNS
10_1101-2021_01_08_425885	305	16	.	.	.
10_1101-2021_01_08_425885	306	1	3	3	CD
10_1101-2021_01_08_425885	306	2	Discussion	Discussion	NNP
10_1101-2021_01_08_425885	306	3	In	in	IN
10_1101-2021_01_08_425885	306	4	this	this	DT
10_1101-2021_01_08_425885	306	5	study	study	NN
10_1101-2021_01_08_425885	306	6	,	,	,
10_1101-2021_01_08_425885	306	7	we	-PRON-	PRP
10_1101-2021_01_08_425885	306	8	explored	explore	VBD
10_1101-2021_01_08_425885	306	9	two	two	CD
10_1101-2021_01_08_425885	306	10	approaches	approach	NNS
10_1101-2021_01_08_425885	306	11	to	to	IN
10_1101-2021_01_08_425885	306	12	computing	compute	VBG
10_1101-2021_01_08_425885	306	13	the	the	DT
10_1101-2021_01_08_425885	306	14	curvature	curvature	NN
10_1101-2021_01_08_425885	306	15	of	of	IN
10_1101-2021_01_08_425885	306	16	data	datum	NNS
10_1101-2021_01_08_425885	306	17	manifolds	manifold	NNS
10_1101-2021_01_08_425885	306	18	using	use	VBG
10_1101-2021_01_08_425885	306	19	tools	tool	NNS
10_1101-2021_01_08_425885	306	20	from	from	IN
10_1101-2021_01_08_425885	306	21	twin	twin	JJ
10_1101-2021_01_08_425885	306	22	branches	branch	NNS
10_1101-2021_01_08_425885	306	23	of	of	IN
10_1101-2021_01_08_425885	306	24	differential	differential	NN
10_1101-2021_01_08_425885	306	25	geometry	geometry	NN
10_1101-2021_01_08_425885	306	26	.	.	.
10_1101-2021_01_08_425885	307	1	Despite	despite	IN
10_1101-2021_01_08_425885	307	2	the	the	DT
10_1101-2021_01_08_425885	307	3	prevalence	prevalence	NN
10_1101-2021_01_08_425885	307	4	of	of	IN
10_1101-2021_01_08_425885	307	5	the	the	DT
10_1101-2021_01_08_425885	307	6	Laplace	Laplace	NNP
10_1101-2021_01_08_425885	307	7	-	-	HYPH
10_1101-2021_01_08_425885	307	8	Beltrami	Beltrami	NNP
10_1101-2021_01_08_425885	307	9	operator	operator	NN
10_1101-2021_01_08_425885	307	10	in	in	IN
10_1101-2021_01_08_425885	307	11	geometric	geometric	JJ
10_1101-2021_01_08_425885	307	12	data	datum	NNS
10_1101-2021_01_08_425885	307	13	analysis	analysis	NN
10_1101-2021_01_08_425885	307	14	[	[	-LRB-
10_1101-2021_01_08_425885	307	15	14	14	CD
10_1101-2021_01_08_425885	307	16	,	,	,
10_1101-2021_01_08_425885	307	17	26	26	CD
10_1101-2021_01_08_425885	307	18	,	,	,
10_1101-2021_01_08_425885	307	19	27	27	CD
10_1101-2021_01_08_425885	307	20	,	,	,
10_1101-2021_01_08_425885	307	21	28	28	CD
10_1101-2021_01_08_425885	307	22	,	,	,
10_1101-2021_01_08_425885	307	23	29	29	CD
10_1101-2021_01_08_425885	307	24	]	]	-RRB-
10_1101-2021_01_08_425885	307	25	,	,	,
10_1101-2021_01_08_425885	307	26	an	an	DT
10_1101-2021_01_08_425885	307	27	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	307	28	approach	approach	NN
10_1101-2021_01_08_425885	307	29	to	to	IN
10_1101-2021_01_08_425885	307	30	computing	compute	VBG
10_1101-2021_01_08_425885	307	31	scalar	scalar	JJ
10_1101-2021_01_08_425885	307	32	curvature	curvature	NN
10_1101-2021_01_08_425885	307	33	relying	relying	NN
10_1101-2021_01_08_425885	307	34	on	on	IN
10_1101-2021_01_08_425885	307	35	this	this	DT
10_1101-2021_01_08_425885	307	36	operator	operator	NN
10_1101-2021_01_08_425885	307	37	’s	’s	POS
10_1101-2021_01_08_425885	307	38	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	307	39	was	be	VBD
10_1101-2021_01_08_425885	307	40	determined	determined	JJ
10_1101-2021_01_08_425885	307	41	to	to	TO
10_1101-2021_01_08_425885	307	42	be	be	VB
10_1101-2021_01_08_425885	307	43	infeasible	infeasible	JJ
10_1101-2021_01_08_425885	307	44	for	for	IN
10_1101-2021_01_08_425885	307	45	sample	sample	NN
10_1101-2021_01_08_425885	307	46	sizes	size	NNS
10_1101-2021_01_08_425885	307	47	of	of	IN
10_1101-2021_01_08_425885	307	48	N	N	NNP
10_1101-2021_01_08_425885	307	49	≈	≈	NNP
10_1101-2021_01_08_425885	307	50	104	104	CD
10_1101-2021_01_08_425885	307	51	typical	typical	JJ
10_1101-2021_01_08_425885	307	52	of	of	IN
10_1101-2021_01_08_425885	307	53	current	current	JJ
10_1101-2021_01_08_425885	307	54	scRNAseq	scrnaseq	JJ
10_1101-2021_01_08_425885	307	55	datasets	dataset	NNS
10_1101-2021_01_08_425885	307	56	.	.	.
10_1101-2021_01_08_425885	308	1	Although	although	IN
10_1101-2021_01_08_425885	308	2	methods	method	NNS
10_1101-2021_01_08_425885	308	3	such	such	JJ
10_1101-2021_01_08_425885	308	4	as	as	IN
10_1101-2021_01_08_425885	308	5	MAGIC	magic	NN
10_1101-2021_01_08_425885	308	6	[	[	-LRB-
10_1101-2021_01_08_425885	308	7	45	45	CD
10_1101-2021_01_08_425885	308	8	]	]	-RRB-
10_1101-2021_01_08_425885	308	9	and	and	CC
10_1101-2021_01_08_425885	308	10	diffusion	diffusion	NN
10_1101-2021_01_08_425885	308	11	pseudotime	pseudotime	NN
10_1101-2021_01_08_425885	308	12	[	[	-LRB-
10_1101-2021_01_08_425885	308	13	46	46	CD
10_1101-2021_01_08_425885	308	14	]	]	-RRB-
10_1101-2021_01_08_425885	308	15	apply	apply	VB
10_1101-2021_01_08_425885	308	16	the	the	DT
10_1101-2021_01_08_425885	308	17	Laplace	Laplace	NNP
10_1101-2021_01_08_425885	308	18	-	-	HYPH
10_1101-2021_01_08_425885	308	19	Beltrami	Beltrami	NNP
10_1101-2021_01_08_425885	308	20	operator	operator	NN
10_1101-2021_01_08_425885	308	21	to	to	TO
10_1101-2021_01_08_425885	308	22	smooth	smooth	VB
10_1101-2021_01_08_425885	308	23	scRNAseq	scrnaseq	JJ
10_1101-2021_01_08_425885	308	24	data	datum	NNS
10_1101-2021_01_08_425885	308	25	and	and	CC
10_1101-2021_01_08_425885	308	26	infer	infer	JJ
10_1101-2021_01_08_425885	308	27	cell	cell	NN
10_1101-2021_01_08_425885	308	28	differentiation	differentiation	NN
10_1101-2021_01_08_425885	308	29	trajectories	trajectory	NNS
10_1101-2021_01_08_425885	308	30	respectively	respectively	RB
10_1101-2021_01_08_425885	308	31	,	,	,
10_1101-2021_01_08_425885	308	32	using	use	VBG
10_1101-2021_01_08_425885	308	33	information	information	NN
10_1101-2021_01_08_425885	308	34	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	308	35	to	to	IN
10_1101-2021_01_08_425885	308	36	the	the	DT
10_1101-2021_01_08_425885	308	37	manifold	manifold	NN
10_1101-2021_01_08_425885	308	38	,	,	,
10_1101-2021_01_08_425885	308	39	our	-PRON-	PRP$
10_1101-2021_01_08_425885	308	40	results	result	NNS
10_1101-2021_01_08_425885	308	41	suggest	suggest	VBP
10_1101-2021_01_08_425885	308	42	that	that	IN
10_1101-2021_01_08_425885	308	43	the	the	DT
10_1101-2021_01_08_425885	308	44	embedding	embedding	NN
10_1101-2021_01_08_425885	308	45	of	of	IN
10_1101-2021_01_08_425885	308	46	the	the	DT
10_1101-2021_01_08_425885	308	47	manifold	manifold	NN
10_1101-2021_01_08_425885	308	48	in	in	IN
10_1101-2021_01_08_425885	308	49	the	the	DT
10_1101-2021_01_08_425885	308	50	ambient	ambient	JJ
10_1101-2021_01_08_425885	308	51	space	space	NN
10_1101-2021_01_08_425885	308	52	provides	provide	VBZ
10_1101-2021_01_08_425885	308	53	valuable	valuable	JJ
10_1101-2021_01_08_425885	308	54	information	information	NN
10_1101-2021_01_08_425885	308	55	necessary	necessary	JJ
10_1101-2021_01_08_425885	308	56	for	for	IN
10_1101-2021_01_08_425885	308	57	estimating	estimate	VBG
10_1101-2021_01_08_425885	308	58	the	the	DT
10_1101-2021_01_08_425885	308	59	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	308	60	curvature	curvature	NN
10_1101-2021_01_08_425885	308	61	.	.	.
10_1101-2021_01_08_425885	309	1	This	this	DT
10_1101-2021_01_08_425885	309	2	observation	observation	NN
10_1101-2021_01_08_425885	309	3	is	be	VBZ
10_1101-2021_01_08_425885	309	4	perhaps	perhaps	RB
10_1101-2021_01_08_425885	309	5	implicit	implicit	JJ
10_1101-2021_01_08_425885	309	6	in	in	IN
10_1101-2021_01_08_425885	309	7	recent	recent	JJ
10_1101-2021_01_08_425885	309	8	tools	tool	NNS
10_1101-2021_01_08_425885	309	9	for	for	IN
10_1101-2021_01_08_425885	309	10	estimating	estimate	VBG
10_1101-2021_01_08_425885	309	11	the	the	DT
10_1101-2021_01_08_425885	309	12	Laplace	Laplace	NNP
10_1101-2021_01_08_425885	309	13	-	-	HYPH
10_1101-2021_01_08_425885	309	14	Beltrami	Beltrami	NNP
10_1101-2021_01_08_425885	309	15	operator	operator	NN
10_1101-2021_01_08_425885	309	16	,	,	,
10_1101-2021_01_08_425885	309	17	which	which	WDT
10_1101-2021_01_08_425885	309	18	first	first	RB
10_1101-2021_01_08_425885	309	19	use	use	VBP
10_1101-2021_01_08_425885	309	20	moving	move	VBG
10_1101-2021_01_08_425885	309	21	local	local	JJ
10_1101-2021_01_08_425885	309	22	least	least	JJS
10_1101-2021_01_08_425885	309	23	-	-	HYPH
10_1101-2021_01_08_425885	309	24	squares	square	NNS
10_1101-2021_01_08_425885	309	25	to	to	TO
10_1101-2021_01_08_425885	309	26	approximate	approximate	VB
10_1101-2021_01_08_425885	309	27	a	a	DT
10_1101-2021_01_08_425885	309	28	surface	surface	NN
10_1101-2021_01_08_425885	309	29	,	,	,
10_1101-2021_01_08_425885	309	30	thereby	thereby	RB
10_1101-2021_01_08_425885	309	31	incorporating	incorporate	VBG
10_1101-2021_01_08_425885	309	32	information	information	NN
10_1101-2021_01_08_425885	309	33	from	from	IN
10_1101-2021_01_08_425885	309	34	the	the	DT
10_1101-2021_01_08_425885	309	35	ambient	ambient	JJ
10_1101-2021_01_08_425885	309	36	space	space	NN
10_1101-2021_01_08_425885	309	37	[	[	-LRB-
10_1101-2021_01_08_425885	309	38	29	29	CD
10_1101-2021_01_08_425885	309	39	]	]	-RRB-
10_1101-2021_01_08_425885	309	40	.	.	.
10_1101-2021_01_08_425885	310	1	18	18	CD
10_1101-2021_01_08_425885	310	2	.CC	.CC	:
10_1101-2021_01_08_425885	310	3	-	-	HYPH
10_1101-2021_01_08_425885	310	4	BY	by	IN
10_1101-2021_01_08_425885	310	5	-	-	HYPH
10_1101-2021_01_08_425885	310	6	NC	NC	NNP
10_1101-2021_01_08_425885	310	7	-	-	HYPH
10_1101-2021_01_08_425885	310	8	ND	ND	NNP
10_1101-2021_01_08_425885	310	9	4.0	4.0	CD
10_1101-2021_01_08_425885	310	10	International	International	NNP
10_1101-2021_01_08_425885	310	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	310	12	under	under	IN
10_1101-2021_01_08_425885	310	13	a	a	DT
10_1101-2021_01_08_425885	310	14	(	(	-LRB-
10_1101-2021_01_08_425885	310	15	which	which	WDT
10_1101-2021_01_08_425885	310	16	was	be	VBD
10_1101-2021_01_08_425885	310	17	not	not	RB
10_1101-2021_01_08_425885	310	18	certified	certify	VBN
10_1101-2021_01_08_425885	310	19	by	by	IN
10_1101-2021_01_08_425885	310	20	peer	peer	NN
10_1101-2021_01_08_425885	310	21	review	review	NN
10_1101-2021_01_08_425885	310	22	)	)	-RRB-
10_1101-2021_01_08_425885	310	23	is	be	VBZ
10_1101-2021_01_08_425885	310	24	the	the	DT
10_1101-2021_01_08_425885	310	25	author	author	NN
10_1101-2021_01_08_425885	310	26	/	/	SYM
10_1101-2021_01_08_425885	310	27	funder	funder	NN
10_1101-2021_01_08_425885	310	28	,	,	,
10_1101-2021_01_08_425885	310	29	who	who	WP
10_1101-2021_01_08_425885	310	30	has	have	VBZ
10_1101-2021_01_08_425885	310	31	granted	grant	VBN
10_1101-2021_01_08_425885	310	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	310	33	a	a	DT
10_1101-2021_01_08_425885	310	34	license	license	NN
10_1101-2021_01_08_425885	310	35	to	to	TO
10_1101-2021_01_08_425885	310	36	display	display	VB
10_1101-2021_01_08_425885	310	37	the	the	DT
10_1101-2021_01_08_425885	310	38	preprint	preprint	NN
10_1101-2021_01_08_425885	310	39	in	in	IN
10_1101-2021_01_08_425885	310	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	310	41	.	.	.
10_1101-2021_01_08_425885	311	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	311	2	is	be	VBZ
10_1101-2021_01_08_425885	311	3	made	make	VBN
10_1101-2021_01_08_425885	311	4	The	the	DT
10_1101-2021_01_08_425885	311	5	copyright	copyright	NN
10_1101-2021_01_08_425885	311	6	holder	holder	NN
10_1101-2021_01_08_425885	311	7	for	for	IN
10_1101-2021_01_08_425885	311	8	this	this	DT
10_1101-2021_01_08_425885	311	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	311	10	version	version	NN
10_1101-2021_01_08_425885	311	11	posted	post	VBD
10_1101-2021_01_08_425885	311	12	January	January	NNP
10_1101-2021_01_08_425885	311	13	8	8	CD
10_1101-2021_01_08_425885	311	14	,	,	,
10_1101-2021_01_08_425885	311	15	2021	2021	CD
10_1101-2021_01_08_425885	311	16	.	.	.
10_1101-2021_01_08_425885	311	17	;	;	:
10_1101-2021_01_08_425885	311	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	311	19	:	:	:
10_1101-2021_01_08_425885	311	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	311	21	preprint	preprint	NN
10_1101-2021_01_08_425885	311	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	311	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	RB
10_1101-2021_01_08_425885	311	24	Certainly	certainly	RB
10_1101-2021_01_08_425885	311	25	,	,	,
10_1101-2021_01_08_425885	311	26	we	-PRON-	PRP
10_1101-2021_01_08_425885	311	27	found	find	VBD
10_1101-2021_01_08_425885	311	28	that	that	IN
10_1101-2021_01_08_425885	311	29	an	an	DT
10_1101-2021_01_08_425885	311	30	extrinsic	extrinsic	JJ
10_1101-2021_01_08_425885	311	31	approach	approach	NN
10_1101-2021_01_08_425885	311	32	in	in	IN
10_1101-2021_01_08_425885	311	33	which	which	WDT
10_1101-2021_01_08_425885	311	34	the	the	DT
10_1101-2021_01_08_425885	311	35	embedding	embedding	NN
10_1101-2021_01_08_425885	311	36	is	be	VBZ
10_1101-2021_01_08_425885	311	37	retained	retain	VBN
10_1101-2021_01_08_425885	311	38	,	,	,
10_1101-2021_01_08_425885	311	39	and	and	CC
10_1101-2021_01_08_425885	311	40	curvature	curvature	NN
10_1101-2021_01_08_425885	311	41	is	be	VBZ
10_1101-2021_01_08_425885	311	42	determined	determine	VBN
10_1101-2021_01_08_425885	311	43	by	by	IN
10_1101-2021_01_08_425885	311	44	local	local	JJ
10_1101-2021_01_08_425885	311	45	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	311	46	fitting	fitting	NN
10_1101-2021_01_08_425885	311	47	of	of	IN
10_1101-2021_01_08_425885	311	48	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	311	49	in	in	IN
10_1101-2021_01_08_425885	311	50	ambient	ambient	JJ
10_1101-2021_01_08_425885	311	51	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	311	52	,	,	,
10_1101-2021_01_08_425885	311	53	is	be	VBZ
10_1101-2021_01_08_425885	311	54	feasible	feasible	JJ
10_1101-2021_01_08_425885	311	55	given	give	VBN
10_1101-2021_01_08_425885	311	56	the	the	DT
10_1101-2021_01_08_425885	311	57	sample	sample	NN
10_1101-2021_01_08_425885	311	58	size	size	NN
10_1101-2021_01_08_425885	311	59	and	and	CC
10_1101-2021_01_08_425885	311	60	degree	degree	NN
10_1101-2021_01_08_425885	311	61	of	of	IN
10_1101-2021_01_08_425885	311	62	noise	noise	NN
10_1101-2021_01_08_425885	311	63	in	in	IN
10_1101-2021_01_08_425885	311	64	real	real	JJ
10_1101-2021_01_08_425885	311	65	-	-	HYPH
10_1101-2021_01_08_425885	311	66	world	world	NN
10_1101-2021_01_08_425885	311	67	datasets	dataset	NNS
10_1101-2021_01_08_425885	311	68	.	.	.
10_1101-2021_01_08_425885	312	1	To	to	TO
10_1101-2021_01_08_425885	312	2	obtain	obtain	VB
10_1101-2021_01_08_425885	312	3	the	the	DT
10_1101-2021_01_08_425885	312	4	scalar	scalar	JJ
10_1101-2021_01_08_425885	312	5	curvature	curvature	NN
10_1101-2021_01_08_425885	312	6	of	of	IN
10_1101-2021_01_08_425885	312	7	data	datum	NNS
10_1101-2021_01_08_425885	312	8	manifolds	manifold	NNS
10_1101-2021_01_08_425885	312	9	,	,	,
10_1101-2021_01_08_425885	312	10	our	-PRON-	PRP$
10_1101-2021_01_08_425885	312	11	algorithm	algorithm	NNP
10_1101-2021_01_08_425885	312	12	first	first	RB
10_1101-2021_01_08_425885	312	13	computes	compute	VBZ
10_1101-2021_01_08_425885	312	14	the	the	DT
10_1101-2021_01_08_425885	312	15	full	full	JJ
10_1101-2021_01_08_425885	312	16	Riemannian	riemannian	JJ
10_1101-2021_01_08_425885	312	17	curvature	curvature	NN
10_1101-2021_01_08_425885	312	18	tensor	tensor	NN
10_1101-2021_01_08_425885	312	19	.	.	.
10_1101-2021_01_08_425885	313	1	For	for	IN
10_1101-2021_01_08_425885	313	2	other	other	JJ
10_1101-2021_01_08_425885	313	3	applications	application	NNS
10_1101-2021_01_08_425885	313	4	,	,	,
10_1101-2021_01_08_425885	313	5	this	this	DT
10_1101-2021_01_08_425885	313	6	tensor	tensor	NN
10_1101-2021_01_08_425885	313	7	can	can	MD
10_1101-2021_01_08_425885	313	8	be	be	VB
10_1101-2021_01_08_425885	313	9	used	use	VBN
10_1101-2021_01_08_425885	313	10	to	to	TO
10_1101-2021_01_08_425885	313	11	compute	compute	VB
10_1101-2021_01_08_425885	313	12	other	other	JJ
10_1101-2021_01_08_425885	313	13	geometric	geometric	JJ
10_1101-2021_01_08_425885	313	14	quantities	quantity	NNS
10_1101-2021_01_08_425885	313	15	,	,	,
10_1101-2021_01_08_425885	313	16	such	such	JJ
10_1101-2021_01_08_425885	313	17	as	as	IN
10_1101-2021_01_08_425885	313	18	Ricci	Ricci	NNP
10_1101-2021_01_08_425885	313	19	curvature	curvature	NN
10_1101-2021_01_08_425885	313	20	,	,	,
10_1101-2021_01_08_425885	313	21	or	or	CC
10_1101-2021_01_08_425885	313	22	may	may	MD
10_1101-2021_01_08_425885	313	23	itself	-PRON-	PRP
10_1101-2021_01_08_425885	313	24	be	be	VB
10_1101-2021_01_08_425885	313	25	of	of	IN
10_1101-2021_01_08_425885	313	26	interest	interest	NN
10_1101-2021_01_08_425885	313	27	.	.	.
10_1101-2021_01_08_425885	314	1	More	more	RBR
10_1101-2021_01_08_425885	314	2	generally	generally	RB
10_1101-2021_01_08_425885	314	3	,	,	,
10_1101-2021_01_08_425885	314	4	we	-PRON-	PRP
10_1101-2021_01_08_425885	314	5	focused	focus	VBD
10_1101-2021_01_08_425885	314	6	on	on	IN
10_1101-2021_01_08_425885	314	7	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	314	8	curvature	curvature	NN
10_1101-2021_01_08_425885	314	9	because	because	IN
10_1101-2021_01_08_425885	314	10	we	-PRON-	PRP
10_1101-2021_01_08_425885	314	11	were	be	VBD
10_1101-2021_01_08_425885	314	12	interested	interested	JJ
10_1101-2021_01_08_425885	314	13	in	in	IN
10_1101-2021_01_08_425885	314	14	geometric	geometric	JJ
10_1101-2021_01_08_425885	314	15	properties	property	NNS
10_1101-2021_01_08_425885	314	16	of	of	IN
10_1101-2021_01_08_425885	314	17	the	the	DT
10_1101-2021_01_08_425885	314	18	manifolds	manifold	NNS
10_1101-2021_01_08_425885	314	19	independent	independent	JJ
10_1101-2021_01_08_425885	314	20	of	of	IN
10_1101-2021_01_08_425885	314	21	their	-PRON-	PRP$
10_1101-2021_01_08_425885	314	22	embeddings	embedding	NNS
10_1101-2021_01_08_425885	314	23	.	.	.
10_1101-2021_01_08_425885	315	1	However	however	RB
10_1101-2021_01_08_425885	315	2	,	,	,
10_1101-2021_01_08_425885	315	3	the	the	DT
10_1101-2021_01_08_425885	315	4	Second	Second	NNP
10_1101-2021_01_08_425885	315	5	Fundamental	Fundamental	NNP
10_1101-2021_01_08_425885	315	6	Form	Form	NNP
10_1101-2021_01_08_425885	315	7	used	use	VBD
10_1101-2021_01_08_425885	315	8	in	in	IN
10_1101-2021_01_08_425885	315	9	our	-PRON-	PRP$
10_1101-2021_01_08_425885	315	10	approach	approach	NN
10_1101-2021_01_08_425885	315	11	to	to	TO
10_1101-2021_01_08_425885	315	12	compute	compute	VB
10_1101-2021_01_08_425885	315	13	the	the	DT
10_1101-2021_01_08_425885	315	14	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	315	15	curvature	curvature	NN
10_1101-2021_01_08_425885	315	16	can	can	MD
10_1101-2021_01_08_425885	315	17	be	be	VB
10_1101-2021_01_08_425885	315	18	used	use	VBN
10_1101-2021_01_08_425885	315	19	to	to	TO
10_1101-2021_01_08_425885	315	20	obtain	obtain	VB
10_1101-2021_01_08_425885	315	21	all	all	PDT
10_1101-2021_01_08_425885	315	22	the	the	DT
10_1101-2021_01_08_425885	315	23	information	information	NN
10_1101-2021_01_08_425885	315	24	about	about	IN
10_1101-2021_01_08_425885	315	25	the	the	DT
10_1101-2021_01_08_425885	315	26	extrinsic	extrinsic	NN
10_1101-2021_01_08_425885	315	27	curvature	curvature	NN
10_1101-2021_01_08_425885	315	28	as	as	RB
10_1101-2021_01_08_425885	315	29	well	well	RB
10_1101-2021_01_08_425885	315	30	.	.	.
10_1101-2021_01_08_425885	316	1	Indeed	indeed	RB
10_1101-2021_01_08_425885	316	2	,	,	,
10_1101-2021_01_08_425885	316	3	hkij(p	hkij(p	ADD
10_1101-2021_01_08_425885	316	4	)	)	-RRB-
10_1101-2021_01_08_425885	316	5	exactly	exactly	RB
10_1101-2021_01_08_425885	316	6	quantifies	quantify	VBZ
10_1101-2021_01_08_425885	316	7	the	the	DT
10_1101-2021_01_08_425885	316	8	extent	extent	NN
10_1101-2021_01_08_425885	316	9	to	to	TO
10_1101-2021_01_08_425885	316	10	which	which	WDT
10_1101-2021_01_08_425885	316	11	the	the	DT
10_1101-2021_01_08_425885	316	12	manifold	manifold	JJ
10_1101-2021_01_08_425885	316	13	deviates	deviate	NNS
10_1101-2021_01_08_425885	316	14	in	in	IN
10_1101-2021_01_08_425885	316	15	the	the	DT
10_1101-2021_01_08_425885	316	16	kth	kth	JJ
10_1101-2021_01_08_425885	316	17	normal	normal	JJ
10_1101-2021_01_08_425885	316	18	direction	direction	NN
10_1101-2021_01_08_425885	316	19	from	from	IN
10_1101-2021_01_08_425885	316	20	the	the	DT
10_1101-2021_01_08_425885	316	21	ij	ij	JJ
10_1101-2021_01_08_425885	316	22	-	-	HYPH
10_1101-2021_01_08_425885	316	23	tangent	tangent	JJ
10_1101-2021_01_08_425885	316	24	plane	plane	NN
10_1101-2021_01_08_425885	316	25	at	at	IN
10_1101-2021_01_08_425885	316	26	point	point	NN
10_1101-2021_01_08_425885	316	27	p.	p.	NN
10_1101-2021_01_08_425885	316	28	A	a	DT
10_1101-2021_01_08_425885	316	29	key	key	JJ
10_1101-2021_01_08_425885	316	30	limitation	limitation	NN
10_1101-2021_01_08_425885	316	31	of	of	IN
10_1101-2021_01_08_425885	316	32	our	-PRON-	PRP$
10_1101-2021_01_08_425885	316	33	algorithm	algorithm	NN
10_1101-2021_01_08_425885	316	34	is	be	VBZ
10_1101-2021_01_08_425885	316	35	that	that	IN
10_1101-2021_01_08_425885	316	36	the	the	DT
10_1101-2021_01_08_425885	316	37	manifold	manifold	JJ
10_1101-2021_01_08_425885	316	38	dimension	dimension	NN
10_1101-2021_01_08_425885	316	39	must	must	MD
10_1101-2021_01_08_425885	316	40	be	be	VB
10_1101-2021_01_08_425885	316	41	specified	specify	VBN
10_1101-2021_01_08_425885	316	42	by	by	IN
10_1101-2021_01_08_425885	316	43	the	the	DT
10_1101-2021_01_08_425885	316	44	user	user	NN
10_1101-2021_01_08_425885	316	45	.	.	.
10_1101-2021_01_08_425885	317	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	317	2	also	also	RB
10_1101-2021_01_08_425885	317	3	assumed	assume	VBD
10_1101-2021_01_08_425885	317	4	that	that	IN
10_1101-2021_01_08_425885	317	5	the	the	DT
10_1101-2021_01_08_425885	317	6	manifold	manifold	JJ
10_1101-2021_01_08_425885	317	7	dimension	dimension	NN
10_1101-2021_01_08_425885	317	8	is	be	VBZ
10_1101-2021_01_08_425885	317	9	the	the	DT
10_1101-2021_01_08_425885	317	10	same	same	JJ
10_1101-2021_01_08_425885	317	11	at	at	IN
10_1101-2021_01_08_425885	317	12	every	every	DT
10_1101-2021_01_08_425885	317	13	point	point	NN
10_1101-2021_01_08_425885	317	14	in	in	IN
10_1101-2021_01_08_425885	317	15	a	a	DT
10_1101-2021_01_08_425885	317	16	dataset	dataset	NN
10_1101-2021_01_08_425885	317	17	.	.	.
10_1101-2021_01_08_425885	318	1	Extending	extend	VBG
10_1101-2021_01_08_425885	318	2	the	the	DT
10_1101-2021_01_08_425885	318	3	algorithm	algorithm	NN
10_1101-2021_01_08_425885	318	4	to	to	TO
10_1101-2021_01_08_425885	318	5	determine	determine	VB
10_1101-2021_01_08_425885	318	6	the	the	DT
10_1101-2021_01_08_425885	318	7	manifold	manifold	JJ
10_1101-2021_01_08_425885	318	8	dimension	dimension	NN
10_1101-2021_01_08_425885	318	9	from	from	IN
10_1101-2021_01_08_425885	318	10	the	the	DT
10_1101-2021_01_08_425885	318	11	data	datum	NNS
10_1101-2021_01_08_425885	318	12	itself	-PRON-	PRP
10_1101-2021_01_08_425885	318	13	,	,	,
10_1101-2021_01_08_425885	318	14	potentially	potentially	RB
10_1101-2021_01_08_425885	318	15	in	in	IN
10_1101-2021_01_08_425885	318	16	a	a	DT
10_1101-2021_01_08_425885	318	17	position	position	NN
10_1101-2021_01_08_425885	318	18	-	-	HYPH
10_1101-2021_01_08_425885	318	19	dependent	dependent	JJ
10_1101-2021_01_08_425885	318	20	manner	manner	NN
10_1101-2021_01_08_425885	318	21	,	,	,
10_1101-2021_01_08_425885	318	22	may	may	MD
10_1101-2021_01_08_425885	318	23	prove	prove	VB
10_1101-2021_01_08_425885	318	24	useful	useful	JJ
10_1101-2021_01_08_425885	318	25	.	.	.
10_1101-2021_01_08_425885	319	1	In	in	IN
10_1101-2021_01_08_425885	319	2	addition	addition	NN
10_1101-2021_01_08_425885	319	3	,	,	,
10_1101-2021_01_08_425885	319	4	there	there	EX
10_1101-2021_01_08_425885	319	5	is	be	VBZ
10_1101-2021_01_08_425885	319	6	no	no	DT
10_1101-2021_01_08_425885	319	7	inherently	inherently	RB
10_1101-2021_01_08_425885	319	8	correct	correct	JJ
10_1101-2021_01_08_425885	319	9	length	length	NN
10_1101-2021_01_08_425885	319	10	scale	scale	NN
10_1101-2021_01_08_425885	319	11	over	over	IN
10_1101-2021_01_08_425885	319	12	which	which	WDT
10_1101-2021_01_08_425885	319	13	curvature	curvature	NN
10_1101-2021_01_08_425885	319	14	should	should	MD
10_1101-2021_01_08_425885	319	15	be	be	VB
10_1101-2021_01_08_425885	319	16	computed	compute	VBN
10_1101-2021_01_08_425885	319	17	for	for	IN
10_1101-2021_01_08_425885	319	18	a	a	DT
10_1101-2021_01_08_425885	319	19	data	data	NN
10_1101-2021_01_08_425885	319	20	manifold	manifold	NN
10_1101-2021_01_08_425885	319	21	.	.	.
10_1101-2021_01_08_425885	320	1	Our	-PRON-	PRP$
10_1101-2021_01_08_425885	320	2	algorithm	algorithm	NN
10_1101-2021_01_08_425885	320	3	chooses	choose	VBZ
10_1101-2021_01_08_425885	320	4	a	a	DT
10_1101-2021_01_08_425885	320	5	length	length	NN
10_1101-2021_01_08_425885	320	6	scale	scale	NN
10_1101-2021_01_08_425885	320	7	that	that	WDT
10_1101-2021_01_08_425885	320	8	varies	vary	VBZ
10_1101-2021_01_08_425885	320	9	from	from	IN
10_1101-2021_01_08_425885	320	10	one	one	CD
10_1101-2021_01_08_425885	320	11	part	part	NN
10_1101-2021_01_08_425885	320	12	of	of	IN
10_1101-2021_01_08_425885	320	13	the	the	DT
10_1101-2021_01_08_425885	320	14	data	datum	NNS
10_1101-2021_01_08_425885	320	15	manifold	manifold	NN
10_1101-2021_01_08_425885	320	16	to	to	IN
10_1101-2021_01_08_425885	320	17	another	another	DT
10_1101-2021_01_08_425885	320	18	according	accord	VBG
10_1101-2021_01_08_425885	320	19	to	to	IN
10_1101-2021_01_08_425885	320	20	the	the	DT
10_1101-2021_01_08_425885	320	21	density	density	NN
10_1101-2021_01_08_425885	320	22	of	of	IN
10_1101-2021_01_08_425885	320	23	points	point	NNS
10_1101-2021_01_08_425885	320	24	,	,	,
10_1101-2021_01_08_425885	320	25	and	and	CC
10_1101-2021_01_08_425885	320	26	is	be	VBZ
10_1101-2021_01_08_425885	320	27	tuned	tune	VBN
10_1101-2021_01_08_425885	320	28	to	to	TO
10_1101-2021_01_08_425885	320	29	achieve	achieve	VB
10_1101-2021_01_08_425885	320	30	a	a	DT
10_1101-2021_01_08_425885	320	31	user	user	NN
10_1101-2021_01_08_425885	320	32	-	-	HYPH
10_1101-2021_01_08_425885	320	33	specified	specify	VBN
10_1101-2021_01_08_425885	320	34	level	level	NN
10_1101-2021_01_08_425885	320	35	of	of	IN
10_1101-2021_01_08_425885	320	36	uncertainty	uncertainty	NN
10_1101-2021_01_08_425885	320	37	in	in	IN
10_1101-2021_01_08_425885	320	38	the	the	DT
10_1101-2021_01_08_425885	320	39	computed	compute	VBN
10_1101-2021_01_08_425885	320	40	curvature	curvature	NN
10_1101-2021_01_08_425885	320	41	.	.	.
10_1101-2021_01_08_425885	321	1	For	for	IN
10_1101-2021_01_08_425885	321	2	some	some	DT
10_1101-2021_01_08_425885	321	3	applications	application	NNS
10_1101-2021_01_08_425885	321	4	,	,	,
10_1101-2021_01_08_425885	321	5	it	-PRON-	PRP
10_1101-2021_01_08_425885	321	6	might	may	MD
10_1101-2021_01_08_425885	321	7	be	be	VB
10_1101-2021_01_08_425885	321	8	more	more	RBR
10_1101-2021_01_08_425885	321	9	sensible	sensible	JJ
10_1101-2021_01_08_425885	321	10	to	to	TO
10_1101-2021_01_08_425885	321	11	fix	fix	VB
10_1101-2021_01_08_425885	321	12	a	a	DT
10_1101-2021_01_08_425885	321	13	desired	desire	VBN
10_1101-2021_01_08_425885	321	14	length	length	NN
10_1101-2021_01_08_425885	321	15	scale	scale	NN
10_1101-2021_01_08_425885	321	16	for	for	IN
10_1101-2021_01_08_425885	321	17	computing	compute	VBG
10_1101-2021_01_08_425885	321	18	the	the	DT
10_1101-2021_01_08_425885	321	19	curvature	curvature	NN
10_1101-2021_01_08_425885	321	20	.	.	.
10_1101-2021_01_08_425885	322	1	As	as	IN
10_1101-2021_01_08_425885	322	2	a	a	DT
10_1101-2021_01_08_425885	322	3	demonstration	demonstration	NN
10_1101-2021_01_08_425885	322	4	of	of	IN
10_1101-2021_01_08_425885	322	5	our	-PRON-	PRP$
10_1101-2021_01_08_425885	322	6	algorithm	algorithm	NN
10_1101-2021_01_08_425885	322	7	,	,	,
10_1101-2021_01_08_425885	322	8	we	-PRON-	PRP
10_1101-2021_01_08_425885	322	9	computed	compute	VBD
10_1101-2021_01_08_425885	322	10	the	the	DT
10_1101-2021_01_08_425885	322	11	scalar	scalar	JJ
10_1101-2021_01_08_425885	322	12	curvature	curvature	NN
10_1101-2021_01_08_425885	322	13	of	of	IN
10_1101-2021_01_08_425885	322	14	image	image	NN
10_1101-2021_01_08_425885	322	15	patches	patch	NNS
10_1101-2021_01_08_425885	322	16	,	,	,
10_1101-2021_01_08_425885	322	17	and	and	CC
10_1101-2021_01_08_425885	322	18	found	find	VBD
10_1101-2021_01_08_425885	322	19	that	that	IN
10_1101-2021_01_08_425885	322	20	it	-PRON-	PRP
10_1101-2021_01_08_425885	322	21	was	be	VBD
10_1101-2021_01_08_425885	322	22	consistent	consistent	JJ
10_1101-2021_01_08_425885	322	23	with	with	IN
10_1101-2021_01_08_425885	322	24	that	that	DT
10_1101-2021_01_08_425885	322	25	of	of	IN
10_1101-2021_01_08_425885	322	26	a	a	DT
10_1101-2021_01_08_425885	322	27	Klein	Klein	NNP
10_1101-2021_01_08_425885	322	28	bottle	bottle	NN
10_1101-2021_01_08_425885	322	29	.	.	.
10_1101-2021_01_08_425885	323	1	This	this	DT
10_1101-2021_01_08_425885	323	2	observation	observation	NN
10_1101-2021_01_08_425885	323	3	further	further	RB
10_1101-2021_01_08_425885	323	4	validates	validate	VBZ
10_1101-2021_01_08_425885	323	5	the	the	DT
10_1101-2021_01_08_425885	323	6	claim	claim	NN
10_1101-2021_01_08_425885	323	7	by	by	IN
10_1101-2021_01_08_425885	323	8	Carlsson	Carlsson	NNP
10_1101-2021_01_08_425885	323	9	et	et	FW
10_1101-2021_01_08_425885	323	10	al	al	NNP
10_1101-2021_01_08_425885	323	11	.	.	.
10_1101-2021_01_08_425885	324	1	who	who	WP
10_1101-2021_01_08_425885	324	2	showed	show	VBD
10_1101-2021_01_08_425885	324	3	that	that	IN
10_1101-2021_01_08_425885	324	4	image	image	NN
10_1101-2021_01_08_425885	324	5	patches	patch	NNS
10_1101-2021_01_08_425885	324	6	have	have	VBP
10_1101-2021_01_08_425885	324	7	the	the	DT
10_1101-2021_01_08_425885	324	8	topology	topology	NN
10_1101-2021_01_08_425885	324	9	of	of	IN
10_1101-2021_01_08_425885	324	10	a	a	DT
10_1101-2021_01_08_425885	324	11	Klein	Klein	NNP
10_1101-2021_01_08_425885	324	12	bottle	bottle	NN
10_1101-2021_01_08_425885	324	13	[	[	-LRB-
10_1101-2021_01_08_425885	324	14	21	21	CD
10_1101-2021_01_08_425885	324	15	]	]	-RRB-
10_1101-2021_01_08_425885	324	16	.	.	.
10_1101-2021_01_08_425885	325	1	Unlike	unlike	IN
10_1101-2021_01_08_425885	325	2	the	the	DT
10_1101-2021_01_08_425885	325	3	Klein	Klein	NNP
10_1101-2021_01_08_425885	325	4	bottle	bottle	NN
10_1101-2021_01_08_425885	325	5	parameterization	parameterization	NN
10_1101-2021_01_08_425885	325	6	of	of	IN
10_1101-2021_01_08_425885	325	7	image	image	NN
10_1101-2021_01_08_425885	325	8	patches	patch	NNS
10_1101-2021_01_08_425885	325	9	however	however	RB
10_1101-2021_01_08_425885	325	10	,	,	,
10_1101-2021_01_08_425885	325	11	no	no	DT
10_1101-2021_01_08_425885	325	12	definitive	definitive	JJ
10_1101-2021_01_08_425885	325	13	analytical	analytical	JJ
10_1101-2021_01_08_425885	325	14	form	form	NN
10_1101-2021_01_08_425885	325	15	has	have	VBZ
10_1101-2021_01_08_425885	325	16	been	be	VBN
10_1101-2021_01_08_425885	325	17	established	establish	VBN
10_1101-2021_01_08_425885	325	18	for	for	IN
10_1101-2021_01_08_425885	325	19	scRNAseq	scrnaseq	JJ
10_1101-2021_01_08_425885	325	20	datasets	dataset	NNS
10_1101-2021_01_08_425885	325	21	.	.	.
10_1101-2021_01_08_425885	326	1	Recent	recent	JJ
10_1101-2021_01_08_425885	326	2	work	work	NN
10_1101-2021_01_08_425885	326	3	has	have	VBZ
10_1101-2021_01_08_425885	326	4	suggested	suggest	VBN
10_1101-2021_01_08_425885	326	5	the	the	DT
10_1101-2021_01_08_425885	326	6	use	use	NN
10_1101-2021_01_08_425885	326	7	of	of	IN
10_1101-2021_01_08_425885	326	8	hyperbolic	hyperbolic	JJ
10_1101-2021_01_08_425885	326	9	geometry	geometry	NN
10_1101-2021_01_08_425885	326	10	to	to	TO
10_1101-2021_01_08_425885	326	11	model	model	VB
10_1101-2021_01_08_425885	326	12	branching	branch	VBG
10_1101-2021_01_08_425885	326	13	cell	cell	NN
10_1101-2021_01_08_425885	326	14	differentiation	differentiation	NN
10_1101-2021_01_08_425885	326	15	trajectories	trajectory	NNS
10_1101-2021_01_08_425885	326	16	[	[	-LRB-
10_1101-2021_01_08_425885	326	17	47	47	CD
10_1101-2021_01_08_425885	326	18	]	]	-RRB-
10_1101-2021_01_08_425885	326	19	and	and	CC
10_1101-2021_01_08_425885	326	20	specific	specific	JJ
10_1101-2021_01_08_425885	326	21	manifolds	manifold	NNS
10_1101-2021_01_08_425885	326	22	have	have	VBP
10_1101-2021_01_08_425885	326	23	been	be	VBN
10_1101-2021_01_08_425885	326	24	proposed	propose	VBN
10_1101-2021_01_08_425885	326	25	to	to	IN
10_1101-2021_01_08_425885	326	26	model	model	VB
10_1101-2021_01_08_425885	326	27	reaction	reaction	NN
10_1101-2021_01_08_425885	326	28	networks	network	NNS
10_1101-2021_01_08_425885	326	29	[	[	-LRB-
10_1101-2021_01_08_425885	326	30	48	48	CD
10_1101-2021_01_08_425885	326	31	]	]	-RRB-
10_1101-2021_01_08_425885	326	32	,	,	,
10_1101-2021_01_08_425885	326	33	which	which	WDT
10_1101-2021_01_08_425885	326	34	may	may	MD
10_1101-2021_01_08_425885	326	35	be	be	VB
10_1101-2021_01_08_425885	326	36	applicable	applicable	JJ
10_1101-2021_01_08_425885	326	37	to	to	IN
10_1101-2021_01_08_425885	326	38	scRNAseq	scrnaseq	VB
10_1101-2021_01_08_425885	326	39	data	datum	NNS
10_1101-2021_01_08_425885	326	40	.	.	.
10_1101-2021_01_08_425885	327	1	These	these	DT
10_1101-2021_01_08_425885	327	2	proposed	propose	VBN
10_1101-2021_01_08_425885	327	3	manifolds	manifold	NNS
10_1101-2021_01_08_425885	327	4	can	can	MD
10_1101-2021_01_08_425885	327	5	be	be	VB
10_1101-2021_01_08_425885	327	6	validated	validate	VBN
10_1101-2021_01_08_425885	327	7	or	or	CC
10_1101-2021_01_08_425885	327	8	improved	improve	VBN
10_1101-2021_01_08_425885	327	9	using	use	VBG
10_1101-2021_01_08_425885	327	10	knowledge	knowledge	NN
10_1101-2021_01_08_425885	327	11	of	of	IN
10_1101-2021_01_08_425885	327	12	the	the	DT
10_1101-2021_01_08_425885	327	13	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	327	14	geometry	geometry	NN
10_1101-2021_01_08_425885	327	15	of	of	IN
10_1101-2021_01_08_425885	327	16	scRNAseq	scrnaseq	NN
10_1101-2021_01_08_425885	327	17	datasets	dataset	NNS
10_1101-2021_01_08_425885	327	18	.	.	.
10_1101-2021_01_08_425885	328	1	Finally	finally	RB
10_1101-2021_01_08_425885	328	2	,	,	,
10_1101-2021_01_08_425885	328	3	incorporating	incorporate	VBG
10_1101-2021_01_08_425885	328	4	information	information	NN
10_1101-2021_01_08_425885	328	5	about	about	IN
10_1101-2021_01_08_425885	328	6	curvature	curvature	NN
10_1101-2021_01_08_425885	328	7	may	may	MD
10_1101-2021_01_08_425885	328	8	provide	provide	VB
10_1101-2021_01_08_425885	328	9	a	a	DT
10_1101-2021_01_08_425885	328	10	more	more	RBR
10_1101-2021_01_08_425885	328	11	principled	principled	JJ
10_1101-2021_01_08_425885	328	12	approach	approach	NN
10_1101-2021_01_08_425885	328	13	for	for	IN
10_1101-2021_01_08_425885	328	14	developing	develop	VBG
10_1101-2021_01_08_425885	328	15	dimensionality	dimensionality	NN
10_1101-2021_01_08_425885	328	16	reduction	reduction	NN
10_1101-2021_01_08_425885	328	17	and	and	CC
10_1101-2021_01_08_425885	328	18	visualization	visualization	NN
10_1101-2021_01_08_425885	328	19	tools	tool	NNS
10_1101-2021_01_08_425885	328	20	.	.	.
10_1101-2021_01_08_425885	329	1	19	19	CD
10_1101-2021_01_08_425885	329	2	.CC	.CC	:
10_1101-2021_01_08_425885	329	3	-	-	HYPH
10_1101-2021_01_08_425885	329	4	BY	by	IN
10_1101-2021_01_08_425885	329	5	-	-	HYPH
10_1101-2021_01_08_425885	329	6	NC	NC	NNP
10_1101-2021_01_08_425885	329	7	-	-	HYPH
10_1101-2021_01_08_425885	329	8	ND	ND	NNP
10_1101-2021_01_08_425885	329	9	4.0	4.0	CD
10_1101-2021_01_08_425885	329	10	International	International	NNP
10_1101-2021_01_08_425885	329	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	329	12	under	under	IN
10_1101-2021_01_08_425885	329	13	a	a	DT
10_1101-2021_01_08_425885	329	14	(	(	-LRB-
10_1101-2021_01_08_425885	329	15	which	which	WDT
10_1101-2021_01_08_425885	329	16	was	be	VBD
10_1101-2021_01_08_425885	329	17	not	not	RB
10_1101-2021_01_08_425885	329	18	certified	certify	VBN
10_1101-2021_01_08_425885	329	19	by	by	IN
10_1101-2021_01_08_425885	329	20	peer	peer	NN
10_1101-2021_01_08_425885	329	21	review	review	NN
10_1101-2021_01_08_425885	329	22	)	)	-RRB-
10_1101-2021_01_08_425885	329	23	is	be	VBZ
10_1101-2021_01_08_425885	329	24	the	the	DT
10_1101-2021_01_08_425885	329	25	author	author	NN
10_1101-2021_01_08_425885	329	26	/	/	SYM
10_1101-2021_01_08_425885	329	27	funder	funder	NN
10_1101-2021_01_08_425885	329	28	,	,	,
10_1101-2021_01_08_425885	329	29	who	who	WP
10_1101-2021_01_08_425885	329	30	has	have	VBZ
10_1101-2021_01_08_425885	329	31	granted	grant	VBN
10_1101-2021_01_08_425885	329	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	329	33	a	a	DT
10_1101-2021_01_08_425885	329	34	license	license	NN
10_1101-2021_01_08_425885	329	35	to	to	TO
10_1101-2021_01_08_425885	329	36	display	display	VB
10_1101-2021_01_08_425885	329	37	the	the	DT
10_1101-2021_01_08_425885	329	38	preprint	preprint	NN
10_1101-2021_01_08_425885	329	39	in	in	IN
10_1101-2021_01_08_425885	329	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	329	41	.	.	.
10_1101-2021_01_08_425885	330	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	330	2	is	be	VBZ
10_1101-2021_01_08_425885	330	3	made	make	VBN
10_1101-2021_01_08_425885	330	4	The	the	DT
10_1101-2021_01_08_425885	330	5	copyright	copyright	NN
10_1101-2021_01_08_425885	330	6	holder	holder	NN
10_1101-2021_01_08_425885	330	7	for	for	IN
10_1101-2021_01_08_425885	330	8	this	this	DT
10_1101-2021_01_08_425885	330	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	330	10	version	version	NN
10_1101-2021_01_08_425885	330	11	posted	post	VBD
10_1101-2021_01_08_425885	330	12	January	January	NNP
10_1101-2021_01_08_425885	330	13	8	8	CD
10_1101-2021_01_08_425885	330	14	,	,	,
10_1101-2021_01_08_425885	330	15	2021	2021	CD
10_1101-2021_01_08_425885	330	16	.	.	.
10_1101-2021_01_08_425885	330	17	;	;	:
10_1101-2021_01_08_425885	330	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	330	19	:	:	:
10_1101-2021_01_08_425885	330	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	330	21	preprint	preprint	NN
10_1101-2021_01_08_425885	330	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	330	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NN
10_1101-2021_01_08_425885	330	24	4	4	CD
10_1101-2021_01_08_425885	330	25	Methods	Methods	NNP
10_1101-2021_01_08_425885	330	26	4.1	4.1	CD
10_1101-2021_01_08_425885	330	27	Differential	Differential	NNP
10_1101-2021_01_08_425885	330	28	Geometry	Geometry	NNP
10_1101-2021_01_08_425885	330	29	of	of	IN
10_1101-2021_01_08_425885	330	30	Theoretical	theoretical	JJ
10_1101-2021_01_08_425885	330	31	Manifolds	Manifolds	NNPS
10_1101-2021_01_08_425885	330	32	Here	here	RB
10_1101-2021_01_08_425885	330	33	we	-PRON-	PRP
10_1101-2021_01_08_425885	330	34	briefly	briefly	RB
10_1101-2021_01_08_425885	330	35	discuss	discuss	VBP
10_1101-2021_01_08_425885	330	36	how	how	WRB
10_1101-2021_01_08_425885	330	37	to	to	TO
10_1101-2021_01_08_425885	330	38	compute	compute	VB
10_1101-2021_01_08_425885	330	39	the	the	DT
10_1101-2021_01_08_425885	330	40	scalar	scalar	JJ
10_1101-2021_01_08_425885	330	41	curvature	curvature	NN
10_1101-2021_01_08_425885	330	42	of	of	IN
10_1101-2021_01_08_425885	330	43	,	,	,
10_1101-2021_01_08_425885	330	44	and	and	CC
10_1101-2021_01_08_425885	330	45	sample	sample	VB
10_1101-2021_01_08_425885	330	46	from	from	IN
10_1101-2021_01_08_425885	330	47	,	,	,
10_1101-2021_01_08_425885	330	48	theoretical	theoretical	JJ
10_1101-2021_01_08_425885	330	49	manifolds	manifold	NNS
10_1101-2021_01_08_425885	330	50	given	give	VBD
10_1101-2021_01_08_425885	330	51	a	a	DT
10_1101-2021_01_08_425885	330	52	parameterization	parameterization	NN
10_1101-2021_01_08_425885	330	53	.	.	.
10_1101-2021_01_08_425885	331	1	For	for	IN
10_1101-2021_01_08_425885	331	2	a	a	DT
10_1101-2021_01_08_425885	331	3	d	d	NN
10_1101-2021_01_08_425885	331	4	-	-	HYPH
10_1101-2021_01_08_425885	331	5	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	331	6	manifold	manifold	NN
10_1101-2021_01_08_425885	331	7	,	,	,
10_1101-2021_01_08_425885	331	8	M	M	NNP
10_1101-2021_01_08_425885	331	9	,	,	,
10_1101-2021_01_08_425885	331	10	with	with	IN
10_1101-2021_01_08_425885	331	11	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	331	12	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	331	13	{	{	-LRB-
10_1101-2021_01_08_425885	331	14	x1	x1	NNP
10_1101-2021_01_08_425885	331	15	,	,	,
10_1101-2021_01_08_425885	331	16	...	...	:
10_1101-2021_01_08_425885	331	17	,	,	,
10_1101-2021_01_08_425885	331	18	xd	xd	NNP
10_1101-2021_01_08_425885	331	19	}	}	-RRB-
10_1101-2021_01_08_425885	331	20	and	and	CC
10_1101-2021_01_08_425885	331	21	embedding	embed	VBG
10_1101-2021_01_08_425885	331	22	in	in	RP
10_1101-2021_01_08_425885	331	23	Rn	Rn	NNS
10_1101-2021_01_08_425885	331	24	given	give	VBN
10_1101-2021_01_08_425885	331	25	by	by	IN
10_1101-2021_01_08_425885	331	26	f(x1	f(x1	NNP
10_1101-2021_01_08_425885	331	27	,	,	,
10_1101-2021_01_08_425885	331	28	...	...	:
10_1101-2021_01_08_425885	331	29	,	,	,
10_1101-2021_01_08_425885	331	30	xd	xd	NNP
10_1101-2021_01_08_425885	331	31	)	)	-RRB-
10_1101-2021_01_08_425885	331	32	,	,	,
10_1101-2021_01_08_425885	331	33	the	the	DT
10_1101-2021_01_08_425885	331	34	metric	metric	NN
10_1101-2021_01_08_425885	331	35	is	be	VBZ
10_1101-2021_01_08_425885	331	36	:	:	:
10_1101-2021_01_08_425885	331	37	gij	gij	NNP
10_1101-2021_01_08_425885	331	38	=	=	SYM
10_1101-2021_01_08_425885	331	39	∂fT	∂fT	NNP
10_1101-2021_01_08_425885	331	40	∂xi	∂xi	,
10_1101-2021_01_08_425885	331	41	∂f	∂f	.
10_1101-2021_01_08_425885	331	42	∂xj	∂xj	,
10_1101-2021_01_08_425885	331	43	(	(	-LRB-
10_1101-2021_01_08_425885	331	44	8)	8)	CD
10_1101-2021_01_08_425885	331	45	The	the	DT
10_1101-2021_01_08_425885	331	46	scalar	scalar	JJ
10_1101-2021_01_08_425885	331	47	curvature	curvature	NN
10_1101-2021_01_08_425885	331	48	of	of	IN
10_1101-2021_01_08_425885	331	49	M	m	NN
10_1101-2021_01_08_425885	331	50	can	can	MD
10_1101-2021_01_08_425885	331	51	then	then	RB
10_1101-2021_01_08_425885	331	52	be	be	VB
10_1101-2021_01_08_425885	331	53	derived	derive	VBN
10_1101-2021_01_08_425885	331	54	analytically	analytically	RB
10_1101-2021_01_08_425885	331	55	in	in	IN
10_1101-2021_01_08_425885	331	56	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	331	57	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	331	58	in	in	IN
10_1101-2021_01_08_425885	331	59	terms	term	NNS
10_1101-2021_01_08_425885	331	60	of	of	IN
10_1101-2021_01_08_425885	331	61	the	the	DT
10_1101-2021_01_08_425885	331	62	metric	metric	JJ
10_1101-2021_01_08_425885	331	63	as	as	IN
10_1101-2021_01_08_425885	331	64	S	S	NNP
10_1101-2021_01_08_425885	331	65	=	=	SYM
10_1101-2021_01_08_425885	331	66	gij	gij	NNP
10_1101-2021_01_08_425885	331	67	(	(	-LRB-
10_1101-2021_01_08_425885	331	68	Γkij	Γkij	NNP
10_1101-2021_01_08_425885	331	69	,	,	,
10_1101-2021_01_08_425885	331	70	k	k	NN
10_1101-2021_01_08_425885	331	71	−	−	NNP
10_1101-2021_01_08_425885	331	72	Γ	Γ	NNP
10_1101-2021_01_08_425885	331	73	k	k	NN
10_1101-2021_01_08_425885	331	74	ik	ik	NN
10_1101-2021_01_08_425885	331	75	,	,	,
10_1101-2021_01_08_425885	331	76	j	j	NNP
10_1101-2021_01_08_425885	331	77	+	+	CC
10_1101-2021_01_08_425885	331	78	Γ	Γ	NNP
10_1101-2021_01_08_425885	331	79	l	l	NN
10_1101-2021_01_08_425885	331	80	ijΓ	ijΓ	NNP
10_1101-2021_01_08_425885	331	81	k	k	NN
10_1101-2021_01_08_425885	331	82	kl	kl	NNP
10_1101-2021_01_08_425885	331	83	−	−	NNP
10_1101-2021_01_08_425885	331	84	Γ	Γ	NNP
10_1101-2021_01_08_425885	331	85	l	l	NN
10_1101-2021_01_08_425885	331	86	ikΓ	ikΓ	NNP
10_1101-2021_01_08_425885	331	87	k	k	NN
10_1101-2021_01_08_425885	331	88	jl	jl	NN
10_1101-2021_01_08_425885	331	89	)	)	-RRB-
10_1101-2021_01_08_425885	331	90	(	(	-LRB-
10_1101-2021_01_08_425885	331	91	9	9	CD
10_1101-2021_01_08_425885	331	92	)	)	-RRB-
10_1101-2021_01_08_425885	331	93	where	where	WRB
10_1101-2021_01_08_425885	331	94	the	the	DT
10_1101-2021_01_08_425885	331	95	Γijks	Γijks	NNP
10_1101-2021_01_08_425885	331	96	are	be	VBP
10_1101-2021_01_08_425885	331	97	Christoffel	christoffel	NN
10_1101-2021_01_08_425885	331	98	symbols	symbol	NNS
10_1101-2021_01_08_425885	331	99	given	give	VBN
10_1101-2021_01_08_425885	331	100	by	by	IN
10_1101-2021_01_08_425885	331	101	Γijk	Γijk	NNP
10_1101-2021_01_08_425885	331	102	=	=	SYM
10_1101-2021_01_08_425885	331	103	gil	gil	NNP
10_1101-2021_01_08_425885	331	104	2	2	CD
10_1101-2021_01_08_425885	331	105	(	(	-LRB-
10_1101-2021_01_08_425885	331	106	∂glj	∂glj	$
10_1101-2021_01_08_425885	331	107	∂xk	∂xk	NN
10_1101-2021_01_08_425885	331	108	+	+	SYM
10_1101-2021_01_08_425885	331	109	∂glk	∂glk	$
10_1101-2021_01_08_425885	331	110	∂xj	∂xj	NFP
10_1101-2021_01_08_425885	331	111	−	−	NNP
10_1101-2021_01_08_425885	331	112	∂gjk	∂gjk	CD
10_1101-2021_01_08_425885	331	113	∂xl	∂xl	.
10_1101-2021_01_08_425885	331	114	)	)	-RRB-
10_1101-2021_01_08_425885	331	115	(	(	-LRB-
10_1101-2021_01_08_425885	331	116	10	10	CD
10_1101-2021_01_08_425885	331	117	)	)	-RRB-
10_1101-2021_01_08_425885	331	118	and	and	CC
10_1101-2021_01_08_425885	331	119	Γijk	Γijk	NNP
10_1101-2021_01_08_425885	331	120	,	,	,
10_1101-2021_01_08_425885	331	121	l=	l=	NNP
10_1101-2021_01_08_425885	331	122	∂Γijk	∂Γijk	.
10_1101-2021_01_08_425885	331	123	∂xl	∂xl	NFP
10_1101-2021_01_08_425885	331	124	.	.	.
10_1101-2021_01_08_425885	332	1	To	to	TO
10_1101-2021_01_08_425885	332	2	draw	draw	VB
10_1101-2021_01_08_425885	332	3	points	point	NNS
10_1101-2021_01_08_425885	332	4	from	from	IN
10_1101-2021_01_08_425885	332	5	M	M	NNP
10_1101-2021_01_08_425885	332	6	with	with	IN
10_1101-2021_01_08_425885	332	7	ai	ai	NNP
10_1101-2021_01_08_425885	332	8	≤	≤	NNP
10_1101-2021_01_08_425885	332	9	xi	xi	NNP
10_1101-2021_01_08_425885	332	10	≤	≤	NNP
10_1101-2021_01_08_425885	332	11	bi	bi	NNP
10_1101-2021_01_08_425885	332	12	so	so	IN
10_1101-2021_01_08_425885	332	13	that	that	IN
10_1101-2021_01_08_425885	332	14	the	the	DT
10_1101-2021_01_08_425885	332	15	embedded	embed	VBN
10_1101-2021_01_08_425885	332	16	manifold	manifold	NN
10_1101-2021_01_08_425885	332	17	is	be	VBZ
10_1101-2021_01_08_425885	332	18	uniformly	uniformly	RB
10_1101-2021_01_08_425885	332	19	sampled	sample	VBN
10_1101-2021_01_08_425885	332	20	in	in	IN
10_1101-2021_01_08_425885	332	21	Rn	Rn	NNP
10_1101-2021_01_08_425885	332	22	,	,	,
10_1101-2021_01_08_425885	332	23	we	-PRON-	PRP
10_1101-2021_01_08_425885	332	24	use	use	VBP
10_1101-2021_01_08_425885	332	25	rejection	rejection	NN
10_1101-2021_01_08_425885	332	26	sampling	sampling	NN
10_1101-2021_01_08_425885	332	27	.	.	.
10_1101-2021_01_08_425885	333	1	For	for	IN
10_1101-2021_01_08_425885	333	2	paired	pair	VBN
10_1101-2021_01_08_425885	333	3	random	random	JJ
10_1101-2021_01_08_425885	333	4	variables	variable	NNS
10_1101-2021_01_08_425885	333	5	x	x	SYM
10_1101-2021_01_08_425885	333	6	∼	∼	NN
10_1101-2021_01_08_425885	333	7	Uniform(a	uniform(a	NN
10_1101-2021_01_08_425885	333	8	,	,	,
10_1101-2021_01_08_425885	333	9	b	b	LS
10_1101-2021_01_08_425885	333	10	)	)	-RRB-
10_1101-2021_01_08_425885	333	11	and	and	CC
10_1101-2021_01_08_425885	333	12	y	y	NNP
10_1101-2021_01_08_425885	333	13	∼	∼	NNP
10_1101-2021_01_08_425885	333	14	Uniform(0	Uniform(0	NNP
10_1101-2021_01_08_425885	333	15	,	,	,
10_1101-2021_01_08_425885	333	16	max	max	NNP
10_1101-2021_01_08_425885	333	17	√	√	NNP
10_1101-2021_01_08_425885	333	18	det	det	NNP
10_1101-2021_01_08_425885	333	19	g	g	NNP
10_1101-2021_01_08_425885	333	20	)	)	-RRB-
10_1101-2021_01_08_425885	333	21	,	,	,
10_1101-2021_01_08_425885	333	22	we	-PRON-	PRP
10_1101-2021_01_08_425885	333	23	retain	retain	VBP
10_1101-2021_01_08_425885	333	24	x	x	SYM
10_1101-2021_01_08_425885	333	25	as	as	IN
10_1101-2021_01_08_425885	333	26	a	a	DT
10_1101-2021_01_08_425885	333	27	sample	sample	NN
10_1101-2021_01_08_425885	333	28	point	point	NN
10_1101-2021_01_08_425885	333	29	if	if	IN
10_1101-2021_01_08_425885	333	30	√	√	NNP
10_1101-2021_01_08_425885	333	31	det	det	NN
10_1101-2021_01_08_425885	333	32	g	g	NNP
10_1101-2021_01_08_425885	333	33	∣∣	∣∣	NNP
10_1101-2021_01_08_425885	333	34	x	x	NNP
10_1101-2021_01_08_425885	333	35	≤	≤	NNP
10_1101-2021_01_08_425885	333	36	y.	y.	NNP
10_1101-2021_01_08_425885	334	1	4.2	4.2	CD
10_1101-2021_01_08_425885	334	2	Details	detail	NNS
10_1101-2021_01_08_425885	334	3	of	of	IN
10_1101-2021_01_08_425885	334	4	Intrinsic	Intrinsic	NNP
10_1101-2021_01_08_425885	334	5	Approach	Approach	NNP
10_1101-2021_01_08_425885	334	6	to	to	IN
10_1101-2021_01_08_425885	334	7	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	334	8	Estimation	estimation	NN
10_1101-2021_01_08_425885	334	9	Here	here	RB
10_1101-2021_01_08_425885	334	10	we	-PRON-	PRP
10_1101-2021_01_08_425885	334	11	explain	explain	VBP
10_1101-2021_01_08_425885	334	12	how	how	WRB
10_1101-2021_01_08_425885	334	13	we	-PRON-	PRP
10_1101-2021_01_08_425885	334	14	used	use	VBD
10_1101-2021_01_08_425885	334	15	Equations	Equations	NNP
10_1101-2021_01_08_425885	334	16	2	2	CD
10_1101-2021_01_08_425885	334	17	-	-	SYM
10_1101-2021_01_08_425885	334	18	4	4	CD
10_1101-2021_01_08_425885	334	19	on	on	IN
10_1101-2021_01_08_425885	334	20	the	the	DT
10_1101-2021_01_08_425885	334	21	simplest	simple	JJS
10_1101-2021_01_08_425885	334	22	of	of	IN
10_1101-2021_01_08_425885	334	23	toy	toy	NN
10_1101-2021_01_08_425885	334	24	manifolds	manifold	NNS
10_1101-2021_01_08_425885	334	25	,	,	,
10_1101-2021_01_08_425885	334	26	the	the	DT
10_1101-2021_01_08_425885	334	27	noise	noise	NN
10_1101-2021_01_08_425885	334	28	-	-	HYPH
10_1101-2021_01_08_425885	334	29	free	free	JJ
10_1101-2021_01_08_425885	334	30	2-dimensional	2-dimensional	CD
10_1101-2021_01_08_425885	334	31	hollow	hollow	JJ
10_1101-2021_01_08_425885	334	32	unit	unit	NN
10_1101-2021_01_08_425885	334	33	sphere	sphere	VBD
10_1101-2021_01_08_425885	334	34	,	,	,
10_1101-2021_01_08_425885	334	35	S2	S2	NNP
10_1101-2021_01_08_425885	334	36	,	,	,
10_1101-2021_01_08_425885	334	37	to	to	TO
10_1101-2021_01_08_425885	334	38	obtain	obtain	VB
10_1101-2021_01_08_425885	334	39	an	an	DT
10_1101-2021_01_08_425885	334	40	estimate	estimate	NN
10_1101-2021_01_08_425885	334	41	of	of	IN
10_1101-2021_01_08_425885	334	42	the	the	DT
10_1101-2021_01_08_425885	334	43	average	average	JJ
10_1101-2021_01_08_425885	334	44	scalar	scalar	JJ
10_1101-2021_01_08_425885	334	45	curvature	curvature	NN
10_1101-2021_01_08_425885	334	46	.	.	.
10_1101-2021_01_08_425885	335	1	The	the	DT
10_1101-2021_01_08_425885	335	2	true	true	JJ
10_1101-2021_01_08_425885	335	3	scalar	scalar	JJ
10_1101-2021_01_08_425885	335	4	curvature	curvature	NN
10_1101-2021_01_08_425885	335	5	is	be	VBZ
10_1101-2021_01_08_425885	335	6	S(p	s(p	XX
10_1101-2021_01_08_425885	335	7	)	)	-RRB-
10_1101-2021_01_08_425885	335	8	=	=	NFP
10_1101-2021_01_08_425885	335	9	2	2	CD
10_1101-2021_01_08_425885	335	10	∀p	∀p	CD
10_1101-2021_01_08_425885	335	11	∈	∈	NNP
10_1101-2021_01_08_425885	335	12	M.	M.	NNP
10_1101-2021_01_08_425885	335	13	For	for	IN
10_1101-2021_01_08_425885	335	14	the	the	DT
10_1101-2021_01_08_425885	335	15	remainder	remainder	NN
10_1101-2021_01_08_425885	335	16	of	of	IN
10_1101-2021_01_08_425885	335	17	this	this	DT
10_1101-2021_01_08_425885	335	18	section	section	NN
10_1101-2021_01_08_425885	335	19	,	,	,
10_1101-2021_01_08_425885	335	20	we	-PRON-	PRP
10_1101-2021_01_08_425885	335	21	adopt	adopt	VBP
10_1101-2021_01_08_425885	335	22	the	the	DT
10_1101-2021_01_08_425885	335	23	convention	convention	NN
10_1101-2021_01_08_425885	335	24	that	that	IN
10_1101-2021_01_08_425885	335	25	symbols	symbol	NNS
10_1101-2021_01_08_425885	335	26	with	with	IN
10_1101-2021_01_08_425885	335	27	overbars	overbar	NNS
10_1101-2021_01_08_425885	335	28	are	be	VBP
10_1101-2021_01_08_425885	335	29	estimates	estimate	NNS
10_1101-2021_01_08_425885	335	30	of	of	IN
10_1101-2021_01_08_425885	335	31	the	the	DT
10_1101-2021_01_08_425885	335	32	corresponding	corresponding	JJ
10_1101-2021_01_08_425885	335	33	unaccented	unaccented	JJ
10_1101-2021_01_08_425885	335	34	quantities	quantity	NNS
10_1101-2021_01_08_425885	335	35	.	.	.
10_1101-2021_01_08_425885	336	1	4.2.1	4.2.1	CD
10_1101-2021_01_08_425885	336	2	Approach	Approach	NNP
10_1101-2021_01_08_425885	336	3	for	for	IN
10_1101-2021_01_08_425885	336	4	S2	s2	NN
10_1101-2021_01_08_425885	336	5	Our	-PRON-	PRP$
10_1101-2021_01_08_425885	336	6	approach	approach	NN
10_1101-2021_01_08_425885	336	7	mirrors	mirror	VBZ
10_1101-2021_01_08_425885	336	8	the	the	DT
10_1101-2021_01_08_425885	336	9	treatment	treatment	NN
10_1101-2021_01_08_425885	336	10	in	in	IN
10_1101-2021_01_08_425885	336	11	[	[	-LRB-
10_1101-2021_01_08_425885	336	12	27	27	CD
10_1101-2021_01_08_425885	336	13	]	]	-RRB-
10_1101-2021_01_08_425885	336	14	,	,	,
10_1101-2021_01_08_425885	336	15	in	in	IN
10_1101-2021_01_08_425885	336	16	which	which	WDT
10_1101-2021_01_08_425885	336	17	heat	heat	NN
10_1101-2021_01_08_425885	336	18	-	-	HYPH
10_1101-2021_01_08_425885	336	19	traces	trace	NNS
10_1101-2021_01_08_425885	336	20	are	be	VBP
10_1101-2021_01_08_425885	336	21	fit	fit	JJ
10_1101-2021_01_08_425885	336	22	over	over	IN
10_1101-2021_01_08_425885	336	23	various	various	JJ
10_1101-2021_01_08_425885	336	24	intervals	interval	NNS
10_1101-2021_01_08_425885	336	25	[	[	-LRB-
10_1101-2021_01_08_425885	336	26	x1,x2	x1,x2	NN
10_1101-2021_01_08_425885	336	27	]	]	-RRB-
10_1101-2021_01_08_425885	336	28	with	with	IN
10_1101-2021_01_08_425885	336	29	x1	x1	NNP
10_1101-2021_01_08_425885	336	30	≥	≥	UH
10_1101-2021_01_08_425885	336	31	0	0	CD
10_1101-2021_01_08_425885	336	32	,	,	,
10_1101-2021_01_08_425885	336	33	to	to	IN
10_1101-2021_01_08_425885	336	34	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	336	35	polynomials	polynomial	NNS
10_1101-2021_01_08_425885	336	36	p2(x	p2(x	ADD
10_1101-2021_01_08_425885	336	37	)	)	-RRB-
10_1101-2021_01_08_425885	336	38	=	=	NFP
10_1101-2021_01_08_425885	336	39	c0	c0	NNP
10_1101-2021_01_08_425885	336	40	+	+	CC
10_1101-2021_01_08_425885	336	41	c1x	c1x	NNP
10_1101-2021_01_08_425885	336	42	+	+	CD
10_1101-2021_01_08_425885	336	43	c2x2	c2x2	NN
10_1101-2021_01_08_425885	336	44	to	to	TO
10_1101-2021_01_08_425885	336	45	estimate	estimate	VB
10_1101-2021_01_08_425885	336	46	the	the	DT
10_1101-2021_01_08_425885	336	47	geometric	geometric	JJ
10_1101-2021_01_08_425885	336	48	quantities	quantity	NNS
10_1101-2021_01_08_425885	336	49	in	in	IN
10_1101-2021_01_08_425885	336	50	Equation	Equation	NNP
10_1101-2021_01_08_425885	336	51	2	2	CD
10_1101-2021_01_08_425885	336	52	.	.	.
10_1101-2021_01_08_425885	337	1	Here	here	RB
10_1101-2021_01_08_425885	337	2	,	,	,
10_1101-2021_01_08_425885	337	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	337	4	constrained	constrain	VBD
10_1101-2021_01_08_425885	337	5	the	the	DT
10_1101-2021_01_08_425885	337	6	form	form	NN
10_1101-2021_01_08_425885	337	7	of	of	IN
10_1101-2021_01_08_425885	337	8	p2(x	p2(x	NNP
10_1101-2021_01_08_425885	337	9	)	)	-RRB-
10_1101-2021_01_08_425885	337	10	for	for	IN
10_1101-2021_01_08_425885	337	11	fitting	fit	VBG
10_1101-2021_01_08_425885	337	12	by	by	IN
10_1101-2021_01_08_425885	337	13	assuming	assume	VBG
10_1101-2021_01_08_425885	337	14	that	that	DT
10_1101-2021_01_08_425885	337	15	(	(	-LRB-
10_1101-2021_01_08_425885	337	16	i	i	NN
10_1101-2021_01_08_425885	337	17	)	)	-RRB-
10_1101-2021_01_08_425885	337	18	the	the	DT
10_1101-2021_01_08_425885	337	19	manifold	manifold	NN
10_1101-2021_01_08_425885	337	20	is	be	VBZ
10_1101-2021_01_08_425885	337	21	boundary	boundary	JJ
10_1101-2021_01_08_425885	337	22	-	-	HYPH
10_1101-2021_01_08_425885	337	23	less	less	JJR
10_1101-2021_01_08_425885	337	24	(	(	-LRB-
10_1101-2021_01_08_425885	337	25	so	so	IN
10_1101-2021_01_08_425885	337	26	that	that	IN
10_1101-2021_01_08_425885	337	27	c1	c1	NN
10_1101-2021_01_08_425885	337	28	=	=	SYM
10_1101-2021_01_08_425885	337	29	c1	c1	NN
10_1101-2021_01_08_425885	337	30	=	=	SYM
10_1101-2021_01_08_425885	337	31	0	0	NFP
10_1101-2021_01_08_425885	337	32	and	and	CC
10_1101-2021_01_08_425885	337	33	the	the	DT
10_1101-2021_01_08_425885	337	34	second	second	JJ
10_1101-2021_01_08_425885	337	35	boundary	boundary	JJ
10_1101-2021_01_08_425885	337	36	term	term	NN
10_1101-2021_01_08_425885	337	37	for	for	IN
10_1101-2021_01_08_425885	337	38	c2	c2	NNP
10_1101-2021_01_08_425885	337	39	vanishes	vanishe	NNS
10_1101-2021_01_08_425885	337	40	)	)	-RRB-
10_1101-2021_01_08_425885	337	41	,	,	,
10_1101-2021_01_08_425885	337	42	(	(	-LRB-
10_1101-2021_01_08_425885	337	43	ii	ii	LS
10_1101-2021_01_08_425885	337	44	)	)	-RRB-
10_1101-2021_01_08_425885	337	45	the	the	DT
10_1101-2021_01_08_425885	337	46	volume	volume	NN
10_1101-2021_01_08_425885	337	47	is	be	VBZ
10_1101-2021_01_08_425885	337	48	known	know	VBN
10_1101-2021_01_08_425885	337	49	(	(	-LRB-
10_1101-2021_01_08_425885	337	50	so	so	IN
10_1101-2021_01_08_425885	337	51	that	that	IN
10_1101-2021_01_08_425885	337	52	20	20	CD
10_1101-2021_01_08_425885	337	53	.CC	.CC	NFP
10_1101-2021_01_08_425885	337	54	-	-	HYPH
10_1101-2021_01_08_425885	337	55	BY	by	IN
10_1101-2021_01_08_425885	337	56	-	-	HYPH
10_1101-2021_01_08_425885	337	57	NC	NC	NNP
10_1101-2021_01_08_425885	337	58	-	-	HYPH
10_1101-2021_01_08_425885	337	59	ND	ND	NNP
10_1101-2021_01_08_425885	337	60	4.0	4.0	CD
10_1101-2021_01_08_425885	337	61	International	International	NNP
10_1101-2021_01_08_425885	337	62	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	337	63	under	under	IN
10_1101-2021_01_08_425885	337	64	a	a	DT
10_1101-2021_01_08_425885	337	65	(	(	-LRB-
10_1101-2021_01_08_425885	337	66	which	which	WDT
10_1101-2021_01_08_425885	337	67	was	be	VBD
10_1101-2021_01_08_425885	337	68	not	not	RB
10_1101-2021_01_08_425885	337	69	certified	certify	VBN
10_1101-2021_01_08_425885	337	70	by	by	IN
10_1101-2021_01_08_425885	337	71	peer	peer	NN
10_1101-2021_01_08_425885	337	72	review	review	NN
10_1101-2021_01_08_425885	337	73	)	)	-RRB-
10_1101-2021_01_08_425885	337	74	is	be	VBZ
10_1101-2021_01_08_425885	337	75	the	the	DT
10_1101-2021_01_08_425885	337	76	author	author	NN
10_1101-2021_01_08_425885	337	77	/	/	SYM
10_1101-2021_01_08_425885	337	78	funder	funder	NN
10_1101-2021_01_08_425885	337	79	,	,	,
10_1101-2021_01_08_425885	337	80	who	who	WP
10_1101-2021_01_08_425885	337	81	has	have	VBZ
10_1101-2021_01_08_425885	337	82	granted	grant	VBN
10_1101-2021_01_08_425885	337	83	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	337	84	a	a	DT
10_1101-2021_01_08_425885	337	85	license	license	NN
10_1101-2021_01_08_425885	337	86	to	to	TO
10_1101-2021_01_08_425885	337	87	display	display	VB
10_1101-2021_01_08_425885	337	88	the	the	DT
10_1101-2021_01_08_425885	337	89	preprint	preprint	NN
10_1101-2021_01_08_425885	337	90	in	in	IN
10_1101-2021_01_08_425885	337	91	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	337	92	.	.	.
10_1101-2021_01_08_425885	338	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	338	2	is	be	VBZ
10_1101-2021_01_08_425885	338	3	made	make	VBN
10_1101-2021_01_08_425885	338	4	The	the	DT
10_1101-2021_01_08_425885	338	5	copyright	copyright	NN
10_1101-2021_01_08_425885	338	6	holder	holder	NN
10_1101-2021_01_08_425885	338	7	for	for	IN
10_1101-2021_01_08_425885	338	8	this	this	DT
10_1101-2021_01_08_425885	338	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	338	10	version	version	NN
10_1101-2021_01_08_425885	338	11	posted	post	VBD
10_1101-2021_01_08_425885	338	12	January	January	NNP
10_1101-2021_01_08_425885	338	13	8	8	CD
10_1101-2021_01_08_425885	338	14	,	,	,
10_1101-2021_01_08_425885	338	15	2021	2021	CD
10_1101-2021_01_08_425885	338	16	.	.	.
10_1101-2021_01_08_425885	338	17	;	;	:
10_1101-2021_01_08_425885	338	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	338	19	:	:	:
10_1101-2021_01_08_425885	338	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	338	21	preprint	preprint	NN
10_1101-2021_01_08_425885	338	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	NNP
10_1101-2021_01_08_425885	338	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NNP
10_1101-2021_01_08_425885	338	24	c0	c0	NNP
10_1101-2021_01_08_425885	338	25	=	=	SYM
10_1101-2021_01_08_425885	338	26	c0	c0	NNP
10_1101-2021_01_08_425885	338	27	=	=	SYM
10_1101-2021_01_08_425885	338	28	4π	4π	NNP
10_1101-2021_01_08_425885	338	29	)	)	-RRB-
10_1101-2021_01_08_425885	338	30	,	,	,
10_1101-2021_01_08_425885	338	31	and	and	CC
10_1101-2021_01_08_425885	338	32	(	(	-LRB-
10_1101-2021_01_08_425885	338	33	iii	iii	NNP
10_1101-2021_01_08_425885	338	34	)	)	-RRB-
10_1101-2021_01_08_425885	338	35	the	the	DT
10_1101-2021_01_08_425885	338	36	scalar	scalar	JJ
10_1101-2021_01_08_425885	338	37	curvature	curvature	NN
10_1101-2021_01_08_425885	338	38	is	be	VBZ
10_1101-2021_01_08_425885	338	39	constant	constant	JJ
10_1101-2021_01_08_425885	338	40	(	(	-LRB-
10_1101-2021_01_08_425885	338	41	so	so	IN
10_1101-2021_01_08_425885	338	42	that	that	IN
10_1101-2021_01_08_425885	338	43	c2	c2	NNP
10_1101-2021_01_08_425885	338	44	=	=	SYM
10_1101-2021_01_08_425885	338	45	2π	2π	NNP
10_1101-2021_01_08_425885	338	46	3	3	CD
10_1101-2021_01_08_425885	338	47	S	S	NNP
10_1101-2021_01_08_425885	338	48	)	)	-RRB-
10_1101-2021_01_08_425885	338	49	,	,	,
10_1101-2021_01_08_425885	338	50	yielding	yield	VBG
10_1101-2021_01_08_425885	338	51	p2(x	p2(x	NNP
10_1101-2021_01_08_425885	338	52	)	)	-RRB-
10_1101-2021_01_08_425885	338	53	=	=	NFP
10_1101-2021_01_08_425885	338	54	4π	4π	CD
10_1101-2021_01_08_425885	338	55	+	+	SYM
10_1101-2021_01_08_425885	338	56	2π	2π	CD
10_1101-2021_01_08_425885	338	57	3	3	CD
10_1101-2021_01_08_425885	338	58	Sx2	sx2	NN
10_1101-2021_01_08_425885	338	59	.	.	.
10_1101-2021_01_08_425885	339	1	These	these	DT
10_1101-2021_01_08_425885	339	2	are	be	VBP
10_1101-2021_01_08_425885	339	3	strong	strong	JJ
10_1101-2021_01_08_425885	339	4	assumptions	assumption	NNS
10_1101-2021_01_08_425885	339	5	that	that	WDT
10_1101-2021_01_08_425885	339	6	will	will	MD
10_1101-2021_01_08_425885	339	7	not	not	RB
10_1101-2021_01_08_425885	339	8	hold	hold	VB
10_1101-2021_01_08_425885	339	9	for	for	IN
10_1101-2021_01_08_425885	339	10	an	an	DT
10_1101-2021_01_08_425885	339	11	arbitrary	arbitrary	JJ
10_1101-2021_01_08_425885	339	12	manifold	manifold	NN
10_1101-2021_01_08_425885	339	13	,	,	,
10_1101-2021_01_08_425885	339	14	which	which	WDT
10_1101-2021_01_08_425885	339	15	already	already	RB
10_1101-2021_01_08_425885	339	16	precludes	preclude	VBZ
10_1101-2021_01_08_425885	339	17	this	this	DT
10_1101-2021_01_08_425885	339	18	as	as	IN
10_1101-2021_01_08_425885	339	19	a	a	DT
10_1101-2021_01_08_425885	339	20	generic	generic	JJ
10_1101-2021_01_08_425885	339	21	procedure	procedure	NN
10_1101-2021_01_08_425885	339	22	.	.	.
10_1101-2021_01_08_425885	340	1	Nonetheless	nonetheless	RB
10_1101-2021_01_08_425885	340	2	,	,	,
10_1101-2021_01_08_425885	340	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	340	4	proceeded	proceed	VBD
10_1101-2021_01_08_425885	340	5	for	for	IN
10_1101-2021_01_08_425885	340	6	S2	s2	NN
10_1101-2021_01_08_425885	340	7	to	to	TO
10_1101-2021_01_08_425885	340	8	see	see	VB
10_1101-2021_01_08_425885	340	9	if	if	IN
10_1101-2021_01_08_425885	340	10	even	even	RB
10_1101-2021_01_08_425885	340	11	with	with	IN
10_1101-2021_01_08_425885	340	12	this	this	DT
10_1101-2021_01_08_425885	340	13	privileged	privileged	JJ
10_1101-2021_01_08_425885	340	14	information	information	NN
10_1101-2021_01_08_425885	340	15	,	,	,
10_1101-2021_01_08_425885	340	16	the	the	DT
10_1101-2021_01_08_425885	340	17	scalar	scalar	JJ
10_1101-2021_01_08_425885	340	18	curvature	curvature	NN
10_1101-2021_01_08_425885	340	19	could	could	MD
10_1101-2021_01_08_425885	340	20	be	be	VB
10_1101-2021_01_08_425885	340	21	estimated	estimate	VBN
10_1101-2021_01_08_425885	340	22	accurately	accurately	RB
10_1101-2021_01_08_425885	340	23	.	.	.
10_1101-2021_01_08_425885	341	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	341	2	declared	declare	VBD
10_1101-2021_01_08_425885	341	3	an	an	DT
10_1101-2021_01_08_425885	341	4	estimate	estimate	NN
10_1101-2021_01_08_425885	341	5	to	to	TO
10_1101-2021_01_08_425885	341	6	be	be	VB
10_1101-2021_01_08_425885	341	7	accurate	accurate	JJ
10_1101-2021_01_08_425885	341	8	on	on	IN
10_1101-2021_01_08_425885	341	9	the	the	DT
10_1101-2021_01_08_425885	341	10	interval	interval	NN
10_1101-2021_01_08_425885	341	11	[	[	-LRB-
10_1101-2021_01_08_425885	341	12	x1,x2	x1,x2	NNP
10_1101-2021_01_08_425885	341	13	]	]	-RRB-
10_1101-2021_01_08_425885	341	14	if	if	IN
10_1101-2021_01_08_425885	341	15	S	S	NNP
10_1101-2021_01_08_425885	341	16	has	have	VBZ
10_1101-2021_01_08_425885	341	17	error	error	NN
10_1101-2021_01_08_425885	341	18	within	within	IN
10_1101-2021_01_08_425885	341	19	±0.5	±0.5	NNP
10_1101-2021_01_08_425885	341	20	i.e.	i.e.	FW
10_1101-2021_01_08_425885	342	1	S	S	NNP
10_1101-2021_01_08_425885	342	2	∈	∈	NNP
10_1101-2021_01_08_425885	342	3	[	[	-LRB-
10_1101-2021_01_08_425885	342	4	1.5	1.5	CD
10_1101-2021_01_08_425885	342	5	,	,	,
10_1101-2021_01_08_425885	342	6	2.5	2.5	CD
10_1101-2021_01_08_425885	342	7	]	]	-RRB-
10_1101-2021_01_08_425885	342	8	.	.	.
10_1101-2021_01_08_425885	343	1	All	all	DT
10_1101-2021_01_08_425885	343	2	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	343	3	fits	fit	NNS
10_1101-2021_01_08_425885	343	4	were	be	VBD
10_1101-2021_01_08_425885	343	5	performed	perform	VBN
10_1101-2021_01_08_425885	343	6	in	in	IN
10_1101-2021_01_08_425885	343	7	MATLAB	MATLAB	NNP
10_1101-2021_01_08_425885	343	8	using	use	VBG
10_1101-2021_01_08_425885	343	9	the	the	DT
10_1101-2021_01_08_425885	343	10	lsqnonlin	lsqnonlin	NNP
10_1101-2021_01_08_425885	343	11	function	function	NN
10_1101-2021_01_08_425885	343	12	(	(	-LRB-
10_1101-2021_01_08_425885	343	13	‘	'	``
10_1101-2021_01_08_425885	343	14	StepTolerance’=1e-3	StepTolerance’=1e-3	NNP
10_1101-2021_01_08_425885	343	15	,	,	,
10_1101-2021_01_08_425885	343	16	‘	'	''
10_1101-2021_01_08_425885	343	17	FunctionTolerance’=1e-6	FunctionTolerance’=1e-6	NNP
10_1101-2021_01_08_425885	343	18	)	)	-RRB-
10_1101-2021_01_08_425885	343	19	.	.	.
10_1101-2021_01_08_425885	344	1	First	first	RB
10_1101-2021_01_08_425885	344	2	,	,	,
10_1101-2021_01_08_425885	344	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	344	4	evaluated	evaluate	VBD
10_1101-2021_01_08_425885	344	5	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	344	6	)	)	-RRB-
10_1101-2021_01_08_425885	344	7	using	use	VBG
10_1101-2021_01_08_425885	344	8	analytical	analytical	JJ
10_1101-2021_01_08_425885	344	9	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	344	10	for	for	IN
10_1101-2021_01_08_425885	344	11	S2	s2	NN
10_1101-2021_01_08_425885	344	12	given	give	VBN
10_1101-2021_01_08_425885	344	13	by	by	IN
10_1101-2021_01_08_425885	344	14	λ(`−1)2	λ(`−1)2	NN
10_1101-2021_01_08_425885	344	15	+	+	SYM
10_1101-2021_01_08_425885	344	16	1	1	CD
10_1101-2021_01_08_425885	344	17	,	,	,
10_1101-2021_01_08_425885	344	18	...	...	NFP
10_1101-2021_01_08_425885	344	19	,	,	,
10_1101-2021_01_08_425885	344	20	λ`2	λ`2	NNP
10_1101-2021_01_08_425885	344	21	=	=	SYM
10_1101-2021_01_08_425885	344	22	`	`	''
10_1101-2021_01_08_425885	344	23	(	(	-LRB-
10_1101-2021_01_08_425885	344	24	`	`	''
10_1101-2021_01_08_425885	344	25	−	−	NNP
10_1101-2021_01_08_425885	344	26	1	1	CD
10_1101-2021_01_08_425885	344	27	)	)	-RRB-
10_1101-2021_01_08_425885	344	28	,	,	,
10_1101-2021_01_08_425885	344	29	`	`	''
10_1101-2021_01_08_425885	344	30	>	>	XX
10_1101-2021_01_08_425885	344	31	0	0	CD
10_1101-2021_01_08_425885	344	32	,	,	,
10_1101-2021_01_08_425885	344	33	and	and	CC
10_1101-2021_01_08_425885	344	34	let	let	VB
10_1101-2021_01_08_425885	344	35	Dm	Dm	NNP
10_1101-2021_01_08_425885	344	36	be	be	VB
10_1101-2021_01_08_425885	344	37	the	the	DT
10_1101-2021_01_08_425885	344	38	collection	collection	NN
10_1101-2021_01_08_425885	344	39	of	of	IN
10_1101-2021_01_08_425885	344	40	all	all	DT
10_1101-2021_01_08_425885	344	41	intervals	interval	NNS
10_1101-2021_01_08_425885	344	42	for	for	IN
10_1101-2021_01_08_425885	344	43	which	which	WDT
10_1101-2021_01_08_425885	344	44	fits	fit	VBZ
10_1101-2021_01_08_425885	344	45	to	to	IN
10_1101-2021_01_08_425885	344	46	p2(x	p2(x	ADD
10_1101-2021_01_08_425885	344	47	)	)	-RRB-
10_1101-2021_01_08_425885	344	48	yielded	yield	VBD
10_1101-2021_01_08_425885	344	49	accurate	accurate	JJ
10_1101-2021_01_08_425885	344	50	S.	S.	NNP
10_1101-2021_01_08_425885	344	51	Dm	Dm	NNP
10_1101-2021_01_08_425885	344	52	corresponds	correspond	VBZ
10_1101-2021_01_08_425885	344	53	to	to	IN
10_1101-2021_01_08_425885	344	54	intervals	interval	NNS
10_1101-2021_01_08_425885	344	55	where	where	WRB
10_1101-2021_01_08_425885	344	56	Equation	equation	NN
10_1101-2021_01_08_425885	344	57	4	4	CD
10_1101-2021_01_08_425885	344	58	is	be	VBZ
10_1101-2021_01_08_425885	344	59	accurate	accurate	JJ
10_1101-2021_01_08_425885	344	60	to	to	IN
10_1101-2021_01_08_425885	344	61	our	-PRON-	PRP$
10_1101-2021_01_08_425885	344	62	desired	desire	VBN
10_1101-2021_01_08_425885	344	63	tolerance	tolerance	NN
10_1101-2021_01_08_425885	344	64	when	when	WRB
10_1101-2021_01_08_425885	344	65	the	the	DT
10_1101-2021_01_08_425885	344	66	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	344	67	are	be	VBP
10_1101-2021_01_08_425885	344	68	known	know	VBN
10_1101-2021_01_08_425885	344	69	exactly	exactly	RB
10_1101-2021_01_08_425885	344	70	.	.	.
10_1101-2021_01_08_425885	345	1	Next	next	RB
10_1101-2021_01_08_425885	345	2	,	,	,
10_1101-2021_01_08_425885	345	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	345	4	uniformly	uniformly	RB
10_1101-2021_01_08_425885	345	5	sampled	sample	VBD
10_1101-2021_01_08_425885	345	6	N	n	NN
10_1101-2021_01_08_425885	345	7	=	=	SYM
10_1101-2021_01_08_425885	345	8	104	104	CD
10_1101-2021_01_08_425885	345	9	points	point	NNS
10_1101-2021_01_08_425885	345	10	from	from	IN
10_1101-2021_01_08_425885	345	11	S2	s2	NN
10_1101-2021_01_08_425885	345	12	(	(	-LRB-
10_1101-2021_01_08_425885	345	13	see	see	VB
10_1101-2021_01_08_425885	345	14	Figure	figure	NN
10_1101-2021_01_08_425885	345	15	1A	1a	NN
10_1101-2021_01_08_425885	345	16	;	;	:
10_1101-2021_01_08_425885	345	17	Methods	Methods	NNP
10_1101-2021_01_08_425885	345	18	Section	Section	NNP
10_1101-2021_01_08_425885	345	19	4.4.1.1	4.4.1.1	CD
10_1101-2021_01_08_425885	345	20	)	)	-RRB-
10_1101-2021_01_08_425885	345	21	,	,	,
10_1101-2021_01_08_425885	345	22	estimated	estimate	VBD
10_1101-2021_01_08_425885	345	23	∆M	∆M	NNP
10_1101-2021_01_08_425885	345	24	using	use	VBG
10_1101-2021_01_08_425885	345	25	the	the	DT
10_1101-2021_01_08_425885	345	26	random	random	JJ
10_1101-2021_01_08_425885	345	27	walk	walk	NN
10_1101-2021_01_08_425885	345	28	Graph	Graph	NNP
10_1101-2021_01_08_425885	345	29	Laplacian	Laplacian	NNP
10_1101-2021_01_08_425885	345	30	with	with	IN
10_1101-2021_01_08_425885	345	31	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	345	32	kernel	kernel	NN
10_1101-2021_01_08_425885	345	33	(	(	-LRB-
10_1101-2021_01_08_425885	345	34	see	see	VB
10_1101-2021_01_08_425885	345	35	Equation	Equation	NNP
10_1101-2021_01_08_425885	345	36	15	15	CD
10_1101-2021_01_08_425885	345	37	in	in	IN
10_1101-2021_01_08_425885	345	38	Methods	Methods	NNP
10_1101-2021_01_08_425885	345	39	Section	Section	NNP
10_1101-2021_01_08_425885	345	40	4.2.5	4.2.5	CD
10_1101-2021_01_08_425885	345	41	)	)	-RRB-
10_1101-2021_01_08_425885	345	42	,	,	,
10_1101-2021_01_08_425885	345	43	and	and	CC
10_1101-2021_01_08_425885	345	44	computed	compute	VBD
10_1101-2021_01_08_425885	345	45	empirical	empirical	JJ
10_1101-2021_01_08_425885	345	46	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	345	47	,	,	,
10_1101-2021_01_08_425885	345	48	λk	λk	NNP
10_1101-2021_01_08_425885	345	49	,	,	,
10_1101-2021_01_08_425885	345	50	from	from	IN
10_1101-2021_01_08_425885	345	51	∆M	∆M	NNP
10_1101-2021_01_08_425885	345	52	.	.	.
10_1101-2021_01_08_425885	346	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	346	2	selected	select	VBD
10_1101-2021_01_08_425885	346	3	N	n	CC
10_1101-2021_01_08_425885	346	4	=	=	SYM
10_1101-2021_01_08_425885	346	5	10	10	CD
10_1101-2021_01_08_425885	346	6	4	4	CD
10_1101-2021_01_08_425885	346	7	as	as	IN
10_1101-2021_01_08_425885	346	8	it	-PRON-	PRP
10_1101-2021_01_08_425885	346	9	is	be	VBZ
10_1101-2021_01_08_425885	346	10	the	the	DT
10_1101-2021_01_08_425885	346	11	same	same	JJ
10_1101-2021_01_08_425885	346	12	order	order	NN
10_1101-2021_01_08_425885	346	13	of	of	IN
10_1101-2021_01_08_425885	346	14	magnitude	magnitude	NN
10_1101-2021_01_08_425885	346	15	as	as	IN
10_1101-2021_01_08_425885	346	16	the	the	DT
10_1101-2021_01_08_425885	346	17	sample	sample	NN
10_1101-2021_01_08_425885	346	18	size	size	NN
10_1101-2021_01_08_425885	346	19	of	of	IN
10_1101-2021_01_08_425885	346	20	current	current	JJ
10_1101-2021_01_08_425885	346	21	scRNAseq	scrnaseq	JJ
10_1101-2021_01_08_425885	346	22	experiments	experiment	NNS
10_1101-2021_01_08_425885	346	23	,	,	,
10_1101-2021_01_08_425885	346	24	and	and	CC
10_1101-2021_01_08_425885	346	25	is	be	VBZ
10_1101-2021_01_08_425885	346	26	sufficient	sufficient	JJ
10_1101-2021_01_08_425885	346	27	to	to	TO
10_1101-2021_01_08_425885	346	28	identify	identify	VB
10_1101-2021_01_08_425885	346	29	M	M	NNP
10_1101-2021_01_08_425885	346	30	as	as	IN
10_1101-2021_01_08_425885	346	31	S2	s2	NN
10_1101-2021_01_08_425885	346	32	by	by	IN
10_1101-2021_01_08_425885	346	33	eye	eye	NN
10_1101-2021_01_08_425885	346	34	(	(	-LRB-
10_1101-2021_01_08_425885	346	35	see	see	VB
10_1101-2021_01_08_425885	346	36	Figure	Figure	NNP
10_1101-2021_01_08_425885	346	37	1A	1a	NN
10_1101-2021_01_08_425885	346	38	)	)	-RRB-
10_1101-2021_01_08_425885	346	39	.	.	.
10_1101-2021_01_08_425885	347	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	347	2	verified	verify	VBD
10_1101-2021_01_08_425885	347	3	if	if	IN
10_1101-2021_01_08_425885	347	4	estimates	estimate	NNS
10_1101-2021_01_08_425885	347	5	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	347	6	)	)	-RRB-
10_1101-2021_01_08_425885	347	7	,	,	,
10_1101-2021_01_08_425885	347	8	obtained	obtain	VBN
10_1101-2021_01_08_425885	347	9	by	by	IN
10_1101-2021_01_08_425885	347	10	evaluating	evaluate	VBG
10_1101-2021_01_08_425885	347	11	Equation	Equation	NNP
10_1101-2021_01_08_425885	347	12	3	3	CD
10_1101-2021_01_08_425885	347	13	using	use	VBG
10_1101-2021_01_08_425885	347	14	λk	λk	NNP
10_1101-2021_01_08_425885	347	15	,	,	,
10_1101-2021_01_08_425885	347	16	when	when	WRB
10_1101-2021_01_08_425885	347	17	fit	fit	JJ
10_1101-2021_01_08_425885	347	18	as	as	IN
10_1101-2021_01_08_425885	347	19	described	describe	VBN
10_1101-2021_01_08_425885	347	20	above	above	RB
10_1101-2021_01_08_425885	347	21	to	to	IN
10_1101-2021_01_08_425885	347	22	p2(x	p2(x	NNP
10_1101-2021_01_08_425885	347	23	)	)	-RRB-
10_1101-2021_01_08_425885	347	24	over	over	IN
10_1101-2021_01_08_425885	347	25	intervals	interval	NNS
10_1101-2021_01_08_425885	347	26	in	in	IN
10_1101-2021_01_08_425885	347	27	Dm	Dm	NNP
10_1101-2021_01_08_425885	347	28	,	,	,
10_1101-2021_01_08_425885	347	29	recapitulated	recapitulate	VBD
10_1101-2021_01_08_425885	347	30	the	the	DT
10_1101-2021_01_08_425885	347	31	accurate	accurate	JJ
10_1101-2021_01_08_425885	347	32	S	s	NN
10_1101-2021_01_08_425885	347	33	obtained	obtain	VBD
10_1101-2021_01_08_425885	347	34	using	use	VBG
10_1101-2021_01_08_425885	347	35	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	347	36	)	)	-RRB-
10_1101-2021_01_08_425885	347	37	.	.	.
10_1101-2021_01_08_425885	348	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	348	2	restricted	restrict	VBD
10_1101-2021_01_08_425885	348	3	our	-PRON-	PRP$
10_1101-2021_01_08_425885	348	4	attention	attention	NN
10_1101-2021_01_08_425885	348	5	to	to	IN
10_1101-2021_01_08_425885	348	6	Dm	Dm	NNP
10_1101-2021_01_08_425885	348	7	for	for	IN
10_1101-2021_01_08_425885	348	8	calculations	calculation	NNS
10_1101-2021_01_08_425885	348	9	using	use	VBG
10_1101-2021_01_08_425885	348	10	empirical	empirical	JJ
10_1101-2021_01_08_425885	348	11	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	348	12	,	,	,
10_1101-2021_01_08_425885	348	13	since	since	IN
10_1101-2021_01_08_425885	348	14	it	-PRON-	PRP
10_1101-2021_01_08_425885	348	15	is	be	VBZ
10_1101-2021_01_08_425885	348	16	only	only	RB
10_1101-2021_01_08_425885	348	17	over	over	IN
10_1101-2021_01_08_425885	348	18	intervals	interval	NNS
10_1101-2021_01_08_425885	348	19	in	in	IN
10_1101-2021_01_08_425885	348	20	Dm	Dm	NNP
10_1101-2021_01_08_425885	348	21	that	that	IN
10_1101-2021_01_08_425885	348	22	it	-PRON-	PRP
10_1101-2021_01_08_425885	348	23	is	be	VBZ
10_1101-2021_01_08_425885	348	24	even	even	RB
10_1101-2021_01_08_425885	348	25	theoretically	theoretically	RB
10_1101-2021_01_08_425885	348	26	possible	possible	JJ
10_1101-2021_01_08_425885	348	27	to	to	TO
10_1101-2021_01_08_425885	348	28	compute	compute	VB
10_1101-2021_01_08_425885	348	29	scalar	scalar	JJ
10_1101-2021_01_08_425885	348	30	curvature	curvature	NN
10_1101-2021_01_08_425885	348	31	to	to	IN
10_1101-2021_01_08_425885	348	32	the	the	DT
10_1101-2021_01_08_425885	348	33	desired	desire	VBN
10_1101-2021_01_08_425885	348	34	accuracy	accuracy	NN
10_1101-2021_01_08_425885	348	35	.	.	.
10_1101-2021_01_08_425885	349	1	Below	below	RB
10_1101-2021_01_08_425885	349	2	,	,	,
10_1101-2021_01_08_425885	349	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	349	4	report	report	VBP
10_1101-2021_01_08_425885	349	5	our	-PRON-	PRP$
10_1101-2021_01_08_425885	349	6	findings	finding	NNS
10_1101-2021_01_08_425885	349	7	for	for	IN
10_1101-2021_01_08_425885	349	8	different	different	JJ
10_1101-2021_01_08_425885	349	9	m.	m.	NN
10_1101-2021_01_08_425885	349	10	4.2.2	4.2.2	CD
10_1101-2021_01_08_425885	349	11	Infinite	Infinite	NNP
10_1101-2021_01_08_425885	349	12	Series	Series	NNP
10_1101-2021_01_08_425885	349	13	We	-PRON-	PRP
10_1101-2021_01_08_425885	349	14	first	first	RB
10_1101-2021_01_08_425885	349	15	applied	apply	VBD
10_1101-2021_01_08_425885	349	16	this	this	DT
10_1101-2021_01_08_425885	349	17	approach	approach	NN
10_1101-2021_01_08_425885	349	18	to	to	IN
10_1101-2021_01_08_425885	349	19	the	the	DT
10_1101-2021_01_08_425885	349	20	ideal	ideal	JJ
10_1101-2021_01_08_425885	349	21	case	case	NN
10_1101-2021_01_08_425885	349	22	in	in	IN
10_1101-2021_01_08_425885	349	23	Equation	Equation	NNP
10_1101-2021_01_08_425885	349	24	3	3	CD
10_1101-2021_01_08_425885	349	25	,	,	,
10_1101-2021_01_08_425885	349	26	where	where	WRB
10_1101-2021_01_08_425885	349	27	infinite	infinite	JJ
10_1101-2021_01_08_425885	349	28	analytical	analytical	JJ
10_1101-2021_01_08_425885	349	29	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	349	30	are	be	VBP
10_1101-2021_01_08_425885	349	31	available	available	JJ
10_1101-2021_01_08_425885	349	32	.	.	.
10_1101-2021_01_08_425885	350	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	350	2	computed	compute	VBD
10_1101-2021_01_08_425885	350	3	z∞(x	z∞(x	NN
10_1101-2021_01_08_425885	350	4	)	)	-RRB-
10_1101-2021_01_08_425885	350	5	(	(	-LRB-
10_1101-2021_01_08_425885	350	6	shown	show	VBN
10_1101-2021_01_08_425885	350	7	as	as	IN
10_1101-2021_01_08_425885	350	8	a	a	DT
10_1101-2021_01_08_425885	350	9	black	black	JJ
10_1101-2021_01_08_425885	350	10	line	line	NN
10_1101-2021_01_08_425885	350	11	in	in	IN
10_1101-2021_01_08_425885	350	12	Figure	Figure	NNP
10_1101-2021_01_08_425885	350	13	S1A	s1a	NN
10_1101-2021_01_08_425885	350	14	)	)	-RRB-
10_1101-2021_01_08_425885	350	15	and	and	CC
10_1101-2021_01_08_425885	350	16	obtained	obtain	VBN
10_1101-2021_01_08_425885	350	17	S	S	NNP
10_1101-2021_01_08_425885	350	18	by	by	IN
10_1101-2021_01_08_425885	350	19	fitting	fit	VBG
10_1101-2021_01_08_425885	350	20	p2(x	p2(x	NNP
10_1101-2021_01_08_425885	350	21	)	)	-RRB-
10_1101-2021_01_08_425885	350	22	over	over	IN
10_1101-2021_01_08_425885	350	23	various	various	JJ
10_1101-2021_01_08_425885	350	24	intervals	interval	NNS
10_1101-2021_01_08_425885	350	25	as	as	IN
10_1101-2021_01_08_425885	350	26	described	describe	VBN
10_1101-2021_01_08_425885	350	27	above	above	RB
10_1101-2021_01_08_425885	350	28	.	.	.
10_1101-2021_01_08_425885	351	1	Figure	figure	NN
10_1101-2021_01_08_425885	351	2	S1B	s1b	NN
10_1101-2021_01_08_425885	351	3	shows	show	VBZ
10_1101-2021_01_08_425885	351	4	that	that	IN
10_1101-2021_01_08_425885	351	5	D∞	D∞	NNP
10_1101-2021_01_08_425885	351	6	is	be	VBZ
10_1101-2021_01_08_425885	351	7	comprised	comprise	VBN
10_1101-2021_01_08_425885	351	8	of	of	IN
10_1101-2021_01_08_425885	351	9	intervals	interval	NNS
10_1101-2021_01_08_425885	351	10	with	with	IN
10_1101-2021_01_08_425885	351	11	0	0	CD
10_1101-2021_01_08_425885	351	12	≤	≤	NN
10_1101-2021_01_08_425885	351	13	x1	x1	NNP
10_1101-2021_01_08_425885	351	14	<	<	XX
10_1101-2021_01_08_425885	351	15	x2	x2	NNP
10_1101-2021_01_08_425885	351	16	.	.	.
10_1101-2021_01_08_425885	352	1	1.15	1.15	CD
10_1101-2021_01_08_425885	352	2	.	.	.
10_1101-2021_01_08_425885	353	1	For	for	IN
10_1101-2021_01_08_425885	353	2	x2	x2	NNP
10_1101-2021_01_08_425885	353	3	&	&	CC
10_1101-2021_01_08_425885	353	4	1.15	1.15	CD
10_1101-2021_01_08_425885	353	5	,	,	,
10_1101-2021_01_08_425885	353	6	errors	error	NNS
10_1101-2021_01_08_425885	353	7	from	from	IN
10_1101-2021_01_08_425885	353	8	neglecting	neglect	VBG
10_1101-2021_01_08_425885	353	9	higher	high	JJR
10_1101-2021_01_08_425885	353	10	-	-	HYPH
10_1101-2021_01_08_425885	353	11	order	order	NN
10_1101-2021_01_08_425885	353	12	terms	term	NNS
10_1101-2021_01_08_425885	353	13	o(x	o(x	$
10_1101-2021_01_08_425885	353	14	3	3	CD
10_1101-2021_01_08_425885	353	15	)	)	-RRB-
10_1101-2021_01_08_425885	353	16	in	in	IN
10_1101-2021_01_08_425885	353	17	Equation	equation	NN
10_1101-2021_01_08_425885	353	18	4	4	CD
10_1101-2021_01_08_425885	353	19	dominate	dominate	NN
10_1101-2021_01_08_425885	353	20	.	.	.
10_1101-2021_01_08_425885	354	1	Since	since	IN
10_1101-2021_01_08_425885	354	2	zm(x	zm(x	CD
10_1101-2021_01_08_425885	354	3	)	)	-RRB-
10_1101-2021_01_08_425885	354	4	converges	converge	NNS
10_1101-2021_01_08_425885	354	5	from	from	IN
10_1101-2021_01_08_425885	354	6	∞	∞	NNP
10_1101-2021_01_08_425885	354	7	,	,	,
10_1101-2021_01_08_425885	354	8	x2	x2	NNP
10_1101-2021_01_08_425885	354	9	.	.	.
10_1101-2021_01_08_425885	355	1	1.15	1.15	CD
10_1101-2021_01_08_425885	355	2	necessarily	necessarily	RB
10_1101-2021_01_08_425885	355	3	holds	hold	VBZ
10_1101-2021_01_08_425885	355	4	for	for	IN
10_1101-2021_01_08_425885	355	5	any	any	DT
10_1101-2021_01_08_425885	355	6	interval	interval	NN
10_1101-2021_01_08_425885	355	7	in	in	IN
10_1101-2021_01_08_425885	355	8	Dm∀m	Dm∀m	NNP
10_1101-2021_01_08_425885	355	9	.	.	.
10_1101-2021_01_08_425885	356	1	4.2.3	4.2.3	NNP
10_1101-2021_01_08_425885	356	2	Truncated	Truncated	NNP
10_1101-2021_01_08_425885	356	3	Series	Series	NNP
10_1101-2021_01_08_425885	356	4	We	-PRON-	PRP
10_1101-2021_01_08_425885	356	5	next	next	RB
10_1101-2021_01_08_425885	356	6	considered	consider	VBD
10_1101-2021_01_08_425885	356	7	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	356	8	)	)	-RRB-
10_1101-2021_01_08_425885	356	9	for	for	IN
10_1101-2021_01_08_425885	356	10	m	m	NNP
10_1101-2021_01_08_425885	356	11	<	<	XX
10_1101-2021_01_08_425885	356	12	N	N	NNP
10_1101-2021_01_08_425885	356	13	,	,	,
10_1101-2021_01_08_425885	356	14	since	since	IN
10_1101-2021_01_08_425885	356	15	in	in	IN
10_1101-2021_01_08_425885	356	16	practice	practice	NN
10_1101-2021_01_08_425885	356	17	,	,	,
10_1101-2021_01_08_425885	356	18	we	-PRON-	PRP
10_1101-2021_01_08_425885	356	19	will	will	MD
10_1101-2021_01_08_425885	356	20	only	only	RB
10_1101-2021_01_08_425885	356	21	have	have	VB
10_1101-2021_01_08_425885	356	22	access	access	NN
10_1101-2021_01_08_425885	356	23	to	to	IN
10_1101-2021_01_08_425885	356	24	as	as	RB
10_1101-2021_01_08_425885	356	25	many	many	JJ
10_1101-2021_01_08_425885	356	26	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	356	27	as	as	IN
10_1101-2021_01_08_425885	356	28	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	356	29	(	(	-LRB-
10_1101-2021_01_08_425885	356	30	N	n	NN
10_1101-2021_01_08_425885	356	31	)	)	-RRB-
10_1101-2021_01_08_425885	356	32	.	.	.
10_1101-2021_01_08_425885	357	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	357	2	computed	compute	VBD
10_1101-2021_01_08_425885	357	3	z1000(x	z1000(x	NNP
10_1101-2021_01_08_425885	357	4	)	)	-RRB-
10_1101-2021_01_08_425885	357	5	using	use	VBG
10_1101-2021_01_08_425885	357	6	Equation	equation	NN
10_1101-2021_01_08_425885	357	7	3	3	CD
10_1101-2021_01_08_425885	357	8	(	(	-LRB-
10_1101-2021_01_08_425885	357	9	shown	show	VBN
10_1101-2021_01_08_425885	357	10	as	as	IN
10_1101-2021_01_08_425885	357	11	a	a	DT
10_1101-2021_01_08_425885	357	12	solid	solid	JJ
10_1101-2021_01_08_425885	357	13	blue	blue	JJ
10_1101-2021_01_08_425885	357	14	line	line	NN
10_1101-2021_01_08_425885	357	15	in	in	IN
10_1101-2021_01_08_425885	357	16	Figure	Figure	NNP
10_1101-2021_01_08_425885	357	17	S1A	s1a	NN
10_1101-2021_01_08_425885	357	18	)	)	-RRB-
10_1101-2021_01_08_425885	357	19	,	,	,
10_1101-2021_01_08_425885	357	20	and	and	CC
10_1101-2021_01_08_425885	357	21	obtained	obtain	VBN
10_1101-2021_01_08_425885	357	22	S	S	NNP
10_1101-2021_01_08_425885	357	23	by	by	IN
10_1101-2021_01_08_425885	357	24	fitting	fit	VBG
10_1101-2021_01_08_425885	357	25	p2(x	p2(x	ADD
10_1101-2021_01_08_425885	357	26	)	)	-RRB-
10_1101-2021_01_08_425885	357	27	(	(	-LRB-
10_1101-2021_01_08_425885	357	28	see	see	VB
10_1101-2021_01_08_425885	357	29	Figure	Figure	NNP
10_1101-2021_01_08_425885	357	30	S1C	S1C	NNP
10_1101-2021_01_08_425885	357	31	)	)	-RRB-
10_1101-2021_01_08_425885	357	32	.	.	.
10_1101-2021_01_08_425885	358	1	Intervals	interval	NNS
10_1101-2021_01_08_425885	358	2	in	in	IN
10_1101-2021_01_08_425885	358	3	D1000	D1000	NNP
10_1101-2021_01_08_425885	358	4	roughly	roughly	RB
10_1101-2021_01_08_425885	358	5	satisfy	satisfy	VBP
10_1101-2021_01_08_425885	358	6	0.25	0.25	CD
10_1101-2021_01_08_425885	358	7	.	.	.
10_1101-2021_01_08_425885	359	1	x1	x1	NNP
10_1101-2021_01_08_425885	359	2	<	<	XX
10_1101-2021_01_08_425885	359	3	x2	x2	NNP
10_1101-2021_01_08_425885	359	4	.	.	.
10_1101-2021_01_08_425885	360	1	1.15	1.15	CD
10_1101-2021_01_08_425885	360	2	.	.	.
10_1101-2021_01_08_425885	361	1	However	however	RB
10_1101-2021_01_08_425885	361	2	,	,	,
10_1101-2021_01_08_425885	361	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	361	4	found	find	VBD
10_1101-2021_01_08_425885	361	5	that	that	IN
10_1101-2021_01_08_425885	361	6	z1000(x	z1000(x	NNP
10_1101-2021_01_08_425885	361	7	)	)	-RRB-
10_1101-2021_01_08_425885	361	8	(	(	-LRB-
10_1101-2021_01_08_425885	361	9	shown	show	VBN
10_1101-2021_01_08_425885	361	10	as	as	IN
10_1101-2021_01_08_425885	361	11	a	a	DT
10_1101-2021_01_08_425885	361	12	dashed	dash	VBN
10_1101-2021_01_08_425885	361	13	blue	blue	JJ
10_1101-2021_01_08_425885	361	14	line	line	NN
10_1101-2021_01_08_425885	361	15	in	in	IN
10_1101-2021_01_08_425885	361	16	Figure	Figure	NNP
10_1101-2021_01_08_425885	361	17	S1A	s1a	NN
10_1101-2021_01_08_425885	361	18	)	)	-RRB-
10_1101-2021_01_08_425885	361	19	deviated	deviate	VBN
10_1101-2021_01_08_425885	361	20	markedly	markedly	RB
10_1101-2021_01_08_425885	361	21	from	from	IN
10_1101-2021_01_08_425885	361	22	z1000(x	z1000(x	NNP
10_1101-2021_01_08_425885	361	23	)	)	-RRB-
10_1101-2021_01_08_425885	361	24	in	in	IN
10_1101-2021_01_08_425885	361	25	the	the	DT
10_1101-2021_01_08_425885	361	26	rough	rough	JJ
10_1101-2021_01_08_425885	361	27	interval	interval	NN
10_1101-2021_01_08_425885	361	28	[	[	-LRB-
10_1101-2021_01_08_425885	361	29	0.1	0.1	CD
10_1101-2021_01_08_425885	361	30	,	,	,
10_1101-2021_01_08_425885	361	31	0.75	0.75	CD
10_1101-2021_01_08_425885	361	32	]	]	-RRB-
10_1101-2021_01_08_425885	361	33	,	,	,
10_1101-2021_01_08_425885	361	34	which	which	WDT
10_1101-2021_01_08_425885	361	35	has	have	VBZ
10_1101-2021_01_08_425885	361	36	significant	significant	JJ
10_1101-2021_01_08_425885	361	37	overlap	overlap	NN
10_1101-2021_01_08_425885	361	38	with	with	IN
10_1101-2021_01_08_425885	361	39	D1000	D1000	NNP
10_1101-2021_01_08_425885	361	40	.	.	.
10_1101-2021_01_08_425885	362	1	Consequently	consequently	RB
10_1101-2021_01_08_425885	362	2	,	,	,
10_1101-2021_01_08_425885	362	3	when	when	WRB
10_1101-2021_01_08_425885	362	4	we	-PRON-	PRP
10_1101-2021_01_08_425885	362	5	21	21	CD
10_1101-2021_01_08_425885	362	6	.CC	.CC	:
10_1101-2021_01_08_425885	362	7	-	-	HYPH
10_1101-2021_01_08_425885	362	8	BY	by	IN
10_1101-2021_01_08_425885	362	9	-	-	HYPH
10_1101-2021_01_08_425885	362	10	NC	NC	NNP
10_1101-2021_01_08_425885	362	11	-	-	HYPH
10_1101-2021_01_08_425885	362	12	ND	ND	NNP
10_1101-2021_01_08_425885	362	13	4.0	4.0	CD
10_1101-2021_01_08_425885	362	14	International	International	NNP
10_1101-2021_01_08_425885	362	15	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	362	16	under	under	IN
10_1101-2021_01_08_425885	362	17	a	a	DT
10_1101-2021_01_08_425885	362	18	(	(	-LRB-
10_1101-2021_01_08_425885	362	19	which	which	WDT
10_1101-2021_01_08_425885	362	20	was	be	VBD
10_1101-2021_01_08_425885	362	21	not	not	RB
10_1101-2021_01_08_425885	362	22	certified	certify	VBN
10_1101-2021_01_08_425885	362	23	by	by	IN
10_1101-2021_01_08_425885	362	24	peer	peer	NN
10_1101-2021_01_08_425885	362	25	review	review	NN
10_1101-2021_01_08_425885	362	26	)	)	-RRB-
10_1101-2021_01_08_425885	362	27	is	be	VBZ
10_1101-2021_01_08_425885	362	28	the	the	DT
10_1101-2021_01_08_425885	362	29	author	author	NN
10_1101-2021_01_08_425885	362	30	/	/	SYM
10_1101-2021_01_08_425885	362	31	funder	funder	NN
10_1101-2021_01_08_425885	362	32	,	,	,
10_1101-2021_01_08_425885	362	33	who	who	WP
10_1101-2021_01_08_425885	362	34	has	have	VBZ
10_1101-2021_01_08_425885	362	35	granted	grant	VBN
10_1101-2021_01_08_425885	362	36	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	362	37	a	a	DT
10_1101-2021_01_08_425885	362	38	license	license	NN
10_1101-2021_01_08_425885	362	39	to	to	TO
10_1101-2021_01_08_425885	362	40	display	display	VB
10_1101-2021_01_08_425885	362	41	the	the	DT
10_1101-2021_01_08_425885	362	42	preprint	preprint	NN
10_1101-2021_01_08_425885	362	43	in	in	IN
10_1101-2021_01_08_425885	362	44	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	362	45	.	.	.
10_1101-2021_01_08_425885	363	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	363	2	is	be	VBZ
10_1101-2021_01_08_425885	363	3	made	make	VBN
10_1101-2021_01_08_425885	363	4	The	the	DT
10_1101-2021_01_08_425885	363	5	copyright	copyright	NN
10_1101-2021_01_08_425885	363	6	holder	holder	NN
10_1101-2021_01_08_425885	363	7	for	for	IN
10_1101-2021_01_08_425885	363	8	this	this	DT
10_1101-2021_01_08_425885	363	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	363	10	version	version	NN
10_1101-2021_01_08_425885	363	11	posted	post	VBD
10_1101-2021_01_08_425885	363	12	January	January	NNP
10_1101-2021_01_08_425885	363	13	8	8	CD
10_1101-2021_01_08_425885	363	14	,	,	,
10_1101-2021_01_08_425885	363	15	2021	2021	CD
10_1101-2021_01_08_425885	363	16	.	.	.
10_1101-2021_01_08_425885	363	17	;	;	:
10_1101-2021_01_08_425885	363	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	363	19	:	:	:
10_1101-2021_01_08_425885	363	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	363	21	preprint	preprint	NN
10_1101-2021_01_08_425885	363	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	363	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	RB
10_1101-2021_01_08_425885	363	24	fit	fit	JJ
10_1101-2021_01_08_425885	363	25	p2(x	p2(x	NNP
10_1101-2021_01_08_425885	363	26	)	)	-RRB-
10_1101-2021_01_08_425885	363	27	to	to	IN
10_1101-2021_01_08_425885	363	28	z1000(x	z1000(x	NNP
10_1101-2021_01_08_425885	363	29	)	)	-RRB-
10_1101-2021_01_08_425885	363	30	on	on	IN
10_1101-2021_01_08_425885	363	31	D1000	D1000	NNP
10_1101-2021_01_08_425885	363	32	,	,	,
10_1101-2021_01_08_425885	363	33	the	the	DT
10_1101-2021_01_08_425885	363	34	resulting	result	VBG
10_1101-2021_01_08_425885	363	35	S	S	NNP
10_1101-2021_01_08_425885	363	36	was	be	VBD
10_1101-2021_01_08_425885	363	37	not	not	RB
10_1101-2021_01_08_425885	363	38	accurate	accurate	JJ
10_1101-2021_01_08_425885	363	39	for	for	IN
10_1101-2021_01_08_425885	363	40	any	any	DT
10_1101-2021_01_08_425885	363	41	interval	interval	NN
10_1101-2021_01_08_425885	363	42	in	in	IN
10_1101-2021_01_08_425885	363	43	D1000	D1000	NNP
10_1101-2021_01_08_425885	363	44	(	(	-LRB-
10_1101-2021_01_08_425885	363	45	see	see	VB
10_1101-2021_01_08_425885	363	46	Figure	figure	NN
10_1101-2021_01_08_425885	363	47	S1D	s1d	NN
10_1101-2021_01_08_425885	363	48	)	)	-RRB-
10_1101-2021_01_08_425885	363	49	.	.	.
10_1101-2021_01_08_425885	364	1	Note	note	VB
10_1101-2021_01_08_425885	364	2	that	that	IN
10_1101-2021_01_08_425885	364	3	this	this	DT
10_1101-2021_01_08_425885	364	4	inaccuracy	inaccuracy	NN
10_1101-2021_01_08_425885	364	5	was	be	VBD
10_1101-2021_01_08_425885	364	6	not	not	RB
10_1101-2021_01_08_425885	364	7	a	a	DT
10_1101-2021_01_08_425885	364	8	consequence	consequence	NN
10_1101-2021_01_08_425885	364	9	of	of	IN
10_1101-2021_01_08_425885	364	10	not	not	RB
10_1101-2021_01_08_425885	364	11	using	use	VBG
10_1101-2021_01_08_425885	364	12	all	all	DT
10_1101-2021_01_08_425885	364	13	N	n	NN
10_1101-2021_01_08_425885	364	14	available	available	JJ
10_1101-2021_01_08_425885	364	15	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	364	16	.	.	.
10_1101-2021_01_08_425885	365	1	While	while	IN
10_1101-2021_01_08_425885	365	2	picking	pick	VBG
10_1101-2021_01_08_425885	365	3	m	m	NN
10_1101-2021_01_08_425885	365	4	=	=	SYM
10_1101-2021_01_08_425885	365	5	N	n	NN
10_1101-2021_01_08_425885	365	6	would	would	MD
10_1101-2021_01_08_425885	365	7	reduce	reduce	VB
10_1101-2021_01_08_425885	365	8	the	the	DT
10_1101-2021_01_08_425885	365	9	lower	low	JJR
10_1101-2021_01_08_425885	365	10	bound	bind	VBN
10_1101-2021_01_08_425885	365	11	on	on	IN
10_1101-2021_01_08_425885	365	12	valid	valid	JJ
10_1101-2021_01_08_425885	365	13	intervals	interval	NNS
10_1101-2021_01_08_425885	365	14	in	in	IN
10_1101-2021_01_08_425885	365	15	Dm	Dm	NNP
10_1101-2021_01_08_425885	365	16	(	(	-LRB-
10_1101-2021_01_08_425885	365	17	since	since	IN
10_1101-2021_01_08_425885	365	18	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	365	19	)	)	-RRB-
10_1101-2021_01_08_425885	365	20	converges	converge	NNS
10_1101-2021_01_08_425885	365	21	from	from	IN
10_1101-2021_01_08_425885	365	22	∞	∞	NNP
10_1101-2021_01_08_425885	365	23	)	)	-RRB-
10_1101-2021_01_08_425885	365	24	,	,	,
10_1101-2021_01_08_425885	365	25	it	-PRON-	PRP
10_1101-2021_01_08_425885	365	26	is	be	VBZ
10_1101-2021_01_08_425885	365	27	exactly	exactly	RB
10_1101-2021_01_08_425885	365	28	for	for	IN
10_1101-2021_01_08_425885	365	29	small	small	JJ
10_1101-2021_01_08_425885	365	30	x1	x1	NN
10_1101-2021_01_08_425885	365	31	that	that	WDT
10_1101-2021_01_08_425885	365	32	S	S	NNP
10_1101-2021_01_08_425885	365	33	obtained	obtain	VBD
10_1101-2021_01_08_425885	365	34	from	from	IN
10_1101-2021_01_08_425885	365	35	z1000(x	z1000(x	NNP
10_1101-2021_01_08_425885	365	36	)	)	-RRB-
10_1101-2021_01_08_425885	365	37	is	be	VBZ
10_1101-2021_01_08_425885	365	38	already	already	RB
10_1101-2021_01_08_425885	365	39	over	over	RB
10_1101-2021_01_08_425885	365	40	-	-	HYPH
10_1101-2021_01_08_425885	365	41	estimated	estimate	VBN
10_1101-2021_01_08_425885	365	42	as	as	IN
10_1101-2021_01_08_425885	365	43	shown	show	VBN
10_1101-2021_01_08_425885	365	44	in	in	IN
10_1101-2021_01_08_425885	365	45	Figure	Figure	NNP
10_1101-2021_01_08_425885	365	46	S1D.	S1D.	NNP
10_1101-2021_01_08_425885	366	1	Since	since	IN
10_1101-2021_01_08_425885	366	2	zm2	zm2	NNP
10_1101-2021_01_08_425885	366	3	(	(	-LRB-
10_1101-2021_01_08_425885	366	4	x	x	NNP
10_1101-2021_01_08_425885	366	5	)	)	-RRB-
10_1101-2021_01_08_425885	366	6	>	>	NNP
10_1101-2021_01_08_425885	366	7	zm1	zm1	NNP
10_1101-2021_01_08_425885	366	8	(	(	-LRB-
10_1101-2021_01_08_425885	366	9	x	x	NNP
10_1101-2021_01_08_425885	366	10	)	)	-RRB-
10_1101-2021_01_08_425885	366	11	∀x	∀x	NNP
10_1101-2021_01_08_425885	366	12	,	,	,
10_1101-2021_01_08_425885	366	13	m2	m2	NNP
10_1101-2021_01_08_425885	366	14	>	>	NNP
10_1101-2021_01_08_425885	366	15	m1	m1	NNP
10_1101-2021_01_08_425885	366	16	,	,	,
10_1101-2021_01_08_425885	366	17	using	use	VBG
10_1101-2021_01_08_425885	366	18	a	a	DT
10_1101-2021_01_08_425885	366	19	truncated	truncate	VBN
10_1101-2021_01_08_425885	366	20	series	series	NN
10_1101-2021_01_08_425885	366	21	with	with	IN
10_1101-2021_01_08_425885	366	22	a	a	DT
10_1101-2021_01_08_425885	366	23	larger	large	JJR
10_1101-2021_01_08_425885	366	24	m	m	NN
10_1101-2021_01_08_425885	366	25	would	would	MD
10_1101-2021_01_08_425885	366	26	simply	simply	RB
10_1101-2021_01_08_425885	366	27	exaggerate	exaggerate	VB
10_1101-2021_01_08_425885	366	28	the	the	DT
10_1101-2021_01_08_425885	366	29	difference	difference	NN
10_1101-2021_01_08_425885	366	30	between	between	IN
10_1101-2021_01_08_425885	366	31	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	366	32	)	)	-RRB-
10_1101-2021_01_08_425885	366	33	and	and	CC
10_1101-2021_01_08_425885	366	34	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	366	35	)	)	-RRB-
10_1101-2021_01_08_425885	366	36	for	for	IN
10_1101-2021_01_08_425885	366	37	small	small	JJ
10_1101-2021_01_08_425885	366	38	x	x	NNS
10_1101-2021_01_08_425885	366	39	and	and	CC
10_1101-2021_01_08_425885	366	40	cause	cause	VB
10_1101-2021_01_08_425885	366	41	scalar	scalar	JJ
10_1101-2021_01_08_425885	366	42	curvatures	curvature	NNS
10_1101-2021_01_08_425885	366	43	estimated	estimate	VBN
10_1101-2021_01_08_425885	366	44	using	use	VBG
10_1101-2021_01_08_425885	366	45	the	the	DT
10_1101-2021_01_08_425885	366	46	latter	latter	JJ
10_1101-2021_01_08_425885	366	47	to	to	TO
10_1101-2021_01_08_425885	366	48	be	be	VB
10_1101-2021_01_08_425885	366	49	further	further	RB
10_1101-2021_01_08_425885	366	50	over	over	RB
10_1101-2021_01_08_425885	366	51	-	-	HYPH
10_1101-2021_01_08_425885	366	52	estimated	estimate	VBN
10_1101-2021_01_08_425885	366	53	.	.	.
10_1101-2021_01_08_425885	367	1	Following	follow	VBG
10_1101-2021_01_08_425885	367	2	this	this	DT
10_1101-2021_01_08_425885	367	3	line	line	NN
10_1101-2021_01_08_425885	367	4	of	of	IN
10_1101-2021_01_08_425885	367	5	thought	thought	NN
10_1101-2021_01_08_425885	367	6	,	,	,
10_1101-2021_01_08_425885	367	7	we	-PRON-	PRP
10_1101-2021_01_08_425885	367	8	reasoned	reason	VBD
10_1101-2021_01_08_425885	367	9	that	that	IN
10_1101-2021_01_08_425885	367	10	picking	pick	VBG
10_1101-2021_01_08_425885	367	11	a	a	DT
10_1101-2021_01_08_425885	367	12	fewer	few	JJR
10_1101-2021_01_08_425885	367	13	number	number	NN
10_1101-2021_01_08_425885	367	14	of	of	IN
10_1101-2021_01_08_425885	367	15	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	367	16	may	may	MD
10_1101-2021_01_08_425885	367	17	ameliorate	ameliorate	VB
10_1101-2021_01_08_425885	367	18	the	the	DT
10_1101-2021_01_08_425885	367	19	issue	issue	NN
10_1101-2021_01_08_425885	367	20	.	.	.
10_1101-2021_01_08_425885	368	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	368	2	selected	select	VBD
10_1101-2021_01_08_425885	368	3	m	m	NN
10_1101-2021_01_08_425885	368	4	=	=	SYM
10_1101-2021_01_08_425885	368	5	49	49	CD
10_1101-2021_01_08_425885	368	6	(	(	-LRB-
10_1101-2021_01_08_425885	368	7	instead	instead	RB
10_1101-2021_01_08_425885	368	8	of	of	IN
10_1101-2021_01_08_425885	368	9	a	a	DT
10_1101-2021_01_08_425885	368	10	round	round	JJ
10_1101-2021_01_08_425885	368	11	number	number	NN
10_1101-2021_01_08_425885	368	12	like	like	IN
10_1101-2021_01_08_425885	368	13	m	m	NN
10_1101-2021_01_08_425885	368	14	=	=	SYM
10_1101-2021_01_08_425885	368	15	50	50	CD
10_1101-2021_01_08_425885	368	16	so	so	IN
10_1101-2021_01_08_425885	368	17	that	that	IN
10_1101-2021_01_08_425885	368	18	all	all	DT
10_1101-2021_01_08_425885	368	19	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	368	20	of	of	IN
10_1101-2021_01_08_425885	368	21	a	a	DT
10_1101-2021_01_08_425885	368	22	given	give	VBN
10_1101-2021_01_08_425885	368	23	multiplicity	multiplicity	NN
10_1101-2021_01_08_425885	368	24	are	be	VBP
10_1101-2021_01_08_425885	368	25	included	include	VBN
10_1101-2021_01_08_425885	368	26	)	)	-RRB-
10_1101-2021_01_08_425885	368	27	and	and	CC
10_1101-2021_01_08_425885	368	28	repeated	repeat	VBN
10_1101-2021_01_08_425885	368	29	this	this	DT
10_1101-2021_01_08_425885	368	30	analysis	analysis	NN
10_1101-2021_01_08_425885	368	31	for	for	IN
10_1101-2021_01_08_425885	368	32	the	the	DT
10_1101-2021_01_08_425885	368	33	same	same	JJ
10_1101-2021_01_08_425885	368	34	set	set	NN
10_1101-2021_01_08_425885	368	35	of	of	IN
10_1101-2021_01_08_425885	368	36	N	n	NN
10_1101-2021_01_08_425885	368	37	=	=	SYM
10_1101-2021_01_08_425885	368	38	104	104	CD
10_1101-2021_01_08_425885	368	39	points	point	NNS
10_1101-2021_01_08_425885	368	40	.	.	.
10_1101-2021_01_08_425885	369	1	z49(x	z49(x	NNP
10_1101-2021_01_08_425885	369	2	)	)	-RRB-
10_1101-2021_01_08_425885	369	3	is	be	VBZ
10_1101-2021_01_08_425885	369	4	shown	show	VBN
10_1101-2021_01_08_425885	369	5	as	as	IN
10_1101-2021_01_08_425885	369	6	a	a	DT
10_1101-2021_01_08_425885	369	7	solid	solid	JJ
10_1101-2021_01_08_425885	369	8	red	red	JJ
10_1101-2021_01_08_425885	369	9	line	line	NN
10_1101-2021_01_08_425885	369	10	in	in	IN
10_1101-2021_01_08_425885	369	11	Figure	Figure	NNP
10_1101-2021_01_08_425885	369	12	S1A	s1a	NN
10_1101-2021_01_08_425885	369	13	and	and	CC
10_1101-2021_01_08_425885	369	14	the	the	DT
10_1101-2021_01_08_425885	369	15	intervals	interval	NNS
10_1101-2021_01_08_425885	369	16	over	over	IN
10_1101-2021_01_08_425885	369	17	which	which	WDT
10_1101-2021_01_08_425885	369	18	fits	fit	VBZ
10_1101-2021_01_08_425885	369	19	to	to	IN
10_1101-2021_01_08_425885	369	20	p2(x	p2(x	ADD
10_1101-2021_01_08_425885	369	21	)	)	-RRB-
10_1101-2021_01_08_425885	369	22	yield	yield	VBP
10_1101-2021_01_08_425885	369	23	accurate	accurate	JJ
10_1101-2021_01_08_425885	369	24	S	S	NNP
10_1101-2021_01_08_425885	369	25	,	,	,
10_1101-2021_01_08_425885	369	26	D49	D49	NNP
10_1101-2021_01_08_425885	369	27	,	,	,
10_1101-2021_01_08_425885	369	28	are	be	VBP
10_1101-2021_01_08_425885	369	29	shown	show	VBN
10_1101-2021_01_08_425885	369	30	in	in	IN
10_1101-2021_01_08_425885	369	31	Figure	Figure	NNP
10_1101-2021_01_08_425885	369	32	S1E.	S1E.	NNP
10_1101-2021_01_08_425885	370	1	While	while	IN
10_1101-2021_01_08_425885	370	2	z49(x	z49(x	NNP
10_1101-2021_01_08_425885	370	3	)	)	-RRB-
10_1101-2021_01_08_425885	370	4	(	(	-LRB-
10_1101-2021_01_08_425885	370	5	shown	show	VBN
10_1101-2021_01_08_425885	370	6	as	as	IN
10_1101-2021_01_08_425885	370	7	a	a	DT
10_1101-2021_01_08_425885	370	8	dashed	dash	VBN
10_1101-2021_01_08_425885	370	9	red	red	JJ
10_1101-2021_01_08_425885	370	10	line	line	NN
10_1101-2021_01_08_425885	370	11	in	in	IN
10_1101-2021_01_08_425885	370	12	Figure	Figure	NNP
10_1101-2021_01_08_425885	370	13	S1A	s1a	NN
10_1101-2021_01_08_425885	370	14	)	)	-RRB-
10_1101-2021_01_08_425885	370	15	has	have	VBZ
10_1101-2021_01_08_425885	370	16	a	a	DT
10_1101-2021_01_08_425885	370	17	much	much	RB
10_1101-2021_01_08_425885	370	18	smaller	small	JJR
10_1101-2021_01_08_425885	370	19	deviation	deviation	NN
10_1101-2021_01_08_425885	370	20	from	from	IN
10_1101-2021_01_08_425885	370	21	z49(x	z49(x	NNP
10_1101-2021_01_08_425885	370	22	)	)	-RRB-
10_1101-2021_01_08_425885	370	23	than	than	IN
10_1101-2021_01_08_425885	370	24	z1000(x	z1000(x	NNP
10_1101-2021_01_08_425885	370	25	)	)	-RRB-
10_1101-2021_01_08_425885	370	26	did	do	VBD
10_1101-2021_01_08_425885	370	27	from	from	IN
10_1101-2021_01_08_425885	370	28	z1000(x	z1000(x	NNP
10_1101-2021_01_08_425885	370	29	)	)	-RRB-
10_1101-2021_01_08_425885	370	30	,	,	,
10_1101-2021_01_08_425885	370	31	no	no	DT
10_1101-2021_01_08_425885	370	32	estimate	estimate	NN
10_1101-2021_01_08_425885	370	33	of	of	IN
10_1101-2021_01_08_425885	370	34	S	S	NNP
10_1101-2021_01_08_425885	370	35	obtained	obtain	VBN
10_1101-2021_01_08_425885	370	36	from	from	IN
10_1101-2021_01_08_425885	370	37	fits	fit	NNS
10_1101-2021_01_08_425885	370	38	of	of	IN
10_1101-2021_01_08_425885	370	39	z49(x	z49(x	NN
10_1101-2021_01_08_425885	370	40	)	)	-RRB-
10_1101-2021_01_08_425885	370	41	to	to	IN
10_1101-2021_01_08_425885	370	42	p2(x	p2(x	NNP
10_1101-2021_01_08_425885	370	43	)	)	-RRB-
10_1101-2021_01_08_425885	370	44	on	on	IN
10_1101-2021_01_08_425885	370	45	D49	D49	NNP
10_1101-2021_01_08_425885	370	46	were	be	VBD
10_1101-2021_01_08_425885	370	47	sufficiently	sufficiently	RB
10_1101-2021_01_08_425885	370	48	accurate	accurate	JJ
10_1101-2021_01_08_425885	370	49	once	once	RB
10_1101-2021_01_08_425885	370	50	again	again	RB
10_1101-2021_01_08_425885	370	51	(	(	-LRB-
10_1101-2021_01_08_425885	370	52	see	see	VB
10_1101-2021_01_08_425885	370	53	Figure	Figure	NNP
10_1101-2021_01_08_425885	370	54	S1F	S1F	NNP
10_1101-2021_01_08_425885	370	55	)	)	-RRB-
10_1101-2021_01_08_425885	370	56	.	.	.
10_1101-2021_01_08_425885	371	1	4.2.4	4.2.4	NNP
10_1101-2021_01_08_425885	371	2	Eigenvalue	Eigenvalue	NNP
10_1101-2021_01_08_425885	371	3	Convergence	Convergence	NNP
10_1101-2021_01_08_425885	371	4	We	-PRON-	PRP
10_1101-2021_01_08_425885	371	5	refrained	refrain	VBD
10_1101-2021_01_08_425885	371	6	from	from	IN
10_1101-2021_01_08_425885	371	7	reducing	reduce	VBG
10_1101-2021_01_08_425885	371	8	m	m	NNP
10_1101-2021_01_08_425885	371	9	further	further	RB
10_1101-2021_01_08_425885	371	10	to	to	TO
10_1101-2021_01_08_425885	371	11	improve	improve	VB
10_1101-2021_01_08_425885	371	12	agreement	agreement	NN
10_1101-2021_01_08_425885	371	13	between	between	IN
10_1101-2021_01_08_425885	371	14	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	371	15	)	)	-RRB-
10_1101-2021_01_08_425885	371	16	and	and	CC
10_1101-2021_01_08_425885	371	17	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	371	18	)	)	-RRB-
10_1101-2021_01_08_425885	371	19	after	after	IN
10_1101-2021_01_08_425885	371	20	noting	note	VBG
10_1101-2021_01_08_425885	371	21	that	that	IN
10_1101-2021_01_08_425885	371	22	the	the	DT
10_1101-2021_01_08_425885	371	23	size	size	NN
10_1101-2021_01_08_425885	371	24	of	of	IN
10_1101-2021_01_08_425885	371	25	the	the	DT
10_1101-2021_01_08_425885	371	26	intervals	interval	NNS
10_1101-2021_01_08_425885	371	27	in	in	IN
10_1101-2021_01_08_425885	371	28	Dm	Dm	NNP
10_1101-2021_01_08_425885	371	29	shrink	shrink	VBP
10_1101-2021_01_08_425885	371	30	with	with	IN
10_1101-2021_01_08_425885	371	31	m.	m.	NN
10_1101-2021_01_08_425885	371	32	Though	though	IN
10_1101-2021_01_08_425885	371	33	we	-PRON-	PRP
10_1101-2021_01_08_425885	371	34	may	may	MD
10_1101-2021_01_08_425885	371	35	have	have	VB
10_1101-2021_01_08_425885	371	36	a	a	DT
10_1101-2021_01_08_425885	371	37	better	well	JJR
10_1101-2021_01_08_425885	371	38	chance	chance	NN
10_1101-2021_01_08_425885	371	39	of	of	IN
10_1101-2021_01_08_425885	371	40	computing	compute	VBG
10_1101-2021_01_08_425885	371	41	accurate	accurate	JJ
10_1101-2021_01_08_425885	371	42	S	S	NNP
10_1101-2021_01_08_425885	371	43	with	with	IN
10_1101-2021_01_08_425885	371	44	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	371	45	)	)	-RRB-
10_1101-2021_01_08_425885	371	46	on	on	IN
10_1101-2021_01_08_425885	371	47	Dm	Dm	NNP
10_1101-2021_01_08_425885	371	48	for	for	IN
10_1101-2021_01_08_425885	371	49	smaller	small	JJR
10_1101-2021_01_08_425885	371	50	m	m	NN
10_1101-2021_01_08_425885	371	51	,	,	,
10_1101-2021_01_08_425885	371	52	recall	recall	VB
10_1101-2021_01_08_425885	371	53	that	that	IN
10_1101-2021_01_08_425885	371	54	in	in	IN
10_1101-2021_01_08_425885	371	55	practice	practice	NN
10_1101-2021_01_08_425885	371	56	we	-PRON-	PRP
10_1101-2021_01_08_425885	371	57	will	will	MD
10_1101-2021_01_08_425885	371	58	not	not	RB
10_1101-2021_01_08_425885	371	59	have	have	VB
10_1101-2021_01_08_425885	371	60	Dm	Dm	NNP
10_1101-2021_01_08_425885	371	61	available	available	JJ
10_1101-2021_01_08_425885	371	62	to	to	IN
10_1101-2021_01_08_425885	371	63	us	-PRON-	PRP
10_1101-2021_01_08_425885	371	64	since	since	IN
10_1101-2021_01_08_425885	371	65	the	the	DT
10_1101-2021_01_08_425885	371	66	analytical	analytical	JJ
10_1101-2021_01_08_425885	371	67	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	371	68	will	will	MD
10_1101-2021_01_08_425885	371	69	be	be	VB
10_1101-2021_01_08_425885	371	70	unknown	unknown	JJ
10_1101-2021_01_08_425885	371	71	.	.	.
10_1101-2021_01_08_425885	372	1	Therefore	therefore	RB
10_1101-2021_01_08_425885	372	2	,	,	,
10_1101-2021_01_08_425885	372	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	372	4	simply	simply	RB
10_1101-2021_01_08_425885	372	5	shift	shift	VBP
10_1101-2021_01_08_425885	372	6	the	the	DT
10_1101-2021_01_08_425885	372	7	problem	problem	NN
10_1101-2021_01_08_425885	372	8	to	to	IN
10_1101-2021_01_08_425885	372	9	one	one	CD
10_1101-2021_01_08_425885	372	10	of	of	IN
10_1101-2021_01_08_425885	372	11	choosing	choose	VBG
10_1101-2021_01_08_425885	372	12	an	an	DT
10_1101-2021_01_08_425885	372	13	interval	interval	NN
10_1101-2021_01_08_425885	372	14	that	that	WDT
10_1101-2021_01_08_425885	372	15	will	will	MD
10_1101-2021_01_08_425885	372	16	yield	yield	VB
10_1101-2021_01_08_425885	372	17	an	an	DT
10_1101-2021_01_08_425885	372	18	accurate	accurate	JJ
10_1101-2021_01_08_425885	372	19	S	S	NNP
10_1101-2021_01_08_425885	372	20	,	,	,
10_1101-2021_01_08_425885	372	21	from	from	IN
10_1101-2021_01_08_425885	372	22	a	a	DT
10_1101-2021_01_08_425885	372	23	shrinking	shrink	VBG
10_1101-2021_01_08_425885	372	24	pool	pool	NN
10_1101-2021_01_08_425885	372	25	of	of	IN
10_1101-2021_01_08_425885	372	26	intervals	interval	NNS
10_1101-2021_01_08_425885	372	27	that	that	WDT
10_1101-2021_01_08_425885	372	28	could	could	MD
10_1101-2021_01_08_425885	372	29	even	even	RB
10_1101-2021_01_08_425885	372	30	theoretically	theoretically	RB
10_1101-2021_01_08_425885	372	31	yield	yield	VB
10_1101-2021_01_08_425885	372	32	an	an	DT
10_1101-2021_01_08_425885	372	33	accurate	accurate	JJ
10_1101-2021_01_08_425885	372	34	estimate	estimate	NN
10_1101-2021_01_08_425885	372	35	.	.	.
10_1101-2021_01_08_425885	373	1	Instead	instead	RB
10_1101-2021_01_08_425885	373	2	,	,	,
10_1101-2021_01_08_425885	373	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	373	4	compared	compare	VBD
10_1101-2021_01_08_425885	373	5	the	the	DT
10_1101-2021_01_08_425885	373	6	estimated	estimate	VBN
10_1101-2021_01_08_425885	373	7	λks	λks	NNP
10_1101-2021_01_08_425885	373	8	with	with	IN
10_1101-2021_01_08_425885	373	9	their	-PRON-	PRP$
10_1101-2021_01_08_425885	373	10	true	true	JJ
10_1101-2021_01_08_425885	373	11	values	value	NNS
10_1101-2021_01_08_425885	373	12	,	,	,
10_1101-2021_01_08_425885	373	13	λk	λk	NNP
10_1101-2021_01_08_425885	373	14	,	,	,
10_1101-2021_01_08_425885	373	15	and	and	CC
10_1101-2021_01_08_425885	373	16	observed	observe	VBD
10_1101-2021_01_08_425885	373	17	that	that	IN
10_1101-2021_01_08_425885	373	18	the	the	DT
10_1101-2021_01_08_425885	373	19	former	former	JJ
10_1101-2021_01_08_425885	373	20	con-	con-	NN
10_1101-2021_01_08_425885	373	21	sistently	sistently	RB
10_1101-2021_01_08_425885	373	22	under	under	IN
10_1101-2021_01_08_425885	373	23	-	-	HYPH
10_1101-2021_01_08_425885	373	24	estimate	estimate	VB
10_1101-2021_01_08_425885	373	25	the	the	DT
10_1101-2021_01_08_425885	373	26	latter	latter	JJ
10_1101-2021_01_08_425885	373	27	(	(	-LRB-
10_1101-2021_01_08_425885	373	28	see	see	VB
10_1101-2021_01_08_425885	373	29	Figure	Figure	NNP
10_1101-2021_01_08_425885	373	30	S1H	s1h	NN
10_1101-2021_01_08_425885	373	31	)	)	-RRB-
10_1101-2021_01_08_425885	373	32	.	.	.
10_1101-2021_01_08_425885	374	1	Furthermore	furthermore	RB
10_1101-2021_01_08_425885	374	2	,	,	,
10_1101-2021_01_08_425885	374	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	374	4	found	find	VBD
10_1101-2021_01_08_425885	374	5	that	that	IN
10_1101-2021_01_08_425885	374	6	the	the	DT
10_1101-2021_01_08_425885	374	7	fractional	fractional	JJ
10_1101-2021_01_08_425885	374	8	error	error	NN
10_1101-2021_01_08_425885	374	9	grows	grow	VBZ
10_1101-2021_01_08_425885	374	10	with	with	IN
10_1101-2021_01_08_425885	374	11	k	k	NN
10_1101-2021_01_08_425885	374	12	,	,	,
10_1101-2021_01_08_425885	374	13	exceeding	exceed	VBG
10_1101-2021_01_08_425885	374	14	60	60	CD
10_1101-2021_01_08_425885	374	15	%	%	NN
10_1101-2021_01_08_425885	374	16	for	for	IN
10_1101-2021_01_08_425885	374	17	k	k	NN
10_1101-2021_01_08_425885	374	18	=	=	SYM
10_1101-2021_01_08_425885	374	19	37	37	CD
10_1101-2021_01_08_425885	374	20	,	,	,
10_1101-2021_01_08_425885	374	21	...	...	NFP
10_1101-2021_01_08_425885	374	22	,	,	,
10_1101-2021_01_08_425885	374	23	49	49	CD
10_1101-2021_01_08_425885	374	24	.	.	.
10_1101-2021_01_08_425885	375	1	Therefore	therefore	RB
10_1101-2021_01_08_425885	375	2	,	,	,
10_1101-2021_01_08_425885	375	3	z49(x	z49(x	NNP
10_1101-2021_01_08_425885	375	4	)	)	-RRB-
10_1101-2021_01_08_425885	375	5	will	will	MD
10_1101-2021_01_08_425885	375	6	only	only	RB
10_1101-2021_01_08_425885	375	7	be	be	VB
10_1101-2021_01_08_425885	375	8	accurate	accurate	JJ
10_1101-2021_01_08_425885	375	9	if	if	IN
10_1101-2021_01_08_425885	375	10	N	N	NNP
10_1101-2021_01_08_425885	375	11	is	be	VBZ
10_1101-2021_01_08_425885	375	12	large	large	JJ
10_1101-2021_01_08_425885	375	13	enough	enough	RB
10_1101-2021_01_08_425885	375	14	to	to	TO
10_1101-2021_01_08_425885	375	15	limit	limit	VB
10_1101-2021_01_08_425885	375	16	the	the	DT
10_1101-2021_01_08_425885	375	17	fractional	fractional	JJ
10_1101-2021_01_08_425885	375	18	error	error	NN
10_1101-2021_01_08_425885	375	19	.	.	.
10_1101-2021_01_08_425885	376	1	To	to	TO
10_1101-2021_01_08_425885	376	2	determine	determine	VB
10_1101-2021_01_08_425885	376	3	the	the	DT
10_1101-2021_01_08_425885	376	4	required	required	JJ
10_1101-2021_01_08_425885	376	5	tolerance	tolerance	NN
10_1101-2021_01_08_425885	376	6	on	on	IN
10_1101-2021_01_08_425885	376	7	the	the	DT
10_1101-2021_01_08_425885	376	8	fractional	fractional	JJ
10_1101-2021_01_08_425885	376	9	error	error	NN
10_1101-2021_01_08_425885	376	10	,	,	,
10_1101-2021_01_08_425885	376	11	we	-PRON-	PRP
10_1101-2021_01_08_425885	376	12	constructed	construct	VBD
10_1101-2021_01_08_425885	376	13	a	a	DT
10_1101-2021_01_08_425885	376	14	truncated	truncate	VBN
10_1101-2021_01_08_425885	376	15	series	series	NN
10_1101-2021_01_08_425885	376	16	analo-	analo-	NN
10_1101-2021_01_08_425885	376	17	gous	gous	JJ
10_1101-2021_01_08_425885	376	18	to	to	IN
10_1101-2021_01_08_425885	376	19	Equation	Equation	NNP
10_1101-2021_01_08_425885	376	20	3	3	CD
10_1101-2021_01_08_425885	376	21	,	,	,
10_1101-2021_01_08_425885	376	22	but	but	CC
10_1101-2021_01_08_425885	376	23	with	with	IN
10_1101-2021_01_08_425885	376	24	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	376	25	interpolated	interpolate	VBN
10_1101-2021_01_08_425885	376	26	between	between	IN
10_1101-2021_01_08_425885	376	27	the	the	DT
10_1101-2021_01_08_425885	376	28	analytical	analytical	JJ
10_1101-2021_01_08_425885	376	29	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	376	30	and	and	CC
10_1101-2021_01_08_425885	376	31	the	the	DT
10_1101-2021_01_08_425885	376	32	empirical	empirical	JJ
10_1101-2021_01_08_425885	376	33	22	22	CD
10_1101-2021_01_08_425885	376	34	.CC	.CC	:
10_1101-2021_01_08_425885	376	35	-	-	HYPH
10_1101-2021_01_08_425885	376	36	BY	by	IN
10_1101-2021_01_08_425885	376	37	-	-	HYPH
10_1101-2021_01_08_425885	376	38	NC	NC	NNP
10_1101-2021_01_08_425885	376	39	-	-	HYPH
10_1101-2021_01_08_425885	376	40	ND	ND	NNP
10_1101-2021_01_08_425885	376	41	4.0	4.0	CD
10_1101-2021_01_08_425885	376	42	International	International	NNP
10_1101-2021_01_08_425885	376	43	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	376	44	under	under	IN
10_1101-2021_01_08_425885	376	45	a	a	DT
10_1101-2021_01_08_425885	376	46	(	(	-LRB-
10_1101-2021_01_08_425885	376	47	which	which	WDT
10_1101-2021_01_08_425885	376	48	was	be	VBD
10_1101-2021_01_08_425885	376	49	not	not	RB
10_1101-2021_01_08_425885	376	50	certified	certify	VBN
10_1101-2021_01_08_425885	376	51	by	by	IN
10_1101-2021_01_08_425885	376	52	peer	peer	NN
10_1101-2021_01_08_425885	376	53	review	review	NN
10_1101-2021_01_08_425885	376	54	)	)	-RRB-
10_1101-2021_01_08_425885	376	55	is	be	VBZ
10_1101-2021_01_08_425885	376	56	the	the	DT
10_1101-2021_01_08_425885	376	57	author	author	NN
10_1101-2021_01_08_425885	376	58	/	/	SYM
10_1101-2021_01_08_425885	376	59	funder	funder	NN
10_1101-2021_01_08_425885	376	60	,	,	,
10_1101-2021_01_08_425885	376	61	who	who	WP
10_1101-2021_01_08_425885	376	62	has	have	VBZ
10_1101-2021_01_08_425885	376	63	granted	grant	VBN
10_1101-2021_01_08_425885	376	64	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	376	65	a	a	DT
10_1101-2021_01_08_425885	376	66	license	license	NN
10_1101-2021_01_08_425885	376	67	to	to	TO
10_1101-2021_01_08_425885	376	68	display	display	VB
10_1101-2021_01_08_425885	376	69	the	the	DT
10_1101-2021_01_08_425885	376	70	preprint	preprint	NN
10_1101-2021_01_08_425885	376	71	in	in	IN
10_1101-2021_01_08_425885	376	72	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	376	73	.	.	.
10_1101-2021_01_08_425885	377	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	377	2	is	be	VBZ
10_1101-2021_01_08_425885	377	3	made	make	VBN
10_1101-2021_01_08_425885	377	4	The	the	DT
10_1101-2021_01_08_425885	377	5	copyright	copyright	NN
10_1101-2021_01_08_425885	377	6	holder	holder	NN
10_1101-2021_01_08_425885	377	7	for	for	IN
10_1101-2021_01_08_425885	377	8	this	this	DT
10_1101-2021_01_08_425885	377	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	377	10	version	version	NN
10_1101-2021_01_08_425885	377	11	posted	post	VBD
10_1101-2021_01_08_425885	377	12	January	January	NNP
10_1101-2021_01_08_425885	377	13	8	8	CD
10_1101-2021_01_08_425885	377	14	,	,	,
10_1101-2021_01_08_425885	377	15	2021	2021	CD
10_1101-2021_01_08_425885	377	16	.	.	.
10_1101-2021_01_08_425885	377	17	;	;	:
10_1101-2021_01_08_425885	377	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	377	19	:	:	:
10_1101-2021_01_08_425885	377	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	377	21	preprint	preprint	NN
10_1101-2021_01_08_425885	377	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	377	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	CD
10_1101-2021_01_08_425885	377	24	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	377	25	determined	determine	VBN
10_1101-2021_01_08_425885	377	26	for	for	IN
10_1101-2021_01_08_425885	377	27	N	n	NN
10_1101-2021_01_08_425885	377	28	=	=	SYM
10_1101-2021_01_08_425885	377	29	10000	10000	CD
10_1101-2021_01_08_425885	377	30	,	,	,
10_1101-2021_01_08_425885	377	31	according	accord	VBG
10_1101-2021_01_08_425885	377	32	to	to	IN
10_1101-2021_01_08_425885	377	33	a	a	DT
10_1101-2021_01_08_425885	377	34	parameter	parameter	NN
10_1101-2021_01_08_425885	377	35	f	f	XX
10_1101-2021_01_08_425885	377	36	:	:	:
10_1101-2021_01_08_425885	377	37	z̃m(x	z̃m(x	NNP
10_1101-2021_01_08_425885	377	38	;	;	:
10_1101-2021_01_08_425885	377	39	f	f	LS
10_1101-2021_01_08_425885	377	40	)	)	-RRB-
10_1101-2021_01_08_425885	377	41	=	=	NFP
10_1101-2021_01_08_425885	377	42	(	(	-LRB-
10_1101-2021_01_08_425885	377	43	4π	4π	LS
10_1101-2021_01_08_425885	377	44	)	)	-RRB-
10_1101-2021_01_08_425885	377	45	d/2xd	d/2xd	NNP
10_1101-2021_01_08_425885	377	46	m∑	m∑	NNP
10_1101-2021_01_08_425885	377	47	k=1	k=1	JJ
10_1101-2021_01_08_425885	377	48	e−λ̃k(f)x	e−λ̃k(f)x	CD
10_1101-2021_01_08_425885	377	49	2	2	CD
10_1101-2021_01_08_425885	377	50	λ̃k(f	λ̃k(f	NNPS
10_1101-2021_01_08_425885	377	51	)	)	-RRB-
10_1101-2021_01_08_425885	377	52	=	=	NFP
10_1101-2021_01_08_425885	377	53	λk	λk	NN
10_1101-2021_01_08_425885	377	54	+	+	CC
10_1101-2021_01_08_425885	377	55	f(λk	f(λk	CD
10_1101-2021_01_08_425885	377	56	−λk	−λk	CD
10_1101-2021_01_08_425885	377	57	)	)	-RRB-
10_1101-2021_01_08_425885	377	58	(	(	-LRB-
10_1101-2021_01_08_425885	377	59	11	11	CD
10_1101-2021_01_08_425885	377	60	)	)	-RRB-
10_1101-2021_01_08_425885	377	61	f	f	NN
10_1101-2021_01_08_425885	377	62	signifies	signify	VBZ
10_1101-2021_01_08_425885	377	63	that	that	IN
10_1101-2021_01_08_425885	377	64	the	the	DT
10_1101-2021_01_08_425885	377	65	fractional	fractional	JJ
10_1101-2021_01_08_425885	377	66	error	error	NN
10_1101-2021_01_08_425885	377	67	of	of	IN
10_1101-2021_01_08_425885	377	68	the	the	DT
10_1101-2021_01_08_425885	377	69	interpolated	interpolate	VBN
10_1101-2021_01_08_425885	377	70	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	377	71	is	be	VBZ
10_1101-2021_01_08_425885	377	72	reduced	reduce	VBN
10_1101-2021_01_08_425885	377	73	by	by	IN
10_1101-2021_01_08_425885	377	74	1−f	1−f	CD
10_1101-2021_01_08_425885	377	75	relative	relative	JJ
10_1101-2021_01_08_425885	377	76	to	to	IN
10_1101-2021_01_08_425885	377	77	the	the	DT
10_1101-2021_01_08_425885	377	78	empirical	empirical	JJ
10_1101-2021_01_08_425885	377	79	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	377	80	determined	determine	VBN
10_1101-2021_01_08_425885	377	81	for	for	IN
10_1101-2021_01_08_425885	377	82	N	n	NN
10_1101-2021_01_08_425885	377	83	=	=	SYM
10_1101-2021_01_08_425885	377	84	10000	10000	CD
10_1101-2021_01_08_425885	377	85	.	.	.
10_1101-2021_01_08_425885	378	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	378	2	found	find	VBD
10_1101-2021_01_08_425885	378	3	that	that	IN
10_1101-2021_01_08_425885	378	4	f	f	NNP
10_1101-2021_01_08_425885	378	5	≤	≤	NNP
10_1101-2021_01_08_425885	378	6	0.23	0.23	CD
10_1101-2021_01_08_425885	378	7	is	be	VBZ
10_1101-2021_01_08_425885	378	8	needed	need	VBN
10_1101-2021_01_08_425885	378	9	so	so	IN
10_1101-2021_01_08_425885	378	10	that	that	IN
10_1101-2021_01_08_425885	378	11	z̃49(x	z̃49(x	NNP
10_1101-2021_01_08_425885	378	12	;	;	:
10_1101-2021_01_08_425885	378	13	f	f	LS
10_1101-2021_01_08_425885	378	14	)	)	-RRB-
10_1101-2021_01_08_425885	378	15	(	(	-LRB-
10_1101-2021_01_08_425885	378	16	shown	show	VBN
10_1101-2021_01_08_425885	378	17	as	as	IN
10_1101-2021_01_08_425885	378	18	a	a	DT
10_1101-2021_01_08_425885	378	19	green	green	JJ
10_1101-2021_01_08_425885	378	20	line	line	NN
10_1101-2021_01_08_425885	378	21	in	in	IN
10_1101-2021_01_08_425885	378	22	Figure	Figure	NNP
10_1101-2021_01_08_425885	378	23	S1A	s1a	NN
10_1101-2021_01_08_425885	378	24	)	)	-RRB-
10_1101-2021_01_08_425885	378	25	fit	fit	NN
10_1101-2021_01_08_425885	378	26	to	to	IN
10_1101-2021_01_08_425885	378	27	p2(x	p2(x	ADD
10_1101-2021_01_08_425885	378	28	)	)	-RRB-
10_1101-2021_01_08_425885	378	29	yields	yield	NNS
10_1101-2021_01_08_425885	378	30	accurate	accurate	VBP
10_1101-2021_01_08_425885	378	31	S	S	NNP
10_1101-2021_01_08_425885	378	32	on	on	IN
10_1101-2021_01_08_425885	378	33	half	half	PDT
10_1101-2021_01_08_425885	378	34	the	the	DT
10_1101-2021_01_08_425885	378	35	intervals	interval	NNS
10_1101-2021_01_08_425885	378	36	in	in	IN
10_1101-2021_01_08_425885	378	37	D49	D49	NNP
10_1101-2021_01_08_425885	378	38	(	(	-LRB-
10_1101-2021_01_08_425885	378	39	see	see	VB
10_1101-2021_01_08_425885	378	40	Figure	figure	NN
10_1101-2021_01_08_425885	378	41	S1	s1	NN
10_1101-2021_01_08_425885	378	42	G	g	NN
10_1101-2021_01_08_425885	378	43	)	)	-RRB-
10_1101-2021_01_08_425885	378	44	.	.	.
10_1101-2021_01_08_425885	379	1	Given	give	VBN
10_1101-2021_01_08_425885	379	2	that	that	IN
10_1101-2021_01_08_425885	379	3	the	the	DT
10_1101-2021_01_08_425885	379	4	fractional	fractional	JJ
10_1101-2021_01_08_425885	379	5	error	error	NN
10_1101-2021_01_08_425885	379	6	in	in	IN
10_1101-2021_01_08_425885	379	7	estimating	estimate	VBG
10_1101-2021_01_08_425885	379	8	λ37	λ37	NN
10_1101-2021_01_08_425885	379	9	,	,	,
10_1101-2021_01_08_425885	379	10	...	...	:
10_1101-2021_01_08_425885	379	11	,	,	,
10_1101-2021_01_08_425885	379	12	λ49	λ49	NNP
10_1101-2021_01_08_425885	379	13	by	by	IN
10_1101-2021_01_08_425885	379	14	λ37	λ37	NNP
10_1101-2021_01_08_425885	379	15	,	,	,
10_1101-2021_01_08_425885	379	16	...	...	:
10_1101-2021_01_08_425885	379	17	,	,	,
10_1101-2021_01_08_425885	379	18	λ49	λ49	NNP
10_1101-2021_01_08_425885	379	19	is	be	VBZ
10_1101-2021_01_08_425885	379	20	60	60	CD
10_1101-2021_01_08_425885	379	21	%	%	NN
10_1101-2021_01_08_425885	379	22	when	when	WRB
10_1101-2021_01_08_425885	379	23	N	n	NN
10_1101-2021_01_08_425885	379	24	=	=	SYM
10_1101-2021_01_08_425885	379	25	10000	10000	CD
10_1101-2021_01_08_425885	379	26	,	,	,
10_1101-2021_01_08_425885	379	27	how	how	WRB
10_1101-2021_01_08_425885	379	28	large	large	JJ
10_1101-2021_01_08_425885	379	29	does	do	VBZ
10_1101-2021_01_08_425885	379	30	N	n	PRP
10_1101-2021_01_08_425885	379	31	have	have	VB
10_1101-2021_01_08_425885	379	32	to	to	TO
10_1101-2021_01_08_425885	379	33	be	be	VB
10_1101-2021_01_08_425885	379	34	to	to	TO
10_1101-2021_01_08_425885	379	35	reduce	reduce	VB
10_1101-2021_01_08_425885	379	36	this	this	DT
10_1101-2021_01_08_425885	379	37	fractional	fractional	JJ
10_1101-2021_01_08_425885	379	38	error	error	NN
10_1101-2021_01_08_425885	379	39	to	to	IN
10_1101-2021_01_08_425885	379	40	60	60	CD
10_1101-2021_01_08_425885	379	41	%	%	NN
10_1101-2021_01_08_425885	379	42	×	×	CD
10_1101-2021_01_08_425885	379	43	0.23	0.23	CD
10_1101-2021_01_08_425885	379	44	≈	≈	NN
10_1101-2021_01_08_425885	379	45	14	14	CD
10_1101-2021_01_08_425885	379	46	%	%	NN
10_1101-2021_01_08_425885	379	47	?	?	.
10_1101-2021_01_08_425885	380	1	A	a	DT
10_1101-2021_01_08_425885	380	2	convergence	convergence	NN
10_1101-2021_01_08_425885	380	3	rate	rate	NN
10_1101-2021_01_08_425885	380	4	for	for	IN
10_1101-2021_01_08_425885	380	5	the	the	DT
10_1101-2021_01_08_425885	380	6	fractional	fractional	JJ
10_1101-2021_01_08_425885	380	7	error	error	NN
10_1101-2021_01_08_425885	380	8	is	be	VBZ
10_1101-2021_01_08_425885	380	9	given	give	VBN
10_1101-2021_01_08_425885	380	10	in	in	IN
10_1101-2021_01_08_425885	380	11	Theorem	theorem	NN
10_1101-2021_01_08_425885	380	12	1	1	CD
10_1101-2021_01_08_425885	380	13	of	of	IN
10_1101-2021_01_08_425885	380	14	[	[	-LRB-
10_1101-2021_01_08_425885	380	15	30	30	CD
10_1101-2021_01_08_425885	380	16	]	]	-RRB-
10_1101-2021_01_08_425885	380	17	.	.	.
10_1101-2021_01_08_425885	381	1	For	for	IN
10_1101-2021_01_08_425885	381	2	2-dimensional	2-dimensional	CD
10_1101-2021_01_08_425885	381	3	manifolds	manifold	NNS
10_1101-2021_01_08_425885	381	4	:	:	:
10_1101-2021_01_08_425885	381	5	∣∣λk	∣∣λk	NN
10_1101-2021_01_08_425885	381	6	−λk∣∣	−λk∣∣	NNP
10_1101-2021_01_08_425885	381	7	λk	λk	FW
10_1101-2021_01_08_425885	381	8	=	=	FW
10_1101-2021_01_08_425885	381	9	O	o	FW
10_1101-2021_01_08_425885	381	10	(	(	-LRB-
10_1101-2021_01_08_425885	381	11	(	(	-LRB-
10_1101-2021_01_08_425885	381	12	log	log	NNP
10_1101-2021_01_08_425885	381	13	N	n	CD
10_1101-2021_01_08_425885	381	14	)	)	-RRB-
10_1101-2021_01_08_425885	381	15	3	3	CD
10_1101-2021_01_08_425885	381	16	8	8	CD
10_1101-2021_01_08_425885	381	17	N	n	CD
10_1101-2021_01_08_425885	381	18	1	1	CD
10_1101-2021_01_08_425885	381	19	4	4	CD
10_1101-2021_01_08_425885	381	20	)	)	-RRB-
10_1101-2021_01_08_425885	381	21	(	(	-LRB-
10_1101-2021_01_08_425885	381	22	12	12	CD
10_1101-2021_01_08_425885	381	23	)	)	-RRB-
10_1101-2021_01_08_425885	381	24	Assuming	assume	VBG
10_1101-2021_01_08_425885	381	25	that	that	IN
10_1101-2021_01_08_425885	381	26	the	the	DT
10_1101-2021_01_08_425885	381	27	big	big	JJ
10_1101-2021_01_08_425885	381	28	-	-	HYPH
10_1101-2021_01_08_425885	381	29	O	o	NN
10_1101-2021_01_08_425885	381	30	bound	bind	VBN
10_1101-2021_01_08_425885	381	31	is	be	VBZ
10_1101-2021_01_08_425885	381	32	sharp	sharp	JJ
10_1101-2021_01_08_425885	381	33	at	at	IN
10_1101-2021_01_08_425885	381	34	N	n	NN
10_1101-2021_01_08_425885	381	35	=	=	SYM
10_1101-2021_01_08_425885	381	36	104	104	CD
10_1101-2021_01_08_425885	381	37	for	for	IN
10_1101-2021_01_08_425885	381	38	k	k	NN
10_1101-2021_01_08_425885	381	39	=	=	SYM
10_1101-2021_01_08_425885	381	40	37	37	CD
10_1101-2021_01_08_425885	381	41	,	,	,
10_1101-2021_01_08_425885	381	42	...	...	NFP
10_1101-2021_01_08_425885	381	43	,	,	,
10_1101-2021_01_08_425885	381	44	49	49	CD
10_1101-2021_01_08_425885	381	45	(	(	-LRB-
10_1101-2021_01_08_425885	381	46	i.e.	i.e.	FW
10_1101-2021_01_08_425885	382	1	the	the	DT
10_1101-2021_01_08_425885	382	2	prefactor	prefactor	NN
10_1101-2021_01_08_425885	382	3	is	be	VBZ
10_1101-2021_01_08_425885	382	4	given	give	VBN
10_1101-2021_01_08_425885	382	5	by	by	IN
10_1101-2021_01_08_425885	382	6	0.6	0.6	CD
10_1101-2021_01_08_425885	382	7	10000	10000	CD
10_1101-2021_01_08_425885	382	8	1	1	CD
10_1101-2021_01_08_425885	382	9	4	4	CD
10_1101-2021_01_08_425885	382	10	log(10000	log(10000	CD
10_1101-2021_01_08_425885	382	11	)	)	-RRB-
10_1101-2021_01_08_425885	382	12	3	3	CD
10_1101-2021_01_08_425885	382	13	8	8	CD
10_1101-2021_01_08_425885	382	14	≈	≈	NN
10_1101-2021_01_08_425885	382	15	2.61	2.61	CD
10_1101-2021_01_08_425885	382	16	)	)	-RRB-
10_1101-2021_01_08_425885	382	17	,	,	,
10_1101-2021_01_08_425885	382	18	we	-PRON-	PRP
10_1101-2021_01_08_425885	382	19	extrapolated	extrapolate	VBD
10_1101-2021_01_08_425885	382	20	that	that	IN
10_1101-2021_01_08_425885	382	21	at	at	RB
10_1101-2021_01_08_425885	382	22	least	least	JJS
10_1101-2021_01_08_425885	382	23	N	n	NN
10_1101-2021_01_08_425885	382	24	=	=	SYM
10_1101-2021_01_08_425885	382	25	107	107	CD
10_1101-2021_01_08_425885	382	26	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	382	27	are	be	VBP
10_1101-2021_01_08_425885	382	28	needed	need	VBN
10_1101-2021_01_08_425885	382	29	to	to	TO
10_1101-2021_01_08_425885	382	30	reduce	reduce	VB
10_1101-2021_01_08_425885	382	31	the	the	DT
10_1101-2021_01_08_425885	382	32	fractional	fractional	JJ
10_1101-2021_01_08_425885	382	33	error	error	NN
10_1101-2021_01_08_425885	382	34	to	to	IN
10_1101-2021_01_08_425885	382	35	14	14	CD
10_1101-2021_01_08_425885	382	36	%	%	NN
10_1101-2021_01_08_425885	382	37	(	(	-LRB-
10_1101-2021_01_08_425885	382	38	see	see	VB
10_1101-2021_01_08_425885	382	39	Figure	Figure	NNP
10_1101-2021_01_08_425885	382	40	S1H	s1h	NN
10_1101-2021_01_08_425885	382	41	)	)	-RRB-
10_1101-2021_01_08_425885	382	42	.	.	.
10_1101-2021_01_08_425885	383	1	Equation	equation	NN
10_1101-2021_01_08_425885	383	2	12	12	CD
10_1101-2021_01_08_425885	383	3	also	also	RB
10_1101-2021_01_08_425885	383	4	applies	apply	VBZ
10_1101-2021_01_08_425885	383	5	to	to	IN
10_1101-2021_01_08_425885	383	6	empirical	empirical	JJ
10_1101-2021_01_08_425885	383	7	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	383	8	of	of	IN
10_1101-2021_01_08_425885	383	9	∆M	∆M	NNP
10_1101-2021_01_08_425885	383	10	constructed	construct	VBN
10_1101-2021_01_08_425885	383	11	from	from	IN
10_1101-2021_01_08_425885	383	12	weighted	weight	VBN
10_1101-2021_01_08_425885	383	13	kNN	kNN	NNS
10_1101-2021_01_08_425885	383	14	and	and	CC
10_1101-2021_01_08_425885	383	15	r	r	NN
10_1101-2021_01_08_425885	383	16	-	-	HYPH
10_1101-2021_01_08_425885	383	17	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	383	18	kernels	kernel	NNS
10_1101-2021_01_08_425885	383	19	instead	instead	RB
10_1101-2021_01_08_425885	383	20	of	of	IN
10_1101-2021_01_08_425885	383	21	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	383	22	kernels	kernel	NNS
10_1101-2021_01_08_425885	383	23	(	(	-LRB-
10_1101-2021_01_08_425885	383	24	see	see	VB
10_1101-2021_01_08_425885	383	25	Methods	Methods	NNP
10_1101-2021_01_08_425885	383	26	Section	Section	NNP
10_1101-2021_01_08_425885	383	27	4.2.5	4.2.5	CD
10_1101-2021_01_08_425885	383	28	)	)	-RRB-
10_1101-2021_01_08_425885	383	29	.	.	.
10_1101-2021_01_08_425885	384	1	However	however	RB
10_1101-2021_01_08_425885	384	2	,	,	,
10_1101-2021_01_08_425885	384	3	the	the	DT
10_1101-2021_01_08_425885	384	4	prefactor	prefactor	NN
10_1101-2021_01_08_425885	384	5	in	in	IN
10_1101-2021_01_08_425885	384	6	Equation	Equation	NNP
10_1101-2021_01_08_425885	384	7	12	12	CD
10_1101-2021_01_08_425885	384	8	is	be	VBZ
10_1101-2021_01_08_425885	384	9	actually	actually	RB
10_1101-2021_01_08_425885	384	10	worse	bad	JJR
10_1101-2021_01_08_425885	384	11	for	for	IN
10_1101-2021_01_08_425885	384	12	these	these	DT
10_1101-2021_01_08_425885	384	13	estimators	estimator	NNS
10_1101-2021_01_08_425885	384	14	since	since	IN
10_1101-2021_01_08_425885	384	15	their	-PRON-	PRP$
10_1101-2021_01_08_425885	384	16	empirical	empirical	JJ
10_1101-2021_01_08_425885	384	17	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	384	18	have	have	VBP
10_1101-2021_01_08_425885	384	19	larger	large	JJR
10_1101-2021_01_08_425885	384	20	fractional	fractional	JJ
10_1101-2021_01_08_425885	384	21	errors	error	NNS
10_1101-2021_01_08_425885	384	22	at	at	IN
10_1101-2021_01_08_425885	384	23	N	n	NN
10_1101-2021_01_08_425885	384	24	=	=	SYM
10_1101-2021_01_08_425885	384	25	10000	10000	CD
10_1101-2021_01_08_425885	384	26	(	(	-LRB-
10_1101-2021_01_08_425885	384	27	see	see	VB
10_1101-2021_01_08_425885	384	28	Figure	Figure	NNP
10_1101-2021_01_08_425885	384	29	S1H	S1H	NNP
10_1101-2021_01_08_425885	384	30	)	)	-RRB-
10_1101-2021_01_08_425885	384	31	,	,	,
10_1101-2021_01_08_425885	384	32	so	so	IN
10_1101-2021_01_08_425885	384	33	that	that	IN
10_1101-2021_01_08_425885	384	34	even	even	RB
10_1101-2021_01_08_425885	384	35	larger	large	JJR
10_1101-2021_01_08_425885	384	36	N	n	NN
10_1101-2021_01_08_425885	384	37	would	would	MD
10_1101-2021_01_08_425885	384	38	be	be	VB
10_1101-2021_01_08_425885	384	39	required	require	VBN
10_1101-2021_01_08_425885	384	40	to	to	TO
10_1101-2021_01_08_425885	384	41	attain	attain	VB
10_1101-2021_01_08_425885	384	42	the	the	DT
10_1101-2021_01_08_425885	384	43	desired	desire	VBN
10_1101-2021_01_08_425885	384	44	fractional	fractional	JJ
10_1101-2021_01_08_425885	384	45	error	error	NN
10_1101-2021_01_08_425885	384	46	.	.	.
10_1101-2021_01_08_425885	385	1	Lastly	lastly	RB
10_1101-2021_01_08_425885	385	2	,	,	,
10_1101-2021_01_08_425885	385	3	note	note	VB
10_1101-2021_01_08_425885	385	4	that	that	IN
10_1101-2021_01_08_425885	385	5	while	while	IN
10_1101-2021_01_08_425885	385	6	we	-PRON-	PRP
10_1101-2021_01_08_425885	385	7	had	have	VBD
10_1101-2021_01_08_425885	385	8	analytical	analytical	JJ
10_1101-2021_01_08_425885	385	9	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	385	10	available	available	JJ
10_1101-2021_01_08_425885	385	11	with	with	IN
10_1101-2021_01_08_425885	385	12	which	which	WDT
10_1101-2021_01_08_425885	385	13	to	to	TO
10_1101-2021_01_08_425885	385	14	ascertain	ascertain	VB
10_1101-2021_01_08_425885	385	15	m	m	NNP
10_1101-2021_01_08_425885	385	16	=	=	SYM
10_1101-2021_01_08_425885	385	17	49	49	CD
10_1101-2021_01_08_425885	385	18	as	as	IN
10_1101-2021_01_08_425885	385	19	suitable	suitable	JJ
10_1101-2021_01_08_425885	385	20	,	,	,
10_1101-2021_01_08_425885	385	21	the	the	DT
10_1101-2021_01_08_425885	385	22	naive	naive	JJ
10_1101-2021_01_08_425885	385	23	approach	approach	NN
10_1101-2021_01_08_425885	385	24	of	of	IN
10_1101-2021_01_08_425885	385	25	simply	simply	RB
10_1101-2021_01_08_425885	385	26	using	use	VBG
10_1101-2021_01_08_425885	385	27	all	all	DT
10_1101-2021_01_08_425885	385	28	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	385	29	available	available	JJ
10_1101-2021_01_08_425885	385	30	(	(	-LRB-
10_1101-2021_01_08_425885	385	31	m	m	NNP
10_1101-2021_01_08_425885	385	32	=	=	SYM
10_1101-2021_01_08_425885	385	33	N	N	NNP
10_1101-2021_01_08_425885	385	34	)	)	-RRB-
10_1101-2021_01_08_425885	385	35	,	,	,
10_1101-2021_01_08_425885	385	36	would	would	MD
10_1101-2021_01_08_425885	385	37	require	require	VB
10_1101-2021_01_08_425885	385	38	sample	sample	NN
10_1101-2021_01_08_425885	385	39	sizes	size	NNS
10_1101-2021_01_08_425885	385	40	that	that	WDT
10_1101-2021_01_08_425885	385	41	are	be	VBP
10_1101-2021_01_08_425885	385	42	even	even	RB
10_1101-2021_01_08_425885	385	43	larger	large	JJR
10_1101-2021_01_08_425885	385	44	by	by	IN
10_1101-2021_01_08_425885	385	45	several	several	JJ
10_1101-2021_01_08_425885	385	46	more	more	JJR
10_1101-2021_01_08_425885	385	47	orders	order	NNS
10_1101-2021_01_08_425885	385	48	of	of	IN
10_1101-2021_01_08_425885	385	49	magnitude	magnitude	NN
10_1101-2021_01_08_425885	385	50	.	.	.
10_1101-2021_01_08_425885	386	1	4.2.5	4.2.5	LS
10_1101-2021_01_08_425885	386	2	Estimating	estimate	VBG
10_1101-2021_01_08_425885	386	3	the	the	DT
10_1101-2021_01_08_425885	386	4	Laplace	Laplace	NNP
10_1101-2021_01_08_425885	386	5	-	-	HYPH
10_1101-2021_01_08_425885	386	6	Beltrami	Beltrami	NNP
10_1101-2021_01_08_425885	386	7	Operator	Operator	NNP
10_1101-2021_01_08_425885	386	8	from	from	IN
10_1101-2021_01_08_425885	386	9	Data	Data	NNP
10_1101-2021_01_08_425885	386	10	For	for	IN
10_1101-2021_01_08_425885	386	11	N	N	NNP
10_1101-2021_01_08_425885	386	12	points	point	NNS
10_1101-2021_01_08_425885	386	13	,	,	,
10_1101-2021_01_08_425885	386	14	{	{	-LRB-
10_1101-2021_01_08_425885	386	15	Xi	Xi	NNP
10_1101-2021_01_08_425885	386	16	}	}	-RRB-
10_1101-2021_01_08_425885	386	17	∈	∈	NNP
10_1101-2021_01_08_425885	386	18	Rn	Rn	NNP
10_1101-2021_01_08_425885	386	19	,	,	,
10_1101-2021_01_08_425885	386	20	sampled	sample	VBN
10_1101-2021_01_08_425885	386	21	from	from	IN
10_1101-2021_01_08_425885	386	22	M	M	NNP
10_1101-2021_01_08_425885	386	23	,	,	,
10_1101-2021_01_08_425885	386	24	we	-PRON-	PRP
10_1101-2021_01_08_425885	386	25	estimated	estimate	VBD
10_1101-2021_01_08_425885	386	26	∆M	∆M	NNP
10_1101-2021_01_08_425885	386	27	by	by	IN
10_1101-2021_01_08_425885	386	28	normalizing	normalize	VBG
10_1101-2021_01_08_425885	386	29	the	the	DT
10_1101-2021_01_08_425885	386	30	weight	weight	NN
10_1101-2021_01_08_425885	386	31	matrix	matrix	NN
10_1101-2021_01_08_425885	386	32	W	W	NNP
10_1101-2021_01_08_425885	386	33	(	(	-LRB-
10_1101-2021_01_08_425885	386	34	see	see	VB
10_1101-2021_01_08_425885	386	35	below	below	RB
10_1101-2021_01_08_425885	386	36	)	)	-RRB-
10_1101-2021_01_08_425885	386	37	using	use	VBG
10_1101-2021_01_08_425885	386	38	the	the	DT
10_1101-2021_01_08_425885	386	39	random	random	JJ
10_1101-2021_01_08_425885	386	40	walk	walk	NN
10_1101-2021_01_08_425885	386	41	normalization	normalization	NN
10_1101-2021_01_08_425885	386	42	[	[	-LRB-
10_1101-2021_01_08_425885	386	43	30	30	CD
10_1101-2021_01_08_425885	386	44	,	,	,
10_1101-2021_01_08_425885	386	45	49	49	CD
10_1101-2021_01_08_425885	386	46	]	]	-RRB-
10_1101-2021_01_08_425885	386	47	.	.	.
10_1101-2021_01_08_425885	387	1	∆M	∆M	NNP
10_1101-2021_01_08_425885	387	2	constructed	construct	VBD
10_1101-2021_01_08_425885	387	3	using	use	VBG
10_1101-2021_01_08_425885	387	4	this	this	DT
10_1101-2021_01_08_425885	387	5	normalization	normalization	NN
10_1101-2021_01_08_425885	387	6	converges	converge	VBZ
10_1101-2021_01_08_425885	387	7	to	to	IN
10_1101-2021_01_08_425885	387	8	∆M	∆M	NNP
10_1101-2021_01_08_425885	387	9	when	when	WRB
10_1101-2021_01_08_425885	387	10	samples	sample	NNS
10_1101-2021_01_08_425885	387	11	are	be	VBP
10_1101-2021_01_08_425885	387	12	drawn	draw	VBN
10_1101-2021_01_08_425885	387	13	uniformly	uniformly	RB
10_1101-2021_01_08_425885	387	14	from	from	IN
10_1101-2021_01_08_425885	387	15	the	the	DT
10_1101-2021_01_08_425885	387	16	embedding	embedding	NN
10_1101-2021_01_08_425885	387	17	of	of	IN
10_1101-2021_01_08_425885	387	18	M	M	NNP
10_1101-2021_01_08_425885	387	19	in	in	IN
10_1101-2021_01_08_425885	387	20	Rn	Rn	NNP
10_1101-2021_01_08_425885	387	21	,	,	,
10_1101-2021_01_08_425885	387	22	as	as	IN
10_1101-2021_01_08_425885	387	23	was	be	VBD
10_1101-2021_01_08_425885	387	24	done	do	VBN
10_1101-2021_01_08_425885	387	25	in	in	IN
10_1101-2021_01_08_425885	387	26	our	-PRON-	PRP$
10_1101-2021_01_08_425885	387	27	analysis	analysis	NN
10_1101-2021_01_08_425885	387	28	.	.	.
10_1101-2021_01_08_425885	388	1	∆M	∆m	JJ
10_1101-2021_01_08_425885	388	2	=	=	SYM
10_1101-2021_01_08_425885	388	3	4	4	CD
10_1101-2021_01_08_425885	388	4	�	�	NNS
10_1101-2021_01_08_425885	388	5	(	(	-LRB-
10_1101-2021_01_08_425885	388	6	IN	in	IN
10_1101-2021_01_08_425885	388	7	−D−1W	−D−1W	NNP
10_1101-2021_01_08_425885	388	8	)	)	-RRB-
10_1101-2021_01_08_425885	388	9	D	D	NNP
10_1101-2021_01_08_425885	388	10	=	=	NFP
10_1101-2021_01_08_425885	388	11	diag{W1	diag{W1	.
10_1101-2021_01_08_425885	388	12	}	}	-RRB-
10_1101-2021_01_08_425885	388	13	(	(	-LRB-
10_1101-2021_01_08_425885	388	14	13	13	CD
10_1101-2021_01_08_425885	388	15	)	)	-RRB-
10_1101-2021_01_08_425885	388	16	23	23	CD
10_1101-2021_01_08_425885	388	17	.CC	.CC	:
10_1101-2021_01_08_425885	388	18	-	-	HYPH
10_1101-2021_01_08_425885	388	19	BY	by	IN
10_1101-2021_01_08_425885	388	20	-	-	HYPH
10_1101-2021_01_08_425885	388	21	NC	NC	NNP
10_1101-2021_01_08_425885	388	22	-	-	HYPH
10_1101-2021_01_08_425885	388	23	ND	ND	NNP
10_1101-2021_01_08_425885	388	24	4.0	4.0	CD
10_1101-2021_01_08_425885	388	25	International	International	NNP
10_1101-2021_01_08_425885	388	26	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	388	27	under	under	IN
10_1101-2021_01_08_425885	388	28	a	a	DT
10_1101-2021_01_08_425885	388	29	(	(	-LRB-
10_1101-2021_01_08_425885	388	30	which	which	WDT
10_1101-2021_01_08_425885	388	31	was	be	VBD
10_1101-2021_01_08_425885	388	32	not	not	RB
10_1101-2021_01_08_425885	388	33	certified	certify	VBN
10_1101-2021_01_08_425885	388	34	by	by	IN
10_1101-2021_01_08_425885	388	35	peer	peer	NN
10_1101-2021_01_08_425885	388	36	review	review	NN
10_1101-2021_01_08_425885	388	37	)	)	-RRB-
10_1101-2021_01_08_425885	388	38	is	be	VBZ
10_1101-2021_01_08_425885	388	39	the	the	DT
10_1101-2021_01_08_425885	388	40	author	author	NN
10_1101-2021_01_08_425885	388	41	/	/	SYM
10_1101-2021_01_08_425885	388	42	funder	funder	NN
10_1101-2021_01_08_425885	388	43	,	,	,
10_1101-2021_01_08_425885	388	44	who	who	WP
10_1101-2021_01_08_425885	388	45	has	have	VBZ
10_1101-2021_01_08_425885	388	46	granted	grant	VBN
10_1101-2021_01_08_425885	388	47	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	388	48	a	a	DT
10_1101-2021_01_08_425885	388	49	license	license	NN
10_1101-2021_01_08_425885	388	50	to	to	TO
10_1101-2021_01_08_425885	388	51	display	display	VB
10_1101-2021_01_08_425885	388	52	the	the	DT
10_1101-2021_01_08_425885	388	53	preprint	preprint	NN
10_1101-2021_01_08_425885	388	54	in	in	IN
10_1101-2021_01_08_425885	388	55	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	388	56	.	.	.
10_1101-2021_01_08_425885	389	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	389	2	is	be	VBZ
10_1101-2021_01_08_425885	389	3	made	make	VBN
10_1101-2021_01_08_425885	389	4	The	the	DT
10_1101-2021_01_08_425885	389	5	copyright	copyright	NN
10_1101-2021_01_08_425885	389	6	holder	holder	NN
10_1101-2021_01_08_425885	389	7	for	for	IN
10_1101-2021_01_08_425885	389	8	this	this	DT
10_1101-2021_01_08_425885	389	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	389	10	version	version	NN
10_1101-2021_01_08_425885	389	11	posted	post	VBD
10_1101-2021_01_08_425885	389	12	January	January	NNP
10_1101-2021_01_08_425885	389	13	8	8	CD
10_1101-2021_01_08_425885	389	14	,	,	,
10_1101-2021_01_08_425885	389	15	2021	2021	CD
10_1101-2021_01_08_425885	389	16	.	.	.
10_1101-2021_01_08_425885	389	17	;	;	:
10_1101-2021_01_08_425885	389	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	389	19	:	:	:
10_1101-2021_01_08_425885	389	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	389	21	preprint	preprint	NN
10_1101-2021_01_08_425885	389	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	389	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NNP
10_1101-2021_01_08_425885	389	24	IN	IN	NNP
10_1101-2021_01_08_425885	389	25	is	be	VBZ
10_1101-2021_01_08_425885	389	26	the	the	DT
10_1101-2021_01_08_425885	389	27	N	N	NNP
10_1101-2021_01_08_425885	389	28	×N	×n	CD
10_1101-2021_01_08_425885	389	29	identity	identity	NN
10_1101-2021_01_08_425885	389	30	matrix	matrix	NN
10_1101-2021_01_08_425885	389	31	,	,	,
10_1101-2021_01_08_425885	389	32	1	1	CD
10_1101-2021_01_08_425885	389	33	∈	∈	NNP
10_1101-2021_01_08_425885	389	34	RN	RN	NNP
10_1101-2021_01_08_425885	389	35	is	be	VBZ
10_1101-2021_01_08_425885	389	36	a	a	DT
10_1101-2021_01_08_425885	389	37	vector	vector	NN
10_1101-2021_01_08_425885	389	38	of	of	IN
10_1101-2021_01_08_425885	389	39	ones	one	NNS
10_1101-2021_01_08_425885	389	40	and	and	CC
10_1101-2021_01_08_425885	389	41	the	the	DT
10_1101-2021_01_08_425885	389	42	kernel	kernel	NN
10_1101-2021_01_08_425885	389	43	width	width	NN
10_1101-2021_01_08_425885	389	44	,	,	,
10_1101-2021_01_08_425885	389	45	�	�	NNP
10_1101-2021_01_08_425885	389	46	,	,	,
10_1101-2021_01_08_425885	389	47	is	be	VBZ
10_1101-2021_01_08_425885	389	48	set	set	VBN
10_1101-2021_01_08_425885	389	49	to	to	TO
10_1101-2021_01_08_425885	389	50	match	match	VB
10_1101-2021_01_08_425885	389	51	that	that	WDT
10_1101-2021_01_08_425885	389	52	used	use	VBN
10_1101-2021_01_08_425885	389	53	in	in	IN
10_1101-2021_01_08_425885	389	54	Theorem	theorem	NN
10_1101-2021_01_08_425885	389	55	1	1	CD
10_1101-2021_01_08_425885	389	56	of	of	IN
10_1101-2021_01_08_425885	389	57	[	[	-LRB-
10_1101-2021_01_08_425885	389	58	30	30	CD
10_1101-2021_01_08_425885	389	59	]	]	-RRB-
10_1101-2021_01_08_425885	389	60	:	:	:
10_1101-2021_01_08_425885	389	61	�	�	ADD
10_1101-2021_01_08_425885	389	62	=	=	NFP
10_1101-2021_01_08_425885	389	63	(	(	-LRB-
10_1101-2021_01_08_425885	389	64	log	log	NNP
10_1101-2021_01_08_425885	389	65	N	n	CD
10_1101-2021_01_08_425885	389	66	)	)	-RRB-
10_1101-2021_01_08_425885	389	67	3	3	CD
10_1101-2021_01_08_425885	389	68	8	8	CD
10_1101-2021_01_08_425885	389	69	N	n	CD
10_1101-2021_01_08_425885	389	70	1	1	CD
10_1101-2021_01_08_425885	389	71	4	4	CD
10_1101-2021_01_08_425885	389	72	(	(	-LRB-
10_1101-2021_01_08_425885	389	73	14	14	CD
10_1101-2021_01_08_425885	389	74	)	)	-RRB-
10_1101-2021_01_08_425885	389	75	Throughout	throughout	IN
10_1101-2021_01_08_425885	389	76	our	-PRON-	PRP$
10_1101-2021_01_08_425885	389	77	analysis	analysis	NN
10_1101-2021_01_08_425885	389	78	,	,	,
10_1101-2021_01_08_425885	389	79	we	-PRON-	PRP
10_1101-2021_01_08_425885	389	80	used	use	VBD
10_1101-2021_01_08_425885	389	81	W	W	NNP
10_1101-2021_01_08_425885	389	82	=	=	SYM
10_1101-2021_01_08_425885	389	83	Wg	Wg	NNP
10_1101-2021_01_08_425885	389	84	,	,	,
10_1101-2021_01_08_425885	389	85	the	the	DT
10_1101-2021_01_08_425885	389	86	weight	weight	NN
10_1101-2021_01_08_425885	389	87	matrix	matrix	NN
10_1101-2021_01_08_425885	389	88	with	with	IN
10_1101-2021_01_08_425885	389	89	entries	entry	NNS
10_1101-2021_01_08_425885	389	90	given	give	VBN
10_1101-2021_01_08_425885	389	91	by	by	IN
10_1101-2021_01_08_425885	389	92	a	a	DT
10_1101-2021_01_08_425885	389	93	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	389	94	kernel	kernel	NN
10_1101-2021_01_08_425885	389	95	:	:	:
10_1101-2021_01_08_425885	389	96	[	[	-LRB-
10_1101-2021_01_08_425885	389	97	Wg]i	wg]i	FW
10_1101-2021_01_08_425885	389	98	,	,	,
10_1101-2021_01_08_425885	389	99	j	j	NNP
10_1101-2021_01_08_425885	389	100	=	=	SYM
10_1101-2021_01_08_425885	389	101	exp(−‖Xi	exp(−‖Xi	NNP
10_1101-2021_01_08_425885	389	102	−Xj‖22/	−Xj‖22/	NNP
10_1101-2021_01_08_425885	389	103	�	�	NNP
10_1101-2021_01_08_425885	389	104	)	)	-RRB-
10_1101-2021_01_08_425885	389	105	−	−	NNP
10_1101-2021_01_08_425885	389	106	δi	δi	NNP
10_1101-2021_01_08_425885	389	107	,	,	,
10_1101-2021_01_08_425885	389	108	j	j	NNP
10_1101-2021_01_08_425885	389	109	(	(	-LRB-
10_1101-2021_01_08_425885	389	110	15	15	CD
10_1101-2021_01_08_425885	389	111	)	)	-RRB-
10_1101-2021_01_08_425885	389	112	To	to	TO
10_1101-2021_01_08_425885	389	113	check	check	VB
10_1101-2021_01_08_425885	389	114	whether	whether	IN
10_1101-2021_01_08_425885	389	115	other	other	JJ
10_1101-2021_01_08_425885	389	116	estimators	estimator	NNS
10_1101-2021_01_08_425885	389	117	had	have	VBD
10_1101-2021_01_08_425885	389	118	more	more	RBR
10_1101-2021_01_08_425885	389	119	benign	benign	JJ
10_1101-2021_01_08_425885	389	120	prefactors	prefactor	NNS
10_1101-2021_01_08_425885	389	121	for	for	IN
10_1101-2021_01_08_425885	389	122	eigenvalue	eigenvalue	NN
10_1101-2021_01_08_425885	389	123	convergence	convergence	NN
10_1101-2021_01_08_425885	389	124	(	(	-LRB-
10_1101-2021_01_08_425885	389	125	see	see	VB
10_1101-2021_01_08_425885	389	126	Figure	Figure	NNP
10_1101-2021_01_08_425885	389	127	S1H	S1H	NNP
10_1101-2021_01_08_425885	389	128	)	)	-RRB-
10_1101-2021_01_08_425885	389	129	,	,	,
10_1101-2021_01_08_425885	389	130	we	-PRON-	PRP
10_1101-2021_01_08_425885	389	131	also	also	RB
10_1101-2021_01_08_425885	389	132	considered	consider	VBD
10_1101-2021_01_08_425885	389	133	the	the	DT
10_1101-2021_01_08_425885	389	134	weighted	weighted	JJ
10_1101-2021_01_08_425885	389	135	kNN	kNN	NNP
10_1101-2021_01_08_425885	389	136	kernel	kernel	NN
10_1101-2021_01_08_425885	389	137	,	,	,
10_1101-2021_01_08_425885	389	138	WkNN	WkNN	NNP
10_1101-2021_01_08_425885	389	139	,	,	,
10_1101-2021_01_08_425885	389	140	and	and	CC
10_1101-2021_01_08_425885	389	141	the	the	DT
10_1101-2021_01_08_425885	389	142	r	r	JJ
10_1101-2021_01_08_425885	389	143	-	-	HYPH
10_1101-2021_01_08_425885	389	144	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	389	145	kernel	kernel	NN
10_1101-2021_01_08_425885	389	146	,	,	,
10_1101-2021_01_08_425885	389	147	Wr	Wr	NNP
10_1101-2021_01_08_425885	389	148	,	,	,
10_1101-2021_01_08_425885	389	149	with	with	IN
10_1101-2021_01_08_425885	389	150	r	r	NN
10_1101-2021_01_08_425885	389	151	=	=	SYM
10_1101-2021_01_08_425885	389	152	�	�	NNP
10_1101-2021_01_08_425885	389	153	[	[	-LRB-
10_1101-2021_01_08_425885	389	154	50	50	CD
10_1101-2021_01_08_425885	389	155	]	]	-RRB-
10_1101-2021_01_08_425885	389	156	:	:	:
10_1101-2021_01_08_425885	389	157	[	[	-LRB-
10_1101-2021_01_08_425885	389	158	WkNN	WkNN	NNP
10_1101-2021_01_08_425885	389	159	]	]	-RRB-
10_1101-2021_01_08_425885	389	160	i	i	NNP
10_1101-2021_01_08_425885	389	161	,	,	,
10_1101-2021_01_08_425885	389	162	j	j	NNP
10_1101-2021_01_08_425885	389	163	=	=	NFP
10_1101-2021_01_08_425885	389	164	[	[	-LRB-
10_1101-2021_01_08_425885	389	165	WG]i	WG]i	NNP
10_1101-2021_01_08_425885	389	166	,	,	,
10_1101-2021_01_08_425885	389	167	j	j	NNP
10_1101-2021_01_08_425885	389	168	[	[	-LRB-
10_1101-2021_01_08_425885	389	169	1kNN(j)(i	1knn(j)(i	CD
10_1101-2021_01_08_425885	389	170	)	)	-RRB-
10_1101-2021_01_08_425885	389	171	OR	or	CC
10_1101-2021_01_08_425885	389	172	1kNN(i)(j	1knn(i)(j	CD
10_1101-2021_01_08_425885	389	173	)	)	-RRB-
10_1101-2021_01_08_425885	389	174	]	]	-RRB-
10_1101-2021_01_08_425885	389	175	[	[	-LRB-
10_1101-2021_01_08_425885	389	176	Wr]i	Wr]i	NNP
10_1101-2021_01_08_425885	389	177	,	,	,
10_1101-2021_01_08_425885	389	178	j	j	NNP
10_1101-2021_01_08_425885	389	179	=	=	SYM
10_1101-2021_01_08_425885	389	180	1BXi(r)(Xj	1bxi(r)(xj	CD
10_1101-2021_01_08_425885	389	181	)	)	-RRB-
10_1101-2021_01_08_425885	389	182	−	−	NNP
10_1101-2021_01_08_425885	389	183	δi	δi	NNP
10_1101-2021_01_08_425885	389	184	,	,	,
10_1101-2021_01_08_425885	389	185	j	j	NNP
10_1101-2021_01_08_425885	389	186	(	(	-LRB-
10_1101-2021_01_08_425885	389	187	16	16	CD
10_1101-2021_01_08_425885	389	188	)	)	-RRB-
10_1101-2021_01_08_425885	389	189	kNN(i	kNN(i	NNP
10_1101-2021_01_08_425885	389	190	)	)	-RRB-
10_1101-2021_01_08_425885	389	191	is	be	VBZ
10_1101-2021_01_08_425885	389	192	the	the	DT
10_1101-2021_01_08_425885	389	193	set	set	NN
10_1101-2021_01_08_425885	389	194	of	of	IN
10_1101-2021_01_08_425885	389	195	indices	index	NNS
10_1101-2021_01_08_425885	389	196	of	of	IN
10_1101-2021_01_08_425885	389	197	the	the	DT
10_1101-2021_01_08_425885	389	198	k	k	NNP
10_1101-2021_01_08_425885	389	199	-	-	HYPH
10_1101-2021_01_08_425885	389	200	nearest	near	JJS
10_1101-2021_01_08_425885	389	201	neighbors	neighbor	NNS
10_1101-2021_01_08_425885	389	202	of	of	IN
10_1101-2021_01_08_425885	389	203	point	point	NN
10_1101-2021_01_08_425885	389	204	i	i	PRP
10_1101-2021_01_08_425885	389	205	in	in	IN
10_1101-2021_01_08_425885	389	206	Rn	Rn	NNP
10_1101-2021_01_08_425885	389	207	,	,	,
10_1101-2021_01_08_425885	389	208	BXi(r	bxi(r	ADD
10_1101-2021_01_08_425885	389	209	)	)	-RRB-
10_1101-2021_01_08_425885	389	210	is	be	VBZ
10_1101-2021_01_08_425885	389	211	the	the	DT
10_1101-2021_01_08_425885	389	212	n	n	JJ
10_1101-2021_01_08_425885	389	213	-	-	HYPH
10_1101-2021_01_08_425885	389	214	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	389	215	ball	ball	NN
10_1101-2021_01_08_425885	389	216	of	of	IN
10_1101-2021_01_08_425885	389	217	radius	radius	NNP
10_1101-2021_01_08_425885	389	218	r	r	NNP
10_1101-2021_01_08_425885	389	219	centred	centre	VBD
10_1101-2021_01_08_425885	389	220	at	at	IN
10_1101-2021_01_08_425885	389	221	Xi	Xi	NNP
10_1101-2021_01_08_425885	389	222	,	,	,
10_1101-2021_01_08_425885	389	223	and	and	CC
10_1101-2021_01_08_425885	389	224	1A(x	1a(x	LS
10_1101-2021_01_08_425885	389	225	)	)	-RRB-
10_1101-2021_01_08_425885	389	226	is	be	VBZ
10_1101-2021_01_08_425885	389	227	the	the	DT
10_1101-2021_01_08_425885	389	228	indicator	indicator	NN
10_1101-2021_01_08_425885	389	229	function	function	NN
10_1101-2021_01_08_425885	389	230	for	for	IN
10_1101-2021_01_08_425885	389	231	x	x	NNS
10_1101-2021_01_08_425885	389	232	∈	∈	NNP
10_1101-2021_01_08_425885	389	233	A.	a.	NN
10_1101-2021_01_08_425885	390	1	4.3	4.3	CD
10_1101-2021_01_08_425885	390	2	Details	detail	NNS
10_1101-2021_01_08_425885	390	3	of	of	IN
10_1101-2021_01_08_425885	390	4	Extrinsic	Extrinsic	NNP
10_1101-2021_01_08_425885	390	5	Approach	Approach	NNP
10_1101-2021_01_08_425885	390	6	to	to	IN
10_1101-2021_01_08_425885	390	7	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	390	8	Estimation	Estimation	NNP
10_1101-2021_01_08_425885	390	9	4.3.1	4.3.1	CD
10_1101-2021_01_08_425885	390	10	Quadratic	Quadratic	NNP
10_1101-2021_01_08_425885	390	11	Regression	Regression	NNP
10_1101-2021_01_08_425885	390	12	on	on	IN
10_1101-2021_01_08_425885	390	13	Local	Local	NNP
10_1101-2021_01_08_425885	390	14	Neighborhoods	Neighborhoods	NNPS
10_1101-2021_01_08_425885	390	15	of	of	IN
10_1101-2021_01_08_425885	390	16	Data	Data	NNPS
10_1101-2021_01_08_425885	390	17	Here	here	RB
10_1101-2021_01_08_425885	390	18	we	-PRON-	PRP
10_1101-2021_01_08_425885	390	19	describe	describe	VBP
10_1101-2021_01_08_425885	390	20	the	the	DT
10_1101-2021_01_08_425885	390	21	regression	regression	NN
10_1101-2021_01_08_425885	390	22	model	model	NN
10_1101-2021_01_08_425885	390	23	for	for	IN
10_1101-2021_01_08_425885	390	24	computing	compute	VBG
10_1101-2021_01_08_425885	390	25	the	the	DT
10_1101-2021_01_08_425885	390	26	coefficients	coefficient	NNS
10_1101-2021_01_08_425885	390	27	of	of	IN
10_1101-2021_01_08_425885	390	28	the	the	DT
10_1101-2021_01_08_425885	390	29	Second	Second	NNP
10_1101-2021_01_08_425885	390	30	Fundamental	Fundamental	NNP
10_1101-2021_01_08_425885	390	31	Form	Form	NNP
10_1101-2021_01_08_425885	390	32	,	,	,
10_1101-2021_01_08_425885	390	33	hkij	hkij	NNP
10_1101-2021_01_08_425885	390	34	,	,	,
10_1101-2021_01_08_425885	390	35	at	at	IN
10_1101-2021_01_08_425885	390	36	a	a	DT
10_1101-2021_01_08_425885	390	37	particular	particular	JJ
10_1101-2021_01_08_425885	390	38	point	point	NN
10_1101-2021_01_08_425885	390	39	p.	p.	NN
10_1101-2021_01_08_425885	390	40	As	as	IN
10_1101-2021_01_08_425885	390	41	described	describe	VBN
10_1101-2021_01_08_425885	390	42	in	in	IN
10_1101-2021_01_08_425885	390	43	the	the	DT
10_1101-2021_01_08_425885	390	44	main	main	JJ
10_1101-2021_01_08_425885	390	45	text	text	NN
10_1101-2021_01_08_425885	390	46	,	,	,
10_1101-2021_01_08_425885	390	47	after	after	IN
10_1101-2021_01_08_425885	390	48	performing	perform	VBG
10_1101-2021_01_08_425885	390	49	PCA	PCA	NNP
10_1101-2021_01_08_425885	390	50	on	on	IN
10_1101-2021_01_08_425885	390	51	a	a	DT
10_1101-2021_01_08_425885	390	52	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	390	53	of	of	IN
10_1101-2021_01_08_425885	390	54	Np	Np	NNP
10_1101-2021_01_08_425885	390	55	points	point	NNS
10_1101-2021_01_08_425885	390	56	around	around	IN
10_1101-2021_01_08_425885	390	57	p	p	NN
10_1101-2021_01_08_425885	390	58	in	in	IN
10_1101-2021_01_08_425885	390	59	Rn	Rn	NNS
10_1101-2021_01_08_425885	390	60	,	,	,
10_1101-2021_01_08_425885	390	61	each	each	DT
10_1101-2021_01_08_425885	390	62	point	point	NN
10_1101-2021_01_08_425885	390	63	in	in	IN
10_1101-2021_01_08_425885	390	64	the	the	DT
10_1101-2021_01_08_425885	390	65	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	390	66	can	can	MD
10_1101-2021_01_08_425885	390	67	be	be	VB
10_1101-2021_01_08_425885	390	68	described	describe	VBN
10_1101-2021_01_08_425885	390	69	in	in	IN
10_1101-2021_01_08_425885	390	70	terms	term	NNS
10_1101-2021_01_08_425885	390	71	of	of	IN
10_1101-2021_01_08_425885	390	72	d	d	NN
10_1101-2021_01_08_425885	390	73	tangent	tangent	NN
10_1101-2021_01_08_425885	390	74	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	390	75	,	,	,
10_1101-2021_01_08_425885	390	76	ti	ti	NN
10_1101-2021_01_08_425885	390	77	,	,	,
10_1101-2021_01_08_425885	390	78	and	and	CC
10_1101-2021_01_08_425885	390	79	n−d	n−d	NNP
10_1101-2021_01_08_425885	390	80	normal	normal	JJ
10_1101-2021_01_08_425885	390	81	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	390	82	,	,	,
10_1101-2021_01_08_425885	390	83	nk	nk	NNP
10_1101-2021_01_08_425885	390	84	.	.	.
10_1101-2021_01_08_425885	391	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	391	2	defer	defer	VBP
10_1101-2021_01_08_425885	391	3	discussion	discussion	NN
10_1101-2021_01_08_425885	391	4	of	of	IN
10_1101-2021_01_08_425885	391	5	how	how	WRB
10_1101-2021_01_08_425885	391	6	the	the	DT
10_1101-2021_01_08_425885	391	7	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	391	8	is	be	VBZ
10_1101-2021_01_08_425885	391	9	selected	select	VBN
10_1101-2021_01_08_425885	391	10	to	to	IN
10_1101-2021_01_08_425885	391	11	Methods	Methods	NNP
10_1101-2021_01_08_425885	391	12	Section	Section	NNP
10_1101-2021_01_08_425885	391	13	4.3.2	4.3.2	CD
10_1101-2021_01_08_425885	391	14	.	.	.
10_1101-2021_01_08_425885	392	1	The	the	DT
10_1101-2021_01_08_425885	392	2	nks	nk	NNS
10_1101-2021_01_08_425885	392	3	are	be	VBP
10_1101-2021_01_08_425885	392	4	treated	treat	VBN
10_1101-2021_01_08_425885	392	5	as	as	IN
10_1101-2021_01_08_425885	392	6	dependent	dependent	JJ
10_1101-2021_01_08_425885	392	7	variables	variable	NNS
10_1101-2021_01_08_425885	392	8	that	that	WDT
10_1101-2021_01_08_425885	392	9	can	can	MD
10_1101-2021_01_08_425885	392	10	be	be	VB
10_1101-2021_01_08_425885	392	11	modelled	model	VBN
10_1101-2021_01_08_425885	392	12	as	as	IN
10_1101-2021_01_08_425885	392	13	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	392	14	functions	function	NNS
10_1101-2021_01_08_425885	392	15	of	of	IN
10_1101-2021_01_08_425885	392	16	the	the	DT
10_1101-2021_01_08_425885	392	17	tis	tis	NN
10_1101-2021_01_08_425885	392	18	,	,	,
10_1101-2021_01_08_425885	392	19	which	which	WDT
10_1101-2021_01_08_425885	392	20	are	be	VBP
10_1101-2021_01_08_425885	392	21	taken	take	VBN
10_1101-2021_01_08_425885	392	22	to	to	TO
10_1101-2021_01_08_425885	392	23	be	be	VB
10_1101-2021_01_08_425885	392	24	independent	independent	JJ
10_1101-2021_01_08_425885	392	25	variables	variable	NNS
10_1101-2021_01_08_425885	392	26	.	.	.
10_1101-2021_01_08_425885	393	1	See	see	VB
10_1101-2021_01_08_425885	393	2	Equation	Equation	NNP
10_1101-2021_01_08_425885	393	3	17	17	CD
10_1101-2021_01_08_425885	393	4	below	below	RB
10_1101-2021_01_08_425885	393	5	.	.	.
10_1101-2021_01_08_425885	394	1	Linear	linear	JJ
10_1101-2021_01_08_425885	394	2	terms	term	NNS
10_1101-2021_01_08_425885	394	3	are	be	VBP
10_1101-2021_01_08_425885	394	4	excluded	exclude	VBN
10_1101-2021_01_08_425885	394	5	since	since	IN
10_1101-2021_01_08_425885	394	6	they	-PRON-	PRP
10_1101-2021_01_08_425885	394	7	ought	ought	MD
10_1101-2021_01_08_425885	394	8	to	to	TO
10_1101-2021_01_08_425885	394	9	have	have	VB
10_1101-2021_01_08_425885	394	10	zero	zero	CD
10_1101-2021_01_08_425885	394	11	coefficients	coefficient	NNS
10_1101-2021_01_08_425885	394	12	in	in	IN
10_1101-2021_01_08_425885	394	13	the	the	DT
10_1101-2021_01_08_425885	394	14	tangent	tangent	JJ
10_1101-2021_01_08_425885	394	15	basis	basis	NN
10_1101-2021_01_08_425885	394	16	.	.	.
10_1101-2021_01_08_425885	395	1	Constant	constant	JJ
10_1101-2021_01_08_425885	395	2	terms	term	NNS
10_1101-2021_01_08_425885	395	3	,	,	,
10_1101-2021_01_08_425885	395	4	Ck	Ck	NNP
10_1101-2021_01_08_425885	395	5	,	,	,
10_1101-2021_01_08_425885	395	6	are	be	VBP
10_1101-2021_01_08_425885	395	7	included	include	VBN
10_1101-2021_01_08_425885	395	8	to	to	TO
10_1101-2021_01_08_425885	395	9	account	account	VB
10_1101-2021_01_08_425885	395	10	for	for	IN
10_1101-2021_01_08_425885	395	11	affine	affine	NN
10_1101-2021_01_08_425885	395	12	shifts	shift	NNS
10_1101-2021_01_08_425885	395	13	.	.	.
10_1101-2021_01_08_425885	396	1	Since	since	IN
10_1101-2021_01_08_425885	396	2	hkij	hkij	NNP
10_1101-2021_01_08_425885	396	3	=	=	SYM
10_1101-2021_01_08_425885	396	4	h	h	NNP
10_1101-2021_01_08_425885	396	5	k	k	NNP
10_1101-2021_01_08_425885	396	6	ji	ji	NNP
10_1101-2021_01_08_425885	396	7	according	accord	VBG
10_1101-2021_01_08_425885	396	8	to	to	IN
10_1101-2021_01_08_425885	396	9	Equation	Equation	NNP
10_1101-2021_01_08_425885	396	10	5	5	CD
10_1101-2021_01_08_425885	396	11	,	,	,
10_1101-2021_01_08_425885	396	12	in	in	IN
10_1101-2021_01_08_425885	396	13	practice	practice	NN
10_1101-2021_01_08_425885	396	14	we	-PRON-	PRP
10_1101-2021_01_08_425885	396	15	only	only	RB
10_1101-2021_01_08_425885	396	16	consider	consider	VBP
10_1101-2021_01_08_425885	396	17	titj	titj	NN
10_1101-2021_01_08_425885	396	18	and	and	CC
10_1101-2021_01_08_425885	396	19	h	h	NNP
10_1101-2021_01_08_425885	396	20	k	k	NNP
10_1101-2021_01_08_425885	396	21	ij	ij	NNP
10_1101-2021_01_08_425885	396	22	for	for	IN
10_1101-2021_01_08_425885	396	23	j	j	NNP
10_1101-2021_01_08_425885	396	24	≥	≥	UH
10_1101-2021_01_08_425885	396	25	i	i	PRP
10_1101-2021_01_08_425885	396	26	so	so	RB
10_1101-2021_01_08_425885	396	27	that	that	IN
10_1101-2021_01_08_425885	396	28	t	t	NN
10_1101-2021_01_08_425885	396	29	and	and	CC
10_1101-2021_01_08_425885	396	30	h	h	NN
10_1101-2021_01_08_425885	396	31	in	in	IN
10_1101-2021_01_08_425885	396	32	Equation	Equation	NNP
10_1101-2021_01_08_425885	396	33	17	17	CD
10_1101-2021_01_08_425885	396	34	have	have	VBP
10_1101-2021_01_08_425885	396	35	linearly	linearly	JJ
10_1101-2021_01_08_425885	396	36	independent	independent	JJ
10_1101-2021_01_08_425885	396	37	columns	column	NNS
10_1101-2021_01_08_425885	396	38	,	,	,
10_1101-2021_01_08_425885	396	39	though	though	IN
10_1101-2021_01_08_425885	396	40	we	-PRON-	PRP
10_1101-2021_01_08_425885	396	41	write	write	VBP
10_1101-2021_01_08_425885	396	42	the	the	DT
10_1101-2021_01_08_425885	396	43	full	full	JJ
10_1101-2021_01_08_425885	396	44	form	form	NN
10_1101-2021_01_08_425885	396	45	here	here	RB
10_1101-2021_01_08_425885	396	46	for	for	IN
10_1101-2021_01_08_425885	396	47	simplicity	simplicity	NN
10_1101-2021_01_08_425885	396	48	.	.	.
10_1101-2021_01_08_425885	397	1	24	24	CD
10_1101-2021_01_08_425885	397	2	.CC	.CC	:
10_1101-2021_01_08_425885	397	3	-	-	HYPH
10_1101-2021_01_08_425885	397	4	BY	by	IN
10_1101-2021_01_08_425885	397	5	-	-	HYPH
10_1101-2021_01_08_425885	397	6	NC	NC	NNP
10_1101-2021_01_08_425885	397	7	-	-	HYPH
10_1101-2021_01_08_425885	397	8	ND	ND	NNP
10_1101-2021_01_08_425885	397	9	4.0	4.0	CD
10_1101-2021_01_08_425885	397	10	International	International	NNP
10_1101-2021_01_08_425885	397	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	397	12	under	under	IN
10_1101-2021_01_08_425885	397	13	a	a	DT
10_1101-2021_01_08_425885	397	14	(	(	-LRB-
10_1101-2021_01_08_425885	397	15	which	which	WDT
10_1101-2021_01_08_425885	397	16	was	be	VBD
10_1101-2021_01_08_425885	397	17	not	not	RB
10_1101-2021_01_08_425885	397	18	certified	certify	VBN
10_1101-2021_01_08_425885	397	19	by	by	IN
10_1101-2021_01_08_425885	397	20	peer	peer	NN
10_1101-2021_01_08_425885	397	21	review	review	NN
10_1101-2021_01_08_425885	397	22	)	)	-RRB-
10_1101-2021_01_08_425885	397	23	is	be	VBZ
10_1101-2021_01_08_425885	397	24	the	the	DT
10_1101-2021_01_08_425885	397	25	author	author	NN
10_1101-2021_01_08_425885	397	26	/	/	SYM
10_1101-2021_01_08_425885	397	27	funder	funder	NN
10_1101-2021_01_08_425885	397	28	,	,	,
10_1101-2021_01_08_425885	397	29	who	who	WP
10_1101-2021_01_08_425885	397	30	has	have	VBZ
10_1101-2021_01_08_425885	397	31	granted	grant	VBN
10_1101-2021_01_08_425885	397	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	397	33	a	a	DT
10_1101-2021_01_08_425885	397	34	license	license	NN
10_1101-2021_01_08_425885	397	35	to	to	TO
10_1101-2021_01_08_425885	397	36	display	display	VB
10_1101-2021_01_08_425885	397	37	the	the	DT
10_1101-2021_01_08_425885	397	38	preprint	preprint	NN
10_1101-2021_01_08_425885	397	39	in	in	IN
10_1101-2021_01_08_425885	397	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	397	41	.	.	.
10_1101-2021_01_08_425885	398	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	398	2	is	be	VBZ
10_1101-2021_01_08_425885	398	3	made	make	VBN
10_1101-2021_01_08_425885	398	4	The	the	DT
10_1101-2021_01_08_425885	398	5	copyright	copyright	NN
10_1101-2021_01_08_425885	398	6	holder	holder	NN
10_1101-2021_01_08_425885	398	7	for	for	IN
10_1101-2021_01_08_425885	398	8	this	this	DT
10_1101-2021_01_08_425885	398	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	398	10	version	version	NN
10_1101-2021_01_08_425885	398	11	posted	post	VBD
10_1101-2021_01_08_425885	398	12	January	January	NNP
10_1101-2021_01_08_425885	398	13	8	8	CD
10_1101-2021_01_08_425885	398	14	,	,	,
10_1101-2021_01_08_425885	398	15	2021	2021	CD
10_1101-2021_01_08_425885	398	16	.	.	.
10_1101-2021_01_08_425885	398	17	;	;	:
10_1101-2021_01_08_425885	398	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	398	19	:	:	:
10_1101-2021_01_08_425885	398	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	398	21	preprint	preprint	NN
10_1101-2021_01_08_425885	398	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	398	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	RB
10_1101-2021_01_08_425885	398	24	n	n	NN
10_1101-2021_01_08_425885	398	25	=	=	SYM
10_1101-2021_01_08_425885	398	26	th	th	NN
10_1101-2021_01_08_425885	398	27	+	+	SYM
10_1101-2021_01_08_425885	398	28	E	e	NN
10_1101-2021_01_08_425885	398	29	n	n	NN
10_1101-2021_01_08_425885	398	30	=	=	SYM
10_1101-2021_01_08_425885	398	31			NNP
10_1101-2021_01_08_425885	398	32			NNP
10_1101-2021_01_08_425885	398	33	n	n	JJ
10_1101-2021_01_08_425885	398	34	(	(	-LRB-
10_1101-2021_01_08_425885	398	35	1	1	CD
10_1101-2021_01_08_425885	398	36	)	)	-RRB-
10_1101-2021_01_08_425885	398	37	1	1	CD
10_1101-2021_01_08_425885	398	38	.	.	.
10_1101-2021_01_08_425885	399	1	.	.	.
10_1101-2021_01_08_425885	400	1	.	.	.
10_1101-2021_01_08_425885	401	1	n	n	NNP
10_1101-2021_01_08_425885	401	2	(	(	-LRB-
10_1101-2021_01_08_425885	401	3	1	1	CD
10_1101-2021_01_08_425885	401	4	)	)	-RRB-
10_1101-2021_01_08_425885	401	5	n−d	n−d	NNP
10_1101-2021_01_08_425885	401	6	...	...	:
10_1101-2021_01_08_425885	401	7	.	.	.
10_1101-2021_01_08_425885	402	1	.	.	.
10_1101-2021_01_08_425885	403	1	.	.	.
10_1101-2021_01_08_425885	404	1	...	...	NFP
10_1101-2021_01_08_425885	404	2	n	n	NNP
10_1101-2021_01_08_425885	404	3	(	(	-LRB-
10_1101-2021_01_08_425885	404	4	Np	Np	NNP
10_1101-2021_01_08_425885	404	5	)	)	-RRB-
10_1101-2021_01_08_425885	404	6	1	1	CD
10_1101-2021_01_08_425885	404	7	.	.	.
10_1101-2021_01_08_425885	405	1	.	.	.
10_1101-2021_01_08_425885	406	1	.	.	.
10_1101-2021_01_08_425885	407	1	n	n	LS
10_1101-2021_01_08_425885	407	2	(	(	-LRB-
10_1101-2021_01_08_425885	407	3	Np	Np	NNP
10_1101-2021_01_08_425885	407	4	)	)	-RRB-
10_1101-2021_01_08_425885	407	5	n−d	n−d	.
10_1101-2021_01_08_425885	407	6			NNP
10_1101-2021_01_08_425885	407	7			NNP
10_1101-2021_01_08_425885	407	8	t	t	NNP
10_1101-2021_01_08_425885	407	9	=	=	SYM
10_1101-2021_01_08_425885	407	10			NNP
10_1101-2021_01_08_425885	407	11			NNP
10_1101-2021_01_08_425885	407	12	1	1	CD
10_1101-2021_01_08_425885	407	13	t	t	NN
10_1101-2021_01_08_425885	407	14	(	(	-LRB-
10_1101-2021_01_08_425885	407	15	1	1	CD
10_1101-2021_01_08_425885	407	16	)	)	-RRB-
10_1101-2021_01_08_425885	407	17	1	1	CD
10_1101-2021_01_08_425885	407	18	t	t	NN
10_1101-2021_01_08_425885	407	19	(	(	-LRB-
10_1101-2021_01_08_425885	407	20	1	1	CD
10_1101-2021_01_08_425885	407	21	)	)	-RRB-
10_1101-2021_01_08_425885	407	22	1	1	CD
10_1101-2021_01_08_425885	407	23	.	.	.
10_1101-2021_01_08_425885	408	1	.	.	.
10_1101-2021_01_08_425885	409	1	.	.	.
10_1101-2021_01_08_425885	410	1	t	t	NNP
10_1101-2021_01_08_425885	410	2	(	(	-LRB-
10_1101-2021_01_08_425885	410	3	1	1	CD
10_1101-2021_01_08_425885	410	4	)	)	-RRB-
10_1101-2021_01_08_425885	410	5	1	1	CD
10_1101-2021_01_08_425885	410	6	t	t	NN
10_1101-2021_01_08_425885	410	7	(	(	-LRB-
10_1101-2021_01_08_425885	410	8	1	1	CD
10_1101-2021_01_08_425885	410	9	)	)	-RRB-
10_1101-2021_01_08_425885	410	10	d	d	NNP
10_1101-2021_01_08_425885	410	11	t	t	NNP
10_1101-2021_01_08_425885	410	12	(	(	-LRB-
10_1101-2021_01_08_425885	410	13	1	1	CD
10_1101-2021_01_08_425885	410	14	)	)	-RRB-
10_1101-2021_01_08_425885	410	15	2	2	CD
10_1101-2021_01_08_425885	410	16	t	t	NN
10_1101-2021_01_08_425885	410	17	(	(	-LRB-
10_1101-2021_01_08_425885	410	18	1	1	CD
10_1101-2021_01_08_425885	410	19	)	)	-RRB-
10_1101-2021_01_08_425885	410	20	1	1	CD
10_1101-2021_01_08_425885	410	21	.	.	.
10_1101-2021_01_08_425885	411	1	.	.	.
10_1101-2021_01_08_425885	412	1	.	.	.
10_1101-2021_01_08_425885	413	1	t	t	NNP
10_1101-2021_01_08_425885	413	2	(	(	-LRB-
10_1101-2021_01_08_425885	413	3	1	1	CD
10_1101-2021_01_08_425885	413	4	)	)	-RRB-
10_1101-2021_01_08_425885	413	5	d	d	NNP
10_1101-2021_01_08_425885	413	6	t	t	NNP
10_1101-2021_01_08_425885	413	7	(	(	-LRB-
10_1101-2021_01_08_425885	413	8	1	1	CD
10_1101-2021_01_08_425885	413	9	)	)	-RRB-
10_1101-2021_01_08_425885	413	10	d	d	NN
10_1101-2021_01_08_425885	413	11	...	...	NFP
10_1101-2021_01_08_425885	413	12	...	...	:
10_1101-2021_01_08_425885	413	13	.	.	.
10_1101-2021_01_08_425885	414	1	.	.	.
10_1101-2021_01_08_425885	415	1	.	.	.
10_1101-2021_01_08_425885	416	1	...	...	NFP
10_1101-2021_01_08_425885	416	2	...	...	:
10_1101-2021_01_08_425885	416	3	.	.	.
10_1101-2021_01_08_425885	417	1	.	.	.
10_1101-2021_01_08_425885	418	1	.	.	.
10_1101-2021_01_08_425885	419	1	...	...	NFP
10_1101-2021_01_08_425885	419	2	1	1	CD
10_1101-2021_01_08_425885	419	3	t	t	NN
10_1101-2021_01_08_425885	419	4	(	(	-LRB-
10_1101-2021_01_08_425885	419	5	Np	Np	NNP
10_1101-2021_01_08_425885	419	6	)	)	-RRB-
10_1101-2021_01_08_425885	419	7	1	1	CD
10_1101-2021_01_08_425885	419	8	t	t	NN
10_1101-2021_01_08_425885	419	9	(	(	-LRB-
10_1101-2021_01_08_425885	419	10	Np	Np	NNP
10_1101-2021_01_08_425885	419	11	)	)	-RRB-
10_1101-2021_01_08_425885	419	12	1	1	CD
10_1101-2021_01_08_425885	419	13	.	.	.
10_1101-2021_01_08_425885	420	1	.	.	.
10_1101-2021_01_08_425885	421	1	.	.	.
10_1101-2021_01_08_425885	422	1	t	t	NNP
10_1101-2021_01_08_425885	422	2	(	(	-LRB-
10_1101-2021_01_08_425885	422	3	Np	Np	NNP
10_1101-2021_01_08_425885	422	4	)	)	-RRB-
10_1101-2021_01_08_425885	422	5	1	1	CD
10_1101-2021_01_08_425885	422	6	t	t	NN
10_1101-2021_01_08_425885	422	7	(	(	-LRB-
10_1101-2021_01_08_425885	422	8	Np	Np	NNP
10_1101-2021_01_08_425885	422	9	)	)	-RRB-
10_1101-2021_01_08_425885	422	10	d	d	NN
10_1101-2021_01_08_425885	422	11	t	t	NN
10_1101-2021_01_08_425885	422	12	(	(	-LRB-
10_1101-2021_01_08_425885	422	13	Np	Np	NNP
10_1101-2021_01_08_425885	422	14	)	)	-RRB-
10_1101-2021_01_08_425885	422	15	2	2	CD
10_1101-2021_01_08_425885	422	16	t	t	NN
10_1101-2021_01_08_425885	422	17	(	(	-LRB-
10_1101-2021_01_08_425885	422	18	Np	Np	NNP
10_1101-2021_01_08_425885	422	19	)	)	-RRB-
10_1101-2021_01_08_425885	422	20	1	1	CD
10_1101-2021_01_08_425885	422	21	.	.	.
10_1101-2021_01_08_425885	423	1	.	.	.
10_1101-2021_01_08_425885	424	1	.	.	.
10_1101-2021_01_08_425885	425	1	t	t	NNP
10_1101-2021_01_08_425885	425	2	(	(	-LRB-
10_1101-2021_01_08_425885	425	3	Np	Np	NNP
10_1101-2021_01_08_425885	425	4	)	)	-RRB-
10_1101-2021_01_08_425885	425	5	d	d	NN
10_1101-2021_01_08_425885	425	6	t	t	NNP
10_1101-2021_01_08_425885	425	7	(	(	-LRB-
10_1101-2021_01_08_425885	425	8	Np	Np	NNP
10_1101-2021_01_08_425885	425	9	)	)	-RRB-
10_1101-2021_01_08_425885	425	10	d	d	NN
10_1101-2021_01_08_425885	425	11			NNP
10_1101-2021_01_08_425885	425	12			NNP
10_1101-2021_01_08_425885	425	13	h	h	NNP
10_1101-2021_01_08_425885	425	14	=	=	SYM
10_1101-2021_01_08_425885	425	15			NNP
10_1101-2021_01_08_425885	425	16			NNP
10_1101-2021_01_08_425885	425	17	C1	C1	NNP
10_1101-2021_01_08_425885	425	18	h	h	NNP
10_1101-2021_01_08_425885	425	19	1	1	CD
10_1101-2021_01_08_425885	425	20	1,1	1,1	CD
10_1101-2021_01_08_425885	425	21	.	.	.
10_1101-2021_01_08_425885	426	1	.	.	.
10_1101-2021_01_08_425885	427	1	.	.	.
10_1101-2021_01_08_425885	428	1	h	h	NNP
10_1101-2021_01_08_425885	428	2	1	1	CD
10_1101-2021_01_08_425885	428	3	1,d	1,d	CD
10_1101-2021_01_08_425885	428	4	h	h	NN
10_1101-2021_01_08_425885	428	5	1	1	CD
10_1101-2021_01_08_425885	428	6	2,1	2,1	CD
10_1101-2021_01_08_425885	428	7	.	.	.
10_1101-2021_01_08_425885	429	1	.	.	.
10_1101-2021_01_08_425885	430	1	.	.	.
10_1101-2021_01_08_425885	431	1	h	h	NNP
10_1101-2021_01_08_425885	431	2	1	1	CD
10_1101-2021_01_08_425885	431	3	d	d	NN
10_1101-2021_01_08_425885	431	4	,	,	,
10_1101-2021_01_08_425885	431	5	d	d	NNP
10_1101-2021_01_08_425885	431	6	...	...	NFP
10_1101-2021_01_08_425885	431	7	...	...	:
10_1101-2021_01_08_425885	431	8	.	.	.
10_1101-2021_01_08_425885	432	1	.	.	.
10_1101-2021_01_08_425885	433	1	.	.	.
10_1101-2021_01_08_425885	434	1	...	...	NFP
10_1101-2021_01_08_425885	434	2	...	...	:
10_1101-2021_01_08_425885	434	3	.	.	.
10_1101-2021_01_08_425885	435	1	.	.	.
10_1101-2021_01_08_425885	436	1	.	.	.
10_1101-2021_01_08_425885	437	1	...	...	NFP
10_1101-2021_01_08_425885	437	2	Cn−d	Cn−d	NNP
10_1101-2021_01_08_425885	437	3	h	h	NNP
10_1101-2021_01_08_425885	437	4	n−d	n−d	NNP
10_1101-2021_01_08_425885	437	5	1,1	1,1	CD
10_1101-2021_01_08_425885	437	6	.	.	.
10_1101-2021_01_08_425885	438	1	.	.	.
10_1101-2021_01_08_425885	439	1	.	.	.
10_1101-2021_01_08_425885	440	1	h	h	LS
10_1101-2021_01_08_425885	440	2	n−d	n−d	NNP
10_1101-2021_01_08_425885	440	3	1,d	1,d	CD
10_1101-2021_01_08_425885	440	4	h	h	NN
10_1101-2021_01_08_425885	440	5	n−d	n−d	NNP
10_1101-2021_01_08_425885	440	6	2,1	2,1	CD
10_1101-2021_01_08_425885	440	7	.	.	.
10_1101-2021_01_08_425885	441	1	.	.	.
10_1101-2021_01_08_425885	442	1	.	.	.
10_1101-2021_01_08_425885	443	1	h	h	LS
10_1101-2021_01_08_425885	443	2	n−d	n−d	NNP
10_1101-2021_01_08_425885	443	3	d	d	NN
10_1101-2021_01_08_425885	443	4	,	,	,
10_1101-2021_01_08_425885	443	5	d	d	LS
10_1101-2021_01_08_425885	443	6			NNP
10_1101-2021_01_08_425885	443	7			NNP
10_1101-2021_01_08_425885	443	8	T	t	NN
10_1101-2021_01_08_425885	443	9	E	e	NN
10_1101-2021_01_08_425885	443	10	=	=	SYM
10_1101-2021_01_08_425885	443	11			NNP
10_1101-2021_01_08_425885	443	12			NNP
10_1101-2021_01_08_425885	443	13	ε	ε	NN
10_1101-2021_01_08_425885	443	14	(	(	-LRB-
10_1101-2021_01_08_425885	443	15	1	1	CD
10_1101-2021_01_08_425885	443	16	)	)	-RRB-
10_1101-2021_01_08_425885	443	17	1	1	CD
10_1101-2021_01_08_425885	443	18	.	.	.
10_1101-2021_01_08_425885	444	1	.	.	.
10_1101-2021_01_08_425885	445	1	.	.	.
10_1101-2021_01_08_425885	446	1	ε	ε	NNP
10_1101-2021_01_08_425885	446	2	(	(	-LRB-
10_1101-2021_01_08_425885	446	3	1	1	CD
10_1101-2021_01_08_425885	446	4	)	)	-RRB-
10_1101-2021_01_08_425885	446	5	n−d	n−d	NNP
10_1101-2021_01_08_425885	446	6	...	...	:
10_1101-2021_01_08_425885	446	7	.	.	.
10_1101-2021_01_08_425885	447	1	.	.	.
10_1101-2021_01_08_425885	448	1	.	.	.
10_1101-2021_01_08_425885	449	1	...	...	NFP
10_1101-2021_01_08_425885	449	2	ε	ε	LS
10_1101-2021_01_08_425885	449	3	(	(	-LRB-
10_1101-2021_01_08_425885	449	4	Np	Np	NNP
10_1101-2021_01_08_425885	449	5	)	)	-RRB-
10_1101-2021_01_08_425885	449	6	1	1	CD
10_1101-2021_01_08_425885	449	7	.	.	.
10_1101-2021_01_08_425885	450	1	.	.	.
10_1101-2021_01_08_425885	451	1	.	.	.
10_1101-2021_01_08_425885	452	1	ε	ε	LS
10_1101-2021_01_08_425885	452	2	(	(	-LRB-
10_1101-2021_01_08_425885	452	3	Np	Np	NNP
10_1101-2021_01_08_425885	452	4	)	)	-RRB-
10_1101-2021_01_08_425885	452	5	n−d	n−d	.
10_1101-2021_01_08_425885	452	6			NNP
10_1101-2021_01_08_425885	452	7			NNPS
10_1101-2021_01_08_425885	452	8	=	=	SYM
10_1101-2021_01_08_425885	452	9			NNP
10_1101-2021_01_08_425885	452	10			NNP
10_1101-2021_01_08_425885	452	11	ε(1	ε(1	NNP
10_1101-2021_01_08_425885	452	12	)	)	-RRB-
10_1101-2021_01_08_425885	452	13	T	T	NNP
10_1101-2021_01_08_425885	452	14	...	...	:
10_1101-2021_01_08_425885	452	15	ε(Np	ε(Np	NNP
10_1101-2021_01_08_425885	452	16	)	)	-RRB-
10_1101-2021_01_08_425885	452	17	T	T	NNP
10_1101-2021_01_08_425885	452	18			NNP
10_1101-2021_01_08_425885	452	19			CD
10_1101-2021_01_08_425885	452	20	(	(	-LRB-
10_1101-2021_01_08_425885	452	21	17	17	CD
10_1101-2021_01_08_425885	452	22	)	)	-RRB-
10_1101-2021_01_08_425885	452	23	Regression	regression	NN
10_1101-2021_01_08_425885	452	24	yields	yield	VBZ
10_1101-2021_01_08_425885	452	25	the	the	DT
10_1101-2021_01_08_425885	452	26	following	follow	VBG
10_1101-2021_01_08_425885	452	27	least	least	JJS
10_1101-2021_01_08_425885	452	28	-	-	HYPH
10_1101-2021_01_08_425885	452	29	squares	square	NNS
10_1101-2021_01_08_425885	452	30	solution	solution	NN
10_1101-2021_01_08_425885	452	31	:	:	:
10_1101-2021_01_08_425885	452	32	ĥ	ĥ	NNP
10_1101-2021_01_08_425885	452	33	=	=	NFP
10_1101-2021_01_08_425885	452	34	(	(	-LRB-
10_1101-2021_01_08_425885	452	35	tT	tT	NNP
10_1101-2021_01_08_425885	452	36	t)−1tT	t)−1tt	NN
10_1101-2021_01_08_425885	452	37	n	n	NN
10_1101-2021_01_08_425885	452	38	Σε	σε	NN
10_1101-2021_01_08_425885	452	39	=	=	NFP
10_1101-2021_01_08_425885	452	40	(	(	-LRB-
10_1101-2021_01_08_425885	452	41	n	n	IN
10_1101-2021_01_08_425885	452	42	−	−	NNP
10_1101-2021_01_08_425885	452	43	tĥ)T	tĥ)t	NN
10_1101-2021_01_08_425885	452	44	(	(	-LRB-
10_1101-2021_01_08_425885	452	45	n	n	CC
10_1101-2021_01_08_425885	452	46	−	−	NNP
10_1101-2021_01_08_425885	452	47	tĥ	tĥ	ADD
10_1101-2021_01_08_425885	452	48	)	)	-RRB-
10_1101-2021_01_08_425885	452	49	Np	Np	NNP
10_1101-2021_01_08_425885	452	50	Σh	Σh	NNP
10_1101-2021_01_08_425885	452	51	=	=	FW
10_1101-2021_01_08_425885	452	52	Σε	σε	FW
10_1101-2021_01_08_425885	452	53	⊗	⊗	NN
10_1101-2021_01_08_425885	452	54	(	(	-LRB-
10_1101-2021_01_08_425885	452	55	tT	tT	NNP
10_1101-2021_01_08_425885	452	56	t)−1	t)−1	FW
10_1101-2021_01_08_425885	452	57	(	(	-LRB-
10_1101-2021_01_08_425885	452	58	18	18	CD
10_1101-2021_01_08_425885	452	59	)	)	-RRB-
10_1101-2021_01_08_425885	452	60	where	where	WRB
10_1101-2021_01_08_425885	452	61	ĥ	ĥ	NNP
10_1101-2021_01_08_425885	452	62	is	be	VBZ
10_1101-2021_01_08_425885	452	63	the	the	DT
10_1101-2021_01_08_425885	452	64	matrix	matrix	NN
10_1101-2021_01_08_425885	452	65	of	of	IN
10_1101-2021_01_08_425885	452	66	estimates	estimate	NNS
10_1101-2021_01_08_425885	452	67	of	of	IN
10_1101-2021_01_08_425885	452	68	the	the	DT
10_1101-2021_01_08_425885	452	69	Second	Second	NNP
10_1101-2021_01_08_425885	452	70	Fundamental	Fundamental	NNP
10_1101-2021_01_08_425885	452	71	Form	Form	NNP
10_1101-2021_01_08_425885	452	72	,	,	,
10_1101-2021_01_08_425885	452	73	Σε	Σε	NNP
10_1101-2021_01_08_425885	452	74	is	be	VBZ
10_1101-2021_01_08_425885	452	75	the	the	DT
10_1101-2021_01_08_425885	452	76	estimated	estimate	VBN
10_1101-2021_01_08_425885	452	77	covariance	covariance	NN
10_1101-2021_01_08_425885	452	78	structure	structure	NN
10_1101-2021_01_08_425885	452	79	of	of	IN
10_1101-2021_01_08_425885	452	80	the	the	DT
10_1101-2021_01_08_425885	452	81	residuals	residual	NNS
10_1101-2021_01_08_425885	452	82	so	so	IN
10_1101-2021_01_08_425885	452	83	that	that	IN
10_1101-2021_01_08_425885	452	84	ε(i	ε(i	XX
10_1101-2021_01_08_425885	452	85	)	)	-RRB-
10_1101-2021_01_08_425885	452	86	∼	∼	NNP
10_1101-2021_01_08_425885	452	87	N(0	N(0	NNP
10_1101-2021_01_08_425885	452	88	,	,	,
10_1101-2021_01_08_425885	452	89	Σε	Σε	NNP
10_1101-2021_01_08_425885	452	90	)	)	-RRB-
10_1101-2021_01_08_425885	452	91	,	,	,
10_1101-2021_01_08_425885	452	92	and	and	CC
10_1101-2021_01_08_425885	452	93	Σh	Σh	NNP
10_1101-2021_01_08_425885	452	94	is	be	VBZ
10_1101-2021_01_08_425885	452	95	the	the	DT
10_1101-2021_01_08_425885	452	96	covariance	covariance	NN
10_1101-2021_01_08_425885	452	97	matrix	matrix	NN
10_1101-2021_01_08_425885	452	98	for	for	IN
10_1101-2021_01_08_425885	452	99	ĥ.	ĥ.	NNP
10_1101-2021_01_08_425885	453	1	⊗	⊗	NNP
10_1101-2021_01_08_425885	453	2	denotes	denote	VBZ
10_1101-2021_01_08_425885	453	3	the	the	DT
10_1101-2021_01_08_425885	453	4	Kronecker	Kronecker	NNP
10_1101-2021_01_08_425885	453	5	product	product	NN
10_1101-2021_01_08_425885	453	6	.	.	.
10_1101-2021_01_08_425885	454	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	454	2	used	use	VBD
10_1101-2021_01_08_425885	454	3	the	the	DT
10_1101-2021_01_08_425885	454	4	mvregress	mvregress	JJ
10_1101-2021_01_08_425885	454	5	function	function	NN
10_1101-2021_01_08_425885	454	6	in	in	IN
10_1101-2021_01_08_425885	454	7	MATLAB	MATLAB	NNP
10_1101-2021_01_08_425885	454	8	to	to	TO
10_1101-2021_01_08_425885	454	9	perform	perform	VB
10_1101-2021_01_08_425885	454	10	this	this	DT
10_1101-2021_01_08_425885	454	11	regression	regression	NN
10_1101-2021_01_08_425885	454	12	in	in	IN
10_1101-2021_01_08_425885	454	13	our	-PRON-	PRP$
10_1101-2021_01_08_425885	454	14	code	code	NN
10_1101-2021_01_08_425885	454	15	.	.	.
10_1101-2021_01_08_425885	455	1	When	when	WRB
10_1101-2021_01_08_425885	455	2	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	455	3	are	be	VBP
10_1101-2021_01_08_425885	455	4	sampled	sample	VBN
10_1101-2021_01_08_425885	455	5	exactly	exactly	RB
10_1101-2021_01_08_425885	455	6	from	from	IN
10_1101-2021_01_08_425885	455	7	an	an	DT
10_1101-2021_01_08_425885	455	8	analytical	analytical	JJ
10_1101-2021_01_08_425885	455	9	manifold	manifold	NN
10_1101-2021_01_08_425885	455	10	,	,	,
10_1101-2021_01_08_425885	455	11	Σε	Σε	NNP
10_1101-2021_01_08_425885	455	12	measures	measure	VBZ
10_1101-2021_01_08_425885	455	13	the	the	DT
10_1101-2021_01_08_425885	455	14	contribution	contribution	NN
10_1101-2021_01_08_425885	455	15	of	of	IN
10_1101-2021_01_08_425885	455	16	higher	high	JJR
10_1101-2021_01_08_425885	455	17	-	-	HYPH
10_1101-2021_01_08_425885	455	18	order	order	NN
10_1101-2021_01_08_425885	455	19	terms	term	NNS
10_1101-2021_01_08_425885	455	20	.	.	.
10_1101-2021_01_08_425885	456	1	In	in	IN
10_1101-2021_01_08_425885	456	2	the	the	DT
10_1101-2021_01_08_425885	456	3	limit	limit	NN
10_1101-2021_01_08_425885	456	4	of	of	IN
10_1101-2021_01_08_425885	456	5	infinite	infinite	JJ
10_1101-2021_01_08_425885	456	6	sampling	sampling	NN
10_1101-2021_01_08_425885	456	7	and	and	CC
10_1101-2021_01_08_425885	456	8	infinitesimally	infinitesimally	RB
10_1101-2021_01_08_425885	456	9	small	small	JJ
10_1101-2021_01_08_425885	456	10	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	456	11	,	,	,
10_1101-2021_01_08_425885	456	12	Σε	Σε	NNP
10_1101-2021_01_08_425885	456	13	→	→	SYM
10_1101-2021_01_08_425885	456	14	0	0	CD
10_1101-2021_01_08_425885	456	15	.	.	.
10_1101-2021_01_08_425885	457	1	When	when	WRB
10_1101-2021_01_08_425885	457	2	observational	observational	JJ
10_1101-2021_01_08_425885	457	3	noise	noise	NN
10_1101-2021_01_08_425885	457	4	is	be	VBZ
10_1101-2021_01_08_425885	457	5	present	present	JJ
10_1101-2021_01_08_425885	457	6	(	(	-LRB-
10_1101-2021_01_08_425885	457	7	discussed	discuss	VBN
10_1101-2021_01_08_425885	457	8	in	in	IN
10_1101-2021_01_08_425885	457	9	Methods	Methods	NNP
10_1101-2021_01_08_425885	457	10	Section	Section	NNP
10_1101-2021_01_08_425885	457	11	4.4.2.2	4.4.2.2	CD
10_1101-2021_01_08_425885	457	12	)	)	-RRB-
10_1101-2021_01_08_425885	457	13	,	,	,
10_1101-2021_01_08_425885	457	14	Σε	Σε	NNP
10_1101-2021_01_08_425885	457	15	also	also	RB
10_1101-2021_01_08_425885	457	16	depends	depend	VBZ
10_1101-2021_01_08_425885	457	17	on	on	IN
10_1101-2021_01_08_425885	457	18	the	the	DT
10_1101-2021_01_08_425885	457	19	magnitude	magnitude	NN
10_1101-2021_01_08_425885	457	20	of	of	IN
10_1101-2021_01_08_425885	457	21	the	the	DT
10_1101-2021_01_08_425885	457	22	noise	noise	NN
10_1101-2021_01_08_425885	457	23	(	(	-LRB-
10_1101-2021_01_08_425885	457	24	σ	σ	NN
10_1101-2021_01_08_425885	457	25	in	in	IN
10_1101-2021_01_08_425885	457	26	Equation	Equation	NNP
10_1101-2021_01_08_425885	457	27	28	28	CD
10_1101-2021_01_08_425885	457	28	)	)	-RRB-
10_1101-2021_01_08_425885	457	29	.	.	.
10_1101-2021_01_08_425885	458	1	25	25	CD
10_1101-2021_01_08_425885	458	2	.CC	.CC	:
10_1101-2021_01_08_425885	458	3	-	-	HYPH
10_1101-2021_01_08_425885	458	4	BY	by	IN
10_1101-2021_01_08_425885	458	5	-	-	HYPH
10_1101-2021_01_08_425885	458	6	NC	NC	NNP
10_1101-2021_01_08_425885	458	7	-	-	HYPH
10_1101-2021_01_08_425885	458	8	ND	ND	NNP
10_1101-2021_01_08_425885	458	9	4.0	4.0	CD
10_1101-2021_01_08_425885	458	10	International	International	NNP
10_1101-2021_01_08_425885	458	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	458	12	under	under	IN
10_1101-2021_01_08_425885	458	13	a	a	DT
10_1101-2021_01_08_425885	458	14	(	(	-LRB-
10_1101-2021_01_08_425885	458	15	which	which	WDT
10_1101-2021_01_08_425885	458	16	was	be	VBD
10_1101-2021_01_08_425885	458	17	not	not	RB
10_1101-2021_01_08_425885	458	18	certified	certify	VBN
10_1101-2021_01_08_425885	458	19	by	by	IN
10_1101-2021_01_08_425885	458	20	peer	peer	NN
10_1101-2021_01_08_425885	458	21	review	review	NN
10_1101-2021_01_08_425885	458	22	)	)	-RRB-
10_1101-2021_01_08_425885	458	23	is	be	VBZ
10_1101-2021_01_08_425885	458	24	the	the	DT
10_1101-2021_01_08_425885	458	25	author	author	NN
10_1101-2021_01_08_425885	458	26	/	/	SYM
10_1101-2021_01_08_425885	458	27	funder	funder	NN
10_1101-2021_01_08_425885	458	28	,	,	,
10_1101-2021_01_08_425885	458	29	who	who	WP
10_1101-2021_01_08_425885	458	30	has	have	VBZ
10_1101-2021_01_08_425885	458	31	granted	grant	VBN
10_1101-2021_01_08_425885	458	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	458	33	a	a	DT
10_1101-2021_01_08_425885	458	34	license	license	NN
10_1101-2021_01_08_425885	458	35	to	to	TO
10_1101-2021_01_08_425885	458	36	display	display	VB
10_1101-2021_01_08_425885	458	37	the	the	DT
10_1101-2021_01_08_425885	458	38	preprint	preprint	NN
10_1101-2021_01_08_425885	458	39	in	in	IN
10_1101-2021_01_08_425885	458	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	458	41	.	.	.
10_1101-2021_01_08_425885	459	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	459	2	is	be	VBZ
10_1101-2021_01_08_425885	459	3	made	make	VBN
10_1101-2021_01_08_425885	459	4	The	the	DT
10_1101-2021_01_08_425885	459	5	copyright	copyright	NN
10_1101-2021_01_08_425885	459	6	holder	holder	NN
10_1101-2021_01_08_425885	459	7	for	for	IN
10_1101-2021_01_08_425885	459	8	this	this	DT
10_1101-2021_01_08_425885	459	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	459	10	version	version	NN
10_1101-2021_01_08_425885	459	11	posted	post	VBD
10_1101-2021_01_08_425885	459	12	January	January	NNP
10_1101-2021_01_08_425885	459	13	8	8	CD
10_1101-2021_01_08_425885	459	14	,	,	,
10_1101-2021_01_08_425885	459	15	2021	2021	CD
10_1101-2021_01_08_425885	459	16	.	.	.
10_1101-2021_01_08_425885	459	17	;	;	:
10_1101-2021_01_08_425885	459	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	459	19	:	:	:
10_1101-2021_01_08_425885	459	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	459	21	preprint	preprint	NN
10_1101-2021_01_08_425885	459	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	459	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NN
10_1101-2021_01_08_425885	459	24	4.3.2	4.3.2	CD
10_1101-2021_01_08_425885	459	25	Selecting	select	VBG
10_1101-2021_01_08_425885	459	26	Local	Local	NNP
10_1101-2021_01_08_425885	459	27	Neighborhoods	Neighborhoods	NNPS
10_1101-2021_01_08_425885	459	28	for	for	IN
10_1101-2021_01_08_425885	459	29	Regression	regression	NN
10_1101-2021_01_08_425885	459	30	Here	here	RB
10_1101-2021_01_08_425885	459	31	we	-PRON-	PRP
10_1101-2021_01_08_425885	459	32	describe	describe	VBP
10_1101-2021_01_08_425885	459	33	the	the	DT
10_1101-2021_01_08_425885	459	34	procedure	procedure	NN
10_1101-2021_01_08_425885	459	35	for	for	IN
10_1101-2021_01_08_425885	459	36	selecting	select	VBG
10_1101-2021_01_08_425885	459	37	a	a	DT
10_1101-2021_01_08_425885	459	38	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	459	39	around	around	IN
10_1101-2021_01_08_425885	459	40	each	each	DT
10_1101-2021_01_08_425885	459	41	point	point	NN
10_1101-2021_01_08_425885	459	42	p	p	NN
10_1101-2021_01_08_425885	459	43	for	for	IN
10_1101-2021_01_08_425885	459	44	computing	compute	VBG
10_1101-2021_01_08_425885	459	45	the	the	DT
10_1101-2021_01_08_425885	459	46	Second	Second	NNP
10_1101-2021_01_08_425885	459	47	Fundamental	Fundamental	NNP
10_1101-2021_01_08_425885	459	48	Form	Form	NNP
10_1101-2021_01_08_425885	459	49	.	.	.
10_1101-2021_01_08_425885	460	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	460	2	adopt	adopt	VBP
10_1101-2021_01_08_425885	460	3	the	the	DT
10_1101-2021_01_08_425885	460	4	simplest	simple	JJS
10_1101-2021_01_08_425885	460	5	approach	approach	NN
10_1101-2021_01_08_425885	460	6	of	of	IN
10_1101-2021_01_08_425885	460	7	selecting	select	VBG
10_1101-2021_01_08_425885	460	8	the	the	DT
10_1101-2021_01_08_425885	460	9	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	460	10	to	to	TO
10_1101-2021_01_08_425885	460	11	be	be	VB
10_1101-2021_01_08_425885	460	12	a	a	DT
10_1101-2021_01_08_425885	460	13	ball	ball	NN
10_1101-2021_01_08_425885	460	14	of	of	IN
10_1101-2021_01_08_425885	460	15	radius	radius	NN
10_1101-2021_01_08_425885	460	16	r	r	NNP
10_1101-2021_01_08_425885	460	17	centred	centre	VBD
10_1101-2021_01_08_425885	460	18	at	at	IN
10_1101-2021_01_08_425885	460	19	p	p	NN
10_1101-2021_01_08_425885	460	20	,	,	,
10_1101-2021_01_08_425885	460	21	Bp(r	Bp(r	NNP
10_1101-2021_01_08_425885	460	22	)	)	-RRB-
10_1101-2021_01_08_425885	460	23	.	.	.
10_1101-2021_01_08_425885	461	1	If	if	IN
10_1101-2021_01_08_425885	461	2	r(p	r(p	NNP
10_1101-2021_01_08_425885	461	3	)	)	-RRB-
10_1101-2021_01_08_425885	461	4	is	be	VBZ
10_1101-2021_01_08_425885	461	5	not	not	RB
10_1101-2021_01_08_425885	461	6	specified	specify	VBN
10_1101-2021_01_08_425885	461	7	,	,	,
10_1101-2021_01_08_425885	461	8	we	-PRON-	PRP
10_1101-2021_01_08_425885	461	9	set	set	VBD
10_1101-2021_01_08_425885	461	10	it	-PRON-	PRP
10_1101-2021_01_08_425885	461	11	according	accord	VBG
10_1101-2021_01_08_425885	461	12	to	to	IN
10_1101-2021_01_08_425885	461	13	statistical	statistical	JJ
10_1101-2021_01_08_425885	461	14	rather	rather	RB
10_1101-2021_01_08_425885	461	15	than	than	IN
10_1101-2021_01_08_425885	461	16	geometric	geometric	JJ
10_1101-2021_01_08_425885	461	17	principles	principle	NNS
10_1101-2021_01_08_425885	461	18	,	,	,
10_1101-2021_01_08_425885	461	19	since	since	IN
10_1101-2021_01_08_425885	461	20	the	the	DT
10_1101-2021_01_08_425885	461	21	geom-	geom-	JJ
10_1101-2021_01_08_425885	461	22	etry	etry	NN
10_1101-2021_01_08_425885	461	23	of	of	IN
10_1101-2021_01_08_425885	461	24	the	the	DT
10_1101-2021_01_08_425885	461	25	manifold	manifold	NN
10_1101-2021_01_08_425885	461	26	may	may	MD
10_1101-2021_01_08_425885	461	27	be	be	VB
10_1101-2021_01_08_425885	461	28	non	non	JJ
10_1101-2021_01_08_425885	461	29	-	-	JJ
10_1101-2021_01_08_425885	461	30	trivial	trivial	JJ
10_1101-2021_01_08_425885	461	31	and	and	CC
10_1101-2021_01_08_425885	461	32	unknown	unknown	JJ
10_1101-2021_01_08_425885	461	33	a	a	DT
10_1101-2021_01_08_425885	461	34	priori	priori	FW
10_1101-2021_01_08_425885	461	35	.	.	.
10_1101-2021_01_08_425885	462	1	Specifically	specifically	RB
10_1101-2021_01_08_425885	462	2	,	,	,
10_1101-2021_01_08_425885	462	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	462	4	set	set	VBD
10_1101-2021_01_08_425885	462	5	r(p	r(p	NNP
10_1101-2021_01_08_425885	462	6	)	)	-RRB-
10_1101-2021_01_08_425885	462	7	so	so	IN
10_1101-2021_01_08_425885	462	8	that	that	IN
10_1101-2021_01_08_425885	462	9	the	the	DT
10_1101-2021_01_08_425885	462	10	elements	element	NNS
10_1101-2021_01_08_425885	462	11	in	in	IN
10_1101-2021_01_08_425885	462	12	the	the	DT
10_1101-2021_01_08_425885	462	13	covariance	covariance	NN
10_1101-2021_01_08_425885	462	14	matrix	matrix	NN
10_1101-2021_01_08_425885	462	15	,	,	,
10_1101-2021_01_08_425885	462	16	Σh	Σh	NNP
10_1101-2021_01_08_425885	462	17	,	,	,
10_1101-2021_01_08_425885	462	18	are	be	VBP
10_1101-2021_01_08_425885	462	19	upper	upper	RB
10_1101-2021_01_08_425885	462	20	-	-	HYPH
10_1101-2021_01_08_425885	462	21	bounded	bound	VBN
10_1101-2021_01_08_425885	462	22	by	by	IN
10_1101-2021_01_08_425885	462	23	σ	σ	NNP
10_1101-2021_01_08_425885	462	24	2	2	CD
10_1101-2021_01_08_425885	462	25	h	h	NN
10_1101-2021_01_08_425885	462	26	,	,	,
10_1101-2021_01_08_425885	462	27	the	the	DT
10_1101-2021_01_08_425885	462	28	square	square	NN
10_1101-2021_01_08_425885	462	29	of	of	IN
10_1101-2021_01_08_425885	462	30	the	the	DT
10_1101-2021_01_08_425885	462	31	specified	specify	VBN
10_1101-2021_01_08_425885	462	32	target	target	NN
10_1101-2021_01_08_425885	462	33	uncertainty	uncertainty	NN
10_1101-2021_01_08_425885	462	34	.	.	.
10_1101-2021_01_08_425885	463	1	The	the	DT
10_1101-2021_01_08_425885	463	2	largest	large	JJS
10_1101-2021_01_08_425885	463	3	elements	element	NNS
10_1101-2021_01_08_425885	463	4	in	in	IN
10_1101-2021_01_08_425885	463	5	Σh	Σh	NNP
10_1101-2021_01_08_425885	463	6	are	be	VBP
10_1101-2021_01_08_425885	463	7	the	the	DT
10_1101-2021_01_08_425885	463	8	variance	variance	NN
10_1101-2021_01_08_425885	463	9	terms	term	NNS
10_1101-2021_01_08_425885	463	10	on	on	IN
10_1101-2021_01_08_425885	463	11	the	the	DT
10_1101-2021_01_08_425885	463	12	main	main	JJ
10_1101-2021_01_08_425885	463	13	diagonal	diagonal	JJ
10_1101-2021_01_08_425885	463	14	,	,	,
10_1101-2021_01_08_425885	463	15	corresponding	correspond	VBG
10_1101-2021_01_08_425885	463	16	to	to	IN
10_1101-2021_01_08_425885	463	17	the	the	DT
10_1101-2021_01_08_425885	463	18	squares	square	NNS
10_1101-2021_01_08_425885	463	19	of	of	IN
10_1101-2021_01_08_425885	463	20	the	the	DT
10_1101-2021_01_08_425885	463	21	standard	standard	JJ
10_1101-2021_01_08_425885	463	22	errors	error	NNS
10_1101-2021_01_08_425885	463	23	,	,	,
10_1101-2021_01_08_425885	463	24	σhk	σhk	NNP
10_1101-2021_01_08_425885	463	25	ij	ij	NNP
10_1101-2021_01_08_425885	463	26	,	,	,
10_1101-2021_01_08_425885	463	27	for	for	IN
10_1101-2021_01_08_425885	463	28	the	the	DT
10_1101-2021_01_08_425885	463	29	coefficients	coefficient	NNS
10_1101-2021_01_08_425885	463	30	hkij	hkij	NNP
10_1101-2021_01_08_425885	463	31	.	.	.
10_1101-2021_01_08_425885	464	1	By	by	IN
10_1101-2021_01_08_425885	464	2	inspection	inspection	NN
10_1101-2021_01_08_425885	464	3	of	of	IN
10_1101-2021_01_08_425885	464	4	Equation	Equation	NNP
10_1101-2021_01_08_425885	464	5	18	18	CD
10_1101-2021_01_08_425885	464	6	:	:	:
10_1101-2021_01_08_425885	464	7	σ2	σ2	NNP
10_1101-2021_01_08_425885	464	8	hk	hk	NNP
10_1101-2021_01_08_425885	464	9	ij	ij	NNP
10_1101-2021_01_08_425885	464	10	=	=	NFP
10_1101-2021_01_08_425885	464	11	[	[	-LRB-
10_1101-2021_01_08_425885	464	12	diag	diag	JJ
10_1101-2021_01_08_425885	464	13	Σε]k	σε]k	CD
10_1101-2021_01_08_425885	464	14	[	[	-LRB-
10_1101-2021_01_08_425885	464	15	diag	diag	NNP
10_1101-2021_01_08_425885	464	16	(	(	-LRB-
10_1101-2021_01_08_425885	464	17	t′t)−1	t′t)−1	NN
10_1101-2021_01_08_425885	464	18	]	]	-RRB-
10_1101-2021_01_08_425885	464	19	(	(	-LRB-
10_1101-2021_01_08_425885	464	20	ij	ij	NNP
10_1101-2021_01_08_425885	464	21	)	)	-RRB-
10_1101-2021_01_08_425885	464	22	(	(	-LRB-
10_1101-2021_01_08_425885	464	23	19	19	CD
10_1101-2021_01_08_425885	464	24	)	)	-RRB-
10_1101-2021_01_08_425885	464	25	where	where	WRB
10_1101-2021_01_08_425885	464	26	[	[	-LRB-
10_1101-2021_01_08_425885	464	27	diag	diag	NNP
10_1101-2021_01_08_425885	464	28	Σε]k	σε]k	CD
10_1101-2021_01_08_425885	464	29	is	be	VBZ
10_1101-2021_01_08_425885	464	30	the	the	DT
10_1101-2021_01_08_425885	464	31	diagonal	diagonal	JJ
10_1101-2021_01_08_425885	464	32	entry	entry	NN
10_1101-2021_01_08_425885	464	33	of	of	IN
10_1101-2021_01_08_425885	464	34	Σε	Σε	NNP
10_1101-2021_01_08_425885	464	35	corresponding	correspond	VBG
10_1101-2021_01_08_425885	464	36	to	to	IN
10_1101-2021_01_08_425885	464	37	the	the	DT
10_1101-2021_01_08_425885	464	38	k	k	XX
10_1101-2021_01_08_425885	464	39	th	th	XX
10_1101-2021_01_08_425885	464	40	normal	normal	JJ
10_1101-2021_01_08_425885	464	41	direction	direction	NN
10_1101-2021_01_08_425885	464	42	and	and	CC
10_1101-2021_01_08_425885	464	43	[	[	-LRB-
10_1101-2021_01_08_425885	464	44	diag	diag	NNP
10_1101-2021_01_08_425885	464	45	(	(	-LRB-
10_1101-2021_01_08_425885	464	46	t′t)−1	t′t)−1	NN
10_1101-2021_01_08_425885	464	47	]	]	-RRB-
10_1101-2021_01_08_425885	464	48	(	(	-LRB-
10_1101-2021_01_08_425885	464	49	ij	ij	NNP
10_1101-2021_01_08_425885	464	50	)	)	-RRB-
10_1101-2021_01_08_425885	464	51	is	be	VBZ
10_1101-2021_01_08_425885	464	52	the	the	DT
10_1101-2021_01_08_425885	464	53	diagonal	diagonal	JJ
10_1101-2021_01_08_425885	464	54	entry	entry	NN
10_1101-2021_01_08_425885	464	55	in	in	IN
10_1101-2021_01_08_425885	464	56	(	(	-LRB-
10_1101-2021_01_08_425885	464	57	t′t)−1	t′t)−1	NN
10_1101-2021_01_08_425885	464	58	for	for	IN
10_1101-2021_01_08_425885	464	59	which	which	WDT
10_1101-2021_01_08_425885	464	60	the	the	DT
10_1101-2021_01_08_425885	464	61	corresponding	correspond	VBG
10_1101-2021_01_08_425885	464	62	entry	entry	NN
10_1101-2021_01_08_425885	464	63	in	in	IN
10_1101-2021_01_08_425885	464	64	t′t	t′t	NNP
10_1101-2021_01_08_425885	464	65	is	be	VBZ
10_1101-2021_01_08_425885	464	66	∼	∼	FW
10_1101-2021_01_08_425885	464	67	∑	∑	.
10_1101-2021_01_08_425885	464	68	l(t	l(t	NNP
10_1101-2021_01_08_425885	464	69	(	(	-LRB-
10_1101-2021_01_08_425885	464	70	l	l	NN
10_1101-2021_01_08_425885	464	71	)	)	-RRB-
10_1101-2021_01_08_425885	464	72	i	i	PRP
10_1101-2021_01_08_425885	464	73	t	t	VBP
10_1101-2021_01_08_425885	464	74	(	(	-LRB-
10_1101-2021_01_08_425885	464	75	l	l	NN
10_1101-2021_01_08_425885	464	76	)	)	-RRB-
10_1101-2021_01_08_425885	464	77	j	j	NNP
10_1101-2021_01_08_425885	464	78	)	)	-RRB-
10_1101-2021_01_08_425885	464	79	2	2	CD
10_1101-2021_01_08_425885	464	80	.	.	.
10_1101-2021_01_08_425885	465	1	Increasing	increase	VBG
10_1101-2021_01_08_425885	465	2	r(p	r(p	NNP
10_1101-2021_01_08_425885	465	3	)	)	-RRB-
10_1101-2021_01_08_425885	465	4	monotonically	monotonically	RB
10_1101-2021_01_08_425885	465	5	increases	increase	VBZ
10_1101-2021_01_08_425885	465	6	both	both	DT
10_1101-2021_01_08_425885	465	7	Np(r	Np(r	NNP
10_1101-2021_01_08_425885	465	8	)	)	-RRB-
10_1101-2021_01_08_425885	465	9	,	,	,
10_1101-2021_01_08_425885	465	10	the	the	DT
10_1101-2021_01_08_425885	465	11	number	number	NN
10_1101-2021_01_08_425885	465	12	of	of	IN
10_1101-2021_01_08_425885	465	13	points	point	NNS
10_1101-2021_01_08_425885	465	14	in	in	IN
10_1101-2021_01_08_425885	465	15	Bp(r	Bp(r	NNP
10_1101-2021_01_08_425885	465	16	)	)	-RRB-
10_1101-2021_01_08_425885	465	17	,	,	,
10_1101-2021_01_08_425885	465	18	and	and	CC
10_1101-2021_01_08_425885	465	19	the	the	DT
10_1101-2021_01_08_425885	465	20	average	average	JJ
10_1101-2021_01_08_425885	465	21	magnitude	magnitude	NN
10_1101-2021_01_08_425885	465	22	of	of	IN
10_1101-2021_01_08_425885	465	23	elements	element	NNS
10_1101-2021_01_08_425885	465	24	in	in	IN
10_1101-2021_01_08_425885	465	25	t	t	NN
10_1101-2021_01_08_425885	465	26	,	,	,
10_1101-2021_01_08_425885	465	27	both	both	DT
10_1101-2021_01_08_425885	465	28	of	of	IN
10_1101-2021_01_08_425885	465	29	which	which	WDT
10_1101-2021_01_08_425885	465	30	reduce	reduce	VBP
10_1101-2021_01_08_425885	465	31	σhk	σhk	NN
10_1101-2021_01_08_425885	465	32	ij	ij	NNP
10_1101-2021_01_08_425885	465	33	.	.	.
10_1101-2021_01_08_425885	466	1	To	to	TO
10_1101-2021_01_08_425885	466	2	avoid	avoid	VB
10_1101-2021_01_08_425885	466	3	sweeping	sweep	VBG
10_1101-2021_01_08_425885	466	4	r(p	r(p	NNP
10_1101-2021_01_08_425885	466	5	)	)	-RRB-
10_1101-2021_01_08_425885	466	6	to	to	TO
10_1101-2021_01_08_425885	466	7	find	find	VB
10_1101-2021_01_08_425885	466	8	the	the	DT
10_1101-2021_01_08_425885	466	9	minimum	minimum	JJ
10_1101-2021_01_08_425885	466	10	value	value	NN
10_1101-2021_01_08_425885	466	11	such	such	JJ
10_1101-2021_01_08_425885	466	12	that	that	IN
10_1101-2021_01_08_425885	466	13	max	max	NNP
10_1101-2021_01_08_425885	466	14	σhk	σhk	NNP
10_1101-2021_01_08_425885	466	15	ij	ij	NNP
10_1101-2021_01_08_425885	466	16	<	<	XX
10_1101-2021_01_08_425885	466	17	σh	σh	NNP
10_1101-2021_01_08_425885	466	18	,	,	,
10_1101-2021_01_08_425885	466	19	which	which	WDT
10_1101-2021_01_08_425885	466	20	is	be	VBZ
10_1101-2021_01_08_425885	466	21	computationally	computationally	RB
10_1101-2021_01_08_425885	466	22	expensive	expensive	JJ
10_1101-2021_01_08_425885	466	23	,	,	,
10_1101-2021_01_08_425885	466	24	for	for	IN
10_1101-2021_01_08_425885	466	25	each	each	DT
10_1101-2021_01_08_425885	466	26	point	point	NN
10_1101-2021_01_08_425885	466	27	we	-PRON-	PRP
10_1101-2021_01_08_425885	466	28	instead	instead	RB
10_1101-2021_01_08_425885	466	29	model	model	VBP
10_1101-2021_01_08_425885	466	30	the	the	DT
10_1101-2021_01_08_425885	466	31	dependence	dependence	NN
10_1101-2021_01_08_425885	466	32	of	of	IN
10_1101-2021_01_08_425885	466	33	Np(r	Np(r	NNP
10_1101-2021_01_08_425885	466	34	)	)	-RRB-
10_1101-2021_01_08_425885	466	35	on	on	IN
10_1101-2021_01_08_425885	466	36	r	r	NN
10_1101-2021_01_08_425885	466	37	as	as	IN
10_1101-2021_01_08_425885	466	38	Np(r	Np(r	NNP
10_1101-2021_01_08_425885	466	39	)	)	-RRB-
10_1101-2021_01_08_425885	466	40	∼	∼	NN
10_1101-2021_01_08_425885	466	41	rd	rd	NNP
10_1101-2021_01_08_425885	466	42	′	′	NNP
10_1101-2021_01_08_425885	466	43	(	(	-LRB-
10_1101-2021_01_08_425885	466	44	20	20	CD
10_1101-2021_01_08_425885	466	45	)	)	-RRB-
10_1101-2021_01_08_425885	466	46	so	so	RB
10_1101-2021_01_08_425885	466	47	that	that	IN
10_1101-2021_01_08_425885	466	48	σ2	σ2	NNP
10_1101-2021_01_08_425885	466	49	hk	hk	NNP
10_1101-2021_01_08_425885	466	50	ij	ij	NNP
10_1101-2021_01_08_425885	466	51	∼	∼	NNP
10_1101-2021_01_08_425885	466	52	1	1	CD
10_1101-2021_01_08_425885	466	53	rd	rd	NNP
10_1101-2021_01_08_425885	466	54	′+4	′+4	NNP
10_1101-2021_01_08_425885	466	55	(	(	-LRB-
10_1101-2021_01_08_425885	466	56	21	21	CD
10_1101-2021_01_08_425885	466	57	)	)	-RRB-
10_1101-2021_01_08_425885	466	58	To	to	TO
10_1101-2021_01_08_425885	466	59	determine	determine	VB
10_1101-2021_01_08_425885	466	60	d′	d′	NN
10_1101-2021_01_08_425885	466	61	,	,	,
10_1101-2021_01_08_425885	466	62	Np(r	Np(r	NNP
10_1101-2021_01_08_425885	466	63	)	)	-RRB-
10_1101-2021_01_08_425885	466	64	is	be	VBZ
10_1101-2021_01_08_425885	466	65	counted	count	VBN
10_1101-2021_01_08_425885	466	66	at	at	IN
10_1101-2021_01_08_425885	466	67	10	10	CD
10_1101-2021_01_08_425885	466	68	log	log	NN
10_1101-2021_01_08_425885	466	69	-	-	HYPH
10_1101-2021_01_08_425885	466	70	spaced	space	VBN
10_1101-2021_01_08_425885	466	71	distances	distance	NNS
10_1101-2021_01_08_425885	466	72	,	,	,
10_1101-2021_01_08_425885	466	73	ri	ri	NNP
10_1101-2021_01_08_425885	466	74	,	,	,
10_1101-2021_01_08_425885	466	75	and	and	CC
10_1101-2021_01_08_425885	466	76	a	a	DT
10_1101-2021_01_08_425885	466	77	line	line	NN
10_1101-2021_01_08_425885	466	78	is	be	VBZ
10_1101-2021_01_08_425885	466	79	fit	fit	JJ
10_1101-2021_01_08_425885	466	80	to	to	IN
10_1101-2021_01_08_425885	466	81	the	the	DT
10_1101-2021_01_08_425885	466	82	(	(	-LRB-
10_1101-2021_01_08_425885	466	83	log	log	NNP
10_1101-2021_01_08_425885	466	84	ri	ri	NNP
10_1101-2021_01_08_425885	466	85	,	,	,
10_1101-2021_01_08_425885	466	86	log	log	NNP
10_1101-2021_01_08_425885	466	87	Np(ri	Np(ri	NNP
10_1101-2021_01_08_425885	466	88	)	)	-RRB-
10_1101-2021_01_08_425885	466	89	)	)	-RRB-
10_1101-2021_01_08_425885	466	90	pairs	pair	NNS
10_1101-2021_01_08_425885	466	91	for	for	IN
10_1101-2021_01_08_425885	466	92	i	i	PRP
10_1101-2021_01_08_425885	466	93	∈{2	∈{2	NNP
10_1101-2021_01_08_425885	466	94	,	,	,
10_1101-2021_01_08_425885	466	95	...	...	:
10_1101-2021_01_08_425885	466	96	,	,	,
10_1101-2021_01_08_425885	466	97	8	8	CD
10_1101-2021_01_08_425885	466	98	}	}	-RRB-
10_1101-2021_01_08_425885	466	99	.	.	.
10_1101-2021_01_08_425885	467	1	r1	r1	NNP
10_1101-2021_01_08_425885	467	2	is	be	VBZ
10_1101-2021_01_08_425885	467	3	set	set	VBN
10_1101-2021_01_08_425885	467	4	to	to	TO
10_1101-2021_01_08_425885	467	5	be	be	VB
10_1101-2021_01_08_425885	467	6	the	the	DT
10_1101-2021_01_08_425885	467	7	distance	distance	NN
10_1101-2021_01_08_425885	467	8	from	from	IN
10_1101-2021_01_08_425885	467	9	p	p	NN
10_1101-2021_01_08_425885	467	10	to	to	IN
10_1101-2021_01_08_425885	467	11	the	the	DT
10_1101-2021_01_08_425885	467	12	(	(	-LRB-
10_1101-2021_01_08_425885	467	13	d(d+1	d(d+1	NNP
10_1101-2021_01_08_425885	467	14	)	)	-RRB-
10_1101-2021_01_08_425885	467	15	2	2	CD
10_1101-2021_01_08_425885	467	16	+	+	SYM
10_1101-2021_01_08_425885	467	17	1	1	CD
10_1101-2021_01_08_425885	467	18	)	)	-RRB-
10_1101-2021_01_08_425885	467	19	-closest	-closest	CD
10_1101-2021_01_08_425885	467	20	point	point	NN
10_1101-2021_01_08_425885	467	21	to	to	IN
10_1101-2021_01_08_425885	467	22	p	p	NN
10_1101-2021_01_08_425885	467	23	(	(	-LRB-
10_1101-2021_01_08_425885	467	24	the	the	DT
10_1101-2021_01_08_425885	467	25	minimum	minimum	JJ
10_1101-2021_01_08_425885	467	26	number	number	NN
10_1101-2021_01_08_425885	467	27	of	of	IN
10_1101-2021_01_08_425885	467	28	points	point	NNS
10_1101-2021_01_08_425885	467	29	needed	need	VBN
10_1101-2021_01_08_425885	467	30	for	for	IN
10_1101-2021_01_08_425885	467	31	regression	regression	NN
10_1101-2021_01_08_425885	467	32	)	)	-RRB-
10_1101-2021_01_08_425885	467	33	.	.	.
10_1101-2021_01_08_425885	468	1	r10	r10	NN
10_1101-2021_01_08_425885	468	2	is	be	VBZ
10_1101-2021_01_08_425885	468	3	set	set	VBN
10_1101-2021_01_08_425885	468	4	to	to	TO
10_1101-2021_01_08_425885	468	5	be	be	VB
10_1101-2021_01_08_425885	468	6	the	the	DT
10_1101-2021_01_08_425885	468	7	distance	distance	NN
10_1101-2021_01_08_425885	468	8	from	from	IN
10_1101-2021_01_08_425885	468	9	p	p	NN
10_1101-2021_01_08_425885	468	10	to	to	IN
10_1101-2021_01_08_425885	468	11	the	the	DT
10_1101-2021_01_08_425885	468	12	furthest	furth	JJS
10_1101-2021_01_08_425885	468	13	point	point	NN
10_1101-2021_01_08_425885	468	14	from	from	IN
10_1101-2021_01_08_425885	468	15	p.	p.	NN
10_1101-2021_01_08_425885	468	16	To	to	TO
10_1101-2021_01_08_425885	468	17	solve	solve	VB
10_1101-2021_01_08_425885	468	18	for	for	IN
10_1101-2021_01_08_425885	468	19	r	r	NN
10_1101-2021_01_08_425885	468	20	,	,	,
10_1101-2021_01_08_425885	468	21	we	-PRON-	PRP
10_1101-2021_01_08_425885	468	22	first	first	RB
10_1101-2021_01_08_425885	468	23	guess	guess	VBP
10_1101-2021_01_08_425885	468	24	rg	rg	NNP
10_1101-2021_01_08_425885	468	25	=	=	SYM
10_1101-2021_01_08_425885	468	26	r1	r1	NN
10_1101-2021_01_08_425885	468	27	,	,	,
10_1101-2021_01_08_425885	468	28	perform	perform	VB
10_1101-2021_01_08_425885	468	29	regression	regression	NN
10_1101-2021_01_08_425885	468	30	on	on	IN
10_1101-2021_01_08_425885	468	31	the	the	DT
10_1101-2021_01_08_425885	468	32	set	set	NN
10_1101-2021_01_08_425885	468	33	of	of	IN
10_1101-2021_01_08_425885	468	34	points	point	NNS
10_1101-2021_01_08_425885	468	35	in	in	IN
10_1101-2021_01_08_425885	468	36	Bp(rg	Bp(rg	NNP
10_1101-2021_01_08_425885	468	37	)	)	-RRB-
10_1101-2021_01_08_425885	468	38	and	and	CC
10_1101-2021_01_08_425885	468	39	assign	assign	NNP
10_1101-2021_01_08_425885	468	40	σ	σ	NNP
10_1101-2021_01_08_425885	468	41	2	2	CD
10_1101-2021_01_08_425885	468	42	g	g	NNP
10_1101-2021_01_08_425885	468	43	to	to	TO
10_1101-2021_01_08_425885	468	44	be	be	VB
10_1101-2021_01_08_425885	468	45	the	the	DT
10_1101-2021_01_08_425885	468	46	largest	large	JJS
10_1101-2021_01_08_425885	468	47	diagonal	diagonal	JJ
10_1101-2021_01_08_425885	468	48	entry	entry	NN
10_1101-2021_01_08_425885	468	49	in	in	IN
10_1101-2021_01_08_425885	468	50	Σh	Σh	NNP
10_1101-2021_01_08_425885	468	51	.	.	.
10_1101-2021_01_08_425885	469	1	If	if	IN
10_1101-2021_01_08_425885	469	2	∣∣∣σgσh	∣∣∣σgσh	NN
10_1101-2021_01_08_425885	469	3	−	−	NNP
10_1101-2021_01_08_425885	469	4	1∣∣∣	1∣∣∣	CD
10_1101-2021_01_08_425885	469	5	is	be	VBZ
10_1101-2021_01_08_425885	469	6	within	within	IN
10_1101-2021_01_08_425885	469	7	a	a	DT
10_1101-2021_01_08_425885	469	8	desired	desire	VBN
10_1101-2021_01_08_425885	469	9	tolerance	tolerance	NN
10_1101-2021_01_08_425885	469	10	,	,	,
10_1101-2021_01_08_425885	469	11	we	-PRON-	PRP
10_1101-2021_01_08_425885	469	12	set	set	VBP
10_1101-2021_01_08_425885	469	13	r	r	NN
10_1101-2021_01_08_425885	469	14	=	=	SYM
10_1101-2021_01_08_425885	469	15	rg	rg	FW
10_1101-2021_01_08_425885	469	16	,	,	,
10_1101-2021_01_08_425885	469	17	or	or	CC
10_1101-2021_01_08_425885	469	18	else	else	RB
10_1101-2021_01_08_425885	469	19	we	-PRON-	PRP
10_1101-2021_01_08_425885	469	20	update	update	VBP
10_1101-2021_01_08_425885	469	21	rg	rg	NNP
10_1101-2021_01_08_425885	469	22	as	as	IN
10_1101-2021_01_08_425885	469	23	shown	show	VBN
10_1101-2021_01_08_425885	469	24	and	and	CC
10_1101-2021_01_08_425885	469	25	iterate	iterate	VB
10_1101-2021_01_08_425885	469	26	to	to	IN
10_1101-2021_01_08_425885	469	27	convergence	convergence	NN
10_1101-2021_01_08_425885	469	28	.	.	.
10_1101-2021_01_08_425885	470	1	rg	rg	NNP
10_1101-2021_01_08_425885	470	2	←	←	NNP
10_1101-2021_01_08_425885	470	3	rg	rg	NNP
10_1101-2021_01_08_425885	470	4	(	(	-LRB-
10_1101-2021_01_08_425885	470	5	σg	σg	NNP
10_1101-2021_01_08_425885	470	6	σh	σh	NNP
10_1101-2021_01_08_425885	470	7	)	)	-RRB-
10_1101-2021_01_08_425885	470	8	2	2	CD
10_1101-2021_01_08_425885	470	9	d′+4	d′+4	.
10_1101-2021_01_08_425885	470	10	(	(	-LRB-
10_1101-2021_01_08_425885	470	11	22	22	CD
10_1101-2021_01_08_425885	470	12	)	)	-RRB-
10_1101-2021_01_08_425885	470	13	For	for	IN
10_1101-2021_01_08_425885	470	14	large	large	JJ
10_1101-2021_01_08_425885	470	15	datasets	dataset	NNS
10_1101-2021_01_08_425885	470	16	,	,	,
10_1101-2021_01_08_425885	470	17	we	-PRON-	PRP
10_1101-2021_01_08_425885	470	18	speed	speed	VBP
10_1101-2021_01_08_425885	470	19	up	up	RP
10_1101-2021_01_08_425885	470	20	computation	computation	NN
10_1101-2021_01_08_425885	470	21	by	by	IN
10_1101-2021_01_08_425885	470	22	only	only	RB
10_1101-2021_01_08_425885	470	23	selecting	select	VBG
10_1101-2021_01_08_425885	470	24	r	r	NN
10_1101-2021_01_08_425885	470	25	in	in	IN
10_1101-2021_01_08_425885	470	26	this	this	DT
10_1101-2021_01_08_425885	470	27	manner	manner	NN
10_1101-2021_01_08_425885	470	28	for	for	IN
10_1101-2021_01_08_425885	470	29	a	a	DT
10_1101-2021_01_08_425885	470	30	subset	subset	NN
10_1101-2021_01_08_425885	470	31	of	of	IN
10_1101-2021_01_08_425885	470	32	Ncalib	Ncalib	NNP
10_1101-2021_01_08_425885	470	33	≤	≤	NNP
10_1101-2021_01_08_425885	470	34	N	N	NNP
10_1101-2021_01_08_425885	470	35	26	26	CD
10_1101-2021_01_08_425885	470	36	.CC	.CC	:
10_1101-2021_01_08_425885	470	37	-	-	HYPH
10_1101-2021_01_08_425885	470	38	BY	by	IN
10_1101-2021_01_08_425885	470	39	-	-	HYPH
10_1101-2021_01_08_425885	470	40	NC	NC	NNP
10_1101-2021_01_08_425885	470	41	-	-	HYPH
10_1101-2021_01_08_425885	470	42	ND	ND	NNP
10_1101-2021_01_08_425885	470	43	4.0	4.0	CD
10_1101-2021_01_08_425885	470	44	International	International	NNP
10_1101-2021_01_08_425885	470	45	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	470	46	under	under	IN
10_1101-2021_01_08_425885	470	47	a	a	DT
10_1101-2021_01_08_425885	470	48	(	(	-LRB-
10_1101-2021_01_08_425885	470	49	which	which	WDT
10_1101-2021_01_08_425885	470	50	was	be	VBD
10_1101-2021_01_08_425885	470	51	not	not	RB
10_1101-2021_01_08_425885	470	52	certified	certify	VBN
10_1101-2021_01_08_425885	470	53	by	by	IN
10_1101-2021_01_08_425885	470	54	peer	peer	NN
10_1101-2021_01_08_425885	470	55	review	review	NN
10_1101-2021_01_08_425885	470	56	)	)	-RRB-
10_1101-2021_01_08_425885	470	57	is	be	VBZ
10_1101-2021_01_08_425885	470	58	the	the	DT
10_1101-2021_01_08_425885	470	59	author	author	NN
10_1101-2021_01_08_425885	470	60	/	/	SYM
10_1101-2021_01_08_425885	470	61	funder	funder	NN
10_1101-2021_01_08_425885	470	62	,	,	,
10_1101-2021_01_08_425885	470	63	who	who	WP
10_1101-2021_01_08_425885	470	64	has	have	VBZ
10_1101-2021_01_08_425885	470	65	granted	grant	VBN
10_1101-2021_01_08_425885	470	66	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	470	67	a	a	DT
10_1101-2021_01_08_425885	470	68	license	license	NN
10_1101-2021_01_08_425885	470	69	to	to	TO
10_1101-2021_01_08_425885	470	70	display	display	VB
10_1101-2021_01_08_425885	470	71	the	the	DT
10_1101-2021_01_08_425885	470	72	preprint	preprint	NN
10_1101-2021_01_08_425885	470	73	in	in	IN
10_1101-2021_01_08_425885	470	74	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	470	75	.	.	.
10_1101-2021_01_08_425885	471	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	471	2	is	be	VBZ
10_1101-2021_01_08_425885	471	3	made	make	VBN
10_1101-2021_01_08_425885	471	4	The	the	DT
10_1101-2021_01_08_425885	471	5	copyright	copyright	NN
10_1101-2021_01_08_425885	471	6	holder	holder	NN
10_1101-2021_01_08_425885	471	7	for	for	IN
10_1101-2021_01_08_425885	471	8	this	this	DT
10_1101-2021_01_08_425885	471	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	471	10	version	version	NN
10_1101-2021_01_08_425885	471	11	posted	post	VBD
10_1101-2021_01_08_425885	471	12	January	January	NNP
10_1101-2021_01_08_425885	471	13	8	8	CD
10_1101-2021_01_08_425885	471	14	,	,	,
10_1101-2021_01_08_425885	471	15	2021	2021	CD
10_1101-2021_01_08_425885	471	16	.	.	.
10_1101-2021_01_08_425885	471	17	;	;	:
10_1101-2021_01_08_425885	471	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	471	19	:	:	:
10_1101-2021_01_08_425885	471	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	471	21	preprint	preprint	NN
10_1101-2021_01_08_425885	471	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	NNP
10_1101-2021_01_08_425885	471	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	RB
10_1101-2021_01_08_425885	471	24	randomly	randomly	RB
10_1101-2021_01_08_425885	471	25	selected	select	VBN
10_1101-2021_01_08_425885	471	26	calibration	calibration	NN
10_1101-2021_01_08_425885	471	27	points	point	NNS
10_1101-2021_01_08_425885	471	28	.	.	.
10_1101-2021_01_08_425885	472	1	All	all	DT
10_1101-2021_01_08_425885	472	2	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	472	3	in	in	IN
10_1101-2021_01_08_425885	472	4	the	the	DT
10_1101-2021_01_08_425885	472	5	Voronoi	Voronoi	NNP
10_1101-2021_01_08_425885	472	6	cell	cell	NN
10_1101-2021_01_08_425885	472	7	of	of	IN
10_1101-2021_01_08_425885	472	8	each	each	DT
10_1101-2021_01_08_425885	472	9	calibration	calibration	NN
10_1101-2021_01_08_425885	472	10	point	point	NN
10_1101-2021_01_08_425885	472	11	are	be	VBP
10_1101-2021_01_08_425885	472	12	then	then	RB
10_1101-2021_01_08_425885	472	13	assigned	assign	VBN
10_1101-2021_01_08_425885	472	14	the	the	DT
10_1101-2021_01_08_425885	472	15	same	same	JJ
10_1101-2021_01_08_425885	472	16	r	r	NN
10_1101-2021_01_08_425885	472	17	as	as	IN
10_1101-2021_01_08_425885	472	18	the	the	DT
10_1101-2021_01_08_425885	472	19	calibration	calibration	NN
10_1101-2021_01_08_425885	472	20	point	point	NN
10_1101-2021_01_08_425885	472	21	.	.	.
10_1101-2021_01_08_425885	473	1	Unless	unless	IN
10_1101-2021_01_08_425885	473	2	otherwise	otherwise	RB
10_1101-2021_01_08_425885	473	3	specified	specified	JJ
10_1101-2021_01_08_425885	473	4	Ncalib	Ncalib	NNP
10_1101-2021_01_08_425885	473	5	=	=	SYM
10_1101-2021_01_08_425885	473	6	N.	N.	NNP
10_1101-2021_01_08_425885	473	7	4.3.3	4.3.3	NNP
10_1101-2021_01_08_425885	473	8	Goodness	Goodness	NNP
10_1101-2021_01_08_425885	473	9	-	-	HYPH
10_1101-2021_01_08_425885	473	10	of	of	IN
10_1101-2021_01_08_425885	473	11	-	-	HYPH
10_1101-2021_01_08_425885	473	12	Fit	fit	NN
10_1101-2021_01_08_425885	473	13	Test	Test	NNP
10_1101-2021_01_08_425885	473	14	for	for	IN
10_1101-2021_01_08_425885	473	15	Quadratic	Quadratic	NNP
10_1101-2021_01_08_425885	473	16	Regression	Regression	NNP
10_1101-2021_01_08_425885	473	17	For	for	IN
10_1101-2021_01_08_425885	473	18	a	a	DT
10_1101-2021_01_08_425885	473	19	fixed	fix	VBN
10_1101-2021_01_08_425885	473	20	density	density	NN
10_1101-2021_01_08_425885	473	21	of	of	IN
10_1101-2021_01_08_425885	473	22	points	point	NNS
10_1101-2021_01_08_425885	473	23	,	,	,
10_1101-2021_01_08_425885	473	24	there	there	EX
10_1101-2021_01_08_425885	473	25	is	be	VBZ
10_1101-2021_01_08_425885	473	26	a	a	DT
10_1101-2021_01_08_425885	473	27	fundamental	fundamental	JJ
10_1101-2021_01_08_425885	473	28	trade	trade	NN
10_1101-2021_01_08_425885	473	29	-	-	HYPH
10_1101-2021_01_08_425885	473	30	off	off	NN
10_1101-2021_01_08_425885	473	31	between	between	IN
10_1101-2021_01_08_425885	473	32	reducing	reduce	VBG
10_1101-2021_01_08_425885	473	33	uncertainty	uncertainty	NN
10_1101-2021_01_08_425885	473	34	in	in	IN
10_1101-2021_01_08_425885	473	35	the	the	DT
10_1101-2021_01_08_425885	473	36	hkijs	hkijs	NN
10_1101-2021_01_08_425885	473	37	and	and	CC
10_1101-2021_01_08_425885	473	38	the	the	DT
10_1101-2021_01_08_425885	473	39	validity	validity	NN
10_1101-2021_01_08_425885	473	40	of	of	IN
10_1101-2021_01_08_425885	473	41	approximating	approximate	VBG
10_1101-2021_01_08_425885	473	42	local	local	JJ
10_1101-2021_01_08_425885	473	43	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	473	44	with	with	IN
10_1101-2021_01_08_425885	473	45	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	473	46	fits	fit	NNS
10_1101-2021_01_08_425885	473	47	.	.	.
10_1101-2021_01_08_425885	474	1	To	to	TO
10_1101-2021_01_08_425885	474	2	reduce	reduce	VB
10_1101-2021_01_08_425885	474	3	σh	σh	NNP
10_1101-2021_01_08_425885	474	4	,	,	,
10_1101-2021_01_08_425885	474	5	more	more	JJR
10_1101-2021_01_08_425885	474	6	points	point	NNS
10_1101-2021_01_08_425885	474	7	must	must	MD
10_1101-2021_01_08_425885	474	8	be	be	VB
10_1101-2021_01_08_425885	474	9	included	include	VBN
10_1101-2021_01_08_425885	474	10	in	in	IN
10_1101-2021_01_08_425885	474	11	the	the	DT
10_1101-2021_01_08_425885	474	12	fit	fit	NN
10_1101-2021_01_08_425885	474	13	,	,	,
10_1101-2021_01_08_425885	474	14	but	but	CC
10_1101-2021_01_08_425885	474	15	a	a	DT
10_1101-2021_01_08_425885	474	16	larger	large	JJR
10_1101-2021_01_08_425885	474	17	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	474	18	may	may	MD
10_1101-2021_01_08_425885	474	19	not	not	RB
10_1101-2021_01_08_425885	474	20	be	be	VB
10_1101-2021_01_08_425885	474	21	well	well	RB
10_1101-2021_01_08_425885	474	22	-	-	HYPH
10_1101-2021_01_08_425885	474	23	modelled	model	VBN
10_1101-2021_01_08_425885	474	24	by	by	IN
10_1101-2021_01_08_425885	474	25	only	only	JJ
10_1101-2021_01_08_425885	474	26	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	474	27	terms	term	NNS
10_1101-2021_01_08_425885	474	28	.	.	.
10_1101-2021_01_08_425885	475	1	Conversely	conversely	RB
10_1101-2021_01_08_425885	475	2	,	,	,
10_1101-2021_01_08_425885	475	3	d(d+1	d(d+1	NNP
10_1101-2021_01_08_425885	475	4	)	)	-RRB-
10_1101-2021_01_08_425885	475	5	2	2	CD
10_1101-2021_01_08_425885	475	6	+	+	SYM
10_1101-2021_01_08_425885	475	7	1	1	CD
10_1101-2021_01_08_425885	475	8	points	point	NNS
10_1101-2021_01_08_425885	475	9	are	be	VBP
10_1101-2021_01_08_425885	475	10	sufficient	sufficient	JJ
10_1101-2021_01_08_425885	475	11	to	to	TO
10_1101-2021_01_08_425885	475	12	perform	perform	VB
10_1101-2021_01_08_425885	475	13	the	the	DT
10_1101-2021_01_08_425885	475	14	regression	regression	NN
10_1101-2021_01_08_425885	475	15	,	,	,
10_1101-2021_01_08_425885	475	16	but	but	CC
10_1101-2021_01_08_425885	475	17	there	there	EX
10_1101-2021_01_08_425885	475	18	is	be	VBZ
10_1101-2021_01_08_425885	475	19	then	then	RB
10_1101-2021_01_08_425885	475	20	large	large	JJ
10_1101-2021_01_08_425885	475	21	uncertainty	uncertainty	NN
10_1101-2021_01_08_425885	475	22	in	in	IN
10_1101-2021_01_08_425885	475	23	the	the	DT
10_1101-2021_01_08_425885	475	24	estimate	estimate	NN
10_1101-2021_01_08_425885	475	25	of	of	IN
10_1101-2021_01_08_425885	475	26	hkij	hkij	NNP
10_1101-2021_01_08_425885	475	27	.	.	.
10_1101-2021_01_08_425885	476	1	Since	since	IN
10_1101-2021_01_08_425885	476	2	our	-PRON-	PRP$
10_1101-2021_01_08_425885	476	3	approach	approach	NN
10_1101-2021_01_08_425885	476	4	is	be	VBZ
10_1101-2021_01_08_425885	476	5	to	to	TO
10_1101-2021_01_08_425885	476	6	choose	choose	VB
10_1101-2021_01_08_425885	476	7	a	a	DT
10_1101-2021_01_08_425885	476	8	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	476	9	size	size	NN
10_1101-2021_01_08_425885	476	10	to	to	TO
10_1101-2021_01_08_425885	476	11	achieve	achieve	VB
10_1101-2021_01_08_425885	476	12	a	a	DT
10_1101-2021_01_08_425885	476	13	target	target	NN
10_1101-2021_01_08_425885	476	14	σh	σh	NNP
10_1101-2021_01_08_425885	476	15	,	,	,
10_1101-2021_01_08_425885	476	16	we	-PRON-	PRP
10_1101-2021_01_08_425885	476	17	include	include	VBP
10_1101-2021_01_08_425885	476	18	a	a	DT
10_1101-2021_01_08_425885	476	19	companion	companion	NN
10_1101-2021_01_08_425885	476	20	goodness	goodness	NN
10_1101-2021_01_08_425885	476	21	-	-	HYPH
10_1101-2021_01_08_425885	476	22	of	of	IN
10_1101-2021_01_08_425885	476	23	-	-	HYPH
10_1101-2021_01_08_425885	476	24	fit	fit	NN
10_1101-2021_01_08_425885	476	25	(	(	-LRB-
10_1101-2021_01_08_425885	476	26	GOF	GOF	NNP
10_1101-2021_01_08_425885	476	27	)	)	-RRB-
10_1101-2021_01_08_425885	476	28	statistic	statistic	NN
10_1101-2021_01_08_425885	476	29	measuring	measuring	NN
10_1101-2021_01_08_425885	476	30	how	how	WRB
10_1101-2021_01_08_425885	476	31	well	well	RB
10_1101-2021_01_08_425885	476	32	the	the	DT
10_1101-2021_01_08_425885	476	33	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	476	34	is	be	VBZ
10_1101-2021_01_08_425885	476	35	fit	fit	JJ
10_1101-2021_01_08_425885	476	36	by	by	IN
10_1101-2021_01_08_425885	476	37	a	a	DT
10_1101-2021_01_08_425885	476	38	quadratic	quadratic	NN
10_1101-2021_01_08_425885	476	39	.	.	.
10_1101-2021_01_08_425885	477	1	Namely	namely	RB
10_1101-2021_01_08_425885	477	2	,	,	,
10_1101-2021_01_08_425885	477	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	477	4	use	use	VBP
10_1101-2021_01_08_425885	477	5	Mardia	Mardia	NNP
10_1101-2021_01_08_425885	477	6	’s	’s	POS
10_1101-2021_01_08_425885	477	7	test	test	NN
10_1101-2021_01_08_425885	477	8	on	on	IN
10_1101-2021_01_08_425885	477	9	the	the	DT
10_1101-2021_01_08_425885	477	10	residuals	residual	NNS
10_1101-2021_01_08_425885	477	11	from	from	IN
10_1101-2021_01_08_425885	477	12	regression	regression	NN
10_1101-2021_01_08_425885	477	13	(	(	-LRB-
10_1101-2021_01_08_425885	477	14	ε(i	ε(i	NNP
10_1101-2021_01_08_425885	477	15	)	)	-RRB-
10_1101-2021_01_08_425885	477	16	in	in	IN
10_1101-2021_01_08_425885	477	17	Equation	Equation	NNP
10_1101-2021_01_08_425885	477	18	17	17	CD
10_1101-2021_01_08_425885	477	19	)	)	-RRB-
10_1101-2021_01_08_425885	477	20	,	,	,
10_1101-2021_01_08_425885	477	21	which	which	WDT
10_1101-2021_01_08_425885	477	22	yields	yield	VBZ
10_1101-2021_01_08_425885	477	23	a	a	DT
10_1101-2021_01_08_425885	477	24	p	p	NN
10_1101-2021_01_08_425885	477	25	-	-	HYPH
10_1101-2021_01_08_425885	477	26	value	value	NN
10_1101-2021_01_08_425885	477	27	for	for	IN
10_1101-2021_01_08_425885	477	28	the	the	DT
10_1101-2021_01_08_425885	477	29	null	null	JJ
10_1101-2021_01_08_425885	477	30	hypothesis	hypothesis	NN
10_1101-2021_01_08_425885	477	31	that	that	WDT
10_1101-2021_01_08_425885	477	32	the	the	DT
10_1101-2021_01_08_425885	477	33	residuals	residual	NNS
10_1101-2021_01_08_425885	477	34	are	be	VBP
10_1101-2021_01_08_425885	477	35	normally	normally	RB
10_1101-2021_01_08_425885	477	36	distributed	distribute	VBN
10_1101-2021_01_08_425885	477	37	[	[	-LRB-
10_1101-2021_01_08_425885	477	38	51	51	CD
10_1101-2021_01_08_425885	477	39	]	]	-RRB-
10_1101-2021_01_08_425885	477	40	.	.	.
10_1101-2021_01_08_425885	478	1	When	when	WRB
10_1101-2021_01_08_425885	478	2	the	the	DT
10_1101-2021_01_08_425885	478	3	p	p	NN
10_1101-2021_01_08_425885	478	4	-	-	HYPH
10_1101-2021_01_08_425885	478	5	values	value	NNS
10_1101-2021_01_08_425885	478	6	are	be	VBP
10_1101-2021_01_08_425885	478	7	small	small	JJ
10_1101-2021_01_08_425885	478	8	,	,	,
10_1101-2021_01_08_425885	478	9	the	the	DT
10_1101-2021_01_08_425885	478	10	quadratic	quadratic	NNP
10_1101-2021_01_08_425885	478	11	regression	regression	NN
10_1101-2021_01_08_425885	478	12	model	model	NN
10_1101-2021_01_08_425885	478	13	is	be	VBZ
10_1101-2021_01_08_425885	478	14	unlikely	unlikely	JJ
10_1101-2021_01_08_425885	478	15	to	to	TO
10_1101-2021_01_08_425885	478	16	be	be	VB
10_1101-2021_01_08_425885	478	17	valid	valid	JJ
10_1101-2021_01_08_425885	478	18	.	.	.
10_1101-2021_01_08_425885	479	1	In	in	IN
10_1101-2021_01_08_425885	479	2	this	this	DT
10_1101-2021_01_08_425885	479	3	case	case	NN
10_1101-2021_01_08_425885	479	4	,	,	,
10_1101-2021_01_08_425885	479	5	curvatures	curvature	NNS
10_1101-2021_01_08_425885	479	6	computed	compute	VBD
10_1101-2021_01_08_425885	479	7	using	use	VBG
10_1101-2021_01_08_425885	479	8	the	the	DT
10_1101-2021_01_08_425885	479	9	resulting	result	VBG
10_1101-2021_01_08_425885	479	10	hkij	hkij	NNP
10_1101-2021_01_08_425885	479	11	may	may	MD
10_1101-2021_01_08_425885	479	12	be	be	VB
10_1101-2021_01_08_425885	479	13	suspect	suspect	JJ
10_1101-2021_01_08_425885	479	14	regardless	regardless	RB
10_1101-2021_01_08_425885	479	15	of	of	IN
10_1101-2021_01_08_425885	479	16	the	the	DT
10_1101-2021_01_08_425885	479	17	tightness	tightness	NN
10_1101-2021_01_08_425885	479	18	of	of	IN
10_1101-2021_01_08_425885	479	19	the	the	DT
10_1101-2021_01_08_425885	479	20	errorbars	errorbar	NNS
10_1101-2021_01_08_425885	479	21	,	,	,
10_1101-2021_01_08_425885	479	22	and	and	CC
10_1101-2021_01_08_425885	479	23	the	the	DT
10_1101-2021_01_08_425885	479	24	user	user	NN
10_1101-2021_01_08_425885	479	25	may	may	MD
10_1101-2021_01_08_425885	479	26	want	want	VB
10_1101-2021_01_08_425885	479	27	to	to	TO
10_1101-2021_01_08_425885	479	28	consider	consider	VB
10_1101-2021_01_08_425885	479	29	increasing	increase	VBG
10_1101-2021_01_08_425885	479	30	σh	σh	NNP
10_1101-2021_01_08_425885	479	31	to	to	TO
10_1101-2021_01_08_425885	479	32	reduce	reduce	VB
10_1101-2021_01_08_425885	479	33	the	the	DT
10_1101-2021_01_08_425885	479	34	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	479	35	size	size	NN
10_1101-2021_01_08_425885	479	36	.	.	.
10_1101-2021_01_08_425885	480	1	However	however	RB
10_1101-2021_01_08_425885	480	2	,	,	,
10_1101-2021_01_08_425885	480	3	the	the	DT
10_1101-2021_01_08_425885	480	4	poor	poor	JJ
10_1101-2021_01_08_425885	480	5	GOF	GOF	NNP
10_1101-2021_01_08_425885	480	6	may	may	MD
10_1101-2021_01_08_425885	480	7	not	not	RB
10_1101-2021_01_08_425885	480	8	be	be	VB
10_1101-2021_01_08_425885	480	9	of	of	IN
10_1101-2021_01_08_425885	480	10	concern	concern	NN
10_1101-2021_01_08_425885	480	11	if	if	IN
10_1101-2021_01_08_425885	480	12	the	the	DT
10_1101-2021_01_08_425885	480	13	length	length	NN
10_1101-2021_01_08_425885	480	14	scale	scale	NN
10_1101-2021_01_08_425885	480	15	of	of	IN
10_1101-2021_01_08_425885	480	16	interest	interest	NN
10_1101-2021_01_08_425885	480	17	is	be	VBZ
10_1101-2021_01_08_425885	480	18	larger	large	JJR
10_1101-2021_01_08_425885	480	19	than	than	IN
10_1101-2021_01_08_425885	480	20	the	the	DT
10_1101-2021_01_08_425885	480	21	fluctuations	fluctuation	NNS
10_1101-2021_01_08_425885	480	22	in	in	IN
10_1101-2021_01_08_425885	480	23	the	the	DT
10_1101-2021_01_08_425885	480	24	manifold	manifold	NN
10_1101-2021_01_08_425885	480	25	which	which	WDT
10_1101-2021_01_08_425885	480	26	give	give	VBP
10_1101-2021_01_08_425885	480	27	rise	rise	NN
10_1101-2021_01_08_425885	480	28	to	to	IN
10_1101-2021_01_08_425885	480	29	the	the	DT
10_1101-2021_01_08_425885	480	30	non	non	JJ
10_1101-2021_01_08_425885	480	31	-	-	JJ
10_1101-2021_01_08_425885	480	32	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	480	33	residuals	residual	NNS
10_1101-2021_01_08_425885	480	34	(	(	-LRB-
10_1101-2021_01_08_425885	480	35	see	see	VB
10_1101-2021_01_08_425885	480	36	Methods	Methods	NNP
10_1101-2021_01_08_425885	480	37	Section	Section	NNP
10_1101-2021_01_08_425885	480	38	4.3.5	4.3.5	CD
10_1101-2021_01_08_425885	480	39	)	)	-RRB-
10_1101-2021_01_08_425885	480	40	.	.	.
10_1101-2021_01_08_425885	481	1	Note	note	VB
10_1101-2021_01_08_425885	481	2	that	that	IN
10_1101-2021_01_08_425885	481	3	Mardia	Mardia	NNP
10_1101-2021_01_08_425885	481	4	’s	’s	POS
10_1101-2021_01_08_425885	481	5	test	test	NN
10_1101-2021_01_08_425885	481	6	is	be	VBZ
10_1101-2021_01_08_425885	481	7	relatively	relatively	RB
10_1101-2021_01_08_425885	481	8	weak	weak	JJ
10_1101-2021_01_08_425885	481	9	since	since	IN
10_1101-2021_01_08_425885	481	10	it	-PRON-	PRP
10_1101-2021_01_08_425885	481	11	may	may	MD
10_1101-2021_01_08_425885	481	12	yield	yield	VB
10_1101-2021_01_08_425885	481	13	false	false	JJ
10_1101-2021_01_08_425885	481	14	negatives	negative	NNS
10_1101-2021_01_08_425885	481	15	for	for	IN
10_1101-2021_01_08_425885	481	16	heteroskedastic	heteroskedastic	JJ
10_1101-2021_01_08_425885	481	17	residuals	residual	NNS
10_1101-2021_01_08_425885	481	18	.	.	.
10_1101-2021_01_08_425885	482	1	This	this	DT
10_1101-2021_01_08_425885	482	2	GOF	GOF	NNP
10_1101-2021_01_08_425885	482	3	measure	measure	NN
10_1101-2021_01_08_425885	482	4	is	be	VBZ
10_1101-2021_01_08_425885	482	5	therefore	therefore	RB
10_1101-2021_01_08_425885	482	6	only	only	RB
10_1101-2021_01_08_425885	482	7	provided	provide	VBN
10_1101-2021_01_08_425885	482	8	as	as	IN
10_1101-2021_01_08_425885	482	9	a	a	DT
10_1101-2021_01_08_425885	482	10	computationally	computationally	RB
10_1101-2021_01_08_425885	482	11	cheap	cheap	JJ
10_1101-2021_01_08_425885	482	12	consistency	consistency	NN
10_1101-2021_01_08_425885	482	13	check	check	NN
10_1101-2021_01_08_425885	482	14	.	.	.
10_1101-2021_01_08_425885	483	1	Ideally	ideally	RB
10_1101-2021_01_08_425885	483	2	,	,	,
10_1101-2021_01_08_425885	483	3	the	the	DT
10_1101-2021_01_08_425885	483	4	density	density	NN
10_1101-2021_01_08_425885	483	5	of	of	IN
10_1101-2021_01_08_425885	483	6	sampled	sample	VBN
10_1101-2021_01_08_425885	483	7	points	point	NNS
10_1101-2021_01_08_425885	483	8	is	be	VBZ
10_1101-2021_01_08_425885	483	9	sufficiently	sufficiently	RB
10_1101-2021_01_08_425885	483	10	high	high	JJ
10_1101-2021_01_08_425885	483	11	to	to	IN
10_1101-2021_01_08_425885	483	12	(	(	-LRB-
10_1101-2021_01_08_425885	483	13	i	i	PRP
10_1101-2021_01_08_425885	483	14	)	)	-RRB-
10_1101-2021_01_08_425885	483	15	permit	permit	VBP
10_1101-2021_01_08_425885	483	16	small	small	JJ
10_1101-2021_01_08_425885	483	17	σh	σh	NNP
10_1101-2021_01_08_425885	483	18	and	and	CC
10_1101-2021_01_08_425885	483	19	(	(	-LRB-
10_1101-2021_01_08_425885	483	20	ii	ii	NNP
10_1101-2021_01_08_425885	483	21	)	)	-RRB-
10_1101-2021_01_08_425885	483	22	produce	produce	VBP
10_1101-2021_01_08_425885	483	23	GOF	GOF	NNP
10_1101-2021_01_08_425885	483	24	p	p	NN
10_1101-2021_01_08_425885	483	25	-	-	HYPH
10_1101-2021_01_08_425885	483	26	values	value	NNS
10_1101-2021_01_08_425885	483	27	that	that	WDT
10_1101-2021_01_08_425885	483	28	are	be	VBP
10_1101-2021_01_08_425885	483	29	uniformly	uniformly	RB
10_1101-2021_01_08_425885	483	30	distributed	distribute	VBN
10_1101-2021_01_08_425885	483	31	(	(	-LRB-
10_1101-2021_01_08_425885	483	32	consistent	consistent	JJ
10_1101-2021_01_08_425885	483	33	with	with	IN
10_1101-2021_01_08_425885	483	34	the	the	DT
10_1101-2021_01_08_425885	483	35	null	null	JJ
10_1101-2021_01_08_425885	483	36	model	model	NN
10_1101-2021_01_08_425885	483	37	)	)	-RRB-
10_1101-2021_01_08_425885	483	38	and	and	CC
10_1101-2021_01_08_425885	483	39	spatially	spatially	RB
10_1101-2021_01_08_425885	483	40	uncorrelated	uncorrelated	JJ
10_1101-2021_01_08_425885	483	41	.	.	.
10_1101-2021_01_08_425885	484	1	4.3.4	4.3.4	CD
10_1101-2021_01_08_425885	484	2	Standard	Standard	NNP
10_1101-2021_01_08_425885	484	3	Error	Error	NNP
10_1101-2021_01_08_425885	484	4	and	and	CC
10_1101-2021_01_08_425885	484	5	Bias	Bias	NNP
10_1101-2021_01_08_425885	484	6	of	of	IN
10_1101-2021_01_08_425885	484	7	Scalar	Scalar	NNP
10_1101-2021_01_08_425885	484	8	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	484	9	Estimate	Estimate	NNP
10_1101-2021_01_08_425885	484	10	Here	here	RB
10_1101-2021_01_08_425885	484	11	we	-PRON-	PRP
10_1101-2021_01_08_425885	484	12	discuss	discuss	VBP
10_1101-2021_01_08_425885	484	13	how	how	WRB
10_1101-2021_01_08_425885	484	14	we	-PRON-	PRP
10_1101-2021_01_08_425885	484	15	compute	compute	VBP
10_1101-2021_01_08_425885	484	16	the	the	DT
10_1101-2021_01_08_425885	484	17	standard	standard	JJ
10_1101-2021_01_08_425885	484	18	error	error	NN
10_1101-2021_01_08_425885	484	19	,	,	,
10_1101-2021_01_08_425885	484	20	σS	σS	NNP
10_1101-2021_01_08_425885	484	21	,	,	,
10_1101-2021_01_08_425885	484	22	of	of	IN
10_1101-2021_01_08_425885	484	23	the	the	DT
10_1101-2021_01_08_425885	484	24	estimate	estimate	NN
10_1101-2021_01_08_425885	484	25	for	for	IN
10_1101-2021_01_08_425885	484	26	S	S	NNP
10_1101-2021_01_08_425885	484	27	and	and	CC
10_1101-2021_01_08_425885	484	28	note	note	VB
10_1101-2021_01_08_425885	484	29	sources	source	NNS
10_1101-2021_01_08_425885	484	30	of	of	IN
10_1101-2021_01_08_425885	484	31	estimator	estimator	NN
10_1101-2021_01_08_425885	484	32	bias	bias	NN
10_1101-2021_01_08_425885	484	33	.	.	.
10_1101-2021_01_08_425885	485	1	Since	since	IN
10_1101-2021_01_08_425885	485	2	the	the	DT
10_1101-2021_01_08_425885	485	3	Riemannian	riemannian	JJ
10_1101-2021_01_08_425885	485	4	curvature	curvature	NN
10_1101-2021_01_08_425885	485	5	tensor	tensor	NN
10_1101-2021_01_08_425885	485	6	in	in	IN
10_1101-2021_01_08_425885	485	7	Equation	Equation	NNP
10_1101-2021_01_08_425885	485	8	6	6	CD
10_1101-2021_01_08_425885	485	9	is	be	VBZ
10_1101-2021_01_08_425885	485	10	a	a	DT
10_1101-2021_01_08_425885	485	11	bilinear	bilinear	JJ
10_1101-2021_01_08_425885	485	12	form	form	NN
10_1101-2021_01_08_425885	485	13	and	and	CC
10_1101-2021_01_08_425885	485	14	the	the	DT
10_1101-2021_01_08_425885	485	15	tensor	tensor	NN
10_1101-2021_01_08_425885	485	16	contraction	contraction	NN
10_1101-2021_01_08_425885	485	17	in	in	IN
10_1101-2021_01_08_425885	485	18	Equation	Equation	NNP
10_1101-2021_01_08_425885	485	19	7	7	CD
10_1101-2021_01_08_425885	485	20	is	be	VBZ
10_1101-2021_01_08_425885	485	21	a	a	DT
10_1101-2021_01_08_425885	485	22	straightforward	straightforward	JJ
10_1101-2021_01_08_425885	485	23	sum	sum	NN
10_1101-2021_01_08_425885	485	24	,	,	,
10_1101-2021_01_08_425885	485	25	σS	σS	NNP
10_1101-2021_01_08_425885	485	26	can	can	MD
10_1101-2021_01_08_425885	485	27	be	be	VB
10_1101-2021_01_08_425885	485	28	computed	compute	VBN
10_1101-2021_01_08_425885	485	29	using	use	VBG
10_1101-2021_01_08_425885	485	30	simple	simple	JJ
10_1101-2021_01_08_425885	485	31	error	error	NN
10_1101-2021_01_08_425885	485	32	propagation	propagation	NN
10_1101-2021_01_08_425885	485	33	formulas	formula	NNS
10_1101-2021_01_08_425885	485	34	in	in	IN
10_1101-2021_01_08_425885	485	35	terms	term	NNS
10_1101-2021_01_08_425885	485	36	of	of	IN
10_1101-2021_01_08_425885	485	37	the	the	DT
10_1101-2021_01_08_425885	485	38	uncertainties	uncertainty	NNS
10_1101-2021_01_08_425885	485	39	from	from	IN
10_1101-2021_01_08_425885	485	40	regression	regression	NN
10_1101-2021_01_08_425885	485	41	.	.	.
10_1101-2021_01_08_425885	486	1	Specifically	specifically	RB
10_1101-2021_01_08_425885	486	2	,	,	,
10_1101-2021_01_08_425885	486	3	the	the	DT
10_1101-2021_01_08_425885	486	4	standard	standard	JJ
10_1101-2021_01_08_425885	486	5	error	error	NN
10_1101-2021_01_08_425885	486	6	we	-PRON-	PRP
10_1101-2021_01_08_425885	486	7	report	report	VBP
10_1101-2021_01_08_425885	486	8	is	be	VBZ
10_1101-2021_01_08_425885	486	9	the	the	DT
10_1101-2021_01_08_425885	486	10	first	first	JJ
10_1101-2021_01_08_425885	486	11	-	-	HYPH
10_1101-2021_01_08_425885	486	12	order	order	NN
10_1101-2021_01_08_425885	486	13	approximation	approximation	NN
10_1101-2021_01_08_425885	486	14	to	to	IN
10_1101-2021_01_08_425885	486	15	the	the	DT
10_1101-2021_01_08_425885	486	16	second	second	JJ
10_1101-2021_01_08_425885	486	17	moment	moment	NN
10_1101-2021_01_08_425885	486	18	of	of	IN
10_1101-2021_01_08_425885	486	19	a	a	DT
10_1101-2021_01_08_425885	486	20	function	function	NN
10_1101-2021_01_08_425885	486	21	of	of	IN
10_1101-2021_01_08_425885	486	22	random	random	JJ
10_1101-2021_01_08_425885	486	23	variables	variable	NNS
10_1101-2021_01_08_425885	486	24	:	:	:
10_1101-2021_01_08_425885	486	25	σS	σs	NN
10_1101-2021_01_08_425885	486	26	=	=	SYM
10_1101-2021_01_08_425885	486	27	√	√	NNP
10_1101-2021_01_08_425885	486	28	JT	jt	NN
10_1101-2021_01_08_425885	486	29	ΣhJ	σhj	NN
10_1101-2021_01_08_425885	486	30	(	(	-LRB-
10_1101-2021_01_08_425885	486	31	23	23	CD
10_1101-2021_01_08_425885	486	32	)	)	-RRB-
10_1101-2021_01_08_425885	486	33	where	where	WRB
10_1101-2021_01_08_425885	486	34	J	J	NNP
10_1101-2021_01_08_425885	486	35	=	=	SYM
10_1101-2021_01_08_425885	486	36	∂S	∂S	.
10_1101-2021_01_08_425885	486	37	∂hk	∂hk	NN
10_1101-2021_01_08_425885	486	38	ij	ij	NNP
10_1101-2021_01_08_425885	486	39	∣∣∣	∣∣∣	NNP
10_1101-2021_01_08_425885	486	40	ĥ	ĥ	NNP
10_1101-2021_01_08_425885	486	41	.	.	.
10_1101-2021_01_08_425885	487	1	27	27	CD
10_1101-2021_01_08_425885	487	2	.CC	.CC	:
10_1101-2021_01_08_425885	487	3	-	-	HYPH
10_1101-2021_01_08_425885	487	4	BY	by	IN
10_1101-2021_01_08_425885	487	5	-	-	HYPH
10_1101-2021_01_08_425885	487	6	NC	NC	NNP
10_1101-2021_01_08_425885	487	7	-	-	HYPH
10_1101-2021_01_08_425885	487	8	ND	ND	NNP
10_1101-2021_01_08_425885	487	9	4.0	4.0	CD
10_1101-2021_01_08_425885	487	10	International	International	NNP
10_1101-2021_01_08_425885	487	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	487	12	under	under	IN
10_1101-2021_01_08_425885	487	13	a	a	DT
10_1101-2021_01_08_425885	487	14	(	(	-LRB-
10_1101-2021_01_08_425885	487	15	which	which	WDT
10_1101-2021_01_08_425885	487	16	was	be	VBD
10_1101-2021_01_08_425885	487	17	not	not	RB
10_1101-2021_01_08_425885	487	18	certified	certify	VBN
10_1101-2021_01_08_425885	487	19	by	by	IN
10_1101-2021_01_08_425885	487	20	peer	peer	NN
10_1101-2021_01_08_425885	487	21	review	review	NN
10_1101-2021_01_08_425885	487	22	)	)	-RRB-
10_1101-2021_01_08_425885	487	23	is	be	VBZ
10_1101-2021_01_08_425885	487	24	the	the	DT
10_1101-2021_01_08_425885	487	25	author	author	NN
10_1101-2021_01_08_425885	487	26	/	/	SYM
10_1101-2021_01_08_425885	487	27	funder	funder	NN
10_1101-2021_01_08_425885	487	28	,	,	,
10_1101-2021_01_08_425885	487	29	who	who	WP
10_1101-2021_01_08_425885	487	30	has	have	VBZ
10_1101-2021_01_08_425885	487	31	granted	grant	VBN
10_1101-2021_01_08_425885	487	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	487	33	a	a	DT
10_1101-2021_01_08_425885	487	34	license	license	NN
10_1101-2021_01_08_425885	487	35	to	to	TO
10_1101-2021_01_08_425885	487	36	display	display	VB
10_1101-2021_01_08_425885	487	37	the	the	DT
10_1101-2021_01_08_425885	487	38	preprint	preprint	NN
10_1101-2021_01_08_425885	487	39	in	in	IN
10_1101-2021_01_08_425885	487	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	487	41	.	.	.
10_1101-2021_01_08_425885	488	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	488	2	is	be	VBZ
10_1101-2021_01_08_425885	488	3	made	make	VBN
10_1101-2021_01_08_425885	488	4	The	the	DT
10_1101-2021_01_08_425885	488	5	copyright	copyright	NN
10_1101-2021_01_08_425885	488	6	holder	holder	NN
10_1101-2021_01_08_425885	488	7	for	for	IN
10_1101-2021_01_08_425885	488	8	this	this	DT
10_1101-2021_01_08_425885	488	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	488	10	version	version	NN
10_1101-2021_01_08_425885	488	11	posted	post	VBD
10_1101-2021_01_08_425885	488	12	January	January	NNP
10_1101-2021_01_08_425885	488	13	8	8	CD
10_1101-2021_01_08_425885	488	14	,	,	,
10_1101-2021_01_08_425885	488	15	2021	2021	CD
10_1101-2021_01_08_425885	488	16	.	.	.
10_1101-2021_01_08_425885	488	17	;	;	:
10_1101-2021_01_08_425885	488	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	488	19	:	:	:
10_1101-2021_01_08_425885	488	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	488	21	preprint	preprint	NN
10_1101-2021_01_08_425885	488	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	488	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	RB
10_1101-2021_01_08_425885	488	24	It	-PRON-	PRP
10_1101-2021_01_08_425885	488	25	is	be	VBZ
10_1101-2021_01_08_425885	488	26	important	important	JJ
10_1101-2021_01_08_425885	488	27	to	to	TO
10_1101-2021_01_08_425885	488	28	note	note	VB
10_1101-2021_01_08_425885	488	29	that	that	IN
10_1101-2021_01_08_425885	488	30	our	-PRON-	PRP$
10_1101-2021_01_08_425885	488	31	estimate	estimate	NN
10_1101-2021_01_08_425885	488	32	for	for	IN
10_1101-2021_01_08_425885	488	33	S	S	NNP
10_1101-2021_01_08_425885	488	34	is	be	VBZ
10_1101-2021_01_08_425885	488	35	biased	biased	JJ
10_1101-2021_01_08_425885	488	36	and	and	CC
10_1101-2021_01_08_425885	488	37	not	not	RB
10_1101-2021_01_08_425885	488	38	normally	normally	RB
10_1101-2021_01_08_425885	488	39	distributed	distribute	VBN
10_1101-2021_01_08_425885	488	40	.	.	.
10_1101-2021_01_08_425885	489	1	First	first	RB
10_1101-2021_01_08_425885	489	2	,	,	,
10_1101-2021_01_08_425885	489	3	the	the	DT
10_1101-2021_01_08_425885	489	4	hkijs	hkijs	NN
10_1101-2021_01_08_425885	489	5	are	be	VBP
10_1101-2021_01_08_425885	489	6	only	only	RB
10_1101-2021_01_08_425885	489	7	normally	normally	RB
10_1101-2021_01_08_425885	489	8	distributed	distribute	VBN
10_1101-2021_01_08_425885	489	9	when	when	WRB
10_1101-2021_01_08_425885	489	10	the	the	DT
10_1101-2021_01_08_425885	489	11	residuals	residual	NNS
10_1101-2021_01_08_425885	489	12	(	(	-LRB-
10_1101-2021_01_08_425885	489	13	ε(i	ε(i	NNP
10_1101-2021_01_08_425885	489	14	)	)	-RRB-
10_1101-2021_01_08_425885	489	15	in	in	IN
10_1101-2021_01_08_425885	489	16	Equation	Equation	NNP
10_1101-2021_01_08_425885	489	17	17	17	CD
10_1101-2021_01_08_425885	489	18	)	)	-RRB-
10_1101-2021_01_08_425885	489	19	themselves	-PRON-	PRP
10_1101-2021_01_08_425885	489	20	are	be	VBP
10_1101-2021_01_08_425885	489	21	normally	normally	RB
10_1101-2021_01_08_425885	489	22	distributed	distribute	VBN
10_1101-2021_01_08_425885	489	23	.	.	.
10_1101-2021_01_08_425885	490	1	Second	second	JJ
10_1101-2021_01_08_425885	490	2	,	,	,
10_1101-2021_01_08_425885	490	3	even	even	RB
10_1101-2021_01_08_425885	490	4	when	when	WRB
10_1101-2021_01_08_425885	490	5	the	the	DT
10_1101-2021_01_08_425885	490	6	hkijs	hkijs	NN
10_1101-2021_01_08_425885	490	7	are	be	VBP
10_1101-2021_01_08_425885	490	8	normally	normally	RB
10_1101-2021_01_08_425885	490	9	distributed	distribute	VBN
10_1101-2021_01_08_425885	490	10	,	,	,
10_1101-2021_01_08_425885	490	11	our	-PRON-	PRP$
10_1101-2021_01_08_425885	490	12	estimate	estimate	NN
10_1101-2021_01_08_425885	490	13	of	of	IN
10_1101-2021_01_08_425885	490	14	S	S	NNP
10_1101-2021_01_08_425885	490	15	will	will	MD
10_1101-2021_01_08_425885	490	16	not	not	RB
10_1101-2021_01_08_425885	490	17	be	be	VB
10_1101-2021_01_08_425885	490	18	due	due	IN
10_1101-2021_01_08_425885	490	19	to	to	IN
10_1101-2021_01_08_425885	490	20	its	-PRON-	PRP$
10_1101-2021_01_08_425885	490	21	bilinear	bilinear	NN
10_1101-2021_01_08_425885	490	22	dependence	dependence	NN
10_1101-2021_01_08_425885	490	23	on	on	IN
10_1101-2021_01_08_425885	490	24	hkij	hkij	NNP
10_1101-2021_01_08_425885	490	25	.	.	.
10_1101-2021_01_08_425885	491	1	Lastly	lastly	RB
10_1101-2021_01_08_425885	491	2	,	,	,
10_1101-2021_01_08_425885	491	3	estimates	estimate	VBZ
10_1101-2021_01_08_425885	491	4	for	for	IN
10_1101-2021_01_08_425885	491	5	S	S	NNP
10_1101-2021_01_08_425885	491	6	can	can	MD
10_1101-2021_01_08_425885	491	7	be	be	VB
10_1101-2021_01_08_425885	491	8	biased	bias	VBN
10_1101-2021_01_08_425885	491	9	in	in	IN
10_1101-2021_01_08_425885	491	10	a	a	DT
10_1101-2021_01_08_425885	491	11	manifold	manifold	JJ
10_1101-2021_01_08_425885	491	12	-	-	HYPH
10_1101-2021_01_08_425885	491	13	dependent	dependent	JJ
10_1101-2021_01_08_425885	491	14	and	and	CC
10_1101-2021_01_08_425885	491	15	even	even	RB
10_1101-2021_01_08_425885	491	16	position-	position-	XX
10_1101-2021_01_08_425885	491	17	dependent	dependent	JJ
10_1101-2021_01_08_425885	491	18	way	way	NN
10_1101-2021_01_08_425885	491	19	.	.	.
10_1101-2021_01_08_425885	492	1	For	for	IN
10_1101-2021_01_08_425885	492	2	instance	instance	NN
10_1101-2021_01_08_425885	492	3	,	,	,
10_1101-2021_01_08_425885	492	4	the	the	DT
10_1101-2021_01_08_425885	492	5	analytical	analytical	JJ
10_1101-2021_01_08_425885	492	6	scalar	scalar	JJ
10_1101-2021_01_08_425885	492	7	curvature	curvature	NN
10_1101-2021_01_08_425885	492	8	of	of	IN
10_1101-2021_01_08_425885	492	9	S2	s2	NN
10_1101-2021_01_08_425885	492	10	embedded	embed	VBN
10_1101-2021_01_08_425885	492	11	in	in	IN
10_1101-2021_01_08_425885	492	12	R3	r3	NN
10_1101-2021_01_08_425885	492	13	is	be	VBZ
10_1101-2021_01_08_425885	492	14	given	give	VBN
10_1101-2021_01_08_425885	492	15	by	by	IN
10_1101-2021_01_08_425885	492	16	S	S	NNP
10_1101-2021_01_08_425885	492	17	=	=	SYM
10_1101-2021_01_08_425885	492	18	8(h111h122−	8(h111h122−	NNP
10_1101-2021_01_08_425885	492	19	h112h	h112h	ADD
10_1101-2021_01_08_425885	492	20	1	1	CD
10_1101-2021_01_08_425885	492	21	21	21	CD
10_1101-2021_01_08_425885	492	22	)	)	-RRB-
10_1101-2021_01_08_425885	492	23	,	,	,
10_1101-2021_01_08_425885	492	24	with	with	IN
10_1101-2021_01_08_425885	492	25	h	h	NNP
10_1101-2021_01_08_425885	492	26	1	1	CD
10_1101-2021_01_08_425885	492	27	11	11	CD
10_1101-2021_01_08_425885	492	28	=	=	SYM
10_1101-2021_01_08_425885	492	29	h	h	NN
10_1101-2021_01_08_425885	492	30	1	1	CD
10_1101-2021_01_08_425885	492	31	22	22	CD
10_1101-2021_01_08_425885	492	32	=	=	SYM
10_1101-2021_01_08_425885	492	33	1/2	1/2	CD
10_1101-2021_01_08_425885	492	34	and	and	CC
10_1101-2021_01_08_425885	492	35	h	h	NN
10_1101-2021_01_08_425885	492	36	1	1	CD
10_1101-2021_01_08_425885	492	37	12	12	CD
10_1101-2021_01_08_425885	492	38	=	=	SYM
10_1101-2021_01_08_425885	492	39	h	h	NNP
10_1101-2021_01_08_425885	492	40	1	1	CD
10_1101-2021_01_08_425885	492	41	21	21	CD
10_1101-2021_01_08_425885	492	42	=	=	SYM
10_1101-2021_01_08_425885	492	43	0	0	CD
10_1101-2021_01_08_425885	492	44	.	.	.
10_1101-2021_01_08_425885	493	1	Numerically	numerically	RB
10_1101-2021_01_08_425885	493	2	however	however	RB
10_1101-2021_01_08_425885	493	3	,	,	,
10_1101-2021_01_08_425885	493	4	the	the	DT
10_1101-2021_01_08_425885	493	5	symmetric	symmetric	JJ
10_1101-2021_01_08_425885	493	6	off	off	IN
10_1101-2021_01_08_425885	493	7	-	-	HYPH
10_1101-2021_01_08_425885	493	8	diagonal	diagonal	JJ
10_1101-2021_01_08_425885	493	9	terms	term	NNS
10_1101-2021_01_08_425885	493	10	will	will	MD
10_1101-2021_01_08_425885	493	11	never	never	RB
10_1101-2021_01_08_425885	493	12	be	be	VB
10_1101-2021_01_08_425885	493	13	exactly	exactly	RB
10_1101-2021_01_08_425885	493	14	0	0	CD
10_1101-2021_01_08_425885	493	15	so	so	RB
10_1101-2021_01_08_425885	493	16	S	S	NNP
10_1101-2021_01_08_425885	493	17	will	will	MD
10_1101-2021_01_08_425885	493	18	be	be	VB
10_1101-2021_01_08_425885	493	19	systematically	systematically	RB
10_1101-2021_01_08_425885	493	20	under	under	RB
10_1101-2021_01_08_425885	493	21	-	-	HYPH
10_1101-2021_01_08_425885	493	22	estimated	estimate	VBN
10_1101-2021_01_08_425885	493	23	.	.	.
10_1101-2021_01_08_425885	494	1	This	this	DT
10_1101-2021_01_08_425885	494	2	is	be	VBZ
10_1101-2021_01_08_425885	494	3	apparent	apparent	JJ
10_1101-2021_01_08_425885	494	4	in	in	IN
10_1101-2021_01_08_425885	494	5	the	the	DT
10_1101-2021_01_08_425885	494	6	left	left	JJ
10_1101-2021_01_08_425885	494	7	tail	tail	NN
10_1101-2021_01_08_425885	494	8	of	of	IN
10_1101-2021_01_08_425885	494	9	the	the	DT
10_1101-2021_01_08_425885	494	10	blue	blue	JJ
10_1101-2021_01_08_425885	494	11	histogram	histogram	NNP
10_1101-2021_01_08_425885	494	12	in	in	IN
10_1101-2021_01_08_425885	494	13	Figure	Figure	NNP
10_1101-2021_01_08_425885	494	14	2I.	2i.	CD
10_1101-2021_01_08_425885	495	1	In	in	IN
10_1101-2021_01_08_425885	495	2	our	-PRON-	PRP$
10_1101-2021_01_08_425885	495	3	experience	experience	NN
10_1101-2021_01_08_425885	495	4	,	,	,
10_1101-2021_01_08_425885	495	5	adding	add	VBG
10_1101-2021_01_08_425885	495	6	isotropic	isotropic	JJ
10_1101-2021_01_08_425885	495	7	noise	noise	NN
10_1101-2021_01_08_425885	495	8	of	of	IN
10_1101-2021_01_08_425885	495	9	small	small	JJ
10_1101-2021_01_08_425885	495	10	magnitude	magnitude	NN
10_1101-2021_01_08_425885	495	11	tends	tend	VBZ
10_1101-2021_01_08_425885	495	12	to	to	TO
10_1101-2021_01_08_425885	495	13	remove	remove	VB
10_1101-2021_01_08_425885	495	14	the	the	DT
10_1101-2021_01_08_425885	495	15	skew	skew	JJ
10_1101-2021_01_08_425885	495	16	,	,	,
10_1101-2021_01_08_425885	495	17	presumably	presumably	RB
10_1101-2021_01_08_425885	495	18	because	because	IN
10_1101-2021_01_08_425885	495	19	then	then	RB
10_1101-2021_01_08_425885	495	20	the	the	DT
10_1101-2021_01_08_425885	495	21	residuals	residual	NNS
10_1101-2021_01_08_425885	495	22	more	more	RBR
10_1101-2021_01_08_425885	495	23	closely	closely	RB
10_1101-2021_01_08_425885	495	24	match	match	VBP
10_1101-2021_01_08_425885	495	25	the	the	DT
10_1101-2021_01_08_425885	495	26	regression	regression	NN
10_1101-2021_01_08_425885	495	27	assumptions	assumption	NNS
10_1101-2021_01_08_425885	495	28	(	(	-LRB-
10_1101-2021_01_08_425885	495	29	see	see	VB
10_1101-2021_01_08_425885	495	30	for	for	IN
10_1101-2021_01_08_425885	495	31	example	example	NN
10_1101-2021_01_08_425885	495	32	Figure	figure	NN
10_1101-2021_01_08_425885	495	33	S2B	S2B	NNP
10_1101-2021_01_08_425885	495	34	,	,	,
10_1101-2021_01_08_425885	495	35	where	where	WRB
10_1101-2021_01_08_425885	495	36	the	the	DT
10_1101-2021_01_08_425885	495	37	left	left	JJ
10_1101-2021_01_08_425885	495	38	tail	tail	NN
10_1101-2021_01_08_425885	495	39	disappears	disappear	VBZ
10_1101-2021_01_08_425885	495	40	for	for	IN
10_1101-2021_01_08_425885	495	41	σ	σ	NN
10_1101-2021_01_08_425885	495	42	=	=	SYM
10_1101-2021_01_08_425885	495	43	0.001	0.001	CD
10_1101-2021_01_08_425885	495	44	)	)	-RRB-
10_1101-2021_01_08_425885	495	45	.	.	.
10_1101-2021_01_08_425885	496	1	Furthermore	furthermore	RB
10_1101-2021_01_08_425885	496	2	,	,	,
10_1101-2021_01_08_425885	496	3	in	in	IN
10_1101-2021_01_08_425885	496	4	our	-PRON-	PRP$
10_1101-2021_01_08_425885	496	5	examples	example	NNS
10_1101-2021_01_08_425885	496	6	,	,	,
10_1101-2021_01_08_425885	496	7	we	-PRON-	PRP
10_1101-2021_01_08_425885	496	8	observed	observe	VBD
10_1101-2021_01_08_425885	496	9	that	that	IN
10_1101-2021_01_08_425885	496	10	computed	compute	VBD
10_1101-2021_01_08_425885	496	11	scalar	scalar	JJ
10_1101-2021_01_08_425885	496	12	curvatures	curvature	NNS
10_1101-2021_01_08_425885	496	13	were	be	VBD
10_1101-2021_01_08_425885	496	14	less	less	RBR
10_1101-2021_01_08_425885	496	15	biased	biased	JJ
10_1101-2021_01_08_425885	496	16	when	when	WRB
10_1101-2021_01_08_425885	496	17	the	the	DT
10_1101-2021_01_08_425885	496	18	ambient	ambient	NN
10_1101-2021_01_08_425885	496	19	and/or	and/or	CC
10_1101-2021_01_08_425885	496	20	manifold	manifold	JJ
10_1101-2021_01_08_425885	496	21	dimensions	dimension	NNS
10_1101-2021_01_08_425885	496	22	were	be	VBD
10_1101-2021_01_08_425885	496	23	large	large	JJ
10_1101-2021_01_08_425885	496	24	.	.	.
10_1101-2021_01_08_425885	497	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	497	2	speculate	speculate	VBP
10_1101-2021_01_08_425885	497	3	that	that	IN
10_1101-2021_01_08_425885	497	4	this	this	DT
10_1101-2021_01_08_425885	497	5	is	be	VBZ
10_1101-2021_01_08_425885	497	6	because	because	IN
10_1101-2021_01_08_425885	497	7	the	the	DT
10_1101-2021_01_08_425885	497	8	increased	increase	VBN
10_1101-2021_01_08_425885	497	9	number	number	NN
10_1101-2021_01_08_425885	497	10	of	of	IN
10_1101-2021_01_08_425885	497	11	terms	term	NNS
10_1101-2021_01_08_425885	497	12	(	(	-LRB-
10_1101-2021_01_08_425885	497	13	with	with	IN
10_1101-2021_01_08_425885	497	14	alternating	alternate	VBG
10_1101-2021_01_08_425885	497	15	signs	sign	NNS
10_1101-2021_01_08_425885	497	16	)	)	-RRB-
10_1101-2021_01_08_425885	497	17	in	in	IN
10_1101-2021_01_08_425885	497	18	Equations	Equations	NNP
10_1101-2021_01_08_425885	497	19	6	6	CD
10_1101-2021_01_08_425885	497	20	and	and	CC
10_1101-2021_01_08_425885	497	21	7	7	CD
10_1101-2021_01_08_425885	497	22	leads	lead	NNS
10_1101-2021_01_08_425885	497	23	to	to	IN
10_1101-2021_01_08_425885	497	24	cancellation	cancellation	NN
10_1101-2021_01_08_425885	497	25	of	of	IN
10_1101-2021_01_08_425885	497	26	errors	error	NNS
10_1101-2021_01_08_425885	497	27	,	,	,
10_1101-2021_01_08_425885	497	28	which	which	WDT
10_1101-2021_01_08_425885	497	29	is	be	VBZ
10_1101-2021_01_08_425885	497	30	likely	likely	JJ
10_1101-2021_01_08_425885	497	31	why	why	WRB
10_1101-2021_01_08_425885	497	32	the	the	DT
10_1101-2021_01_08_425885	497	33	accuracy	accuracy	NN
10_1101-2021_01_08_425885	497	34	of	of	IN
10_1101-2021_01_08_425885	497	35	computed	compute	VBN
10_1101-2021_01_08_425885	497	36	scalar	scalar	JJ
10_1101-2021_01_08_425885	497	37	curvatures	curvature	NNS
10_1101-2021_01_08_425885	497	38	was	be	VBD
10_1101-2021_01_08_425885	497	39	higher	high	JJR
10_1101-2021_01_08_425885	497	40	for	for	IN
10_1101-2021_01_08_425885	497	41	S3	S3	NNP
10_1101-2021_01_08_425885	497	42	,	,	,
10_1101-2021_01_08_425885	497	43	S5	s5	NN
10_1101-2021_01_08_425885	497	44	and	and	CC
10_1101-2021_01_08_425885	497	45	S7	s7	NN
10_1101-2021_01_08_425885	497	46	than	than	IN
10_1101-2021_01_08_425885	497	47	S2	s2	NN
10_1101-2021_01_08_425885	497	48	,	,	,
10_1101-2021_01_08_425885	497	49	and	and	CC
10_1101-2021_01_08_425885	497	50	the	the	DT
10_1101-2021_01_08_425885	497	51	distribution	distribution	NN
10_1101-2021_01_08_425885	497	52	of	of	IN
10_1101-2021_01_08_425885	497	53	scalar	scalar	JJ
10_1101-2021_01_08_425885	497	54	curvatures	curvature	NNS
10_1101-2021_01_08_425885	497	55	less	less	RBR
10_1101-2021_01_08_425885	497	56	skewed	skewed	JJ
10_1101-2021_01_08_425885	497	57	(	(	-LRB-
10_1101-2021_01_08_425885	497	58	see	see	VB
10_1101-2021_01_08_425885	497	59	Figure	figure	NN
10_1101-2021_01_08_425885	497	60	2I	2i	NN
10_1101-2021_01_08_425885	497	61	)	)	-RRB-
10_1101-2021_01_08_425885	497	62	.	.	.
10_1101-2021_01_08_425885	498	1	4.3.5	4.3.5	CD
10_1101-2021_01_08_425885	498	2	Note	note	NN
10_1101-2021_01_08_425885	498	3	on	on	IN
10_1101-2021_01_08_425885	498	4	Length	Length	NNP
10_1101-2021_01_08_425885	498	5	Scales	scale	NNS
10_1101-2021_01_08_425885	498	6	Here	here	RB
10_1101-2021_01_08_425885	498	7	we	-PRON-	PRP
10_1101-2021_01_08_425885	498	8	make	make	VBP
10_1101-2021_01_08_425885	498	9	three	three	CD
10_1101-2021_01_08_425885	498	10	remarks	remark	NNS
10_1101-2021_01_08_425885	498	11	regarding	regard	VBG
10_1101-2021_01_08_425885	498	12	length	length	NN
10_1101-2021_01_08_425885	498	13	scales	scale	NNS
10_1101-2021_01_08_425885	498	14	relevant	relevant	JJ
10_1101-2021_01_08_425885	498	15	both	both	CC
10_1101-2021_01_08_425885	498	16	for	for	IN
10_1101-2021_01_08_425885	498	17	considering	consider	VBG
10_1101-2021_01_08_425885	498	18	curvature	curvature	JJ
10_1101-2021_01_08_425885	498	19	theoretically	theoretically	RB
10_1101-2021_01_08_425885	498	20	and	and	CC
10_1101-2021_01_08_425885	498	21	for	for	IN
10_1101-2021_01_08_425885	498	22	applying	apply	VBG
10_1101-2021_01_08_425885	498	23	our	-PRON-	PRP$
10_1101-2021_01_08_425885	498	24	algorithm	algorithm	NN
10_1101-2021_01_08_425885	498	25	.	.	.
10_1101-2021_01_08_425885	499	1	First	first	RB
10_1101-2021_01_08_425885	499	2	,	,	,
10_1101-2021_01_08_425885	499	3	note	note	VB
10_1101-2021_01_08_425885	499	4	that	that	IN
10_1101-2021_01_08_425885	499	5	scalar	scalar	JJ
10_1101-2021_01_08_425885	499	6	curvature	curvature	NN
10_1101-2021_01_08_425885	499	7	has	have	VBZ
10_1101-2021_01_08_425885	499	8	units	unit	NNS
10_1101-2021_01_08_425885	499	9	of	of	IN
10_1101-2021_01_08_425885	499	10	inverse	inverse	NN
10_1101-2021_01_08_425885	499	11	length	length	NN
10_1101-2021_01_08_425885	499	12	squared	square	VBD
10_1101-2021_01_08_425885	499	13	.	.	.
10_1101-2021_01_08_425885	500	1	Therefore	therefore	RB
10_1101-2021_01_08_425885	500	2	,	,	,
10_1101-2021_01_08_425885	500	3	scaling	scale	VBG
10_1101-2021_01_08_425885	500	4	all	all	PDT
10_1101-2021_01_08_425885	500	5	the	the	DT
10_1101-2021_01_08_425885	500	6	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	500	7	of	of	IN
10_1101-2021_01_08_425885	500	8	the	the	DT
10_1101-2021_01_08_425885	500	9	points	point	NNS
10_1101-2021_01_08_425885	500	10	on	on	IN
10_1101-2021_01_08_425885	500	11	a	a	DT
10_1101-2021_01_08_425885	500	12	manifold	manifold	NN
10_1101-2021_01_08_425885	500	13	by	by	IN
10_1101-2021_01_08_425885	500	14	a	a	DT
10_1101-2021_01_08_425885	500	15	factor	factor	NN
10_1101-2021_01_08_425885	500	16	L	L	NNP
10_1101-2021_01_08_425885	500	17	,	,	,
10_1101-2021_01_08_425885	500	18	changes	change	VBZ
10_1101-2021_01_08_425885	500	19	the	the	DT
10_1101-2021_01_08_425885	500	20	scalar	scalar	JJ
10_1101-2021_01_08_425885	500	21	curvature	curvature	NN
10_1101-2021_01_08_425885	500	22	at	at	IN
10_1101-2021_01_08_425885	500	23	all	all	DT
10_1101-2021_01_08_425885	500	24	points	point	NNS
10_1101-2021_01_08_425885	500	25	by	by	IN
10_1101-2021_01_08_425885	500	26	L−2	L−2	,
10_1101-2021_01_08_425885	500	27	.	.	.
10_1101-2021_01_08_425885	501	1	Thus	thus	RB
10_1101-2021_01_08_425885	501	2	,	,	,
10_1101-2021_01_08_425885	501	3	it	-PRON-	PRP
10_1101-2021_01_08_425885	501	4	is	be	VBZ
10_1101-2021_01_08_425885	501	5	always	always	RB
10_1101-2021_01_08_425885	501	6	important	important	JJ
10_1101-2021_01_08_425885	501	7	to	to	TO
10_1101-2021_01_08_425885	501	8	contextualize	contextualize	VB
10_1101-2021_01_08_425885	501	9	the	the	DT
10_1101-2021_01_08_425885	501	10	scalar	scalar	JJ
10_1101-2021_01_08_425885	501	11	curvature	curvature	NN
10_1101-2021_01_08_425885	501	12	in	in	IN
10_1101-2021_01_08_425885	501	13	terms	term	NNS
10_1101-2021_01_08_425885	501	14	of	of	IN
10_1101-2021_01_08_425885	501	15	the	the	DT
10_1101-2021_01_08_425885	501	16	global	global	JJ
10_1101-2021_01_08_425885	501	17	length	length	NN
10_1101-2021_01_08_425885	501	18	scale	scale	NN
10_1101-2021_01_08_425885	501	19	associated	associate	VBN
10_1101-2021_01_08_425885	501	20	with	with	IN
10_1101-2021_01_08_425885	501	21	the	the	DT
10_1101-2021_01_08_425885	501	22	manifold	manifold	NN
10_1101-2021_01_08_425885	501	23	.	.	.
10_1101-2021_01_08_425885	502	1	For	for	IN
10_1101-2021_01_08_425885	502	2	example	example	NN
10_1101-2021_01_08_425885	502	3	,	,	,
10_1101-2021_01_08_425885	502	4	the	the	DT
10_1101-2021_01_08_425885	502	5	scalar	scalar	JJ
10_1101-2021_01_08_425885	502	6	curvature	curvature	NN
10_1101-2021_01_08_425885	502	7	of	of	IN
10_1101-2021_01_08_425885	502	8	Sd	Sd	NNP
10_1101-2021_01_08_425885	502	9	with	with	IN
10_1101-2021_01_08_425885	502	10	radius	radius	NN
10_1101-2021_01_08_425885	502	11	R	r	NN
10_1101-2021_01_08_425885	502	12	is	be	VBZ
10_1101-2021_01_08_425885	502	13	Sd(p	Sd(p	NNP
10_1101-2021_01_08_425885	502	14	)	)	-RRB-
10_1101-2021_01_08_425885	502	15	=	=	NFP
10_1101-2021_01_08_425885	502	16	d(d−1	d(d−1	NNP
10_1101-2021_01_08_425885	502	17	)	)	-RRB-
10_1101-2021_01_08_425885	502	18	R2	R2	NNP
10_1101-2021_01_08_425885	502	19	∀p	∀p	NNP
10_1101-2021_01_08_425885	502	20	∈	∈	NNP
10_1101-2021_01_08_425885	502	21	M	m	NN
10_1101-2021_01_08_425885	502	22	(	(	-LRB-
10_1101-2021_01_08_425885	502	23	here	here	RB
10_1101-2021_01_08_425885	502	24	L	l	NN
10_1101-2021_01_08_425885	502	25	=	=	SYM
10_1101-2021_01_08_425885	502	26	R	r	NN
10_1101-2021_01_08_425885	502	27	)	)	-RRB-
10_1101-2021_01_08_425885	502	28	.	.	.
10_1101-2021_01_08_425885	503	1	In	in	IN
10_1101-2021_01_08_425885	503	2	the	the	DT
10_1101-2021_01_08_425885	503	3	case	case	NN
10_1101-2021_01_08_425885	503	4	of	of	IN
10_1101-2021_01_08_425885	503	5	the	the	DT
10_1101-2021_01_08_425885	503	6	toy	toy	NN
10_1101-2021_01_08_425885	503	7	models	model	NNS
10_1101-2021_01_08_425885	503	8	shown	show	VBN
10_1101-2021_01_08_425885	503	9	in	in	IN
10_1101-2021_01_08_425885	503	10	Figure	Figure	NNP
10_1101-2021_01_08_425885	503	11	2	2	CD
10_1101-2021_01_08_425885	503	12	,	,	,
10_1101-2021_01_08_425885	503	13	the	the	DT
10_1101-2021_01_08_425885	503	14	global	global	JJ
10_1101-2021_01_08_425885	503	15	length	length	NN
10_1101-2021_01_08_425885	503	16	scale	scale	NN
10_1101-2021_01_08_425885	503	17	is	be	VBZ
10_1101-2021_01_08_425885	503	18	L	L	NNP
10_1101-2021_01_08_425885	503	19	≈	≈	NNP
10_1101-2021_01_08_425885	503	20	1	1	CD
10_1101-2021_01_08_425885	503	21	(	(	-LRB-
10_1101-2021_01_08_425885	503	22	see	see	VB
10_1101-2021_01_08_425885	503	23	Methods	Methods	NNP
10_1101-2021_01_08_425885	503	24	Section	Section	NNP
10_1101-2021_01_08_425885	503	25	4.4.1	4.4.1	CD
10_1101-2021_01_08_425885	503	26	)	)	-RRB-
10_1101-2021_01_08_425885	503	27	.	.	.
10_1101-2021_01_08_425885	504	1	For	for	IN
10_1101-2021_01_08_425885	504	2	the	the	DT
10_1101-2021_01_08_425885	504	3	image	image	NN
10_1101-2021_01_08_425885	504	4	patch	patch	NN
10_1101-2021_01_08_425885	504	5	dataset	dataset	NNP
10_1101-2021_01_08_425885	504	6	,	,	,
10_1101-2021_01_08_425885	504	7	a	a	DT
10_1101-2021_01_08_425885	504	8	normalization	normalization	NN
10_1101-2021_01_08_425885	504	9	is	be	VBZ
10_1101-2021_01_08_425885	504	10	applied	apply	VBN
10_1101-2021_01_08_425885	504	11	which	which	WDT
10_1101-2021_01_08_425885	504	12	places	place	VBZ
10_1101-2021_01_08_425885	504	13	all	all	DT
10_1101-2021_01_08_425885	504	14	patches	patch	NNS
10_1101-2021_01_08_425885	504	15	on	on	IN
10_1101-2021_01_08_425885	504	16	S7	S7	NNP
10_1101-2021_01_08_425885	504	17	(	(	-LRB-
10_1101-2021_01_08_425885	504	18	see	see	VB
10_1101-2021_01_08_425885	504	19	Methods	Methods	NNP
10_1101-2021_01_08_425885	504	20	Section	Section	NNP
10_1101-2021_01_08_425885	504	21	4.5.2	4.5.2	CD
10_1101-2021_01_08_425885	504	22	)	)	-RRB-
10_1101-2021_01_08_425885	504	23	,	,	,
10_1101-2021_01_08_425885	504	24	so	so	IN
10_1101-2021_01_08_425885	504	25	that	that	IN
10_1101-2021_01_08_425885	504	26	the	the	DT
10_1101-2021_01_08_425885	504	27	global	global	JJ
10_1101-2021_01_08_425885	504	28	scale	scale	NN
10_1101-2021_01_08_425885	504	29	is	be	VBZ
10_1101-2021_01_08_425885	504	30	again	again	RB
10_1101-2021_01_08_425885	504	31	L	L	NNP
10_1101-2021_01_08_425885	504	32	=	=	SYM
10_1101-2021_01_08_425885	504	33	1	1	CD
10_1101-2021_01_08_425885	504	34	.	.	.
10_1101-2021_01_08_425885	505	1	For	for	IN
10_1101-2021_01_08_425885	505	2	scRNAseq	scrnaseq	JJ
10_1101-2021_01_08_425885	505	3	data	datum	NNS
10_1101-2021_01_08_425885	505	4	,	,	,
10_1101-2021_01_08_425885	505	5	we	-PRON-	PRP
10_1101-2021_01_08_425885	505	6	computed	compute	VBD
10_1101-2021_01_08_425885	505	7	scalar	scalar	JJ
10_1101-2021_01_08_425885	505	8	curvature	curvature	NN
10_1101-2021_01_08_425885	505	9	on	on	IN
10_1101-2021_01_08_425885	505	10	the	the	DT
10_1101-2021_01_08_425885	505	11	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	505	12	after	after	IN
10_1101-2021_01_08_425885	505	13	preprocessing	preprocesse	VBG
10_1101-2021_01_08_425885	505	14	(	(	-LRB-
10_1101-2021_01_08_425885	505	15	see	see	VB
10_1101-2021_01_08_425885	505	16	Methods	Methods	NNP
10_1101-2021_01_08_425885	505	17	Section	Section	NNP
10_1101-2021_01_08_425885	505	18	4.6.1	4.6.1	CD
10_1101-2021_01_08_425885	505	19	)	)	-RRB-
10_1101-2021_01_08_425885	505	20	,	,	,
10_1101-2021_01_08_425885	505	21	without	without	IN
10_1101-2021_01_08_425885	505	22	imposing	impose	VBG
10_1101-2021_01_08_425885	505	23	any	any	DT
10_1101-2021_01_08_425885	505	24	additional	additional	JJ
10_1101-2021_01_08_425885	505	25	scaling	scale	VBG
10_1101-2021_01_08_425885	505	26	correction	correction	NN
10_1101-2021_01_08_425885	505	27	to	to	TO
10_1101-2021_01_08_425885	505	28	achieve	achieve	VB
10_1101-2021_01_08_425885	505	29	a	a	DT
10_1101-2021_01_08_425885	505	30	standardized	standardized	JJ
10_1101-2021_01_08_425885	505	31	global	global	JJ
10_1101-2021_01_08_425885	505	32	length	length	NN
10_1101-2021_01_08_425885	505	33	scale	scale	NN
10_1101-2021_01_08_425885	505	34	.	.	.
10_1101-2021_01_08_425885	506	1	Since	since	IN
10_1101-2021_01_08_425885	506	2	other	other	JJ
10_1101-2021_01_08_425885	506	3	custom	custom	NN
10_1101-2021_01_08_425885	506	4	analyses	analysis	NNS
10_1101-2021_01_08_425885	506	5	also	also	RB
10_1101-2021_01_08_425885	506	6	use	use	VBP
10_1101-2021_01_08_425885	506	7	these	these	DT
10_1101-2021_01_08_425885	506	8	same	same	JJ
10_1101-2021_01_08_425885	506	9	boilerplate	boilerplate	NN
10_1101-2021_01_08_425885	506	10	preprocessing	preprocessing	NN
10_1101-2021_01_08_425885	506	11	steps	step	NNS
10_1101-2021_01_08_425885	506	12	,	,	,
10_1101-2021_01_08_425885	506	13	computing	compute	VBG
10_1101-2021_01_08_425885	506	14	scalar	scalar	JJ
10_1101-2021_01_08_425885	506	15	curvatures	curvature	NNS
10_1101-2021_01_08_425885	506	16	in	in	IN
10_1101-2021_01_08_425885	506	17	the	the	DT
10_1101-2021_01_08_425885	506	18	context	context	NN
10_1101-2021_01_08_425885	506	19	of	of	IN
10_1101-2021_01_08_425885	506	20	the	the	DT
10_1101-2021_01_08_425885	506	21	global	global	JJ
10_1101-2021_01_08_425885	506	22	length	length	NN
10_1101-2021_01_08_425885	506	23	scale	scale	NN
10_1101-2021_01_08_425885	506	24	of	of	IN
10_1101-2021_01_08_425885	506	25	the	the	DT
10_1101-2021_01_08_425885	506	26	preprocessed	preprocesse	VBN
10_1101-2021_01_08_425885	506	27	data	data	NN
10_1101-2021_01_08_425885	506	28	is	be	VBZ
10_1101-2021_01_08_425885	506	29	sensible	sensible	JJ
10_1101-2021_01_08_425885	506	30	.	.	.
10_1101-2021_01_08_425885	507	1	For	for	IN
10_1101-2021_01_08_425885	507	2	all	all	DT
10_1101-2021_01_08_425885	507	3	three	three	CD
10_1101-2021_01_08_425885	507	4	scRNAseq	scrnaseq	NN
10_1101-2021_01_08_425885	507	5	datasets	dataset	NNS
10_1101-2021_01_08_425885	507	6	,	,	,
10_1101-2021_01_08_425885	507	7	the	the	DT
10_1101-2021_01_08_425885	507	8	global	global	JJ
10_1101-2021_01_08_425885	507	9	length	length	NN
10_1101-2021_01_08_425885	507	10	scale	scale	NN
10_1101-2021_01_08_425885	507	11	happened	happen	VBD
10_1101-2021_01_08_425885	507	12	to	to	TO
10_1101-2021_01_08_425885	507	13	be	be	VB
10_1101-2021_01_08_425885	507	14	L	L	NNP
10_1101-2021_01_08_425885	507	15	≈	≈	NNP
10_1101-2021_01_08_425885	507	16	20	20	CD
10_1101-2021_01_08_425885	507	17	(	(	-LRB-
10_1101-2021_01_08_425885	507	18	see	see	VB
10_1101-2021_01_08_425885	507	19	Methods	Methods	NNP
10_1101-2021_01_08_425885	507	20	Section	Section	NNP
10_1101-2021_01_08_425885	507	21	4.6.4	4.6.4	CD
10_1101-2021_01_08_425885	507	22	)	)	-RRB-
10_1101-2021_01_08_425885	507	23	.	.	.
10_1101-2021_01_08_425885	508	1	Second	second	RB
10_1101-2021_01_08_425885	508	2	,	,	,
10_1101-2021_01_08_425885	508	3	since	since	IN
10_1101-2021_01_08_425885	508	4	hkij	hkij	NNP
10_1101-2021_01_08_425885	508	5	is	be	VBZ
10_1101-2021_01_08_425885	508	6	a	a	DT
10_1101-2021_01_08_425885	508	7	dimension	dimension	NN
10_1101-2021_01_08_425885	508	8	-	-	HYPH
10_1101-2021_01_08_425885	508	9	ful	ful	JJ
10_1101-2021_01_08_425885	508	10	quantity	quantity	NN
10_1101-2021_01_08_425885	508	11	(	(	-LRB-
10_1101-2021_01_08_425885	508	12	which	which	WDT
10_1101-2021_01_08_425885	508	13	scales	scale	VBZ
10_1101-2021_01_08_425885	508	14	as	as	IN
10_1101-2021_01_08_425885	508	15	L	L	NNP
10_1101-2021_01_08_425885	508	16	−1	−1	NNP
10_1101-2021_01_08_425885	508	17	)	)	-RRB-
10_1101-2021_01_08_425885	508	18	,	,	,
10_1101-2021_01_08_425885	508	19	to	to	TO
10_1101-2021_01_08_425885	508	20	keep	keep	VB
10_1101-2021_01_08_425885	508	21	the	the	DT
10_1101-2021_01_08_425885	508	22	ratio	ratio	NN
10_1101-2021_01_08_425885	508	23	of	of	IN
10_1101-2021_01_08_425885	508	24	σS	σs	NN
10_1101-2021_01_08_425885	508	25	to	to	IN
10_1101-2021_01_08_425885	508	26	S	S	NNP
10_1101-2021_01_08_425885	508	27	fixed	fix	VBN
10_1101-2021_01_08_425885	508	28	when	when	WRB
10_1101-2021_01_08_425885	508	29	all	all	DT
10_1101-2021_01_08_425885	508	30	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	508	31	are	be	VBP
10_1101-2021_01_08_425885	508	32	scaled	scale	VBN
10_1101-2021_01_08_425885	508	33	by	by	IN
10_1101-2021_01_08_425885	508	34	L	L	NNP
10_1101-2021_01_08_425885	508	35	,	,	,
10_1101-2021_01_08_425885	508	36	σh	σh	NNP
10_1101-2021_01_08_425885	508	37	needs	need	VBZ
10_1101-2021_01_08_425885	508	38	to	to	TO
10_1101-2021_01_08_425885	508	39	be	be	VB
10_1101-2021_01_08_425885	508	40	scaled	scale	VBN
10_1101-2021_01_08_425885	508	41	by	by	IN
10_1101-2021_01_08_425885	508	42	L	L	NNP
10_1101-2021_01_08_425885	508	43	−1	−1	NNP
10_1101-2021_01_08_425885	508	44	.	.	.
10_1101-2021_01_08_425885	509	1	28	28	CD
10_1101-2021_01_08_425885	509	2	.CC	.CC	:
10_1101-2021_01_08_425885	509	3	-	-	:
10_1101-2021_01_08_425885	509	4	BY	by	IN
10_1101-2021_01_08_425885	509	5	-	-	HYPH
10_1101-2021_01_08_425885	509	6	NC	NC	NNP
10_1101-2021_01_08_425885	509	7	-	-	HYPH
10_1101-2021_01_08_425885	509	8	ND	ND	NNP
10_1101-2021_01_08_425885	509	9	4.0	4.0	CD
10_1101-2021_01_08_425885	509	10	International	International	NNP
10_1101-2021_01_08_425885	509	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	509	12	under	under	IN
10_1101-2021_01_08_425885	509	13	a	a	DT
10_1101-2021_01_08_425885	509	14	(	(	-LRB-
10_1101-2021_01_08_425885	509	15	which	which	WDT
10_1101-2021_01_08_425885	509	16	was	be	VBD
10_1101-2021_01_08_425885	509	17	not	not	RB
10_1101-2021_01_08_425885	509	18	certified	certify	VBN
10_1101-2021_01_08_425885	509	19	by	by	IN
10_1101-2021_01_08_425885	509	20	peer	peer	NN
10_1101-2021_01_08_425885	509	21	review	review	NN
10_1101-2021_01_08_425885	509	22	)	)	-RRB-
10_1101-2021_01_08_425885	509	23	is	be	VBZ
10_1101-2021_01_08_425885	509	24	the	the	DT
10_1101-2021_01_08_425885	509	25	author	author	NN
10_1101-2021_01_08_425885	509	26	/	/	SYM
10_1101-2021_01_08_425885	509	27	funder	funder	NN
10_1101-2021_01_08_425885	509	28	,	,	,
10_1101-2021_01_08_425885	509	29	who	who	WP
10_1101-2021_01_08_425885	509	30	has	have	VBZ
10_1101-2021_01_08_425885	509	31	granted	grant	VBN
10_1101-2021_01_08_425885	509	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	509	33	a	a	DT
10_1101-2021_01_08_425885	509	34	license	license	NN
10_1101-2021_01_08_425885	509	35	to	to	TO
10_1101-2021_01_08_425885	509	36	display	display	VB
10_1101-2021_01_08_425885	509	37	the	the	DT
10_1101-2021_01_08_425885	509	38	preprint	preprint	NN
10_1101-2021_01_08_425885	509	39	in	in	IN
10_1101-2021_01_08_425885	509	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	509	41	.	.	.
10_1101-2021_01_08_425885	510	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	510	2	is	be	VBZ
10_1101-2021_01_08_425885	510	3	made	make	VBN
10_1101-2021_01_08_425885	510	4	The	the	DT
10_1101-2021_01_08_425885	510	5	copyright	copyright	NN
10_1101-2021_01_08_425885	510	6	holder	holder	NN
10_1101-2021_01_08_425885	510	7	for	for	IN
10_1101-2021_01_08_425885	510	8	this	this	DT
10_1101-2021_01_08_425885	510	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	510	10	version	version	NN
10_1101-2021_01_08_425885	510	11	posted	post	VBD
10_1101-2021_01_08_425885	510	12	January	January	NNP
10_1101-2021_01_08_425885	510	13	8	8	CD
10_1101-2021_01_08_425885	510	14	,	,	,
10_1101-2021_01_08_425885	510	15	2021	2021	CD
10_1101-2021_01_08_425885	510	16	.	.	.
10_1101-2021_01_08_425885	510	17	;	;	:
10_1101-2021_01_08_425885	510	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	510	19	:	:	:
10_1101-2021_01_08_425885	510	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	510	21	preprint	preprint	NN
10_1101-2021_01_08_425885	510	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	510	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	RB
10_1101-2021_01_08_425885	510	24	Lastly	Lastly	NNP
10_1101-2021_01_08_425885	510	25	,	,	,
10_1101-2021_01_08_425885	510	26	we	-PRON-	PRP
10_1101-2021_01_08_425885	510	27	note	note	VBP
10_1101-2021_01_08_425885	510	28	that	that	IN
10_1101-2021_01_08_425885	510	29	our	-PRON-	PRP$
10_1101-2021_01_08_425885	510	30	choice	choice	NN
10_1101-2021_01_08_425885	510	31	of	of	IN
10_1101-2021_01_08_425885	510	32	σh	σh	NNP
10_1101-2021_01_08_425885	510	33	sets	set	VBZ
10_1101-2021_01_08_425885	510	34	local	local	JJ
10_1101-2021_01_08_425885	510	35	length	length	NN
10_1101-2021_01_08_425885	510	36	scales	scale	NNS
10_1101-2021_01_08_425885	510	37	that	that	WDT
10_1101-2021_01_08_425885	510	38	are	be	VBP
10_1101-2021_01_08_425885	510	39	statistically	statistically	RB
10_1101-2021_01_08_425885	510	40	rather	rather	RB
10_1101-2021_01_08_425885	510	41	than	than	IN
10_1101-2021_01_08_425885	510	42	geometrically	geometrically	RB
10_1101-2021_01_08_425885	510	43	informed	informed	JJ
10_1101-2021_01_08_425885	510	44	:	:	:
10_1101-2021_01_08_425885	510	45	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	510	46	are	be	VBP
10_1101-2021_01_08_425885	510	47	chosen	choose	VBN
10_1101-2021_01_08_425885	510	48	to	to	IN
10_1101-2021_01_08_425885	510	49	upper	upper	JJ
10_1101-2021_01_08_425885	510	50	bound	bind	VBD
10_1101-2021_01_08_425885	510	51	the	the	DT
10_1101-2021_01_08_425885	510	52	uncertainty	uncertainty	NN
10_1101-2021_01_08_425885	510	53	in	in	IN
10_1101-2021_01_08_425885	510	54	estimates	estimate	NNS
10_1101-2021_01_08_425885	510	55	obtained	obtain	VBN
10_1101-2021_01_08_425885	510	56	from	from	IN
10_1101-2021_01_08_425885	510	57	regression	regression	NN
10_1101-2021_01_08_425885	510	58	.	.	.
10_1101-2021_01_08_425885	511	1	This	this	DT
10_1101-2021_01_08_425885	511	2	length	length	NN
10_1101-2021_01_08_425885	511	3	scale	scale	NN
10_1101-2021_01_08_425885	511	4	can	can	MD
10_1101-2021_01_08_425885	511	5	also	also	RB
10_1101-2021_01_08_425885	511	6	be	be	VB
10_1101-2021_01_08_425885	511	7	understood	understand	VBN
10_1101-2021_01_08_425885	511	8	in	in	IN
10_1101-2021_01_08_425885	511	9	terms	term	NNS
10_1101-2021_01_08_425885	511	10	of	of	IN
10_1101-2021_01_08_425885	511	11	a	a	DT
10_1101-2021_01_08_425885	511	12	bias	bias	NN
10_1101-2021_01_08_425885	511	13	-	-	HYPH
10_1101-2021_01_08_425885	511	14	variance	variance	NN
10_1101-2021_01_08_425885	511	15	trade	trade	NN
10_1101-2021_01_08_425885	511	16	-	-	HYPH
10_1101-2021_01_08_425885	511	17	off	off	NN
10_1101-2021_01_08_425885	511	18	.	.	.
10_1101-2021_01_08_425885	512	1	Large	large	JJ
10_1101-2021_01_08_425885	512	2	length	length	NN
10_1101-2021_01_08_425885	512	3	scales	scale	NNS
10_1101-2021_01_08_425885	512	4	reduce	reduce	VBP
10_1101-2021_01_08_425885	512	5	variance	variance	NN
10_1101-2021_01_08_425885	512	6	but	but	CC
10_1101-2021_01_08_425885	512	7	may	may	MD
10_1101-2021_01_08_425885	512	8	introduce	introduce	VB
10_1101-2021_01_08_425885	512	9	a	a	DT
10_1101-2021_01_08_425885	512	10	bias	bias	NN
10_1101-2021_01_08_425885	512	11	if	if	IN
10_1101-2021_01_08_425885	512	12	the	the	DT
10_1101-2021_01_08_425885	512	13	resulting	result	VBG
10_1101-2021_01_08_425885	512	14	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	512	15	are	be	VBP
10_1101-2021_01_08_425885	512	16	larger	large	JJR
10_1101-2021_01_08_425885	512	17	than	than	IN
10_1101-2021_01_08_425885	512	18	features	feature	NNS
10_1101-2021_01_08_425885	512	19	on	on	IN
10_1101-2021_01_08_425885	512	20	the	the	DT
10_1101-2021_01_08_425885	512	21	manifold	manifold	NN
10_1101-2021_01_08_425885	512	22	.	.	.
10_1101-2021_01_08_425885	513	1	This	this	DT
10_1101-2021_01_08_425885	513	2	manifests	manifest	VBZ
10_1101-2021_01_08_425885	513	3	as	as	IN
10_1101-2021_01_08_425885	513	4	poor	poor	JJ
10_1101-2021_01_08_425885	513	5	GOFs	gof	NNS
10_1101-2021_01_08_425885	513	6	and	and	CC
10_1101-2021_01_08_425885	513	7	can	can	MD
10_1101-2021_01_08_425885	513	8	be	be	VB
10_1101-2021_01_08_425885	513	9	corrected	correct	VBN
10_1101-2021_01_08_425885	513	10	by	by	IN
10_1101-2021_01_08_425885	513	11	finer	finer	NNP
10_1101-2021_01_08_425885	513	12	sampling	sampling	NN
10_1101-2021_01_08_425885	513	13	.	.	.
10_1101-2021_01_08_425885	514	1	However	however	RB
10_1101-2021_01_08_425885	514	2	,	,	,
10_1101-2021_01_08_425885	514	3	for	for	IN
10_1101-2021_01_08_425885	514	4	manifolds	manifold	NNS
10_1101-2021_01_08_425885	514	5	with	with	IN
10_1101-2021_01_08_425885	514	6	features	feature	NNS
10_1101-2021_01_08_425885	514	7	at	at	IN
10_1101-2021_01_08_425885	514	8	different	different	JJ
10_1101-2021_01_08_425885	514	9	length	length	NN
10_1101-2021_01_08_425885	514	10	scales	scale	NNS
10_1101-2021_01_08_425885	514	11	(	(	-LRB-
10_1101-2021_01_08_425885	514	12	such	such	JJ
10_1101-2021_01_08_425885	514	13	as	as	IN
10_1101-2021_01_08_425885	514	14	a	a	DT
10_1101-2021_01_08_425885	514	15	golf	golf	NN
10_1101-2021_01_08_425885	514	16	ball	ball	NN
10_1101-2021_01_08_425885	514	17	,	,	,
10_1101-2021_01_08_425885	514	18	which	which	WDT
10_1101-2021_01_08_425885	514	19	can	can	MD
10_1101-2021_01_08_425885	514	20	be	be	VB
10_1101-2021_01_08_425885	514	21	treated	treat	VBN
10_1101-2021_01_08_425885	514	22	as	as	IN
10_1101-2021_01_08_425885	514	23	dimples	dimple	NNS
10_1101-2021_01_08_425885	514	24	superimposed	superimpose	VBN
10_1101-2021_01_08_425885	514	25	on	on	IN
10_1101-2021_01_08_425885	514	26	S2	s2	NN
10_1101-2021_01_08_425885	514	27	)	)	-RRB-
10_1101-2021_01_08_425885	514	28	,	,	,
10_1101-2021_01_08_425885	514	29	neigh-	neigh-	JJ
10_1101-2021_01_08_425885	514	30	borhoods	borhood	NNS
10_1101-2021_01_08_425885	514	31	chosen	choose	VBN
10_1101-2021_01_08_425885	514	32	by	by	IN
10_1101-2021_01_08_425885	514	33	this	this	DT
10_1101-2021_01_08_425885	514	34	heuristic	heuristic	NN
10_1101-2021_01_08_425885	514	35	can	can	MD
10_1101-2021_01_08_425885	514	36	also	also	RB
10_1101-2021_01_08_425885	514	37	be	be	VB
10_1101-2021_01_08_425885	514	38	much	much	RB
10_1101-2021_01_08_425885	514	39	smaller	small	JJR
10_1101-2021_01_08_425885	514	40	than	than	IN
10_1101-2021_01_08_425885	514	41	the	the	DT
10_1101-2021_01_08_425885	514	42	feature	feature	NN
10_1101-2021_01_08_425885	514	43	of	of	IN
10_1101-2021_01_08_425885	514	44	interest	interest	NN
10_1101-2021_01_08_425885	514	45	,	,	,
10_1101-2021_01_08_425885	514	46	so	so	IN
10_1101-2021_01_08_425885	514	47	that	that	IN
10_1101-2021_01_08_425885	514	48	fine	fine	JJ
10_1101-2021_01_08_425885	514	49	-	-	HYPH
10_1101-2021_01_08_425885	514	50	scale	scale	NN
10_1101-2021_01_08_425885	514	51	curvature	curvature	NN
10_1101-2021_01_08_425885	514	52	fluctuations	fluctuation	NNS
10_1101-2021_01_08_425885	514	53	are	be	VBP
10_1101-2021_01_08_425885	514	54	detected	detect	VBN
10_1101-2021_01_08_425885	514	55	(	(	-LRB-
10_1101-2021_01_08_425885	514	56	dimples	dimple	NNS
10_1101-2021_01_08_425885	514	57	)	)	-RRB-
10_1101-2021_01_08_425885	514	58	while	while	IN
10_1101-2021_01_08_425885	514	59	coarser	coarser	NN
10_1101-2021_01_08_425885	514	60	features	feature	NNS
10_1101-2021_01_08_425885	514	61	are	be	VBP
10_1101-2021_01_08_425885	514	62	neglected	neglect	VBN
10_1101-2021_01_08_425885	514	63	(	(	-LRB-
10_1101-2021_01_08_425885	514	64	S2	s2	NN
10_1101-2021_01_08_425885	514	65	)	)	-RRB-
10_1101-2021_01_08_425885	514	66	.	.	.
10_1101-2021_01_08_425885	515	1	Regardless	regardless	RB
10_1101-2021_01_08_425885	515	2	,	,	,
10_1101-2021_01_08_425885	515	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	515	4	de-	de-	RB
10_1101-2021_01_08_425885	515	5	fault	fault	VBP
10_1101-2021_01_08_425885	515	6	to	to	IN
10_1101-2021_01_08_425885	515	7	this	this	DT
10_1101-2021_01_08_425885	515	8	statistical	statistical	JJ
10_1101-2021_01_08_425885	515	9	approach	approach	NN
10_1101-2021_01_08_425885	515	10	because	because	IN
10_1101-2021_01_08_425885	515	11	in	in	IN
10_1101-2021_01_08_425885	515	12	general	general	JJ
10_1101-2021_01_08_425885	515	13	,	,	,
10_1101-2021_01_08_425885	515	14	the	the	DT
10_1101-2021_01_08_425885	515	15	length	length	NN
10_1101-2021_01_08_425885	515	16	scale	scale	NN
10_1101-2021_01_08_425885	515	17	of	of	IN
10_1101-2021_01_08_425885	515	18	relevant	relevant	JJ
10_1101-2021_01_08_425885	515	19	features	feature	NNS
10_1101-2021_01_08_425885	515	20	on	on	IN
10_1101-2021_01_08_425885	515	21	a	a	DT
10_1101-2021_01_08_425885	515	22	data	data	NN
10_1101-2021_01_08_425885	515	23	manifold	manifold	NN
10_1101-2021_01_08_425885	515	24	will	will	MD
10_1101-2021_01_08_425885	515	25	not	not	RB
10_1101-2021_01_08_425885	515	26	be	be	VB
10_1101-2021_01_08_425885	515	27	uniform	uniform	JJ
10_1101-2021_01_08_425885	515	28	across	across	IN
10_1101-2021_01_08_425885	515	29	the	the	DT
10_1101-2021_01_08_425885	515	30	manifold	manifold	NN
10_1101-2021_01_08_425885	515	31	or	or	CC
10_1101-2021_01_08_425885	515	32	known	know	VBN
10_1101-2021_01_08_425885	515	33	a	a	DT
10_1101-2021_01_08_425885	515	34	priori	priori	FW
10_1101-2021_01_08_425885	515	35	.	.	.
10_1101-2021_01_08_425885	516	1	However	however	RB
10_1101-2021_01_08_425885	516	2	,	,	,
10_1101-2021_01_08_425885	516	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	516	4	also	also	RB
10_1101-2021_01_08_425885	516	5	provide	provide	VBP
10_1101-2021_01_08_425885	516	6	the	the	DT
10_1101-2021_01_08_425885	516	7	ability	ability	NN
10_1101-2021_01_08_425885	516	8	to	to	TO
10_1101-2021_01_08_425885	516	9	manually	manually	RB
10_1101-2021_01_08_425885	516	10	set	set	VB
10_1101-2021_01_08_425885	516	11	position	position	NN
10_1101-2021_01_08_425885	516	12	-	-	HYPH
10_1101-2021_01_08_425885	516	13	dependent	dependent	JJ
10_1101-2021_01_08_425885	516	14	r(p	r(p	NNP
10_1101-2021_01_08_425885	516	15	)	)	-RRB-
10_1101-2021_01_08_425885	516	16	in	in	IN
10_1101-2021_01_08_425885	516	17	the	the	DT
10_1101-2021_01_08_425885	516	18	software	software	NN
10_1101-2021_01_08_425885	516	19	to	to	TO
10_1101-2021_01_08_425885	516	20	facilitate	facilitate	VB
10_1101-2021_01_08_425885	516	21	ad	ad	FW
10_1101-2021_01_08_425885	516	22	hoc	hoc	FW
10_1101-2021_01_08_425885	516	23	computation	computation	NN
10_1101-2021_01_08_425885	516	24	of	of	IN
10_1101-2021_01_08_425885	516	25	curvatures	curvature	NNS
10_1101-2021_01_08_425885	516	26	at	at	IN
10_1101-2021_01_08_425885	516	27	any	any	DT
10_1101-2021_01_08_425885	516	28	length	length	NN
10_1101-2021_01_08_425885	516	29	scale	scale	NN
10_1101-2021_01_08_425885	516	30	of	of	IN
10_1101-2021_01_08_425885	516	31	interest	interest	NN
10_1101-2021_01_08_425885	516	32	.	.	.
10_1101-2021_01_08_425885	517	1	4.4	4.4	CD
10_1101-2021_01_08_425885	517	2	Details	detail	NNS
10_1101-2021_01_08_425885	517	3	of	of	IN
10_1101-2021_01_08_425885	517	4	Toy	Toy	NNP
10_1101-2021_01_08_425885	517	5	Manifold	Manifold	NNP
10_1101-2021_01_08_425885	517	6	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	517	7	Computations	Computations	NNPS
10_1101-2021_01_08_425885	517	8	4.4.1	4.4.1	CD
10_1101-2021_01_08_425885	517	9	Analytical	analytical	JJ
10_1101-2021_01_08_425885	517	10	Forms	form	NNS
10_1101-2021_01_08_425885	517	11	Here	here	RB
10_1101-2021_01_08_425885	517	12	we	-PRON-	PRP
10_1101-2021_01_08_425885	517	13	provide	provide	VBP
10_1101-2021_01_08_425885	517	14	analytical	analytical	JJ
10_1101-2021_01_08_425885	517	15	forms	form	NNS
10_1101-2021_01_08_425885	517	16	for	for	IN
10_1101-2021_01_08_425885	517	17	the	the	DT
10_1101-2021_01_08_425885	517	18	toy	toy	NN
10_1101-2021_01_08_425885	517	19	manifolds	manifold	NNS
10_1101-2021_01_08_425885	517	20	shown	show	VBN
10_1101-2021_01_08_425885	517	21	in	in	IN
10_1101-2021_01_08_425885	517	22	Figures	Figures	NNP
10_1101-2021_01_08_425885	517	23	2	2	CD
10_1101-2021_01_08_425885	517	24	and	and	CC
10_1101-2021_01_08_425885	517	25	S2	s2	NN
10_1101-2021_01_08_425885	517	26	.	.	.
10_1101-2021_01_08_425885	518	1	4.4.1.1	4.4.1.1	CD
10_1101-2021_01_08_425885	518	2	Hypersphere	Hypersphere	NNP
10_1101-2021_01_08_425885	518	3	The	the	DT
10_1101-2021_01_08_425885	518	4	d	d	NNP
10_1101-2021_01_08_425885	518	5	-	-	HYPH
10_1101-2021_01_08_425885	518	6	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	518	7	unit	unit	NN
10_1101-2021_01_08_425885	518	8	hypersphere	hypersphere	RB
10_1101-2021_01_08_425885	518	9	,	,	,
10_1101-2021_01_08_425885	518	10	Sd	Sd	NNP
10_1101-2021_01_08_425885	518	11	,	,	,
10_1101-2021_01_08_425885	518	12	has	have	VBZ
10_1101-2021_01_08_425885	518	13	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	518	14	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	518	15	θ1	θ1	JJ
10_1101-2021_01_08_425885	518	16	∈	∈	NNP
10_1101-2021_01_08_425885	518	17	[	[	-LRB-
10_1101-2021_01_08_425885	518	18	0	0	CD
10_1101-2021_01_08_425885	518	19	,	,	,
10_1101-2021_01_08_425885	518	20	2π	2π	LS
10_1101-2021_01_08_425885	518	21	]	]	-RRB-
10_1101-2021_01_08_425885	518	22	,	,	,
10_1101-2021_01_08_425885	518	23	θ2	θ2	NNP
10_1101-2021_01_08_425885	518	24	,	,	,
10_1101-2021_01_08_425885	518	25	...	...	:
10_1101-2021_01_08_425885	518	26	,	,	,
10_1101-2021_01_08_425885	518	27	θd	θd	VB
10_1101-2021_01_08_425885	518	28	∈	∈	NNP
10_1101-2021_01_08_425885	518	29	[	[	-LRB-
10_1101-2021_01_08_425885	518	30	−π	−π	NN
10_1101-2021_01_08_425885	518	31	2	2	CD
10_1101-2021_01_08_425885	518	32	,	,	,
10_1101-2021_01_08_425885	518	33	π	π	CD
10_1101-2021_01_08_425885	518	34	2	2	CD
10_1101-2021_01_08_425885	518	35	]	]	-RRB-
10_1101-2021_01_08_425885	518	36	and	and	CC
10_1101-2021_01_08_425885	518	37	ambient	ambient	JJ
10_1101-2021_01_08_425885	518	38	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	518	39	in	in	IN
10_1101-2021_01_08_425885	518	40	Rd+1	Rd+1	NNP
10_1101-2021_01_08_425885	518	41	given	give	VBN
10_1101-2021_01_08_425885	518	42	by	by	IN
10_1101-2021_01_08_425885	518	43	:	:	:
10_1101-2021_01_08_425885	518	44	xi	xi	NNP
10_1101-2021_01_08_425885	518	45	=	=	SYM
10_1101-2021_01_08_425885	518	46			-LRB-
10_1101-2021_01_08_425885	518	47			NNP
10_1101-2021_01_08_425885	518	48	∏d	∏d	NNP
10_1101-2021_01_08_425885	518	49	j=1	j=1	NN
10_1101-2021_01_08_425885	518	50	cos	cos	NNP
10_1101-2021_01_08_425885	518	51	θj	θj	NNP
10_1101-2021_01_08_425885	518	52	,	,	,
10_1101-2021_01_08_425885	518	53	i	i	PRP
10_1101-2021_01_08_425885	518	54	=	=	SYM
10_1101-2021_01_08_425885	518	55	1	1	CD
10_1101-2021_01_08_425885	518	56	sin	sin	NN
10_1101-2021_01_08_425885	518	57	θi−1	θi−1	NNP
10_1101-2021_01_08_425885	518	58	∏d	∏d	NNP
10_1101-2021_01_08_425885	518	59	j	j	NNP
10_1101-2021_01_08_425885	518	60	=	=	SYM
10_1101-2021_01_08_425885	518	61	i	i	PRP
10_1101-2021_01_08_425885	518	62	cos	cos	NNP
10_1101-2021_01_08_425885	518	63	θj	θj	NNP
10_1101-2021_01_08_425885	518	64	,	,	,
10_1101-2021_01_08_425885	518	65	1	1	CD
10_1101-2021_01_08_425885	518	66	<	<	XX
10_1101-2021_01_08_425885	518	67	i	i	PRP
10_1101-2021_01_08_425885	518	68	≤	≤	VBP
10_1101-2021_01_08_425885	518	69	d	d	NN
10_1101-2021_01_08_425885	518	70	+	+	SYM
10_1101-2021_01_08_425885	518	71	1	1	CD
10_1101-2021_01_08_425885	518	72	(	(	-LRB-
10_1101-2021_01_08_425885	518	73	24	24	CD
10_1101-2021_01_08_425885	518	74	)	)	-RRB-
10_1101-2021_01_08_425885	518	75	Using	use	VBG
10_1101-2021_01_08_425885	518	76	the	the	DT
10_1101-2021_01_08_425885	518	77	relations	relation	NNS
10_1101-2021_01_08_425885	518	78	in	in	IN
10_1101-2021_01_08_425885	518	79	Methods	Methods	NNP
10_1101-2021_01_08_425885	518	80	Sections	Sections	NNP
10_1101-2021_01_08_425885	518	81	4.1	4.1	CD
10_1101-2021_01_08_425885	518	82	,	,	,
10_1101-2021_01_08_425885	518	83	the	the	DT
10_1101-2021_01_08_425885	518	84	scalar	scalar	JJ
10_1101-2021_01_08_425885	518	85	curvature	curvature	NN
10_1101-2021_01_08_425885	518	86	is	be	VBZ
10_1101-2021_01_08_425885	518	87	given	give	VBN
10_1101-2021_01_08_425885	518	88	by	by	IN
10_1101-2021_01_08_425885	518	89	Sd(p	Sd(p	NNP
10_1101-2021_01_08_425885	518	90	)	)	-RRB-
10_1101-2021_01_08_425885	518	91	=	=	NFP
10_1101-2021_01_08_425885	518	92	d(d	d(d	NN
10_1101-2021_01_08_425885	518	93	−	−	NNP
10_1101-2021_01_08_425885	518	94	1	1	CD
10_1101-2021_01_08_425885	518	95	)	)	-RRB-
10_1101-2021_01_08_425885	518	96	∀p	∀p	.
10_1101-2021_01_08_425885	518	97	∈	∈	NNP
10_1101-2021_01_08_425885	518	98	M.	M.	NNP
10_1101-2021_01_08_425885	518	99	To	to	TO
10_1101-2021_01_08_425885	518	100	draw	draw	VB
10_1101-2021_01_08_425885	518	101	uniform	uniform	JJ
10_1101-2021_01_08_425885	518	102	samples	sample	NNS
10_1101-2021_01_08_425885	518	103	from	from	IN
10_1101-2021_01_08_425885	518	104	Sd	Sd	NNP
10_1101-2021_01_08_425885	518	105	,	,	,
10_1101-2021_01_08_425885	518	106	instead	instead	RB
10_1101-2021_01_08_425885	518	107	of	of	IN
10_1101-2021_01_08_425885	518	108	applying	apply	VBG
10_1101-2021_01_08_425885	518	109	rejection	rejection	NN
10_1101-2021_01_08_425885	518	110	sampling	sample	VBG
10_1101-2021_01_08_425885	518	111	on	on	IN
10_1101-2021_01_08_425885	518	112	these	these	DT
10_1101-2021_01_08_425885	518	113	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	518	114	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	518	115	as	as	IN
10_1101-2021_01_08_425885	518	116	described	describe	VBN
10_1101-2021_01_08_425885	518	117	in	in	IN
10_1101-2021_01_08_425885	518	118	Methods	Methods	NNP
10_1101-2021_01_08_425885	518	119	Section	Section	NNP
10_1101-2021_01_08_425885	518	120	4.1	4.1	CD
10_1101-2021_01_08_425885	518	121	,	,	,
10_1101-2021_01_08_425885	518	122	it	-PRON-	PRP
10_1101-2021_01_08_425885	518	123	is	be	VBZ
10_1101-2021_01_08_425885	518	124	more	more	RBR
10_1101-2021_01_08_425885	518	125	straightforward	straightforward	JJ
10_1101-2021_01_08_425885	518	126	to	to	TO
10_1101-2021_01_08_425885	518	127	let	let	VB
10_1101-2021_01_08_425885	518	128	xi	xi	NNP
10_1101-2021_01_08_425885	518	129	∼N(0	∼N(0	NNP
10_1101-2021_01_08_425885	518	130	,	,	,
10_1101-2021_01_08_425885	518	131	1	1	CD
10_1101-2021_01_08_425885	518	132	)	)	-RRB-
10_1101-2021_01_08_425885	518	133	and	and	CC
10_1101-2021_01_08_425885	518	134	scale	scale	VB
10_1101-2021_01_08_425885	518	135	the	the	DT
10_1101-2021_01_08_425885	518	136	resulting	result	VBG
10_1101-2021_01_08_425885	518	137	vector	vector	NN
10_1101-2021_01_08_425885	518	138	(	(	-LRB-
10_1101-2021_01_08_425885	518	139	x1	x1	NNP
10_1101-2021_01_08_425885	518	140	,	,	,
10_1101-2021_01_08_425885	518	141	...	...	:
10_1101-2021_01_08_425885	518	142	,	,	,
10_1101-2021_01_08_425885	518	143	xd+1	xd+1	NNP
10_1101-2021_01_08_425885	518	144	)	)	-RRB-
10_1101-2021_01_08_425885	518	145	to	to	TO
10_1101-2021_01_08_425885	518	146	have	have	VB
10_1101-2021_01_08_425885	518	147	unit	unit	NN
10_1101-2021_01_08_425885	518	148	norm	norm	NN
10_1101-2021_01_08_425885	518	149	.	.	.
10_1101-2021_01_08_425885	519	1	29	29	CD
10_1101-2021_01_08_425885	519	2	.CC	.CC	:
10_1101-2021_01_08_425885	519	3	-	-	HYPH
10_1101-2021_01_08_425885	519	4	BY	by	IN
10_1101-2021_01_08_425885	519	5	-	-	HYPH
10_1101-2021_01_08_425885	519	6	NC	NC	NNP
10_1101-2021_01_08_425885	519	7	-	-	HYPH
10_1101-2021_01_08_425885	519	8	ND	ND	NNP
10_1101-2021_01_08_425885	519	9	4.0	4.0	CD
10_1101-2021_01_08_425885	519	10	International	International	NNP
10_1101-2021_01_08_425885	519	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	519	12	under	under	IN
10_1101-2021_01_08_425885	519	13	a	a	DT
10_1101-2021_01_08_425885	519	14	(	(	-LRB-
10_1101-2021_01_08_425885	519	15	which	which	WDT
10_1101-2021_01_08_425885	519	16	was	be	VBD
10_1101-2021_01_08_425885	519	17	not	not	RB
10_1101-2021_01_08_425885	519	18	certified	certify	VBN
10_1101-2021_01_08_425885	519	19	by	by	IN
10_1101-2021_01_08_425885	519	20	peer	peer	NN
10_1101-2021_01_08_425885	519	21	review	review	NN
10_1101-2021_01_08_425885	519	22	)	)	-RRB-
10_1101-2021_01_08_425885	519	23	is	be	VBZ
10_1101-2021_01_08_425885	519	24	the	the	DT
10_1101-2021_01_08_425885	519	25	author	author	NN
10_1101-2021_01_08_425885	519	26	/	/	SYM
10_1101-2021_01_08_425885	519	27	funder	funder	NN
10_1101-2021_01_08_425885	519	28	,	,	,
10_1101-2021_01_08_425885	519	29	who	who	WP
10_1101-2021_01_08_425885	519	30	has	have	VBZ
10_1101-2021_01_08_425885	519	31	granted	grant	VBN
10_1101-2021_01_08_425885	519	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	519	33	a	a	DT
10_1101-2021_01_08_425885	519	34	license	license	NN
10_1101-2021_01_08_425885	519	35	to	to	TO
10_1101-2021_01_08_425885	519	36	display	display	VB
10_1101-2021_01_08_425885	519	37	the	the	DT
10_1101-2021_01_08_425885	519	38	preprint	preprint	NN
10_1101-2021_01_08_425885	519	39	in	in	IN
10_1101-2021_01_08_425885	519	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	519	41	.	.	.
10_1101-2021_01_08_425885	520	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	520	2	is	be	VBZ
10_1101-2021_01_08_425885	520	3	made	make	VBN
10_1101-2021_01_08_425885	520	4	The	the	DT
10_1101-2021_01_08_425885	520	5	copyright	copyright	NN
10_1101-2021_01_08_425885	520	6	holder	holder	NN
10_1101-2021_01_08_425885	520	7	for	for	IN
10_1101-2021_01_08_425885	520	8	this	this	DT
10_1101-2021_01_08_425885	520	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	520	10	version	version	NN
10_1101-2021_01_08_425885	520	11	posted	post	VBD
10_1101-2021_01_08_425885	520	12	January	January	NNP
10_1101-2021_01_08_425885	520	13	8	8	CD
10_1101-2021_01_08_425885	520	14	,	,	,
10_1101-2021_01_08_425885	520	15	2021	2021	CD
10_1101-2021_01_08_425885	520	16	.	.	.
10_1101-2021_01_08_425885	520	17	;	;	:
10_1101-2021_01_08_425885	520	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	520	19	:	:	:
10_1101-2021_01_08_425885	520	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	520	21	preprint	preprint	NN
10_1101-2021_01_08_425885	520	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	520	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	RB
10_1101-2021_01_08_425885	520	24	4.4.1.2	4.4.1.2	CD
10_1101-2021_01_08_425885	520	25	One	one	CD
10_1101-2021_01_08_425885	520	26	-	-	HYPH
10_1101-2021_01_08_425885	520	27	Sheet	sheet	NN
10_1101-2021_01_08_425885	520	28	Hyperboloid	Hyperboloid	NNP
10_1101-2021_01_08_425885	520	29	The	the	DT
10_1101-2021_01_08_425885	520	30	one	one	CD
10_1101-2021_01_08_425885	520	31	-	-	HYPH
10_1101-2021_01_08_425885	520	32	sheet	sheet	NN
10_1101-2021_01_08_425885	520	33	hyperboloid	hyperboloid	NN
10_1101-2021_01_08_425885	520	34	,	,	,
10_1101-2021_01_08_425885	520	35	H22	H22	NNP
10_1101-2021_01_08_425885	520	36	,	,	,
10_1101-2021_01_08_425885	520	37	has	have	VBZ
10_1101-2021_01_08_425885	520	38	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	520	39	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	520	40	θ	θ	NNP
10_1101-2021_01_08_425885	520	41	∈	∈	RB
10_1101-2021_01_08_425885	520	42	[	[	-LRB-
10_1101-2021_01_08_425885	520	43	0	0	CD
10_1101-2021_01_08_425885	520	44	,	,	,
10_1101-2021_01_08_425885	520	45	2π	2π	CD
10_1101-2021_01_08_425885	520	46	]	]	-RRB-
10_1101-2021_01_08_425885	520	47	,	,	,
10_1101-2021_01_08_425885	520	48	u	u	NNP
10_1101-2021_01_08_425885	520	49	∈	∈	NNP
10_1101-2021_01_08_425885	520	50	R	R	NNP
10_1101-2021_01_08_425885	520	51	and	and	CC
10_1101-2021_01_08_425885	520	52	ambient	ambient	JJ
10_1101-2021_01_08_425885	520	53	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	520	54	in	in	IN
10_1101-2021_01_08_425885	520	55	R3	r3	NN
10_1101-2021_01_08_425885	520	56	given	give	VBN
10_1101-2021_01_08_425885	520	57	by	by	IN
10_1101-2021_01_08_425885	520	58	:	:	:
10_1101-2021_01_08_425885	520	59	x	x	LS
10_1101-2021_01_08_425885	520	60	=	=	SYM
10_1101-2021_01_08_425885	520	61	a	a	DT
10_1101-2021_01_08_425885	520	62	cos	cos	NNP
10_1101-2021_01_08_425885	520	63	θ	θ	NNP
10_1101-2021_01_08_425885	520	64	√	√	NNP
10_1101-2021_01_08_425885	520	65	u2	u2	NN
10_1101-2021_01_08_425885	520	66	+	+	CC
10_1101-2021_01_08_425885	520	67	1	1	CD
10_1101-2021_01_08_425885	520	68	y	y	NN
10_1101-2021_01_08_425885	520	69	=	=	SYM
10_1101-2021_01_08_425885	520	70	b	b	NN
10_1101-2021_01_08_425885	520	71	sin	sin	NN
10_1101-2021_01_08_425885	520	72	θ	θ	NNP
10_1101-2021_01_08_425885	520	73	√	√	NNP
10_1101-2021_01_08_425885	520	74	u2	u2	NN
10_1101-2021_01_08_425885	520	75	+	+	CC
10_1101-2021_01_08_425885	520	76	1	1	CD
10_1101-2021_01_08_425885	520	77	z	z	NN
10_1101-2021_01_08_425885	520	78	=	=	SYM
10_1101-2021_01_08_425885	520	79	cu	cu	XX
10_1101-2021_01_08_425885	520	80	(	(	-LRB-
10_1101-2021_01_08_425885	520	81	25	25	CD
10_1101-2021_01_08_425885	520	82	)	)	-RRB-
10_1101-2021_01_08_425885	520	83	For	for	IN
10_1101-2021_01_08_425885	520	84	Figure	Figure	NNP
10_1101-2021_01_08_425885	520	85	2E	2e	NN
10_1101-2021_01_08_425885	520	86	,	,	,
10_1101-2021_01_08_425885	520	87	F	F	NNP
10_1101-2021_01_08_425885	520	88	,	,	,
10_1101-2021_01_08_425885	520	89	we	-PRON-	PRP
10_1101-2021_01_08_425885	520	90	used	use	VBD
10_1101-2021_01_08_425885	520	91	a	a	NN
10_1101-2021_01_08_425885	520	92	=	=	SYM
10_1101-2021_01_08_425885	520	93	b	b	NN
10_1101-2021_01_08_425885	520	94	=	=	SYM
10_1101-2021_01_08_425885	520	95	2	2	CD
10_1101-2021_01_08_425885	520	96	and	and	CC
10_1101-2021_01_08_425885	520	97	c	c	NN
10_1101-2021_01_08_425885	520	98	=	=	SYM
10_1101-2021_01_08_425885	520	99	1	1	CD
10_1101-2021_01_08_425885	520	100	.	.	.
10_1101-2021_01_08_425885	521	1	Using	use	VBG
10_1101-2021_01_08_425885	521	2	the	the	DT
10_1101-2021_01_08_425885	521	3	relations	relation	NNS
10_1101-2021_01_08_425885	521	4	in	in	IN
10_1101-2021_01_08_425885	521	5	Methods	Methods	NNP
10_1101-2021_01_08_425885	521	6	Sections	Sections	NNP
10_1101-2021_01_08_425885	521	7	4.1	4.1	CD
10_1101-2021_01_08_425885	521	8	,	,	,
10_1101-2021_01_08_425885	521	9	the	the	DT
10_1101-2021_01_08_425885	521	10	scalar	scalar	JJ
10_1101-2021_01_08_425885	521	11	curvature	curvature	NN
10_1101-2021_01_08_425885	521	12	is	be	VBZ
10_1101-2021_01_08_425885	521	13	given	give	VBN
10_1101-2021_01_08_425885	521	14	by	by	IN
10_1101-2021_01_08_425885	521	15	S(z	S(z	NNP
10_1101-2021_01_08_425885	521	16	)	)	-RRB-
10_1101-2021_01_08_425885	521	17	=	=	NFP
10_1101-2021_01_08_425885	521	18	−	−	NNP
10_1101-2021_01_08_425885	521	19	2	2	CD
10_1101-2021_01_08_425885	521	20	(	(	-LRB-
10_1101-2021_01_08_425885	521	21	5z2	5z2	CD
10_1101-2021_01_08_425885	521	22	+	+	SYM
10_1101-2021_01_08_425885	521	23	1)2	1)2	CD
10_1101-2021_01_08_425885	521	24	.	.	.
10_1101-2021_01_08_425885	522	1	To	to	TO
10_1101-2021_01_08_425885	522	2	avoid	avoid	VB
10_1101-2021_01_08_425885	522	3	edge	edge	NN
10_1101-2021_01_08_425885	522	4	effects	effect	NNS
10_1101-2021_01_08_425885	522	5	in	in	IN
10_1101-2021_01_08_425885	522	6	the	the	DT
10_1101-2021_01_08_425885	522	7	z	z	NN
10_1101-2021_01_08_425885	522	8	-	-	HYPH
10_1101-2021_01_08_425885	522	9	direction	direction	NN
10_1101-2021_01_08_425885	522	10	,	,	,
10_1101-2021_01_08_425885	522	11	we	-PRON-	PRP
10_1101-2021_01_08_425885	522	12	constrained	constrain	VBD
10_1101-2021_01_08_425885	522	13	u	u	NNP
10_1101-2021_01_08_425885	522	14	∈	∈	NNP
10_1101-2021_01_08_425885	522	15	[	[	-LRB-
10_1101-2021_01_08_425885	522	16	−2	−2	NNP
10_1101-2021_01_08_425885	522	17	,	,	,
10_1101-2021_01_08_425885	522	18	2	2	CD
10_1101-2021_01_08_425885	522	19	]	]	-RRB-
10_1101-2021_01_08_425885	522	20	,	,	,
10_1101-2021_01_08_425885	522	21	and	and	CC
10_1101-2021_01_08_425885	522	22	sampled	sample	VBN
10_1101-2021_01_08_425885	522	23	points	point	NNS
10_1101-2021_01_08_425885	522	24	as	as	IN
10_1101-2021_01_08_425885	522	25	described	describe	VBN
10_1101-2021_01_08_425885	522	26	in	in	IN
10_1101-2021_01_08_425885	522	27	Methods	Methods	NNP
10_1101-2021_01_08_425885	522	28	Section	Section	NNP
10_1101-2021_01_08_425885	522	29	4.1	4.1	CD
10_1101-2021_01_08_425885	522	30	until	until	IN
10_1101-2021_01_08_425885	522	31	a	a	DT
10_1101-2021_01_08_425885	522	32	subset	subset	NN
10_1101-2021_01_08_425885	522	33	of	of	IN
10_1101-2021_01_08_425885	522	34	N	n	NN
10_1101-2021_01_08_425885	522	35	=	=	SYM
10_1101-2021_01_08_425885	522	36	104	104	CD
10_1101-2021_01_08_425885	522	37	had	have	VBD
10_1101-2021_01_08_425885	522	38	u	u	PRP
10_1101-2021_01_08_425885	522	39	∈	∈	NNP
10_1101-2021_01_08_425885	522	40	[	[	-LRB-
10_1101-2021_01_08_425885	522	41	−1	−1	NNP
10_1101-2021_01_08_425885	522	42	,	,	,
10_1101-2021_01_08_425885	522	43	1	1	CD
10_1101-2021_01_08_425885	522	44	]	]	-RRB-
10_1101-2021_01_08_425885	522	45	.	.	.
10_1101-2021_01_08_425885	523	1	Scalar	scalar	JJ
10_1101-2021_01_08_425885	523	2	curvature	curvature	NN
10_1101-2021_01_08_425885	523	3	was	be	VBD
10_1101-2021_01_08_425885	523	4	computed	compute	VBN
10_1101-2021_01_08_425885	523	5	and	and	CC
10_1101-2021_01_08_425885	523	6	visualized	visualize	VBN
10_1101-2021_01_08_425885	523	7	for	for	IN
10_1101-2021_01_08_425885	523	8	these	these	DT
10_1101-2021_01_08_425885	523	9	N	n	NN
10_1101-2021_01_08_425885	523	10	=	=	SYM
10_1101-2021_01_08_425885	523	11	104	104	CD
10_1101-2021_01_08_425885	523	12	points	point	NNS
10_1101-2021_01_08_425885	523	13	.	.	.
10_1101-2021_01_08_425885	524	1	4.4.1.3	4.4.1.3	LS
10_1101-2021_01_08_425885	524	2	Ring	Ring	NNP
10_1101-2021_01_08_425885	524	3	Torus	Torus	NNP
10_1101-2021_01_08_425885	524	4	The	the	DT
10_1101-2021_01_08_425885	524	5	2-dimensional	2-dimensional	CD
10_1101-2021_01_08_425885	524	6	ring	ring	NN
10_1101-2021_01_08_425885	524	7	torus	torus	NN
10_1101-2021_01_08_425885	524	8	,	,	,
10_1101-2021_01_08_425885	524	9	T	T	NNP
10_1101-2021_01_08_425885	524	10	2	2	CD
10_1101-2021_01_08_425885	524	11	,	,	,
10_1101-2021_01_08_425885	524	12	has	have	VBZ
10_1101-2021_01_08_425885	524	13	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	524	14	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	524	15	θ	θ	NNP
10_1101-2021_01_08_425885	524	16	,	,	,
10_1101-2021_01_08_425885	524	17	φ	φ	NNP
10_1101-2021_01_08_425885	524	18	∈	∈	NNP
10_1101-2021_01_08_425885	524	19	[	[	-LRB-
10_1101-2021_01_08_425885	524	20	0	0	CD
10_1101-2021_01_08_425885	524	21	,	,	,
10_1101-2021_01_08_425885	524	22	2π	2π	CD
10_1101-2021_01_08_425885	524	23	]	]	-RRB-
10_1101-2021_01_08_425885	524	24	and	and	CC
10_1101-2021_01_08_425885	524	25	ambi-	ambi-	NN
10_1101-2021_01_08_425885	524	26	ent	ent	NN
10_1101-2021_01_08_425885	524	27	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	524	28	in	in	IN
10_1101-2021_01_08_425885	524	29	R3	r3	NN
10_1101-2021_01_08_425885	524	30	given	give	VBN
10_1101-2021_01_08_425885	524	31	by	by	IN
10_1101-2021_01_08_425885	524	32	:	:	:
10_1101-2021_01_08_425885	524	33	x	x	LS
10_1101-2021_01_08_425885	524	34	=	=	NFP
10_1101-2021_01_08_425885	524	35	(	(	-LRB-
10_1101-2021_01_08_425885	524	36	R	r	NN
10_1101-2021_01_08_425885	524	37	+	+	CC
10_1101-2021_01_08_425885	524	38	r	r	NN
10_1101-2021_01_08_425885	524	39	cos	cos	NNP
10_1101-2021_01_08_425885	524	40	θ	θ	NNP
10_1101-2021_01_08_425885	524	41	)	)	-RRB-
10_1101-2021_01_08_425885	524	42	cos	cos	NNP
10_1101-2021_01_08_425885	524	43	φ	φ	NNP
10_1101-2021_01_08_425885	524	44	y	y	NNP
10_1101-2021_01_08_425885	524	45	=	=	NFP
10_1101-2021_01_08_425885	524	46	(	(	-LRB-
10_1101-2021_01_08_425885	524	47	R	r	NN
10_1101-2021_01_08_425885	524	48	+	+	CC
10_1101-2021_01_08_425885	524	49	r	r	NN
10_1101-2021_01_08_425885	524	50	cos	cos	NNP
10_1101-2021_01_08_425885	524	51	θ	θ	NNP
10_1101-2021_01_08_425885	524	52	)	)	-RRB-
10_1101-2021_01_08_425885	524	53	sin	sin	NN
10_1101-2021_01_08_425885	524	54	φ	φ	NN
10_1101-2021_01_08_425885	524	55	z	z	NN
10_1101-2021_01_08_425885	524	56	=	=	SYM
10_1101-2021_01_08_425885	524	57	r	r	NN
10_1101-2021_01_08_425885	524	58	sin	sin	NN
10_1101-2021_01_08_425885	524	59	θ	θ	NNP
10_1101-2021_01_08_425885	524	60	(	(	-LRB-
10_1101-2021_01_08_425885	524	61	26	26	CD
10_1101-2021_01_08_425885	524	62	)	)	-RRB-
10_1101-2021_01_08_425885	524	63	For	for	IN
10_1101-2021_01_08_425885	524	64	Figure	figure	NN
10_1101-2021_01_08_425885	524	65	2G	2g	NN
10_1101-2021_01_08_425885	524	66	,	,	,
10_1101-2021_01_08_425885	524	67	H	h	NN
10_1101-2021_01_08_425885	524	68	,	,	,
10_1101-2021_01_08_425885	524	69	we	-PRON-	PRP
10_1101-2021_01_08_425885	524	70	used	use	VBD
10_1101-2021_01_08_425885	524	71	R	r	NN
10_1101-2021_01_08_425885	524	72	=	=	SYM
10_1101-2021_01_08_425885	524	73	2.5	2.5	CD
10_1101-2021_01_08_425885	524	74	and	and	CC
10_1101-2021_01_08_425885	524	75	r	r	NNP
10_1101-2021_01_08_425885	524	76	=	=	SYM
10_1101-2021_01_08_425885	524	77	0.5	0.5	CD
10_1101-2021_01_08_425885	524	78	.	.	.
10_1101-2021_01_08_425885	525	1	Using	use	VBG
10_1101-2021_01_08_425885	525	2	the	the	DT
10_1101-2021_01_08_425885	525	3	relations	relation	NNS
10_1101-2021_01_08_425885	525	4	in	in	IN
10_1101-2021_01_08_425885	525	5	Methods	Methods	NNP
10_1101-2021_01_08_425885	525	6	Sections	Sections	NNP
10_1101-2021_01_08_425885	525	7	4.1	4.1	CD
10_1101-2021_01_08_425885	525	8	,	,	,
10_1101-2021_01_08_425885	525	9	the	the	DT
10_1101-2021_01_08_425885	525	10	scalar	scalar	JJ
10_1101-2021_01_08_425885	525	11	curvature	curvature	NN
10_1101-2021_01_08_425885	525	12	is	be	VBZ
10_1101-2021_01_08_425885	525	13	given	give	VBN
10_1101-2021_01_08_425885	525	14	by	by	IN
10_1101-2021_01_08_425885	525	15	S(θ	s(θ	NN
10_1101-2021_01_08_425885	525	16	)	)	-RRB-
10_1101-2021_01_08_425885	525	17	=	=	NFP
10_1101-2021_01_08_425885	525	18	8	8	CD
10_1101-2021_01_08_425885	525	19	cos(θ	cos(θ	CD
10_1101-2021_01_08_425885	525	20	)	)	-RRB-
10_1101-2021_01_08_425885	525	21	5+cos(θ	5+cos(θ	NNP
10_1101-2021_01_08_425885	525	22	)	)	-RRB-
10_1101-2021_01_08_425885	525	23	.	.	.
10_1101-2021_01_08_425885	526	1	4.4.1.4	4.4.1.4	CD
10_1101-2021_01_08_425885	526	2	Hypercube	Hypercube	NNP
10_1101-2021_01_08_425885	526	3	The	the	DT
10_1101-2021_01_08_425885	526	4	m	m	NNP
10_1101-2021_01_08_425885	526	5	-	-	HYPH
10_1101-2021_01_08_425885	526	6	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	526	7	cube	cube	NN
10_1101-2021_01_08_425885	526	8	of	of	IN
10_1101-2021_01_08_425885	526	9	side	side	NNP
10_1101-2021_01_08_425885	526	10	length	length	NN
10_1101-2021_01_08_425885	526	11	r	r	NNP
10_1101-2021_01_08_425885	526	12	,	,	,
10_1101-2021_01_08_425885	526	13	Dmr	Dmr	NNP
10_1101-2021_01_08_425885	526	14	,	,	,
10_1101-2021_01_08_425885	526	15	has	have	VBZ
10_1101-2021_01_08_425885	526	16	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	526	17	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	526	18	z1	z1	NNP
10_1101-2021_01_08_425885	526	19	,	,	,
10_1101-2021_01_08_425885	526	20	...	...	:
10_1101-2021_01_08_425885	526	21	,	,	,
10_1101-2021_01_08_425885	526	22	zm	zm	NNP
10_1101-2021_01_08_425885	526	23	∈	∈	NNP
10_1101-2021_01_08_425885	526	24	[	[	-LRB-
10_1101-2021_01_08_425885	526	25	−r/2,r/2	−r/2,r/2	NN
10_1101-2021_01_08_425885	526	26	]	]	-RRB-
10_1101-2021_01_08_425885	526	27	,	,	,
10_1101-2021_01_08_425885	526	28	and	and	CC
10_1101-2021_01_08_425885	526	29	ambient	ambient	JJ
10_1101-2021_01_08_425885	526	30	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	526	31	in	in	IN
10_1101-2021_01_08_425885	526	32	Rn	Rn	NNS
10_1101-2021_01_08_425885	526	33	for	for	IN
10_1101-2021_01_08_425885	526	34	n	n	NN
10_1101-2021_01_08_425885	526	35	≥	≥	NN
10_1101-2021_01_08_425885	526	36	m	m	NN
10_1101-2021_01_08_425885	526	37	given	give	VBN
10_1101-2021_01_08_425885	526	38	by	by	IN
10_1101-2021_01_08_425885	526	39	:	:	:
10_1101-2021_01_08_425885	526	40	xi	xi	NNP
10_1101-2021_01_08_425885	526	41	=	=	SYM
10_1101-2021_01_08_425885	526	42			-LRB-
10_1101-2021_01_08_425885	526	43			NNP
10_1101-2021_01_08_425885	526	44	zi	zi	NNP
10_1101-2021_01_08_425885	526	45	,	,	,
10_1101-2021_01_08_425885	526	46	1	1	CD
10_1101-2021_01_08_425885	526	47	≤	≤	NNP
10_1101-2021_01_08_425885	526	48	i	i	PRP
10_1101-2021_01_08_425885	526	49	≤	≤	NNP
10_1101-2021_01_08_425885	526	50	m	m	NNP
10_1101-2021_01_08_425885	526	51	0	0	CD
10_1101-2021_01_08_425885	526	52	,	,	,
10_1101-2021_01_08_425885	526	53	m	m	NNP
10_1101-2021_01_08_425885	526	54	<	<	XX
10_1101-2021_01_08_425885	526	55	i	i	PRP
10_1101-2021_01_08_425885	526	56	≤	≤	VBP
10_1101-2021_01_08_425885	526	57	n	n	CC
10_1101-2021_01_08_425885	526	58	(	(	-LRB-
10_1101-2021_01_08_425885	526	59	27	27	CD
10_1101-2021_01_08_425885	526	60	)	)	-RRB-
10_1101-2021_01_08_425885	526	61	Using	use	VBG
10_1101-2021_01_08_425885	526	62	the	the	DT
10_1101-2021_01_08_425885	526	63	relations	relation	NNS
10_1101-2021_01_08_425885	526	64	in	in	IN
10_1101-2021_01_08_425885	526	65	Methods	Methods	NNP
10_1101-2021_01_08_425885	526	66	Sections	Sections	NNP
10_1101-2021_01_08_425885	526	67	4.1	4.1	CD
10_1101-2021_01_08_425885	526	68	,	,	,
10_1101-2021_01_08_425885	526	69	the	the	DT
10_1101-2021_01_08_425885	526	70	scalar	scalar	JJ
10_1101-2021_01_08_425885	526	71	curvature	curvature	NN
10_1101-2021_01_08_425885	526	72	is	be	VBZ
10_1101-2021_01_08_425885	526	73	given	give	VBN
10_1101-2021_01_08_425885	526	74	by	by	IN
10_1101-2021_01_08_425885	526	75	S(p	s(p	NN
10_1101-2021_01_08_425885	526	76	)	)	-RRB-
10_1101-2021_01_08_425885	526	77	=	=	NFP
10_1101-2021_01_08_425885	526	78	0	0	NFP
10_1101-2021_01_08_425885	526	79	∀p	∀p	NNS
10_1101-2021_01_08_425885	526	80	∈	∈	NNP
10_1101-2021_01_08_425885	526	81	M.	M.	NNP
10_1101-2021_01_08_425885	526	82	4.4.2	4.4.2	NNP
10_1101-2021_01_08_425885	526	83	Practical	Practical	NNP
10_1101-2021_01_08_425885	526	84	Issues	Issues	NNPS
10_1101-2021_01_08_425885	526	85	for	for	IN
10_1101-2021_01_08_425885	526	86	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	526	87	Estimation	Estimation	NNP
10_1101-2021_01_08_425885	526	88	on	on	IN
10_1101-2021_01_08_425885	526	89	Real	real	JJ
10_1101-2021_01_08_425885	526	90	-	-	HYPH
10_1101-2021_01_08_425885	526	91	World	world	NN
10_1101-2021_01_08_425885	526	92	Datasets	dataset	NNS
10_1101-2021_01_08_425885	526	93	For	for	IN
10_1101-2021_01_08_425885	526	94	real	real	JJ
10_1101-2021_01_08_425885	526	95	-	-	HYPH
10_1101-2021_01_08_425885	526	96	world	world	NN
10_1101-2021_01_08_425885	526	97	data	datum	NNS
10_1101-2021_01_08_425885	526	98	,	,	,
10_1101-2021_01_08_425885	526	99	small	small	JJ
10_1101-2021_01_08_425885	526	100	sample	sample	NN
10_1101-2021_01_08_425885	526	101	size	size	NN
10_1101-2021_01_08_425885	526	102	is	be	VBZ
10_1101-2021_01_08_425885	526	103	only	only	RB
10_1101-2021_01_08_425885	526	104	one	one	CD
10_1101-2021_01_08_425885	526	105	of	of	IN
10_1101-2021_01_08_425885	526	106	the	the	DT
10_1101-2021_01_08_425885	526	107	potential	potential	JJ
10_1101-2021_01_08_425885	526	108	confounders	confounder	NNS
10_1101-2021_01_08_425885	526	109	for	for	IN
10_1101-2021_01_08_425885	526	110	accurately	accurately	RB
10_1101-2021_01_08_425885	526	111	estimating	estimate	VBG
10_1101-2021_01_08_425885	526	112	curvature	curvature	JJ
10_1101-2021_01_08_425885	526	113	.	.	.
10_1101-2021_01_08_425885	527	1	Here	here	RB
10_1101-2021_01_08_425885	527	2	,	,	,
10_1101-2021_01_08_425885	527	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	527	4	report	report	VBP
10_1101-2021_01_08_425885	527	5	how	how	WRB
10_1101-2021_01_08_425885	527	6	our	-PRON-	PRP$
10_1101-2021_01_08_425885	527	7	algorithm	algorithm	NN
10_1101-2021_01_08_425885	527	8	fares	fare	VBZ
10_1101-2021_01_08_425885	527	9	when	when	WRB
10_1101-2021_01_08_425885	527	10	four	four	CD
10_1101-2021_01_08_425885	527	11	other	other	JJ
10_1101-2021_01_08_425885	527	12	real	real	JJ
10_1101-2021_01_08_425885	527	13	-	-	HYPH
10_1101-2021_01_08_425885	527	14	world	world	NN
10_1101-2021_01_08_425885	527	15	confounders	confounder	NNS
10_1101-2021_01_08_425885	527	16	are	be	VBP
10_1101-2021_01_08_425885	527	17	applied	apply	VBN
10_1101-2021_01_08_425885	527	18	to	to	IN
10_1101-2021_01_08_425885	527	19	toy	toy	NN
10_1101-2021_01_08_425885	527	20	manifolds	manifold	NNS
10_1101-2021_01_08_425885	527	21	:	:	:
10_1101-2021_01_08_425885	527	22	non	non	JJ
10_1101-2021_01_08_425885	527	23	-	-	JJ
10_1101-2021_01_08_425885	527	24	uniform	uniform	JJ
10_1101-2021_01_08_425885	527	25	sampling	sampling	NN
10_1101-2021_01_08_425885	527	26	,	,	,
10_1101-2021_01_08_425885	527	27	observational	observational	JJ
10_1101-2021_01_08_425885	527	28	noise	noise	NN
10_1101-2021_01_08_425885	527	29	,	,	,
10_1101-2021_01_08_425885	527	30	large	large	JJ
10_1101-2021_01_08_425885	527	31	ambient	ambient	JJ
10_1101-2021_01_08_425885	527	32	dimension	dimension	NN
10_1101-2021_01_08_425885	527	33	n	n	NN
10_1101-2021_01_08_425885	527	34	,	,	,
10_1101-2021_01_08_425885	527	35	and	and	CC
10_1101-2021_01_08_425885	527	36	uncertainty	uncertainty	NN
10_1101-2021_01_08_425885	527	37	in	in	IN
10_1101-2021_01_08_425885	527	38	30	30	CD
10_1101-2021_01_08_425885	527	39	.CC	.CC	,
10_1101-2021_01_08_425885	527	40	-	-	HYPH
10_1101-2021_01_08_425885	527	41	BY	by	IN
10_1101-2021_01_08_425885	527	42	-	-	HYPH
10_1101-2021_01_08_425885	527	43	NC	NC	NNP
10_1101-2021_01_08_425885	527	44	-	-	HYPH
10_1101-2021_01_08_425885	527	45	ND	ND	NNP
10_1101-2021_01_08_425885	527	46	4.0	4.0	CD
10_1101-2021_01_08_425885	527	47	International	International	NNP
10_1101-2021_01_08_425885	527	48	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	527	49	under	under	IN
10_1101-2021_01_08_425885	527	50	a	a	DT
10_1101-2021_01_08_425885	527	51	(	(	-LRB-
10_1101-2021_01_08_425885	527	52	which	which	WDT
10_1101-2021_01_08_425885	527	53	was	be	VBD
10_1101-2021_01_08_425885	527	54	not	not	RB
10_1101-2021_01_08_425885	527	55	certified	certify	VBN
10_1101-2021_01_08_425885	527	56	by	by	IN
10_1101-2021_01_08_425885	527	57	peer	peer	NN
10_1101-2021_01_08_425885	527	58	review	review	NN
10_1101-2021_01_08_425885	527	59	)	)	-RRB-
10_1101-2021_01_08_425885	527	60	is	be	VBZ
10_1101-2021_01_08_425885	527	61	the	the	DT
10_1101-2021_01_08_425885	527	62	author	author	NN
10_1101-2021_01_08_425885	527	63	/	/	SYM
10_1101-2021_01_08_425885	527	64	funder	funder	NN
10_1101-2021_01_08_425885	527	65	,	,	,
10_1101-2021_01_08_425885	527	66	who	who	WP
10_1101-2021_01_08_425885	527	67	has	have	VBZ
10_1101-2021_01_08_425885	527	68	granted	grant	VBN
10_1101-2021_01_08_425885	527	69	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	527	70	a	a	DT
10_1101-2021_01_08_425885	527	71	license	license	NN
10_1101-2021_01_08_425885	527	72	to	to	TO
10_1101-2021_01_08_425885	527	73	display	display	VB
10_1101-2021_01_08_425885	527	74	the	the	DT
10_1101-2021_01_08_425885	527	75	preprint	preprint	NN
10_1101-2021_01_08_425885	527	76	in	in	IN
10_1101-2021_01_08_425885	527	77	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	527	78	.	.	.
10_1101-2021_01_08_425885	528	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	528	2	is	be	VBZ
10_1101-2021_01_08_425885	528	3	made	make	VBN
10_1101-2021_01_08_425885	528	4	The	the	DT
10_1101-2021_01_08_425885	528	5	copyright	copyright	NN
10_1101-2021_01_08_425885	528	6	holder	holder	NN
10_1101-2021_01_08_425885	528	7	for	for	IN
10_1101-2021_01_08_425885	528	8	this	this	DT
10_1101-2021_01_08_425885	528	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	528	10	version	version	NN
10_1101-2021_01_08_425885	528	11	posted	post	VBD
10_1101-2021_01_08_425885	528	12	January	January	NNP
10_1101-2021_01_08_425885	528	13	8	8	CD
10_1101-2021_01_08_425885	528	14	,	,	,
10_1101-2021_01_08_425885	528	15	2021	2021	CD
10_1101-2021_01_08_425885	528	16	.	.	.
10_1101-2021_01_08_425885	528	17	;	;	:
10_1101-2021_01_08_425885	528	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	528	19	:	:	:
10_1101-2021_01_08_425885	528	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	528	21	preprint	preprint	NN
10_1101-2021_01_08_425885	528	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	528	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	VB
10_1101-2021_01_08_425885	528	24	the	the	DT
10_1101-2021_01_08_425885	528	25	manifold	manifold	JJ
10_1101-2021_01_08_425885	528	26	dimension	dimension	NN
10_1101-2021_01_08_425885	528	27	d.	d.	NNP
10_1101-2021_01_08_425885	528	28	4.4.2.1	4.4.2.1	CD
10_1101-2021_01_08_425885	528	29	Non	non	JJ
10_1101-2021_01_08_425885	528	30	-	-	JJ
10_1101-2021_01_08_425885	528	31	Uniform	uniform	NN
10_1101-2021_01_08_425885	528	32	Sampling	sampling	NN
10_1101-2021_01_08_425885	528	33	We	-PRON-	PRP
10_1101-2021_01_08_425885	528	34	expect	expect	VBP
10_1101-2021_01_08_425885	528	35	our	-PRON-	PRP$
10_1101-2021_01_08_425885	528	36	approach	approach	NN
10_1101-2021_01_08_425885	528	37	to	to	TO
10_1101-2021_01_08_425885	528	38	handle	handle	VB
10_1101-2021_01_08_425885	528	39	non	non	JJ
10_1101-2021_01_08_425885	528	40	-	-	JJ
10_1101-2021_01_08_425885	528	41	uniform	uniform	JJ
10_1101-2021_01_08_425885	528	42	sampling	sampling	NN
10_1101-2021_01_08_425885	528	43	of	of	IN
10_1101-2021_01_08_425885	528	44	the	the	DT
10_1101-2021_01_08_425885	528	45	man-	man-	NNP
10_1101-2021_01_08_425885	528	46	ifold	ifold	NN
10_1101-2021_01_08_425885	528	47	gracefully	gracefully	RB
10_1101-2021_01_08_425885	528	48	:	:	:
10_1101-2021_01_08_425885	528	49	smaller	small	JJR
10_1101-2021_01_08_425885	528	50	(	(	-LRB-
10_1101-2021_01_08_425885	528	51	larger	large	JJR
10_1101-2021_01_08_425885	528	52	)	)	-RRB-
10_1101-2021_01_08_425885	528	53	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	528	54	will	will	MD
10_1101-2021_01_08_425885	528	55	be	be	VB
10_1101-2021_01_08_425885	528	56	used	use	VBN
10_1101-2021_01_08_425885	528	57	on	on	IN
10_1101-2021_01_08_425885	528	58	densely	densely	RB
10_1101-2021_01_08_425885	528	59	(	(	-LRB-
10_1101-2021_01_08_425885	528	60	sparsely	sparsely	RB
10_1101-2021_01_08_425885	528	61	)	)	-RRB-
10_1101-2021_01_08_425885	528	62	sampled	sample	VBN
10_1101-2021_01_08_425885	528	63	portions	portion	NNS
10_1101-2021_01_08_425885	528	64	of	of	IN
10_1101-2021_01_08_425885	528	65	the	the	DT
10_1101-2021_01_08_425885	528	66	manifold	manifold	NN
10_1101-2021_01_08_425885	528	67	to	to	TO
10_1101-2021_01_08_425885	528	68	encapsulate	encapsulate	VB
10_1101-2021_01_08_425885	528	69	the	the	DT
10_1101-2021_01_08_425885	528	70	number	number	NN
10_1101-2021_01_08_425885	528	71	of	of	IN
10_1101-2021_01_08_425885	528	72	points	point	NNS
10_1101-2021_01_08_425885	528	73	needed	need	VBN
10_1101-2021_01_08_425885	528	74	to	to	TO
10_1101-2021_01_08_425885	528	75	achieve	achieve	VB
10_1101-2021_01_08_425885	528	76	σh	σh	NNP
10_1101-2021_01_08_425885	528	77	.	.	.
10_1101-2021_01_08_425885	529	1	To	to	TO
10_1101-2021_01_08_425885	529	2	computationally	computationally	RB
10_1101-2021_01_08_425885	529	3	verify	verify	VB
10_1101-2021_01_08_425885	529	4	the	the	DT
10_1101-2021_01_08_425885	529	5	robustness	robustness	NN
10_1101-2021_01_08_425885	529	6	of	of	IN
10_1101-2021_01_08_425885	529	7	our	-PRON-	PRP$
10_1101-2021_01_08_425885	529	8	tool	tool	NN
10_1101-2021_01_08_425885	529	9	to	to	IN
10_1101-2021_01_08_425885	529	10	non	non	JJ
10_1101-2021_01_08_425885	529	11	-	-	JJ
10_1101-2021_01_08_425885	529	12	uniform	uniform	JJ
10_1101-2021_01_08_425885	529	13	sampling	sampling	NN
10_1101-2021_01_08_425885	529	14	,	,	,
10_1101-2021_01_08_425885	529	15	we	-PRON-	PRP
10_1101-2021_01_08_425885	529	16	constructed	construct	VBD
10_1101-2021_01_08_425885	529	17	a	a	DT
10_1101-2021_01_08_425885	529	18	toy	toy	NN
10_1101-2021_01_08_425885	529	19	model	model	NN
10_1101-2021_01_08_425885	529	20	to	to	TO
10_1101-2021_01_08_425885	529	21	roughly	roughly	RB
10_1101-2021_01_08_425885	529	22	match	match	VB
10_1101-2021_01_08_425885	529	23	the	the	DT
10_1101-2021_01_08_425885	529	24	(	(	-LRB-
10_1101-2021_01_08_425885	529	25	n	n	NN
10_1101-2021_01_08_425885	529	26	,	,	,
10_1101-2021_01_08_425885	529	27	d	d	NN
10_1101-2021_01_08_425885	529	28	,	,	,
10_1101-2021_01_08_425885	529	29	L	l	NN
10_1101-2021_01_08_425885	529	30	)	)	-RRB-
10_1101-2021_01_08_425885	529	31	parameters	parameter	NNS
10_1101-2021_01_08_425885	529	32	for	for	IN
10_1101-2021_01_08_425885	529	33	the	the	DT
10_1101-2021_01_08_425885	529	34	scRNAseq	scrnaseq	JJ
10_1101-2021_01_08_425885	529	35	datasets	dataset	NNS
10_1101-2021_01_08_425885	529	36	explored	explore	VBN
10_1101-2021_01_08_425885	529	37	in	in	IN
10_1101-2021_01_08_425885	529	38	the	the	DT
10_1101-2021_01_08_425885	529	39	paper	paper	NN
10_1101-2021_01_08_425885	529	40	,	,	,
10_1101-2021_01_08_425885	529	41	for	for	IN
10_1101-2021_01_08_425885	529	42	which	which	WDT
10_1101-2021_01_08_425885	529	43	non	non	JJ
10_1101-2021_01_08_425885	529	44	-	-	JJ
10_1101-2021_01_08_425885	529	45	zero	zero	CD
10_1101-2021_01_08_425885	529	46	scalar	scalar	JJ
10_1101-2021_01_08_425885	529	47	curvatures	curvature	NNS
10_1101-2021_01_08_425885	529	48	seemed	seem	VBD
10_1101-2021_01_08_425885	529	49	to	to	TO
10_1101-2021_01_08_425885	529	50	appear	appear	VB
10_1101-2021_01_08_425885	529	51	at	at	IN
10_1101-2021_01_08_425885	529	52	smaller	small	JJR
10_1101-2021_01_08_425885	529	53	length	length	NN
10_1101-2021_01_08_425885	529	54	scales	scale	NNS
10_1101-2021_01_08_425885	529	55	/	/	SYM
10_1101-2021_01_08_425885	529	56	higher	high	JJR
10_1101-2021_01_08_425885	529	57	densities	density	NNS
10_1101-2021_01_08_425885	529	58	.	.	.
10_1101-2021_01_08_425885	530	1	Specifically	specifically	RB
10_1101-2021_01_08_425885	530	2	,	,	,
10_1101-2021_01_08_425885	530	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	530	4	wanted	want	VBD
10_1101-2021_01_08_425885	530	5	to	to	TO
10_1101-2021_01_08_425885	530	6	verify	verify	VB
10_1101-2021_01_08_425885	530	7	that	that	DT
10_1101-2021_01_08_425885	530	8	non	non	JJ
10_1101-2021_01_08_425885	530	9	-	-	JJ
10_1101-2021_01_08_425885	530	10	zero	zero	CD
10_1101-2021_01_08_425885	530	11	scalar	scalar	JJ
10_1101-2021_01_08_425885	530	12	curvatures	curvature	NNS
10_1101-2021_01_08_425885	530	13	do	do	VBP
10_1101-2021_01_08_425885	530	14	not	not	RB
10_1101-2021_01_08_425885	530	15	appear	appear	VB
10_1101-2021_01_08_425885	530	16	artifactually	artifactually	RB
10_1101-2021_01_08_425885	530	17	at	at	IN
10_1101-2021_01_08_425885	530	18	specific	specific	JJ
10_1101-2021_01_08_425885	530	19	length	length	NN
10_1101-2021_01_08_425885	530	20	scales	scale	NNS
10_1101-2021_01_08_425885	530	21	due	due	JJ
10_1101-2021_01_08_425885	530	22	to	to	IN
10_1101-2021_01_08_425885	530	23	sharp	sharp	JJ
10_1101-2021_01_08_425885	530	24	changes	change	NNS
10_1101-2021_01_08_425885	530	25	in	in	IN
10_1101-2021_01_08_425885	530	26	the	the	DT
10_1101-2021_01_08_425885	530	27	local	local	JJ
10_1101-2021_01_08_425885	530	28	density	density	NN
10_1101-2021_01_08_425885	530	29	of	of	IN
10_1101-2021_01_08_425885	530	30	points	point	NNS
10_1101-2021_01_08_425885	530	31	sampled	sample	VBN
10_1101-2021_01_08_425885	530	32	from	from	IN
10_1101-2021_01_08_425885	530	33	a	a	DT
10_1101-2021_01_08_425885	530	34	flat	flat	JJ
10_1101-2021_01_08_425885	530	35	manifold	manifold	NN
10_1101-2021_01_08_425885	530	36	.	.	.
10_1101-2021_01_08_425885	531	1	To	to	IN
10_1101-2021_01_08_425885	531	2	this	this	DT
10_1101-2021_01_08_425885	531	3	end	end	NN
10_1101-2021_01_08_425885	531	4	,	,	,
10_1101-2021_01_08_425885	531	5	we	-PRON-	PRP
10_1101-2021_01_08_425885	531	6	formed	form	VBD
10_1101-2021_01_08_425885	531	7	a	a	DT
10_1101-2021_01_08_425885	531	8	dataset	dataset	NN
10_1101-2021_01_08_425885	531	9	with	with	IN
10_1101-2021_01_08_425885	531	10	a	a	DT
10_1101-2021_01_08_425885	531	11	sparse	sparse	JJ
10_1101-2021_01_08_425885	531	12	periphery	periphery	NN
10_1101-2021_01_08_425885	531	13	and	and	CC
10_1101-2021_01_08_425885	531	14	dense	dense	JJ
10_1101-2021_01_08_425885	531	15	core	core	NN
10_1101-2021_01_08_425885	531	16	by	by	IN
10_1101-2021_01_08_425885	531	17	uniformly	uniformly	RB
10_1101-2021_01_08_425885	531	18	sampling	sample	VBG
10_1101-2021_01_08_425885	531	19	N1	N1	NNP
10_1101-2021_01_08_425885	531	20	=	=	SYM
10_1101-2021_01_08_425885	531	21	10	10	CD
10_1101-2021_01_08_425885	531	22	4	4	CD
10_1101-2021_01_08_425885	531	23	points	point	NNS
10_1101-2021_01_08_425885	531	24	from	from	IN
10_1101-2021_01_08_425885	531	25	D310	D310	NNP
10_1101-2021_01_08_425885	531	26	to	to	TO
10_1101-2021_01_08_425885	531	27	establish	establish	VB
10_1101-2021_01_08_425885	531	28	a	a	DT
10_1101-2021_01_08_425885	531	29	background	background	NN
10_1101-2021_01_08_425885	531	30	density	density	NN
10_1101-2021_01_08_425885	531	31	equal	equal	JJ
10_1101-2021_01_08_425885	531	32	to	to	IN
10_1101-2021_01_08_425885	531	33	10	10	CD
10_1101-2021_01_08_425885	531	34	points	point	NNS
10_1101-2021_01_08_425885	531	35	per	per	IN
10_1101-2021_01_08_425885	531	36	unit	unit	NN
10_1101-2021_01_08_425885	531	37	volume	volume	NN
10_1101-2021_01_08_425885	531	38	,	,	,
10_1101-2021_01_08_425885	531	39	and	and	CC
10_1101-2021_01_08_425885	531	40	N2	N2	NNP
10_1101-2021_01_08_425885	531	41	=	=	SYM
10_1101-2021_01_08_425885	531	42	10	10	CD
10_1101-2021_01_08_425885	531	43	3	3	CD
10_1101-2021_01_08_425885	531	44	points	point	NNS
10_1101-2021_01_08_425885	531	45	from	from	IN
10_1101-2021_01_08_425885	531	46	D31	D31	NNP
10_1101-2021_01_08_425885	531	47	to	to	TO
10_1101-2021_01_08_425885	531	48	create	create	VB
10_1101-2021_01_08_425885	531	49	a	a	DT
10_1101-2021_01_08_425885	531	50	core	core	NN
10_1101-2021_01_08_425885	531	51	density	density	NN
10_1101-2021_01_08_425885	531	52	roughly	roughly	RB
10_1101-2021_01_08_425885	531	53	equal	equal	JJ
10_1101-2021_01_08_425885	531	54	to	to	IN
10_1101-2021_01_08_425885	531	55	103	103	CD
10_1101-2021_01_08_425885	531	56	points	point	NNS
10_1101-2021_01_08_425885	531	57	per	per	IN
10_1101-2021_01_08_425885	531	58	unit	unit	NN
10_1101-2021_01_08_425885	531	59	volume	volume	NN
10_1101-2021_01_08_425885	531	60	(	(	-LRB-
10_1101-2021_01_08_425885	531	61	see	see	VB
10_1101-2021_01_08_425885	531	62	Methods	Methods	NNP
10_1101-2021_01_08_425885	531	63	Section	Section	NNP
10_1101-2021_01_08_425885	531	64	4.4.1.4	4.4.1.4	CD
10_1101-2021_01_08_425885	531	65	)	)	-RRB-
10_1101-2021_01_08_425885	531	66	.	.	.
10_1101-2021_01_08_425885	532	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	532	2	embedded	embed	VBD
10_1101-2021_01_08_425885	532	3	these	these	DT
10_1101-2021_01_08_425885	532	4	points	point	NNS
10_1101-2021_01_08_425885	532	5	in	in	IN
10_1101-2021_01_08_425885	532	6	R11	R11	NNP
10_1101-2021_01_08_425885	532	7	by	by	IN
10_1101-2021_01_08_425885	532	8	adding	add	VBG
10_1101-2021_01_08_425885	532	9	isotropic	isotropic	JJ
10_1101-2021_01_08_425885	532	10	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	532	11	noise	noise	NN
10_1101-2021_01_08_425885	532	12	with	with	IN
10_1101-2021_01_08_425885	532	13	σ	σ	NNP
10_1101-2021_01_08_425885	532	14	=	=	SYM
10_1101-2021_01_08_425885	532	15	0.01	0.01	CD
10_1101-2021_01_08_425885	532	16	to	to	IN
10_1101-2021_01_08_425885	532	17	the	the	DT
10_1101-2021_01_08_425885	532	18	eight	eight	CD
10_1101-2021_01_08_425885	532	19	normal	normal	JJ
10_1101-2021_01_08_425885	532	20	directions	direction	NNS
10_1101-2021_01_08_425885	532	21	,	,	,
10_1101-2021_01_08_425885	532	22	for	for	IN
10_1101-2021_01_08_425885	532	23	all	all	DT
10_1101-2021_01_08_425885	532	24	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	532	25	.	.	.
10_1101-2021_01_08_425885	533	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	533	2	computed	compute	VBD
10_1101-2021_01_08_425885	533	3	scalar	scalar	JJ
10_1101-2021_01_08_425885	533	4	curvature	curvature	NN
10_1101-2021_01_08_425885	533	5	on	on	IN
10_1101-2021_01_08_425885	533	6	this	this	DT
10_1101-2021_01_08_425885	533	7	dataset	dataset	NN
10_1101-2021_01_08_425885	533	8	for	for	IN
10_1101-2021_01_08_425885	533	9	a	a	DT
10_1101-2021_01_08_425885	533	10	fixed	fix	VBN
10_1101-2021_01_08_425885	533	11	σh	σh	NN
10_1101-2021_01_08_425885	533	12	(	(	-LRB-
10_1101-2021_01_08_425885	533	13	see	see	VB
10_1101-2021_01_08_425885	533	14	Methods	Methods	NNP
10_1101-2021_01_08_425885	533	15	Section	Section	NNP
10_1101-2021_01_08_425885	533	16	4.4.3	4.4.3	NNS
10_1101-2021_01_08_425885	533	17	)	)	-RRB-
10_1101-2021_01_08_425885	533	18	and	and	CC
10_1101-2021_01_08_425885	533	19	found	find	VBD
10_1101-2021_01_08_425885	533	20	no	no	DT
10_1101-2021_01_08_425885	533	21	significant	significant	JJ
10_1101-2021_01_08_425885	533	22	deviation	deviation	NN
10_1101-2021_01_08_425885	533	23	from	from	IN
10_1101-2021_01_08_425885	533	24	the	the	DT
10_1101-2021_01_08_425885	533	25	true	true	JJ
10_1101-2021_01_08_425885	533	26	value	value	NN
10_1101-2021_01_08_425885	533	27	of	of	IN
10_1101-2021_01_08_425885	533	28	zero	zero	CD
10_1101-2021_01_08_425885	533	29	in	in	IN
10_1101-2021_01_08_425885	533	30	either	either	CC
10_1101-2021_01_08_425885	533	31	the	the	DT
10_1101-2021_01_08_425885	533	32	sparse	sparse	JJ
10_1101-2021_01_08_425885	533	33	or	or	CC
10_1101-2021_01_08_425885	533	34	dense	dense	JJ
10_1101-2021_01_08_425885	533	35	regions	region	NNS
10_1101-2021_01_08_425885	533	36	(	(	-LRB-
10_1101-2021_01_08_425885	533	37	see	see	VB
10_1101-2021_01_08_425885	533	38	Figure	Figure	NNP
10_1101-2021_01_08_425885	533	39	S2A	s2a	NN
10_1101-2021_01_08_425885	533	40	)	)	-RRB-
10_1101-2021_01_08_425885	533	41	.	.	.
10_1101-2021_01_08_425885	534	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	534	2	next	next	RB
10_1101-2021_01_08_425885	534	3	computed	compute	VBD
10_1101-2021_01_08_425885	534	4	scalar	scalar	JJ
10_1101-2021_01_08_425885	534	5	curvatures	curvature	NNS
10_1101-2021_01_08_425885	534	6	at	at	IN
10_1101-2021_01_08_425885	534	7	three	three	CD
10_1101-2021_01_08_425885	534	8	fixed	fix	VBN
10_1101-2021_01_08_425885	534	9	length	length	NN
10_1101-2021_01_08_425885	534	10	scales	scale	NNS
10_1101-2021_01_08_425885	534	11	corresponding	correspond	VBG
10_1101-2021_01_08_425885	534	12	to	to	IN
10_1101-2021_01_08_425885	534	13	the	the	DT
10_1101-2021_01_08_425885	534	14	5	5	CD
10_1101-2021_01_08_425885	534	15	,	,	,
10_1101-2021_01_08_425885	534	16	50	50	CD
10_1101-2021_01_08_425885	534	17	,	,	,
10_1101-2021_01_08_425885	534	18	and	and	CC
10_1101-2021_01_08_425885	534	19	95%-ile	95%-ile	CD
10_1101-2021_01_08_425885	534	20	r	r	NN
10_1101-2021_01_08_425885	534	21	values	value	NNS
10_1101-2021_01_08_425885	534	22	obtained	obtain	VBN
10_1101-2021_01_08_425885	534	23	using	use	VBG
10_1101-2021_01_08_425885	534	24	the	the	DT
10_1101-2021_01_08_425885	534	25	specified	specify	VBN
10_1101-2021_01_08_425885	534	26	σh	σh	NNP
10_1101-2021_01_08_425885	534	27	(	(	-LRB-
10_1101-2021_01_08_425885	534	28	r	r	NNP
10_1101-2021_01_08_425885	534	29	=	=	SYM
10_1101-2021_01_08_425885	534	30	0.54	0.54	CD
10_1101-2021_01_08_425885	534	31	,	,	,
10_1101-2021_01_08_425885	534	32	0.90	0.90	CD
10_1101-2021_01_08_425885	534	33	and	and	CC
10_1101-2021_01_08_425885	534	34	1.22	1.22	CD
10_1101-2021_01_08_425885	534	35	respectively	respectively	RB
10_1101-2021_01_08_425885	534	36	)	)	-RRB-
10_1101-2021_01_08_425885	534	37	and	and	CC
10_1101-2021_01_08_425885	534	38	again	again	RB
10_1101-2021_01_08_425885	534	39	saw	see	VBD
10_1101-2021_01_08_425885	534	40	no	no	DT
10_1101-2021_01_08_425885	534	41	deviation	deviation	NN
10_1101-2021_01_08_425885	534	42	from	from	IN
10_1101-2021_01_08_425885	534	43	zero	zero	CD
10_1101-2021_01_08_425885	534	44	scalar	scalar	JJ
10_1101-2021_01_08_425885	534	45	curvature	curvature	NN
10_1101-2021_01_08_425885	534	46	for	for	IN
10_1101-2021_01_08_425885	534	47	points	point	NNS
10_1101-2021_01_08_425885	534	48	in	in	IN
10_1101-2021_01_08_425885	534	49	either	either	CC
10_1101-2021_01_08_425885	534	50	the	the	DT
10_1101-2021_01_08_425885	534	51	sparse	sparse	JJ
10_1101-2021_01_08_425885	534	52	or	or	CC
10_1101-2021_01_08_425885	534	53	dense	dense	JJ
10_1101-2021_01_08_425885	534	54	region	region	NN
10_1101-2021_01_08_425885	534	55	(	(	-LRB-
10_1101-2021_01_08_425885	534	56	see	see	VB
10_1101-2021_01_08_425885	534	57	Figure	Figure	NNP
10_1101-2021_01_08_425885	534	58	S2A	s2a	NN
10_1101-2021_01_08_425885	534	59	)	)	-RRB-
10_1101-2021_01_08_425885	534	60	.	.	.
10_1101-2021_01_08_425885	535	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	535	2	repeated	repeat	VBD
10_1101-2021_01_08_425885	535	3	this	this	DT
10_1101-2021_01_08_425885	535	4	analysis	analysis	NN
10_1101-2021_01_08_425885	535	5	for	for	IN
10_1101-2021_01_08_425885	535	6	N2	N2	NNP
10_1101-2021_01_08_425885	535	7	=	=	SYM
10_1101-2021_01_08_425885	535	8	10	10	CD
10_1101-2021_01_08_425885	535	9	4	4	CD
10_1101-2021_01_08_425885	535	10	and	and	CC
10_1101-2021_01_08_425885	535	11	again	again	RB
10_1101-2021_01_08_425885	535	12	saw	see	VBD
10_1101-2021_01_08_425885	535	13	no	no	DT
10_1101-2021_01_08_425885	535	14	deviation	deviation	NN
10_1101-2021_01_08_425885	535	15	from	from	IN
10_1101-2021_01_08_425885	535	16	zero	zero	CD
10_1101-2021_01_08_425885	535	17	scalar	scalar	JJ
10_1101-2021_01_08_425885	535	18	curvature	curvature	NN
10_1101-2021_01_08_425885	535	19	,	,	,
10_1101-2021_01_08_425885	535	20	regardless	regardless	RB
10_1101-2021_01_08_425885	535	21	of	of	IN
10_1101-2021_01_08_425885	535	22	whether	whether	IN
10_1101-2021_01_08_425885	535	23	variable	variable	JJ
10_1101-2021_01_08_425885	535	24	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	535	25	sizes	size	NNS
10_1101-2021_01_08_425885	535	26	or	or	CC
10_1101-2021_01_08_425885	535	27	fixed	fix	VBN
10_1101-2021_01_08_425885	535	28	length	length	NN
10_1101-2021_01_08_425885	535	29	scales	scale	NNS
10_1101-2021_01_08_425885	535	30	(	(	-LRB-
10_1101-2021_01_08_425885	535	31	r	r	NN
10_1101-2021_01_08_425885	535	32	=	=	SYM
10_1101-2021_01_08_425885	535	33	0.37	0.37	CD
10_1101-2021_01_08_425885	535	34	,	,	,
10_1101-2021_01_08_425885	535	35	0.63	0.63	CD
10_1101-2021_01_08_425885	535	36	and	and	CC
10_1101-2021_01_08_425885	535	37	1.42	1.42	CD
10_1101-2021_01_08_425885	535	38	corresponding	correspond	VBG
10_1101-2021_01_08_425885	535	39	to	to	IN
10_1101-2021_01_08_425885	535	40	the	the	DT
10_1101-2021_01_08_425885	535	41	same	same	JJ
10_1101-2021_01_08_425885	535	42	percentiles	percentile	NNS
10_1101-2021_01_08_425885	535	43	)	)	-RRB-
10_1101-2021_01_08_425885	535	44	were	be	VBD
10_1101-2021_01_08_425885	535	45	used	use	VBN
10_1101-2021_01_08_425885	535	46	(	(	-LRB-
10_1101-2021_01_08_425885	535	47	see	see	VB
10_1101-2021_01_08_425885	535	48	Figure	Figure	NNP
10_1101-2021_01_08_425885	535	49	S2A	s2a	NN
10_1101-2021_01_08_425885	535	50	)	)	-RRB-
10_1101-2021_01_08_425885	535	51	.	.	.
10_1101-2021_01_08_425885	536	1	4.4.2.2	4.4.2.2	CD
10_1101-2021_01_08_425885	536	2	Observational	Observational	NNP
10_1101-2021_01_08_425885	536	3	Noise	Noise	NNP
10_1101-2021_01_08_425885	536	4	Every	every	DT
10_1101-2021_01_08_425885	536	5	ambient	ambient	JJ
10_1101-2021_01_08_425885	536	6	coordinate	coordinate	NN
10_1101-2021_01_08_425885	536	7	can	can	MD
10_1101-2021_01_08_425885	536	8	be	be	VB
10_1101-2021_01_08_425885	536	9	considered	consider	VBN
10_1101-2021_01_08_425885	536	10	a	a	DT
10_1101-2021_01_08_425885	536	11	measured	measure	VBN
10_1101-2021_01_08_425885	536	12	observable	observable	JJ
10_1101-2021_01_08_425885	536	13	with	with	IN
10_1101-2021_01_08_425885	536	14	its	-PRON-	PRP$
10_1101-2021_01_08_425885	536	15	own	own	JJ
10_1101-2021_01_08_425885	536	16	observational	observational	JJ
10_1101-2021_01_08_425885	536	17	noise	noise	NN
10_1101-2021_01_08_425885	536	18	.	.	.
10_1101-2021_01_08_425885	537	1	Assuming	assume	VBG
10_1101-2021_01_08_425885	537	2	each	each	DT
10_1101-2021_01_08_425885	537	3	observable	observable	JJ
10_1101-2021_01_08_425885	537	4	is	be	VBZ
10_1101-2021_01_08_425885	537	5	distorted	distort	VBN
10_1101-2021_01_08_425885	537	6	by	by	IN
10_1101-2021_01_08_425885	537	7	independent	independent	JJ
10_1101-2021_01_08_425885	537	8	,	,	,
10_1101-2021_01_08_425885	537	9	isotropic	isotropic	JJ
10_1101-2021_01_08_425885	537	10	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	537	11	noise	noise	NN
10_1101-2021_01_08_425885	537	12	with	with	IN
10_1101-2021_01_08_425885	537	13	variance	variance	NN
10_1101-2021_01_08_425885	537	14	σ2	σ2	NNP
10_1101-2021_01_08_425885	537	15	(	(	-LRB-
10_1101-2021_01_08_425885	537	16	sometimes	sometimes	RB
10_1101-2021_01_08_425885	537	17	referred	refer	VBN
10_1101-2021_01_08_425885	537	18	to	to	IN
10_1101-2021_01_08_425885	537	19	as	as	IN
10_1101-2021_01_08_425885	537	20	convolutional	convolutional	JJ
10_1101-2021_01_08_425885	537	21	noise	noise	NN
10_1101-2021_01_08_425885	537	22	[	[	-LRB-
10_1101-2021_01_08_425885	537	23	37	37	CD
10_1101-2021_01_08_425885	537	24	]	]	-RRB-
10_1101-2021_01_08_425885	537	25	)	)	-RRB-
10_1101-2021_01_08_425885	537	26	,	,	,
10_1101-2021_01_08_425885	537	27	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	537	28	X	x	NN
10_1101-2021_01_08_425885	537	29	∈	∈	NNP
10_1101-2021_01_08_425885	537	30	Rn	Rn	NNS
10_1101-2021_01_08_425885	537	31	sampled	sample	VBN
10_1101-2021_01_08_425885	537	32	from	from	IN
10_1101-2021_01_08_425885	537	33	an	an	DT
10_1101-2021_01_08_425885	537	34	embedded	embed	VBN
10_1101-2021_01_08_425885	537	35	manifold	manifold	NN
10_1101-2021_01_08_425885	537	36	M	M	NNP
10_1101-2021_01_08_425885	537	37	are	be	VBP
10_1101-2021_01_08_425885	537	38	modelled	model	VBN
10_1101-2021_01_08_425885	537	39	by	by	IN
10_1101-2021_01_08_425885	537	40	:	:	:
10_1101-2021_01_08_425885	537	41	X	X	NNS
10_1101-2021_01_08_425885	537	42	=	=	SYM
10_1101-2021_01_08_425885	537	43	x	x	SYM
10_1101-2021_01_08_425885	537	44	+	+	SYM
10_1101-2021_01_08_425885	537	45	N(0,σI	n(0,σi	NN
10_1101-2021_01_08_425885	537	46	)	)	-RRB-
10_1101-2021_01_08_425885	537	47	,	,	,
10_1101-2021_01_08_425885	537	48	x	x	LS
10_1101-2021_01_08_425885	537	49	∈	∈	NNP
10_1101-2021_01_08_425885	537	50	M	M	NNP
10_1101-2021_01_08_425885	537	51	(	(	-LRB-
10_1101-2021_01_08_425885	537	52	28	28	CD
10_1101-2021_01_08_425885	537	53	)	)	-RRB-
10_1101-2021_01_08_425885	537	54	To	to	TO
10_1101-2021_01_08_425885	537	55	study	study	VB
10_1101-2021_01_08_425885	537	56	the	the	DT
10_1101-2021_01_08_425885	537	57	sensitivity	sensitivity	NN
10_1101-2021_01_08_425885	537	58	of	of	IN
10_1101-2021_01_08_425885	537	59	our	-PRON-	PRP$
10_1101-2021_01_08_425885	537	60	algorithm	algorithm	NN
10_1101-2021_01_08_425885	537	61	to	to	TO
10_1101-2021_01_08_425885	537	62	noise	noise	VB
10_1101-2021_01_08_425885	537	63	,	,	,
10_1101-2021_01_08_425885	537	64	we	-PRON-	PRP
10_1101-2021_01_08_425885	537	65	uniformly	uniformly	RB
10_1101-2021_01_08_425885	537	66	sampled	sample	VBD
10_1101-2021_01_08_425885	537	67	N	n	NN
10_1101-2021_01_08_425885	537	68	=	=	SYM
10_1101-2021_01_08_425885	537	69	104	104	CD
10_1101-2021_01_08_425885	537	70	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	537	71	from	from	IN
10_1101-2021_01_08_425885	537	72	S2	S2	NNP
10_1101-2021_01_08_425885	537	73	∈	∈	NNP
10_1101-2021_01_08_425885	537	74	R3	R3	NNP
10_1101-2021_01_08_425885	537	75	,	,	,
10_1101-2021_01_08_425885	537	76	added	add	VBD
10_1101-2021_01_08_425885	537	77	convolutional	convolutional	JJ
10_1101-2021_01_08_425885	537	78	noise	noise	NN
10_1101-2021_01_08_425885	537	79	with	with	IN
10_1101-2021_01_08_425885	537	80	σ	σ	NNP
10_1101-2021_01_08_425885	537	81	ranging	range	VBG
10_1101-2021_01_08_425885	537	82	over	over	IN
10_1101-2021_01_08_425885	537	83	several	several	JJ
10_1101-2021_01_08_425885	537	84	orders	order	NNS
10_1101-2021_01_08_425885	537	85	of	of	IN
10_1101-2021_01_08_425885	537	86	magnitude	magnitude	NN
10_1101-2021_01_08_425885	537	87	,	,	,
10_1101-2021_01_08_425885	537	88	and	and	CC
10_1101-2021_01_08_425885	537	89	estimated	estimate	VBN
10_1101-2021_01_08_425885	537	90	scalar	scalar	JJ
10_1101-2021_01_08_425885	537	91	curvatures	curvature	NNS
10_1101-2021_01_08_425885	537	92	using	use	VBG
10_1101-2021_01_08_425885	537	93	a	a	DT
10_1101-2021_01_08_425885	537	94	fixed	fix	VBN
10_1101-2021_01_08_425885	537	95	σh	σh	NN
10_1101-2021_01_08_425885	537	96	(	(	-LRB-
10_1101-2021_01_08_425885	537	97	see	see	VB
10_1101-2021_01_08_425885	537	98	Methods	Methods	NNP
10_1101-2021_01_08_425885	537	99	Section	Section	NNP
10_1101-2021_01_08_425885	537	100	4.4.3	4.4.3	CD
10_1101-2021_01_08_425885	537	101	)	)	-RRB-
10_1101-2021_01_08_425885	537	102	.	.	.
10_1101-2021_01_08_425885	538	1	For	for	IN
10_1101-2021_01_08_425885	538	2	small	small	JJ
10_1101-2021_01_08_425885	538	3	σ	σ	NNS
10_1101-2021_01_08_425885	538	4	,	,	,
10_1101-2021_01_08_425885	538	5	the	the	DT
10_1101-2021_01_08_425885	538	6	distribution	distribution	NN
10_1101-2021_01_08_425885	538	7	of	of	IN
10_1101-2021_01_08_425885	538	8	scalar	scalar	JJ
10_1101-2021_01_08_425885	538	9	curvatures	curvature	NNS
10_1101-2021_01_08_425885	538	10	was	be	VBD
10_1101-2021_01_08_425885	538	11	centred	centre	VBN
10_1101-2021_01_08_425885	538	12	31	31	CD
10_1101-2021_01_08_425885	538	13	.CC	.CC	:
10_1101-2021_01_08_425885	538	14	-	-	HYPH
10_1101-2021_01_08_425885	538	15	BY	by	IN
10_1101-2021_01_08_425885	538	16	-	-	HYPH
10_1101-2021_01_08_425885	538	17	NC	NC	NNP
10_1101-2021_01_08_425885	538	18	-	-	HYPH
10_1101-2021_01_08_425885	538	19	ND	ND	NNP
10_1101-2021_01_08_425885	538	20	4.0	4.0	CD
10_1101-2021_01_08_425885	538	21	International	International	NNP
10_1101-2021_01_08_425885	538	22	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	538	23	under	under	IN
10_1101-2021_01_08_425885	538	24	a	a	DT
10_1101-2021_01_08_425885	538	25	(	(	-LRB-
10_1101-2021_01_08_425885	538	26	which	which	WDT
10_1101-2021_01_08_425885	538	27	was	be	VBD
10_1101-2021_01_08_425885	538	28	not	not	RB
10_1101-2021_01_08_425885	538	29	certified	certify	VBN
10_1101-2021_01_08_425885	538	30	by	by	IN
10_1101-2021_01_08_425885	538	31	peer	peer	NN
10_1101-2021_01_08_425885	538	32	review	review	NN
10_1101-2021_01_08_425885	538	33	)	)	-RRB-
10_1101-2021_01_08_425885	538	34	is	be	VBZ
10_1101-2021_01_08_425885	538	35	the	the	DT
10_1101-2021_01_08_425885	538	36	author	author	NN
10_1101-2021_01_08_425885	538	37	/	/	SYM
10_1101-2021_01_08_425885	538	38	funder	funder	NN
10_1101-2021_01_08_425885	538	39	,	,	,
10_1101-2021_01_08_425885	538	40	who	who	WP
10_1101-2021_01_08_425885	538	41	has	have	VBZ
10_1101-2021_01_08_425885	538	42	granted	grant	VBN
10_1101-2021_01_08_425885	538	43	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	538	44	a	a	DT
10_1101-2021_01_08_425885	538	45	license	license	NN
10_1101-2021_01_08_425885	538	46	to	to	TO
10_1101-2021_01_08_425885	538	47	display	display	VB
10_1101-2021_01_08_425885	538	48	the	the	DT
10_1101-2021_01_08_425885	538	49	preprint	preprint	NN
10_1101-2021_01_08_425885	538	50	in	in	IN
10_1101-2021_01_08_425885	538	51	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	538	52	.	.	.
10_1101-2021_01_08_425885	539	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	539	2	is	be	VBZ
10_1101-2021_01_08_425885	539	3	made	make	VBN
10_1101-2021_01_08_425885	539	4	The	the	DT
10_1101-2021_01_08_425885	539	5	copyright	copyright	NN
10_1101-2021_01_08_425885	539	6	holder	holder	NN
10_1101-2021_01_08_425885	539	7	for	for	IN
10_1101-2021_01_08_425885	539	8	this	this	DT
10_1101-2021_01_08_425885	539	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	539	10	version	version	NN
10_1101-2021_01_08_425885	539	11	posted	post	VBD
10_1101-2021_01_08_425885	539	12	January	January	NNP
10_1101-2021_01_08_425885	539	13	8	8	CD
10_1101-2021_01_08_425885	539	14	,	,	,
10_1101-2021_01_08_425885	539	15	2021	2021	CD
10_1101-2021_01_08_425885	539	16	.	.	.
10_1101-2021_01_08_425885	539	17	;	;	:
10_1101-2021_01_08_425885	539	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	539	19	:	:	:
10_1101-2021_01_08_425885	539	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	539	21	preprint	preprint	NN
10_1101-2021_01_08_425885	539	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	539	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	RB
10_1101-2021_01_08_425885	539	24	on	on	IN
10_1101-2021_01_08_425885	539	25	the	the	DT
10_1101-2021_01_08_425885	539	26	true	true	JJ
10_1101-2021_01_08_425885	539	27	value	value	NN
10_1101-2021_01_08_425885	539	28	of	of	IN
10_1101-2021_01_08_425885	539	29	2	2	CD
10_1101-2021_01_08_425885	539	30	,	,	,
10_1101-2021_01_08_425885	539	31	but	but	CC
10_1101-2021_01_08_425885	539	32	once	once	RB
10_1101-2021_01_08_425885	539	33	σ	σ	NNP
10_1101-2021_01_08_425885	539	34	became	become	VBD
10_1101-2021_01_08_425885	539	35	large	large	JJ
10_1101-2021_01_08_425885	539	36	(	(	-LRB-
10_1101-2021_01_08_425885	539	37	≈	≈	NNP
10_1101-2021_01_08_425885	539	38	10	10	CD
10_1101-2021_01_08_425885	539	39	%	%	NN
10_1101-2021_01_08_425885	539	40	of	of	IN
10_1101-2021_01_08_425885	539	41	S2	s2	NN
10_1101-2021_01_08_425885	539	42	’s	’s	NNP
10_1101-2021_01_08_425885	539	43	radius	radius	NN
10_1101-2021_01_08_425885	539	44	)	)	-RRB-
10_1101-2021_01_08_425885	539	45	,	,	,
10_1101-2021_01_08_425885	539	46	the	the	DT
10_1101-2021_01_08_425885	539	47	estimated	estimate	VBN
10_1101-2021_01_08_425885	539	48	scalar	scalar	JJ
10_1101-2021_01_08_425885	539	49	curvatures	curvature	NNS
10_1101-2021_01_08_425885	539	50	approached	approach	VBD
10_1101-2021_01_08_425885	539	51	0	0	NFP
10_1101-2021_01_08_425885	539	52	(	(	-LRB-
10_1101-2021_01_08_425885	539	53	see	see	VB
10_1101-2021_01_08_425885	539	54	Figure	Figure	NNP
10_1101-2021_01_08_425885	539	55	S2B	S2B	NNP
10_1101-2021_01_08_425885	539	56	)	)	-RRB-
10_1101-2021_01_08_425885	539	57	.	.	.
10_1101-2021_01_08_425885	540	1	Noise	noise	NN
10_1101-2021_01_08_425885	540	2	in	in	IN
10_1101-2021_01_08_425885	540	3	the	the	DT
10_1101-2021_01_08_425885	540	4	regression	regression	NN
10_1101-2021_01_08_425885	540	5	context	context	NN
10_1101-2021_01_08_425885	540	6	does	do	VBZ
10_1101-2021_01_08_425885	540	7	not	not	RB
10_1101-2021_01_08_425885	540	8	change	change	VB
10_1101-2021_01_08_425885	540	9	the	the	DT
10_1101-2021_01_08_425885	540	10	expectation	expectation	NN
10_1101-2021_01_08_425885	540	11	value	value	NN
10_1101-2021_01_08_425885	540	12	of	of	IN
10_1101-2021_01_08_425885	540	13	any	any	DT
10_1101-2021_01_08_425885	540	14	estimated	estimate	VBN
10_1101-2021_01_08_425885	540	15	parameter	parameter	NN
10_1101-2021_01_08_425885	540	16	.	.	.
10_1101-2021_01_08_425885	541	1	The	the	DT
10_1101-2021_01_08_425885	541	2	apparent	apparent	JJ
10_1101-2021_01_08_425885	541	3	flattening	flattening	NN
10_1101-2021_01_08_425885	541	4	that	that	WDT
10_1101-2021_01_08_425885	541	5	is	be	VBZ
10_1101-2021_01_08_425885	541	6	observed	observe	VBN
10_1101-2021_01_08_425885	541	7	therefore	therefore	RB
10_1101-2021_01_08_425885	541	8	indicates	indicate	VBZ
10_1101-2021_01_08_425885	541	9	that	that	IN
10_1101-2021_01_08_425885	541	10	X	X	NNP
10_1101-2021_01_08_425885	541	11	(	(	-LRB-
10_1101-2021_01_08_425885	541	12	obtained	obtain	VBN
10_1101-2021_01_08_425885	541	13	from	from	IN
10_1101-2021_01_08_425885	541	14	convoluting	convolute	VBG
10_1101-2021_01_08_425885	541	15	M	M	NNP
10_1101-2021_01_08_425885	541	16	)	)	-RRB-
10_1101-2021_01_08_425885	541	17	,	,	,
10_1101-2021_01_08_425885	541	18	has	have	VBZ
10_1101-2021_01_08_425885	541	19	a	a	DT
10_1101-2021_01_08_425885	541	20	geometry	geometry	NN
10_1101-2021_01_08_425885	541	21	that	that	WDT
10_1101-2021_01_08_425885	541	22	is	be	VBZ
10_1101-2021_01_08_425885	541	23	not	not	RB
10_1101-2021_01_08_425885	541	24	trivially	trivially	RB
10_1101-2021_01_08_425885	541	25	related	related	JJ
10_1101-2021_01_08_425885	541	26	to	to	IN
10_1101-2021_01_08_425885	541	27	M.	M.	NNP
10_1101-2021_01_08_425885	541	28	Certainly	Certainly	NNP
10_1101-2021_01_08_425885	541	29	for	for	IN
10_1101-2021_01_08_425885	541	30	σ	σ	NNP
10_1101-2021_01_08_425885	541	31	≈	≈	NNP
10_1101-2021_01_08_425885	541	32	1	1	CD
10_1101-2021_01_08_425885	541	33	,	,	,
10_1101-2021_01_08_425885	541	34	X	X	NNP
10_1101-2021_01_08_425885	541	35	does	do	VBZ
10_1101-2021_01_08_425885	541	36	not	not	RB
10_1101-2021_01_08_425885	541	37	even	even	RB
10_1101-2021_01_08_425885	541	38	preserve	preserve	VB
10_1101-2021_01_08_425885	541	39	the	the	DT
10_1101-2021_01_08_425885	541	40	topology	topology	NN
10_1101-2021_01_08_425885	541	41	of	of	IN
10_1101-2021_01_08_425885	541	42	M	M	NNP
10_1101-2021_01_08_425885	541	43	as	as	IN
10_1101-2021_01_08_425885	541	44	S2	S2	NNP
10_1101-2021_01_08_425885	541	45	.	.	.
10_1101-2021_01_08_425885	542	1	From	from	IN
10_1101-2021_01_08_425885	542	2	a	a	DT
10_1101-2021_01_08_425885	542	3	practical	practical	JJ
10_1101-2021_01_08_425885	542	4	perspective	perspective	NN
10_1101-2021_01_08_425885	542	5	,	,	,
10_1101-2021_01_08_425885	542	6	it	-PRON-	PRP
10_1101-2021_01_08_425885	542	7	suffices	suffice	VBZ
10_1101-2021_01_08_425885	542	8	to	to	TO
10_1101-2021_01_08_425885	542	9	say	say	VB
10_1101-2021_01_08_425885	542	10	that	that	IN
10_1101-2021_01_08_425885	542	11	small	small	JJ
10_1101-2021_01_08_425885	542	12	convolutional	convolutional	JJ
10_1101-2021_01_08_425885	542	13	noise	noise	NN
10_1101-2021_01_08_425885	542	14	can	can	MD
10_1101-2021_01_08_425885	542	15	be	be	VB
10_1101-2021_01_08_425885	542	16	handled	handle	VBN
10_1101-2021_01_08_425885	542	17	by	by	IN
10_1101-2021_01_08_425885	542	18	simple	simple	JJ
10_1101-2021_01_08_425885	542	19	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	542	20	regression	regression	NN
10_1101-2021_01_08_425885	542	21	,	,	,
10_1101-2021_01_08_425885	542	22	while	while	IN
10_1101-2021_01_08_425885	542	23	large	large	JJ
10_1101-2021_01_08_425885	542	24	convolutional	convolutional	JJ
10_1101-2021_01_08_425885	542	25	noise	noise	NN
10_1101-2021_01_08_425885	542	26	obfuscates	obfuscate	VBZ
10_1101-2021_01_08_425885	542	27	the	the	DT
10_1101-2021_01_08_425885	542	28	original	original	JJ
10_1101-2021_01_08_425885	542	29	manifold	manifold	NN
10_1101-2021_01_08_425885	542	30	.	.	.
10_1101-2021_01_08_425885	543	1	These	these	DT
10_1101-2021_01_08_425885	543	2	observations	observation	NNS
10_1101-2021_01_08_425885	543	3	are	be	VBP
10_1101-2021_01_08_425885	543	4	consistent	consistent	JJ
10_1101-2021_01_08_425885	543	5	with	with	IN
10_1101-2021_01_08_425885	543	6	literature	literature	NN
10_1101-2021_01_08_425885	543	7	defining	define	VBG
10_1101-2021_01_08_425885	543	8	a	a	DT
10_1101-2021_01_08_425885	543	9	manifold	manifold	NN
10_1101-2021_01_08_425885	543	10	’s	’s	POS
10_1101-2021_01_08_425885	543	11	reach	reach	VB
10_1101-2021_01_08_425885	543	12	[	[	-LRB-
10_1101-2021_01_08_425885	543	13	34	34	CD
10_1101-2021_01_08_425885	543	14	,	,	,
10_1101-2021_01_08_425885	543	15	35	35	CD
10_1101-2021_01_08_425885	543	16	]	]	-RRB-
10_1101-2021_01_08_425885	543	17	,	,	,
10_1101-2021_01_08_425885	543	18	a	a	DT
10_1101-2021_01_08_425885	543	19	noise	noise	NN
10_1101-2021_01_08_425885	543	20	scale	scale	NN
10_1101-2021_01_08_425885	543	21	beyond	beyond	IN
10_1101-2021_01_08_425885	543	22	which	which	WDT
10_1101-2021_01_08_425885	543	23	noisy	noisy	JJ
10_1101-2021_01_08_425885	543	24	samples	sample	NNS
10_1101-2021_01_08_425885	543	25	can	can	MD
10_1101-2021_01_08_425885	543	26	not	not	RB
10_1101-2021_01_08_425885	543	27	be	be	VB
10_1101-2021_01_08_425885	543	28	uniquely	uniquely	RB
10_1101-2021_01_08_425885	543	29	associated	associate	VBN
10_1101-2021_01_08_425885	543	30	to	to	IN
10_1101-2021_01_08_425885	543	31	a	a	DT
10_1101-2021_01_08_425885	543	32	point	point	NN
10_1101-2021_01_08_425885	543	33	on	on	IN
10_1101-2021_01_08_425885	543	34	the	the	DT
10_1101-2021_01_08_425885	543	35	noise	noise	NN
10_1101-2021_01_08_425885	543	36	-	-	HYPH
10_1101-2021_01_08_425885	543	37	free	free	JJ
10_1101-2021_01_08_425885	543	38	manifold	manifold	NN
10_1101-2021_01_08_425885	543	39	.	.	.
10_1101-2021_01_08_425885	544	1	When	when	WRB
10_1101-2021_01_08_425885	544	2	σ	σ	PRP
10_1101-2021_01_08_425885	544	3	exceeds	exceed	VBZ
10_1101-2021_01_08_425885	544	4	the	the	DT
10_1101-2021_01_08_425885	544	5	manifold	manifold	NN
10_1101-2021_01_08_425885	544	6	’s	’s	POS
10_1101-2021_01_08_425885	544	7	reach	reach	VB
10_1101-2021_01_08_425885	544	8	,	,	,
10_1101-2021_01_08_425885	544	9	the	the	DT
10_1101-2021_01_08_425885	544	10	relationship	relationship	NN
10_1101-2021_01_08_425885	544	11	between	between	IN
10_1101-2021_01_08_425885	544	12	the	the	DT
10_1101-2021_01_08_425885	544	13	empirical	empirical	JJ
10_1101-2021_01_08_425885	544	14	density	density	NN
10_1101-2021_01_08_425885	544	15	of	of	IN
10_1101-2021_01_08_425885	544	16	sampled	sample	VBN
10_1101-2021_01_08_425885	544	17	points	point	NNS
10_1101-2021_01_08_425885	544	18	and	and	CC
10_1101-2021_01_08_425885	544	19	the	the	DT
10_1101-2021_01_08_425885	544	20	original	original	JJ
10_1101-2021_01_08_425885	544	21	manifold	manifold	NN
10_1101-2021_01_08_425885	544	22	is	be	VBZ
10_1101-2021_01_08_425885	544	23	non	non	JJ
10_1101-2021_01_08_425885	544	24	-	-	JJ
10_1101-2021_01_08_425885	544	25	trivial	trivial	JJ
10_1101-2021_01_08_425885	544	26	even	even	RB
10_1101-2021_01_08_425885	544	27	for	for	IN
10_1101-2021_01_08_425885	544	28	a	a	DT
10_1101-2021_01_08_425885	544	29	relatively	relatively	RB
10_1101-2021_01_08_425885	544	30	forgiving	forgiving	JJ
10_1101-2021_01_08_425885	544	31	model	model	NN
10_1101-2021_01_08_425885	544	32	of	of	IN
10_1101-2021_01_08_425885	544	33	manifold	manifold	JJ
10_1101-2021_01_08_425885	544	34	-	-	HYPH
10_1101-2021_01_08_425885	544	35	orthogonal	orthogonal	JJ
10_1101-2021_01_08_425885	544	36	noise	noise	NN
10_1101-2021_01_08_425885	544	37	.	.	.
10_1101-2021_01_08_425885	545	1	The	the	DT
10_1101-2021_01_08_425885	545	2	ridge	ridge	NN
10_1101-2021_01_08_425885	545	3	manifold	manifold	NN
10_1101-2021_01_08_425885	545	4	[	[	-LRB-
10_1101-2021_01_08_425885	545	5	36	36	CD
10_1101-2021_01_08_425885	545	6	,	,	,
10_1101-2021_01_08_425885	545	7	37	37	CD
10_1101-2021_01_08_425885	545	8	]	]	-RRB-
10_1101-2021_01_08_425885	545	9	of	of	IN
10_1101-2021_01_08_425885	545	10	an	an	DT
10_1101-2021_01_08_425885	545	11	empirical	empirical	JJ
10_1101-2021_01_08_425885	545	12	density	density	NN
10_1101-2021_01_08_425885	545	13	has	have	VBZ
10_1101-2021_01_08_425885	545	14	also	also	RB
10_1101-2021_01_08_425885	545	15	been	be	VBN
10_1101-2021_01_08_425885	545	16	defined	define	VBN
10_1101-2021_01_08_425885	545	17	as	as	IN
10_1101-2021_01_08_425885	545	18	an	an	DT
10_1101-2021_01_08_425885	545	19	alternative	alternative	NN
10_1101-2021_01_08_425885	545	20	to	to	IN
10_1101-2021_01_08_425885	545	21	the	the	DT
10_1101-2021_01_08_425885	545	22	unwieldy	unwieldy	JJ
10_1101-2021_01_08_425885	545	23	task	task	NN
10_1101-2021_01_08_425885	545	24	of	of	IN
10_1101-2021_01_08_425885	545	25	deconvoluting	deconvolute	VBG
10_1101-2021_01_08_425885	545	26	noisy	noisy	JJ
10_1101-2021_01_08_425885	545	27	samples	sample	NNS
10_1101-2021_01_08_425885	545	28	to	to	TO
10_1101-2021_01_08_425885	545	29	recover	recover	VB
10_1101-2021_01_08_425885	545	30	a	a	DT
10_1101-2021_01_08_425885	545	31	noise	noise	NN
10_1101-2021_01_08_425885	545	32	-	-	HYPH
10_1101-2021_01_08_425885	545	33	free	free	JJ
10_1101-2021_01_08_425885	545	34	manifold	manifold	NN
10_1101-2021_01_08_425885	545	35	.	.	.
10_1101-2021_01_08_425885	546	1	This	this	DT
10_1101-2021_01_08_425885	546	2	definition	definition	NN
10_1101-2021_01_08_425885	546	3	avoids	avoid	VBZ
10_1101-2021_01_08_425885	546	4	the	the	DT
10_1101-2021_01_08_425885	546	5	notion	notion	NN
10_1101-2021_01_08_425885	546	6	of	of	IN
10_1101-2021_01_08_425885	546	7	a	a	DT
10_1101-2021_01_08_425885	546	8	noise	noise	NN
10_1101-2021_01_08_425885	546	9	-	-	HYPH
10_1101-2021_01_08_425885	546	10	free	free	JJ
10_1101-2021_01_08_425885	546	11	manifold	manifold	NN
10_1101-2021_01_08_425885	546	12	altogether	altogether	RB
10_1101-2021_01_08_425885	546	13	and	and	CC
10_1101-2021_01_08_425885	546	14	instead	instead	RB
10_1101-2021_01_08_425885	546	15	defines	define	VBZ
10_1101-2021_01_08_425885	546	16	manifolds	manifold	NNS
10_1101-2021_01_08_425885	546	17	as	as	IN
10_1101-2021_01_08_425885	546	18	ridges	ridge	NNS
10_1101-2021_01_08_425885	546	19	,	,	,
10_1101-2021_01_08_425885	546	20	contours	contour	NNS
10_1101-2021_01_08_425885	546	21	along	along	IN
10_1101-2021_01_08_425885	546	22	which	which	WDT
10_1101-2021_01_08_425885	546	23	the	the	DT
10_1101-2021_01_08_425885	546	24	empirical	empirical	JJ
10_1101-2021_01_08_425885	546	25	density	density	NN
10_1101-2021_01_08_425885	546	26	of	of	IN
10_1101-2021_01_08_425885	546	27	points	point	NNS
10_1101-2021_01_08_425885	546	28	is	be	VBZ
10_1101-2021_01_08_425885	546	29	maximized	maximize	VBN
10_1101-2021_01_08_425885	546	30	.	.	.
10_1101-2021_01_08_425885	547	1	4.4.2.3	4.4.2.3	CD
10_1101-2021_01_08_425885	547	2	Large	Large	NNP
10_1101-2021_01_08_425885	547	3	Ambient	Ambient	NNP
10_1101-2021_01_08_425885	547	4	Dimension	dimension	NN
10_1101-2021_01_08_425885	547	5	A	a	DT
10_1101-2021_01_08_425885	547	6	high	high	JJ
10_1101-2021_01_08_425885	547	7	-	-	HYPH
10_1101-2021_01_08_425885	547	8	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	547	9	dataset	dataset	NN
10_1101-2021_01_08_425885	547	10	may	may	MD
10_1101-2021_01_08_425885	547	11	have	have	VB
10_1101-2021_01_08_425885	547	12	an	an	DT
10_1101-2021_01_08_425885	547	13	ambient	ambient	JJ
10_1101-2021_01_08_425885	547	14	space	space	NN
10_1101-2021_01_08_425885	547	15	comprised	comprise	VBN
10_1101-2021_01_08_425885	547	16	of	of	IN
10_1101-2021_01_08_425885	547	17	tens	ten	NNS
10_1101-2021_01_08_425885	547	18	of	of	IN
10_1101-2021_01_08_425885	547	19	thousands	thousand	NNS
10_1101-2021_01_08_425885	547	20	of	of	IN
10_1101-2021_01_08_425885	547	21	observables	observable	NNS
10_1101-2021_01_08_425885	547	22	,	,	,
10_1101-2021_01_08_425885	547	23	i.e.	i.e.	FW
10_1101-2021_01_08_425885	548	1	n	n	CC
10_1101-2021_01_08_425885	548	2	is	be	VBZ
10_1101-2021_01_08_425885	548	3	very	very	RB
10_1101-2021_01_08_425885	548	4	large	large	JJ
10_1101-2021_01_08_425885	548	5	.	.	.
10_1101-2021_01_08_425885	549	1	Meanwhile	meanwhile	RB
10_1101-2021_01_08_425885	549	2	,	,	,
10_1101-2021_01_08_425885	549	3	the	the	DT
10_1101-2021_01_08_425885	549	4	underlying	underlying	JJ
10_1101-2021_01_08_425885	549	5	manifold	manifold	JJ
10_1101-2021_01_08_425885	549	6	dimension	dimension	NN
10_1101-2021_01_08_425885	549	7	,	,	,
10_1101-2021_01_08_425885	549	8	d	d	NNP
10_1101-2021_01_08_425885	549	9	,	,	,
10_1101-2021_01_08_425885	549	10	may	may	MD
10_1101-2021_01_08_425885	549	11	be	be	VB
10_1101-2021_01_08_425885	549	12	small	small	JJ
10_1101-2021_01_08_425885	549	13	.	.	.
10_1101-2021_01_08_425885	550	1	Since	since	IN
10_1101-2021_01_08_425885	550	2	convolutional	convolutional	JJ
10_1101-2021_01_08_425885	550	3	noise	noise	NN
10_1101-2021_01_08_425885	550	4	occurs	occur	VBZ
10_1101-2021_01_08_425885	550	5	in	in	IN
10_1101-2021_01_08_425885	550	6	n	n	DT
10_1101-2021_01_08_425885	550	7	dimensions	dimension	NNS
10_1101-2021_01_08_425885	550	8	,	,	,
10_1101-2021_01_08_425885	550	9	will	will	MD
10_1101-2021_01_08_425885	550	10	a	a	DT
10_1101-2021_01_08_425885	550	11	low	low	JJ
10_1101-2021_01_08_425885	550	12	-	-	HYPH
10_1101-2021_01_08_425885	550	13	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	550	14	manifold	manifold	NN
10_1101-2021_01_08_425885	550	15	still	still	RB
10_1101-2021_01_08_425885	550	16	be	be	VB
10_1101-2021_01_08_425885	550	17	discernable	discernable	JJ
10_1101-2021_01_08_425885	550	18	?	?	.
10_1101-2021_01_08_425885	551	1	To	to	TO
10_1101-2021_01_08_425885	551	2	explore	explore	VB
10_1101-2021_01_08_425885	551	3	this	this	DT
10_1101-2021_01_08_425885	551	4	,	,	,
10_1101-2021_01_08_425885	551	5	we	-PRON-	PRP
10_1101-2021_01_08_425885	551	6	uniformly	uniformly	RB
10_1101-2021_01_08_425885	551	7	sampled	sample	VBD
10_1101-2021_01_08_425885	551	8	N	n	NN
10_1101-2021_01_08_425885	551	9	=	=	SYM
10_1101-2021_01_08_425885	551	10	104	104	CD
10_1101-2021_01_08_425885	551	11	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	551	12	from	from	IN
10_1101-2021_01_08_425885	551	13	S2	S2	NNP
10_1101-2021_01_08_425885	551	14	∈	∈	NNP
10_1101-2021_01_08_425885	551	15	R3	R3	NNP
10_1101-2021_01_08_425885	551	16	,	,	,
10_1101-2021_01_08_425885	551	17	embedded	embed	VBD
10_1101-2021_01_08_425885	551	18	these	these	DT
10_1101-2021_01_08_425885	551	19	points	point	NNS
10_1101-2021_01_08_425885	551	20	in	in	IN
10_1101-2021_01_08_425885	551	21	Rn	Rn	NNS
10_1101-2021_01_08_425885	551	22	for	for	IN
10_1101-2021_01_08_425885	551	23	a	a	DT
10_1101-2021_01_08_425885	551	24	range	range	NN
10_1101-2021_01_08_425885	551	25	of	of	IN
10_1101-2021_01_08_425885	551	26	n	n	NN
10_1101-2021_01_08_425885	551	27	up	up	IN
10_1101-2021_01_08_425885	551	28	to	to	TO
10_1101-2021_01_08_425885	551	29	100	100	CD
10_1101-2021_01_08_425885	551	30	,	,	,
10_1101-2021_01_08_425885	551	31	and	and	CC
10_1101-2021_01_08_425885	551	32	added	add	VBD
10_1101-2021_01_08_425885	551	33	convolutional	convolutional	JJ
10_1101-2021_01_08_425885	551	34	noise	noise	NN
10_1101-2021_01_08_425885	551	35	of	of	IN
10_1101-2021_01_08_425885	551	36	magnitude	magnitude	NNP
10_1101-2021_01_08_425885	551	37	σ	σ	NNP
10_1101-2021_01_08_425885	551	38	=	=	SYM
10_1101-2021_01_08_425885	551	39	0.01	0.01	CD
10_1101-2021_01_08_425885	551	40	,	,	,
10_1101-2021_01_08_425885	551	41	0.03	0.03	CD
10_1101-2021_01_08_425885	551	42	,	,	,
10_1101-2021_01_08_425885	551	43	and	and	CC
10_1101-2021_01_08_425885	551	44	0.05	0.05	CD
10_1101-2021_01_08_425885	551	45	in	in	IN
10_1101-2021_01_08_425885	551	46	the	the	DT
10_1101-2021_01_08_425885	551	47	n	n	JJ
10_1101-2021_01_08_425885	551	48	-	-	HYPH
10_1101-2021_01_08_425885	551	49	dimensional	dimensional	JJ
10_1101-2021_01_08_425885	551	50	ambient	ambient	JJ
10_1101-2021_01_08_425885	551	51	space	space	NN
10_1101-2021_01_08_425885	551	52	.	.	.
10_1101-2021_01_08_425885	552	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	552	2	computed	compute	VBD
10_1101-2021_01_08_425885	552	3	curvatures	curvature	NNS
10_1101-2021_01_08_425885	552	4	for	for	IN
10_1101-2021_01_08_425885	552	5	all	all	DT
10_1101-2021_01_08_425885	552	6	combinations	combination	NNS
10_1101-2021_01_08_425885	552	7	of	of	IN
10_1101-2021_01_08_425885	552	8	n	n	NN
10_1101-2021_01_08_425885	552	9	and	and	CC
10_1101-2021_01_08_425885	552	10	σ	σ	NNP
10_1101-2021_01_08_425885	552	11	using	use	VBG
10_1101-2021_01_08_425885	552	12	a	a	DT
10_1101-2021_01_08_425885	552	13	fixed	fix	VBN
10_1101-2021_01_08_425885	552	14	σh	σh	NN
10_1101-2021_01_08_425885	552	15	(	(	-LRB-
10_1101-2021_01_08_425885	552	16	see	see	VB
10_1101-2021_01_08_425885	552	17	Methods	Methods	NNP
10_1101-2021_01_08_425885	552	18	Section	Section	NNP
10_1101-2021_01_08_425885	552	19	4.4.3	4.4.3	CD
10_1101-2021_01_08_425885	552	20	)	)	-RRB-
10_1101-2021_01_08_425885	552	21	.	.	.
10_1101-2021_01_08_425885	553	1	As	as	IN
10_1101-2021_01_08_425885	553	2	n	n	NN
10_1101-2021_01_08_425885	553	3	or	or	CC
10_1101-2021_01_08_425885	553	4	σ	σ	NN
10_1101-2021_01_08_425885	553	5	increased	increase	VBD
10_1101-2021_01_08_425885	553	6	,	,	,
10_1101-2021_01_08_425885	553	7	the	the	DT
10_1101-2021_01_08_425885	553	8	algorithmically	algorithmically	RB
10_1101-2021_01_08_425885	553	9	chosen	choose	VBN
10_1101-2021_01_08_425885	553	10	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	553	11	sizes	size	NNS
10_1101-2021_01_08_425885	553	12	,	,	,
10_1101-2021_01_08_425885	553	13	r(p	r(p	NNP
10_1101-2021_01_08_425885	553	14	)	)	-RRB-
10_1101-2021_01_08_425885	553	15	,	,	,
10_1101-2021_01_08_425885	553	16	expanded	expand	VBD
10_1101-2021_01_08_425885	553	17	to	to	TO
10_1101-2021_01_08_425885	553	18	include	include	VB
10_1101-2021_01_08_425885	553	19	enough	enough	JJ
10_1101-2021_01_08_425885	553	20	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	553	21	to	to	TO
10_1101-2021_01_08_425885	553	22	maintain	maintain	VB
10_1101-2021_01_08_425885	553	23	the	the	DT
10_1101-2021_01_08_425885	553	24	desired	desire	VBN
10_1101-2021_01_08_425885	553	25	σh	σh	NN
10_1101-2021_01_08_425885	553	26	.	.	.
10_1101-2021_01_08_425885	554	1	The	the	DT
10_1101-2021_01_08_425885	554	2	distribution	distribution	NN
10_1101-2021_01_08_425885	554	3	of	of	IN
10_1101-2021_01_08_425885	554	4	estimated	estimate	VBN
10_1101-2021_01_08_425885	554	5	scalar	scalar	JJ
10_1101-2021_01_08_425885	554	6	curvatures	curvature	NNS
10_1101-2021_01_08_425885	554	7	(	(	-LRB-
10_1101-2021_01_08_425885	554	8	shown	show	VBN
10_1101-2021_01_08_425885	554	9	in	in	IN
10_1101-2021_01_08_425885	554	10	Figure	Figure	NNP
10_1101-2021_01_08_425885	554	11	S2C	s2c	NN
10_1101-2021_01_08_425885	554	12	)	)	-RRB-
10_1101-2021_01_08_425885	554	13	is	be	VBZ
10_1101-2021_01_08_425885	554	14	centred	centre	VBN
10_1101-2021_01_08_425885	554	15	on	on	IN
10_1101-2021_01_08_425885	554	16	the	the	DT
10_1101-2021_01_08_425885	554	17	true	true	JJ
10_1101-2021_01_08_425885	554	18	value	value	NN
10_1101-2021_01_08_425885	554	19	of	of	IN
10_1101-2021_01_08_425885	554	20	2	2	CD
10_1101-2021_01_08_425885	554	21	for	for	IN
10_1101-2021_01_08_425885	554	22	n	n	NN
10_1101-2021_01_08_425885	554	23	<	<	XX
10_1101-2021_01_08_425885	554	24	80	80	CD
10_1101-2021_01_08_425885	554	25	and	and	CC
10_1101-2021_01_08_425885	554	26	σ	σ	NNP
10_1101-2021_01_08_425885	554	27	≤	≤	NNP
10_1101-2021_01_08_425885	554	28	0.05	0.05	CD
10_1101-2021_01_08_425885	554	29	.	.	.
10_1101-2021_01_08_425885	555	1	However	however	RB
10_1101-2021_01_08_425885	555	2	,	,	,
10_1101-2021_01_08_425885	555	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	555	4	observed	observe	VBD
10_1101-2021_01_08_425885	555	5	that	that	IN
10_1101-2021_01_08_425885	555	6	r	r	NNP
10_1101-2021_01_08_425885	555	7	was	be	VBD
10_1101-2021_01_08_425885	555	8	far	far	RB
10_1101-2021_01_08_425885	555	9	less	less	RBR
10_1101-2021_01_08_425885	555	10	sensitive	sensitive	JJ
10_1101-2021_01_08_425885	555	11	to	to	IN
10_1101-2021_01_08_425885	555	12	changes	change	NNS
10_1101-2021_01_08_425885	555	13	in	in	IN
10_1101-2021_01_08_425885	555	14	n	n	NN
10_1101-2021_01_08_425885	555	15	than	than	IN
10_1101-2021_01_08_425885	555	16	changes	change	NNS
10_1101-2021_01_08_425885	555	17	in	in	IN
10_1101-2021_01_08_425885	555	18	σ	σ	NN
10_1101-2021_01_08_425885	555	19	.	.	.
10_1101-2021_01_08_425885	556	1	For	for	IN
10_1101-2021_01_08_425885	556	2	example	example	NN
10_1101-2021_01_08_425885	556	3	,	,	,
10_1101-2021_01_08_425885	556	4	exploding	explode	VBG
10_1101-2021_01_08_425885	556	5	n	n	CC
10_1101-2021_01_08_425885	556	6	from	from	IN
10_1101-2021_01_08_425885	556	7	3	3	CD
10_1101-2021_01_08_425885	556	8	to	to	IN
10_1101-2021_01_08_425885	556	9	100	100	CD
10_1101-2021_01_08_425885	556	10	at	at	IN
10_1101-2021_01_08_425885	556	11	σ	σ	NN
10_1101-2021_01_08_425885	556	12	=	=	SYM
10_1101-2021_01_08_425885	556	13	0.01	0.01	CD
10_1101-2021_01_08_425885	556	14	and	and	CC
10_1101-2021_01_08_425885	556	15	tripling	triple	VBG
10_1101-2021_01_08_425885	556	16	σ	σ	NNP
10_1101-2021_01_08_425885	556	17	from	from	IN
10_1101-2021_01_08_425885	556	18	0.01	0.01	CD
10_1101-2021_01_08_425885	556	19	to	to	IN
10_1101-2021_01_08_425885	556	20	0.03	0.03	CD
10_1101-2021_01_08_425885	556	21	at	at	IN
10_1101-2021_01_08_425885	556	22	n	n	NN
10_1101-2021_01_08_425885	556	23	=	=	SYM
10_1101-2021_01_08_425885	556	24	3	3	CD
10_1101-2021_01_08_425885	556	25	required	require	VBD
10_1101-2021_01_08_425885	556	26	a	a	DT
10_1101-2021_01_08_425885	556	27	comparable	comparable	JJ
10_1101-2021_01_08_425885	556	28	increase	increase	NN
10_1101-2021_01_08_425885	556	29	in	in	IN
10_1101-2021_01_08_425885	556	30	r	r	NN
10_1101-2021_01_08_425885	556	31	(	(	-LRB-
10_1101-2021_01_08_425885	556	32	see	see	VB
10_1101-2021_01_08_425885	556	33	Figure	Figure	NNP
10_1101-2021_01_08_425885	556	34	S2C	s2c	NN
10_1101-2021_01_08_425885	556	35	)	)	-RRB-
10_1101-2021_01_08_425885	556	36	.	.	.
10_1101-2021_01_08_425885	557	1	Therefore	therefore	RB
10_1101-2021_01_08_425885	557	2	,	,	,
10_1101-2021_01_08_425885	557	3	consistent	consistent	JJ
10_1101-2021_01_08_425885	557	4	with	with	IN
10_1101-2021_01_08_425885	557	5	the	the	DT
10_1101-2021_01_08_425885	557	6	results	result	NNS
10_1101-2021_01_08_425885	557	7	of	of	IN
10_1101-2021_01_08_425885	557	8	Methods	Methods	NNP
10_1101-2021_01_08_425885	557	9	Section	Section	NNP
10_1101-2021_01_08_425885	557	10	4.4.2.2	4.4.2.2	CD
10_1101-2021_01_08_425885	557	11	,	,	,
10_1101-2021_01_08_425885	557	12	as	as	RB
10_1101-2021_01_08_425885	557	13	long	long	RB
10_1101-2021_01_08_425885	557	14	as	as	IN
10_1101-2021_01_08_425885	557	15	the	the	DT
10_1101-2021_01_08_425885	557	16	noise	noise	NN
10_1101-2021_01_08_425885	557	17	scale	scale	NN
10_1101-2021_01_08_425885	557	18	σ	σ	NNP
10_1101-2021_01_08_425885	557	19	is	be	VBZ
10_1101-2021_01_08_425885	557	20	small	small	JJ
10_1101-2021_01_08_425885	557	21	,	,	,
10_1101-2021_01_08_425885	557	22	a	a	DT
10_1101-2021_01_08_425885	557	23	large	large	JJ
10_1101-2021_01_08_425885	557	24	ambient	ambient	JJ
10_1101-2021_01_08_425885	557	25	dimension	dimension	NN
10_1101-2021_01_08_425885	557	26	n	n	CC
10_1101-2021_01_08_425885	557	27	is	be	VBZ
10_1101-2021_01_08_425885	557	28	not	not	RB
10_1101-2021_01_08_425885	557	29	a	a	DT
10_1101-2021_01_08_425885	557	30	confounder	confounder	NN
10_1101-2021_01_08_425885	557	31	.	.	.
10_1101-2021_01_08_425885	558	1	Practically	practically	RB
10_1101-2021_01_08_425885	558	2	however	however	RB
10_1101-2021_01_08_425885	558	3	,	,	,
10_1101-2021_01_08_425885	558	4	to	to	TO
10_1101-2021_01_08_425885	558	5	shorten	shorten	VB
10_1101-2021_01_08_425885	558	6	computational	computational	JJ
10_1101-2021_01_08_425885	558	7	overhead	overhead	NN
10_1101-2021_01_08_425885	558	8	and	and	CC
10_1101-2021_01_08_425885	558	9	avoid	avoid	VB
10_1101-2021_01_08_425885	558	10	the	the	DT
10_1101-2021_01_08_425885	558	11	large	large	JJ
10_1101-2021_01_08_425885	558	12	-	-	HYPH
10_1101-2021_01_08_425885	558	13	n	n	NN
10_1101-2021_01_08_425885	558	14	-	-	HYPH
10_1101-2021_01_08_425885	558	15	and	and	CC
10_1101-2021_01_08_425885	558	16	-	-	HYPH
10_1101-2021_01_08_425885	558	17	σ	σ	NN
10_1101-2021_01_08_425885	558	18	case	case	NN
10_1101-2021_01_08_425885	558	19	,	,	,
10_1101-2021_01_08_425885	558	20	it	-PRON-	PRP
10_1101-2021_01_08_425885	558	21	is	be	VBZ
10_1101-2021_01_08_425885	558	22	still	still	RB
10_1101-2021_01_08_425885	558	23	helpful	helpful	JJ
10_1101-2021_01_08_425885	558	24	to	to	TO
10_1101-2021_01_08_425885	558	25	reduce	reduce	VB
10_1101-2021_01_08_425885	558	26	the	the	DT
10_1101-2021_01_08_425885	558	27	ambient	ambient	JJ
10_1101-2021_01_08_425885	558	28	dimension	dimension	NN
10_1101-2021_01_08_425885	558	29	by	by	IN
10_1101-2021_01_08_425885	558	30	projecting	project	VBG
10_1101-2021_01_08_425885	558	31	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	558	32	to	to	IN
10_1101-2021_01_08_425885	558	33	an	an	DT
10_1101-2021_01_08_425885	558	34	affine	affine	NN
10_1101-2021_01_08_425885	558	35	subspace	subspace	NN
10_1101-2021_01_08_425885	558	36	containing	contain	VBG
10_1101-2021_01_08_425885	558	37	the	the	DT
10_1101-2021_01_08_425885	558	38	manifold	manifold	NN
10_1101-2021_01_08_425885	558	39	(	(	-LRB-
10_1101-2021_01_08_425885	558	40	e.g.	e.g.	RB
10_1101-2021_01_08_425885	559	1	by	by	IN
10_1101-2021_01_08_425885	559	2	PCA	PCA	NNP
10_1101-2021_01_08_425885	559	3	)	)	-RRB-
10_1101-2021_01_08_425885	559	4	.	.	.
10_1101-2021_01_08_425885	560	1	Such	such	PDT
10_1101-2021_01_08_425885	560	2	a	a	DT
10_1101-2021_01_08_425885	560	3	transformation	transformation	NN
10_1101-2021_01_08_425885	560	4	does	do	VBZ
10_1101-2021_01_08_425885	560	5	not	not	RB
10_1101-2021_01_08_425885	560	6	change	change	VB
10_1101-2021_01_08_425885	560	7	the	the	DT
10_1101-2021_01_08_425885	560	8	intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	560	9	curvature	curvature	NN
10_1101-2021_01_08_425885	560	10	.	.	.
10_1101-2021_01_08_425885	561	1	32	32	CD
10_1101-2021_01_08_425885	561	2	.CC	.CC	:
10_1101-2021_01_08_425885	561	3	-	-	HYPH
10_1101-2021_01_08_425885	561	4	BY	by	IN
10_1101-2021_01_08_425885	561	5	-	-	HYPH
10_1101-2021_01_08_425885	561	6	NC	NC	NNP
10_1101-2021_01_08_425885	561	7	-	-	HYPH
10_1101-2021_01_08_425885	561	8	ND	ND	NNP
10_1101-2021_01_08_425885	561	9	4.0	4.0	CD
10_1101-2021_01_08_425885	561	10	International	International	NNP
10_1101-2021_01_08_425885	561	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	561	12	under	under	IN
10_1101-2021_01_08_425885	561	13	a	a	DT
10_1101-2021_01_08_425885	561	14	(	(	-LRB-
10_1101-2021_01_08_425885	561	15	which	which	WDT
10_1101-2021_01_08_425885	561	16	was	be	VBD
10_1101-2021_01_08_425885	561	17	not	not	RB
10_1101-2021_01_08_425885	561	18	certified	certify	VBN
10_1101-2021_01_08_425885	561	19	by	by	IN
10_1101-2021_01_08_425885	561	20	peer	peer	NN
10_1101-2021_01_08_425885	561	21	review	review	NN
10_1101-2021_01_08_425885	561	22	)	)	-RRB-
10_1101-2021_01_08_425885	561	23	is	be	VBZ
10_1101-2021_01_08_425885	561	24	the	the	DT
10_1101-2021_01_08_425885	561	25	author	author	NN
10_1101-2021_01_08_425885	561	26	/	/	SYM
10_1101-2021_01_08_425885	561	27	funder	funder	NN
10_1101-2021_01_08_425885	561	28	,	,	,
10_1101-2021_01_08_425885	561	29	who	who	WP
10_1101-2021_01_08_425885	561	30	has	have	VBZ
10_1101-2021_01_08_425885	561	31	granted	grant	VBN
10_1101-2021_01_08_425885	561	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	561	33	a	a	DT
10_1101-2021_01_08_425885	561	34	license	license	NN
10_1101-2021_01_08_425885	561	35	to	to	TO
10_1101-2021_01_08_425885	561	36	display	display	VB
10_1101-2021_01_08_425885	561	37	the	the	DT
10_1101-2021_01_08_425885	561	38	preprint	preprint	NN
10_1101-2021_01_08_425885	561	39	in	in	IN
10_1101-2021_01_08_425885	561	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	561	41	.	.	.
10_1101-2021_01_08_425885	562	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	562	2	is	be	VBZ
10_1101-2021_01_08_425885	562	3	made	make	VBN
10_1101-2021_01_08_425885	562	4	The	the	DT
10_1101-2021_01_08_425885	562	5	copyright	copyright	NN
10_1101-2021_01_08_425885	562	6	holder	holder	NN
10_1101-2021_01_08_425885	562	7	for	for	IN
10_1101-2021_01_08_425885	562	8	this	this	DT
10_1101-2021_01_08_425885	562	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	562	10	version	version	NN
10_1101-2021_01_08_425885	562	11	posted	post	VBD
10_1101-2021_01_08_425885	562	12	January	January	NNP
10_1101-2021_01_08_425885	562	13	8	8	CD
10_1101-2021_01_08_425885	562	14	,	,	,
10_1101-2021_01_08_425885	562	15	2021	2021	CD
10_1101-2021_01_08_425885	562	16	.	.	.
10_1101-2021_01_08_425885	562	17	;	;	:
10_1101-2021_01_08_425885	562	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	562	19	:	:	:
10_1101-2021_01_08_425885	562	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	562	21	preprint	preprint	NN
10_1101-2021_01_08_425885	562	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	562	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	RB
10_1101-2021_01_08_425885	562	24	4.4.2.4	4.4.2.4	CD
10_1101-2021_01_08_425885	562	25	Choice	Choice	NNP
10_1101-2021_01_08_425885	562	26	of	of	IN
10_1101-2021_01_08_425885	562	27	Manifold	Manifold	NNP
10_1101-2021_01_08_425885	562	28	Dimension	Dimension	NNP
10_1101-2021_01_08_425885	562	29	The	the	DT
10_1101-2021_01_08_425885	562	30	last	last	JJ
10_1101-2021_01_08_425885	562	31	practical	practical	JJ
10_1101-2021_01_08_425885	562	32	consideration	consideration	NN
10_1101-2021_01_08_425885	562	33	is	be	VBZ
10_1101-2021_01_08_425885	562	34	accurate	accurate	JJ
10_1101-2021_01_08_425885	562	35	selection	selection	NN
10_1101-2021_01_08_425885	562	36	of	of	IN
10_1101-2021_01_08_425885	562	37	the	the	DT
10_1101-2021_01_08_425885	562	38	manifold	manifold	JJ
10_1101-2021_01_08_425885	562	39	dimension	dimension	NN
10_1101-2021_01_08_425885	562	40	,	,	,
10_1101-2021_01_08_425885	562	41	d	d	NNP
10_1101-2021_01_08_425885	562	42	,	,	,
10_1101-2021_01_08_425885	562	43	which	which	WDT
10_1101-2021_01_08_425885	562	44	we	-PRON-	PRP
10_1101-2021_01_08_425885	562	45	have	have	VBP
10_1101-2021_01_08_425885	562	46	so	so	RB
10_1101-2021_01_08_425885	562	47	far	far	RB
10_1101-2021_01_08_425885	562	48	assumed	assume	VBN
10_1101-2021_01_08_425885	562	49	to	to	TO
10_1101-2021_01_08_425885	562	50	be	be	VB
10_1101-2021_01_08_425885	562	51	known	know	VBN
10_1101-2021_01_08_425885	562	52	.	.	.
10_1101-2021_01_08_425885	563	1	There	there	EX
10_1101-2021_01_08_425885	563	2	is	be	VBZ
10_1101-2021_01_08_425885	563	3	no	no	DT
10_1101-2021_01_08_425885	563	4	consensus	consensus	NN
10_1101-2021_01_08_425885	563	5	on	on	IN
10_1101-2021_01_08_425885	563	6	the	the	DT
10_1101-2021_01_08_425885	563	7	definition	definition	NN
10_1101-2021_01_08_425885	563	8	of	of	IN
10_1101-2021_01_08_425885	563	9	d	d	NN
10_1101-2021_01_08_425885	563	10	for	for	IN
10_1101-2021_01_08_425885	563	11	a	a	DT
10_1101-2021_01_08_425885	563	12	dataset	dataset	NN
10_1101-2021_01_08_425885	563	13	,	,	,
10_1101-2021_01_08_425885	563	14	so	so	RB
10_1101-2021_01_08_425885	563	15	various	various	JJ
10_1101-2021_01_08_425885	563	16	disciplines	discipline	NNS
10_1101-2021_01_08_425885	563	17	have	have	VBP
10_1101-2021_01_08_425885	563	18	devised	devise	VBN
10_1101-2021_01_08_425885	563	19	different	different	JJ
10_1101-2021_01_08_425885	563	20	heuristics	heuristic	NNS
10_1101-2021_01_08_425885	563	21	to	to	TO
10_1101-2021_01_08_425885	563	22	determine	determine	VB
10_1101-2021_01_08_425885	563	23	d	d	NN
10_1101-2021_01_08_425885	563	24	in	in	IN
10_1101-2021_01_08_425885	563	25	a	a	DT
10_1101-2021_01_08_425885	563	26	data	data	NN
10_1101-2021_01_08_425885	563	27	-	-	HYPH
10_1101-2021_01_08_425885	563	28	driven	drive	VBN
10_1101-2021_01_08_425885	563	29	fashion	fashion	NN
10_1101-2021_01_08_425885	563	30	[	[	-LRB-
10_1101-2021_01_08_425885	563	31	52	52	CD
10_1101-2021_01_08_425885	563	32	]	]	-RRB-
10_1101-2021_01_08_425885	563	33	.	.	.
10_1101-2021_01_08_425885	564	1	From	from	IN
10_1101-2021_01_08_425885	564	2	the	the	DT
10_1101-2021_01_08_425885	564	3	regression	regression	NN
10_1101-2021_01_08_425885	564	4	perspective	perspective	NN
10_1101-2021_01_08_425885	564	5	,	,	,
10_1101-2021_01_08_425885	564	6	any	any	DT
10_1101-2021_01_08_425885	564	7	d	d	NN
10_1101-2021_01_08_425885	564	8	>	>	NN
10_1101-2021_01_08_425885	564	9	0	0	CD
10_1101-2021_01_08_425885	564	10	corresponds	correspond	NNS
10_1101-2021_01_08_425885	564	11	to	to	IN
10_1101-2021_01_08_425885	564	12	a	a	DT
10_1101-2021_01_08_425885	564	13	well	well	RB
10_1101-2021_01_08_425885	564	14	-	-	HYPH
10_1101-2021_01_08_425885	564	15	defined	define	VBN
10_1101-2021_01_08_425885	564	16	regression	regression	NN
10_1101-2021_01_08_425885	564	17	problem	problem	NN
10_1101-2021_01_08_425885	564	18	.	.	.
10_1101-2021_01_08_425885	565	1	The	the	DT
10_1101-2021_01_08_425885	565	2	choice	choice	NN
10_1101-2021_01_08_425885	565	3	of	of	IN
10_1101-2021_01_08_425885	565	4	d	d	NN
10_1101-2021_01_08_425885	565	5	merely	merely	RB
10_1101-2021_01_08_425885	565	6	determines	determine	VBZ
10_1101-2021_01_08_425885	565	7	how	how	WRB
10_1101-2021_01_08_425885	565	8	local	local	JJ
10_1101-2021_01_08_425885	565	9	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	565	10	are	be	VBP
10_1101-2021_01_08_425885	565	11	partitioned	partition	VBN
10_1101-2021_01_08_425885	565	12	into	into	IN
10_1101-2021_01_08_425885	565	13	independent	independent	JJ
10_1101-2021_01_08_425885	565	14	(	(	-LRB-
10_1101-2021_01_08_425885	565	15	tangent	tangent	NN
10_1101-2021_01_08_425885	565	16	)	)	-RRB-
10_1101-2021_01_08_425885	565	17	and	and	CC
10_1101-2021_01_08_425885	565	18	dependent	dependent	JJ
10_1101-2021_01_08_425885	565	19	(	(	-LRB-
10_1101-2021_01_08_425885	565	20	normal	normal	JJ
10_1101-2021_01_08_425885	565	21	)	)	-RRB-
10_1101-2021_01_08_425885	565	22	variables	variable	NNS
10_1101-2021_01_08_425885	565	23	.	.	.
10_1101-2021_01_08_425885	566	1	However	however	RB
10_1101-2021_01_08_425885	566	2	,	,	,
10_1101-2021_01_08_425885	566	3	in	in	IN
10_1101-2021_01_08_425885	566	4	our	-PRON-	PRP$
10_1101-2021_01_08_425885	566	5	algorithm	algorithm	NN
10_1101-2021_01_08_425885	566	6	we	-PRON-	PRP
10_1101-2021_01_08_425885	566	7	noticed	notice	VBD
10_1101-2021_01_08_425885	566	8	that	that	IN
10_1101-2021_01_08_425885	566	9	some	some	DT
10_1101-2021_01_08_425885	566	10	choices	choice	NNS
10_1101-2021_01_08_425885	566	11	of	of	IN
10_1101-2021_01_08_425885	566	12	d	d	NN
10_1101-2021_01_08_425885	566	13	result	result	NN
10_1101-2021_01_08_425885	566	14	in	in	IN
10_1101-2021_01_08_425885	566	15	exces-	exces-	NNP
10_1101-2021_01_08_425885	566	16	sively	sively	RB
10_1101-2021_01_08_425885	566	17	large	large	JJ
10_1101-2021_01_08_425885	566	18	r(p	r(p	NNP
10_1101-2021_01_08_425885	566	19	)	)	-RRB-
10_1101-2021_01_08_425885	566	20	for	for	IN
10_1101-2021_01_08_425885	566	21	a	a	DT
10_1101-2021_01_08_425885	566	22	fixed	fix	VBN
10_1101-2021_01_08_425885	566	23	σh	σh	NN
10_1101-2021_01_08_425885	566	24	.	.	.
10_1101-2021_01_08_425885	567	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	567	2	explored	explore	VBD
10_1101-2021_01_08_425885	567	3	this	this	DT
10_1101-2021_01_08_425885	567	4	further	further	RB
10_1101-2021_01_08_425885	567	5	using	use	VBG
10_1101-2021_01_08_425885	567	6	two	two	CD
10_1101-2021_01_08_425885	567	7	toy	toy	NN
10_1101-2021_01_08_425885	567	8	manifolds	manifold	NNS
10_1101-2021_01_08_425885	567	9	and	and	CC
10_1101-2021_01_08_425885	567	10	discovered	discover	VBD
10_1101-2021_01_08_425885	567	11	a	a	DT
10_1101-2021_01_08_425885	567	12	signature	signature	NN
10_1101-2021_01_08_425885	567	13	indicating	indicate	VBG
10_1101-2021_01_08_425885	567	14	that	that	IN
10_1101-2021_01_08_425885	567	15	the	the	DT
10_1101-2021_01_08_425885	567	16	specified	specify	VBN
10_1101-2021_01_08_425885	567	17	manifold	manifold	JJ
10_1101-2021_01_08_425885	567	18	dimension	dimension	NN
10_1101-2021_01_08_425885	567	19	may	may	MD
10_1101-2021_01_08_425885	567	20	be	be	VB
10_1101-2021_01_08_425885	567	21	incorrect	incorrect	JJ
10_1101-2021_01_08_425885	567	22	.	.	.
10_1101-2021_01_08_425885	568	1	The	the	DT
10_1101-2021_01_08_425885	568	2	manifolds	manifold	NNS
10_1101-2021_01_08_425885	568	3	considered	consider	VBN
10_1101-2021_01_08_425885	568	4	were	be	VBD
10_1101-2021_01_08_425885	568	5	S3	S3	NNP
10_1101-2021_01_08_425885	568	6	⊂	⊂	CD
10_1101-2021_01_08_425885	568	7	R5	R5	NNP
10_1101-2021_01_08_425885	568	8	convoluted	convolute	VBN
10_1101-2021_01_08_425885	568	9	by	by	IN
10_1101-2021_01_08_425885	568	10	isotropic	isotropic	JJ
10_1101-2021_01_08_425885	568	11	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	568	12	noise	noise	NN
10_1101-2021_01_08_425885	568	13	with	with	IN
10_1101-2021_01_08_425885	568	14	σ	σ	NNP
10_1101-2021_01_08_425885	568	15	=	=	SYM
10_1101-2021_01_08_425885	568	16	0.01	0.01	CD
10_1101-2021_01_08_425885	568	17	and	and	CC
10_1101-2021_01_08_425885	568	18	S2	S2	NNP
10_1101-2021_01_08_425885	568	19	×S2	×S2	NNP
10_1101-2021_01_08_425885	568	20	⊂	⊂	CD
10_1101-2021_01_08_425885	568	21	R6	R6	NNP
10_1101-2021_01_08_425885	568	22	,	,	,
10_1101-2021_01_08_425885	568	23	for	for	IN
10_1101-2021_01_08_425885	568	24	which	which	WDT
10_1101-2021_01_08_425885	568	25	d∗	d∗	NN
10_1101-2021_01_08_425885	568	26	,	,	,
10_1101-2021_01_08_425885	568	27	the	the	DT
10_1101-2021_01_08_425885	568	28	true	true	JJ
10_1101-2021_01_08_425885	568	29	manifold	manifold	JJ
10_1101-2021_01_08_425885	568	30	dimension	dimension	NN
10_1101-2021_01_08_425885	568	31	,	,	,
10_1101-2021_01_08_425885	568	32	is	be	VBZ
10_1101-2021_01_08_425885	568	33	d∗	d∗	NN
10_1101-2021_01_08_425885	568	34	=	=	SYM
10_1101-2021_01_08_425885	568	35	3	3	CD
10_1101-2021_01_08_425885	568	36	and	and	CC
10_1101-2021_01_08_425885	568	37	d∗	d∗	NN
10_1101-2021_01_08_425885	568	38	=	=	SYM
10_1101-2021_01_08_425885	568	39	4	4	CD
10_1101-2021_01_08_425885	568	40	respectively	respectively	RB
10_1101-2021_01_08_425885	568	41	.	.	.
10_1101-2021_01_08_425885	569	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	569	2	uniformly	uniformly	RB
10_1101-2021_01_08_425885	569	3	sampled	sample	VBD
10_1101-2021_01_08_425885	569	4	N	n	NN
10_1101-2021_01_08_425885	569	5	=	=	SYM
10_1101-2021_01_08_425885	569	6	104	104	CD
10_1101-2021_01_08_425885	569	7	points	point	NNS
10_1101-2021_01_08_425885	569	8	from	from	IN
10_1101-2021_01_08_425885	569	9	each	each	DT
10_1101-2021_01_08_425885	569	10	manifold	manifold	JJ
10_1101-2021_01_08_425885	569	11	and	and	CC
10_1101-2021_01_08_425885	569	12	estimated	estimate	VBN
10_1101-2021_01_08_425885	569	13	scalar	scalar	JJ
10_1101-2021_01_08_425885	569	14	curvatures	curvature	NNS
10_1101-2021_01_08_425885	569	15	by	by	IN
10_1101-2021_01_08_425885	569	16	holding	hold	VBG
10_1101-2021_01_08_425885	569	17	σh	σh	NNP
10_1101-2021_01_08_425885	569	18	fixed	fix	VBN
10_1101-2021_01_08_425885	569	19	for	for	IN
10_1101-2021_01_08_425885	569	20	different	different	JJ
10_1101-2021_01_08_425885	569	21	d	d	NN
10_1101-2021_01_08_425885	569	22	(	(	-LRB-
10_1101-2021_01_08_425885	569	23	see	see	VB
10_1101-2021_01_08_425885	569	24	Methods	Methods	NNP
10_1101-2021_01_08_425885	569	25	Section	Section	NNP
10_1101-2021_01_08_425885	569	26	4.4.3	4.4.3	CD
10_1101-2021_01_08_425885	569	27	)	)	-RRB-
10_1101-2021_01_08_425885	569	28	.	.	.
10_1101-2021_01_08_425885	570	1	For	for	IN
10_1101-2021_01_08_425885	570	2	both	both	DT
10_1101-2021_01_08_425885	570	3	manifolds	manifold	NNS
10_1101-2021_01_08_425885	570	4	,	,	,
10_1101-2021_01_08_425885	570	5	the	the	DT
10_1101-2021_01_08_425885	570	6	average	average	JJ
10_1101-2021_01_08_425885	570	7	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	570	8	size	size	NN
10_1101-2021_01_08_425885	570	9	,	,	,
10_1101-2021_01_08_425885	570	10	r	r	NNP
10_1101-2021_01_08_425885	570	11	,	,	,
10_1101-2021_01_08_425885	570	12	was	be	VBD
10_1101-2021_01_08_425885	570	13	much	much	RB
10_1101-2021_01_08_425885	570	14	larger	large	JJR
10_1101-2021_01_08_425885	570	15	for	for	IN
10_1101-2021_01_08_425885	570	16	d	d	NNP
10_1101-2021_01_08_425885	570	17	>	>	NNP
10_1101-2021_01_08_425885	570	18	d∗	d∗	NN
10_1101-2021_01_08_425885	570	19	and	and	CC
10_1101-2021_01_08_425885	570	20	d	d	NNP
10_1101-2021_01_08_425885	570	21	<	<	XX
10_1101-2021_01_08_425885	570	22	d∗	d∗	NN
10_1101-2021_01_08_425885	570	23	,	,	,
10_1101-2021_01_08_425885	570	24	than	than	IN
10_1101-2021_01_08_425885	570	25	for	for	IN
10_1101-2021_01_08_425885	570	26	d	d	NN
10_1101-2021_01_08_425885	570	27	=	=	SYM
10_1101-2021_01_08_425885	570	28	d∗	d∗	NN
10_1101-2021_01_08_425885	570	29	(	(	-LRB-
10_1101-2021_01_08_425885	570	30	see	see	VB
10_1101-2021_01_08_425885	570	31	Figure	Figure	NNP
10_1101-2021_01_08_425885	570	32	S2D	s2d	NN
10_1101-2021_01_08_425885	570	33	)	)	-RRB-
10_1101-2021_01_08_425885	570	34	.	.	.
10_1101-2021_01_08_425885	571	1	In	in	IN
10_1101-2021_01_08_425885	571	2	the	the	DT
10_1101-2021_01_08_425885	571	3	case	case	NN
10_1101-2021_01_08_425885	571	4	of	of	IN
10_1101-2021_01_08_425885	571	5	S3	S3	NNP
10_1101-2021_01_08_425885	571	6	,	,	,
10_1101-2021_01_08_425885	571	7	for	for	IN
10_1101-2021_01_08_425885	571	8	d	d	NN
10_1101-2021_01_08_425885	571	9	<	<	XX
10_1101-2021_01_08_425885	571	10	d∗	d∗	NN
10_1101-2021_01_08_425885	571	11	,	,	,
10_1101-2021_01_08_425885	571	12	the	the	DT
10_1101-2021_01_08_425885	571	13	average	average	JJ
10_1101-2021_01_08_425885	571	14	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	571	15	size	size	NN
10_1101-2021_01_08_425885	571	16	was	be	VBD
10_1101-2021_01_08_425885	571	17	even	even	RB
10_1101-2021_01_08_425885	571	18	larger	large	JJR
10_1101-2021_01_08_425885	571	19	than	than	IN
10_1101-2021_01_08_425885	571	20	the	the	DT
10_1101-2021_01_08_425885	571	21	global	global	JJ
10_1101-2021_01_08_425885	571	22	length	length	NN
10_1101-2021_01_08_425885	571	23	scale	scale	NN
10_1101-2021_01_08_425885	571	24	,	,	,
10_1101-2021_01_08_425885	571	25	L	l	NN
10_1101-2021_01_08_425885	571	26	,	,	,
10_1101-2021_01_08_425885	571	27	of	of	IN
10_1101-2021_01_08_425885	571	28	the	the	DT
10_1101-2021_01_08_425885	571	29	manifold	manifold	NN
10_1101-2021_01_08_425885	571	30	.	.	.
10_1101-2021_01_08_425885	572	1	Since	since	IN
10_1101-2021_01_08_425885	572	2	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	572	3	sizes	size	NNS
10_1101-2021_01_08_425885	572	4	are	be	VBP
10_1101-2021_01_08_425885	572	5	chosen	choose	VBN
10_1101-2021_01_08_425885	572	6	to	to	TO
10_1101-2021_01_08_425885	572	7	achieve	achieve	VB
10_1101-2021_01_08_425885	572	8	a	a	DT
10_1101-2021_01_08_425885	572	9	target	target	NN
10_1101-2021_01_08_425885	572	10	σh	σh	NNP
10_1101-2021_01_08_425885	572	11	,	,	,
10_1101-2021_01_08_425885	572	12	manually	manually	RB
10_1101-2021_01_08_425885	572	13	decreasing	decrease	VBG
10_1101-2021_01_08_425885	572	14	r(p	r(p	NNP
10_1101-2021_01_08_425885	572	15	)	)	-RRB-
10_1101-2021_01_08_425885	572	16	is	be	VBZ
10_1101-2021_01_08_425885	572	17	counter	counter	JJ
10_1101-2021_01_08_425885	572	18	-	-	JJ
10_1101-2021_01_08_425885	572	19	productive	productive	JJ
10_1101-2021_01_08_425885	572	20	and	and	CC
10_1101-2021_01_08_425885	572	21	simply	simply	RB
10_1101-2021_01_08_425885	572	22	increases	increase	VBZ
10_1101-2021_01_08_425885	572	23	the	the	DT
10_1101-2021_01_08_425885	572	24	uncertainty	uncertainty	NN
10_1101-2021_01_08_425885	572	25	from	from	IN
10_1101-2021_01_08_425885	572	26	regression	regression	NN
10_1101-2021_01_08_425885	572	27	above	above	IN
10_1101-2021_01_08_425885	572	28	σh	σh	NNP
10_1101-2021_01_08_425885	572	29	.	.	.
10_1101-2021_01_08_425885	573	1	The	the	DT
10_1101-2021_01_08_425885	573	2	large	large	JJ
10_1101-2021_01_08_425885	573	3	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	573	4	sizes	size	NNS
10_1101-2021_01_08_425885	573	5	that	that	WDT
10_1101-2021_01_08_425885	573	6	emerged	emerge	VBD
10_1101-2021_01_08_425885	573	7	for	for	IN
10_1101-2021_01_08_425885	573	8	both	both	DT
10_1101-2021_01_08_425885	573	9	d	d	NN
10_1101-2021_01_08_425885	573	10	>	>	XX
10_1101-2021_01_08_425885	573	11	d∗	d∗	NN
10_1101-2021_01_08_425885	573	12	and	and	CC
10_1101-2021_01_08_425885	573	13	d	d	NNP
10_1101-2021_01_08_425885	573	14	<	<	XX
10_1101-2021_01_08_425885	573	15	d∗	d∗	NN
10_1101-2021_01_08_425885	573	16	can	can	MD
10_1101-2021_01_08_425885	573	17	be	be	VB
10_1101-2021_01_08_425885	573	18	understood	understand	VBN
10_1101-2021_01_08_425885	573	19	in	in	IN
10_1101-2021_01_08_425885	573	20	terms	term	NNS
10_1101-2021_01_08_425885	573	21	of	of	IN
10_1101-2021_01_08_425885	573	22	the	the	DT
10_1101-2021_01_08_425885	573	23	mis	mis	NN
10_1101-2021_01_08_425885	573	24	-	-	HYPH
10_1101-2021_01_08_425885	573	25	assignment	assignment	NN
10_1101-2021_01_08_425885	573	26	of	of	IN
10_1101-2021_01_08_425885	573	27	normal	normal	JJ
10_1101-2021_01_08_425885	573	28	vectors	vector	NNS
10_1101-2021_01_08_425885	573	29	to	to	IN
10_1101-2021_01_08_425885	573	30	the	the	DT
10_1101-2021_01_08_425885	573	31	tangent	tangent	NN
10_1101-2021_01_08_425885	573	32	space	space	NN
10_1101-2021_01_08_425885	573	33	,	,	,
10_1101-2021_01_08_425885	573	34	or	or	CC
10_1101-2021_01_08_425885	573	35	vice	vice	RB
10_1101-2021_01_08_425885	573	36	versa	versa	RB
10_1101-2021_01_08_425885	573	37	.	.	.
10_1101-2021_01_08_425885	574	1	According	accord	VBG
10_1101-2021_01_08_425885	574	2	to	to	IN
10_1101-2021_01_08_425885	574	3	Equation	Equation	NNP
10_1101-2021_01_08_425885	574	4	19	19	CD
10_1101-2021_01_08_425885	574	5	,	,	,
10_1101-2021_01_08_425885	574	6	σhk	σhk	NNP
10_1101-2021_01_08_425885	574	7	ij	ij	VBP
10_1101-2021_01_08_425885	574	8	increases	increase	NNS
10_1101-2021_01_08_425885	574	9	with	with	IN
10_1101-2021_01_08_425885	574	10	large	large	JJ
10_1101-2021_01_08_425885	574	11	variation	variation	NN
10_1101-2021_01_08_425885	574	12	in	in	IN
10_1101-2021_01_08_425885	574	13	the	the	DT
10_1101-2021_01_08_425885	574	14	normal	normal	JJ
10_1101-2021_01_08_425885	574	15	direction	direction	NN
10_1101-2021_01_08_425885	574	16	(	(	-LRB-
10_1101-2021_01_08_425885	574	17	[	[	-LRB-
10_1101-2021_01_08_425885	574	18	diag	diag	NNP
10_1101-2021_01_08_425885	574	19	Σε]k	σε]k	CD
10_1101-2021_01_08_425885	574	20	)	)	-RRB-
10_1101-2021_01_08_425885	574	21	,	,	,
10_1101-2021_01_08_425885	574	22	or	or	CC
10_1101-2021_01_08_425885	574	23	with	with	IN
10_1101-2021_01_08_425885	574	24	small	small	JJ
10_1101-2021_01_08_425885	574	25	variation	variation	NN
10_1101-2021_01_08_425885	574	26	in	in	IN
10_1101-2021_01_08_425885	574	27	the	the	DT
10_1101-2021_01_08_425885	574	28	tangent	tangent	NN
10_1101-2021_01_08_425885	574	29	direction	direction	NN
10_1101-2021_01_08_425885	574	30	(	(	-LRB-
10_1101-2021_01_08_425885	574	31	[	[	-LRB-
10_1101-2021_01_08_425885	574	32	diag	diag	NNP
10_1101-2021_01_08_425885	574	33	(	(	-LRB-
10_1101-2021_01_08_425885	574	34	t′t)−1	t′t)−1	NN
10_1101-2021_01_08_425885	574	35	]	]	-RRB-
10_1101-2021_01_08_425885	574	36	(	(	-LRB-
10_1101-2021_01_08_425885	574	37	ij	ij	NNP
10_1101-2021_01_08_425885	574	38	)	)	-RRB-
10_1101-2021_01_08_425885	574	39	)	)	-RRB-
10_1101-2021_01_08_425885	574	40	.	.	.
10_1101-2021_01_08_425885	575	1	When	when	WRB
10_1101-2021_01_08_425885	575	2	we	-PRON-	PRP
10_1101-2021_01_08_425885	575	3	choose	choose	VBP
10_1101-2021_01_08_425885	575	4	d	d	LS
10_1101-2021_01_08_425885	575	5	>	>	XX
10_1101-2021_01_08_425885	575	6	d∗	d∗	NN
10_1101-2021_01_08_425885	575	7	,	,	,
10_1101-2021_01_08_425885	575	8	we	-PRON-	PRP
10_1101-2021_01_08_425885	575	9	mis	mis	VBP
10_1101-2021_01_08_425885	575	10	-	-	HYPH
10_1101-2021_01_08_425885	575	11	attribute	attribute	VB
10_1101-2021_01_08_425885	575	12	a	a	DT
10_1101-2021_01_08_425885	575	13	normal	normal	JJ
10_1101-2021_01_08_425885	575	14	direction	direction	NN
10_1101-2021_01_08_425885	575	15	with	with	IN
10_1101-2021_01_08_425885	575	16	small	small	JJ
10_1101-2021_01_08_425885	575	17	variation	variation	NN
10_1101-2021_01_08_425885	575	18	[	[	-LRB-
10_1101-2021_01_08_425885	575	19	diag	diag	VBD
10_1101-2021_01_08_425885	575	20	Σε]k	σε]k	CD
10_1101-2021_01_08_425885	575	21	as	as	IN
10_1101-2021_01_08_425885	575	22	an	an	DT
10_1101-2021_01_08_425885	575	23	independent	independent	JJ
10_1101-2021_01_08_425885	575	24	variable	variable	NN
10_1101-2021_01_08_425885	575	25	,	,	,
10_1101-2021_01_08_425885	575	26	whereas	whereas	IN
10_1101-2021_01_08_425885	575	27	variation	variation	NN
10_1101-2021_01_08_425885	575	28	along	along	IN
10_1101-2021_01_08_425885	575	29	the	the	DT
10_1101-2021_01_08_425885	575	30	true	true	JJ
10_1101-2021_01_08_425885	575	31	tangent	tangent	NN
10_1101-2021_01_08_425885	575	32	space	space	NN
10_1101-2021_01_08_425885	575	33	is	be	VBZ
10_1101-2021_01_08_425885	575	34	�	�	NNP
10_1101-2021_01_08_425885	575	35	[	[	-LRB-
10_1101-2021_01_08_425885	575	36	diag	diag	VBD
10_1101-2021_01_08_425885	575	37	Σε]k	σε]k	CD
10_1101-2021_01_08_425885	575	38	.	.	.
10_1101-2021_01_08_425885	575	39	r	r	NNP
10_1101-2021_01_08_425885	575	40	must	must	MD
10_1101-2021_01_08_425885	575	41	therefore	therefore	RB
10_1101-2021_01_08_425885	575	42	be	be	VB
10_1101-2021_01_08_425885	575	43	increased	increase	VBN
10_1101-2021_01_08_425885	575	44	to	to	TO
10_1101-2021_01_08_425885	575	45	compensate	compensate	VB
10_1101-2021_01_08_425885	575	46	for	for	IN
10_1101-2021_01_08_425885	575	47	the	the	DT
10_1101-2021_01_08_425885	575	48	lack	lack	NN
10_1101-2021_01_08_425885	575	49	of	of	IN
10_1101-2021_01_08_425885	575	50	variation	variation	NN
10_1101-2021_01_08_425885	575	51	along	along	IN
10_1101-2021_01_08_425885	575	52	this	this	DT
10_1101-2021_01_08_425885	575	53	direction	direction	NN
10_1101-2021_01_08_425885	575	54	mis	mis	NN
10_1101-2021_01_08_425885	575	55	-	-	HYPH
10_1101-2021_01_08_425885	575	56	classified	classify	VBN
10_1101-2021_01_08_425885	575	57	as	as	IN
10_1101-2021_01_08_425885	575	58	tangent	tangent	NN
10_1101-2021_01_08_425885	575	59	.	.	.
10_1101-2021_01_08_425885	576	1	When	when	WRB
10_1101-2021_01_08_425885	576	2	d	d	NNP
10_1101-2021_01_08_425885	576	3	<	<	XX
10_1101-2021_01_08_425885	576	4	d∗	d∗	NN
10_1101-2021_01_08_425885	576	5	,	,	,
10_1101-2021_01_08_425885	576	6	we	-PRON-	PRP
10_1101-2021_01_08_425885	576	7	have	have	VBP
10_1101-2021_01_08_425885	576	8	spuriously	spuriously	RB
10_1101-2021_01_08_425885	576	9	assigned	assign	VBN
10_1101-2021_01_08_425885	576	10	a	a	DT
10_1101-2021_01_08_425885	576	11	tangent	tangent	NN
10_1101-2021_01_08_425885	576	12	direction	direction	NN
10_1101-2021_01_08_425885	576	13	with	with	IN
10_1101-2021_01_08_425885	576	14	large	large	JJ
10_1101-2021_01_08_425885	576	15	variation	variation	NN
10_1101-2021_01_08_425885	576	16	to	to	TO
10_1101-2021_01_08_425885	576	17	be	be	VB
10_1101-2021_01_08_425885	576	18	a	a	DT
10_1101-2021_01_08_425885	576	19	normal	normal	JJ
10_1101-2021_01_08_425885	576	20	direction	direction	NN
10_1101-2021_01_08_425885	576	21	.	.	.
10_1101-2021_01_08_425885	577	1	Since	since	IN
10_1101-2021_01_08_425885	577	2	this	this	DT
10_1101-2021_01_08_425885	577	3	spurious	spurious	JJ
10_1101-2021_01_08_425885	577	4	normal	normal	JJ
10_1101-2021_01_08_425885	577	5	coordinate	coordinate	NN
10_1101-2021_01_08_425885	577	6	can	can	MD
10_1101-2021_01_08_425885	577	7	not	not	RB
10_1101-2021_01_08_425885	577	8	be	be	VB
10_1101-2021_01_08_425885	577	9	well	well	RB
10_1101-2021_01_08_425885	577	10	-	-	HYPH
10_1101-2021_01_08_425885	577	11	approximated	approximate	VBN
10_1101-2021_01_08_425885	577	12	as	as	IN
10_1101-2021_01_08_425885	577	13	a	a	DT
10_1101-2021_01_08_425885	577	14	function	function	NN
10_1101-2021_01_08_425885	577	15	of	of	IN
10_1101-2021_01_08_425885	577	16	tangent	tangent	NN
10_1101-2021_01_08_425885	577	17	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	577	18	from	from	IN
10_1101-2021_01_08_425885	577	19	which	which	WDT
10_1101-2021_01_08_425885	577	20	it	-PRON-	PRP
10_1101-2021_01_08_425885	577	21	is	be	VBZ
10_1101-2021_01_08_425885	577	22	linearly	linearly	RB
10_1101-2021_01_08_425885	577	23	independent	independent	JJ
10_1101-2021_01_08_425885	577	24	,	,	,
10_1101-2021_01_08_425885	577	25	the	the	DT
10_1101-2021_01_08_425885	577	26	perceived	perceive	VBN
10_1101-2021_01_08_425885	577	27	noise	noise	NN
10_1101-2021_01_08_425885	577	28	scale	scale	NN
10_1101-2021_01_08_425885	577	29	(	(	-LRB-
10_1101-2021_01_08_425885	577	30	[	[	-LRB-
10_1101-2021_01_08_425885	577	31	diag	diag	NNP
10_1101-2021_01_08_425885	577	32	Σε]k	σε]k	CD
10_1101-2021_01_08_425885	577	33	)	)	-RRB-
10_1101-2021_01_08_425885	577	34	is	be	VBZ
10_1101-2021_01_08_425885	577	35	exaggerated	exaggerate	VBN
10_1101-2021_01_08_425885	577	36	so	so	IN
10_1101-2021_01_08_425885	577	37	that	that	IN
10_1101-2021_01_08_425885	577	38	a	a	DT
10_1101-2021_01_08_425885	577	39	larger	large	JJR
10_1101-2021_01_08_425885	577	40	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	577	41	is	be	VBZ
10_1101-2021_01_08_425885	577	42	needed	need	VBN
10_1101-2021_01_08_425885	577	43	to	to	TO
10_1101-2021_01_08_425885	577	44	attain	attain	VB
10_1101-2021_01_08_425885	577	45	σh	σh	NNP
10_1101-2021_01_08_425885	577	46	.	.	.
10_1101-2021_01_08_425885	578	1	This	this	DT
10_1101-2021_01_08_425885	578	2	suggests	suggest	VBZ
10_1101-2021_01_08_425885	578	3	a	a	DT
10_1101-2021_01_08_425885	578	4	crude	crude	JJ
10_1101-2021_01_08_425885	578	5	,	,	,
10_1101-2021_01_08_425885	578	6	operational	operational	JJ
10_1101-2021_01_08_425885	578	7	definition	definition	NN
10_1101-2021_01_08_425885	578	8	of	of	IN
10_1101-2021_01_08_425885	578	9	what	what	WP
10_1101-2021_01_08_425885	578	10	constitutes	constitute	VBZ
10_1101-2021_01_08_425885	578	11	an	an	DT
10_1101-2021_01_08_425885	578	12	incorrect	incorrect	JJ
10_1101-2021_01_08_425885	578	13	choice	choice	NN
10_1101-2021_01_08_425885	578	14	of	of	IN
10_1101-2021_01_08_425885	578	15	d.	d.	NNP
10_1101-2021_01_08_425885	578	16	When	when	WRB
10_1101-2021_01_08_425885	578	17	σhk	σhk	NNP
10_1101-2021_01_08_425885	578	18	ij	ij	NNP
10_1101-2021_01_08_425885	578	19	is	be	VBZ
10_1101-2021_01_08_425885	578	20	large	large	JJ
10_1101-2021_01_08_425885	578	21	relative	relative	JJ
10_1101-2021_01_08_425885	578	22	to	to	IN
10_1101-2021_01_08_425885	578	23	the	the	DT
10_1101-2021_01_08_425885	578	24	uncertainty	uncertainty	NN
10_1101-2021_01_08_425885	578	25	in	in	IN
10_1101-2021_01_08_425885	578	26	other	other	JJ
10_1101-2021_01_08_425885	578	27	coefficients	coefficient	NNS
10_1101-2021_01_08_425885	578	28	,	,	,
10_1101-2021_01_08_425885	578	29	there	there	EX
10_1101-2021_01_08_425885	578	30	is	be	VBZ
10_1101-2021_01_08_425885	578	31	either	either	CC
10_1101-2021_01_08_425885	578	32	too	too	RB
10_1101-2021_01_08_425885	578	33	little	little	JJ
10_1101-2021_01_08_425885	578	34	variation	variation	NN
10_1101-2021_01_08_425885	578	35	along	along	IN
10_1101-2021_01_08_425885	578	36	the	the	DT
10_1101-2021_01_08_425885	578	37	ith	ith	NNP
10_1101-2021_01_08_425885	578	38	and	and	CC
10_1101-2021_01_08_425885	578	39	jth	jth	NNP
10_1101-2021_01_08_425885	578	40	tangent	tangent	NN
10_1101-2021_01_08_425885	578	41	directions	direction	NNS
10_1101-2021_01_08_425885	578	42	,	,	,
10_1101-2021_01_08_425885	578	43	or	or	CC
10_1101-2021_01_08_425885	578	44	too	too	RB
10_1101-2021_01_08_425885	578	45	much	much	JJ
10_1101-2021_01_08_425885	578	46	variation	variation	NN
10_1101-2021_01_08_425885	578	47	along	along	IN
10_1101-2021_01_08_425885	578	48	the	the	DT
10_1101-2021_01_08_425885	578	49	kth	kth	JJ
10_1101-2021_01_08_425885	578	50	normal	normal	JJ
10_1101-2021_01_08_425885	578	51	direction	direction	NN
10_1101-2021_01_08_425885	578	52	.	.	.
10_1101-2021_01_08_425885	579	1	In	in	IN
10_1101-2021_01_08_425885	579	2	the	the	DT
10_1101-2021_01_08_425885	579	3	former	former	JJ
10_1101-2021_01_08_425885	579	4	case	case	NN
10_1101-2021_01_08_425885	579	5	,	,	,
10_1101-2021_01_08_425885	579	6	the	the	DT
10_1101-2021_01_08_425885	579	7	ith	ith	NNP
10_1101-2021_01_08_425885	579	8	or	or	CC
10_1101-2021_01_08_425885	579	9	jth	jth	NNP
10_1101-2021_01_08_425885	579	10	tangent	tangent	NN
10_1101-2021_01_08_425885	579	11	direction	direction	NN
10_1101-2021_01_08_425885	579	12	might	may	MD
10_1101-2021_01_08_425885	579	13	be	be	VB
10_1101-2021_01_08_425885	579	14	more	more	RBR
10_1101-2021_01_08_425885	579	15	appropriately	appropriately	RB
10_1101-2021_01_08_425885	579	16	classified	classify	VBN
10_1101-2021_01_08_425885	579	17	as	as	IN
10_1101-2021_01_08_425885	579	18	a	a	DT
10_1101-2021_01_08_425885	579	19	normal	normal	JJ
10_1101-2021_01_08_425885	579	20	direction	direction	NN
10_1101-2021_01_08_425885	579	21	(	(	-LRB-
10_1101-2021_01_08_425885	579	22	d	d	NN
10_1101-2021_01_08_425885	579	23	is	be	VBZ
10_1101-2021_01_08_425885	579	24	too	too	RB
10_1101-2021_01_08_425885	579	25	large	large	JJ
10_1101-2021_01_08_425885	579	26	and	and	CC
10_1101-2021_01_08_425885	579	27	should	should	MD
10_1101-2021_01_08_425885	579	28	be	be	VB
10_1101-2021_01_08_425885	579	29	decreased	decrease	VBN
10_1101-2021_01_08_425885	579	30	)	)	-RRB-
10_1101-2021_01_08_425885	579	31	,	,	,
10_1101-2021_01_08_425885	579	32	while	while	IN
10_1101-2021_01_08_425885	579	33	in	in	IN
10_1101-2021_01_08_425885	579	34	the	the	DT
10_1101-2021_01_08_425885	579	35	latter	latter	JJ
10_1101-2021_01_08_425885	579	36	case	case	NN
10_1101-2021_01_08_425885	579	37	,	,	,
10_1101-2021_01_08_425885	579	38	the	the	DT
10_1101-2021_01_08_425885	579	39	kth	kth	JJ
10_1101-2021_01_08_425885	579	40	normal	normal	JJ
10_1101-2021_01_08_425885	579	41	direction	direction	NN
10_1101-2021_01_08_425885	579	42	might	may	MD
10_1101-2021_01_08_425885	579	43	be	be	VB
10_1101-2021_01_08_425885	579	44	more	more	RBR
10_1101-2021_01_08_425885	579	45	appropriately	appropriately	RB
10_1101-2021_01_08_425885	579	46	classified	classify	VBN
10_1101-2021_01_08_425885	579	47	as	as	IN
10_1101-2021_01_08_425885	579	48	a	a	DT
10_1101-2021_01_08_425885	579	49	tangent	tangent	NN
10_1101-2021_01_08_425885	579	50	direction	direction	NN
10_1101-2021_01_08_425885	579	51	(	(	-LRB-
10_1101-2021_01_08_425885	579	52	d	d	NN
10_1101-2021_01_08_425885	579	53	is	be	VBZ
10_1101-2021_01_08_425885	579	54	too	too	RB
10_1101-2021_01_08_425885	579	55	small	small	JJ
10_1101-2021_01_08_425885	579	56	and	and	CC
10_1101-2021_01_08_425885	579	57	should	should	MD
10_1101-2021_01_08_425885	579	58	be	be	VB
10_1101-2021_01_08_425885	579	59	increased	increase	VBN
10_1101-2021_01_08_425885	579	60	)	)	-RRB-
10_1101-2021_01_08_425885	579	61	.	.	.
10_1101-2021_01_08_425885	580	1	When	when	WRB
10_1101-2021_01_08_425885	580	2	this	this	DT
10_1101-2021_01_08_425885	580	3	criterion	criterion	NN
10_1101-2021_01_08_425885	580	4	is	be	VBZ
10_1101-2021_01_08_425885	580	5	applied	apply	VBN
10_1101-2021_01_08_425885	580	6	point	point	NN
10_1101-2021_01_08_425885	580	7	-	-	HYPH
10_1101-2021_01_08_425885	580	8	wise	wise	JJ
10_1101-2021_01_08_425885	580	9	,	,	,
10_1101-2021_01_08_425885	580	10	33	33	CD
10_1101-2021_01_08_425885	580	11	.CC	.CC	,
10_1101-2021_01_08_425885	580	12	-	-	HYPH
10_1101-2021_01_08_425885	580	13	BY	by	IN
10_1101-2021_01_08_425885	580	14	-	-	HYPH
10_1101-2021_01_08_425885	580	15	NC	NC	NNP
10_1101-2021_01_08_425885	580	16	-	-	HYPH
10_1101-2021_01_08_425885	580	17	ND	ND	NNP
10_1101-2021_01_08_425885	580	18	4.0	4.0	CD
10_1101-2021_01_08_425885	580	19	International	International	NNP
10_1101-2021_01_08_425885	580	20	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	580	21	under	under	IN
10_1101-2021_01_08_425885	580	22	a	a	DT
10_1101-2021_01_08_425885	580	23	(	(	-LRB-
10_1101-2021_01_08_425885	580	24	which	which	WDT
10_1101-2021_01_08_425885	580	25	was	be	VBD
10_1101-2021_01_08_425885	580	26	not	not	RB
10_1101-2021_01_08_425885	580	27	certified	certify	VBN
10_1101-2021_01_08_425885	580	28	by	by	IN
10_1101-2021_01_08_425885	580	29	peer	peer	NN
10_1101-2021_01_08_425885	580	30	review	review	NN
10_1101-2021_01_08_425885	580	31	)	)	-RRB-
10_1101-2021_01_08_425885	580	32	is	be	VBZ
10_1101-2021_01_08_425885	580	33	the	the	DT
10_1101-2021_01_08_425885	580	34	author	author	NN
10_1101-2021_01_08_425885	580	35	/	/	SYM
10_1101-2021_01_08_425885	580	36	funder	funder	NN
10_1101-2021_01_08_425885	580	37	,	,	,
10_1101-2021_01_08_425885	580	38	who	who	WP
10_1101-2021_01_08_425885	580	39	has	have	VBZ
10_1101-2021_01_08_425885	580	40	granted	grant	VBN
10_1101-2021_01_08_425885	580	41	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	580	42	a	a	DT
10_1101-2021_01_08_425885	580	43	license	license	NN
10_1101-2021_01_08_425885	580	44	to	to	TO
10_1101-2021_01_08_425885	580	45	display	display	VB
10_1101-2021_01_08_425885	580	46	the	the	DT
10_1101-2021_01_08_425885	580	47	preprint	preprint	NN
10_1101-2021_01_08_425885	580	48	in	in	IN
10_1101-2021_01_08_425885	580	49	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	580	50	.	.	.
10_1101-2021_01_08_425885	581	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	581	2	is	be	VBZ
10_1101-2021_01_08_425885	581	3	made	make	VBN
10_1101-2021_01_08_425885	581	4	The	the	DT
10_1101-2021_01_08_425885	581	5	copyright	copyright	NN
10_1101-2021_01_08_425885	581	6	holder	holder	NN
10_1101-2021_01_08_425885	581	7	for	for	IN
10_1101-2021_01_08_425885	581	8	this	this	DT
10_1101-2021_01_08_425885	581	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	581	10	version	version	NN
10_1101-2021_01_08_425885	581	11	posted	post	VBD
10_1101-2021_01_08_425885	581	12	January	January	NNP
10_1101-2021_01_08_425885	581	13	8	8	CD
10_1101-2021_01_08_425885	581	14	,	,	,
10_1101-2021_01_08_425885	581	15	2021	2021	CD
10_1101-2021_01_08_425885	581	16	.	.	.
10_1101-2021_01_08_425885	581	17	;	;	:
10_1101-2021_01_08_425885	581	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	581	19	:	:	:
10_1101-2021_01_08_425885	581	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	581	21	preprint	preprint	NN
10_1101-2021_01_08_425885	581	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	581	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	RB
10_1101-2021_01_08_425885	581	24	there	there	EX
10_1101-2021_01_08_425885	581	25	may	may	MD
10_1101-2021_01_08_425885	581	26	be	be	VB
10_1101-2021_01_08_425885	581	27	a	a	DT
10_1101-2021_01_08_425885	581	28	different	different	JJ
10_1101-2021_01_08_425885	581	29	acceptable	acceptable	JJ
10_1101-2021_01_08_425885	581	30	choice	choice	NN
10_1101-2021_01_08_425885	581	31	of	of	IN
10_1101-2021_01_08_425885	581	32	d	d	NN
10_1101-2021_01_08_425885	581	33	for	for	IN
10_1101-2021_01_08_425885	581	34	different	different	JJ
10_1101-2021_01_08_425885	581	35	parts	part	NNS
10_1101-2021_01_08_425885	581	36	of	of	IN
10_1101-2021_01_08_425885	581	37	the	the	DT
10_1101-2021_01_08_425885	581	38	manifold	manifold	NN
10_1101-2021_01_08_425885	581	39	.	.	.
10_1101-2021_01_08_425885	582	1	When	when	WRB
10_1101-2021_01_08_425885	582	2	this	this	DT
10_1101-2021_01_08_425885	582	3	criterion	criterion	NN
10_1101-2021_01_08_425885	582	4	is	be	VBZ
10_1101-2021_01_08_425885	582	5	generalized	generalize	VBN
10_1101-2021_01_08_425885	582	6	over	over	IN
10_1101-2021_01_08_425885	582	7	the	the	DT
10_1101-2021_01_08_425885	582	8	entire	entire	JJ
10_1101-2021_01_08_425885	582	9	manifold	manifold	NN
10_1101-2021_01_08_425885	582	10	,	,	,
10_1101-2021_01_08_425885	582	11	a	a	DT
10_1101-2021_01_08_425885	582	12	σh	σh	NN
10_1101-2021_01_08_425885	582	13	yielding	yield	VBG
10_1101-2021_01_08_425885	582	14	a	a	DT
10_1101-2021_01_08_425885	582	15	flat	flat	JJ
10_1101-2021_01_08_425885	582	16	distribution	distribution	NN
10_1101-2021_01_08_425885	582	17	of	of	IN
10_1101-2021_01_08_425885	582	18	GOF	GOF	NNP
10_1101-2021_01_08_425885	582	19	p	p	NN
10_1101-2021_01_08_425885	582	20	-	-	HYPH
10_1101-2021_01_08_425885	582	21	values	value	NNS
10_1101-2021_01_08_425885	582	22	when	when	WRB
10_1101-2021_01_08_425885	582	23	the	the	DT
10_1101-2021_01_08_425885	582	24	manifold	manifold	JJ
10_1101-2021_01_08_425885	582	25	dimension	dimension	NN
10_1101-2021_01_08_425885	582	26	is	be	VBZ
10_1101-2021_01_08_425885	582	27	specified	specify	VBN
10_1101-2021_01_08_425885	582	28	to	to	TO
10_1101-2021_01_08_425885	582	29	be	be	VB
10_1101-2021_01_08_425885	582	30	d	d	NN
10_1101-2021_01_08_425885	582	31	will	will	MD
10_1101-2021_01_08_425885	582	32	also	also	RB
10_1101-2021_01_08_425885	582	33	yield	yield	VB
10_1101-2021_01_08_425885	582	34	a	a	DT
10_1101-2021_01_08_425885	582	35	flat	flat	JJ
10_1101-2021_01_08_425885	582	36	distribution	distribution	NN
10_1101-2021_01_08_425885	582	37	for	for	IN
10_1101-2021_01_08_425885	582	38	d	d	NN
10_1101-2021_01_08_425885	582	39	+	+	SYM
10_1101-2021_01_08_425885	582	40	1	1	CD
10_1101-2021_01_08_425885	582	41	but	but	CC
10_1101-2021_01_08_425885	582	42	not	not	RB
10_1101-2021_01_08_425885	582	43	necessarily	necessarily	RB
10_1101-2021_01_08_425885	582	44	for	for	IN
10_1101-2021_01_08_425885	582	45	d	d	NN
10_1101-2021_01_08_425885	582	46	−	−	NNP
10_1101-2021_01_08_425885	582	47	1	1	CD
10_1101-2021_01_08_425885	582	48	:	:	:
10_1101-2021_01_08_425885	582	49	if	if	IN
10_1101-2021_01_08_425885	582	50	residuals	residual	NNS
10_1101-2021_01_08_425885	582	51	in	in	IN
10_1101-2021_01_08_425885	582	52	n−d	n−d	NNP
10_1101-2021_01_08_425885	582	53	dimensions	dimension	NNS
10_1101-2021_01_08_425885	582	54	are	be	VBP
10_1101-2021_01_08_425885	582	55	well	well	RB
10_1101-2021_01_08_425885	582	56	-	-	HYPH
10_1101-2021_01_08_425885	582	57	modelled	model	VBN
10_1101-2021_01_08_425885	582	58	by	by	IN
10_1101-2021_01_08_425885	582	59	a	a	DT
10_1101-2021_01_08_425885	582	60	multivariate	multivariate	NN
10_1101-2021_01_08_425885	582	61	Gaussian	Gaussian	NNP
10_1101-2021_01_08_425885	582	62	,	,	,
10_1101-2021_01_08_425885	582	63	so	so	RB
10_1101-2021_01_08_425885	582	64	too	too	RB
10_1101-2021_01_08_425885	582	65	will	will	MD
10_1101-2021_01_08_425885	582	66	residuals	residual	NNS
10_1101-2021_01_08_425885	582	67	in	in	IN
10_1101-2021_01_08_425885	582	68	n−d−1	n−d−1	NNP
10_1101-2021_01_08_425885	582	69	dimensions	dimension	NNS
10_1101-2021_01_08_425885	582	70	,	,	,
10_1101-2021_01_08_425885	582	71	but	but	CC
10_1101-2021_01_08_425885	582	72	not	not	RB
10_1101-2021_01_08_425885	582	73	necessarily	necessarily	RB
10_1101-2021_01_08_425885	582	74	residuals	residual	NNS
10_1101-2021_01_08_425885	582	75	in	in	IN
10_1101-2021_01_08_425885	582	76	n	n	IN
10_1101-2021_01_08_425885	582	77	−	−	NNP
10_1101-2021_01_08_425885	582	78	d	d	NN
10_1101-2021_01_08_425885	582	79	+	+	SYM
10_1101-2021_01_08_425885	582	80	1	1	CD
10_1101-2021_01_08_425885	582	81	dimensions	dimension	NNS
10_1101-2021_01_08_425885	582	82	(	(	-LRB-
10_1101-2021_01_08_425885	582	83	see	see	VB
10_1101-2021_01_08_425885	582	84	Figure	figure	NN
10_1101-2021_01_08_425885	582	85	S2D	s2d	NN
10_1101-2021_01_08_425885	582	86	)	)	-RRB-
10_1101-2021_01_08_425885	582	87	.	.	.
10_1101-2021_01_08_425885	583	1	Our	-PRON-	PRP$
10_1101-2021_01_08_425885	583	2	observations	observation	NNS
10_1101-2021_01_08_425885	583	3	are	be	VBP
10_1101-2021_01_08_425885	583	4	consistent	consistent	JJ
10_1101-2021_01_08_425885	583	5	with	with	IN
10_1101-2021_01_08_425885	583	6	manifolds	manifold	NNS
10_1101-2021_01_08_425885	583	7	in	in	IN
10_1101-2021_01_08_425885	583	8	literature	literature	NN
10_1101-2021_01_08_425885	583	9	with	with	IN
10_1101-2021_01_08_425885	583	10	multiple	multiple	JJ
10_1101-2021_01_08_425885	583	11	possible	possible	JJ
10_1101-2021_01_08_425885	583	12	manifold	manifold	JJ
10_1101-2021_01_08_425885	583	13	dimensions	dimension	NNS
10_1101-2021_01_08_425885	583	14	(	(	-LRB-
10_1101-2021_01_08_425885	583	15	like	like	IN
10_1101-2021_01_08_425885	583	16	the	the	DT
10_1101-2021_01_08_425885	583	17	helix	helix	JJ
10_1101-2021_01_08_425885	583	18	manifold	manifold	NN
10_1101-2021_01_08_425885	583	19	in	in	IN
10_1101-2021_01_08_425885	583	20	[	[	-LRB-
10_1101-2021_01_08_425885	583	21	36	36	CD
10_1101-2021_01_08_425885	583	22	]	]	-RRB-
10_1101-2021_01_08_425885	583	23	)	)	-RRB-
10_1101-2021_01_08_425885	583	24	,	,	,
10_1101-2021_01_08_425885	583	25	and	and	CC
10_1101-2021_01_08_425885	583	26	which	which	WDT
10_1101-2021_01_08_425885	583	27	could	could	MD
10_1101-2021_01_08_425885	583	28	generally	generally	RB
10_1101-2021_01_08_425885	583	29	arise	arise	VB
10_1101-2021_01_08_425885	583	30	from	from	IN
10_1101-2021_01_08_425885	583	31	non	non	JJ
10_1101-2021_01_08_425885	583	32	-	-	JJ
10_1101-2021_01_08_425885	583	33	isotropic	isotropic	JJ
10_1101-2021_01_08_425885	583	34	noise	noise	NN
10_1101-2021_01_08_425885	583	35	or	or	CC
10_1101-2021_01_08_425885	583	36	non	non	JJ
10_1101-2021_01_08_425885	583	37	-	-	JJ
10_1101-2021_01_08_425885	583	38	uniform	uniform	JJ
10_1101-2021_01_08_425885	583	39	sampling	sampling	NN
10_1101-2021_01_08_425885	583	40	.	.	.
10_1101-2021_01_08_425885	584	1	4.4.3	4.4.3	NNP
10_1101-2021_01_08_425885	584	2	Parameters	Parameters	NNPS
10_1101-2021_01_08_425885	584	3	for	for	IN
10_1101-2021_01_08_425885	584	4	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	584	5	Estimation	Estimation	NNP
10_1101-2021_01_08_425885	584	6	For	for	IN
10_1101-2021_01_08_425885	584	7	each	each	DT
10_1101-2021_01_08_425885	584	8	manifold	manifold	NN
10_1101-2021_01_08_425885	584	9	in	in	IN
10_1101-2021_01_08_425885	584	10	Figure	Figure	NNP
10_1101-2021_01_08_425885	584	11	2	2	CD
10_1101-2021_01_08_425885	584	12	,	,	,
10_1101-2021_01_08_425885	584	13	we	-PRON-	PRP
10_1101-2021_01_08_425885	584	14	chose	choose	VBD
10_1101-2021_01_08_425885	584	15	σh	σh	NNP
10_1101-2021_01_08_425885	584	16	so	so	IN
10_1101-2021_01_08_425885	584	17	that	that	IN
10_1101-2021_01_08_425885	584	18	the	the	DT
10_1101-2021_01_08_425885	584	19	fraction	fraction	NN
10_1101-2021_01_08_425885	584	20	of	of	IN
10_1101-2021_01_08_425885	584	21	points	point	NNS
10_1101-2021_01_08_425885	584	22	with	with	IN
10_1101-2021_01_08_425885	584	23	GOF	GOF	NNP
10_1101-2021_01_08_425885	584	24	p	p	NN
10_1101-2021_01_08_425885	584	25	-	-	HYPH
10_1101-2021_01_08_425885	584	26	value	value	NN
10_1101-2021_01_08_425885	584	27	≤	≤	NNP
10_1101-2021_01_08_425885	584	28	α	α	NNP
10_1101-2021_01_08_425885	584	29	=	=	SYM
10_1101-2021_01_08_425885	584	30	0.05	0.05	CD
10_1101-2021_01_08_425885	584	31	most	most	RBS
10_1101-2021_01_08_425885	584	32	closely	closely	RB
10_1101-2021_01_08_425885	584	33	matched	match	VBN
10_1101-2021_01_08_425885	584	34	the	the	DT
10_1101-2021_01_08_425885	584	35	null	null	JJ
10_1101-2021_01_08_425885	584	36	model	model	NN
10_1101-2021_01_08_425885	584	37	of	of	IN
10_1101-2021_01_08_425885	584	38	normally	normally	RB
10_1101-2021_01_08_425885	584	39	distributed	distribute	VBN
10_1101-2021_01_08_425885	584	40	residuals	residual	NNS
10_1101-2021_01_08_425885	584	41	consistent	consistent	JJ
10_1101-2021_01_08_425885	584	42	with	with	IN
10_1101-2021_01_08_425885	584	43	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	584	44	sizes	size	VBZ
10_1101-2021_01_08_425885	584	45	well	well	RB
10_1101-2021_01_08_425885	584	46	-	-	HYPH
10_1101-2021_01_08_425885	584	47	approximated	approximate	VBN
10_1101-2021_01_08_425885	584	48	by	by	IN
10_1101-2021_01_08_425885	584	49	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	584	50	regression	regression	NN
10_1101-2021_01_08_425885	584	51	(	(	-LRB-
10_1101-2021_01_08_425885	584	52	see	see	VB
10_1101-2021_01_08_425885	584	53	Section	Section	NNP
10_1101-2021_01_08_425885	584	54	4.3.3	4.3.3	CD
10_1101-2021_01_08_425885	584	55	)	)	-RRB-
10_1101-2021_01_08_425885	584	56	.	.	.
10_1101-2021_01_08_425885	585	1	σh	σh	NNP
10_1101-2021_01_08_425885	585	2	=	=	FW
10_1101-2021_01_08_425885	585	3	(	(	-LRB-
10_1101-2021_01_08_425885	585	4	0.017	0.017	CD
10_1101-2021_01_08_425885	585	5	,	,	,
10_1101-2021_01_08_425885	585	6	0.020	0.020	CD
10_1101-2021_01_08_425885	585	7	,	,	,
10_1101-2021_01_08_425885	585	8	0.028	0.028	CD
10_1101-2021_01_08_425885	585	9	,	,	,
10_1101-2021_01_08_425885	585	10	0.055	0.055	CD
10_1101-2021_01_08_425885	585	11	,	,	,
10_1101-2021_01_08_425885	585	12	0.022	0.022	CD
10_1101-2021_01_08_425885	585	13	,	,	,
10_1101-2021_01_08_425885	585	14	0.030	0.030	CD
10_1101-2021_01_08_425885	585	15	)	)	-RRB-
10_1101-2021_01_08_425885	585	16	for	for	IN
10_1101-2021_01_08_425885	585	17	(	(	-LRB-
10_1101-2021_01_08_425885	585	18	S2,S3,S5,S7,H22,T	s2,s3,s5,s7,h22,t	PRP$
10_1101-2021_01_08_425885	585	19	2	2	CD
10_1101-2021_01_08_425885	585	20	)	)	-RRB-
10_1101-2021_01_08_425885	585	21	resulted	result	VBD
10_1101-2021_01_08_425885	585	22	in	in	IN
10_1101-2021_01_08_425885	585	23	(	(	-LRB-
10_1101-2021_01_08_425885	585	24	7.4	7.4	CD
10_1101-2021_01_08_425885	585	25	,	,	,
10_1101-2021_01_08_425885	585	26	3.5	3.5	CD
10_1101-2021_01_08_425885	585	27	,	,	,
10_1101-2021_01_08_425885	585	28	1.4	1.4	CD
10_1101-2021_01_08_425885	585	29	,	,	,
10_1101-2021_01_08_425885	585	30	2.8	2.8	CD
10_1101-2021_01_08_425885	585	31	,	,	,
10_1101-2021_01_08_425885	585	32	7.4	7.4	CD
10_1101-2021_01_08_425885	585	33	,	,	,
10_1101-2021_01_08_425885	585	34	4.0)%	4.0)%	NNP
10_1101-2021_01_08_425885	585	35	of	of	IN
10_1101-2021_01_08_425885	585	36	points	point	NNS
10_1101-2021_01_08_425885	585	37	having	have	VBG
10_1101-2021_01_08_425885	585	38	GOF	GOF	NNP
10_1101-2021_01_08_425885	585	39	p	p	NN
10_1101-2021_01_08_425885	585	40	-	-	HYPH
10_1101-2021_01_08_425885	585	41	values	value	NNS
10_1101-2021_01_08_425885	585	42	≤	≤	NNP
10_1101-2021_01_08_425885	585	43	α	α	NNP
10_1101-2021_01_08_425885	585	44	=	=	SYM
10_1101-2021_01_08_425885	585	45	0.05	0.05	CD
10_1101-2021_01_08_425885	585	46	.	.	.
10_1101-2021_01_08_425885	586	1	Theoretically	theoretically	RB
10_1101-2021_01_08_425885	586	2	,	,	,
10_1101-2021_01_08_425885	586	3	max	max	NNP
10_1101-2021_01_08_425885	586	4	|hkij|	|hkij|	NNP
10_1101-2021_01_08_425885	586	5	=	=	SYM
10_1101-2021_01_08_425885	586	6	(	(	-LRB-
10_1101-2021_01_08_425885	586	7	0.5	0.5	CD
10_1101-2021_01_08_425885	586	8	,	,	,
10_1101-2021_01_08_425885	586	9	2	2	CD
10_1101-2021_01_08_425885	586	10	,	,	,
10_1101-2021_01_08_425885	586	11	2.5	2.5	CD
10_1101-2021_01_08_425885	586	12	)	)	-RRB-
10_1101-2021_01_08_425885	586	13	for	for	IN
10_1101-2021_01_08_425885	586	14	(	(	-LRB-
10_1101-2021_01_08_425885	586	15	S	S	NNP
10_1101-2021_01_08_425885	586	16	d	d	NNP
10_1101-2021_01_08_425885	586	17	,	,	,
10_1101-2021_01_08_425885	586	18	H22,T	h22,t	NN
10_1101-2021_01_08_425885	586	19	2	2	CD
10_1101-2021_01_08_425885	586	20	)	)	-RRB-
10_1101-2021_01_08_425885	586	21	so	so	CC
10_1101-2021_01_08_425885	586	22	our	-PRON-	PRP$
10_1101-2021_01_08_425885	586	23	choices	choice	NNS
10_1101-2021_01_08_425885	586	24	for	for	IN
10_1101-2021_01_08_425885	586	25	σh	σh	NNP
10_1101-2021_01_08_425885	586	26	result	result	NN
10_1101-2021_01_08_425885	586	27	in	in	IN
10_1101-2021_01_08_425885	586	28	small	small	JJ
10_1101-2021_01_08_425885	586	29	fractional	fractional	JJ
10_1101-2021_01_08_425885	586	30	errors	error	NNS
10_1101-2021_01_08_425885	586	31	in	in	IN
10_1101-2021_01_08_425885	586	32	all	all	DT
10_1101-2021_01_08_425885	586	33	cases	case	NNS
10_1101-2021_01_08_425885	586	34	.	.	.
10_1101-2021_01_08_425885	587	1	For	for	IN
10_1101-2021_01_08_425885	587	2	Figure	figure	NN
10_1101-2021_01_08_425885	587	3	S2A	s2a	NN
10_1101-2021_01_08_425885	587	4	,	,	,
10_1101-2021_01_08_425885	587	5	we	-PRON-	PRP
10_1101-2021_01_08_425885	587	6	set	set	VBP
10_1101-2021_01_08_425885	587	7	σh	σh	NNP
10_1101-2021_01_08_425885	587	8	=	=	FW
10_1101-2021_01_08_425885	587	9	(	(	-LRB-
10_1101-2021_01_08_425885	587	10	0.02	0.02	CD
10_1101-2021_01_08_425885	587	11	,	,	,
10_1101-2021_01_08_425885	587	12	0.01	0.01	CD
10_1101-2021_01_08_425885	587	13	)	)	-RRB-
10_1101-2021_01_08_425885	587	14	for	for	IN
10_1101-2021_01_08_425885	587	15	N2	N2	NNP
10_1101-2021_01_08_425885	587	16	=	=	SYM
10_1101-2021_01_08_425885	587	17	(	(	-LRB-
10_1101-2021_01_08_425885	587	18	10	10	CD
10_1101-2021_01_08_425885	587	19	3	3	CD
10_1101-2021_01_08_425885	587	20	,	,	,
10_1101-2021_01_08_425885	587	21	104	104	CD
10_1101-2021_01_08_425885	587	22	)	)	-RRB-
10_1101-2021_01_08_425885	587	23	respectively	respectively	RB
10_1101-2021_01_08_425885	587	24	which	which	WDT
10_1101-2021_01_08_425885	587	25	resulted	result	VBD
10_1101-2021_01_08_425885	587	26	in	in	IN
10_1101-2021_01_08_425885	587	27	(	(	-LRB-
10_1101-2021_01_08_425885	587	28	1.6	1.6	CD
10_1101-2021_01_08_425885	587	29	,	,	,
10_1101-2021_01_08_425885	587	30	2.5)%	2.5)%	CD
10_1101-2021_01_08_425885	587	31	of	of	IN
10_1101-2021_01_08_425885	587	32	points	point	NNS
10_1101-2021_01_08_425885	587	33	having	have	VBG
10_1101-2021_01_08_425885	587	34	GOF	GOF	NNP
10_1101-2021_01_08_425885	587	35	p	p	NN
10_1101-2021_01_08_425885	587	36	-	-	HYPH
10_1101-2021_01_08_425885	587	37	values	value	NNS
10_1101-2021_01_08_425885	587	38	≤	≤	NNP
10_1101-2021_01_08_425885	587	39	α	α	NNP
10_1101-2021_01_08_425885	587	40	=	=	SYM
10_1101-2021_01_08_425885	587	41	0.05	0.05	CD
10_1101-2021_01_08_425885	587	42	.	.	.
10_1101-2021_01_08_425885	588	1	For	for	IN
10_1101-2021_01_08_425885	588	2	all	all	DT
10_1101-2021_01_08_425885	588	3	other	other	JJ
10_1101-2021_01_08_425885	588	4	panels	panel	NNS
10_1101-2021_01_08_425885	588	5	in	in	IN
10_1101-2021_01_08_425885	588	6	Figure	Figure	NNP
10_1101-2021_01_08_425885	588	7	S2	s2	NN
10_1101-2021_01_08_425885	588	8	,	,	,
10_1101-2021_01_08_425885	588	9	where	where	WRB
10_1101-2021_01_08_425885	588	10	we	-PRON-	PRP
10_1101-2021_01_08_425885	588	11	were	be	VBD
10_1101-2021_01_08_425885	588	12	interested	interested	JJ
10_1101-2021_01_08_425885	588	13	in	in	IN
10_1101-2021_01_08_425885	588	14	ascertaining	ascertain	VBG
10_1101-2021_01_08_425885	588	15	the	the	DT
10_1101-2021_01_08_425885	588	16	sensitivity	sensitivity	NN
10_1101-2021_01_08_425885	588	17	to	to	IN
10_1101-2021_01_08_425885	588	18	different	different	JJ
10_1101-2021_01_08_425885	588	19	confounders	confounder	NNS
10_1101-2021_01_08_425885	588	20	,	,	,
10_1101-2021_01_08_425885	588	21	instead	instead	RB
10_1101-2021_01_08_425885	588	22	of	of	IN
10_1101-2021_01_08_425885	588	23	minimizing	minimize	VBG
10_1101-2021_01_08_425885	588	24	uncertainty	uncertainty	NN
10_1101-2021_01_08_425885	588	25	per	per	FW
10_1101-2021_01_08_425885	588	26	se	se	FW
10_1101-2021_01_08_425885	588	27	,	,	,
10_1101-2021_01_08_425885	588	28	we	-PRON-	PRP
10_1101-2021_01_08_425885	588	29	used	use	VBD
10_1101-2021_01_08_425885	588	30	a	a	DT
10_1101-2021_01_08_425885	588	31	fixed	fix	VBN
10_1101-2021_01_08_425885	588	32	value	value	NN
10_1101-2021_01_08_425885	588	33	of	of	IN
10_1101-2021_01_08_425885	588	34	σh	σh	NNP
10_1101-2021_01_08_425885	588	35	=	=	SYM
10_1101-2021_01_08_425885	588	36	0.05	0.05	CD
10_1101-2021_01_08_425885	588	37	.	.	.
10_1101-2021_01_08_425885	589	1	This	this	DT
10_1101-2021_01_08_425885	589	2	choice	choice	NN
10_1101-2021_01_08_425885	589	3	resulted	result	VBD
10_1101-2021_01_08_425885	589	4	in	in	IN
10_1101-2021_01_08_425885	589	5	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	589	6	small	small	JJ
10_1101-2021_01_08_425885	589	7	enough	enough	RB
10_1101-2021_01_08_425885	589	8	to	to	TO
10_1101-2021_01_08_425885	589	9	be	be	VB
10_1101-2021_01_08_425885	589	10	well	well	RB
10_1101-2021_01_08_425885	589	11	-	-	HYPH
10_1101-2021_01_08_425885	589	12	approximated	approximate	VBN
10_1101-2021_01_08_425885	589	13	by	by	IN
10_1101-2021_01_08_425885	589	14	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	589	15	regression	regression	NN
10_1101-2021_01_08_425885	589	16	,	,	,
10_1101-2021_01_08_425885	589	17	manifesting	manifest	VBG
10_1101-2021_01_08_425885	589	18	as	as	IN
10_1101-2021_01_08_425885	589	19	a	a	DT
10_1101-2021_01_08_425885	589	20	roughly	roughly	RB
10_1101-2021_01_08_425885	589	21	uniform	uniform	JJ
10_1101-2021_01_08_425885	589	22	distribution	distribution	NN
10_1101-2021_01_08_425885	589	23	of	of	IN
10_1101-2021_01_08_425885	589	24	GOF	GOF	NNP
10_1101-2021_01_08_425885	589	25	p	p	NN
10_1101-2021_01_08_425885	589	26	-	-	HYPH
10_1101-2021_01_08_425885	589	27	values	value	NNS
10_1101-2021_01_08_425885	589	28	in	in	IN
10_1101-2021_01_08_425885	589	29	all	all	DT
10_1101-2021_01_08_425885	589	30	cases	case	NNS
10_1101-2021_01_08_425885	589	31	.	.	.
10_1101-2021_01_08_425885	590	1	4.5	4.5	CD
10_1101-2021_01_08_425885	590	2	Details	detail	NNS
10_1101-2021_01_08_425885	590	3	of	of	IN
10_1101-2021_01_08_425885	590	4	Image	Image	NNP
10_1101-2021_01_08_425885	590	5	Patch	Patch	NNP
10_1101-2021_01_08_425885	590	6	Dataset	Dataset	NNP
10_1101-2021_01_08_425885	590	7	and	and	CC
10_1101-2021_01_08_425885	590	8	Klein	Klein	NNP
10_1101-2021_01_08_425885	590	9	Bottle	Bottle	NNP
10_1101-2021_01_08_425885	590	10	Manifolds	Manifolds	NNP
10_1101-2021_01_08_425885	590	11	4.5.1	4.5.1	CD
10_1101-2021_01_08_425885	590	12	Notation	Notation	NNP
10_1101-2021_01_08_425885	590	13	and	and	CC
10_1101-2021_01_08_425885	590	14	Preliminaries	Preliminaries	NNPS
10_1101-2021_01_08_425885	590	15	First	first	RB
10_1101-2021_01_08_425885	590	16	we	-PRON-	PRP
10_1101-2021_01_08_425885	590	17	introduce	introduce	VBP
10_1101-2021_01_08_425885	590	18	some	some	DT
10_1101-2021_01_08_425885	590	19	notation	notation	NN
10_1101-2021_01_08_425885	590	20	needed	need	VBN
10_1101-2021_01_08_425885	590	21	to	to	TO
10_1101-2021_01_08_425885	590	22	describe	describe	VB
10_1101-2021_01_08_425885	590	23	the	the	DT
10_1101-2021_01_08_425885	590	24	image	image	NN
10_1101-2021_01_08_425885	590	25	patch	patch	NN
10_1101-2021_01_08_425885	590	26	dataset	dataset	NN
10_1101-2021_01_08_425885	590	27	.	.	.
10_1101-2021_01_08_425885	591	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	591	2	refer	refer	VBP
10_1101-2021_01_08_425885	591	3	readers	reader	NNS
10_1101-2021_01_08_425885	591	4	to	to	IN
10_1101-2021_01_08_425885	591	5	[	[	-LRB-
10_1101-2021_01_08_425885	591	6	21	21	CD
10_1101-2021_01_08_425885	591	7	,	,	,
10_1101-2021_01_08_425885	591	8	40	40	CD
10_1101-2021_01_08_425885	591	9	]	]	-RRB-
10_1101-2021_01_08_425885	591	10	for	for	IN
10_1101-2021_01_08_425885	591	11	a	a	DT
10_1101-2021_01_08_425885	591	12	more	more	RBR
10_1101-2021_01_08_425885	591	13	detailed	detailed	JJ
10_1101-2021_01_08_425885	591	14	exposition	exposition	NN
10_1101-2021_01_08_425885	591	15	.	.	.
10_1101-2021_01_08_425885	592	1	Let	let	VB
10_1101-2021_01_08_425885	592	2	P	p	PRP
10_1101-2021_01_08_425885	592	3	be	be	VB
10_1101-2021_01_08_425885	592	4	the	the	DT
10_1101-2021_01_08_425885	592	5	space	space	NN
10_1101-2021_01_08_425885	592	6	of	of	IN
10_1101-2021_01_08_425885	592	7	all	all	DT
10_1101-2021_01_08_425885	592	8	bivariate	bivariate	JJ
10_1101-2021_01_08_425885	592	9	polynomials	polynomial	NNS
10_1101-2021_01_08_425885	592	10	p	p	XX
10_1101-2021_01_08_425885	592	11	:	:	:
10_1101-2021_01_08_425885	592	12	R	r	NN
10_1101-2021_01_08_425885	592	13	×	×	NN
10_1101-2021_01_08_425885	592	14	R	r	NN
10_1101-2021_01_08_425885	592	15	→	→	SYM
10_1101-2021_01_08_425885	592	16	R	r	NN
10_1101-2021_01_08_425885	592	17	with	with	IN
10_1101-2021_01_08_425885	592	18	p	p	NN
10_1101-2021_01_08_425885	592	19	∈	∈	NNP
10_1101-2021_01_08_425885	592	20	P	p	NN
10_1101-2021_01_08_425885	592	21	,	,	,
10_1101-2021_01_08_425885	592	22	h	h	NN
10_1101-2021_01_08_425885	592	23	:	:	:
10_1101-2021_01_08_425885	592	24	P	p	NN
10_1101-2021_01_08_425885	592	25	→	→	SYM
10_1101-2021_01_08_425885	592	26	R9	r9	VB
10_1101-2021_01_08_425885	592	27	the	the	DT
10_1101-2021_01_08_425885	592	28	vectorization	vectorization	NN
10_1101-2021_01_08_425885	592	29	operator	operator	NN
10_1101-2021_01_08_425885	592	30	given	give	VBN
10_1101-2021_01_08_425885	592	31	by	by	IN
10_1101-2021_01_08_425885	592	32	h(p	h(p	NNP
10_1101-2021_01_08_425885	592	33	)	)	-RRB-
10_1101-2021_01_08_425885	592	34	=	=	NFP
10_1101-2021_01_08_425885	592	35	[	[	-LRB-
10_1101-2021_01_08_425885	592	36	p(−1	p(−1	JJ
10_1101-2021_01_08_425885	592	37	,	,	,
10_1101-2021_01_08_425885	592	38	1),p(−1	1),p(−1	NNP
10_1101-2021_01_08_425885	592	39	,	,	,
10_1101-2021_01_08_425885	592	40	0),p(−1,−1),p(0	0),p(−1,−1),p(0	CD
10_1101-2021_01_08_425885	592	41	,	,	,
10_1101-2021_01_08_425885	592	42	1),p(0	1),p(0	CD
10_1101-2021_01_08_425885	592	43	,	,	,
10_1101-2021_01_08_425885	592	44	0),p(0,−1	0),p(0,−1	NNP
10_1101-2021_01_08_425885	592	45	)	)	-RRB-
10_1101-2021_01_08_425885	592	46	,	,	,
10_1101-2021_01_08_425885	592	47	p(1	p(1	NNP
10_1101-2021_01_08_425885	592	48	,	,	,
10_1101-2021_01_08_425885	592	49	1),p(1	1),p(1	CD
10_1101-2021_01_08_425885	592	50	,	,	,
10_1101-2021_01_08_425885	592	51	0),p(1,−1)]T	0),p(1,−1)]t	CD
10_1101-2021_01_08_425885	592	52	,	,	,
10_1101-2021_01_08_425885	592	53	u	u	NN
10_1101-2021_01_08_425885	592	54	:	:	:
10_1101-2021_01_08_425885	592	55	Rm	Rm	NNP
10_1101-2021_01_08_425885	592	56	→Sm−1	→Sm−1	VBZ
10_1101-2021_01_08_425885	592	57	the	the	DT
10_1101-2021_01_08_425885	592	58	normalization	normalization	NN
10_1101-2021_01_08_425885	592	59	operator	operator	NN
10_1101-2021_01_08_425885	592	60	given	give	VBN
10_1101-2021_01_08_425885	592	61	by	by	IN
10_1101-2021_01_08_425885	592	62	u(v	u(v	NNP
10_1101-2021_01_08_425885	592	63	)	)	-RRB-
10_1101-2021_01_08_425885	592	64	=	=	NFP
10_1101-2021_01_08_425885	592	65	v‖v‖2	v‖v‖2	NNP
10_1101-2021_01_08_425885	592	66	,	,	,
10_1101-2021_01_08_425885	592	67	and	and	CC
10_1101-2021_01_08_425885	592	68	c	c	NN
10_1101-2021_01_08_425885	592	69	:	:	:
10_1101-2021_01_08_425885	592	70	R	r	NN
10_1101-2021_01_08_425885	592	71	9	9	CD
10_1101-2021_01_08_425885	592	72	→	→	SYM
10_1101-2021_01_08_425885	592	73	R8	R8	VBZ
10_1101-2021_01_08_425885	592	74	the	the	DT
10_1101-2021_01_08_425885	592	75	projection	projection	NN
10_1101-2021_01_08_425885	592	76	operator	operator	NN
10_1101-2021_01_08_425885	592	77	given	give	VBN
10_1101-2021_01_08_425885	592	78	by	by	IN
10_1101-2021_01_08_425885	592	79	c(y	c(y	NNP
10_1101-2021_01_08_425885	592	80	)	)	-RRB-
10_1101-2021_01_08_425885	592	81	=	=	NFP
10_1101-2021_01_08_425885	592	82	ΛATy	ΛATy	NNS
10_1101-2021_01_08_425885	592	83	,	,	,
10_1101-2021_01_08_425885	592	84	where	where	WRB
10_1101-2021_01_08_425885	592	85	A	a	NN
10_1101-2021_01_08_425885	592	86	=	=	SYM
10_1101-2021_01_08_425885	592	87	[	[	-LRB-
10_1101-2021_01_08_425885	592	88	e1	e1	NN
10_1101-2021_01_08_425885	592	89	.	.	.
10_1101-2021_01_08_425885	593	1	.	.	.
10_1101-2021_01_08_425885	594	1	.	.	.
10_1101-2021_01_08_425885	595	1	e8	e8	NNP
10_1101-2021_01_08_425885	595	2	]	]	-RRB-
10_1101-2021_01_08_425885	595	3	,	,	,
10_1101-2021_01_08_425885	595	4	Λ	λ	NN
10_1101-2021_01_08_425885	595	5	=	=	SYM
10_1101-2021_01_08_425885	595	6	diag	diag	VBP
10_1101-2021_01_08_425885	595	7	{	{	-LRB-
10_1101-2021_01_08_425885	595	8	1‖e1‖22	1‖e1‖22	NNS
10_1101-2021_01_08_425885	595	9	,	,	,
10_1101-2021_01_08_425885	595	10	...	...	NFP
10_1101-2021_01_08_425885	595	11	,	,	,
10_1101-2021_01_08_425885	595	12	1	1	CD
10_1101-2021_01_08_425885	595	13	‖e8‖22	‖e8‖22	NNP
10_1101-2021_01_08_425885	595	14	}	}	-RRB-
10_1101-2021_01_08_425885	595	15	,	,	,
10_1101-2021_01_08_425885	595	16	and	and	CC
10_1101-2021_01_08_425885	595	17	{	{	-LRB-
10_1101-2021_01_08_425885	595	18	ei	ei	NNP
10_1101-2021_01_08_425885	595	19	}	}	-RRB-
10_1101-2021_01_08_425885	595	20	34	34	CD
10_1101-2021_01_08_425885	595	21	.CC	.CC	NFP
10_1101-2021_01_08_425885	595	22	-	-	HYPH
10_1101-2021_01_08_425885	595	23	BY	by	IN
10_1101-2021_01_08_425885	595	24	-	-	HYPH
10_1101-2021_01_08_425885	595	25	NC	NC	NNP
10_1101-2021_01_08_425885	595	26	-	-	HYPH
10_1101-2021_01_08_425885	595	27	ND	ND	NNP
10_1101-2021_01_08_425885	595	28	4.0	4.0	CD
10_1101-2021_01_08_425885	595	29	International	International	NNP
10_1101-2021_01_08_425885	595	30	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	595	31	under	under	IN
10_1101-2021_01_08_425885	595	32	a	a	DT
10_1101-2021_01_08_425885	595	33	(	(	-LRB-
10_1101-2021_01_08_425885	595	34	which	which	WDT
10_1101-2021_01_08_425885	595	35	was	be	VBD
10_1101-2021_01_08_425885	595	36	not	not	RB
10_1101-2021_01_08_425885	595	37	certified	certify	VBN
10_1101-2021_01_08_425885	595	38	by	by	IN
10_1101-2021_01_08_425885	595	39	peer	peer	NN
10_1101-2021_01_08_425885	595	40	review	review	NN
10_1101-2021_01_08_425885	595	41	)	)	-RRB-
10_1101-2021_01_08_425885	595	42	is	be	VBZ
10_1101-2021_01_08_425885	595	43	the	the	DT
10_1101-2021_01_08_425885	595	44	author	author	NN
10_1101-2021_01_08_425885	595	45	/	/	SYM
10_1101-2021_01_08_425885	595	46	funder	funder	NN
10_1101-2021_01_08_425885	595	47	,	,	,
10_1101-2021_01_08_425885	595	48	who	who	WP
10_1101-2021_01_08_425885	595	49	has	have	VBZ
10_1101-2021_01_08_425885	595	50	granted	grant	VBN
10_1101-2021_01_08_425885	595	51	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	595	52	a	a	DT
10_1101-2021_01_08_425885	595	53	license	license	NN
10_1101-2021_01_08_425885	595	54	to	to	TO
10_1101-2021_01_08_425885	595	55	display	display	VB
10_1101-2021_01_08_425885	595	56	the	the	DT
10_1101-2021_01_08_425885	595	57	preprint	preprint	NN
10_1101-2021_01_08_425885	595	58	in	in	IN
10_1101-2021_01_08_425885	595	59	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	595	60	.	.	.
10_1101-2021_01_08_425885	596	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	596	2	is	be	VBZ
10_1101-2021_01_08_425885	596	3	made	make	VBN
10_1101-2021_01_08_425885	596	4	The	the	DT
10_1101-2021_01_08_425885	596	5	copyright	copyright	NN
10_1101-2021_01_08_425885	596	6	holder	holder	NN
10_1101-2021_01_08_425885	596	7	for	for	IN
10_1101-2021_01_08_425885	596	8	this	this	DT
10_1101-2021_01_08_425885	596	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	596	10	version	version	NN
10_1101-2021_01_08_425885	596	11	posted	post	VBD
10_1101-2021_01_08_425885	596	12	January	January	NNP
10_1101-2021_01_08_425885	596	13	8	8	CD
10_1101-2021_01_08_425885	596	14	,	,	,
10_1101-2021_01_08_425885	596	15	2021	2021	CD
10_1101-2021_01_08_425885	596	16	.	.	.
10_1101-2021_01_08_425885	596	17	;	;	:
10_1101-2021_01_08_425885	596	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	596	19	:	:	:
10_1101-2021_01_08_425885	596	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	596	21	preprint	preprint	NN
10_1101-2021_01_08_425885	596	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	NNP
10_1101-2021_01_08_425885	596	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	CD
10_1101-2021_01_08_425885	596	24	are	be	VBP
10_1101-2021_01_08_425885	596	25	vectorized	vectorize	VBN
10_1101-2021_01_08_425885	596	26	basis	basis	NN
10_1101-2021_01_08_425885	596	27	vectors	vector	NNS
10_1101-2021_01_08_425885	596	28	for	for	IN
10_1101-2021_01_08_425885	596	29	the	the	DT
10_1101-2021_01_08_425885	596	30	2-dimensional	2-dimensional	CD
10_1101-2021_01_08_425885	596	31	discrete	discrete	JJ
10_1101-2021_01_08_425885	596	32	cosine	cosine	NN
10_1101-2021_01_08_425885	596	33	transform	transform	NN
10_1101-2021_01_08_425885	596	34	(	(	-LRB-
10_1101-2021_01_08_425885	596	35	DCT	dct	NN
10_1101-2021_01_08_425885	596	36	)	)	-RRB-
10_1101-2021_01_08_425885	596	37	applied	apply	VBD
10_1101-2021_01_08_425885	596	38	to	to	IN
10_1101-2021_01_08_425885	596	39	3x3	3x3	CD
10_1101-2021_01_08_425885	596	40	patches	patch	NNS
10_1101-2021_01_08_425885	596	41	:	:	:
10_1101-2021_01_08_425885	596	42	e1	e1	NNP
10_1101-2021_01_08_425885	596	43	=	=	NFP
10_1101-2021_01_08_425885	596	44	[	[	-LRB-
10_1101-2021_01_08_425885	596	45	1	1	CD
10_1101-2021_01_08_425885	596	46	,	,	,
10_1101-2021_01_08_425885	596	47	0,−1	0,−1	CD
10_1101-2021_01_08_425885	596	48	,	,	,
10_1101-2021_01_08_425885	596	49	1	1	CD
10_1101-2021_01_08_425885	596	50	,	,	,
10_1101-2021_01_08_425885	596	51	0,−1	0,−1	CD
10_1101-2021_01_08_425885	596	52	,	,	,
10_1101-2021_01_08_425885	596	53	1	1	CD
10_1101-2021_01_08_425885	596	54	,	,	,
10_1101-2021_01_08_425885	596	55	0,−1]T/	0,−1]T/	.
10_1101-2021_01_08_425885	596	56	√	√	NNP
10_1101-2021_01_08_425885	596	57	6	6	CD
10_1101-2021_01_08_425885	596	58	e2	e2	NN
10_1101-2021_01_08_425885	596	59	=	=	SYM
10_1101-2021_01_08_425885	596	60	[	[	-LRB-
10_1101-2021_01_08_425885	596	61	1	1	CD
10_1101-2021_01_08_425885	596	62	,	,	,
10_1101-2021_01_08_425885	596	63	1	1	CD
10_1101-2021_01_08_425885	596	64	,	,	,
10_1101-2021_01_08_425885	596	65	1	1	CD
10_1101-2021_01_08_425885	596	66	,	,	,
10_1101-2021_01_08_425885	596	67	0	0	CD
10_1101-2021_01_08_425885	596	68	,	,	,
10_1101-2021_01_08_425885	596	69	0	0	CD
10_1101-2021_01_08_425885	596	70	,	,	,
10_1101-2021_01_08_425885	596	71	0,−1,−1,−1]T/	0,−1,−1,−1]t/	CD
10_1101-2021_01_08_425885	596	72	√	√	NNP
10_1101-2021_01_08_425885	596	73	6	6	CD
10_1101-2021_01_08_425885	596	74	e3	e3	NN
10_1101-2021_01_08_425885	596	75	=	=	NFP
10_1101-2021_01_08_425885	596	76	[	[	-LRB-
10_1101-2021_01_08_425885	596	77	1,−2	1,−2	CD
10_1101-2021_01_08_425885	596	78	,	,	,
10_1101-2021_01_08_425885	596	79	1	1	CD
10_1101-2021_01_08_425885	596	80	,	,	,
10_1101-2021_01_08_425885	596	81	1,−2	1,−2	CD
10_1101-2021_01_08_425885	596	82	,	,	,
10_1101-2021_01_08_425885	596	83	1	1	CD
10_1101-2021_01_08_425885	596	84	,	,	,
10_1101-2021_01_08_425885	596	85	1,−2	1,−2	CD
10_1101-2021_01_08_425885	596	86	,	,	,
10_1101-2021_01_08_425885	596	87	1]T/	1]t/	CD
10_1101-2021_01_08_425885	596	88	√	√	NN
10_1101-2021_01_08_425885	596	89	54	54	CD
10_1101-2021_01_08_425885	596	90	e4	e4	NN
10_1101-2021_01_08_425885	596	91	=	=	SYM
10_1101-2021_01_08_425885	596	92	[	[	-LRB-
10_1101-2021_01_08_425885	596	93	1	1	CD
10_1101-2021_01_08_425885	596	94	,	,	,
10_1101-2021_01_08_425885	596	95	1	1	CD
10_1101-2021_01_08_425885	596	96	,	,	,
10_1101-2021_01_08_425885	596	97	1,−2,−2,−2	1,−2,−2,−2	CD
10_1101-2021_01_08_425885	596	98	,	,	,
10_1101-2021_01_08_425885	596	99	1	1	CD
10_1101-2021_01_08_425885	596	100	,	,	,
10_1101-2021_01_08_425885	596	101	1	1	CD
10_1101-2021_01_08_425885	596	102	,	,	,
10_1101-2021_01_08_425885	596	103	1]T/	1]t/	CD
10_1101-2021_01_08_425885	596	104	√	√	NN
10_1101-2021_01_08_425885	596	105	54	54	CD
10_1101-2021_01_08_425885	596	106	e5	e5	NN
10_1101-2021_01_08_425885	596	107	=	=	NNS
10_1101-2021_01_08_425885	596	108	[	[	-LRB-
10_1101-2021_01_08_425885	596	109	1	1	CD
10_1101-2021_01_08_425885	596	110	,	,	,
10_1101-2021_01_08_425885	596	111	0,−1	0,−1	CD
10_1101-2021_01_08_425885	596	112	,	,	,
10_1101-2021_01_08_425885	596	113	0	0	CD
10_1101-2021_01_08_425885	596	114	,	,	,
10_1101-2021_01_08_425885	596	115	0	0	CD
10_1101-2021_01_08_425885	596	116	,	,	,
10_1101-2021_01_08_425885	596	117	0,−1	0,−1	CD
10_1101-2021_01_08_425885	596	118	,	,	,
10_1101-2021_01_08_425885	596	119	0	0	CD
10_1101-2021_01_08_425885	596	120	,	,	,
10_1101-2021_01_08_425885	596	121	1]T/	1]t/	CD
10_1101-2021_01_08_425885	596	122	√	√	NN
10_1101-2021_01_08_425885	596	123	8	8	CD
10_1101-2021_01_08_425885	596	124	e6	e6	NN
10_1101-2021_01_08_425885	596	125	=	=	:
10_1101-2021_01_08_425885	596	126	[	[	-LRB-
10_1101-2021_01_08_425885	596	127	1	1	CD
10_1101-2021_01_08_425885	596	128	,	,	,
10_1101-2021_01_08_425885	596	129	0,−1,−2	0,−1,−2	CD
10_1101-2021_01_08_425885	596	130	,	,	,
10_1101-2021_01_08_425885	596	131	0	0	CD
10_1101-2021_01_08_425885	596	132	,	,	,
10_1101-2021_01_08_425885	596	133	2	2	CD
10_1101-2021_01_08_425885	596	134	,	,	,
10_1101-2021_01_08_425885	596	135	1	1	CD
10_1101-2021_01_08_425885	596	136	,	,	,
10_1101-2021_01_08_425885	596	137	0,−1]T/	0,−1]T/	.
10_1101-2021_01_08_425885	596	138	√	√	NNP
10_1101-2021_01_08_425885	596	139	48	48	CD
10_1101-2021_01_08_425885	596	140	e7	e7	NN
10_1101-2021_01_08_425885	596	141	=	=	SYM
10_1101-2021_01_08_425885	596	142	[	[	-LRB-
10_1101-2021_01_08_425885	596	143	1,−2	1,−2	CD
10_1101-2021_01_08_425885	596	144	,	,	,
10_1101-2021_01_08_425885	596	145	1	1	CD
10_1101-2021_01_08_425885	596	146	,	,	,
10_1101-2021_01_08_425885	596	147	0	0	CD
10_1101-2021_01_08_425885	596	148	,	,	,
10_1101-2021_01_08_425885	596	149	0	0	CD
10_1101-2021_01_08_425885	596	150	,	,	,
10_1101-2021_01_08_425885	596	151	0,−1	0,−1	CD
10_1101-2021_01_08_425885	596	152	,	,	,
10_1101-2021_01_08_425885	596	153	2,−1]T/	2,−1]t/	CD
10_1101-2021_01_08_425885	596	154	√	√	NNP
10_1101-2021_01_08_425885	596	155	48	48	CD
10_1101-2021_01_08_425885	596	156	e8	e8	NNS
10_1101-2021_01_08_425885	596	157	=	=	SYM
10_1101-2021_01_08_425885	596	158	[	[	-LRB-
10_1101-2021_01_08_425885	596	159	1,−2	1,−2	CD
10_1101-2021_01_08_425885	596	160	,	,	,
10_1101-2021_01_08_425885	596	161	1,−2	1,−2	CD
10_1101-2021_01_08_425885	596	162	,	,	,
10_1101-2021_01_08_425885	596	163	4,−2	4,−2	CD
10_1101-2021_01_08_425885	596	164	,	,	,
10_1101-2021_01_08_425885	596	165	1,−2	1,−2	CD
10_1101-2021_01_08_425885	596	166	,	,	,
10_1101-2021_01_08_425885	596	167	1]T/	1]t/	CD
10_1101-2021_01_08_425885	596	168	√	√	NN
10_1101-2021_01_08_425885	596	169	216	216	CD
10_1101-2021_01_08_425885	596	170	(	(	-LRB-
10_1101-2021_01_08_425885	596	171	29	29	CD
10_1101-2021_01_08_425885	596	172	)	)	-RRB-
10_1101-2021_01_08_425885	596	173	By	by	IN
10_1101-2021_01_08_425885	596	174	inspection	inspection	NN
10_1101-2021_01_08_425885	596	175	,	,	,
10_1101-2021_01_08_425885	596	176	e1	e1	NNP
10_1101-2021_01_08_425885	596	177	is	be	VBZ
10_1101-2021_01_08_425885	596	178	the	the	DT
10_1101-2021_01_08_425885	596	179	basis	basis	NN
10_1101-2021_01_08_425885	596	180	vector	vector	NN
10_1101-2021_01_08_425885	596	181	for	for	IN
10_1101-2021_01_08_425885	596	182	patches	patch	NNS
10_1101-2021_01_08_425885	596	183	with	with	IN
10_1101-2021_01_08_425885	596	184	horizontal	horizontal	JJ
10_1101-2021_01_08_425885	596	185	stripes	stripe	NNS
10_1101-2021_01_08_425885	596	186	and	and	CC
10_1101-2021_01_08_425885	596	187	linear	linear	JJ
10_1101-2021_01_08_425885	596	188	gradients	gradient	NNS
10_1101-2021_01_08_425885	596	189	,	,	,
10_1101-2021_01_08_425885	596	190	e2	e2	NN
10_1101-2021_01_08_425885	596	191	for	for	IN
10_1101-2021_01_08_425885	596	192	patches	patch	NNS
10_1101-2021_01_08_425885	596	193	with	with	IN
10_1101-2021_01_08_425885	596	194	vertical	vertical	JJ
10_1101-2021_01_08_425885	596	195	stripes	stripe	NNS
10_1101-2021_01_08_425885	596	196	and	and	CC
10_1101-2021_01_08_425885	596	197	linear	linear	JJ
10_1101-2021_01_08_425885	596	198	gradients	gradient	NNS
10_1101-2021_01_08_425885	596	199	,	,	,
10_1101-2021_01_08_425885	596	200	e3	e3	FW
10_1101-2021_01_08_425885	596	201	for	for	IN
10_1101-2021_01_08_425885	596	202	patches	patch	NNS
10_1101-2021_01_08_425885	596	203	with	with	IN
10_1101-2021_01_08_425885	596	204	horizontal	horizontal	JJ
10_1101-2021_01_08_425885	596	205	stripes	stripe	NNS
10_1101-2021_01_08_425885	596	206	and	and	CC
10_1101-2021_01_08_425885	596	207	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	596	208	gradients	gradient	NNS
10_1101-2021_01_08_425885	596	209	,	,	,
10_1101-2021_01_08_425885	596	210	e4	e4	NNP
10_1101-2021_01_08_425885	596	211	for	for	IN
10_1101-2021_01_08_425885	596	212	patches	patch	NNS
10_1101-2021_01_08_425885	596	213	with	with	IN
10_1101-2021_01_08_425885	596	214	vertical	vertical	JJ
10_1101-2021_01_08_425885	596	215	stripes	stripe	NNS
10_1101-2021_01_08_425885	596	216	and	and	CC
10_1101-2021_01_08_425885	596	217	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	596	218	gradients	gradient	NNS
10_1101-2021_01_08_425885	596	219	,	,	,
10_1101-2021_01_08_425885	596	220	and	and	CC
10_1101-2021_01_08_425885	596	221	e5	e5	VB
10_1101-2021_01_08_425885	596	222	for	for	IN
10_1101-2021_01_08_425885	596	223	diagonally	diagonally	RB
10_1101-2021_01_08_425885	596	224	-	-	HYPH
10_1101-2021_01_08_425885	596	225	oriented	orient	VBN
10_1101-2021_01_08_425885	596	226	patches	patch	NNS
10_1101-2021_01_08_425885	596	227	with	with	IN
10_1101-2021_01_08_425885	596	228	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	596	229	gradients	gradient	NNS
10_1101-2021_01_08_425885	596	230	.	.	.
10_1101-2021_01_08_425885	597	1	All	all	PDT
10_1101-2021_01_08_425885	597	2	the	the	DT
10_1101-2021_01_08_425885	597	3	patches	patch	NNS
10_1101-2021_01_08_425885	597	4	produced	produce	VBN
10_1101-2021_01_08_425885	597	5	by	by	IN
10_1101-2021_01_08_425885	597	6	the	the	DT
10_1101-2021_01_08_425885	597	7	embedding	embedding	NN
10_1101-2021_01_08_425885	597	8	k0	k0	NNP
10_1101-2021_01_08_425885	597	9	in	in	IN
10_1101-2021_01_08_425885	597	10	Equation	Equation	NNP
10_1101-2021_01_08_425885	597	11	31	31	CD
10_1101-2021_01_08_425885	597	12	below	below	RB
10_1101-2021_01_08_425885	597	13	and	and	CC
10_1101-2021_01_08_425885	597	14	visualized	visualize	VBN
10_1101-2021_01_08_425885	597	15	in	in	IN
10_1101-2021_01_08_425885	597	16	Figure	figure	NN
10_1101-2021_01_08_425885	597	17	3B	3b	NN
10_1101-2021_01_08_425885	597	18	can	can	MD
10_1101-2021_01_08_425885	597	19	be	be	VB
10_1101-2021_01_08_425885	597	20	written	write	VBN
10_1101-2021_01_08_425885	597	21	as	as	IN
10_1101-2021_01_08_425885	597	22	a	a	DT
10_1101-2021_01_08_425885	597	23	linear	linear	JJ
10_1101-2021_01_08_425885	597	24	combination	combination	NN
10_1101-2021_01_08_425885	597	25	of	of	IN
10_1101-2021_01_08_425885	597	26	these	these	DT
10_1101-2021_01_08_425885	597	27	5	5	CD
10_1101-2021_01_08_425885	597	28	basis	basis	NN
10_1101-2021_01_08_425885	597	29	vectors	vector	NNS
10_1101-2021_01_08_425885	597	30	.	.	.
10_1101-2021_01_08_425885	598	1	Next	next	RB
10_1101-2021_01_08_425885	598	2	,	,	,
10_1101-2021_01_08_425885	598	3	note	note	VB
10_1101-2021_01_08_425885	598	4	that	that	IN
10_1101-2021_01_08_425885	598	5	the	the	DT
10_1101-2021_01_08_425885	598	6	components	component	NNS
10_1101-2021_01_08_425885	598	7	in	in	IN
10_1101-2021_01_08_425885	598	8	each	each	DT
10_1101-2021_01_08_425885	598	9	ei	ei	NNP
10_1101-2021_01_08_425885	598	10	sum	sum	NN
10_1101-2021_01_08_425885	598	11	to	to	IN
10_1101-2021_01_08_425885	598	12	0	0	CD
10_1101-2021_01_08_425885	598	13	,	,	,
10_1101-2021_01_08_425885	598	14	so	so	IN
10_1101-2021_01_08_425885	598	15	that	that	IN
10_1101-2021_01_08_425885	598	16	the	the	DT
10_1101-2021_01_08_425885	598	17	projection	projection	NN
10_1101-2021_01_08_425885	598	18	operator	operator	NN
10_1101-2021_01_08_425885	598	19	,	,	,
10_1101-2021_01_08_425885	598	20	c	c	NNP
10_1101-2021_01_08_425885	598	21	,	,	,
10_1101-2021_01_08_425885	598	22	additionally	additionally	RB
10_1101-2021_01_08_425885	598	23	serves	serve	VBZ
10_1101-2021_01_08_425885	598	24	to	to	TO
10_1101-2021_01_08_425885	598	25	remove	remove	VB
10_1101-2021_01_08_425885	598	26	the	the	DT
10_1101-2021_01_08_425885	598	27	mean	mean	NN
10_1101-2021_01_08_425885	598	28	.	.	.
10_1101-2021_01_08_425885	599	1	Finally	finally	RB
10_1101-2021_01_08_425885	599	2	,	,	,
10_1101-2021_01_08_425885	599	3	observe	observe	VB
10_1101-2021_01_08_425885	599	4	that	that	IN
10_1101-2021_01_08_425885	599	5	the	the	DT
10_1101-2021_01_08_425885	599	6	vector	vector	NN
10_1101-2021_01_08_425885	599	7	norm	norm	NN
10_1101-2021_01_08_425885	599	8	formed	form	VBN
10_1101-2021_01_08_425885	599	9	under	under	IN
10_1101-2021_01_08_425885	599	10	D	d	NN
10_1101-2021_01_08_425885	599	11	=	=	SYM
10_1101-2021_01_08_425885	599	12	AΛ2AT	AΛ2AT	NNP
10_1101-2021_01_08_425885	599	13	(	(	-LRB-
10_1101-2021_01_08_425885	599	14	referred	refer	VBN
10_1101-2021_01_08_425885	599	15	to	to	IN
10_1101-2021_01_08_425885	599	16	hereafter	hereafter	RB
10_1101-2021_01_08_425885	599	17	as	as	IN
10_1101-2021_01_08_425885	599	18	the	the	DT
10_1101-2021_01_08_425885	599	19	D	d	JJ
10_1101-2021_01_08_425885	599	20	-	-	HYPH
10_1101-2021_01_08_425885	599	21	norm	norm	NN
10_1101-2021_01_08_425885	599	22	following	follow	VBG
10_1101-2021_01_08_425885	599	23	[	[	-LRB-
10_1101-2021_01_08_425885	599	24	40	40	CD
10_1101-2021_01_08_425885	599	25	]	]	-RRB-
10_1101-2021_01_08_425885	599	26	)	)	-RRB-
10_1101-2021_01_08_425885	599	27	measures	measure	VBZ
10_1101-2021_01_08_425885	599	28	the	the	DT
10_1101-2021_01_08_425885	599	29	contrast	contrast	NN
10_1101-2021_01_08_425885	599	30	in	in	IN
10_1101-2021_01_08_425885	599	31	a	a	DT
10_1101-2021_01_08_425885	599	32	3x3	3x3	CD
10_1101-2021_01_08_425885	599	33	patch	patch	NN
10_1101-2021_01_08_425885	599	34	since	since	IN
10_1101-2021_01_08_425885	599	35	‖v‖D	‖v‖D	NNP
10_1101-2021_01_08_425885	599	36	=	=	SYM
10_1101-2021_01_08_425885	599	37	√	√	NNP
10_1101-2021_01_08_425885	599	38	vTDv	vTDv	NNP
10_1101-2021_01_08_425885	599	39	=	=	SYM
10_1101-2021_01_08_425885	599	40	1	1	CD
10_1101-2021_01_08_425885	599	41	2	2	CD
10_1101-2021_01_08_425885	599	42	√∑	√∑	NNP
10_1101-2021_01_08_425885	599	43	i	i	PRP
10_1101-2021_01_08_425885	599	44	∑	∑	.
10_1101-2021_01_08_425885	599	45	j∼i	j∼i	NNP
10_1101-2021_01_08_425885	599	46	(	(	-LRB-
10_1101-2021_01_08_425885	599	47	vi	vi	NNP
10_1101-2021_01_08_425885	599	48	−vj)2	−vj)2	NNP
10_1101-2021_01_08_425885	599	49	(	(	-LRB-
10_1101-2021_01_08_425885	599	50	30	30	CD
10_1101-2021_01_08_425885	599	51	)	)	-RRB-
10_1101-2021_01_08_425885	599	52	where	where	WRB
10_1101-2021_01_08_425885	599	53	j	j	NNP
10_1101-2021_01_08_425885	599	54	∼	∼	NNP
10_1101-2021_01_08_425885	599	55	i	i	PRP
10_1101-2021_01_08_425885	599	56	refers	refer	VBZ
10_1101-2021_01_08_425885	599	57	to	to	IN
10_1101-2021_01_08_425885	599	58	all	all	DT
10_1101-2021_01_08_425885	599	59	vertical	vertical	JJ
10_1101-2021_01_08_425885	599	60	and	and	CC
10_1101-2021_01_08_425885	599	61	horizontal	horizontal	JJ
10_1101-2021_01_08_425885	599	62	neighbors	neighbor	NNS
10_1101-2021_01_08_425885	599	63	,	,	,
10_1101-2021_01_08_425885	599	64	j	j	NNP
10_1101-2021_01_08_425885	599	65	,	,	,
10_1101-2021_01_08_425885	599	66	of	of	IN
10_1101-2021_01_08_425885	599	67	a	a	DT
10_1101-2021_01_08_425885	599	68	pixel	pixel	NN
10_1101-2021_01_08_425885	599	69	i	i	PRP
10_1101-2021_01_08_425885	599	70	in	in	IN
10_1101-2021_01_08_425885	599	71	the	the	DT
10_1101-2021_01_08_425885	599	72	preimage	preimage	NN
10_1101-2021_01_08_425885	599	73	of	of	IN
10_1101-2021_01_08_425885	599	74	v	v	NN
10_1101-2021_01_08_425885	599	75	under	under	IN
10_1101-2021_01_08_425885	599	76	h.	h.	NN
10_1101-2021_01_08_425885	599	77	The	the	DT
10_1101-2021_01_08_425885	599	78	ei	ei	NNP
10_1101-2021_01_08_425885	599	79	are	be	VBP
10_1101-2021_01_08_425885	599	80	normalized	normalized	JJ
10_1101-2021_01_08_425885	599	81	so	so	IN
10_1101-2021_01_08_425885	599	82	that	that	IN
10_1101-2021_01_08_425885	599	83	‖ei‖D	‖ei‖d	NN
10_1101-2021_01_08_425885	599	84	=	=	SYM
10_1101-2021_01_08_425885	599	85	1	1	CD
10_1101-2021_01_08_425885	599	86	.	.	.
10_1101-2021_01_08_425885	600	1	4.5.2	4.5.2	CD
10_1101-2021_01_08_425885	600	2	Image	Image	NNP
10_1101-2021_01_08_425885	600	3	Dataset	Dataset	NNP
10_1101-2021_01_08_425885	600	4	We	-PRON-	PRP
10_1101-2021_01_08_425885	600	5	used	use	VBD
10_1101-2021_01_08_425885	600	6	the	the	DT
10_1101-2021_01_08_425885	600	7	same	same	JJ
10_1101-2021_01_08_425885	600	8	van	van	NNP
10_1101-2021_01_08_425885	600	9	Hateren	Hateren	NNP
10_1101-2021_01_08_425885	600	10	IML	IML	NNP
10_1101-2021_01_08_425885	600	11	dataset	dataset	NN
10_1101-2021_01_08_425885	600	12	[	[	-LRB-
10_1101-2021_01_08_425885	600	13	41	41	CD
10_1101-2021_01_08_425885	600	14	]	]	-RRB-
10_1101-2021_01_08_425885	600	15	consisting	consist	VBG
10_1101-2021_01_08_425885	600	16	of	of	IN
10_1101-2021_01_08_425885	600	17	4167	4167	CD
10_1101-2021_01_08_425885	600	18	greyscale	greyscale	JJ
10_1101-2021_01_08_425885	600	19	images	image	NNS
10_1101-2021_01_08_425885	600	20	of	of	IN
10_1101-2021_01_08_425885	600	21	size	size	NN
10_1101-2021_01_08_425885	600	22	1532x1020	1532x1020	NN
10_1101-2021_01_08_425885	600	23	pixels	pixel	NNS
10_1101-2021_01_08_425885	600	24	studied	study	VBN
10_1101-2021_01_08_425885	600	25	by	by	IN
10_1101-2021_01_08_425885	600	26	Carlsson	Carlsson	NNP
10_1101-2021_01_08_425885	600	27	et	et	FW
10_1101-2021_01_08_425885	600	28	al	al	NNP
10_1101-2021_01_08_425885	600	29	.	.	.
10_1101-2021_01_08_425885	601	1	in	in	IN
10_1101-2021_01_08_425885	601	2	[	[	-LRB-
10_1101-2021_01_08_425885	601	3	21	21	CD
10_1101-2021_01_08_425885	601	4	]	]	-RRB-
10_1101-2021_01_08_425885	601	5	and	and	CC
10_1101-2021_01_08_425885	601	6	followed	follow	VBD
10_1101-2021_01_08_425885	601	7	the	the	DT
10_1101-2021_01_08_425885	601	8	same	same	JJ
10_1101-2021_01_08_425885	601	9	preprocessing	preprocessing	NN
10_1101-2021_01_08_425885	601	10	steps	step	NNS
10_1101-2021_01_08_425885	601	11	used	use	VBN
10_1101-2021_01_08_425885	601	12	there	there	RB
10_1101-2021_01_08_425885	601	13	.	.	.
10_1101-2021_01_08_425885	602	1	In	in	IN
10_1101-2021_01_08_425885	602	2	short	short	JJ
10_1101-2021_01_08_425885	602	3	,	,	,
10_1101-2021_01_08_425885	602	4	we	-PRON-	PRP
10_1101-2021_01_08_425885	602	5	applied	apply	VBD
10_1101-2021_01_08_425885	602	6	a	a	DT
10_1101-2021_01_08_425885	602	7	log1p	log1p	NN
10_1101-2021_01_08_425885	602	8	transformation	transformation	NN
10_1101-2021_01_08_425885	602	9	to	to	IN
10_1101-2021_01_08_425885	602	10	all	all	DT
10_1101-2021_01_08_425885	602	11	pixel	pixel	NN
10_1101-2021_01_08_425885	602	12	values	value	NNS
10_1101-2021_01_08_425885	602	13	and	and	CC
10_1101-2021_01_08_425885	602	14	randomly	randomly	RB
10_1101-2021_01_08_425885	602	15	sampled	sample	VBD
10_1101-2021_01_08_425885	602	16	5	5	CD
10_1101-2021_01_08_425885	602	17	×	×	CD
10_1101-2021_01_08_425885	602	18	103	103	CD
10_1101-2021_01_08_425885	602	19	(	(	-LRB-
10_1101-2021_01_08_425885	602	20	possibly	possibly	RB
10_1101-2021_01_08_425885	602	21	overlapping	overlap	VBG
10_1101-2021_01_08_425885	602	22	)	)	-RRB-
10_1101-2021_01_08_425885	602	23	3x3	3x3	CD
10_1101-2021_01_08_425885	602	24	patches	patch	NNS
10_1101-2021_01_08_425885	602	25	from	from	IN
10_1101-2021_01_08_425885	602	26	each	each	DT
10_1101-2021_01_08_425885	602	27	image	image	NN
10_1101-2021_01_08_425885	602	28	.	.	.
10_1101-2021_01_08_425885	603	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	603	2	indexed	index	VBD
10_1101-2021_01_08_425885	603	3	the	the	DT
10_1101-2021_01_08_425885	603	4	pixels	pixel	NNS
10_1101-2021_01_08_425885	603	5	in	in	IN
10_1101-2021_01_08_425885	603	6	each	each	DT
10_1101-2021_01_08_425885	603	7	patch	patch	NN
10_1101-2021_01_08_425885	603	8	using	use	VBG
10_1101-2021_01_08_425885	603	9	standard	standard	JJ
10_1101-2021_01_08_425885	603	10	Cartesian	cartesian	JJ
10_1101-2021_01_08_425885	603	11	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	603	12	with	with	IN
10_1101-2021_01_08_425885	603	13	the	the	DT
10_1101-2021_01_08_425885	603	14	middle	middle	JJ
10_1101-2021_01_08_425885	603	15	pixel	pixel	NNP
10_1101-2021_01_08_425885	603	16	as	as	IN
10_1101-2021_01_08_425885	603	17	the	the	DT
10_1101-2021_01_08_425885	603	18	origin	origin	NN
10_1101-2021_01_08_425885	603	19	,	,	,
10_1101-2021_01_08_425885	603	20	so	so	IN
10_1101-2021_01_08_425885	603	21	that	that	IN
10_1101-2021_01_08_425885	603	22	log	log	NN
10_1101-2021_01_08_425885	603	23	-	-	HYPH
10_1101-2021_01_08_425885	603	24	transformed	transform	VBN
10_1101-2021_01_08_425885	603	25	pixel	pixel	NN
10_1101-2021_01_08_425885	603	26	values	value	NNS
10_1101-2021_01_08_425885	603	27	are	be	VBP
10_1101-2021_01_08_425885	603	28	given	give	VBN
10_1101-2021_01_08_425885	603	29	by	by	IN
10_1101-2021_01_08_425885	603	30	p(x	p(x	NNS
10_1101-2021_01_08_425885	603	31	,	,	,
10_1101-2021_01_08_425885	603	32	y),x	y),x	NNP
10_1101-2021_01_08_425885	603	33	∈{−1	∈{−1	NNP
10_1101-2021_01_08_425885	603	34	,	,	,
10_1101-2021_01_08_425885	603	35	0	0	CD
10_1101-2021_01_08_425885	603	36	,	,	,
10_1101-2021_01_08_425885	603	37	1},y	1},y	CD
10_1101-2021_01_08_425885	603	38	∈{−1	∈{−1	CD
10_1101-2021_01_08_425885	603	39	,	,	,
10_1101-2021_01_08_425885	603	40	0	0	CD
10_1101-2021_01_08_425885	603	41	,	,	,
10_1101-2021_01_08_425885	603	42	1	1	CD
10_1101-2021_01_08_425885	603	43	}	}	-RRB-
10_1101-2021_01_08_425885	603	44	.	.	.
10_1101-2021_01_08_425885	604	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	604	2	35	35	CD
10_1101-2021_01_08_425885	604	3	.CC	.CC	:
10_1101-2021_01_08_425885	604	4	-	-	HYPH
10_1101-2021_01_08_425885	604	5	BY	by	IN
10_1101-2021_01_08_425885	604	6	-	-	HYPH
10_1101-2021_01_08_425885	604	7	NC	NC	NNP
10_1101-2021_01_08_425885	604	8	-	-	HYPH
10_1101-2021_01_08_425885	604	9	ND	ND	NNP
10_1101-2021_01_08_425885	604	10	4.0	4.0	CD
10_1101-2021_01_08_425885	604	11	International	International	NNP
10_1101-2021_01_08_425885	604	12	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	604	13	under	under	IN
10_1101-2021_01_08_425885	604	14	a	a	DT
10_1101-2021_01_08_425885	604	15	(	(	-LRB-
10_1101-2021_01_08_425885	604	16	which	which	WDT
10_1101-2021_01_08_425885	604	17	was	be	VBD
10_1101-2021_01_08_425885	604	18	not	not	RB
10_1101-2021_01_08_425885	604	19	certified	certify	VBN
10_1101-2021_01_08_425885	604	20	by	by	IN
10_1101-2021_01_08_425885	604	21	peer	peer	NN
10_1101-2021_01_08_425885	604	22	review	review	NN
10_1101-2021_01_08_425885	604	23	)	)	-RRB-
10_1101-2021_01_08_425885	604	24	is	be	VBZ
10_1101-2021_01_08_425885	604	25	the	the	DT
10_1101-2021_01_08_425885	604	26	author	author	NN
10_1101-2021_01_08_425885	604	27	/	/	SYM
10_1101-2021_01_08_425885	604	28	funder	funder	NN
10_1101-2021_01_08_425885	604	29	,	,	,
10_1101-2021_01_08_425885	604	30	who	who	WP
10_1101-2021_01_08_425885	604	31	has	have	VBZ
10_1101-2021_01_08_425885	604	32	granted	grant	VBN
10_1101-2021_01_08_425885	604	33	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	604	34	a	a	DT
10_1101-2021_01_08_425885	604	35	license	license	NN
10_1101-2021_01_08_425885	604	36	to	to	TO
10_1101-2021_01_08_425885	604	37	display	display	VB
10_1101-2021_01_08_425885	604	38	the	the	DT
10_1101-2021_01_08_425885	604	39	preprint	preprint	NN
10_1101-2021_01_08_425885	604	40	in	in	IN
10_1101-2021_01_08_425885	604	41	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	604	42	.	.	.
10_1101-2021_01_08_425885	605	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	605	2	is	be	VBZ
10_1101-2021_01_08_425885	605	3	made	make	VBN
10_1101-2021_01_08_425885	605	4	The	the	DT
10_1101-2021_01_08_425885	605	5	copyright	copyright	NN
10_1101-2021_01_08_425885	605	6	holder	holder	NN
10_1101-2021_01_08_425885	605	7	for	for	IN
10_1101-2021_01_08_425885	605	8	this	this	DT
10_1101-2021_01_08_425885	605	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	605	10	version	version	NN
10_1101-2021_01_08_425885	605	11	posted	post	VBD
10_1101-2021_01_08_425885	605	12	January	January	NNP
10_1101-2021_01_08_425885	605	13	8	8	CD
10_1101-2021_01_08_425885	605	14	,	,	,
10_1101-2021_01_08_425885	605	15	2021	2021	CD
10_1101-2021_01_08_425885	605	16	.	.	.
10_1101-2021_01_08_425885	605	17	;	;	:
10_1101-2021_01_08_425885	605	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	605	19	:	:	:
10_1101-2021_01_08_425885	605	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	605	21	preprint	preprint	NN
10_1101-2021_01_08_425885	605	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	605	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	RB
10_1101-2021_01_08_425885	605	24	then	then	RB
10_1101-2021_01_08_425885	605	25	applied	apply	VBD
10_1101-2021_01_08_425885	605	26	h	h	NNP
10_1101-2021_01_08_425885	605	27	to	to	TO
10_1101-2021_01_08_425885	605	28	vectorize	vectorize	VB
10_1101-2021_01_08_425885	605	29	each	each	DT
10_1101-2021_01_08_425885	605	30	patch	patch	NN
10_1101-2021_01_08_425885	605	31	p	p	NN
10_1101-2021_01_08_425885	605	32	,	,	,
10_1101-2021_01_08_425885	605	33	and	and	CC
10_1101-2021_01_08_425885	605	34	retained	retain	VBD
10_1101-2021_01_08_425885	605	35	the	the	DT
10_1101-2021_01_08_425885	605	36	high	high	JJ
10_1101-2021_01_08_425885	605	37	-	-	HYPH
10_1101-2021_01_08_425885	605	38	contrast	contrast	NN
10_1101-2021_01_08_425885	605	39	patches	patch	NNS
10_1101-2021_01_08_425885	605	40	comprising	comprise	VBG
10_1101-2021_01_08_425885	605	41	the	the	DT
10_1101-2021_01_08_425885	605	42	top	top	JJ
10_1101-2021_01_08_425885	605	43	quintile	quintile	NN
10_1101-2021_01_08_425885	605	44	of	of	IN
10_1101-2021_01_08_425885	605	45	D	d	NN
10_1101-2021_01_08_425885	605	46	-	-	HYPH
10_1101-2021_01_08_425885	605	47	norms	norm	NNS
10_1101-2021_01_08_425885	605	48	for	for	IN
10_1101-2021_01_08_425885	605	49	each	each	DT
10_1101-2021_01_08_425885	605	50	image	image	NN
10_1101-2021_01_08_425885	605	51	,	,	,
10_1101-2021_01_08_425885	605	52	resulting	result	VBG
10_1101-2021_01_08_425885	605	53	in	in	IN
10_1101-2021_01_08_425885	605	54	N	N	NNP
10_1101-2021_01_08_425885	605	55	≈	≈	NNP
10_1101-2021_01_08_425885	605	56	4.2	4.2	CD
10_1101-2021_01_08_425885	605	57	×	×	CD
10_1101-2021_01_08_425885	605	58	106	106	CD
10_1101-2021_01_08_425885	605	59	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	605	60	.	.	.
10_1101-2021_01_08_425885	606	1	Next	next	RB
10_1101-2021_01_08_425885	606	2	,	,	,
10_1101-2021_01_08_425885	606	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	606	4	normalized	normalize	VBD
10_1101-2021_01_08_425885	606	5	these	these	DT
10_1101-2021_01_08_425885	606	6	high	high	JJ
10_1101-2021_01_08_425885	606	7	-	-	HYPH
10_1101-2021_01_08_425885	606	8	contrast	contrast	NN
10_1101-2021_01_08_425885	606	9	vectorized	vectorize	VBN
10_1101-2021_01_08_425885	606	10	patches	patch	NNS
10_1101-2021_01_08_425885	606	11	using	use	VBG
10_1101-2021_01_08_425885	606	12	the	the	DT
10_1101-2021_01_08_425885	606	13	composition	composition	NN
10_1101-2021_01_08_425885	606	14	u	u	NNP
10_1101-2021_01_08_425885	606	15	◦	◦	NNP
10_1101-2021_01_08_425885	606	16	c	c	NNP
10_1101-2021_01_08_425885	606	17	,	,	,
10_1101-2021_01_08_425885	606	18	resulting	result	VBG
10_1101-2021_01_08_425885	606	19	in	in	IN
10_1101-2021_01_08_425885	606	20	a	a	DT
10_1101-2021_01_08_425885	606	21	set	set	NN
10_1101-2021_01_08_425885	606	22	of	of	IN
10_1101-2021_01_08_425885	606	23	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	606	24	on	on	IN
10_1101-2021_01_08_425885	606	25	S7	S7	NNP
10_1101-2021_01_08_425885	606	26	⊂	⊂	CD
10_1101-2021_01_08_425885	606	27	R8	r8	NN
10_1101-2021_01_08_425885	606	28	.	.	.
10_1101-2021_01_08_425885	607	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	607	2	determined	determine	VBD
10_1101-2021_01_08_425885	607	3	the	the	DT
10_1101-2021_01_08_425885	607	4	density	density	NN
10_1101-2021_01_08_425885	607	5	of	of	IN
10_1101-2021_01_08_425885	607	6	these	these	DT
10_1101-2021_01_08_425885	607	7	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	607	8	in	in	IN
10_1101-2021_01_08_425885	607	9	R8	R8	NNP
10_1101-2021_01_08_425885	607	10	using	use	VBG
10_1101-2021_01_08_425885	607	11	the	the	DT
10_1101-2021_01_08_425885	607	12	kNN	kNN	NNP
10_1101-2021_01_08_425885	607	13	density	density	NN
10_1101-2021_01_08_425885	607	14	estimator	estimator	NN
10_1101-2021_01_08_425885	607	15	with	with	IN
10_1101-2021_01_08_425885	607	16	k	k	NNP
10_1101-2021_01_08_425885	607	17	=	=	SYM
10_1101-2021_01_08_425885	607	18	100	100	CD
10_1101-2021_01_08_425885	607	19	,	,	,
10_1101-2021_01_08_425885	607	20	and	and	CC
10_1101-2021_01_08_425885	607	21	retained	retain	VBD
10_1101-2021_01_08_425885	607	22	the	the	DT
10_1101-2021_01_08_425885	607	23	densest	dense	JJS
10_1101-2021_01_08_425885	607	24	decile	decile	NN
10_1101-2021_01_08_425885	607	25	,	,	,
10_1101-2021_01_08_425885	607	26	which	which	WDT
10_1101-2021_01_08_425885	607	27	yielded	yield	VBD
10_1101-2021_01_08_425885	607	28	N	N	NNP
10_1101-2021_01_08_425885	607	29	≈	≈	NNP
10_1101-2021_01_08_425885	607	30	4.2	4.2	CD
10_1101-2021_01_08_425885	607	31	×	×	CD
10_1101-2021_01_08_425885	607	32	105	105	CD
10_1101-2021_01_08_425885	607	33	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	607	34	.	.	.
10_1101-2021_01_08_425885	608	1	This	this	DT
10_1101-2021_01_08_425885	608	2	dense	dense	JJ
10_1101-2021_01_08_425885	608	3	subset	subset	NN
10_1101-2021_01_08_425885	608	4	of	of	IN
10_1101-2021_01_08_425885	608	5	high	high	JJ
10_1101-2021_01_08_425885	608	6	-	-	HYPH
10_1101-2021_01_08_425885	608	7	contrast	contrast	NN
10_1101-2021_01_08_425885	608	8	normalized	normalized	JJ
10_1101-2021_01_08_425885	608	9	patches	patch	NNS
10_1101-2021_01_08_425885	608	10	was	be	VBD
10_1101-2021_01_08_425885	608	11	found	find	VBN
10_1101-2021_01_08_425885	608	12	using	use	VBG
10_1101-2021_01_08_425885	608	13	topological	topological	JJ
10_1101-2021_01_08_425885	608	14	data	datum	NNS
10_1101-2021_01_08_425885	608	15	analysis	analysis	NN
10_1101-2021_01_08_425885	608	16	in	in	IN
10_1101-2021_01_08_425885	608	17	[	[	-LRB-
10_1101-2021_01_08_425885	608	18	21	21	CD
10_1101-2021_01_08_425885	608	19	]	]	-RRB-
10_1101-2021_01_08_425885	608	20	to	to	TO
10_1101-2021_01_08_425885	608	21	be	be	VB
10_1101-2021_01_08_425885	608	22	a	a	DT
10_1101-2021_01_08_425885	608	23	Klein	Klein	NNP
10_1101-2021_01_08_425885	608	24	bottle	bottle	NN
10_1101-2021_01_08_425885	608	25	,	,	,
10_1101-2021_01_08_425885	608	26	K2	K2	NNP
10_1101-2021_01_08_425885	608	27	⊂	⊂	CD
10_1101-2021_01_08_425885	608	28	S7	S7	NNP
10_1101-2021_01_08_425885	608	29	,	,	,
10_1101-2021_01_08_425885	608	30	and	and	CC
10_1101-2021_01_08_425885	608	31	is	be	VBZ
10_1101-2021_01_08_425885	608	32	studied	study	VBN
10_1101-2021_01_08_425885	608	33	in	in	IN
10_1101-2021_01_08_425885	608	34	Figures	figure	NNS
10_1101-2021_01_08_425885	608	35	3D	3d	NN
10_1101-2021_01_08_425885	608	36	,	,	,
10_1101-2021_01_08_425885	608	37	I	-PRON-	PRP
10_1101-2021_01_08_425885	608	38	and	and	CC
10_1101-2021_01_08_425885	608	39	S3B.	s3b.	VB
10_1101-2021_01_08_425885	609	1	To	to	TO
10_1101-2021_01_08_425885	609	2	generate	generate	VB
10_1101-2021_01_08_425885	609	3	the	the	DT
10_1101-2021_01_08_425885	609	4	augmented	augment	VBN
10_1101-2021_01_08_425885	609	5	image	image	NN
10_1101-2021_01_08_425885	609	6	patch	patch	NN
10_1101-2021_01_08_425885	609	7	dataset	dataset	NN
10_1101-2021_01_08_425885	609	8	used	use	VBN
10_1101-2021_01_08_425885	609	9	in	in	IN
10_1101-2021_01_08_425885	609	10	Figures	figure	NNS
10_1101-2021_01_08_425885	609	11	3J	3J	NNP
10_1101-2021_01_08_425885	609	12	and	and	CC
10_1101-2021_01_08_425885	609	13	S3E	s3e	NN
10_1101-2021_01_08_425885	609	14	,	,	,
10_1101-2021_01_08_425885	609	15	F	F	NNP
10_1101-2021_01_08_425885	609	16	,	,	,
10_1101-2021_01_08_425885	609	17	we	-PRON-	PRP
10_1101-2021_01_08_425885	609	18	first	first	RB
10_1101-2021_01_08_425885	609	19	considered	consider	VBD
10_1101-2021_01_08_425885	609	20	all	all	DT
10_1101-2021_01_08_425885	609	21	N	n	NN
10_1101-2021_01_08_425885	609	22	≈	≈	NNP
10_1101-2021_01_08_425885	609	23	1.3	1.3	CD
10_1101-2021_01_08_425885	609	24	×	×	CD
10_1101-2021_01_08_425885	609	25	109	109	CD
10_1101-2021_01_08_425885	609	26	vectorized	vectorize	VBN
10_1101-2021_01_08_425885	609	27	high	high	JJ
10_1101-2021_01_08_425885	609	28	-	-	HYPH
10_1101-2021_01_08_425885	609	29	contrast	contrast	NN
10_1101-2021_01_08_425885	609	30	patches	patch	NNS
10_1101-2021_01_08_425885	609	31	in	in	IN
10_1101-2021_01_08_425885	609	32	the	the	DT
10_1101-2021_01_08_425885	609	33	van	van	NNP
10_1101-2021_01_08_425885	609	34	Hateren	Hateren	NNP
10_1101-2021_01_08_425885	609	35	IML	IML	NNP
10_1101-2021_01_08_425885	609	36	dataset	dataset	VBD
10_1101-2021_01_08_425885	609	37	using	use	VBG
10_1101-2021_01_08_425885	609	38	the	the	DT
10_1101-2021_01_08_425885	609	39	same	same	JJ
10_1101-2021_01_08_425885	609	40	procedure	procedure	NN
10_1101-2021_01_08_425885	609	41	described	describe	VBN
10_1101-2021_01_08_425885	609	42	above	above	IN
10_1101-2021_01_08_425885	609	43	(	(	-LRB-
10_1101-2021_01_08_425885	609	44	each	each	DT
10_1101-2021_01_08_425885	609	45	of	of	IN
10_1101-2021_01_08_425885	609	46	the	the	DT
10_1101-2021_01_08_425885	609	47	4167	4167	CD
10_1101-2021_01_08_425885	609	48	images	image	NNS
10_1101-2021_01_08_425885	609	49	yields	yield	NNS
10_1101-2021_01_08_425885	609	50	1530	1530	CD
10_1101-2021_01_08_425885	609	51	×	×	NN
10_1101-2021_01_08_425885	609	52	1018	1018	CD
10_1101-2021_01_08_425885	609	53	patches	patch	NNS
10_1101-2021_01_08_425885	609	54	,	,	,
10_1101-2021_01_08_425885	609	55	of	of	IN
10_1101-2021_01_08_425885	609	56	which	which	WDT
10_1101-2021_01_08_425885	609	57	the	the	DT
10_1101-2021_01_08_425885	609	58	top	top	JJ
10_1101-2021_01_08_425885	609	59	20	20	CD
10_1101-2021_01_08_425885	609	60	%	%	NN
10_1101-2021_01_08_425885	609	61	by	by	IN
10_1101-2021_01_08_425885	609	62	D	d	NN
10_1101-2021_01_08_425885	609	63	-	-	HYPH
10_1101-2021_01_08_425885	609	64	norm	norm	NN
10_1101-2021_01_08_425885	609	65	are	be	VBP
10_1101-2021_01_08_425885	609	66	retained	retain	VBN
10_1101-2021_01_08_425885	609	67	per	per	IN
10_1101-2021_01_08_425885	609	68	image	image	NN
10_1101-2021_01_08_425885	609	69	)	)	-RRB-
10_1101-2021_01_08_425885	609	70	.	.	.
10_1101-2021_01_08_425885	610	1	These	these	DT
10_1101-2021_01_08_425885	610	2	were	be	VBD
10_1101-2021_01_08_425885	610	3	normalized	normalize	VBN
10_1101-2021_01_08_425885	610	4	by	by	IN
10_1101-2021_01_08_425885	610	5	u	u	NNP
10_1101-2021_01_08_425885	610	6	◦	◦	NNP
10_1101-2021_01_08_425885	610	7	c	c	NNP
10_1101-2021_01_08_425885	610	8	as	as	IN
10_1101-2021_01_08_425885	610	9	before	before	IN
10_1101-2021_01_08_425885	610	10	to	to	TO
10_1101-2021_01_08_425885	610	11	place	place	VB
10_1101-2021_01_08_425885	610	12	them	-PRON-	PRP
10_1101-2021_01_08_425885	610	13	on	on	IN
10_1101-2021_01_08_425885	610	14	S7	S7	NNP
10_1101-2021_01_08_425885	610	15	⊂	⊂	CD
10_1101-2021_01_08_425885	610	16	R8	r8	NN
10_1101-2021_01_08_425885	610	17	.	.	.
10_1101-2021_01_08_425885	611	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	611	2	again	again	RB
10_1101-2021_01_08_425885	611	3	wanted	want	VBD
10_1101-2021_01_08_425885	611	4	to	to	TO
10_1101-2021_01_08_425885	611	5	retain	retain	VB
10_1101-2021_01_08_425885	611	6	the	the	DT
10_1101-2021_01_08_425885	611	7	densest	dense	JJS
10_1101-2021_01_08_425885	611	8	decile	decile	NN
10_1101-2021_01_08_425885	611	9	of	of	IN
10_1101-2021_01_08_425885	611	10	points	point	NNS
10_1101-2021_01_08_425885	611	11	,	,	,
10_1101-2021_01_08_425885	611	12	since	since	IN
10_1101-2021_01_08_425885	611	13	only	only	RB
10_1101-2021_01_08_425885	611	14	these	these	DT
10_1101-2021_01_08_425885	611	15	have	have	VBP
10_1101-2021_01_08_425885	611	16	the	the	DT
10_1101-2021_01_08_425885	611	17	topology	topology	NN
10_1101-2021_01_08_425885	611	18	of	of	IN
10_1101-2021_01_08_425885	611	19	a	a	DT
10_1101-2021_01_08_425885	611	20	Klein	Klein	NNP
10_1101-2021_01_08_425885	611	21	bottle	bottle	NN
10_1101-2021_01_08_425885	611	22	.	.	.
10_1101-2021_01_08_425885	612	1	Mirroring	mirror	VBG
10_1101-2021_01_08_425885	612	2	the	the	DT
10_1101-2021_01_08_425885	612	3	approach	approach	NN
10_1101-2021_01_08_425885	612	4	in	in	IN
10_1101-2021_01_08_425885	612	5	[	[	-LRB-
10_1101-2021_01_08_425885	612	6	21	21	CD
10_1101-2021_01_08_425885	612	7	]	]	-RRB-
10_1101-2021_01_08_425885	612	8	where	where	WRB
10_1101-2021_01_08_425885	612	9	the	the	DT
10_1101-2021_01_08_425885	612	10	k	k	NN
10_1101-2021_01_08_425885	612	11	used	use	VBN
10_1101-2021_01_08_425885	612	12	in	in	IN
10_1101-2021_01_08_425885	612	13	the	the	DT
10_1101-2021_01_08_425885	612	14	kNN	kNN	NNP
10_1101-2021_01_08_425885	612	15	estimator	estimator	NN
10_1101-2021_01_08_425885	612	16	was	be	VBD
10_1101-2021_01_08_425885	612	17	scaled	scale	VBN
10_1101-2021_01_08_425885	612	18	with	with	IN
10_1101-2021_01_08_425885	612	19	sample	sample	NN
10_1101-2021_01_08_425885	612	20	size	size	NN
10_1101-2021_01_08_425885	612	21	,	,	,
10_1101-2021_01_08_425885	612	22	k	k	NNP
10_1101-2021_01_08_425885	612	23	=	=	SYM
10_1101-2021_01_08_425885	612	24	102	102	CD
10_1101-2021_01_08_425885	612	25	used	use	VBN
10_1101-2021_01_08_425885	612	26	for	for	IN
10_1101-2021_01_08_425885	612	27	N	N	NNP
10_1101-2021_01_08_425885	612	28	≈	≈	NNP
10_1101-2021_01_08_425885	612	29	4.2	4.2	CD
10_1101-2021_01_08_425885	612	30	×	×	CD
10_1101-2021_01_08_425885	612	31	106	106	CD
10_1101-2021_01_08_425885	612	32	corresponds	correspond	NNS
10_1101-2021_01_08_425885	612	33	to	to	IN
10_1101-2021_01_08_425885	612	34	k	k	NN
10_1101-2021_01_08_425885	612	35	=	=	SYM
10_1101-2021_01_08_425885	612	36	102	102	CD
10_1101-2021_01_08_425885	612	37	×	×	CD
10_1101-2021_01_08_425885	612	38	1.3×10	1.3×10	CD
10_1101-2021_01_08_425885	612	39	9	9	CD
10_1101-2021_01_08_425885	612	40	4.2×106	4.2×106	CD
10_1101-2021_01_08_425885	612	41	≈	≈	NN
10_1101-2021_01_08_425885	612	42	3	3	CD
10_1101-2021_01_08_425885	612	43	×	×	CD
10_1101-2021_01_08_425885	612	44	10	10	CD
10_1101-2021_01_08_425885	612	45	4	4	CD
10_1101-2021_01_08_425885	612	46	for	for	IN
10_1101-2021_01_08_425885	612	47	N	N	NNP
10_1101-2021_01_08_425885	612	48	≈	≈	NNP
10_1101-2021_01_08_425885	612	49	1.3	1.3	CD
10_1101-2021_01_08_425885	612	50	×	×	CD
10_1101-2021_01_08_425885	612	51	109	109	CD
10_1101-2021_01_08_425885	612	52	.	.	.
10_1101-2021_01_08_425885	613	1	Computing	compute	VBG
10_1101-2021_01_08_425885	613	2	k	k	NN
10_1101-2021_01_08_425885	613	3	≈	≈	NN
10_1101-2021_01_08_425885	613	4	3	3	CD
10_1101-2021_01_08_425885	613	5	×	×	CD
10_1101-2021_01_08_425885	613	6	104	104	CD
10_1101-2021_01_08_425885	613	7	neighbors	neighbor	NNS
10_1101-2021_01_08_425885	613	8	for	for	IN
10_1101-2021_01_08_425885	613	9	all	all	DT
10_1101-2021_01_08_425885	613	10	N	N	NNP
10_1101-2021_01_08_425885	613	11	≈	≈	NNP
10_1101-2021_01_08_425885	613	12	1.3	1.3	CD
10_1101-2021_01_08_425885	613	13	×	×	NN
10_1101-2021_01_08_425885	613	14	109	109	CD
10_1101-2021_01_08_425885	613	15	points	point	NNS
10_1101-2021_01_08_425885	613	16	is	be	VBZ
10_1101-2021_01_08_425885	613	17	prohibitive	prohibitive	JJ
10_1101-2021_01_08_425885	613	18	however	however	RB
10_1101-2021_01_08_425885	613	19	.	.	.
10_1101-2021_01_08_425885	614	1	To	to	TO
10_1101-2021_01_08_425885	614	2	determine	determine	VB
10_1101-2021_01_08_425885	614	3	a	a	DT
10_1101-2021_01_08_425885	614	4	reasonable	reasonable	JJ
10_1101-2021_01_08_425885	614	5	smaller	small	JJR
10_1101-2021_01_08_425885	614	6	value	value	NN
10_1101-2021_01_08_425885	614	7	of	of	IN
10_1101-2021_01_08_425885	614	8	k	k	NN
10_1101-2021_01_08_425885	614	9	,	,	,
10_1101-2021_01_08_425885	614	10	we	-PRON-	PRP
10_1101-2021_01_08_425885	614	11	randomly	randomly	RB
10_1101-2021_01_08_425885	614	12	selected	select	VBD
10_1101-2021_01_08_425885	614	13	2	2	CD
10_1101-2021_01_08_425885	614	14	×	×	CD
10_1101-2021_01_08_425885	614	15	104	104	CD
10_1101-2021_01_08_425885	614	16	points	point	NNS
10_1101-2021_01_08_425885	614	17	from	from	IN
10_1101-2021_01_08_425885	614	18	the	the	DT
10_1101-2021_01_08_425885	614	19	set	set	NN
10_1101-2021_01_08_425885	614	20	of	of	IN
10_1101-2021_01_08_425885	614	21	N	N	NNP
10_1101-2021_01_08_425885	614	22	≈	≈	NNP
10_1101-2021_01_08_425885	614	23	1.3	1.3	CD
10_1101-2021_01_08_425885	614	24	×	×	CD
10_1101-2021_01_08_425885	614	25	109	109	CD
10_1101-2021_01_08_425885	614	26	on	on	IN
10_1101-2021_01_08_425885	614	27	which	which	WDT
10_1101-2021_01_08_425885	614	28	to	to	TO
10_1101-2021_01_08_425885	614	29	compare	compare	VB
10_1101-2021_01_08_425885	614	30	estimators	estimator	NNS
10_1101-2021_01_08_425885	614	31	and	and	CC
10_1101-2021_01_08_425885	614	32	found	find	VBD
10_1101-2021_01_08_425885	614	33	that	that	IN
10_1101-2021_01_08_425885	614	34	90	90	CD
10_1101-2021_01_08_425885	614	35	%	%	NN
10_1101-2021_01_08_425885	614	36	of	of	IN
10_1101-2021_01_08_425885	614	37	points	point	NNS
10_1101-2021_01_08_425885	614	38	in	in	IN
10_1101-2021_01_08_425885	614	39	the	the	DT
10_1101-2021_01_08_425885	614	40	densest	dense	JJS
10_1101-2021_01_08_425885	614	41	decile	decile	NN
10_1101-2021_01_08_425885	614	42	as	as	IN
10_1101-2021_01_08_425885	614	43	computed	compute	VBN
10_1101-2021_01_08_425885	614	44	with	with	IN
10_1101-2021_01_08_425885	614	45	k	k	NN
10_1101-2021_01_08_425885	614	46	=	=	SYM
10_1101-2021_01_08_425885	614	47	3	3	CD
10_1101-2021_01_08_425885	614	48	×	×	NN
10_1101-2021_01_08_425885	614	49	104	104	CD
10_1101-2021_01_08_425885	614	50	also	also	RB
10_1101-2021_01_08_425885	614	51	appeared	appear	VBD
10_1101-2021_01_08_425885	614	52	in	in	IN
10_1101-2021_01_08_425885	614	53	the	the	DT
10_1101-2021_01_08_425885	614	54	densest	dense	JJS
10_1101-2021_01_08_425885	614	55	decile	decile	NN
10_1101-2021_01_08_425885	614	56	computed	compute	VBD
10_1101-2021_01_08_425885	614	57	using	use	VBG
10_1101-2021_01_08_425885	614	58	k	k	NN
10_1101-2021_01_08_425885	614	59	=	=	SYM
10_1101-2021_01_08_425885	614	60	6	6	CD
10_1101-2021_01_08_425885	614	61	×	×	CD
10_1101-2021_01_08_425885	614	62	102	102	CD
10_1101-2021_01_08_425885	614	63	.	.	.
10_1101-2021_01_08_425885	615	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	615	2	therefore	therefore	RB
10_1101-2021_01_08_425885	615	3	used	use	VBD
10_1101-2021_01_08_425885	615	4	the	the	DT
10_1101-2021_01_08_425885	615	5	latter	latter	JJ
10_1101-2021_01_08_425885	615	6	value	value	NN
10_1101-2021_01_08_425885	615	7	for	for	IN
10_1101-2021_01_08_425885	615	8	density	density	NN
10_1101-2021_01_08_425885	615	9	estimation	estimation	NN
10_1101-2021_01_08_425885	615	10	and	and	CC
10_1101-2021_01_08_425885	615	11	retained	retain	VBD
10_1101-2021_01_08_425885	615	12	the	the	DT
10_1101-2021_01_08_425885	615	13	N	N	NNP
10_1101-2021_01_08_425885	615	14	≈	≈	NNP
10_1101-2021_01_08_425885	615	15	1.3	1.3	CD
10_1101-2021_01_08_425885	615	16	×	×	CD
10_1101-2021_01_08_425885	615	17	108	108	CD
10_1101-2021_01_08_425885	615	18	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	615	19	comprising	comprise	VBG
10_1101-2021_01_08_425885	615	20	the	the	DT
10_1101-2021_01_08_425885	615	21	densest	dense	JJS
10_1101-2021_01_08_425885	615	22	decile	decile	NN
10_1101-2021_01_08_425885	615	23	.	.	.
10_1101-2021_01_08_425885	616	1	4.5.3	4.5.3	CD
10_1101-2021_01_08_425885	616	2	Parametric	Parametric	NNP
10_1101-2021_01_08_425885	616	3	Family	Family	NNP
10_1101-2021_01_08_425885	616	4	of	of	IN
10_1101-2021_01_08_425885	616	5	Klein	Klein	NNP
10_1101-2021_01_08_425885	616	6	Bottle	Bottle	NNP
10_1101-2021_01_08_425885	616	7	Embeddings	Embeddings	NNP
10_1101-2021_01_08_425885	616	8	Let	Let	VBD
10_1101-2021_01_08_425885	616	9	θ	θ	NNP
10_1101-2021_01_08_425885	616	10	,	,	,
10_1101-2021_01_08_425885	616	11	φ	φ	LS
10_1101-2021_01_08_425885	616	12	∈	∈	NNP
10_1101-2021_01_08_425885	616	13	[	[	-LRB-
10_1101-2021_01_08_425885	616	14	0	0	CD
10_1101-2021_01_08_425885	616	15	,	,	,
10_1101-2021_01_08_425885	616	16	2π	2π	CD
10_1101-2021_01_08_425885	616	17	]	]	-RRB-
10_1101-2021_01_08_425885	616	18	.	.	.
10_1101-2021_01_08_425885	617	1	Bivariate	bivariate	JJ
10_1101-2021_01_08_425885	617	2	polynomials	polynomial	NNS
10_1101-2021_01_08_425885	617	3	parameterized	parameterize	VBN
10_1101-2021_01_08_425885	617	4	by	by	IN
10_1101-2021_01_08_425885	617	5	(	(	-LRB-
10_1101-2021_01_08_425885	617	6	θ	θ	NNP
10_1101-2021_01_08_425885	617	7	,	,	,
10_1101-2021_01_08_425885	617	8	φ	φ	NNP
10_1101-2021_01_08_425885	617	9	)	)	-RRB-
10_1101-2021_01_08_425885	617	10	,	,	,
10_1101-2021_01_08_425885	617	11	kθ	kθ	NNP
10_1101-2021_01_08_425885	617	12	,	,	,
10_1101-2021_01_08_425885	617	13	φ	φ	NNP
10_1101-2021_01_08_425885	617	14	∈	∈	NNP
10_1101-2021_01_08_425885	617	15	Kθ	Kθ	NNP
10_1101-2021_01_08_425885	617	16	,	,	,
10_1101-2021_01_08_425885	617	17	φ	φ	NNP
10_1101-2021_01_08_425885	617	18	⊂	⊂	CD
10_1101-2021_01_08_425885	617	19	P	p	NN
10_1101-2021_01_08_425885	617	20	,	,	,
10_1101-2021_01_08_425885	617	21	that	that	WDT
10_1101-2021_01_08_425885	617	22	satisfy	satisfy	VBP
10_1101-2021_01_08_425885	617	23	kθ	kθ	NNP
10_1101-2021_01_08_425885	617	24	,	,	,
10_1101-2021_01_08_425885	617	25	φ	φ	NNP
10_1101-2021_01_08_425885	617	26	=	=	SYM
10_1101-2021_01_08_425885	617	27	kθ+π,2π−φ	kθ+π,2π−φ	NN
10_1101-2021_01_08_425885	617	28	form	form	NN
10_1101-2021_01_08_425885	617	29	a	a	DT
10_1101-2021_01_08_425885	617	30	Klein	Klein	NNP
10_1101-2021_01_08_425885	617	31	bottle	bottle	NN
10_1101-2021_01_08_425885	617	32	,	,	,
10_1101-2021_01_08_425885	617	33	K	K	NNP
10_1101-2021_01_08_425885	617	34	2	2	CD
10_1101-2021_01_08_425885	617	35	:	:	:
10_1101-2021_01_08_425885	617	36	the	the	DT
10_1101-2021_01_08_425885	617	37	(	(	-LRB-
10_1101-2021_01_08_425885	617	38	θ	θ	NNP
10_1101-2021_01_08_425885	617	39	,	,	,
10_1101-2021_01_08_425885	617	40	φ	φ	NNP
10_1101-2021_01_08_425885	617	41	)	)	-RRB-
10_1101-2021_01_08_425885	617	42	∼	∼	NNP
10_1101-2021_01_08_425885	617	43	(	(	-LRB-
10_1101-2021_01_08_425885	617	44	θ	θ	NNP
10_1101-2021_01_08_425885	617	45	+	+	SYM
10_1101-2021_01_08_425885	617	46	π	π	NN
10_1101-2021_01_08_425885	617	47	,	,	,
10_1101-2021_01_08_425885	617	48	2π	2π	CD
10_1101-2021_01_08_425885	617	49	−	−	NNP
10_1101-2021_01_08_425885	617	50	φ	φ	NN
10_1101-2021_01_08_425885	617	51	)	)	-RRB-
10_1101-2021_01_08_425885	617	52	similarity	similarity	NN
10_1101-2021_01_08_425885	617	53	relation	relation	NN
10_1101-2021_01_08_425885	617	54	results	result	NNS
10_1101-2021_01_08_425885	617	55	in	in	IN
10_1101-2021_01_08_425885	617	56	edges	edge	NNS
10_1101-2021_01_08_425885	617	57	being	be	VBG
10_1101-2021_01_08_425885	617	58	glued	glue	VBN
10_1101-2021_01_08_425885	617	59	together	together	RB
10_1101-2021_01_08_425885	617	60	in	in	IN
10_1101-2021_01_08_425885	617	61	the	the	DT
10_1101-2021_01_08_425885	617	62	manner	manner	NN
10_1101-2021_01_08_425885	617	63	definitional	definitional	JJ
10_1101-2021_01_08_425885	617	64	of	of	IN
10_1101-2021_01_08_425885	617	65	a	a	DT
10_1101-2021_01_08_425885	617	66	Klein	Klein	NNP
10_1101-2021_01_08_425885	617	67	bottle	bottle	NN
10_1101-2021_01_08_425885	617	68	’s	’s	NN
10_1101-2021_01_08_425885	617	69	topology	topology	NN
10_1101-2021_01_08_425885	617	70	(	(	-LRB-
10_1101-2021_01_08_425885	617	71	shown	show	VBN
10_1101-2021_01_08_425885	617	72	in	in	IN
10_1101-2021_01_08_425885	617	73	Figure	Figure	NNP
10_1101-2021_01_08_425885	617	74	3B	3b	NN
10_1101-2021_01_08_425885	617	75	)	)	-RRB-
10_1101-2021_01_08_425885	617	76	.	.	.
10_1101-2021_01_08_425885	618	1	The	the	DT
10_1101-2021_01_08_425885	618	2	candidate	candidate	NN
10_1101-2021_01_08_425885	618	3	Klein	Klein	NNP
10_1101-2021_01_08_425885	618	4	bottle	bottle	NN
10_1101-2021_01_08_425885	618	5	embedding	embed	VBG
10_1101-2021_01_08_425885	618	6	supplied	supply	VBN
10_1101-2021_01_08_425885	618	7	in	in	IN
10_1101-2021_01_08_425885	618	8	[	[	-LRB-
10_1101-2021_01_08_425885	618	9	21	21	CD
10_1101-2021_01_08_425885	618	10	]	]	-RRB-
10_1101-2021_01_08_425885	618	11	to	to	TO
10_1101-2021_01_08_425885	618	12	model	model	VB
10_1101-2021_01_08_425885	618	13	image	image	NN
10_1101-2021_01_08_425885	618	14	patch	patch	NN
10_1101-2021_01_08_425885	618	15	data	data	NN
10_1101-2021_01_08_425885	618	16	satisfies	satisfie	NNS
10_1101-2021_01_08_425885	618	17	the	the	DT
10_1101-2021_01_08_425885	618	18	similarity	similarity	NN
10_1101-2021_01_08_425885	618	19	relation	relation	NN
10_1101-2021_01_08_425885	618	20	∀x	∀x	NNP
10_1101-2021_01_08_425885	618	21	,	,	,
10_1101-2021_01_08_425885	618	22	y	y	NNP
10_1101-2021_01_08_425885	618	23	:	:	:
10_1101-2021_01_08_425885	618	24	k0	k0	NNP
10_1101-2021_01_08_425885	618	25	≡	≡	NNP
10_1101-2021_01_08_425885	618	26	k0θ	k0θ	NNP
10_1101-2021_01_08_425885	618	27	,	,	,
10_1101-2021_01_08_425885	618	28	φ(x	φ(x	NNP
10_1101-2021_01_08_425885	618	29	,	,	,
10_1101-2021_01_08_425885	618	30	y	y	NNP
10_1101-2021_01_08_425885	618	31	)	)	-RRB-
10_1101-2021_01_08_425885	618	32	=	=	SYM
10_1101-2021_01_08_425885	618	33	cos	cos	NNP
10_1101-2021_01_08_425885	618	34	φ	φ	NNP
10_1101-2021_01_08_425885	618	35	[	[	-LRB-
10_1101-2021_01_08_425885	618	36	x	x	SYM
10_1101-2021_01_08_425885	618	37	cos	cos	NNP
10_1101-2021_01_08_425885	618	38	θ	θ	NNP
10_1101-2021_01_08_425885	618	39	+	+	SYM
10_1101-2021_01_08_425885	618	40	y	y	NNP
10_1101-2021_01_08_425885	618	41	sin	sin	NN
10_1101-2021_01_08_425885	618	42	θ	θ	NNP
10_1101-2021_01_08_425885	618	43	]	]	-RRB-
10_1101-2021_01_08_425885	618	44	2	2	CD
10_1101-2021_01_08_425885	618	45	+	+	SYM
10_1101-2021_01_08_425885	618	46	sin	sin	NN
10_1101-2021_01_08_425885	618	47	φ	φ	NN
10_1101-2021_01_08_425885	618	48	[	[	-LRB-
10_1101-2021_01_08_425885	618	49	x	x	SYM
10_1101-2021_01_08_425885	618	50	cos	cos	NNP
10_1101-2021_01_08_425885	618	51	θ	θ	NNP
10_1101-2021_01_08_425885	618	52	+	+	SYM
10_1101-2021_01_08_425885	618	53	y	y	NNP
10_1101-2021_01_08_425885	618	54	sin	sin	NN
10_1101-2021_01_08_425885	618	55	θ	θ	NNP
10_1101-2021_01_08_425885	618	56	]	]	-RRB-
10_1101-2021_01_08_425885	618	57	(	(	-LRB-
10_1101-2021_01_08_425885	618	58	31	31	CD
10_1101-2021_01_08_425885	618	59	)	)	-RRB-
10_1101-2021_01_08_425885	618	60	Note	note	VB
10_1101-2021_01_08_425885	618	61	that	that	IN
10_1101-2021_01_08_425885	618	62	any	any	DT
10_1101-2021_01_08_425885	618	63	kθ	kθ	NN
10_1101-2021_01_08_425885	618	64	,	,	,
10_1101-2021_01_08_425885	618	65	φ	φ	NNP
10_1101-2021_01_08_425885	618	66	∈	∈	NNP
10_1101-2021_01_08_425885	618	67	Kθ	Kθ	NNP
10_1101-2021_01_08_425885	618	68	,	,	,
10_1101-2021_01_08_425885	618	69	φ	φ	DT
10_1101-2021_01_08_425885	618	70	can	can	MD
10_1101-2021_01_08_425885	618	71	be	be	VB
10_1101-2021_01_08_425885	618	72	decomposed	decompose	VBN
10_1101-2021_01_08_425885	618	73	as	as	IN
10_1101-2021_01_08_425885	618	74	:	:	:
10_1101-2021_01_08_425885	618	75	kθ	kθ	NNP
10_1101-2021_01_08_425885	618	76	,	,	,
10_1101-2021_01_08_425885	618	77	φ	φ	NNP
10_1101-2021_01_08_425885	618	78	=	=	SYM
10_1101-2021_01_08_425885	618	79	C	C	NNP
10_1101-2021_01_08_425885	618	80	+	+	CC
10_1101-2021_01_08_425885	618	81	κθ	κθ	NN
10_1101-2021_01_08_425885	618	82	+	+	SYM
10_1101-2021_01_08_425885	618	83	κφ	κφ	XX
10_1101-2021_01_08_425885	618	84	+	+	CC
10_1101-2021_01_08_425885	618	85	κθ	κθ	UH
10_1101-2021_01_08_425885	618	86	,	,	,
10_1101-2021_01_08_425885	618	87	φ	φ	NNP
10_1101-2021_01_08_425885	618	88	(	(	-LRB-
10_1101-2021_01_08_425885	618	89	32	32	CD
10_1101-2021_01_08_425885	618	90	)	)	-RRB-
10_1101-2021_01_08_425885	618	91	36	36	CD
10_1101-2021_01_08_425885	618	92	.CC	.CC	NFP
10_1101-2021_01_08_425885	618	93	-	-	HYPH
10_1101-2021_01_08_425885	618	94	BY	by	IN
10_1101-2021_01_08_425885	618	95	-	-	HYPH
10_1101-2021_01_08_425885	618	96	NC	NC	NNP
10_1101-2021_01_08_425885	618	97	-	-	HYPH
10_1101-2021_01_08_425885	618	98	ND	ND	NNP
10_1101-2021_01_08_425885	618	99	4.0	4.0	CD
10_1101-2021_01_08_425885	618	100	International	International	NNP
10_1101-2021_01_08_425885	618	101	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	618	102	under	under	IN
10_1101-2021_01_08_425885	618	103	a	a	DT
10_1101-2021_01_08_425885	618	104	(	(	-LRB-
10_1101-2021_01_08_425885	618	105	which	which	WDT
10_1101-2021_01_08_425885	618	106	was	be	VBD
10_1101-2021_01_08_425885	618	107	not	not	RB
10_1101-2021_01_08_425885	618	108	certified	certify	VBN
10_1101-2021_01_08_425885	618	109	by	by	IN
10_1101-2021_01_08_425885	618	110	peer	peer	NN
10_1101-2021_01_08_425885	618	111	review	review	NN
10_1101-2021_01_08_425885	618	112	)	)	-RRB-
10_1101-2021_01_08_425885	618	113	is	be	VBZ
10_1101-2021_01_08_425885	618	114	the	the	DT
10_1101-2021_01_08_425885	618	115	author	author	NN
10_1101-2021_01_08_425885	618	116	/	/	SYM
10_1101-2021_01_08_425885	618	117	funder	funder	NN
10_1101-2021_01_08_425885	618	118	,	,	,
10_1101-2021_01_08_425885	618	119	who	who	WP
10_1101-2021_01_08_425885	618	120	has	have	VBZ
10_1101-2021_01_08_425885	618	121	granted	grant	VBN
10_1101-2021_01_08_425885	618	122	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	618	123	a	a	DT
10_1101-2021_01_08_425885	618	124	license	license	NN
10_1101-2021_01_08_425885	618	125	to	to	TO
10_1101-2021_01_08_425885	618	126	display	display	VB
10_1101-2021_01_08_425885	618	127	the	the	DT
10_1101-2021_01_08_425885	618	128	preprint	preprint	NN
10_1101-2021_01_08_425885	618	129	in	in	IN
10_1101-2021_01_08_425885	618	130	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	618	131	.	.	.
10_1101-2021_01_08_425885	619	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	619	2	is	be	VBZ
10_1101-2021_01_08_425885	619	3	made	make	VBN
10_1101-2021_01_08_425885	619	4	The	the	DT
10_1101-2021_01_08_425885	619	5	copyright	copyright	NN
10_1101-2021_01_08_425885	619	6	holder	holder	NN
10_1101-2021_01_08_425885	619	7	for	for	IN
10_1101-2021_01_08_425885	619	8	this	this	DT
10_1101-2021_01_08_425885	619	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	619	10	version	version	NN
10_1101-2021_01_08_425885	619	11	posted	post	VBD
10_1101-2021_01_08_425885	619	12	January	January	NNP
10_1101-2021_01_08_425885	619	13	8	8	CD
10_1101-2021_01_08_425885	619	14	,	,	,
10_1101-2021_01_08_425885	619	15	2021	2021	CD
10_1101-2021_01_08_425885	619	16	.	.	.
10_1101-2021_01_08_425885	619	17	;	;	:
10_1101-2021_01_08_425885	619	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	619	19	:	:	:
10_1101-2021_01_08_425885	619	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	619	21	preprint	preprint	NN
10_1101-2021_01_08_425885	619	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	619	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NN
10_1101-2021_01_08_425885	619	24	where	where	WRB
10_1101-2021_01_08_425885	619	25	κθ	κθ	NNP
10_1101-2021_01_08_425885	619	26	=	=	-RRB-
10_1101-2021_01_08_425885	619	27	κθ+π	κθ+π	UH
10_1101-2021_01_08_425885	619	28	,	,	,
10_1101-2021_01_08_425885	619	29	κφ	κφ	NNP
10_1101-2021_01_08_425885	619	30	=	=	SYM
10_1101-2021_01_08_425885	619	31	κ2π−φ	κ2π−φ	NNP
10_1101-2021_01_08_425885	619	32	and	and	CC
10_1101-2021_01_08_425885	619	33	κθ	κθ	NNP
10_1101-2021_01_08_425885	619	34	,	,	,
10_1101-2021_01_08_425885	619	35	φ	φ	NNP
10_1101-2021_01_08_425885	619	36	=	=	SYM
10_1101-2021_01_08_425885	619	37	κθ+π,2π−φ	κθ+π,2π−φ	NNP
10_1101-2021_01_08_425885	619	38	.	.	.
10_1101-2021_01_08_425885	620	1	The	the	DT
10_1101-2021_01_08_425885	620	2	first	first	JJ
10_1101-2021_01_08_425885	620	3	three	three	CD
10_1101-2021_01_08_425885	620	4	terms	term	NNS
10_1101-2021_01_08_425885	620	5	can	can	MD
10_1101-2021_01_08_425885	620	6	be	be	VB
10_1101-2021_01_08_425885	620	7	understood	understand	VBN
10_1101-2021_01_08_425885	620	8	as	as	IN
10_1101-2021_01_08_425885	620	9	constant	constant	JJ
10_1101-2021_01_08_425885	620	10	,	,	,
10_1101-2021_01_08_425885	620	11	θ	θ	NN
10_1101-2021_01_08_425885	620	12	-	-	HYPH
10_1101-2021_01_08_425885	620	13	dependent	dependent	JJ
10_1101-2021_01_08_425885	620	14	and	and	CC
10_1101-2021_01_08_425885	620	15	φ	φ	JJ
10_1101-2021_01_08_425885	620	16	-	-	HYPH
10_1101-2021_01_08_425885	620	17	dependent	dependent	JJ
10_1101-2021_01_08_425885	620	18	phases	phase	NNS
10_1101-2021_01_08_425885	620	19	respectively	respectively	RB
10_1101-2021_01_08_425885	620	20	.	.	.
10_1101-2021_01_08_425885	621	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	621	2	sought	seek	VBD
10_1101-2021_01_08_425885	621	3	an	an	DT
10_1101-2021_01_08_425885	621	4	embedding	embedding	NN
10_1101-2021_01_08_425885	621	5	of	of	IN
10_1101-2021_01_08_425885	621	6	the	the	DT
10_1101-2021_01_08_425885	621	7	Klein	Klein	NNP
10_1101-2021_01_08_425885	621	8	bottle	bottle	NN
10_1101-2021_01_08_425885	621	9	for	for	IN
10_1101-2021_01_08_425885	621	10	which	which	WDT
10_1101-2021_01_08_425885	621	11	the	the	DT
10_1101-2021_01_08_425885	621	12	sum	sum	NN
10_1101-2021_01_08_425885	621	13	of	of	IN
10_1101-2021_01_08_425885	621	14	Euclidean	euclidean	JJ
10_1101-2021_01_08_425885	621	15	distances	distance	NNS
10_1101-2021_01_08_425885	621	16	from	from	IN
10_1101-2021_01_08_425885	621	17	each	each	DT
10_1101-2021_01_08_425885	621	18	image	image	NN
10_1101-2021_01_08_425885	621	19	patch	patch	NN
10_1101-2021_01_08_425885	621	20	to	to	IN
10_1101-2021_01_08_425885	621	21	its	-PRON-	PRP$
10_1101-2021_01_08_425885	621	22	closest	close	JJS
10_1101-2021_01_08_425885	621	23	point	point	NN
10_1101-2021_01_08_425885	621	24	on	on	IN
10_1101-2021_01_08_425885	621	25	the	the	DT
10_1101-2021_01_08_425885	621	26	embedding	embedding	NN
10_1101-2021_01_08_425885	621	27	is	be	VBZ
10_1101-2021_01_08_425885	621	28	minimized	minimize	VBN
10_1101-2021_01_08_425885	621	29	.	.	.
10_1101-2021_01_08_425885	622	1	To	to	TO
10_1101-2021_01_08_425885	622	2	accomplish	accomplish	VB
10_1101-2021_01_08_425885	622	3	this	this	DT
10_1101-2021_01_08_425885	622	4	,	,	,
10_1101-2021_01_08_425885	622	5	we	-PRON-	PRP
10_1101-2021_01_08_425885	622	6	constructed	construct	VBD
10_1101-2021_01_08_425885	622	7	a	a	DT
10_1101-2021_01_08_425885	622	8	parametric	parametric	JJ
10_1101-2021_01_08_425885	622	9	family	family	NN
10_1101-2021_01_08_425885	622	10	of	of	IN
10_1101-2021_01_08_425885	622	11	models	model	NNS
10_1101-2021_01_08_425885	622	12	for	for	IN
10_1101-2021_01_08_425885	622	13	each	each	DT
10_1101-2021_01_08_425885	622	14	of	of	IN
10_1101-2021_01_08_425885	622	15	the	the	DT
10_1101-2021_01_08_425885	622	16	four	four	CD
10_1101-2021_01_08_425885	622	17	terms	term	NNS
10_1101-2021_01_08_425885	622	18	in	in	IN
10_1101-2021_01_08_425885	622	19	Equation	Equation	NNP
10_1101-2021_01_08_425885	622	20	32	32	CD
10_1101-2021_01_08_425885	622	21	.	.	.
10_1101-2021_01_08_425885	623	1	The	the	DT
10_1101-2021_01_08_425885	623	2	first	first	JJ
10_1101-2021_01_08_425885	623	3	three	three	CD
10_1101-2021_01_08_425885	623	4	of	of	IN
10_1101-2021_01_08_425885	623	5	these	these	DT
10_1101-2021_01_08_425885	623	6	are	be	VBP
10_1101-2021_01_08_425885	623	7	most	most	RBS
10_1101-2021_01_08_425885	623	8	conveniently	conveniently	RB
10_1101-2021_01_08_425885	623	9	expressed	express	VBN
10_1101-2021_01_08_425885	623	10	directly	directly	RB
10_1101-2021_01_08_425885	623	11	in	in	IN
10_1101-2021_01_08_425885	623	12	the	the	DT
10_1101-2021_01_08_425885	623	13	DCT	dct	NN
10_1101-2021_01_08_425885	623	14	basis	basis	NN
10_1101-2021_01_08_425885	623	15	.	.	.
10_1101-2021_01_08_425885	624	1	(	(	-LRB-
10_1101-2021_01_08_425885	624	2	c	c	NNP
10_1101-2021_01_08_425885	624	3	◦	◦	NNP
10_1101-2021_01_08_425885	624	4	h	h	NNP
10_1101-2021_01_08_425885	624	5	)	)	-RRB-
10_1101-2021_01_08_425885	624	6	(	(	-LRB-
10_1101-2021_01_08_425885	624	7	C	c	NN
10_1101-2021_01_08_425885	624	8	)	)	-RRB-
10_1101-2021_01_08_425885	624	9	=	=	NFP
10_1101-2021_01_08_425885	624	10	NC	NC	NNP
10_1101-2021_01_08_425885	624	11	8∑	8∑	NN
10_1101-2021_01_08_425885	624	12	i=1	i=1	NN
10_1101-2021_01_08_425885	624	13	µiei	µiei	NN
10_1101-2021_01_08_425885	624	14	(	(	-LRB-
10_1101-2021_01_08_425885	624	15	c	c	NNP
10_1101-2021_01_08_425885	624	16	◦	◦	NNP
10_1101-2021_01_08_425885	624	17	h	h	NNP
10_1101-2021_01_08_425885	624	18	)	)	-RRB-
10_1101-2021_01_08_425885	624	19	(	(	-LRB-
10_1101-2021_01_08_425885	624	20	κθ	κθ	NNP
10_1101-2021_01_08_425885	624	21	)	)	-RRB-
10_1101-2021_01_08_425885	624	22	=	=	SYM
10_1101-2021_01_08_425885	624	23	8∑	8∑	NNP
10_1101-2021_01_08_425885	624	24	i=1	i=1	NNPS
10_1101-2021_01_08_425885	624	25			NNP
10_1101-2021_01_08_425885	624	26			NNPS
10_1101-2021_01_08_425885	624	27	Nθ∑	Nθ∑	NNP
10_1101-2021_01_08_425885	624	28	j=2	j=2	NNP
10_1101-2021_01_08_425885	624	29	j	j	NNP
10_1101-2021_01_08_425885	624	30	even	even	RB
10_1101-2021_01_08_425885	624	31	βi	βi	RB
10_1101-2021_01_08_425885	624	32	,	,	,
10_1101-2021_01_08_425885	624	33	j	j	NNP
10_1101-2021_01_08_425885	624	34	cos(jθ	cos(jθ	NNP
10_1101-2021_01_08_425885	624	35	)	)	-RRB-
10_1101-2021_01_08_425885	624	36	+	+	CC
10_1101-2021_01_08_425885	624	37	γi	γi	NNP
10_1101-2021_01_08_425885	624	38	,	,	,
10_1101-2021_01_08_425885	624	39	j	j	NNP
10_1101-2021_01_08_425885	624	40	sin(jθ	sin(jθ	NNP
10_1101-2021_01_08_425885	624	41	)	)	-RRB-
10_1101-2021_01_08_425885	624	42			NNS
10_1101-2021_01_08_425885	624	43			CD
10_1101-2021_01_08_425885	624	44	ei	ei	NN
10_1101-2021_01_08_425885	624	45	(	(	-LRB-
10_1101-2021_01_08_425885	624	46	c	c	NNP
10_1101-2021_01_08_425885	624	47	◦	◦	NNP
10_1101-2021_01_08_425885	624	48	h	h	NNP
10_1101-2021_01_08_425885	624	49	)	)	-RRB-
10_1101-2021_01_08_425885	624	50	(	(	-LRB-
10_1101-2021_01_08_425885	624	51	κφ	κφ	NNP
10_1101-2021_01_08_425885	624	52	)	)	-RRB-
10_1101-2021_01_08_425885	624	53	=	=	SYM
10_1101-2021_01_08_425885	624	54	8∑	8∑	NNP
10_1101-2021_01_08_425885	624	55	i=1	i=1	NNPS
10_1101-2021_01_08_425885	624	56			NNP
10_1101-2021_01_08_425885	624	57	Nφ∑	Nφ∑	NNP
10_1101-2021_01_08_425885	624	58	j=1	j=1	NNS
10_1101-2021_01_08_425885	624	59	ζi	ζi	NNP
10_1101-2021_01_08_425885	624	60	,	,	,
10_1101-2021_01_08_425885	624	61	j	j	NNP
10_1101-2021_01_08_425885	624	62	cos(jφ	cos(jφ	NNP
10_1101-2021_01_08_425885	624	63	)	)	-RRB-
10_1101-2021_01_08_425885	624	64			NNP
10_1101-2021_01_08_425885	624	65	ei	ei	CD
10_1101-2021_01_08_425885	624	66	(	(	-LRB-
10_1101-2021_01_08_425885	624	67	33	33	CD
10_1101-2021_01_08_425885	624	68	)	)	-RRB-
10_1101-2021_01_08_425885	624	69	NC	NC	NNP
10_1101-2021_01_08_425885	624	70	is	be	VBZ
10_1101-2021_01_08_425885	624	71	a	a	DT
10_1101-2021_01_08_425885	624	72	Boolean	boolean	JJ
10_1101-2021_01_08_425885	624	73	variable	variable	NN
10_1101-2021_01_08_425885	624	74	,	,	,
10_1101-2021_01_08_425885	624	75	and	and	CC
10_1101-2021_01_08_425885	624	76	Nθ	nθ	UH
10_1101-2021_01_08_425885	624	77	and	and	CC
10_1101-2021_01_08_425885	624	78	Nφ	Nφ	NNP
10_1101-2021_01_08_425885	624	79	control	control	VB
10_1101-2021_01_08_425885	624	80	the	the	DT
10_1101-2021_01_08_425885	624	81	number	number	NN
10_1101-2021_01_08_425885	624	82	of	of	IN
10_1101-2021_01_08_425885	624	83	terms	term	NNS
10_1101-2021_01_08_425885	624	84	in	in	IN
10_1101-2021_01_08_425885	624	85	the	the	DT
10_1101-2021_01_08_425885	624	86	inner	inner	JJ
10_1101-2021_01_08_425885	624	87	sum	sum	NN
10_1101-2021_01_08_425885	624	88	for	for	IN
10_1101-2021_01_08_425885	624	89	(	(	-LRB-
10_1101-2021_01_08_425885	624	90	c	c	NN
10_1101-2021_01_08_425885	624	91	◦	◦	NNP
10_1101-2021_01_08_425885	624	92	h	h	NNP
10_1101-2021_01_08_425885	624	93	)	)	-RRB-
10_1101-2021_01_08_425885	624	94	(	(	-LRB-
10_1101-2021_01_08_425885	624	95	κθ	κθ	NNP
10_1101-2021_01_08_425885	624	96	)	)	-RRB-
10_1101-2021_01_08_425885	624	97	and	and	CC
10_1101-2021_01_08_425885	624	98	(	(	-LRB-
10_1101-2021_01_08_425885	624	99	c	c	NN
10_1101-2021_01_08_425885	624	100	◦	◦	NNP
10_1101-2021_01_08_425885	624	101	h	h	NNP
10_1101-2021_01_08_425885	624	102	)	)	-RRB-
10_1101-2021_01_08_425885	624	103	(	(	-LRB-
10_1101-2021_01_08_425885	624	104	κφ	κφ	NN
10_1101-2021_01_08_425885	624	105	)	)	-RRB-
10_1101-2021_01_08_425885	624	106	respectively	respectively	RB
10_1101-2021_01_08_425885	624	107	.	.	.
10_1101-2021_01_08_425885	625	1	The	the	DT
10_1101-2021_01_08_425885	625	2	expression	expression	NN
10_1101-2021_01_08_425885	625	3	for	for	IN
10_1101-2021_01_08_425885	625	4	(	(	-LRB-
10_1101-2021_01_08_425885	625	5	c	c	NN
10_1101-2021_01_08_425885	625	6	◦	◦	NNP
10_1101-2021_01_08_425885	625	7	h	h	NNP
10_1101-2021_01_08_425885	625	8	)	)	-RRB-
10_1101-2021_01_08_425885	625	9	(	(	-LRB-
10_1101-2021_01_08_425885	625	10	κθ	κθ	NNP
10_1101-2021_01_08_425885	625	11	)	)	-RRB-
10_1101-2021_01_08_425885	625	12	only	only	RB
10_1101-2021_01_08_425885	625	13	includes	include	VBZ
10_1101-2021_01_08_425885	625	14	even	even	RB
10_1101-2021_01_08_425885	625	15	coefficients	coefficient	NNS
10_1101-2021_01_08_425885	625	16	for	for	IN
10_1101-2021_01_08_425885	625	17	θ	θ	NNP
10_1101-2021_01_08_425885	625	18	so	so	IN
10_1101-2021_01_08_425885	625	19	that	that	IN
10_1101-2021_01_08_425885	625	20	the	the	DT
10_1101-2021_01_08_425885	625	21	similarity	similarity	NN
10_1101-2021_01_08_425885	625	22	relation	relation	NN
10_1101-2021_01_08_425885	625	23	(	(	-LRB-
10_1101-2021_01_08_425885	625	24	θ	θ	NNP
10_1101-2021_01_08_425885	625	25	)	)	-RRB-
10_1101-2021_01_08_425885	625	26	∼	∼	NNP
10_1101-2021_01_08_425885	625	27	(	(	-LRB-
10_1101-2021_01_08_425885	625	28	θ	θ	NNP
10_1101-2021_01_08_425885	625	29	+	+	SYM
10_1101-2021_01_08_425885	625	30	π	π	NN
10_1101-2021_01_08_425885	625	31	)	)	-RRB-
10_1101-2021_01_08_425885	625	32	is	be	VBZ
10_1101-2021_01_08_425885	625	33	satisfied	satisfied	JJ
10_1101-2021_01_08_425885	625	34	.	.	.
10_1101-2021_01_08_425885	626	1	The	the	DT
10_1101-2021_01_08_425885	626	2	expression	expression	NN
10_1101-2021_01_08_425885	626	3	for	for	IN
10_1101-2021_01_08_425885	626	4	(	(	-LRB-
10_1101-2021_01_08_425885	626	5	c	c	NN
10_1101-2021_01_08_425885	626	6	◦	◦	NNP
10_1101-2021_01_08_425885	626	7	h	h	NNP
10_1101-2021_01_08_425885	626	8	)	)	-RRB-
10_1101-2021_01_08_425885	626	9	(	(	-LRB-
10_1101-2021_01_08_425885	626	10	κφ	κφ	NNP
10_1101-2021_01_08_425885	626	11	)	)	-RRB-
10_1101-2021_01_08_425885	626	12	only	only	RB
10_1101-2021_01_08_425885	626	13	includes	include	VBZ
10_1101-2021_01_08_425885	626	14	cosine	cosine	NN
10_1101-2021_01_08_425885	626	15	terms	term	NNS
10_1101-2021_01_08_425885	626	16	so	so	IN
10_1101-2021_01_08_425885	626	17	that	that	IN
10_1101-2021_01_08_425885	626	18	the	the	DT
10_1101-2021_01_08_425885	626	19	similarity	similarity	NN
10_1101-2021_01_08_425885	626	20	relation	relation	NN
10_1101-2021_01_08_425885	626	21	(	(	-LRB-
10_1101-2021_01_08_425885	626	22	φ	φ	NNP
10_1101-2021_01_08_425885	626	23	)	)	-RRB-
10_1101-2021_01_08_425885	626	24	∼	∼	NNP
10_1101-2021_01_08_425885	626	25	(	(	-LRB-
10_1101-2021_01_08_425885	626	26	2π	2π	NNP
10_1101-2021_01_08_425885	626	27	−φ	−φ	CD
10_1101-2021_01_08_425885	626	28	)	)	-RRB-
10_1101-2021_01_08_425885	626	29	is	be	VBZ
10_1101-2021_01_08_425885	626	30	satisfied	satisfied	JJ
10_1101-2021_01_08_425885	626	31	.	.	.
10_1101-2021_01_08_425885	627	1	For	for	IN
10_1101-2021_01_08_425885	627	2	κθ	κθ	NNP
10_1101-2021_01_08_425885	627	3	,	,	,
10_1101-2021_01_08_425885	627	4	φ	φ	UH
10_1101-2021_01_08_425885	627	5	,	,	,
10_1101-2021_01_08_425885	627	6	we	-PRON-	PRP
10_1101-2021_01_08_425885	627	7	refrained	refrain	VBD
10_1101-2021_01_08_425885	627	8	from	from	IN
10_1101-2021_01_08_425885	627	9	writing	write	VBG
10_1101-2021_01_08_425885	627	10	a	a	DT
10_1101-2021_01_08_425885	627	11	Fourier	Fourier	NNP
10_1101-2021_01_08_425885	627	12	series	series	NN
10_1101-2021_01_08_425885	627	13	-	-	HYPH
10_1101-2021_01_08_425885	627	14	like	like	JJ
10_1101-2021_01_08_425885	627	15	expansion	expansion	NN
10_1101-2021_01_08_425885	627	16	because	because	IN
10_1101-2021_01_08_425885	627	17	we	-PRON-	PRP
10_1101-2021_01_08_425885	627	18	wanted	want	VBD
10_1101-2021_01_08_425885	627	19	to	to	TO
10_1101-2021_01_08_425885	627	20	preserve	preserve	VB
10_1101-2021_01_08_425885	627	21	the	the	DT
10_1101-2021_01_08_425885	627	22	interpretation	interpretation	NN
10_1101-2021_01_08_425885	627	23	of	of	IN
10_1101-2021_01_08_425885	627	24	θ	θ	NNP
10_1101-2021_01_08_425885	627	25	and	and	CC
10_1101-2021_01_08_425885	627	26	φ	φ	NNP
10_1101-2021_01_08_425885	627	27	as	as	IN
10_1101-2021_01_08_425885	627	28	parameters	parameter	NNS
10_1101-2021_01_08_425885	627	29	controlling	control	VBG
10_1101-2021_01_08_425885	627	30	the	the	DT
10_1101-2021_01_08_425885	627	31	orientation	orientation	NN
10_1101-2021_01_08_425885	627	32	and	and	CC
10_1101-2021_01_08_425885	627	33	gradient	gradient	NN
10_1101-2021_01_08_425885	627	34	respectively	respectively	RB
10_1101-2021_01_08_425885	627	35	[	[	-LRB-
10_1101-2021_01_08_425885	627	36	21	21	CD
10_1101-2021_01_08_425885	627	37	]	]	-RRB-
10_1101-2021_01_08_425885	627	38	.	.	.
10_1101-2021_01_08_425885	628	1	Instead	instead	RB
10_1101-2021_01_08_425885	628	2	,	,	,
10_1101-2021_01_08_425885	628	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	628	4	devised	devise	VBD
10_1101-2021_01_08_425885	628	5	the	the	DT
10_1101-2021_01_08_425885	628	6	following	follow	VBG
10_1101-2021_01_08_425885	628	7	form	form	NN
10_1101-2021_01_08_425885	628	8	,	,	,
10_1101-2021_01_08_425885	628	9	which	which	WDT
10_1101-2021_01_08_425885	628	10	we	-PRON-	PRP
10_1101-2021_01_08_425885	628	11	motivate	motivate	VBP
10_1101-2021_01_08_425885	628	12	further	further	RB
10_1101-2021_01_08_425885	628	13	below	below	RB
10_1101-2021_01_08_425885	628	14	:	:	:
10_1101-2021_01_08_425885	628	15	κθ	κθ	NNP
10_1101-2021_01_08_425885	628	16	,	,	,
10_1101-2021_01_08_425885	628	17	φ(x	φ(x	NNP
10_1101-2021_01_08_425885	628	18	,	,	,
10_1101-2021_01_08_425885	628	19	y	y	NNP
10_1101-2021_01_08_425885	628	20	)	)	-RRB-
10_1101-2021_01_08_425885	628	21	=	=	SYM
10_1101-2021_01_08_425885	628	22	Mφ∑	Mφ∑	NNP
10_1101-2021_01_08_425885	628	23	l=1	l=1	JJ
10_1101-2021_01_08_425885	628	24	cosl(φ	cosl(φ	NNP
10_1101-2021_01_08_425885	628	25	)	)	-RRB-
10_1101-2021_01_08_425885	628	26			NNP
10_1101-2021_01_08_425885	628	27			NNP
10_1101-2021_01_08_425885	628	28	s+t≤Mθ∑	s+t≤Mθ∑	NNP
10_1101-2021_01_08_425885	628	29	0≤s	0≤s	NNP
10_1101-2021_01_08_425885	628	30	,	,	,
10_1101-2021_01_08_425885	628	31	t≤Mθ	t≤mθ	DT
10_1101-2021_01_08_425885	628	32	1	1	CD
10_1101-2021_01_08_425885	628	33	<	<	XX
10_1101-2021_01_08_425885	628	34	s+t	s+t	NNP
10_1101-2021_01_08_425885	628	35	even	even	RB
10_1101-2021_01_08_425885	628	36	ηl	ηl	RB
10_1101-2021_01_08_425885	628	37	,	,	,
10_1101-2021_01_08_425885	628	38	s	s	NNP
10_1101-2021_01_08_425885	628	39	,	,	,
10_1101-2021_01_08_425885	628	40	t(x	t(x	NNP
10_1101-2021_01_08_425885	628	41	cos	cos	NNP
10_1101-2021_01_08_425885	628	42	θ	θ	NNP
10_1101-2021_01_08_425885	628	43	)	)	-RRB-
10_1101-2021_01_08_425885	628	44	s(y	s(y	NNP
10_1101-2021_01_08_425885	628	45	sin	sin	NN
10_1101-2021_01_08_425885	628	46	θ)t	θ)t	NNP
10_1101-2021_01_08_425885	628	47			NNP
10_1101-2021_01_08_425885	628	48			NNP
10_1101-2021_01_08_425885	628	49	+	+	SYM
10_1101-2021_01_08_425885	628	50	Mφ∑	Mφ∑	NNP
10_1101-2021_01_08_425885	628	51	l=1	l=1	NNP
10_1101-2021_01_08_425885	628	52	l	l	NNP
10_1101-2021_01_08_425885	628	53	odd	odd	JJ
10_1101-2021_01_08_425885	628	54	sinl(φ	sinl(φ	NNP
10_1101-2021_01_08_425885	628	55	)	)	-RRB-
10_1101-2021_01_08_425885	628	56			NNP
10_1101-2021_01_08_425885	628	57			ADD
10_1101-2021_01_08_425885	628	58	s+t≤Mθ∑	s+t≤Mθ∑	NNP
10_1101-2021_01_08_425885	628	59	0≤s	0≤s	NNP
10_1101-2021_01_08_425885	628	60	,	,	,
10_1101-2021_01_08_425885	628	61	t≤Mθ	t≤mθ	DT
10_1101-2021_01_08_425885	628	62	s+t	s+t	NNP
10_1101-2021_01_08_425885	628	63	odd	odd	JJ
10_1101-2021_01_08_425885	628	64	ϑl	ϑl	NNP
10_1101-2021_01_08_425885	628	65	,	,	,
10_1101-2021_01_08_425885	628	66	s	s	NNP
10_1101-2021_01_08_425885	628	67	,	,	,
10_1101-2021_01_08_425885	628	68	t(x	t(x	NNP
10_1101-2021_01_08_425885	628	69	cos	cos	NNP
10_1101-2021_01_08_425885	628	70	θ	θ	NNP
10_1101-2021_01_08_425885	628	71	)	)	-RRB-
10_1101-2021_01_08_425885	628	72	s(y	s(y	NNP
10_1101-2021_01_08_425885	628	73	sin	sin	NN
10_1101-2021_01_08_425885	628	74	θ)t	θ)t	NNP
10_1101-2021_01_08_425885	628	75			NNP
10_1101-2021_01_08_425885	628	76			CD
10_1101-2021_01_08_425885	628	77	(	(	-LRB-
10_1101-2021_01_08_425885	628	78	34	34	CD
10_1101-2021_01_08_425885	628	79	)	)	-RRB-
10_1101-2021_01_08_425885	628	80	The	the	DT
10_1101-2021_01_08_425885	628	81	expression	expression	NN
10_1101-2021_01_08_425885	628	82	for	for	IN
10_1101-2021_01_08_425885	628	83	(	(	-LRB-
10_1101-2021_01_08_425885	628	84	c	c	NN
10_1101-2021_01_08_425885	628	85	◦	◦	NNP
10_1101-2021_01_08_425885	628	86	h	h	NNP
10_1101-2021_01_08_425885	628	87	)	)	-RRB-
10_1101-2021_01_08_425885	628	88	(	(	-LRB-
10_1101-2021_01_08_425885	628	89	κθ	κθ	UH
10_1101-2021_01_08_425885	628	90	,	,	,
10_1101-2021_01_08_425885	628	91	φ	φ	LS
10_1101-2021_01_08_425885	628	92	)	)	-RRB-
10_1101-2021_01_08_425885	628	93	is	be	VBZ
10_1101-2021_01_08_425885	628	94	unwieldy	unwieldy	JJ
10_1101-2021_01_08_425885	628	95	but	but	CC
10_1101-2021_01_08_425885	628	96	we	-PRON-	PRP
10_1101-2021_01_08_425885	628	97	note	note	VBP
10_1101-2021_01_08_425885	628	98	the	the	DT
10_1101-2021_01_08_425885	628	99	following	follow	VBG
10_1101-2021_01_08_425885	628	100	identities	identity	NNS
10_1101-2021_01_08_425885	628	101	for	for	IN
10_1101-2021_01_08_425885	628	102	monomials	monomial	NNS
10_1101-2021_01_08_425885	628	103	of	of	IN
10_1101-2021_01_08_425885	628	104	the	the	DT
10_1101-2021_01_08_425885	628	105	form	form	NN
10_1101-2021_01_08_425885	628	106	37	37	CD
10_1101-2021_01_08_425885	628	107	.CC	.CC	,
10_1101-2021_01_08_425885	628	108	-	-	HYPH
10_1101-2021_01_08_425885	628	109	BY	by	IN
10_1101-2021_01_08_425885	628	110	-	-	HYPH
10_1101-2021_01_08_425885	628	111	NC	NC	NNP
10_1101-2021_01_08_425885	628	112	-	-	HYPH
10_1101-2021_01_08_425885	628	113	ND	ND	NNP
10_1101-2021_01_08_425885	628	114	4.0	4.0	CD
10_1101-2021_01_08_425885	628	115	International	International	NNP
10_1101-2021_01_08_425885	628	116	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	628	117	under	under	IN
10_1101-2021_01_08_425885	628	118	a	a	DT
10_1101-2021_01_08_425885	628	119	(	(	-LRB-
10_1101-2021_01_08_425885	628	120	which	which	WDT
10_1101-2021_01_08_425885	628	121	was	be	VBD
10_1101-2021_01_08_425885	628	122	not	not	RB
10_1101-2021_01_08_425885	628	123	certified	certify	VBN
10_1101-2021_01_08_425885	628	124	by	by	IN
10_1101-2021_01_08_425885	628	125	peer	peer	NN
10_1101-2021_01_08_425885	628	126	review	review	NN
10_1101-2021_01_08_425885	628	127	)	)	-RRB-
10_1101-2021_01_08_425885	628	128	is	be	VBZ
10_1101-2021_01_08_425885	628	129	the	the	DT
10_1101-2021_01_08_425885	628	130	author	author	NN
10_1101-2021_01_08_425885	628	131	/	/	SYM
10_1101-2021_01_08_425885	628	132	funder	funder	NN
10_1101-2021_01_08_425885	628	133	,	,	,
10_1101-2021_01_08_425885	628	134	who	who	WP
10_1101-2021_01_08_425885	628	135	has	have	VBZ
10_1101-2021_01_08_425885	628	136	granted	grant	VBN
10_1101-2021_01_08_425885	628	137	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	628	138	a	a	DT
10_1101-2021_01_08_425885	628	139	license	license	NN
10_1101-2021_01_08_425885	628	140	to	to	TO
10_1101-2021_01_08_425885	628	141	display	display	VB
10_1101-2021_01_08_425885	628	142	the	the	DT
10_1101-2021_01_08_425885	628	143	preprint	preprint	NN
10_1101-2021_01_08_425885	628	144	in	in	IN
10_1101-2021_01_08_425885	628	145	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	628	146	.	.	.
10_1101-2021_01_08_425885	629	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	629	2	is	be	VBZ
10_1101-2021_01_08_425885	629	3	made	make	VBN
10_1101-2021_01_08_425885	629	4	The	the	DT
10_1101-2021_01_08_425885	629	5	copyright	copyright	NN
10_1101-2021_01_08_425885	629	6	holder	holder	NN
10_1101-2021_01_08_425885	629	7	for	for	IN
10_1101-2021_01_08_425885	629	8	this	this	DT
10_1101-2021_01_08_425885	629	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	629	10	version	version	NN
10_1101-2021_01_08_425885	629	11	posted	post	VBD
10_1101-2021_01_08_425885	629	12	January	January	NNP
10_1101-2021_01_08_425885	629	13	8	8	CD
10_1101-2021_01_08_425885	629	14	,	,	,
10_1101-2021_01_08_425885	629	15	2021	2021	CD
10_1101-2021_01_08_425885	629	16	.	.	.
10_1101-2021_01_08_425885	629	17	;	;	:
10_1101-2021_01_08_425885	629	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	629	19	:	:	:
10_1101-2021_01_08_425885	629	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	629	21	preprint	preprint	NN
10_1101-2021_01_08_425885	629	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	629	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NN
10_1101-2021_01_08_425885	629	24	q(x	q(x	NNP
10_1101-2021_01_08_425885	629	25	,	,	,
10_1101-2021_01_08_425885	629	26	y	y	NNP
10_1101-2021_01_08_425885	629	27	)	)	-RRB-
10_1101-2021_01_08_425885	629	28	=	=	SYM
10_1101-2021_01_08_425885	629	29	xsyt	xsyt	NNP
10_1101-2021_01_08_425885	629	30	,	,	,
10_1101-2021_01_08_425885	629	31	which	which	WDT
10_1101-2021_01_08_425885	629	32	can	can	MD
10_1101-2021_01_08_425885	629	33	then	then	RB
10_1101-2021_01_08_425885	629	34	be	be	VB
10_1101-2021_01_08_425885	629	35	applied	apply	VBN
10_1101-2021_01_08_425885	629	36	term	term	NN
10_1101-2021_01_08_425885	629	37	-	-	HYPH
10_1101-2021_01_08_425885	629	38	wise	wise	JJ
10_1101-2021_01_08_425885	629	39	to	to	IN
10_1101-2021_01_08_425885	629	40	κθ	κθ	NNP
10_1101-2021_01_08_425885	629	41	,	,	,
10_1101-2021_01_08_425885	629	42	φ	φ	UH
10_1101-2021_01_08_425885	629	43	.	.	.
10_1101-2021_01_08_425885	630	1	(	(	-LRB-
10_1101-2021_01_08_425885	630	2	c	c	NNP
10_1101-2021_01_08_425885	630	3	◦	◦	NNP
10_1101-2021_01_08_425885	630	4	h	h	NNP
10_1101-2021_01_08_425885	630	5	)	)	-RRB-
10_1101-2021_01_08_425885	630	6	(	(	-LRB-
10_1101-2021_01_08_425885	630	7	q	q	NNP
10_1101-2021_01_08_425885	630	8	)	)	-RRB-
10_1101-2021_01_08_425885	630	9	=	=	NFP
10_1101-2021_01_08_425885	630	10			NFP
10_1101-2021_01_08_425885	630	11			NNP
10_1101-2021_01_08_425885	630	12	√	√	NNP
10_1101-2021_01_08_425885	630	13	6e1	6e1	CD
10_1101-2021_01_08_425885	630	14	,	,	,
10_1101-2021_01_08_425885	630	15	if	if	IN
10_1101-2021_01_08_425885	630	16	s	s	FW
10_1101-2021_01_08_425885	630	17	=	=	SYM
10_1101-2021_01_08_425885	630	18	0	0	CD
10_1101-2021_01_08_425885	630	19	and	and	CC
10_1101-2021_01_08_425885	630	20	t	t	NN
10_1101-2021_01_08_425885	630	21	odd	odd	JJ
10_1101-2021_01_08_425885	630	22	−	−	NNP
10_1101-2021_01_08_425885	630	23	√	√	NNP
10_1101-2021_01_08_425885	630	24	6e2	6e2	NNP
10_1101-2021_01_08_425885	630	25	,	,	,
10_1101-2021_01_08_425885	630	26	if	if	IN
10_1101-2021_01_08_425885	630	27	t	t	NN
10_1101-2021_01_08_425885	630	28	=	=	SYM
10_1101-2021_01_08_425885	630	29	0	0	CD
10_1101-2021_01_08_425885	630	30	and	and	CC
10_1101-2021_01_08_425885	630	31	s	s	POS
10_1101-2021_01_08_425885	630	32	odd	odd	JJ
10_1101-2021_01_08_425885	630	33	√	√	NNP
10_1101-2021_01_08_425885	630	34	6e3	6e3	CD
10_1101-2021_01_08_425885	630	35	,	,	,
10_1101-2021_01_08_425885	630	36	if	if	IN
10_1101-2021_01_08_425885	630	37	s	s	FW
10_1101-2021_01_08_425885	630	38	=	=	SYM
10_1101-2021_01_08_425885	630	39	0	0	CD
10_1101-2021_01_08_425885	630	40	and	and	CC
10_1101-2021_01_08_425885	630	41	t	t	NN
10_1101-2021_01_08_425885	630	42	even	even	RB
10_1101-2021_01_08_425885	630	43	√	√	NNP
10_1101-2021_01_08_425885	630	44	6e4	6e4	CD
10_1101-2021_01_08_425885	630	45	,	,	,
10_1101-2021_01_08_425885	630	46	if	if	IN
10_1101-2021_01_08_425885	630	47	t	t	NN
10_1101-2021_01_08_425885	630	48	=	=	SYM
10_1101-2021_01_08_425885	630	49	0	0	CD
10_1101-2021_01_08_425885	630	50	and	and	CC
10_1101-2021_01_08_425885	630	51	s	s	NN
10_1101-2021_01_08_425885	630	52	even	even	RB
10_1101-2021_01_08_425885	630	53	−	−	NNP
10_1101-2021_01_08_425885	630	54	√	√	NNP
10_1101-2021_01_08_425885	630	55	8e5	8e5	NNP
10_1101-2021_01_08_425885	630	56	,	,	,
10_1101-2021_01_08_425885	630	57	if	if	IN
10_1101-2021_01_08_425885	630	58	s	s	NNP
10_1101-2021_01_08_425885	630	59	odd	odd	JJ
10_1101-2021_01_08_425885	630	60	and	and	CC
10_1101-2021_01_08_425885	630	61	t	t	NNP
10_1101-2021_01_08_425885	630	62	odd	odd	JJ
10_1101-2021_01_08_425885	630	63	2	2	CD
10_1101-2021_01_08_425885	630	64	√	√	NNP
10_1101-2021_01_08_425885	630	65	6	6	CD
10_1101-2021_01_08_425885	630	66	3	3	CD
10_1101-2021_01_08_425885	630	67	e1	e1	NN
10_1101-2021_01_08_425885	630	68	+	+	CC
10_1101-2021_01_08_425885	630	69	4	4	CD
10_1101-2021_01_08_425885	630	70	√	√	NN
10_1101-2021_01_08_425885	630	71	3	3	CD
10_1101-2021_01_08_425885	630	72	3	3	CD
10_1101-2021_01_08_425885	630	73	e6	e6	NNS
10_1101-2021_01_08_425885	630	74	,	,	,
10_1101-2021_01_08_425885	630	75	if	if	IN
10_1101-2021_01_08_425885	630	76	s	s	NNP
10_1101-2021_01_08_425885	630	77	>	>	XX
10_1101-2021_01_08_425885	630	78	0	0	CD
10_1101-2021_01_08_425885	630	79	even	even	RB
10_1101-2021_01_08_425885	630	80	and	and	CC
10_1101-2021_01_08_425885	630	81	t	t	NNP
10_1101-2021_01_08_425885	630	82	odd	odd	JJ
10_1101-2021_01_08_425885	630	83	−2	−2	NNP
10_1101-2021_01_08_425885	630	84	√	√	NNP
10_1101-2021_01_08_425885	630	85	6	6	CD
10_1101-2021_01_08_425885	630	86	3	3	CD
10_1101-2021_01_08_425885	630	87	e2	e2	NN
10_1101-2021_01_08_425885	630	88	−	−	NNP
10_1101-2021_01_08_425885	630	89	4	4	CD
10_1101-2021_01_08_425885	630	90	√	√	NN
10_1101-2021_01_08_425885	630	91	3	3	CD
10_1101-2021_01_08_425885	630	92	3	3	CD
10_1101-2021_01_08_425885	630	93	e7	e7	NN
10_1101-2021_01_08_425885	630	94	,	,	,
10_1101-2021_01_08_425885	630	95	if	if	IN
10_1101-2021_01_08_425885	630	96	t	t	NNP
10_1101-2021_01_08_425885	630	97	>	>	XX
10_1101-2021_01_08_425885	630	98	0	0	NFP
10_1101-2021_01_08_425885	630	99	even	even	RB
10_1101-2021_01_08_425885	630	100	and	and	CC
10_1101-2021_01_08_425885	630	101	s	s	POS
10_1101-2021_01_08_425885	630	102	odd	odd	JJ
10_1101-2021_01_08_425885	630	103	2	2	CD
10_1101-2021_01_08_425885	630	104	√	√	NNP
10_1101-2021_01_08_425885	630	105	6	6	CD
10_1101-2021_01_08_425885	630	106	3	3	CD
10_1101-2021_01_08_425885	630	107	(	(	-LRB-
10_1101-2021_01_08_425885	630	108	e3	e3	NNP
10_1101-2021_01_08_425885	630	109	+	+	SYM
10_1101-2021_01_08_425885	630	110	e4	e4	NN
10_1101-2021_01_08_425885	630	111	+	+	SYM
10_1101-2021_01_08_425885	630	112	e8	e8	NNS
10_1101-2021_01_08_425885	630	113	)	)	-RRB-
10_1101-2021_01_08_425885	630	114	,	,	,
10_1101-2021_01_08_425885	630	115	if	if	IN
10_1101-2021_01_08_425885	630	116	s	s	NNP
10_1101-2021_01_08_425885	630	117	>	>	VBP
10_1101-2021_01_08_425885	630	118	0	0	CD
10_1101-2021_01_08_425885	630	119	even	even	RB
10_1101-2021_01_08_425885	630	120	and	and	CC
10_1101-2021_01_08_425885	630	121	t	t	NNP
10_1101-2021_01_08_425885	630	122	>	>	XX
10_1101-2021_01_08_425885	630	123	0	0	NFP
10_1101-2021_01_08_425885	630	124	even	even	RB
10_1101-2021_01_08_425885	630	125	(	(	-LRB-
10_1101-2021_01_08_425885	630	126	35	35	CD
10_1101-2021_01_08_425885	630	127	)	)	-RRB-
10_1101-2021_01_08_425885	630	128	Note	note	VB
10_1101-2021_01_08_425885	630	129	that	that	IN
10_1101-2021_01_08_425885	630	130	the	the	DT
10_1101-2021_01_08_425885	630	131	first	first	JJ
10_1101-2021_01_08_425885	630	132	inner	inner	JJ
10_1101-2021_01_08_425885	630	133	sum	sum	NN
10_1101-2021_01_08_425885	630	134	in	in	IN
10_1101-2021_01_08_425885	630	135	Equation	Equation	NNP
10_1101-2021_01_08_425885	630	136	34	34	CD
10_1101-2021_01_08_425885	630	137	is	be	VBZ
10_1101-2021_01_08_425885	630	138	a	a	DT
10_1101-2021_01_08_425885	630	139	linear	linear	JJ
10_1101-2021_01_08_425885	630	140	combination	combination	NN
10_1101-2021_01_08_425885	630	141	of	of	IN
10_1101-2021_01_08_425885	630	142	basis	basis	NN
10_1101-2021_01_08_425885	630	143	vectors	vector	NNS
10_1101-2021_01_08_425885	630	144	encoding	encode	VBG
10_1101-2021_01_08_425885	630	145	purely	purely	RB
10_1101-2021_01_08_425885	630	146	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	630	147	gradients	gradient	NNS
10_1101-2021_01_08_425885	630	148	(	(	-LRB-
10_1101-2021_01_08_425885	630	149	e3	e3	NNP
10_1101-2021_01_08_425885	630	150	,	,	,
10_1101-2021_01_08_425885	630	151	e4	e4	NNP
10_1101-2021_01_08_425885	630	152	,	,	,
10_1101-2021_01_08_425885	630	153	e5	e5	NNP
10_1101-2021_01_08_425885	630	154	and	and	CC
10_1101-2021_01_08_425885	630	155	e8	e8	NNS
10_1101-2021_01_08_425885	630	156	)	)	-RRB-
10_1101-2021_01_08_425885	630	157	,	,	,
10_1101-2021_01_08_425885	630	158	weighted	weight	VBN
10_1101-2021_01_08_425885	630	159	by	by	IN
10_1101-2021_01_08_425885	630	160	even	even	RB
10_1101-2021_01_08_425885	630	161	trigonometric	trigonometric	JJ
10_1101-2021_01_08_425885	630	162	functions	function	NNS
10_1101-2021_01_08_425885	630	163	of	of	IN
10_1101-2021_01_08_425885	630	164	θ	θ	NNP
10_1101-2021_01_08_425885	630	165	.	.	.
10_1101-2021_01_08_425885	631	1	The	the	DT
10_1101-2021_01_08_425885	631	2	prefactors	prefactor	NNS
10_1101-2021_01_08_425885	631	3	on	on	IN
10_1101-2021_01_08_425885	631	4	this	this	DT
10_1101-2021_01_08_425885	631	5	inner	inner	JJ
10_1101-2021_01_08_425885	631	6	sum	sum	NN
10_1101-2021_01_08_425885	631	7	are	be	VBP
10_1101-2021_01_08_425885	631	8	functions	function	NNS
10_1101-2021_01_08_425885	631	9	that	that	WDT
10_1101-2021_01_08_425885	631	10	are	be	VBP
10_1101-2021_01_08_425885	631	11	even	even	RB
10_1101-2021_01_08_425885	631	12	in	in	IN
10_1101-2021_01_08_425885	631	13	φ	φ	NN
10_1101-2021_01_08_425885	631	14	.	.	.
10_1101-2021_01_08_425885	632	1	This	this	DT
10_1101-2021_01_08_425885	632	2	inner	inner	JJ
10_1101-2021_01_08_425885	632	3	sum	sum	NN
10_1101-2021_01_08_425885	632	4	and	and	CC
10_1101-2021_01_08_425885	632	5	its	-PRON-	PRP$
10_1101-2021_01_08_425885	632	6	prefactor	prefactor	NN
10_1101-2021_01_08_425885	632	7	therefore	therefore	RB
10_1101-2021_01_08_425885	632	8	jointly	jointly	RB
10_1101-2021_01_08_425885	632	9	satisfy	satisfy	VBP
10_1101-2021_01_08_425885	632	10	the	the	DT
10_1101-2021_01_08_425885	632	11	similarity	similarity	NN
10_1101-2021_01_08_425885	632	12	relation	relation	NN
10_1101-2021_01_08_425885	632	13	(	(	-LRB-
10_1101-2021_01_08_425885	632	14	θ	θ	NNP
10_1101-2021_01_08_425885	632	15	,	,	,
10_1101-2021_01_08_425885	632	16	φ	φ	NNP
10_1101-2021_01_08_425885	632	17	)	)	-RRB-
10_1101-2021_01_08_425885	632	18	∼	∼	NNP
10_1101-2021_01_08_425885	632	19	(	(	-LRB-
10_1101-2021_01_08_425885	632	20	θ	θ	NNP
10_1101-2021_01_08_425885	632	21	+	+	SYM
10_1101-2021_01_08_425885	632	22	π	π	NN
10_1101-2021_01_08_425885	632	23	,	,	,
10_1101-2021_01_08_425885	632	24	2π−φ	2π−φ	LS
10_1101-2021_01_08_425885	632	25	)	)	-RRB-
10_1101-2021_01_08_425885	632	26	by	by	IN
10_1101-2021_01_08_425885	632	27	independently	independently	RB
10_1101-2021_01_08_425885	632	28	satisfying	satisfy	VBG
10_1101-2021_01_08_425885	632	29	(	(	-LRB-
10_1101-2021_01_08_425885	632	30	θ	θ	NNP
10_1101-2021_01_08_425885	632	31	)	)	-RRB-
10_1101-2021_01_08_425885	632	32	∼	∼	NNP
10_1101-2021_01_08_425885	632	33	(	(	-LRB-
10_1101-2021_01_08_425885	632	34	θ	θ	NNP
10_1101-2021_01_08_425885	632	35	+	+	SYM
10_1101-2021_01_08_425885	632	36	π	π	NN
10_1101-2021_01_08_425885	632	37	)	)	-RRB-
10_1101-2021_01_08_425885	632	38	and	and	CC
10_1101-2021_01_08_425885	632	39	(	(	-LRB-
10_1101-2021_01_08_425885	632	40	φ	φ	NN
10_1101-2021_01_08_425885	632	41	)	)	-RRB-
10_1101-2021_01_08_425885	632	42	∼	∼	NNP
10_1101-2021_01_08_425885	632	43	(	(	-LRB-
10_1101-2021_01_08_425885	632	44	2π−φ	2π−φ	NNP
10_1101-2021_01_08_425885	632	45	)	)	-RRB-
10_1101-2021_01_08_425885	632	46	.	.	.
10_1101-2021_01_08_425885	633	1	Meanwhile	meanwhile	RB
10_1101-2021_01_08_425885	633	2	,	,	,
10_1101-2021_01_08_425885	633	3	the	the	DT
10_1101-2021_01_08_425885	633	4	second	second	JJ
10_1101-2021_01_08_425885	633	5	inner	inner	JJ
10_1101-2021_01_08_425885	633	6	sum	sum	NN
10_1101-2021_01_08_425885	633	7	in	in	IN
10_1101-2021_01_08_425885	633	8	Equation	Equation	NNP
10_1101-2021_01_08_425885	633	9	34	34	CD
10_1101-2021_01_08_425885	633	10	is	be	VBZ
10_1101-2021_01_08_425885	633	11	a	a	DT
10_1101-2021_01_08_425885	633	12	linear	linear	JJ
10_1101-2021_01_08_425885	633	13	combination	combination	NN
10_1101-2021_01_08_425885	633	14	of	of	IN
10_1101-2021_01_08_425885	633	15	basis	basis	NN
10_1101-2021_01_08_425885	633	16	vectors	vector	NNS
10_1101-2021_01_08_425885	633	17	containing	contain	VBG
10_1101-2021_01_08_425885	633	18	linear	linear	JJ
10_1101-2021_01_08_425885	633	19	gradients	gradient	NNS
10_1101-2021_01_08_425885	633	20	(	(	-LRB-
10_1101-2021_01_08_425885	633	21	e1	e1	NN
10_1101-2021_01_08_425885	633	22	,	,	,
10_1101-2021_01_08_425885	633	23	e2	e2	NN
10_1101-2021_01_08_425885	633	24	,	,	,
10_1101-2021_01_08_425885	633	25	e6	e6	NN
10_1101-2021_01_08_425885	633	26	and	and	CC
10_1101-2021_01_08_425885	633	27	e7	e7	NNP
10_1101-2021_01_08_425885	633	28	)	)	-RRB-
10_1101-2021_01_08_425885	633	29	,	,	,
10_1101-2021_01_08_425885	633	30	weighted	weight	VBN
10_1101-2021_01_08_425885	633	31	by	by	IN
10_1101-2021_01_08_425885	633	32	odd	odd	JJ
10_1101-2021_01_08_425885	633	33	trigonometric	trigonometric	JJ
10_1101-2021_01_08_425885	633	34	functions	function	NNS
10_1101-2021_01_08_425885	633	35	of	of	IN
10_1101-2021_01_08_425885	633	36	θ	θ	NNP
10_1101-2021_01_08_425885	633	37	.	.	.
10_1101-2021_01_08_425885	634	1	The	the	DT
10_1101-2021_01_08_425885	634	2	prefactors	prefactor	NNS
10_1101-2021_01_08_425885	634	3	on	on	IN
10_1101-2021_01_08_425885	634	4	this	this	DT
10_1101-2021_01_08_425885	634	5	inner	inner	JJ
10_1101-2021_01_08_425885	634	6	sum	sum	NN
10_1101-2021_01_08_425885	634	7	are	be	VBP
10_1101-2021_01_08_425885	634	8	functions	function	NNS
10_1101-2021_01_08_425885	634	9	that	that	WDT
10_1101-2021_01_08_425885	634	10	are	be	VBP
10_1101-2021_01_08_425885	634	11	odd	odd	JJ
10_1101-2021_01_08_425885	634	12	in	in	IN
10_1101-2021_01_08_425885	634	13	φ	φ	NN
10_1101-2021_01_08_425885	634	14	.	.	.
10_1101-2021_01_08_425885	635	1	This	this	DT
10_1101-2021_01_08_425885	635	2	inner	inner	JJ
10_1101-2021_01_08_425885	635	3	sum	sum	NN
10_1101-2021_01_08_425885	635	4	and	and	CC
10_1101-2021_01_08_425885	635	5	its	-PRON-	PRP$
10_1101-2021_01_08_425885	635	6	prefactor	prefactor	NN
10_1101-2021_01_08_425885	635	7	therefore	therefore	RB
10_1101-2021_01_08_425885	635	8	jointly	jointly	RB
10_1101-2021_01_08_425885	635	9	satisfy	satisfy	VBP
10_1101-2021_01_08_425885	635	10	the	the	DT
10_1101-2021_01_08_425885	635	11	similarity	similarity	NN
10_1101-2021_01_08_425885	635	12	relation	relation	NN
10_1101-2021_01_08_425885	635	13	(	(	-LRB-
10_1101-2021_01_08_425885	635	14	θ	θ	NNP
10_1101-2021_01_08_425885	635	15	,	,	,
10_1101-2021_01_08_425885	635	16	φ	φ	NNP
10_1101-2021_01_08_425885	635	17	)	)	-RRB-
10_1101-2021_01_08_425885	635	18	∼	∼	NNP
10_1101-2021_01_08_425885	635	19	(	(	-LRB-
10_1101-2021_01_08_425885	635	20	θ	θ	NNP
10_1101-2021_01_08_425885	635	21	+	+	SYM
10_1101-2021_01_08_425885	635	22	π	π	NN
10_1101-2021_01_08_425885	635	23	,	,	,
10_1101-2021_01_08_425885	635	24	2π	2π	CD
10_1101-2021_01_08_425885	635	25	−	−	NNP
10_1101-2021_01_08_425885	635	26	φ	φ	NNP
10_1101-2021_01_08_425885	635	27	)	)	-RRB-
10_1101-2021_01_08_425885	635	28	,	,	,
10_1101-2021_01_08_425885	635	29	by	by	IN
10_1101-2021_01_08_425885	635	30	independently	independently	RB
10_1101-2021_01_08_425885	635	31	satisfying	satisfy	VBG
10_1101-2021_01_08_425885	635	32	(	(	-LRB-
10_1101-2021_01_08_425885	635	33	θ	θ	NNP
10_1101-2021_01_08_425885	635	34	)	)	-RRB-
10_1101-2021_01_08_425885	635	35	∼	∼	NNP
10_1101-2021_01_08_425885	635	36	−(θ	−(θ	NNP
10_1101-2021_01_08_425885	635	37	+	+	SYM
10_1101-2021_01_08_425885	635	38	π	π	NN
10_1101-2021_01_08_425885	635	39	)	)	-RRB-
10_1101-2021_01_08_425885	635	40	and	and	CC
10_1101-2021_01_08_425885	635	41	(	(	-LRB-
10_1101-2021_01_08_425885	635	42	φ	φ	NN
10_1101-2021_01_08_425885	635	43	)	)	-RRB-
10_1101-2021_01_08_425885	635	44	∼	∼	NN
10_1101-2021_01_08_425885	635	45	−(2π	−(2π	ADD
10_1101-2021_01_08_425885	635	46	−	−	NNP
10_1101-2021_01_08_425885	635	47	φ	φ	NNP
10_1101-2021_01_08_425885	635	48	)	)	-RRB-
10_1101-2021_01_08_425885	635	49	.	.	.
10_1101-2021_01_08_425885	636	1	Since	since	IN
10_1101-2021_01_08_425885	636	2	the	the	DT
10_1101-2021_01_08_425885	636	3	trigonometric	trigonometric	JJ
10_1101-2021_01_08_425885	636	4	functions	function	NNS
10_1101-2021_01_08_425885	636	5	of	of	IN
10_1101-2021_01_08_425885	636	6	θ	θ	NNS
10_1101-2021_01_08_425885	636	7	are	be	VBP
10_1101-2021_01_08_425885	636	8	coupled	couple	VBN
10_1101-2021_01_08_425885	636	9	to	to	IN
10_1101-2021_01_08_425885	636	10	(	(	-LRB-
10_1101-2021_01_08_425885	636	11	x	x	NN
10_1101-2021_01_08_425885	636	12	,	,	,
10_1101-2021_01_08_425885	636	13	y	y	NNP
10_1101-2021_01_08_425885	636	14	)	)	-RRB-
10_1101-2021_01_08_425885	636	15	,	,	,
10_1101-2021_01_08_425885	636	16	θ	θ	NNP
10_1101-2021_01_08_425885	636	17	controls	control	VBZ
10_1101-2021_01_08_425885	636	18	the	the	DT
10_1101-2021_01_08_425885	636	19	rotation	rotation	NN
10_1101-2021_01_08_425885	636	20	of	of	IN
10_1101-2021_01_08_425885	636	21	stripes	stripe	NNS
10_1101-2021_01_08_425885	636	22	in	in	IN
10_1101-2021_01_08_425885	636	23	the	the	DT
10_1101-2021_01_08_425885	636	24	image	image	NN
10_1101-2021_01_08_425885	636	25	patches	patch	NNS
10_1101-2021_01_08_425885	636	26	,	,	,
10_1101-2021_01_08_425885	636	27	just	just	RB
10_1101-2021_01_08_425885	636	28	as	as	IN
10_1101-2021_01_08_425885	636	29	in	in	IN
10_1101-2021_01_08_425885	636	30	k0	k0	NNP
10_1101-2021_01_08_425885	636	31	.	.	.
10_1101-2021_01_08_425885	637	1	Similarly	similarly	RB
10_1101-2021_01_08_425885	637	2	,	,	,
10_1101-2021_01_08_425885	637	3	since	since	IN
10_1101-2021_01_08_425885	637	4	the	the	DT
10_1101-2021_01_08_425885	637	5	prefactors	prefactor	NNS
10_1101-2021_01_08_425885	637	6	on	on	IN
10_1101-2021_01_08_425885	637	7	the	the	DT
10_1101-2021_01_08_425885	637	8	inner	inner	JJ
10_1101-2021_01_08_425885	637	9	sums	sum	NNS
10_1101-2021_01_08_425885	637	10	are	be	VBP
10_1101-2021_01_08_425885	637	11	functions	function	NNS
10_1101-2021_01_08_425885	637	12	of	of	IN
10_1101-2021_01_08_425885	637	13	φ	φ	NN
10_1101-2021_01_08_425885	637	14	,	,	,
10_1101-2021_01_08_425885	637	15	φ	φ	LS
10_1101-2021_01_08_425885	637	16	controls	control	VBZ
10_1101-2021_01_08_425885	637	17	the	the	DT
10_1101-2021_01_08_425885	637	18	relative	relative	JJ
10_1101-2021_01_08_425885	637	19	contribution	contribution	NN
10_1101-2021_01_08_425885	637	20	of	of	IN
10_1101-2021_01_08_425885	637	21	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	637	22	gradients	gradient	NNS
10_1101-2021_01_08_425885	637	23	(	(	-LRB-
10_1101-2021_01_08_425885	637	24	e3	e3	NNP
10_1101-2021_01_08_425885	637	25	,	,	,
10_1101-2021_01_08_425885	637	26	e4	e4	NNP
10_1101-2021_01_08_425885	637	27	,	,	,
10_1101-2021_01_08_425885	637	28	e5	e5	NN
10_1101-2021_01_08_425885	637	29	and	and	CC
10_1101-2021_01_08_425885	637	30	e8	e8	NNS
10_1101-2021_01_08_425885	637	31	in	in	IN
10_1101-2021_01_08_425885	637	32	the	the	DT
10_1101-2021_01_08_425885	637	33	first	first	JJ
10_1101-2021_01_08_425885	637	34	inner	inner	JJ
10_1101-2021_01_08_425885	637	35	sum	sum	NN
10_1101-2021_01_08_425885	637	36	)	)	-RRB-
10_1101-2021_01_08_425885	637	37	and	and	CC
10_1101-2021_01_08_425885	637	38	linear	linear	JJ
10_1101-2021_01_08_425885	637	39	gradients	gradient	NNS
10_1101-2021_01_08_425885	637	40	(	(	-LRB-
10_1101-2021_01_08_425885	637	41	e1	e1	NN
10_1101-2021_01_08_425885	637	42	,	,	,
10_1101-2021_01_08_425885	637	43	e2	e2	NN
10_1101-2021_01_08_425885	637	44	,	,	,
10_1101-2021_01_08_425885	637	45	e6	e6	NNP
10_1101-2021_01_08_425885	637	46	and	and	CC
10_1101-2021_01_08_425885	637	47	e7	e7	NNP
10_1101-2021_01_08_425885	637	48	in	in	IN
10_1101-2021_01_08_425885	637	49	the	the	DT
10_1101-2021_01_08_425885	637	50	second	second	JJ
10_1101-2021_01_08_425885	637	51	inner	inner	JJ
10_1101-2021_01_08_425885	637	52	sum	sum	NN
10_1101-2021_01_08_425885	637	53	)	)	-RRB-
10_1101-2021_01_08_425885	637	54	.	.	.
10_1101-2021_01_08_425885	638	1	Lastly	lastly	RB
10_1101-2021_01_08_425885	638	2	,	,	,
10_1101-2021_01_08_425885	638	3	the	the	DT
10_1101-2021_01_08_425885	638	4	boundary	boundary	JJ
10_1101-2021_01_08_425885	638	5	conditions	condition	NNS
10_1101-2021_01_08_425885	638	6	for	for	IN
10_1101-2021_01_08_425885	638	7	θ	θ	NN
10_1101-2021_01_08_425885	638	8	and	and	CC
10_1101-2021_01_08_425885	638	9	φ	φ	NN
10_1101-2021_01_08_425885	638	10	in	in	IN
10_1101-2021_01_08_425885	638	11	this	this	DT
10_1101-2021_01_08_425885	638	12	parameterization	parameterization	NN
10_1101-2021_01_08_425885	638	13	of	of	IN
10_1101-2021_01_08_425885	638	14	κθ	κθ	NNP
10_1101-2021_01_08_425885	638	15	,	,	,
10_1101-2021_01_08_425885	638	16	φ	φ	NNP
10_1101-2021_01_08_425885	638	17	,	,	,
10_1101-2021_01_08_425885	638	18	yield	yield	NN
10_1101-2021_01_08_425885	638	19	patches	patch	NNS
10_1101-2021_01_08_425885	638	20	with	with	IN
10_1101-2021_01_08_425885	638	21	vertical	vertical	JJ
10_1101-2021_01_08_425885	638	22	(	(	-LRB-
10_1101-2021_01_08_425885	638	23	horizontal	horizontal	JJ
10_1101-2021_01_08_425885	638	24	)	)	-RRB-
10_1101-2021_01_08_425885	638	25	stripes	stripe	VBZ
10_1101-2021_01_08_425885	638	26	when	when	WRB
10_1101-2021_01_08_425885	638	27	θ	θ	NNP
10_1101-2021_01_08_425885	638	28	=	=	SYM
10_1101-2021_01_08_425885	638	29	0	0	NFP
10_1101-2021_01_08_425885	638	30	(	(	-LRB-
10_1101-2021_01_08_425885	638	31	θ	θ	NNP
10_1101-2021_01_08_425885	638	32	=	=	SYM
10_1101-2021_01_08_425885	638	33	π	π	NN
10_1101-2021_01_08_425885	638	34	2	2	CD
10_1101-2021_01_08_425885	638	35	)	)	-RRB-
10_1101-2021_01_08_425885	638	36	,	,	,
10_1101-2021_01_08_425885	638	37	and	and	CC
10_1101-2021_01_08_425885	638	38	linear	linear	JJ
10_1101-2021_01_08_425885	638	39	(	(	-LRB-
10_1101-2021_01_08_425885	638	40	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	638	41	)	)	-RRB-
10_1101-2021_01_08_425885	638	42	gradients	gradient	NNS
10_1101-2021_01_08_425885	638	43	when	when	WRB
10_1101-2021_01_08_425885	638	44	φ	φ	NN
10_1101-2021_01_08_425885	638	45	=	=	SYM
10_1101-2021_01_08_425885	638	46	π	π	NN
10_1101-2021_01_08_425885	638	47	2	2	CD
10_1101-2021_01_08_425885	638	48	,	,	,
10_1101-2021_01_08_425885	638	49	3π	3π	CD
10_1101-2021_01_08_425885	638	50	2	2	CD
10_1101-2021_01_08_425885	638	51	(	(	-LRB-
10_1101-2021_01_08_425885	638	52	φ	φ	NNP
10_1101-2021_01_08_425885	638	53	=	=	SYM
10_1101-2021_01_08_425885	638	54	0,π	0,π	CD
10_1101-2021_01_08_425885	638	55	)	)	-RRB-
10_1101-2021_01_08_425885	638	56	just	just	RB
10_1101-2021_01_08_425885	638	57	as	as	IN
10_1101-2021_01_08_425885	638	58	in	in	IN
10_1101-2021_01_08_425885	638	59	k0	k0	NNP
10_1101-2021_01_08_425885	638	60	.	.	.
10_1101-2021_01_08_425885	639	1	A	a	DT
10_1101-2021_01_08_425885	639	2	Klein	Klein	NNP
10_1101-2021_01_08_425885	639	3	bottle	bottle	NN
10_1101-2021_01_08_425885	639	4	embedding	embed	VBG
10_1101-2021_01_08_425885	639	5	belonging	belong	VBG
10_1101-2021_01_08_425885	639	6	to	to	IN
10_1101-2021_01_08_425885	639	7	this	this	DT
10_1101-2021_01_08_425885	639	8	parametric	parametric	JJ
10_1101-2021_01_08_425885	639	9	family	family	NN
10_1101-2021_01_08_425885	639	10	,	,	,
10_1101-2021_01_08_425885	639	11	kαθ	kαθ	NNP
10_1101-2021_01_08_425885	639	12	,	,	,
10_1101-2021_01_08_425885	639	13	φ	φ	NNP
10_1101-2021_01_08_425885	639	14	∈	∈	NNP
10_1101-2021_01_08_425885	639	15	Kθ	Kθ	NNP
10_1101-2021_01_08_425885	639	16	,	,	,
10_1101-2021_01_08_425885	639	17	φ	φ	NNP
10_1101-2021_01_08_425885	639	18	,	,	,
10_1101-2021_01_08_425885	639	19	can	can	MD
10_1101-2021_01_08_425885	639	20	therefore	therefore	RB
10_1101-2021_01_08_425885	639	21	be	be	VB
10_1101-2021_01_08_425885	639	22	specified	specify	VBN
10_1101-2021_01_08_425885	639	23	in	in	IN
10_1101-2021_01_08_425885	639	24	terms	term	NNS
10_1101-2021_01_08_425885	639	25	of	of	IN
10_1101-2021_01_08_425885	639	26	a	a	DT
10_1101-2021_01_08_425885	639	27	vector	vector	NN
10_1101-2021_01_08_425885	639	28	F	f	NN
10_1101-2021_01_08_425885	639	29	=	=	NFP
10_1101-2021_01_08_425885	639	30	[	[	-LRB-
10_1101-2021_01_08_425885	639	31	NC	NC	NNP
10_1101-2021_01_08_425885	639	32	,	,	,
10_1101-2021_01_08_425885	639	33	Nθ	nθ	UH
10_1101-2021_01_08_425885	639	34	,	,	,
10_1101-2021_01_08_425885	639	35	Nφ	Nφ	NNP
10_1101-2021_01_08_425885	639	36	,	,	,
10_1101-2021_01_08_425885	639	37	Mθ	Mθ	NNP
10_1101-2021_01_08_425885	639	38	,	,	,
10_1101-2021_01_08_425885	639	39	Mφ	Mφ	NNP
10_1101-2021_01_08_425885	639	40	]	]	-RRB-
10_1101-2021_01_08_425885	639	41	defining	define	VBG
10_1101-2021_01_08_425885	639	42	its	-PRON-	PRP$
10_1101-2021_01_08_425885	639	43	functional	functional	JJ
10_1101-2021_01_08_425885	639	44	form	form	NN
10_1101-2021_01_08_425885	639	45	,	,	,
10_1101-2021_01_08_425885	639	46	and	and	CC
10_1101-2021_01_08_425885	639	47	a	a	DT
10_1101-2021_01_08_425885	639	48	corresponding	corresponding	JJ
10_1101-2021_01_08_425885	639	49	coefficient	coefficient	JJ
10_1101-2021_01_08_425885	639	50	vector	vector	NN
10_1101-2021_01_08_425885	639	51	α	α	NN
10_1101-2021_01_08_425885	639	52	=	=	SYM
10_1101-2021_01_08_425885	639	53	[	[	-LRB-
10_1101-2021_01_08_425885	639	54	µi	µi	UH
10_1101-2021_01_08_425885	639	55	,	,	,
10_1101-2021_01_08_425885	639	56	...	...	:
10_1101-2021_01_08_425885	639	57	,	,	,
10_1101-2021_01_08_425885	639	58	βi	βi	XX
10_1101-2021_01_08_425885	639	59	,	,	,
10_1101-2021_01_08_425885	639	60	...	...	:
10_1101-2021_01_08_425885	639	61	,	,	,
10_1101-2021_01_08_425885	639	62	γi	γi	NNP
10_1101-2021_01_08_425885	639	63	,	,	,
10_1101-2021_01_08_425885	639	64	...	...	:
10_1101-2021_01_08_425885	639	65	,	,	,
10_1101-2021_01_08_425885	639	66	ζi	ζi	NNP
10_1101-2021_01_08_425885	639	67	,	,	,
10_1101-2021_01_08_425885	639	68	...	...	:
10_1101-2021_01_08_425885	639	69	,	,	,
10_1101-2021_01_08_425885	639	70	ηi	ηi	VB
10_1101-2021_01_08_425885	639	71	,	,	,
10_1101-2021_01_08_425885	639	72	...	...	:
10_1101-2021_01_08_425885	639	73	,	,	,
10_1101-2021_01_08_425885	639	74	ϑi	ϑi	NNP
10_1101-2021_01_08_425885	639	75	]	]	-RRB-
10_1101-2021_01_08_425885	639	76	.	.	.
10_1101-2021_01_08_425885	640	1	In	in	IN
10_1101-2021_01_08_425885	640	2	this	this	DT
10_1101-2021_01_08_425885	640	3	parametric	parametric	JJ
10_1101-2021_01_08_425885	640	4	family	family	NN
10_1101-2021_01_08_425885	640	5	of	of	IN
10_1101-2021_01_08_425885	640	6	Klein	Klein	NNP
10_1101-2021_01_08_425885	640	7	bottle	bottle	NN
10_1101-2021_01_08_425885	640	8	embeddings	embedding	NNS
10_1101-2021_01_08_425885	640	9	,	,	,
10_1101-2021_01_08_425885	640	10	k	k	NN
10_1101-2021_01_08_425885	640	11	0	0	CD
10_1101-2021_01_08_425885	640	12	corresponds	correspond	NNS
10_1101-2021_01_08_425885	640	13	to	to	IN
10_1101-2021_01_08_425885	640	14	F	f	NN
10_1101-2021_01_08_425885	640	15	=	=	NFP
10_1101-2021_01_08_425885	640	16	[	[	-LRB-
10_1101-2021_01_08_425885	640	17	0	0	CD
10_1101-2021_01_08_425885	640	18	,	,	,
10_1101-2021_01_08_425885	640	19	0	0	CD
10_1101-2021_01_08_425885	640	20	,	,	,
10_1101-2021_01_08_425885	640	21	0	0	CD
10_1101-2021_01_08_425885	640	22	,	,	,
10_1101-2021_01_08_425885	640	23	2	2	CD
10_1101-2021_01_08_425885	640	24	,	,	,
10_1101-2021_01_08_425885	640	25	1	1	CD
10_1101-2021_01_08_425885	640	26	]	]	-RRB-
10_1101-2021_01_08_425885	640	27	with	with	IN
10_1101-2021_01_08_425885	640	28	α	α	XX
10_1101-2021_01_08_425885	640	29	=	=	NNS
10_1101-2021_01_08_425885	640	30	[	[	-LRB-
10_1101-2021_01_08_425885	640	31	η1,2,0,η1,1,1,η1,0,2,ϑ1,0,1,ϑ1,1,0	η1,2,0,η1,1,1,η1,0,2,ϑ1,0,1,ϑ1,1,0	NNP
10_1101-2021_01_08_425885	640	32	]	]	-RRB-
10_1101-2021_01_08_425885	640	33	=	=	NFP
10_1101-2021_01_08_425885	640	34	[	[	-LRB-
10_1101-2021_01_08_425885	640	35	1	1	CD
10_1101-2021_01_08_425885	640	36	,	,	,
10_1101-2021_01_08_425885	640	37	2	2	CD
10_1101-2021_01_08_425885	640	38	,	,	,
10_1101-2021_01_08_425885	640	39	1	1	CD
10_1101-2021_01_08_425885	640	40	,	,	,
10_1101-2021_01_08_425885	640	41	1	1	CD
10_1101-2021_01_08_425885	640	42	,	,	,
10_1101-2021_01_08_425885	640	43	1	1	CD
10_1101-2021_01_08_425885	640	44	]	]	-RRB-
10_1101-2021_01_08_425885	640	45	.	.	.
10_1101-2021_01_08_425885	641	1	Note	note	VB
10_1101-2021_01_08_425885	641	2	that	that	IN
10_1101-2021_01_08_425885	641	3	since	since	IN
10_1101-2021_01_08_425885	641	4	curvatures	curvature	NNS
10_1101-2021_01_08_425885	641	5	are	be	VBP
10_1101-2021_01_08_425885	641	6	only	only	RB
10_1101-2021_01_08_425885	641	7	computed	compute	VBN
10_1101-2021_01_08_425885	641	8	on	on	IN
10_1101-2021_01_08_425885	641	9	the	the	DT
10_1101-2021_01_08_425885	641	10	embedding	embedding	NN
10_1101-2021_01_08_425885	641	11	after	after	IN
10_1101-2021_01_08_425885	641	12	normalization	normalization	NN
10_1101-2021_01_08_425885	641	13	,	,	,
10_1101-2021_01_08_425885	641	14	α	α	NNP
10_1101-2021_01_08_425885	641	15	is	be	VBZ
10_1101-2021_01_08_425885	641	16	only	only	RB
10_1101-2021_01_08_425885	641	17	meaningfully	meaningfully	RB
10_1101-2021_01_08_425885	641	18	defined	define	VBN
10_1101-2021_01_08_425885	641	19	up	up	RP
10_1101-2021_01_08_425885	641	20	to	to	IN
10_1101-2021_01_08_425885	641	21	a	a	DT
10_1101-2021_01_08_425885	641	22	multiplicative	multiplicative	JJ
10_1101-2021_01_08_425885	641	23	constant	constant	NN
10_1101-2021_01_08_425885	641	24	.	.	.
10_1101-2021_01_08_425885	642	1	38	38	CD
10_1101-2021_01_08_425885	642	2	.CC	.CC	:
10_1101-2021_01_08_425885	642	3	-	-	HYPH
10_1101-2021_01_08_425885	642	4	BY	by	IN
10_1101-2021_01_08_425885	642	5	-	-	HYPH
10_1101-2021_01_08_425885	642	6	NC	NC	NNP
10_1101-2021_01_08_425885	642	7	-	-	HYPH
10_1101-2021_01_08_425885	642	8	ND	ND	NNP
10_1101-2021_01_08_425885	642	9	4.0	4.0	CD
10_1101-2021_01_08_425885	642	10	International	International	NNP
10_1101-2021_01_08_425885	642	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	642	12	under	under	IN
10_1101-2021_01_08_425885	642	13	a	a	DT
10_1101-2021_01_08_425885	642	14	(	(	-LRB-
10_1101-2021_01_08_425885	642	15	which	which	WDT
10_1101-2021_01_08_425885	642	16	was	be	VBD
10_1101-2021_01_08_425885	642	17	not	not	RB
10_1101-2021_01_08_425885	642	18	certified	certify	VBN
10_1101-2021_01_08_425885	642	19	by	by	IN
10_1101-2021_01_08_425885	642	20	peer	peer	NN
10_1101-2021_01_08_425885	642	21	review	review	NN
10_1101-2021_01_08_425885	642	22	)	)	-RRB-
10_1101-2021_01_08_425885	642	23	is	be	VBZ
10_1101-2021_01_08_425885	642	24	the	the	DT
10_1101-2021_01_08_425885	642	25	author	author	NN
10_1101-2021_01_08_425885	642	26	/	/	SYM
10_1101-2021_01_08_425885	642	27	funder	funder	NN
10_1101-2021_01_08_425885	642	28	,	,	,
10_1101-2021_01_08_425885	642	29	who	who	WP
10_1101-2021_01_08_425885	642	30	has	have	VBZ
10_1101-2021_01_08_425885	642	31	granted	grant	VBN
10_1101-2021_01_08_425885	642	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	642	33	a	a	DT
10_1101-2021_01_08_425885	642	34	license	license	NN
10_1101-2021_01_08_425885	642	35	to	to	TO
10_1101-2021_01_08_425885	642	36	display	display	VB
10_1101-2021_01_08_425885	642	37	the	the	DT
10_1101-2021_01_08_425885	642	38	preprint	preprint	NN
10_1101-2021_01_08_425885	642	39	in	in	IN
10_1101-2021_01_08_425885	642	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	642	41	.	.	.
10_1101-2021_01_08_425885	643	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	643	2	is	be	VBZ
10_1101-2021_01_08_425885	643	3	made	make	VBN
10_1101-2021_01_08_425885	643	4	The	the	DT
10_1101-2021_01_08_425885	643	5	copyright	copyright	NN
10_1101-2021_01_08_425885	643	6	holder	holder	NN
10_1101-2021_01_08_425885	643	7	for	for	IN
10_1101-2021_01_08_425885	643	8	this	this	DT
10_1101-2021_01_08_425885	643	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	643	10	version	version	NN
10_1101-2021_01_08_425885	643	11	posted	post	VBD
10_1101-2021_01_08_425885	643	12	January	January	NNP
10_1101-2021_01_08_425885	643	13	8	8	CD
10_1101-2021_01_08_425885	643	14	,	,	,
10_1101-2021_01_08_425885	643	15	2021	2021	CD
10_1101-2021_01_08_425885	643	16	.	.	.
10_1101-2021_01_08_425885	643	17	;	;	:
10_1101-2021_01_08_425885	643	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	643	19	:	:	:
10_1101-2021_01_08_425885	643	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	643	21	preprint	preprint	NN
10_1101-2021_01_08_425885	643	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	643	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	RB
10_1101-2021_01_08_425885	643	24	4.5.4	4.5.4	CD
10_1101-2021_01_08_425885	643	25	Associating	Associating	NNP
10_1101-2021_01_08_425885	643	26	Image	Image	NNP
10_1101-2021_01_08_425885	643	27	Patches	Patches	NNPS
10_1101-2021_01_08_425885	643	28	to	to	IN
10_1101-2021_01_08_425885	643	29	a	a	DT
10_1101-2021_01_08_425885	643	30	Klein	Klein	NNP
10_1101-2021_01_08_425885	643	31	Bottle	Bottle	NNP
10_1101-2021_01_08_425885	643	32	Embedding	embed	VBG
10_1101-2021_01_08_425885	643	33	For	for	IN
10_1101-2021_01_08_425885	643	34	a	a	DT
10_1101-2021_01_08_425885	643	35	given	give	VBN
10_1101-2021_01_08_425885	643	36	Klein	Klein	NNP
10_1101-2021_01_08_425885	643	37	bottle	bottle	NN
10_1101-2021_01_08_425885	643	38	embedding	embedding	NN
10_1101-2021_01_08_425885	643	39	,	,	,
10_1101-2021_01_08_425885	643	40	kαθ	kαθ	NNP
10_1101-2021_01_08_425885	643	41	,	,	,
10_1101-2021_01_08_425885	643	42	φ	φ	NNP
10_1101-2021_01_08_425885	643	43	∈	∈	NNP
10_1101-2021_01_08_425885	643	44	Kθ	Kθ	NNP
10_1101-2021_01_08_425885	643	45	,	,	,
10_1101-2021_01_08_425885	643	46	φ	φ	UH
10_1101-2021_01_08_425885	643	47	,	,	,
10_1101-2021_01_08_425885	643	48	we	-PRON-	PRP
10_1101-2021_01_08_425885	643	49	associated	associate	VBD
10_1101-2021_01_08_425885	643	50	each	each	DT
10_1101-2021_01_08_425885	643	51	datapoint	datapoint	JJ
10_1101-2021_01_08_425885	643	52	vi	vi	NNP
10_1101-2021_01_08_425885	643	53	(	(	-LRB-
10_1101-2021_01_08_425885	643	54	already	already	RB
10_1101-2021_01_08_425885	643	55	vectorized	vectorize	VBN
10_1101-2021_01_08_425885	643	56	and	and	CC
10_1101-2021_01_08_425885	643	57	normalized	normalize	VBN
10_1101-2021_01_08_425885	643	58	by	by	IN
10_1101-2021_01_08_425885	643	59	u	u	NNP
10_1101-2021_01_08_425885	643	60	◦	◦	NNP
10_1101-2021_01_08_425885	643	61	c	c	NNP
10_1101-2021_01_08_425885	643	62	◦	◦	NNP
10_1101-2021_01_08_425885	643	63	h	h	NNP
10_1101-2021_01_08_425885	643	64	)	)	-RRB-
10_1101-2021_01_08_425885	643	65	to	to	IN
10_1101-2021_01_08_425885	643	66	the	the	DT
10_1101-2021_01_08_425885	643	67	closest	close	JJS
10_1101-2021_01_08_425885	643	68	point	point	NN
10_1101-2021_01_08_425885	643	69	on	on	IN
10_1101-2021_01_08_425885	643	70	kαθ	kαθ	NNP
10_1101-2021_01_08_425885	643	71	,	,	,
10_1101-2021_01_08_425885	643	72	φ	φ	NN
10_1101-2021_01_08_425885	643	73	by	by	IN
10_1101-2021_01_08_425885	643	74	minimizing	minimize	VBG
10_1101-2021_01_08_425885	643	75	the	the	DT
10_1101-2021_01_08_425885	643	76	Euclidean	euclidean	JJ
10_1101-2021_01_08_425885	643	77	distance	distance	NN
10_1101-2021_01_08_425885	643	78	in	in	IN
10_1101-2021_01_08_425885	643	79	R	r	NN
10_1101-2021_01_08_425885	643	80	8	8	CD
10_1101-2021_01_08_425885	643	81	:	:	:
10_1101-2021_01_08_425885	643	82	(	(	-LRB-
10_1101-2021_01_08_425885	643	83	θ̂i	θ̂i	NNP
10_1101-2021_01_08_425885	643	84	,	,	,
10_1101-2021_01_08_425885	643	85	φ̂i	φ̂i	NNP
10_1101-2021_01_08_425885	643	86	)	)	-RRB-
10_1101-2021_01_08_425885	643	87	=	=	SYM
10_1101-2021_01_08_425885	643	88	argminθ	argminθ	NNS
10_1101-2021_01_08_425885	643	89	,	,	,
10_1101-2021_01_08_425885	643	90	φ‖(u	φ‖(u	NNP
10_1101-2021_01_08_425885	643	91	◦	◦	NNP
10_1101-2021_01_08_425885	643	92	c	c	NNP
10_1101-2021_01_08_425885	643	93	◦	◦	NNP
10_1101-2021_01_08_425885	643	94	h	h	NNP
10_1101-2021_01_08_425885	643	95	)	)	-RRB-
10_1101-2021_01_08_425885	643	96	(	(	-LRB-
10_1101-2021_01_08_425885	643	97	kαθ	kαθ	NNP
10_1101-2021_01_08_425885	643	98	,	,	,
10_1101-2021_01_08_425885	643	99	φ	φ	LS
10_1101-2021_01_08_425885	643	100	)	)	-RRB-
10_1101-2021_01_08_425885	643	101	−vi‖22	−vi‖22	NNP
10_1101-2021_01_08_425885	643	102	(	(	-LRB-
10_1101-2021_01_08_425885	643	103	36	36	CD
10_1101-2021_01_08_425885	643	104	)	)	-RRB-
10_1101-2021_01_08_425885	643	105	We	-PRON-	PRP
10_1101-2021_01_08_425885	643	106	solved	solve	VBD
10_1101-2021_01_08_425885	643	107	this	this	DT
10_1101-2021_01_08_425885	643	108	minimization	minimization	NN
10_1101-2021_01_08_425885	643	109	using	use	VBG
10_1101-2021_01_08_425885	643	110	the	the	DT
10_1101-2021_01_08_425885	643	111	lsqnonlin	lsqnonlin	NNP
10_1101-2021_01_08_425885	643	112	function	function	NN
10_1101-2021_01_08_425885	643	113	(	(	-LRB-
10_1101-2021_01_08_425885	643	114	‘	'	``
10_1101-2021_01_08_425885	643	115	StepTolerance’=1e-3	StepTolerance’=1e-3	NNP
10_1101-2021_01_08_425885	643	116	,	,	,
10_1101-2021_01_08_425885	643	117	‘	'	''
10_1101-2021_01_08_425885	643	118	FunctionTolerance’=1e-6	FunctionTolerance’=1e-6	NNP
10_1101-2021_01_08_425885	643	119	)	)	-RRB-
10_1101-2021_01_08_425885	643	120	in	in	IN
10_1101-2021_01_08_425885	643	121	MATLAB	MATLAB	NNP
10_1101-2021_01_08_425885	643	122	,	,	,
10_1101-2021_01_08_425885	643	123	supplying	supply	VBG
10_1101-2021_01_08_425885	643	124	initial	initial	JJ
10_1101-2021_01_08_425885	643	125	conditions	condition	NNS
10_1101-2021_01_08_425885	643	126	corresponding	correspond	VBG
10_1101-2021_01_08_425885	643	127	to	to	IN
10_1101-2021_01_08_425885	643	128	analytical	analytical	JJ
10_1101-2021_01_08_425885	643	129	values	value	NNS
10_1101-2021_01_08_425885	643	130	for	for	IN
10_1101-2021_01_08_425885	643	131	a	a	DT
10_1101-2021_01_08_425885	643	132	point	point	NN
10_1101-2021_01_08_425885	643	133	on	on	IN
10_1101-2021_01_08_425885	643	134	k0	k0	NNP
10_1101-2021_01_08_425885	643	135	:	:	:
10_1101-2021_01_08_425885	643	136	θ̂i	θ̂i	NNP
10_1101-2021_01_08_425885	643	137	=	=	SYM
10_1101-2021_01_08_425885	643	138	arctan	arctan	NNP
10_1101-2021_01_08_425885	643	139	e1	e1	NN
10_1101-2021_01_08_425885	643	140	Tvi	Tvi	NNP
10_1101-2021_01_08_425885	643	141	−e2Tvi	−e2Tvi	NNP
10_1101-2021_01_08_425885	643	142	(	(	-LRB-
10_1101-2021_01_08_425885	643	143	vi∈(u	vi∈(u	NNP
10_1101-2021_01_08_425885	643	144	◦	◦	NNP
10_1101-2021_01_08_425885	643	145	c	c	NNP
10_1101-2021_01_08_425885	643	146	◦	◦	NNP
10_1101-2021_01_08_425885	643	147	h)(k0	h)(k0	NNP
10_1101-2021_01_08_425885	643	148	)	)	-RRB-
10_1101-2021_01_08_425885	643	149	=	=	NFP
10_1101-2021_01_08_425885	643	150	arctan	arctan	NNP
10_1101-2021_01_08_425885	643	151	sin	sin	NN
10_1101-2021_01_08_425885	643	152	φ̂i	φ̂i	NNP
10_1101-2021_01_08_425885	643	153	sin	sin	NN
10_1101-2021_01_08_425885	643	154	θ̂i	θ̂i	NNP
10_1101-2021_01_08_425885	643	155	sin	sin	VB
10_1101-2021_01_08_425885	643	156	φ̂i	φ̂i	NNP
10_1101-2021_01_08_425885	643	157	cos	cos	IN
10_1101-2021_01_08_425885	643	158	θ̂i	θ̂i	NNP
10_1101-2021_01_08_425885	643	159	)	)	-RRB-
10_1101-2021_01_08_425885	643	160	φ̂i	φ̂i	NNP
10_1101-2021_01_08_425885	643	161	=	=	SYM
10_1101-2021_01_08_425885	643	162	arctan	arctan	NNP
10_1101-2021_01_08_425885	643	163	√	√	NNP
10_1101-2021_01_08_425885	643	164	(	(	-LRB-
10_1101-2021_01_08_425885	643	165	e1Tvi)2	e1tvi)2	ADD
10_1101-2021_01_08_425885	643	166	+	+	NFP
10_1101-2021_01_08_425885	643	167	(	(	-LRB-
10_1101-2021_01_08_425885	643	168	e2Tvi)2	e2tvi)2	FW
10_1101-2021_01_08_425885	643	169	(	(	-LRB-
10_1101-2021_01_08_425885	643	170	e3Tvi	e3tvi	NN
10_1101-2021_01_08_425885	643	171	)	)	-RRB-
10_1101-2021_01_08_425885	643	172	+	+	CC
10_1101-2021_01_08_425885	643	173	e4Tvi	e4Tvi	NNP
10_1101-2021_01_08_425885	643	174			NNP
10_1101-2021_01_08_425885	643	175	vi∈(u	vi∈(u	NN
10_1101-2021_01_08_425885	643	176	◦	◦	NNP
10_1101-2021_01_08_425885	643	177	c	c	NNP
10_1101-2021_01_08_425885	643	178	◦	◦	NNP
10_1101-2021_01_08_425885	643	179	h)(k0)=	h)(k0)=	NNP
10_1101-2021_01_08_425885	643	180	arctan	arctan	NN
10_1101-2021_01_08_425885	643	181	√	√	NNP
10_1101-2021_01_08_425885	643	182	sin2	sin2	NN
10_1101-2021_01_08_425885	643	183	φ̂i	φ̂i	NNP
10_1101-2021_01_08_425885	643	184	cos2	cos2	NNP
10_1101-2021_01_08_425885	643	185	φ̂i	φ̂i	NNP
10_1101-2021_01_08_425885	643	186			CD
10_1101-2021_01_08_425885	643	187			NNP
10_1101-2021_01_08_425885	643	188	(	(	-LRB-
10_1101-2021_01_08_425885	643	189	37	37	CD
10_1101-2021_01_08_425885	643	190	)	)	-RRB-
10_1101-2021_01_08_425885	643	191	We	-PRON-	PRP
10_1101-2021_01_08_425885	643	192	constrained	constrain	VBD
10_1101-2021_01_08_425885	643	193	solutions	solution	NNS
10_1101-2021_01_08_425885	643	194	to	to	IN
10_1101-2021_01_08_425885	643	195	θ̂i	θ̂i	NNP
10_1101-2021_01_08_425885	643	196	∈	∈	NNP
10_1101-2021_01_08_425885	643	197	[	[	-LRB-
10_1101-2021_01_08_425885	643	198	0,π	0,π	NN
10_1101-2021_01_08_425885	643	199	]	]	-RRB-
10_1101-2021_01_08_425885	643	200	and	and	CC
10_1101-2021_01_08_425885	643	201	φ̂i	φ̂i	NNP
10_1101-2021_01_08_425885	643	202	=	=	NFP
10_1101-2021_01_08_425885	643	203	[	[	-LRB-
10_1101-2021_01_08_425885	643	204	0	0	CD
10_1101-2021_01_08_425885	643	205	,	,	,
10_1101-2021_01_08_425885	643	206	2π	2π	LS
10_1101-2021_01_08_425885	643	207	]	]	-RRB-
10_1101-2021_01_08_425885	643	208	according	accord	VBG
10_1101-2021_01_08_425885	643	209	to	to	IN
10_1101-2021_01_08_425885	643	210	the	the	DT
10_1101-2021_01_08_425885	643	211	(	(	-LRB-
10_1101-2021_01_08_425885	643	212	θ	θ	NNP
10_1101-2021_01_08_425885	643	213	,	,	,
10_1101-2021_01_08_425885	643	214	φ	φ	NN
10_1101-2021_01_08_425885	643	215	)	)	-RRB-
10_1101-2021_01_08_425885	643	216	similarity	similarity	NN
10_1101-2021_01_08_425885	643	217	relation	relation	NN
10_1101-2021_01_08_425885	643	218	.	.	.
10_1101-2021_01_08_425885	644	1	4.5.5	4.5.5	CD
10_1101-2021_01_08_425885	644	2	Optimal	Optimal	NNP
10_1101-2021_01_08_425885	644	3	Klein	Klein	NNP
10_1101-2021_01_08_425885	644	4	Bottle	Bottle	NNP
10_1101-2021_01_08_425885	644	5	Embedding	Embedding	NNP
10_1101-2021_01_08_425885	644	6	Let	Let	NNP
10_1101-2021_01_08_425885	644	7	kα̂θ	kα̂θ	NNP
10_1101-2021_01_08_425885	644	8	,	,	,
10_1101-2021_01_08_425885	644	9	φ	φ	NNP
10_1101-2021_01_08_425885	644	10	∈	∈	NNP
10_1101-2021_01_08_425885	644	11	Kθ	Kθ	NNP
10_1101-2021_01_08_425885	644	12	,	,	,
10_1101-2021_01_08_425885	644	13	φ	φ	LS
10_1101-2021_01_08_425885	644	14	be	be	VB
10_1101-2021_01_08_425885	644	15	the	the	DT
10_1101-2021_01_08_425885	644	16	Klein	Klein	NNP
10_1101-2021_01_08_425885	644	17	bottle	bottle	NN
10_1101-2021_01_08_425885	644	18	embedding	embed	VBG
10_1101-2021_01_08_425885	644	19	that	that	WDT
10_1101-2021_01_08_425885	644	20	minimizes	minimize	VBZ
10_1101-2021_01_08_425885	644	21	the	the	DT
10_1101-2021_01_08_425885	644	22	sum	sum	NN
10_1101-2021_01_08_425885	644	23	of	of	IN
10_1101-2021_01_08_425885	644	24	Euclidean	euclidean	JJ
10_1101-2021_01_08_425885	644	25	distances	distance	NNS
10_1101-2021_01_08_425885	644	26	in	in	IN
10_1101-2021_01_08_425885	644	27	R	r	NN
10_1101-2021_01_08_425885	644	28	8	8	CD
10_1101-2021_01_08_425885	644	29	between	between	IN
10_1101-2021_01_08_425885	644	30	each	each	DT
10_1101-2021_01_08_425885	644	31	image	image	NN
10_1101-2021_01_08_425885	644	32	patch	patch	NN
10_1101-2021_01_08_425885	644	33	and	and	CC
10_1101-2021_01_08_425885	644	34	the	the	DT
10_1101-2021_01_08_425885	644	35	closest	close	JJS
10_1101-2021_01_08_425885	644	36	point	point	NN
10_1101-2021_01_08_425885	644	37	on	on	IN
10_1101-2021_01_08_425885	644	38	the	the	DT
10_1101-2021_01_08_425885	644	39	embedding	embedding	NN
10_1101-2021_01_08_425885	644	40	.	.	.
10_1101-2021_01_08_425885	645	1	To	to	TO
10_1101-2021_01_08_425885	645	2	determine	determine	VB
10_1101-2021_01_08_425885	645	3	kα̂θ	kα̂θ	NNP
10_1101-2021_01_08_425885	645	4	,	,	,
10_1101-2021_01_08_425885	645	5	φ	φ	NNP
10_1101-2021_01_08_425885	645	6	given	give	VBN
10_1101-2021_01_08_425885	645	7	a	a	DT
10_1101-2021_01_08_425885	645	8	functional	functional	JJ
10_1101-2021_01_08_425885	645	9	form	form	NN
10_1101-2021_01_08_425885	645	10	F	F	NNP
10_1101-2021_01_08_425885	645	11	,	,	,
10_1101-2021_01_08_425885	645	12	we	-PRON-	PRP
10_1101-2021_01_08_425885	645	13	initialized	initialize	VBD
10_1101-2021_01_08_425885	645	14	the	the	DT
10_1101-2021_01_08_425885	645	15	coefficient	coefficient	NN
10_1101-2021_01_08_425885	645	16	vector	vector	NN
10_1101-2021_01_08_425885	645	17	α̂	α̂	NNP
10_1101-2021_01_08_425885	645	18	to	to	TO
10_1101-2021_01_08_425885	645	19	have	have	VB
10_1101-2021_01_08_425885	645	20	zero	zero	CD
10_1101-2021_01_08_425885	645	21	entries	entry	NNS
10_1101-2021_01_08_425885	645	22	everywhere	everywhere	RB
10_1101-2021_01_08_425885	645	23	except	except	IN
10_1101-2021_01_08_425885	645	24	for	for	IN
10_1101-2021_01_08_425885	645	25	the	the	DT
10_1101-2021_01_08_425885	645	26	values	value	NNS
10_1101-2021_01_08_425885	645	27	used	use	VBN
10_1101-2021_01_08_425885	645	28	in	in	IN
10_1101-2021_01_08_425885	645	29	k0	k0	NNP
10_1101-2021_01_08_425885	645	30	.	.	.
10_1101-2021_01_08_425885	646	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	646	2	then	then	RB
10_1101-2021_01_08_425885	646	3	iterated	iterate	VBD
10_1101-2021_01_08_425885	646	4	between	between	IN
10_1101-2021_01_08_425885	646	5	optimizing	optimize	VBG
10_1101-2021_01_08_425885	646	6	for	for	IN
10_1101-2021_01_08_425885	646	7	(	(	-LRB-
10_1101-2021_01_08_425885	646	8	θ̂i	θ̂i	NNP
10_1101-2021_01_08_425885	646	9	,	,	,
10_1101-2021_01_08_425885	646	10	φ̂i	φ̂i	NNP
10_1101-2021_01_08_425885	646	11	)	)	-RRB-
10_1101-2021_01_08_425885	646	12	according	accord	VBG
10_1101-2021_01_08_425885	646	13	to	to	IN
10_1101-2021_01_08_425885	646	14	Equation	Equation	NNP
10_1101-2021_01_08_425885	646	15	36	36	CD
10_1101-2021_01_08_425885	646	16	and	and	CC
10_1101-2021_01_08_425885	646	17	for	for	IN
10_1101-2021_01_08_425885	646	18	α̂	α̂	NNP
10_1101-2021_01_08_425885	646	19	as	as	IN
10_1101-2021_01_08_425885	646	20	shown	show	VBN
10_1101-2021_01_08_425885	646	21	below	below	IN
10_1101-2021_01_08_425885	646	22	using	use	VBG
10_1101-2021_01_08_425885	646	23	least	least	JJS
10_1101-2021_01_08_425885	646	24	-	-	HYPH
10_1101-2021_01_08_425885	646	25	squares	square	NNS
10_1101-2021_01_08_425885	646	26	,	,	,
10_1101-2021_01_08_425885	646	27	until	until	IN
10_1101-2021_01_08_425885	646	28	convergence	convergence	NN
10_1101-2021_01_08_425885	646	29	:	:	:
10_1101-2021_01_08_425885	646	30	α̂	α̂	ADD
10_1101-2021_01_08_425885	646	31	=	=	SYM
10_1101-2021_01_08_425885	646	32	argminα	argminα	NNP
10_1101-2021_01_08_425885	646	33	∑	∑	XX
10_1101-2021_01_08_425885	646	34	i	i	NN
10_1101-2021_01_08_425885	646	35	‖(u	‖(u	NNS
10_1101-2021_01_08_425885	646	36	◦	◦	NNP
10_1101-2021_01_08_425885	646	37	c	c	NNP
10_1101-2021_01_08_425885	646	38	◦	◦	NNP
10_1101-2021_01_08_425885	646	39	h	h	NNP
10_1101-2021_01_08_425885	646	40	)	)	-RRB-
10_1101-2021_01_08_425885	646	41	(	(	-LRB-
10_1101-2021_01_08_425885	646	42	kα	kα	FW
10_1101-2021_01_08_425885	646	43	θ̂i	θ̂i	NNP
10_1101-2021_01_08_425885	646	44	,	,	,
10_1101-2021_01_08_425885	646	45	φ̂i	φ̂i	NNP
10_1101-2021_01_08_425885	646	46	)	)	-RRB-
10_1101-2021_01_08_425885	646	47	−vi‖22	−vi‖22	NNP
10_1101-2021_01_08_425885	646	48	(	(	-LRB-
10_1101-2021_01_08_425885	646	49	38	38	CD
10_1101-2021_01_08_425885	646	50	)	)	-RRB-
10_1101-2021_01_08_425885	646	51	k1	k1	NNP
10_1101-2021_01_08_425885	646	52	≡	≡	NNP
10_1101-2021_01_08_425885	646	53	kα̂θ	kα̂θ	NNP
10_1101-2021_01_08_425885	646	54	,	,	,
10_1101-2021_01_08_425885	646	55	φ	φ	NNP
10_1101-2021_01_08_425885	646	56	is	be	VBZ
10_1101-2021_01_08_425885	646	57	the	the	DT
10_1101-2021_01_08_425885	646	58	optimized	optimize	VBN
10_1101-2021_01_08_425885	646	59	Klein	Klein	NNP
10_1101-2021_01_08_425885	646	60	bottle	bottle	NN
10_1101-2021_01_08_425885	646	61	embedding	embed	VBG
10_1101-2021_01_08_425885	646	62	corresponding	correspond	VBG
10_1101-2021_01_08_425885	646	63	to	to	IN
10_1101-2021_01_08_425885	646	64	F	f	NN
10_1101-2021_01_08_425885	646	65	=	=	NFP
10_1101-2021_01_08_425885	646	66	[	[	-LRB-
10_1101-2021_01_08_425885	646	67	1	1	CD
10_1101-2021_01_08_425885	646	68	,	,	,
10_1101-2021_01_08_425885	646	69	10	10	CD
10_1101-2021_01_08_425885	646	70	,	,	,
10_1101-2021_01_08_425885	646	71	10	10	CD
10_1101-2021_01_08_425885	646	72	,	,	,
10_1101-2021_01_08_425885	646	73	20	20	CD
10_1101-2021_01_08_425885	646	74	,	,	,
10_1101-2021_01_08_425885	646	75	10	10	CD
10_1101-2021_01_08_425885	646	76	]	]	-RRB-
10_1101-2021_01_08_425885	646	77	,	,	,
10_1101-2021_01_08_425885	646	78	for	for	IN
10_1101-2021_01_08_425885	646	79	which	which	WDT
10_1101-2021_01_08_425885	646	80	results	result	NNS
10_1101-2021_01_08_425885	646	81	are	be	VBP
10_1101-2021_01_08_425885	646	82	shown	show	VBN
10_1101-2021_01_08_425885	646	83	in	in	IN
10_1101-2021_01_08_425885	646	84	Figures	figure	NNS
10_1101-2021_01_08_425885	646	85	3H	3h	NN
10_1101-2021_01_08_425885	646	86	and	and	CC
10_1101-2021_01_08_425885	646	87	S3D.	S3D.	NNS
10_1101-2021_01_08_425885	647	1	4.5.6	4.5.6	CD
10_1101-2021_01_08_425885	647	2	Noisy	Noisy	NNP
10_1101-2021_01_08_425885	647	3	Klein	Klein	NNP
10_1101-2021_01_08_425885	647	4	Bottle	Bottle	NNP
10_1101-2021_01_08_425885	647	5	Embeddings	Embeddings	NNP
10_1101-2021_01_08_425885	647	6	The	the	DT
10_1101-2021_01_08_425885	647	7	set	set	NN
10_1101-2021_01_08_425885	647	8	of	of	IN
10_1101-2021_01_08_425885	647	9	N	N	NNP
10_1101-2021_01_08_425885	647	10	≈	≈	NNP
10_1101-2021_01_08_425885	647	11	4.2×105	4.2×105	CD
10_1101-2021_01_08_425885	647	12	image	image	NN
10_1101-2021_01_08_425885	647	13	patches	patch	NNS
10_1101-2021_01_08_425885	647	14	was	be	VBD
10_1101-2021_01_08_425885	647	15	associated	associate	VBN
10_1101-2021_01_08_425885	647	16	to	to	IN
10_1101-2021_01_08_425885	647	17	k0	k0	NNP
10_1101-2021_01_08_425885	647	18	according	accord	VBG
10_1101-2021_01_08_425885	647	19	to	to	IN
10_1101-2021_01_08_425885	647	20	the	the	DT
10_1101-2021_01_08_425885	647	21	procedure	procedure	NN
10_1101-2021_01_08_425885	647	22	described	describe	VBN
10_1101-2021_01_08_425885	647	23	in	in	IN
10_1101-2021_01_08_425885	647	24	Methods	Methods	NNP
10_1101-2021_01_08_425885	647	25	Section	Section	NNP
10_1101-2021_01_08_425885	647	26	4.5.4	4.5.4	CD
10_1101-2021_01_08_425885	647	27	,	,	,
10_1101-2021_01_08_425885	647	28	yielding	yield	VBG
10_1101-2021_01_08_425885	647	29	(	(	-LRB-
10_1101-2021_01_08_425885	647	30	θ̂i	θ̂i	NNP
10_1101-2021_01_08_425885	647	31	,	,	,
10_1101-2021_01_08_425885	647	32	φ̂i	φ̂i	NNP
10_1101-2021_01_08_425885	647	33	)	)	-RRB-
10_1101-2021_01_08_425885	647	34	values	value	NNS
10_1101-2021_01_08_425885	647	35	.	.	.
10_1101-2021_01_08_425885	648	1	Isotropic	isotropic	JJ
10_1101-2021_01_08_425885	648	2	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	648	3	noise	noise	NN
10_1101-2021_01_08_425885	648	4	of	of	IN
10_1101-2021_01_08_425885	648	5	magnitude	magnitude	NN
10_1101-2021_01_08_425885	648	6	sσ	sσ	NNP
10_1101-2021_01_08_425885	648	7	was	be	VBD
10_1101-2021_01_08_425885	648	8	added	add	VBN
10_1101-2021_01_08_425885	648	9	element	element	NN
10_1101-2021_01_08_425885	648	10	-	-	HYPH
10_1101-2021_01_08_425885	648	11	wise	wise	JJ
10_1101-2021_01_08_425885	648	12	in	in	IN
10_1101-2021_01_08_425885	648	13	R9	R9	NNP
10_1101-2021_01_08_425885	648	14	(	(	-LRB-
10_1101-2021_01_08_425885	648	15	prior	prior	RB
10_1101-2021_01_08_425885	648	16	to	to	IN
10_1101-2021_01_08_425885	648	17	normalization	normalization	NN
10_1101-2021_01_08_425885	648	18	by	by	IN
10_1101-2021_01_08_425885	648	19	u	u	NNP
10_1101-2021_01_08_425885	648	20	◦	◦	NNP
10_1101-2021_01_08_425885	648	21	c	c	NNP
10_1101-2021_01_08_425885	648	22	)	)	-RRB-
10_1101-2021_01_08_425885	648	23	to	to	IN
10_1101-2021_01_08_425885	648	24	h(k0	h(k0	NNP
10_1101-2021_01_08_425885	648	25	θ̂i	θ̂i	NNP
10_1101-2021_01_08_425885	648	26	,	,	,
10_1101-2021_01_08_425885	648	27	φ̂i	φ̂i	NNP
10_1101-2021_01_08_425885	648	28	)	)	-RRB-
10_1101-2021_01_08_425885	648	29	,	,	,
10_1101-2021_01_08_425885	648	30	where	where	WRB
10_1101-2021_01_08_425885	648	31	s	s	NNP
10_1101-2021_01_08_425885	648	32	=	=	SYM
10_1101-2021_01_08_425885	648	33	mediani{‖h(k0	mediani{‖h(k0	NNP
10_1101-2021_01_08_425885	648	34	θ̂i	θ̂i	NNP
10_1101-2021_01_08_425885	648	35	,	,	,
10_1101-2021_01_08_425885	648	36	φ̂i	φ̂i	NNP
10_1101-2021_01_08_425885	648	37	)	)	-RRB-
10_1101-2021_01_08_425885	648	38	‖2	‖2	NNP
10_1101-2021_01_08_425885	648	39	}	}	-RRB-
10_1101-2021_01_08_425885	648	40	≈	≈	NNP
10_1101-2021_01_08_425885	648	41	2.451	2.451	CD
10_1101-2021_01_08_425885	648	42	.	.	.
10_1101-2021_01_08_425885	649	1	Figures	figure	NNS
10_1101-2021_01_08_425885	649	2	3F	3f	NN
10_1101-2021_01_08_425885	649	3	,	,	,
10_1101-2021_01_08_425885	649	4	G	g	NN
10_1101-2021_01_08_425885	649	5	and	and	CC
10_1101-2021_01_08_425885	649	6	S3A	S3A	NNP
10_1101-2021_01_08_425885	649	7	correspond	correspond	NN
10_1101-2021_01_08_425885	649	8	to	to	TO
10_1101-2021_01_08_425885	649	9	noise	noise	VB
10_1101-2021_01_08_425885	649	10	with	with	IN
10_1101-2021_01_08_425885	649	11	σ	σ	NNP
10_1101-2021_01_08_425885	649	12	=	=	SYM
10_1101-2021_01_08_425885	649	13	0.007	0.007	CD
10_1101-2021_01_08_425885	649	14	,	,	,
10_1101-2021_01_08_425885	649	15	0.01	0.01	CD
10_1101-2021_01_08_425885	649	16	and	and	CC
10_1101-2021_01_08_425885	649	17	0.03	0.03	CD
10_1101-2021_01_08_425885	649	18	.	.	.
10_1101-2021_01_08_425885	650	1	39	39	CD
10_1101-2021_01_08_425885	650	2	.CC	.CC	:
10_1101-2021_01_08_425885	650	3	-	-	HYPH
10_1101-2021_01_08_425885	650	4	BY	by	IN
10_1101-2021_01_08_425885	650	5	-	-	HYPH
10_1101-2021_01_08_425885	650	6	NC	NC	NNP
10_1101-2021_01_08_425885	650	7	-	-	HYPH
10_1101-2021_01_08_425885	650	8	ND	ND	NNP
10_1101-2021_01_08_425885	650	9	4.0	4.0	CD
10_1101-2021_01_08_425885	650	10	International	International	NNP
10_1101-2021_01_08_425885	650	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	650	12	under	under	IN
10_1101-2021_01_08_425885	650	13	a	a	DT
10_1101-2021_01_08_425885	650	14	(	(	-LRB-
10_1101-2021_01_08_425885	650	15	which	which	WDT
10_1101-2021_01_08_425885	650	16	was	be	VBD
10_1101-2021_01_08_425885	650	17	not	not	RB
10_1101-2021_01_08_425885	650	18	certified	certify	VBN
10_1101-2021_01_08_425885	650	19	by	by	IN
10_1101-2021_01_08_425885	650	20	peer	peer	NN
10_1101-2021_01_08_425885	650	21	review	review	NN
10_1101-2021_01_08_425885	650	22	)	)	-RRB-
10_1101-2021_01_08_425885	650	23	is	be	VBZ
10_1101-2021_01_08_425885	650	24	the	the	DT
10_1101-2021_01_08_425885	650	25	author	author	NN
10_1101-2021_01_08_425885	650	26	/	/	SYM
10_1101-2021_01_08_425885	650	27	funder	funder	NN
10_1101-2021_01_08_425885	650	28	,	,	,
10_1101-2021_01_08_425885	650	29	who	who	WP
10_1101-2021_01_08_425885	650	30	has	have	VBZ
10_1101-2021_01_08_425885	650	31	granted	grant	VBN
10_1101-2021_01_08_425885	650	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	650	33	a	a	DT
10_1101-2021_01_08_425885	650	34	license	license	NN
10_1101-2021_01_08_425885	650	35	to	to	TO
10_1101-2021_01_08_425885	650	36	display	display	VB
10_1101-2021_01_08_425885	650	37	the	the	DT
10_1101-2021_01_08_425885	650	38	preprint	preprint	NN
10_1101-2021_01_08_425885	650	39	in	in	IN
10_1101-2021_01_08_425885	650	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	650	41	.	.	.
10_1101-2021_01_08_425885	651	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	651	2	is	be	VBZ
10_1101-2021_01_08_425885	651	3	made	make	VBN
10_1101-2021_01_08_425885	651	4	The	the	DT
10_1101-2021_01_08_425885	651	5	copyright	copyright	NN
10_1101-2021_01_08_425885	651	6	holder	holder	NN
10_1101-2021_01_08_425885	651	7	for	for	IN
10_1101-2021_01_08_425885	651	8	this	this	DT
10_1101-2021_01_08_425885	651	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	651	10	version	version	NN
10_1101-2021_01_08_425885	651	11	posted	post	VBD
10_1101-2021_01_08_425885	651	12	January	January	NNP
10_1101-2021_01_08_425885	651	13	8	8	CD
10_1101-2021_01_08_425885	651	14	,	,	,
10_1101-2021_01_08_425885	651	15	2021	2021	CD
10_1101-2021_01_08_425885	651	16	.	.	.
10_1101-2021_01_08_425885	651	17	;	;	:
10_1101-2021_01_08_425885	651	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	651	19	:	:	:
10_1101-2021_01_08_425885	651	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	651	21	preprint	preprint	NN
10_1101-2021_01_08_425885	651	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	651	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NN
10_1101-2021_01_08_425885	651	24	4.5.7	4.5.7	CD
10_1101-2021_01_08_425885	651	25	Parameters	Parameters	NNPS
10_1101-2021_01_08_425885	651	26	for	for	IN
10_1101-2021_01_08_425885	651	27	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	651	28	Estimation	Estimation	NNP
10_1101-2021_01_08_425885	651	29	For	for	IN
10_1101-2021_01_08_425885	651	30	all	all	DT
10_1101-2021_01_08_425885	651	31	scalar	scalar	JJ
10_1101-2021_01_08_425885	651	32	curvature	curvature	JJ
10_1101-2021_01_08_425885	651	33	computations	computation	NNS
10_1101-2021_01_08_425885	651	34	on	on	IN
10_1101-2021_01_08_425885	651	35	image	image	NN
10_1101-2021_01_08_425885	651	36	patch	patch	NN
10_1101-2021_01_08_425885	651	37	datasets	dataset	NNS
10_1101-2021_01_08_425885	651	38	and	and	CC
10_1101-2021_01_08_425885	651	39	Klein	Klein	NNP
10_1101-2021_01_08_425885	651	40	bottle	bottle	NN
10_1101-2021_01_08_425885	651	41	embeddings	embedding	NNS
10_1101-2021_01_08_425885	651	42	,	,	,
10_1101-2021_01_08_425885	651	43	we	-PRON-	PRP
10_1101-2021_01_08_425885	651	44	set	set	VBP
10_1101-2021_01_08_425885	651	45	d	d	NNS
10_1101-2021_01_08_425885	651	46	=	=	SYM
10_1101-2021_01_08_425885	651	47	2	2	CD
10_1101-2021_01_08_425885	651	48	and	and	CC
10_1101-2021_01_08_425885	651	49	Ncalib	Ncalib	NNP
10_1101-2021_01_08_425885	651	50	=	=	SYM
10_1101-2021_01_08_425885	651	51	10	10	CD
10_1101-2021_01_08_425885	651	52	4	4	CD
10_1101-2021_01_08_425885	651	53	.	.	.
10_1101-2021_01_08_425885	652	1	Unless	unless	IN
10_1101-2021_01_08_425885	652	2	the	the	DT
10_1101-2021_01_08_425885	652	3	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	652	4	were	be	VBD
10_1101-2021_01_08_425885	652	5	manually	manually	RB
10_1101-2021_01_08_425885	652	6	specified	specify	VBN
10_1101-2021_01_08_425885	652	7	,	,	,
10_1101-2021_01_08_425885	652	8	we	-PRON-	PRP
10_1101-2021_01_08_425885	652	9	used	use	VBD
10_1101-2021_01_08_425885	652	10	σh	σh	NNP
10_1101-2021_01_08_425885	652	11	=	=	SYM
10_1101-2021_01_08_425885	652	12	0.1	0.1	CD
10_1101-2021_01_08_425885	652	13	,	,	,
10_1101-2021_01_08_425885	652	14	which	which	WDT
10_1101-2021_01_08_425885	652	15	yielded	yield	VBD
10_1101-2021_01_08_425885	652	16	a	a	DT
10_1101-2021_01_08_425885	652	17	flat	flat	JJ
10_1101-2021_01_08_425885	652	18	distribution	distribution	NN
10_1101-2021_01_08_425885	652	19	of	of	IN
10_1101-2021_01_08_425885	652	20	GOF	GOF	NNP
10_1101-2021_01_08_425885	652	21	p	p	NN
10_1101-2021_01_08_425885	652	22	-	-	HYPH
10_1101-2021_01_08_425885	652	23	values	value	NNS
10_1101-2021_01_08_425885	652	24	(	(	-LRB-
10_1101-2021_01_08_425885	652	25	2.5	2.5	CD
10_1101-2021_01_08_425885	652	26	%	%	NN
10_1101-2021_01_08_425885	652	27	of	of	IN
10_1101-2021_01_08_425885	652	28	points	point	NNS
10_1101-2021_01_08_425885	652	29	reported	report	VBD
10_1101-2021_01_08_425885	652	30	GOF	GOF	NNP
10_1101-2021_01_08_425885	652	31	p	p	NN
10_1101-2021_01_08_425885	652	32	-	-	HYPH
10_1101-2021_01_08_425885	652	33	values	value	NNS
10_1101-2021_01_08_425885	652	34	≤	≤	NNP
10_1101-2021_01_08_425885	652	35	α	α	NNP
10_1101-2021_01_08_425885	652	36	=	=	SYM
10_1101-2021_01_08_425885	652	37	0.05	0.05	CD
10_1101-2021_01_08_425885	652	38	)	)	-RRB-
10_1101-2021_01_08_425885	652	39	for	for	IN
10_1101-2021_01_08_425885	652	40	the	the	DT
10_1101-2021_01_08_425885	652	41	set	set	NN
10_1101-2021_01_08_425885	652	42	of	of	IN
10_1101-2021_01_08_425885	652	43	N	N	NNP
10_1101-2021_01_08_425885	652	44	≈	≈	NNP
10_1101-2021_01_08_425885	652	45	4.2×105	4.2×105	CD
10_1101-2021_01_08_425885	652	46	points	point	NNS
10_1101-2021_01_08_425885	652	47	on	on	IN
10_1101-2021_01_08_425885	652	48	k0	k0	NNP
10_1101-2021_01_08_425885	652	49	closest	close	JJS
10_1101-2021_01_08_425885	652	50	to	to	IN
10_1101-2021_01_08_425885	652	51	the	the	DT
10_1101-2021_01_08_425885	652	52	image	image	NN
10_1101-2021_01_08_425885	652	53	patches	patch	NNS
10_1101-2021_01_08_425885	652	54	(	(	-LRB-
10_1101-2021_01_08_425885	652	55	shown	show	VBN
10_1101-2021_01_08_425885	652	56	in	in	IN
10_1101-2021_01_08_425885	652	57	Figure	Figure	NNP
10_1101-2021_01_08_425885	652	58	3E	3e	NN
10_1101-2021_01_08_425885	652	59	)	)	-RRB-
10_1101-2021_01_08_425885	652	60	.	.	.
10_1101-2021_01_08_425885	653	1	4.6	4.6	CD
10_1101-2021_01_08_425885	653	2	Details	detail	NNS
10_1101-2021_01_08_425885	653	3	of	of	IN
10_1101-2021_01_08_425885	653	4	scRNASeq	scRNASeq	NNP
10_1101-2021_01_08_425885	653	5	Datasets	dataset	VBZ
10_1101-2021_01_08_425885	653	6	The	the	DT
10_1101-2021_01_08_425885	653	7	PBMC	pbmc	NN
10_1101-2021_01_08_425885	653	8	dataset	dataset	NN
10_1101-2021_01_08_425885	653	9	provided	provide	VBN
10_1101-2021_01_08_425885	653	10	by	by	IN
10_1101-2021_01_08_425885	653	11	10x	10x	NNPS
10_1101-2021_01_08_425885	653	12	Genomics	Genomics	NNP
10_1101-2021_01_08_425885	653	13	is	be	VBZ
10_1101-2021_01_08_425885	653	14	comprised	comprise	VBN
10_1101-2021_01_08_425885	653	15	of	of	IN
10_1101-2021_01_08_425885	653	16	N	n	NN
10_1101-2021_01_08_425885	653	17	=	=	SYM
10_1101-2021_01_08_425885	653	18	10194	10194	CD
10_1101-2021_01_08_425885	653	19	PBMCs	pbmc	NNS
10_1101-2021_01_08_425885	653	20	collected	collect	VBD
10_1101-2021_01_08_425885	653	21	from	from	IN
10_1101-2021_01_08_425885	653	22	a	a	DT
10_1101-2021_01_08_425885	653	23	healthy	healthy	JJ
10_1101-2021_01_08_425885	653	24	donor	donor	NN
10_1101-2021_01_08_425885	653	25	[	[	-LRB-
10_1101-2021_01_08_425885	653	26	42	42	CD
10_1101-2021_01_08_425885	653	27	]	]	-RRB-
10_1101-2021_01_08_425885	653	28	.	.	.
10_1101-2021_01_08_425885	654	1	The	the	DT
10_1101-2021_01_08_425885	654	2	mouse	mouse	NN
10_1101-2021_01_08_425885	654	3	gastrulation	gastrulation	NN
10_1101-2021_01_08_425885	654	4	dataset	dataset	NN
10_1101-2021_01_08_425885	654	5	consists	consist	VBZ
10_1101-2021_01_08_425885	654	6	of	of	IN
10_1101-2021_01_08_425885	654	7	N	n	NN
10_1101-2021_01_08_425885	654	8	=	=	SYM
10_1101-2021_01_08_425885	654	9	116312	116312	CD
10_1101-2021_01_08_425885	654	10	cells	cell	NNS
10_1101-2021_01_08_425885	654	11	collected	collect	VBN
10_1101-2021_01_08_425885	654	12	at	at	IN
10_1101-2021_01_08_425885	654	13	nine	nine	CD
10_1101-2021_01_08_425885	654	14	6-hour	6-hour	CD
10_1101-2021_01_08_425885	654	15	intervals	interval	NNS
10_1101-2021_01_08_425885	654	16	from	from	IN
10_1101-2021_01_08_425885	654	17	embryonic	embryonic	JJ
10_1101-2021_01_08_425885	654	18	day	day	NN
10_1101-2021_01_08_425885	654	19	6.5	6.5	CD
10_1101-2021_01_08_425885	654	20	to	to	TO
10_1101-2021_01_08_425885	654	21	8.5	8.5	CD
10_1101-2021_01_08_425885	654	22	[	[	-LRB-
10_1101-2021_01_08_425885	654	23	43	43	CD
10_1101-2021_01_08_425885	654	24	]	]	-RRB-
10_1101-2021_01_08_425885	654	25	.	.	.
10_1101-2021_01_08_425885	655	1	The	the	DT
10_1101-2021_01_08_425885	655	2	mouse	mouse	NN
10_1101-2021_01_08_425885	655	3	brain	brain	NN
10_1101-2021_01_08_425885	655	4	dataset	dataset	NN
10_1101-2021_01_08_425885	655	5	is	be	VBZ
10_1101-2021_01_08_425885	655	6	a	a	DT
10_1101-2021_01_08_425885	655	7	benchmark	benchmark	NN
10_1101-2021_01_08_425885	655	8	from	from	IN
10_1101-2021_01_08_425885	655	9	10x	10x	NNPS
10_1101-2021_01_08_425885	655	10	Genomics	Genomics	NNP
10_1101-2021_01_08_425885	655	11	consisting	consist	VBG
10_1101-2021_01_08_425885	655	12	of	of	IN
10_1101-2021_01_08_425885	655	13	N	n	NN
10_1101-2021_01_08_425885	655	14	=	=	SYM
10_1101-2021_01_08_425885	655	15	1306127	1306127	CD
10_1101-2021_01_08_425885	655	16	cells	cell	NNS
10_1101-2021_01_08_425885	655	17	collected	collect	VBN
10_1101-2021_01_08_425885	655	18	from	from	IN
10_1101-2021_01_08_425885	655	19	the	the	DT
10_1101-2021_01_08_425885	655	20	cortex	cortex	NNP
10_1101-2021_01_08_425885	655	21	,	,	,
10_1101-2021_01_08_425885	655	22	hippocampus	hippocampus	NNP
10_1101-2021_01_08_425885	655	23	and	and	CC
10_1101-2021_01_08_425885	655	24	ventricular	ventricular	NNP
10_1101-2021_01_08_425885	655	25	zone	zone	NN
10_1101-2021_01_08_425885	655	26	of	of	IN
10_1101-2021_01_08_425885	655	27	two	two	CD
10_1101-2021_01_08_425885	655	28	embryonic	embryonic	JJ
10_1101-2021_01_08_425885	655	29	mice	mouse	NNS
10_1101-2021_01_08_425885	655	30	sacked	sack	VBN
10_1101-2021_01_08_425885	655	31	at	at	IN
10_1101-2021_01_08_425885	655	32	embryonic	embryonic	NNP
10_1101-2021_01_08_425885	655	33	day	day	NN
10_1101-2021_01_08_425885	655	34	18	18	CD
10_1101-2021_01_08_425885	655	35	[	[	-LRB-
10_1101-2021_01_08_425885	655	36	44	44	CD
10_1101-2021_01_08_425885	655	37	]	]	-RRB-
10_1101-2021_01_08_425885	655	38	.	.	.
10_1101-2021_01_08_425885	656	1	4.6.1	4.6.1	NNP
10_1101-2021_01_08_425885	656	2	Preprocessing	Preprocessing	NNP
10_1101-2021_01_08_425885	656	3	For	for	IN
10_1101-2021_01_08_425885	656	4	the	the	DT
10_1101-2021_01_08_425885	656	5	PBMC	PBMC	NNP
10_1101-2021_01_08_425885	656	6	dataset	dataset	NN
10_1101-2021_01_08_425885	656	7	,	,	,
10_1101-2021_01_08_425885	656	8	we	-PRON-	PRP
10_1101-2021_01_08_425885	656	9	applied	apply	VBD
10_1101-2021_01_08_425885	656	10	standard	standard	JJ
10_1101-2021_01_08_425885	656	11	preprocessing	preprocessing	NN
10_1101-2021_01_08_425885	656	12	steps	step	NNS
10_1101-2021_01_08_425885	656	13	using	use	VBG
10_1101-2021_01_08_425885	656	14	Seurat	Seurat	NNP
10_1101-2021_01_08_425885	656	15	v3.1.2	v3.1.2	NNP
10_1101-2021_01_08_425885	656	16	[	[	-LRB-
10_1101-2021_01_08_425885	656	17	53	53	CD
10_1101-2021_01_08_425885	656	18	]	]	-RRB-
10_1101-2021_01_08_425885	656	19	with	with	IN
10_1101-2021_01_08_425885	656	20	default	default	NN
10_1101-2021_01_08_425885	656	21	function	function	NN
10_1101-2021_01_08_425885	656	22	arguments	argument	NNS
10_1101-2021_01_08_425885	656	23	,	,	,
10_1101-2021_01_08_425885	656	24	to	to	TO
10_1101-2021_01_08_425885	656	25	extract	extract	VB
10_1101-2021_01_08_425885	656	26	PC	pc	NN
10_1101-2021_01_08_425885	656	27	projections	projection	NNS
10_1101-2021_01_08_425885	656	28	and	and	CC
10_1101-2021_01_08_425885	656	29	UMAP	UMAP	NNP
10_1101-2021_01_08_425885	656	30	coordinates	coordinate	VBZ
10_1101-2021_01_08_425885	656	31	ourselves	-PRON-	PRP
10_1101-2021_01_08_425885	656	32	.	.	.
10_1101-2021_01_08_425885	657	1	Specifically	specifically	RB
10_1101-2021_01_08_425885	657	2	,	,	,
10_1101-2021_01_08_425885	657	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	657	4	removed	remove	VBD
10_1101-2021_01_08_425885	657	5	cells	cell	NNS
10_1101-2021_01_08_425885	657	6	where	where	WRB
10_1101-2021_01_08_425885	657	7	the	the	DT
10_1101-2021_01_08_425885	657	8	percentage	percentage	NN
10_1101-2021_01_08_425885	657	9	of	of	IN
10_1101-2021_01_08_425885	657	10	transcripts	transcript	NNS
10_1101-2021_01_08_425885	657	11	corresponding	correspond	VBG
10_1101-2021_01_08_425885	657	12	to	to	IN
10_1101-2021_01_08_425885	657	13	mitochondrial	mitochondrial	NN
10_1101-2021_01_08_425885	657	14	genes	gene	NNS
10_1101-2021_01_08_425885	657	15	exceeded	exceed	VBD
10_1101-2021_01_08_425885	657	16	15	15	CD
10_1101-2021_01_08_425885	657	17	%	%	NN
10_1101-2021_01_08_425885	657	18	,	,	,
10_1101-2021_01_08_425885	657	19	or	or	CC
10_1101-2021_01_08_425885	657	20	which	which	WDT
10_1101-2021_01_08_425885	657	21	had	have	VBD
10_1101-2021_01_08_425885	657	22	fewer	few	JJR
10_1101-2021_01_08_425885	657	23	than	than	IN
10_1101-2021_01_08_425885	657	24	500	500	CD
10_1101-2021_01_08_425885	657	25	transcripts	transcript	NNS
10_1101-2021_01_08_425885	657	26	.	.	.
10_1101-2021_01_08_425885	658	1	This	this	DT
10_1101-2021_01_08_425885	658	2	reduced	reduce	VBD
10_1101-2021_01_08_425885	658	3	the	the	DT
10_1101-2021_01_08_425885	658	4	number	number	NN
10_1101-2021_01_08_425885	658	5	of	of	IN
10_1101-2021_01_08_425885	658	6	cells	cell	NNS
10_1101-2021_01_08_425885	658	7	from	from	IN
10_1101-2021_01_08_425885	658	8	10194	10194	CD
10_1101-2021_01_08_425885	658	9	to	to	IN
10_1101-2021_01_08_425885	658	10	9385	9385	CD
10_1101-2021_01_08_425885	658	11	.	.	.
10_1101-2021_01_08_425885	659	1	On	on	IN
10_1101-2021_01_08_425885	659	2	this	this	DT
10_1101-2021_01_08_425885	659	3	filtered	filtered	JJ
10_1101-2021_01_08_425885	659	4	set	set	NN
10_1101-2021_01_08_425885	659	5	,	,	,
10_1101-2021_01_08_425885	659	6	we	-PRON-	PRP
10_1101-2021_01_08_425885	659	7	normalized	normalize	VBD
10_1101-2021_01_08_425885	659	8	the	the	DT
10_1101-2021_01_08_425885	659	9	data	datum	NNS
10_1101-2021_01_08_425885	659	10	(	(	-LRB-
10_1101-2021_01_08_425885	659	11	NormalizeData(normalization.method=‘LogNormalize	normalizedata(normalization.method=‘lognormalize	NN
10_1101-2021_01_08_425885	659	12	’	'	''
10_1101-2021_01_08_425885	659	13	,	,	,
10_1101-2021_01_08_425885	659	14	scale.factor=10000	scale.factor=10000	NNP
10_1101-2021_01_08_425885	659	15	)	)	-RRB-
10_1101-2021_01_08_425885	659	16	)	)	-RRB-
10_1101-2021_01_08_425885	659	17	,	,	,
10_1101-2021_01_08_425885	659	18	retained	retain	VBD
10_1101-2021_01_08_425885	659	19	the	the	DT
10_1101-2021_01_08_425885	659	20	2000	2000	CD
10_1101-2021_01_08_425885	659	21	most	most	RBS
10_1101-2021_01_08_425885	659	22	variable	variable	JJ
10_1101-2021_01_08_425885	659	23	genes	gene	NNS
10_1101-2021_01_08_425885	659	24	(	(	-LRB-
10_1101-2021_01_08_425885	659	25	FindVariableFeatures(selection.method=‘vst	FindVariableFeatures(selection.method=‘vst	NNP
10_1101-2021_01_08_425885	659	26	’	'	''
10_1101-2021_01_08_425885	659	27	,	,	,
10_1101-2021_01_08_425885	659	28	nfeatures=2000	nfeatures=2000	NNP
10_1101-2021_01_08_425885	659	29	)	)	-RRB-
10_1101-2021_01_08_425885	659	30	)	)	-RRB-
10_1101-2021_01_08_425885	659	31	,	,	,
10_1101-2021_01_08_425885	659	32	and	and	CC
10_1101-2021_01_08_425885	659	33	scaled	scale	VBD
10_1101-2021_01_08_425885	659	34	the	the	DT
10_1101-2021_01_08_425885	659	35	data	datum	NNS
10_1101-2021_01_08_425885	659	36	(	(	-LRB-
10_1101-2021_01_08_425885	659	37	ScaleData	ScaleData	NNP
10_1101-2021_01_08_425885	659	38	)	)	-RRB-
10_1101-2021_01_08_425885	659	39	.	.	.
10_1101-2021_01_08_425885	660	1	Next	next	RB
10_1101-2021_01_08_425885	660	2	,	,	,
10_1101-2021_01_08_425885	660	3	we	-PRON-	PRP
10_1101-2021_01_08_425885	660	4	performed	perform	VBD
10_1101-2021_01_08_425885	660	5	linear	linear	JJ
10_1101-2021_01_08_425885	660	6	dimensionality	dimensionality	NN
10_1101-2021_01_08_425885	660	7	reduction	reduction	NN
10_1101-2021_01_08_425885	660	8	using	use	VBG
10_1101-2021_01_08_425885	660	9	PCA	PCA	NNP
10_1101-2021_01_08_425885	660	10	down	down	RB
10_1101-2021_01_08_425885	660	11	to	to	IN
10_1101-2021_01_08_425885	660	12	50	50	CD
10_1101-2021_01_08_425885	660	13	dimensions	dimension	NNS
10_1101-2021_01_08_425885	660	14	(	(	-LRB-
10_1101-2021_01_08_425885	660	15	RunPCA(npcs=50	RunPCA(npcs=50	NNP
10_1101-2021_01_08_425885	660	16	)	)	-RRB-
10_1101-2021_01_08_425885	660	17	)	)	-RRB-
10_1101-2021_01_08_425885	660	18	and	and	CC
10_1101-2021_01_08_425885	660	19	generated	generate	VBN
10_1101-2021_01_08_425885	660	20	UMAP	UMAP	NNP
10_1101-2021_01_08_425885	660	21	coordinates	coordinate	VBZ
10_1101-2021_01_08_425885	660	22	for	for	IN
10_1101-2021_01_08_425885	660	23	visualization	visualization	NN
10_1101-2021_01_08_425885	660	24	(	(	-LRB-
10_1101-2021_01_08_425885	660	25	RunUMAP(dims	RunUMAP(dims	NFP
10_1101-2021_01_08_425885	660	26	=	=	SYM
10_1101-2021_01_08_425885	660	27	1:30	1:30	CD
10_1101-2021_01_08_425885	660	28	)	)	-RRB-
10_1101-2021_01_08_425885	660	29	)	)	-RRB-
10_1101-2021_01_08_425885	660	30	.	.	.
10_1101-2021_01_08_425885	661	1	For	for	IN
10_1101-2021_01_08_425885	661	2	the	the	DT
10_1101-2021_01_08_425885	661	3	gastrulation	gastrulation	NN
10_1101-2021_01_08_425885	661	4	(	(	-LRB-
10_1101-2021_01_08_425885	661	5	brain	brain	NN
10_1101-2021_01_08_425885	661	6	)	)	-RRB-
10_1101-2021_01_08_425885	661	7	dataset	dataset	NN
10_1101-2021_01_08_425885	661	8	,	,	,
10_1101-2021_01_08_425885	661	9	we	-PRON-	PRP
10_1101-2021_01_08_425885	661	10	did	do	VBD
10_1101-2021_01_08_425885	661	11	not	not	RB
10_1101-2021_01_08_425885	661	12	preprocess	preprocess	VB
10_1101-2021_01_08_425885	661	13	the	the	DT
10_1101-2021_01_08_425885	661	14	data	datum	NNS
10_1101-2021_01_08_425885	661	15	ourselves	-PRON-	PRP
10_1101-2021_01_08_425885	661	16	but	but	CC
10_1101-2021_01_08_425885	661	17	instead	instead	RB
10_1101-2021_01_08_425885	661	18	directly	directly	RB
10_1101-2021_01_08_425885	661	19	used	use	VBD
10_1101-2021_01_08_425885	661	20	the	the	DT
10_1101-2021_01_08_425885	661	21	50	50	CD
10_1101-2021_01_08_425885	661	22	(	(	-LRB-
10_1101-2021_01_08_425885	661	23	20	20	CD
10_1101-2021_01_08_425885	661	24	)	)	-RRB-
10_1101-2021_01_08_425885	661	25	PC	pc	NN
10_1101-2021_01_08_425885	661	26	projections	projection	NNS
10_1101-2021_01_08_425885	661	27	and	and	CC
10_1101-2021_01_08_425885	661	28	UMAP	UMAP	NNP
10_1101-2021_01_08_425885	661	29	(	(	-LRB-
10_1101-2021_01_08_425885	661	30	t	t	NNP
10_1101-2021_01_08_425885	661	31	-	-	HYPH
10_1101-2021_01_08_425885	661	32	SNE	SNE	NNP
10_1101-2021_01_08_425885	661	33	)	)	-RRB-
10_1101-2021_01_08_425885	661	34	visualization	visualization	NN
10_1101-2021_01_08_425885	661	35	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	661	36	provided	provide	VBN
10_1101-2021_01_08_425885	661	37	with	with	IN
10_1101-2021_01_08_425885	661	38	the	the	DT
10_1101-2021_01_08_425885	661	39	dataset	dataset	NN
10_1101-2021_01_08_425885	661	40	.	.	.
10_1101-2021_01_08_425885	662	1	Please	please	UH
10_1101-2021_01_08_425885	662	2	refer	refer	VB
10_1101-2021_01_08_425885	662	3	to	to	IN
10_1101-2021_01_08_425885	662	4	[	[	-LRB-
10_1101-2021_01_08_425885	662	5	43	43	CD
10_1101-2021_01_08_425885	662	6	,	,	,
10_1101-2021_01_08_425885	662	7	44	44	CD
10_1101-2021_01_08_425885	662	8	]	]	-RRB-
10_1101-2021_01_08_425885	662	9	for	for	IN
10_1101-2021_01_08_425885	662	10	additional	additional	JJ
10_1101-2021_01_08_425885	662	11	details	detail	NNS
10_1101-2021_01_08_425885	662	12	.	.	.
10_1101-2021_01_08_425885	663	1	4.6.2	4.6.2	CD
10_1101-2021_01_08_425885	663	2	Cell	Cell	NNP
10_1101-2021_01_08_425885	663	3	Type	Type	NNP
10_1101-2021_01_08_425885	663	4	Annotations	Annotations	NNPS
10_1101-2021_01_08_425885	663	5	For	for	IN
10_1101-2021_01_08_425885	663	6	the	the	DT
10_1101-2021_01_08_425885	663	7	PBMC	PBMC	NNP
10_1101-2021_01_08_425885	663	8	dataset	dataset	NN
10_1101-2021_01_08_425885	663	9	,	,	,
10_1101-2021_01_08_425885	663	10	the	the	DT
10_1101-2021_01_08_425885	663	11	AddModuleScore(ctrl=5	AddModuleScore(ctrl=5	NNP
10_1101-2021_01_08_425885	663	12	)	)	-RRB-
10_1101-2021_01_08_425885	663	13	function	function	NN
10_1101-2021_01_08_425885	663	14	was	be	VBD
10_1101-2021_01_08_425885	663	15	used	use	VBN
10_1101-2021_01_08_425885	663	16	to	to	TO
10_1101-2021_01_08_425885	663	17	compute	compute	VB
10_1101-2021_01_08_425885	663	18	the	the	DT
10_1101-2021_01_08_425885	663	19	per	per	IN
10_1101-2021_01_08_425885	663	20	-	-	HYPH
10_1101-2021_01_08_425885	663	21	cell	cell	NN
10_1101-2021_01_08_425885	663	22	average	average	JJ
10_1101-2021_01_08_425885	663	23	expression	expression	NN
10_1101-2021_01_08_425885	663	24	of	of	IN
10_1101-2021_01_08_425885	663	25	marker	marker	NN
10_1101-2021_01_08_425885	663	26	genes	gene	NNS
10_1101-2021_01_08_425885	663	27	corresponding	correspond	VBG
10_1101-2021_01_08_425885	663	28	to	to	IN
10_1101-2021_01_08_425885	663	29	seven	seven	CD
10_1101-2021_01_08_425885	663	30	different	different	JJ
10_1101-2021_01_08_425885	663	31	cell	cell	NN
10_1101-2021_01_08_425885	663	32	types	type	NNS
10_1101-2021_01_08_425885	663	33	[	[	-LRB-
10_1101-2021_01_08_425885	663	34	54	54	CD
10_1101-2021_01_08_425885	663	35	]	]	-RRB-
10_1101-2021_01_08_425885	663	36	.	.	.
10_1101-2021_01_08_425885	664	1	To	to	TO
10_1101-2021_01_08_425885	664	2	prepare	prepare	VB
10_1101-2021_01_08_425885	664	3	Figure	figure	NN
10_1101-2021_01_08_425885	664	4	S4A	s4a	NN
10_1101-2021_01_08_425885	664	5	,	,	,
10_1101-2021_01_08_425885	664	6	each	each	DT
10_1101-2021_01_08_425885	664	7	cell	cell	NN
10_1101-2021_01_08_425885	664	8	was	be	VBD
10_1101-2021_01_08_425885	664	9	assigned	assign	VBN
10_1101-2021_01_08_425885	664	10	the	the	DT
10_1101-2021_01_08_425885	664	11	cell	cell	NN
10_1101-2021_01_08_425885	664	12	type	type	NN
10_1101-2021_01_08_425885	664	13	for	for	IN
10_1101-2021_01_08_425885	664	14	which	which	WDT
10_1101-2021_01_08_425885	664	15	its	-PRON-	PRP$
10_1101-2021_01_08_425885	664	16	average	average	JJ
10_1101-2021_01_08_425885	664	17	marker	marker	NN
10_1101-2021_01_08_425885	664	18	gene	gene	NN
10_1101-2021_01_08_425885	664	19	expression	expression	NN
10_1101-2021_01_08_425885	664	20	was	be	VBD
10_1101-2021_01_08_425885	664	21	the	the	DT
10_1101-2021_01_08_425885	664	22	highest	high	JJS
10_1101-2021_01_08_425885	664	23	.	.	.
10_1101-2021_01_08_425885	665	1	Cell	cell	NN
10_1101-2021_01_08_425885	665	2	type	type	NN
10_1101-2021_01_08_425885	665	3	annotations	annotation	NNS
10_1101-2021_01_08_425885	665	4	for	for	IN
10_1101-2021_01_08_425885	665	5	the	the	DT
10_1101-2021_01_08_425885	665	6	gastrulation	gastrulation	NN
10_1101-2021_01_08_425885	665	7	dataset	dataset	NN
10_1101-2021_01_08_425885	665	8	(	(	-LRB-
10_1101-2021_01_08_425885	665	9	see	see	VB
10_1101-2021_01_08_425885	665	10	Figure	figure	NN
10_1101-2021_01_08_425885	665	11	S5A	S5A	NNS
10_1101-2021_01_08_425885	665	12	)	)	-RRB-
10_1101-2021_01_08_425885	665	13	were	be	VBD
10_1101-2021_01_08_425885	665	14	sourced	source	VBN
10_1101-2021_01_08_425885	665	15	from	from	IN
10_1101-2021_01_08_425885	665	16	Figure	figure	NN
10_1101-2021_01_08_425885	665	17	1C	1c	NN
10_1101-2021_01_08_425885	665	18	of	of	IN
10_1101-2021_01_08_425885	665	19	[	[	-LRB-
10_1101-2021_01_08_425885	665	20	43	43	CD
10_1101-2021_01_08_425885	665	21	]	]	-RRB-
10_1101-2021_01_08_425885	665	22	.	.	.
10_1101-2021_01_08_425885	666	1	Cell	cell	NN
10_1101-2021_01_08_425885	666	2	type	type	NN
10_1101-2021_01_08_425885	666	3	40	40	CD
10_1101-2021_01_08_425885	666	4	.CC	.CC	NFP
10_1101-2021_01_08_425885	666	5	-	-	HYPH
10_1101-2021_01_08_425885	666	6	BY	by	IN
10_1101-2021_01_08_425885	666	7	-	-	HYPH
10_1101-2021_01_08_425885	666	8	NC	NC	NNP
10_1101-2021_01_08_425885	666	9	-	-	HYPH
10_1101-2021_01_08_425885	666	10	ND	ND	NNP
10_1101-2021_01_08_425885	666	11	4.0	4.0	CD
10_1101-2021_01_08_425885	666	12	International	International	NNP
10_1101-2021_01_08_425885	666	13	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	666	14	under	under	IN
10_1101-2021_01_08_425885	666	15	a	a	DT
10_1101-2021_01_08_425885	666	16	(	(	-LRB-
10_1101-2021_01_08_425885	666	17	which	which	WDT
10_1101-2021_01_08_425885	666	18	was	be	VBD
10_1101-2021_01_08_425885	666	19	not	not	RB
10_1101-2021_01_08_425885	666	20	certified	certify	VBN
10_1101-2021_01_08_425885	666	21	by	by	IN
10_1101-2021_01_08_425885	666	22	peer	peer	NN
10_1101-2021_01_08_425885	666	23	review	review	NN
10_1101-2021_01_08_425885	666	24	)	)	-RRB-
10_1101-2021_01_08_425885	666	25	is	be	VBZ
10_1101-2021_01_08_425885	666	26	the	the	DT
10_1101-2021_01_08_425885	666	27	author	author	NN
10_1101-2021_01_08_425885	666	28	/	/	SYM
10_1101-2021_01_08_425885	666	29	funder	funder	NN
10_1101-2021_01_08_425885	666	30	,	,	,
10_1101-2021_01_08_425885	666	31	who	who	WP
10_1101-2021_01_08_425885	666	32	has	have	VBZ
10_1101-2021_01_08_425885	666	33	granted	grant	VBN
10_1101-2021_01_08_425885	666	34	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	666	35	a	a	DT
10_1101-2021_01_08_425885	666	36	license	license	NN
10_1101-2021_01_08_425885	666	37	to	to	TO
10_1101-2021_01_08_425885	666	38	display	display	VB
10_1101-2021_01_08_425885	666	39	the	the	DT
10_1101-2021_01_08_425885	666	40	preprint	preprint	NN
10_1101-2021_01_08_425885	666	41	in	in	IN
10_1101-2021_01_08_425885	666	42	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	666	43	.	.	.
10_1101-2021_01_08_425885	667	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	667	2	is	be	VBZ
10_1101-2021_01_08_425885	667	3	made	make	VBN
10_1101-2021_01_08_425885	667	4	The	the	DT
10_1101-2021_01_08_425885	667	5	copyright	copyright	NN
10_1101-2021_01_08_425885	667	6	holder	holder	NN
10_1101-2021_01_08_425885	667	7	for	for	IN
10_1101-2021_01_08_425885	667	8	this	this	DT
10_1101-2021_01_08_425885	667	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	667	10	version	version	NN
10_1101-2021_01_08_425885	667	11	posted	post	VBD
10_1101-2021_01_08_425885	667	12	January	January	NNP
10_1101-2021_01_08_425885	667	13	8	8	CD
10_1101-2021_01_08_425885	667	14	,	,	,
10_1101-2021_01_08_425885	667	15	2021	2021	CD
10_1101-2021_01_08_425885	667	16	.	.	.
10_1101-2021_01_08_425885	667	17	;	;	:
10_1101-2021_01_08_425885	667	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	667	19	:	:	:
10_1101-2021_01_08_425885	667	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	667	21	preprint	preprint	NN
10_1101-2021_01_08_425885	667	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	NNP
10_1101-2021_01_08_425885	667	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NN
10_1101-2021_01_08_425885	667	24	annotations	annotation	NNS
10_1101-2021_01_08_425885	667	25	for	for	IN
10_1101-2021_01_08_425885	667	26	the	the	DT
10_1101-2021_01_08_425885	667	27	brain	brain	NN
10_1101-2021_01_08_425885	667	28	dataset	dataset	NN
10_1101-2021_01_08_425885	667	29	(	(	-LRB-
10_1101-2021_01_08_425885	667	30	see	see	VB
10_1101-2021_01_08_425885	667	31	Figure	Figure	NNP
10_1101-2021_01_08_425885	667	32	S6A	s6a	NN
10_1101-2021_01_08_425885	667	33	)	)	-RRB-
10_1101-2021_01_08_425885	667	34	are	be	VBP
10_1101-2021_01_08_425885	667	35	predicted	predict	VBN
10_1101-2021_01_08_425885	667	36	labels	label	NNS
10_1101-2021_01_08_425885	667	37	sourced	source	VBN
10_1101-2021_01_08_425885	667	38	from	from	IN
10_1101-2021_01_08_425885	667	39	[	[	-LRB-
10_1101-2021_01_08_425885	667	40	55	55	CD
10_1101-2021_01_08_425885	667	41	]	]	-RRB-
10_1101-2021_01_08_425885	667	42	.	.	.
10_1101-2021_01_08_425885	668	1	4.6.3	4.6.3	VBZ
10_1101-2021_01_08_425885	668	2	Statistical	statistical	JJ
10_1101-2021_01_08_425885	668	3	Tests	Tests	NNPS
10_1101-2021_01_08_425885	668	4	Here	here	RB
10_1101-2021_01_08_425885	668	5	we	-PRON-	PRP
10_1101-2021_01_08_425885	668	6	describe	describe	VBP
10_1101-2021_01_08_425885	668	7	the	the	DT
10_1101-2021_01_08_425885	668	8	statistical	statistical	JJ
10_1101-2021_01_08_425885	668	9	tests	test	NNS
10_1101-2021_01_08_425885	668	10	applied	apply	VBN
10_1101-2021_01_08_425885	668	11	to	to	IN
10_1101-2021_01_08_425885	668	12	scalar	scalar	JJ
10_1101-2021_01_08_425885	668	13	curvatures	curvature	NNS
10_1101-2021_01_08_425885	668	14	computed	compute	VBN
10_1101-2021_01_08_425885	668	15	for	for	IN
10_1101-2021_01_08_425885	668	16	the	the	DT
10_1101-2021_01_08_425885	668	17	scRNAseq	scrnaseq	JJ
10_1101-2021_01_08_425885	668	18	datasets	dataset	NNS
10_1101-2021_01_08_425885	668	19	.	.	.
10_1101-2021_01_08_425885	669	1	4.6.3.1	4.6.3.1	CD
10_1101-2021_01_08_425885	669	2	Spatial	Spatial	NNP
10_1101-2021_01_08_425885	669	3	Precision	Precision	NNP
10_1101-2021_01_08_425885	669	4	of	of	IN
10_1101-2021_01_08_425885	669	5	Errorbars	Errorbars	NNPS
10_1101-2021_01_08_425885	669	6	Let	Let	VBD
10_1101-2021_01_08_425885	669	7	m	m	TO
10_1101-2021_01_08_425885	669	8	be	be	VB
10_1101-2021_01_08_425885	669	9	the	the	DT
10_1101-2021_01_08_425885	669	10	fraction	fraction	NN
10_1101-2021_01_08_425885	669	11	of	of	IN
10_1101-2021_01_08_425885	669	12	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	669	13	with	with	IN
10_1101-2021_01_08_425885	669	14	95	95	CD
10_1101-2021_01_08_425885	669	15	%	%	NN
10_1101-2021_01_08_425885	669	16	CIs	ci	NNS
10_1101-2021_01_08_425885	669	17	containing	contain	VBG
10_1101-2021_01_08_425885	669	18	the	the	DT
10_1101-2021_01_08_425885	669	19	scalar	scalar	JJ
10_1101-2021_01_08_425885	669	20	curvatures	curvature	NNS
10_1101-2021_01_08_425885	669	21	reported	report	VBN
10_1101-2021_01_08_425885	669	22	by	by	IN
10_1101-2021_01_08_425885	669	23	their	-PRON-	PRP$
10_1101-2021_01_08_425885	669	24	respective	respective	JJ
10_1101-2021_01_08_425885	669	25	kNNs	knns	NN
10_1101-2021_01_08_425885	669	26	.	.	.
10_1101-2021_01_08_425885	670	1	To	to	TO
10_1101-2021_01_08_425885	670	2	check	check	VB
10_1101-2021_01_08_425885	670	3	whether	whether	IN
10_1101-2021_01_08_425885	670	4	m	m	NNP
10_1101-2021_01_08_425885	670	5	was	be	VBD
10_1101-2021_01_08_425885	670	6	significantly	significantly	RB
10_1101-2021_01_08_425885	670	7	larger	large	JJR
10_1101-2021_01_08_425885	670	8	than	than	IN
10_1101-2021_01_08_425885	670	9	chance	chance	NN
10_1101-2021_01_08_425885	670	10	,	,	,
10_1101-2021_01_08_425885	670	11	we	-PRON-	PRP
10_1101-2021_01_08_425885	670	12	used	use	VBD
10_1101-2021_01_08_425885	670	13	a	a	DT
10_1101-2021_01_08_425885	670	14	permutation	permutation	NN
10_1101-2021_01_08_425885	670	15	test	test	NN
10_1101-2021_01_08_425885	670	16	.	.	.
10_1101-2021_01_08_425885	671	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	671	2	randomly	randomly	RB
10_1101-2021_01_08_425885	671	3	assigned	assign	VBD
10_1101-2021_01_08_425885	671	4	the	the	DT
10_1101-2021_01_08_425885	671	5	kNN	knn	NN
10_1101-2021_01_08_425885	671	6	of	of	IN
10_1101-2021_01_08_425885	671	7	each	each	DT
10_1101-2021_01_08_425885	671	8	datapoint	datapoint	NN
10_1101-2021_01_08_425885	671	9	to	to	TO
10_1101-2021_01_08_425885	671	10	be	be	VB
10_1101-2021_01_08_425885	671	11	one	one	CD
10_1101-2021_01_08_425885	671	12	of	of	IN
10_1101-2021_01_08_425885	671	13	the	the	DT
10_1101-2021_01_08_425885	671	14	N	N	NNP
10_1101-2021_01_08_425885	671	15	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	671	16	in	in	IN
10_1101-2021_01_08_425885	671	17	the	the	DT
10_1101-2021_01_08_425885	671	18	dataset	dataset	NN
10_1101-2021_01_08_425885	671	19	and	and	CC
10_1101-2021_01_08_425885	671	20	computed	compute	VBD
10_1101-2021_01_08_425885	671	21	m.	m.	NN
10_1101-2021_01_08_425885	671	22	We	-PRON-	PRP
10_1101-2021_01_08_425885	671	23	repeated	repeat	VBD
10_1101-2021_01_08_425885	671	24	the	the	DT
10_1101-2021_01_08_425885	671	25	procedure	procedure	NN
10_1101-2021_01_08_425885	671	26	T	t	NN
10_1101-2021_01_08_425885	671	27	=	=	SYM
10_1101-2021_01_08_425885	671	28	1000	1000	CD
10_1101-2021_01_08_425885	671	29	times	time	NNS
10_1101-2021_01_08_425885	671	30	to	to	TO
10_1101-2021_01_08_425885	671	31	generate	generate	VB
10_1101-2021_01_08_425885	671	32	an	an	DT
10_1101-2021_01_08_425885	671	33	empirical	empirical	JJ
10_1101-2021_01_08_425885	671	34	distribution	distribution	NN
10_1101-2021_01_08_425885	671	35	of	of	IN
10_1101-2021_01_08_425885	671	36	m	m	NN
10_1101-2021_01_08_425885	671	37	for	for	IN
10_1101-2021_01_08_425885	671	38	the	the	DT
10_1101-2021_01_08_425885	671	39	null	null	JJ
10_1101-2021_01_08_425885	671	40	model	model	NN
10_1101-2021_01_08_425885	671	41	of	of	IN
10_1101-2021_01_08_425885	671	42	random	random	JJ
10_1101-2021_01_08_425885	671	43	neighbors	neighbor	NNS
10_1101-2021_01_08_425885	671	44	.	.	.
10_1101-2021_01_08_425885	672	1	The	the	DT
10_1101-2021_01_08_425885	672	2	reported	report	VBN
10_1101-2021_01_08_425885	672	3	p	p	NN
10_1101-2021_01_08_425885	672	4	-	-	HYPH
10_1101-2021_01_08_425885	672	5	value	value	NN
10_1101-2021_01_08_425885	672	6	for	for	IN
10_1101-2021_01_08_425885	672	7	each	each	DT
10_1101-2021_01_08_425885	672	8	k	k	NN
10_1101-2021_01_08_425885	672	9	is	be	VBZ
10_1101-2021_01_08_425885	672	10	the	the	DT
10_1101-2021_01_08_425885	672	11	fraction	fraction	NN
10_1101-2021_01_08_425885	672	12	of	of	IN
10_1101-2021_01_08_425885	672	13	the	the	DT
10_1101-2021_01_08_425885	672	14	T	T	NNP
10_1101-2021_01_08_425885	672	15	trials	trial	NNS
10_1101-2021_01_08_425885	672	16	for	for	IN
10_1101-2021_01_08_425885	672	17	which	which	WDT
10_1101-2021_01_08_425885	672	18	m	m	NNP
10_1101-2021_01_08_425885	672	19	was	be	VBD
10_1101-2021_01_08_425885	672	20	greater	great	JJR
10_1101-2021_01_08_425885	672	21	than	than	IN
10_1101-2021_01_08_425885	672	22	the	the	DT
10_1101-2021_01_08_425885	672	23	value	value	NN
10_1101-2021_01_08_425885	672	24	computed	compute	VBN
10_1101-2021_01_08_425885	672	25	for	for	IN
10_1101-2021_01_08_425885	672	26	data	datum	NNS
10_1101-2021_01_08_425885	672	27	.	.	.
10_1101-2021_01_08_425885	673	1	See	see	VB
10_1101-2021_01_08_425885	673	2	Figures	Figures	NNP
10_1101-2021_01_08_425885	673	3	S4D	s4d	NN
10_1101-2021_01_08_425885	673	4	,	,	,
10_1101-2021_01_08_425885	673	5	S5D	S5D	NNP
10_1101-2021_01_08_425885	673	6	and	and	CC
10_1101-2021_01_08_425885	673	7	S6D.	S6D.	NNP
10_1101-2021_01_08_425885	674	1	4.6.3.2	4.6.3.2	CD
10_1101-2021_01_08_425885	674	2	Sensitivity	sensitivity	NN
10_1101-2021_01_08_425885	674	3	to	to	IN
10_1101-2021_01_08_425885	674	4	Cell	cell	NN
10_1101-2021_01_08_425885	674	5	Downsampling	downsample	VBG
10_1101-2021_01_08_425885	674	6	To	to	TO
10_1101-2021_01_08_425885	674	7	check	check	VB
10_1101-2021_01_08_425885	674	8	the	the	DT
10_1101-2021_01_08_425885	674	9	sensitivity	sensitivity	NN
10_1101-2021_01_08_425885	674	10	of	of	IN
10_1101-2021_01_08_425885	674	11	the	the	DT
10_1101-2021_01_08_425885	674	12	computed	computed	JJ
10_1101-2021_01_08_425885	674	13	scalar	scalar	JJ
10_1101-2021_01_08_425885	674	14	curvatures	curvature	NNS
10_1101-2021_01_08_425885	674	15	to	to	IN
10_1101-2021_01_08_425885	674	16	the	the	DT
10_1101-2021_01_08_425885	674	17	average	average	JJ
10_1101-2021_01_08_425885	674	18	density	density	NN
10_1101-2021_01_08_425885	674	19	of	of	IN
10_1101-2021_01_08_425885	674	20	cells	cell	NNS
10_1101-2021_01_08_425885	674	21	,	,	,
10_1101-2021_01_08_425885	674	22	we	-PRON-	PRP
10_1101-2021_01_08_425885	674	23	discarded	discard	VBD
10_1101-2021_01_08_425885	674	24	f%	f%	NNP
10_1101-2021_01_08_425885	674	25	of	of	IN
10_1101-2021_01_08_425885	674	26	cells	cell	NNS
10_1101-2021_01_08_425885	674	27	at	at	IN
10_1101-2021_01_08_425885	674	28	random	random	JJ
10_1101-2021_01_08_425885	674	29	from	from	IN
10_1101-2021_01_08_425885	674	30	the	the	DT
10_1101-2021_01_08_425885	674	31	ambient	ambient	JJ
10_1101-2021_01_08_425885	674	32	space	space	NN
10_1101-2021_01_08_425885	674	33	computed	compute	VBD
10_1101-2021_01_08_425885	674	34	using	use	VBG
10_1101-2021_01_08_425885	674	35	the	the	DT
10_1101-2021_01_08_425885	674	36	original	original	JJ
10_1101-2021_01_08_425885	674	37	set	set	NN
10_1101-2021_01_08_425885	674	38	of	of	IN
10_1101-2021_01_08_425885	674	39	N	n	NN
10_1101-2021_01_08_425885	674	40	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	674	41	,	,	,
10_1101-2021_01_08_425885	674	42	and	and	CC
10_1101-2021_01_08_425885	674	43	recomputed	recompute	VBN
10_1101-2021_01_08_425885	674	44	scalar	scalar	JJ
10_1101-2021_01_08_425885	674	45	curvatures	curvature	NNS
10_1101-2021_01_08_425885	674	46	using	use	VBG
10_1101-2021_01_08_425885	674	47	the	the	DT
10_1101-2021_01_08_425885	674	48	same	same	JJ
10_1101-2021_01_08_425885	674	49	ambient	ambient	JJ
10_1101-2021_01_08_425885	674	50	dimension	dimension	NN
10_1101-2021_01_08_425885	674	51	,	,	,
10_1101-2021_01_08_425885	674	52	manifold	manifold	JJ
10_1101-2021_01_08_425885	674	53	dimension	dimension	NN
10_1101-2021_01_08_425885	674	54	and	and	CC
10_1101-2021_01_08_425885	674	55	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	674	56	sizes	size	NNS
10_1101-2021_01_08_425885	674	57	as	as	IN
10_1101-2021_01_08_425885	674	58	for	for	IN
10_1101-2021_01_08_425885	674	59	the	the	DT
10_1101-2021_01_08_425885	674	60	original	original	JJ
10_1101-2021_01_08_425885	674	61	dataset	dataset	NN
10_1101-2021_01_08_425885	674	62	(	(	-LRB-
10_1101-2021_01_08_425885	674	63	see	see	VB
10_1101-2021_01_08_425885	674	64	Methods	Methods	NNP
10_1101-2021_01_08_425885	674	65	Section	Section	NNP
10_1101-2021_01_08_425885	674	66	4.6.4	4.6.4	CD
10_1101-2021_01_08_425885	674	67	)	)	-RRB-
10_1101-2021_01_08_425885	674	68	.	.	.
10_1101-2021_01_08_425885	675	1	Let	let	VB
10_1101-2021_01_08_425885	675	2	m	m	PRP
10_1101-2021_01_08_425885	675	3	be	be	VB
10_1101-2021_01_08_425885	675	4	the	the	DT
10_1101-2021_01_08_425885	675	5	fraction	fraction	NN
10_1101-2021_01_08_425885	675	6	of	of	IN
10_1101-2021_01_08_425885	675	7	downsampled	downsampled	JJ
10_1101-2021_01_08_425885	675	8	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	675	9	with	with	IN
10_1101-2021_01_08_425885	675	10	95	95	CD
10_1101-2021_01_08_425885	675	11	%	%	NN
10_1101-2021_01_08_425885	675	12	CIs	ci	NNS
10_1101-2021_01_08_425885	675	13	containing	contain	VBG
10_1101-2021_01_08_425885	675	14	the	the	DT
10_1101-2021_01_08_425885	675	15	scalar	scalar	JJ
10_1101-2021_01_08_425885	675	16	curvatures	curvature	NNS
10_1101-2021_01_08_425885	675	17	originally	originally	RB
10_1101-2021_01_08_425885	675	18	reported	report	VBN
10_1101-2021_01_08_425885	675	19	.	.	.
10_1101-2021_01_08_425885	676	1	Since	since	IN
10_1101-2021_01_08_425885	676	2	the	the	DT
10_1101-2021_01_08_425885	676	3	CIs	ci	NNS
10_1101-2021_01_08_425885	676	4	grow	grow	VBP
10_1101-2021_01_08_425885	676	5	as	as	IN
10_1101-2021_01_08_425885	676	6	f	f	NNP
10_1101-2021_01_08_425885	676	7	increases	increase	VBZ
10_1101-2021_01_08_425885	676	8	,	,	,
10_1101-2021_01_08_425885	676	9	we	-PRON-	PRP
10_1101-2021_01_08_425885	676	10	checked	check	VBD
10_1101-2021_01_08_425885	676	11	whether	whether	IN
10_1101-2021_01_08_425885	676	12	m	m	NNP
10_1101-2021_01_08_425885	676	13	was	be	VBD
10_1101-2021_01_08_425885	676	14	significantly	significantly	RB
10_1101-2021_01_08_425885	676	15	larger	large	JJR
10_1101-2021_01_08_425885	676	16	than	than	IN
10_1101-2021_01_08_425885	676	17	chance	chance	NN
10_1101-2021_01_08_425885	676	18	by	by	IN
10_1101-2021_01_08_425885	676	19	using	use	VBG
10_1101-2021_01_08_425885	676	20	a	a	DT
10_1101-2021_01_08_425885	676	21	permutation	permutation	NN
10_1101-2021_01_08_425885	676	22	test	test	NN
10_1101-2021_01_08_425885	676	23	.	.	.
10_1101-2021_01_08_425885	677	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	677	2	randomly	randomly	RB
10_1101-2021_01_08_425885	677	3	paired	pair	VBD
10_1101-2021_01_08_425885	677	4	each	each	DT
10_1101-2021_01_08_425885	677	5	of	of	IN
10_1101-2021_01_08_425885	677	6	the	the	DT
10_1101-2021_01_08_425885	677	7	95	95	CD
10_1101-2021_01_08_425885	677	8	%	%	NN
10_1101-2021_01_08_425885	677	9	CIs	ci	NNS
10_1101-2021_01_08_425885	677	10	computed	compute	VBD
10_1101-2021_01_08_425885	677	11	after	after	IN
10_1101-2021_01_08_425885	677	12	downsampling	downsample	VBG
10_1101-2021_01_08_425885	677	13	,	,	,
10_1101-2021_01_08_425885	677	14	to	to	IN
10_1101-2021_01_08_425885	677	15	one	one	CD
10_1101-2021_01_08_425885	677	16	of	of	IN
10_1101-2021_01_08_425885	677	17	the	the	DT
10_1101-2021_01_08_425885	677	18	scalar	scalar	JJ
10_1101-2021_01_08_425885	677	19	curvatures	curvature	NNS
10_1101-2021_01_08_425885	677	20	reported	report	VBN
10_1101-2021_01_08_425885	677	21	by	by	IN
10_1101-2021_01_08_425885	677	22	the	the	DT
10_1101-2021_01_08_425885	677	23	downsampled	downsampled	JJ
10_1101-2021_01_08_425885	677	24	points	point	NNS
10_1101-2021_01_08_425885	677	25	for	for	IN
10_1101-2021_01_08_425885	677	26	the	the	DT
10_1101-2021_01_08_425885	677	27	original	original	JJ
10_1101-2021_01_08_425885	677	28	dataset	dataset	NN
10_1101-2021_01_08_425885	677	29	,	,	,
10_1101-2021_01_08_425885	677	30	and	and	CC
10_1101-2021_01_08_425885	677	31	computed	compute	VBD
10_1101-2021_01_08_425885	677	32	m.	m.	NN
10_1101-2021_01_08_425885	677	33	We	-PRON-	PRP
10_1101-2021_01_08_425885	677	34	repeated	repeat	VBD
10_1101-2021_01_08_425885	677	35	the	the	DT
10_1101-2021_01_08_425885	677	36	procedure	procedure	NN
10_1101-2021_01_08_425885	677	37	T	t	NN
10_1101-2021_01_08_425885	677	38	=	=	SYM
10_1101-2021_01_08_425885	677	39	1000	1000	CD
10_1101-2021_01_08_425885	677	40	times	time	NNS
10_1101-2021_01_08_425885	677	41	to	to	TO
10_1101-2021_01_08_425885	677	42	generate	generate	VB
10_1101-2021_01_08_425885	677	43	an	an	DT
10_1101-2021_01_08_425885	677	44	empirical	empirical	JJ
10_1101-2021_01_08_425885	677	45	distribution	distribution	NN
10_1101-2021_01_08_425885	677	46	of	of	IN
10_1101-2021_01_08_425885	677	47	m	m	NN
10_1101-2021_01_08_425885	677	48	for	for	IN
10_1101-2021_01_08_425885	677	49	the	the	DT
10_1101-2021_01_08_425885	677	50	null	null	JJ
10_1101-2021_01_08_425885	677	51	model	model	NN
10_1101-2021_01_08_425885	677	52	.	.	.
10_1101-2021_01_08_425885	678	1	The	the	DT
10_1101-2021_01_08_425885	678	2	reported	report	VBN
10_1101-2021_01_08_425885	678	3	p	p	NN
10_1101-2021_01_08_425885	678	4	-	-	HYPH
10_1101-2021_01_08_425885	678	5	value	value	NN
10_1101-2021_01_08_425885	678	6	for	for	IN
10_1101-2021_01_08_425885	678	7	each	each	DT
10_1101-2021_01_08_425885	678	8	f	f	NN
10_1101-2021_01_08_425885	678	9	is	be	VBZ
10_1101-2021_01_08_425885	678	10	the	the	DT
10_1101-2021_01_08_425885	678	11	fraction	fraction	NN
10_1101-2021_01_08_425885	678	12	of	of	IN
10_1101-2021_01_08_425885	678	13	the	the	DT
10_1101-2021_01_08_425885	678	14	T	T	NNP
10_1101-2021_01_08_425885	678	15	trials	trial	NNS
10_1101-2021_01_08_425885	678	16	for	for	IN
10_1101-2021_01_08_425885	678	17	which	which	WDT
10_1101-2021_01_08_425885	678	18	m	m	NNP
10_1101-2021_01_08_425885	678	19	was	be	VBD
10_1101-2021_01_08_425885	678	20	greater	great	JJR
10_1101-2021_01_08_425885	678	21	than	than	IN
10_1101-2021_01_08_425885	678	22	the	the	DT
10_1101-2021_01_08_425885	678	23	value	value	NN
10_1101-2021_01_08_425885	678	24	computed	compute	VBN
10_1101-2021_01_08_425885	678	25	for	for	IN
10_1101-2021_01_08_425885	678	26	data	datum	NNS
10_1101-2021_01_08_425885	678	27	.	.	.
10_1101-2021_01_08_425885	679	1	See	see	VB
10_1101-2021_01_08_425885	679	2	Figures	Figures	NNP
10_1101-2021_01_08_425885	679	3	S4I	s4i	NN
10_1101-2021_01_08_425885	679	4	,	,	,
10_1101-2021_01_08_425885	679	5	S5I	S5I	NNS
10_1101-2021_01_08_425885	679	6	and	and	CC
10_1101-2021_01_08_425885	679	7	S6I.	S6I.	NNP
10_1101-2021_01_08_425885	680	1	4.6.3.3	4.6.3.3	LS
10_1101-2021_01_08_425885	680	2	Sensitivity	sensitivity	NN
10_1101-2021_01_08_425885	680	3	to	to	IN
10_1101-2021_01_08_425885	680	4	Transcript	Transcript	NNP
10_1101-2021_01_08_425885	680	5	Downsampling	downsample	VBG
10_1101-2021_01_08_425885	680	6	To	to	TO
10_1101-2021_01_08_425885	680	7	check	check	VB
10_1101-2021_01_08_425885	680	8	the	the	DT
10_1101-2021_01_08_425885	680	9	sensitivity	sensitivity	NN
10_1101-2021_01_08_425885	680	10	of	of	IN
10_1101-2021_01_08_425885	680	11	the	the	DT
10_1101-2021_01_08_425885	680	12	computed	computed	JJ
10_1101-2021_01_08_425885	680	13	scalar	scalar	JJ
10_1101-2021_01_08_425885	680	14	curvatures	curvature	NNS
10_1101-2021_01_08_425885	680	15	to	to	IN
10_1101-2021_01_08_425885	680	16	the	the	DT
10_1101-2021_01_08_425885	680	17	capture	capture	NN
10_1101-2021_01_08_425885	680	18	efficiency	efficiency	NN
10_1101-2021_01_08_425885	680	19	and	and	CC
10_1101-2021_01_08_425885	680	20	sequencing	sequence	VBG
10_1101-2021_01_08_425885	680	21	depth	depth	NN
10_1101-2021_01_08_425885	680	22	of	of	IN
10_1101-2021_01_08_425885	680	23	the	the	DT
10_1101-2021_01_08_425885	680	24	data	datum	NNS
10_1101-2021_01_08_425885	680	25	,	,	,
10_1101-2021_01_08_425885	680	26	we	-PRON-	PRP
10_1101-2021_01_08_425885	680	27	discarded	discard	VBD
10_1101-2021_01_08_425885	680	28	f%	f%	NNP
10_1101-2021_01_08_425885	680	29	of	of	IN
10_1101-2021_01_08_425885	680	30	transcripts	transcript	NNS
10_1101-2021_01_08_425885	680	31	at	at	IN
10_1101-2021_01_08_425885	680	32	random	random	JJ
10_1101-2021_01_08_425885	680	33	from	from	IN
10_1101-2021_01_08_425885	680	34	the	the	DT
10_1101-2021_01_08_425885	680	35	single	single	JJ
10_1101-2021_01_08_425885	680	36	-	-	HYPH
10_1101-2021_01_08_425885	680	37	cell	cell	NN
10_1101-2021_01_08_425885	680	38	count	count	NN
10_1101-2021_01_08_425885	680	39	matrix	matrix	NN
10_1101-2021_01_08_425885	680	40	for	for	IN
10_1101-2021_01_08_425885	680	41	the	the	DT
10_1101-2021_01_08_425885	680	42	PBMC	PBMC	NNP
10_1101-2021_01_08_425885	680	43	dataset	dataset	NN
10_1101-2021_01_08_425885	680	44	,	,	,
10_1101-2021_01_08_425885	680	45	then	then	RB
10_1101-2021_01_08_425885	680	46	performed	perform	VBD
10_1101-2021_01_08_425885	680	47	the	the	DT
10_1101-2021_01_08_425885	680	48	same	same	JJ
10_1101-2021_01_08_425885	680	49	preprocessing	preprocessing	NN
10_1101-2021_01_08_425885	680	50	steps	step	NNS
10_1101-2021_01_08_425885	680	51	described	describe	VBN
10_1101-2021_01_08_425885	680	52	in	in	IN
10_1101-2021_01_08_425885	680	53	Methods	Methods	NNP
10_1101-2021_01_08_425885	680	54	Section	Section	NNP
10_1101-2021_01_08_425885	680	55	4.6.1	4.6.1	CD
10_1101-2021_01_08_425885	680	56	.	.	.
10_1101-2021_01_08_425885	681	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	681	2	recomputed	recompute	VBD
10_1101-2021_01_08_425885	681	3	scalar	scalar	JJ
10_1101-2021_01_08_425885	681	4	curvatures	curvature	NNS
10_1101-2021_01_08_425885	681	5	using	use	VBG
10_1101-2021_01_08_425885	681	6	the	the	DT
10_1101-2021_01_08_425885	681	7	same	same	JJ
10_1101-2021_01_08_425885	681	8	ambient	ambient	JJ
10_1101-2021_01_08_425885	681	9	dimension	dimension	NN
10_1101-2021_01_08_425885	681	10	,	,	,
10_1101-2021_01_08_425885	681	11	manifold	manifold	JJ
10_1101-2021_01_08_425885	681	12	dimension	dimension	NN
10_1101-2021_01_08_425885	681	13	and	and	CC
10_1101-2021_01_08_425885	681	14	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	681	15	sizes	size	NNS
10_1101-2021_01_08_425885	681	16	as	as	IN
10_1101-2021_01_08_425885	681	17	for	for	IN
10_1101-2021_01_08_425885	681	18	the	the	DT
10_1101-2021_01_08_425885	681	19	original	original	JJ
10_1101-2021_01_08_425885	681	20	dataset	dataset	NN
10_1101-2021_01_08_425885	681	21	(	(	-LRB-
10_1101-2021_01_08_425885	681	22	see	see	VB
10_1101-2021_01_08_425885	681	23	Methods	Methods	NNP
10_1101-2021_01_08_425885	681	24	Section	Section	NNP
10_1101-2021_01_08_425885	681	25	4.6.4	4.6.4	CD
10_1101-2021_01_08_425885	681	26	)	)	-RRB-
10_1101-2021_01_08_425885	681	27	.	.	.
10_1101-2021_01_08_425885	682	1	Let	let	VB
10_1101-2021_01_08_425885	682	2	m	m	PRP
10_1101-2021_01_08_425885	682	3	be	be	VB
10_1101-2021_01_08_425885	682	4	the	the	DT
10_1101-2021_01_08_425885	682	5	fraction	fraction	NN
10_1101-2021_01_08_425885	682	6	of	of	IN
10_1101-2021_01_08_425885	682	7	datapoints	datapoint	NNS
10_1101-2021_01_08_425885	682	8	with	with	IN
10_1101-2021_01_08_425885	682	9	95	95	CD
10_1101-2021_01_08_425885	682	10	%	%	NN
10_1101-2021_01_08_425885	682	11	CIs	ci	NNS
10_1101-2021_01_08_425885	682	12	containing	contain	VBG
10_1101-2021_01_08_425885	682	13	the	the	DT
10_1101-2021_01_08_425885	682	14	scalar	scalar	JJ
10_1101-2021_01_08_425885	682	15	curvatures	curvature	NNS
10_1101-2021_01_08_425885	682	16	originally	originally	RB
10_1101-2021_01_08_425885	682	17	reported	report	VBN
10_1101-2021_01_08_425885	682	18	.	.	.
10_1101-2021_01_08_425885	683	1	To	to	TO
10_1101-2021_01_08_425885	683	2	check	check	VB
10_1101-2021_01_08_425885	683	3	whether	whether	IN
10_1101-2021_01_08_425885	683	4	m	m	NNP
10_1101-2021_01_08_425885	683	5	was	be	VBD
10_1101-2021_01_08_425885	683	6	significantly	significantly	RB
10_1101-2021_01_08_425885	683	7	larger	large	JJR
10_1101-2021_01_08_425885	683	8	than	than	IN
10_1101-2021_01_08_425885	683	9	chance	chance	NN
10_1101-2021_01_08_425885	683	10	,	,	,
10_1101-2021_01_08_425885	683	11	we	-PRON-	PRP
10_1101-2021_01_08_425885	683	12	used	use	VBD
10_1101-2021_01_08_425885	683	13	a	a	DT
10_1101-2021_01_08_425885	683	14	permutation	permutation	NN
10_1101-2021_01_08_425885	683	15	test	test	NN
10_1101-2021_01_08_425885	683	16	.	.	.
10_1101-2021_01_08_425885	684	1	We	-PRON-	PRP
10_1101-2021_01_08_425885	684	2	randomly	randomly	RB
10_1101-2021_01_08_425885	684	3	paired	pair	VBD
10_1101-2021_01_08_425885	684	4	each	each	DT
10_1101-2021_01_08_425885	684	5	of	of	IN
10_1101-2021_01_08_425885	684	6	the	the	DT
10_1101-2021_01_08_425885	684	7	95	95	CD
10_1101-2021_01_08_425885	684	8	%	%	NN
10_1101-2021_01_08_425885	684	9	CIs	ci	NNS
10_1101-2021_01_08_425885	684	10	computed	compute	VBD
10_1101-2021_01_08_425885	684	11	after	after	IN
10_1101-2021_01_08_425885	684	12	downsampling	downsample	VBG
10_1101-2021_01_08_425885	684	13	transcripts	transcript	NNS
10_1101-2021_01_08_425885	684	14	,	,	,
10_1101-2021_01_08_425885	684	15	to	to	IN
10_1101-2021_01_08_425885	684	16	one	one	CD
10_1101-2021_01_08_425885	684	17	of	of	IN
10_1101-2021_01_08_425885	684	18	the	the	DT
10_1101-2021_01_08_425885	684	19	scalar	scalar	JJ
10_1101-2021_01_08_425885	684	20	curvatures	curvature	NNS
10_1101-2021_01_08_425885	684	21	computed	compute	VBD
10_1101-2021_01_08_425885	684	22	for	for	IN
10_1101-2021_01_08_425885	684	23	the	the	DT
10_1101-2021_01_08_425885	684	24	original	original	JJ
10_1101-2021_01_08_425885	684	25	41	41	CD
10_1101-2021_01_08_425885	684	26	.CC	.CC	,
10_1101-2021_01_08_425885	684	27	-	-	HYPH
10_1101-2021_01_08_425885	684	28	BY	by	IN
10_1101-2021_01_08_425885	684	29	-	-	HYPH
10_1101-2021_01_08_425885	684	30	NC	NC	NNP
10_1101-2021_01_08_425885	684	31	-	-	HYPH
10_1101-2021_01_08_425885	684	32	ND	ND	NNP
10_1101-2021_01_08_425885	684	33	4.0	4.0	CD
10_1101-2021_01_08_425885	684	34	International	International	NNP
10_1101-2021_01_08_425885	684	35	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	684	36	under	under	IN
10_1101-2021_01_08_425885	684	37	a	a	DT
10_1101-2021_01_08_425885	684	38	(	(	-LRB-
10_1101-2021_01_08_425885	684	39	which	which	WDT
10_1101-2021_01_08_425885	684	40	was	be	VBD
10_1101-2021_01_08_425885	684	41	not	not	RB
10_1101-2021_01_08_425885	684	42	certified	certify	VBN
10_1101-2021_01_08_425885	684	43	by	by	IN
10_1101-2021_01_08_425885	684	44	peer	peer	NN
10_1101-2021_01_08_425885	684	45	review	review	NN
10_1101-2021_01_08_425885	684	46	)	)	-RRB-
10_1101-2021_01_08_425885	684	47	is	be	VBZ
10_1101-2021_01_08_425885	684	48	the	the	DT
10_1101-2021_01_08_425885	684	49	author	author	NN
10_1101-2021_01_08_425885	684	50	/	/	SYM
10_1101-2021_01_08_425885	684	51	funder	funder	NN
10_1101-2021_01_08_425885	684	52	,	,	,
10_1101-2021_01_08_425885	684	53	who	who	WP
10_1101-2021_01_08_425885	684	54	has	have	VBZ
10_1101-2021_01_08_425885	684	55	granted	grant	VBN
10_1101-2021_01_08_425885	684	56	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	684	57	a	a	DT
10_1101-2021_01_08_425885	684	58	license	license	NN
10_1101-2021_01_08_425885	684	59	to	to	TO
10_1101-2021_01_08_425885	684	60	display	display	VB
10_1101-2021_01_08_425885	684	61	the	the	DT
10_1101-2021_01_08_425885	684	62	preprint	preprint	NN
10_1101-2021_01_08_425885	684	63	in	in	IN
10_1101-2021_01_08_425885	684	64	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	684	65	.	.	.
10_1101-2021_01_08_425885	685	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	685	2	is	be	VBZ
10_1101-2021_01_08_425885	685	3	made	make	VBN
10_1101-2021_01_08_425885	685	4	The	the	DT
10_1101-2021_01_08_425885	685	5	copyright	copyright	NN
10_1101-2021_01_08_425885	685	6	holder	holder	NN
10_1101-2021_01_08_425885	685	7	for	for	IN
10_1101-2021_01_08_425885	685	8	this	this	DT
10_1101-2021_01_08_425885	685	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	685	10	version	version	NN
10_1101-2021_01_08_425885	685	11	posted	post	VBD
10_1101-2021_01_08_425885	685	12	January	January	NNP
10_1101-2021_01_08_425885	685	13	8	8	CD
10_1101-2021_01_08_425885	685	14	,	,	,
10_1101-2021_01_08_425885	685	15	2021	2021	CD
10_1101-2021_01_08_425885	685	16	.	.	.
10_1101-2021_01_08_425885	685	17	;	;	:
10_1101-2021_01_08_425885	685	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	685	19	:	:	:
10_1101-2021_01_08_425885	685	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	685	21	preprint	preprint	NN
10_1101-2021_01_08_425885	685	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	NNP
10_1101-2021_01_08_425885	685	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NNP
10_1101-2021_01_08_425885	685	24	dataset	dataset	NNP
10_1101-2021_01_08_425885	685	25	,	,	,
10_1101-2021_01_08_425885	685	26	and	and	CC
10_1101-2021_01_08_425885	685	27	computed	compute	VBD
10_1101-2021_01_08_425885	685	28	m.	m.	NN
10_1101-2021_01_08_425885	685	29	We	-PRON-	PRP
10_1101-2021_01_08_425885	685	30	repeated	repeat	VBD
10_1101-2021_01_08_425885	685	31	the	the	DT
10_1101-2021_01_08_425885	685	32	procedure	procedure	NN
10_1101-2021_01_08_425885	685	33	T	t	NN
10_1101-2021_01_08_425885	685	34	=	=	SYM
10_1101-2021_01_08_425885	685	35	1000	1000	CD
10_1101-2021_01_08_425885	685	36	times	time	NNS
10_1101-2021_01_08_425885	685	37	to	to	TO
10_1101-2021_01_08_425885	685	38	generate	generate	VB
10_1101-2021_01_08_425885	685	39	an	an	DT
10_1101-2021_01_08_425885	685	40	empirical	empirical	JJ
10_1101-2021_01_08_425885	685	41	distribution	distribution	NN
10_1101-2021_01_08_425885	685	42	of	of	IN
10_1101-2021_01_08_425885	685	43	m	m	NN
10_1101-2021_01_08_425885	685	44	for	for	IN
10_1101-2021_01_08_425885	685	45	the	the	DT
10_1101-2021_01_08_425885	685	46	null	null	JJ
10_1101-2021_01_08_425885	685	47	model	model	NN
10_1101-2021_01_08_425885	685	48	.	.	.
10_1101-2021_01_08_425885	686	1	The	the	DT
10_1101-2021_01_08_425885	686	2	reported	report	VBN
10_1101-2021_01_08_425885	686	3	p	p	NN
10_1101-2021_01_08_425885	686	4	-	-	HYPH
10_1101-2021_01_08_425885	686	5	value	value	NN
10_1101-2021_01_08_425885	686	6	for	for	IN
10_1101-2021_01_08_425885	686	7	each	each	DT
10_1101-2021_01_08_425885	686	8	f	f	NN
10_1101-2021_01_08_425885	686	9	is	be	VBZ
10_1101-2021_01_08_425885	686	10	the	the	DT
10_1101-2021_01_08_425885	686	11	fraction	fraction	NN
10_1101-2021_01_08_425885	686	12	of	of	IN
10_1101-2021_01_08_425885	686	13	the	the	DT
10_1101-2021_01_08_425885	686	14	T	T	NNP
10_1101-2021_01_08_425885	686	15	trials	trial	NNS
10_1101-2021_01_08_425885	686	16	for	for	IN
10_1101-2021_01_08_425885	686	17	which	which	WDT
10_1101-2021_01_08_425885	686	18	m	m	NNP
10_1101-2021_01_08_425885	686	19	was	be	VBD
10_1101-2021_01_08_425885	686	20	greater	great	JJR
10_1101-2021_01_08_425885	686	21	than	than	IN
10_1101-2021_01_08_425885	686	22	the	the	DT
10_1101-2021_01_08_425885	686	23	value	value	NN
10_1101-2021_01_08_425885	686	24	computed	compute	VBN
10_1101-2021_01_08_425885	686	25	for	for	IN
10_1101-2021_01_08_425885	686	26	data	datum	NNS
10_1101-2021_01_08_425885	686	27	.	.	.
10_1101-2021_01_08_425885	687	1	See	see	VB
10_1101-2021_01_08_425885	687	2	Figure	figure	NN
10_1101-2021_01_08_425885	687	3	S4J.	s4j.	NN
10_1101-2021_01_08_425885	688	1	4.6.4	4.6.4	CD
10_1101-2021_01_08_425885	688	2	Parameters	Parameters	NNPS
10_1101-2021_01_08_425885	688	3	for	for	IN
10_1101-2021_01_08_425885	688	4	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	688	5	Estimation	Estimation	NNP
10_1101-2021_01_08_425885	688	6	Let	let	VBP
10_1101-2021_01_08_425885	688	7	the	the	DT
10_1101-2021_01_08_425885	688	8	variance	variance	NN
10_1101-2021_01_08_425885	688	9	explained	explain	VBN
10_1101-2021_01_08_425885	688	10	by	by	IN
10_1101-2021_01_08_425885	688	11	the	the	DT
10_1101-2021_01_08_425885	688	12	ith	ith	NNP
10_1101-2021_01_08_425885	688	13	PC	PC	NNP
10_1101-2021_01_08_425885	688	14	be	be	VB
10_1101-2021_01_08_425885	688	15	given	give	VBN
10_1101-2021_01_08_425885	688	16	by	by	IN
10_1101-2021_01_08_425885	688	17	σ2i	σ2i	NNP
10_1101-2021_01_08_425885	688	18	and	and	CC
10_1101-2021_01_08_425885	688	19	the	the	DT
10_1101-2021_01_08_425885	688	20	cumulative	cumulative	JJ
10_1101-2021_01_08_425885	688	21	fractional	fractional	JJ
10_1101-2021_01_08_425885	688	22	variance	variance	NN
10_1101-2021_01_08_425885	688	23	of	of	IN
10_1101-2021_01_08_425885	688	24	the	the	DT
10_1101-2021_01_08_425885	688	25	first	first	JJ
10_1101-2021_01_08_425885	688	26	m	m	NNP
10_1101-2021_01_08_425885	688	27	PCs	pc	NNS
10_1101-2021_01_08_425885	688	28	by	by	IN
10_1101-2021_01_08_425885	688	29	cm	cm	NNP
10_1101-2021_01_08_425885	688	30	=	=	SYM
10_1101-2021_01_08_425885	688	31	∑m	∑m	.
10_1101-2021_01_08_425885	688	32	i=1	i=1	NNP
10_1101-2021_01_08_425885	688	33	σ	σ	NNP
10_1101-2021_01_08_425885	688	34	2	2	CD
10_1101-2021_01_08_425885	688	35	i∑	i∑	UH
10_1101-2021_01_08_425885	688	36	i	i	PRP
10_1101-2021_01_08_425885	688	37	σ2	σ2	VBP
10_1101-2021_01_08_425885	688	38	i	i	PRP
10_1101-2021_01_08_425885	688	39	.	.	.
10_1101-2021_01_08_425885	689	1	For	for	IN
10_1101-2021_01_08_425885	689	2	each	each	DT
10_1101-2021_01_08_425885	689	3	dataset	dataset	NN
10_1101-2021_01_08_425885	689	4	,	,	,
10_1101-2021_01_08_425885	689	5	we	-PRON-	PRP
10_1101-2021_01_08_425885	689	6	selected	select	VBD
10_1101-2021_01_08_425885	689	7	the	the	DT
10_1101-2021_01_08_425885	689	8	ambient	ambient	JJ
10_1101-2021_01_08_425885	689	9	dimension	dimension	NN
10_1101-2021_01_08_425885	689	10	as	as	IN
10_1101-2021_01_08_425885	689	11	n	n	NNP
10_1101-2021_01_08_425885	689	12	=	=	SYM
10_1101-2021_01_08_425885	689	13	argmaxm{cm|cm	argmaxm{cm|cm	NNP
10_1101-2021_01_08_425885	689	14	≤	≤	NNP
10_1101-2021_01_08_425885	689	15	0.8	0.8	CD
10_1101-2021_01_08_425885	689	16	}	}	-RRB-
10_1101-2021_01_08_425885	689	17	,	,	,
10_1101-2021_01_08_425885	689	18	the	the	DT
10_1101-2021_01_08_425885	689	19	manifold	manifold	JJ
10_1101-2021_01_08_425885	689	20	dimension	dimension	NN
10_1101-2021_01_08_425885	689	21	as	as	IN
10_1101-2021_01_08_425885	689	22	d	d	NNP
10_1101-2021_01_08_425885	689	23	=	=	SYM
10_1101-2021_01_08_425885	689	24	argmaxm{cm|cm	argmaxm{cm|cm	ADD
10_1101-2021_01_08_425885	689	25	≤	≤	NNP
10_1101-2021_01_08_425885	689	26	0.64	0.64	CD
10_1101-2021_01_08_425885	689	27	}	}	-RRB-
10_1101-2021_01_08_425885	689	28	,	,	,
10_1101-2021_01_08_425885	689	29	and	and	CC
10_1101-2021_01_08_425885	689	30	considered	consider	VBN
10_1101-2021_01_08_425885	689	31	the	the	DT
10_1101-2021_01_08_425885	689	32	global	global	JJ
10_1101-2021_01_08_425885	689	33	length	length	NN
10_1101-2021_01_08_425885	689	34	scale	scale	NN
10_1101-2021_01_08_425885	689	35	to	to	TO
10_1101-2021_01_08_425885	689	36	be	be	VB
10_1101-2021_01_08_425885	689	37	L	l	NN
10_1101-2021_01_08_425885	689	38	=	=	SYM
10_1101-2021_01_08_425885	689	39	3σd	3σd	NN
10_1101-2021_01_08_425885	689	40	.	.	.
10_1101-2021_01_08_425885	690	1	(	(	-LRB-
10_1101-2021_01_08_425885	690	2	n	n	NN
10_1101-2021_01_08_425885	690	3	,	,	,
10_1101-2021_01_08_425885	690	4	d	d	NN
10_1101-2021_01_08_425885	690	5	,	,	,
10_1101-2021_01_08_425885	690	6	L	l	NN
10_1101-2021_01_08_425885	690	7	)	)	-RRB-
10_1101-2021_01_08_425885	690	8	=	=	NFP
10_1101-2021_01_08_425885	690	9	(	(	-LRB-
10_1101-2021_01_08_425885	690	10	8	8	CD
10_1101-2021_01_08_425885	690	11	,	,	,
10_1101-2021_01_08_425885	690	12	3	3	CD
10_1101-2021_01_08_425885	690	13	,	,	,
10_1101-2021_01_08_425885	690	14	18.3	18.3	CD
10_1101-2021_01_08_425885	690	15	)	)	-RRB-
10_1101-2021_01_08_425885	690	16	,	,	,
10_1101-2021_01_08_425885	690	17	(	(	-LRB-
10_1101-2021_01_08_425885	690	18	11	11	CD
10_1101-2021_01_08_425885	690	19	,	,	,
10_1101-2021_01_08_425885	690	20	3	3	CD
10_1101-2021_01_08_425885	690	21	,	,	,
10_1101-2021_01_08_425885	690	22	19.1	19.1	CD
10_1101-2021_01_08_425885	690	23	)	)	-RRB-
10_1101-2021_01_08_425885	690	24	and	and	CC
10_1101-2021_01_08_425885	690	25	(	(	-LRB-
10_1101-2021_01_08_425885	690	26	9	9	CD
10_1101-2021_01_08_425885	690	27	,	,	,
10_1101-2021_01_08_425885	690	28	5	5	CD
10_1101-2021_01_08_425885	690	29	,	,	,
10_1101-2021_01_08_425885	690	30	24.9	24.9	CD
10_1101-2021_01_08_425885	690	31	)	)	-RRB-
10_1101-2021_01_08_425885	690	32	for	for	IN
10_1101-2021_01_08_425885	690	33	the	the	DT
10_1101-2021_01_08_425885	690	34	PBMC	PBMC	NNS
10_1101-2021_01_08_425885	690	35	,	,	,
10_1101-2021_01_08_425885	690	36	gastrulation	gastrulation	NN
10_1101-2021_01_08_425885	690	37	and	and	CC
10_1101-2021_01_08_425885	690	38	brain	brain	NN
10_1101-2021_01_08_425885	690	39	datasets	dataset	NNS
10_1101-2021_01_08_425885	690	40	respectively	respectively	RB
10_1101-2021_01_08_425885	690	41	.	.	.
10_1101-2021_01_08_425885	691	1	For	for	IN
10_1101-2021_01_08_425885	691	2	the	the	DT
10_1101-2021_01_08_425885	691	3	three	three	CD
10_1101-2021_01_08_425885	691	4	datasets	dataset	NNS
10_1101-2021_01_08_425885	691	5	,	,	,
10_1101-2021_01_08_425885	691	6	we	-PRON-	PRP
10_1101-2021_01_08_425885	691	7	computed	compute	VBD
10_1101-2021_01_08_425885	691	8	scalar	scalar	JJ
10_1101-2021_01_08_425885	691	9	curvatures	curvature	NNS
10_1101-2021_01_08_425885	691	10	for	for	IN
10_1101-2021_01_08_425885	691	11	manifold	manifold	JJ
10_1101-2021_01_08_425885	691	12	dimensions	dimension	NNS
10_1101-2021_01_08_425885	691	13	d−	d−	NNP
10_1101-2021_01_08_425885	691	14	1	1	CD
10_1101-2021_01_08_425885	691	15	,	,	,
10_1101-2021_01_08_425885	691	16	d	d	NN
10_1101-2021_01_08_425885	691	17	and	and	CC
10_1101-2021_01_08_425885	691	18	d	d	NNP
10_1101-2021_01_08_425885	691	19	+	+	SYM
10_1101-2021_01_08_425885	691	20	1	1	CD
10_1101-2021_01_08_425885	691	21	.	.	.
10_1101-2021_01_08_425885	692	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	692	2	was	be	VBD
10_1101-2021_01_08_425885	692	3	not	not	RB
10_1101-2021_01_08_425885	692	4	always	always	RB
10_1101-2021_01_08_425885	692	5	possible	possible	JJ
10_1101-2021_01_08_425885	692	6	to	to	TO
10_1101-2021_01_08_425885	692	7	select	select	VB
10_1101-2021_01_08_425885	692	8	σh	σh	NNP
10_1101-2021_01_08_425885	692	9	for	for	IN
10_1101-2021_01_08_425885	692	10	each	each	DT
10_1101-2021_01_08_425885	692	11	dataset	dataset	NN
10_1101-2021_01_08_425885	692	12	and	and	CC
10_1101-2021_01_08_425885	692	13	manifold	manifold	JJ
10_1101-2021_01_08_425885	692	14	dimension	dimension	NN
10_1101-2021_01_08_425885	692	15	,	,	,
10_1101-2021_01_08_425885	692	16	so	so	IN
10_1101-2021_01_08_425885	692	17	that	that	IN
10_1101-2021_01_08_425885	692	18	the	the	DT
10_1101-2021_01_08_425885	692	19	distribution	distribution	NN
10_1101-2021_01_08_425885	692	20	of	of	IN
10_1101-2021_01_08_425885	692	21	GOF	GOF	NNP
10_1101-2021_01_08_425885	692	22	p	p	NN
10_1101-2021_01_08_425885	692	23	-	-	HYPH
10_1101-2021_01_08_425885	692	24	values	value	NNS
10_1101-2021_01_08_425885	692	25	was	be	VBD
10_1101-2021_01_08_425885	692	26	flat	flat	JJ
10_1101-2021_01_08_425885	692	27	,	,	,
10_1101-2021_01_08_425885	692	28	according	accord	VBG
10_1101-2021_01_08_425885	692	29	to	to	IN
10_1101-2021_01_08_425885	692	30	our	-PRON-	PRP$
10_1101-2021_01_08_425885	692	31	usual	usual	JJ
10_1101-2021_01_08_425885	692	32	heuristic	heuristic	NN
10_1101-2021_01_08_425885	692	33	.	.	.
10_1101-2021_01_08_425885	693	1	For	for	IN
10_1101-2021_01_08_425885	693	2	consistency	consistency	NN
10_1101-2021_01_08_425885	693	3	,	,	,
10_1101-2021_01_08_425885	693	4	we	-PRON-	PRP
10_1101-2021_01_08_425885	693	5	therefore	therefore	RB
10_1101-2021_01_08_425885	693	6	picked	pick	VBD
10_1101-2021_01_08_425885	693	7	σh	σh	NNP
10_1101-2021_01_08_425885	693	8	so	so	IN
10_1101-2021_01_08_425885	693	9	that	that	IN
10_1101-2021_01_08_425885	693	10	1/3	1/3	CD
10_1101-2021_01_08_425885	693	11	of	of	IN
10_1101-2021_01_08_425885	693	12	points	point	NNS
10_1101-2021_01_08_425885	693	13	had	have	VBD
10_1101-2021_01_08_425885	693	14	GOF	GOF	NNP
10_1101-2021_01_08_425885	693	15	p	p	NN
10_1101-2021_01_08_425885	693	16	-	-	HYPH
10_1101-2021_01_08_425885	693	17	values	value	NNS
10_1101-2021_01_08_425885	693	18	≤	≤	NNP
10_1101-2021_01_08_425885	693	19	α	α	NNP
10_1101-2021_01_08_425885	693	20	=	=	SYM
10_1101-2021_01_08_425885	693	21	0.05	0.05	CD
10_1101-2021_01_08_425885	693	22	.	.	.
10_1101-2021_01_08_425885	694	1	For	for	IN
10_1101-2021_01_08_425885	694	2	manifold	manifold	JJ
10_1101-2021_01_08_425885	694	3	dimension	dimension	NN
10_1101-2021_01_08_425885	694	4	(	(	-LRB-
10_1101-2021_01_08_425885	694	5	d	d	NNP
10_1101-2021_01_08_425885	694	6	−	−	NNP
10_1101-2021_01_08_425885	694	7	1,d	1,d	CD
10_1101-2021_01_08_425885	694	8	,	,	,
10_1101-2021_01_08_425885	694	9	d	d	NN
10_1101-2021_01_08_425885	694	10	+	+	SYM
10_1101-2021_01_08_425885	694	11	1	1	CD
10_1101-2021_01_08_425885	694	12	)	)	-RRB-
10_1101-2021_01_08_425885	694	13	,	,	,
10_1101-2021_01_08_425885	694	14	σh	σh	NNP
10_1101-2021_01_08_425885	694	15	=	=	FW
10_1101-2021_01_08_425885	694	16	(	(	-LRB-
10_1101-2021_01_08_425885	694	17	0.031	0.031	CD
10_1101-2021_01_08_425885	694	18	,	,	,
10_1101-2021_01_08_425885	694	19	0.041	0.041	CD
10_1101-2021_01_08_425885	694	20	,	,	,
10_1101-2021_01_08_425885	694	21	0.045	0.045	CD
10_1101-2021_01_08_425885	694	22	)	)	-RRB-
10_1101-2021_01_08_425885	694	23	,	,	,
10_1101-2021_01_08_425885	694	24	(	(	-LRB-
10_1101-2021_01_08_425885	694	25	0.036	0.036	CD
10_1101-2021_01_08_425885	694	26	,	,	,
10_1101-2021_01_08_425885	694	27	0.044	0.044	CD
10_1101-2021_01_08_425885	694	28	,	,	,
10_1101-2021_01_08_425885	694	29	0.053	0.053	CD
10_1101-2021_01_08_425885	694	30	)	)	-RRB-
10_1101-2021_01_08_425885	694	31	and	and	CC
10_1101-2021_01_08_425885	694	32	(	(	-LRB-
10_1101-2021_01_08_425885	694	33	0.034	0.034	CD
10_1101-2021_01_08_425885	694	34	,	,	,
10_1101-2021_01_08_425885	694	35	0.050	0.050	CD
10_1101-2021_01_08_425885	694	36	,	,	,
10_1101-2021_01_08_425885	694	37	0.055	0.055	CD
10_1101-2021_01_08_425885	694	38	)	)	-RRB-
10_1101-2021_01_08_425885	694	39	for	for	IN
10_1101-2021_01_08_425885	694	40	the	the	DT
10_1101-2021_01_08_425885	694	41	PBMC	PBMC	NNS
10_1101-2021_01_08_425885	694	42	,	,	,
10_1101-2021_01_08_425885	694	43	gastrulation	gastrulation	NN
10_1101-2021_01_08_425885	694	44	and	and	CC
10_1101-2021_01_08_425885	694	45	brain	brain	NN
10_1101-2021_01_08_425885	694	46	datasets	dataset	NNS
10_1101-2021_01_08_425885	694	47	respectively	respectively	RB
10_1101-2021_01_08_425885	694	48	.	.	.
10_1101-2021_01_08_425885	695	1	5	5	CD
10_1101-2021_01_08_425885	695	2	Acknowledgements	Acknowledgements	NNPS
10_1101-2021_01_08_425885	695	3	DS	DS	NNP
10_1101-2021_01_08_425885	695	4	was	be	VBD
10_1101-2021_01_08_425885	695	5	funded	fund	VBN
10_1101-2021_01_08_425885	695	6	in	in	IN
10_1101-2021_01_08_425885	695	7	part	part	NN
10_1101-2021_01_08_425885	695	8	by	by	IN
10_1101-2021_01_08_425885	695	9	the	the	DT
10_1101-2021_01_08_425885	695	10	Natural	Natural	NNP
10_1101-2021_01_08_425885	695	11	Sciences	Sciences	NNPS
10_1101-2021_01_08_425885	695	12	and	and	CC
10_1101-2021_01_08_425885	695	13	Engineering	Engineering	NNP
10_1101-2021_01_08_425885	695	14	Research	Research	NNP
10_1101-2021_01_08_425885	695	15	Council	Council	NNP
10_1101-2021_01_08_425885	695	16	of	of	IN
10_1101-2021_01_08_425885	695	17	Canada	Canada	NNP
10_1101-2021_01_08_425885	695	18	(	(	-LRB-
10_1101-2021_01_08_425885	695	19	NSERC	NSERC	NNP
10_1101-2021_01_08_425885	695	20	PGSD2	PGSD2	NNP
10_1101-2021_01_08_425885	695	21	-	-	HYPH
10_1101-2021_01_08_425885	695	22	517131	517131	CD
10_1101-2021_01_08_425885	695	23	-	-	HYPH
10_1101-2021_01_08_425885	695	24	2018	2018	CD
10_1101-2021_01_08_425885	695	25	)	)	-RRB-
10_1101-2021_01_08_425885	695	26	.	.	.
10_1101-2021_01_08_425885	696	1	SW	SW	NNP
10_1101-2021_01_08_425885	696	2	was	be	VBD
10_1101-2021_01_08_425885	696	3	supported	support	VBN
10_1101-2021_01_08_425885	696	4	by	by	IN
10_1101-2021_01_08_425885	696	5	NCI	NCI	NNP
10_1101-2021_01_08_425885	696	6	U54-CA225088	U54-CA225088	NNP
10_1101-2021_01_08_425885	696	7	and	and	CC
10_1101-2021_01_08_425885	696	8	NIH	NIH	NNP
10_1101-2021_01_08_425885	696	9	NIGMS	NIGMS	NNP
10_1101-2021_01_08_425885	696	10	T32	T32	NNP
10_1101-2021_01_08_425885	696	11	GM008313	gm008313	NN
10_1101-2021_01_08_425885	696	12	.	.	.
10_1101-2021_01_08_425885	697	1	DS	DS	NNP
10_1101-2021_01_08_425885	697	2	and	and	CC
10_1101-2021_01_08_425885	697	3	SH	SH	NNP
10_1101-2021_01_08_425885	697	4	acknowledge	acknowledge	XX
10_1101-2021_01_08_425885	697	5	funding	funding	NN
10_1101-2021_01_08_425885	697	6	from	from	IN
10_1101-2021_01_08_425885	697	7	NIH	NIH	NNP
10_1101-2021_01_08_425885	697	8	NIGMS	NIGMS	NNP
10_1101-2021_01_08_425885	697	9	R00GM118910	R00GM118910	NNP
10_1101-2021_01_08_425885	697	10	,	,	,
10_1101-2021_01_08_425885	697	11	U19	U19	NNP
10_1101-2021_01_08_425885	697	12	Systems	Systems	NNPS
10_1101-2021_01_08_425885	697	13	Immunology	Immunology	NNP
10_1101-2021_01_08_425885	697	14	Pilot	Pilot	NNP
10_1101-2021_01_08_425885	697	15	Project	Project	NNP
10_1101-2021_01_08_425885	697	16	Grant	Grant	NNP
10_1101-2021_01_08_425885	697	17	at	at	IN
10_1101-2021_01_08_425885	697	18	Harvard	Harvard	NNP
10_1101-2021_01_08_425885	697	19	University	University	NNP
10_1101-2021_01_08_425885	697	20	,	,	,
10_1101-2021_01_08_425885	697	21	and	and	CC
10_1101-2021_01_08_425885	697	22	the	the	DT
10_1101-2021_01_08_425885	697	23	Harvard	Harvard	NNP
10_1101-2021_01_08_425885	697	24	University	University	NNP
10_1101-2021_01_08_425885	697	25	William	William	NNP
10_1101-2021_01_08_425885	697	26	F.	F.	NNP
10_1101-2021_01_08_425885	697	27	Milton	Milton	NNP
10_1101-2021_01_08_425885	697	28	Fund	Fund	NNP
10_1101-2021_01_08_425885	697	29	.	.	.
10_1101-2021_01_08_425885	698	1	The	the	DT
10_1101-2021_01_08_425885	698	2	authors	author	NNS
10_1101-2021_01_08_425885	698	3	would	would	MD
10_1101-2021_01_08_425885	698	4	like	like	VB
10_1101-2021_01_08_425885	698	5	to	to	TO
10_1101-2021_01_08_425885	698	6	thank	thank	VB
10_1101-2021_01_08_425885	698	7	Peter	Peter	NNP
10_1101-2021_01_08_425885	698	8	Kharchenko	Kharchenko	NNP
10_1101-2021_01_08_425885	698	9	and	and	CC
10_1101-2021_01_08_425885	698	10	Allon	Allon	NNP
10_1101-2021_01_08_425885	698	11	Klein	Klein	NNP
10_1101-2021_01_08_425885	698	12	for	for	IN
10_1101-2021_01_08_425885	698	13	helpful	helpful	JJ
10_1101-2021_01_08_425885	698	14	discussions	discussion	NNS
10_1101-2021_01_08_425885	698	15	.	.	.
10_1101-2021_01_08_425885	699	1	Portions	portion	NNS
10_1101-2021_01_08_425885	699	2	of	of	IN
10_1101-2021_01_08_425885	699	3	this	this	DT
10_1101-2021_01_08_425885	699	4	research	research	NN
10_1101-2021_01_08_425885	699	5	were	be	VBD
10_1101-2021_01_08_425885	699	6	conducted	conduct	VBN
10_1101-2021_01_08_425885	699	7	on	on	IN
10_1101-2021_01_08_425885	699	8	the	the	DT
10_1101-2021_01_08_425885	699	9	O2	O2	NNP
10_1101-2021_01_08_425885	699	10	High	High	NNP
10_1101-2021_01_08_425885	699	11	Performance	Performance	NNP
10_1101-2021_01_08_425885	699	12	Compute	Compute	NNP
10_1101-2021_01_08_425885	699	13	Cluster	Cluster	NNP
10_1101-2021_01_08_425885	699	14	,	,	,
10_1101-2021_01_08_425885	699	15	supported	support	VBN
10_1101-2021_01_08_425885	699	16	by	by	IN
10_1101-2021_01_08_425885	699	17	the	the	DT
10_1101-2021_01_08_425885	699	18	Research	Research	NNP
10_1101-2021_01_08_425885	699	19	Computing	Computing	NNP
10_1101-2021_01_08_425885	699	20	Group	Group	NNP
10_1101-2021_01_08_425885	699	21	,	,	,
10_1101-2021_01_08_425885	699	22	at	at	IN
10_1101-2021_01_08_425885	699	23	Harvard	Harvard	NNP
10_1101-2021_01_08_425885	699	24	Medical	Medical	NNP
10_1101-2021_01_08_425885	699	25	School	School	NNP
10_1101-2021_01_08_425885	699	26	.	.	.
10_1101-2021_01_08_425885	700	1	See	see	VB
10_1101-2021_01_08_425885	700	2	http://rc.hms.harvard.edu	http://rc.hms.harvard.edu	NNS
10_1101-2021_01_08_425885	700	3	for	for	IN
10_1101-2021_01_08_425885	700	4	more	more	JJR
10_1101-2021_01_08_425885	700	5	information	information	NN
10_1101-2021_01_08_425885	700	6	.	.	.
10_1101-2021_01_08_425885	701	1	6	6	CD
10_1101-2021_01_08_425885	701	2	Data	Data	NNPS
10_1101-2021_01_08_425885	701	3	and	and	CC
10_1101-2021_01_08_425885	701	4	Code	Code	NNP
10_1101-2021_01_08_425885	701	5	Availability	Availability	NNP
10_1101-2021_01_08_425885	701	6	The	the	DT
10_1101-2021_01_08_425885	701	7	van	van	NN
10_1101-2021_01_08_425885	701	8	Hateren	Hateren	NNP
10_1101-2021_01_08_425885	701	9	IML	IML	NNP
10_1101-2021_01_08_425885	701	10	dataset	dataset	NN
10_1101-2021_01_08_425885	701	11	is	be	VBZ
10_1101-2021_01_08_425885	701	12	available	available	JJ
10_1101-2021_01_08_425885	701	13	at	at	IN
10_1101-2021_01_08_425885	701	14	http://bethgelab.org/datasets/vanhateren	http://bethgelab.org/datasets/vanhateren	NNP
10_1101-2021_01_08_425885	701	15	and	and	CC
10_1101-2021_01_08_425885	701	16	was	be	VBD
10_1101-2021_01_08_425885	701	17	loaded	load	VBN
10_1101-2021_01_08_425885	701	18	according	accord	VBG
10_1101-2021_01_08_425885	701	19	to	to	IN
10_1101-2021_01_08_425885	701	20	the	the	DT
10_1101-2021_01_08_425885	701	21	instructions	instruction	NNS
10_1101-2021_01_08_425885	701	22	there	there	RB
10_1101-2021_01_08_425885	701	23	.	.	.
10_1101-2021_01_08_425885	702	1	The	the	DT
10_1101-2021_01_08_425885	702	2	PBMC	PBMC	NNP
10_1101-2021_01_08_425885	702	3	dataset	dataset	NN
10_1101-2021_01_08_425885	702	4	is	be	VBZ
10_1101-2021_01_08_425885	702	5	available	available	JJ
10_1101-2021_01_08_425885	702	6	at	at	IN
10_1101-2021_01_08_425885	702	7	https://support.10xgenomics	https://support.10xgenomic	NNS
10_1101-2021_01_08_425885	702	8	.	.	.
10_1101-2021_01_08_425885	703	1	com	com	NN
10_1101-2021_01_08_425885	703	2	/	/	SYM
10_1101-2021_01_08_425885	703	3	single	single	JJ
10_1101-2021_01_08_425885	703	4	-	-	HYPH
10_1101-2021_01_08_425885	703	5	cell	cell	NN
10_1101-2021_01_08_425885	703	6	-	-	HYPH
10_1101-2021_01_08_425885	703	7	gene	gene	NN
10_1101-2021_01_08_425885	703	8	-	-	HYPH
10_1101-2021_01_08_425885	703	9	expression	expression	NN
10_1101-2021_01_08_425885	703	10	/	/	SYM
10_1101-2021_01_08_425885	703	11	datasets/4.0.0	datasets/4.0.0	NNP
10_1101-2021_01_08_425885	703	12	/	/	SYM
10_1101-2021_01_08_425885	703	13	Parent_NGSC3_DI_PBMC	Parent_NGSC3_DI_PBMC	NNP
10_1101-2021_01_08_425885	703	14	.	.	.
10_1101-2021_01_08_425885	704	1	The	the	DT
10_1101-2021_01_08_425885	704	2	gastrulation	gastrulation	NN
10_1101-2021_01_08_425885	704	3	dataset	dataset	NN
10_1101-2021_01_08_425885	704	4	can	can	MD
10_1101-2021_01_08_425885	704	5	be	be	VB
10_1101-2021_01_08_425885	704	6	retrieved	retrieve	VBN
10_1101-2021_01_08_425885	704	7	using	use	VBG
10_1101-2021_01_08_425885	704	8	instructions	instruction	NNS
10_1101-2021_01_08_425885	704	9	found	find	VBN
10_1101-2021_01_08_425885	704	10	at	at	IN
10_1101-2021_01_08_425885	704	11	https://github.com/MarioniLab/EmbryoTimecourse2018	https://github.com/MarioniLab/EmbryoTimecourse2018	NNP
10_1101-2021_01_08_425885	704	12	.	.	.
10_1101-2021_01_08_425885	705	1	42	42	CD
10_1101-2021_01_08_425885	705	2	.CC	.CC	:
10_1101-2021_01_08_425885	705	3	-	-	HYPH
10_1101-2021_01_08_425885	705	4	BY	by	IN
10_1101-2021_01_08_425885	705	5	-	-	HYPH
10_1101-2021_01_08_425885	705	6	NC	NC	NNP
10_1101-2021_01_08_425885	705	7	-	-	HYPH
10_1101-2021_01_08_425885	705	8	ND	ND	NNP
10_1101-2021_01_08_425885	705	9	4.0	4.0	CD
10_1101-2021_01_08_425885	705	10	International	International	NNP
10_1101-2021_01_08_425885	705	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	705	12	under	under	IN
10_1101-2021_01_08_425885	705	13	a	a	DT
10_1101-2021_01_08_425885	705	14	(	(	-LRB-
10_1101-2021_01_08_425885	705	15	which	which	WDT
10_1101-2021_01_08_425885	705	16	was	be	VBD
10_1101-2021_01_08_425885	705	17	not	not	RB
10_1101-2021_01_08_425885	705	18	certified	certify	VBN
10_1101-2021_01_08_425885	705	19	by	by	IN
10_1101-2021_01_08_425885	705	20	peer	peer	NN
10_1101-2021_01_08_425885	705	21	review	review	NN
10_1101-2021_01_08_425885	705	22	)	)	-RRB-
10_1101-2021_01_08_425885	705	23	is	be	VBZ
10_1101-2021_01_08_425885	705	24	the	the	DT
10_1101-2021_01_08_425885	705	25	author	author	NN
10_1101-2021_01_08_425885	705	26	/	/	SYM
10_1101-2021_01_08_425885	705	27	funder	funder	NN
10_1101-2021_01_08_425885	705	28	,	,	,
10_1101-2021_01_08_425885	705	29	who	who	WP
10_1101-2021_01_08_425885	705	30	has	have	VBZ
10_1101-2021_01_08_425885	705	31	granted	grant	VBN
10_1101-2021_01_08_425885	705	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	705	33	a	a	DT
10_1101-2021_01_08_425885	705	34	license	license	NN
10_1101-2021_01_08_425885	705	35	to	to	TO
10_1101-2021_01_08_425885	705	36	display	display	VB
10_1101-2021_01_08_425885	705	37	the	the	DT
10_1101-2021_01_08_425885	705	38	preprint	preprint	NN
10_1101-2021_01_08_425885	705	39	in	in	IN
10_1101-2021_01_08_425885	705	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	705	41	.	.	.
10_1101-2021_01_08_425885	706	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	706	2	is	be	VBZ
10_1101-2021_01_08_425885	706	3	made	make	VBN
10_1101-2021_01_08_425885	706	4	The	the	DT
10_1101-2021_01_08_425885	706	5	copyright	copyright	NN
10_1101-2021_01_08_425885	706	6	holder	holder	NN
10_1101-2021_01_08_425885	706	7	for	for	IN
10_1101-2021_01_08_425885	706	8	this	this	DT
10_1101-2021_01_08_425885	706	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	706	10	version	version	NN
10_1101-2021_01_08_425885	706	11	posted	post	VBD
10_1101-2021_01_08_425885	706	12	January	January	NNP
10_1101-2021_01_08_425885	706	13	8	8	CD
10_1101-2021_01_08_425885	706	14	,	,	,
10_1101-2021_01_08_425885	706	15	2021	2021	CD
10_1101-2021_01_08_425885	706	16	.	.	.
10_1101-2021_01_08_425885	706	17	;	;	:
10_1101-2021_01_08_425885	706	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	706	19	:	:	:
10_1101-2021_01_08_425885	706	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	706	21	preprint	preprint	NN
10_1101-2021_01_08_425885	706	22	http://rc.hms.harvard.edu	http://rc.hms.harvard.edu	NN
10_1101-2021_01_08_425885	706	23	http://bethgelab.org/datasets/vanhateren	http://bethgelab.org/datasets/vanhateren	VBP
10_1101-2021_01_08_425885	706	24	https://support.10xgenomics.com/single-cell-gene-expression/datasets/4.0.0/Parent_NGSC3_DI_PBMC	https://support.10xgenomics.com/single-cell-gene-expression/datasets/4.0.0/parent_ngsc3_di_pbmc	CD
10_1101-2021_01_08_425885	706	25	https://support.10xgenomics.com/single-cell-gene-expression/datasets/4.0.0/Parent_NGSC3_DI_PBMC	https://support.10xgenomics.com/single-cell-gene-expression/datasets/4.0.0/Parent_NGSC3_DI_PBMC	NNP
10_1101-2021_01_08_425885	706	26	https://github.com/MarioniLab/EmbryoTimecourse2018	https://github.com/MarioniLab/EmbryoTimecourse2018	NNP
10_1101-2021_01_08_425885	706	27	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	706	28	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	VB
10_1101-2021_01_08_425885	706	29	The	the	DT
10_1101-2021_01_08_425885	706	30	brain	brain	NN
10_1101-2021_01_08_425885	706	31	dataset	dataset	NN
10_1101-2021_01_08_425885	706	32	is	be	VBZ
10_1101-2021_01_08_425885	706	33	available	available	JJ
10_1101-2021_01_08_425885	706	34	at	at	IN
10_1101-2021_01_08_425885	706	35	https://support.10xgenomics.com/single-cell-gene-expression/	https://support.10xgenomics.com/single-cell-gene-expression/	NNP
10_1101-2021_01_08_425885	706	36	datasets/1.3.0/1M_neurons	datasets/1.3.0/1m_neuron	NNS
10_1101-2021_01_08_425885	706	37	.	.	.
10_1101-2021_01_08_425885	707	1	The	the	DT
10_1101-2021_01_08_425885	707	2	software	software	NN
10_1101-2021_01_08_425885	707	3	package	package	NN
10_1101-2021_01_08_425885	707	4	described	describe	VBN
10_1101-2021_01_08_425885	707	5	here	here	RB
10_1101-2021_01_08_425885	707	6	to	to	TO
10_1101-2021_01_08_425885	707	7	compute	compute	VB
10_1101-2021_01_08_425885	707	8	scalar	scalar	JJ
10_1101-2021_01_08_425885	707	9	curvature	curvature	NN
10_1101-2021_01_08_425885	707	10	is	be	VBZ
10_1101-2021_01_08_425885	707	11	avail-	avail-	PRP$
10_1101-2021_01_08_425885	707	12	able	able	JJ
10_1101-2021_01_08_425885	707	13	at	at	IN
10_1101-2021_01_08_425885	707	14	https://gitlab.com/hormozlab/ManifoldCurvature	https://gitlab.com/hormozlab/manifoldcurvature	NN
10_1101-2021_01_08_425885	707	15	.	.	.
10_1101-2021_01_08_425885	708	1	All	all	DT
10_1101-2021_01_08_425885	708	2	code	code	NN
10_1101-2021_01_08_425885	708	3	and	and	CC
10_1101-2021_01_08_425885	708	4	instructions	instruction	NNS
10_1101-2021_01_08_425885	708	5	to	to	TO
10_1101-2021_01_08_425885	708	6	reproduce	reproduce	VB
10_1101-2021_01_08_425885	708	7	the	the	DT
10_1101-2021_01_08_425885	708	8	numerics	numeric	NNS
10_1101-2021_01_08_425885	708	9	and	and	CC
10_1101-2021_01_08_425885	708	10	figures	figure	NNS
10_1101-2021_01_08_425885	708	11	in	in	IN
10_1101-2021_01_08_425885	708	12	this	this	DT
10_1101-2021_01_08_425885	708	13	study	study	NN
10_1101-2021_01_08_425885	708	14	will	will	MD
10_1101-2021_01_08_425885	708	15	be	be	VB
10_1101-2021_01_08_425885	708	16	made	make	VBN
10_1101-2021_01_08_425885	708	17	available	available	JJ
10_1101-2021_01_08_425885	708	18	upon	upon	IN
10_1101-2021_01_08_425885	708	19	publication	publication	NN
10_1101-2021_01_08_425885	708	20	.	.	.
10_1101-2021_01_08_425885	709	1	43	43	CD
10_1101-2021_01_08_425885	709	2	.CC	.CC	:
10_1101-2021_01_08_425885	709	3	-	-	HYPH
10_1101-2021_01_08_425885	709	4	BY	by	IN
10_1101-2021_01_08_425885	709	5	-	-	HYPH
10_1101-2021_01_08_425885	709	6	NC	NC	NNP
10_1101-2021_01_08_425885	709	7	-	-	HYPH
10_1101-2021_01_08_425885	709	8	ND	ND	NNP
10_1101-2021_01_08_425885	709	9	4.0	4.0	CD
10_1101-2021_01_08_425885	709	10	International	International	NNP
10_1101-2021_01_08_425885	709	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	709	12	under	under	IN
10_1101-2021_01_08_425885	709	13	a	a	DT
10_1101-2021_01_08_425885	709	14	(	(	-LRB-
10_1101-2021_01_08_425885	709	15	which	which	WDT
10_1101-2021_01_08_425885	709	16	was	be	VBD
10_1101-2021_01_08_425885	709	17	not	not	RB
10_1101-2021_01_08_425885	709	18	certified	certify	VBN
10_1101-2021_01_08_425885	709	19	by	by	IN
10_1101-2021_01_08_425885	709	20	peer	peer	NN
10_1101-2021_01_08_425885	709	21	review	review	NN
10_1101-2021_01_08_425885	709	22	)	)	-RRB-
10_1101-2021_01_08_425885	709	23	is	be	VBZ
10_1101-2021_01_08_425885	709	24	the	the	DT
10_1101-2021_01_08_425885	709	25	author	author	NN
10_1101-2021_01_08_425885	709	26	/	/	SYM
10_1101-2021_01_08_425885	709	27	funder	funder	NN
10_1101-2021_01_08_425885	709	28	,	,	,
10_1101-2021_01_08_425885	709	29	who	who	WP
10_1101-2021_01_08_425885	709	30	has	have	VBZ
10_1101-2021_01_08_425885	709	31	granted	grant	VBN
10_1101-2021_01_08_425885	709	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	709	33	a	a	DT
10_1101-2021_01_08_425885	709	34	license	license	NN
10_1101-2021_01_08_425885	709	35	to	to	TO
10_1101-2021_01_08_425885	709	36	display	display	VB
10_1101-2021_01_08_425885	709	37	the	the	DT
10_1101-2021_01_08_425885	709	38	preprint	preprint	NN
10_1101-2021_01_08_425885	709	39	in	in	IN
10_1101-2021_01_08_425885	709	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	709	41	.	.	.
10_1101-2021_01_08_425885	710	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	710	2	is	be	VBZ
10_1101-2021_01_08_425885	710	3	made	make	VBN
10_1101-2021_01_08_425885	710	4	The	the	DT
10_1101-2021_01_08_425885	710	5	copyright	copyright	NN
10_1101-2021_01_08_425885	710	6	holder	holder	NN
10_1101-2021_01_08_425885	710	7	for	for	IN
10_1101-2021_01_08_425885	710	8	this	this	DT
10_1101-2021_01_08_425885	710	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	710	10	version	version	NN
10_1101-2021_01_08_425885	710	11	posted	post	VBD
10_1101-2021_01_08_425885	710	12	January	January	NNP
10_1101-2021_01_08_425885	710	13	8	8	CD
10_1101-2021_01_08_425885	710	14	,	,	,
10_1101-2021_01_08_425885	710	15	2021	2021	CD
10_1101-2021_01_08_425885	710	16	.	.	.
10_1101-2021_01_08_425885	710	17	;	;	:
10_1101-2021_01_08_425885	710	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	710	19	:	:	:
10_1101-2021_01_08_425885	710	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	710	21	preprint	preprint	NN
10_1101-2021_01_08_425885	710	22	https://support.10xgenomics.com/single-cell-gene-expression/datasets/1.3.0/1M_neurons	https://support.10xgenomics.com/single-cell-gene-expression/datasets/1.3.0/1m_neuron	NNS
10_1101-2021_01_08_425885	710	23	https://support.10xgenomics.com/single-cell-gene-expression/datasets/1.3.0/1M_neurons	https://support.10xgenomics.com/single-cell-gene-expression/datasets/1.3.0/1m_neuron	NNS
10_1101-2021_01_08_425885	710	24	https://gitlab.com/hormozlab/ManifoldCurvature	https://gitlab.com/hormozlab/manifoldcurvature	NN
10_1101-2021_01_08_425885	710	25	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	NNP
10_1101-2021_01_08_425885	710	26	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NN
10_1101-2021_01_08_425885	710	27	7	7	CD
10_1101-2021_01_08_425885	710	28	Supplementary	Supplementary	NNP
10_1101-2021_01_08_425885	710	29	Figures	Figures	NNPS
10_1101-2021_01_08_425885	710	30	44	44	CD
10_1101-2021_01_08_425885	710	31	.CC	.CC	,
10_1101-2021_01_08_425885	710	32	-	-	HYPH
10_1101-2021_01_08_425885	710	33	BY	by	IN
10_1101-2021_01_08_425885	710	34	-	-	HYPH
10_1101-2021_01_08_425885	710	35	NC	NC	NNP
10_1101-2021_01_08_425885	710	36	-	-	HYPH
10_1101-2021_01_08_425885	710	37	ND	ND	NNP
10_1101-2021_01_08_425885	710	38	4.0	4.0	CD
10_1101-2021_01_08_425885	710	39	International	International	NNP
10_1101-2021_01_08_425885	710	40	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	710	41	under	under	IN
10_1101-2021_01_08_425885	710	42	a	a	DT
10_1101-2021_01_08_425885	710	43	(	(	-LRB-
10_1101-2021_01_08_425885	710	44	which	which	WDT
10_1101-2021_01_08_425885	710	45	was	be	VBD
10_1101-2021_01_08_425885	710	46	not	not	RB
10_1101-2021_01_08_425885	710	47	certified	certify	VBN
10_1101-2021_01_08_425885	710	48	by	by	IN
10_1101-2021_01_08_425885	710	49	peer	peer	NN
10_1101-2021_01_08_425885	710	50	review	review	NN
10_1101-2021_01_08_425885	710	51	)	)	-RRB-
10_1101-2021_01_08_425885	710	52	is	be	VBZ
10_1101-2021_01_08_425885	710	53	the	the	DT
10_1101-2021_01_08_425885	710	54	author	author	NN
10_1101-2021_01_08_425885	710	55	/	/	SYM
10_1101-2021_01_08_425885	710	56	funder	funder	NN
10_1101-2021_01_08_425885	710	57	,	,	,
10_1101-2021_01_08_425885	710	58	who	who	WP
10_1101-2021_01_08_425885	710	59	has	have	VBZ
10_1101-2021_01_08_425885	710	60	granted	grant	VBN
10_1101-2021_01_08_425885	710	61	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	710	62	a	a	DT
10_1101-2021_01_08_425885	710	63	license	license	NN
10_1101-2021_01_08_425885	710	64	to	to	TO
10_1101-2021_01_08_425885	710	65	display	display	VB
10_1101-2021_01_08_425885	710	66	the	the	DT
10_1101-2021_01_08_425885	710	67	preprint	preprint	NN
10_1101-2021_01_08_425885	710	68	in	in	IN
10_1101-2021_01_08_425885	710	69	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	710	70	.	.	.
10_1101-2021_01_08_425885	711	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	711	2	is	be	VBZ
10_1101-2021_01_08_425885	711	3	made	make	VBN
10_1101-2021_01_08_425885	711	4	The	the	DT
10_1101-2021_01_08_425885	711	5	copyright	copyright	NN
10_1101-2021_01_08_425885	711	6	holder	holder	NN
10_1101-2021_01_08_425885	711	7	for	for	IN
10_1101-2021_01_08_425885	711	8	this	this	DT
10_1101-2021_01_08_425885	711	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	711	10	version	version	NN
10_1101-2021_01_08_425885	711	11	posted	post	VBD
10_1101-2021_01_08_425885	711	12	January	January	NNP
10_1101-2021_01_08_425885	711	13	8	8	CD
10_1101-2021_01_08_425885	711	14	,	,	,
10_1101-2021_01_08_425885	711	15	2021	2021	CD
10_1101-2021_01_08_425885	711	16	.	.	.
10_1101-2021_01_08_425885	711	17	;	;	:
10_1101-2021_01_08_425885	711	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	711	19	:	:	:
10_1101-2021_01_08_425885	711	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	711	21	preprint	preprint	NN
10_1101-2021_01_08_425885	711	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	711	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NN
10_1101-2021_01_08_425885	711	24	A	A	NNP
10_1101-2021_01_08_425885	711	25	B	b	NN
10_1101-2021_01_08_425885	711	26	C	c	NN
10_1101-2021_01_08_425885	711	27	D	d	NN
10_1101-2021_01_08_425885	711	28	E	e	NN
10_1101-2021_01_08_425885	711	29	F	f	NN
10_1101-2021_01_08_425885	711	30	H	h	NN
10_1101-2021_01_08_425885	711	31	G	g	NN
10_1101-2021_01_08_425885	711	32	Figure	figure	NN
10_1101-2021_01_08_425885	711	33	S1	s1	NN
10_1101-2021_01_08_425885	711	34	:	:	:
10_1101-2021_01_08_425885	711	35	The	the	DT
10_1101-2021_01_08_425885	711	36	scalar	scalar	JJ
10_1101-2021_01_08_425885	711	37	curvature	curvature	NN
10_1101-2021_01_08_425885	711	38	of	of	IN
10_1101-2021_01_08_425885	711	39	S2	s2	NN
10_1101-2021_01_08_425885	711	40	is	be	VBZ
10_1101-2021_01_08_425885	711	41	poorly	poorly	RB
10_1101-2021_01_08_425885	711	42	estimated	estimate	VBN
10_1101-2021_01_08_425885	711	43	using	use	VBG
10_1101-2021_01_08_425885	711	44	the	the	DT
10_1101-2021_01_08_425885	711	45	Laplace	Laplace	NNP
10_1101-2021_01_08_425885	711	46	-	-	HYPH
10_1101-2021_01_08_425885	711	47	Beltrami	Beltrami	NNP
10_1101-2021_01_08_425885	711	48	operator	operator	NN
10_1101-2021_01_08_425885	711	49	.	.	.
10_1101-2021_01_08_425885	712	1	(	(	-LRB-
10_1101-2021_01_08_425885	712	2	A	a	NN
10_1101-2021_01_08_425885	712	3	)	)	-RRB-
10_1101-2021_01_08_425885	712	4	The	the	DT
10_1101-2021_01_08_425885	712	5	heat	heat	NN
10_1101-2021_01_08_425885	712	6	-	-	HYPH
10_1101-2021_01_08_425885	712	7	trace	trace	NN
10_1101-2021_01_08_425885	712	8	with	with	IN
10_1101-2021_01_08_425885	712	9	m	m	NN
10_1101-2021_01_08_425885	712	10	terms	term	NNS
10_1101-2021_01_08_425885	712	11	,	,	,
10_1101-2021_01_08_425885	712	12	(	(	-LRB-
10_1101-2021_01_08_425885	712	13	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	712	14	)	)	-RRB-
10_1101-2021_01_08_425885	712	15	in	in	IN
10_1101-2021_01_08_425885	712	16	Equation	Equation	NNP
10_1101-2021_01_08_425885	712	17	3	3	CD
10_1101-2021_01_08_425885	712	18	)	)	-RRB-
10_1101-2021_01_08_425885	712	19	is	be	VBZ
10_1101-2021_01_08_425885	712	20	shown	show	VBN
10_1101-2021_01_08_425885	712	21	for	for	IN
10_1101-2021_01_08_425885	712	22	m	m	NN
10_1101-2021_01_08_425885	712	23	=	=	SYM
10_1101-2021_01_08_425885	712	24	∞	∞	FW
10_1101-2021_01_08_425885	712	25	(	(	-LRB-
10_1101-2021_01_08_425885	712	26	black	black	NNP
10_1101-2021_01_08_425885	712	27	)	)	-RRB-
10_1101-2021_01_08_425885	712	28	,	,	,
10_1101-2021_01_08_425885	712	29	m	m	NN
10_1101-2021_01_08_425885	712	30	=	=	SYM
10_1101-2021_01_08_425885	712	31	1000	1000	CD
10_1101-2021_01_08_425885	712	32	(	(	-LRB-
10_1101-2021_01_08_425885	712	33	solid	solid	JJ
10_1101-2021_01_08_425885	712	34	blue	blue	NN
10_1101-2021_01_08_425885	712	35	)	)	-RRB-
10_1101-2021_01_08_425885	712	36	and	and	CC
10_1101-2021_01_08_425885	712	37	m	m	NN
10_1101-2021_01_08_425885	712	38	=	=	SYM
10_1101-2021_01_08_425885	712	39	49	49	CD
10_1101-2021_01_08_425885	712	40	(	(	-LRB-
10_1101-2021_01_08_425885	712	41	solid	solid	JJ
10_1101-2021_01_08_425885	712	42	red	red	NNP
10_1101-2021_01_08_425885	712	43	)	)	-RRB-
10_1101-2021_01_08_425885	712	44	,	,	,
10_1101-2021_01_08_425885	712	45	when	when	WRB
10_1101-2021_01_08_425885	712	46	evaluated	evaluate	VBN
10_1101-2021_01_08_425885	712	47	with	with	IN
10_1101-2021_01_08_425885	712	48	analytical	analytical	JJ
10_1101-2021_01_08_425885	712	49	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	712	50	for	for	IN
10_1101-2021_01_08_425885	712	51	S2	s2	NN
10_1101-2021_01_08_425885	712	52	.	.	.
10_1101-2021_01_08_425885	713	1	Empirical	empirical	JJ
10_1101-2021_01_08_425885	713	2	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	713	3	were	be	VBD
10_1101-2021_01_08_425885	713	4	obtained	obtain	VBN
10_1101-2021_01_08_425885	713	5	by	by	IN
10_1101-2021_01_08_425885	713	6	uniformly	uniformly	RB
10_1101-2021_01_08_425885	713	7	sampling	sample	VBG
10_1101-2021_01_08_425885	713	8	N	n	NN
10_1101-2021_01_08_425885	713	9	=	=	SYM
10_1101-2021_01_08_425885	713	10	104	104	CD
10_1101-2021_01_08_425885	713	11	points	point	NNS
10_1101-2021_01_08_425885	713	12	from	from	IN
10_1101-2021_01_08_425885	713	13	S2	s2	NN
10_1101-2021_01_08_425885	713	14	(	(	-LRB-
10_1101-2021_01_08_425885	713	15	see	see	VB
10_1101-2021_01_08_425885	713	16	Figure	figure	NN
10_1101-2021_01_08_425885	713	17	1A	1a	NN
10_1101-2021_01_08_425885	713	18	;	;	:
10_1101-2021_01_08_425885	713	19	Methods	Methods	NNP
10_1101-2021_01_08_425885	713	20	Section	Section	NNP
10_1101-2021_01_08_425885	713	21	4.4.1.1	4.4.1.1	CD
10_1101-2021_01_08_425885	713	22	)	)	-RRB-
10_1101-2021_01_08_425885	713	23	and	and	CC
10_1101-2021_01_08_425885	713	24	estimating	estimate	VBG
10_1101-2021_01_08_425885	713	25	the	the	DT
10_1101-2021_01_08_425885	713	26	Laplace	Laplace	NNP
10_1101-2021_01_08_425885	713	27	-	-	HYPH
10_1101-2021_01_08_425885	713	28	Beltrami	Beltrami	NNP
10_1101-2021_01_08_425885	713	29	(	(	-LRB-
10_1101-2021_01_08_425885	713	30	LB	LB	NNP
10_1101-2021_01_08_425885	713	31	)	)	-RRB-
10_1101-2021_01_08_425885	713	32	operator	operator	NN
10_1101-2021_01_08_425885	713	33	using	use	VBG
10_1101-2021_01_08_425885	713	34	Equations	Equations	NNP
10_1101-2021_01_08_425885	713	35	13	13	CD
10_1101-2021_01_08_425885	713	36	-	-	SYM
10_1101-2021_01_08_425885	713	37	15	15	CD
10_1101-2021_01_08_425885	713	38	.	.	.
10_1101-2021_01_08_425885	714	1	The	the	DT
10_1101-2021_01_08_425885	714	2	heat	heat	NN
10_1101-2021_01_08_425885	714	3	-	-	HYPH
10_1101-2021_01_08_425885	714	4	trace	trace	NN
10_1101-2021_01_08_425885	714	5	evaluated	evaluate	VBD
10_1101-2021_01_08_425885	714	6	using	use	VBG
10_1101-2021_01_08_425885	714	7	these	these	DT
10_1101-2021_01_08_425885	714	8	empirical	empirical	JJ
10_1101-2021_01_08_425885	714	9	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	714	10	,	,	,
10_1101-2021_01_08_425885	714	11	zm	zm	NNP
10_1101-2021_01_08_425885	714	12	,	,	,
10_1101-2021_01_08_425885	714	13	is	be	VBZ
10_1101-2021_01_08_425885	714	14	shown	show	VBN
10_1101-2021_01_08_425885	714	15	for	for	IN
10_1101-2021_01_08_425885	714	16	m	m	NN
10_1101-2021_01_08_425885	714	17	=	=	SYM
10_1101-2021_01_08_425885	714	18	1000	1000	CD
10_1101-2021_01_08_425885	714	19	(	(	-LRB-
10_1101-2021_01_08_425885	714	20	dashed	dash	VBN
10_1101-2021_01_08_425885	714	21	blue	blue	NNP
10_1101-2021_01_08_425885	714	22	)	)	-RRB-
10_1101-2021_01_08_425885	714	23	and	and	CC
10_1101-2021_01_08_425885	714	24	m	m	NN
10_1101-2021_01_08_425885	714	25	=	=	SYM
10_1101-2021_01_08_425885	714	26	49	49	CD
10_1101-2021_01_08_425885	714	27	(	(	-LRB-
10_1101-2021_01_08_425885	714	28	dashed	dash	VBN
10_1101-2021_01_08_425885	714	29	red	red	NNP
10_1101-2021_01_08_425885	714	30	)	)	-RRB-
10_1101-2021_01_08_425885	714	31	.	.	.
10_1101-2021_01_08_425885	715	1	The	the	DT
10_1101-2021_01_08_425885	715	2	heat	heat	NN
10_1101-2021_01_08_425885	715	3	-	-	HYPH
10_1101-2021_01_08_425885	715	4	trace	trace	NN
10_1101-2021_01_08_425885	715	5	evaluated	evaluate	VBD
10_1101-2021_01_08_425885	715	6	using	use	VBG
10_1101-2021_01_08_425885	715	7	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	715	8	obtained	obtain	VBN
10_1101-2021_01_08_425885	715	9	by	by	IN
10_1101-2021_01_08_425885	715	10	interpolating	interpolate	VBG
10_1101-2021_01_08_425885	715	11	between	between	IN
10_1101-2021_01_08_425885	715	12	the	the	DT
10_1101-2021_01_08_425885	715	13	analytical	analytical	JJ
10_1101-2021_01_08_425885	715	14	and	and	CC
10_1101-2021_01_08_425885	715	15	empirical	empirical	JJ
10_1101-2021_01_08_425885	715	16	values	value	NNS
10_1101-2021_01_08_425885	715	17	(	(	-LRB-
10_1101-2021_01_08_425885	715	18	z̃m(x	z̃m(x	NNP
10_1101-2021_01_08_425885	715	19	;	;	:
10_1101-2021_01_08_425885	715	20	f	f	LS
10_1101-2021_01_08_425885	715	21	)	)	-RRB-
10_1101-2021_01_08_425885	715	22	in	in	IN
10_1101-2021_01_08_425885	715	23	Equation	Equation	NNP
10_1101-2021_01_08_425885	715	24	11	11	CD
10_1101-2021_01_08_425885	715	25	)	)	-RRB-
10_1101-2021_01_08_425885	715	26	is	be	VBZ
10_1101-2021_01_08_425885	715	27	shown	show	VBN
10_1101-2021_01_08_425885	715	28	for	for	IN
10_1101-2021_01_08_425885	715	29	m	m	NNP
10_1101-2021_01_08_425885	715	30	=	=	SYM
10_1101-2021_01_08_425885	715	31	49	49	CD
10_1101-2021_01_08_425885	715	32	and	and	CC
10_1101-2021_01_08_425885	715	33	f	f	NNP
10_1101-2021_01_08_425885	715	34	=	=	SYM
10_1101-2021_01_08_425885	715	35	0.23	0.23	CD
10_1101-2021_01_08_425885	715	36	(	(	-LRB-
10_1101-2021_01_08_425885	715	37	solid	solid	JJ
10_1101-2021_01_08_425885	715	38	green	green	NN
10_1101-2021_01_08_425885	715	39	)	)	-RRB-
10_1101-2021_01_08_425885	715	40	.	.	.
10_1101-2021_01_08_425885	716	1	f	f	NNP
10_1101-2021_01_08_425885	716	2	signifies	signify	VBZ
10_1101-2021_01_08_425885	716	3	that	that	IN
10_1101-2021_01_08_425885	716	4	the	the	DT
10_1101-2021_01_08_425885	716	5	fractional	fractional	JJ
10_1101-2021_01_08_425885	716	6	error	error	NN
10_1101-2021_01_08_425885	716	7	of	of	IN
10_1101-2021_01_08_425885	716	8	the	the	DT
10_1101-2021_01_08_425885	716	9	interpolated	interpolate	VBN
10_1101-2021_01_08_425885	716	10	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	716	11	is	be	VBZ
10_1101-2021_01_08_425885	716	12	reduced	reduce	VBN
10_1101-2021_01_08_425885	716	13	by	by	IN
10_1101-2021_01_08_425885	716	14	1−f	1−f	CD
10_1101-2021_01_08_425885	716	15	relative	relative	JJ
10_1101-2021_01_08_425885	716	16	to	to	IN
10_1101-2021_01_08_425885	716	17	the	the	DT
10_1101-2021_01_08_425885	716	18	empirical	empirical	JJ
10_1101-2021_01_08_425885	716	19	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	716	20	.	.	.
10_1101-2021_01_08_425885	717	1	f	f	LS
10_1101-2021_01_08_425885	717	2	=	=	SYM
10_1101-2021_01_08_425885	717	3	0	0	CD
10_1101-2021_01_08_425885	717	4	corresponds	correspond	NNS
10_1101-2021_01_08_425885	717	5	to	to	IN
10_1101-2021_01_08_425885	717	6	the	the	DT
10_1101-2021_01_08_425885	717	7	analytical	analytical	JJ
10_1101-2021_01_08_425885	717	8	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	717	9	while	while	IN
10_1101-2021_01_08_425885	717	10	f	f	NN
10_1101-2021_01_08_425885	717	11	=	=	SYM
10_1101-2021_01_08_425885	717	12	1	1	CD
10_1101-2021_01_08_425885	717	13	corresponds	correspond	NNS
10_1101-2021_01_08_425885	717	14	to	to	IN
10_1101-2021_01_08_425885	717	15	the	the	DT
10_1101-2021_01_08_425885	717	16	empirical	empirical	JJ
10_1101-2021_01_08_425885	717	17	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	717	18	.	.	.
10_1101-2021_01_08_425885	718	1	The	the	DT
10_1101-2021_01_08_425885	718	2	white	white	JJ
10_1101-2021_01_08_425885	718	3	region	region	NN
10_1101-2021_01_08_425885	718	4	bounded	bound	VBN
10_1101-2021_01_08_425885	718	5	by	by	IN
10_1101-2021_01_08_425885	718	6	[	[	-LRB-
10_1101-2021_01_08_425885	718	7	x1,x2	x1,x2	NNP
10_1101-2021_01_08_425885	718	8	]	]	-RRB-
10_1101-2021_01_08_425885	718	9	indicates	indicate	VBZ
10_1101-2021_01_08_425885	718	10	a	a	DT
10_1101-2021_01_08_425885	718	11	candidate	candidate	NN
10_1101-2021_01_08_425885	718	12	interval	interval	NN
10_1101-2021_01_08_425885	718	13	over	over	IN
10_1101-2021_01_08_425885	718	14	which	which	WDT
10_1101-2021_01_08_425885	718	15	to	to	TO
10_1101-2021_01_08_425885	718	16	fit	fit	VB
10_1101-2021_01_08_425885	718	17	a	a	DT
10_1101-2021_01_08_425885	718	18	heat	heat	NN
10_1101-2021_01_08_425885	718	19	-	-	HYPH
10_1101-2021_01_08_425885	718	20	trace	trace	NN
10_1101-2021_01_08_425885	718	21	to	to	IN
10_1101-2021_01_08_425885	718	22	a	a	DT
10_1101-2021_01_08_425885	718	23	quadratic	quadratic	NN
10_1101-2021_01_08_425885	718	24	in	in	IN
10_1101-2021_01_08_425885	718	25	order	order	NN
10_1101-2021_01_08_425885	718	26	to	to	TO
10_1101-2021_01_08_425885	718	27	extract	extract	VB
10_1101-2021_01_08_425885	718	28	an	an	DT
10_1101-2021_01_08_425885	718	29	estimate	estimate	NN
10_1101-2021_01_08_425885	718	30	for	for	IN
10_1101-2021_01_08_425885	718	31	the	the	DT
10_1101-2021_01_08_425885	718	32	scalar	scalar	JJ
10_1101-2021_01_08_425885	718	33	curvature	curvature	NN
10_1101-2021_01_08_425885	718	34	(	(	-LRB-
10_1101-2021_01_08_425885	718	35	see	see	VB
10_1101-2021_01_08_425885	718	36	Equations	Equations	NNP
10_1101-2021_01_08_425885	718	37	2	2	CD
10_1101-2021_01_08_425885	718	38	-	-	SYM
10_1101-2021_01_08_425885	718	39	4	4	CD
10_1101-2021_01_08_425885	718	40	;	;	:
10_1101-2021_01_08_425885	718	41	Methods	Methods	NNP
10_1101-2021_01_08_425885	718	42	Section	Section	NNP
10_1101-2021_01_08_425885	718	43	4.2.1	4.2.1	CD
10_1101-2021_01_08_425885	718	44	)	)	-RRB-
10_1101-2021_01_08_425885	718	45	.	.	.
10_1101-2021_01_08_425885	719	1	On	on	IN
10_1101-2021_01_08_425885	719	2	the	the	DT
10_1101-2021_01_08_425885	719	3	one	one	CD
10_1101-2021_01_08_425885	719	4	hand	hand	NN
10_1101-2021_01_08_425885	719	5	,	,	,
10_1101-2021_01_08_425885	719	6	since	since	IN
10_1101-2021_01_08_425885	719	7	the	the	DT
10_1101-2021_01_08_425885	719	8	knee	knee	NN
10_1101-2021_01_08_425885	719	9	of	of	IN
10_1101-2021_01_08_425885	719	10	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	719	11	)	)	-RRB-
10_1101-2021_01_08_425885	719	12	shifts	shift	VBZ
10_1101-2021_01_08_425885	719	13	to	to	IN
10_1101-2021_01_08_425885	719	14	the	the	DT
10_1101-2021_01_08_425885	719	15	left	left	NN
10_1101-2021_01_08_425885	719	16	as	as	IN
10_1101-2021_01_08_425885	719	17	m	m	NNP
10_1101-2021_01_08_425885	719	18	increases	increase	NNS
10_1101-2021_01_08_425885	719	19	(	(	-LRB-
10_1101-2021_01_08_425885	719	20	i.e.	i.e.	FW
10_1101-2021_01_08_425885	720	1	zm(x	zm(x	JJ
10_1101-2021_01_08_425885	720	2	)	)	-RRB-
10_1101-2021_01_08_425885	720	3	converges	converge	NNS
10_1101-2021_01_08_425885	720	4	from	from	IN
10_1101-2021_01_08_425885	720	5	∞	∞	NNP
10_1101-2021_01_08_425885	720	6	)	)	-RRB-
10_1101-2021_01_08_425885	720	7	,	,	,
10_1101-2021_01_08_425885	720	8	larger	large	JJR
10_1101-2021_01_08_425885	720	9	m	m	NN
10_1101-2021_01_08_425885	720	10	results	result	NNS
10_1101-2021_01_08_425885	720	11	in	in	IN
10_1101-2021_01_08_425885	720	12	more	more	JJR
10_1101-2021_01_08_425885	720	13	intervals	interval	NNS
10_1101-2021_01_08_425885	720	14	for	for	IN
10_1101-2021_01_08_425885	720	15	which	which	WDT
10_1101-2021_01_08_425885	720	16	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	720	17	)	)	-RRB-
10_1101-2021_01_08_425885	720	18	well	well	RB
10_1101-2021_01_08_425885	720	19	-	-	HYPH
10_1101-2021_01_08_425885	720	20	approximates	approximate	NNS
10_1101-2021_01_08_425885	720	21	z∞(x	z∞(x	NN
10_1101-2021_01_08_425885	720	22	)	)	-RRB-
10_1101-2021_01_08_425885	720	23	and	and	CC
10_1101-2021_01_08_425885	720	24	will	will	MD
10_1101-2021_01_08_425885	720	25	therefore	therefore	RB
10_1101-2021_01_08_425885	720	26	yield	yield	VB
10_1101-2021_01_08_425885	720	27	accurate	accurate	JJ
10_1101-2021_01_08_425885	720	28	scalar	scalar	JJ
10_1101-2021_01_08_425885	720	29	curvature	curvature	NN
10_1101-2021_01_08_425885	720	30	estimates	estimate	NNS
10_1101-2021_01_08_425885	720	31	.	.	.
10_1101-2021_01_08_425885	721	1	On	on	IN
10_1101-2021_01_08_425885	721	2	the	the	DT
10_1101-2021_01_08_425885	721	3	other	other	JJ
10_1101-2021_01_08_425885	721	4	hand	hand	NN
10_1101-2021_01_08_425885	721	5	,	,	,
10_1101-2021_01_08_425885	721	6	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	721	7	)	)	-RRB-
10_1101-2021_01_08_425885	721	8	becomes	become	VBZ
10_1101-2021_01_08_425885	721	9	a	a	DT
10_1101-2021_01_08_425885	721	10	worse	bad	JJR
10_1101-2021_01_08_425885	721	11	estimator	estimator	NN
10_1101-2021_01_08_425885	721	12	for	for	IN
10_1101-2021_01_08_425885	721	13	zm(x	zm(x	NNP
10_1101-2021_01_08_425885	721	14	)	)	-RRB-
10_1101-2021_01_08_425885	721	15	as	as	IN
10_1101-2021_01_08_425885	721	16	m	m	NNP
10_1101-2021_01_08_425885	721	17	increases	increase	NNS
10_1101-2021_01_08_425885	721	18	.	.	.
10_1101-2021_01_08_425885	722	1	(	(	-LRB-
10_1101-2021_01_08_425885	722	2	B	b	NN
10_1101-2021_01_08_425885	722	3	)	)	-RRB-
10_1101-2021_01_08_425885	722	4	Scalar	Scalar	NNP
10_1101-2021_01_08_425885	722	5	curvatures	curvature	NNS
10_1101-2021_01_08_425885	722	6	estimated	estimate	VBN
10_1101-2021_01_08_425885	722	7	by	by	IN
10_1101-2021_01_08_425885	722	8	fitting	fit	VBG
10_1101-2021_01_08_425885	722	9	z∞(x	z∞(x	NN
10_1101-2021_01_08_425885	722	10	)	)	-RRB-
10_1101-2021_01_08_425885	722	11	to	to	IN
10_1101-2021_01_08_425885	722	12	a	a	DT
10_1101-2021_01_08_425885	722	13	quadratic	quadratic	NN
10_1101-2021_01_08_425885	722	14	over	over	IN
10_1101-2021_01_08_425885	722	15	different	different	JJ
10_1101-2021_01_08_425885	722	16	intervals	interval	NNS
10_1101-2021_01_08_425885	722	17	[	[	-LRB-
10_1101-2021_01_08_425885	722	18	x1,x2	x1,x2	NNP
10_1101-2021_01_08_425885	722	19	]	]	-RRB-
10_1101-2021_01_08_425885	722	20	as	as	IN
10_1101-2021_01_08_425885	722	21	defined	define	VBN
10_1101-2021_01_08_425885	722	22	in	in	IN
10_1101-2021_01_08_425885	722	23	(	(	-LRB-
10_1101-2021_01_08_425885	722	24	A	a	NN
10_1101-2021_01_08_425885	722	25	)	)	-RRB-
10_1101-2021_01_08_425885	722	26	.	.	.
10_1101-2021_01_08_425885	723	1	Scalar	scalar	JJ
10_1101-2021_01_08_425885	723	2	curvatures	curvature	NNS
10_1101-2021_01_08_425885	723	3	are	be	VBP
10_1101-2021_01_08_425885	723	4	shown	show	VBN
10_1101-2021_01_08_425885	723	5	in	in	IN
10_1101-2021_01_08_425885	723	6	color	color	NN
10_1101-2021_01_08_425885	723	7	for	for	IN
10_1101-2021_01_08_425885	723	8	intervals	interval	NNS
10_1101-2021_01_08_425885	723	9	yielding	yield	VBG
10_1101-2021_01_08_425885	723	10	accurate	accurate	JJ
10_1101-2021_01_08_425885	723	11	estimates	estimate	NNS
10_1101-2021_01_08_425885	723	12	(	(	-LRB-
10_1101-2021_01_08_425885	723	13	S	s	NN
10_1101-2021_01_08_425885	723	14	∈	∈	NNP
10_1101-2021_01_08_425885	723	15	[	[	-LRB-
10_1101-2021_01_08_425885	723	16	1.5	1.5	CD
10_1101-2021_01_08_425885	723	17	,	,	,
10_1101-2021_01_08_425885	723	18	2.5	2.5	CD
10_1101-2021_01_08_425885	723	19	]	]	-RRB-
10_1101-2021_01_08_425885	723	20	)	)	-RRB-
10_1101-2021_01_08_425885	723	21	.	.	.
10_1101-2021_01_08_425885	724	1	This	this	DT
10_1101-2021_01_08_425885	724	2	colored	colored	JJ
10_1101-2021_01_08_425885	724	3	region	region	NN
10_1101-2021_01_08_425885	724	4	corresponds	correspond	VBZ
10_1101-2021_01_08_425885	724	5	to	to	IN
10_1101-2021_01_08_425885	724	6	D∞.	d∞.	ADD
10_1101-2021_01_08_425885	725	1	(	(	-LRB-
10_1101-2021_01_08_425885	725	2	C	C	NNP
10_1101-2021_01_08_425885	725	3	)	)	-RRB-
10_1101-2021_01_08_425885	725	4	As	as	IN
10_1101-2021_01_08_425885	725	5	in	in	IN
10_1101-2021_01_08_425885	725	6	(	(	-LRB-
10_1101-2021_01_08_425885	725	7	B	b	NN
10_1101-2021_01_08_425885	725	8	)	)	-RRB-
10_1101-2021_01_08_425885	725	9	but	but	CC
10_1101-2021_01_08_425885	725	10	with	with	IN
10_1101-2021_01_08_425885	725	11	estimates	estimate	NNS
10_1101-2021_01_08_425885	725	12	obtained	obtain	VBN
10_1101-2021_01_08_425885	725	13	by	by	IN
10_1101-2021_01_08_425885	725	14	fitting	fit	VBG
10_1101-2021_01_08_425885	725	15	a	a	DT
10_1101-2021_01_08_425885	725	16	quadratic	quadratic	NN
10_1101-2021_01_08_425885	725	17	to	to	IN
10_1101-2021_01_08_425885	725	18	z1000(x	z1000(x	NNP
10_1101-2021_01_08_425885	725	19	)	)	-RRB-
10_1101-2021_01_08_425885	725	20	.	.	.
10_1101-2021_01_08_425885	726	1	The	the	DT
10_1101-2021_01_08_425885	726	2	colored	colored	JJ
10_1101-2021_01_08_425885	726	3	region	region	NN
10_1101-2021_01_08_425885	726	4	corresponds	correspond	VBZ
10_1101-2021_01_08_425885	726	5	to	to	IN
10_1101-2021_01_08_425885	726	6	D1000	D1000	NNP
10_1101-2021_01_08_425885	726	7	.	.	.
10_1101-2021_01_08_425885	727	1	By	by	IN
10_1101-2021_01_08_425885	727	2	inspection	inspection	NN
10_1101-2021_01_08_425885	727	3	,	,	,
10_1101-2021_01_08_425885	727	4	D1000	D1000	NNP
10_1101-2021_01_08_425885	727	5	⊂	⊂	CD
10_1101-2021_01_08_425885	727	6	D∞.	d∞.	NN
10_1101-2021_01_08_425885	728	1	(	(	-LRB-
10_1101-2021_01_08_425885	728	2	D	D	NNP
10_1101-2021_01_08_425885	728	3	)	)	-RRB-
10_1101-2021_01_08_425885	728	4	Scalar	scalar	JJ
10_1101-2021_01_08_425885	728	5	curvatures	curvature	NNS
10_1101-2021_01_08_425885	728	6	estimated	estimate	VBN
10_1101-2021_01_08_425885	728	7	by	by	IN
10_1101-2021_01_08_425885	728	8	fitting	fit	VBG
10_1101-2021_01_08_425885	728	9	z1000(x	z1000(x	NNP
10_1101-2021_01_08_425885	728	10	)	)	-RRB-
10_1101-2021_01_08_425885	728	11	to	to	IN
10_1101-2021_01_08_425885	728	12	a	a	DT
10_1101-2021_01_08_425885	728	13	quadratic	quadratic	NN
10_1101-2021_01_08_425885	728	14	over	over	IN
10_1101-2021_01_08_425885	728	15	each	each	DT
10_1101-2021_01_08_425885	728	16	interval	interval	NN
10_1101-2021_01_08_425885	728	17	in	in	IN
10_1101-2021_01_08_425885	728	18	D1000	D1000	NNP
10_1101-2021_01_08_425885	728	19	.	.	.
10_1101-2021_01_08_425885	729	1	Though	though	IN
10_1101-2021_01_08_425885	729	2	D1000	D1000	NNP
10_1101-2021_01_08_425885	729	3	was	be	VBD
10_1101-2021_01_08_425885	729	4	constructed	construct	VBN
10_1101-2021_01_08_425885	729	5	using	use	VBG
10_1101-2021_01_08_425885	729	6	only	only	JJ
10_1101-2021_01_08_425885	729	7	intervals	interval	NNS
10_1101-2021_01_08_425885	729	8	which	which	WDT
10_1101-2021_01_08_425885	729	9	yielded	yield	VBD
10_1101-2021_01_08_425885	729	10	an	an	DT
10_1101-2021_01_08_425885	729	11	accurate	accurate	JJ
10_1101-2021_01_08_425885	729	12	scalar	scalar	JJ
10_1101-2021_01_08_425885	729	13	curvature	curvature	JJ
10_1101-2021_01_08_425885	729	14	estimate	estimate	NN
10_1101-2021_01_08_425885	729	15	when	when	WRB
10_1101-2021_01_08_425885	729	16	analytical	analytical	JJ
10_1101-2021_01_08_425885	729	17	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	729	18	were	be	VBD
10_1101-2021_01_08_425885	729	19	used	use	VBN
10_1101-2021_01_08_425885	729	20	in	in	IN
10_1101-2021_01_08_425885	729	21	the	the	DT
10_1101-2021_01_08_425885	729	22	heat	heat	NN
10_1101-2021_01_08_425885	729	23	-	-	HYPH
10_1101-2021_01_08_425885	729	24	trace	trace	NN
10_1101-2021_01_08_425885	729	25	,	,	,
10_1101-2021_01_08_425885	729	26	no	no	DT
10_1101-2021_01_08_425885	729	27	interval	interval	NN
10_1101-2021_01_08_425885	729	28	in	in	IN
10_1101-2021_01_08_425885	729	29	D1000	D1000	NNP
10_1101-2021_01_08_425885	729	30	yields	yield	VBZ
10_1101-2021_01_08_425885	729	31	an	an	DT
10_1101-2021_01_08_425885	729	32	accurate	accurate	JJ
10_1101-2021_01_08_425885	729	33	scalar	scalar	JJ
10_1101-2021_01_08_425885	729	34	curvature	curvature	JJ
10_1101-2021_01_08_425885	729	35	estimate	estimate	NN
10_1101-2021_01_08_425885	729	36	when	when	WRB
10_1101-2021_01_08_425885	729	37	the	the	DT
10_1101-2021_01_08_425885	729	38	same	same	JJ
10_1101-2021_01_08_425885	729	39	number	number	NN
10_1101-2021_01_08_425885	729	40	of	of	IN
10_1101-2021_01_08_425885	729	41	empirical	empirical	JJ
10_1101-2021_01_08_425885	729	42	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	729	43	are	be	VBP
10_1101-2021_01_08_425885	729	44	used	use	VBN
10_1101-2021_01_08_425885	729	45	in	in	IN
10_1101-2021_01_08_425885	729	46	the	the	DT
10_1101-2021_01_08_425885	729	47	heat	heat	NN
10_1101-2021_01_08_425885	729	48	-	-	HYPH
10_1101-2021_01_08_425885	729	49	trace	trace	NN
10_1101-2021_01_08_425885	729	50	instead	instead	RB
10_1101-2021_01_08_425885	729	51	.	.	.
10_1101-2021_01_08_425885	730	1	(	(	-LRB-
10_1101-2021_01_08_425885	730	2	E	e	NN
10_1101-2021_01_08_425885	730	3	)	)	-RRB-
10_1101-2021_01_08_425885	730	4	As	as	IN
10_1101-2021_01_08_425885	730	5	in	in	IN
10_1101-2021_01_08_425885	730	6	(	(	-LRB-
10_1101-2021_01_08_425885	730	7	B	b	NN
10_1101-2021_01_08_425885	730	8	)	)	-RRB-
10_1101-2021_01_08_425885	730	9	but	but	CC
10_1101-2021_01_08_425885	730	10	with	with	IN
10_1101-2021_01_08_425885	730	11	estimates	estimate	NNS
10_1101-2021_01_08_425885	730	12	obtained	obtain	VBN
10_1101-2021_01_08_425885	730	13	by	by	IN
10_1101-2021_01_08_425885	730	14	fitting	fit	VBG
10_1101-2021_01_08_425885	730	15	a	a	DT
10_1101-2021_01_08_425885	730	16	quadratic	quadratic	NN
10_1101-2021_01_08_425885	730	17	to	to	IN
10_1101-2021_01_08_425885	730	18	z49(x	z49(x	NNP
10_1101-2021_01_08_425885	730	19	)	)	-RRB-
10_1101-2021_01_08_425885	730	20	.	.	.
10_1101-2021_01_08_425885	731	1	The	the	DT
10_1101-2021_01_08_425885	731	2	colored	colored	JJ
10_1101-2021_01_08_425885	731	3	region	region	NN
10_1101-2021_01_08_425885	731	4	corresponds	correspond	VBZ
10_1101-2021_01_08_425885	731	5	to	to	IN
10_1101-2021_01_08_425885	731	6	D49	D49	NNP
10_1101-2021_01_08_425885	731	7	.	.	.
10_1101-2021_01_08_425885	732	1	By	by	IN
10_1101-2021_01_08_425885	732	2	inspection	inspection	NN
10_1101-2021_01_08_425885	732	3	,	,	,
10_1101-2021_01_08_425885	732	4	D49	D49	NNP
10_1101-2021_01_08_425885	732	5	⊂	⊂	CD
10_1101-2021_01_08_425885	732	6	D1000	D1000	NNP
10_1101-2021_01_08_425885	732	7	(	(	-LRB-
10_1101-2021_01_08_425885	732	8	F	F	NNP
10_1101-2021_01_08_425885	732	9	)	)	-RRB-
10_1101-2021_01_08_425885	732	10	As	as	IN
10_1101-2021_01_08_425885	732	11	in	in	IN
10_1101-2021_01_08_425885	732	12	(	(	-LRB-
10_1101-2021_01_08_425885	732	13	D	d	NN
10_1101-2021_01_08_425885	732	14	)	)	-RRB-
10_1101-2021_01_08_425885	732	15	but	but	CC
10_1101-2021_01_08_425885	732	16	with	with	IN
10_1101-2021_01_08_425885	732	17	estimates	estimate	NNS
10_1101-2021_01_08_425885	732	18	obtained	obtain	VBN
10_1101-2021_01_08_425885	732	19	by	by	IN
10_1101-2021_01_08_425885	732	20	fitting	fit	VBG
10_1101-2021_01_08_425885	732	21	z49(x	z49(x	NNP
10_1101-2021_01_08_425885	732	22	)	)	-RRB-
10_1101-2021_01_08_425885	732	23	to	to	IN
10_1101-2021_01_08_425885	732	24	a	a	DT
10_1101-2021_01_08_425885	732	25	quadratic	quadratic	NN
10_1101-2021_01_08_425885	732	26	over	over	IN
10_1101-2021_01_08_425885	732	27	each	each	DT
10_1101-2021_01_08_425885	732	28	interval	interval	NN
10_1101-2021_01_08_425885	732	29	in	in	IN
10_1101-2021_01_08_425885	732	30	D49	D49	NNP
10_1101-2021_01_08_425885	732	31	.	.	.
10_1101-2021_01_08_425885	733	1	No	no	DT
10_1101-2021_01_08_425885	733	2	estimate	estimate	NN
10_1101-2021_01_08_425885	733	3	is	be	VBZ
10_1101-2021_01_08_425885	733	4	accurate	accurate	JJ
10_1101-2021_01_08_425885	733	5	just	just	RB
10_1101-2021_01_08_425885	733	6	as	as	IN
10_1101-2021_01_08_425885	733	7	in	in	IN
10_1101-2021_01_08_425885	733	8	(	(	-LRB-
10_1101-2021_01_08_425885	733	9	D	d	NN
10_1101-2021_01_08_425885	733	10	)	)	-RRB-
10_1101-2021_01_08_425885	733	11	.	.	.
10_1101-2021_01_08_425885	734	1	(	(	-LRB-
10_1101-2021_01_08_425885	734	2	G	g	NN
10_1101-2021_01_08_425885	734	3	)	)	-RRB-
10_1101-2021_01_08_425885	734	4	As	as	IN
10_1101-2021_01_08_425885	734	5	in	in	IN
10_1101-2021_01_08_425885	734	6	(	(	-LRB-
10_1101-2021_01_08_425885	734	7	F	f	NN
10_1101-2021_01_08_425885	734	8	)	)	-RRB-
10_1101-2021_01_08_425885	734	9	but	but	CC
10_1101-2021_01_08_425885	734	10	with	with	IN
10_1101-2021_01_08_425885	734	11	estimates	estimate	NNS
10_1101-2021_01_08_425885	734	12	obtained	obtain	VBN
10_1101-2021_01_08_425885	734	13	by	by	IN
10_1101-2021_01_08_425885	734	14	fitting	fit	VBG
10_1101-2021_01_08_425885	734	15	z̃49(x	z̃49(x	NNS
10_1101-2021_01_08_425885	734	16	;	;	:
10_1101-2021_01_08_425885	734	17	f	f	NNP
10_1101-2021_01_08_425885	734	18	=	=	SYM
10_1101-2021_01_08_425885	734	19	0.23	0.23	CD
10_1101-2021_01_08_425885	734	20	)	)	-RRB-
10_1101-2021_01_08_425885	734	21	to	to	IN
10_1101-2021_01_08_425885	734	22	a	a	DT
10_1101-2021_01_08_425885	734	23	quadratic	quadratic	NN
10_1101-2021_01_08_425885	734	24	over	over	IN
10_1101-2021_01_08_425885	734	25	each	each	DT
10_1101-2021_01_08_425885	734	26	interval	interval	NN
10_1101-2021_01_08_425885	734	27	in	in	IN
10_1101-2021_01_08_425885	734	28	D49	D49	NNP
10_1101-2021_01_08_425885	734	29	.	.	.
10_1101-2021_01_08_425885	735	1	f	f	LS
10_1101-2021_01_08_425885	735	2	=	=	SYM
10_1101-2021_01_08_425885	735	3	0.23	0.23	CD
10_1101-2021_01_08_425885	735	4	was	be	VBD
10_1101-2021_01_08_425885	735	5	chosen	choose	VBN
10_1101-2021_01_08_425885	735	6	so	so	IN
10_1101-2021_01_08_425885	735	7	that	that	IN
10_1101-2021_01_08_425885	735	8	half	half	PDT
10_1101-2021_01_08_425885	735	9	the	the	DT
10_1101-2021_01_08_425885	735	10	intervals	interval	NNS
10_1101-2021_01_08_425885	735	11	in	in	IN
10_1101-2021_01_08_425885	735	12	D49	D49	NNP
10_1101-2021_01_08_425885	735	13	yield	yield	VBP
10_1101-2021_01_08_425885	735	14	an	an	DT
10_1101-2021_01_08_425885	735	15	accurate	accurate	JJ
10_1101-2021_01_08_425885	735	16	scalar	scalar	JJ
10_1101-2021_01_08_425885	735	17	curvature	curvature	NN
10_1101-2021_01_08_425885	735	18	estimate	estimate	NN
10_1101-2021_01_08_425885	735	19	.	.	.
10_1101-2021_01_08_425885	736	1	(	(	-LRB-
10_1101-2021_01_08_425885	736	2	H	h	NN
10_1101-2021_01_08_425885	736	3	)	)	-RRB-
10_1101-2021_01_08_425885	736	4	(	(	-LRB-
10_1101-2021_01_08_425885	736	5	Left	leave	VBN
10_1101-2021_01_08_425885	736	6	)	)	-RRB-
10_1101-2021_01_08_425885	736	7	The	the	DT
10_1101-2021_01_08_425885	736	8	fractional	fractional	JJ
10_1101-2021_01_08_425885	736	9	error	error	NN
10_1101-2021_01_08_425885	736	10	in	in	IN
10_1101-2021_01_08_425885	736	11	the	the	DT
10_1101-2021_01_08_425885	736	12	first	first	JJ
10_1101-2021_01_08_425885	736	13	49	49	CD
10_1101-2021_01_08_425885	736	14	empirical	empirical	JJ
10_1101-2021_01_08_425885	736	15	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	736	16	of	of	IN
10_1101-2021_01_08_425885	736	17	the	the	DT
10_1101-2021_01_08_425885	736	18	LB	LB	NNP
10_1101-2021_01_08_425885	736	19	estimator	estimator	NN
10_1101-2021_01_08_425885	736	20	from	from	IN
10_1101-2021_01_08_425885	736	21	(	(	-LRB-
10_1101-2021_01_08_425885	736	22	A	a	NN
10_1101-2021_01_08_425885	736	23	)	)	-RRB-
10_1101-2021_01_08_425885	736	24	is	be	VBZ
10_1101-2021_01_08_425885	736	25	shown	show	VBN
10_1101-2021_01_08_425885	736	26	in	in	IN
10_1101-2021_01_08_425885	736	27	red	red	NN
10_1101-2021_01_08_425885	736	28	.	.	.
10_1101-2021_01_08_425885	737	1	This	this	DT
10_1101-2021_01_08_425885	737	2	operator	operator	NN
10_1101-2021_01_08_425885	737	3	was	be	VBD
10_1101-2021_01_08_425885	737	4	computed	compute	VBN
10_1101-2021_01_08_425885	737	5	using	use	VBG
10_1101-2021_01_08_425885	737	6	the	the	DT
10_1101-2021_01_08_425885	737	7	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	737	8	kernel	kernel	NN
10_1101-2021_01_08_425885	737	9	(	(	-LRB-
10_1101-2021_01_08_425885	737	10	Wg	Wg	NNP
10_1101-2021_01_08_425885	737	11	in	in	IN
10_1101-2021_01_08_425885	737	12	Equation	Equation	NNP
10_1101-2021_01_08_425885	737	13	15	15	CD
10_1101-2021_01_08_425885	737	14	)	)	-RRB-
10_1101-2021_01_08_425885	737	15	.	.	.
10_1101-2021_01_08_425885	738	1	Eigenvalues	Eigenvalues	NNP
10_1101-2021_01_08_425885	738	2	37	37	CD
10_1101-2021_01_08_425885	738	3	-	-	SYM
10_1101-2021_01_08_425885	738	4	49	49	CD
10_1101-2021_01_08_425885	738	5	have	have	VBP
10_1101-2021_01_08_425885	738	6	a	a	DT
10_1101-2021_01_08_425885	738	7	fractional	fractional	JJ
10_1101-2021_01_08_425885	738	8	error	error	NN
10_1101-2021_01_08_425885	738	9	of	of	IN
10_1101-2021_01_08_425885	738	10	60	60	CD
10_1101-2021_01_08_425885	738	11	%	%	NN
10_1101-2021_01_08_425885	738	12	.	.	.
10_1101-2021_01_08_425885	739	1	The	the	DT
10_1101-2021_01_08_425885	739	2	fractional	fractional	JJ
10_1101-2021_01_08_425885	739	3	error	error	NN
10_1101-2021_01_08_425885	739	4	of	of	IN
10_1101-2021_01_08_425885	739	5	the	the	DT
10_1101-2021_01_08_425885	739	6	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	739	7	of	of	IN
10_1101-2021_01_08_425885	739	8	LB	LB	NNP
10_1101-2021_01_08_425885	739	9	estimators	estimator	NNS
10_1101-2021_01_08_425885	739	10	computed	compute	VBD
10_1101-2021_01_08_425885	739	11	on	on	IN
10_1101-2021_01_08_425885	739	12	the	the	DT
10_1101-2021_01_08_425885	739	13	same	same	JJ
10_1101-2021_01_08_425885	739	14	N	n	NN
10_1101-2021_01_08_425885	739	15	=	=	SYM
10_1101-2021_01_08_425885	739	16	104	104	CD
10_1101-2021_01_08_425885	739	17	points	point	NNS
10_1101-2021_01_08_425885	739	18	but	but	CC
10_1101-2021_01_08_425885	739	19	using	use	VBG
10_1101-2021_01_08_425885	739	20	the	the	DT
10_1101-2021_01_08_425885	739	21	weighted	weighted	JJ
10_1101-2021_01_08_425885	739	22	kNN	kNN	NNS
10_1101-2021_01_08_425885	739	23	and	and	CC
10_1101-2021_01_08_425885	739	24	r	r	NN
10_1101-2021_01_08_425885	739	25	-	-	HYPH
10_1101-2021_01_08_425885	739	26	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	739	27	kernels	kernel	NNS
10_1101-2021_01_08_425885	739	28	(	(	-LRB-
10_1101-2021_01_08_425885	739	29	WkNN	WkNN	NNP
10_1101-2021_01_08_425885	739	30	and	and	CC
10_1101-2021_01_08_425885	739	31	Wr	Wr	NNP
10_1101-2021_01_08_425885	739	32	respectively	respectively	RB
10_1101-2021_01_08_425885	739	33	in	in	IN
10_1101-2021_01_08_425885	739	34	Equation	Equation	NNP
10_1101-2021_01_08_425885	739	35	16	16	CD
10_1101-2021_01_08_425885	739	36	)	)	-RRB-
10_1101-2021_01_08_425885	739	37	is	be	VBZ
10_1101-2021_01_08_425885	739	38	also	also	RB
10_1101-2021_01_08_425885	739	39	plotted	plot	VBN
10_1101-2021_01_08_425885	739	40	.	.	.
10_1101-2021_01_08_425885	740	1	Positive	positive	JJ
10_1101-2021_01_08_425885	740	2	error	error	NN
10_1101-2021_01_08_425885	740	3	indicates	indicate	VBZ
10_1101-2021_01_08_425885	740	4	under	under	IN
10_1101-2021_01_08_425885	740	5	-	-	HYPH
10_1101-2021_01_08_425885	740	6	estimation	estimation	NN
10_1101-2021_01_08_425885	740	7	.	.	.
10_1101-2021_01_08_425885	741	1	(	(	-LRB-
10_1101-2021_01_08_425885	741	2	Right	right	UH
10_1101-2021_01_08_425885	741	3	)	)	-RRB-
10_1101-2021_01_08_425885	741	4	Projected	project	VBN
10_1101-2021_01_08_425885	741	5	fractional	fractional	JJ
10_1101-2021_01_08_425885	741	6	error	error	NN
10_1101-2021_01_08_425885	741	7	for	for	IN
10_1101-2021_01_08_425885	741	8	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	741	9	37	37	CD
10_1101-2021_01_08_425885	741	10	-	-	SYM
10_1101-2021_01_08_425885	741	11	49	49	CD
10_1101-2021_01_08_425885	741	12	of	of	IN
10_1101-2021_01_08_425885	741	13	the	the	DT
10_1101-2021_01_08_425885	741	14	LB	LB	NNP
10_1101-2021_01_08_425885	741	15	estimator	estimator	NN
10_1101-2021_01_08_425885	741	16	with	with	IN
10_1101-2021_01_08_425885	741	17	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	741	18	kernel	kernel	NN
10_1101-2021_01_08_425885	741	19	computed	compute	VBD
10_1101-2021_01_08_425885	741	20	using	use	VBG
10_1101-2021_01_08_425885	741	21	a	a	DT
10_1101-2021_01_08_425885	741	22	larger	large	JJR
10_1101-2021_01_08_425885	741	23	sample	sample	NN
10_1101-2021_01_08_425885	741	24	size	size	NN
10_1101-2021_01_08_425885	741	25	(	(	-LRB-
10_1101-2021_01_08_425885	741	26	N	n	NN
10_1101-2021_01_08_425885	741	27	)	)	-RRB-
10_1101-2021_01_08_425885	741	28	.	.	.
10_1101-2021_01_08_425885	742	1	The	the	DT
10_1101-2021_01_08_425885	742	2	projection	projection	NN
10_1101-2021_01_08_425885	742	3	is	be	VBZ
10_1101-2021_01_08_425885	742	4	based	base	VBN
10_1101-2021_01_08_425885	742	5	on	on	IN
10_1101-2021_01_08_425885	742	6	the	the	DT
10_1101-2021_01_08_425885	742	7	convergence	convergence	NN
10_1101-2021_01_08_425885	742	8	rate	rate	NN
10_1101-2021_01_08_425885	742	9	given	give	VBN
10_1101-2021_01_08_425885	742	10	in	in	IN
10_1101-2021_01_08_425885	742	11	Theorem	theorem	NN
10_1101-2021_01_08_425885	742	12	1	1	CD
10_1101-2021_01_08_425885	742	13	of	of	IN
10_1101-2021_01_08_425885	742	14	[	[	-LRB-
10_1101-2021_01_08_425885	742	15	30	30	CD
10_1101-2021_01_08_425885	742	16	]	]	-RRB-
10_1101-2021_01_08_425885	742	17	,	,	,
10_1101-2021_01_08_425885	742	18	assuming	assume	VBG
10_1101-2021_01_08_425885	742	19	that	that	IN
10_1101-2021_01_08_425885	742	20	the	the	DT
10_1101-2021_01_08_425885	742	21	big	big	JJ
10_1101-2021_01_08_425885	742	22	-	-	HYPH
10_1101-2021_01_08_425885	742	23	O	o	NN
10_1101-2021_01_08_425885	742	24	bound	bind	VBN
10_1101-2021_01_08_425885	742	25	is	be	VBZ
10_1101-2021_01_08_425885	742	26	sharp	sharp	JJ
10_1101-2021_01_08_425885	742	27	at	at	IN
10_1101-2021_01_08_425885	742	28	N	n	NN
10_1101-2021_01_08_425885	742	29	=	=	SYM
10_1101-2021_01_08_425885	742	30	104	104	CD
10_1101-2021_01_08_425885	742	31	for	for	IN
10_1101-2021_01_08_425885	742	32	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	742	33	37	37	CD
10_1101-2021_01_08_425885	742	34	-	-	SYM
10_1101-2021_01_08_425885	742	35	49	49	CD
10_1101-2021_01_08_425885	742	36	.	.	.
10_1101-2021_01_08_425885	743	1	The	the	DT
10_1101-2021_01_08_425885	743	2	dashed	dash	VBN
10_1101-2021_01_08_425885	743	3	green	green	JJ
10_1101-2021_01_08_425885	743	4	line	line	NN
10_1101-2021_01_08_425885	743	5	corresponds	correspond	VBZ
10_1101-2021_01_08_425885	743	6	to	to	IN
10_1101-2021_01_08_425885	743	7	the	the	DT
10_1101-2021_01_08_425885	743	8	14	14	CD
10_1101-2021_01_08_425885	743	9	%	%	NN
10_1101-2021_01_08_425885	743	10	fractional	fractional	JJ
10_1101-2021_01_08_425885	743	11	error	error	NN
10_1101-2021_01_08_425885	743	12	needed	need	VBN
10_1101-2021_01_08_425885	743	13	for	for	IN
10_1101-2021_01_08_425885	743	14	scalar	scalar	JJ
10_1101-2021_01_08_425885	743	15	curvatures	curvature	NNS
10_1101-2021_01_08_425885	743	16	to	to	TO
10_1101-2021_01_08_425885	743	17	be	be	VB
10_1101-2021_01_08_425885	743	18	accurately	accurately	RB
10_1101-2021_01_08_425885	743	19	estimated	estimate	VBN
10_1101-2021_01_08_425885	743	20	for	for	IN
10_1101-2021_01_08_425885	743	21	half	half	PDT
10_1101-2021_01_08_425885	743	22	the	the	DT
10_1101-2021_01_08_425885	743	23	intervals	interval	NNS
10_1101-2021_01_08_425885	743	24	in	in	IN
10_1101-2021_01_08_425885	743	25	D49	D49	NNP
10_1101-2021_01_08_425885	743	26	.	.	.
10_1101-2021_01_08_425885	744	1	This	this	DT
10_1101-2021_01_08_425885	744	2	corresponds	correspond	VBZ
10_1101-2021_01_08_425885	744	3	to	to	IN
10_1101-2021_01_08_425885	744	4	f	f	NN
10_1101-2021_01_08_425885	744	5	=	=	SYM
10_1101-2021_01_08_425885	744	6	0.23	0.23	CD
10_1101-2021_01_08_425885	744	7	in	in	IN
10_1101-2021_01_08_425885	744	8	(	(	-LRB-
10_1101-2021_01_08_425885	744	9	G	g	NN
10_1101-2021_01_08_425885	744	10	)	)	-RRB-
10_1101-2021_01_08_425885	744	11	since	since	IN
10_1101-2021_01_08_425885	744	12	60	60	CD
10_1101-2021_01_08_425885	744	13	%	%	NN
10_1101-2021_01_08_425885	744	14	×f	×f	NN
10_1101-2021_01_08_425885	744	15	=	=	SYM
10_1101-2021_01_08_425885	744	16	14	14	CD
10_1101-2021_01_08_425885	744	17	%	%	NN
10_1101-2021_01_08_425885	744	18	.	.	.
10_1101-2021_01_08_425885	745	1	For	for	IN
10_1101-2021_01_08_425885	745	2	the	the	DT
10_1101-2021_01_08_425885	745	3	LB	LB	NNP
10_1101-2021_01_08_425885	745	4	estimator	estimator	NN
10_1101-2021_01_08_425885	745	5	computed	compute	VBD
10_1101-2021_01_08_425885	745	6	using	use	VBG
10_1101-2021_01_08_425885	745	7	the	the	DT
10_1101-2021_01_08_425885	745	8	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	745	9	kernel	kernel	NN
10_1101-2021_01_08_425885	745	10	,	,	,
10_1101-2021_01_08_425885	745	11	achieving	achieve	VBG
10_1101-2021_01_08_425885	745	12	this	this	DT
10_1101-2021_01_08_425885	745	13	fractional	fractional	JJ
10_1101-2021_01_08_425885	745	14	error	error	NN
10_1101-2021_01_08_425885	745	15	requires	require	VBZ
10_1101-2021_01_08_425885	745	16	N	N	NNP
10_1101-2021_01_08_425885	745	17	≈	≈	NNP
10_1101-2021_01_08_425885	745	18	107	107	CD
10_1101-2021_01_08_425885	745	19	.	.	.
10_1101-2021_01_08_425885	746	1	Since	since	IN
10_1101-2021_01_08_425885	746	2	LB	LB	NNP
10_1101-2021_01_08_425885	746	3	estimators	estimator	NNS
10_1101-2021_01_08_425885	746	4	computed	compute	VBD
10_1101-2021_01_08_425885	746	5	using	use	VBG
10_1101-2021_01_08_425885	746	6	the	the	DT
10_1101-2021_01_08_425885	746	7	other	other	JJ
10_1101-2021_01_08_425885	746	8	kernels	kernel	NNS
10_1101-2021_01_08_425885	746	9	have	have	VBP
10_1101-2021_01_08_425885	746	10	the	the	DT
10_1101-2021_01_08_425885	746	11	same	same	JJ
10_1101-2021_01_08_425885	746	12	convergence	convergence	NN
10_1101-2021_01_08_425885	746	13	rate	rate	NN
10_1101-2021_01_08_425885	746	14	but	but	CC
10_1101-2021_01_08_425885	746	15	larger	large	JJR
10_1101-2021_01_08_425885	746	16	fractional	fractional	JJ
10_1101-2021_01_08_425885	746	17	error	error	NN
10_1101-2021_01_08_425885	746	18	at	at	IN
10_1101-2021_01_08_425885	746	19	N	n	NN
10_1101-2021_01_08_425885	746	20	=	=	SYM
10_1101-2021_01_08_425885	746	21	104	104	CD
10_1101-2021_01_08_425885	746	22	,	,	,
10_1101-2021_01_08_425885	746	23	these	these	DT
10_1101-2021_01_08_425885	746	24	estimators	estimator	NNS
10_1101-2021_01_08_425885	746	25	would	would	MD
10_1101-2021_01_08_425885	746	26	require	require	VB
10_1101-2021_01_08_425885	746	27	even	even	RB
10_1101-2021_01_08_425885	746	28	larger	large	JJR
10_1101-2021_01_08_425885	746	29	N	n	NN
10_1101-2021_01_08_425885	746	30	to	to	TO
10_1101-2021_01_08_425885	746	31	achieve	achieve	VB
10_1101-2021_01_08_425885	746	32	the	the	DT
10_1101-2021_01_08_425885	746	33	desired	desire	VBN
10_1101-2021_01_08_425885	746	34	14	14	CD
10_1101-2021_01_08_425885	746	35	%	%	NN
10_1101-2021_01_08_425885	746	36	fractional	fractional	JJ
10_1101-2021_01_08_425885	746	37	error	error	NN
10_1101-2021_01_08_425885	746	38	.	.	.
10_1101-2021_01_08_425885	747	1	45	45	CD
10_1101-2021_01_08_425885	747	2	.CC	.CC	:
10_1101-2021_01_08_425885	747	3	-	-	HYPH
10_1101-2021_01_08_425885	747	4	BY	by	IN
10_1101-2021_01_08_425885	747	5	-	-	HYPH
10_1101-2021_01_08_425885	747	6	NC	NC	NNP
10_1101-2021_01_08_425885	747	7	-	-	HYPH
10_1101-2021_01_08_425885	747	8	ND	ND	NNP
10_1101-2021_01_08_425885	747	9	4.0	4.0	CD
10_1101-2021_01_08_425885	747	10	International	International	NNP
10_1101-2021_01_08_425885	747	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	747	12	under	under	IN
10_1101-2021_01_08_425885	747	13	a	a	DT
10_1101-2021_01_08_425885	747	14	(	(	-LRB-
10_1101-2021_01_08_425885	747	15	which	which	WDT
10_1101-2021_01_08_425885	747	16	was	be	VBD
10_1101-2021_01_08_425885	747	17	not	not	RB
10_1101-2021_01_08_425885	747	18	certified	certify	VBN
10_1101-2021_01_08_425885	747	19	by	by	IN
10_1101-2021_01_08_425885	747	20	peer	peer	NN
10_1101-2021_01_08_425885	747	21	review	review	NN
10_1101-2021_01_08_425885	747	22	)	)	-RRB-
10_1101-2021_01_08_425885	747	23	is	be	VBZ
10_1101-2021_01_08_425885	747	24	the	the	DT
10_1101-2021_01_08_425885	747	25	author	author	NN
10_1101-2021_01_08_425885	747	26	/	/	SYM
10_1101-2021_01_08_425885	747	27	funder	funder	NN
10_1101-2021_01_08_425885	747	28	,	,	,
10_1101-2021_01_08_425885	747	29	who	who	WP
10_1101-2021_01_08_425885	747	30	has	have	VBZ
10_1101-2021_01_08_425885	747	31	granted	grant	VBN
10_1101-2021_01_08_425885	747	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	747	33	a	a	DT
10_1101-2021_01_08_425885	747	34	license	license	NN
10_1101-2021_01_08_425885	747	35	to	to	TO
10_1101-2021_01_08_425885	747	36	display	display	VB
10_1101-2021_01_08_425885	747	37	the	the	DT
10_1101-2021_01_08_425885	747	38	preprint	preprint	NN
10_1101-2021_01_08_425885	747	39	in	in	IN
10_1101-2021_01_08_425885	747	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	747	41	.	.	.
10_1101-2021_01_08_425885	748	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	748	2	is	be	VBZ
10_1101-2021_01_08_425885	748	3	made	make	VBN
10_1101-2021_01_08_425885	748	4	The	the	DT
10_1101-2021_01_08_425885	748	5	copyright	copyright	NN
10_1101-2021_01_08_425885	748	6	holder	holder	NN
10_1101-2021_01_08_425885	748	7	for	for	IN
10_1101-2021_01_08_425885	748	8	this	this	DT
10_1101-2021_01_08_425885	748	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	748	10	version	version	NN
10_1101-2021_01_08_425885	748	11	posted	post	VBD
10_1101-2021_01_08_425885	748	12	January	January	NNP
10_1101-2021_01_08_425885	748	13	8	8	CD
10_1101-2021_01_08_425885	748	14	,	,	,
10_1101-2021_01_08_425885	748	15	2021	2021	CD
10_1101-2021_01_08_425885	748	16	.	.	.
10_1101-2021_01_08_425885	748	17	;	;	:
10_1101-2021_01_08_425885	748	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	748	19	:	:	:
10_1101-2021_01_08_425885	748	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	748	21	preprint	preprint	NN
10_1101-2021_01_08_425885	748	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	748	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NN
10_1101-2021_01_08_425885	748	24	A	A	NNP
10_1101-2021_01_08_425885	748	25	B	b	NN
10_1101-2021_01_08_425885	748	26	C	c	NN
10_1101-2021_01_08_425885	748	27	D	D	NNP
10_1101-2021_01_08_425885	748	28	Figure	figure	NN
10_1101-2021_01_08_425885	748	29	S2	s2	NN
10_1101-2021_01_08_425885	748	30	:	:	:
10_1101-2021_01_08_425885	748	31	Sensitivity	sensitivity	NN
10_1101-2021_01_08_425885	748	32	of	of	IN
10_1101-2021_01_08_425885	748	33	algorithm	algorithm	NN
10_1101-2021_01_08_425885	748	34	to	to	IN
10_1101-2021_01_08_425885	748	35	real	real	JJ
10_1101-2021_01_08_425885	748	36	-	-	HYPH
10_1101-2021_01_08_425885	748	37	world	world	NN
10_1101-2021_01_08_425885	748	38	confounders	confounder	NNS
10_1101-2021_01_08_425885	748	39	.	.	.
10_1101-2021_01_08_425885	749	1	(	(	-LRB-
10_1101-2021_01_08_425885	749	2	A	a	NN
10_1101-2021_01_08_425885	749	3	)	)	-RRB-
10_1101-2021_01_08_425885	749	4	(	(	-LRB-
10_1101-2021_01_08_425885	749	5	Left	leave	VBN
10_1101-2021_01_08_425885	749	6	)	)	-RRB-
10_1101-2021_01_08_425885	749	7	A	a	DT
10_1101-2021_01_08_425885	749	8	dataset	dataset	NN
10_1101-2021_01_08_425885	749	9	with	with	IN
10_1101-2021_01_08_425885	749	10	a	a	DT
10_1101-2021_01_08_425885	749	11	sparse	sparse	JJ
10_1101-2021_01_08_425885	749	12	periphery	periphery	NN
10_1101-2021_01_08_425885	749	13	and	and	CC
10_1101-2021_01_08_425885	749	14	a	a	DT
10_1101-2021_01_08_425885	749	15	dense	dense	JJ
10_1101-2021_01_08_425885	749	16	core	core	NN
10_1101-2021_01_08_425885	749	17	was	be	VBD
10_1101-2021_01_08_425885	749	18	formed	form	VBN
10_1101-2021_01_08_425885	749	19	by	by	IN
10_1101-2021_01_08_425885	749	20	uniformly	uniformly	RB
10_1101-2021_01_08_425885	749	21	sampling	sample	VBG
10_1101-2021_01_08_425885	749	22	N1	N1	NNP
10_1101-2021_01_08_425885	749	23	=	=	SYM
10_1101-2021_01_08_425885	749	24	10	10	CD
10_1101-2021_01_08_425885	749	25	4	4	CD
10_1101-2021_01_08_425885	749	26	points	point	NNS
10_1101-2021_01_08_425885	749	27	from	from	IN
10_1101-2021_01_08_425885	749	28	the	the	DT
10_1101-2021_01_08_425885	749	29	3-dimensional	3-dimensional	CD
10_1101-2021_01_08_425885	749	30	cube	cube	NN
10_1101-2021_01_08_425885	749	31	of	of	IN
10_1101-2021_01_08_425885	749	32	side	side	NN
10_1101-2021_01_08_425885	749	33	-	-	HYPH
10_1101-2021_01_08_425885	749	34	length	length	NN
10_1101-2021_01_08_425885	749	35	10	10	CD
10_1101-2021_01_08_425885	749	36	,	,	,
10_1101-2021_01_08_425885	749	37	D310	D310	NNP
10_1101-2021_01_08_425885	749	38	,	,	,
10_1101-2021_01_08_425885	749	39	and	and	CC
10_1101-2021_01_08_425885	749	40	N2	N2	NNP
10_1101-2021_01_08_425885	749	41	=	=	SYM
10_1101-2021_01_08_425885	749	42	10	10	CD
10_1101-2021_01_08_425885	749	43	3	3	CD
10_1101-2021_01_08_425885	749	44	points	point	NNS
10_1101-2021_01_08_425885	749	45	from	from	IN
10_1101-2021_01_08_425885	749	46	the	the	DT
10_1101-2021_01_08_425885	749	47	3-dimensional	3-dimensional	CD
10_1101-2021_01_08_425885	749	48	cube	cube	NN
10_1101-2021_01_08_425885	749	49	of	of	IN
10_1101-2021_01_08_425885	749	50	side	side	NN
10_1101-2021_01_08_425885	749	51	-	-	HYPH
10_1101-2021_01_08_425885	749	52	length	length	NN
10_1101-2021_01_08_425885	749	53	1	1	CD
10_1101-2021_01_08_425885	749	54	,	,	,
10_1101-2021_01_08_425885	749	55	D31	D31	NNP
10_1101-2021_01_08_425885	749	56	(	(	-LRB-
10_1101-2021_01_08_425885	749	57	see	see	VB
10_1101-2021_01_08_425885	749	58	Methods	Methods	NNP
10_1101-2021_01_08_425885	749	59	Section	Section	NNP
10_1101-2021_01_08_425885	749	60	4.4.1.4	4.4.1.4	CD
10_1101-2021_01_08_425885	749	61	)	)	-RRB-
10_1101-2021_01_08_425885	749	62	.	.	.
10_1101-2021_01_08_425885	750	1	These	these	DT
10_1101-2021_01_08_425885	750	2	points	point	NNS
10_1101-2021_01_08_425885	750	3	were	be	VBD
10_1101-2021_01_08_425885	750	4	embedded	embed	VBN
10_1101-2021_01_08_425885	750	5	in	in	IN
10_1101-2021_01_08_425885	750	6	R11	R11	NNP
10_1101-2021_01_08_425885	750	7	and	and	CC
10_1101-2021_01_08_425885	750	8	padded	pad	VBN
10_1101-2021_01_08_425885	750	9	with	with	IN
10_1101-2021_01_08_425885	750	10	isotropic	isotropic	JJ
10_1101-2021_01_08_425885	750	11	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	750	12	noise	noise	NN
10_1101-2021_01_08_425885	750	13	of	of	IN
10_1101-2021_01_08_425885	750	14	magnitude	magnitude	NN
10_1101-2021_01_08_425885	750	15	σ	σ	NNP
10_1101-2021_01_08_425885	750	16	=	=	SYM
10_1101-2021_01_08_425885	750	17	0.01	0.01	CD
10_1101-2021_01_08_425885	750	18	in	in	IN
10_1101-2021_01_08_425885	750	19	the	the	DT
10_1101-2021_01_08_425885	750	20	8	8	CD
10_1101-2021_01_08_425885	750	21	normal	normal	JJ
10_1101-2021_01_08_425885	750	22	directions	direction	NNS
10_1101-2021_01_08_425885	750	23	.	.	.
10_1101-2021_01_08_425885	751	1	Scalar	scalar	JJ
10_1101-2021_01_08_425885	751	2	curvatures	curvature	NNS
10_1101-2021_01_08_425885	751	3	(	(	-LRB-
10_1101-2021_01_08_425885	751	4	S	s	NN
10_1101-2021_01_08_425885	751	5	)	)	-RRB-
10_1101-2021_01_08_425885	751	6	were	be	VBD
10_1101-2021_01_08_425885	751	7	computed	compute	VBN
10_1101-2021_01_08_425885	751	8	on	on	IN
10_1101-2021_01_08_425885	751	9	this	this	DT
10_1101-2021_01_08_425885	751	10	dataset	dataset	NN
10_1101-2021_01_08_425885	751	11	of	of	IN
10_1101-2021_01_08_425885	751	12	N1	N1	NNP
10_1101-2021_01_08_425885	751	13	+	+	CC
10_1101-2021_01_08_425885	751	14	N2	N2	NNP
10_1101-2021_01_08_425885	751	15	points	point	NNS
10_1101-2021_01_08_425885	751	16	by	by	IN
10_1101-2021_01_08_425885	751	17	setting	set	VBG
10_1101-2021_01_08_425885	751	18	σh	σh	NNP
10_1101-2021_01_08_425885	751	19	and	and	CC
10_1101-2021_01_08_425885	751	20	are	be	VBP
10_1101-2021_01_08_425885	751	21	plotted	plot	VBN
10_1101-2021_01_08_425885	751	22	against	against	IN
10_1101-2021_01_08_425885	751	23	their	-PRON-	PRP$
10_1101-2021_01_08_425885	751	24	standard	standard	JJ
10_1101-2021_01_08_425885	751	25	errors	error	NNS
10_1101-2021_01_08_425885	751	26	(	(	-LRB-
10_1101-2021_01_08_425885	751	27	σS	σs	NN
10_1101-2021_01_08_425885	751	28	)	)	-RRB-
10_1101-2021_01_08_425885	751	29	in	in	IN
10_1101-2021_01_08_425885	751	30	the	the	DT
10_1101-2021_01_08_425885	751	31	leftmost	leftmost	JJ
10_1101-2021_01_08_425885	751	32	panel	panel	NN
10_1101-2021_01_08_425885	751	33	.	.	.
10_1101-2021_01_08_425885	752	1	Curvature	curvature	JJ
10_1101-2021_01_08_425885	752	2	computations	computation	NNS
10_1101-2021_01_08_425885	752	3	were	be	VBD
10_1101-2021_01_08_425885	752	4	also	also	RB
10_1101-2021_01_08_425885	752	5	performed	perform	VBN
10_1101-2021_01_08_425885	752	6	at	at	IN
10_1101-2021_01_08_425885	752	7	fixed	fix	VBN
10_1101-2021_01_08_425885	752	8	length	length	NN
10_1101-2021_01_08_425885	752	9	scales	scale	NNS
10_1101-2021_01_08_425885	752	10	corresponding	correspond	VBG
10_1101-2021_01_08_425885	752	11	to	to	IN
10_1101-2021_01_08_425885	752	12	the	the	DT
10_1101-2021_01_08_425885	752	13	5	5	CD
10_1101-2021_01_08_425885	752	14	,	,	,
10_1101-2021_01_08_425885	752	15	50	50	CD
10_1101-2021_01_08_425885	752	16	and	and	CC
10_1101-2021_01_08_425885	752	17	95%-ile	95%-ile	CD
10_1101-2021_01_08_425885	752	18	values	value	NNS
10_1101-2021_01_08_425885	752	19	for	for	IN
10_1101-2021_01_08_425885	752	20	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	752	21	size	size	NN
10_1101-2021_01_08_425885	752	22	(	(	-LRB-
10_1101-2021_01_08_425885	752	23	left	leave	VBN
10_1101-2021_01_08_425885	752	24	to	to	IN
10_1101-2021_01_08_425885	752	25	right	right	NN
10_1101-2021_01_08_425885	752	26	)	)	-RRB-
10_1101-2021_01_08_425885	752	27	used	use	VBN
10_1101-2021_01_08_425885	752	28	in	in	IN
10_1101-2021_01_08_425885	752	29	the	the	DT
10_1101-2021_01_08_425885	752	30	leftmost	leftmost	JJ
10_1101-2021_01_08_425885	752	31	panel	panel	NN
10_1101-2021_01_08_425885	752	32	(	(	-LRB-
10_1101-2021_01_08_425885	752	33	r	r	NN
10_1101-2021_01_08_425885	752	34	=	=	SYM
10_1101-2021_01_08_425885	752	35	0.54	0.54	CD
10_1101-2021_01_08_425885	752	36	,	,	,
10_1101-2021_01_08_425885	752	37	0.90	0.90	CD
10_1101-2021_01_08_425885	752	38	and	and	CC
10_1101-2021_01_08_425885	752	39	1.22	1.22	CD
10_1101-2021_01_08_425885	752	40	respectively	respectively	RB
10_1101-2021_01_08_425885	752	41	)	)	-RRB-
10_1101-2021_01_08_425885	752	42	.	.	.
10_1101-2021_01_08_425885	753	1	Here	here	RB
10_1101-2021_01_08_425885	753	2	,	,	,
10_1101-2021_01_08_425885	753	3	points	point	NNS
10_1101-2021_01_08_425885	753	4	for	for	IN
10_1101-2021_01_08_425885	753	5	which	which	WDT
10_1101-2021_01_08_425885	753	6	the	the	DT
10_1101-2021_01_08_425885	753	7	chosen	choose	VBN
10_1101-2021_01_08_425885	753	8	r	r	NN
10_1101-2021_01_08_425885	753	9	led	lead	VBD
10_1101-2021_01_08_425885	753	10	to	to	IN
10_1101-2021_01_08_425885	753	11	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	753	12	with	with	IN
10_1101-2021_01_08_425885	753	13	insufficient	insufficient	JJ
10_1101-2021_01_08_425885	753	14	points	point	NNS
10_1101-2021_01_08_425885	753	15	for	for	IN
10_1101-2021_01_08_425885	753	16	regression	regression	NN
10_1101-2021_01_08_425885	753	17	are	be	VBP
10_1101-2021_01_08_425885	753	18	not	not	RB
10_1101-2021_01_08_425885	753	19	shown	show	VBN
10_1101-2021_01_08_425885	753	20	.	.	.
10_1101-2021_01_08_425885	754	1	For	for	IN
10_1101-2021_01_08_425885	754	2	large	large	JJ
10_1101-2021_01_08_425885	754	3	length	length	NN
10_1101-2021_01_08_425885	754	4	scales	scale	NNS
10_1101-2021_01_08_425885	754	5	,	,	,
10_1101-2021_01_08_425885	754	6	all	all	DT
10_1101-2021_01_08_425885	754	7	points	point	NNS
10_1101-2021_01_08_425885	754	8	in	in	IN
10_1101-2021_01_08_425885	754	9	the	the	DT
10_1101-2021_01_08_425885	754	10	dense	dense	JJ
10_1101-2021_01_08_425885	754	11	region	region	NN
10_1101-2021_01_08_425885	754	12	are	be	VBP
10_1101-2021_01_08_425885	754	13	able	able	JJ
10_1101-2021_01_08_425885	754	14	to	to	TO
10_1101-2021_01_08_425885	754	15	report	report	VB
10_1101-2021_01_08_425885	754	16	curvatures	curvature	NNS
10_1101-2021_01_08_425885	754	17	but	but	CC
10_1101-2021_01_08_425885	754	18	are	be	VBP
10_1101-2021_01_08_425885	754	19	crowded	crowd	VBN
10_1101-2021_01_08_425885	754	20	into	into	IN
10_1101-2021_01_08_425885	754	21	the	the	DT
10_1101-2021_01_08_425885	754	22	apex	apex	NN
10_1101-2021_01_08_425885	754	23	of	of	IN
10_1101-2021_01_08_425885	754	24	the	the	DT
10_1101-2021_01_08_425885	754	25	plots	plot	NNS
10_1101-2021_01_08_425885	754	26	.	.	.
10_1101-2021_01_08_425885	755	1	The	the	DT
10_1101-2021_01_08_425885	755	2	N1	n1	NN
10_1101-2021_01_08_425885	755	3	(	(	-LRB-
10_1101-2021_01_08_425885	755	4	N2	n2	NN
10_1101-2021_01_08_425885	755	5	)	)	-RRB-
10_1101-2021_01_08_425885	755	6	sparse	sparse	RB
10_1101-2021_01_08_425885	755	7	(	(	-LRB-
10_1101-2021_01_08_425885	755	8	dense	dense	JJ
10_1101-2021_01_08_425885	755	9	)	)	-RRB-
10_1101-2021_01_08_425885	755	10	points	point	NNS
10_1101-2021_01_08_425885	755	11	are	be	VBP
10_1101-2021_01_08_425885	755	12	shown	show	VBN
10_1101-2021_01_08_425885	755	13	in	in	IN
10_1101-2021_01_08_425885	755	14	blue	blue	JJ
10_1101-2021_01_08_425885	755	15	(	(	-LRB-
10_1101-2021_01_08_425885	755	16	green	green	JJ
10_1101-2021_01_08_425885	755	17	)	)	-RRB-
10_1101-2021_01_08_425885	755	18	.	.	.
10_1101-2021_01_08_425885	756	1	Points	point	NNS
10_1101-2021_01_08_425885	756	2	enclosed	enclose	VBN
10_1101-2021_01_08_425885	756	3	by	by	IN
10_1101-2021_01_08_425885	756	4	the	the	DT
10_1101-2021_01_08_425885	756	5	red	red	JJ
10_1101-2021_01_08_425885	756	6	lines	line	NNS
10_1101-2021_01_08_425885	756	7	have	have	VBP
10_1101-2021_01_08_425885	756	8	95	95	CD
10_1101-2021_01_08_425885	756	9	%	%	NN
10_1101-2021_01_08_425885	756	10	CIs	ci	NNS
10_1101-2021_01_08_425885	756	11	including	include	VBG
10_1101-2021_01_08_425885	756	12	the	the	DT
10_1101-2021_01_08_425885	756	13	true	true	JJ
10_1101-2021_01_08_425885	756	14	value	value	NN
10_1101-2021_01_08_425885	756	15	of	of	IN
10_1101-2021_01_08_425885	756	16	zero	zero	CD
10_1101-2021_01_08_425885	756	17	.	.	.
10_1101-2021_01_08_425885	757	1	The	the	DT
10_1101-2021_01_08_425885	757	2	right	right	JJ
10_1101-2021_01_08_425885	757	3	four	four	CD
10_1101-2021_01_08_425885	757	4	panels	panel	NNS
10_1101-2021_01_08_425885	757	5	show	show	VBP
10_1101-2021_01_08_425885	757	6	analogous	analogous	JJ
10_1101-2021_01_08_425885	757	7	results	result	NNS
10_1101-2021_01_08_425885	757	8	when	when	WRB
10_1101-2021_01_08_425885	757	9	N2	N2	NNP
10_1101-2021_01_08_425885	757	10	=	=	SYM
10_1101-2021_01_08_425885	757	11	10	10	CD
10_1101-2021_01_08_425885	757	12	4	4	CD
10_1101-2021_01_08_425885	757	13	.	.	.
10_1101-2021_01_08_425885	758	1	Here	here	RB
10_1101-2021_01_08_425885	758	2	the	the	DT
10_1101-2021_01_08_425885	758	3	the	the	DT
10_1101-2021_01_08_425885	758	4	5	5	CD
10_1101-2021_01_08_425885	758	5	,	,	,
10_1101-2021_01_08_425885	758	6	50	50	CD
10_1101-2021_01_08_425885	758	7	and	and	CC
10_1101-2021_01_08_425885	758	8	95%-ile	95%-ile	CD
10_1101-2021_01_08_425885	758	9	values	value	NNS
10_1101-2021_01_08_425885	758	10	for	for	IN
10_1101-2021_01_08_425885	758	11	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	758	12	size	size	NN
10_1101-2021_01_08_425885	758	13	are	be	VBP
10_1101-2021_01_08_425885	758	14	r	r	NNP
10_1101-2021_01_08_425885	758	15	=	=	SYM
10_1101-2021_01_08_425885	758	16	0.37	0.37	CD
10_1101-2021_01_08_425885	758	17	,	,	,
10_1101-2021_01_08_425885	758	18	0.63	0.63	CD
10_1101-2021_01_08_425885	758	19	and	and	CC
10_1101-2021_01_08_425885	758	20	1.42	1.42	CD
10_1101-2021_01_08_425885	758	21	respectively	respectively	RB
10_1101-2021_01_08_425885	758	22	.	.	.
10_1101-2021_01_08_425885	759	1	See	see	VB
10_1101-2021_01_08_425885	759	2	Methods	Methods	NNP
10_1101-2021_01_08_425885	759	3	Section	Section	NNP
10_1101-2021_01_08_425885	759	4	4.4.2.1	4.4.2.1	CD
10_1101-2021_01_08_425885	759	5	.	.	.
10_1101-2021_01_08_425885	760	1	(	(	-LRB-
10_1101-2021_01_08_425885	760	2	B	b	NN
10_1101-2021_01_08_425885	760	3	)	)	-RRB-
10_1101-2021_01_08_425885	760	4	Distribution	distribution	NN
10_1101-2021_01_08_425885	760	5	of	of	IN
10_1101-2021_01_08_425885	760	6	scalar	scalar	JJ
10_1101-2021_01_08_425885	760	7	curvatures	curvature	NNS
10_1101-2021_01_08_425885	760	8	computed	compute	VBD
10_1101-2021_01_08_425885	760	9	for	for	IN
10_1101-2021_01_08_425885	760	10	N	n	NN
10_1101-2021_01_08_425885	760	11	=	=	SYM
10_1101-2021_01_08_425885	760	12	104	104	CD
10_1101-2021_01_08_425885	760	13	points	point	NNS
10_1101-2021_01_08_425885	760	14	uniformly	uniformly	RB
10_1101-2021_01_08_425885	760	15	sampled	sample	VBN
10_1101-2021_01_08_425885	760	16	from	from	IN
10_1101-2021_01_08_425885	760	17	S2	s2	NN
10_1101-2021_01_08_425885	760	18	⊂	⊂	CD
10_1101-2021_01_08_425885	760	19	R3	r3	NN
10_1101-2021_01_08_425885	760	20	and	and	CC
10_1101-2021_01_08_425885	760	21	convoluted	convolute	VBN
10_1101-2021_01_08_425885	760	22	with	with	IN
10_1101-2021_01_08_425885	760	23	isotropic	isotropic	JJ
10_1101-2021_01_08_425885	760	24	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	760	25	noise	noise	NN
10_1101-2021_01_08_425885	760	26	of	of	IN
10_1101-2021_01_08_425885	760	27	magnitude	magnitude	NN
10_1101-2021_01_08_425885	760	28	σ	σ	NNP
10_1101-2021_01_08_425885	760	29	in	in	IN
10_1101-2021_01_08_425885	760	30	R3	R3	NNP
10_1101-2021_01_08_425885	760	31	.	.	.
10_1101-2021_01_08_425885	761	1	Noise	noise	NN
10_1101-2021_01_08_425885	761	2	confounds	confound	VBZ
10_1101-2021_01_08_425885	761	3	accurate	accurate	JJ
10_1101-2021_01_08_425885	761	4	scalar	scalar	JJ
10_1101-2021_01_08_425885	761	5	curvature	curvature	JJ
10_1101-2021_01_08_425885	761	6	computation	computation	NN
10_1101-2021_01_08_425885	761	7	when	when	WRB
10_1101-2021_01_08_425885	761	8	σ	σ	NN
10_1101-2021_01_08_425885	761	9	is	be	VBZ
10_1101-2021_01_08_425885	761	10	roughly	roughly	RB
10_1101-2021_01_08_425885	761	11	10	10	CD
10_1101-2021_01_08_425885	761	12	%	%	NN
10_1101-2021_01_08_425885	761	13	of	of	IN
10_1101-2021_01_08_425885	761	14	the	the	DT
10_1101-2021_01_08_425885	761	15	sphere	sphere	NN
10_1101-2021_01_08_425885	761	16	’s	’s	POS
10_1101-2021_01_08_425885	761	17	radius	radius	NN
10_1101-2021_01_08_425885	761	18	.	.	.
10_1101-2021_01_08_425885	762	1	The	the	DT
10_1101-2021_01_08_425885	762	2	deviation	deviation	NN
10_1101-2021_01_08_425885	762	3	of	of	IN
10_1101-2021_01_08_425885	762	4	the	the	DT
10_1101-2021_01_08_425885	762	5	estimated	estimate	VBN
10_1101-2021_01_08_425885	762	6	scalar	scalar	JJ
10_1101-2021_01_08_425885	762	7	curvatures	curvature	NNS
10_1101-2021_01_08_425885	762	8	from	from	IN
10_1101-2021_01_08_425885	762	9	the	the	DT
10_1101-2021_01_08_425885	762	10	true	true	JJ
10_1101-2021_01_08_425885	762	11	value	value	NN
10_1101-2021_01_08_425885	762	12	of	of	IN
10_1101-2021_01_08_425885	762	13	2	2	CD
10_1101-2021_01_08_425885	762	14	(	(	-LRB-
10_1101-2021_01_08_425885	762	15	shown	show	VBN
10_1101-2021_01_08_425885	762	16	as	as	IN
10_1101-2021_01_08_425885	762	17	a	a	DT
10_1101-2021_01_08_425885	762	18	dashed	dash	VBN
10_1101-2021_01_08_425885	762	19	red	red	JJ
10_1101-2021_01_08_425885	762	20	line	line	NN
10_1101-2021_01_08_425885	762	21	)	)	-RRB-
10_1101-2021_01_08_425885	762	22	for	for	IN
10_1101-2021_01_08_425885	762	23	σ	σ	NN
10_1101-2021_01_08_425885	762	24	≥	≥	CD
10_1101-2021_01_08_425885	762	25	0.1	0.1	CD
10_1101-2021_01_08_425885	762	26	reflects	reflect	VBZ
10_1101-2021_01_08_425885	762	27	the	the	DT
10_1101-2021_01_08_425885	762	28	nontrivial	nontrivial	JJ
10_1101-2021_01_08_425885	762	29	geometry	geometry	NN
10_1101-2021_01_08_425885	762	30	of	of	IN
10_1101-2021_01_08_425885	762	31	a	a	DT
10_1101-2021_01_08_425885	762	32	manifold	manifold	NN
10_1101-2021_01_08_425885	762	33	convoluted	convolute	VBN
10_1101-2021_01_08_425885	762	34	by	by	IN
10_1101-2021_01_08_425885	762	35	noise	noise	NN
10_1101-2021_01_08_425885	762	36	.	.	.
10_1101-2021_01_08_425885	763	1	See	see	VB
10_1101-2021_01_08_425885	763	2	Methods	Methods	NNP
10_1101-2021_01_08_425885	763	3	Section	Section	NNP
10_1101-2021_01_08_425885	763	4	4.4.2.2	4.4.2.2	CD
10_1101-2021_01_08_425885	763	5	.	.	.
10_1101-2021_01_08_425885	764	1	(	(	-LRB-
10_1101-2021_01_08_425885	764	2	C	C	NNP
10_1101-2021_01_08_425885	764	3	)	)	-RRB-
10_1101-2021_01_08_425885	764	4	(	(	-LRB-
10_1101-2021_01_08_425885	764	5	Left	left	NN
10_1101-2021_01_08_425885	764	6	)	)	-RRB-
10_1101-2021_01_08_425885	764	7	N	n	NN
10_1101-2021_01_08_425885	764	8	=	=	SYM
10_1101-2021_01_08_425885	764	9	104	104	CD
10_1101-2021_01_08_425885	764	10	points	point	NNS
10_1101-2021_01_08_425885	764	11	were	be	VBD
10_1101-2021_01_08_425885	764	12	uniformly	uniformly	RB
10_1101-2021_01_08_425885	764	13	sampled	sample	VBN
10_1101-2021_01_08_425885	764	14	from	from	IN
10_1101-2021_01_08_425885	764	15	S2	s2	NN
10_1101-2021_01_08_425885	764	16	and	and	CC
10_1101-2021_01_08_425885	764	17	embedded	embed	VBN
10_1101-2021_01_08_425885	764	18	in	in	IN
10_1101-2021_01_08_425885	764	19	Rn	Rn	NNP
10_1101-2021_01_08_425885	764	20	.	.	.
10_1101-2021_01_08_425885	765	1	Isotropic	isotropic	JJ
10_1101-2021_01_08_425885	765	2	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	765	3	noise	noise	NN
10_1101-2021_01_08_425885	765	4	of	of	IN
10_1101-2021_01_08_425885	765	5	magnitude	magnitude	NN
10_1101-2021_01_08_425885	765	6	σ	σ	NNP
10_1101-2021_01_08_425885	765	7	was	be	VBD
10_1101-2021_01_08_425885	765	8	applied	apply	VBN
10_1101-2021_01_08_425885	765	9	to	to	IN
10_1101-2021_01_08_425885	765	10	each	each	DT
10_1101-2021_01_08_425885	765	11	of	of	IN
10_1101-2021_01_08_425885	765	12	the	the	DT
10_1101-2021_01_08_425885	765	13	n	n	JJ
10_1101-2021_01_08_425885	765	14	ambient	ambient	JJ
10_1101-2021_01_08_425885	765	15	dimensions	dimension	NNS
10_1101-2021_01_08_425885	765	16	.	.	.
10_1101-2021_01_08_425885	766	1	Scalar	scalar	JJ
10_1101-2021_01_08_425885	766	2	curvatures	curvature	NNS
10_1101-2021_01_08_425885	766	3	computed	compute	VBN
10_1101-2021_01_08_425885	766	4	by	by	IN
10_1101-2021_01_08_425885	766	5	keeping	keep	VBG
10_1101-2021_01_08_425885	766	6	σh	σh	NNP
10_1101-2021_01_08_425885	766	7	fixed	fix	VBN
10_1101-2021_01_08_425885	766	8	for	for	IN
10_1101-2021_01_08_425885	766	9	all	all	DT
10_1101-2021_01_08_425885	766	10	n	n	NN
10_1101-2021_01_08_425885	766	11	and	and	CC
10_1101-2021_01_08_425885	766	12	σ	σ	NNP
10_1101-2021_01_08_425885	766	13	,	,	,
10_1101-2021_01_08_425885	766	14	recapitulated	recapitulate	VBD
10_1101-2021_01_08_425885	766	15	the	the	DT
10_1101-2021_01_08_425885	766	16	true	true	JJ
10_1101-2021_01_08_425885	766	17	value	value	NN
10_1101-2021_01_08_425885	766	18	of	of	IN
10_1101-2021_01_08_425885	766	19	2	2	CD
10_1101-2021_01_08_425885	766	20	(	(	-LRB-
10_1101-2021_01_08_425885	766	21	shown	show	VBN
10_1101-2021_01_08_425885	766	22	as	as	IN
10_1101-2021_01_08_425885	766	23	dashed	dash	VBN
10_1101-2021_01_08_425885	766	24	red	red	JJ
10_1101-2021_01_08_425885	766	25	lines	line	NNS
10_1101-2021_01_08_425885	766	26	)	)	-RRB-
10_1101-2021_01_08_425885	766	27	for	for	IN
10_1101-2021_01_08_425885	766	28	n	n	NNP
10_1101-2021_01_08_425885	766	29	≤	≤	NNP
10_1101-2021_01_08_425885	766	30	80	80	CD
10_1101-2021_01_08_425885	766	31	and	and	CC
10_1101-2021_01_08_425885	766	32	σ	σ	NNP
10_1101-2021_01_08_425885	766	33	≤	≤	NNP
10_1101-2021_01_08_425885	766	34	0.05	0.05	CD
10_1101-2021_01_08_425885	766	35	.	.	.
10_1101-2021_01_08_425885	767	1	(	(	-LRB-
10_1101-2021_01_08_425885	767	2	Right	right	UH
10_1101-2021_01_08_425885	767	3	)	)	-RRB-
10_1101-2021_01_08_425885	767	4	The	the	DT
10_1101-2021_01_08_425885	767	5	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	767	6	size	size	NN
10_1101-2021_01_08_425885	767	7	(	(	-LRB-
10_1101-2021_01_08_425885	767	8	r	r	NN
10_1101-2021_01_08_425885	767	9	)	)	-RRB-
10_1101-2021_01_08_425885	767	10	necessary	necessary	JJ
10_1101-2021_01_08_425885	767	11	to	to	TO
10_1101-2021_01_08_425885	767	12	attain	attain	VB
10_1101-2021_01_08_425885	767	13	σh	σh	NNP
10_1101-2021_01_08_425885	767	14	is	be	VBZ
10_1101-2021_01_08_425885	767	15	less	less	RBR
10_1101-2021_01_08_425885	767	16	sensitive	sensitive	JJ
10_1101-2021_01_08_425885	767	17	to	to	IN
10_1101-2021_01_08_425885	767	18	changes	change	NNS
10_1101-2021_01_08_425885	767	19	in	in	IN
10_1101-2021_01_08_425885	767	20	n	n	NN
10_1101-2021_01_08_425885	767	21	than	than	IN
10_1101-2021_01_08_425885	767	22	changes	change	NNS
10_1101-2021_01_08_425885	767	23	in	in	IN
10_1101-2021_01_08_425885	767	24	σ	σ	NN
10_1101-2021_01_08_425885	767	25	.	.	.
10_1101-2021_01_08_425885	768	1	See	see	VB
10_1101-2021_01_08_425885	768	2	Methods	Methods	NNP
10_1101-2021_01_08_425885	768	3	Section	Section	NNP
10_1101-2021_01_08_425885	768	4	4.4.2.3	4.4.2.3	CD
10_1101-2021_01_08_425885	768	5	.	.	.
10_1101-2021_01_08_425885	769	1	(	(	-LRB-
10_1101-2021_01_08_425885	769	2	D	d	NN
10_1101-2021_01_08_425885	769	3	)	)	-RRB-
10_1101-2021_01_08_425885	769	4	N	n	NN
10_1101-2021_01_08_425885	769	5	=	=	SYM
10_1101-2021_01_08_425885	769	6	104	104	CD
10_1101-2021_01_08_425885	769	7	points	point	NNS
10_1101-2021_01_08_425885	769	8	were	be	VBD
10_1101-2021_01_08_425885	769	9	uniformly	uniformly	RB
10_1101-2021_01_08_425885	769	10	sampled	sample	VBN
10_1101-2021_01_08_425885	769	11	from	from	IN
10_1101-2021_01_08_425885	769	12	(	(	-LRB-
10_1101-2021_01_08_425885	769	13	left	left	RB
10_1101-2021_01_08_425885	769	14	)	)	-RRB-
10_1101-2021_01_08_425885	769	15	S3	S3	NNP
10_1101-2021_01_08_425885	769	16	⊂	⊂	CD
10_1101-2021_01_08_425885	769	17	R5	r5	NN
10_1101-2021_01_08_425885	769	18	convoluted	convolute	VBD
10_1101-2021_01_08_425885	769	19	with	with	IN
10_1101-2021_01_08_425885	769	20	isotropic	isotropic	JJ
10_1101-2021_01_08_425885	769	21	Gaussian	gaussian	JJ
10_1101-2021_01_08_425885	769	22	noise	noise	NN
10_1101-2021_01_08_425885	769	23	in	in	IN
10_1101-2021_01_08_425885	769	24	the	the	DT
10_1101-2021_01_08_425885	769	25	ambient	ambient	JJ
10_1101-2021_01_08_425885	769	26	space	space	NN
10_1101-2021_01_08_425885	769	27	with	with	IN
10_1101-2021_01_08_425885	769	28	σ	σ	NNP
10_1101-2021_01_08_425885	769	29	=	=	SYM
10_1101-2021_01_08_425885	769	30	0.01	0.01	CD
10_1101-2021_01_08_425885	769	31	and	and	CC
10_1101-2021_01_08_425885	769	32	(	(	-LRB-
10_1101-2021_01_08_425885	769	33	right	right	UH
10_1101-2021_01_08_425885	769	34	)	)	-RRB-
10_1101-2021_01_08_425885	769	35	S2	s2	NN
10_1101-2021_01_08_425885	769	36	×S2	×S2	NNP
10_1101-2021_01_08_425885	769	37	⊂	⊂	CD
10_1101-2021_01_08_425885	769	38	R6	R6	NNP
10_1101-2021_01_08_425885	769	39	.	.	.
10_1101-2021_01_08_425885	770	1	To	to	TO
10_1101-2021_01_08_425885	770	2	investigate	investigate	VB
10_1101-2021_01_08_425885	770	3	the	the	DT
10_1101-2021_01_08_425885	770	4	effects	effect	NNS
10_1101-2021_01_08_425885	770	5	of	of	IN
10_1101-2021_01_08_425885	770	6	choosing	choose	VBG
10_1101-2021_01_08_425885	770	7	the	the	DT
10_1101-2021_01_08_425885	770	8	manifold	manifold	JJ
10_1101-2021_01_08_425885	770	9	dimension	dimension	NN
10_1101-2021_01_08_425885	770	10	,	,	,
10_1101-2021_01_08_425885	770	11	d	d	NNP
10_1101-2021_01_08_425885	770	12	,	,	,
10_1101-2021_01_08_425885	770	13	differently	differently	RB
10_1101-2021_01_08_425885	770	14	than	than	IN
10_1101-2021_01_08_425885	770	15	the	the	DT
10_1101-2021_01_08_425885	770	16	true	true	JJ
10_1101-2021_01_08_425885	770	17	value	value	NN
10_1101-2021_01_08_425885	770	18	,	,	,
10_1101-2021_01_08_425885	770	19	d∗	d∗	NN
10_1101-2021_01_08_425885	770	20	,	,	,
10_1101-2021_01_08_425885	770	21	σh	σh	NNP
10_1101-2021_01_08_425885	770	22	was	be	VBD
10_1101-2021_01_08_425885	770	23	kept	keep	VBN
10_1101-2021_01_08_425885	770	24	fixed	fix	VBN
10_1101-2021_01_08_425885	770	25	,	,	,
10_1101-2021_01_08_425885	770	26	and	and	CC
10_1101-2021_01_08_425885	770	27	scalar	scalar	JJ
10_1101-2021_01_08_425885	770	28	curvatures	curvature	NNS
10_1101-2021_01_08_425885	770	29	were	be	VBD
10_1101-2021_01_08_425885	770	30	computed	compute	VBN
10_1101-2021_01_08_425885	770	31	for	for	IN
10_1101-2021_01_08_425885	770	32	d	d	NN
10_1101-2021_01_08_425885	770	33	=	=	SYM
10_1101-2021_01_08_425885	770	34	d	d	NNP
10_1101-2021_01_08_425885	770	35	∗−1	∗−1	NNP
10_1101-2021_01_08_425885	770	36	(	(	-LRB-
10_1101-2021_01_08_425885	770	37	cyan	cyan	NNP
10_1101-2021_01_08_425885	770	38	)	)	-RRB-
10_1101-2021_01_08_425885	770	39	,	,	,
10_1101-2021_01_08_425885	770	40	d	d	NNP
10_1101-2021_01_08_425885	770	41	=	=	SYM
10_1101-2021_01_08_425885	770	42	d∗	d∗	NN
10_1101-2021_01_08_425885	770	43	+	+	CC
10_1101-2021_01_08_425885	770	44	1	1	CD
10_1101-2021_01_08_425885	770	45	(	(	-LRB-
10_1101-2021_01_08_425885	770	46	magenta	magenta	NNP
10_1101-2021_01_08_425885	770	47	)	)	-RRB-
10_1101-2021_01_08_425885	770	48	and	and	CC
10_1101-2021_01_08_425885	770	49	d	d	NNP
10_1101-2021_01_08_425885	770	50	=	=	SYM
10_1101-2021_01_08_425885	770	51	d∗	d∗	NN
10_1101-2021_01_08_425885	770	52	(	(	-LRB-
10_1101-2021_01_08_425885	770	53	green	green	NN
10_1101-2021_01_08_425885	770	54	)	)	-RRB-
10_1101-2021_01_08_425885	770	55	.	.	.
10_1101-2021_01_08_425885	771	1	The	the	DT
10_1101-2021_01_08_425885	771	2	panels	panel	NNS
10_1101-2021_01_08_425885	771	3	show	show	VBP
10_1101-2021_01_08_425885	771	4	the	the	DT
10_1101-2021_01_08_425885	771	5	distribution	distribution	NN
10_1101-2021_01_08_425885	771	6	of	of	IN
10_1101-2021_01_08_425885	771	7	(	(	-LRB-
10_1101-2021_01_08_425885	771	8	left	leave	VBN
10_1101-2021_01_08_425885	771	9	to	to	IN
10_1101-2021_01_08_425885	771	10	right	right	JJ
10_1101-2021_01_08_425885	771	11	)	)	-RRB-
10_1101-2021_01_08_425885	771	12	scalar	scalar	JJ
10_1101-2021_01_08_425885	771	13	curvatures	curvature	NNS
10_1101-2021_01_08_425885	771	14	(	(	-LRB-
10_1101-2021_01_08_425885	771	15	S	S	NNP
10_1101-2021_01_08_425885	771	16	)	)	-RRB-
10_1101-2021_01_08_425885	771	17	,	,	,
10_1101-2021_01_08_425885	771	18	standard	standard	JJ
10_1101-2021_01_08_425885	771	19	errors	error	NNS
10_1101-2021_01_08_425885	771	20	(	(	-LRB-
10_1101-2021_01_08_425885	771	21	σS	σs	NN
10_1101-2021_01_08_425885	771	22	)	)	-RRB-
10_1101-2021_01_08_425885	771	23	and	and	CC
10_1101-2021_01_08_425885	771	24	GOF	GOF	NNP
10_1101-2021_01_08_425885	771	25	p	p	NN
10_1101-2021_01_08_425885	771	26	-	-	HYPH
10_1101-2021_01_08_425885	771	27	values	value	NNS
10_1101-2021_01_08_425885	771	28	.	.	.
10_1101-2021_01_08_425885	772	1	The	the	DT
10_1101-2021_01_08_425885	772	2	true	true	JJ
10_1101-2021_01_08_425885	772	3	value	value	NN
10_1101-2021_01_08_425885	772	4	of	of	IN
10_1101-2021_01_08_425885	772	5	the	the	DT
10_1101-2021_01_08_425885	772	6	scalar	scalar	JJ
10_1101-2021_01_08_425885	772	7	curvature	curvature	NN
10_1101-2021_01_08_425885	772	8	(	(	-LRB-
10_1101-2021_01_08_425885	772	9	at	at	IN
10_1101-2021_01_08_425885	772	10	d	d	NN
10_1101-2021_01_08_425885	772	11	=	=	SYM
10_1101-2021_01_08_425885	772	12	d∗	d∗	NN
10_1101-2021_01_08_425885	772	13	)	)	-RRB-
10_1101-2021_01_08_425885	772	14	is	be	VBZ
10_1101-2021_01_08_425885	772	15	constant	constant	JJ
10_1101-2021_01_08_425885	772	16	across	across	IN
10_1101-2021_01_08_425885	772	17	both	both	DT
10_1101-2021_01_08_425885	772	18	manifolds	manifold	NNS
10_1101-2021_01_08_425885	772	19	and	and	CC
10_1101-2021_01_08_425885	772	20	shown	show	VBN
10_1101-2021_01_08_425885	772	21	as	as	IN
10_1101-2021_01_08_425885	772	22	a	a	DT
10_1101-2021_01_08_425885	772	23	dashed	dash	VBN
10_1101-2021_01_08_425885	772	24	red	red	JJ
10_1101-2021_01_08_425885	772	25	line	line	NN
10_1101-2021_01_08_425885	772	26	.	.	.
10_1101-2021_01_08_425885	773	1	The	the	DT
10_1101-2021_01_08_425885	773	2	average	average	JJ
10_1101-2021_01_08_425885	773	3	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	773	4	size	size	NN
10_1101-2021_01_08_425885	773	5	(	(	-LRB-
10_1101-2021_01_08_425885	773	6	r	r	NNP
10_1101-2021_01_08_425885	773	7	averaged	average	VBD
10_1101-2021_01_08_425885	773	8	over	over	IN
10_1101-2021_01_08_425885	773	9	all	all	DT
10_1101-2021_01_08_425885	773	10	points	point	NNS
10_1101-2021_01_08_425885	773	11	)	)	-RRB-
10_1101-2021_01_08_425885	773	12	is	be	VBZ
10_1101-2021_01_08_425885	773	13	much	much	RB
10_1101-2021_01_08_425885	773	14	larger	large	JJR
10_1101-2021_01_08_425885	773	15	for	for	IN
10_1101-2021_01_08_425885	773	16	both	both	DT
10_1101-2021_01_08_425885	773	17	d	d	NN
10_1101-2021_01_08_425885	773	18	=	=	SYM
10_1101-2021_01_08_425885	773	19	d∗	d∗	NN
10_1101-2021_01_08_425885	773	20	−	−	NNP
10_1101-2021_01_08_425885	773	21	1	1	CD
10_1101-2021_01_08_425885	773	22	and	and	CC
10_1101-2021_01_08_425885	773	23	d	d	NN
10_1101-2021_01_08_425885	773	24	=	=	SYM
10_1101-2021_01_08_425885	773	25	d∗	d∗	NN
10_1101-2021_01_08_425885	773	26	+	+	CC
10_1101-2021_01_08_425885	773	27	1	1	CD
10_1101-2021_01_08_425885	773	28	than	than	IN
10_1101-2021_01_08_425885	773	29	for	for	IN
10_1101-2021_01_08_425885	773	30	d	d	NN
10_1101-2021_01_08_425885	773	31	=	=	SYM
10_1101-2021_01_08_425885	773	32	d∗	d∗	NN
10_1101-2021_01_08_425885	773	33	as	as	IN
10_1101-2021_01_08_425885	773	34	shown	show	VBN
10_1101-2021_01_08_425885	773	35	in	in	IN
10_1101-2021_01_08_425885	773	36	the	the	DT
10_1101-2021_01_08_425885	773	37	legend	legend	NN
10_1101-2021_01_08_425885	773	38	.	.	.
10_1101-2021_01_08_425885	774	1	For	for	IN
10_1101-2021_01_08_425885	774	2	the	the	DT
10_1101-2021_01_08_425885	774	3	same	same	JJ
10_1101-2021_01_08_425885	774	4	σh	σh	NN
10_1101-2021_01_08_425885	774	5	,	,	,
10_1101-2021_01_08_425885	774	6	d	d	NNP
10_1101-2021_01_08_425885	774	7	=	=	SYM
10_1101-2021_01_08_425885	774	8	d	d	NNP
10_1101-2021_01_08_425885	774	9	∗−	∗−	NNP
10_1101-2021_01_08_425885	774	10	1	1	CD
10_1101-2021_01_08_425885	774	11	also	also	RB
10_1101-2021_01_08_425885	774	12	leads	lead	VBZ
10_1101-2021_01_08_425885	774	13	to	to	IN
10_1101-2021_01_08_425885	774	14	a	a	DT
10_1101-2021_01_08_425885	774	15	more	more	RBR
10_1101-2021_01_08_425885	774	16	skewed	skewed	JJ
10_1101-2021_01_08_425885	774	17	distribution	distribution	NN
10_1101-2021_01_08_425885	774	18	of	of	IN
10_1101-2021_01_08_425885	774	19	GOF	GOF	NNP
10_1101-2021_01_08_425885	774	20	p	p	NN
10_1101-2021_01_08_425885	774	21	-	-	HYPH
10_1101-2021_01_08_425885	774	22	values	value	NNS
10_1101-2021_01_08_425885	774	23	relative	relative	JJ
10_1101-2021_01_08_425885	774	24	to	to	IN
10_1101-2021_01_08_425885	774	25	d	d	NN
10_1101-2021_01_08_425885	774	26	=	=	SYM
10_1101-2021_01_08_425885	774	27	d∗	d∗	NN
10_1101-2021_01_08_425885	774	28	,	,	,
10_1101-2021_01_08_425885	774	29	while	while	IN
10_1101-2021_01_08_425885	774	30	the	the	DT
10_1101-2021_01_08_425885	774	31	distribution	distribution	NN
10_1101-2021_01_08_425885	774	32	for	for	IN
10_1101-2021_01_08_425885	774	33	d	d	NN
10_1101-2021_01_08_425885	774	34	=	=	SYM
10_1101-2021_01_08_425885	774	35	d∗	d∗	NN
10_1101-2021_01_08_425885	774	36	+	+	CC
10_1101-2021_01_08_425885	774	37	1	1	CD
10_1101-2021_01_08_425885	774	38	is	be	VBZ
10_1101-2021_01_08_425885	774	39	still	still	RB
10_1101-2021_01_08_425885	774	40	flat	flat	JJ
10_1101-2021_01_08_425885	774	41	.	.	.
10_1101-2021_01_08_425885	775	1	See	see	VB
10_1101-2021_01_08_425885	775	2	Methods	method	NNS
10_1101-2021_01_08_425885	775	3	Section	Section	NNP
10_1101-2021_01_08_425885	775	4	4.4.2.4	4.4.2.4	CD
10_1101-2021_01_08_425885	775	5	.	.	.
10_1101-2021_01_08_425885	776	1	46	46	CD
10_1101-2021_01_08_425885	776	2	.CC	.CC	:
10_1101-2021_01_08_425885	776	3	-	-	HYPH
10_1101-2021_01_08_425885	776	4	BY	by	IN
10_1101-2021_01_08_425885	776	5	-	-	HYPH
10_1101-2021_01_08_425885	776	6	NC	NC	NNP
10_1101-2021_01_08_425885	776	7	-	-	HYPH
10_1101-2021_01_08_425885	776	8	ND	ND	NNP
10_1101-2021_01_08_425885	776	9	4.0	4.0	CD
10_1101-2021_01_08_425885	776	10	International	International	NNP
10_1101-2021_01_08_425885	776	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	776	12	under	under	IN
10_1101-2021_01_08_425885	776	13	a	a	DT
10_1101-2021_01_08_425885	776	14	(	(	-LRB-
10_1101-2021_01_08_425885	776	15	which	which	WDT
10_1101-2021_01_08_425885	776	16	was	be	VBD
10_1101-2021_01_08_425885	776	17	not	not	RB
10_1101-2021_01_08_425885	776	18	certified	certify	VBN
10_1101-2021_01_08_425885	776	19	by	by	IN
10_1101-2021_01_08_425885	776	20	peer	peer	NN
10_1101-2021_01_08_425885	776	21	review	review	NN
10_1101-2021_01_08_425885	776	22	)	)	-RRB-
10_1101-2021_01_08_425885	776	23	is	be	VBZ
10_1101-2021_01_08_425885	776	24	the	the	DT
10_1101-2021_01_08_425885	776	25	author	author	NN
10_1101-2021_01_08_425885	776	26	/	/	SYM
10_1101-2021_01_08_425885	776	27	funder	funder	NN
10_1101-2021_01_08_425885	776	28	,	,	,
10_1101-2021_01_08_425885	776	29	who	who	WP
10_1101-2021_01_08_425885	776	30	has	have	VBZ
10_1101-2021_01_08_425885	776	31	granted	grant	VBN
10_1101-2021_01_08_425885	776	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	776	33	a	a	DT
10_1101-2021_01_08_425885	776	34	license	license	NN
10_1101-2021_01_08_425885	776	35	to	to	TO
10_1101-2021_01_08_425885	776	36	display	display	VB
10_1101-2021_01_08_425885	776	37	the	the	DT
10_1101-2021_01_08_425885	776	38	preprint	preprint	NN
10_1101-2021_01_08_425885	776	39	in	in	IN
10_1101-2021_01_08_425885	776	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	776	41	.	.	.
10_1101-2021_01_08_425885	777	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	777	2	is	be	VBZ
10_1101-2021_01_08_425885	777	3	made	make	VBN
10_1101-2021_01_08_425885	777	4	The	the	DT
10_1101-2021_01_08_425885	777	5	copyright	copyright	NN
10_1101-2021_01_08_425885	777	6	holder	holder	NN
10_1101-2021_01_08_425885	777	7	for	for	IN
10_1101-2021_01_08_425885	777	8	this	this	DT
10_1101-2021_01_08_425885	777	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	777	10	version	version	NN
10_1101-2021_01_08_425885	777	11	posted	post	VBD
10_1101-2021_01_08_425885	777	12	January	January	NNP
10_1101-2021_01_08_425885	777	13	8	8	CD
10_1101-2021_01_08_425885	777	14	,	,	,
10_1101-2021_01_08_425885	777	15	2021	2021	CD
10_1101-2021_01_08_425885	777	16	.	.	.
10_1101-2021_01_08_425885	777	17	;	;	:
10_1101-2021_01_08_425885	777	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	777	19	:	:	:
10_1101-2021_01_08_425885	777	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	777	21	preprint	preprint	NN
10_1101-2021_01_08_425885	777	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	777	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NN
10_1101-2021_01_08_425885	777	24	A	A	NNP
10_1101-2021_01_08_425885	777	25	B	b	NN
10_1101-2021_01_08_425885	777	26	C	c	NN
10_1101-2021_01_08_425885	777	27	D	d	NN
10_1101-2021_01_08_425885	777	28	E	e	NN
10_1101-2021_01_08_425885	777	29	F	F	NNP
10_1101-2021_01_08_425885	777	30	Figure	Figure	NNP
10_1101-2021_01_08_425885	777	31	S3	s3	NN
10_1101-2021_01_08_425885	777	32	:	:	:
10_1101-2021_01_08_425885	777	33	Additional	additional	JJ
10_1101-2021_01_08_425885	777	34	details	detail	NNS
10_1101-2021_01_08_425885	777	35	of	of	IN
10_1101-2021_01_08_425885	777	36	the	the	DT
10_1101-2021_01_08_425885	777	37	image	image	NN
10_1101-2021_01_08_425885	777	38	patch	patch	NN
10_1101-2021_01_08_425885	777	39	dataset	dataset	NN
10_1101-2021_01_08_425885	777	40	and	and	CC
10_1101-2021_01_08_425885	777	41	Klein	Klein	NNP
10_1101-2021_01_08_425885	777	42	bottle	bottle	NN
10_1101-2021_01_08_425885	777	43	embeddings	embedding	NNS
10_1101-2021_01_08_425885	777	44	(	(	-LRB-
10_1101-2021_01_08_425885	777	45	related	relate	VBN
10_1101-2021_01_08_425885	777	46	to	to	IN
10_1101-2021_01_08_425885	777	47	Figure	Figure	NNP
10_1101-2021_01_08_425885	777	48	3	3	CD
10_1101-2021_01_08_425885	777	49	)	)	-RRB-
10_1101-2021_01_08_425885	777	50	.	.	.
10_1101-2021_01_08_425885	778	1	(	(	-LRB-
10_1101-2021_01_08_425885	778	2	A	a	NN
10_1101-2021_01_08_425885	778	3	)	)	-RRB-
10_1101-2021_01_08_425885	778	4	To	to	TO
10_1101-2021_01_08_425885	778	5	compute	compute	VB
10_1101-2021_01_08_425885	778	6	scalar	scalar	JJ
10_1101-2021_01_08_425885	778	7	curvatures	curvature	NNS
10_1101-2021_01_08_425885	778	8	for	for	IN
10_1101-2021_01_08_425885	778	9	Figure	Figure	NNP
10_1101-2021_01_08_425885	778	10	3E	3e	NN
10_1101-2021_01_08_425885	778	11	,	,	,
10_1101-2021_01_08_425885	778	12	each	each	DT
10_1101-2021_01_08_425885	778	13	image	image	NN
10_1101-2021_01_08_425885	778	14	patch	patch	NN
10_1101-2021_01_08_425885	778	15	was	be	VBD
10_1101-2021_01_08_425885	778	16	associated	associate	VBN
10_1101-2021_01_08_425885	778	17	to	to	IN
10_1101-2021_01_08_425885	778	18	the	the	DT
10_1101-2021_01_08_425885	778	19	(	(	-LRB-
10_1101-2021_01_08_425885	778	20	θ0,φ0	θ0,φ0	NN
10_1101-2021_01_08_425885	778	21	)	)	-RRB-
10_1101-2021_01_08_425885	778	22	coordinates	coordinate	VBZ
10_1101-2021_01_08_425885	778	23	of	of	IN
10_1101-2021_01_08_425885	778	24	the	the	DT
10_1101-2021_01_08_425885	778	25	closest	close	JJS
10_1101-2021_01_08_425885	778	26	point	point	NN
10_1101-2021_01_08_425885	778	27	on	on	IN
10_1101-2021_01_08_425885	778	28	k0	k0	NNP
10_1101-2021_01_08_425885	778	29	.	.	.
10_1101-2021_01_08_425885	779	1	Here	here	RB
10_1101-2021_01_08_425885	779	2	we	-PRON-	PRP
10_1101-2021_01_08_425885	779	3	select	select	VBP
10_1101-2021_01_08_425885	779	4	a	a	DT
10_1101-2021_01_08_425885	779	5	handful	handful	NN
10_1101-2021_01_08_425885	779	6	of	of	IN
10_1101-2021_01_08_425885	779	7	these	these	DT
10_1101-2021_01_08_425885	779	8	associated	associate	VBN
10_1101-2021_01_08_425885	779	9	points	point	NNS
10_1101-2021_01_08_425885	779	10	on	on	IN
10_1101-2021_01_08_425885	779	11	k0	k0	NNP
10_1101-2021_01_08_425885	779	12	(	(	-LRB-
10_1101-2021_01_08_425885	779	13	shown	show	VBN
10_1101-2021_01_08_425885	779	14	in	in	IN
10_1101-2021_01_08_425885	779	15	black	black	JJ
10_1101-2021_01_08_425885	779	16	)	)	-RRB-
10_1101-2021_01_08_425885	779	17	and	and	CC
10_1101-2021_01_08_425885	779	18	visualize	visualize	VB
10_1101-2021_01_08_425885	779	19	how	how	WRB
10_1101-2021_01_08_425885	779	20	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	779	21	chosen	choose	VBN
10_1101-2021_01_08_425885	779	22	in	in	IN
10_1101-2021_01_08_425885	779	23	R8	R8	NNP
10_1101-2021_01_08_425885	779	24	to	to	TO
10_1101-2021_01_08_425885	779	25	compute	compute	VB
10_1101-2021_01_08_425885	779	26	scalar	scalar	JJ
10_1101-2021_01_08_425885	779	27	curvatures	curvature	NNS
10_1101-2021_01_08_425885	779	28	for	for	IN
10_1101-2021_01_08_425885	779	29	Figure	Figure	NNP
10_1101-2021_01_08_425885	779	30	3E	3e	NN
10_1101-2021_01_08_425885	779	31	appear	appear	VB
10_1101-2021_01_08_425885	779	32	in	in	IN
10_1101-2021_01_08_425885	779	33	(	(	-LRB-
10_1101-2021_01_08_425885	779	34	θ0,φ0	θ0,φ0	NN
10_1101-2021_01_08_425885	779	35	)	)	-RRB-
10_1101-2021_01_08_425885	779	36	coordinates	coordinate	VBZ
10_1101-2021_01_08_425885	779	37	(	(	-LRB-
10_1101-2021_01_08_425885	779	38	shown	show	VBN
10_1101-2021_01_08_425885	779	39	in	in	IN
10_1101-2021_01_08_425885	779	40	red	red	NN
10_1101-2021_01_08_425885	779	41	)	)	-RRB-
10_1101-2021_01_08_425885	779	42	.	.	.
10_1101-2021_01_08_425885	780	1	When	when	WRB
10_1101-2021_01_08_425885	780	2	noise	noise	NN
10_1101-2021_01_08_425885	780	3	of	of	IN
10_1101-2021_01_08_425885	780	4	increasing	increase	VBG
10_1101-2021_01_08_425885	780	5	magnitude	magnitude	NN
10_1101-2021_01_08_425885	780	6	,	,	,
10_1101-2021_01_08_425885	780	7	σ	σ	NN
10_1101-2021_01_08_425885	780	8	,	,	,
10_1101-2021_01_08_425885	780	9	is	be	VBZ
10_1101-2021_01_08_425885	780	10	added	add	VBN
10_1101-2021_01_08_425885	780	11	to	to	IN
10_1101-2021_01_08_425885	780	12	the	the	DT
10_1101-2021_01_08_425885	780	13	set	set	NN
10_1101-2021_01_08_425885	780	14	of	of	IN
10_1101-2021_01_08_425885	780	15	closest	close	JJS
10_1101-2021_01_08_425885	780	16	points	point	NNS
10_1101-2021_01_08_425885	780	17	on	on	IN
10_1101-2021_01_08_425885	780	18	k0	k0	NNP
10_1101-2021_01_08_425885	780	19	(	(	-LRB-
10_1101-2021_01_08_425885	780	20	see	see	VB
10_1101-2021_01_08_425885	780	21	Methods	Methods	NNP
10_1101-2021_01_08_425885	780	22	Section	Section	NNP
10_1101-2021_01_08_425885	780	23	4.5.6	4.5.6	CD
10_1101-2021_01_08_425885	780	24	)	)	-RRB-
10_1101-2021_01_08_425885	780	25	,	,	,
10_1101-2021_01_08_425885	780	26	the	the	DT
10_1101-2021_01_08_425885	780	27	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	780	28	size	size	NN
10_1101-2021_01_08_425885	780	29	at	at	IN
10_1101-2021_01_08_425885	780	30	each	each	DT
10_1101-2021_01_08_425885	780	31	point	point	NN
10_1101-2021_01_08_425885	780	32	grows	grow	VBZ
10_1101-2021_01_08_425885	780	33	until	until	IN
10_1101-2021_01_08_425885	780	34	σh	σh	NNP
10_1101-2021_01_08_425885	780	35	is	be	VBZ
10_1101-2021_01_08_425885	780	36	attained	attain	VBN
10_1101-2021_01_08_425885	780	37	.	.	.
10_1101-2021_01_08_425885	781	1	(	(	-LRB-
10_1101-2021_01_08_425885	781	2	B	b	NN
10_1101-2021_01_08_425885	781	3	)	)	-RRB-
10_1101-2021_01_08_425885	781	4	As	as	IN
10_1101-2021_01_08_425885	781	5	in	in	IN
10_1101-2021_01_08_425885	781	6	(	(	-LRB-
10_1101-2021_01_08_425885	781	7	A	a	NN
10_1101-2021_01_08_425885	781	8	)	)	-RRB-
10_1101-2021_01_08_425885	781	9	,	,	,
10_1101-2021_01_08_425885	781	10	but	but	CC
10_1101-2021_01_08_425885	781	11	showing	show	VBG
10_1101-2021_01_08_425885	781	12	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	781	13	used	use	VBN
10_1101-2021_01_08_425885	781	14	in	in	IN
10_1101-2021_01_08_425885	781	15	computing	compute	VBG
10_1101-2021_01_08_425885	781	16	the	the	DT
10_1101-2021_01_08_425885	781	17	scalar	scalar	JJ
10_1101-2021_01_08_425885	781	18	curvatures	curvature	NNS
10_1101-2021_01_08_425885	781	19	in	in	IN
10_1101-2021_01_08_425885	781	20	Figure	Figure	NNP
10_1101-2021_01_08_425885	781	21	3D	3d	NN
10_1101-2021_01_08_425885	781	22	for	for	IN
10_1101-2021_01_08_425885	781	23	the	the	DT
10_1101-2021_01_08_425885	781	24	image	image	NN
10_1101-2021_01_08_425885	781	25	patch	patch	NN
10_1101-2021_01_08_425885	781	26	dataset	dataset	NN
10_1101-2021_01_08_425885	781	27	.	.	.
10_1101-2021_01_08_425885	782	1	Note	note	VB
10_1101-2021_01_08_425885	782	2	the	the	DT
10_1101-2021_01_08_425885	782	3	close	close	JJ
10_1101-2021_01_08_425885	782	4	correspondence	correspondence	NN
10_1101-2021_01_08_425885	782	5	in	in	IN
10_1101-2021_01_08_425885	782	6	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	782	7	size	size	NN
10_1101-2021_01_08_425885	782	8	with	with	IN
10_1101-2021_01_08_425885	782	9	σ	σ	NNP
10_1101-2021_01_08_425885	782	10	=	=	SYM
10_1101-2021_01_08_425885	782	11	0.03	0.03	CD
10_1101-2021_01_08_425885	782	12	in	in	IN
10_1101-2021_01_08_425885	782	13	(	(	-LRB-
10_1101-2021_01_08_425885	782	14	A	a	NN
10_1101-2021_01_08_425885	782	15	)	)	-RRB-
10_1101-2021_01_08_425885	782	16	.	.	.
10_1101-2021_01_08_425885	783	1	(	(	-LRB-
10_1101-2021_01_08_425885	783	2	C	C	NNP
10_1101-2021_01_08_425885	783	3	)	)	-RRB-
10_1101-2021_01_08_425885	783	4	Scalar	Scalar	NNP
10_1101-2021_01_08_425885	783	5	curvatures	curvature	NNS
10_1101-2021_01_08_425885	783	6	computed	compute	VBD
10_1101-2021_01_08_425885	783	7	for	for	IN
10_1101-2021_01_08_425885	783	8	the	the	DT
10_1101-2021_01_08_425885	783	9	set	set	NN
10_1101-2021_01_08_425885	783	10	of	of	IN
10_1101-2021_01_08_425885	783	11	closest	close	JJS
10_1101-2021_01_08_425885	783	12	points	point	NNS
10_1101-2021_01_08_425885	783	13	(	(	-LRB-
10_1101-2021_01_08_425885	783	14	θ0,φ0	θ0,φ0	NN
10_1101-2021_01_08_425885	783	15	)	)	-RRB-
10_1101-2021_01_08_425885	783	16	on	on	IN
10_1101-2021_01_08_425885	783	17	k	k	NNP
10_1101-2021_01_08_425885	783	18	0	0	CD
10_1101-2021_01_08_425885	783	19	as	as	IN
10_1101-2021_01_08_425885	783	20	in	in	IN
10_1101-2021_01_08_425885	783	21	Figure	Figure	NNP
10_1101-2021_01_08_425885	783	22	3E	3e	NN
10_1101-2021_01_08_425885	783	23	,	,	,
10_1101-2021_01_08_425885	783	24	but	but	CC
10_1101-2021_01_08_425885	783	25	using	use	VBG
10_1101-2021_01_08_425885	783	26	the	the	DT
10_1101-2021_01_08_425885	783	27	same	same	JJ
10_1101-2021_01_08_425885	783	28	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	783	29	sizes	size	NNS
10_1101-2021_01_08_425885	783	30	determined	determine	VBN
10_1101-2021_01_08_425885	783	31	for	for	IN
10_1101-2021_01_08_425885	783	32	the	the	DT
10_1101-2021_01_08_425885	783	33	image	image	NN
10_1101-2021_01_08_425885	783	34	patch	patch	NN
10_1101-2021_01_08_425885	783	35	dataset	dataset	NN
10_1101-2021_01_08_425885	783	36	shown	show	VBN
10_1101-2021_01_08_425885	783	37	in	in	IN
10_1101-2021_01_08_425885	783	38	Figure	Figure	NNP
10_1101-2021_01_08_425885	783	39	3D	3d	NN
10_1101-2021_01_08_425885	783	40	,	,	,
10_1101-2021_01_08_425885	783	41	some	some	DT
10_1101-2021_01_08_425885	783	42	of	of	IN
10_1101-2021_01_08_425885	783	43	which	which	WDT
10_1101-2021_01_08_425885	783	44	are	be	VBP
10_1101-2021_01_08_425885	783	45	visualized	visualize	VBN
10_1101-2021_01_08_425885	783	46	in	in	IN
10_1101-2021_01_08_425885	783	47	(	(	-LRB-
10_1101-2021_01_08_425885	783	48	B	b	NN
10_1101-2021_01_08_425885	783	49	)	)	-RRB-
10_1101-2021_01_08_425885	783	50	.	.	.
10_1101-2021_01_08_425885	784	1	(	(	-LRB-
10_1101-2021_01_08_425885	784	2	D	d	NN
10_1101-2021_01_08_425885	784	3	)	)	-RRB-
10_1101-2021_01_08_425885	784	4	As	as	IN
10_1101-2021_01_08_425885	784	5	in	in	IN
10_1101-2021_01_08_425885	784	6	(	(	-LRB-
10_1101-2021_01_08_425885	784	7	A	a	NN
10_1101-2021_01_08_425885	784	8	)	)	-RRB-
10_1101-2021_01_08_425885	784	9	but	but	CC
10_1101-2021_01_08_425885	784	10	showing	show	VBG
10_1101-2021_01_08_425885	784	11	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	784	12	used	use	VBN
10_1101-2021_01_08_425885	784	13	in	in	IN
10_1101-2021_01_08_425885	784	14	computing	compute	VBG
10_1101-2021_01_08_425885	784	15	the	the	DT
10_1101-2021_01_08_425885	784	16	scalar	scalar	JJ
10_1101-2021_01_08_425885	784	17	curvatures	curvature	NNS
10_1101-2021_01_08_425885	784	18	in	in	IN
10_1101-2021_01_08_425885	784	19	Figure	Figure	NNP
10_1101-2021_01_08_425885	784	20	3H	3h	NN
10_1101-2021_01_08_425885	784	21	for	for	IN
10_1101-2021_01_08_425885	784	22	the	the	DT
10_1101-2021_01_08_425885	784	23	set	set	NN
10_1101-2021_01_08_425885	784	24	of	of	IN
10_1101-2021_01_08_425885	784	25	closest	close	JJS
10_1101-2021_01_08_425885	784	26	points	point	NNS
10_1101-2021_01_08_425885	784	27	on	on	IN
10_1101-2021_01_08_425885	784	28	k1	k1	NNP
10_1101-2021_01_08_425885	784	29	.	.	.
10_1101-2021_01_08_425885	785	1	Neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	785	2	are	be	VBP
10_1101-2021_01_08_425885	785	3	visualized	visualize	VBN
10_1101-2021_01_08_425885	785	4	on	on	IN
10_1101-2021_01_08_425885	785	5	(	(	-LRB-
10_1101-2021_01_08_425885	785	6	θ0,φ0	θ0,φ0	NN
10_1101-2021_01_08_425885	785	7	)	)	-RRB-
10_1101-2021_01_08_425885	785	8	coordinates	coordinate	VBZ
10_1101-2021_01_08_425885	785	9	instead	instead	RB
10_1101-2021_01_08_425885	785	10	of	of	IN
10_1101-2021_01_08_425885	785	11	(	(	-LRB-
10_1101-2021_01_08_425885	785	12	θ1,φ1	θ1,φ1	NN
10_1101-2021_01_08_425885	785	13	)	)	-RRB-
10_1101-2021_01_08_425885	785	14	coordinates	coordinate	VBZ
10_1101-2021_01_08_425885	785	15	for	for	IN
10_1101-2021_01_08_425885	785	16	ease	ease	NN
10_1101-2021_01_08_425885	785	17	of	of	IN
10_1101-2021_01_08_425885	785	18	comparison	comparison	NN
10_1101-2021_01_08_425885	785	19	.	.	.
10_1101-2021_01_08_425885	786	1	(	(	-LRB-
10_1101-2021_01_08_425885	786	2	E	e	NN
10_1101-2021_01_08_425885	786	3	)	)	-RRB-
10_1101-2021_01_08_425885	786	4	As	as	IN
10_1101-2021_01_08_425885	786	5	in	in	IN
10_1101-2021_01_08_425885	786	6	(	(	-LRB-
10_1101-2021_01_08_425885	786	7	B	b	NN
10_1101-2021_01_08_425885	786	8	)	)	-RRB-
10_1101-2021_01_08_425885	786	9	but	but	CC
10_1101-2021_01_08_425885	786	10	showing	show	VBG
10_1101-2021_01_08_425885	786	11	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	786	12	used	use	VBN
10_1101-2021_01_08_425885	786	13	in	in	IN
10_1101-2021_01_08_425885	786	14	computing	compute	VBG
10_1101-2021_01_08_425885	786	15	the	the	DT
10_1101-2021_01_08_425885	786	16	scalar	scalar	JJ
10_1101-2021_01_08_425885	786	17	curvatures	curvature	NNS
10_1101-2021_01_08_425885	786	18	in	in	IN
10_1101-2021_01_08_425885	786	19	Figure	Figure	NNP
10_1101-2021_01_08_425885	786	20	3J	3j	NN
10_1101-2021_01_08_425885	786	21	for	for	IN
10_1101-2021_01_08_425885	786	22	the	the	DT
10_1101-2021_01_08_425885	786	23	augmented	augment	VBN
10_1101-2021_01_08_425885	786	24	image	image	NN
10_1101-2021_01_08_425885	786	25	patch	patch	NN
10_1101-2021_01_08_425885	786	26	dataset	dataset	NN
10_1101-2021_01_08_425885	786	27	.	.	.
10_1101-2021_01_08_425885	787	1	(	(	-LRB-
10_1101-2021_01_08_425885	787	2	F	F	NNP
10_1101-2021_01_08_425885	787	3	)	)	-RRB-
10_1101-2021_01_08_425885	787	4	Scalar	Scalar	NNP
10_1101-2021_01_08_425885	787	5	curvatures	curvature	NNS
10_1101-2021_01_08_425885	787	6	computed	compute	VBD
10_1101-2021_01_08_425885	787	7	for	for	IN
10_1101-2021_01_08_425885	787	8	the	the	DT
10_1101-2021_01_08_425885	787	9	augmented	augment	VBN
10_1101-2021_01_08_425885	787	10	image	image	NN
10_1101-2021_01_08_425885	787	11	patch	patch	NN
10_1101-2021_01_08_425885	787	12	dataset	dataset	VBN
10_1101-2021_01_08_425885	787	13	with	with	IN
10_1101-2021_01_08_425885	787	14	N	N	NNP
10_1101-2021_01_08_425885	787	15	≈	≈	NNP
10_1101-2021_01_08_425885	787	16	1.3	1.3	CD
10_1101-2021_01_08_425885	787	17	×	×	CD
10_1101-2021_01_08_425885	787	18	108	108	CD
10_1101-2021_01_08_425885	787	19	points	point	NNS
10_1101-2021_01_08_425885	787	20	as	as	IN
10_1101-2021_01_08_425885	787	21	in	in	IN
10_1101-2021_01_08_425885	787	22	Figure	Figure	NNP
10_1101-2021_01_08_425885	787	23	3J	3j	NN
10_1101-2021_01_08_425885	787	24	,	,	,
10_1101-2021_01_08_425885	787	25	but	but	CC
10_1101-2021_01_08_425885	787	26	using	use	VBG
10_1101-2021_01_08_425885	787	27	the	the	DT
10_1101-2021_01_08_425885	787	28	same	same	JJ
10_1101-2021_01_08_425885	787	29	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	787	30	sizes	size	NNS
10_1101-2021_01_08_425885	787	31	determined	determine	VBN
10_1101-2021_01_08_425885	787	32	for	for	IN
10_1101-2021_01_08_425885	787	33	the	the	DT
10_1101-2021_01_08_425885	787	34	original	original	JJ
10_1101-2021_01_08_425885	787	35	image	image	NN
10_1101-2021_01_08_425885	787	36	patch	patch	NN
10_1101-2021_01_08_425885	787	37	dataset	dataset	VBN
10_1101-2021_01_08_425885	787	38	with	with	IN
10_1101-2021_01_08_425885	787	39	N	N	NNP
10_1101-2021_01_08_425885	787	40	≈	≈	NNP
10_1101-2021_01_08_425885	787	41	4.2	4.2	CD
10_1101-2021_01_08_425885	787	42	×	×	CD
10_1101-2021_01_08_425885	787	43	105	105	CD
10_1101-2021_01_08_425885	787	44	shown	show	VBN
10_1101-2021_01_08_425885	787	45	in	in	IN
10_1101-2021_01_08_425885	787	46	Figure	figure	NN
10_1101-2021_01_08_425885	787	47	3D	3d	NN
10_1101-2021_01_08_425885	787	48	and	and	CC
10_1101-2021_01_08_425885	787	49	(	(	-LRB-
10_1101-2021_01_08_425885	787	50	B	b	NN
10_1101-2021_01_08_425885	787	51	)	)	-RRB-
10_1101-2021_01_08_425885	787	52	.	.	.
10_1101-2021_01_08_425885	788	1	Note	note	VB
10_1101-2021_01_08_425885	788	2	the	the	DT
10_1101-2021_01_08_425885	788	3	close	close	JJ
10_1101-2021_01_08_425885	788	4	correspondence	correspondence	NN
10_1101-2021_01_08_425885	788	5	with	with	IN
10_1101-2021_01_08_425885	788	6	Figure	figure	NN
10_1101-2021_01_08_425885	788	7	3D.	3d.	CD
10_1101-2021_01_08_425885	789	1	47	47	CD
10_1101-2021_01_08_425885	789	2	.CC	.CC	:
10_1101-2021_01_08_425885	789	3	-	-	HYPH
10_1101-2021_01_08_425885	789	4	BY	by	IN
10_1101-2021_01_08_425885	789	5	-	-	HYPH
10_1101-2021_01_08_425885	789	6	NC	NC	NNP
10_1101-2021_01_08_425885	789	7	-	-	HYPH
10_1101-2021_01_08_425885	789	8	ND	ND	NNP
10_1101-2021_01_08_425885	789	9	4.0	4.0	CD
10_1101-2021_01_08_425885	789	10	International	International	NNP
10_1101-2021_01_08_425885	789	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	789	12	under	under	IN
10_1101-2021_01_08_425885	789	13	a	a	DT
10_1101-2021_01_08_425885	789	14	(	(	-LRB-
10_1101-2021_01_08_425885	789	15	which	which	WDT
10_1101-2021_01_08_425885	789	16	was	be	VBD
10_1101-2021_01_08_425885	789	17	not	not	RB
10_1101-2021_01_08_425885	789	18	certified	certify	VBN
10_1101-2021_01_08_425885	789	19	by	by	IN
10_1101-2021_01_08_425885	789	20	peer	peer	NN
10_1101-2021_01_08_425885	789	21	review	review	NN
10_1101-2021_01_08_425885	789	22	)	)	-RRB-
10_1101-2021_01_08_425885	789	23	is	be	VBZ
10_1101-2021_01_08_425885	789	24	the	the	DT
10_1101-2021_01_08_425885	789	25	author	author	NN
10_1101-2021_01_08_425885	789	26	/	/	SYM
10_1101-2021_01_08_425885	789	27	funder	funder	NN
10_1101-2021_01_08_425885	789	28	,	,	,
10_1101-2021_01_08_425885	789	29	who	who	WP
10_1101-2021_01_08_425885	789	30	has	have	VBZ
10_1101-2021_01_08_425885	789	31	granted	grant	VBN
10_1101-2021_01_08_425885	789	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	789	33	a	a	DT
10_1101-2021_01_08_425885	789	34	license	license	NN
10_1101-2021_01_08_425885	789	35	to	to	TO
10_1101-2021_01_08_425885	789	36	display	display	VB
10_1101-2021_01_08_425885	789	37	the	the	DT
10_1101-2021_01_08_425885	789	38	preprint	preprint	NN
10_1101-2021_01_08_425885	789	39	in	in	IN
10_1101-2021_01_08_425885	789	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	789	41	.	.	.
10_1101-2021_01_08_425885	790	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	790	2	is	be	VBZ
10_1101-2021_01_08_425885	790	3	made	make	VBN
10_1101-2021_01_08_425885	790	4	The	the	DT
10_1101-2021_01_08_425885	790	5	copyright	copyright	NN
10_1101-2021_01_08_425885	790	6	holder	holder	NN
10_1101-2021_01_08_425885	790	7	for	for	IN
10_1101-2021_01_08_425885	790	8	this	this	DT
10_1101-2021_01_08_425885	790	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	790	10	version	version	NN
10_1101-2021_01_08_425885	790	11	posted	post	VBD
10_1101-2021_01_08_425885	790	12	January	January	NNP
10_1101-2021_01_08_425885	790	13	8	8	CD
10_1101-2021_01_08_425885	790	14	,	,	,
10_1101-2021_01_08_425885	790	15	2021	2021	CD
10_1101-2021_01_08_425885	790	16	.	.	.
10_1101-2021_01_08_425885	790	17	;	;	:
10_1101-2021_01_08_425885	790	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	790	19	:	:	:
10_1101-2021_01_08_425885	790	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	790	21	preprint	preprint	NN
10_1101-2021_01_08_425885	790	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	NNP
10_1101-2021_01_08_425885	790	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NN
10_1101-2021_01_08_425885	790	24	J	J	NNP
10_1101-2021_01_08_425885	790	25	C	C	NNP
10_1101-2021_01_08_425885	790	26	D	d	NN
10_1101-2021_01_08_425885	790	27	E	e	NN
10_1101-2021_01_08_425885	790	28	H	h	NN
10_1101-2021_01_08_425885	790	29	G	g	NN
10_1101-2021_01_08_425885	790	30	F	f	NN
10_1101-2021_01_08_425885	790	31	I	i	NN
10_1101-2021_01_08_425885	790	32	A	A	NNP
10_1101-2021_01_08_425885	790	33	B	B	NNP
10_1101-2021_01_08_425885	790	34	Figure	Figure	NNP
10_1101-2021_01_08_425885	790	35	S4	s4	NN
10_1101-2021_01_08_425885	790	36	48	48	CD
10_1101-2021_01_08_425885	790	37	.CC	.CC	:
10_1101-2021_01_08_425885	790	38	-	-	HYPH
10_1101-2021_01_08_425885	790	39	BY	by	IN
10_1101-2021_01_08_425885	790	40	-	-	HYPH
10_1101-2021_01_08_425885	790	41	NC	NC	NNP
10_1101-2021_01_08_425885	790	42	-	-	HYPH
10_1101-2021_01_08_425885	790	43	ND	ND	NNP
10_1101-2021_01_08_425885	790	44	4.0	4.0	CD
10_1101-2021_01_08_425885	790	45	International	International	NNP
10_1101-2021_01_08_425885	790	46	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	790	47	under	under	IN
10_1101-2021_01_08_425885	790	48	a	a	DT
10_1101-2021_01_08_425885	790	49	(	(	-LRB-
10_1101-2021_01_08_425885	790	50	which	which	WDT
10_1101-2021_01_08_425885	790	51	was	be	VBD
10_1101-2021_01_08_425885	790	52	not	not	RB
10_1101-2021_01_08_425885	790	53	certified	certify	VBN
10_1101-2021_01_08_425885	790	54	by	by	IN
10_1101-2021_01_08_425885	790	55	peer	peer	NN
10_1101-2021_01_08_425885	790	56	review	review	NN
10_1101-2021_01_08_425885	790	57	)	)	-RRB-
10_1101-2021_01_08_425885	790	58	is	be	VBZ
10_1101-2021_01_08_425885	790	59	the	the	DT
10_1101-2021_01_08_425885	790	60	author	author	NN
10_1101-2021_01_08_425885	790	61	/	/	SYM
10_1101-2021_01_08_425885	790	62	funder	funder	NN
10_1101-2021_01_08_425885	790	63	,	,	,
10_1101-2021_01_08_425885	790	64	who	who	WP
10_1101-2021_01_08_425885	790	65	has	have	VBZ
10_1101-2021_01_08_425885	790	66	granted	grant	VBN
10_1101-2021_01_08_425885	790	67	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	790	68	a	a	DT
10_1101-2021_01_08_425885	790	69	license	license	NN
10_1101-2021_01_08_425885	790	70	to	to	TO
10_1101-2021_01_08_425885	790	71	display	display	VB
10_1101-2021_01_08_425885	790	72	the	the	DT
10_1101-2021_01_08_425885	790	73	preprint	preprint	NN
10_1101-2021_01_08_425885	790	74	in	in	IN
10_1101-2021_01_08_425885	790	75	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	790	76	.	.	.
10_1101-2021_01_08_425885	791	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	791	2	is	be	VBZ
10_1101-2021_01_08_425885	791	3	made	make	VBN
10_1101-2021_01_08_425885	791	4	The	the	DT
10_1101-2021_01_08_425885	791	5	copyright	copyright	NN
10_1101-2021_01_08_425885	791	6	holder	holder	NN
10_1101-2021_01_08_425885	791	7	for	for	IN
10_1101-2021_01_08_425885	791	8	this	this	DT
10_1101-2021_01_08_425885	791	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	791	10	version	version	NN
10_1101-2021_01_08_425885	791	11	posted	post	VBD
10_1101-2021_01_08_425885	791	12	January	January	NNP
10_1101-2021_01_08_425885	791	13	8	8	CD
10_1101-2021_01_08_425885	791	14	,	,	,
10_1101-2021_01_08_425885	791	15	2021	2021	CD
10_1101-2021_01_08_425885	791	16	.	.	.
10_1101-2021_01_08_425885	791	17	;	;	:
10_1101-2021_01_08_425885	791	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	791	19	:	:	:
10_1101-2021_01_08_425885	791	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	791	21	preprint	preprint	NN
10_1101-2021_01_08_425885	791	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	NNP
10_1101-2021_01_08_425885	791	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NNP
10_1101-2021_01_08_425885	791	24	Figure	figure	NN
10_1101-2021_01_08_425885	791	25	S4	s4	NN
10_1101-2021_01_08_425885	791	26	:	:	:
10_1101-2021_01_08_425885	791	27	Additional	additional	JJ
10_1101-2021_01_08_425885	791	28	details	detail	NNS
10_1101-2021_01_08_425885	791	29	of	of	IN
10_1101-2021_01_08_425885	791	30	the	the	DT
10_1101-2021_01_08_425885	791	31	PBMC	PBMC	NNP
10_1101-2021_01_08_425885	791	32	scRNAseq	scRNAseq	NNP
10_1101-2021_01_08_425885	791	33	dataset	dataset	NNP
10_1101-2021_01_08_425885	791	34	(	(	-LRB-
10_1101-2021_01_08_425885	791	35	related	related	JJ
10_1101-2021_01_08_425885	791	36	to	to	IN
10_1101-2021_01_08_425885	791	37	Figure	Figure	NNP
10_1101-2021_01_08_425885	791	38	4	4	CD
10_1101-2021_01_08_425885	791	39	)	)	-RRB-
10_1101-2021_01_08_425885	791	40	.	.	.
10_1101-2021_01_08_425885	792	1	(	(	-LRB-
10_1101-2021_01_08_425885	792	2	A	a	DT
10_1101-2021_01_08_425885	792	3	)	)	-RRB-
10_1101-2021_01_08_425885	792	4	Cell	cell	NN
10_1101-2021_01_08_425885	792	5	types	type	NNS
10_1101-2021_01_08_425885	792	6	overlaid	overlay	VBD
10_1101-2021_01_08_425885	792	7	onto	onto	IN
10_1101-2021_01_08_425885	792	8	UMAP	UMAP	NNP
10_1101-2021_01_08_425885	792	9	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	792	10	and	and	CC
10_1101-2021_01_08_425885	792	11	sorted	sort	VBD
10_1101-2021_01_08_425885	792	12	in	in	IN
10_1101-2021_01_08_425885	792	13	decreasing	decrease	VBG
10_1101-2021_01_08_425885	792	14	order	order	NN
10_1101-2021_01_08_425885	792	15	of	of	IN
10_1101-2021_01_08_425885	792	16	abundance	abundance	NN
10_1101-2021_01_08_425885	792	17	in	in	IN
10_1101-2021_01_08_425885	792	18	the	the	DT
10_1101-2021_01_08_425885	792	19	legend	legend	NN
10_1101-2021_01_08_425885	792	20	.	.	.
10_1101-2021_01_08_425885	793	1	Cells	cell	NNS
10_1101-2021_01_08_425885	793	2	were	be	VBD
10_1101-2021_01_08_425885	793	3	annotated	annotate	VBN
10_1101-2021_01_08_425885	793	4	as	as	IN
10_1101-2021_01_08_425885	793	5	described	describe	VBN
10_1101-2021_01_08_425885	793	6	in	in	IN
10_1101-2021_01_08_425885	793	7	Methods	Methods	NNP
10_1101-2021_01_08_425885	793	8	Section	Section	NNP
10_1101-2021_01_08_425885	793	9	4.6.2	4.6.2	CD
10_1101-2021_01_08_425885	793	10	.	.	.
10_1101-2021_01_08_425885	794	1	(	(	-LRB-
10_1101-2021_01_08_425885	794	2	B	b	NN
10_1101-2021_01_08_425885	794	3	)	)	-RRB-
10_1101-2021_01_08_425885	794	4	A	a	DT
10_1101-2021_01_08_425885	794	5	goodness	goodness	NN
10_1101-2021_01_08_425885	794	6	-	-	HYPH
10_1101-2021_01_08_425885	794	7	of	of	IN
10_1101-2021_01_08_425885	794	8	-	-	HYPH
10_1101-2021_01_08_425885	794	9	fit	fit	NNP
10_1101-2021_01_08_425885	794	10	p	p	NN
10_1101-2021_01_08_425885	794	11	-	-	HYPH
10_1101-2021_01_08_425885	794	12	value	value	NN
10_1101-2021_01_08_425885	794	13	was	be	VBD
10_1101-2021_01_08_425885	794	14	computed	compute	VBN
10_1101-2021_01_08_425885	794	15	for	for	IN
10_1101-2021_01_08_425885	794	16	each	each	DT
10_1101-2021_01_08_425885	794	17	point	point	NN
10_1101-2021_01_08_425885	794	18	by	by	IN
10_1101-2021_01_08_425885	794	19	applying	apply	VBG
10_1101-2021_01_08_425885	794	20	Mardia	Mardia	NNP
10_1101-2021_01_08_425885	794	21	’s	’s	POS
10_1101-2021_01_08_425885	794	22	test	test	NN
10_1101-2021_01_08_425885	794	23	to	to	IN
10_1101-2021_01_08_425885	794	24	the	the	DT
10_1101-2021_01_08_425885	794	25	residuals	residual	NNS
10_1101-2021_01_08_425885	794	26	obtained	obtain	VBN
10_1101-2021_01_08_425885	794	27	from	from	IN
10_1101-2021_01_08_425885	794	28	fitting	fit	VBG
10_1101-2021_01_08_425885	794	29	the	the	DT
10_1101-2021_01_08_425885	794	30	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	794	31	around	around	IN
10_1101-2021_01_08_425885	794	32	the	the	DT
10_1101-2021_01_08_425885	794	33	point	point	NN
10_1101-2021_01_08_425885	794	34	to	to	IN
10_1101-2021_01_08_425885	794	35	a	a	DT
10_1101-2021_01_08_425885	794	36	quadratic	quadratic	JJ
10_1101-2021_01_08_425885	794	37	function	function	NN
10_1101-2021_01_08_425885	794	38	(	(	-LRB-
10_1101-2021_01_08_425885	794	39	see	see	VB
10_1101-2021_01_08_425885	794	40	Methods	Methods	NNP
10_1101-2021_01_08_425885	794	41	Section	Section	NNP
10_1101-2021_01_08_425885	794	42	4.3.3	4.3.3	CD
10_1101-2021_01_08_425885	794	43	)	)	-RRB-
10_1101-2021_01_08_425885	794	44	.	.	.
10_1101-2021_01_08_425885	795	1	These	these	DT
10_1101-2021_01_08_425885	795	2	p	p	NN
10_1101-2021_01_08_425885	795	3	-	-	HYPH
10_1101-2021_01_08_425885	795	4	values	value	NNS
10_1101-2021_01_08_425885	795	5	are	be	VBP
10_1101-2021_01_08_425885	795	6	visualized	visualize	VBN
10_1101-2021_01_08_425885	795	7	on	on	IN
10_1101-2021_01_08_425885	795	8	UMAP	UMAP	NNP
10_1101-2021_01_08_425885	795	9	coordinates	coordinate	VBZ
10_1101-2021_01_08_425885	795	10	corresponding	correspond	VBG
10_1101-2021_01_08_425885	795	11	to	to	IN
10_1101-2021_01_08_425885	795	12	each	each	DT
10_1101-2021_01_08_425885	795	13	point	point	NN
10_1101-2021_01_08_425885	795	14	(	(	-LRB-
10_1101-2021_01_08_425885	795	15	left	left	RB
10_1101-2021_01_08_425885	795	16	)	)	-RRB-
10_1101-2021_01_08_425885	795	17	and	and	CC
10_1101-2021_01_08_425885	795	18	their	-PRON-	PRP$
10_1101-2021_01_08_425885	795	19	empirical	empirical	JJ
10_1101-2021_01_08_425885	795	20	distribution	distribution	NN
10_1101-2021_01_08_425885	795	21	is	be	VBZ
10_1101-2021_01_08_425885	795	22	shown	show	VBN
10_1101-2021_01_08_425885	795	23	using	use	VBG
10_1101-2021_01_08_425885	795	24	a	a	DT
10_1101-2021_01_08_425885	795	25	histogram	histogram	NN
10_1101-2021_01_08_425885	795	26	(	(	-LRB-
10_1101-2021_01_08_425885	795	27	right	right	UH
10_1101-2021_01_08_425885	795	28	)	)	-RRB-
10_1101-2021_01_08_425885	795	29	.	.	.
10_1101-2021_01_08_425885	796	1	Small	small	JJ
10_1101-2021_01_08_425885	796	2	p	p	NN
10_1101-2021_01_08_425885	796	3	-	-	HYPH
10_1101-2021_01_08_425885	796	4	values	value	NNS
10_1101-2021_01_08_425885	796	5	suggest	suggest	VBP
10_1101-2021_01_08_425885	796	6	that	that	IN
10_1101-2021_01_08_425885	796	7	the	the	DT
10_1101-2021_01_08_425885	796	8	residuals	residual	NNS
10_1101-2021_01_08_425885	796	9	are	be	VBP
10_1101-2021_01_08_425885	796	10	non	non	JJ
10_1101-2021_01_08_425885	796	11	-	-	JJ
10_1101-2021_01_08_425885	796	12	normal	normal	JJ
10_1101-2021_01_08_425885	796	13	so	so	IN
10_1101-2021_01_08_425885	796	14	that	that	IN
10_1101-2021_01_08_425885	796	15	approximating	approximate	VBG
10_1101-2021_01_08_425885	796	16	local	local	JJ
10_1101-2021_01_08_425885	796	17	neighborhoods	neighborhood	NNS
10_1101-2021_01_08_425885	796	18	as	as	IN
10_1101-2021_01_08_425885	796	19	quadratic	quadratic	NNP
10_1101-2021_01_08_425885	796	20	may	may	MD
10_1101-2021_01_08_425885	796	21	not	not	RB
10_1101-2021_01_08_425885	796	22	be	be	VB
10_1101-2021_01_08_425885	796	23	valid	valid	JJ
10_1101-2021_01_08_425885	796	24	.	.	.
10_1101-2021_01_08_425885	797	1	(	(	-LRB-
10_1101-2021_01_08_425885	797	2	C	C	NNP
10_1101-2021_01_08_425885	797	3	)	)	-RRB-
10_1101-2021_01_08_425885	797	4	Pearson	Pearson	NNP
10_1101-2021_01_08_425885	797	5	correlation	correlation	NN
10_1101-2021_01_08_425885	797	6	between	between	IN
10_1101-2021_01_08_425885	797	7	the	the	DT
10_1101-2021_01_08_425885	797	8	scalar	scalar	JJ
10_1101-2021_01_08_425885	797	9	curvature	curvature	NN
10_1101-2021_01_08_425885	797	10	reported	report	VBN
10_1101-2021_01_08_425885	797	11	by	by	IN
10_1101-2021_01_08_425885	797	12	each	each	DT
10_1101-2021_01_08_425885	797	13	point	point	NN
10_1101-2021_01_08_425885	797	14	and	and	CC
10_1101-2021_01_08_425885	797	15	its	-PRON-	PRP$
10_1101-2021_01_08_425885	797	16	kth	kth	NN
10_1101-2021_01_08_425885	797	17	-	-	HYPH
10_1101-2021_01_08_425885	797	18	nearest	near	JJS
10_1101-2021_01_08_425885	797	19	neighbor	neighbor	NN
10_1101-2021_01_08_425885	797	20	(	(	-LRB-
10_1101-2021_01_08_425885	797	21	kNN	kNN	NNP
10_1101-2021_01_08_425885	797	22	)	)	-RRB-
10_1101-2021_01_08_425885	797	23	for	for	IN
10_1101-2021_01_08_425885	797	24	different	different	JJ
10_1101-2021_01_08_425885	797	25	k	k	NNP
10_1101-2021_01_08_425885	797	26	(	(	-LRB-
10_1101-2021_01_08_425885	797	27	shown	show	VBN
10_1101-2021_01_08_425885	797	28	in	in	IN
10_1101-2021_01_08_425885	797	29	blue	blue	NNP
10_1101-2021_01_08_425885	797	30	)	)	-RRB-
10_1101-2021_01_08_425885	797	31	.	.	.
10_1101-2021_01_08_425885	798	1	The	the	DT
10_1101-2021_01_08_425885	798	2	red	red	JJ
10_1101-2021_01_08_425885	798	3	bar	bar	NN
10_1101-2021_01_08_425885	798	4	shows	show	VBZ
10_1101-2021_01_08_425885	798	5	the	the	DT
10_1101-2021_01_08_425885	798	6	mean	mean	JJ
10_1101-2021_01_08_425885	798	7	and	and	CC
10_1101-2021_01_08_425885	798	8	standard	standard	JJ
10_1101-2021_01_08_425885	798	9	deviation	deviation	NN
10_1101-2021_01_08_425885	798	10	of	of	IN
10_1101-2021_01_08_425885	798	11	the	the	DT
10_1101-2021_01_08_425885	798	12	Pearson	Pearson	NNP
10_1101-2021_01_08_425885	798	13	correlation	correlation	NN
10_1101-2021_01_08_425885	798	14	when	when	WRB
10_1101-2021_01_08_425885	798	15	neighbors	neighbor	NNS
10_1101-2021_01_08_425885	798	16	are	be	VBP
10_1101-2021_01_08_425885	798	17	chosen	choose	VBN
10_1101-2021_01_08_425885	798	18	randomly	randomly	RB
10_1101-2021_01_08_425885	798	19	over	over	IN
10_1101-2021_01_08_425885	798	20	1000	1000	CD
10_1101-2021_01_08_425885	798	21	trials	trial	NNS
10_1101-2021_01_08_425885	798	22	(	(	-LRB-
10_1101-2021_01_08_425885	798	23	*	*	NFP
10_1101-2021_01_08_425885	798	24	p	p	NN
10_1101-2021_01_08_425885	798	25	<	<	XX
10_1101-2021_01_08_425885	798	26	10−6	10−6	CD
10_1101-2021_01_08_425885	798	27	)	)	-RRB-
10_1101-2021_01_08_425885	798	28	.	.	.
10_1101-2021_01_08_425885	799	1	(	(	-LRB-
10_1101-2021_01_08_425885	799	2	D	d	NN
10_1101-2021_01_08_425885	799	3	)	)	-RRB-
10_1101-2021_01_08_425885	799	4	The	the	DT
10_1101-2021_01_08_425885	799	5	percentage	percentage	NN
10_1101-2021_01_08_425885	799	6	of	of	IN
10_1101-2021_01_08_425885	799	7	points	point	NNS
10_1101-2021_01_08_425885	799	8	with	with	IN
10_1101-2021_01_08_425885	799	9	95	95	CD
10_1101-2021_01_08_425885	799	10	%	%	NN
10_1101-2021_01_08_425885	799	11	CIs	ci	NNS
10_1101-2021_01_08_425885	799	12	containing	contain	VBG
10_1101-2021_01_08_425885	799	13	the	the	DT
10_1101-2021_01_08_425885	799	14	scalar	scalar	JJ
10_1101-2021_01_08_425885	799	15	curvatures	curvature	NNS
10_1101-2021_01_08_425885	799	16	reported	report	VBN
10_1101-2021_01_08_425885	799	17	by	by	IN
10_1101-2021_01_08_425885	799	18	their	-PRON-	PRP$
10_1101-2021_01_08_425885	799	19	respective	respective	JJ
10_1101-2021_01_08_425885	799	20	kNNs	knns	NN
10_1101-2021_01_08_425885	799	21	(	(	-LRB-
10_1101-2021_01_08_425885	799	22	shown	show	VBN
10_1101-2021_01_08_425885	799	23	in	in	IN
10_1101-2021_01_08_425885	799	24	blue	blue	NNP
10_1101-2021_01_08_425885	799	25	)	)	-RRB-
10_1101-2021_01_08_425885	799	26	.	.	.
10_1101-2021_01_08_425885	800	1	The	the	DT
10_1101-2021_01_08_425885	800	2	red	red	JJ
10_1101-2021_01_08_425885	800	3	bar	bar	NN
10_1101-2021_01_08_425885	800	4	shows	show	VBZ
10_1101-2021_01_08_425885	800	5	the	the	DT
10_1101-2021_01_08_425885	800	6	mean	mean	JJ
10_1101-2021_01_08_425885	800	7	and	and	CC
10_1101-2021_01_08_425885	800	8	standard	standard	JJ
10_1101-2021_01_08_425885	800	9	deviation	deviation	NN
10_1101-2021_01_08_425885	800	10	of	of	IN
10_1101-2021_01_08_425885	800	11	this	this	DT
10_1101-2021_01_08_425885	800	12	percentage	percentage	NN
10_1101-2021_01_08_425885	800	13	when	when	WRB
10_1101-2021_01_08_425885	800	14	neighbors	neighbor	NNS
10_1101-2021_01_08_425885	800	15	are	be	VBP
10_1101-2021_01_08_425885	800	16	chosen	choose	VBN
10_1101-2021_01_08_425885	800	17	randomly	randomly	RB
10_1101-2021_01_08_425885	800	18	over	over	IN
10_1101-2021_01_08_425885	800	19	1000	1000	CD
10_1101-2021_01_08_425885	800	20	trials	trial	NNS
10_1101-2021_01_08_425885	800	21	(	(	-LRB-
10_1101-2021_01_08_425885	800	22	*	*	NFP
10_1101-2021_01_08_425885	800	23	p	p	NN
10_1101-2021_01_08_425885	800	24	<	<	XX
10_1101-2021_01_08_425885	800	25	0.001	0.001	CD
10_1101-2021_01_08_425885	800	26	;	;	:
10_1101-2021_01_08_425885	800	27	see	see	VB
10_1101-2021_01_08_425885	800	28	Methods	Methods	NNP
10_1101-2021_01_08_425885	800	29	Section	Section	NNP
10_1101-2021_01_08_425885	800	30	4.6.3.1	4.6.3.1	CD
10_1101-2021_01_08_425885	800	31	)	)	-RRB-
10_1101-2021_01_08_425885	800	32	.	.	.
10_1101-2021_01_08_425885	801	1	(	(	-LRB-
10_1101-2021_01_08_425885	801	2	E	e	NN
10_1101-2021_01_08_425885	801	3	)	)	-RRB-
10_1101-2021_01_08_425885	801	4	The	the	DT
10_1101-2021_01_08_425885	801	5	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	801	6	size	size	NN
10_1101-2021_01_08_425885	801	7	(	(	-LRB-
10_1101-2021_01_08_425885	801	8	r	r	NN
10_1101-2021_01_08_425885	801	9	)	)	-RRB-
10_1101-2021_01_08_425885	801	10	used	use	VBN
10_1101-2021_01_08_425885	801	11	for	for	IN
10_1101-2021_01_08_425885	801	12	computing	compute	VBG
10_1101-2021_01_08_425885	801	13	scalar	scalar	JJ
10_1101-2021_01_08_425885	801	14	curvature	curvature	NN
10_1101-2021_01_08_425885	801	15	at	at	IN
10_1101-2021_01_08_425885	801	16	each	each	DT
10_1101-2021_01_08_425885	801	17	point	point	NN
10_1101-2021_01_08_425885	801	18	,	,	,
10_1101-2021_01_08_425885	801	19	overlaid	overlay	VBN
10_1101-2021_01_08_425885	801	20	onto	onto	IN
10_1101-2021_01_08_425885	801	21	UMAP	UMAP	NNP
10_1101-2021_01_08_425885	801	22	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	801	23	(	(	-LRB-
10_1101-2021_01_08_425885	801	24	left	left	RB
10_1101-2021_01_08_425885	801	25	)	)	-RRB-
10_1101-2021_01_08_425885	801	26	and	and	CC
10_1101-2021_01_08_425885	801	27	a	a	DT
10_1101-2021_01_08_425885	801	28	corresponding	correspond	VBG
10_1101-2021_01_08_425885	801	29	histogram	histogram	NN
10_1101-2021_01_08_425885	801	30	of	of	IN
10_1101-2021_01_08_425885	801	31	the	the	DT
10_1101-2021_01_08_425885	801	32	empirical	empirical	JJ
10_1101-2021_01_08_425885	801	33	distribution	distribution	NN
10_1101-2021_01_08_425885	801	34	(	(	-LRB-
10_1101-2021_01_08_425885	801	35	right	right	RB
10_1101-2021_01_08_425885	801	36	)	)	-RRB-
10_1101-2021_01_08_425885	801	37	.	.	.
10_1101-2021_01_08_425885	802	1	The	the	DT
10_1101-2021_01_08_425885	802	2	dashed	dash	VBN
10_1101-2021_01_08_425885	802	3	red	red	JJ
10_1101-2021_01_08_425885	802	4	lines	line	NNS
10_1101-2021_01_08_425885	802	5	correspond	correspond	VBP
10_1101-2021_01_08_425885	802	6	to	to	IN
10_1101-2021_01_08_425885	802	7	the	the	DT
10_1101-2021_01_08_425885	802	8	25	25	CD
10_1101-2021_01_08_425885	802	9	,	,	,
10_1101-2021_01_08_425885	802	10	50	50	CD
10_1101-2021_01_08_425885	802	11	,	,	,
10_1101-2021_01_08_425885	802	12	and	and	CC
10_1101-2021_01_08_425885	802	13	75%-ile	75%-ile	CD
10_1101-2021_01_08_425885	802	14	values	value	NNS
10_1101-2021_01_08_425885	802	15	of	of	IN
10_1101-2021_01_08_425885	802	16	r(p	r(p	NNP
10_1101-2021_01_08_425885	802	17	)	)	-RRB-
10_1101-2021_01_08_425885	802	18	used	use	VBN
10_1101-2021_01_08_425885	802	19	for	for	IN
10_1101-2021_01_08_425885	802	20	computing	compute	VBG
10_1101-2021_01_08_425885	802	21	scalar	scalar	JJ
10_1101-2021_01_08_425885	802	22	curvatures	curvature	NNS
10_1101-2021_01_08_425885	802	23	at	at	IN
10_1101-2021_01_08_425885	802	24	fixed	fix	VBN
10_1101-2021_01_08_425885	802	25	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	802	26	sizes	size	NNS
10_1101-2021_01_08_425885	802	27	for	for	IN
10_1101-2021_01_08_425885	802	28	Figure	figure	NN
10_1101-2021_01_08_425885	802	29	4C.	4c.	CD
10_1101-2021_01_08_425885	803	1	See	see	VB
10_1101-2021_01_08_425885	803	2	Methods	Methods	NNP
10_1101-2021_01_08_425885	803	3	Section	Section	NNP
10_1101-2021_01_08_425885	803	4	4.3.2	4.3.2	CD
10_1101-2021_01_08_425885	803	5	.	.	.
10_1101-2021_01_08_425885	804	1	(	(	-LRB-
10_1101-2021_01_08_425885	804	2	F	f	NN
10_1101-2021_01_08_425885	804	3	)	)	-RRB-
10_1101-2021_01_08_425885	804	4	The	the	DT
10_1101-2021_01_08_425885	804	5	number	number	NN
10_1101-2021_01_08_425885	804	6	of	of	IN
10_1101-2021_01_08_425885	804	7	points	point	NNS
10_1101-2021_01_08_425885	804	8	in	in	IN
10_1101-2021_01_08_425885	804	9	each	each	DT
10_1101-2021_01_08_425885	804	10	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	804	11	(	(	-LRB-
10_1101-2021_01_08_425885	804	12	corresponding	correspond	VBG
10_1101-2021_01_08_425885	804	13	to	to	IN
10_1101-2021_01_08_425885	804	14	the	the	DT
10_1101-2021_01_08_425885	804	15	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	804	16	sizes	size	NNS
10_1101-2021_01_08_425885	804	17	in	in	IN
10_1101-2021_01_08_425885	804	18	(	(	-LRB-
10_1101-2021_01_08_425885	804	19	E	e	NN
10_1101-2021_01_08_425885	804	20	)	)	-RRB-
10_1101-2021_01_08_425885	804	21	)	)	-RRB-
10_1101-2021_01_08_425885	804	22	overlaid	overlay	VBN
10_1101-2021_01_08_425885	804	23	onto	onto	IN
10_1101-2021_01_08_425885	804	24	UMAP	UMAP	NNP
10_1101-2021_01_08_425885	804	25	co-	co-	VBN
10_1101-2021_01_08_425885	804	26	ordinates	ordinate	NNS
10_1101-2021_01_08_425885	804	27	(	(	-LRB-
10_1101-2021_01_08_425885	804	28	left	leave	VBN
10_1101-2021_01_08_425885	804	29	)	)	-RRB-
10_1101-2021_01_08_425885	804	30	and	and	CC
10_1101-2021_01_08_425885	804	31	a	a	DT
10_1101-2021_01_08_425885	804	32	corresponding	correspond	VBG
10_1101-2021_01_08_425885	804	33	histogram	histogram	NN
10_1101-2021_01_08_425885	804	34	of	of	IN
10_1101-2021_01_08_425885	804	35	the	the	DT
10_1101-2021_01_08_425885	804	36	empirical	empirical	JJ
10_1101-2021_01_08_425885	804	37	distribution	distribution	NN
10_1101-2021_01_08_425885	804	38	(	(	-LRB-
10_1101-2021_01_08_425885	804	39	middle	middle	NNP
10_1101-2021_01_08_425885	804	40	)	)	-RRB-
10_1101-2021_01_08_425885	804	41	.	.	.
10_1101-2021_01_08_425885	805	1	(	(	-LRB-
10_1101-2021_01_08_425885	805	2	Right	right	UH
10_1101-2021_01_08_425885	805	3	)	)	-RRB-
10_1101-2021_01_08_425885	805	4	The	the	DT
10_1101-2021_01_08_425885	805	5	set	set	NN
10_1101-2021_01_08_425885	805	6	of	of	IN
10_1101-2021_01_08_425885	805	7	neighbors	neighbor	NNS
10_1101-2021_01_08_425885	805	8	used	use	VBN
10_1101-2021_01_08_425885	805	9	for	for	IN
10_1101-2021_01_08_425885	805	10	computing	compute	VBG
10_1101-2021_01_08_425885	805	11	scalar	scalar	JJ
10_1101-2021_01_08_425885	805	12	curvature	curvature	NN
10_1101-2021_01_08_425885	805	13	(	(	-LRB-
10_1101-2021_01_08_425885	805	14	purple	purple	NN
10_1101-2021_01_08_425885	805	15	)	)	-RRB-
10_1101-2021_01_08_425885	805	16	is	be	VBZ
10_1101-2021_01_08_425885	805	17	visualized	visualize	VBN
10_1101-2021_01_08_425885	805	18	on	on	IN
10_1101-2021_01_08_425885	805	19	UMAP	UMAP	NNP
10_1101-2021_01_08_425885	805	20	coordinates	coordinate	VBZ
10_1101-2021_01_08_425885	805	21	for	for	IN
10_1101-2021_01_08_425885	805	22	a	a	DT
10_1101-2021_01_08_425885	805	23	handful	handful	NN
10_1101-2021_01_08_425885	805	24	of	of	IN
10_1101-2021_01_08_425885	805	25	points	point	NNS
10_1101-2021_01_08_425885	805	26	(	(	-LRB-
10_1101-2021_01_08_425885	805	27	black	black	JJ
10_1101-2021_01_08_425885	805	28	)	)	-RRB-
10_1101-2021_01_08_425885	805	29	.	.	.
10_1101-2021_01_08_425885	806	1	(	(	-LRB-
10_1101-2021_01_08_425885	806	2	G	G	NNP
10_1101-2021_01_08_425885	806	3	)	)	-RRB-
10_1101-2021_01_08_425885	806	4	Scalar	Scalar	NNP
10_1101-2021_01_08_425885	806	5	curvatures	curvature	NNS
10_1101-2021_01_08_425885	806	6	were	be	VBD
10_1101-2021_01_08_425885	806	7	computed	compute	VBN
10_1101-2021_01_08_425885	806	8	for	for	IN
10_1101-2021_01_08_425885	806	9	manifold	manifold	JJ
10_1101-2021_01_08_425885	806	10	dimension	dimension	NN
10_1101-2021_01_08_425885	806	11	d−	d−	NNP
10_1101-2021_01_08_425885	806	12	1	1	CD
10_1101-2021_01_08_425885	806	13	(	(	-LRB-
10_1101-2021_01_08_425885	806	14	left	left	RB
10_1101-2021_01_08_425885	806	15	)	)	-RRB-
10_1101-2021_01_08_425885	806	16	and	and	CC
10_1101-2021_01_08_425885	806	17	d	d	NN
10_1101-2021_01_08_425885	806	18	+	+	SYM
10_1101-2021_01_08_425885	806	19	1	1	CD
10_1101-2021_01_08_425885	806	20	(	(	-LRB-
10_1101-2021_01_08_425885	806	21	right	right	RB
10_1101-2021_01_08_425885	806	22	)	)	-RRB-
10_1101-2021_01_08_425885	806	23	.	.	.
10_1101-2021_01_08_425885	807	1	They	-PRON-	PRP
10_1101-2021_01_08_425885	807	2	are	be	VBP
10_1101-2021_01_08_425885	807	3	plotted	plot	VBN
10_1101-2021_01_08_425885	807	4	here	here	RB
10_1101-2021_01_08_425885	807	5	on	on	IN
10_1101-2021_01_08_425885	807	6	UMAP	UMAP	NNP
10_1101-2021_01_08_425885	807	7	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	807	8	after	after	IN
10_1101-2021_01_08_425885	807	9	smoothing	smooth	VBG
10_1101-2021_01_08_425885	807	10	over	over	IN
10_1101-2021_01_08_425885	807	11	the	the	DT
10_1101-2021_01_08_425885	807	12	same	same	JJ
10_1101-2021_01_08_425885	807	13	set	set	NN
10_1101-2021_01_08_425885	807	14	of	of	IN
10_1101-2021_01_08_425885	807	15	k	k	NN
10_1101-2021_01_08_425885	807	16	=	=	SYM
10_1101-2021_01_08_425885	807	17	250	250	CD
10_1101-2021_01_08_425885	807	18	neighbors	neighbor	NNS
10_1101-2021_01_08_425885	807	19	used	use	VBN
10_1101-2021_01_08_425885	807	20	in	in	IN
10_1101-2021_01_08_425885	807	21	Figure	figure	NN
10_1101-2021_01_08_425885	807	22	4A.	4a.	NN
10_1101-2021_01_08_425885	808	1	See	see	VB
10_1101-2021_01_08_425885	808	2	Methods	Methods	NNP
10_1101-2021_01_08_425885	808	3	Section	Section	NNP
10_1101-2021_01_08_425885	808	4	4.6.4	4.6.4	CD
10_1101-2021_01_08_425885	808	5	.	.	.
10_1101-2021_01_08_425885	809	1	(	(	-LRB-
10_1101-2021_01_08_425885	809	2	H	h	NN
10_1101-2021_01_08_425885	809	3	)	)	-RRB-
10_1101-2021_01_08_425885	809	4	The	the	DT
10_1101-2021_01_08_425885	809	5	total	total	JJ
10_1101-2021_01_08_425885	809	6	number	number	NN
10_1101-2021_01_08_425885	809	7	of	of	IN
10_1101-2021_01_08_425885	809	8	transcripts	transcript	NNS
10_1101-2021_01_08_425885	809	9	observed	observe	VBN
10_1101-2021_01_08_425885	809	10	in	in	IN
10_1101-2021_01_08_425885	809	11	each	each	DT
10_1101-2021_01_08_425885	809	12	cell	cell	NN
10_1101-2021_01_08_425885	809	13	overlaid	overlay	VBN
10_1101-2021_01_08_425885	809	14	onto	onto	IN
10_1101-2021_01_08_425885	809	15	UMAP	UMAP	NNP
10_1101-2021_01_08_425885	809	16	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	809	17	.	.	.
10_1101-2021_01_08_425885	810	1	(	(	-LRB-
10_1101-2021_01_08_425885	810	2	I	i	NN
10_1101-2021_01_08_425885	810	3	)	)	-RRB-
10_1101-2021_01_08_425885	810	4	Scalar	scalar	JJ
10_1101-2021_01_08_425885	810	5	curvatures	curvature	NNS
10_1101-2021_01_08_425885	810	6	were	be	VBD
10_1101-2021_01_08_425885	810	7	computed	compute	VBN
10_1101-2021_01_08_425885	810	8	after	after	IN
10_1101-2021_01_08_425885	810	9	downsampling	downsample	VBG
10_1101-2021_01_08_425885	810	10	the	the	DT
10_1101-2021_01_08_425885	810	11	number	number	NN
10_1101-2021_01_08_425885	810	12	of	of	IN
10_1101-2021_01_08_425885	810	13	cells	cell	NNS
10_1101-2021_01_08_425885	810	14	in	in	IN
10_1101-2021_01_08_425885	810	15	the	the	DT
10_1101-2021_01_08_425885	810	16	ambient	ambient	JJ
10_1101-2021_01_08_425885	810	17	space	space	NN
10_1101-2021_01_08_425885	810	18	by	by	IN
10_1101-2021_01_08_425885	810	19	a	a	DT
10_1101-2021_01_08_425885	810	20	factor	factor	NN
10_1101-2021_01_08_425885	810	21	of	of	IN
10_1101-2021_01_08_425885	810	22	2	2	CD
10_1101-2021_01_08_425885	810	23	(	(	-LRB-
10_1101-2021_01_08_425885	810	24	left	left	RB
10_1101-2021_01_08_425885	810	25	)	)	-RRB-
10_1101-2021_01_08_425885	810	26	and	and	CC
10_1101-2021_01_08_425885	810	27	4	4	CD
10_1101-2021_01_08_425885	810	28	(	(	-LRB-
10_1101-2021_01_08_425885	810	29	middle	middle	NNP
10_1101-2021_01_08_425885	810	30	)	)	-RRB-
10_1101-2021_01_08_425885	810	31	,	,	,
10_1101-2021_01_08_425885	810	32	using	use	VBG
10_1101-2021_01_08_425885	810	33	the	the	DT
10_1101-2021_01_08_425885	810	34	same	same	JJ
10_1101-2021_01_08_425885	810	35	ambient	ambient	JJ
10_1101-2021_01_08_425885	810	36	dimension	dimension	NN
10_1101-2021_01_08_425885	810	37	,	,	,
10_1101-2021_01_08_425885	810	38	manifold	manifold	JJ
10_1101-2021_01_08_425885	810	39	dimension	dimension	NN
10_1101-2021_01_08_425885	810	40	and	and	CC
10_1101-2021_01_08_425885	810	41	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	810	42	sizes	size	NNS
10_1101-2021_01_08_425885	810	43	determined	determine	VBN
10_1101-2021_01_08_425885	810	44	for	for	IN
10_1101-2021_01_08_425885	810	45	the	the	DT
10_1101-2021_01_08_425885	810	46	original	original	JJ
10_1101-2021_01_08_425885	810	47	dataset	dataset	NN
10_1101-2021_01_08_425885	810	48	.	.	.
10_1101-2021_01_08_425885	811	1	They	-PRON-	PRP
10_1101-2021_01_08_425885	811	2	are	be	VBP
10_1101-2021_01_08_425885	811	3	plotted	plot	VBN
10_1101-2021_01_08_425885	811	4	here	here	RB
10_1101-2021_01_08_425885	811	5	on	on	IN
10_1101-2021_01_08_425885	811	6	UMAP	UMAP	NNP
10_1101-2021_01_08_425885	811	7	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	811	8	after	after	IN
10_1101-2021_01_08_425885	811	9	smoothing	smooth	VBG
10_1101-2021_01_08_425885	811	10	over	over	IN
10_1101-2021_01_08_425885	811	11	the	the	DT
10_1101-2021_01_08_425885	811	12	same	same	JJ
10_1101-2021_01_08_425885	811	13	set	set	NN
10_1101-2021_01_08_425885	811	14	of	of	IN
10_1101-2021_01_08_425885	811	15	neighbors	neighbor	NNS
10_1101-2021_01_08_425885	811	16	(	(	-LRB-
10_1101-2021_01_08_425885	811	17	which	which	WDT
10_1101-2021_01_08_425885	811	18	survive	survive	VBP
10_1101-2021_01_08_425885	811	19	downsampling	downsample	VBG
10_1101-2021_01_08_425885	811	20	)	)	-RRB-
10_1101-2021_01_08_425885	811	21	used	use	VBN
10_1101-2021_01_08_425885	811	22	in	in	IN
10_1101-2021_01_08_425885	811	23	Figure	figure	NN
10_1101-2021_01_08_425885	811	24	4A.	4a.	NN
10_1101-2021_01_08_425885	812	1	(	(	-LRB-
10_1101-2021_01_08_425885	812	2	Right	right	UH
10_1101-2021_01_08_425885	812	3	)	)	-RRB-
10_1101-2021_01_08_425885	812	4	The	the	DT
10_1101-2021_01_08_425885	812	5	percentage	percentage	NN
10_1101-2021_01_08_425885	812	6	of	of	IN
10_1101-2021_01_08_425885	812	7	points	point	NNS
10_1101-2021_01_08_425885	812	8	in	in	IN
10_1101-2021_01_08_425885	812	9	the	the	DT
10_1101-2021_01_08_425885	812	10	downsampled	downsampled	JJ
10_1101-2021_01_08_425885	812	11	datasets	dataset	NNS
10_1101-2021_01_08_425885	812	12	with	with	IN
10_1101-2021_01_08_425885	812	13	a	a	DT
10_1101-2021_01_08_425885	812	14	95	95	CD
10_1101-2021_01_08_425885	812	15	%	%	NN
10_1101-2021_01_08_425885	812	16	CI	ci	NN
10_1101-2021_01_08_425885	812	17	containing	contain	VBG
10_1101-2021_01_08_425885	812	18	the	the	DT
10_1101-2021_01_08_425885	812	19	originally	originally	RB
10_1101-2021_01_08_425885	812	20	reported	report	VBN
10_1101-2021_01_08_425885	812	21	scalar	scalar	JJ
10_1101-2021_01_08_425885	812	22	curvature	curvature	NN
10_1101-2021_01_08_425885	812	23	(	(	-LRB-
10_1101-2021_01_08_425885	812	24	blue	blue	JJ
10_1101-2021_01_08_425885	812	25	)	)	-RRB-
10_1101-2021_01_08_425885	812	26	,	,	,
10_1101-2021_01_08_425885	812	27	and	and	CC
10_1101-2021_01_08_425885	812	28	likewise	likewise	RB
10_1101-2021_01_08_425885	812	29	for	for	IN
10_1101-2021_01_08_425885	812	30	a	a	DT
10_1101-2021_01_08_425885	812	31	negative	negative	JJ
10_1101-2021_01_08_425885	812	32	control	control	NN
10_1101-2021_01_08_425885	812	33	obtained	obtain	VBN
10_1101-2021_01_08_425885	812	34	by	by	IN
10_1101-2021_01_08_425885	812	35	randomly	randomly	RB
10_1101-2021_01_08_425885	812	36	pairing	pair	VBG
10_1101-2021_01_08_425885	812	37	95	95	CD
10_1101-2021_01_08_425885	812	38	%	%	NN
10_1101-2021_01_08_425885	812	39	CIs	ci	NNS
10_1101-2021_01_08_425885	812	40	and	and	CC
10_1101-2021_01_08_425885	812	41	originally	originally	RB
10_1101-2021_01_08_425885	812	42	reported	report	VBD
10_1101-2021_01_08_425885	812	43	scalar	scalar	JJ
10_1101-2021_01_08_425885	812	44	curvatures	curvature	NNS
10_1101-2021_01_08_425885	812	45	for	for	IN
10_1101-2021_01_08_425885	812	46	points	point	NNS
10_1101-2021_01_08_425885	812	47	in	in	IN
10_1101-2021_01_08_425885	812	48	the	the	DT
10_1101-2021_01_08_425885	812	49	downsampled	downsampled	JJ
10_1101-2021_01_08_425885	812	50	dataset	dataset	NN
10_1101-2021_01_08_425885	812	51	(	(	-LRB-
10_1101-2021_01_08_425885	812	52	red	red	NNP
10_1101-2021_01_08_425885	812	53	)	)	-RRB-
10_1101-2021_01_08_425885	812	54	.	.	.
10_1101-2021_01_08_425885	813	1	Errorbars	errorbar	NNS
10_1101-2021_01_08_425885	813	2	for	for	IN
10_1101-2021_01_08_425885	813	3	the	the	DT
10_1101-2021_01_08_425885	813	4	negative	negative	JJ
10_1101-2021_01_08_425885	813	5	control	control	NN
10_1101-2021_01_08_425885	813	6	are	be	VBP
10_1101-2021_01_08_425885	813	7	the	the	DT
10_1101-2021_01_08_425885	813	8	standard	standard	JJ
10_1101-2021_01_08_425885	813	9	deviation	deviation	NN
10_1101-2021_01_08_425885	813	10	of	of	IN
10_1101-2021_01_08_425885	813	11	this	this	DT
10_1101-2021_01_08_425885	813	12	percentage	percentage	NN
10_1101-2021_01_08_425885	813	13	over	over	IN
10_1101-2021_01_08_425885	813	14	1000	1000	CD
10_1101-2021_01_08_425885	813	15	trials	trial	NNS
10_1101-2021_01_08_425885	813	16	with	with	IN
10_1101-2021_01_08_425885	813	17	different	different	JJ
10_1101-2021_01_08_425885	813	18	random	random	JJ
10_1101-2021_01_08_425885	813	19	pairings	pairing	NNS
10_1101-2021_01_08_425885	813	20	(	(	-LRB-
10_1101-2021_01_08_425885	813	21	*	*	NFP
10_1101-2021_01_08_425885	813	22	p	p	NN
10_1101-2021_01_08_425885	813	23	<	<	XX
10_1101-2021_01_08_425885	813	24	0.001	0.001	CD
10_1101-2021_01_08_425885	813	25	;	;	:
10_1101-2021_01_08_425885	813	26	see	see	VB
10_1101-2021_01_08_425885	813	27	Methods	Methods	NNP
10_1101-2021_01_08_425885	813	28	Section	Section	NNP
10_1101-2021_01_08_425885	813	29	4.6.3.2	4.6.3.2	CD
10_1101-2021_01_08_425885	813	30	)	)	-RRB-
10_1101-2021_01_08_425885	813	31	.	.	.
10_1101-2021_01_08_425885	814	1	(	(	-LRB-
10_1101-2021_01_08_425885	814	2	J	J	NNP
10_1101-2021_01_08_425885	814	3	)	)	-RRB-
10_1101-2021_01_08_425885	814	4	Scalar	Scalar	NNP
10_1101-2021_01_08_425885	814	5	curvatures	curvature	NNS
10_1101-2021_01_08_425885	814	6	were	be	VBD
10_1101-2021_01_08_425885	814	7	computed	compute	VBN
10_1101-2021_01_08_425885	814	8	after	after	IN
10_1101-2021_01_08_425885	814	9	downsampling	downsample	VBG
10_1101-2021_01_08_425885	814	10	the	the	DT
10_1101-2021_01_08_425885	814	11	number	number	NN
10_1101-2021_01_08_425885	814	12	of	of	IN
10_1101-2021_01_08_425885	814	13	transcripts	transcript	NNS
10_1101-2021_01_08_425885	814	14	by	by	IN
10_1101-2021_01_08_425885	814	15	a	a	DT
10_1101-2021_01_08_425885	814	16	factor	factor	NN
10_1101-2021_01_08_425885	814	17	of	of	IN
10_1101-2021_01_08_425885	814	18	2	2	CD
10_1101-2021_01_08_425885	814	19	(	(	-LRB-
10_1101-2021_01_08_425885	814	20	left	left	RB
10_1101-2021_01_08_425885	814	21	)	)	-RRB-
10_1101-2021_01_08_425885	814	22	and	and	CC
10_1101-2021_01_08_425885	814	23	4	4	CD
10_1101-2021_01_08_425885	814	24	(	(	-LRB-
10_1101-2021_01_08_425885	814	25	middle	middle	NNP
10_1101-2021_01_08_425885	814	26	)	)	-RRB-
10_1101-2021_01_08_425885	814	27	,	,	,
10_1101-2021_01_08_425885	814	28	using	use	VBG
10_1101-2021_01_08_425885	814	29	the	the	DT
10_1101-2021_01_08_425885	814	30	same	same	JJ
10_1101-2021_01_08_425885	814	31	ambient	ambient	JJ
10_1101-2021_01_08_425885	814	32	dimension	dimension	NN
10_1101-2021_01_08_425885	814	33	,	,	,
10_1101-2021_01_08_425885	814	34	manifold	manifold	JJ
10_1101-2021_01_08_425885	814	35	dimension	dimension	NN
10_1101-2021_01_08_425885	814	36	and	and	CC
10_1101-2021_01_08_425885	814	37	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	814	38	sizes	size	NNS
10_1101-2021_01_08_425885	814	39	determined	determine	VBN
10_1101-2021_01_08_425885	814	40	for	for	IN
10_1101-2021_01_08_425885	814	41	the	the	DT
10_1101-2021_01_08_425885	814	42	original	original	JJ
10_1101-2021_01_08_425885	814	43	dataset	dataset	NN
10_1101-2021_01_08_425885	814	44	.	.	.
10_1101-2021_01_08_425885	815	1	They	-PRON-	PRP
10_1101-2021_01_08_425885	815	2	are	be	VBP
10_1101-2021_01_08_425885	815	3	plotted	plot	VBN
10_1101-2021_01_08_425885	815	4	here	here	RB
10_1101-2021_01_08_425885	815	5	on	on	IN
10_1101-2021_01_08_425885	815	6	UMAP	UMAP	NNP
10_1101-2021_01_08_425885	815	7	coordinates	coordinate	NNS
10_1101-2021_01_08_425885	815	8	after	after	IN
10_1101-2021_01_08_425885	815	9	smoothing	smooth	VBG
10_1101-2021_01_08_425885	815	10	over	over	IN
10_1101-2021_01_08_425885	815	11	the	the	DT
10_1101-2021_01_08_425885	815	12	same	same	JJ
10_1101-2021_01_08_425885	815	13	set	set	NN
10_1101-2021_01_08_425885	815	14	of	of	IN
10_1101-2021_01_08_425885	815	15	k	k	NN
10_1101-2021_01_08_425885	815	16	=	=	SYM
10_1101-2021_01_08_425885	815	17	250	250	CD
10_1101-2021_01_08_425885	815	18	neighbors	neighbor	NNS
10_1101-2021_01_08_425885	815	19	used	use	VBN
10_1101-2021_01_08_425885	815	20	in	in	IN
10_1101-2021_01_08_425885	815	21	Figure	figure	NN
10_1101-2021_01_08_425885	815	22	4A.	4a.	NN
10_1101-2021_01_08_425885	816	1	(	(	-LRB-
10_1101-2021_01_08_425885	816	2	Right	right	UH
10_1101-2021_01_08_425885	816	3	)	)	-RRB-
10_1101-2021_01_08_425885	816	4	The	the	DT
10_1101-2021_01_08_425885	816	5	percentage	percentage	NN
10_1101-2021_01_08_425885	816	6	of	of	IN
10_1101-2021_01_08_425885	816	7	points	point	NNS
10_1101-2021_01_08_425885	816	8	in	in	IN
10_1101-2021_01_08_425885	816	9	the	the	DT
10_1101-2021_01_08_425885	816	10	downsampled	downsampled	JJ
10_1101-2021_01_08_425885	816	11	datasets	dataset	NNS
10_1101-2021_01_08_425885	816	12	with	with	IN
10_1101-2021_01_08_425885	816	13	a	a	DT
10_1101-2021_01_08_425885	816	14	95	95	CD
10_1101-2021_01_08_425885	816	15	%	%	NN
10_1101-2021_01_08_425885	816	16	CI	ci	NN
10_1101-2021_01_08_425885	816	17	containing	contain	VBG
10_1101-2021_01_08_425885	816	18	the	the	DT
10_1101-2021_01_08_425885	816	19	originally	originally	RB
10_1101-2021_01_08_425885	816	20	reported	report	VBN
10_1101-2021_01_08_425885	816	21	scalar	scalar	JJ
10_1101-2021_01_08_425885	816	22	curvature	curvature	NN
10_1101-2021_01_08_425885	816	23	(	(	-LRB-
10_1101-2021_01_08_425885	816	24	blue	blue	JJ
10_1101-2021_01_08_425885	816	25	)	)	-RRB-
10_1101-2021_01_08_425885	816	26	,	,	,
10_1101-2021_01_08_425885	816	27	and	and	CC
10_1101-2021_01_08_425885	816	28	likewise	likewise	RB
10_1101-2021_01_08_425885	816	29	for	for	IN
10_1101-2021_01_08_425885	816	30	a	a	DT
10_1101-2021_01_08_425885	816	31	negative	negative	JJ
10_1101-2021_01_08_425885	816	32	control	control	NN
10_1101-2021_01_08_425885	816	33	obtained	obtain	VBN
10_1101-2021_01_08_425885	816	34	by	by	IN
10_1101-2021_01_08_425885	816	35	randomly	randomly	RB
10_1101-2021_01_08_425885	816	36	pairing	pair	VBG
10_1101-2021_01_08_425885	816	37	95	95	CD
10_1101-2021_01_08_425885	816	38	%	%	NN
10_1101-2021_01_08_425885	816	39	CIs	ci	NNS
10_1101-2021_01_08_425885	816	40	and	and	CC
10_1101-2021_01_08_425885	816	41	originally	originally	RB
10_1101-2021_01_08_425885	816	42	reported	report	VBD
10_1101-2021_01_08_425885	816	43	scalar	scalar	JJ
10_1101-2021_01_08_425885	816	44	curvatures	curvature	NNS
10_1101-2021_01_08_425885	816	45	for	for	IN
10_1101-2021_01_08_425885	816	46	points	point	NNS
10_1101-2021_01_08_425885	816	47	in	in	IN
10_1101-2021_01_08_425885	816	48	the	the	DT
10_1101-2021_01_08_425885	816	49	downsampled	downsampled	JJ
10_1101-2021_01_08_425885	816	50	dataset	dataset	NN
10_1101-2021_01_08_425885	816	51	(	(	-LRB-
10_1101-2021_01_08_425885	816	52	red	red	NNP
10_1101-2021_01_08_425885	816	53	)	)	-RRB-
10_1101-2021_01_08_425885	816	54	.	.	.
10_1101-2021_01_08_425885	817	1	Errorbars	errorbar	NNS
10_1101-2021_01_08_425885	817	2	for	for	IN
10_1101-2021_01_08_425885	817	3	the	the	DT
10_1101-2021_01_08_425885	817	4	negative	negative	JJ
10_1101-2021_01_08_425885	817	5	control	control	NN
10_1101-2021_01_08_425885	817	6	are	be	VBP
10_1101-2021_01_08_425885	817	7	the	the	DT
10_1101-2021_01_08_425885	817	8	standard	standard	JJ
10_1101-2021_01_08_425885	817	9	deviation	deviation	NN
10_1101-2021_01_08_425885	817	10	of	of	IN
10_1101-2021_01_08_425885	817	11	this	this	DT
10_1101-2021_01_08_425885	817	12	percentage	percentage	NN
10_1101-2021_01_08_425885	817	13	over	over	IN
10_1101-2021_01_08_425885	817	14	1000	1000	CD
10_1101-2021_01_08_425885	817	15	trials	trial	NNS
10_1101-2021_01_08_425885	817	16	with	with	IN
10_1101-2021_01_08_425885	817	17	different	different	JJ
10_1101-2021_01_08_425885	817	18	random	random	JJ
10_1101-2021_01_08_425885	817	19	pairings	pairing	NNS
10_1101-2021_01_08_425885	817	20	(	(	-LRB-
10_1101-2021_01_08_425885	817	21	*	*	NFP
10_1101-2021_01_08_425885	817	22	p	p	NN
10_1101-2021_01_08_425885	817	23	<	<	XX
10_1101-2021_01_08_425885	817	24	0.001	0.001	CD
10_1101-2021_01_08_425885	817	25	;	;	:
10_1101-2021_01_08_425885	817	26	see	see	VB
10_1101-2021_01_08_425885	817	27	Methods	Methods	NNP
10_1101-2021_01_08_425885	817	28	Section	Section	NNP
10_1101-2021_01_08_425885	817	29	4.6.3.3	4.6.3.3	CD
10_1101-2021_01_08_425885	817	30	)	)	-RRB-
10_1101-2021_01_08_425885	817	31	.	.	.
10_1101-2021_01_08_425885	818	1	49	49	CD
10_1101-2021_01_08_425885	818	2	.CC	.CC	:
10_1101-2021_01_08_425885	818	3	-	-	HYPH
10_1101-2021_01_08_425885	818	4	BY	by	IN
10_1101-2021_01_08_425885	818	5	-	-	HYPH
10_1101-2021_01_08_425885	818	6	NC	NC	NNP
10_1101-2021_01_08_425885	818	7	-	-	HYPH
10_1101-2021_01_08_425885	818	8	ND	ND	NNP
10_1101-2021_01_08_425885	818	9	4.0	4.0	CD
10_1101-2021_01_08_425885	818	10	International	International	NNP
10_1101-2021_01_08_425885	818	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	818	12	under	under	IN
10_1101-2021_01_08_425885	818	13	a	a	DT
10_1101-2021_01_08_425885	818	14	(	(	-LRB-
10_1101-2021_01_08_425885	818	15	which	which	WDT
10_1101-2021_01_08_425885	818	16	was	be	VBD
10_1101-2021_01_08_425885	818	17	not	not	RB
10_1101-2021_01_08_425885	818	18	certified	certify	VBN
10_1101-2021_01_08_425885	818	19	by	by	IN
10_1101-2021_01_08_425885	818	20	peer	peer	NN
10_1101-2021_01_08_425885	818	21	review	review	NN
10_1101-2021_01_08_425885	818	22	)	)	-RRB-
10_1101-2021_01_08_425885	818	23	is	be	VBZ
10_1101-2021_01_08_425885	818	24	the	the	DT
10_1101-2021_01_08_425885	818	25	author	author	NN
10_1101-2021_01_08_425885	818	26	/	/	SYM
10_1101-2021_01_08_425885	818	27	funder	funder	NN
10_1101-2021_01_08_425885	818	28	,	,	,
10_1101-2021_01_08_425885	818	29	who	who	WP
10_1101-2021_01_08_425885	818	30	has	have	VBZ
10_1101-2021_01_08_425885	818	31	granted	grant	VBN
10_1101-2021_01_08_425885	818	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	818	33	a	a	DT
10_1101-2021_01_08_425885	818	34	license	license	NN
10_1101-2021_01_08_425885	818	35	to	to	TO
10_1101-2021_01_08_425885	818	36	display	display	VB
10_1101-2021_01_08_425885	818	37	the	the	DT
10_1101-2021_01_08_425885	818	38	preprint	preprint	NN
10_1101-2021_01_08_425885	818	39	in	in	IN
10_1101-2021_01_08_425885	818	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	818	41	.	.	.
10_1101-2021_01_08_425885	819	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	819	2	is	be	VBZ
10_1101-2021_01_08_425885	819	3	made	make	VBN
10_1101-2021_01_08_425885	819	4	The	the	DT
10_1101-2021_01_08_425885	819	5	copyright	copyright	NN
10_1101-2021_01_08_425885	819	6	holder	holder	NN
10_1101-2021_01_08_425885	819	7	for	for	IN
10_1101-2021_01_08_425885	819	8	this	this	DT
10_1101-2021_01_08_425885	819	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	819	10	version	version	NN
10_1101-2021_01_08_425885	819	11	posted	post	VBD
10_1101-2021_01_08_425885	819	12	January	January	NNP
10_1101-2021_01_08_425885	819	13	8	8	CD
10_1101-2021_01_08_425885	819	14	,	,	,
10_1101-2021_01_08_425885	819	15	2021	2021	CD
10_1101-2021_01_08_425885	819	16	.	.	.
10_1101-2021_01_08_425885	819	17	;	;	:
10_1101-2021_01_08_425885	819	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	819	19	:	:	:
10_1101-2021_01_08_425885	819	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	819	21	preprint	preprint	NN
10_1101-2021_01_08_425885	819	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	UH
10_1101-2021_01_08_425885	819	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NNP
10_1101-2021_01_08_425885	819	24	B	b	NN
10_1101-2021_01_08_425885	819	25	C	C	NNP
10_1101-2021_01_08_425885	819	26	D	d	NN
10_1101-2021_01_08_425885	819	27	E	e	NN
10_1101-2021_01_08_425885	819	28	H	h	NN
10_1101-2021_01_08_425885	819	29	G	g	NN
10_1101-2021_01_08_425885	819	30	F	f	NN
10_1101-2021_01_08_425885	819	31	I	i	NN
10_1101-2021_01_08_425885	819	32	A	a	DT
10_1101-2021_01_08_425885	819	33	Figure	figure	NN
10_1101-2021_01_08_425885	819	34	S5	s5	NN
10_1101-2021_01_08_425885	819	35	:	:	:
10_1101-2021_01_08_425885	819	36	Additional	additional	JJ
10_1101-2021_01_08_425885	819	37	details	detail	NNS
10_1101-2021_01_08_425885	819	38	of	of	IN
10_1101-2021_01_08_425885	819	39	the	the	DT
10_1101-2021_01_08_425885	819	40	gastrulation	gastrulation	NN
10_1101-2021_01_08_425885	819	41	scRNAseq	scRNAseq	NNP
10_1101-2021_01_08_425885	819	42	dataset	dataset	FW
10_1101-2021_01_08_425885	819	43	(	(	-LRB-
10_1101-2021_01_08_425885	819	44	related	related	JJ
10_1101-2021_01_08_425885	819	45	to	to	IN
10_1101-2021_01_08_425885	819	46	Figure	Figure	NNP
10_1101-2021_01_08_425885	819	47	4	4	CD
10_1101-2021_01_08_425885	819	48	)	)	-RRB-
10_1101-2021_01_08_425885	819	49	.	.	.
10_1101-2021_01_08_425885	820	1	Panels	panel	NNS
10_1101-2021_01_08_425885	820	2	as	as	IN
10_1101-2021_01_08_425885	820	3	in	in	IN
10_1101-2021_01_08_425885	820	4	Figure	Figure	NNP
10_1101-2021_01_08_425885	820	5	S4	s4	NN
10_1101-2021_01_08_425885	820	6	.	.	.
10_1101-2021_01_08_425885	821	1	50	50	CD
10_1101-2021_01_08_425885	821	2	.CC	.CC	:
10_1101-2021_01_08_425885	821	3	-	-	HYPH
10_1101-2021_01_08_425885	821	4	BY	by	IN
10_1101-2021_01_08_425885	821	5	-	-	HYPH
10_1101-2021_01_08_425885	821	6	NC	NC	NNP
10_1101-2021_01_08_425885	821	7	-	-	HYPH
10_1101-2021_01_08_425885	821	8	ND	ND	NNP
10_1101-2021_01_08_425885	821	9	4.0	4.0	CD
10_1101-2021_01_08_425885	821	10	International	International	NNP
10_1101-2021_01_08_425885	821	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	821	12	under	under	IN
10_1101-2021_01_08_425885	821	13	a	a	DT
10_1101-2021_01_08_425885	821	14	(	(	-LRB-
10_1101-2021_01_08_425885	821	15	which	which	WDT
10_1101-2021_01_08_425885	821	16	was	be	VBD
10_1101-2021_01_08_425885	821	17	not	not	RB
10_1101-2021_01_08_425885	821	18	certified	certify	VBN
10_1101-2021_01_08_425885	821	19	by	by	IN
10_1101-2021_01_08_425885	821	20	peer	peer	NN
10_1101-2021_01_08_425885	821	21	review	review	NN
10_1101-2021_01_08_425885	821	22	)	)	-RRB-
10_1101-2021_01_08_425885	821	23	is	be	VBZ
10_1101-2021_01_08_425885	821	24	the	the	DT
10_1101-2021_01_08_425885	821	25	author	author	NN
10_1101-2021_01_08_425885	821	26	/	/	SYM
10_1101-2021_01_08_425885	821	27	funder	funder	NN
10_1101-2021_01_08_425885	821	28	,	,	,
10_1101-2021_01_08_425885	821	29	who	who	WP
10_1101-2021_01_08_425885	821	30	has	have	VBZ
10_1101-2021_01_08_425885	821	31	granted	grant	VBN
10_1101-2021_01_08_425885	821	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	821	33	a	a	DT
10_1101-2021_01_08_425885	821	34	license	license	NN
10_1101-2021_01_08_425885	821	35	to	to	TO
10_1101-2021_01_08_425885	821	36	display	display	VB
10_1101-2021_01_08_425885	821	37	the	the	DT
10_1101-2021_01_08_425885	821	38	preprint	preprint	NN
10_1101-2021_01_08_425885	821	39	in	in	IN
10_1101-2021_01_08_425885	821	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	821	41	.	.	.
10_1101-2021_01_08_425885	822	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	822	2	is	be	VBZ
10_1101-2021_01_08_425885	822	3	made	make	VBN
10_1101-2021_01_08_425885	822	4	The	the	DT
10_1101-2021_01_08_425885	822	5	copyright	copyright	NN
10_1101-2021_01_08_425885	822	6	holder	holder	NN
10_1101-2021_01_08_425885	822	7	for	for	IN
10_1101-2021_01_08_425885	822	8	this	this	DT
10_1101-2021_01_08_425885	822	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	822	10	version	version	NN
10_1101-2021_01_08_425885	822	11	posted	post	VBD
10_1101-2021_01_08_425885	822	12	January	January	NNP
10_1101-2021_01_08_425885	822	13	8	8	CD
10_1101-2021_01_08_425885	822	14	,	,	,
10_1101-2021_01_08_425885	822	15	2021	2021	CD
10_1101-2021_01_08_425885	822	16	.	.	.
10_1101-2021_01_08_425885	822	17	;	;	:
10_1101-2021_01_08_425885	822	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	822	19	:	:	:
10_1101-2021_01_08_425885	822	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	822	21	preprint	preprint	NN
10_1101-2021_01_08_425885	822	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	UH
10_1101-2021_01_08_425885	822	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	NNP
10_1101-2021_01_08_425885	822	24	B	b	NN
10_1101-2021_01_08_425885	822	25	C	C	NNP
10_1101-2021_01_08_425885	822	26	D	d	NN
10_1101-2021_01_08_425885	822	27	E	e	NN
10_1101-2021_01_08_425885	822	28	H	h	NN
10_1101-2021_01_08_425885	822	29	G	g	NN
10_1101-2021_01_08_425885	822	30	F	f	NN
10_1101-2021_01_08_425885	822	31	I	i	NN
10_1101-2021_01_08_425885	822	32	A	a	DT
10_1101-2021_01_08_425885	822	33	Figure	figure	NN
10_1101-2021_01_08_425885	822	34	S6	s6	NN
10_1101-2021_01_08_425885	822	35	:	:	:
10_1101-2021_01_08_425885	822	36	Additional	additional	JJ
10_1101-2021_01_08_425885	822	37	details	detail	NNS
10_1101-2021_01_08_425885	822	38	of	of	IN
10_1101-2021_01_08_425885	822	39	the	the	DT
10_1101-2021_01_08_425885	822	40	brain	brain	NN
10_1101-2021_01_08_425885	822	41	scRNAseq	scRNAseq	VBN
10_1101-2021_01_08_425885	822	42	dataset	dataset	NN
10_1101-2021_01_08_425885	822	43	(	(	-LRB-
10_1101-2021_01_08_425885	822	44	related	related	JJ
10_1101-2021_01_08_425885	822	45	to	to	IN
10_1101-2021_01_08_425885	822	46	Figure	Figure	NNP
10_1101-2021_01_08_425885	822	47	4	4	CD
10_1101-2021_01_08_425885	822	48	)	)	-RRB-
10_1101-2021_01_08_425885	822	49	.	.	.
10_1101-2021_01_08_425885	823	1	Panels	panel	NNS
10_1101-2021_01_08_425885	823	2	as	as	IN
10_1101-2021_01_08_425885	823	3	in	in	IN
10_1101-2021_01_08_425885	823	4	Figure	Figure	NNP
10_1101-2021_01_08_425885	823	5	S4	s4	NN
10_1101-2021_01_08_425885	823	6	but	but	CC
10_1101-2021_01_08_425885	823	7	with	with	IN
10_1101-2021_01_08_425885	823	8	t	t	NNP
10_1101-2021_01_08_425885	823	9	-	-	HYPH
10_1101-2021_01_08_425885	823	10	SNE	SNE	NNP
10_1101-2021_01_08_425885	823	11	instead	instead	RB
10_1101-2021_01_08_425885	823	12	of	of	IN
10_1101-2021_01_08_425885	823	13	UMAP	umap	JJ
10_1101-2021_01_08_425885	823	14	plots	plot	NNS
10_1101-2021_01_08_425885	823	15	.	.	.
10_1101-2021_01_08_425885	824	1	51	51	CD
10_1101-2021_01_08_425885	824	2	.CC	.CC	:
10_1101-2021_01_08_425885	824	3	-	-	HYPH
10_1101-2021_01_08_425885	824	4	BY	by	IN
10_1101-2021_01_08_425885	824	5	-	-	HYPH
10_1101-2021_01_08_425885	824	6	NC	NC	NNP
10_1101-2021_01_08_425885	824	7	-	-	HYPH
10_1101-2021_01_08_425885	824	8	ND	ND	NNP
10_1101-2021_01_08_425885	824	9	4.0	4.0	CD
10_1101-2021_01_08_425885	824	10	International	International	NNP
10_1101-2021_01_08_425885	824	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	824	12	under	under	IN
10_1101-2021_01_08_425885	824	13	a	a	DT
10_1101-2021_01_08_425885	824	14	(	(	-LRB-
10_1101-2021_01_08_425885	824	15	which	which	WDT
10_1101-2021_01_08_425885	824	16	was	be	VBD
10_1101-2021_01_08_425885	824	17	not	not	RB
10_1101-2021_01_08_425885	824	18	certified	certify	VBN
10_1101-2021_01_08_425885	824	19	by	by	IN
10_1101-2021_01_08_425885	824	20	peer	peer	NN
10_1101-2021_01_08_425885	824	21	review	review	NN
10_1101-2021_01_08_425885	824	22	)	)	-RRB-
10_1101-2021_01_08_425885	824	23	is	be	VBZ
10_1101-2021_01_08_425885	824	24	the	the	DT
10_1101-2021_01_08_425885	824	25	author	author	NN
10_1101-2021_01_08_425885	824	26	/	/	SYM
10_1101-2021_01_08_425885	824	27	funder	funder	NN
10_1101-2021_01_08_425885	824	28	,	,	,
10_1101-2021_01_08_425885	824	29	who	who	WP
10_1101-2021_01_08_425885	824	30	has	have	VBZ
10_1101-2021_01_08_425885	824	31	granted	grant	VBN
10_1101-2021_01_08_425885	824	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	824	33	a	a	DT
10_1101-2021_01_08_425885	824	34	license	license	NN
10_1101-2021_01_08_425885	824	35	to	to	TO
10_1101-2021_01_08_425885	824	36	display	display	VB
10_1101-2021_01_08_425885	824	37	the	the	DT
10_1101-2021_01_08_425885	824	38	preprint	preprint	NN
10_1101-2021_01_08_425885	824	39	in	in	IN
10_1101-2021_01_08_425885	824	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	824	41	.	.	.
10_1101-2021_01_08_425885	825	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	825	2	is	be	VBZ
10_1101-2021_01_08_425885	825	3	made	make	VBN
10_1101-2021_01_08_425885	825	4	The	the	DT
10_1101-2021_01_08_425885	825	5	copyright	copyright	NN
10_1101-2021_01_08_425885	825	6	holder	holder	NN
10_1101-2021_01_08_425885	825	7	for	for	IN
10_1101-2021_01_08_425885	825	8	this	this	DT
10_1101-2021_01_08_425885	825	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	825	10	version	version	NN
10_1101-2021_01_08_425885	825	11	posted	post	VBD
10_1101-2021_01_08_425885	825	12	January	January	NNP
10_1101-2021_01_08_425885	825	13	8	8	CD
10_1101-2021_01_08_425885	825	14	,	,	,
10_1101-2021_01_08_425885	825	15	2021	2021	CD
10_1101-2021_01_08_425885	825	16	.	.	.
10_1101-2021_01_08_425885	825	17	;	;	:
10_1101-2021_01_08_425885	825	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	825	19	:	:	:
10_1101-2021_01_08_425885	825	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	825	21	preprint	preprint	NN
10_1101-2021_01_08_425885	825	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	825	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	JJ
10_1101-2021_01_08_425885	825	24	References	reference	NNS
10_1101-2021_01_08_425885	825	25	[	[	-LRB-
10_1101-2021_01_08_425885	825	26	1	1	CD
10_1101-2021_01_08_425885	825	27	]	]	-RRB-
10_1101-2021_01_08_425885	825	28	A.	a.	NN
10_1101-2021_01_08_425885	825	29	M.	M.	NNP
10_1101-2021_01_08_425885	825	30	Klein	Klein	NNP
10_1101-2021_01_08_425885	825	31	,	,	,
10_1101-2021_01_08_425885	825	32	L.	L.	NNP
10_1101-2021_01_08_425885	825	33	Mazutis	Mazutis	NNP
10_1101-2021_01_08_425885	825	34	,	,	,
10_1101-2021_01_08_425885	825	35	I.	I.	NNP
10_1101-2021_01_08_425885	825	36	Akartuna	Akartuna	NNP
10_1101-2021_01_08_425885	825	37	,	,	,
10_1101-2021_01_08_425885	825	38	N.	N.	NNP
10_1101-2021_01_08_425885	825	39	Tallapragada	Tallapragada	NNP
10_1101-2021_01_08_425885	825	40	,	,	,
10_1101-2021_01_08_425885	825	41	A.	a.	NN
10_1101-2021_01_08_425885	825	42	Veres	vere	NNS
10_1101-2021_01_08_425885	825	43	,	,	,
10_1101-2021_01_08_425885	825	44	V.	V.	NNP
10_1101-2021_01_08_425885	825	45	Li	Li	NNP
10_1101-2021_01_08_425885	825	46	,	,	,
10_1101-2021_01_08_425885	825	47	L.	L.	NNP
10_1101-2021_01_08_425885	825	48	Peshkin	Peshkin	NNP
10_1101-2021_01_08_425885	825	49	,	,	,
10_1101-2021_01_08_425885	825	50	D.	D.	NNP
10_1101-2021_01_08_425885	825	51	A.	a.	NN
10_1101-2021_01_08_425885	825	52	Weitz	Weitz	NNP
10_1101-2021_01_08_425885	825	53	,	,	,
10_1101-2021_01_08_425885	825	54	and	and	CC
10_1101-2021_01_08_425885	825	55	M.	M.	NNP
10_1101-2021_01_08_425885	825	56	W.	W.	NNP
10_1101-2021_01_08_425885	825	57	Kirschner	Kirschner	NNP
10_1101-2021_01_08_425885	825	58	.	.	.
10_1101-2021_01_08_425885	826	1	Droplet	Droplet	NNP
10_1101-2021_01_08_425885	826	2	barcoding	barcode	VBG
10_1101-2021_01_08_425885	826	3	for	for	IN
10_1101-2021_01_08_425885	826	4	single	single	JJ
10_1101-2021_01_08_425885	826	5	-	-	HYPH
10_1101-2021_01_08_425885	826	6	cell	cell	NN
10_1101-2021_01_08_425885	826	7	transcriptomics	transcriptomic	NNS
10_1101-2021_01_08_425885	826	8	applied	apply	VBN
10_1101-2021_01_08_425885	826	9	to	to	IN
10_1101-2021_01_08_425885	826	10	embryonic	embryonic	JJ
10_1101-2021_01_08_425885	826	11	stem	stem	NN
10_1101-2021_01_08_425885	826	12	cells	cell	NNS
10_1101-2021_01_08_425885	826	13	.	.	.
10_1101-2021_01_08_425885	827	1	Cell	cell	NN
10_1101-2021_01_08_425885	827	2	,	,	,
10_1101-2021_01_08_425885	827	3	161(5):1187–1201	161(5):1187–1201	CD
10_1101-2021_01_08_425885	827	4	,	,	,
10_1101-2021_01_08_425885	827	5	2015	2015	CD
10_1101-2021_01_08_425885	827	6	.	.	.
10_1101-2021_01_08_425885	828	1	[	[	-LRB-
10_1101-2021_01_08_425885	828	2	2	2	LS
10_1101-2021_01_08_425885	828	3	]	]	-RRB-
10_1101-2021_01_08_425885	828	4	E.	E.	NNP
10_1101-2021_01_08_425885	828	5	Z.	Z.	NNP
10_1101-2021_01_08_425885	828	6	Macosko	Macosko	NNP
10_1101-2021_01_08_425885	828	7	,	,	,
10_1101-2021_01_08_425885	828	8	A.	A.	NNP
10_1101-2021_01_08_425885	828	9	Basu	Basu	NNP
10_1101-2021_01_08_425885	828	10	,	,	,
10_1101-2021_01_08_425885	828	11	R.	R.	NNP
10_1101-2021_01_08_425885	828	12	Satija	Satija	NNP
10_1101-2021_01_08_425885	828	13	,	,	,
10_1101-2021_01_08_425885	828	14	J.	J.	NNP
10_1101-2021_01_08_425885	828	15	Nemesh	Nemesh	NNP
10_1101-2021_01_08_425885	828	16	,	,	,
10_1101-2021_01_08_425885	828	17	K.	K.	NNP
10_1101-2021_01_08_425885	828	18	Shekhar	Shekhar	NNP
10_1101-2021_01_08_425885	828	19	,	,	,
10_1101-2021_01_08_425885	828	20	M.	M.	NNP
10_1101-2021_01_08_425885	828	21	Goldman	Goldman	NNP
10_1101-2021_01_08_425885	828	22	,	,	,
10_1101-2021_01_08_425885	828	23	I.	I.	NNP
10_1101-2021_01_08_425885	828	24	Tirosh	Tirosh	NNP
10_1101-2021_01_08_425885	828	25	,	,	,
10_1101-2021_01_08_425885	828	26	A.	A.	NNP
10_1101-2021_01_08_425885	828	27	R.	R.	NNP
10_1101-2021_01_08_425885	828	28	Bialas	Bialas	NNP
10_1101-2021_01_08_425885	828	29	,	,	,
10_1101-2021_01_08_425885	828	30	N.	N.	NNP
10_1101-2021_01_08_425885	828	31	Kamitaki	Kamitaki	NNP
10_1101-2021_01_08_425885	828	32	,	,	,
10_1101-2021_01_08_425885	828	33	E.	E.	NNP
10_1101-2021_01_08_425885	828	34	M.	M.	NNP
10_1101-2021_01_08_425885	828	35	Martersteck	Martersteck	NNP
10_1101-2021_01_08_425885	828	36	,	,	,
10_1101-2021_01_08_425885	828	37	J.	J.	NNP
10_1101-2021_01_08_425885	828	38	J.	J.	NNP
10_1101-2021_01_08_425885	828	39	Trombetta	Trombetta	NNP
10_1101-2021_01_08_425885	828	40	,	,	,
10_1101-2021_01_08_425885	828	41	D.	D.	NNP
10_1101-2021_01_08_425885	828	42	A.	a.	NN
10_1101-2021_01_08_425885	828	43	Weitz	Weitz	NNP
10_1101-2021_01_08_425885	828	44	,	,	,
10_1101-2021_01_08_425885	828	45	J.	J.	NNP
10_1101-2021_01_08_425885	828	46	R.	R.	NNP
10_1101-2021_01_08_425885	828	47	Sanes	Sanes	NNP
10_1101-2021_01_08_425885	828	48	,	,	,
10_1101-2021_01_08_425885	828	49	A.	A.	NNP
10_1101-2021_01_08_425885	828	50	K.	K.	NNP
10_1101-2021_01_08_425885	828	51	Shalek	Shalek	NNP
10_1101-2021_01_08_425885	828	52	,	,	,
10_1101-2021_01_08_425885	828	53	A.	a.	NN
10_1101-2021_01_08_425885	828	54	Regev	Regev	NNP
10_1101-2021_01_08_425885	828	55	,	,	,
10_1101-2021_01_08_425885	828	56	and	and	CC
10_1101-2021_01_08_425885	828	57	S.	S.	NNP
10_1101-2021_01_08_425885	828	58	A.	a.	NN
10_1101-2021_01_08_425885	828	59	McCarroll	McCarroll	NNP
10_1101-2021_01_08_425885	828	60	.	.	.
10_1101-2021_01_08_425885	829	1	Highly	highly	RB
10_1101-2021_01_08_425885	829	2	parallel	parallel	JJ
10_1101-2021_01_08_425885	829	3	genome	genome	NN
10_1101-2021_01_08_425885	829	4	-	-	HYPH
10_1101-2021_01_08_425885	829	5	wide	wide	JJ
10_1101-2021_01_08_425885	829	6	expression	expression	NN
10_1101-2021_01_08_425885	829	7	profiling	profiling	NN
10_1101-2021_01_08_425885	829	8	of	of	IN
10_1101-2021_01_08_425885	829	9	individual	individual	JJ
10_1101-2021_01_08_425885	829	10	cells	cell	NNS
10_1101-2021_01_08_425885	829	11	using	use	VBG
10_1101-2021_01_08_425885	829	12	nanoliter	nanoliter	JJ
10_1101-2021_01_08_425885	829	13	droplets	droplet	NNS
10_1101-2021_01_08_425885	829	14	.	.	.
10_1101-2021_01_08_425885	830	1	Cell	cell	NN
10_1101-2021_01_08_425885	830	2	,	,	,
10_1101-2021_01_08_425885	830	3	161(5):1202–1214	161(5):1202–1214	NNS
10_1101-2021_01_08_425885	830	4	,	,	,
10_1101-2021_01_08_425885	830	5	2015	2015	CD
10_1101-2021_01_08_425885	830	6	.	.	.
10_1101-2021_01_08_425885	831	1	[	[	-LRB-
10_1101-2021_01_08_425885	831	2	3	3	LS
10_1101-2021_01_08_425885	831	3	]	]	-RRB-
10_1101-2021_01_08_425885	831	4	G.	G.	NNP
10_1101-2021_01_08_425885	831	5	X.	X.	NNP
10_1101-2021_01_08_425885	831	6	Y.	Y.	NNP
10_1101-2021_01_08_425885	831	7	Zheng	Zheng	NNP
10_1101-2021_01_08_425885	831	8	,	,	,
10_1101-2021_01_08_425885	831	9	J.	J.	NNP
10_1101-2021_01_08_425885	831	10	M.	M.	NNP
10_1101-2021_01_08_425885	831	11	Terry	Terry	NNP
10_1101-2021_01_08_425885	831	12	,	,	,
10_1101-2021_01_08_425885	831	13	P.	P.	NNP
10_1101-2021_01_08_425885	831	14	Belgrader	Belgrader	NNP
10_1101-2021_01_08_425885	831	15	,	,	,
10_1101-2021_01_08_425885	831	16	P.	P.	NNP
10_1101-2021_01_08_425885	831	17	Ryvkin	Ryvkin	NNP
10_1101-2021_01_08_425885	831	18	,	,	,
10_1101-2021_01_08_425885	831	19	Z.	Z.	NNP
10_1101-2021_01_08_425885	831	20	W.	W.	NNP
10_1101-2021_01_08_425885	831	21	Bent	Bent	NNP
10_1101-2021_01_08_425885	831	22	,	,	,
10_1101-2021_01_08_425885	831	23	R.	R.	NNP
10_1101-2021_01_08_425885	831	24	Wilson	Wilson	NNP
10_1101-2021_01_08_425885	831	25	,	,	,
10_1101-2021_01_08_425885	831	26	S.	S.	NNP
10_1101-2021_01_08_425885	831	27	B.	B.	NNP
10_1101-2021_01_08_425885	831	28	Ziraldo	Ziraldo	NNP
10_1101-2021_01_08_425885	831	29	,	,	,
10_1101-2021_01_08_425885	831	30	T.	T.	NNP
10_1101-2021_01_08_425885	831	31	D.	D.	NNP
10_1101-2021_01_08_425885	831	32	Wheeler	Wheeler	NNP
10_1101-2021_01_08_425885	831	33	,	,	,
10_1101-2021_01_08_425885	831	34	G.	G.	NNP
10_1101-2021_01_08_425885	831	35	P.	P.	NNP
10_1101-2021_01_08_425885	831	36	McDermott	McDermott	NNP
10_1101-2021_01_08_425885	831	37	,	,	,
10_1101-2021_01_08_425885	831	38	J.	J.	NNP
10_1101-2021_01_08_425885	831	39	Zhu	Zhu	NNP
10_1101-2021_01_08_425885	831	40	,	,	,
10_1101-2021_01_08_425885	831	41	M.	M.	NNP
10_1101-2021_01_08_425885	831	42	T.	T.	NNP
10_1101-2021_01_08_425885	831	43	Gregory	Gregory	NNP
10_1101-2021_01_08_425885	831	44	,	,	,
10_1101-2021_01_08_425885	831	45	J.	J.	NNP
10_1101-2021_01_08_425885	831	46	Shuga	Shuga	NNP
10_1101-2021_01_08_425885	831	47	,	,	,
10_1101-2021_01_08_425885	831	48	L.	L.	NNP
10_1101-2021_01_08_425885	831	49	Montesclaros	Montesclaros	NNP
10_1101-2021_01_08_425885	831	50	,	,	,
10_1101-2021_01_08_425885	831	51	J.	J.	NNP
10_1101-2021_01_08_425885	831	52	G.	G.	NNP
10_1101-2021_01_08_425885	831	53	Underwood	Underwood	NNP
10_1101-2021_01_08_425885	831	54	,	,	,
10_1101-2021_01_08_425885	831	55	D.	D.	NNP
10_1101-2021_01_08_425885	831	56	A.	A.	NNP
10_1101-2021_01_08_425885	831	57	Masquelier	Masquelier	NNP
10_1101-2021_01_08_425885	831	58	,	,	,
10_1101-2021_01_08_425885	831	59	S.	S.	NNP
10_1101-2021_01_08_425885	831	60	Y.	Y.	NNP
10_1101-2021_01_08_425885	831	61	Nishimura	Nishimura	NNP
10_1101-2021_01_08_425885	831	62	,	,	,
10_1101-2021_01_08_425885	831	63	M.	M.	NNP
10_1101-2021_01_08_425885	831	64	Schnall	Schnall	NNP
10_1101-2021_01_08_425885	831	65	-	-	HYPH
10_1101-2021_01_08_425885	831	66	Levin	Levin	NNP
10_1101-2021_01_08_425885	831	67	,	,	,
10_1101-2021_01_08_425885	831	68	P.	P.	NNP
10_1101-2021_01_08_425885	831	69	W.	W.	NNP
10_1101-2021_01_08_425885	831	70	Wyatt	Wyatt	NNP
10_1101-2021_01_08_425885	831	71	,	,	,
10_1101-2021_01_08_425885	831	72	C.	C.	NNP
10_1101-2021_01_08_425885	831	73	M.	M.	NNP
10_1101-2021_01_08_425885	831	74	Hindson	Hindson	NNP
10_1101-2021_01_08_425885	831	75	,	,	,
10_1101-2021_01_08_425885	831	76	R.	R.	NNP
10_1101-2021_01_08_425885	831	77	Bharadwaj	Bharadwaj	NNP
10_1101-2021_01_08_425885	831	78	,	,	,
10_1101-2021_01_08_425885	831	79	A.	a.	NN
10_1101-2021_01_08_425885	831	80	Wong	Wong	NNP
10_1101-2021_01_08_425885	831	81	,	,	,
10_1101-2021_01_08_425885	831	82	K.	K.	NNP
10_1101-2021_01_08_425885	831	83	D.	D.	NNP
10_1101-2021_01_08_425885	831	84	Ness	Ness	NNP
10_1101-2021_01_08_425885	831	85	,	,	,
10_1101-2021_01_08_425885	831	86	L.	L.	NNP
10_1101-2021_01_08_425885	831	87	W.	W.	NNP
10_1101-2021_01_08_425885	831	88	Beppu	Beppu	NNP
10_1101-2021_01_08_425885	831	89	,	,	,
10_1101-2021_01_08_425885	831	90	H.	H.	NNP
10_1101-2021_01_08_425885	831	91	J.	J.	NNP
10_1101-2021_01_08_425885	831	92	Deeg	Deeg	NNP
10_1101-2021_01_08_425885	831	93	,	,	,
10_1101-2021_01_08_425885	831	94	C.	C.	NNP
10_1101-2021_01_08_425885	831	95	McFarland	McFarland	NNP
10_1101-2021_01_08_425885	831	96	,	,	,
10_1101-2021_01_08_425885	831	97	K.	K.	NNP
10_1101-2021_01_08_425885	831	98	R.	R.	NNP
10_1101-2021_01_08_425885	831	99	Loeb	Loeb	NNP
10_1101-2021_01_08_425885	831	100	,	,	,
10_1101-2021_01_08_425885	831	101	W.	W.	NNP
10_1101-2021_01_08_425885	831	102	J.	J.	NNP
10_1101-2021_01_08_425885	831	103	Valente	Valente	NNP
10_1101-2021_01_08_425885	831	104	,	,	,
10_1101-2021_01_08_425885	831	105	N.	N.	NNP
10_1101-2021_01_08_425885	831	106	G.	G.	NNP
10_1101-2021_01_08_425885	831	107	Ericson	Ericson	NNP
10_1101-2021_01_08_425885	831	108	,	,	,
10_1101-2021_01_08_425885	831	109	E.	E.	NNP
10_1101-2021_01_08_425885	831	110	A.	A.	NNP
10_1101-2021_01_08_425885	831	111	Stevens	Stevens	NNP
10_1101-2021_01_08_425885	831	112	,	,	,
10_1101-2021_01_08_425885	831	113	J.	J.	NNP
10_1101-2021_01_08_425885	831	114	P.	P.	NNP
10_1101-2021_01_08_425885	831	115	Radich	Radich	NNP
10_1101-2021_01_08_425885	831	116	,	,	,
10_1101-2021_01_08_425885	831	117	T.	T.	NNP
10_1101-2021_01_08_425885	831	118	S.	S.	NNP
10_1101-2021_01_08_425885	831	119	Mikkelsen	Mikkelsen	NNP
10_1101-2021_01_08_425885	831	120	,	,	,
10_1101-2021_01_08_425885	831	121	B.	B.	NNP
10_1101-2021_01_08_425885	831	122	J.	J.	NNP
10_1101-2021_01_08_425885	831	123	Hindson	Hindson	NNP
10_1101-2021_01_08_425885	831	124	,	,	,
10_1101-2021_01_08_425885	831	125	and	and	CC
10_1101-2021_01_08_425885	831	126	J.	J.	NNP
10_1101-2021_01_08_425885	831	127	H.	H.	NNP
10_1101-2021_01_08_425885	831	128	Bielas	Bielas	NNP
10_1101-2021_01_08_425885	831	129	.	.	.
10_1101-2021_01_08_425885	832	1	Massively	massively	RB
10_1101-2021_01_08_425885	832	2	parallel	parallel	JJ
10_1101-2021_01_08_425885	832	3	digital	digital	JJ
10_1101-2021_01_08_425885	832	4	transcriptional	transcriptional	JJ
10_1101-2021_01_08_425885	832	5	profiling	profiling	NN
10_1101-2021_01_08_425885	832	6	of	of	IN
10_1101-2021_01_08_425885	832	7	single	single	JJ
10_1101-2021_01_08_425885	832	8	cells	cell	NNS
10_1101-2021_01_08_425885	832	9	.	.	.
10_1101-2021_01_08_425885	833	1	Nature	Nature	NNP
10_1101-2021_01_08_425885	833	2	Communications	Communications	NNPS
10_1101-2021_01_08_425885	833	3	,	,	,
10_1101-2021_01_08_425885	833	4	8(1):1–12	8(1):1–12	CD
10_1101-2021_01_08_425885	833	5	,	,	,
10_1101-2021_01_08_425885	833	6	2017	2017	CD
10_1101-2021_01_08_425885	833	7	.	.	.
10_1101-2021_01_08_425885	834	1	[	[	-LRB-
10_1101-2021_01_08_425885	834	2	4	4	CD
10_1101-2021_01_08_425885	834	3	]	]	-RRB-
10_1101-2021_01_08_425885	834	4	D.	D.	NNP
10_1101-2021_01_08_425885	834	5	R.	R.	NNP
10_1101-2021_01_08_425885	834	6	Bandura	Bandura	NNP
10_1101-2021_01_08_425885	834	7	,	,	,
10_1101-2021_01_08_425885	834	8	V.	V.	NNP
10_1101-2021_01_08_425885	834	9	I.	I.	NNP
10_1101-2021_01_08_425885	834	10	Baranov	Baranov	NNP
10_1101-2021_01_08_425885	834	11	,	,	,
10_1101-2021_01_08_425885	834	12	O.	O.	NNP
10_1101-2021_01_08_425885	834	13	I.	I.	NNP
10_1101-2021_01_08_425885	834	14	Ornatsky	Ornatsky	NNP
10_1101-2021_01_08_425885	834	15	,	,	,
10_1101-2021_01_08_425885	834	16	A.	a.	NN
10_1101-2021_01_08_425885	834	17	Antonov	Antonov	NNP
10_1101-2021_01_08_425885	834	18	,	,	,
10_1101-2021_01_08_425885	834	19	R.	R.	NNP
10_1101-2021_01_08_425885	834	20	Kinach	Kinach	NNP
10_1101-2021_01_08_425885	834	21	,	,	,
10_1101-2021_01_08_425885	834	22	X.	X.	NNP
10_1101-2021_01_08_425885	834	23	Lou	Lou	NNP
10_1101-2021_01_08_425885	834	24	,	,	,
10_1101-2021_01_08_425885	834	25	S.	S.	NNP
10_1101-2021_01_08_425885	834	26	Pavlov	Pavlov	NNP
10_1101-2021_01_08_425885	834	27	,	,	,
10_1101-2021_01_08_425885	834	28	S.	S.	NNP
10_1101-2021_01_08_425885	834	29	Voro-	Voro-	NNP
10_1101-2021_01_08_425885	834	30	biev	biev	NN
10_1101-2021_01_08_425885	834	31	,	,	,
10_1101-2021_01_08_425885	834	32	J.	J.	NNP
10_1101-2021_01_08_425885	834	33	E.	E.	NNP
10_1101-2021_01_08_425885	834	34	Dick	Dick	NNP
10_1101-2021_01_08_425885	834	35	,	,	,
10_1101-2021_01_08_425885	834	36	and	and	CC
10_1101-2021_01_08_425885	834	37	S.	S.	NNP
10_1101-2021_01_08_425885	834	38	D.	D.	NNP
10_1101-2021_01_08_425885	834	39	Tanner	Tanner	NNP
10_1101-2021_01_08_425885	834	40	.	.	.
10_1101-2021_01_08_425885	835	1	Mass	mass	NN
10_1101-2021_01_08_425885	835	2	cytometry	cytometry	NN
10_1101-2021_01_08_425885	835	3	:	:	:
10_1101-2021_01_08_425885	835	4	technique	technique	NN
10_1101-2021_01_08_425885	835	5	for	for	IN
10_1101-2021_01_08_425885	835	6	real	real	JJ
10_1101-2021_01_08_425885	835	7	time	time	NN
10_1101-2021_01_08_425885	835	8	single	single	JJ
10_1101-2021_01_08_425885	835	9	cell	cell	NN
10_1101-2021_01_08_425885	835	10	multitarget	multitarget	NN
10_1101-2021_01_08_425885	835	11	immunoassay	immunoassay	NNP
10_1101-2021_01_08_425885	835	12	based	base	VBN
10_1101-2021_01_08_425885	835	13	on	on	IN
10_1101-2021_01_08_425885	835	14	inductively	inductively	RB
10_1101-2021_01_08_425885	835	15	coupled	couple	VBN
10_1101-2021_01_08_425885	835	16	plasma	plasma	NN
10_1101-2021_01_08_425885	835	17	time	time	NN
10_1101-2021_01_08_425885	835	18	-	-	HYPH
10_1101-2021_01_08_425885	835	19	of	of	IN
10_1101-2021_01_08_425885	835	20	-	-	HYPH
10_1101-2021_01_08_425885	835	21	flight	flight	NN
10_1101-2021_01_08_425885	835	22	mass	mass	NN
10_1101-2021_01_08_425885	835	23	spectrometry	spectrometry	NN
10_1101-2021_01_08_425885	835	24	.	.	.
10_1101-2021_01_08_425885	836	1	Analytical	Analytical	NNP
10_1101-2021_01_08_425885	836	2	Chem-	Chem-	NNP
10_1101-2021_01_08_425885	836	3	istry	istry	NN
10_1101-2021_01_08_425885	836	4	,	,	,
10_1101-2021_01_08_425885	836	5	81(16):6813–6822	81(16):6813–6822	CD
10_1101-2021_01_08_425885	836	6	,	,	,
10_1101-2021_01_08_425885	836	7	2009	2009	CD
10_1101-2021_01_08_425885	836	8	.	.	.
10_1101-2021_01_08_425885	837	1	[	[	-LRB-
10_1101-2021_01_08_425885	837	2	5	5	CD
10_1101-2021_01_08_425885	837	3	]	]	-RRB-
10_1101-2021_01_08_425885	837	4	C.	C.	NNP
10_1101-2021_01_08_425885	837	5	Giesen	Giesen	NNP
10_1101-2021_01_08_425885	837	6	,	,	,
10_1101-2021_01_08_425885	837	7	H.	H.	NNP
10_1101-2021_01_08_425885	837	8	A.	A.	NNP
10_1101-2021_01_08_425885	837	9	O.	O.	NNP
10_1101-2021_01_08_425885	837	10	Wang	Wang	NNP
10_1101-2021_01_08_425885	837	11	,	,	,
10_1101-2021_01_08_425885	837	12	D.	D.	NNP
10_1101-2021_01_08_425885	837	13	Schapiro	Schapiro	NNP
10_1101-2021_01_08_425885	837	14	,	,	,
10_1101-2021_01_08_425885	837	15	N.	N.	NNP
10_1101-2021_01_08_425885	837	16	Zivanovic	Zivanovic	NNP
10_1101-2021_01_08_425885	837	17	,	,	,
10_1101-2021_01_08_425885	837	18	A.	A.	NNP
10_1101-2021_01_08_425885	837	19	Jacobs	Jacobs	NNP
10_1101-2021_01_08_425885	837	20	,	,	,
10_1101-2021_01_08_425885	837	21	B.	B.	NNP
10_1101-2021_01_08_425885	837	22	Hattendorf	Hattendorf	NNP
10_1101-2021_01_08_425885	837	23	,	,	,
10_1101-2021_01_08_425885	837	24	P.	P.	NNP
10_1101-2021_01_08_425885	837	25	J.	J.	NNP
10_1101-2021_01_08_425885	837	26	Schüffler	Schüffler	NNP
10_1101-2021_01_08_425885	837	27	,	,	,
10_1101-2021_01_08_425885	837	28	D.	D.	NNP
10_1101-2021_01_08_425885	837	29	Grolimund	Grolimund	NNP
10_1101-2021_01_08_425885	837	30	,	,	,
10_1101-2021_01_08_425885	837	31	J.	J.	NNP
10_1101-2021_01_08_425885	837	32	M.	M.	NNP
10_1101-2021_01_08_425885	837	33	Buhmann	Buhmann	NNP
10_1101-2021_01_08_425885	837	34	,	,	,
10_1101-2021_01_08_425885	837	35	S.	S.	NNP
10_1101-2021_01_08_425885	837	36	Brandt	Brandt	NNP
10_1101-2021_01_08_425885	837	37	,	,	,
10_1101-2021_01_08_425885	837	38	Z.	Z.	NNP
10_1101-2021_01_08_425885	837	39	Varga	Varga	NNP
10_1101-2021_01_08_425885	837	40	,	,	,
10_1101-2021_01_08_425885	837	41	P.	P.	NNP
10_1101-2021_01_08_425885	837	42	J.	J.	NNP
10_1101-2021_01_08_425885	838	1	Wild	Wild	NNP
10_1101-2021_01_08_425885	838	2	,	,	,
10_1101-2021_01_08_425885	838	3	D.	D.	NNP
10_1101-2021_01_08_425885	838	4	Günther	Günther	NNP
10_1101-2021_01_08_425885	838	5	,	,	,
10_1101-2021_01_08_425885	838	6	and	and	CC
10_1101-2021_01_08_425885	838	7	B.	B.	NNP
10_1101-2021_01_08_425885	838	8	Bodenmiller	Bodenmiller	NNP
10_1101-2021_01_08_425885	838	9	.	.	.
10_1101-2021_01_08_425885	839	1	Highly	highly	RB
10_1101-2021_01_08_425885	839	2	multiplexed	multiplexed	JJ
10_1101-2021_01_08_425885	839	3	imaging	imaging	NN
10_1101-2021_01_08_425885	839	4	of	of	IN
10_1101-2021_01_08_425885	839	5	tumor	tumor	NN
10_1101-2021_01_08_425885	839	6	tissues	tissue	NNS
10_1101-2021_01_08_425885	839	7	with	with	IN
10_1101-2021_01_08_425885	839	8	subcellular	subcellular	JJ
10_1101-2021_01_08_425885	839	9	resolution	resolution	NN
10_1101-2021_01_08_425885	839	10	by	by	IN
10_1101-2021_01_08_425885	839	11	mass	mass	NN
10_1101-2021_01_08_425885	839	12	cytometry	cytometry	NN
10_1101-2021_01_08_425885	839	13	.	.	.
10_1101-2021_01_08_425885	840	1	Nature	Nature	NNP
10_1101-2021_01_08_425885	840	2	Methods	Methods	NNPS
10_1101-2021_01_08_425885	840	3	,	,	,
10_1101-2021_01_08_425885	840	4	11(4):417–422	11(4):417–422	CD
10_1101-2021_01_08_425885	840	5	,	,	,
10_1101-2021_01_08_425885	840	6	2014	2014	CD
10_1101-2021_01_08_425885	840	7	.	.	.
10_1101-2021_01_08_425885	841	1	[	[	-LRB-
10_1101-2021_01_08_425885	841	2	6	6	CD
10_1101-2021_01_08_425885	841	3	]	]	-RRB-
10_1101-2021_01_08_425885	841	4	J	J	NNP
10_1101-2021_01_08_425885	841	5	-	-	HYPH
10_1101-2021_01_08_425885	841	6	R.	R.	NNP
10_1101-2021_01_08_425885	841	7	Lin	Lin	NNP
10_1101-2021_01_08_425885	841	8	,	,	,
10_1101-2021_01_08_425885	841	9	M.	M.	NNP
10_1101-2021_01_08_425885	841	10	Fallahi	Fallahi	NNP
10_1101-2021_01_08_425885	841	11	-	-	HYPH
10_1101-2021_01_08_425885	841	12	Sichani	Sichani	NNP
10_1101-2021_01_08_425885	841	13	,	,	,
10_1101-2021_01_08_425885	841	14	J	J	NNP
10_1101-2021_01_08_425885	841	15	-	-	HYPH
10_1101-2021_01_08_425885	841	16	Y.	Y.	NNP
10_1101-2021_01_08_425885	842	1	Chen	Chen	NNP
10_1101-2021_01_08_425885	842	2	,	,	,
10_1101-2021_01_08_425885	842	3	and	and	CC
10_1101-2021_01_08_425885	842	4	P.	P.	NNP
10_1101-2021_01_08_425885	842	5	K.	K.	NNP
10_1101-2021_01_08_425885	842	6	Sorger	Sorger	NNP
10_1101-2021_01_08_425885	842	7	.	.	.
10_1101-2021_01_08_425885	843	1	Cyclic	cyclic	JJ
10_1101-2021_01_08_425885	843	2	immunofluorescence	immunofluorescence	NN
10_1101-2021_01_08_425885	843	3	(	(	-LRB-
10_1101-2021_01_08_425885	843	4	CycIF	CycIF	NNP
10_1101-2021_01_08_425885	843	5	)	)	-RRB-
10_1101-2021_01_08_425885	843	6	,	,	,
10_1101-2021_01_08_425885	843	7	a	a	DT
10_1101-2021_01_08_425885	843	8	highly	highly	RB
10_1101-2021_01_08_425885	843	9	multiplexed	multiplexed	JJ
10_1101-2021_01_08_425885	843	10	method	method	NN
10_1101-2021_01_08_425885	843	11	for	for	IN
10_1101-2021_01_08_425885	843	12	single	single	JJ
10_1101-2021_01_08_425885	843	13	-	-	HYPH
10_1101-2021_01_08_425885	843	14	cell	cell	NN
10_1101-2021_01_08_425885	843	15	imaging	imaging	NN
10_1101-2021_01_08_425885	843	16	.	.	.
10_1101-2021_01_08_425885	844	1	Current	Current	NNP
10_1101-2021_01_08_425885	844	2	Protocols	Protocols	NNPS
10_1101-2021_01_08_425885	844	3	in	in	IN
10_1101-2021_01_08_425885	844	4	Chemical	Chemical	NNP
10_1101-2021_01_08_425885	844	5	Biology	Biology	NNP
10_1101-2021_01_08_425885	844	6	,	,	,
10_1101-2021_01_08_425885	844	7	8(4):251–264	8(4):251–264	CD
10_1101-2021_01_08_425885	844	8	,	,	,
10_1101-2021_01_08_425885	844	9	2016	2016	CD
10_1101-2021_01_08_425885	844	10	.	.	.
10_1101-2021_01_08_425885	845	1	[	[	-LRB-
10_1101-2021_01_08_425885	845	2	7	7	CD
10_1101-2021_01_08_425885	845	3	]	]	-RRB-
10_1101-2021_01_08_425885	845	4	J	J	NNP
10_1101-2021_01_08_425885	845	5	-	-	HYPH
10_1101-2021_01_08_425885	845	6	R.	R.	NNP
10_1101-2021_01_08_425885	845	7	Lin	Lin	NNP
10_1101-2021_01_08_425885	845	8	,	,	,
10_1101-2021_01_08_425885	845	9	B.	B.	NNP
10_1101-2021_01_08_425885	845	10	Izar	Izar	NNP
10_1101-2021_01_08_425885	845	11	,	,	,
10_1101-2021_01_08_425885	845	12	S.	S.	NNP
10_1101-2021_01_08_425885	845	13	Wang	Wang	NNP
10_1101-2021_01_08_425885	845	14	,	,	,
10_1101-2021_01_08_425885	845	15	C.	C.	NNP
10_1101-2021_01_08_425885	845	16	Yapp	Yapp	NNP
10_1101-2021_01_08_425885	845	17	,	,	,
10_1101-2021_01_08_425885	845	18	S.	S.	NNP
10_1101-2021_01_08_425885	845	19	Mei	Mei	NNP
10_1101-2021_01_08_425885	845	20	,	,	,
10_1101-2021_01_08_425885	845	21	P.	P.	NNP
10_1101-2021_01_08_425885	845	22	M.	M.	NNP
10_1101-2021_01_08_425885	845	23	Shah	Shah	NNP
10_1101-2021_01_08_425885	845	24	,	,	,
10_1101-2021_01_08_425885	845	25	S.	S.	NNP
10_1101-2021_01_08_425885	845	26	Santagata	Santagata	NNP
10_1101-2021_01_08_425885	845	27	,	,	,
10_1101-2021_01_08_425885	845	28	and	and	CC
10_1101-2021_01_08_425885	845	29	P.	P.	NNP
10_1101-2021_01_08_425885	845	30	K.	K.	NNP
10_1101-2021_01_08_425885	845	31	Sorger	Sorger	NNP
10_1101-2021_01_08_425885	845	32	.	.	.
10_1101-2021_01_08_425885	846	1	Highly	highly	RB
10_1101-2021_01_08_425885	846	2	multiplexed	multiplexed	JJ
10_1101-2021_01_08_425885	846	3	immunofluorescence	immunofluorescence	NN
10_1101-2021_01_08_425885	846	4	imaging	imaging	NN
10_1101-2021_01_08_425885	846	5	of	of	IN
10_1101-2021_01_08_425885	846	6	human	human	JJ
10_1101-2021_01_08_425885	846	7	tissues	tissue	NNS
10_1101-2021_01_08_425885	846	8	and	and	CC
10_1101-2021_01_08_425885	846	9	tumors	tumor	NNS
10_1101-2021_01_08_425885	846	10	using	use	VBG
10_1101-2021_01_08_425885	846	11	t	t	NN
10_1101-2021_01_08_425885	846	12	-	-	HYPH
10_1101-2021_01_08_425885	846	13	CyCIF	CyCIF	NNS
10_1101-2021_01_08_425885	846	14	and	and	CC
10_1101-2021_01_08_425885	846	15	conventional	conventional	JJ
10_1101-2021_01_08_425885	846	16	optical	optical	JJ
10_1101-2021_01_08_425885	846	17	microscopes	microscope	NNS
10_1101-2021_01_08_425885	846	18	.	.	.
10_1101-2021_01_08_425885	847	1	eLife	elife	NN
10_1101-2021_01_08_425885	847	2	,	,	,
10_1101-2021_01_08_425885	847	3	7	7	CD
10_1101-2021_01_08_425885	847	4	,	,	,
10_1101-2021_01_08_425885	847	5	2018	2018	CD
10_1101-2021_01_08_425885	847	6	.	.	.
10_1101-2021_01_08_425885	848	1	[	[	-LRB-
10_1101-2021_01_08_425885	848	2	8	8	CD
10_1101-2021_01_08_425885	848	3	]	]	-RRB-
10_1101-2021_01_08_425885	848	4	L.	L.	NNP
10_1101-2021_01_08_425885	848	5	H.	H.	NNP
10_1101-2021_01_08_425885	848	6	Nguyen	Nguyen	NNP
10_1101-2021_01_08_425885	848	7	and	and	CC
10_1101-2021_01_08_425885	848	8	S.	S.	NNP
10_1101-2021_01_08_425885	848	9	Holmes	Holmes	NNP
10_1101-2021_01_08_425885	848	10	.	.	.
10_1101-2021_01_08_425885	849	1	Ten	ten	CD
10_1101-2021_01_08_425885	849	2	quick	quick	JJ
10_1101-2021_01_08_425885	849	3	tips	tip	NNS
10_1101-2021_01_08_425885	849	4	for	for	IN
10_1101-2021_01_08_425885	849	5	effective	effective	JJ
10_1101-2021_01_08_425885	849	6	dimensionality	dimensionality	NN
10_1101-2021_01_08_425885	849	7	reduction	reduction	NN
10_1101-2021_01_08_425885	849	8	.	.	.
10_1101-2021_01_08_425885	850	1	PLoS	PLoS	NNP
10_1101-2021_01_08_425885	850	2	Computational	Computational	NNP
10_1101-2021_01_08_425885	850	3	Biology	Biology	NNP
10_1101-2021_01_08_425885	850	4	,	,	,
10_1101-2021_01_08_425885	850	5	15(6):e1006907	15(6):e1006907	CD
10_1101-2021_01_08_425885	850	6	,	,	,
10_1101-2021_01_08_425885	850	7	2019	2019	CD
10_1101-2021_01_08_425885	850	8	.	.	.
10_1101-2021_01_08_425885	851	1	52	52	CD
10_1101-2021_01_08_425885	851	2	.CC	.CC	:
10_1101-2021_01_08_425885	851	3	-	-	HYPH
10_1101-2021_01_08_425885	851	4	BY	by	IN
10_1101-2021_01_08_425885	851	5	-	-	HYPH
10_1101-2021_01_08_425885	851	6	NC	NC	NNP
10_1101-2021_01_08_425885	851	7	-	-	HYPH
10_1101-2021_01_08_425885	851	8	ND	ND	NNP
10_1101-2021_01_08_425885	851	9	4.0	4.0	CD
10_1101-2021_01_08_425885	851	10	International	International	NNP
10_1101-2021_01_08_425885	851	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	851	12	under	under	IN
10_1101-2021_01_08_425885	851	13	a	a	DT
10_1101-2021_01_08_425885	851	14	(	(	-LRB-
10_1101-2021_01_08_425885	851	15	which	which	WDT
10_1101-2021_01_08_425885	851	16	was	be	VBD
10_1101-2021_01_08_425885	851	17	not	not	RB
10_1101-2021_01_08_425885	851	18	certified	certify	VBN
10_1101-2021_01_08_425885	851	19	by	by	IN
10_1101-2021_01_08_425885	851	20	peer	peer	NN
10_1101-2021_01_08_425885	851	21	review	review	NN
10_1101-2021_01_08_425885	851	22	)	)	-RRB-
10_1101-2021_01_08_425885	851	23	is	be	VBZ
10_1101-2021_01_08_425885	851	24	the	the	DT
10_1101-2021_01_08_425885	851	25	author	author	NN
10_1101-2021_01_08_425885	851	26	/	/	SYM
10_1101-2021_01_08_425885	851	27	funder	funder	NN
10_1101-2021_01_08_425885	851	28	,	,	,
10_1101-2021_01_08_425885	851	29	who	who	WP
10_1101-2021_01_08_425885	851	30	has	have	VBZ
10_1101-2021_01_08_425885	851	31	granted	grant	VBN
10_1101-2021_01_08_425885	851	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	851	33	a	a	DT
10_1101-2021_01_08_425885	851	34	license	license	NN
10_1101-2021_01_08_425885	851	35	to	to	TO
10_1101-2021_01_08_425885	851	36	display	display	VB
10_1101-2021_01_08_425885	851	37	the	the	DT
10_1101-2021_01_08_425885	851	38	preprint	preprint	NN
10_1101-2021_01_08_425885	851	39	in	in	IN
10_1101-2021_01_08_425885	851	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	851	41	.	.	.
10_1101-2021_01_08_425885	852	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	852	2	is	be	VBZ
10_1101-2021_01_08_425885	852	3	made	make	VBN
10_1101-2021_01_08_425885	852	4	The	the	DT
10_1101-2021_01_08_425885	852	5	copyright	copyright	NN
10_1101-2021_01_08_425885	852	6	holder	holder	NN
10_1101-2021_01_08_425885	852	7	for	for	IN
10_1101-2021_01_08_425885	852	8	this	this	DT
10_1101-2021_01_08_425885	852	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	852	10	version	version	NN
10_1101-2021_01_08_425885	852	11	posted	post	VBD
10_1101-2021_01_08_425885	852	12	January	January	NNP
10_1101-2021_01_08_425885	852	13	8	8	CD
10_1101-2021_01_08_425885	852	14	,	,	,
10_1101-2021_01_08_425885	852	15	2021	2021	CD
10_1101-2021_01_08_425885	852	16	.	.	.
10_1101-2021_01_08_425885	852	17	;	;	:
10_1101-2021_01_08_425885	852	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	852	19	:	:	:
10_1101-2021_01_08_425885	852	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	852	21	preprint	preprint	NN
10_1101-2021_01_08_425885	852	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	852	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	CD
10_1101-2021_01_08_425885	852	24	[	[	-LRB-
10_1101-2021_01_08_425885	852	25	9	9	CD
10_1101-2021_01_08_425885	852	26	]	]	-RRB-
10_1101-2021_01_08_425885	852	27	J.	J.	NNP
10_1101-2021_01_08_425885	853	1	B.	B.	NNP
10_1101-2021_01_08_425885	853	2	Tenenbaum	Tenenbaum	NNP
10_1101-2021_01_08_425885	853	3	.	.	.
10_1101-2021_01_08_425885	854	1	A	a	DT
10_1101-2021_01_08_425885	854	2	global	global	JJ
10_1101-2021_01_08_425885	854	3	geometric	geometric	JJ
10_1101-2021_01_08_425885	854	4	framework	framework	NN
10_1101-2021_01_08_425885	854	5	for	for	IN
10_1101-2021_01_08_425885	854	6	nonlinear	nonlinear	JJ
10_1101-2021_01_08_425885	854	7	dimensionality	dimensionality	NN
10_1101-2021_01_08_425885	854	8	reduction	reduction	NN
10_1101-2021_01_08_425885	854	9	.	.	.
10_1101-2021_01_08_425885	855	1	Science	science	NN
10_1101-2021_01_08_425885	855	2	,	,	,
10_1101-2021_01_08_425885	855	3	290(5500):2319–2323	290(5500):2319–2323	CD
10_1101-2021_01_08_425885	855	4	,	,	,
10_1101-2021_01_08_425885	855	5	2000	2000	CD
10_1101-2021_01_08_425885	855	6	.	.	.
10_1101-2021_01_08_425885	856	1	[	[	-LRB-
10_1101-2021_01_08_425885	856	2	10	10	CD
10_1101-2021_01_08_425885	856	3	]	]	-RRB-
10_1101-2021_01_08_425885	856	4	L.	L.	NNP
10_1101-2021_01_08_425885	856	5	van	van	NNP
10_1101-2021_01_08_425885	856	6	der	der	NNP
10_1101-2021_01_08_425885	856	7	Maaten	Maaten	NNP
10_1101-2021_01_08_425885	856	8	and	and	CC
10_1101-2021_01_08_425885	856	9	G.	G.	NNP
10_1101-2021_01_08_425885	856	10	Hinton	Hinton	NNP
10_1101-2021_01_08_425885	856	11	.	.	.
10_1101-2021_01_08_425885	857	1	Visualizing	visualize	VBG
10_1101-2021_01_08_425885	857	2	data	datum	NNS
10_1101-2021_01_08_425885	857	3	using	use	VBG
10_1101-2021_01_08_425885	857	4	t	t	NNP
10_1101-2021_01_08_425885	857	5	-	-	HYPH
10_1101-2021_01_08_425885	857	6	SNE	SNE	NNP
10_1101-2021_01_08_425885	857	7	.	.	.
10_1101-2021_01_08_425885	858	1	Journal	Journal	NNP
10_1101-2021_01_08_425885	858	2	of	of	IN
10_1101-2021_01_08_425885	858	3	Machine	Machine	NNP
10_1101-2021_01_08_425885	858	4	Learning	Learning	NNP
10_1101-2021_01_08_425885	858	5	Research	Research	NNP
10_1101-2021_01_08_425885	858	6	,	,	,
10_1101-2021_01_08_425885	858	7	9(Nov):2579–2605	9(nov):2579–2605	CD
10_1101-2021_01_08_425885	858	8	,	,	,
10_1101-2021_01_08_425885	858	9	2008	2008	CD
10_1101-2021_01_08_425885	858	10	.	.	.
10_1101-2021_01_08_425885	859	1	[	[	-LRB-
10_1101-2021_01_08_425885	859	2	11	11	CD
10_1101-2021_01_08_425885	859	3	]	]	-RRB-
10_1101-2021_01_08_425885	859	4	E.	E.	NNP
10_1101-2021_01_08_425885	859	5	Becht	Becht	NNP
10_1101-2021_01_08_425885	859	6	,	,	,
10_1101-2021_01_08_425885	859	7	L.	L.	NNP
10_1101-2021_01_08_425885	859	8	McInnes	McInnes	NNP
10_1101-2021_01_08_425885	859	9	,	,	,
10_1101-2021_01_08_425885	859	10	J.	J.	NNP
10_1101-2021_01_08_425885	859	11	Healy	Healy	NNP
10_1101-2021_01_08_425885	859	12	,	,	,
10_1101-2021_01_08_425885	859	13	C	C	NNP
10_1101-2021_01_08_425885	859	14	-	-	HYPH
10_1101-2021_01_08_425885	859	15	A.	a.	NN
10_1101-2021_01_08_425885	860	1	Dutertre	Dutertre	NNP
10_1101-2021_01_08_425885	860	2	,	,	,
10_1101-2021_01_08_425885	860	3	I.	I.	NNP
10_1101-2021_01_08_425885	860	4	W.	W.	NNP
10_1101-2021_01_08_425885	860	5	H.	H.	NNP
10_1101-2021_01_08_425885	860	6	Kwok	Kwok	NNP
10_1101-2021_01_08_425885	860	7	,	,	,
10_1101-2021_01_08_425885	860	8	L.	L.	NNP
10_1101-2021_01_08_425885	860	9	G.	G.	NNP
10_1101-2021_01_08_425885	860	10	Ng	Ng	NNP
10_1101-2021_01_08_425885	860	11	,	,	,
10_1101-2021_01_08_425885	860	12	F.	F.	NNP
10_1101-2021_01_08_425885	860	13	Ginhoux	Ginhoux	NNP
10_1101-2021_01_08_425885	860	14	,	,	,
10_1101-2021_01_08_425885	860	15	and	and	CC
10_1101-2021_01_08_425885	860	16	E.	E.	NNP
10_1101-2021_01_08_425885	860	17	W.	W.	NNP
10_1101-2021_01_08_425885	860	18	Newell	Newell	NNP
10_1101-2021_01_08_425885	860	19	.	.	.
10_1101-2021_01_08_425885	861	1	Dimensionality	dimensionality	NN
10_1101-2021_01_08_425885	861	2	reduction	reduction	NN
10_1101-2021_01_08_425885	861	3	for	for	IN
10_1101-2021_01_08_425885	861	4	visualizing	visualize	VBG
10_1101-2021_01_08_425885	861	5	single	single	JJ
10_1101-2021_01_08_425885	861	6	-	-	HYPH
10_1101-2021_01_08_425885	861	7	cell	cell	NN
10_1101-2021_01_08_425885	861	8	data	datum	NNS
10_1101-2021_01_08_425885	861	9	using	use	VBG
10_1101-2021_01_08_425885	861	10	UMAP	UMAP	NNP
10_1101-2021_01_08_425885	861	11	.	.	.
10_1101-2021_01_08_425885	862	1	Nature	Nature	NNP
10_1101-2021_01_08_425885	862	2	Biotechnology	Biotechnology	NNP
10_1101-2021_01_08_425885	862	3	,	,	,
10_1101-2021_01_08_425885	862	4	37(1):38–44	37(1):38–44	CD
10_1101-2021_01_08_425885	862	5	,	,	,
10_1101-2021_01_08_425885	862	6	2018	2018	CD
10_1101-2021_01_08_425885	862	7	.	.	.
10_1101-2021_01_08_425885	863	1	[	[	-LRB-
10_1101-2021_01_08_425885	863	2	12	12	CD
10_1101-2021_01_08_425885	863	3	]	]	-RRB-
10_1101-2021_01_08_425885	863	4	A.	a.	NN
10_1101-2021_01_08_425885	863	5	Hatcher	Hatcher	NNP
10_1101-2021_01_08_425885	863	6	.	.	.
10_1101-2021_01_08_425885	864	1	Algebraic	Algebraic	NNP
10_1101-2021_01_08_425885	864	2	Topology	Topology	NNP
10_1101-2021_01_08_425885	864	3	.	.	.
10_1101-2021_01_08_425885	865	1	Cambridge	Cambridge	NNP
10_1101-2021_01_08_425885	865	2	University	University	NNP
10_1101-2021_01_08_425885	865	3	Press	Press	NNP
10_1101-2021_01_08_425885	865	4	,	,	,
10_1101-2021_01_08_425885	865	5	2001	2001	CD
10_1101-2021_01_08_425885	865	6	.	.	.
10_1101-2021_01_08_425885	866	1	[	[	-LRB-
10_1101-2021_01_08_425885	866	2	13	13	CD
10_1101-2021_01_08_425885	866	3	]	]	-RRB-
10_1101-2021_01_08_425885	866	4	R.	R.	NNP
10_1101-2021_01_08_425885	866	5	Ghrist	Ghrist	NNP
10_1101-2021_01_08_425885	866	6	.	.	.
10_1101-2021_01_08_425885	867	1	Barcodes	barcodes	IN
10_1101-2021_01_08_425885	867	2	:	:	:
10_1101-2021_01_08_425885	867	3	the	the	DT
10_1101-2021_01_08_425885	867	4	persistent	persistent	JJ
10_1101-2021_01_08_425885	867	5	topology	topology	NN
10_1101-2021_01_08_425885	867	6	of	of	IN
10_1101-2021_01_08_425885	867	7	data	datum	NNS
10_1101-2021_01_08_425885	867	8	.	.	.
10_1101-2021_01_08_425885	868	1	Bulletin	bulletin	NN
10_1101-2021_01_08_425885	868	2	of	of	IN
10_1101-2021_01_08_425885	868	3	the	the	DT
10_1101-2021_01_08_425885	868	4	American	American	NNP
10_1101-2021_01_08_425885	868	5	Mathematical	Mathematical	NNP
10_1101-2021_01_08_425885	868	6	Society	Society	NNP
10_1101-2021_01_08_425885	868	7	,	,	,
10_1101-2021_01_08_425885	868	8	45(01):61–76	45(01):61–76	CD
10_1101-2021_01_08_425885	868	9	,	,	,
10_1101-2021_01_08_425885	868	10	2007	2007	CD
10_1101-2021_01_08_425885	868	11	.	.	.
10_1101-2021_01_08_425885	869	1	[	[	-LRB-
10_1101-2021_01_08_425885	869	2	14	14	CD
10_1101-2021_01_08_425885	869	3	]	]	-RRB-
10_1101-2021_01_08_425885	869	4	D.	D.	NNP
10_1101-2021_01_08_425885	869	5	Perrault	Perrault	NNP
10_1101-2021_01_08_425885	869	6	-	-	HYPH
10_1101-2021_01_08_425885	869	7	Joncas	Joncas	NNP
10_1101-2021_01_08_425885	869	8	and	and	CC
10_1101-2021_01_08_425885	869	9	M.	M.	NNP
10_1101-2021_01_08_425885	869	10	Meilâ.	Meilâ.	NNP
10_1101-2021_01_08_425885	870	1	Non	non	JJ
10_1101-2021_01_08_425885	870	2	-	-	JJ
10_1101-2021_01_08_425885	870	3	linear	linear	JJ
10_1101-2021_01_08_425885	870	4	dimensionality	dimensionality	NN
10_1101-2021_01_08_425885	870	5	reduction	reduction	NN
10_1101-2021_01_08_425885	870	6	:	:	:
10_1101-2021_01_08_425885	870	7	Riemannian	riemannian	JJ
10_1101-2021_01_08_425885	870	8	metric	metric	JJ
10_1101-2021_01_08_425885	870	9	estimation	estimation	NN
10_1101-2021_01_08_425885	870	10	and	and	CC
10_1101-2021_01_08_425885	870	11	the	the	DT
10_1101-2021_01_08_425885	870	12	problem	problem	NN
10_1101-2021_01_08_425885	870	13	of	of	IN
10_1101-2021_01_08_425885	870	14	geometric	geometric	JJ
10_1101-2021_01_08_425885	870	15	discovery	discovery	NN
10_1101-2021_01_08_425885	870	16	.	.	.
10_1101-2021_01_08_425885	871	1	arXiv	arXiv	NNP
10_1101-2021_01_08_425885	871	2	,	,	,
10_1101-2021_01_08_425885	871	3	2013	2013	CD
10_1101-2021_01_08_425885	871	4	.	.	.
10_1101-2021_01_08_425885	872	1	[	[	-LRB-
10_1101-2021_01_08_425885	872	2	15	15	CD
10_1101-2021_01_08_425885	872	3	]	]	-RRB-
10_1101-2021_01_08_425885	872	4	J.	J.	NNP
10_1101-2021_01_08_425885	872	5	M.	M.	NNP
10_1101-2021_01_08_425885	872	6	Lee	Lee	NNP
10_1101-2021_01_08_425885	872	7	.	.	.
10_1101-2021_01_08_425885	873	1	Riemannian	Riemannian	NNP
10_1101-2021_01_08_425885	873	2	Manifolds	Manifolds	NNP
10_1101-2021_01_08_425885	873	3	:	:	:
10_1101-2021_01_08_425885	873	4	An	an	DT
10_1101-2021_01_08_425885	873	5	Introduction	introduction	NN
10_1101-2021_01_08_425885	873	6	to	to	IN
10_1101-2021_01_08_425885	873	7	Curvature	curvature	NN
10_1101-2021_01_08_425885	873	8	(	(	-LRB-
10_1101-2021_01_08_425885	873	9	Graduate	Graduate	NNP
10_1101-2021_01_08_425885	873	10	Texts	Texts	NNP
10_1101-2021_01_08_425885	873	11	in	in	IN
10_1101-2021_01_08_425885	873	12	Mathematics	Mathematics	NNP
10_1101-2021_01_08_425885	873	13	)	)	-RRB-
10_1101-2021_01_08_425885	873	14	.	.	.
10_1101-2021_01_08_425885	874	1	Springer	Springer	NNP
10_1101-2021_01_08_425885	874	2	,	,	,
10_1101-2021_01_08_425885	874	3	1997	1997	CD
10_1101-2021_01_08_425885	874	4	.	.	.
10_1101-2021_01_08_425885	875	1	[	[	-LRB-
10_1101-2021_01_08_425885	875	2	16	16	CD
10_1101-2021_01_08_425885	875	3	]	]	-RRB-
10_1101-2021_01_08_425885	875	4	A.	a.	NN
10_1101-2021_01_08_425885	875	5	Zomorodian	Zomorodian	NNP
10_1101-2021_01_08_425885	875	6	and	and	CC
10_1101-2021_01_08_425885	875	7	G.	G.	NNP
10_1101-2021_01_08_425885	875	8	Carlsson	Carlsson	NNP
10_1101-2021_01_08_425885	875	9	.	.	.
10_1101-2021_01_08_425885	876	1	Computing	compute	VBG
10_1101-2021_01_08_425885	876	2	persistent	persistent	JJ
10_1101-2021_01_08_425885	876	3	homology	homology	NN
10_1101-2021_01_08_425885	876	4	.	.	.
10_1101-2021_01_08_425885	877	1	Discrete	Discrete	NNP
10_1101-2021_01_08_425885	877	2	&	&	CC
10_1101-2021_01_08_425885	877	3	Computational	Computational	NNP
10_1101-2021_01_08_425885	877	4	Geometry	Geometry	NNP
10_1101-2021_01_08_425885	877	5	,	,	,
10_1101-2021_01_08_425885	877	6	33(2):249–274	33(2):249–274	CD
10_1101-2021_01_08_425885	877	7	,	,	,
10_1101-2021_01_08_425885	877	8	2004	2004	CD
10_1101-2021_01_08_425885	877	9	.	.	.
10_1101-2021_01_08_425885	878	1	[	[	-LRB-
10_1101-2021_01_08_425885	878	2	17	17	CD
10_1101-2021_01_08_425885	878	3	]	]	-RRB-
10_1101-2021_01_08_425885	878	4	G.	G.	NNP
10_1101-2021_01_08_425885	878	5	Carlsson	Carlsson	NNP
10_1101-2021_01_08_425885	878	6	.	.	.
10_1101-2021_01_08_425885	879	1	Topology	topology	NN
10_1101-2021_01_08_425885	879	2	and	and	CC
10_1101-2021_01_08_425885	879	3	data	datum	NNS
10_1101-2021_01_08_425885	879	4	.	.	.
10_1101-2021_01_08_425885	880	1	Bulletin	bulletin	NN
10_1101-2021_01_08_425885	880	2	of	of	IN
10_1101-2021_01_08_425885	880	3	the	the	DT
10_1101-2021_01_08_425885	880	4	American	American	NNP
10_1101-2021_01_08_425885	880	5	Mathematical	Mathematical	NNP
10_1101-2021_01_08_425885	880	6	Society	Society	NNP
10_1101-2021_01_08_425885	880	7	,	,	,
10_1101-2021_01_08_425885	880	8	46(2):255–308	46(2):255–308	CD
10_1101-2021_01_08_425885	880	9	,	,	,
10_1101-2021_01_08_425885	880	10	2009	2009	CD
10_1101-2021_01_08_425885	880	11	.	.	.
10_1101-2021_01_08_425885	881	1	[	[	-LRB-
10_1101-2021_01_08_425885	881	2	18	18	CD
10_1101-2021_01_08_425885	881	3	]	]	-RRB-
10_1101-2021_01_08_425885	881	4	M.	M.	NNP
10_1101-2021_01_08_425885	881	5	Bernstein	Bernstein	NNP
10_1101-2021_01_08_425885	881	6	,	,	,
10_1101-2021_01_08_425885	881	7	V.	V.	NNP
10_1101-2021_01_08_425885	881	8	De	De	NNP
10_1101-2021_01_08_425885	881	9	Silva	Silva	NNP
10_1101-2021_01_08_425885	881	10	,	,	,
10_1101-2021_01_08_425885	881	11	J.	J.	NNP
10_1101-2021_01_08_425885	881	12	C.	C.	NNP
10_1101-2021_01_08_425885	881	13	Langford	Langford	NNP
10_1101-2021_01_08_425885	881	14	,	,	,
10_1101-2021_01_08_425885	881	15	and	and	CC
10_1101-2021_01_08_425885	881	16	J.	J.	NNP
10_1101-2021_01_08_425885	882	1	B.	B.	NNP
10_1101-2021_01_08_425885	882	2	Tenenbaum	Tenenbaum	NNP
10_1101-2021_01_08_425885	882	3	.	.	.
10_1101-2021_01_08_425885	883	1	Graph	graph	NN
10_1101-2021_01_08_425885	883	2	approximations	approximation	NNS
10_1101-2021_01_08_425885	883	3	to	to	IN
10_1101-2021_01_08_425885	883	4	geodesics	geodesic	NNS
10_1101-2021_01_08_425885	883	5	on	on	IN
10_1101-2021_01_08_425885	883	6	embedded	embed	VBN
10_1101-2021_01_08_425885	883	7	manifolds	manifold	NNS
10_1101-2021_01_08_425885	883	8	.	.	.
10_1101-2021_01_08_425885	884	1	Technical	technical	JJ
10_1101-2021_01_08_425885	884	2	report	report	NN
10_1101-2021_01_08_425885	884	3	,	,	,
10_1101-2021_01_08_425885	884	4	Department	Department	NNP
10_1101-2021_01_08_425885	884	5	of	of	IN
10_1101-2021_01_08_425885	884	6	Psychology	Psychology	NNP
10_1101-2021_01_08_425885	884	7	,	,	,
10_1101-2021_01_08_425885	884	8	Stanford	Stanford	NNP
10_1101-2021_01_08_425885	884	9	University	University	NNP
10_1101-2021_01_08_425885	884	10	,	,	,
10_1101-2021_01_08_425885	884	11	2000	2000	CD
10_1101-2021_01_08_425885	884	12	.	.	.
10_1101-2021_01_08_425885	885	1	[	[	-LRB-
10_1101-2021_01_08_425885	885	2	19	19	CD
10_1101-2021_01_08_425885	885	3	]	]	-RRB-
10_1101-2021_01_08_425885	885	4	F.	F.	NNP
10_1101-2021_01_08_425885	885	5	Chazal	Chazal	NNP
10_1101-2021_01_08_425885	885	6	,	,	,
10_1101-2021_01_08_425885	885	7	M.	M.	NNP
10_1101-2021_01_08_425885	885	8	Glisse	Glisse	NNP
10_1101-2021_01_08_425885	885	9	,	,	,
10_1101-2021_01_08_425885	885	10	C.	C.	NNP
10_1101-2021_01_08_425885	885	11	Labruère	Labruère	NNP
10_1101-2021_01_08_425885	885	12	,	,	,
10_1101-2021_01_08_425885	885	13	and	and	CC
10_1101-2021_01_08_425885	885	14	B.	B.	NNP
10_1101-2021_01_08_425885	885	15	Michel	Michel	NNP
10_1101-2021_01_08_425885	885	16	.	.	.
10_1101-2021_01_08_425885	886	1	Convergence	convergence	NN
10_1101-2021_01_08_425885	886	2	rates	rate	NNS
10_1101-2021_01_08_425885	886	3	for	for	IN
10_1101-2021_01_08_425885	886	4	persistence	persistence	NN
10_1101-2021_01_08_425885	886	5	diagram	diagram	NN
10_1101-2021_01_08_425885	886	6	estimation	estimation	NN
10_1101-2021_01_08_425885	886	7	in	in	IN
10_1101-2021_01_08_425885	886	8	topological	topological	JJ
10_1101-2021_01_08_425885	886	9	data	datum	NNS
10_1101-2021_01_08_425885	886	10	analysis	analysis	NN
10_1101-2021_01_08_425885	886	11	.	.	.
10_1101-2021_01_08_425885	887	1	Journal	Journal	NNP
10_1101-2021_01_08_425885	887	2	of	of	IN
10_1101-2021_01_08_425885	887	3	Machine	Machine	NNP
10_1101-2021_01_08_425885	887	4	Learning	Learning	NNP
10_1101-2021_01_08_425885	887	5	Research	Research	NNP
10_1101-2021_01_08_425885	887	6	,	,	,
10_1101-2021_01_08_425885	887	7	16(1):3603–3635	16(1):3603–3635	CD
10_1101-2021_01_08_425885	887	8	,	,	,
10_1101-2021_01_08_425885	887	9	2015	2015	CD
10_1101-2021_01_08_425885	887	10	.	.	.
10_1101-2021_01_08_425885	888	1	[	[	-LRB-
10_1101-2021_01_08_425885	888	2	20	20	CD
10_1101-2021_01_08_425885	888	3	]	]	-RRB-
10_1101-2021_01_08_425885	888	4	C.	C.	NNP
10_1101-2021_01_08_425885	888	5	R.	R.	NNP
10_1101-2021_01_08_425885	888	6	Genovese	Genovese	NNP
10_1101-2021_01_08_425885	888	7	,	,	,
10_1101-2021_01_08_425885	888	8	M.	M.	NNP
10_1101-2021_01_08_425885	888	9	Perone	Perone	NNP
10_1101-2021_01_08_425885	888	10	-	-	HYPH
10_1101-2021_01_08_425885	888	11	Pacifico	Pacifico	NNP
10_1101-2021_01_08_425885	888	12	,	,	,
10_1101-2021_01_08_425885	888	13	I.	I.	NNP
10_1101-2021_01_08_425885	888	14	Verdinelli	Verdinelli	NNP
10_1101-2021_01_08_425885	888	15	,	,	,
10_1101-2021_01_08_425885	888	16	and	and	CC
10_1101-2021_01_08_425885	888	17	L.	L.	NNP
10_1101-2021_01_08_425885	888	18	Wasserman	Wasserman	NNP
10_1101-2021_01_08_425885	888	19	.	.	.
10_1101-2021_01_08_425885	889	1	Minimax	Minimax	NNP
10_1101-2021_01_08_425885	889	2	manifold	manifold	JJ
10_1101-2021_01_08_425885	889	3	estimation	estimation	NN
10_1101-2021_01_08_425885	889	4	.	.	.
10_1101-2021_01_08_425885	890	1	Journal	Journal	NNP
10_1101-2021_01_08_425885	890	2	of	of	IN
10_1101-2021_01_08_425885	890	3	Machine	Machine	NNP
10_1101-2021_01_08_425885	890	4	Learning	Learning	NNP
10_1101-2021_01_08_425885	890	5	Research	Research	NNP
10_1101-2021_01_08_425885	890	6	,	,	,
10_1101-2021_01_08_425885	890	7	13(1):1263–1291	13(1):1263–1291	CD
10_1101-2021_01_08_425885	890	8	,	,	,
10_1101-2021_01_08_425885	890	9	2012	2012	CD
10_1101-2021_01_08_425885	890	10	.	.	.
10_1101-2021_01_08_425885	891	1	[	[	-LRB-
10_1101-2021_01_08_425885	891	2	21	21	CD
10_1101-2021_01_08_425885	891	3	]	]	-RRB-
10_1101-2021_01_08_425885	891	4	G.	G.	NNP
10_1101-2021_01_08_425885	891	5	Carlsson	Carlsson	NNP
10_1101-2021_01_08_425885	891	6	,	,	,
10_1101-2021_01_08_425885	891	7	T.	T.	NNP
10_1101-2021_01_08_425885	891	8	Ishkhanov	Ishkhanov	NNP
10_1101-2021_01_08_425885	891	9	,	,	,
10_1101-2021_01_08_425885	891	10	V.	V.	NNP
10_1101-2021_01_08_425885	891	11	De	De	NNP
10_1101-2021_01_08_425885	891	12	Silva	Silva	NNP
10_1101-2021_01_08_425885	891	13	,	,	,
10_1101-2021_01_08_425885	891	14	and	and	CC
10_1101-2021_01_08_425885	891	15	A.	A.	NNP
10_1101-2021_01_08_425885	891	16	Zomorodian	Zomorodian	NNP
10_1101-2021_01_08_425885	891	17	.	.	.
10_1101-2021_01_08_425885	892	1	On	on	IN
10_1101-2021_01_08_425885	892	2	the	the	DT
10_1101-2021_01_08_425885	892	3	local	local	JJ
10_1101-2021_01_08_425885	892	4	behavior	behavior	NN
10_1101-2021_01_08_425885	892	5	of	of	IN
10_1101-2021_01_08_425885	892	6	spaces	space	NNS
10_1101-2021_01_08_425885	892	7	of	of	IN
10_1101-2021_01_08_425885	892	8	natural	natural	JJ
10_1101-2021_01_08_425885	892	9	images	image	NNS
10_1101-2021_01_08_425885	892	10	.	.	.
10_1101-2021_01_08_425885	893	1	International	International	NNP
10_1101-2021_01_08_425885	893	2	Journal	Journal	NNP
10_1101-2021_01_08_425885	893	3	of	of	IN
10_1101-2021_01_08_425885	893	4	Computer	Computer	NNP
10_1101-2021_01_08_425885	893	5	Vision	Vision	NNP
10_1101-2021_01_08_425885	893	6	,	,	,
10_1101-2021_01_08_425885	893	7	76(1):1–12	76(1):1–12	CD
10_1101-2021_01_08_425885	893	8	,	,	,
10_1101-2021_01_08_425885	893	9	2008	2008	CD
10_1101-2021_01_08_425885	893	10	.	.	.
10_1101-2021_01_08_425885	894	1	[	[	-LRB-
10_1101-2021_01_08_425885	894	2	22	22	CD
10_1101-2021_01_08_425885	894	3	]	]	-RRB-
10_1101-2021_01_08_425885	894	4	P.	P.	NNP
10_1101-2021_01_08_425885	894	5	Lawson	Lawson	NNP
10_1101-2021_01_08_425885	894	6	,	,	,
10_1101-2021_01_08_425885	894	7	A.	a.	NN
10_1101-2021_01_08_425885	895	1	B.	B.	NNP
10_1101-2021_01_08_425885	895	2	Sholl	Sholl	NNP
10_1101-2021_01_08_425885	895	3	,	,	,
10_1101-2021_01_08_425885	895	4	J.	J.	NNP
10_1101-2021_01_08_425885	895	5	Q.	Q.	NNP
10_1101-2021_01_08_425885	896	1	Brown	Brown	NNP
10_1101-2021_01_08_425885	896	2	,	,	,
10_1101-2021_01_08_425885	896	3	B.	B.	NNP
10_1101-2021_01_08_425885	896	4	T.	T.	NNP
10_1101-2021_01_08_425885	896	5	Fasy	Fasy	NNP
10_1101-2021_01_08_425885	896	6	,	,	,
10_1101-2021_01_08_425885	896	7	and	and	CC
10_1101-2021_01_08_425885	896	8	C.	C.	NNP
10_1101-2021_01_08_425885	896	9	Wenk	Wenk	NNP
10_1101-2021_01_08_425885	896	10	.	.	.
10_1101-2021_01_08_425885	897	1	Persistent	persistent	JJ
10_1101-2021_01_08_425885	897	2	homology	homology	NN
10_1101-2021_01_08_425885	897	3	for	for	IN
10_1101-2021_01_08_425885	897	4	the	the	DT
10_1101-2021_01_08_425885	897	5	quantitative	quantitative	JJ
10_1101-2021_01_08_425885	897	6	evaluation	evaluation	NN
10_1101-2021_01_08_425885	897	7	of	of	IN
10_1101-2021_01_08_425885	897	8	architectural	architectural	JJ
10_1101-2021_01_08_425885	897	9	features	feature	NNS
10_1101-2021_01_08_425885	897	10	in	in	IN
10_1101-2021_01_08_425885	897	11	prostate	prostate	NN
10_1101-2021_01_08_425885	897	12	cancer	cancer	NN
10_1101-2021_01_08_425885	897	13	histology	histology	NN
10_1101-2021_01_08_425885	897	14	.	.	.
10_1101-2021_01_08_425885	898	1	Scientific	Scientific	NNP
10_1101-2021_01_08_425885	898	2	Reports	Reports	NNPS
10_1101-2021_01_08_425885	898	3	,	,	,
10_1101-2021_01_08_425885	898	4	9(1):1–15	9(1):1–15	CD
10_1101-2021_01_08_425885	898	5	,	,	,
10_1101-2021_01_08_425885	898	6	2019	2019	CD
10_1101-2021_01_08_425885	898	7	.	.	.
10_1101-2021_01_08_425885	899	1	53	53	CD
10_1101-2021_01_08_425885	899	2	.CC	.CC	:
10_1101-2021_01_08_425885	899	3	-	-	HYPH
10_1101-2021_01_08_425885	899	4	BY	by	IN
10_1101-2021_01_08_425885	899	5	-	-	HYPH
10_1101-2021_01_08_425885	899	6	NC	NC	NNP
10_1101-2021_01_08_425885	899	7	-	-	HYPH
10_1101-2021_01_08_425885	899	8	ND	ND	NNP
10_1101-2021_01_08_425885	899	9	4.0	4.0	CD
10_1101-2021_01_08_425885	899	10	International	International	NNP
10_1101-2021_01_08_425885	899	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	899	12	under	under	IN
10_1101-2021_01_08_425885	899	13	a	a	DT
10_1101-2021_01_08_425885	899	14	(	(	-LRB-
10_1101-2021_01_08_425885	899	15	which	which	WDT
10_1101-2021_01_08_425885	899	16	was	be	VBD
10_1101-2021_01_08_425885	899	17	not	not	RB
10_1101-2021_01_08_425885	899	18	certified	certify	VBN
10_1101-2021_01_08_425885	899	19	by	by	IN
10_1101-2021_01_08_425885	899	20	peer	peer	NN
10_1101-2021_01_08_425885	899	21	review	review	NN
10_1101-2021_01_08_425885	899	22	)	)	-RRB-
10_1101-2021_01_08_425885	899	23	is	be	VBZ
10_1101-2021_01_08_425885	899	24	the	the	DT
10_1101-2021_01_08_425885	899	25	author	author	NN
10_1101-2021_01_08_425885	899	26	/	/	SYM
10_1101-2021_01_08_425885	899	27	funder	funder	NN
10_1101-2021_01_08_425885	899	28	,	,	,
10_1101-2021_01_08_425885	899	29	who	who	WP
10_1101-2021_01_08_425885	899	30	has	have	VBZ
10_1101-2021_01_08_425885	899	31	granted	grant	VBN
10_1101-2021_01_08_425885	899	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	899	33	a	a	DT
10_1101-2021_01_08_425885	899	34	license	license	NN
10_1101-2021_01_08_425885	899	35	to	to	TO
10_1101-2021_01_08_425885	899	36	display	display	VB
10_1101-2021_01_08_425885	899	37	the	the	DT
10_1101-2021_01_08_425885	899	38	preprint	preprint	NN
10_1101-2021_01_08_425885	899	39	in	in	IN
10_1101-2021_01_08_425885	899	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	899	41	.	.	.
10_1101-2021_01_08_425885	900	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	900	2	is	be	VBZ
10_1101-2021_01_08_425885	900	3	made	make	VBN
10_1101-2021_01_08_425885	900	4	The	the	DT
10_1101-2021_01_08_425885	900	5	copyright	copyright	NN
10_1101-2021_01_08_425885	900	6	holder	holder	NN
10_1101-2021_01_08_425885	900	7	for	for	IN
10_1101-2021_01_08_425885	900	8	this	this	DT
10_1101-2021_01_08_425885	900	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	900	10	version	version	NN
10_1101-2021_01_08_425885	900	11	posted	post	VBD
10_1101-2021_01_08_425885	900	12	January	January	NNP
10_1101-2021_01_08_425885	900	13	8	8	CD
10_1101-2021_01_08_425885	900	14	,	,	,
10_1101-2021_01_08_425885	900	15	2021	2021	CD
10_1101-2021_01_08_425885	900	16	.	.	.
10_1101-2021_01_08_425885	900	17	;	;	:
10_1101-2021_01_08_425885	900	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	900	19	:	:	:
10_1101-2021_01_08_425885	900	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	900	21	preprint	preprint	NN
10_1101-2021_01_08_425885	900	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	900	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	CD
10_1101-2021_01_08_425885	900	24	[	[	-LRB-
10_1101-2021_01_08_425885	900	25	23	23	CD
10_1101-2021_01_08_425885	900	26	]	]	-RRB-
10_1101-2021_01_08_425885	900	27	J.	J.	NNP
10_1101-2021_01_08_425885	900	28	M.	M.	NNP
10_1101-2021_01_08_425885	900	29	Chan	Chan	NNP
10_1101-2021_01_08_425885	900	30	,	,	,
10_1101-2021_01_08_425885	900	31	G.	G.	NNP
10_1101-2021_01_08_425885	900	32	Carlsson	Carlsson	NNP
10_1101-2021_01_08_425885	900	33	,	,	,
10_1101-2021_01_08_425885	900	34	and	and	CC
10_1101-2021_01_08_425885	900	35	R.	R.	NNP
10_1101-2021_01_08_425885	900	36	Rabadan	Rabadan	NNP
10_1101-2021_01_08_425885	900	37	.	.	.
10_1101-2021_01_08_425885	901	1	Topology	topology	NN
10_1101-2021_01_08_425885	901	2	of	of	IN
10_1101-2021_01_08_425885	901	3	viral	viral	JJ
10_1101-2021_01_08_425885	901	4	evolution	evolution	NN
10_1101-2021_01_08_425885	901	5	.	.	.
10_1101-2021_01_08_425885	902	1	Proceedings	proceeding	NNS
10_1101-2021_01_08_425885	902	2	of	of	IN
10_1101-2021_01_08_425885	902	3	the	the	DT
10_1101-2021_01_08_425885	902	4	National	National	NNP
10_1101-2021_01_08_425885	902	5	Academy	Academy	NNP
10_1101-2021_01_08_425885	902	6	of	of	IN
10_1101-2021_01_08_425885	902	7	Sciences	Sciences	NNPS
10_1101-2021_01_08_425885	902	8	,	,	,
10_1101-2021_01_08_425885	902	9	110(46):18566–18571	110(46):18566–18571	CD
10_1101-2021_01_08_425885	902	10	,	,	,
10_1101-2021_01_08_425885	902	11	2013	2013	CD
10_1101-2021_01_08_425885	902	12	.	.	.
10_1101-2021_01_08_425885	903	1	[	[	-LRB-
10_1101-2021_01_08_425885	903	2	24	24	CD
10_1101-2021_01_08_425885	903	3	]	]	-RRB-
10_1101-2021_01_08_425885	903	4	P.	P.	NNP
10_1101-2021_01_08_425885	903	5	G.	G.	NNP
10_1101-2021_01_08_425885	903	6	Cámara	Cámara	NNP
10_1101-2021_01_08_425885	903	7	,	,	,
10_1101-2021_01_08_425885	903	8	A.	A.	NNP
10_1101-2021_01_08_425885	903	9	J.	J.	NNP
10_1101-2021_01_08_425885	903	10	Levine	Levine	NNP
10_1101-2021_01_08_425885	903	11	,	,	,
10_1101-2021_01_08_425885	903	12	and	and	CC
10_1101-2021_01_08_425885	903	13	R.	R.	NNP
10_1101-2021_01_08_425885	903	14	Rabadán	Rabadán	NNP
10_1101-2021_01_08_425885	903	15	.	.	.
10_1101-2021_01_08_425885	904	1	Inference	inference	NN
10_1101-2021_01_08_425885	904	2	of	of	IN
10_1101-2021_01_08_425885	904	3	ancestral	ancestral	JJ
10_1101-2021_01_08_425885	904	4	recombination	recombination	NN
10_1101-2021_01_08_425885	904	5	graphs	graphs	NN
10_1101-2021_01_08_425885	904	6	through	through	IN
10_1101-2021_01_08_425885	904	7	topological	topological	JJ
10_1101-2021_01_08_425885	904	8	data	datum	NNS
10_1101-2021_01_08_425885	904	9	analysis	analysis	NN
10_1101-2021_01_08_425885	904	10	.	.	.
10_1101-2021_01_08_425885	905	1	PLoS	PLoS	NNP
10_1101-2021_01_08_425885	905	2	Computational	Computational	NNP
10_1101-2021_01_08_425885	905	3	Biology	Biology	NNP
10_1101-2021_01_08_425885	905	4	,	,	,
10_1101-2021_01_08_425885	905	5	12(8):e1005071	12(8):e1005071	CD
10_1101-2021_01_08_425885	905	6	,	,	,
10_1101-2021_01_08_425885	905	7	2016	2016	CD
10_1101-2021_01_08_425885	905	8	.	.	.
10_1101-2021_01_08_425885	906	1	[	[	-LRB-
10_1101-2021_01_08_425885	906	2	25	25	CD
10_1101-2021_01_08_425885	906	3	]	]	-RRB-
10_1101-2021_01_08_425885	906	4	E.	E.	NNP
10_1101-2021_01_08_425885	906	5	Abbott	Abbott	NNP
10_1101-2021_01_08_425885	906	6	.	.	.
10_1101-2021_01_08_425885	907	1	Flatland	flatland	NN
10_1101-2021_01_08_425885	907	2	:	:	:
10_1101-2021_01_08_425885	907	3	A	a	DT
10_1101-2021_01_08_425885	907	4	Romance	Romance	NNP
10_1101-2021_01_08_425885	907	5	of	of	IN
10_1101-2021_01_08_425885	907	6	Many	many	JJ
10_1101-2021_01_08_425885	907	7	Dimensions	dimension	NNS
10_1101-2021_01_08_425885	907	8	.	.	.
10_1101-2021_01_08_425885	908	1	Princeton	Princeton	NNP
10_1101-2021_01_08_425885	908	2	University	University	NNP
10_1101-2021_01_08_425885	908	3	Press	Press	NNP
10_1101-2021_01_08_425885	908	4	,	,	,
10_1101-2021_01_08_425885	908	5	1991	1991	CD
10_1101-2021_01_08_425885	908	6	.	.	.
10_1101-2021_01_08_425885	909	1	[	[	-LRB-
10_1101-2021_01_08_425885	909	2	26	26	CD
10_1101-2021_01_08_425885	909	3	]	]	-RRB-
10_1101-2021_01_08_425885	909	4	M.	M.	NNP
10_1101-2021_01_08_425885	909	5	Belkin	Belkin	NNP
10_1101-2021_01_08_425885	909	6	and	and	CC
10_1101-2021_01_08_425885	909	7	P.	P.	NNP
10_1101-2021_01_08_425885	909	8	Niyogi	Niyogi	NNP
10_1101-2021_01_08_425885	909	9	.	.	.
10_1101-2021_01_08_425885	910	1	Laplacian	laplacian	JJ
10_1101-2021_01_08_425885	910	2	eigenmaps	eigenmap	NNS
10_1101-2021_01_08_425885	910	3	and	and	CC
10_1101-2021_01_08_425885	910	4	spectral	spectral	JJ
10_1101-2021_01_08_425885	910	5	techniques	technique	NNS
10_1101-2021_01_08_425885	910	6	for	for	IN
10_1101-2021_01_08_425885	910	7	embedding	embed	VBG
10_1101-2021_01_08_425885	910	8	and	and	CC
10_1101-2021_01_08_425885	910	9	clustering	clustering	NN
10_1101-2021_01_08_425885	910	10	.	.	.
10_1101-2021_01_08_425885	911	1	Advances	advance	NNS
10_1101-2021_01_08_425885	911	2	in	in	IN
10_1101-2021_01_08_425885	911	3	Neural	Neural	NNP
10_1101-2021_01_08_425885	911	4	Information	Information	NNP
10_1101-2021_01_08_425885	911	5	Processing	Processing	NNP
10_1101-2021_01_08_425885	911	6	Systems	Systems	NNPS
10_1101-2021_01_08_425885	911	7	,	,	,
10_1101-2021_01_08_425885	911	8	14:585–591	14:585–591	CD
10_1101-2021_01_08_425885	911	9	,	,	,
10_1101-2021_01_08_425885	911	10	2001	2001	CD
10_1101-2021_01_08_425885	911	11	.	.	.
10_1101-2021_01_08_425885	912	1	[	[	-LRB-
10_1101-2021_01_08_425885	912	2	27	27	CD
10_1101-2021_01_08_425885	912	3	]	]	-RRB-
10_1101-2021_01_08_425885	912	4	M.	M.	NNP
10_1101-2021_01_08_425885	912	5	Reuter	Reuter	NNP
10_1101-2021_01_08_425885	912	6	,	,	,
10_1101-2021_01_08_425885	912	7	F	F	NNP
10_1101-2021_01_08_425885	912	8	-	-	HYPH
10_1101-2021_01_08_425885	912	9	E.	E.	NNP
10_1101-2021_01_08_425885	912	10	Wolter	Wolter	NNP
10_1101-2021_01_08_425885	912	11	,	,	,
10_1101-2021_01_08_425885	912	12	and	and	CC
10_1101-2021_01_08_425885	912	13	N.	N.	NNP
10_1101-2021_01_08_425885	912	14	Peinecke	Peinecke	NNP
10_1101-2021_01_08_425885	912	15	.	.	.
10_1101-2021_01_08_425885	913	1	Laplace	Laplace	NNP
10_1101-2021_01_08_425885	913	2	–	–	:
10_1101-2021_01_08_425885	913	3	Beltrami	Beltrami	NNP
10_1101-2021_01_08_425885	913	4	spectra	spectra	NN
10_1101-2021_01_08_425885	913	5	as	as	IN
10_1101-2021_01_08_425885	913	6	‘	'	``
10_1101-2021_01_08_425885	913	7	Shape	Shape	NNP
10_1101-2021_01_08_425885	913	8	-	-	HYPH
10_1101-2021_01_08_425885	913	9	DNA	DNA	NNP
10_1101-2021_01_08_425885	913	10	’	'	''
10_1101-2021_01_08_425885	913	11	of	of	IN
10_1101-2021_01_08_425885	913	12	surfaces	surface	NNS
10_1101-2021_01_08_425885	913	13	and	and	CC
10_1101-2021_01_08_425885	913	14	solids	solid	NNS
10_1101-2021_01_08_425885	913	15	.	.	.
10_1101-2021_01_08_425885	914	1	Computer	computer	NN
10_1101-2021_01_08_425885	914	2	-	-	HYPH
10_1101-2021_01_08_425885	914	3	Aided	aid	VBN
10_1101-2021_01_08_425885	914	4	Design	Design	NNP
10_1101-2021_01_08_425885	914	5	,	,	,
10_1101-2021_01_08_425885	914	6	38(4):342–366	38(4):342–366	CD
10_1101-2021_01_08_425885	914	7	,	,	,
10_1101-2021_01_08_425885	914	8	2006	2006	CD
10_1101-2021_01_08_425885	914	9	.	.	.
10_1101-2021_01_08_425885	915	1	[	[	-LRB-
10_1101-2021_01_08_425885	915	2	28	28	CD
10_1101-2021_01_08_425885	915	3	]	]	-RRB-
10_1101-2021_01_08_425885	915	4	M.	M.	NNP
10_1101-2021_01_08_425885	915	5	Belkin	Belkin	NNP
10_1101-2021_01_08_425885	915	6	,	,	,
10_1101-2021_01_08_425885	915	7	J.	J.	NNP
10_1101-2021_01_08_425885	916	1	Sun	Sun	NNP
10_1101-2021_01_08_425885	916	2	,	,	,
10_1101-2021_01_08_425885	916	3	and	and	CC
10_1101-2021_01_08_425885	916	4	Y.	Y.	NNP
10_1101-2021_01_08_425885	916	5	Wang	Wang	NNP
10_1101-2021_01_08_425885	916	6	.	.	.
10_1101-2021_01_08_425885	917	1	Constructing	construct	VBG
10_1101-2021_01_08_425885	917	2	Laplace	Laplace	NNP
10_1101-2021_01_08_425885	917	3	operator	operator	NN
10_1101-2021_01_08_425885	917	4	from	from	IN
10_1101-2021_01_08_425885	917	5	point	point	NN
10_1101-2021_01_08_425885	917	6	clouds	cloud	NNS
10_1101-2021_01_08_425885	917	7	in	in	IN
10_1101-2021_01_08_425885	917	8	Rd	Rd	NNP
10_1101-2021_01_08_425885	917	9	.	.	.
10_1101-2021_01_08_425885	918	1	In	in	IN
10_1101-2021_01_08_425885	918	2	Proceedings	Proceedings	NNP
10_1101-2021_01_08_425885	918	3	of	of	IN
10_1101-2021_01_08_425885	918	4	the	the	DT
10_1101-2021_01_08_425885	918	5	Twentieth	Twentieth	NNP
10_1101-2021_01_08_425885	918	6	Annual	Annual	NNP
10_1101-2021_01_08_425885	918	7	ACM	ACM	NNP
10_1101-2021_01_08_425885	918	8	-	-	HYPH
10_1101-2021_01_08_425885	918	9	SIAM	SIAM	NNP
10_1101-2021_01_08_425885	918	10	Symposium	Symposium	NNP
10_1101-2021_01_08_425885	918	11	on	on	IN
10_1101-2021_01_08_425885	918	12	Discrete	Discrete	NNP
10_1101-2021_01_08_425885	918	13	Algorithms	Algorithms	NNP
10_1101-2021_01_08_425885	918	14	,	,	,
10_1101-2021_01_08_425885	918	15	pages	page	NNS
10_1101-2021_01_08_425885	918	16	1031–1040	1031–1040	CD
10_1101-2021_01_08_425885	918	17	,	,	,
10_1101-2021_01_08_425885	918	18	2009	2009	CD
10_1101-2021_01_08_425885	918	19	.	.	.
10_1101-2021_01_08_425885	919	1	[	[	-LRB-
10_1101-2021_01_08_425885	919	2	29	29	CD
10_1101-2021_01_08_425885	919	3	]	]	-RRB-
10_1101-2021_01_08_425885	919	4	J.	J.	NNP
10_1101-2021_01_08_425885	919	5	Liang	Liang	NNP
10_1101-2021_01_08_425885	919	6	,	,	,
10_1101-2021_01_08_425885	919	7	R.	R.	NNP
10_1101-2021_01_08_425885	919	8	Lai	Lai	NNP
10_1101-2021_01_08_425885	919	9	,	,	,
10_1101-2021_01_08_425885	919	10	T.	T.	NNP
10_1101-2021_01_08_425885	919	11	W.	W.	NNP
10_1101-2021_01_08_425885	919	12	Wong	Wong	NNP
10_1101-2021_01_08_425885	919	13	,	,	,
10_1101-2021_01_08_425885	919	14	and	and	CC
10_1101-2021_01_08_425885	919	15	H.	H.	NNP
10_1101-2021_01_08_425885	919	16	Zhao	Zhao	NNP
10_1101-2021_01_08_425885	919	17	.	.	.
10_1101-2021_01_08_425885	920	1	Geometric	geometric	JJ
10_1101-2021_01_08_425885	920	2	understanding	understanding	NN
10_1101-2021_01_08_425885	920	3	of	of	IN
10_1101-2021_01_08_425885	920	4	point	point	NN
10_1101-2021_01_08_425885	920	5	clouds	cloud	NNS
10_1101-2021_01_08_425885	920	6	using	use	VBG
10_1101-2021_01_08_425885	920	7	Laplace-	Laplace-	NNP
10_1101-2021_01_08_425885	920	8	Beltrami	Beltrami	NNP
10_1101-2021_01_08_425885	920	9	operator	operator	NN
10_1101-2021_01_08_425885	920	10	.	.	.
10_1101-2021_01_08_425885	921	1	In	in	IN
10_1101-2021_01_08_425885	921	2	IEEE	IEEE	NNP
10_1101-2021_01_08_425885	921	3	Conference	Conference	NNP
10_1101-2021_01_08_425885	921	4	on	on	IN
10_1101-2021_01_08_425885	921	5	Computer	Computer	NNP
10_1101-2021_01_08_425885	921	6	Vision	Vision	NNP
10_1101-2021_01_08_425885	921	7	and	and	CC
10_1101-2021_01_08_425885	921	8	Pattern	Pattern	NNP
10_1101-2021_01_08_425885	921	9	Recognition	Recognition	NNP
10_1101-2021_01_08_425885	921	10	,	,	,
10_1101-2021_01_08_425885	921	11	pages	page	VBZ
10_1101-2021_01_08_425885	921	12	214–221	214–221	CD
10_1101-2021_01_08_425885	921	13	,	,	,
10_1101-2021_01_08_425885	921	14	2012	2012	CD
10_1101-2021_01_08_425885	921	15	.	.	.
10_1101-2021_01_08_425885	922	1	[	[	-LRB-
10_1101-2021_01_08_425885	922	2	30	30	CD
10_1101-2021_01_08_425885	922	3	]	]	-RRB-
10_1101-2021_01_08_425885	922	4	N.	N.	NNP
10_1101-2021_01_08_425885	922	5	G.	G.	NNP
10_1101-2021_01_08_425885	922	6	Trillos	Trillos	NNP
10_1101-2021_01_08_425885	922	7	,	,	,
10_1101-2021_01_08_425885	922	8	M.	M.	NNP
10_1101-2021_01_08_425885	922	9	Gerlach	Gerlach	NNP
10_1101-2021_01_08_425885	922	10	,	,	,
10_1101-2021_01_08_425885	922	11	M.	M.	NNP
10_1101-2021_01_08_425885	922	12	Hein	Hein	NNP
10_1101-2021_01_08_425885	922	13	,	,	,
10_1101-2021_01_08_425885	922	14	and	and	CC
10_1101-2021_01_08_425885	922	15	D.	D.	NNP
10_1101-2021_01_08_425885	922	16	Slepčev	Slepčev	NNP
10_1101-2021_01_08_425885	922	17	.	.	.
10_1101-2021_01_08_425885	923	1	Error	error	NN
10_1101-2021_01_08_425885	923	2	estimates	estimate	NNS
10_1101-2021_01_08_425885	923	3	for	for	IN
10_1101-2021_01_08_425885	923	4	spectral	spectral	JJ
10_1101-2021_01_08_425885	923	5	convergence	convergence	NN
10_1101-2021_01_08_425885	923	6	of	of	IN
10_1101-2021_01_08_425885	923	7	the	the	DT
10_1101-2021_01_08_425885	923	8	graph	graph	NN
10_1101-2021_01_08_425885	923	9	Laplacian	Laplacian	NNP
10_1101-2021_01_08_425885	923	10	on	on	IN
10_1101-2021_01_08_425885	923	11	random	random	JJ
10_1101-2021_01_08_425885	923	12	geometric	geometric	JJ
10_1101-2021_01_08_425885	923	13	graphs	graphs	NN
10_1101-2021_01_08_425885	923	14	toward	toward	IN
10_1101-2021_01_08_425885	923	15	the	the	DT
10_1101-2021_01_08_425885	923	16	Laplace	Laplace	NNP
10_1101-2021_01_08_425885	923	17	–	–	:
10_1101-2021_01_08_425885	923	18	Beltrami	Beltrami	NNP
10_1101-2021_01_08_425885	923	19	operator	operator	NN
10_1101-2021_01_08_425885	923	20	.	.	.
10_1101-2021_01_08_425885	924	1	Foundations	foundation	NNS
10_1101-2021_01_08_425885	924	2	of	of	IN
10_1101-2021_01_08_425885	924	3	Computational	Computational	NNP
10_1101-2021_01_08_425885	924	4	Mathematics	Mathematics	NNPS
10_1101-2021_01_08_425885	924	5	,	,	,
10_1101-2021_01_08_425885	924	6	20(4):827–887	20(4):827–887	CD
10_1101-2021_01_08_425885	924	7	,	,	,
10_1101-2021_01_08_425885	924	8	2020	2020	CD
10_1101-2021_01_08_425885	924	9	.	.	.
10_1101-2021_01_08_425885	925	1	[	[	-LRB-
10_1101-2021_01_08_425885	925	2	31	31	CD
10_1101-2021_01_08_425885	925	3	]	]	-RRB-
10_1101-2021_01_08_425885	925	4	H.	H.	NNP
10_1101-2021_01_08_425885	925	5	P.	P.	NNP
10_1101-2021_01_08_425885	925	6	McKean	McKean	NNP
10_1101-2021_01_08_425885	925	7	Jr.	Jr.	NNP
10_1101-2021_01_08_425885	925	8	and	and	CC
10_1101-2021_01_08_425885	925	9	I.	I.	NNP
10_1101-2021_01_08_425885	925	10	M.	M.	NNP
10_1101-2021_01_08_425885	925	11	Singer	Singer	NNP
10_1101-2021_01_08_425885	925	12	.	.	.
10_1101-2021_01_08_425885	926	1	Curvature	curvature	NN
10_1101-2021_01_08_425885	926	2	and	and	CC
10_1101-2021_01_08_425885	926	3	the	the	DT
10_1101-2021_01_08_425885	926	4	eigenvalues	eigenvalue	NNS
10_1101-2021_01_08_425885	926	5	of	of	IN
10_1101-2021_01_08_425885	926	6	the	the	DT
10_1101-2021_01_08_425885	926	7	Laplacian	Laplacian	NNP
10_1101-2021_01_08_425885	926	8	.	.	.
10_1101-2021_01_08_425885	927	1	Journal	Journal	NNP
10_1101-2021_01_08_425885	927	2	of	of	IN
10_1101-2021_01_08_425885	927	3	Differential	Differential	NNP
10_1101-2021_01_08_425885	927	4	Geometry	Geometry	NNP
10_1101-2021_01_08_425885	927	5	,	,	,
10_1101-2021_01_08_425885	927	6	1(1	1(1	NNP
10_1101-2021_01_08_425885	927	7	-	-	HYPH
10_1101-2021_01_08_425885	927	8	2):43–69	2):43–69	NNP
10_1101-2021_01_08_425885	927	9	,	,	,
10_1101-2021_01_08_425885	927	10	1967	1967	CD
10_1101-2021_01_08_425885	927	11	.	.	.
10_1101-2021_01_08_425885	928	1	[	[	-LRB-
10_1101-2021_01_08_425885	928	2	32	32	CD
10_1101-2021_01_08_425885	928	3	]	]	-RRB-
10_1101-2021_01_08_425885	928	4	B.	B.	NNP
10_1101-2021_01_08_425885	928	5	Andrews	Andrews	NNP
10_1101-2021_01_08_425885	928	6	.	.	.
10_1101-2021_01_08_425885	929	1	Lectures	lecture	NNS
10_1101-2021_01_08_425885	929	2	on	on	IN
10_1101-2021_01_08_425885	929	3	Differential	Differential	NNP
10_1101-2021_01_08_425885	929	4	Geometry	Geometry	NNP
10_1101-2021_01_08_425885	929	5	.	.	.
10_1101-2021_01_08_425885	930	1	https://maths-people.anu.edu.au/~andrews/DG	https://maths-people.anu.edu.au/~andrews/DG	NNP
10_1101-2021_01_08_425885	930	2	.	.	.
10_1101-2021_01_08_425885	931	1	Australian	Australian	NNP
10_1101-2021_01_08_425885	931	2	National	National	NNP
10_1101-2021_01_08_425885	931	3	University	University	NNP
10_1101-2021_01_08_425885	931	4	.	.	.
10_1101-2021_01_08_425885	932	1	[	[	-LRB-
10_1101-2021_01_08_425885	932	2	33	33	CD
10_1101-2021_01_08_425885	932	3	]	]	-RRB-
10_1101-2021_01_08_425885	932	4	I.	I.	NNP
10_1101-2021_01_08_425885	932	5	T.	T.	NNP
10_1101-2021_01_08_425885	932	6	Jolliffe	Jolliffe	NNP
10_1101-2021_01_08_425885	932	7	and	and	CC
10_1101-2021_01_08_425885	932	8	J.	J.	NNP
10_1101-2021_01_08_425885	932	9	Cadima	Cadima	NNP
10_1101-2021_01_08_425885	932	10	.	.	.
10_1101-2021_01_08_425885	933	1	Principal	principal	JJ
10_1101-2021_01_08_425885	933	2	component	component	NN
10_1101-2021_01_08_425885	933	3	analysis	analysis	NN
10_1101-2021_01_08_425885	933	4	:	:	:
10_1101-2021_01_08_425885	933	5	a	a	DT
10_1101-2021_01_08_425885	933	6	review	review	NN
10_1101-2021_01_08_425885	933	7	and	and	CC
10_1101-2021_01_08_425885	933	8	recent	recent	JJ
10_1101-2021_01_08_425885	933	9	developments	development	NNS
10_1101-2021_01_08_425885	933	10	.	.	.
10_1101-2021_01_08_425885	934	1	Philosophical	philosophical	JJ
10_1101-2021_01_08_425885	934	2	Transactions	Transactions	NNPS
10_1101-2021_01_08_425885	934	3	of	of	IN
10_1101-2021_01_08_425885	934	4	the	the	DT
10_1101-2021_01_08_425885	934	5	Royal	Royal	NNP
10_1101-2021_01_08_425885	934	6	Society	Society	NNP
10_1101-2021_01_08_425885	934	7	A	A	NNP
10_1101-2021_01_08_425885	934	8	:	:	:
10_1101-2021_01_08_425885	934	9	Mathematical	mathematical	JJ
10_1101-2021_01_08_425885	934	10	,	,	,
10_1101-2021_01_08_425885	934	11	Physical	Physical	NNP
10_1101-2021_01_08_425885	934	12	and	and	CC
10_1101-2021_01_08_425885	934	13	Engineering	Engineering	NNP
10_1101-2021_01_08_425885	934	14	Sciences	Sciences	NNPS
10_1101-2021_01_08_425885	934	15	,	,	,
10_1101-2021_01_08_425885	934	16	374(2065):20150202	374(2065):20150202	CD
10_1101-2021_01_08_425885	934	17	,	,	,
10_1101-2021_01_08_425885	934	18	2016	2016	CD
10_1101-2021_01_08_425885	934	19	.	.	.
10_1101-2021_01_08_425885	935	1	[	[	-LRB-
10_1101-2021_01_08_425885	935	2	34	34	CD
10_1101-2021_01_08_425885	935	3	]	]	-RRB-
10_1101-2021_01_08_425885	935	4	H.	H.	NNP
10_1101-2021_01_08_425885	935	5	Federer	Federer	NNP
10_1101-2021_01_08_425885	935	6	.	.	.
10_1101-2021_01_08_425885	936	1	Curvature	curvature	JJ
10_1101-2021_01_08_425885	936	2	measures	measure	NNS
10_1101-2021_01_08_425885	936	3	.	.	.
10_1101-2021_01_08_425885	937	1	Transactions	transaction	NNS
10_1101-2021_01_08_425885	937	2	of	of	IN
10_1101-2021_01_08_425885	937	3	the	the	DT
10_1101-2021_01_08_425885	937	4	American	American	NNP
10_1101-2021_01_08_425885	937	5	Mathematical	Mathematical	NNP
10_1101-2021_01_08_425885	937	6	Society	Society	NNP
10_1101-2021_01_08_425885	937	7	,	,	,
10_1101-2021_01_08_425885	937	8	93(3):418–418	93(3):418–418	CD
10_1101-2021_01_08_425885	937	9	,	,	,
10_1101-2021_01_08_425885	937	10	1959	1959	CD
10_1101-2021_01_08_425885	937	11	.	.	.
10_1101-2021_01_08_425885	938	1	[	[	-LRB-
10_1101-2021_01_08_425885	938	2	35	35	CD
10_1101-2021_01_08_425885	938	3	]	]	-RRB-
10_1101-2021_01_08_425885	938	4	P.	P.	NNP
10_1101-2021_01_08_425885	938	5	Niyogi	Niyogi	NNP
10_1101-2021_01_08_425885	938	6	,	,	,
10_1101-2021_01_08_425885	938	7	S.	S.	NNP
10_1101-2021_01_08_425885	938	8	Smale	Smale	NNP
10_1101-2021_01_08_425885	938	9	,	,	,
10_1101-2021_01_08_425885	938	10	and	and	CC
10_1101-2021_01_08_425885	938	11	S.	S.	NNP
10_1101-2021_01_08_425885	938	12	Weinberger	Weinberger	NNP
10_1101-2021_01_08_425885	938	13	.	.	.
10_1101-2021_01_08_425885	939	1	Finding	find	VBG
10_1101-2021_01_08_425885	939	2	the	the	DT
10_1101-2021_01_08_425885	939	3	homology	homology	NN
10_1101-2021_01_08_425885	939	4	of	of	IN
10_1101-2021_01_08_425885	939	5	submanifolds	submanifold	NNS
10_1101-2021_01_08_425885	939	6	with	with	IN
10_1101-2021_01_08_425885	939	7	high	high	JJ
10_1101-2021_01_08_425885	939	8	confidence	confidence	NN
10_1101-2021_01_08_425885	939	9	from	from	IN
10_1101-2021_01_08_425885	939	10	random	random	JJ
10_1101-2021_01_08_425885	939	11	samples	sample	NNS
10_1101-2021_01_08_425885	939	12	.	.	.
10_1101-2021_01_08_425885	940	1	Discrete	Discrete	NNP
10_1101-2021_01_08_425885	940	2	&	&	CC
10_1101-2021_01_08_425885	940	3	Computational	Computational	NNP
10_1101-2021_01_08_425885	940	4	Geometry	Geometry	NNP
10_1101-2021_01_08_425885	940	5	,	,	,
10_1101-2021_01_08_425885	940	6	39(1	39(1	CD
10_1101-2021_01_08_425885	940	7	-	-	HYPH
10_1101-2021_01_08_425885	940	8	3):419–441	3):419–441	CD
10_1101-2021_01_08_425885	940	9	,	,	,
10_1101-2021_01_08_425885	940	10	2008	2008	CD
10_1101-2021_01_08_425885	940	11	.	.	.
10_1101-2021_01_08_425885	941	1	54	54	CD
10_1101-2021_01_08_425885	941	2	.CC	.CC	:
10_1101-2021_01_08_425885	941	3	-	-	HYPH
10_1101-2021_01_08_425885	941	4	BY	by	IN
10_1101-2021_01_08_425885	941	5	-	-	HYPH
10_1101-2021_01_08_425885	941	6	NC	NC	NNP
10_1101-2021_01_08_425885	941	7	-	-	HYPH
10_1101-2021_01_08_425885	941	8	ND	ND	NNP
10_1101-2021_01_08_425885	941	9	4.0	4.0	CD
10_1101-2021_01_08_425885	941	10	International	International	NNP
10_1101-2021_01_08_425885	941	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	941	12	under	under	IN
10_1101-2021_01_08_425885	941	13	a	a	DT
10_1101-2021_01_08_425885	941	14	(	(	-LRB-
10_1101-2021_01_08_425885	941	15	which	which	WDT
10_1101-2021_01_08_425885	941	16	was	be	VBD
10_1101-2021_01_08_425885	941	17	not	not	RB
10_1101-2021_01_08_425885	941	18	certified	certify	VBN
10_1101-2021_01_08_425885	941	19	by	by	IN
10_1101-2021_01_08_425885	941	20	peer	peer	NN
10_1101-2021_01_08_425885	941	21	review	review	NN
10_1101-2021_01_08_425885	941	22	)	)	-RRB-
10_1101-2021_01_08_425885	941	23	is	be	VBZ
10_1101-2021_01_08_425885	941	24	the	the	DT
10_1101-2021_01_08_425885	941	25	author	author	NN
10_1101-2021_01_08_425885	941	26	/	/	SYM
10_1101-2021_01_08_425885	941	27	funder	funder	NN
10_1101-2021_01_08_425885	941	28	,	,	,
10_1101-2021_01_08_425885	941	29	who	who	WP
10_1101-2021_01_08_425885	941	30	has	have	VBZ
10_1101-2021_01_08_425885	941	31	granted	grant	VBN
10_1101-2021_01_08_425885	941	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	941	33	a	a	DT
10_1101-2021_01_08_425885	941	34	license	license	NN
10_1101-2021_01_08_425885	941	35	to	to	TO
10_1101-2021_01_08_425885	941	36	display	display	VB
10_1101-2021_01_08_425885	941	37	the	the	DT
10_1101-2021_01_08_425885	941	38	preprint	preprint	NN
10_1101-2021_01_08_425885	941	39	in	in	IN
10_1101-2021_01_08_425885	941	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	941	41	.	.	.
10_1101-2021_01_08_425885	942	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	942	2	is	be	VBZ
10_1101-2021_01_08_425885	942	3	made	make	VBN
10_1101-2021_01_08_425885	942	4	The	the	DT
10_1101-2021_01_08_425885	942	5	copyright	copyright	NN
10_1101-2021_01_08_425885	942	6	holder	holder	NN
10_1101-2021_01_08_425885	942	7	for	for	IN
10_1101-2021_01_08_425885	942	8	this	this	DT
10_1101-2021_01_08_425885	942	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	942	10	version	version	NN
10_1101-2021_01_08_425885	942	11	posted	post	VBD
10_1101-2021_01_08_425885	942	12	January	January	NNP
10_1101-2021_01_08_425885	942	13	8	8	CD
10_1101-2021_01_08_425885	942	14	,	,	,
10_1101-2021_01_08_425885	942	15	2021	2021	CD
10_1101-2021_01_08_425885	942	16	.	.	.
10_1101-2021_01_08_425885	942	17	;	;	:
10_1101-2021_01_08_425885	942	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	942	19	:	:	:
10_1101-2021_01_08_425885	942	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	942	21	preprint	preprint	NN
10_1101-2021_01_08_425885	942	22	https://maths-people.anu.edu.au/~andrews/DG	https://maths-people.anu.edu.au/~andrews/dg	NN
10_1101-2021_01_08_425885	942	23	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	942	24	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	CD
10_1101-2021_01_08_425885	942	25	[	[	-LRB-
10_1101-2021_01_08_425885	942	26	36	36	CD
10_1101-2021_01_08_425885	942	27	]	]	-RRB-
10_1101-2021_01_08_425885	942	28	U.	U.	NNP
10_1101-2021_01_08_425885	942	29	Ozertem	Ozertem	NNP
10_1101-2021_01_08_425885	942	30	and	and	CC
10_1101-2021_01_08_425885	942	31	D.	D.	NNP
10_1101-2021_01_08_425885	942	32	Erdogmus	Erdogmus	NNP
10_1101-2021_01_08_425885	942	33	.	.	.
10_1101-2021_01_08_425885	943	1	Locally	locally	RB
10_1101-2021_01_08_425885	943	2	defined	define	VBN
10_1101-2021_01_08_425885	943	3	principal	principal	JJ
10_1101-2021_01_08_425885	943	4	curves	curve	NNS
10_1101-2021_01_08_425885	943	5	and	and	CC
10_1101-2021_01_08_425885	943	6	surfaces	surface	NNS
10_1101-2021_01_08_425885	943	7	.	.	.
10_1101-2021_01_08_425885	944	1	Journal	Journal	NNP
10_1101-2021_01_08_425885	944	2	of	of	IN
10_1101-2021_01_08_425885	944	3	Machine	Machine	NNP
10_1101-2021_01_08_425885	944	4	Learning	Learning	NNP
10_1101-2021_01_08_425885	944	5	Research	Research	NNP
10_1101-2021_01_08_425885	944	6	,	,	,
10_1101-2021_01_08_425885	944	7	12:1249–1286	12:1249–1286	CD
10_1101-2021_01_08_425885	944	8	,	,	,
10_1101-2021_01_08_425885	944	9	2011	2011	CD
10_1101-2021_01_08_425885	944	10	.	.	.
10_1101-2021_01_08_425885	945	1	[	[	-LRB-
10_1101-2021_01_08_425885	945	2	37	37	CD
10_1101-2021_01_08_425885	945	3	]	]	-RRB-
10_1101-2021_01_08_425885	945	4	C.	C.	NNP
10_1101-2021_01_08_425885	945	5	R.	R.	NNP
10_1101-2021_01_08_425885	945	6	Genovese	Genovese	NNP
10_1101-2021_01_08_425885	945	7	,	,	,
10_1101-2021_01_08_425885	945	8	M.	M.	NNP
10_1101-2021_01_08_425885	945	9	Perone	Perone	NNP
10_1101-2021_01_08_425885	945	10	-	-	HYPH
10_1101-2021_01_08_425885	945	11	Pacifico	Pacifico	NNP
10_1101-2021_01_08_425885	945	12	,	,	,
10_1101-2021_01_08_425885	945	13	I.	I.	NNP
10_1101-2021_01_08_425885	945	14	Verdinelli	Verdinelli	NNP
10_1101-2021_01_08_425885	945	15	,	,	,
10_1101-2021_01_08_425885	945	16	and	and	CC
10_1101-2021_01_08_425885	945	17	L.	L.	NNP
10_1101-2021_01_08_425885	945	18	Wasserman	Wasserman	NNP
10_1101-2021_01_08_425885	945	19	.	.	.
10_1101-2021_01_08_425885	946	1	Nonparametric	nonparametric	JJ
10_1101-2021_01_08_425885	946	2	ridge	ridge	NN
10_1101-2021_01_08_425885	946	3	estimation	estimation	NN
10_1101-2021_01_08_425885	946	4	.	.	.
10_1101-2021_01_08_425885	947	1	The	the	DT
10_1101-2021_01_08_425885	947	2	Annals	Annals	NNPS
10_1101-2021_01_08_425885	947	3	of	of	IN
10_1101-2021_01_08_425885	947	4	Statistics	Statistics	NNPS
10_1101-2021_01_08_425885	947	5	,	,	,
10_1101-2021_01_08_425885	947	6	42(4):1511–1545	42(4):1511–1545	CD
10_1101-2021_01_08_425885	947	7	,	,	,
10_1101-2021_01_08_425885	947	8	2014	2014	CD
10_1101-2021_01_08_425885	947	9	.	.	.
10_1101-2021_01_08_425885	948	1	[	[	-LRB-
10_1101-2021_01_08_425885	948	2	38	38	CD
10_1101-2021_01_08_425885	948	3	]	]	-RRB-
10_1101-2021_01_08_425885	948	4	R.	R.	NNP
10_1101-2021_01_08_425885	948	5	W.	W.	NNP
10_1101-2021_01_08_425885	948	6	Buccigrossi	Buccigrossi	NNP
10_1101-2021_01_08_425885	948	7	and	and	CC
10_1101-2021_01_08_425885	948	8	E.	E.	NNP
10_1101-2021_01_08_425885	948	9	P.	P.	NNP
10_1101-2021_01_08_425885	948	10	Simoncelli	Simoncelli	NNP
10_1101-2021_01_08_425885	948	11	.	.	.
10_1101-2021_01_08_425885	949	1	Image	image	NN
10_1101-2021_01_08_425885	949	2	compression	compression	NN
10_1101-2021_01_08_425885	949	3	via	via	IN
10_1101-2021_01_08_425885	949	4	joint	joint	JJ
10_1101-2021_01_08_425885	949	5	statistical	statistical	JJ
10_1101-2021_01_08_425885	949	6	characterization	characterization	NN
10_1101-2021_01_08_425885	949	7	in	in	IN
10_1101-2021_01_08_425885	949	8	the	the	DT
10_1101-2021_01_08_425885	949	9	wavelet	wavelet	NN
10_1101-2021_01_08_425885	949	10	domain	domain	NN
10_1101-2021_01_08_425885	949	11	.	.	.
10_1101-2021_01_08_425885	950	1	IEEE	IEEE	NNP
10_1101-2021_01_08_425885	950	2	Transactions	transaction	NNS
10_1101-2021_01_08_425885	950	3	on	on	IN
10_1101-2021_01_08_425885	950	4	Image	Image	NNP
10_1101-2021_01_08_425885	950	5	Processing	Processing	NNP
10_1101-2021_01_08_425885	950	6	,	,	,
10_1101-2021_01_08_425885	950	7	8(12):1688–1701	8(12):1688–1701	CD
10_1101-2021_01_08_425885	950	8	,	,	,
10_1101-2021_01_08_425885	950	9	1999	1999	CD
10_1101-2021_01_08_425885	950	10	.	.	.
10_1101-2021_01_08_425885	951	1	[	[	-LRB-
10_1101-2021_01_08_425885	951	2	39	39	CD
10_1101-2021_01_08_425885	951	3	]	]	-RRB-
10_1101-2021_01_08_425885	951	4	J.	J.	NNP
10_1101-2021_01_08_425885	951	5	Malik	Malik	NNP
10_1101-2021_01_08_425885	951	6	,	,	,
10_1101-2021_01_08_425885	951	7	S.	S.	NNP
10_1101-2021_01_08_425885	951	8	Belongie	Belongie	NNP
10_1101-2021_01_08_425885	951	9	,	,	,
10_1101-2021_01_08_425885	951	10	T.	T.	NNP
10_1101-2021_01_08_425885	951	11	Leung	Leung	NNP
10_1101-2021_01_08_425885	951	12	,	,	,
10_1101-2021_01_08_425885	951	13	and	and	CC
10_1101-2021_01_08_425885	951	14	J.	J.	NNP
10_1101-2021_01_08_425885	951	15	Shi	Shi	NNP
10_1101-2021_01_08_425885	951	16	.	.	.
10_1101-2021_01_08_425885	952	1	Contour	contour	NN
10_1101-2021_01_08_425885	952	2	and	and	CC
10_1101-2021_01_08_425885	952	3	texture	texture	VB
10_1101-2021_01_08_425885	952	4	analysis	analysis	NN
10_1101-2021_01_08_425885	952	5	for	for	IN
10_1101-2021_01_08_425885	952	6	image	image	NN
10_1101-2021_01_08_425885	952	7	segmentation	segmentation	NN
10_1101-2021_01_08_425885	952	8	.	.	.
10_1101-2021_01_08_425885	953	1	International	International	NNP
10_1101-2021_01_08_425885	953	2	Journal	Journal	NNP
10_1101-2021_01_08_425885	953	3	of	of	IN
10_1101-2021_01_08_425885	953	4	Computer	Computer	NNP
10_1101-2021_01_08_425885	953	5	Vision	Vision	NNP
10_1101-2021_01_08_425885	953	6	,	,	,
10_1101-2021_01_08_425885	953	7	43(1):7–27	43(1):7–27	CD
10_1101-2021_01_08_425885	953	8	,	,	,
10_1101-2021_01_08_425885	953	9	2001	2001	CD
10_1101-2021_01_08_425885	953	10	.	.	.
10_1101-2021_01_08_425885	954	1	[	[	-LRB-
10_1101-2021_01_08_425885	954	2	40	40	CD
10_1101-2021_01_08_425885	954	3	]	]	-RRB-
10_1101-2021_01_08_425885	954	4	A.	a.	NN
10_1101-2021_01_08_425885	955	1	B.	B.	NNP
10_1101-2021_01_08_425885	955	2	Lee	Lee	NNP
10_1101-2021_01_08_425885	955	3	,	,	,
10_1101-2021_01_08_425885	955	4	K.	K.	NNP
10_1101-2021_01_08_425885	955	5	S.	S.	NNP
10_1101-2021_01_08_425885	955	6	Pedersen	Pedersen	NNP
10_1101-2021_01_08_425885	955	7	,	,	,
10_1101-2021_01_08_425885	955	8	and	and	CC
10_1101-2021_01_08_425885	955	9	D.	D.	NNP
10_1101-2021_01_08_425885	955	10	Mumford	Mumford	NNP
10_1101-2021_01_08_425885	955	11	.	.	.
10_1101-2021_01_08_425885	956	1	The	the	DT
10_1101-2021_01_08_425885	956	2	nonlinear	nonlinear	JJ
10_1101-2021_01_08_425885	956	3	statistics	statistic	NNS
10_1101-2021_01_08_425885	956	4	of	of	IN
10_1101-2021_01_08_425885	956	5	high	high	JJ
10_1101-2021_01_08_425885	956	6	-	-	HYPH
10_1101-2021_01_08_425885	956	7	contrast	contrast	NN
10_1101-2021_01_08_425885	956	8	patches	patch	NNS
10_1101-2021_01_08_425885	956	9	in	in	IN
10_1101-2021_01_08_425885	956	10	natural	natural	JJ
10_1101-2021_01_08_425885	956	11	images	image	NNS
10_1101-2021_01_08_425885	956	12	.	.	.
10_1101-2021_01_08_425885	957	1	International	International	NNP
10_1101-2021_01_08_425885	957	2	Journal	Journal	NNP
10_1101-2021_01_08_425885	957	3	of	of	IN
10_1101-2021_01_08_425885	957	4	Computer	Computer	NNP
10_1101-2021_01_08_425885	957	5	Vision	Vision	NNP
10_1101-2021_01_08_425885	957	6	,	,	,
10_1101-2021_01_08_425885	957	7	54(1	54(1	CD
10_1101-2021_01_08_425885	957	8	-	-	HYPH
10_1101-2021_01_08_425885	957	9	2):83–103	2):83–103	CD
10_1101-2021_01_08_425885	957	10	,	,	,
10_1101-2021_01_08_425885	957	11	2003	2003	CD
10_1101-2021_01_08_425885	957	12	.	.	.
10_1101-2021_01_08_425885	958	1	[	[	-LRB-
10_1101-2021_01_08_425885	958	2	41	41	CD
10_1101-2021_01_08_425885	958	3	]	]	-RRB-
10_1101-2021_01_08_425885	958	4	J.	J.	NNP
10_1101-2021_01_08_425885	958	5	H.	H.	NNP
10_1101-2021_01_08_425885	958	6	van	van	NNP
10_1101-2021_01_08_425885	958	7	Hateren	Hateren	NNP
10_1101-2021_01_08_425885	958	8	and	and	CC
10_1101-2021_01_08_425885	958	9	A.	A.	NNP
10_1101-2021_01_08_425885	958	10	van	van	NNP
10_1101-2021_01_08_425885	958	11	der	der	NNP
10_1101-2021_01_08_425885	958	12	Schaaf	Schaaf	NNP
10_1101-2021_01_08_425885	958	13	.	.	.
10_1101-2021_01_08_425885	959	1	Independent	independent	JJ
10_1101-2021_01_08_425885	959	2	component	component	NN
10_1101-2021_01_08_425885	959	3	filters	filter	NNS
10_1101-2021_01_08_425885	959	4	of	of	IN
10_1101-2021_01_08_425885	959	5	natural	natural	JJ
10_1101-2021_01_08_425885	959	6	images	image	NNS
10_1101-2021_01_08_425885	959	7	compared	compare	VBN
10_1101-2021_01_08_425885	959	8	with	with	IN
10_1101-2021_01_08_425885	959	9	simple	simple	JJ
10_1101-2021_01_08_425885	959	10	cells	cell	NNS
10_1101-2021_01_08_425885	959	11	in	in	IN
10_1101-2021_01_08_425885	959	12	primary	primary	JJ
10_1101-2021_01_08_425885	959	13	visual	visual	JJ
10_1101-2021_01_08_425885	959	14	cortex	cortex	NN
10_1101-2021_01_08_425885	959	15	.	.	.
10_1101-2021_01_08_425885	960	1	Proceedings	proceeding	NNS
10_1101-2021_01_08_425885	960	2	:	:	:
10_1101-2021_01_08_425885	960	3	Biological	Biological	NNP
10_1101-2021_01_08_425885	960	4	Sciences	Sciences	NNPS
10_1101-2021_01_08_425885	960	5	,	,	,
10_1101-2021_01_08_425885	960	6	265(1394):359–366	265(1394):359–366	CD
10_1101-2021_01_08_425885	960	7	,	,	,
10_1101-2021_01_08_425885	960	8	1998	1998	CD
10_1101-2021_01_08_425885	960	9	.	.	.
10_1101-2021_01_08_425885	961	1	[	[	-LRB-
10_1101-2021_01_08_425885	961	2	42	42	CD
10_1101-2021_01_08_425885	961	3	]	]	-RRB-
10_1101-2021_01_08_425885	961	4	10x	10x	NNPS
10_1101-2021_01_08_425885	961	5	Genomics	Genomics	NNP
10_1101-2021_01_08_425885	961	6	.	.	.
10_1101-2021_01_08_425885	962	1	PBMCs	pbmc	NNS
10_1101-2021_01_08_425885	962	2	from	from	IN
10_1101-2021_01_08_425885	962	3	a	a	DT
10_1101-2021_01_08_425885	962	4	Healthy	healthy	JJ
10_1101-2021_01_08_425885	962	5	Donor	donor	NN
10_1101-2021_01_08_425885	962	6	:	:	:
10_1101-2021_01_08_425885	962	7	Whole	Whole	NNP
10_1101-2021_01_08_425885	962	8	Transcriptome	Transcriptome	NNP
10_1101-2021_01_08_425885	962	9	Analysis	Analysis	NNP
10_1101-2021_01_08_425885	962	10	.	.	.
10_1101-2021_01_08_425885	963	1	https://support	https://support	UH
10_1101-2021_01_08_425885	963	2	.	.	.
10_1101-2021_01_08_425885	964	1	10xgenomics.com/single-cell-gene-expression/datasets/4.0.0/Parent_NGSC3_DI_PBMC	10xgenomics.com/single-cell-gene-expression/datasets/4.0.0/parent_ngsc3_di_pbmc	CD
10_1101-2021_01_08_425885	964	2	,	,	,
10_1101-2021_01_08_425885	964	3	2020	2020	CD
10_1101-2021_01_08_425885	964	4	.	.	.
10_1101-2021_01_08_425885	965	1	[	[	-LRB-
10_1101-2021_01_08_425885	965	2	43	43	CD
10_1101-2021_01_08_425885	965	3	]	]	-RRB-
10_1101-2021_01_08_425885	965	4	B.	B.	NNP
10_1101-2021_01_08_425885	965	5	Pijuan	Pijuan	NNP
10_1101-2021_01_08_425885	965	6	-	-	HYPH
10_1101-2021_01_08_425885	965	7	Sala	Sala	NNP
10_1101-2021_01_08_425885	965	8	,	,	,
10_1101-2021_01_08_425885	965	9	J.	J.	NNP
10_1101-2021_01_08_425885	966	1	A.	A.	NNP
10_1101-2021_01_08_425885	966	2	Griffiths	Griffiths	NNP
10_1101-2021_01_08_425885	966	3	,	,	,
10_1101-2021_01_08_425885	966	4	C.	C.	NNP
10_1101-2021_01_08_425885	966	5	Guibentif	Guibentif	NNP
10_1101-2021_01_08_425885	966	6	,	,	,
10_1101-2021_01_08_425885	966	7	T.	T.	NNP
10_1101-2021_01_08_425885	966	8	W.	W.	NNP
10_1101-2021_01_08_425885	966	9	Hiscock	Hiscock	NNP
10_1101-2021_01_08_425885	966	10	,	,	,
10_1101-2021_01_08_425885	966	11	W.	W.	NNP
10_1101-2021_01_08_425885	966	12	Jawaid	Jawaid	NNP
10_1101-2021_01_08_425885	966	13	,	,	,
10_1101-2021_01_08_425885	966	14	F.	F.	NNP
10_1101-2021_01_08_425885	966	15	J.	J.	NNP
10_1101-2021_01_08_425885	966	16	Calero	Calero	NNP
10_1101-2021_01_08_425885	966	17	-	-	HYPH
10_1101-2021_01_08_425885	966	18	Nieto	Nieto	NNP
10_1101-2021_01_08_425885	966	19	,	,	,
10_1101-2021_01_08_425885	966	20	C.	C.	NNP
10_1101-2021_01_08_425885	966	21	Mulas	Mulas	NNP
10_1101-2021_01_08_425885	966	22	,	,	,
10_1101-2021_01_08_425885	966	23	X.	X.	NNP
10_1101-2021_01_08_425885	966	24	Ibarra	Ibarra	NNP
10_1101-2021_01_08_425885	966	25	-	-	HYPH
10_1101-2021_01_08_425885	966	26	Soria	Soria	NNP
10_1101-2021_01_08_425885	966	27	,	,	,
10_1101-2021_01_08_425885	966	28	R.	R.	NNP
10_1101-2021_01_08_425885	966	29	C.	C.	NNP
10_1101-2021_01_08_425885	966	30	V.	V.	NNP
10_1101-2021_01_08_425885	966	31	Tyser	Tyser	NNP
10_1101-2021_01_08_425885	966	32	,	,	,
10_1101-2021_01_08_425885	966	33	D.	D.	NNP
10_1101-2021_01_08_425885	966	34	L.	L.	NNP
10_1101-2021_01_08_425885	966	35	L.	L.	NNP
10_1101-2021_01_08_425885	966	36	Ho	Ho	NNP
10_1101-2021_01_08_425885	966	37	,	,	,
10_1101-2021_01_08_425885	966	38	W.	W.	NNP
10_1101-2021_01_08_425885	966	39	Reik	Reik	NNP
10_1101-2021_01_08_425885	966	40	,	,	,
10_1101-2021_01_08_425885	966	41	S.	S.	NNP
10_1101-2021_01_08_425885	966	42	Srinivas	Srinivas	NNP
10_1101-2021_01_08_425885	966	43	,	,	,
10_1101-2021_01_08_425885	966	44	B.	B.	NNP
10_1101-2021_01_08_425885	966	45	D.	D.	NNP
10_1101-2021_01_08_425885	966	46	Simons	Simons	NNP
10_1101-2021_01_08_425885	966	47	,	,	,
10_1101-2021_01_08_425885	966	48	J.	J.	NNP
10_1101-2021_01_08_425885	966	49	Nichols	Nichols	NNP
10_1101-2021_01_08_425885	966	50	,	,	,
10_1101-2021_01_08_425885	966	51	J.	J.	NNP
10_1101-2021_01_08_425885	966	52	C.	C.	NNP
10_1101-2021_01_08_425885	966	53	Marioni	Marioni	NNP
10_1101-2021_01_08_425885	966	54	,	,	,
10_1101-2021_01_08_425885	966	55	and	and	CC
10_1101-2021_01_08_425885	966	56	B.	B.	NNP
10_1101-2021_01_08_425885	966	57	Göttgens	Göttgens	NNPS
10_1101-2021_01_08_425885	966	58	.	.	.
10_1101-2021_01_08_425885	967	1	A	a	DT
10_1101-2021_01_08_425885	967	2	single	single	JJ
10_1101-2021_01_08_425885	967	3	-	-	HYPH
10_1101-2021_01_08_425885	967	4	cell	cell	NN
10_1101-2021_01_08_425885	967	5	molecular	molecular	JJ
10_1101-2021_01_08_425885	967	6	map	map	NN
10_1101-2021_01_08_425885	967	7	of	of	IN
10_1101-2021_01_08_425885	967	8	mouse	mouse	NN
10_1101-2021_01_08_425885	967	9	gastrulation	gastrulation	NN
10_1101-2021_01_08_425885	967	10	and	and	CC
10_1101-2021_01_08_425885	967	11	early	early	JJ
10_1101-2021_01_08_425885	967	12	organogenesis	organogenesis	NN
10_1101-2021_01_08_425885	967	13	.	.	.
10_1101-2021_01_08_425885	968	1	Nature	nature	NN
10_1101-2021_01_08_425885	968	2	,	,	,
10_1101-2021_01_08_425885	968	3	566(7745):490–495	566(7745):490–495	NNP
10_1101-2021_01_08_425885	968	4	,	,	,
10_1101-2021_01_08_425885	968	5	2019	2019	CD
10_1101-2021_01_08_425885	968	6	.	.	.
10_1101-2021_01_08_425885	969	1	[	[	-LRB-
10_1101-2021_01_08_425885	969	2	44	44	CD
10_1101-2021_01_08_425885	969	3	]	]	-RRB-
10_1101-2021_01_08_425885	969	4	10x	10x	NNPS
10_1101-2021_01_08_425885	969	5	Genomics	Genomics	NNP
10_1101-2021_01_08_425885	969	6	.	.	.
10_1101-2021_01_08_425885	970	1	1.3	1.3	CD
10_1101-2021_01_08_425885	970	2	Million	Million	NNP
10_1101-2021_01_08_425885	970	3	Brain	Brain	NNP
10_1101-2021_01_08_425885	970	4	Cells	cell	NNS
10_1101-2021_01_08_425885	970	5	from	from	IN
10_1101-2021_01_08_425885	970	6	E18	E18	NNP
10_1101-2021_01_08_425885	970	7	Mice	mouse	NNS
10_1101-2021_01_08_425885	970	8	.	.	.
10_1101-2021_01_08_425885	971	1	https://support.10xgenomics.com/	https://support.10xgenomics.com/	NNP
10_1101-2021_01_08_425885	971	2	single	single	JJ
10_1101-2021_01_08_425885	971	3	-	-	HYPH
10_1101-2021_01_08_425885	971	4	cell	cell	NN
10_1101-2021_01_08_425885	971	5	-	-	HYPH
10_1101-2021_01_08_425885	971	6	gene	gene	NN
10_1101-2021_01_08_425885	971	7	-	-	HYPH
10_1101-2021_01_08_425885	971	8	expression	expression	NN
10_1101-2021_01_08_425885	971	9	/	/	SYM
10_1101-2021_01_08_425885	971	10	datasets/1.3.0/1M_neurons	datasets/1.3.0/1m_neuron	NNS
10_1101-2021_01_08_425885	971	11	,	,	,
10_1101-2021_01_08_425885	971	12	2017	2017	CD
10_1101-2021_01_08_425885	971	13	.	.	.
10_1101-2021_01_08_425885	972	1	[	[	-LRB-
10_1101-2021_01_08_425885	972	2	45	45	CD
10_1101-2021_01_08_425885	972	3	]	]	-RRB-
10_1101-2021_01_08_425885	972	4	D.	D.	NNP
10_1101-2021_01_08_425885	972	5	van	van	NNP
10_1101-2021_01_08_425885	972	6	Dijk	Dijk	NNP
10_1101-2021_01_08_425885	972	7	,	,	,
10_1101-2021_01_08_425885	972	8	R.	R.	NNP
10_1101-2021_01_08_425885	972	9	Sharma	Sharma	NNP
10_1101-2021_01_08_425885	972	10	,	,	,
10_1101-2021_01_08_425885	972	11	J.	J.	NNP
10_1101-2021_01_08_425885	972	12	Nainys	Nainys	NNP
10_1101-2021_01_08_425885	972	13	,	,	,
10_1101-2021_01_08_425885	972	14	K.	K.	NNP
10_1101-2021_01_08_425885	972	15	Yim	Yim	NNP
10_1101-2021_01_08_425885	972	16	,	,	,
10_1101-2021_01_08_425885	972	17	P.	P.	NNP
10_1101-2021_01_08_425885	972	18	Kathail	Kathail	NNP
10_1101-2021_01_08_425885	972	19	,	,	,
10_1101-2021_01_08_425885	972	20	A.	A.	NNP
10_1101-2021_01_08_425885	972	21	J.	J.	NNP
10_1101-2021_01_08_425885	972	22	Carr	Carr	NNP
10_1101-2021_01_08_425885	972	23	,	,	,
10_1101-2021_01_08_425885	972	24	C.	C.	NNP
10_1101-2021_01_08_425885	972	25	Burdziak	Burdziak	NNP
10_1101-2021_01_08_425885	972	26	,	,	,
10_1101-2021_01_08_425885	972	27	K.	K.	NNP
10_1101-2021_01_08_425885	972	28	R.	R.	NNP
10_1101-2021_01_08_425885	972	29	Moon	Moon	NNP
10_1101-2021_01_08_425885	972	30	,	,	,
10_1101-2021_01_08_425885	972	31	C.	C.	NNP
10_1101-2021_01_08_425885	972	32	L.	L.	NNP
10_1101-2021_01_08_425885	972	33	Chaffer	Chaffer	NNP
10_1101-2021_01_08_425885	972	34	,	,	,
10_1101-2021_01_08_425885	972	35	D.	D.	NNP
10_1101-2021_01_08_425885	972	36	Pattabiraman	Pattabiraman	NNP
10_1101-2021_01_08_425885	972	37	,	,	,
10_1101-2021_01_08_425885	972	38	B.	B.	NNP
10_1101-2021_01_08_425885	972	39	Bierie	Bierie	NNP
10_1101-2021_01_08_425885	972	40	,	,	,
10_1101-2021_01_08_425885	972	41	L.	L.	NNP
10_1101-2021_01_08_425885	972	42	Mazutis	Mazutis	NNP
10_1101-2021_01_08_425885	972	43	,	,	,
10_1101-2021_01_08_425885	972	44	G.	G.	NNP
10_1101-2021_01_08_425885	972	45	Wolf	Wolf	NNP
10_1101-2021_01_08_425885	972	46	,	,	,
10_1101-2021_01_08_425885	972	47	S.	S.	NNP
10_1101-2021_01_08_425885	972	48	Krishnaswamy	Krishnaswamy	NNP
10_1101-2021_01_08_425885	972	49	,	,	,
10_1101-2021_01_08_425885	972	50	and	and	CC
10_1101-2021_01_08_425885	972	51	D.	D.	NNP
10_1101-2021_01_08_425885	972	52	Pe’er	Pe’er	NNP
10_1101-2021_01_08_425885	972	53	.	.	.
10_1101-2021_01_08_425885	973	1	Recovering	recover	VBG
10_1101-2021_01_08_425885	973	2	gene	gene	NN
10_1101-2021_01_08_425885	973	3	interactions	interaction	NNS
10_1101-2021_01_08_425885	973	4	from	from	IN
10_1101-2021_01_08_425885	973	5	single	single	JJ
10_1101-2021_01_08_425885	973	6	-	-	HYPH
10_1101-2021_01_08_425885	973	7	cell	cell	NN
10_1101-2021_01_08_425885	973	8	data	datum	NNS
10_1101-2021_01_08_425885	973	9	using	use	VBG
10_1101-2021_01_08_425885	973	10	data	datum	NNS
10_1101-2021_01_08_425885	973	11	diffusion	diffusion	NN
10_1101-2021_01_08_425885	973	12	.	.	.
10_1101-2021_01_08_425885	974	1	Cell	cell	NN
10_1101-2021_01_08_425885	974	2	,	,	,
10_1101-2021_01_08_425885	974	3	174(3):716–729	174(3):716–729	CD
10_1101-2021_01_08_425885	974	4	,	,	,
10_1101-2021_01_08_425885	974	5	2018	2018	CD
10_1101-2021_01_08_425885	974	6	.	.	.
10_1101-2021_01_08_425885	975	1	[	[	-LRB-
10_1101-2021_01_08_425885	975	2	46	46	CD
10_1101-2021_01_08_425885	975	3	]	]	-RRB-
10_1101-2021_01_08_425885	975	4	L.	L.	NNP
10_1101-2021_01_08_425885	975	5	Haghverdi	Haghverdi	NNP
10_1101-2021_01_08_425885	975	6	,	,	,
10_1101-2021_01_08_425885	975	7	M.	M.	NNP
10_1101-2021_01_08_425885	975	8	Büttner	Büttner	NNP
10_1101-2021_01_08_425885	975	9	,	,	,
10_1101-2021_01_08_425885	975	10	F.	F.	NNP
10_1101-2021_01_08_425885	975	11	A.	a.	NN
10_1101-2021_01_08_425885	975	12	Wolf	Wolf	NNP
10_1101-2021_01_08_425885	975	13	,	,	,
10_1101-2021_01_08_425885	975	14	F.	F.	NNP
10_1101-2021_01_08_425885	975	15	Buettner	Buettner	NNP
10_1101-2021_01_08_425885	975	16	,	,	,
10_1101-2021_01_08_425885	975	17	and	and	CC
10_1101-2021_01_08_425885	975	18	F.	F.	NNP
10_1101-2021_01_08_425885	975	19	J.	J.	NNP
10_1101-2021_01_08_425885	975	20	Theis	Theis	NNP
10_1101-2021_01_08_425885	975	21	.	.	.
10_1101-2021_01_08_425885	976	1	Diffusion	diffusion	NN
10_1101-2021_01_08_425885	976	2	pseudotime	pseudotime	NN
10_1101-2021_01_08_425885	976	3	robustly	robustly	RB
10_1101-2021_01_08_425885	976	4	reconstructs	reconstruct	VBZ
10_1101-2021_01_08_425885	976	5	lineage	lineage	NN
10_1101-2021_01_08_425885	976	6	branching	branching	NN
10_1101-2021_01_08_425885	976	7	.	.	.
10_1101-2021_01_08_425885	977	1	Nature	Nature	NNP
10_1101-2021_01_08_425885	977	2	Methods	Methods	NNPS
10_1101-2021_01_08_425885	977	3	,	,	,
10_1101-2021_01_08_425885	977	4	13(10):845–848	13(10):845–848	CD
10_1101-2021_01_08_425885	977	5	,	,	,
10_1101-2021_01_08_425885	977	6	2016	2016	CD
10_1101-2021_01_08_425885	977	7	.	.	.
10_1101-2021_01_08_425885	978	1	[	[	-LRB-
10_1101-2021_01_08_425885	978	2	47	47	CD
10_1101-2021_01_08_425885	978	3	]	]	-RRB-
10_1101-2021_01_08_425885	978	4	A.	a.	NN
10_1101-2021_01_08_425885	978	5	Klimovskaia	Klimovskaia	NNP
10_1101-2021_01_08_425885	978	6	,	,	,
10_1101-2021_01_08_425885	978	7	D.	D.	NNP
10_1101-2021_01_08_425885	978	8	Lopez	Lopez	NNP
10_1101-2021_01_08_425885	978	9	-	-	HYPH
10_1101-2021_01_08_425885	978	10	Paz	Paz	NNP
10_1101-2021_01_08_425885	978	11	,	,	,
10_1101-2021_01_08_425885	978	12	L.	L.	NNP
10_1101-2021_01_08_425885	978	13	Bottou	Bottou	NNP
10_1101-2021_01_08_425885	978	14	,	,	,
10_1101-2021_01_08_425885	978	15	and	and	CC
10_1101-2021_01_08_425885	978	16	M.	M.	NNP
10_1101-2021_01_08_425885	978	17	Nickel	Nickel	NNP
10_1101-2021_01_08_425885	978	18	.	.	.
10_1101-2021_01_08_425885	979	1	Poincaré	Poincaré	NNP
10_1101-2021_01_08_425885	979	2	maps	map	NNS
10_1101-2021_01_08_425885	979	3	for	for	IN
10_1101-2021_01_08_425885	979	4	analyzing	analyze	VBG
10_1101-2021_01_08_425885	979	5	complex	complex	JJ
10_1101-2021_01_08_425885	979	6	hierar-	hierar-	JJ
10_1101-2021_01_08_425885	979	7	chies	chie	NNS
10_1101-2021_01_08_425885	979	8	in	in	IN
10_1101-2021_01_08_425885	979	9	single	single	JJ
10_1101-2021_01_08_425885	979	10	-	-	HYPH
10_1101-2021_01_08_425885	979	11	cell	cell	NN
10_1101-2021_01_08_425885	979	12	data	datum	NNS
10_1101-2021_01_08_425885	979	13	.	.	.
10_1101-2021_01_08_425885	980	1	Nature	Nature	NNP
10_1101-2021_01_08_425885	980	2	Communications	Communications	NNPS
10_1101-2021_01_08_425885	980	3	,	,	,
10_1101-2021_01_08_425885	980	4	11(1):1–9	11(1):1–9	CD
10_1101-2021_01_08_425885	980	5	,	,	,
10_1101-2021_01_08_425885	980	6	2020	2020	CD
10_1101-2021_01_08_425885	980	7	.	.	.
10_1101-2021_01_08_425885	981	1	55	55	CD
10_1101-2021_01_08_425885	981	2	.CC	.CC	:
10_1101-2021_01_08_425885	981	3	-	-	HYPH
10_1101-2021_01_08_425885	981	4	BY	by	IN
10_1101-2021_01_08_425885	981	5	-	-	HYPH
10_1101-2021_01_08_425885	981	6	NC	NC	NNP
10_1101-2021_01_08_425885	981	7	-	-	HYPH
10_1101-2021_01_08_425885	981	8	ND	ND	NNP
10_1101-2021_01_08_425885	981	9	4.0	4.0	CD
10_1101-2021_01_08_425885	981	10	International	International	NNP
10_1101-2021_01_08_425885	981	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	981	12	under	under	IN
10_1101-2021_01_08_425885	981	13	a	a	DT
10_1101-2021_01_08_425885	981	14	(	(	-LRB-
10_1101-2021_01_08_425885	981	15	which	which	WDT
10_1101-2021_01_08_425885	981	16	was	be	VBD
10_1101-2021_01_08_425885	981	17	not	not	RB
10_1101-2021_01_08_425885	981	18	certified	certify	VBN
10_1101-2021_01_08_425885	981	19	by	by	IN
10_1101-2021_01_08_425885	981	20	peer	peer	NN
10_1101-2021_01_08_425885	981	21	review	review	NN
10_1101-2021_01_08_425885	981	22	)	)	-RRB-
10_1101-2021_01_08_425885	981	23	is	be	VBZ
10_1101-2021_01_08_425885	981	24	the	the	DT
10_1101-2021_01_08_425885	981	25	author	author	NN
10_1101-2021_01_08_425885	981	26	/	/	SYM
10_1101-2021_01_08_425885	981	27	funder	funder	NN
10_1101-2021_01_08_425885	981	28	,	,	,
10_1101-2021_01_08_425885	981	29	who	who	WP
10_1101-2021_01_08_425885	981	30	has	have	VBZ
10_1101-2021_01_08_425885	981	31	granted	grant	VBN
10_1101-2021_01_08_425885	981	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	981	33	a	a	DT
10_1101-2021_01_08_425885	981	34	license	license	NN
10_1101-2021_01_08_425885	981	35	to	to	TO
10_1101-2021_01_08_425885	981	36	display	display	VB
10_1101-2021_01_08_425885	981	37	the	the	DT
10_1101-2021_01_08_425885	981	38	preprint	preprint	NN
10_1101-2021_01_08_425885	981	39	in	in	IN
10_1101-2021_01_08_425885	981	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	981	41	.	.	.
10_1101-2021_01_08_425885	982	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	982	2	is	be	VBZ
10_1101-2021_01_08_425885	982	3	made	make	VBN
10_1101-2021_01_08_425885	982	4	The	the	DT
10_1101-2021_01_08_425885	982	5	copyright	copyright	NN
10_1101-2021_01_08_425885	982	6	holder	holder	NN
10_1101-2021_01_08_425885	982	7	for	for	IN
10_1101-2021_01_08_425885	982	8	this	this	DT
10_1101-2021_01_08_425885	982	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	982	10	version	version	NN
10_1101-2021_01_08_425885	982	11	posted	post	VBD
10_1101-2021_01_08_425885	982	12	January	January	NNP
10_1101-2021_01_08_425885	982	13	8	8	CD
10_1101-2021_01_08_425885	982	14	,	,	,
10_1101-2021_01_08_425885	982	15	2021	2021	CD
10_1101-2021_01_08_425885	982	16	.	.	.
10_1101-2021_01_08_425885	982	17	;	;	:
10_1101-2021_01_08_425885	982	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	982	19	:	:	:
10_1101-2021_01_08_425885	982	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	982	21	preprint	preprint	JJ
10_1101-2021_01_08_425885	982	22	https://support.10xgenomics.com/single-cell-gene-expression/datasets/4.0.0/Parent_NGSC3_DI_PBMC	https://support.10xgenomics.com/single-cell-gene-expression/datasets/4.0.0/parent_ngsc3_di_pbmc	CD
10_1101-2021_01_08_425885	982	23	https://support.10xgenomics.com/single-cell-gene-expression/datasets/4.0.0/Parent_NGSC3_DI_PBMC	https://support.10xgenomics.com/single-cell-gene-expression/datasets/4.0.0/parent_ngsc3_di_pbmc	CD
10_1101-2021_01_08_425885	982	24	https://support.10xgenomics.com/single-cell-gene-expression/datasets/1.3.0/1M_neurons	https://support.10xgenomics.com/single-cell-gene-expression/datasets/1.3.0/1M_neurons	NNP
10_1101-2021_01_08_425885	982	25	https://support.10xgenomics.com/single-cell-gene-expression/datasets/1.3.0/1M_neurons	https://support.10xgenomics.com/single-cell-gene-expression/datasets/1.3.0/1M_neurons	NNP
10_1101-2021_01_08_425885	982	26	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	ADD
10_1101-2021_01_08_425885	982	27	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	CD
10_1101-2021_01_08_425885	982	28	[	[	-LRB-
10_1101-2021_01_08_425885	982	29	48	48	CD
10_1101-2021_01_08_425885	982	30	]	]	-RRB-
10_1101-2021_01_08_425885	982	31	S.	S.	NNP
10_1101-2021_01_08_425885	982	32	Wang	Wang	NNP
10_1101-2021_01_08_425885	982	33	,	,	,
10_1101-2021_01_08_425885	982	34	J	J	NNP
10_1101-2021_01_08_425885	982	35	-	-	HYPH
10_1101-2021_01_08_425885	982	36	R.	R.	NNP
10_1101-2021_01_08_425885	982	37	Lin	Lin	NNP
10_1101-2021_01_08_425885	982	38	,	,	,
10_1101-2021_01_08_425885	982	39	E.	E.	NNP
10_1101-2021_01_08_425885	982	40	D.	D.	NNP
10_1101-2021_01_08_425885	982	41	Sontag	Sontag	NNP
10_1101-2021_01_08_425885	982	42	,	,	,
10_1101-2021_01_08_425885	982	43	and	and	CC
10_1101-2021_01_08_425885	982	44	P.	P.	NNP
10_1101-2021_01_08_425885	982	45	K.	K.	NNP
10_1101-2021_01_08_425885	982	46	Sorger	Sorger	NNP
10_1101-2021_01_08_425885	982	47	.	.	.
10_1101-2021_01_08_425885	983	1	Inferring	infer	VBG
10_1101-2021_01_08_425885	983	2	reaction	reaction	NN
10_1101-2021_01_08_425885	983	3	network	network	NN
10_1101-2021_01_08_425885	983	4	structure	structure	NN
10_1101-2021_01_08_425885	983	5	from	from	IN
10_1101-2021_01_08_425885	983	6	single	single	JJ
10_1101-2021_01_08_425885	983	7	-	-	HYPH
10_1101-2021_01_08_425885	983	8	cell	cell	NN
10_1101-2021_01_08_425885	983	9	,	,	,
10_1101-2021_01_08_425885	983	10	multiplex	multiplex	NNP
10_1101-2021_01_08_425885	983	11	data	datum	NNS
10_1101-2021_01_08_425885	983	12	,	,	,
10_1101-2021_01_08_425885	983	13	using	use	VBG
10_1101-2021_01_08_425885	983	14	toric	toric	JJ
10_1101-2021_01_08_425885	983	15	systems	system	NNS
10_1101-2021_01_08_425885	983	16	theory	theory	NN
10_1101-2021_01_08_425885	983	17	.	.	.
10_1101-2021_01_08_425885	984	1	PLoS	PLoS	NNP
10_1101-2021_01_08_425885	984	2	Computational	Computational	NNP
10_1101-2021_01_08_425885	984	3	Biology	Biology	NNP
10_1101-2021_01_08_425885	984	4	,	,	,
10_1101-2021_01_08_425885	984	5	15(12):e1007311	15(12):e1007311	CD
10_1101-2021_01_08_425885	984	6	,	,	,
10_1101-2021_01_08_425885	984	7	2019	2019	CD
10_1101-2021_01_08_425885	984	8	.	.	.
10_1101-2021_01_08_425885	985	1	[	[	-LRB-
10_1101-2021_01_08_425885	985	2	49	49	CD
10_1101-2021_01_08_425885	985	3	]	]	-RRB-
10_1101-2021_01_08_425885	985	4	M.	M.	NNP
10_1101-2021_01_08_425885	985	5	Hein	Hein	NNP
10_1101-2021_01_08_425885	985	6	,	,	,
10_1101-2021_01_08_425885	985	7	J	J	NNP
10_1101-2021_01_08_425885	985	8	-	-	HYPH
10_1101-2021_01_08_425885	985	9	Y.	Y.	NNP
10_1101-2021_01_08_425885	986	1	Audibert	Audibert	NNP
10_1101-2021_01_08_425885	986	2	,	,	,
10_1101-2021_01_08_425885	986	3	and	and	CC
10_1101-2021_01_08_425885	986	4	U.	U.	NNP
10_1101-2021_01_08_425885	986	5	von	von	NNP
10_1101-2021_01_08_425885	986	6	Luxburg	Luxburg	NNP
10_1101-2021_01_08_425885	986	7	.	.	.
10_1101-2021_01_08_425885	987	1	Graph	Graph	NNP
10_1101-2021_01_08_425885	987	2	Laplacians	Laplacians	NNPS
10_1101-2021_01_08_425885	987	3	and	and	CC
10_1101-2021_01_08_425885	987	4	their	-PRON-	PRP$
10_1101-2021_01_08_425885	987	5	convergence	convergence	NN
10_1101-2021_01_08_425885	987	6	on	on	IN
10_1101-2021_01_08_425885	987	7	random	random	JJ
10_1101-2021_01_08_425885	987	8	neighborhood	neighborhood	NN
10_1101-2021_01_08_425885	987	9	graphs	graphs	NN
10_1101-2021_01_08_425885	987	10	.	.	.
10_1101-2021_01_08_425885	988	1	Journal	Journal	NNP
10_1101-2021_01_08_425885	988	2	of	of	IN
10_1101-2021_01_08_425885	988	3	Machine	Machine	NNP
10_1101-2021_01_08_425885	988	4	Learning	Learning	NNP
10_1101-2021_01_08_425885	988	5	Research	Research	NNP
10_1101-2021_01_08_425885	988	6	,	,	,
10_1101-2021_01_08_425885	988	7	8(48):1325–1370	8(48):1325–1370	CD
10_1101-2021_01_08_425885	988	8	,	,	,
10_1101-2021_01_08_425885	988	9	2007	2007	CD
10_1101-2021_01_08_425885	988	10	.	.	.
10_1101-2021_01_08_425885	989	1	[	[	-LRB-
10_1101-2021_01_08_425885	989	2	50	50	CD
10_1101-2021_01_08_425885	989	3	]	]	-RRB-
10_1101-2021_01_08_425885	989	4	D.	D.	NNP
10_1101-2021_01_08_425885	989	5	Ting	Ting	NNP
10_1101-2021_01_08_425885	989	6	,	,	,
10_1101-2021_01_08_425885	989	7	L.	L.	NNP
10_1101-2021_01_08_425885	989	8	Huang	Huang	NNP
10_1101-2021_01_08_425885	989	9	,	,	,
10_1101-2021_01_08_425885	989	10	and	and	CC
10_1101-2021_01_08_425885	989	11	M.	M.	NNP
10_1101-2021_01_08_425885	989	12	Jordan	Jordan	NNP
10_1101-2021_01_08_425885	989	13	.	.	.
10_1101-2021_01_08_425885	990	1	An	an	DT
10_1101-2021_01_08_425885	990	2	analysis	analysis	NN
10_1101-2021_01_08_425885	990	3	of	of	IN
10_1101-2021_01_08_425885	990	4	the	the	DT
10_1101-2021_01_08_425885	990	5	convergence	convergence	NN
10_1101-2021_01_08_425885	990	6	of	of	IN
10_1101-2021_01_08_425885	990	7	graph	graph	NNP
10_1101-2021_01_08_425885	990	8	Laplacians	Laplacians	NNPS
10_1101-2021_01_08_425885	990	9	.	.	.
10_1101-2021_01_08_425885	991	1	arXiv	arXiv	NNP
10_1101-2021_01_08_425885	991	2	,	,	,
10_1101-2021_01_08_425885	991	3	2011	2011	CD
10_1101-2021_01_08_425885	991	4	.	.	.
10_1101-2021_01_08_425885	992	1	[	[	-LRB-
10_1101-2021_01_08_425885	992	2	51	51	CD
10_1101-2021_01_08_425885	992	3	]	]	-RRB-
10_1101-2021_01_08_425885	992	4	K.	K.	NNP
10_1101-2021_01_08_425885	992	5	V.	V.	NNP
10_1101-2021_01_08_425885	992	6	Mardia	Mardia	NNP
10_1101-2021_01_08_425885	992	7	.	.	.
10_1101-2021_01_08_425885	993	1	Measures	measure	NNS
10_1101-2021_01_08_425885	993	2	of	of	IN
10_1101-2021_01_08_425885	993	3	multivariate	multivariate	JJ
10_1101-2021_01_08_425885	993	4	skewness	skewness	NN
10_1101-2021_01_08_425885	993	5	and	and	CC
10_1101-2021_01_08_425885	993	6	kurtosis	kurtosis	NN
10_1101-2021_01_08_425885	993	7	with	with	IN
10_1101-2021_01_08_425885	993	8	applications	application	NNS
10_1101-2021_01_08_425885	993	9	.	.	.
10_1101-2021_01_08_425885	994	1	Biometrika	Biometrika	NNP
10_1101-2021_01_08_425885	994	2	,	,	,
10_1101-2021_01_08_425885	994	3	57(3):519	57(3):519	CD
10_1101-2021_01_08_425885	994	4	–	–	:
10_1101-2021_01_08_425885	994	5	530	530	CD
10_1101-2021_01_08_425885	994	6	,	,	,
10_1101-2021_01_08_425885	994	7	1970	1970	CD
10_1101-2021_01_08_425885	994	8	.	.	.
10_1101-2021_01_08_425885	995	1	[	[	-LRB-
10_1101-2021_01_08_425885	995	2	52	52	CD
10_1101-2021_01_08_425885	995	3	]	]	-RRB-
10_1101-2021_01_08_425885	995	4	P.	P.	NNP
10_1101-2021_01_08_425885	995	5	Campadelli	Campadelli	NNP
10_1101-2021_01_08_425885	995	6	,	,	,
10_1101-2021_01_08_425885	995	7	E.	E.	NNP
10_1101-2021_01_08_425885	995	8	Casiraghi	Casiraghi	NNP
10_1101-2021_01_08_425885	995	9	,	,	,
10_1101-2021_01_08_425885	995	10	C.	C.	NNP
10_1101-2021_01_08_425885	995	11	Ceruti	Ceruti	NNP
10_1101-2021_01_08_425885	995	12	,	,	,
10_1101-2021_01_08_425885	995	13	and	and	CC
10_1101-2021_01_08_425885	995	14	A.	A.	NNP
10_1101-2021_01_08_425885	995	15	Rozza	Rozza	NNP
10_1101-2021_01_08_425885	995	16	.	.	.
10_1101-2021_01_08_425885	996	1	Intrinsic	intrinsic	JJ
10_1101-2021_01_08_425885	996	2	dimension	dimension	NN
10_1101-2021_01_08_425885	996	3	estimation	estimation	NN
10_1101-2021_01_08_425885	996	4	:	:	:
10_1101-2021_01_08_425885	996	5	Relevant	relevant	JJ
10_1101-2021_01_08_425885	996	6	tech-	tech-	JJ
10_1101-2021_01_08_425885	996	7	niques	nique	NNS
10_1101-2021_01_08_425885	996	8	and	and	CC
10_1101-2021_01_08_425885	996	9	a	a	DT
10_1101-2021_01_08_425885	996	10	benchmark	benchmark	JJ
10_1101-2021_01_08_425885	996	11	framework	framework	NN
10_1101-2021_01_08_425885	996	12	.	.	.
10_1101-2021_01_08_425885	997	1	Mathematical	Mathematical	NNP
10_1101-2021_01_08_425885	997	2	Problems	Problems	NNPS
10_1101-2021_01_08_425885	997	3	in	in	IN
10_1101-2021_01_08_425885	997	4	Engineering	Engineering	NNP
10_1101-2021_01_08_425885	997	5	,	,	,
10_1101-2021_01_08_425885	997	6	2015:1–21	2015:1–21	CD
10_1101-2021_01_08_425885	997	7	,	,	,
10_1101-2021_01_08_425885	997	8	2015	2015	CD
10_1101-2021_01_08_425885	997	9	.	.	.
10_1101-2021_01_08_425885	998	1	[	[	-LRB-
10_1101-2021_01_08_425885	998	2	53	53	CD
10_1101-2021_01_08_425885	998	3	]	]	-RRB-
10_1101-2021_01_08_425885	998	4	A.	a.	NN
10_1101-2021_01_08_425885	998	5	Butler	Butler	NNP
10_1101-2021_01_08_425885	998	6	,	,	,
10_1101-2021_01_08_425885	998	7	P.	P.	NNP
10_1101-2021_01_08_425885	998	8	Hoffman	Hoffman	NNP
10_1101-2021_01_08_425885	998	9	,	,	,
10_1101-2021_01_08_425885	998	10	P.	P.	NNP
10_1101-2021_01_08_425885	998	11	Smibert	Smibert	NNP
10_1101-2021_01_08_425885	998	12	,	,	,
10_1101-2021_01_08_425885	998	13	E.	E.	NNP
10_1101-2021_01_08_425885	998	14	Papalexi	Papalexi	NNP
10_1101-2021_01_08_425885	998	15	,	,	,
10_1101-2021_01_08_425885	998	16	and	and	CC
10_1101-2021_01_08_425885	998	17	R.	R.	NNP
10_1101-2021_01_08_425885	998	18	Satija	Satija	NNP
10_1101-2021_01_08_425885	998	19	.	.	.
10_1101-2021_01_08_425885	999	1	Integrating	integrate	VBG
10_1101-2021_01_08_425885	999	2	single	single	JJ
10_1101-2021_01_08_425885	999	3	-	-	HYPH
10_1101-2021_01_08_425885	999	4	cell	cell	NN
10_1101-2021_01_08_425885	999	5	transcriptomic	transcriptomic	JJ
10_1101-2021_01_08_425885	999	6	data	datum	NNS
10_1101-2021_01_08_425885	999	7	across	across	IN
10_1101-2021_01_08_425885	999	8	different	different	JJ
10_1101-2021_01_08_425885	999	9	conditions	condition	NNS
10_1101-2021_01_08_425885	999	10	,	,	,
10_1101-2021_01_08_425885	999	11	technologies	technology	NNS
10_1101-2021_01_08_425885	999	12	,	,	,
10_1101-2021_01_08_425885	999	13	and	and	CC
10_1101-2021_01_08_425885	999	14	species	specie	NNS
10_1101-2021_01_08_425885	999	15	.	.	.
10_1101-2021_01_08_425885	1000	1	Nature	Nature	NNP
10_1101-2021_01_08_425885	1000	2	Biotechnology	Biotechnology	NNP
10_1101-2021_01_08_425885	1000	3	,	,	,
10_1101-2021_01_08_425885	1000	4	36(5):411–420	36(5):411–420	CD
10_1101-2021_01_08_425885	1000	5	,	,	,
10_1101-2021_01_08_425885	1000	6	2018	2018	CD
10_1101-2021_01_08_425885	1000	7	.	.	.
10_1101-2021_01_08_425885	1001	1	[	[	-LRB-
10_1101-2021_01_08_425885	1001	2	54	54	CD
10_1101-2021_01_08_425885	1001	3	]	]	-RRB-
10_1101-2021_01_08_425885	1001	4	Y.	Y.	NNP
10_1101-2021_01_08_425885	1001	5	Hu	Hu	NNP
10_1101-2021_01_08_425885	1001	6	,	,	,
10_1101-2021_01_08_425885	1001	7	M.	M.	NNP
10_1101-2021_01_08_425885	1001	8	Ranganathan	Ranganathan	NNP
10_1101-2021_01_08_425885	1001	9	,	,	,
10_1101-2021_01_08_425885	1001	10	C.	C.	NNP
10_1101-2021_01_08_425885	1001	11	Shu	Shu	NNP
10_1101-2021_01_08_425885	1001	12	,	,	,
10_1101-2021_01_08_425885	1001	13	X.	X.	NNP
10_1101-2021_01_08_425885	1001	14	Liang	Liang	NNP
10_1101-2021_01_08_425885	1001	15	,	,	,
10_1101-2021_01_08_425885	1001	16	S.	S.	NNP
10_1101-2021_01_08_425885	1001	17	Ganesh	Ganesh	NNP
10_1101-2021_01_08_425885	1001	18	,	,	,
10_1101-2021_01_08_425885	1001	19	A.	A.	NNP
10_1101-2021_01_08_425885	1001	20	Osafo	Osafo	NNP
10_1101-2021_01_08_425885	1001	21	-	-	HYPH
10_1101-2021_01_08_425885	1001	22	Addo	Addo	NNP
10_1101-2021_01_08_425885	1001	23	,	,	,
10_1101-2021_01_08_425885	1001	24	C.	C.	NNP
10_1101-2021_01_08_425885	1001	25	Yan	Yan	NNP
10_1101-2021_01_08_425885	1001	26	,	,	,
10_1101-2021_01_08_425885	1001	27	X.	X.	NNP
10_1101-2021_01_08_425885	1001	28	Zhang	Zhang	NNP
10_1101-2021_01_08_425885	1001	29	,	,	,
10_1101-2021_01_08_425885	1001	30	B.	B.	NNP
10_1101-2021_01_08_425885	1001	31	E.	E.	NNP
10_1101-2021_01_08_425885	1001	32	Aouizerat	Aouizerat	NNP
10_1101-2021_01_08_425885	1001	33	,	,	,
10_1101-2021_01_08_425885	1001	34	J.	J.	NNP
10_1101-2021_01_08_425885	1001	35	H.	H.	NNP
10_1101-2021_01_08_425885	1001	36	Krystal	Krystal	NNP
10_1101-2021_01_08_425885	1001	37	,	,	,
10_1101-2021_01_08_425885	1001	38	D.	D.	NNP
10_1101-2021_01_08_425885	1001	39	C.	C.	NNP
10_1101-2021_01_08_425885	1001	40	D’Souza	D’Souza	NNP
10_1101-2021_01_08_425885	1001	41	,	,	,
10_1101-2021_01_08_425885	1001	42	and	and	CC
10_1101-2021_01_08_425885	1001	43	K.	K.	NNP
10_1101-2021_01_08_425885	1001	44	Xu	Xu	NNP
10_1101-2021_01_08_425885	1001	45	.	.	.
10_1101-2021_01_08_425885	1002	1	Single	single	JJ
10_1101-2021_01_08_425885	1002	2	-	-	HYPH
10_1101-2021_01_08_425885	1002	3	cell	cell	NN
10_1101-2021_01_08_425885	1002	4	transcriptome	transcriptome	DT
10_1101-2021_01_08_425885	1002	5	mapping	mapping	NN
10_1101-2021_01_08_425885	1002	6	identifies	identify	VBZ
10_1101-2021_01_08_425885	1002	7	common	common	JJ
10_1101-2021_01_08_425885	1002	8	and	and	CC
10_1101-2021_01_08_425885	1002	9	cell	cell	NN
10_1101-2021_01_08_425885	1002	10	-	-	HYPH
10_1101-2021_01_08_425885	1002	11	type	type	NN
10_1101-2021_01_08_425885	1002	12	specific	specific	JJ
10_1101-2021_01_08_425885	1002	13	genes	gene	NNS
10_1101-2021_01_08_425885	1002	14	affected	affect	VBN
10_1101-2021_01_08_425885	1002	15	by	by	IN
10_1101-2021_01_08_425885	1002	16	acute	acute	JJ
10_1101-2021_01_08_425885	1002	17	delta9-tetrahydrocannabinol	delta9-tetrahydrocannabinol	NNP
10_1101-2021_01_08_425885	1002	18	in	in	IN
10_1101-2021_01_08_425885	1002	19	humans	human	NNS
10_1101-2021_01_08_425885	1002	20	.	.	.
10_1101-2021_01_08_425885	1003	1	Scientific	Scientific	NNP
10_1101-2021_01_08_425885	1003	2	Reports	Reports	NNPS
10_1101-2021_01_08_425885	1003	3	,	,	,
10_1101-2021_01_08_425885	1003	4	10(1):1–14	10(1):1–14	CD
10_1101-2021_01_08_425885	1003	5	,	,	,
10_1101-2021_01_08_425885	1003	6	2020	2020	CD
10_1101-2021_01_08_425885	1003	7	.	.	.
10_1101-2021_01_08_425885	1004	1	[	[	-LRB-
10_1101-2021_01_08_425885	1004	2	55	55	CD
10_1101-2021_01_08_425885	1004	3	]	]	-RRB-
10_1101-2021_01_08_425885	1004	4	K.	K.	NNP
10_1101-2021_01_08_425885	1004	5	Xie	Xie	NNP
10_1101-2021_01_08_425885	1004	6	,	,	,
10_1101-2021_01_08_425885	1004	7	Y.	Y.	NNP
10_1101-2021_01_08_425885	1004	8	Huang	Huang	NNP
10_1101-2021_01_08_425885	1004	9	,	,	,
10_1101-2021_01_08_425885	1004	10	F.	F.	NNP
10_1101-2021_01_08_425885	1004	11	Zeng	Zeng	NNP
10_1101-2021_01_08_425885	1004	12	,	,	,
10_1101-2021_01_08_425885	1004	13	Z.	Z.	NNP
10_1101-2021_01_08_425885	1004	14	Liu	Liu	NNP
10_1101-2021_01_08_425885	1004	15	,	,	,
10_1101-2021_01_08_425885	1004	16	and	and	CC
10_1101-2021_01_08_425885	1004	17	T.	T.	NNP
10_1101-2021_01_08_425885	1004	18	Chen	Chen	NNP
10_1101-2021_01_08_425885	1004	19	.	.	.
10_1101-2021_01_08_425885	1005	1	scAIDE	scaide	XX
10_1101-2021_01_08_425885	1005	2	:	:	:
10_1101-2021_01_08_425885	1005	3	clustering	cluster	VBG
10_1101-2021_01_08_425885	1005	4	of	of	IN
10_1101-2021_01_08_425885	1005	5	large	large	JJ
10_1101-2021_01_08_425885	1005	6	-	-	HYPH
10_1101-2021_01_08_425885	1005	7	scale	scale	NN
10_1101-2021_01_08_425885	1005	8	single	single	JJ
10_1101-2021_01_08_425885	1005	9	-	-	HYPH
10_1101-2021_01_08_425885	1005	10	cell	cell	NN
10_1101-2021_01_08_425885	1005	11	RNA	RNA	NNP
10_1101-2021_01_08_425885	1005	12	-	-	HYPH
10_1101-2021_01_08_425885	1005	13	seq	seq	NN
10_1101-2021_01_08_425885	1005	14	data	datum	NNS
10_1101-2021_01_08_425885	1005	15	reveals	reveal	NNS
10_1101-2021_01_08_425885	1005	16	putative	putative	JJ
10_1101-2021_01_08_425885	1005	17	and	and	CC
10_1101-2021_01_08_425885	1005	18	rare	rare	JJ
10_1101-2021_01_08_425885	1005	19	cell	cell	NN
10_1101-2021_01_08_425885	1005	20	types	type	NNS
10_1101-2021_01_08_425885	1005	21	.	.	.
10_1101-2021_01_08_425885	1006	1	NAR	NAR	NNP
10_1101-2021_01_08_425885	1006	2	Genomics	Genomics	NNP
10_1101-2021_01_08_425885	1006	3	and	and	CC
10_1101-2021_01_08_425885	1006	4	Bioinformatics	Bioinformatics	NNP
10_1101-2021_01_08_425885	1006	5	,	,	,
10_1101-2021_01_08_425885	1006	6	2(4	2(4	NNP
10_1101-2021_01_08_425885	1006	7	)	)	-RRB-
10_1101-2021_01_08_425885	1006	8	,	,	,
10_1101-2021_01_08_425885	1006	9	2020	2020	CD
10_1101-2021_01_08_425885	1006	10	.	.	.
10_1101-2021_01_08_425885	1007	1	56	56	CD
10_1101-2021_01_08_425885	1007	2	.CC	.CC	:
10_1101-2021_01_08_425885	1007	3	-	-	HYPH
10_1101-2021_01_08_425885	1007	4	BY	by	IN
10_1101-2021_01_08_425885	1007	5	-	-	HYPH
10_1101-2021_01_08_425885	1007	6	NC	NC	NNP
10_1101-2021_01_08_425885	1007	7	-	-	HYPH
10_1101-2021_01_08_425885	1007	8	ND	ND	NNP
10_1101-2021_01_08_425885	1007	9	4.0	4.0	CD
10_1101-2021_01_08_425885	1007	10	International	International	NNP
10_1101-2021_01_08_425885	1007	11	licenseavailable	licenseavailable	NN
10_1101-2021_01_08_425885	1007	12	under	under	IN
10_1101-2021_01_08_425885	1007	13	a	a	DT
10_1101-2021_01_08_425885	1007	14	(	(	-LRB-
10_1101-2021_01_08_425885	1007	15	which	which	WDT
10_1101-2021_01_08_425885	1007	16	was	be	VBD
10_1101-2021_01_08_425885	1007	17	not	not	RB
10_1101-2021_01_08_425885	1007	18	certified	certify	VBN
10_1101-2021_01_08_425885	1007	19	by	by	IN
10_1101-2021_01_08_425885	1007	20	peer	peer	NN
10_1101-2021_01_08_425885	1007	21	review	review	NN
10_1101-2021_01_08_425885	1007	22	)	)	-RRB-
10_1101-2021_01_08_425885	1007	23	is	be	VBZ
10_1101-2021_01_08_425885	1007	24	the	the	DT
10_1101-2021_01_08_425885	1007	25	author	author	NN
10_1101-2021_01_08_425885	1007	26	/	/	SYM
10_1101-2021_01_08_425885	1007	27	funder	funder	NN
10_1101-2021_01_08_425885	1007	28	,	,	,
10_1101-2021_01_08_425885	1007	29	who	who	WP
10_1101-2021_01_08_425885	1007	30	has	have	VBZ
10_1101-2021_01_08_425885	1007	31	granted	grant	VBN
10_1101-2021_01_08_425885	1007	32	bioRxiv	biorxiv	IN
10_1101-2021_01_08_425885	1007	33	a	a	DT
10_1101-2021_01_08_425885	1007	34	license	license	NN
10_1101-2021_01_08_425885	1007	35	to	to	TO
10_1101-2021_01_08_425885	1007	36	display	display	VB
10_1101-2021_01_08_425885	1007	37	the	the	DT
10_1101-2021_01_08_425885	1007	38	preprint	preprint	NN
10_1101-2021_01_08_425885	1007	39	in	in	IN
10_1101-2021_01_08_425885	1007	40	perpetuity	perpetuity	NN
10_1101-2021_01_08_425885	1007	41	.	.	.
10_1101-2021_01_08_425885	1008	1	It	-PRON-	PRP
10_1101-2021_01_08_425885	1008	2	is	be	VBZ
10_1101-2021_01_08_425885	1008	3	made	make	VBN
10_1101-2021_01_08_425885	1008	4	The	the	DT
10_1101-2021_01_08_425885	1008	5	copyright	copyright	NN
10_1101-2021_01_08_425885	1008	6	holder	holder	NN
10_1101-2021_01_08_425885	1008	7	for	for	IN
10_1101-2021_01_08_425885	1008	8	this	this	DT
10_1101-2021_01_08_425885	1008	9	preprintthis	preprintthis	NN
10_1101-2021_01_08_425885	1008	10	version	version	NN
10_1101-2021_01_08_425885	1008	11	posted	post	VBD
10_1101-2021_01_08_425885	1008	12	January	January	NNP
10_1101-2021_01_08_425885	1008	13	8	8	CD
10_1101-2021_01_08_425885	1008	14	,	,	,
10_1101-2021_01_08_425885	1008	15	2021	2021	CD
10_1101-2021_01_08_425885	1008	16	.	.	.
10_1101-2021_01_08_425885	1008	17	;	;	:
10_1101-2021_01_08_425885	1008	18	https://doi.org/10.1101/2021.01.08.425885doi	https://doi.org/10.1101/2021.01.08.425885doi	ADD
10_1101-2021_01_08_425885	1008	19	:	:	:
10_1101-2021_01_08_425885	1008	20	bioRxiv	biorxiv	VB
10_1101-2021_01_08_425885	1008	21	preprint	preprint	NN
10_1101-2021_01_08_425885	1008	22	https://doi.org/10.1101/2021.01.08.425885	https://doi.org/10.1101/2021.01.08.425885	VBZ
10_1101-2021_01_08_425885	1008	23	http://creativecommons.org/licenses/by-nc-nd/4.0/	http://creativecommons.org/licenses/by-nc-nd/4.0/	RB
10_1101-2021_01_08_425885	1008	24	Introduction	Introduction	NNP
10_1101-2021_01_08_425885	1008	25	Results	Results	NNPS
10_1101-2021_01_08_425885	1008	26	Estimators	Estimators	NNPS
10_1101-2021_01_08_425885	1008	27	of	of	IN
10_1101-2021_01_08_425885	1008	28	the	the	DT
10_1101-2021_01_08_425885	1008	29	Laplace	Laplace	NNP
10_1101-2021_01_08_425885	1008	30	-	-	HYPH
10_1101-2021_01_08_425885	1008	31	Beltrami	Beltrami	NNP
10_1101-2021_01_08_425885	1008	32	Operator	Operator	NNP
10_1101-2021_01_08_425885	1008	33	Yield	Yield	NNP
10_1101-2021_01_08_425885	1008	34	Inaccurate	Inaccurate	NNP
10_1101-2021_01_08_425885	1008	35	Scalar	Scalar	NNP
10_1101-2021_01_08_425885	1008	36	Curvatures	curvature	VBZ
10_1101-2021_01_08_425885	1008	37	Curvature	curvature	NN
10_1101-2021_01_08_425885	1008	38	Can	Can	MD
10_1101-2021_01_08_425885	1008	39	Be	be	VB
10_1101-2021_01_08_425885	1008	40	Computed	compute	VBN
10_1101-2021_01_08_425885	1008	41	Accurately	accurately	RB
10_1101-2021_01_08_425885	1008	42	Using	use	VBG
10_1101-2021_01_08_425885	1008	43	the	the	DT
10_1101-2021_01_08_425885	1008	44	Second	Second	NNP
10_1101-2021_01_08_425885	1008	45	Fundamental	Fundamental	NNP
10_1101-2021_01_08_425885	1008	46	Form	Form	NNP
10_1101-2021_01_08_425885	1008	47	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	1008	48	of	of	IN
10_1101-2021_01_08_425885	1008	49	Image	Image	NNP
10_1101-2021_01_08_425885	1008	50	Patch	Patch	NNP
10_1101-2021_01_08_425885	1008	51	Manifold	Manifold	NNP
10_1101-2021_01_08_425885	1008	52	is	be	VBZ
10_1101-2021_01_08_425885	1008	53	Consistent	consistent	JJ
10_1101-2021_01_08_425885	1008	54	with	with	IN
10_1101-2021_01_08_425885	1008	55	a	a	DT
10_1101-2021_01_08_425885	1008	56	Noisy	Noisy	NNP
10_1101-2021_01_08_425885	1008	57	Klein	Klein	NNP
10_1101-2021_01_08_425885	1008	58	Bottle	Bottle	NNP
10_1101-2021_01_08_425885	1008	59	scRNAseq	scRNAseq	NNP
10_1101-2021_01_08_425885	1008	60	Datasets	dataset	NNS
10_1101-2021_01_08_425885	1008	61	have	have	VBP
10_1101-2021_01_08_425885	1008	62	Non	non	JJ
10_1101-2021_01_08_425885	1008	63	-	-	JJ
10_1101-2021_01_08_425885	1008	64	Trivial	trivial	JJ
10_1101-2021_01_08_425885	1008	65	Intrinsic	Intrinsic	NNP
10_1101-2021_01_08_425885	1008	66	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	1008	67	Discussion	Discussion	NNP
10_1101-2021_01_08_425885	1008	68	Methods	Methods	NNP
10_1101-2021_01_08_425885	1008	69	Differential	Differential	NNP
10_1101-2021_01_08_425885	1008	70	Geometry	Geometry	NNP
10_1101-2021_01_08_425885	1008	71	of	of	IN
10_1101-2021_01_08_425885	1008	72	Theoretical	Theoretical	NNP
10_1101-2021_01_08_425885	1008	73	Manifolds	Manifolds	NNPS
10_1101-2021_01_08_425885	1008	74	Details	Details	NNP
10_1101-2021_01_08_425885	1008	75	of	of	IN
10_1101-2021_01_08_425885	1008	76	Intrinsic	Intrinsic	NNP
10_1101-2021_01_08_425885	1008	77	Approach	Approach	NNP
10_1101-2021_01_08_425885	1008	78	to	to	IN
10_1101-2021_01_08_425885	1008	79	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	1008	80	Estimation	Estimation	NNP
10_1101-2021_01_08_425885	1008	81	Approach	Approach	NNP
10_1101-2021_01_08_425885	1008	82	for	for	IN
10_1101-2021_01_08_425885	1008	83	S2	S2	NNP
10_1101-2021_01_08_425885	1008	84	Infinite	Infinite	NNP
10_1101-2021_01_08_425885	1008	85	Series	Series	NNP
10_1101-2021_01_08_425885	1008	86	Truncated	Truncated	NNP
10_1101-2021_01_08_425885	1008	87	Series	Series	NNP
10_1101-2021_01_08_425885	1008	88	Eigenvalue	Eigenvalue	NNP
10_1101-2021_01_08_425885	1008	89	Convergence	Convergence	NNP
10_1101-2021_01_08_425885	1008	90	Estimating	Estimating	NNP
10_1101-2021_01_08_425885	1008	91	the	the	DT
10_1101-2021_01_08_425885	1008	92	Laplace	Laplace	NNP
10_1101-2021_01_08_425885	1008	93	-	-	HYPH
10_1101-2021_01_08_425885	1008	94	Beltrami	Beltrami	NNP
10_1101-2021_01_08_425885	1008	95	Operator	Operator	NNP
10_1101-2021_01_08_425885	1008	96	from	from	IN
10_1101-2021_01_08_425885	1008	97	Data	Data	NNP
10_1101-2021_01_08_425885	1008	98	Details	Details	NNP
10_1101-2021_01_08_425885	1008	99	of	of	IN
10_1101-2021_01_08_425885	1008	100	Extrinsic	Extrinsic	NNP
10_1101-2021_01_08_425885	1008	101	Approach	Approach	NNP
10_1101-2021_01_08_425885	1008	102	to	to	IN
10_1101-2021_01_08_425885	1008	103	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	1008	104	Estimation	estimation	NN
10_1101-2021_01_08_425885	1008	105	Quadratic	Quadratic	NNP
10_1101-2021_01_08_425885	1008	106	Regression	Regression	NNP
10_1101-2021_01_08_425885	1008	107	on	on	IN
10_1101-2021_01_08_425885	1008	108	Local	Local	NNP
10_1101-2021_01_08_425885	1008	109	Neighborhoods	Neighborhoods	NNPS
10_1101-2021_01_08_425885	1008	110	of	of	IN
10_1101-2021_01_08_425885	1008	111	Data	Data	NNP
10_1101-2021_01_08_425885	1008	112	Selecting	Selecting	NNP
10_1101-2021_01_08_425885	1008	113	Local	Local	NNP
10_1101-2021_01_08_425885	1008	114	Neighborhoods	Neighborhoods	NNPS
10_1101-2021_01_08_425885	1008	115	for	for	IN
10_1101-2021_01_08_425885	1008	116	Regression	Regression	NNP
10_1101-2021_01_08_425885	1008	117	Goodness	Goodness	NNP
10_1101-2021_01_08_425885	1008	118	-	-	HYPH
10_1101-2021_01_08_425885	1008	119	of	of	IN
10_1101-2021_01_08_425885	1008	120	-	-	HYPH
10_1101-2021_01_08_425885	1008	121	Fit	fit	NN
10_1101-2021_01_08_425885	1008	122	Test	Test	NNP
10_1101-2021_01_08_425885	1008	123	for	for	IN
10_1101-2021_01_08_425885	1008	124	Quadratic	Quadratic	NNP
10_1101-2021_01_08_425885	1008	125	Regression	Regression	NNP
10_1101-2021_01_08_425885	1008	126	Standard	Standard	NNP
10_1101-2021_01_08_425885	1008	127	Error	Error	NNP
10_1101-2021_01_08_425885	1008	128	and	and	CC
10_1101-2021_01_08_425885	1008	129	Bias	Bias	NNP
10_1101-2021_01_08_425885	1008	130	of	of	IN
10_1101-2021_01_08_425885	1008	131	Scalar	Scalar	NNP
10_1101-2021_01_08_425885	1008	132	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	1008	133	Estimate	Estimate	NNP
10_1101-2021_01_08_425885	1008	134	Note	Note	NNP
10_1101-2021_01_08_425885	1008	135	on	on	IN
10_1101-2021_01_08_425885	1008	136	Length	Length	NNP
10_1101-2021_01_08_425885	1008	137	Scales	Scales	NNP
10_1101-2021_01_08_425885	1008	138	Details	Details	NNP
10_1101-2021_01_08_425885	1008	139	of	of	IN
10_1101-2021_01_08_425885	1008	140	Toy	Toy	NNP
10_1101-2021_01_08_425885	1008	141	Manifold	Manifold	NNP
10_1101-2021_01_08_425885	1008	142	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	1008	143	Computations	Computations	NNPS
10_1101-2021_01_08_425885	1008	144	Analytical	Analytical	NNP
10_1101-2021_01_08_425885	1008	145	Forms	form	NNS
10_1101-2021_01_08_425885	1008	146	Hypersphere	Hypersphere	NNP
10_1101-2021_01_08_425885	1008	147	One	one	CD
10_1101-2021_01_08_425885	1008	148	-	-	HYPH
10_1101-2021_01_08_425885	1008	149	Sheet	Sheet	NNP
10_1101-2021_01_08_425885	1008	150	Hyperboloid	Hyperboloid	NNP
10_1101-2021_01_08_425885	1008	151	Ring	Ring	NNP
10_1101-2021_01_08_425885	1008	152	Torus	Torus	NNP
10_1101-2021_01_08_425885	1008	153	Hypercube	Hypercube	NNP
10_1101-2021_01_08_425885	1008	154	Practical	Practical	NNP
10_1101-2021_01_08_425885	1008	155	Issues	Issues	NNPS
10_1101-2021_01_08_425885	1008	156	for	for	IN
10_1101-2021_01_08_425885	1008	157	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	1008	158	Estimation	Estimation	NNP
10_1101-2021_01_08_425885	1008	159	on	on	IN
10_1101-2021_01_08_425885	1008	160	Real	real	JJ
10_1101-2021_01_08_425885	1008	161	-	-	HYPH
10_1101-2021_01_08_425885	1008	162	World	world	NN
10_1101-2021_01_08_425885	1008	163	Datasets	dataset	NNS
10_1101-2021_01_08_425885	1008	164	Non	non	JJ
10_1101-2021_01_08_425885	1008	165	-	-	JJ
10_1101-2021_01_08_425885	1008	166	Uniform	uniform	JJ
10_1101-2021_01_08_425885	1008	167	Sampling	Sampling	NNP
10_1101-2021_01_08_425885	1008	168	Observational	Observational	NNP
10_1101-2021_01_08_425885	1008	169	Noise	Noise	NNP
10_1101-2021_01_08_425885	1008	170	Large	Large	NNP
10_1101-2021_01_08_425885	1008	171	Ambient	Ambient	NNP
10_1101-2021_01_08_425885	1008	172	Dimension	Dimension	NNP
10_1101-2021_01_08_425885	1008	173	Choice	Choice	NNP
10_1101-2021_01_08_425885	1008	174	of	of	IN
10_1101-2021_01_08_425885	1008	175	Manifold	Manifold	NNP
10_1101-2021_01_08_425885	1008	176	Dimension	Dimension	NNP
10_1101-2021_01_08_425885	1008	177	Parameters	Parameters	NNPS
10_1101-2021_01_08_425885	1008	178	for	for	IN
10_1101-2021_01_08_425885	1008	179	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	1008	180	Estimation	Estimation	NNP
10_1101-2021_01_08_425885	1008	181	Details	Details	NNPS
10_1101-2021_01_08_425885	1008	182	of	of	IN
10_1101-2021_01_08_425885	1008	183	Image	Image	NNP
10_1101-2021_01_08_425885	1008	184	Patch	Patch	NNP
10_1101-2021_01_08_425885	1008	185	Dataset	Dataset	NNP
10_1101-2021_01_08_425885	1008	186	and	and	CC
10_1101-2021_01_08_425885	1008	187	Klein	Klein	NNP
10_1101-2021_01_08_425885	1008	188	Bottle	Bottle	NNP
10_1101-2021_01_08_425885	1008	189	Manifolds	Manifolds	NNPS
10_1101-2021_01_08_425885	1008	190	Notation	Notation	NNP
10_1101-2021_01_08_425885	1008	191	and	and	CC
10_1101-2021_01_08_425885	1008	192	Preliminaries	Preliminaries	NNPS
10_1101-2021_01_08_425885	1008	193	Image	Image	NNP
10_1101-2021_01_08_425885	1008	194	Dataset	Dataset	NNP
10_1101-2021_01_08_425885	1008	195	Parametric	Parametric	NNP
10_1101-2021_01_08_425885	1008	196	Family	Family	NNP
10_1101-2021_01_08_425885	1008	197	of	of	IN
10_1101-2021_01_08_425885	1008	198	Klein	Klein	NNP
10_1101-2021_01_08_425885	1008	199	Bottle	Bottle	NNP
10_1101-2021_01_08_425885	1008	200	Embeddings	Embeddings	NNP
10_1101-2021_01_08_425885	1008	201	Associating	Associating	NNP
10_1101-2021_01_08_425885	1008	202	Image	image	NN
10_1101-2021_01_08_425885	1008	203	Patches	Patches	NNPS
10_1101-2021_01_08_425885	1008	204	to	to	IN
10_1101-2021_01_08_425885	1008	205	a	a	DT
10_1101-2021_01_08_425885	1008	206	Klein	Klein	NNP
10_1101-2021_01_08_425885	1008	207	Bottle	Bottle	NNP
10_1101-2021_01_08_425885	1008	208	Embedding	embed	VBG
10_1101-2021_01_08_425885	1008	209	Optimal	Optimal	NNP
10_1101-2021_01_08_425885	1008	210	Klein	Klein	NNP
10_1101-2021_01_08_425885	1008	211	Bottle	bottle	NN
10_1101-2021_01_08_425885	1008	212	Embedding	embed	VBG
10_1101-2021_01_08_425885	1008	213	Noisy	Noisy	NNP
10_1101-2021_01_08_425885	1008	214	Klein	Klein	NNP
10_1101-2021_01_08_425885	1008	215	Bottle	Bottle	NNP
10_1101-2021_01_08_425885	1008	216	Embeddings	Embeddings	NNP
10_1101-2021_01_08_425885	1008	217	Parameters	Parameters	NNPS
10_1101-2021_01_08_425885	1008	218	for	for	IN
10_1101-2021_01_08_425885	1008	219	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	1008	220	Estimation	Estimation	NNP
10_1101-2021_01_08_425885	1008	221	Details	Details	NNPS
10_1101-2021_01_08_425885	1008	222	of	of	IN
10_1101-2021_01_08_425885	1008	223	scRNASeq	scRNASeq	NNP
10_1101-2021_01_08_425885	1008	224	Datasets	dataset	VBZ
10_1101-2021_01_08_425885	1008	225	Preprocessing	preprocesse	VBG
10_1101-2021_01_08_425885	1008	226	Cell	Cell	NNP
10_1101-2021_01_08_425885	1008	227	Type	Type	NNP
10_1101-2021_01_08_425885	1008	228	Annotations	Annotations	NNP
10_1101-2021_01_08_425885	1008	229	Statistical	Statistical	NNP
10_1101-2021_01_08_425885	1008	230	Tests	Tests	NNPS
10_1101-2021_01_08_425885	1008	231	Spatial	Spatial	NNP
10_1101-2021_01_08_425885	1008	232	Precision	Precision	NNP
10_1101-2021_01_08_425885	1008	233	of	of	IN
10_1101-2021_01_08_425885	1008	234	Errorbars	Errorbars	NNPS
10_1101-2021_01_08_425885	1008	235	Sensitivity	Sensitivity	NNP
10_1101-2021_01_08_425885	1008	236	to	to	IN
10_1101-2021_01_08_425885	1008	237	Cell	Cell	NNP
10_1101-2021_01_08_425885	1008	238	Downsampling	downsample	VBG
10_1101-2021_01_08_425885	1008	239	Sensitivity	sensitivity	NN
10_1101-2021_01_08_425885	1008	240	to	to	IN
10_1101-2021_01_08_425885	1008	241	Transcript	Transcript	NNP
10_1101-2021_01_08_425885	1008	242	Downsampling	Downsampling	NNP
10_1101-2021_01_08_425885	1008	243	Parameters	Parameters	NNPS
10_1101-2021_01_08_425885	1008	244	for	for	IN
10_1101-2021_01_08_425885	1008	245	Curvature	Curvature	NNP
10_1101-2021_01_08_425885	1008	246	Estimation	Estimation	NNP
10_1101-2021_01_08_425885	1008	247	Acknowledgements	Acknowledgements	NNPS
10_1101-2021_01_08_425885	1008	248	Data	Data	NNPS
10_1101-2021_01_08_425885	1008	249	and	and	CC
10_1101-2021_01_08_425885	1008	250	Code	Code	NNP
10_1101-2021_01_08_425885	1008	251	Availability	Availability	NNP
10_1101-2021_01_08_425885	1008	252	Supplementary	Supplementary	NNP
10_1101-2021_01_08_425885	1008	253	Figures	Figures	NNPS
10_1101-2021_01_08_425885	1008	254	References	reference	NNS