id	sid	tid	token	lemma	pos
cord-194157-ak2gc3nz	1	1	key	key	NN
cord-194157-ak2gc3nz	1	2	:	:	:
cord-194157-ak2gc3nz	1	3	cord-194157-ak2gc3nz	cord-194157-ak2gc3nz	NNP
cord-194157-ak2gc3nz	2	1	authors	author	NNS
cord-194157-ak2gc3nz	2	2	:	:	:
cord-194157-ak2gc3nz	2	3	Clum	Clum	NNP
cord-194157-ak2gc3nz	2	4	,	,	,
cord-194157-ak2gc3nz	2	5	Charles	Charles	NNP
cord-194157-ak2gc3nz	2	6	;	;	:
cord-194157-ak2gc3nz	2	7	Mixon	Mixon	NNP
cord-194157-ak2gc3nz	2	8	,	,	,
cord-194157-ak2gc3nz	2	9	Dustin	Dustin	NNP
cord-194157-ak2gc3nz	2	10	G.	G.	NNP
cord-194157-ak2gc3nz	2	11	title	title	NN
cord-194157-ak2gc3nz	2	12	:	:	:
cord-194157-ak2gc3nz	3	1	Parameter	parameter	NN
cord-194157-ak2gc3nz	3	2	estimation	estimation	NN
cord-194157-ak2gc3nz	3	3	in	in	IN
cord-194157-ak2gc3nz	3	4	the	the	DT
cord-194157-ak2gc3nz	3	5	SIR	SIR	NNP
cord-194157-ak2gc3nz	3	6	model	model	NN
cord-194157-ak2gc3nz	3	7	from	from	IN
cord-194157-ak2gc3nz	3	8	early	early	JJ
cord-194157-ak2gc3nz	3	9	infections	infection	NNS
cord-194157-ak2gc3nz	3	10	date	date	NN
cord-194157-ak2gc3nz	3	11	:	:	:
cord-194157-ak2gc3nz	3	12	2020	2020	CD
cord-194157-ak2gc3nz	3	13	-	-	HYPH
cord-194157-ak2gc3nz	3	14	08	08	CD
cord-194157-ak2gc3nz	3	15	-	-	SYM
cord-194157-ak2gc3nz	3	16	10	10	CD
cord-194157-ak2gc3nz	3	17	journal	journal	NN
cord-194157-ak2gc3nz	3	18	:	:	:
cord-194157-ak2gc3nz	4	1	nan	nan	NNP
cord-194157-ak2gc3nz	4	2	DOI	DOI	NNP
cord-194157-ak2gc3nz	4	3	:	:	:
cord-194157-ak2gc3nz	4	4	nan	nan	NNP
cord-194157-ak2gc3nz	4	5	sha	sha	NNP
cord-194157-ak2gc3nz	4	6	:	:	:
cord-194157-ak2gc3nz	4	7	6a01b1983cead2f2b390b38f2eaf0c3cb4c56c59	6a01b1983cead2f2b390b38f2eaf0c3cb4c56c59	CD
cord-194157-ak2gc3nz	4	8	doc_id	doc_id	CD
cord-194157-ak2gc3nz	4	9	:	:	:
cord-194157-ak2gc3nz	4	10	194157	194157	CD
cord-194157-ak2gc3nz	4	11	cord_uid	cord_uid	NNS
cord-194157-ak2gc3nz	4	12	:	:	:
cord-194157-ak2gc3nz	5	1	ak2gc3nz	ak2gc3nz	NNP
cord-194157-ak2gc3nz	5	2	A	a	DT
cord-194157-ak2gc3nz	5	3	standard	standard	JJ
cord-194157-ak2gc3nz	5	4	model	model	NN
cord-194157-ak2gc3nz	5	5	for	for	IN
cord-194157-ak2gc3nz	5	6	epidemics	epidemic	NNS
cord-194157-ak2gc3nz	5	7	is	be	VBZ
cord-194157-ak2gc3nz	5	8	the	the	DT
cord-194157-ak2gc3nz	5	9	SIR	SIR	NNP
cord-194157-ak2gc3nz	5	10	model	model	NN
cord-194157-ak2gc3nz	5	11	on	on	IN
cord-194157-ak2gc3nz	5	12	a	a	DT
cord-194157-ak2gc3nz	5	13	graph	graph	NN
cord-194157-ak2gc3nz	5	14	.	.	.
cord-194157-ak2gc3nz	6	1	We	-PRON-	PRP
cord-194157-ak2gc3nz	6	2	introduce	introduce	VBP
cord-194157-ak2gc3nz	6	3	a	a	DT
cord-194157-ak2gc3nz	6	4	simple	simple	JJ
cord-194157-ak2gc3nz	6	5	algorithm	algorithm	NN
cord-194157-ak2gc3nz	6	6	that	that	WDT
cord-194157-ak2gc3nz	6	7	uses	use	VBZ
cord-194157-ak2gc3nz	6	8	the	the	DT
cord-194157-ak2gc3nz	6	9	early	early	JJ
cord-194157-ak2gc3nz	6	10	infection	infection	NN
cord-194157-ak2gc3nz	6	11	times	time	NNS
cord-194157-ak2gc3nz	6	12	from	from	IN
cord-194157-ak2gc3nz	6	13	a	a	DT
cord-194157-ak2gc3nz	6	14	sample	sample	NN
cord-194157-ak2gc3nz	6	15	path	path	NN
cord-194157-ak2gc3nz	6	16	of	of	IN
cord-194157-ak2gc3nz	6	17	the	the	DT
cord-194157-ak2gc3nz	6	18	SIR	SIR	NNP
cord-194157-ak2gc3nz	6	19	model	model	NN
cord-194157-ak2gc3nz	6	20	to	to	TO
cord-194157-ak2gc3nz	6	21	estimate	estimate	VB
cord-194157-ak2gc3nz	6	22	the	the	DT
cord-194157-ak2gc3nz	6	23	parameters	parameter	NNS
cord-194157-ak2gc3nz	6	24	this	this	DT
cord-194157-ak2gc3nz	6	25	model	model	NN
cord-194157-ak2gc3nz	6	26	,	,	,
cord-194157-ak2gc3nz	6	27	and	and	CC
cord-194157-ak2gc3nz	6	28	we	-PRON-	PRP
cord-194157-ak2gc3nz	6	29	provide	provide	VBP
cord-194157-ak2gc3nz	6	30	a	a	DT
cord-194157-ak2gc3nz	6	31	performance	performance	NN
cord-194157-ak2gc3nz	6	32	guarantee	guarantee	NN
cord-194157-ak2gc3nz	6	33	in	in	IN
cord-194157-ak2gc3nz	6	34	the	the	DT
cord-194157-ak2gc3nz	6	35	setting	setting	NN
cord-194157-ak2gc3nz	6	36	of	of	IN
cord-194157-ak2gc3nz	6	37	locally	locally	RB
cord-194157-ak2gc3nz	6	38	tree	tree	NN
cord-194157-ak2gc3nz	6	39	-	-	HYPH
cord-194157-ak2gc3nz	6	40	like	like	JJ
cord-194157-ak2gc3nz	6	41	graphs	graph	NNS
cord-194157-ak2gc3nz	6	42	.	.	.
cord-194157-ak2gc3nz	7	1	During	during	IN
cord-194157-ak2gc3nz	7	2	an	an	DT
cord-194157-ak2gc3nz	7	3	epidemic	epidemic	NN
cord-194157-ak2gc3nz	7	4	,	,	,
cord-194157-ak2gc3nz	7	5	government	government	NN
cord-194157-ak2gc3nz	7	6	leaders	leader	NNS
cord-194157-ak2gc3nz	7	7	are	be	VBP
cord-194157-ak2gc3nz	7	8	expected	expect	VBN
cord-194157-ak2gc3nz	7	9	to	to	TO
cord-194157-ak2gc3nz	7	10	help	help	VB
cord-194157-ak2gc3nz	7	11	maintain	maintain	VB
cord-194157-ak2gc3nz	7	12	public	public	JJ
cord-194157-ak2gc3nz	7	13	health	health	NN
cord-194157-ak2gc3nz	7	14	while	while	IN
cord-194157-ak2gc3nz	7	15	simultaneously	simultaneously	RB
cord-194157-ak2gc3nz	7	16	preventing	prevent	VBG
cord-194157-ak2gc3nz	7	17	an	an	DT
cord-194157-ak2gc3nz	7	18	economic	economic	JJ
cord-194157-ak2gc3nz	7	19	meltdown	meltdown	NN
cord-194157-ak2gc3nz	7	20	.	.	.
cord-194157-ak2gc3nz	8	1	In	in	IN
cord-194157-ak2gc3nz	8	2	the	the	DT
cord-194157-ak2gc3nz	8	3	absence	absence	NN
cord-194157-ak2gc3nz	8	4	of	of	IN
cord-194157-ak2gc3nz	8	5	a	a	DT
cord-194157-ak2gc3nz	8	6	vaccine	vaccine	NN
cord-194157-ak2gc3nz	8	7	,	,	,
cord-194157-ak2gc3nz	8	8	decision	decision	NN
cord-194157-ak2gc3nz	8	9	makers	maker	NNS
cord-194157-ak2gc3nz	8	10	must	must	MD
cord-194157-ak2gc3nz	8	11	choose	choose	VB
cord-194157-ak2gc3nz	8	12	between	between	IN
cord-194157-ak2gc3nz	8	13	various	various	JJ
cord-194157-ak2gc3nz	8	14	non	non	JJ
cord-194157-ak2gc3nz	8	15	-	-	JJ
cord-194157-ak2gc3nz	8	16	pharmaceutical	pharmaceutical	JJ
cord-194157-ak2gc3nz	8	17	interventions	intervention	NNS
cord-194157-ak2gc3nz	8	18	.	.	.
cord-194157-ak2gc3nz	9	1	This	this	DT
cord-194157-ak2gc3nz	9	2	decision	decision	NN
cord-194157-ak2gc3nz	9	3	requires	require	VBZ
cord-194157-ak2gc3nz	9	4	an	an	DT
cord-194157-ak2gc3nz	9	5	informative	informative	JJ
cord-194157-ak2gc3nz	9	6	forecast	forecast	NN
cord-194157-ak2gc3nz	9	7	of	of	IN
cord-194157-ak2gc3nz	9	8	the	the	DT
cord-194157-ak2gc3nz	9	9	epidemic	epidemic	NN
cord-194157-ak2gc3nz	9	10	at	at	IN
cord-194157-ak2gc3nz	9	11	a	a	DT
cord-194157-ak2gc3nz	9	12	very	very	RB
cord-194157-ak2gc3nz	9	13	early	early	JJ
cord-194157-ak2gc3nz	9	14	time	time	NN
cord-194157-ak2gc3nz	9	15	.	.	.
cord-194157-ak2gc3nz	10	1	To	to	TO
cord-194157-ak2gc3nz	10	2	obtain	obtain	VB
cord-194157-ak2gc3nz	10	3	such	such	PDT
cord-194157-ak2gc3nz	10	4	a	a	DT
cord-194157-ak2gc3nz	10	5	forecast	forecast	NN
cord-194157-ak2gc3nz	10	6	,	,	,
cord-194157-ak2gc3nz	10	7	it	-PRON-	PRP
cord-194157-ak2gc3nz	10	8	is	be	VBZ
cord-194157-ak2gc3nz	10	9	helpful	helpful	JJ
cord-194157-ak2gc3nz	10	10	to	to	TO
cord-194157-ak2gc3nz	10	11	have	have	VB
cord-194157-ak2gc3nz	10	12	a	a	DT
cord-194157-ak2gc3nz	10	13	parametrized	parametrize	VBN
cord-194157-ak2gc3nz	10	14	model	model	NN
cord-194157-ak2gc3nz	10	15	for	for	IN
cord-194157-ak2gc3nz	10	16	epidemics	epidemic	NNS
cord-194157-ak2gc3nz	10	17	.	.	.
cord-194157-ak2gc3nz	11	1	What	what	WP
cord-194157-ak2gc3nz	11	2	follows	follow	VBZ
cord-194157-ak2gc3nz	11	3	is	be	VBZ
cord-194157-ak2gc3nz	11	4	a	a	DT
cord-194157-ak2gc3nz	11	5	particularly	particularly	RB
cord-194157-ak2gc3nz	11	6	popular	popular	JJ
cord-194157-ak2gc3nz	11	7	compartmental	compartmental	JJ
cord-194157-ak2gc3nz	11	8	model	model	NN
cord-194157-ak2gc3nz	11	9	that	that	WDT
cord-194157-ak2gc3nz	11	10	originates	originate	VBZ
cord-194157-ak2gc3nz	11	11	from	from	IN
cord-194157-ak2gc3nz	11	12	the	the	DT
cord-194157-ak2gc3nz	11	13	classic	classic	JJ
cord-194157-ak2gc3nz	11	14	work	work	NN
cord-194157-ak2gc3nz	11	15	of	of	IN
cord-194157-ak2gc3nz	11	16	Kermack	Kermack	NNP
cord-194157-ak2gc3nz	11	17	and	and	CC
cord-194157-ak2gc3nz	11	18	McKendrick	McKendrick	NNP
cord-194157-ak2gc3nz	11	19	[	[	-LRB-
cord-194157-ak2gc3nz	11	20	4	4	CD
cord-194157-ak2gc3nz	11	21	]	]	-RRB-
cord-194157-ak2gc3nz	11	22	.	.	.
cord-194157-ak2gc3nz	12	1	Definition	definition	NN
cord-194157-ak2gc3nz	12	2	1	1	CD
cord-194157-ak2gc3nz	12	3	(	(	-LRB-
cord-194157-ak2gc3nz	12	4	SIR	SIR	NNP
cord-194157-ak2gc3nz	12	5	model	model	NN
cord-194157-ak2gc3nz	12	6	)	)	-RRB-
cord-194157-ak2gc3nz	12	7	.	.	.
cord-194157-ak2gc3nz	13	1	Fix	fix	VB
cord-194157-ak2gc3nz	13	2	a	a	DT
cord-194157-ak2gc3nz	13	3	simple	simple	JJ
cord-194157-ak2gc3nz	13	4	,	,	,
cord-194157-ak2gc3nz	13	5	connected	connected	JJ
cord-194157-ak2gc3nz	13	6	graph	graph	NN
cord-194157-ak2gc3nz	13	7	G	g	NN
cord-194157-ak2gc3nz	13	8	and	and	CC
cord-194157-ak2gc3nz	13	9	parameters	parameter	NNS
cord-194157-ak2gc3nz	13	10	λ	λ	NN
cord-194157-ak2gc3nz	13	11	,	,	,
cord-194157-ak2gc3nz	13	12	µ	µ	NN
cord-194157-ak2gc3nz	13	13	≥	≥	CD
cord-194157-ak2gc3nz	13	14	0	0	CD
cord-194157-ak2gc3nz	13	15	.	.	.
cord-194157-ak2gc3nz	14	1	Consider	consider	VB
cord-194157-ak2gc3nz	14	2	a	a	DT
cord-194157-ak2gc3nz	14	3	continuous	continuous	JJ
cord-194157-ak2gc3nz	14	4	-	-	HYPH
cord-194157-ak2gc3nz	14	5	time	time	NN
cord-194157-ak2gc3nz	14	6	Markov	Markov	NNP
cord-194157-ak2gc3nz	14	7	chain	chain	NN
cord-194157-ak2gc3nz	14	8	in	in	IN
cord-194157-ak2gc3nz	14	9	which	which	WDT
cord-194157-ak2gc3nz	14	10	the	the	DT
cord-194157-ak2gc3nz	14	11	state	state	NN
cord-194157-ak2gc3nz	14	12	is	be	VBZ
cord-194157-ak2gc3nz	14	13	a	a	DT
cord-194157-ak2gc3nz	14	14	partition	partition	NN
cord-194157-ak2gc3nz	14	15	(	(	-LRB-
cord-194157-ak2gc3nz	14	16	S	s	NN
cord-194157-ak2gc3nz	14	17	,	,	,
cord-194157-ak2gc3nz	14	18	I	-PRON-	PRP
cord-194157-ak2gc3nz	14	19	,	,	,
cord-194157-ak2gc3nz	14	20	R	r	NN
cord-194157-ak2gc3nz	14	21	)	)	-RRB-
cord-194157-ak2gc3nz	14	22	of	of	IN
cord-194157-ak2gc3nz	14	23	V	V	NNP
cord-194157-ak2gc3nz	14	24	(	(	-LRB-
cord-194157-ak2gc3nz	14	25	G	G	NNP
cord-194157-ak2gc3nz	14	26	)	)	-RRB-
cord-194157-ak2gc3nz	14	27	.	.	.
cord-194157-ak2gc3nz	15	1	For	for	IN
cord-194157-ak2gc3nz	15	2	the	the	DT
cord-194157-ak2gc3nz	15	3	initial	initial	JJ
cord-194157-ak2gc3nz	15	4	state	state	NN
cord-194157-ak2gc3nz	15	5	,	,	,
cord-194157-ak2gc3nz	15	6	draw	draw	VB
cord-194157-ak2gc3nz	15	7	v	v	NN
cord-194157-ak2gc3nz	15	8	∼	∼	NNP
cord-194157-ak2gc3nz	15	9	Unif(V	unif(v	NN
cord-194157-ak2gc3nz	15	10	(	(	-LRB-
cord-194157-ak2gc3nz	15	11	G	G	NNP
cord-194157-ak2gc3nz	15	12	)	)	-RRB-
cord-194157-ak2gc3nz	15	13	)	)	-RRB-
cord-194157-ak2gc3nz	15	14	and	and	CC
cord-194157-ak2gc3nz	15	15	put	put	VBN
cord-194157-ak2gc3nz	15	16	In	in	IN
cord-194157-ak2gc3nz	15	17	fact	fact	NN
cord-194157-ak2gc3nz	15	18	,	,	,
cord-194157-ak2gc3nz	15	19	(	(	-LRB-
cord-194157-ak2gc3nz	15	20	s(t	s(t	NNP
cord-194157-ak2gc3nz	15	21	)	)	-RRB-
cord-194157-ak2gc3nz	15	22	,	,	,
cord-194157-ak2gc3nz	15	23	i(t	i(t	NNP
cord-194157-ak2gc3nz	15	24	)	)	-RRB-
cord-194157-ak2gc3nz	15	25	,	,	,
cord-194157-ak2gc3nz	15	26	r(t	r(t	NNP
cord-194157-ak2gc3nz	15	27	)	)	-RRB-
cord-194157-ak2gc3nz	15	28	)	)	-RRB-
cord-194157-ak2gc3nz	15	29	is	be	VBZ
cord-194157-ak2gc3nz	15	30	also	also	RB
cord-194157-ak2gc3nz	15	31	a	a	DT
cord-194157-ak2gc3nz	15	32	continuous	continuous	JJ
cord-194157-ak2gc3nz	15	33	-	-	HYPH
cord-194157-ak2gc3nz	15	34	time	time	NN
cord-194157-ak2gc3nz	15	35	Markov	Markov	NNP
cord-194157-ak2gc3nz	15	36	chain	chain	NN
cord-194157-ak2gc3nz	15	37	in	in	IN
cord-194157-ak2gc3nz	15	38	this	this	DT
cord-194157-ak2gc3nz	15	39	case	case	NN
cord-194157-ak2gc3nz	15	40	.	.	.
cord-194157-ak2gc3nz	16	1	The	the	DT
cord-194157-ak2gc3nz	16	2	initial	initial	JJ
cord-194157-ak2gc3nz	16	3	conditions	condition	NNS
cord-194157-ak2gc3nz	16	4	are	be	VBP
cord-194157-ak2gc3nz	16	5	s(0	s(0	CD
cord-194157-ak2gc3nz	16	6	)	)	-RRB-
cord-194157-ak2gc3nz	17	1	=	=	SYM
cord-194157-ak2gc3nz	17	2	n	n	NN
cord-194157-ak2gc3nz	17	3	−	−	NNP
cord-194157-ak2gc3nz	17	4	1	1	CD
cord-194157-ak2gc3nz	17	5	,	,	,
cord-194157-ak2gc3nz	17	6	i(0	i(0	NNP
cord-194157-ak2gc3nz	17	7	)	)	-RRB-
cord-194157-ak2gc3nz	17	8	=	=	SYM
cord-194157-ak2gc3nz	17	9	1	1	CD
cord-194157-ak2gc3nz	17	10	,	,	,
cord-194157-ak2gc3nz	17	11	r(0	r(0	NNP
cord-194157-ak2gc3nz	17	12	)	)	-RRB-
cord-194157-ak2gc3nz	17	13	=	=	SYM
cord-194157-ak2gc3nz	17	14	0	0	CD
cord-194157-ak2gc3nz	17	15	,	,	,
cord-194157-ak2gc3nz	17	16	and	and	CC
cord-194157-ak2gc3nz	17	17	the	the	DT
cord-194157-ak2gc3nz	17	18	process	process	NN
cord-194157-ak2gc3nz	17	19	transitions	transition	NNS
cord-194157-ak2gc3nz	17	20	(	(	-LRB-
cord-194157-ak2gc3nz	17	21	s	s	NNP
cord-194157-ak2gc3nz	17	22	,	,	,
cord-194157-ak2gc3nz	17	23	i	i	PRP
cord-194157-ak2gc3nz	17	24	,	,	,
cord-194157-ak2gc3nz	17	25	r	r	LS
cord-194157-ak2gc3nz	17	26	)	)	-RRB-
cord-194157-ak2gc3nz	18	1	→	→	NFP
cord-194157-ak2gc3nz	18	2	(	(	-LRB-
cord-194157-ak2gc3nz	18	3	s	s	NNP
cord-194157-ak2gc3nz	18	4	−	−	NNP
cord-194157-ak2gc3nz	18	5	1	1	CD
cord-194157-ak2gc3nz	18	6	,	,	,
cord-194157-ak2gc3nz	18	7	i	i	PRP
cord-194157-ak2gc3nz	18	8	+	+	SYM
cord-194157-ak2gc3nz	18	9	1	1	CD
cord-194157-ak2gc3nz	18	10	,	,	,
cord-194157-ak2gc3nz	18	11	r	r	LS
cord-194157-ak2gc3nz	18	12	)	)	-RRB-
cord-194157-ak2gc3nz	18	13	with	with	IN
cord-194157-ak2gc3nz	18	14	rate	rate	NN
cord-194157-ak2gc3nz	18	15	λis	λis	NN
cord-194157-ak2gc3nz	18	16	and	and	CC
cord-194157-ak2gc3nz	18	17	(	(	-LRB-
cord-194157-ak2gc3nz	18	18	s	s	NNP
cord-194157-ak2gc3nz	18	19	,	,	,
cord-194157-ak2gc3nz	18	20	i	i	PRP
cord-194157-ak2gc3nz	18	21	,	,	,
cord-194157-ak2gc3nz	18	22	r	r	LS
cord-194157-ak2gc3nz	18	23	)	)	-RRB-
cord-194157-ak2gc3nz	19	1	→	→	NFP
cord-194157-ak2gc3nz	19	2	(	(	-LRB-
cord-194157-ak2gc3nz	19	3	s	s	NNP
cord-194157-ak2gc3nz	19	4	,	,	,
cord-194157-ak2gc3nz	19	5	i	i	PRP
cord-194157-ak2gc3nz	19	6	−	−	NNP
cord-194157-ak2gc3nz	19	7	1	1	CD
cord-194157-ak2gc3nz	19	8	,	,	,
cord-194157-ak2gc3nz	20	1	r	r	LS
cord-194157-ak2gc3nz	20	2	+	+	SYM
cord-194157-ak2gc3nz	20	3	1	1	CD
cord-194157-ak2gc3nz	20	4	)	)	-RRB-
cord-194157-ak2gc3nz	20	5	with	with	IN
cord-194157-ak2gc3nz	20	6	rate	rate	NN
cord-194157-ak2gc3nz	20	7	µi	µi	NN
cord-194157-ak2gc3nz	20	8	.	.	.
cord-194157-ak2gc3nz	21	1	Assuming	assume	VBG
cord-194157-ak2gc3nz	21	2	n	n	CC
cord-194157-ak2gc3nz	21	3	is	be	VBZ
cord-194157-ak2gc3nz	21	4	large	large	JJ
cord-194157-ak2gc3nz	21	5	and	and	CC
cord-194157-ak2gc3nz	21	6	λn	λn	XX
cord-194157-ak2gc3nz	21	7	=	=	NN
cord-194157-ak2gc3nz	21	8	:	:	:
cord-194157-ak2gc3nz	21	9	β	β	NNP
cord-194157-ak2gc3nz	21	10	,	,	,
cord-194157-ak2gc3nz	21	11	then	then	RB
cord-194157-ak2gc3nz	21	12	putting	put	VBG
cord-194157-ak2gc3nz	21	13	σ	σ	NN
cord-194157-ak2gc3nz	21	14	:	:	:
cord-194157-ak2gc3nz	21	15	=	=	NFP
cord-194157-ak2gc3nz	21	16	s	s	NNP
cord-194157-ak2gc3nz	21	17	/	/	SYM
cord-194157-ak2gc3nz	21	18	n	n	NNP
cord-194157-ak2gc3nz	21	19	,	,	,
cord-194157-ak2gc3nz	21	20	ι	ι	NNS
cord-194157-ak2gc3nz	21	21	:	:	:
cord-194157-ak2gc3nz	21	22	=	=	NFP
cord-194157-ak2gc3nz	21	23	i	i	NNP
cord-194157-ak2gc3nz	21	24	/	/	SYM
cord-194157-ak2gc3nz	21	25	n	n	NNP
cord-194157-ak2gc3nz	21	26	,	,	,
cord-194157-ak2gc3nz	21	27	and	and	CC
cord-194157-ak2gc3nz	21	28	ρ	ρ	NN
cord-194157-ak2gc3nz	21	29	:	:	:
cord-194157-ak2gc3nz	21	30	=	=	NFP
cord-194157-ak2gc3nz	21	31	r	r	NNP
cord-194157-ak2gc3nz	21	32	/	/	SYM
cord-194157-ak2gc3nz	21	33	n	n	CC
cord-194157-ak2gc3nz	21	34	,	,	,
cord-194157-ak2gc3nz	21	35	we	-PRON-	PRP
cord-194157-ak2gc3nz	21	36	may	may	MD
cord-194157-ak2gc3nz	21	37	pass	pass	VB
cord-194157-ak2gc3nz	21	38	to	to	IN
cord-194157-ak2gc3nz	21	39	the	the	DT
cord-194157-ak2gc3nz	21	40	mean	mean	JJ
cord-194157-ak2gc3nz	21	41	-	-	HYPH
cord-194157-ak2gc3nz	21	42	field	field	NN
cord-194157-ak2gc3nz	21	43	approximation	approximation	NN
cord-194157-ak2gc3nz	21	44	:	:	:
cord-194157-ak2gc3nz	21	45	This	this	DT
cord-194157-ak2gc3nz	21	46	approximation	approximation	NN
cord-194157-ak2gc3nz	21	47	is	be	VBZ
cord-194157-ak2gc3nz	21	48	popular	popular	JJ
cord-194157-ak2gc3nz	21	49	because	because	IN
cord-194157-ak2gc3nz	21	50	it	-PRON-	PRP
cord-194157-ak2gc3nz	21	51	is	be	VBZ
cord-194157-ak2gc3nz	21	52	much	much	RB
cord-194157-ak2gc3nz	21	53	easier	easy	JJR
cord-194157-ak2gc3nz	21	54	to	to	TO
cord-194157-ak2gc3nz	21	55	interact	interact	VB
cord-194157-ak2gc3nz	21	56	with	with	IN
cord-194157-ak2gc3nz	21	57	.	.	.
cord-194157-ak2gc3nz	22	1	The	the	DT
cord-194157-ak2gc3nz	22	2	approximation	approximation	NN
cord-194157-ak2gc3nz	22	3	is	be	VBZ
cord-194157-ak2gc3nz	22	4	good	good	JJ
cord-194157-ak2gc3nz	22	5	once	once	IN
cord-194157-ak2gc3nz	22	6	the	the	DT
cord-194157-ak2gc3nz	22	7	number	number	NN
cord-194157-ak2gc3nz	22	8	of	of	IN
cord-194157-ak2gc3nz	22	9	infected	infected	JJ
cord-194157-ak2gc3nz	22	10	vertices	vertex	NNS
cord-194157-ak2gc3nz	22	11	becomes	become	VBZ
cord-194157-ak2gc3nz	22	12	a	a	DT
cord-194157-ak2gc3nz	22	13	fraction	fraction	NN
cord-194157-ak2gc3nz	22	14	of	of	IN
cord-194157-ak2gc3nz	22	15	n	n	NN
cord-194157-ak2gc3nz	22	16	,	,	,
cord-194157-ak2gc3nz	22	17	and	and	CC
cord-194157-ak2gc3nz	22	18	the	the	DT
cord-194157-ak2gc3nz	22	19	approximation	approximation	NN
cord-194157-ak2gc3nz	22	20	is	be	VBZ
cord-194157-ak2gc3nz	22	21	better	well	JJR
cord-194157-ak2gc3nz	22	22	when	when	WRB
cord-194157-ak2gc3nz	22	23	this	this	DT
cord-194157-ak2gc3nz	22	24	fraction	fraction	NN
cord-194157-ak2gc3nz	22	25	is	be	VBZ
cord-194157-ak2gc3nz	22	26	larger	large	JJR
cord-194157-ak2gc3nz	22	27	[	[	-LRB-
cord-194157-ak2gc3nz	22	28	5	5	CD
cord-194157-ak2gc3nz	22	29	]	]	-RRB-
cord-194157-ak2gc3nz	22	30	.	.	.
cord-194157-ak2gc3nz	23	1	This	this	DT
cord-194157-ak2gc3nz	23	2	suggests	suggest	VBZ
cord-194157-ak2gc3nz	23	3	an	an	DT
cord-194157-ak2gc3nz	23	4	initial	initial	JJ
cord-194157-ak2gc3nz	23	5	condition	condition	NN
cord-194157-ak2gc3nz	23	6	of	of	IN
cord-194157-ak2gc3nz	23	7	the	the	DT
cord-194157-ak2gc3nz	23	8	form	form	NN
cord-194157-ak2gc3nz	23	9	σ(t	σ(t	CD
cord-194157-ak2gc3nz	23	10	0	0	NFP
cord-194157-ak2gc3nz	23	11	)	)	-RRB-
cord-194157-ak2gc3nz	24	1	=	=	NFP
cord-194157-ak2gc3nz	25	1	1	1	LS
cord-194157-ak2gc3nz	25	2	−	−	NN
cord-194157-ak2gc3nz	25	3	δ	δ	NN
cord-194157-ak2gc3nz	25	4	−	−	NN
cord-194157-ak2gc3nz	25	5	γ	γ	NN
cord-194157-ak2gc3nz	25	6	,	,	,
cord-194157-ak2gc3nz	25	7	ι(t	ι(t	NNP
cord-194157-ak2gc3nz	25	8	0	0	NFP
cord-194157-ak2gc3nz	25	9	)	)	-RRB-
cord-194157-ak2gc3nz	25	10	=	=	NFP
cord-194157-ak2gc3nz	26	1	δ	δ	NN
cord-194157-ak2gc3nz	26	2	,	,	,
cord-194157-ak2gc3nz	26	3	ρ(t	ρ(t	NNP
cord-194157-ak2gc3nz	26	4	0	0	NFP
cord-194157-ak2gc3nz	26	5	)	)	-RRB-
cord-194157-ak2gc3nz	27	1	=	=	NFP
cord-194157-ak2gc3nz	27	2	γ	γ	NN
cord-194157-ak2gc3nz	27	3	for	for	IN
cord-194157-ak2gc3nz	27	4	some	some	DT
cord-194157-ak2gc3nz	27	5	small	small	JJ
cord-194157-ak2gc3nz	27	6	t	t	NN
cord-194157-ak2gc3nz	27	7	0	0	CD
cord-194157-ak2gc3nz	27	8	,	,	,
cord-194157-ak2gc3nz	27	9	δ	δ	NN
cord-194157-ak2gc3nz	27	10	,	,	,
cord-194157-ak2gc3nz	27	11	γ	γ	NN
cord-194157-ak2gc3nz	27	12	>	>	XX
cord-194157-ak2gc3nz	27	13	0	0	NFP
cord-194157-ak2gc3nz	27	14	.	.	.
cord-194157-ak2gc3nz	28	1	For	for	IN
cord-194157-ak2gc3nz	28	2	simplicity	simplicity	NN
cord-194157-ak2gc3nz	28	3	,	,	,
cord-194157-ak2gc3nz	28	4	we	-PRON-	PRP
cord-194157-ak2gc3nz	28	5	translate	translate	VBP
cord-194157-ak2gc3nz	28	6	time	time	NN
cord-194157-ak2gc3nz	29	1	so	so	IN
cord-194157-ak2gc3nz	29	2	that	that	IN
cord-194157-ak2gc3nz	29	3	t	t	NN
cord-194157-ak2gc3nz	29	4	0	0	CD
cord-194157-ak2gc3nz	29	5	=	=	SYM
cord-194157-ak2gc3nz	29	6	0	0	CD
cord-194157-ak2gc3nz	29	7	.	.	.
cord-194157-ak2gc3nz	30	1	We	-PRON-	PRP
cord-194157-ak2gc3nz	30	2	argue	argue	VBP
cord-194157-ak2gc3nz	30	3	there	there	EX
cord-194157-ak2gc3nz	30	4	is	be	VBZ
cord-194157-ak2gc3nz	30	5	no	no	DT
cord-194157-ak2gc3nz	30	6	hope	hope	NN
cord-194157-ak2gc3nz	30	7	of	of	IN
cord-194157-ak2gc3nz	30	8	determining	determine	VBG
cord-194157-ak2gc3nz	30	9	(	(	-LRB-
cord-194157-ak2gc3nz	30	10	β	β	NN
cord-194157-ak2gc3nz	30	11	,	,	,
cord-194157-ak2gc3nz	30	12	µ	µ	LS
cord-194157-ak2gc3nz	30	13	)	)	-RRB-
cord-194157-ak2gc3nz	30	14	from	from	IN
cord-194157-ak2gc3nz	30	15	data	datum	NNS
cord-194157-ak2gc3nz	30	16	of	of	IN
cord-194157-ak2gc3nz	30	17	the	the	DT
cord-194157-ak2gc3nz	30	18	form	form	NN
cord-194157-ak2gc3nz	30	19	{	{	-LRB-
cord-194157-ak2gc3nz	30	20	ι(t	ι(t	NNP
cord-194157-ak2gc3nz	30	21	)	)	-RRB-
cord-194157-ak2gc3nz	30	22	+	+	CC
cord-194157-ak2gc3nz	30	23	ρ(t	ρ(t	NNP
cord-194157-ak2gc3nz	30	24	)	)	-RRB-
cord-194157-ak2gc3nz	30	25	}	}	-RRB-
cord-194157-ak2gc3nz	31	1	t∈[0	t∈[0	NN
cord-194157-ak2gc3nz	31	2	,	,	,
cord-194157-ak2gc3nz	31	3	]	]	-RRB-
cord-194157-ak2gc3nz	31	4	for	for	IN
cord-194157-ak2gc3nz	31	5	small	small	JJ
cord-194157-ak2gc3nz	31	6	>	>	XX
cord-194157-ak2gc3nz	31	7	0	0	CD
cord-194157-ak2gc3nz	31	8	.	.	.
cord-194157-ak2gc3nz	32	1	(	(	-LRB-
cord-194157-ak2gc3nz	32	2	While	while	IN
cord-194157-ak2gc3nz	32	3	the	the	DT
cord-194157-ak2gc3nz	32	4	following	follow	VBG
cord-194157-ak2gc3nz	32	5	argument	argument	NN
cord-194157-ak2gc3nz	32	6	is	be	VBZ
cord-194157-ak2gc3nz	32	7	not	not	RB
cord-194157-ak2gc3nz	32	8	rigorous	rigorous	JJ
cord-194157-ak2gc3nz	32	9	,	,	,
cord-194157-ak2gc3nz	32	10	it	-PRON-	PRP
cord-194157-ak2gc3nz	32	11	conveys	convey	VBZ
cord-194157-ak2gc3nz	32	12	the	the	DT
cord-194157-ak2gc3nz	32	13	main	main	JJ
cord-194157-ak2gc3nz	32	14	idea	idea	NN
cord-194157-ak2gc3nz	32	15	.	.	.
cord-194157-ak2gc3nz	32	16	)	)	-RRB-
cord-194157-ak2gc3nz	33	1	Notice	notice	VB
cord-194157-ak2gc3nz	33	2	that	that	IN
cord-194157-ak2gc3nz	33	3	for	for	IN
cord-194157-ak2gc3nz	33	4	t	t	NN
cord-194157-ak2gc3nz	33	5	∈	∈	NN
cord-194157-ak2gc3nz	33	6	[	[	-LRB-
cord-194157-ak2gc3nz	33	7	0	0	NFP
cord-194157-ak2gc3nz	33	8	,	,	,
cord-194157-ak2gc3nz	33	9	]	]	-RRB-
cord-194157-ak2gc3nz	33	10	,	,	,
cord-194157-ak2gc3nz	33	11	it	-PRON-	PRP
cord-194157-ak2gc3nz	33	12	holds	hold	VBZ
cord-194157-ak2gc3nz	33	13	that	that	DT
cord-194157-ak2gc3nz	33	14	σ(t	σ(t	NN
cord-194157-ak2gc3nz	33	15	)	)	-RRB-
cord-194157-ak2gc3nz	34	1	≈	≈	NNP
cord-194157-ak2gc3nz	34	2	1	1	CD
cord-194157-ak2gc3nz	34	3	,	,	,
cord-194157-ak2gc3nz	34	4	and	and	CC
cord-194157-ak2gc3nz	34	5	so	so	RB
cord-194157-ak2gc3nz	34	6	ι(t	ι(t	NNP
cord-194157-ak2gc3nz	34	7	)	)	-RRB-
cord-194157-ak2gc3nz	35	1	≈	≈	NNP
cord-194157-ak2gc3nz	35	2	δe	δe	NNP
cord-194157-ak2gc3nz	36	1	(	(	-LRB-
cord-194157-ak2gc3nz	36	2	β−µ)t	β−µ)t	CD
cord-194157-ak2gc3nz	36	3	and	and	CC
cord-194157-ak2gc3nz	36	4	Then	then	RB
cord-194157-ak2gc3nz	36	5	our	-PRON-	PRP$
cord-194157-ak2gc3nz	36	6	data	datum	NNS
cord-194157-ak2gc3nz	36	7	takes	take	VBZ
cord-194157-ak2gc3nz	36	8	the	the	DT
cord-194157-ak2gc3nz	36	9	form	form	NN
cord-194157-ak2gc3nz	37	1	δ	δ	NNP
cord-194157-ak2gc3nz	38	1	·	·	NFP
cord-194157-ak2gc3nz	38	2	e	e	NN
cord-194157-ak2gc3nz	38	3	(	(	-LRB-
cord-194157-ak2gc3nz	38	4	β−µ)t	β−µ)t	NN
cord-194157-ak2gc3nz	38	5	=	=	SYM
cord-194157-ak2gc3nz	38	6	:	:	:
cord-194157-ak2gc3nz	38	7	a	a	DT
cord-194157-ak2gc3nz	39	1	+	+	CC
cord-194157-ak2gc3nz	39	2	be	be	VB
cord-194157-ak2gc3nz	39	3	ct	ct	NNP
cord-194157-ak2gc3nz	39	4	.	.	.
cord-194157-ak2gc3nz	40	1	We	-PRON-	PRP
cord-194157-ak2gc3nz	40	2	can	can	MD
cord-194157-ak2gc3nz	40	3	expect	expect	VB
cord-194157-ak2gc3nz	40	4	to	to	TO
cord-194157-ak2gc3nz	40	5	determine	determine	VB
cord-194157-ak2gc3nz	40	6	a	a	DT
cord-194157-ak2gc3nz	40	7	,	,	,
cord-194157-ak2gc3nz	40	8	b	b	NN
cord-194157-ak2gc3nz	40	9	,	,	,
cord-194157-ak2gc3nz	40	10	and	and	CC
cord-194157-ak2gc3nz	40	11	c	c	NN
cord-194157-ak2gc3nz	40	12	by	by	IN
cord-194157-ak2gc3nz	40	13	curve	curve	NN
cord-194157-ak2gc3nz	40	14	fitting	fitting	NN
cord-194157-ak2gc3nz	40	15	.	.	.
cord-194157-ak2gc3nz	41	1	However	however	RB
cord-194157-ak2gc3nz	41	2	,	,	,
cord-194157-ak2gc3nz	41	3	we	-PRON-	PRP
cord-194157-ak2gc3nz	41	4	do	do	VBP
cord-194157-ak2gc3nz	41	5	n't	not	RB
cord-194157-ak2gc3nz	41	6	know	know	VB
cord-194157-ak2gc3nz	41	7	δ	δ	NN
cord-194157-ak2gc3nz	41	8	or	or	CC
cord-194157-ak2gc3nz	41	9	γ	γ	NN
cord-194157-ak2gc3nz	41	10	,	,	,
cord-194157-ak2gc3nz	41	11	but	but	CC
cord-194157-ak2gc3nz	41	12	rather	rather	RB
cord-194157-ak2gc3nz	41	13	their	-PRON-	PRP$
cord-194157-ak2gc3nz	41	14	sum	sum	NN
cord-194157-ak2gc3nz	41	15	.	.	.
cord-194157-ak2gc3nz	42	1	As	as	IN
cord-194157-ak2gc3nz	42	2	such	such	JJ
cord-194157-ak2gc3nz	42	3	,	,	,
cord-194157-ak2gc3nz	42	4	we	-PRON-	PRP
cord-194157-ak2gc3nz	42	5	claim	claim	VBP
cord-194157-ak2gc3nz	42	6	that	that	IN
cord-194157-ak2gc3nz	42	7	(	(	-LRB-
cord-194157-ak2gc3nz	42	8	a	a	DT
cord-194157-ak2gc3nz	42	9	,	,	,
cord-194157-ak2gc3nz	42	10	b	b	NN
cord-194157-ak2gc3nz	42	11	,	,	,
cord-194157-ak2gc3nz	42	12	c	c	LS
cord-194157-ak2gc3nz	42	13	)	)	-RRB-
cord-194157-ak2gc3nz	42	14	only	only	RB
cord-194157-ak2gc3nz	42	15	determines	determine	VBZ
cord-194157-ak2gc3nz	42	16	β	β	NN
cord-194157-ak2gc3nz	42	17	−	−	CD
cord-194157-ak2gc3nz	42	18	µ.	µ.	NN
cord-194157-ak2gc3nz	43	1	Indeed	indeed	RB
cord-194157-ak2gc3nz	43	2	,	,	,
cord-194157-ak2gc3nz	43	3	for	for	IN
cord-194157-ak2gc3nz	43	4	every	every	DT
cord-194157-ak2gc3nz	43	5	choice	choice	NN
cord-194157-ak2gc3nz	43	6	of	of	IN
cord-194157-ak2gc3nz	43	7	(	(	-LRB-
cord-194157-ak2gc3nz	43	8	β	β	NN
cord-194157-ak2gc3nz	43	9	,	,	,
cord-194157-ak2gc3nz	43	10	µ	µ	LS
cord-194157-ak2gc3nz	43	11	)	)	-RRB-
cord-194157-ak2gc3nz	43	12	such	such	JJ
cord-194157-ak2gc3nz	43	13	that	that	DT
cord-194157-ak2gc3nz	44	1	β	β	NNP
cord-194157-ak2gc3nz	44	2	−	−	NNP
cord-194157-ak2gc3nz	44	3	µ	µ	NN
cord-194157-ak2gc3nz	44	4	=	=	SYM
cord-194157-ak2gc3nz	44	5	c	c	NN
cord-194157-ak2gc3nz	44	6	,	,	,
cord-194157-ak2gc3nz	44	7	it	-PRON-	PRP
cord-194157-ak2gc3nz	44	8	could	could	MD
cord-194157-ak2gc3nz	44	9	be	be	VB
cord-194157-ak2gc3nz	44	10	the	the	DT
cord-194157-ak2gc3nz	44	11	case	case	NN
cord-194157-ak2gc3nz	44	12	that	that	IN
cord-194157-ak2gc3nz	44	13	which	which	WDT
cord-194157-ak2gc3nz	44	14	would	would	MD
cord-194157-ak2gc3nz	44	15	then	then	RB
cord-194157-ak2gc3nz	44	16	be	be	VB
cord-194157-ak2gc3nz	44	17	consistent	consistent	JJ
cord-194157-ak2gc3nz	44	18	with	with	IN
cord-194157-ak2gc3nz	44	19	the	the	DT
cord-194157-ak2gc3nz	44	20	data	datum	NNS
cord-194157-ak2gc3nz	44	21	(	(	-LRB-
cord-194157-ak2gc3nz	44	22	a	a	NN
cord-194157-ak2gc3nz	44	23	,	,	,
cord-194157-ak2gc3nz	44	24	b	b	NN
cord-194157-ak2gc3nz	44	25	,	,	,
cord-194157-ak2gc3nz	44	26	c	c	NNP
cord-194157-ak2gc3nz	44	27	)	)	-RRB-
cord-194157-ak2gc3nz	44	28	.	.	.
cord-194157-ak2gc3nz	45	1	Of	of	RB
cord-194157-ak2gc3nz	45	2	course	course	RB
cord-194157-ak2gc3nz	45	3	,	,	,
cord-194157-ak2gc3nz	45	4	additional	additional	JJ
cord-194157-ak2gc3nz	45	5	information	information	NN
cord-194157-ak2gc3nz	45	6	about	about	IN
cord-194157-ak2gc3nz	45	7	(	(	-LRB-
cord-194157-ak2gc3nz	45	8	β	β	NN
cord-194157-ak2gc3nz	45	9	,	,	,
cord-194157-ak2gc3nz	45	10	µ	µ	NNP
cord-194157-ak2gc3nz	45	11	)	)	-RRB-
cord-194157-ak2gc3nz	45	12	could	could	MD
cord-194157-ak2gc3nz	45	13	conceivably	conceivably	RB
cord-194157-ak2gc3nz	45	14	be	be	VB
cord-194157-ak2gc3nz	45	15	extracted	extract	VBN
cord-194157-ak2gc3nz	45	16	from	from	IN
cord-194157-ak2gc3nz	45	17	higher	high	JJR
cord-194157-ak2gc3nz	45	18	-	-	HYPH
cord-194157-ak2gc3nz	45	19	order	order	NN
cord-194157-ak2gc3nz	45	20	terms	term	NNS
cord-194157-ak2gc3nz	45	21	,	,	,
cord-194157-ak2gc3nz	45	22	since	since	IN
cord-194157-ak2gc3nz	45	23	a	a	DT
cord-194157-ak2gc3nz	45	24	+	+	NN
cord-194157-ak2gc3nz	45	25	be	be	VB
cord-194157-ak2gc3nz	45	26	ct	ct	NNP
cord-194157-ak2gc3nz	45	27	is	be	VBZ
cord-194157-ak2gc3nz	45	28	merely	merely	RB
cord-194157-ak2gc3nz	45	29	an	an	DT
cord-194157-ak2gc3nz	45	30	approximation	approximation	NN
cord-194157-ak2gc3nz	45	31	of	of	IN
cord-194157-ak2gc3nz	45	32	ι(t	ι(t	NNP
cord-194157-ak2gc3nz	45	33	)	)	-RRB-
cord-194157-ak2gc3nz	45	34	+	+	CC
cord-194157-ak2gc3nz	45	35	ρ(t	ρ(t	NNP
cord-194157-ak2gc3nz	45	36	)	)	-RRB-
cord-194157-ak2gc3nz	45	37	.	.	.
cord-194157-ak2gc3nz	46	1	However	however	RB
cord-194157-ak2gc3nz	46	2	,	,	,
cord-194157-ak2gc3nz	46	3	we	-PRON-	PRP
cord-194157-ak2gc3nz	46	4	expect	expect	VBP
cord-194157-ak2gc3nz	46	5	any	any	DT
cord-194157-ak2gc3nz	46	6	such	such	JJ
cord-194157-ak2gc3nz	46	7	signal	signal	NN
cord-194157-ak2gc3nz	46	8	to	to	TO
cord-194157-ak2gc3nz	46	9	be	be	VB
cord-194157-ak2gc3nz	46	10	dwarfed	dwarf	VBN
cord-194157-ak2gc3nz	46	11	by	by	IN
cord-194157-ak2gc3nz	46	12	noise	noise	NN
cord-194157-ak2gc3nz	46	13	in	in	IN
cord-194157-ak2gc3nz	46	14	the	the	DT
cord-194157-ak2gc3nz	46	15	data	datum	NNS
cord-194157-ak2gc3nz	46	16	.	.	.
cord-194157-ak2gc3nz	47	1	While	while	IN
cord-194157-ak2gc3nz	47	2	the	the	DT
cord-194157-ak2gc3nz	47	3	short	short	JJ
cord-194157-ak2gc3nz	47	4	-	-	HYPH
cord-194157-ak2gc3nz	47	5	term	term	NN
cord-194157-ak2gc3nz	47	6	behavior	behavior	NN
cord-194157-ak2gc3nz	47	7	of	of	IN
cord-194157-ak2gc3nz	47	8	ι	ι	NNS
cord-194157-ak2gc3nz	47	9	is	be	VBZ
cord-194157-ak2gc3nz	47	10	exponential	exponential	JJ
cord-194157-ak2gc3nz	47	11	with	with	IN
cord-194157-ak2gc3nz	47	12	rate	rate	NN
cord-194157-ak2gc3nz	47	13	β	β	NN
cord-194157-ak2gc3nz	47	14	−	−	CD
cord-194157-ak2gc3nz	47	15	µ	µ	NN
cord-194157-ak2gc3nz	47	16	,	,	,
cord-194157-ak2gc3nz	47	17	the	the	DT
cord-194157-ak2gc3nz	47	18	long	long	JJ
cord-194157-ak2gc3nz	47	19	-	-	HYPH
cord-194157-ak2gc3nz	47	20	term	term	NN
cord-194157-ak2gc3nz	47	21	behavior	behavior	NN
cord-194157-ak2gc3nz	47	22	is	be	VBZ
cord-194157-ak2gc3nz	47	23	instead	instead	RB
cord-194157-ak2gc3nz	47	24	governed	govern	VBN
cord-194157-ak2gc3nz	47	25	by	by	IN
cord-194157-ak2gc3nz	47	26	the	the	DT
cord-194157-ak2gc3nz	47	27	quotient	quotient	NN
cord-194157-ak2gc3nz	47	28	R	r	NN
cord-194157-ak2gc3nz	47	29	0	0	CD
cord-194157-ak2gc3nz	47	30	:	:	:
cord-194157-ak2gc3nz	48	1	=	=	NFP
cord-194157-ak2gc3nz	49	1	β/µ	β/µ	RB
cord-194157-ak2gc3nz	49	2	,	,	,
cord-194157-ak2gc3nz	49	3	known	know	VBN
cord-194157-ak2gc3nz	49	4	as	as	IN
cord-194157-ak2gc3nz	49	5	the	the	DT
cord-194157-ak2gc3nz	49	6	basic	basic	JJ
cord-194157-ak2gc3nz	49	7	reproductive	reproductive	JJ
cord-194157-ak2gc3nz	49	8	number	number	NN
cord-194157-ak2gc3nz	49	9	.	.	.
cord-194157-ak2gc3nz	50	1	This	this	DT
cord-194157-ak2gc3nz	50	2	can	can	MD
cord-194157-ak2gc3nz	50	3	be	be	VB
cord-194157-ak2gc3nz	50	4	seen	see	VBN
cord-194157-ak2gc3nz	50	5	by	by	IN
cord-194157-ak2gc3nz	50	6	dilating	dilate	VBG
cord-194157-ak2gc3nz	50	7	time	time	NN
cord-194157-ak2gc3nz	50	8	by	by	IN
cord-194157-ak2gc3nz	50	9	substituting	substitute	VBG
cord-194157-ak2gc3nz	50	10	s	s	NN
cord-194157-ak2gc3nz	50	11	=	=	SYM
cord-194157-ak2gc3nz	50	12	µt	µt	NNP
cord-194157-ak2gc3nz	50	13	.	.	.
cord-194157-ak2gc3nz	51	1	In	in	IN
cord-194157-ak2gc3nz	51	2	this	this	DT
cord-194157-ak2gc3nz	51	3	variable	variable	NN
cord-194157-ak2gc3nz	51	4	,	,	,
cord-194157-ak2gc3nz	51	5	the	the	DT
cord-194157-ak2gc3nz	51	6	mean	mean	JJ
cord-194157-ak2gc3nz	51	7	-	-	HYPH
cord-194157-ak2gc3nz	51	8	field	field	NN
cord-194157-ak2gc3nz	51	9	approximation	approximation	NN
cord-194157-ak2gc3nz	51	10	instead	instead	RB
cord-194157-ak2gc3nz	51	11	takes	take	VBZ
cord-194157-ak2gc3nz	51	12	the	the	DT
cord-194157-ak2gc3nz	51	13	form	form	NN
cord-194157-ak2gc3nz	51	14	That	that	WDT
cord-194157-ak2gc3nz	51	15	is	is	RB
cord-194157-ak2gc3nz	51	16	,	,	,
cord-194157-ak2gc3nz	51	17	R	R	NNP
cord-194157-ak2gc3nz	51	18	0	0	NFP
cord-194157-ak2gc3nz	51	19	(	(	-LRB-
cord-194157-ak2gc3nz	51	20	together	together	RB
cord-194157-ak2gc3nz	51	21	with	with	IN
cord-194157-ak2gc3nz	51	22	initial	initial	JJ
cord-194157-ak2gc3nz	51	23	conditions	condition	NNS
cord-194157-ak2gc3nz	51	24	)	)	-RRB-
cord-194157-ak2gc3nz	51	25	determines	determine	VBZ
cord-194157-ak2gc3nz	51	26	ι	ι	NNS
cord-194157-ak2gc3nz	51	27	modulo	modulo	JJ
cord-194157-ak2gc3nz	51	28	time	time	NN
cord-194157-ak2gc3nz	51	29	dilation	dilation	NN
cord-194157-ak2gc3nz	51	30	,	,	,
cord-194157-ak2gc3nz	51	31	and	and	CC
cord-194157-ak2gc3nz	51	32	notably	notably	RB
cord-194157-ak2gc3nz	51	33	,	,	,
cord-194157-ak2gc3nz	51	34	whether	whether	IN
cord-194157-ak2gc3nz	51	35	the	the	DT
cord-194157-ak2gc3nz	51	36	curve	curve	NN
cord-194157-ak2gc3nz	51	37	ever	ever	RB
cord-194157-ak2gc3nz	51	38	exceeds	exceed	VBZ
cord-194157-ak2gc3nz	51	39	the	the	DT
cord-194157-ak2gc3nz	51	40	capacity	capacity	NN
cord-194157-ak2gc3nz	51	41	of	of	IN
cord-194157-ak2gc3nz	51	42	the	the	DT
cord-194157-ak2gc3nz	51	43	medical	medical	JJ
cord-194157-ak2gc3nz	51	44	care	care	NN
cord-194157-ak2gc3nz	51	45	system	system	NN
cord-194157-ak2gc3nz	51	46	.	.	.
cord-194157-ak2gc3nz	52	1	However	however	RB
cord-194157-ak2gc3nz	52	2	,	,	,
cord-194157-ak2gc3nz	52	3	R	r	NN
cord-194157-ak2gc3nz	52	4	0	0	CD
cord-194157-ak2gc3nz	52	5	=	=	NFP
cord-194157-ak2gc3nz	53	1	β/µ	β/µ	UH
cord-194157-ak2gc3nz	53	2	can	can	MD
cord-194157-ak2gc3nz	53	3	not	not	RB
cord-194157-ak2gc3nz	53	4	be	be	VB
cord-194157-ak2gc3nz	53	5	determined	determine	VBN
cord-194157-ak2gc3nz	53	6	from	from	IN
cord-194157-ak2gc3nz	53	7	β	β	NNP
cord-194157-ak2gc3nz	53	8	−	−	CD
cord-194157-ak2gc3nz	53	9	µ.	µ.	NN
cord-194157-ak2gc3nz	54	1	Overall	overall	RB
cord-194157-ak2gc3nz	54	2	,	,	,
cord-194157-ak2gc3nz	54	3	the	the	DT
cord-194157-ak2gc3nz	54	4	complete	complete	JJ
cord-194157-ak2gc3nz	54	5	graph	graph	NN
cord-194157-ak2gc3nz	54	6	is	be	VBZ
cord-194157-ak2gc3nz	54	7	not	not	RB
cord-194157-ak2gc3nz	54	8	amenable	amenable	JJ
cord-194157-ak2gc3nz	54	9	to	to	IN
cord-194157-ak2gc3nz	54	10	determining	determine	VBG
cord-194157-ak2gc3nz	54	11	(	(	-LRB-
cord-194157-ak2gc3nz	54	12	λ	λ	NN
cord-194157-ak2gc3nz	54	13	,	,	,
cord-194157-ak2gc3nz	54	14	µ	µ	NN
cord-194157-ak2gc3nz	54	15	)	)	-RRB-
cord-194157-ak2gc3nz	54	16	from	from	IN
cord-194157-ak2gc3nz	54	17	{	{	-LRB-
cord-194157-ak2gc3nz	54	18	U	u	NN
cord-194157-ak2gc3nz	54	19	(	(	-LRB-
cord-194157-ak2gc3nz	54	20	t	t	NN
cord-194157-ak2gc3nz	54	21	)	)	-RRB-
cord-194157-ak2gc3nz	54	22	}	}	-RRB-
cord-194157-ak2gc3nz	54	23	t∈[0	t∈[0	NN
cord-194157-ak2gc3nz	54	24	,	,	,
cord-194157-ak2gc3nz	54	25	]	]	-RRB-
cord-194157-ak2gc3nz	54	26	.	.	.
cord-194157-ak2gc3nz	55	1	However	however	RB
cord-194157-ak2gc3nz	55	2	,	,	,
cord-194157-ak2gc3nz	55	3	real	real	JJ
cord-194157-ak2gc3nz	55	4	-	-	HYPH
cord-194157-ak2gc3nz	55	5	world	world	NN
cord-194157-ak2gc3nz	55	6	social	social	JJ
cord-194157-ak2gc3nz	55	7	networks	network	NNS
cord-194157-ak2gc3nz	55	8	are	be	VBP
cord-194157-ak2gc3nz	55	9	far	far	RB
cord-194157-ak2gc3nz	55	10	from	from	IN
cord-194157-ak2gc3nz	55	11	complete	complete	JJ
cord-194157-ak2gc3nz	55	12	.	.	.
cord-194157-ak2gc3nz	56	1	Like	like	IN
cord-194157-ak2gc3nz	56	2	social	social	JJ
cord-194157-ak2gc3nz	56	3	networks	network	NNS
cord-194157-ak2gc3nz	56	4	,	,	,
cord-194157-ak2gc3nz	56	5	expander	expander	NN
cord-194157-ak2gc3nz	56	6	graphs	graph	NNS
cord-194157-ak2gc3nz	56	7	have	have	VBP
cord-194157-ak2gc3nz	56	8	low	low	JJ
cord-194157-ak2gc3nz	56	9	degree	degree	NN
cord-194157-ak2gc3nz	56	10	,	,	,
cord-194157-ak2gc3nz	56	11	but	but	CC
cord-194157-ak2gc3nz	56	12	considering	consider	VBG
cord-194157-ak2gc3nz	56	13	their	-PRON-	PRP$
cord-194157-ak2gc3nz	56	14	spectral	spectral	JJ
cord-194157-ak2gc3nz	56	15	properties	property	NNS
cord-194157-ak2gc3nz	56	16	,	,	,
cord-194157-ak2gc3nz	56	17	one	one	PRP
cord-194157-ak2gc3nz	56	18	might	may	MD
cord-194157-ak2gc3nz	56	19	presume	presume	VB
cord-194157-ak2gc3nz	56	20	that	that	IN
cord-194157-ak2gc3nz	56	21	they	-PRON-	PRP
cord-194157-ak2gc3nz	56	22	are	be	VBP
cord-194157-ak2gc3nz	56	23	just	just	RB
cord-194157-ak2gc3nz	56	24	as	as	RB
cord-194157-ak2gc3nz	56	25	opaque	opaque	JJ
cord-194157-ak2gc3nz	56	26	as	as	IN
cord-194157-ak2gc3nz	56	27	the	the	DT
cord-194157-ak2gc3nz	56	28	complete	complete	JJ
cord-194157-ak2gc3nz	56	29	graph	graph	NN
cord-194157-ak2gc3nz	56	30	.	.	.
cord-194157-ak2gc3nz	57	1	Surprisingly	surprisingly	RB
cord-194157-ak2gc3nz	57	2	,	,	,
cord-194157-ak2gc3nz	57	3	this	this	DT
cord-194157-ak2gc3nz	57	4	is	be	VBZ
cord-194157-ak2gc3nz	57	5	not	not	RB
cord-194157-ak2gc3nz	57	6	correct	correct	JJ
cord-194157-ak2gc3nz	57	7	!	!	.
cord-194157-ak2gc3nz	58	1	In	in	IN
cord-194157-ak2gc3nz	58	2	this	this	DT
cord-194157-ak2gc3nz	58	3	paper	paper	NN
cord-194157-ak2gc3nz	58	4	,	,	,
cord-194157-ak2gc3nz	58	5	we	-PRON-	PRP
cord-194157-ak2gc3nz	58	6	show	show	VBP
cord-194157-ak2gc3nz	58	7	how	how	WRB
cord-194157-ak2gc3nz	58	8	certain	certain	JJ
cord-194157-ak2gc3nz	58	9	graphs	graph	NNS
cord-194157-ak2gc3nz	58	10	(	(	-LRB-
cord-194157-ak2gc3nz	58	11	including	include	VBG
cord-194157-ak2gc3nz	58	12	certain	certain	JJ
cord-194157-ak2gc3nz	58	13	expander	expander	NN
cord-194157-ak2gc3nz	58	14	graphs	graph	NNS
cord-194157-ak2gc3nz	58	15	)	)	-RRB-
cord-194157-ak2gc3nz	58	16	are	be	VBP
cord-194157-ak2gc3nz	58	17	provably	provably	RB
cord-194157-ak2gc3nz	58	18	amenable	amenable	JJ
cord-194157-ak2gc3nz	58	19	to	to	IN
cord-194157-ak2gc3nz	58	20	determining	determine	VBG
cord-194157-ak2gc3nz	58	21	(	(	-LRB-
cord-194157-ak2gc3nz	58	22	λ	λ	NN
cord-194157-ak2gc3nz	58	23	,	,	,
cord-194157-ak2gc3nz	58	24	µ	µ	NN
cord-194157-ak2gc3nz	58	25	)	)	-RRB-
cord-194157-ak2gc3nz	58	26	from	from	IN
cord-194157-ak2gc3nz	58	27	{	{	-LRB-
cord-194157-ak2gc3nz	58	28	U	u	NN
cord-194157-ak2gc3nz	58	29	(	(	-LRB-
cord-194157-ak2gc3nz	58	30	t	t	NN
cord-194157-ak2gc3nz	58	31	)	)	-RRB-
cord-194157-ak2gc3nz	58	32	}	}	-RRB-
cord-194157-ak2gc3nz	58	33	t∈[0	t∈[0	NN
cord-194157-ak2gc3nz	58	34	,	,	,
cord-194157-ak2gc3nz	58	35	]	]	-RRB-
cord-194157-ak2gc3nz	58	36	.	.	.
cord-194157-ak2gc3nz	59	1	In	in	IN
cord-194157-ak2gc3nz	59	2	the	the	DT
cord-194157-ak2gc3nz	59	3	following	following	JJ
cord-194157-ak2gc3nz	59	4	section	section	NN
cord-194157-ak2gc3nz	59	5	,	,	,
cord-194157-ak2gc3nz	59	6	we	-PRON-	PRP
cord-194157-ak2gc3nz	59	7	introduce	introduce	VBP
cord-194157-ak2gc3nz	59	8	our	-PRON-	PRP$
cord-194157-ak2gc3nz	59	9	approach	approach	NN
cord-194157-ak2gc3nz	59	10	.	.	.
cord-194157-ak2gc3nz	60	1	Specifically	specifically	RB
cord-194157-ak2gc3nz	60	2	,	,	,
cord-194157-ak2gc3nz	60	3	we	-PRON-	PRP
cord-194157-ak2gc3nz	60	4	isolate	isolate	VBP
cord-194157-ak2gc3nz	60	5	infections	infection	NNS
cord-194157-ak2gc3nz	60	6	that	that	WDT
cord-194157-ak2gc3nz	60	7	pass	pass	VBP
cord-194157-ak2gc3nz	60	8	across	across	IN
cord-194157-ak2gc3nz	60	9	bridges	bridge	NNS
cord-194157-ak2gc3nz	60	10	in	in	IN
cord-194157-ak2gc3nz	60	11	a	a	DT
cord-194157-ak2gc3nz	60	12	local	local	JJ
cord-194157-ak2gc3nz	60	13	subgraph	subgraph	NN
cord-194157-ak2gc3nz	60	14	of	of	IN
cord-194157-ak2gc3nz	60	15	the	the	DT
cord-194157-ak2gc3nz	60	16	social	social	JJ
cord-194157-ak2gc3nz	60	17	network	network	NN
cord-194157-ak2gc3nz	60	18	,	,	,
cord-194157-ak2gc3nz	60	19	and	and	CC
cord-194157-ak2gc3nz	60	20	then	then	RB
cord-194157-ak2gc3nz	60	21	we	-PRON-	PRP
cord-194157-ak2gc3nz	60	22	estimate	estimate	VBP
cord-194157-ak2gc3nz	60	23	λ	λ	NN
cord-194157-ak2gc3nz	60	24	and	and	CC
cord-194157-ak2gc3nz	60	25	µ	µ	NN
cord-194157-ak2gc3nz	60	26	from	from	IN
cord-194157-ak2gc3nz	60	27	these	these	DT
cord-194157-ak2gc3nz	60	28	infection	infection	NN
cord-194157-ak2gc3nz	60	29	statistics	statistic	NNS
cord-194157-ak2gc3nz	60	30	.	.	.
cord-194157-ak2gc3nz	61	1	Section	section	NN
cord-194157-ak2gc3nz	61	2	3	3	CD
cord-194157-ak2gc3nz	61	3	gives	give	VBZ
cord-194157-ak2gc3nz	61	4	the	the	DT
cord-194157-ak2gc3nz	61	5	proof	proof	NN
cord-194157-ak2gc3nz	61	6	of	of	IN
cord-194157-ak2gc3nz	61	7	our	-PRON-	PRP$
cord-194157-ak2gc3nz	61	8	main	main	JJ
cord-194157-ak2gc3nz	61	9	result	result	NN
cord-194157-ak2gc3nz	61	10	:	:	:
cord-194157-ak2gc3nz	61	11	that	that	IN
cord-194157-ak2gc3nz	61	12	our	-PRON-	PRP$
cord-194157-ak2gc3nz	61	13	approach	approach	NN
cord-194157-ak2gc3nz	61	14	provides	provide	VBZ
cord-194157-ak2gc3nz	61	15	decent	decent	JJ
cord-194157-ak2gc3nz	61	16	estimates	estimate	NNS
cord-194157-ak2gc3nz	61	17	of	of	IN
cord-194157-ak2gc3nz	61	18	λ	λ	NN
cord-194157-ak2gc3nz	61	19	and	and	CC
cord-194157-ak2gc3nz	61	20	µ	µ	NN
cord-194157-ak2gc3nz	61	21	in	in	IN
cord-194157-ak2gc3nz	61	22	the	the	DT
cord-194157-ak2gc3nz	61	23	setting	setting	NN
cord-194157-ak2gc3nz	61	24	of	of	IN
cord-194157-ak2gc3nz	61	25	locally	locally	RB
cord-194157-ak2gc3nz	61	26	tree	tree	NN
cord-194157-ak2gc3nz	61	27	-	-	HYPH
cord-194157-ak2gc3nz	61	28	like	like	JJ
cord-194157-ak2gc3nz	61	29	graphs	graph	NNS
cord-194157-ak2gc3nz	61	30	.	.	.
cord-194157-ak2gc3nz	62	1	Our	-PRON-	PRP$
cord-194157-ak2gc3nz	62	2	proof	proof	NN
cord-194157-ak2gc3nz	62	3	makes	make	VBZ
cord-194157-ak2gc3nz	62	4	use	use	NN
cord-194157-ak2gc3nz	62	5	of	of	IN
cord-194157-ak2gc3nz	62	6	the	the	DT
cord-194157-ak2gc3nz	62	7	vast	vast	JJ
cord-194157-ak2gc3nz	62	8	literature	literature	NN
cord-194157-ak2gc3nz	62	9	on	on	IN
cord-194157-ak2gc3nz	62	10	SIR	SIR	NNP
cord-194157-ak2gc3nz	62	11	dynamics	dynamic	NNS
cord-194157-ak2gc3nz	62	12	on	on	IN
cord-194157-ak2gc3nz	62	13	infinite	infinite	JJ
cord-194157-ak2gc3nz	62	14	trees	tree	NNS
cord-194157-ak2gc3nz	62	15	.	.	.
cord-194157-ak2gc3nz	63	1	We	-PRON-	PRP
cord-194157-ak2gc3nz	63	2	conclude	conclude	VBP
cord-194157-ak2gc3nz	63	3	in	in	IN
cord-194157-ak2gc3nz	63	4	Section	section	NN
cord-194157-ak2gc3nz	63	5	4	4	CD
cord-194157-ak2gc3nz	63	6	with	with	IN
cord-194157-ak2gc3nz	63	7	a	a	DT
cord-194157-ak2gc3nz	63	8	discussion	discussion	NN
cord-194157-ak2gc3nz	63	9	of	of	IN
cord-194157-ak2gc3nz	63	10	opportunities	opportunity	NNS
cord-194157-ak2gc3nz	63	11	for	for	IN
cord-194157-ak2gc3nz	63	12	future	future	JJ
cord-194157-ak2gc3nz	63	13	work	work	NN
cord-194157-ak2gc3nz	63	14	.	.	.
cord-194157-ak2gc3nz	64	1	We	-PRON-	PRP
cord-194157-ak2gc3nz	64	2	start	start	VBP
cord-194157-ak2gc3nz	64	3	with	with	IN
cord-194157-ak2gc3nz	64	4	the	the	DT
cord-194157-ak2gc3nz	64	5	simple	simple	JJ
cord-194157-ak2gc3nz	64	6	example	example	NN
cord-194157-ak2gc3nz	64	7	in	in	IN
cord-194157-ak2gc3nz	64	8	which	which	WDT
cord-194157-ak2gc3nz	64	9	G	g	NN
cord-194157-ak2gc3nz	64	10	=	=	SYM
cord-194157-ak2gc3nz	64	11	K	K	NNP
cord-194157-ak2gc3nz	64	12	2	2	CD
cord-194157-ak2gc3nz	64	13	.	.	.
cord-194157-ak2gc3nz	65	1	According	accord	VBG
cord-194157-ak2gc3nz	65	2	to	to	IN
cord-194157-ak2gc3nz	65	3	the	the	DT
cord-194157-ak2gc3nz	65	4	SIR	SIR	NNP
cord-194157-ak2gc3nz	65	5	process	process	NN
cord-194157-ak2gc3nz	65	6	,	,	,
cord-194157-ak2gc3nz	65	7	one	one	CD
cord-194157-ak2gc3nz	65	8	of	of	IN
cord-194157-ak2gc3nz	65	9	the	the	DT
cord-194157-ak2gc3nz	65	10	two	two	CD
cord-194157-ak2gc3nz	65	11	vertices	vertex	NNS
cord-194157-ak2gc3nz	65	12	is	be	VBZ
cord-194157-ak2gc3nz	65	13	infected	infect	VBN
cord-194157-ak2gc3nz	65	14	,	,	,
cord-194157-ak2gc3nz	65	15	and	and	CC
cord-194157-ak2gc3nz	65	16	then	then	RB
cord-194157-ak2gc3nz	65	17	it	-PRON-	PRP
cord-194157-ak2gc3nz	65	18	either	either	CC
cord-194157-ak2gc3nz	65	19	infects	infect	VBZ
cord-194157-ak2gc3nz	65	20	the	the	DT
cord-194157-ak2gc3nz	65	21	other	other	JJ
cord-194157-ak2gc3nz	65	22	vertex	vertex	NN
cord-194157-ak2gc3nz	65	23	or	or	CC
cord-194157-ak2gc3nz	65	24	it	-PRON-	PRP
cord-194157-ak2gc3nz	65	25	recovers	recover	VBZ
cord-194157-ak2gc3nz	65	26	before	before	IN
cord-194157-ak2gc3nz	65	27	doing	do	VBG
cord-194157-ak2gc3nz	65	28	so	so	RB
cord-194157-ak2gc3nz	65	29	.	.	.
cord-194157-ak2gc3nz	66	1	Let	let	VB
cord-194157-ak2gc3nz	66	2	Z	z	PRP
cord-194157-ak2gc3nz	66	3	denote	denote	VB
cord-194157-ak2gc3nz	66	4	the	the	DT
cord-194157-ak2gc3nz	66	5	random	random	JJ
cord-194157-ak2gc3nz	66	6	amount	amount	NN
cord-194157-ak2gc3nz	66	7	of	of	IN
cord-194157-ak2gc3nz	66	8	time	time	NN
cord-194157-ak2gc3nz	66	9	it	-PRON-	PRP
cord-194157-ak2gc3nz	66	10	takes	take	VBZ
cord-194157-ak2gc3nz	66	11	for	for	IN
cord-194157-ak2gc3nz	66	12	the	the	DT
cord-194157-ak2gc3nz	66	13	second	second	JJ
cord-194157-ak2gc3nz	66	14	vertex	vertex	NN
cord-194157-ak2gc3nz	66	15	to	to	TO
cord-194157-ak2gc3nz	66	16	become	become	VB
cord-194157-ak2gc3nz	66	17	infected	infected	JJ
cord-194157-ak2gc3nz	66	18	.	.	.
cord-194157-ak2gc3nz	67	1	Notice	notice	VB
cord-194157-ak2gc3nz	67	2	that	that	DT
cord-194157-ak2gc3nz	67	3	Z	z	NN
cord-194157-ak2gc3nz	68	1	=	=	NFP
cord-194157-ak2gc3nz	68	2	∞	∞	NNP
cord-194157-ak2gc3nz	68	3	with	with	IN
cord-194157-ak2gc3nz	68	4	probability	probability	NN
cord-194157-ak2gc3nz	68	5	µ	µ	NN
cord-194157-ak2gc3nz	68	6	λ+µ	λ+µ	ADD
cord-194157-ak2gc3nz	68	7	.	.	.
cord-194157-ak2gc3nz	69	1	On	on	IN
cord-194157-ak2gc3nz	69	2	the	the	DT
cord-194157-ak2gc3nz	69	3	other	other	JJ
cord-194157-ak2gc3nz	69	4	hand	hand	NN
cord-194157-ak2gc3nz	69	5	,	,	,
cord-194157-ak2gc3nz	69	6	if	if	IN
cord-194157-ak2gc3nz	69	7	we	-PRON-	PRP
cord-194157-ak2gc3nz	69	8	condition	condition	VBP
cord-194157-ak2gc3nz	69	9	on	on	IN
cord-194157-ak2gc3nz	69	10	the	the	DT
cord-194157-ak2gc3nz	69	11	event	event	NN
cord-194157-ak2gc3nz	69	12	Z	z	NN
cord-194157-ak2gc3nz	69	13	<	<	XX
cord-194157-ak2gc3nz	70	1	∞	∞	NNP
cord-194157-ak2gc3nz	70	2	,	,	,
cord-194157-ak2gc3nz	70	3	then	then	RB
cord-194157-ak2gc3nz	70	4	the	the	DT
cord-194157-ak2gc3nz	70	5	distribution	distribution	NN
cord-194157-ak2gc3nz	70	6	of	of	IN
cord-194157-ak2gc3nz	70	7	Z	Z	NNP
cord-194157-ak2gc3nz	70	8	is	be	VBZ
cord-194157-ak2gc3nz	70	9	exponential	exponential	JJ
cord-194157-ak2gc3nz	70	10	with	with	IN
cord-194157-ak2gc3nz	70	11	rate	rate	NN
cord-194157-ak2gc3nz	70	12	λ	λ	NN
cord-194157-ak2gc3nz	70	13	+	+	CC
cord-194157-ak2gc3nz	70	14	µ.	µ.	NN
cord-194157-ak2gc3nz	71	1	(	(	-LRB-
cord-194157-ak2gc3nz	71	2	This	this	DT
cord-194157-ak2gc3nz	71	3	is	be	VBZ
cord-194157-ak2gc3nz	71	4	a	a	DT
cord-194157-ak2gc3nz	71	5	consequence	consequence	NN
cord-194157-ak2gc3nz	71	6	of	of	IN
cord-194157-ak2gc3nz	71	7	the	the	DT
cord-194157-ak2gc3nz	71	8	fact	fact	NN
cord-194157-ak2gc3nz	71	9	that	that	IN
cord-194157-ak2gc3nz	71	10	the	the	DT
cord-194157-ak2gc3nz	71	11	minimum	minimum	NN
cord-194157-ak2gc3nz	71	12	and	and	CC
cord-194157-ak2gc3nz	71	13	minimizer	minimizer	NN
cord-194157-ak2gc3nz	71	14	of	of	IN
cord-194157-ak2gc3nz	71	15	independent	independent	JJ
cord-194157-ak2gc3nz	71	16	exponential	exponential	JJ
cord-194157-ak2gc3nz	71	17	random	random	JJ
cord-194157-ak2gc3nz	71	18	variables	variable	NNS
cord-194157-ak2gc3nz	71	19	are	be	VBP
cord-194157-ak2gc3nz	71	20	independent	independent	JJ
cord-194157-ak2gc3nz	71	21	.	.	.
cord-194157-ak2gc3nz	71	22	)	)	-RRB-
cord-194157-ak2gc3nz	72	1	Notice	notice	VB
cord-194157-ak2gc3nz	72	2	that	that	IN
cord-194157-ak2gc3nz	72	3	if	if	IN
cord-194157-ak2gc3nz	72	4	we	-PRON-	PRP
cord-194157-ak2gc3nz	72	5	could	could	MD
cord-194157-ak2gc3nz	72	6	estimate	estimate	VB
cord-194157-ak2gc3nz	72	7	then	then	RB
cord-194157-ak2gc3nz	72	8	we	-PRON-	PRP
cord-194157-ak2gc3nz	72	9	could	could	MD
cord-194157-ak2gc3nz	72	10	recover	recover	VB
cord-194157-ak2gc3nz	72	11	(	(	-LRB-
cord-194157-ak2gc3nz	72	12	λ	λ	NN
cord-194157-ak2gc3nz	72	13	,	,	,
cord-194157-ak2gc3nz	72	14	µ	µ	NNP
cord-194157-ak2gc3nz	72	15	)	)	-RRB-
cord-194157-ak2gc3nz	72	16	,	,	,
cord-194157-ak2gc3nz	72	17	as	as	IN
cord-194157-ak2gc3nz	72	18	desired	desire	VBN
cord-194157-ak2gc3nz	72	19	.	.	.
cord-194157-ak2gc3nz	73	1	For	for	IN
cord-194157-ak2gc3nz	73	2	example	example	NN
cord-194157-ak2gc3nz	73	3	,	,	,
cord-194157-ak2gc3nz	73	4	if	if	IN
cord-194157-ak2gc3nz	73	5	we	-PRON-	PRP
cord-194157-ak2gc3nz	73	6	had	have	VBD
cord-194157-ak2gc3nz	73	7	access	access	NN
cord-194157-ak2gc3nz	73	8	to	to	IN
cord-194157-ak2gc3nz	73	9	multiple	multiple	JJ
cord-194157-ak2gc3nz	73	10	independent	independent	JJ
cord-194157-ak2gc3nz	73	11	draws	draw	NNS
cord-194157-ak2gc3nz	73	12	of	of	IN
cord-194157-ak2gc3nz	73	13	the	the	DT
cord-194157-ak2gc3nz	73	14	SIR	SIR	NNP
cord-194157-ak2gc3nz	73	15	model	model	NN
cord-194157-ak2gc3nz	73	16	on	on	IN
cord-194157-ak2gc3nz	73	17	K	K	NNP
cord-194157-ak2gc3nz	73	18	2	2	CD
cord-194157-ak2gc3nz	73	19	,	,	,
cord-194157-ak2gc3nz	73	20	then	then	RB
cord-194157-ak2gc3nz	73	21	we	-PRON-	PRP
cord-194157-ak2gc3nz	73	22	could	could	MD
cord-194157-ak2gc3nz	73	23	obtain	obtain	VB
cord-194157-ak2gc3nz	73	24	such	such	JJ
cord-194157-ak2gc3nz	73	25	estimates	estimate	NNS
cord-194157-ak2gc3nz	73	26	.	.	.
cord-194157-ak2gc3nz	74	1	For	for	IN
cord-194157-ak2gc3nz	74	2	certain	certain	JJ
cord-194157-ak2gc3nz	74	3	types	type	NNS
cord-194157-ak2gc3nz	74	4	of	of	IN
cord-194157-ak2gc3nz	74	5	graphs	graph	NNS
cord-194157-ak2gc3nz	74	6	,	,	,
cord-194157-ak2gc3nz	74	7	we	-PRON-	PRP
cord-194157-ak2gc3nz	74	8	can	can	MD
cord-194157-ak2gc3nz	74	9	actually	actually	RB
cord-194157-ak2gc3nz	74	10	simulate	simulate	VB
cord-194157-ak2gc3nz	74	11	this	this	DT
cord-194157-ak2gc3nz	74	12	setup	setup	NN
cord-194157-ak2gc3nz	74	13	,	,	,
cord-194157-ak2gc3nz	74	14	and	and	CC
cord-194157-ak2gc3nz	74	15	this	this	DT
cord-194157-ak2gc3nz	74	16	is	be	VBZ
cord-194157-ak2gc3nz	74	17	the	the	DT
cord-194157-ak2gc3nz	74	18	main	main	JJ
cord-194157-ak2gc3nz	74	19	idea	idea	NN
cord-194157-ak2gc3nz	74	20	of	of	IN
cord-194157-ak2gc3nz	74	21	our	-PRON-	PRP$
cord-194157-ak2gc3nz	74	22	approach	approach	NN
cord-194157-ak2gc3nz	74	23	.	.	.
cord-194157-ak2gc3nz	75	1	In	in	IN
cord-194157-ak2gc3nz	75	2	practice	practice	NN
cord-194157-ak2gc3nz	75	3	,	,	,
cord-194157-ak2gc3nz	75	4	we	-PRON-	PRP
cord-194157-ak2gc3nz	75	5	will	will	MD
cord-194157-ak2gc3nz	75	6	not	not	RB
cord-194157-ak2gc3nz	75	7	have	have	VB
cord-194157-ak2gc3nz	75	8	the	the	DT
cord-194157-ak2gc3nz	75	9	time	time	NN
cord-194157-ak2gc3nz	75	10	to	to	TO
cord-194157-ak2gc3nz	75	11	determine	determine	VB
cord-194157-ak2gc3nz	75	12	whether	whether	IN
cord-194157-ak2gc3nz	75	13	Z	z	NN
cord-194157-ak2gc3nz	75	14	<	<	XX
cord-194157-ak2gc3nz	75	15	∞	∞	NNP
cord-194157-ak2gc3nz	75	16	,	,	,
cord-194157-ak2gc3nz	75	17	and	and	CC
cord-194157-ak2gc3nz	75	18	so	so	RB
cord-194157-ak2gc3nz	75	19	we	-PRON-	PRP
cord-194157-ak2gc3nz	75	20	instead	instead	RB
cord-194157-ak2gc3nz	75	21	truncate	truncate	VBP
cord-194157-ak2gc3nz	75	22	Z	z	NN
cord-194157-ak2gc3nz	75	23	←	←	NN
cord-194157-ak2gc3nz	75	24	min{Z	min{z	NN
cord-194157-ak2gc3nz	75	25	,	,	,
cord-194157-ak2gc3nz	75	26	τ	τ	NN
cord-194157-ak2gc3nz	75	27	}	}	-RRB-
cord-194157-ak2gc3nz	75	28	for	for	IN
cord-194157-ak2gc3nz	75	29	some	some	DT
cord-194157-ak2gc3nz	75	30	threshold	threshold	NN
cord-194157-ak2gc3nz	75	31	τ	τ	NN
cord-194157-ak2gc3nz	75	32	>	>	XX
cord-194157-ak2gc3nz	75	33	0	0	NFP
cord-194157-ak2gc3nz	75	34	.	.	.
cord-194157-ak2gc3nz	76	1	In	in	IN
cord-194157-ak2gc3nz	76	2	particular	particular	JJ
cord-194157-ak2gc3nz	76	3	,	,	,
cord-194157-ak2gc3nz	76	4	we	-PRON-	PRP
cord-194157-ak2gc3nz	76	5	write	write	VBP
cord-194157-ak2gc3nz	76	6	Z	Z	NNP
cord-194157-ak2gc3nz	76	7	∼	∼	NNP
cord-194157-ak2gc3nz	76	8	CI(λ	CI(λ	NNP
cord-194157-ak2gc3nz	76	9	,	,	,
cord-194157-ak2gc3nz	76	10	µ	µ	NN
cord-194157-ak2gc3nz	76	11	,	,	,
cord-194157-ak2gc3nz	76	12	τ	τ	NN
cord-194157-ak2gc3nz	76	13	)	)	-RRB-
cord-194157-ak2gc3nz	76	14	to	to	TO
cord-194157-ak2gc3nz	76	15	denote	denote	VB
cord-194157-ak2gc3nz	76	16	a	a	DT
cord-194157-ak2gc3nz	76	17	random	random	JJ
cord-194157-ak2gc3nz	76	18	variable	variable	NN
cord-194157-ak2gc3nz	76	19	with	with	IN
cord-194157-ak2gc3nz	76	20	distribution	distribution	NN
cord-194157-ak2gc3nz	76	21	We	-PRON-	PRP
cord-194157-ak2gc3nz	76	22	seek	seek	VBP
cord-194157-ak2gc3nz	76	23	to	to	TO
cord-194157-ak2gc3nz	76	24	estimate	estimate	VB
cord-194157-ak2gc3nz	76	25	λ	λ	NN
cord-194157-ak2gc3nz	76	26	and	and	CC
cord-194157-ak2gc3nz	76	27	µ	µ	NN
cord-194157-ak2gc3nz	76	28	given	give	VBN
cord-194157-ak2gc3nz	76	29	τ	τ	NN
cord-194157-ak2gc3nz	76	30	and	and	CC
cord-194157-ak2gc3nz	76	31	estimates	estimate	NNS
cord-194157-ak2gc3nz	76	32	of	of	IN
cord-194157-ak2gc3nz	76	33	the	the	DT
cord-194157-ak2gc3nz	76	34	following	following	JJ
cord-194157-ak2gc3nz	76	35	quantities	quantity	NNS
cord-194157-ak2gc3nz	76	36	:	:	:
cord-194157-ak2gc3nz	76	37	First	first	RB
cord-194157-ak2gc3nz	76	38	,	,	,
cord-194157-ak2gc3nz	76	39	we	-PRON-	PRP
cord-194157-ak2gc3nz	76	40	show	show	VBP
cord-194157-ak2gc3nz	76	41	that	that	IN
cord-194157-ak2gc3nz	76	42	good	good	JJ
cord-194157-ak2gc3nz	76	43	estimates	estimate	NNS
cord-194157-ak2gc3nz	76	44	of	of	IN
cord-194157-ak2gc3nz	76	45	p	p	NN
cord-194157-ak2gc3nz	76	46	and	and	CC
cord-194157-ak2gc3nz	76	47	q	q	NN
cord-194157-ak2gc3nz	76	48	yield	yield	VB
cord-194157-ak2gc3nz	76	49	good	good	JJ
cord-194157-ak2gc3nz	76	50	estimates	estimate	NNS
cord-194157-ak2gc3nz	76	51	of	of	IN
cord-194157-ak2gc3nz	76	52	λ	λ	NN
cord-194157-ak2gc3nz	76	53	and	and	CC
cord-194157-ak2gc3nz	76	54	µ	µ	NN
cord-194157-ak2gc3nz	77	1	:	:	:
cord-194157-ak2gc3nz	77	2	Lemma	Lemma	NNP
cord-194157-ak2gc3nz	77	3	4	4	CD
cord-194157-ak2gc3nz	77	4	.	.	.
cord-194157-ak2gc3nz	78	1	Suppose	suppose	VB
cord-194157-ak2gc3nz	78	2	m	m	NN
cord-194157-ak2gc3nz	78	3	:	:	:
cord-194157-ak2gc3nz	78	4	=	=	NFP
cord-194157-ak2gc3nz	78	5	(	(	-LRB-
cord-194157-ak2gc3nz	78	6	λ	λ	NN
cord-194157-ak2gc3nz	78	7	+	+	CC
cord-194157-ak2gc3nz	78	8	µ)τ	µ)τ	NNP
cord-194157-ak2gc3nz	78	9	≥	≥	CD
cord-194157-ak2gc3nz	78	10	2	2	CD
cord-194157-ak2gc3nz	78	11	,	,	,
cord-194157-ak2gc3nz	78	12	and	and	CC
cord-194157-ak2gc3nz	78	13	take	take	VB
cord-194157-ak2gc3nz	78	14	P	p	NN
cord-194157-ak2gc3nz	78	15	and	and	CC
cord-194157-ak2gc3nz	78	16	Q	q	NN
cord-194157-ak2gc3nz	78	17	such	such	JJ
cord-194157-ak2gc3nz	78	18	that	that	IN
cord-194157-ak2gc3nz	78	19	for	for	IN
cord-194157-ak2gc3nz	78	20	some	some	DT
cord-194157-ak2gc3nz	78	21	>	>	XX
cord-194157-ak2gc3nz	78	22	0	0	CD
cord-194157-ak2gc3nz	78	23	.	.	.
cord-194157-ak2gc3nz	79	1	Then	then	RB
cord-194157-ak2gc3nz	79	2	Proof	Proof	NNP
cord-194157-ak2gc3nz	79	3	.	.	.
cord-194157-ak2gc3nz	80	1	First	first	RB
cord-194157-ak2gc3nz	80	2	,	,	,
cord-194157-ak2gc3nz	80	3	observe	observe	VB
cord-194157-ak2gc3nz	80	4	that	that	IN
cord-194157-ak2gc3nz	80	5	Since	since	IN
cord-194157-ak2gc3nz	80	6	m	m	NN
cord-194157-ak2gc3nz	80	7	≥	≥	CD
cord-194157-ak2gc3nz	80	8	2	2	CD
cord-194157-ak2gc3nz	80	9	,	,	,
cord-194157-ak2gc3nz	80	10	we	-PRON-	PRP
cord-194157-ak2gc3nz	80	11	have	have	VBP
cord-194157-ak2gc3nz	81	1	(	(	-LRB-
cord-194157-ak2gc3nz	81	2	m	m	NN
cord-194157-ak2gc3nz	81	3	+	+	CC
cord-194157-ak2gc3nz	81	4	1)e	1)e	CD
cord-194157-ak2gc3nz	81	5	−m	−m	NNP
cord-194157-ak2gc3nz	81	6	≤	≤	NNPS
cord-194157-ak2gc3nz	81	7	1/2	1/2	CD
cord-194157-ak2gc3nz	81	8	,	,	,
cord-194157-ak2gc3nz	81	9	and	and	CC
cord-194157-ak2gc3nz	82	1	so	so	RB
cord-194157-ak2gc3nz	82	2	Thus	thus	RB
cord-194157-ak2gc3nz	82	3	,	,	,
cord-194157-ak2gc3nz	82	4	and	and	CC
cord-194157-ak2gc3nz	82	5	similarly	similarly	RB
cord-194157-ak2gc3nz	82	6	for	for	IN
cord-194157-ak2gc3nz	82	7	(	(	-LRB-
cord-194157-ak2gc3nz	82	8	1	1	CD
cord-194157-ak2gc3nz	82	9	−	−	NN
cord-194157-ak2gc3nz	82	10	P	p	NN
cord-194157-ak2gc3nz	82	11	)	)	-RRB-
cord-194157-ak2gc3nz	83	1	/Q.	/Q.	.
cord-194157-ak2gc3nz	84	1	Next	next	RB
cord-194157-ak2gc3nz	84	2	,	,	,
cord-194157-ak2gc3nz	84	3	we	-PRON-	PRP
cord-194157-ak2gc3nz	84	4	produce	produce	VBP
cord-194157-ak2gc3nz	84	5	estimates	estimate	NNS
cord-194157-ak2gc3nz	84	6	P	p	NN
cord-194157-ak2gc3nz	84	7	and	and	CC
cord-194157-ak2gc3nz	84	8	Q	Q	NNP
cord-194157-ak2gc3nz	84	9	given	give	VBN
cord-194157-ak2gc3nz	84	10	independent	independent	JJ
cord-194157-ak2gc3nz	84	11	realizations	realization	NNS
cord-194157-ak2gc3nz	84	12	of	of	IN
cord-194157-ak2gc3nz	84	13	Z	z	NN
cord-194157-ak2gc3nz	84	14	:	:	:
cord-194157-ak2gc3nz	84	15	Proof	proof	NN
cord-194157-ak2gc3nz	84	16	.	.	.
cord-194157-ak2gc3nz	85	1	For	for	IN
cord-194157-ak2gc3nz	85	2	convenience	convenience	NN
cord-194157-ak2gc3nz	85	3	,	,	,
cord-194157-ak2gc3nz	85	4	we	-PRON-	PRP
cord-194157-ak2gc3nz	85	5	put	put	VBP
cord-194157-ak2gc3nz	85	6	k	k	NN
cord-194157-ak2gc3nz	85	7	:	:	:
cord-194157-ak2gc3nz	85	8	=	=	SYM
cord-194157-ak2gc3nz	85	9	|A|	|a|	XX
cord-194157-ak2gc3nz	85	10	and	and	CC
cord-194157-ak2gc3nz	85	11	identify	identify	VB
cord-194157-ak2gc3nz	85	12	A	a	DT
cord-194157-ak2gc3nz	85	13	=	=	:
cord-194157-ak2gc3nz	85	14	[	[	-LRB-
cord-194157-ak2gc3nz	85	15	k	k	NNP
cord-194157-ak2gc3nz	85	16	]	]	-RRB-
cord-194157-ak2gc3nz	85	17	.	.	.
cord-194157-ak2gc3nz	86	1	We	-PRON-	PRP
cord-194157-ak2gc3nz	86	2	have	have	VBP
cord-194157-ak2gc3nz	86	3	EL	EL	NNP
cord-194157-ak2gc3nz	86	4	i	i	PRP
cord-194157-ak2gc3nz	86	5	=	=	SYM
cord-194157-ak2gc3nz	86	6	p	p	NN
cord-194157-ak2gc3nz	86	7	,	,	,
cord-194157-ak2gc3nz	87	1	Var	Var	NNP
cord-194157-ak2gc3nz	87	2	L	L	NNP
cord-194157-ak2gc3nz	87	3	i	i	NN
cord-194157-ak2gc3nz	87	4	=	=	VBZ
cord-194157-ak2gc3nz	87	5	p(1	p(1	NN
cord-194157-ak2gc3nz	87	6	−	−	NN
cord-194157-ak2gc3nz	87	7	p	p	NN
cord-194157-ak2gc3nz	87	8	)	)	-RRB-
cord-194157-ak2gc3nz	87	9	,	,	,
cord-194157-ak2gc3nz	87	10	and	and	CC
cord-194157-ak2gc3nz	88	1	L	L	NNP
cord-194157-ak2gc3nz	88	2	i	i	PRP
cord-194157-ak2gc3nz	88	3	∈	∈	VBP
cord-194157-ak2gc3nz	88	4	[	[	-LRB-
cord-194157-ak2gc3nz	88	5	0	0	CD
cord-194157-ak2gc3nz	88	6	,	,	,
cord-194157-ak2gc3nz	88	7	1	1	CD
cord-194157-ak2gc3nz	88	8	]	]	-RRB-
cord-194157-ak2gc3nz	88	9	almost	almost	RB
cord-194157-ak2gc3nz	88	10	surely	surely	RB
cord-194157-ak2gc3nz	88	11	.	.	.
cord-194157-ak2gc3nz	89	1	As	as	IN
cord-194157-ak2gc3nz	89	2	such	such	JJ
cord-194157-ak2gc3nz	89	3	,	,	,
cord-194157-ak2gc3nz	89	4	we	-PRON-	PRP
cord-194157-ak2gc3nz	89	5	may	may	MD
cord-194157-ak2gc3nz	89	6	apply	apply	VB
cord-194157-ak2gc3nz	89	7	Bernstein	Bernstein	NNP
cord-194157-ak2gc3nz	89	8	's	's	POS
cord-194157-ak2gc3nz	89	9	inequality	inequality	NN
cord-194157-ak2gc3nz	89	10	for	for	IN
cord-194157-ak2gc3nz	89	11	bounded	bound	VBN
cord-194157-ak2gc3nz	89	12	random	random	JJ
cord-194157-ak2gc3nz	89	13	variables	variable	NNS
cord-194157-ak2gc3nz	89	14	(	(	-LRB-
cord-194157-ak2gc3nz	89	15	see	see	VB
cord-194157-ak2gc3nz	90	1	Theorem	theorem	NN
cord-194157-ak2gc3nz	90	2	2.8.4	2.8.4	CD
cord-194157-ak2gc3nz	90	3	in	in	IN
cord-194157-ak2gc3nz	90	4	[	[	-LRB-
cord-194157-ak2gc3nz	90	5	7	7	CD
cord-194157-ak2gc3nz	90	6	]	]	-RRB-
cord-194157-ak2gc3nz	91	1	):	):	NNP
cord-194157-ak2gc3nz	92	1	Put	put	VB
cord-194157-ak2gc3nz	92	2	δ	δ	NN
cord-194157-ak2gc3nz	92	3	=	=	SYM
cord-194157-ak2gc3nz	92	4	1	1	CD
cord-194157-ak2gc3nz	92	5	−	−	NN
cord-194157-ak2gc3nz	92	6	e	e	NN
cord-194157-ak2gc3nz	92	7	−	−	NN
cord-194157-ak2gc3nz	92	8	.	.	.
cord-194157-ak2gc3nz	93	1	Then	then	RB
cord-194157-ak2gc3nz	93	2	both	both	DT
cord-194157-ak2gc3nz	93	3	of	of	IN
cord-194157-ak2gc3nz	93	4	the	the	DT
cord-194157-ak2gc3nz	93	5	following	following	JJ
cord-194157-ak2gc3nz	93	6	hold	hold	NN
cord-194157-ak2gc3nz	93	7	with	with	IN
cord-194157-ak2gc3nz	93	8	probability	probability	NN
cord-194157-ak2gc3nz	93	9	1	1	CD
cord-194157-ak2gc3nz	93	10	−	−	CD
cord-194157-ak2gc3nz	93	11	2e	2e	NN
cord-194157-ak2gc3nz	93	12	−c	−c	NNP
cord-194157-ak2gc3nz	93	13	kp(1−p	kp(1−p	NNP
cord-194157-ak2gc3nz	93	14	)	)	-RRB-
cord-194157-ak2gc3nz	93	15	:	:	:
cord-194157-ak2gc3nz	93	16	Note	note	VB
cord-194157-ak2gc3nz	93	17	that	that	IN
cord-194157-ak2gc3nz	93	18	this	this	DT
cord-194157-ak2gc3nz	93	19	implies	imply	VBZ
cord-194157-ak2gc3nz	93	20	Next	next	RB
cord-194157-ak2gc3nz	93	21	,	,	,
cord-194157-ak2gc3nz	93	22	we	-PRON-	PRP
cord-194157-ak2gc3nz	93	23	estimate	estimate	VBP
cord-194157-ak2gc3nz	93	24	Q.	Q.	NNP
cord-194157-ak2gc3nz	93	25	Conditioned	condition	VBN
cord-194157-ak2gc3nz	93	26	on	on	IN
cord-194157-ak2gc3nz	93	27	A	A	NNP
cord-194157-ak2gc3nz	93	28	,	,	,
cord-194157-ak2gc3nz	93	29	the	the	DT
cord-194157-ak2gc3nz	93	30	random	random	JJ
cord-194157-ak2gc3nz	93	31	variables	variable	NNS
cord-194157-ak2gc3nz	93	32	{	{	-LRB-
cord-194157-ak2gc3nz	93	33	Z	Z	NNP
cord-194157-ak2gc3nz	93	34	a	a	DT
cord-194157-ak2gc3nz	93	35	}	}	-RRB-
cord-194157-ak2gc3nz	93	36	a∈A	a∈a	NN
cord-194157-ak2gc3nz	93	37	are	be	VBP
cord-194157-ak2gc3nz	93	38	all	all	DT
cord-194157-ak2gc3nz	93	39	distributed	distribute	VBN
cord-194157-ak2gc3nz	93	40	like	like	IN
cord-194157-ak2gc3nz	93	41	a	a	DT
cord-194157-ak2gc3nz	93	42	τ	τ	NN
cord-194157-ak2gc3nz	93	43	-truncated	-truncated	:
cord-194157-ak2gc3nz	93	44	version	version	NN
cord-194157-ak2gc3nz	93	45	Y	Y	NNP
cord-194157-ak2gc3nz	93	46	of	of	IN
cord-194157-ak2gc3nz	93	47	a	a	DT
cord-194157-ak2gc3nz	93	48	random	random	JJ
cord-194157-ak2gc3nz	93	49	variable	variable	NN
cord-194157-ak2gc3nz	93	50	X	x	NN
cord-194157-ak2gc3nz	93	51	∼	∼	NNP
cord-194157-ak2gc3nz	93	52	Exp(λ	Exp(λ	NNPS
cord-194157-ak2gc3nz	93	53	+	+	CC
cord-194157-ak2gc3nz	93	54	µ	µ	NN
cord-194157-ak2gc3nz	93	55	)	)	-RRB-
cord-194157-ak2gc3nz	93	56	,	,	,
cord-194157-ak2gc3nz	93	57	and	and	CC
cord-194157-ak2gc3nz	93	58	there	there	EX
cord-194157-ak2gc3nz	93	59	exist	exist	VBP
cord-194157-ak2gc3nz	93	60	absolute	absolute	JJ
cord-194157-ak2gc3nz	93	61	constants	constant	NNS
cord-194157-ak2gc3nz	93	62	C	C	NNP
cord-194157-ak2gc3nz	93	63	1	1	CD
cord-194157-ak2gc3nz	93	64	,	,	,
cord-194157-ak2gc3nz	94	1	C	c	NN
cord-194157-ak2gc3nz	94	2	2	2	CD
cord-194157-ak2gc3nz	94	3	>	>	SYM
cord-194157-ak2gc3nz	94	4	0	0	NFP
cord-194157-ak2gc3nz	94	5	such	such	JJ
cord-194157-ak2gc3nz	94	6	that	that	IN
cord-194157-ak2gc3nz	94	7	As	as	IN
cord-194157-ak2gc3nz	94	8	such	such	JJ
cord-194157-ak2gc3nz	94	9	,	,	,
cord-194157-ak2gc3nz	94	10	we	-PRON-	PRP
cord-194157-ak2gc3nz	94	11	may	may	MD
cord-194157-ak2gc3nz	94	12	apply	apply	VB
cord-194157-ak2gc3nz	94	13	Bernstein	Bernstein	NNP
cord-194157-ak2gc3nz	94	14	's	's	POS
cord-194157-ak2gc3nz	94	15	inequality	inequality	NN
cord-194157-ak2gc3nz	94	16	for	for	IN
cord-194157-ak2gc3nz	94	17	subexponential	subexponential	JJ
cord-194157-ak2gc3nz	94	18	random	random	JJ
cord-194157-ak2gc3nz	94	19	variables	variable	NNS
cord-194157-ak2gc3nz	94	20	(	(	-LRB-
cord-194157-ak2gc3nz	94	21	see	see	VB
cord-194157-ak2gc3nz	95	1	Theorem	theorem	NN
cord-194157-ak2gc3nz	95	2	2.8.1	2.8.1	NN
cord-194157-ak2gc3nz	95	3	in	in	IN
cord-194157-ak2gc3nz	95	4	[	[	-LRB-
cord-194157-ak2gc3nz	95	5	7	7	CD
cord-194157-ak2gc3nz	95	6	]	]	-RRB-
cord-194157-ak2gc3nz	96	1	):	):	NNP
cord-194157-ak2gc3nz	97	1	The	the	DT
cord-194157-ak2gc3nz	97	2	result	result	NN
cord-194157-ak2gc3nz	97	3	follows	follow	VBZ
cord-194157-ak2gc3nz	97	4	from	from	IN
cord-194157-ak2gc3nz	97	5	the	the	DT
cord-194157-ak2gc3nz	97	6	union	union	NN
cord-194157-ak2gc3nz	97	7	bound	bind	VBN
cord-194157-ak2gc3nz	97	8	.	.	.
cord-194157-ak2gc3nz	98	1	If	if	IN
cord-194157-ak2gc3nz	98	2	we	-PRON-	PRP
cord-194157-ak2gc3nz	98	3	had	have	VBD
cord-194157-ak2gc3nz	98	4	access	access	NN
cord-194157-ak2gc3nz	98	5	to	to	IN
cord-194157-ak2gc3nz	98	6	the	the	DT
cord-194157-ak2gc3nz	98	7	infected	infected	JJ
cord-194157-ak2gc3nz	98	8	vertices	vertex	NNS
cord-194157-ak2gc3nz	98	9	at	at	IN
cord-194157-ak2gc3nz	98	10	time	time	NN
cord-194157-ak2gc3nz	98	11	t	t	NNP
cord-194157-ak2gc3nz	98	12	0	0	CD
cord-194157-ak2gc3nz	98	13	,	,	,
cord-194157-ak2gc3nz	98	14	we	-PRON-	PRP
cord-194157-ak2gc3nz	98	15	could	could	MD
cord-194157-ak2gc3nz	98	16	use	use	VB
cord-194157-ak2gc3nz	98	17	the	the	DT
cord-194157-ak2gc3nz	98	18	formulas	formula	NNS
cord-194157-ak2gc3nz	98	19	in	in	IN
cord-194157-ak2gc3nz	98	20	Lemma	Lemma	NNP
cord-194157-ak2gc3nz	98	21	5	5	CD
cord-194157-ak2gc3nz	98	22	to	to	TO
cord-194157-ak2gc3nz	98	23	obtain	obtain	VB
cord-194157-ak2gc3nz	98	24	estimators	estimator	NNS
cord-194157-ak2gc3nz	98	25	of	of	IN
cord-194157-ak2gc3nz	98	26	the	the	DT
cord-194157-ak2gc3nz	98	27	SIR	SIR	NNP
cord-194157-ak2gc3nz	98	28	parameters	parameter	NNS
cord-194157-ak2gc3nz	98	29	that	that	WDT
cord-194157-ak2gc3nz	98	30	provide	provide	VBP
cord-194157-ak2gc3nz	98	31	a	a	DT
cord-194157-ak2gc3nz	98	32	good	good	JJ
cord-194157-ak2gc3nz	98	33	approximation	approximation	NN
cord-194157-ak2gc3nz	98	34	to	to	IN
cord-194157-ak2gc3nz	98	35	the	the	DT
cord-194157-ak2gc3nz	98	36	true	true	JJ
cord-194157-ak2gc3nz	98	37	parameters	parameter	NNS
cord-194157-ak2gc3nz	98	38	:	:	:
cord-194157-ak2gc3nz	98	39	Lemma	Lemma	NNP
cord-194157-ak2gc3nz	98	40	6	6	CD
cord-194157-ak2gc3nz	98	41	.	.	.
cord-194157-ak2gc3nz	99	1	Consider	consider	VB
cord-194157-ak2gc3nz	99	2	the	the	DT
cord-194157-ak2gc3nz	99	3	SIR	SIR	NNP
cord-194157-ak2gc3nz	99	4	model	model	NN
cord-194157-ak2gc3nz	99	5	on	on	IN
cord-194157-ak2gc3nz	99	6	a	a	DT
cord-194157-ak2gc3nz	99	7	graph	graph	NN
cord-194157-ak2gc3nz	99	8	G	g	NN
cord-194157-ak2gc3nz	99	9	with	with	IN
cord-194157-ak2gc3nz	99	10	parameters	parameter	NNS
cord-194157-ak2gc3nz	99	11	λ	λ	NN
cord-194157-ak2gc3nz	99	12	and	and	CC
cord-194157-ak2gc3nz	99	13	µ.	µ.	NN
cord-194157-ak2gc3nz	99	14	Select	Select	NNP
cord-194157-ak2gc3nz	99	15	r	r	NNP
cord-194157-ak2gc3nz	99	16	,	,	,
cord-194157-ak2gc3nz	99	17	t	t	NNP
cord-194157-ak2gc3nz	99	18	0	0	CD
cord-194157-ak2gc3nz	99	19	,	,	,
cord-194157-ak2gc3nz	99	20	t	t	NN
cord-194157-ak2gc3nz	99	21	1	1	CD
cord-194157-ak2gc3nz	99	22	>	>	SYM
cord-194157-ak2gc3nz	99	23	0	0	NFP
cord-194157-ak2gc3nz	99	24	and	and	CC
cord-194157-ak2gc3nz	99	25	put	put	VB
cord-194157-ak2gc3nz	99	26	τ	τ	NN
cord-194157-ak2gc3nz	99	27	:	:	:
cord-194157-ak2gc3nz	99	28	=	=	NFP
cord-194157-ak2gc3nz	100	1	t	t	NNP
cord-194157-ak2gc3nz	100	2	1	1	CD
cord-194157-ak2gc3nz	100	3	−	−	NNP
cord-194157-ak2gc3nz	100	4	t	t	NN
cord-194157-ak2gc3nz	100	5	0	0	CD
cord-194157-ak2gc3nz	100	6	.	.	.
cord-194157-ak2gc3nz	101	1	Let	let	VB
cord-194157-ak2gc3nz	101	2	B(r	B(r	NNS
cord-194157-ak2gc3nz	101	3	)	)	-RRB-
cord-194157-ak2gc3nz	101	4	denote	denote	VB
cord-194157-ak2gc3nz	101	5	the	the	DT
cord-194157-ak2gc3nz	101	6	subgraph	subgraph	NN
cord-194157-ak2gc3nz	101	7	of	of	IN
cord-194157-ak2gc3nz	101	8	G	g	NN
cord-194157-ak2gc3nz	101	9	induced	induce	VBN
cord-194157-ak2gc3nz	101	10	by	by	IN
cord-194157-ak2gc3nz	101	11	vertices	vertex	NNS
cord-194157-ak2gc3nz	101	12	of	of	IN
cord-194157-ak2gc3nz	101	13	distance	distance	NN
cord-194157-ak2gc3nz	101	14	at	at	IN
cord-194157-ak2gc3nz	101	15	most	most	RBS
cord-194157-ak2gc3nz	101	16	r	r	NN
cord-194157-ak2gc3nz	101	17	from	from	IN
cord-194157-ak2gc3nz	101	18	U	U	NNP
cord-194157-ak2gc3nz	101	19	(	(	-LRB-
cord-194157-ak2gc3nz	101	20	0	0	NFP
cord-194157-ak2gc3nz	101	21	)	)	-RRB-
cord-194157-ak2gc3nz	101	22	.	.	.
cord-194157-ak2gc3nz	102	1	The	the	DT
cord-194157-ak2gc3nz	102	2	set	set	NN
cord-194157-ak2gc3nz	102	3	of	of	IN
cord-194157-ak2gc3nz	102	4	bridges	bridge	NNS
cord-194157-ak2gc3nz	102	5	in	in	IN
cord-194157-ak2gc3nz	102	6	B(r	B(r	NNS
cord-194157-ak2gc3nz	102	7	)	)	-RRB-
cord-194157-ak2gc3nz	102	8	with	with	IN
cord-194157-ak2gc3nz	102	9	one	one	CD
cord-194157-ak2gc3nz	102	10	vertex	vertex	NN
cord-194157-ak2gc3nz	102	11	in	in	IN
cord-194157-ak2gc3nz	102	12	I(t	I(t	NNP
cord-194157-ak2gc3nz	102	13	0	0	CD
cord-194157-ak2gc3nz	102	14	)	)	-RRB-
cord-194157-ak2gc3nz	102	15	and	and	CC
cord-194157-ak2gc3nz	102	16	another	another	DT
cord-194157-ak2gc3nz	102	17	vertex	vertex	NN
cord-194157-ak2gc3nz	102	18	in	in	IN
cord-194157-ak2gc3nz	102	19	For	for	IN
cord-194157-ak2gc3nz	102	20	any	any	DT
cord-194157-ak2gc3nz	102	21	fixed	fixed	JJ
cord-194157-ak2gc3nz	102	22	k	k	NN
cord-194157-ak2gc3nz	102	23	,	,	,
cord-194157-ak2gc3nz	102	24	>	>	XX
cord-194157-ak2gc3nz	102	25	0	0	NFP
cord-194157-ak2gc3nz	102	26	,	,	,
cord-194157-ak2gc3nz	102	27	define	define	VB
cord-194157-ak2gc3nz	102	28	the	the	DT
cord-194157-ak2gc3nz	102	29	events	event	NNS
cord-194157-ak2gc3nz	102	30	Proof	Proof	NNP
cord-194157-ak2gc3nz	102	31	.	.	.
cord-194157-ak2gc3nz	103	1	Let	let	VB
cord-194157-ak2gc3nz	103	2	S	S	NNP
cord-194157-ak2gc3nz	103	3	denote	denote	VB
cord-194157-ak2gc3nz	103	4	the	the	DT
cord-194157-ak2gc3nz	103	5	vertices	vertex	NNS
cord-194157-ak2gc3nz	103	6	in	in	IN
cord-194157-ak2gc3nz	103	7	G	g	NN
cord-194157-ak2gc3nz	103	8	of	of	IN
cord-194157-ak2gc3nz	103	9	distance	distance	NN
cord-194157-ak2gc3nz	104	1	exactly	exactly	RB
cord-194157-ak2gc3nz	104	2	r	r	VBN
cord-194157-ak2gc3nz	104	3	from	from	IN
cord-194157-ak2gc3nz	104	4	U	U	NNP
cord-194157-ak2gc3nz	104	5	(	(	-LRB-
cord-194157-ak2gc3nz	104	6	0	0	NFP
cord-194157-ak2gc3nz	104	7	)	)	-RRB-
cord-194157-ak2gc3nz	104	8	.	.	.
cord-194157-ak2gc3nz	105	1	Notice	notice	VB
cord-194157-ak2gc3nz	105	2	that	that	IN
cord-194157-ak2gc3nz	105	3	for	for	IN
cord-194157-ak2gc3nz	105	4	every	every	DT
cord-194157-ak2gc3nz	105	5	vertex	vertex	NN
cord-194157-ak2gc3nz	105	6	v	v	NN
cord-194157-ak2gc3nz	105	7	∈	∈	NN
cord-194157-ak2gc3nz	105	8	V	v	NN
cord-194157-ak2gc3nz	105	9	(	(	-LRB-
cord-194157-ak2gc3nz	105	10	B(r	B(r	NNS
cord-194157-ak2gc3nz	105	11	)	)	-RRB-
cord-194157-ak2gc3nz	105	12	)	)	-RRB-
cord-194157-ak2gc3nz	106	1	\	\	LS
cord-194157-ak2gc3nz	107	1	S	S	NNP
cord-194157-ak2gc3nz	107	2	,	,	,
cord-194157-ak2gc3nz	107	3	the	the	DT
cord-194157-ak2gc3nz	107	4	edges	edge	NNS
cord-194157-ak2gc3nz	107	5	incident	incident	NN
cord-194157-ak2gc3nz	107	6	to	to	IN
cord-194157-ak2gc3nz	107	7	v	v	NN
cord-194157-ak2gc3nz	107	8	in	in	IN
cord-194157-ak2gc3nz	107	9	B(r	B(r	NNS
cord-194157-ak2gc3nz	107	10	)	)	-RRB-
cord-194157-ak2gc3nz	107	11	are	be	VBP
cord-194157-ak2gc3nz	107	12	precisely	precisely	RB
cord-194157-ak2gc3nz	107	13	the	the	DT
cord-194157-ak2gc3nz	107	14	edges	edge	NNS
cord-194157-ak2gc3nz	107	15	incident	incident	NN
cord-194157-ak2gc3nz	107	16	to	to	IN
cord-194157-ak2gc3nz	107	17	v	v	NN
cord-194157-ak2gc3nz	107	18	in	in	IN
cord-194157-ak2gc3nz	107	19	G.	G.	NNP
cord-194157-ak2gc3nz	108	1	As	as	IN
cord-194157-ak2gc3nz	108	2	such	such	JJ
cord-194157-ak2gc3nz	108	3	,	,	,
cord-194157-ak2gc3nz	108	4	the	the	DT
cord-194157-ak2gc3nz	108	5	SIR	SIR	NNP
cord-194157-ak2gc3nz	108	6	processes	process	VBZ
cord-194157-ak2gc3nz	108	7	on	on	IN
cord-194157-ak2gc3nz	108	8	G	g	NN
cord-194157-ak2gc3nz	108	9	and	and	CC
cord-194157-ak2gc3nz	108	10	on	on	IN
cord-194157-ak2gc3nz	108	11	B(r	B(r	NNS
cord-194157-ak2gc3nz	108	12	)	)	-RRB-
cord-194157-ak2gc3nz	108	13	are	be	VBP
cord-194157-ak2gc3nz	108	14	identical	identical	JJ
cord-194157-ak2gc3nz	108	15	until	until	IN
cord-194157-ak2gc3nz	108	16	the	the	DT
cord-194157-ak2gc3nz	108	17	stopping	stop	VBG
cord-194157-ak2gc3nz	108	18	time	time	NN
cord-194157-ak2gc3nz	108	19	Let	let	VB
cord-194157-ak2gc3nz	108	20	B(r	B(r	NNS
cord-194157-ak2gc3nz	108	21	)	)	-RRB-
cord-194157-ak2gc3nz	108	22	denote	denote	VB
cord-194157-ak2gc3nz	108	23	the	the	DT
cord-194157-ak2gc3nz	108	24	subgraph	subgraph	NN
cord-194157-ak2gc3nz	108	25	of	of	IN
cord-194157-ak2gc3nz	108	26	G	g	NN
cord-194157-ak2gc3nz	108	27	induced	induce	VBN
cord-194157-ak2gc3nz	108	28	by	by	IN
cord-194157-ak2gc3nz	108	29	vertices	vertex	NNS
cord-194157-ak2gc3nz	108	30	of	of	IN
cord-194157-ak2gc3nz	108	31	distance	distance	NN
cord-194157-ak2gc3nz	108	32	at	at	IN
cord-194157-ak2gc3nz	108	33	most	most	RBS
cord-194157-ak2gc3nz	108	34	r	r	NN
cord-194157-ak2gc3nz	108	35	from	from	IN
cord-194157-ak2gc3nz	108	36	the	the	DT
cord-194157-ak2gc3nz	108	37	minimizer	minimizer	NN
cord-194157-ak2gc3nz	108	38	of	of	IN
cord-194157-ak2gc3nz	108	39	T	T	NNP
cord-194157-ak2gc3nz	108	40	.	.	.
cord-194157-ak2gc3nz	109	1	For	for	IN
cord-194157-ak2gc3nz	109	2	each	each	DT
cord-194157-ak2gc3nz	109	3	quantity	quantity	NN
cord-194157-ak2gc3nz	109	4	T	t	NN
cord-194157-ak2gc3nz	109	5	(	(	-LRB-
cord-194157-ak2gc3nz	109	6	v	v	NN
cord-194157-ak2gc3nz	109	7	)	)	-RRB-
cord-194157-ak2gc3nz	109	8	,	,	,
cord-194157-ak2gc3nz	109	9	Z	Z	NNP
cord-194157-ak2gc3nz	109	10	a	a	NNP
cord-194157-ak2gc3nz	109	11	,	,	,
cord-194157-ak2gc3nz	109	12	A	a	DT
cord-194157-ak2gc3nz	109	13	I	i	NN
cord-194157-ak2gc3nz	109	14	,	,	,
cord-194157-ak2gc3nz	109	15	A	a	DT
cord-194157-ak2gc3nz	109	16	I	i	NN
cord-194157-ak2gc3nz	109	17	,	,	,
cord-194157-ak2gc3nz	109	18	B	B	NNP
cord-194157-ak2gc3nz	109	19	a	a	DT
cord-194157-ak2gc3nz	109	20	,	,	,
cord-194157-ak2gc3nz	109	21	b(a	b(a	NNP
cord-194157-ak2gc3nz	109	22	)	)	-RRB-
cord-194157-ak2gc3nz	109	23	,	,	,
cord-194157-ak2gc3nz	109	24	P	p	NN
cord-194157-ak2gc3nz	109	25	,	,	,
cord-194157-ak2gc3nz	109	26	Q	Q	NNP
cord-194157-ak2gc3nz	109	27	,	,	,
cord-194157-ak2gc3nz	109	28	λ	λ	NN
cord-194157-ak2gc3nz	109	29	I	i	NN
cord-194157-ak2gc3nz	109	30	,	,	,
cord-194157-ak2gc3nz	109	31	μ	μ	NN
cord-194157-ak2gc3nz	109	32	I	-PRON-	PRP
cord-194157-ak2gc3nz	109	33	defined	define	VBD
cord-194157-ak2gc3nz	109	34	in	in	IN
cord-194157-ak2gc3nz	109	35	the	the	DT
cord-194157-ak2gc3nz	109	36	statement	statement	NN
cord-194157-ak2gc3nz	109	37	of	of	IN
cord-194157-ak2gc3nz	109	38	the	the	DT
cord-194157-ak2gc3nz	109	39	lemma	lemma	NN
cord-194157-ak2gc3nz	109	40	,	,	,
cord-194157-ak2gc3nz	109	41	there	there	EX
cord-194157-ak2gc3nz	109	42	is	be	VBZ
cord-194157-ak2gc3nz	109	43	a	a	DT
cord-194157-ak2gc3nz	109	44	corresponding	correspond	VBG
cord-194157-ak2gc3nz	109	45	quantity	quantity	NN
cord-194157-ak2gc3nz	109	46	defined	define	VBN
cord-194157-ak2gc3nz	109	47	by	by	IN
cord-194157-ak2gc3nz	109	48	replacing	replace	VBG
cord-194157-ak2gc3nz	109	49	the	the	DT
cord-194157-ak2gc3nz	109	50	SIR	SIR	NNP
cord-194157-ak2gc3nz	109	51	process	process	NN
cord-194157-ak2gc3nz	109	52	on	on	IN
cord-194157-ak2gc3nz	109	53	G	g	NN
cord-194157-ak2gc3nz	109	54	with	with	IN
cord-194157-ak2gc3nz	109	55	the	the	DT
cord-194157-ak2gc3nz	109	56	SIR	SIR	NNP
cord-194157-ak2gc3nz	109	57	process	process	NN
cord-194157-ak2gc3nz	109	58	on	on	IN
cord-194157-ak2gc3nz	109	59	B(r	B(r	NNPS
cord-194157-ak2gc3nz	109	60	)	)	-RRB-
cord-194157-ak2gc3nz	109	61	,	,	,
cord-194157-ak2gc3nz	109	62	and	and	CC
cord-194157-ak2gc3nz	109	63	we	-PRON-	PRP
cord-194157-ak2gc3nz	109	64	denote	denote	VBP
cord-194157-ak2gc3nz	109	65	these	these	DT
cord-194157-ak2gc3nz	109	66	variables	variable	NNS
cord-194157-ak2gc3nz	109	67	byT	byT	VBN
cord-194157-ak2gc3nz	110	1	(	(	-LRB-
cord-194157-ak2gc3nz	110	2	v),Z	v),Z	``
cord-194157-ak2gc3nz	110	3	a	a	NNP
cord-194157-ak2gc3nz	110	4	,	,	,
cord-194157-ak2gc3nz	110	5	Ã	Ã	NNP
cord-194157-ak2gc3nz	110	6	,	,	,
cord-194157-ak2gc3nz	110	7	Ã	Ã	NNP
cord-194157-ak2gc3nz	110	8	,	,	,
cord-194157-ak2gc3nz	111	1	B	B	NNP
cord-194157-ak2gc3nz	111	2	a	a	DT
cord-194157-ak2gc3nz	111	3	,	,	,
cord-194157-ak2gc3nz	111	4	b(a),P	b(a),p	UH
cord-194157-ak2gc3nz	111	5	,	,	,
cord-194157-ak2gc3nz	111	6	Q	Q	NNP
cord-194157-ak2gc3nz	111	7	,	,	,
cord-194157-ak2gc3nz	111	8	λ	λ	NN
cord-194157-ak2gc3nz	111	9	,	,	,
cord-194157-ak2gc3nz	111	10	μ	μ	NN
cord-194157-ak2gc3nz	111	11	.	.	.
cord-194157-ak2gc3nz	112	1	Each	each	DT
cord-194157-ak2gc3nz	112	2	of	of	IN
cord-194157-ak2gc3nz	112	3	these	these	DT
cord-194157-ak2gc3nz	112	4	variables	variable	NNS
cord-194157-ak2gc3nz	112	5	equals	equal	VBZ
cord-194157-ak2gc3nz	112	6	its	-PRON-	PRP$
cord-194157-ak2gc3nz	112	7	counterpart	counterpart	NN
cord-194157-ak2gc3nz	112	8	over	over	IN
cord-194157-ak2gc3nz	112	9	the	the	DT
cord-194157-ak2gc3nz	112	10	event	event	NN
cord-194157-ak2gc3nz	112	11	It	-PRON-	PRP
cord-194157-ak2gc3nz	112	12	remains	remain	VBZ
cord-194157-ak2gc3nz	112	13	to	to	TO
cord-194157-ak2gc3nz	112	14	bound	bound	VB
cord-194157-ak2gc3nz	112	15	P(F|E	P(F|E	NNP
cord-194157-ak2gc3nz	112	16	2	2	CD
cord-194157-ak2gc3nz	112	17	)	)	-RRB-
cord-194157-ak2gc3nz	112	18	.	.	.
cord-194157-ak2gc3nz	113	1	Conditioned	condition	VBN
cord-194157-ak2gc3nz	113	2	onÃ	onã	CD
cord-194157-ak2gc3nz	113	3	and	and	CC
cord-194157-ak2gc3nz	113	4	{	{	-LRB-
cord-194157-ak2gc3nz	113	5	b(a	b(a	NN
cord-194157-ak2gc3nz	113	6	)	)	-RRB-
cord-194157-ak2gc3nz	113	7	}	}	-RRB-
cord-194157-ak2gc3nz	114	1	a∈Ã	a∈ã	RB
cord-194157-ak2gc3nz	114	2	,	,	,
cord-194157-ak2gc3nz	114	3	then	then	RB
cord-194157-ak2gc3nz	114	4	for	for	IN
cord-194157-ak2gc3nz	114	5	each	each	DT
cord-194157-ak2gc3nz	114	6	a	a	DT
cord-194157-ak2gc3nz	114	7	∈Ã	∈ã	NN
cord-194157-ak2gc3nz	114	8	,	,	,
cord-194157-ak2gc3nz	114	9	the	the	DT
cord-194157-ak2gc3nz	114	10	Markov	Markov	NNP
cord-194157-ak2gc3nz	114	11	property	property	NN
cord-194157-ak2gc3nz	114	12	implies	imply	VBZ
cord-194157-ak2gc3nz	114	13	thatZ	thatZ	NNP
cord-194157-ak2gc3nz	114	14	a	a	DT
cord-194157-ak2gc3nz	114	15	has	have	VBZ
cord-194157-ak2gc3nz	114	16	distribution	distribution	NN
cord-194157-ak2gc3nz	114	17	CI(λ	CI(λ	NNP
cord-194157-ak2gc3nz	114	18	,	,	,
cord-194157-ak2gc3nz	114	19	µ	µ	NN
cord-194157-ak2gc3nz	114	20	,	,	,
cord-194157-ak2gc3nz	114	21	τ	τ	NN
cord-194157-ak2gc3nz	114	22	)	)	-RRB-
cord-194157-ak2gc3nz	114	23	.	.	.
cord-194157-ak2gc3nz	115	1	Also	also	RB
cord-194157-ak2gc3nz	115	2	,	,	,
cord-194157-ak2gc3nz	115	3	the	the	DT
cord-194157-ak2gc3nz	115	4	vertices	vertex	NNS
cord-194157-ak2gc3nz	115	5	{	{	-LRB-
cord-194157-ak2gc3nz	115	6	b(a	b(a	NNP
cord-194157-ak2gc3nz	115	7	)	)	-RRB-
cord-194157-ak2gc3nz	115	8	}	}	-RRB-
cord-194157-ak2gc3nz	115	9	a∈Ã	a∈Ã	NNS
cord-194157-ak2gc3nz	115	10	are	be	VBP
cord-194157-ak2gc3nz	115	11	pairwise	pairwise	JJ
cord-194157-ak2gc3nz	115	12	distinct	distinct	JJ
cord-194157-ak2gc3nz	115	13	almost	almost	RB
cord-194157-ak2gc3nz	115	14	surely	surely	RB
cord-194157-ak2gc3nz	115	15	.	.	.
cord-194157-ak2gc3nz	116	1	Indeed	indeed	RB
cord-194157-ak2gc3nz	116	2	,	,	,
cord-194157-ak2gc3nz	116	3	ifb(a	ifb(a	ADD
cord-194157-ak2gc3nz	116	4	)	)	-RRB-
cord-194157-ak2gc3nz	117	1	=	=	NFP
cord-194157-ak2gc3nz	117	2	b(a	b(a	NNP
cord-194157-ak2gc3nz	117	3	)	)	-RRB-
cord-194157-ak2gc3nz	117	4	,	,	,
cord-194157-ak2gc3nz	117	5	then	then	RB
cord-194157-ak2gc3nz	117	6	if	if	IN
cord-194157-ak2gc3nz	117	7	we	-PRON-	PRP
cord-194157-ak2gc3nz	117	8	delete	delete	VBP
cord-194157-ak2gc3nz	117	9	the	the	DT
cord-194157-ak2gc3nz	117	10	edge	edge	NN
cord-194157-ak2gc3nz	117	11	{	{	-LRB-
cord-194157-ak2gc3nz	117	12	a	a	NN
cord-194157-ak2gc3nz	117	13	,	,	,
cord-194157-ak2gc3nz	117	14	b(a	b(a	NNP
cord-194157-ak2gc3nz	117	15	)	)	-RRB-
cord-194157-ak2gc3nz	117	16	}	}	-RRB-
cord-194157-ak2gc3nz	117	17	,	,	,
cord-194157-ak2gc3nz	117	18	we	-PRON-	PRP
cord-194157-ak2gc3nz	117	19	can	can	MD
cord-194157-ak2gc3nz	117	20	still	still	RB
cord-194157-ak2gc3nz	117	21	traverse	traverse	VB
cord-194157-ak2gc3nz	117	22	a	a	DT
cord-194157-ak2gc3nz	117	23	walk	walk	NN
cord-194157-ak2gc3nz	117	24	from	from	IN
cord-194157-ak2gc3nz	117	25	a	a	DT
cord-194157-ak2gc3nz	117	26	to	to	IN
cord-194157-ak2gc3nz	117	27	U	U	NNP
cord-194157-ak2gc3nz	117	28	(	(	-LRB-
cord-194157-ak2gc3nz	117	29	0	0	NFP
cord-194157-ak2gc3nz	117	30	)	)	-RRB-
cord-194157-ak2gc3nz	117	31	to	to	IN
cord-194157-ak2gc3nz	117	32	a	a	DT
cord-194157-ak2gc3nz	117	33	tob(a	tob(a	NN
cord-194157-ak2gc3nz	117	34	)	)	-RRB-
cord-194157-ak2gc3nz	118	1	=	=	NFP
cord-194157-ak2gc3nz	118	2	b(a	b(a	NNP
cord-194157-ak2gc3nz	118	3	)	)	-RRB-
cord-194157-ak2gc3nz	118	4	,	,	,
cord-194157-ak2gc3nz	118	5	implying	imply	VBG
cord-194157-ak2gc3nz	118	6	{	{	-LRB-
cord-194157-ak2gc3nz	118	7	a	a	DT
cord-194157-ak2gc3nz	118	8	,	,	,
cord-194157-ak2gc3nz	118	9	b(a	b(a	NNP
cord-194157-ak2gc3nz	118	10	)	)	-RRB-
cord-194157-ak2gc3nz	118	11	}	}	-RRB-
cord-194157-ak2gc3nz	118	12	was	be	VBD
cord-194157-ak2gc3nz	118	13	not	not	RB
cord-194157-ak2gc3nz	118	14	a	a	DT
cord-194157-ak2gc3nz	118	15	bridge	bridge	NN
cord-194157-ak2gc3nz	118	16	.	.	.
cord-194157-ak2gc3nz	119	1	As	as	IN
cord-194157-ak2gc3nz	119	2	such	such	JJ
cord-194157-ak2gc3nz	119	3	,	,	,
cord-194157-ak2gc3nz	119	4	conditioned	condition	VBN
cord-194157-ak2gc3nz	119	5	onÃ	onã	CD
cord-194157-ak2gc3nz	119	6	and	and	CC
cord-194157-ak2gc3nz	119	7	{	{	-LRB-
cord-194157-ak2gc3nz	119	8	b(a	b(a	NNP
cord-194157-ak2gc3nz	119	9	)	)	-RRB-
cord-194157-ak2gc3nz	119	10	}	}	-RRB-
cord-194157-ak2gc3nz	119	11	a∈Ã	a∈ã	RB
cord-194157-ak2gc3nz	119	12	,	,	,
cord-194157-ak2gc3nz	119	13	the	the	DT
cord-194157-ak2gc3nz	119	14	variables	variable	NNS
cord-194157-ak2gc3nz	119	15	{	{	-LRB-
cord-194157-ak2gc3nz	119	16	Z	Z	NNP
cord-194157-ak2gc3nz	119	17	a	a	DT
cord-194157-ak2gc3nz	119	18	}	}	-RRB-
cord-194157-ak2gc3nz	119	19	a∈Ã	a∈Ã	NNS
cord-194157-ak2gc3nz	119	20	are	be	VBP
cord-194157-ak2gc3nz	119	21	jointly	jointly	RB
cord-194157-ak2gc3nz	119	22	independent	independent	JJ
cord-194157-ak2gc3nz	119	23	.	.	.
cord-194157-ak2gc3nz	120	1	Then	then	RB
cord-194157-ak2gc3nz	120	2	Lemmas	Lemmas	NNP
cord-194157-ak2gc3nz	120	3	4	4	CD
cord-194157-ak2gc3nz	120	4	and	and	CC
cord-194157-ak2gc3nz	120	5	5	5	CD
cord-194157-ak2gc3nz	120	6	together	together	RB
cord-194157-ak2gc3nz	120	7	imply	imply	NN
cord-194157-ak2gc3nz	120	8	Of	of	RB
cord-194157-ak2gc3nz	120	9	course	course	RB
cord-194157-ak2gc3nz	120	10	,	,	,
cord-194157-ak2gc3nz	120	11	in	in	IN
cord-194157-ak2gc3nz	120	12	our	-PRON-	PRP$
cord-194157-ak2gc3nz	120	13	setup	setup	NN
cord-194157-ak2gc3nz	120	14	,	,	,
cord-194157-ak2gc3nz	120	15	we	-PRON-	PRP
cord-194157-ak2gc3nz	120	16	do	do	VBP
cord-194157-ak2gc3nz	120	17	not	not	RB
cord-194157-ak2gc3nz	120	18	have	have	VB
cord-194157-ak2gc3nz	120	19	access	access	NN
cord-194157-ak2gc3nz	120	20	to	to	IN
cord-194157-ak2gc3nz	120	21	I(t	I(t	NNP
cord-194157-ak2gc3nz	120	22	0	0	CD
cord-194157-ak2gc3nz	120	23	)	)	-RRB-
cord-194157-ak2gc3nz	120	24	,	,	,
cord-194157-ak2gc3nz	120	25	but	but	CC
cord-194157-ak2gc3nz	120	26	rather	rather	RB
cord-194157-ak2gc3nz	120	27	U	u	PRP
cord-194157-ak2gc3nz	120	28	(	(	-LRB-
cord-194157-ak2gc3nz	120	29	t	t	NN
cord-194157-ak2gc3nz	120	30	0	0	CD
cord-194157-ak2gc3nz	120	31	)	)	-RRB-
cord-194157-ak2gc3nz	120	32	=	=	NFP
cord-194157-ak2gc3nz	121	1	I(t	I(t	NNP
cord-194157-ak2gc3nz	121	2	0	0	CD
cord-194157-ak2gc3nz	121	3	)	)	-RRB-
cord-194157-ak2gc3nz	122	1	∪	∪	NNP
cord-194157-ak2gc3nz	122	2	R(t	R(t	NNP
cord-194157-ak2gc3nz	122	3	0	0	NFP
cord-194157-ak2gc3nz	122	4	)	)	-RRB-
cord-194157-ak2gc3nz	123	1	,	,	,
cord-194157-ak2gc3nz	124	1	and	and	CC
cord-194157-ak2gc3nz	124	2	so	so	RB
cord-194157-ak2gc3nz	124	3	we	-PRON-	PRP
cord-194157-ak2gc3nz	124	4	can	can	MD
cord-194157-ak2gc3nz	124	5	not	not	RB
cord-194157-ak2gc3nz	124	6	apply	apply	VB
cord-194157-ak2gc3nz	124	7	Lemma	Lemma	NNP
cord-194157-ak2gc3nz	124	8	6	6	CD
cord-194157-ak2gc3nz	124	9	directly	directly	RB
cord-194157-ak2gc3nz	124	10	.	.	.
cord-194157-ak2gc3nz	125	1	Instead	instead	RB
cord-194157-ak2gc3nz	125	2	,	,	,
cord-194157-ak2gc3nz	125	3	we	-PRON-	PRP
cord-194157-ak2gc3nz	125	4	assume	assume	VBP
cord-194157-ak2gc3nz	125	5	that	that	IN
cord-194157-ak2gc3nz	125	6	λ	λ	NN
cord-194157-ak2gc3nz	125	7	is	be	VBZ
cord-194157-ak2gc3nz	125	8	sufficiently	sufficiently	RB
cord-194157-ak2gc3nz	125	9	large	large	JJ
cord-194157-ak2gc3nz	125	10	compared	compare	VBN
cord-194157-ak2gc3nz	125	11	to	to	IN
cord-194157-ak2gc3nz	125	12	µ	µ	NN
cord-194157-ak2gc3nz	125	13	that	that	WDT
cord-194157-ak2gc3nz	125	14	U	u	NN
cord-194157-ak2gc3nz	125	15	(	(	-LRB-
cord-194157-ak2gc3nz	125	16	t	t	NN
cord-194157-ak2gc3nz	125	17	0	0	CD
cord-194157-ak2gc3nz	125	18	)	)	-RRB-
cord-194157-ak2gc3nz	125	19	is	be	VBZ
cord-194157-ak2gc3nz	125	20	a	a	DT
cord-194157-ak2gc3nz	125	21	decent	decent	JJ
cord-194157-ak2gc3nz	125	22	approximation	approximation	NN
cord-194157-ak2gc3nz	125	23	of	of	IN
cord-194157-ak2gc3nz	125	24	I(t	I(t	NNP
cord-194157-ak2gc3nz	125	25	0	0	CD
cord-194157-ak2gc3nz	125	26	)	)	-RRB-
cord-194157-ak2gc3nz	125	27	.	.	.
cord-194157-ak2gc3nz	126	1	This	this	DT
cord-194157-ak2gc3nz	126	2	approach	approach	NN
cord-194157-ak2gc3nz	126	3	is	be	VBZ
cord-194157-ak2gc3nz	126	4	summarized	summarize	VBN
cord-194157-ak2gc3nz	126	5	in	in	IN
cord-194157-ak2gc3nz	126	6	Algorithm	Algorithm	NNP
cord-194157-ak2gc3nz	126	7	1	1	CD
cord-194157-ak2gc3nz	126	8	.	.	.
cord-194157-ak2gc3nz	127	1	As	as	IN
cord-194157-ak2gc3nz	127	2	we	-PRON-	PRP
cord-194157-ak2gc3nz	127	3	will	will	MD
cord-194157-ak2gc3nz	127	4	see	see	VB
cord-194157-ak2gc3nz	127	5	,	,	,
cord-194157-ak2gc3nz	127	6	the	the	DT
cord-194157-ak2gc3nz	127	7	approximation	approximation	NN
cord-194157-ak2gc3nz	127	8	I(t	I(t	NNP
cord-194157-ak2gc3nz	127	9	0	0	CD
cord-194157-ak2gc3nz	127	10	)	)	-RRB-
cord-194157-ak2gc3nz	128	1	≈	≈	NNP
cord-194157-ak2gc3nz	128	2	U	U	NNP
cord-194157-ak2gc3nz	128	3	(	(	-LRB-
cord-194157-ak2gc3nz	128	4	t	t	NN
cord-194157-ak2gc3nz	128	5	0	0	CD
cord-194157-ak2gc3nz	128	6	)	)	-RRB-
cord-194157-ak2gc3nz	128	7	introduces	introduce	VBZ
cord-194157-ak2gc3nz	128	8	some	some	DT
cord-194157-ak2gc3nz	128	9	error	error	NN
cord-194157-ak2gc3nz	128	10	in	in	IN
cord-194157-ak2gc3nz	128	11	our	-PRON-	PRP$
cord-194157-ak2gc3nz	128	12	estimators	estimator	NNS
cord-194157-ak2gc3nz	128	13	.	.	.
cord-194157-ak2gc3nz	129	1	To	to	TO
cord-194157-ak2gc3nz	129	2	analyze	analyze	VB
cord-194157-ak2gc3nz	129	3	the	the	DT
cord-194157-ak2gc3nz	129	4	performance	performance	NN
cord-194157-ak2gc3nz	129	5	of	of	IN
cord-194157-ak2gc3nz	129	6	Algorithm	algorithm	NN
cord-194157-ak2gc3nz	129	7	1	1	CD
cord-194157-ak2gc3nz	129	8	,	,	,
cord-194157-ak2gc3nz	129	9	it	-PRON-	PRP
cord-194157-ak2gc3nz	129	10	is	be	VBZ
cord-194157-ak2gc3nz	129	11	convenient	convenient	JJ
cord-194157-ak2gc3nz	129	12	to	to	TO
cord-194157-ak2gc3nz	129	13	focus	focus	VB
cord-194157-ak2gc3nz	129	14	on	on	IN
cord-194157-ak2gc3nz	129	15	a	a	DT
cord-194157-ak2gc3nz	129	16	certain	certain	JJ
cord-194157-ak2gc3nz	129	17	(	(	-LRB-
cord-194157-ak2gc3nz	129	18	large	large	JJ
cord-194157-ak2gc3nz	129	19	)	)	-RRB-
cord-194157-ak2gc3nz	129	20	family	family	NN
cord-194157-ak2gc3nz	129	21	of	of	IN
cord-194157-ak2gc3nz	129	22	graphs	graph	NNS
cord-194157-ak2gc3nz	129	23	.	.	.
cord-194157-ak2gc3nz	130	1	We	-PRON-	PRP
cord-194157-ak2gc3nz	130	2	say	say	VBP
cord-194157-ak2gc3nz	130	3	a	a	DT
cord-194157-ak2gc3nz	130	4	graph	graph	NN
cord-194157-ak2gc3nz	130	5	G	g	NN
cord-194157-ak2gc3nz	130	6	is	be	VBZ
cord-194157-ak2gc3nz	130	7	(	(	-LRB-
cord-194157-ak2gc3nz	130	8	r	r	NN
cord-194157-ak2gc3nz	130	9	,	,	,
cord-194157-ak2gc3nz	130	10	η)-locally	η)-locally	RB
cord-194157-ak2gc3nz	130	11	tree	tree	NN
cord-194157-ak2gc3nz	130	12	-	-	HYPH
cord-194157-ak2gc3nz	130	13	like	like	JJ
cord-194157-ak2gc3nz	130	14	if	if	IN
cord-194157-ak2gc3nz	130	15	for	for	IN
cord-194157-ak2gc3nz	130	16	a	a	DT
cord-194157-ak2gc3nz	130	17	fraction	fraction	NN
cord-194157-ak2gc3nz	130	18	1	1	CD
cord-194157-ak2gc3nz	130	19	−	−	CD
cord-194157-ak2gc3nz	130	20	η	η	NN
cord-194157-ak2gc3nz	130	21	of	of	IN
cord-194157-ak2gc3nz	130	22	the	the	DT
cord-194157-ak2gc3nz	130	23	vertices	vertex	NNS
cord-194157-ak2gc3nz	130	24	v	v	NN
cord-194157-ak2gc3nz	130	25	∈	∈	NN
cord-194157-ak2gc3nz	130	26	V	v	NN
cord-194157-ak2gc3nz	130	27	(	(	-LRB-
cord-194157-ak2gc3nz	130	28	G	G	NNP
cord-194157-ak2gc3nz	130	29	)	)	-RRB-
cord-194157-ak2gc3nz	130	30	,	,	,
cord-194157-ak2gc3nz	130	31	it	-PRON-	PRP
cord-194157-ak2gc3nz	130	32	holds	hold	VBZ
cord-194157-ak2gc3nz	130	33	that	that	IN
cord-194157-ak2gc3nz	130	34	the	the	DT
cord-194157-ak2gc3nz	130	35	subgraph	subgraph	NN
cord-194157-ak2gc3nz	130	36	induced	induce	VBN
cord-194157-ak2gc3nz	130	37	by	by	IN
cord-194157-ak2gc3nz	130	38	the	the	DT
cord-194157-ak2gc3nz	130	39	vertices	vertex	NNS
cord-194157-ak2gc3nz	130	40	of	of	IN
cord-194157-ak2gc3nz	130	41	distance	distance	NN
cord-194157-ak2gc3nz	130	42	at	at	IN
cord-194157-ak2gc3nz	130	43	most	most	JJS
cord-194157-ak2gc3nz	130	44	r	r	NN
cord-194157-ak2gc3nz	130	45	from	from	IN
cord-194157-ak2gc3nz	130	46	v	v	NN
cord-194157-ak2gc3nz	130	47	is	be	VBZ
cord-194157-ak2gc3nz	130	48	a	a	DT
cord-194157-ak2gc3nz	130	49	tree	tree	NN
cord-194157-ak2gc3nz	130	50	.	.	.
cord-194157-ak2gc3nz	131	1	For	for	IN
cord-194157-ak2gc3nz	131	2	example	example	NN
cord-194157-ak2gc3nz	131	3	,	,	,
cord-194157-ak2gc3nz	131	4	it	-PRON-	PRP
cord-194157-ak2gc3nz	131	5	is	be	VBZ
cord-194157-ak2gc3nz	131	6	known	know	VBN
cord-194157-ak2gc3nz	131	7	that	that	IN
cord-194157-ak2gc3nz	131	8	for	for	IN
cord-194157-ak2gc3nz	131	9	every	every	DT
cord-194157-ak2gc3nz	131	10	fixed	fix	VBN
cord-194157-ak2gc3nz	131	11	choice	choice	NN
cord-194157-ak2gc3nz	131	12	of	of	IN
cord-194157-ak2gc3nz	131	13	d	d	NN
cord-194157-ak2gc3nz	131	14	∈	∈	NNP
cord-194157-ak2gc3nz	131	15	N	N	NNP
cord-194157-ak2gc3nz	131	16	with	with	IN
cord-194157-ak2gc3nz	131	17	d	d	NN
cord-194157-ak2gc3nz	131	18	>	>	XX
cord-194157-ak2gc3nz	131	19	1	1	CD
cord-194157-ak2gc3nz	131	20	and	and	CC
cord-194157-ak2gc3nz	131	21	c	c	NN
cord-194157-ak2gc3nz	131	22	∈	∈	NN
cord-194157-ak2gc3nz	131	23	(	(	-LRB-
cord-194157-ak2gc3nz	131	24	0	0	CD
cord-194157-ak2gc3nz	131	25	,	,	,
cord-194157-ak2gc3nz	131	26	1	1	CD
cord-194157-ak2gc3nz	131	27	4	4	CD
cord-194157-ak2gc3nz	131	28	)	)	-RRB-
cord-194157-ak2gc3nz	131	29	,	,	,
cord-194157-ak2gc3nz	131	30	there	there	EX
cord-194157-ak2gc3nz	131	31	exists	exist	VBZ
cord-194157-ak2gc3nz	131	32	γ	γ	NN
cord-194157-ak2gc3nz	131	33	>	>	XX
cord-194157-ak2gc3nz	131	34	0	0	NFP
cord-194157-ak2gc3nz	132	1	such	such	JJ
cord-194157-ak2gc3nz	132	2	that	that	IN
cord-194157-ak2gc3nz	132	3	a	a	DT
cord-194157-ak2gc3nz	132	4	random	random	JJ
cord-194157-ak2gc3nz	132	5	d	d	NN
cord-194157-ak2gc3nz	132	6	-	-	HYPH
cord-194157-ak2gc3nz	132	7	regular	regular	JJ
cord-194157-ak2gc3nz	132	8	graph	graph	NN
cord-194157-ak2gc3nz	132	9	on	on	IN
cord-194157-ak2gc3nz	132	10	n	n	NN
cord-194157-ak2gc3nz	132	11	vertices	vertex	NNS
cord-194157-ak2gc3nz	132	12	is	be	VBZ
cord-194157-ak2gc3nz	132	13	(	(	-LRB-
cord-194157-ak2gc3nz	132	14	c	c	NN
cord-194157-ak2gc3nz	132	15	log	log	NN
cord-194157-ak2gc3nz	132	16	d−1	d−1	NNP
cord-194157-ak2gc3nz	132	17	n	n	NN
cord-194157-ak2gc3nz	132	18	,	,	,
cord-194157-ak2gc3nz	132	19	n	n	NNP
cord-194157-ak2gc3nz	132	20	−γ	−γ	NNP
cord-194157-ak2gc3nz	132	21	)	)	-RRB-
cord-194157-ak2gc3nz	133	1	-locally	-locally	RB
cord-194157-ak2gc3nz	133	2	tree	tree	NN
cord-194157-ak2gc3nz	133	3	-	-	HYPH
cord-194157-ak2gc3nz	133	4	like	like	JJ
cord-194157-ak2gc3nz	133	5	with	with	IN
cord-194157-ak2gc3nz	133	6	probability	probability	NN
cord-194157-ak2gc3nz	133	7	approaching	approach	VBG
cord-194157-ak2gc3nz	133	8	1	1	CD
cord-194157-ak2gc3nz	133	9	as	as	IN
cord-194157-ak2gc3nz	133	10	n	n	CC
cord-194157-ak2gc3nz	133	11	→	→	NN
cord-194157-ak2gc3nz	133	12	∞	∞	NNP
cord-194157-ak2gc3nz	133	13	;	;	:
cord-194157-ak2gc3nz	133	14	see	see	VB
cord-194157-ak2gc3nz	133	15	Proposition	Proposition	NNP
cord-194157-ak2gc3nz	133	16	4.1	4.1	CD
cord-194157-ak2gc3nz	133	17	in	in	IN
cord-194157-ak2gc3nz	133	18	[	[	-LRB-
cord-194157-ak2gc3nz	133	19	2	2	CD
cord-194157-ak2gc3nz	133	20	]	]	-RRB-
cord-194157-ak2gc3nz	133	21	.	.	.
cord-194157-ak2gc3nz	134	1	By	by	IN
cord-194157-ak2gc3nz	134	2	focusing	focus	VBG
cord-194157-ak2gc3nz	134	3	on	on	IN
cord-194157-ak2gc3nz	134	4	this	this	DT
cord-194157-ak2gc3nz	134	5	class	class	NN
cord-194157-ak2gc3nz	134	6	of	of	IN
cord-194157-ak2gc3nz	134	7	graphs	graph	NNS
cord-194157-ak2gc3nz	134	8	,	,	,
cord-194157-ak2gc3nz	134	9	we	-PRON-	PRP
cord-194157-ak2gc3nz	134	10	may	may	MD
cord-194157-ak2gc3nz	134	11	apply	apply	VB
cord-194157-ak2gc3nz	134	12	the	the	DT
cord-194157-ak2gc3nz	134	13	vast	vast	JJ
cord-194157-ak2gc3nz	134	14	literature	literature	NN
cord-194157-ak2gc3nz	134	15	on	on	IN
cord-194157-ak2gc3nz	134	16	SIR	SIR	NNP
cord-194157-ak2gc3nz	134	17	dynamics	dynamic	NNS
cord-194157-ak2gc3nz	134	18	on	on	IN
cord-194157-ak2gc3nz	134	19	infinite	infinite	JJ
cord-194157-ak2gc3nz	134	20	trees	tree	NNS
cord-194157-ak2gc3nz	134	21	to	to	TO
cord-194157-ak2gc3nz	134	22	help	help	VB
cord-194157-ak2gc3nz	134	23	analyze	analyze	VB
cord-194157-ak2gc3nz	134	24	the	the	DT
cord-194157-ak2gc3nz	134	25	performance	performance	NN
cord-194157-ak2gc3nz	134	26	of	of	IN
cord-194157-ak2gc3nz	134	27	Algorithm	Algorithm	NNP
cord-194157-ak2gc3nz	134	28	1	1	CD
cord-194157-ak2gc3nz	134	29	.	.	.
cord-194157-ak2gc3nz	135	1	Theorem	theorem	NN
cord-194157-ak2gc3nz	135	2	7	7	CD
cord-194157-ak2gc3nz	135	3	(	(	-LRB-
cord-194157-ak2gc3nz	135	4	Main	Main	NNP
cord-194157-ak2gc3nz	135	5	Result	Result	NNP
cord-194157-ak2gc3nz	135	6	)	)	-RRB-
cord-194157-ak2gc3nz	135	7	.	.	.
cord-194157-ak2gc3nz	136	1	Fix	fix	VB
cord-194157-ak2gc3nz	136	2	d	d	NN
cord-194157-ak2gc3nz	136	3	∈	∈	NN
cord-194157-ak2gc3nz	137	1	N	n	CD
cord-194157-ak2gc3nz	137	2	with	with	IN
cord-194157-ak2gc3nz	137	3	d	d	NNP
cord-194157-ak2gc3nz	137	4	≥	≥	CD
cord-194157-ak2gc3nz	137	5	3	3	CD
cord-194157-ak2gc3nz	137	6	and	and	CC
cord-194157-ak2gc3nz	137	7	c	c	NNP
cord-194157-ak2gc3nz	137	8	,	,	,
cord-194157-ak2gc3nz	137	9	γ	γ	NN
cord-194157-ak2gc3nz	137	10	>	>	XX
cord-194157-ak2gc3nz	137	11	0	0	CD
cord-194157-ak2gc3nz	137	12	,	,	,
cord-194157-ak2gc3nz	137	13	and	and	CC
cord-194157-ak2gc3nz	137	14	consider	consider	VB
cord-194157-ak2gc3nz	137	15	any	any	DT
cord-194157-ak2gc3nz	137	16	sequence	sequence	NN
cord-194157-ak2gc3nz	137	17	of	of	IN
cord-194157-ak2gc3nz	137	18	d	d	JJ
cord-194157-ak2gc3nz	137	19	-	-	HYPH
cord-194157-ak2gc3nz	137	20	regular	regular	JJ
cord-194157-ak2gc3nz	137	21	,	,	,
cord-194157-ak2gc3nz	138	1	(	(	-LRB-
cord-194157-ak2gc3nz	138	2	c	c	LS
cord-194157-ak2gc3nz	138	3	log	log	NN
cord-194157-ak2gc3nz	138	4	d−1	d−1	NNP
cord-194157-ak2gc3nz	138	5	n	n	NN
cord-194157-ak2gc3nz	138	6	,	,	,
cord-194157-ak2gc3nz	138	7	n	n	NNP
cord-194157-ak2gc3nz	138	8	−γ	−γ	NNP
cord-194157-ak2gc3nz	138	9	)	)	-RRB-
cord-194157-ak2gc3nz	139	1	-locally	-locally	RB
cord-194157-ak2gc3nz	139	2	tree	tree	NN
cord-194157-ak2gc3nz	139	3	-	-	HYPH
cord-194157-ak2gc3nz	139	4	like	like	JJ
cord-194157-ak2gc3nz	139	5	graphs	graph	NNS
cord-194157-ak2gc3nz	139	6	on	on	IN
cord-194157-ak2gc3nz	139	7	n	n	NN
cord-194157-ak2gc3nz	139	8	vertices	vertex	NNS
cord-194157-ak2gc3nz	139	9	with	with	IN
cord-194157-ak2gc3nz	139	10	n	n	NNP
cord-194157-ak2gc3nz	139	11	→	→	NN
cord-194157-ak2gc3nz	139	12	∞.	∞.	NNP
cord-194157-ak2gc3nz	139	13	Select	Select	NNP
cord-194157-ak2gc3nz	139	14	any	any	DT
cord-194157-ak2gc3nz	139	15	α	α	NN
cord-194157-ak2gc3nz	139	16	and	and	CC
cord-194157-ak2gc3nz	139	17	β	β	NN
cord-194157-ak2gc3nz	139	18	such	such	JJ
cord-194157-ak2gc3nz	139	19	that	that	DT
cord-194157-ak2gc3nz	140	1	0	0	NFP
cord-194157-ak2gc3nz	140	2	<	<	XX
cord-194157-ak2gc3nz	140	3	α	α	XX
cord-194157-ak2gc3nz	140	4	<	<	XX
cord-194157-ak2gc3nz	140	5	β	β	XX
cord-194157-ak2gc3nz	140	6	<	<	XX
cord-194157-ak2gc3nz	140	7	c	c	NNP
cord-194157-ak2gc3nz	140	8	2e(d−1)λ	2e(d−1)λ	CD
cord-194157-ak2gc3nz	140	9	,	,	,
cord-194157-ak2gc3nz	140	10	and	and	CC
cord-194157-ak2gc3nz	140	11	put	put	VBN
cord-194157-ak2gc3nz	140	12	For	for	IN
cord-194157-ak2gc3nz	140	13	each	each	DT
cord-194157-ak2gc3nz	140	14	n	n	NN
cord-194157-ak2gc3nz	141	1	,	,	,
cord-194157-ak2gc3nz	141	2	let	let	VB
cord-194157-ak2gc3nz	141	3	E	e	NN
cord-194157-ak2gc3nz	141	4	0	0	CD
cord-194157-ak2gc3nz	141	5	denote	denote	VB
cord-194157-ak2gc3nz	141	6	the	the	DT
cord-194157-ak2gc3nz	141	7	event	event	NN
cord-194157-ak2gc3nz	141	8	that	that	IN
cord-194157-ak2gc3nz	141	9	the	the	DT
cord-194157-ak2gc3nz	141	10	subgraph	subgraph	NN
cord-194157-ak2gc3nz	141	11	B(r	B(r	NNS
cord-194157-ak2gc3nz	141	12	)	)	-RRB-
cord-194157-ak2gc3nz	141	13	induced	induce	VBN
cord-194157-ak2gc3nz	141	14	by	by	IN
cord-194157-ak2gc3nz	141	15	vertices	vertex	NNS
cord-194157-ak2gc3nz	141	16	of	of	IN
cord-194157-ak2gc3nz	141	17	distance	distance	NN
cord-194157-ak2gc3nz	141	18	at	at	IN
cord-194157-ak2gc3nz	141	19	most	most	RBS
cord-194157-ak2gc3nz	141	20	r	r	NN
cord-194157-ak2gc3nz	141	21	from	from	IN
cord-194157-ak2gc3nz	141	22	U	U	NNP
cord-194157-ak2gc3nz	141	23	(	(	-LRB-
cord-194157-ak2gc3nz	141	24	0	0	NFP
cord-194157-ak2gc3nz	141	25	)	)	-RRB-
cord-194157-ak2gc3nz	141	26	is	be	VBZ
cord-194157-ak2gc3nz	141	27	a	a	DT
cord-194157-ak2gc3nz	141	28	tree	tree	NN
cord-194157-ak2gc3nz	141	29	,	,	,
cord-194157-ak2gc3nz	141	30	and	and	CC
cord-194157-ak2gc3nz	141	31	let	let	VB
cord-194157-ak2gc3nz	141	32	E	e	NN
cord-194157-ak2gc3nz	141	33	∞	∞	NNP
cord-194157-ak2gc3nz	141	34	denote	denote	VB
cord-194157-ak2gc3nz	141	35	the	the	DT
cord-194157-ak2gc3nz	141	36	event	event	NN
cord-194157-ak2gc3nz	141	37	that	that	WDT
cord-194157-ak2gc3nz	141	38	U	U	NNP
cord-194157-ak2gc3nz	141	39	(	(	-LRB-
cord-194157-ak2gc3nz	141	40	∞	∞	NNP
cord-194157-ak2gc3nz	141	41	)	)	-RRB-
cord-194157-ak2gc3nz	141	42	contains	contain	VBZ
cord-194157-ak2gc3nz	141	43	a	a	DT
cord-194157-ak2gc3nz	141	44	vertex	vertex	NN
cord-194157-ak2gc3nz	141	45	of	of	IN
cord-194157-ak2gc3nz	141	46	distance	distance	NN
cord-194157-ak2gc3nz	141	47	greater	great	JJR
cord-194157-ak2gc3nz	141	48	than	than	IN
cord-194157-ak2gc3nz	141	49	r	r	NN
cord-194157-ak2gc3nz	141	50	from	from	IN
cord-194157-ak2gc3nz	141	51	U	U	NNP
cord-194157-ak2gc3nz	141	52	(	(	-LRB-
cord-194157-ak2gc3nz	141	53	0	0	NFP
cord-194157-ak2gc3nz	141	54	)	)	-RRB-
cord-194157-ak2gc3nz	141	55	.	.	.
cord-194157-ak2gc3nz	142	1	Suppose	suppose	VB
cord-194157-ak2gc3nz	142	2	λ	λ	NN
cord-194157-ak2gc3nz	142	3	≥	≥	CD
cord-194157-ak2gc3nz	142	4	6µ	6µ	CD
cord-194157-ak2gc3nz	142	5	>	>	XX
cord-194157-ak2gc3nz	142	6	0	0	CD
cord-194157-ak2gc3nz	142	7	.	.	.
cord-194157-ak2gc3nz	143	1	Then	then	RB
cord-194157-ak2gc3nz	143	2	one	one	CD
cord-194157-ak2gc3nz	143	3	of	of	IN
cord-194157-ak2gc3nz	143	4	the	the	DT
cord-194157-ak2gc3nz	143	5	following	following	NN
cord-194157-ak2gc3nz	143	6	holds	hold	VBZ
cord-194157-ak2gc3nz	143	7	:	:	:
cord-194157-ak2gc3nz	143	8	,	,	,
cord-194157-ak2gc3nz	143	9	meaning	mean	VBG
cord-194157-ak2gc3nz	143	10	there	there	EX
cord-194157-ak2gc3nz	143	11	is	be	VBZ
cord-194157-ak2gc3nz	143	12	a	a	DT
cord-194157-ak2gc3nz	143	13	subsequence	subsequence	NN
cord-194157-ak2gc3nz	143	14	of	of	IN
cord-194157-ak2gc3nz	143	15	n	n	NN
cord-194157-ak2gc3nz	143	16	for	for	IN
cord-194157-ak2gc3nz	143	17	which	which	WDT
cord-194157-ak2gc3nz	143	18	,	,	,
cord-194157-ak2gc3nz	143	19	with	with	IN
cord-194157-ak2gc3nz	143	20	probability	probability	NN
cord-194157-ak2gc3nz	143	21	at	at	IN
cord-194157-ak2gc3nz	143	22	least	least	JJS
cord-194157-ak2gc3nz	143	23	1	1	CD
cord-194157-ak2gc3nz	143	24	−	−	NNP
cord-194157-ak2gc3nz	143	25	o(1	o(1	NNP
cord-194157-ak2gc3nz	143	26	)	)	-RRB-
cord-194157-ak2gc3nz	143	27	,	,	,
cord-194157-ak2gc3nz	143	28	no	no	DT
cord-194157-ak2gc3nz	143	29	vertex	vertex	NN
cord-194157-ak2gc3nz	143	30	outside	outside	IN
cord-194157-ak2gc3nz	143	31	of	of	IN
cord-194157-ak2gc3nz	143	32	B(r	B(r	NNS
cord-194157-ak2gc3nz	143	33	)	)	-RRB-
cord-194157-ak2gc3nz	143	34	will	will	MD
cord-194157-ak2gc3nz	143	35	ever	ever	RB
cord-194157-ak2gc3nz	143	36	be	be	VB
cord-194157-ak2gc3nz	143	37	infected	infect	VBN
cord-194157-ak2gc3nz	143	38	,	,	,
cord-194157-ak2gc3nz	143	39	in	in	IN
cord-194157-ak2gc3nz	143	40	which	which	WDT
cord-194157-ak2gc3nz	143	41	case	case	NN
cord-194157-ak2gc3nz	143	42	the	the	DT
cord-194157-ak2gc3nz	143	43	infection	infection	NN
cord-194157-ak2gc3nz	143	44	does	do	VBZ
cord-194157-ak2gc3nz	143	45	not	not	RB
cord-194157-ak2gc3nz	143	46	spread	spread	VB
cord-194157-ak2gc3nz	143	47	to	to	IN
cord-194157-ak2gc3nz	143	48	even	even	RB
cord-194157-ak2gc3nz	143	49	a	a	DT
cord-194157-ak2gc3nz	143	50	constant	constant	JJ
cord-194157-ak2gc3nz	143	51	fraction	fraction	NN
cord-194157-ak2gc3nz	143	52	of	of	IN
cord-194157-ak2gc3nz	143	53	the	the	DT
cord-194157-ak2gc3nz	143	54	graph	graph	NN
cord-194157-ak2gc3nz	143	55	.	.	.
cord-194157-ak2gc3nz	144	1	(	(	-LRB-
cord-194157-ak2gc3nz	144	2	b	b	LS
cord-194157-ak2gc3nz	144	3	)	)	-RRB-
cord-194157-ak2gc3nz	144	4	For	for	IN
cord-194157-ak2gc3nz	144	5	each	each	DT
cord-194157-ak2gc3nz	144	6	n	n	NN
cord-194157-ak2gc3nz	144	7	,	,	,
cord-194157-ak2gc3nz	144	8	the	the	DT
cord-194157-ak2gc3nz	144	9	following	following	NN
cord-194157-ak2gc3nz	144	10	holds	hold	VBZ
cord-194157-ak2gc3nz	144	11	:	:	:
cord-194157-ak2gc3nz	144	12	with	with	IN
cord-194157-ak2gc3nz	144	13	probability	probability	NN
cord-194157-ak2gc3nz	144	14	tending	tend	VBG
cord-194157-ak2gc3nz	144	15	to	to	IN
cord-194157-ak2gc3nz	144	16	1	1	CD
cord-194157-ak2gc3nz	144	17	as	as	IN
cord-194157-ak2gc3nz	144	18	n	n	NNP
cord-194157-ak2gc3nz	144	19	→	→	NN
cord-194157-ak2gc3nz	144	20	∞.	∞.	NNP
cord-194157-ak2gc3nz	144	21	.	.	.
cord-194157-ak2gc3nz	145	1	The	the	DT
cord-194157-ak2gc3nz	145	2	proof	proof	NN
cord-194157-ak2gc3nz	145	3	is	be	VBZ
cord-194157-ak2gc3nz	145	4	given	give	VBN
cord-194157-ak2gc3nz	145	5	in	in	IN
cord-194157-ak2gc3nz	145	6	the	the	DT
cord-194157-ak2gc3nz	145	7	next	next	JJ
cord-194157-ak2gc3nz	145	8	section	section	NN
cord-194157-ak2gc3nz	145	9	,	,	,
cord-194157-ak2gc3nz	145	10	and	and	CC
cord-194157-ak2gc3nz	145	11	Figure	figure	NN
cord-194157-ak2gc3nz	145	12	1	1	CD
cord-194157-ak2gc3nz	145	13	illustrates	illustrate	VBZ
cord-194157-ak2gc3nz	145	14	the	the	DT
cord-194157-ak2gc3nz	145	15	actual	actual	JJ
cord-194157-ak2gc3nz	145	16	behavior	behavior	NN
cord-194157-ak2gc3nz	145	17	of	of	IN
cord-194157-ak2gc3nz	145	18	Algorithm	Algorithm	NNP
cord-194157-ak2gc3nz	145	19	1	1	CD
cord-194157-ak2gc3nz	145	20	for	for	IN
cord-194157-ak2gc3nz	145	21	comparison	comparison	NN
cord-194157-ak2gc3nz	145	22	.	.	.
cord-194157-ak2gc3nz	146	1	The	the	DT
cord-194157-ak2gc3nz	146	2	factors	factor	NNS
cord-194157-ak2gc3nz	146	3	of	of	IN
cord-194157-ak2gc3nz	146	4	8	8	CD
cord-194157-ak2gc3nz	146	5	in	in	IN
cord-194157-ak2gc3nz	146	6	(	(	-LRB-
cord-194157-ak2gc3nz	146	7	1	1	CD
cord-194157-ak2gc3nz	146	8	)	)	-RRB-
cord-194157-ak2gc3nz	146	9	are	be	VBP
cord-194157-ak2gc3nz	146	10	due	due	JJ
cord-194157-ak2gc3nz	146	11	to	to	IN
cord-194157-ak2gc3nz	146	12	the	the	DT
cord-194157-ak2gc3nz	146	13	approximation	approximation	NN
cord-194157-ak2gc3nz	146	14	I(t	I(t	NNP
cord-194157-ak2gc3nz	146	15	0	0	CD
cord-194157-ak2gc3nz	146	16	)	)	-RRB-
cord-194157-ak2gc3nz	147	1	≈	≈	NNP
cord-194157-ak2gc3nz	147	2	U	U	NNP
cord-194157-ak2gc3nz	147	3	(	(	-LRB-
cord-194157-ak2gc3nz	147	4	t	t	NN
cord-194157-ak2gc3nz	147	5	0	0	CD
cord-194157-ak2gc3nz	147	6	)	)	-RRB-
cord-194157-ak2gc3nz	147	7	,	,	,
cord-194157-ak2gc3nz	147	8	and	and	CC
cord-194157-ak2gc3nz	147	9	they	-PRON-	PRP
cord-194157-ak2gc3nz	147	10	have	have	VBP
cord-194157-ak2gc3nz	147	11	not	not	RB
cord-194157-ak2gc3nz	147	12	been	be	VBN
cord-194157-ak2gc3nz	147	13	optimized	optimize	VBN
cord-194157-ak2gc3nz	147	14	.	.	.
cord-194157-ak2gc3nz	148	1	We	-PRON-	PRP
cord-194157-ak2gc3nz	148	2	suspect	suspect	VBP
cord-194157-ak2gc3nz	148	3	that	that	IN
cord-194157-ak2gc3nz	148	4	these	these	DT
cord-194157-ak2gc3nz	148	5	factors	factor	NNS
cord-194157-ak2gc3nz	148	6	can	can	MD
cord-194157-ak2gc3nz	148	7	be	be	VB
cord-194157-ak2gc3nz	148	8	replaced	replace	VBN
cord-194157-ak2gc3nz	148	9	by	by	IN
cord-194157-ak2gc3nz	148	10	terms	term	NNS
cord-194157-ak2gc3nz	148	11	that	that	WDT
cord-194157-ak2gc3nz	148	12	approach	approach	VBP
cord-194157-ak2gc3nz	148	13	1	1	CD
cord-194157-ak2gc3nz	148	14	as	as	IN
cord-194157-ak2gc3nz	148	15	d	d	NNP
cord-194157-ak2gc3nz	148	16	→	→	NN
cord-194157-ak2gc3nz	148	17	∞	∞	NNP
cord-194157-ak2gc3nz	148	18	,	,	,
cord-194157-ak2gc3nz	148	19	but	but	CC
cord-194157-ak2gc3nz	148	20	this	this	DT
cord-194157-ak2gc3nz	148	21	requires	require	VBZ
cord-194157-ak2gc3nz	148	22	a	a	DT
cord-194157-ak2gc3nz	148	23	different	different	JJ
cord-194157-ak2gc3nz	148	24	technique	technique	NN
cord-194157-ak2gc3nz	148	25	.	.	.
cord-194157-ak2gc3nz	149	1	We	-PRON-	PRP
cord-194157-ak2gc3nz	149	2	also	also	RB
cord-194157-ak2gc3nz	149	3	suspect	suspect	VBP
cord-194157-ak2gc3nz	149	4	the	the	DT
cord-194157-ak2gc3nz	149	5	hypothesis	hypothesis	NN
cord-194157-ak2gc3nz	149	6	λ	λ	NN
cord-194157-ak2gc3nz	149	7	≥	≥	CD
cord-194157-ak2gc3nz	149	8	6µ	6µ	CD
cord-194157-ak2gc3nz	149	9	is	be	VBZ
cord-194157-ak2gc3nz	149	10	an	an	DT
cord-194157-ak2gc3nz	149	11	artifact	artifact	NN
cord-194157-ak2gc3nz	149	12	of	of	IN
cord-194157-ak2gc3nz	149	13	our	-PRON-	PRP$
cord-194157-ak2gc3nz	149	14	proof	proof	NN
cord-194157-ak2gc3nz	149	15	.	.	.
cord-194157-ak2gc3nz	150	1	As	as	IN
cord-194157-ak2gc3nz	150	2	the	the	DT
cord-194157-ak2gc3nz	150	3	following	follow	VBG
cord-194157-ak2gc3nz	150	4	lemma	lemma	NN
cord-194157-ak2gc3nz	150	5	indicates	indicate	VBZ
cord-194157-ak2gc3nz	150	6	,	,	,
cord-194157-ak2gc3nz	150	7	the	the	DT
cord-194157-ak2gc3nz	150	8	threshold	threshold	NN
cord-194157-ak2gc3nz	150	9	(	(	-LRB-
cord-194157-ak2gc3nz	150	10	d	d	NN
cord-194157-ak2gc3nz	150	11	−	−	NNP
cord-194157-ak2gc3nz	150	12	2)λ	2)λ	CD
cord-194157-ak2gc3nz	151	1	>	>	XX
cord-194157-ak2gc3nz	152	1	µ	µ	NNP
cord-194157-ak2gc3nz	152	2	would	would	MD
cord-194157-ak2gc3nz	152	3	be	be	VB
cord-194157-ak2gc3nz	152	4	more	more	RBR
cord-194157-ak2gc3nz	152	5	natural	natural	JJ
cord-194157-ak2gc3nz	152	6	;	;	:
cord-194157-ak2gc3nz	152	7	this	this	DT
cord-194157-ak2gc3nz	152	8	threshold	threshold	NN
cord-194157-ak2gc3nz	152	9	arises	arise	VBZ
cord-194157-ak2gc3nz	152	10	from	from	IN
cord-194157-ak2gc3nz	152	11	standard	standard	JJ
cord-194157-ak2gc3nz	152	12	results	result	NNS
cord-194157-ak2gc3nz	152	13	on	on	IN
cord-194157-ak2gc3nz	152	14	Galton	Galton	NNP
cord-194157-ak2gc3nz	152	15	-	-	HYPH
cord-194157-ak2gc3nz	152	16	Watson	Watson	NNP
cord-194157-ak2gc3nz	152	17	processes	process	VBZ
cord-194157-ak2gc3nz	152	18	(	(	-LRB-
cord-194157-ak2gc3nz	152	19	see	see	VB
cord-194157-ak2gc3nz	152	20	the	the	DT
cord-194157-ak2gc3nz	152	21	lecture	lecture	NN
cord-194157-ak2gc3nz	152	22	notes	note	NNS
cord-194157-ak2gc3nz	152	23	[	[	-LRB-
cord-194157-ak2gc3nz	152	24	1	1	CD
cord-194157-ak2gc3nz	152	25	]	]	-RRB-
cord-194157-ak2gc3nz	152	26	,	,	,
cord-194157-ak2gc3nz	152	27	for	for	IN
cord-194157-ak2gc3nz	152	28	example	example	NN
cord-194157-ak2gc3nz	152	29	)	)	-RRB-
cord-194157-ak2gc3nz	152	30	.	.	.
cord-194157-ak2gc3nz	153	1	Lemma	Lemma	NNP
cord-194157-ak2gc3nz	153	2	8	8	CD
cord-194157-ak2gc3nz	153	3	.	.	.
cord-194157-ak2gc3nz	154	1	Consider	consider	VB
cord-194157-ak2gc3nz	154	2	any	any	DT
cord-194157-ak2gc3nz	154	3	sequence	sequence	NN
cord-194157-ak2gc3nz	154	4	{	{	-LRB-
cord-194157-ak2gc3nz	154	5	G	g	NN
cord-194157-ak2gc3nz	154	6	n	n	NN
cord-194157-ak2gc3nz	154	7	}	}	-RRB-
cord-194157-ak2gc3nz	154	8	of	of	IN
cord-194157-ak2gc3nz	154	9	d	d	JJ
cord-194157-ak2gc3nz	154	10	-	-	JJ
cord-194157-ak2gc3nz	154	11	regular	regular	JJ
cord-194157-ak2gc3nz	154	12	graphs	graph	NNS
cord-194157-ak2gc3nz	154	13	on	on	IN
cord-194157-ak2gc3nz	154	14	n	n	NN
cord-194157-ak2gc3nz	154	15	vertices	vertex	NNS
cord-194157-ak2gc3nz	154	16	with	with	IN
cord-194157-ak2gc3nz	155	1	n	n	LS
cord-194157-ak2gc3nz	155	2	→	→	NN
cord-194157-ak2gc3nz	155	3	∞	∞	NNP
cord-194157-ak2gc3nz	155	4	such	such	JJ
cord-194157-ak2gc3nz	155	5	that	that	IN
cord-194157-ak2gc3nz	155	6	G	g	NN
cord-194157-ak2gc3nz	155	7	n	n	NN
cord-194157-ak2gc3nz	155	8	is	be	VBZ
cord-194157-ak2gc3nz	155	9	(	(	-LRB-
cord-194157-ak2gc3nz	155	10	r	r	NNP
cord-194157-ak2gc3nz	155	11	n	n	NN
cord-194157-ak2gc3nz	155	12	,	,	,
cord-194157-ak2gc3nz	155	13	η	η	NN
cord-194157-ak2gc3nz	155	14	n	n	NN
cord-194157-ak2gc3nz	155	15	)	)	-RRB-
cord-194157-ak2gc3nz	155	16	-locally	-locally	HYPH
cord-194157-ak2gc3nz	155	17	tree	tree	NN
cord-194157-ak2gc3nz	155	18	-	-	HYPH
cord-194157-ak2gc3nz	155	19	like	like	JJ
cord-194157-ak2gc3nz	155	20	with	with	IN
cord-194157-ak2gc3nz	155	21	r	r	NN
cord-194157-ak2gc3nz	155	22	n	n	NN
cord-194157-ak2gc3nz	156	1	→	→	IN
cord-194157-ak2gc3nz	156	2	∞	∞	NNP
cord-194157-ak2gc3nz	156	3	and	and	CC
cord-194157-ak2gc3nz	156	4	η	η	NN
cord-194157-ak2gc3nz	156	5	n	n	NN
cord-194157-ak2gc3nz	156	6	→	→	SYM
cord-194157-ak2gc3nz	156	7	0	0	CD
cord-194157-ak2gc3nz	156	8	.	.	.
cord-194157-ak2gc3nz	157	1	For	for	IN
cord-194157-ak2gc3nz	157	2	each	each	DT
cord-194157-ak2gc3nz	157	3	n	n	NN
cord-194157-ak2gc3nz	157	4	,	,	,
cord-194157-ak2gc3nz	157	5	consider	consider	VB
cord-194157-ak2gc3nz	157	6	the	the	DT
cord-194157-ak2gc3nz	157	7	SIR	SIR	NNP
cord-194157-ak2gc3nz	157	8	model	model	NN
cord-194157-ak2gc3nz	157	9	on	on	IN
cord-194157-ak2gc3nz	157	10	G	G	NNP
cord-194157-ak2gc3nz	157	11	n	n	NN
cord-194157-ak2gc3nz	157	12	with	with	IN
cord-194157-ak2gc3nz	157	13	parameters	parameter	NNS
cord-194157-ak2gc3nz	157	14	λ	λ	NN
cord-194157-ak2gc3nz	157	15	and	and	CC
cord-194157-ak2gc3nz	157	16	µ	µ	NN
cord-194157-ak2gc3nz	157	17	,	,	,
cord-194157-ak2gc3nz	157	18	and	and	CC
cord-194157-ak2gc3nz	157	19	let	let	VB
cord-194157-ak2gc3nz	157	20	E	e	NN
cord-194157-ak2gc3nz	157	21	∞	∞	NNP
cord-194157-ak2gc3nz	157	22	denote	denote	VB
cord-194157-ak2gc3nz	157	23	the	the	DT
cord-194157-ak2gc3nz	157	24	event	event	NN
cord-194157-ak2gc3nz	157	25	that	that	WDT
cord-194157-ak2gc3nz	157	26	U	U	NNP
cord-194157-ak2gc3nz	157	27	(	(	-LRB-
cord-194157-ak2gc3nz	157	28	∞	∞	NNP
cord-194157-ak2gc3nz	157	29	)	)	-RRB-
cord-194157-ak2gc3nz	157	30	contains	contain	VBZ
cord-194157-ak2gc3nz	157	31	a	a	DT
cord-194157-ak2gc3nz	157	32	vertex	vertex	NN
cord-194157-ak2gc3nz	157	33	of	of	IN
cord-194157-ak2gc3nz	157	34	distance	distance	NN
cord-194157-ak2gc3nz	157	35	greater	great	JJR
cord-194157-ak2gc3nz	157	36	than	than	IN
cord-194157-ak2gc3nz	157	37	r	r	NN
cord-194157-ak2gc3nz	157	38	from	from	IN
cord-194157-ak2gc3nz	157	39	U	U	NNP
cord-194157-ak2gc3nz	157	40	(	(	-LRB-
cord-194157-ak2gc3nz	157	41	0	0	NFP
cord-194157-ak2gc3nz	157	42	)	)	-RRB-
cord-194157-ak2gc3nz	157	43	.	.	.
cord-194157-ak2gc3nz	158	1	Proof	proof	NN
cord-194157-ak2gc3nz	158	2	.	.	.
cord-194157-ak2gc3nz	159	1	Restrict	restrict	VB
cord-194157-ak2gc3nz	159	2	to	to	IN
cord-194157-ak2gc3nz	159	3	the	the	DT
cord-194157-ak2gc3nz	159	4	event	event	NN
cord-194157-ak2gc3nz	159	5	E	e	NN
cord-194157-ak2gc3nz	159	6	0	0	NN
cord-194157-ak2gc3nz	159	7	,	,	,
cord-194157-ak2gc3nz	159	8	and	and	CC
cord-194157-ak2gc3nz	159	9	put	put	VBN
cord-194157-ak2gc3nz	159	10	{	{	-LRB-
cord-194157-ak2gc3nz	159	11	v	v	NN
cord-194157-ak2gc3nz	159	12	}	}	-RRB-
cord-194157-ak2gc3nz	159	13	=	=	SYM
cord-194157-ak2gc3nz	159	14	U	u	NN
cord-194157-ak2gc3nz	159	15	(	(	-LRB-
cord-194157-ak2gc3nz	159	16	0	0	NFP
cord-194157-ak2gc3nz	159	17	)	)	-RRB-
cord-194157-ak2gc3nz	159	18	.	.	.
cord-194157-ak2gc3nz	160	1	Deleting	delete	VBG
cord-194157-ak2gc3nz	160	2	v	v	LS
cord-194157-ak2gc3nz	160	3	from	from	IN
cord-194157-ak2gc3nz	160	4	B(r	B(r	NNP
cord-194157-ak2gc3nz	160	5	n	n	NNP
cord-194157-ak2gc3nz	160	6	)	)	-RRB-
cord-194157-ak2gc3nz	160	7	produces	produce	VBZ
cord-194157-ak2gc3nz	160	8	d	d	XX
cord-194157-ak2gc3nz	160	9	connected	connect	VBN
cord-194157-ak2gc3nz	160	10	components	component	NNS
cord-194157-ak2gc3nz	160	11	,	,	,
cord-194157-ak2gc3nz	160	12	each	each	DT
cord-194157-ak2gc3nz	160	13	of	of	IN
cord-194157-ak2gc3nz	160	14	which	which	WDT
cord-194157-ak2gc3nz	160	15	can	can	MD
cord-194157-ak2gc3nz	160	16	be	be	VB
cord-194157-ak2gc3nz	160	17	viewed	view	VBN
cord-194157-ak2gc3nz	160	18	as	as	IN
cord-194157-ak2gc3nz	160	19	a	a	DT
cord-194157-ak2gc3nz	160	20	subgraph	subgraph	NN
cord-194157-ak2gc3nz	160	21	of	of	IN
cord-194157-ak2gc3nz	160	22	the	the	DT
cord-194157-ak2gc3nz	160	23	infinite	infinite	JJ
cord-194157-ak2gc3nz	160	24	(	(	-LRB-
cord-194157-ak2gc3nz	160	25	d	d	NNP
cord-194157-ak2gc3nz	160	26	−	−	NNP
cord-194157-ak2gc3nz	160	27	1)-ary	1)-ary	CD
cord-194157-ak2gc3nz	160	28	tree	tree	NN
cord-194157-ak2gc3nz	160	29	T	T	NNP
cord-194157-ak2gc3nz	160	30	that	that	WDT
cord-194157-ak2gc3nz	160	31	is	be	VBZ
cord-194157-ak2gc3nz	160	32	rooted	root	VBN
cord-194157-ak2gc3nz	160	33	by	by	IN
cord-194157-ak2gc3nz	160	34	the	the	DT
cord-194157-ak2gc3nz	160	35	corresponding	correspond	VBG
cord-194157-ak2gc3nz	160	36	neighbor	neighbor	NN
cord-194157-ak2gc3nz	160	37	w	w	NNP
cord-194157-ak2gc3nz	160	38	of	of	IN
cord-194157-ak2gc3nz	160	39	v.	v.	NNP
cord-194157-ak2gc3nz	161	1	The	the	DT
cord-194157-ak2gc3nz	161	2	SIR	SIR	NNP
cord-194157-ak2gc3nz	161	3	evolution	evolution	NN
cord-194157-ak2gc3nz	161	4	on	on	IN
cord-194157-ak2gc3nz	161	5	T	T	NNP
cord-194157-ak2gc3nz	161	6	determines	determine	VBZ
cord-194157-ak2gc3nz	161	7	a	a	DT
cord-194157-ak2gc3nz	161	8	Galton	Galton	NNP
cord-194157-ak2gc3nz	161	9	-	-	HYPH
cord-194157-ak2gc3nz	161	10	Watson	Watson	NNP
cord-194157-ak2gc3nz	161	11	process	process	NN
cord-194157-ak2gc3nz	161	12	that	that	WDT
cord-194157-ak2gc3nz	161	13	gives	give	VBZ
cord-194157-ak2gc3nz	161	14	the	the	DT
cord-194157-ak2gc3nz	161	15	eventual	eventual	JJ
cord-194157-ak2gc3nz	161	16	number	number	NN
cord-194157-ak2gc3nz	161	17	Z	z	NN
cord-194157-ak2gc3nz	161	18	m	m	NNP
cord-194157-ak2gc3nz	161	19	of	of	IN
cord-194157-ak2gc3nz	161	20	unsusceptible	unsusceptible	JJ
cord-194157-ak2gc3nz	161	21	vertices	vertex	NNS
cord-194157-ak2gc3nz	161	22	at	at	IN
cord-194157-ak2gc3nz	161	23	distance	distance	NN
cord-194157-ak2gc3nz	161	24	m	m	NNP
cord-194157-ak2gc3nz	161	25	≥	≥	CD
cord-194157-ak2gc3nz	161	26	1	1	CD
cord-194157-ak2gc3nz	161	27	from	from	IN
cord-194157-ak2gc3nz	161	28	w	w	NN
cord-194157-ak2gc3nz	161	29	:	:	:
cord-194157-ak2gc3nz	161	30	where	where	WRB
cord-194157-ak2gc3nz	161	31	X	X	NNP
cord-194157-ak2gc3nz	161	32	m	m	NNP
cord-194157-ak2gc3nz	161	33	,	,	,
cord-194157-ak2gc3nz	161	34	k	k	NNP
cord-194157-ak2gc3nz	161	35	denotes	denote	VBZ
cord-194157-ak2gc3nz	161	36	the	the	DT
cord-194157-ak2gc3nz	161	37	number	number	NN
cord-194157-ak2gc3nz	161	38	of	of	IN
cord-194157-ak2gc3nz	161	39	vertices	vertex	NNS
cord-194157-ak2gc3nz	161	40	infected	infect	VBN
cord-194157-ak2gc3nz	161	41	by	by	IN
cord-194157-ak2gc3nz	161	42	the	the	DT
cord-194157-ak2gc3nz	161	43	kth	kth	NNP
cord-194157-ak2gc3nz	161	44	infected	infected	JJ
cord-194157-ak2gc3nz	161	45	vertex	vertex	NN
cord-194157-ak2gc3nz	161	46	in	in	IN
cord-194157-ak2gc3nz	161	47	T	t	NN
cord-194157-ak2gc3nz	161	48	that	that	WDT
cord-194157-ak2gc3nz	161	49	has	have	VBZ
cord-194157-ak2gc3nz	161	50	distance	distance	NN
cord-194157-ak2gc3nz	161	51	m	m	NNP
cord-194157-ak2gc3nz	161	52	from	from	IN
cord-194157-ak2gc3nz	161	53	w.	w.	NNP
cord-194157-ak2gc3nz	162	1	The	the	DT
cord-194157-ak2gc3nz	162	2	random	random	JJ
cord-194157-ak2gc3nz	162	3	variables	variable	NNS
cord-194157-ak2gc3nz	162	4	{	{	-LRB-
cord-194157-ak2gc3nz	162	5	X	x	NN
cord-194157-ak2gc3nz	162	6	n	n	NN
cord-194157-ak2gc3nz	162	7	,	,	,
cord-194157-ak2gc3nz	162	8	k	k	NNP
cord-194157-ak2gc3nz	162	9	}	}	-RRB-
cord-194157-ak2gc3nz	162	10	n	n	NNP
cord-194157-ak2gc3nz	162	11	,	,	,
cord-194157-ak2gc3nz	162	12	k≥1	k≥1	NNPS
cord-194157-ak2gc3nz	162	13	are	be	VBP
cord-194157-ak2gc3nz	162	14	independent	independent	JJ
cord-194157-ak2gc3nz	162	15	with	with	IN
cord-194157-ak2gc3nz	162	16	distribution	distribution	NN
cord-194157-ak2gc3nz	162	17	matching	match	VBG
cord-194157-ak2gc3nz	162	18	a	a	DT
cord-194157-ak2gc3nz	162	19	random	random	JJ
cord-194157-ak2gc3nz	162	20	variable	variable	NN
cord-194157-ak2gc3nz	162	21	that	that	WDT
cord-194157-ak2gc3nz	162	22	we	-PRON-	PRP
cord-194157-ak2gc3nz	162	23	denote	denote	VBP
cord-194157-ak2gc3nz	162	24	X.	X.	.
cord-194157-ak2gc3nz	163	1	We	-PRON-	PRP
cord-194157-ak2gc3nz	163	2	can	can	MD
cord-194157-ak2gc3nz	163	3	describe	describe	VB
cord-194157-ak2gc3nz	163	4	the	the	DT
cord-194157-ak2gc3nz	163	5	distribution	distribution	NN
cord-194157-ak2gc3nz	163	6	of	of	IN
cord-194157-ak2gc3nz	163	7	X	x	NN
cord-194157-ak2gc3nz	163	8	as	as	IN
cord-194157-ak2gc3nz	163	9	follows	follow	VBZ
cord-194157-ak2gc3nz	163	10	.	.	.
cord-194157-ak2gc3nz	164	1	Draw	draw	VB
cord-194157-ak2gc3nz	164	2	random	random	JJ
cord-194157-ak2gc3nz	164	3	variables	variable	NNS
cord-194157-ak2gc3nz	165	1	T	T	NNP
cord-194157-ak2gc3nz	165	2	∼	∼	NNP
cord-194157-ak2gc3nz	165	3	Exp(µ	Exp(µ	NNP
cord-194157-ak2gc3nz	165	4	)	)	-RRB-
cord-194157-ak2gc3nz	165	5	and	and	CC
cord-194157-ak2gc3nz	165	6	C	C	NNP
cord-194157-ak2gc3nz	165	7	1	1	CD
cord-194157-ak2gc3nz	165	8	,	,	,
cord-194157-ak2gc3nz	165	9	.	.	.
cord-194157-ak2gc3nz	165	10	.	.	.
cord-194157-ak2gc3nz	165	11	.	.	.
cord-194157-ak2gc3nz	166	1	,	,	,
cord-194157-ak2gc3nz	166	2	C	C	NNP
cord-194157-ak2gc3nz	166	3	d−1	d−1	NNP
cord-194157-ak2gc3nz	166	4	∼	∼	NNP
cord-194157-ak2gc3nz	166	5	Exp(λ	Exp(λ	NNPS
cord-194157-ak2gc3nz	166	6	)	)	-RRB-
cord-194157-ak2gc3nz	166	7	.	.	.
cord-194157-ak2gc3nz	167	1	If	if	IN
cord-194157-ak2gc3nz	167	2	N	n	CD
cord-194157-ak2gc3nz	167	3	denotes	denote	VBZ
cord-194157-ak2gc3nz	167	4	the	the	DT
cord-194157-ak2gc3nz	167	5	number	number	NN
cord-194157-ak2gc3nz	167	6	of	of	IN
cord-194157-ak2gc3nz	167	7	k	k	NN
cord-194157-ak2gc3nz	167	8	∈	∈	NN
cord-194157-ak2gc3nz	167	9	[	[	-LRB-
cord-194157-ak2gc3nz	167	10	d	d	NN
cord-194157-ak2gc3nz	167	11	−	−	NNP
cord-194157-ak2gc3nz	167	12	1	1	CD
cord-194157-ak2gc3nz	167	13	]	]	-RRB-
cord-194157-ak2gc3nz	167	14	for	for	IN
cord-194157-ak2gc3nz	167	15	which	which	WDT
cord-194157-ak2gc3nz	168	1	C	C	NNP
cord-194157-ak2gc3nz	168	2	k	k	XX
cord-194157-ak2gc3nz	168	3	<	<	XX
cord-194157-ak2gc3nz	168	4	T	T	NNP
cord-194157-ak2gc3nz	168	5	,	,	,
cord-194157-ak2gc3nz	168	6	then	then	RB
cord-194157-ak2gc3nz	168	7	N	N	NNP
cord-194157-ak2gc3nz	168	8	is	be	VBZ
cord-194157-ak2gc3nz	168	9	distributed	distribute	VBN
cord-194157-ak2gc3nz	168	10	like	like	IN
cord-194157-ak2gc3nz	168	11	X.	X.	NNP
cord-194157-ak2gc3nz	168	12	Conditioned	condition	VBN
cord-194157-ak2gc3nz	168	13	on	on	IN
cord-194157-ak2gc3nz	168	14	T	T	NNP
cord-194157-ak2gc3nz	168	15	,	,	,
cord-194157-ak2gc3nz	168	16	this	this	DT
cord-194157-ak2gc3nz	168	17	number	number	NN
cord-194157-ak2gc3nz	168	18	is	be	VBZ
cord-194157-ak2gc3nz	168	19	a	a	DT
cord-194157-ak2gc3nz	168	20	binomial	binomial	NN
cord-194157-ak2gc3nz	168	21	with	with	IN
cord-194157-ak2gc3nz	168	22	parameters	parameter	NNS
cord-194157-ak2gc3nz	168	23	d	d	NNP
cord-194157-ak2gc3nz	168	24	−	−	NNP
cord-194157-ak2gc3nz	168	25	1	1	CD
cord-194157-ak2gc3nz	168	26	and	and	CC
cord-194157-ak2gc3nz	168	27	1	1	CD
cord-194157-ak2gc3nz	168	28	−	−	NN
cord-194157-ak2gc3nz	168	29	e	e	NN
cord-194157-ak2gc3nz	168	30	−λT	−λT	NNP
cord-194157-ak2gc3nz	168	31	.	.	.
cord-194157-ak2gc3nz	169	1	Hence	hence	RB
cord-194157-ak2gc3nz	169	2	,	,	,
cord-194157-ak2gc3nz	169	3	Since	since	IN
cord-194157-ak2gc3nz	169	4	in	in	IN
cord-194157-ak2gc3nz	169	5	addition	addition	NN
cord-194157-ak2gc3nz	169	6	,	,	,
cord-194157-ak2gc3nz	169	7	it	-PRON-	PRP
cord-194157-ak2gc3nz	169	8	holds	hold	VBZ
cord-194157-ak2gc3nz	169	9	that	that	IN
cord-194157-ak2gc3nz	169	10	P{X	p{x	NN
cord-194157-ak2gc3nz	169	11	>	>	XX
cord-194157-ak2gc3nz	169	12	1	1	CD
cord-194157-ak2gc3nz	169	13	}	}	-RRB-
cord-194157-ak2gc3nz	169	14	>	>	XX
cord-194157-ak2gc3nz	169	15	0	0	CD
cord-194157-ak2gc3nz	169	16	,	,	,
cord-194157-ak2gc3nz	169	17	Theorem	theorem	NN
cord-194157-ak2gc3nz	169	18	1.7	1.7	CD
cord-194157-ak2gc3nz	169	19	in	in	IN
cord-194157-ak2gc3nz	169	20	[	[	-LRB-
cord-194157-ak2gc3nz	169	21	1	1	CD
cord-194157-ak2gc3nz	169	22	]	]	-RRB-
cord-194157-ak2gc3nz	169	23	gives	give	VBZ
cord-194157-ak2gc3nz	169	24	that	that	DT
cord-194157-ak2gc3nz	169	25	∞	∞	NNP
cord-194157-ak2gc3nz	169	26	m=1	m=1	NN
cord-194157-ak2gc3nz	169	27	Z	Z	NNP
cord-194157-ak2gc3nz	169	28	m	m	NNP
cord-194157-ak2gc3nz	169	29	is	be	VBZ
cord-194157-ak2gc3nz	169	30	finite	finite	JJ
cord-194157-ak2gc3nz	169	31	almost	almost	RB
cord-194157-ak2gc3nz	169	32	surely	surely	RB
cord-194157-ak2gc3nz	169	33	.	.	.
cord-194157-ak2gc3nz	170	1	Put	put	VB
cord-194157-ak2gc3nz	170	2	M	M	NNP
cord-194157-ak2gc3nz	171	1	:	:	:
cord-194157-ak2gc3nz	171	2	=	=	NFP
cord-194157-ak2gc3nz	171	3	sup{m	sup{m	NNP
cord-194157-ak2gc3nz	171	4	:	:	:
cord-194157-ak2gc3nz	172	1	Z	z	NN
cord-194157-ak2gc3nz	172	2	m	m	NN
cord-194157-ak2gc3nz	172	3	>	>	XX
cord-194157-ak2gc3nz	172	4	0	0	CD
cord-194157-ak2gc3nz	172	5	}	}	-RRB-
cord-194157-ak2gc3nz	172	6	.	.	.
cord-194157-ak2gc3nz	173	1	Then	then	RB
cord-194157-ak2gc3nz	173	2	M	M	NNP
cord-194157-ak2gc3nz	173	3	<	<	XX
cord-194157-ak2gc3nz	174	1	∞	∞	NNP
cord-194157-ak2gc3nz	174	2	almost	almost	RB
cord-194157-ak2gc3nz	174	3	surely	surely	RB
cord-194157-ak2gc3nz	174	4	.	.	.
cord-194157-ak2gc3nz	175	1	In	in	IN
cord-194157-ak2gc3nz	175	2	particular	particular	JJ
cord-194157-ak2gc3nz	175	3	,	,	,
cord-194157-ak2gc3nz	175	4	a	a	DT
cord-194157-ak2gc3nz	175	5	union	union	NN
cord-194157-ak2gc3nz	175	6	bound	bind	VBN
cord-194157-ak2gc3nz	175	7	over	over	IN
cord-194157-ak2gc3nz	175	8	the	the	DT
cord-194157-ak2gc3nz	175	9	d	d	XX
cord-194157-ak2gc3nz	175	10	different	different	JJ
cord-194157-ak2gc3nz	175	11	neighbors	neighbor	NNS
cord-194157-ak2gc3nz	175	12	of	of	IN
cord-194157-ak2gc3nz	175	13	v	v	NN
cord-194157-ak2gc3nz	175	14	gives	give	VBZ
cord-194157-ak2gc3nz	175	15	where	where	WRB
cord-194157-ak2gc3nz	175	16	the	the	DT
cord-194157-ak2gc3nz	175	17	last	last	JJ
cord-194157-ak2gc3nz	175	18	step	step	NN
cord-194157-ak2gc3nz	175	19	uses	use	VBZ
cord-194157-ak2gc3nz	175	20	the	the	DT
cord-194157-ak2gc3nz	175	21	fact	fact	NN
cord-194157-ak2gc3nz	175	22	that	that	IN
cord-194157-ak2gc3nz	175	23	the	the	DT
cord-194157-ak2gc3nz	175	24	survivor	survivor	NN
cord-194157-ak2gc3nz	175	25	function	function	NN
cord-194157-ak2gc3nz	175	26	of	of	IN
cord-194157-ak2gc3nz	175	27	M	M	NNP
cord-194157-ak2gc3nz	175	28	vanishes	vanish	VBZ
cord-194157-ak2gc3nz	175	29	at	at	IN
cord-194157-ak2gc3nz	175	30	infinity	infinity	NN
cord-194157-ak2gc3nz	175	31	.	.	.
cord-194157-ak2gc3nz	176	1	Restrict	restrict	VB
cord-194157-ak2gc3nz	176	2	to	to	IN
cord-194157-ak2gc3nz	176	3	the	the	DT
cord-194157-ak2gc3nz	176	4	event	event	NN
cord-194157-ak2gc3nz	176	5	E	e	NN
cord-194157-ak2gc3nz	176	6	0	0	NN
cord-194157-ak2gc3nz	176	7	,	,	,
cord-194157-ak2gc3nz	176	8	and	and	CC
cord-194157-ak2gc3nz	176	9	put	put	VBN
cord-194157-ak2gc3nz	176	10	{	{	-LRB-
cord-194157-ak2gc3nz	176	11	v	v	NN
cord-194157-ak2gc3nz	176	12	}	}	-RRB-
cord-194157-ak2gc3nz	176	13	=	=	SYM
cord-194157-ak2gc3nz	176	14	U	u	NN
cord-194157-ak2gc3nz	176	15	(	(	-LRB-
cord-194157-ak2gc3nz	176	16	0	0	NFP
cord-194157-ak2gc3nz	176	17	)	)	-RRB-
cord-194157-ak2gc3nz	176	18	.	.	.
cord-194157-ak2gc3nz	177	1	As	as	IN
cord-194157-ak2gc3nz	177	2	before	before	RB
cord-194157-ak2gc3nz	177	3	,	,	,
cord-194157-ak2gc3nz	177	4	we	-PRON-	PRP
cord-194157-ak2gc3nz	177	5	identify	identify	VBP
cord-194157-ak2gc3nz	177	6	a	a	DT
cord-194157-ak2gc3nz	177	7	Galton	Galton	NNP
cord-194157-ak2gc3nz	177	8	-	-	HYPH
cord-194157-ak2gc3nz	177	9	Watson	Watson	NNP
cord-194157-ak2gc3nz	177	10	process	process	NN
cord-194157-ak2gc3nz	177	11	to	to	TO
cord-194157-ak2gc3nz	177	12	analyze	analyze	VB
cord-194157-ak2gc3nz	177	13	,	,	,
cord-194157-ak2gc3nz	177	14	but	but	CC
cord-194157-ak2gc3nz	177	15	this	this	DT
cord-194157-ak2gc3nz	177	16	one	one	NN
cord-194157-ak2gc3nz	177	17	is	be	VBZ
cord-194157-ak2gc3nz	177	18	slightly	slightly	RB
cord-194157-ak2gc3nz	177	19	different	different	JJ
cord-194157-ak2gc3nz	177	20	:	:	:
cord-194157-ak2gc3nz	177	21	Delete	delete	VB
cord-194157-ak2gc3nz	177	22	one	one	CD
cord-194157-ak2gc3nz	177	23	of	of	IN
cord-194157-ak2gc3nz	177	24	the	the	DT
cord-194157-ak2gc3nz	177	25	neighbors	neighbor	NNS
cord-194157-ak2gc3nz	177	26	of	of	IN
cord-194157-ak2gc3nz	177	27	v	v	NN
cord-194157-ak2gc3nz	177	28	from	from	IN
cord-194157-ak2gc3nz	177	29	B(r	B(r	NNP
cord-194157-ak2gc3nz	177	30	n	n	NNP
cord-194157-ak2gc3nz	177	31	)	)	-RRB-
cord-194157-ak2gc3nz	177	32	and	and	CC
cord-194157-ak2gc3nz	177	33	identify	identify	VB
cord-194157-ak2gc3nz	177	34	the	the	DT
cord-194157-ak2gc3nz	177	35	connected	connected	JJ
cord-194157-ak2gc3nz	177	36	component	component	NN
cord-194157-ak2gc3nz	177	37	C	c	NN
cord-194157-ak2gc3nz	177	38	containing	contain	VBG
cord-194157-ak2gc3nz	177	39	v	v	NN
cord-194157-ak2gc3nz	177	40	with	with	IN
cord-194157-ak2gc3nz	177	41	a	a	DT
cord-194157-ak2gc3nz	177	42	subgraph	subgraph	NN
cord-194157-ak2gc3nz	177	43	of	of	IN
cord-194157-ak2gc3nz	177	44	a	a	DT
cord-194157-ak2gc3nz	177	45	(	(	-LRB-
cord-194157-ak2gc3nz	177	46	d	d	NNP
cord-194157-ak2gc3nz	177	47	−	−	NN
cord-194157-ak2gc3nz	177	48	1)-ary	1)-ary	CD
cord-194157-ak2gc3nz	177	49	tree	tree	NN
cord-194157-ak2gc3nz	177	50	T	T	NNP
cord-194157-ak2gc3nz	177	51	with	with	IN
cord-194157-ak2gc3nz	177	52	root	root	NN
cord-194157-ak2gc3nz	177	53	v.	v.	IN
cord-194157-ak2gc3nz	177	54	The	the	DT
cord-194157-ak2gc3nz	177	55	SIR	SIR	NNP
cord-194157-ak2gc3nz	177	56	evolution	evolution	NN
cord-194157-ak2gc3nz	177	57	on	on	IN
cord-194157-ak2gc3nz	177	58	T	T	NNP
cord-194157-ak2gc3nz	177	59	determines	determine	VBZ
cord-194157-ak2gc3nz	177	60	a	a	DT
cord-194157-ak2gc3nz	177	61	Galton	Galton	NNP
cord-194157-ak2gc3nz	177	62	-	-	HYPH
cord-194157-ak2gc3nz	177	63	Watson	Watson	NNP
cord-194157-ak2gc3nz	177	64	process	process	NN
cord-194157-ak2gc3nz	177	65	that	that	WDT
cord-194157-ak2gc3nz	177	66	gives	give	VBZ
cord-194157-ak2gc3nz	177	67	the	the	DT
cord-194157-ak2gc3nz	177	68	eventual	eventual	JJ
cord-194157-ak2gc3nz	177	69	number	number	NN
cord-194157-ak2gc3nz	177	70	Z	z	NN
cord-194157-ak2gc3nz	177	71	m	m	NNP
cord-194157-ak2gc3nz	177	72	of	of	IN
cord-194157-ak2gc3nz	177	73	unsusceptible	unsusceptible	JJ
cord-194157-ak2gc3nz	177	74	vertices	vertex	NNS
cord-194157-ak2gc3nz	177	75	at	at	IN
cord-194157-ak2gc3nz	177	76	distance	distance	NN
cord-194157-ak2gc3nz	177	77	m	m	NNP
cord-194157-ak2gc3nz	177	78	≥	≥	CD
cord-194157-ak2gc3nz	177	79	1	1	CD
cord-194157-ak2gc3nz	177	80	from	from	IN
cord-194157-ak2gc3nz	177	81	v	v	NN
cord-194157-ak2gc3nz	177	82	:	:	:
cord-194157-ak2gc3nz	177	83	where	where	WRB
cord-194157-ak2gc3nz	177	84	X	X	NNP
cord-194157-ak2gc3nz	177	85	m	m	NNP
cord-194157-ak2gc3nz	177	86	,	,	,
cord-194157-ak2gc3nz	177	87	k	k	NNP
cord-194157-ak2gc3nz	177	88	denotes	denote	VBZ
cord-194157-ak2gc3nz	177	89	the	the	DT
cord-194157-ak2gc3nz	177	90	number	number	NN
cord-194157-ak2gc3nz	177	91	of	of	IN
cord-194157-ak2gc3nz	177	92	vertices	vertex	NNS
cord-194157-ak2gc3nz	177	93	infected	infect	VBN
cord-194157-ak2gc3nz	177	94	by	by	IN
cord-194157-ak2gc3nz	177	95	the	the	DT
cord-194157-ak2gc3nz	177	96	kth	kth	NNP
cord-194157-ak2gc3nz	177	97	infected	infected	JJ
cord-194157-ak2gc3nz	177	98	vertex	vertex	NN
cord-194157-ak2gc3nz	177	99	in	in	IN
cord-194157-ak2gc3nz	177	100	T	t	NN
cord-194157-ak2gc3nz	177	101	that	that	WDT
cord-194157-ak2gc3nz	177	102	has	have	VBZ
cord-194157-ak2gc3nz	177	103	distance	distance	NN
cord-194157-ak2gc3nz	177	104	m	m	NNP
cord-194157-ak2gc3nz	177	105	from	from	IN
cord-194157-ak2gc3nz	177	106	v.	v.	IN
cord-194157-ak2gc3nz	177	107	The	the	DT
cord-194157-ak2gc3nz	177	108	random	random	JJ
cord-194157-ak2gc3nz	177	109	variables	variable	NNS
cord-194157-ak2gc3nz	177	110	{	{	-LRB-
cord-194157-ak2gc3nz	177	111	X	X	NNP
cord-194157-ak2gc3nz	177	112	m	m	NNP
cord-194157-ak2gc3nz	177	113	,	,	,
cord-194157-ak2gc3nz	177	114	k	k	NNP
cord-194157-ak2gc3nz	177	115	}	}	-RRB-
cord-194157-ak2gc3nz	177	116	m	m	NNP
cord-194157-ak2gc3nz	177	117	,	,	,
cord-194157-ak2gc3nz	177	118	k≥1	k≥1	NNP
cord-194157-ak2gc3nz	178	1	are	be	VBP
cord-194157-ak2gc3nz	178	2	independent	independent	JJ
cord-194157-ak2gc3nz	178	3	with	with	IN
cord-194157-ak2gc3nz	178	4	distribution	distribution	NN
cord-194157-ak2gc3nz	178	5	matching	match	VBG
cord-194157-ak2gc3nz	178	6	a	a	DT
cord-194157-ak2gc3nz	178	7	random	random	JJ
cord-194157-ak2gc3nz	178	8	variable	variable	NN
cord-194157-ak2gc3nz	178	9	that	that	WDT
cord-194157-ak2gc3nz	178	10	we	-PRON-	PRP
cord-194157-ak2gc3nz	178	11	denote	denote	VBP
cord-194157-ak2gc3nz	178	12	X.	X.	.
cord-194157-ak2gc3nz	179	1	We	-PRON-	PRP
cord-194157-ak2gc3nz	179	2	see	see	VBP
cord-194157-ak2gc3nz	179	3	that	that	IN
cord-194157-ak2gc3nz	179	4	P(E	P(E	NNP
cord-194157-ak2gc3nz	179	5	c	c	NN
cord-194157-ak2gc3nz	180	1	∞	∞	NNP
cord-194157-ak2gc3nz	180	2	|E	|e	CD
cord-194157-ak2gc3nz	180	3	0	0	NFP
cord-194157-ak2gc3nz	180	4	)	)	-RRB-
cord-194157-ak2gc3nz	180	5	is	be	VBZ
cord-194157-ak2gc3nz	180	6	at	at	IN
cord-194157-ak2gc3nz	180	7	most	most	JJS
cord-194157-ak2gc3nz	180	8	the	the	DT
cord-194157-ak2gc3nz	180	9	extinction	extinction	NN
cord-194157-ak2gc3nz	180	10	probability	probability	NN
cord-194157-ak2gc3nz	180	11	q	q	NN
cord-194157-ak2gc3nz	180	12	of	of	IN
cord-194157-ak2gc3nz	180	13	this	this	DT
cord-194157-ak2gc3nz	180	14	process	process	NN
cord-194157-ak2gc3nz	180	15	.	.	.
cord-194157-ak2gc3nz	181	1	By	by	IN
cord-194157-ak2gc3nz	181	2	Theorem	Theorem	NNP
cord-194157-ak2gc3nz	181	3	1	1	CD
cord-194157-ak2gc3nz	181	4	.	.	.
cord-194157-ak2gc3nz	181	5	 	 	_SP
cord-194157-ak2gc3nz	182	1	it	-PRON-	PRP
cord-194157-ak2gc3nz	182	2	follows	follow	VBZ
cord-194157-ak2gc3nz	182	3	that	that	IN
cord-194157-ak2gc3nz	182	4	q	q	NNP
cord-194157-ak2gc3nz	182	5	≤	≤	NN
cord-194157-ak2gc3nz	182	6	p	p	NN
cord-194157-ak2gc3nz	182	7	0	0	CD
cord-194157-ak2gc3nz	182	8	1−p	1−p	CD
cord-194157-ak2gc3nz	182	9	0	0	CD
cord-194157-ak2gc3nz	182	10	−p	−p	NNP
cord-194157-ak2gc3nz	182	11	1	1	CD
cord-194157-ak2gc3nz	182	12	.	.	.
cord-194157-ak2gc3nz	183	1	Before	before	IN
cord-194157-ak2gc3nz	183	2	estimating	estimate	VBG
cord-194157-ak2gc3nz	183	3	p	p	NN
cord-194157-ak2gc3nz	183	4	0	0	CD
cord-194157-ak2gc3nz	183	5	and	and	CC
cord-194157-ak2gc3nz	183	6	p	p	NN
cord-194157-ak2gc3nz	183	7	1	1	CD
cord-194157-ak2gc3nz	183	8	,	,	,
cord-194157-ak2gc3nz	183	9	it	-PRON-	PRP
cord-194157-ak2gc3nz	183	10	is	be	VBZ
cord-194157-ak2gc3nz	183	11	helpful	helpful	JJ
cord-194157-ak2gc3nz	183	12	to	to	TO
cord-194157-ak2gc3nz	183	13	introduce	introduce	VB
cord-194157-ak2gc3nz	183	14	some	some	DT
cord-194157-ak2gc3nz	183	15	notation	notation	NN
cord-194157-ak2gc3nz	183	16	.	.	.
cord-194157-ak2gc3nz	184	1	An	an	DT
cord-194157-ak2gc3nz	184	2	infected	infected	JJ
cord-194157-ak2gc3nz	184	3	parent	parent	NN
cord-194157-ak2gc3nz	184	4	with	with	IN
cord-194157-ak2gc3nz	184	5	d	d	NNP
cord-194157-ak2gc3nz	184	6	−	−	NNP
cord-194157-ak2gc3nz	184	7	1	1	CD
cord-194157-ak2gc3nz	184	8	children	child	NNS
cord-194157-ak2gc3nz	184	9	infects	infect	VBZ
cord-194157-ak2gc3nz	184	10	X	X	NNS
cord-194157-ak2gc3nz	184	11	of	of	IN
cord-194157-ak2gc3nz	184	12	these	these	DT
cord-194157-ak2gc3nz	184	13	children	child	NNS
cord-194157-ak2gc3nz	184	14	.	.	.
cord-194157-ak2gc3nz	185	1	The	the	DT
cord-194157-ak2gc3nz	185	2	parent	parent	NN
cord-194157-ak2gc3nz	185	3	recovers	recover	VBZ
cord-194157-ak2gc3nz	185	4	exponentially	exponentially	RB
cord-194157-ak2gc3nz	185	5	with	with	IN
cord-194157-ak2gc3nz	185	6	rate	rate	NN
cord-194157-ak2gc3nz	185	7	µ	µ	NN
cord-194157-ak2gc3nz	185	8	,	,	,
cord-194157-ak2gc3nz	185	9	and	and	CC
cord-194157-ak2gc3nz	185	10	we	-PRON-	PRP
cord-194157-ak2gc3nz	185	11	let	let	VBP
cord-194157-ak2gc3nz	185	12	R	r	NN
cord-194157-ak2gc3nz	185	13	denote	denote	VB
cord-194157-ak2gc3nz	185	14	the	the	DT
cord-194157-ak2gc3nz	185	15	recovery	recovery	NN
cord-194157-ak2gc3nz	185	16	time	time	NN
cord-194157-ak2gc3nz	185	17	.	.	.
cord-194157-ak2gc3nz	186	1	Simultaneously	simultaneously	RB
cord-194157-ak2gc3nz	186	2	,	,	,
cord-194157-ak2gc3nz	186	3	each	each	DT
cord-194157-ak2gc3nz	186	4	child	child	NN
cord-194157-ak2gc3nz	186	5	is	be	VBZ
cord-194157-ak2gc3nz	186	6	infected	infect	VBN
cord-194157-ak2gc3nz	186	7	exponentially	exponentially	RB
cord-194157-ak2gc3nz	186	8	with	with	IN
cord-194157-ak2gc3nz	186	9	rate	rate	NN
cord-194157-ak2gc3nz	186	10	λ	λ	NN
cord-194157-ak2gc3nz	186	11	,	,	,
cord-194157-ak2gc3nz	186	12	and	and	CC
cord-194157-ak2gc3nz	186	13	so	so	RB
cord-194157-ak2gc3nz	186	14	we	-PRON-	PRP
cord-194157-ak2gc3nz	186	15	denote	denote	VBP
cord-194157-ak2gc3nz	186	16	independent	independent	JJ
cord-194157-ak2gc3nz	186	17	random	random	JJ
cord-194157-ak2gc3nz	186	18	variables	variable	NNS
cord-194157-ak2gc3nz	187	1	I	-PRON-	PRP
cord-194157-ak2gc3nz	187	2	i	i	PRP
cord-194157-ak2gc3nz	187	3	∼	∼	VBP
cord-194157-ak2gc3nz	187	4	Exp(λ	Exp(λ	NNPS
cord-194157-ak2gc3nz	187	5	)	)	-RRB-
cord-194157-ak2gc3nz	187	6	such	such	JJ
cord-194157-ak2gc3nz	187	7	that	that	WDT
cord-194157-ak2gc3nz	187	8	gives	give	VBZ
cord-194157-ak2gc3nz	187	9	the	the	DT
cord-194157-ak2gc3nz	187	10	time	time	NN
cord-194157-ak2gc3nz	187	11	of	of	IN
cord-194157-ak2gc3nz	187	12	infection	infection	NN
cord-194157-ak2gc3nz	187	13	for	for	IN
cord-194157-ak2gc3nz	187	14	child	child	NN
cord-194157-ak2gc3nz	187	15	i.	i.	NN
cord-194157-ak2gc3nz	188	1	Then	then	RB
cord-194157-ak2gc3nz	188	2	Next	Next	NNP
cord-194157-ak2gc3nz	188	3	,	,	,
cord-194157-ak2gc3nz	188	4	the	the	DT
cord-194157-ak2gc3nz	188	5	order	order	NN
cord-194157-ak2gc3nz	188	6	statistic	statistic	NN
cord-194157-ak2gc3nz	188	7	I	-PRON-	PRP
cord-194157-ak2gc3nz	188	8	(	(	-LRB-
cord-194157-ak2gc3nz	188	9	2	2	CD
cord-194157-ak2gc3nz	188	10	)	)	-RRB-
cord-194157-ak2gc3nz	188	11	has	have	VBZ
cord-194157-ak2gc3nz	188	12	the	the	DT
cord-194157-ak2gc3nz	188	13	same	same	JJ
cord-194157-ak2gc3nz	188	14	distribution	distribution	NN
cord-194157-ak2gc3nz	188	15	as	as	IN
cord-194157-ak2gc3nz	188	16	1	1	CD
cord-194157-ak2gc3nz	188	17	This	this	DT
cord-194157-ak2gc3nz	188	18	identity	identity	NN
cord-194157-ak2gc3nz	188	19	combined	combine	VBN
cord-194157-ak2gc3nz	188	20	with	with	IN
cord-194157-ak2gc3nz	188	21	the	the	DT
cord-194157-ak2gc3nz	188	22	fact	fact	NN
cord-194157-ak2gc3nz	188	23	that	that	IN
cord-194157-ak2gc3nz	188	24	x	x	NN
cord-194157-ak2gc3nz	188	25	→	→	WDT
cord-194157-ak2gc3nz	188	26	µx	µx	NN
cord-194157-ak2gc3nz	188	27	µ+λx	µ+λx	NNP
cord-194157-ak2gc3nz	188	28	is	be	VBZ
cord-194157-ak2gc3nz	188	29	an	an	DT
cord-194157-ak2gc3nz	188	30	increasing	increase	VBG
cord-194157-ak2gc3nz	188	31	function	function	NN
cord-194157-ak2gc3nz	188	32	gives	give	VBZ
cord-194157-ak2gc3nz	188	33	3	3	CD
cord-194157-ak2gc3nz	188	34	Proof	Proof	NNP
cord-194157-ak2gc3nz	188	35	of	of	IN
cord-194157-ak2gc3nz	188	36	Theorem	Theorem	NNP
cord-194157-ak2gc3nz	188	37	7	7	CD
cord-194157-ak2gc3nz	188	38	The	the	DT
cord-194157-ak2gc3nz	188	39	last	last	JJ
cord-194157-ak2gc3nz	188	40	statement	statement	NN
cord-194157-ak2gc3nz	188	41	follows	follow	VBZ
cord-194157-ak2gc3nz	188	42	from	from	IN
cord-194157-ak2gc3nz	188	43	Lemma	Lemma	NNP
cord-194157-ak2gc3nz	188	44	8	8	CD
cord-194157-ak2gc3nz	188	45	.	.	.
cord-194157-ak2gc3nz	189	1	To	to	TO
cord-194157-ak2gc3nz	189	2	prove	prove	VB
cord-194157-ak2gc3nz	189	3	the	the	DT
cord-194157-ak2gc3nz	189	4	remainder	remainder	NN
cord-194157-ak2gc3nz	189	5	of	of	IN
cord-194157-ak2gc3nz	189	6	the	the	DT
cord-194157-ak2gc3nz	189	7	result	result	NN
cord-194157-ak2gc3nz	189	8	,	,	,
cord-194157-ak2gc3nz	189	9	we	-PRON-	PRP
cord-194157-ak2gc3nz	189	10	will	will	MD
cord-194157-ak2gc3nz	189	11	assume	assume	VB
cord-194157-ak2gc3nz	189	12	that	that	IN
cord-194157-ak2gc3nz	189	13	(	(	-LRB-
cord-194157-ak2gc3nz	189	14	a	a	LS
cord-194157-ak2gc3nz	189	15	)	)	-RRB-
cord-194157-ak2gc3nz	189	16	does	do	VBZ
cord-194157-ak2gc3nz	189	17	not	not	RB
cord-194157-ak2gc3nz	189	18	hold	hold	VB
cord-194157-ak2gc3nz	189	19	and	and	CC
cord-194157-ak2gc3nz	189	20	prove	prove	VB
cord-194157-ak2gc3nz	189	21	that	that	DT
cord-194157-ak2gc3nz	189	22	(	(	-LRB-
cord-194157-ak2gc3nz	189	23	b	b	NN
cord-194157-ak2gc3nz	189	24	)	)	-RRB-
cord-194157-ak2gc3nz	189	25	holds	hold	VBZ
cord-194157-ak2gc3nz	189	26	.	.	.
cord-194157-ak2gc3nz	190	1	Since	since	IN
cord-194157-ak2gc3nz	190	2	(	(	-LRB-
cord-194157-ak2gc3nz	190	3	a	a	DT
cord-194157-ak2gc3nz	190	4	)	)	-RRB-
cord-194157-ak2gc3nz	190	5	does	do	VBZ
cord-194157-ak2gc3nz	190	6	not	not	RB
cord-194157-ak2gc3nz	190	7	hold	hold	VB
cord-194157-ak2gc3nz	190	8	,	,	,
cord-194157-ak2gc3nz	190	9	there	there	EX
cord-194157-ak2gc3nz	190	10	exists	exist	VBZ
cord-194157-ak2gc3nz	191	1	some	some	DT
cord-194157-ak2gc3nz	191	2	κ	κ	NN
cord-194157-ak2gc3nz	191	3	>	>	XX
cord-194157-ak2gc3nz	191	4	0	0	NFP
cord-194157-ak2gc3nz	191	5	such	such	JJ
cord-194157-ak2gc3nz	191	6	that	that	IN
cord-194157-ak2gc3nz	191	7	P(E	P(E	NNP
cord-194157-ak2gc3nz	191	8	0	0	CD
cord-194157-ak2gc3nz	192	1	∩	∩	UH
cord-194157-ak2gc3nz	192	2	E	E	NNP
cord-194157-ak2gc3nz	192	3	∞	∞	NNP
cord-194157-ak2gc3nz	192	4	)	)	-RRB-
cord-194157-ak2gc3nz	193	1	>	>	XX
cord-194157-ak2gc3nz	194	1	κ	κ	LS
cord-194157-ak2gc3nz	194	2	for	for	IN
cord-194157-ak2gc3nz	194	3	all	all	DT
cord-194157-ak2gc3nz	194	4	sufficiently	sufficiently	RB
cord-194157-ak2gc3nz	194	5	large	large	JJ
cord-194157-ak2gc3nz	194	6	n.	n.	NN
cord-194157-ak2gc3nz	194	7	Select	Select	NNP
cord-194157-ak2gc3nz	194	8	n	n	NNP
cord-194157-ak2gc3nz	194	9	sufficiently	sufficiently	RB
cord-194157-ak2gc3nz	194	10	large	large	JJ
cord-194157-ak2gc3nz	194	11	,	,	,
cord-194157-ak2gc3nz	194	12	and	and	CC
cord-194157-ak2gc3nz	194	13	let	let	VB
cord-194157-ak2gc3nz	194	14	F	F	NNP
cord-194157-ak2gc3nz	194	15	denote	denote	VB
cord-194157-ak2gc3nz	194	16	the	the	DT
cord-194157-ak2gc3nz	194	17	failure	failure	NN
cord-194157-ak2gc3nz	194	18	event	event	NN
cord-194157-ak2gc3nz	194	19	that	that	WDT
cord-194157-ak2gc3nz	194	20	(	(	-LRB-
cord-194157-ak2gc3nz	194	21	1	1	CD
cord-194157-ak2gc3nz	194	22	)	)	-RRB-
cord-194157-ak2gc3nz	194	23	does	do	VBZ
cord-194157-ak2gc3nz	194	24	not	not	RB
cord-194157-ak2gc3nz	194	25	hold	hold	VB
cord-194157-ak2gc3nz	194	26	for	for	IN
cord-194157-ak2gc3nz	194	27	some	some	DT
cord-194157-ak2gc3nz	194	28	o(1	o(1	NNP
cord-194157-ak2gc3nz	194	29	)	)	-RRB-
cord-194157-ak2gc3nz	194	30	function	function	NN
cord-194157-ak2gc3nz	194	31	to	to	TO
cord-194157-ak2gc3nz	194	32	be	be	VB
cord-194157-ak2gc3nz	194	33	identified	identify	VBN
cord-194157-ak2gc3nz	194	34	later	later	RB
cord-194157-ak2gc3nz	194	35	.	.	.
cord-194157-ak2gc3nz	195	1	We	-PRON-	PRP
cord-194157-ak2gc3nz	195	2	wish	wish	VBP
cord-194157-ak2gc3nz	195	3	to	to	TO
cord-194157-ak2gc3nz	195	4	show	show	VB
cord-194157-ak2gc3nz	195	5	that	that	IN
cord-194157-ak2gc3nz	195	6	P(F|E	p(f|e	NN
cord-194157-ak2gc3nz	195	7	0	0	CD
cord-194157-ak2gc3nz	196	1	∩	∩	UH
cord-194157-ak2gc3nz	196	2	E	E	NNP
cord-194157-ak2gc3nz	196	3	∞	∞	NNP
cord-194157-ak2gc3nz	196	4	)	)	-RRB-
cord-194157-ak2gc3nz	196	5	=	=	NFP
cord-194157-ak2gc3nz	196	6	o(1	o(1	NNP
cord-194157-ak2gc3nz	196	7	)	)	-RRB-
cord-194157-ak2gc3nz	196	8	.	.	.
cord-194157-ak2gc3nz	197	1	Let	let	VB
cord-194157-ak2gc3nz	197	2	E	e	NN
cord-194157-ak2gc3nz	197	3	1	1	CD
cord-194157-ak2gc3nz	197	4	denote	denote	VB
cord-194157-ak2gc3nz	197	5	the	the	DT
cord-194157-ak2gc3nz	197	6	event	event	NN
cord-194157-ak2gc3nz	197	7	that	that	DT
cord-194157-ak2gc3nz	198	1	U	U	NNP
cord-194157-ak2gc3nz	198	2	(	(	-LRB-
cord-194157-ak2gc3nz	198	3	t	t	NN
cord-194157-ak2gc3nz	198	4	1	1	CD
cord-194157-ak2gc3nz	198	5	)	)	-RRB-
cord-194157-ak2gc3nz	198	6	∪	∪	NNP
cord-194157-ak2gc3nz	198	7	∂U	∂u	CD
cord-194157-ak2gc3nz	199	1	(	(	-LRB-
cord-194157-ak2gc3nz	199	2	t	t	NN
cord-194157-ak2gc3nz	199	3	1	1	CD
cord-194157-ak2gc3nz	199	4	)	)	-RRB-
cord-194157-ak2gc3nz	199	5	is	be	VBZ
cord-194157-ak2gc3nz	199	6	contained	contain	VBN
cord-194157-ak2gc3nz	199	7	within	within	IN
cord-194157-ak2gc3nz	199	8	distance	distance	NN
cord-194157-ak2gc3nz	199	9	r	r	NN
cord-194157-ak2gc3nz	199	10	of	of	IN
cord-194157-ak2gc3nz	199	11	U	U	NNP
cord-194157-ak2gc3nz	199	12	(	(	-LRB-
cord-194157-ak2gc3nz	199	13	0	0	NFP
cord-194157-ak2gc3nz	199	14	)	)	-RRB-
cord-194157-ak2gc3nz	199	15	.	.	.
cord-194157-ak2gc3nz	200	1	In	in	IN
cord-194157-ak2gc3nz	200	2	particular	particular	JJ
cord-194157-ak2gc3nz	200	3	,	,	,
cord-194157-ak2gc3nz	200	4	on	on	IN
cord-194157-ak2gc3nz	200	5	the	the	DT
cord-194157-ak2gc3nz	200	6	event	event	NN
cord-194157-ak2gc3nz	200	7	E	e	NN
cord-194157-ak2gc3nz	200	8	0	0	CD
cord-194157-ak2gc3nz	201	1	∩	∩	NN
cord-194157-ak2gc3nz	201	2	E	E	NNP
cord-194157-ak2gc3nz	201	3	1	1	CD
cord-194157-ak2gc3nz	201	4	,	,	,
cord-194157-ak2gc3nz	201	5	all	all	DT
cord-194157-ak2gc3nz	201	6	of	of	IN
cord-194157-ak2gc3nz	201	7	infected	infected	JJ
cord-194157-ak2gc3nz	201	8	and	and	CC
cord-194157-ak2gc3nz	201	9	recovered	recover	VBN
cord-194157-ak2gc3nz	201	10	vertices	vertex	NNS
cord-194157-ak2gc3nz	201	11	at	at	IN
cord-194157-ak2gc3nz	201	12	time	time	NN
cord-194157-ak2gc3nz	201	13	t	t	NNP
cord-194157-ak2gc3nz	201	14	1	1	CD
cord-194157-ak2gc3nz	201	15	reside	reside	VBP
cord-194157-ak2gc3nz	201	16	in	in	IN
cord-194157-ak2gc3nz	201	17	a	a	DT
cord-194157-ak2gc3nz	201	18	tree	tree	NN
cord-194157-ak2gc3nz	201	19	with	with	IN
cord-194157-ak2gc3nz	201	20	root	root	NN
cord-194157-ak2gc3nz	201	21	U	u	NN
cord-194157-ak2gc3nz	201	22	(	(	-LRB-
cord-194157-ak2gc3nz	201	23	0	0	NFP
cord-194157-ak2gc3nz	201	24	)	)	-RRB-
cord-194157-ak2gc3nz	201	25	.	.	.
cord-194157-ak2gc3nz	202	1	Also	also	RB
cord-194157-ak2gc3nz	202	2	,	,	,
cord-194157-ak2gc3nz	202	3	selecting	select	VBG
cord-194157-ak2gc3nz	202	4	k	k	NN
cord-194157-ak2gc3nz	202	5	:	:	:
cord-194157-ak2gc3nz	202	6	=	=	NFP
cord-194157-ak2gc3nz	202	7	α(µ+λ	α(µ+λ	NNP
cord-194157-ak2gc3nz	202	8	)	)	-RRB-
cord-194157-ak2gc3nz	202	9	·	·	NFP
cord-194157-ak2gc3nz	202	10	c	c	LS
cord-194157-ak2gc3nz	202	11	log	log	NN
cord-194157-ak2gc3nz	202	12	d−1	d−1	NNP
cord-194157-ak2gc3nz	202	13	n	n	NN
cord-194157-ak2gc3nz	202	14	,	,	,
cord-194157-ak2gc3nz	202	15	let	let	VB
cord-194157-ak2gc3nz	202	16	E	e	NN
cord-194157-ak2gc3nz	202	17	2	2	CD
cord-194157-ak2gc3nz	202	18	denote	denote	VB
cord-194157-ak2gc3nz	202	19	the	the	DT
cord-194157-ak2gc3nz	202	20	event	event	NN
cord-194157-ak2gc3nz	202	21	that	that	IN
cord-194157-ak2gc3nz	202	22	|U	|U	NFP
cord-194157-ak2gc3nz	202	23	(	(	-LRB-
cord-194157-ak2gc3nz	202	24	t	t	NN
cord-194157-ak2gc3nz	202	25	0	0	CD
cord-194157-ak2gc3nz	202	26	)	)	-RRB-
cord-194157-ak2gc3nz	203	1	|	|	NNP
cord-194157-ak2gc3nz	204	1	≥	≥	CD
cord-194157-ak2gc3nz	205	1	k.	k.	NNP
cord-194157-ak2gc3nz	206	1	We	-PRON-	PRP
cord-194157-ak2gc3nz	206	2	will	will	MD
cord-194157-ak2gc3nz	206	3	make	make	VB
cord-194157-ak2gc3nz	206	4	use	use	NN
cord-194157-ak2gc3nz	206	5	of	of	IN
cord-194157-ak2gc3nz	206	6	two	two	CD
cord-194157-ak2gc3nz	206	7	simple	simple	JJ
cord-194157-ak2gc3nz	206	8	inequalities	inequality	NNS
cord-194157-ak2gc3nz	206	9	involving	involve	VBG
cord-194157-ak2gc3nz	206	10	arbitrary	arbitrary	JJ
cord-194157-ak2gc3nz	206	11	events	event	NNS
cord-194157-ak2gc3nz	206	12	A	a	NN
cord-194157-ak2gc3nz	206	13	,	,	,
cord-194157-ak2gc3nz	206	14	B	b	NN
cord-194157-ak2gc3nz	206	15	,	,	,
cord-194157-ak2gc3nz	206	16	and	and	CC
cord-194157-ak2gc3nz	206	17	C.	C.	NNP
cord-194157-ak2gc3nz	206	18	First	First	NNP
cord-194157-ak2gc3nz	206	19	,	,	,
cord-194157-ak2gc3nz	207	1	Furthermore	furthermore	RB
cord-194157-ak2gc3nz	207	2	,	,	,
cord-194157-ak2gc3nz	207	3	if	if	IN
cord-194157-ak2gc3nz	207	4	P(C	P(C	NNP
cord-194157-ak2gc3nz	207	5	c	c	NN
cord-194157-ak2gc3nz	207	6	|B	|b	CD
cord-194157-ak2gc3nz	207	7	)	)	-RRB-
cord-194157-ak2gc3nz	207	8	=	=	SYM
cord-194157-ak2gc3nz	207	9	1	1	CD
cord-194157-ak2gc3nz	207	10	,	,	,
cord-194157-ak2gc3nz	207	11	then	then	RB
cord-194157-ak2gc3nz	207	12	Two	two	CD
cord-194157-ak2gc3nz	207	13	applications	application	NNS
cord-194157-ak2gc3nz	207	14	of	of	IN
cord-194157-ak2gc3nz	207	15	(	(	-LRB-
cord-194157-ak2gc3nz	207	16	2	2	CD
cord-194157-ak2gc3nz	207	17	)	)	-RRB-
cord-194157-ak2gc3nz	207	18	gives	give	VBZ
cord-194157-ak2gc3nz	207	19	To	to	TO
cord-194157-ak2gc3nz	207	20	bound	bound	VB
cord-194157-ak2gc3nz	207	21	the	the	DT
cord-194157-ak2gc3nz	207	22	third	third	JJ
cord-194157-ak2gc3nz	207	23	term	term	NN
cord-194157-ak2gc3nz	207	24	in	in	IN
cord-194157-ak2gc3nz	207	25	(	(	-LRB-
cord-194157-ak2gc3nz	207	26	4	4	CD
cord-194157-ak2gc3nz	207	27	)	)	-RRB-
cord-194157-ak2gc3nz	207	28	,	,	,
cord-194157-ak2gc3nz	207	29	we	-PRON-	PRP
cord-194157-ak2gc3nz	207	30	let	let	VBP
cord-194157-ak2gc3nz	207	31	P	p	NN
cord-194157-ak2gc3nz	207	32	λ,µ	λ,µ	NNP
cord-194157-ak2gc3nz	207	33	denote	denote	VB
cord-194157-ak2gc3nz	207	34	the	the	DT
cord-194157-ak2gc3nz	207	35	probability	probability	NN
cord-194157-ak2gc3nz	207	36	measure	measure	NN
cord-194157-ak2gc3nz	207	37	corresponding	correspond	VBG
cord-194157-ak2gc3nz	207	38	to	to	IN
cord-194157-ak2gc3nz	207	39	the	the	DT
cord-194157-ak2gc3nz	207	40	SIR	SIR	NNP
cord-194157-ak2gc3nz	207	41	model	model	NN
cord-194157-ak2gc3nz	207	42	with	with	IN
cord-194157-ak2gc3nz	207	43	parameters	parameter	NNS
cord-194157-ak2gc3nz	207	44	λ	λ	NN
cord-194157-ak2gc3nz	207	45	and	and	CC
cord-194157-ak2gc3nz	207	46	µ.	µ.	NN
cord-194157-ak2gc3nz	208	1	Then	then	RB
cord-194157-ak2gc3nz	208	2	,	,	,
cord-194157-ak2gc3nz	208	3	for	for	IN
cord-194157-ak2gc3nz	208	4	sufficiently	sufficiently	RB
cord-194157-ak2gc3nz	208	5	large	large	JJ
cord-194157-ak2gc3nz	208	6	n	n	NN
cord-194157-ak2gc3nz	208	7	,	,	,
cord-194157-ak2gc3nz	208	8	we	-PRON-	PRP
cord-194157-ak2gc3nz	208	9	have	have	VBP
cord-194157-ak2gc3nz	209	1	As	as	IN
cord-194157-ak2gc3nz	209	2	such	such	JJ
cord-194157-ak2gc3nz	209	3	,	,	,
cord-194157-ak2gc3nz	209	4	it	-PRON-	PRP
cord-194157-ak2gc3nz	209	5	suffices	suffice	VBZ
cord-194157-ak2gc3nz	209	6	to	to	TO
cord-194157-ak2gc3nz	209	7	show	show	VB
cord-194157-ak2gc3nz	209	8	that	that	IN
cord-194157-ak2gc3nz	209	9	P	p	NN
cord-194157-ak2gc3nz	209	10	λ,0	λ,0	NN
cord-194157-ak2gc3nz	209	11	(	(	-LRB-
cord-194157-ak2gc3nz	209	12	E	e	NN
cord-194157-ak2gc3nz	209	13	0	0	NN
cord-194157-ak2gc3nz	209	14	∩	∩	NN
cord-194157-ak2gc3nz	209	15	E	e	NN
cord-194157-ak2gc3nz	209	16	c	c	NN
cord-194157-ak2gc3nz	209	17	1	1	CD
cord-194157-ak2gc3nz	209	18	)	)	-RRB-
cord-194157-ak2gc3nz	209	19	=	=	NFP
cord-194157-ak2gc3nz	209	20	o(1	o(1	NNP
cord-194157-ak2gc3nz	209	21	)	)	-RRB-
cord-194157-ak2gc3nz	209	22	.	.	.
cord-194157-ak2gc3nz	210	1	We	-PRON-	PRP
cord-194157-ak2gc3nz	210	2	accomplish	accomplish	VBP
cord-194157-ak2gc3nz	210	3	this	this	DT
cord-194157-ak2gc3nz	210	4	by	by	IN
cord-194157-ak2gc3nz	210	5	analyzing	analyze	VBG
cord-194157-ak2gc3nz	210	6	the	the	DT
cord-194157-ak2gc3nz	210	7	corresponding	correspond	VBG
cord-194157-ak2gc3nz	210	8	branching	branching	NN
cord-194157-ak2gc3nz	210	9	process	process	NN
cord-194157-ak2gc3nz	210	10	:	:	:
cord-194157-ak2gc3nz	210	11	Lemma	Lemma	NNP
cord-194157-ak2gc3nz	210	12	9	9	CD
cord-194157-ak2gc3nz	210	13	.	.	.
cord-194157-ak2gc3nz	211	1	Let	let	VB
cord-194157-ak2gc3nz	211	2	G	G	NNP
cord-194157-ak2gc3nz	211	3	denote	denote	VB
cord-194157-ak2gc3nz	211	4	the	the	DT
cord-194157-ak2gc3nz	211	5	infinite	infinite	JJ
cord-194157-ak2gc3nz	211	6	d	d	NNP
cord-194157-ak2gc3nz	211	7	-	-	HYPH
cord-194157-ak2gc3nz	211	8	ary	ary	JJ
cord-194157-ak2gc3nz	211	9	tree	tree	NN
cord-194157-ak2gc3nz	211	10	.	.	.
cord-194157-ak2gc3nz	212	1	Consider	consider	VB
cord-194157-ak2gc3nz	212	2	the	the	DT
cord-194157-ak2gc3nz	212	3	process	process	NN
cord-194157-ak2gc3nz	212	4	{	{	-LRB-
cord-194157-ak2gc3nz	212	5	H	h	NN
cord-194157-ak2gc3nz	212	6	t	t	NN
cord-194157-ak2gc3nz	212	7	}	}	-RRB-
cord-194157-ak2gc3nz	212	8	t≥0	t≥0	NN
cord-194157-ak2gc3nz	212	9	of	of	IN
cord-194157-ak2gc3nz	212	10	induced	induce	VBN
cord-194157-ak2gc3nz	212	11	subgraphs	subgraphs	NN
cord-194157-ak2gc3nz	212	12	of	of	IN
cord-194157-ak2gc3nz	212	13	G	g	NN
cord-194157-ak2gc3nz	212	14	in	in	IN
cord-194157-ak2gc3nz	212	15	which	which	WDT
cord-194157-ak2gc3nz	212	16	H	h	NN
cord-194157-ak2gc3nz	212	17	0	0	CD
cord-194157-ak2gc3nz	212	18	is	be	VBZ
cord-194157-ak2gc3nz	212	19	induced	induce	VBN
cord-194157-ak2gc3nz	212	20	by	by	IN
cord-194157-ak2gc3nz	212	21	the	the	DT
cord-194157-ak2gc3nz	212	22	root	root	NN
cord-194157-ak2gc3nz	212	23	vertex	vertex	NN
cord-194157-ak2gc3nz	212	24	,	,	,
cord-194157-ak2gc3nz	212	25	and	and	CC
cord-194157-ak2gc3nz	212	26	then	then	RB
cord-194157-ak2gc3nz	212	27	for	for	IN
cord-194157-ak2gc3nz	212	28	each	each	DT
cord-194157-ak2gc3nz	212	29	v	v	NN
cord-194157-ak2gc3nz	212	30	∈	∈	NN
cord-194157-ak2gc3nz	212	31	V	v	NN
cord-194157-ak2gc3nz	212	32	(	(	-LRB-
cord-194157-ak2gc3nz	212	33	G)\V	G)\V	NNP
cord-194157-ak2gc3nz	212	34	(	(	-LRB-
cord-194157-ak2gc3nz	212	35	H	h	NN
cord-194157-ak2gc3nz	212	36	t	t	NN
cord-194157-ak2gc3nz	212	37	)	)	-RRB-
cord-194157-ak2gc3nz	212	38	that	that	WDT
cord-194157-ak2gc3nz	212	39	is	be	VBZ
cord-194157-ak2gc3nz	212	40	a	a	DT
cord-194157-ak2gc3nz	212	41	G	g	NN
cord-194157-ak2gc3nz	212	42	-	-	HYPH
cord-194157-ak2gc3nz	212	43	child	child	NN
cord-194157-ak2gc3nz	212	44	of	of	IN
cord-194157-ak2gc3nz	212	45	some	some	DT
cord-194157-ak2gc3nz	212	46	vertex	vertex	NN
cord-194157-ak2gc3nz	212	47	in	in	IN
cord-194157-ak2gc3nz	212	48	H	h	NN
cord-194157-ak2gc3nz	212	49	t	t	NN
cord-194157-ak2gc3nz	213	1	,	,	,
cord-194157-ak2gc3nz	213	2	it	-PRON-	PRP
cord-194157-ak2gc3nz	213	3	holds	hold	VBZ
cord-194157-ak2gc3nz	213	4	that	that	DT
cord-194157-ak2gc3nz	213	5	v	v	NN
cord-194157-ak2gc3nz	213	6	is	be	VBZ
cord-194157-ak2gc3nz	213	7	added	add	VBN
cord-194157-ak2gc3nz	213	8	to	to	IN
cord-194157-ak2gc3nz	213	9	H	H	NNP
cord-194157-ak2gc3nz	213	10	t	t	NN
cord-194157-ak2gc3nz	213	11	at	at	IN
cord-194157-ak2gc3nz	213	12	unit	unit	NN
cord-194157-ak2gc3nz	213	13	rate	rate	NN
cord-194157-ak2gc3nz	213	14	.	.	.
cord-194157-ak2gc3nz	214	1	Let	let	VB
cord-194157-ak2gc3nz	214	2	B	b	NN
cord-194157-ak2gc3nz	214	3	m	m	NNP
cord-194157-ak2gc3nz	214	4	denote	denote	VB
cord-194157-ak2gc3nz	214	5	the	the	DT
cord-194157-ak2gc3nz	214	6	first	first	JJ
cord-194157-ak2gc3nz	214	7	time	time	NN
cord-194157-ak2gc3nz	214	8	at	at	IN
cord-194157-ak2gc3nz	214	9	which	which	WDT
cord-194157-ak2gc3nz	214	10	a	a	DT
cord-194157-ak2gc3nz	214	11	vertex	vertex	NN
cord-194157-ak2gc3nz	214	12	of	of	IN
cord-194157-ak2gc3nz	214	13	distance	distance	NN
cord-194157-ak2gc3nz	214	14	m	m	NNP
cord-194157-ak2gc3nz	214	15	from	from	IN
cord-194157-ak2gc3nz	214	16	the	the	DT
cord-194157-ak2gc3nz	214	17	root	root	NN
cord-194157-ak2gc3nz	214	18	vertex	vertex	NN
cord-194157-ak2gc3nz	214	19	of	of	IN
cord-194157-ak2gc3nz	214	20	G	G	NNP
cord-194157-ak2gc3nz	214	21	is	be	VBZ
cord-194157-ak2gc3nz	214	22	added	add	VBN
cord-194157-ak2gc3nz	214	23	to	to	IN
cord-194157-ak2gc3nz	214	24	H	H	NNP
cord-194157-ak2gc3nz	214	25	t	t	NN
cord-194157-ak2gc3nz	214	26	.	.	.
cord-194157-ak2gc3nz	215	1	Then	then	RB
cord-194157-ak2gc3nz	215	2	B	b	NN
cord-194157-ak2gc3nz	215	3	m	m	NN
cord-194157-ak2gc3nz	215	4	≥	≥	NN
cord-194157-ak2gc3nz	215	5	m/(2ed	m/(2ed	NN
cord-194157-ak2gc3nz	215	6	)	)	-RRB-
cord-194157-ak2gc3nz	215	7	with	with	IN
cord-194157-ak2gc3nz	215	8	probability	probability	NN
cord-194157-ak2gc3nz	215	9	≥	≥	CD
cord-194157-ak2gc3nz	215	10	1	1	CD
cord-194157-ak2gc3nz	215	11	−	−	NN
cord-194157-ak2gc3nz	215	12	e	e	NN
cord-194157-ak2gc3nz	215	13	−m/2	−m/2	NN
cord-194157-ak2gc3nz	215	14	.	.	.
cord-194157-ak2gc3nz	216	1	Proof	proof	NN
cord-194157-ak2gc3nz	216	2	.	.	.
cord-194157-ak2gc3nz	217	1	Let	let	VB
cord-194157-ak2gc3nz	217	2	B	B	NNP
cord-194157-ak2gc3nz	217	3	m	m	NNP
cord-194157-ak2gc3nz	217	4	,	,	,
cord-194157-ak2gc3nz	217	5	r	r	LS
cord-194157-ak2gc3nz	217	6	denote	denote	VB
cord-194157-ak2gc3nz	217	7	the	the	DT
cord-194157-ak2gc3nz	217	8	rth	rth	NNP
cord-194157-ak2gc3nz	217	9	time	time	NN
cord-194157-ak2gc3nz	217	10	at	at	IN
cord-194157-ak2gc3nz	217	11	which	which	WDT
cord-194157-ak2gc3nz	217	12	a	a	DT
cord-194157-ak2gc3nz	217	13	vertex	vertex	NN
cord-194157-ak2gc3nz	217	14	of	of	IN
cord-194157-ak2gc3nz	217	15	distance	distance	NN
cord-194157-ak2gc3nz	217	16	m	m	NNP
cord-194157-ak2gc3nz	217	17	from	from	IN
cord-194157-ak2gc3nz	217	18	the	the	DT
cord-194157-ak2gc3nz	217	19	root	root	NN
cord-194157-ak2gc3nz	217	20	vertex	vertex	NN
cord-194157-ak2gc3nz	217	21	of	of	IN
cord-194157-ak2gc3nz	217	22	G	G	NNP
cord-194157-ak2gc3nz	217	23	is	be	VBZ
cord-194157-ak2gc3nz	217	24	added	add	VBN
cord-194157-ak2gc3nz	217	25	to	to	IN
cord-194157-ak2gc3nz	217	26	H	H	NNP
cord-194157-ak2gc3nz	217	27	t	t	NN
cord-194157-ak2gc3nz	217	28	,	,	,
cord-194157-ak2gc3nz	217	29	and	and	CC
cord-194157-ak2gc3nz	217	30	note	note	VB
cord-194157-ak2gc3nz	217	31	that	that	DT
cord-194157-ak2gc3nz	217	32	B	b	NN
cord-194157-ak2gc3nz	217	33	m	m	NN
cord-194157-ak2gc3nz	217	34	=	=	NN
cord-194157-ak2gc3nz	217	35	B	b	NN
cord-194157-ak2gc3nz	217	36	m,1	m,1	NN
cord-194157-ak2gc3nz	217	37	.	.	.
cord-194157-ak2gc3nz	218	1	Let	let	VB
cord-194157-ak2gc3nz	218	2	c	c	NN
cord-194157-ak2gc3nz	218	3	,	,	,
cord-194157-ak2gc3nz	218	4	θ	θ	NN
cord-194157-ak2gc3nz	218	5	>	>	XX
cord-194157-ak2gc3nz	218	6	0	0	NFP
cord-194157-ak2gc3nz	218	7	be	be	VB
cord-194157-ak2gc3nz	218	8	given	give	VBN
cord-194157-ak2gc3nz	218	9	(	(	-LRB-
cord-194157-ak2gc3nz	218	10	to	to	TO
cord-194157-ak2gc3nz	218	11	be	be	VB
cord-194157-ak2gc3nz	218	12	selected	select	VBN
cord-194157-ak2gc3nz	218	13	later	later	RB
cord-194157-ak2gc3nz	218	14	)	)	-RRB-
cord-194157-ak2gc3nz	218	15	.	.	.
cord-194157-ak2gc3nz	219	1	Then	then	RB
cord-194157-ak2gc3nz	219	2	Markov	Markov	NNP
cord-194157-ak2gc3nz	219	3	's	's	POS
cord-194157-ak2gc3nz	219	4	inequality	inequality	NN
cord-194157-ak2gc3nz	219	5	gives	give	VBZ
cord-194157-ak2gc3nz	219	6	where	where	WRB
cord-194157-ak2gc3nz	219	7	the	the	DT
cord-194157-ak2gc3nz	219	8	last	last	JJ
cord-194157-ak2gc3nz	219	9	identity	identity	NN
cord-194157-ak2gc3nz	219	10	,	,	,
cord-194157-ak2gc3nz	219	11	which	which	WDT
cord-194157-ak2gc3nz	219	12	appears	appear	VBZ
cord-194157-ak2gc3nz	219	13	in	in	IN
cord-194157-ak2gc3nz	219	14	Theorem	Theorem	NNP
cord-194157-ak2gc3nz	219	15	1	1	CD
cord-194157-ak2gc3nz	219	16	in	in	IN
cord-194157-ak2gc3nz	219	17	[	[	-LRB-
cord-194157-ak2gc3nz	219	18	5	5	CD
cord-194157-ak2gc3nz	219	19	]	]	-RRB-
cord-194157-ak2gc3nz	219	20	,	,	,
cord-194157-ak2gc3nz	219	21	follows	follow	VBZ
cord-194157-ak2gc3nz	219	22	from	from	IN
cord-194157-ak2gc3nz	219	23	analyzing	analyze	VBG
cord-194157-ak2gc3nz	219	24	a	a	DT
cord-194157-ak2gc3nz	219	25	certain	certain	JJ
cord-194157-ak2gc3nz	219	26	martingale	martingale	NN
cord-194157-ak2gc3nz	219	27	.	.	.
cord-194157-ak2gc3nz	220	1	In	in	IN
cord-194157-ak2gc3nz	220	2	our	-PRON-	PRP$
cord-194157-ak2gc3nz	220	3	case	case	NN
cord-194157-ak2gc3nz	220	4	,	,	,
cord-194157-ak2gc3nz	220	5	X	x	NN
cord-194157-ak2gc3nz	220	6	0	0	CD
cord-194157-ak2gc3nz	220	7	:	:	:
cord-194157-ak2gc3nz	220	8	=	=	NFP
cord-194157-ak2gc3nz	221	1	B	b	NN
cord-194157-ak2gc3nz	221	2	1,1	1,1	CD
cord-194157-ak2gc3nz	221	3	∼	∼	NNP
cord-194157-ak2gc3nz	221	4	Exp(d	Exp(d	NNP
cord-194157-ak2gc3nz	221	5	)	)	-RRB-
cord-194157-ak2gc3nz	221	6	and	and	CC
cord-194157-ak2gc3nz	222	1	X	X	NNP
cord-194157-ak2gc3nz	222	2	r	r	NN
cord-194157-ak2gc3nz	222	3	:	:	:
cord-194157-ak2gc3nz	222	4	=	=	NFP
cord-194157-ak2gc3nz	222	5	B	b	NN
cord-194157-ak2gc3nz	223	1	1,r+1	1,r+1	LS
cord-194157-ak2gc3nz	223	2	−	−	NN
cord-194157-ak2gc3nz	223	3	B	b	NN
cord-194157-ak2gc3nz	223	4	1,r	1,r	CD
cord-194157-ak2gc3nz	223	5	∼	∼	NNP
cord-194157-ak2gc3nz	223	6	Exp(d	Exp(d	NNP
cord-194157-ak2gc3nz	223	7	−	−	NNP
cord-194157-ak2gc3nz	223	8	r	r	NN
cord-194157-ak2gc3nz	223	9	)	)	-RRB-
cord-194157-ak2gc3nz	223	10	for	for	IN
cord-194157-ak2gc3nz	223	11	r	r	LS
cord-194157-ak2gc3nz	223	12	∈	∈	NN
cord-194157-ak2gc3nz	223	13	{	{	-LRB-
cord-194157-ak2gc3nz	223	14	1	1	CD
cord-194157-ak2gc3nz	223	15	,	,	,
cord-194157-ak2gc3nz	223	16	.	.	.
cord-194157-ak2gc3nz	223	17	.	.	.
cord-194157-ak2gc3nz	223	18	.	.	.
cord-194157-ak2gc3nz	224	1	,	,	,
cord-194157-ak2gc3nz	224	2	d	d	NNP
cord-194157-ak2gc3nz	224	3	−	−	NNP
cord-194157-ak2gc3nz	224	4	1	1	CD
cord-194157-ak2gc3nz	224	5	}	}	-RRB-
cord-194157-ak2gc3nz	224	6	are	be	VBP
cord-194157-ak2gc3nz	224	7	independent	independent	JJ
cord-194157-ak2gc3nz	224	8	.	.	.
cord-194157-ak2gc3nz	225	1	It	-PRON-	PRP
cord-194157-ak2gc3nz	225	2	follows	follow	VBZ
cord-194157-ak2gc3nz	225	3	that	that	IN
cord-194157-ak2gc3nz	225	4	Overall	Overall	NNP
cord-194157-ak2gc3nz	225	5	,	,	,
cord-194157-ak2gc3nz	225	6	Selecting	select	VBG
cord-194157-ak2gc3nz	225	7	θ	θ	NN
cord-194157-ak2gc3nz	225	8	=	=	SYM
cord-194157-ak2gc3nz	225	9	ed	ed	NN
cord-194157-ak2gc3nz	225	10	and	and	CC
cord-194157-ak2gc3nz	225	11	c	c	NN
cord-194157-ak2gc3nz	225	12	=	=	SYM
cord-194157-ak2gc3nz	225	13	1/(2ed	1/(2ed	CD
cord-194157-ak2gc3nz	225	14	)	)	-RRB-
cord-194157-ak2gc3nz	225	15	gives	give	VBZ
cord-194157-ak2gc3nz	225	16	the	the	DT
cord-194157-ak2gc3nz	225	17	result	result	NN
cord-194157-ak2gc3nz	225	18	.	.	.
cord-194157-ak2gc3nz	226	1	Lemma	Lemma	NNP
cord-194157-ak2gc3nz	226	2	10	10	CD
cord-194157-ak2gc3nz	226	3	.	.	.
cord-194157-ak2gc3nz	227	1	Suppose	suppose	VB
cord-194157-ak2gc3nz	227	2	G	g	NN
cord-194157-ak2gc3nz	227	3	is	be	VBZ
cord-194157-ak2gc3nz	227	4	(	(	-LRB-
cord-194157-ak2gc3nz	227	5	r	r	NN
cord-194157-ak2gc3nz	227	6	,	,	,
cord-194157-ak2gc3nz	227	7	η)-locally	η)-locally	RB
cord-194157-ak2gc3nz	227	8	tree	tree	NN
cord-194157-ak2gc3nz	227	9	-	-	HYPH
cord-194157-ak2gc3nz	227	10	like	like	JJ
cord-194157-ak2gc3nz	227	11	,	,	,
cord-194157-ak2gc3nz	227	12	consider	consider	VB
cord-194157-ak2gc3nz	227	13	the	the	DT
cord-194157-ak2gc3nz	227	14	SIR	SIR	NNP
cord-194157-ak2gc3nz	227	15	process	process	NN
cord-194157-ak2gc3nz	227	16	on	on	IN
cord-194157-ak2gc3nz	227	17	G	g	NN
cord-194157-ak2gc3nz	227	18	with	with	IN
cord-194157-ak2gc3nz	227	19	µ	µ	NN
cord-194157-ak2gc3nz	227	20	=	=	SYM
cord-194157-ak2gc3nz	227	21	0	0	CD
cord-194157-ak2gc3nz	227	22	,	,	,
cord-194157-ak2gc3nz	227	23	and	and	CC
cord-194157-ak2gc3nz	227	24	take	take	VB
cord-194157-ak2gc3nz	227	25	any	any	DT
cord-194157-ak2gc3nz	227	26	t	t	NN
cord-194157-ak2gc3nz	227	27	1	1	CD
cord-194157-ak2gc3nz	227	28	≤	≤	NNP
cord-194157-ak2gc3nz	227	29	r−2	r−2	NNP
cord-194157-ak2gc3nz	227	30	2e(d−1)λ	2e(d−1)λ	CD
cord-194157-ak2gc3nz	227	31	.	.	.
cord-194157-ak2gc3nz	228	1	Then	then	RB
cord-194157-ak2gc3nz	228	2	P(E	P(E	NNP
cord-194157-ak2gc3nz	228	3	c	c	NN
cord-194157-ak2gc3nz	228	4	1	1	CD
cord-194157-ak2gc3nz	228	5	|E	|e	CD
cord-194157-ak2gc3nz	228	6	0	0	NFP
cord-194157-ak2gc3nz	228	7	)	)	-RRB-
cord-194157-ak2gc3nz	228	8	≤	≤	NNP
cord-194157-ak2gc3nz	228	9	2e	2e	NNP
cord-194157-ak2gc3nz	228	10	−(r−2)/2	−(r−2)/2	NNP
cord-194157-ak2gc3nz	228	11	.	.	.
cord-194157-ak2gc3nz	229	1	Proof	proof	NN
cord-194157-ak2gc3nz	229	2	.	.	.
cord-194157-ak2gc3nz	230	1	By	by	IN
cord-194157-ak2gc3nz	230	2	time	time	NN
cord-194157-ak2gc3nz	230	3	dilation	dilation	NN
cord-194157-ak2gc3nz	230	4	,	,	,
cord-194157-ak2gc3nz	230	5	we	-PRON-	PRP
cord-194157-ak2gc3nz	230	6	may	may	MD
cord-194157-ak2gc3nz	230	7	take	take	VB
cord-194157-ak2gc3nz	230	8	λ	λ	NN
cord-194157-ak2gc3nz	230	9	=	=	SYM
cord-194157-ak2gc3nz	230	10	1	1	CD
cord-194157-ak2gc3nz	230	11	without	without	IN
cord-194157-ak2gc3nz	230	12	loss	loss	NN
cord-194157-ak2gc3nz	230	13	of	of	IN
cord-194157-ak2gc3nz	230	14	generality	generality	NN
cord-194157-ak2gc3nz	230	15	.	.	.
cord-194157-ak2gc3nz	231	1	Condition	condition	NN
cord-194157-ak2gc3nz	231	2	on	on	IN
cord-194157-ak2gc3nz	231	3	E	e	NN
cord-194157-ak2gc3nz	231	4	0	0	CD
cord-194157-ak2gc3nz	231	5	.	.	.
cord-194157-ak2gc3nz	232	1	After	after	IN
cord-194157-ak2gc3nz	232	2	time	time	NN
cord-194157-ak2gc3nz	232	3	T	T	NNP
cord-194157-ak2gc3nz	232	4	∼	∼	NNP
cord-194157-ak2gc3nz	232	5	Exp(d	Exp(d	NNP
cord-194157-ak2gc3nz	232	6	)	)	-RRB-
cord-194157-ak2gc3nz	232	7	,	,	,
cord-194157-ak2gc3nz	232	8	there	there	EX
cord-194157-ak2gc3nz	232	9	are	be	VBP
cord-194157-ak2gc3nz	232	10	two	two	CD
cord-194157-ak2gc3nz	232	11	infected	infected	JJ
cord-194157-ak2gc3nz	232	12	vertices	vertex	NNS
cord-194157-ak2gc3nz	232	13	u	u	NN
cord-194157-ak2gc3nz	232	14	and	and	CC
cord-194157-ak2gc3nz	232	15	v.	v.	IN
cord-194157-ak2gc3nz	232	16	Removing	remove	VBG
cord-194157-ak2gc3nz	232	17	the	the	DT
cord-194157-ak2gc3nz	232	18	edge	edge	NN
cord-194157-ak2gc3nz	232	19	{	{	-LRB-
cord-194157-ak2gc3nz	232	20	u	u	NN
cord-194157-ak2gc3nz	232	21	,	,	,
cord-194157-ak2gc3nz	232	22	v	v	LS
cord-194157-ak2gc3nz	232	23	}	}	-RRB-
cord-194157-ak2gc3nz	232	24	from	from	IN
cord-194157-ak2gc3nz	232	25	H	H	NNP
cord-194157-ak2gc3nz	232	26	produces	produce	VBZ
cord-194157-ak2gc3nz	232	27	two	two	CD
cord-194157-ak2gc3nz	232	28	(	(	-LRB-
cord-194157-ak2gc3nz	232	29	d	d	NNP
cord-194157-ak2gc3nz	232	30	−	−	NNP
cord-194157-ak2gc3nz	232	31	1)-ary	1)-ary	CD
cord-194157-ak2gc3nz	232	32	trees	tree	NNS
cord-194157-ak2gc3nz	232	33	,	,	,
cord-194157-ak2gc3nz	232	34	with	with	IN
cord-194157-ak2gc3nz	232	35	root	root	NN
cord-194157-ak2gc3nz	232	36	vertices	vertex	NNS
cord-194157-ak2gc3nz	232	37	u	u	NNP
cord-194157-ak2gc3nz	232	38	and	and	CC
cord-194157-ak2gc3nz	232	39	v.	v.	CC
cord-194157-ak2gc3nz	232	40	Extend	extend	VB
cord-194157-ak2gc3nz	232	41	these	these	DT
cord-194157-ak2gc3nz	232	42	trees	tree	NNS
cord-194157-ak2gc3nz	232	43	to	to	IN
cord-194157-ak2gc3nz	232	44	infinite	infinite	JJ
cord-194157-ak2gc3nz	232	45	(	(	-LRB-
cord-194157-ak2gc3nz	232	46	d−1)-ary	d−1)-ary	JJ
cord-194157-ak2gc3nz	232	47	trees	tree	NNS
cord-194157-ak2gc3nz	232	48	H	h	NN
cord-194157-ak2gc3nz	232	49	u	u	NN
cord-194157-ak2gc3nz	232	50	and	and	CC
cord-194157-ak2gc3nz	232	51	H	h	NN
cord-194157-ak2gc3nz	232	52	v	v	NN
cord-194157-ak2gc3nz	232	53	.	.	.
cord-194157-ak2gc3nz	233	1	Let	let	VB
cord-194157-ak2gc3nz	233	2	B	b	NN
cord-194157-ak2gc3nz	233	3	u	u	PRP
cord-194157-ak2gc3nz	233	4	denote	denote	VB
cord-194157-ak2gc3nz	233	5	the	the	DT
cord-194157-ak2gc3nz	233	6	first	first	JJ
cord-194157-ak2gc3nz	233	7	time	time	NN
cord-194157-ak2gc3nz	233	8	at	at	IN
cord-194157-ak2gc3nz	233	9	which	which	WDT
cord-194157-ak2gc3nz	233	10	a	a	DT
cord-194157-ak2gc3nz	233	11	vertex	vertex	NN
cord-194157-ak2gc3nz	233	12	of	of	IN
cord-194157-ak2gc3nz	233	13	distance	distance	NN
cord-194157-ak2gc3nz	233	14	r	r	NNP
cord-194157-ak2gc3nz	233	15	−	−	CD
cord-194157-ak2gc3nz	233	16	2	2	CD
cord-194157-ak2gc3nz	233	17	from	from	IN
cord-194157-ak2gc3nz	233	18	the	the	DT
cord-194157-ak2gc3nz	233	19	root	root	NN
cord-194157-ak2gc3nz	233	20	vertex	vertex	NN
cord-194157-ak2gc3nz	233	21	is	be	VBZ
cord-194157-ak2gc3nz	233	22	infected	infect	VBN
cord-194157-ak2gc3nz	233	23	in	in	IN
cord-194157-ak2gc3nz	233	24	H	H	NNP
cord-194157-ak2gc3nz	233	25	u	u	NN
cord-194157-ak2gc3nz	233	26	,	,	,
cord-194157-ak2gc3nz	233	27	and	and	CC
cord-194157-ak2gc3nz	233	28	similarly	similarly	RB
cord-194157-ak2gc3nz	233	29	for	for	IN
cord-194157-ak2gc3nz	233	30	B	B	NNP
cord-194157-ak2gc3nz	233	31	v	v	NN
cord-194157-ak2gc3nz	233	32	.	.	.
cord-194157-ak2gc3nz	234	1	Then	then	RB
cord-194157-ak2gc3nz	234	2	by	by	IN
cord-194157-ak2gc3nz	234	3	assumption	assumption	NN
cord-194157-ak2gc3nz	234	4	on	on	IN
cord-194157-ak2gc3nz	234	5	t	t	NNP
cord-194157-ak2gc3nz	234	6	1	1	CD
cord-194157-ak2gc3nz	234	7	,	,	,
cord-194157-ak2gc3nz	234	8	we	-PRON-	PRP
cord-194157-ak2gc3nz	234	9	have	have	VBP
cord-194157-ak2gc3nz	234	10	Finally	finally	RB
cord-194157-ak2gc3nz	234	11	,	,	,
cord-194157-ak2gc3nz	234	12	we	-PRON-	PRP
cord-194157-ak2gc3nz	234	13	apply	apply	VBP
cord-194157-ak2gc3nz	234	14	the	the	DT
cord-194157-ak2gc3nz	234	15	union	union	NN
cord-194157-ak2gc3nz	234	16	bound	bind	VBN
cord-194157-ak2gc3nz	234	17	and	and	CC
cord-194157-ak2gc3nz	234	18	Lemma	Lemma	NNP
cord-194157-ak2gc3nz	234	19	9	9	CD
cord-194157-ak2gc3nz	234	20	to	to	TO
cord-194157-ak2gc3nz	234	21	get	get	VB
cord-194157-ak2gc3nz	234	22	Overall	overall	RB
cord-194157-ak2gc3nz	234	23	,	,	,
cord-194157-ak2gc3nz	234	24	(	(	-LRB-
cord-194157-ak2gc3nz	234	25	5	5	LS
cord-194157-ak2gc3nz	234	26	)	)	-RRB-
cord-194157-ak2gc3nz	234	27	and	and	CC
cord-194157-ak2gc3nz	234	28	Lemma	Lemma	NNP
cord-194157-ak2gc3nz	234	29	10	10	CD
cord-194157-ak2gc3nz	234	30	together	together	RB
cord-194157-ak2gc3nz	235	1	give	give	VB
cord-194157-ak2gc3nz	235	2	P(E	P(E	NNP
cord-194157-ak2gc3nz	235	3	c	c	NN
cord-194157-ak2gc3nz	235	4	1	1	CD
cord-194157-ak2gc3nz	235	5	|E	|e	CD
cord-194157-ak2gc3nz	235	6	0	0	CD
cord-194157-ak2gc3nz	236	1	∩	∩	UH
cord-194157-ak2gc3nz	236	2	E	E	NNP
cord-194157-ak2gc3nz	236	3	∞	∞	NNP
cord-194157-ak2gc3nz	236	4	)	)	-RRB-
cord-194157-ak2gc3nz	236	5	=	=	NFP
cord-194157-ak2gc3nz	236	6	o(1	o(1	NNP
cord-194157-ak2gc3nz	236	7	)	)	-RRB-
cord-194157-ak2gc3nz	236	8	.	.	.
cord-194157-ak2gc3nz	237	1	Next	next	RB
cord-194157-ak2gc3nz	237	2	,	,	,
cord-194157-ak2gc3nz	237	3	we	-PRON-	PRP
cord-194157-ak2gc3nz	237	4	may	may	MD
cord-194157-ak2gc3nz	237	5	combine	combine	VB
cord-194157-ak2gc3nz	237	6	this	this	DT
cord-194157-ak2gc3nz	237	7	bound	bind	VBN
cord-194157-ak2gc3nz	237	8	with	with	IN
cord-194157-ak2gc3nz	237	9	(	(	-LRB-
cord-194157-ak2gc3nz	237	10	3	3	CD
cord-194157-ak2gc3nz	237	11	)	)	-RRB-
cord-194157-ak2gc3nz	237	12	to	to	TO
cord-194157-ak2gc3nz	237	13	bound	bound	VB
cord-194157-ak2gc3nz	237	14	the	the	DT
cord-194157-ak2gc3nz	237	15	second	second	JJ
cord-194157-ak2gc3nz	237	16	term	term	NN
cord-194157-ak2gc3nz	237	17	in	in	IN
cord-194157-ak2gc3nz	237	18	(	(	-LRB-
cord-194157-ak2gc3nz	237	19	4	4	CD
cord-194157-ak2gc3nz	237	20	)	)	-RRB-
cord-194157-ak2gc3nz	237	21	:	:	:
cord-194157-ak2gc3nz	237	22	(	(	-LRB-
cord-194157-ak2gc3nz	237	23	1	1	CD
cord-194157-ak2gc3nz	237	24	)	)	-RRB-
cord-194157-ak2gc3nz	237	25	.	.	.
cord-194157-ak2gc3nz	238	1	To	to	IN
cord-194157-ak2gc3nz	238	2	this	this	DT
cord-194157-ak2gc3nz	238	3	end	end	NN
cord-194157-ak2gc3nz	238	4	,	,	,
cord-194157-ak2gc3nz	238	5	it	-PRON-	PRP
cord-194157-ak2gc3nz	238	6	is	be	VBZ
cord-194157-ak2gc3nz	238	7	convenient	convenient	JJ
cord-194157-ak2gc3nz	238	8	to	to	TO
cord-194157-ak2gc3nz	238	9	consider	consider	VB
cord-194157-ak2gc3nz	238	10	the	the	DT
cord-194157-ak2gc3nz	238	11	stopping	stopping	JJ
cord-194157-ak2gc3nz	238	12	time	time	NN
cord-194157-ak2gc3nz	238	13	T	t	NN
cord-194157-ak2gc3nz	238	14	0	0	CD
cord-194157-ak2gc3nz	238	15	:	:	:
cord-194157-ak2gc3nz	239	1	=	=	NFP
cord-194157-ak2gc3nz	240	1	inf{t	inf{t	NNP
cord-194157-ak2gc3nz	240	2	:	:	:
cord-194157-ak2gc3nz	241	1	t	t	NNP
cord-194157-ak2gc3nz	241	2	0	0	CD
cord-194157-ak2gc3nz	241	3	and	and	CC
cord-194157-ak2gc3nz	241	4	c	c	NN
cord-194157-ak2gc3nz	241	5	<	<	XX
cord-194157-ak2gc3nz	241	6	1	1	CD
cord-194157-ak2gc3nz	241	7	,	,	,
cord-194157-ak2gc3nz	241	8	it	-PRON-	PRP
cord-194157-ak2gc3nz	241	9	follows	follow	VBZ
cord-194157-ak2gc3nz	241	10	that	that	DT
cord-194157-ak2gc3nz	241	11	Next	Next	NNP
cord-194157-ak2gc3nz	241	12	,	,	,
cord-194157-ak2gc3nz	241	13	our	-PRON-	PRP$
cord-194157-ak2gc3nz	241	14	assumptions	assumption	NNS
cord-194157-ak2gc3nz	241	15	that	that	IN
cord-194157-ak2gc3nz	241	16	α	α	NN
cord-194157-ak2gc3nz	241	17	<	<	XX
cord-194157-ak2gc3nz	241	18	c	c	NNP
cord-194157-ak2gc3nz	241	19	2e(d−1)λ	2e(d−1)λ	CD
cord-194157-ak2gc3nz	241	20	,	,	,
cord-194157-ak2gc3nz	241	21	(	(	-LRB-
cord-194157-ak2gc3nz	241	22	d	d	NN
cord-194157-ak2gc3nz	241	23	−	−	NNP
cord-194157-ak2gc3nz	241	24	2)λ	2)λ	CD
cord-194157-ak2gc3nz	242	1	>	>	XX
cord-194157-ak2gc3nz	242	2	µ	µ	XX
cord-194157-ak2gc3nz	242	3	,	,	,
cord-194157-ak2gc3nz	242	4	and	and	CC
cord-194157-ak2gc3nz	242	5	c	c	NN
cord-194157-ak2gc3nz	242	6	<	<	XX
cord-194157-ak2gc3nz	242	7	1	1	CD
cord-194157-ak2gc3nz	242	8	together	together	RB
cord-194157-ak2gc3nz	242	9	imply	imply	VBP
cord-194157-ak2gc3nz	242	10	from	from	IN
cord-194157-ak2gc3nz	242	11	which	which	WDT
cord-194157-ak2gc3nz	242	12	it	-PRON-	PRP
cord-194157-ak2gc3nz	242	13	follows	follow	VBZ
cord-194157-ak2gc3nz	242	14	that	that	DT
cord-194157-ak2gc3nz	243	1	k	k	NNP
cord-194157-ak2gc3nz	243	2	<	<	NNP
cord-194157-ak2gc3nz	243	3	r.	r.	NNP
cord-194157-ak2gc3nz	244	1	On	on	IN
cord-194157-ak2gc3nz	244	2	the	the	DT
cord-194157-ak2gc3nz	244	3	event	event	NN
cord-194157-ak2gc3nz	245	1	E	E	NNP
cord-194157-ak2gc3nz	245	2	∞	∞	NNP
cord-194157-ak2gc3nz	245	3	,	,	,
cord-194157-ak2gc3nz	245	4	it	-PRON-	PRP
cord-194157-ak2gc3nz	245	5	holds	hold	VBZ
cord-194157-ak2gc3nz	245	6	that	that	IN
cord-194157-ak2gc3nz	245	7	U	U	NNP
cord-194157-ak2gc3nz	245	8	(	(	-LRB-
cord-194157-ak2gc3nz	245	9	∞	∞	NNP
cord-194157-ak2gc3nz	245	10	)	)	-RRB-
cord-194157-ak2gc3nz	245	11	induces	induce	VBZ
cord-194157-ak2gc3nz	245	12	a	a	DT
cord-194157-ak2gc3nz	245	13	tree	tree	NN
cord-194157-ak2gc3nz	245	14	that	that	WDT
cord-194157-ak2gc3nz	245	15	contains	contain	VBZ
cord-194157-ak2gc3nz	245	16	a	a	DT
cord-194157-ak2gc3nz	245	17	path	path	NN
cord-194157-ak2gc3nz	245	18	of	of	IN
cord-194157-ak2gc3nz	245	19	length	length	NN
cord-194157-ak2gc3nz	245	20	greater	great	JJR
cord-194157-ak2gc3nz	245	21	than	than	IN
cord-194157-ak2gc3nz	245	22	r	r	NNP
cord-194157-ak2gc3nz	245	23	,	,	,
cord-194157-ak2gc3nz	245	24	from	from	IN
cord-194157-ak2gc3nz	245	25	which	which	WDT
cord-194157-ak2gc3nz	245	26	is	be	VBZ
cord-194157-ak2gc3nz	245	27	follows	follow	VBZ
cord-194157-ak2gc3nz	245	28	that	that	DT
cord-194157-ak2gc3nz	245	29	|U	|u	CD
cord-194157-ak2gc3nz	245	30	(	(	-LRB-
cord-194157-ak2gc3nz	245	31	∞)|	∞)|	NNP
cord-194157-ak2gc3nz	245	32	>	>	XX
cord-194157-ak2gc3nz	245	33	r.	r.	NNP
cord-194157-ak2gc3nz	246	1	As	as	IN
cord-194157-ak2gc3nz	246	2	such	such	JJ
cord-194157-ak2gc3nz	246	3	,	,	,
cord-194157-ak2gc3nz	246	4	This	this	DT
cord-194157-ak2gc3nz	246	5	allows	allow	VBZ
cord-194157-ak2gc3nz	246	6	us	-PRON-	PRP
cord-194157-ak2gc3nz	246	7	to	to	TO
cord-194157-ak2gc3nz	246	8	continue	continue	VB
cord-194157-ak2gc3nz	246	9	(	(	-LRB-
cord-194157-ak2gc3nz	246	10	7	7	CD
cord-194157-ak2gc3nz	246	11	)	)	-RRB-
cord-194157-ak2gc3nz	246	12	:	:	:
cord-194157-ak2gc3nz	246	13	To	to	TO
cord-194157-ak2gc3nz	246	14	continue	continue	VB
cord-194157-ak2gc3nz	246	15	,	,	,
cord-194157-ak2gc3nz	246	16	we	-PRON-	PRP
cord-194157-ak2gc3nz	246	17	show	show	VBP
cord-194157-ak2gc3nz	246	18	that	that	IN
cord-194157-ak2gc3nz	246	19	P	P	NNP
cord-194157-ak2gc3nz	246	20	(	(	-LRB-
cord-194157-ak2gc3nz	246	21	Proof	Proof	NNP
cord-194157-ak2gc3nz	246	22	.	.	.
cord-194157-ak2gc3nz	247	1	The	the	DT
cord-194157-ak2gc3nz	247	2	random	random	JJ
cord-194157-ak2gc3nz	247	3	number	number	NN
cord-194157-ak2gc3nz	247	4	N	n	CD
cord-194157-ak2gc3nz	247	5	of	of	IN
cord-194157-ak2gc3nz	247	6	transitions	transition	NNS
cord-194157-ak2gc3nz	247	7	that	that	WDT
cord-194157-ak2gc3nz	247	8	occur	occur	VBP
cord-194157-ak2gc3nz	247	9	over	over	IN
cord-194157-ak2gc3nz	247	10	the	the	DT
cord-194157-ak2gc3nz	247	11	interval	interval	NN
cord-194157-ak2gc3nz	247	12	(	(	-LRB-
cord-194157-ak2gc3nz	247	13	0	0	NFP
cord-194157-ak2gc3nz	247	14	,	,	,
cord-194157-ak2gc3nz	247	15	T	T	NNP
cord-194157-ak2gc3nz	247	16	0	0	NFP
cord-194157-ak2gc3nz	247	17	]	]	-RRB-
cord-194157-ak2gc3nz	247	18	is	be	VBZ
cord-194157-ak2gc3nz	247	19	given	give	VBN
cord-194157-ak2gc3nz	247	20	by	by	IN
cord-194157-ak2gc3nz	247	21	Conditioned	condition	VBN
cord-194157-ak2gc3nz	247	22	on	on	IN
cord-194157-ak2gc3nz	247	23	the	the	DT
cord-194157-ak2gc3nz	247	24	sequence	sequence	NN
cord-194157-ak2gc3nz	247	25	of	of	IN
cord-194157-ak2gc3nz	247	26	states	state	NNS
cord-194157-ak2gc3nz	247	27	of	of	IN
cord-194157-ak2gc3nz	247	28	the	the	DT
cord-194157-ak2gc3nz	247	29	discrete	discrete	JJ
cord-194157-ak2gc3nz	247	30	time	time	NN
cord-194157-ak2gc3nz	247	31	Markov	Markov	NNP
cord-194157-ak2gc3nz	247	32	chain	chain	NN
cord-194157-ak2gc3nz	247	33	{	{	-LRB-
cord-194157-ak2gc3nz	247	34	M	M	NNP
cord-194157-ak2gc3nz	247	35	n	n	NNP
cord-194157-ak2gc3nz	247	36	}	}	-RRB-
cord-194157-ak2gc3nz	247	37	n≥0	n≥0	NNP
cord-194157-ak2gc3nz	247	38	,	,	,
cord-194157-ak2gc3nz	247	39	the	the	DT
cord-194157-ak2gc3nz	247	40	transition	transition	NN
cord-194157-ak2gc3nz	247	41	times	time	NNS
cord-194157-ak2gc3nz	247	42	{	{	-LRB-
cord-194157-ak2gc3nz	247	43	X	x	NN
cord-194157-ak2gc3nz	247	44	n	n	NN
cord-194157-ak2gc3nz	247	45	}	}	-RRB-
cord-194157-ak2gc3nz	247	46	n≥1	n≥1	NN
cord-194157-ak2gc3nz	247	47	are	be	VBP
cord-194157-ak2gc3nz	247	48	independent	independent	JJ
cord-194157-ak2gc3nz	247	49	and	and	CC
cord-194157-ak2gc3nz	247	50	exponentially	exponentially	RB
cord-194157-ak2gc3nz	247	51	distributed	distribute	VBN
cord-194157-ak2gc3nz	247	52	with	with	IN
cord-194157-ak2gc3nz	247	53	(	(	-LRB-
cord-194157-ak2gc3nz	247	54	deterministic	deterministic	JJ
cord-194157-ak2gc3nz	247	55	)	)	-RRB-
cord-194157-ak2gc3nz	247	56	parameters	parameter	NNS
cord-194157-ak2gc3nz	247	57	λe(I	λe(I	NNP
cord-194157-ak2gc3nz	247	58	n	n	NN
cord-194157-ak2gc3nz	247	59	,	,	,
cord-194157-ak2gc3nz	247	60	S	S	NNP
cord-194157-ak2gc3nz	247	61	n	n	NN
cord-194157-ak2gc3nz	247	62	)	)	-RRB-
cord-194157-ak2gc3nz	248	1	+	+	CC
cord-194157-ak2gc3nz	248	2	µ|I	µ|i	NN
cord-194157-ak2gc3nz	248	3	n	n	NN
cord-194157-ak2gc3nz	248	4	|	|	NNP
cord-194157-ak2gc3nz	248	5	.	.	.
cord-194157-ak2gc3nz	249	1	For	for	IN
cord-194157-ak2gc3nz	249	2	any	any	DT
cord-194157-ak2gc3nz	249	3	sequence	sequence	NN
cord-194157-ak2gc3nz	249	4	of	of	IN
cord-194157-ak2gc3nz	249	5	states	state	NNS
cord-194157-ak2gc3nz	249	6	in	in	IN
cord-194157-ak2gc3nz	249	7	the	the	DT
cord-194157-ak2gc3nz	249	8	event	event	NN
cord-194157-ak2gc3nz	249	9	{	{	-LRB-
cord-194157-ak2gc3nz	249	10	T	t	NN
cord-194157-ak2gc3nz	249	11	0	0	CD
cord-194157-ak2gc3nz	249	12	<	<	XX
cord-194157-ak2gc3nz	249	13	∞	∞	NNP
cord-194157-ak2gc3nz	249	14	}	}	-RRB-
cord-194157-ak2gc3nz	249	15	,	,	,
cord-194157-ak2gc3nz	249	16	the	the	DT
cord-194157-ak2gc3nz	249	17	first	first	JJ
cord-194157-ak2gc3nz	249	18	N	n	CD
cord-194157-ak2gc3nz	249	19	of	of	IN
cord-194157-ak2gc3nz	249	20	these	these	DT
cord-194157-ak2gc3nz	249	21	parameters	parameter	NNS
cord-194157-ak2gc3nz	249	22	are	be	VBP
cord-194157-ak2gc3nz	249	23	all	all	RB
cord-194157-ak2gc3nz	249	24	at	at	IN
cord-194157-ak2gc3nz	249	25	least	least	JJS
cord-194157-ak2gc3nz	249	26	µ	µ	NN
cord-194157-ak2gc3nz	249	27	+	+	CC
cord-194157-ak2gc3nz	249	28	λ	λ	NN
cord-194157-ak2gc3nz	249	29	.	.	.
cord-194157-ak2gc3nz	250	1	Put	put	NN
cord-194157-ak2gc3nz	250	2	E	e	NN
cord-194157-ak2gc3nz	250	3	:	:	:
cord-194157-ak2gc3nz	250	4	=	=	NFP
cord-194157-ak2gc3nz	250	5	{	{	-LRB-
cord-194157-ak2gc3nz	250	6	T	t	NN
cord-194157-ak2gc3nz	250	7	0	0	CD
cord-194157-ak2gc3nz	250	8	<	<	XX
cord-194157-ak2gc3nz	251	1	∞	∞	NNP
cord-194157-ak2gc3nz	251	2	}	}	-RRB-
cord-194157-ak2gc3nz	251	3	and	and	CC
cord-194157-ak2gc3nz	251	4	denote	denote	VB
cord-194157-ak2gc3nz	251	5	P	p	NN
cord-194157-ak2gc3nz	251	6	E	e	NN
cord-194157-ak2gc3nz	251	7	(	(	-LRB-
cord-194157-ak2gc3nz	251	8	A	a	NN
cord-194157-ak2gc3nz	251	9	)	)	-RRB-
cord-194157-ak2gc3nz	251	10	:	:	:
cord-194157-ak2gc3nz	251	11	=	=	NFP
cord-194157-ak2gc3nz	251	12	P(A|E	P(A|E	NNP
cord-194157-ak2gc3nz	251	13	)	)	-RRB-
cord-194157-ak2gc3nz	251	14	.	.	.
cord-194157-ak2gc3nz	252	1	Then	then	RB
cord-194157-ak2gc3nz	252	2	Put	put	VB
cord-194157-ak2gc3nz	252	3	t	t	NN
cord-194157-ak2gc3nz	252	4	0	0	CD
cord-194157-ak2gc3nz	252	5	:	:	:
cord-194157-ak2gc3nz	252	6	=	=	SYM
cord-194157-ak2gc3nz	252	7	4k	4k	CD
cord-194157-ak2gc3nz	253	1	µ+λ	µ+λ	UH
cord-194157-ak2gc3nz	253	2	.	.	.
cord-194157-ak2gc3nz	254	1	Conditioning	conditioning	NN
cord-194157-ak2gc3nz	254	2	on	on	IN
cord-194157-ak2gc3nz	254	3	N	N	NNP
cord-194157-ak2gc3nz	254	4	,	,	,
cord-194157-ak2gc3nz	254	5	we	-PRON-	PRP
cord-194157-ak2gc3nz	254	6	may	may	MD
cord-194157-ak2gc3nz	254	7	apply	apply	VB
cord-194157-ak2gc3nz	254	8	Bernstein	Bernstein	NNP
cord-194157-ak2gc3nz	254	9	's	's	POS
cord-194157-ak2gc3nz	254	10	inequality	inequality	NN
cord-194157-ak2gc3nz	254	11	for	for	IN
cord-194157-ak2gc3nz	254	12	subexponential	subexponential	JJ
cord-194157-ak2gc3nz	254	13	random	random	JJ
cord-194157-ak2gc3nz	254	14	variables	variable	NNS
cord-194157-ak2gc3nz	254	15	(	(	-LRB-
cord-194157-ak2gc3nz	255	1	see	see	VB
cord-194157-ak2gc3nz	256	1	Theorem	theorem	NN
cord-194157-ak2gc3nz	256	2	2.8.1	2.8.1	NN
cord-194157-ak2gc3nz	256	3	in	in	IN
cord-194157-ak2gc3nz	256	4	[	[	-LRB-
cord-194157-ak2gc3nz	256	5	7	7	CD
cord-194157-ak2gc3nz	256	6	]	]	-RRB-
cord-194157-ak2gc3nz	256	7	)	)	-RRB-
cord-194157-ak2gc3nz	256	8	.	.	.
cord-194157-ak2gc3nz	257	1	In	in	IN
cord-194157-ak2gc3nz	257	2	particular	particular	JJ
cord-194157-ak2gc3nz	257	3	,	,	,
cord-194157-ak2gc3nz	257	4	we	-PRON-	PRP
cord-194157-ak2gc3nz	257	5	let	let	VBP
cord-194157-ak2gc3nz	257	6	C	c	NN
cord-194157-ak2gc3nz	257	7	>	>	XX
cord-194157-ak2gc3nz	257	8	0	0	NFP
cord-194157-ak2gc3nz	257	9	denote	denote	VBP
cord-194157-ak2gc3nz	257	10	a	a	DT
cord-194157-ak2gc3nz	257	11	universal	universal	JJ
cord-194157-ak2gc3nz	257	12	constant	constant	NN
cord-194157-ak2gc3nz	258	1	such	such	JJ
cord-194157-ak2gc3nz	258	2	that	that	IN
cord-194157-ak2gc3nz	258	3	any	any	DT
cord-194157-ak2gc3nz	258	4	random	random	JJ
cord-194157-ak2gc3nz	258	5	variable	variable	NN
cord-194157-ak2gc3nz	258	6	of	of	IN
cord-194157-ak2gc3nz	258	7	the	the	DT
cord-194157-ak2gc3nz	258	8	form	form	NN
cord-194157-ak2gc3nz	258	9	X	x	NN
cord-194157-ak2gc3nz	258	10	∼	∼	NNP
cord-194157-ak2gc3nz	258	11	Exp(λ	Exp(λ	NNPS
cord-194157-ak2gc3nz	258	12	)	)	-RRB-
cord-194157-ak2gc3nz	258	13	satisfies	satisfy	VBZ
cord-194157-ak2gc3nz	258	14	X	X	NNP
cord-194157-ak2gc3nz	258	15	−	−	NNP
cord-194157-ak2gc3nz	258	16	EX	EX	NNP
cord-194157-ak2gc3nz	258	17	ψ	ψ	NN
cord-194157-ak2gc3nz	258	18	1	1	CD
cord-194157-ak2gc3nz	258	19	≤	≤	NN
cord-194157-ak2gc3nz	258	20	C	c	NN
cord-194157-ak2gc3nz	258	21	λ	λ	NN
cord-194157-ak2gc3nz	258	22	.	.	.
cord-194157-ak2gc3nz	259	1	Then	then	RB
cord-194157-ak2gc3nz	259	2	where	where	WRB
cord-194157-ak2gc3nz	259	3	the	the	DT
cord-194157-ak2gc3nz	259	4	last	last	JJ
cord-194157-ak2gc3nz	259	5	step	step	NN
cord-194157-ak2gc3nz	259	6	applies	apply	VBZ
cord-194157-ak2gc3nz	259	7	the	the	DT
cord-194157-ak2gc3nz	259	8	bound	bound	JJ
cord-194157-ak2gc3nz	259	9	N	n	NN
cord-194157-ak2gc3nz	259	10	≤	≤	NNPS
cord-194157-ak2gc3nz	259	11	2k	2k	NNP
cord-194157-ak2gc3nz	259	12	and	and	CC
cord-194157-ak2gc3nz	259	13	c	c	NN
cord-194157-ak2gc3nz	259	14	1	1	CD
cord-194157-ak2gc3nz	259	15	:	:	:
cord-194157-ak2gc3nz	259	16	=	=	SYM
cord-194157-ak2gc3nz	259	17	2c	2c	NNP
cord-194157-ak2gc3nz	259	18	max(C	max(C	NNP
cord-194157-ak2gc3nz	259	19	2	2	CD
cord-194157-ak2gc3nz	259	20	,	,	,
cord-194157-ak2gc3nz	259	21	C	C	NNP
cord-194157-ak2gc3nz	259	22	)	)	-RRB-
cord-194157-ak2gc3nz	259	23	.	.	.
cord-194157-ak2gc3nz	260	1	Overall	overall	RB
cord-194157-ak2gc3nz	260	2	,	,	,
cord-194157-ak2gc3nz	260	3	(	(	-LRB-
cord-194157-ak2gc3nz	260	4	6	6	CD
cord-194157-ak2gc3nz	260	5	)	)	-RRB-
cord-194157-ak2gc3nz	260	6	,	,	,
cord-194157-ak2gc3nz	260	7	(	(	-LRB-
cord-194157-ak2gc3nz	260	8	8)	8)	NNP
cord-194157-ak2gc3nz	260	9	and	and	CC
cord-194157-ak2gc3nz	260	10	Lemma	Lemma	NNP
cord-194157-ak2gc3nz	260	11	11	11	CD
cord-194157-ak2gc3nz	260	12	together	together	RB
cord-194157-ak2gc3nz	260	13	give	give	VBP
cord-194157-ak2gc3nz	260	14	that	that	IN
cord-194157-ak2gc3nz	260	15	the	the	DT
cord-194157-ak2gc3nz	260	16	second	second	JJ
cord-194157-ak2gc3nz	260	17	term	term	NN
cord-194157-ak2gc3nz	260	18	in	in	IN
cord-194157-ak2gc3nz	260	19	(	(	-LRB-
cord-194157-ak2gc3nz	260	20	4	4	LS
cord-194157-ak2gc3nz	260	21	)	)	-RRB-
cord-194157-ak2gc3nz	260	22	is	be	VBZ
cord-194157-ak2gc3nz	260	23	o	o	NN
cord-194157-ak2gc3nz	260	24	(	(	-LRB-
cord-194157-ak2gc3nz	260	25	1	1	CD
cord-194157-ak2gc3nz	260	26	)	)	-RRB-
cord-194157-ak2gc3nz	260	27	.	.	.
cord-194157-ak2gc3nz	261	1	It	-PRON-	PRP
cord-194157-ak2gc3nz	261	2	remains	remain	VBZ
cord-194157-ak2gc3nz	261	3	to	to	TO
cord-194157-ak2gc3nz	261	4	show	show	VB
cord-194157-ak2gc3nz	261	5	that	that	IN
cord-194157-ak2gc3nz	261	6	the	the	DT
cord-194157-ak2gc3nz	261	7	first	first	JJ
cord-194157-ak2gc3nz	261	8	term	term	NN
cord-194157-ak2gc3nz	261	9	in	in	IN
cord-194157-ak2gc3nz	261	10	(	(	-LRB-
cord-194157-ak2gc3nz	261	11	4	4	LS
cord-194157-ak2gc3nz	261	12	)	)	-RRB-
cord-194157-ak2gc3nz	261	13	is	be	VBZ
cord-194157-ak2gc3nz	261	14	o	o	NN
cord-194157-ak2gc3nz	261	15	(	(	-LRB-
cord-194157-ak2gc3nz	261	16	1	1	CD
cord-194157-ak2gc3nz	261	17	)	)	-RRB-
cord-194157-ak2gc3nz	261	18	.	.	.
cord-194157-ak2gc3nz	262	1	To	to	IN
cord-194157-ak2gc3nz	262	2	this	this	DT
cord-194157-ak2gc3nz	262	3	end	end	NN
cord-194157-ak2gc3nz	262	4	,	,	,
cord-194157-ak2gc3nz	262	5	we	-PRON-	PRP
cord-194157-ak2gc3nz	262	6	first	first	RB
cord-194157-ak2gc3nz	262	7	show	show	VBP
cord-194157-ak2gc3nz	262	8	that	that	IN
cord-194157-ak2gc3nz	262	9	P	p	NN
cord-194157-ak2gc3nz	262	10	(	(	-LRB-
cord-194157-ak2gc3nz	262	11	where	where	WRB
cord-194157-ak2gc3nz	262	12	the	the	DT
cord-194157-ak2gc3nz	262	13	last	last	JJ
cord-194157-ak2gc3nz	262	14	step	step	NN
cord-194157-ak2gc3nz	262	15	applies	apply	VBZ
cord-194157-ak2gc3nz	262	16	(	(	-LRB-
cord-194157-ak2gc3nz	262	17	8)	8)	NNP
cord-194157-ak2gc3nz	262	18	and	and	CC
cord-194157-ak2gc3nz	262	19	Lemma	Lemma	NNP
cord-194157-ak2gc3nz	262	20	11	11	CD
cord-194157-ak2gc3nz	262	21	.	.	.
cord-194157-ak2gc3nz	263	1	Combining	combine	VBG
cord-194157-ak2gc3nz	263	2	this	this	DT
cord-194157-ak2gc3nz	263	3	with	with	IN
cord-194157-ak2gc3nz	263	4	(	(	-LRB-
cord-194157-ak2gc3nz	263	5	5	5	CD
cord-194157-ak2gc3nz	263	6	)	)	-RRB-
cord-194157-ak2gc3nz	263	7	and	and	CC
cord-194157-ak2gc3nz	263	8	Lemma	Lemma	NNP
cord-194157-ak2gc3nz	263	9	10	10	CD
cord-194157-ak2gc3nz	263	10	after	after	IN
cord-194157-ak2gc3nz	263	11	a	a	DT
cord-194157-ak2gc3nz	263	12	union	union	NN
cord-194157-ak2gc3nz	263	13	bound	bind	VBN
cord-194157-ak2gc3nz	263	14	then	then	RB
cord-194157-ak2gc3nz	263	15	gives	give	VBZ
cord-194157-ak2gc3nz	263	16	as	as	IN
cord-194157-ak2gc3nz	263	17	claimed	claim	VBN
cord-194157-ak2gc3nz	263	18	.	.	.
cord-194157-ak2gc3nz	264	1	As	as	IN
cord-194157-ak2gc3nz	264	2	such	such	JJ
cord-194157-ak2gc3nz	264	3	,	,	,
cord-194157-ak2gc3nz	264	4	it	-PRON-	PRP
cord-194157-ak2gc3nz	264	5	suffices	suffice	VBZ
cord-194157-ak2gc3nz	264	6	to	to	TO
cord-194157-ak2gc3nz	264	7	show	show	VB
cord-194157-ak2gc3nz	264	8	that	that	DT
cord-194157-ak2gc3nz	264	9	.	.	.
cord-194157-ak2gc3nz	265	1	For	for	IN
cord-194157-ak2gc3nz	265	2	this	this	DT
cord-194157-ak2gc3nz	265	3	,	,	,
cord-194157-ak2gc3nz	265	4	it	-PRON-	PRP
cord-194157-ak2gc3nz	265	5	is	be	VBZ
cord-194157-ak2gc3nz	265	6	convenient	convenient	JJ
cord-194157-ak2gc3nz	265	7	to	to	TO
cord-194157-ak2gc3nz	265	8	consider	consider	VB
cord-194157-ak2gc3nz	265	9	the	the	DT
cord-194157-ak2gc3nz	265	10	event	event	NN
cord-194157-ak2gc3nz	266	1	A	a	DT
cord-194157-ak2gc3nz	266	2	t	t	NN
cord-194157-ak2gc3nz	266	3	0	0	CD
cord-194157-ak2gc3nz	266	4	=	=	NFP
cord-194157-ak2gc3nz	266	5	{	{	-LRB-
cord-194157-ak2gc3nz	266	6	e(I(t	e(I(t	VBZ
cord-194157-ak2gc3nz	266	7	0	0	NFP
cord-194157-ak2gc3nz	266	8	)	)	-RRB-
cord-194157-ak2gc3nz	266	9	,	,	,
cord-194157-ak2gc3nz	266	10	S(t	S(t	NNS
cord-194157-ak2gc3nz	266	11	0	0	CD
cord-194157-ak2gc3nz	266	12	)	)	-RRB-
cord-194157-ak2gc3nz	266	13	)	)	-RRB-
cord-194157-ak2gc3nz	267	1	>	>	XX
cord-194157-ak2gc3nz	268	1	0	0	LS
cord-194157-ak2gc3nz	268	2	}	}	-RRB-
cord-194157-ak2gc3nz	268	3	that	that	IN
cord-194157-ak2gc3nz	268	4	the	the	DT
cord-194157-ak2gc3nz	268	5	infection	infection	NN
cord-194157-ak2gc3nz	268	6	is	be	VBZ
cord-194157-ak2gc3nz	268	7	still	still	RB
cord-194157-ak2gc3nz	268	8	spreading	spread	VBG
cord-194157-ak2gc3nz	268	9	at	at	IN
cord-194157-ak2gc3nz	268	10	time	time	NN
cord-194157-ak2gc3nz	268	11	t	t	NN
cord-194157-ak2gc3nz	268	12	0	0	CD
cord-194157-ak2gc3nz	268	13	.	.	.
cord-194157-ak2gc3nz	269	1	Since	since	IN
cord-194157-ak2gc3nz	269	2	E	e	NN
cord-194157-ak2gc3nz	269	3	1	1	CD
cord-194157-ak2gc3nz	269	4	is	be	VBZ
cord-194157-ak2gc3nz	269	5	the	the	DT
cord-194157-ak2gc3nz	269	6	event	event	NN
cord-194157-ak2gc3nz	269	7	that	that	IN
cord-194157-ak2gc3nz	269	8	the	the	DT
cord-194157-ak2gc3nz	269	9	infection	infection	NN
cord-194157-ak2gc3nz	269	10	stays	stay	VBZ
cord-194157-ak2gc3nz	269	11	within	within	IN
cord-194157-ak2gc3nz	269	12	B(r	B(r	NNS
cord-194157-ak2gc3nz	269	13	)	)	-RRB-
cord-194157-ak2gc3nz	269	14	up	up	IN
cord-194157-ak2gc3nz	269	15	to	to	IN
cord-194157-ak2gc3nz	269	16	time	time	NN
cord-194157-ak2gc3nz	269	17	t	t	NNP
cord-194157-ak2gc3nz	269	18	1	1	CD
cord-194157-ak2gc3nz	269	19	(	(	-LRB-
cord-194157-ak2gc3nz	269	20	i.e.	i.e.	FW
cord-194157-ak2gc3nz	269	21	,	,	,
cord-194157-ak2gc3nz	269	22	after	after	IN
cord-194157-ak2gc3nz	269	23	t	t	NN
cord-194157-ak2gc3nz	269	24	0	0	CD
cord-194157-ak2gc3nz	269	25	)	)	-RRB-
cord-194157-ak2gc3nz	269	26	and	and	CC
cord-194157-ak2gc3nz	269	27	E	E	NNP
cord-194157-ak2gc3nz	269	28	∞	∞	NNP
cord-194157-ak2gc3nz	269	29	is	be	VBZ
cord-194157-ak2gc3nz	269	30	the	the	DT
cord-194157-ak2gc3nz	269	31	event	event	NN
cord-194157-ak2gc3nz	269	32	that	that	IN
cord-194157-ak2gc3nz	269	33	the	the	DT
cord-194157-ak2gc3nz	269	34	infection	infection	NN
cord-194157-ak2gc3nz	269	35	eventually	eventually	RB
cord-194157-ak2gc3nz	269	36	escapes	escape	VBZ
cord-194157-ak2gc3nz	269	37	B(r	B(r	NNS
cord-194157-ak2gc3nz	269	38	)	)	-RRB-
cord-194157-ak2gc3nz	269	39	,	,	,
cord-194157-ak2gc3nz	269	40	it	-PRON-	PRP
cord-194157-ak2gc3nz	269	41	follows	follow	VBZ
cord-194157-ak2gc3nz	269	42	that	that	IN
cord-194157-ak2gc3nz	269	43	Since	since	IN
cord-194157-ak2gc3nz	269	44	λ	λ	NN
cord-194157-ak2gc3nz	269	45	≥	≥	CD
cord-194157-ak2gc3nz	269	46	6µ	6µ	CD
cord-194157-ak2gc3nz	269	47	and	and	CC
cord-194157-ak2gc3nz	269	48	d	d	NN
cord-194157-ak2gc3nz	269	49	≥	≥	CD
cord-194157-ak2gc3nz	269	50	3	3	CD
cord-194157-ak2gc3nz	269	51	,	,	,
cord-194157-ak2gc3nz	269	52	we	-PRON-	PRP
cord-194157-ak2gc3nz	269	53	may	may	MD
cord-194157-ak2gc3nz	269	54	select	select	VB
cord-194157-ak2gc3nz	269	55	any	any	DT
cord-194157-ak2gc3nz	269	56	∈	∈	NN
cord-194157-ak2gc3nz	269	57	(	(	-LRB-
cord-194157-ak2gc3nz	269	58	2µ	2µ	NNP
cord-194157-ak2gc3nz	269	59	µ+λ	µ+λ	NNP
cord-194157-ak2gc3nz	269	60	,	,	,
cord-194157-ak2gc3nz	269	61	1	1	CD
cord-194157-ak2gc3nz	269	62	−	−	NN
cord-194157-ak2gc3nz	269	63	2	2	CD
cord-194157-ak2gc3nz	269	64	d	d	NN
cord-194157-ak2gc3nz	269	65	)	)	-RRB-
cord-194157-ak2gc3nz	269	66	;	;	:
cord-194157-ak2gc3nz	269	67	we	-PRON-	PRP
cord-194157-ak2gc3nz	269	68	will	will	MD
cord-194157-ak2gc3nz	269	69	refine	refine	VB
cord-194157-ak2gc3nz	269	70	our	-PRON-	PRP$
cord-194157-ak2gc3nz	269	71	choice	choice	NN
cord-194157-ak2gc3nz	269	72	later	later	RB
cord-194157-ak2gc3nz	269	73	.	.	.
cord-194157-ak2gc3nz	270	1	Defining	define	VBG
cord-194157-ak2gc3nz	270	2	B	b	NN
cord-194157-ak2gc3nz	270	3	t	t	NN
cord-194157-ak2gc3nz	270	4	0	0	CD
cord-194157-ak2gc3nz	270	5	:	:	:
cord-194157-ak2gc3nz	270	6	=	=	NFP
cord-194157-ak2gc3nz	270	7	{	{	-LRB-
cord-194157-ak2gc3nz	270	8	|R(t	|R(t	NNP
cord-194157-ak2gc3nz	270	9	0	0	CD
cord-194157-ak2gc3nz	270	10	)	)	-RRB-
cord-194157-ak2gc3nz	271	1	|	|	NNP
cord-194157-ak2gc3nz	272	1	<	<	XX
cord-194157-ak2gc3nz	272	2	|U	|U	.
cord-194157-ak2gc3nz	273	1	(	(	-LRB-
cord-194157-ak2gc3nz	273	2	t	t	NN
cord-194157-ak2gc3nz	273	3	0	0	CD
cord-194157-ak2gc3nz	273	4	)	)	-RRB-
cord-194157-ak2gc3nz	273	5	|	|	NFP
cord-194157-ak2gc3nz	273	6	}	}	-RRB-
cord-194157-ak2gc3nz	273	7	,	,	,
cord-194157-ak2gc3nz	273	8	we	-PRON-	PRP
cord-194157-ak2gc3nz	273	9	then	then	RB
cord-194157-ak2gc3nz	273	10	have	have	VBP
cord-194157-ak2gc3nz	273	11	We	-PRON-	PRP
cord-194157-ak2gc3nz	273	12	bound	bind	VBN
cord-194157-ak2gc3nz	273	13	the	the	DT
cord-194157-ak2gc3nz	273	14	first	first	JJ
cord-194157-ak2gc3nz	273	15	term	term	NN
cord-194157-ak2gc3nz	273	16	of	of	IN
cord-194157-ak2gc3nz	273	17	(	(	-LRB-
cord-194157-ak2gc3nz	273	18	9	9	CD
cord-194157-ak2gc3nz	273	19	)	)	-RRB-
cord-194157-ak2gc3nz	273	20	by	by	IN
cord-194157-ak2gc3nz	273	21	analyzing	analyze	VBG
cord-194157-ak2gc3nz	273	22	the	the	DT
cord-194157-ak2gc3nz	273	23	underlying	underlie	VBG
cord-194157-ak2gc3nz	273	24	discrete	discrete	JJ
cord-194157-ak2gc3nz	273	25	time	time	NN
cord-194157-ak2gc3nz	273	26	Markov	Markov	NNP
cord-194157-ak2gc3nz	273	27	chain	chain	NN
cord-194157-ak2gc3nz	273	28	:	:	:
cord-194157-ak2gc3nz	274	1	Almost	almost	RB
cord-194157-ak2gc3nz	274	2	surely	surely	RB
cord-194157-ak2gc3nz	274	3	,	,	,
cord-194157-ak2gc3nz	274	4	the	the	DT
cord-194157-ak2gc3nz	274	5	end	end	NN
cord-194157-ak2gc3nz	274	6	state	state	NN
cord-194157-ak2gc3nz	274	7	of	of	IN
cord-194157-ak2gc3nz	274	8	this	this	DT
cord-194157-ak2gc3nz	274	9	process	process	NN
cord-194157-ak2gc3nz	274	10	takes	take	VBZ
cord-194157-ak2gc3nz	274	11	the	the	DT
cord-194157-ak2gc3nz	274	12	form	form	NN
cord-194157-ak2gc3nz	274	13	(	(	-LRB-
cord-194157-ak2gc3nz	274	14	S	S	NNP
cord-194157-ak2gc3nz	274	15	,	,	,
cord-194157-ak2gc3nz	274	16	∅	∅	NNP
cord-194157-ak2gc3nz	274	17	,	,	,
cord-194157-ak2gc3nz	274	18	V	v	NN
cord-194157-ak2gc3nz	274	19	(	(	-LRB-
cord-194157-ak2gc3nz	274	20	G	g	NN
cord-194157-ak2gc3nz	274	21	)	)	-RRB-
cord-194157-ak2gc3nz	274	22	\	\	NNP
cord-194157-ak2gc3nz	274	23	S	S	NNP
cord-194157-ak2gc3nz	274	24	)	)	-RRB-
cord-194157-ak2gc3nz	274	25	.	.	.
cord-194157-ak2gc3nz	275	1	Importantly	importantly	RB
cord-194157-ak2gc3nz	275	2	,	,	,
cord-194157-ak2gc3nz	275	3	{	{	-LRB-
cord-194157-ak2gc3nz	275	4	M	m	NN
cord-194157-ak2gc3nz	275	5	n	n	NNP
cord-194157-ak2gc3nz	275	6	}	}	-RRB-
cord-194157-ak2gc3nz	275	7	n≥0	n≥0	NNP
cord-194157-ak2gc3nz	275	8	is	be	VBZ
cord-194157-ak2gc3nz	275	9	a	a	DT
cord-194157-ak2gc3nz	275	10	discrete	discrete	JJ
cord-194157-ak2gc3nz	275	11	time	time	NN
cord-194157-ak2gc3nz	275	12	Markov	Markov	NNP
cord-194157-ak2gc3nz	275	13	chain	chain	NN
cord-194157-ak2gc3nz	275	14	in	in	IN
cord-194157-ak2gc3nz	275	15	which	which	WDT
cord-194157-ak2gc3nz	275	16	,	,	,
cord-194157-ak2gc3nz	275	17	conditioned	condition	VBN
cord-194157-ak2gc3nz	275	18	on	on	IN
cord-194157-ak2gc3nz	275	19	M	M	NNP
cord-194157-ak2gc3nz	275	20	n	n	NNP
cord-194157-ak2gc3nz	275	21	,	,	,
cord-194157-ak2gc3nz	275	22	it	-PRON-	PRP
cord-194157-ak2gc3nz	275	23	holds	hold	VBZ
cord-194157-ak2gc3nz	275	24	that	that	IN
cord-194157-ak2gc3nz	275	25	R	r	NN
cord-194157-ak2gc3nz	275	26	n+1	n+1	NN
cord-194157-ak2gc3nz	275	27	strictly	strictly	RB
cord-194157-ak2gc3nz	275	28	contains	contain	VBZ
cord-194157-ak2gc3nz	275	29	R	R	NNP
cord-194157-ak2gc3nz	275	30	n	n	NN
cord-194157-ak2gc3nz	275	31	with	with	IN
cord-194157-ak2gc3nz	275	32	probability	probability	NN
cord-194157-ak2gc3nz	276	1	µ|I	µ|i	NN
cord-194157-ak2gc3nz	276	2	n	n	NN
cord-194157-ak2gc3nz	276	3	|	|	NNP
cord-194157-ak2gc3nz	276	4	λe(I	λe(I	NNP
cord-194157-ak2gc3nz	276	5	n	n	NNP
cord-194157-ak2gc3nz	276	6	,	,	,
cord-194157-ak2gc3nz	276	7	S	S	NNP
cord-194157-ak2gc3nz	276	8	n	n	NN
cord-194157-ak2gc3nz	276	9	)	)	-RRB-
cord-194157-ak2gc3nz	276	10	+	+	CC
cord-194157-ak2gc3nz	277	1	µ|I	µ|I	NNP
cord-194157-ak2gc3nz	277	2	n	n	NN
cord-194157-ak2gc3nz	277	3	|	|	NNP
cord-194157-ak2gc3nz	277	4	.	.	.
cord-194157-ak2gc3nz	278	1	We	-PRON-	PRP
cord-194157-ak2gc3nz	278	2	will	will	MD
cord-194157-ak2gc3nz	278	3	consider	consider	VB
cord-194157-ak2gc3nz	278	4	this	this	DT
cord-194157-ak2gc3nz	278	5	process	process	NN
cord-194157-ak2gc3nz	278	6	until	until	IN
cord-194157-ak2gc3nz	278	7	the	the	DT
cord-194157-ak2gc3nz	278	8	stopping	stop	VBG
cord-194157-ak2gc3nz	278	9	time	time	NN
cord-194157-ak2gc3nz	278	10	N	n	NN
cord-194157-ak2gc3nz	278	11	:	:	:
cord-194157-ak2gc3nz	278	12	=	=	NFP
cord-194157-ak2gc3nz	279	1	inf{n	inf{n	NNP
cord-194157-ak2gc3nz	279	2	:	:	:
cord-194157-ak2gc3nz	280	1	e(I	e(I	NNP
cord-194157-ak2gc3nz	280	2	n	n	NN
cord-194157-ak2gc3nz	280	3	,	,	,
cord-194157-ak2gc3nz	280	4	S	S	NNP
cord-194157-ak2gc3nz	280	5	n	n	NN
cord-194157-ak2gc3nz	280	6	)	)	-RRB-
cord-194157-ak2gc3nz	280	7	=	=	SYM
cord-194157-ak2gc3nz	280	8	0	0	CD
cord-194157-ak2gc3nz	280	9	}	}	-RRB-
cord-194157-ak2gc3nz	280	10	.	.	.
cord-194157-ak2gc3nz	281	1	Specifically	specifically	RB
cord-194157-ak2gc3nz	281	2	,	,	,
cord-194157-ak2gc3nz	281	3	for	for	IN
cord-194157-ak2gc3nz	281	4	each	each	DT
cord-194157-ak2gc3nz	281	5	n	n	NN
cord-194157-ak2gc3nz	281	6	∈	∈	NN
cord-194157-ak2gc3nz	281	7	{	{	-LRB-
cord-194157-ak2gc3nz	281	8	1	1	CD
cord-194157-ak2gc3nz	281	9	,	,	,
cord-194157-ak2gc3nz	281	10	.	.	.
cord-194157-ak2gc3nz	281	11	.	.	.
cord-194157-ak2gc3nz	281	12	.	.	.
cord-194157-ak2gc3nz	282	1	,	,	,
cord-194157-ak2gc3nz	282	2	N	n	LS
cord-194157-ak2gc3nz	282	3	}	}	-RRB-
cord-194157-ak2gc3nz	282	4	,	,	,
cord-194157-ak2gc3nz	282	5	let	let	VBD
cord-194157-ak2gc3nz	282	6	X	x	NN
cord-194157-ak2gc3nz	282	7	n	n	NNP
cord-194157-ak2gc3nz	282	8	indicate	indicate	VB
cord-194157-ak2gc3nz	282	9	whether	whether	IN
cord-194157-ak2gc3nz	282	10	the	the	DT
cord-194157-ak2gc3nz	282	11	nth	nth	NNP
cord-194157-ak2gc3nz	282	12	transition	transition	NN
cord-194157-ak2gc3nz	282	13	recovers	recover	VBZ
cord-194157-ak2gc3nz	282	14	a	a	DT
cord-194157-ak2gc3nz	282	15	vertex	vertex	NN
cord-194157-ak2gc3nz	282	16	,	,	,
cord-194157-ak2gc3nz	282	17	i.e.	i.e.	FW
cord-194157-ak2gc3nz	282	18	,	,	,
cord-194157-ak2gc3nz	282	19	R	r	NN
cord-194157-ak2gc3nz	282	20	n	n	NN
cord-194157-ak2gc3nz	282	21	strictly	strictly	RB
cord-194157-ak2gc3nz	282	22	contains	contain	VBZ
cord-194157-ak2gc3nz	282	23	R	r	NN
cord-194157-ak2gc3nz	282	24	n−1	n−1	NNS
cord-194157-ak2gc3nz	282	25	.	.	.
cord-194157-ak2gc3nz	283	1	For	for	IN
cord-194157-ak2gc3nz	283	2	each	each	DT
cord-194157-ak2gc3nz	283	3	n	n	NN
cord-194157-ak2gc3nz	283	4	>	>	XX
cord-194157-ak2gc3nz	283	5	N	n	CD
cord-194157-ak2gc3nz	283	6	,	,	,
cord-194157-ak2gc3nz	283	7	let	let	VB
cord-194157-ak2gc3nz	283	8	X	x	NN
cord-194157-ak2gc3nz	283	9	n	n	NN
cord-194157-ak2gc3nz	283	10	be	be	VB
cord-194157-ak2gc3nz	283	11	Bernoulli	Bernoulli	NNP
cord-194157-ak2gc3nz	283	12	with	with	IN
cord-194157-ak2gc3nz	283	13	success	success	NN
cord-194157-ak2gc3nz	283	14	probability	probability	NN
cord-194157-ak2gc3nz	283	15	µ	µ	NN
cord-194157-ak2gc3nz	283	16	µ+λ	µ+λ	NN
cord-194157-ak2gc3nz	283	17	,	,	,
cord-194157-ak2gc3nz	283	18	all	all	DT
cord-194157-ak2gc3nz	283	19	of	of	IN
cord-194157-ak2gc3nz	283	20	which	which	WDT
cord-194157-ak2gc3nz	283	21	are	be	VBP
cord-194157-ak2gc3nz	283	22	independent	independent	JJ
cord-194157-ak2gc3nz	283	23	of	of	IN
cord-194157-ak2gc3nz	283	24	each	each	DT
cord-194157-ak2gc3nz	283	25	other	other	JJ
cord-194157-ak2gc3nz	283	26	and	and	CC
cord-194157-ak2gc3nz	283	27	of	of	IN
cord-194157-ak2gc3nz	283	28	M	M	NNP
cord-194157-ak2gc3nz	283	29	N	N	NNP
cord-194157-ak2gc3nz	283	30	.	.	.
cord-194157-ak2gc3nz	284	1	Put	Put	NNP
cord-194157-ak2gc3nz	284	2	M	m	NN
cord-194157-ak2gc3nz	284	3	n	n	NN
cord-194157-ak2gc3nz	285	1	:	:	:
cord-194157-ak2gc3nz	285	2	=	=	SYM
cord-194157-ak2gc3nz	285	3	M	M	NNP
cord-194157-ak2gc3nz	285	4	min(n	min(n	NNP
cord-194157-ak2gc3nz	285	5	,	,	,
cord-194157-ak2gc3nz	285	6	N	N	NNP
cord-194157-ak2gc3nz	285	7	)	)	-RRB-
cord-194157-ak2gc3nz	285	8	.	.	.
cord-194157-ak2gc3nz	286	1	Let	let	VB
cord-194157-ak2gc3nz	286	2	P	p	NN
cord-194157-ak2gc3nz	286	3	n	n	CC
cord-194157-ak2gc3nz	286	4	denote	denote	VB
cord-194157-ak2gc3nz	286	5	the	the	DT
cord-194157-ak2gc3nz	286	6	(	(	-LRB-
cord-194157-ak2gc3nz	286	7	random	random	JJ
cord-194157-ak2gc3nz	286	8	)	)	-RRB-
cord-194157-ak2gc3nz	286	9	probability	probability	NN
cord-194157-ak2gc3nz	286	10	measure	measure	NN
cord-194157-ak2gc3nz	286	11	conditioned	condition	VBN
cord-194157-ak2gc3nz	286	12	on	on	IN
cord-194157-ak2gc3nz	286	13	the	the	DT
cord-194157-ak2gc3nz	286	14	state	state	NN
cord-194157-ak2gc3nz	286	15	history	history	NN
cord-194157-ak2gc3nz	286	16	{	{	-LRB-
cord-194157-ak2gc3nz	286	17	M	M	NNP
cord-194157-ak2gc3nz	286	18	j	j	NNP
cord-194157-ak2gc3nz	286	19	}	}	-RRB-
cord-194157-ak2gc3nz	286	20	n	n	CC
cord-194157-ak2gc3nz	286	21	j=0	j=0	NNS
cord-194157-ak2gc3nz	286	22	.	.	.
cord-194157-ak2gc3nz	287	1	Notice	notice	VB
cord-194157-ak2gc3nz	287	2	that	that	IN
cord-194157-ak2gc3nz	287	3	in	in	IN
cord-194157-ak2gc3nz	287	4	the	the	DT
cord-194157-ak2gc3nz	287	5	event	event	NN
cord-194157-ak2gc3nz	287	6	{	{	-LRB-
cord-194157-ak2gc3nz	287	7	n	n	NN
cord-194157-ak2gc3nz	287	8	<	<	XX
cord-194157-ak2gc3nz	287	9	N	N	NNP
cord-194157-ak2gc3nz	287	10	}	}	-RRB-
cord-194157-ak2gc3nz	287	11	,	,	,
cord-194157-ak2gc3nz	287	12	we	-PRON-	PRP
cord-194157-ak2gc3nz	287	13	have	have	VBP
cord-194157-ak2gc3nz	287	14	the	the	DT
cord-194157-ak2gc3nz	287	15	bound	bind	VBN
cord-194157-ak2gc3nz	287	16	P	p	NN
cord-194157-ak2gc3nz	287	17	n	n	NN
cord-194157-ak2gc3nz	287	18	{	{	-LRB-
cord-194157-ak2gc3nz	287	19	X	x	NN
cord-194157-ak2gc3nz	287	20	n+1	n+1	NN
cord-194157-ak2gc3nz	287	21	=	=	SYM
cord-194157-ak2gc3nz	287	22	1	1	CD
cord-194157-ak2gc3nz	287	23	}	}	-RRB-
cord-194157-ak2gc3nz	288	1	=	=	NFP
cord-194157-ak2gc3nz	289	1	P{X	P{X	NNP
cord-194157-ak2gc3nz	289	2	n+1	n+1	NN
cord-194157-ak2gc3nz	289	3	=	=	.
cord-194157-ak2gc3nz	290	1	1|M	1|M	NNP
cord-194157-ak2gc3nz	290	2	n	n	NNP
cord-194157-ak2gc3nz	290	3	}	}	-RRB-
cord-194157-ak2gc3nz	290	4	=	=	.
cord-194157-ak2gc3nz	291	1	µ|I	µ|i	NN
cord-194157-ak2gc3nz	292	1	n	n	NNP
cord-194157-ak2gc3nz	292	2	|	|	NNP
cord-194157-ak2gc3nz	292	3	λe(I	λe(I	NNP
cord-194157-ak2gc3nz	292	4	n	n	NNP
cord-194157-ak2gc3nz	292	5	,	,	,
cord-194157-ak2gc3nz	292	6	S	S	NNP
cord-194157-ak2gc3nz	292	7	n	n	NN
cord-194157-ak2gc3nz	292	8	)	)	-RRB-
cord-194157-ak2gc3nz	292	9	+	+	CC
cord-194157-ak2gc3nz	292	10	µ|I	µ|i	NN
cord-194157-ak2gc3nz	292	11	n	n	NN
cord-194157-ak2gc3nz	292	12	|	|	NNP
cord-194157-ak2gc3nz	292	13	≤	≤	NN
cord-194157-ak2gc3nz	292	14	µ	µ	NN
cord-194157-ak2gc3nz	292	15	µ	µ	NN
cord-194157-ak2gc3nz	292	16	+	+	CC
cord-194157-ak2gc3nz	292	17	λ	λ	NN
cord-194157-ak2gc3nz	292	18	almost	almost	RB
cord-194157-ak2gc3nz	292	19	surely	surely	RB
cord-194157-ak2gc3nz	292	20	.	.	.
cord-194157-ak2gc3nz	293	1	Meanwhile	meanwhile	RB
cord-194157-ak2gc3nz	293	2	,	,	,
cord-194157-ak2gc3nz	293	3	in	in	IN
cord-194157-ak2gc3nz	293	4	the	the	DT
cord-194157-ak2gc3nz	293	5	complementary	complementary	JJ
cord-194157-ak2gc3nz	293	6	event	event	NN
cord-194157-ak2gc3nz	293	7	{	{	-LRB-
cord-194157-ak2gc3nz	293	8	n	n	NNP
cord-194157-ak2gc3nz	293	9	≥	≥	NNP
cord-194157-ak2gc3nz	293	10	N	N	NNP
cord-194157-ak2gc3nz	293	11	}	}	-RRB-
cord-194157-ak2gc3nz	293	12	,	,	,
cord-194157-ak2gc3nz	293	13	X	X	NNP
cord-194157-ak2gc3nz	293	14	n+1	n+1	NN
cord-194157-ak2gc3nz	293	15	is	be	VBZ
cord-194157-ak2gc3nz	293	16	Bernoulli	Bernoulli	NNP
cord-194157-ak2gc3nz	293	17	with	with	IN
cord-194157-ak2gc3nz	293	18	success	success	NN
cord-194157-ak2gc3nz	293	19	probability	probability	NN
cord-194157-ak2gc3nz	293	20	λ	λ	NN
cord-194157-ak2gc3nz	293	21	µ+λ	µ+λ	NN
cord-194157-ak2gc3nz	293	22	and	and	CC
cord-194157-ak2gc3nz	293	23	independent	independent	NN
cord-194157-ak2gc3nz	293	24	of	of	IN
cord-194157-ak2gc3nz	293	25	M	M	NNP
cord-194157-ak2gc3nz	293	26	n	n	NNP
cord-194157-ak2gc3nz	293	27	,	,	,
cord-194157-ak2gc3nz	293	28	and	and	CC
cord-194157-ak2gc3nz	293	29	so	so	RB
cord-194157-ak2gc3nz	293	30	P	p	NN
cord-194157-ak2gc3nz	293	31	n	n	NN
cord-194157-ak2gc3nz	293	32	{	{	-LRB-
cord-194157-ak2gc3nz	293	33	X	x	NN
cord-194157-ak2gc3nz	293	34	n+1	n+1	NN
cord-194157-ak2gc3nz	293	35	=	=	SYM
cord-194157-ak2gc3nz	293	36	1	1	CD
cord-194157-ak2gc3nz	293	37	}	}	-RRB-
cord-194157-ak2gc3nz	294	1	=	=	NFP
cord-194157-ak2gc3nz	295	1	P{X	P{X	NNP
cord-194157-ak2gc3nz	295	2	n+1	n+1	NN
cord-194157-ak2gc3nz	295	3	=	=	.
cord-194157-ak2gc3nz	296	1	1|M	1|M	NNP
cord-194157-ak2gc3nz	296	2	n	n	NNP
cord-194157-ak2gc3nz	296	3	}	}	-RRB-
cord-194157-ak2gc3nz	296	4	=	=	.
cord-194157-ak2gc3nz	297	1	P{X	P{X	NNP
cord-194157-ak2gc3nz	298	1	n+1	n+1	NN
cord-194157-ak2gc3nz	298	2	=	=	.
cord-194157-ak2gc3nz	299	1	1	1	LS
cord-194157-ak2gc3nz	299	2	}	}	-RRB-
cord-194157-ak2gc3nz	299	3	=	=	.
cord-194157-ak2gc3nz	300	1	µ	µ	LS
cord-194157-ak2gc3nz	300	2	µ	µ	NN
cord-194157-ak2gc3nz	300	3	+	+	CC
cord-194157-ak2gc3nz	300	4	λ	λ	NN
cord-194157-ak2gc3nz	300	5	almost	almost	RB
cord-194157-ak2gc3nz	300	6	surely	surely	RB
cord-194157-ak2gc3nz	300	7	.	.	.
cord-194157-ak2gc3nz	301	1	Overall	overall	RB
cord-194157-ak2gc3nz	301	2	,	,	,
cord-194157-ak2gc3nz	301	3	P	p	NN
cord-194157-ak2gc3nz	301	4	n	n	NN
cord-194157-ak2gc3nz	301	5	{	{	-LRB-
cord-194157-ak2gc3nz	301	6	X	x	NN
cord-194157-ak2gc3nz	301	7	n+1	n+1	NN
cord-194157-ak2gc3nz	301	8	=	=	SYM
cord-194157-ak2gc3nz	301	9	1	1	CD
cord-194157-ak2gc3nz	301	10	}	}	-RRB-
cord-194157-ak2gc3nz	301	11	≤	≤	VBZ
cord-194157-ak2gc3nz	301	12	µ	µ	NN
cord-194157-ak2gc3nz	301	13	µ+λ	µ+λ	NN
cord-194157-ak2gc3nz	301	14	almost	almost	RB
cord-194157-ak2gc3nz	301	15	surely	surely	RB
cord-194157-ak2gc3nz	301	16	.	.	.
cord-194157-ak2gc3nz	302	1	Next	next	RB
cord-194157-ak2gc3nz	302	2	,	,	,
cord-194157-ak2gc3nz	302	3	let	let	VB
cord-194157-ak2gc3nz	302	4	J	J	NNP
cord-194157-ak2gc3nz	302	5	denote	denote	VB
cord-194157-ak2gc3nz	302	6	a	a	DT
cord-194157-ak2gc3nz	302	7	set	set	NN
cord-194157-ak2gc3nz	302	8	of	of	IN
cord-194157-ak2gc3nz	302	9	positive	positive	JJ
cord-194157-ak2gc3nz	302	10	integers	integer	NNS
cord-194157-ak2gc3nz	302	11	j	j	NNP
cord-194157-ak2gc3nz	302	12	1	1	CD
cord-194157-ak2gc3nz	302	13	<	<	XX
cord-194157-ak2gc3nz	302	14	·	·	NFP
cord-194157-ak2gc3nz	302	15	·	·	NFP
cord-194157-ak2gc3nz	302	16	·	·	NFP
cord-194157-ak2gc3nz	302	17	<	<	XX
cord-194157-ak2gc3nz	303	1	j	j	NNP
cord-194157-ak2gc3nz	303	2	m	m	NNP
cord-194157-ak2gc3nz	303	3	.	.	.
cord-194157-ak2gc3nz	304	1	Then	then	RB
cord-194157-ak2gc3nz	304	2	the	the	DT
cord-194157-ak2gc3nz	304	3	law	law	NN
cord-194157-ak2gc3nz	304	4	of	of	IN
cord-194157-ak2gc3nz	304	5	total	total	JJ
cord-194157-ak2gc3nz	304	6	probability	probability	NN
cord-194157-ak2gc3nz	304	7	gives	give	VBZ
cord-194157-ak2gc3nz	304	8	Next	Next	NNP
cord-194157-ak2gc3nz	304	9	,	,	,
cord-194157-ak2gc3nz	304	10	P	p	NN
cord-194157-ak2gc3nz	304	11	jm−1	jm−1	NNP
cord-194157-ak2gc3nz	305	1	{	{	-LRB-
cord-194157-ak2gc3nz	305	2	X	x	NN
cord-194157-ak2gc3nz	305	3	j	j	NN
cord-194157-ak2gc3nz	305	4	=	=	SYM
cord-194157-ak2gc3nz	305	5	1	1	CD
cord-194157-ak2gc3nz	305	6	∀j	∀j	NNP
cord-194157-ak2gc3nz	305	7	∈	∈	NNP
cord-194157-ak2gc3nz	305	8	J	J	NNP
cord-194157-ak2gc3nz	305	9	\	\	NNP
cord-194157-ak2gc3nz	305	10	{	{	-LRB-
cord-194157-ak2gc3nz	305	11	j	j	NNP
cord-194157-ak2gc3nz	305	12	m	m	NNP
cord-194157-ak2gc3nz	305	13	}	}	-RRB-
cord-194157-ak2gc3nz	305	14	}	}	-RRB-
cord-194157-ak2gc3nz	305	15	∈	∈	VB
cord-194157-ak2gc3nz	305	16	{	{	-LRB-
cord-194157-ak2gc3nz	305	17	0	0	CD
cord-194157-ak2gc3nz	305	18	,	,	,
cord-194157-ak2gc3nz	305	19	1	1	CD
cord-194157-ak2gc3nz	305	20	}	}	-RRB-
cord-194157-ak2gc3nz	305	21	,	,	,
cord-194157-ak2gc3nz	305	22	and	and	CC
cord-194157-ak2gc3nz	305	23	so	so	RB
cord-194157-ak2gc3nz	305	24	Take	take	VB
cord-194157-ak2gc3nz	305	25	expectations	expectation	NNS
cord-194157-ak2gc3nz	305	26	of	of	IN
cord-194157-ak2gc3nz	305	27	both	both	DT
cord-194157-ak2gc3nz	305	28	sides	side	NNS
cord-194157-ak2gc3nz	305	29	and	and	CC
cord-194157-ak2gc3nz	305	30	apply	apply	VBP
cord-194157-ak2gc3nz	305	31	induction	induction	NN
cord-194157-ak2gc3nz	305	32	to	to	TO
cord-194157-ak2gc3nz	305	33	get	get	VB
cord-194157-ak2gc3nz	305	34	Next	Next	NNP
cord-194157-ak2gc3nz	305	35	,	,	,
cord-194157-ak2gc3nz	305	36	let	let	VB
cord-194157-ak2gc3nz	305	37	N	n	CD
cord-194157-ak2gc3nz	305	38	0	0	CD
cord-194157-ak2gc3nz	305	39	denote	denote	VB
cord-194157-ak2gc3nz	305	40	the	the	DT
cord-194157-ak2gc3nz	305	41	number	number	NN
cord-194157-ak2gc3nz	305	42	of	of	IN
cord-194157-ak2gc3nz	305	43	transitions	transition	NNS
cord-194157-ak2gc3nz	305	44	that	that	WDT
cord-194157-ak2gc3nz	305	45	have	have	VBP
cord-194157-ak2gc3nz	305	46	occurred	occur	VBN
cord-194157-ak2gc3nz	305	47	by	by	IN
cord-194157-ak2gc3nz	305	48	time	time	NN
cord-194157-ak2gc3nz	305	49	t	t	NN
cord-194157-ak2gc3nz	305	50	0	0	CD
cord-194157-ak2gc3nz	305	51	.	.	.
cord-194157-ak2gc3nz	306	1	In	in	IN
cord-194157-ak2gc3nz	306	2	the	the	DT
cord-194157-ak2gc3nz	306	3	event	event	NN
cord-194157-ak2gc3nz	306	4	A	a	DT
cord-194157-ak2gc3nz	306	5	t	t	NN
cord-194157-ak2gc3nz	306	6	0	0	CD
cord-194157-ak2gc3nz	306	7	,	,	,
cord-194157-ak2gc3nz	306	8	it	-PRON-	PRP
cord-194157-ak2gc3nz	306	9	holds	hold	VBZ
cord-194157-ak2gc3nz	306	10	that	that	IN
cord-194157-ak2gc3nz	306	11	N	n	NN
cord-194157-ak2gc3nz	306	12	0	0	CD
cord-194157-ak2gc3nz	306	13	<	<	XX
cord-194157-ak2gc3nz	306	14	N	N	NNP
cord-194157-ak2gc3nz	306	15	,	,	,
cord-194157-ak2gc3nz	306	16	and	and	CC
cord-194157-ak2gc3nz	306	17	so	so	RB
cord-194157-ak2gc3nz	306	18	|R(t	|r(t	JJ
cord-194157-ak2gc3nz	306	19	0	0	NFP
cord-194157-ak2gc3nz	306	20	)	)	-RRB-
cord-194157-ak2gc3nz	307	1	|	|	NNP
cord-194157-ak2gc3nz	308	1	=	=	SYM
cord-194157-ak2gc3nz	308	2	N	n	NN
cord-194157-ak2gc3nz	308	3	0	0	CD
cord-194157-ak2gc3nz	309	1	j=1	j=1	NNP
cord-194157-ak2gc3nz	309	2	X	X	NNP
cord-194157-ak2gc3nz	309	3	j	j	NNP
cord-194157-ak2gc3nz	309	4	.	.	.
cord-194157-ak2gc3nz	310	1	Also	also	RB
cord-194157-ak2gc3nz	310	2	,	,	,
cord-194157-ak2gc3nz	310	3	we	-PRON-	PRP
cord-194157-ak2gc3nz	310	4	have	have	VBP
cord-194157-ak2gc3nz	310	5	N	n	CD
cord-194157-ak2gc3nz	310	6	0	0	CD
cord-194157-ak2gc3nz	310	7	≤	≤	NNP
cord-194157-ak2gc3nz	310	8	2|U	2|u	NN
cord-194157-ak2gc3nz	310	9	(	(	-LRB-
cord-194157-ak2gc3nz	310	10	t	t	NN
cord-194157-ak2gc3nz	310	11	0	0	CD
cord-194157-ak2gc3nz	310	12	)	)	-RRB-
cord-194157-ak2gc3nz	310	13	|	|	NNS
cord-194157-ak2gc3nz	310	14	.	.	.
cord-194157-ak2gc3nz	311	1	As	as	IN
cord-194157-ak2gc3nz	311	2	such	such	JJ
cord-194157-ak2gc3nz	311	3	,	,	,
cord-194157-ak2gc3nz	311	4	µ+λ	µ+λ	''
cord-194157-ak2gc3nz	311	5	.	.	.
cord-194157-ak2gc3nz	312	1	This	this	DT
cord-194157-ak2gc3nz	312	2	then	then	RB
cord-194157-ak2gc3nz	312	3	gives	give	VBZ
cord-194157-ak2gc3nz	312	4	Overall	Overall	NNP
cord-194157-ak2gc3nz	312	5	,	,	,
cord-194157-ak2gc3nz	313	1	Lemma	Lemma	NNP
cord-194157-ak2gc3nz	313	2	12	12	CD
cord-194157-ak2gc3nz	313	3	gives	give	VBZ
cord-194157-ak2gc3nz	313	4	that	that	IN
cord-194157-ak2gc3nz	313	5	the	the	DT
cord-194157-ak2gc3nz	313	6	first	first	JJ
cord-194157-ak2gc3nz	313	7	term	term	NN
cord-194157-ak2gc3nz	313	8	in	in	IN
cord-194157-ak2gc3nz	313	9	(	(	-LRB-
cord-194157-ak2gc3nz	313	10	9	9	CD
cord-194157-ak2gc3nz	313	11	)	)	-RRB-
cord-194157-ak2gc3nz	313	12	is	be	VBZ
cord-194157-ak2gc3nz	313	13	o(1	o(1	NNP
cord-194157-ak2gc3nz	313	14	)	)	-RRB-
cord-194157-ak2gc3nz	313	15	.	.	.
cord-194157-ak2gc3nz	314	1	It	-PRON-	PRP
cord-194157-ak2gc3nz	314	2	remains	remain	VBZ
cord-194157-ak2gc3nz	314	3	to	to	TO
cord-194157-ak2gc3nz	314	4	bound	bind	VBN
cord-194157-ak2gc3nz	314	5	to	to	IN
cord-194157-ak2gc3nz	314	6	second	second	JJ
cord-194157-ak2gc3nz	314	7	term	term	NN
cord-194157-ak2gc3nz	314	8	in	in	IN
cord-194157-ak2gc3nz	314	9	(	(	-LRB-
cord-194157-ak2gc3nz	314	10	9	9	CD
cord-194157-ak2gc3nz	314	11	)	)	-RRB-
cord-194157-ak2gc3nz	314	12	.	.	.
cord-194157-ak2gc3nz	315	1	To	to	TO
cord-194157-ak2gc3nz	315	2	do	do	VB
cord-194157-ak2gc3nz	315	3	so	so	RB
cord-194157-ak2gc3nz	315	4	,	,	,
cord-194157-ak2gc3nz	315	5	we	-PRON-	PRP
cord-194157-ak2gc3nz	315	6	restrict	restrict	VBP
cord-194157-ak2gc3nz	315	7	to	to	IN
cord-194157-ak2gc3nz	315	8	the	the	DT
cord-194157-ak2gc3nz	315	9	event	event	NN
cord-194157-ak2gc3nz	315	10	E	e	NN
cord-194157-ak2gc3nz	315	11	0	0	CD
cord-194157-ak2gc3nz	316	1	∩	∩	NN
cord-194157-ak2gc3nz	316	2	E	e	NN
cord-194157-ak2gc3nz	316	3	1	1	CD
cord-194157-ak2gc3nz	317	1	∩	∩	NN
cord-194157-ak2gc3nz	317	2	E	e	NN
cord-194157-ak2gc3nz	317	3	2	2	CD
cord-194157-ak2gc3nz	318	1	∩	∩	UH
cord-194157-ak2gc3nz	318	2	B	B	NNP
cord-194157-ak2gc3nz	318	3	t	t	NN
cord-194157-ak2gc3nz	318	4	0	0	CD
cord-194157-ak2gc3nz	318	5	and	and	CC
cord-194157-ak2gc3nz	318	6	argue	argue	VBP
cord-194157-ak2gc3nz	318	7	that	that	IN
cord-194157-ak2gc3nz	318	8	F	F	NNP
cord-194157-ak2gc3nz	318	9	occurs	occur	VBZ
cord-194157-ak2gc3nz	318	10	with	with	IN
cord-194157-ak2gc3nz	318	11	probability	probability	NN
cord-194157-ak2gc3nz	318	12	o(1	o(1	NNP
cord-194157-ak2gc3nz	318	13	)	)	-RRB-
cord-194157-ak2gc3nz	318	14	.	.	.
cord-194157-ak2gc3nz	319	1	We	-PRON-	PRP
cord-194157-ak2gc3nz	319	2	adopt	adopt	VBP
cord-194157-ak2gc3nz	319	3	the	the	DT
cord-194157-ak2gc3nz	319	4	notation	notation	NN
cord-194157-ak2gc3nz	319	5	from	from	IN
cord-194157-ak2gc3nz	319	6	Lemma	Lemma	NNP
cord-194157-ak2gc3nz	319	7	6	6	CD
cord-194157-ak2gc3nz	319	8	and	and	CC
cord-194157-ak2gc3nz	319	9	Algorithm	Algorithm	NNP
cord-194157-ak2gc3nz	319	10	1	1	CD
cord-194157-ak2gc3nz	319	11	.	.	.
cord-194157-ak2gc3nz	320	1	Since	since	IN
cord-194157-ak2gc3nz	320	2	B(r	B(r	NNS
cord-194157-ak2gc3nz	320	3	)	)	-RRB-
cord-194157-ak2gc3nz	320	4	is	be	VBZ
cord-194157-ak2gc3nz	320	5	a	a	DT
cord-194157-ak2gc3nz	320	6	tree	tree	NN
cord-194157-ak2gc3nz	320	7	,	,	,
cord-194157-ak2gc3nz	320	8	A	a	DT
cord-194157-ak2gc3nz	320	9	consists	consists	NN
cord-194157-ak2gc3nz	320	10	of	of	IN
cord-194157-ak2gc3nz	320	11	the	the	DT
cord-194157-ak2gc3nz	320	12	vertices	vertex	NNS
cord-194157-ak2gc3nz	320	13	in	in	IN
cord-194157-ak2gc3nz	320	14	U	U	NNP
cord-194157-ak2gc3nz	320	15	(	(	-LRB-
cord-194157-ak2gc3nz	320	16	t	t	NN
cord-194157-ak2gc3nz	320	17	0	0	CD
cord-194157-ak2gc3nz	320	18	)	)	-RRB-
cord-194157-ak2gc3nz	320	19	that	that	WDT
cord-194157-ak2gc3nz	320	20	have	have	VBP
cord-194157-ak2gc3nz	320	21	a	a	DT
cord-194157-ak2gc3nz	320	22	neighbor	neighbor	NN
cord-194157-ak2gc3nz	320	23	in	in	IN
cord-194157-ak2gc3nz	320	24	S(t	S(t	NNP
cord-194157-ak2gc3nz	320	25	0	0	CD
cord-194157-ak2gc3nz	320	26	)	)	-RRB-
cord-194157-ak2gc3nz	320	27	,	,	,
cord-194157-ak2gc3nz	320	28	while	while	IN
cord-194157-ak2gc3nz	320	29	A	a	DT
cord-194157-ak2gc3nz	320	30	I	i	NN
cord-194157-ak2gc3nz	320	31	=	=	NFP
cord-194157-ak2gc3nz	321	1	A	a	DT
cord-194157-ak2gc3nz	321	2	∩	∩	NN
cord-194157-ak2gc3nz	321	3	I(t	I(t	NNP
cord-194157-ak2gc3nz	321	4	0	0	CD
cord-194157-ak2gc3nz	321	5	)	)	-RRB-
cord-194157-ak2gc3nz	321	6	.	.	.
cord-194157-ak2gc3nz	322	1	For	for	IN
cord-194157-ak2gc3nz	322	2	every	every	DT
cord-194157-ak2gc3nz	322	3	a	a	DT
cord-194157-ak2gc3nz	322	4	∈	∈	NN
cord-194157-ak2gc3nz	322	5	A	a	NN
cord-194157-ak2gc3nz	322	6	\	\	NN
cord-194157-ak2gc3nz	322	7	A	a	NN
cord-194157-ak2gc3nz	322	8	I	i	NN
cord-194157-ak2gc3nz	322	9	⊆	⊆	NN
cord-194157-ak2gc3nz	322	10	R(t	r(t	NN
cord-194157-ak2gc3nz	322	11	0	0	CD
cord-194157-ak2gc3nz	322	12	)	)	-RRB-
cord-194157-ak2gc3nz	322	13	,	,	,
cord-194157-ak2gc3nz	322	14	since	since	IN
cord-194157-ak2gc3nz	322	15	a	a	DT
cord-194157-ak2gc3nz	322	16	can	can	MD
cord-194157-ak2gc3nz	322	17	not	not	RB
cord-194157-ak2gc3nz	322	18	infect	infect	VB
cord-194157-ak2gc3nz	322	19	b(a	b(a	NNP
cord-194157-ak2gc3nz	322	20	)	)	-RRB-
cord-194157-ak2gc3nz	322	21	,	,	,
cord-194157-ak2gc3nz	322	22	it	-PRON-	PRP
cord-194157-ak2gc3nz	322	23	holds	hold	VBZ
cord-194157-ak2gc3nz	322	24	that	that	IN
cord-194157-ak2gc3nz	322	25	Z	z	NN
cord-194157-ak2gc3nz	322	26	a	a	NN
cord-194157-ak2gc3nz	322	27	=	=	SYM
cord-194157-ak2gc3nz	322	28	τ	τ	NN
cord-194157-ak2gc3nz	322	29	.	.	.
cord-194157-ak2gc3nz	323	1	It	-PRON-	PRP
cord-194157-ak2gc3nz	323	2	follows	follow	VBZ
cord-194157-ak2gc3nz	323	3	that	that	IN
cord-194157-ak2gc3nz	323	4	Q	q	NN
cord-194157-ak2gc3nz	323	5	=	=	NN
cord-194157-ak2gc3nz	323	6	Q	Q	NNP
cord-194157-ak2gc3nz	323	7	I	I	NNP
cord-194157-ak2gc3nz	323	8	and	and	CC
cord-194157-ak2gc3nz	323	9	P	p	NN
cord-194157-ak2gc3nz	323	10	=	=	SYM
cord-194157-ak2gc3nz	323	11	|A	|a	CD
cord-194157-ak2gc3nz	324	1	I	-PRON-	PRP
cord-194157-ak2gc3nz	324	2	|	|	NNP
cord-194157-ak2gc3nz	325	1	|A|	|A|	NFP
cord-194157-ak2gc3nz	325	2	P	p	NN
cord-194157-ak2gc3nz	325	3	I	i	NN
cord-194157-ak2gc3nz	325	4	,	,	,
cord-194157-ak2gc3nz	325	5	and	and	CC
cord-194157-ak2gc3nz	325	6	sô	sô	DT
cord-194157-ak2gc3nz	325	7	λ	λ	NN
cord-194157-ak2gc3nz	325	8	λ	λ	NN
cord-194157-ak2gc3nz	325	9	I	i	NN
cord-194157-ak2gc3nz	325	10	=	=	NFP
cord-194157-ak2gc3nz	326	1	P	p	NN
cord-194157-ak2gc3nz	326	2	P	p	NN
cord-194157-ak2gc3nz	326	3	I	i	NN
cord-194157-ak2gc3nz	327	1	=	=	NFP
cord-194157-ak2gc3nz	328	1	|A	|a	CD
cord-194157-ak2gc3nz	329	1	I	-PRON-	PRP
cord-194157-ak2gc3nz	329	2	|	|	NNP
cord-194157-ak2gc3nz	329	3	|A|	|A|	NNP
cord-194157-ak2gc3nz	329	4	,	,	,
cord-194157-ak2gc3nz	330	1	μ	μ	NN
cord-194157-ak2gc3nz	331	1	µ	µ	UH
cord-194157-ak2gc3nz	331	2	I	i	NN
cord-194157-ak2gc3nz	331	3	=	=	SYM
cord-194157-ak2gc3nz	331	4	1	1	CD
cord-194157-ak2gc3nz	331	5	−	−	NN
cord-194157-ak2gc3nz	331	6	P	p	NN
cord-194157-ak2gc3nz	331	7	1	1	CD
cord-194157-ak2gc3nz	331	8	−	−	NN
cord-194157-ak2gc3nz	332	1	P	p	NN
cord-194157-ak2gc3nz	333	1	I	-PRON-	PRP
cord-194157-ak2gc3nz	333	2	=	=	VBZ
cord-194157-ak2gc3nz	333	3	1	1	CD
cord-194157-ak2gc3nz	333	4	−	−	NN
cord-194157-ak2gc3nz	333	5	|A	|a	CD
cord-194157-ak2gc3nz	334	1	I	-PRON-	PRP
cord-194157-ak2gc3nz	334	2	|	|	NNP
cord-194157-ak2gc3nz	334	3	|A|	|a|	XX
cord-194157-ak2gc3nz	335	1	P	p	NN
cord-194157-ak2gc3nz	336	1	I	-PRON-	PRP
cord-194157-ak2gc3nz	337	1	1	1	LS
cord-194157-ak2gc3nz	337	2	−	−	NN
cord-194157-ak2gc3nz	337	3	P	p	NN
cord-194157-ak2gc3nz	338	1	I	-PRON-	PRP
cord-194157-ak2gc3nz	338	2	=	=	NFP
cord-194157-ak2gc3nz	339	1	1	1	LS
cord-194157-ak2gc3nz	339	2	+	+	CC
cord-194157-ak2gc3nz	340	1	1	1	LS
cord-194157-ak2gc3nz	340	2	−	−	NN
cord-194157-ak2gc3nz	341	1	|A	|a	CD
cord-194157-ak2gc3nz	342	1	I	-PRON-	PRP
cord-194157-ak2gc3nz	342	2	|	|	NNP
cord-194157-ak2gc3nz	343	1	|A|	|a|	UH
cord-194157-ak2gc3nz	343	2	·	·	NFP
cord-194157-ak2gc3nz	343	3	P	p	NN
cord-194157-ak2gc3nz	344	1	I	-PRON-	PRP
cord-194157-ak2gc3nz	345	1	1	1	LS
cord-194157-ak2gc3nz	345	2	−	−	NN
cord-194157-ak2gc3nz	345	3	P	p	NN
cord-194157-ak2gc3nz	345	4	I	i	NN
cord-194157-ak2gc3nz	345	5	.	.	.
cord-194157-ak2gc3nz	346	1	As	as	IN
cord-194157-ak2gc3nz	346	2	such	such	JJ
cord-194157-ak2gc3nz	346	3	,	,	,
cord-194157-ak2gc3nz	346	4	λ	λ	NN
cord-194157-ak2gc3nz	346	5	λ	λ	NN
cord-194157-ak2gc3nz	346	6	I	i	NN
cord-194157-ak2gc3nz	346	7	≤	≤	NNP
cord-194157-ak2gc3nz	346	8	1	1	CD
cord-194157-ak2gc3nz	346	9	andμ	andμ	NNP
cord-194157-ak2gc3nz	346	10	µ	µ	NNP
cord-194157-ak2gc3nz	346	11	I	i	NN
cord-194157-ak2gc3nz	346	12	≥	≥	CD
cord-194157-ak2gc3nz	346	13	1	1	CD
cord-194157-ak2gc3nz	346	14	.	.	.
cord-194157-ak2gc3nz	347	1	To	to	TO
cord-194157-ak2gc3nz	347	2	obtain	obtain	VB
cord-194157-ak2gc3nz	347	3	bounds	bound	NNS
cord-194157-ak2gc3nz	347	4	in	in	IN
cord-194157-ak2gc3nz	347	5	the	the	DT
cord-194157-ak2gc3nz	347	6	other	other	JJ
cord-194157-ak2gc3nz	347	7	directions	direction	NNS
cord-194157-ak2gc3nz	347	8	,	,	,
cord-194157-ak2gc3nz	347	9	we	-PRON-	PRP
cord-194157-ak2gc3nz	347	10	require	require	VBP
cord-194157-ak2gc3nz	347	11	a	a	DT
cord-194157-ak2gc3nz	347	12	lemma	lemma	NN
cord-194157-ak2gc3nz	347	13	:	:	:
cord-194157-ak2gc3nz	347	14	 	 	_SP
cord-194157-ak2gc3nz	348	1	In	in	IN
cord-194157-ak2gc3nz	348	2	this	this	DT
cord-194157-ak2gc3nz	348	3	paper	paper	NN
cord-194157-ak2gc3nz	348	4	,	,	,
cord-194157-ak2gc3nz	348	5	we	-PRON-	PRP
cord-194157-ak2gc3nz	348	6	introduced	introduce	VBD
cord-194157-ak2gc3nz	348	7	a	a	DT
cord-194157-ak2gc3nz	348	8	simple	simple	JJ
cord-194157-ak2gc3nz	348	9	algorithm	algorithm	NN
cord-194157-ak2gc3nz	348	10	to	to	TO
cord-194157-ak2gc3nz	348	11	estimate	estimate	VB
cord-194157-ak2gc3nz	348	12	SIR	SIR	NNP
cord-194157-ak2gc3nz	348	13	parameters	parameter	NNS
cord-194157-ak2gc3nz	348	14	from	from	IN
cord-194157-ak2gc3nz	348	15	early	early	JJ
cord-194157-ak2gc3nz	348	16	infections	infection	NNS
cord-194157-ak2gc3nz	348	17	.	.	.
cord-194157-ak2gc3nz	349	1	There	there	EX
cord-194157-ak2gc3nz	349	2	are	be	VBP
cord-194157-ak2gc3nz	349	3	many	many	JJ
cord-194157-ak2gc3nz	349	4	interesting	interesting	JJ
cord-194157-ak2gc3nz	349	5	directions	direction	NNS
cord-194157-ak2gc3nz	349	6	for	for	IN
cord-194157-ak2gc3nz	349	7	future	future	JJ
cord-194157-ak2gc3nz	349	8	work	work	NN
cord-194157-ak2gc3nz	349	9	.	.	.
cord-194157-ak2gc3nz	350	1	First	first	RB
cord-194157-ak2gc3nz	350	2	,	,	,
cord-194157-ak2gc3nz	350	3	we	-PRON-	PRP
cord-194157-ak2gc3nz	350	4	do	do	VBP
cord-194157-ak2gc3nz	350	5	not	not	RB
cord-194157-ak2gc3nz	350	6	believe	believe	VB
cord-194157-ak2gc3nz	350	7	that	that	IN
cord-194157-ak2gc3nz	350	8	Theorem	theorem	NN
cord-194157-ak2gc3nz	350	9	7	7	CD
cord-194157-ak2gc3nz	350	10	captures	capture	VBZ
cord-194157-ak2gc3nz	350	11	the	the	DT
cord-194157-ak2gc3nz	350	12	true	true	JJ
cord-194157-ak2gc3nz	350	13	performance	performance	NN
cord-194157-ak2gc3nz	350	14	of	of	IN
cord-194157-ak2gc3nz	350	15	Algorithm	algorithm	NN
cord-194157-ak2gc3nz	350	16	1	1	CD
cord-194157-ak2gc3nz	350	17	,	,	,
cord-194157-ak2gc3nz	350	18	especially	especially	RB
cord-194157-ak2gc3nz	350	19	in	in	IN
cord-194157-ak2gc3nz	350	20	light	light	NN
cord-194157-ak2gc3nz	350	21	of	of	IN
cord-194157-ak2gc3nz	350	22	Figure	figure	NN
cord-194157-ak2gc3nz	350	23	1	1	CD
cord-194157-ak2gc3nz	350	24	,	,	,
cord-194157-ak2gc3nz	350	25	and	and	CC
cord-194157-ak2gc3nz	350	26	this	this	DT
cord-194157-ak2gc3nz	350	27	warrants	warrant	VBZ
cord-194157-ak2gc3nz	350	28	further	further	JJ
cord-194157-ak2gc3nz	350	29	investigation	investigation	NN
cord-194157-ak2gc3nz	350	30	.	.	.
cord-194157-ak2gc3nz	351	1	Next	next	RB
cord-194157-ak2gc3nz	351	2	,	,	,
cord-194157-ak2gc3nz	351	3	it	-PRON-	PRP
cord-194157-ak2gc3nz	351	4	would	would	MD
cord-194157-ak2gc3nz	351	5	be	be	VB
cord-194157-ak2gc3nz	351	6	interesting	interesting	JJ
cord-194157-ak2gc3nz	351	7	to	to	TO
cord-194157-ak2gc3nz	351	8	consider	consider	VB
cord-194157-ak2gc3nz	351	9	other	other	JJ
cord-194157-ak2gc3nz	351	10	types	type	NNS
cord-194157-ak2gc3nz	351	11	of	of	IN
cord-194157-ak2gc3nz	351	12	estimators	estimator	NNS
cord-194157-ak2gc3nz	351	13	.	.	.
cord-194157-ak2gc3nz	352	1	Notice	notice	VB
cord-194157-ak2gc3nz	352	2	that	that	IN
cord-194157-ak2gc3nz	352	3	since	since	IN
cord-194157-ak2gc3nz	352	4	Algorithm	algorithm	NN
cord-194157-ak2gc3nz	352	5	1	1	CD
cord-194157-ak2gc3nz	352	6	explicitly	explicitly	RB
cord-194157-ak2gc3nz	352	7	makes	make	VBZ
cord-194157-ak2gc3nz	352	8	use	use	NN
cord-194157-ak2gc3nz	352	9	of	of	IN
cord-194157-ak2gc3nz	352	10	certain	certain	JJ
cord-194157-ak2gc3nz	352	11	properties	property	NNS
cord-194157-ak2gc3nz	352	12	of	of	IN
cord-194157-ak2gc3nz	352	13	the	the	DT
cord-194157-ak2gc3nz	352	14	underlying	underlie	VBG
cord-194157-ak2gc3nz	352	15	graph	graph	NN
cord-194157-ak2gc3nz	352	16	,	,	,
cord-194157-ak2gc3nz	352	17	it	-PRON-	PRP
cord-194157-ak2gc3nz	352	18	is	be	VBZ
cord-194157-ak2gc3nz	352	19	clear	clear	JJ
cord-194157-ak2gc3nz	352	20	why	why	WRB
cord-194157-ak2gc3nz	352	21	it	-PRON-	PRP
cord-194157-ak2gc3nz	352	22	fails	fail	VBZ
cord-194157-ak2gc3nz	352	23	for	for	IN
cord-194157-ak2gc3nz	352	24	the	the	DT
cord-194157-ak2gc3nz	352	25	complete	complete	JJ
cord-194157-ak2gc3nz	352	26	graph	graph	NN
cord-194157-ak2gc3nz	352	27	.	.	.
cord-194157-ak2gc3nz	353	1	Does	do	VBZ
cord-194157-ak2gc3nz	353	2	the	the	DT
cord-194157-ak2gc3nz	353	3	behavior	behavior	NN
cord-194157-ak2gc3nz	353	4	of	of	IN
cord-194157-ak2gc3nz	353	5	the	the	DT
cord-194157-ak2gc3nz	353	6	maximum	maximum	JJ
cord-194157-ak2gc3nz	353	7	likelihood	likelihood	NN
cord-194157-ak2gc3nz	353	8	estimator	estimator	NN
cord-194157-ak2gc3nz	353	9	have	have	VBP
cord-194157-ak2gc3nz	353	10	a	a	DT
cord-194157-ak2gc3nz	353	11	similarly	similarly	RB
cord-194157-ak2gc3nz	353	12	transparent	transparent	JJ
cord-194157-ak2gc3nz	353	13	dependence	dependence	NN
cord-194157-ak2gc3nz	353	14	on	on	IN
cord-194157-ak2gc3nz	353	15	the	the	DT
cord-194157-ak2gc3nz	353	16	underlying	underlie	VBG
cord-194157-ak2gc3nz	353	17	graph	graph	NN
cord-194157-ak2gc3nz	353	18	?	?	.
cord-194157-ak2gc3nz	354	1	We	-PRON-	PRP
cord-194157-ak2gc3nz	354	2	focused	focus	VBD
cord-194157-ak2gc3nz	354	3	on	on	IN
cord-194157-ak2gc3nz	354	4	locally	locally	RB
cord-194157-ak2gc3nz	354	5	tree	tree	NN
cord-194157-ak2gc3nz	354	6	-	-	HYPH
cord-194157-ak2gc3nz	354	7	like	like	JJ
cord-194157-ak2gc3nz	354	8	graphs	graph	NNS
cord-194157-ak2gc3nz	354	9	in	in	IN
cord-194157-ak2gc3nz	354	10	part	part	NN
cord-194157-ak2gc3nz	354	11	because	because	IN
cord-194157-ak2gc3nz	354	12	there	there	EX
cord-194157-ak2gc3nz	354	13	is	be	VBZ
cord-194157-ak2gc3nz	354	14	a	a	DT
cord-194157-ak2gc3nz	354	15	rich	rich	JJ
cord-194157-ak2gc3nz	354	16	literature	literature	NN
cord-194157-ak2gc3nz	354	17	on	on	IN
cord-194157-ak2gc3nz	354	18	SIR	SIR	NNP
cord-194157-ak2gc3nz	354	19	dynamics	dynamic	NNS
cord-194157-ak2gc3nz	354	20	over	over	IN
cord-194157-ak2gc3nz	354	21	infinite	infinite	JJ
cord-194157-ak2gc3nz	354	22	trees	tree	NNS
cord-194157-ak2gc3nz	354	23	,	,	,
cord-194157-ak2gc3nz	354	24	but	but	CC
cord-194157-ak2gc3nz	354	25	it	-PRON-	PRP
cord-194157-ak2gc3nz	354	26	would	would	MD
cord-194157-ak2gc3nz	354	27	be	be	VB
cord-194157-ak2gc3nz	354	28	interesting	interesting	JJ
cord-194157-ak2gc3nz	354	29	to	to	TO
cord-194157-ak2gc3nz	354	30	analyze	analyze	VB
cord-194157-ak2gc3nz	354	31	the	the	DT
cord-194157-ak2gc3nz	354	32	performance	performance	NN
cord-194157-ak2gc3nz	354	33	of	of	IN
cord-194157-ak2gc3nz	354	34	Algorithm	Algorithm	NNP
cord-194157-ak2gc3nz	354	35	1	1	CD
cord-194157-ak2gc3nz	354	36	on	on	IN
cord-194157-ak2gc3nz	354	37	other	other	JJ
cord-194157-ak2gc3nz	354	38	graph	graph	NN
cord-194157-ak2gc3nz	354	39	families	family	NNS
cord-194157-ak2gc3nz	354	40	.	.	.
cord-194157-ak2gc3nz	355	1	Also	also	RB
cord-194157-ak2gc3nz	355	2	,	,	,
cord-194157-ak2gc3nz	355	3	there	there	EX
cord-194157-ak2gc3nz	355	4	is	be	VBZ
cord-194157-ak2gc3nz	355	5	a	a	DT
cord-194157-ak2gc3nz	355	6	multitude	multitude	NN
cord-194157-ak2gc3nz	355	7	of	of	IN
cord-194157-ak2gc3nz	355	8	compartmental	compartmental	JJ
cord-194157-ak2gc3nz	355	9	models	model	NNS
cord-194157-ak2gc3nz	355	10	for	for	IN
cord-194157-ak2gc3nz	355	11	epidemics	epidemic	NNS
cord-194157-ak2gc3nz	355	12	with	with	IN
cord-194157-ak2gc3nz	355	13	various	various	JJ
cord-194157-ak2gc3nz	355	14	choices	choice	NNS
cord-194157-ak2gc3nz	355	15	of	of	IN
cord-194157-ak2gc3nz	355	16	probability	probability	NN
cord-194157-ak2gc3nz	355	17	distributions	distribution	NNS
cord-194157-ak2gc3nz	355	18	for	for	IN
cord-194157-ak2gc3nz	355	19	transition	transition	NN
cord-194157-ak2gc3nz	355	20	times	time	NNS
cord-194157-ak2gc3nz	355	21	between	between	IN
cord-194157-ak2gc3nz	355	22	compartments	compartment	NNS
cord-194157-ak2gc3nz	355	23	.	.	.
cord-194157-ak2gc3nz	356	1	Finally	finally	RB
cord-194157-ak2gc3nz	356	2	,	,	,
cord-194157-ak2gc3nz	356	3	one	one	PRP
cord-194157-ak2gc3nz	356	4	might	may	MD
cord-194157-ak2gc3nz	356	5	consider	consider	VB
cord-194157-ak2gc3nz	356	6	alternative	alternative	JJ
cord-194157-ak2gc3nz	356	7	models	model	NNS
cord-194157-ak2gc3nz	356	8	for	for	IN
cord-194157-ak2gc3nz	356	9	what	what	WDT
cord-194157-ak2gc3nz	356	10	data	data	NN
cord-194157-ak2gc3nz	356	11	is	be	VBZ
cord-194157-ak2gc3nz	356	12	available	available	JJ
cord-194157-ak2gc3nz	356	13	.	.	.
cord-194157-ak2gc3nz	357	1	For	for	IN
cord-194157-ak2gc3nz	357	2	example	example	NN
cord-194157-ak2gc3nz	357	3	,	,	,
cord-194157-ak2gc3nz	357	4	to	to	TO
cord-194157-ak2gc3nz	357	5	model	model	VB
cord-194157-ak2gc3nz	357	6	asymptomatic	asymptomatic	JJ
cord-194157-ak2gc3nz	357	7	infections	infection	NNS
cord-194157-ak2gc3nz	357	8	,	,	,
cord-194157-ak2gc3nz	357	9	one	one	PRP
cord-194157-ak2gc3nz	357	10	might	may	MD
cord-194157-ak2gc3nz	357	11	assume	assume	VB
cord-194157-ak2gc3nz	357	12	that	that	IN
cord-194157-ak2gc3nz	357	13	a	a	DT
cord-194157-ak2gc3nz	357	14	random	random	JJ
cord-194157-ak2gc3nz	357	15	fraction	fraction	NN
cord-194157-ak2gc3nz	357	16	of	of	IN
cord-194157-ak2gc3nz	357	17	infected	infected	JJ
cord-194157-ak2gc3nz	357	18	vertices	vertex	NNS
cord-194157-ak2gc3nz	357	19	are	be	VBP
cord-194157-ak2gc3nz	357	20	not	not	RB
cord-194157-ak2gc3nz	357	21	known	know	VBN
cord-194157-ak2gc3nz	357	22	to	to	TO
cord-194157-ak2gc3nz	357	23	be	be	VB
cord-194157-ak2gc3nz	357	24	infected	infect	VBN
cord-194157-ak2gc3nz	357	25	.	.	.
cord-194157-ak2gc3nz	358	1	The	the	DT
cord-194157-ak2gc3nz	358	2	simple	simple	JJ
cord-194157-ak2gc3nz	358	3	Galton	Galton	NNP
cord-194157-ak2gc3nz	358	4	-	-	HYPH
cord-194157-ak2gc3nz	358	5	Watson	Watson	NNP
cord-194157-ak2gc3nz	358	6	process	process	NN
cord-194157-ak2gc3nz	358	7	:	:	:
cord-194157-ak2gc3nz	358	8	Classical	classical	JJ
cord-194157-ak2gc3nz	358	9	approach	approach	NN
cord-194157-ak2gc3nz	358	10	Local	Local	NNP
cord-194157-ak2gc3nz	358	11	Kesten	Kesten	NNP
cord-194157-ak2gc3nz	358	12	-	-	HYPH
cord-194157-ak2gc3nz	358	13	McKay	McKay	NNP
cord-194157-ak2gc3nz	358	14	law	law	NN
cord-194157-ak2gc3nz	358	15	for	for	IN
cord-194157-ak2gc3nz	358	16	random	random	JJ
cord-194157-ak2gc3nz	358	17	regular	regular	JJ
cord-194157-ak2gc3nz	358	18	graphs	graph	NNS
cord-194157-ak2gc3nz	359	1	The	the	DT
cord-194157-ak2gc3nz	359	2	first	first	JJ
cord-194157-ak2gc3nz	359	3	birth	birth	NN
cord-194157-ak2gc3nz	359	4	problem	problem	NN
cord-194157-ak2gc3nz	359	5	for	for	IN
cord-194157-ak2gc3nz	359	6	an	an	DT
cord-194157-ak2gc3nz	359	7	age	age	NN
cord-194157-ak2gc3nz	359	8	-	-	HYPH
cord-194157-ak2gc3nz	359	9	dependent	dependent	JJ
cord-194157-ak2gc3nz	359	10	branching	branching	NN
cord-194157-ak2gc3nz	359	11	process	process	NN
cord-194157-ak2gc3nz	360	1	A	a	DT
cord-194157-ak2gc3nz	360	2	Contribution	contribution	NN
cord-194157-ak2gc3nz	360	3	to	to	IN
cord-194157-ak2gc3nz	360	4	the	the	DT
cord-194157-ak2gc3nz	360	5	Mathematical	Mathematical	NNP
cord-194157-ak2gc3nz	360	6	Theory	Theory	NNP
cord-194157-ak2gc3nz	360	7	of	of	IN
cord-194157-ak2gc3nz	360	8	Epidemics	Epidemics	NNPS
cord-194157-ak2gc3nz	360	9	Limit	limit	VBP
cord-194157-ak2gc3nz	360	10	theorems	theorem	NNS
cord-194157-ak2gc3nz	360	11	for	for	IN
cord-194157-ak2gc3nz	360	12	sequences	sequence	NNS
cord-194157-ak2gc3nz	360	13	of	of	IN
cord-194157-ak2gc3nz	360	14	jump	jump	NN
cord-194157-ak2gc3nz	360	15	Markov	Markov	NNP
cord-194157-ak2gc3nz	360	16	processes	process	VBZ
cord-194157-ak2gc3nz	360	17	Early	early	JJ
cord-194157-ak2gc3nz	360	18	transmission	transmission	NN
cord-194157-ak2gc3nz	360	19	dynamics	dynamic	NNS
cord-194157-ak2gc3nz	360	20	in	in	IN
cord-194157-ak2gc3nz	360	21	Wuhan	Wuhan	NNP
cord-194157-ak2gc3nz	360	22	,	,	,
cord-194157-ak2gc3nz	360	23	China	China	NNP
cord-194157-ak2gc3nz	360	24	,	,	,
cord-194157-ak2gc3nz	360	25	of	of	IN
cord-194157-ak2gc3nz	360	26	novel	novel	JJ
cord-194157-ak2gc3nz	360	27	coronavirusinfected	coronavirusinfecte	VBN
cord-194157-ak2gc3nz	360	28	pneumonia	pneumonia	NN
cord-194157-ak2gc3nz	360	29	High	High	NNP
cord-194157-ak2gc3nz	360	30	-	-	HYPH
cord-194157-ak2gc3nz	360	31	dimensional	dimensional	JJ
cord-194157-ak2gc3nz	360	32	probability	probability	NN
cord-194157-ak2gc3nz	360	33	:	:	:
cord-194157-ak2gc3nz	360	34	An	an	DT
cord-194157-ak2gc3nz	360	35	introduction	introduction	NN
cord-194157-ak2gc3nz	360	36	with	with	IN
cord-194157-ak2gc3nz	360	37	applications	application	NNS
cord-194157-ak2gc3nz	360	38	in	in	IN
cord-194157-ak2gc3nz	360	39	data	datum	NNS
cord-194157-ak2gc3nz	360	40	science	science	NN
cord-194157-ak2gc3nz	361	1	The	the	DT
cord-194157-ak2gc3nz	361	2	authors	author	NNS
cord-194157-ak2gc3nz	361	3	thank	thank	VBP
cord-194157-ak2gc3nz	361	4	Boris	Boris	NNP
cord-194157-ak2gc3nz	361	5	Alexeev	Alexeev	NNP
cord-194157-ak2gc3nz	361	6	for	for	IN
cord-194157-ak2gc3nz	361	7	interesting	interesting	JJ
cord-194157-ak2gc3nz	361	8	discussions	discussion	NNS
cord-194157-ak2gc3nz	361	9	that	that	WDT
cord-194157-ak2gc3nz	361	10	inspired	inspire	VBD
cord-194157-ak2gc3nz	361	11	this	this	DT
cord-194157-ak2gc3nz	361	12	work	work	NN
cord-194157-ak2gc3nz	361	13	.	.	.
cord-194157-ak2gc3nz	362	1	DGM	DGM	NNP
cord-194157-ak2gc3nz	362	2	was	be	VBD
cord-194157-ak2gc3nz	362	3	partially	partially	RB
cord-194157-ak2gc3nz	362	4	supported	support	VBN
cord-194157-ak2gc3nz	362	5	by	by	IN
cord-194157-ak2gc3nz	362	6	AFOSR	AFOSR	NNP
cord-194157-ak2gc3nz	362	7	FA9550	FA9550	NNP
cord-194157-ak2gc3nz	362	8	-	-	HYPH
cord-194157-ak2gc3nz	362	9	18	18	CD
cord-194157-ak2gc3nz	362	10	-	-	HYPH
cord-194157-ak2gc3nz	362	11	1	1	CD
cord-194157-ak2gc3nz	362	12	-	-	HYPH
cord-194157-ak2gc3nz	362	13	0107	0107	CD
cord-194157-ak2gc3nz	362	14	and	and	CC
cord-194157-ak2gc3nz	362	15	NSF	NSF	NNP
cord-194157-ak2gc3nz	362	16	DMS	DMS	NNP
cord-194157-ak2gc3nz	362	17	1829955	1829955	CD
cord-194157-ak2gc3nz	362	18	.	.	.
cord-194157-ak2gc3nz	363	1	Since	since	IN
cord-194157-ak2gc3nz	363	2	U	U	NNP
cord-194157-ak2gc3nz	363	3	(	(	-LRB-
cord-194157-ak2gc3nz	363	4	t	t	NN
cord-194157-ak2gc3nz	363	5	0	0	CD
cord-194157-ak2gc3nz	363	6	)	)	-RRB-
cord-194157-ak2gc3nz	363	7	induces	induce	VBZ
cord-194157-ak2gc3nz	363	8	a	a	DT
cord-194157-ak2gc3nz	363	9	subtree	subtree	NN
cord-194157-ak2gc3nz	363	10	of	of	IN
cord-194157-ak2gc3nz	363	11	G	g	NN
cord-194157-ak2gc3nz	363	12	,	,	,
cord-194157-ak2gc3nz	363	13	Lemma	Lemma	NNP
cord-194157-ak2gc3nz	363	14	13	13	CD
cord-194157-ak2gc3nz	363	15	gives	give	VBZ
cord-194157-ak2gc3nz	363	16	that	that	DT
cord-194157-ak2gc3nz	363	17	|A|	|A|	NNP
cord-194157-ak2gc3nz	363	18	≥	≥	NN
cord-194157-ak2gc3nz	363	19	(	(	-LRB-
cord-194157-ak2gc3nz	363	20	1	1	CD
cord-194157-ak2gc3nz	363	21	−	−	NN
cord-194157-ak2gc3nz	363	22	2	2	CD
cord-194157-ak2gc3nz	363	23	d	d	NN
cord-194157-ak2gc3nz	363	24	)	)	-RRB-
cord-194157-ak2gc3nz	364	1	|U	|U	.
cord-194157-ak2gc3nz	365	1	(	(	-LRB-
cord-194157-ak2gc3nz	365	2	t	t	NN
cord-194157-ak2gc3nz	365	3	0	0	CD
cord-194157-ak2gc3nz	365	4	)	)	-RRB-
cord-194157-ak2gc3nz	365	5	|	|	NNP
cord-194157-ak2gc3nz	365	6	,	,	,
cord-194157-ak2gc3nz	365	7	and	and	CC
cord-194157-ak2gc3nz	365	8	sowhere	sowhere	NNP
cord-194157-ak2gc3nz	365	9	the	the	DT
cord-194157-ak2gc3nz	365	10	last	last	JJ
cord-194157-ak2gc3nz	365	11	two	two	CD
cord-194157-ak2gc3nz	365	12	steps	step	NNS
cord-194157-ak2gc3nz	365	13	use	use	VBP
cord-194157-ak2gc3nz	365	14	the	the	DT
cord-194157-ak2gc3nz	365	15	fact	fact	NN
cord-194157-ak2gc3nz	365	16	that	that	IN
cord-194157-ak2gc3nz	365	17	d	d	NNP
cord-194157-ak2gc3nz	365	18	≥	≥	CD
cord-194157-ak2gc3nz	365	19	3	3	CD
cord-194157-ak2gc3nz	365	20	and	and	CC
cord-194157-ak2gc3nz	365	21	the	the	DT
cord-194157-ak2gc3nz	365	22	choice	choice	NN
cord-194157-ak2gc3nz	365	23	=	=	,
cord-194157-ak2gc3nz	365	24	(	(	-LRB-
cord-194157-ak2gc3nz	365	25	1	1	CD
cord-194157-ak2gc3nz	365	26	+	+	SYM
cord-194157-ak2gc3nz	365	27	0	0	CD
cord-194157-ak2gc3nz	365	28	)	)	-RRB-
cord-194157-ak2gc3nz	365	29	2µ	2µ	CD
cord-194157-ak2gc3nz	366	1	µ+λ	µ+λ	VB
cord-194157-ak2gc3nz	366	2	for	for	IN
cord-194157-ak2gc3nz	366	3	some	some	DT
cord-194157-ak2gc3nz	366	4	small	small	JJ
cord-194157-ak2gc3nz	366	5	0	0	CD
cord-194157-ak2gc3nz	366	6	>	>	XX
cord-194157-ak2gc3nz	366	7	0	0	NFP
cord-194157-ak2gc3nz	366	8	.	.	.
cord-194157-ak2gc3nz	367	1	It	-PRON-	PRP
cord-194157-ak2gc3nz	367	2	follows	follow	VBZ
cord-194157-ak2gc3nz	367	3	thatwhere	thatwhere	RB
cord-194157-ak2gc3nz	367	4	the	the	DT
cord-194157-ak2gc3nz	367	5	last	last	JJ
cord-194157-ak2gc3nz	367	6	two	two	CD
cord-194157-ak2gc3nz	367	7	steps	step	NNS
cord-194157-ak2gc3nz	367	8	use	use	VBP
cord-194157-ak2gc3nz	367	9	the	the	DT
cord-194157-ak2gc3nz	367	10	facts	fact	NNS
cord-194157-ak2gc3nz	367	11	that	that	WDT
cord-194157-ak2gc3nz	367	12	λ	λ	NN
cord-194157-ak2gc3nz	367	13	≥	≥	CD
cord-194157-ak2gc3nz	367	14	6µ	6µ	CD
cord-194157-ak2gc3nz	367	15	and	and	CC
cord-194157-ak2gc3nz	367	16	0	0	NFP
cord-194157-ak2gc3nz	367	17	is	be	VBZ
cord-194157-ak2gc3nz	367	18	small	small	JJ
cord-194157-ak2gc3nz	367	19	.	.	.
cord-194157-ak2gc3nz	368	1	Next	next	RB
cord-194157-ak2gc3nz	368	2	,	,	,
cord-194157-ak2gc3nz	368	3	considerSincek	considerSincek	NNP
cord-194157-ak2gc3nz	368	4	and	and	CC
cord-194157-ak2gc3nz	368	5	τ	τ	NN
cord-194157-ak2gc3nz	368	6	both	both	DT
cord-194157-ak2gc3nz	368	7	increase	increase	VBP
cord-194157-ak2gc3nz	368	8	with	with	IN
cord-194157-ak2gc3nz	368	9	factors	factor	NNS
cord-194157-ak2gc3nz	368	10	of	of	IN
cord-194157-ak2gc3nz	368	11	log	log	NN
cord-194157-ak2gc3nz	368	12	n	n	NN
cord-194157-ak2gc3nz	368	13	,	,	,
cord-194157-ak2gc3nz	368	14	Lemma	Lemma	NNP
cord-194157-ak2gc3nz	368	15	6	6	CD
cord-194157-ak2gc3nz	368	16	implies	imply	VBZ
cord-194157-ak2gc3nz	368	17	that	that	DT
cord-194157-ak2gc3nz	369	1	(	(	-LRB-
cord-194157-ak2gc3nz	369	2	λ	λ	NN
cord-194157-ak2gc3nz	369	3	I	-PRON-	PRP
cord-194157-ak2gc3nz	369	4	,	,	,
cord-194157-ak2gc3nz	369	5	μ	μ	NN
cord-194157-ak2gc3nz	369	6	I	i	NN
cord-194157-ak2gc3nz	369	7	)	)	-RRB-
cord-194157-ak2gc3nz	369	8	converges	converge	VBZ
cord-194157-ak2gc3nz	369	9	to	to	IN
cord-194157-ak2gc3nz	369	10	(	(	-LRB-
cord-194157-ak2gc3nz	369	11	λ	λ	NN
cord-194157-ak2gc3nz	369	12	,	,	,
cord-194157-ak2gc3nz	369	13	µ	µ	NN
cord-194157-ak2gc3nz	369	14	)	)	-RRB-
cord-194157-ak2gc3nz	369	15	in	in	IN
cord-194157-ak2gc3nz	369	16	probability	probability	NN
cord-194157-ak2gc3nz	369	17	.	.	.
cord-194157-ak2gc3nz	370	1	As	as	IN
cord-194157-ak2gc3nz	370	2	such	such	JJ
cord-194157-ak2gc3nz	370	3	,	,	,
cord-194157-ak2gc3nz	370	4	where	where	WRB
cord-194157-ak2gc3nz	370	5	the	the	DT
cord-194157-ak2gc3nz	370	6	last	last	JJ
cord-194157-ak2gc3nz	370	7	step	step	NN
cord-194157-ak2gc3nz	370	8	holds	hold	VBZ
cord-194157-ak2gc3nz	370	9	when	when	WRB
cord-194157-ak2gc3nz	370	10	n	n	NN
cord-194157-ak2gc3nz	370	11	is	be	VBZ
cord-194157-ak2gc3nz	370	12	large	large	JJ
cord-194157-ak2gc3nz	370	13	.	.	.
cord-194157-ak2gc3nz	371	1	The	the	DT
cord-194157-ak2gc3nz	371	2	result	result	NN
cord-194157-ak2gc3nz	371	3	then	then	RB
cord-194157-ak2gc3nz	371	4	follows	follow	VBZ
cord-194157-ak2gc3nz	371	5	from	from	IN
cord-194157-ak2gc3nz	371	6	the	the	DT
cord-194157-ak2gc3nz	371	7	fact	fact	NN
cord-194157-ak2gc3nz	371	8	that	that	IN
cord-194157-ak2gc3nz	371	9	(	(	-LRB-
cord-194157-ak2gc3nz	371	10	λ	λ	NN
cord-194157-ak2gc3nz	371	11	I	-PRON-	PRP
cord-194157-ak2gc3nz	371	12	,	,	,
cord-194157-ak2gc3nz	371	13	μ	μ	NN
cord-194157-ak2gc3nz	371	14	I	i	NN
cord-194157-ak2gc3nz	371	15	)	)	-RRB-
cord-194157-ak2gc3nz	371	16	converges	converge	VBZ
cord-194157-ak2gc3nz	371	17	to	to	IN
cord-194157-ak2gc3nz	371	18	(	(	-LRB-
cord-194157-ak2gc3nz	371	19	λ	λ	NN
cord-194157-ak2gc3nz	371	20	,	,	,
cord-194157-ak2gc3nz	371	21	µ	µ	NN
cord-194157-ak2gc3nz	371	22	)	)	-RRB-
cord-194157-ak2gc3nz	371	23	in	in	IN
cord-194157-ak2gc3nz	371	24	probability	probability	NN
cord-194157-ak2gc3nz	371	25	.	.	.