id sid tid token lemma pos cord-326314-9ycht8gi 1 1 key key NN cord-326314-9ycht8gi 1 2 : : : cord-326314-9ycht8gi 2 1 cord-326314 cord-326314 NNP cord-326314-9ycht8gi 2 2 - - HYPH cord-326314-9ycht8gi 2 3 9ycht8gi 9ycht8gi CD cord-326314-9ycht8gi 2 4 authors author NNS cord-326314-9ycht8gi 2 5 : : : cord-326314-9ycht8gi 2 6 Armstrong Armstrong NNP cord-326314-9ycht8gi 2 7 , , , cord-326314-9ycht8gi 2 8 Eve Eve NNP cord-326314-9ycht8gi 2 9 ; ; : cord-326314-9ycht8gi 2 10 Runge Runge NNP cord-326314-9ycht8gi 2 11 , , , cord-326314-9ycht8gi 2 12 Manuela Manuela NNP cord-326314-9ycht8gi 2 13 ; ; : cord-326314-9ycht8gi 2 14 Gerardin Gerardin NNP cord-326314-9ycht8gi 2 15 , , , cord-326314-9ycht8gi 2 16 Jaline Jaline NNP cord-326314-9ycht8gi 2 17 title title NN cord-326314-9ycht8gi 2 18 : : : cord-326314-9ycht8gi 2 19 Identifying identify VBG cord-326314-9ycht8gi 2 20 the the DT cord-326314-9ycht8gi 2 21 measurements measurement NNS cord-326314-9ycht8gi 2 22 required require VBN cord-326314-9ycht8gi 2 23 to to TO cord-326314-9ycht8gi 2 24 estimate estimate VB cord-326314-9ycht8gi 2 25 rates rate NNS cord-326314-9ycht8gi 2 26 of of IN cord-326314-9ycht8gi 2 27 COVID-19 covid-19 JJ cord-326314-9ycht8gi 2 28 transmission transmission NN cord-326314-9ycht8gi 2 29 , , , cord-326314-9ycht8gi 2 30 infection infection NN cord-326314-9ycht8gi 2 31 , , , cord-326314-9ycht8gi 2 32 and and CC cord-326314-9ycht8gi 2 33 detection detection NN cord-326314-9ycht8gi 2 34 , , , cord-326314-9ycht8gi 2 35 using use VBG cord-326314-9ycht8gi 2 36 variational variational JJ cord-326314-9ycht8gi 2 37 data datum NNS cord-326314-9ycht8gi 2 38 assimilation assimilation NN cord-326314-9ycht8gi 2 39 date date NN cord-326314-9ycht8gi 2 40 : : : cord-326314-9ycht8gi 2 41 2020 2020 CD cord-326314-9ycht8gi 2 42 - - HYPH cord-326314-9ycht8gi 2 43 11 11 CD cord-326314-9ycht8gi 2 44 - - HYPH cord-326314-9ycht8gi 2 45 02 02 CD cord-326314-9ycht8gi 2 46 journal journal NN cord-326314-9ycht8gi 2 47 : : : cord-326314-9ycht8gi 3 1 Infect infect VB cord-326314-9ycht8gi 3 2 Dis Dis NNP cord-326314-9ycht8gi 3 3 Model Model NNP cord-326314-9ycht8gi 3 4 DOI doi NN cord-326314-9ycht8gi 3 5 : : : cord-326314-9ycht8gi 3 6 10.1016 10.1016 CD cord-326314-9ycht8gi 3 7 / / SYM cord-326314-9ycht8gi 3 8 j.idm.2020.10.010 j.idm.2020.10.010 NNP cord-326314-9ycht8gi 3 9 sha sha NNP cord-326314-9ycht8gi 3 10 : : : cord-326314-9ycht8gi 4 1 583564c42e6c7e41c9c83c2b6091e8f9061142f8 583564c42e6c7e41c9c83c2b6091e8f9061142f8 NNP cord-326314-9ycht8gi 4 2 doc_id doc_id CD cord-326314-9ycht8gi 4 3 : : : cord-326314-9ycht8gi 5 1 326314 326314 CD cord-326314-9ycht8gi 5 2 cord_uid cord_uid NN cord-326314-9ycht8gi 5 3 : : : cord-326314-9ycht8gi 6 1 9ycht8gi 9ycht8gi CD cord-326314-9ycht8gi 7 1 We -PRON- PRP cord-326314-9ycht8gi 7 2 demonstrate demonstrate VBP cord-326314-9ycht8gi 7 3 the the DT cord-326314-9ycht8gi 7 4 ability ability NN cord-326314-9ycht8gi 7 5 of of IN cord-326314-9ycht8gi 7 6 statistical statistical JJ cord-326314-9ycht8gi 7 7 data data NN cord-326314-9ycht8gi 7 8 assimilation assimilation NN cord-326314-9ycht8gi 7 9 ( ( -LRB- cord-326314-9ycht8gi 7 10 SDA SDA NNP cord-326314-9ycht8gi 7 11 ) ) -RRB- cord-326314-9ycht8gi 7 12 to to TO cord-326314-9ycht8gi 7 13 identify identify VB cord-326314-9ycht8gi 7 14 the the DT cord-326314-9ycht8gi 7 15 measurements measurement NNS cord-326314-9ycht8gi 7 16 required require VBN cord-326314-9ycht8gi 7 17 for for IN cord-326314-9ycht8gi 7 18 accurate accurate JJ cord-326314-9ycht8gi 7 19 state state NN cord-326314-9ycht8gi 7 20 and and CC cord-326314-9ycht8gi 7 21 parameter parameter NN cord-326314-9ycht8gi 7 22 estimation estimation NN cord-326314-9ycht8gi 7 23 in in IN cord-326314-9ycht8gi 7 24 an an DT cord-326314-9ycht8gi 7 25 epidemiological epidemiological JJ cord-326314-9ycht8gi 7 26 model model NN cord-326314-9ycht8gi 7 27 for for IN cord-326314-9ycht8gi 7 28 the the DT cord-326314-9ycht8gi 7 29 novel novel JJ cord-326314-9ycht8gi 7 30 coronavirus coronavirus NN cord-326314-9ycht8gi 7 31 disease disease NN cord-326314-9ycht8gi 7 32 COVID-19 COVID-19 NNP cord-326314-9ycht8gi 7 33 . . . cord-326314-9ycht8gi 8 1 Our -PRON- PRP$ cord-326314-9ycht8gi 8 2 context context NN cord-326314-9ycht8gi 8 3 is be VBZ cord-326314-9ycht8gi 8 4 an an DT cord-326314-9ycht8gi 8 5 effort effort NN cord-326314-9ycht8gi 8 6 to to TO cord-326314-9ycht8gi 8 7 inform inform VB cord-326314-9ycht8gi 8 8 policy policy NN cord-326314-9ycht8gi 8 9 regarding regard VBG cord-326314-9ycht8gi 8 10 social social JJ cord-326314-9ycht8gi 8 11 behavior behavior NN cord-326314-9ycht8gi 8 12 , , , cord-326314-9ycht8gi 8 13 to to TO cord-326314-9ycht8gi 8 14 mitigate mitigate VB cord-326314-9ycht8gi 8 15 strain strain NN cord-326314-9ycht8gi 8 16 on on IN cord-326314-9ycht8gi 8 17 hospital hospital NN cord-326314-9ycht8gi 8 18 capacity capacity NN cord-326314-9ycht8gi 8 19 . . . cord-326314-9ycht8gi 9 1 The the DT cord-326314-9ycht8gi 9 2 model model NN cord-326314-9ycht8gi 9 3 unknowns unknown NNS cord-326314-9ycht8gi 9 4 are be VBP cord-326314-9ycht8gi 9 5 taken take VBN cord-326314-9ycht8gi 9 6 to to TO cord-326314-9ycht8gi 9 7 be be VB cord-326314-9ycht8gi 9 8 : : : cord-326314-9ycht8gi 9 9 the the DT cord-326314-9ycht8gi 9 10 time time NN cord-326314-9ycht8gi 9 11 - - HYPH cord-326314-9ycht8gi 9 12 varying vary VBG cord-326314-9ycht8gi 9 13 transmission transmission NN cord-326314-9ycht8gi 9 14 rate rate NN cord-326314-9ycht8gi 9 15 , , , cord-326314-9ycht8gi 9 16 the the DT cord-326314-9ycht8gi 9 17 fraction fraction NN cord-326314-9ycht8gi 9 18 of of IN cord-326314-9ycht8gi 9 19 exposed expose VBN cord-326314-9ycht8gi 9 20 cases case NNS cord-326314-9ycht8gi 9 21 that that WDT cord-326314-9ycht8gi 9 22 require require VBP cord-326314-9ycht8gi 9 23 hospitalization hospitalization NN cord-326314-9ycht8gi 9 24 , , , cord-326314-9ycht8gi 9 25 and and CC cord-326314-9ycht8gi 9 26 the the DT cord-326314-9ycht8gi 9 27 time time NN cord-326314-9ycht8gi 9 28 - - HYPH cord-326314-9ycht8gi 9 29 varying vary VBG cord-326314-9ycht8gi 9 30 detection detection NN cord-326314-9ycht8gi 9 31 probabilities probability NNS cord-326314-9ycht8gi 9 32 of of IN cord-326314-9ycht8gi 9 33 new new JJ cord-326314-9ycht8gi 9 34 asymptomatic asymptomatic JJ cord-326314-9ycht8gi 9 35 and and CC cord-326314-9ycht8gi 9 36 symptomatic symptomatic JJ cord-326314-9ycht8gi 9 37 cases case NNS cord-326314-9ycht8gi 9 38 . . . cord-326314-9ycht8gi 10 1 In in IN cord-326314-9ycht8gi 10 2 simulations simulation NNS cord-326314-9ycht8gi 10 3 , , , cord-326314-9ycht8gi 10 4 we -PRON- PRP cord-326314-9ycht8gi 10 5 obtain obtain VBP cord-326314-9ycht8gi 10 6 estimates estimate NNS cord-326314-9ycht8gi 10 7 of of IN cord-326314-9ycht8gi 10 8 undetected undetected JJ cord-326314-9ycht8gi 10 9 ( ( -LRB- cord-326314-9ycht8gi 10 10 that that RB cord-326314-9ycht8gi 10 11 is is RB cord-326314-9ycht8gi 10 12 , , , cord-326314-9ycht8gi 10 13 unmeasured unmeasured JJ cord-326314-9ycht8gi 10 14 ) ) -RRB- cord-326314-9ycht8gi 10 15 infectious infectious JJ cord-326314-9ycht8gi 10 16 populations population NNS cord-326314-9ycht8gi 10 17 , , , cord-326314-9ycht8gi 10 18 by by IN cord-326314-9ycht8gi 10 19 measuring measure VBG cord-326314-9ycht8gi 10 20 the the DT cord-326314-9ycht8gi 10 21 detected detect VBN cord-326314-9ycht8gi 10 22 cases case NNS cord-326314-9ycht8gi 10 23 together together RB cord-326314-9ycht8gi 10 24 with with IN cord-326314-9ycht8gi 10 25 the the DT cord-326314-9ycht8gi 10 26 recovered recovered JJ cord-326314-9ycht8gi 10 27 and and CC cord-326314-9ycht8gi 10 28 dead dead JJ cord-326314-9ycht8gi 10 29 - - : cord-326314-9ycht8gi 10 30 and and CC cord-326314-9ycht8gi 10 31 without without IN cord-326314-9ycht8gi 10 32 assumed assume VBN cord-326314-9ycht8gi 10 33 knowledge knowledge NN cord-326314-9ycht8gi 10 34 of of IN cord-326314-9ycht8gi 10 35 the the DT cord-326314-9ycht8gi 10 36 detection detection NN cord-326314-9ycht8gi 10 37 rates rate NNS cord-326314-9ycht8gi 10 38 . . . cord-326314-9ycht8gi 11 1 Given give VBN cord-326314-9ycht8gi 11 2 a a DT cord-326314-9ycht8gi 11 3 noiseless noiseless JJ cord-326314-9ycht8gi 11 4 measurement measurement NN cord-326314-9ycht8gi 11 5 of of IN cord-326314-9ycht8gi 11 6 the the DT cord-326314-9ycht8gi 11 7 recovered recover VBN cord-326314-9ycht8gi 11 8 population population NN cord-326314-9ycht8gi 11 9 , , , cord-326314-9ycht8gi 11 10 excellent excellent JJ cord-326314-9ycht8gi 11 11 estimates estimate NNS cord-326314-9ycht8gi 11 12 of of IN cord-326314-9ycht8gi 11 13 all all DT cord-326314-9ycht8gi 11 14 quantities quantity NNS cord-326314-9ycht8gi 11 15 are be VBP cord-326314-9ycht8gi 11 16 obtained obtain VBN cord-326314-9ycht8gi 11 17 using use VBG cord-326314-9ycht8gi 11 18 a a DT cord-326314-9ycht8gi 11 19 temporal temporal JJ cord-326314-9ycht8gi 11 20 baseline baseline NN cord-326314-9ycht8gi 11 21 of of IN cord-326314-9ycht8gi 11 22 101 101 CD cord-326314-9ycht8gi 11 23 days day NNS cord-326314-9ycht8gi 11 24 , , , cord-326314-9ycht8gi 11 25 with with IN cord-326314-9ycht8gi 11 26 the the DT cord-326314-9ycht8gi 11 27 exception exception NN cord-326314-9ycht8gi 11 28 of of IN cord-326314-9ycht8gi 11 29 the the DT cord-326314-9ycht8gi 11 30 time time NN cord-326314-9ycht8gi 11 31 - - HYPH cord-326314-9ycht8gi 11 32 varying vary VBG cord-326314-9ycht8gi 11 33 transmission transmission NN cord-326314-9ycht8gi 11 34 rate rate NN cord-326314-9ycht8gi 11 35 at at IN cord-326314-9ycht8gi 11 36 times time NNS cord-326314-9ycht8gi 11 37 prior prior RB cord-326314-9ycht8gi 11 38 to to IN cord-326314-9ycht8gi 11 39 the the DT cord-326314-9ycht8gi 11 40 implementation implementation NN cord-326314-9ycht8gi 11 41 of of IN cord-326314-9ycht8gi 11 42 social social JJ cord-326314-9ycht8gi 11 43 distancing distancing NN cord-326314-9ycht8gi 11 44 . . . cord-326314-9ycht8gi 12 1 With with IN cord-326314-9ycht8gi 12 2 low low JJ cord-326314-9ycht8gi 12 3 noise noise NN cord-326314-9ycht8gi 12 4 added add VBN cord-326314-9ycht8gi 12 5 to to IN cord-326314-9ycht8gi 12 6 the the DT cord-326314-9ycht8gi 12 7 recovered recover VBN cord-326314-9ycht8gi 12 8 population population NN cord-326314-9ycht8gi 12 9 , , , cord-326314-9ycht8gi 12 10 accurate accurate JJ cord-326314-9ycht8gi 12 11 state state NN cord-326314-9ycht8gi 12 12 estimates estimate NNS cord-326314-9ycht8gi 12 13 require require VBP cord-326314-9ycht8gi 12 14 a a DT cord-326314-9ycht8gi 12 15 lengthening lengthening NN cord-326314-9ycht8gi 12 16 of of IN cord-326314-9ycht8gi 12 17 the the DT cord-326314-9ycht8gi 12 18 temporal temporal JJ cord-326314-9ycht8gi 12 19 baseline baseline NN cord-326314-9ycht8gi 12 20 of of IN cord-326314-9ycht8gi 12 21 measurements measurement NNS cord-326314-9ycht8gi 12 22 . . . cord-326314-9ycht8gi 13 1 Estimates estimate NNS cord-326314-9ycht8gi 13 2 of of IN cord-326314-9ycht8gi 13 3 all all DT cord-326314-9ycht8gi 13 4 parameters parameter NNS cord-326314-9ycht8gi 13 5 are be VBP cord-326314-9ycht8gi 13 6 sensitive sensitive JJ cord-326314-9ycht8gi 13 7 to to IN cord-326314-9ycht8gi 13 8 the the DT cord-326314-9ycht8gi 13 9 contamination contamination NN cord-326314-9ycht8gi 13 10 , , , cord-326314-9ycht8gi 13 11 highlighting highlight VBG cord-326314-9ycht8gi 13 12 the the DT cord-326314-9ycht8gi 13 13 need need NN cord-326314-9ycht8gi 13 14 for for IN cord-326314-9ycht8gi 13 15 accurate accurate JJ cord-326314-9ycht8gi 13 16 and and CC cord-326314-9ycht8gi 13 17 uniform uniform JJ cord-326314-9ycht8gi 13 18 methods method NNS cord-326314-9ycht8gi 13 19 of of IN cord-326314-9ycht8gi 13 20 reporting reporting NN cord-326314-9ycht8gi 13 21 . . . cord-326314-9ycht8gi 14 1 The the DT cord-326314-9ycht8gi 14 2 aim aim NN cord-326314-9ycht8gi 14 3 of of IN cord-326314-9ycht8gi 14 4 this this DT cord-326314-9ycht8gi 14 5 paper paper NN cord-326314-9ycht8gi 14 6 is be VBZ cord-326314-9ycht8gi 14 7 to to TO cord-326314-9ycht8gi 14 8 exemplify exemplify VB cord-326314-9ycht8gi 14 9 the the DT cord-326314-9ycht8gi 14 10 power power NN cord-326314-9ycht8gi 14 11 of of IN cord-326314-9ycht8gi 14 12 SDA SDA NNP cord-326314-9ycht8gi 14 13 to to TO cord-326314-9ycht8gi 14 14 determine determine VB cord-326314-9ycht8gi 14 15 what what WP cord-326314-9ycht8gi 14 16 properties property NNS cord-326314-9ycht8gi 14 17 of of IN cord-326314-9ycht8gi 14 18 measurements measurement NNS cord-326314-9ycht8gi 14 19 will will MD cord-326314-9ycht8gi 14 20 yield yield VB cord-326314-9ycht8gi 14 21 estimates estimate NNS cord-326314-9ycht8gi 14 22 of of IN cord-326314-9ycht8gi 14 23 unknown unknown JJ cord-326314-9ycht8gi 14 24 parameters parameter NNS cord-326314-9ycht8gi 14 25 to to IN cord-326314-9ycht8gi 14 26 a a DT cord-326314-9ycht8gi 14 27 desired desire VBN cord-326314-9ycht8gi 14 28 precision precision NN cord-326314-9ycht8gi 14 29 , , , cord-326314-9ycht8gi 14 30 in in IN cord-326314-9ycht8gi 14 31 a a DT cord-326314-9ycht8gi 14 32 model model NN cord-326314-9ycht8gi 14 33 with with IN cord-326314-9ycht8gi 14 34 the the DT cord-326314-9ycht8gi 14 35 complexity complexity NN cord-326314-9ycht8gi 14 36 required require VBN cord-326314-9ycht8gi 14 37 to to TO cord-326314-9ycht8gi 14 38 capture capture VB cord-326314-9ycht8gi 14 39 important important JJ cord-326314-9ycht8gi 14 40 features feature NNS cord-326314-9ycht8gi 14 41 of of IN cord-326314-9ycht8gi 14 42 the the DT cord-326314-9ycht8gi 14 43 COVID-19 COVID-19 NNP cord-326314-9ycht8gi 14 44 pandemic pandemic NN cord-326314-9ycht8gi 14 45 . . . cord-326314-9ycht8gi 15 1 The the DT cord-326314-9ycht8gi 15 2 coronavirus coronavirus NN cord-326314-9ycht8gi 15 3 disease disease NN cord-326314-9ycht8gi 15 4 2019 2019 CD cord-326314-9ycht8gi 16 1 ( ( -LRB- cord-326314-9ycht8gi 16 2 COVID- COVID- NNP cord-326314-9ycht8gi 16 3 19 19 CD cord-326314-9ycht8gi 16 4 ) ) -RRB- cord-326314-9ycht8gi 16 5 is be VBZ cord-326314-9ycht8gi 16 6 burdening burden VBG cord-326314-9ycht8gi 16 7 health health NN cord-326314-9ycht8gi 16 8 care care NN cord-326314-9ycht8gi 16 9 systems system NNS cord-326314-9ycht8gi 16 10 worldwide worldwide RB cord-326314-9ycht8gi 16 11 , , , cord-326314-9ycht8gi 16 12 threatening threaten VBG cord-326314-9ycht8gi 16 13 physical physical JJ cord-326314-9ycht8gi 16 14 and and CC cord-326314-9ycht8gi 16 15 psychological psychological JJ cord-326314-9ycht8gi 16 16 health health NN cord-326314-9ycht8gi 16 17 , , , cord-326314-9ycht8gi 16 18 and and CC cord-326314-9ycht8gi 16 19 devastating devastate VBG cord-326314-9ycht8gi 16 20 the the DT cord-326314-9ycht8gi 16 21 global global JJ cord-326314-9ycht8gi 16 22 economy economy NN cord-326314-9ycht8gi 16 23 . . . cord-326314-9ycht8gi 17 1 Individual individual JJ cord-326314-9ycht8gi 17 2 countries country NNS cord-326314-9ycht8gi 17 3 and and CC cord-326314-9ycht8gi 17 4 states state NNS cord-326314-9ycht8gi 17 5 are be VBP cord-326314-9ycht8gi 17 6 tasked task VBN cord-326314-9ycht8gi 17 7 demonstrate demonstrate VBP cord-326314-9ycht8gi 17 8 the the DT cord-326314-9ycht8gi 17 9 power power NN cord-326314-9ycht8gi 17 10 and and CC cord-326314-9ycht8gi 17 11 versatility versatility NN cord-326314-9ycht8gi 17 12 of of IN cord-326314-9ycht8gi 17 13 the the DT cord-326314-9ycht8gi 17 14 SDA SDA NNP cord-326314-9ycht8gi 17 15 technique technique NN cord-326314-9ycht8gi 17 16 to to TO cord-326314-9ycht8gi 17 17 explore explore VB cord-326314-9ycht8gi 17 18 what what WP cord-326314-9ycht8gi 17 19 is be VBZ cord-326314-9ycht8gi 17 20 required require VBN cord-326314-9ycht8gi 17 21 of of IN cord-326314-9ycht8gi 17 22 measurements measurement NNS cord-326314-9ycht8gi 17 23 to to TO cord-326314-9ycht8gi 17 24 complete complete VB cord-326314-9ycht8gi 17 25 a a DT cord-326314-9ycht8gi 17 26 model model NN cord-326314-9ycht8gi 17 27 with with IN cord-326314-9ycht8gi 17 28 a a DT cord-326314-9ycht8gi 17 29 dimension dimension NN cord-326314-9ycht8gi 17 30 sufficiently sufficiently RB cord-326314-9ycht8gi 17 31 high high JJ cord-326314-9ycht8gi 17 32 to to TO cord-326314-9ycht8gi 17 33 capture capture VB cord-326314-9ycht8gi 17 34 the the DT cord-326314-9ycht8gi 17 35 policy policy NN cord-326314-9ycht8gi 17 36 - - HYPH cord-326314-9ycht8gi 17 37 relevant relevant JJ cord-326314-9ycht8gi 17 38 complexities complexity NNS cord-326314-9ycht8gi 17 39 of of IN cord-326314-9ycht8gi 17 40 COVID-19 covid-19 JJ cord-326314-9ycht8gi 17 41 transmission transmission NN cord-326314-9ycht8gi 17 42 and and CC cord-326314-9ycht8gi 17 43 containment containment NN cord-326314-9ycht8gi 17 44 -an -an NNS cord-326314-9ycht8gi 17 45 examination examination NN cord-326314-9ycht8gi 17 46 that that WDT cord-326314-9ycht8gi 17 47 has have VBZ cord-326314-9ycht8gi 17 48 not not RB cord-326314-9ycht8gi 17 49 previously previously RB cord-326314-9ycht8gi 17 50 been be VBN cord-326314-9ycht8gi 17 51 done do VBN cord-326314-9ycht8gi 17 52 . . . cord-326314-9ycht8gi 18 1 To to IN cord-326314-9ycht8gi 18 2 this this DT cord-326314-9ycht8gi 18 3 end end NN cord-326314-9ycht8gi 18 4 , , , cord-326314-9ycht8gi 18 5 we -PRON- PRP cord-326314-9ycht8gi 18 6 sought seek VBD cord-326314-9ycht8gi 18 7 to to TO cord-326314-9ycht8gi 18 8 estimate estimate VB cord-326314-9ycht8gi 18 9 the the DT cord-326314-9ycht8gi 18 10 parameters parameter NNS cord-326314-9ycht8gi 18 11 noted note VBN cord-326314-9ycht8gi 18 12 above above RB cord-326314-9ycht8gi 18 13 , , , cord-326314-9ycht8gi 18 14 using use VBG cord-326314-9ycht8gi 18 15 simulated simulated JJ cord-326314-9ycht8gi 18 16 data datum NNS cord-326314-9ycht8gi 18 17 representing represent VBG cord-326314-9ycht8gi 18 18 a a DT cord-326314-9ycht8gi 18 19 metropolitan metropolitan JJ cord-326314-9ycht8gi 18 20 - - HYPH cord-326314-9ycht8gi 18 21 area area NN cord-326314-9ycht8gi 18 22 population population NN cord-326314-9ycht8gi 18 23 loosely loosely RB cord-326314-9ycht8gi 18 24 based base VBN cord-326314-9ycht8gi 18 25 on on IN cord-326314-9ycht8gi 18 26 New New NNP cord-326314-9ycht8gi 18 27 York York NNP cord-326314-9ycht8gi 18 28 City City NNP cord-326314-9ycht8gi 18 29 . . . cord-326314-9ycht8gi 19 1 We -PRON- PRP cord-326314-9ycht8gi 19 2 examined examine VBD cord-326314-9ycht8gi 19 3 the the DT cord-326314-9ycht8gi 19 4 sensitivity sensitivity NN cord-326314-9ycht8gi 19 5 of of IN cord-326314-9ycht8gi 19 6 estimations estimation NNS cord-326314-9ycht8gi 19 7 to to IN cord-326314-9ycht8gi 19 8 : : : cord-326314-9ycht8gi 19 9 i i LS cord-326314-9ycht8gi 19 10 ) ) -RRB- cord-326314-9ycht8gi 19 11 the the DT cord-326314-9ycht8gi 19 12 subpopulations subpopulation NNS cord-326314-9ycht8gi 19 13 that that WDT cord-326314-9ycht8gi 19 14 were be VBD cord-326314-9ycht8gi 19 15 sampled sample VBN cord-326314-9ycht8gi 19 16 , , , cord-326314-9ycht8gi 19 17 ii ii LS cord-326314-9ycht8gi 19 18 ) ) -RRB- cord-326314-9ycht8gi 19 19 the the DT cord-326314-9ycht8gi 19 20 temporal temporal JJ cord-326314-9ycht8gi 19 21 baseline baseline NN cord-326314-9ycht8gi 19 22 of of IN cord-326314-9ycht8gi 19 23 sampling sampling NN cord-326314-9ycht8gi 19 24 , , , cord-326314-9ycht8gi 19 25 and and CC cord-326314-9ycht8gi 19 26 iii iii LS cord-326314-9ycht8gi 19 27 ) ) -RRB- cord-326314-9ycht8gi 19 28 uncertainty uncertainty NN cord-326314-9ycht8gi 19 29 in in IN cord-326314-9ycht8gi 19 30 the the DT cord-326314-9ycht8gi 19 31 sampling sampling NN cord-326314-9ycht8gi 19 32 . . . cord-326314-9ycht8gi 20 1 Results result NNS cord-326314-9ycht8gi 20 2 using use VBG cord-326314-9ycht8gi 20 3 simulated simulated JJ cord-326314-9ycht8gi 20 4 data datum NNS cord-326314-9ycht8gi 20 5 are be VBP cord-326314-9ycht8gi 20 6 threefold threefold JJ cord-326314-9ycht8gi 20 7 . . . cord-326314-9ycht8gi 21 1 First first RB cord-326314-9ycht8gi 21 2 , , , cord-326314-9ycht8gi 21 3 reasonable reasonable JJ cord-326314-9ycht8gi 21 4 estimations estimation NNS cord-326314-9ycht8gi 21 5 of of IN cord-326314-9ycht8gi 21 6 time time NN cord-326314-9ycht8gi 21 7 - - HYPH cord-326314-9ycht8gi 21 8 varying vary VBG cord-326314-9ycht8gi 21 9 detection detection NN cord-326314-9ycht8gi 21 10 probabilities probability NNS cord-326314-9ycht8gi 21 11 require require VBP cord-326314-9ycht8gi 21 12 the the DT cord-326314-9ycht8gi 21 13 reporting reporting NN cord-326314-9ycht8gi 21 14 of of IN cord-326314-9ycht8gi 21 15 new new JJ cord-326314-9ycht8gi 21 16 detected detected JJ cord-326314-9ycht8gi 21 17 cases case NNS cord-326314-9ycht8gi 21 18 ( ( -LRB- cord-326314-9ycht8gi 21 19 asymptomatic asymptomatic JJ cord-326314-9ycht8gi 21 20 and and CC cord-326314-9ycht8gi 21 21 symptomatic symptomatic JJ cord-326314-9ycht8gi 21 22 ) ) -RRB- cord-326314-9ycht8gi 21 23 , , , cord-326314-9ycht8gi 21 24 dead dead JJ cord-326314-9ycht8gi 21 25 , , , cord-326314-9ycht8gi 21 26 and and CC cord-326314-9ycht8gi 21 27 recovered recover VBD cord-326314-9ycht8gi 21 28 . . . cord-326314-9ycht8gi 22 1 Second second RB cord-326314-9ycht8gi 22 2 , , , cord-326314-9ycht8gi 22 3 given give VBN cord-326314-9ycht8gi 22 4 noiseless noiseless JJ cord-326314-9ycht8gi 22 5 measurements measurement NNS cord-326314-9ycht8gi 22 6 , , , cord-326314-9ycht8gi 22 7 a a DT cord-326314-9ycht8gi 22 8 temporal temporal JJ cord-326314-9ycht8gi 22 9 baseline baseline NN cord-326314-9ycht8gi 22 10 of of IN cord-326314-9ycht8gi 22 11 101 101 CD cord-326314-9ycht8gi 22 12 days day NNS cord-326314-9ycht8gi 22 13 is be VBZ cord-326314-9ycht8gi 22 14 sufficient sufficient JJ cord-326314-9ycht8gi 22 15 for for IN cord-326314-9ycht8gi 22 16 the the DT cord-326314-9ycht8gi 22 17 SDA SDA NNP cord-326314-9ycht8gi 22 18 procedure procedure NN cord-326314-9ycht8gi 22 19 to to TO cord-326314-9ycht8gi 22 20 capture capture VB cord-326314-9ycht8gi 22 21 the the DT cord-326314-9ycht8gi 22 22 general general JJ cord-326314-9ycht8gi 22 23 trends trend NNS cord-326314-9ycht8gi 22 24 in in IN cord-326314-9ycht8gi 22 25 the the DT cord-326314-9ycht8gi 22 26 evolution evolution NN cord-326314-9ycht8gi 22 27 of of IN cord-326314-9ycht8gi 22 28 the the DT cord-326314-9ycht8gi 22 29 model model NN cord-326314-9ycht8gi 22 30 populations population NNS cord-326314-9ycht8gi 22 31 , , , cord-326314-9ycht8gi 22 32 the the DT cord-326314-9ycht8gi 22 33 detection detection NN cord-326314-9ycht8gi 22 34 probabilities probability NNS cord-326314-9ycht8gi 22 35 , , , cord-326314-9ycht8gi 22 36 and and CC cord-326314-9ycht8gi 22 37 the the DT cord-326314-9ycht8gi 22 38 time time NN cord-326314-9ycht8gi 22 39 - - HYPH cord-326314-9ycht8gi 22 40 varying vary VBG cord-326314-9ycht8gi 22 41 transmission transmission NN cord-326314-9ycht8gi 22 42 rate rate NN cord-326314-9ycht8gi 22 43 following follow VBG cord-326314-9ycht8gi 22 44 the the DT cord-326314-9ycht8gi 22 45 implementation implementation NN cord-326314-9ycht8gi 22 46 of of IN cord-326314-9ycht8gi 22 47 social social JJ cord-326314-9ycht8gi 22 48 distancing distancing NN cord-326314-9ycht8gi 22 49 . . . cord-326314-9ycht8gi 23 1 Importantly importantly RB cord-326314-9ycht8gi 23 2 , , , cord-326314-9ycht8gi 23 3 the the DT cord-326314-9ycht8gi 23 4 information information NN cord-326314-9ycht8gi 23 5 contained contain VBN cord-326314-9ycht8gi 23 6 in in IN cord-326314-9ycht8gi 23 7 the the DT cord-326314-9ycht8gi 23 8 measured measure VBN cord-326314-9ycht8gi 23 9 detected detect VBN cord-326314-9ycht8gi 23 10 populations population NNS cord-326314-9ycht8gi 23 11 propagates propagate VBZ cord-326314-9ycht8gi 23 12 successfully successfully RB cord-326314-9ycht8gi 23 13 to to IN cord-326314-9ycht8gi 23 14 the the DT cord-326314-9ycht8gi 23 15 estimation estimation NN cord-326314-9ycht8gi 23 16 of of IN cord-326314-9ycht8gi 23 17 the the DT cord-326314-9ycht8gi 23 18 numbers number NNS cord-326314-9ycht8gi 23 19 of of IN cord-326314-9ycht8gi 23 20 severe severe JJ cord-326314-9ycht8gi 23 21 undetected undetected JJ cord-326314-9ycht8gi 23 22 cases case NNS cord-326314-9ycht8gi 23 23 . . . cord-326314-9ycht8gi 24 1 Third third RB cord-326314-9ycht8gi 24 2 , , , cord-326314-9ycht8gi 24 3 the the DT cord-326314-9ycht8gi 24 4 state state NN cord-326314-9ycht8gi 24 5 evolution evolution NN cord-326314-9ycht8gi 24 6 -and -and : cord-326314-9ycht8gi 24 7 importantly importantly RB cord-326314-9ycht8gi 24 8 the the DT cord-326314-9ycht8gi 24 9 populations population NNS cord-326314-9ycht8gi 24 10 requiring require VBG cord-326314-9ycht8gi 24 11 inpatient inpatient JJ cord-326314-9ycht8gi 24 12 care care NN cord-326314-9ycht8gi 24 13 -tolerates -tolerate VBZ cord-326314-9ycht8gi 24 14 low low JJ cord-326314-9ycht8gi 24 15 ( ( -LRB- cord-326314-9ycht8gi 24 16 ∼ ∼ NN cord-326314-9ycht8gi 24 17 five five CD cord-326314-9ycht8gi 24 18 percent percent NN cord-326314-9ycht8gi 24 19 ) ) -RRB- cord-326314-9ycht8gi 24 20 noise noise NN cord-326314-9ycht8gi 24 21 , , , cord-326314-9ycht8gi 24 22 given give VBN cord-326314-9ycht8gi 24 23 a a DT cord-326314-9ycht8gi 24 24 doubling doubling NN cord-326314-9ycht8gi 24 25 of of IN cord-326314-9ycht8gi 24 26 the the DT cord-326314-9ycht8gi 24 27 temporal temporal JJ cord-326314-9ycht8gi 24 28 baseline baseline NN cord-326314-9ycht8gi 24 29 of of IN cord-326314-9ycht8gi 24 30 measurements measurement NNS cord-326314-9ycht8gi 24 31 ; ; : cord-326314-9ycht8gi 24 32 the the DT cord-326314-9ycht8gi 24 33 parameter parameter NN cord-326314-9ycht8gi 24 34 estimates estimate NNS cord-326314-9ycht8gi 24 35 do do VBP cord-326314-9ycht8gi 24 36 not not RB cord-326314-9ycht8gi 24 37 tolerate tolerate VB cord-326314-9ycht8gi 24 38 this this DT cord-326314-9ycht8gi 24 39 contamination contamination NN cord-326314-9ycht8gi 24 40 . . . cord-326314-9ycht8gi 25 1 Finally finally RB cord-326314-9ycht8gi 25 2 , , , cord-326314-9ycht8gi 25 3 we -PRON- PRP cord-326314-9ycht8gi 25 4 discuss discuss VBP cord-326314-9ycht8gi 25 5 necessary necessary JJ cord-326314-9ycht8gi 25 6 modifications modification NNS cord-326314-9ycht8gi 25 7 prior prior RB cord-326314-9ycht8gi 25 8 to to IN cord-326314-9ycht8gi 25 9 testing test VBG cord-326314-9ycht8gi 25 10 with with IN cord-326314-9ycht8gi 25 11 real real JJ cord-326314-9ycht8gi 25 12 data datum NNS cord-326314-9ycht8gi 25 13 , , , cord-326314-9ycht8gi 25 14 including include VBG cord-326314-9ycht8gi 25 15 lowering lower VBG cord-326314-9ycht8gi 25 16 the the DT cord-326314-9ycht8gi 25 17 sensitivity sensitivity NN cord-326314-9ycht8gi 25 18 of of IN cord-326314-9ycht8gi 25 19 parameter parameter NN cord-326314-9ycht8gi 25 20 estimates estimate NNS cord-326314-9ycht8gi 25 21 to to IN cord-326314-9ycht8gi 25 22 noise noise NN cord-326314-9ycht8gi 25 23 in in IN cord-326314-9ycht8gi 25 24 data datum NNS cord-326314-9ycht8gi 25 25 . . . cord-326314-9ycht8gi 26 1 The the DT cord-326314-9ycht8gi 26 2 model model NN cord-326314-9ycht8gi 26 3 is be VBZ cord-326314-9ycht8gi 26 4 written write VBN cord-326314-9ycht8gi 26 5 in in IN cord-326314-9ycht8gi 26 6 22 22 CD cord-326314-9ycht8gi 26 7 state state NN cord-326314-9ycht8gi 26 8 variables variable NNS cord-326314-9ycht8gi 26 9 , , , cord-326314-9ycht8gi 26 10 each each DT cord-326314-9ycht8gi 26 11 representing represent VBG cord-326314-9ycht8gi 26 12 a a DT cord-326314-9ycht8gi 26 13 subpopulation subpopulation NN cord-326314-9ycht8gi 26 14 of of IN cord-326314-9ycht8gi 26 15 people people NNS cord-326314-9ycht8gi 26 16 ; ; : cord-326314-9ycht8gi 26 17 the the DT cord-326314-9ycht8gi 26 18 total total JJ cord-326314-9ycht8gi 26 19 population population NN cord-326314-9ycht8gi 26 20 is be VBZ cord-326314-9ycht8gi 26 21 conserved conserve VBN cord-326314-9ycht8gi 26 22 . . . cord-326314-9ycht8gi 27 1 Figure figure NN cord-326314-9ycht8gi 27 2 1 1 CD cord-326314-9ycht8gi 27 3 shows show VBZ cord-326314-9ycht8gi 27 4 a a DT cord-326314-9ycht8gi 27 5 schematic schematic NN cord-326314-9ycht8gi 27 6 of of IN cord-326314-9ycht8gi 27 7 the the DT cord-326314-9ycht8gi 27 8 model model NN cord-326314-9ycht8gi 27 9 structure structure NN cord-326314-9ycht8gi 27 10 . . . cord-326314-9ycht8gi 28 1 Each each DT cord-326314-9ycht8gi 28 2 member member NN cord-326314-9ycht8gi 28 3 of of IN cord-326314-9ycht8gi 28 4 a a DT cord-326314-9ycht8gi 28 5 Population Population NNP cord-326314-9ycht8gi 28 6 S S NNP cord-326314-9ycht8gi 28 7 that that WDT cord-326314-9ycht8gi 28 8 becomes become VBZ cord-326314-9ycht8gi 28 9 Exposed expose VBN cord-326314-9ycht8gi 28 10 ( ( -LRB- cord-326314-9ycht8gi 28 11 E e NN cord-326314-9ycht8gi 28 12 ) ) -RRB- cord-326314-9ycht8gi 28 13 ultimately ultimately RB cord-326314-9ycht8gi 28 14 reaches reach VBZ cord-326314-9ycht8gi 28 15 either either CC cord-326314-9ycht8gi 28 16 the the DT cord-326314-9ycht8gi 28 17 Recovered Recovered NNP cord-326314-9ycht8gi 28 18 ( ( -LRB- cord-326314-9ycht8gi 28 19 R r NN cord-326314-9ycht8gi 28 20 ) ) -RRB- cord-326314-9ycht8gi 28 21 or or CC cord-326314-9ycht8gi 28 22 Dead Dead NNP cord-326314-9ycht8gi 28 23 ( ( -LRB- cord-326314-9ycht8gi 28 24 D D NNP cord-326314-9ycht8gi 28 25 ) ) -RRB- cord-326314-9ycht8gi 28 26 state state NN cord-326314-9ycht8gi 28 27 . . . cord-326314-9ycht8gi 29 1 Absent absent JJ cord-326314-9ycht8gi 29 2 additive additive NN cord-326314-9ycht8gi 29 3 noise noise NN cord-326314-9ycht8gi 29 4 , , , cord-326314-9ycht8gi 29 5 the the DT cord-326314-9ycht8gi 29 6 model model NN cord-326314-9ycht8gi 29 7 is be VBZ cord-326314-9ycht8gi 29 8 deterministic deterministic JJ cord-326314-9ycht8gi 29 9 . . . cord-326314-9ycht8gi 30 1 Five five CD cord-326314-9ycht8gi 30 2 variables variable NNS cord-326314-9ycht8gi 30 3 correspond correspond VBP cord-326314-9ycht8gi 30 4 to to IN cord-326314-9ycht8gi 30 5 measured measure VBN cord-326314-9ycht8gi 30 6 quantities quantity NNS cord-326314-9ycht8gi 30 7 in in IN cord-326314-9ycht8gi 30 8 the the DT cord-326314-9ycht8gi 30 9 inference inference NN cord-326314-9ycht8gi 30 10 experiments experiment NNS cord-326314-9ycht8gi 30 11 . . . cord-326314-9ycht8gi 31 1 As as IN cord-326314-9ycht8gi 31 2 noted note VBN cord-326314-9ycht8gi 31 3 , , , cord-326314-9ycht8gi 31 4 the the DT cord-326314-9ycht8gi 31 5 model model NN cord-326314-9ycht8gi 31 6 is be VBZ cord-326314-9ycht8gi 31 7 written write VBN cord-326314-9ycht8gi 31 8 with with IN cord-326314-9ycht8gi 31 9 the the DT cord-326314-9ycht8gi 31 10 aim aim NN cord-326314-9ycht8gi 31 11 to to TO cord-326314-9ycht8gi 31 12 inform inform VB cord-326314-9ycht8gi 31 13 policy policy NN cord-326314-9ycht8gi 31 14 on on IN cord-326314-9ycht8gi 31 15 social social JJ cord-326314-9ycht8gi 31 16 behavior behavior NN cord-326314-9ycht8gi 31 17 and and CC cord-326314-9ycht8gi 31 18 contact contact NN cord-326314-9ycht8gi 31 19 tracing trace VBG cord-326314-9ycht8gi 31 20 so so IN cord-326314-9ycht8gi 31 21 as as IN cord-326314-9ycht8gi 31 22 to to TO cord-326314-9ycht8gi 31 23 avoid avoid VB cord-326314-9ycht8gi 31 24 exceeding exceed VBG cord-326314-9ycht8gi 31 25 hospital hospital NN cord-326314-9ycht8gi 31 26 capacity capacity NN cord-326314-9ycht8gi 31 27 . . . cord-326314-9ycht8gi 32 1 To to IN cord-326314-9ycht8gi 32 2 this this DT cord-326314-9ycht8gi 32 3 end end NN cord-326314-9ycht8gi 32 4 , , , cord-326314-9ycht8gi 32 5 the the DT cord-326314-9ycht8gi 32 6 model model NN cord-326314-9ycht8gi 32 7 resolves resolve VBZ cord-326314-9ycht8gi 32 8 asymptomatic asymptomatic JJ cord-326314-9ycht8gi 32 9 - - HYPH cord-326314-9ycht8gi 32 10 versus versus IN cord-326314-9ycht8gi 32 11 - - HYPH cord-326314-9ycht8gi 32 12 symptomatic symptomatic JJ cord-326314-9ycht8gi 32 13 cases case NNS cord-326314-9ycht8gi 32 14 , , , cord-326314-9ycht8gi 32 15 undetected undetected JJ cord-326314-9ycht8gi 32 16 - - HYPH cord-326314-9ycht8gi 32 17 versus versus NN cord-326314-9ycht8gi 32 18 - - HYPH cord-326314-9ycht8gi 32 19 detected detect VBN cord-326314-9ycht8gi 32 20 cases case NNS cord-326314-9ycht8gi 32 21 , , , cord-326314-9ycht8gi 32 22 and and CC cord-326314-9ycht8gi 32 23 the the DT cord-326314-9ycht8gi 32 24 two two CD cord-326314-9ycht8gi 32 25 tiers tier NNS cord-326314-9ycht8gi 32 26 of of IN cord-326314-9ycht8gi 32 27 hospital hospital NN cord-326314-9ycht8gi 32 28 needs need NNS cord-326314-9ycht8gi 32 29 : : : cord-326314-9ycht8gi 32 30 the the DT cord-326314-9ycht8gi 32 31 general general JJ cord-326314-9ycht8gi 32 32 ( ( -LRB- cord-326314-9ycht8gi 32 33 inpatient inpatient JJ cord-326314-9ycht8gi 32 34 , , , cord-326314-9ycht8gi 32 35 nonintensive nonintensive NNP cord-326314-9ycht8gi 32 36 care care NN cord-326314-9ycht8gi 32 37 unit unit NN cord-326314-9ycht8gi 32 38 ( ( -LRB- cord-326314-9ycht8gi 32 39 ICU ICU NNP cord-326314-9ycht8gi 32 40 ) ) -RRB- cord-326314-9ycht8gi 32 41 ) ) -RRB- cord-326314-9ycht8gi 33 1 H h NN cord-326314-9ycht8gi 33 2 versus versus IN cord-326314-9ycht8gi 33 3 the the DT cord-326314-9ycht8gi 33 4 critical critical JJ cord-326314-9ycht8gi 33 5 care care NN cord-326314-9ycht8gi 33 6 ( ( -LRB- cord-326314-9ycht8gi 33 7 ICU ICU NNP cord-326314-9ycht8gi 33 8 ) ) -RRB- cord-326314-9ycht8gi 33 9 C C NNP cord-326314-9ycht8gi 33 10 populations population NNS cord-326314-9ycht8gi 33 11 . . . cord-326314-9ycht8gi 34 1 The the DT cord-326314-9ycht8gi 34 2 resolution resolution NN cord-326314-9ycht8gi 34 3 of of IN cord-326314-9ycht8gi 34 4 asymptomatic asymptomatic JJ cord-326314-9ycht8gi 34 5 versus versus IN cord-326314-9ycht8gi 34 6 symptomatic symptomatic JJ cord-326314-9ycht8gi 34 7 cases case NNS cord-326314-9ycht8gi 34 8 was be VBD cord-326314-9ycht8gi 34 9 motivated motivate VBN cord-326314-9ycht8gi 34 10 by by IN cord-326314-9ycht8gi 34 11 an an DT cord-326314-9ycht8gi 34 12 interest interest NN cord-326314-9ycht8gi 34 13 in in IN cord-326314-9ycht8gi 34 14 what what WDT cord-326314-9ycht8gi 34 15 interventions intervention NNS cord-326314-9ycht8gi 34 16 are be VBP cord-326314-9ycht8gi 34 17 necessary necessary JJ cord-326314-9ycht8gi 34 18 to to TO cord-326314-9ycht8gi 34 19 control control VB cord-326314-9ycht8gi 34 20 the the DT cord-326314-9ycht8gi 34 21 epidemic epidemic NN cord-326314-9ycht8gi 34 22 . . . cord-326314-9ycht8gi 35 1 For for IN cord-326314-9ycht8gi 35 2 example example NN cord-326314-9ycht8gi 35 3 , , , cord-326314-9ycht8gi 35 4 is be VBZ cord-326314-9ycht8gi 35 5 it -PRON- PRP cord-326314-9ycht8gi 35 6 sufficient sufficient JJ cord-326314-9ycht8gi 35 7 to to TO cord-326314-9ycht8gi 35 8 focus focus VB cord-326314-9ycht8gi 35 9 only only RB cord-326314-9ycht8gi 35 10 on on IN cord-326314-9ycht8gi 35 11 symptomatic symptomatic JJ cord-326314-9ycht8gi 35 12 individuals individual NNS cord-326314-9ycht8gi 35 13 , , , cord-326314-9ycht8gi 35 14 or or CC cord-326314-9ycht8gi 35 15 must must MD cord-326314-9ycht8gi 35 16 we -PRON- PRP cord-326314-9ycht8gi 35 17 also also RB cord-326314-9ycht8gi 35 18 target target VB cord-326314-9ycht8gi 35 19 and and CC cord-326314-9ycht8gi 35 20 address address VB cord-326314-9ycht8gi 35 21 asymptomatic asymptomatic JJ cord-326314-9ycht8gi 35 22 individuals individual NNS cord-326314-9ycht8gi 35 23 who who WP cord-326314-9ycht8gi 35 24 may may MD cord-326314-9ycht8gi 35 25 not not RB cord-326314-9ycht8gi 35 26 even even RB cord-326314-9ycht8gi 35 27 realize realize VB cord-326314-9ycht8gi 35 28 they -PRON- PRP cord-326314-9ycht8gi 35 29 are be VBP cord-326314-9ycht8gi 35 30 infected infect VBN cord-326314-9ycht8gi 35 31 ? ? . cord-326314-9ycht8gi 36 1 The the DT cord-326314-9ycht8gi 36 2 detected detected JJ cord-326314-9ycht8gi 36 3 and and CC cord-326314-9ycht8gi 36 4 undetected undetected JJ cord-326314-9ycht8gi 36 5 populations population NNS cord-326314-9ycht8gi 36 6 exist exist VBP cord-326314-9ycht8gi 36 7 for for IN cord-326314-9ycht8gi 36 8 two two CD cord-326314-9ycht8gi 36 9 reasons reason NNS cord-326314-9ycht8gi 36 10 . . . cord-326314-9ycht8gi 37 1 First first RB cord-326314-9ycht8gi 37 2 , , , cord-326314-9ycht8gi 37 3 we -PRON- PRP cord-326314-9ycht8gi 37 4 seek seek VBP cord-326314-9ycht8gi 37 5 to to TO cord-326314-9ycht8gi 37 6 account account VB cord-326314-9ycht8gi 37 7 for for IN cord-326314-9ycht8gi 37 8 underreporting underreporting NN cord-326314-9ycht8gi 37 9 of of IN cord-326314-9ycht8gi 37 10 cases case NNS cord-326314-9ycht8gi 37 11 and and CC cord-326314-9ycht8gi 37 12 deaths death NNS cord-326314-9ycht8gi 37 13 . . . cord-326314-9ycht8gi 38 1 Second second RB cord-326314-9ycht8gi 38 2 , , , cord-326314-9ycht8gi 38 3 we -PRON- PRP cord-326314-9ycht8gi 38 4 desire desire VBP cord-326314-9ycht8gi 38 5 a a DT cord-326314-9ycht8gi 38 6 model model NN cord-326314-9ycht8gi 38 7 structure structure NN cord-326314-9ycht8gi 38 8 that that WDT cord-326314-9ycht8gi 38 9 can can MD cord-326314-9ycht8gi 38 10 simulate simulate VB cord-326314-9ycht8gi 38 11 the the DT cord-326314-9ycht8gi 38 12 impact impact NN cord-326314-9ycht8gi 38 13 of of IN cord-326314-9ycht8gi 38 14 increasing increase VBG cord-326314-9ycht8gi 38 15 detection detection NN cord-326314-9ycht8gi 38 16 rates rate NNS cord-326314-9ycht8gi 38 17 on on IN cord-326314-9ycht8gi 38 18 disease disease NN cord-326314-9ycht8gi 38 19 transmission transmission NN cord-326314-9ycht8gi 38 20 , , , cord-326314-9ycht8gi 38 21 including include VBG cord-326314-9ycht8gi 38 22 the the DT cord-326314-9ycht8gi 38 23 impact impact NN cord-326314-9ycht8gi 38 24 of of IN cord-326314-9ycht8gi 38 25 contact contact NN cord-326314-9ycht8gi 38 26 tracing tracing NN cord-326314-9ycht8gi 38 27 . . . cord-326314-9ycht8gi 39 1 Thus thus RB cord-326314-9ycht8gi 39 2 the the DT cord-326314-9ycht8gi 39 3 model model NN cord-326314-9ycht8gi 39 4 was be VBD cord-326314-9ycht8gi 39 5 3 3 CD cord-326314-9ycht8gi 39 6 J J NNP cord-326314-9ycht8gi 39 7 o o NN cord-326314-9ycht8gi 39 8 u u NN cord-326314-9ycht8gi 39 9 r r NN cord-326314-9ycht8gi 39 10 n n NN cord-326314-9ycht8gi 39 11 a a DT cord-326314-9ycht8gi 39 12 l l NN cord-326314-9ycht8gi 39 13 P p NN cord-326314-9ycht8gi 39 14 r r NN cord-326314-9ycht8gi 39 15 e e NN cord-326314-9ycht8gi 39 16 -p -p NN cord-326314-9ycht8gi 40 1 r r NNP cord-326314-9ycht8gi 40 2 o o NN cord-326314-9ycht8gi 40 3 o o NN cord-326314-9ycht8gi 40 4 f f NN cord-326314-9ycht8gi 40 5 structured structure VBN cord-326314-9ycht8gi 40 6 from from IN cord-326314-9ycht8gi 40 7 the the DT cord-326314-9ycht8gi 40 8 beginning beginning NN cord-326314-9ycht8gi 40 9 so so IN cord-326314-9ycht8gi 40 10 that that IN cord-326314-9ycht8gi 40 11 we -PRON- PRP cord-326314-9ycht8gi 40 12 might may MD cord-326314-9ycht8gi 40 13 examine examine VB cord-326314-9ycht8gi 40 14 the the DT cord-326314-9ycht8gi 40 15 effects effect NNS cord-326314-9ycht8gi 40 16 of of IN cord-326314-9ycht8gi 40 17 interventions intervention NNS cord-326314-9ycht8gi 40 18 that that WDT cord-326314-9ycht8gi 40 19 were be VBD cord-326314-9ycht8gi 40 20 imposed impose VBN cord-326314-9ycht8gi 40 21 later later RB cord-326314-9ycht8gi 40 22 on on RB cord-326314-9ycht8gi 40 23 . . . cord-326314-9ycht8gi 41 1 The the DT cord-326314-9ycht8gi 41 2 ultimate ultimate JJ cord-326314-9ycht8gi 41 3 aim aim NN cord-326314-9ycht8gi 41 4 here here RB cord-326314-9ycht8gi 41 5 is be VBZ cord-326314-9ycht8gi 41 6 to to TO cord-326314-9ycht8gi 41 7 inform inform VB cord-326314-9ycht8gi 41 8 policy policy NN cord-326314-9ycht8gi 41 9 on on IN cord-326314-9ycht8gi 41 10 the the DT cord-326314-9ycht8gi 41 11 requirements requirement NNS cord-326314-9ycht8gi 41 12 for for IN cord-326314-9ycht8gi 41 13 containing contain VBG cord-326314-9ycht8gi 41 14 the the DT cord-326314-9ycht8gi 41 15 epidemic epidemic NN cord-326314-9ycht8gi 41 16 . . . cord-326314-9ycht8gi 42 1 We -PRON- PRP cord-326314-9ycht8gi 42 2 included include VBD cord-326314-9ycht8gi 42 3 both both DT cord-326314-9ycht8gi 42 4 H H NNP cord-326314-9ycht8gi 42 5 and and CC cord-326314-9ycht8gi 42 6 C C NNP cord-326314-9ycht8gi 42 7 populations population NNS cord-326314-9ycht8gi 42 8 because because IN cord-326314-9ycht8gi 42 9 hospital hospital NN cord-326314-9ycht8gi 42 10 inpatient inpatient NN cord-326314-9ycht8gi 42 11 and and CC cord-326314-9ycht8gi 42 12 ICU ICU NNP cord-326314-9ycht8gi 42 13 bed bed NN cord-326314-9ycht8gi 42 14 capacities capacity NNS cord-326314-9ycht8gi 42 15 are be VBP cord-326314-9ycht8gi 42 16 the the DT cord-326314-9ycht8gi 42 17 key key JJ cord-326314-9ycht8gi 42 18 health health NN cord-326314-9ycht8gi 42 19 system system NN cord-326314-9ycht8gi 42 20 metrics metric NNS cord-326314-9ycht8gi 42 21 that that WDT cord-326314-9ycht8gi 42 22 we -PRON- PRP cord-326314-9ycht8gi 42 23 aim aim VBP cord-326314-9ycht8gi 42 24 to to TO cord-326314-9ycht8gi 42 25 avoid avoid VB cord-326314-9ycht8gi 42 26 straining strain VBG cord-326314-9ycht8gi 42 27 . . . cord-326314-9ycht8gi 43 1 Any any DT cord-326314-9ycht8gi 43 2 policy policy NN cord-326314-9ycht8gi 43 3 that that WDT cord-326314-9ycht8gi 43 4 we -PRON- PRP cord-326314-9ycht8gi 43 5 consider consider VBP cord-326314-9ycht8gi 43 6 must must MD cord-326314-9ycht8gi 43 7 include include VB cord-326314-9ycht8gi 43 8 predictions prediction NNS cord-326314-9ycht8gi 43 9 on on IN cord-326314-9ycht8gi 43 10 inpatient inpatient JJ cord-326314-9ycht8gi 43 11 and and CC cord-326314-9ycht8gi 43 12 ICU ICU NNP cord-326314-9ycht8gi 43 13 bed bed NN cord-326314-9ycht8gi 43 14 needs need VBZ cord-326314-9ycht8gi 43 15 . . . cord-326314-9ycht8gi 44 1 Preparing prepare VBG cord-326314-9ycht8gi 44 2 for for IN cord-326314-9ycht8gi 44 3 those those DT cord-326314-9ycht8gi 44 4 needs need NNS cord-326314-9ycht8gi 44 5 is be VBZ cord-326314-9ycht8gi 44 6 a a DT cord-326314-9ycht8gi 44 7 key key JJ cord-326314-9ycht8gi 44 8 response response NN cord-326314-9ycht8gi 44 9 if if IN cord-326314-9ycht8gi 44 10 or or CC cord-326314-9ycht8gi 44 11 when when WRB cord-326314-9ycht8gi 44 12 the the DT cord-326314-9ycht8gi 44 13 epidemic epidemic NN cord-326314-9ycht8gi 44 14 grows grow VBZ cord-326314-9ycht8gi 44 15 uncontrolled uncontrolled JJ cord-326314-9ycht8gi 44 16 . . . cord-326314-9ycht8gi 45 1 For for IN cord-326314-9ycht8gi 45 2 details detail NNS cord-326314-9ycht8gi 45 3 of of IN cord-326314-9ycht8gi 45 4 the the DT cord-326314-9ycht8gi 45 5 model model NN cord-326314-9ycht8gi 45 6 , , , cord-326314-9ycht8gi 45 7 including include VBG cord-326314-9ycht8gi 45 8 the the DT cord-326314-9ycht8gi 45 9 differential differential JJ cord-326314-9ycht8gi 45 10 equations equation NNS cord-326314-9ycht8gi 45 11 describing describe VBG cord-326314-9ycht8gi 45 12 the the DT cord-326314-9ycht8gi 45 13 mass mass JJ cord-326314-9ycht8gi 45 14 action action NN cord-326314-9ycht8gi 45 15 between between IN cord-326314-9ycht8gi 45 16 susceptible susceptible JJ cord-326314-9ycht8gi 45 17 and and CC cord-326314-9ycht8gi 45 18 infectious infectious JJ cord-326314-9ycht8gi 45 19 individuals individual NNS cord-326314-9ycht8gi 45 20 and and CC cord-326314-9ycht8gi 45 21 the the DT cord-326314-9ycht8gi 45 22 disease disease NN cord-326314-9ycht8gi 45 23 progression progression NN cord-326314-9ycht8gi 45 24 through through IN cord-326314-9ycht8gi 45 25 different different JJ cord-326314-9ycht8gi 45 26 sub sub NN cord-326314-9ycht8gi 45 27 - - NNS cord-326314-9ycht8gi 45 28 populations population NNS cord-326314-9ycht8gi 45 29 , , , cord-326314-9ycht8gi 45 30 see see VB cord-326314-9ycht8gi 45 31 Appendix Appendix NNP cord-326314-9ycht8gi 45 32 A. a. NN cord-326314-9ycht8gi 45 33 SDA SDA NNP cord-326314-9ycht8gi 45 34 is be VBZ cord-326314-9ycht8gi 45 35 an an DT cord-326314-9ycht8gi 45 36 inference inference NN cord-326314-9ycht8gi 45 37 procedure procedure NN cord-326314-9ycht8gi 45 38 , , , cord-326314-9ycht8gi 45 39 or or CC cord-326314-9ycht8gi 45 40 a a DT cord-326314-9ycht8gi 45 41 type type NN cord-326314-9ycht8gi 45 42 of of IN cord-326314-9ycht8gi 45 43 machine machine NN cord-326314-9ycht8gi 45 44 learning learning NN cord-326314-9ycht8gi 45 45 , , , cord-326314-9ycht8gi 45 46 in in IN cord-326314-9ycht8gi 45 47 which which WDT cord-326314-9ycht8gi 45 48 a a DT cord-326314-9ycht8gi 45 49 model model NN cord-326314-9ycht8gi 45 50 dynamical dynamical JJ cord-326314-9ycht8gi 45 51 system system NN cord-326314-9ycht8gi 45 52 is be VBZ cord-326314-9ycht8gi 45 53 assumed assume VBN cord-326314-9ycht8gi 45 54 to to TO cord-326314-9ycht8gi 45 55 underlie underlie VB cord-326314-9ycht8gi 45 56 any any DT cord-326314-9ycht8gi 45 57 measured measure VBN cord-326314-9ycht8gi 45 58 quantities quantity NNS cord-326314-9ycht8gi 45 59 . . . cord-326314-9ycht8gi 46 1 This this DT cord-326314-9ycht8gi 46 2 model model NN cord-326314-9ycht8gi 46 3 F F NNP cord-326314-9ycht8gi 46 4 can can MD cord-326314-9ycht8gi 46 5 be be VB cord-326314-9ycht8gi 46 6 written write VBN cord-326314-9ycht8gi 46 7 as as IN cord-326314-9ycht8gi 46 8 a a DT cord-326314-9ycht8gi 46 9 set set NN cord-326314-9ycht8gi 46 10 of of IN cord-326314-9ycht8gi 46 11 D d NN cord-326314-9ycht8gi 46 12 ordinary ordinary JJ cord-326314-9ycht8gi 46 13 differential differential JJ cord-326314-9ycht8gi 46 14 equations equation NNS cord-326314-9ycht8gi 46 15 that that WDT cord-326314-9ycht8gi 46 16 evolve evolve VBP cord-326314-9ycht8gi 46 17 in in IN cord-326314-9ycht8gi 46 18 some some DT cord-326314-9ycht8gi 46 19 parameterization parameterization NN cord-326314-9ycht8gi 46 20 t t NN cord-326314-9ycht8gi 46 21 as as IN cord-326314-9ycht8gi 46 22 : : : cord-326314-9ycht8gi 46 23 where where WRB cord-326314-9ycht8gi 46 24 the the DT cord-326314-9ycht8gi 46 25 components component NNS cord-326314-9ycht8gi 46 26 x x : cord-326314-9ycht8gi 46 27 a a DT cord-326314-9ycht8gi 46 28 of of IN cord-326314-9ycht8gi 46 29 the the DT cord-326314-9ycht8gi 46 30 vector vector NN cord-326314-9ycht8gi 46 31 x x NN cord-326314-9ycht8gi 46 32 are be VBP cord-326314-9ycht8gi 46 33 the the DT cord-326314-9ycht8gi 46 34 model model NN cord-326314-9ycht8gi 46 35 state state NN cord-326314-9ycht8gi 46 36 variables variable NNS cord-326314-9ycht8gi 46 37 , , , cord-326314-9ycht8gi 46 38 and and CC cord-326314-9ycht8gi 46 39 unknown unknown JJ cord-326314-9ycht8gi 46 40 parameters parameter NNS cord-326314-9ycht8gi 46 41 to to TO cord-326314-9ycht8gi 46 42 be be VB cord-326314-9ycht8gi 46 43 estimated estimate VBN cord-326314-9ycht8gi 46 44 are be VBP cord-326314-9ycht8gi 46 45 contained contain VBN cord-326314-9ycht8gi 46 46 in in IN cord-326314-9ycht8gi 46 47 p(t p(t NNP cord-326314-9ycht8gi 46 48 ) ) -RRB- cord-326314-9ycht8gi 46 49 . . . cord-326314-9ycht8gi 47 1 A a DT cord-326314-9ycht8gi 47 2 subset subset JJ cord-326314-9ycht8gi 47 3 L l NN cord-326314-9ycht8gi 47 4 of of IN cord-326314-9ycht8gi 47 5 the the DT cord-326314-9ycht8gi 47 6 D D NNP cord-326314-9ycht8gi 47 7 state state NN cord-326314-9ycht8gi 47 8 variables variable NNS cord-326314-9ycht8gi 47 9 is be VBZ cord-326314-9ycht8gi 47 10 associated associate VBN cord-326314-9ycht8gi 47 11 with with IN cord-326314-9ycht8gi 47 12 measured measure VBN cord-326314-9ycht8gi 47 13 quantities quantity NNS cord-326314-9ycht8gi 47 14 . . . cord-326314-9ycht8gi 48 1 One one PRP cord-326314-9ycht8gi 48 2 seeks seek VBZ cord-326314-9ycht8gi 48 3 to to TO cord-326314-9ycht8gi 48 4 estimate estimate VB cord-326314-9ycht8gi 48 5 the the DT cord-326314-9ycht8gi 48 6 p p NN cord-326314-9ycht8gi 48 7 unknown unknown JJ cord-326314-9ycht8gi 48 8 parameters parameter NNS cord-326314-9ycht8gi 48 9 and and CC cord-326314-9ycht8gi 48 10 the the DT cord-326314-9ycht8gi 48 11 evolution evolution NN cord-326314-9ycht8gi 48 12 of of IN cord-326314-9ycht8gi 48 13 all all DT cord-326314-9ycht8gi 48 14 state state NN cord-326314-9ycht8gi 48 15 variables variable NNS cord-326314-9ycht8gi 48 16 that that WDT cord-326314-9ycht8gi 48 17 is be VBZ cord-326314-9ycht8gi 48 18 consistent consistent JJ cord-326314-9ycht8gi 48 19 with with IN cord-326314-9ycht8gi 48 20 the the DT cord-326314-9ycht8gi 48 21 L L NNP cord-326314-9ycht8gi 48 22 measurements measurement NNS cord-326314-9ycht8gi 48 23 . . . cord-326314-9ycht8gi 49 1 A a DT cord-326314-9ycht8gi 49 2 prerequisite prerequisite NN cord-326314-9ycht8gi 49 3 for for IN cord-326314-9ycht8gi 49 4 estimation estimation NN cord-326314-9ycht8gi 49 5 using use VBG cord-326314-9ycht8gi 49 6 real real JJ cord-326314-9ycht8gi 49 7 data data NN cord-326314-9ycht8gi 49 8 is be VBZ cord-326314-9ycht8gi 49 9 the the DT cord-326314-9ycht8gi 49 10 design design NN cord-326314-9ycht8gi 49 11 of of IN cord-326314-9ycht8gi 49 12 simulated simulated JJ cord-326314-9ycht8gi 49 13 experiments experiment NNS cord-326314-9ycht8gi 49 14 , , , cord-326314-9ycht8gi 49 15 wherein wherein WRB cord-326314-9ycht8gi 49 16 the the DT cord-326314-9ycht8gi 49 17 true true JJ cord-326314-9ycht8gi 49 18 values value NNS cord-326314-9ycht8gi 49 19 of of IN cord-326314-9ycht8gi 49 20 parameters parameter NNS cord-326314-9ycht8gi 49 21 are be VBP cord-326314-9ycht8gi 49 22 known know VBN cord-326314-9ycht8gi 49 23 . . . cord-326314-9ycht8gi 50 1 In in IN cord-326314-9ycht8gi 50 2 addition addition NN cord-326314-9ycht8gi 50 3 to to IN cord-326314-9ycht8gi 50 4 providing provide VBG cord-326314-9ycht8gi 50 5 a a DT cord-326314-9ycht8gi 50 6 consistency consistency NN cord-326314-9ycht8gi 50 7 check check NN cord-326314-9ycht8gi 50 8 , , , cord-326314-9ycht8gi 50 9 simulated simulated JJ cord-326314-9ycht8gi 50 10 experiments experiment NNS cord-326314-9ycht8gi 50 11 offer offer VBP cord-326314-9ycht8gi 50 12 the the DT cord-326314-9ycht8gi 50 13 opportunity opportunity NN cord-326314-9ycht8gi 50 14 to to TO cord-326314-9ycht8gi 50 15 ascertain ascertain VB cord-326314-9ycht8gi 50 16 which which WDT cord-326314-9ycht8gi 50 17 and and CC cord-326314-9ycht8gi 50 18 how how WRB cord-326314-9ycht8gi 50 19 few few JJ cord-326314-9ycht8gi 50 20 experimental experimental JJ cord-326314-9ycht8gi 50 21 measurements measurement NNS cord-326314-9ycht8gi 50 22 , , , cord-326314-9ycht8gi 50 23 in in IN cord-326314-9ycht8gi 50 24 principle principle NN cord-326314-9ycht8gi 50 25 , , , cord-326314-9ycht8gi 50 26 are be VBP cord-326314-9ycht8gi 50 27 necessary necessary JJ cord-326314-9ycht8gi 50 28 and and CC cord-326314-9ycht8gi 50 29 sufficient sufficient JJ cord-326314-9ycht8gi 50 30 to to TO cord-326314-9ycht8gi 50 31 complete complete VB cord-326314-9ycht8gi 50 32 a a DT cord-326314-9ycht8gi 50 33 model model NN cord-326314-9ycht8gi 50 34 . . . cord-326314-9ycht8gi 51 1 method method NN cord-326314-9ycht8gi 51 2 , , , cord-326314-9ycht8gi 51 3 and and CC cord-326314-9ycht8gi 51 4 we -PRON- PRP cord-326314-9ycht8gi 51 5 employ employ VBP cord-326314-9ycht8gi 51 6 a a DT cord-326314-9ycht8gi 51 7 method method NN cord-326314-9ycht8gi 51 8 of of IN cord-326314-9ycht8gi 51 9 annealing anneal VBG cord-326314-9ycht8gi 51 10 to to TO cord-326314-9ycht8gi 51 11 identify identify VB cord-326314-9ycht8gi 51 12 a a DT cord-326314-9ycht8gi 51 13 lowest low JJS cord-326314-9ycht8gi 51 14 minumum minumum JJ cord-326314-9ycht8gi 51 15 -a -a NN cord-326314-9ycht8gi 51 16 procedure procedure NN cord-326314-9ycht8gi 51 17 that that WDT cord-326314-9ycht8gi 51 18 has have VBZ cord-326314-9ycht8gi 51 19 been be VBN cord-326314-9ycht8gi 51 20 referred refer VBN cord-326314-9ycht8gi 51 21 to to IN cord-326314-9ycht8gi 51 22 loosely loosely RB cord-326314-9ycht8gi 51 23 in in IN cord-326314-9ycht8gi 51 24 the the DT cord-326314-9ycht8gi 51 25 literature literature NN cord-326314-9ycht8gi 51 26 as as IN cord-326314-9ycht8gi 51 27 variational variational JJ cord-326314-9ycht8gi 51 28 annealing annealing NN cord-326314-9ycht8gi 51 29 ( ( -LRB- cord-326314-9ycht8gi 51 30 VA VA NNP cord-326314-9ycht8gi 51 31 ) ) -RRB- cord-326314-9ycht8gi 51 32 . . . cord-326314-9ycht8gi 52 1 The the DT cord-326314-9ycht8gi 52 2 cost cost NN cord-326314-9ycht8gi 52 3 function function NN cord-326314-9ycht8gi 52 4 A a NN cord-326314-9ycht8gi 52 5 0 0 NFP cord-326314-9ycht8gi 52 6 used use VBN cord-326314-9ycht8gi 52 7 in in IN cord-326314-9ycht8gi 52 8 this this DT cord-326314-9ycht8gi 52 9 paper paper NN cord-326314-9ycht8gi 52 10 is be VBZ cord-326314-9ycht8gi 52 11 written write VBN cord-326314-9ycht8gi 52 12 as as IN cord-326314-9ycht8gi 52 13 : : : cord-326314-9ycht8gi 52 14 One one PRP cord-326314-9ycht8gi 52 15 seeks seek VBZ cord-326314-9ycht8gi 52 16 the the DT cord-326314-9ycht8gi 52 17 path path NN cord-326314-9ycht8gi 52 18 X x NN cord-326314-9ycht8gi 52 19 0 0 CD cord-326314-9ycht8gi 53 1 = = SYM cord-326314-9ycht8gi 53 2 x(0 x(0 NNP cord-326314-9ycht8gi 53 3 ) ) -RRB- cord-326314-9ycht8gi 53 4 , , , cord-326314-9ycht8gi 53 5 ... ... NFP cord-326314-9ycht8gi 53 6 , , , cord-326314-9ycht8gi 53 7 x(N x(n LS cord-326314-9ycht8gi 53 8 ) ) -RRB- cord-326314-9ycht8gi 53 9 , , , cord-326314-9ycht8gi 53 10 p(0 p(0 NNP cord-326314-9ycht8gi 53 11 ) ) -RRB- cord-326314-9ycht8gi 53 12 , , , cord-326314-9ycht8gi 53 13 ... ... : cord-326314-9ycht8gi 54 1 p(N p(N NNP cord-326314-9ycht8gi 54 2 ) ) -RRB- cord-326314-9ycht8gi 54 3 in in IN cord-326314-9ycht8gi 54 4 state state NN cord-326314-9ycht8gi 54 5 space space NN cord-326314-9ycht8gi 54 6 on on IN cord-326314-9ycht8gi 54 7 which which WDT cord-326314-9ycht8gi 54 8 A a NN cord-326314-9ycht8gi 54 9 0 0 CD cord-326314-9ycht8gi 54 10 attains attain VBZ cord-326314-9ycht8gi 54 11 a a DT cord-326314-9ycht8gi 54 12 minimum minimum JJ cord-326314-9ycht8gi 54 13 value value NN cord-326314-9ycht8gi 54 14 1 1 CD cord-326314-9ycht8gi 54 15 . . . cord-326314-9ycht8gi 55 1 Note note VB cord-326314-9ycht8gi 55 2 that that IN cord-326314-9ycht8gi 55 3 Equation equation NN cord-326314-9ycht8gi 55 4 1 1 CD cord-326314-9ycht8gi 55 5 is be VBZ cord-326314-9ycht8gi 55 6 shorthand shorthand NN cord-326314-9ycht8gi 55 7 ; ; : cord-326314-9ycht8gi 55 8 for for IN cord-326314-9ycht8gi 55 9 the the DT cord-326314-9ycht8gi 55 10 full full JJ cord-326314-9ycht8gi 55 11 form form NN cord-326314-9ycht8gi 55 12 , , , cord-326314-9ycht8gi 55 13 see see VB cord-326314-9ycht8gi 55 14 Appendix Appendix NNP cord-326314-9ycht8gi 55 15 A A NNP cord-326314-9ycht8gi 55 16 of of IN cord-326314-9ycht8gi 55 17 Ref Ref NNP cord-326314-9ycht8gi 55 18 [ [ -LRB- cord-326314-9ycht8gi 55 19 18 18 CD cord-326314-9ycht8gi 55 20 ] ] -RRB- cord-326314-9ycht8gi 55 21 . . . cord-326314-9ycht8gi 56 1 For for IN cord-326314-9ycht8gi 56 2 a a DT cord-326314-9ycht8gi 56 3 derivation derivation NN cord-326314-9ycht8gi 56 4 -beginning -beginne VBG cord-326314-9ycht8gi 56 5 with with IN cord-326314-9ycht8gi 56 6 the the DT cord-326314-9ycht8gi 56 7 physical physical JJ cord-326314-9ycht8gi 56 8 Action Action NNP cord-326314-9ycht8gi 56 9 of of IN cord-326314-9ycht8gi 56 10 a a DT cord-326314-9ycht8gi 56 11 particle particle NN cord-326314-9ycht8gi 56 12 in in IN cord-326314-9ycht8gi 56 13 state state NN cord-326314-9ycht8gi 56 14 space space NN cord-326314-9ycht8gi 56 15 -see -see : cord-326314-9ycht8gi 56 16 Ref ref NN cord-326314-9ycht8gi 56 17 [ [ -LRB- cord-326314-9ycht8gi 56 18 26 26 CD cord-326314-9ycht8gi 56 19 ] ] -RRB- cord-326314-9ycht8gi 56 20 . . . cord-326314-9ycht8gi 57 1 The the DT cord-326314-9ycht8gi 57 2 first first JJ cord-326314-9ycht8gi 57 3 squared squared JJ cord-326314-9ycht8gi 57 4 term term NN cord-326314-9ycht8gi 57 5 of of IN cord-326314-9ycht8gi 57 6 Equation equation NN cord-326314-9ycht8gi 57 7 1 1 CD cord-326314-9ycht8gi 57 8 governs govern VBZ cord-326314-9ycht8gi 57 9 the the DT cord-326314-9ycht8gi 57 10 transfer transfer NN cord-326314-9ycht8gi 57 11 of of IN cord-326314-9ycht8gi 57 12 information information NN cord-326314-9ycht8gi 57 13 from from IN cord-326314-9ycht8gi 57 14 measurements measurement NNS cord-326314-9ycht8gi 57 15 y y NNP cord-326314-9ycht8gi 57 16 l l NNP cord-326314-9ycht8gi 57 17 to to TO cord-326314-9ycht8gi 57 18 model model VB cord-326314-9ycht8gi 57 19 states state NNS cord-326314-9ycht8gi 57 20 x x SYM cord-326314-9ycht8gi 57 21 l l NNP cord-326314-9ycht8gi 57 22 . . . cord-326314-9ycht8gi 58 1 The the DT cord-326314-9ycht8gi 58 2 summation summation NN cord-326314-9ycht8gi 58 3 on on IN cord-326314-9ycht8gi 58 4 j j NNP cord-326314-9ycht8gi 58 5 runs run VBZ cord-326314-9ycht8gi 58 6 over over IN cord-326314-9ycht8gi 58 7 all all DT cord-326314-9ycht8gi 58 8 discretized discretize VBN cord-326314-9ycht8gi 58 9 timepoints timepoint NNS cord-326314-9ycht8gi 58 10 J J NNP cord-326314-9ycht8gi 58 11 at at IN cord-326314-9ycht8gi 58 12 which which WDT cord-326314-9ycht8gi 58 13 measurements measurement NNS cord-326314-9ycht8gi 58 14 are be VBP cord-326314-9ycht8gi 58 15 made make VBN cord-326314-9ycht8gi 58 16 , , , cord-326314-9ycht8gi 58 17 which which WDT cord-326314-9ycht8gi 58 18 may may MD cord-326314-9ycht8gi 58 19 be be VB cord-326314-9ycht8gi 58 20 a a DT cord-326314-9ycht8gi 58 21 subset subset NN cord-326314-9ycht8gi 58 22 of of IN cord-326314-9ycht8gi 58 23 all all DT cord-326314-9ycht8gi 58 24 integrated integrate VBN cord-326314-9ycht8gi 58 25 model model NN cord-326314-9ycht8gi 58 26 timepoints timepoint NNS cord-326314-9ycht8gi 58 27 . . . cord-326314-9ycht8gi 59 1 The the DT cord-326314-9ycht8gi 59 2 summation summation NN cord-326314-9ycht8gi 59 3 on on IN cord-326314-9ycht8gi 59 4 l l NNP cord-326314-9ycht8gi 59 5 is be VBZ cord-326314-9ycht8gi 59 6 taken take VBN cord-326314-9ycht8gi 59 7 over over RP cord-326314-9ycht8gi 59 8 all all DT cord-326314-9ycht8gi 59 9 L l NN cord-326314-9ycht8gi 59 10 measured measure VBN cord-326314-9ycht8gi 59 11 quantities quantity NNS cord-326314-9ycht8gi 59 12 . . . cord-326314-9ycht8gi 60 1 The the DT cord-326314-9ycht8gi 60 2 second second JJ cord-326314-9ycht8gi 60 3 squared squared JJ cord-326314-9ycht8gi 60 4 term term NN cord-326314-9ycht8gi 60 5 of of IN cord-326314-9ycht8gi 60 6 Equation equation NN cord-326314-9ycht8gi 60 7 1 1 CD cord-326314-9ycht8gi 60 8 incorporates incorporate VBZ cord-326314-9ycht8gi 60 9 the the DT cord-326314-9ycht8gi 60 10 model model NN cord-326314-9ycht8gi 60 11 evolution evolution NN cord-326314-9ycht8gi 60 12 of of IN cord-326314-9ycht8gi 60 13 all all DT cord-326314-9ycht8gi 60 14 D d NN cord-326314-9ycht8gi 60 15 state state NN cord-326314-9ycht8gi 60 16 variables variable NNS cord-326314-9ycht8gi 61 1 x x SYM cord-326314-9ycht8gi 61 2 a a LS cord-326314-9ycht8gi 61 3 . . . cord-326314-9ycht8gi 62 1 The the DT cord-326314-9ycht8gi 62 2 term term NN cord-326314-9ycht8gi 62 3 f f FW cord-326314-9ycht8gi 62 4 a a NN cord-326314-9ycht8gi 62 5 ( ( -LRB- cord-326314-9ycht8gi 62 6 x(n x(n NNP cord-326314-9ycht8gi 62 7 ) ) -RRB- cord-326314-9ycht8gi 62 8 ) ) -RRB- cord-326314-9ycht8gi 62 9 is be VBZ cord-326314-9ycht8gi 62 10 defined define VBN cord-326314-9ycht8gi 62 11 , , , cord-326314-9ycht8gi 62 12 for for IN cord-326314-9ycht8gi 62 13 discretization discretization NN cord-326314-9ycht8gi 62 14 , , , cord-326314-9ycht8gi 62 15 as as IN cord-326314-9ycht8gi 62 16 : : : cord-326314-9ycht8gi 62 17 1 1 CD cord-326314-9ycht8gi 62 18 2 2 CD cord-326314-9ycht8gi 62 19 [ [ -LRB- cord-326314-9ycht8gi 62 20 F F NNP cord-326314-9ycht8gi 62 21 a a NN cord-326314-9ycht8gi 62 22 ( ( -LRB- cord-326314-9ycht8gi 62 23 x(n x(n NNP cord-326314-9ycht8gi 62 24 ) ) -RRB- cord-326314-9ycht8gi 62 25 ) ) -RRB- cord-326314-9ycht8gi 62 26 + + CC cord-326314-9ycht8gi 62 27 F F NNP cord-326314-9ycht8gi 62 28 a a NNP cord-326314-9ycht8gi 62 29 ( ( -LRB- cord-326314-9ycht8gi 62 30 x(n x(n NNP cord-326314-9ycht8gi 62 31 + + SYM cord-326314-9ycht8gi 62 32 1 1 CD cord-326314-9ycht8gi 62 33 ) ) -RRB- cord-326314-9ycht8gi 62 34 ) ) -RRB- cord-326314-9ycht8gi 62 35 ] ] -RRB- cord-326314-9ycht8gi 62 36 . . . cord-326314-9ycht8gi 63 1 The the DT cord-326314-9ycht8gi 63 2 outer outer JJ cord-326314-9ycht8gi 63 3 sum sum NN cord-326314-9ycht8gi 63 4 on on IN cord-326314-9ycht8gi 63 5 n n NN cord-326314-9ycht8gi 63 6 is be VBZ cord-326314-9ycht8gi 63 7 taken take VBN cord-326314-9ycht8gi 63 8 over over RP cord-326314-9ycht8gi 63 9 all all DT cord-326314-9ycht8gi 63 10 discretized discretize VBN cord-326314-9ycht8gi 63 11 timepoints timepoint NNS cord-326314-9ycht8gi 63 12 of of IN cord-326314-9ycht8gi 63 13 the the DT cord-326314-9ycht8gi 63 14 model model NN cord-326314-9ycht8gi 63 15 equations equation NNS cord-326314-9ycht8gi 63 16 of of IN cord-326314-9ycht8gi 63 17 motion motion NN cord-326314-9ycht8gi 63 18 . . . cord-326314-9ycht8gi 64 1 The the DT cord-326314-9ycht8gi 64 2 sum sum NN cord-326314-9ycht8gi 64 3 on on IN cord-326314-9ycht8gi 64 4 a a DT cord-326314-9ycht8gi 64 5 is be VBZ cord-326314-9ycht8gi 64 6 taken take VBN cord-326314-9ycht8gi 64 7 over over RP cord-326314-9ycht8gi 64 8 all all DT cord-326314-9ycht8gi 64 9 D d NN cord-326314-9ycht8gi 64 10 state state NN cord-326314-9ycht8gi 64 11 variables variable NNS cord-326314-9ycht8gi 64 12 . . . cord-326314-9ycht8gi 65 1 R r NN cord-326314-9ycht8gi 65 2 m m NN cord-326314-9ycht8gi 65 3 and and CC cord-326314-9ycht8gi 65 4 R R NNP cord-326314-9ycht8gi 65 5 f f NNP cord-326314-9ycht8gi 65 6 are be VBP cord-326314-9ycht8gi 65 7 inverse inverse JJ cord-326314-9ycht8gi 65 8 covariance covariance NN cord-326314-9ycht8gi 65 9 matrices matrix NNS cord-326314-9ycht8gi 65 10 for for IN cord-326314-9ycht8gi 65 11 the the DT cord-326314-9ycht8gi 65 12 measurement measurement NN cord-326314-9ycht8gi 65 13 and and CC cord-326314-9ycht8gi 65 14 model model NN cord-326314-9ycht8gi 65 15 errors error NNS cord-326314-9ycht8gi 65 16 , , , cord-326314-9ycht8gi 65 17 respectively respectively RB cord-326314-9ycht8gi 65 18 . . . cord-326314-9ycht8gi 66 1 We -PRON- PRP cord-326314-9ycht8gi 66 2 take take VBP cord-326314-9ycht8gi 66 3 each each DT cord-326314-9ycht8gi 66 4 matrix matrix NN cord-326314-9ycht8gi 66 5 to to TO cord-326314-9ycht8gi 66 6 be be VB cord-326314-9ycht8gi 66 7 diagonal diagonal JJ cord-326314-9ycht8gi 66 8 and and CC cord-326314-9ycht8gi 66 9 treat treat VB cord-326314-9ycht8gi 66 10 them -PRON- PRP cord-326314-9ycht8gi 66 11 as as IN cord-326314-9ycht8gi 66 12 relative relative JJ cord-326314-9ycht8gi 66 13 weighting weighting NN cord-326314-9ycht8gi 66 14 terms term NNS cord-326314-9ycht8gi 66 15 , , , cord-326314-9ycht8gi 66 16 whose whose WP$ cord-326314-9ycht8gi 66 17 utility utility NN cord-326314-9ycht8gi 66 18 will will MD cord-326314-9ycht8gi 66 19 be be VB cord-326314-9ycht8gi 66 20 described describe VBN cord-326314-9ycht8gi 66 21 below below IN cord-326314-9ycht8gi 66 22 in in IN cord-326314-9ycht8gi 66 23 this this DT cord-326314-9ycht8gi 66 24 Section section NN cord-326314-9ycht8gi 66 25 . . . cord-326314-9ycht8gi 67 1 The the DT cord-326314-9ycht8gi 67 2 procedure procedure NN cord-326314-9ycht8gi 67 3 searches search VBZ cord-326314-9ycht8gi 67 4 a a DT cord-326314-9ycht8gi 67 5 ( ( -LRB- cord-326314-9ycht8gi 67 6 D D NNP cord-326314-9ycht8gi 67 7 ( ( -LRB- cord-326314-9ycht8gi 67 8 N n NN cord-326314-9ycht8gi 67 9 + + SYM cord-326314-9ycht8gi 67 10 1 1 CD cord-326314-9ycht8gi 67 11 ) ) -RRB- cord-326314-9ycht8gi 67 12 + + CC cord-326314-9ycht8gi 67 13 p p NN cord-326314-9ycht8gi 67 14 ( ( -LRB- cord-326314-9ycht8gi 67 15 N N NNP cord-326314-9ycht8gi 67 16 + + CC cord-326314-9ycht8gi 67 17 1))-dimensional 1))-dimensional CD cord-326314-9ycht8gi 67 18 state state NN cord-326314-9ycht8gi 67 19 space space NN cord-326314-9ycht8gi 67 20 , , , cord-326314-9ycht8gi 67 21 where where WRB cord-326314-9ycht8gi 67 22 D D NNP cord-326314-9ycht8gi 67 23 is be VBZ cord-326314-9ycht8gi 67 24 the the DT cord-326314-9ycht8gi 67 25 number number NN cord-326314-9ycht8gi 67 26 of of IN cord-326314-9ycht8gi 67 27 state state NN cord-326314-9ycht8gi 67 28 variables variable NNS cord-326314-9ycht8gi 67 29 , , , cord-326314-9ycht8gi 67 30 N N NNP cord-326314-9ycht8gi 67 31 is be VBZ cord-326314-9ycht8gi 67 32 the the DT cord-326314-9ycht8gi 67 33 number number NN cord-326314-9ycht8gi 67 34 of of IN cord-326314-9ycht8gi 67 35 discretized discretize VBN cord-326314-9ycht8gi 67 36 steps step NNS cord-326314-9ycht8gi 67 37 , , , cord-326314-9ycht8gi 67 38 and and CC cord-326314-9ycht8gi 67 39 p p NN cord-326314-9ycht8gi 67 40 is be VBZ cord-326314-9ycht8gi 67 41 the the DT cord-326314-9ycht8gi 67 42 number number NN cord-326314-9ycht8gi 67 43 of of IN cord-326314-9ycht8gi 67 44 unknown unknown JJ cord-326314-9ycht8gi 67 45 parameters parameter NNS cord-326314-9ycht8gi 67 46 . . . cord-326314-9ycht8gi 68 1 To to TO cord-326314-9ycht8gi 68 2 perform perform VB cord-326314-9ycht8gi 68 3 simulated simulated JJ cord-326314-9ycht8gi 68 4 experiments experiment NNS cord-326314-9ycht8gi 68 5 , , , cord-326314-9ycht8gi 68 6 the the DT cord-326314-9ycht8gi 68 7 equations equation NNS cord-326314-9ycht8gi 68 8 of of IN cord-326314-9ycht8gi 68 9 motion motion NN cord-326314-9ycht8gi 68 10 are be VBP cord-326314-9ycht8gi 68 11 integrated integrate VBN cord-326314-9ycht8gi 68 12 forward forward RB cord-326314-9ycht8gi 68 13 to to TO cord-326314-9ycht8gi 68 14 yield yield VB cord-326314-9ycht8gi 68 15 simulated simulated JJ cord-326314-9ycht8gi 68 16 data datum NNS cord-326314-9ycht8gi 68 17 , , , cord-326314-9ycht8gi 68 18 and and CC cord-326314-9ycht8gi 68 19 the the DT cord-326314-9ycht8gi 68 20 VA VA NNP cord-326314-9ycht8gi 68 21 procedure procedure NN cord-326314-9ycht8gi 68 22 is be VBZ cord-326314-9ycht8gi 68 23 challenged challenge VBN cord-326314-9ycht8gi 68 24 to to TO cord-326314-9ycht8gi 68 25 infer infer VB cord-326314-9ycht8gi 68 26 the the DT cord-326314-9ycht8gi 68 27 parameters parameter NNS cord-326314-9ycht8gi 68 28 and and CC cord-326314-9ycht8gi 68 29 the the DT cord-326314-9ycht8gi 68 30 evolution evolution NN cord-326314-9ycht8gi 68 31 of of IN cord-326314-9ycht8gi 68 32 all all DT cord-326314-9ycht8gi 68 33 state state NN cord-326314-9ycht8gi 68 34 variablesmeasured variablesmeasured JJ cord-326314-9ycht8gi 68 35 and and CC cord-326314-9ycht8gi 68 36 unmeasured unmeasured JJ cord-326314-9ycht8gi 68 37 -that -that NN cord-326314-9ycht8gi 68 38 generated generate VBD cord-326314-9ycht8gi 68 39 the the DT cord-326314-9ycht8gi 68 40 simulated simulated JJ cord-326314-9ycht8gi 68 41 data datum NNS cord-326314-9ycht8gi 68 42 . . . cord-326314-9ycht8gi 69 1 This this DT cord-326314-9ycht8gi 69 2 specific specific JJ cord-326314-9ycht8gi 69 3 formulation formulation NN cord-326314-9ycht8gi 69 4 has have VBZ cord-326314-9ycht8gi 69 5 been be VBN cord-326314-9ycht8gi 69 6 tested test VBN cord-326314-9ycht8gi 69 7 with with IN cord-326314-9ycht8gi 69 8 chaotic chaotic JJ cord-326314-9ycht8gi 69 9 models model NNS cord-326314-9ycht8gi 69 10 [ [ -LRB- cord-326314-9ycht8gi 69 11 27 27 CD cord-326314-9ycht8gi 69 12 ] ] -RRB- cord-326314-9ycht8gi 69 13 [ [ -LRB- cord-326314-9ycht8gi 69 14 28 28 CD cord-326314-9ycht8gi 69 15 ] ] -RRB- cord-326314-9ycht8gi 69 16 [ [ -LRB- cord-326314-9ycht8gi 69 17 29 29 CD cord-326314-9ycht8gi 69 18 ] ] -RRB- cord-326314-9ycht8gi 69 19 [ [ -LRB- cord-326314-9ycht8gi 69 20 30 30 CD cord-326314-9ycht8gi 69 21 ] ] -RRB- cord-326314-9ycht8gi 69 22 , , , cord-326314-9ycht8gi 69 23 and and CC cord-326314-9ycht8gi 69 24 used use VBD cord-326314-9ycht8gi 69 25 to to TO cord-326314-9ycht8gi 69 26 estimate estimate VB cord-326314-9ycht8gi 69 27 parameters parameter NNS cord-326314-9ycht8gi 69 28 in in IN cord-326314-9ycht8gi 69 29 models model NNS cord-326314-9ycht8gi 69 30 of of IN cord-326314-9ycht8gi 69 31 biological biological JJ cord-326314-9ycht8gi 69 32 neurons neuron NNS cord-326314-9ycht8gi 69 33 [ [ -LRB- cord-326314-9ycht8gi 69 34 13 13 CD cord-326314-9ycht8gi 69 35 , , , cord-326314-9ycht8gi 69 36 14 14 CD cord-326314-9ycht8gi 69 37 , , , cord-326314-9ycht8gi 69 38 16 16 CD cord-326314-9ycht8gi 69 39 , , , cord-326314-9ycht8gi 69 40 18 18 CD cord-326314-9ycht8gi 69 41 , , , cord-326314-9ycht8gi 69 42 31 31 CD cord-326314-9ycht8gi 69 43 , , , cord-326314-9ycht8gi 69 44 32 32 CD cord-326314-9ycht8gi 69 45 ] ] -RRB- cord-326314-9ycht8gi 69 46 , , , cord-326314-9ycht8gi 69 47 as as RB cord-326314-9ycht8gi 69 48 well well RB cord-326314-9ycht8gi 69 49 as as IN cord-326314-9ycht8gi 69 50 astrophysical astrophysical JJ cord-326314-9ycht8gi 69 51 scenarios scenario NNS cord-326314-9ycht8gi 69 52 [ [ -LRB- cord-326314-9ycht8gi 69 53 33 33 CD cord-326314-9ycht8gi 69 54 ] ] -RRB- cord-326314-9ycht8gi 69 55 . . . cord-326314-9ycht8gi 70 1 Our -PRON- PRP$ cord-326314-9ycht8gi 70 2 model model NN cord-326314-9ycht8gi 70 3 is be VBZ cord-326314-9ycht8gi 70 4 nonlinear nonlinear JJ cord-326314-9ycht8gi 70 5 , , , cord-326314-9ycht8gi 70 6 and and CC cord-326314-9ycht8gi 70 7 thus thus RB cord-326314-9ycht8gi 70 8 the the DT cord-326314-9ycht8gi 70 9 cost cost NN cord-326314-9ycht8gi 70 10 function function NN cord-326314-9ycht8gi 70 11 surface surface NN cord-326314-9ycht8gi 70 12 is be VBZ cord-326314-9ycht8gi 70 13 non non JJ cord-326314-9ycht8gi 70 14 - - JJ cord-326314-9ycht8gi 70 15 convex convex JJ cord-326314-9ycht8gi 70 16 . . . cord-326314-9ycht8gi 71 1 For for IN cord-326314-9ycht8gi 71 2 this this DT cord-326314-9ycht8gi 71 3 reason reason NN cord-326314-9ycht8gi 71 4 , , , cord-326314-9ycht8gi 71 5 we -PRON- PRP cord-326314-9ycht8gi 71 6 iterate iterate VBP cord-326314-9ycht8gi 71 7 -or -or DT cord-326314-9ycht8gi 72 1 anneal anneal VB cord-326314-9ycht8gi 72 2 -in -in . cord-326314-9ycht8gi 73 1 terms term NNS cord-326314-9ycht8gi 73 2 of of IN cord-326314-9ycht8gi 73 3 the the DT cord-326314-9ycht8gi 73 4 ratio ratio NN cord-326314-9ycht8gi 73 5 of of IN cord-326314-9ycht8gi 73 6 model model NN cord-326314-9ycht8gi 73 7 and and CC cord-326314-9ycht8gi 73 8 measurement measurement NN cord-326314-9ycht8gi 73 9 error error NN cord-326314-9ycht8gi 73 10 , , , cord-326314-9ycht8gi 73 11 with with IN cord-326314-9ycht8gi 73 12 the the DT cord-326314-9ycht8gi 73 13 aim aim NN cord-326314-9ycht8gi 73 14 to to TO cord-326314-9ycht8gi 73 15 gradually gradually RB cord-326314-9ycht8gi 73 16 freeze freeze VB cord-326314-9ycht8gi 73 17 out out RP cord-326314-9ycht8gi 73 18 a a DT cord-326314-9ycht8gi 73 19 1 1 CD cord-326314-9ycht8gi 74 1 It -PRON- PRP cord-326314-9ycht8gi 74 2 may may MD cord-326314-9ycht8gi 74 3 interest interest VB cord-326314-9ycht8gi 74 4 the the DT cord-326314-9ycht8gi 74 5 reader reader NN cord-326314-9ycht8gi 74 6 that that IN cord-326314-9ycht8gi 74 7 one one PRP cord-326314-9ycht8gi 74 8 can can MD cord-326314-9ycht8gi 74 9 derive derive VB cord-326314-9ycht8gi 74 10 this this DT cord-326314-9ycht8gi 74 11 cost cost NN cord-326314-9ycht8gi 74 12 function function NN cord-326314-9ycht8gi 74 13 by by IN cord-326314-9ycht8gi 74 14 considering consider VBG cord-326314-9ycht8gi 74 15 the the DT cord-326314-9ycht8gi 74 16 classical classical JJ cord-326314-9ycht8gi 74 17 physical physical JJ cord-326314-9ycht8gi 74 18 Action Action NNP cord-326314-9ycht8gi 74 19 on on IN cord-326314-9ycht8gi 74 20 a a DT cord-326314-9ycht8gi 74 21 path path NN cord-326314-9ycht8gi 74 22 in in IN cord-326314-9ycht8gi 74 23 a a DT cord-326314-9ycht8gi 74 24 state state NN cord-326314-9ycht8gi 74 25 space space NN cord-326314-9ycht8gi 74 26 , , , cord-326314-9ycht8gi 74 27 where where WRB cord-326314-9ycht8gi 74 28 the the DT cord-326314-9ycht8gi 74 29 path path NN cord-326314-9ycht8gi 74 30 of of IN cord-326314-9ycht8gi 74 31 lowest low JJS cord-326314-9ycht8gi 74 32 Action Action NNP cord-326314-9ycht8gi 74 33 corresponds correspond VBZ cord-326314-9ycht8gi 74 34 to to IN cord-326314-9ycht8gi 74 35 the the DT cord-326314-9ycht8gi 74 36 correct correct JJ cord-326314-9ycht8gi 74 37 solution solution NN cord-326314-9ycht8gi 74 38 [ [ -LRB- cord-326314-9ycht8gi 74 39 26 26 CD cord-326314-9ycht8gi 74 40 ] ] -RRB- cord-326314-9ycht8gi 74 41 5 5 CD cord-326314-9ycht8gi 74 42 J j NN cord-326314-9ycht8gi 74 43 o o NN cord-326314-9ycht8gi 74 44 u u NN cord-326314-9ycht8gi 74 45 r r NN cord-326314-9ycht8gi 74 46 n n NN cord-326314-9ycht8gi 74 47 a a DT cord-326314-9ycht8gi 74 48 l l NN cord-326314-9ycht8gi 74 49 P p NN cord-326314-9ycht8gi 74 50 r r NN cord-326314-9ycht8gi 74 51 e e NN cord-326314-9ycht8gi 74 52 -p -p NN cord-326314-9ycht8gi 75 1 r r LS cord-326314-9ycht8gi 75 2 o o NN cord-326314-9ycht8gi 76 1 o o UH cord-326314-9ycht8gi 76 2 f f NNP cord-326314-9ycht8gi 76 3 lowest low JJS cord-326314-9ycht8gi 76 4 minimum minimum NN cord-326314-9ycht8gi 76 5 . . . cord-326314-9ycht8gi 77 1 This this DT cord-326314-9ycht8gi 77 2 procedure procedure NN cord-326314-9ycht8gi 77 3 was be VBD cord-326314-9ycht8gi 77 4 introduced introduce VBN cord-326314-9ycht8gi 77 5 in in IN cord-326314-9ycht8gi 77 6 Ref Ref NNP cord-326314-9ycht8gi 77 7 [ [ -LRB- cord-326314-9ycht8gi 77 8 34 34 CD cord-326314-9ycht8gi 77 9 ] ] -RRB- cord-326314-9ycht8gi 77 10 , , , cord-326314-9ycht8gi 77 11 and and CC cord-326314-9ycht8gi 77 12 has have VBZ cord-326314-9ycht8gi 77 13 since since IN cord-326314-9ycht8gi 77 14 been be VBN cord-326314-9ycht8gi 77 15 used use VBN cord-326314-9ycht8gi 77 16 in in IN cord-326314-9ycht8gi 77 17 combination combination NN cord-326314-9ycht8gi 77 18 with with IN cord-326314-9ycht8gi 77 19 variational variational JJ cord-326314-9ycht8gi 77 20 optimization optimization NN cord-326314-9ycht8gi 77 21 on on IN cord-326314-9ycht8gi 77 22 nonlinear nonlinear JJ cord-326314-9ycht8gi 77 23 models model NNS cord-326314-9ycht8gi 77 24 in in IN cord-326314-9ycht8gi 77 25 Refs ref NNS cord-326314-9ycht8gi 77 26 [ [ -LRB- cord-326314-9ycht8gi 77 27 11 11 CD cord-326314-9ycht8gi 77 28 , , , cord-326314-9ycht8gi 77 29 18 18 CD cord-326314-9ycht8gi 77 30 , , , cord-326314-9ycht8gi 77 31 31 31 CD cord-326314-9ycht8gi 77 32 , , , cord-326314-9ycht8gi 77 33 33 33 CD cord-326314-9ycht8gi 77 34 ] ] -RRB- cord-326314-9ycht8gi 77 35 above above RB cord-326314-9ycht8gi 77 36 . . . cord-326314-9ycht8gi 78 1 The the DT cord-326314-9ycht8gi 78 2 annealing annealing NN cord-326314-9ycht8gi 78 3 works work VBZ cord-326314-9ycht8gi 78 4 as as IN cord-326314-9ycht8gi 78 5 follows follow VBZ cord-326314-9ycht8gi 78 6 . . . cord-326314-9ycht8gi 79 1 We -PRON- PRP cord-326314-9ycht8gi 79 2 first first RB cord-326314-9ycht8gi 79 3 define define VBP cord-326314-9ycht8gi 79 4 the the DT cord-326314-9ycht8gi 79 5 coefficient coefficient NN cord-326314-9ycht8gi 79 6 of of IN cord-326314-9ycht8gi 79 7 measurement measurement NN cord-326314-9ycht8gi 79 8 error error NN cord-326314-9ycht8gi 79 9 R r NN cord-326314-9ycht8gi 79 10 m m NN cord-326314-9ycht8gi 79 11 to to TO cord-326314-9ycht8gi 79 12 be be VB cord-326314-9ycht8gi 79 13 1.0 1.0 CD cord-326314-9ycht8gi 79 14 , , , cord-326314-9ycht8gi 79 15 and and CC cord-326314-9ycht8gi 79 16 write write VB cord-326314-9ycht8gi 79 17 the the DT cord-326314-9ycht8gi 79 18 coefficient coefficient NN cord-326314-9ycht8gi 79 19 of of IN cord-326314-9ycht8gi 79 20 model model NN cord-326314-9ycht8gi 79 21 error error NN cord-326314-9ycht8gi 79 22 R r NN cord-326314-9ycht8gi 79 23 f f NN cord-326314-9ycht8gi 79 24 as as IN cord-326314-9ycht8gi 79 25 : : : cord-326314-9ycht8gi 79 26 R r NN cord-326314-9ycht8gi 79 27 f f NN cord-326314-9ycht8gi 79 28 = = NN cord-326314-9ycht8gi 79 29 R r NN cord-326314-9ycht8gi 79 30 f f NN cord-326314-9ycht8gi 79 31 , , , cord-326314-9ycht8gi 79 32 0 0 NFP cord-326314-9ycht8gi 79 33 α α NN cord-326314-9ycht8gi 79 34 β β NN cord-326314-9ycht8gi 79 35 , , , cord-326314-9ycht8gi 79 36 where where WRB cord-326314-9ycht8gi 79 37 R R NNP cord-326314-9ycht8gi 79 38 f f NN cord-326314-9ycht8gi 79 39 , , , cord-326314-9ycht8gi 79 40 0 0 NFP cord-326314-9ycht8gi 79 41 is be VBZ cord-326314-9ycht8gi 79 42 a a DT cord-326314-9ycht8gi 79 43 small small JJ cord-326314-9ycht8gi 79 44 number number NN cord-326314-9ycht8gi 79 45 near near IN cord-326314-9ycht8gi 79 46 zero zero CD cord-326314-9ycht8gi 79 47 , , , cord-326314-9ycht8gi 79 48 α α NN cord-326314-9ycht8gi 79 49 is be VBZ cord-326314-9ycht8gi 79 50 a a DT cord-326314-9ycht8gi 79 51 small small JJ cord-326314-9ycht8gi 79 52 number number NN cord-326314-9ycht8gi 79 53 greater great JJR cord-326314-9ycht8gi 79 54 than than IN cord-326314-9ycht8gi 79 55 1.0 1.0 CD cord-326314-9ycht8gi 79 56 , , , cord-326314-9ycht8gi 79 57 and and CC cord-326314-9ycht8gi 79 58 β β NN cord-326314-9ycht8gi 79 59 is be VBZ cord-326314-9ycht8gi 79 60 initialized initialize VBN cord-326314-9ycht8gi 79 61 at at IN cord-326314-9ycht8gi 79 62 zero zero CD cord-326314-9ycht8gi 79 63 . . . cord-326314-9ycht8gi 80 1 Parameter parameter NN cord-326314-9ycht8gi 80 2 β β NN cord-326314-9ycht8gi 80 3 is be VBZ cord-326314-9ycht8gi 80 4 our -PRON- PRP$ cord-326314-9ycht8gi 80 5 annealing annealing NN cord-326314-9ycht8gi 80 6 parameter parameter NN cord-326314-9ycht8gi 80 7 . . . cord-326314-9ycht8gi 81 1 For for IN cord-326314-9ycht8gi 81 2 the the DT cord-326314-9ycht8gi 81 3 case case NN cord-326314-9ycht8gi 81 4 in in IN cord-326314-9ycht8gi 81 5 which which WDT cord-326314-9ycht8gi 81 6 β β NN cord-326314-9ycht8gi 81 7 = = SYM cord-326314-9ycht8gi 81 8 0 0 NFP cord-326314-9ycht8gi 81 9 , , , cord-326314-9ycht8gi 81 10 relatively relatively RB cord-326314-9ycht8gi 81 11 free free JJ cord-326314-9ycht8gi 81 12 from from IN cord-326314-9ycht8gi 81 13 model model NN cord-326314-9ycht8gi 81 14 constraints constraint NNS cord-326314-9ycht8gi 81 15 the the DT cord-326314-9ycht8gi 81 16 cost cost NN cord-326314-9ycht8gi 81 17 function function NN cord-326314-9ycht8gi 81 18 surface surface NN cord-326314-9ycht8gi 81 19 is be VBZ cord-326314-9ycht8gi 81 20 smooth smooth JJ cord-326314-9ycht8gi 81 21 and and CC cord-326314-9ycht8gi 81 22 there there EX cord-326314-9ycht8gi 81 23 exists exist VBZ cord-326314-9ycht8gi 81 24 one one CD cord-326314-9ycht8gi 81 25 minimum minimum NN cord-326314-9ycht8gi 81 26 of of IN cord-326314-9ycht8gi 81 27 the the DT cord-326314-9ycht8gi 81 28 variational variational JJ cord-326314-9ycht8gi 81 29 problem problem NN cord-326314-9ycht8gi 81 30 that that WDT cord-326314-9ycht8gi 81 31 is be VBZ cord-326314-9ycht8gi 81 32 consistent consistent JJ cord-326314-9ycht8gi 81 33 with with IN cord-326314-9ycht8gi 81 34 the the DT cord-326314-9ycht8gi 81 35 measurements measurement NNS cord-326314-9ycht8gi 81 36 . . . cord-326314-9ycht8gi 82 1 We -PRON- PRP cord-326314-9ycht8gi 82 2 obtain obtain VBP cord-326314-9ycht8gi 82 3 an an DT cord-326314-9ycht8gi 82 4 estimate estimate NN cord-326314-9ycht8gi 82 5 of of IN cord-326314-9ycht8gi 82 6 that that DT cord-326314-9ycht8gi 82 7 minimum minimum NN cord-326314-9ycht8gi 82 8 . . . cord-326314-9ycht8gi 83 1 Then then RB cord-326314-9ycht8gi 83 2 we -PRON- PRP cord-326314-9ycht8gi 83 3 increase increase VBP cord-326314-9ycht8gi 83 4 the the DT cord-326314-9ycht8gi 83 5 weight weight NN cord-326314-9ycht8gi 83 6 of of IN cord-326314-9ycht8gi 83 7 the the DT cord-326314-9ycht8gi 83 8 model model NN cord-326314-9ycht8gi 83 9 term term NN cord-326314-9ycht8gi 83 10 slightly slightly RB cord-326314-9ycht8gi 83 11 , , , cord-326314-9ycht8gi 83 12 via via IN cord-326314-9ycht8gi 83 13 an an DT cord-326314-9ycht8gi 83 14 integer integ JJR cord-326314-9ycht8gi 83 15 increment increment NN cord-326314-9ycht8gi 83 16 in in IN cord-326314-9ycht8gi 83 17 β β NN cord-326314-9ycht8gi 83 18 , , , cord-326314-9ycht8gi 83 19 and and CC cord-326314-9ycht8gi 83 20 recalculate recalculate VB cord-326314-9ycht8gi 83 21 the the DT cord-326314-9ycht8gi 83 22 cost cost NN cord-326314-9ycht8gi 83 23 . . . cord-326314-9ycht8gi 84 1 We -PRON- PRP cord-326314-9ycht8gi 84 2 do do VBP cord-326314-9ycht8gi 84 3 this this DT cord-326314-9ycht8gi 84 4 recursively recursively RB cord-326314-9ycht8gi 84 5 , , , cord-326314-9ycht8gi 84 6 toward toward IN cord-326314-9ycht8gi 84 7 the the DT cord-326314-9ycht8gi 84 8 deterministic deterministic JJ cord-326314-9ycht8gi 84 9 limit limit NN cord-326314-9ycht8gi 84 10 of of IN cord-326314-9ycht8gi 84 11 R r NN cord-326314-9ycht8gi 84 12 f f NN cord-326314-9ycht8gi 84 13 R r NN cord-326314-9ycht8gi 84 14 m m NN cord-326314-9ycht8gi 84 15 . . . cord-326314-9ycht8gi 85 1 The the DT cord-326314-9ycht8gi 85 2 aim aim NN cord-326314-9ycht8gi 85 3 is be VBZ cord-326314-9ycht8gi 85 4 to to TO cord-326314-9ycht8gi 85 5 remain remain VB cord-326314-9ycht8gi 85 6 sufficiently sufficiently RB cord-326314-9ycht8gi 85 7 near near JJ cord-326314-9ycht8gi 85 8 to to IN cord-326314-9ycht8gi 85 9 the the DT cord-326314-9ycht8gi 85 10 lowest low JJS cord-326314-9ycht8gi 85 11 minimum minimum NN cord-326314-9ycht8gi 85 12 to to TO cord-326314-9ycht8gi 85 13 not not RB cord-326314-9ycht8gi 85 14 become become VB cord-326314-9ycht8gi 85 15 trapped trap VBN cord-326314-9ycht8gi 85 16 in in IN cord-326314-9ycht8gi 85 17 a a DT cord-326314-9ycht8gi 85 18 local local JJ cord-326314-9ycht8gi 85 19 minimum minimum NN cord-326314-9ycht8gi 85 20 as as IN cord-326314-9ycht8gi 85 21 the the DT cord-326314-9ycht8gi 85 22 surface surface NN cord-326314-9ycht8gi 85 23 becomes become VBZ cord-326314-9ycht8gi 85 24 resolved resolve VBN cord-326314-9ycht8gi 85 25 . . . cord-326314-9ycht8gi 86 1 We -PRON- PRP cord-326314-9ycht8gi 86 2 will will MD cord-326314-9ycht8gi 86 3 show show VB cord-326314-9ycht8gi 86 4 in in IN cord-326314-9ycht8gi 86 5 Results result NNS cord-326314-9ycht8gi 86 6 that that IN cord-326314-9ycht8gi 86 7 a a DT cord-326314-9ycht8gi 86 8 plot plot NN cord-326314-9ycht8gi 86 9 of of IN cord-326314-9ycht8gi 86 10 the the DT cord-326314-9ycht8gi 86 11 cost cost NN cord-326314-9ycht8gi 86 12 as as IN cord-326314-9ycht8gi 86 13 a a DT cord-326314-9ycht8gi 86 14 function function NN cord-326314-9ycht8gi 86 15 of of IN cord-326314-9ycht8gi 86 16 β β NN cord-326314-9ycht8gi 86 17 reveals reveal VBZ cord-326314-9ycht8gi 86 18 whether whether IN cord-326314-9ycht8gi 86 19 a a DT cord-326314-9ycht8gi 86 20 solution solution NN cord-326314-9ycht8gi 86 21 has have VBZ cord-326314-9ycht8gi 86 22 been be VBN cord-326314-9ycht8gi 86 23 found find VBN cord-326314-9ycht8gi 86 24 that that WDT cord-326314-9ycht8gi 86 25 is be VBZ cord-326314-9ycht8gi 86 26 consistent consistent JJ cord-326314-9ycht8gi 86 27 with with IN cord-326314-9ycht8gi 86 28 both both DT cord-326314-9ycht8gi 86 29 measurements measurement NNS cord-326314-9ycht8gi 86 30 and and CC cord-326314-9ycht8gi 86 31 model model NN cord-326314-9ycht8gi 86 32 . . . cord-326314-9ycht8gi 87 1 We -PRON- PRP cord-326314-9ycht8gi 87 2 based base VBD cord-326314-9ycht8gi 87 3 our -PRON- PRP$ cord-326314-9ycht8gi 87 4 simulated simulated JJ cord-326314-9ycht8gi 87 5 locality locality NN cord-326314-9ycht8gi 87 6 loosely loosely RB cord-326314-9ycht8gi 87 7 on on IN cord-326314-9ycht8gi 87 8 New New NNP cord-326314-9ycht8gi 87 9 York York NNP cord-326314-9ycht8gi 87 10 City City NNP cord-326314-9ycht8gi 87 11 , , , cord-326314-9ycht8gi 87 12 with with IN cord-326314-9ycht8gi 87 13 a a DT cord-326314-9ycht8gi 87 14 population population NN cord-326314-9ycht8gi 87 15 of of IN cord-326314-9ycht8gi 87 16 9 9 CD cord-326314-9ycht8gi 87 17 million million CD cord-326314-9ycht8gi 87 18 . . . cord-326314-9ycht8gi 88 1 For for IN cord-326314-9ycht8gi 88 2 simplicity simplicity NN cord-326314-9ycht8gi 88 3 , , , cord-326314-9ycht8gi 88 4 we -PRON- PRP cord-326314-9ycht8gi 88 5 assume assume VBP cord-326314-9ycht8gi 88 6 a a DT cord-326314-9ycht8gi 88 7 closed closed JJ cord-326314-9ycht8gi 88 8 population population NN cord-326314-9ycht8gi 88 9 . . . cord-326314-9ycht8gi 89 1 Simulations simulation NNS cord-326314-9ycht8gi 89 2 ran run VBD cord-326314-9ycht8gi 89 3 from from IN cord-326314-9ycht8gi 89 4 an an DT cord-326314-9ycht8gi 89 5 initial initial JJ cord-326314-9ycht8gi 89 6 time time NN cord-326314-9ycht8gi 89 7 t t NN cord-326314-9ycht8gi 89 8 0 0 CD cord-326314-9ycht8gi 89 9 of of IN cord-326314-9ycht8gi 89 10 four four CD cord-326314-9ycht8gi 89 11 days day NNS cord-326314-9ycht8gi 89 12 prior prior RB cord-326314-9ycht8gi 89 13 to to IN cord-326314-9ycht8gi 89 14 2020 2020 CD cord-326314-9ycht8gi 89 15 March March NNP cord-326314-9ycht8gi 89 16 1 1 CD cord-326314-9ycht8gi 89 17 , , , cord-326314-9ycht8gi 89 18 the the DT cord-326314-9ycht8gi 89 19 date date NN cord-326314-9ycht8gi 89 20 of of IN cord-326314-9ycht8gi 89 21 the the DT cord-326314-9ycht8gi 89 22 first first JJ cord-326314-9ycht8gi 89 23 reported report VBN cord-326314-9ycht8gi 89 24 COVID-19 COVID-19 NNP cord-326314-9ycht8gi 89 25 case case NN cord-326314-9ycht8gi 89 26 in in IN cord-326314-9ycht8gi 89 27 New New NNP cord-326314-9ycht8gi 89 28 York York NNP cord-326314-9ycht8gi 89 29 City City NNP cord-326314-9ycht8gi 89 30 [ [ -LRB- cord-326314-9ycht8gi 89 31 35 35 CD cord-326314-9ycht8gi 89 32 ] ] -RRB- cord-326314-9ycht8gi 89 33 . . . cord-326314-9ycht8gi 90 1 At at IN cord-326314-9ycht8gi 90 2 time time NN cord-326314-9ycht8gi 90 3 t t NNP cord-326314-9ycht8gi 90 4 0 0 CD cord-326314-9ycht8gi 90 5 , , , cord-326314-9ycht8gi 90 6 there there EX cord-326314-9ycht8gi 90 7 existed exist VBD cord-326314-9ycht8gi 90 8 one one CD cord-326314-9ycht8gi 90 9 detected detect VBD cord-326314-9ycht8gi 90 10 symptomatic symptomatic JJ cord-326314-9ycht8gi 90 11 case case NN cord-326314-9ycht8gi 90 12 within within IN cord-326314-9ycht8gi 90 13 the the DT cord-326314-9ycht8gi 90 14 population population NN cord-326314-9ycht8gi 90 15 of of IN cord-326314-9ycht8gi 90 16 9 9 CD cord-326314-9ycht8gi 90 17 million million CD cord-326314-9ycht8gi 90 18 . . . cord-326314-9ycht8gi 91 1 In in IN cord-326314-9ycht8gi 91 2 addition addition NN cord-326314-9ycht8gi 91 3 to to IN cord-326314-9ycht8gi 91 4 that that DT cord-326314-9ycht8gi 91 5 one one CD cord-326314-9ycht8gi 91 6 initial initial JJ cord-326314-9ycht8gi 91 7 detected detect VBN cord-326314-9ycht8gi 91 8 case case NN cord-326314-9ycht8gi 91 9 , , , cord-326314-9ycht8gi 91 10 we -PRON- PRP cord-326314-9ycht8gi 91 11 took take VBD cord-326314-9ycht8gi 91 12 as as IN cord-326314-9ycht8gi 91 13 our -PRON- PRP$ cord-326314-9ycht8gi 91 14 initial initial JJ cord-326314-9ycht8gi 91 15 conditions condition NNS cord-326314-9ycht8gi 91 16 on on IN cord-326314-9ycht8gi 91 17 the the DT cord-326314-9ycht8gi 91 18 populations population NNS cord-326314-9ycht8gi 91 19 to to TO cord-326314-9ycht8gi 91 20 be be VB cord-326314-9ycht8gi 91 21 : : : cord-326314-9ycht8gi 91 22 50 50 CD cord-326314-9ycht8gi 91 23 undetected undetected JJ cord-326314-9ycht8gi 91 24 asymptomatics asymptomatic NNS cord-326314-9ycht8gi 91 25 , , , cord-326314-9ycht8gi 91 26 10 10 CD cord-326314-9ycht8gi 91 27 undetected undetected JJ cord-326314-9ycht8gi 91 28 mild mild JJ cord-326314-9ycht8gi 91 29 symptomatics symptomatic NNS cord-326314-9ycht8gi 91 30 , , , cord-326314-9ycht8gi 91 31 and and CC cord-326314-9ycht8gi 91 32 one one CD cord-326314-9ycht8gi 91 33 undetected undetected JJ cord-326314-9ycht8gi 91 34 severe severe JJ cord-326314-9ycht8gi 91 35 symptomatic symptomatic JJ cord-326314-9ycht8gi 91 36 . . . cord-326314-9ycht8gi 92 1 2 2 LS cord-326314-9ycht8gi 93 1 We -PRON- PRP cord-326314-9ycht8gi 93 2 chose choose VBD cord-326314-9ycht8gi 93 3 five five CD cord-326314-9ycht8gi 93 4 quantities quantity NNS cord-326314-9ycht8gi 93 5 as as IN cord-326314-9ycht8gi 93 6 unknown unknown JJ cord-326314-9ycht8gi 93 7 parameters parameter NNS cord-326314-9ycht8gi 93 8 to to TO cord-326314-9ycht8gi 93 9 be be VB cord-326314-9ycht8gi 93 10 estimated estimate VBN cord-326314-9ycht8gi 93 11 ( ( -LRB- cord-326314-9ycht8gi 93 12 Table table NN cord-326314-9ycht8gi 93 13 1 1 CD cord-326314-9ycht8gi 93 14 ) ) -RRB- cord-326314-9ycht8gi 93 15 : : : cord-326314-9ycht8gi 93 16 1 1 LS cord-326314-9ycht8gi 93 17 ) ) -RRB- cord-326314-9ycht8gi 93 18 the the DT cord-326314-9ycht8gi 93 19 time time NN cord-326314-9ycht8gi 93 20 - - HYPH cord-326314-9ycht8gi 93 21 varying vary VBG cord-326314-9ycht8gi 93 22 transmission transmission NN cord-326314-9ycht8gi 93 23 rate rate NN cord-326314-9ycht8gi 94 1 K K NNP cord-326314-9ycht8gi 94 2 i i PRP cord-326314-9ycht8gi 94 3 ( ( -LRB- cord-326314-9ycht8gi 94 4 t t NN cord-326314-9ycht8gi 94 5 ) ) -RRB- cord-326314-9ycht8gi 95 1 ; ; : cord-326314-9ycht8gi 95 2 2 2 LS cord-326314-9ycht8gi 95 3 ) ) -RRB- cord-326314-9ycht8gi 95 4 the the DT cord-326314-9ycht8gi 95 5 detection detection NN cord-326314-9ycht8gi 95 6 probability probability NN cord-326314-9ycht8gi 95 7 of of IN cord-326314-9ycht8gi 95 8 mild mild JJ cord-326314-9ycht8gi 95 9 symptomatic symptomatic JJ cord-326314-9ycht8gi 95 10 cases case NNS cord-326314-9ycht8gi 95 11 d d XX cord-326314-9ycht8gi 95 12 Sym sym NN cord-326314-9ycht8gi 95 13 ( ( -LRB- cord-326314-9ycht8gi 95 14 t t NN cord-326314-9ycht8gi 95 15 ) ) -RRB- cord-326314-9ycht8gi 95 16 , , . cord-326314-9ycht8gi 96 1 3 3 LS cord-326314-9ycht8gi 96 2 ) ) -RRB- cord-326314-9ycht8gi 96 3 the the DT cord-326314-9ycht8gi 96 4 detection detection NN cord-326314-9ycht8gi 96 5 probability probability NN cord-326314-9ycht8gi 96 6 of of IN cord-326314-9ycht8gi 96 7 severe severe JJ cord-326314-9ycht8gi 96 8 symptomatic symptomatic JJ cord-326314-9ycht8gi 96 9 cases case NNS cord-326314-9ycht8gi 96 10 d d XX cord-326314-9ycht8gi 96 11 Sys Sys NNP cord-326314-9ycht8gi 96 12 ( ( -LRB- cord-326314-9ycht8gi 96 13 t t NN cord-326314-9ycht8gi 96 14 ) ) -RRB- cord-326314-9ycht8gi 96 15 , , , cord-326314-9ycht8gi 96 16 4 4 LS cord-326314-9ycht8gi 96 17 ) ) -RRB- cord-326314-9ycht8gi 96 18 the the DT cord-326314-9ycht8gi 96 19 fraction fraction NN cord-326314-9ycht8gi 96 20 of of IN cord-326314-9ycht8gi 96 21 cases case NNS cord-326314-9ycht8gi 96 22 that that WDT cord-326314-9ycht8gi 96 23 become become VBP cord-326314-9ycht8gi 96 24 symptomatic symptomatic JJ cord-326314-9ycht8gi 96 25 f f NN cord-326314-9ycht8gi 96 26 sympt sympt NN cord-326314-9ycht8gi 96 27 , , , cord-326314-9ycht8gi 96 28 and and CC cord-326314-9ycht8gi 96 29 5 5 LS cord-326314-9ycht8gi 96 30 ) ) -RRB- cord-326314-9ycht8gi 96 31 the the DT cord-326314-9ycht8gi 96 32 fraction fraction NN cord-326314-9ycht8gi 96 33 of of IN cord-326314-9ycht8gi 96 34 symptomatic symptomatic JJ cord-326314-9ycht8gi 96 35 cases case NNS cord-326314-9ycht8gi 96 36 that that WDT cord-326314-9ycht8gi 96 37 become become VBP cord-326314-9ycht8gi 96 38 severe severe JJ cord-326314-9ycht8gi 96 39 enough enough RB cord-326314-9ycht8gi 96 40 to to TO cord-326314-9ycht8gi 96 41 require require VB cord-326314-9ycht8gi 96 42 hospitalization hospitalization NN cord-326314-9ycht8gi 96 43 f f NN cord-326314-9ycht8gi 96 44 severe severe JJ cord-326314-9ycht8gi 96 45 . . . cord-326314-9ycht8gi 97 1 Here here RB cord-326314-9ycht8gi 97 2 we -PRON- PRP cord-326314-9ycht8gi 97 3 summarize summarize VBP cord-326314-9ycht8gi 97 4 the the DT cord-326314-9ycht8gi 97 5 key key JJ cord-326314-9ycht8gi 97 6 features feature NNS cord-326314-9ycht8gi 97 7 that that WDT cord-326314-9ycht8gi 97 8 we -PRON- PRP cord-326314-9ycht8gi 97 9 sought seek VBD cord-326314-9ycht8gi 97 10 to to TO cord-326314-9ycht8gi 97 11 capture capture VB cord-326314-9ycht8gi 97 12 in in IN cord-326314-9ycht8gi 97 13 modeling model VBG cord-326314-9ycht8gi 97 14 these these DT cord-326314-9ycht8gi 97 15 parameters parameter NNS cord-326314-9ycht8gi 97 16 ; ; : cord-326314-9ycht8gi 97 17 for for IN cord-326314-9ycht8gi 97 18 their -PRON- PRP$ cord-326314-9ycht8gi 97 19 mathematical mathematical JJ cord-326314-9ycht8gi 97 20 formulatons formulaton NNS cord-326314-9ycht8gi 97 21 , , , cord-326314-9ycht8gi 97 22 see see VB cord-326314-9ycht8gi 97 23 Appendix Appendix NNP cord-326314-9ycht8gi 97 24 B. B. NNP cord-326314-9ycht8gi 98 1 The the DT cord-326314-9ycht8gi 98 2 transmission transmission NN cord-326314-9ycht8gi 98 3 rate rate NN cord-326314-9ycht8gi 99 1 K K NNP cord-326314-9ycht8gi 99 2 i i PRP cord-326314-9ycht8gi 99 3 ( ( -LRB- cord-326314-9ycht8gi 99 4 often often RB cord-326314-9ycht8gi 99 5 referred refer VBN cord-326314-9ycht8gi 99 6 to to IN cord-326314-9ycht8gi 99 7 as as IN cord-326314-9ycht8gi 99 8 the the DT cord-326314-9ycht8gi 99 9 effective effective JJ cord-326314-9ycht8gi 99 10 contact contact NN cord-326314-9ycht8gi 99 11 rate rate NN cord-326314-9ycht8gi 99 12 ) ) -RRB- cord-326314-9ycht8gi 99 13 in in IN cord-326314-9ycht8gi 99 14 a a DT cord-326314-9ycht8gi 99 15 given give VBN cord-326314-9ycht8gi 99 16 population population NN cord-326314-9ycht8gi 99 17 for for IN cord-326314-9ycht8gi 99 18 a a DT cord-326314-9ycht8gi 99 19 given give VBN cord-326314-9ycht8gi 99 20 infectious infectious JJ cord-326314-9ycht8gi 99 21 disease disease NN cord-326314-9ycht8gi 99 22 is be VBZ cord-326314-9ycht8gi 99 23 measured measure VBN cord-326314-9ycht8gi 99 24 in in IN cord-326314-9ycht8gi 99 25 effective effective JJ cord-326314-9ycht8gi 99 26 contacts contact NNS cord-326314-9ycht8gi 99 27 per per IN cord-326314-9ycht8gi 99 28 unit unit NN cord-326314-9ycht8gi 99 29 time time NN cord-326314-9ycht8gi 99 30 . . . cord-326314-9ycht8gi 100 1 This this DT cord-326314-9ycht8gi 100 2 may may MD cord-326314-9ycht8gi 100 3 be be VB cord-326314-9ycht8gi 100 4 expressed express VBN cord-326314-9ycht8gi 100 5 as as IN cord-326314-9ycht8gi 100 6 the the DT cord-326314-9ycht8gi 100 7 total total JJ cord-326314-9ycht8gi 100 8 contact contact NN cord-326314-9ycht8gi 100 9 rate rate NN cord-326314-9ycht8gi 100 10 multiplied multiply VBN cord-326314-9ycht8gi 100 11 by by IN cord-326314-9ycht8gi 100 12 the the DT cord-326314-9ycht8gi 100 13 risk risk NN cord-326314-9ycht8gi 100 14 of of IN cord-326314-9ycht8gi 100 15 infection infection NN cord-326314-9ycht8gi 100 16 , , , cord-326314-9ycht8gi 100 17 given give VBN cord-326314-9ycht8gi 100 18 contact contact NN cord-326314-9ycht8gi 100 19 between between IN cord-326314-9ycht8gi 100 20 an an DT cord-326314-9ycht8gi 100 21 infectious infectious JJ cord-326314-9ycht8gi 100 22 and and CC cord-326314-9ycht8gi 100 23 a a DT cord-326314-9ycht8gi 100 24 susceptible susceptible JJ cord-326314-9ycht8gi 100 25 individual individual NN cord-326314-9ycht8gi 100 26 . . . cord-326314-9ycht8gi 101 1 The the DT cord-326314-9ycht8gi 101 2 contact contact NN cord-326314-9ycht8gi 101 3 rate rate NN cord-326314-9ycht8gi 101 4 , , , cord-326314-9ycht8gi 101 5 in in IN cord-326314-9ycht8gi 101 6 turn turn NN cord-326314-9ycht8gi 101 7 , , , cord-326314-9ycht8gi 101 8 can can MD cord-326314-9ycht8gi 101 9 be be VB cord-326314-9ycht8gi 101 10 impacted impact VBN cord-326314-9ycht8gi 101 11 by by IN cord-326314-9ycht8gi 101 12 amendments amendment NNS cord-326314-9ycht8gi 101 13 to to IN cord-326314-9ycht8gi 101 14 social social JJ cord-326314-9ycht8gi 101 15 behavior behavior NN cord-326314-9ycht8gi 101 16 3 3 CD cord-326314-9ycht8gi 101 17 . . . cord-326314-9ycht8gi 102 1 As as IN cord-326314-9ycht8gi 102 2 a a DT cord-326314-9ycht8gi 102 3 first first JJ cord-326314-9ycht8gi 102 4 step step NN cord-326314-9ycht8gi 102 5 in in IN cord-326314-9ycht8gi 102 6 applying apply VBG cord-326314-9ycht8gi 102 7 SDA SDA NNP cord-326314-9ycht8gi 102 8 to to IN cord-326314-9ycht8gi 102 9 a a DT cord-326314-9ycht8gi 102 10 high high JJ cord-326314-9ycht8gi 102 11 - - HYPH cord-326314-9ycht8gi 102 12 dimensional dimensional JJ cord-326314-9ycht8gi 102 13 epidemiological epidemiological JJ cord-326314-9ycht8gi 102 14 model model NN cord-326314-9ycht8gi 102 15 , , , cord-326314-9ycht8gi 102 16 we -PRON- PRP cord-326314-9ycht8gi 102 17 chose choose VBD cord-326314-9ycht8gi 102 18 to to TO cord-326314-9ycht8gi 102 19 condense condense VB cord-326314-9ycht8gi 102 20 the the DT cord-326314-9ycht8gi 102 21 significance significance NN cord-326314-9ycht8gi 102 22 of of IN cord-326314-9ycht8gi 102 23 K K NNP cord-326314-9ycht8gi 102 24 i i PRP cord-326314-9ycht8gi 102 25 into into IN cord-326314-9ycht8gi 102 26 a a DT cord-326314-9ycht8gi 102 27 relatively relatively RB cord-326314-9ycht8gi 102 28 simple simple JJ cord-326314-9ycht8gi 102 29 mathematical mathematical JJ cord-326314-9ycht8gi 102 30 form form NN cord-326314-9ycht8gi 102 31 . . . cord-326314-9ycht8gi 103 1 We -PRON- PRP cord-326314-9ycht8gi 103 2 assumed assume VBD cord-326314-9ycht8gi 103 3 that that IN cord-326314-9ycht8gi 103 4 K K NNP cord-326314-9ycht8gi 103 5 i i PRP cord-326314-9ycht8gi 103 6 was be VBD cord-326314-9ycht8gi 103 7 constant constant JJ cord-326314-9ycht8gi 103 8 prior prior RB cord-326314-9ycht8gi 103 9 to to IN cord-326314-9ycht8gi 103 10 the the DT cord-326314-9ycht8gi 103 11 implementation implementation NN cord-326314-9ycht8gi 103 12 of of IN cord-326314-9ycht8gi 103 13 a a DT cord-326314-9ycht8gi 103 14 social social JJ cord-326314-9ycht8gi 103 15 - - HYPH cord-326314-9ycht8gi 103 16 distancing distance VBG cord-326314-9ycht8gi 103 17 mandate mandate NN cord-326314-9ycht8gi 103 18 , , , cord-326314-9ycht8gi 103 19 which which WDT cord-326314-9ycht8gi 103 20 then then RB cord-326314-9ycht8gi 103 21 effected effect VBD cord-326314-9ycht8gi 103 22 a a DT cord-326314-9ycht8gi 103 23 rapid rapid JJ cord-326314-9ycht8gi 103 24 transition transition NN cord-326314-9ycht8gi 103 25 of of IN cord-326314-9ycht8gi 103 26 K K NNP cord-326314-9ycht8gi 103 27 i i PRP cord-326314-9ycht8gi 103 28 to to IN cord-326314-9ycht8gi 103 29 a a DT cord-326314-9ycht8gi 103 30 lower low JJR cord-326314-9ycht8gi 103 31 constant constant JJ cord-326314-9ycht8gi 103 32 value value NN cord-326314-9ycht8gi 103 33 . . . cord-326314-9ycht8gi 104 1 Specifically specifically RB cord-326314-9ycht8gi 104 2 , , , cord-326314-9ycht8gi 104 3 we -PRON- PRP cord-326314-9ycht8gi 104 4 modeled model VBD cord-326314-9ycht8gi 104 5 K K NNP cord-326314-9ycht8gi 104 6 i i PRP cord-326314-9ycht8gi 104 7 as as IN cord-326314-9ycht8gi 104 8 a a DT cord-326314-9ycht8gi 104 9 smooth smooth JJ cord-326314-9ycht8gi 104 10 approximation approximation NN cord-326314-9ycht8gi 104 11 to to IN cord-326314-9ycht8gi 104 12 a a DT cord-326314-9ycht8gi 104 13 Heaviside Heaviside NNP cord-326314-9ycht8gi 104 14 function function NN cord-326314-9ycht8gi 104 15 that that WDT cord-326314-9ycht8gi 104 16 begins begin VBZ cord-326314-9ycht8gi 104 17 its -PRON- PRP$ cord-326314-9ycht8gi 104 18 decline decline NN cord-326314-9ycht8gi 104 19 on on IN cord-326314-9ycht8gi 104 20 March March NNP cord-326314-9ycht8gi 104 21 22 22 CD cord-326314-9ycht8gi 104 22 , , , cord-326314-9ycht8gi 104 23 the the DT cord-326314-9ycht8gi 104 24 date date NN cord-326314-9ycht8gi 104 25 that that WDT cord-326314-9ycht8gi 104 26 the the DT cord-326314-9ycht8gi 104 27 stay stay VB cord-326314-9ycht8gi 104 28 - - HYPH cord-326314-9ycht8gi 104 29 at at IN cord-326314-9ycht8gi 104 30 - - HYPH cord-326314-9ycht8gi 104 31 home home NN cord-326314-9ycht8gi 104 32 order order NN cord-326314-9ycht8gi 104 33 took take VBD cord-326314-9ycht8gi 104 34 effect effect NN cord-326314-9ycht8gi 104 35 in in IN cord-326314-9ycht8gi 104 36 New New NNP cord-326314-9ycht8gi 104 37 York York NNP cord-326314-9ycht8gi 104 38 City City NNP cord-326314-9ycht8gi 104 39 [ [ -LRB- cord-326314-9ycht8gi 104 40 39 39 CD cord-326314-9ycht8gi 104 41 ] ] -RRB- cord-326314-9ycht8gi 104 42 : : : cord-326314-9ycht8gi 104 43 25 25 CD cord-326314-9ycht8gi 104 44 days day NNS cord-326314-9ycht8gi 104 45 after after IN cord-326314-9ycht8gi 104 46 time time NN cord-326314-9ycht8gi 104 47 t t NN cord-326314-9ycht8gi 104 48 0 0 CD cord-326314-9ycht8gi 104 49 . . . cord-326314-9ycht8gi 105 1 For for IN cord-326314-9ycht8gi 105 2 further further JJ cord-326314-9ycht8gi 105 3 simplicity simplicity NN cord-326314-9ycht8gi 105 4 , , , cord-326314-9ycht8gi 105 5 we -PRON- PRP cord-326314-9ycht8gi 105 6 took take VBD cord-326314-9ycht8gi 105 7 K K NNP cord-326314-9ycht8gi 105 8 i i PRP cord-326314-9ycht8gi 105 9 to to TO cord-326314-9ycht8gi 105 10 reflect reflect VB cord-326314-9ycht8gi 105 11 a a DT cord-326314-9ycht8gi 105 12 single single JJ cord-326314-9ycht8gi 105 13 implementation implementation NN cord-326314-9ycht8gi 105 14 of of IN cord-326314-9ycht8gi 105 15 a a DT cord-326314-9ycht8gi 105 16 social social JJ cord-326314-9ycht8gi 105 17 distancing distancing NN cord-326314-9ycht8gi 105 18 protocol protocol NN cord-326314-9ycht8gi 105 19 , , , cord-326314-9ycht8gi 105 20 and and CC cord-326314-9ycht8gi 105 21 adherence adherence NN cord-326314-9ycht8gi 105 22 to to IN cord-326314-9ycht8gi 105 23 that that DT cord-326314-9ycht8gi 105 24 protocol protocol NN cord-326314-9ycht8gi 105 25 throughout throughout IN cord-326314-9ycht8gi 105 26 the the DT cord-326314-9ycht8gi 105 27 remaining remain VBG cord-326314-9ycht8gi 105 28 temporal temporal JJ cord-326314-9ycht8gi 105 29 baseline baseline NN cord-326314-9ycht8gi 105 30 of of IN cord-326314-9ycht8gi 105 31 estimation estimation NN cord-326314-9ycht8gi 105 32 . . . cord-326314-9ycht8gi 106 1 Detection detection NN cord-326314-9ycht8gi 106 2 rates rate NNS cord-326314-9ycht8gi 106 3 impact impact VBP cord-326314-9ycht8gi 106 4 the the DT cord-326314-9ycht8gi 106 5 sizes size NNS cord-326314-9ycht8gi 106 6 of of IN cord-326314-9ycht8gi 106 7 the the DT cord-326314-9ycht8gi 106 8 subpopulations subpopulation NNS cord-326314-9ycht8gi 106 9 entering enter VBG cord-326314-9ycht8gi 106 10 hospitals hospital NNS cord-326314-9ycht8gi 106 11 , , , cord-326314-9ycht8gi 106 12 and and CC cord-326314-9ycht8gi 106 13 their -PRON- PRP$ cord-326314-9ycht8gi 106 14 values value NNS cord-326314-9ycht8gi 106 15 are be VBP cord-326314-9ycht8gi 106 16 highly highly RB cord-326314-9ycht8gi 106 17 uncertain uncertain JJ cord-326314-9ycht8gi 106 18 [ [ -LRB- cord-326314-9ycht8gi 106 19 3 3 CD cord-326314-9ycht8gi 106 20 , , , cord-326314-9ycht8gi 106 21 4 4 CD cord-326314-9ycht8gi 106 22 ] ] -RRB- cord-326314-9ycht8gi 106 23 . . . cord-326314-9ycht8gi 107 1 Thus thus RB cord-326314-9ycht8gi 107 2 we -PRON- PRP cord-326314-9ycht8gi 107 3 took take VBD cord-326314-9ycht8gi 107 4 these these DT cord-326314-9ycht8gi 107 5 quantities quantity NNS cord-326314-9ycht8gi 107 6 to to TO cord-326314-9ycht8gi 107 7 be be VB cord-326314-9ycht8gi 107 8 unknown unknown JJ cord-326314-9ycht8gi 107 9 , , , cord-326314-9ycht8gi 107 10 and and CC cord-326314-9ycht8gi 107 11 -as -as CD cord-326314-9ycht8gi 107 12 detection detection NN cord-326314-9ycht8gi 107 13 methods method NNS cord-326314-9ycht8gi 107 14 will will MD cord-326314-9ycht8gi 107 15 evolve evolve VB cord-326314-9ycht8gi 107 16 -time -time NN cord-326314-9ycht8gi 107 17 - - HYPH cord-326314-9ycht8gi 107 18 varying varying NN cord-326314-9ycht8gi 107 19 . . . cord-326314-9ycht8gi 108 1 We -PRON- PRP cord-326314-9ycht8gi 108 2 also also RB cord-326314-9ycht8gi 108 3 optimistically optimistically RB cord-326314-9ycht8gi 108 4 assumed assume VBD cord-326314-9ycht8gi 108 5 that that IN cord-326314-9ycht8gi 108 6 the the DT cord-326314-9ycht8gi 108 7 methods method NNS cord-326314-9ycht8gi 108 8 will will MD cord-326314-9ycht8gi 108 9 improve improve VB cord-326314-9ycht8gi 108 10 , , , cord-326314-9ycht8gi 108 11 and and CC cord-326314-9ycht8gi 108 12 thus thus RB cord-326314-9ycht8gi 108 13 we -PRON- PRP cord-326314-9ycht8gi 108 14 described describe VBD cord-326314-9ycht8gi 108 15 them -PRON- PRP cord-326314-9ycht8gi 108 16 as as IN cord-326314-9ycht8gi 108 17 increasing increase VBG cord-326314-9ycht8gi 108 18 functions function NNS cord-326314-9ycht8gi 108 19 of of IN cord-326314-9ycht8gi 108 20 time time NN cord-326314-9ycht8gi 108 21 . . . cord-326314-9ycht8gi 109 1 We -PRON- PRP cord-326314-9ycht8gi 109 2 used use VBD cord-326314-9ycht8gi 109 3 smoothly smoothly RB cord-326314-9ycht8gi 109 4 - - HYPH cord-326314-9ycht8gi 109 5 varying vary VBG cord-326314-9ycht8gi 109 6 forms form NNS cord-326314-9ycht8gi 109 7 , , , cord-326314-9ycht8gi 109 8 the the DT cord-326314-9ycht8gi 109 9 first first JJ cord-326314-9ycht8gi 109 10 linear linear NN cord-326314-9ycht8gi 109 11 and and CC cord-326314-9ycht8gi 109 12 the the DT cord-326314-9ycht8gi 109 13 second second JJ cord-326314-9ycht8gi 109 14 quadratic quadratic NN cord-326314-9ycht8gi 109 15 , , , cord-326314-9ycht8gi 109 16 to to TO cord-326314-9ycht8gi 109 17 preclude preclude VB cord-326314-9ycht8gi 109 18 symmetries symmetry NNS cord-326314-9ycht8gi 109 19 in in IN cord-326314-9ycht8gi 109 20 the the DT cord-326314-9ycht8gi 109 21 model model NN cord-326314-9ycht8gi 109 22 equations equation NNS cord-326314-9ycht8gi 109 23 . . . cord-326314-9ycht8gi 110 1 Meanwhile meanwhile RB cord-326314-9ycht8gi 110 2 , , , cord-326314-9ycht8gi 110 3 we -PRON- PRP cord-326314-9ycht8gi 110 4 took take VBD cord-326314-9ycht8gi 110 5 the the DT cord-326314-9ycht8gi 110 6 detection detection NN cord-326314-9ycht8gi 110 7 probability probability NN cord-326314-9ycht8gi 110 8 for for IN cord-326314-9ycht8gi 110 9 asymptomatic asymptomatic JJ cord-326314-9ycht8gi 110 10 cases case NNS cord-326314-9ycht8gi 110 11 ( ( -LRB- cord-326314-9ycht8gi 110 12 d d XX cord-326314-9ycht8gi 110 13 As as IN cord-326314-9ycht8gi 110 14 ) ) -RRB- cord-326314-9ycht8gi 110 15 to to TO cord-326314-9ycht8gi 110 16 be be VB cord-326314-9ycht8gi 110 17 known know VBN cord-326314-9ycht8gi 110 18 and and CC cord-326314-9ycht8gi 110 19 zero zero CD cord-326314-9ycht8gi 110 20 , , , cord-326314-9ycht8gi 110 21 a a DT cord-326314-9ycht8gi 110 22 reasonable reasonable JJ cord-326314-9ycht8gi 110 23 reflection reflection NN cord-326314-9ycht8gi 110 24 of of IN cord-326314-9ycht8gi 110 25 the the DT cord-326314-9ycht8gi 110 26 state state NN cord-326314-9ycht8gi 110 27 of of IN cord-326314-9ycht8gi 110 28 testing testing NN cord-326314-9ycht8gi 110 29 in in IN cord-326314-9ycht8gi 110 30 that that DT cord-326314-9ycht8gi 110 31 population population NN cord-326314-9ycht8gi 110 32 during during IN cord-326314-9ycht8gi 110 33 our -PRON- PRP$ cord-326314-9ycht8gi 110 34 study study NN cord-326314-9ycht8gi 110 35 period period NN cord-326314-9ycht8gi 110 36 . . . cord-326314-9ycht8gi 111 1 Finally finally RB cord-326314-9ycht8gi 111 2 , , , cord-326314-9ycht8gi 111 3 we -PRON- PRP cord-326314-9ycht8gi 111 4 assigned assign VBD cord-326314-9ycht8gi 111 5 as as IN cord-326314-9ycht8gi 111 6 unknowns unknown NNS cord-326314-9ycht8gi 111 7 the the DT cord-326314-9ycht8gi 111 8 fraction fraction NN cord-326314-9ycht8gi 111 9 of of IN cord-326314-9ycht8gi 111 10 cases case NNS cord-326314-9ycht8gi 111 11 that that WDT cord-326314-9ycht8gi 111 12 become become VBP cord-326314-9ycht8gi 111 13 symptomatic symptomatic JJ cord-326314-9ycht8gi 111 14 ( ( -LRB- cord-326314-9ycht8gi 111 15 f f FW cord-326314-9ycht8gi 111 16 sympt sympt NNP cord-326314-9ycht8gi 111 17 ) ) -RRB- cord-326314-9ycht8gi 111 18 and and CC cord-326314-9ycht8gi 111 19 fraction fraction NN cord-326314-9ycht8gi 111 20 of of IN cord-326314-9ycht8gi 111 21 symptomatic symptomatic JJ cord-326314-9ycht8gi 111 22 cases case NNS cord-326314-9ycht8gi 111 23 that that WDT cord-326314-9ycht8gi 111 24 become become VBP cord-326314-9ycht8gi 111 25 sufficiently sufficiently RB cord-326314-9ycht8gi 111 26 severe severe JJ cord-326314-9ycht8gi 111 27 to to TO cord-326314-9ycht8gi 111 28 require require VB cord-326314-9ycht8gi 111 29 hospitalization hospitalization NN cord-326314-9ycht8gi 111 30 ( ( -LRB- cord-326314-9ycht8gi 111 31 f f NNP cord-326314-9ycht8gi 111 32 severe severe JJ cord-326314-9ycht8gi 111 33 ) ) -RRB- cord-326314-9ycht8gi 111 34 , , , cord-326314-9ycht8gi 111 35 as as IN cord-326314-9ycht8gi 111 36 these these DT cord-326314-9ycht8gi 111 37 fractions fraction NNS cord-326314-9ycht8gi 111 38 possess possess VBP cord-326314-9ycht8gi 111 39 high high JJ cord-326314-9ycht8gi 111 40 uncertainties uncertainty NNS cord-326314-9ycht8gi 112 1 ( ( -LRB- cord-326314-9ycht8gi 112 2 Refs ref NNS cord-326314-9ycht8gi 112 3 [ [ -LRB- cord-326314-9ycht8gi 112 4 40 40 CD cord-326314-9ycht8gi 112 5 ] ] -RRB- cord-326314-9ycht8gi 112 6 and and CC cord-326314-9ycht8gi 112 7 [ [ -LRB- cord-326314-9ycht8gi 112 8 41 41 CD cord-326314-9ycht8gi 112 9 ] ] -RRB- cord-326314-9ycht8gi 112 10 , , , cord-326314-9ycht8gi 112 11 respectively respectively RB cord-326314-9ycht8gi 112 12 ) ) -RRB- cord-326314-9ycht8gi 112 13 . . . cord-326314-9ycht8gi 113 1 As as IN cord-326314-9ycht8gi 113 2 they -PRON- PRP cord-326314-9ycht8gi 113 3 reflect reflect VBP cord-326314-9ycht8gi 113 4 an an DT cord-326314-9ycht8gi 113 5 intrinsic intrinsic JJ cord-326314-9ycht8gi 113 6 property property NN cord-326314-9ycht8gi 113 7 of of IN cord-326314-9ycht8gi 113 8 the the DT cord-326314-9ycht8gi 113 9 disease disease NN cord-326314-9ycht8gi 113 10 , , , cord-326314-9ycht8gi 113 11 we -PRON- PRP cord-326314-9ycht8gi 113 12 took take VBD cord-326314-9ycht8gi 113 13 them -PRON- PRP cord-326314-9ycht8gi 113 14 to to TO cord-326314-9ycht8gi 113 15 be be VB cord-326314-9ycht8gi 113 16 constants constant NNS cord-326314-9ycht8gi 113 17 . . . cord-326314-9ycht8gi 114 1 All all DT cord-326314-9ycht8gi 114 2 other other JJ cord-326314-9ycht8gi 114 3 model model NN cord-326314-9ycht8gi 114 4 parameters parameter NNS cord-326314-9ycht8gi 114 5 were be VBD cord-326314-9ycht8gi 114 6 taken take VBN cord-326314-9ycht8gi 114 7 to to TO cord-326314-9ycht8gi 114 8 be be VB cord-326314-9ycht8gi 114 9 known know VBN cord-326314-9ycht8gi 114 10 and and CC cord-326314-9ycht8gi 114 11 constant constant JJ cord-326314-9ycht8gi 115 1 ( ( -LRB- cord-326314-9ycht8gi 115 2 Appendix Appendix NNP cord-326314-9ycht8gi 115 3 A A NNP cord-326314-9ycht8gi 115 4 ) ) -RRB- cord-326314-9ycht8gi 115 5 ; ; : cord-326314-9ycht8gi 115 6 however however RB cord-326314-9ycht8gi 115 7 , , , cord-326314-9ycht8gi 115 8 the the DT cord-326314-9ycht8gi 115 9 values value NNS cord-326314-9ycht8gi 115 10 of of IN cord-326314-9ycht8gi 115 11 many many JJ cord-326314-9ycht8gi 115 12 other other JJ cord-326314-9ycht8gi 115 13 model model NN cord-326314-9ycht8gi 115 14 parameters parameter NNS cord-326314-9ycht8gi 115 15 also also RB cord-326314-9ycht8gi 115 16 possess possess VBP cord-326314-9ycht8gi 115 17 significant significant JJ cord-326314-9ycht8gi 115 18 uncertainties uncertainty NNS cord-326314-9ycht8gi 115 19 given give VBN cord-326314-9ycht8gi 115 20 the the DT cord-326314-9ycht8gi 115 21 reported report VBN cord-326314-9ycht8gi 115 22 data datum NNS cord-326314-9ycht8gi 115 23 , , , cord-326314-9ycht8gi 115 24 including include VBG cord-326314-9ycht8gi 115 25 , , , cord-326314-9ycht8gi 115 26 for for IN cord-326314-9ycht8gi 115 27 example example NN cord-326314-9ycht8gi 115 28 , , , cord-326314-9ycht8gi 115 29 the the DT cord-326314-9ycht8gi 115 30 fraction fraction NN cord-326314-9ycht8gi 115 31 of of IN cord-326314-9ycht8gi 115 32 those those DT cord-326314-9ycht8gi 115 33 hospitalized hospitalize VBN cord-326314-9ycht8gi 115 34 that that WDT cord-326314-9ycht8gi 115 35 require require VBP cord-326314-9ycht8gi 115 36 ICU ICU NNP cord-326314-9ycht8gi 115 37 care care NN cord-326314-9ycht8gi 115 38 . . . cord-326314-9ycht8gi 116 1 Future future JJ cord-326314-9ycht8gi 116 2 VA VA NNP cord-326314-9ycht8gi 116 3 experiments experiment NNS cord-326314-9ycht8gi 116 4 can can MD cord-326314-9ycht8gi 116 5 treat treat VB cord-326314-9ycht8gi 116 6 these these DT cord-326314-9ycht8gi 116 7 quantities quantity NNS cord-326314-9ycht8gi 116 8 as as IN cord-326314-9ycht8gi 116 9 unknowns unknown NNS cord-326314-9ycht8gi 116 10 as as RB cord-326314-9ycht8gi 116 11 well well RB cord-326314-9ycht8gi 116 12 . . . cord-326314-9ycht8gi 117 1 The the DT cord-326314-9ycht8gi 117 2 simulated simulated JJ cord-326314-9ycht8gi 117 3 experiments experiment NNS cord-326314-9ycht8gi 117 4 are be VBP cord-326314-9ycht8gi 117 5 summarized summarize VBN cord-326314-9ycht8gi 117 6 in in IN cord-326314-9ycht8gi 117 7 the the DT cord-326314-9ycht8gi 117 8 schematic schematic NN cord-326314-9ycht8gi 117 9 of of IN cord-326314-9ycht8gi 117 10 The the DT cord-326314-9ycht8gi 117 11 base base NN cord-326314-9ycht8gi 117 12 experiment experiment NN cord-326314-9ycht8gi 117 13 ( ( -LRB- cord-326314-9ycht8gi 117 14 i i PRP cord-326314-9ycht8gi 117 15 in in IN cord-326314-9ycht8gi 117 16 Figure Figure NNP cord-326314-9ycht8gi 117 17 2 2 CD cord-326314-9ycht8gi 117 18 ) ) -RRB- cord-326314-9ycht8gi 117 19 possesses possess VBZ cord-326314-9ycht8gi 117 20 the the DT cord-326314-9ycht8gi 117 21 following follow VBG cord-326314-9ycht8gi 117 22 features feature NNS cord-326314-9ycht8gi 117 23 : : : cord-326314-9ycht8gi 117 24 a a LS cord-326314-9ycht8gi 117 25 ) ) -RRB- cord-326314-9ycht8gi 117 26 five five CD cord-326314-9ycht8gi 117 27 measured measure VBN cord-326314-9ycht8gi 117 28 populations population NNS cord-326314-9ycht8gi 117 29 : : : cord-326314-9ycht8gi 117 30 detected detect VBN cord-326314-9ycht8gi 117 31 asymptomatic asymptomatic JJ cord-326314-9ycht8gi 118 1 As as IN cord-326314-9ycht8gi 118 2 det det NNP cord-326314-9ycht8gi 118 3 , , , cord-326314-9ycht8gi 118 4 detected detect VBD cord-326314-9ycht8gi 118 5 mild mild JJ cord-326314-9ycht8gi 118 6 symptomatic symptomatic JJ cord-326314-9ycht8gi 118 7 Sym sym NN cord-326314-9ycht8gi 118 8 det det NN cord-326314-9ycht8gi 118 9 , , , cord-326314-9ycht8gi 118 10 detected detect VBD cord-326314-9ycht8gi 118 11 severe severe JJ cord-326314-9ycht8gi 118 12 symptomatic symptomatic JJ cord-326314-9ycht8gi 118 13 Sys Sys NNP cord-326314-9ycht8gi 118 14 det det NN cord-326314-9ycht8gi 118 15 , , , cord-326314-9ycht8gi 118 16 Recovered recovered JJ cord-326314-9ycht8gi 118 17 R R NNP cord-326314-9ycht8gi 118 18 , , , cord-326314-9ycht8gi 118 19 and and CC cord-326314-9ycht8gi 118 20 Dead Dead NNP cord-326314-9ycht8gi 118 21 D d NN cord-326314-9ycht8gi 118 22 ; ; : cord-326314-9ycht8gi 118 23 b b LS cord-326314-9ycht8gi 118 24 ) ) -RRB- cord-326314-9ycht8gi 118 25 a a DT cord-326314-9ycht8gi 118 26 temporal temporal JJ cord-326314-9ycht8gi 118 27 baseline baseline NN cord-326314-9ycht8gi 118 28 of of IN cord-326314-9ycht8gi 118 29 101 101 CD cord-326314-9ycht8gi 118 30 days day NNS cord-326314-9ycht8gi 118 31 , , , cord-326314-9ycht8gi 118 32 beginning begin VBG cord-326314-9ycht8gi 118 33 on on IN cord-326314-9ycht8gi 118 34 2020 2020 CD cord-326314-9ycht8gi 118 35 February February NNP cord-326314-9ycht8gi 118 36 26 26 CD cord-326314-9ycht8gi 118 37 ; ; : cord-326314-9ycht8gi 118 38 c c LS cord-326314-9ycht8gi 118 39 ) ) -RRB- cord-326314-9ycht8gi 118 40 no no DT cord-326314-9ycht8gi 118 41 noise noise NN cord-326314-9ycht8gi 118 42 in in IN cord-326314-9ycht8gi 118 43 measurements measurement NNS cord-326314-9ycht8gi 118 44 . . . cord-326314-9ycht8gi 119 1 3 3 LS cord-326314-9ycht8gi 120 1 The the DT cord-326314-9ycht8gi 120 2 reproduction reproduction NN cord-326314-9ycht8gi 120 3 number number NN cord-326314-9ycht8gi 120 4 R r NN cord-326314-9ycht8gi 120 5 0 0 CD cord-326314-9ycht8gi 120 6 , , , cord-326314-9ycht8gi 120 7 in in IN cord-326314-9ycht8gi 120 8 the the DT cord-326314-9ycht8gi 120 9 simplest simple JJS cord-326314-9ycht8gi 120 10 SIR SIR NNP cord-326314-9ycht8gi 120 11 form form NN cord-326314-9ycht8gi 120 12 , , , cord-326314-9ycht8gi 120 13 can can MD cord-326314-9ycht8gi 120 14 be be VB cord-326314-9ycht8gi 120 15 written write VBN cord-326314-9ycht8gi 120 16 as as IN cord-326314-9ycht8gi 120 17 the the DT cord-326314-9ycht8gi 120 18 effective effective JJ cord-326314-9ycht8gi 120 19 contact contact NN cord-326314-9ycht8gi 120 20 rate rate NN cord-326314-9ycht8gi 120 21 divided divide VBN cord-326314-9ycht8gi 120 22 by by IN cord-326314-9ycht8gi 120 23 the the DT cord-326314-9ycht8gi 120 24 recovery recovery NN cord-326314-9ycht8gi 120 25 rate rate NN cord-326314-9ycht8gi 120 26 . . . cord-326314-9ycht8gi 121 1 In in IN cord-326314-9ycht8gi 121 2 practice practice NN cord-326314-9ycht8gi 121 3 , , , cord-326314-9ycht8gi 121 4 R r NN cord-326314-9ycht8gi 121 5 0 0 CD cord-326314-9ycht8gi 121 6 is be VBZ cord-326314-9ycht8gi 121 7 a a DT cord-326314-9ycht8gi 121 8 challenge challenge NN cord-326314-9ycht8gi 121 9 to to TO cord-326314-9ycht8gi 121 10 infer infer VB cord-326314-9ycht8gi 121 11 [ [ -LRB- cord-326314-9ycht8gi 121 12 22 22 CD cord-326314-9ycht8gi 121 13 , , , cord-326314-9ycht8gi 121 14 [ [ -LRB- cord-326314-9ycht8gi 121 15 36 36 CD cord-326314-9ycht8gi 121 16 ] ] -RRB- cord-326314-9ycht8gi 121 17 [ [ -LRB- cord-326314-9ycht8gi 121 18 37 37 CD cord-326314-9ycht8gi 121 19 ] ] -RRB- cord-326314-9ycht8gi 121 20 [ [ -LRB- cord-326314-9ycht8gi 121 21 38 38 CD cord-326314-9ycht8gi 121 22 ] ] -RRB- cord-326314-9ycht8gi 121 23 . . . cord-326314-9ycht8gi 122 1 7 7 LS cord-326314-9ycht8gi 122 2 J J NNP cord-326314-9ycht8gi 122 3 o o NN cord-326314-9ycht8gi 122 4 u u NN cord-326314-9ycht8gi 122 5 r r NN cord-326314-9ycht8gi 122 6 n n NN cord-326314-9ycht8gi 122 7 a a DT cord-326314-9ycht8gi 122 8 l l NN cord-326314-9ycht8gi 122 9 P p NN cord-326314-9ycht8gi 122 10 r r NN cord-326314-9ycht8gi 122 11 e e NN cord-326314-9ycht8gi 122 12 -p -p NN cord-326314-9ycht8gi 123 1 r r LS cord-326314-9ycht8gi 124 1 o o UH cord-326314-9ycht8gi 125 1 o o UH cord-326314-9ycht8gi 125 2 f f NNP cord-326314-9ycht8gi 126 1 The the DT cord-326314-9ycht8gi 126 2 three three CD cord-326314-9ycht8gi 126 3 variations variation NNS cord-326314-9ycht8gi 126 4 on on IN cord-326314-9ycht8gi 126 5 this this DT cord-326314-9ycht8gi 126 6 basic basic JJ cord-326314-9ycht8gi 126 7 experiment experiment NN cord-326314-9ycht8gi 126 8 ( ( -LRB- cord-326314-9ycht8gi 126 9 ii ii NNP cord-326314-9ycht8gi 126 10 through through IN cord-326314-9ycht8gi 126 11 iv iv CD cord-326314-9ycht8gi 126 12 in in IN cord-326314-9ycht8gi 126 13 Figure figure NN cord-326314-9ycht8gi 126 14 2 2 CD cord-326314-9ycht8gi 126 15 ) ) -RRB- cord-326314-9ycht8gi 126 16 , , , cord-326314-9ycht8gi 126 17 incorporate incorporate VB cord-326314-9ycht8gi 126 18 the the DT cord-326314-9ycht8gi 126 19 following follow VBG cord-326314-9ycht8gi 126 20 independent independent JJ cord-326314-9ycht8gi 126 21 changes change NNS cord-326314-9ycht8gi 126 22 . . . cord-326314-9ycht8gi 127 1 In in IN cord-326314-9ycht8gi 127 2 Experiment Experiment NNP cord-326314-9ycht8gi 127 3 ii ii NNP cord-326314-9ycht8gi 127 4 , , , cord-326314-9ycht8gi 127 5 the the DT cord-326314-9ycht8gi 127 6 R r NN cord-326314-9ycht8gi 127 7 population population NN cord-326314-9ycht8gi 127 8 is be VBZ cord-326314-9ycht8gi 127 9 not not RB cord-326314-9ycht8gi 127 10 measured measure VBN cord-326314-9ycht8gi 127 11 -an -an NNS cord-326314-9ycht8gi 127 12 example example NN cord-326314-9ycht8gi 127 13 designed design VBN cord-326314-9ycht8gi 127 14 to to TO cord-326314-9ycht8gi 127 15 reflect reflect VB cord-326314-9ycht8gi 127 16 the the DT cord-326314-9ycht8gi 127 17 current current JJ cord-326314-9ycht8gi 127 18 situation situation NN cord-326314-9ycht8gi 127 19 in in IN cord-326314-9ycht8gi 127 20 some some DT cord-326314-9ycht8gi 127 21 localities locality NNS cord-326314-9ycht8gi 127 22 ( ( -LRB- cord-326314-9ycht8gi 128 1 e.g. e.g. IN cord-326314-9ycht8gi 128 2 Refs Refs NNPS cord-326314-9ycht8gi 128 3 [ [ -LRB- cord-326314-9ycht8gi 128 4 3 3 CD cord-326314-9ycht8gi 128 5 , , , cord-326314-9ycht8gi 128 6 4 4 CD cord-326314-9ycht8gi 128 7 ] ] -RRB- cord-326314-9ycht8gi 128 8 ) ) -RRB- cord-326314-9ycht8gi 128 9 . . . cord-326314-9ycht8gi 129 1 Experiment experiment NN cord-326314-9ycht8gi 129 2 iii iii NNP cord-326314-9ycht8gi 129 3 includes include VBZ cord-326314-9ycht8gi 129 4 a a DT cord-326314-9ycht8gi 129 5 ∼ ∼ NNP cord-326314-9ycht8gi 129 6 five five CD cord-326314-9ycht8gi 129 7 percent percent NN cord-326314-9ycht8gi 129 8 noise noise NN cord-326314-9ycht8gi 129 9 level level NN cord-326314-9ycht8gi 129 10 ( ( -LRB- cord-326314-9ycht8gi 129 11 for for IN cord-326314-9ycht8gi 129 12 the the DT cord-326314-9ycht8gi 129 13 form form NN cord-326314-9ycht8gi 129 14 of of IN cord-326314-9ycht8gi 129 15 additive additive NN cord-326314-9ycht8gi 129 16 noise noise NN cord-326314-9ycht8gi 129 17 , , , cord-326314-9ycht8gi 129 18 see see VB cord-326314-9ycht8gi 129 19 Appendix Appendix NNP cord-326314-9ycht8gi 129 20 C C NNP cord-326314-9ycht8gi 129 21 ) ) -RRB- cord-326314-9ycht8gi 129 22 in in IN cord-326314-9ycht8gi 129 23 the the DT cord-326314-9ycht8gi 129 24 simulated simulated JJ cord-326314-9ycht8gi 129 25 R r NN cord-326314-9ycht8gi 129 26 data data NN cord-326314-9ycht8gi 129 27 , , , cord-326314-9ycht8gi 129 28 and and CC cord-326314-9ycht8gi 129 29 Experiment Experiment NNP cord-326314-9ycht8gi 129 30 iv iv CD cord-326314-9ycht8gi 129 31 includes include VBZ cord-326314-9ycht8gi 129 32 that that DT cord-326314-9ycht8gi 129 33 noise noise NN cord-326314-9ycht8gi 129 34 level level NN cord-326314-9ycht8gi 129 35 in in IN cord-326314-9ycht8gi 129 36 addition addition NN cord-326314-9ycht8gi 129 37 to to IN cord-326314-9ycht8gi 129 38 a a DT cord-326314-9ycht8gi 129 39 doubled double VBN cord-326314-9ycht8gi 129 40 temporal temporal JJ cord-326314-9ycht8gi 129 41 baseline baseline NN cord-326314-9ycht8gi 129 42 . . . cord-326314-9ycht8gi 130 1 For for IN cord-326314-9ycht8gi 130 2 each each DT cord-326314-9ycht8gi 130 3 experiment experiment NN cord-326314-9ycht8gi 130 4 , , , cord-326314-9ycht8gi 130 5 twenty twenty CD cord-326314-9ycht8gi 130 6 independent independent JJ cord-326314-9ycht8gi 130 7 calculations calculation NNS cord-326314-9ycht8gi 130 8 were be VBD cord-326314-9ycht8gi 130 9 initiated initiate VBN cord-326314-9ycht8gi 130 10 in in IN cord-326314-9ycht8gi 130 11 parallel parallel JJ cord-326314-9ycht8gi 130 12 searches search NNS cord-326314-9ycht8gi 130 13 , , , cord-326314-9ycht8gi 130 14 each each DT cord-326314-9ycht8gi 130 15 with with IN cord-326314-9ycht8gi 130 16 a a DT cord-326314-9ycht8gi 130 17 randomly randomly RB cord-326314-9ycht8gi 130 18 - - HYPH cord-326314-9ycht8gi 130 19 generated generate VBN cord-326314-9ycht8gi 130 20 set set NN cord-326314-9ycht8gi 130 21 of of IN cord-326314-9ycht8gi 130 22 initial initial JJ cord-326314-9ycht8gi 130 23 conditions condition NNS cord-326314-9ycht8gi 130 24 on on IN cord-326314-9ycht8gi 130 25 state state NN cord-326314-9ycht8gi 130 26 variable variable NN cord-326314-9ycht8gi 130 27 and and CC cord-326314-9ycht8gi 130 28 parameter parameter NN cord-326314-9ycht8gi 130 29 values value NNS cord-326314-9ycht8gi 130 30 . . . cord-326314-9ycht8gi 131 1 For for IN cord-326314-9ycht8gi 131 2 technical technical JJ cord-326314-9ycht8gi 131 3 details detail NNS cord-326314-9ycht8gi 131 4 of of IN cord-326314-9ycht8gi 131 5 all all DT cord-326314-9ycht8gi 131 6 experimental experimental JJ cord-326314-9ycht8gi 131 7 designs design NNS cord-326314-9ycht8gi 131 8 and and CC cord-326314-9ycht8gi 131 9 implementation implementation NN cord-326314-9ycht8gi 131 10 , , , cord-326314-9ycht8gi 131 11 see see VB cord-326314-9ycht8gi 131 12 Appendix Appendix NNP cord-326314-9ycht8gi 131 13 C. C. NNP cord-326314-9ycht8gi 132 1 The the DT cord-326314-9ycht8gi 132 2 salient salient JJ cord-326314-9ycht8gi 132 3 results result NNS cord-326314-9ycht8gi 132 4 for for IN cord-326314-9ycht8gi 132 5 the the DT cord-326314-9ycht8gi 132 6 simulated simulated JJ cord-326314-9ycht8gi 132 7 experiments experiment NNS cord-326314-9ycht8gi 132 8 i i PRP cord-326314-9ycht8gi 132 9 through through IN cord-326314-9ycht8gi 132 10 iv iv CD cord-326314-9ycht8gi 132 11 are be VBP cord-326314-9ycht8gi 132 12 as as IN cord-326314-9ycht8gi 132 13 follows follow VBZ cord-326314-9ycht8gi 132 14 : : : cord-326314-9ycht8gi 133 1 i i PRP cord-326314-9ycht8gi 133 2 Table Table NNP cord-326314-9ycht8gi 133 3 2 2 CD cord-326314-9ycht8gi 133 4 . . . cord-326314-9ycht8gi 134 1 The the DT cord-326314-9ycht8gi 134 2 base base NN cord-326314-9ycht8gi 134 3 experiment experiment NN cord-326314-9ycht8gi 134 4 that that WDT cord-326314-9ycht8gi 134 5 employed employ VBD cord-326314-9ycht8gi 134 6 five five CD cord-326314-9ycht8gi 134 7 noiseless noiseless JJ cord-326314-9ycht8gi 134 8 measured measure VBN cord-326314-9ycht8gi 134 9 populations population NNS cord-326314-9ycht8gi 134 10 over over IN cord-326314-9ycht8gi 134 11 101 101 CD cord-326314-9ycht8gi 134 12 days day NNS cord-326314-9ycht8gi 134 13 yielded yield VBD cord-326314-9ycht8gi 134 14 an an DT cord-326314-9ycht8gi 134 15 excellent excellent JJ cord-326314-9ycht8gi 134 16 solution solution NN cord-326314-9ycht8gi 134 17 in in IN cord-326314-9ycht8gi 134 18 terms term NNS cord-326314-9ycht8gi 134 19 of of IN cord-326314-9ycht8gi 134 20 model model NN cord-326314-9ycht8gi 134 21 evolution evolution NN cord-326314-9ycht8gi 134 22 and and CC cord-326314-9ycht8gi 134 23 parameter parameter NN cord-326314-9ycht8gi 134 24 estimates estimate NNS cord-326314-9ycht8gi 134 25 . . . cord-326314-9ycht8gi 135 1 Prior prior RB cord-326314-9ycht8gi 135 2 to to IN cord-326314-9ycht8gi 135 3 examining examine VBG cord-326314-9ycht8gi 135 4 the the DT cord-326314-9ycht8gi 135 5 solution solution NN cord-326314-9ycht8gi 135 6 , , , cord-326314-9ycht8gi 135 7 we -PRON- PRP cord-326314-9ycht8gi 135 8 shall shall MD cord-326314-9ycht8gi 135 9 first first RB cord-326314-9ycht8gi 135 10 show show VB cord-326314-9ycht8gi 135 11 the the DT cord-326314-9ycht8gi 135 12 cost cost NN cord-326314-9ycht8gi 135 13 function function NN cord-326314-9ycht8gi 135 14 versus versus IN cord-326314-9ycht8gi 135 15 the the DT cord-326314-9ycht8gi 135 16 annealing annealing NN cord-326314-9ycht8gi 135 17 parameter parameter NN cord-326314-9ycht8gi 135 18 β β NN cord-326314-9ycht8gi 135 19 , , , cord-326314-9ycht8gi 135 20 as as IN cord-326314-9ycht8gi 135 21 this this DT cord-326314-9ycht8gi 135 22 distribution distribution NN cord-326314-9ycht8gi 135 23 can can MD cord-326314-9ycht8gi 135 24 serve serve VB cord-326314-9ycht8gi 135 25 as as IN cord-326314-9ycht8gi 135 26 a a DT cord-326314-9ycht8gi 135 27 tool tool NN cord-326314-9ycht8gi 135 28 for for IN cord-326314-9ycht8gi 135 29 assessing assess VBG cord-326314-9ycht8gi 135 30 the the DT cord-326314-9ycht8gi 135 31 significance significance NN cord-326314-9ycht8gi 135 32 of of IN cord-326314-9ycht8gi 135 33 a a DT cord-326314-9ycht8gi 135 34 solution solution NN cord-326314-9ycht8gi 135 35 . . . cord-326314-9ycht8gi 136 1 Figure figure NN cord-326314-9ycht8gi 136 2 3 3 CD cord-326314-9ycht8gi 136 3 shows show VBZ cord-326314-9ycht8gi 136 4 the the DT cord-326314-9ycht8gi 136 5 evolution evolution NN cord-326314-9ycht8gi 136 6 of of IN cord-326314-9ycht8gi 136 7 the the DT cord-326314-9ycht8gi 136 8 cost cost NN cord-326314-9ycht8gi 136 9 throughout throughout IN cord-326314-9ycht8gi 136 10 annealing anneal VBG cord-326314-9ycht8gi 136 11 , , , cord-326314-9ycht8gi 136 12 for for IN cord-326314-9ycht8gi 136 13 the the DT cord-326314-9ycht8gi 136 14 ten ten CD cord-326314-9ycht8gi 136 15 distinct distinct JJ cord-326314-9ycht8gi 136 16 independent independent JJ cord-326314-9ycht8gi 136 17 paths path NNS cord-326314-9ycht8gi 136 18 that that WDT cord-326314-9ycht8gi 136 19 were be VBD cord-326314-9ycht8gi 136 20 initiated initiate VBN cord-326314-9ycht8gi 136 21 ; ; : cord-326314-9ycht8gi 136 22 the the DT cord-326314-9ycht8gi 136 23 x x NN cord-326314-9ycht8gi 136 24 - - HYPH cord-326314-9ycht8gi 136 25 axis axis NN cord-326314-9ycht8gi 136 26 shows show VBZ cord-326314-9ycht8gi 136 27 the the DT cord-326314-9ycht8gi 136 28 value value NN cord-326314-9ycht8gi 136 29 of of IN cord-326314-9ycht8gi 136 30 Annealing Annealing NNP cord-326314-9ycht8gi 136 31 Parameter Parameter NNP cord-326314-9ycht8gi 136 32 β β NN cord-326314-9ycht8gi 136 33 , , , cord-326314-9ycht8gi 136 34 or or CC cord-326314-9ycht8gi 136 35 : : : cord-326314-9ycht8gi 136 36 the the DT cord-326314-9ycht8gi 136 37 increasing increase VBG cord-326314-9ycht8gi 136 38 rigidity rigidity NN cord-326314-9ycht8gi 136 39 of of IN cord-326314-9ycht8gi 136 40 the the DT cord-326314-9ycht8gi 136 41 model model NN cord-326314-9ycht8gi 136 42 constraint constraint NN cord-326314-9ycht8gi 136 43 . . . cord-326314-9ycht8gi 137 1 At at IN cord-326314-9ycht8gi 137 2 the the DT cord-326314-9ycht8gi 137 3 start start NN cord-326314-9ycht8gi 137 4 of of IN cord-326314-9ycht8gi 137 5 iterations iteration NNS cord-326314-9ycht8gi 137 6 , , , cord-326314-9ycht8gi 137 7 the the DT cord-326314-9ycht8gi 137 8 cost cost NN cord-326314-9ycht8gi 137 9 function function NN cord-326314-9ycht8gi 137 10 is be VBZ cord-326314-9ycht8gi 137 11 mainly mainly RB cord-326314-9ycht8gi 137 12 fitting fit VBG cord-326314-9ycht8gi 137 13 the the DT cord-326314-9ycht8gi 137 14 measurements measurement NNS cord-326314-9ycht8gi 137 15 to to IN cord-326314-9ycht8gi 137 16 data datum NNS cord-326314-9ycht8gi 137 17 , , , cord-326314-9ycht8gi 137 18 and and CC cord-326314-9ycht8gi 137 19 its -PRON- PRP$ cord-326314-9ycht8gi 137 20 value value NN cord-326314-9ycht8gi 137 21 begins begin VBZ cord-326314-9ycht8gi 137 22 to to TO cord-326314-9ycht8gi 137 23 climb climb VB cord-326314-9ycht8gi 137 24 as as IN cord-326314-9ycht8gi 137 25 the the DT cord-326314-9ycht8gi 137 26 model model NN cord-326314-9ycht8gi 137 27 penalty penalty NN cord-326314-9ycht8gi 137 28 is be VBZ cord-326314-9ycht8gi 137 29 gradually gradually RB cord-326314-9ycht8gi 137 30 imposed impose VBN cord-326314-9ycht8gi 137 31 . . . cord-326314-9ycht8gi 138 1 If if IN cord-326314-9ycht8gi 138 2 the the DT cord-326314-9ycht8gi 138 3 procedure procedure NN cord-326314-9ycht8gi 138 4 finds find VBZ cord-326314-9ycht8gi 138 5 a a DT cord-326314-9ycht8gi 138 6 solution solution NN cord-326314-9ycht8gi 138 7 8 8 CD cord-326314-9ycht8gi 138 8 J j NN cord-326314-9ycht8gi 138 9 o o NN cord-326314-9ycht8gi 138 10 u u NN cord-326314-9ycht8gi 138 11 r r NN cord-326314-9ycht8gi 138 12 n n NN cord-326314-9ycht8gi 138 13 a a DT cord-326314-9ycht8gi 138 14 l l NN cord-326314-9ycht8gi 138 15 P p NN cord-326314-9ycht8gi 138 16 r r NN cord-326314-9ycht8gi 138 17 e e NN cord-326314-9ycht8gi 138 18 -p -p NN cord-326314-9ycht8gi 139 1 r r LS cord-326314-9ycht8gi 140 1 o o UH cord-326314-9ycht8gi 141 1 o o UH cord-326314-9ycht8gi 141 2 f f NN cord-326314-9ycht8gi 141 3 that that WDT cord-326314-9ycht8gi 141 4 is be VBZ cord-326314-9ycht8gi 141 5 consistent consistent JJ cord-326314-9ycht8gi 141 6 not not RB cord-326314-9ycht8gi 141 7 only only RB cord-326314-9ycht8gi 141 8 with with IN cord-326314-9ycht8gi 141 9 the the DT cord-326314-9ycht8gi 141 10 measurements measurement NNS cord-326314-9ycht8gi 141 11 , , , cord-326314-9ycht8gi 141 12 but but CC cord-326314-9ycht8gi 141 13 also also RB cord-326314-9ycht8gi 141 14 with with IN cord-326314-9ycht8gi 141 15 the the DT cord-326314-9ycht8gi 141 16 model model NN cord-326314-9ycht8gi 141 17 , , , cord-326314-9ycht8gi 141 18 then then RB cord-326314-9ycht8gi 141 19 the the DT cord-326314-9ycht8gi 141 20 cost cost NN cord-326314-9ycht8gi 141 21 will will MD cord-326314-9ycht8gi 141 22 plateau plateau NN cord-326314-9ycht8gi 141 23 . . . cord-326314-9ycht8gi 142 1 In in IN cord-326314-9ycht8gi 142 2 prior prior RB cord-326314-9ycht8gi 142 3 to to IN cord-326314-9ycht8gi 142 4 its -PRON- PRP$ cord-326314-9ycht8gi 142 5 steep steep JJ cord-326314-9ycht8gi 142 6 decline decline NN cord-326314-9ycht8gi 142 7 . . . cord-326314-9ycht8gi 143 1 We -PRON- PRP cord-326314-9ycht8gi 143 2 noted note VBD cord-326314-9ycht8gi 143 3 no no DT cord-326314-9ycht8gi 143 4 improvement improvement NN cord-326314-9ycht8gi 143 5 in in IN cord-326314-9ycht8gi 143 6 this this DT cord-326314-9ycht8gi 143 7 estimate estimate NN cord-326314-9ycht8gi 143 8 for for IN cord-326314-9ycht8gi 143 9 K K NNP cord-326314-9ycht8gi 143 10 i i NNP cord-326314-9ycht8gi 143 11 ( ( -LRB- cord-326314-9ycht8gi 143 12 t t NN cord-326314-9ycht8gi 143 13 ) ) -RRB- cord-326314-9ycht8gi 143 14 , , , cord-326314-9ycht8gi 143 15 following follow VBG cord-326314-9ycht8gi 143 16 a a DT cord-326314-9ycht8gi 143 17 tenfold tenfold JJ cord-326314-9ycht8gi 143 18 increase increase NN cord-326314-9ycht8gi 143 19 in in IN cord-326314-9ycht8gi 143 20 the the DT cord-326314-9ycht8gi 143 21 temporal temporal JJ cord-326314-9ycht8gi 143 22 resolution resolution NN cord-326314-9ycht8gi 143 23 of of IN cord-326314-9ycht8gi 143 24 measurements measurement NNS cord-326314-9ycht8gi 143 25 ( ( -LRB- cord-326314-9ycht8gi 143 26 not not RB cord-326314-9ycht8gi 143 27 shown show VBN cord-326314-9ycht8gi 143 28 ) ) -RRB- cord-326314-9ycht8gi 143 29 . . . cord-326314-9ycht8gi 144 1 The the DT cord-326314-9ycht8gi 144 2 procedure procedure NN cord-326314-9ycht8gi 144 3 does do VBZ cord-326314-9ycht8gi 144 4 appear appear VB cord-326314-9ycht8gi 144 5 to to TO cord-326314-9ycht8gi 144 6 recognize recognize VB cord-326314-9ycht8gi 144 7 that that IN cord-326314-9ycht8gi 144 8 a a DT cord-326314-9ycht8gi 144 9 fast fast JJ cord-326314-9ycht8gi 144 10 transition transition NN cord-326314-9ycht8gi 144 11 in in IN cord-326314-9ycht8gi 144 12 the the DT cord-326314-9ycht8gi 144 13 value value NN cord-326314-9ycht8gi 144 14 of of IN cord-326314-9ycht8gi 144 15 K K NNP cord-326314-9ycht8gi 145 1 i i PRP cord-326314-9ycht8gi 145 2 occurred occur VBD cord-326314-9ycht8gi 145 3 at at IN cord-326314-9ycht8gi 145 4 early early JJ cord-326314-9ycht8gi 145 5 times time NNS cord-326314-9ycht8gi 145 6 , , , cord-326314-9ycht8gi 145 7 and and CC cord-326314-9ycht8gi 145 8 that that IN cord-326314-9ycht8gi 145 9 that that DT cord-326314-9ycht8gi 145 10 value value NN cord-326314-9ycht8gi 145 11 was be VBD cord-326314-9ycht8gi 145 12 previously previously RB cord-326314-9ycht8gi 145 13 higher high JJR cord-326314-9ycht8gi 145 14 . . . cord-326314-9ycht8gi 146 1 It -PRON- PRP cord-326314-9ycht8gi 146 2 will will MD cord-326314-9ycht8gi 146 3 be be VB cord-326314-9ycht8gi 146 4 important important JJ cord-326314-9ycht8gi 146 5 to to TO cord-326314-9ycht8gi 146 6 investigate investigate VB cord-326314-9ycht8gi 146 7 the the DT cord-326314-9ycht8gi 146 8 reason reason NN cord-326314-9ycht8gi 146 9 for for IN cord-326314-9ycht8gi 146 10 this this DT cord-326314-9ycht8gi 146 11 failure failure NN cord-326314-9ycht8gi 146 12 in in IN cord-326314-9ycht8gi 146 13 the the DT cord-326314-9ycht8gi 146 14 estimation estimation NN cord-326314-9ycht8gi 146 15 of of IN cord-326314-9ycht8gi 146 16 K K NNP cord-326314-9ycht8gi 146 17 i i PRP cord-326314-9ycht8gi 146 18 at at IN cord-326314-9ycht8gi 146 19 early early JJ cord-326314-9ycht8gi 146 20 times time NNS cord-326314-9ycht8gi 146 21 , , , cord-326314-9ycht8gi 146 22 to to TO cord-326314-9ycht8gi 146 23 rule rule VB cord-326314-9ycht8gi 146 24 out out RP cord-326314-9ycht8gi 146 25 numerical numerical JJ cord-326314-9ycht8gi 146 26 issues issue NNS cord-326314-9ycht8gi 146 27 involved involve VBN cord-326314-9ycht8gi 146 28 with with IN cord-326314-9ycht8gi 146 29 the the DT cord-326314-9ycht8gi 146 30 quickly quickly RB cord-326314-9ycht8gi 146 31 - - HYPH cord-326314-9ycht8gi 146 32 changing change VBG cord-326314-9ycht8gi 146 33 derivative derivative JJ cord-326314-9ycht8gi 146 34 4 4 CD cord-326314-9ycht8gi 146 35 . . . cord-326314-9ycht8gi 147 1 Figure figure NN cord-326314-9ycht8gi 147 2 5 5 CD cord-326314-9ycht8gi 147 3 shows show VBZ cord-326314-9ycht8gi 147 4 the the DT cord-326314-9ycht8gi 147 5 cost cost NN cord-326314-9ycht8gi 147 6 as as IN cord-326314-9ycht8gi 147 7 a a DT cord-326314-9ycht8gi 147 8 function function NN cord-326314-9ycht8gi 147 9 of of IN cord-326314-9ycht8gi 147 10 annealing anneal VBG cord-326314-9ycht8gi 147 11 for for IN cord-326314-9ycht8gi 147 12 the the DT cord-326314-9ycht8gi 147 13 case case NN cord-326314-9ycht8gi 147 14 with with IN cord-326314-9ycht8gi 147 15 no no DT cord-326314-9ycht8gi 147 16 measurement measurement NN cord-326314-9ycht8gi 147 17 of of IN cord-326314-9ycht8gi 147 18 Recovered Recovered NNP cord-326314-9ycht8gi 147 19 Population Population NNP cord-326314-9ycht8gi 147 20 R. R. NNP cord-326314-9ycht8gi 147 21 Without without IN cord-326314-9ycht8gi 147 22 examining examine VBG cord-326314-9ycht8gi 147 23 the the DT cord-326314-9ycht8gi 147 24 estimates estimate NNS cord-326314-9ycht8gi 147 25 , , , cord-326314-9ycht8gi 147 26 we -PRON- PRP cord-326314-9ycht8gi 147 27 know know VBP cord-326314-9ycht8gi 147 28 from from IN cord-326314-9ycht8gi 147 29 the the DT cord-326314-9ycht8gi 147 30 Cost(β Cost(β NNP cord-326314-9ycht8gi 147 31 ) ) -RRB- cord-326314-9ycht8gi 147 32 plot plot NN cord-326314-9ycht8gi 147 33 that that WDT cord-326314-9ycht8gi 147 34 no no DT cord-326314-9ycht8gi 147 35 solution solution NN cord-326314-9ycht8gi 147 36 has have VBZ cord-326314-9ycht8gi 147 37 been be VBN cord-326314-9ycht8gi 147 38 found find VBN cord-326314-9ycht8gi 147 39 that that WDT cord-326314-9ycht8gi 147 40 is be VBZ cord-326314-9ycht8gi 147 41 consistent consistent JJ cord-326314-9ycht8gi 147 42 with with IN cord-326314-9ycht8gi 147 43 both both DT cord-326314-9ycht8gi 147 44 measurements measurement NNS cord-326314-9ycht8gi 147 45 and and CC cord-326314-9ycht8gi 147 46 model model NN cord-326314-9ycht8gi 148 1 : : : cord-326314-9ycht8gi 148 2 no no DT cord-326314-9ycht8gi 148 3 plateau plateau NN cord-326314-9ycht8gi 148 4 is be VBZ cord-326314-9ycht8gi 148 5 reached reach VBN cord-326314-9ycht8gi 148 6 . . . cord-326314-9ycht8gi 149 1 Rather rather RB cord-326314-9ycht8gi 149 2 , , , cord-326314-9ycht8gi 149 3 as as IN cord-326314-9ycht8gi 149 4 the the DT cord-326314-9ycht8gi 149 5 model model NN cord-326314-9ycht8gi 149 6 constraint constraint NN cord-326314-9ycht8gi 149 7 strengthens strengthen VBZ cord-326314-9ycht8gi 149 8 , , , cord-326314-9ycht8gi 149 9 the the DT cord-326314-9ycht8gi 149 10 cost cost NN cord-326314-9ycht8gi 149 11 increases increase VBZ cord-326314-9ycht8gi 149 12 exponentially exponentially RB cord-326314-9ycht8gi 149 13 . . . cord-326314-9ycht8gi 150 1 Indeed indeed RB cord-326314-9ycht8gi 150 2 , , , cord-326314-9ycht8gi 150 3 Figure figure NN cord-326314-9ycht8gi 150 4 6 6 CD cord-326314-9ycht8gi 150 5 shows show VBZ cord-326314-9ycht8gi 150 6 the the DT cord-326314-9ycht8gi 150 7 estimation estimation NN cord-326314-9ycht8gi 150 8 , , , cord-326314-9ycht8gi 150 9 taken take VBN cord-326314-9ycht8gi 150 10 at at IN cord-326314-9ycht8gi 150 11 β β NN cord-326314-9ycht8gi 150 12 = = SYM cord-326314-9ycht8gi 150 13 2 2 CD cord-326314-9ycht8gi 150 14 , , , cord-326314-9ycht8gi 150 15 prior prior RB cord-326314-9ycht8gi 150 16 to to IN cord-326314-9ycht8gi 150 17 the the DT cord-326314-9ycht8gi 150 18 runaway runaway JJ cord-326314-9ycht8gi 150 19 behavior behavior NN cord-326314-9ycht8gi 150 20 . . . cord-326314-9ycht8gi 151 1 Note note VB cord-326314-9ycht8gi 151 2 the the DT cord-326314-9ycht8gi 151 3 excellent excellent JJ cord-326314-9ycht8gi 151 4 fit fit NN cord-326314-9ycht8gi 151 5 to to IN cord-326314-9ycht8gi 151 6 the the DT cord-326314-9ycht8gi 151 7 measured measure VBN cord-326314-9ycht8gi 151 8 states state NNS cord-326314-9ycht8gi 151 9 and and CC cord-326314-9ycht8gi 151 10 simultaneous simultaneous JJ cord-326314-9ycht8gi 151 11 poor poor JJ cord-326314-9ycht8gi 151 12 fit fit NN cord-326314-9ycht8gi 151 13 to to IN cord-326314-9ycht8gi 151 14 the the DT cord-326314-9ycht8gi 151 15 unmeasured unmeasured JJ cord-326314-9ycht8gi 151 16 states state NNS cord-326314-9ycht8gi 151 17 . . . cord-326314-9ycht8gi 152 1 As as IN cord-326314-9ycht8gi 152 2 no no DT cord-326314-9ycht8gi 152 3 stable stable JJ cord-326314-9ycht8gi 152 4 solution solution NN cord-326314-9ycht8gi 152 5 is be VBZ cord-326314-9ycht8gi 152 6 found find VBN cord-326314-9ycht8gi 152 7 at at IN cord-326314-9ycht8gi 152 8 high high JJ cord-326314-9ycht8gi 152 9 β β NN cord-326314-9ycht8gi 152 10 , , , cord-326314-9ycht8gi 152 11 we -PRON- PRP cord-326314-9ycht8gi 152 12 conclude conclude VBP cord-326314-9ycht8gi 152 13 that that IN cord-326314-9ycht8gi 152 14 there there EX cord-326314-9ycht8gi 152 15 exists exist VBZ cord-326314-9ycht8gi 152 16 insufficient insufficient JJ cord-326314-9ycht8gi 152 17 information information NN cord-326314-9ycht8gi 152 18 in in IN cord-326314-9ycht8gi 153 1 As as IN cord-326314-9ycht8gi 153 2 det det NNP cord-326314-9ycht8gi 153 3 , , , cord-326314-9ycht8gi 153 4 Sym Sym NNP cord-326314-9ycht8gi 153 5 det det NNP cord-326314-9ycht8gi 153 6 , , , cord-326314-9ycht8gi 153 7 Sys Sys NNP cord-326314-9ycht8gi 153 8 det det NNP cord-326314-9ycht8gi 153 9 , , , cord-326314-9ycht8gi 153 10 and and CC cord-326314-9ycht8gi 153 11 D d NN cord-326314-9ycht8gi 153 12 alone alone RB cord-326314-9ycht8gi 153 13 to to TO cord-326314-9ycht8gi 153 14 corral corral VB cord-326314-9ycht8gi 153 15 the the DT cord-326314-9ycht8gi 153 16 procedure procedure NN cord-326314-9ycht8gi 153 17 into into IN cord-326314-9ycht8gi 153 18 a a DT cord-326314-9ycht8gi 153 19 region region NN cord-326314-9ycht8gi 153 20 of of IN cord-326314-9ycht8gi 153 21 state state NN cord-326314-9ycht8gi 153 22 - - HYPH cord-326314-9ycht8gi 153 23 and and CC cord-326314-9ycht8gi 153 24 - - HYPH cord-326314-9ycht8gi 153 25 parameter parameter NN cord-326314-9ycht8gi 153 26 space space NN cord-326314-9ycht8gi 153 27 in in IN cord-326314-9ycht8gi 153 28 which which WDT cord-326314-9ycht8gi 153 29 a a DT cord-326314-9ycht8gi 153 30 model model NN cord-326314-9ycht8gi 153 31 solution solution NN cord-326314-9ycht8gi 153 32 is be VBZ cord-326314-9ycht8gi 153 33 possible possible JJ cord-326314-9ycht8gi 153 34 . . . cord-326314-9ycht8gi 154 1 We -PRON- PRP cord-326314-9ycht8gi 154 2 repeated repeat VBD cord-326314-9ycht8gi 154 3 this this DT cord-326314-9ycht8gi 154 4 experiment experiment NN cord-326314-9ycht8gi 154 5 with with IN cord-326314-9ycht8gi 154 6 a a DT cord-326314-9ycht8gi 154 7 doubled double VBN cord-326314-9ycht8gi 154 8 baseline baseline NN cord-326314-9ycht8gi 154 9 of of IN cord-326314-9ycht8gi 154 10 201 201 CD cord-326314-9ycht8gi 154 11 days day NNS cord-326314-9ycht8gi 154 12 , , , cord-326314-9ycht8gi 154 13 and and CC cord-326314-9ycht8gi 154 14 noted note VBD cord-326314-9ycht8gi 154 15 no no DT cord-326314-9ycht8gi 154 16 improvement improvement NN cord-326314-9ycht8gi 154 17 ( ( -LRB- cord-326314-9ycht8gi 154 18 not not RB cord-326314-9ycht8gi 154 19 shown show VBN cord-326314-9ycht8gi 154 20 ) ) -RRB- cord-326314-9ycht8gi 154 21 . . . cord-326314-9ycht8gi 155 1 In in IN cord-326314-9ycht8gi 155 2 Experiment Experiment NNP cord-326314-9ycht8gi 155 3 iii iii NNP cord-326314-9ycht8gi 155 4 , , , cord-326314-9ycht8gi 155 5 the the DT cord-326314-9ycht8gi 155 6 low low JJ cord-326314-9ycht8gi 155 7 noise noise NN cord-326314-9ycht8gi 155 8 added add VBN cord-326314-9ycht8gi 155 9 to to IN cord-326314-9ycht8gi 155 10 R R NNP cord-326314-9ycht8gi 155 11 yielded yield VBD cord-326314-9ycht8gi 155 12 a a DT cord-326314-9ycht8gi 155 13 poor poor JJ cord-326314-9ycht8gi 155 14 state state NN cord-326314-9ycht8gi 155 15 and and CC cord-326314-9ycht8gi 155 16 parameter parameter NN cord-326314-9ycht8gi 155 17 estimate estimate NN cord-326314-9ycht8gi 155 18 ( ( -LRB- cord-326314-9ycht8gi 155 19 not not RB cord-326314-9ycht8gi 155 20 shown show VBN cord-326314-9ycht8gi 155 21 ) ) -RRB- cord-326314-9ycht8gi 155 22 . . . cord-326314-9ycht8gi 156 1 With with IN cord-326314-9ycht8gi 156 2 a a DT cord-326314-9ycht8gi 156 3 doubled double VBN cord-326314-9ycht8gi 156 4 temporal temporal JJ cord-326314-9ycht8gi 156 5 baseline baseline NN cord-326314-9ycht8gi 156 6 of of IN cord-326314-9ycht8gi 156 7 measurements measurement NNS cord-326314-9ycht8gi 156 8 ( ( -LRB- cord-326314-9ycht8gi 156 9 Experiment experiment NN cord-326314-9ycht8gi 156 10 iv iv CD cord-326314-9ycht8gi 156 11 ) ) -RRB- cord-326314-9ycht8gi 156 12 , , , cord-326314-9ycht8gi 156 13 however however RB cord-326314-9ycht8gi 156 14 , , , cord-326314-9ycht8gi 156 15 the the DT cord-326314-9ycht8gi 156 16 state state NN cord-326314-9ycht8gi 156 17 estimate estimate NN cord-326314-9ycht8gi 156 18 became become VBD cord-326314-9ycht8gi 156 19 robust robust JJ cord-326314-9ycht8gi 156 20 to to IN cord-326314-9ycht8gi 156 21 the the DT cord-326314-9ycht8gi 156 22 contamination contamination NN cord-326314-9ycht8gi 156 23 . . . cord-326314-9ycht8gi 157 1 Figure figure NN cord-326314-9ycht8gi 157 2 7 7 CD cord-326314-9ycht8gi 157 3 shows show VBZ cord-326314-9ycht8gi 157 4 this this DT cord-326314-9ycht8gi 157 5 estimate estimate NN cord-326314-9ycht8gi 157 6 . . . cord-326314-9ycht8gi 158 1 While while IN cord-326314-9ycht8gi 158 2 the the DT cord-326314-9ycht8gi 158 3 ∼ ∼ NNP cord-326314-9ycht8gi 158 4 five five CD cord-326314-9ycht8gi 158 5 percent percent NN cord-326314-9ycht8gi 158 6 noise noise NN cord-326314-9ycht8gi 158 7 added add VBN cord-326314-9ycht8gi 158 8 to to IN cord-326314-9ycht8gi 158 9 Population population NN cord-326314-9ycht8gi 158 10 R r NN cord-326314-9ycht8gi 158 11 propagates propagate VBZ cord-326314-9ycht8gi 158 12 to to IN cord-326314-9ycht8gi 158 13 the the DT cord-326314-9ycht8gi 158 14 unmeasured unmeasured JJ cord-326314-9ycht8gi 158 15 States States NNP cord-326314-9ycht8gi 158 16 S S NNP cord-326314-9ycht8gi 158 17 , , , cord-326314-9ycht8gi 158 18 E E NNP cord-326314-9ycht8gi 158 19 , , , cord-326314-9ycht8gi 158 20 and and CC cord-326314-9ycht8gi 158 21 P p NN cord-326314-9ycht8gi 158 22 , , , cord-326314-9ycht8gi 158 23 the the DT cord-326314-9ycht8gi 158 24 general general JJ cord-326314-9ycht8gi 158 25 state state NN cord-326314-9ycht8gi 158 26 evolution evolution NN cord-326314-9ycht8gi 158 27 is be VBZ cord-326314-9ycht8gi 158 28 still still RB cord-326314-9ycht8gi 158 29 captured capture VBN cord-326314-9ycht8gi 158 30 well well RB cord-326314-9ycht8gi 158 31 . . . cord-326314-9ycht8gi 159 1 Importantly importantly RB cord-326314-9ycht8gi 159 2 , , , cord-326314-9ycht8gi 159 3 the the DT cord-326314-9ycht8gi 159 4 populations population NNS cord-326314-9ycht8gi 159 5 entering enter VBG cord-326314-9ycht8gi 159 6 the the DT cord-326314-9ycht8gi 159 7 hospital hospital NN cord-326314-9ycht8gi 159 8 are be VBP cord-326314-9ycht8gi 159 9 well well RB cord-326314-9ycht8gi 159 10 estimated estimate VBN cord-326314-9ycht8gi 159 11 . . . cord-326314-9ycht8gi 160 1 Note note VB cord-326314-9ycht8gi 160 2 that that IN cord-326314-9ycht8gi 160 3 some some DT cord-326314-9ycht8gi 160 4 low low JJ cord-326314-9ycht8gi 160 5 state state NN cord-326314-9ycht8gi 160 6 estimates estimate NNS cord-326314-9ycht8gi 160 7 ( ( -LRB- cord-326314-9ycht8gi 160 8 e.g. e.g. RB cord-326314-9ycht8gi 160 9 As as IN cord-326314-9ycht8gi 160 10 ) ) -RRB- cord-326314-9ycht8gi 160 11 are be VBP cord-326314-9ycht8gi 160 12 not not RB cord-326314-9ycht8gi 160 13 perfectly perfectly RB cord-326314-9ycht8gi 160 14 offset offset VBN cord-326314-9ycht8gi 160 15 by by IN cord-326314-9ycht8gi 160 16 high high JJ cord-326314-9ycht8gi 160 17 estimates estimate NNS cord-326314-9ycht8gi 160 18 ( ( -LRB- cord-326314-9ycht8gi 160 19 e.g. e.g. RB cord-326314-9ycht8gi 160 20 Sym Sym NNP cord-326314-9ycht8gi 160 21 ) ) -RRB- cord-326314-9ycht8gi 160 22 . . . cord-326314-9ycht8gi 161 1 The the DT cord-326314-9ycht8gi 161 2 addition addition NN cord-326314-9ycht8gi 161 3 of of IN cord-326314-9ycht8gi 161 4 noise noise NN cord-326314-9ycht8gi 161 5 in in IN cord-326314-9ycht8gi 161 6 these these DT cord-326314-9ycht8gi 161 7 numbers number NNS cord-326314-9ycht8gi 161 8 -by -by : cord-326314-9ycht8gi 161 9 definition definition NN cord-326314-9ycht8gi 161 10 -breaks -breaks . cord-326314-9ycht8gi 162 1 the the DT cord-326314-9ycht8gi 162 2 conservation conservation NN cord-326314-9ycht8gi 162 3 of of IN cord-326314-9ycht8gi 162 4 the the DT cord-326314-9ycht8gi 162 5 population population NN cord-326314-9ycht8gi 162 6 . . . cord-326314-9ycht8gi 163 1 Finally finally RB cord-326314-9ycht8gi 163 2 , , , cord-326314-9ycht8gi 163 3 the the DT cord-326314-9ycht8gi 163 4 parameter parameter NN cord-326314-9ycht8gi 163 5 estimates estimate VBZ cord-326314-9ycht8gi 163 6 for for IN cord-326314-9ycht8gi 163 7 Experiment experiment NN cord-326314-9ycht8gi 163 8 iv iv LS cord-326314-9ycht8gi 163 9 do do VBP cord-326314-9ycht8gi 163 10 not not RB cord-326314-9ycht8gi 163 11 survive survive VB cord-326314-9ycht8gi 163 12 the the DT cord-326314-9ycht8gi 163 13 added add VBN cord-326314-9ycht8gi 163 14 contamination contamination NN cord-326314-9ycht8gi 163 15 ( ( -LRB- cord-326314-9ycht8gi 163 16 not not RB cord-326314-9ycht8gi 163 17 shown show VBN cord-326314-9ycht8gi 163 18 ) ) -RRB- cord-326314-9ycht8gi 163 19 . . . cord-326314-9ycht8gi 164 1 We -PRON- PRP cord-326314-9ycht8gi 164 2 have have VBP cord-326314-9ycht8gi 164 3 endeavoured endeavour VBN cord-326314-9ycht8gi 164 4 to to TO cord-326314-9ycht8gi 164 5 illustrate illustrate VB cord-326314-9ycht8gi 164 6 the the DT cord-326314-9ycht8gi 164 7 potential potential NN cord-326314-9ycht8gi 164 8 of of IN cord-326314-9ycht8gi 164 9 SDA SDA NNP cord-326314-9ycht8gi 164 10 to to TO cord-326314-9ycht8gi 164 11 systematically systematically RB cord-326314-9ycht8gi 164 12 identify identify VB cord-326314-9ycht8gi 164 13 the the DT cord-326314-9ycht8gi 164 14 specific specific JJ cord-326314-9ycht8gi 164 15 measurements measurement NNS cord-326314-9ycht8gi 164 16 , , , cord-326314-9ycht8gi 164 17 temporal temporal JJ cord-326314-9ycht8gi 164 18 baseline baseline NN cord-326314-9ycht8gi 164 19 of of IN cord-326314-9ycht8gi 164 20 measurements measurement NNS cord-326314-9ycht8gi 164 21 , , , cord-326314-9ycht8gi 164 22 and and CC cord-326314-9ycht8gi 164 23 degree degree NN cord-326314-9ycht8gi 164 24 of of IN cord-326314-9ycht8gi 164 25 measurement measurement NN cord-326314-9ycht8gi 164 26 accuracy accuracy NN cord-326314-9ycht8gi 164 27 , , , cord-326314-9ycht8gi 164 28 required require VBN cord-326314-9ycht8gi 164 29 to to TO cord-326314-9ycht8gi 164 30 estimate estimate VB cord-326314-9ycht8gi 164 31 unknown unknown JJ cord-326314-9ycht8gi 164 32 model model NN cord-326314-9ycht8gi 164 33 parameters parameter NNS cord-326314-9ycht8gi 164 34 in in IN cord-326314-9ycht8gi 164 35 a a DT cord-326314-9ycht8gi 164 36 high high JJ cord-326314-9ycht8gi 164 37 - - HYPH cord-326314-9ycht8gi 164 38 dimensional dimensional JJ cord-326314-9ycht8gi 164 39 model model NN cord-326314-9ycht8gi 164 40 designed design VBN cord-326314-9ycht8gi 164 41 to to TO cord-326314-9ycht8gi 164 42 examine examine VB cord-326314-9ycht8gi 164 43 the the DT cord-326314-9ycht8gi 164 44 complex complex JJ cord-326314-9ycht8gi 164 45 problems problem NNS cord-326314-9ycht8gi 164 46 that that WDT cord-326314-9ycht8gi 164 47 COVID-19 covid-19 VBP cord-326314-9ycht8gi 164 48 presents present VBZ cord-326314-9ycht8gi 164 49 to to IN cord-326314-9ycht8gi 164 50 hospitals hospital NNS cord-326314-9ycht8gi 164 51 . . . cord-326314-9ycht8gi 165 1 In in IN cord-326314-9ycht8gi 165 2 light light NN cord-326314-9ycht8gi 165 3 of of IN cord-326314-9ycht8gi 165 4 our -PRON- PRP$ cord-326314-9ycht8gi 165 5 assumed assumed JJ cord-326314-9ycht8gi 165 6 knowledge knowledge NN cord-326314-9ycht8gi 165 7 of of IN cord-326314-9ycht8gi 165 8 some some DT cord-326314-9ycht8gi 165 9 model model NN cord-326314-9ycht8gi 165 10 parameters parameter NNS cord-326314-9ycht8gi 165 11 , , , cord-326314-9ycht8gi 165 12 we -PRON- PRP cord-326314-9ycht8gi 165 13 restrict restrict VBP cord-326314-9ycht8gi 165 14 our -PRON- PRP$ cord-326314-9ycht8gi 165 15 conclusions conclusion NNS cord-326314-9ycht8gi 165 16 to to IN cord-326314-9ycht8gi 165 17 general general JJ cord-326314-9ycht8gi 165 18 comments comment NNS cord-326314-9ycht8gi 165 19 . . . cord-326314-9ycht8gi 166 1 We -PRON- PRP cord-326314-9ycht8gi 166 2 emphasize emphasize VBP cord-326314-9ycht8gi 166 3 that that DT cord-326314-9ycht8gi 166 4 estimation estimation NN cord-326314-9ycht8gi 166 5 of of IN cord-326314-9ycht8gi 166 6 the the DT cord-326314-9ycht8gi 166 7 full full JJ cord-326314-9ycht8gi 166 8 model model NN cord-326314-9ycht8gi 166 9 state state NN cord-326314-9ycht8gi 166 10 requires require VBZ cord-326314-9ycht8gi 166 11 measurements measurement NNS cord-326314-9ycht8gi 166 12 of of IN cord-326314-9ycht8gi 166 13 the the DT cord-326314-9ycht8gi 166 14 detected detect VBN cord-326314-9ycht8gi 166 15 cases case NNS cord-326314-9ycht8gi 166 16 but but CC cord-326314-9ycht8gi 166 17 not not RB cord-326314-9ycht8gi 166 18 the the DT cord-326314-9ycht8gi 166 19 undetected undetected JJ cord-326314-9ycht8gi 166 20 , , , cord-326314-9ycht8gi 166 21 provided provide VBN cord-326314-9ycht8gi 166 22 that that IN cord-326314-9ycht8gi 166 23 the the DT cord-326314-9ycht8gi 166 24 recovered recover VBN cord-326314-9ycht8gi 166 25 and and CC cord-326314-9ycht8gi 166 26 dead dead JJ cord-326314-9ycht8gi 166 27 are be VBP cord-326314-9ycht8gi 166 28 also also RB cord-326314-9ycht8gi 166 29 measured measure VBN cord-326314-9ycht8gi 166 30 . . . cord-326314-9ycht8gi 167 1 The the DT cord-326314-9ycht8gi 167 2 state state NN cord-326314-9ycht8gi 167 3 evolution evolution NN cord-326314-9ycht8gi 167 4 is be VBZ cord-326314-9ycht8gi 167 5 tolerant tolerant JJ cord-326314-9ycht8gi 167 6 to to IN cord-326314-9ycht8gi 167 7 low low JJ cord-326314-9ycht8gi 167 8 noise noise NN cord-326314-9ycht8gi 167 9 in in IN cord-326314-9ycht8gi 167 10 these these DT cord-326314-9ycht8gi 167 11 measurements measurement NNS cord-326314-9ycht8gi 167 12 , , , cord-326314-9ycht8gi 167 13 while while IN cord-326314-9ycht8gi 167 14 the the DT cord-326314-9ycht8gi 167 15 parameter parameter NN cord-326314-9ycht8gi 167 16 estimates estimate NNS cord-326314-9ycht8gi 167 17 are be VBP cord-326314-9ycht8gi 167 18 not not RB cord-326314-9ycht8gi 167 19 . . . cord-326314-9ycht8gi 168 1 The the DT cord-326314-9ycht8gi 168 2 ultimate ultimate JJ cord-326314-9ycht8gi 168 3 aim aim NN cord-326314-9ycht8gi 168 4 of of IN cord-326314-9ycht8gi 168 5 SDA SDA NNP cord-326314-9ycht8gi 168 6 is be VBZ cord-326314-9ycht8gi 168 7 to to TO cord-326314-9ycht8gi 168 8 test test VB cord-326314-9ycht8gi 168 9 the the DT cord-326314-9ycht8gi 168 10 validity validity NN cord-326314-9ycht8gi 168 11 of of IN cord-326314-9ycht8gi 168 12 model model NN cord-326314-9ycht8gi 168 13 estimation estimation NN cord-326314-9ycht8gi 168 14 using use VBG cord-326314-9ycht8gi 168 15 real real JJ cord-326314-9ycht8gi 168 16 data datum NNS cord-326314-9ycht8gi 168 17 , , , cord-326314-9ycht8gi 168 18 via via IN cord-326314-9ycht8gi 168 19 prediction prediction NN cord-326314-9ycht8gi 168 20 . . . cord-326314-9ycht8gi 169 1 In in IN cord-326314-9ycht8gi 169 2 advance advance NN cord-326314-9ycht8gi 169 3 of of IN cord-326314-9ycht8gi 169 4 that that DT cord-326314-9ycht8gi 169 5 step step NN cord-326314-9ycht8gi 169 6 , , , cord-326314-9ycht8gi 169 7 we -PRON- PRP cord-326314-9ycht8gi 169 8 are be VBP cord-326314-9ycht8gi 169 9 performing perform VBG cord-326314-9ycht8gi 169 10 a a DT cord-326314-9ycht8gi 169 11 detailed detailed JJ cord-326314-9ycht8gi 169 12 study study NN cord-326314-9ycht8gi 169 13 of of IN cord-326314-9ycht8gi 169 14 the the DT cord-326314-9ycht8gi 169 15 model model NN cord-326314-9ycht8gi 169 16 's 's POS cord-326314-9ycht8gi 169 17 sensitivity sensitivity NN cord-326314-9ycht8gi 169 18 to to IN cord-326314-9ycht8gi 169 19 contamination contamination NN cord-326314-9ycht8gi 169 20 in in IN cord-326314-9ycht8gi 169 21 the the DT cord-326314-9ycht8gi 169 22 measurable measurable JJ cord-326314-9ycht8gi 169 23 populations population NNS cord-326314-9ycht8gi 170 1 As as IN cord-326314-9ycht8gi 170 2 det det NNP cord-326314-9ycht8gi 170 3 , , , cord-326314-9ycht8gi 170 4 Sym Sym NNP cord-326314-9ycht8gi 170 5 det det NNP cord-326314-9ycht8gi 170 6 , , , cord-326314-9ycht8gi 170 7 Sys Sys NNP cord-326314-9ycht8gi 170 8 det det NNP cord-326314-9ycht8gi 170 9 , , , cord-326314-9ycht8gi 170 10 R R NNP cord-326314-9ycht8gi 170 11 , , , cord-326314-9ycht8gi 170 12 and and CC cord-326314-9ycht8gi 170 13 D. D. NNP cord-326314-9ycht8gi 171 1 Concurrently concurrently RB cord-326314-9ycht8gi 171 2 we -PRON- PRP cord-326314-9ycht8gi 171 3 are be VBP cord-326314-9ycht8gi 171 4 examining examine VBG cord-326314-9ycht8gi 171 5 means mean NNS cord-326314-9ycht8gi 171 6 to to TO cord-326314-9ycht8gi 171 7 render render VB cord-326314-9ycht8gi 171 8 the the DT cord-326314-9ycht8gi 171 9 parameter parameter NN cord-326314-9ycht8gi 171 10 estimation estimation NN cord-326314-9ycht8gi 171 11 less less RBR cord-326314-9ycht8gi 171 12 sensitive sensitive JJ cord-326314-9ycht8gi 171 13 to to IN cord-326314-9ycht8gi 171 14 noise noise NN cord-326314-9ycht8gi 171 15 , , , cord-326314-9ycht8gi 171 16 via via IN cord-326314-9ycht8gi 171 17 various various JJ cord-326314-9ycht8gi 171 18 additional additional JJ cord-326314-9ycht8gi 171 19 equality equality NN cord-326314-9ycht8gi 171 20 constraints constraint NNS cord-326314-9ycht8gi 171 21 in in IN cord-326314-9ycht8gi 171 22 the the DT cord-326314-9ycht8gi 171 23 cost cost NN cord-326314-9ycht8gi 171 24 function function NN cord-326314-9ycht8gi 171 25 , , , cord-326314-9ycht8gi 171 26 and and CC cord-326314-9ycht8gi 171 27 loosening loosen VBG cord-326314-9ycht8gi 171 28 the the DT cord-326314-9ycht8gi 171 29 assumption assumption NN cord-326314-9ycht8gi 171 30 of of IN cord-326314-9ycht8gi 171 31 Gaussian Gaussian NNP cord-326314-9ycht8gi 171 32 - - HYPH cord-326314-9ycht8gi 171 33 distributed distribute VBN cord-326314-9ycht8gi 171 34 noise noise NN cord-326314-9ycht8gi 171 35 . . . cord-326314-9ycht8gi 172 1 In in IN cord-326314-9ycht8gi 172 2 particular particular JJ cord-326314-9ycht8gi 172 3 , , , cord-326314-9ycht8gi 172 4 we -PRON- PRP cord-326314-9ycht8gi 172 5 shall shall MD cord-326314-9ycht8gi 172 6 require require VB cord-326314-9ycht8gi 172 7 that that IN cord-326314-9ycht8gi 172 8 the the DT cord-326314-9ycht8gi 172 9 time time NN cord-326314-9ycht8gi 172 10 - - HYPH cord-326314-9ycht8gi 172 11 varying vary VBG cord-326314-9ycht8gi 172 12 parameters parameter NNS cord-326314-9ycht8gi 172 13 be be VB cord-326314-9ycht8gi 172 14 smoothly smoothly RB cord-326314-9ycht8gi 172 15 - - HYPH cord-326314-9ycht8gi 172 16 varying vary VBG cord-326314-9ycht8gi 172 17 . . . cord-326314-9ycht8gi 173 1 It -PRON- PRP cord-326314-9ycht8gi 173 2 will will MD cord-326314-9ycht8gi 173 3 be be VB cord-326314-9ycht8gi 173 4 important important JJ cord-326314-9ycht8gi 173 5 to to TO cord-326314-9ycht8gi 173 6 examine examine VB cord-326314-9ycht8gi 173 7 the the DT cord-326314-9ycht8gi 173 8 stability stability NN cord-326314-9ycht8gi 173 9 of of IN cord-326314-9ycht8gi 173 10 the the DT cord-326314-9ycht8gi 173 11 SDA SDA NNP cord-326314-9ycht8gi 173 12 procedure procedure NN cord-326314-9ycht8gi 173 13 over over IN cord-326314-9ycht8gi 173 14 a a DT cord-326314-9ycht8gi 173 15 range range NN cord-326314-9ycht8gi 173 16 of of IN cord-326314-9ycht8gi 173 17 choices choice NNS cord-326314-9ycht8gi 173 18 for for IN cord-326314-9ycht8gi 173 19 parameter parameter NN cord-326314-9ycht8gi 173 20 values value NNS cord-326314-9ycht8gi 173 21 and and CC cord-326314-9ycht8gi 173 22 initial initial JJ cord-326314-9ycht8gi 173 23 numbers number NNS cord-326314-9ycht8gi 173 24 for for IN cord-326314-9ycht8gi 173 25 the the DT cord-326314-9ycht8gi 173 26 infected infected JJ cord-326314-9ycht8gi 173 27 populations population NNS cord-326314-9ycht8gi 173 28 . . . cord-326314-9ycht8gi 174 1 This this DT cord-326314-9ycht8gi 174 2 procedure procedure NN cord-326314-9ycht8gi 174 3 can can MD cord-326314-9ycht8gi 174 4 be be VB cord-326314-9ycht8gi 174 5 expanded expand VBN cord-326314-9ycht8gi 174 6 in in IN cord-326314-9ycht8gi 174 7 many many JJ cord-326314-9ycht8gi 174 8 directions direction NNS cord-326314-9ycht8gi 174 9 . . . cord-326314-9ycht8gi 175 1 Currently currently RB cord-326314-9ycht8gi 175 2 we -PRON- PRP cord-326314-9ycht8gi 175 3 are be VBP cord-326314-9ycht8gi 175 4 working work VBG cord-326314-9ycht8gi 175 5 to to TO cord-326314-9ycht8gi 175 6 divide divide VB cord-326314-9ycht8gi 175 7 the the DT cord-326314-9ycht8gi 175 8 model model NN cord-326314-9ycht8gi 175 9 subpopulations subpopulation NNS cord-326314-9ycht8gi 175 10 by by IN cord-326314-9ycht8gi 175 11 age age NN cord-326314-9ycht8gi 175 12 , , , cord-326314-9ycht8gi 175 13 and and CC cord-326314-9ycht8gi 175 14 to to TO cord-326314-9ycht8gi 175 15 include include VB cord-326314-9ycht8gi 175 16 age age NN cord-326314-9ycht8gi 175 17 - - HYPH cord-326314-9ycht8gi 175 18 specific specific JJ cord-326314-9ycht8gi 175 19 parameters parameter NNS cord-326314-9ycht8gi 175 20 such such JJ cord-326314-9ycht8gi 175 21 as as IN cord-326314-9ycht8gi 175 22 susceptibility susceptibility NN cord-326314-9ycht8gi 175 23 and and CC cord-326314-9ycht8gi 175 24 the the DT cord-326314-9ycht8gi 175 25 likelihood likelihood NN cord-326314-9ycht8gi 175 26 of of IN cord-326314-9ycht8gi 175 27 requiring require VBG cord-326314-9ycht8gi 175 28 hospitalization hospitalization NN cord-326314-9ycht8gi 175 29 and and CC cord-326314-9ycht8gi 175 30 intensive intensive JJ cord-326314-9ycht8gi 175 31 care care NN cord-326314-9ycht8gi 175 32 . . . cord-326314-9ycht8gi 176 1 Specifically specifically RB cord-326314-9ycht8gi 176 2 , , , cord-326314-9ycht8gi 176 3 SDA SDA NNP cord-326314-9ycht8gi 176 4 might may MD cord-326314-9ycht8gi 176 5 inform inform VB cord-326314-9ycht8gi 176 6 the the DT cord-326314-9ycht8gi 176 7 question question NN cord-326314-9ycht8gi 176 8 of of IN cord-326314-9ycht8gi 176 9 whether whether IN cord-326314-9ycht8gi 176 10 the the DT cord-326314-9ycht8gi 176 11 contact contact NN cord-326314-9ycht8gi 176 12 matrices matrix NNS cord-326314-9ycht8gi 176 13 among among IN cord-326314-9ycht8gi 176 14 age age NN cord-326314-9ycht8gi 176 15 groups group NNS cord-326314-9ycht8gi 176 16 are be VBP cord-326314-9ycht8gi 176 17 non non JJ cord-326314-9ycht8gi 176 18 - - JJ cord-326314-9ycht8gi 176 19 stationary stationary JJ cord-326314-9ycht8gi 176 20 -a -a HYPH cord-326314-9ycht8gi 176 21 question question NN cord-326314-9ycht8gi 176 22 of of IN cord-326314-9ycht8gi 176 23 high high JJ cord-326314-9ycht8gi 176 24 interest interest NN cord-326314-9ycht8gi 176 25 for for IN cord-326314-9ycht8gi 176 26 predicting predict VBG cord-326314-9ycht8gi 176 27 age age NN cord-326314-9ycht8gi 176 28 - - HYPH cord-326314-9ycht8gi 176 29 dependent dependent JJ cord-326314-9ycht8gi 176 30 susceptibility susceptibility NN cord-326314-9ycht8gi 176 31 during during IN cord-326314-9ycht8gi 176 32 a a DT cord-326314-9ycht8gi 176 33 second second JJ cord-326314-9ycht8gi 176 34 wave wave NN cord-326314-9ycht8gi 176 35 [ [ -LRB- cord-326314-9ycht8gi 176 36 42 42 CD cord-326314-9ycht8gi 176 37 ] ] -RRB- cord-326314-9ycht8gi 176 38 of of IN cord-326314-9ycht8gi 176 39 the the DT cord-326314-9ycht8gi 176 40 virus virus NN cord-326314-9ycht8gi 176 41 . . . cord-326314-9ycht8gi 177 1 Other other JJ cord-326314-9ycht8gi 177 2 avenues avenue NNS cord-326314-9ycht8gi 177 3 for for IN cord-326314-9ycht8gi 177 4 expansion expansion NN cord-326314-9ycht8gi 177 5 are be VBP cord-326314-9ycht8gi 177 6 as as IN cord-326314-9ycht8gi 177 7 follows follow VBZ cord-326314-9ycht8gi 177 8 : : : cord-326314-9ycht8gi 177 9 1 1 LS cord-326314-9ycht8gi 177 10 ) ) -RRB- cord-326314-9ycht8gi 177 11 define define VB cord-326314-9ycht8gi 177 12 additional additional JJ cord-326314-9ycht8gi 177 13 model model NN cord-326314-9ycht8gi 177 14 parameters parameter NNS cord-326314-9ycht8gi 177 15 as as IN cord-326314-9ycht8gi 177 16 unknowns unknown NNS cord-326314-9ycht8gi 177 17 to to TO cord-326314-9ycht8gi 177 18 be be VB cord-326314-9ycht8gi 177 19 estimated estimate VBN cord-326314-9ycht8gi 177 20 , , , cord-326314-9ycht8gi 177 21 including include VBG cord-326314-9ycht8gi 177 22 the the DT cord-326314-9ycht8gi 177 23 fraction fraction NN cord-326314-9ycht8gi 177 24 of of IN cord-326314-9ycht8gi 177 25 patients patient NNS cord-326314-9ycht8gi 177 26 hospitalized hospitalize VBN cord-326314-9ycht8gi 177 27 , , , cord-326314-9ycht8gi 177 28 the the DT cord-326314-9ycht8gi 177 29 fraction fraction NN cord-326314-9ycht8gi 177 30 who who WP cord-326314-9ycht8gi 177 31 enter enter VBP cord-326314-9ycht8gi 177 32 critical critical JJ cord-326314-9ycht8gi 177 33 care care NN cord-326314-9ycht8gi 177 34 , , , cord-326314-9ycht8gi 177 35 and and CC cord-326314-9ycht8gi 177 36 the the DT cord-326314-9ycht8gi 177 37 various various JJ cord-326314-9ycht8gi 177 38 timescales timescale NNS cord-326314-9ycht8gi 177 39 governing govern VBG cord-326314-9ycht8gi 177 40 the the DT cord-326314-9ycht8gi 177 41 reaction reaction NN cord-326314-9ycht8gi 177 42 equations equation NNS cord-326314-9ycht8gi 177 43 ; ; : cord-326314-9ycht8gi 177 44 2 2 LS cord-326314-9ycht8gi 177 45 ) ) -RRB- cord-326314-9ycht8gi 177 46 impose impose VB cord-326314-9ycht8gi 177 47 various various JJ cord-326314-9ycht8gi 177 48 constraints constraint NNS cord-326314-9ycht8gi 177 49 regarding regard VBG cord-326314-9ycht8gi 177 50 the the DT cord-326314-9ycht8gi 177 51 unknown unknown JJ cord-326314-9ycht8gi 177 52 time time NN cord-326314-9ycht8gi 177 53 - - HYPH cord-326314-9ycht8gi 177 54 varying vary VBG cord-326314-9ycht8gi 177 55 quantities quantity NNS cord-326314-9ycht8gi 177 56 , , , cord-326314-9ycht8gi 177 57 particularly particularly RB cord-326314-9ycht8gi 177 58 transmission transmission NN cord-326314-9ycht8gi 177 59 rate rate NN cord-326314-9ycht8gi 178 1 K K NNP cord-326314-9ycht8gi 178 2 i i PRP cord-326314-9ycht8gi 178 3 ( ( -LRB- cord-326314-9ycht8gi 178 4 t t NN cord-326314-9ycht8gi 178 5 ) ) -RRB- cord-326314-9ycht8gi 178 6 , , , cord-326314-9ycht8gi 178 7 and and CC cord-326314-9ycht8gi 178 8 identifying identify VBG cord-326314-9ycht8gi 178 9 which which WDT cord-326314-9ycht8gi 178 10 forms form VBZ cord-326314-9ycht8gi 178 11 permit permit VBP cord-326314-9ycht8gi 178 12 a a DT cord-326314-9ycht8gi 178 13 solution solution NN cord-326314-9ycht8gi 178 14 consistent consistent JJ cord-326314-9ycht8gi 178 15 with with IN cord-326314-9ycht8gi 178 16 measurements measurement NNS cord-326314-9ycht8gi 178 17 ; ; : cord-326314-9ycht8gi 178 18 3 3 LS cord-326314-9ycht8gi 178 19 ) ) -RRB- cord-326314-9ycht8gi 178 20 examine examine VB cord-326314-9ycht8gi 178 21 model model NN cord-326314-9ycht8gi 178 22 sensitivity sensitivity NN cord-326314-9ycht8gi 178 23 to to IN cord-326314-9ycht8gi 178 24 the the DT cord-326314-9ycht8gi 178 25 initial initial JJ cord-326314-9ycht8gi 178 26 numbers number NNS cord-326314-9ycht8gi 178 27 within within IN cord-326314-9ycht8gi 178 28 each each DT cord-326314-9ycht8gi 178 29 population population NN cord-326314-9ycht8gi 178 30 ; ; : cord-326314-9ycht8gi 178 31 4 4 LS cord-326314-9ycht8gi 178 32 ) ) -RRB- cord-326314-9ycht8gi 178 33 examine examine VB cord-326314-9ycht8gi 178 34 model model NN cord-326314-9ycht8gi 178 35 sensitivity sensitivity NN cord-326314-9ycht8gi 178 36 to to IN cord-326314-9ycht8gi 178 37 the the DT cord-326314-9ycht8gi 178 38 temporal temporal JJ cord-326314-9ycht8gi 178 39 frequency frequency NN cord-326314-9ycht8gi 178 40 of of IN cord-326314-9ycht8gi 178 41 data datum NNS cord-326314-9ycht8gi 178 42 sampling sampling NN cord-326314-9ycht8gi 178 43 . . . cord-326314-9ycht8gi 179 1 Moreover moreover RB cord-326314-9ycht8gi 179 2 , , , cord-326314-9ycht8gi 179 3 it -PRON- PRP cord-326314-9ycht8gi 179 4 is be VBZ cord-326314-9ycht8gi 179 5 our -PRON- PRP$ cord-326314-9ycht8gi 179 6 hope hope NN cord-326314-9ycht8gi 179 7 that that IN cord-326314-9ycht8gi 179 8 the the DT cord-326314-9ycht8gi 179 9 procedure procedure NN cord-326314-9ycht8gi 179 10 described describe VBN cord-326314-9ycht8gi 179 11 in in IN cord-326314-9ycht8gi 179 12 this this DT cord-326314-9ycht8gi 179 13 paper paper NN cord-326314-9ycht8gi 179 14 can can MD cord-326314-9ycht8gi 179 15 guide guide VB cord-326314-9ycht8gi 179 16 the the DT cord-326314-9ycht8gi 179 17 application application NN cord-326314-9ycht8gi 179 18 of of IN cord-326314-9ycht8gi 179 19 SDA SDA NNP cord-326314-9ycht8gi 179 20 to to IN cord-326314-9ycht8gi 179 21 a a DT cord-326314-9ycht8gi 179 22 host host NN cord-326314-9ycht8gi 179 23 of of IN cord-326314-9ycht8gi 179 24 complicated complicated JJ cord-326314-9ycht8gi 179 25 questions question NNS cord-326314-9ycht8gi 179 26 surrounding surround VBG cord-326314-9ycht8gi 179 27 COVID-19 covid-19 CD cord-326314-9ycht8gi 179 28 . . . cord-326314-9ycht8gi 180 1 Thank thank VBP cord-326314-9ycht8gi 180 2 you -PRON- PRP cord-326314-9ycht8gi 180 3 to to IN cord-326314-9ycht8gi 180 4 Patrick Patrick NNP cord-326314-9ycht8gi 180 5 Clay Clay NNP cord-326314-9ycht8gi 180 6 from from IN cord-326314-9ycht8gi 180 7 the the DT cord-326314-9ycht8gi 180 8 University University NNP cord-326314-9ycht8gi 180 9 of of IN cord-326314-9ycht8gi 180 10 Michigan Michigan NNP cord-326314-9ycht8gi 180 11 for for IN cord-326314-9ycht8gi 180 12 discussions discussion NNS cord-326314-9ycht8gi 180 13 on on IN cord-326314-9ycht8gi 180 14 inferring infer VBG cord-326314-9ycht8gi 180 15 exposure exposure NN cord-326314-9ycht8gi 180 16 rates rate NNS cord-326314-9ycht8gi 180 17 given give VBN cord-326314-9ycht8gi 180 18 social social JJ cord-326314-9ycht8gi 180 19 distancing distancing NN cord-326314-9ycht8gi 180 20 protocols protocol NNS cord-326314-9ycht8gi 180 21 . . . cord-326314-9ycht8gi 181 1 and and CC cord-326314-9ycht8gi 181 2 f f LS cord-326314-9ycht8gi 181 3 severe severe JJ cord-326314-9ycht8gi 181 4 are be VBP cord-326314-9ycht8gi 181 5 constant constant JJ cord-326314-9ycht8gi 181 6 numbers number NNS cord-326314-9ycht8gi 181 7 , , , cord-326314-9ycht8gi 181 8 as as IN cord-326314-9ycht8gi 181 9 they -PRON- PRP cord-326314-9ycht8gi 181 10 are be VBP cord-326314-9ycht8gi 181 11 assumed assume VBN cord-326314-9ycht8gi 181 12 to to TO cord-326314-9ycht8gi 181 13 reflect reflect VB cord-326314-9ycht8gi 181 14 an an DT cord-326314-9ycht8gi 181 15 intrinsic intrinsic JJ cord-326314-9ycht8gi 181 16 property property NN cord-326314-9ycht8gi 181 17 of of IN cord-326314-9ycht8gi 181 18 the the DT cord-326314-9ycht8gi 181 19 disease disease NN cord-326314-9ycht8gi 181 20 . . . cord-326314-9ycht8gi 182 1 The the DT cord-326314-9ycht8gi 182 2 detection detection NN cord-326314-9ycht8gi 182 3 probability probability NN cord-326314-9ycht8gi 182 4 of of IN cord-326314-9ycht8gi 182 5 asymptomatic asymptomatic JJ cord-326314-9ycht8gi 182 6 cases case NNS cord-326314-9ycht8gi 182 7 is be VBZ cord-326314-9ycht8gi 182 8 taken take VBN cord-326314-9ycht8gi 182 9 to to TO cord-326314-9ycht8gi 182 10 be be VB cord-326314-9ycht8gi 182 11 known know VBN cord-326314-9ycht8gi 182 12 and and CC cord-326314-9ycht8gi 182 13 zero zero CD cord-326314-9ycht8gi 182 14 . . . cord-326314-9ycht8gi 183 1 [ [ -LRB- cord-326314-9ycht8gi 183 2 40 40 CD cord-326314-9ycht8gi 183 3 ] ] -RRB- cord-326314-9ycht8gi 183 4 and and CC cord-326314-9ycht8gi 183 5 [ [ -LRB- cord-326314-9ycht8gi 183 6 41 41 CD cord-326314-9ycht8gi 183 7 ] ] -RRB- cord-326314-9ycht8gi 183 8 . . . cord-326314-9ycht8gi 184 1 For for IN cord-326314-9ycht8gi 184 2 Experiments experiment NNS cord-326314-9ycht8gi 184 3 i i PRP cord-326314-9ycht8gi 184 4 and and CC cord-326314-9ycht8gi 184 5 iv iv NNP cord-326314-9ycht8gi 184 6 , , , cord-326314-9ycht8gi 184 7 the the DT cord-326314-9ycht8gi 184 8 reported report VBN cord-326314-9ycht8gi 184 9 numbers number NNS cord-326314-9ycht8gi 184 10 are be VBP cord-326314-9ycht8gi 184 11 taken take VBN cord-326314-9ycht8gi 184 12 from from IN cord-326314-9ycht8gi 184 13 the the DT cord-326314-9ycht8gi 184 14 annealing anneal VBG cord-326314-9ycht8gi 184 15 iteration iteration NN cord-326314-9ycht8gi 184 16 with with IN cord-326314-9ycht8gi 184 17 a a DT cord-326314-9ycht8gi 184 18 value value NN cord-326314-9ycht8gi 184 19 of of IN cord-326314-9ycht8gi 184 20 parameter parameter NN cord-326314-9ycht8gi 184 21 β β NN cord-326314-9ycht8gi 184 22 of of IN cord-326314-9ycht8gi 184 23 32 32 CD cord-326314-9ycht8gi 184 24 and and CC cord-326314-9ycht8gi 184 25 40 40 CD cord-326314-9ycht8gi 184 26 , , , cord-326314-9ycht8gi 184 27 respectively respectively RB cord-326314-9ycht8gi 184 28 : : : cord-326314-9ycht8gi 184 29 once once IN cord-326314-9ycht8gi 184 30 the the DT cord-326314-9ycht8gi 184 31 deterministic deterministic JJ cord-326314-9ycht8gi 184 32 limit limit NN cord-326314-9ycht8gi 184 33 has have VBZ cord-326314-9ycht8gi 184 34 been be VBN cord-326314-9ycht8gi 184 35 reached reach VBN cord-326314-9ycht8gi 184 36 ( ( -LRB- cord-326314-9ycht8gi 184 37 see see VB cord-326314-9ycht8gi 184 38 text text NN cord-326314-9ycht8gi 184 39 ) ) -RRB- cord-326314-9ycht8gi 184 40 . . . cord-326314-9ycht8gi 185 1 For for IN cord-326314-9ycht8gi 185 2 Experiment Experiment NNP cord-326314-9ycht8gi 185 3 ii ii NNP cord-326314-9ycht8gi 185 4 , , , cord-326314-9ycht8gi 185 5 an an DT cord-326314-9ycht8gi 185 6 attempt attempt NN cord-326314-9ycht8gi 185 7 was be VBD cord-326314-9ycht8gi 185 8 made make VBN cord-326314-9ycht8gi 185 9 to to TO cord-326314-9ycht8gi 185 10 retrieve retrieve VB cord-326314-9ycht8gi 185 11 parameter parameter NN cord-326314-9ycht8gi 185 12 estimates estimate NNS cord-326314-9ycht8gi 185 13 at at IN cord-326314-9ycht8gi 185 14 β β NN cord-326314-9ycht8gi 185 15 = = SYM cord-326314-9ycht8gi 185 16 2 2 CD cord-326314-9ycht8gi 185 17 ; ; : cord-326314-9ycht8gi 185 18 that that DT cord-326314-9ycht8gi 185 19 is be VBZ cord-326314-9ycht8gi 185 20 : : : cord-326314-9ycht8gi 185 21 before before IN cord-326314-9ycht8gi 185 22 the the DT cord-326314-9ycht8gi 185 23 solution solution NN cord-326314-9ycht8gi 185 24 grows grow VBZ cord-326314-9ycht8gi 185 25 unstable unstable JJ cord-326314-9ycht8gi 185 26 exponentially exponentially RB cord-326314-9ycht8gi 185 27 ( ( -LRB- cord-326314-9ycht8gi 185 28 see see VB cord-326314-9ycht8gi 185 29 Figure figure NN cord-326314-9ycht8gi 185 30 5 5 CD cord-326314-9ycht8gi 185 31 ) ) -RRB- cord-326314-9ycht8gi 185 32 . . . cord-326314-9ycht8gi 186 1 See see VB cord-326314-9ycht8gi 186 2 specific specific JJ cord-326314-9ycht8gi 186 3 subsections subsection NNS cord-326314-9ycht8gi 186 4 for for IN cord-326314-9ycht8gi 186 5 details detail NNS cord-326314-9ycht8gi 186 6 of of IN cord-326314-9ycht8gi 186 7 each each DT cord-326314-9ycht8gi 186 8 experiment experiment NN cord-326314-9ycht8gi 186 9 . . . cord-326314-9ycht8gi 186 10 _SP cord-326314-9ycht8gi 187 1 The the DT cord-326314-9ycht8gi 187 2 blue blue JJ cord-326314-9ycht8gi 187 3 notation notation NN cord-326314-9ycht8gi 187 4 specified specify VBN cord-326314-9ycht8gi 187 5 by by IN cord-326314-9ycht8gi 187 6 overbrackets overbracket NNS cord-326314-9ycht8gi 187 7 denotes denote VBZ cord-326314-9ycht8gi 187 8 the the DT cord-326314-9ycht8gi 187 9 correspondence correspondence NN cord-326314-9ycht8gi 187 10 of of IN cord-326314-9ycht8gi 187 11 specific specific JJ cord-326314-9ycht8gi 187 12 terms term NNS cord-326314-9ycht8gi 187 13 to to IN cord-326314-9ycht8gi 187 14 the the DT cord-326314-9ycht8gi 187 15 reactions reaction NNS cord-326314-9ycht8gi 187 16 between between IN cord-326314-9ycht8gi 187 17 the the DT cord-326314-9ycht8gi 187 18 populations population NNS cord-326314-9ycht8gi 187 19 depicted depict VBN cord-326314-9ycht8gi 187 20 in in IN cord-326314-9ycht8gi 187 21 Figure figure NN cord-326314-9ycht8gi 187 22 1 1 CD cord-326314-9ycht8gi 187 23 . . . cord-326314-9ycht8gi 188 1 J J NNP cord-326314-9ycht8gi 188 2 o o NN cord-326314-9ycht8gi 188 3 u u NN cord-326314-9ycht8gi 188 4 r r NN cord-326314-9ycht8gi 188 5 n n NN cord-326314-9ycht8gi 188 6 a a DT cord-326314-9ycht8gi 188 7 l l NN cord-326314-9ycht8gi 188 8 P p NN cord-326314-9ycht8gi 188 9 r r NN cord-326314-9ycht8gi 188 10 e e NN cord-326314-9ycht8gi 188 11 -p -p NN cord-326314-9ycht8gi 188 12 r r NN cord-326314-9ycht8gi 189 1 o o UH cord-326314-9ycht8gi 189 2 o o NN cord-326314-9ycht8gi 189 3 f f NN cord-326314-9ycht8gi 190 1 t t NNP cord-326314-9ycht8gi 190 2 D D NNP cord-326314-9ycht8gi 190 3 Time Time NNP cord-326314-9ycht8gi 190 4 from from IN cord-326314-9ycht8gi 190 5 entering enter VBG cord-326314-9ycht8gi 190 6 critical critical JJ cord-326314-9ycht8gi 190 7 care care NN cord-326314-9ycht8gi 190 8 to to IN cord-326314-9ycht8gi 190 9 death death NN cord-326314-9ycht8gi 190 10 , , , cord-326314-9ycht8gi 190 11 for for IN cord-326314-9ycht8gi 190 12 severe severe JJ cord-326314-9ycht8gi 190 13 symptomatics symptomatic NNS cord-326314-9ycht8gi 190 14 5.0 5.0 CD cord-326314-9ycht8gi 190 15 [ [ -LRB- cord-326314-9ycht8gi 190 16 50 50 CD cord-326314-9ycht8gi 190 17 ] ] -RRB- cord-326314-9ycht8gi 191 1 a a DT cord-326314-9ycht8gi 191 2 As as IN cord-326314-9ycht8gi 191 3 described describe VBN cord-326314-9ycht8gi 191 4 in in IN cord-326314-9ycht8gi 191 5 [ [ -LRB- cord-326314-9ycht8gi 191 6 45 45 CD cord-326314-9ycht8gi 191 7 ] ] -RRB- cord-326314-9ycht8gi 191 8 , , , cord-326314-9ycht8gi 191 9 viral viral JJ cord-326314-9ycht8gi 191 10 load load NN cord-326314-9ycht8gi 191 11 can can MD cord-326314-9ycht8gi 191 12 be be VB cord-326314-9ycht8gi 191 13 high high JJ cord-326314-9ycht8gi 191 14 and and CC cord-326314-9ycht8gi 191 15 detectable detectable JJ cord-326314-9ycht8gi 191 16 for for IN cord-326314-9ycht8gi 191 17 up up IN cord-326314-9ycht8gi 191 18 to to TO cord-326314-9ycht8gi 191 19 20 20 CD cord-326314-9ycht8gi 191 20 days day NNS cord-326314-9ycht8gi 191 21 . . . cord-326314-9ycht8gi 192 1 We -PRON- PRP cord-326314-9ycht8gi 192 2 choose choose VBP cord-326314-9ycht8gi 192 3 a a DT cord-326314-9ycht8gi 192 4 shorter short JJR cord-326314-9ycht8gi 192 5 duration duration NN cord-326314-9ycht8gi 192 6 of of IN cord-326314-9ycht8gi 192 7 infectiousness infectiousness NN cord-326314-9ycht8gi 192 8 to to TO cord-326314-9ycht8gi 192 9 capture capture VB cord-326314-9ycht8gi 192 10 the the DT cord-326314-9ycht8gi 192 11 time time NN cord-326314-9ycht8gi 192 12 during during IN cord-326314-9ycht8gi 192 13 which which WDT cord-326314-9ycht8gi 192 14 transmissibility transmissibility NN cord-326314-9ycht8gi 192 15 is be VBZ cord-326314-9ycht8gi 192 16 highest high JJS cord-326314-9ycht8gi 192 17 . . . cord-326314-9ycht8gi 193 1 J J NNP cord-326314-9ycht8gi 193 2 o o NN cord-326314-9ycht8gi 193 3 u u NN cord-326314-9ycht8gi 193 4 r r NN cord-326314-9ycht8gi 193 5 n n NN cord-326314-9ycht8gi 193 6 a a DT cord-326314-9ycht8gi 193 7 l l NN cord-326314-9ycht8gi 193 8 P p NN cord-326314-9ycht8gi 193 9 r r NN cord-326314-9ycht8gi 193 10 e e NN cord-326314-9ycht8gi 193 11 -p -p NN cord-326314-9ycht8gi 194 1 r r NN cord-326314-9ycht8gi 194 2 o o NN cord-326314-9ycht8gi 194 3 o o NN cord-326314-9ycht8gi 194 4 f f NN cord-326314-9ycht8gi 194 5 Appendix Appendix NNP cord-326314-9ycht8gi 194 6 B B NNP cord-326314-9ycht8gi 194 7 : : : cord-326314-9ycht8gi 195 1 Unknown unknown JJ cord-326314-9ycht8gi 195 2 time time NN cord-326314-9ycht8gi 195 3 - - HYPH cord-326314-9ycht8gi 195 4 varying vary VBG cord-326314-9ycht8gi 195 5 parameters parameter NNS cord-326314-9ycht8gi 195 6 to to TO cord-326314-9ycht8gi 195 7 be be VB cord-326314-9ycht8gi 195 8 estimated estimate VBN cord-326314-9ycht8gi 195 9 The the DT cord-326314-9ycht8gi 195 10 unknown unknown JJ cord-326314-9ycht8gi 195 11 parameters parameter NNS cord-326314-9ycht8gi 195 12 assumed assume VBN cord-326314-9ycht8gi 195 13 to to TO cord-326314-9ycht8gi 195 14 be be VB cord-326314-9ycht8gi 195 15 time time NN cord-326314-9ycht8gi 195 16 - - HYPH cord-326314-9ycht8gi 195 17 varying vary VBG cord-326314-9ycht8gi 196 1 are be VBP cord-326314-9ycht8gi 196 2 the the DT cord-326314-9ycht8gi 196 3 transmission transmission NN cord-326314-9ycht8gi 196 4 rate rate NN cord-326314-9ycht8gi 196 5 K K NNP cord-326314-9ycht8gi 196 6 i i NNP cord-326314-9ycht8gi 196 7 , , , cord-326314-9ycht8gi 196 8 and and CC cord-326314-9ycht8gi 196 9 the the DT cord-326314-9ycht8gi 196 10 detection detection NN cord-326314-9ycht8gi 196 11 probabilities probability NNS cord-326314-9ycht8gi 196 12 d d NNP cord-326314-9ycht8gi 196 13 Sym Sym NNP cord-326314-9ycht8gi 196 14 and and CC cord-326314-9ycht8gi 196 15 d d NNP cord-326314-9ycht8gi 196 16 Sys Sys NNP cord-326314-9ycht8gi 196 17 for for IN cord-326314-9ycht8gi 196 18 mild mild JJ cord-326314-9ycht8gi 196 19 and and CC cord-326314-9ycht8gi 196 20 severe severe JJ cord-326314-9ycht8gi 196 21 symptomatic symptomatic JJ cord-326314-9ycht8gi 196 22 cases case NNS cord-326314-9ycht8gi 196 23 , , , cord-326314-9ycht8gi 196 24 respectively respectively RB cord-326314-9ycht8gi 196 25 . . . cord-326314-9ycht8gi 197 1 The the DT cord-326314-9ycht8gi 197 2 transmission transmission NN cord-326314-9ycht8gi 197 3 rate rate NN cord-326314-9ycht8gi 197 4 in in IN cord-326314-9ycht8gi 197 5 a a DT cord-326314-9ycht8gi 197 6 given give VBN cord-326314-9ycht8gi 197 7 population population NN cord-326314-9ycht8gi 197 8 for for IN cord-326314-9ycht8gi 197 9 a a DT cord-326314-9ycht8gi 197 10 given give VBN cord-326314-9ycht8gi 197 11 infectious infectious JJ cord-326314-9ycht8gi 197 12 disease disease NN cord-326314-9ycht8gi 197 13 is be VBZ cord-326314-9ycht8gi 197 14 measured measure VBN cord-326314-9ycht8gi 197 15 in in IN cord-326314-9ycht8gi 197 16 effective effective JJ cord-326314-9ycht8gi 197 17 contacts contact NNS cord-326314-9ycht8gi 197 18 per per IN cord-326314-9ycht8gi 197 19 unit unit NN cord-326314-9ycht8gi 197 20 time time NN cord-326314-9ycht8gi 197 21 . . . cord-326314-9ycht8gi 198 1 This this DT cord-326314-9ycht8gi 198 2 may may MD cord-326314-9ycht8gi 198 3 be be VB cord-326314-9ycht8gi 198 4 expressed express VBN cord-326314-9ycht8gi 198 5 as as IN cord-326314-9ycht8gi 198 6 the the DT cord-326314-9ycht8gi 198 7 total total JJ cord-326314-9ycht8gi 198 8 contact contact NN cord-326314-9ycht8gi 198 9 rate rate NN cord-326314-9ycht8gi 198 10 ( ( -LRB- cord-326314-9ycht8gi 198 11 the the DT cord-326314-9ycht8gi 198 12 total total JJ cord-326314-9ycht8gi 198 13 number number NN cord-326314-9ycht8gi 198 14 of of IN cord-326314-9ycht8gi 198 15 contacts contact NNS cord-326314-9ycht8gi 198 16 , , , cord-326314-9ycht8gi 198 17 effective effective JJ cord-326314-9ycht8gi 198 18 or or CC cord-326314-9ycht8gi 198 19 not not RB cord-326314-9ycht8gi 198 20 , , , cord-326314-9ycht8gi 198 21 per per IN cord-326314-9ycht8gi 198 22 unit unit NN cord-326314-9ycht8gi 198 23 time time NN cord-326314-9ycht8gi 198 24 ) ) -RRB- cord-326314-9ycht8gi 198 25 , , , cord-326314-9ycht8gi 198 26 multiplied multiply VBN cord-326314-9ycht8gi 198 27 by by IN cord-326314-9ycht8gi 198 28 the the DT cord-326314-9ycht8gi 198 29 risk risk NN cord-326314-9ycht8gi 198 30 of of IN cord-326314-9ycht8gi 198 31 infection infection NN cord-326314-9ycht8gi 198 32 , , , cord-326314-9ycht8gi 198 33 given give VBN cord-326314-9ycht8gi 198 34 contact contact NN cord-326314-9ycht8gi 198 35 between between IN cord-326314-9ycht8gi 198 36 an an DT cord-326314-9ycht8gi 198 37 infectious infectious JJ cord-326314-9ycht8gi 198 38 and and CC cord-326314-9ycht8gi 198 39 a a DT cord-326314-9ycht8gi 198 40 susceptible susceptible JJ cord-326314-9ycht8gi 198 41 individual individual NN cord-326314-9ycht8gi 198 42 . . . cord-326314-9ycht8gi 199 1 The the DT cord-326314-9ycht8gi 199 2 total total JJ cord-326314-9ycht8gi 199 3 contact contact NN cord-326314-9ycht8gi 199 4 rate rate NN cord-326314-9ycht8gi 199 5 can can MD cord-326314-9ycht8gi 199 6 be be VB cord-326314-9ycht8gi 199 7 impacted impact VBN cord-326314-9ycht8gi 199 8 by by IN cord-326314-9ycht8gi 199 9 social social JJ cord-326314-9ycht8gi 199 10 behavior behavior NN cord-326314-9ycht8gi 199 11 . . . cord-326314-9ycht8gi 200 1 In in IN cord-326314-9ycht8gi 200 2 this this DT cord-326314-9ycht8gi 200 3 first first JJ cord-326314-9ycht8gi 200 4 employment employment NN cord-326314-9ycht8gi 200 5 of of IN cord-326314-9ycht8gi 200 6 SDA SDA NNP cord-326314-9ycht8gi 200 7 upon upon IN cord-326314-9ycht8gi 200 8 a a DT cord-326314-9ycht8gi 200 9 pandemic pandemic JJ cord-326314-9ycht8gi 200 10 model model NN cord-326314-9ycht8gi 200 11 of of IN cord-326314-9ycht8gi 200 12 such such JJ cord-326314-9ycht8gi 200 13 high high JJ cord-326314-9ycht8gi 200 14 dimensionality dimensionality NN cord-326314-9ycht8gi 200 15 , , , cord-326314-9ycht8gi 200 16 we -PRON- PRP cord-326314-9ycht8gi 200 17 chose choose VBD cord-326314-9ycht8gi 200 18 to to TO cord-326314-9ycht8gi 200 19 represent represent VB cord-326314-9ycht8gi 200 20 K K NNP cord-326314-9ycht8gi 200 21 i i PRP cord-326314-9ycht8gi 200 22 as as IN cord-326314-9ycht8gi 200 23 a a DT cord-326314-9ycht8gi 200 24 relatively relatively RB cord-326314-9ycht8gi 200 25 constant constant JJ cord-326314-9ycht8gi 200 26 value value NN cord-326314-9ycht8gi 200 27 that that WDT cord-326314-9ycht8gi 200 28 undergoes undergo VBZ cord-326314-9ycht8gi 200 29 one one CD cord-326314-9ycht8gi 200 30 rapid rapid JJ cord-326314-9ycht8gi 200 31 transition transition NN cord-326314-9ycht8gi 200 32 corresponding correspond VBG cord-326314-9ycht8gi 200 33 to to IN cord-326314-9ycht8gi 200 34 a a DT cord-326314-9ycht8gi 200 35 single single JJ cord-326314-9ycht8gi 200 36 social social JJ cord-326314-9ycht8gi 200 37 distancing distancing NN cord-326314-9ycht8gi 200 38 mandate mandate NN cord-326314-9ycht8gi 200 39 . . . cord-326314-9ycht8gi 201 1 As as IN cord-326314-9ycht8gi 201 2 noted note VBN cord-326314-9ycht8gi 201 3 in in IN cord-326314-9ycht8gi 201 4 Experiments experiment NNS cord-326314-9ycht8gi 201 5 , , , cord-326314-9ycht8gi 201 6 social social JJ cord-326314-9ycht8gi 201 7 distancing distancing NN cord-326314-9ycht8gi 201 8 rules rule NNS cord-326314-9ycht8gi 201 9 were be VBD cord-326314-9ycht8gi 201 10 imposed impose VBN cord-326314-9ycht8gi 201 11 in in IN cord-326314-9ycht8gi 201 12 New New NNP cord-326314-9ycht8gi 201 13 York York NNP cord-326314-9ycht8gi 201 14 City City NNP cord-326314-9ycht8gi 201 15 roughly roughly RB cord-326314-9ycht8gi 201 16 25 25 CD cord-326314-9ycht8gi 201 17 days day NNS cord-326314-9ycht8gi 201 18 following follow VBG cord-326314-9ycht8gi 201 19 the the DT cord-326314-9ycht8gi 201 20 first first JJ cord-326314-9ycht8gi 201 21 reported report VBN cord-326314-9ycht8gi 201 22 case case NN cord-326314-9ycht8gi 201 23 . . . cord-326314-9ycht8gi 202 1 We -PRON- PRP cord-326314-9ycht8gi 202 2 thus thus RB cord-326314-9ycht8gi 202 3 chose choose VBD cord-326314-9ycht8gi 202 4 K K NNP cord-326314-9ycht8gi 202 5 i i PRP cord-326314-9ycht8gi 202 6 to to TO cord-326314-9ycht8gi 202 7 transition transition VB cord-326314-9ycht8gi 202 8 between between IN cord-326314-9ycht8gi 202 9 two two CD cord-326314-9ycht8gi 202 10 relatively relatively RB cord-326314-9ycht8gi 202 11 constant constant JJ cord-326314-9ycht8gi 202 12 levels level NNS cord-326314-9ycht8gi 202 13 , , , cord-326314-9ycht8gi 202 14 roughly roughly RB cord-326314-9ycht8gi 202 15 25 25 CD cord-326314-9ycht8gi 202 16 days day NNS cord-326314-9ycht8gi 202 17 following follow VBG cord-326314-9ycht8gi 202 18 time time NN cord-326314-9ycht8gi 202 19 t t NN cord-326314-9ycht8gi 202 20 0 0 CD cord-326314-9ycht8gi 202 21 . . . cord-326314-9ycht8gi 203 1 Specifically specifically RB cord-326314-9ycht8gi 203 2 , , , cord-326314-9ycht8gi 203 3 we -PRON- PRP cord-326314-9ycht8gi 203 4 wrote write VBD cord-326314-9ycht8gi 203 5 K K NNP cord-326314-9ycht8gi 203 6 i i PRP cord-326314-9ycht8gi 203 7 ( ( -LRB- cord-326314-9ycht8gi 203 8 t t NN cord-326314-9ycht8gi 203 9 ) ) -RRB- cord-326314-9ycht8gi 204 1 [ [ -LRB- cord-326314-9ycht8gi 204 2 51 51 CD cord-326314-9ycht8gi 204 3 ] ] -RRB- cord-326314-9ycht8gi 204 4 as as IN cord-326314-9ycht8gi 204 5 : : : cord-326314-9ycht8gi 204 6 The the DT cord-326314-9ycht8gi 204 7 parameter parameter NN cord-326314-9ycht8gi 204 8 T t NN cord-326314-9ycht8gi 204 9 was be VBD cord-326314-9ycht8gi 204 10 set set VBN cord-326314-9ycht8gi 204 11 to to IN cord-326314-9ycht8gi 204 12 25 25 CD cord-326314-9ycht8gi 204 13 , , , cord-326314-9ycht8gi 204 14 beginning begin VBG cord-326314-9ycht8gi 204 15 four four CD cord-326314-9ycht8gi 204 16 days day NNS cord-326314-9ycht8gi 204 17 prior prior RB cord-326314-9ycht8gi 204 18 to to IN cord-326314-9ycht8gi 204 19 the the DT cord-326314-9ycht8gi 204 20 first first JJ cord-326314-9ycht8gi 204 21 report report NN cord-326314-9ycht8gi 204 22 of of IN cord-326314-9ycht8gi 204 23 a a DT cord-326314-9ycht8gi 204 24 detection detection NN cord-326314-9ycht8gi 204 25 in in IN cord-326314-9ycht8gi 204 26 NYC NYC NNP cord-326314-9ycht8gi 204 27 [ [ -LRB- cord-326314-9ycht8gi 204 28 35 35 CD cord-326314-9ycht8gi 204 29 ] ] -RRB- cord-326314-9ycht8gi 204 30 to to IN cord-326314-9ycht8gi 204 31 the the DT cord-326314-9ycht8gi 204 32 imposition imposition NN cord-326314-9ycht8gi 204 33 of of IN cord-326314-9ycht8gi 204 34 a a DT cord-326314-9ycht8gi 204 35 stay stay VB cord-326314-9ycht8gi 204 36 - - HYPH cord-326314-9ycht8gi 204 37 home home NN cord-326314-9ycht8gi 204 38 order order NN cord-326314-9ycht8gi 204 39 in in IN cord-326314-9ycht8gi 204 40 NYC NYC NNP cord-326314-9ycht8gi 204 41 on on IN cord-326314-9ycht8gi 204 42 March March NNP cord-326314-9ycht8gi 204 43 22 22 CD cord-326314-9ycht8gi 204 44 [ [ -LRB- cord-326314-9ycht8gi 204 45 39 39 CD cord-326314-9ycht8gi 204 46 ] ] -RRB- cord-326314-9ycht8gi 204 47 . . . cord-326314-9ycht8gi 205 1 The the DT cord-326314-9ycht8gi 205 2 parameter parameter NN cord-326314-9ycht8gi 205 3 s s NN cord-326314-9ycht8gi 205 4 governs govern VBZ cord-326314-9ycht8gi 205 5 the the DT cord-326314-9ycht8gi 205 6 steepness steepness NN cord-326314-9ycht8gi 205 7 of of IN cord-326314-9ycht8gi 205 8 the the DT cord-326314-9ycht8gi 205 9 transformation transformation NN cord-326314-9ycht8gi 205 10 , , , cord-326314-9ycht8gi 205 11 and and CC cord-326314-9ycht8gi 205 12 was be VBD cord-326314-9ycht8gi 205 13 set set VBN cord-326314-9ycht8gi 205 14 to to IN cord-326314-9ycht8gi 205 15 10 10 CD cord-326314-9ycht8gi 205 16 . . . cord-326314-9ycht8gi 206 1 Parameters parameter NNS cord-326314-9ycht8gi 206 2 f f NNP cord-326314-9ycht8gi 206 3 and and CC cord-326314-9ycht8gi 206 4 ξ ξ NNS cord-326314-9ycht8gi 206 5 were be VBD cord-326314-9ycht8gi 206 6 then then RB cord-326314-9ycht8gi 206 7 adjusted adjust VBN cord-326314-9ycht8gi 206 8 to to IN cord-326314-9ycht8gi 206 9 1.2 1.2 CD cord-326314-9ycht8gi 206 10 and and CC cord-326314-9ycht8gi 206 11 1.5 1.5 CD cord-326314-9ycht8gi 206 12 , , , cord-326314-9ycht8gi 206 13 to to TO cord-326314-9ycht8gi 206 14 achieve achieve VB cord-326314-9ycht8gi 206 15 a a DT cord-326314-9ycht8gi 206 16 transition transition NN cord-326314-9ycht8gi 206 17 from from IN cord-326314-9ycht8gi 206 18 about about IN cord-326314-9ycht8gi 206 19 1.4 1.4 CD cord-326314-9ycht8gi 206 20 to to IN cord-326314-9ycht8gi 206 21 0.3 0.3 CD cord-326314-9ycht8gi 206 22 . . . cord-326314-9ycht8gi 207 1 For for IN cord-326314-9ycht8gi 207 2 detection detection NN cord-326314-9ycht8gi 207 3 probabilities probability NNS cord-326314-9ycht8gi 207 4 d d NN cord-326314-9ycht8gi 207 5 Sym Sym NNP cord-326314-9ycht8gi 207 6 and and CC cord-326314-9ycht8gi 207 7 d d NNP cord-326314-9ycht8gi 207 8 Sys Sys NNP cord-326314-9ycht8gi 207 9 , , , cord-326314-9ycht8gi 207 10 a a DT cord-326314-9ycht8gi 207 11 linear linear JJ cord-326314-9ycht8gi 207 12 and and CC cord-326314-9ycht8gi 207 13 quadratic quadratic JJ cord-326314-9ycht8gi 207 14 form form NN cord-326314-9ycht8gi 207 15 , , , cord-326314-9ycht8gi 207 16 respectively respectively RB cord-326314-9ycht8gi 207 17 , , , cord-326314-9ycht8gi 207 18 were be VBD cord-326314-9ycht8gi 207 19 chosen choose VBN cord-326314-9ycht8gi 207 20 to to TO cord-326314-9ycht8gi 207 21 preclude preclude VB cord-326314-9ycht8gi 207 22 symmetries symmetry NNS cord-326314-9ycht8gi 207 23 , , , cord-326314-9ycht8gi 207 24 and and CC cord-326314-9ycht8gi 207 25 both both DT cord-326314-9ycht8gi 207 26 were be VBD cord-326314-9ycht8gi 207 27 optimistically optimistically RB cord-326314-9ycht8gi 207 28 taken take VBN cord-326314-9ycht8gi 207 29 to to TO cord-326314-9ycht8gi 207 30 increase increase VB cord-326314-9ycht8gi 207 31 with with IN cord-326314-9ycht8gi 207 32 time time NN cord-326314-9ycht8gi 207 33 : : : cord-326314-9ycht8gi 208 1 dSym(t dSym(t NNP cord-326314-9ycht8gi 208 2 ) ) -RRB- cord-326314-9ycht8gi 208 3 = = SYM cord-326314-9ycht8gi 208 4 0.2 0.2 CD cord-326314-9ycht8gi 208 5 · · NFP cord-326314-9ycht8gi 208 6 t t NNP cord-326314-9ycht8gi 208 7 dSys(t dSys(t NNP cord-326314-9ycht8gi 208 8 ) ) -RRB- cord-326314-9ycht8gi 209 1 = = NFP cord-326314-9ycht8gi 210 1 0.1 0.1 NFP cord-326314-9ycht8gi 210 2 · · NFP cord-326314-9ycht8gi 210 3 t t NN cord-326314-9ycht8gi 210 4 2 2 CD cord-326314-9ycht8gi 211 1 Finally finally RB cord-326314-9ycht8gi 211 2 , , , cord-326314-9ycht8gi 211 3 each each DT cord-326314-9ycht8gi 211 4 time time NN cord-326314-9ycht8gi 211 5 series series NN cord-326314-9ycht8gi 211 6 was be VBD cord-326314-9ycht8gi 211 7 normalized normalize VBN cord-326314-9ycht8gi 211 8 to to IN cord-326314-9ycht8gi 211 9 the the DT cord-326314-9ycht8gi 211 10 range range NN cord-326314-9ycht8gi 211 11 : : : cord-326314-9ycht8gi 211 12 [ [ -LRB- cord-326314-9ycht8gi 211 13 0:1 0:1 NNP cord-326314-9ycht8gi 211 14 ] ] -RRB- cord-326314-9ycht8gi 211 15 , , , cord-326314-9ycht8gi 211 16 via via IN cord-326314-9ycht8gi 211 17 division division NN cord-326314-9ycht8gi 211 18 by by IN cord-326314-9ycht8gi 211 19 their -PRON- PRP$ cord-326314-9ycht8gi 211 20 respective respective JJ cord-326314-9ycht8gi 211 21 maximum maximum JJ cord-326314-9ycht8gi 211 22 values value NNS cord-326314-9ycht8gi 211 23 . . . cord-326314-9ycht8gi 212 1 The the DT cord-326314-9ycht8gi 212 2 simulated simulated JJ cord-326314-9ycht8gi 212 3 data datum NNS cord-326314-9ycht8gi 212 4 were be VBD cord-326314-9ycht8gi 212 5 generated generate VBN cord-326314-9ycht8gi 212 6 by by IN cord-326314-9ycht8gi 212 7 integrating integrate VBG cord-326314-9ycht8gi 212 8 the the DT cord-326314-9ycht8gi 212 9 reaction reaction NN cord-326314-9ycht8gi 212 10 equations equation NNS cord-326314-9ycht8gi 212 11 ( ( -LRB- cord-326314-9ycht8gi 212 12 Appendix Appendix NNP cord-326314-9ycht8gi 212 13 A A NNP cord-326314-9ycht8gi 212 14 ) ) -RRB- cord-326314-9ycht8gi 212 15 via via IN cord-326314-9ycht8gi 212 16 a a DT cord-326314-9ycht8gi 212 17 fourth fourth JJ cord-326314-9ycht8gi 212 18 - - HYPH cord-326314-9ycht8gi 212 19 order order NN cord-326314-9ycht8gi 212 20 adaptive adaptive JJ cord-326314-9ycht8gi 212 21 Runge Runge NNP cord-326314-9ycht8gi 212 22 - - HYPH cord-326314-9ycht8gi 212 23 Kutta Kutta NNP cord-326314-9ycht8gi 212 24 method method NN cord-326314-9ycht8gi 212 25 encoded encode VBN cord-326314-9ycht8gi 212 26 in in IN cord-326314-9ycht8gi 212 27 the the DT cord-326314-9ycht8gi 212 28 Python Python NNP cord-326314-9ycht8gi 212 29 package package NN cord-326314-9ycht8gi 212 30 odeINT odeint RB cord-326314-9ycht8gi 212 31 . . . cord-326314-9ycht8gi 213 1 A a DT cord-326314-9ycht8gi 213 2 step step NN cord-326314-9ycht8gi 213 3 size size NN cord-326314-9ycht8gi 213 4 of of IN cord-326314-9ycht8gi 213 5 one one CD cord-326314-9ycht8gi 213 6 ( ( -LRB- cord-326314-9ycht8gi 213 7 day day NN cord-326314-9ycht8gi 213 8 ) ) -RRB- cord-326314-9ycht8gi 213 9 was be VBD cord-326314-9ycht8gi 213 10 used use VBN cord-326314-9ycht8gi 213 11 to to TO cord-326314-9ycht8gi 213 12 record record VB cord-326314-9ycht8gi 213 13 the the DT cord-326314-9ycht8gi 213 14 output output NN cord-326314-9ycht8gi 213 15 . . . cord-326314-9ycht8gi 214 1 Except except IN cord-326314-9ycht8gi 214 2 for for IN cord-326314-9ycht8gi 214 3 the the DT cord-326314-9ycht8gi 214 4 one one CD cord-326314-9ycht8gi 214 5 instance instance NN cord-326314-9ycht8gi 214 6 noted note VBN cord-326314-9ycht8gi 214 7 in in IN cord-326314-9ycht8gi 214 8 Results result NNS cord-326314-9ycht8gi 214 9 regarding regard VBG cord-326314-9ycht8gi 215 1 Experiment experiment NN cord-326314-9ycht8gi 215 2 i i PRP cord-326314-9ycht8gi 215 3 , , , cord-326314-9ycht8gi 215 4 we -PRON- PRP cord-326314-9ycht8gi 215 5 did do VBD cord-326314-9ycht8gi 215 6 not not RB cord-326314-9ycht8gi 215 7 examine examine VB cord-326314-9ycht8gi 215 8 the the DT cord-326314-9ycht8gi 215 9 sensitivity sensitivity NN cord-326314-9ycht8gi 215 10 of of IN cord-326314-9ycht8gi 215 11 estimations estimation NNS cord-326314-9ycht8gi 215 12 to to IN cord-326314-9ycht8gi 215 13 the the DT cord-326314-9ycht8gi 215 14 temporal temporal JJ cord-326314-9ycht8gi 215 15 sparsity sparsity NN cord-326314-9ycht8gi 215 16 of of IN cord-326314-9ycht8gi 215 17 measurements measurement NNS cord-326314-9ycht8gi 215 18 . . . cord-326314-9ycht8gi 216 1 The the DT cord-326314-9ycht8gi 216 2 initial initial JJ cord-326314-9ycht8gi 216 3 conditions condition NNS cord-326314-9ycht8gi 216 4 on on IN cord-326314-9ycht8gi 216 5 the the DT cord-326314-9ycht8gi 216 6 populations population NNS cord-326314-9ycht8gi 216 7 were be VBD cord-326314-9ycht8gi 216 8 : : : cord-326314-9ycht8gi 216 9 S s NN cord-326314-9ycht8gi 216 10 0 0 CD cord-326314-9ycht8gi 216 11 = = NFP cord-326314-9ycht8gi 217 1 N N NNP cord-326314-9ycht8gi 217 2 − − NN cord-326314-9ycht8gi 217 3 1 1 CD cord-326314-9ycht8gi 218 1 ( ( -LRB- cord-326314-9ycht8gi 218 2 where where WRB cord-326314-9ycht8gi 218 3 N N NNP cord-326314-9ycht8gi 218 4 is be VBZ cord-326314-9ycht8gi 218 5 the the DT cord-326314-9ycht8gi 218 6 total total JJ cord-326314-9ycht8gi 218 7 population population NN cord-326314-9ycht8gi 218 8 ) ) -RRB- cord-326314-9ycht8gi 218 9 , , . cord-326314-9ycht8gi 219 1 As as IN cord-326314-9ycht8gi 219 2 0 0 CD cord-326314-9ycht8gi 219 3 = = SYM cord-326314-9ycht8gi 219 4 1 1 CD cord-326314-9ycht8gi 219 5 , , , cord-326314-9ycht8gi 219 6 and and CC cord-326314-9ycht8gi 219 7 zero zero CD cord-326314-9ycht8gi 219 8 for for IN cord-326314-9ycht8gi 219 9 all all DT cord-326314-9ycht8gi 219 10 others other NNS cord-326314-9ycht8gi 219 11 . . . cord-326314-9ycht8gi 220 1 For for IN cord-326314-9ycht8gi 220 2 the the DT cord-326314-9ycht8gi 220 3 noise noise NN cord-326314-9ycht8gi 220 4 experiments experiment NNS cord-326314-9ycht8gi 220 5 , , , cord-326314-9ycht8gi 220 6 the the DT cord-326314-9ycht8gi 220 7 noise noise NN cord-326314-9ycht8gi 220 8 added add VBN cord-326314-9ycht8gi 220 9 to to IN cord-326314-9ycht8gi 220 10 the the DT cord-326314-9ycht8gi 220 11 simulated simulated JJ cord-326314-9ycht8gi 220 12 Sym sym NN cord-326314-9ycht8gi 220 13 det det NN cord-326314-9ycht8gi 220 14 , , , cord-326314-9ycht8gi 220 15 Sys Sys NNP cord-326314-9ycht8gi 220 16 det det NNP cord-326314-9ycht8gi 220 17 , , , cord-326314-9ycht8gi 220 18 and and CC cord-326314-9ycht8gi 220 19 R R NNP cord-326314-9ycht8gi 220 20 data datum NNS cord-326314-9ycht8gi 220 21 were be VBD cord-326314-9ycht8gi 220 22 generated generate VBN cord-326314-9ycht8gi 220 23 by by IN cord-326314-9ycht8gi 220 24 Python Python NNP cord-326314-9ycht8gi 220 25 's 's POS cord-326314-9ycht8gi 220 26 numpy.random.normal numpy.random.normal JJ cord-326314-9ycht8gi 220 27 package package NN cord-326314-9ycht8gi 220 28 , , , cord-326314-9ycht8gi 220 29 which which WDT cord-326314-9ycht8gi 220 30 defines define VBZ cord-326314-9ycht8gi 220 31 a a DT cord-326314-9ycht8gi 220 32 normal normal JJ cord-326314-9ycht8gi 220 33 distribution distribution NN cord-326314-9ycht8gi 220 34 of of IN cord-326314-9ycht8gi 220 35 noise noise NN cord-326314-9ycht8gi 220 36 . . . cord-326314-9ycht8gi 221 1 For for IN cord-326314-9ycht8gi 221 2 the the DT cord-326314-9ycht8gi 221 3 " " `` cord-326314-9ycht8gi 221 4 low low JJ cord-326314-9ycht8gi 221 5 - - HYPH cord-326314-9ycht8gi 221 6 noise noise NN cord-326314-9ycht8gi 221 7 " " '' cord-326314-9ycht8gi 221 8 24 24 CD cord-326314-9ycht8gi 221 9 J J NNP cord-326314-9ycht8gi 221 10 o o NN cord-326314-9ycht8gi 221 11 u u NN cord-326314-9ycht8gi 221 12 r r NN cord-326314-9ycht8gi 221 13 n n NN cord-326314-9ycht8gi 221 14 a a DT cord-326314-9ycht8gi 221 15 l l NN cord-326314-9ycht8gi 221 16 P p NN cord-326314-9ycht8gi 221 17 r r NN cord-326314-9ycht8gi 221 18 e e NN cord-326314-9ycht8gi 222 1 -p -p : cord-326314-9ycht8gi 223 1 r r NNP cord-326314-9ycht8gi 223 2 o o NN cord-326314-9ycht8gi 223 3 o o NN cord-326314-9ycht8gi 223 4 f f NN cord-326314-9ycht8gi 223 5 experiments experiment NNS cord-326314-9ycht8gi 223 6 , , , cord-326314-9ycht8gi 223 7 we -PRON- PRP cord-326314-9ycht8gi 223 8 set set VBD cord-326314-9ycht8gi 223 9 the the DT cord-326314-9ycht8gi 223 10 standard standard JJ cord-326314-9ycht8gi 223 11 deviation deviation NN cord-326314-9ycht8gi 223 12 to to TO cord-326314-9ycht8gi 223 13 be be VB cord-326314-9ycht8gi 223 14 the the DT cord-326314-9ycht8gi 223 15 respective respective JJ cord-326314-9ycht8gi 223 16 mean mean NN cord-326314-9ycht8gi 223 17 of of IN cord-326314-9ycht8gi 223 18 each each DT cord-326314-9ycht8gi 223 19 distribution distribution NN cord-326314-9ycht8gi 223 20 , , , cord-326314-9ycht8gi 223 21 divided divide VBN cord-326314-9ycht8gi 223 22 by by IN cord-326314-9ycht8gi 223 23 100 100 CD cord-326314-9ycht8gi 223 24 . . . cord-326314-9ycht8gi 224 1 For for IN cord-326314-9ycht8gi 224 2 the the DT cord-326314-9ycht8gi 224 3 experiments experiment NNS cord-326314-9ycht8gi 224 4 using use VBG cord-326314-9ycht8gi 224 5 higher high JJR cord-326314-9ycht8gi 224 6 noise noise NN cord-326314-9ycht8gi 224 7 , , , cord-326314-9ycht8gi 224 8 we -PRON- PRP cord-326314-9ycht8gi 224 9 multiplied multiply VBD cord-326314-9ycht8gi 224 10 that that IN cord-326314-9ycht8gi 224 11 original original JJ cord-326314-9ycht8gi 224 12 level level NN cord-326314-9ycht8gi 224 13 by by IN cord-326314-9ycht8gi 224 14 a a DT cord-326314-9ycht8gi 224 15 factor factor NN cord-326314-9ycht8gi 224 16 of of IN cord-326314-9ycht8gi 224 17 ten ten CD cord-326314-9ycht8gi 224 18 . . . cord-326314-9ycht8gi 225 1 For for IN cord-326314-9ycht8gi 225 2 each each DT cord-326314-9ycht8gi 225 3 noisy noisy JJ cord-326314-9ycht8gi 225 4 data datum NNS cord-326314-9ycht8gi 225 5 set set VBN cord-326314-9ycht8gi 225 6 , , , cord-326314-9ycht8gi 225 7 the the DT cord-326314-9ycht8gi 225 8 absolute absolute JJ cord-326314-9ycht8gi 225 9 value value NN cord-326314-9ycht8gi 225 10 of of IN cord-326314-9ycht8gi 225 11 the the DT cord-326314-9ycht8gi 225 12 minimum minimum NN cord-326314-9ycht8gi 225 13 was be VBD cord-326314-9ycht8gi 225 14 then then RB cord-326314-9ycht8gi 225 15 added add VBN cord-326314-9ycht8gi 225 16 to to IN cord-326314-9ycht8gi 225 17 each each DT cord-326314-9ycht8gi 225 18 data data NN cord-326314-9ycht8gi 225 19 point point NN cord-326314-9ycht8gi 225 20 , , , cord-326314-9ycht8gi 225 21 so so IN cord-326314-9ycht8gi 225 22 that that IN cord-326314-9ycht8gi 225 23 the the DT cord-326314-9ycht8gi 225 24 population population NN cord-326314-9ycht8gi 225 25 did do VBD cord-326314-9ycht8gi 225 26 not not RB cord-326314-9ycht8gi 225 27 drop drop VB cord-326314-9ycht8gi 225 28 below below IN cord-326314-9ycht8gi 225 29 zero zero CD cord-326314-9ycht8gi 225 30 . . . cord-326314-9ycht8gi 226 1 The the DT cord-326314-9ycht8gi 226 2 optimization optimization NN cord-326314-9ycht8gi 226 3 was be VBD cord-326314-9ycht8gi 226 4 performed perform VBN cord-326314-9ycht8gi 226 5 via via IN cord-326314-9ycht8gi 226 6 the the DT cord-326314-9ycht8gi 226 7 open open JJ cord-326314-9ycht8gi 226 8 - - HYPH cord-326314-9ycht8gi 226 9 source source NN cord-326314-9ycht8gi 226 10 Interior Interior NNP cord-326314-9ycht8gi 226 11 - - HYPH cord-326314-9ycht8gi 226 12 point point NN cord-326314-9ycht8gi 226 13 Optimizer Optimizer NNP cord-326314-9ycht8gi 226 14 ( ( -LRB- cord-326314-9ycht8gi 226 15 Ipopt Ipopt NNP cord-326314-9ycht8gi 226 16 ) ) -RRB- cord-326314-9ycht8gi 226 17 [ [ -LRB- cord-326314-9ycht8gi 226 18 52 52 CD cord-326314-9ycht8gi 226 19 ] ] -RRB- cord-326314-9ycht8gi 226 20 . . . cord-326314-9ycht8gi 227 1 Ipopt Ipopt NNP cord-326314-9ycht8gi 227 2 uses use VBZ cord-326314-9ycht8gi 227 3 a a DT cord-326314-9ycht8gi 227 4 Simpson Simpson NNP cord-326314-9ycht8gi 227 5 's 's POS cord-326314-9ycht8gi 227 6 rule rule NN cord-326314-9ycht8gi 227 7 method method NN cord-326314-9ycht8gi 227 8 of of IN cord-326314-9ycht8gi 227 9 finite finite JJ cord-326314-9ycht8gi 227 10 differences difference NNS cord-326314-9ycht8gi 227 11 to to TO cord-326314-9ycht8gi 227 12 discretize discretize VB cord-326314-9ycht8gi 227 13 the the DT cord-326314-9ycht8gi 227 14 state state NN cord-326314-9ycht8gi 227 15 space space NN cord-326314-9ycht8gi 227 16 , , , cord-326314-9ycht8gi 227 17 a a DT cord-326314-9ycht8gi 227 18 Newton Newton NNP cord-326314-9ycht8gi 227 19 's 's POS cord-326314-9ycht8gi 227 20 method method NN cord-326314-9ycht8gi 227 21 to to TO cord-326314-9ycht8gi 227 22 search search VB cord-326314-9ycht8gi 227 23 , , , cord-326314-9ycht8gi 227 24 and and CC cord-326314-9ycht8gi 227 25 a a DT cord-326314-9ycht8gi 227 26 barrier barrier NN cord-326314-9ycht8gi 227 27 method method NN cord-326314-9ycht8gi 227 28 to to TO cord-326314-9ycht8gi 227 29 impose impose VB cord-326314-9ycht8gi 227 30 user user NN cord-326314-9ycht8gi 227 31 - - HYPH cord-326314-9ycht8gi 227 32 defined define VBN cord-326314-9ycht8gi 227 33 bounds bound NNS cord-326314-9ycht8gi 227 34 that that WDT cord-326314-9ycht8gi 227 35 are be VBP cord-326314-9ycht8gi 227 36 placed place VBN cord-326314-9ycht8gi 227 37 upon upon IN cord-326314-9ycht8gi 227 38 the the DT cord-326314-9ycht8gi 227 39 searches search NNS cord-326314-9ycht8gi 227 40 . . . cord-326314-9ycht8gi 228 1 We -PRON- PRP cord-326314-9ycht8gi 228 2 note note VBP cord-326314-9ycht8gi 228 3 that that IN cord-326314-9ycht8gi 228 4 Ipopt Ipopt NNP cord-326314-9ycht8gi 228 5 's 's POS cord-326314-9ycht8gi 228 6 search search NN cord-326314-9ycht8gi 228 7 algorithm algorithm NN cord-326314-9ycht8gi 228 8 treats treat VBZ cord-326314-9ycht8gi 228 9 state state NN cord-326314-9ycht8gi 228 10 variables variable NNS cord-326314-9ycht8gi 228 11 as as IN cord-326314-9ycht8gi 228 12 independent independent JJ cord-326314-9ycht8gi 228 13 quantities quantity NNS cord-326314-9ycht8gi 228 14 , , , cord-326314-9ycht8gi 228 15 which which WDT cord-326314-9ycht8gi 228 16 is be VBZ cord-326314-9ycht8gi 228 17 not not RB cord-326314-9ycht8gi 228 18 the the DT cord-326314-9ycht8gi 228 19 case case NN cord-326314-9ycht8gi 228 20 for for IN cord-326314-9ycht8gi 228 21 a a DT cord-326314-9ycht8gi 228 22 model model NN cord-326314-9ycht8gi 228 23 involving involve VBG cord-326314-9ycht8gi 228 24 a a DT cord-326314-9ycht8gi 228 25 closed closed JJ cord-326314-9ycht8gi 228 26 population population NN cord-326314-9ycht8gi 228 27 . . . cord-326314-9ycht8gi 229 1 This this DT cord-326314-9ycht8gi 229 2 feature feature NN cord-326314-9ycht8gi 229 3 did do VBD cord-326314-9ycht8gi 229 4 not not RB cord-326314-9ycht8gi 229 5 affect affect VB cord-326314-9ycht8gi 229 6 the the DT cord-326314-9ycht8gi 229 7 results result NNS cord-326314-9ycht8gi 229 8 of of IN cord-326314-9ycht8gi 229 9 this this DT cord-326314-9ycht8gi 229 10 paper paper NN cord-326314-9ycht8gi 229 11 . . . cord-326314-9ycht8gi 230 1 Those those DT cord-326314-9ycht8gi 230 2 interested interested JJ cord-326314-9ycht8gi 230 3 in in IN cord-326314-9ycht8gi 230 4 expanding expand VBG cord-326314-9ycht8gi 230 5 the the DT cord-326314-9ycht8gi 230 6 use use NN cord-326314-9ycht8gi 230 7 of of IN cord-326314-9ycht8gi 230 8 this this DT cord-326314-9ycht8gi 230 9 tool tool NN cord-326314-9ycht8gi 230 10 , , , cord-326314-9ycht8gi 230 11 however however RB cord-326314-9ycht8gi 230 12 , , , cord-326314-9ycht8gi 230 13 might may MD cord-326314-9ycht8gi 230 14 keep keep VB cord-326314-9ycht8gi 230 15 in in IN cord-326314-9ycht8gi 230 16 mind mind NN cord-326314-9ycht8gi 230 17 this this DT cord-326314-9ycht8gi 230 18 feature feature NN cord-326314-9ycht8gi 230 19 . . . cord-326314-9ycht8gi 231 1 One one PRP cord-326314-9ycht8gi 231 2 might may MD cord-326314-9ycht8gi 231 3 negate negate VB cord-326314-9ycht8gi 231 4 undesired undesired JJ cord-326314-9ycht8gi 231 5 effects effect NNS cord-326314-9ycht8gi 231 6 by by IN cord-326314-9ycht8gi 231 7 , , , cord-326314-9ycht8gi 231 8 for for IN cord-326314-9ycht8gi 231 9 example example NN cord-326314-9ycht8gi 231 10 , , , cord-326314-9ycht8gi 231 11 imposing impose VBG cord-326314-9ycht8gi 231 12 equality equality NN cord-326314-9ycht8gi 231 13 constraints constraint NNS cord-326314-9ycht8gi 231 14 into into IN cord-326314-9ycht8gi 231 15 the the DT cord-326314-9ycht8gi 231 16 cost cost NN cord-326314-9ycht8gi 231 17 function function NN cord-326314-9ycht8gi 231 18 that that WDT cord-326314-9ycht8gi 231 19 enforce enforce VBP cord-326314-9ycht8gi 231 20 the the DT cord-326314-9ycht8gi 231 21 conservation conservation NN cord-326314-9ycht8gi 231 22 of of IN cord-326314-9ycht8gi 231 23 N. N. NNP cord-326314-9ycht8gi 231 24 Within within IN cord-326314-9ycht8gi 231 25 the the DT cord-326314-9ycht8gi 231 26 annealing annealing NN cord-326314-9ycht8gi 231 27 procedure procedure NN cord-326314-9ycht8gi 231 28 described describe VBN cord-326314-9ycht8gi 231 29 in in IN cord-326314-9ycht8gi 231 30 Methods method NNS cord-326314-9ycht8gi 231 31 , , , cord-326314-9ycht8gi 231 32 the the DT cord-326314-9ycht8gi 231 33 parameter parameter NN cord-326314-9ycht8gi 231 34 α α NN cord-326314-9ycht8gi 231 35 was be VBD cord-326314-9ycht8gi 231 36 set set VBN cord-326314-9ycht8gi 231 37 to to IN cord-326314-9ycht8gi 231 38 2.0 2.0 CD cord-326314-9ycht8gi 231 39 , , , cord-326314-9ycht8gi 231 40 and and CC cord-326314-9ycht8gi 231 41 β β NN cord-326314-9ycht8gi 231 42 ran run VBD cord-326314-9ycht8gi 231 43 from from IN cord-326314-9ycht8gi 231 44 0 0 CD cord-326314-9ycht8gi 231 45 to to IN cord-326314-9ycht8gi 231 46 38 38 CD cord-326314-9ycht8gi 231 47 in in IN cord-326314-9ycht8gi 231 48 increments increment NNS cord-326314-9ycht8gi 231 49 of of IN cord-326314-9ycht8gi 231 50 1 1 CD cord-326314-9ycht8gi 231 51 . . . cord-326314-9ycht8gi 232 1 The the DT cord-326314-9ycht8gi 232 2 inverse inverse NN cord-326314-9ycht8gi 232 3 covariance covariance NN cord-326314-9ycht8gi 232 4 matrix matrix NN cord-326314-9ycht8gi 232 5 for for IN cord-326314-9ycht8gi 232 6 measurement measurement NN cord-326314-9ycht8gi 232 7 error error NN cord-326314-9ycht8gi 232 8 ( ( -LRB- cord-326314-9ycht8gi 232 9 R R NNP cord-326314-9ycht8gi 232 10 m m NN cord-326314-9ycht8gi 232 11 ) ) -RRB- cord-326314-9ycht8gi 232 12 was be VBD cord-326314-9ycht8gi 232 13 set set VBN cord-326314-9ycht8gi 232 14 to to IN cord-326314-9ycht8gi 232 15 1.0 1.0 CD cord-326314-9ycht8gi 232 16 , , , cord-326314-9ycht8gi 232 17 and and CC cord-326314-9ycht8gi 232 18 the the DT cord-326314-9ycht8gi 232 19 initial initial JJ cord-326314-9ycht8gi 232 20 value value NN cord-326314-9ycht8gi 232 21 of of IN cord-326314-9ycht8gi 232 22 the the DT cord-326314-9ycht8gi 232 23 inverse inverse NN cord-326314-9ycht8gi 232 24 covariance covariance NN cord-326314-9ycht8gi 232 25 matrix matrix NN cord-326314-9ycht8gi 232 26 for for IN cord-326314-9ycht8gi 232 27 model model NN cord-326314-9ycht8gi 232 28 error error NN cord-326314-9ycht8gi 232 29 ( ( -LRB- cord-326314-9ycht8gi 232 30 R r NN cord-326314-9ycht8gi 232 31 f f NN cord-326314-9ycht8gi 232 32 , , , cord-326314-9ycht8gi 232 33 0 0 CD cord-326314-9ycht8gi 232 34 ) ) -RRB- cord-326314-9ycht8gi 232 35 was be VBD cord-326314-9ycht8gi 232 36 set set VBN cord-326314-9ycht8gi 232 37 to to IN cord-326314-9ycht8gi 232 38 10 10 CD cord-326314-9ycht8gi 232 39 −7 −7 NN cord-326314-9ycht8gi 232 40 . . . cord-326314-9ycht8gi 233 1 For for IN cord-326314-9ycht8gi 233 2 each each DT cord-326314-9ycht8gi 233 3 of of IN cord-326314-9ycht8gi 233 4 the the DT cord-326314-9ycht8gi 233 5 four four CD cord-326314-9ycht8gi 233 6 simulated simulate VBN cord-326314-9ycht8gi 233 7 experiments experiment NNS cord-326314-9ycht8gi 233 8 , , , cord-326314-9ycht8gi 233 9 twenty twenty CD cord-326314-9ycht8gi 233 10 paths path NNS cord-326314-9ycht8gi 233 11 were be VBD cord-326314-9ycht8gi 233 12 searched search VBN cord-326314-9ycht8gi 233 13 , , , cord-326314-9ycht8gi 233 14 beginning begin VBG cord-326314-9ycht8gi 233 15 at at IN cord-326314-9ycht8gi 233 16 randomlygenerated randomlygenerate VBN cord-326314-9ycht8gi 233 17 initial initial JJ cord-326314-9ycht8gi 233 18 conditions condition NNS cord-326314-9ycht8gi 233 19 for for IN cord-326314-9ycht8gi 233 20 parameters parameter NNS cord-326314-9ycht8gi 233 21 and and CC cord-326314-9ycht8gi 233 22 state state NN cord-326314-9ycht8gi 233 23 variables variable NNS cord-326314-9ycht8gi 233 24 . . . cord-326314-9ycht8gi 234 1 All all DT cord-326314-9ycht8gi 234 2 simulations simulation NNS cord-326314-9ycht8gi 234 3 were be VBD cord-326314-9ycht8gi 234 4 run run VBN cord-326314-9ycht8gi 234 5 on on IN cord-326314-9ycht8gi 234 6 a a DT cord-326314-9ycht8gi 234 7 720-core 720-core CD cord-326314-9ycht8gi 234 8 , , , cord-326314-9ycht8gi 234 9 1440-GB 1440-gb CD cord-326314-9ycht8gi 234 10 , , , cord-326314-9ycht8gi 234 11 64-bit 64-bit CD cord-326314-9ycht8gi 234 12 CPU cpu NN cord-326314-9ycht8gi 234 13 cluster cluster NN cord-326314-9ycht8gi 234 14 . . . cord-326314-9ycht8gi 235 1 IHME IHME NNP cord-326314-9ycht8gi 235 2 COVID-19 COVID-19 NNP cord-326314-9ycht8gi 235 3 health health NN cord-326314-9ycht8gi 235 4 service service NN cord-326314-9ycht8gi 235 5 utilization utilization NN cord-326314-9ycht8gi 235 6 forecasting forecasting NNP cord-326314-9ycht8gi 235 7 Team Team NNP cord-326314-9ycht8gi 235 8 and and CC cord-326314-9ycht8gi 235 9 Christopher Christopher NNP cord-326314-9ycht8gi 235 10 JL JL NNP cord-326314-9ycht8gi 235 11 Murray Murray NNP cord-326314-9ycht8gi 235 12 . . . cord-326314-9ycht8gi 236 1 Forecasting forecast VBG cord-326314-9ycht8gi 236 2 COVID-19 covid-19 JJ cord-326314-9ycht8gi 236 3 impact impact NN cord-326314-9ycht8gi 236 4 on on IN cord-326314-9ycht8gi 236 5 hospital hospital NN cord-326314-9ycht8gi 236 6 bed bed NN cord-326314-9ycht8gi 236 7 - - HYPH cord-326314-9ycht8gi 236 8 days day NNS cord-326314-9ycht8gi 236 9 , , , cord-326314-9ycht8gi 236 10 ICU ICU NNP cord-326314-9ycht8gi 236 11 - - HYPH cord-326314-9ycht8gi 236 12 days day NNS cord-326314-9ycht8gi 236 13 , , , cord-326314-9ycht8gi 236 14 ventilator ventilator NN cord-326314-9ycht8gi 236 15 - - HYPH cord-326314-9ycht8gi 236 16 days day NNS cord-326314-9ycht8gi 236 17 and and CC cord-326314-9ycht8gi 236 18 deaths death NNS cord-326314-9ycht8gi 236 19 by by IN cord-326314-9ycht8gi 236 20 US US NNP cord-326314-9ycht8gi 236 21 state state NN cord-326314-9ycht8gi 236 22 in in IN cord-326314-9ycht8gi 236 23 the the DT cord-326314-9ycht8gi 236 24 next next JJ cord-326314-9ycht8gi 236 25 4 4 CD cord-326314-9ycht8gi 236 26 months month NNS cord-326314-9ycht8gi 236 27 . . . cord-326314-9ycht8gi 237 1 medRxiv medRxiv NNS cord-326314-9ycht8gi 237 2 , , , cord-326314-9ycht8gi 237 3 page page NN cord-326314-9ycht8gi 237 4 2020.03 2020.03 CD cord-326314-9ycht8gi 238 1 The the DT cord-326314-9ycht8gi 238 2 need need NN cord-326314-9ycht8gi 238 3 for for IN cord-326314-9ycht8gi 238 4 data data NN cord-326314-9ycht8gi 238 5 innovation innovation NN cord-326314-9ycht8gi 238 6 in in IN cord-326314-9ycht8gi 238 7 the the DT cord-326314-9ycht8gi 238 8 time time NN cord-326314-9ycht8gi 238 9 of of IN cord-326314-9ycht8gi 238 10 covid-19 covid-19 NNP cord-326314-9ycht8gi 238 11 Estimating Estimating NNP cord-326314-9ycht8gi 238 12 the the DT cord-326314-9ycht8gi 238 13 early early JJ cord-326314-9ycht8gi 238 14 death death NN cord-326314-9ycht8gi 238 15 toll toll NN cord-326314-9ycht8gi 238 16 of of IN cord-326314-9ycht8gi 238 17 covid-19 covid-19 NNP cord-326314-9ycht8gi 238 18 in in IN cord-326314-9ycht8gi 238 19 the the DT cord-326314-9ycht8gi 238 20 united united NNP cord-326314-9ycht8gi 238 21 states states NNP cord-326314-9ycht8gi 238 22 Substantial substantial JJ cord-326314-9ycht8gi 238 23 undocumented undocumented JJ cord-326314-9ycht8gi 238 24 infection infection NN cord-326314-9ycht8gi 238 25 facilitates facilitate VBZ cord-326314-9ycht8gi 238 26 the the DT cord-326314-9ycht8gi 238 27 rapid rapid JJ cord-326314-9ycht8gi 238 28 dissemination dissemination NN cord-326314-9ycht8gi 238 29 of of IN cord-326314-9ycht8gi 238 30 novel novel JJ cord-326314-9ycht8gi 238 31 coronavirus coronavirus NN cord-326314-9ycht8gi 238 32 ( ( -LRB- cord-326314-9ycht8gi 238 33 sars sars NNP cord-326314-9ycht8gi 238 34 - - HYPH cord-326314-9ycht8gi 238 35 cov-2 cov-2 LS cord-326314-9ycht8gi 238 36 ) ) -RRB- cord-326314-9ycht8gi 238 37 Inverse inverse NN cord-326314-9ycht8gi 238 38 problem problem NN cord-326314-9ycht8gi 238 39 theory theory NN cord-326314-9ycht8gi 238 40 and and CC cord-326314-9ycht8gi 238 41 methods method NNS cord-326314-9ycht8gi 238 42 for for IN cord-326314-9ycht8gi 238 43 model model NN cord-326314-9ycht8gi 238 44 parameter parameter NN cord-326314-9ycht8gi 238 45 estimation estimation NN cord-326314-9ycht8gi 238 46 Numerical numerical JJ cord-326314-9ycht8gi 238 47 weather weather NN cord-326314-9ycht8gi 238 48 prediction prediction NN cord-326314-9ycht8gi 238 49 Atmospheric atmospheric JJ cord-326314-9ycht8gi 238 50 modeling modeling NN cord-326314-9ycht8gi 238 51 , , , cord-326314-9ycht8gi 238 52 data datum NNS cord-326314-9ycht8gi 238 53 assimilation assimilation NN cord-326314-9ycht8gi 238 54 and and CC cord-326314-9ycht8gi 238 55 predictability predictability NN cord-326314-9ycht8gi 238 56 Data data NN cord-326314-9ycht8gi 238 57 assimilation assimilation NN cord-326314-9ycht8gi 238 58 : : : cord-326314-9ycht8gi 238 59 the the DT cord-326314-9ycht8gi 238 60 ensemble ensemble NN cord-326314-9ycht8gi 238 61 Kalman Kalman NNP cord-326314-9ycht8gi 238 62 filter filter NN cord-326314-9ycht8gi 238 63 Practical practical JJ cord-326314-9ycht8gi 238 64 methods method NNS cord-326314-9ycht8gi 238 65 for for IN cord-326314-9ycht8gi 238 66 optimal optimal JJ cord-326314-9ycht8gi 238 67 control control NN cord-326314-9ycht8gi 238 68 and and CC cord-326314-9ycht8gi 238 69 estimation estimation NN cord-326314-9ycht8gi 238 70 using use VBG cord-326314-9ycht8gi 238 71 nonlinear nonlinear JJ cord-326314-9ycht8gi 238 72 programming programming NN cord-326314-9ycht8gi 239 1 The the DT cord-326314-9ycht8gi 239 2 number number NN cord-326314-9ycht8gi 239 3 of of IN cord-326314-9ycht8gi 239 4 required require VBN cord-326314-9ycht8gi 239 5 observations observation NNS cord-326314-9ycht8gi 239 6 in in IN cord-326314-9ycht8gi 239 7 data data NN cord-326314-9ycht8gi 239 8 assimilation assimilation NN cord-326314-9ycht8gi 239 9 for for IN cord-326314-9ycht8gi 239 10 a a DT cord-326314-9ycht8gi 239 11 shallow shallow JJ cord-326314-9ycht8gi 239 12 - - HYPH cord-326314-9ycht8gi 239 13 water water NN cord-326314-9ycht8gi 239 14 flow flow NN cord-326314-9ycht8gi 239 15 Estimating estimate VBG cord-326314-9ycht8gi 239 16 the the DT cord-326314-9ycht8gi 239 17 state state NN cord-326314-9ycht8gi 239 18 of of IN cord-326314-9ycht8gi 239 19 a a DT cord-326314-9ycht8gi 239 20 geophysical geophysical JJ cord-326314-9ycht8gi 239 21 system system NN cord-326314-9ycht8gi 239 22 with with IN cord-326314-9ycht8gi 239 23 sparse sparse JJ cord-326314-9ycht8gi 239 24 observations observation NNS cord-326314-9ycht8gi 239 25 : : : cord-326314-9ycht8gi 239 26 time time NN cord-326314-9ycht8gi 239 27 delay delay NN cord-326314-9ycht8gi 239 28 methods method NNS cord-326314-9ycht8gi 239 29 to to TO cord-326314-9ycht8gi 239 30 achieve achieve VB cord-326314-9ycht8gi 239 31 accurate accurate JJ cord-326314-9ycht8gi 239 32 initial initial JJ cord-326314-9ycht8gi 239 33 states state NNS cord-326314-9ycht8gi 239 34 for for IN cord-326314-9ycht8gi 239 35 prediction prediction NN cord-326314-9ycht8gi 240 1 Kalman Kalman NNP cord-326314-9ycht8gi 240 2 meets meet VBZ cord-326314-9ycht8gi 240 3 neuron neuron NN cord-326314-9ycht8gi 240 4 : : : cord-326314-9ycht8gi 240 5 the the DT cord-326314-9ycht8gi 240 6 emerging emerge VBG cord-326314-9ycht8gi 240 7 intersection intersection NN cord-326314-9ycht8gi 240 8 of of IN cord-326314-9ycht8gi 240 9 control control NN cord-326314-9ycht8gi 240 10 theory theory NN cord-326314-9ycht8gi 240 11 with with IN cord-326314-9ycht8gi 240 12 neuroscience neuroscience NN cord-326314-9ycht8gi 240 13 Dynamical dynamical JJ cord-326314-9ycht8gi 240 14 estimation estimation NN cord-326314-9ycht8gi 240 15 of of IN cord-326314-9ycht8gi 240 16 neuron neuron NN cord-326314-9ycht8gi 240 17 and and CC cord-326314-9ycht8gi 240 18 network network NN cord-326314-9ycht8gi 240 19 properties property NNS cord-326314-9ycht8gi 241 1 i i PRP cord-326314-9ycht8gi 241 2 : : : cord-326314-9ycht8gi 241 3 variational variational JJ cord-326314-9ycht8gi 241 4 methods method NNS cord-326314-9ycht8gi 242 1 Dynamical dynamical JJ cord-326314-9ycht8gi 242 2 estimation estimation NN cord-326314-9ycht8gi 242 3 of of IN cord-326314-9ycht8gi 242 4 neuron neuron NN cord-326314-9ycht8gi 242 5 and and CC cord-326314-9ycht8gi 242 6 network network NN cord-326314-9ycht8gi 242 7 properties property NNS cord-326314-9ycht8gi 242 8 ii ii NNP cord-326314-9ycht8gi 242 9 : : : cord-326314-9ycht8gi 242 10 path path NNP cord-326314-9ycht8gi 242 11 integral integral NNP cord-326314-9ycht8gi 242 12 monte monte NNP cord-326314-9ycht8gi 242 13 carlo carlo NNP cord-326314-9ycht8gi 242 14 methods method NNS cord-326314-9ycht8gi 242 15 Real real JJ cord-326314-9ycht8gi 242 16 - - HYPH cord-326314-9ycht8gi 242 17 time time NN cord-326314-9ycht8gi 242 18 tracking tracking NN cord-326314-9ycht8gi 242 19 of of IN cord-326314-9ycht8gi 242 20 neuronal neuronal JJ cord-326314-9ycht8gi 242 21 network network NN cord-326314-9ycht8gi 242 22 structure structure NN cord-326314-9ycht8gi 242 23 using use VBG cord-326314-9ycht8gi 242 24 data datum NNS cord-326314-9ycht8gi 242 25 assimilation assimilation NN cord-326314-9ycht8gi 242 26 Estimating estimate VBG cord-326314-9ycht8gi 242 27 parameters parameter NNS cord-326314-9ycht8gi 242 28 and and CC cord-326314-9ycht8gi 242 29 predicting predict VBG cord-326314-9ycht8gi 242 30 membrane membrane NN cord-326314-9ycht8gi 242 31 voltages voltage NNS cord-326314-9ycht8gi 242 32 with with IN cord-326314-9ycht8gi 242 33 conductance conductance NN cord-326314-9ycht8gi 242 34 - - HYPH cord-326314-9ycht8gi 242 35 based base VBN cord-326314-9ycht8gi 242 36 neuron neuron NN cord-326314-9ycht8gi 242 37 models model NNS cord-326314-9ycht8gi 243 1 Automatic automatic JJ cord-326314-9ycht8gi 243 2 construction construction NN cord-326314-9ycht8gi 243 3 of of IN cord-326314-9ycht8gi 243 4 predictive predictive JJ cord-326314-9ycht8gi 243 5 neuron neuron NN cord-326314-9ycht8gi 243 6 models model NNS cord-326314-9ycht8gi 243 7 through through IN cord-326314-9ycht8gi 243 8 large large JJ cord-326314-9ycht8gi 243 9 scale scale NN cord-326314-9ycht8gi 243 10 assimilation assimilation NN cord-326314-9ycht8gi 243 11 of of IN cord-326314-9ycht8gi 243 12 electrophysiological electrophysiological JJ cord-326314-9ycht8gi 243 13 data datum NNS cord-326314-9ycht8gi 243 14 Statistical statistical JJ cord-326314-9ycht8gi 243 15 data datum NNS cord-326314-9ycht8gi 243 16 assimilation assimilation NN cord-326314-9ycht8gi 243 17 for for IN cord-326314-9ycht8gi 243 18 estimating estimate VBG cord-326314-9ycht8gi 243 19 electrophysiology electrophysiology NN cord-326314-9ycht8gi 243 20 simultaneously simultaneously RB cord-326314-9ycht8gi 243 21 with with IN cord-326314-9ycht8gi 243 22 connectivity connectivity NN cord-326314-9ycht8gi 243 23 within within IN cord-326314-9ycht8gi 243 24 a a DT cord-326314-9ycht8gi 243 25 biological biological JJ cord-326314-9ycht8gi 243 26 neuronal neuronal JJ cord-326314-9ycht8gi 243 27 network network NN cord-326314-9ycht8gi 243 28 Towards towards IN cord-326314-9ycht8gi 243 29 real real JJ cord-326314-9ycht8gi 243 30 time time NN cord-326314-9ycht8gi 243 31 epidemiology epidemiology NN cord-326314-9ycht8gi 243 32 : : : cord-326314-9ycht8gi 243 33 data data NN cord-326314-9ycht8gi 243 34 assimilation assimilation NN cord-326314-9ycht8gi 243 35 , , , cord-326314-9ycht8gi 243 36 modeling modeling NN cord-326314-9ycht8gi 243 37 and and CC cord-326314-9ycht8gi 243 38 anomaly anomaly NN cord-326314-9ycht8gi 243 39 detection detection NN cord-326314-9ycht8gi 243 40 of of IN cord-326314-9ycht8gi 243 41 health health NN cord-326314-9ycht8gi 243 42 surveillance surveillance NN cord-326314-9ycht8gi 243 43 data datum NNS cord-326314-9ycht8gi 243 44 streams stream VBZ cord-326314-9ycht8gi 243 45 Variational Variational NNP cord-326314-9ycht8gi 243 46 data datum NNS cord-326314-9ycht8gi 243 47 assimilation assimilation NN cord-326314-9ycht8gi 243 48 with with IN cord-326314-9ycht8gi 243 49 epidemic epidemic NN cord-326314-9ycht8gi 243 50 models model NNS cord-326314-9ycht8gi 243 51 Bayesian Bayesian NNP cord-326314-9ycht8gi 243 52 tracking tracking NN cord-326314-9ycht8gi 243 53 of of IN cord-326314-9ycht8gi 243 54 emerging emerge VBG cord-326314-9ycht8gi 243 55 epidemics epidemic NNS cord-326314-9ycht8gi 243 56 using use VBG cord-326314-9ycht8gi 243 57 ensemble ensemble JJ cord-326314-9ycht8gi 243 58 optimal optimal JJ cord-326314-9ycht8gi 243 59 statistical statistical JJ cord-326314-9ycht8gi 243 60 interpolation interpolation NN cord-326314-9ycht8gi 243 61 Real real JJ cord-326314-9ycht8gi 243 62 time time NN cord-326314-9ycht8gi 243 63 bayesian bayesian JJ cord-326314-9ycht8gi 243 64 estimation estimation NN cord-326314-9ycht8gi 243 65 of of IN cord-326314-9ycht8gi 243 66 the the DT cord-326314-9ycht8gi 243 67 epidemic epidemic NN cord-326314-9ycht8gi 243 68 potential potential NN cord-326314-9ycht8gi 243 69 of of IN cord-326314-9ycht8gi 243 70 emerging emerge VBG cord-326314-9ycht8gi 243 71 infectious infectious JJ cord-326314-9ycht8gi 243 72 diseases disease NNS cord-326314-9ycht8gi 243 73 Adjoint Adjoint NNP cord-326314-9ycht8gi 243 74 - - HYPH cord-326314-9ycht8gi 243 75 based base VBN cord-326314-9ycht8gi 243 76 data datum NNS cord-326314-9ycht8gi 243 77 assimilation assimilation NN cord-326314-9ycht8gi 243 78 of of IN cord-326314-9ycht8gi 243 79 an an DT cord-326314-9ycht8gi 243 80 epidemiology epidemiology NN cord-326314-9ycht8gi 243 81 model model NN cord-326314-9ycht8gi 243 82 for for IN cord-326314-9ycht8gi 243 83 the the DT cord-326314-9ycht8gi 243 84 covid-19 covid-19 CD cord-326314-9ycht8gi 243 85 pandemic pandemic NN cord-326314-9ycht8gi 243 86 in in IN cord-326314-9ycht8gi 243 87 2020 2020 CD cord-326314-9ycht8gi 244 1 An an DT cord-326314-9ycht8gi 244 2 epidemiological epidemiological JJ cord-326314-9ycht8gi 244 3 modelling modelling NN cord-326314-9ycht8gi 244 4 approach approach NN cord-326314-9ycht8gi 244 5 for for IN cord-326314-9ycht8gi 244 6 covid19 covid19 NNP cord-326314-9ycht8gi 244 7 via via IN cord-326314-9ycht8gi 244 8 data data NN cord-326314-9ycht8gi 244 9 assimilation assimilation NN cord-326314-9ycht8gi 244 10 Efficient efficient JJ cord-326314-9ycht8gi 244 11 bayesian bayesian JJ cord-326314-9ycht8gi 244 12 inference inference NN cord-326314-9ycht8gi 244 13 of of IN cord-326314-9ycht8gi 244 14 fully fully RB cord-326314-9ycht8gi 244 15 stochastic stochastic JJ cord-326314-9ycht8gi 244 16 epidemiological epidemiological JJ cord-326314-9ycht8gi 244 17 models model NNS cord-326314-9ycht8gi 244 18 with with IN cord-326314-9ycht8gi 244 19 applications application NNS cord-326314-9ycht8gi 244 20 to to IN cord-326314-9ycht8gi 244 21 covid-19 covid-19 VB cord-326314-9ycht8gi 244 22 Predicting predict VBG cord-326314-9ycht8gi 244 23 the the DT cord-326314-9ycht8gi 244 24 future future NN cord-326314-9ycht8gi 244 25 : : : cord-326314-9ycht8gi 244 26 completing complete VBG cord-326314-9ycht8gi 244 27 models model NNS cord-326314-9ycht8gi 244 28 of of IN cord-326314-9ycht8gi 244 29 observed observed JJ cord-326314-9ycht8gi 244 30 complex complex JJ cord-326314-9ycht8gi 244 31 systems system NNS cord-326314-9ycht8gi 244 32 Dynamical dynamical JJ cord-326314-9ycht8gi 244 33 parameter parameter NN cord-326314-9ycht8gi 244 34 and and CC cord-326314-9ycht8gi 244 35 state state NN cord-326314-9ycht8gi 244 36 estimation estimation NN cord-326314-9ycht8gi 244 37 in in IN cord-326314-9ycht8gi 244 38 neuron neuron NN cord-326314-9ycht8gi 244 39 models model NNS cord-326314-9ycht8gi 244 40 . . . cord-326314-9ycht8gi 245 1 The the DT cord-326314-9ycht8gi 245 2 dynamic dynamic JJ cord-326314-9ycht8gi 245 3 brain brain NN cord-326314-9ycht8gi 245 4 : : : cord-326314-9ycht8gi 245 5 an an DT cord-326314-9ycht8gi 245 6 exploration exploration NN cord-326314-9ycht8gi 245 7 of of IN cord-326314-9ycht8gi 245 8 neuronal neuronal JJ cord-326314-9ycht8gi 245 9 variability variability NN cord-326314-9ycht8gi 245 10 and and CC cord-326314-9ycht8gi 245 11 its -PRON- PRP$ cord-326314-9ycht8gi 245 12 functional functional JJ cord-326314-9ycht8gi 245 13 significance significance NN cord-326314-9ycht8gi 245 14 Estimating estimate VBG cord-326314-9ycht8gi 245 15 the the DT cord-326314-9ycht8gi 245 16 biophysical biophysical JJ cord-326314-9ycht8gi 245 17 properties property NNS cord-326314-9ycht8gi 245 18 of of IN cord-326314-9ycht8gi 245 19 neurons neuron NNS cord-326314-9ycht8gi 245 20 with with IN cord-326314-9ycht8gi 245 21 intracellular intracellular JJ cord-326314-9ycht8gi 245 22 calcium calcium NN cord-326314-9ycht8gi 245 23 dynamics dynamic NNS cord-326314-9ycht8gi 245 24 Accurate accurate JJ cord-326314-9ycht8gi 245 25 state state NN cord-326314-9ycht8gi 245 26 and and CC cord-326314-9ycht8gi 245 27 parameter parameter NN cord-326314-9ycht8gi 245 28 estimation estimation NN cord-326314-9ycht8gi 245 29 in in IN cord-326314-9ycht8gi 245 30 nonlinear nonlinear JJ cord-326314-9ycht8gi 245 31 systems system NNS cord-326314-9ycht8gi 245 32 with with IN cord-326314-9ycht8gi 245 33 sparse sparse JJ cord-326314-9ycht8gi 245 34 observations observation NNS cord-326314-9ycht8gi 245 35 Improved improve VBN cord-326314-9ycht8gi 245 36 variational variational JJ cord-326314-9ycht8gi 245 37 methods method NNS cord-326314-9ycht8gi 245 38 in in IN cord-326314-9ycht8gi 245 39 statistical statistical JJ cord-326314-9ycht8gi 245 40 data data NN cord-326314-9ycht8gi 245 41 assimilation assimilation NN cord-326314-9ycht8gi 245 42 Nonlinear Nonlinear NNP cord-326314-9ycht8gi 245 43 statistical statistical JJ cord-326314-9ycht8gi 245 44 data data NN cord-326314-9ycht8gi 245 45 assimilation assimilation NN cord-326314-9ycht8gi 245 46 for for IN cord-326314-9ycht8gi 245 47 HVC HVC NNP cord-326314-9ycht8gi 245 48 RA RA NNP cord-326314-9ycht8gi 245 49 neurons neuron NNS cord-326314-9ycht8gi 245 50 in in IN cord-326314-9ycht8gi 245 51 the the DT cord-326314-9ycht8gi 245 52 avian avian JJ cord-326314-9ycht8gi 245 53 song song NN cord-326314-9ycht8gi 245 54 system system NN cord-326314-9ycht8gi 245 55 Data Data NNP cord-326314-9ycht8gi 245 56 assimilation assimilation NN cord-326314-9ycht8gi 245 57 of of IN cord-326314-9ycht8gi 245 58 membrane membrane NN cord-326314-9ycht8gi 245 59 dynamics dynamic NNS cord-326314-9ycht8gi 245 60 and and CC cord-326314-9ycht8gi 245 61 channel channel NN cord-326314-9ycht8gi 245 62 kinetics kinetic NNS cord-326314-9ycht8gi 245 63 with with IN cord-326314-9ycht8gi 245 64 a a DT cord-326314-9ycht8gi 245 65 neuromorphic neuromorphic JJ cord-326314-9ycht8gi 245 66 integrated integrate VBN cord-326314-9ycht8gi 245 67 circuit circuit NN cord-326314-9ycht8gi 246 1 An an DT cord-326314-9ycht8gi 246 2 optimization optimization NN cord-326314-9ycht8gi 246 3 - - HYPH cord-326314-9ycht8gi 246 4 based base VBN cord-326314-9ycht8gi 246 5 approach approach NN cord-326314-9ycht8gi 246 6 to to IN cord-326314-9ycht8gi 246 7 calculating calculate VBG cord-326314-9ycht8gi 246 8 neutrino neutrino NN cord-326314-9ycht8gi 246 9 flavor flavor NN cord-326314-9ycht8gi 246 10 evolution evolution NN cord-326314-9ycht8gi 246 11 Systematic systematic JJ cord-326314-9ycht8gi 246 12 variational variational JJ cord-326314-9ycht8gi 246 13 method method NN cord-326314-9ycht8gi 246 14 for for IN cord-326314-9ycht8gi 246 15 statistical statistical JJ cord-326314-9ycht8gi 246 16 nonlinear nonlinear JJ cord-326314-9ycht8gi 246 17 state state NN cord-326314-9ycht8gi 246 18 and and CC cord-326314-9ycht8gi 246 19 parameter parameter NN cord-326314-9ycht8gi 246 20 estimation estimation NN cord-326314-9ycht8gi 246 21 Improved improve VBN cord-326314-9ycht8gi 246 22 inference inference NN cord-326314-9ycht8gi 246 23 of of IN cord-326314-9ycht8gi 246 24 time time NN cord-326314-9ycht8gi 246 25 - - HYPH cord-326314-9ycht8gi 246 26 varying vary VBG cord-326314-9ycht8gi 246 27 reproduction reproduction NN cord-326314-9ycht8gi 246 28 numbers number NNS cord-326314-9ycht8gi 246 29 during during IN cord-326314-9ycht8gi 246 30 infectious infectious JJ cord-326314-9ycht8gi 246 31 disease disease NN cord-326314-9ycht8gi 246 32 outbreaks outbreak NNS cord-326314-9ycht8gi 247 1 A a DT cord-326314-9ycht8gi 247 2 new new JJ cord-326314-9ycht8gi 247 3 framework framework NN cord-326314-9ycht8gi 247 4 and and CC cord-326314-9ycht8gi 247 5 software software NN cord-326314-9ycht8gi 247 6 to to TO cord-326314-9ycht8gi 247 7 estimate estimate VB cord-326314-9ycht8gi 247 8 time time NN cord-326314-9ycht8gi 247 9 - - HYPH cord-326314-9ycht8gi 247 10 varying vary VBG cord-326314-9ycht8gi 247 11 reproduction reproduction NN cord-326314-9ycht8gi 247 12 numbers number NNS cord-326314-9ycht8gi 247 13 during during IN cord-326314-9ycht8gi 247 14 epidemics epidemic NNS cord-326314-9ycht8gi 247 15 Different different JJ cord-326314-9ycht8gi 247 16 epidemic epidemic NN cord-326314-9ycht8gi 247 17 curves curve NNS cord-326314-9ycht8gi 247 18 for for IN cord-326314-9ycht8gi 247 19 severe severe JJ cord-326314-9ycht8gi 247 20 acute acute JJ cord-326314-9ycht8gi 247 21 respiratory respiratory JJ cord-326314-9ycht8gi 247 22 syndrome syndrome NN cord-326314-9ycht8gi 247 23 reveal reveal VBP cord-326314-9ycht8gi 247 24 similar similar JJ cord-326314-9ycht8gi 247 25 impacts impact NNS cord-326314-9ycht8gi 247 26 of of IN cord-326314-9ycht8gi 247 27 control control NN cord-326314-9ycht8gi 247 28 measures measure NNS cord-326314-9ycht8gi 247 29 PAUSE pause VB cord-326314-9ycht8gi 247 30 order order NN cord-326314-9ycht8gi 247 31 in in IN cord-326314-9ycht8gi 247 32 New New NNP cord-326314-9ycht8gi 247 33 York York NNP cord-326314-9ycht8gi 247 34 City City NNP cord-326314-9ycht8gi 247 35 takes take VBZ cord-326314-9ycht8gi 247 36 effect effect NN cord-326314-9ycht8gi 247 37 Getting get VBG cord-326314-9ycht8gi 247 38 a a DT cord-326314-9ycht8gi 247 39 handle handle NN cord-326314-9ycht8gi 247 40 on on IN cord-326314-9ycht8gi 247 41 asymptomatic asymptomatic JJ cord-326314-9ycht8gi 247 42 SARS SARS NNP cord-326314-9ycht8gi 247 43 - - HYPH cord-326314-9ycht8gi 247 44 CoV-2 CoV-2 NNP cord-326314-9ycht8gi 247 45 infection infection NN cord-326314-9ycht8gi 247 46 Estimating estimate VBG cord-326314-9ycht8gi 247 47 the the DT cord-326314-9ycht8gi 247 48 burden burden NN cord-326314-9ycht8gi 247 49 of of IN cord-326314-9ycht8gi 247 50 sars sars NNP cord-326314-9ycht8gi 248 1 -cov-2 -cov-2 : cord-326314-9ycht8gi 248 2 in in IN cord-326314-9ycht8gi 248 3 france france NNP cord-326314-9ycht8gi 249 1 As as IN cord-326314-9ycht8gi 249 2 Americans Americans NNPS cord-326314-9ycht8gi 249 3 Brace Brace NNP cord-326314-9ycht8gi 249 4 for for IN cord-326314-9ycht8gi 249 5 Second Second NNP cord-326314-9ycht8gi 249 6 Wave Wave NNP cord-326314-9ycht8gi 249 7 of of IN cord-326314-9ycht8gi 249 8 COVID-19 COVID-19 NNP cord-326314-9ycht8gi 249 9 Substantial substantial JJ cord-326314-9ycht8gi 249 10 undocumented undocumented JJ cord-326314-9ycht8gi 249 11 infection infection NN cord-326314-9ycht8gi 249 12 facilitates facilitate VBZ cord-326314-9ycht8gi 249 13 the the DT cord-326314-9ycht8gi 249 14 rapid rapid JJ cord-326314-9ycht8gi 249 15 dissemination dissemination NN cord-326314-9ycht8gi 249 16 of of IN cord-326314-9ycht8gi 249 17 novel novel JJ cord-326314-9ycht8gi 249 18 coronavirus coronavirus NN cord-326314-9ycht8gi 249 19 ( ( -LRB- cord-326314-9ycht8gi 249 20 SARS SARS NNP cord-326314-9ycht8gi 249 21 - - HYPH cord-326314-9ycht8gi 249 22 CoV-2 CoV-2 NNP cord-326314-9ycht8gi 249 23 ) ) -RRB- cord-326314-9ycht8gi 249 24 Estimation estimation NN cord-326314-9ycht8gi 249 25 of of IN cord-326314-9ycht8gi 249 26 incubation incubation NN cord-326314-9ycht8gi 249 27 period period NN cord-326314-9ycht8gi 249 28 distribution distribution NN cord-326314-9ycht8gi 249 29 of of IN cord-326314-9ycht8gi 249 30 COVID-19 COVID-19 NNP cord-326314-9ycht8gi 249 31 using use VBG cord-326314-9ycht8gi 249 32 disease disease NN cord-326314-9ycht8gi 249 33 onset onset NN cord-326314-9ycht8gi 249 34 forward forward RB cord-326314-9ycht8gi 249 35 time time NN cord-326314-9ycht8gi 249 36 : : : cord-326314-9ycht8gi 249 37 a a DT cord-326314-9ycht8gi 249 38 novel novel JJ cord-326314-9ycht8gi 249 39 cross cross JJ cord-326314-9ycht8gi 249 40 - - JJ cord-326314-9ycht8gi 249 41 sectional sectional JJ cord-326314-9ycht8gi 249 42 and and CC cord-326314-9ycht8gi 249 43 forward forward RB cord-326314-9ycht8gi 249 44 follow follow VB cord-326314-9ycht8gi 249 45 - - HYPH cord-326314-9ycht8gi 249 46 up up NN cord-326314-9ycht8gi 249 47 study study NN cord-326314-9ycht8gi 249 48 . . . cord-326314-9ycht8gi 250 1 medRxiv medRxiv NNS cord-326314-9ycht8gi 250 2 , , , cord-326314-9ycht8gi 250 3 page page NN cord-326314-9ycht8gi 250 4 2020.03.06 2020.03.06 CD cord-326314-9ycht8gi 250 5 Virological virological JJ cord-326314-9ycht8gi 250 6 assessment assessment NN cord-326314-9ycht8gi 250 7 of of IN cord-326314-9ycht8gi 250 8 hospitalized hospitalize VBN cord-326314-9ycht8gi 250 9 patients patient NNS cord-326314-9ycht8gi 250 10 with with IN cord-326314-9ycht8gi 250 11 COVID-2019 COVID-2019 NNP cord-326314-9ycht8gi 250 12 Incidence Incidence NNP cord-326314-9ycht8gi 250 13 , , , cord-326314-9ycht8gi 250 14 clinical clinical JJ cord-326314-9ycht8gi 250 15 outcomes outcome NNS cord-326314-9ycht8gi 250 16 , , , cord-326314-9ycht8gi 250 17 and and CC cord-326314-9ycht8gi 250 18 transmission transmission NN cord-326314-9ycht8gi 250 19 dynamics dynamic NNS cord-326314-9ycht8gi 250 20 of of IN cord-326314-9ycht8gi 250 21 hospitalized hospitalize VBN cord-326314-9ycht8gi 250 22 2019 2019 CD cord-326314-9ycht8gi 250 23 coronavirus coronavirus NN cord-326314-9ycht8gi 250 24 disease disease NN cord-326314-9ycht8gi 250 25 among among IN cord-326314-9ycht8gi 250 26 9,596,321 9,596,321 CD cord-326314-9ycht8gi 250 27 individuals individual NNS cord-326314-9ycht8gi 250 28 residing reside VBG cord-326314-9ycht8gi 250 29 in in IN cord-326314-9ycht8gi 250 30 california california NNP cord-326314-9ycht8gi 250 31 and and CC cord-326314-9ycht8gi 250 32 washington washington NNP cord-326314-9ycht8gi 250 33 Clinical Clinical NNP cord-326314-9ycht8gi 250 34 Characteristics Characteristics NNPS cord-326314-9ycht8gi 250 35 of of IN cord-326314-9ycht8gi 250 36 138 138 CD cord-326314-9ycht8gi 250 37 Hospitalized hospitalize VBN cord-326314-9ycht8gi 250 38 Patients patient NNS cord-326314-9ycht8gi 250 39 With with IN cord-326314-9ycht8gi 250 40 2019 2019 CD cord-326314-9ycht8gi 250 41 Novel Novel NNP cord-326314-9ycht8gi 250 42 Coronavirus Coronavirus NNP cord-326314-9ycht8gi 250 43 - - HYPH cord-326314-9ycht8gi 250 44 Infected Infected NNP cord-326314-9ycht8gi 250 45 Pneumonia Pneumonia NNP cord-326314-9ycht8gi 250 46 Clinical Clinical NNP cord-326314-9ycht8gi 250 47 features feature NNS cord-326314-9ycht8gi 250 48 of of IN cord-326314-9ycht8gi 250 49 patients patient NNS cord-326314-9ycht8gi 250 50 infected infect VBN cord-326314-9ycht8gi 250 51 with with IN cord-326314-9ycht8gi 250 52 2019 2019 CD cord-326314-9ycht8gi 250 53 novel novel JJ cord-326314-9ycht8gi 250 54 coronavirus coronavirus NN cord-326314-9ycht8gi 250 55 in in IN cord-326314-9ycht8gi 250 56 wuhan wuhan NNP cord-326314-9ycht8gi 250 57 , , , cord-326314-9ycht8gi 250 58 china china NNP cord-326314-9ycht8gi 250 59 . . . cord-326314-9ycht8gi 251 1 The the DT cord-326314-9ycht8gi 251 2 lancet lancet NN cord-326314-9ycht8gi 251 3 Epidemiology epidemiology NN cord-326314-9ycht8gi 251 4 and and CC cord-326314-9ycht8gi 251 5 transmission transmission NN cord-326314-9ycht8gi 251 6 of of IN cord-326314-9ycht8gi 251 7 covid-19 covid-19 NNP cord-326314-9ycht8gi 251 8 in in IN cord-326314-9ycht8gi 251 9 shenzhen shenzhen NNP cord-326314-9ycht8gi 251 10 china china NNP cord-326314-9ycht8gi 251 11 : : : cord-326314-9ycht8gi 251 12 Analysis Analysis NNP cord-326314-9ycht8gi 251 13 of of IN cord-326314-9ycht8gi 251 14 391 391 CD cord-326314-9ycht8gi 251 15 cases case NNS cord-326314-9ycht8gi 251 16 and and CC cord-326314-9ycht8gi 251 17 1,286 1,286 CD cord-326314-9ycht8gi 251 18 of of IN cord-326314-9ycht8gi 251 19 their -PRON- PRP$ cord-326314-9ycht8gi 251 20 close close JJ cord-326314-9ycht8gi 251 21 contacts contact NNS cord-326314-9ycht8gi 251 22 Clinical clinical JJ cord-326314-9ycht8gi 251 23 course course NN cord-326314-9ycht8gi 251 24 and and CC cord-326314-9ycht8gi 251 25 outcomes outcome NNS cord-326314-9ycht8gi 251 26 of of IN cord-326314-9ycht8gi 251 27 critically critically RB cord-326314-9ycht8gi 251 28 ill ill JJ cord-326314-9ycht8gi 251 29 patients patient NNS cord-326314-9ycht8gi 251 30 with with IN cord-326314-9ycht8gi 251 31 sars sars NNP cord-326314-9ycht8gi 251 32 - - HYPH cord-326314-9ycht8gi 251 33 cov-2 cov-2 NNP cord-326314-9ycht8gi 251 34 pneumonia pneumonia NN cord-326314-9ycht8gi 251 35 in in IN cord-326314-9ycht8gi 251 36 wuhan wuhan NNP cord-326314-9ycht8gi 251 37 , , , cord-326314-9ycht8gi 251 38 china china NNP cord-326314-9ycht8gi 251 39 : : : cord-326314-9ycht8gi 251 40 a a DT cord-326314-9ycht8gi 251 41 single single RB cord-326314-9ycht8gi 251 42 - - HYPH cord-326314-9ycht8gi 251 43 centered centered JJ cord-326314-9ycht8gi 251 44 , , , cord-326314-9ycht8gi 251 45 retrospective retrospective JJ cord-326314-9ycht8gi 251 46 , , , cord-326314-9ycht8gi 251 47 observational observational JJ cord-326314-9ycht8gi 251 48 study study NN cord-326314-9ycht8gi 251 49 . . . cord-326314-9ycht8gi 252 1 The the DT cord-326314-9ycht8gi 252 2 Lancet Lancet NNP cord-326314-9ycht8gi 252 3 Respiratory respiratory JJ cord-326314-9ycht8gi 252 4 Medicine medicine NN cord-326314-9ycht8gi 253 1 An an DT cord-326314-9ycht8gi 253 2 updated update VBN cord-326314-9ycht8gi 253 3 estimation estimation NN cord-326314-9ycht8gi 253 4 of of IN cord-326314-9ycht8gi 253 5 the the DT cord-326314-9ycht8gi 253 6 risk risk NN cord-326314-9ycht8gi 253 7 of of IN cord-326314-9ycht8gi 253 8 transmission transmission NN cord-326314-9ycht8gi 253 9 of of IN cord-326314-9ycht8gi 253 10 the the DT cord-326314-9ycht8gi 253 11 novel novel JJ cord-326314-9ycht8gi 253 12 coronavirus coronavirus NN cord-326314-9ycht8gi 253 13 ( ( -LRB- cord-326314-9ycht8gi 253 14 2019-ncov 2019-ncov CD cord-326314-9ycht8gi 253 15 ) ) -RRB- cord-326314-9ycht8gi 253 16 Short short JJ cord-326314-9ycht8gi 253 17 tutorial tutorial NN cord-326314-9ycht8gi 253 18 : : : cord-326314-9ycht8gi 253 19 getting get VBG cord-326314-9ycht8gi 253 20 started start VBN cord-326314-9ycht8gi 253 21 with with IN cord-326314-9ycht8gi 253 22 ipopt ipopt NNP cord-326314-9ycht8gi 253 23 in in IN cord-326314-9ycht8gi 253 24 90 90 CD cord-326314-9ycht8gi 253 25 minutes minute NNS