id sid tid token lemma pos q811kh06t41 1 1 the the DET q811kh06t41 1 2 most most ADV q811kh06t41 1 3 important important ADJ q811kh06t41 1 4 error error NOUN q811kh06t41 1 5 - - PUNCT q811kh06t41 1 6 generating generate VERB q811kh06t41 1 7 events event NOUN q811kh06t41 1 8 in in ADP q811kh06t41 1 9 network network NOUN q811kh06t41 1 10 control control NOUN q811kh06t41 1 11 systems system NOUN q811kh06t41 1 12 are be AUX q811kh06t41 1 13 known know VERB q811kh06t41 1 14 to to PART q811kh06t41 1 15 be be AUX q811kh06t41 1 16 : : PUNCT q811kh06t41 1 17 time time NOUN q811kh06t41 1 18 - - PUNCT q811kh06t41 1 19 variant variant NOUN q811kh06t41 1 20 communication communication NOUN q811kh06t41 1 21 delays delay NOUN q811kh06t41 1 22 , , PUNCT q811kh06t41 1 23 packet packet NOUN q811kh06t41 1 24 drops drop VERB q811kh06t41 1 25 , , PUNCT q811kh06t41 1 26 bandwidth bandwidth ADJ q811kh06t41 1 27 limitations limitation NOUN q811kh06t41 1 28 , , PUNCT q811kh06t41 1 29 and and CCONJ q811kh06t41 1 30 synchronization synchronization NOUN q811kh06t41 1 31 errors error NOUN q811kh06t41 1 32 . . PUNCT q811kh06t41 2 1 synchronization synchronization NOUN q811kh06t41 2 2 errors error NOUN q811kh06t41 2 3 constitute constitute VERB q811kh06t41 2 4 an an DET q811kh06t41 2 5 important important ADJ q811kh06t41 2 6 and and CCONJ q811kh06t41 2 7 often often ADV q811kh06t41 2 8 overlooked overlook VERB q811kh06t41 2 9 network network NOUN q811kh06t41 2 10 induced induce VERB q811kh06t41 2 11 non non ADJ q811kh06t41 2 12 - - ADJ q811kh06t41 2 13 ideal ideal ADJ q811kh06t41 2 14 behavior behavior NOUN q811kh06t41 2 15 . . PUNCT q811kh06t41 3 1 little little ADJ q811kh06t41 3 2 is be AUX q811kh06t41 3 3 known know VERB q811kh06t41 3 4 about about ADP q811kh06t41 3 5 their their PRON q811kh06t41 3 6 effects effect NOUN q811kh06t41 3 7 on on ADP q811kh06t41 3 8 system system NOUN q811kh06t41 3 9 stability stability NOUN q811kh06t41 3 10 and and CCONJ q811kh06t41 3 11 performance performance NOUN q811kh06t41 3 12 robustness robustness NOUN q811kh06t41 3 13 . . PUNCT q811kh06t41 4 1 therefore therefore ADV q811kh06t41 4 2 studying study VERB q811kh06t41 4 3 and and CCONJ q811kh06t41 4 4 understanding understand VERB q811kh06t41 4 5 synchronization synchronization NOUN q811kh06t41 4 6 errors error NOUN q811kh06t41 4 7 is be AUX q811kh06t41 4 8 the the DET q811kh06t41 4 9 primary primary ADJ q811kh06t41 4 10 objective objective NOUN q811kh06t41 4 11 of of ADP q811kh06t41 4 12 this this DET q811kh06t41 4 13 thesis thesis NOUN q811kh06t41 4 14 . . PUNCT q811kh06t41 5 1 most most ADJ q811kh06t41 5 2 literature literature NOUN q811kh06t41 5 3 either either CCONJ q811kh06t41 5 4 assumes assume VERB q811kh06t41 5 5 that that SCONJ q811kh06t41 5 6 all all DET q811kh06t41 5 7 subsystems subsystem NOUN q811kh06t41 5 8 are be AUX q811kh06t41 5 9 working work VERB q811kh06t41 5 10 synchronously synchronously ADV q811kh06t41 5 11 or or CCONJ q811kh06t41 5 12 use use VERB q811kh06t41 5 13 a a DET q811kh06t41 5 14 continuous continuous ADJ q811kh06t41 5 15 - - PUNCT q811kh06t41 5 16 time time NOUN q811kh06t41 5 17 model model NOUN q811kh06t41 5 18 , , PUNCT q811kh06t41 5 19 to to PART q811kh06t41 5 20 circumvent circumvent VERB q811kh06t41 5 21 the the DET q811kh06t41 5 22 difficulties difficulty NOUN q811kh06t41 5 23 of of ADP q811kh06t41 5 24 the the DET q811kh06t41 5 25 desynchronized desynchronized ADJ q811kh06t41 5 26 discrete discrete ADJ q811kh06t41 5 27 - - PUNCT q811kh06t41 5 28 time time NOUN q811kh06t41 5 29 approach approach NOUN q811kh06t41 5 30 . . PUNCT q811kh06t41 6 1 only only ADV q811kh06t41 6 2 a a DET q811kh06t41 6 3 few few ADJ q811kh06t41 6 4 papers paper NOUN q811kh06t41 6 5 proposed propose VERB q811kh06t41 6 6 a a DET q811kh06t41 6 7 desynchronized desynchronized ADJ q811kh06t41 6 8 discrete discrete ADJ q811kh06t41 6 9 time time NOUN q811kh06t41 6 10 model model NOUN q811kh06t41 6 11 , , PUNCT q811kh06t41 6 12 using use VERB q811kh06t41 6 13 certain certain ADJ q811kh06t41 6 14 idealized idealized ADJ q811kh06t41 6 15 assumptions assumption NOUN q811kh06t41 6 16 . . PUNCT q811kh06t41 7 1 in in ADP q811kh06t41 7 2 this this DET q811kh06t41 7 3 thesis thesis NOUN q811kh06t41 7 4 we we PRON q811kh06t41 7 5 present present VERB q811kh06t41 7 6 two two NUM q811kh06t41 7 7 new new ADJ q811kh06t41 7 8 models model NOUN q811kh06t41 7 9 that that PRON q811kh06t41 7 10 efficiently efficiently ADV q811kh06t41 7 11 capture capture VERB q811kh06t41 7 12 the the DET q811kh06t41 7 13 salient salient ADJ q811kh06t41 7 14 effects effect NOUN q811kh06t41 7 15 of of ADP q811kh06t41 7 16 synchronization synchronization NOUN q811kh06t41 7 17 errors error NOUN q811kh06t41 7 18 in in ADP q811kh06t41 7 19 interconnected interconnect VERB q811kh06t41 7 20 discrete discrete ADJ q811kh06t41 7 21 - - PUNCT q811kh06t41 7 22 time time NOUN q811kh06t41 7 23 systems system NOUN q811kh06t41 7 24 : : PUNCT q811kh06t41 7 25 a a DET q811kh06t41 7 26 state state NOUN q811kh06t41 7 27 - - PUNCT q811kh06t41 7 28 space space NOUN q811kh06t41 7 29 based base VERB q811kh06t41 7 30 model model NOUN q811kh06t41 7 31 , , PUNCT q811kh06t41 7 32 and and CCONJ q811kh06t41 7 33 a a DET q811kh06t41 7 34 system system NOUN q811kh06t41 7 35 description description NOUN q811kh06t41 7 36 based base VERB q811kh06t41 7 37 on on ADP q811kh06t41 7 38 infinite infinite ADJ q811kh06t41 7 39 dimensional dimensional ADJ q811kh06t41 7 40 toeplitz toeplitz NOUN q811kh06t41 7 41 like like ADP q811kh06t41 7 42 operators operator NOUN q811kh06t41 7 43 . . PUNCT q811kh06t41 8 1 we we PRON q811kh06t41 8 2 first first ADJ q811kh06t41 8 3 model model NOUN q811kh06t41 8 4 and and CCONJ q811kh06t41 8 5 perform perform VERB q811kh06t41 8 6 stability stability NOUN q811kh06t41 8 7 analysis analysis NOUN q811kh06t41 8 8 for for ADP q811kh06t41 8 9 systems system NOUN q811kh06t41 8 10 with with ADP q811kh06t41 8 11 identical identical ADJ q811kh06t41 8 12 clock clock NOUN q811kh06t41 8 13 frequencies frequency NOUN q811kh06t41 8 14 that that PRON q811kh06t41 8 15 are be AUX q811kh06t41 8 16 operating operate VERB q811kh06t41 8 17 asynchronously asynchronously ADV q811kh06t41 8 18 . . PUNCT q811kh06t41 9 1 this this DET q811kh06t41 9 2 class class NOUN q811kh06t41 9 3 of of ADP q811kh06t41 9 4 systems system NOUN q811kh06t41 9 5 finds find VERB q811kh06t41 9 6 applications application NOUN q811kh06t41 9 7 in in ADP q811kh06t41 9 8 high high ADJ q811kh06t41 9 9 - - PUNCT q811kh06t41 9 10 speed speed NOUN q811kh06t41 9 11 circuitry circuitry NOUN q811kh06t41 9 12 . . PUNCT q811kh06t41 10 1 the the DET q811kh06t41 10 2 introduced introduce VERB q811kh06t41 10 3 stability stability NOUN q811kh06t41 10 4 analysis analysis NOUN q811kh06t41 10 5 utilizes utilize VERB q811kh06t41 10 6 spectral spectral ADJ q811kh06t41 10 7 methods method NOUN q811kh06t41 10 8 , , PUNCT q811kh06t41 10 9 and and CCONJ q811kh06t41 10 10 a a DET q811kh06t41 10 11 proposed propose VERB q811kh06t41 10 12 fault fault NOUN q811kh06t41 10 13 detection detection NOUN q811kh06t41 10 14 algorithm algorithm PROPN q811kh06t41 10 15 identifies identify VERB q811kh06t41 10 16 desynchronized desynchronized PROPN q811kh06t41 10 17 sub sub NOUN q811kh06t41 10 18 - - NOUN q811kh06t41 10 19 systems system NOUN q811kh06t41 10 20 . . PUNCT q811kh06t41 11 1 for for ADP q811kh06t41 11 2 the the DET q811kh06t41 11 3 case case NOUN q811kh06t41 11 4 of of ADP q811kh06t41 11 5 a a DET q811kh06t41 11 6 two two NUM q811kh06t41 11 7 system system NOUN q811kh06t41 11 8 control control NOUN q811kh06t41 11 9 loop loop NOUN q811kh06t41 11 10 , , PUNCT q811kh06t41 11 11 it it PRON q811kh06t41 11 12 is be AUX q811kh06t41 11 13 shown show VERB q811kh06t41 11 14 that that SCONJ q811kh06t41 11 15 the the DET q811kh06t41 11 16 nature nature NOUN q811kh06t41 11 17 of of ADP q811kh06t41 11 18 the the DET q811kh06t41 11 19 period period NOUN q811kh06t41 11 20 ratio ratio NOUN q811kh06t41 11 21 $ $ SYM q811kh06t41 11 22 frac{t_1}{t_2}$ frac{t_1}{t_2}$ NOUN q811kh06t41 11 23 profoundly profoundly ADV q811kh06t41 11 24 affects affect VERB q811kh06t41 11 25 system system NOUN q811kh06t41 11 26 behavior behavior NOUN q811kh06t41 11 27 . . PUNCT q811kh06t41 12 1 the the DET q811kh06t41 12 2 case case NOUN q811kh06t41 12 3 of of ADP q811kh06t41 12 4 commensurate commensurate ADJ q811kh06t41 12 5 rates rate NOUN q811kh06t41 12 6 $ $ SYM q811kh06t41 12 7 frac{t_1}{t_2}$ frac{t_1}{t_2}$ NOUN q811kh06t41 12 8 is be AUX q811kh06t41 12 9 tackled tackle VERB q811kh06t41 12 10 using use VERB q811kh06t41 12 11 both both PRON q811kh06t41 12 12 , , PUNCT q811kh06t41 12 13 the the DET q811kh06t41 12 14 state state NOUN q811kh06t41 12 15 - - PUNCT q811kh06t41 12 16 space space NOUN q811kh06t41 12 17 approach approach NOUN q811kh06t41 12 18 and and CCONJ q811kh06t41 12 19 the the DET q811kh06t41 12 20 infinite infinite ADJ q811kh06t41 12 21 - - PUNCT q811kh06t41 12 22 dimensional dimensional ADJ q811kh06t41 12 23 operator operator NOUN q811kh06t41 12 24 approach approach NOUN q811kh06t41 12 25 . . PUNCT q811kh06t41 13 1 from from ADP q811kh06t41 13 2 the the DET q811kh06t41 13 3 state state NOUN q811kh06t41 13 4 - - PUNCT q811kh06t41 13 5 space space NOUN q811kh06t41 13 6 description description NOUN q811kh06t41 13 7 it it PRON q811kh06t41 13 8 follows follow VERB q811kh06t41 13 9 that that SCONJ q811kh06t41 13 10 the the DET q811kh06t41 13 11 system system NOUN q811kh06t41 13 12 is be AUX q811kh06t41 13 13 equivalent equivalent ADJ q811kh06t41 13 14 to to ADP q811kh06t41 13 15 a a DET q811kh06t41 13 16 periodic periodic ADJ q811kh06t41 13 17 , , PUNCT q811kh06t41 13 18 time time NOUN q811kh06t41 13 19 - - PUNCT q811kh06t41 13 20 variant variant NOUN q811kh06t41 13 21 , , PUNCT q811kh06t41 13 22 discrete discrete ADJ q811kh06t41 13 23 - - PUNCT q811kh06t41 13 24 time time NOUN q811kh06t41 13 25 system system NOUN q811kh06t41 13 26 . . PUNCT q811kh06t41 14 1 stability stability NOUN q811kh06t41 14 2 analysis analysis NOUN q811kh06t41 14 3 is be AUX q811kh06t41 14 4 then then ADV q811kh06t41 14 5 performed perform VERB q811kh06t41 14 6 using use VERB q811kh06t41 14 7 the the DET q811kh06t41 14 8 classical classical ADJ q811kh06t41 14 9 spectral spectral ADJ q811kh06t41 14 10 techniques technique NOUN q811kh06t41 14 11 . . PUNCT q811kh06t41 15 1 the the DET q811kh06t41 15 2 toeplitz toeplitz PROPN q811kh06t41 15 3 based base VERB q811kh06t41 15 4 approach approach NOUN q811kh06t41 15 5 reveals reveal VERB q811kh06t41 15 6 an an DET q811kh06t41 15 7 underlying underlie VERB q811kh06t41 15 8 periodic periodic ADJ q811kh06t41 15 9 matrix matrix NOUN q811kh06t41 15 10 block block NOUN q811kh06t41 15 11 pattern pattern NOUN q811kh06t41 15 12 in in ADP q811kh06t41 15 13 the the DET q811kh06t41 15 14 infinite infinite ADJ q811kh06t41 15 15 - - PUNCT q811kh06t41 15 16 dimensional dimensional ADJ q811kh06t41 15 17 matrix matrix NOUN q811kh06t41 15 18 representation representation NOUN q811kh06t41 15 19 . . PUNCT q811kh06t41 16 1 this this DET q811kh06t41 16 2 periodicity periodicity NOUN q811kh06t41 16 3 property property NOUN q811kh06t41 16 4 is be AUX q811kh06t41 16 5 utilized utilize VERB q811kh06t41 16 6 to to PART q811kh06t41 16 7 derive derive VERB q811kh06t41 16 8 equivalent equivalent ADJ q811kh06t41 16 9 stability stability NOUN q811kh06t41 16 10 conditions condition NOUN q811kh06t41 16 11 . . PUNCT q811kh06t41 17 1 finally finally ADV q811kh06t41 17 2 , , PUNCT q811kh06t41 17 3 we we PRON q811kh06t41 17 4 investigate investigate VERB q811kh06t41 17 5 the the DET q811kh06t41 17 6 case case NOUN q811kh06t41 17 7 of of ADP q811kh06t41 17 8 irrational irrational ADJ q811kh06t41 17 9 ratios ratio NOUN q811kh06t41 17 10 $ $ SYM q811kh06t41 17 11 frac{t_1}{t_2}$ frac{t_1}{t_2}$ NOUN q811kh06t41 17 12 , , PUNCT q811kh06t41 17 13 using use VERB q811kh06t41 17 14 the the DET q811kh06t41 17 15 two two NUM q811kh06t41 17 16 above above ADV q811kh06t41 17 17 - - PUNCT q811kh06t41 17 18 mentioned mention VERB q811kh06t41 17 19 approaches approach NOUN q811kh06t41 17 20 . . PUNCT q811kh06t41 18 1 it it PRON q811kh06t41 18 2 is be AUX q811kh06t41 18 3 shown show VERB q811kh06t41 18 4 that that SCONJ q811kh06t41 18 5 the the DET q811kh06t41 18 6 infinite infinite ADJ q811kh06t41 18 7 - - PUNCT q811kh06t41 18 8 dimensional dimensional ADJ q811kh06t41 18 9 matrix matrix NOUN q811kh06t41 18 10 representation representation NOUN q811kh06t41 18 11 always always ADV q811kh06t41 18 12 admits admit VERB q811kh06t41 18 13 a a DET q811kh06t41 18 14 sparse sparse ADJ q811kh06t41 18 15 factorization factorization NOUN q811kh06t41 18 16 . . PUNCT q811kh06t41 19 1 this this DET q811kh06t41 19 2 amazing amazing ADJ q811kh06t41 19 3 property property NOUN q811kh06t41 19 4 will will AUX q811kh06t41 19 5 enable enable VERB q811kh06t41 19 6 the the DET q811kh06t41 19 7 formulation formulation NOUN q811kh06t41 19 8 of of ADP q811kh06t41 19 9 future future ADJ q811kh06t41 19 10 stability stability NOUN q811kh06t41 19 11 conditions condition NOUN q811kh06t41 19 12 and and CCONJ q811kh06t41 19 13 computationally computationally ADV q811kh06t41 19 14 efficient efficient ADJ q811kh06t41 19 15 algorithms algorithm NOUN q811kh06t41 19 16 . . PUNCT q811kh06t41 20 1 based base VERB q811kh06t41 20 2 on on ADP q811kh06t41 20 3 the the DET q811kh06t41 20 4 state state NOUN q811kh06t41 20 5 - - PUNCT q811kh06t41 20 6 space space NOUN q811kh06t41 20 7 model model NOUN q811kh06t41 20 8 , , PUNCT q811kh06t41 20 9 a a DET q811kh06t41 20 10 sufficient sufficient ADJ q811kh06t41 20 11 stability stability NOUN q811kh06t41 20 12 condition condition NOUN q811kh06t41 20 13 is be AUX q811kh06t41 20 14 derived derive VERB q811kh06t41 20 15 , , PUNCT q811kh06t41 20 16 that that PRON q811kh06t41 20 17 can can AUX q811kh06t41 20 18 be be AUX q811kh06t41 20 19 made make VERB q811kh06t41 20 20 arbitrarily arbitrarily ADV q811kh06t41 20 21 close close ADJ q811kh06t41 20 22 to to ADP q811kh06t41 20 23 being be AUX q811kh06t41 20 24 necessary necessary ADJ q811kh06t41 20 25 at at ADP q811kh06t41 20 26 the the DET q811kh06t41 20 27 expense expense NOUN q811kh06t41 20 28 of of ADP q811kh06t41 20 29 increased increase VERB q811kh06t41 20 30 computations computation NOUN q811kh06t41 20 31 . . PUNCT q811kh06t41 21 1 the the DET q811kh06t41 21 2 case case NOUN q811kh06t41 21 3 of of ADP q811kh06t41 21 4 period period NOUN q811kh06t41 21 5 ratio ratio NOUN q811kh06t41 21 6 uncertainties uncertainty NOUN q811kh06t41 21 7 is be AUX q811kh06t41 21 8 also also ADV q811kh06t41 21 9 addressed address VERB q811kh06t41 21 10 . . PUNCT