id	sid	tid	token	lemma	pos
cord-243070-0b06zk1q	1	1	key	key	ADJ
cord-243070-0b06zk1q	1	2	:	:	PUNCT
cord-243070-0b06zk1q	1	3	cord-243070	cord-243070	NOUN
cord-243070-0b06zk1q	1	4	-	-	PUNCT
cord-243070-0b06zk1q	1	5	0b06zk1q	0b06zk1q	NOUN
cord-243070-0b06zk1q	1	6	authors	author	NOUN
cord-243070-0b06zk1q	1	7	:	:	PUNCT
cord-243070-0b06zk1q	1	8	lesniewski	lesniewski	PROPN
cord-243070-0b06zk1q	1	9	,	,	PUNCT
cord-243070-0b06zk1q	1	10	andrew	andrew	PROPN
cord-243070-0b06zk1q	1	11	title	title	PROPN
cord-243070-0b06zk1q	1	12	:	:	PUNCT
cord-243070-0b06zk1q	1	13	epidemic	epidemic	NOUN
cord-243070-0b06zk1q	1	14	control	control	NOUN
cord-243070-0b06zk1q	1	15	via	via	ADP
cord-243070-0b06zk1q	1	16	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	1	17	optimal	optimal	ADJ
cord-243070-0b06zk1q	1	18	control	control	NOUN
cord-243070-0b06zk1q	1	19	date	date	NOUN
cord-243070-0b06zk1q	1	20	:	:	PUNCT
cord-243070-0b06zk1q	1	21	2020	2020	NUM
cord-243070-0b06zk1q	1	22	-	-	SYM
cord-243070-0b06zk1q	1	23	04	04	NUM
cord-243070-0b06zk1q	1	24	-	-	PUNCT
cord-243070-0b06zk1q	1	25	14	14	NUM
cord-243070-0b06zk1q	1	26	journal	journal	NOUN
cord-243070-0b06zk1q	1	27	:	:	PUNCT
cord-243070-0b06zk1q	1	28	nan	nan	PROPN
cord-243070-0b06zk1q	1	29	doi	doi	PROPN
cord-243070-0b06zk1q	1	30	:	:	PUNCT
cord-243070-0b06zk1q	1	31	nan	nan	PROPN
cord-243070-0b06zk1q	1	32	sha	shall	AUX
cord-243070-0b06zk1q	1	33	:	:	PUNCT
cord-243070-0b06zk1q	2	1	doc_id	doc_id	X
cord-243070-0b06zk1q	2	2	:	:	PUNCT
cord-243070-0b06zk1q	2	3	243070	243070	NUM
cord-243070-0b06zk1q	3	1	cord_uid	cord_uid	PROPN
cord-243070-0b06zk1q	3	2	:	:	PUNCT
cord-243070-0b06zk1q	3	3	0b06zk1q	0b06zk1q	PROPN
cord-243070-0b06zk1q	3	4	we	we	PRON
cord-243070-0b06zk1q	3	5	study	study	VERB
cord-243070-0b06zk1q	3	6	the	the	DET
cord-243070-0b06zk1q	3	7	problem	problem	NOUN
cord-243070-0b06zk1q	3	8	of	of	ADP
cord-243070-0b06zk1q	3	9	optimal	optimal	ADJ
cord-243070-0b06zk1q	3	10	control	control	NOUN
cord-243070-0b06zk1q	3	11	of	of	ADP
cord-243070-0b06zk1q	3	12	the	the	DET
cord-243070-0b06zk1q	3	13	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	3	14	sir	sir	NOUN
cord-243070-0b06zk1q	3	15	model	model	NOUN
cord-243070-0b06zk1q	3	16	.	.	PUNCT
cord-243070-0b06zk1q	4	1	models	model	NOUN
cord-243070-0b06zk1q	4	2	of	of	ADP
cord-243070-0b06zk1q	4	3	this	this	DET
cord-243070-0b06zk1q	4	4	type	type	NOUN
cord-243070-0b06zk1q	4	5	are	be	AUX
cord-243070-0b06zk1q	4	6	used	use	VERB
cord-243070-0b06zk1q	4	7	in	in	ADP
cord-243070-0b06zk1q	4	8	mathematical	mathematical	ADJ
cord-243070-0b06zk1q	4	9	epidemiology	epidemiology	NOUN
cord-243070-0b06zk1q	4	10	to	to	PART
cord-243070-0b06zk1q	4	11	capture	capture	VERB
cord-243070-0b06zk1q	4	12	the	the	DET
cord-243070-0b06zk1q	4	13	time	time	NOUN
cord-243070-0b06zk1q	4	14	evolution	evolution	NOUN
cord-243070-0b06zk1q	4	15	of	of	ADP
cord-243070-0b06zk1q	4	16	highly	highly	ADV
cord-243070-0b06zk1q	4	17	infectious	infectious	ADJ
cord-243070-0b06zk1q	4	18	diseases	disease	NOUN
cord-243070-0b06zk1q	4	19	such	such	ADJ
cord-243070-0b06zk1q	4	20	as	as	ADP
cord-243070-0b06zk1q	4	21	covid-19	covid-19	PROPN
cord-243070-0b06zk1q	4	22	.	.	PUNCT
cord-243070-0b06zk1q	5	1	our	our	PRON
cord-243070-0b06zk1q	5	2	approach	approach	NOUN
cord-243070-0b06zk1q	5	3	relies	rely	VERB
cord-243070-0b06zk1q	5	4	on	on	ADP
cord-243070-0b06zk1q	5	5	reformulating	reformulate	VERB
cord-243070-0b06zk1q	5	6	the	the	DET
cord-243070-0b06zk1q	5	7	hamilton	hamilton	PROPN
cord-243070-0b06zk1q	5	8	-	-	PUNCT
cord-243070-0b06zk1q	5	9	jacobi	jacobi	PROPN
cord-243070-0b06zk1q	5	10	-	-	PUNCT
cord-243070-0b06zk1q	5	11	bellman	bellman	NOUN
cord-243070-0b06zk1q	5	12	equation	equation	NOUN
cord-243070-0b06zk1q	5	13	as	as	ADP
cord-243070-0b06zk1q	5	14	a	a	DET
cord-243070-0b06zk1q	5	15	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	5	16	minimum	minimum	NOUN
cord-243070-0b06zk1q	5	17	principle	principle	NOUN
cord-243070-0b06zk1q	5	18	.	.	PUNCT
cord-243070-0b06zk1q	6	1	this	this	DET
cord-243070-0b06zk1q	6	2	results	result	VERB
cord-243070-0b06zk1q	6	3	in	in	ADP
cord-243070-0b06zk1q	6	4	a	a	DET
cord-243070-0b06zk1q	6	5	system	system	NOUN
cord-243070-0b06zk1q	6	6	of	of	ADP
cord-243070-0b06zk1q	6	7	forward	forward	ADV
cord-243070-0b06zk1q	6	8	backward	backward	ADJ
cord-243070-0b06zk1q	6	9	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	6	10	differential	differential	ADJ
cord-243070-0b06zk1q	6	11	equations	equation	NOUN
cord-243070-0b06zk1q	6	12	,	,	PUNCT
cord-243070-0b06zk1q	6	13	which	which	PRON
cord-243070-0b06zk1q	6	14	is	be	AUX
cord-243070-0b06zk1q	6	15	amenable	amenable	ADJ
cord-243070-0b06zk1q	6	16	to	to	ADP
cord-243070-0b06zk1q	6	17	numerical	numerical	ADJ
cord-243070-0b06zk1q	6	18	solution	solution	NOUN
cord-243070-0b06zk1q	6	19	via	via	ADP
cord-243070-0b06zk1q	6	20	monte	monte	PROPN
cord-243070-0b06zk1q	6	21	carlo	carlo	PROPN
cord-243070-0b06zk1q	6	22	simulations	simulation	NOUN
cord-243070-0b06zk1q	6	23	.	.	PUNCT
cord-243070-0b06zk1q	7	1	we	we	PRON
cord-243070-0b06zk1q	7	2	present	present	VERB
cord-243070-0b06zk1q	7	3	a	a	DET
cord-243070-0b06zk1q	7	4	number	number	NOUN
cord-243070-0b06zk1q	7	5	of	of	ADP
cord-243070-0b06zk1q	7	6	numerical	numerical	ADJ
cord-243070-0b06zk1q	7	7	solutions	solution	NOUN
cord-243070-0b06zk1q	7	8	of	of	ADP
cord-243070-0b06zk1q	7	9	the	the	DET
cord-243070-0b06zk1q	7	10	system	system	NOUN
cord-243070-0b06zk1q	7	11	under	under	ADP
cord-243070-0b06zk1q	7	12	a	a	DET
cord-243070-0b06zk1q	7	13	variety	variety	NOUN
cord-243070-0b06zk1q	7	14	of	of	ADP
cord-243070-0b06zk1q	7	15	scenarios	scenario	NOUN
cord-243070-0b06zk1q	7	16	.	.	PUNCT
cord-243070-0b06zk1q	8	1	the	the	DET
cord-243070-0b06zk1q	8	2	classic	classic	ADJ
cord-243070-0b06zk1q	8	3	sir	sir	PROPN
cord-243070-0b06zk1q	8	4	model	model	NOUN
cord-243070-0b06zk1q	8	5	,	,	PUNCT
cord-243070-0b06zk1q	8	6	originally	originally	ADV
cord-243070-0b06zk1q	8	7	proposed	propose	VERB
cord-243070-0b06zk1q	8	8	in	in	ADP
cord-243070-0b06zk1q	8	9	[	[	X
cord-243070-0b06zk1q	8	10	15	15	NUM
cord-243070-0b06zk1q	8	11	]	]	PUNCT
cord-243070-0b06zk1q	8	12	,	,	PUNCT
cord-243070-0b06zk1q	8	13	is	be	AUX
cord-243070-0b06zk1q	8	14	the	the	DET
cord-243070-0b06zk1q	8	15	standard	standard	ADJ
cord-243070-0b06zk1q	8	16	tool	tool	NOUN
cord-243070-0b06zk1q	8	17	of	of	ADP
cord-243070-0b06zk1q	8	18	mathematical	mathematical	ADJ
cord-243070-0b06zk1q	8	19	epidemiology	epidemiology	NOUN
cord-243070-0b06zk1q	8	20	[	[	PUNCT
cord-243070-0b06zk1q	8	21	4	4	NUM
cord-243070-0b06zk1q	8	22	]	]	X
cord-243070-0b06zk1q	8	23	for	for	ADP
cord-243070-0b06zk1q	8	24	quantitative	quantitative	ADJ
cord-243070-0b06zk1q	8	25	analysis	analysis	NOUN
cord-243070-0b06zk1q	8	26	of	of	ADP
cord-243070-0b06zk1q	8	27	the	the	DET
cord-243070-0b06zk1q	8	28	spread	spread	NOUN
cord-243070-0b06zk1q	8	29	of	of	ADP
cord-243070-0b06zk1q	8	30	an	an	DET
cord-243070-0b06zk1q	8	31	epidemic	epidemic	NOUN
cord-243070-0b06zk1q	8	32	.	.	PUNCT
cord-243070-0b06zk1q	9	1	it	it	PRON
cord-243070-0b06zk1q	9	2	describes	describe	VERB
cord-243070-0b06zk1q	9	3	the	the	DET
cord-243070-0b06zk1q	9	4	state	state	NOUN
cord-243070-0b06zk1q	9	5	of	of	ADP
cord-243070-0b06zk1q	9	6	the	the	DET
cord-243070-0b06zk1q	9	7	affected	affected	ADJ
cord-243070-0b06zk1q	9	8	population	population	NOUN
cord-243070-0b06zk1q	9	9	in	in	ADP
cord-243070-0b06zk1q	9	10	terms	term	NOUN
cord-243070-0b06zk1q	9	11	of	of	ADP
cord-243070-0b06zk1q	9	12	three	three	NUM
cord-243070-0b06zk1q	9	13	state	state	NOUN
cord-243070-0b06zk1q	9	14	variables	variable	NOUN
cord-243070-0b06zk1q	9	15	,	,	PUNCT
cord-243070-0b06zk1q	9	16	traditionally	traditionally	ADV
cord-243070-0b06zk1q	9	17	denoted	denote	VERB
cord-243070-0b06zk1q	9	18	by	by	ADP
cord-243070-0b06zk1q	9	19	s	s	PROPN
cord-243070-0b06zk1q	9	20	,	,	PUNCT
cord-243070-0b06zk1q	9	21	i	i	PROPN
cord-243070-0b06zk1q	9	22	,	,	PUNCT
cord-243070-0b06zk1q	9	23	and	and	CCONJ
cord-243070-0b06zk1q	9	24	r	r	X
cord-243070-0b06zk1q	9	25	:	:	PUNCT
cord-243070-0b06zk1q	9	26	(	(	PUNCT
cord-243070-0b06zk1q	9	27	i	i	NOUN
cord-243070-0b06zk1q	9	28	)	)	PUNCT
cord-243070-0b06zk1q	9	29	0	0	NUM
cord-243070-0b06zk1q	10	1	≤	≤	PROPN
cord-243070-0b06zk1q	10	2	s	s	PROPN
cord-243070-0b06zk1q	10	3	≤	≤	PROPN
cord-243070-0b06zk1q	10	4	1	1	NUM
cord-243070-0b06zk1q	10	5	,	,	PUNCT
cord-243070-0b06zk1q	10	6	the	the	DET
cord-243070-0b06zk1q	10	7	fraction	fraction	NOUN
cord-243070-0b06zk1q	10	8	of	of	ADP
cord-243070-0b06zk1q	10	9	individuals	individual	NOUN
cord-243070-0b06zk1q	10	10	who	who	PRON
cord-243070-0b06zk1q	10	11	are	be	AUX
cord-243070-0b06zk1q	10	12	susceptible	susceptible	ADJ
cord-243070-0b06zk1q	10	13	to	to	ADP
cord-243070-0b06zk1q	10	14	the	the	DET
cord-243070-0b06zk1q	10	15	disease	disease	NOUN
cord-243070-0b06zk1q	10	16	.	.	PUNCT
cord-243070-0b06zk1q	11	1	(	(	PUNCT
cord-243070-0b06zk1q	11	2	ii	ii	PROPN
cord-243070-0b06zk1q	11	3	)	)	PUNCT
cord-243070-0b06zk1q	11	4	0	0	NUM
cord-243070-0b06zk1q	12	1	≤	≤	NOUN
cord-243070-0b06zk1q	13	1	i	i	NOUN
cord-243070-0b06zk1q	13	2	≤	≤	PROPN
cord-243070-0b06zk1q	13	3	1	1	NUM
cord-243070-0b06zk1q	13	4	,	,	PUNCT
cord-243070-0b06zk1q	13	5	the	the	DET
cord-243070-0b06zk1q	13	6	fraction	fraction	NOUN
cord-243070-0b06zk1q	13	7	of	of	ADP
cord-243070-0b06zk1q	13	8	individuals	individual	NOUN
cord-243070-0b06zk1q	13	9	who	who	PRON
cord-243070-0b06zk1q	13	10	are	be	AUX
cord-243070-0b06zk1q	13	11	infected	infect	VERB
cord-243070-0b06zk1q	13	12	with	with	ADP
cord-243070-0b06zk1q	13	13	the	the	DET
cord-243070-0b06zk1q	13	14	disease	disease	NOUN
cord-243070-0b06zk1q	13	15	.	.	PUNCT
cord-243070-0b06zk1q	14	1	(	(	PUNCT
cord-243070-0b06zk1q	14	2	iii	iii	NUM
cord-243070-0b06zk1q	14	3	)	)	PUNCT
cord-243070-0b06zk1q	14	4	0	0	NUM
cord-243070-0b06zk1q	15	1	≤	≤	PROPN
cord-243070-0b06zk1q	15	2	r	r	NOUN
cord-243070-0b06zk1q	15	3	≤	≤	PROPN
cord-243070-0b06zk1q	15	4	1	1	NUM
cord-243070-0b06zk1q	15	5	,	,	PUNCT
cord-243070-0b06zk1q	15	6	the	the	DET
cord-243070-0b06zk1q	15	7	fraction	fraction	NOUN
cord-243070-0b06zk1q	15	8	of	of	ADP
cord-243070-0b06zk1q	15	9	individuals	individual	NOUN
cord-243070-0b06zk1q	15	10	who	who	PRON
cord-243070-0b06zk1q	15	11	have	have	AUX
cord-243070-0b06zk1q	15	12	been	be	AUX
cord-243070-0b06zk1q	15	13	removed	remove	VERB
cord-243070-0b06zk1q	15	14	and	and	CCONJ
cord-243070-0b06zk1q	15	15	are	be	AUX
cord-243070-0b06zk1q	15	16	immune	immune	ADJ
cord-243070-0b06zk1q	15	17	to	to	ADP
cord-243070-0b06zk1q	15	18	the	the	DET
cord-243070-0b06zk1q	15	19	disease	disease	NOUN
cord-243070-0b06zk1q	15	20	.	.	PUNCT
cord-243070-0b06zk1q	16	1	note	note	VERB
cord-243070-0b06zk1q	16	2	that	that	SCONJ
cord-243070-0b06zk1q	16	3	,	,	PUNCT
cord-243070-0b06zk1q	16	4	in	in	ADP
cord-243070-0b06zk1q	16	5	this	this	DET
cord-243070-0b06zk1q	16	6	simplified	simplified	ADJ
cord-243070-0b06zk1q	16	7	model	model	NOUN
cord-243070-0b06zk1q	16	8	,	,	PUNCT
cord-243070-0b06zk1q	16	9	r	r	NOUN
cord-243070-0b06zk1q	16	10	includes	include	VERB
cord-243070-0b06zk1q	16	11	the	the	DET
cord-243070-0b06zk1q	16	12	individuals	individual	NOUN
cord-243070-0b06zk1q	16	13	who	who	PRON
cord-243070-0b06zk1q	16	14	have	have	AUX
cord-243070-0b06zk1q	16	15	left	leave	VERB
cord-243070-0b06zk1q	16	16	the	the	DET
cord-243070-0b06zk1q	16	17	population	population	NOUN
cord-243070-0b06zk1q	16	18	through	through	ADP
cord-243070-0b06zk1q	16	19	mortality	mortality	NOUN
cord-243070-0b06zk1q	16	20	.	.	PUNCT
cord-243070-0b06zk1q	17	1	the	the	DET
cord-243070-0b06zk1q	17	2	model	model	NOUN
cord-243070-0b06zk1q	17	3	dynamics	dynamic	NOUN
cord-243070-0b06zk1q	17	4	is	be	AUX
cord-243070-0b06zk1q	17	5	given	give	VERB
cord-243070-0b06zk1q	17	6	as	as	ADP
cord-243070-0b06zk1q	17	7	the	the	DET
cord-243070-0b06zk1q	17	8	following	follow	VERB
cord-243070-0b06zk1q	17	9	dynamical	dynamical	ADJ
cord-243070-0b06zk1q	17	10	system	system	NOUN
cord-243070-0b06zk1q	17	11	:	:	PUNCT
cord-243070-0b06zk1q	17	12	,	,	PUNCT
cord-243070-0b06zk1q	17	13	where	where	SCONJ
cord-243070-0b06zk1q	17	14	the	the	DET
cord-243070-0b06zk1q	17	15	constant	constant	ADJ
cord-243070-0b06zk1q	17	16	parameters	parameter	NOUN
cord-243070-0b06zk1q	17	17	β	β	NOUN
cord-243070-0b06zk1q	17	18	>	>	X
cord-243070-0b06zk1q	17	19	0	0	NUM
cord-243070-0b06zk1q	17	20	and	and	CCONJ
cord-243070-0b06zk1q	17	21	γ	γ	X
cord-243070-0b06zk1q	17	22	>	>	X
cord-243070-0b06zk1q	17	23	0	0	PUNCT
cord-243070-0b06zk1q	17	24	are	be	AUX
cord-243070-0b06zk1q	17	25	called	call	VERB
cord-243070-0b06zk1q	17	26	the	the	DET
cord-243070-0b06zk1q	17	27	infection	infection	NOUN
cord-243070-0b06zk1q	17	28	rate	rate	NOUN
cord-243070-0b06zk1q	17	29	and	and	CCONJ
cord-243070-0b06zk1q	17	30	recovery	recovery	NOUN
cord-243070-0b06zk1q	17	31	rate	rate	NOUN
cord-243070-0b06zk1q	17	32	,	,	PUNCT
cord-243070-0b06zk1q	17	33	respectively	respectively	ADV
cord-243070-0b06zk1q	17	34	.	.	PUNCT
cord-243070-0b06zk1q	18	1	the	the	DET
cord-243070-0b06zk1q	18	2	evolution	evolution	NOUN
cord-243070-0b06zk1q	18	3	above	above	ADV
cord-243070-0b06zk1q	18	4	is	be	AUX
cord-243070-0b06zk1q	18	5	subject	subject	ADJ
cord-243070-0b06zk1q	18	6	to	to	ADP
cord-243070-0b06zk1q	18	7	the	the	DET
cord-243070-0b06zk1q	18	8	initial	initial	ADJ
cord-243070-0b06zk1q	18	9	conditions	condition	NOUN
cord-243070-0b06zk1q	18	10	:	:	PUNCT
cord-243070-0b06zk1q	18	11	(	(	PUNCT
cord-243070-0b06zk1q	18	12	notice	notice	VERB
cord-243070-0b06zk1q	18	13	that	that	SCONJ
cord-243070-0b06zk1q	18	14	this	this	DET
cord-243070-0b06zk1q	18	15	dynamics	dynamic	NOUN
cord-243070-0b06zk1q	18	16	obeys	obey	VERB
cord-243070-0b06zk1q	18	17	the	the	DET
cord-243070-0b06zk1q	18	18	conservation	conservation	NOUN
cord-243070-0b06zk1q	18	19	law	law	NOUN
cord-243070-0b06zk1q	18	20	consistent	consistent	ADJ
cord-243070-0b06zk1q	18	21	with	with	ADP
cord-243070-0b06zk1q	18	22	the	the	DET
cord-243070-0b06zk1q	18	23	assumption	assumption	NOUN
cord-243070-0b06zk1q	18	24	that	that	SCONJ
cord-243070-0b06zk1q	18	25	the	the	DET
cord-243070-0b06zk1q	18	26	variables	variable	NOUN
cord-243070-0b06zk1q	18	27	s	s	PROPN
cord-243070-0b06zk1q	18	28	,	,	PUNCT
cord-243070-0b06zk1q	18	29	i	i	PROPN
cord-243070-0b06zk1q	18	30	,	,	PUNCT
cord-243070-0b06zk1q	18	31	and	and	CCONJ
cord-243070-0b06zk1q	18	32	r	r	NOUN
cord-243070-0b06zk1q	18	33	represent	represent	VERB
cord-243070-0b06zk1q	18	34	population	population	NOUN
cord-243070-0b06zk1q	18	35	fractions	fraction	NOUN
cord-243070-0b06zk1q	18	36	.	.	PUNCT
cord-243070-0b06zk1q	19	1	this	this	PRON
cord-243070-0b06zk1q	19	2	means	mean	VERB
cord-243070-0b06zk1q	19	3	that	that	SCONJ
cord-243070-0b06zk1q	19	4	the	the	DET
cord-243070-0b06zk1q	19	5	variable	variable	ADJ
cord-243070-0b06zk1q	19	6	r	r	NOUN
cord-243070-0b06zk1q	19	7	is	be	AUX
cord-243070-0b06zk1q	19	8	,	,	PUNCT
cord-243070-0b06zk1q	19	9	in	in	ADP
cord-243070-0b06zk1q	19	10	a	a	DET
cord-243070-0b06zk1q	19	11	way	way	NOUN
cord-243070-0b06zk1q	19	12	,	,	PUNCT
cord-243070-0b06zk1q	19	13	redundant	redundant	ADJ
cord-243070-0b06zk1q	19	14	,	,	PUNCT
cord-243070-0b06zk1q	19	15	as	as	SCONJ
cord-243070-0b06zk1q	19	16	its	its	PRON
cord-243070-0b06zk1q	19	17	current	current	ADJ
cord-243070-0b06zk1q	19	18	value	value	NOUN
cord-243070-0b06zk1q	19	19	does	do	AUX
cord-243070-0b06zk1q	19	20	not	not	PART
cord-243070-0b06zk1q	19	21	affect	affect	VERB
cord-243070-0b06zk1q	19	22	the	the	DET
cord-243070-0b06zk1q	19	23	dynamics	dynamic	NOUN
cord-243070-0b06zk1q	19	24	of	of	ADP
cord-243070-0b06zk1q	19	25	s	s	NOUN
cord-243070-0b06zk1q	19	26	and	and	CCONJ
cord-243070-0b06zk1q	19	27	i	i	NOUN
cord-243070-0b06zk1q	19	28	,	,	PUNCT
cord-243070-0b06zk1q	19	29	and	and	CCONJ
cord-243070-0b06zk1q	19	30	it	it	PRON
cord-243070-0b06zk1q	19	31	can	can	AUX
cord-243070-0b06zk1q	19	32	be	be	AUX
cord-243070-0b06zk1q	19	33	computed	compute	VERB
cord-243070-0b06zk1q	19	34	in	in	ADP
cord-243070-0b06zk1q	19	35	a	a	DET
cord-243070-0b06zk1q	19	36	straightforward	straightforward	ADJ
cord-243070-0b06zk1q	19	37	manner	manner	NOUN
cord-243070-0b06zk1q	19	38	from	from	ADP
cord-243070-0b06zk1q	19	39	(	(	PUNCT
cord-243070-0b06zk1q	19	40	3	3	NUM
cord-243070-0b06zk1q	19	41	)	)	PUNCT
cord-243070-0b06zk1q	19	42	.	.	PUNCT
cord-243070-0b06zk1q	20	1	it	it	PRON
cord-243070-0b06zk1q	20	2	is	be	AUX
cord-243070-0b06zk1q	20	3	thus	thus	ADV
cord-243070-0b06zk1q	20	4	natural	natural	ADJ
cord-243070-0b06zk1q	20	5	to	to	PART
cord-243070-0b06zk1q	20	6	consider	consider	VERB
cord-243070-0b06zk1q	20	7	the	the	DET
cord-243070-0b06zk1q	20	8	two	two	NUM
cord-243070-0b06zk1q	20	9	dimensional	dimensional	ADJ
cord-243070-0b06zk1q	20	10	system	system	NOUN
cord-243070-0b06zk1q	20	11	defined	define	VERB
cord-243070-0b06zk1q	20	12	by	by	ADP
cord-243070-0b06zk1q	20	13	s	s	NOUN
cord-243070-0b06zk1q	20	14	,	,	PUNCT
cord-243070-0b06zk1q	20	15	i	i	PRON
cord-243070-0b06zk1q	20	16	only	only	ADV
cord-243070-0b06zk1q	20	17	.	.	PUNCT
cord-243070-0b06zk1q	21	1	eventually	eventually	ADV
cord-243070-0b06zk1q	21	2	every	every	DET
cord-243070-0b06zk1q	21	3	epidemic	epidemic	NOUN
cord-243070-0b06zk1q	21	4	comes	come	VERB
cord-243070-0b06zk1q	21	5	to	to	ADP
cord-243070-0b06zk1q	21	6	a	a	DET
cord-243070-0b06zk1q	21	7	natural	natural	ADJ
cord-243070-0b06zk1q	21	8	halt	halt	NOUN
cord-243070-0b06zk1q	21	9	1	1	NUM
cord-243070-0b06zk1q	21	10	,	,	PUNCT
cord-243070-0b06zk1q	21	11	but	but	CCONJ
cord-243070-0b06zk1q	21	12	its	its	PRON
cord-243070-0b06zk1q	21	13	impact	impact	NOUN
cord-243070-0b06zk1q	21	14	on	on	ADP
cord-243070-0b06zk1q	21	15	the	the	DET
cord-243070-0b06zk1q	21	16	population	population	NOUN
cord-243070-0b06zk1q	21	17	may	may	AUX
cord-243070-0b06zk1q	21	18	be	be	AUX
cord-243070-0b06zk1q	21	19	very	very	ADV
cord-243070-0b06zk1q	21	20	serious	serious	ADJ
cord-243070-0b06zk1q	21	21	.	.	PUNCT
cord-243070-0b06zk1q	22	1	the	the	DET
cord-243070-0b06zk1q	22	2	overall	overall	ADJ
cord-243070-0b06zk1q	22	3	objective	objective	NOUN
cord-243070-0b06zk1q	22	4	of	of	ADP
cord-243070-0b06zk1q	22	5	epidemic	epidemic	NOUN
cord-243070-0b06zk1q	22	6	control	control	NOUN
cord-243070-0b06zk1q	22	7	is	be	AUX
cord-243070-0b06zk1q	22	8	to	to	PART
cord-243070-0b06zk1q	22	9	slow	slow	VERB
cord-243070-0b06zk1q	22	10	down	down	ADP
cord-243070-0b06zk1q	22	11	the	the	DET
cord-243070-0b06zk1q	22	12	spread	spread	NOUN
cord-243070-0b06zk1q	22	13	of	of	ADP
cord-243070-0b06zk1q	22	14	infection	infection	NOUN
cord-243070-0b06zk1q	22	15	in	in	ADP
cord-243070-0b06zk1q	22	16	a	a	DET
cord-243070-0b06zk1q	22	17	way	way	NOUN
cord-243070-0b06zk1q	22	18	that	that	PRON
cord-243070-0b06zk1q	22	19	it	it	PRON
cord-243070-0b06zk1q	22	20	does	do	AUX
cord-243070-0b06zk1q	22	21	not	not	PART
cord-243070-0b06zk1q	22	22	overwhelm	overwhelm	VERB
cord-243070-0b06zk1q	22	23	the	the	DET
cord-243070-0b06zk1q	22	24	healthcare	healthcare	NOUN
cord-243070-0b06zk1q	22	25	system	system	NOUN
cord-243070-0b06zk1q	22	26	and	and	CCONJ
cord-243070-0b06zk1q	22	27	it	it	PRON
cord-243070-0b06zk1q	22	28	allows	allow	VERB
cord-243070-0b06zk1q	22	29	the	the	DET
cord-243070-0b06zk1q	22	30	economy	economy	NOUN
cord-243070-0b06zk1q	22	31	to	to	PART
cord-243070-0b06zk1q	22	32	function	function	VERB
cord-243070-0b06zk1q	22	33	.	.	PUNCT
cord-243070-0b06zk1q	23	1	all	all	PRON
cord-243070-0b06zk1q	23	2	of	of	ADP
cord-243070-0b06zk1q	23	3	this	this	PRON
cord-243070-0b06zk1q	23	4	should	should	AUX
cord-243070-0b06zk1q	23	5	be	be	AUX
cord-243070-0b06zk1q	23	6	done	do	VERB
cord-243070-0b06zk1q	23	7	within	within	ADP
cord-243070-0b06zk1q	23	8	the	the	DET
cord-243070-0b06zk1q	23	9	limits	limit	NOUN
cord-243070-0b06zk1q	23	10	of	of	ADP
cord-243070-0b06zk1q	23	11	available	available	ADJ
cord-243070-0b06zk1q	23	12	resources	resource	NOUN
cord-243070-0b06zk1q	23	13	.	.	PUNCT
cord-243070-0b06zk1q	24	1	in	in	ADP
cord-243070-0b06zk1q	24	2	this	this	DET
cord-243070-0b06zk1q	24	3	note	note	NOUN
cord-243070-0b06zk1q	24	4	we	we	PRON
cord-243070-0b06zk1q	24	5	study	study	VERB
cord-243070-0b06zk1q	24	6	the	the	DET
cord-243070-0b06zk1q	24	7	problem	problem	NOUN
cord-243070-0b06zk1q	24	8	of	of	ADP
cord-243070-0b06zk1q	24	9	optimal	optimal	ADJ
cord-243070-0b06zk1q	24	10	control	control	NOUN
cord-243070-0b06zk1q	24	11	of	of	ADP
cord-243070-0b06zk1q	24	12	an	an	DET
cord-243070-0b06zk1q	24	13	epidemic	epidemic	NOUN
cord-243070-0b06zk1q	24	14	modeled	model	VERB
cord-243070-0b06zk1q	24	15	by	by	ADP
cord-243070-0b06zk1q	24	16	means	mean	NOUN
cord-243070-0b06zk1q	24	17	of	of	ADP
cord-243070-0b06zk1q	24	18	a	a	DET
cord-243070-0b06zk1q	24	19	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	24	20	extension	extension	NOUN
cord-243070-0b06zk1q	24	21	of	of	ADP
cord-243070-0b06zk1q	24	22	the	the	DET
cord-243070-0b06zk1q	24	23	sir	sir	PROPN
cord-243070-0b06zk1q	24	24	model	model	NOUN
cord-243070-0b06zk1q	24	25	(	(	PUNCT
cord-243070-0b06zk1q	24	26	see	see	VERB
cord-243070-0b06zk1q	24	27	section	section	NOUN
cord-243070-0b06zk1q	24	28	2	2	NUM
cord-243070-0b06zk1q	24	29	for	for	ADP
cord-243070-0b06zk1q	24	30	definition	definition	NOUN
cord-243070-0b06zk1q	24	31	)	)	PUNCT
cord-243070-0b06zk1q	24	32	.	.	PUNCT
cord-243070-0b06zk1q	25	1	we	we	PRON
cord-243070-0b06zk1q	25	2	assume	assume	VERB
cord-243070-0b06zk1q	25	3	that	that	SCONJ
cord-243070-0b06zk1q	25	4	the	the	DET
cord-243070-0b06zk1q	25	5	controlling	control	VERB
cord-243070-0b06zk1q	25	6	agent	agent	NOUN
cord-243070-0b06zk1q	25	7	(	(	PUNCT
cord-243070-0b06zk1q	25	8	"	"	PUNCT
cord-243070-0b06zk1q	25	9	government	government	NOUN
cord-243070-0b06zk1q	25	10	"	"	PUNCT
cord-243070-0b06zk1q	25	11	)	)	PUNCT
cord-243070-0b06zk1q	25	12	has	have	VERB
cord-243070-0b06zk1q	25	13	the	the	DET
cord-243070-0b06zk1q	25	14	ability	ability	NOUN
cord-243070-0b06zk1q	25	15	to	to	PART
cord-243070-0b06zk1q	25	16	impact	impact	VERB
cord-243070-0b06zk1q	25	17	the	the	DET
cord-243070-0b06zk1q	25	18	spread	spread	NOUN
cord-243070-0b06zk1q	25	19	of	of	ADP
cord-243070-0b06zk1q	25	20	the	the	DET
cord-243070-0b06zk1q	25	21	disease	disease	NOUN
cord-243070-0b06zk1q	25	22	through	through	ADP
cord-243070-0b06zk1q	25	23	one	one	NUM
cord-243070-0b06zk1q	25	24	of	of	ADP
cord-243070-0b06zk1q	25	25	the	the	DET
cord-243070-0b06zk1q	25	26	policies	policy	NOUN
cord-243070-0b06zk1q	25	27	(	(	PUNCT
cord-243070-0b06zk1q	25	28	or	or	CCONJ
cord-243070-0b06zk1q	25	29	the	the	DET
cord-243070-0b06zk1q	25	30	combination	combination	NOUN
cord-243070-0b06zk1q	25	31	of	of	ADP
cord-243070-0b06zk1q	25	32	both	both	PRON
cord-243070-0b06zk1q	25	33	):	):	PUNCT
cord-243070-0b06zk1q	25	34	(	(	PUNCT
cord-243070-0b06zk1q	25	35	i	i	NOUN
cord-243070-0b06zk1q	25	36	)	)	PUNCT
cord-243070-0b06zk1q	25	37	vaccination	vaccination	NOUN
cord-243070-0b06zk1q	25	38	of	of	ADP
cord-243070-0b06zk1q	25	39	susceptible	susceptible	ADJ
cord-243070-0b06zk1q	25	40	individuals	individual	NOUN
cord-243070-0b06zk1q	25	41	,	,	PUNCT
cord-243070-0b06zk1q	25	42	with	with	ADP
cord-243070-0b06zk1q	25	43	rate	rate	NOUN
cord-243070-0b06zk1q	25	44	v.	v.	ADP
cord-243070-0b06zk1q	25	45	this	this	PRON
cord-243070-0b06zk1q	25	46	makes	make	VERB
cord-243070-0b06zk1q	25	47	the	the	DET
cord-243070-0b06zk1q	25	48	fraction	fraction	NOUN
cord-243070-0b06zk1q	25	49	vs	vs	ADP
cord-243070-0b06zk1q	25	50	of	of	ADP
cord-243070-0b06zk1q	25	51	the	the	DET
cord-243070-0b06zk1q	25	52	susceptible	susceptible	ADJ
cord-243070-0b06zk1q	25	53	population	population	NOUN
cord-243070-0b06zk1q	25	54	immune	immune	ADJ
cord-243070-0b06zk1q	25	55	to	to	ADP
cord-243070-0b06zk1q	25	56	the	the	DET
cord-243070-0b06zk1q	25	57	disease	disease	NOUN
cord-243070-0b06zk1q	25	58	.	.	PUNCT
cord-243070-0b06zk1q	26	1	(	(	PUNCT
cord-243070-0b06zk1q	26	2	ii	ii	PROPN
cord-243070-0b06zk1q	26	3	)	)	PUNCT
cord-243070-0b06zk1q	26	4	isolation	isolation	NOUN
cord-243070-0b06zk1q	26	5	of	of	ADP
cord-243070-0b06zk1q	26	6	infected	infected	ADJ
cord-243070-0b06zk1q	26	7	individuals	individual	NOUN
cord-243070-0b06zk1q	26	8	,	,	PUNCT
cord-243070-0b06zk1q	26	9	with	with	ADP
cord-243070-0b06zk1q	26	10	rate	rate	NOUN
cord-243070-0b06zk1q	26	11	i.	i.	PROPN
cord-243070-0b06zk1q	26	12	this	this	PRON
cord-243070-0b06zk1q	26	13	removes	remove	VERB
cord-243070-0b06zk1q	26	14	the	the	DET
cord-243070-0b06zk1q	26	15	fraction	fraction	NOUN
cord-243070-0b06zk1q	26	16	ii	ii	PROPN
cord-243070-0b06zk1q	26	17	of	of	ADP
cord-243070-0b06zk1q	26	18	the	the	DET
cord-243070-0b06zk1q	26	19	infected	infected	ADJ
cord-243070-0b06zk1q	26	20	population	population	NOUN
cord-243070-0b06zk1q	26	21	and	and	CCONJ
cord-243070-0b06zk1q	26	22	prevents	prevent	VERB
cord-243070-0b06zk1q	26	23	it	it	PRON
cord-243070-0b06zk1q	26	24	from	from	ADP
cord-243070-0b06zk1q	26	25	spreading	spread	VERB
cord-243070-0b06zk1q	26	26	the	the	DET
cord-243070-0b06zk1q	26	27	disease	disease	NOUN
cord-243070-0b06zk1q	26	28	.	.	PUNCT
cord-243070-0b06zk1q	27	1	the	the	DET
cord-243070-0b06zk1q	27	2	controlled	control	VERB
cord-243070-0b06zk1q	27	3	dynamics	dynamic	NOUN
cord-243070-0b06zk1q	27	4	of	of	ADP
cord-243070-0b06zk1q	27	5	the	the	DET
cord-243070-0b06zk1q	27	6	sir	sir	PROPN
cord-243070-0b06zk1q	27	7	model	model	NOUN
cord-243070-0b06zk1q	27	8	reads	read	VERB
cord-243070-0b06zk1q	27	9	[	[	X
cord-243070-0b06zk1q	27	10	1	1	NUM
cord-243070-0b06zk1q	27	11	]	]	PUNCT
cord-243070-0b06zk1q	27	12	,	,	PUNCT
cord-243070-0b06zk1q	27	13	[	[	X
cord-243070-0b06zk1q	27	14	13	13	NUM
cord-243070-0b06zk1q	27	15	]	]	PUNCT
cord-243070-0b06zk1q	27	16	:	:	PUNCT
cord-243070-0b06zk1q	27	17	r(t	r(t	NOUN
cord-243070-0b06zk1q	27	18	)	)	PUNCT
cord-243070-0b06zk1q	27	19	=	=	NOUN
cord-243070-0b06zk1q	27	20	v(t)s(t	v(t)s(t	PROPN
cord-243070-0b06zk1q	27	21	)	)	PUNCT
cord-243070-0b06zk1q	27	22	+	+	CCONJ
cord-243070-0b06zk1q	27	23	(	(	PUNCT
cord-243070-0b06zk1q	27	24	γ	γ	PROPN
cord-243070-0b06zk1q	27	25	+	+	CCONJ
cord-243070-0b06zk1q	27	26	i(t))i(t	i(t))i(t	PROPN
cord-243070-0b06zk1q	27	27	)	)	PUNCT
cord-243070-0b06zk1q	27	28	.	.	PUNCT
cord-243070-0b06zk1q	28	1	for	for	ADP
cord-243070-0b06zk1q	28	2	efficiency	efficiency	NOUN
cord-243070-0b06zk1q	28	3	,	,	PUNCT
cord-243070-0b06zk1q	28	4	we	we	PRON
cord-243070-0b06zk1q	28	5	will	will	AUX
cord-243070-0b06zk1q	28	6	be	be	AUX
cord-243070-0b06zk1q	28	7	using	use	VERB
cord-243070-0b06zk1q	28	8	the	the	DET
cord-243070-0b06zk1q	28	9	notation	notation	NOUN
cord-243070-0b06zk1q	28	10	x	x	SYM
cord-243070-0b06zk1q	28	11	1	1	NUM
cord-243070-0b06zk1q	28	12	=	=	X
cord-243070-0b06zk1q	28	13	s	s	NOUN
cord-243070-0b06zk1q	28	14	and	and	CCONJ
cord-243070-0b06zk1q	28	15	x	x	NOUN
cord-243070-0b06zk1q	28	16	2	2	NUM
cord-243070-0b06zk1q	28	17	=	=	NOUN
cord-243070-0b06zk1q	28	18	i	i	NOUN
cord-243070-0b06zk1q	28	19	throughout	throughout	ADP
cord-243070-0b06zk1q	28	20	the	the	DET
cord-243070-0b06zk1q	28	21	remainder	remainder	NOUN
cord-243070-0b06zk1q	28	22	of	of	ADP
cord-243070-0b06zk1q	28	23	the	the	DET
cord-243070-0b06zk1q	28	24	paper	paper	NOUN
cord-243070-0b06zk1q	28	25	.	.	PUNCT
cord-243070-0b06zk1q	29	1	mathematical	mathematical	ADJ
cord-243070-0b06zk1q	29	2	models	model	NOUN
cord-243070-0b06zk1q	29	3	are	be	AUX
cord-243070-0b06zk1q	29	4	only	only	ADV
cord-243070-0b06zk1q	29	5	as	as	ADV
cord-243070-0b06zk1q	29	6	good	good	ADJ
cord-243070-0b06zk1q	29	7	as	as	ADP
cord-243070-0b06zk1q	29	8	(	(	PUNCT
cord-243070-0b06zk1q	29	9	i	i	NOUN
cord-243070-0b06zk1q	29	10	)	)	PUNCT
cord-243070-0b06zk1q	29	11	their	their	PRON
cord-243070-0b06zk1q	29	12	analytic	analytic	ADJ
cord-243070-0b06zk1q	29	13	specifications	specification	NOUN
cord-243070-0b06zk1q	29	14	,	,	PUNCT
cord-243070-0b06zk1q	29	15	and	and	CCONJ
cord-243070-0b06zk1q	29	16	(	(	PUNCT
cord-243070-0b06zk1q	29	17	ii	ii	PROPN
cord-243070-0b06zk1q	29	18	)	)	PUNCT
cord-243070-0b06zk1q	29	19	the	the	DET
cord-243070-0b06zk1q	29	20	data	datum	NOUN
cord-243070-0b06zk1q	29	21	that	that	PRON
cord-243070-0b06zk1q	29	22	fuel	fuel	VERB
cord-243070-0b06zk1q	29	23	them	they	PRON
cord-243070-0b06zk1q	29	24	.	.	PUNCT
cord-243070-0b06zk1q	30	1	during	during	ADP
cord-243070-0b06zk1q	30	2	initial	initial	ADJ
cord-243070-0b06zk1q	30	3	phases	phase	NOUN
cord-243070-0b06zk1q	30	4	of	of	ADP
cord-243070-0b06zk1q	30	5	an	an	DET
cord-243070-0b06zk1q	30	6	epidemic	epidemic	NOUN
cord-243070-0b06zk1q	30	7	the	the	DET
cord-243070-0b06zk1q	30	8	available	available	ADJ
cord-243070-0b06zk1q	30	9	data	datum	NOUN
cord-243070-0b06zk1q	30	10	tend	tend	VERB
cord-243070-0b06zk1q	30	11	to	to	PART
cord-243070-0b06zk1q	30	12	be	be	AUX
cord-243070-0b06zk1q	30	13	of	of	ADP
cord-243070-0b06zk1q	30	14	limited	limited	ADJ
cord-243070-0b06zk1q	30	15	usefulness	usefulness	NOUN
cord-243070-0b06zk1q	30	16	:	:	PUNCT
cord-243070-0b06zk1q	30	17	because	because	SCONJ
cord-243070-0b06zk1q	30	18	of	of	ADP
cord-243070-0b06zk1q	30	19	the	the	DET
cord-243070-0b06zk1q	30	20	lack	lack	NOUN
cord-243070-0b06zk1q	30	21	of	of	ADP
cord-243070-0b06zk1q	30	22	reliable	reliable	ADJ
cord-243070-0b06zk1q	30	23	large	large	ADJ
cord-243070-0b06zk1q	30	24	scale	scale	NOUN
cord-243070-0b06zk1q	30	25	testing	testing	NOUN
cord-243070-0b06zk1q	30	26	,	,	PUNCT
cord-243070-0b06zk1q	30	27	it	it	PRON
cord-243070-0b06zk1q	30	28	is	be	AUX
cord-243070-0b06zk1q	30	29	not	not	PART
cord-243070-0b06zk1q	30	30	really	really	ADV
cord-243070-0b06zk1q	30	31	known	know	VERB
cord-243070-0b06zk1q	30	32	what	what	DET
cord-243070-0b06zk1q	30	33	fractions	fraction	NOUN
cord-243070-0b06zk1q	30	34	of	of	ADP
cord-243070-0b06zk1q	30	35	the	the	DET
cord-243070-0b06zk1q	30	36	population	population	NOUN
cord-243070-0b06zk1q	30	37	fall	fall	VERB
cord-243070-0b06zk1q	30	38	into	into	ADP
cord-243070-0b06zk1q	30	39	the	the	DET
cord-243070-0b06zk1q	30	40	different	different	ADJ
cord-243070-0b06zk1q	30	41	compartments	compartment	NOUN
cord-243070-0b06zk1q	30	42	s	s	PROPN
cord-243070-0b06zk1q	30	43	,	,	PUNCT
cord-243070-0b06zk1q	30	44	i	i	PROPN
cord-243070-0b06zk1q	30	45	,	,	PUNCT
cord-243070-0b06zk1q	30	46	and	and	CCONJ
cord-243070-0b06zk1q	30	47	r.	r.	PROPN
cord-243070-0b06zk1q	30	48	this	this	PRON
cord-243070-0b06zk1q	30	49	may	may	AUX
cord-243070-0b06zk1q	30	50	lead	lead	VERB
cord-243070-0b06zk1q	30	51	to	to	ADP
cord-243070-0b06zk1q	30	52	a	a	DET
cord-243070-0b06zk1q	30	53	panic	panic	NOUN
cord-243070-0b06zk1q	30	54	reaction	reaction	NOUN
cord-243070-0b06zk1q	30	55	of	of	ADP
cord-243070-0b06zk1q	30	56	the	the	DET
cord-243070-0b06zk1q	30	57	population	population	NOUN
cord-243070-0b06zk1q	30	58	and	and	CCONJ
cord-243070-0b06zk1q	30	59	a	a	DET
cord-243070-0b06zk1q	30	60	chaotic	chaotic	ADJ
cord-243070-0b06zk1q	30	61	and	and	CCONJ
cord-243070-0b06zk1q	30	62	economically	economically	ADV
cord-243070-0b06zk1q	30	63	devastating	devastating	ADJ
cord-243070-0b06zk1q	30	64	public	public	ADJ
cord-243070-0b06zk1q	30	65	health	health	NOUN
cord-243070-0b06zk1q	30	66	response	response	NOUN
cord-243070-0b06zk1q	30	67	to	to	ADP
cord-243070-0b06zk1q	30	68	the	the	DET
cord-243070-0b06zk1q	30	69	epidemic	epidemic	NOUN
cord-243070-0b06zk1q	30	70	.	.	PUNCT
cord-243070-0b06zk1q	31	1	in	in	ADP
cord-243070-0b06zk1q	31	2	the	the	DET
cord-243070-0b06zk1q	31	3	absence	absence	NOUN
cord-243070-0b06zk1q	31	4	of	of	ADP
cord-243070-0b06zk1q	31	5	an	an	DET
cord-243070-0b06zk1q	31	6	effective	effective	ADJ
cord-243070-0b06zk1q	31	7	vaccine	vaccine	NOUN
cord-243070-0b06zk1q	31	8	(	(	PUNCT
cord-243070-0b06zk1q	31	9	which	which	PRON
cord-243070-0b06zk1q	31	10	would	would	AUX
cord-243070-0b06zk1q	31	11	allow	allow	VERB
cord-243070-0b06zk1q	31	12	to	to	PART
cord-243070-0b06zk1q	31	13	immunize	immunize	VERB
cord-243070-0b06zk1q	31	14	a	a	DET
cord-243070-0b06zk1q	31	15	portion	portion	NOUN
cord-243070-0b06zk1q	31	16	of	of	ADP
cord-243070-0b06zk1q	31	17	the	the	DET
cord-243070-0b06zk1q	31	18	population	population	NOUN
cord-243070-0b06zk1q	31	19	)	)	PUNCT
cord-243070-0b06zk1q	32	1	the	the	DET
cord-243070-0b06zk1q	32	2	optimal	optimal	ADJ
cord-243070-0b06zk1q	32	3	policy	policy	NOUN
cord-243070-0b06zk1q	32	4	is	be	AUX
cord-243070-0b06zk1q	32	5	to	to	PART
cord-243070-0b06zk1q	32	6	isolate	isolate	VERB
cord-243070-0b06zk1q	32	7	at	at	ADP
cord-243070-0b06zk1q	32	8	least	least	ADJ
cord-243070-0b06zk1q	32	9	a	a	DET
cord-243070-0b06zk1q	32	10	significant	significant	ADJ
cord-243070-0b06zk1q	32	11	fraction	fraction	NOUN
cord-243070-0b06zk1q	32	12	of	of	ADP
cord-243070-0b06zk1q	32	13	the	the	DET
cord-243070-0b06zk1q	32	14	infected	infect	VERB
cord-243070-0b06zk1q	32	15	individuals	individual	NOUN
cord-243070-0b06zk1q	32	16	so	so	SCONJ
cord-243070-0b06zk1q	32	17	that	that	SCONJ
cord-243070-0b06zk1q	32	18	the	the	DET
cord-243070-0b06zk1q	32	19	basic	basic	ADJ
cord-243070-0b06zk1q	32	20	reproduction	reproduction	NOUN
cord-243070-0b06zk1q	32	21	ratio	ratio	NOUN
cord-243070-0b06zk1q	32	22	r	r	NOUN
cord-243070-0b06zk1q	32	23	0	0	PUNCT
cord-243070-0b06zk1q	32	24	can	can	AUX
cord-243070-0b06zk1q	32	25	be	be	AUX
cord-243070-0b06zk1q	32	26	brought	bring	VERB
cord-243070-0b06zk1q	32	27	significantly	significantly	ADV
cord-243070-0b06zk1q	32	28	below	below	ADP
cord-243070-0b06zk1q	32	29	one	one	NUM
cord-243070-0b06zk1q	32	30	.	.	PUNCT
cord-243070-0b06zk1q	33	1	since	since	SCONJ
cord-243070-0b06zk1q	33	2	we	we	PRON
cord-243070-0b06zk1q	33	3	lack	lack	VERB
cord-243070-0b06zk1q	33	4	the	the	DET
cord-243070-0b06zk1q	33	5	knowledge	knowledge	NOUN
cord-243070-0b06zk1q	33	6	who	who	PRON
cord-243070-0b06zk1q	33	7	is	be	AUX
cord-243070-0b06zk1q	33	8	infected	infect	VERB
cord-243070-0b06zk1q	33	9	and	and	CCONJ
cord-243070-0b06zk1q	33	10	who	who	PRON
cord-243070-0b06zk1q	33	11	is	be	AUX
cord-243070-0b06zk1q	33	12	not	not	PART
cord-243070-0b06zk1q	33	13	,	,	PUNCT
cord-243070-0b06zk1q	33	14	the	the	DET
cord-243070-0b06zk1q	33	15	public	public	ADJ
cord-243070-0b06zk1q	33	16	health	health	NOUN
cord-243070-0b06zk1q	33	17	response	response	NOUN
cord-243070-0b06zk1q	33	18	is	be	AUX
cord-243070-0b06zk1q	33	19	to	to	PART
cord-243070-0b06zk1q	33	20	try	try	VERB
cord-243070-0b06zk1q	33	21	to	to	PART
cord-243070-0b06zk1q	33	22	isolate	isolate	VERB
cord-243070-0b06zk1q	33	23	everyone	everyone	PRON
cord-243070-0b06zk1q	33	24	,	,	PUNCT
cord-243070-0b06zk1q	33	25	whether	whether	SCONJ
cord-243070-0b06zk1q	33	26	susceptible	susceptible	ADJ
cord-243070-0b06zk1q	33	27	,	,	PUNCT
cord-243070-0b06zk1q	33	28	infected	infect	VERB
cord-243070-0b06zk1q	33	29	or	or	CCONJ
cord-243070-0b06zk1q	33	30	immune	immune	ADJ
cord-243070-0b06zk1q	33	31	.	.	PUNCT
cord-243070-0b06zk1q	34	1	these	these	DET
cord-243070-0b06zk1q	34	2	circumstances	circumstance	NOUN
cord-243070-0b06zk1q	34	3	impose	impose	VERB
cord-243070-0b06zk1q	34	4	a	a	DET
cord-243070-0b06zk1q	34	5	serious	serious	ADJ
cord-243070-0b06zk1q	34	6	limitation	limitation	NOUN
cord-243070-0b06zk1q	34	7	on	on	ADP
cord-243070-0b06zk1q	34	8	practical	practical	ADJ
cord-243070-0b06zk1q	34	9	applicability	applicability	NOUN
cord-243070-0b06zk1q	34	10	of	of	ADP
cord-243070-0b06zk1q	34	11	the	the	DET
cord-243070-0b06zk1q	34	12	approach	approach	NOUN
cord-243070-0b06zk1q	34	13	to	to	ADP
cord-243070-0b06zk1q	34	14	optimal	optimal	ADJ
cord-243070-0b06zk1q	34	15	epidemic	epidemic	NOUN
cord-243070-0b06zk1q	34	16	control	control	NOUN
cord-243070-0b06zk1q	34	17	discussed	discuss	VERB
cord-243070-0b06zk1q	34	18	in	in	ADP
cord-243070-0b06zk1q	34	19	this	this	DET
cord-243070-0b06zk1q	34	20	paper	paper	NOUN
cord-243070-0b06zk1q	34	21	,	,	PUNCT
cord-243070-0b06zk1q	34	22	as	as	ADV
cord-243070-0b06zk1q	34	23	well	well	ADV
cord-243070-0b06zk1q	34	24	as	as	ADP
cord-243070-0b06zk1q	34	25	other	other	ADJ
cord-243070-0b06zk1q	34	26	quantitative	quantitative	ADJ
cord-243070-0b06zk1q	34	27	approaches	approach	NOUN
cord-243070-0b06zk1q	34	28	.	.	PUNCT
cord-243070-0b06zk1q	35	1	unless	unless	SCONJ
cord-243070-0b06zk1q	35	2	the	the	DET
cord-243070-0b06zk1q	35	3	inputs	input	NOUN
cord-243070-0b06zk1q	35	4	to	to	ADP
cord-243070-0b06zk1q	35	5	the	the	DET
cord-243070-0b06zk1q	35	6	model	model	NOUN
cord-243070-0b06zk1q	35	7	(	(	PUNCT
cord-243070-0b06zk1q	35	8	β	β	NOUN
cord-243070-0b06zk1q	35	9	,	,	PUNCT
cord-243070-0b06zk1q	35	10	γ	γ	PROPN
cord-243070-0b06zk1q	35	11	,	,	PUNCT
cord-243070-0b06zk1q	35	12	and	and	CCONJ
cord-243070-0b06zk1q	35	13	the	the	DET
cord-243070-0b06zk1q	35	14	current	current	ADJ
cord-243070-0b06zk1q	35	15	snapshots	snapshot	NOUN
cord-243070-0b06zk1q	35	16	of	of	ADP
cord-243070-0b06zk1q	35	17	s	s	NOUN
cord-243070-0b06zk1q	35	18	and	and	CCONJ
cord-243070-0b06zk1q	35	19	i	i	NOUN
cord-243070-0b06zk1q	35	20	)	)	PUNCT
cord-243070-0b06zk1q	35	21	can	can	AUX
cord-243070-0b06zk1q	35	22	reliably	reliably	ADV
cord-243070-0b06zk1q	35	23	be	be	AUX
cord-243070-0b06zk1q	35	24	estimated	estimate	VERB
cord-243070-0b06zk1q	35	25	from	from	ADP
cord-243070-0b06zk1q	35	26	the	the	DET
cord-243070-0b06zk1q	35	27	available	available	ADJ
cord-243070-0b06zk1q	35	28	data	datum	NOUN
cord-243070-0b06zk1q	35	29	,	,	PUNCT
cord-243070-0b06zk1q	35	30	the	the	DET
cord-243070-0b06zk1q	35	31	model	model	NOUN
cord-243070-0b06zk1q	35	32	's	's	PART
cord-243070-0b06zk1q	35	33	output	output	NOUN
cord-243070-0b06zk1q	35	34	is	be	AUX
cord-243070-0b06zk1q	35	35	unreliable	unreliable	ADJ
cord-243070-0b06zk1q	35	36	2	2	NUM
cord-243070-0b06zk1q	35	37	.	.	PUNCT
cord-243070-0b06zk1q	36	1	the	the	DET
cord-243070-0b06zk1q	36	2	paper	paper	NOUN
cord-243070-0b06zk1q	36	3	is	be	AUX
cord-243070-0b06zk1q	36	4	organized	organize	VERB
cord-243070-0b06zk1q	36	5	as	as	SCONJ
cord-243070-0b06zk1q	36	6	follows	follow	VERB
cord-243070-0b06zk1q	36	7	.	.	PUNCT
cord-243070-0b06zk1q	37	1	in	in	ADP
cord-243070-0b06zk1q	37	2	section	section	NOUN
cord-243070-0b06zk1q	37	3	2	2	NUM
cord-243070-0b06zk1q	37	4	we	we	PRON
cord-243070-0b06zk1q	37	5	review	review	VERB
cord-243070-0b06zk1q	37	6	the	the	DET
cord-243070-0b06zk1q	37	7	formulation	formulation	NOUN
cord-243070-0b06zk1q	37	8	of	of	ADP
cord-243070-0b06zk1q	37	9	the	the	DET
cord-243070-0b06zk1q	37	10	continuous	continuous	ADJ
cord-243070-0b06zk1q	37	11	time	time	NOUN
cord-243070-0b06zk1q	37	12	stochastic	stochastic	NOUN
cord-243070-0b06zk1q	37	13	sir	sir	NOUN
cord-243070-0b06zk1q	37	14	model	model	NOUN
cord-243070-0b06zk1q	37	15	.	.	PUNCT
cord-243070-0b06zk1q	38	1	the	the	DET
cord-243070-0b06zk1q	38	2	optimal	optimal	ADJ
cord-243070-0b06zk1q	38	3	control	control	NOUN
cord-243070-0b06zk1q	38	4	problem	problem	NOUN
cord-243070-0b06zk1q	38	5	for	for	ADP
cord-243070-0b06zk1q	38	6	the	the	DET
cord-243070-0b06zk1q	38	7	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	38	8	sir	sir	NOUN
cord-243070-0b06zk1q	38	9	model	model	NOUN
cord-243070-0b06zk1q	38	10	is	be	AUX
cord-243070-0b06zk1q	38	11	formulated	formulate	VERB
cord-243070-0b06zk1q	38	12	in	in	ADP
cord-243070-0b06zk1q	38	13	section	section	NOUN
cord-243070-0b06zk1q	38	14	3	3	NUM
cord-243070-0b06zk1q	38	15	.	.	PUNCT
cord-243070-0b06zk1q	39	1	the	the	DET
cord-243070-0b06zk1q	39	2	optimal	optimal	ADJ
cord-243070-0b06zk1q	39	3	control	control	NOUN
cord-243070-0b06zk1q	39	4	problem	problem	NOUN
cord-243070-0b06zk1q	39	5	is	be	AUX
cord-243070-0b06zk1q	39	6	recast	recast	VERB
cord-243070-0b06zk1q	39	7	as	as	ADP
cord-243070-0b06zk1q	39	8	the	the	DET
cord-243070-0b06zk1q	39	9	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	39	10	minimum	minimum	ADJ
cord-243070-0b06zk1q	39	11	principle	principle	NOUN
cord-243070-0b06zk1q	39	12	problem	problem	NOUN
cord-243070-0b06zk1q	39	13	and	and	CCONJ
cord-243070-0b06zk1q	39	14	formulated	formulate	VERB
cord-243070-0b06zk1q	39	15	in	in	ADP
cord-243070-0b06zk1q	39	16	terms	term	NOUN
cord-243070-0b06zk1q	39	17	of	of	ADP
cord-243070-0b06zk1q	39	18	a	a	DET
cord-243070-0b06zk1q	39	19	system	system	NOUN
cord-243070-0b06zk1q	39	20	of	of	ADP
cord-243070-0b06zk1q	39	21	forward	forward	ADV
cord-243070-0b06zk1q	39	22	backward	backward	ADJ
cord-243070-0b06zk1q	39	23	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	39	24	differential	differential	ADJ
cord-243070-0b06zk1q	39	25	equations	equation	NOUN
cord-243070-0b06zk1q	39	26	(	(	PUNCT
cord-243070-0b06zk1q	39	27	fbsde	fbsde	PROPN
cord-243070-0b06zk1q	39	28	)	)	PUNCT
cord-243070-0b06zk1q	39	29	.	.	PUNCT
cord-243070-0b06zk1q	40	1	we	we	PRON
cord-243070-0b06zk1q	40	2	present	present	VERB
cord-243070-0b06zk1q	40	3	an	an	DET
cord-243070-0b06zk1q	40	4	algorithm	algorithm	NOUN
cord-243070-0b06zk1q	40	5	for	for	ADP
cord-243070-0b06zk1q	40	6	solving	solve	VERB
cord-243070-0b06zk1q	40	7	this	this	DET
cord-243070-0b06zk1q	40	8	system	system	NOUN
cord-243070-0b06zk1q	40	9	in	in	ADP
cord-243070-0b06zk1q	40	10	section	section	NOUN
cord-243070-0b06zk1q	40	11	5	5	NUM
cord-243070-0b06zk1q	40	12	.	.	PUNCT
cord-243070-0b06zk1q	41	1	this	this	DET
cord-243070-0b06zk1q	41	2	section	section	NOUN
cord-243070-0b06zk1q	41	3	presents	present	VERB
cord-243070-0b06zk1q	41	4	also	also	ADV
cord-243070-0b06zk1q	41	5	the	the	DET
cord-243070-0b06zk1q	41	6	results	result	NOUN
cord-243070-0b06zk1q	41	7	of	of	ADP
cord-243070-0b06zk1q	41	8	a	a	DET
cord-243070-0b06zk1q	41	9	number	number	NOUN
cord-243070-0b06zk1q	41	10	2	2	NUM
cord-243070-0b06zk1q	41	11	"	"	PUNCT
cord-243070-0b06zk1q	41	12	this	this	PRON
cord-243070-0b06zk1q	41	13	is	be	AUX
cord-243070-0b06zk1q	41	14	indeed	indeed	ADV
cord-243070-0b06zk1q	41	15	a	a	DET
cord-243070-0b06zk1q	41	16	mystery	mystery	NOUN
cord-243070-0b06zk1q	41	17	,	,	PUNCT
cord-243070-0b06zk1q	41	18	"	"	PUNCT
cord-243070-0b06zk1q	41	19	watson	watson	PROPN
cord-243070-0b06zk1q	41	20	remarked	remark	VERB
cord-243070-0b06zk1q	41	21	.	.	PUNCT
cord-243070-0b06zk1q	42	1	"	"	PUNCT
cord-243070-0b06zk1q	42	2	what	what	PRON
cord-243070-0b06zk1q	42	3	do	do	AUX
cord-243070-0b06zk1q	42	4	you	you	PRON
cord-243070-0b06zk1q	42	5	imagine	imagine	VERB
cord-243070-0b06zk1q	42	6	that	that	SCONJ
cord-243070-0b06zk1q	42	7	it	it	PRON
cord-243070-0b06zk1q	42	8	means	mean	VERB
cord-243070-0b06zk1q	42	9	?	?	PUNCT
cord-243070-0b06zk1q	42	10	"	"	PUNCT
cord-243070-0b06zk1q	43	1	"	"	PUNCT
cord-243070-0b06zk1q	43	2	i	i	PRON
cord-243070-0b06zk1q	43	3	have	have	VERB
cord-243070-0b06zk1q	43	4	no	no	DET
cord-243070-0b06zk1q	43	5	data	data	NOUN
cord-243070-0b06zk1q	43	6	yet	yet	ADV
cord-243070-0b06zk1q	43	7	,	,	PUNCT
cord-243070-0b06zk1q	43	8	"	"	PUNCT
cord-243070-0b06zk1q	43	9	holmes	holme	NOUN
cord-243070-0b06zk1q	43	10	replied	reply	VERB
cord-243070-0b06zk1q	43	11	.	.	PUNCT
cord-243070-0b06zk1q	44	1	"	"	PUNCT
cord-243070-0b06zk1q	44	2	it	it	PRON
cord-243070-0b06zk1q	44	3	is	be	AUX
cord-243070-0b06zk1q	44	4	a	a	DET
cord-243070-0b06zk1q	44	5	capital	capital	NOUN
cord-243070-0b06zk1q	44	6	mistake	mistake	NOUN
cord-243070-0b06zk1q	44	7	to	to	PART
cord-243070-0b06zk1q	44	8	theorise	theorise	VERB
cord-243070-0b06zk1q	44	9	before	before	SCONJ
cord-243070-0b06zk1q	44	10	one	one	PRON
cord-243070-0b06zk1q	44	11	has	have	VERB
cord-243070-0b06zk1q	44	12	data	datum	NOUN
cord-243070-0b06zk1q	44	13	.	.	PUNCT
cord-243070-0b06zk1q	45	1	insensibly	insensibly	ADV
cord-243070-0b06zk1q	45	2	one	one	NUM
cord-243070-0b06zk1q	45	3	begins	begin	VERB
cord-243070-0b06zk1q	45	4	to	to	PART
cord-243070-0b06zk1q	45	5	twist	twist	VERB
cord-243070-0b06zk1q	45	6	facts	fact	NOUN
cord-243070-0b06zk1q	45	7	to	to	PART
cord-243070-0b06zk1q	45	8	suit	suit	VERB
cord-243070-0b06zk1q	45	9	theories	theory	NOUN
cord-243070-0b06zk1q	45	10	,	,	PUNCT
cord-243070-0b06zk1q	45	11	instead	instead	ADV
cord-243070-0b06zk1q	45	12	of	of	ADP
cord-243070-0b06zk1q	45	13	theories	theory	NOUN
cord-243070-0b06zk1q	45	14	to	to	PART
cord-243070-0b06zk1q	45	15	suit	suit	VERB
cord-243070-0b06zk1q	45	16	facts	fact	NOUN
cord-243070-0b06zk1q	45	17	.	.	PUNCT
cord-243070-0b06zk1q	45	18	"	"	PUNCT
cord-243070-0b06zk1q	46	1	[	[	PUNCT
cord-243070-0b06zk1q	46	2	8	8	NUM
cord-243070-0b06zk1q	46	3	]	]	PUNCT
cord-243070-0b06zk1q	46	4	of	of	ADP
cord-243070-0b06zk1q	46	5	numerical	numerical	ADJ
cord-243070-0b06zk1q	46	6	experiments	experiment	NOUN
cord-243070-0b06zk1q	46	7	involving	involve	VERB
cord-243070-0b06zk1q	46	8	the	the	DET
cord-243070-0b06zk1q	46	9	three	three	NUM
cord-243070-0b06zk1q	46	10	mitigation	mitigation	NOUN
cord-243070-0b06zk1q	46	11	policies	policy	NOUN
cord-243070-0b06zk1q	46	12	within	within	ADP
cord-243070-0b06zk1q	46	13	various	various	ADJ
cord-243070-0b06zk1q	46	14	cost	cost	NOUN
cord-243070-0b06zk1q	46	15	function	function	NOUN
cord-243070-0b06zk1q	46	16	regimes	regime	NOUN
cord-243070-0b06zk1q	46	17	.	.	PUNCT
cord-243070-0b06zk1q	47	1	acknowledgement	acknowledgement	NOUN
cord-243070-0b06zk1q	47	2	.	.	PUNCT
cord-243070-0b06zk1q	48	1	i	i	PRON
cord-243070-0b06zk1q	48	2	would	would	AUX
cord-243070-0b06zk1q	48	3	like	like	VERB
cord-243070-0b06zk1q	48	4	to	to	PART
cord-243070-0b06zk1q	48	5	thank	thank	VERB
cord-243070-0b06zk1q	48	6	nicholas	nicholas	PROPN
cord-243070-0b06zk1q	48	7	lesniewski	lesniewski	PROPN
cord-243070-0b06zk1q	48	8	for	for	ADP
cord-243070-0b06zk1q	48	9	numerous	numerous	ADJ
cord-243070-0b06zk1q	48	10	discussions	discussion	NOUN
cord-243070-0b06zk1q	48	11	.	.	PUNCT
cord-243070-0b06zk1q	49	1	we	we	PRON
cord-243070-0b06zk1q	49	2	consider	consider	VERB
cord-243070-0b06zk1q	49	3	a	a	DET
cord-243070-0b06zk1q	49	4	continuous	continuous	ADJ
cord-243070-0b06zk1q	49	5	time	time	NOUN
cord-243070-0b06zk1q	49	6	stochastic	stochastic	NOUN
cord-243070-0b06zk1q	49	7	extension	extension	NOUN
cord-243070-0b06zk1q	49	8	of	of	ADP
cord-243070-0b06zk1q	49	9	the	the	DET
cord-243070-0b06zk1q	49	10	deterministic	deterministic	ADJ
cord-243070-0b06zk1q	49	11	sir	sir	NOUN
cord-243070-0b06zk1q	49	12	model	model	NOUN
cord-243070-0b06zk1q	49	13	,	,	PUNCT
cord-243070-0b06zk1q	49	14	see	see	VERB
cord-243070-0b06zk1q	49	15	[	[	X
cord-243070-0b06zk1q	49	16	3	3	NUM
cord-243070-0b06zk1q	49	17	]	]	PUNCT
cord-243070-0b06zk1q	49	18	and	and	CCONJ
cord-243070-0b06zk1q	49	19	references	reference	NOUN
cord-243070-0b06zk1q	49	20	therein	therein	ADV
cord-243070-0b06zk1q	49	21	.	.	PUNCT
cord-243070-0b06zk1q	50	1	let	let	VERB
cord-243070-0b06zk1q	50	2	w	w	PROPN
cord-243070-0b06zk1q	50	3	t	t	PROPN
cord-243070-0b06zk1q	50	4	denote	denote	VERB
cord-243070-0b06zk1q	50	5	the	the	DET
cord-243070-0b06zk1q	50	6	standard	standard	ADJ
cord-243070-0b06zk1q	50	7	brownian	brownian	ADJ
cord-243070-0b06zk1q	50	8	motion	motion	NOUN
cord-243070-0b06zk1q	50	9	,	,	PUNCT
cord-243070-0b06zk1q	50	10	and	and	CCONJ
cord-243070-0b06zk1q	50	11	leṫ	leṫ	NOUN
cord-243070-0b06zk1q	50	12	w	w	PROPN
cord-243070-0b06zk1q	50	13	t	t	PROPN
cord-243070-0b06zk1q	50	14	denote	denote	VERB
cord-243070-0b06zk1q	50	15	the	the	DET
cord-243070-0b06zk1q	50	16	white	white	ADJ
cord-243070-0b06zk1q	50	17	noise	noise	NOUN
cord-243070-0b06zk1q	50	18	process	process	NOUN
cord-243070-0b06zk1q	50	19	.	.	PUNCT
cord-243070-0b06zk1q	51	1	we	we	PRON
cord-243070-0b06zk1q	51	2	assume	assume	VERB
cord-243070-0b06zk1q	51	3	that	that	SCONJ
cord-243070-0b06zk1q	51	4	the	the	DET
cord-243070-0b06zk1q	51	5	infection	infection	NOUN
cord-243070-0b06zk1q	51	6	rate	rate	NOUN
cord-243070-0b06zk1q	51	7	β	β	NOUN
cord-243070-0b06zk1q	51	8	is	be	AUX
cord-243070-0b06zk1q	51	9	subject	subject	ADJ
cord-243070-0b06zk1q	51	10	to	to	ADP
cord-243070-0b06zk1q	51	11	random	random	ADJ
cord-243070-0b06zk1q	51	12	shocks	shock	NOUN
cord-243070-0b06zk1q	51	13	,	,	PUNCT
cord-243070-0b06zk1q	51	14	rather	rather	ADV
cord-243070-0b06zk1q	51	15	than	than	ADP
cord-243070-0b06zk1q	51	16	being	be	AUX
cord-243070-0b06zk1q	51	17	constant	constant	ADJ
cord-243070-0b06zk1q	51	18	,	,	PUNCT
cord-243070-0b06zk1q	51	19	namely	namely	ADV
cord-243070-0b06zk1q	51	20	while	while	SCONJ
cord-243070-0b06zk1q	51	21	the	the	DET
cord-243070-0b06zk1q	51	22	recovery	recovery	NOUN
cord-243070-0b06zk1q	51	23	rate	rate	NOUN
cord-243070-0b06zk1q	51	24	γ	γ	PRON
cord-243070-0b06zk1q	51	25	remains	remain	VERB
cord-243070-0b06zk1q	51	26	constant	constant	ADJ
cord-243070-0b06zk1q	51	27	.	.	PUNCT
cord-243070-0b06zk1q	52	1	here	here	ADV
cord-243070-0b06zk1q	52	2	σ	σ	PROPN
cord-243070-0b06zk1q	52	3	>	>	X
cord-243070-0b06zk1q	52	4	0	0	NUM
cord-243070-0b06zk1q	52	5	is	be	AUX
cord-243070-0b06zk1q	52	6	a	a	DET
cord-243070-0b06zk1q	52	7	constant	constant	ADJ
cord-243070-0b06zk1q	52	8	volatility	volatility	NOUN
cord-243070-0b06zk1q	52	9	parameter	parameter	NOUN
cord-243070-0b06zk1q	52	10	.	.	PUNCT
cord-243070-0b06zk1q	53	1	this	this	PRON
cord-243070-0b06zk1q	53	2	leads	lead	VERB
cord-243070-0b06zk1q	53	3	to	to	ADP
cord-243070-0b06zk1q	53	4	the	the	DET
cord-243070-0b06zk1q	53	5	following	follow	VERB
cord-243070-0b06zk1q	53	6	system	system	NOUN
cord-243070-0b06zk1q	53	7	of	of	ADP
cord-243070-0b06zk1q	53	8	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	53	9	differential	differential	ADJ
cord-243070-0b06zk1q	53	10	equations	equation	NOUN
cord-243070-0b06zk1q	53	11	(	(	PUNCT
cord-243070-0b06zk1q	53	12	sde	sde	PROPN
cord-243070-0b06zk1q	53	13	)	)	PUNCT
cord-243070-0b06zk1q	53	14	,	,	PUNCT
cord-243070-0b06zk1q	53	15	driven	drive	VERB
cord-243070-0b06zk1q	53	16	by	by	ADP
cord-243070-0b06zk1q	53	17	w	w	PROPN
cord-243070-0b06zk1q	53	18	t	t	PROPN
cord-243070-0b06zk1q	53	19	with	with	ADP
cord-243070-0b06zk1q	53	20	the	the	DET
cord-243070-0b06zk1q	53	21	initial	initial	ADJ
cord-243070-0b06zk1q	53	22	conditions	condition	NOUN
cord-243070-0b06zk1q	53	23	the	the	DET
cord-243070-0b06zk1q	53	24	third	third	ADJ
cord-243070-0b06zk1q	53	25	component	component	NOUN
cord-243070-0b06zk1q	53	26	of	of	ADP
cord-243070-0b06zk1q	53	27	the	the	DET
cord-243070-0b06zk1q	53	28	process	process	NOUN
cord-243070-0b06zk1q	53	29	,	,	PUNCT
cord-243070-0b06zk1q	53	30	x	x	SYM
cord-243070-0b06zk1q	53	31	3	3	NUM
cord-243070-0b06zk1q	53	32	=	=	SYM
cord-243070-0b06zk1q	53	33	r	r	NOUN
cord-243070-0b06zk1q	53	34	,	,	PUNCT
cord-243070-0b06zk1q	53	35	follows	follow	VERB
cord-243070-0b06zk1q	53	36	the	the	DET
cord-243070-0b06zk1q	53	37	dynamics	dynamic	NOUN
cord-243070-0b06zk1q	53	38	which	which	PRON
cord-243070-0b06zk1q	53	39	implies	imply	VERB
cord-243070-0b06zk1q	53	40	that	that	SCONJ
cord-243070-0b06zk1q	53	41	the	the	DET
cord-243070-0b06zk1q	53	42	conservation	conservation	NOUN
cord-243070-0b06zk1q	53	43	law	law	NOUN
cord-243070-0b06zk1q	53	44	continues	continue	VERB
cord-243070-0b06zk1q	53	45	to	to	PART
cord-243070-0b06zk1q	53	46	hold	hold	VERB
cord-243070-0b06zk1q	53	47	in	in	ADP
cord-243070-0b06zk1q	53	48	the	the	DET
cord-243070-0b06zk1q	53	49	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	53	50	model	model	NOUN
cord-243070-0b06zk1q	53	51	.	.	PUNCT
cord-243070-0b06zk1q	54	1	notice	notice	VERB
cord-243070-0b06zk1q	54	2	that	that	SCONJ
cord-243070-0b06zk1q	54	3	,	,	PUNCT
cord-243070-0b06zk1q	54	4	under	under	ADP
cord-243070-0b06zk1q	54	5	the	the	DET
cord-243070-0b06zk1q	54	6	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	54	7	sir	sir	NOUN
cord-243070-0b06zk1q	54	8	model	model	NOUN
cord-243070-0b06zk1q	54	9	(	(	PUNCT
cord-243070-0b06zk1q	54	10	6	6	NUM
cord-243070-0b06zk1q	54	11	)	)	PUNCT
cord-243070-0b06zk1q	54	12	,	,	PUNCT
cord-243070-0b06zk1q	54	13	an	an	DET
cord-243070-0b06zk1q	54	14	epidemic	epidemic	NOUN
cord-243070-0b06zk1q	54	15	eventually	eventually	ADV
cord-243070-0b06zk1q	54	16	comes	come	VERB
cord-243070-0b06zk1q	54	17	to	to	ADP
cord-243070-0b06zk1q	54	18	a	a	DET
cord-243070-0b06zk1q	54	19	natural	natural	ADJ
cord-243070-0b06zk1q	54	20	end	end	NOUN
cord-243070-0b06zk1q	54	21	.	.	PUNCT
cord-243070-0b06zk1q	55	1	more	more	ADV
cord-243070-0b06zk1q	55	2	precisely	precisely	ADV
cord-243070-0b06zk1q	55	3	,	,	PUNCT
cord-243070-0b06zk1q	55	4	the	the	DET
cord-243070-0b06zk1q	55	5	solution	solution	NOUN
cord-243070-0b06zk1q	55	6	(	(	PUNCT
cord-243070-0b06zk1q	55	7	x	x	X
cord-243070-0b06zk1q	55	8	1,t	1,t	NOUN
cord-243070-0b06zk1q	55	9	,	,	PUNCT
cord-243070-0b06zk1q	55	10	x	x	PUNCT
cord-243070-0b06zk1q	55	11	2,t	2,t	NUM
cord-243070-0b06zk1q	55	12	)	)	PUNCT
cord-243070-0b06zk1q	55	13	=	=	NOUN
cord-243070-0b06zk1q	55	14	(	(	PUNCT
cord-243070-0b06zk1q	55	15	0	0	NUM
cord-243070-0b06zk1q	55	16	,	,	PUNCT
cord-243070-0b06zk1q	55	17	0	0	NUM
cord-243070-0b06zk1q	55	18	)	)	PUNCT
cord-243070-0b06zk1q	55	19	to	to	ADP
cord-243070-0b06zk1q	55	20	(	(	PUNCT
cord-243070-0b06zk1q	55	21	6	6	NUM
cord-243070-0b06zk1q	55	22	)	)	PUNCT
cord-243070-0b06zk1q	55	23	is	be	AUX
cord-243070-0b06zk1q	55	24	stable	stable	ADJ
cord-243070-0b06zk1q	55	25	in	in	ADP
cord-243070-0b06zk1q	55	26	probability	probability	NOUN
cord-243070-0b06zk1q	55	27	[	[	X
cord-243070-0b06zk1q	55	28	16	16	NUM
cord-243070-0b06zk1q	55	29	]	]	PUNCT
cord-243070-0b06zk1q	55	30	.	.	PUNCT
cord-243070-0b06zk1q	56	1	in	in	ADP
cord-243070-0b06zk1q	56	2	order	order	NOUN
cord-243070-0b06zk1q	56	3	to	to	PART
cord-243070-0b06zk1q	56	4	see	see	VERB
cord-243070-0b06zk1q	56	5	it	it	PRON
cord-243070-0b06zk1q	56	6	,	,	PUNCT
cord-243070-0b06zk1q	56	7	we	we	PRON
cord-243070-0b06zk1q	56	8	set	set	VERB
cord-243070-0b06zk1q	56	9	for	for	ADP
cord-243070-0b06zk1q	56	10	0	0	NUM
cord-243070-0b06zk1q	56	11	≤	≤	PROPN
cord-243070-0b06zk1q	57	1	x	x	PUNCT
cord-243070-0b06zk1q	58	1	i	i	PRON
cord-243070-0b06zk1q	58	2	≤	≤	PROPN
cord-243070-0b06zk1q	58	3	1	1	NUM
cord-243070-0b06zk1q	58	4	,	,	PUNCT
cord-243070-0b06zk1q	58	5	i	i	NOUN
cord-243070-0b06zk1q	58	6	=	=	NOUN
cord-243070-0b06zk1q	58	7	1	1	NUM
cord-243070-0b06zk1q	58	8	,	,	PUNCT
cord-243070-0b06zk1q	58	9	2	2	NUM
cord-243070-0b06zk1q	58	10	,	,	PUNCT
cord-243070-0b06zk1q	58	11	and	and	CCONJ
cord-243070-0b06zk1q	58	12	fixed	fix	VERB
cord-243070-0b06zk1q	59	1	0	0	NUM
cord-243070-0b06zk1q	59	2	<	<	X
cord-243070-0b06zk1q	60	1	ρ	ρ	X
cord-243070-0b06zk1q	61	1	<	<	X
cord-243070-0b06zk1q	61	2	β	β	X
cord-243070-0b06zk1q	61	3	/	/	SYM
cord-243070-0b06zk1q	61	4	γ	γ	NOUN
cord-243070-0b06zk1q	61	5	.	.	PROPN
cord-243070-0b06zk1q	61	6	then	then	ADV
cord-243070-0b06zk1q	61	7	v	v	X
cord-243070-0b06zk1q	61	8	ρ	ρ	NOUN
cord-243070-0b06zk1q	61	9	(	(	PUNCT
cord-243070-0b06zk1q	61	10	0	0	NUM
cord-243070-0b06zk1q	61	11	,	,	PUNCT
cord-243070-0b06zk1q	61	12	0	0	NUM
cord-243070-0b06zk1q	61	13	)	)	PUNCT
cord-243070-0b06zk1q	61	14	=	=	NOUN
cord-243070-0b06zk1q	61	15	0	0	NUM
cord-243070-0b06zk1q	61	16	,	,	PUNCT
cord-243070-0b06zk1q	61	17	and	and	CCONJ
cord-243070-0b06zk1q	61	18	v	v	ADP
cord-243070-0b06zk1q	61	19	ρ	ρ	NOUN
cord-243070-0b06zk1q	61	20	(	(	PUNCT
cord-243070-0b06zk1q	61	21	x	x	SYM
cord-243070-0b06zk1q	61	22	1	1	NUM
cord-243070-0b06zk1q	61	23	,	,	PUNCT
cord-243070-0b06zk1q	61	24	x	x	PUNCT
cord-243070-0b06zk1q	61	25	2	2	NUM
cord-243070-0b06zk1q	61	26	)	)	PUNCT
cord-243070-0b06zk1q	61	27	>	>	PUNCT
cord-243070-0b06zk1q	61	28	0	0	NUM
cord-243070-0b06zk1q	61	29	in	in	ADP
cord-243070-0b06zk1q	61	30	a	a	DET
cord-243070-0b06zk1q	61	31	neighborhood	neighborhood	NOUN
cord-243070-0b06zk1q	61	32	of	of	ADP
cord-243070-0b06zk1q	61	33	(	(	PUNCT
cord-243070-0b06zk1q	61	34	0.0	0.0	NUM
cord-243070-0b06zk1q	61	35	)	)	PUNCT
cord-243070-0b06zk1q	61	36	.	.	PUNCT
cord-243070-0b06zk1q	62	1	furthermore	furthermore	ADV
cord-243070-0b06zk1q	62	2	,	,	PUNCT
cord-243070-0b06zk1q	62	3	denoting	denote	VERB
cord-243070-0b06zk1q	62	4	by	by	ADP
cord-243070-0b06zk1q	62	5	l	l	PROPN
cord-243070-0b06zk1q	62	6	the	the	DET
cord-243070-0b06zk1q	62	7	generator	generator	NOUN
cord-243070-0b06zk1q	62	8	of	of	ADP
cord-243070-0b06zk1q	62	9	the	the	DET
cord-243070-0b06zk1q	62	10	process(6	process(6	PROPN
cord-243070-0b06zk1q	62	11	)	)	PUNCT
cord-243070-0b06zk1q	62	12	,	,	PUNCT
cord-243070-0b06zk1q	62	13	we	we	PRON
cord-243070-0b06zk1q	62	14	verify	verify	VERB
cord-243070-0b06zk1q	62	15	that	that	SCONJ
cord-243070-0b06zk1q	62	16	in	in	ADP
cord-243070-0b06zk1q	62	17	other	other	ADJ
cord-243070-0b06zk1q	62	18	words	word	NOUN
cord-243070-0b06zk1q	62	19	,	,	PUNCT
cord-243070-0b06zk1q	62	20	v	v	X
cord-243070-0b06zk1q	62	21	ρ	ρ	NOUN
cord-243070-0b06zk1q	62	22	(	(	PUNCT
cord-243070-0b06zk1q	62	23	x	x	SYM
cord-243070-0b06zk1q	62	24	1	1	NUM
cord-243070-0b06zk1q	62	25	,	,	PUNCT
cord-243070-0b06zk1q	62	26	x	x	SYM
cord-243070-0b06zk1q	62	27	2	2	X
cord-243070-0b06zk1q	62	28	)	)	PUNCT
cord-243070-0b06zk1q	62	29	is	be	AUX
cord-243070-0b06zk1q	62	30	a	a	DET
cord-243070-0b06zk1q	62	31	lyapunov	lyapunov	ADJ
cord-243070-0b06zk1q	62	32	function	function	NOUN
cord-243070-0b06zk1q	62	33	for	for	ADP
cord-243070-0b06zk1q	62	34	(	(	PUNCT
cord-243070-0b06zk1q	62	35	6	6	NUM
cord-243070-0b06zk1q	62	36	)	)	PUNCT
cord-243070-0b06zk1q	62	37	and	and	CCONJ
cord-243070-0b06zk1q	62	38	our	our	PRON
cord-243070-0b06zk1q	62	39	claim	claim	NOUN
cord-243070-0b06zk1q	62	40	follows	follow	VERB
cord-243070-0b06zk1q	62	41	from	from	ADP
cord-243070-0b06zk1q	62	42	theorem	theorem	NOUN
cord-243070-0b06zk1q	62	43	5.3	5.3	NUM
cord-243070-0b06zk1q	62	44	in	in	ADP
cord-243070-0b06zk1q	62	45	[	[	X
cord-243070-0b06zk1q	62	46	16	16	NUM
cord-243070-0b06zk1q	62	47	]	]	PUNCT
cord-243070-0b06zk1q	62	48	.	.	PUNCT
cord-243070-0b06zk1q	63	1	the	the	DET
cord-243070-0b06zk1q	63	2	model	model	NOUN
cord-243070-0b06zk1q	63	3	(	(	PUNCT
cord-243070-0b06zk1q	63	4	6	6	NUM
cord-243070-0b06zk1q	63	5	)	)	PUNCT
cord-243070-0b06zk1q	63	6	is	be	AUX
cord-243070-0b06zk1q	63	7	a	a	DET
cord-243070-0b06zk1q	63	8	one	one	NUM
cord-243070-0b06zk1q	63	9	factor	factor	NOUN
cord-243070-0b06zk1q	63	10	model	model	NOUN
cord-243070-0b06zk1q	63	11	,	,	PUNCT
cord-243070-0b06zk1q	63	12	driven	drive	VERB
cord-243070-0b06zk1q	63	13	by	by	ADP
cord-243070-0b06zk1q	63	14	a	a	DET
cord-243070-0b06zk1q	63	15	single	single	ADJ
cord-243070-0b06zk1q	63	16	source	source	NOUN
cord-243070-0b06zk1q	63	17	of	of	ADP
cord-243070-0b06zk1q	63	18	randomness	randomness	NOUN
cord-243070-0b06zk1q	63	19	.	.	PUNCT
cord-243070-0b06zk1q	64	1	there	there	PRON
cord-243070-0b06zk1q	64	2	is	be	VERB
cord-243070-0b06zk1q	64	3	a	a	DET
cord-243070-0b06zk1q	64	4	natural	natural	ADJ
cord-243070-0b06zk1q	64	5	two	two	NUM
cord-243070-0b06zk1q	64	6	-	-	PUNCT
cord-243070-0b06zk1q	64	7	factor	factor	NOUN
cord-243070-0b06zk1q	64	8	version	version	NOUN
cord-243070-0b06zk1q	64	9	of	of	ADP
cord-243070-0b06zk1q	64	10	the	the	DET
cord-243070-0b06zk1q	64	11	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	64	12	sir	sir	NOUN
cord-243070-0b06zk1q	64	13	model	model	NOUN
cord-243070-0b06zk1q	65	1	[	[	X
cord-243070-0b06zk1q	65	2	18	18	NUM
cord-243070-0b06zk1q	65	3	]	]	PUNCT
cord-243070-0b06zk1q	65	4	,	,	PUNCT
cord-243070-0b06zk1q	65	5	in	in	ADP
cord-243070-0b06zk1q	65	6	which	which	PRON
cord-243070-0b06zk1q	65	7	also	also	ADV
cord-243070-0b06zk1q	65	8	the	the	DET
cord-243070-0b06zk1q	65	9	recovery	recovery	NOUN
cord-243070-0b06zk1q	65	10	rate	rate	NOUN
cord-243070-0b06zk1q	65	11	γ	γ	NOUN
cord-243070-0b06zk1q	65	12	is	be	AUX
cord-243070-0b06zk1q	65	13	allowed	allow	VERB
cord-243070-0b06zk1q	65	14	to	to	PART
cord-243070-0b06zk1q	65	15	be	be	AUX
cord-243070-0b06zk1q	65	16	subject	subject	ADJ
cord-243070-0b06zk1q	65	17	to	to	ADP
cord-243070-0b06zk1q	65	18	white	white	ADJ
cord-243070-0b06zk1q	65	19	noise	noise	NOUN
cord-243070-0b06zk1q	65	20	shocks	shock	NOUN
cord-243070-0b06zk1q	65	21	.	.	PUNCT
cord-243070-0b06zk1q	66	1	for	for	ADP
cord-243070-0b06zk1q	66	2	simplicity	simplicity	NOUN
cord-243070-0b06zk1q	66	3	,	,	PUNCT
cord-243070-0b06zk1q	66	4	our	our	PRON
cord-243070-0b06zk1q	66	5	analysis	analysis	NOUN
cord-243070-0b06zk1q	66	6	will	will	AUX
cord-243070-0b06zk1q	66	7	focus	focus	VERB
cord-243070-0b06zk1q	66	8	on	on	ADP
cord-243070-0b06zk1q	66	9	the	the	DET
cord-243070-0b06zk1q	66	10	one	one	NUM
cord-243070-0b06zk1q	66	11	-	-	PUNCT
cord-243070-0b06zk1q	66	12	factor	factor	NOUN
cord-243070-0b06zk1q	66	13	model	model	NOUN
cord-243070-0b06zk1q	66	14	(	(	PUNCT
cord-243070-0b06zk1q	66	15	6	6	NUM
cord-243070-0b06zk1q	66	16	)	)	PUNCT
cord-243070-0b06zk1q	66	17	.	.	PUNCT
cord-243070-0b06zk1q	67	1	we	we	PRON
cord-243070-0b06zk1q	67	2	frame	frame	VERB
cord-243070-0b06zk1q	67	3	the	the	DET
cord-243070-0b06zk1q	67	4	problem	problem	NOUN
cord-243070-0b06zk1q	67	5	of	of	ADP
cord-243070-0b06zk1q	67	6	epidemic	epidemic	NOUN
cord-243070-0b06zk1q	67	7	control	control	NOUN
cord-243070-0b06zk1q	67	8	as	as	ADP
cord-243070-0b06zk1q	67	9	a	a	DET
cord-243070-0b06zk1q	67	10	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	67	11	control	control	NOUN
cord-243070-0b06zk1q	67	12	problem	problem	NOUN
cord-243070-0b06zk1q	67	13	[	[	X
cord-243070-0b06zk1q	67	14	2	2	NUM
cord-243070-0b06zk1q	67	15	]	]	PUNCT
cord-243070-0b06zk1q	67	16	.	.	PUNCT
cord-243070-0b06zk1q	68	1	we	we	PRON
cord-243070-0b06zk1q	68	2	denote	denote	VERB
cord-243070-0b06zk1q	68	3	by	by	ADP
cord-243070-0b06zk1q	68	4	u	u	PROPN
cord-243070-0b06zk1q	68	5	=	=	PROPN
cord-243070-0b06zk1q	68	6	(	(	PUNCT
cord-243070-0b06zk1q	68	7	u	u	NOUN
cord-243070-0b06zk1q	68	8	1	1	NUM
cord-243070-0b06zk1q	68	9	,	,	PUNCT
cord-243070-0b06zk1q	68	10	u	u	NOUN
cord-243070-0b06zk1q	68	11	2	2	NUM
cord-243070-0b06zk1q	68	12	)	)	PUNCT
cord-243070-0b06zk1q	68	13	≡	≡	PROPN
cord-243070-0b06zk1q	68	14	(	(	PUNCT
cord-243070-0b06zk1q	68	15	v	v	NOUN
cord-243070-0b06zk1q	68	16	,	,	PUNCT
cord-243070-0b06zk1q	68	17	i	i	PROPN
cord-243070-0b06zk1q	68	18	)	)	PUNCT
cord-243070-0b06zk1q	68	19	the	the	DET
cord-243070-0b06zk1q	68	20	vaccination	vaccination	NOUN
cord-243070-0b06zk1q	68	21	and	and	CCONJ
cord-243070-0b06zk1q	68	22	isolation	isolation	NOUN
cord-243070-0b06zk1q	68	23	controls	control	NOUN
cord-243070-0b06zk1q	68	24	,	,	PUNCT
cord-243070-0b06zk1q	68	25	and	and	CCONJ
cord-243070-0b06zk1q	68	26	we	we	PRON
cord-243070-0b06zk1q	68	27	denote	denote	VERB
cord-243070-0b06zk1q	68	28	the	the	DET
cord-243070-0b06zk1q	68	29	controlled	control	VERB
cord-243070-0b06zk1q	68	30	process	process	NOUN
cord-243070-0b06zk1q	68	31	by	by	ADP
cord-243070-0b06zk1q	68	32	x	x	PROPN
cord-243070-0b06zk1q	68	33	u	u	PROPN
cord-243070-0b06zk1q	68	34	t	t	NOUN
cord-243070-0b06zk1q	68	35	.	.	PUNCT
cord-243070-0b06zk1q	69	1	generalizing	generalize	VERB
cord-243070-0b06zk1q	69	2	the	the	DET
cord-243070-0b06zk1q	69	3	deterministic	deterministic	ADJ
cord-243070-0b06zk1q	69	4	specification	specification	NOUN
cord-243070-0b06zk1q	69	5	(	(	PUNCT
cord-243070-0b06zk1q	69	6	4	4	NUM
cord-243070-0b06zk1q	69	7	)	)	PUNCT
cord-243070-0b06zk1q	69	8	to	to	ADP
cord-243070-0b06zk1q	69	9	the	the	DET
cord-243070-0b06zk1q	69	10	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	69	11	case	case	NOUN
cord-243070-0b06zk1q	69	12	,	,	PUNCT
cord-243070-0b06zk1q	69	13	we	we	PRON
cord-243070-0b06zk1q	69	14	assume	assume	VERB
cord-243070-0b06zk1q	69	15	that	that	SCONJ
cord-243070-0b06zk1q	69	16	the	the	DET
cord-243070-0b06zk1q	69	17	dynamics	dynamic	NOUN
cord-243070-0b06zk1q	69	18	of	of	ADP
cord-243070-0b06zk1q	69	19	x	x	SYM
cord-243070-0b06zk1q	69	20	u	u	PROPN
cord-243070-0b06zk1q	69	21	t	t	PROPN
cord-243070-0b06zk1q	69	22	is	be	AUX
cord-243070-0b06zk1q	69	23	given	give	VERB
cord-243070-0b06zk1q	69	24	by	by	ADP
cord-243070-0b06zk1q	69	25	:	:	PUNCT
cord-243070-0b06zk1q	69	26	subject	subject	ADJ
cord-243070-0b06zk1q	69	27	to	to	ADP
cord-243070-0b06zk1q	69	28	initial	initial	ADJ
cord-243070-0b06zk1q	69	29	conditions	condition	NOUN
cord-243070-0b06zk1q	69	30	(	(	PUNCT
cord-243070-0b06zk1q	69	31	7	7	NUM
cord-243070-0b06zk1q	69	32	)	)	PUNCT
cord-243070-0b06zk1q	69	33	.	.	PUNCT
cord-243070-0b06zk1q	70	1	two	two	NUM
cord-243070-0b06zk1q	70	2	special	special	ADJ
cord-243070-0b06zk1q	70	3	cases	case	NOUN
cord-243070-0b06zk1q	70	4	of	of	ADP
cord-243070-0b06zk1q	70	5	the	the	DET
cord-243070-0b06zk1q	70	6	controlled	control	VERB
cord-243070-0b06zk1q	70	7	process	process	NOUN
cord-243070-0b06zk1q	70	8	are	be	AUX
cord-243070-0b06zk1q	70	9	of	of	ADP
cord-243070-0b06zk1q	70	10	interest	interest	NOUN
cord-243070-0b06zk1q	70	11	.	.	PUNCT
cord-243070-0b06zk1q	71	1	if	if	SCONJ
cord-243070-0b06zk1q	71	2	a	a	DET
cord-243070-0b06zk1q	71	3	vaccine	vaccine	NOUN
cord-243070-0b06zk1q	71	4	against	against	ADP
cord-243070-0b06zk1q	71	5	the	the	DET
cord-243070-0b06zk1q	71	6	disease	disease	NOUN
cord-243070-0b06zk1q	71	7	is	be	AUX
cord-243070-0b06zk1q	71	8	unavailable	unavailable	ADJ
cord-243070-0b06zk1q	71	9	,	,	PUNCT
cord-243070-0b06zk1q	71	10	we	we	PRON
cord-243070-0b06zk1q	71	11	set	set	VERB
cord-243070-0b06zk1q	71	12	u	u	NOUN
cord-243070-0b06zk1q	71	13	1	1	NUM
cord-243070-0b06zk1q	71	14	=	=	NOUN
cord-243070-0b06zk1q	71	15	0	0	NUM
cord-243070-0b06zk1q	71	16	in	in	ADP
cord-243070-0b06zk1q	71	17	the	the	DET
cord-243070-0b06zk1q	71	18	equation	equation	NOUN
cord-243070-0b06zk1q	71	19	above	above	ADV
cord-243070-0b06zk1q	71	20	,	,	PUNCT
cord-243070-0b06zk1q	71	21	which	which	PRON
cord-243070-0b06zk1q	71	22	yields	yield	VERB
cord-243070-0b06zk1q	71	23	the	the	DET
cord-243070-0b06zk1q	71	24	following	follow	VERB
cord-243070-0b06zk1q	71	25	controlled	control	VERB
cord-243070-0b06zk1q	71	26	process	process	NOUN
cord-243070-0b06zk1q	71	27	:	:	PUNCT
cord-243070-0b06zk1q	71	28	we	we	PRON
cord-243070-0b06zk1q	71	29	will	will	AUX
cord-243070-0b06zk1q	71	30	refer	refer	VERB
cord-243070-0b06zk1q	71	31	to	to	ADP
cord-243070-0b06zk1q	71	32	this	this	DET
cord-243070-0b06zk1q	71	33	policy	policy	NOUN
cord-243070-0b06zk1q	71	34	as	as	ADP
cord-243070-0b06zk1q	71	35	an	an	DET
cord-243070-0b06zk1q	71	36	isolation	isolation	NOUN
cord-243070-0b06zk1q	71	37	policy	policy	NOUN
cord-243070-0b06zk1q	71	38	.	.	PUNCT
cord-243070-0b06zk1q	72	1	similarly	similarly	ADV
cord-243070-0b06zk1q	72	2	,	,	PUNCT
cord-243070-0b06zk1q	72	3	we	we	PRON
cord-243070-0b06zk1q	72	4	can	can	AUX
cord-243070-0b06zk1q	72	5	consider	consider	VERB
cord-243070-0b06zk1q	72	6	a	a	DET
cord-243070-0b06zk1q	72	7	vaccination	vaccination	NOUN
cord-243070-0b06zk1q	72	8	policy	policy	NOUN
cord-243070-0b06zk1q	72	9	,	,	PUNCT
cord-243070-0b06zk1q	72	10	for	for	ADP
cord-243070-0b06zk1q	72	11	which	which	PRON
cord-243070-0b06zk1q	72	12	u	u	PROPN
cord-243070-0b06zk1q	72	13	2	2	NUM
cord-243070-0b06zk1q	72	14	=	=	NOUN
cord-243070-0b06zk1q	72	15	0	0	NUM
cord-243070-0b06zk1q	72	16	.	.	PUNCT
cord-243070-0b06zk1q	73	1	in	in	ADP
cord-243070-0b06zk1q	73	2	this	this	DET
cord-243070-0b06zk1q	73	3	case	case	NOUN
cord-243070-0b06zk1q	73	4	the	the	DET
cord-243070-0b06zk1q	73	5	controlled	control	VERB
cord-243070-0b06zk1q	73	6	dynamics	dynamic	NOUN
cord-243070-0b06zk1q	73	7	reads	read	VERB
cord-243070-0b06zk1q	73	8	dx	dx	PROPN
cord-243070-0b06zk1q	73	9	u	u	PROPN
cord-243070-0b06zk1q	73	10	we	we	PRON
cord-243070-0b06zk1q	73	11	assume	assume	VERB
cord-243070-0b06zk1q	73	12	a	a	DET
cord-243070-0b06zk1q	73	13	finite	finite	ADJ
cord-243070-0b06zk1q	73	14	time	time	NOUN
cord-243070-0b06zk1q	73	15	horizon	horizon	VERB
cord-243070-0b06zk1q	73	16	t	t	PROPN
cord-243070-0b06zk1q	73	17	<	<	X
cord-243070-0b06zk1q	74	1	∞.	∞.	PROPN
cord-243070-0b06zk1q	74	2	the	the	DET
cord-243070-0b06zk1q	74	3	controlling	control	VERB
cord-243070-0b06zk1q	74	4	agent	agent	NOUN
cord-243070-0b06zk1q	74	5	's	's	PART
cord-243070-0b06zk1q	74	6	objective	objective	NOUN
cord-243070-0b06zk1q	74	7	is	be	AUX
cord-243070-0b06zk1q	74	8	to	to	PART
cord-243070-0b06zk1q	74	9	minimize	minimize	VERB
cord-243070-0b06zk1q	74	10	a	a	DET
cord-243070-0b06zk1q	74	11	running	running	NOUN
cord-243070-0b06zk1q	74	12	cost	cost	NOUN
cord-243070-0b06zk1q	74	13	function	function	NOUN
cord-243070-0b06zk1q	74	14	c(x	c(x	NOUN
cord-243070-0b06zk1q	74	15	t	t	PROPN
cord-243070-0b06zk1q	74	16	,	,	PUNCT
cord-243070-0b06zk1q	74	17	u	u	PROPN
cord-243070-0b06zk1q	74	18	t	t	NOUN
cord-243070-0b06zk1q	74	19	)	)	PUNCT
cord-243070-0b06zk1q	74	20	and	and	CCONJ
cord-243070-0b06zk1q	74	21	the	the	DET
cord-243070-0b06zk1q	74	22	terminal	terminal	ADJ
cord-243070-0b06zk1q	74	23	value	value	NOUN
cord-243070-0b06zk1q	74	24	function	function	VERB
cord-243070-0b06zk1q	74	25	g(x	g(x	PROPN
cord-243070-0b06zk1q	74	26	t	t	PROPN
cord-243070-0b06zk1q	74	27	)	)	PUNCT
cord-243070-0b06zk1q	74	28	.	.	PUNCT
cord-243070-0b06zk1q	75	1	in	in	ADP
cord-243070-0b06zk1q	75	2	other	other	ADJ
cord-243070-0b06zk1q	75	3	words	word	NOUN
cord-243070-0b06zk1q	75	4	,	,	PUNCT
cord-243070-0b06zk1q	75	5	we	we	PRON
cord-243070-0b06zk1q	75	6	are	be	AUX
cord-243070-0b06zk1q	75	7	seeking	seek	VERB
cord-243070-0b06zk1q	75	8	a	a	DET
cord-243070-0b06zk1q	75	9	policy	policy	NOUN
cord-243070-0b06zk1q	75	10	u	u	NOUN
cord-243070-0b06zk1q	75	11	*	*	PUNCT
cord-243070-0b06zk1q	75	12	such	such	ADJ
cord-243070-0b06zk1q	75	13	that	that	SCONJ
cord-243070-0b06zk1q	75	14	we	we	PRON
cord-243070-0b06zk1q	75	15	consider	consider	VERB
cord-243070-0b06zk1q	75	16	the	the	DET
cord-243070-0b06zk1q	75	17	following	follow	VERB
cord-243070-0b06zk1q	75	18	cost	cost	NOUN
cord-243070-0b06zk1q	75	19	function	function	NOUN
cord-243070-0b06zk1q	75	20	:	:	PUNCT
cord-243070-0b06zk1q	75	21	where	where	SCONJ
cord-243070-0b06zk1q	75	22	for	for	ADP
cord-243070-0b06zk1q	75	23	i	i	PRON
cord-243070-0b06zk1q	75	24	=	=	NOUN
cord-243070-0b06zk1q	75	25	1	1	NUM
cord-243070-0b06zk1q	75	26	,	,	PUNCT
cord-243070-0b06zk1q	75	27	2	2	NUM
cord-243070-0b06zk1q	75	28	.	.	X
cord-243070-0b06zk1q	76	1	in	in	ADP
cord-243070-0b06zk1q	76	2	other	other	ADJ
cord-243070-0b06zk1q	76	3	words	word	NOUN
cord-243070-0b06zk1q	76	4	,	,	PUNCT
cord-243070-0b06zk1q	76	5	the	the	DET
cord-243070-0b06zk1q	76	6	running	running	NOUN
cord-243070-0b06zk1q	76	7	cost	cost	NOUN
cord-243070-0b06zk1q	76	8	of	of	ADP
cord-243070-0b06zk1q	76	9	vaccination	vaccination	NOUN
cord-243070-0b06zk1q	76	10	is	be	AUX
cord-243070-0b06zk1q	76	11	assumed	assume	VERB
cord-243070-0b06zk1q	76	12	to	to	PART
cord-243070-0b06zk1q	76	13	be	be	AUX
cord-243070-0b06zk1q	76	14	proportional	proportional	ADJ
cord-243070-0b06zk1q	76	15	to	to	ADP
cord-243070-0b06zk1q	76	16	the	the	DET
cord-243070-0b06zk1q	76	17	number	number	NOUN
cord-243070-0b06zk1q	76	18	of	of	ADP
cord-243070-0b06zk1q	76	19	susceptible	susceptible	ADJ
cord-243070-0b06zk1q	76	20	individuals	individual	NOUN
cord-243070-0b06zk1q	76	21	,	,	PUNCT
cord-243070-0b06zk1q	76	22	while	while	SCONJ
cord-243070-0b06zk1q	76	23	the	the	DET
cord-243070-0b06zk1q	76	24	cost	cost	NOUN
cord-243070-0b06zk1q	76	25	of	of	ADP
cord-243070-0b06zk1q	76	26	isolation	isolation	NOUN
cord-243070-0b06zk1q	76	27	is	be	AUX
cord-243070-0b06zk1q	76	28	assumed	assume	VERB
cord-243070-0b06zk1q	76	29	to	to	PART
cord-243070-0b06zk1q	76	30	be	be	AUX
cord-243070-0b06zk1q	76	31	proportional	proportional	ADJ
cord-243070-0b06zk1q	76	32	to	to	ADP
cord-243070-0b06zk1q	76	33	the	the	DET
cord-243070-0b06zk1q	76	34	number	number	NOUN
cord-243070-0b06zk1q	76	35	of	of	ADP
cord-243070-0b06zk1q	76	36	infected	infected	ADJ
cord-243070-0b06zk1q	76	37	individuals	individual	NOUN
cord-243070-0b06zk1q	76	38	.	.	PUNCT
cord-243070-0b06zk1q	77	1	the	the	DET
cord-243070-0b06zk1q	77	2	coefficients	coefficient	NOUN
cord-243070-0b06zk1q	77	3	l	l	PROPN
cord-243070-0b06zk1q	77	4	i	i	PRON
cord-243070-0b06zk1q	77	5	>	>	X
cord-243070-0b06zk1q	77	6	0	0	NUM
cord-243070-0b06zk1q	77	7	,	,	PUNCT
cord-243070-0b06zk1q	77	8	m	m	X
cord-243070-0b06zk1q	77	9	i	i	PRON
cord-243070-0b06zk1q	77	10	,	,	PUNCT
cord-243070-0b06zk1q	77	11	n	n	ADV
cord-243070-0b06zk1q	77	12	i	i	PRON
cord-243070-0b06zk1q	77	13	are	be	AUX
cord-243070-0b06zk1q	77	14	determined	determine	VERB
cord-243070-0b06zk1q	77	15	by	by	ADP
cord-243070-0b06zk1q	77	16	the	the	DET
cord-243070-0b06zk1q	77	17	overall	overall	ADJ
cord-243070-0b06zk1q	77	18	cost	cost	NOUN
cord-243070-0b06zk1q	77	19	of	of	ADP
cord-243070-0b06zk1q	77	20	following	follow	VERB
cord-243070-0b06zk1q	77	21	the	the	DET
cord-243070-0b06zk1q	77	22	mitigation	mitigation	NOUN
cord-243070-0b06zk1q	77	23	policy	policy	NOUN
cord-243070-0b06zk1q	77	24	.	.	PUNCT
cord-243070-0b06zk1q	78	1	in	in	ADP
cord-243070-0b06zk1q	78	2	particular	particular	ADJ
cord-243070-0b06zk1q	78	3	,	,	PUNCT
cord-243070-0b06zk1q	78	4	they	they	PRON
cord-243070-0b06zk1q	78	5	should	should	AUX
cord-243070-0b06zk1q	78	6	be	be	AUX
cord-243070-0b06zk1q	78	7	selected	select	VERB
cord-243070-0b06zk1q	78	8	so	so	SCONJ
cord-243070-0b06zk1q	78	9	that	that	SCONJ
cord-243070-0b06zk1q	78	10	the	the	DET
cord-243070-0b06zk1q	78	11	running	running	NOUN
cord-243070-0b06zk1q	78	12	cost	cost	NOUN
cord-243070-0b06zk1q	78	13	functions	function	NOUN
cord-243070-0b06zk1q	78	14	are	be	AUX
cord-243070-0b06zk1q	78	15	strictly	strictly	ADV
cord-243070-0b06zk1q	78	16	positive	positive	ADJ
cord-243070-0b06zk1q	78	17	.	.	PUNCT
cord-243070-0b06zk1q	79	1	as	as	SCONJ
cord-243070-0b06zk1q	79	2	the	the	DET
cord-243070-0b06zk1q	79	3	terminal	terminal	ADJ
cord-243070-0b06zk1q	79	4	value	value	NOUN
cord-243070-0b06zk1q	79	5	function	function	NOUN
cord-243070-0b06zk1q	79	6	we	we	PRON
cord-243070-0b06zk1q	79	7	take	take	VERB
cord-243070-0b06zk1q	79	8	the	the	DET
cord-243070-0b06zk1q	79	9	transmission	transmission	NOUN
cord-243070-0b06zk1q	79	10	rate	rate	NOUN
cord-243070-0b06zk1q	79	11	of	of	ADP
cord-243070-0b06zk1q	79	12	the	the	DET
cord-243070-0b06zk1q	79	13	infection	infection	NOUN
cord-243070-0b06zk1q	79	14	[	[	PUNCT
cord-243070-0b06zk1q	79	15	13	13	NUM
cord-243070-0b06zk1q	79	16	]	]	PUNCT
cord-243070-0b06zk1q	79	17	,	,	PUNCT
cord-243070-0b06zk1q	79	18	namely	namely	ADV
cord-243070-0b06zk1q	79	19	we	we	PRON
cord-243070-0b06zk1q	79	20	now	now	ADV
cord-243070-0b06zk1q	79	21	invoke	invoke	VERB
cord-243070-0b06zk1q	79	22	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	79	23	dynamic	dynamic	ADJ
cord-243070-0b06zk1q	79	24	programming	programming	NOUN
cord-243070-0b06zk1q	79	25	,	,	PUNCT
cord-243070-0b06zk1q	79	26	see	see	VERB
cord-243070-0b06zk1q	79	27	eg	eg	NOUN
cord-243070-0b06zk1q	79	28	.	.	PUNCT
cord-243070-0b06zk1q	80	1	[	[	X
cord-243070-0b06zk1q	80	2	10	10	NUM
cord-243070-0b06zk1q	80	3	]	]	PUNCT
cord-243070-0b06zk1q	80	4	,	,	PUNCT
cord-243070-0b06zk1q	80	5	[	[	X
cord-243070-0b06zk1q	80	6	21	21	NUM
cord-243070-0b06zk1q	80	7	]	]	PUNCT
cord-243070-0b06zk1q	80	8	.	.	PUNCT
cord-243070-0b06zk1q	81	1	the	the	DET
cord-243070-0b06zk1q	81	2	key	key	ADJ
cord-243070-0b06zk1q	81	3	element	element	NOUN
cord-243070-0b06zk1q	81	4	of	of	ADP
cord-243070-0b06zk1q	81	5	this	this	DET
cord-243070-0b06zk1q	81	6	approach	approach	NOUN
cord-243070-0b06zk1q	81	7	is	be	AUX
cord-243070-0b06zk1q	81	8	the	the	DET
cord-243070-0b06zk1q	81	9	value	value	NOUN
cord-243070-0b06zk1q	81	10	function	function	NOUN
cord-243070-0b06zk1q	81	11	j(t	j(t	PROPN
cord-243070-0b06zk1q	81	12	,	,	PUNCT
cord-243070-0b06zk1q	81	13	x	x	PROPN
cord-243070-0b06zk1q	81	14	,	,	PUNCT
cord-243070-0b06zk1q	81	15	y	y	PROPN
cord-243070-0b06zk1q	81	16	)	)	PUNCT
cord-243070-0b06zk1q	81	17	.	.	PUNCT
cord-243070-0b06zk1q	82	1	it	it	PRON
cord-243070-0b06zk1q	82	2	is	be	AUX
cord-243070-0b06zk1q	82	3	determined	determine	VERB
cord-243070-0b06zk1q	82	4	by	by	ADP
cord-243070-0b06zk1q	82	5	two	two	NUM
cord-243070-0b06zk1q	82	6	requirements	requirement	NOUN
cord-243070-0b06zk1q	82	7	:	:	PUNCT
cord-243070-0b06zk1q	82	8	(	(	PUNCT
cord-243070-0b06zk1q	82	9	b1	b1	NOUN
cord-243070-0b06zk1q	82	10	)	)	PUNCT
cord-243070-0b06zk1q	82	11	it	it	PRON
cord-243070-0b06zk1q	82	12	satisfies	satisfy	VERB
cord-243070-0b06zk1q	82	13	bellman	bellman	PROPN
cord-243070-0b06zk1q	82	14	's	's	PART
cord-243070-0b06zk1q	82	15	principle	principle	NOUN
cord-243070-0b06zk1q	82	16	of	of	ADP
cord-243070-0b06zk1q	82	17	optimality	optimality	NOUN
cord-243070-0b06zk1q	82	18	,	,	PUNCT
cord-243070-0b06zk1q	82	19	for	for	ADP
cord-243070-0b06zk1q	82	20	all	all	PRON
cord-243070-0b06zk1q	83	1	0	0	NUM
cord-243070-0b06zk1q	83	2	≤	≤	PROPN
cord-243070-0b06zk1q	84	1	t	t	X
cord-243070-0b06zk1q	84	2	<	<	X
cord-243070-0b06zk1q	84	3	t	t	PROPN
cord-243070-0b06zk1q	84	4	,	,	PUNCT
cord-243070-0b06zk1q	84	5	where	where	SCONJ
cord-243070-0b06zk1q	84	6	e	e	PROPN
cord-243070-0b06zk1q	84	7	t	t	PROPN
cord-243070-0b06zk1q	84	8	denotes	denote	VERB
cord-243070-0b06zk1q	84	9	conditional	conditional	ADJ
cord-243070-0b06zk1q	84	10	expectation	expectation	NOUN
cord-243070-0b06zk1q	84	11	with	with	ADP
cord-243070-0b06zk1q	84	12	respect	respect	NOUN
cord-243070-0b06zk1q	84	13	to	to	ADP
cord-243070-0b06zk1q	84	14	the	the	DET
cord-243070-0b06zk1q	84	15	information	information	NOUN
cord-243070-0b06zk1q	84	16	set	set	VERB
cord-243070-0b06zk1q	84	17	at	at	ADP
cord-243070-0b06zk1q	84	18	time	time	NOUN
cord-243070-0b06zk1q	84	19	t	t	NOUN
cord-243070-0b06zk1q	84	20	,	,	PUNCT
cord-243070-0b06zk1q	84	21	and	and	CCONJ
cord-243070-0b06zk1q	84	22	where	where	SCONJ
cord-243070-0b06zk1q	84	23	the	the	DET
cord-243070-0b06zk1q	84	24	minimum	minimum	NOUN
cord-243070-0b06zk1q	84	25	is	be	AUX
cord-243070-0b06zk1q	84	26	taken	take	VERB
cord-243070-0b06zk1q	84	27	over	over	ADP
cord-243070-0b06zk1q	84	28	all	all	DET
cord-243070-0b06zk1q	84	29	admissible	admissible	ADJ
cord-243070-0b06zk1q	84	30	controls	control	NOUN
cord-243070-0b06zk1q	84	31	u	u	PROPN
cord-243070-0b06zk1q	84	32	t	t	PROPN
cord-243070-0b06zk1q	84	33	,	,	PUNCT
cord-243070-0b06zk1q	84	34	[	[	X
cord-243070-0b06zk1q	84	35	10	10	NUM
cord-243070-0b06zk1q	84	36	]	]	PUNCT
cord-243070-0b06zk1q	84	37	.	.	PUNCT
cord-243070-0b06zk1q	85	1	(	(	PUNCT
cord-243070-0b06zk1q	85	2	b2	b2	NOUN
cord-243070-0b06zk1q	85	3	)	)	PUNCT
cord-243070-0b06zk1q	85	4	it	it	PRON
cord-243070-0b06zk1q	85	5	satisfies	satisfy	VERB
cord-243070-0b06zk1q	85	6	the	the	DET
cord-243070-0b06zk1q	85	7	terminal	terminal	ADJ
cord-243070-0b06zk1q	85	8	condition	condition	NOUN
cord-243070-0b06zk1q	85	9	,	,	PUNCT
cord-243070-0b06zk1q	85	10	using	use	VERB
cord-243070-0b06zk1q	85	11	ito	ito	PROPN
cord-243070-0b06zk1q	85	12	's	's	PART
cord-243070-0b06zk1q	85	13	lemma	lemma	NOUN
cord-243070-0b06zk1q	85	14	,	,	PUNCT
cord-243070-0b06zk1q	85	15	we	we	PRON
cord-243070-0b06zk1q	85	16	verify	verify	VERB
cord-243070-0b06zk1q	85	17	that	that	SCONJ
cord-243070-0b06zk1q	85	18	these	these	DET
cord-243070-0b06zk1q	85	19	two	two	NUM
cord-243070-0b06zk1q	85	20	conditions	condition	NOUN
cord-243070-0b06zk1q	85	21	lead	lead	VERB
cord-243070-0b06zk1q	85	22	to	to	ADP
cord-243070-0b06zk1q	85	23	the	the	DET
cord-243070-0b06zk1q	85	24	following	follow	VERB
cord-243070-0b06zk1q	85	25	nonlinear	nonlinear	ADJ
cord-243070-0b06zk1q	85	26	partial	partial	ADJ
cord-243070-0b06zk1q	85	27	differential	differential	ADJ
cord-243070-0b06zk1q	85	28	equation	equation	NOUN
cord-243070-0b06zk1q	85	29	for	for	ADP
cord-243070-0b06zk1q	85	30	the	the	DET
cord-243070-0b06zk1q	85	31	value	value	NOUN
cord-243070-0b06zk1q	85	32	function	function	NOUN
cord-243070-0b06zk1q	85	33	,	,	PUNCT
cord-243070-0b06zk1q	85	34	namely	namely	ADV
cord-243070-0b06zk1q	85	35	the	the	DET
cord-243070-0b06zk1q	85	36	stochastic	stochastic	PROPN
cord-243070-0b06zk1q	85	37	hamilton	hamilton	PROPN
cord-243070-0b06zk1q	85	38	-	-	PUNCT
cord-243070-0b06zk1q	85	39	jacobi	jacobi	PROPN
cord-243070-0b06zk1q	85	40	-	-	PUNCT
cord-243070-0b06zk1q	85	41	bellman	bellman	PROPN
cord-243070-0b06zk1q	85	42	equation	equation	NOUN
cord-243070-0b06zk1q	85	43	:	:	PUNCT
cord-243070-0b06zk1q	85	44	subject	subject	ADJ
cord-243070-0b06zk1q	85	45	to	to	ADP
cord-243070-0b06zk1q	85	46	the	the	DET
cord-243070-0b06zk1q	85	47	terminal	terminal	ADJ
cord-243070-0b06zk1q	85	48	condition	condition	NOUN
cord-243070-0b06zk1q	85	49	as	as	ADP
cord-243070-0b06zk1q	85	50	the	the	DET
cord-243070-0b06zk1q	85	51	first	first	ADJ
cord-243070-0b06zk1q	85	52	step	step	NOUN
cord-243070-0b06zk1q	85	53	towards	towards	ADP
cord-243070-0b06zk1q	85	54	solving	solve	VERB
cord-243070-0b06zk1q	85	55	the	the	DET
cord-243070-0b06zk1q	85	56	hjb	hjb	PROPN
cord-243070-0b06zk1q	85	57	equation	equation	NOUN
cord-243070-0b06zk1q	85	58	(	(	PUNCT
cord-243070-0b06zk1q	85	59	21	21	NUM
cord-243070-0b06zk1q	85	60	)	)	PUNCT
cord-243070-0b06zk1q	85	61	,	,	PUNCT
cord-243070-0b06zk1q	85	62	we	we	PRON
cord-243070-0b06zk1q	85	63	let	let	VERB
cord-243070-0b06zk1q	85	64	u	u	PRON
cord-243070-0b06zk1q	85	65	=	=	NOUN
cord-243070-0b06zk1q	85	66	u	u	NOUN
cord-243070-0b06zk1q	85	67	*	*	PUNCT
cord-243070-0b06zk1q	85	68	denote	denote	VERB
cord-243070-0b06zk1q	85	69	the	the	DET
cord-243070-0b06zk1q	85	70	minimizer	minimizer	NOUN
cord-243070-0b06zk1q	85	71	of	of	ADP
cord-243070-0b06zk1q	85	72	the	the	DET
cord-243070-0b06zk1q	85	73	expression	expression	NOUN
cord-243070-0b06zk1q	85	74	inside	inside	ADP
cord-243070-0b06zk1q	85	75	the	the	DET
cord-243070-0b06zk1q	85	76	curly	curly	ADJ
cord-243070-0b06zk1q	85	77	parentheses	parenthesis	NOUN
cord-243070-0b06zk1q	85	78	in	in	ADP
cord-243070-0b06zk1q	85	79	(	(	PUNCT
cord-243070-0b06zk1q	85	80	21	21	NUM
cord-243070-0b06zk1q	85	81	)	)	PUNCT
cord-243070-0b06zk1q	85	82	.	.	PUNCT
cord-243070-0b06zk1q	86	1	in	in	ADP
cord-243070-0b06zk1q	86	2	other	other	ADJ
cord-243070-0b06zk1q	86	3	words	word	NOUN
cord-243070-0b06zk1q	86	4	,	,	PUNCT
cord-243070-0b06zk1q	86	5	u	u	NOUN
cord-243070-0b06zk1q	86	6	*	*	PUNCT
cord-243070-0b06zk1q	86	7	satisfies	satisfie	NOUN
cord-243070-0b06zk1q	86	8	which	which	PRON
cord-243070-0b06zk1q	86	9	leads	lead	VERB
cord-243070-0b06zk1q	86	10	to	to	ADP
cord-243070-0b06zk1q	86	11	the	the	DET
cord-243070-0b06zk1q	86	12	following	follow	VERB
cord-243070-0b06zk1q	86	13	first	first	ADJ
cord-243070-0b06zk1q	86	14	order	order	NOUN
cord-243070-0b06zk1q	86	15	condition	condition	NOUN
cord-243070-0b06zk1q	86	16	on	on	ADP
cord-243070-0b06zk1q	86	17	u	u	PROPN
cord-243070-0b06zk1q	86	18	*	*	PUNCT
cord-243070-0b06zk1q	86	19	:	:	PUNCT
cord-243070-0b06zk1q	86	20	substituting	substitute	VERB
cord-243070-0b06zk1q	86	21	u	u	PROPN
cord-243070-0b06zk1q	86	22	*	*	PUNCT
cord-243070-0b06zk1q	86	23	back	back	ADV
cord-243070-0b06zk1q	86	24	to	to	ADP
cord-243070-0b06zk1q	86	25	the	the	DET
cord-243070-0b06zk1q	86	26	hjb	hjb	PROPN
cord-243070-0b06zk1q	86	27	equation	equation	NOUN
cord-243070-0b06zk1q	86	28	yields	yield	VERB
cord-243070-0b06zk1q	86	29	the	the	DET
cord-243070-0b06zk1q	86	30	equatioṅ	equatioṅ	NOUN
cord-243070-0b06zk1q	86	31	we	we	PRON
cord-243070-0b06zk1q	86	32	do	do	AUX
cord-243070-0b06zk1q	86	33	not	not	PART
cord-243070-0b06zk1q	86	34	believe	believe	VERB
cord-243070-0b06zk1q	86	35	that	that	SCONJ
cord-243070-0b06zk1q	86	36	the	the	DET
cord-243070-0b06zk1q	86	37	solution	solution	NOUN
cord-243070-0b06zk1q	86	38	to	to	ADP
cord-243070-0b06zk1q	86	39	this	this	DET
cord-243070-0b06zk1q	86	40	equation	equation	NOUN
cord-243070-0b06zk1q	86	41	can	can	AUX
cord-243070-0b06zk1q	86	42	be	be	AUX
cord-243070-0b06zk1q	86	43	explicitly	explicitly	ADV
cord-243070-0b06zk1q	86	44	represented	represent	VERB
cord-243070-0b06zk1q	86	45	in	in	ADP
cord-243070-0b06zk1q	86	46	terms	term	NOUN
cord-243070-0b06zk1q	86	47	of	of	ADP
cord-243070-0b06zk1q	86	48	standard	standard	ADJ
cord-243070-0b06zk1q	86	49	functions	function	NOUN
cord-243070-0b06zk1q	86	50	.	.	PUNCT
cord-243070-0b06zk1q	87	1	this	this	PRON
cord-243070-0b06zk1q	87	2	is	be	AUX
cord-243070-0b06zk1q	87	3	a	a	DET
cord-243070-0b06zk1q	87	4	three	three	NUM
cord-243070-0b06zk1q	87	5	dimensional	dimensional	ADJ
cord-243070-0b06zk1q	87	6	partial	partial	ADJ
cord-243070-0b06zk1q	87	7	differential	differential	ADJ
cord-243070-0b06zk1q	87	8	equation	equation	NOUN
cord-243070-0b06zk1q	87	9	,	,	PUNCT
cord-243070-0b06zk1q	87	10	and	and	CCONJ
cord-243070-0b06zk1q	87	11	solving	solve	VERB
cord-243070-0b06zk1q	87	12	it	it	PRON
cord-243070-0b06zk1q	87	13	numerically	numerically	ADV
cord-243070-0b06zk1q	87	14	may	may	AUX
cord-243070-0b06zk1q	87	15	pose	pose	VERB
cord-243070-0b06zk1q	87	16	challenges	challenge	NOUN
cord-243070-0b06zk1q	87	17	.	.	PUNCT
cord-243070-0b06zk1q	88	1	rather	rather	ADV
cord-243070-0b06zk1q	88	2	than	than	ADP
cord-243070-0b06zk1q	88	3	following	follow	VERB
cord-243070-0b06zk1q	88	4	this	this	DET
cord-243070-0b06zk1q	88	5	path	path	NOUN
cord-243070-0b06zk1q	88	6	,	,	PUNCT
cord-243070-0b06zk1q	88	7	we	we	PRON
cord-243070-0b06zk1q	88	8	shall	shall	AUX
cord-243070-0b06zk1q	88	9	invoke	invoke	VERB
cord-243070-0b06zk1q	88	10	the	the	DET
cord-243070-0b06zk1q	88	11	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	88	12	minimum	minimum	NOUN
cord-243070-0b06zk1q	88	13	principle	principle	NOUN
cord-243070-0b06zk1q	88	14	and	and	CCONJ
cord-243070-0b06zk1q	88	15	reformulate	reformulate	VERB
cord-243070-0b06zk1q	88	16	the	the	DET
cord-243070-0b06zk1q	88	17	problem	problem	NOUN
cord-243070-0b06zk1q	88	18	as	as	ADP
cord-243070-0b06zk1q	88	19	a	a	DET
cord-243070-0b06zk1q	88	20	system	system	NOUN
cord-243070-0b06zk1q	88	21	of	of	ADP
cord-243070-0b06zk1q	88	22	fbsdes	fbsde	NOUN
cord-243070-0b06zk1q	88	23	.	.	PUNCT
cord-243070-0b06zk1q	89	1	among	among	ADP
cord-243070-0b06zk1q	89	2	the	the	DET
cord-243070-0b06zk1q	89	3	advantages	advantage	NOUN
cord-243070-0b06zk1q	89	4	of	of	ADP
cord-243070-0b06zk1q	89	5	this	this	DET
cord-243070-0b06zk1q	89	6	approach	approach	NOUN
cord-243070-0b06zk1q	89	7	is	be	AUX
cord-243070-0b06zk1q	89	8	that	that	SCONJ
cord-243070-0b06zk1q	89	9	it	it	PRON
cord-243070-0b06zk1q	89	10	might	might	AUX
cord-243070-0b06zk1q	89	11	be	be	AUX
cord-243070-0b06zk1q	89	12	amenable	amenable	ADJ
cord-243070-0b06zk1q	89	13	to	to	ADP
cord-243070-0b06zk1q	89	14	a	a	DET
cord-243070-0b06zk1q	89	15	deep	deep	ADJ
cord-243070-0b06zk1q	89	16	learning	learning	NOUN
cord-243070-0b06zk1q	89	17	approach	approach	NOUN
cord-243070-0b06zk1q	89	18	via	via	ADP
cord-243070-0b06zk1q	89	19	the	the	DET
cord-243070-0b06zk1q	89	20	method	method	NOUN
cord-243070-0b06zk1q	89	21	advocated	advocate	VERB
cord-243070-0b06zk1q	89	22	in	in	ADP
cord-243070-0b06zk1q	89	23	[	[	X
cord-243070-0b06zk1q	89	24	14	14	NUM
cord-243070-0b06zk1q	89	25	]	]	PUNCT
cord-243070-0b06zk1q	89	26	.	.	PUNCT
cord-243070-0b06zk1q	90	1	the	the	DET
cord-243070-0b06zk1q	90	2	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	90	3	minimum	minimum	NOUN
cord-243070-0b06zk1q	90	4	principle	principle	NOUN
cord-243070-0b06zk1q	90	5	,	,	PUNCT
cord-243070-0b06zk1q	90	6	see	see	VERB
cord-243070-0b06zk1q	90	7	[	[	X
cord-243070-0b06zk1q	90	8	21	21	NUM
cord-243070-0b06zk1q	90	9	]	]	PUNCT
cord-243070-0b06zk1q	90	10	and	and	CCONJ
cord-243070-0b06zk1q	90	11	references	reference	NOUN
cord-243070-0b06zk1q	90	12	therein	therein	ADV
cord-243070-0b06zk1q	90	13	,	,	PUNCT
cord-243070-0b06zk1q	90	14	offers	offer	VERB
cord-243070-0b06zk1q	90	15	an	an	DET
cord-243070-0b06zk1q	90	16	alternative	alternative	ADJ
cord-243070-0b06zk1q	90	17	approach	approach	NOUN
cord-243070-0b06zk1q	90	18	to	to	ADP
cord-243070-0b06zk1q	90	19	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	90	20	optimal	optimal	ADJ
cord-243070-0b06zk1q	90	21	control	control	NOUN
cord-243070-0b06zk1q	90	22	.	.	PUNCT
cord-243070-0b06zk1q	91	1	it	it	PRON
cord-243070-0b06zk1q	91	2	is	be	AUX
cord-243070-0b06zk1q	91	3	a	a	DET
cord-243070-0b06zk1q	91	4	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	91	5	version	version	NOUN
cord-243070-0b06zk1q	91	6	of	of	ADP
cord-243070-0b06zk1q	91	7	pontryagin	pontryagin	NOUN
cord-243070-0b06zk1q	91	8	's	's	PART
cord-243070-0b06zk1q	91	9	minimum	minimum	ADJ
cord-243070-0b06zk1q	91	10	principle	principle	NOUN
cord-243070-0b06zk1q	91	11	introduced	introduce	VERB
cord-243070-0b06zk1q	91	12	in	in	ADP
cord-243070-0b06zk1q	91	13	the	the	DET
cord-243070-0b06zk1q	91	14	context	context	NOUN
cord-243070-0b06zk1q	91	15	of	of	ADP
cord-243070-0b06zk1q	91	16	deterministic	deterministic	ADJ
cord-243070-0b06zk1q	91	17	optimal	optimal	ADJ
cord-243070-0b06zk1q	91	18	control	control	NOUN
cord-243070-0b06zk1q	91	19	[	[	PUNCT
cord-243070-0b06zk1q	91	20	22	22	NUM
cord-243070-0b06zk1q	91	21	]	]	PUNCT
cord-243070-0b06zk1q	91	22	.	.	PUNCT
cord-243070-0b06zk1q	92	1	it	it	PRON
cord-243070-0b06zk1q	92	2	also	also	ADV
cord-243070-0b06zk1q	92	3	offers	offer	VERB
cord-243070-0b06zk1q	92	4	an	an	DET
cord-243070-0b06zk1q	92	5	effective	effective	ADJ
cord-243070-0b06zk1q	92	6	numerical	numerical	ADJ
cord-243070-0b06zk1q	92	7	methodology	methodology	NOUN
cord-243070-0b06zk1q	92	8	to	to	ADP
cord-243070-0b06zk1q	92	9	solving	solve	VERB
cord-243070-0b06zk1q	92	10	the	the	DET
cord-243070-0b06zk1q	92	11	hjb	hjb	PROPN
cord-243070-0b06zk1q	92	12	equation	equation	NOUN
cord-243070-0b06zk1q	92	13	(	(	PUNCT
cord-243070-0b06zk1q	92	14	24	24	NUM
cord-243070-0b06zk1q	92	15	)	)	PUNCT
cord-243070-0b06zk1q	92	16	via	via	ADP
cord-243070-0b06zk1q	92	17	monte	monte	PROPN
cord-243070-0b06zk1q	92	18	carlo	carlo	PROPN
cord-243070-0b06zk1q	92	19	simulations	simulation	NOUN
cord-243070-0b06zk1q	92	20	.	.	PUNCT
cord-243070-0b06zk1q	93	1	in	in	ADP
cord-243070-0b06zk1q	93	2	this	this	DET
cord-243070-0b06zk1q	93	3	approach	approach	NOUN
cord-243070-0b06zk1q	93	4	,	,	PUNCT
cord-243070-0b06zk1q	93	5	the	the	DET
cord-243070-0b06zk1q	93	6	key	key	ADJ
cord-243070-0b06zk1q	93	7	object	object	NOUN
cord-243070-0b06zk1q	93	8	is	be	AUX
cord-243070-0b06zk1q	93	9	the	the	DET
cord-243070-0b06zk1q	93	10	hamiltonian	hamiltonian	ADJ
cord-243070-0b06zk1q	93	11	function	function	NOUN
cord-243070-0b06zk1q	93	12	h	h	PROPN
cord-243070-0b06zk1q	93	13	=	=	X
cord-243070-0b06zk1q	93	14	h(x	h(x	PROPN
cord-243070-0b06zk1q	93	15	,	,	PUNCT
cord-243070-0b06zk1q	93	16	u	u	PROPN
cord-243070-0b06zk1q	93	17	,	,	PUNCT
cord-243070-0b06zk1q	93	18	y	y	PROPN
cord-243070-0b06zk1q	93	19	,	,	PUNCT
cord-243070-0b06zk1q	93	20	z	z	PROPN
cord-243070-0b06zk1q	93	21	)	)	PUNCT
cord-243070-0b06zk1q	93	22	of	of	ADP
cord-243070-0b06zk1q	93	23	four	four	NUM
cord-243070-0b06zk1q	93	24	arguments	argument	NOUN
cord-243070-0b06zk1q	93	25	and	and	CCONJ
cord-243070-0b06zk1q	93	26	a	a	DET
cord-243070-0b06zk1q	93	27	system	system	NOUN
cord-243070-0b06zk1q	93	28	of	of	ADP
cord-243070-0b06zk1q	93	29	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	93	30	differential	differential	ADJ
cord-243070-0b06zk1q	93	31	equations	equation	NOUN
cord-243070-0b06zk1q	93	32	,	,	PUNCT
cord-243070-0b06zk1q	93	33	both	both	CCONJ
cord-243070-0b06zk1q	93	34	forward	forward	ADV
cord-243070-0b06zk1q	93	35	and	and	CCONJ
cord-243070-0b06zk1q	93	36	backward	backward	ADJ
cord-243070-0b06zk1q	93	37	,	,	PUNCT
cord-243070-0b06zk1q	93	38	determined	determine	VERB
cord-243070-0b06zk1q	93	39	by	by	ADP
cord-243070-0b06zk1q	93	40	h.	h.	PROPN
cord-243070-0b06zk1q	93	41	specifically	specifically	ADV
cord-243070-0b06zk1q	93	42	,	,	PUNCT
cord-243070-0b06zk1q	93	43	for	for	ADP
cord-243070-0b06zk1q	93	44	the	the	DET
cord-243070-0b06zk1q	93	45	case	case	NOUN
cord-243070-0b06zk1q	93	46	of	of	ADP
cord-243070-0b06zk1q	93	47	the	the	DET
cord-243070-0b06zk1q	93	48	controlled	control	VERB
cord-243070-0b06zk1q	93	49	stochastic	stochastic	NOUN
cord-243070-0b06zk1q	93	50	sir	sir	NOUN
cord-243070-0b06zk1q	93	51	model	model	NOUN
cord-243070-0b06zk1q	93	52	(	(	PUNCT
cord-243070-0b06zk1q	93	53	14	14	NUM
cord-243070-0b06zk1q	93	54	)	)	PUNCT
cord-243070-0b06zk1q	93	55	,	,	PUNCT
cord-243070-0b06zk1q	93	56	we	we	PRON
cord-243070-0b06zk1q	93	57	have	have	VERB
cord-243070-0b06zk1q	93	58	x	x	PROPN
cord-243070-0b06zk1q	93	59	,	,	PUNCT
cord-243070-0b06zk1q	93	60	u	u	PROPN
cord-243070-0b06zk1q	93	61	,	,	PUNCT
cord-243070-0b06zk1q	93	62	y	y	PROPN
cord-243070-0b06zk1q	93	63	,	,	PUNCT
cord-243070-0b06zk1q	93	64	z	z	PROPN
cord-243070-0b06zk1q	93	65	∈	∈	NOUN
cord-243070-0b06zk1q	93	66	r	r	NOUN
cord-243070-0b06zk1q	93	67	2	2	NUM
cord-243070-0b06zk1q	93	68	,	,	PUNCT
cord-243070-0b06zk1q	93	69	and	and	CCONJ
cord-243070-0b06zk1q	93	70	the	the	DET
cord-243070-0b06zk1q	93	71	hamiltonian	hamiltonian	ADJ
cord-243070-0b06zk1q	93	72	function	function	NOUN
cord-243070-0b06zk1q	93	73	reads	read	VERB
cord-243070-0b06zk1q	93	74	:	:	PUNCT
cord-243070-0b06zk1q	93	75	we	we	PRON
cord-243070-0b06zk1q	93	76	consider	consider	VERB
cord-243070-0b06zk1q	93	77	the	the	DET
cord-243070-0b06zk1q	93	78	following	follow	VERB
cord-243070-0b06zk1q	93	79	system	system	NOUN
cord-243070-0b06zk1q	93	80	of	of	ADP
cord-243070-0b06zk1q	93	81	stochastic	stochastic	PROPN
cord-243070-0b06zk1q	93	82	hamilton	hamilton	PROPN
cord-243070-0b06zk1q	93	83	's	's	PART
cord-243070-0b06zk1q	93	84	equations	equation	NOUN
cord-243070-0b06zk1q	93	85	:	:	PUNCT
cord-243070-0b06zk1q	93	86	and	and	CCONJ
cord-243070-0b06zk1q	93	87	where	where	SCONJ
cord-243070-0b06zk1q	93	88	equation	equation	NOUN
cord-243070-0b06zk1q	93	89	(	(	PUNCT
cord-243070-0b06zk1q	93	90	26	26	NUM
cord-243070-0b06zk1q	93	91	)	)	PUNCT
cord-243070-0b06zk1q	93	92	is	be	AUX
cord-243070-0b06zk1q	93	93	merely	merely	ADV
cord-243070-0b06zk1q	93	94	an	an	DET
cord-243070-0b06zk1q	93	95	alternative	alternative	ADJ
cord-243070-0b06zk1q	93	96	way	way	NOUN
cord-243070-0b06zk1q	93	97	of	of	ADP
cord-243070-0b06zk1q	93	98	writing	write	VERB
cord-243070-0b06zk1q	93	99	the	the	DET
cord-243070-0b06zk1q	93	100	underlying	underlie	VERB
cord-243070-0b06zk1q	93	101	controlled	control	VERB
cord-243070-0b06zk1q	93	102	diffusion	diffusion	NOUN
cord-243070-0b06zk1q	93	103	process	process	NOUN
cord-243070-0b06zk1q	93	104	(	(	PUNCT
cord-243070-0b06zk1q	93	105	14	14	NUM
cord-243070-0b06zk1q	93	106	)	)	PUNCT
cord-243070-0b06zk1q	93	107	,	,	PUNCT
cord-243070-0b06zk1q	93	108	while	while	SCONJ
cord-243070-0b06zk1q	93	109	equation	equation	NOUN
cord-243070-0b06zk1q	93	110	(	(	PUNCT
cord-243070-0b06zk1q	93	111	27	27	NUM
cord-243070-0b06zk1q	93	112	)	)	PUNCT
cord-243070-0b06zk1q	93	113	reflects	reflect	VERB
cord-243070-0b06zk1q	93	114	the	the	DET
cord-243070-0b06zk1q	93	115	dynamics	dynamic	NOUN
cord-243070-0b06zk1q	93	116	of	of	ADP
cord-243070-0b06zk1q	93	117	the	the	DET
cord-243070-0b06zk1q	93	118	control	control	NOUN
cord-243070-0b06zk1q	93	119	variables	variable	NOUN
cord-243070-0b06zk1q	93	120	given	give	VERB
cord-243070-0b06zk1q	93	121	the	the	DET
cord-243070-0b06zk1q	93	122	running	running	NOUN
cord-243070-0b06zk1q	93	123	cost	cost	NOUN
cord-243070-0b06zk1q	93	124	function	function	NOUN
cord-243070-0b06zk1q	93	125	.	.	PUNCT
cord-243070-0b06zk1q	94	1	note	note	VERB
cord-243070-0b06zk1q	94	2	that	that	SCONJ
cord-243070-0b06zk1q	94	3	while	while	SCONJ
cord-243070-0b06zk1q	94	4	the	the	DET
cord-243070-0b06zk1q	94	5	first	first	ADJ
cord-243070-0b06zk1q	94	6	of	of	ADP
cord-243070-0b06zk1q	94	7	the	the	DET
cord-243070-0b06zk1q	94	8	equations	equation	NOUN
cord-243070-0b06zk1q	94	9	(	(	PUNCT
cord-243070-0b06zk1q	94	10	26	26	NUM
cord-243070-0b06zk1q	94	11	)	)	PUNCT
cord-243070-0b06zk1q	94	12	is	be	AUX
cord-243070-0b06zk1q	94	13	a	a	DET
cord-243070-0b06zk1q	94	14	standard	standard	ADJ
cord-243070-0b06zk1q	94	15	(	(	PUNCT
cord-243070-0b06zk1q	94	16	forward	forward	ADV
cord-243070-0b06zk1q	94	17	)	)	PUNCT
cord-243070-0b06zk1q	94	18	sde	sde	PROPN
cord-243070-0b06zk1q	94	19	,	,	PUNCT
cord-243070-0b06zk1q	94	20	the	the	DET
cord-243070-0b06zk1q	94	21	second	second	ADJ
cord-243070-0b06zk1q	94	22	one	one	NOUN
cord-243070-0b06zk1q	94	23	is	be	AUX
cord-243070-0b06zk1q	94	24	a	a	DET
cord-243070-0b06zk1q	94	25	backward	backward	ADJ
cord-243070-0b06zk1q	94	26	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	94	27	differential	differential	ADJ
cord-243070-0b06zk1q	94	28	equation	equation	NOUN
cord-243070-0b06zk1q	94	29	(	(	PUNCT
cord-243070-0b06zk1q	94	30	bsde	bsde	PROPN
cord-243070-0b06zk1q	94	31	)	)	PUNCT
cord-243070-0b06zk1q	94	32	,	,	PUNCT
cord-243070-0b06zk1q	94	33	see	see	VERB
cord-243070-0b06zk1q	94	34	e.g.	e.g.	ADV
cord-243070-0b06zk1q	94	35	[	[	X
cord-243070-0b06zk1q	94	36	9	9	NUM
cord-243070-0b06zk1q	94	37	]	]	PUNCT
cord-243070-0b06zk1q	94	38	.	.	PUNCT
cord-243070-0b06zk1q	95	1	explicitly	explicitly	ADV
cord-243070-0b06zk1q	95	2	,	,	PUNCT
cord-243070-0b06zk1q	95	3	these	these	DET
cord-243070-0b06zk1q	95	4	four	four	NUM
cord-243070-0b06zk1q	95	5	equations	equation	NOUN
cord-243070-0b06zk1q	95	6	can	can	AUX
cord-243070-0b06zk1q	95	7	be	be	AUX
cord-243070-0b06zk1q	95	8	stated	state	VERB
cord-243070-0b06zk1q	95	9	as	as	ADP
cord-243070-0b06zk1q	95	10	subject	subject	ADJ
cord-243070-0b06zk1q	95	11	to	to	ADP
cord-243070-0b06zk1q	95	12	the	the	DET
cord-243070-0b06zk1q	95	13	boundary	boundary	ADJ
cord-243070-0b06zk1q	95	14	conditions	condition	NOUN
cord-243070-0b06zk1q	95	15	in	in	ADP
cord-243070-0b06zk1q	95	16	(	(	PUNCT
cord-243070-0b06zk1q	95	17	26	26	NUM
cord-243070-0b06zk1q	95	18	)	)	PUNCT
cord-243070-0b06zk1q	95	19	.	.	PUNCT
cord-243070-0b06zk1q	96	1	then	then	ADV
cord-243070-0b06zk1q	96	2	u	u	PROPN
cord-243070-0b06zk1q	96	3	*	*	PUNCT
cord-243070-0b06zk1q	96	4	is	be	AUX
cord-243070-0b06zk1q	96	5	an	an	DET
cord-243070-0b06zk1q	96	6	optimal	optimal	ADJ
cord-243070-0b06zk1q	96	7	control	control	NOUN
cord-243070-0b06zk1q	96	8	,	,	PUNCT
cord-243070-0b06zk1q	96	9	i.e.	i.e.	X
cord-243070-0b06zk1q	96	10	it	it	PRON
cord-243070-0b06zk1q	96	11	satisfies	satisfy	VERB
cord-243070-0b06zk1q	96	12	the	the	DET
cord-243070-0b06zk1q	96	13	optimality	optimality	ADJ
cord-243070-0b06zk1q	96	14	condition	condition	NOUN
cord-243070-0b06zk1q	96	15	(	(	PUNCT
cord-243070-0b06zk1q	96	16	15	15	NUM
cord-243070-0b06zk1q	96	17	)	)	PUNCT
cord-243070-0b06zk1q	96	18	.	.	PUNCT
cord-243070-0b06zk1q	97	1	in	in	ADP
cord-243070-0b06zk1q	97	2	fact	fact	NOUN
cord-243070-0b06zk1q	97	3	,	,	PUNCT
cord-243070-0b06zk1q	97	4	there	there	PRON
cord-243070-0b06zk1q	97	5	is	be	VERB
cord-243070-0b06zk1q	97	6	a	a	DET
cord-243070-0b06zk1q	97	7	direct	direct	ADJ
cord-243070-0b06zk1q	97	8	link	link	NOUN
cord-243070-0b06zk1q	97	9	between	between	ADP
cord-243070-0b06zk1q	97	10	the	the	DET
cord-243070-0b06zk1q	97	11	hamilton	hamilton	PROPN
cord-243070-0b06zk1q	97	12	function	function	PROPN
cord-243070-0b06zk1q	97	13	h	h	PROPN
cord-243070-0b06zk1q	97	14	and	and	CCONJ
cord-243070-0b06zk1q	97	15	the	the	DET
cord-243070-0b06zk1q	97	16	value	value	NOUN
cord-243070-0b06zk1q	97	17	function	function	NOUN
cord-243070-0b06zk1q	97	18	j	j	PROPN
cord-243070-0b06zk1q	97	19	(	(	PUNCT
cord-243070-0b06zk1q	97	20	also	also	ADV
cord-243070-0b06zk1q	97	21	known	know	VERB
cord-243070-0b06zk1q	97	22	in	in	ADP
cord-243070-0b06zk1q	97	23	classical	classical	ADJ
cord-243070-0b06zk1q	97	24	dynamics	dynamic	NOUN
cord-243070-0b06zk1q	97	25	as	as	ADP
cord-243070-0b06zk1q	97	26	the	the	DET
cord-243070-0b06zk1q	97	27	action	action	NOUN
cord-243070-0b06zk1q	97	28	function	function	NOUN
cord-243070-0b06zk1q	97	29	)	)	PUNCT
cord-243070-0b06zk1q	97	30	.	.	PUNCT
cord-243070-0b06zk1q	98	1	namely	namely	ADV
cord-243070-0b06zk1q	98	2	,	,	PUNCT
cord-243070-0b06zk1q	98	3	we	we	PRON
cord-243070-0b06zk1q	98	4	set	set	VERB
cord-243070-0b06zk1q	98	5	[	[	PUNCT
cord-243070-0b06zk1q	98	6	21	21	NUM
cord-243070-0b06zk1q	98	7	]	]	PUNCT
cord-243070-0b06zk1q	98	8	,	,	PUNCT
cord-243070-0b06zk1q	98	9	[	[	X
cord-243070-0b06zk1q	98	10	23	23	NUM
cord-243070-0b06zk1q	98	11	]	]	PUNCT
cord-243070-0b06zk1q	98	12	:	:	PUNCT
cord-243070-0b06zk1q	98	13	if	if	SCONJ
cord-243070-0b06zk1q	98	14	u	u	PROPN
cord-243070-0b06zk1q	98	15	*	*	PUNCT
cord-243070-0b06zk1q	98	16	is	be	AUX
cord-243070-0b06zk1q	98	17	an	an	DET
cord-243070-0b06zk1q	98	18	optimal	optimal	ADJ
cord-243070-0b06zk1q	98	19	control	control	NOUN
cord-243070-0b06zk1q	98	20	and	and	CCONJ
cord-243070-0b06zk1q	98	21	x	x	X
cord-243070-0b06zk1q	98	22	*	*	PUNCT
cord-243070-0b06zk1q	98	23	denotes	denote	VERB
cord-243070-0b06zk1q	98	24	the	the	DET
cord-243070-0b06zk1q	98	25	corresponding	corresponding	ADJ
cord-243070-0b06zk1q	98	26	optimal	optimal	ADJ
cord-243070-0b06zk1q	98	27	diffusion	diffusion	NOUN
cord-243070-0b06zk1q	98	28	process	process	NOUN
cord-243070-0b06zk1q	98	29	,	,	PUNCT
cord-243070-0b06zk1q	98	30	then	then	ADV
cord-243070-0b06zk1q	98	31	the	the	DET
cord-243070-0b06zk1q	98	32	pair	pair	NOUN
cord-243070-0b06zk1q	98	33	is	be	AUX
cord-243070-0b06zk1q	98	34	the	the	DET
cord-243070-0b06zk1q	98	35	solution	solution	NOUN
cord-243070-0b06zk1q	98	36	to	to	ADP
cord-243070-0b06zk1q	98	37	the	the	DET
cord-243070-0b06zk1q	98	38	bsde	bsde	PROPN
cord-243070-0b06zk1q	98	39	(	(	PUNCT
cord-243070-0b06zk1q	98	40	27	27	NUM
cord-243070-0b06zk1q	98	41	)	)	PUNCT
cord-243070-0b06zk1q	98	42	.	.	PUNCT
cord-243070-0b06zk1q	99	1	going	go	VERB
cord-243070-0b06zk1q	99	2	back	back	ADV
cord-243070-0b06zk1q	99	3	to	to	ADP
cord-243070-0b06zk1q	99	4	the	the	DET
cord-243070-0b06zk1q	99	5	main	main	ADJ
cord-243070-0b06zk1q	99	6	line	line	NOUN
cord-243070-0b06zk1q	99	7	of	of	ADP
cord-243070-0b06zk1q	99	8	reasoning	reasoning	NOUN
cord-243070-0b06zk1q	99	9	,	,	PUNCT
cord-243070-0b06zk1q	99	10	we	we	PRON
cord-243070-0b06zk1q	99	11	find	find	VERB
cord-243070-0b06zk1q	99	12	that	that	SCONJ
cord-243070-0b06zk1q	99	13	u	u	PROPN
cord-243070-0b06zk1q	99	14	*	*	PUNCT
cord-243070-0b06zk1q	99	15	has	have	VERB
cord-243070-0b06zk1q	99	16	to	to	PART
cord-243070-0b06zk1q	99	17	satisfy	satisfy	VERB
cord-243070-0b06zk1q	99	18	from	from	ADP
cord-243070-0b06zk1q	99	19	equations	equation	NOUN
cord-243070-0b06zk1q	99	20	(	(	PUNCT
cord-243070-0b06zk1q	99	21	32	32	NUM
cord-243070-0b06zk1q	99	22	)	)	PUNCT
cord-243070-0b06zk1q	99	23	we	we	PRON
cord-243070-0b06zk1q	99	24	see	see	VERB
cord-243070-0b06zk1q	99	25	that	that	PRON
cord-243070-0b06zk1q	99	26	,	,	PUNCT
cord-243070-0b06zk1q	99	27	up	up	ADP
cord-243070-0b06zk1q	99	28	to	to	ADP
cord-243070-0b06zk1q	99	29	a	a	DET
cord-243070-0b06zk1q	99	30	simple	simple	ADJ
cord-243070-0b06zk1q	99	31	linear	linear	ADJ
cord-243070-0b06zk1q	99	32	transformation	transformation	NOUN
cord-243070-0b06zk1q	99	33	,	,	PUNCT
cord-243070-0b06zk1q	99	34	y	y	PROPN
cord-243070-0b06zk1q	99	35	t	t	PROPN
cord-243070-0b06zk1q	99	36	is	be	AUX
cord-243070-0b06zk1q	99	37	essentially	essentially	ADV
cord-243070-0b06zk1q	99	38	the	the	DET
cord-243070-0b06zk1q	99	39	optimal	optimal	ADJ
cord-243070-0b06zk1q	99	40	policy	policy	NOUN
cord-243070-0b06zk1q	99	41	.	.	PUNCT
cord-243070-0b06zk1q	100	1	furthermore	furthermore	ADV
cord-243070-0b06zk1q	100	2	,	,	PUNCT
cord-243070-0b06zk1q	100	3	the	the	DET
cord-243070-0b06zk1q	100	4	process	process	NOUN
cord-243070-0b06zk1q	100	5	z	z	NOUN
cord-243070-0b06zk1q	100	6	t	t	PROPN
cord-243070-0b06zk1q	100	7	can	can	AUX
cord-243070-0b06zk1q	100	8	be	be	AUX
cord-243070-0b06zk1q	100	9	thought	think	VERB
cord-243070-0b06zk1q	100	10	of	of	ADP
cord-243070-0b06zk1q	100	11	as	as	ADP
cord-243070-0b06zk1q	100	12	the	the	DET
cord-243070-0b06zk1q	100	13	sensitivity	sensitivity	NOUN
cord-243070-0b06zk1q	100	14	of	of	ADP
cord-243070-0b06zk1q	100	15	the	the	DET
cord-243070-0b06zk1q	100	16	optimal	optimal	ADJ
cord-243070-0b06zk1q	100	17	policy	policy	NOUN
cord-243070-0b06zk1q	100	18	to	to	ADP
cord-243070-0b06zk1q	100	19	the	the	DET
cord-243070-0b06zk1q	100	20	underlying	underlie	VERB
cord-243070-0b06zk1q	100	21	process	process	NOUN
cord-243070-0b06zk1q	100	22	x	x	SYM
cord-243070-0b06zk1q	100	23	t	t	PROPN
cord-243070-0b06zk1q	100	24	(	(	PUNCT
cord-243070-0b06zk1q	100	25	multiplied	multiply	VERB
cord-243070-0b06zk1q	100	26	by	by	ADP
cord-243070-0b06zk1q	100	27	the	the	DET
cord-243070-0b06zk1q	100	28	instantaneous	instantaneous	ADJ
cord-243070-0b06zk1q	100	29	volatility	volatility	NOUN
cord-243070-0b06zk1q	100	30	of	of	ADP
cord-243070-0b06zk1q	100	31	that	that	DET
cord-243070-0b06zk1q	100	32	process	process	NOUN
cord-243070-0b06zk1q	100	33	)	)	PUNCT
cord-243070-0b06zk1q	100	34	.	.	PUNCT
cord-243070-0b06zk1q	101	1	substituting	substitute	VERB
cord-243070-0b06zk1q	101	2	this	this	DET
cord-243070-0b06zk1q	101	3	expression	expression	NOUN
cord-243070-0b06zk1q	101	4	into	into	ADP
cord-243070-0b06zk1q	101	5	(	(	PUNCT
cord-243070-0b06zk1q	101	6	29	29	NUM
cord-243070-0b06zk1q	101	7	)	)	PUNCT
cord-243070-0b06zk1q	101	8	,	,	PUNCT
cord-243070-0b06zk1q	101	9	we	we	PRON
cord-243070-0b06zk1q	101	10	find	find	VERB
cord-243070-0b06zk1q	101	11	that	that	SCONJ
cord-243070-0b06zk1q	101	12	the	the	DET
cord-243070-0b06zk1q	101	13	optimal	optimal	ADJ
cord-243070-0b06zk1q	101	14	process	process	NOUN
cord-243070-0b06zk1q	101	15	has	have	VERB
cord-243070-0b06zk1q	101	16	to	to	PART
cord-243070-0b06zk1q	101	17	follow	follow	VERB
cord-243070-0b06zk1q	101	18	the	the	DET
cord-243070-0b06zk1q	101	19	dynamics	dynamic	NOUN
cord-243070-0b06zk1q	101	20	:	:	PUNCT
cord-243070-0b06zk1q	101	21	subject	subject	ADJ
cord-243070-0b06zk1q	101	22	to	to	ADP
cord-243070-0b06zk1q	101	23	the	the	DET
cord-243070-0b06zk1q	101	24	boundary	boundary	ADJ
cord-243070-0b06zk1q	101	25	conditions	condition	NOUN
cord-243070-0b06zk1q	101	26	in	in	ADP
cord-243070-0b06zk1q	101	27	(	(	PUNCT
cord-243070-0b06zk1q	101	28	26	26	NUM
cord-243070-0b06zk1q	101	29	)	)	PUNCT
cord-243070-0b06zk1q	101	30	and	and	CCONJ
cord-243070-0b06zk1q	101	31	(	(	PUNCT
cord-243070-0b06zk1q	101	32	27	27	NUM
cord-243070-0b06zk1q	101	33	)	)	PUNCT
cord-243070-0b06zk1q	101	34	.	.	PUNCT
cord-243070-0b06zk1q	102	1	in	in	ADP
cord-243070-0b06zk1q	102	2	particular	particular	ADJ
cord-243070-0b06zk1q	102	3	,	,	PUNCT
cord-243070-0b06zk1q	102	4	the	the	DET
cord-243070-0b06zk1q	102	5	isolation	isolation	NOUN
cord-243070-0b06zk1q	102	6	only	only	ADV
cord-243070-0b06zk1q	102	7	and	and	CCONJ
cord-243070-0b06zk1q	102	8	vaccination	vaccination	NOUN
cord-243070-0b06zk1q	102	9	only	only	ADV
cord-243070-0b06zk1q	102	10	policies	policy	NOUN
cord-243070-0b06zk1q	102	11	are	be	AUX
cord-243070-0b06zk1q	102	12	given	give	VERB
cord-243070-0b06zk1q	102	13	by	by	ADP
cord-243070-0b06zk1q	102	14	the	the	DET
cord-243070-0b06zk1q	102	15	following	follow	VERB
cord-243070-0b06zk1q	102	16	systems	system	NOUN
cord-243070-0b06zk1q	102	17	of	of	ADP
cord-243070-0b06zk1q	102	18	fbsdes	fbsde	NOUN
cord-243070-0b06zk1q	102	19	:	:	PUNCT
cord-243070-0b06zk1q	102	20	and	and	CCONJ
cord-243070-0b06zk1q	102	21	respectively	respectively	ADV
cord-243070-0b06zk1q	102	22	.	.	PUNCT
cord-243070-0b06zk1q	103	1	even	even	ADV
cord-243070-0b06zk1q	103	2	though	though	SCONJ
cord-243070-0b06zk1q	103	3	derived	derive	VERB
cord-243070-0b06zk1q	103	4	in	in	ADP
cord-243070-0b06zk1q	103	5	the	the	DET
cord-243070-0b06zk1q	103	6	context	context	NOUN
cord-243070-0b06zk1q	103	7	of	of	ADP
cord-243070-0b06zk1q	103	8	a	a	DET
cord-243070-0b06zk1q	103	9	meaningful	meaningful	ADJ
cord-243070-0b06zk1q	103	10	underlying	underlying	ADJ
cord-243070-0b06zk1q	103	11	dynamics	dynamic	NOUN
cord-243070-0b06zk1q	103	12	,	,	PUNCT
cord-243070-0b06zk1q	103	13	there	there	PRON
cord-243070-0b06zk1q	103	14	is	be	VERB
cord-243070-0b06zk1q	103	15	no	no	DET
cord-243070-0b06zk1q	103	16	a	a	DET
cord-243070-0b06zk1q	103	17	priori	priori	ADJ
cord-243070-0b06zk1q	103	18	reason	reason	NOUN
cord-243070-0b06zk1q	103	19	why	why	SCONJ
cord-243070-0b06zk1q	103	20	these	these	DET
cord-243070-0b06zk1q	103	21	equations	equation	NOUN
cord-243070-0b06zk1q	103	22	should	should	AUX
cord-243070-0b06zk1q	103	23	have	have	VERB
cord-243070-0b06zk1q	103	24	solutions	solution	NOUN
cord-243070-0b06zk1q	103	25	.	.	PUNCT
cord-243070-0b06zk1q	104	1	the	the	DET
cord-243070-0b06zk1q	104	2	drivers	driver	NOUN
cord-243070-0b06zk1q	104	3	of	of	ADP
cord-243070-0b06zk1q	104	4	the	the	DET
cord-243070-0b06zk1q	104	5	backward	backward	ADJ
cord-243070-0b06zk1q	104	6	equations	equation	NOUN
cord-243070-0b06zk1q	104	7	above	above	ADV
cord-243070-0b06zk1q	104	8	contain	contain	VERB
cord-243070-0b06zk1q	104	9	terms	term	NOUN
cord-243070-0b06zk1q	104	10	quadratic	quadratic	ADJ
cord-243070-0b06zk1q	104	11	in	in	ADP
cord-243070-0b06zk1q	104	12	y	y	PROPN
cord-243070-0b06zk1q	104	13	,	,	PUNCT
cord-243070-0b06zk1q	104	14	and	and	CCONJ
cord-243070-0b06zk1q	104	15	so	so	ADV
cord-243070-0b06zk1q	104	16	the	the	DET
cord-243070-0b06zk1q	104	17	standard	standard	ADJ
cord-243070-0b06zk1q	104	18	existence	existence	NOUN
cord-243070-0b06zk1q	104	19	theorems	theorem	VERB
cord-243070-0b06zk1q	104	20	[	[	X
cord-243070-0b06zk1q	104	21	9	9	NUM
cord-243070-0b06zk1q	104	22	]	]	X
cord-243070-0b06zk1q	104	23	do	do	AUX
cord-243070-0b06zk1q	104	24	not	not	PART
cord-243070-0b06zk1q	104	25	apply	apply	VERB
cord-243070-0b06zk1q	104	26	.	.	PUNCT
cord-243070-0b06zk1q	105	1	we	we	PRON
cord-243070-0b06zk1q	105	2	proceed	proceed	VERB
cord-243070-0b06zk1q	105	3	in	in	ADP
cord-243070-0b06zk1q	105	4	the	the	DET
cord-243070-0b06zk1q	105	5	following	following	NOUN
cord-243070-0b06zk1q	105	6	assuming	assume	VERB
cord-243070-0b06zk1q	105	7	that	that	SCONJ
cord-243070-0b06zk1q	105	8	these	these	DET
cord-243070-0b06zk1q	105	9	systems	system	NOUN
cord-243070-0b06zk1q	105	10	do	do	AUX
cord-243070-0b06zk1q	105	11	,	,	PUNCT
cord-243070-0b06zk1q	105	12	in	in	ADP
cord-243070-0b06zk1q	105	13	fact	fact	NOUN
cord-243070-0b06zk1q	105	14	,	,	PUNCT
cord-243070-0b06zk1q	105	15	have	have	VERB
cord-243070-0b06zk1q	105	16	solutions	solution	NOUN
cord-243070-0b06zk1q	105	17	.	.	PUNCT
cord-243070-0b06zk1q	106	1	in	in	ADP
cord-243070-0b06zk1q	106	2	this	this	DET
cord-243070-0b06zk1q	106	3	section	section	NOUN
cord-243070-0b06zk1q	106	4	we	we	PRON
cord-243070-0b06zk1q	106	5	discuss	discuss	VERB
cord-243070-0b06zk1q	106	6	a	a	DET
cord-243070-0b06zk1q	106	7	numerical	numerical	ADJ
cord-243070-0b06zk1q	106	8	algorithm	algorithm	NOUN
cord-243070-0b06zk1q	106	9	for	for	ADP
cord-243070-0b06zk1q	106	10	solving	solve	VERB
cord-243070-0b06zk1q	106	11	the	the	DET
cord-243070-0b06zk1q	106	12	system	system	NOUN
cord-243070-0b06zk1q	106	13	(	(	PUNCT
cord-243070-0b06zk1q	106	14	34	34	NUM
cord-243070-0b06zk1q	106	15	)	)	PUNCT
cord-243070-0b06zk1q	106	16	.	.	PUNCT
cord-243070-0b06zk1q	107	1	applying	apply	VERB
cord-243070-0b06zk1q	107	2	this	this	DET
cord-243070-0b06zk1q	107	3	methodology	methodology	NOUN
cord-243070-0b06zk1q	107	4	in	in	ADP
cord-243070-0b06zk1q	107	5	a	a	DET
cord-243070-0b06zk1q	107	6	number	number	NOUN
cord-243070-0b06zk1q	107	7	of	of	ADP
cord-243070-0b06zk1q	107	8	numerical	numerical	ADJ
cord-243070-0b06zk1q	107	9	experiments	experiment	NOUN
cord-243070-0b06zk1q	107	10	,	,	PUNCT
cord-243070-0b06zk1q	107	11	we	we	PRON
cord-243070-0b06zk1q	107	12	present	present	VERB
cord-243070-0b06zk1q	107	13	compelling	compelling	ADJ
cord-243070-0b06zk1q	107	14	evidence	evidence	NOUN
cord-243070-0b06zk1q	107	15	that	that	PRON
cord-243070-0b06zk1q	107	16	solutions	solution	VERB
cord-243070-0b06zk1q	107	17	to	to	ADP
cord-243070-0b06zk1q	107	18	(	(	PUNCT
cord-243070-0b06zk1q	107	19	34	34	NUM
cord-243070-0b06zk1q	107	20	)	)	PUNCT
cord-243070-0b06zk1q	107	21	exist	exist	VERB
cord-243070-0b06zk1q	107	22	and	and	CCONJ
cord-243070-0b06zk1q	107	23	are	be	AUX
cord-243070-0b06zk1q	107	24	meaningful	meaningful	ADJ
cord-243070-0b06zk1q	107	25	over	over	ADP
cord-243070-0b06zk1q	107	26	a	a	DET
cord-243070-0b06zk1q	107	27	wide	wide	ADJ
cord-243070-0b06zk1q	107	28	range	range	NOUN
cord-243070-0b06zk1q	107	29	of	of	ADP
cord-243070-0b06zk1q	107	30	model	model	NOUN
cord-243070-0b06zk1q	107	31	parameters	parameter	NOUN
cord-243070-0b06zk1q	107	32	.	.	PUNCT
cord-243070-0b06zk1q	108	1	we	we	PRON
cord-243070-0b06zk1q	108	2	start	start	VERB
cord-243070-0b06zk1q	108	3	by	by	ADP
cord-243070-0b06zk1q	108	4	describing	describe	VERB
cord-243070-0b06zk1q	108	5	a	a	DET
cord-243070-0b06zk1q	108	6	method	method	NOUN
cord-243070-0b06zk1q	108	7	for	for	ADP
cord-243070-0b06zk1q	108	8	discretization	discretization	NOUN
cord-243070-0b06zk1q	108	9	of	of	ADP
cord-243070-0b06zk1q	108	10	the	the	DET
cord-243070-0b06zk1q	108	11	basic	basic	ADJ
cord-243070-0b06zk1q	108	12	fbsde	fbsde	PROPN
cord-243070-0b06zk1q	108	13	system	system	NOUN
cord-243070-0b06zk1q	108	14	(	(	PUNCT
cord-243070-0b06zk1q	108	15	34	34	NUM
cord-243070-0b06zk1q	108	16	)	)	PUNCT
cord-243070-0b06zk1q	108	17	.	.	PUNCT
cord-243070-0b06zk1q	109	1	we	we	PRON
cord-243070-0b06zk1q	109	2	notice	notice	VERB
cord-243070-0b06zk1q	109	3	first	first	ADV
cord-243070-0b06zk1q	109	4	that	that	SCONJ
cord-243070-0b06zk1q	109	5	the	the	DET
cord-243070-0b06zk1q	109	6	two	two	NUM
cord-243070-0b06zk1q	109	7	dimensional	dimensional	ADJ
cord-243070-0b06zk1q	109	8	system	system	NOUN
cord-243070-0b06zk1q	109	9	defined	define	VERB
cord-243070-0b06zk1q	109	10	by	by	ADP
cord-243070-0b06zk1q	109	11	the	the	DET
cord-243070-0b06zk1q	109	12	state	state	NOUN
cord-243070-0b06zk1q	109	13	variables	variable	NOUN
cord-243070-0b06zk1q	109	14	s	s	PROPN
cord-243070-0b06zk1q	109	15	,	,	PUNCT
cord-243070-0b06zk1q	109	16	i	i	PRON
cord-243070-0b06zk1q	109	17	is	be	AUX
cord-243070-0b06zk1q	109	18	in	in	ADP
cord-243070-0b06zk1q	109	19	fact	fact	NOUN
cord-243070-0b06zk1q	109	20	hamiltonian	hamiltonian	ADJ
cord-243070-0b06zk1q	110	1	[	[	X
cord-243070-0b06zk1q	110	2	17	17	NUM
cord-243070-0b06zk1q	110	3	]	]	PUNCT
cord-243070-0b06zk1q	110	4	.	.	PUNCT
cord-243070-0b06zk1q	111	1	namely	namely	ADV
cord-243070-0b06zk1q	111	2	,	,	PUNCT
cord-243070-0b06zk1q	111	3	we	we	PRON
cord-243070-0b06zk1q	111	4	define	define	VERB
cord-243070-0b06zk1q	111	5	new	new	ADJ
cord-243070-0b06zk1q	111	6	(	(	PUNCT
cord-243070-0b06zk1q	111	7	canonical	canonical	ADJ
cord-243070-0b06zk1q	111	8	)	)	PUNCT
cord-243070-0b06zk1q	111	9	variables	variable	NOUN
cord-243070-0b06zk1q	111	10	and	and	CCONJ
cord-243070-0b06zk1q	111	11	it	it	PRON
cord-243070-0b06zk1q	111	12	is	be	AUX
cord-243070-0b06zk1q	111	13	easy	easy	ADJ
cord-243070-0b06zk1q	111	14	to	to	PART
cord-243070-0b06zk1q	111	15	verify	verify	VERB
cord-243070-0b06zk1q	111	16	that	that	SCONJ
cord-243070-0b06zk1q	111	17	d	d	PROPN
cord-243070-0b06zk1q	111	18	dt	dt	PROPN
cord-243070-0b06zk1q	111	19	under	under	ADP
cord-243070-0b06zk1q	111	20	the	the	DET
cord-243070-0b06zk1q	111	21	dynamics	dynamic	NOUN
cord-243070-0b06zk1q	111	22	(	(	PUNCT
cord-243070-0b06zk1q	111	23	1	1	NUM
cord-243070-0b06zk1q	111	24	)	)	PUNCT
cord-243070-0b06zk1q	111	25	.	.	PUNCT
cord-243070-0b06zk1q	112	1	the	the	DET
cord-243070-0b06zk1q	112	2	system	system	NOUN
cord-243070-0b06zk1q	112	3	(	(	PUNCT
cord-243070-0b06zk1q	112	4	1	1	NUM
cord-243070-0b06zk1q	112	5	)	)	PUNCT
cord-243070-0b06zk1q	112	6	can	can	AUX
cord-243070-0b06zk1q	112	7	be	be	AUX
cord-243070-0b06zk1q	112	8	explicitly	explicitly	ADV
cord-243070-0b06zk1q	112	9	written	write	VERB
cord-243070-0b06zk1q	112	10	in	in	ADP
cord-243070-0b06zk1q	112	11	the	the	DET
cord-243070-0b06zk1q	112	12	hamilton	hamilton	PROPN
cord-243070-0b06zk1q	112	13	forṁ	forṁ	PROPN
cord-243070-0b06zk1q	112	14	notice	notice	VERB
cord-243070-0b06zk1q	112	15	also	also	ADV
cord-243070-0b06zk1q	112	16	that	that	SCONJ
cord-243070-0b06zk1q	112	17	the	the	DET
cord-243070-0b06zk1q	112	18	hamiltonian	hamiltonian	ADJ
cord-243070-0b06zk1q	112	19	function	function	NOUN
cord-243070-0b06zk1q	112	20	is	be	AUX
cord-243070-0b06zk1q	112	21	separable	separable	ADJ
cord-243070-0b06zk1q	112	22	,	,	PUNCT
cord-243070-0b06zk1q	112	23	i.e.	i.e.	X
cord-243070-0b06zk1q	112	24	it	it	PRON
cord-243070-0b06zk1q	112	25	is	be	AUX
cord-243070-0b06zk1q	112	26	of	of	ADP
cord-243070-0b06zk1q	112	27	the	the	DET
cord-243070-0b06zk1q	112	28	form	form	NOUN
cord-243070-0b06zk1q	112	29	h(p	h(p	NOUN
cord-243070-0b06zk1q	112	30	,	,	PUNCT
cord-243070-0b06zk1q	112	31	q	q	NOUN
cord-243070-0b06zk1q	112	32	)	)	PUNCT
cord-243070-0b06zk1q	112	33	=	=	NOUN
cord-243070-0b06zk1q	112	34	t	t	NOUN
cord-243070-0b06zk1q	112	35	(	(	PUNCT
cord-243070-0b06zk1q	112	36	p	p	NOUN
cord-243070-0b06zk1q	112	37	)	)	PUNCT
cord-243070-0b06zk1q	112	38	+	+	NOUN
cord-243070-0b06zk1q	113	1	v	v	X
cord-243070-0b06zk1q	114	1	(	(	PUNCT
cord-243070-0b06zk1q	114	2	q	q	NOUN
cord-243070-0b06zk1q	114	3	)	)	PUNCT
cord-243070-0b06zk1q	114	4	4	4	NUM
cord-243070-0b06zk1q	114	5	.	.	PUNCT
cord-243070-0b06zk1q	115	1	a	a	DET
cord-243070-0b06zk1q	115	2	convenient	convenient	ADJ
cord-243070-0b06zk1q	115	3	discretization	discretization	NOUN
cord-243070-0b06zk1q	115	4	to	to	ADP
cord-243070-0b06zk1q	115	5	(	(	PUNCT
cord-243070-0b06zk1q	115	6	6	6	NUM
cord-243070-0b06zk1q	115	7	)	)	PUNCT
cord-243070-0b06zk1q	115	8	can	can	AUX
cord-243070-0b06zk1q	115	9	be	be	AUX
cord-243070-0b06zk1q	115	10	formulated	formulate	VERB
cord-243070-0b06zk1q	115	11	in	in	ADP
cord-243070-0b06zk1q	115	12	terms	term	NOUN
cord-243070-0b06zk1q	115	13	of	of	ADP
cord-243070-0b06zk1q	115	14	the	the	DET
cord-243070-0b06zk1q	115	15	canonical	canonical	ADJ
cord-243070-0b06zk1q	115	16	variables	variable	NOUN
cord-243070-0b06zk1q	115	17	(	(	PUNCT
cord-243070-0b06zk1q	115	18	p	p	PROPN
cord-243070-0b06zk1q	115	19	t	t	PROPN
cord-243070-0b06zk1q	115	20	,	,	PUNCT
cord-243070-0b06zk1q	115	21	q	q	NOUN
cord-243070-0b06zk1q	115	22	t	t	NOUN
cord-243070-0b06zk1q	115	23	)	)	PUNCT
cord-243070-0b06zk1q	115	24	=	=	PROPN
cord-243070-0b06zk1q	115	25	(	(	PUNCT
cord-243070-0b06zk1q	115	26	−	−	PROPN
cord-243070-0b06zk1q	115	27	log	log	PROPN
cord-243070-0b06zk1q	115	28	x	x	SYM
cord-243070-0b06zk1q	115	29	2,t	2,t	NUM
cord-243070-0b06zk1q	115	30	,	,	PUNCT
cord-243070-0b06zk1q	115	31	−	−	PROPN
cord-243070-0b06zk1q	115	32	log	log	PROPN
cord-243070-0b06zk1q	115	33	x	x	SYM
cord-243070-0b06zk1q	115	34	1,t	1,t	NOUN
cord-243070-0b06zk1q	115	35	)	)	PUNCT
cord-243070-0b06zk1q	115	36	as	as	SCONJ
cord-243070-0b06zk1q	115	37	follows	follow	VERB
cord-243070-0b06zk1q	115	38	[	[	X
cord-243070-0b06zk1q	115	39	18	18	NUM
cord-243070-0b06zk1q	115	40	]	]	PUNCT
cord-243070-0b06zk1q	115	41	.	.	PUNCT
cord-243070-0b06zk1q	116	1	choose	choose	VERB
cord-243070-0b06zk1q	116	2	the	the	DET
cord-243070-0b06zk1q	116	3	number	number	NOUN
cord-243070-0b06zk1q	116	4	of	of	ADP
cord-243070-0b06zk1q	116	5	steps	step	NOUN
cord-243070-0b06zk1q	116	6	n	n	ADV
cord-243070-0b06zk1q	116	7	,	,	PUNCT
cord-243070-0b06zk1q	116	8	define	define	VERB
cord-243070-0b06zk1q	116	9	the	the	DET
cord-243070-0b06zk1q	116	10	time	time	NOUN
cord-243070-0b06zk1q	116	11	step	step	NOUN
cord-243070-0b06zk1q	116	12	δ	δ	NOUN
cord-243070-0b06zk1q	116	13	=	=	SYM
cord-243070-0b06zk1q	116	14	t	t	NOUN
cord-243070-0b06zk1q	116	15	/n	/n	PUNCT
cord-243070-0b06zk1q	116	16	,	,	PUNCT
cord-243070-0b06zk1q	116	17	set	set	VERB
cord-243070-0b06zk1q	116	18	t	t	PROPN
cord-243070-0b06zk1q	116	19	n	n	PROPN
cord-243070-0b06zk1q	116	20	=	=	PROPN
cord-243070-0b06zk1q	116	21	nδ	nδ	PROPN
cord-243070-0b06zk1q	116	22	for	for	ADP
cord-243070-0b06zk1q	116	23	n	n	PRON
cord-243070-0b06zk1q	116	24	=	=	NOUN
cord-243070-0b06zk1q	116	25	0	0	NUM
cord-243070-0b06zk1q	116	26	,	,	PUNCT
cord-243070-0b06zk1q	116	27	1	1	NUM
cord-243070-0b06zk1q	116	28	,	,	PUNCT
cord-243070-0b06zk1q	116	29	.	.	PUNCT
cord-243070-0b06zk1q	116	30	.	.	PUNCT
cord-243070-0b06zk1q	116	31	.	.	PUNCT
cord-243070-0b06zk1q	116	32	,	,	PUNCT
cord-243070-0b06zk1q	116	33	n	n	X
cord-243070-0b06zk1q	116	34	,	,	PUNCT
cord-243070-0b06zk1q	116	35	and	and	CCONJ
cord-243070-0b06zk1q	116	36	use	use	VERB
cord-243070-0b06zk1q	116	37	simplified	simplify	VERB
cord-243070-0b06zk1q	116	38	(	(	PUNCT
cord-243070-0b06zk1q	116	39	p	p	PROPN
cord-243070-0b06zk1q	116	40	n	n	PROPN
cord-243070-0b06zk1q	116	41	,	,	PUNCT
cord-243070-0b06zk1q	116	42	q	q	NOUN
cord-243070-0b06zk1q	116	43	n	n	NOUN
cord-243070-0b06zk1q	116	44	)	)	PUNCT
cord-243070-0b06zk1q	116	45	≡	≡	PROPN
cord-243070-0b06zk1q	116	46	(	(	PUNCT
cord-243070-0b06zk1q	116	47	p	p	PROPN
cord-243070-0b06zk1q	116	48	tn	tn	PROPN
cord-243070-0b06zk1q	116	49	,	,	PUNCT
cord-243070-0b06zk1q	116	50	q	q	PROPN
cord-243070-0b06zk1q	116	51	tn	tn	PROPN
cord-243070-0b06zk1q	116	52	)	)	PUNCT
cord-243070-0b06zk1q	116	53	.	.	PUNCT
cord-243070-0b06zk1q	117	1	this	this	PRON
cord-243070-0b06zk1q	117	2	yields	yield	VERB
cord-243070-0b06zk1q	117	3	the	the	DET
cord-243070-0b06zk1q	117	4	following	follow	VERB
cord-243070-0b06zk1q	117	5	euler	euler	NOUN
cord-243070-0b06zk1q	117	6	scheme	scheme	NOUN
cord-243070-0b06zk1q	117	7	:	:	PUNCT
cord-243070-0b06zk1q	117	8	for	for	ADP
cord-243070-0b06zk1q	117	9	n	n	NOUN
cord-243070-0b06zk1q	117	10	=	=	NOUN
cord-243070-0b06zk1q	117	11	0	0	NUM
cord-243070-0b06zk1q	117	12	,	,	PUNCT
cord-243070-0b06zk1q	117	13	1	1	NUM
cord-243070-0b06zk1q	117	14	,	,	PUNCT
cord-243070-0b06zk1q	117	15	.	.	PUNCT
cord-243070-0b06zk1q	117	16	.	.	PUNCT
cord-243070-0b06zk1q	117	17	.	.	PUNCT
cord-243070-0b06zk1q	118	1	,	,	PUNCT
cord-243070-0b06zk1q	118	2	n	n	ADV
cord-243070-0b06zk1q	118	3	−	−	PROPN
cord-243070-0b06zk1q	118	4	1	1	NUM
cord-243070-0b06zk1q	118	5	.	.	PUNCT
cord-243070-0b06zk1q	119	1	here	here	ADV
cord-243070-0b06zk1q	119	2	,	,	PUNCT
cord-243070-0b06zk1q	119	3	the	the	DET
cord-243070-0b06zk1q	119	4	brownian	brownian	ADJ
cord-243070-0b06zk1q	119	5	motion	motion	NOUN
cord-243070-0b06zk1q	119	6	increments	increment	NOUN
cord-243070-0b06zk1q	119	7	∆w	∆w	PROPN
cord-243070-0b06zk1q	119	8	=	=	SYM
cord-243070-0b06zk1q	119	9	w	w	PROPN
cord-243070-0b06zk1q	119	10	(	(	PUNCT
cord-243070-0b06zk1q	119	11	n+1)δ	n+1)δ	PROPN
cord-243070-0b06zk1q	119	12	−	−	PROPN
cord-243070-0b06zk1q	119	13	w	w	PROPN
cord-243070-0b06zk1q	119	14	nδ	nδ	PROPN
cord-243070-0b06zk1q	119	15	are	be	AUX
cord-243070-0b06zk1q	119	16	independent	independent	ADJ
cord-243070-0b06zk1q	119	17	variates	variate	NOUN
cord-243070-0b06zk1q	119	18	drawn	draw	VERB
cord-243070-0b06zk1q	119	19	from	from	ADP
cord-243070-0b06zk1q	119	20	the	the	DET
cord-243070-0b06zk1q	119	21	normal	normal	ADJ
cord-243070-0b06zk1q	119	22	distribution	distribution	NOUN
cord-243070-0b06zk1q	119	23	n	n	NOUN
cord-243070-0b06zk1q	119	24	(	(	PUNCT
cord-243070-0b06zk1q	119	25	0	0	NUM
cord-243070-0b06zk1q	119	26	,	,	PUNCT
cord-243070-0b06zk1q	119	27	δ	δ	PROPN
cord-243070-0b06zk1q	119	28	)	)	PUNCT
cord-243070-0b06zk1q	119	29	.	.	PUNCT
cord-243070-0b06zk1q	120	1	at	at	ADP
cord-243070-0b06zk1q	120	2	each	each	DET
cord-243070-0b06zk1q	120	3	iteration	iteration	NOUN
cord-243070-0b06zk1q	120	4	step	step	NOUN
cord-243070-0b06zk1q	120	5	also	also	ADV
cord-243070-0b06zk1q	120	6	have	have	VERB
cord-243070-0b06zk1q	120	7	to	to	PART
cord-243070-0b06zk1q	120	8	to	to	PART
cord-243070-0b06zk1q	120	9	floor	floor	VERB
cord-243070-0b06zk1q	120	10	q	q	NOUN
cord-243070-0b06zk1q	120	11	n+1	n+1	PROPN
cord-243070-0b06zk1q	120	12	and	and	CCONJ
cord-243070-0b06zk1q	120	13	p	p	NOUN
cord-243070-0b06zk1q	120	14	n+1	n+1	PROPN
cord-243070-0b06zk1q	120	15	at	at	ADP
cord-243070-0b06zk1q	120	16	0	0	NUM
cord-243070-0b06zk1q	120	17	,	,	PUNCT
cord-243070-0b06zk1q	120	18	q	q	NOUN
cord-243070-0b06zk1q	120	19	n+1	n+1	NOUN
cord-243070-0b06zk1q	120	20	=	=	SYM
cord-243070-0b06zk1q	120	21	max(q	max(q	X
cord-243070-0b06zk1q	120	22	n+1	n+1	NUM
cord-243070-0b06zk1q	120	23	,	,	PUNCT
cord-243070-0b06zk1q	120	24	0	0	NUM
cord-243070-0b06zk1q	120	25	)	)	PUNCT
cord-243070-0b06zk1q	120	26	,	,	PUNCT
cord-243070-0b06zk1q	120	27	p	p	PROPN
cord-243070-0b06zk1q	120	28	n+1	n+1	PROPN
cord-243070-0b06zk1q	120	29	=	=	SYM
cord-243070-0b06zk1q	120	30	max(p	max(p	X
cord-243070-0b06zk1q	120	31	n+1	n+1	PROPN
cord-243070-0b06zk1q	120	32	,	,	PUNCT
cord-243070-0b06zk1q	120	33	0	0	NUM
cord-243070-0b06zk1q	120	34	)	)	PUNCT
cord-243070-0b06zk1q	120	35	,	,	PUNCT
cord-243070-0b06zk1q	120	36	so	so	SCONJ
cord-243070-0b06zk1q	120	37	that	that	SCONJ
cord-243070-0b06zk1q	120	38	e	e	PROPN
cord-243070-0b06zk1q	120	39	−qn	−qn	PROPN
cord-243070-0b06zk1q	120	40	,	,	PUNCT
cord-243070-0b06zk1q	120	41	e	e	NOUN
cord-243070-0b06zk1q	120	42	−pn	−pn	PROPN
cord-243070-0b06zk1q	120	43	≤	≤	PROPN
cord-243070-0b06zk1q	120	44	1	1	NUM
cord-243070-0b06zk1q	120	45	.	.	PUNCT
cord-243070-0b06zk1q	121	1	approximating	approximate	VERB
cord-243070-0b06zk1q	121	2	the	the	DET
cord-243070-0b06zk1q	121	3	backward	backward	ADJ
cord-243070-0b06zk1q	121	4	equations	equation	NOUN
cord-243070-0b06zk1q	121	5	of	of	ADP
cord-243070-0b06zk1q	121	6	the	the	DET
cord-243070-0b06zk1q	121	7	system	system	NOUN
cord-243070-0b06zk1q	121	8	(	(	PUNCT
cord-243070-0b06zk1q	121	9	34	34	NUM
cord-243070-0b06zk1q	121	10	)	)	PUNCT
cord-243070-0b06zk1q	121	11	leads	lead	VERB
cord-243070-0b06zk1q	121	12	to	to	ADP
cord-243070-0b06zk1q	121	13	the	the	DET
cord-243070-0b06zk1q	121	14	following	follow	VERB
cord-243070-0b06zk1q	121	15	backward	backward	PROPN
cord-243070-0b06zk1q	121	16	euler	euler	NOUN
cord-243070-0b06zk1q	121	17	scheme	scheme	NOUN
cord-243070-0b06zk1q	121	18	:	:	PUNCT
cord-243070-0b06zk1q	121	19	where	where	SCONJ
cord-243070-0b06zk1q	121	20	denote	denote	ADJ
cord-243070-0b06zk1q	121	21	the	the	DET
cord-243070-0b06zk1q	121	22	generators	generator	NOUN
cord-243070-0b06zk1q	121	23	of	of	ADP
cord-243070-0b06zk1q	121	24	the	the	DET
cord-243070-0b06zk1q	121	25	two	two	NUM
cord-243070-0b06zk1q	121	26	bsdes	bsde	NOUN
cord-243070-0b06zk1q	121	27	.	.	PUNCT
cord-243070-0b06zk1q	122	1	starting	start	VERB
cord-243070-0b06zk1q	122	2	with	with	ADP
cord-243070-0b06zk1q	122	3	the	the	DET
cord-243070-0b06zk1q	122	4	terminal	terminal	ADJ
cord-243070-0b06zk1q	122	5	condition	condition	NOUN
cord-243070-0b06zk1q	122	6	we	we	PRON
cord-243070-0b06zk1q	122	7	will	will	AUX
cord-243070-0b06zk1q	122	8	move	move	VERB
cord-243070-0b06zk1q	122	9	backward	backward	ADV
cord-243070-0b06zk1q	122	10	in	in	ADP
cord-243070-0b06zk1q	122	11	time	time	NOUN
cord-243070-0b06zk1q	122	12	with	with	ADP
cord-243070-0b06zk1q	122	13	computing	computing	PROPN
cord-243070-0b06zk1q	122	14	y	y	PROPN
cord-243070-0b06zk1q	122	15	n	n	PROPN
cord-243070-0b06zk1q	122	16	and	and	CCONJ
cord-243070-0b06zk1q	122	17	z	z	PROPN
cord-243070-0b06zk1q	122	18	n	n	ADV
cord-243070-0b06zk1q	122	19	,	,	PUNCT
cord-243070-0b06zk1q	122	20	for	for	ADP
cord-243070-0b06zk1q	122	21	n	n	PRON
cord-243070-0b06zk1q	122	22	=	=	PROPN
cord-243070-0b06zk1q	122	23	n	n	NOUN
cord-243070-0b06zk1q	122	24	−	−	PROPN
cord-243070-0b06zk1q	122	25	1	1	NUM
cord-243070-0b06zk1q	122	26	,	,	PUNCT
cord-243070-0b06zk1q	122	27	.	.	PUNCT
cord-243070-0b06zk1q	122	28	.	.	PUNCT
cord-243070-0b06zk1q	122	29	.	.	PUNCT
cord-243070-0b06zk1q	123	1	,	,	PUNCT
cord-243070-0b06zk1q	123	2	0	0	X
cord-243070-0b06zk1q	123	3	.	.	PUNCT
cord-243070-0b06zk1q	123	4	notice	notice	VERB
cord-243070-0b06zk1q	123	5	that	that	SCONJ
cord-243070-0b06zk1q	123	6	two	two	NUM
cord-243070-0b06zk1q	123	7	difficulties	difficulty	NOUN
cord-243070-0b06zk1q	123	8	arise	arise	VERB
cord-243070-0b06zk1q	123	9	while	while	SCONJ
cord-243070-0b06zk1q	123	10	doing	do	VERB
cord-243070-0b06zk1q	123	11	so	so	ADV
cord-243070-0b06zk1q	123	12	:	:	PUNCT
cord-243070-0b06zk1q	123	13	(	(	PUNCT
cord-243070-0b06zk1q	123	14	i	i	NOUN
cord-243070-0b06zk1q	123	15	)	)	PUNCT
cord-243070-0b06zk1q	123	16	the	the	DET
cord-243070-0b06zk1q	123	17	y	y	PROPN
cord-243070-0b06zk1q	123	18	n	n	PROPN
cord-243070-0b06zk1q	123	19	's	's	PROPN
cord-243070-0b06zk1q	123	20	in	in	ADP
cord-243070-0b06zk1q	123	21	(	(	PUNCT
cord-243070-0b06zk1q	123	22	42	42	NUM
cord-243070-0b06zk1q	123	23	)	)	PUNCT
cord-243070-0b06zk1q	123	24	are	be	AUX
cord-243070-0b06zk1q	123	25	not	not	PART
cord-243070-0b06zk1q	123	26	necessarily	necessarily	ADV
cord-243070-0b06zk1q	123	27	adapted	adapt	VERB
cord-243070-0b06zk1q	123	28	,	,	PUNCT
cord-243070-0b06zk1q	123	29	and	and	CCONJ
cord-243070-0b06zk1q	123	30	(	(	PUNCT
cord-243070-0b06zk1q	123	31	ii	ii	PROPN
cord-243070-0b06zk1q	123	32	)	)	PUNCT
cord-243070-0b06zk1q	123	33	they	they	PRON
cord-243070-0b06zk1q	123	34	depend	depend	VERB
cord-243070-0b06zk1q	123	35	on	on	ADP
cord-243070-0b06zk1q	123	36	z	z	PROPN
cord-243070-0b06zk1q	123	37	n	n	NOUN
cord-243070-0b06zk1q	123	38	.	.	PUNCT
cord-243070-0b06zk1q	124	1	these	these	DET
cord-243070-0b06zk1q	124	2	two	two	NUM
cord-243070-0b06zk1q	124	3	problems	problem	NOUN
cord-243070-0b06zk1q	124	4	can	can	AUX
cord-243070-0b06zk1q	124	5	be	be	AUX
cord-243070-0b06zk1q	124	6	solved	solve	VERB
cord-243070-0b06zk1q	124	7	by	by	ADP
cord-243070-0b06zk1q	124	8	taking	take	VERB
cord-243070-0b06zk1q	124	9	conditional	conditional	ADJ
cord-243070-0b06zk1q	124	10	expectations	expectation	NOUN
cord-243070-0b06zk1q	124	11	e	e	PROPN
cord-243070-0b06zk1q	124	12	n	n	PUNCT
cord-243070-0b06zk1q	124	13	(	(	PUNCT
cord-243070-0b06zk1q	124	14	·	·	PUNCT
cord-243070-0b06zk1q	124	15	)	)	PUNCT
cord-243070-0b06zk1q	124	16	=	=	NOUN
cord-243070-0b06zk1q	124	17	e	e	NOUN
cord-243070-0b06zk1q	124	18	(	(	PUNCT
cord-243070-0b06zk1q	124	19	·	·	PUNCT
cord-243070-0b06zk1q	124	20	|	|	NOUN
cord-243070-0b06zk1q	124	21	x	x	SYM
cord-243070-0b06zk1q	124	22	0	0	NUM
cord-243070-0b06zk1q	124	23	,	,	PUNCT
cord-243070-0b06zk1q	124	24	x	x	PUNCT
cord-243070-0b06zk1q	124	25	1	1	NUM
cord-243070-0b06zk1q	124	26	,	,	PUNCT
cord-243070-0b06zk1q	124	27	.	.	PUNCT
cord-243070-0b06zk1q	124	28	.	.	PUNCT
cord-243070-0b06zk1q	124	29	.	.	PUNCT
cord-243070-0b06zk1q	125	1	,	,	PUNCT
cord-243070-0b06zk1q	125	2	x	x	NOUN
cord-243070-0b06zk1q	125	3	n	n	X
cord-243070-0b06zk1q	125	4	)	)	PUNCT
cord-243070-0b06zk1q	125	5	on	on	ADP
cord-243070-0b06zk1q	125	6	time	time	NOUN
cord-243070-0b06zk1q	125	7	t	t	PROPN
cord-243070-0b06zk1q	125	8	n	n	PROPN
cord-243070-0b06zk1q	125	9	.	.	PUNCT
cord-243070-0b06zk1q	126	1	this	this	PRON
cord-243070-0b06zk1q	126	2	leads	lead	VERB
cord-243070-0b06zk1q	126	3	to	to	ADP
cord-243070-0b06zk1q	126	4	the	the	DET
cord-243070-0b06zk1q	126	5	following	following	ADJ
cord-243070-0b06zk1q	126	6	condition	condition	NOUN
cord-243070-0b06zk1q	126	7	:	:	PUNCT
cord-243070-0b06zk1q	126	8	this	this	PRON
cord-243070-0b06zk1q	126	9	is	be	AUX
cord-243070-0b06zk1q	126	10	an	an	DET
cord-243070-0b06zk1q	126	11	implicit	implicit	ADJ
cord-243070-0b06zk1q	126	12	scheme	scheme	NOUN
cord-243070-0b06zk1q	126	13	,	,	PUNCT
cord-243070-0b06zk1q	126	14	which	which	PRON
cord-243070-0b06zk1q	126	15	may	may	AUX
cord-243070-0b06zk1q	126	16	slow	slow	VERB
cord-243070-0b06zk1q	126	17	down	down	ADP
cord-243070-0b06zk1q	126	18	the	the	DET
cord-243070-0b06zk1q	126	19	computations	computation	NOUN
cord-243070-0b06zk1q	126	20	.	.	PUNCT
cord-243070-0b06zk1q	127	1	however	however	ADV
cord-243070-0b06zk1q	127	2	,	,	PUNCT
cord-243070-0b06zk1q	127	3	we	we	PRON
cord-243070-0b06zk1q	127	4	can	can	AUX
cord-243070-0b06zk1q	127	5	easily	easily	ADV
cord-243070-0b06zk1q	127	6	replace	replace	VERB
cord-243070-0b06zk1q	127	7	it	it	PRON
cord-243070-0b06zk1q	127	8	with	with	ADP
cord-243070-0b06zk1q	127	9	an	an	DET
cord-243070-0b06zk1q	127	10	explicit	explicit	ADJ
cord-243070-0b06zk1q	127	11	scheme	scheme	NOUN
cord-243070-0b06zk1q	127	12	of	of	ADP
cord-243070-0b06zk1q	127	13	the	the	DET
cord-243070-0b06zk1q	127	14	same	same	ADJ
cord-243070-0b06zk1q	127	15	order	order	NOUN
cord-243070-0b06zk1q	127	16	:	:	PUNCT
cord-243070-0b06zk1q	127	17	in	in	ADP
cord-243070-0b06zk1q	127	18	order	order	NOUN
cord-243070-0b06zk1q	127	19	to	to	PART
cord-243070-0b06zk1q	127	20	determine	determine	VERB
cord-243070-0b06zk1q	127	21	z	z	NOUN
cord-243070-0b06zk1q	127	22	i	i	NOUN
cord-243070-0b06zk1q	127	23	,	,	PUNCT
cord-243070-0b06zk1q	127	24	n	n	ADV
cord-243070-0b06zk1q	127	25	,	,	PUNCT
cord-243070-0b06zk1q	127	26	i	i	PRON
cord-243070-0b06zk1q	127	27	=	=	NOUN
cord-243070-0b06zk1q	127	28	1	1	NUM
cord-243070-0b06zk1q	127	29	,	,	PUNCT
cord-243070-0b06zk1q	127	30	2	2	NUM
cord-243070-0b06zk1q	127	31	,	,	PUNCT
cord-243070-0b06zk1q	127	32	we	we	PRON
cord-243070-0b06zk1q	127	33	multiply	multiply	VERB
cord-243070-0b06zk1q	127	34	(	(	PUNCT
cord-243070-0b06zk1q	127	35	42	42	NUM
cord-243070-0b06zk1q	127	36	)	)	PUNCT
cord-243070-0b06zk1q	127	37	by	by	ADP
cord-243070-0b06zk1q	127	38	an	an	DET
cord-243070-0b06zk1q	127	39	increment	increment	NOUN
cord-243070-0b06zk1q	127	40	∆w	∆w	PROPN
cord-243070-0b06zk1q	127	41	n	n	NOUN
cord-243070-0b06zk1q	127	42	and	and	CCONJ
cord-243070-0b06zk1q	127	43	take	take	VERB
cord-243070-0b06zk1q	127	44	conditional	conditional	ADJ
cord-243070-0b06zk1q	127	45	expectations	expectation	NOUN
cord-243070-0b06zk1q	127	46	.	.	PUNCT
cord-243070-0b06zk1q	128	1	this	this	DET
cord-243070-0b06zk1q	128	2	yields	yield	NOUN
cord-243070-0b06zk1q	128	3	and	and	CCONJ
cord-243070-0b06zk1q	128	4	hence	hence	ADV
cord-243070-0b06zk1q	128	5	we	we	PRON
cord-243070-0b06zk1q	128	6	obtain	obtain	VERB
cord-243070-0b06zk1q	128	7	the	the	DET
cord-243070-0b06zk1q	128	8	following	follow	VERB
cord-243070-0b06zk1q	128	9	expression	expression	NOUN
cord-243070-0b06zk1q	128	10	for	for	ADP
cord-243070-0b06zk1q	128	11	z	z	PROPN
cord-243070-0b06zk1q	128	12	i	i	NOUN
cord-243070-0b06zk1q	128	13	,	,	PUNCT
cord-243070-0b06zk1q	128	14	n	n	ADV
cord-243070-0b06zk1q	128	15	:	:	PUNCT
cord-243070-0b06zk1q	128	16	in	in	ADP
cord-243070-0b06zk1q	128	17	summary	summary	NOUN
cord-243070-0b06zk1q	128	18	,	,	PUNCT
cord-243070-0b06zk1q	128	19	we	we	PRON
cord-243070-0b06zk1q	128	20	are	be	AUX
cord-243070-0b06zk1q	128	21	led	lead	VERB
cord-243070-0b06zk1q	128	22	to	to	ADP
cord-243070-0b06zk1q	128	23	the	the	DET
cord-243070-0b06zk1q	128	24	following	follow	VERB
cord-243070-0b06zk1q	128	25	discrete	discrete	ADJ
cord-243070-0b06zk1q	128	26	time	time	NOUN
cord-243070-0b06zk1q	128	27	scheme	scheme	NOUN
cord-243070-0b06zk1q	128	28	for	for	ADP
cord-243070-0b06zk1q	128	29	solving	solve	VERB
cord-243070-0b06zk1q	128	30	(	(	PUNCT
cord-243070-0b06zk1q	128	31	42	42	NUM
cord-243070-0b06zk1q	128	32	):	):	PUNCT
cord-243070-0b06zk1q	128	33	for	for	ADP
cord-243070-0b06zk1q	128	34	n	n	PRON
cord-243070-0b06zk1q	128	35	=	=	PROPN
cord-243070-0b06zk1q	128	36	n	n	NOUN
cord-243070-0b06zk1q	128	37	−	−	PROPN
cord-243070-0b06zk1q	128	38	1	1	NUM
cord-243070-0b06zk1q	128	39	,	,	PUNCT
cord-243070-0b06zk1q	128	40	.	.	PUNCT
cord-243070-0b06zk1q	128	41	.	.	PUNCT
cord-243070-0b06zk1q	128	42	.	.	PUNCT
cord-243070-0b06zk1q	129	1	,	,	PUNCT
cord-243070-0b06zk1q	129	2	0	0	X
cord-243070-0b06zk1q	129	3	.	.	PUNCT
cord-243070-0b06zk1q	129	4	note	note	VERB
cord-243070-0b06zk1q	129	5	that	that	SCONJ
cord-243070-0b06zk1q	129	6	simulating	simulate	VERB
cord-243070-0b06zk1q	129	7	this	this	DET
cord-243070-0b06zk1q	129	8	system	system	NOUN
cord-243070-0b06zk1q	129	9	requires	require	VERB
cord-243070-0b06zk1q	129	10	numerical	numerical	ADJ
cord-243070-0b06zk1q	129	11	estimation	estimation	NOUN
cord-243070-0b06zk1q	129	12	of	of	ADP
cord-243070-0b06zk1q	129	13	the	the	DET
cord-243070-0b06zk1q	129	14	conditional	conditional	ADJ
cord-243070-0b06zk1q	129	15	expected	expect	VERB
cord-243070-0b06zk1q	129	16	values	value	NOUN
cord-243070-0b06zk1q	129	17	e	e	PROPN
cord-243070-0b06zk1q	129	18	n	n	PUNCT
cord-243070-0b06zk1q	129	19	(	(	PUNCT
cord-243070-0b06zk1q	129	20	·	·	PUNCT
cord-243070-0b06zk1q	129	21	)	)	PUNCT
cord-243070-0b06zk1q	129	22	in	in	ADP
cord-243070-0b06zk1q	129	23	the	the	DET
cord-243070-0b06zk1q	129	24	formulas	formula	NOUN
cord-243070-0b06zk1q	129	25	above	above	ADV
cord-243070-0b06zk1q	129	26	.	.	PUNCT
cord-243070-0b06zk1q	130	1	we	we	PRON
cord-243070-0b06zk1q	130	2	discuss	discuss	VERB
cord-243070-0b06zk1q	130	3	this	this	DET
cord-243070-0b06zk1q	130	4	issue	issue	NOUN
cord-243070-0b06zk1q	130	5	in	in	ADP
cord-243070-0b06zk1q	130	6	the	the	DET
cord-243070-0b06zk1q	130	7	following	follow	VERB
cord-243070-0b06zk1q	130	8	section	section	NOUN
cord-243070-0b06zk1q	130	9	.	.	PUNCT
cord-243070-0b06zk1q	131	1	a	a	DET
cord-243070-0b06zk1q	131	2	practical	practical	ADJ
cord-243070-0b06zk1q	131	3	and	and	CCONJ
cord-243070-0b06zk1q	131	4	powerful	powerful	ADJ
cord-243070-0b06zk1q	131	5	method	method	NOUN
cord-243070-0b06zk1q	131	6	of	of	ADP
cord-243070-0b06zk1q	131	7	computing	compute	VERB
cord-243070-0b06zk1q	131	8	the	the	DET
cord-243070-0b06zk1q	131	9	conditional	conditional	ADJ
cord-243070-0b06zk1q	131	10	expected	expect	VERB
cord-243070-0b06zk1q	131	11	values	value	NOUN
cord-243070-0b06zk1q	131	12	in	in	ADP
cord-243070-0b06zk1q	131	13	(	(	PUNCT
cord-243070-0b06zk1q	131	14	45	45	NUM
cord-243070-0b06zk1q	131	15	)	)	PUNCT
cord-243070-0b06zk1q	131	16	is	be	AUX
cord-243070-0b06zk1q	131	17	the	the	DET
cord-243070-0b06zk1q	131	18	longstaff	longstaff	NOUN
cord-243070-0b06zk1q	131	19	-	-	PUNCT
cord-243070-0b06zk1q	131	20	schwartz	schwartz	NOUN
cord-243070-0b06zk1q	131	21	regression	regression	NOUN
cord-243070-0b06zk1q	131	22	method	method	NOUN
cord-243070-0b06zk1q	131	23	originally	originally	ADV
cord-243070-0b06zk1q	131	24	developed	develop	VERB
cord-243070-0b06zk1q	131	25	for	for	ADP
cord-243070-0b06zk1q	131	26	modeling	model	VERB
cord-243070-0b06zk1q	131	27	american	american	ADJ
cord-243070-0b06zk1q	131	28	options	option	NOUN
cord-243070-0b06zk1q	131	29	[	[	X
cord-243070-0b06zk1q	131	30	20	20	NUM
cord-243070-0b06zk1q	131	31	]	]	PUNCT
cord-243070-0b06zk1q	131	32	.	.	PUNCT
cord-243070-0b06zk1q	132	1	we	we	PRON
cord-243070-0b06zk1q	132	2	use	use	VERB
cord-243070-0b06zk1q	132	3	a	a	DET
cord-243070-0b06zk1q	132	4	variant	variant	NOUN
cord-243070-0b06zk1q	132	5	of	of	ADP
cord-243070-0b06zk1q	132	6	this	this	DET
cord-243070-0b06zk1q	132	7	method	method	NOUN
cord-243070-0b06zk1q	132	8	that	that	PRON
cord-243070-0b06zk1q	132	9	involves	involve	VERB
cord-243070-0b06zk1q	132	10	the	the	DET
cord-243070-0b06zk1q	132	11	hermite	hermite	PROPN
cord-243070-0b06zk1q	132	12	polynomials	polynomial	NOUN
cord-243070-0b06zk1q	132	13	,	,	PUNCT
cord-243070-0b06zk1q	132	14	and	and	CCONJ
cord-243070-0b06zk1q	132	15	that	that	PRON
cord-243070-0b06zk1q	132	16	was	be	AUX
cord-243070-0b06zk1q	132	17	used	use	VERB
cord-243070-0b06zk1q	132	18	for	for	ADP
cord-243070-0b06zk1q	132	19	a	a	DET
cord-243070-0b06zk1q	132	20	similar	similar	ADJ
cord-243070-0b06zk1q	132	21	purpose	purpose	NOUN
cord-243070-0b06zk1q	132	22	in	in	ADP
cord-243070-0b06zk1q	132	23	[	[	X
cord-243070-0b06zk1q	132	24	19	19	NUM
cord-243070-0b06zk1q	132	25	]	]	PUNCT
cord-243070-0b06zk1q	132	26	.	.	PUNCT
cord-243070-0b06zk1q	133	1	this	this	DET
cord-243070-0b06zk1q	133	2	choice	choice	NOUN
cord-243070-0b06zk1q	133	3	is	be	AUX
cord-243070-0b06zk1q	133	4	natural	natural	ADJ
cord-243070-0b06zk1q	133	5	,	,	PUNCT
cord-243070-0b06zk1q	133	6	as	as	ADP
cord-243070-0b06zk1q	133	7	conditional	conditional	ADJ
cord-243070-0b06zk1q	133	8	expectations	expectation	NOUN
cord-243070-0b06zk1q	133	9	of	of	ADP
cord-243070-0b06zk1q	133	10	hermite	hermite	ADJ
cord-243070-0b06zk1q	133	11	polynomials	polynomial	NOUN
cord-243070-0b06zk1q	133	12	of	of	ADP
cord-243070-0b06zk1q	133	13	a	a	DET
cord-243070-0b06zk1q	133	14	gaussian	gaussian	ADJ
cord-243070-0b06zk1q	133	15	random	random	ADJ
cord-243070-0b06zk1q	133	16	variable	variable	NOUN
cord-243070-0b06zk1q	133	17	lead	lead	NOUN
cord-243070-0b06zk1q	133	18	to	to	ADP
cord-243070-0b06zk1q	133	19	simple	simple	ADJ
cord-243070-0b06zk1q	133	20	closed	closed	ADJ
cord-243070-0b06zk1q	133	21	form	form	NOUN
cord-243070-0b06zk1q	133	22	expressions	expression	NOUN
cord-243070-0b06zk1q	133	23	.	.	PUNCT
cord-243070-0b06zk1q	134	1	let	let	VERB
cord-243070-0b06zk1q	134	2	he	he	PRON
cord-243070-0b06zk1q	135	1	k	k	PROPN
cord-243070-0b06zk1q	135	2	(	(	PUNCT
cord-243070-0b06zk1q	135	3	x	x	X
cord-243070-0b06zk1q	135	4	)	)	PUNCT
cord-243070-0b06zk1q	135	5	,	,	PUNCT
cord-243070-0b06zk1q	135	6	k	k	PROPN
cord-243070-0b06zk1q	135	7	=	=	SYM
cord-243070-0b06zk1q	135	8	0	0	NUM
cord-243070-0b06zk1q	135	9	,	,	PUNCT
cord-243070-0b06zk1q	135	10	1	1	NUM
cord-243070-0b06zk1q	135	11	,	,	PUNCT
cord-243070-0b06zk1q	135	12	.	.	PUNCT
cord-243070-0b06zk1q	135	13	.	.	PUNCT
cord-243070-0b06zk1q	135	14	.	.	PUNCT
cord-243070-0b06zk1q	135	15	,	,	PUNCT
cord-243070-0b06zk1q	135	16	denote	denote	VERB
cord-243070-0b06zk1q	135	17	the	the	DET
cord-243070-0b06zk1q	135	18	k	k	X
cord-243070-0b06zk1q	135	19	-	-	PUNCT
cord-243070-0b06zk1q	135	20	th	th	VERB
cord-243070-0b06zk1q	135	21	normalized	normalize	VERB
cord-243070-0b06zk1q	135	22	hermite	hermite	PROPN
cord-243070-0b06zk1q	135	23	polynomial	polynomial	NOUN
cord-243070-0b06zk1q	135	24	corresponding	corresponding	NOUN
cord-243070-0b06zk1q	135	25	to	to	ADP
cord-243070-0b06zk1q	135	26	the	the	DET
cord-243070-0b06zk1q	135	27	standard	standard	ADJ
cord-243070-0b06zk1q	135	28	gaussian	gaussian	ADJ
cord-243070-0b06zk1q	135	29	measure	measure	NOUN
cord-243070-0b06zk1q	135	30	dµ(x	dµ(x	NOUN
cord-243070-0b06zk1q	135	31	)	)	PUNCT
cord-243070-0b06zk1q	135	32	=	=	NOUN
cord-243070-0b06zk1q	135	33	(	(	PUNCT
cord-243070-0b06zk1q	135	34	2π	2π	NUM
cord-243070-0b06zk1q	135	35	)	)	PUNCT
cord-243070-0b06zk1q	136	1	−1/2	−1/2	NOUN
cord-243070-0b06zk1q	136	2	e	e	NOUN
cord-243070-0b06zk1q	136	3	−x	−x	NOUN
cord-243070-0b06zk1q	136	4	2	2	NUM
cord-243070-0b06zk1q	136	5	/2	/2	NUM
cord-243070-0b06zk1q	136	6	dx	dx	PROPN
cord-243070-0b06zk1q	136	7	.	.	PUNCT
cord-243070-0b06zk1q	137	1	these	these	DET
cord-243070-0b06zk1q	137	2	functions	function	NOUN
cord-243070-0b06zk1q	137	3	form	form	VERB
cord-243070-0b06zk1q	137	4	an	an	DET
cord-243070-0b06zk1q	137	5	orthonormal	orthonormal	ADJ
cord-243070-0b06zk1q	137	6	basis	basis	NOUN
cord-243070-0b06zk1q	137	7	for	for	ADP
cord-243070-0b06zk1q	137	8	the	the	DET
cord-243070-0b06zk1q	137	9	hilbert	hilbert	ADJ
cord-243070-0b06zk1q	137	10	space	space	NOUN
cord-243070-0b06zk1q	137	11	l	l	PROPN
cord-243070-0b06zk1q	137	12	2	2	NUM
cord-243070-0b06zk1q	137	13	r	r	NOUN
cord-243070-0b06zk1q	137	14	,	,	PUNCT
cord-243070-0b06zk1q	137	15	dµ	dµ	INTJ
cord-243070-0b06zk1q	137	16	.	.	PUNCT
cord-243070-0b06zk1q	138	1	the	the	DET
cord-243070-0b06zk1q	138	2	key	key	ADJ
cord-243070-0b06zk1q	138	3	property	property	NOUN
cord-243070-0b06zk1q	138	4	of	of	ADP
cord-243070-0b06zk1q	138	5	he	he	PRON
cord-243070-0b06zk1q	138	6	k	k	NOUN
cord-243070-0b06zk1q	138	7	(	(	PUNCT
cord-243070-0b06zk1q	138	8	x	x	X
cord-243070-0b06zk1q	138	9	)	)	PUNCT
cord-243070-0b06zk1q	138	10	is	be	AUX
cord-243070-0b06zk1q	138	11	the	the	DET
cord-243070-0b06zk1q	138	12	following	follow	VERB
cord-243070-0b06zk1q	138	13	addition	addition	NOUN
cord-243070-0b06zk1q	138	14	formula	formula	NOUN
cord-243070-0b06zk1q	138	15	for	for	ADP
cord-243070-0b06zk1q	138	16	χ	χ	NUM
cord-243070-0b06zk1q	138	17	∈	∈	NOUN
cord-243070-0b06zk1q	138	18	[	[	X
cord-243070-0b06zk1q	138	19	0	0	NUM
cord-243070-0b06zk1q	138	20	,	,	PUNCT
cord-243070-0b06zk1q	138	21	1	1	NUM
cord-243070-0b06zk1q	138	22	]	]	PUNCT
cord-243070-0b06zk1q	138	23	and	and	CCONJ
cord-243070-0b06zk1q	138	24	w	w	INTJ
cord-243070-0b06zk1q	138	25	,	,	PUNCT
cord-243070-0b06zk1q	138	26	x	x	NOUN
cord-243070-0b06zk1q	138	27	∈	∈	NOUN
cord-243070-0b06zk1q	138	28	r	r	NOUN
cord-243070-0b06zk1q	138	29	:	:	PUNCT
cord-243070-0b06zk1q	138	30	consequently	consequently	ADV
cord-243070-0b06zk1q	138	31	,	,	PUNCT
cord-243070-0b06zk1q	138	32	integrating	integrate	VERB
cord-243070-0b06zk1q	138	33	over	over	ADP
cord-243070-0b06zk1q	138	34	x	x	NOUN
cord-243070-0b06zk1q	138	35	with	with	ADP
cord-243070-0b06zk1q	138	36	respect	respect	NOUN
cord-243070-0b06zk1q	138	37	to	to	ADP
cord-243070-0b06zk1q	138	38	to	to	ADP
cord-243070-0b06zk1q	138	39	the	the	DET
cord-243070-0b06zk1q	138	40	measure	measure	NOUN
cord-243070-0b06zk1q	138	41	µ	µ	X
cord-243070-0b06zk1q	138	42	yields	yield	VERB
cord-243070-0b06zk1q	138	43	the	the	DET
cord-243070-0b06zk1q	138	44	following	follow	VERB
cord-243070-0b06zk1q	138	45	conditioning	conditioning	NOUN
cord-243070-0b06zk1q	138	46	rule	rule	NOUN
cord-243070-0b06zk1q	138	47	:	:	PUNCT
cord-243070-0b06zk1q	138	48	here	here	ADV
cord-243070-0b06zk1q	138	49	,	,	PUNCT
cord-243070-0b06zk1q	138	50	w	w	PROPN
cord-243070-0b06zk1q	138	51	,	,	PUNCT
cord-243070-0b06zk1q	138	52	x	x	PUNCT
cord-243070-0b06zk1q	138	53	are	be	AUX
cord-243070-0b06zk1q	138	54	independent	independent	ADJ
cord-243070-0b06zk1q	138	55	standard	standard	ADJ
cord-243070-0b06zk1q	138	56	normal	normal	ADJ
cord-243070-0b06zk1q	138	57	random	random	ADJ
cord-243070-0b06zk1q	138	58	variables	variable	NOUN
cord-243070-0b06zk1q	138	59	.	.	PUNCT
cord-243070-0b06zk1q	139	1	we	we	PRON
cord-243070-0b06zk1q	139	2	shall	shall	AUX
cord-243070-0b06zk1q	139	3	use	use	VERB
cord-243070-0b06zk1q	139	4	this	this	DET
cord-243070-0b06zk1q	139	5	relation	relation	NOUN
cord-243070-0b06zk1q	139	6	in	in	ADP
cord-243070-0b06zk1q	139	7	order	order	NOUN
cord-243070-0b06zk1q	139	8	to	to	PART
cord-243070-0b06zk1q	139	9	estimate	estimate	VERB
cord-243070-0b06zk1q	139	10	the	the	DET
cord-243070-0b06zk1q	139	11	conditional	conditional	ADJ
cord-243070-0b06zk1q	139	12	expected	expect	VERB
cord-243070-0b06zk1q	139	13	values	value	NOUN
cord-243070-0b06zk1q	139	14	in	in	ADP
cord-243070-0b06zk1q	139	15	(	(	PUNCT
cord-243070-0b06zk1q	139	16	45	45	NUM
cord-243070-0b06zk1q	139	17	)	)	PUNCT
cord-243070-0b06zk1q	139	18	.	.	PUNCT
cord-243070-0b06zk1q	140	1	we	we	PRON
cord-243070-0b06zk1q	140	2	set	set	VERB
cord-243070-0b06zk1q	140	3	w	w	PROPN
cord-243070-0b06zk1q	140	4	ti	ti	PROPN
cord-243070-0b06zk1q	140	5	=	=	X
cord-243070-0b06zk1q	140	6	√	√	PUNCT
cord-243070-0b06zk1q	141	1	t	t	PROPN
cord-243070-0b06zk1q	141	2	i	i	PRON
cord-243070-0b06zk1q	142	1	w	w	ADP
cord-243070-0b06zk1q	142	2	i	i	PRON
cord-243070-0b06zk1q	142	3	,	,	PUNCT
cord-243070-0b06zk1q	142	4	for	for	ADP
cord-243070-0b06zk1q	142	5	i	i	PRON
cord-243070-0b06zk1q	142	6	=	=	NOUN
cord-243070-0b06zk1q	142	7	1	1	NUM
cord-243070-0b06zk1q	142	8	,	,	PUNCT
cord-243070-0b06zk1q	142	9	.	.	PUNCT
cord-243070-0b06zk1q	142	10	.	.	PUNCT
cord-243070-0b06zk1q	142	11	.	.	PUNCT
cord-243070-0b06zk1q	143	1	,	,	PUNCT
cord-243070-0b06zk1q	143	2	m	m	PROPN
cord-243070-0b06zk1q	143	3	,	,	PUNCT
cord-243070-0b06zk1q	143	4	where	where	SCONJ
cord-243070-0b06zk1q	143	5	w	w	PROPN
cord-243070-0b06zk1q	143	6	i	i	PRON
cord-243070-0b06zk1q	143	7	is	be	AUX
cord-243070-0b06zk1q	143	8	an	an	DET
cord-243070-0b06zk1q	143	9	n	n	ADV
cord-243070-0b06zk1q	143	10	-	-	ADJ
cord-243070-0b06zk1q	143	11	dimensional	dimensional	ADJ
cord-243070-0b06zk1q	143	12	standard	standard	ADJ
cord-243070-0b06zk1q	143	13	normal	normal	ADJ
cord-243070-0b06zk1q	143	14	random	random	ADJ
cord-243070-0b06zk1q	143	15	variable	variable	NOUN
cord-243070-0b06zk1q	143	16	.	.	PUNCT
cord-243070-0b06zk1q	144	1	we	we	PRON
cord-243070-0b06zk1q	144	2	notice	notice	VERB
cord-243070-0b06zk1q	144	3	that	that	SCONJ
cord-243070-0b06zk1q	144	4	where	where	SCONJ
cord-243070-0b06zk1q	144	5	χ	χ	X
cord-243070-0b06zk1q	144	6	i	i	PRON
cord-243070-0b06zk1q	144	7	=	=	SYM
cord-243070-0b06zk1q	144	8	t	t	NOUN
cord-243070-0b06zk1q	144	9	i	i	NOUN
cord-243070-0b06zk1q	144	10	/t	/t	PUNCT
cord-243070-0b06zk1q	144	11	i+1	i+1	PUNCT
cord-243070-0b06zk1q	144	12	,	,	PUNCT
cord-243070-0b06zk1q	144	13	and	and	CCONJ
cord-243070-0b06zk1q	144	14	where	where	SCONJ
cord-243070-0b06zk1q	144	15	x	x	PROPN
cord-243070-0b06zk1q	144	16	i	i	PRON
cord-243070-0b06zk1q	144	17	is	be	AUX
cord-243070-0b06zk1q	144	18	standard	standard	ADJ
cord-243070-0b06zk1q	144	19	normal	normal	ADJ
cord-243070-0b06zk1q	144	20	and	and	CCONJ
cord-243070-0b06zk1q	144	21	independent	independent	ADJ
cord-243070-0b06zk1q	144	22	of	of	ADP
cord-243070-0b06zk1q	144	23	w	w	PROPN
cord-243070-0b06zk1q	144	24	i	i	PROPN
cord-243070-0b06zk1q	144	25	.	.	PUNCT
cord-243070-0b06zk1q	145	1	in	in	ADP
cord-243070-0b06zk1q	145	2	the	the	DET
cord-243070-0b06zk1q	145	3	following	following	NOUN
cord-243070-0b06zk1q	145	4	,	,	PUNCT
cord-243070-0b06zk1q	145	5	we	we	PRON
cord-243070-0b06zk1q	145	6	shall	shall	AUX
cord-243070-0b06zk1q	145	7	use	use	VERB
cord-243070-0b06zk1q	145	8	this	this	DET
cord-243070-0b06zk1q	145	9	decomposition	decomposition	NOUN
cord-243070-0b06zk1q	145	10	in	in	ADP
cord-243070-0b06zk1q	145	11	conjunction	conjunction	NOUN
cord-243070-0b06zk1q	145	12	with	with	ADP
cord-243070-0b06zk1q	145	13	(	(	PUNCT
cord-243070-0b06zk1q	145	14	47	47	NUM
cord-243070-0b06zk1q	145	15	)	)	PUNCT
cord-243070-0b06zk1q	145	16	.	.	PUNCT
cord-243070-0b06zk1q	146	1	now	now	ADV
cord-243070-0b06zk1q	146	2	,	,	PUNCT
cord-243070-0b06zk1q	146	3	we	we	PRON
cord-243070-0b06zk1q	146	4	assume	assume	VERB
cord-243070-0b06zk1q	146	5	the	the	DET
cord-243070-0b06zk1q	146	6	following	follow	VERB
cord-243070-0b06zk1q	146	7	linear	linear	ADJ
cord-243070-0b06zk1q	146	8	architecture	architecture	NOUN
cord-243070-0b06zk1q	146	9	:	:	PUNCT
cord-243070-0b06zk1q	146	10	where	where	SCONJ
cord-243070-0b06zk1q	146	11	k	k	PROPN
cord-243070-0b06zk1q	146	12	is	be	AUX
cord-243070-0b06zk1q	146	13	the	the	DET
cord-243070-0b06zk1q	146	14	cutoff	cutoff	NOUN
cord-243070-0b06zk1q	146	15	value	value	NOUN
cord-243070-0b06zk1q	146	16	of	of	ADP
cord-243070-0b06zk1q	146	17	the	the	DET
cord-243070-0b06zk1q	146	18	order	order	NOUN
cord-243070-0b06zk1q	146	19	of	of	ADP
cord-243070-0b06zk1q	146	20	the	the	DET
cord-243070-0b06zk1q	146	21	hermite	hermite	PROPN
cord-243070-0b06zk1q	146	22	polynomials	polynomial	NOUN
cord-243070-0b06zk1q	146	23	.	.	PUNCT
cord-243070-0b06zk1q	147	1	this	this	PRON
cord-243070-0b06zk1q	147	2	is	be	AUX
cord-243070-0b06zk1q	147	3	simply	simply	ADV
cord-243070-0b06zk1q	147	4	a	a	DET
cord-243070-0b06zk1q	147	5	truncated	truncate	VERB
cord-243070-0b06zk1q	147	6	expansion	expansion	NOUN
cord-243070-0b06zk1q	147	7	of	of	ADP
cord-243070-0b06zk1q	147	8	the	the	DET
cord-243070-0b06zk1q	147	9	random	random	ADJ
cord-243070-0b06zk1q	147	10	variable	variable	PROPN
cord-243070-0b06zk1q	147	11	y	y	PROPN
cord-243070-0b06zk1q	147	12	i+1	i+1	X
cord-243070-0b06zk1q	147	13	in	in	ADP
cord-243070-0b06zk1q	147	14	terms	term	NOUN
cord-243070-0b06zk1q	147	15	of	of	ADP
cord-243070-0b06zk1q	147	16	the	the	DET
cord-243070-0b06zk1q	147	17	orthonormal	orthonormal	ADJ
cord-243070-0b06zk1q	147	18	basis	basis	NOUN
cord-243070-0b06zk1q	147	19	he	he	PRON
cord-243070-0b06zk1q	147	20	k	k	PROPN
cord-243070-0b06zk1q	147	21	(	(	PUNCT
cord-243070-0b06zk1q	147	22	w	w	NOUN
cord-243070-0b06zk1q	147	23	i+1	i+1	PUNCT
cord-243070-0b06zk1q	147	24	)	)	PUNCT
cord-243070-0b06zk1q	147	25	.	.	PUNCT
cord-243070-0b06zk1q	148	1	the	the	DET
cord-243070-0b06zk1q	148	2	values	value	NOUN
cord-243070-0b06zk1q	148	3	of	of	ADP
cord-243070-0b06zk1q	148	4	the	the	DET
cord-243070-0b06zk1q	148	5	fourier	fourier	NOUN
cord-243070-0b06zk1q	148	6	coefficients	coefficient	NOUN
cord-243070-0b06zk1q	148	7	are	be	AUX
cord-243070-0b06zk1q	148	8	estimated	estimate	VERB
cord-243070-0b06zk1q	148	9	by	by	ADP
cord-243070-0b06zk1q	148	10	means	mean	NOUN
cord-243070-0b06zk1q	148	11	of	of	ADP
cord-243070-0b06zk1q	148	12	ordinary	ordinary	ADJ
cord-243070-0b06zk1q	148	13	least	least	ADJ
cord-243070-0b06zk1q	148	14	square	square	ADJ
cord-243070-0b06zk1q	148	15	regression	regression	NOUN
cord-243070-0b06zk1q	148	16	.	.	PUNCT
cord-243070-0b06zk1q	149	1	then	then	ADV
cord-243070-0b06zk1q	149	2	,	,	PUNCT
cord-243070-0b06zk1q	149	3	as	as	ADP
cord-243070-0b06zk1q	149	4	a	a	DET
cord-243070-0b06zk1q	149	5	consequence	consequence	NOUN
cord-243070-0b06zk1q	149	6	of	of	ADP
cord-243070-0b06zk1q	149	7	the	the	DET
cord-243070-0b06zk1q	149	8	conditioning	conditioning	NOUN
cord-243070-0b06zk1q	149	9	rule	rule	NOUN
cord-243070-0b06zk1q	149	10	(	(	PUNCT
cord-243070-0b06zk1q	149	11	47	47	NUM
cord-243070-0b06zk1q	149	12	)	)	PUNCT
cord-243070-0b06zk1q	149	13	,	,	PUNCT
cord-243070-0b06zk1q	149	14	in	in	ADP
cord-243070-0b06zk1q	149	15	other	other	ADJ
cord-243070-0b06zk1q	149	16	words	word	NOUN
cord-243070-0b06zk1q	149	17	,	,	PUNCT
cord-243070-0b06zk1q	149	18	conditioning	condition	VERB
cord-243070-0b06zk1q	149	19	y	y	PROPN
cord-243070-0b06zk1q	149	20	i+1	i+1	PUNCT
cord-243070-0b06zk1q	149	21	on	on	ADP
cord-243070-0b06zk1q	149	22	w	w	PROPN
cord-243070-0b06zk1q	150	1	i	i	PRON
cord-243070-0b06zk1q	150	2	is	be	AUX
cord-243070-0b06zk1q	150	3	equivalent	equivalent	ADJ
cord-243070-0b06zk1q	150	4	to	to	ADP
cord-243070-0b06zk1q	150	5	multiplying	multiply	VERB
cord-243070-0b06zk1q	150	6	its	its	PRON
cord-243070-0b06zk1q	150	7	fourier	fourier	NOUN
cord-243070-0b06zk1q	150	8	coefficients	coefficient	NOUN
cord-243070-0b06zk1q	150	9	g	g	PROPN
cord-243070-0b06zk1q	150	10	k	k	PROPN
cord-243070-0b06zk1q	150	11	by	by	ADP
cord-243070-0b06zk1q	150	12	the	the	DET
cord-243070-0b06zk1q	150	13	factor	factor	NOUN
cord-243070-0b06zk1q	150	14	χ	χ	X
cord-243070-0b06zk1q	150	15	k/2	k/2	NOUN
cord-243070-0b06zk1q	151	1	i	i	PRON
cord-243070-0b06zk1q	151	2	.	.	PUNCT
cord-243070-0b06zk1q	152	1	this	this	PRON
cord-243070-0b06zk1q	152	2	allows	allow	VERB
cord-243070-0b06zk1q	152	3	us	we	PRON
cord-243070-0b06zk1q	152	4	to	to	PART
cord-243070-0b06zk1q	152	5	calculate	calculate	VERB
cord-243070-0b06zk1q	152	6	the	the	DET
cord-243070-0b06zk1q	152	7	first	first	ADJ
cord-243070-0b06zk1q	152	8	term	term	NOUN
cord-243070-0b06zk1q	152	9	on	on	ADP
cord-243070-0b06zk1q	152	10	the	the	DET
cord-243070-0b06zk1q	152	11	right	right	ADJ
cord-243070-0b06zk1q	152	12	hand	hand	NOUN
cord-243070-0b06zk1q	152	13	side	side	NOUN
cord-243070-0b06zk1q	152	14	of	of	ADP
cord-243070-0b06zk1q	152	15	the	the	DET
cord-243070-0b06zk1q	152	16	third	third	ADJ
cord-243070-0b06zk1q	152	17	equation	equation	NOUN
cord-243070-0b06zk1q	152	18	in	in	ADP
cord-243070-0b06zk1q	152	19	(	(	PUNCT
cord-243070-0b06zk1q	152	20	45	45	NUM
cord-243070-0b06zk1q	152	21	)	)	PUNCT
cord-243070-0b06zk1q	152	22	.	.	PUNCT
cord-243070-0b06zk1q	153	1	in	in	ADP
cord-243070-0b06zk1q	153	2	order	order	NOUN
cord-243070-0b06zk1q	153	3	to	to	PART
cord-243070-0b06zk1q	153	4	calculate	calculate	VERB
cord-243070-0b06zk1q	153	5	the	the	DET
cord-243070-0b06zk1q	153	6	second	second	ADJ
cord-243070-0b06zk1q	153	7	term	term	NOUN
cord-243070-0b06zk1q	153	8	,	,	PUNCT
cord-243070-0b06zk1q	153	9	we	we	PRON
cord-243070-0b06zk1q	153	10	substitute	substitute	VERB
cord-243070-0b06zk1q	153	11	the	the	DET
cord-243070-0b06zk1q	153	12	explicit	explicit	ADJ
cord-243070-0b06zk1q	153	13	formula	formula	NOUN
cord-243070-0b06zk1q	153	14	for	for	ADP
cord-243070-0b06zk1q	153	15	z	z	PROPN
cord-243070-0b06zk1q	153	16	n	n	NOUN
cord-243070-0b06zk1q	153	17	into	into	ADP
cord-243070-0b06zk1q	153	18	the	the	DET
cord-243070-0b06zk1q	153	19	generators	generator	NOUN
cord-243070-0b06zk1q	153	20	(	(	PUNCT
cord-243070-0b06zk1q	153	21	43	43	NUM
cord-243070-0b06zk1q	153	22	)	)	PUNCT
cord-243070-0b06zk1q	153	23	and	and	CCONJ
cord-243070-0b06zk1q	153	24	repeat	repeat	VERB
cord-243070-0b06zk1q	153	25	the	the	DET
cord-243070-0b06zk1q	153	26	calculations	calculation	NOUN
cord-243070-0b06zk1q	153	27	in	in	ADP
cord-243070-0b06zk1q	153	28	(	(	PUNCT
cord-243070-0b06zk1q	153	29	49	49	NUM
cord-243070-0b06zk1q	153	30	)	)	PUNCT
cord-243070-0b06zk1q	153	31	and	and	CCONJ
cord-243070-0b06zk1q	153	32	(	(	PUNCT
cord-243070-0b06zk1q	153	33	50	50	NUM
cord-243070-0b06zk1q	153	34	)	)	PUNCT
cord-243070-0b06zk1q	153	35	with	with	ADP
cord-243070-0b06zk1q	153	36	y	y	PROPN
cord-243070-0b06zk1q	153	37	n+1	n+1	PROPN
cord-243070-0b06zk1q	153	38	replaced	replace	VERB
cord-243070-0b06zk1q	153	39	by	by	ADP
cord-243070-0b06zk1q	153	40	y	y	PROPN
cord-243070-0b06zk1q	153	41	n+1	n+1	PROPN
cord-243070-0b06zk1q	153	42	+	+	CCONJ
cord-243070-0b06zk1q	153	43	f	f	PROPN
cord-243070-0b06zk1q	153	44	(	(	PUNCT
cord-243070-0b06zk1q	153	45	x	x	NOUN
cord-243070-0b06zk1q	153	46	n	n	PROPN
cord-243070-0b06zk1q	153	47	,	,	PUNCT
cord-243070-0b06zk1q	153	48	y	y	PROPN
cord-243070-0b06zk1q	153	49	n	n	PROPN
cord-243070-0b06zk1q	153	50	,	,	PUNCT
cord-243070-0b06zk1q	153	51	z	z	NOUN
cord-243070-0b06zk1q	153	52	n	n	NOUN
cord-243070-0b06zk1q	153	53	)	)	PUNCT
cord-243070-0b06zk1q	153	54	δ	δ	PROPN
cord-243070-0b06zk1q	153	55	.	.	PUNCT
cord-243070-0b06zk1q	154	1	for	for	ADP
cord-243070-0b06zk1q	154	2	numerical	numerical	ADJ
cord-243070-0b06zk1q	154	3	experiments	experiment	NOUN
cord-243070-0b06zk1q	154	4	within	within	ADP
cord-243070-0b06zk1q	154	5	the	the	DET
cord-243070-0b06zk1q	154	6	framework	framework	NOUN
cord-243070-0b06zk1q	154	7	developed	develop	VERB
cord-243070-0b06zk1q	154	8	above	above	ADV
cord-243070-0b06zk1q	154	9	,	,	PUNCT
cord-243070-0b06zk1q	154	10	we	we	PRON
cord-243070-0b06zk1q	154	11	assume	assume	VERB
cord-243070-0b06zk1q	154	12	a	a	DET
cord-243070-0b06zk1q	154	13	time	time	NOUN
cord-243070-0b06zk1q	154	14	horizon	horizon	NOUN
cord-243070-0b06zk1q	154	15	of	of	ADP
cord-243070-0b06zk1q	154	16	1	1	NUM
cord-243070-0b06zk1q	154	17	year	year	NOUN
cord-243070-0b06zk1q	154	18	(	(	PUNCT
cord-243070-0b06zk1q	154	19	365	365	NUM
cord-243070-0b06zk1q	154	20	days	day	NOUN
cord-243070-0b06zk1q	154	21	)	)	PUNCT
cord-243070-0b06zk1q	154	22	,	,	PUNCT
cord-243070-0b06zk1q	154	23	and	and	CCONJ
cord-243070-0b06zk1q	154	24	choose	choose	VERB
cord-243070-0b06zk1q	154	25	the	the	DET
cord-243070-0b06zk1q	154	26	sir	sir	PROPN
cord-243070-0b06zk1q	154	27	model	model	NOUN
cord-243070-0b06zk1q	154	28	parameters	parameter	NOUN
cord-243070-0b06zk1q	154	29	as	as	SCONJ
cord-243070-0b06zk1q	154	30	follows	follow	VERB
cord-243070-0b06zk1q	154	31	:	:	PUNCT
cord-243070-0b06zk1q	154	32	β	β	PROPN
cord-243070-0b06zk1q	154	33	=	=	NOUN
cord-243070-0b06zk1q	154	34	38.0	38.0	NUM
cord-243070-0b06zk1q	154	35	,	,	PUNCT
cord-243070-0b06zk1q	154	36	γ	γ	PROPN
cord-243070-0b06zk1q	154	37	=	=	NOUN
cord-243070-0b06zk1q	154	38	11.5	11.5	NUM
cord-243070-0b06zk1q	154	39	,	,	PUNCT
cord-243070-0b06zk1q	154	40	s	s	NOUN
cord-243070-0b06zk1q	154	41	0	0	NUM
cord-243070-0b06zk1q	154	42	=	=	NOUN
cord-243070-0b06zk1q	154	43	0.999	0.999	NUM
cord-243070-0b06zk1q	154	44	,	,	PUNCT
cord-243070-0b06zk1q	154	45	these	these	DET
cord-243070-0b06zk1q	154	46	parameters	parameter	NOUN
cord-243070-0b06zk1q	154	47	are	be	AUX
cord-243070-0b06zk1q	154	48	purely	purely	ADV
cord-243070-0b06zk1q	154	49	hypothetical	hypothetical	ADJ
cord-243070-0b06zk1q	154	50	,	,	PUNCT
cord-243070-0b06zk1q	154	51	and	and	CCONJ
cord-243070-0b06zk1q	154	52	they	they	PRON
cord-243070-0b06zk1q	154	53	do	do	AUX
cord-243070-0b06zk1q	154	54	not	not	PART
cord-243070-0b06zk1q	154	55	arise	arise	VERB
cord-243070-0b06zk1q	154	56	from	from	ADP
cord-243070-0b06zk1q	154	57	the	the	DET
cord-243070-0b06zk1q	154	58	calibration	calibration	NOUN
cord-243070-0b06zk1q	154	59	to	to	ADP
cord-243070-0b06zk1q	154	60	any	any	DET
cord-243070-0b06zk1q	154	61	actually	actually	ADV
cord-243070-0b06zk1q	154	62	reported	report	VERB
cord-243070-0b06zk1q	154	63	data	datum	NOUN
cord-243070-0b06zk1q	154	64	.	.	PUNCT
cord-243070-0b06zk1q	155	1	the	the	DET
cord-243070-0b06zk1q	155	2	corresponding	corresponding	ADJ
cord-243070-0b06zk1q	155	3	value	value	NOUN
cord-243070-0b06zk1q	155	4	of	of	ADP
cord-243070-0b06zk1q	155	5	the	the	DET
cord-243070-0b06zk1q	155	6	basic	basic	ADJ
cord-243070-0b06zk1q	155	7	reproduction	reproduction	NOUN
cord-243070-0b06zk1q	155	8	ratio	ratio	NOUN
cord-243070-0b06zk1q	155	9	r	r	NOUN
cord-243070-0b06zk1q	155	10	0	0	NUM
cord-243070-0b06zk1q	155	11	=	=	SYM
cord-243070-0b06zk1q	155	12	s	s	X
cord-243070-0b06zk1q	155	13	0	0	NUM
cord-243070-0b06zk1q	155	14	β	β	NOUN
cord-243070-0b06zk1q	155	15	/	/	SYM
cord-243070-0b06zk1q	155	16	γ	γ	NOUN
cord-243070-0b06zk1q	155	17	is	be	AUX
cord-243070-0b06zk1q	155	18	3.30	3.30	NUM
cord-243070-0b06zk1q	155	19	and	and	CCONJ
cord-243070-0b06zk1q	155	20	it	it	PRON
cord-243070-0b06zk1q	155	21	indicates	indicate	VERB
cord-243070-0b06zk1q	155	22	a	a	DET
cord-243070-0b06zk1q	155	23	highly	highly	ADV
cord-243070-0b06zk1q	155	24	infectious	infectious	ADJ
cord-243070-0b06zk1q	155	25	disease	disease	NOUN
cord-243070-0b06zk1q	155	26	such	such	ADJ
cord-243070-0b06zk1q	155	27	as	as	ADP
cord-243070-0b06zk1q	155	28	covid-19	covid-19	PROPN
cord-243070-0b06zk1q	155	29	.	.	PUNCT
cord-243070-0b06zk1q	156	1	we	we	PRON
cord-243070-0b06zk1q	156	2	choose	choose	VERB
cord-243070-0b06zk1q	156	3	the	the	DET
cord-243070-0b06zk1q	156	4	diffusion	diffusion	NOUN
cord-243070-0b06zk1q	156	5	parameter	parameter	NOUN
cord-243070-0b06zk1q	156	6	σ	σ	PROPN
cord-243070-0b06zk1q	156	7	=	=	NOUN
cord-243070-0b06zk1q	156	8	3.1	3.1	NUM
cord-243070-0b06zk1q	156	9	.	.	PUNCT
cord-243070-0b06zk1q	157	1	(	(	PUNCT
cord-243070-0b06zk1q	157	2	52	52	NUM
cord-243070-0b06zk1q	157	3	)	)	PUNCT
cord-243070-0b06zk1q	157	4	a	a	DET
cord-243070-0b06zk1q	157	5	typical	typical	ADJ
cord-243070-0b06zk1q	157	6	scenario	scenario	NOUN
cord-243070-0b06zk1q	157	7	generated	generate	VERB
cord-243070-0b06zk1q	157	8	by	by	ADP
cord-243070-0b06zk1q	157	9	this	this	DET
cord-243070-0b06zk1q	157	10	model	model	NOUN
cord-243070-0b06zk1q	157	11	is	be	AUX
cord-243070-0b06zk1q	157	12	graphed	graph	VERB
cord-243070-0b06zk1q	157	13	in	in	ADP
cord-243070-0b06zk1q	157	14	figure	figure	NOUN
cord-243070-0b06zk1q	157	15	1	1	NUM
cord-243070-0b06zk1q	157	16	.	.	PUNCT
cord-243070-0b06zk1q	158	1	for	for	ADP
cord-243070-0b06zk1q	158	2	solving	solve	VERB
cord-243070-0b06zk1q	158	3	the	the	DET
cord-243070-0b06zk1q	158	4	fbsde	fbsde	PROPN
cord-243070-0b06zk1q	158	5	system	system	NOUN
cord-243070-0b06zk1q	158	6	(	(	PUNCT
cord-243070-0b06zk1q	158	7	34	34	NUM
cord-243070-0b06zk1q	158	8	)	)	PUNCT
cord-243070-0b06zk1q	158	9	we	we	PRON
cord-243070-0b06zk1q	158	10	generate	generate	VERB
cord-243070-0b06zk1q	158	11	2	2	NUM
cord-243070-0b06zk1q	158	12	,	,	PUNCT
cord-243070-0b06zk1q	158	13	000	000	NUM
cord-243070-0b06zk1q	158	14	scenarios	scenario	NOUN
cord-243070-0b06zk1q	158	15	(	(	PUNCT
cord-243070-0b06zk1q	158	16	monte	monte	PROPN
cord-243070-0b06zk1q	158	17	carlo	carlo	PROPN
cord-243070-0b06zk1q	158	18	paths	path	NOUN
cord-243070-0b06zk1q	158	19	)	)	PUNCT
cord-243070-0b06zk1q	158	20	using	use	VERB
cord-243070-0b06zk1q	158	21	the	the	DET
cord-243070-0b06zk1q	158	22	low	low	ADJ
cord-243070-0b06zk1q	158	23	variance	variance	NOUN
cord-243070-0b06zk1q	158	24	spectral	spectral	ADJ
cord-243070-0b06zk1q	158	25	decomposition	decomposition	NOUN
cord-243070-0b06zk1q	158	26	method	method	NOUN
cord-243070-0b06zk1q	158	27	.	.	PUNCT
cord-243070-0b06zk1q	159	1	each	each	DET
cord-243070-0b06zk1q	159	2	scenario	scenario	NOUN
cord-243070-0b06zk1q	159	3	is	be	AUX
cord-243070-0b06zk1q	159	4	based	base	VERB
cord-243070-0b06zk1q	159	5	on	on	ADP
cord-243070-0b06zk1q	159	6	daily	daily	ADJ
cord-243070-0b06zk1q	159	7	sampling	sampling	NOUN
cord-243070-0b06zk1q	159	8	,	,	PUNCT
cord-243070-0b06zk1q	159	9	i.e.	i.e.	X
cord-243070-0b06zk1q	159	10	n	n	NOUN
cord-243070-0b06zk1q	159	11	=	=	NOUN
cord-243070-0b06zk1q	159	12	365	365	NUM
cord-243070-0b06zk1q	159	13	.	.	PUNCT
cord-243070-0b06zk1q	160	1	for	for	ADP
cord-243070-0b06zk1q	160	2	calculating	calculate	VERB
cord-243070-0b06zk1q	160	3	the	the	DET
cord-243070-0b06zk1q	160	4	conditional	conditional	ADJ
cord-243070-0b06zk1q	160	5	expectations	expectation	NOUN
cord-243070-0b06zk1q	160	6	in	in	ADP
cord-243070-0b06zk1q	160	7	the	the	DET
cord-243070-0b06zk1q	160	8	longstaff	longstaff	PROPN
cord-243070-0b06zk1q	160	9	-	-	PUNCT
cord-243070-0b06zk1q	160	10	schwartz	schwartz	NOUN
cord-243070-0b06zk1q	160	11	regression	regression	NOUN
cord-243070-0b06zk1q	160	12	we	we	PRON
cord-243070-0b06zk1q	160	13	use	use	VERB
cord-243070-0b06zk1q	160	14	the	the	DET
cord-243070-0b06zk1q	160	15	cutoff	cutoff	NOUN
cord-243070-0b06zk1q	160	16	value	value	NOUN
cord-243070-0b06zk1q	160	17	of	of	ADP
cord-243070-0b06zk1q	160	18	k	k	PROPN
cord-243070-0b06zk1q	160	19	=	=	SYM
cord-243070-0b06zk1q	160	20	4	4	NUM
cord-243070-0b06zk1q	160	21	.	.	PUNCT
cord-243070-0b06zk1q	161	1	the	the	DET
cord-243070-0b06zk1q	161	2	expectation	expectation	NOUN
cord-243070-0b06zk1q	161	3	behind	behind	ADP
cord-243070-0b06zk1q	161	4	this	this	DET
cord-243070-0b06zk1q	161	5	choice	choice	NOUN
cord-243070-0b06zk1q	161	6	is	be	AUX
cord-243070-0b06zk1q	161	7	that	that	SCONJ
cord-243070-0b06zk1q	161	8	we	we	PRON
cord-243070-0b06zk1q	161	9	obtain	obtain	VERB
cord-243070-0b06zk1q	161	10	the	the	DET
cord-243070-0b06zk1q	161	11	accuracy	accuracy	NOUN
cord-243070-0b06zk1q	161	12	of	of	ADP
cord-243070-0b06zk1q	161	13	four	four	NUM
cord-243070-0b06zk1q	161	14	sigma	sigma	NOUN
cord-243070-0b06zk1q	161	15	.	.	PUNCT
cord-243070-0b06zk1q	162	1	we	we	PRON
cord-243070-0b06zk1q	162	2	attempt	attempt	VERB
cord-243070-0b06zk1q	162	3	to	to	PART
cord-243070-0b06zk1q	162	4	construct	construct	VERB
cord-243070-0b06zk1q	162	5	a	a	DET
cord-243070-0b06zk1q	162	6	numerical	numerical	ADJ
cord-243070-0b06zk1q	162	7	solution	solution	NOUN
cord-243070-0b06zk1q	162	8	to	to	ADP
cord-243070-0b06zk1q	162	9	(	(	PUNCT
cord-243070-0b06zk1q	162	10	34	34	NUM
cord-243070-0b06zk1q	162	11	)	)	PUNCT
cord-243070-0b06zk1q	162	12	through	through	ADP
cord-243070-0b06zk1q	162	13	the	the	DET
cord-243070-0b06zk1q	162	14	following	follow	VERB
cord-243070-0b06zk1q	162	15	iterative	iterative	ADJ
cord-243070-0b06zk1q	162	16	procedure	procedure	NOUN
cord-243070-0b06zk1q	162	17	.	.	PUNCT
cord-243070-0b06zk1q	163	1	we	we	PRON
cord-243070-0b06zk1q	163	2	start	start	VERB
cord-243070-0b06zk1q	163	3	by	by	ADP
cord-243070-0b06zk1q	163	4	generating	generate	VERB
cord-243070-0b06zk1q	163	5	initial	initial	PROPN
cord-243070-0b06zk1q	163	6	monte	monte	PROPN
cord-243070-0b06zk1q	163	7	carlo	carlo	PROPN
cord-243070-0b06zk1q	163	8	paths	paths	PROPN
cord-243070-0b06zk1q	163	9	x	x	PROPN
cord-243070-0b06zk1q	163	10	(	(	PUNCT
cord-243070-0b06zk1q	163	11	0	0	NUM
cord-243070-0b06zk1q	163	12	)	)	PUNCT
cord-243070-0b06zk1q	163	13	t	t	NOUN
cord-243070-0b06zk1q	163	14	using	use	VERB
cord-243070-0b06zk1q	163	15	the	the	DET
cord-243070-0b06zk1q	163	16	(	(	PUNCT
cord-243070-0b06zk1q	163	17	discretized	discretized	ADJ
cord-243070-0b06zk1q	163	18	version	version	NOUN
cord-243070-0b06zk1q	163	19	of	of	ADP
cord-243070-0b06zk1q	163	20	the	the	DET
cord-243070-0b06zk1q	163	21	)	)	PUNCT
cord-243070-0b06zk1q	163	22	raw	raw	ADJ
cord-243070-0b06zk1q	163	23	process	process	NOUN
cord-243070-0b06zk1q	163	24	(	(	PUNCT
cord-243070-0b06zk1q	163	25	6	6	NUM
cord-243070-0b06zk1q	163	26	)	)	PUNCT
cord-243070-0b06zk1q	163	27	.	.	PUNCT
cord-243070-0b06zk1q	164	1	for	for	ADP
cord-243070-0b06zk1q	164	2	the	the	DET
cord-243070-0b06zk1q	164	3	initial	initial	ADJ
cord-243070-0b06zk1q	164	4	guess	guess	NOUN
cord-243070-0b06zk1q	164	5	of	of	ADP
cord-243070-0b06zk1q	164	6	y	y	PROPN
cord-243070-0b06zk1q	164	7	t	t	PROPN
cord-243070-0b06zk1q	164	8	we	we	PRON
cord-243070-0b06zk1q	164	9	take	take	VERB
cord-243070-0b06zk1q	164	10	y	y	PROPN
cord-243070-0b06zk1q	164	11	notice	notice	NOUN
cord-243070-0b06zk1q	164	12	that	that	SCONJ
cord-243070-0b06zk1q	164	13	this	this	PRON
cord-243070-0b06zk1q	164	14	is	be	AUX
cord-243070-0b06zk1q	164	15	not	not	PART
cord-243070-0b06zk1q	164	16	at	at	ADP
cord-243070-0b06zk1q	164	17	solution	solution	NOUN
cord-243070-0b06zk1q	164	18	to	to	ADP
cord-243070-0b06zk1q	164	19	the	the	DET
cord-243070-0b06zk1q	164	20	backward	backward	ADJ
cord-243070-0b06zk1q	164	21	equations	equation	NOUN
cord-243070-0b06zk1q	164	22	in	in	ADP
cord-243070-0b06zk1q	164	23	(	(	PUNCT
cord-243070-0b06zk1q	164	24	34	34	NUM
cord-243070-0b06zk1q	164	25	)	)	PUNCT
cord-243070-0b06zk1q	164	26	,	,	PUNCT
cord-243070-0b06zk1q	164	27	it	it	PRON
cord-243070-0b06zk1q	164	28	merely	merely	ADV
cord-243070-0b06zk1q	164	29	satisfies	satisfy	VERB
cord-243070-0b06zk1q	164	30	the	the	DET
cord-243070-0b06zk1q	164	31	terminal	terminal	ADJ
cord-243070-0b06zk1q	164	32	condition	condition	NOUN
cord-243070-0b06zk1q	164	33	.	.	PUNCT
cord-243070-0b06zk1q	165	1	after	after	ADP
cord-243070-0b06zk1q	165	2	this	this	PRON
cord-243070-0b06zk1q	165	3	,	,	PUNCT
cord-243070-0b06zk1q	165	4	we	we	PRON
cord-243070-0b06zk1q	165	5	iterate	iterate	VERB
cord-243070-0b06zk1q	165	6	for	for	ADP
cord-243070-0b06zk1q	165	7	k	k	PROPN
cord-243070-0b06zk1q	165	8	=	=	NOUN
cord-243070-0b06zk1q	165	9	0	0	NUM
cord-243070-0b06zk1q	165	10	,	,	PUNCT
cord-243070-0b06zk1q	165	11	1	1	NUM
cord-243070-0b06zk1q	165	12	,	,	PUNCT
cord-243070-0b06zk1q	165	13	.	.	PUNCT
cord-243070-0b06zk1q	165	14	.	.	PUNCT
cord-243070-0b06zk1q	165	15	.	.	PUNCT
cord-243070-0b06zk1q	166	1	,	,	PUNCT
cord-243070-0b06zk1q	166	2	until	until	SCONJ
cord-243070-0b06zk1q	166	3	the	the	DET
cord-243070-0b06zk1q	166	4	stopping	stopping	NOUN
cord-243070-0b06zk1q	166	5	criterion	criterion	NOUN
cord-243070-0b06zk1q	166	6	is	be	AUX
cord-243070-0b06zk1q	166	7	satisfied	satisfied	ADJ
cord-243070-0b06zk1q	166	8	or	or	CCONJ
cord-243070-0b06zk1q	166	9	the	the	DET
cord-243070-0b06zk1q	166	10	maximum	maximum	ADJ
cord-243070-0b06zk1q	166	11	number	number	NOUN
cord-243070-0b06zk1q	166	12	of	of	ADP
cord-243070-0b06zk1q	166	13	iterations	iteration	NOUN
cord-243070-0b06zk1q	166	14	is	be	AUX
cord-243070-0b06zk1q	166	15	reached	reach	VERB
cord-243070-0b06zk1q	166	16	.	.	PUNCT
cord-243070-0b06zk1q	167	1	for	for	ADP
cord-243070-0b06zk1q	167	2	the	the	DET
cord-243070-0b06zk1q	167	3	stopping	stopping	NOUN
cord-243070-0b06zk1q	167	4	criterion	criterion	NOUN
cord-243070-0b06zk1q	167	5	we	we	PRON
cord-243070-0b06zk1q	167	6	choose	choose	VERB
cord-243070-0b06zk1q	167	7	the	the	DET
cord-243070-0b06zk1q	167	8	condition	condition	NOUN
cord-243070-0b06zk1q	167	9	that	that	SCONJ
cord-243070-0b06zk1q	167	10	the	the	DET
cord-243070-0b06zk1q	167	11	average	average	ADJ
cord-243070-0b06zk1q	167	12	l	l	NOUN
cord-243070-0b06zk1q	167	13	2	2	NUM
cord-243070-0b06zk1q	167	14	-norm	-norm	NOUN
cord-243070-0b06zk1q	167	15	change	change	NOUN
cord-243070-0b06zk1q	167	16	of	of	ADP
cord-243070-0b06zk1q	167	17	a	a	DET
cord-243070-0b06zk1q	167	18	monte	monte	PROPN
cord-243070-0b06zk1q	167	19	carlo	carlo	PROPN
cord-243070-0b06zk1q	167	20	path	path	PROPN
cord-243070-0b06zk1q	167	21	falls	fall	VERB
cord-243070-0b06zk1q	167	22	below	below	ADP
cord-243070-0b06zk1q	167	23	a	a	DET
cord-243070-0b06zk1q	167	24	tolerance	tolerance	NOUN
cord-243070-0b06zk1q	167	25	threshold	threshold	NOUN
cord-243070-0b06zk1q	167	26	of	of	ADP
cord-243070-0b06zk1q	167	27	10	10	NUM
cord-243070-0b06zk1q	167	28	−8	−8	NOUN
cord-243070-0b06zk1q	167	29	.	.	PUNCT
cord-243070-0b06zk1q	168	1	we	we	PRON
cord-243070-0b06zk1q	168	2	make	make	VERB
cord-243070-0b06zk1q	168	3	various	various	ADJ
cord-243070-0b06zk1q	168	4	choices	choice	NOUN
cord-243070-0b06zk1q	168	5	of	of	ADP
cord-243070-0b06zk1q	168	6	the	the	DET
cord-243070-0b06zk1q	168	7	coefficients	coefficient	NOUN
cord-243070-0b06zk1q	168	8	l	l	PROPN
cord-243070-0b06zk1q	168	9	,	,	PUNCT
cord-243070-0b06zk1q	168	10	m	m	VERB
cord-243070-0b06zk1q	168	11	,	,	PUNCT
cord-243070-0b06zk1q	168	12	n	n	ADV
cord-243070-0b06zk1q	168	13	defining	define	VERB
cord-243070-0b06zk1q	168	14	the	the	DET
cord-243070-0b06zk1q	168	15	running	running	NOUN
cord-243070-0b06zk1q	168	16	cost	cost	NOUN
cord-243070-0b06zk1q	168	17	functions	function	NOUN
cord-243070-0b06zk1q	168	18	.	.	PUNCT
cord-243070-0b06zk1q	169	1	depending	depend	VERB
cord-243070-0b06zk1q	169	2	on	on	ADP
cord-243070-0b06zk1q	169	3	the	the	DET
cord-243070-0b06zk1q	169	4	values	value	NOUN
cord-243070-0b06zk1q	169	5	of	of	ADP
cord-243070-0b06zk1q	169	6	these	these	DET
cord-243070-0b06zk1q	169	7	coefficients	coefficient	NOUN
cord-243070-0b06zk1q	169	8	,	,	PUNCT
cord-243070-0b06zk1q	169	9	the	the	DET
cord-243070-0b06zk1q	169	10	iterative	iterative	ADJ
cord-243070-0b06zk1q	169	11	process	process	NOUN
cord-243070-0b06zk1q	169	12	described	describe	VERB
cord-243070-0b06zk1q	169	13	above	above	ADP
cord-243070-0b06zk1q	169	14	converges	converge	NOUN
cord-243070-0b06zk1q	169	15	to	to	ADP
cord-243070-0b06zk1q	169	16	a	a	DET
cord-243070-0b06zk1q	169	17	meaningful	meaningful	ADJ
cord-243070-0b06zk1q	169	18	solution	solution	NOUN
cord-243070-0b06zk1q	169	19	or	or	CCONJ
cord-243070-0b06zk1q	169	20	it	it	PRON
cord-243070-0b06zk1q	169	21	diverges	diverge	VERB
cord-243070-0b06zk1q	169	22	.	.	PUNCT
cord-243070-0b06zk1q	170	1	at	at	ADP
cord-243070-0b06zk1q	170	2	this	this	DET
cord-243070-0b06zk1q	170	3	point	point	NOUN
cord-243070-0b06zk1q	170	4	,	,	PUNCT
cord-243070-0b06zk1q	170	5	it	it	PRON
cord-243070-0b06zk1q	170	6	is	be	AUX
cord-243070-0b06zk1q	170	7	unclear	unclear	ADJ
cord-243070-0b06zk1q	170	8	what	what	PRON
cord-243070-0b06zk1q	170	9	choices	choice	NOUN
cord-243070-0b06zk1q	170	10	of	of	ADP
cord-243070-0b06zk1q	170	11	the	the	DET
cord-243070-0b06zk1q	170	12	coefficients	coefficient	NOUN
cord-243070-0b06zk1q	170	13	lead	lead	VERB
cord-243070-0b06zk1q	170	14	to	to	ADP
cord-243070-0b06zk1q	170	15	what	what	PRON
cord-243070-0b06zk1q	170	16	outcomes	outcome	NOUN
cord-243070-0b06zk1q	170	17	,	,	PUNCT
cord-243070-0b06zk1q	170	18	but	but	CCONJ
cord-243070-0b06zk1q	170	19	it	it	PRON
cord-243070-0b06zk1q	170	20	appears	appear	VERB
cord-243070-0b06zk1q	170	21	that	that	SCONJ
cord-243070-0b06zk1q	170	22	there	there	PRON
cord-243070-0b06zk1q	170	23	are	be	VERB
cord-243070-0b06zk1q	170	24	well	well	ADV
cord-243070-0b06zk1q	170	25	defined	define	VERB
cord-243070-0b06zk1q	170	26	basins	basin	NOUN
cord-243070-0b06zk1q	170	27	of	of	ADP
cord-243070-0b06zk1q	170	28	convergence	convergence	NOUN
cord-243070-0b06zk1q	170	29	in	in	ADP
cord-243070-0b06zk1q	170	30	the	the	DET
cord-243070-0b06zk1q	170	31	space	space	NOUN
cord-243070-0b06zk1q	170	32	of	of	ADP
cord-243070-0b06zk1q	170	33	the	the	DET
cord-243070-0b06zk1q	170	34	parameters	parameter	NOUN
cord-243070-0b06zk1q	170	35	.	.	PUNCT
cord-243070-0b06zk1q	171	1	we	we	PRON
cord-243070-0b06zk1q	171	2	first	first	ADV
cord-243070-0b06zk1q	171	3	consider	consider	VERB
cord-243070-0b06zk1q	171	4	a	a	DET
cord-243070-0b06zk1q	171	5	high	high	ADJ
cord-243070-0b06zk1q	171	6	cost	cost	NOUN
cord-243070-0b06zk1q	171	7	policy	policy	NOUN
cord-243070-0b06zk1q	171	8	.	.	PUNCT
cord-243070-0b06zk1q	172	1	figures	figure	NOUN
cord-243070-0b06zk1q	172	2	2	2	NUM
cord-243070-0b06zk1q	172	3	-5	-5	NOUN
cord-243070-0b06zk1q	172	4	show	show	VERB
cord-243070-0b06zk1q	172	5	the	the	DET
cord-243070-0b06zk1q	172	6	graphs	graph	NOUN
cord-243070-0b06zk1q	172	7	of	of	ADP
cord-243070-0b06zk1q	172	8	the	the	DET
cord-243070-0b06zk1q	172	9	solutions	solution	NOUN
cord-243070-0b06zk1q	172	10	assuming	assume	VERB
cord-243070-0b06zk1q	172	11	the	the	DET
cord-243070-0b06zk1q	172	12	following	follow	VERB
cord-243070-0b06zk1q	172	13	parameters	parameter	NOUN
cord-243070-0b06zk1q	172	14	of	of	ADP
cord-243070-0b06zk1q	172	15	the	the	DET
cord-243070-0b06zk1q	172	16	quadratic	quadratic	ADJ
cord-243070-0b06zk1q	172	17	polynomial	polynomial	NOUN
cord-243070-0b06zk1q	172	18	in	in	ADP
cord-243070-0b06zk1q	172	19	the	the	DET
cord-243070-0b06zk1q	172	20	running	running	NOUN
cord-243070-0b06zk1q	172	21	cost	cost	NOUN
cord-243070-0b06zk1q	172	22	function	function	NOUN
cord-243070-0b06zk1q	172	23	c	c	PROPN
cord-243070-0b06zk1q	172	24	2	2	NUM
cord-243070-0b06zk1q	172	25	(	(	PUNCT
cord-243070-0b06zk1q	172	26	u	u	NOUN
cord-243070-0b06zk1q	172	27	2	2	NUM
cord-243070-0b06zk1q	172	28	,	,	PUNCT
cord-243070-0b06zk1q	172	29	x	x	PUNCT
cord-243070-0b06zk1q	172	30	2	2	NUM
cord-243070-0b06zk1q	172	31	):	):	PUNCT
cord-243070-0b06zk1q	172	32	unlike	unlike	ADP
cord-243070-0b06zk1q	172	33	figure	figure	NOUN
cord-243070-0b06zk1q	172	34	1	1	NUM
cord-243070-0b06zk1q	172	35	,	,	PUNCT
cord-243070-0b06zk1q	172	36	the	the	DET
cord-243070-0b06zk1q	172	37	curves	curve	NOUN
cord-243070-0b06zk1q	172	38	in	in	ADP
cord-243070-0b06zk1q	172	39	all	all	DET
cord-243070-0b06zk1q	172	40	graphs	graph	NOUN
cord-243070-0b06zk1q	172	41	below	below	ADV
cord-243070-0b06zk1q	172	42	show	show	VERB
cord-243070-0b06zk1q	172	43	the	the	DET
cord-243070-0b06zk1q	172	44	averages	average	NOUN
cord-243070-0b06zk1q	172	45	of	of	ADP
cord-243070-0b06zk1q	172	46	the	the	DET
cord-243070-0b06zk1q	172	47	corresponding	corresponding	ADJ
cord-243070-0b06zk1q	172	48	quantities	quantity	NOUN
cord-243070-0b06zk1q	172	49	over	over	ADP
cord-243070-0b06zk1q	172	50	2,000	2,000	NUM
cord-243070-0b06zk1q	172	51	monte	monte	PROPN
cord-243070-0b06zk1q	172	52	carlo	carlo	PROPN
cord-243070-0b06zk1q	172	53	paths	path	NOUN
cord-243070-0b06zk1q	172	54	.	.	PUNCT
cord-243070-0b06zk1q	173	1	under	under	ADP
cord-243070-0b06zk1q	173	2	this	this	DET
cord-243070-0b06zk1q	173	3	running	running	NOUN
cord-243070-0b06zk1q	173	4	cost	cost	NOUN
cord-243070-0b06zk1q	173	5	function	function	NOUN
cord-243070-0b06zk1q	173	6	,	,	PUNCT
cord-243070-0b06zk1q	173	7	the	the	DET
cord-243070-0b06zk1q	173	8	optimal	optimal	ADJ
cord-243070-0b06zk1q	173	9	policy	policy	NOUN
cord-243070-0b06zk1q	173	10	is	be	AUX
cord-243070-0b06zk1q	173	11	to	to	PART
cord-243070-0b06zk1q	173	12	implement	implement	VERB
cord-243070-0b06zk1q	173	13	a	a	DET
cord-243070-0b06zk1q	173	14	draconian	draconian	ADJ
cord-243070-0b06zk1q	173	15	isolation	isolation	NOUN
cord-243070-0b06zk1q	173	16	regime	regime	NOUN
cord-243070-0b06zk1q	173	17	,	,	PUNCT
cord-243070-0b06zk1q	173	18	which	which	PRON
cord-243070-0b06zk1q	173	19	leads	lead	VERB
cord-243070-0b06zk1q	173	20	to	to	ADP
cord-243070-0b06zk1q	173	21	a	a	DET
cord-243070-0b06zk1q	173	22	rapid	rapid	ADJ
cord-243070-0b06zk1q	173	23	drop	drop	NOUN
cord-243070-0b06zk1q	173	24	in	in	ADP
cord-243070-0b06zk1q	173	25	infections	infection	NOUN
cord-243070-0b06zk1q	173	26	,	,	PUNCT
cord-243070-0b06zk1q	173	27	while	while	SCONJ
cord-243070-0b06zk1q	173	28	keeping	keep	VERB
cord-243070-0b06zk1q	173	29	the	the	DET
cord-243070-0b06zk1q	173	30	susceptible	susceptible	ADJ
cord-243070-0b06zk1q	173	31	fraction	fraction	NOUN
cord-243070-0b06zk1q	173	32	of	of	ADP
cord-243070-0b06zk1q	173	33	the	the	DET
cord-243070-0b06zk1q	173	34	population	population	NOUN
cord-243070-0b06zk1q	173	35	at	at	ADP
cord-243070-0b06zk1q	173	36	a	a	DET
cord-243070-0b06zk1q	173	37	very	very	ADV
cord-243070-0b06zk1q	173	38	high	high	ADJ
cord-243070-0b06zk1q	173	39	level	level	NOUN
cord-243070-0b06zk1q	173	40	.	.	PUNCT
cord-243070-0b06zk1q	174	1	on	on	ADP
cord-243070-0b06zk1q	174	2	the	the	DET
cord-243070-0b06zk1q	174	3	other	other	ADJ
cord-243070-0b06zk1q	174	4	hand	hand	NOUN
cord-243070-0b06zk1q	174	5	,	,	PUNCT
cord-243070-0b06zk1q	174	6	figures	figure	VERB
cord-243070-0b06zk1q	174	7	6	6	NUM
cord-243070-0b06zk1q	174	8	-9	-9	PROPN
cord-243070-0b06zk1q	174	9	show	show	VERB
cord-243070-0b06zk1q	174	10	the	the	DET
cord-243070-0b06zk1q	174	11	plots	plot	NOUN
cord-243070-0b06zk1q	174	12	of	of	ADP
cord-243070-0b06zk1q	174	13	the	the	DET
cord-243070-0b06zk1q	174	14	solutions	solution	NOUN
cord-243070-0b06zk1q	174	15	assuming	assume	VERB
cord-243070-0b06zk1q	174	16	a	a	DET
cord-243070-0b06zk1q	174	17	low	low	ADJ
cord-243070-0b06zk1q	174	18	cost	cost	NOUN
cord-243070-0b06zk1q	174	19	policy	policy	NOUN
cord-243070-0b06zk1q	174	20	,	,	PUNCT
cord-243070-0b06zk1q	174	21	with	with	ADP
cord-243070-0b06zk1q	174	22	the	the	DET
cord-243070-0b06zk1q	174	23	following	follow	VERB
cord-243070-0b06zk1q	174	24	parameters	parameter	NOUN
cord-243070-0b06zk1q	174	25	of	of	ADP
cord-243070-0b06zk1q	174	26	the	the	DET
cord-243070-0b06zk1q	174	27	quadratic	quadratic	ADJ
cord-243070-0b06zk1q	174	28	polynomial	polynomial	NOUN
cord-243070-0b06zk1q	174	29	in	in	ADP
cord-243070-0b06zk1q	174	30	the	the	DET
cord-243070-0b06zk1q	174	31	running	running	NOUN
cord-243070-0b06zk1q	174	32	cost	cost	NOUN
cord-243070-0b06zk1q	174	33	function	function	NOUN
cord-243070-0b06zk1q	174	34	c	c	PROPN
cord-243070-0b06zk1q	174	35	2	2	NUM
cord-243070-0b06zk1q	174	36	(	(	PUNCT
cord-243070-0b06zk1q	174	37	u	u	NOUN
cord-243070-0b06zk1q	174	38	2	2	NUM
cord-243070-0b06zk1q	174	39	,	,	PUNCT
cord-243070-0b06zk1q	174	40	x	x	NOUN
cord-243070-0b06zk1q	174	41	2	2	NUM
cord-243070-0b06zk1q	174	42	):	):	PUNCT
cord-243070-0b06zk1q	174	43	under	under	ADP
cord-243070-0b06zk1q	174	44	this	this	DET
cord-243070-0b06zk1q	174	45	running	running	NOUN
cord-243070-0b06zk1q	174	46	cost	cost	NOUN
cord-243070-0b06zk1q	174	47	function	function	NOUN
cord-243070-0b06zk1q	174	48	,	,	PUNCT
cord-243070-0b06zk1q	174	49	the	the	DET
cord-243070-0b06zk1q	174	50	optimal	optimal	ADJ
cord-243070-0b06zk1q	174	51	policy	policy	NOUN
cord-243070-0b06zk1q	174	52	is	be	AUX
cord-243070-0b06zk1q	174	53	a	a	DET
cord-243070-0b06zk1q	174	54	moderate	moderate	ADJ
cord-243070-0b06zk1q	174	55	isolation	isolation	NOUN
cord-243070-0b06zk1q	174	56	regime	regime	NOUN
cord-243070-0b06zk1q	174	57	.	.	PUNCT
cord-243070-0b06zk1q	175	1	following	follow	VERB
cord-243070-0b06zk1q	175	2	this	this	DET
cord-243070-0b06zk1q	175	3	policy	policy	NOUN
cord-243070-0b06zk1q	175	4	,	,	PUNCT
cord-243070-0b06zk1q	175	5	the	the	DET
cord-243070-0b06zk1q	175	6	isolation	isolation	NOUN
cord-243070-0b06zk1q	175	7	rate	rate	NOUN
cord-243070-0b06zk1q	175	8	is	be	AUX
cord-243070-0b06zk1q	175	9	high	high	ADJ
cord-243070-0b06zk1q	175	10	,	,	PUNCT
cord-243070-0b06zk1q	175	11	as	as	SCONJ
cord-243070-0b06zk1q	175	12	the	the	DET
cord-243070-0b06zk1q	175	13	infections	infection	NOUN
cord-243070-0b06zk1q	175	14	are	be	AUX
cord-243070-0b06zk1q	175	15	low	low	ADJ
cord-243070-0b06zk1q	175	16	,	,	PUNCT
cord-243070-0b06zk1q	175	17	and	and	CCONJ
cord-243070-0b06zk1q	175	18	then	then	ADV
cord-243070-0b06zk1q	175	19	it	it	PRON
cord-243070-0b06zk1q	175	20	declines	decline	VERB
cord-243070-0b06zk1q	175	21	over	over	ADP
cord-243070-0b06zk1q	175	22	time	time	NOUN
cord-243070-0b06zk1q	175	23	while	while	SCONJ
cord-243070-0b06zk1q	175	24	the	the	DET
cord-243070-0b06zk1q	175	25	epidemic	epidemic	NOUN
cord-243070-0b06zk1q	175	26	develops	develop	VERB
cord-243070-0b06zk1q	175	27	.	.	PUNCT
cord-243070-0b06zk1q	176	1	unlike	unlike	ADP
cord-243070-0b06zk1q	176	2	the	the	DET
cord-243070-0b06zk1q	176	3	policy	policy	NOUN
cord-243070-0b06zk1q	176	4	above	above	ADV
cord-243070-0b06zk1q	176	5	,	,	PUNCT
cord-243070-0b06zk1q	176	6	this	this	PRON
cord-243070-0b06zk1q	176	7	leads	lead	VERB
cord-243070-0b06zk1q	176	8	to	to	ADP
cord-243070-0b06zk1q	176	9	a	a	DET
cord-243070-0b06zk1q	176	10	gradual	gradual	ADJ
cord-243070-0b06zk1q	176	11	decline	decline	NOUN
cord-243070-0b06zk1q	176	12	in	in	ADP
cord-243070-0b06zk1q	176	13	both	both	CCONJ
cord-243070-0b06zk1q	176	14	the	the	DET
cord-243070-0b06zk1q	176	15	infected	infected	ADJ
cord-243070-0b06zk1q	176	16	and	and	CCONJ
cord-243070-0b06zk1q	176	17	susceptible	susceptible	ADJ
cord-243070-0b06zk1q	176	18	fractions	fraction	NOUN
cord-243070-0b06zk1q	176	19	of	of	ADP
cord-243070-0b06zk1q	176	20	the	the	DET
cord-243070-0b06zk1q	176	21	population	population	NOUN
cord-243070-0b06zk1q	176	22	.	.	PUNCT
cord-243070-0b06zk1q	177	1	consider	consider	VERB
cord-243070-0b06zk1q	177	2	now	now	ADV
cord-243070-0b06zk1q	177	3	the	the	DET
cord-243070-0b06zk1q	177	4	case	case	NOUN
cord-243070-0b06zk1q	177	5	of	of	ADP
cord-243070-0b06zk1q	177	6	an	an	DET
cord-243070-0b06zk1q	177	7	optimal	optimal	ADJ
cord-243070-0b06zk1q	177	8	vaccination	vaccination	NOUN
cord-243070-0b06zk1q	177	9	strategy	strategy	NOUN
cord-243070-0b06zk1q	177	10	.	.	PUNCT
cord-243070-0b06zk1q	178	1	again	again	ADV
cord-243070-0b06zk1q	178	2	,	,	PUNCT
cord-243070-0b06zk1q	178	3	we	we	PRON
cord-243070-0b06zk1q	178	4	make	make	VERB
cord-243070-0b06zk1q	178	5	two	two	NUM
cord-243070-0b06zk1q	178	6	choices	choice	NOUN
cord-243070-0b06zk1q	178	7	of	of	ADP
cord-243070-0b06zk1q	178	8	the	the	DET
cord-243070-0b06zk1q	178	9	running	running	NOUN
cord-243070-0b06zk1q	178	10	cost	cost	NOUN
cord-243070-0b06zk1q	178	11	function	function	NOUN
cord-243070-0b06zk1q	178	12	:	:	PUNCT
cord-243070-0b06zk1q	178	13	high	high	ADJ
cord-243070-0b06zk1q	178	14	cost	cost	NOUN
cord-243070-0b06zk1q	178	15	and	and	CCONJ
cord-243070-0b06zk1q	178	16	low	low	ADJ
cord-243070-0b06zk1q	178	17	cost	cost	NOUN
cord-243070-0b06zk1q	178	18	.	.	PUNCT
cord-243070-0b06zk1q	179	1	for	for	ADP
cord-243070-0b06zk1q	179	2	the	the	DET
cord-243070-0b06zk1q	179	3	high	high	ADJ
cord-243070-0b06zk1q	179	4	cost	cost	NOUN
cord-243070-0b06zk1q	179	5	case	case	NOUN
cord-243070-0b06zk1q	179	6	we	we	PRON
cord-243070-0b06zk1q	179	7	choose	choose	VERB
cord-243070-0b06zk1q	179	8	the	the	DET
cord-243070-0b06zk1q	179	9	parameters	parameter	NOUN
cord-243070-0b06zk1q	179	10	as	as	SCONJ
cord-243070-0b06zk1q	179	11	follows	follow	VERB
cord-243070-0b06zk1q	179	12	:	:	PUNCT
cord-243070-0b06zk1q	179	13	the	the	DET
cord-243070-0b06zk1q	179	14	results	result	NOUN
cord-243070-0b06zk1q	179	15	of	of	ADP
cord-243070-0b06zk1q	179	16	monte	monte	PROPN
cord-243070-0b06zk1q	179	17	carlo	carlo	PROPN
cord-243070-0b06zk1q	179	18	simulations	simulation	NOUN
cord-243070-0b06zk1q	179	19	for	for	ADP
cord-243070-0b06zk1q	179	20	this	this	DET
cord-243070-0b06zk1q	179	21	cost	cost	NOUN
cord-243070-0b06zk1q	179	22	function	function	NOUN
cord-243070-0b06zk1q	179	23	are	be	AUX
cord-243070-0b06zk1q	179	24	plotted	plot	VERB
cord-243070-0b06zk1q	179	25	in	in	ADP
cord-243070-0b06zk1q	179	26	figures	figure	NOUN
cord-243070-0b06zk1q	179	27	10	10	NUM
cord-243070-0b06zk1q	179	28	-13	-13	PUNCT
cord-243070-0b06zk1q	179	29	.	.	PUNCT
cord-243070-0b06zk1q	180	1	they	they	PRON
cord-243070-0b06zk1q	180	2	parallel	parallel	VERB
cord-243070-0b06zk1q	180	3	the	the	DET
cord-243070-0b06zk1q	180	4	results	result	NOUN
cord-243070-0b06zk1q	180	5	presented	present	VERB
cord-243070-0b06zk1q	180	6	above	above	ADP
cord-243070-0b06zk1q	180	7	in	in	ADP
cord-243070-0b06zk1q	180	8	the	the	DET
cord-243070-0b06zk1q	180	9	case	case	NOUN
cord-243070-0b06zk1q	180	10	of	of	ADP
cord-243070-0b06zk1q	180	11	high	high	ADJ
cord-243070-0b06zk1q	180	12	cost	cost	NOUN
cord-243070-0b06zk1q	180	13	isolation	isolation	NOUN
cord-243070-0b06zk1q	180	14	mitigation	mitigation	NOUN
cord-243070-0b06zk1q	180	15	.	.	PUNCT
cord-243070-0b06zk1q	181	1	the	the	DET
cord-243070-0b06zk1q	181	2	optimal	optimal	ADJ
cord-243070-0b06zk1q	181	3	policy	policy	NOUN
cord-243070-0b06zk1q	181	4	is	be	AUX
cord-243070-0b06zk1q	181	5	a	a	DET
cord-243070-0b06zk1q	181	6	massive	massive	ADJ
cord-243070-0b06zk1q	181	7	vaccination	vaccination	NOUN
cord-243070-0b06zk1q	181	8	campaign	campaign	NOUN
cord-243070-0b06zk1q	181	9	that	that	PRON
cord-243070-0b06zk1q	181	10	dramatically	dramatically	ADV
cord-243070-0b06zk1q	181	11	reduces	reduce	VERB
cord-243070-0b06zk1q	181	12	the	the	DET
cord-243070-0b06zk1q	181	13	susceptible	susceptible	ADJ
cord-243070-0b06zk1q	181	14	fraction	fraction	NOUN
cord-243070-0b06zk1q	181	15	of	of	ADP
cord-243070-0b06zk1q	181	16	the	the	DET
cord-243070-0b06zk1q	181	17	population	population	NOUN
cord-243070-0b06zk1q	181	18	and	and	CCONJ
cord-243070-0b06zk1q	181	19	leads	lead	VERB
cord-243070-0b06zk1q	181	20	to	to	ADP
cord-243070-0b06zk1q	181	21	significantly	significantly	ADV
cord-243070-0b06zk1q	181	22	lower	low	ADJ
cord-243070-0b06zk1q	181	23	infections	infection	NOUN
cord-243070-0b06zk1q	181	24	.	.	PUNCT
cord-243070-0b06zk1q	182	1	population	population	NOUN
cord-243070-0b06zk1q	182	2	biology	biology	NOUN
cord-243070-0b06zk1q	182	3	of	of	ADP
cord-243070-0b06zk1q	182	4	infectious	infectious	ADJ
cord-243070-0b06zk1q	182	5	diseases	disease	NOUN
cord-243070-0b06zk1q	182	6	:	:	PUNCT
cord-243070-0b06zk1q	182	7	part	part	NOUN
cord-243070-0b06zk1q	182	8	i	i	PRON
cord-243070-0b06zk1q	182	9	dynamic	dynamic	ADJ
cord-243070-0b06zk1q	182	10	programming	programming	NOUN
cord-243070-0b06zk1q	182	11	time	time	NOUN
cord-243070-0b06zk1q	182	12	-	-	PUNCT
cord-243070-0b06zk1q	182	13	optimal	optimal	ADJ
cord-243070-0b06zk1q	182	14	control	control	NOUN
cord-243070-0b06zk1q	182	15	strategies	strategy	NOUN
cord-243070-0b06zk1q	182	16	in	in	ADP
cord-243070-0b06zk1q	182	17	sir	sir	PROPN
cord-243070-0b06zk1q	182	18	epidemic	epidemic	PROPN
cord-243070-0b06zk1q	182	19	models	model	VERB
cord-243070-0b06zk1q	182	20	mathematical	mathematical	ADJ
cord-243070-0b06zk1q	182	21	models	model	NOUN
cord-243070-0b06zk1q	182	22	in	in	ADP
cord-243070-0b06zk1q	182	23	epidemiology	epidemiology	NOUN
cord-243070-0b06zk1q	182	24	stochastic	stochastic	NOUN
cord-243070-0b06zk1q	182	25	epidemic	epidemic	NOUN
cord-243070-0b06zk1q	182	26	models	model	NOUN
cord-243070-0b06zk1q	182	27	:	:	PUNCT
cord-243070-0b06zk1q	182	28	a	a	DET
cord-243070-0b06zk1q	182	29	survey	survey	NOUN
cord-243070-0b06zk1q	182	30	deterministic	deterministic	ADJ
cord-243070-0b06zk1q	182	31	and	and	CCONJ
cord-243070-0b06zk1q	182	32	stochastic	stochastic	NOUN
cord-243070-0b06zk1q	182	33	models	model	NOUN
cord-243070-0b06zk1q	182	34	for	for	ADP
cord-243070-0b06zk1q	182	35	recurrent	recurrent	ADJ
cord-243070-0b06zk1q	182	36	epidemics	epidemic	NOUN
cord-243070-0b06zk1q	182	37	discrete	discrete	ADJ
cord-243070-0b06zk1q	182	38	time	time	NOUN
cord-243070-0b06zk1q	182	39	approximation	approximation	NOUN
cord-243070-0b06zk1q	182	40	and	and	CCONJ
cord-243070-0b06zk1q	182	41	monte	monte	PROPN
cord-243070-0b06zk1q	182	42	-	-	PUNCT
cord-243070-0b06zk1q	182	43	carlo	carlo	PROPN
cord-243070-0b06zk1q	182	44	simulation	simulation	NOUN
cord-243070-0b06zk1q	182	45	of	of	ADP
cord-243070-0b06zk1q	182	46	backward	backward	ADJ
cord-243070-0b06zk1q	182	47	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	182	48	differential	differential	ADJ
cord-243070-0b06zk1q	182	49	equations	equation	NOUN
cord-243070-0b06zk1q	182	50	,	,	PUNCT
cord-243070-0b06zk1q	182	51	stochastic	stochastic	NOUN
cord-243070-0b06zk1q	182	52	processes	process	NOUN
cord-243070-0b06zk1q	182	53	and	and	CCONJ
cord-243070-0b06zk1q	182	54	their	their	PRON
cord-243070-0b06zk1q	182	55	applications	application	NOUN
cord-243070-0b06zk1q	182	56	a	a	DET
cord-243070-0b06zk1q	182	57	scandal	scandal	NOUN
cord-243070-0b06zk1q	182	58	in	in	ADP
cord-243070-0b06zk1q	182	59	bohemia	bohemia	ADJ
cord-243070-0b06zk1q	182	60	,	,	PUNCT
cord-243070-0b06zk1q	182	61	(	(	PUNCT
cord-243070-0b06zk1q	182	62	1891	1891	NUM
cord-243070-0b06zk1q	182	63	)	)	PUNCT
cord-243070-0b06zk1q	182	64	,	,	PUNCT
cord-243070-0b06zk1q	182	65	included	include	VERB
cord-243070-0b06zk1q	182	66	in	in	ADP
cord-243070-0b06zk1q	182	67	the	the	DET
cord-243070-0b06zk1q	182	68	adventures	adventure	NOUN
cord-243070-0b06zk1q	182	69	of	of	ADP
cord-243070-0b06zk1q	182	70	sherlock	sherlock	NOUN
cord-243070-0b06zk1q	182	71	holmes	holmes	PROPN
cord-243070-0b06zk1q	182	72	backward	backward	PROPN
cord-243070-0b06zk1q	182	73	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	182	74	differential	differential	ADJ
cord-243070-0b06zk1q	182	75	equations	equation	NOUN
cord-243070-0b06zk1q	182	76	in	in	ADP
cord-243070-0b06zk1q	182	77	finance	finance	NOUN
cord-243070-0b06zk1q	182	78	controlled	control	VERB
cord-243070-0b06zk1q	182	79	markov	markov	NOUN
cord-243070-0b06zk1q	182	80	processes	process	NOUN
cord-243070-0b06zk1q	182	81	and	and	CCONJ
cord-243070-0b06zk1q	182	82	viscosity	viscosity	NOUN
cord-243070-0b06zk1q	182	83	solutions	solution	NOUN
cord-243070-0b06zk1q	182	84	a	a	DET
cord-243070-0b06zk1q	182	85	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	182	86	differential	differential	ADJ
cord-243070-0b06zk1q	182	87	equation	equation	NOUN
cord-243070-0b06zk1q	182	88	sis	sis	NOUN
cord-243070-0b06zk1q	182	89	epidemic	epidemic	NOUN
cord-243070-0b06zk1q	182	90	model	model	NOUN
cord-243070-0b06zk1q	182	91	geometric	geometric	PROPN
cord-243070-0b06zk1q	182	92	numerical	numerical	ADJ
cord-243070-0b06zk1q	182	93	integration	integration	NOUN
cord-243070-0b06zk1q	182	94	illustrated	illustrate	VERB
cord-243070-0b06zk1q	182	95	by	by	ADP
cord-243070-0b06zk1q	182	96	the	the	DET
cord-243070-0b06zk1q	182	97	störmerverlet	störmerverlet	NOUN
cord-243070-0b06zk1q	182	98	method	method	NOUN
cord-243070-0b06zk1q	182	99	optimal	optimal	ADJ
cord-243070-0b06zk1q	182	100	control	control	NOUN
cord-243070-0b06zk1q	182	101	of	of	ADP
cord-243070-0b06zk1q	182	102	epidemics	epidemic	NOUN
cord-243070-0b06zk1q	182	103	with	with	ADP
cord-243070-0b06zk1q	182	104	limited	limited	ADJ
cord-243070-0b06zk1q	182	105	resources	resource	NOUN
cord-243070-0b06zk1q	182	106	solving	solve	VERB
cord-243070-0b06zk1q	182	107	high	high	ADJ
cord-243070-0b06zk1q	182	108	-	-	PUNCT
cord-243070-0b06zk1q	182	109	dimensional	dimensional	ADJ
cord-243070-0b06zk1q	182	110	partial	partial	ADJ
cord-243070-0b06zk1q	182	111	differential	differential	ADJ
cord-243070-0b06zk1q	182	112	equations	equation	NOUN
cord-243070-0b06zk1q	182	113	using	use	VERB
cord-243070-0b06zk1q	182	114	deep	deep	ADJ
cord-243070-0b06zk1q	182	115	learning	learn	VERB
cord-243070-0b06zk1q	182	116	a	a	DET
cord-243070-0b06zk1q	182	117	contribution	contribution	NOUN
cord-243070-0b06zk1q	182	118	to	to	ADP
cord-243070-0b06zk1q	182	119	the	the	DET
cord-243070-0b06zk1q	182	120	mathematical	mathematical	ADJ
cord-243070-0b06zk1q	182	121	theory	theory	NOUN
cord-243070-0b06zk1q	182	122	of	of	ADP
cord-243070-0b06zk1q	182	123	epidemics	epidemic	NOUN
cord-243070-0b06zk1q	182	124	stochastic	stochastic	NOUN
cord-243070-0b06zk1q	182	125	stability	stability	NOUN
cord-243070-0b06zk1q	182	126	of	of	ADP
cord-243070-0b06zk1q	182	127	differential	differential	ADJ
cord-243070-0b06zk1q	182	128	equations	equation	NOUN
cord-243070-0b06zk1q	182	129	simulating	simulate	VERB
cord-243070-0b06zk1q	182	130	hamiltonian	hamiltonian	ADJ
cord-243070-0b06zk1q	182	131	dynamics	dynamic	NOUN
cord-243070-0b06zk1q	182	132	options	option	NOUN
cord-243070-0b06zk1q	182	133	on	on	ADP
cord-243070-0b06zk1q	182	134	infectious	infectious	ADJ
cord-243070-0b06zk1q	182	135	diseases	disease	NOUN
cord-243070-0b06zk1q	182	136	managing	manage	VERB
cord-243070-0b06zk1q	182	137	counterparty	counterparty	NOUN
cord-243070-0b06zk1q	182	138	credit	credit	NOUN
cord-243070-0b06zk1q	182	139	risk	risk	NOUN
cord-243070-0b06zk1q	182	140	via	via	ADP
cord-243070-0b06zk1q	182	141	backward	backward	ADJ
cord-243070-0b06zk1q	182	142	stochastic	stochastic	ADJ
cord-243070-0b06zk1q	182	143	differential	differential	ADJ
cord-243070-0b06zk1q	182	144	equations	equation	NOUN
cord-243070-0b06zk1q	182	145	valuing	value	VERB
cord-243070-0b06zk1q	182	146	american	american	ADJ
cord-243070-0b06zk1q	182	147	options	option	NOUN
cord-243070-0b06zk1q	182	148	by	by	ADP
cord-243070-0b06zk1q	182	149	simulation	simulation	NOUN
cord-243070-0b06zk1q	182	150	:	:	PUNCT
cord-243070-0b06zk1q	182	151	a	a	DET
cord-243070-0b06zk1q	182	152	simple	simple	ADJ
cord-243070-0b06zk1q	182	153	least	least	ADJ
cord-243070-0b06zk1q	182	154	-	-	PUNCT
cord-243070-0b06zk1q	182	155	squares	square	NOUN
cord-243070-0b06zk1q	182	156	approach	approach	NOUN
cord-243070-0b06zk1q	182	157	continuous	continuous	ADJ
cord-243070-0b06zk1q	182	158	-	-	PUNCT
cord-243070-0b06zk1q	182	159	time	time	NOUN
cord-243070-0b06zk1q	182	160	stochastic	stochastic	NOUN
cord-243070-0b06zk1q	182	161	control	control	NOUN
cord-243070-0b06zk1q	182	162	and	and	CCONJ
cord-243070-0b06zk1q	182	163	optimization	optimization	NOUN
cord-243070-0b06zk1q	182	164	with	with	ADP
cord-243070-0b06zk1q	182	165	financial	financial	ADJ
cord-243070-0b06zk1q	182	166	applications	application	NOUN
cord-243070-0b06zk1q	182	167	the	the	DET
cord-243070-0b06zk1q	182	168	mathematical	mathematical	ADJ
cord-243070-0b06zk1q	182	169	theory	theory	NOUN
cord-243070-0b06zk1q	182	170	of	of	ADP
cord-243070-0b06zk1q	182	171	optimal	optimal	ADJ
cord-243070-0b06zk1q	182	172	processes	process	NOUN
cord-243070-0b06zk1q	182	173	stochastic	stochastic	NOUN
cord-243070-0b06zk1q	182	174	controls	control	NOUN
cord-243070-0b06zk1q	182	175	:	:	PUNCT
cord-243070-0b06zk1q	182	176	hamiltonian	hamiltonian	ADJ
cord-243070-0b06zk1q	182	177	systems	system	NOUN
cord-243070-0b06zk1q	182	178	and	and	CCONJ
cord-243070-0b06zk1q	182	179	hjb	hjb	NOUN
cord-243070-0b06zk1q	182	180	equations	equation	NOUN
