id	sid	tid	token	lemma	pos
cord-329276-tfrjw743	1	1	key	key	NN
cord-329276-tfrjw743	1	2	:	:	:
cord-329276-tfrjw743	1	3	cord-329276-tfrjw743	cord-329276-tfrjw743	NNP
cord-329276-tfrjw743	1	4	authors	author	NNS
cord-329276-tfrjw743	1	5	:	:	:
cord-329276-tfrjw743	1	6	Ledzewicz	ledzewicz	NN
cord-329276-tfrjw743	1	7	,	,	,
cord-329276-tfrjw743	1	8	Urszula	Urszula	NNP
cord-329276-tfrjw743	1	9	;	;	:
cord-329276-tfrjw743	1	10	Schättler	Schättler	NNP
cord-329276-tfrjw743	1	11	,	,	,
cord-329276-tfrjw743	1	12	Heinz	Heinz	NNP
cord-329276-tfrjw743	1	13	title	title	NN
cord-329276-tfrjw743	1	14	:	:	:
cord-329276-tfrjw743	2	1	On	on	IN
cord-329276-tfrjw743	2	2	the	the	DT
cord-329276-tfrjw743	2	3	Role	role	NN
cord-329276-tfrjw743	2	4	of	of	IN
cord-329276-tfrjw743	2	5	the	the	DT
cord-329276-tfrjw743	2	6	Objective	Objective	NNP
cord-329276-tfrjw743	2	7	in	in	IN
cord-329276-tfrjw743	2	8	the	the	DT
cord-329276-tfrjw743	2	9	Optimization	Optimization	NNP
cord-329276-tfrjw743	2	10	of	of	IN
cord-329276-tfrjw743	2	11	Compartmental	Compartmental	NNP
cord-329276-tfrjw743	2	12	Models	Models	NNPS
cord-329276-tfrjw743	2	13	for	for	IN
cord-329276-tfrjw743	2	14	Biomedical	Biomedical	NNP
cord-329276-tfrjw743	2	15	Therapies	Therapies	NNP
cord-329276-tfrjw743	2	16	date	date	NN
cord-329276-tfrjw743	2	17	:	:	:
cord-329276-tfrjw743	2	18	2020	2020	CD
cord-329276-tfrjw743	2	19	-	-	HYPH
cord-329276-tfrjw743	2	20	09	09	CD
cord-329276-tfrjw743	2	21	-	-	SYM
cord-329276-tfrjw743	2	22	30	30	CD
cord-329276-tfrjw743	2	23	journal	journal	NN
cord-329276-tfrjw743	2	24	:	:	:
cord-329276-tfrjw743	2	25	J	J	NNP
cord-329276-tfrjw743	2	26	Optim	Optim	NNP
cord-329276-tfrjw743	2	27	Theory	Theory	NNP
cord-329276-tfrjw743	3	1	Appl	Appl	NNP
cord-329276-tfrjw743	3	2	DOI	DOI	NNP
cord-329276-tfrjw743	3	3	:	:	:
cord-329276-tfrjw743	4	1	10.1007	10.1007	CD
cord-329276-tfrjw743	4	2	/	/	SYM
cord-329276-tfrjw743	4	3	s10957	s10957	CD
cord-329276-tfrjw743	4	4	-	-	HYPH
cord-329276-tfrjw743	4	5	020	020	CD
cord-329276-tfrjw743	4	6	-	-	HYPH
cord-329276-tfrjw743	4	7	01754	01754	CD
cord-329276-tfrjw743	4	8	-	-	SYM
cord-329276-tfrjw743	4	9	2	2	CD
cord-329276-tfrjw743	4	10	sha	sha	NNP
cord-329276-tfrjw743	4	11	:	:	:
cord-329276-tfrjw743	4	12	d305e9d98bc9da4cb24371180ab1fcaf8adb4163	d305e9d98bc9da4cb24371180ab1fcaf8adb4163	NNP
cord-329276-tfrjw743	4	13	doc_id	doc_id	CD
cord-329276-tfrjw743	4	14	:	:	:
cord-329276-tfrjw743	5	1	329276	329276	CD
cord-329276-tfrjw743	5	2	cord_uid	cord_uid	NNS
cord-329276-tfrjw743	5	3	:	:	:
cord-329276-tfrjw743	6	1	tfrjw743	tfrjw743	NNP
cord-329276-tfrjw743	7	1	We	-PRON-	PRP
cord-329276-tfrjw743	7	2	review	review	VBP
cord-329276-tfrjw743	7	3	and	and	CC
cord-329276-tfrjw743	7	4	discuss	discuss	VB
cord-329276-tfrjw743	7	5	results	result	NNS
cord-329276-tfrjw743	7	6	obtained	obtain	VBN
cord-329276-tfrjw743	7	7	through	through	IN
cord-329276-tfrjw743	7	8	an	an	DT
cord-329276-tfrjw743	7	9	application	application	NN
cord-329276-tfrjw743	7	10	of	of	IN
cord-329276-tfrjw743	7	11	tools	tool	NNS
cord-329276-tfrjw743	7	12	of	of	IN
cord-329276-tfrjw743	7	13	nonlinear	nonlinear	JJ
cord-329276-tfrjw743	7	14	optimal	optimal	JJ
cord-329276-tfrjw743	7	15	control	control	NN
cord-329276-tfrjw743	7	16	to	to	IN
cord-329276-tfrjw743	7	17	biomedical	biomedical	JJ
cord-329276-tfrjw743	7	18	problems	problem	NNS
cord-329276-tfrjw743	7	19	.	.	.
cord-329276-tfrjw743	8	1	We	-PRON-	PRP
cord-329276-tfrjw743	8	2	discuss	discuss	VBP
cord-329276-tfrjw743	8	3	various	various	JJ
cord-329276-tfrjw743	8	4	aspects	aspect	NNS
cord-329276-tfrjw743	8	5	of	of	IN
cord-329276-tfrjw743	8	6	the	the	DT
cord-329276-tfrjw743	8	7	modeling	modeling	NN
cord-329276-tfrjw743	8	8	of	of	IN
cord-329276-tfrjw743	8	9	the	the	DT
cord-329276-tfrjw743	8	10	dynamics	dynamic	NNS
cord-329276-tfrjw743	8	11	(	(	-LRB-
cord-329276-tfrjw743	8	12	such	such	JJ
cord-329276-tfrjw743	8	13	as	as	IN
cord-329276-tfrjw743	8	14	growth	growth	NN
cord-329276-tfrjw743	8	15	and	and	CC
cord-329276-tfrjw743	8	16	interaction	interaction	NN
cord-329276-tfrjw743	8	17	terms	term	NNS
cord-329276-tfrjw743	8	18	)	)	-RRB-
cord-329276-tfrjw743	8	19	,	,	,
cord-329276-tfrjw743	8	20	modeling	modeling	NN
cord-329276-tfrjw743	8	21	of	of	IN
cord-329276-tfrjw743	8	22	treatment	treatment	NN
cord-329276-tfrjw743	8	23	(	(	-LRB-
cord-329276-tfrjw743	8	24	including	include	VBG
cord-329276-tfrjw743	8	25	pharmacometrics	pharmacometric	NNS
cord-329276-tfrjw743	8	26	of	of	IN
cord-329276-tfrjw743	8	27	the	the	DT
cord-329276-tfrjw743	8	28	drugs	drug	NNS
cord-329276-tfrjw743	8	29	)	)	-RRB-
cord-329276-tfrjw743	8	30	,	,	,
cord-329276-tfrjw743	8	31	and	and	CC
cord-329276-tfrjw743	8	32	give	give	VB
cord-329276-tfrjw743	8	33	special	special	JJ
cord-329276-tfrjw743	8	34	attention	attention	NN
cord-329276-tfrjw743	8	35	to	to	IN
cord-329276-tfrjw743	8	36	the	the	DT
cord-329276-tfrjw743	8	37	choice	choice	NN
cord-329276-tfrjw743	8	38	of	of	IN
cord-329276-tfrjw743	8	39	the	the	DT
cord-329276-tfrjw743	8	40	objective	objective	JJ
cord-329276-tfrjw743	8	41	functional	functional	JJ
cord-329276-tfrjw743	8	42	to	to	TO
cord-329276-tfrjw743	8	43	be	be	VB
cord-329276-tfrjw743	8	44	minimized	minimize	VBN
cord-329276-tfrjw743	8	45	.	.	.
cord-329276-tfrjw743	9	1	Indeed	indeed	RB
cord-329276-tfrjw743	9	2	,	,	,
cord-329276-tfrjw743	9	3	many	many	JJ
cord-329276-tfrjw743	9	4	properties	property	NNS
cord-329276-tfrjw743	9	5	of	of	IN
cord-329276-tfrjw743	9	6	optimal	optimal	JJ
cord-329276-tfrjw743	9	7	solutions	solution	NNS
cord-329276-tfrjw743	9	8	are	be	VBP
cord-329276-tfrjw743	9	9	predestined	predestine	VBN
cord-329276-tfrjw743	9	10	by	by	IN
cord-329276-tfrjw743	9	11	this	this	DT
cord-329276-tfrjw743	9	12	choice	choice	NN
cord-329276-tfrjw743	9	13	which	which	WDT
cord-329276-tfrjw743	9	14	often	often	RB
cord-329276-tfrjw743	9	15	is	be	VBZ
cord-329276-tfrjw743	9	16	only	only	RB
cord-329276-tfrjw743	9	17	made	make	VBN
cord-329276-tfrjw743	9	18	casually	casually	RB
cord-329276-tfrjw743	9	19	using	use	VBG
cord-329276-tfrjw743	9	20	some	some	DT
cord-329276-tfrjw743	9	21	simple	simple	JJ
cord-329276-tfrjw743	9	22	ad	ad	FW
cord-329276-tfrjw743	9	23	hoc	hoc	FW
cord-329276-tfrjw743	9	24	heuristics	heuristic	NNS
cord-329276-tfrjw743	9	25	.	.	.
cord-329276-tfrjw743	10	1	We	-PRON-	PRP
cord-329276-tfrjw743	10	2	discuss	discuss	VBP
cord-329276-tfrjw743	10	3	means	mean	NNS
cord-329276-tfrjw743	10	4	to	to	TO
cord-329276-tfrjw743	10	5	improve	improve	VB
cord-329276-tfrjw743	10	6	this	this	DT
cord-329276-tfrjw743	10	7	choice	choice	NN
cord-329276-tfrjw743	10	8	by	by	IN
cord-329276-tfrjw743	10	9	taking	take	VBG
cord-329276-tfrjw743	10	10	into	into	IN
cord-329276-tfrjw743	10	11	account	account	NN
cord-329276-tfrjw743	10	12	the	the	DT
cord-329276-tfrjw743	10	13	underlying	underlie	VBG
cord-329276-tfrjw743	10	14	biology	biology	NN
cord-329276-tfrjw743	10	15	of	of	IN
cord-329276-tfrjw743	10	16	the	the	DT
cord-329276-tfrjw743	10	17	problem	problem	NN
cord-329276-tfrjw743	10	18	.	.	.
cord-329276-tfrjw743	11	1	Optimal	optimal	JJ
cord-329276-tfrjw743	11	2	control	control	NN
cord-329276-tfrjw743	11	3	is	be	VBZ
cord-329276-tfrjw743	11	4	a	a	DT
cord-329276-tfrjw743	11	5	methodology	methodology	NN
cord-329276-tfrjw743	11	6	to	to	TO
cord-329276-tfrjw743	11	7	obtain	obtain	VB
cord-329276-tfrjw743	11	8	well	well	RB
cord-329276-tfrjw743	11	9	thought	think	VBN
cord-329276-tfrjw743	11	10	through	through	IN
cord-329276-tfrjw743	11	11	solutions	solution	NNS
cord-329276-tfrjw743	11	12	to	to	IN
cord-329276-tfrjw743	11	13	practical	practical	JJ
cord-329276-tfrjw743	11	14	problems	problem	NNS
cord-329276-tfrjw743	11	15	for	for	IN
cord-329276-tfrjw743	11	16	dynamical	dynamical	JJ
cord-329276-tfrjw743	11	17	processes	process	NNS
cord-329276-tfrjw743	11	18	.	.	.
cord-329276-tfrjw743	12	1	It	-PRON-	PRP
cord-329276-tfrjw743	12	2	has	have	VBZ
cord-329276-tfrjw743	12	3	found	find	VBN
cord-329276-tfrjw743	12	4	numerous	numerous	JJ
cord-329276-tfrjw743	12	5	applications	application	NNS
cord-329276-tfrjw743	12	6	in	in	IN
cord-329276-tfrjw743	12	7	the	the	DT
cord-329276-tfrjw743	12	8	sciences	science	NNS
cord-329276-tfrjw743	12	9	and	and	CC
cord-329276-tfrjw743	12	10	has	have	VBZ
cord-329276-tfrjw743	12	11	become	become	VBN
cord-329276-tfrjw743	12	12	a	a	DT
cord-329276-tfrjw743	12	13	staple	staple	NN
cord-329276-tfrjw743	12	14	of	of	IN
cord-329276-tfrjw743	12	15	engineering	engineering	NN
cord-329276-tfrjw743	12	16	design	design	NN
cord-329276-tfrjw743	12	17	,	,	,
cord-329276-tfrjw743	12	18	but	but	CC
cord-329276-tfrjw743	12	19	applications	application	NNS
cord-329276-tfrjw743	12	20	to	to	IN
cord-329276-tfrjw743	12	21	biomedical	biomedical	JJ
cord-329276-tfrjw743	12	22	problems	problem	NNS
cord-329276-tfrjw743	12	23	are	be	VBP
cord-329276-tfrjw743	12	24	less	less	RBR
cord-329276-tfrjw743	12	25	well	well	RB
cord-329276-tfrjw743	12	26	known	known	JJ
cord-329276-tfrjw743	12	27	.	.	.
cord-329276-tfrjw743	13	1	Yet	yet	RB
cord-329276-tfrjw743	13	2	,	,	,
cord-329276-tfrjw743	13	3	optimal	optimal	JJ
cord-329276-tfrjw743	13	4	control	control	NN
cord-329276-tfrjw743	13	5	as	as	IN
cord-329276-tfrjw743	13	6	a	a	DT
cord-329276-tfrjw743	13	7	tool	tool	NN
cord-329276-tfrjw743	13	8	in	in	IN
cord-329276-tfrjw743	13	9	the	the	DT
cord-329276-tfrjw743	13	10	analysis	analysis	NN
cord-329276-tfrjw743	13	11	of	of	IN
cord-329276-tfrjw743	13	12	mathematical	mathematical	JJ
cord-329276-tfrjw743	13	13	models	model	NNS
cord-329276-tfrjw743	13	14	of	of	IN
cord-329276-tfrjw743	13	15	cancer	cancer	NN
cord-329276-tfrjw743	13	16	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	13	17	dates	date	VBZ
cord-329276-tfrjw743	13	18	back	back	RB
cord-329276-tfrjw743	13	19	to	to	IN
cord-329276-tfrjw743	13	20	the	the	DT
cord-329276-tfrjw743	13	21	1970s	1970	NNS
cord-329276-tfrjw743	13	22	and	and	CC
cord-329276-tfrjw743	13	23	1980s	1980	NNS
cord-329276-tfrjw743	13	24	(	(	-LRB-
cord-329276-tfrjw743	13	25	e.g.	e.g.	RB
cord-329276-tfrjw743	13	26	,	,	,
cord-329276-tfrjw743	13	27	see	see	VB
cord-329276-tfrjw743	13	28	[	[	-LRB-
cord-329276-tfrjw743	13	29	1	1	CD
cord-329276-tfrjw743	13	30	]	]	-RRB-
cord-329276-tfrjw743	14	1	[	[	-LRB-
cord-329276-tfrjw743	14	2	2	2	LS
cord-329276-tfrjw743	14	3	]	]	-RRB-
cord-329276-tfrjw743	14	4	[	[	-LRB-
cord-329276-tfrjw743	14	5	3	3	CD
cord-329276-tfrjw743	14	6	]	]	-RRB-
cord-329276-tfrjw743	14	7	[	[	-LRB-
cord-329276-tfrjw743	14	8	4	4	CD
cord-329276-tfrjw743	14	9	]	]	-RRB-
cord-329276-tfrjw743	14	10	[	[	-LRB-
cord-329276-tfrjw743	14	11	5	5	CD
cord-329276-tfrjw743	14	12	]	]	-RRB-
cord-329276-tfrjw743	14	13	[	[	-LRB-
cord-329276-tfrjw743	14	14	6	6	CD
cord-329276-tfrjw743	14	15	]	]	-RRB-
cord-329276-tfrjw743	14	16	)	)	-RRB-
cord-329276-tfrjw743	14	17	,	,	,
cord-329276-tfrjw743	14	18	and	and	CC
cord-329276-tfrjw743	14	19	these	these	DT
cord-329276-tfrjw743	14	20	efforts	effort	NNS
cord-329276-tfrjw743	14	21	have	have	VBP
cord-329276-tfrjw743	14	22	continued	continue	VBN
cord-329276-tfrjw743	14	23	actively	actively	RB
cord-329276-tfrjw743	14	24	throughout	throughout	IN
cord-329276-tfrjw743	14	25	the	the	DT
cord-329276-tfrjw743	14	26	years	year	NNS
cord-329276-tfrjw743	14	27	to	to	IN
cord-329276-tfrjw743	14	28	the	the	DT
cord-329276-tfrjw743	14	29	present	present	JJ
cord-329276-tfrjw743	14	30	day	day	NN
cord-329276-tfrjw743	14	31	(	(	-LRB-
cord-329276-tfrjw743	14	32	e.g.	e.g.	RB
cord-329276-tfrjw743	14	33	,	,	,
cord-329276-tfrjw743	14	34	see	see	VB
cord-329276-tfrjw743	14	35	[	[	-LRB-
cord-329276-tfrjw743	14	36	7	7	CD
cord-329276-tfrjw743	14	37	]	]	-RRB-
cord-329276-tfrjw743	14	38	[	[	-LRB-
cord-329276-tfrjw743	14	39	8	8	CD
cord-329276-tfrjw743	14	40	]	]	-RRB-
cord-329276-tfrjw743	14	41	[	[	-LRB-
cord-329276-tfrjw743	14	42	9	9	CD
cord-329276-tfrjw743	14	43	]	]	-RRB-
cord-329276-tfrjw743	14	44	[	[	-LRB-
cord-329276-tfrjw743	14	45	10	10	CD
cord-329276-tfrjw743	14	46	]	]	-RRB-
cord-329276-tfrjw743	14	47	[	[	-LRB-
cord-329276-tfrjw743	14	48	11	11	CD
cord-329276-tfrjw743	14	49	]	]	-RRB-
cord-329276-tfrjw743	14	50	[	[	-LRB-
cord-329276-tfrjw743	14	51	12	12	CD
cord-329276-tfrjw743	14	52	]	]	-RRB-
cord-329276-tfrjw743	14	53	[	[	-LRB-
cord-329276-tfrjw743	14	54	13	13	CD
cord-329276-tfrjw743	14	55	]	]	-RRB-
cord-329276-tfrjw743	14	56	[	[	-LRB-
cord-329276-tfrjw743	14	57	14	14	CD
cord-329276-tfrjw743	14	58	]	]	-RRB-
cord-329276-tfrjw743	14	59	and	and	CC
cord-329276-tfrjw743	14	60	the	the	DT
cord-329276-tfrjw743	14	61	many	many	JJ
cord-329276-tfrjw743	14	62	references	reference	NNS
cord-329276-tfrjw743	14	63	in	in	IN
cord-329276-tfrjw743	14	64	[	[	-LRB-
cord-329276-tfrjw743	14	65	15	15	CD
cord-329276-tfrjw743	14	66	]	]	-RRB-
cord-329276-tfrjw743	14	67	)	)	-RRB-
cord-329276-tfrjw743	14	68	.	.	.
cord-329276-tfrjw743	15	1	In	in	IN
cord-329276-tfrjw743	15	2	the	the	DT
cord-329276-tfrjw743	15	3	modeling	modeling	NN
cord-329276-tfrjw743	15	4	,	,	,
cord-329276-tfrjw743	15	5	considerable	considerable	JJ
cord-329276-tfrjw743	15	6	attention	attention	NN
cord-329276-tfrjw743	15	7	is	be	VBZ
cord-329276-tfrjw743	15	8	given	give	VBN
cord-329276-tfrjw743	15	9	to	to	IN
cord-329276-tfrjw743	15	10	the	the	DT
cord-329276-tfrjw743	15	11	formulation	formulation	NN
cord-329276-tfrjw743	15	12	of	of	IN
cord-329276-tfrjw743	15	13	the	the	DT
cord-329276-tfrjw743	15	14	underlying	underlie	VBG
cord-329276-tfrjw743	15	15	dynamics	dynamic	NNS
cord-329276-tfrjw743	15	16	.	.	.
cord-329276-tfrjw743	16	1	Based	base	VBN
cord-329276-tfrjw743	16	2	on	on	IN
cord-329276-tfrjw743	16	3	the	the	DT
cord-329276-tfrjw743	16	4	tremendous	tremendous	JJ
cord-329276-tfrjw743	16	5	progress	progress	NN
cord-329276-tfrjw743	16	6	that	that	WDT
cord-329276-tfrjw743	16	7	has	have	VBZ
cord-329276-tfrjw743	16	8	been	be	VBN
cord-329276-tfrjw743	16	9	made	make	VBN
cord-329276-tfrjw743	16	10	over	over	IN
cord-329276-tfrjw743	16	11	the	the	DT
cord-329276-tfrjw743	16	12	years	year	NNS
cord-329276-tfrjw743	16	13	in	in	IN
cord-329276-tfrjw743	16	14	understanding	understand	VBG
cord-329276-tfrjw743	16	15	biomedical	biomedical	JJ
cord-329276-tfrjw743	16	16	problems	problem	NNS
cord-329276-tfrjw743	16	17	,	,	,
cord-329276-tfrjw743	16	18	and	and	CC
cord-329276-tfrjw743	16	19	cancer	cancer	NN
cord-329276-tfrjw743	16	20	in	in	IN
cord-329276-tfrjw743	16	21	particular	particular	JJ
cord-329276-tfrjw743	16	22	,	,	,
cord-329276-tfrjw743	16	23	even	even	RB
cord-329276-tfrjw743	16	24	minimally	minimally	RB
cord-329276-tfrjw743	16	25	parameterized	parameterize	VBN
cord-329276-tfrjw743	16	26	models	model	NNS
cord-329276-tfrjw743	16	27	are	be	VBP
cord-329276-tfrjw743	16	28	generally	generally	RB
cord-329276-tfrjw743	16	29	well	well	RB
cord-329276-tfrjw743	16	30	thought	think	VBN
cord-329276-tfrjw743	16	31	through	through	IN
cord-329276-tfrjw743	16	32	and	and	CC
cord-329276-tfrjw743	16	33	realistic	realistic	JJ
cord-329276-tfrjw743	16	34	.	.	.
cord-329276-tfrjw743	17	1	As	as	IN
cord-329276-tfrjw743	17	2	a	a	DT
cord-329276-tfrjw743	17	3	matter	matter	NN
cord-329276-tfrjw743	17	4	of	of	IN
cord-329276-tfrjw743	17	5	fact	fact	NN
cord-329276-tfrjw743	17	6	,	,	,
cord-329276-tfrjw743	17	7	however	however	RB
cord-329276-tfrjw743	17	8	,	,	,
cord-329276-tfrjw743	17	9	considerably	considerably	RB
cord-329276-tfrjw743	17	10	less	less	JJR
cord-329276-tfrjw743	17	11	effort	effort	NN
cord-329276-tfrjw743	17	12	is	be	VBZ
cord-329276-tfrjw743	17	13	made	make	VBN
cord-329276-tfrjw743	17	14	when	when	WRB
cord-329276-tfrjw743	17	15	the	the	DT
cord-329276-tfrjw743	17	16	objective	objective	NN
cord-329276-tfrjw743	17	17	is	be	VBZ
cord-329276-tfrjw743	17	18	formulated	formulate	VBN
cord-329276-tfrjw743	17	19	that	that	WDT
cord-329276-tfrjw743	17	20	will	will	MD
cord-329276-tfrjw743	17	21	be	be	VB
cord-329276-tfrjw743	17	22	imposed	impose	VBN
cord-329276-tfrjw743	17	23	on	on	IN
cord-329276-tfrjw743	17	24	the	the	DT
cord-329276-tfrjw743	17	25	process	process	NN
cord-329276-tfrjw743	17	26	.	.	.
cord-329276-tfrjw743	18	1	Omnipresent	omnipresent	JJ
cord-329276-tfrjw743	18	2	are	be	VBP
cord-329276-tfrjw743	18	3	the	the	DT
cord-329276-tfrjw743	18	4	papers	paper	NNS
cord-329276-tfrjw743	18	5	in	in	IN
cord-329276-tfrjw743	18	6	which	which	WDT
cord-329276-tfrjw743	18	7	the	the	DT
cord-329276-tfrjw743	18	8	formulation	formulation	NN
cord-329276-tfrjw743	18	9	of	of	IN
cord-329276-tfrjw743	18	10	the	the	DT
cord-329276-tfrjw743	18	11	criterion	criterion	NN
cord-329276-tfrjw743	18	12	at	at	IN
cord-329276-tfrjw743	18	13	best	good	JJS
cord-329276-tfrjw743	18	14	is	be	VBZ
cord-329276-tfrjw743	18	15	a	a	DT
cord-329276-tfrjw743	18	16	mere	mere	JJ
cord-329276-tfrjw743	18	17	after	after	NN
cord-329276-tfrjw743	18	18	-	-	HYPH
cord-329276-tfrjw743	18	19	thought	thought	NN
cord-329276-tfrjw743	18	20	rested	rest	VBD
cord-329276-tfrjw743	18	21	in	in	IN
cord-329276-tfrjw743	18	22	questionable	questionable	JJ
cord-329276-tfrjw743	18	23	heuristics	heuristic	NNS
cord-329276-tfrjw743	18	24	based	base	VBN
cord-329276-tfrjw743	18	25	on	on	IN
cord-329276-tfrjw743	18	26	the	the	DT
cord-329276-tfrjw743	18	27	notion	notion	NN
cord-329276-tfrjw743	18	28	of	of	IN
cord-329276-tfrjw743	18	29	a	a	DT
cord-329276-tfrjw743	18	30	"	"	``
cord-329276-tfrjw743	18	31	systemic	systemic	JJ
cord-329276-tfrjw743	18	32	cost"-whatever	cost"-whatever	NNS
cord-329276-tfrjw743	18	33	that	that	WDT
cord-329276-tfrjw743	18	34	may	may	MD
cord-329276-tfrjw743	18	35	be	be	VB
cord-329276-tfrjw743	18	36	.	.	.
cord-329276-tfrjw743	19	1	Naturally	naturally	RB
cord-329276-tfrjw743	19	2	,	,	,
cord-329276-tfrjw743	19	3	the	the	DT
cord-329276-tfrjw743	19	4	choice	choice	NN
cord-329276-tfrjw743	19	5	of	of	IN
cord-329276-tfrjw743	19	6	the	the	DT
cord-329276-tfrjw743	19	7	objective	objective	NN
cord-329276-tfrjw743	19	8	in	in	IN
cord-329276-tfrjw743	19	9	an	an	DT
cord-329276-tfrjw743	19	10	optimal	optimal	JJ
cord-329276-tfrjw743	19	11	control	control	NN
cord-329276-tfrjw743	19	12	problem	problem	NN
cord-329276-tfrjw743	19	13	is	be	VBZ
cord-329276-tfrjw743	19	14	a	a	DT
cord-329276-tfrjw743	19	15	very	very	RB
cord-329276-tfrjw743	19	16	important	important	JJ
cord-329276-tfrjw743	19	17	aspect	aspect	NN
cord-329276-tfrjw743	19	18	of	of	IN
cord-329276-tfrjw743	19	19	the	the	DT
cord-329276-tfrjw743	19	20	overall	overall	JJ
cord-329276-tfrjw743	19	21	approach	approach	NN
cord-329276-tfrjw743	19	22	and	and	CC
cord-329276-tfrjw743	19	23	quite	quite	RB
cord-329276-tfrjw743	19	24	often	often	RB
cord-329276-tfrjw743	19	25	it	-PRON-	PRP
cord-329276-tfrjw743	19	26	is	be	VBZ
cord-329276-tfrjw743	19	27	here	here	RB
cord-329276-tfrjw743	19	28	where	where	WRB
cord-329276-tfrjw743	19	29	what	what	WP
cord-329276-tfrjw743	19	30	will	will	MD
cord-329276-tfrjw743	19	31	be	be	VB
cord-329276-tfrjw743	19	32	eventual	eventual	JJ
cord-329276-tfrjw743	19	33	properties	property	NNS
cord-329276-tfrjw743	19	34	of	of	IN
cord-329276-tfrjw743	19	35	the	the	DT
cord-329276-tfrjw743	19	36	optimal	optimal	JJ
cord-329276-tfrjw743	19	37	solution	solution	NN
cord-329276-tfrjw743	19	38	are	be	VBP
cord-329276-tfrjw743	19	39	already	already	RB
cord-329276-tfrjw743	19	40	determined	determine	VBN
cord-329276-tfrjw743	19	41	.	.	.
cord-329276-tfrjw743	20	1	One	one	PRP
cord-329276-tfrjw743	20	2	should	should	MD
cord-329276-tfrjw743	20	3	not	not	RB
cord-329276-tfrjw743	20	4	confuse	confuse	VB
cord-329276-tfrjw743	20	5	this	this	DT
cord-329276-tfrjw743	20	6	with	with	IN
cord-329276-tfrjw743	20	7	obtaining	obtain	VBG
cord-329276-tfrjw743	20	8	meaningful	meaningful	JJ
cord-329276-tfrjw743	20	9	information	information	NN
cord-329276-tfrjw743	20	10	on	on	IN
cord-329276-tfrjw743	20	11	the	the	DT
cord-329276-tfrjw743	20	12	underlying	underlie	VBG
cord-329276-tfrjw743	20	13	biological	biological	JJ
cord-329276-tfrjw743	20	14	problem	problem	NN
cord-329276-tfrjw743	20	15	.	.	.
cord-329276-tfrjw743	21	1	While	while	IN
cord-329276-tfrjw743	21	2	,	,	,
cord-329276-tfrjw743	21	3	on	on	IN
cord-329276-tfrjw743	21	4	the	the	DT
cord-329276-tfrjw743	21	5	one	one	CD
cord-329276-tfrjw743	21	6	hand	hand	NN
cord-329276-tfrjw743	21	7	,	,	,
cord-329276-tfrjw743	21	8	it	-PRON-	PRP
cord-329276-tfrjw743	21	9	is	be	VBZ
cord-329276-tfrjw743	21	10	not	not	RB
cord-329276-tfrjw743	21	11	that	that	RB
cord-329276-tfrjw743	21	12	straightforward	straightforward	JJ
cord-329276-tfrjw743	21	13	to	to	TO
cord-329276-tfrjw743	21	14	come	come	VB
cord-329276-tfrjw743	21	15	up	up	RP
cord-329276-tfrjw743	21	16	with	with	IN
cord-329276-tfrjw743	21	17	a	a	DT
cord-329276-tfrjw743	21	18	proper	proper	JJ
cord-329276-tfrjw743	21	19	objective	objective	JJ
cord-329276-tfrjw743	21	20	criterion	criterion	NN
cord-329276-tfrjw743	21	21	in	in	IN
cord-329276-tfrjw743	21	22	biological	biological	JJ
cord-329276-tfrjw743	21	23	problems	problem	NNS
cord-329276-tfrjw743	21	24	,	,	,
cord-329276-tfrjw743	21	25	on	on	IN
cord-329276-tfrjw743	21	26	the	the	DT
cord-329276-tfrjw743	21	27	other	other	JJ
cord-329276-tfrjw743	21	28	hand	hand	NN
cord-329276-tfrjw743	21	29	,	,	,
cord-329276-tfrjw743	21	30	choosing	choose	VBG
cord-329276-tfrjw743	21	31	the	the	DT
cord-329276-tfrjw743	21	32	objective	objective	NN
cord-329276-tfrjw743	21	33	based	base	VBN
cord-329276-tfrjw743	21	34	on	on	IN
cord-329276-tfrjw743	21	35	mathematical	mathematical	JJ
cord-329276-tfrjw743	21	36	tractability	tractability	NN
cord-329276-tfrjw743	21	37	with	with	IN
cord-329276-tfrjw743	21	38	disregard	disregard	NN
cord-329276-tfrjw743	21	39	of	of	IN
cord-329276-tfrjw743	21	40	its	-PRON-	PRP$
cord-329276-tfrjw743	21	41	meaning	meaning	NN
cord-329276-tfrjw743	21	42	will	will	MD
cord-329276-tfrjw743	21	43	not	not	RB
cord-329276-tfrjw743	21	44	pass	pass	VB
cord-329276-tfrjw743	21	45	muster	muster	NN
cord-329276-tfrjw743	21	46	.	.	.
cord-329276-tfrjw743	22	1	In	in	IN
cord-329276-tfrjw743	22	2	this	this	DT
cord-329276-tfrjw743	22	3	paper	paper	NN
cord-329276-tfrjw743	22	4	,	,	,
cord-329276-tfrjw743	22	5	which	which	WDT
cord-329276-tfrjw743	22	6	is	be	VBZ
cord-329276-tfrjw743	22	7	intended	intend	VBN
cord-329276-tfrjw743	22	8	as	as	IN
cord-329276-tfrjw743	22	9	a	a	DT
cord-329276-tfrjw743	22	10	review	review	NN
cord-329276-tfrjw743	22	11	and	and	CC
cord-329276-tfrjw743	22	12	discussion	discussion	NN
cord-329276-tfrjw743	22	13	,	,	,
cord-329276-tfrjw743	22	14	using	use	VBG
cord-329276-tfrjw743	22	15	mathematical	mathematical	JJ
cord-329276-tfrjw743	22	16	models	model	NNS
cord-329276-tfrjw743	22	17	for	for	IN
cord-329276-tfrjw743	22	18	cancer	cancer	NN
cord-329276-tfrjw743	22	19	treatments	treatment	NNS
cord-329276-tfrjw743	22	20	as	as	IN
cord-329276-tfrjw743	22	21	the	the	DT
cord-329276-tfrjw743	22	22	main	main	JJ
cord-329276-tfrjw743	22	23	vehicle	vehicle	NN
cord-329276-tfrjw743	22	24	of	of	IN
cord-329276-tfrjw743	22	25	presentation	presentation	NN
cord-329276-tfrjw743	22	26	,	,	,
cord-329276-tfrjw743	22	27	we	-PRON-	PRP
cord-329276-tfrjw743	22	28	discuss	discuss	VBP
cord-329276-tfrjw743	22	29	the	the	DT
cord-329276-tfrjw743	22	30	main	main	JJ
cord-329276-tfrjw743	22	31	aspects	aspect	NNS
cord-329276-tfrjw743	22	32	that	that	WDT
cord-329276-tfrjw743	22	33	enter	enter	VBP
cord-329276-tfrjw743	22	34	into	into	IN
cord-329276-tfrjw743	22	35	the	the	DT
cord-329276-tfrjw743	22	36	modeling	modeling	NN
cord-329276-tfrjw743	22	37	of	of	IN
cord-329276-tfrjw743	22	38	biomedical	biomedical	JJ
cord-329276-tfrjw743	22	39	problems	problem	NNS
cord-329276-tfrjw743	22	40	as	as	IN
cord-329276-tfrjw743	22	41	optimal	optimal	JJ
cord-329276-tfrjw743	22	42	control	control	NN
cord-329276-tfrjw743	22	43	problems	problem	NNS
cord-329276-tfrjw743	22	44	.	.	.
cord-329276-tfrjw743	23	1	We	-PRON-	PRP
cord-329276-tfrjw743	23	2	give	give	VBP
cord-329276-tfrjw743	23	3	some	some	DT
cord-329276-tfrjw743	23	4	attention	attention	NN
cord-329276-tfrjw743	23	5	to	to	IN
cord-329276-tfrjw743	23	6	the	the	DT
cord-329276-tfrjw743	23	7	formulation	formulation	NN
cord-329276-tfrjw743	23	8	of	of	IN
cord-329276-tfrjw743	23	9	the	the	DT
cord-329276-tfrjw743	23	10	dynamics	dynamic	NNS
cord-329276-tfrjw743	23	11	(	(	-LRB-
cord-329276-tfrjw743	23	12	such	such	JJ
cord-329276-tfrjw743	23	13	as	as	IN
cord-329276-tfrjw743	23	14	growth	growth	NN
cord-329276-tfrjw743	23	15	and	and	CC
cord-329276-tfrjw743	23	16	interaction	interaction	NN
cord-329276-tfrjw743	23	17	terms	term	NNS
cord-329276-tfrjw743	23	18	for	for	IN
cord-329276-tfrjw743	23	19	the	the	DT
cord-329276-tfrjw743	23	20	population	population	NN
cord-329276-tfrjw743	23	21	)	)	-RRB-
cord-329276-tfrjw743	23	22	and	and	CC
cord-329276-tfrjw743	23	23	treatment	treatment	NN
cord-329276-tfrjw743	23	24	aspects	aspect	NNS
cord-329276-tfrjw743	23	25	,	,	,
cord-329276-tfrjw743	23	26	but	but	CC
cord-329276-tfrjw743	23	27	our	-PRON-	PRP$
cord-329276-tfrjw743	23	28	emphasis	emphasis	NN
cord-329276-tfrjw743	23	29	will	will	MD
cord-329276-tfrjw743	23	30	be	be	VB
cord-329276-tfrjw743	23	31	on	on	IN
cord-329276-tfrjw743	23	32	the	the	DT
cord-329276-tfrjw743	23	33	formulation	formulation	NN
cord-329276-tfrjw743	23	34	of	of	IN
cord-329276-tfrjw743	23	35	the	the	DT
cord-329276-tfrjw743	23	36	objective	objective	NN
cord-329276-tfrjw743	23	37	to	to	TO
cord-329276-tfrjw743	23	38	be	be	VB
cord-329276-tfrjw743	23	39	minimized	minimize	VBN
cord-329276-tfrjw743	23	40	.	.	.
cord-329276-tfrjw743	24	1	We	-PRON-	PRP
cord-329276-tfrjw743	24	2	stress	stress	VBP
cord-329276-tfrjw743	24	3	the	the	DT
cord-329276-tfrjw743	24	4	need	need	NN
cord-329276-tfrjw743	24	5	for	for	IN
cord-329276-tfrjw743	24	6	a	a	DT
cord-329276-tfrjw743	24	7	meaningful	meaningful	JJ
cord-329276-tfrjw743	24	8	interpretation	interpretation	NN
cord-329276-tfrjw743	24	9	of	of	IN
cord-329276-tfrjw743	24	10	the	the	DT
cord-329276-tfrjw743	24	11	objective	objective	NN
cord-329276-tfrjw743	24	12	.	.	.
cord-329276-tfrjw743	25	1	This	this	DT
cord-329276-tfrjw743	25	2	should	should	MD
cord-329276-tfrjw743	25	3	be	be	VB
cord-329276-tfrjw743	25	4	related	relate	VBN
cord-329276-tfrjw743	25	5	to	to	IN
cord-329276-tfrjw743	25	6	side	side	JJ
cord-329276-tfrjw743	25	7	effects	effect	NNS
cord-329276-tfrjw743	25	8	of	of	IN
cord-329276-tfrjw743	25	9	the	the	DT
cord-329276-tfrjw743	25	10	treatment	treatment	NN
cord-329276-tfrjw743	25	11	in	in	IN
cord-329276-tfrjw743	25	12	models	model	NNS
cord-329276-tfrjw743	25	13	for	for	IN
cord-329276-tfrjw743	25	14	cancer	cancer	NN
cord-329276-tfrjw743	25	15	therapies	therapy	NNS
cord-329276-tfrjw743	25	16	and/or	and/or	CC
cord-329276-tfrjw743	25	17	to	to	IN
cord-329276-tfrjw743	25	18	the	the	DT
cord-329276-tfrjw743	25	19	actual	actual	JJ
cord-329276-tfrjw743	25	20	cost	cost	NN
cord-329276-tfrjw743	25	21	.	.	.
cord-329276-tfrjw743	26	1	Yet	yet	RB
cord-329276-tfrjw743	26	2	,	,	,
cord-329276-tfrjw743	26	3	such	such	JJ
cord-329276-tfrjw743	26	4	costs	cost	NNS
cord-329276-tfrjw743	26	5	are	be	VBP
cord-329276-tfrjw743	26	6	not	not	RB
cord-329276-tfrjw743	26	7	always	always	RB
cord-329276-tfrjw743	26	8	easily	easily	RB
cord-329276-tfrjw743	26	9	quantifiable	quantifiable	JJ
cord-329276-tfrjw743	26	10	.	.	.
cord-329276-tfrjw743	27	1	Just	just	RB
cord-329276-tfrjw743	27	2	think	think	VB
cord-329276-tfrjw743	27	3	of	of	IN
cord-329276-tfrjw743	27	4	'	'	``
cord-329276-tfrjw743	27	5	social	social	JJ
cord-329276-tfrjw743	27	6	distancing	distancing	NN
cord-329276-tfrjw743	27	7	'	'	''
cord-329276-tfrjw743	27	8	during	during	IN
cord-329276-tfrjw743	27	9	an	an	DT
cord-329276-tfrjw743	27	10	epidemic	epidemic	NN
cord-329276-tfrjw743	27	11	and	and	CC
cord-329276-tfrjw743	27	12	its	-PRON-	PRP$
cord-329276-tfrjw743	27	13	effects	effect	NNS
cord-329276-tfrjw743	27	14	on	on	IN
cord-329276-tfrjw743	27	15	the	the	DT
cord-329276-tfrjw743	27	16	economy	economy	NN
cord-329276-tfrjw743	27	17	.	.	.
cord-329276-tfrjw743	28	1	Using	use	VBG
cord-329276-tfrjw743	28	2	examples	example	NNS
cord-329276-tfrjw743	28	3	from	from	IN
cord-329276-tfrjw743	28	4	our	-PRON-	PRP$
cord-329276-tfrjw743	28	5	work	work	NN
cord-329276-tfrjw743	28	6	,	,	,
cord-329276-tfrjw743	28	7	we	-PRON-	PRP
cord-329276-tfrjw743	28	8	illustrate	illustrate	VBP
cord-329276-tfrjw743	28	9	how	how	WRB
cord-329276-tfrjw743	28	10	information	information	NN
cord-329276-tfrjw743	28	11	from	from	IN
cord-329276-tfrjw743	28	12	the	the	DT
cord-329276-tfrjw743	28	13	underlying	underlie	VBG
cord-329276-tfrjw743	28	14	biology	biology	NN
cord-329276-tfrjw743	28	15	or	or	CC
cord-329276-tfrjw743	28	16	medically	medically	RB
cord-329276-tfrjw743	28	17	relevant	relevant	JJ
cord-329276-tfrjw743	28	18	limitations	limitation	NNS
cord-329276-tfrjw743	28	19	can	can	MD
cord-329276-tfrjw743	28	20	be	be	VB
cord-329276-tfrjw743	28	21	used	use	VBN
cord-329276-tfrjw743	28	22	to	to	TO
cord-329276-tfrjw743	28	23	formulate	formulate	VB
cord-329276-tfrjw743	28	24	the	the	DT
cord-329276-tfrjw743	28	25	optimization	optimization	NN
cord-329276-tfrjw743	28	26	criterion	criterion	NN
cord-329276-tfrjw743	28	27	so	so	IN
cord-329276-tfrjw743	28	28	that	that	IN
cord-329276-tfrjw743	28	29	optimal	optimal	JJ
cord-329276-tfrjw743	28	30	solutions	solution	NNS
cord-329276-tfrjw743	28	31	then	then	RB
cord-329276-tfrjw743	28	32	give	give	VBP
cord-329276-tfrjw743	28	33	meaningful	meaningful	JJ
cord-329276-tfrjw743	28	34	information	information	NN
cord-329276-tfrjw743	28	35	for	for	IN
cord-329276-tfrjw743	28	36	the	the	DT
cord-329276-tfrjw743	28	37	underlying	underlie	VBG
cord-329276-tfrjw743	28	38	biomedical	biomedical	JJ
cord-329276-tfrjw743	28	39	problem	problem	NN
cord-329276-tfrjw743	28	40	.	.	.
cord-329276-tfrjw743	29	1	We	-PRON-	PRP
cord-329276-tfrjw743	29	2	point	point	VBP
cord-329276-tfrjw743	29	3	out	out	RP
cord-329276-tfrjw743	29	4	some	some	DT
cord-329276-tfrjw743	29	5	pitfalls	pitfall	NNS
cord-329276-tfrjw743	29	6	to	to	TO
cord-329276-tfrjw743	29	7	be	be	VB
cord-329276-tfrjw743	29	8	avoided	avoid	VBN
cord-329276-tfrjw743	29	9	,	,	,
cord-329276-tfrjw743	29	10	but	but	CC
cord-329276-tfrjw743	29	11	also	also	RB
cord-329276-tfrjw743	29	12	make	make	VB
cord-329276-tfrjw743	29	13	useful	useful	JJ
cord-329276-tfrjw743	29	14	simplifications	simplification	NNS
cord-329276-tfrjw743	29	15	in	in	IN
cord-329276-tfrjw743	29	16	the	the	DT
cord-329276-tfrjw743	29	17	modeling	modeling	NN
cord-329276-tfrjw743	29	18	,	,	,
cord-329276-tfrjw743	29	19	both	both	CC
cord-329276-tfrjw743	29	20	in	in	IN
cord-329276-tfrjw743	29	21	the	the	DT
cord-329276-tfrjw743	29	22	dynamics	dynamic	NNS
cord-329276-tfrjw743	29	23	and	and	CC
cord-329276-tfrjw743	29	24	the	the	DT
cord-329276-tfrjw743	29	25	objective	objective	NN
cord-329276-tfrjw743	29	26	.	.	.
cord-329276-tfrjw743	30	1	In	in	IN
cord-329276-tfrjw743	30	2	this	this	DT
cord-329276-tfrjw743	30	3	section	section	NN
cord-329276-tfrjw743	30	4	,	,	,
cord-329276-tfrjw743	30	5	a	a	DT
cord-329276-tfrjw743	30	6	general	general	JJ
cord-329276-tfrjw743	30	7	model	model	NN
cord-329276-tfrjw743	30	8	is	be	VBZ
cord-329276-tfrjw743	30	9	formulated	formulate	VBN
cord-329276-tfrjw743	30	10	which	which	WDT
cord-329276-tfrjw743	30	11	represents	represent	VBZ
cord-329276-tfrjw743	30	12	a	a	DT
cord-329276-tfrjw743	30	13	class	class	NN
cord-329276-tfrjw743	30	14	of	of	IN
cord-329276-tfrjw743	30	15	dynamical	dynamical	JJ
cord-329276-tfrjw743	30	16	systems	system	NNS
cord-329276-tfrjw743	30	17	common	common	JJ
cord-329276-tfrjw743	30	18	in	in	IN
cord-329276-tfrjw743	30	19	the	the	DT
cord-329276-tfrjw743	30	20	modeling	modeling	NN
cord-329276-tfrjw743	30	21	of	of	IN
cord-329276-tfrjw743	30	22	biomedical	biomedical	JJ
cord-329276-tfrjw743	30	23	therapies	therapy	NNS
cord-329276-tfrjw743	30	24	.	.	.
cord-329276-tfrjw743	31	1	These	these	DT
cord-329276-tfrjw743	31	2	models	model	NNS
cord-329276-tfrjw743	31	3	are	be	VBP
cord-329276-tfrjw743	31	4	affine	affine	JJ
cord-329276-tfrjw743	31	5	in	in	IN
cord-329276-tfrjw743	31	6	the	the	DT
cord-329276-tfrjw743	31	7	controls	control	NNS
cord-329276-tfrjw743	32	1	u	u	NNP
cord-329276-tfrjw743	32	2	∈	∈	NN
cord-329276-tfrjw743	32	3	R	r	NN
cord-329276-tfrjw743	32	4	m	m	NN
cord-329276-tfrjw743	32	5	with	with	IN
cord-329276-tfrjw743	32	6	states	state	NNS
cord-329276-tfrjw743	32	7	x	x	.
cord-329276-tfrjw743	33	1	∈	∈	NN
cord-329276-tfrjw743	33	2	R	r	NN
cord-329276-tfrjw743	33	3	n	n	NN
cord-329276-tfrjw743	33	4	+	+	NN
cord-329276-tfrjw743	33	5	.	.	.
cord-329276-tfrjw743	34	1	The	the	DT
cord-329276-tfrjw743	34	2	components	component	NNS
cord-329276-tfrjw743	35	1	x	x	LS
cord-329276-tfrjw743	36	1	i	i	PRP
cord-329276-tfrjw743	36	2	,	,	,
cord-329276-tfrjw743	36	3	i	i	PRP
cord-329276-tfrjw743	36	4	=	=	SYM
cord-329276-tfrjw743	36	5	1	1	CD
cord-329276-tfrjw743	36	6	,	,	,
cord-329276-tfrjw743	36	7	.	.	.
cord-329276-tfrjw743	36	8	.	.	.
cord-329276-tfrjw743	36	9	.	.	.
cord-329276-tfrjw743	37	1	,	,	,
cord-329276-tfrjw743	37	2	n	n	NNP
cord-329276-tfrjw743	37	3	,	,	,
cord-329276-tfrjw743	37	4	of	of	IN
cord-329276-tfrjw743	37	5	the	the	DT
cord-329276-tfrjw743	37	6	state	state	NN
cord-329276-tfrjw743	37	7	x	x	NNS
cord-329276-tfrjw743	37	8	are	be	VBP
cord-329276-tfrjw743	37	9	nonnegative	nonnegative	JJ
cord-329276-tfrjw743	37	10	numbers	number	NNS
cord-329276-tfrjw743	37	11	which	which	WDT
cord-329276-tfrjw743	37	12	,	,	,
cord-329276-tfrjw743	37	13	in	in	IN
cord-329276-tfrjw743	37	14	a	a	DT
cord-329276-tfrjw743	37	15	typical	typical	JJ
cord-329276-tfrjw743	37	16	example	example	NN
cord-329276-tfrjw743	37	17	,	,	,
cord-329276-tfrjw743	37	18	represent	represent	VBP
cord-329276-tfrjw743	37	19	volumes	volume	NNS
cord-329276-tfrjw743	37	20	or	or	CC
cord-329276-tfrjw743	37	21	cell	cell	NN
cord-329276-tfrjw743	37	22	counts	count	NNS
cord-329276-tfrjw743	37	23	of	of	IN
cord-329276-tfrjw743	37	24	various	various	JJ
cord-329276-tfrjw743	37	25	populations	population	NNS
cord-329276-tfrjw743	37	26	(	(	-LRB-
cord-329276-tfrjw743	37	27	compartments	compartment	NNS
cord-329276-tfrjw743	37	28	)	)	-RRB-
cord-329276-tfrjw743	37	29	of	of	IN
cord-329276-tfrjw743	37	30	cells	cell	NNS
cord-329276-tfrjw743	37	31	relevant	relevant	JJ
cord-329276-tfrjw743	37	32	to	to	IN
cord-329276-tfrjw743	37	33	the	the	DT
cord-329276-tfrjw743	37	34	underlying	underlie	VBG
cord-329276-tfrjw743	37	35	biomedical	biomedical	JJ
cord-329276-tfrjw743	37	36	condition	condition	NN
cord-329276-tfrjw743	37	37	or	or	CC
cord-329276-tfrjw743	37	38	,	,	,
cord-329276-tfrjw743	37	39	in	in	IN
cord-329276-tfrjw743	37	40	epidemiological	epidemiological	JJ
cord-329276-tfrjw743	37	41	models	model	NNS
cord-329276-tfrjw743	37	42	,	,	,
cord-329276-tfrjw743	37	43	population	population	NN
cord-329276-tfrjw743	37	44	counts	count	VBZ
cord-329276-tfrjw743	37	45	in	in	IN
cord-329276-tfrjw743	37	46	various	various	JJ
cord-329276-tfrjw743	37	47	stages	stage	NNS
cord-329276-tfrjw743	37	48	of	of	IN
cord-329276-tfrjw743	37	49	the	the	DT
cord-329276-tfrjw743	37	50	disease	disease	NN
cord-329276-tfrjw743	37	51	.	.	.
cord-329276-tfrjw743	38	1	The	the	DT
cord-329276-tfrjw743	38	2	controls	control	NNS
cord-329276-tfrjw743	38	3	u	u	NNP
cord-329276-tfrjw743	38	4	j	j	NNP
cord-329276-tfrjw743	38	5	,	,	,
cord-329276-tfrjw743	38	6	j	j	NNP
cord-329276-tfrjw743	38	7	=	=	SYM
cord-329276-tfrjw743	38	8	1	1	CD
cord-329276-tfrjw743	38	9	,	,	,
cord-329276-tfrjw743	38	10	.	.	.
cord-329276-tfrjw743	38	11	.	.	.
cord-329276-tfrjw743	38	12	.	.	.
cord-329276-tfrjw743	38	13	,	,	,
cord-329276-tfrjw743	39	1	m	m	LS
cord-329276-tfrjw743	39	2	,	,	,
cord-329276-tfrjw743	39	3	stand	stand	VB
cord-329276-tfrjw743	39	4	for	for	IN
cord-329276-tfrjw743	39	5	possible	possible	JJ
cord-329276-tfrjw743	39	6	external	external	JJ
cord-329276-tfrjw743	39	7	interventions	intervention	NNS
cord-329276-tfrjw743	39	8	and	and	CC
cord-329276-tfrjw743	39	9	strategies	strategy	NNS
cord-329276-tfrjw743	39	10	such	such	JJ
cord-329276-tfrjw743	39	11	as	as	IN
cord-329276-tfrjw743	39	12	drug	drug	NN
cord-329276-tfrjw743	39	13	therapy	therapy	NN
cord-329276-tfrjw743	39	14	in	in	IN
cord-329276-tfrjw743	39	15	cancer	cancer	NN
cord-329276-tfrjw743	39	16	treatments	treatment	NNS
cord-329276-tfrjw743	39	17	or	or	CC
cord-329276-tfrjw743	39	18	vaccination	vaccination	NN
cord-329276-tfrjw743	39	19	efforts	effort	NNS
cord-329276-tfrjw743	39	20	in	in	IN
cord-329276-tfrjw743	39	21	epidemiological	epidemiological	JJ
cord-329276-tfrjw743	39	22	models	model	NNS
cord-329276-tfrjw743	39	23	.	.	.
cord-329276-tfrjw743	40	1	Mathematically	mathematically	RB
cord-329276-tfrjw743	40	2	,	,	,
cord-329276-tfrjw743	40	3	the	the	DT
cord-329276-tfrjw743	40	4	general	general	JJ
cord-329276-tfrjw743	40	5	structure	structure	NN
cord-329276-tfrjw743	40	6	we	-PRON-	PRP
cord-329276-tfrjw743	40	7	consider	consider	VBP
cord-329276-tfrjw743	40	8	in	in	IN
cord-329276-tfrjw743	40	9	this	this	DT
cord-329276-tfrjw743	40	10	paper	paper	NN
cord-329276-tfrjw743	40	11	is	be	VBZ
cord-329276-tfrjw743	40	12	of	of	IN
cord-329276-tfrjw743	40	13	the	the	DT
cord-329276-tfrjw743	40	14	form	form	NN
cord-329276-tfrjw743	40	15	Journal	Journal	NNP
cord-329276-tfrjw743	40	16	of	of	IN
cord-329276-tfrjw743	40	17	Optimization	Optimization	NNP
cord-329276-tfrjw743	40	18	Theory	Theory	NNP
cord-329276-tfrjw743	40	19	and	and	CC
cord-329276-tfrjw743	40	20	Applicationṡ	Applicationṡ	NNP
cord-329276-tfrjw743	40	21	with	with	IN
cord-329276-tfrjw743	40	22	F	F	NNP
cord-329276-tfrjw743	40	23	and	and	CC
cord-329276-tfrjw743	40	24	G	G	NNP
cord-329276-tfrjw743	40	25	typically	typically	RB
cord-329276-tfrjw743	40	26	nonlinear	nonlinear	JJ
cord-329276-tfrjw743	40	27	vector	vector	NN
cord-329276-tfrjw743	40	28	fields	field	NNS
cord-329276-tfrjw743	40	29	called	call	VBD
cord-329276-tfrjw743	40	30	the	the	DT
cord-329276-tfrjw743	40	31	drift	drift	NN
cord-329276-tfrjw743	40	32	and	and	CC
cord-329276-tfrjw743	40	33	control	control	NN
cord-329276-tfrjw743	40	34	vector	vector	NN
cord-329276-tfrjw743	40	35	fields	field	NNS
cord-329276-tfrjw743	40	36	,	,	,
cord-329276-tfrjw743	40	37	respectively	respectively	RB
cord-329276-tfrjw743	40	38	,	,	,
cord-329276-tfrjw743	40	39	and	and	CC
cord-329276-tfrjw743	40	40	U	u	VB
cord-329276-tfrjw743	40	41	the	the	DT
cord-329276-tfrjw743	40	42	control	control	NN
cord-329276-tfrjw743	40	43	set	set	NN
cord-329276-tfrjw743	40	44	which	which	WDT
cord-329276-tfrjw743	40	45	represents	represent	VBZ
cord-329276-tfrjw743	40	46	restrictions	restriction	NNS
cord-329276-tfrjw743	40	47	on	on	IN
cord-329276-tfrjw743	40	48	the	the	DT
cord-329276-tfrjw743	40	49	size	size	NN
cord-329276-tfrjw743	40	50	of	of	IN
cord-329276-tfrjw743	40	51	the	the	DT
cord-329276-tfrjw743	40	52	controls	control	NNS
cord-329276-tfrjw743	40	53	.	.	.
cord-329276-tfrjw743	41	1	The	the	DT
cord-329276-tfrjw743	41	2	drift	drift	NN
cord-329276-tfrjw743	41	3	vector	vector	NN
cord-329276-tfrjw743	41	4	field	field	NN
cord-329276-tfrjw743	41	5	F	F	NNP
cord-329276-tfrjw743	41	6	describes	describe	VBZ
cord-329276-tfrjw743	41	7	the	the	DT
cord-329276-tfrjw743	41	8	underlying	underlie	VBG
cord-329276-tfrjw743	41	9	dynamics	dynamic	NNS
cord-329276-tfrjw743	41	10	of	of	IN
cord-329276-tfrjw743	41	11	the	the	DT
cord-329276-tfrjw743	41	12	system	system	NN
cord-329276-tfrjw743	41	13	without	without	IN
cord-329276-tfrjw743	41	14	any	any	DT
cord-329276-tfrjw743	41	15	outside	outside	JJ
cord-329276-tfrjw743	41	16	interventions	intervention	NNS
cord-329276-tfrjw743	41	17	.	.	.
cord-329276-tfrjw743	42	1	It	-PRON-	PRP
cord-329276-tfrjw743	42	2	generally	generally	RB
cord-329276-tfrjw743	42	3	consists	consist	VBZ
cord-329276-tfrjw743	42	4	of	of	IN
cord-329276-tfrjw743	42	5	various	various	JJ
cord-329276-tfrjw743	42	6	terms	term	NNS
cord-329276-tfrjw743	42	7	which	which	WDT
cord-329276-tfrjw743	42	8	should	should	MD
cord-329276-tfrjw743	42	9	include	include	VB
cord-329276-tfrjw743	42	10	the	the	DT
cord-329276-tfrjw743	42	11	following	follow	VBG
cord-329276-tfrjw743	42	12	aspects	aspect	NNS
cord-329276-tfrjw743	42	13	:	:	:
cord-329276-tfrjw743	42	14	growth	growth	NN
cord-329276-tfrjw743	42	15	terms	term	NNS
cord-329276-tfrjw743	42	16	of	of	IN
cord-329276-tfrjw743	42	17	the	the	DT
cord-329276-tfrjw743	42	18	populations	population	NNS
cord-329276-tfrjw743	42	19	as	as	RB
cord-329276-tfrjw743	42	20	well	well	RB
cord-329276-tfrjw743	42	21	as	as	IN
cord-329276-tfrjw743	42	22	transition	transition	NN
cord-329276-tfrjw743	42	23	and	and	CC
cord-329276-tfrjw743	42	24	interaction	interaction	NN
cord-329276-tfrjw743	42	25	terms	term	NNS
cord-329276-tfrjw743	42	26	between	between	IN
cord-329276-tfrjw743	42	27	the	the	DT
cord-329276-tfrjw743	42	28	various	various	JJ
cord-329276-tfrjw743	42	29	compartments	compartment	NNS
cord-329276-tfrjw743	42	30	.	.	.
cord-329276-tfrjw743	43	1	These	these	DT
cord-329276-tfrjw743	43	2	terms	term	NNS
cord-329276-tfrjw743	43	3	describe	describe	VBP
cord-329276-tfrjw743	43	4	the	the	DT
cord-329276-tfrjw743	43	5	mechanisms	mechanism	NNS
cord-329276-tfrjw743	43	6	behind	behind	IN
cord-329276-tfrjw743	43	7	the	the	DT
cord-329276-tfrjw743	43	8	increase	increase	NN
cord-329276-tfrjw743	43	9	in	in	IN
cord-329276-tfrjw743	43	10	all	all	DT
cord-329276-tfrjw743	43	11	or	or	CC
cord-329276-tfrjw743	43	12	some	some	DT
cord-329276-tfrjw743	43	13	of	of	IN
cord-329276-tfrjw743	43	14	the	the	DT
cord-329276-tfrjw743	43	15	populations	population	NNS
cord-329276-tfrjw743	43	16	in	in	IN
cord-329276-tfrjw743	43	17	the	the	DT
cord-329276-tfrjw743	43	18	compartments	compartment	NNS
cord-329276-tfrjw743	43	19	that	that	WDT
cord-329276-tfrjw743	43	20	define	define	VBP
cord-329276-tfrjw743	43	21	the	the	DT
cord-329276-tfrjw743	43	22	state	state	NN
cord-329276-tfrjw743	43	23	.	.	.
cord-329276-tfrjw743	44	1	These	these	DT
cord-329276-tfrjw743	44	2	mechanisms	mechanism	NNS
cord-329276-tfrjw743	44	3	can	can	MD
cord-329276-tfrjw743	44	4	be	be	VB
cord-329276-tfrjw743	44	5	modeled	model	VBN
cord-329276-tfrjw743	44	6	in	in	IN
cord-329276-tfrjw743	44	7	various	various	JJ
cord-329276-tfrjw743	44	8	ways	way	NNS
cord-329276-tfrjw743	44	9	taking	take	VBG
cord-329276-tfrjw743	44	10	into	into	IN
cord-329276-tfrjw743	44	11	account	account	NN
cord-329276-tfrjw743	44	12	whether	whether	IN
cord-329276-tfrjw743	44	13	or	or	CC
cord-329276-tfrjw743	44	14	not	not	RB
cord-329276-tfrjw743	44	15	such	such	JJ
cord-329276-tfrjw743	44	16	growth	growth	NN
cord-329276-tfrjw743	44	17	saturates	saturate	VBZ
cord-329276-tfrjw743	44	18	or	or	CC
cord-329276-tfrjw743	44	19	not	not	RB
cord-329276-tfrjw743	44	20	.	.	.
cord-329276-tfrjw743	45	1	The	the	DT
cord-329276-tfrjw743	45	2	simplest	simple	JJS
cord-329276-tfrjw743	45	3	model	model	NN
cord-329276-tfrjw743	45	4	for	for	IN
cord-329276-tfrjw743	45	5	a	a	DT
cord-329276-tfrjw743	45	6	single	single	JJ
cord-329276-tfrjw743	45	7	population	population	NN
cord-329276-tfrjw743	45	8	x	x	NN
cord-329276-tfrjw743	45	9	∈	∈	NN
cord-329276-tfrjw743	45	10	R	r	NN
cord-329276-tfrjw743	45	11	is	be	VBZ
cord-329276-tfrjw743	45	12	given	give	VBN
cord-329276-tfrjw743	45	13	by	by	IN
cord-329276-tfrjw743	45	14	exponential	exponential	JJ
cord-329276-tfrjw743	45	15	growth	growth	NN
cord-329276-tfrjw743	45	16	,	,	,
cord-329276-tfrjw743	46	1	x	x	LS
cord-329276-tfrjw743	46	2	=	=	SYM
cord-329276-tfrjw743	46	3	ax	ax	NN
cord-329276-tfrjw743	46	4	,	,	,
cord-329276-tfrjw743	46	5	with	with	IN
cord-329276-tfrjw743	46	6	a	a	DT
cord-329276-tfrjw743	46	7	a	a	DT
cord-329276-tfrjw743	46	8	constant	constant	NN
cord-329276-tfrjw743	46	9	representing	represent	VBG
cord-329276-tfrjw743	46	10	the	the	DT
cord-329276-tfrjw743	46	11	growth	growth	NN
cord-329276-tfrjw743	46	12	rate	rate	NN
cord-329276-tfrjw743	46	13	.	.	.
cord-329276-tfrjw743	47	1	The	the	DT
cord-329276-tfrjw743	47	2	same	same	JJ
cord-329276-tfrjw743	47	3	expression	expression	NN
cord-329276-tfrjw743	47	4	with	with	IN
cord-329276-tfrjw743	47	5	a	a	DT
cord-329276-tfrjw743	47	6	<	<	XX
cord-329276-tfrjw743	47	7	0	0	NFP
cord-329276-tfrjw743	47	8	describes	describe	VBZ
cord-329276-tfrjw743	47	9	a	a	DT
cord-329276-tfrjw743	47	10	basic	basic	JJ
cord-329276-tfrjw743	47	11	death	death	NN
cord-329276-tfrjw743	47	12	term	term	NN
cord-329276-tfrjw743	47	13	of	of	IN
cord-329276-tfrjw743	47	14	the	the	DT
cord-329276-tfrjw743	47	15	population	population	NN
cord-329276-tfrjw743	47	16	and	and	CC
cord-329276-tfrjw743	47	17	,	,	,
cord-329276-tfrjw743	47	18	more	more	RBR
cord-329276-tfrjw743	47	19	generally	generally	RB
cord-329276-tfrjw743	47	20	,	,	,
cord-329276-tfrjw743	47	21	these	these	DT
cord-329276-tfrjw743	47	22	two	two	CD
cord-329276-tfrjw743	47	23	processes	process	NNS
cord-329276-tfrjw743	47	24	can	can	MD
cord-329276-tfrjw743	47	25	be	be	VB
cord-329276-tfrjw743	47	26	combined	combine	VBN
cord-329276-tfrjw743	47	27	with	with	IN
cord-329276-tfrjw743	47	28	a	a	DT
cord-329276-tfrjw743	47	29	describing	describe	VBG
cord-329276-tfrjw743	47	30	the	the	DT
cord-329276-tfrjw743	47	31	net	net	JJ
cord-329276-tfrjw743	47	32	effect	effect	NN
cord-329276-tfrjw743	47	33	.	.	.
cord-329276-tfrjw743	48	1	While	while	IN
cord-329276-tfrjw743	48	2	this	this	DT
cord-329276-tfrjw743	48	3	is	be	VBZ
cord-329276-tfrjw743	48	4	an	an	DT
cord-329276-tfrjw743	48	5	adequate	adequate	JJ
cord-329276-tfrjw743	48	6	model	model	NN
cord-329276-tfrjw743	48	7	for	for	IN
cord-329276-tfrjw743	48	8	some	some	DT
cord-329276-tfrjw743	48	9	phases	phase	NNS
cord-329276-tfrjw743	48	10	of	of	IN
cord-329276-tfrjw743	48	11	the	the	DT
cord-329276-tfrjw743	48	12	dynamics	dynamic	NNS
cord-329276-tfrjw743	48	13	,	,	,
cord-329276-tfrjw743	48	14	often	often	RB
cord-329276-tfrjw743	48	15	used	use	VBN
cord-329276-tfrjw743	48	16	in	in	IN
cord-329276-tfrjw743	48	17	short	short	JJ
cord-329276-tfrjw743	48	18	-	-	HYPH
cord-329276-tfrjw743	48	19	term	term	NN
cord-329276-tfrjw743	48	20	models	model	NNS
cord-329276-tfrjw743	48	21	or	or	CC
cord-329276-tfrjw743	48	22	in	in	IN
cord-329276-tfrjw743	48	23	epidemiology	epidemiology	NN
cord-329276-tfrjw743	48	24	,	,	,
cord-329276-tfrjw743	48	25	over	over	IN
cord-329276-tfrjw743	48	26	longer	long	JJR
cord-329276-tfrjw743	48	27	time	time	NN
cord-329276-tfrjw743	48	28	periods	period	NNS
cord-329276-tfrjw743	48	29	saturation	saturation	NN
cord-329276-tfrjw743	48	30	effects	effect	NNS
cord-329276-tfrjw743	48	31	need	need	VBP
cord-329276-tfrjw743	48	32	to	to	TO
cord-329276-tfrjw743	48	33	be	be	VB
cord-329276-tfrjw743	48	34	taken	take	VBN
cord-329276-tfrjw743	48	35	into	into	IN
cord-329276-tfrjw743	48	36	account	account	NN
cord-329276-tfrjw743	48	37	.	.	.
cord-329276-tfrjw743	49	1	Here	here	RB
cord-329276-tfrjw743	49	2	,	,	,
cord-329276-tfrjw743	49	3	the	the	DT
cord-329276-tfrjw743	49	4	most	most	RBS
cord-329276-tfrjw743	49	5	common	common	JJ
cord-329276-tfrjw743	49	6	models	model	NNS
cord-329276-tfrjw743	49	7	are	be	VBP
cord-329276-tfrjw743	49	8	logistic	logistic	JJ
cord-329276-tfrjw743	49	9	growth	growth	NN
cord-329276-tfrjw743	49	10	,	,	,
cord-329276-tfrjw743	49	11	ẋ	ẋ	NN
cord-329276-tfrjw743	49	12	=	=	SYM
cord-329276-tfrjw743	49	13	ax	ax	NN
cord-329276-tfrjw743	49	14	1	1	CD
cord-329276-tfrjw743	49	15	−	−	NN
cord-329276-tfrjw743	50	1	x	x	SYM
cord-329276-tfrjw743	50	2	K	K	NNP
cord-329276-tfrjw743	50	3	,	,	,
cord-329276-tfrjw743	50	4	with	with	IN
cord-329276-tfrjw743	50	5	K	k	NN
cord-329276-tfrjw743	50	6	denoting	denote	VBG
cord-329276-tfrjw743	50	7	a	a	DT
cord-329276-tfrjw743	50	8	fixed	fix	VBN
cord-329276-tfrjw743	50	9	carrying	carrying	NN
cord-329276-tfrjw743	50	10	capacity	capacity	NN
cord-329276-tfrjw743	50	11	of	of	IN
cord-329276-tfrjw743	50	12	the	the	DT
cord-329276-tfrjw743	50	13	population	population	NN
cord-329276-tfrjw743	50	14	.	.	.
cord-329276-tfrjw743	51	1	Another	another	DT
cord-329276-tfrjw743	51	2	saturation	saturation	NN
cord-329276-tfrjw743	51	3	type	type	NN
cord-329276-tfrjw743	51	4	model	model	NN
cord-329276-tfrjw743	51	5	,	,	,
cord-329276-tfrjw743	51	6	which	which	WDT
cord-329276-tfrjw743	51	7	has	have	VBZ
cord-329276-tfrjw743	51	8	been	be	VBN
cord-329276-tfrjw743	51	9	verified	verify	VBN
cord-329276-tfrjw743	51	10	empirically	empirically	RB
cord-329276-tfrjw743	51	11	as	as	IN
cord-329276-tfrjw743	51	12	the	the	DT
cord-329276-tfrjw743	51	13	model	model	NN
cord-329276-tfrjw743	51	14	for	for	IN
cord-329276-tfrjw743	51	15	late	late	JJ
cord-329276-tfrjw743	51	16	-	-	HYPH
cord-329276-tfrjw743	51	17	stages	stage	NNS
cord-329276-tfrjw743	51	18	in	in	IN
cord-329276-tfrjw743	51	19	breast	breast	NN
cord-329276-tfrjw743	51	20	cancer	cancer	NN
cord-329276-tfrjw743	51	21	[	[	-LRB-
cord-329276-tfrjw743	51	22	16	16	CD
cord-329276-tfrjw743	51	23	,	,	,
cord-329276-tfrjw743	51	24	17	17	CD
cord-329276-tfrjw743	51	25	]	]	-RRB-
cord-329276-tfrjw743	51	26	,	,	,
cord-329276-tfrjw743	51	27	is	be	VBZ
cord-329276-tfrjw743	51	28	Gompertzian	gompertzian	JJ
cord-329276-tfrjw743	51	29	growth	growth	NN
cord-329276-tfrjw743	51	30	of	of	IN
cord-329276-tfrjw743	51	31	the	the	DT
cord-329276-tfrjw743	51	32	formẋ	formẋ	NNP
cord-329276-tfrjw743	51	33	=	=	SYM
cord-329276-tfrjw743	51	34	−ax	−ax	NNP
cord-329276-tfrjw743	51	35	ln	ln	NNP
cord-329276-tfrjw743	51	36	x	x	NNP
cord-329276-tfrjw743	51	37	K	K	NNP
cord-329276-tfrjw743	51	38	.	.	.
cord-329276-tfrjw743	52	1	Logistic	logistic	JJ
cord-329276-tfrjw743	52	2	growth	growth	NN
cord-329276-tfrjw743	52	3	is	be	VBZ
cord-329276-tfrjw743	52	4	often	often	RB
cord-329276-tfrjw743	52	5	preferred	prefer	VBN
cord-329276-tfrjw743	52	6	because	because	IN
cord-329276-tfrjw743	52	7	of	of	IN
cord-329276-tfrjw743	52	8	its	-PRON-	PRP$
cord-329276-tfrjw743	52	9	simpler	simple	JJR
cord-329276-tfrjw743	52	10	mathematical	mathematical	JJ
cord-329276-tfrjw743	52	11	structure	structure	NN
cord-329276-tfrjw743	52	12	.	.	.
cord-329276-tfrjw743	53	1	Other	other	JJ
cord-329276-tfrjw743	53	2	growth	growth	NN
cord-329276-tfrjw743	53	3	models	model	NNS
cord-329276-tfrjw743	53	4	exist	exist	VBP
cord-329276-tfrjw743	53	5	,	,	,
cord-329276-tfrjw743	53	6	but	but	CC
cord-329276-tfrjw743	53	7	are	be	VBP
cord-329276-tfrjw743	53	8	less	less	RBR
cord-329276-tfrjw743	53	9	common	common	JJ
cord-329276-tfrjw743	53	10	(	(	-LRB-
cord-329276-tfrjw743	53	11	e.g.	e.g.	RB
cord-329276-tfrjw743	53	12	,	,	,
cord-329276-tfrjw743	53	13	see	see	VB
cord-329276-tfrjw743	53	14	[	[	-LRB-
cord-329276-tfrjw743	53	15	18	18	CD
cord-329276-tfrjw743	53	16	]	]	-RRB-
cord-329276-tfrjw743	53	17	)	)	-RRB-
cord-329276-tfrjw743	53	18	.	.	.
cord-329276-tfrjw743	54	1	Transition	transition	NN
cord-329276-tfrjw743	54	2	terms	term	NNS
cord-329276-tfrjw743	54	3	model	model	VBP
cord-329276-tfrjw743	54	4	the	the	DT
cord-329276-tfrjw743	54	5	exchanges	exchange	NNS
cord-329276-tfrjw743	54	6	between	between	IN
cord-329276-tfrjw743	54	7	populations	population	NNS
cord-329276-tfrjw743	54	8	.	.	.
cord-329276-tfrjw743	55	1	For	for	IN
cord-329276-tfrjw743	55	2	example	example	NN
cord-329276-tfrjw743	55	3	,	,	,
cord-329276-tfrjw743	55	4	in	in	IN
cord-329276-tfrjw743	55	5	cellcycle	cellcycle	NNP
cord-329276-tfrjw743	55	6	specific	specific	JJ
cord-329276-tfrjw743	55	7	models	model	NNS
cord-329276-tfrjw743	55	8	for	for	IN
cord-329276-tfrjw743	55	9	cancer	cancer	NN
cord-329276-tfrjw743	55	10	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	55	11	[	[	-LRB-
cord-329276-tfrjw743	55	12	8	8	CD
cord-329276-tfrjw743	55	13	]	]	-RRB-
cord-329276-tfrjw743	55	14	,	,	,
cord-329276-tfrjw743	55	15	quiescent	quiescent	JJ
cord-329276-tfrjw743	55	16	and	and	CC
cord-329276-tfrjw743	55	17	proliferating	proliferate	VBG
cord-329276-tfrjw743	55	18	cells	cell	NNS
cord-329276-tfrjw743	55	19	are	be	VBP
cord-329276-tfrjw743	55	20	distinguished	distinguished	JJ
cord-329276-tfrjw743	55	21	and	and	CC
cord-329276-tfrjw743	55	22	proliferating	proliferate	VBG
cord-329276-tfrjw743	55	23	cells	cell	NNS
cord-329276-tfrjw743	55	24	move	move	VBP
cord-329276-tfrjw743	55	25	through	through	IN
cord-329276-tfrjw743	55	26	growth	growth	NN
cord-329276-tfrjw743	55	27	phases	phase	NNS
cord-329276-tfrjw743	55	28	,	,	,
cord-329276-tfrjw743	55	29	synthesis	synthesis	NN
cord-329276-tfrjw743	55	30	and	and	CC
cord-329276-tfrjw743	55	31	mitosis	mitosis	NN
cord-329276-tfrjw743	55	32	,	,	,
cord-329276-tfrjw743	55	33	all	all	DT
cord-329276-tfrjw743	55	34	represented	represent	VBN
cord-329276-tfrjw743	55	35	by	by	IN
cord-329276-tfrjw743	55	36	different	different	JJ
cord-329276-tfrjw743	55	37	coordinates	coordinate	NNS
cord-329276-tfrjw743	55	38	of	of	IN
cord-329276-tfrjw743	55	39	the	the	DT
cord-329276-tfrjw743	55	40	state	state	NN
cord-329276-tfrjw743	55	41	vector	vector	NN
cord-329276-tfrjw743	55	42	x.	x.	NNP
cord-329276-tfrjw743	56	1	Similarly	similarly	RB
cord-329276-tfrjw743	56	2	,	,	,
cord-329276-tfrjw743	56	3	in	in	IN
cord-329276-tfrjw743	56	4	models	model	NNS
cord-329276-tfrjw743	56	5	including	include	VBG
cord-329276-tfrjw743	56	6	drug	drug	NN
cord-329276-tfrjw743	56	7	resistance	resistance	NN
cord-329276-tfrjw743	56	8	,	,	,
cord-329276-tfrjw743	56	9	random	random	JJ
cord-329276-tfrjw743	56	10	changes	change	NNS
cord-329276-tfrjw743	56	11	from	from	IN
cord-329276-tfrjw743	56	12	sensitive	sensitive	JJ
cord-329276-tfrjw743	56	13	to	to	IN
cord-329276-tfrjw743	56	14	resistant	resistant	JJ
cord-329276-tfrjw743	56	15	cells	cell	NNS
cord-329276-tfrjw743	56	16	occur	occur	VBP
cord-329276-tfrjw743	56	17	which	which	WDT
cord-329276-tfrjw743	56	18	,	,	,
cord-329276-tfrjw743	56	19	in	in	IN
cord-329276-tfrjw743	56	20	cases	case	NNS
cord-329276-tfrjw743	56	21	of	of	IN
cord-329276-tfrjw743	56	22	cancer	cancer	NN
cord-329276-tfrjw743	56	23	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	56	24	,	,	,
cord-329276-tfrjw743	56	25	also	also	RB
cord-329276-tfrjw743	56	26	may	may	MD
cord-329276-tfrjw743	56	27	be	be	VB
cord-329276-tfrjw743	56	28	reversible	reversible	JJ
cord-329276-tfrjw743	56	29	.	.	.
cord-329276-tfrjw743	57	1	In	in	IN
cord-329276-tfrjw743	57	2	epidemiological	epidemiological	JJ
cord-329276-tfrjw743	57	3	models	model	NNS
cord-329276-tfrjw743	57	4	,	,	,
cord-329276-tfrjw743	57	5	transitions	transition	NNS
cord-329276-tfrjw743	57	6	between	between	IN
cord-329276-tfrjw743	57	7	sensitive	sensitive	JJ
cord-329276-tfrjw743	57	8	,	,	,
cord-329276-tfrjw743	57	9	exposed	expose	VBN
cord-329276-tfrjw743	57	10	,	,	,
cord-329276-tfrjw743	57	11	infectious	infectious	JJ
cord-329276-tfrjw743	57	12	and	and	CC
cord-329276-tfrjw743	57	13	recovered	recover	VBN
cord-329276-tfrjw743	57	14	individuals	individual	NNS
cord-329276-tfrjw743	57	15	are	be	VBP
cord-329276-tfrjw743	57	16	crucial	crucial	JJ
cord-329276-tfrjw743	57	17	to	to	TO
cord-329276-tfrjw743	57	18	understand	understand	VB
cord-329276-tfrjw743	57	19	the	the	DT
cord-329276-tfrjw743	57	20	spread	spread	NN
cord-329276-tfrjw743	57	21	of	of	IN
cord-329276-tfrjw743	57	22	the	the	DT
cord-329276-tfrjw743	57	23	disease	disease	NN
cord-329276-tfrjw743	57	24	.	.	.
cord-329276-tfrjw743	58	1	All	all	DT
cord-329276-tfrjw743	58	2	such	such	JJ
cord-329276-tfrjw743	58	3	transitions	transition	NNS
cord-329276-tfrjw743	58	4	are	be	VBP
cord-329276-tfrjw743	58	5	generally	generally	RB
cord-329276-tfrjw743	58	6	modeled	model	VBN
cord-329276-tfrjw743	58	7	by	by	IN
cord-329276-tfrjw743	58	8	linear	linear	JJ
cord-329276-tfrjw743	58	9	transition	transition	NN
cord-329276-tfrjw743	58	10	rates	rate	NNS
cord-329276-tfrjw743	58	11	of	of	IN
cord-329276-tfrjw743	58	12	the	the	DT
cord-329276-tfrjw743	58	13	forṁ	forṁ	NN
cord-329276-tfrjw743	58	14	with	with	IN
cord-329276-tfrjw743	58	15	α	α	NN
cord-329276-tfrjw743	58	16	i	i	NN
cord-329276-tfrjw743	58	17	≥	≥	CD
cord-329276-tfrjw743	58	18	0	0	NFP
cord-329276-tfrjw743	58	19	representing	represent	VBG
cord-329276-tfrjw743	58	20	the	the	DT
cord-329276-tfrjw743	58	21	outflow	outflow	NN
cord-329276-tfrjw743	58	22	from	from	IN
cord-329276-tfrjw743	58	23	the	the	DT
cord-329276-tfrjw743	58	24	ith	ith	NNP
cord-329276-tfrjw743	58	25	compartment	compartment	NN
cord-329276-tfrjw743	58	26	and	and	CC
cord-329276-tfrjw743	58	27	β	β	NN
cord-329276-tfrjw743	59	1	i	i	PRP
cord-329276-tfrjw743	59	2	j	j	NNP
cord-329276-tfrjw743	59	3	≥	≥	CD
cord-329276-tfrjw743	59	4	0	0	NFP
cord-329276-tfrjw743	59	5	for	for	IN
cord-329276-tfrjw743	59	6	i	i	PRP
cord-329276-tfrjw743	59	7	=	=	SYM
cord-329276-tfrjw743	59	8	j	j	NNP
cord-329276-tfrjw743	59	9	representing	represent	VBG
cord-329276-tfrjw743	59	10	the	the	DT
cord-329276-tfrjw743	59	11	inflow	inflow	NN
cord-329276-tfrjw743	59	12	from	from	IN
cord-329276-tfrjw743	59	13	the	the	DT
cord-329276-tfrjw743	59	14	jth	jth	NN
cord-329276-tfrjw743	59	15	into	into	IN
cord-329276-tfrjw743	59	16	the	the	DT
cord-329276-tfrjw743	59	17	ith	ith	NNP
cord-329276-tfrjw743	59	18	compartment	compartment	NN
cord-329276-tfrjw743	59	19	.	.	.
cord-329276-tfrjw743	60	1	Cells	cell	NNS
cord-329276-tfrjw743	60	2	in	in	IN
cord-329276-tfrjw743	60	3	various	various	JJ
cord-329276-tfrjw743	60	4	compartments	compartment	NNS
cord-329276-tfrjw743	60	5	stimulate	stimulate	VBP
cord-329276-tfrjw743	60	6	and/or	and/or	CC
cord-329276-tfrjw743	60	7	inhibit	inhibit	VB
cord-329276-tfrjw743	60	8	cells	cell	NNS
cord-329276-tfrjw743	60	9	in	in	IN
cord-329276-tfrjw743	60	10	other	other	JJ
cord-329276-tfrjw743	60	11	compartments	compartment	NNS
cord-329276-tfrjw743	60	12	.	.	.
cord-329276-tfrjw743	61	1	Often	often	RB
cord-329276-tfrjw743	61	2	these	these	DT
cord-329276-tfrjw743	61	3	interactions	interaction	NNS
cord-329276-tfrjw743	61	4	are	be	VBP
cord-329276-tfrjw743	61	5	modeled	model	VBN
cord-329276-tfrjw743	61	6	by	by	IN
cord-329276-tfrjw743	61	7	the	the	DT
cord-329276-tfrjw743	61	8	law	law	NN
cord-329276-tfrjw743	61	9	of	of	IN
cord-329276-tfrjw743	61	10	mass	mass	JJ
cord-329276-tfrjw743	61	11	actions	action	NNS
cord-329276-tfrjw743	61	12	leading	lead	VBG
cord-329276-tfrjw743	61	13	to	to	IN
cord-329276-tfrjw743	61	14	products	product	NNS
cord-329276-tfrjw743	61	15	of	of	IN
cord-329276-tfrjw743	61	16	terms	term	NNS
cord-329276-tfrjw743	61	17	representing	represent	VBG
cord-329276-tfrjw743	61	18	the	the	DT
cord-329276-tfrjw743	61	19	cell	cell	NN
cord-329276-tfrjw743	61	20	counts	count	NNS
cord-329276-tfrjw743	61	21	or	or	CC
cord-329276-tfrjw743	61	22	volumes	volume	NNS
cord-329276-tfrjw743	61	23	in	in	IN
cord-329276-tfrjw743	61	24	various	various	JJ
cord-329276-tfrjw743	61	25	compartments	compartment	NNS
cord-329276-tfrjw743	61	26	.	.	.
cord-329276-tfrjw743	62	1	This	this	DT
cord-329276-tfrjw743	62	2	generates	generate	VBZ
cord-329276-tfrjw743	62	3	expressions	expression	NNS
cord-329276-tfrjw743	62	4	of	of	IN
cord-329276-tfrjw743	62	5	the	the	DT
cord-329276-tfrjw743	62	6	form	form	NN
cord-329276-tfrjw743	63	1	x	x	LS
cord-329276-tfrjw743	64	1	i	i	PRP
cord-329276-tfrjw743	64	2	x	x	SYM
cord-329276-tfrjw743	64	3	j	j	NNP
cord-329276-tfrjw743	64	4	or	or	CC
cord-329276-tfrjw743	64	5	,	,	.
cord-329276-tfrjw743	65	1	more	more	RBR
cord-329276-tfrjw743	65	2	generally	generally	RB
cord-329276-tfrjw743	65	3	,	,	,
cord-329276-tfrjw743	65	4	expressions	expression	NNS
cord-329276-tfrjw743	65	5	which	which	WDT
cord-329276-tfrjw743	65	6	include	include	VBP
cord-329276-tfrjw743	65	7	powers	power	NNS
cord-329276-tfrjw743	65	8	of	of	IN
cord-329276-tfrjw743	65	9	the	the	DT
cord-329276-tfrjw743	65	10	variables	variable	NNS
cord-329276-tfrjw743	65	11	.	.	.
cord-329276-tfrjw743	66	1	The	the	DT
cord-329276-tfrjw743	66	2	simplest	simple	JJS
cord-329276-tfrjw743	66	3	structure	structure	NN
cord-329276-tfrjw743	66	4	shows	show	VBZ
cord-329276-tfrjw743	66	5	up	up	RP
cord-329276-tfrjw743	66	6	in	in	IN
cord-329276-tfrjw743	66	7	epidemiological	epidemiological	JJ
cord-329276-tfrjw743	66	8	models	model	NNS
cord-329276-tfrjw743	66	9	when	when	WRB
cord-329276-tfrjw743	66	10	susceptible	susceptible	JJ
cord-329276-tfrjw743	66	11	and	and	CC
cord-329276-tfrjw743	66	12	infectious	infectious	JJ
cord-329276-tfrjw743	66	13	populations	population	NNS
cord-329276-tfrjw743	66	14	S	s	NN
cord-329276-tfrjw743	67	1	and	and	CC
cord-329276-tfrjw743	67	2	I	-PRON-	PRP
cord-329276-tfrjw743	67	3	interact	interact	VBP
cord-329276-tfrjw743	67	4	generating	generate	VBG
cord-329276-tfrjw743	67	5	an	an	DT
cord-329276-tfrjw743	67	6	outflow	outflow	NN
cord-329276-tfrjw743	67	7	of	of	IN
cord-329276-tfrjw743	67	8	the	the	DT
cord-329276-tfrjw743	67	9	form	form	NN
cord-329276-tfrjw743	68	1	β	β	NNP
cord-329276-tfrjw743	68	2	S	S	NNP
cord-329276-tfrjw743	69	1	I	-PRON-	PRP
cord-329276-tfrjw743	69	2	from	from	IN
cord-329276-tfrjw743	69	3	the	the	DT
cord-329276-tfrjw743	69	4	susceptible	susceptible	JJ
cord-329276-tfrjw743	69	5	compartment	compartment	NN
cord-329276-tfrjw743	69	6	which	which	WDT
cord-329276-tfrjw743	69	7	becomes	become	VBZ
cord-329276-tfrjw743	69	8	an	an	DT
cord-329276-tfrjw743	69	9	inflow	inflow	NN
cord-329276-tfrjw743	69	10	to	to	IN
cord-329276-tfrjw743	69	11	the	the	DT
cord-329276-tfrjw743	69	12	infectious	infectious	JJ
cord-329276-tfrjw743	69	13	population	population	NN
cord-329276-tfrjw743	69	14	I	-PRON-	PRP
cord-329276-tfrjw743	69	15	with	with	IN
cord-329276-tfrjw743	69	16	β	β	NN
cord-329276-tfrjw743	69	17	accounting	account	VBG
cord-329276-tfrjw743	69	18	for	for	IN
cord-329276-tfrjw743	69	19	the	the	DT
cord-329276-tfrjw743	69	20	probability	probability	NN
cord-329276-tfrjw743	69	21	of	of	IN
cord-329276-tfrjw743	69	22	such	such	JJ
cord-329276-tfrjw743	69	23	interactions	interaction	NNS
cord-329276-tfrjw743	69	24	.	.	.
cord-329276-tfrjw743	70	1	Powers	power	NNS
cord-329276-tfrjw743	70	2	arise	arise	VBP
cord-329276-tfrjw743	70	3	,	,	,
cord-329276-tfrjw743	70	4	for	for	IN
cord-329276-tfrjw743	70	5	example	example	NN
cord-329276-tfrjw743	70	6	,	,	,
cord-329276-tfrjw743	70	7	in	in	IN
cord-329276-tfrjw743	70	8	a	a	DT
cord-329276-tfrjw743	70	9	model	model	NN
cord-329276-tfrjw743	70	10	for	for	IN
cord-329276-tfrjw743	70	11	angiogenic	angiogenic	JJ
cord-329276-tfrjw743	70	12	signaling	signal	VBG
cord-329276-tfrjw743	70	13	by	by	IN
cord-329276-tfrjw743	70	14	Hahnfeldt	Hahnfeldt	NNP
cord-329276-tfrjw743	70	15	et	et	NNP
cord-329276-tfrjw743	70	16	al	al	NNP
cord-329276-tfrjw743	70	17	.	.	.
cord-329276-tfrjw743	71	1	[	[	-LRB-
cord-329276-tfrjw743	71	2	19	19	CD
cord-329276-tfrjw743	71	3	]	]	-RRB-
cord-329276-tfrjw743	71	4	where	where	WRB
cord-329276-tfrjw743	71	5	the	the	DT
cord-329276-tfrjw743	71	6	interactions	interaction	NNS
cord-329276-tfrjw743	71	7	are	be	VBP
cord-329276-tfrjw743	71	8	between	between	IN
cord-329276-tfrjw743	71	9	the	the	DT
cord-329276-tfrjw743	71	10	tumor	tumor	NN
cord-329276-tfrjw743	71	11	surface	surface	NN
cord-329276-tfrjw743	71	12	through	through	IN
cord-329276-tfrjw743	71	13	which	which	WDT
cord-329276-tfrjw743	71	14	angiogenic	angiogenic	JJ
cord-329276-tfrjw743	71	15	inhibitors	inhibitor	NNS
cord-329276-tfrjw743	71	16	need	need	VBP
cord-329276-tfrjw743	71	17	to	to	TO
cord-329276-tfrjw743	71	18	be	be	VB
cord-329276-tfrjw743	71	19	released	release	VBN
cord-329276-tfrjw743	71	20	and	and	CC
cord-329276-tfrjw743	71	21	the	the	DT
cord-329276-tfrjw743	71	22	carrying	carrying	NN
cord-329276-tfrjw743	71	23	capacity	capacity	NN
cord-329276-tfrjw743	71	24	of	of	IN
cord-329276-tfrjw743	71	25	the	the	DT
cord-329276-tfrjw743	71	26	vasculature	vasculature	NN
cord-329276-tfrjw743	71	27	.	.	.
cord-329276-tfrjw743	72	1	If	if	IN
cord-329276-tfrjw743	72	2	both	both	DT
cord-329276-tfrjw743	72	3	tumor	tumor	NN
cord-329276-tfrjw743	72	4	volume	volume	NN
cord-329276-tfrjw743	72	5	and	and	CC
cord-329276-tfrjw743	72	6	the	the	DT
cord-329276-tfrjw743	72	7	carrying	carrying	NN
cord-329276-tfrjw743	72	8	capacity	capacity	NN
cord-329276-tfrjw743	72	9	are	be	VBP
cord-329276-tfrjw743	72	10	modeled	model	VBN
cord-329276-tfrjw743	72	11	by	by	IN
cord-329276-tfrjw743	72	12	volumes	volume	NNS
cord-329276-tfrjw743	72	13	p	p	NNP
cord-329276-tfrjw743	72	14	and	and	CC
cord-329276-tfrjw743	72	15	q	q	NNP
cord-329276-tfrjw743	72	16	,	,	,
cord-329276-tfrjw743	72	17	respectively	respectively	RB
cord-329276-tfrjw743	72	18	,	,	,
cord-329276-tfrjw743	72	19	this	this	DT
cord-329276-tfrjw743	72	20	generates	generate	VBZ
cord-329276-tfrjw743	72	21	an	an	DT
cord-329276-tfrjw743	72	22	interaction	interaction	NN
cord-329276-tfrjw743	72	23	term	term	NN
cord-329276-tfrjw743	72	24	of	of	IN
cord-329276-tfrjw743	72	25	the	the	DT
cord-329276-tfrjw743	72	26	form	form	NN
cord-329276-tfrjw743	72	27	p	p	NN
cord-329276-tfrjw743	73	1	2	2	CD
cord-329276-tfrjw743	73	2	3	3	CD
cord-329276-tfrjw743	73	3	q.	q.	NN
cord-329276-tfrjw743	74	1	In	in	IN
cord-329276-tfrjw743	74	2	a	a	DT
cord-329276-tfrjw743	74	3	classical	classical	JJ
cord-329276-tfrjw743	74	4	model	model	NN
cord-329276-tfrjw743	74	5	by	by	IN
cord-329276-tfrjw743	74	6	Stepanova	Stepanova	NNP
cord-329276-tfrjw743	74	7	of	of	IN
cord-329276-tfrjw743	74	8	tumor	tumor	NN
cord-329276-tfrjw743	74	9	immune	immune	JJ
cord-329276-tfrjw743	74	10	system	system	NN
cord-329276-tfrjw743	74	11	interactions	interaction	NNS
cord-329276-tfrjw743	74	12	[	[	-LRB-
cord-329276-tfrjw743	74	13	20	20	CD
cord-329276-tfrjw743	74	14	]	]	-RRB-
cord-329276-tfrjw743	74	15	,	,	,
cord-329276-tfrjw743	74	16	the	the	DT
cord-329276-tfrjw743	74	17	fact	fact	NN
cord-329276-tfrjw743	74	18	that	that	IN
cord-329276-tfrjw743	74	19	the	the	DT
cord-329276-tfrjw743	74	20	immune	immune	JJ
cord-329276-tfrjw743	74	21	system	system	NN
cord-329276-tfrjw743	74	22	is	be	VBZ
cord-329276-tfrjw743	74	23	able	able	JJ
cord-329276-tfrjw743	74	24	to	to	TO
cord-329276-tfrjw743	74	25	control	control	VB
cord-329276-tfrjw743	74	26	small	small	JJ
cord-329276-tfrjw743	74	27	tumors	tumor	NNS
cord-329276-tfrjw743	74	28	,	,	,
cord-329276-tfrjw743	74	29	but	but	CC
cord-329276-tfrjw743	74	30	increasingly	increasingly	RB
cord-329276-tfrjw743	74	31	becomes	become	VBZ
cord-329276-tfrjw743	74	32	overwhelmed	overwhelmed	JJ
cord-329276-tfrjw743	74	33	by	by	IN
cord-329276-tfrjw743	74	34	large	large	JJ
cord-329276-tfrjw743	74	35	tumors	tumor	NNS
cord-329276-tfrjw743	74	36	is	be	VBZ
cord-329276-tfrjw743	74	37	modeled	model	VBN
cord-329276-tfrjw743	74	38	by	by	IN
cord-329276-tfrjw743	74	39	an	an	DT
cord-329276-tfrjw743	74	40	interaction	interaction	NN
cord-329276-tfrjw743	74	41	term	term	NN
cord-329276-tfrjw743	74	42	of	of	IN
cord-329276-tfrjw743	74	43	the	the	DT
cord-329276-tfrjw743	74	44	form	form	NN
cord-329276-tfrjw743	75	1	α	α	NN
cord-329276-tfrjw743	75	2	x	x	SYM
cord-329276-tfrjw743	75	3	−	−	NNP
cord-329276-tfrjw743	76	1	βx	βx	NNP
cord-329276-tfrjw743	77	1	2	2	LS
cord-329276-tfrjw743	77	2	y	y	NN
cord-329276-tfrjw743	77	3	where	where	WRB
cord-329276-tfrjw743	77	4	x	x	NNP
cord-329276-tfrjw743	77	5	represents	represent	VBZ
cord-329276-tfrjw743	77	6	the	the	DT
cord-329276-tfrjw743	77	7	tumor	tumor	NN
cord-329276-tfrjw743	77	8	volume	volume	NN
cord-329276-tfrjw743	77	9	and	and	CC
cord-329276-tfrjw743	77	10	y	y	NNP
cord-329276-tfrjw743	77	11	a	a	DT
cord-329276-tfrjw743	77	12	non	non	JJ
cord-329276-tfrjw743	77	13	-	-	JJ
cord-329276-tfrjw743	77	14	dimensional	dimensional	JJ
cord-329276-tfrjw743	77	15	,	,	,
cord-329276-tfrjw743	77	16	order	order	NN
cord-329276-tfrjw743	77	17	of	of	IN
cord-329276-tfrjw743	77	18	magnitude	magnitude	NN
cord-329276-tfrjw743	77	19	variable	variable	NN
cord-329276-tfrjw743	77	20	related	relate	VBN
cord-329276-tfrjw743	77	21	to	to	IN
cord-329276-tfrjw743	77	22	the	the	DT
cord-329276-tfrjw743	77	23	actions	action	NNS
cord-329276-tfrjw743	77	24	of	of	IN
cord-329276-tfrjw743	77	25	the	the	DT
cord-329276-tfrjw743	77	26	immune	immune	JJ
cord-329276-tfrjw743	77	27	system	system	NN
cord-329276-tfrjw743	77	28	called	call	VBD
cord-329276-tfrjw743	77	29	the	the	DT
cord-329276-tfrjw743	77	30	immunocompetent	immunocompetent	JJ
cord-329276-tfrjw743	77	31	cell	cell	NN
cord-329276-tfrjw743	77	32	density	density	NN
cord-329276-tfrjw743	77	33	.	.	.
cord-329276-tfrjw743	78	1	Here	here	RB
cord-329276-tfrjw743	78	2	,	,	,
cord-329276-tfrjw743	78	3	x	x	NN
cord-329276-tfrjw743	78	4	=	=	SYM
cord-329276-tfrjw743	78	5	1	1	CD
cord-329276-tfrjw743	78	6	β	β	NN
cord-329276-tfrjw743	78	7	corresponds	correspond	VBZ
cord-329276-tfrjw743	78	8	to	to	IN
cord-329276-tfrjw743	78	9	a	a	DT
cord-329276-tfrjw743	78	10	threshold	threshold	NN
cord-329276-tfrjw743	78	11	beyond	beyond	IN
cord-329276-tfrjw743	78	12	which	which	WDT
cord-329276-tfrjw743	78	13	the	the	DT
cord-329276-tfrjw743	78	14	immunological	immunological	JJ
cord-329276-tfrjw743	78	15	system	system	NN
cord-329276-tfrjw743	78	16	becomes	become	VBZ
cord-329276-tfrjw743	78	17	depressed	depressed	JJ
cord-329276-tfrjw743	78	18	by	by	IN
cord-329276-tfrjw743	78	19	the	the	DT
cord-329276-tfrjw743	78	20	growing	grow	VBG
cord-329276-tfrjw743	78	21	tumor	tumor	NN
cord-329276-tfrjw743	78	22	.	.	.
cord-329276-tfrjw743	79	1	The	the	DT
cord-329276-tfrjw743	79	2	coefficients	coefficient	NNS
cord-329276-tfrjw743	79	3	α	α	NN
cord-329276-tfrjw743	79	4	and	and	CC
cord-329276-tfrjw743	79	5	β	β	NN
cord-329276-tfrjw743	79	6	are	be	VBP
cord-329276-tfrjw743	79	7	used	use	VBN
cord-329276-tfrjw743	79	8	to	to	TO
cord-329276-tfrjw743	79	9	calibrate	calibrate	VB
cord-329276-tfrjw743	79	10	these	these	DT
cord-329276-tfrjw743	79	11	interactions	interaction	NNS
cord-329276-tfrjw743	79	12	and	and	CC
cord-329276-tfrjw743	79	13	collectively	collectively	RB
cord-329276-tfrjw743	79	14	describe	describe	VB
cord-329276-tfrjw743	79	15	state	state	NN
cord-329276-tfrjw743	79	16	-	-	HYPH
cord-329276-tfrjw743	79	17	dependent	dependent	JJ
cord-329276-tfrjw743	79	18	interactions	interaction	NNS
cord-329276-tfrjw743	79	19	between	between	IN
cord-329276-tfrjw743	79	20	the	the	DT
cord-329276-tfrjw743	79	21	cancer	cancer	NN
cord-329276-tfrjw743	79	22	cells	cell	NNS
cord-329276-tfrjw743	79	23	and	and	CC
cord-329276-tfrjw743	79	24	the	the	DT
cord-329276-tfrjw743	79	25	immune	immune	JJ
cord-329276-tfrjw743	79	26	system	system	NN
cord-329276-tfrjw743	79	27	.	.	.
cord-329276-tfrjw743	80	1	Limiting	limit	VBG
cord-329276-tfrjw743	80	2	effects	effect	NNS
cord-329276-tfrjw743	80	3	of	of	IN
cord-329276-tfrjw743	80	4	the	the	DT
cord-329276-tfrjw743	80	5	interactions	interaction	NNS
cord-329276-tfrjw743	80	6	between	between	IN
cord-329276-tfrjw743	80	7	various	various	JJ
cord-329276-tfrjw743	80	8	compartments	compartment	NNS
cord-329276-tfrjw743	80	9	can	can	MD
cord-329276-tfrjw743	80	10	be	be	VB
cord-329276-tfrjw743	80	11	taken	take	VBN
cord-329276-tfrjw743	80	12	into	into	IN
cord-329276-tfrjw743	80	13	account	account	NN
cord-329276-tfrjw743	80	14	by	by	IN
cord-329276-tfrjw743	80	15	so	so	RB
cord-329276-tfrjw743	80	16	-	-	HYPH
cord-329276-tfrjw743	80	17	called	call	VBN
cord-329276-tfrjw743	80	18	Michaelis	Michaelis	NNP
cord-329276-tfrjw743	80	19	-	-	HYPH
cord-329276-tfrjw743	80	20	Menten	Menten	NNP
cord-329276-tfrjw743	80	21	terms	term	NNS
cord-329276-tfrjw743	80	22	.	.	.
cord-329276-tfrjw743	81	1	As	as	IN
cord-329276-tfrjw743	81	2	an	an	DT
cord-329276-tfrjw743	81	3	example	example	NN
cord-329276-tfrjw743	81	4	,	,	,
cord-329276-tfrjw743	81	5	in	in	IN
cord-329276-tfrjw743	81	6	a	a	DT
cord-329276-tfrjw743	81	7	model	model	NN
cord-329276-tfrjw743	81	8	for	for	IN
cord-329276-tfrjw743	81	9	CML	CML	NNP
cord-329276-tfrjw743	81	10	(	(	-LRB-
cord-329276-tfrjw743	81	11	chronic	chronic	JJ
cord-329276-tfrjw743	81	12	myeloid	myeloid	NN
cord-329276-tfrjw743	81	13	leukemia	leukemia	NN
cord-329276-tfrjw743	81	14	)	)	-RRB-
cord-329276-tfrjw743	81	15	[	[	-LRB-
cord-329276-tfrjw743	81	16	21	21	CD
cord-329276-tfrjw743	81	17	]	]	-RRB-
cord-329276-tfrjw743	81	18	which	which	WDT
cord-329276-tfrjw743	81	19	includes	include	VBZ
cord-329276-tfrjw743	81	20	proliferating	proliferate	VBG
cord-329276-tfrjw743	81	21	cancer	cancer	NN
cord-329276-tfrjw743	81	22	cells	cell	NNS
cord-329276-tfrjw743	81	23	P	p	NN
cord-329276-tfrjw743	81	24	and	and	CC
cord-329276-tfrjw743	81	25	effector	effector	NN
cord-329276-tfrjw743	81	26	cells	cell	NNS
cord-329276-tfrjw743	81	27	E	E	NNS
cord-329276-tfrjw743	81	28	of	of	IN
cord-329276-tfrjw743	81	29	the	the	DT
cord-329276-tfrjw743	81	30	immune	immune	JJ
cord-329276-tfrjw743	81	31	system	system	NN
cord-329276-tfrjw743	81	32	,	,	,
cord-329276-tfrjw743	81	33	this	this	DT
cord-329276-tfrjw743	81	34	leads	lead	VBZ
cord-329276-tfrjw743	81	35	to	to	IN
cord-329276-tfrjw743	81	36	terms	term	NNS
cord-329276-tfrjw743	81	37	of	of	IN
cord-329276-tfrjw743	81	38	the	the	DT
cord-329276-tfrjw743	81	39	type	type	NN
cord-329276-tfrjw743	81	40	P	p	NN
cord-329276-tfrjw743	81	41	max	max	NN
cord-329276-tfrjw743	81	42	·	·	NFP
cord-329276-tfrjw743	81	43	P	p	NN
cord-329276-tfrjw743	81	44	PC	pc	NN
cord-329276-tfrjw743	81	45	50	50	CD
cord-329276-tfrjw743	81	46	+	+	SYM
cord-329276-tfrjw743	81	47	P	p	NN
cord-329276-tfrjw743	81	48	·	·	NFP
cord-329276-tfrjw743	81	49	E	e	NN
cord-329276-tfrjw743	81	50	with	with	IN
cord-329276-tfrjw743	81	51	P	p	NN
cord-329276-tfrjw743	81	52	max	max	NN
cord-329276-tfrjw743	81	53	denoting	denote	VBG
cord-329276-tfrjw743	81	54	the	the	DT
cord-329276-tfrjw743	81	55	maximum	maximum	JJ
cord-329276-tfrjw743	81	56	possible	possible	JJ
cord-329276-tfrjw743	81	57	effect	effect	NN
cord-329276-tfrjw743	81	58	and	and	CC
cord-329276-tfrjw743	81	59	PC	pc	NN
cord-329276-tfrjw743	81	60	50	50	CD
cord-329276-tfrjw743	81	61	the	the	DT
cord-329276-tfrjw743	81	62	concentration	concentration	NN
cord-329276-tfrjw743	81	63	of	of	IN
cord-329276-tfrjw743	81	64	proliferating	proliferate	VBG
cord-329276-tfrjw743	81	65	cancer	cancer	NN
cord-329276-tfrjw743	81	66	cells	cell	NNS
cord-329276-tfrjw743	81	67	for	for	IN
cord-329276-tfrjw743	81	68	which	which	WDT
cord-329276-tfrjw743	81	69	half	half	NN
cord-329276-tfrjw743	81	70	of	of	IN
cord-329276-tfrjw743	81	71	the	the	DT
cord-329276-tfrjw743	81	72	maximum	maximum	JJ
cord-329276-tfrjw743	81	73	effect	effect	NN
cord-329276-tfrjw743	81	74	is	be	VBZ
cord-329276-tfrjw743	81	75	realized	realize	VBN
cord-329276-tfrjw743	81	76	.	.	.
cord-329276-tfrjw743	82	1	Similar	similar	JJ
cord-329276-tfrjw743	82	2	terms	term	NNS
cord-329276-tfrjw743	82	3	describe	describe	VBP
cord-329276-tfrjw743	82	4	stimulating	stimulate	VBG
cord-329276-tfrjw743	82	5	or	or	CC
cord-329276-tfrjw743	82	6	inhibiting	inhibit	VBG
cord-329276-tfrjw743	82	7	effects	effect	NNS
cord-329276-tfrjw743	82	8	of	of	IN
cord-329276-tfrjw743	82	9	such	such	JJ
cord-329276-tfrjw743	82	10	interactions	interaction	NNS
cord-329276-tfrjw743	82	11	depending	depend	VBG
cord-329276-tfrjw743	82	12	on	on	IN
cord-329276-tfrjw743	82	13	the	the	DT
cord-329276-tfrjw743	82	14	nature	nature	NN
cord-329276-tfrjw743	82	15	of	of	IN
cord-329276-tfrjw743	82	16	the	the	DT
cord-329276-tfrjw743	82	17	variables	variable	NNS
cord-329276-tfrjw743	82	18	.	.	.
cord-329276-tfrjw743	83	1	Important	important	JJ
cord-329276-tfrjw743	83	2	aspects	aspect	NNS
cord-329276-tfrjw743	83	3	of	of	IN
cord-329276-tfrjw743	83	4	the	the	DT
cord-329276-tfrjw743	83	5	uncontrolled	uncontrolled	JJ
cord-329276-tfrjw743	83	6	dynamics	dynamic	NNS
cord-329276-tfrjw743	83	7	are	be	VBP
cord-329276-tfrjw743	83	8	multi	multi	JJ
cord-329276-tfrjw743	83	9	-	-	JJ
cord-329276-tfrjw743	83	10	stability	stability	NN
cord-329276-tfrjw743	83	11	and	and	CC
cord-329276-tfrjw743	83	12	the	the	DT
cord-329276-tfrjw743	83	13	geometry	geometry	NN
cord-329276-tfrjw743	83	14	of	of	IN
cord-329276-tfrjw743	83	15	the	the	DT
cord-329276-tfrjw743	83	16	regions	region	NNS
cord-329276-tfrjw743	83	17	of	of	IN
cord-329276-tfrjw743	83	18	attraction	attraction	NN
cord-329276-tfrjw743	83	19	of	of	IN
cord-329276-tfrjw743	83	20	locally	locally	RB
cord-329276-tfrjw743	83	21	stable	stable	JJ
cord-329276-tfrjw743	83	22	equilibria	equilibrium	NNS
cord-329276-tfrjw743	83	23	.	.	.
cord-329276-tfrjw743	84	1	We	-PRON-	PRP
cord-329276-tfrjw743	84	2	illustrate	illustrate	VBP
cord-329276-tfrjw743	84	3	these	these	DT
cord-329276-tfrjw743	84	4	features	feature	NNS
cord-329276-tfrjw743	84	5	using	use	VBG
cord-329276-tfrjw743	84	6	two	two	CD
cord-329276-tfrjw743	84	7	classical	classical	JJ
cord-329276-tfrjw743	84	8	models	model	NNS
cord-329276-tfrjw743	84	9	for	for	IN
cord-329276-tfrjw743	84	10	tumor	tumor	NN
cord-329276-tfrjw743	84	11	growth	growth	NN
cord-329276-tfrjw743	84	12	and	and	CC
cord-329276-tfrjw743	84	13	its	-PRON-	PRP$
cord-329276-tfrjw743	84	14	interactions	interaction	NNS
cord-329276-tfrjw743	84	15	with	with	IN
cord-329276-tfrjw743	84	16	the	the	DT
cord-329276-tfrjw743	84	17	tumor	tumor	NN
cord-329276-tfrjw743	84	18	micro	micro	JJ
cord-329276-tfrjw743	84	19	-	-	NN
cord-329276-tfrjw743	84	20	environment	environment	NN
cord-329276-tfrjw743	84	21	:	:	:
cord-329276-tfrjw743	84	22	the	the	DT
cord-329276-tfrjw743	84	23	model	model	NN
cord-329276-tfrjw743	84	24	for	for	IN
cord-329276-tfrjw743	84	25	angiogenic	angiogenic	JJ
cord-329276-tfrjw743	84	26	signaling	signal	VBG
cord-329276-tfrjw743	84	27	by	by	IN
cord-329276-tfrjw743	84	28	Hahnfeldt	Hahnfeldt	NNP
cord-329276-tfrjw743	84	29	et	et	NNP
cord-329276-tfrjw743	84	30	al	al	NNP
cord-329276-tfrjw743	84	31	.	.	.
cord-329276-tfrjw743	85	1	[	[	-LRB-
cord-329276-tfrjw743	85	2	19	19	CD
cord-329276-tfrjw743	85	3	]	]	-RRB-
cord-329276-tfrjw743	85	4	and	and	CC
cord-329276-tfrjw743	85	5	Stepanova	Stepanova	NNP
cord-329276-tfrjw743	85	6	's	's	POS
cord-329276-tfrjw743	85	7	model	model	NN
cord-329276-tfrjw743	85	8	for	for	IN
cord-329276-tfrjw743	85	9	tumor	tumor	NN
cord-329276-tfrjw743	85	10	immune	immune	JJ
cord-329276-tfrjw743	85	11	-	-	HYPH
cord-329276-tfrjw743	85	12	system	system	NN
cord-329276-tfrjw743	85	13	interactions	interaction	NNS
cord-329276-tfrjw743	85	14	[	[	-LRB-
cord-329276-tfrjw743	85	15	20	20	CD
cord-329276-tfrjw743	85	16	,	,	,
cord-329276-tfrjw743	85	17	22	22	CD
cord-329276-tfrjw743	85	18	,	,	,
cord-329276-tfrjw743	85	19	23	23	CD
cord-329276-tfrjw743	85	20	]	]	-RRB-
cord-329276-tfrjw743	85	21	.	.	.
cord-329276-tfrjw743	86	1	These	these	DT
cord-329276-tfrjw743	86	2	models	model	NNS
cord-329276-tfrjw743	86	3	also	also	RB
cord-329276-tfrjw743	86	4	serve	serve	VBP
cord-329276-tfrjw743	86	5	as	as	IN
cord-329276-tfrjw743	86	6	illustrations	illustration	NNS
cord-329276-tfrjw743	86	7	for	for	IN
cord-329276-tfrjw743	86	8	the	the	DT
cord-329276-tfrjw743	86	9	general	general	JJ
cord-329276-tfrjw743	86	10	elements	element	NNS
cord-329276-tfrjw743	86	11	of	of	IN
cord-329276-tfrjw743	86	12	the	the	DT
cord-329276-tfrjw743	86	13	dynamics	dynamic	NNS
cord-329276-tfrjw743	86	14	described	describe	VBN
cord-329276-tfrjw743	86	15	above	above	RB
cord-329276-tfrjw743	86	16	.	.	.
cord-329276-tfrjw743	87	1	(	(	-LRB-
cord-329276-tfrjw743	87	2	a	a	LS
cord-329276-tfrjw743	87	3	)	)	-RRB-
cord-329276-tfrjw743	87	4	angiogenic	angiogenic	NN
cord-329276-tfrjw743	87	5	signaling	signal	VBG
cord-329276-tfrjw743	87	6	In	in	IN
cord-329276-tfrjw743	87	7	this	this	DT
cord-329276-tfrjw743	87	8	model	model	NN
cord-329276-tfrjw743	87	9	by	by	IN
cord-329276-tfrjw743	87	10	Hahnfeldt	Hahnfeldt	NNP
cord-329276-tfrjw743	87	11	et	et	NNP
cord-329276-tfrjw743	87	12	al	al	NNP
cord-329276-tfrjw743	87	13	.	.	.
cord-329276-tfrjw743	88	1	[	[	-LRB-
cord-329276-tfrjw743	88	2	19	19	CD
cord-329276-tfrjw743	88	3	]	]	-RRB-
cord-329276-tfrjw743	88	4	,	,	,
cord-329276-tfrjw743	88	5	the	the	DT
cord-329276-tfrjw743	88	6	spatial	spatial	JJ
cord-329276-tfrjw743	88	7	aspects	aspect	NNS
cord-329276-tfrjw743	88	8	of	of	IN
cord-329276-tfrjw743	88	9	the	the	DT
cord-329276-tfrjw743	88	10	underlying	underlie	VBG
cord-329276-tfrjw743	88	11	consumption	consumption	NN
cord-329276-tfrjw743	88	12	-	-	HYPH
cord-329276-tfrjw743	88	13	diffusion	diffusion	NN
cord-329276-tfrjw743	88	14	process	process	NN
cord-329276-tfrjw743	88	15	that	that	WDT
cord-329276-tfrjw743	88	16	stimulate	stimulate	VBP
cord-329276-tfrjw743	88	17	and	and	CC
cord-329276-tfrjw743	88	18	inhibit	inhibit	VBP
cord-329276-tfrjw743	88	19	angiogenesis	angiogenesis	NN
cord-329276-tfrjw743	88	20	are	be	VBP
cord-329276-tfrjw743	88	21	incorporated	incorporate	VBN
cord-329276-tfrjw743	88	22	into	into	IN
cord-329276-tfrjw743	88	23	a	a	DT
cord-329276-tfrjw743	88	24	non	non	JJ
cord-329276-tfrjw743	88	25	-	-	JJ
cord-329276-tfrjw743	88	26	spatial	spatial	JJ
cord-329276-tfrjw743	88	27	2-compartment	2-compartment	CD
cord-329276-tfrjw743	88	28	model	model	NN
cord-329276-tfrjw743	88	29	with	with	IN
cord-329276-tfrjw743	88	30	the	the	DT
cord-329276-tfrjw743	88	31	primary	primary	JJ
cord-329276-tfrjw743	88	32	tumor	tumor	NN
cord-329276-tfrjw743	88	33	volume	volume	NN
cord-329276-tfrjw743	88	34	,	,	,
cord-329276-tfrjw743	88	35	p	p	NN
cord-329276-tfrjw743	88	36	,	,	,
cord-329276-tfrjw743	88	37	and	and	CC
cord-329276-tfrjw743	88	38	the	the	DT
cord-329276-tfrjw743	88	39	carrying	carry	VBG
cord-329276-tfrjw743	88	40	capacity	capacity	NN
cord-329276-tfrjw743	88	41	of	of	IN
cord-329276-tfrjw743	88	42	the	the	DT
cord-329276-tfrjw743	88	43	vasculature	vasculature	NN
cord-329276-tfrjw743	88	44	,	,	,
cord-329276-tfrjw743	88	45	q	q	NNP
cord-329276-tfrjw743	88	46	,	,	,
cord-329276-tfrjw743	88	47	as	as	IN
cord-329276-tfrjw743	88	48	its	-PRON-	PRP$
cord-329276-tfrjw743	88	49	principal	principal	JJ
cord-329276-tfrjw743	88	50	variables	variable	NNS
cord-329276-tfrjw743	88	51	.	.	.
cord-329276-tfrjw743	89	1	The	the	DT
cord-329276-tfrjw743	89	2	dynamics	dynamic	NNS
cord-329276-tfrjw743	89	3	consists	consist	VBZ
cord-329276-tfrjw743	89	4	of	of	IN
cord-329276-tfrjw743	89	5	two	two	CD
cord-329276-tfrjw743	89	6	ODEs	ode	NNS
cord-329276-tfrjw743	89	7	that	that	WDT
cord-329276-tfrjw743	89	8	describe	describe	VBP
cord-329276-tfrjw743	89	9	the	the	DT
cord-329276-tfrjw743	89	10	evolution	evolution	NN
cord-329276-tfrjw743	89	11	of	of	IN
cord-329276-tfrjw743	89	12	the	the	DT
cord-329276-tfrjw743	89	13	tumor	tumor	NN
cord-329276-tfrjw743	89	14	volume	volume	NN
cord-329276-tfrjw743	89	15	and	and	CC
cord-329276-tfrjw743	89	16	its	-PRON-	PRP$
cord-329276-tfrjw743	89	17	carrying	carrying	NN
cord-329276-tfrjw743	89	18	capacity	capacity	NN
cord-329276-tfrjw743	89	19	which	which	WDT
cord-329276-tfrjw743	89	20	are	be	VBP
cord-329276-tfrjw743	89	21	given	give	VBN
cord-329276-tfrjw743	89	22	bẏ	bẏ	IN
cord-329276-tfrjw743	90	1	Thus	thus	RB
cord-329276-tfrjw743	90	2	,	,	,
cord-329276-tfrjw743	90	3	a	a	DT
cord-329276-tfrjw743	90	4	Gompertzian	gompertzian	JJ
cord-329276-tfrjw743	90	5	growth	growth	NN
cord-329276-tfrjw743	90	6	term	term	NN
cord-329276-tfrjw743	90	7	is	be	VBZ
cord-329276-tfrjw743	90	8	used	use	VBN
cord-329276-tfrjw743	90	9	to	to	TO
cord-329276-tfrjw743	90	10	model	model	VB
cord-329276-tfrjw743	90	11	tumor	tumor	NN
cord-329276-tfrjw743	90	12	growth	growth	NN
cord-329276-tfrjw743	90	13	.	.	.
cord-329276-tfrjw743	91	1	The	the	DT
cord-329276-tfrjw743	91	2	carrying	carrying	NN
cord-329276-tfrjw743	91	3	capacity	capacity	NN
cord-329276-tfrjw743	91	4	q	q	NN
cord-329276-tfrjw743	91	5	and	and	CC
cord-329276-tfrjw743	91	6	tumor	tumor	NN
cord-329276-tfrjw743	91	7	volume	volume	NN
cord-329276-tfrjw743	91	8	p	p	NN
cord-329276-tfrjw743	91	9	are	be	VBP
cord-329276-tfrjw743	91	10	balanced	balance	VBN
cord-329276-tfrjw743	91	11	for	for	IN
cord-329276-tfrjw743	91	12	p	p	NN
cord-329276-tfrjw743	92	1	=	=	NFP
cord-329276-tfrjw743	92	2	q	q	NNP
cord-329276-tfrjw743	92	3	,	,	,
cord-329276-tfrjw743	92	4	while	while	IN
cord-329276-tfrjw743	92	5	the	the	DT
cord-329276-tfrjw743	92	6	tumor	tumor	NN
cord-329276-tfrjw743	92	7	volume	volume	NN
cord-329276-tfrjw743	92	8	shrinks	shrink	VBZ
cord-329276-tfrjw743	92	9	for	for	IN
cord-329276-tfrjw743	92	10	inadequate	inadequate	JJ
cord-329276-tfrjw743	92	11	vascular	vascular	JJ
cord-329276-tfrjw743	92	12	support	support	NN
cord-329276-tfrjw743	92	13	(	(	-LRB-
cord-329276-tfrjw743	92	14	q	q	NNP
cord-329276-tfrjw743	92	15	<	<	XX
cord-329276-tfrjw743	92	16	p	p	NN
cord-329276-tfrjw743	92	17	)	)	-RRB-
cord-329276-tfrjw743	92	18	and	and	CC
cord-329276-tfrjw743	92	19	increases	increase	NNS
cord-329276-tfrjw743	92	20	if	if	IN
cord-329276-tfrjw743	92	21	this	this	DT
cord-329276-tfrjw743	92	22	support	support	NN
cord-329276-tfrjw743	92	23	is	be	VBZ
cord-329276-tfrjw743	92	24	plentiful	plentiful	JJ
cord-329276-tfrjw743	92	25	(	(	-LRB-
cord-329276-tfrjw743	92	26	q	q	NN
cord-329276-tfrjw743	92	27	>	>	XX
cord-329276-tfrjw743	92	28	p	p	NN
cord-329276-tfrjw743	92	29	)	)	-RRB-
cord-329276-tfrjw743	92	30	.	.	.
cord-329276-tfrjw743	93	1	Different	different	JJ
cord-329276-tfrjw743	93	2	from	from	IN
cord-329276-tfrjw743	93	3	traditional	traditional	JJ
cord-329276-tfrjw743	93	4	approaches	approach	NNS
cord-329276-tfrjw743	93	5	,	,	,
cord-329276-tfrjw743	93	6	the	the	DT
cord-329276-tfrjw743	93	7	carrying	carrying	NN
cord-329276-tfrjw743	93	8	capacity	capacity	NN
cord-329276-tfrjw743	93	9	is	be	VBZ
cord-329276-tfrjw743	93	10	not	not	RB
cord-329276-tfrjw743	93	11	considered	consider	VBN
cord-329276-tfrjw743	93	12	constant	constant	JJ
cord-329276-tfrjw743	93	13	,	,	,
cord-329276-tfrjw743	93	14	but	but	CC
cord-329276-tfrjw743	93	15	becomes	become	VBZ
cord-329276-tfrjw743	93	16	a	a	DT
cord-329276-tfrjw743	93	17	state	state	NN
cord-329276-tfrjw743	93	18	variable	variable	NN
cord-329276-tfrjw743	93	19	whose	whose	WP$
cord-329276-tfrjw743	93	20	evolution	evolution	NN
cord-329276-tfrjw743	93	21	is	be	VBZ
cord-329276-tfrjw743	93	22	governed	govern	VBN
cord-329276-tfrjw743	93	23	by	by	IN
cord-329276-tfrjw743	93	24	a	a	DT
cord-329276-tfrjw743	93	25	balance	balance	NN
cord-329276-tfrjw743	93	26	of	of	IN
cord-329276-tfrjw743	93	27	stimulatory	stimulatory	JJ
cord-329276-tfrjw743	93	28	and	and	CC
cord-329276-tfrjw743	93	29	inhibitory	inhibitory	JJ
cord-329276-tfrjw743	93	30	effects	effect	NNS
cord-329276-tfrjw743	93	31	.	.	.
cord-329276-tfrjw743	94	1	The	the	DT
cord-329276-tfrjw743	94	2	term	term	NN
cord-329276-tfrjw743	94	3	bp	bp	NNP
cord-329276-tfrjw743	94	4	represents	represent	VBZ
cord-329276-tfrjw743	94	5	the	the	DT
cord-329276-tfrjw743	94	6	stimulation	stimulation	NN
cord-329276-tfrjw743	94	7	of	of	IN
cord-329276-tfrjw743	94	8	the	the	DT
cord-329276-tfrjw743	94	9	vasculature	vasculature	NN
cord-329276-tfrjw743	94	10	by	by	IN
cord-329276-tfrjw743	94	11	the	the	DT
cord-329276-tfrjw743	94	12	tumor	tumor	NN
cord-329276-tfrjw743	94	13	and	and	CC
cord-329276-tfrjw743	94	14	is	be	VBZ
cord-329276-tfrjw743	94	15	taken	take	VBN
cord-329276-tfrjw743	94	16	proportional	proportional	JJ
cord-329276-tfrjw743	94	17	to	to	IN
cord-329276-tfrjw743	94	18	the	the	DT
cord-329276-tfrjw743	94	19	tumor	tumor	NN
cord-329276-tfrjw743	94	20	volume	volume	NN
cord-329276-tfrjw743	94	21	.	.	.
cord-329276-tfrjw743	95	1	The	the	DT
cord-329276-tfrjw743	95	2	term	term	NN
cord-329276-tfrjw743	95	3	dp	dp	NN
cord-329276-tfrjw743	95	4	2	2	CD
cord-329276-tfrjw743	95	5	3	3	CD
cord-329276-tfrjw743	95	6	q	q	NNP
cord-329276-tfrjw743	95	7	models	model	VBZ
cord-329276-tfrjw743	95	8	the	the	DT
cord-329276-tfrjw743	95	9	inhibition	inhibition	NN
cord-329276-tfrjw743	95	10	of	of	IN
cord-329276-tfrjw743	95	11	the	the	DT
cord-329276-tfrjw743	95	12	vasculature	vasculature	NN
cord-329276-tfrjw743	95	13	by	by	IN
cord-329276-tfrjw743	95	14	the	the	DT
cord-329276-tfrjw743	95	15	tumor	tumor	NN
cord-329276-tfrjw743	95	16	which	which	WDT
cord-329276-tfrjw743	95	17	,	,	,
cord-329276-tfrjw743	95	18	as	as	IN
cord-329276-tfrjw743	95	19	mentioned	mention	VBN
cord-329276-tfrjw743	95	20	above	above	RB
cord-329276-tfrjw743	95	21	,	,	,
cord-329276-tfrjw743	95	22	is	be	VBZ
cord-329276-tfrjw743	95	23	represented	represent	VBN
cord-329276-tfrjw743	95	24	as	as	IN
cord-329276-tfrjw743	95	25	an	an	DT
cord-329276-tfrjw743	95	26	interaction	interaction	NN
cord-329276-tfrjw743	95	27	term	term	NN
cord-329276-tfrjw743	95	28	between	between	IN
cord-329276-tfrjw743	95	29	the	the	DT
cord-329276-tfrjw743	95	30	tumor	tumor	NN
cord-329276-tfrjw743	95	31	surface	surface	NN
cord-329276-tfrjw743	95	32	and	and	CC
cord-329276-tfrjw743	95	33	the	the	DT
cord-329276-tfrjw743	95	34	vasculature	vasculature	NN
cord-329276-tfrjw743	95	35	.	.	.
cord-329276-tfrjw743	96	1	The	the	DT
cord-329276-tfrjw743	96	2	coefficients	coefficient	NNS
cord-329276-tfrjw743	96	3	b	b	NN
cord-329276-tfrjw743	96	4	and	and	CC
cord-329276-tfrjw743	96	5	d	d	NN
cord-329276-tfrjw743	96	6	are	be	VBP
cord-329276-tfrjw743	96	7	mnemonically	mnemonically	RB
cord-329276-tfrjw743	96	8	labeled	label	VBN
cord-329276-tfrjw743	96	9	for	for	IN
cord-329276-tfrjw743	96	10	birth	birth	NN
cord-329276-tfrjw743	96	11	and	and	CC
cord-329276-tfrjw743	96	12	death	death	NN
cord-329276-tfrjw743	96	13	,	,	,
cord-329276-tfrjw743	96	14	respectively	respectively	RB
cord-329276-tfrjw743	96	15	.	.	.
cord-329276-tfrjw743	97	1	The	the	DT
cord-329276-tfrjw743	97	2	last	last	JJ
cord-329276-tfrjw743	97	3	term	term	NN
cord-329276-tfrjw743	97	4	−μq	−μq	NN
cord-329276-tfrjw743	97	5	simply	simply	RB
cord-329276-tfrjw743	97	6	represents	represent	VBZ
cord-329276-tfrjw743	97	7	a	a	DT
cord-329276-tfrjw743	97	8	natural	natural	JJ
cord-329276-tfrjw743	97	9	death	death	NN
cord-329276-tfrjw743	97	10	term	term	NN
cord-329276-tfrjw743	97	11	related	relate	VBN
cord-329276-tfrjw743	97	12	to	to	IN
cord-329276-tfrjw743	97	13	the	the	DT
cord-329276-tfrjw743	97	14	vasculature	vasculature	NN
cord-329276-tfrjw743	97	15	.	.	.
cord-329276-tfrjw743	98	1	This	this	DT
cord-329276-tfrjw743	98	2	model	model	NN
cord-329276-tfrjw743	98	3	has	have	VBZ
cord-329276-tfrjw743	98	4	a	a	DT
cord-329276-tfrjw743	98	5	unique	unique	JJ
cord-329276-tfrjw743	98	6	equilibrium	equilibrium	NN
cord-329276-tfrjw743	98	7	at	at	IN
cord-329276-tfrjw743	98	8	which	which	WDT
cord-329276-tfrjw743	98	9	is	be	VBZ
cord-329276-tfrjw743	98	10	globally	globally	RB
cord-329276-tfrjw743	98	11	asymptotically	asymptotically	RB
cord-329276-tfrjw743	98	12	stable	stable	JJ
cord-329276-tfrjw743	98	13	(	(	-LRB-
cord-329276-tfrjw743	98	14	relative	relative	JJ
cord-329276-tfrjw743	98	15	to	to	IN
cord-329276-tfrjw743	98	16	the	the	DT
cord-329276-tfrjw743	98	17	natural	natural	JJ
cord-329276-tfrjw743	98	18	state	state	NN
cord-329276-tfrjw743	98	19	-	-	HYPH
cord-329276-tfrjw743	98	20	space	space	NN
cord-329276-tfrjw743	98	21	D	d	NN
cord-329276-tfrjw743	98	22	=	=	NN
cord-329276-tfrjw743	98	23	{	{	-LRB-
cord-329276-tfrjw743	98	24	(	(	-LRB-
cord-329276-tfrjw743	98	25	p	p	NN
cord-329276-tfrjw743	98	26	,	,	,
cord-329276-tfrjw743	98	27	q	q	NNP
cord-329276-tfrjw743	98	28	)	)	-RRB-
cord-329276-tfrjw743	98	29	:	:	:
cord-329276-tfrjw743	98	30	p	p	NN
cord-329276-tfrjw743	98	31	>	>	XX
cord-329276-tfrjw743	98	32	0	0	CD
cord-329276-tfrjw743	98	33	,	,	,
cord-329276-tfrjw743	98	34	q	q	NN
cord-329276-tfrjw743	98	35	>	>	XX
cord-329276-tfrjw743	98	36	0	0	NFP
cord-329276-tfrjw743	98	37	}	}	-RRB-
cord-329276-tfrjw743	98	38	)	)	-RRB-
cord-329276-tfrjw743	99	1	[	[	-LRB-
cord-329276-tfrjw743	99	2	24	24	CD
cord-329276-tfrjw743	99	3	]	]	-RRB-
cord-329276-tfrjw743	99	4	(	(	-LRB-
cord-329276-tfrjw743	99	5	see	see	VB
cord-329276-tfrjw743	99	6	Fig	Fig	NNP
cord-329276-tfrjw743	99	7	.	.	NNP
cord-329276-tfrjw743	99	8	1	1	CD
cord-329276-tfrjw743	99	9	)	)	-RRB-
cord-329276-tfrjw743	99	10	.	.	.
cord-329276-tfrjw743	100	1	The	the	DT
cord-329276-tfrjw743	100	2	dynamics	dynamic	NNS
cord-329276-tfrjw743	100	3	has	have	VBZ
cord-329276-tfrjw743	100	4	a	a	DT
cord-329276-tfrjw743	100	5	strong	strong	JJ
cord-329276-tfrjw743	100	6	differentialalgebraic	differentialalgebraic	JJ
cord-329276-tfrjw743	100	7	character	character	NN
cord-329276-tfrjw743	100	8	with	with	IN
cord-329276-tfrjw743	100	9	the	the	DT
cord-329276-tfrjw743	100	10	q	q	NN
cord-329276-tfrjw743	100	11	-	-	HYPH
cord-329276-tfrjw743	100	12	dynamics	dynamic	NNS
cord-329276-tfrjw743	100	13	of	of	IN
cord-329276-tfrjw743	100	14	the	the	DT
cord-329276-tfrjw743	100	15	vasculature	vasculature	NN
cord-329276-tfrjw743	100	16	fast	fast	RB
cord-329276-tfrjw743	100	17	and	and	CC
cord-329276-tfrjw743	100	18	the	the	DT
cord-329276-tfrjw743	100	19	p	p	NN
cord-329276-tfrjw743	100	20	-	-	HYPH
cord-329276-tfrjw743	100	21	dynamics	dynamic	NNS
cord-329276-tfrjw743	100	22	for	for	IN
cord-329276-tfrjw743	100	23	the	the	DT
cord-329276-tfrjw743	100	24	tumor	tumor	NN
cord-329276-tfrjw743	100	25	volume	volume	NN
cord-329276-tfrjw743	100	26	slow	slow	JJ
cord-329276-tfrjw743	100	27	.	.	.
cord-329276-tfrjw743	101	1	Essentially	essentially	RB
cord-329276-tfrjw743	101	2	,	,	,
cord-329276-tfrjw743	101	3	the	the	DT
cord-329276-tfrjw743	101	4	system	system	NN
cord-329276-tfrjw743	101	5	follows	follow	VBZ
cord-329276-tfrjw743	101	6	the	the	DT
cord-329276-tfrjw743	101	7	corresponding	correspond	VBG
cord-329276-tfrjw743	101	8	null	null	NN
cord-329276-tfrjw743	101	9	-	-	HYPH
cord-329276-tfrjw743	101	10	cline	cline	JJ
cord-329276-tfrjw743	101	11	(	(	-LRB-
cord-329276-tfrjw743	101	12	defined	define	VBN
cord-329276-tfrjw743	101	13	by	by	IN
cord-329276-tfrjw743	101	14	the	the	DT
cord-329276-tfrjw743	101	15	equationq	equationq	NN
cord-329276-tfrjw743	101	16	=	=	SYM
cord-329276-tfrjw743	101	17	0	0	NFP
cord-329276-tfrjw743	101	18	)	)	-RRB-
cord-329276-tfrjw743	101	19	into	into	IN
cord-329276-tfrjw743	101	20	the	the	DT
cord-329276-tfrjw743	101	21	unique	unique	JJ
cord-329276-tfrjw743	101	22	equilibrium	equilibrium	NN
cord-329276-tfrjw743	101	23	point	point	NN
cord-329276-tfrjw743	101	24	.	.	.
cord-329276-tfrjw743	102	1	For	for	IN
cord-329276-tfrjw743	102	2	realistic	realistic	JJ
cord-329276-tfrjw743	102	3	values	value	NNS
cord-329276-tfrjw743	102	4	of	of	IN
cord-329276-tfrjw743	102	5	the	the	DT
cord-329276-tfrjw743	102	6	parameters	parameter	NNS
cord-329276-tfrjw743	102	7	,	,	,
cord-329276-tfrjw743	102	8	this	this	DT
cord-329276-tfrjw743	102	9	equilibrium	equilibrium	NN
cord-329276-tfrjw743	102	10	is	be	VBZ
cord-329276-tfrjw743	102	11	not	not	RB
cord-329276-tfrjw743	102	12	biologically	biologically	RB
cord-329276-tfrjw743	102	13	viable	viable	JJ
cord-329276-tfrjw743	102	14	and	and	CC
cord-329276-tfrjw743	102	15	therapy	therapy	NN
cord-329276-tfrjw743	102	16	is	be	VBZ
cord-329276-tfrjw743	102	17	needed	need	VBN
cord-329276-tfrjw743	102	18	to	to	TO
cord-329276-tfrjw743	102	19	lower	lower	VB
cord-329276-tfrjw743	102	20	or	or	CC
cord-329276-tfrjw743	102	21	even	even	RB
cord-329276-tfrjw743	102	22	eradicate	eradicate	VB
cord-329276-tfrjw743	102	23	this	this	DT
cord-329276-tfrjw743	102	24	equilibrium	equilibrium	NN
cord-329276-tfrjw743	102	25	point	point	NN
cord-329276-tfrjw743	102	26	.	.	.
cord-329276-tfrjw743	103	1	In	in	IN
cord-329276-tfrjw743	103	2	the	the	DT
cord-329276-tfrjw743	103	3	later	later	JJ
cord-329276-tfrjw743	103	4	case	case	NN
cord-329276-tfrjw743	103	5	,	,	,
cord-329276-tfrjw743	103	6	the	the	DT
cord-329276-tfrjw743	103	7	objective	objective	NN
cord-329276-tfrjw743	103	8	then	then	RB
cord-329276-tfrjw743	103	9	becomes	become	VBZ
cord-329276-tfrjw743	103	10	to	to	TO
cord-329276-tfrjw743	103	11	drive	drive	VB
cord-329276-tfrjw743	103	12	the	the	DT
cord-329276-tfrjw743	103	13	state	state	NN
cord-329276-tfrjw743	103	14	of	of	IN
cord-329276-tfrjw743	103	15	the	the	DT
cord-329276-tfrjw743	103	16	system	system	NN
cord-329276-tfrjw743	103	17	toward	toward	IN
cord-329276-tfrjw743	103	18	the	the	DT
cord-329276-tfrjw743	103	19	singular	singular	JJ
cord-329276-tfrjw743	103	20	point	point	NN
cord-329276-tfrjw743	103	21	(	(	-LRB-
cord-329276-tfrjw743	103	22	p	p	NN
cord-329276-tfrjw743	103	23	,	,	,
cord-329276-tfrjw743	103	24	q	q	NNP
cord-329276-tfrjw743	103	25	)	)	-RRB-
cord-329276-tfrjw743	103	26	=	=	NFP
cord-329276-tfrjw743	103	27	(	(	-LRB-
cord-329276-tfrjw743	103	28	0	0	CD
cord-329276-tfrjw743	103	29	,	,	,
cord-329276-tfrjw743	103	30	0	0	CD
cord-329276-tfrjw743	103	31	)	)	-RRB-
cord-329276-tfrjw743	103	32	.	.	.
cord-329276-tfrjw743	104	1	(	(	-LRB-
cord-329276-tfrjw743	104	2	b	b	LS
cord-329276-tfrjw743	104	3	)	)	-RRB-
cord-329276-tfrjw743	104	4	Tumor	tumor	NN
cord-329276-tfrjw743	104	5	immune	immune	JJ
cord-329276-tfrjw743	104	6	system	system	NN
cord-329276-tfrjw743	104	7	interactions	interaction	NNS
cord-329276-tfrjw743	104	8	In	in	IN
cord-329276-tfrjw743	104	9	this	this	DT
cord-329276-tfrjw743	104	10	by	by	IN
cord-329276-tfrjw743	104	11	now	now	RB
cord-329276-tfrjw743	104	12	classical	classical	JJ
cord-329276-tfrjw743	104	13	mathematical	mathematical	JJ
cord-329276-tfrjw743	104	14	model	model	NN
cord-329276-tfrjw743	104	15	of	of	IN
cord-329276-tfrjw743	104	16	Stepanova	Stepanova	NNP
cord-329276-tfrjw743	104	17	[	[	-LRB-
cord-329276-tfrjw743	104	18	20	20	CD
cord-329276-tfrjw743	104	19	]	]	-RRB-
cord-329276-tfrjw743	104	20	,	,	,
cord-329276-tfrjw743	104	21	two	two	CD
cord-329276-tfrjw743	104	22	ordinary	ordinary	JJ
cord-329276-tfrjw743	104	23	differential	differential	JJ
cord-329276-tfrjw743	104	24	equations	equation	NNS
cord-329276-tfrjw743	104	25	formulate	formulate	VBP
cord-329276-tfrjw743	104	26	the	the	DT
cord-329276-tfrjw743	104	27	aggregated	aggregate	VBN
cord-329276-tfrjw743	104	28	interactions	interaction	NNS
cord-329276-tfrjw743	104	29	between	between	IN
cord-329276-tfrjw743	104	30	cancer	cancer	NN
cord-329276-tfrjw743	104	31	cell	cell	NN
cord-329276-tfrjw743	104	32	growth	growth	NN
cord-329276-tfrjw743	104	33	and	and	CC
cord-329276-tfrjw743	104	34	the	the	DT
cord-329276-tfrjw743	104	35	activities	activity	NNS
cord-329276-tfrjw743	104	36	of	of	IN
cord-329276-tfrjw743	104	37	the	the	DT
cord-329276-tfrjw743	104	38	immune	immune	JJ
cord-329276-tfrjw743	104	39	system	system	NN
cord-329276-tfrjw743	104	40	during	during	IN
cord-329276-tfrjw743	104	41	the	the	DT
cord-329276-tfrjw743	104	42	development	development	NN
cord-329276-tfrjw743	104	43	of	of	IN
cord-329276-tfrjw743	104	44	cancer	cancer	NN
cord-329276-tfrjw743	104	45	.	.	.
cord-329276-tfrjw743	105	1	Precisely	precisely	RB
cord-329276-tfrjw743	105	2	because	because	IN
cord-329276-tfrjw743	105	3	of	of	IN
cord-329276-tfrjw743	105	4	its	-PRON-	PRP$
cord-329276-tfrjw743	105	5	simplicity	simplicity	NN
cord-329276-tfrjw743	105	6	-	-	:
cord-329276-tfrjw743	105	7	a	a	DT
cord-329276-tfrjw743	105	8	few	few	JJ
cord-329276-tfrjw743	105	9	parameters	parameter	NNS
cord-329276-tfrjw743	105	10	incorporate	incorporate	VBP
cord-329276-tfrjw743	105	11	many	many	JJ
cord-329276-tfrjw743	105	12	medically	medically	RB
cord-329276-tfrjw743	105	13	important	important	JJ
cord-329276-tfrjw743	105	14	features	feature	NNS
cord-329276-tfrjw743	105	15	-	-	,
cord-329276-tfrjw743	105	16	the	the	DT
cord-329276-tfrjw743	105	17	underlying	underlying	JJ
cord-329276-tfrjw743	105	18	equations	equation	NNS
cord-329276-tfrjw743	105	19	have	have	VBP
cord-329276-tfrjw743	105	20	been	be	VBN
cord-329276-tfrjw743	105	21	widely	widely	RB
cord-329276-tfrjw743	105	22	accepted	accept	VBN
cord-329276-tfrjw743	105	23	as	as	IN
cord-329276-tfrjw743	105	24	a	a	DT
cord-329276-tfrjw743	105	25	basic	basic	JJ
cord-329276-tfrjw743	105	26	model	model	NN
cord-329276-tfrjw743	105	27	.	.	.
cord-329276-tfrjw743	106	1	The	the	DT
cord-329276-tfrjw743	106	2	main	main	JJ
cord-329276-tfrjw743	106	3	features	feature	NNS
cord-329276-tfrjw743	106	4	of	of	IN
cord-329276-tfrjw743	106	5	tumor	tumor	NN
cord-329276-tfrjw743	106	6	immune	immune	JJ
cord-329276-tfrjw743	106	7	system	system	NN
cord-329276-tfrjw743	106	8	interactions	interaction	NNS
cord-329276-tfrjw743	106	9	are	be	VBP
cord-329276-tfrjw743	106	10	aggregated	aggregate	VBN
cord-329276-tfrjw743	106	11	into	into	IN
cord-329276-tfrjw743	106	12	just	just	RB
cord-329276-tfrjw743	106	13	two	two	CD
cord-329276-tfrjw743	106	14	variables	variable	NNS
cord-329276-tfrjw743	106	15	,	,	,
cord-329276-tfrjw743	106	16	the	the	DT
cord-329276-tfrjw743	106	17	tumor	tumor	NN
cord-329276-tfrjw743	106	18	volume	volume	NN
cord-329276-tfrjw743	106	19	,	,	,
cord-329276-tfrjw743	106	20	p	p	NN
cord-329276-tfrjw743	106	21	,	,	,
cord-329276-tfrjw743	106	22	and	and	CC
cord-329276-tfrjw743	106	23	the	the	DT
cord-329276-tfrjw743	106	24	immunocompetent	immunocompetent	JJ
cord-329276-tfrjw743	106	25	cell	cell	NN
cord-329276-tfrjw743	106	26	densities	density	NNS
cord-329276-tfrjw743	106	27	,	,	,
cord-329276-tfrjw743	106	28	r	r	NNP
cord-329276-tfrjw743	106	29	,	,	,
cord-329276-tfrjw743	106	30	a	a	DT
cord-329276-tfrjw743	106	31	non	non	JJ
cord-329276-tfrjw743	106	32	-	-	JJ
cord-329276-tfrjw743	106	33	dimensional	dimensional	JJ
cord-329276-tfrjw743	106	34	,	,	,
cord-329276-tfrjw743	106	35	order	order	NN
cord-329276-tfrjw743	106	36	of	of	IN
cord-329276-tfrjw743	106	37	magnitude	magnitude	NN
cord-329276-tfrjw743	106	38	quantity	quantity	NN
cord-329276-tfrjw743	106	39	related	relate	VBN
cord-329276-tfrjw743	106	40	to	to	IN
cord-329276-tfrjw743	106	41	various	various	JJ
cord-329276-tfrjw743	106	42	[	[	-LRB-
cord-329276-tfrjw743	106	43	19	19	CD
cord-329276-tfrjw743	106	44	]	]	-RRB-
cord-329276-tfrjw743	106	45	,	,	,
cord-329276-tfrjw743	106	46	a	a	DT
cord-329276-tfrjw743	106	47	fast	fast	JJ
cord-329276-tfrjw743	106	48	growing	grow	VBG
cord-329276-tfrjw743	106	49	cancer	cancer	NN
cord-329276-tfrjw743	106	50	.	.	.
cord-329276-tfrjw743	107	1	The	the	DT
cord-329276-tfrjw743	107	2	almost	almost	RB
cord-329276-tfrjw743	107	3	horizontal	horizontal	JJ
cord-329276-tfrjw743	107	4	segments	segment	NNS
cord-329276-tfrjw743	107	5	indicate	indicate	VBP
cord-329276-tfrjw743	107	6	a	a	DT
cord-329276-tfrjw743	107	7	strong	strong	JJ
cord-329276-tfrjw743	107	8	differential	differential	JJ
cord-329276-tfrjw743	107	9	-	-	HYPH
cord-329276-tfrjw743	107	10	algebraic	algebraic	JJ
cord-329276-tfrjw743	107	11	character	character	NN
cord-329276-tfrjw743	107	12	with	with	IN
cord-329276-tfrjw743	107	13	trajectories	trajectory	NNS
cord-329276-tfrjw743	107	14	eventually	eventually	RB
cord-329276-tfrjw743	107	15	following	follow	VBG
cord-329276-tfrjw743	107	16	theq	theq	NNP
cord-329276-tfrjw743	107	17	-	-	HYPH
cord-329276-tfrjw743	107	18	nullcline	nullcline	NNP
cord-329276-tfrjw743	107	19	defined	define	VBN
cord-329276-tfrjw743	107	20	byq	byq	NN
cord-329276-tfrjw743	107	21	=	=	SYM
cord-329276-tfrjw743	107	22	0	0	CD
cord-329276-tfrjw743	107	23	types	type	NNS
cord-329276-tfrjw743	107	24	of	of	IN
cord-329276-tfrjw743	107	25	immune	immune	JJ
cord-329276-tfrjw743	107	26	cells	cell	NNS
cord-329276-tfrjw743	107	27	(	(	-LRB-
cord-329276-tfrjw743	107	28	T	t	NN
cord-329276-tfrjw743	107	29	-	-	HYPH
cord-329276-tfrjw743	107	30	cells	cell	NNS
cord-329276-tfrjw743	107	31	)	)	-RRB-
cord-329276-tfrjw743	107	32	activated	activate	VBD
cord-329276-tfrjw743	107	33	during	during	IN
cord-329276-tfrjw743	107	34	the	the	DT
cord-329276-tfrjw743	107	35	immune	immune	JJ
cord-329276-tfrjw743	107	36	reaction	reaction	NN
cord-329276-tfrjw743	107	37	.	.	.
cord-329276-tfrjw743	108	1	The	the	DT
cord-329276-tfrjw743	108	2	resulting	result	VBG
cord-329276-tfrjw743	108	3	dynamics	dynamic	NNS
cord-329276-tfrjw743	108	4	takes	take	VBZ
cord-329276-tfrjw743	108	5	the	the	DT
cord-329276-tfrjw743	108	6	following	follow	VBG
cord-329276-tfrjw743	108	7	form	form	NN
cord-329276-tfrjw743	108	8	:	:	:
cord-329276-tfrjw743	108	9	with	with	IN
cord-329276-tfrjw743	108	10	F	F	NNP
cord-329276-tfrjw743	108	11	a	a	DT
cord-329276-tfrjw743	108	12	tumor	tumor	NN
cord-329276-tfrjw743	108	13	growth	growth	NN
cord-329276-tfrjw743	108	14	function	function	NN
cord-329276-tfrjw743	108	15	.	.	.
cord-329276-tfrjw743	109	1	Greek	greek	JJ
cord-329276-tfrjw743	109	2	letters	letter	NNS
cord-329276-tfrjw743	109	3	denote	denote	VBP
cord-329276-tfrjw743	109	4	constant	constant	JJ
cord-329276-tfrjw743	109	5	coefficients	coefficient	NNS
cord-329276-tfrjw743	109	6	which	which	WDT
cord-329276-tfrjw743	109	7	model	model	VBP
cord-329276-tfrjw743	109	8	the	the	DT
cord-329276-tfrjw743	109	9	main	main	JJ
cord-329276-tfrjw743	109	10	interactions	interaction	NNS
cord-329276-tfrjw743	109	11	of	of	IN
cord-329276-tfrjw743	109	12	the	the	DT
cord-329276-tfrjw743	109	13	tumor	tumor	NN
cord-329276-tfrjw743	109	14	with	with	IN
cord-329276-tfrjw743	109	15	the	the	DT
cord-329276-tfrjw743	109	16	immune	immune	JJ
cord-329276-tfrjw743	109	17	system	system	NN
cord-329276-tfrjw743	109	18	.	.	.
cord-329276-tfrjw743	110	1	Various	various	JJ
cord-329276-tfrjw743	110	2	organs	organ	NNS
cord-329276-tfrjw743	110	3	such	such	JJ
cord-329276-tfrjw743	110	4	as	as	IN
cord-329276-tfrjw743	110	5	the	the	DT
cord-329276-tfrjw743	110	6	spleen	spleen	NN
cord-329276-tfrjw743	110	7	,	,	,
cord-329276-tfrjw743	110	8	thymus	thymus	NN
cord-329276-tfrjw743	110	9	,	,	,
cord-329276-tfrjw743	110	10	lymph	lymph	NN
cord-329276-tfrjw743	110	11	nodes	node	NNS
cord-329276-tfrjw743	110	12	and	and	CC
cord-329276-tfrjw743	110	13	bone	bone	NN
cord-329276-tfrjw743	110	14	marrow	marrow	NN
cord-329276-tfrjw743	110	15	,	,	,
cord-329276-tfrjw743	110	16	each	each	DT
cord-329276-tfrjw743	110	17	contribute	contribute	VBP
cord-329276-tfrjw743	110	18	to	to	IN
cord-329276-tfrjw743	110	19	the	the	DT
cord-329276-tfrjw743	110	20	development	development	NN
cord-329276-tfrjw743	110	21	of	of	IN
cord-329276-tfrjw743	110	22	immune	immune	JJ
cord-329276-tfrjw743	110	23	cells	cell	NNS
cord-329276-tfrjw743	110	24	in	in	IN
cord-329276-tfrjw743	110	25	the	the	DT
cord-329276-tfrjw743	110	26	body	body	NN
cord-329276-tfrjw743	110	27	and	and	CC
cord-329276-tfrjw743	110	28	the	the	DT
cord-329276-tfrjw743	110	29	parameter	parameter	NN
cord-329276-tfrjw743	110	30	γ	γ	NN
cord-329276-tfrjw743	110	31	in	in	IN
cord-329276-tfrjw743	110	32	Eq	Eq	NNP
cord-329276-tfrjw743	110	33	.	.	.
cord-329276-tfrjw743	111	1	(	(	-LRB-
cord-329276-tfrjw743	111	2	6	6	CD
cord-329276-tfrjw743	111	3	)	)	-RRB-
cord-329276-tfrjw743	111	4	models	model	NNS
cord-329276-tfrjw743	111	5	a	a	DT
cord-329276-tfrjw743	111	6	combined	combine	VBN
cord-329276-tfrjw743	111	7	rate	rate	NN
cord-329276-tfrjw743	111	8	of	of	IN
cord-329276-tfrjw743	111	9	influx	influx	NN
cord-329276-tfrjw743	111	10	of	of	IN
cord-329276-tfrjw743	111	11	T	T	NNP
cord-329276-tfrjw743	111	12	-	-	HYPH
cord-329276-tfrjw743	111	13	cells	cell	NNS
cord-329276-tfrjw743	111	14	generated	generate	VBN
cord-329276-tfrjw743	111	15	through	through	IN
cord-329276-tfrjw743	111	16	these	these	DT
cord-329276-tfrjw743	111	17	primary	primary	JJ
cord-329276-tfrjw743	111	18	organs	organ	NNS
cord-329276-tfrjw743	111	19	;	;	:
cord-329276-tfrjw743	111	20	δ	δ	NN
cord-329276-tfrjw743	111	21	is	be	VBZ
cord-329276-tfrjw743	111	22	simply	simply	RB
cord-329276-tfrjw743	111	23	the	the	DT
cord-329276-tfrjw743	111	24	rate	rate	NN
cord-329276-tfrjw743	111	25	of	of	IN
cord-329276-tfrjw743	111	26	natural	natural	JJ
cord-329276-tfrjw743	111	27	death	death	NN
cord-329276-tfrjw743	111	28	of	of	IN
cord-329276-tfrjw743	111	29	the	the	DT
cord-329276-tfrjw743	111	30	T	t	NN
cord-329276-tfrjw743	111	31	-	-	HYPH
cord-329276-tfrjw743	111	32	cells	cell	NNS
cord-329276-tfrjw743	111	33	.	.	.
cord-329276-tfrjw743	112	1	The	the	DT
cord-329276-tfrjw743	112	2	first	first	JJ
cord-329276-tfrjw743	112	3	term	term	NN
cord-329276-tfrjw743	112	4	in	in	IN
cord-329276-tfrjw743	112	5	this	this	DT
cord-329276-tfrjw743	112	6	equation	equation	NN
cord-329276-tfrjw743	112	7	models	model	VBZ
cord-329276-tfrjw743	112	8	the	the	DT
cord-329276-tfrjw743	112	9	proliferation	proliferation	NN
cord-329276-tfrjw743	112	10	of	of	IN
cord-329276-tfrjw743	112	11	lymphocytes	lymphocyte	NNS
cord-329276-tfrjw743	112	12	.	.	.
cord-329276-tfrjw743	113	1	For	for	IN
cord-329276-tfrjw743	113	2	small	small	JJ
cord-329276-tfrjw743	113	3	tumors	tumor	NNS
cord-329276-tfrjw743	113	4	,	,	,
cord-329276-tfrjw743	113	5	it	-PRON-	PRP
cord-329276-tfrjw743	113	6	is	be	VBZ
cord-329276-tfrjw743	113	7	stimulated	stimulate	VBN
cord-329276-tfrjw743	113	8	by	by	IN
cord-329276-tfrjw743	113	9	tumor	tumor	NN
cord-329276-tfrjw743	113	10	antigen	antigen	NN
cord-329276-tfrjw743	113	11	and	and	CC
cord-329276-tfrjw743	113	12	this	this	DT
cord-329276-tfrjw743	113	13	effect	effect	NN
cord-329276-tfrjw743	113	14	is	be	VBZ
cord-329276-tfrjw743	113	15	taken	take	VBN
cord-329276-tfrjw743	113	16	to	to	TO
cord-329276-tfrjw743	113	17	be	be	VB
cord-329276-tfrjw743	113	18	proportional	proportional	JJ
cord-329276-tfrjw743	113	19	to	to	IN
cord-329276-tfrjw743	113	20	the	the	DT
cord-329276-tfrjw743	113	21	tumor	tumor	NN
cord-329276-tfrjw743	113	22	volume	volume	NN
cord-329276-tfrjw743	114	1	p.	p.	LS
cord-329276-tfrjw743	114	2	Large	large	JJ
cord-329276-tfrjw743	114	3	tumors	tumor	NNS
cord-329276-tfrjw743	114	4	suppress	suppress	VBP
cord-329276-tfrjw743	114	5	the	the	DT
cord-329276-tfrjw743	114	6	activity	activity	NN
cord-329276-tfrjw743	114	7	of	of	IN
cord-329276-tfrjw743	114	8	the	the	DT
cord-329276-tfrjw743	114	9	immune	immune	JJ
cord-329276-tfrjw743	114	10	system	system	NN
cord-329276-tfrjw743	114	11	,	,	,
cord-329276-tfrjw743	114	12	mostly	mostly	RB
cord-329276-tfrjw743	114	13	because	because	IN
cord-329276-tfrjw743	114	14	of	of	IN
cord-329276-tfrjw743	114	15	a	a	DT
cord-329276-tfrjw743	114	16	general	general	JJ
cord-329276-tfrjw743	114	17	suppression	suppression	NN
cord-329276-tfrjw743	114	18	of	of	IN
cord-329276-tfrjw743	114	19	immune	immune	JJ
cord-329276-tfrjw743	114	20	lymphocytes	lymphocyte	NNS
cord-329276-tfrjw743	114	21	.	.	.
cord-329276-tfrjw743	115	1	This	this	DT
cord-329276-tfrjw743	115	2	feature	feature	NN
cord-329276-tfrjw743	115	3	is	be	VBZ
cord-329276-tfrjw743	115	4	expressed	express	VBN
cord-329276-tfrjw743	115	5	in	in	IN
cord-329276-tfrjw743	115	6	the	the	DT
cord-329276-tfrjw743	115	7	model	model	NN
cord-329276-tfrjw743	115	8	through	through	IN
cord-329276-tfrjw743	115	9	the	the	DT
cord-329276-tfrjw743	115	10	inclusion	inclusion	NN
cord-329276-tfrjw743	115	11	of	of	IN
cord-329276-tfrjw743	115	12	the	the	DT
cord-329276-tfrjw743	115	13	term	term	NN
cord-329276-tfrjw743	115	14	−β	−β	NNP
cord-329276-tfrjw743	115	15	p	p	NN
cord-329276-tfrjw743	115	16	2	2	CD
cord-329276-tfrjw743	115	17	.	.	.
cord-329276-tfrjw743	116	1	Thus	thus	RB
cord-329276-tfrjw743	116	2	,	,	,
cord-329276-tfrjw743	116	3	1	1	CD
cord-329276-tfrjw743	116	4	/	/	SYM
cord-329276-tfrjw743	116	5	β	β	NN
cord-329276-tfrjw743	116	6	corresponds	correspond	VBZ
cord-329276-tfrjw743	116	7	to	to	IN
cord-329276-tfrjw743	116	8	a	a	DT
cord-329276-tfrjw743	116	9	threshold	threshold	NN
cord-329276-tfrjw743	116	10	beyond	beyond	IN
cord-329276-tfrjw743	116	11	which	which	WDT
cord-329276-tfrjw743	116	12	the	the	DT
cord-329276-tfrjw743	116	13	immunological	immunological	JJ
cord-329276-tfrjw743	116	14	system	system	NN
cord-329276-tfrjw743	116	15	becomes	become	VBZ
cord-329276-tfrjw743	116	16	depressed	depressed	JJ
cord-329276-tfrjw743	116	17	by	by	IN
cord-329276-tfrjw743	116	18	the	the	DT
cord-329276-tfrjw743	116	19	growing	grow	VBG
cord-329276-tfrjw743	116	20	tumor	tumor	NN
cord-329276-tfrjw743	116	21	.	.	.
cord-329276-tfrjw743	117	1	The	the	DT
cord-329276-tfrjw743	117	2	coefficients	coefficient	NNS
cord-329276-tfrjw743	117	3	α	α	NN
cord-329276-tfrjw743	117	4	and	and	CC
cord-329276-tfrjw743	117	5	β	β	NN
cord-329276-tfrjw743	117	6	are	be	VBP
cord-329276-tfrjw743	117	7	used	use	VBN
cord-329276-tfrjw743	117	8	to	to	TO
cord-329276-tfrjw743	117	9	calibrate	calibrate	VB
cord-329276-tfrjw743	117	10	these	these	DT
cord-329276-tfrjw743	117	11	interactions	interaction	NNS
cord-329276-tfrjw743	117	12	and	and	CC
cord-329276-tfrjw743	117	13	collectively	collectively	RB
cord-329276-tfrjw743	117	14	describe	describe	VB
cord-329276-tfrjw743	117	15	state	state	NN
cord-329276-tfrjw743	117	16	-	-	HYPH
cord-329276-tfrjw743	117	17	dependent	dependent	JJ
cord-329276-tfrjw743	117	18	influence	influence	NN
cord-329276-tfrjw743	117	19	of	of	IN
cord-329276-tfrjw743	117	20	the	the	DT
cord-329276-tfrjw743	117	21	cancer	cancer	NN
cord-329276-tfrjw743	117	22	cells	cell	NNS
cord-329276-tfrjw743	117	23	on	on	IN
cord-329276-tfrjw743	117	24	the	the	DT
cord-329276-tfrjw743	117	25	stimulation	stimulation	NN
cord-329276-tfrjw743	117	26	of	of	IN
cord-329276-tfrjw743	117	27	the	the	DT
cord-329276-tfrjw743	117	28	immune	immune	JJ
cord-329276-tfrjw743	117	29	system	system	NN
cord-329276-tfrjw743	117	30	.	.	.
cord-329276-tfrjw743	118	1	The	the	DT
cord-329276-tfrjw743	118	2	first	first	JJ
cord-329276-tfrjw743	118	3	equation	equation	NN
cord-329276-tfrjw743	118	4	,	,	,
cord-329276-tfrjw743	118	5	(	(	-LRB-
cord-329276-tfrjw743	118	6	5	5	LS
cord-329276-tfrjw743	118	7	)	)	-RRB-
cord-329276-tfrjw743	118	8	,	,	,
cord-329276-tfrjw743	118	9	models	model	NNS
cord-329276-tfrjw743	118	10	tumor	tumor	VBP
cord-329276-tfrjw743	118	11	growth	growth	NN
cord-329276-tfrjw743	118	12	with	with	IN
cord-329276-tfrjw743	118	13	ξ	ξ	VBZ
cord-329276-tfrjw743	118	14	a	a	DT
cord-329276-tfrjw743	118	15	tumor	tumor	NN
cord-329276-tfrjw743	118	16	growth	growth	NN
cord-329276-tfrjw743	118	17	coefficient	coefficient	NN
cord-329276-tfrjw743	118	18	that	that	WDT
cord-329276-tfrjw743	118	19	has	have	VBZ
cord-329276-tfrjw743	118	20	been	be	VBN
cord-329276-tfrjw743	118	21	separated	separate	VBN
cord-329276-tfrjw743	118	22	from	from	IN
cord-329276-tfrjw743	118	23	the	the	DT
cord-329276-tfrjw743	118	24	qualitative	qualitative	JJ
cord-329276-tfrjw743	118	25	behavior	behavior	NN
cord-329276-tfrjw743	118	26	of	of	IN
cord-329276-tfrjw743	118	27	the	the	DT
cord-329276-tfrjw743	118	28	growth	growth	NN
cord-329276-tfrjw743	118	29	function	function	NN
cord-329276-tfrjw743	118	30	F.	F.	NNP
cord-329276-tfrjw743	119	1	The	the	DT
cord-329276-tfrjw743	119	2	second	second	JJ
cord-329276-tfrjw743	119	3	term	term	NN
cord-329276-tfrjw743	119	4	,	,	,
cord-329276-tfrjw743	119	5	−θ	−θ	NNP
cord-329276-tfrjw743	120	1	pr	pr	NNP
cord-329276-tfrjw743	120	2	,	,	,
cord-329276-tfrjw743	120	3	models	model	VBZ
cord-329276-tfrjw743	120	4	the	the	DT
cord-329276-tfrjw743	120	5	beneficial	beneficial	JJ
cord-329276-tfrjw743	120	6	effects	effect	NNS
cord-329276-tfrjw743	120	7	of	of	IN
cord-329276-tfrjw743	120	8	the	the	DT
cord-329276-tfrjw743	120	9	immune	immune	JJ
cord-329276-tfrjw743	120	10	system	system	NN
cord-329276-tfrjw743	120	11	reaction	reaction	NN
cord-329276-tfrjw743	120	12	on	on	IN
cord-329276-tfrjw743	120	13	the	the	DT
cord-329276-tfrjw743	120	14	cancer	cancer	NN
cord-329276-tfrjw743	120	15	volume	volume	NN
cord-329276-tfrjw743	120	16	and	and	CC
cord-329276-tfrjw743	120	17	θ	θ	NN
cord-329276-tfrjw743	120	18	denotes	denote	VBZ
cord-329276-tfrjw743	120	19	the	the	DT
cord-329276-tfrjw743	120	20	rate	rate	NN
cord-329276-tfrjw743	120	21	at	at	IN
cord-329276-tfrjw743	120	22	which	which	WDT
cord-329276-tfrjw743	120	23	cancer	cancer	NN
cord-329276-tfrjw743	120	24	cells	cell	NNS
cord-329276-tfrjw743	120	25	are	be	VBP
cord-329276-tfrjw743	120	26	eliminated	eliminate	VBN
cord-329276-tfrjw743	120	27	through	through	IN
cord-329276-tfrjw743	120	28	the	the	DT
cord-329276-tfrjw743	120	29	activity	activity	NN
cord-329276-tfrjw743	120	30	of	of	IN
cord-329276-tfrjw743	120	31	T	t	NN
cord-329276-tfrjw743	120	32	-	-	HYPH
cord-329276-tfrjw743	120	33	cells	cell	NNS
cord-329276-tfrjw743	120	34	.	.	.
cord-329276-tfrjw743	121	1	The	the	DT
cord-329276-tfrjw743	121	2	dynamical	dynamical	JJ
cord-329276-tfrjw743	121	3	behavior	behavior	NN
cord-329276-tfrjw743	121	4	of	of	IN
cord-329276-tfrjw743	121	5	this	this	DT
cord-329276-tfrjw743	121	6	system	system	NN
cord-329276-tfrjw743	121	7	is	be	VBZ
cord-329276-tfrjw743	121	8	fundamentally	fundamentally	RB
cord-329276-tfrjw743	121	9	different	different	JJ
cord-329276-tfrjw743	121	10	from	from	IN
cord-329276-tfrjw743	121	11	the	the	DT
cord-329276-tfrjw743	121	12	model	model	NN
cord-329276-tfrjw743	121	13	for	for	IN
cord-329276-tfrjw743	121	14	angiogenic	angiogenic	JJ
cord-329276-tfrjw743	121	15	signaling	signaling	NN
cord-329276-tfrjw743	121	16	.	.	.
cord-329276-tfrjw743	122	1	For	for	IN
cord-329276-tfrjw743	122	2	a	a	DT
cord-329276-tfrjw743	122	3	typical	typical	JJ
cord-329276-tfrjw743	122	4	set	set	NN
cord-329276-tfrjw743	122	5	of	of	IN
cord-329276-tfrjw743	122	6	parameter	parameter	NN
cord-329276-tfrjw743	122	7	values	value	NNS
cord-329276-tfrjw743	122	8	,	,	,
cord-329276-tfrjw743	122	9	the	the	DT
cord-329276-tfrjw743	122	10	dynamics	dynamic	NNS
cord-329276-tfrjw743	122	11	is	be	VBZ
cord-329276-tfrjw743	122	12	multi	multi	JJ
cord-329276-tfrjw743	122	13	-	-	JJ
cord-329276-tfrjw743	122	14	stable	stable	JJ
cord-329276-tfrjw743	122	15	Table	table	NN
cord-329276-tfrjw743	122	16	1	1	CD
cord-329276-tfrjw743	122	17	and	and	CC
cord-329276-tfrjw743	122	18	varying	vary	VBG
cord-329276-tfrjw743	122	19	growth	growth	NN
cord-329276-tfrjw743	122	20	functions	function	NNS
cord-329276-tfrjw743	122	21	F.	f.	NN
cord-329276-tfrjw743	123	1	The	the	DT
cord-329276-tfrjw743	123	2	following	follow	VBG
cord-329276-tfrjw743	123	3	growth	growth	NN
cord-329276-tfrjw743	123	4	functions	function	NNS
cord-329276-tfrjw743	123	5	were	be	VBD
cord-329276-tfrjw743	123	6	used	use	VBN
cord-329276-tfrjw743	123	7	in	in	IN
cord-329276-tfrjw743	123	8	the	the	DT
cord-329276-tfrjw743	123	9	respective	respective	JJ
cord-329276-tfrjw743	123	10	panels	panel	NNS
cord-329276-tfrjw743	123	11	:	:	:
cord-329276-tfrjw743	123	12	a	a	DT
cord-329276-tfrjw743	123	13	Gompertzian	gompertzian	JJ
cord-329276-tfrjw743	123	14	growth	growth	NN
cord-329276-tfrjw743	123	15	:	:	:
cord-329276-tfrjw743	124	1	c	c	NNP
cord-329276-tfrjw743	124	2	generalized	generalize	VBD
cord-329276-tfrjw743	124	3	logistic	logistic	JJ
cord-329276-tfrjw743	124	4	growth	growth	NN
cord-329276-tfrjw743	124	5	with	with	IN
cord-329276-tfrjw743	124	6	exponent	exponent	NN
cord-329276-tfrjw743	124	7	2	2	CD
cord-329276-tfrjw743	124	8	:	:	:
cord-329276-tfrjw743	124	9	,	,	,
cord-329276-tfrjw743	124	10	and	and	CC
cord-329276-tfrjw743	124	11	d	d	LS
cord-329276-tfrjw743	124	12	exponential	exponential	JJ
cord-329276-tfrjw743	124	13	growth	growth	NN
cord-329276-tfrjw743	124	14	:	:	:
cord-329276-tfrjw743	124	15	F	f	NN
cord-329276-tfrjw743	124	16	E	e	NN
cord-329276-tfrjw743	124	17	(	(	-LRB-
cord-329276-tfrjw743	124	18	p	p	NN
cord-329276-tfrjw743	124	19	)	)	-RRB-
cord-329276-tfrjw743	124	20	≡	≡	NN
cord-329276-tfrjw743	125	1	1	1	LS
cord-329276-tfrjw743	125	2	.	.	.
cord-329276-tfrjw743	126	1	The	the	DT
cord-329276-tfrjw743	126	2	points	point	NNS
cord-329276-tfrjw743	126	3	(	(	-LRB-
cord-329276-tfrjw743	126	4	p	p	NN
cord-329276-tfrjw743	126	5	b	b	NN
cord-329276-tfrjw743	126	6	,	,	,
cord-329276-tfrjw743	126	7	r	r	NN
cord-329276-tfrjw743	126	8	b	b	NN
cord-329276-tfrjw743	126	9	)	)	-RRB-
cord-329276-tfrjw743	126	10	and	and	CC
cord-329276-tfrjw743	126	11	(	(	-LRB-
cord-329276-tfrjw743	126	12	p	p	NN
cord-329276-tfrjw743	126	13	m	m	NNP
cord-329276-tfrjw743	126	14	,	,	,
cord-329276-tfrjw743	126	15	r	r	NNP
cord-329276-tfrjw743	126	16	m	m	NN
cord-329276-tfrjw743	126	17	)	)	-RRB-
cord-329276-tfrjw743	126	18	are	be	VBP
cord-329276-tfrjw743	126	19	the	the	DT
cord-329276-tfrjw743	126	20	locally	locally	RB
cord-329276-tfrjw743	126	21	stable	stable	JJ
cord-329276-tfrjw743	126	22	benign	benign	JJ
cord-329276-tfrjw743	126	23	and	and	CC
cord-329276-tfrjw743	126	24	malignant	malignant	JJ
cord-329276-tfrjw743	126	25	equilibria	equilibrium	NNS
cord-329276-tfrjw743	126	26	,	,	,
cord-329276-tfrjw743	126	27	respectively	respectively	RB
cord-329276-tfrjw743	126	28	,	,	,
cord-329276-tfrjw743	126	29	and	and	CC
cord-329276-tfrjw743	126	30	(	(	-LRB-
cord-329276-tfrjw743	126	31	p	p	NNP
cord-329276-tfrjw743	126	32	s	s	NN
cord-329276-tfrjw743	126	33	,	,	,
cord-329276-tfrjw743	126	34	r	r	NNP
cord-329276-tfrjw743	126	35	s	s	NNP
cord-329276-tfrjw743	126	36	)	)	-RRB-
cord-329276-tfrjw743	126	37	denotes	denote	VBZ
cord-329276-tfrjw743	126	38	the	the	DT
cord-329276-tfrjw743	126	39	unstable	unstable	JJ
cord-329276-tfrjw743	126	40	saddle	saddle	NN
cord-329276-tfrjw743	126	41	point	point	NN
cord-329276-tfrjw743	126	42	.	.	.
cord-329276-tfrjw743	127	1	The	the	DT
cord-329276-tfrjw743	127	2	dashed	dash	VBN
cord-329276-tfrjw743	127	3	red	red	JJ
cord-329276-tfrjw743	127	4	curve	curve	NN
cord-329276-tfrjw743	127	5	is	be	VBZ
cord-329276-tfrjw743	127	6	the	the	DT
cord-329276-tfrjw743	127	7	stable	stable	JJ
cord-329276-tfrjw743	127	8	manifold	manifold	NN
cord-329276-tfrjw743	127	9	of	of	IN
cord-329276-tfrjw743	127	10	this	this	DT
cord-329276-tfrjw743	127	11	saddle	saddle	NN
cord-329276-tfrjw743	127	12	and	and	CC
cord-329276-tfrjw743	127	13	the	the	DT
cord-329276-tfrjw743	127	14	system	system	NN
cord-329276-tfrjw743	128	1	has	have	VBZ
cord-329276-tfrjw743	128	2	both	both	DT
cord-329276-tfrjw743	128	3	locally	locally	RB
cord-329276-tfrjw743	128	4	asymptotically	asymptotically	RB
cord-329276-tfrjw743	128	5	stable	stable	JJ
cord-329276-tfrjw743	128	6	microscopic	microscopic	JJ
cord-329276-tfrjw743	128	7	and	and	CC
cord-329276-tfrjw743	128	8	macroscopic	macroscopic	JJ
cord-329276-tfrjw743	128	9	equilibrium	equilibrium	NN
cord-329276-tfrjw743	128	10	points	point	NNS
cord-329276-tfrjw743	128	11	as	as	RB
cord-329276-tfrjw743	128	12	well	well	RB
cord-329276-tfrjw743	128	13	as	as	IN
cord-329276-tfrjw743	128	14	an	an	DT
cord-329276-tfrjw743	128	15	unstable	unstable	JJ
cord-329276-tfrjw743	128	16	saddle	saddle	NN
cord-329276-tfrjw743	128	17	point	point	NN
cord-329276-tfrjw743	128	18	.	.	.
cord-329276-tfrjw743	129	1	Figure	figure	NN
cord-329276-tfrjw743	129	2	2	2	CD
cord-329276-tfrjw743	129	3	shows	show	VBZ
cord-329276-tfrjw743	129	4	phase	phase	NN
cord-329276-tfrjw743	129	5	portraits	portrait	NNS
cord-329276-tfrjw743	129	6	of	of	IN
cord-329276-tfrjw743	129	7	the	the	DT
cord-329276-tfrjw743	129	8	system	system	NN
cord-329276-tfrjw743	129	9	for	for	IN
cord-329276-tfrjw743	129	10	the	the	DT
cord-329276-tfrjw743	129	11	parameter	parameter	NN
cord-329276-tfrjw743	129	12	values	value	NNS
cord-329276-tfrjw743	129	13	listed	list	VBN
cord-329276-tfrjw743	129	14	in	in	IN
cord-329276-tfrjw743	129	15	Table	Table	NNP
cord-329276-tfrjw743	129	16	1	1	CD
cord-329276-tfrjw743	129	17	for	for	IN
cord-329276-tfrjw743	129	18	four	four	CD
cord-329276-tfrjw743	129	19	different	different	JJ
cord-329276-tfrjw743	129	20	growth	growth	NN
cord-329276-tfrjw743	129	21	models	model	NNS
cord-329276-tfrjw743	129	22	which	which	WDT
cord-329276-tfrjw743	129	23	qualitatively	qualitatively	RB
cord-329276-tfrjw743	129	24	all	all	DT
cord-329276-tfrjw743	129	25	exhibit	exhibit	VBP
cord-329276-tfrjw743	129	26	the	the	DT
cord-329276-tfrjw743	129	27	same	same	JJ
cord-329276-tfrjw743	129	28	multi	multi	JJ
cord-329276-tfrjw743	129	29	-	-	NN
cord-329276-tfrjw743	129	30	stability	stability	NN
cord-329276-tfrjw743	129	31	.	.	.
cord-329276-tfrjw743	130	1	At	at	IN
cord-329276-tfrjw743	130	2	the	the	DT
cord-329276-tfrjw743	130	3	microscopic	microscopic	JJ
cord-329276-tfrjw743	130	4	equilibrium	equilibrium	NN
cord-329276-tfrjw743	130	5	point	point	NN
cord-329276-tfrjw743	130	6	,	,	,
cord-329276-tfrjw743	130	7	the	the	DT
cord-329276-tfrjw743	130	8	tumor	tumor	NN
cord-329276-tfrjw743	130	9	volumes	volume	NNS
cord-329276-tfrjw743	130	10	are	be	VBP
cord-329276-tfrjw743	130	11	small	small	JJ
cord-329276-tfrjw743	130	12	and	and	CC
cord-329276-tfrjw743	130	13	immuno	immuno	JJ
cord-329276-tfrjw743	130	14	-	-	JJ
cord-329276-tfrjw743	130	15	competent	competent	JJ
cord-329276-tfrjw743	130	16	cell	cell	NN
cord-329276-tfrjw743	130	17	densities	density	NNS
cord-329276-tfrjw743	130	18	are	be	VBP
cord-329276-tfrjw743	130	19	upregulated	upregulate	VBN
cord-329276-tfrjw743	130	20	.	.	.
cord-329276-tfrjw743	131	1	This	this	DT
cord-329276-tfrjw743	131	2	corresponds	correspond	VBZ
cord-329276-tfrjw743	131	3	to	to	IN
cord-329276-tfrjw743	131	4	a	a	DT
cord-329276-tfrjw743	131	5	situation	situation	NN
cord-329276-tfrjw743	131	6	when	when	WRB
cord-329276-tfrjw743	131	7	the	the	DT
cord-329276-tfrjw743	131	8	immune	immune	JJ
cord-329276-tfrjw743	131	9	system	system	NN
cord-329276-tfrjw743	131	10	is	be	VBZ
cord-329276-tfrjw743	131	11	controlling	control	VBG
cord-329276-tfrjw743	131	12	the	the	DT
cord-329276-tfrjw743	131	13	tumor	tumor	NN
cord-329276-tfrjw743	131	14	.	.	.
cord-329276-tfrjw743	132	1	We	-PRON-	PRP
cord-329276-tfrjw743	132	2	denote	denote	VBP
cord-329276-tfrjw743	132	3	the	the	DT
cord-329276-tfrjw743	132	4	corresponding	corresponding	JJ
cord-329276-tfrjw743	132	5	equilibrium	equilibrium	NN
cord-329276-tfrjw743	132	6	point	point	NN
cord-329276-tfrjw743	132	7	by	by	IN
cord-329276-tfrjw743	132	8	(	(	-LRB-
cord-329276-tfrjw743	132	9	p	p	NN
cord-329276-tfrjw743	132	10	b	b	NN
cord-329276-tfrjw743	132	11	,	,	,
cord-329276-tfrjw743	132	12	r	r	NN
cord-329276-tfrjw743	132	13	b	b	NN
cord-329276-tfrjw743	132	14	)	)	-RRB-
cord-329276-tfrjw743	132	15	and	and	CC
cord-329276-tfrjw743	132	16	call	call	VB
cord-329276-tfrjw743	132	17	it	-PRON-	PRP
cord-329276-tfrjw743	132	18	benign	benign	JJ
cord-329276-tfrjw743	132	19	.	.	.
cord-329276-tfrjw743	133	1	The	the	DT
cord-329276-tfrjw743	133	2	macroscopic	macroscopic	JJ
cord-329276-tfrjw743	133	3	equilibrium	equilibrium	NN
cord-329276-tfrjw743	133	4	point	point	NN
cord-329276-tfrjw743	133	5	is	be	VBZ
cord-329276-tfrjw743	133	6	characterized	characterize	VBN
cord-329276-tfrjw743	133	7	by	by	IN
cord-329276-tfrjw743	133	8	more	more	JJR
cord-329276-tfrjw743	133	9	than	than	IN
cord-329276-tfrjw743	133	10	tenfold	tenfold	RB
cord-329276-tfrjw743	133	11	higher	high	JJR
cord-329276-tfrjw743	133	12	tumor	tumor	NN
cord-329276-tfrjw743	133	13	volumes	volume	NNS
cord-329276-tfrjw743	133	14	and	and	CC
cord-329276-tfrjw743	133	15	depressed	depressed	JJ
cord-329276-tfrjw743	133	16	immunocompetent	immunocompetent	JJ
cord-329276-tfrjw743	133	17	cell	cell	NN
cord-329276-tfrjw743	133	18	densities	density	NNS
cord-329276-tfrjw743	133	19	.	.	.
cord-329276-tfrjw743	134	1	In	in	IN
cord-329276-tfrjw743	134	2	these	these	DT
cord-329276-tfrjw743	134	3	solutions	solution	NNS
cord-329276-tfrjw743	134	4	,	,	,
cord-329276-tfrjw743	134	5	the	the	DT
cord-329276-tfrjw743	134	6	tumor	tumor	NN
cord-329276-tfrjw743	134	7	has	have	VBZ
cord-329276-tfrjw743	134	8	suppressed	suppress	VBN
cord-329276-tfrjw743	134	9	the	the	DT
cord-329276-tfrjw743	134	10	immune	immune	JJ
cord-329276-tfrjw743	134	11	system	system	NN
cord-329276-tfrjw743	134	12	and	and	CC
cord-329276-tfrjw743	134	13	it	-PRON-	PRP
cord-329276-tfrjw743	134	14	almost	almost	RB
cord-329276-tfrjw743	134	15	reached	reach	VBD
cord-329276-tfrjw743	134	16	its	-PRON-	PRP$
cord-329276-tfrjw743	134	17	carrying	carrying	NN
cord-329276-tfrjw743	134	18	capacity	capacity	NN
cord-329276-tfrjw743	134	19	.	.	.
cord-329276-tfrjw743	135	1	We	-PRON-	PRP
cord-329276-tfrjw743	135	2	denote	denote	VBP
cord-329276-tfrjw743	135	3	the	the	DT
cord-329276-tfrjw743	135	4	corresponding	corresponding	JJ
cord-329276-tfrjw743	135	5	equilibrium	equilibrium	NN
cord-329276-tfrjw743	135	6	point	point	NN
cord-329276-tfrjw743	135	7	by	by	IN
cord-329276-tfrjw743	135	8	(	(	-LRB-
cord-329276-tfrjw743	135	9	p	p	NN
cord-329276-tfrjw743	135	10	m	m	NNP
cord-329276-tfrjw743	135	11	,	,	,
cord-329276-tfrjw743	135	12	r	r	NNP
cord-329276-tfrjw743	135	13	m	m	NNP
cord-329276-tfrjw743	135	14	)	)	-RRB-
cord-329276-tfrjw743	135	15	and	and	CC
cord-329276-tfrjw743	135	16	call	call	VB
cord-329276-tfrjw743	135	17	it	-PRON-	PRP
cord-329276-tfrjw743	135	18	malignant	malignant	JJ
cord-329276-tfrjw743	135	19	.	.	.
cord-329276-tfrjw743	136	1	Both	both	DT
cord-329276-tfrjw743	136	2	of	of	IN
cord-329276-tfrjw743	136	3	these	these	DT
cord-329276-tfrjw743	136	4	equilibria	equilibrium	NNS
cord-329276-tfrjw743	136	5	are	be	VBP
cord-329276-tfrjw743	136	6	locally	locally	RB
cord-329276-tfrjw743	136	7	asymptotically	asymptotically	RB
cord-329276-tfrjw743	136	8	stable	stable	JJ
cord-329276-tfrjw743	136	9	,	,	,
cord-329276-tfrjw743	136	10	(	(	-LRB-
cord-329276-tfrjw743	136	11	p	p	NN
cord-329276-tfrjw743	136	12	b	b	NNP
cord-329276-tfrjw743	136	13	,	,	,
cord-329276-tfrjw743	136	14	y	y	NNP
cord-329276-tfrjw743	136	15	b	b	NNP
cord-329276-tfrjw743	136	16	)	)	-RRB-
cord-329276-tfrjw743	136	17	a	a	DT
cord-329276-tfrjw743	136	18	stable	stable	JJ
cord-329276-tfrjw743	136	19	focus	focus	NN
cord-329276-tfrjw743	136	20	and	and	CC
cord-329276-tfrjw743	136	21	(	(	-LRB-
cord-329276-tfrjw743	136	22	p	p	NN
cord-329276-tfrjw743	136	23	m	m	NNP
cord-329276-tfrjw743	136	24	,	,	,
cord-329276-tfrjw743	136	25	r	r	NNP
cord-329276-tfrjw743	136	26	m	m	NN
cord-329276-tfrjw743	136	27	)	)	-RRB-
cord-329276-tfrjw743	136	28	a	a	DT
cord-329276-tfrjw743	136	29	stable	stable	JJ
cord-329276-tfrjw743	136	30	node	node	NN
cord-329276-tfrjw743	136	31	.	.	.
cord-329276-tfrjw743	137	1	We	-PRON-	PRP
cord-329276-tfrjw743	137	2	call	call	VBP
cord-329276-tfrjw743	137	3	the	the	DT
cord-329276-tfrjw743	137	4	regions	region	NNS
cord-329276-tfrjw743	137	5	of	of	IN
cord-329276-tfrjw743	137	6	attraction	attraction	NN
cord-329276-tfrjw743	137	7	associated	associate	VBN
cord-329276-tfrjw743	137	8	with	with	IN
cord-329276-tfrjw743	137	9	the	the	DT
cord-329276-tfrjw743	137	10	benign	benign	JJ
cord-329276-tfrjw743	137	11	and	and	CC
cord-329276-tfrjw743	137	12	malignant	malignant	JJ
cord-329276-tfrjw743	137	13	equilibria	equilibrium	NNS
cord-329276-tfrjw743	137	14	the	the	DT
cord-329276-tfrjw743	137	15	benign	benign	JJ
cord-329276-tfrjw743	137	16	,	,	,
cord-329276-tfrjw743	137	17	respectively	respectively	RB
cord-329276-tfrjw743	137	18	,	,	,
cord-329276-tfrjw743	137	19	the	the	DT
cord-329276-tfrjw743	137	20	malignant	malignant	JJ
cord-329276-tfrjw743	137	21	region	region	NN
cord-329276-tfrjw743	137	22	.	.	.
cord-329276-tfrjw743	138	1	For	for	IN
cord-329276-tfrjw743	138	2	the	the	DT
cord-329276-tfrjw743	138	3	model	model	NN
cord-329276-tfrjw743	138	4	with	with	IN
cord-329276-tfrjw743	138	5	an	an	DT
cord-329276-tfrjw743	138	6	These	these	DT
cord-329276-tfrjw743	138	7	phase	phase	NN
cord-329276-tfrjw743	138	8	portraits	portrait	NNS
cord-329276-tfrjw743	138	9	represent	represent	VBP
cord-329276-tfrjw743	138	10	a	a	DT
cord-329276-tfrjw743	138	11	snapshot	snapshot	NN
cord-329276-tfrjw743	138	12	of	of	IN
cord-329276-tfrjw743	138	13	the	the	DT
cord-329276-tfrjw743	138	14	true	true	JJ
cord-329276-tfrjw743	138	15	dynamics	dynamic	NNS
cord-329276-tfrjw743	138	16	:	:	:
cord-329276-tfrjw743	138	17	a	a	DT
cord-329276-tfrjw743	138	18	stationary	stationary	JJ
cord-329276-tfrjw743	138	19	situation	situation	NN
cord-329276-tfrjw743	138	20	for	for	IN
cord-329276-tfrjw743	138	21	fixed	fix	VBN
cord-329276-tfrjw743	138	22	parameter	parameter	NN
cord-329276-tfrjw743	138	23	values	value	NNS
cord-329276-tfrjw743	138	24	.	.	.
cord-329276-tfrjw743	139	1	Because	because	IN
cord-329276-tfrjw743	139	2	of	of	IN
cord-329276-tfrjw743	139	3	unmodeled	unmodeled	JJ
cord-329276-tfrjw743	139	4	aspects	aspect	NNS
cord-329276-tfrjw743	139	5	of	of	IN
cord-329276-tfrjw743	139	6	the	the	DT
cord-329276-tfrjw743	139	7	dynamics	dynamic	NNS
cord-329276-tfrjw743	139	8	and/or	and/or	CC
cord-329276-tfrjw743	139	9	random	random	JJ
cord-329276-tfrjw743	139	10	events	event	NNS
cord-329276-tfrjw743	139	11	,	,	,
cord-329276-tfrjw743	139	12	however	however	RB
cord-329276-tfrjw743	139	13	,	,	,
cord-329276-tfrjw743	139	14	this	this	DT
cord-329276-tfrjw743	139	15	situation	situation	NN
cord-329276-tfrjw743	139	16	will	will	MD
cord-329276-tfrjw743	139	17	constantly	constantly	RB
cord-329276-tfrjw743	139	18	change	change	VB
cord-329276-tfrjw743	139	19	in	in	IN
cord-329276-tfrjw743	139	20	time	time	NN
cord-329276-tfrjw743	139	21	.	.	.
cord-329276-tfrjw743	140	1	Thus	thus	RB
cord-329276-tfrjw743	140	2	,	,	,
cord-329276-tfrjw743	140	3	it	-PRON-	PRP
cord-329276-tfrjw743	140	4	is	be	VBZ
cord-329276-tfrjw743	140	5	intuitively	intuitively	RB
cord-329276-tfrjw743	140	6	clear	clear	JJ
cord-329276-tfrjw743	140	7	that	that	IN
cord-329276-tfrjw743	140	8	a	a	DT
cord-329276-tfrjw743	140	9	benign	benign	JJ
cord-329276-tfrjw743	140	10	equilibrium	equilibrium	NN
cord-329276-tfrjw743	140	11	solution	solution	NN
cord-329276-tfrjw743	140	12	can	can	MD
cord-329276-tfrjw743	140	13	be	be	VB
cord-329276-tfrjw743	140	14	disrupted	disrupt	VBN
cord-329276-tfrjw743	140	15	by	by	IN
cord-329276-tfrjw743	140	16	events	event	NNS
cord-329276-tfrjw743	140	17	affecting	affect	VBG
cord-329276-tfrjw743	140	18	the	the	DT
cord-329276-tfrjw743	140	19	immune	immune	JJ
cord-329276-tfrjw743	140	20	system	system	NN
cord-329276-tfrjw743	140	21	which	which	WDT
cord-329276-tfrjw743	140	22	were	be	VBD
cord-329276-tfrjw743	140	23	not	not	RB
cord-329276-tfrjw743	140	24	included	include	VBN
cord-329276-tfrjw743	140	25	in	in	IN
cord-329276-tfrjw743	140	26	the	the	DT
cord-329276-tfrjw743	140	27	mathematical	mathematical	JJ
cord-329276-tfrjw743	140	28	modeling	modeling	NN
cord-329276-tfrjw743	140	29	which	which	WDT
cord-329276-tfrjw743	140	30	then	then	RB
cord-329276-tfrjw743	140	31	may	may	MD
cord-329276-tfrjw743	140	32	lead	lead	VB
cord-329276-tfrjw743	140	33	to	to	IN
cord-329276-tfrjw743	140	34	a	a	DT
cord-329276-tfrjw743	140	35	transition	transition	NN
cord-329276-tfrjw743	140	36	of	of	IN
cord-329276-tfrjw743	140	37	the	the	DT
cord-329276-tfrjw743	140	38	state	state	NN
cord-329276-tfrjw743	140	39	into	into	IN
cord-329276-tfrjw743	140	40	the	the	DT
cord-329276-tfrjw743	140	41	malignant	malignant	JJ
cord-329276-tfrjw743	140	42	region	region	NN
cord-329276-tfrjw743	140	43	.	.	.
cord-329276-tfrjw743	141	1	How	how	WRB
cord-329276-tfrjw743	141	2	likely	likely	JJ
cord-329276-tfrjw743	141	3	this	this	DT
cord-329276-tfrjw743	141	4	becomes	become	VBZ
cord-329276-tfrjw743	141	5	is	be	VBZ
cord-329276-tfrjw743	141	6	related	relate	VBN
cord-329276-tfrjw743	141	7	to	to	IN
cord-329276-tfrjw743	141	8	the	the	DT
cord-329276-tfrjw743	141	9	size	size	NN
cord-329276-tfrjw743	141	10	of	of	IN
cord-329276-tfrjw743	141	11	the	the	DT
cord-329276-tfrjw743	141	12	region	region	NN
cord-329276-tfrjw743	141	13	of	of	IN
cord-329276-tfrjw743	141	14	attraction	attraction	NN
cord-329276-tfrjw743	141	15	of	of	IN
cord-329276-tfrjw743	141	16	this	this	DT
cord-329276-tfrjw743	141	17	equilibrium	equilibrium	NN
cord-329276-tfrjw743	141	18	:	:	:
cord-329276-tfrjw743	141	19	If	if	IN
cord-329276-tfrjw743	141	20	the	the	DT
cord-329276-tfrjw743	141	21	benign	benign	JJ
cord-329276-tfrjw743	141	22	region	region	NN
cord-329276-tfrjw743	141	23	is	be	VBZ
cord-329276-tfrjw743	141	24	small	small	JJ
cord-329276-tfrjw743	141	25	,	,	,
cord-329276-tfrjw743	141	26	even	even	RB
cord-329276-tfrjw743	141	27	minor	minor	JJ
cord-329276-tfrjw743	141	28	events	event	NNS
cord-329276-tfrjw743	141	29	may	may	MD
cord-329276-tfrjw743	141	30	bring	bring	VB
cord-329276-tfrjw743	141	31	up	up	RP
cord-329276-tfrjw743	141	32	the	the	DT
cord-329276-tfrjw743	141	33	disease	disease	NN
cord-329276-tfrjw743	141	34	,	,	,
cord-329276-tfrjw743	141	35	whereas	whereas	IN
cord-329276-tfrjw743	141	36	the	the	DT
cord-329276-tfrjw743	141	37	immune	immune	JJ
cord-329276-tfrjw743	141	38	system	system	NN
cord-329276-tfrjw743	141	39	may	may	MD
cord-329276-tfrjw743	141	40	be	be	VB
cord-329276-tfrjw743	141	41	able	able	JJ
cord-329276-tfrjw743	141	42	to	to	TO
cord-329276-tfrjw743	141	43	control	control	VB
cord-329276-tfrjw743	141	44	the	the	DT
cord-329276-tfrjw743	141	45	disease	disease	NN
cord-329276-tfrjw743	141	46	if	if	IN
cord-329276-tfrjw743	141	47	this	this	DT
cord-329276-tfrjw743	141	48	region	region	NN
cord-329276-tfrjw743	141	49	is	be	VBZ
cord-329276-tfrjw743	141	50	large	large	JJ
cord-329276-tfrjw743	141	51	.	.	.
cord-329276-tfrjw743	142	1	While	while	IN
cord-329276-tfrjw743	142	2	there	there	EX
cord-329276-tfrjw743	142	3	exist	exist	VBP
cord-329276-tfrjw743	142	4	good	good	JJ
cord-329276-tfrjw743	142	5	reasons	reason	NNS
cord-329276-tfrjw743	142	6	to	to	TO
cord-329276-tfrjw743	142	7	believe	believe	VB
cord-329276-tfrjw743	142	8	that	that	IN
cord-329276-tfrjw743	142	9	the	the	DT
cord-329276-tfrjw743	142	10	immune	immune	JJ
cord-329276-tfrjw743	142	11	system	system	NN
cord-329276-tfrjw743	142	12	is	be	VBZ
cord-329276-tfrjw743	142	13	able	able	JJ
cord-329276-tfrjw743	142	14	to	to	TO
cord-329276-tfrjw743	142	15	control	control	VB
cord-329276-tfrjw743	142	16	some	some	DT
cord-329276-tfrjw743	142	17	tumors	tumor	NNS
cord-329276-tfrjw743	142	18	initially	initially	RB
cord-329276-tfrjw743	142	19	,	,	,
cord-329276-tfrjw743	142	20	over	over	IN
cord-329276-tfrjw743	142	21	a	a	DT
cord-329276-tfrjw743	142	22	longer	long	JJR
cord-329276-tfrjw743	142	23	period	period	NN
cord-329276-tfrjw743	142	24	of	of	IN
cord-329276-tfrjw743	142	25	time	time	NN
cord-329276-tfrjw743	142	26	,	,	,
cord-329276-tfrjw743	142	27	the	the	DT
cord-329276-tfrjw743	142	28	neoplasm	neoplasm	NN
cord-329276-tfrjw743	142	29	will	will	MD
cord-329276-tfrjw743	142	30	develop	develop	VB
cord-329276-tfrjw743	142	31	various	various	JJ
cord-329276-tfrjw743	142	32	strategies	strategy	NNS
cord-329276-tfrjw743	142	33	to	to	TO
cord-329276-tfrjw743	142	34	evade	evade	VB
cord-329276-tfrjw743	142	35	the	the	DT
cord-329276-tfrjw743	142	36	actions	action	NNS
cord-329276-tfrjw743	142	37	of	of	IN
cord-329276-tfrjw743	142	38	the	the	DT
cord-329276-tfrjw743	142	39	immune	immune	JJ
cord-329276-tfrjw743	142	40	system	system	NN
cord-329276-tfrjw743	142	41	(	(	-LRB-
cord-329276-tfrjw743	142	42	immuno	immuno	JJ
cord-329276-tfrjw743	142	43	-	-	HYPH
cord-329276-tfrjw743	142	44	editing	editing	NN
cord-329276-tfrjw743	142	45	)	)	-RRB-
cord-329276-tfrjw743	142	46	and	and	CC
cord-329276-tfrjw743	142	47	this	this	DT
cord-329276-tfrjw743	142	48	allows	allow	VBZ
cord-329276-tfrjw743	142	49	the	the	DT
cord-329276-tfrjw743	142	50	tumor	tumor	NN
cord-329276-tfrjw743	142	51	to	to	TO
cord-329276-tfrjw743	142	52	recommence	recommence	VB
cord-329276-tfrjw743	142	53	growing	grow	VBG
cord-329276-tfrjw743	142	54	into	into	IN
cord-329276-tfrjw743	142	55	clinically	clinically	RB
cord-329276-tfrjw743	142	56	apparent	apparent	JJ
cord-329276-tfrjw743	142	57	tumors	tumor	NNS
cord-329276-tfrjw743	142	58	and	and	CC
cord-329276-tfrjw743	142	59	eventually	eventually	RB
cord-329276-tfrjw743	142	60	reach	reach	VB
cord-329276-tfrjw743	142	61	its	-PRON-	PRP$
cord-329276-tfrjw743	142	62	carrying	carrying	NN
cord-329276-tfrjw743	142	63	capacity	capacity	NN
cord-329276-tfrjw743	142	64	[	[	-LRB-
cord-329276-tfrjw743	142	65	25	25	CD
cord-329276-tfrjw743	142	66	]	]	-RRB-
cord-329276-tfrjw743	142	67	.	.	.
cord-329276-tfrjw743	143	1	Tumor	tumor	NN
cord-329276-tfrjw743	143	2	-	-	HYPH
cord-329276-tfrjw743	143	3	immune	immune	JJ
cord-329276-tfrjw743	143	4	system	system	NN
cord-329276-tfrjw743	143	5	interactions	interaction	NNS
cord-329276-tfrjw743	143	6	thus	thus	RB
cord-329276-tfrjw743	143	7	exhibit	exhibit	VBP
cord-329276-tfrjw743	143	8	a	a	DT
cord-329276-tfrjw743	143	9	multitude	multitude	NN
cord-329276-tfrjw743	143	10	of	of	IN
cord-329276-tfrjw743	143	11	dynamic	dynamic	JJ
cord-329276-tfrjw743	143	12	properties	property	NNS
cord-329276-tfrjw743	143	13	that	that	WDT
cord-329276-tfrjw743	143	14	include	include	VBP
cord-329276-tfrjw743	143	15	persistence	persistence	NN
cord-329276-tfrjw743	143	16	of	of	IN
cord-329276-tfrjw743	143	17	both	both	CC
cord-329276-tfrjw743	143	18	benign	benign	JJ
cord-329276-tfrjw743	143	19	and	and	CC
cord-329276-tfrjw743	143	20	malignant	malignant	JJ
cord-329276-tfrjw743	143	21	scenarios	scenario	NNS
cord-329276-tfrjw743	143	22	.	.	.
cord-329276-tfrjw743	144	1	From	from	IN
cord-329276-tfrjw743	144	2	a	a	DT
cord-329276-tfrjw743	144	3	practical	practical	JJ
cord-329276-tfrjw743	144	4	point	point	NN
cord-329276-tfrjw743	144	5	of	of	IN
cord-329276-tfrjw743	144	6	view	view	NN
cord-329276-tfrjw743	144	7	,	,	,
cord-329276-tfrjw743	144	8	the	the	DT
cord-329276-tfrjw743	144	9	question	question	NN
cord-329276-tfrjw743	144	10	then	then	RB
cord-329276-tfrjw743	144	11	becomes	become	VBZ
cord-329276-tfrjw743	144	12	how	how	WRB
cord-329276-tfrjw743	144	13	to	to	TO
cord-329276-tfrjw743	144	14	move	move	VB
cord-329276-tfrjw743	144	15	an	an	DT
cord-329276-tfrjw743	144	16	initial	initial	JJ
cord-329276-tfrjw743	144	17	condition	condition	NN
cord-329276-tfrjw743	144	18	that	that	WDT
cord-329276-tfrjw743	144	19	lies	lie	VBZ
cord-329276-tfrjw743	144	20	in	in	IN
cord-329276-tfrjw743	144	21	the	the	DT
cord-329276-tfrjw743	144	22	malignant	malignant	JJ
cord-329276-tfrjw743	144	23	region	region	NN
cord-329276-tfrjw743	144	24	into	into	IN
cord-329276-tfrjw743	144	25	the	the	DT
cord-329276-tfrjw743	144	26	benign	benign	JJ
cord-329276-tfrjw743	144	27	region	region	NN
cord-329276-tfrjw743	144	28	.	.	.
cord-329276-tfrjw743	145	1	This	this	DT
cord-329276-tfrjw743	145	2	requires	require	VBZ
cord-329276-tfrjw743	145	3	therapy	therapy	NN
cord-329276-tfrjw743	145	4	and	and	CC
cord-329276-tfrjw743	145	5	can	can	MD
cord-329276-tfrjw743	145	6	naturally	naturally	RB
cord-329276-tfrjw743	145	7	be	be	VB
cord-329276-tfrjw743	145	8	formulated	formulate	VBN
cord-329276-tfrjw743	145	9	and	and	CC
cord-329276-tfrjw743	145	10	analyzed	analyze	VBN
cord-329276-tfrjw743	145	11	as	as	IN
cord-329276-tfrjw743	145	12	an	an	DT
cord-329276-tfrjw743	145	13	optimal	optimal	JJ
cord-329276-tfrjw743	145	14	control	control	NN
cord-329276-tfrjw743	145	15	problem	problem	NN
cord-329276-tfrjw743	145	16	.	.	.
cord-329276-tfrjw743	146	1	Besides	besides	IN
cord-329276-tfrjw743	146	2	the	the	DT
cord-329276-tfrjw743	146	3	underlying	underlie	VBG
cord-329276-tfrjw743	146	4	dynamics	dynamic	NNS
cord-329276-tfrjw743	146	5	represented	represent	VBN
cord-329276-tfrjw743	146	6	by	by	IN
cord-329276-tfrjw743	146	7	the	the	DT
cord-329276-tfrjw743	146	8	drift	drift	NN
cord-329276-tfrjw743	146	9	vector	vector	NN
cord-329276-tfrjw743	146	10	field	field	NN
cord-329276-tfrjw743	146	11	F	F	NNP
cord-329276-tfrjw743	146	12	,	,	,
cord-329276-tfrjw743	146	13	the	the	DT
cord-329276-tfrjw743	146	14	other	other	JJ
cord-329276-tfrjw743	146	15	essential	essential	JJ
cord-329276-tfrjw743	146	16	ingredient	ingredient	NN
cord-329276-tfrjw743	146	17	in	in	IN
cord-329276-tfrjw743	146	18	biomedical	biomedical	JJ
cord-329276-tfrjw743	146	19	problems	problem	NNS
cord-329276-tfrjw743	146	20	is	be	VBZ
cord-329276-tfrjw743	146	21	a	a	DT
cord-329276-tfrjw743	146	22	mathematical	mathematical	JJ
cord-329276-tfrjw743	146	23	model	model	NN
cord-329276-tfrjw743	146	24	for	for	IN
cord-329276-tfrjw743	146	25	outside	outside	JJ
cord-329276-tfrjw743	146	26	inter	inter	JJ
cord-329276-tfrjw743	146	27	-	-	NNS
cord-329276-tfrjw743	146	28	ventions	vention	NNS
cord-329276-tfrjw743	146	29	.	.	.
cord-329276-tfrjw743	147	1	These	these	DT
cord-329276-tfrjw743	147	2	comprise	comprise	VBP
cord-329276-tfrjw743	147	3	therapies	therapy	NNS
cord-329276-tfrjw743	147	4	aimed	aim	VBN
cord-329276-tfrjw743	147	5	at	at	IN
cord-329276-tfrjw743	147	6	curing	cure	VBG
cord-329276-tfrjw743	147	7	a	a	DT
cord-329276-tfrjw743	147	8	patient	patient	NN
cord-329276-tfrjw743	147	9	in	in	IN
cord-329276-tfrjw743	147	10	cancer	cancer	NN
cord-329276-tfrjw743	147	11	treatment	treatment	NN
cord-329276-tfrjw743	147	12	or	or	CC
cord-329276-tfrjw743	147	13	actions	action	NNS
cord-329276-tfrjw743	147	14	to	to	TO
cord-329276-tfrjw743	147	15	limit	limit	VB
cord-329276-tfrjw743	147	16	the	the	DT
cord-329276-tfrjw743	147	17	spread	spread	NN
cord-329276-tfrjw743	147	18	of	of	IN
cord-329276-tfrjw743	147	19	an	an	DT
cord-329276-tfrjw743	147	20	epidemic	epidemic	NN
cord-329276-tfrjw743	147	21	.	.	.
cord-329276-tfrjw743	148	1	Within	within	IN
cord-329276-tfrjw743	148	2	the	the	DT
cord-329276-tfrjw743	148	3	general	general	JJ
cord-329276-tfrjw743	148	4	structure	structure	NN
cord-329276-tfrjw743	148	5	(	(	-LRB-
cord-329276-tfrjw743	148	6	1	1	CD
cord-329276-tfrjw743	148	7	)	)	-RRB-
cord-329276-tfrjw743	148	8	of	of	IN
cord-329276-tfrjw743	148	9	the	the	DT
cord-329276-tfrjw743	148	10	model	model	NN
cord-329276-tfrjw743	148	11	considered	consider	VBN
cord-329276-tfrjw743	148	12	in	in	IN
cord-329276-tfrjw743	148	13	this	this	DT
cord-329276-tfrjw743	148	14	paper	paper	NN
cord-329276-tfrjw743	148	15	,	,	,
cord-329276-tfrjw743	148	16	the	the	DT
cord-329276-tfrjw743	148	17	effects	effect	NNS
cord-329276-tfrjw743	148	18	of	of	IN
cord-329276-tfrjw743	148	19	these	these	DT
cord-329276-tfrjw743	148	20	actions	action	NNS
cord-329276-tfrjw743	148	21	are	be	VBP
cord-329276-tfrjw743	148	22	modeled	model	VBN
cord-329276-tfrjw743	148	23	linearly	linearly	RB
cord-329276-tfrjw743	148	24	through	through	IN
cord-329276-tfrjw743	148	25	the	the	DT
cord-329276-tfrjw743	148	26	control	control	NN
cord-329276-tfrjw743	148	27	vector	vector	NN
cord-329276-tfrjw743	148	28	fields	field	NNS
cord-329276-tfrjw743	148	29	Here	here	RB
cord-329276-tfrjw743	148	30	the	the	DT
cord-329276-tfrjw743	148	31	control	control	NN
cord-329276-tfrjw743	148	32	variables	variable	NNS
cord-329276-tfrjw743	149	1	u	u	NNP
cord-329276-tfrjw743	149	2	i	i	NNP
cord-329276-tfrjw743	149	3	,	,	,
cord-329276-tfrjw743	149	4	i	i	PRP
cord-329276-tfrjw743	149	5	=	=	SYM
cord-329276-tfrjw743	149	6	1	1	CD
cord-329276-tfrjw743	149	7	,	,	,
cord-329276-tfrjw743	149	8	.	.	.
cord-329276-tfrjw743	149	9	.	.	.
cord-329276-tfrjw743	149	10	.	.	.
cord-329276-tfrjw743	150	1	,	,	,
cord-329276-tfrjw743	150	2	m	m	NNP
cord-329276-tfrjw743	150	3	,	,	,
cord-329276-tfrjw743	150	4	represent	represent	VBP
cord-329276-tfrjw743	150	5	various	various	JJ
cord-329276-tfrjw743	150	6	therapy	therapy	NN
cord-329276-tfrjw743	150	7	options	option	NNS
cord-329276-tfrjw743	150	8	such	such	JJ
cord-329276-tfrjw743	150	9	as	as	IN
cord-329276-tfrjw743	150	10	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	150	11	,	,	,
cord-329276-tfrjw743	150	12	radiotherapy	radiotherapy	NN
cord-329276-tfrjw743	150	13	,	,	,
cord-329276-tfrjw743	150	14	immunotherapy	immunotherapy	NN
cord-329276-tfrjw743	150	15	in	in	IN
cord-329276-tfrjw743	150	16	mathematical	mathematical	JJ
cord-329276-tfrjw743	150	17	models	model	NNS
cord-329276-tfrjw743	150	18	for	for	IN
cord-329276-tfrjw743	150	19	cancer	cancer	NN
cord-329276-tfrjw743	150	20	treatments	treatment	NNS
cord-329276-tfrjw743	150	21	and/or	and/or	CC
cord-329276-tfrjw743	150	22	other	other	JJ
cord-329276-tfrjw743	150	23	available	available	JJ
cord-329276-tfrjw743	150	24	actions	action	NNS
cord-329276-tfrjw743	150	25	to	to	TO
cord-329276-tfrjw743	150	26	influence	influence	VB
cord-329276-tfrjw743	150	27	the	the	DT
cord-329276-tfrjw743	150	28	state	state	NN
cord-329276-tfrjw743	150	29	of	of	IN
cord-329276-tfrjw743	150	30	the	the	DT
cord-329276-tfrjw743	150	31	system	system	NN
cord-329276-tfrjw743	150	32	such	such	JJ
cord-329276-tfrjw743	150	33	as	as	IN
cord-329276-tfrjw743	150	34	,	,	,
cord-329276-tfrjw743	150	35	for	for	IN
cord-329276-tfrjw743	150	36	example	example	NN
cord-329276-tfrjw743	150	37	,	,	,
cord-329276-tfrjw743	150	38	social	social	JJ
cord-329276-tfrjw743	150	39	distancing	distance	VBG
cord-329276-tfrjw743	150	40	measures	measure	NNS
cord-329276-tfrjw743	150	41	in	in	IN
cord-329276-tfrjw743	150	42	epidemiological	epidemiological	JJ
cord-329276-tfrjw743	150	43	models	model	NNS
cord-329276-tfrjw743	150	44	.	.	.
cord-329276-tfrjw743	151	1	The	the	DT
cord-329276-tfrjw743	151	2	components	component	NNS
cord-329276-tfrjw743	151	3	.	.	.
cord-329276-tfrjw743	151	4	.	.	.
cord-329276-tfrjw743	152	1	m	m	NNP
cord-329276-tfrjw743	152	2	,	,	,
cord-329276-tfrjw743	152	3	model	model	VB
cord-329276-tfrjw743	152	4	the	the	DT
cord-329276-tfrjw743	152	5	effects	effect	NNS
cord-329276-tfrjw743	152	6	which	which	WDT
cord-329276-tfrjw743	152	7	the	the	DT
cord-329276-tfrjw743	152	8	jth	jth	NNP
cord-329276-tfrjw743	152	9	intervention	intervention	NN
cord-329276-tfrjw743	152	10	modality	modality	NN
cord-329276-tfrjw743	152	11	u	u	NNP
cord-329276-tfrjw743	152	12	j	j	NNP
cord-329276-tfrjw743	152	13	has	have	VBZ
cord-329276-tfrjw743	152	14	on	on	IN
cord-329276-tfrjw743	152	15	the	the	DT
cord-329276-tfrjw743	152	16	ith	ith	NNP
cord-329276-tfrjw743	152	17	compartment	compartment	NN
cord-329276-tfrjw743	153	1	x	x	LS
cord-329276-tfrjw743	153	2	i	i	PRP
cord-329276-tfrjw743	153	3	of	of	IN
cord-329276-tfrjw743	153	4	the	the	DT
cord-329276-tfrjw743	153	5	state	state	NN
cord-329276-tfrjw743	153	6	.	.	.
cord-329276-tfrjw743	154	1	Generally	generally	RB
cord-329276-tfrjw743	154	2	,	,	,
cord-329276-tfrjw743	154	3	the	the	DT
cord-329276-tfrjw743	154	4	number	number	NN
cord-329276-tfrjw743	154	5	m	m	NN
cord-329276-tfrjw743	154	6	of	of	IN
cord-329276-tfrjw743	154	7	different	different	JJ
cord-329276-tfrjw743	154	8	modalities	modality	NNS
cord-329276-tfrjw743	154	9	for	for	IN
cord-329276-tfrjw743	154	10	outside	outside	JJ
cord-329276-tfrjw743	154	11	interventions	intervention	NNS
cord-329276-tfrjw743	154	12	in	in	IN
cord-329276-tfrjw743	154	13	a	a	DT
cord-329276-tfrjw743	154	14	biomedical	biomedical	JJ
cord-329276-tfrjw743	154	15	problem	problem	NN
cord-329276-tfrjw743	154	16	setting	set	VBG
cord-329276-tfrjw743	154	17	is	be	VBZ
cord-329276-tfrjw743	154	18	small	small	JJ
cord-329276-tfrjw743	154	19	and	and	CC
cord-329276-tfrjw743	154	20	m	m	LS
cord-329276-tfrjw743	154	21	typically	typically	RB
cord-329276-tfrjw743	154	22	lies	lie	VBZ
cord-329276-tfrjw743	154	23	in	in	IN
cord-329276-tfrjw743	154	24	the	the	DT
cord-329276-tfrjw743	154	25	range	range	NN
cord-329276-tfrjw743	154	26	of	of	IN
cord-329276-tfrjw743	154	27	m	m	NN
cord-329276-tfrjw743	154	28	=	=	SYM
cord-329276-tfrjw743	154	29	1	1	CD
cord-329276-tfrjw743	154	30	,	,	,
cord-329276-tfrjw743	154	31	2	2	CD
cord-329276-tfrjw743	154	32	,	,	,
cord-329276-tfrjw743	154	33	3	3	CD
cord-329276-tfrjw743	154	34	.	.	.
cord-329276-tfrjw743	155	1	Even	even	RB
cord-329276-tfrjw743	155	2	for	for	IN
cord-329276-tfrjw743	155	3	the	the	DT
cord-329276-tfrjw743	155	4	current	current	JJ
cord-329276-tfrjw743	155	5	COVID-19	COVID-19	NNP
cord-329276-tfrjw743	155	6	pandemic	pandemic	NN
cord-329276-tfrjw743	155	7	,	,	,
cord-329276-tfrjw743	155	8	in	in	IN
cord-329276-tfrjw743	155	9	essence	essence	NN
cord-329276-tfrjw743	155	10	,	,	,
cord-329276-tfrjw743	155	11	all	all	DT
cord-329276-tfrjw743	155	12	efforts	effort	NNS
cord-329276-tfrjw743	155	13	to	to	TO
cord-329276-tfrjw743	155	14	limit	limit	VB
cord-329276-tfrjw743	155	15	the	the	DT
cord-329276-tfrjw743	155	16	spread	spread	NN
cord-329276-tfrjw743	155	17	of	of	IN
cord-329276-tfrjw743	155	18	the	the	DT
cord-329276-tfrjw743	155	19	pandemic	pandemic	NN
cord-329276-tfrjw743	155	20	are	be	VBP
cord-329276-tfrjw743	155	21	related	relate	VBN
cord-329276-tfrjw743	155	22	to	to	IN
cord-329276-tfrjw743	155	23	social	social	JJ
cord-329276-tfrjw743	155	24	distancing	distancing	NN
cord-329276-tfrjw743	155	25	measures	measure	NNS
cord-329276-tfrjw743	155	26	in	in	IN
cord-329276-tfrjw743	155	27	an	an	DT
cord-329276-tfrjw743	155	28	attempt	attempt	NN
cord-329276-tfrjw743	155	29	to	to	TO
cord-329276-tfrjw743	155	30	lower	lower	VB
cord-329276-tfrjw743	155	31	the	the	DT
cord-329276-tfrjw743	155	32	probabilities	probability	NNS
cord-329276-tfrjw743	155	33	of	of	IN
cord-329276-tfrjw743	155	34	infection	infection	NN
cord-329276-tfrjw743	155	35	.	.	.
cord-329276-tfrjw743	156	1	If	if	IN
cord-329276-tfrjw743	156	2	available	available	JJ
cord-329276-tfrjw743	156	3	,	,	,
cord-329276-tfrjw743	156	4	vaccination	vaccination	NN
cord-329276-tfrjw743	156	5	would	would	MD
cord-329276-tfrjw743	156	6	be	be	VB
cord-329276-tfrjw743	156	7	a	a	DT
cord-329276-tfrjw743	156	8	different	different	JJ
cord-329276-tfrjw743	156	9	second	second	JJ
cord-329276-tfrjw743	156	10	intervention	intervention	NN
cord-329276-tfrjw743	156	11	strategy	strategy	NN
cord-329276-tfrjw743	156	12	,	,	,
cord-329276-tfrjw743	156	13	but	but	CC
cord-329276-tfrjw743	156	14	,	,	,
cord-329276-tfrjw743	156	15	clearly	clearly	RB
cord-329276-tfrjw743	156	16	,	,	,
cord-329276-tfrjw743	156	17	the	the	DT
cord-329276-tfrjw743	156	18	overall	overall	JJ
cord-329276-tfrjw743	156	19	number	number	NN
cord-329276-tfrjw743	156	20	of	of	IN
cord-329276-tfrjw743	156	21	options	option	NNS
cord-329276-tfrjw743	156	22	is	be	VBZ
cord-329276-tfrjw743	156	23	not	not	RB
cord-329276-tfrjw743	156	24	very	very	RB
cord-329276-tfrjw743	156	25	large	large	JJ
cord-329276-tfrjw743	156	26	.	.	.
cord-329276-tfrjw743	157	1	Similarly	similarly	RB
cord-329276-tfrjw743	157	2	,	,	,
cord-329276-tfrjw743	157	3	in	in	IN
cord-329276-tfrjw743	157	4	cancer	cancer	NN
cord-329276-tfrjw743	157	5	therapy	therapy	NN
cord-329276-tfrjw743	157	6	,	,	,
cord-329276-tfrjw743	157	7	the	the	DT
cord-329276-tfrjw743	157	8	number	number	NN
cord-329276-tfrjw743	157	9	of	of	IN
cord-329276-tfrjw743	157	10	possible	possible	JJ
cord-329276-tfrjw743	157	11	qualitatively	qualitatively	RB
cord-329276-tfrjw743	157	12	different	different	JJ
cord-329276-tfrjw743	157	13	treatments	treatment	NNS
cord-329276-tfrjw743	157	14	options	option	NNS
cord-329276-tfrjw743	157	15	is	be	VBZ
cord-329276-tfrjw743	157	16	small	small	JJ
cord-329276-tfrjw743	157	17	.	.	.
cord-329276-tfrjw743	158	1	If	if	IN
cord-329276-tfrjw743	158	2	one	one	PRP
cord-329276-tfrjw743	158	3	ignores	ignore	VBZ
cord-329276-tfrjw743	158	4	surgery	surgery	NN
cord-329276-tfrjw743	158	5	,	,	,
cord-329276-tfrjw743	158	6	as	as	IN
cord-329276-tfrjw743	158	7	this	this	DT
cord-329276-tfrjw743	158	8	is	be	VBZ
cord-329276-tfrjw743	158	9	an	an	DT
cord-329276-tfrjw743	158	10	option	option	NN
cord-329276-tfrjw743	158	11	that	that	WDT
cord-329276-tfrjw743	158	12	would	would	MD
cord-329276-tfrjw743	158	13	be	be	VB
cord-329276-tfrjw743	158	14	pursued	pursue	VBN
cord-329276-tfrjw743	158	15	at	at	IN
cord-329276-tfrjw743	158	16	the	the	DT
cord-329276-tfrjw743	158	17	onset	onset	NN
cord-329276-tfrjw743	158	18	prior	prior	RB
cord-329276-tfrjw743	158	19	to	to	IN
cord-329276-tfrjw743	158	20	any	any	DT
cord-329276-tfrjw743	158	21	time	time	NN
cord-329276-tfrjw743	158	22	frame	frame	NN
cord-329276-tfrjw743	158	23	that	that	WDT
cord-329276-tfrjw743	158	24	typically	typically	RB
cord-329276-tfrjw743	158	25	would	would	MD
cord-329276-tfrjw743	158	26	be	be	VB
cord-329276-tfrjw743	158	27	modeled	model	VBN
cord-329276-tfrjw743	158	28	mathematically	mathematically	RB
cord-329276-tfrjw743	158	29	,	,	,
cord-329276-tfrjw743	158	30	the	the	DT
cord-329276-tfrjw743	158	31	main	main	JJ
cord-329276-tfrjw743	158	32	modalities	modality	NNS
cord-329276-tfrjw743	158	33	are	be	VBP
cord-329276-tfrjw743	158	34	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	158	35	,	,	,
cord-329276-tfrjw743	158	36	radiotherapy	radiotherapy	NN
cord-329276-tfrjw743	158	37	and	and	CC
cord-329276-tfrjw743	158	38	immunotherapy	immunotherapy	NN
cord-329276-tfrjw743	158	39	.	.	.
cord-329276-tfrjw743	159	1	If	if	IN
cord-329276-tfrjw743	159	2	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	159	3	is	be	VBZ
cord-329276-tfrjw743	159	4	given	give	VBN
cord-329276-tfrjw743	159	5	through	through	IN
cord-329276-tfrjw743	159	6	a	a	DT
cord-329276-tfrjw743	159	7	cocktail	cocktail	NN
cord-329276-tfrjw743	159	8	of	of	IN
cord-329276-tfrjw743	159	9	drugs	drug	NNS
cord-329276-tfrjw743	159	10	(	(	-LRB-
cord-329276-tfrjw743	159	11	and	and	CC
cord-329276-tfrjw743	159	12	this	this	DT
cord-329276-tfrjw743	159	13	is	be	VBZ
cord-329276-tfrjw743	159	14	the	the	DT
cord-329276-tfrjw743	159	15	common	common	JJ
cord-329276-tfrjw743	159	16	procedure	procedure	NN
cord-329276-tfrjw743	159	17	)	)	-RRB-
cord-329276-tfrjw743	159	18	,	,	,
cord-329276-tfrjw743	159	19	then	then	RB
cord-329276-tfrjw743	159	20	it	-PRON-	PRP
cord-329276-tfrjw743	159	21	is	be	VBZ
cord-329276-tfrjw743	159	22	still	still	RB
cord-329276-tfrjw743	159	23	typically	typically	RB
cord-329276-tfrjw743	159	24	advantageous	advantageous	JJ
cord-329276-tfrjw743	159	25	to	to	TO
cord-329276-tfrjw743	159	26	model	model	VB
cord-329276-tfrjw743	159	27	the	the	DT
cord-329276-tfrjw743	159	28	effects	effect	NNS
cord-329276-tfrjw743	159	29	of	of	IN
cord-329276-tfrjw743	159	30	the	the	DT
cord-329276-tfrjw743	159	31	combination	combination	NN
cord-329276-tfrjw743	159	32	of	of	IN
cord-329276-tfrjw743	159	33	all	all	PDT
cord-329276-tfrjw743	159	34	the	the	DT
cord-329276-tfrjw743	159	35	drugs	drug	NNS
cord-329276-tfrjw743	159	36	together	together	RB
cord-329276-tfrjw743	160	1	and	and	CC
cord-329276-tfrjw743	160	2	one	one	PRP
cord-329276-tfrjw743	160	3	may	may	MD
cord-329276-tfrjw743	160	4	have	have	VB
cord-329276-tfrjw743	160	5	m	m	CD
cord-329276-tfrjw743	160	6	=	=	SYM
cord-329276-tfrjw743	160	7	1	1	CD
cord-329276-tfrjw743	160	8	,	,	,
cord-329276-tfrjw743	160	9	while	while	IN
cord-329276-tfrjw743	160	10	the	the	DT
cord-329276-tfrjw743	160	11	case	case	NN
cord-329276-tfrjw743	160	12	m	m	NN
cord-329276-tfrjw743	161	1	>	>	XX
cord-329276-tfrjw743	162	1	1	1	LS
cord-329276-tfrjw743	162	2	often	often	RB
cord-329276-tfrjw743	162	3	is	be	VBZ
cord-329276-tfrjw743	162	4	reserved	reserve	VBN
cord-329276-tfrjw743	162	5	for	for	IN
cord-329276-tfrjw743	162	6	true	true	JJ
cord-329276-tfrjw743	162	7	combination	combination	NN
cord-329276-tfrjw743	162	8	therapies	therapy	NNS
cord-329276-tfrjw743	162	9	that	that	WDT
cord-329276-tfrjw743	162	10	combine	combine	VBP
cord-329276-tfrjw743	162	11	,	,	,
cord-329276-tfrjw743	162	12	for	for	IN
cord-329276-tfrjw743	162	13	example	example	NN
cord-329276-tfrjw743	162	14	,	,	,
cord-329276-tfrjw743	162	15	chemo	chemo	NN
cord-329276-tfrjw743	162	16	-	-	,
cord-329276-tfrjw743	162	17	or	or	CC
cord-329276-tfrjw743	162	18	radiotherapy	radiotherapy	NN
cord-329276-tfrjw743	162	19	with	with	IN
cord-329276-tfrjw743	162	20	antiangiogenic	antiangiogenic	JJ
cord-329276-tfrjw743	162	21	treatment	treatment	NN
cord-329276-tfrjw743	162	22	.	.	.
cord-329276-tfrjw743	163	1	Thus	thus	RB
cord-329276-tfrjw743	163	2	,	,	,
cord-329276-tfrjw743	163	3	the	the	DT
cord-329276-tfrjw743	163	4	typical	typical	JJ
cord-329276-tfrjw743	163	5	scenario	scenario	NN
cord-329276-tfrjw743	163	6	is	be	VBZ
cord-329276-tfrjw743	163	7	that	that	IN
cord-329276-tfrjw743	163	8	the	the	DT
cord-329276-tfrjw743	163	9	number	number	NN
cord-329276-tfrjw743	163	10	m	m	NN
cord-329276-tfrjw743	163	11	of	of	IN
cord-329276-tfrjw743	163	12	controls	control	NNS
cord-329276-tfrjw743	163	13	in	in	IN
cord-329276-tfrjw743	163	14	the	the	DT
cord-329276-tfrjw743	163	15	system	system	NN
cord-329276-tfrjw743	163	16	is	be	VBZ
cord-329276-tfrjw743	163	17	small	small	JJ
cord-329276-tfrjw743	163	18	.	.	.
cord-329276-tfrjw743	164	1	The	the	DT
cord-329276-tfrjw743	164	2	particular	particular	JJ
cord-329276-tfrjw743	164	3	mathematical	mathematical	JJ
cord-329276-tfrjw743	164	4	structure	structure	NN
cord-329276-tfrjw743	164	5	considered	consider	VBN
cord-329276-tfrjw743	164	6	in	in	IN
cord-329276-tfrjw743	164	7	Eq	Eq	NNP
cord-329276-tfrjw743	164	8	.	.	.
cord-329276-tfrjw743	165	1	(	(	-LRB-
cord-329276-tfrjw743	165	2	7)-linear	7)-linear	CD
cord-329276-tfrjw743	165	3	in	in	IN
cord-329276-tfrjw743	165	4	u	u	NNP
cord-329276-tfrjw743	165	5	-	-	:
cord-329276-tfrjw743	165	6	clearly	clearly	RB
cord-329276-tfrjw743	165	7	does	do	VBZ
cord-329276-tfrjw743	165	8	not	not	RB
cord-329276-tfrjw743	165	9	cover	cover	VB
cord-329276-tfrjw743	165	10	the	the	DT
cord-329276-tfrjw743	165	11	full	full	JJ
cord-329276-tfrjw743	165	12	range	range	NN
cord-329276-tfrjw743	165	13	of	of	IN
cord-329276-tfrjw743	165	14	possibilities	possibility	NNS
cord-329276-tfrjw743	165	15	,	,	,
cord-329276-tfrjw743	165	16	but	but	CC
cord-329276-tfrjw743	165	17	it	-PRON-	PRP
cord-329276-tfrjw743	165	18	is	be	VBZ
cord-329276-tfrjw743	165	19	worth	worth	JJ
cord-329276-tfrjw743	165	20	emphasizing	emphasize	VBG
cord-329276-tfrjw743	165	21	that	that	IN
cord-329276-tfrjw743	165	22	this	this	DT
cord-329276-tfrjw743	165	23	is	be	VBZ
cord-329276-tfrjw743	165	24	by	by	IN
cord-329276-tfrjw743	165	25	far	far	RB
cord-329276-tfrjw743	165	26	the	the	DT
cord-329276-tfrjw743	165	27	most	most	RBS
cord-329276-tfrjw743	165	28	common	common	JJ
cord-329276-tfrjw743	165	29	,	,	,
cord-329276-tfrjw743	165	30	most	most	RBS
cord-329276-tfrjw743	165	31	important	important	JJ
cord-329276-tfrjw743	165	32	,	,	,
cord-329276-tfrjw743	165	33	and	and	CC
cord-329276-tfrjw743	165	34	,	,	,
cord-329276-tfrjw743	165	35	in	in	IN
cord-329276-tfrjw743	165	36	many	many	JJ
cord-329276-tfrjw743	165	37	aspects	aspect	NNS
cord-329276-tfrjw743	165	38	,	,	,
cord-329276-tfrjw743	165	39	most	most	JJS
cord-329276-tfrjw743	165	40	natural	natural	JJ
cord-329276-tfrjw743	165	41	structure	structure	NN
cord-329276-tfrjw743	165	42	.	.	.
cord-329276-tfrjw743	166	1	Essentially	essentially	RB
cord-329276-tfrjw743	166	2	,	,	,
cord-329276-tfrjw743	166	3	whether	whether	IN
cord-329276-tfrjw743	166	4	or	or	CC
cord-329276-tfrjw743	166	5	not	not	RB
cord-329276-tfrjw743	166	6	a	a	DT
cord-329276-tfrjw743	166	7	control	control	NN
cord-329276-tfrjw743	166	8	affine	affine	JJ
cord-329276-tfrjw743	166	9	model	model	NN
cord-329276-tfrjw743	166	10	(	(	-LRB-
cord-329276-tfrjw743	166	11	7	7	CD
cord-329276-tfrjw743	166	12	)	)	-RRB-
cord-329276-tfrjw743	166	13	is	be	VBZ
cord-329276-tfrjw743	166	14	valid	valid	JJ
cord-329276-tfrjw743	166	15	depends	depend	VBZ
cord-329276-tfrjw743	166	16	on	on	IN
cord-329276-tfrjw743	166	17	the	the	DT
cord-329276-tfrjw743	166	18	choice	choice	NN
cord-329276-tfrjw743	166	19	of	of	IN
cord-329276-tfrjw743	166	20	what	what	WP
cord-329276-tfrjw743	166	21	the	the	DT
cord-329276-tfrjw743	166	22	controls	control	NNS
cord-329276-tfrjw743	166	23	represent	represent	VBP
cord-329276-tfrjw743	166	24	.	.	.
cord-329276-tfrjw743	167	1	If	if	IN
cord-329276-tfrjw743	167	2	the	the	DT
cord-329276-tfrjw743	167	3	controls	control	NNS
cord-329276-tfrjw743	167	4	are	be	VBP
cord-329276-tfrjw743	167	5	tied	tie	VBN
cord-329276-tfrjw743	167	6	in	in	RP
cord-329276-tfrjw743	167	7	with	with	IN
cord-329276-tfrjw743	167	8	the	the	DT
cord-329276-tfrjw743	167	9	effects	effect	NNS
cord-329276-tfrjw743	167	10	of	of	IN
cord-329276-tfrjw743	167	11	treatment	treatment	NN
cord-329276-tfrjw743	167	12	(	(	-LRB-
cord-329276-tfrjw743	167	13	e.g.	e.g.	RB
cord-329276-tfrjw743	167	14	,	,	,
cord-329276-tfrjw743	167	15	the	the	DT
cord-329276-tfrjw743	167	16	control	control	NN
cord-329276-tfrjw743	167	17	represents	represent	VBZ
cord-329276-tfrjw743	167	18	the	the	DT
cord-329276-tfrjw743	167	19	concentration	concentration	NN
cord-329276-tfrjw743	167	20	of	of	IN
cord-329276-tfrjw743	167	21	an	an	DT
cord-329276-tfrjw743	167	22	agent	agent	NN
cord-329276-tfrjw743	167	23	rather	rather	RB
cord-329276-tfrjw743	167	24	than	than	IN
cord-329276-tfrjw743	167	25	its	-PRON-	PRP$
cord-329276-tfrjw743	167	26	dose	dose	NN
cord-329276-tfrjw743	167	27	rate	rate	NN
cord-329276-tfrjw743	167	28	)	)	-RRB-
cord-329276-tfrjw743	167	29	,	,	,
cord-329276-tfrjw743	167	30	then	then	RB
cord-329276-tfrjw743	167	31	this	this	DT
cord-329276-tfrjw743	167	32	model	model	NN
cord-329276-tfrjw743	167	33	may	may	MD
cord-329276-tfrjw743	167	34	not	not	RB
cord-329276-tfrjw743	167	35	be	be	VB
cord-329276-tfrjw743	167	36	appropriate	appropriate	JJ
cord-329276-tfrjw743	167	37	.	.	.
cord-329276-tfrjw743	168	1	If	if	IN
cord-329276-tfrjw743	168	2	,	,	,
cord-329276-tfrjw743	168	3	however	however	RB
cord-329276-tfrjw743	168	4	,	,	,
cord-329276-tfrjw743	168	5	the	the	DT
cord-329276-tfrjw743	168	6	controls	control	NNS
cord-329276-tfrjw743	168	7	u	u	NNP
cord-329276-tfrjw743	168	8	i	i	PRP
cord-329276-tfrjw743	168	9	are	be	VBP
cord-329276-tfrjw743	168	10	related	relate	VBN
cord-329276-tfrjw743	168	11	to	to	IN
cord-329276-tfrjw743	168	12	the	the	DT
cord-329276-tfrjw743	168	13	administration	administration	NN
cord-329276-tfrjw743	168	14	of	of	IN
cord-329276-tfrjw743	168	15	the	the	DT
cord-329276-tfrjw743	168	16	therapies	therapy	NNS
cord-329276-tfrjw743	168	17	(	(	-LRB-
cord-329276-tfrjw743	168	18	dose	dose	NN
cord-329276-tfrjw743	168	19	rates	rate	NNS
cord-329276-tfrjw743	168	20	)	)	-RRB-
cord-329276-tfrjw743	168	21	and	and	CC
cord-329276-tfrjw743	168	22	are	be	VBP
cord-329276-tfrjw743	168	23	separated	separate	VBN
cord-329276-tfrjw743	168	24	from	from	IN
cord-329276-tfrjw743	168	25	their	-PRON-	PRP$
cord-329276-tfrjw743	168	26	effects	effect	NNS
cord-329276-tfrjw743	168	27	,	,	,
cord-329276-tfrjw743	168	28	these	these	DT
cord-329276-tfrjw743	168	29	models	model	NNS
cord-329276-tfrjw743	168	30	will	will	MD
cord-329276-tfrjw743	168	31	be	be	VB
cord-329276-tfrjw743	168	32	linear	linear	JJ
cord-329276-tfrjw743	168	33	in	in	IN
cord-329276-tfrjw743	168	34	the	the	DT
cord-329276-tfrjw743	168	35	controls	control	NNS
cord-329276-tfrjw743	168	36	.	.	.
cord-329276-tfrjw743	169	1	Below	below	IN
cord-329276-tfrjw743	169	2	we	-PRON-	PRP
cord-329276-tfrjw743	169	3	shall	shall	MD
cord-329276-tfrjw743	169	4	discuss	discuss	VB
cord-329276-tfrjw743	169	5	in	in	IN
cord-329276-tfrjw743	169	6	more	more	JJR
cord-329276-tfrjw743	169	7	detail	detail	NN
cord-329276-tfrjw743	169	8	mathematical	mathematical	JJ
cord-329276-tfrjw743	169	9	models	model	NNS
cord-329276-tfrjw743	169	10	for	for	IN
cord-329276-tfrjw743	169	11	drug	drug	NN
cord-329276-tfrjw743	169	12	therapies	therapy	NNS
cord-329276-tfrjw743	169	13	,	,	,
cord-329276-tfrjw743	169	14	but	but	CC
cord-329276-tfrjw743	169	15	we	-PRON-	PRP
cord-329276-tfrjw743	169	16	want	want	VBP
cord-329276-tfrjw743	169	17	to	to	TO
cord-329276-tfrjw743	169	18	mention	mention	VB
cord-329276-tfrjw743	169	19	at	at	IN
cord-329276-tfrjw743	169	20	least	least	JJS
cord-329276-tfrjw743	169	21	in	in	IN
cord-329276-tfrjw743	169	22	passing	pass	VBG
cord-329276-tfrjw743	169	23	the	the	DT
cord-329276-tfrjw743	169	24	main	main	JJ
cord-329276-tfrjw743	169	25	model	model	NN
cord-329276-tfrjw743	169	26	for	for	IN
cord-329276-tfrjw743	169	27	radiotherapy	radiotherapy	NN
cord-329276-tfrjw743	169	28	,	,	,
cord-329276-tfrjw743	169	29	the	the	DT
cord-329276-tfrjw743	169	30	so	so	RB
cord-329276-tfrjw743	169	31	-	-	HYPH
cord-329276-tfrjw743	169	32	called	call	VBN
cord-329276-tfrjw743	169	33	linear	linear	JJ
cord-329276-tfrjw743	169	34	quadratic	quadratic	JJ
cord-329276-tfrjw743	169	35	model	model	NN
cord-329276-tfrjw743	169	36	.	.	.
cord-329276-tfrjw743	170	1	In	in	IN
cord-329276-tfrjw743	170	2	this	this	DT
cord-329276-tfrjw743	170	3	model	model	NN
cord-329276-tfrjw743	170	4	,	,	,
cord-329276-tfrjw743	170	5	the	the	DT
cord-329276-tfrjw743	170	6	probability	probability	NN
cord-329276-tfrjw743	170	7	of	of	IN
cord-329276-tfrjw743	170	8	cell	cell	NN
cord-329276-tfrjw743	170	9	survival	survival	NN
cord-329276-tfrjw743	170	10	is	be	VBZ
cord-329276-tfrjw743	170	11	represented	represent	VBN
cord-329276-tfrjw743	170	12	in	in	IN
cord-329276-tfrjw743	170	13	the	the	DT
cord-329276-tfrjw743	170	14	form	form	NN
cord-329276-tfrjw743	170	15	exp	exp	NN
cord-329276-tfrjw743	170	16	−α	−α	NNP
cord-329276-tfrjw743	171	1	D	D	NNP
cord-329276-tfrjw743	171	2	−	−	NNP
cord-329276-tfrjw743	171	3	β	β	NN
cord-329276-tfrjw743	171	4	D	d	NN
cord-329276-tfrjw743	171	5	2	2	CD
cord-329276-tfrjw743	171	6	where	where	WRB
cord-329276-tfrjw743	171	7	D	D	NNP
cord-329276-tfrjw743	171	8	denotes	denote	VBZ
cord-329276-tfrjw743	171	9	the	the	DT
cord-329276-tfrjw743	171	10	total	total	JJ
cord-329276-tfrjw743	171	11	radiation	radiation	NN
cord-329276-tfrjw743	171	12	dose	dose	NN
cord-329276-tfrjw743	171	13	and	and	CC
cord-329276-tfrjw743	172	1	α	α	NNP
cord-329276-tfrjw743	172	2	and	and	CC
cord-329276-tfrjw743	172	3	β	β	NNP
cord-329276-tfrjw743	172	4	are	be	VBP
cord-329276-tfrjw743	172	5	radiosensitive	radiosensitive	JJ
cord-329276-tfrjw743	172	6	parameters	parameter	NNS
cord-329276-tfrjw743	172	7	.	.	.
cord-329276-tfrjw743	173	1	Briefly	briefly	RB
cord-329276-tfrjw743	173	2	,	,	,
cord-329276-tfrjw743	173	3	the	the	DT
cord-329276-tfrjw743	173	4	rationale	rationale	NN
cord-329276-tfrjw743	173	5	for	for	IN
cord-329276-tfrjw743	173	6	the	the	DT
cord-329276-tfrjw743	173	7	model	model	NN
cord-329276-tfrjw743	173	8	is	be	VBZ
cord-329276-tfrjw743	173	9	as	as	IN
cord-329276-tfrjw743	173	10	follows	follow	VBZ
cord-329276-tfrjw743	173	11	[	[	-LRB-
cord-329276-tfrjw743	173	12	15	15	CD
cord-329276-tfrjw743	173	13	,	,	,
cord-329276-tfrjw743	173	14	26	26	CD
cord-329276-tfrjw743	173	15	]	]	-RRB-
cord-329276-tfrjw743	173	16	:	:	:
cord-329276-tfrjw743	174	1	Radiation	radiation	NN
cord-329276-tfrjw743	174	2	causes	cause	VBZ
cord-329276-tfrjw743	174	3	abnormalities	abnormality	NNS
cord-329276-tfrjw743	174	4	(	(	-LRB-
cord-329276-tfrjw743	174	5	lesions	lesion	NNS
cord-329276-tfrjw743	174	6	)	)	-RRB-
cord-329276-tfrjw743	174	7	that	that	WDT
cord-329276-tfrjw743	174	8	correspond	correspond	VBP
cord-329276-tfrjw743	174	9	to	to	IN
cord-329276-tfrjw743	174	10	ruptures	rupture	NNS
cord-329276-tfrjw743	174	11	of	of	IN
cord-329276-tfrjw743	174	12	the	the	DT
cord-329276-tfrjw743	174	13	molecular	molecular	JJ
cord-329276-tfrjw743	174	14	bonds	bond	NNS
cord-329276-tfrjw743	174	15	on	on	IN
cord-329276-tfrjw743	174	16	the	the	DT
cord-329276-tfrjw743	174	17	double	double	RB
cord-329276-tfrjw743	174	18	-	-	HYPH
cord-329276-tfrjw743	174	19	stranded	strand	VBN
cord-329276-tfrjw743	174	20	DNA	dna	NN
cord-329276-tfrjw743	174	21	.	.	.
cord-329276-tfrjw743	175	1	This	this	DT
cord-329276-tfrjw743	175	2	damage	damage	NN
cord-329276-tfrjw743	175	3	is	be	VBZ
cord-329276-tfrjw743	175	4	made	make	VBN
cord-329276-tfrjw743	175	5	up	up	RP
cord-329276-tfrjw743	175	6	of	of	IN
cord-329276-tfrjw743	175	7	two	two	CD
cord-329276-tfrjw743	175	8	components	component	NNS
cord-329276-tfrjw743	175	9	:	:	:
cord-329276-tfrjw743	175	10	(	(	-LRB-
cord-329276-tfrjw743	175	11	i	i	NN
cord-329276-tfrjw743	175	12	)	)	-RRB-
cord-329276-tfrjw743	175	13	simultaneous	simultaneous	JJ
cord-329276-tfrjw743	175	14	breaks	break	NNS
cord-329276-tfrjw743	175	15	in	in	IN
cord-329276-tfrjw743	175	16	both	both	CC
cord-329276-tfrjw743	175	17	DNA	dna	NN
cord-329276-tfrjw743	175	18	strands	strand	NNS
cord-329276-tfrjw743	175	19	that	that	WDT
cord-329276-tfrjw743	175	20	are	be	VBP
cord-329276-tfrjw743	175	21	caused	cause	VBN
cord-329276-tfrjw743	175	22	by	by	IN
cord-329276-tfrjw743	175	23	a	a	DT
cord-329276-tfrjw743	175	24	single	single	JJ
cord-329276-tfrjw743	175	25	particle	particle	NN
cord-329276-tfrjw743	175	26	and	and	CC
cord-329276-tfrjw743	175	27	(	(	-LRB-
cord-329276-tfrjw743	175	28	ii	ii	NN
cord-329276-tfrjw743	175	29	)	)	-RRB-
cord-329276-tfrjw743	175	30	adjacent	adjacent	JJ
cord-329276-tfrjw743	175	31	(	(	-LRB-
cord-329276-tfrjw743	175	32	both	both	DT
cord-329276-tfrjw743	175	33	in	in	IN
cord-329276-tfrjw743	175	34	location	location	NN
cord-329276-tfrjw743	175	35	and	and	CC
cord-329276-tfrjw743	175	36	time	time	NN
cord-329276-tfrjw743	175	37	)	)	-RRB-
cord-329276-tfrjw743	175	38	breaks	break	VBZ
cord-329276-tfrjw743	175	39	on	on	IN
cord-329276-tfrjw743	175	40	separate	separate	JJ
cord-329276-tfrjw743	175	41	strands	strand	NNS
cord-329276-tfrjw743	175	42	.	.	.
cord-329276-tfrjw743	176	1	While	while	IN
cord-329276-tfrjw743	176	2	a	a	DT
cord-329276-tfrjw743	176	3	double	double	JJ
cord-329276-tfrjw743	176	4	-	-	HYPH
cord-329276-tfrjw743	176	5	strand	strand	NN
cord-329276-tfrjw743	176	6	break	break	NN
cord-329276-tfrjw743	176	7	leads	lead	VBZ
cord-329276-tfrjw743	176	8	to	to	IN
cord-329276-tfrjw743	176	9	a	a	DT
cord-329276-tfrjw743	176	10	loss	loss	NN
cord-329276-tfrjw743	176	11	of	of	IN
cord-329276-tfrjw743	176	12	proliferative	proliferative	JJ
cord-329276-tfrjw743	176	13	abilities	ability	NNS
cord-329276-tfrjw743	176	14	,	,	,
cord-329276-tfrjw743	176	15	a	a	DT
cord-329276-tfrjw743	176	16	single	single	JJ
cord-329276-tfrjw743	176	17	-	-	HYPH
cord-329276-tfrjw743	176	18	strand	strand	NN
cord-329276-tfrjw743	176	19	breakage	breakage	NN
cord-329276-tfrjw743	176	20	is	be	VBZ
cord-329276-tfrjw743	176	21	not	not	RB
cord-329276-tfrjw743	176	22	considered	consider	VBN
cord-329276-tfrjw743	176	23	lethal	lethal	JJ
cord-329276-tfrjw743	176	24	since	since	IN
cord-329276-tfrjw743	176	25	DNA	DNA	NNP
cord-329276-tfrjw743	176	26	has	have	VBZ
cord-329276-tfrjw743	176	27	the	the	DT
cord-329276-tfrjw743	176	28	ability	ability	NN
cord-329276-tfrjw743	176	29	to	to	TO
cord-329276-tfrjw743	176	30	repair	repair	VB
cord-329276-tfrjw743	176	31	it	-PRON-	PRP
cord-329276-tfrjw743	176	32	.	.	.
cord-329276-tfrjw743	177	1	Only	only	RB
cord-329276-tfrjw743	177	2	if	if	IN
cord-329276-tfrjw743	177	3	a	a	DT
cord-329276-tfrjw743	177	4	second	second	JJ
cord-329276-tfrjw743	177	5	adjacent	adjacent	JJ
cord-329276-tfrjw743	177	6	break	break	NN
cord-329276-tfrjw743	177	7	occurs	occur	VBZ
cord-329276-tfrjw743	177	8	on	on	IN
cord-329276-tfrjw743	177	9	the	the	DT
cord-329276-tfrjw743	177	10	other	other	JJ
cord-329276-tfrjw743	177	11	strand	strand	NN
cord-329276-tfrjw743	177	12	before	before	IN
cord-329276-tfrjw743	177	13	the	the	DT
cord-329276-tfrjw743	177	14	first	first	JJ
cord-329276-tfrjw743	177	15	one	one	NN
cord-329276-tfrjw743	177	16	can	can	MD
cord-329276-tfrjw743	177	17	be	be	VB
cord-329276-tfrjw743	177	18	repaired	repair	VBN
cord-329276-tfrjw743	177	19	,	,	,
cord-329276-tfrjw743	177	20	this	this	DT
cord-329276-tfrjw743	177	21	will	will	MD
cord-329276-tfrjw743	177	22	lead	lead	VB
cord-329276-tfrjw743	177	23	to	to	IN
cord-329276-tfrjw743	177	24	loss	loss	NN
cord-329276-tfrjw743	177	25	of	of	IN
cord-329276-tfrjw743	177	26	proliferation	proliferation	NN
cord-329276-tfrjw743	177	27	properties	property	NNS
cord-329276-tfrjw743	177	28	.	.	.
cord-329276-tfrjw743	178	1	Both	both	DT
cord-329276-tfrjw743	178	2	scenarios	scenario	NNS
cord-329276-tfrjw743	178	3	(	(	-LRB-
cord-329276-tfrjw743	178	4	i	i	NN
cord-329276-tfrjw743	178	5	)	)	-RRB-
cord-329276-tfrjw743	178	6	and	and	CC
cord-329276-tfrjw743	178	7	(	(	-LRB-
cord-329276-tfrjw743	178	8	ii	ii	NN
cord-329276-tfrjw743	178	9	)	)	-RRB-
cord-329276-tfrjw743	178	10	are	be	VBP
cord-329276-tfrjw743	178	11	considered	consider	VBN
cord-329276-tfrjw743	178	12	lethal	lethal	JJ
cord-329276-tfrjw743	178	13	in	in	IN
cord-329276-tfrjw743	178	14	the	the	DT
cord-329276-tfrjw743	178	15	sense	sense	NN
cord-329276-tfrjw743	178	16	that	that	IN
cord-329276-tfrjw743	178	17	the	the	DT
cord-329276-tfrjw743	178	18	cell	cell	NN
cord-329276-tfrjw743	178	19	is	be	VBZ
cord-329276-tfrjw743	178	20	no	no	RB
cord-329276-tfrjw743	178	21	longer	longer	RB
cord-329276-tfrjw743	178	22	able	able	JJ
cord-329276-tfrjw743	178	23	to	to	TO
cord-329276-tfrjw743	178	24	proliferate	proliferate	VB
cord-329276-tfrjw743	178	25	.	.	.
cord-329276-tfrjw743	179	1	The	the	DT
cord-329276-tfrjw743	179	2	first	first	JJ
cord-329276-tfrjw743	179	3	situation	situation	NN
cord-329276-tfrjw743	179	4	leads	lead	VBZ
cord-329276-tfrjw743	179	5	to	to	IN
cord-329276-tfrjw743	179	6	a	a	DT
cord-329276-tfrjw743	179	7	linear	linear	JJ
cord-329276-tfrjw743	179	8	term	term	NN
cord-329276-tfrjw743	179	9	in	in	IN
cord-329276-tfrjw743	179	10	the	the	DT
cord-329276-tfrjw743	179	11	cell	cell	NN
cord-329276-tfrjw743	179	12	survival	survival	NN
cord-329276-tfrjw743	179	13	model	model	NN
cord-329276-tfrjw743	179	14	,	,	,
cord-329276-tfrjw743	179	15	while	while	IN
cord-329276-tfrjw743	179	16	the	the	DT
cord-329276-tfrjw743	179	17	second	second	JJ
cord-329276-tfrjw743	179	18	one	one	NN
cord-329276-tfrjw743	179	19	contributes	contribute	VBZ
cord-329276-tfrjw743	179	20	quadratic	quadratic	JJ
cord-329276-tfrjw743	179	21	terms	term	NNS
cord-329276-tfrjw743	179	22	.	.	.
cord-329276-tfrjw743	180	1	This	this	DT
cord-329276-tfrjw743	180	2	is	be	VBZ
cord-329276-tfrjw743	180	3	accounted	account	VBN
cord-329276-tfrjw743	180	4	for	for	IN
cord-329276-tfrjw743	180	5	by	by	IN
cord-329276-tfrjw743	180	6	the	the	DT
cord-329276-tfrjw743	180	7	parameters	parameter	NNS
cord-329276-tfrjw743	180	8	α	α	NNP
cord-329276-tfrjw743	180	9	and	and	CC
cord-329276-tfrjw743	180	10	β	β	NN
cord-329276-tfrjw743	180	11	which	which	WDT
cord-329276-tfrjw743	180	12	are	be	VBP
cord-329276-tfrjw743	180	13	called	call	VBN
cord-329276-tfrjw743	180	14	the	the	DT
cord-329276-tfrjw743	180	15	LQ	LQ	NNP
cord-329276-tfrjw743	180	16	parameters	parameter	NNS
cord-329276-tfrjw743	180	17	.	.	.
cord-329276-tfrjw743	181	1	Repair	repair	NN
cord-329276-tfrjw743	181	2	of	of	IN
cord-329276-tfrjw743	181	3	DNA	dna	NN
cord-329276-tfrjw743	181	4	damage	damage	NN
cord-329276-tfrjw743	181	5	generally	generally	RB
cord-329276-tfrjw743	181	6	is	be	VBZ
cord-329276-tfrjw743	181	7	incomplete	incomplete	JJ
cord-329276-tfrjw743	181	8	.	.	.
cord-329276-tfrjw743	182	1	Once	once	RB
cord-329276-tfrjw743	182	2	this	this	DT
cord-329276-tfrjw743	182	3	is	be	VBZ
cord-329276-tfrjw743	182	4	taken	take	VBN
cord-329276-tfrjw743	182	5	into	into	IN
cord-329276-tfrjw743	182	6	account	account	NN
cord-329276-tfrjw743	182	7	as	as	RB
cord-329276-tfrjw743	182	8	well	well	RB
cord-329276-tfrjw743	182	9	,	,	,
cord-329276-tfrjw743	182	10	then	then	RB
cord-329276-tfrjw743	182	11	the	the	DT
cord-329276-tfrjw743	182	12	surviving	survive	VBG
cord-329276-tfrjw743	182	13	fraction	fraction	NN
cord-329276-tfrjw743	182	14	of	of	IN
cord-329276-tfrjw743	182	15	cancer	cancer	NN
cord-329276-tfrjw743	182	16	cells	cell	NNS
cord-329276-tfrjw743	182	17	can	can	MD
cord-329276-tfrjw743	182	18	be	be	VB
cord-329276-tfrjw743	182	19	represented	represent	VBN
cord-329276-tfrjw743	182	20	in	in	IN
cord-329276-tfrjw743	182	21	the	the	DT
cord-329276-tfrjw743	182	22	form	form	NN
cord-329276-tfrjw743	182	23	with	with	IN
cord-329276-tfrjw743	182	24	u	u	NNP
cord-329276-tfrjw743	182	25	denoting	denote	VBG
cord-329276-tfrjw743	182	26	an	an	DT
cord-329276-tfrjw743	182	27	arbitrary	arbitrary	JJ
cord-329276-tfrjw743	182	28	,	,	,
cord-329276-tfrjw743	182	29	time	time	NN
cord-329276-tfrjw743	182	30	-	-	HYPH
cord-329276-tfrjw743	182	31	varying	vary	VBG
cord-329276-tfrjw743	182	32	dose	dose	NN
cord-329276-tfrjw743	182	33	rate	rate	NN
cord-329276-tfrjw743	182	34	,	,	,
cord-329276-tfrjw743	182	35	u	u	NN
cord-329276-tfrjw743	182	36	=	=	SYM
cord-329276-tfrjw743	182	37	u(t	u(t	NN
cord-329276-tfrjw743	183	1	)	)	-RRB-
cord-329276-tfrjw743	183	2	≥	≥	CD
cord-329276-tfrjw743	183	3	0	0	CD
cord-329276-tfrjw743	183	4	,	,	,
cord-329276-tfrjw743	183	5	over	over	IN
cord-329276-tfrjw743	183	6	the	the	DT
cord-329276-tfrjw743	183	7	therapy	therapy	NN
cord-329276-tfrjw743	183	8	interval	interval	NN
cord-329276-tfrjw743	183	9	[	[	-LRB-
cord-329276-tfrjw743	183	10	0	0	NFP
cord-329276-tfrjw743	183	11	,	,	,
cord-329276-tfrjw743	183	12	T	T	NNP
cord-329276-tfrjw743	183	13	]	]	-RRB-
cord-329276-tfrjw743	183	14	and	and	CC
cord-329276-tfrjw743	183	15	ρ	ρ	LS
cord-329276-tfrjw743	183	16	the	the	DT
cord-329276-tfrjw743	183	17	tissue	tissue	NN
cord-329276-tfrjw743	183	18	repair	repair	NN
cord-329276-tfrjw743	183	19	rate	rate	NN
cord-329276-tfrjw743	183	20	.	.	.
cord-329276-tfrjw743	184	1	The	the	DT
cord-329276-tfrjw743	184	2	total	total	JJ
cord-329276-tfrjw743	184	3	dose	dose	NN
cord-329276-tfrjw743	184	4	D	d	NN
cord-329276-tfrjw743	184	5	is	be	VBZ
cord-329276-tfrjw743	184	6	given	give	VBN
cord-329276-tfrjw743	184	7	by	by	IN
cord-329276-tfrjw743	184	8	D	d	NN
cord-329276-tfrjw743	184	9	=	=	SYM
cord-329276-tfrjw743	184	10	T	t	NN
cord-329276-tfrjw743	184	11	0	0	CD
cord-329276-tfrjw743	184	12	u(t)dt	u(t)dt	ADD
cord-329276-tfrjw743	184	13	.	.	.
cord-329276-tfrjw743	185	1	This	this	DT
cord-329276-tfrjw743	185	2	model	model	NN
cord-329276-tfrjw743	185	3	can	can	MD
cord-329276-tfrjw743	185	4	be	be	VB
cord-329276-tfrjw743	185	5	written	write	VBN
cord-329276-tfrjw743	185	6	in	in	IN
cord-329276-tfrjw743	185	7	a	a	DT
cord-329276-tfrjw743	185	8	control	control	NN
cord-329276-tfrjw743	185	9	-	-	HYPH
cord-329276-tfrjw743	185	10	affine	affine	NN
cord-329276-tfrjw743	185	11	form	form	NN
cord-329276-tfrjw743	185	12	[	[	-LRB-
cord-329276-tfrjw743	185	13	15	15	CD
cord-329276-tfrjw743	185	14	,	,	,
cord-329276-tfrjw743	185	15	27	27	CD
cord-329276-tfrjw743	185	16	]	]	-RRB-
cord-329276-tfrjw743	185	17	as	as	IN
cord-329276-tfrjw743	185	18	follows	follow	VBZ
cord-329276-tfrjw743	185	19	:	:	:
cord-329276-tfrjw743	186	1	Here	here	RB
cord-329276-tfrjw743	186	2	,	,	,
cord-329276-tfrjw743	186	3	p	p	LS
cord-329276-tfrjw743	186	4	once	once	RB
cord-329276-tfrjw743	186	5	more	more	JJR
cord-329276-tfrjw743	186	6	represents	represent	VBZ
cord-329276-tfrjw743	186	7	the	the	DT
cord-329276-tfrjw743	186	8	tumor	tumor	NN
cord-329276-tfrjw743	186	9	volume	volume	NN
cord-329276-tfrjw743	186	10	and	and	CC
cord-329276-tfrjw743	186	11	the	the	DT
cord-329276-tfrjw743	186	12	equation	equation	NN
cord-329276-tfrjw743	186	13	for	for	IN
cord-329276-tfrjw743	186	14	r	r	NN
cord-329276-tfrjw743	186	15	models	model	NNS
cord-329276-tfrjw743	186	16	the	the	DT
cord-329276-tfrjw743	186	17	temporal	temporal	JJ
cord-329276-tfrjw743	186	18	effects	effect	NNS
cord-329276-tfrjw743	186	19	of	of	IN
cord-329276-tfrjw743	186	20	tissue	tissue	NN
cord-329276-tfrjw743	186	21	repair	repair	NN
cord-329276-tfrjw743	186	22	;	;	:
cord-329276-tfrjw743	186	23	α	α	NN
cord-329276-tfrjw743	186	24	and	and	CC
cord-329276-tfrjw743	186	25	β	β	NN
cord-329276-tfrjw743	186	26	are	be	VBP
cord-329276-tfrjw743	186	27	the	the	DT
cord-329276-tfrjw743	186	28	LQ	LQ	NNP
cord-329276-tfrjw743	186	29	parameters	parameter	NNS
cord-329276-tfrjw743	186	30	.	.	.
cord-329276-tfrjw743	187	1	The	the	DT
cord-329276-tfrjw743	187	2	specific	specific	JJ
cord-329276-tfrjw743	187	3	parameter	parameter	NN
cord-329276-tfrjw743	187	4	values	value	NNS
cord-329276-tfrjw743	187	5	depend	depend	VBP
cord-329276-tfrjw743	187	6	on	on	IN
cord-329276-tfrjw743	187	7	the	the	DT
cord-329276-tfrjw743	187	8	tissue	tissue	NN
cord-329276-tfrjw743	187	9	treated	treat	VBN
cord-329276-tfrjw743	187	10	,	,	,
cord-329276-tfrjw743	187	11	and	and	CC
cord-329276-tfrjw743	187	12	there	there	EX
cord-329276-tfrjw743	187	13	will	will	MD
cord-329276-tfrjw743	187	14	be	be	VB
cord-329276-tfrjw743	187	15	separate	separate	JJ
cord-329276-tfrjw743	187	16	equations	equation	NNS
cord-329276-tfrjw743	187	17	modeling	model	VBG
cord-329276-tfrjw743	187	18	the	the	DT
cord-329276-tfrjw743	187	19	effects	effect	NNS
cord-329276-tfrjw743	187	20	on	on	IN
cord-329276-tfrjw743	187	21	cancerous	cancerous	JJ
cord-329276-tfrjw743	187	22	and	and	CC
cord-329276-tfrjw743	187	23	healthy	healthy	JJ
cord-329276-tfrjw743	187	24	tissue	tissue	NN
cord-329276-tfrjw743	187	25	.	.	.
cord-329276-tfrjw743	188	1	The	the	DT
cord-329276-tfrjw743	188	2	control	control	NN
cord-329276-tfrjw743	188	3	u	u	NN
cord-329276-tfrjw743	188	4	represents	represent	VBZ
cord-329276-tfrjw743	188	5	a	a	DT
cord-329276-tfrjw743	188	6	time	time	NN
cord-329276-tfrjw743	188	7	-	-	HYPH
cord-329276-tfrjw743	188	8	varying	vary	VBG
cord-329276-tfrjw743	188	9	fractionated	fractionated	JJ
cord-329276-tfrjw743	188	10	radio	radio	NN
cord-329276-tfrjw743	188	11	-	-	HYPH
cord-329276-tfrjw743	188	12	therapy	therapy	NN
cord-329276-tfrjw743	188	13	dose	dose	NN
cord-329276-tfrjw743	188	14	rate	rate	NN
cord-329276-tfrjw743	188	15	.	.	.
cord-329276-tfrjw743	189	1	The	the	DT
cord-329276-tfrjw743	189	2	linear	linear	JJ
cord-329276-tfrjw743	189	3	model	model	NN
cord-329276-tfrjw743	189	4	in	in	IN
cord-329276-tfrjw743	189	5	u	u	NNP
cord-329276-tfrjw743	189	6	represents	represent	VBZ
cord-329276-tfrjw743	189	7	the	the	DT
cord-329276-tfrjw743	189	8	way	way	NN
cord-329276-tfrjw743	189	9	therapy	therapy	NN
cord-329276-tfrjw743	189	10	is	be	VBZ
cord-329276-tfrjw743	189	11	administered	administer	VBN
cord-329276-tfrjw743	189	12	,	,	,
cord-329276-tfrjw743	189	13	and	and	CC
cord-329276-tfrjw743	189	14	this	this	DT
cord-329276-tfrjw743	189	15	almost	almost	RB
cord-329276-tfrjw743	189	16	always	always	RB
cord-329276-tfrjw743	189	17	is	be	VBZ
cord-329276-tfrjw743	189	18	adequately	adequately	RB
cord-329276-tfrjw743	189	19	modeled	model	VBN
cord-329276-tfrjw743	189	20	by	by	IN
cord-329276-tfrjw743	189	21	a	a	DT
cord-329276-tfrjw743	189	22	linear	linear	JJ
cord-329276-tfrjw743	189	23	term	term	NN
cord-329276-tfrjw743	189	24	.	.	.
cord-329276-tfrjw743	190	1	The	the	DT
cord-329276-tfrjw743	190	2	quadratic	quadratic	JJ
cord-329276-tfrjw743	190	3	effects	effect	NNS
cord-329276-tfrjw743	190	4	of	of	IN
cord-329276-tfrjw743	190	5	radiotherapy	radiotherapy	NN
cord-329276-tfrjw743	190	6	are	be	VBP
cord-329276-tfrjw743	190	7	subsumed	subsume	VBN
cord-329276-tfrjw743	190	8	at	at	IN
cord-329276-tfrjw743	190	9	the	the	DT
cord-329276-tfrjw743	190	10	expense	expense	NN
cord-329276-tfrjw743	190	11	of	of	IN
cord-329276-tfrjw743	190	12	introducing	introduce	VBG
cord-329276-tfrjw743	190	13	the	the	DT
cord-329276-tfrjw743	190	14	extra	extra	JJ
cord-329276-tfrjw743	190	15	state	state	NN
cord-329276-tfrjw743	190	16	variable	variable	NN
cord-329276-tfrjw743	190	17	r	r	NN
cord-329276-tfrjw743	190	18	.	.	.
cord-329276-tfrjw743	191	1	Similarly	similarly	RB
cord-329276-tfrjw743	191	2	,	,	,
cord-329276-tfrjw743	191	3	while	while	IN
cord-329276-tfrjw743	191	4	the	the	DT
cord-329276-tfrjw743	191	5	actions	action	NNS
cord-329276-tfrjw743	191	6	of	of	IN
cord-329276-tfrjw743	191	7	different	different	JJ
cord-329276-tfrjw743	191	8	treatment	treatment	NN
cord-329276-tfrjw743	191	9	modalities	modality	NNS
cord-329276-tfrjw743	191	10	clearly	clearly	RB
cord-329276-tfrjw743	191	11	are	be	VBP
cord-329276-tfrjw743	191	12	interrelated	interrelated	JJ
cord-329276-tfrjw743	191	13	,	,	,
cord-329276-tfrjw743	191	14	this	this	DT
cord-329276-tfrjw743	191	15	concerns	concern	VBZ
cord-329276-tfrjw743	191	16	their	-PRON-	PRP$
cord-329276-tfrjw743	191	17	effects	effect	NNS
cord-329276-tfrjw743	191	18	,	,	,
cord-329276-tfrjw743	191	19	not	not	RB
cord-329276-tfrjw743	191	20	the	the	DT
cord-329276-tfrjw743	191	21	way	way	NN
cord-329276-tfrjw743	191	22	the	the	DT
cord-329276-tfrjw743	191	23	therapies	therapy	NNS
cord-329276-tfrjw743	191	24	are	be	VBP
cord-329276-tfrjw743	191	25	administered	administer	VBN
cord-329276-tfrjw743	191	26	.	.	.
cord-329276-tfrjw743	192	1	If	if	IN
cord-329276-tfrjw743	192	2	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	192	3	is	be	VBZ
cord-329276-tfrjw743	192	4	considered	consider	VBN
cord-329276-tfrjw743	192	5	with	with	IN
cord-329276-tfrjw743	192	6	multiple	multiple	JJ
cord-329276-tfrjw743	192	7	drugs	drug	NNS
cord-329276-tfrjw743	192	8	,	,	,
cord-329276-tfrjw743	192	9	then	then	RB
cord-329276-tfrjw743	192	10	synergistic	synergistic	JJ
cord-329276-tfrjw743	192	11	or	or	CC
cord-329276-tfrjw743	192	12	antagonistic	antagonistic	JJ
cord-329276-tfrjw743	192	13	effects	effect	NNS
cord-329276-tfrjw743	192	14	which	which	WDT
cord-329276-tfrjw743	192	15	can	can	MD
cord-329276-tfrjw743	192	16	not	not	RB
cord-329276-tfrjw743	192	17	be	be	VB
cord-329276-tfrjw743	192	18	modeled	model	VBN
cord-329276-tfrjw743	192	19	linearly	linearly	RB
cord-329276-tfrjw743	192	20	become	become	VBN
cord-329276-tfrjw743	192	21	important	important	JJ
cord-329276-tfrjw743	192	22	.	.	.
cord-329276-tfrjw743	193	1	Aside	aside	RB
cord-329276-tfrjw743	193	2	from	from	IN
cord-329276-tfrjw743	193	3	the	the	DT
cord-329276-tfrjw743	193	4	fact	fact	NN
cord-329276-tfrjw743	193	5	that	that	IN
cord-329276-tfrjw743	193	6	such	such	JJ
cord-329276-tfrjw743	193	7	interactions	interaction	NNS
cord-329276-tfrjw743	193	8	often	often	RB
cord-329276-tfrjw743	193	9	are	be	VBP
cord-329276-tfrjw743	193	10	far	far	RB
cord-329276-tfrjw743	193	11	from	from	IN
cord-329276-tfrjw743	193	12	being	be	VBG
cord-329276-tfrjw743	193	13	understood	understand	VBN
cord-329276-tfrjw743	193	14	,	,	,
cord-329276-tfrjw743	193	15	it	-PRON-	PRP
cord-329276-tfrjw743	193	16	also	also	RB
cord-329276-tfrjw743	193	17	matters	matter	VBZ
cord-329276-tfrjw743	193	18	what	what	WP
cord-329276-tfrjw743	193	19	the	the	DT
cord-329276-tfrjw743	193	20	control	control	NN
cord-329276-tfrjw743	193	21	u	u	NNP
cord-329276-tfrjw743	193	22	represents	represent	VBZ
cord-329276-tfrjw743	193	23	.	.	.
cord-329276-tfrjw743	194	1	If	if	IN
cord-329276-tfrjw743	194	2	the	the	DT
cord-329276-tfrjw743	194	3	control	control	NN
cord-329276-tfrjw743	194	4	represents	represent	VBZ
cord-329276-tfrjw743	194	5	drug	drug	NN
cord-329276-tfrjw743	194	6	concentrations	concentration	NNS
cord-329276-tfrjw743	194	7	,	,	,
cord-329276-tfrjw743	194	8	then	then	RB
cord-329276-tfrjw743	194	9	such	such	JJ
cord-329276-tfrjw743	194	10	interactions	interaction	NNS
cord-329276-tfrjw743	194	11	enter	enter	VBP
cord-329276-tfrjw743	194	12	into	into	IN
cord-329276-tfrjw743	194	13	the	the	DT
cord-329276-tfrjw743	194	14	model	model	NN
cord-329276-tfrjw743	194	15	through	through	IN
cord-329276-tfrjw743	194	16	the	the	DT
cord-329276-tfrjw743	194	17	controls	control	NNS
cord-329276-tfrjw743	194	18	and	and	CC
cord-329276-tfrjw743	194	19	a	a	DT
cord-329276-tfrjw743	194	20	linear	linear	JJ
cord-329276-tfrjw743	194	21	model	model	NN
cord-329276-tfrjw743	194	22	is	be	VBZ
cord-329276-tfrjw743	194	23	inadequate	inadequate	JJ
cord-329276-tfrjw743	194	24	.	.	.
cord-329276-tfrjw743	195	1	On	on	IN
cord-329276-tfrjw743	195	2	the	the	DT
cord-329276-tfrjw743	195	3	other	other	JJ
cord-329276-tfrjw743	195	4	hand	hand	NN
cord-329276-tfrjw743	195	5	,	,	,
cord-329276-tfrjw743	195	6	if	if	IN
cord-329276-tfrjw743	195	7	the	the	DT
cord-329276-tfrjw743	195	8	controls	control	NNS
cord-329276-tfrjw743	195	9	represent	represent	VBP
cord-329276-tfrjw743	195	10	the	the	DT
cord-329276-tfrjw743	195	11	dose	dose	JJ
cord-329276-tfrjw743	195	12	rates	rate	NNS
cord-329276-tfrjw743	195	13	of	of	IN
cord-329276-tfrjw743	195	14	the	the	DT
cord-329276-tfrjw743	195	15	various	various	JJ
cord-329276-tfrjw743	195	16	agents	agent	NNS
cord-329276-tfrjw743	195	17	,	,	,
cord-329276-tfrjw743	195	18	then	then	RB
cord-329276-tfrjw743	195	19	the	the	DT
cord-329276-tfrjw743	195	20	concentrations	concentration	NNS
cord-329276-tfrjw743	195	21	of	of	IN
cord-329276-tfrjw743	195	22	these	these	DT
cord-329276-tfrjw743	195	23	agents	agent	NNS
cord-329276-tfrjw743	195	24	merely	merely	RB
cord-329276-tfrjw743	195	25	become	become	VBP
cord-329276-tfrjw743	195	26	additional	additional	JJ
cord-329276-tfrjw743	195	27	states	state	NNS
cord-329276-tfrjw743	195	28	and	and	CC
cord-329276-tfrjw743	195	29	these	these	DT
cord-329276-tfrjw743	195	30	interactions	interaction	NNS
cord-329276-tfrjw743	195	31	enter	enter	VBP
cord-329276-tfrjw743	195	32	into	into	IN
cord-329276-tfrjw743	195	33	the	the	DT
cord-329276-tfrjw743	195	34	drift	drift	NN
cord-329276-tfrjw743	195	35	vector	vector	NN
cord-329276-tfrjw743	195	36	field	field	NN
cord-329276-tfrjw743	195	37	F	F	NNP
cord-329276-tfrjw743	195	38	of	of	IN
cord-329276-tfrjw743	195	39	a	a	DT
cord-329276-tfrjw743	195	40	generally	generally	RB
cord-329276-tfrjw743	195	41	already	already	RB
cord-329276-tfrjw743	195	42	nonlinear	nonlinear	JJ
cord-329276-tfrjw743	195	43	dynamics	dynamic	NNS
cord-329276-tfrjw743	195	44	.	.	.
cord-329276-tfrjw743	196	1	This	this	DT
cord-329276-tfrjw743	196	2	then	then	RB
cord-329276-tfrjw743	196	3	preserves	preserve	VBZ
cord-329276-tfrjw743	196	4	the	the	DT
cord-329276-tfrjw743	196	5	control	control	NN
cord-329276-tfrjw743	196	6	linear	linear	JJ
cord-329276-tfrjw743	196	7	structure	structure	NN
cord-329276-tfrjw743	196	8	(	(	-LRB-
cord-329276-tfrjw743	196	9	7	7	CD
cord-329276-tfrjw743	196	10	)	)	-RRB-
cord-329276-tfrjw743	196	11	.	.	.
cord-329276-tfrjw743	197	1	In	in	IN
cord-329276-tfrjw743	197	2	essence	essence	NN
cord-329276-tfrjw743	197	3	,	,	,
cord-329276-tfrjw743	197	4	if	if	IN
cord-329276-tfrjw743	197	5	the	the	DT
cord-329276-tfrjw743	197	6	controls	control	NNS
cord-329276-tfrjw743	197	7	u	u	NNP
cord-329276-tfrjw743	197	8	i	i	NNP
cord-329276-tfrjw743	197	9	,	,	,
cord-329276-tfrjw743	197	10	i	i	PRP
cord-329276-tfrjw743	197	11	=	=	SYM
cord-329276-tfrjw743	197	12	1	1	CD
cord-329276-tfrjw743	197	13	,	,	,
cord-329276-tfrjw743	197	14	.	.	.
cord-329276-tfrjw743	197	15	.	.	.
cord-329276-tfrjw743	197	16	.	.	.
cord-329276-tfrjw743	197	17	,	,	,
cord-329276-tfrjw743	197	18	m	m	NNP
cord-329276-tfrjw743	197	19	,	,	,
cord-329276-tfrjw743	197	20	represent	represent	VBP
cord-329276-tfrjw743	197	21	the	the	DT
cord-329276-tfrjw743	197	22	administration	administration	NN
cord-329276-tfrjw743	197	23	of	of	IN
cord-329276-tfrjw743	197	24	the	the	DT
cord-329276-tfrjw743	197	25	therapies	therapy	NNS
cord-329276-tfrjw743	197	26	(	(	-LRB-
cord-329276-tfrjw743	197	27	dose	dose	NN
cord-329276-tfrjw743	197	28	rates	rate	NNS
cord-329276-tfrjw743	197	29	)	)	-RRB-
cord-329276-tfrjw743	197	30	and	and	CC
cord-329276-tfrjw743	197	31	as	as	IN
cord-329276-tfrjw743	197	32	variables	variable	NNS
cord-329276-tfrjw743	197	33	are	be	VBP
cord-329276-tfrjw743	197	34	separated	separate	VBN
cord-329276-tfrjw743	197	35	from	from	IN
cord-329276-tfrjw743	197	36	the	the	DT
cord-329276-tfrjw743	197	37	effects	effect	NNS
cord-329276-tfrjw743	197	38	of	of	IN
cord-329276-tfrjw743	197	39	the	the	DT
cord-329276-tfrjw743	197	40	actions	action	NNS
cord-329276-tfrjw743	197	41	(	(	-LRB-
cord-329276-tfrjw743	197	42	which	which	WDT
cord-329276-tfrjw743	197	43	,	,	,
cord-329276-tfrjw743	197	44	for	for	IN
cord-329276-tfrjw743	197	45	example	example	NN
cord-329276-tfrjw743	197	46	,	,	,
cord-329276-tfrjw743	197	47	depend	depend	VB
cord-329276-tfrjw743	197	48	on	on	IN
cord-329276-tfrjw743	197	49	the	the	DT
cord-329276-tfrjw743	197	50	concentrations	concentration	NNS
cord-329276-tfrjw743	197	51	)	)	-RRB-
cord-329276-tfrjw743	197	52	,	,	,
cord-329276-tfrjw743	197	53	then	then	RB
cord-329276-tfrjw743	197	54	a	a	DT
cord-329276-tfrjw743	197	55	model	model	NN
cord-329276-tfrjw743	197	56	which	which	WDT
cord-329276-tfrjw743	197	57	is	be	VBZ
cord-329276-tfrjw743	197	58	linear	linear	JJ
cord-329276-tfrjw743	197	59	in	in	IN
cord-329276-tfrjw743	197	60	the	the	DT
cord-329276-tfrjw743	197	61	controls	control	NNS
cord-329276-tfrjw743	197	62	is	be	VBZ
cord-329276-tfrjw743	197	63	not	not	RB
cord-329276-tfrjw743	197	64	only	only	RB
cord-329276-tfrjw743	197	65	adequate	adequate	JJ
cord-329276-tfrjw743	197	66	,	,	,
cord-329276-tfrjw743	197	67	but	but	CC
cord-329276-tfrjw743	197	68	is	be	VBZ
cord-329276-tfrjw743	197	69	the	the	DT
cord-329276-tfrjw743	197	70	correct	correct	JJ
cord-329276-tfrjw743	197	71	one	one	CD
cord-329276-tfrjw743	197	72	.	.	.
cord-329276-tfrjw743	198	1	We	-PRON-	PRP
cord-329276-tfrjw743	198	2	expand	expand	VBP
cord-329276-tfrjw743	198	3	further	further	RB
cord-329276-tfrjw743	198	4	on	on	IN
cord-329276-tfrjw743	198	5	this	this	DT
cord-329276-tfrjw743	198	6	for	for	IN
cord-329276-tfrjw743	198	7	the	the	DT
cord-329276-tfrjw743	198	8	case	case	NN
cord-329276-tfrjw743	198	9	of	of	IN
cord-329276-tfrjw743	198	10	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	198	11	and	and	CC
cord-329276-tfrjw743	198	12	,	,	,
cord-329276-tfrjw743	198	13	as	as	IN
cord-329276-tfrjw743	198	14	a	a	DT
cord-329276-tfrjw743	198	15	matter	matter	NN
cord-329276-tfrjw743	198	16	of	of	IN
cord-329276-tfrjw743	198	17	simplicity	simplicity	NN
cord-329276-tfrjw743	198	18	of	of	IN
cord-329276-tfrjw743	198	19	the	the	DT
cord-329276-tfrjw743	198	20	presentation	presentation	NN
cord-329276-tfrjw743	198	21	,	,	,
cord-329276-tfrjw743	198	22	focus	focus	VB
cord-329276-tfrjw743	198	23	on	on	IN
cord-329276-tfrjw743	198	24	the	the	DT
cord-329276-tfrjw743	198	25	case	case	NN
cord-329276-tfrjw743	198	26	of	of	IN
cord-329276-tfrjw743	198	27	a	a	DT
cord-329276-tfrjw743	198	28	single	single	JJ
cord-329276-tfrjw743	198	29	control	control	NN
cord-329276-tfrjw743	198	30	u.	u.	NNP
cord-329276-tfrjw743	198	31	Pharmacodynamics	Pharmacodynamics	NNP
cord-329276-tfrjw743	198	32	is	be	VBZ
cord-329276-tfrjw743	198	33	the	the	DT
cord-329276-tfrjw743	198	34	branch	branch	NN
cord-329276-tfrjw743	198	35	of	of	IN
cord-329276-tfrjw743	198	36	pharmacology	pharmacology	NN
cord-329276-tfrjw743	198	37	which	which	WDT
cord-329276-tfrjw743	198	38	quantifies	quantify	VBZ
cord-329276-tfrjw743	198	39	the	the	DT
cord-329276-tfrjw743	198	40	effects	effect	NNS
cord-329276-tfrjw743	198	41	which	which	WDT
cord-329276-tfrjw743	198	42	a	a	DT
cord-329276-tfrjw743	198	43	drug	drug	NN
cord-329276-tfrjw743	198	44	has	have	VBZ
cord-329276-tfrjw743	198	45	at	at	IN
cord-329276-tfrjw743	198	46	concentration	concentration	NN
cord-329276-tfrjw743	198	47	c.	c.	NN
cord-329276-tfrjw743	199	1	According	accord	VBG
cord-329276-tfrjw743	199	2	to	to	IN
cord-329276-tfrjw743	199	3	the	the	DT
cord-329276-tfrjw743	199	4	law	law	NN
cord-329276-tfrjw743	199	5	of	of	IN
cord-329276-tfrjw743	199	6	mass	mass	JJ
cord-329276-tfrjw743	199	7	action	action	NN
cord-329276-tfrjw743	199	8	,	,	,
cord-329276-tfrjw743	199	9	the	the	DT
cord-329276-tfrjw743	199	10	speed	speed	NN
cord-329276-tfrjw743	199	11	of	of	IN
cord-329276-tfrjw743	199	12	a	a	DT
cord-329276-tfrjw743	199	13	chemical	chemical	JJ
cord-329276-tfrjw743	199	14	reaction	reaction	NN
cord-329276-tfrjw743	199	15	is	be	VBZ
cord-329276-tfrjw743	199	16	proportional	proportional	JJ
cord-329276-tfrjw743	199	17	to	to	IN
cord-329276-tfrjw743	199	18	the	the	DT
cord-329276-tfrjw743	199	19	product	product	NN
cord-329276-tfrjw743	199	20	of	of	IN
cord-329276-tfrjw743	199	21	the	the	DT
cord-329276-tfrjw743	199	22	active	active	JJ
cord-329276-tfrjw743	199	23	masses	masse	NNS
cord-329276-tfrjw743	199	24	(	(	-LRB-
cord-329276-tfrjw743	199	25	concentrations	concentration	NNS
cord-329276-tfrjw743	199	26	)	)	-RRB-
cord-329276-tfrjw743	199	27	of	of	IN
cord-329276-tfrjw743	199	28	the	the	DT
cord-329276-tfrjw743	199	29	reactants	reactant	NNS
cord-329276-tfrjw743	199	30	.	.	.
cord-329276-tfrjw743	200	1	If	if	IN
cord-329276-tfrjw743	200	2	a	a	DT
cord-329276-tfrjw743	200	3	drug	drug	NN
cord-329276-tfrjw743	200	4	is	be	VBZ
cord-329276-tfrjw743	200	5	administered	administer	VBN
cord-329276-tfrjw743	200	6	,	,	,
cord-329276-tfrjw743	200	7	in	in	IN
cord-329276-tfrjw743	200	8	an	an	DT
cord-329276-tfrjw743	200	9	ideal	ideal	JJ
cord-329276-tfrjw743	200	10	situation	situation	NN
cord-329276-tfrjw743	200	11	it	-PRON-	PRP
cord-329276-tfrjw743	200	12	has	have	VBZ
cord-329276-tfrjw743	200	13	been	be	VBN
cord-329276-tfrjw743	200	14	postulated	postulate	VBN
cord-329276-tfrjw743	200	15	that	that	IN
cord-329276-tfrjw743	200	16	cell	cell	NN
cord-329276-tfrjw743	200	17	death	death	NN
cord-329276-tfrjw743	200	18	under	under	IN
cord-329276-tfrjw743	200	19	cancer	cancer	NN
cord-329276-tfrjw743	200	20	drugs	drug	NNS
cord-329276-tfrjw743	200	21	follows	follow	VBZ
cord-329276-tfrjw743	200	22	first	first	JJ
cord-329276-tfrjw743	200	23	-	-	HYPH
cord-329276-tfrjw743	200	24	order	order	NN
cord-329276-tfrjw743	200	25	kinetics	kinetics	NN
cord-329276-tfrjw743	200	26	[	[	-LRB-
cord-329276-tfrjw743	200	27	28	28	CD
cord-329276-tfrjw743	200	28	]	]	-RRB-
cord-329276-tfrjw743	200	29	,	,	,
cord-329276-tfrjw743	200	30	i.e.	i.e.	FW
cord-329276-tfrjw743	200	31	,	,	,
cord-329276-tfrjw743	200	32	the	the	DT
cord-329276-tfrjw743	200	33	decrease	decrease	NN
cord-329276-tfrjw743	200	34	in	in	IN
cord-329276-tfrjw743	200	35	the	the	DT
cord-329276-tfrjw743	200	36	number	number	NN
cord-329276-tfrjw743	200	37	of	of	IN
cord-329276-tfrjw743	200	38	cancer	cancer	NN
cord-329276-tfrjw743	200	39	cells	cell	NNS
cord-329276-tfrjw743	200	40	per	per	IN
cord-329276-tfrjw743	200	41	unit	unit	NN
cord-329276-tfrjw743	200	42	of	of	IN
cord-329276-tfrjw743	200	43	time	time	NN
cord-329276-tfrjw743	200	44	is	be	VBZ
cord-329276-tfrjw743	200	45	proportional	proportional	JJ
cord-329276-tfrjw743	200	46	to	to	IN
cord-329276-tfrjw743	200	47	the	the	DT
cord-329276-tfrjw743	200	48	number	number	NN
cord-329276-tfrjw743	200	49	of	of	IN
cord-329276-tfrjw743	200	50	cancer	cancer	NN
cord-329276-tfrjw743	200	51	cells	cell	NNS
cord-329276-tfrjw743	200	52	with	with	IN
cord-329276-tfrjw743	200	53	the	the	DT
cord-329276-tfrjw743	200	54	rate	rate	NN
cord-329276-tfrjw743	200	55	depending	depend	VBG
cord-329276-tfrjw743	200	56	on	on	IN
cord-329276-tfrjw743	200	57	the	the	DT
cord-329276-tfrjw743	200	58	concentration	concentration	NN
cord-329276-tfrjw743	200	59	of	of	IN
cord-329276-tfrjw743	200	60	the	the	DT
cord-329276-tfrjw743	200	61	anti	anti	JJ
cord-329276-tfrjw743	200	62	-	-	JJ
cord-329276-tfrjw743	200	63	cancer	cancer	JJ
cord-329276-tfrjw743	200	64	drug	drug	NN
cord-329276-tfrjw743	200	65	.	.	.
cord-329276-tfrjw743	201	1	Any	any	DT
cord-329276-tfrjw743	201	2	functional	functional	JJ
cord-329276-tfrjw743	201	3	relation	relation	NN
cord-329276-tfrjw743	201	4	of	of	IN
cord-329276-tfrjw743	201	5	the	the	DT
cord-329276-tfrjw743	201	6	form	form	NN
cord-329276-tfrjw743	201	7	e	e	NN
cord-329276-tfrjw743	201	8	=	=	FW
cord-329276-tfrjw743	201	9	s(c)x	s(c)x	NN
cord-329276-tfrjw743	201	10	with	with	IN
cord-329276-tfrjw743	201	11	x	x	NN
cord-329276-tfrjw743	201	12	denoting	denote	VBG
cord-329276-tfrjw743	201	13	the	the	DT
cord-329276-tfrjw743	201	14	cells	cell	NNS
cord-329276-tfrjw743	201	15	in	in	IN
cord-329276-tfrjw743	201	16	a	a	DT
cord-329276-tfrjw743	201	17	compartment	compartment	NN
cord-329276-tfrjw743	201	18	on	on	IN
cord-329276-tfrjw743	201	19	which	which	WDT
cord-329276-tfrjw743	201	20	the	the	DT
cord-329276-tfrjw743	201	21	drug	drug	NN
cord-329276-tfrjw743	201	22	is	be	VBZ
cord-329276-tfrjw743	201	23	acting	act	VBG
cord-329276-tfrjw743	201	24	(	(	-LRB-
cord-329276-tfrjw743	201	25	e.g.	e.g.	RB
cord-329276-tfrjw743	201	26	,	,	,
cord-329276-tfrjw743	201	27	tumor	tumor	NN
cord-329276-tfrjw743	201	28	cells	cell	NNS
cord-329276-tfrjw743	201	29	,	,	,
cord-329276-tfrjw743	201	30	immune	immune	JJ
cord-329276-tfrjw743	201	31	system	system	NN
cord-329276-tfrjw743	201	32	,	,	,
cord-329276-tfrjw743	201	33	healthy	healthy	JJ
cord-329276-tfrjw743	201	34	cells	cell	NNS
cord-329276-tfrjw743	201	35	,	,	,
cord-329276-tfrjw743	201	36	etc	etc	FW
cord-329276-tfrjw743	201	37	.	.	.
cord-329276-tfrjw743	201	38	)	)	-RRB-
cord-329276-tfrjw743	201	39	and	and	CC
cord-329276-tfrjw743	201	40	the	the	DT
cord-329276-tfrjw743	201	41	coefficient	coefficient	NN
cord-329276-tfrjw743	201	42	s(c	s(c	NNP
cord-329276-tfrjw743	201	43	)	)	-RRB-
cord-329276-tfrjw743	201	44	representing	represent	VBG
cord-329276-tfrjw743	201	45	the	the	DT
cord-329276-tfrjw743	201	46	concentration	concentration	NN
cord-329276-tfrjw743	201	47	dependent	dependent	JJ
cord-329276-tfrjw743	201	48	killing	killing	NN
cord-329276-tfrjw743	201	49	rate	rate	NN
cord-329276-tfrjw743	201	50	of	of	IN
cord-329276-tfrjw743	201	51	the	the	DT
cord-329276-tfrjw743	201	52	drug	drug	NN
cord-329276-tfrjw743	201	53	is	be	VBZ
cord-329276-tfrjw743	201	54	considered	consider	VBN
cord-329276-tfrjw743	201	55	a	a	DT
cord-329276-tfrjw743	201	56	pharmacodynamic	pharmacodynamic	JJ
cord-329276-tfrjw743	201	57	model	model	NN
cord-329276-tfrjw743	201	58	.	.	.
cord-329276-tfrjw743	202	1	A	a	DT
cord-329276-tfrjw743	202	2	linear	linear	JJ
cord-329276-tfrjw743	202	3	model	model	NN
cord-329276-tfrjw743	202	4	of	of	IN
cord-329276-tfrjw743	202	5	the	the	DT
cord-329276-tfrjw743	202	6	form	form	NN
cord-329276-tfrjw743	202	7	s(c	s(c	NNP
cord-329276-tfrjw743	202	8	)	)	-RRB-
cord-329276-tfrjw743	202	9	=	=	NFP
cord-329276-tfrjw743	203	1	ϕc	ϕc	UH
cord-329276-tfrjw743	204	1	with	with	IN
cord-329276-tfrjw743	204	2	ϕ	ϕ	PDT
cord-329276-tfrjw743	204	3	a	a	DT
cord-329276-tfrjw743	204	4	positive	positive	JJ
cord-329276-tfrjw743	204	5	constant	constant	NN
cord-329276-tfrjw743	204	6	,	,	,
cord-329276-tfrjw743	204	7	the	the	DT
cord-329276-tfrjw743	204	8	so	so	RB
cord-329276-tfrjw743	204	9	-	-	HYPH
cord-329276-tfrjw743	204	10	called	call	VBN
cord-329276-tfrjw743	204	11	linear	linear	JJ
cord-329276-tfrjw743	204	12	log	log	NN
cord-329276-tfrjw743	204	13	-	-	HYPH
cord-329276-tfrjw743	204	14	kill	kill	NN
cord-329276-tfrjw743	204	15	hypothesis	hypothesis	NN
cord-329276-tfrjw743	204	16	based	base	VBN
cord-329276-tfrjw743	204	17	on	on	IN
cord-329276-tfrjw743	204	18	Skipper	Skipper	NNP
cord-329276-tfrjw743	204	19	's	's	POS
cord-329276-tfrjw743	204	20	paper	paper	NN
cord-329276-tfrjw743	204	21	[	[	-LRB-
cord-329276-tfrjw743	204	22	28	28	CD
cord-329276-tfrjw743	204	23	]	]	-RRB-
cord-329276-tfrjw743	205	1	,	,	,
cord-329276-tfrjw743	205	2	is	be	VBZ
cord-329276-tfrjw743	205	3	the	the	DT
cord-329276-tfrjw743	205	4	most	most	RBS
cord-329276-tfrjw743	205	5	commonly	commonly	RB
cord-329276-tfrjw743	205	6	used	use	VBN
cord-329276-tfrjw743	205	7	form	form	NN
cord-329276-tfrjw743	205	8	.	.	.
cord-329276-tfrjw743	206	1	Incorporating	incorporate	VBG
cord-329276-tfrjw743	206	2	this	this	DT
cord-329276-tfrjw743	206	3	structure	structure	NN
cord-329276-tfrjw743	206	4	into	into	IN
cord-329276-tfrjw743	206	5	a	a	DT
cord-329276-tfrjw743	206	6	standard	standard	JJ
cord-329276-tfrjw743	206	7	growth	growth	NN
cord-329276-tfrjw743	206	8	law	law	NN
cord-329276-tfrjw743	206	9	results	result	NNS
cord-329276-tfrjw743	206	10	in	in	IN
cord-329276-tfrjw743	206	11	the	the	DT
cord-329276-tfrjw743	206	12	following	follow	VBG
cord-329276-tfrjw743	206	13	growth	growth	NN
cord-329276-tfrjw743	206	14	model	model	NN
cord-329276-tfrjw743	206	15	under	under	IN
cord-329276-tfrjw743	206	16	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	206	17	,	,	,
cord-329276-tfrjw743	206	18	If	if	IN
cord-329276-tfrjw743	206	19	the	the	DT
cord-329276-tfrjw743	206	20	concentration	concentration	NN
cord-329276-tfrjw743	206	21	c	c	NN
cord-329276-tfrjw743	206	22	is	be	VBZ
cord-329276-tfrjw743	206	23	considered	consider	VBN
cord-329276-tfrjw743	206	24	the	the	DT
cord-329276-tfrjw743	206	25	control	control	NN
cord-329276-tfrjw743	206	26	u	u	NN
cord-329276-tfrjw743	206	27	in	in	IN
cord-329276-tfrjw743	206	28	the	the	DT
cord-329276-tfrjw743	206	29	system	system	NN
cord-329276-tfrjw743	206	30	,	,	,
cord-329276-tfrjw743	206	31	u	u	NN
cord-329276-tfrjw743	206	32	=	=	SYM
cord-329276-tfrjw743	206	33	c	c	NN
cord-329276-tfrjw743	206	34	,	,	,
cord-329276-tfrjw743	206	35	then	then	RB
cord-329276-tfrjw743	206	36	the	the	DT
cord-329276-tfrjw743	206	37	linear	linear	JJ
cord-329276-tfrjw743	206	38	log	log	NN
cord-329276-tfrjw743	206	39	-	-	HYPH
cord-329276-tfrjw743	206	40	kill	kill	NN
cord-329276-tfrjw743	206	41	model	model	NN
cord-329276-tfrjw743	206	42	fits	fit	VBZ
cord-329276-tfrjw743	206	43	the	the	DT
cord-329276-tfrjw743	206	44	general	general	JJ
cord-329276-tfrjw743	206	45	linear	linear	JJ
cord-329276-tfrjw743	206	46	form	form	NN
cord-329276-tfrjw743	206	47	(	(	-LRB-
cord-329276-tfrjw743	206	48	7	7	CD
cord-329276-tfrjw743	206	49	)	)	-RRB-
cord-329276-tfrjw743	206	50	.	.	.
cord-329276-tfrjw743	207	1	The	the	DT
cord-329276-tfrjw743	207	2	product	product	NN
cord-329276-tfrjw743	207	3	represents	represent	VBZ
cord-329276-tfrjw743	207	4	an	an	DT
cord-329276-tfrjw743	207	5	interaction	interaction	NN
cord-329276-tfrjw743	207	6	term	term	NN
cord-329276-tfrjw743	207	7	as	as	IN
cord-329276-tfrjw743	207	8	discussed	discuss	VBN
cord-329276-tfrjw743	207	9	in	in	IN
cord-329276-tfrjw743	207	10	Sect	Sect	NNP
cord-329276-tfrjw743	207	11	.	.	.
cord-329276-tfrjw743	208	1	2.1.3	2.1.3	LS
cord-329276-tfrjw743	208	2	.	.	.
cord-329276-tfrjw743	209	1	Such	such	JJ
cord-329276-tfrjw743	209	2	terms	term	NNS
cord-329276-tfrjw743	209	3	can	can	MD
cord-329276-tfrjw743	209	4	be	be	VB
cord-329276-tfrjw743	209	5	both	both	DT
cord-329276-tfrjw743	209	6	inhibiting	inhibit	VBG
cord-329276-tfrjw743	209	7	(	(	-LRB-
cord-329276-tfrjw743	209	8	minus	minus	CC
cord-329276-tfrjw743	209	9	sign	sign	NN
cord-329276-tfrjw743	209	10	)	)	-RRB-
cord-329276-tfrjw743	209	11	and	and	CC
cord-329276-tfrjw743	209	12	stimulating	stimulating	JJ
cord-329276-tfrjw743	209	13	(	(	-LRB-
cord-329276-tfrjw743	209	14	plus	plus	CC
cord-329276-tfrjw743	209	15	sign	sign	NN
cord-329276-tfrjw743	209	16	)	)	-RRB-
cord-329276-tfrjw743	209	17	.	.	.
cord-329276-tfrjw743	210	1	Clearly	clearly	RB
cord-329276-tfrjw743	210	2	,	,	,
cord-329276-tfrjw743	210	3	in	in	IN
cord-329276-tfrjw743	210	4	the	the	DT
cord-329276-tfrjw743	210	5	example	example	NN
cord-329276-tfrjw743	210	6	considered	consider	VBN
cord-329276-tfrjw743	210	7	above	above	RB
cord-329276-tfrjw743	210	8	,	,	,
cord-329276-tfrjw743	210	9	the	the	DT
cord-329276-tfrjw743	210	10	action	action	NN
cord-329276-tfrjw743	210	11	is	be	VBZ
cord-329276-tfrjw743	210	12	inhibiting	inhibit	VBG
cord-329276-tfrjw743	210	13	as	as	IN
cord-329276-tfrjw743	210	14	the	the	DT
cord-329276-tfrjw743	210	15	agent	agent	NN
cord-329276-tfrjw743	210	16	is	be	VBZ
cord-329276-tfrjw743	210	17	cytotoxic	cytotoxic	JJ
cord-329276-tfrjw743	210	18	and	and	CC
cord-329276-tfrjw743	210	19	kills	kill	VBZ
cord-329276-tfrjw743	210	20	the	the	DT
cord-329276-tfrjw743	210	21	cells	cell	NNS
cord-329276-tfrjw743	210	22	.	.	.
cord-329276-tfrjw743	211	1	On	on	IN
cord-329276-tfrjw743	211	2	the	the	DT
cord-329276-tfrjw743	211	3	other	other	JJ
cord-329276-tfrjw743	211	4	hand	hand	NN
cord-329276-tfrjw743	211	5	,	,	,
cord-329276-tfrjw743	211	6	in	in	IN
cord-329276-tfrjw743	211	7	Stepanova	Stepanova	NNP
cord-329276-tfrjw743	211	8	's	's	POS
cord-329276-tfrjw743	211	9	model	model	NN
cord-329276-tfrjw743	211	10	the	the	DT
cord-329276-tfrjw743	211	11	action	action	NN
cord-329276-tfrjw743	211	12	of	of	IN
cord-329276-tfrjw743	211	13	an	an	DT
cord-329276-tfrjw743	211	14	immune	immune	JJ
cord-329276-tfrjw743	211	15	stimulatory	stimulatory	JJ
cord-329276-tfrjw743	211	16	agent	agent	NN
cord-329276-tfrjw743	211	17	(	(	-LRB-
cord-329276-tfrjw743	211	18	such	such	JJ
cord-329276-tfrjw743	211	19	as	as	IN
cord-329276-tfrjw743	211	20	interleukin-2	interleukin-2	IN
cord-329276-tfrjw743	211	21	,	,	,
cord-329276-tfrjw743	211	22	IL-2	IL-2	NNP
cord-329276-tfrjw743	211	23	,	,	,
cord-329276-tfrjw743	211	24	representing	represent	VBG
cord-329276-tfrjw743	211	25	immunotherapy	immunotherapy	NN
cord-329276-tfrjw743	211	26	)	)	-RRB-
cord-329276-tfrjw743	211	27	would	would	MD
cord-329276-tfrjw743	211	28	be	be	VB
cord-329276-tfrjw743	211	29	included	include	VBN
cord-329276-tfrjw743	211	30	through	through	IN
cord-329276-tfrjw743	211	31	the	the	DT
cord-329276-tfrjw743	211	32	addition	addition	NN
cord-329276-tfrjw743	211	33	of	of	IN
cord-329276-tfrjw743	211	34	a	a	DT
cord-329276-tfrjw743	211	35	positive	positive	JJ
cord-329276-tfrjw743	211	36	term	term	NN
cord-329276-tfrjw743	211	37	+	+	CC
cord-329276-tfrjw743	211	38	ρru	ρru	NN
cord-329276-tfrjw743	211	39	into	into	IN
cord-329276-tfrjw743	211	40	Eq	Eq	NNP
cord-329276-tfrjw743	211	41	.	.	.
cord-329276-tfrjw743	212	1	(	(	-LRB-
cord-329276-tfrjw743	212	2	6	6	CD
cord-329276-tfrjw743	212	3	)	)	-RRB-
cord-329276-tfrjw743	212	4	.	.	.
cord-329276-tfrjw743	213	1	While	while	IN
cord-329276-tfrjw743	213	2	a	a	DT
cord-329276-tfrjw743	213	3	linear	linear	JJ
cord-329276-tfrjw743	213	4	model	model	NN
cord-329276-tfrjw743	213	5	s(c	s(c	NNP
cord-329276-tfrjw743	213	6	)	)	-RRB-
cord-329276-tfrjw743	213	7	=	=	SYM
cord-329276-tfrjw743	213	8	ϕc	ϕc	NN
cord-329276-tfrjw743	213	9	is	be	VBZ
cord-329276-tfrjw743	213	10	applicable	applicable	JJ
cord-329276-tfrjw743	213	11	over	over	IN
cord-329276-tfrjw743	213	12	a	a	DT
cord-329276-tfrjw743	213	13	specified	specify	VBN
cord-329276-tfrjw743	213	14	range	range	NN
cord-329276-tfrjw743	213	15	of	of	IN
cord-329276-tfrjw743	213	16	the	the	DT
cord-329276-tfrjw743	213	17	concentration	concentration	NN
cord-329276-tfrjw743	213	18	c	c	NN
cord-329276-tfrjw743	213	19	,	,	,
cord-329276-tfrjw743	213	20	it	-PRON-	PRP
cord-329276-tfrjw743	213	21	is	be	VBZ
cord-329276-tfrjw743	213	22	not	not	RB
cord-329276-tfrjw743	213	23	valid	valid	JJ
cord-329276-tfrjw743	213	24	for	for	IN
cord-329276-tfrjw743	213	25	low	low	JJ
cord-329276-tfrjw743	213	26	or	or	CC
cord-329276-tfrjw743	213	27	high	high	JJ
cord-329276-tfrjw743	213	28	drug	drug	NN
cord-329276-tfrjw743	213	29	concentrations	concentration	NNS
cord-329276-tfrjw743	213	30	.	.	.
cord-329276-tfrjw743	214	1	This	this	DT
cord-329276-tfrjw743	214	2	simply	simply	RB
cord-329276-tfrjw743	214	3	stems	stem	VBZ
cord-329276-tfrjw743	214	4	from	from	IN
cord-329276-tfrjw743	214	5	the	the	DT
cord-329276-tfrjw743	214	6	fact	fact	NN
cord-329276-tfrjw743	214	7	that	that	IN
cord-329276-tfrjw743	214	8	most	most	JJS
cord-329276-tfrjw743	214	9	drugs	drug	NNS
cord-329276-tfrjw743	214	10	have	have	VBP
cord-329276-tfrjw743	214	11	little	little	JJ
cord-329276-tfrjw743	214	12	to	to	TO
cord-329276-tfrjw743	214	13	no	no	DT
cord-329276-tfrjw743	214	14	effect	effect	NN
cord-329276-tfrjw743	214	15	if	if	IN
cord-329276-tfrjw743	214	16	their	-PRON-	PRP$
cord-329276-tfrjw743	214	17	concentrations	concentration	NNS
cord-329276-tfrjw743	214	18	are	be	VBP
cord-329276-tfrjw743	214	19	too	too	RB
cord-329276-tfrjw743	214	20	low	low	JJ
cord-329276-tfrjw743	214	21	and	and	CC
cord-329276-tfrjw743	214	22	,	,	,
cord-329276-tfrjw743	214	23	on	on	IN
cord-329276-tfrjw743	214	24	the	the	DT
cord-329276-tfrjw743	214	25	other	other	JJ
cord-329276-tfrjw743	214	26	hand	hand	NN
cord-329276-tfrjw743	214	27	,	,	,
cord-329276-tfrjw743	214	28	their	-PRON-	PRP$
cord-329276-tfrjw743	214	29	effectiveness	effectiveness	NN
cord-329276-tfrjw743	214	30	saturates	saturate	VBZ
cord-329276-tfrjw743	214	31	at	at	IN
cord-329276-tfrjw743	214	32	high	high	JJ
cord-329276-tfrjw743	214	33	concentrations	concentration	NNS
cord-329276-tfrjw743	214	34	.	.	.
cord-329276-tfrjw743	215	1	If	if	IN
cord-329276-tfrjw743	215	2	side	side	NN
cord-329276-tfrjw743	215	3	effects	effect	NNS
cord-329276-tfrjw743	215	4	allow	allow	VBP
cord-329276-tfrjw743	215	5	,	,	,
cord-329276-tfrjw743	215	6	drugs	drug	NNS
cord-329276-tfrjw743	215	7	are	be	VBP
cord-329276-tfrjw743	215	8	preferably	preferably	RB
cord-329276-tfrjw743	215	9	given	give	VBN
cord-329276-tfrjw743	215	10	in	in	IN
cord-329276-tfrjw743	215	11	the	the	DT
cord-329276-tfrjw743	215	12	upper	upper	JJ
cord-329276-tfrjw743	215	13	range	range	NN
cord-329276-tfrjw743	215	14	of	of	IN
cord-329276-tfrjw743	215	15	this	this	DT
cord-329276-tfrjw743	215	16	dose	dose	JJ
cord-329276-tfrjw743	215	17	-	-	HYPH
cord-329276-tfrjw743	215	18	effect	effect	NN
cord-329276-tfrjw743	215	19	curve	curve	NN
cord-329276-tfrjw743	215	20	and	and	CC
cord-329276-tfrjw743	215	21	an	an	DT
cord-329276-tfrjw743	215	22	E	e	NN
cord-329276-tfrjw743	215	23	max	max	NN
cord-329276-tfrjw743	215	24	model	model	NN
cord-329276-tfrjw743	215	25	of	of	IN
cord-329276-tfrjw743	215	26	the	the	DT
cord-329276-tfrjw743	215	27	form	form	NN
cord-329276-tfrjw743	215	28	describes	describe	VBZ
cord-329276-tfrjw743	215	29	the	the	DT
cord-329276-tfrjw743	215	30	effect	effect	NN
cord-329276-tfrjw743	215	31	of	of	IN
cord-329276-tfrjw743	215	32	"	"	``
cord-329276-tfrjw743	215	33	fast	fast	JJ
cord-329276-tfrjw743	215	34	"	"	''
cord-329276-tfrjw743	215	35	acting	act	VBG
cord-329276-tfrjw743	215	36	drugs	drug	NNS
cord-329276-tfrjw743	215	37	more	more	RBR
cord-329276-tfrjw743	215	38	accurately	accurately	RB
cord-329276-tfrjw743	215	39	for	for	IN
cord-329276-tfrjw743	215	40	high	high	JJ
cord-329276-tfrjw743	215	41	concentrations	concentration	NNS
cord-329276-tfrjw743	215	42	.	.	.
cord-329276-tfrjw743	216	1	Here	here	RB
cord-329276-tfrjw743	216	2	,	,	,
cord-329276-tfrjw743	216	3	EC	EC	NNP
cord-329276-tfrjw743	216	4	50	50	CD
cord-329276-tfrjw743	216	5	denotes	denote	VBZ
cord-329276-tfrjw743	216	6	the	the	DT
cord-329276-tfrjw743	216	7	concentration	concentration	NN
cord-329276-tfrjw743	216	8	at	at	IN
cord-329276-tfrjw743	216	9	which	which	WDT
cord-329276-tfrjw743	216	10	half	half	NN
cord-329276-tfrjw743	216	11	of	of	IN
cord-329276-tfrjw743	216	12	the	the	DT
cord-329276-tfrjw743	216	13	maximum	maximum	JJ
cord-329276-tfrjw743	216	14	effect	effect	NN
cord-329276-tfrjw743	216	15	E	e	NN
cord-329276-tfrjw743	216	16	max	max	NN
cord-329276-tfrjw743	216	17	is	be	VBZ
cord-329276-tfrjw743	216	18	realized	realize	VBN
cord-329276-tfrjw743	216	19	.	.	.
cord-329276-tfrjw743	217	1	Sigmoidal	Sigmoidal	NNP
cord-329276-tfrjw743	217	2	functions	function	NNS
cord-329276-tfrjw743	217	3	also	also	RB
cord-329276-tfrjw743	217	4	capture	capture	VBP
cord-329276-tfrjw743	217	5	the	the	DT
cord-329276-tfrjw743	217	6	behavior	behavior	NN
cord-329276-tfrjw743	217	7	at	at	IN
cord-329276-tfrjw743	217	8	lower	low	JJR
cord-329276-tfrjw743	217	9	concentrations	concentration	NNS
cord-329276-tfrjw743	217	10	.	.	.
cord-329276-tfrjw743	218	1	In	in	IN
cord-329276-tfrjw743	218	2	these	these	DT
cord-329276-tfrjw743	218	3	cases	case	NNS
cord-329276-tfrjw743	218	4	,	,	,
cord-329276-tfrjw743	218	5	if	if	IN
cord-329276-tfrjw743	218	6	the	the	DT
cord-329276-tfrjw743	218	7	drug	drug	NN
cord-329276-tfrjw743	218	8	concentrations	concentration	NNS
cord-329276-tfrjw743	218	9	are	be	VBP
cord-329276-tfrjw743	218	10	used	use	VBN
cord-329276-tfrjw743	218	11	as	as	IN
cord-329276-tfrjw743	218	12	the	the	DT
cord-329276-tfrjw743	218	13	control	control	NN
cord-329276-tfrjw743	218	14	,	,	,
cord-329276-tfrjw743	218	15	after	after	IN
cord-329276-tfrjw743	218	16	normalization	normalization	NN
cord-329276-tfrjw743	218	17	this	this	DT
cord-329276-tfrjw743	218	18	leads	lead	VBZ
cord-329276-tfrjw743	218	19	to	to	IN
cord-329276-tfrjw743	218	20	terms	term	NNS
cord-329276-tfrjw743	218	21	of	of	IN
cord-329276-tfrjw743	218	22	the	the	DT
cord-329276-tfrjw743	218	23	form	form	NN
cord-329276-tfrjw743	218	24	u	u	LS
cord-329276-tfrjw743	218	25	1+u	1+u	CD
cord-329276-tfrjw743	218	26	which	which	WDT
cord-329276-tfrjw743	218	27	no	no	RB
cord-329276-tfrjw743	218	28	longer	longer	RB
cord-329276-tfrjw743	218	29	fit	fit	VBP
cord-329276-tfrjw743	218	30	the	the	DT
cord-329276-tfrjw743	218	31	proposed	propose	VBN
cord-329276-tfrjw743	218	32	structure	structure	NN
cord-329276-tfrjw743	218	33	(	(	-LRB-
cord-329276-tfrjw743	218	34	7	7	CD
cord-329276-tfrjw743	218	35	)	)	-RRB-
cord-329276-tfrjw743	218	36	.	.	.
cord-329276-tfrjw743	219	1	This	this	DT
cord-329276-tfrjw743	219	2	,	,	,
cord-329276-tfrjw743	219	3	however	however	RB
cord-329276-tfrjw743	219	4	,	,	,
cord-329276-tfrjw743	219	5	is	be	VBZ
cord-329276-tfrjw743	219	6	merely	merely	RB
cord-329276-tfrjw743	219	7	caused	cause	VBN
cord-329276-tfrjw743	219	8	by	by	IN
cord-329276-tfrjw743	219	9	using	use	VBG
cord-329276-tfrjw743	219	10	the	the	DT
cord-329276-tfrjw743	219	11	concentrations	concentration	NNS
cord-329276-tfrjw743	219	12	as	as	IN
cord-329276-tfrjw743	219	13	the	the	DT
cord-329276-tfrjw743	219	14	controls	control	NNS
cord-329276-tfrjw743	219	15	.	.	.
cord-329276-tfrjw743	220	1	It	-PRON-	PRP
cord-329276-tfrjw743	220	2	can	can	MD
cord-329276-tfrjw743	220	3	easily	easily	RB
cord-329276-tfrjw743	220	4	be	be	VB
cord-329276-tfrjw743	220	5	removed	remove	VBN
cord-329276-tfrjw743	220	6	by	by	IN
cord-329276-tfrjw743	220	7	changing	change	VBG
cord-329276-tfrjw743	220	8	the	the	DT
cord-329276-tfrjw743	220	9	model	model	NN
cord-329276-tfrjw743	220	10	to	to	TO
cord-329276-tfrjw743	220	11	treat	treat	VB
cord-329276-tfrjw743	220	12	the	the	DT
cord-329276-tfrjw743	220	13	dose	dose	JJ
cord-329276-tfrjw743	220	14	rates	rate	NNS
cord-329276-tfrjw743	220	15	of	of	IN
cord-329276-tfrjw743	220	16	the	the	DT
cord-329276-tfrjw743	220	17	drug	drug	NN
cord-329276-tfrjw743	220	18	administration	administration	NN
cord-329276-tfrjw743	220	19	as	as	IN
cord-329276-tfrjw743	220	20	the	the	DT
cord-329276-tfrjw743	220	21	control	control	NN
cord-329276-tfrjw743	220	22	.	.	.
cord-329276-tfrjw743	221	1	The	the	DT
cord-329276-tfrjw743	221	2	second	second	JJ
cord-329276-tfrjw743	221	3	major	major	JJ
cord-329276-tfrjw743	221	4	aspect	aspect	NN
cord-329276-tfrjw743	221	5	of	of	IN
cord-329276-tfrjw743	221	6	drug	drug	NN
cord-329276-tfrjw743	221	7	delivery	delivery	NN
cord-329276-tfrjw743	221	8	is	be	VBZ
cord-329276-tfrjw743	221	9	pharmacokinetics	pharmacokinetic	NNS
cord-329276-tfrjw743	221	10	.	.	.
cord-329276-tfrjw743	222	1	Pharmacokinetic	pharmacokinetic	JJ
cord-329276-tfrjw743	222	2	equations	equation	NNS
cord-329276-tfrjw743	222	3	model	model	VBP
cord-329276-tfrjw743	222	4	the	the	DT
cord-329276-tfrjw743	222	5	time	time	NN
cord-329276-tfrjw743	222	6	evolution	evolution	NN
cord-329276-tfrjw743	222	7	of	of	IN
cord-329276-tfrjw743	222	8	a	a	DT
cord-329276-tfrjw743	222	9	drug	drug	NN
cord-329276-tfrjw743	222	10	's	's	POS
cord-329276-tfrjw743	222	11	concentration	concentration	NN
cord-329276-tfrjw743	222	12	in	in	IN
cord-329276-tfrjw743	222	13	the	the	DT
cord-329276-tfrjw743	222	14	blood	blood	NN
cord-329276-tfrjw743	222	15	plasma	plasma	NN
cord-329276-tfrjw743	222	16	.	.	.
cord-329276-tfrjw743	223	1	The	the	DT
cord-329276-tfrjw743	223	2	standard	standard	JJ
cord-329276-tfrjw743	223	3	model	model	NN
cord-329276-tfrjw743	223	4	that	that	WDT
cord-329276-tfrjw743	223	5	describes	describe	VBZ
cord-329276-tfrjw743	223	6	the	the	DT
cord-329276-tfrjw743	223	7	concentration	concentration	NN
cord-329276-tfrjw743	223	8	c	c	NN
cord-329276-tfrjw743	223	9	=	=	SYM
cord-329276-tfrjw743	223	10	c(t	c(t	NNP
cord-329276-tfrjw743	223	11	)	)	-RRB-
cord-329276-tfrjw743	223	12	of	of	IN
cord-329276-tfrjw743	223	13	the	the	DT
cord-329276-tfrjw743	223	14	drug	drug	NN
cord-329276-tfrjw743	223	15	in	in	IN
cord-329276-tfrjw743	223	16	the	the	DT
cord-329276-tfrjw743	223	17	bloodstream	bloodstream	NN
cord-329276-tfrjw743	223	18	in	in	IN
cord-329276-tfrjw743	223	19	response	response	NN
cord-329276-tfrjw743	223	20	to	to	IN
cord-329276-tfrjw743	223	21	a	a	DT
cord-329276-tfrjw743	223	22	continuous	continuous	JJ
cord-329276-tfrjw743	223	23	dose	dose	NN
cord-329276-tfrjw743	223	24	rate	rate	NN
cord-329276-tfrjw743	223	25	u	u	NN
cord-329276-tfrjw743	223	26	=	=	NN
cord-329276-tfrjw743	223	27	u(t	u(t	NNP
cord-329276-tfrjw743	223	28	)	)	-RRB-
cord-329276-tfrjw743	223	29	is	be	VBZ
cord-329276-tfrjw743	223	30	one	one	CD
cord-329276-tfrjw743	223	31	of	of	IN
cord-329276-tfrjw743	223	32	exponential	exponential	JJ
cord-329276-tfrjw743	223	33	growth	growth	NN
cord-329276-tfrjw743	223	34	and	and	CC
cord-329276-tfrjw743	223	35	decay	decay	VB
cord-329276-tfrjw743	223	36	given	give	VBN
cord-329276-tfrjw743	223	37	byċ	byċ	NN
cord-329276-tfrjw743	223	38	with	with	IN
cord-329276-tfrjw743	223	39	ρ	ρ	NFP
cord-329276-tfrjw743	223	40	the	the	DT
cord-329276-tfrjw743	223	41	clearance	clearance	NN
cord-329276-tfrjw743	223	42	rate	rate	NN
cord-329276-tfrjw743	223	43	of	of	IN
cord-329276-tfrjw743	223	44	the	the	DT
cord-329276-tfrjw743	223	45	drug	drug	NN
cord-329276-tfrjw743	223	46	.	.	.
cord-329276-tfrjw743	224	1	More	more	RBR
cord-329276-tfrjw743	224	2	generally	generally	RB
cord-329276-tfrjw743	224	3	,	,	,
cord-329276-tfrjw743	224	4	if	if	IN
cord-329276-tfrjw743	224	5	the	the	DT
cord-329276-tfrjw743	224	6	concentrations	concentration	NNS
cord-329276-tfrjw743	224	7	in	in	IN
cord-329276-tfrjw743	224	8	the	the	DT
cord-329276-tfrjw743	224	9	bloodstream	bloodstream	NN
cord-329276-tfrjw743	224	10	are	be	VBP
cord-329276-tfrjw743	224	11	separated	separate	VBN
cord-329276-tfrjw743	224	12	from	from	IN
cord-329276-tfrjw743	224	13	the	the	DT
cord-329276-tfrjw743	224	14	concentrations	concentration	NNS
cord-329276-tfrjw743	224	15	in	in	IN
cord-329276-tfrjw743	224	16	a	a	DT
cord-329276-tfrjw743	224	17	peripheral	peripheral	JJ
cord-329276-tfrjw743	224	18	compartment	compartment	NN
cord-329276-tfrjw743	224	19	(	(	-LRB-
cord-329276-tfrjw743	224	20	such	such	JJ
cord-329276-tfrjw743	224	21	as	as	IN
cord-329276-tfrjw743	224	22	tissue	tissue	NN
cord-329276-tfrjw743	224	23	or	or	CC
cord-329276-tfrjw743	224	24	an	an	DT
cord-329276-tfrjw743	224	25	organ	organ	NN
cord-329276-tfrjw743	224	26	of	of	IN
cord-329276-tfrjw743	224	27	interest	interest	NN
cord-329276-tfrjw743	224	28	)	)	-RRB-
cord-329276-tfrjw743	224	29	and	and	CC
cord-329276-tfrjw743	224	30	the	the	DT
cord-329276-tfrjw743	224	31	interactions	interaction	NNS
cord-329276-tfrjw743	224	32	between	between	IN
cord-329276-tfrjw743	224	33	those	those	DT
cord-329276-tfrjw743	224	34	compartments	compartment	NNS
cord-329276-tfrjw743	224	35	are	be	VBP
cord-329276-tfrjw743	224	36	taken	take	VBN
cord-329276-tfrjw743	224	37	into	into	IN
cord-329276-tfrjw743	224	38	account	account	NN
cord-329276-tfrjw743	224	39	,	,	,
cord-329276-tfrjw743	224	40	a	a	DT
cord-329276-tfrjw743	224	41	two	two	CD
cord-329276-tfrjw743	224	42	-	-	HYPH
cord-329276-tfrjw743	224	43	dimensional	dimensional	JJ
cord-329276-tfrjw743	224	44	linear	linear	JJ
cord-329276-tfrjw743	224	45	system	system	NN
cord-329276-tfrjw743	224	46	with	with	IN
cord-329276-tfrjw743	224	47	positive	positive	JJ
cord-329276-tfrjw743	224	48	eigenvalues	eigenvalue	NNS
cord-329276-tfrjw743	224	49	is	be	VBZ
cord-329276-tfrjw743	224	50	used	use	VBN
cord-329276-tfrjw743	224	51	.	.	.
cord-329276-tfrjw743	225	1	Higher	high	JJR
cord-329276-tfrjw743	225	2	-	-	HYPH
cord-329276-tfrjw743	225	3	dimensional	dimensional	JJ
cord-329276-tfrjw743	225	4	compartmental	compartmental	JJ
cord-329276-tfrjw743	225	5	models	model	NNS
cord-329276-tfrjw743	225	6	are	be	VBP
cord-329276-tfrjw743	225	7	used	use	VBN
cord-329276-tfrjw743	225	8	less	less	RBR
cord-329276-tfrjw743	225	9	frequently	frequently	RB
cord-329276-tfrjw743	225	10	,	,	,
cord-329276-tfrjw743	225	11	but	but	CC
cord-329276-tfrjw743	225	12	arise	arise	VBP
cord-329276-tfrjw743	225	13	,	,	,
cord-329276-tfrjw743	225	14	for	for	IN
cord-329276-tfrjw743	225	15	example	example	NN
cord-329276-tfrjw743	225	16	,	,	,
cord-329276-tfrjw743	225	17	if	if	IN
cord-329276-tfrjw743	225	18	the	the	DT
cord-329276-tfrjw743	225	19	peripheral	peripheral	JJ
cord-329276-tfrjw743	225	20	compartment	compartment	NN
cord-329276-tfrjw743	225	21	is	be	VBZ
cord-329276-tfrjw743	225	22	divided	divide	VBN
cord-329276-tfrjw743	225	23	further	further	RB
cord-329276-tfrjw743	225	24	into	into	IN
cord-329276-tfrjw743	225	25	a	a	DT
cord-329276-tfrjw743	225	26	'	'	``
cord-329276-tfrjw743	225	27	shallow	shallow	JJ
cord-329276-tfrjw743	225	28	'	'	''
cord-329276-tfrjw743	225	29	and	and	CC
cord-329276-tfrjw743	225	30	'	'	``
cord-329276-tfrjw743	225	31	deep	deep	JJ
cord-329276-tfrjw743	225	32	'	'	''
cord-329276-tfrjw743	225	33	compartment	compartment	NN
cord-329276-tfrjw743	225	34	.	.	.
cord-329276-tfrjw743	226	1	For	for	IN
cord-329276-tfrjw743	226	2	example	example	NN
cord-329276-tfrjw743	226	3	,	,	,
cord-329276-tfrjw743	226	4	a	a	DT
cord-329276-tfrjw743	226	5	3-compartment	3-compartment	CD
cord-329276-tfrjw743	226	6	model	model	NN
cord-329276-tfrjw743	226	7	is	be	VBZ
cord-329276-tfrjw743	226	8	often	often	RB
cord-329276-tfrjw743	226	9	used	use	VBN
cord-329276-tfrjw743	226	10	for	for	IN
cord-329276-tfrjw743	226	11	insulin	insulin	NN
cord-329276-tfrjw743	226	12	pumps	pump	NNS
cord-329276-tfrjw743	226	13	[	[	-LRB-
cord-329276-tfrjw743	226	14	29	29	CD
cord-329276-tfrjw743	226	15	]	]	-RRB-
cord-329276-tfrjw743	226	16	.	.	.
cord-329276-tfrjw743	227	1	All	all	PDT
cord-329276-tfrjw743	227	2	these	these	DT
cord-329276-tfrjw743	227	3	models	model	NNS
cord-329276-tfrjw743	227	4	,	,	,
cord-329276-tfrjw743	227	5	however	however	RB
cord-329276-tfrjw743	227	6	,	,	,
cord-329276-tfrjw743	227	7	are	be	VBP
cord-329276-tfrjw743	227	8	described	describe	VBN
cord-329276-tfrjw743	227	9	by	by	IN
cord-329276-tfrjw743	227	10	linear	linear	JJ
cord-329276-tfrjw743	227	11	time	time	NN
cord-329276-tfrjw743	227	12	-	-	HYPH
cord-329276-tfrjw743	227	13	invariant	invariant	JJ
cord-329276-tfrjw743	227	14	systems	system	NNS
cord-329276-tfrjw743	227	15	with	with	IN
cord-329276-tfrjw743	227	16	real	real	JJ
cord-329276-tfrjw743	227	17	eigenvalues	eigenvalue	NNS
cord-329276-tfrjw743	227	18	.	.	.
cord-329276-tfrjw743	228	1	If	if	IN
cord-329276-tfrjw743	228	2	one	one	PRP
cord-329276-tfrjw743	228	3	therefore	therefore	RB
cord-329276-tfrjw743	228	4	introduces	introduce	VBZ
cord-329276-tfrjw743	228	5	the	the	DT
cord-329276-tfrjw743	228	6	drug	drug	NN
cord-329276-tfrjw743	228	7	dose	dose	NN
cord-329276-tfrjw743	228	8	rates	rate	NNS
cord-329276-tfrjw743	228	9	as	as	IN
cord-329276-tfrjw743	228	10	the	the	DT
cord-329276-tfrjw743	228	11	controls	control	NNS
cord-329276-tfrjw743	228	12	,	,	,
cord-329276-tfrjw743	228	13	then	then	RB
cord-329276-tfrjw743	228	14	the	the	DT
cord-329276-tfrjw743	228	15	associated	associate	VBN
cord-329276-tfrjw743	228	16	drug	drug	NN
cord-329276-tfrjw743	228	17	concentrations	concentration	NNS
cord-329276-tfrjw743	229	1	c	c	NNP
cord-329276-tfrjw743	229	2	become	become	VBP
cord-329276-tfrjw743	229	3	state	state	NN
cord-329276-tfrjw743	229	4	variables	variable	NNS
cord-329276-tfrjw743	229	5	and	and	CC
cord-329276-tfrjw743	229	6	thus	thus	RB
cord-329276-tfrjw743	229	7	become	become	VB
cord-329276-tfrjw743	229	8	an	an	DT
cord-329276-tfrjw743	229	9	integral	integral	JJ
cord-329276-tfrjw743	229	10	part	part	NN
cord-329276-tfrjw743	229	11	of	of	IN
cord-329276-tfrjw743	229	12	the	the	DT
cord-329276-tfrjw743	229	13	modeling	modeling	NN
cord-329276-tfrjw743	229	14	of	of	IN
cord-329276-tfrjw743	229	15	the	the	DT
cord-329276-tfrjw743	229	16	uncontrolled	uncontrolled	JJ
cord-329276-tfrjw743	229	17	dynamics	dynamic	NNS
cord-329276-tfrjw743	229	18	that	that	WDT
cord-329276-tfrjw743	229	19	enters	enter	VBZ
cord-329276-tfrjw743	229	20	the	the	DT
cord-329276-tfrjw743	229	21	form	form	NN
cord-329276-tfrjw743	229	22	of	of	IN
cord-329276-tfrjw743	229	23	the	the	DT
cord-329276-tfrjw743	229	24	drift	drift	NN
cord-329276-tfrjw743	229	25	vector	vector	NN
cord-329276-tfrjw743	229	26	field	field	NN
cord-329276-tfrjw743	229	27	F.	F.	NNP
cord-329276-tfrjw743	229	28	In	in	IN
cord-329276-tfrjw743	229	29	particular	particular	JJ
cord-329276-tfrjw743	229	30	,	,	,
cord-329276-tfrjw743	229	31	all	all	PDT
cord-329276-tfrjw743	229	32	the	the	DT
cord-329276-tfrjw743	229	33	nonlinearities	nonlinearitie	NNS
cord-329276-tfrjw743	229	34	that	that	WDT
cord-329276-tfrjw743	229	35	arise	arise	VBP
cord-329276-tfrjw743	229	36	because	because	IN
cord-329276-tfrjw743	229	37	of	of	IN
cord-329276-tfrjw743	229	38	saturation	saturation	NN
cord-329276-tfrjw743	229	39	effects	effect	NNS
cord-329276-tfrjw743	229	40	or	or	CC
cord-329276-tfrjw743	229	41	because	because	IN
cord-329276-tfrjw743	229	42	of	of	IN
cord-329276-tfrjw743	229	43	synergistic	synergistic	JJ
cord-329276-tfrjw743	229	44	properties	property	NNS
cord-329276-tfrjw743	229	45	of	of	IN
cord-329276-tfrjw743	229	46	drug	drug	NN
cord-329276-tfrjw743	229	47	administration	administration	NN
cord-329276-tfrjw743	229	48	are	be	VBP
cord-329276-tfrjw743	229	49	subsumed	subsume	VBN
cord-329276-tfrjw743	229	50	in	in	IN
cord-329276-tfrjw743	229	51	the	the	DT
cord-329276-tfrjw743	229	52	drift	drift	NN
cord-329276-tfrjw743	229	53	vector	vector	NN
cord-329276-tfrjw743	229	54	field	field	NN
cord-329276-tfrjw743	229	55	F	F	NNP
cord-329276-tfrjw743	229	56	,	,	,
cord-329276-tfrjw743	229	57	which	which	WDT
cord-329276-tfrjw743	229	58	,	,	,
cord-329276-tfrjw743	229	59	as	as	IN
cord-329276-tfrjw743	229	60	the	the	DT
cord-329276-tfrjw743	229	61	example	example	NN
cord-329276-tfrjw743	229	62	for	for	IN
cord-329276-tfrjw743	229	63	angiogenic	angiogenic	JJ
cord-329276-tfrjw743	229	64	signaling	signaling	NN
cord-329276-tfrjw743	229	65	shows	show	NNS
cord-329276-tfrjw743	229	66	,	,	,
cord-329276-tfrjw743	229	67	may	may	MD
cord-329276-tfrjw743	229	68	already	already	RB
cord-329276-tfrjw743	229	69	be	be	VB
cord-329276-tfrjw743	229	70	a	a	DT
cord-329276-tfrjw743	229	71	highly	highly	RB
cord-329276-tfrjw743	229	72	nonlinear	nonlinear	JJ
cord-329276-tfrjw743	229	73	vector	vector	NN
cord-329276-tfrjw743	229	74	field	field	NN
cord-329276-tfrjw743	229	75	to	to	TO
cord-329276-tfrjw743	229	76	begin	begin	VB
cord-329276-tfrjw743	229	77	with	with	IN
cord-329276-tfrjw743	229	78	.	.	.
cord-329276-tfrjw743	230	1	Actual	actual	JJ
cord-329276-tfrjw743	230	2	drug	drug	NN
cord-329276-tfrjw743	230	3	administration	administration	NN
cord-329276-tfrjw743	230	4	,	,	,
cord-329276-tfrjw743	230	5	however	however	RB
cord-329276-tfrjw743	230	6	,	,	,
cord-329276-tfrjw743	230	7	is	be	VBZ
cord-329276-tfrjw743	230	8	described	describe	VBN
cord-329276-tfrjw743	230	9	by	by	IN
cord-329276-tfrjw743	230	10	linear	linear	JJ
cord-329276-tfrjw743	230	11	models	model	NNS
cord-329276-tfrjw743	230	12	.	.	.
cord-329276-tfrjw743	231	1	Once	once	IN
cord-329276-tfrjw743	231	2	medical	medical	JJ
cord-329276-tfrjw743	231	3	professionals	professional	NNS
cord-329276-tfrjw743	231	4	have	have	VBP
cord-329276-tfrjw743	231	5	decided	decide	VBN
cord-329276-tfrjw743	231	6	on	on	IN
cord-329276-tfrjw743	231	7	a	a	DT
cord-329276-tfrjw743	231	8	course	course	NN
cord-329276-tfrjw743	231	9	of	of	IN
cord-329276-tfrjw743	231	10	action	action	NN
cord-329276-tfrjw743	231	11	,	,	,
cord-329276-tfrjw743	231	12	a	a	DT
cord-329276-tfrjw743	231	13	number	number	NN
cord-329276-tfrjw743	231	14	of	of	IN
cord-329276-tfrjw743	231	15	natural	natural	JJ
cord-329276-tfrjw743	231	16	questions	question	NNS
cord-329276-tfrjw743	231	17	need	need	VBP
cord-329276-tfrjw743	231	18	to	to	TO
cord-329276-tfrjw743	231	19	be	be	VB
cord-329276-tfrjw743	231	20	answered	answer	VBN
cord-329276-tfrjw743	231	21	:	:	:
cord-329276-tfrjw743	231	22	(	(	-LRB-
cord-329276-tfrjw743	231	23	1	1	LS
cord-329276-tfrjw743	231	24	)	)	-RRB-
cord-329276-tfrjw743	231	25	HOW	how	WRB
cord-329276-tfrjw743	231	26	MUCH	much	JJ
cord-329276-tfrjw743	231	27	of	of	IN
cord-329276-tfrjw743	231	28	the	the	DT
cord-329276-tfrjw743	231	29	agent	agent	NN
cord-329276-tfrjw743	231	30	should	should	MD
cord-329276-tfrjw743	231	31	be	be	VB
cord-329276-tfrjw743	231	32	given	give	VBN
cord-329276-tfrjw743	231	33	?	?	.
cord-329276-tfrjw743	232	1	(	(	-LRB-
cord-329276-tfrjw743	232	2	2	2	LS
cord-329276-tfrjw743	232	3	)	)	-RRB-
cord-329276-tfrjw743	232	4	WHEN	when	WRB
cord-329276-tfrjw743	232	5	and	and	CC
cord-329276-tfrjw743	232	6	HOW	how	WRB
cord-329276-tfrjw743	232	7	OFTEN	often	RB
cord-329276-tfrjw743	232	8	should	should	MD
cord-329276-tfrjw743	232	9	drugs	drug	NNS
cord-329276-tfrjw743	232	10	be	be	VB
cord-329276-tfrjw743	232	11	given	give	VBN
cord-329276-tfrjw743	232	12	?	?	.
cord-329276-tfrjw743	233	1	(	(	-LRB-
cord-329276-tfrjw743	233	2	3	3	LS
cord-329276-tfrjw743	233	3	)	)	-RRB-
cord-329276-tfrjw743	234	1	IN	in	IN
cord-329276-tfrjw743	234	2	WHAT	what	WDT
cord-329276-tfrjw743	234	3	ORDER	order	NN
cord-329276-tfrjw743	234	4	should	should	MD
cord-329276-tfrjw743	234	5	the	the	DT
cord-329276-tfrjw743	234	6	treatments	treatment	NNS
cord-329276-tfrjw743	234	7	be	be	VB
cord-329276-tfrjw743	234	8	applied	apply	VBN
cord-329276-tfrjw743	234	9	?	?	.
cord-329276-tfrjw743	235	1	All	all	PDT
cord-329276-tfrjw743	235	2	these	these	DT
cord-329276-tfrjw743	235	3	questions	question	NNS
cord-329276-tfrjw743	235	4	can	can	MD
cord-329276-tfrjw743	235	5	naturally	naturally	RB
cord-329276-tfrjw743	235	6	be	be	VB
cord-329276-tfrjw743	235	7	answered	answer	VBN
cord-329276-tfrjw743	235	8	within	within	IN
cord-329276-tfrjw743	235	9	the	the	DT
cord-329276-tfrjw743	235	10	framework	framework	NN
cord-329276-tfrjw743	235	11	of	of	IN
cord-329276-tfrjw743	235	12	an	an	DT
cord-329276-tfrjw743	235	13	optimal	optimal	JJ
cord-329276-tfrjw743	235	14	control	control	NN
cord-329276-tfrjw743	235	15	problem	problem	NN
cord-329276-tfrjw743	235	16	.	.	.
cord-329276-tfrjw743	236	1	Clearly	clearly	RB
cord-329276-tfrjw743	236	2	,	,	,
cord-329276-tfrjw743	236	3	we	-PRON-	PRP
cord-329276-tfrjw743	236	4	are	be	VBP
cord-329276-tfrjw743	236	5	only	only	RB
cord-329276-tfrjw743	236	6	dealing	deal	VBG
cord-329276-tfrjw743	236	7	with	with	IN
cord-329276-tfrjw743	236	8	a	a	DT
cord-329276-tfrjw743	236	9	mathematical	mathematical	JJ
cord-329276-tfrjw743	236	10	model	model	NN
cord-329276-tfrjw743	236	11	and	and	CC
cord-329276-tfrjw743	236	12	no	no	DT
cord-329276-tfrjw743	236	13	claims	claim	NNS
cord-329276-tfrjw743	236	14	are	be	VBP
cord-329276-tfrjw743	236	15	made	make	VBN
cord-329276-tfrjw743	236	16	that	that	IN
cord-329276-tfrjw743	236	17	the	the	DT
cord-329276-tfrjw743	236	18	real	real	JJ
cord-329276-tfrjw743	236	19	problem	problem	NN
cord-329276-tfrjw743	236	20	could	could	MD
cord-329276-tfrjw743	236	21	be	be	VB
cord-329276-tfrjw743	236	22	solved	solve	VBN
cord-329276-tfrjw743	236	23	in	in	IN
cord-329276-tfrjw743	236	24	this	this	DT
cord-329276-tfrjw743	236	25	way	way	NN
cord-329276-tfrjw743	236	26	.	.	.
cord-329276-tfrjw743	237	1	But	but	CC
cord-329276-tfrjw743	237	2	interesting	interesting	JJ
cord-329276-tfrjw743	237	3	and	and	CC
cord-329276-tfrjw743	237	4	useful	useful	JJ
cord-329276-tfrjw743	237	5	information	information	NN
cord-329276-tfrjw743	237	6	can	can	MD
cord-329276-tfrjw743	237	7	be	be	VB
cord-329276-tfrjw743	237	8	obtained	obtain	VBN
cord-329276-tfrjw743	237	9	.	.	.
cord-329276-tfrjw743	238	1	To	to	TO
cord-329276-tfrjw743	238	2	give	give	VB
cord-329276-tfrjw743	238	3	a	a	DT
cord-329276-tfrjw743	238	4	concrete	concrete	JJ
cord-329276-tfrjw743	238	5	example	example	NN
cord-329276-tfrjw743	238	6	,	,	,
cord-329276-tfrjw743	238	7	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	238	8	needs	need	VBZ
cord-329276-tfrjw743	238	9	the	the	DT
cord-329276-tfrjw743	238	10	tumor	tumor	NN
cord-329276-tfrjw743	238	11	vasculature	vasculature	NN
cord-329276-tfrjw743	238	12	to	to	TO
cord-329276-tfrjw743	238	13	deliver	deliver	VB
cord-329276-tfrjw743	238	14	cytotoxic	cytotoxic	JJ
cord-329276-tfrjw743	238	15	agents	agent	NNS
cord-329276-tfrjw743	238	16	that	that	WDT
cord-329276-tfrjw743	238	17	kill	kill	VBP
cord-329276-tfrjw743	238	18	the	the	DT
cord-329276-tfrjw743	238	19	tumor	tumor	NN
cord-329276-tfrjw743	238	20	cells	cell	NNS
cord-329276-tfrjw743	238	21	.	.	.
cord-329276-tfrjw743	239	1	It	-PRON-	PRP
cord-329276-tfrjw743	239	2	therefore	therefore	RB
cord-329276-tfrjw743	239	3	was	be	VBD
cord-329276-tfrjw743	239	4	conventional	conventional	JJ
cord-329276-tfrjw743	239	5	wisdom	wisdom	NN
cord-329276-tfrjw743	239	6	to	to	TO
cord-329276-tfrjw743	239	7	first	first	RB
cord-329276-tfrjw743	239	8	give	give	VB
cord-329276-tfrjw743	239	9	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	239	10	when	when	WRB
cord-329276-tfrjw743	239	11	antiangiogenic	antiangiogenic	JJ
cord-329276-tfrjw743	239	12	treatments	treatment	NNS
cord-329276-tfrjw743	239	13	and	and	CC
cord-329276-tfrjw743	239	14	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	239	15	were	be	VBD
cord-329276-tfrjw743	239	16	combined	combine	VBN
cord-329276-tfrjw743	239	17	in	in	IN
cord-329276-tfrjw743	239	18	the	the	DT
cord-329276-tfrjw743	239	19	treatment	treatment	NN
cord-329276-tfrjw743	239	20	of	of	IN
cord-329276-tfrjw743	239	21	cancer	cancer	NN
cord-329276-tfrjw743	239	22	.	.	.
cord-329276-tfrjw743	240	1	This	this	DT
cord-329276-tfrjw743	240	2	notion	notion	NN
cord-329276-tfrjw743	240	3	,	,	,
cord-329276-tfrjw743	240	4	however	however	RB
cord-329276-tfrjw743	240	5	,	,	,
cord-329276-tfrjw743	240	6	was	be	VBD
cord-329276-tfrjw743	240	7	challenged	challenge	VBN
cord-329276-tfrjw743	240	8	by	by	IN
cord-329276-tfrjw743	240	9	Jain	Jain	NNP
cord-329276-tfrjw743	240	10	et	et	NNP
cord-329276-tfrjw743	240	11	al	al	NNP
cord-329276-tfrjw743	240	12	.	.	.
cord-329276-tfrjw743	241	1	[	[	-LRB-
cord-329276-tfrjw743	241	2	30	30	CD
cord-329276-tfrjw743	241	3	,	,	,
cord-329276-tfrjw743	241	4	31	31	CD
cord-329276-tfrjw743	241	5	]	]	-RRB-
cord-329276-tfrjw743	241	6	who	who	WP
cord-329276-tfrjw743	241	7	argued	argue	VBD
cord-329276-tfrjw743	241	8	that	that	IN
cord-329276-tfrjw743	241	9	a	a	DT
cord-329276-tfrjw743	241	10	normalization	normalization	NN
cord-329276-tfrjw743	241	11	of	of	IN
cord-329276-tfrjw743	241	12	the	the	DT
cord-329276-tfrjw743	241	13	vasculature	vasculature	NN
cord-329276-tfrjw743	241	14	(	(	-LRB-
cord-329276-tfrjw743	241	15	"	"	``
cord-329276-tfrjw743	241	16	pruning	prune	VBG
cord-329276-tfrjw743	241	17	"	"	''
cord-329276-tfrjw743	241	18	)	)	-RRB-
cord-329276-tfrjw743	241	19	prior	prior	RB
cord-329276-tfrjw743	241	20	to	to	IN
cord-329276-tfrjw743	241	21	the	the	DT
cord-329276-tfrjw743	241	22	administration	administration	NN
cord-329276-tfrjw743	241	23	of	of	IN
cord-329276-tfrjw743	241	24	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	241	25	is	be	VBZ
cord-329276-tfrjw743	241	26	beneficial	beneficial	JJ
cord-329276-tfrjw743	241	27	for	for	IN
cord-329276-tfrjw743	241	28	the	the	DT
cord-329276-tfrjw743	241	29	delivery	delivery	NN
cord-329276-tfrjw743	241	30	of	of	IN
cord-329276-tfrjw743	241	31	the	the	DT
cord-329276-tfrjw743	241	32	cytotoxic	cytotoxic	JJ
cord-329276-tfrjw743	241	33	agents	agent	NNS
cord-329276-tfrjw743	241	34	and	and	CC
cord-329276-tfrjw743	241	35	that	that	IN
cord-329276-tfrjw743	241	36	it	-PRON-	PRP
cord-329276-tfrjw743	241	37	gives	give	VBZ
cord-329276-tfrjw743	241	38	better	well	JJR
cord-329276-tfrjw743	241	39	results	result	NNS
cord-329276-tfrjw743	241	40	.	.	.
cord-329276-tfrjw743	242	1	These	these	DT
cord-329276-tfrjw743	242	2	findings	finding	NNS
cord-329276-tfrjw743	242	3	can	can	MD
cord-329276-tfrjw743	242	4	be	be	VB
cord-329276-tfrjw743	242	5	strongly	strongly	RB
cord-329276-tfrjw743	242	6	supported	support	VBN
cord-329276-tfrjw743	242	7	through	through	IN
cord-329276-tfrjw743	242	8	a	a	DT
cord-329276-tfrjw743	242	9	mathematical	mathematical	JJ
cord-329276-tfrjw743	242	10	analysis	analysis	NN
cord-329276-tfrjw743	242	11	of	of	IN
cord-329276-tfrjw743	242	12	the	the	DT
cord-329276-tfrjw743	242	13	Hahnfeldt	Hahnfeldt	NNP
cord-329276-tfrjw743	242	14	model	model	NN
cord-329276-tfrjw743	242	15	with	with	IN
cord-329276-tfrjw743	242	16	both	both	DT
cord-329276-tfrjw743	242	17	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	242	18	and	and	CC
cord-329276-tfrjw743	242	19	antiangiogenic	antiangiogenic	JJ
cord-329276-tfrjw743	242	20	therapy	therapy	NN
cord-329276-tfrjw743	242	21	[	[	-LRB-
cord-329276-tfrjw743	242	22	32	32	CD
cord-329276-tfrjw743	242	23	]	]	-RRB-
cord-329276-tfrjw743	242	24	.	.	.
cord-329276-tfrjw743	243	1	Thus	thus	RB
cord-329276-tfrjw743	243	2	,	,	,
cord-329276-tfrjw743	243	3	while	while	IN
cord-329276-tfrjw743	243	4	optimal	optimal	JJ
cord-329276-tfrjw743	243	5	control	control	NN
cord-329276-tfrjw743	243	6	can	can	MD
cord-329276-tfrjw743	243	7	not	not	RB
cord-329276-tfrjw743	243	8	provide	provide	VB
cord-329276-tfrjw743	243	9	the	the	DT
cord-329276-tfrjw743	243	10	ultimate	ultimate	JJ
cord-329276-tfrjw743	243	11	answers	answer	NNS
cord-329276-tfrjw743	243	12	to	to	IN
cord-329276-tfrjw743	243	13	the	the	DT
cord-329276-tfrjw743	243	14	underlying	underlie	VBG
cord-329276-tfrjw743	243	15	problems	problem	NNS
cord-329276-tfrjw743	243	16	,	,	,
cord-329276-tfrjw743	243	17	it	-PRON-	PRP
cord-329276-tfrjw743	243	18	can	can	MD
cord-329276-tfrjw743	243	19	become	become	VB
cord-329276-tfrjw743	243	20	a	a	DT
cord-329276-tfrjw743	243	21	valuable	valuable	JJ
cord-329276-tfrjw743	243	22	tool	tool	NN
cord-329276-tfrjw743	243	23	in	in	IN
cord-329276-tfrjw743	243	24	understanding	understand	VBG
cord-329276-tfrjw743	243	25	these	these	DT
cord-329276-tfrjw743	243	26	processes	process	NNS
cord-329276-tfrjw743	243	27	.	.	.
cord-329276-tfrjw743	244	1	The	the	DT
cord-329276-tfrjw743	244	2	ultimate	ultimate	JJ
cord-329276-tfrjw743	244	3	aim	aim	NN
cord-329276-tfrjw743	244	4	in	in	IN
cord-329276-tfrjw743	244	5	biomedical	biomedical	JJ
cord-329276-tfrjw743	244	6	problem	problem	NN
cord-329276-tfrjw743	244	7	formulations	formulation	NNS
cord-329276-tfrjw743	244	8	is	be	VBZ
cord-329276-tfrjw743	244	9	to	to	TO
cord-329276-tfrjw743	244	10	find	find	VB
cord-329276-tfrjw743	244	11	a	a	DT
cord-329276-tfrjw743	244	12	safe	safe	JJ
cord-329276-tfrjw743	244	13	and	and	CC
cord-329276-tfrjw743	244	14	reasonable	reasonable	JJ
cord-329276-tfrjw743	244	15	strategy	strategy	NN
cord-329276-tfrjw743	244	16	to	to	TO
cord-329276-tfrjw743	244	17	solve	solve	VB
cord-329276-tfrjw743	244	18	the	the	DT
cord-329276-tfrjw743	244	19	underlying	underlying	JJ
cord-329276-tfrjw743	244	20	medical	medical	JJ
cord-329276-tfrjw743	244	21	problem	problem	NN
cord-329276-tfrjw743	244	22	.	.	.
cord-329276-tfrjw743	245	1	By	by	IN
cord-329276-tfrjw743	245	2	adopting	adopt	VBG
cord-329276-tfrjw743	245	3	an	an	DT
cord-329276-tfrjw743	245	4	optimal	optimal	JJ
cord-329276-tfrjw743	245	5	control	control	NN
cord-329276-tfrjw743	245	6	formulation	formulation	NN
cord-329276-tfrjw743	245	7	,	,	,
cord-329276-tfrjw743	245	8	we	-PRON-	PRP
cord-329276-tfrjw743	245	9	are	be	VBP
cord-329276-tfrjw743	245	10	aiming	aim	VBG
cord-329276-tfrjw743	245	11	for	for	IN
cord-329276-tfrjw743	245	12	what	what	WP
cord-329276-tfrjw743	245	13	in	in	IN
cord-329276-tfrjw743	245	14	a	a	DT
cord-329276-tfrjw743	245	15	certain	certain	JJ
cord-329276-tfrjw743	245	16	way	way	NN
cord-329276-tfrjw743	245	17	can	can	MD
cord-329276-tfrjw743	245	18	be	be	VB
cord-329276-tfrjw743	245	19	considered	consider	VBN
cord-329276-tfrjw743	245	20	the	the	DT
cord-329276-tfrjw743	245	21	"	"	``
cord-329276-tfrjw743	245	22	best	good	JJS
cord-329276-tfrjw743	245	23	possible	possible	JJ
cord-329276-tfrjw743	245	24	"	"	''
cord-329276-tfrjw743	245	25	solution	solution	NN
cord-329276-tfrjw743	245	26	.	.	.
cord-329276-tfrjw743	246	1	What	what	WP
cord-329276-tfrjw743	246	2	this	this	DT
cord-329276-tfrjw743	246	3	best	good	JJS
cord-329276-tfrjw743	246	4	possible	possible	JJ
cord-329276-tfrjw743	246	5	solution	solution	NN
cord-329276-tfrjw743	246	6	should	should	MD
cord-329276-tfrjw743	246	7	be	be	VB
cord-329276-tfrjw743	246	8	,	,	,
cord-329276-tfrjw743	246	9	however	however	RB
cord-329276-tfrjw743	246	10	,	,	,
cord-329276-tfrjw743	246	11	is	be	VBZ
cord-329276-tfrjw743	246	12	often	often	RB
cord-329276-tfrjw743	246	13	up	up	IN
cord-329276-tfrjw743	246	14	to	to	IN
cord-329276-tfrjw743	246	15	wide	wide	JJ
cord-329276-tfrjw743	246	16	interpretations	interpretation	NNS
cord-329276-tfrjw743	246	17	.	.	.
cord-329276-tfrjw743	247	1	It	-PRON-	PRP
cord-329276-tfrjw743	247	2	is	be	VBZ
cord-329276-tfrjw743	247	3	here	here	RB
cord-329276-tfrjw743	247	4	that	that	IN
cord-329276-tfrjw743	247	5	the	the	DT
cord-329276-tfrjw743	247	6	role	role	NN
cord-329276-tfrjw743	247	7	of	of	IN
cord-329276-tfrjw743	247	8	the	the	DT
cord-329276-tfrjw743	247	9	objective	objective	JJ
cord-329276-tfrjw743	247	10	functional	functional	JJ
cord-329276-tfrjw743	247	11	chosen	choose	VBN
cord-329276-tfrjw743	247	12	to	to	TO
cord-329276-tfrjw743	247	13	minimize	minimize	VB
cord-329276-tfrjw743	247	14	matters	matter	NNS
cord-329276-tfrjw743	247	15	greatly	greatly	RB
cord-329276-tfrjw743	247	16	-	-	:
cord-329276-tfrjw743	247	17	sometimes	sometimes	RB
cord-329276-tfrjw743	247	18	to	to	IN
cord-329276-tfrjw743	247	19	the	the	DT
cord-329276-tfrjw743	247	20	extent	extent	NN
cord-329276-tfrjw743	247	21	that	that	IN
cord-329276-tfrjw743	247	22	this	this	DT
cord-329276-tfrjw743	247	23	choice	choice	NN
cord-329276-tfrjw743	247	24	already	already	RB
cord-329276-tfrjw743	247	25	preprograms	preprogram	VBZ
cord-329276-tfrjw743	247	26	the	the	DT
cord-329276-tfrjw743	247	27	eventual	eventual	JJ
cord-329276-tfrjw743	247	28	solution	solution	NN
cord-329276-tfrjw743	247	29	.	.	.
cord-329276-tfrjw743	248	1	This	this	DT
cord-329276-tfrjw743	248	2	choice	choice	NN
cord-329276-tfrjw743	248	3	then	then	RB
cord-329276-tfrjw743	248	4	is	be	VBZ
cord-329276-tfrjw743	248	5	the	the	DT
cord-329276-tfrjw743	248	6	third	third	JJ
cord-329276-tfrjw743	248	7	essential	essential	JJ
cord-329276-tfrjw743	248	8	aspect	aspect	NN
cord-329276-tfrjw743	248	9	of	of	IN
cord-329276-tfrjw743	248	10	the	the	DT
cord-329276-tfrjw743	248	11	problem	problem	NN
cord-329276-tfrjw743	248	12	formulation	formulation	NN
cord-329276-tfrjw743	248	13	.	.	.
cord-329276-tfrjw743	249	1	The	the	DT
cord-329276-tfrjw743	249	2	following	follow	VBG
cord-329276-tfrjw743	249	3	general	general	JJ
cord-329276-tfrjw743	249	4	form	form	NN
cord-329276-tfrjw743	249	5	encompasses	encompass	VBZ
cord-329276-tfrjw743	249	6	a	a	DT
cord-329276-tfrjw743	249	7	wide	wide	JJ
cord-329276-tfrjw743	249	8	range	range	NN
cord-329276-tfrjw743	249	9	of	of	IN
cord-329276-tfrjw743	249	10	possibilities	possibility	NNS
cord-329276-tfrjw743	249	11	:	:	:
cord-329276-tfrjw743	249	12	(	(	-LRB-
cord-329276-tfrjw743	249	13	13	13	CD
cord-329276-tfrjw743	249	14	)	)	-RRB-
cord-329276-tfrjw743	250	1	Here	here	RB
cord-329276-tfrjw743	250	2	,	,	,
cord-329276-tfrjw743	250	3	L	L	NNP
cord-329276-tfrjw743	250	4	is	be	VBZ
cord-329276-tfrjw743	250	5	a	a	DT
cord-329276-tfrjw743	250	6	sufficiently	sufficiently	RB
cord-329276-tfrjw743	250	7	smooth	smooth	JJ
cord-329276-tfrjw743	250	8	function	function	NN
cord-329276-tfrjw743	250	9	of	of	IN
cord-329276-tfrjw743	250	10	the	the	DT
cord-329276-tfrjw743	250	11	state	state	NN
cord-329276-tfrjw743	250	12	called	call	VBN
cord-329276-tfrjw743	250	13	the	the	DT
cord-329276-tfrjw743	250	14	Lagrangian	Lagrangian	NNP
cord-329276-tfrjw743	250	15	,	,	,
cord-329276-tfrjw743	250	16	the	the	DT
cord-329276-tfrjw743	250	17	coefficients	coefficient	NNS
cord-329276-tfrjw743	250	18	θ	θ	NNP
cord-329276-tfrjw743	250	19	j	j	NNP
cord-329276-tfrjw743	250	20	,	,	,
cord-329276-tfrjw743	250	21	j	j	NNP
cord-329276-tfrjw743	250	22	=	=	SYM
cord-329276-tfrjw743	250	23	1	1	CD
cord-329276-tfrjw743	250	24	,	,	,
cord-329276-tfrjw743	250	25	.	.	.
cord-329276-tfrjw743	250	26	.	.	.
cord-329276-tfrjw743	250	27	.	.	.
cord-329276-tfrjw743	251	1	,	,	,
cord-329276-tfrjw743	251	2	m	m	NNP
cord-329276-tfrjw743	251	3	,	,	,
cord-329276-tfrjw743	251	4	are	be	VBP
cord-329276-tfrjw743	251	5	nonnegative	nonnegative	JJ
cord-329276-tfrjw743	251	6	weights	weight	NNS
cord-329276-tfrjw743	251	7	and	and	CC
cord-329276-tfrjw743	251	8	ϕ	ϕ	NN
cord-329276-tfrjw743	251	9	is	be	VBZ
cord-329276-tfrjw743	251	10	a	a	DT
cord-329276-tfrjw743	251	11	penalty	penalty	NN
cord-329276-tfrjw743	251	12	function	function	NN
cord-329276-tfrjw743	251	13	on	on	IN
cord-329276-tfrjw743	251	14	the	the	DT
cord-329276-tfrjw743	251	15	terminal	terminal	JJ
cord-329276-tfrjw743	251	16	state	state	NN
cord-329276-tfrjw743	251	17	.	.	.
cord-329276-tfrjw743	252	1	The	the	DT
cord-329276-tfrjw743	252	2	terminal	terminal	JJ
cord-329276-tfrjw743	252	3	time	time	NN
cord-329276-tfrjw743	252	4	T	t	NN
cord-329276-tfrjw743	252	5	can	can	MD
cord-329276-tfrjw743	252	6	be	be	VB
cord-329276-tfrjw743	252	7	fixed	fix	VBN
cord-329276-tfrjw743	252	8	or	or	CC
cord-329276-tfrjw743	252	9	free	free	JJ
cord-329276-tfrjw743	252	10	.	.	.
cord-329276-tfrjw743	253	1	The	the	DT
cord-329276-tfrjw743	253	2	minimization	minimization	NN
cord-329276-tfrjw743	253	3	is	be	VBZ
cord-329276-tfrjw743	253	4	over	over	IN
cord-329276-tfrjw743	253	5	a	a	DT
cord-329276-tfrjw743	253	6	class	class	NN
cord-329276-tfrjw743	253	7	U	u	NN
cord-329276-tfrjw743	253	8	of	of	IN
cord-329276-tfrjw743	253	9	admissible	admissible	JJ
cord-329276-tfrjw743	253	10	controls	control	NNS
cord-329276-tfrjw743	253	11	u	u	PRP
cord-329276-tfrjw743	253	12	which	which	WDT
cord-329276-tfrjw743	253	13	are	be	VBP
cord-329276-tfrjw743	253	14	locally	locally	RB
cord-329276-tfrjw743	253	15	bounded	bound	VBN
cord-329276-tfrjw743	253	16	Lebesgue	Lebesgue	NNP
cord-329276-tfrjw743	253	17	measurable	measurable	JJ
cord-329276-tfrjw743	253	18	functions	function	NNS
cord-329276-tfrjw743	253	19	such	such	JJ
cord-329276-tfrjw743	253	20	that	that	IN
cord-329276-tfrjw743	253	21	the	the	DT
cord-329276-tfrjw743	253	22	associated	associate	VBN
cord-329276-tfrjw743	253	23	controlled	control	VBN
cord-329276-tfrjw743	253	24	trajectory	trajectory	NN
cord-329276-tfrjw743	253	25	(	(	-LRB-
cord-329276-tfrjw743	253	26	x	x	SYM
cord-329276-tfrjw743	253	27	,	,	,
cord-329276-tfrjw743	253	28	u	u	NNP
cord-329276-tfrjw743	253	29	)	)	-RRB-
cord-329276-tfrjw743	253	30	satisfies	satisfy	VBZ
cord-329276-tfrjw743	253	31	all	all	DT
cord-329276-tfrjw743	253	32	other	other	JJ
cord-329276-tfrjw743	253	33	constraints	constraint	NNS
cord-329276-tfrjw743	253	34	imposed	impose	VBN
cord-329276-tfrjw743	253	35	on	on	IN
cord-329276-tfrjw743	253	36	the	the	DT
cord-329276-tfrjw743	253	37	system	system	NN
cord-329276-tfrjw743	253	38	.	.	.
cord-329276-tfrjw743	254	1	These	these	DT
cord-329276-tfrjw743	254	2	generally	generally	RB
cord-329276-tfrjw743	254	3	include	include	VBP
cord-329276-tfrjw743	254	4	control	control	NN
cord-329276-tfrjw743	254	5	-	-	HYPH
cord-329276-tfrjw743	254	6	constraints	constraint	NNS
cord-329276-tfrjw743	254	7	and	and	CC
cord-329276-tfrjw743	254	8	terminal	terminal	NN
cord-329276-tfrjw743	254	9	point	point	NN
cord-329276-tfrjw743	254	10	constraints	constraint	NNS
cord-329276-tfrjw743	254	11	,	,	,
cord-329276-tfrjw743	254	12	but	but	CC
cord-329276-tfrjw743	254	13	could	could	MD
cord-329276-tfrjw743	254	14	also	also	RB
cord-329276-tfrjw743	254	15	come	come	VB
cord-329276-tfrjw743	254	16	from	from	IN
cord-329276-tfrjw743	254	17	a	a	DT
cord-329276-tfrjw743	254	18	wide	wide	JJ
cord-329276-tfrjw743	254	19	variety	variety	NN
cord-329276-tfrjw743	254	20	of	of	IN
cord-329276-tfrjw743	254	21	other	other	JJ
cord-329276-tfrjw743	254	22	restrictions	restriction	NNS
cord-329276-tfrjw743	254	23	imposed	impose	VBN
cord-329276-tfrjw743	254	24	possibly	possibly	RB
cord-329276-tfrjw743	254	25	by	by	IN
cord-329276-tfrjw743	254	26	state	state	NN
cord-329276-tfrjw743	254	27	-	-	HYPH
cord-329276-tfrjw743	254	28	space	space	NN
cord-329276-tfrjw743	254	29	constraints	constraint	NNS
cord-329276-tfrjw743	254	30	or	or	CC
cord-329276-tfrjw743	254	31	other	other	JJ
cord-329276-tfrjw743	254	32	limitations	limitation	NNS
cord-329276-tfrjw743	254	33	inherent	inherent	JJ
cord-329276-tfrjw743	254	34	to	to	IN
cord-329276-tfrjw743	254	35	the	the	DT
cord-329276-tfrjw743	254	36	problem	problem	NN
cord-329276-tfrjw743	254	37	formulation	formulation	NN
cord-329276-tfrjw743	254	38	.	.	.
cord-329276-tfrjw743	255	1	We	-PRON-	PRP
cord-329276-tfrjw743	255	2	discuss	discuss	VBP
cord-329276-tfrjw743	255	3	the	the	DT
cord-329276-tfrjw743	255	4	significance	significance	NN
cord-329276-tfrjw743	255	5	of	of	IN
cord-329276-tfrjw743	255	6	each	each	DT
cord-329276-tfrjw743	255	7	of	of	IN
cord-329276-tfrjw743	255	8	the	the	DT
cord-329276-tfrjw743	255	9	terms	term	NNS
cord-329276-tfrjw743	255	10	starting	start	VBG
cord-329276-tfrjw743	255	11	with	with	IN
cord-329276-tfrjw743	255	12	the	the	DT
cord-329276-tfrjw743	255	13	controls	control	NNS
cord-329276-tfrjw743	255	14	.	.	.
cord-329276-tfrjw743	256	1	Generally	generally	RB
cord-329276-tfrjw743	256	2	,	,	,
cord-329276-tfrjw743	256	3	and	and	CC
cord-329276-tfrjw743	256	4	without	without	IN
cord-329276-tfrjw743	256	5	loss	loss	NN
cord-329276-tfrjw743	256	6	of	of	IN
cord-329276-tfrjw743	256	7	generality	generality	NN
cord-329276-tfrjw743	256	8	,	,	,
cord-329276-tfrjw743	256	9	we	-PRON-	PRP
cord-329276-tfrjw743	256	10	make	make	VBP
cord-329276-tfrjw743	256	11	the	the	DT
cord-329276-tfrjw743	256	12	assumption	assumption	NN
cord-329276-tfrjw743	256	13	that	that	IN
cord-329276-tfrjw743	256	14	the	the	DT
cord-329276-tfrjw743	256	15	controls	control	NNS
cord-329276-tfrjw743	256	16	represent	represent	VBP
cord-329276-tfrjw743	256	17	nonnegative	nonnegative	JJ
cord-329276-tfrjw743	256	18	quantities	quantity	NNS
cord-329276-tfrjw743	256	19	(	(	-LRB-
cord-329276-tfrjw743	256	20	e.g.	e.g.	RB
cord-329276-tfrjw743	256	21	,	,	,
cord-329276-tfrjw743	256	22	dose	dose	NN
cord-329276-tfrjw743	256	23	rates	rate	NNS
cord-329276-tfrjw743	256	24	or	or	CC
cord-329276-tfrjw743	256	25	concentrations	concentration	NNS
cord-329276-tfrjw743	256	26	)	)	-RRB-
cord-329276-tfrjw743	256	27	.	.	.
cord-329276-tfrjw743	257	1	Thus	thus	RB
cord-329276-tfrjw743	257	2	,	,	,
cord-329276-tfrjw743	257	3	the	the	DT
cord-329276-tfrjw743	257	4	control	control	NN
cord-329276-tfrjw743	257	5	term	term	NN
cord-329276-tfrjw743	257	6	m	m	CD
cord-329276-tfrjw743	257	7	j=1	j=1	NNP
cord-329276-tfrjw743	257	8	θ	θ	NNP
cord-329276-tfrjw743	257	9	j	j	NNP
cord-329276-tfrjw743	257	10	u	u	NNP
cord-329276-tfrjw743	257	11	k	k	NNP
cord-329276-tfrjw743	257	12	j	j	NNP
cord-329276-tfrjw743	257	13	(	(	-LRB-
cord-329276-tfrjw743	257	14	t	t	NNP
cord-329276-tfrjw743	257	15	)	)	-RRB-
cord-329276-tfrjw743	257	16	in	in	IN
cord-329276-tfrjw743	257	17	the	the	DT
cord-329276-tfrjw743	257	18	objective	objective	NN
cord-329276-tfrjw743	257	19	(	(	-LRB-
cord-329276-tfrjw743	257	20	13	13	CD
cord-329276-tfrjw743	257	21	)	)	-RRB-
cord-329276-tfrjw743	257	22	for	for	IN
cord-329276-tfrjw743	257	23	k	k	NN
cord-329276-tfrjw743	257	24	=	=	SYM
cord-329276-tfrjw743	257	25	1	1	CD
cord-329276-tfrjw743	258	1	or	or	CC
cord-329276-tfrjw743	258	2	k	k	NN
cord-329276-tfrjw743	258	3	=	=	SYM
cord-329276-tfrjw743	258	4	2	2	CD
cord-329276-tfrjw743	258	5	represents	represent	VBZ
cord-329276-tfrjw743	258	6	a	a	DT
cord-329276-tfrjw743	258	7	weighted	weighted	JJ
cord-329276-tfrjw743	258	8	L	l	NN
cord-329276-tfrjw743	258	9	1	1	CD
cord-329276-tfrjw743	258	10	-or	-or	.
cord-329276-tfrjw743	259	1	L	l	NN
cord-329276-tfrjw743	259	2	2	2	CD
cord-329276-tfrjw743	259	3	-norm	-norm	NN
cord-329276-tfrjw743	259	4	,	,	,
cord-329276-tfrjw743	259	5	respectively	respectively	RB
cord-329276-tfrjw743	259	6	.	.	.
cord-329276-tfrjw743	260	1	Including	include	VBG
cord-329276-tfrjw743	260	2	such	such	PDT
cord-329276-tfrjw743	260	3	a	a	DT
cord-329276-tfrjw743	260	4	positive	positive	JJ
cord-329276-tfrjw743	260	5	and	and	CC
cord-329276-tfrjw743	260	6	increasing	increasing	JJ
cord-329276-tfrjw743	260	7	term	term	NN
cord-329276-tfrjw743	260	8	in	in	IN
cord-329276-tfrjw743	260	9	the	the	DT
cord-329276-tfrjw743	260	10	objective	objective	NN
cord-329276-tfrjw743	260	11	represents	represent	VBZ
cord-329276-tfrjw743	260	12	what	what	WP
cord-329276-tfrjw743	260	13	in	in	IN
cord-329276-tfrjw743	260	14	the	the	DT
cord-329276-tfrjw743	260	15	engineering	engineering	NN
cord-329276-tfrjw743	260	16	literature	literature	NN
cord-329276-tfrjw743	260	17	would	would	MD
cord-329276-tfrjw743	260	18	be	be	VB
cord-329276-tfrjw743	260	19	called	call	VBN
cord-329276-tfrjw743	260	20	a	a	DT
cord-329276-tfrjw743	260	21	soft	soft	JJ
cord-329276-tfrjw743	260	22	modeling	modeling	NN
cord-329276-tfrjw743	260	23	of	of	IN
cord-329276-tfrjw743	260	24	control	control	NN
cord-329276-tfrjw743	260	25	constraints	constraint	NNS
cord-329276-tfrjw743	260	26	.	.	.
cord-329276-tfrjw743	261	1	Clearly	clearly	RB
cord-329276-tfrjw743	261	2	,	,	,
cord-329276-tfrjw743	261	3	medical	medical	JJ
cord-329276-tfrjw743	261	4	treatments	treatment	NNS
cord-329276-tfrjw743	261	5	,	,	,
cord-329276-tfrjw743	261	6	especially	especially	RB
cord-329276-tfrjw743	261	7	the	the	DT
cord-329276-tfrjw743	261	8	strong	strong	JJ
cord-329276-tfrjw743	261	9	treatment	treatment	NN
cord-329276-tfrjw743	261	10	options	option	NNS
cord-329276-tfrjw743	261	11	that	that	WDT
cord-329276-tfrjw743	261	12	need	need	VBP
cord-329276-tfrjw743	261	13	to	to	TO
cord-329276-tfrjw743	261	14	be	be	VB
cord-329276-tfrjw743	261	15	pursued	pursue	VBN
cord-329276-tfrjw743	261	16	in	in	IN
cord-329276-tfrjw743	261	17	cancer	cancer	NN
cord-329276-tfrjw743	261	18	treatment	treatment	NN
cord-329276-tfrjw743	261	19	such	such	JJ
cord-329276-tfrjw743	261	20	as	as	IN
cord-329276-tfrjw743	261	21	chemo	chemo	NN
cord-329276-tfrjw743	261	22	-	-	,
cord-329276-tfrjw743	261	23	or	or	CC
cord-329276-tfrjw743	261	24	radiotherapy	radiotherapy	NN
cord-329276-tfrjw743	261	25	,	,	,
cord-329276-tfrjw743	261	26	have	have	VBP
cord-329276-tfrjw743	261	27	significant	significant	JJ
cord-329276-tfrjw743	261	28	side	side	NN
cord-329276-tfrjw743	261	29	effects	effect	NNS
cord-329276-tfrjw743	261	30	and	and	CC
cord-329276-tfrjw743	261	31	these	these	DT
cord-329276-tfrjw743	261	32	need	need	VBP
cord-329276-tfrjw743	261	33	to	to	TO
cord-329276-tfrjw743	261	34	be	be	VB
cord-329276-tfrjw743	261	35	taken	take	VBN
cord-329276-tfrjw743	261	36	into	into	IN
cord-329276-tfrjw743	261	37	account	account	NN
cord-329276-tfrjw743	261	38	in	in	IN
cord-329276-tfrjw743	261	39	the	the	DT
cord-329276-tfrjw743	261	40	modeling	modeling	NN
cord-329276-tfrjw743	261	41	.	.	.
cord-329276-tfrjw743	262	1	Including	include	VBG
cord-329276-tfrjw743	262	2	the	the	DT
cord-329276-tfrjw743	262	3	control	control	NN
cord-329276-tfrjw743	262	4	term	term	NN
cord-329276-tfrjw743	262	5	in	in	IN
cord-329276-tfrjw743	262	6	the	the	DT
cord-329276-tfrjw743	262	7	objective	objective	NN
cord-329276-tfrjw743	262	8	to	to	TO
cord-329276-tfrjw743	262	9	be	be	VB
cord-329276-tfrjw743	262	10	minimized	minimize	VBN
cord-329276-tfrjw743	262	11	inherently	inherently	RB
cord-329276-tfrjw743	262	12	limits	limit	VBZ
cord-329276-tfrjw743	262	13	the	the	DT
cord-329276-tfrjw743	262	14	use	use	NN
cord-329276-tfrjw743	262	15	of	of	IN
cord-329276-tfrjw743	262	16	the	the	DT
cord-329276-tfrjw743	262	17	controls	control	NNS
cord-329276-tfrjw743	262	18	.	.	.
cord-329276-tfrjw743	263	1	This	this	DT
cord-329276-tfrjw743	263	2	represents	represent	VBZ
cord-329276-tfrjw743	263	3	an	an	DT
cord-329276-tfrjw743	263	4	attempt	attempt	NN
cord-329276-tfrjw743	263	5	to	to	TO
cord-329276-tfrjw743	263	6	make	make	VB
cord-329276-tfrjw743	263	7	a	a	DT
cord-329276-tfrjw743	263	8	reasonable	reasonable	JJ
cord-329276-tfrjw743	263	9	compromise	compromise	NN
cord-329276-tfrjw743	263	10	between	between	IN
cord-329276-tfrjw743	263	11	maximizing	maximize	VBG
cord-329276-tfrjw743	263	12	the	the	DT
cord-329276-tfrjw743	263	13	tumor	tumor	NN
cord-329276-tfrjw743	263	14	kill	kill	NN
cord-329276-tfrjw743	263	15	which	which	WDT
cord-329276-tfrjw743	263	16	requires	require	VBZ
cord-329276-tfrjw743	263	17	to	to	TO
cord-329276-tfrjw743	263	18	give	give	VB
cord-329276-tfrjw743	263	19	a	a	DT
cord-329276-tfrjw743	263	20	large	large	JJ
cord-329276-tfrjw743	263	21	amount	amount	NN
cord-329276-tfrjw743	263	22	of	of	IN
cord-329276-tfrjw743	263	23	drugs	drug	NNS
cord-329276-tfrjw743	263	24	and	and	CC
cord-329276-tfrjw743	263	25	limiting	limit	VBG
cord-329276-tfrjw743	263	26	the	the	DT
cord-329276-tfrjw743	263	27	side	side	NN
cord-329276-tfrjw743	263	28	effects	effect	NNS
cord-329276-tfrjw743	263	29	of	of	IN
cord-329276-tfrjw743	263	30	treatment	treatment	NN
cord-329276-tfrjw743	263	31	(	(	-LRB-
cord-329276-tfrjw743	263	32	these	these	DT
cord-329276-tfrjw743	263	33	are	be	VBP
cord-329276-tfrjw743	263	34	measured	measure	VBN
cord-329276-tfrjw743	263	35	indirectly	indirectly	RB
cord-329276-tfrjw743	263	36	through	through	IN
cord-329276-tfrjw743	263	37	the	the	DT
cord-329276-tfrjw743	263	38	integral	integral	NN
cord-329276-tfrjw743	263	39	of	of	IN
cord-329276-tfrjw743	263	40	the	the	DT
cord-329276-tfrjw743	263	41	control	control	NN
cord-329276-tfrjw743	263	42	)	)	-RRB-
cord-329276-tfrjw743	263	43	which	which	WDT
cord-329276-tfrjw743	263	44	requires	require	VBZ
cord-329276-tfrjw743	263	45	to	to	TO
cord-329276-tfrjw743	263	46	limit	limit	VB
cord-329276-tfrjw743	263	47	this	this	DT
cord-329276-tfrjw743	263	48	amount	amount	NN
cord-329276-tfrjw743	263	49	of	of	IN
cord-329276-tfrjw743	263	50	drugs	drug	NNS
cord-329276-tfrjw743	263	51	.	.	.
cord-329276-tfrjw743	264	1	Whether	whether	IN
cord-329276-tfrjw743	264	2	the	the	DT
cord-329276-tfrjw743	264	3	optimal	optimal	JJ
cord-329276-tfrjw743	264	4	control	control	NN
cord-329276-tfrjw743	264	5	does	do	VBZ
cord-329276-tfrjw743	264	6	this	this	DT
cord-329276-tfrjw743	264	7	adequately	adequately	RB
cord-329276-tfrjw743	264	8	,	,	,
cord-329276-tfrjw743	264	9	then	then	RB
cord-329276-tfrjw743	264	10	becomes	become	VBZ
cord-329276-tfrjw743	264	11	an	an	DT
cord-329276-tfrjw743	264	12	after	after	IN
cord-329276-tfrjw743	264	13	-	-	HYPH
cord-329276-tfrjw743	264	14	thought	thought	NN
cord-329276-tfrjw743	264	15	that	that	WDT
cord-329276-tfrjw743	264	16	always	always	RB
cord-329276-tfrjw743	264	17	needs	need	VBZ
cord-329276-tfrjw743	264	18	to	to	TO
cord-329276-tfrjw743	264	19	be	be	VB
cord-329276-tfrjw743	264	20	checked	check	VBN
cord-329276-tfrjw743	264	21	and	and	CC
cord-329276-tfrjw743	264	22	,	,	,
cord-329276-tfrjw743	264	23	if	if	IN
cord-329276-tfrjw743	264	24	the	the	DT
cord-329276-tfrjw743	264	25	optimal	optimal	JJ
cord-329276-tfrjw743	264	26	solution	solution	NN
cord-329276-tfrjw743	264	27	is	be	VBZ
cord-329276-tfrjw743	264	28	still	still	RB
cord-329276-tfrjw743	264	29	inadequate	inadequate	JJ
cord-329276-tfrjw743	264	30	,	,	,
cord-329276-tfrjw743	264	31	the	the	DT
cord-329276-tfrjw743	264	32	weights	weight	NNS
cord-329276-tfrjw743	264	33	need	need	VBP
cord-329276-tfrjw743	264	34	to	to	TO
cord-329276-tfrjw743	264	35	be	be	VB
cord-329276-tfrjw743	264	36	adjusted	adjust	VBN
cord-329276-tfrjw743	264	37	.	.	.
cord-329276-tfrjw743	265	1	If	if	IN
cord-329276-tfrjw743	265	2	the	the	DT
cord-329276-tfrjw743	265	3	weights	weight	NNS
cord-329276-tfrjw743	265	4	on	on	IN
cord-329276-tfrjw743	265	5	the	the	DT
cord-329276-tfrjw743	265	6	drugs	drug	NNS
cord-329276-tfrjw743	265	7	are	be	VBP
cord-329276-tfrjw743	265	8	too	too	RB
cord-329276-tfrjw743	265	9	small	small	JJ
cord-329276-tfrjw743	265	10	,	,	,
cord-329276-tfrjw743	265	11	optimal	optimal	JJ
cord-329276-tfrjw743	265	12	solutions	solution	NNS
cord-329276-tfrjw743	265	13	will	will	MD
cord-329276-tfrjw743	265	14	simply	simply	RB
cord-329276-tfrjw743	265	15	give	give	VB
cord-329276-tfrjw743	265	16	drugs	drug	NNS
cord-329276-tfrjw743	265	17	all	all	PDT
cord-329276-tfrjw743	265	18	the	the	DT
cord-329276-tfrjw743	265	19	time	time	NN
cord-329276-tfrjw743	265	20	at	at	IN
cord-329276-tfrjw743	265	21	full	full	JJ
cord-329276-tfrjw743	265	22	dose	dose	NN
cord-329276-tfrjw743	265	23	;	;	:
cord-329276-tfrjw743	265	24	if	if	IN
cord-329276-tfrjw743	265	25	the	the	DT
cord-329276-tfrjw743	265	26	weights	weight	NNS
cord-329276-tfrjw743	265	27	are	be	VBP
cord-329276-tfrjw743	265	28	too	too	RB
cord-329276-tfrjw743	265	29	high	high	JJ
cord-329276-tfrjw743	265	30	,	,	,
cord-329276-tfrjw743	265	31	no	no	DT
cord-329276-tfrjw743	265	32	drugs	drug	NNS
cord-329276-tfrjw743	265	33	will	will	MD
cord-329276-tfrjw743	265	34	be	be	VB
cord-329276-tfrjw743	265	35	given	give	VBN
cord-329276-tfrjw743	265	36	.	.	.
cord-329276-tfrjw743	266	1	It	-PRON-	PRP
cord-329276-tfrjw743	266	2	is	be	VBZ
cord-329276-tfrjw743	266	3	clearly	clearly	RB
cord-329276-tfrjw743	266	4	necessary	necessary	JJ
cord-329276-tfrjw743	266	5	to	to	TO
cord-329276-tfrjw743	266	6	calibrate	calibrate	VB
cord-329276-tfrjw743	266	7	the	the	DT
cord-329276-tfrjw743	266	8	weights	weight	NNS
cord-329276-tfrjw743	266	9	to	to	TO
cord-329276-tfrjw743	266	10	obtain	obtain	VB
cord-329276-tfrjw743	266	11	meaningful	meaningful	JJ
cord-329276-tfrjw743	266	12	results	result	NNS
cord-329276-tfrjw743	266	13	.	.	.
cord-329276-tfrjw743	267	1	Such	such	JJ
cord-329276-tfrjw743	267	2	back	back	NN
cord-329276-tfrjw743	267	3	-	-	HYPH
cord-329276-tfrjw743	267	4	and	and	CC
cord-329276-tfrjw743	267	5	-	-	HYPH
cord-329276-tfrjw743	267	6	forth	forth	JJ
cord-329276-tfrjw743	267	7	approaches	approach	NNS
cord-329276-tfrjw743	267	8	are	be	VBP
cord-329276-tfrjw743	267	9	quite	quite	RB
cord-329276-tfrjw743	267	10	common	common	JJ
cord-329276-tfrjw743	267	11	in	in	IN
cord-329276-tfrjw743	267	12	engineering	engineering	NN
cord-329276-tfrjw743	267	13	and	and	CC
cord-329276-tfrjw743	267	14	they	-PRON-	PRP
cord-329276-tfrjw743	267	15	simply	simply	RB
cord-329276-tfrjw743	267	16	reflect	reflect	VBP
cord-329276-tfrjw743	267	17	the	the	DT
cord-329276-tfrjw743	267	18	fact	fact	NN
cord-329276-tfrjw743	267	19	that	that	IN
cord-329276-tfrjw743	267	20	the	the	DT
cord-329276-tfrjw743	267	21	form	form	NN
cord-329276-tfrjw743	267	22	of	of	IN
cord-329276-tfrjw743	267	23	the	the	DT
cord-329276-tfrjw743	267	24	objective	objective	NN
cord-329276-tfrjw743	267	25	,	,	,
cord-329276-tfrjw743	267	26	and	and	CC
cord-329276-tfrjw743	267	27	especially	especially	RB
cord-329276-tfrjw743	267	28	the	the	DT
cord-329276-tfrjw743	267	29	weights	weight	NNS
cord-329276-tfrjw743	267	30	that	that	WDT
cord-329276-tfrjw743	267	31	appear	appear	VBP
cord-329276-tfrjw743	267	32	,	,	,
cord-329276-tfrjw743	267	33	are	be	VBP
cord-329276-tfrjw743	267	34	variables	variable	NNS
cord-329276-tfrjw743	267	35	of	of	IN
cord-329276-tfrjw743	267	36	choice	choice	NN
cord-329276-tfrjw743	267	37	in	in	IN
cord-329276-tfrjw743	267	38	such	such	JJ
cord-329276-tfrjw743	267	39	problems	problem	NNS
cord-329276-tfrjw743	267	40	.	.	.
cord-329276-tfrjw743	268	1	Generally	generally	RB
cord-329276-tfrjw743	268	2	,	,	,
cord-329276-tfrjw743	268	3	and	and	CC
cord-329276-tfrjw743	268	4	this	this	DT
cord-329276-tfrjw743	268	5	is	be	VBZ
cord-329276-tfrjw743	268	6	the	the	DT
cord-329276-tfrjw743	268	7	typical	typical	JJ
cord-329276-tfrjw743	268	8	application	application	NN
cord-329276-tfrjw743	268	9	of	of	IN
cord-329276-tfrjw743	268	10	optimal	optimal	JJ
cord-329276-tfrjw743	268	11	control	control	NN
cord-329276-tfrjw743	268	12	in	in	IN
cord-329276-tfrjw743	268	13	engineering	engineering	NN
cord-329276-tfrjw743	268	14	,	,	,
cord-329276-tfrjw743	268	15	various	various	JJ
cord-329276-tfrjw743	268	16	choices	choice	NNS
cord-329276-tfrjw743	268	17	of	of	IN
cord-329276-tfrjw743	268	18	the	the	DT
cord-329276-tfrjw743	268	19	weights	weight	NNS
cord-329276-tfrjw743	268	20	will	will	MD
cord-329276-tfrjw743	268	21	be	be	VB
cord-329276-tfrjw743	268	22	tested	test	VBN
cord-329276-tfrjw743	268	23	until	until	IN
cord-329276-tfrjw743	268	24	a	a	DT
cord-329276-tfrjw743	268	25	solution	solution	NN
cord-329276-tfrjw743	268	26	has	have	VBZ
cord-329276-tfrjw743	268	27	been	be	VBN
cord-329276-tfrjw743	268	28	found	find	VBN
cord-329276-tfrjw743	268	29	which	which	WDT
cord-329276-tfrjw743	268	30	appears	appear	VBZ
cord-329276-tfrjw743	268	31	adequate	adequate	JJ
cord-329276-tfrjw743	268	32	,	,	,
cord-329276-tfrjw743	268	33	possibly	possibly	RB
cord-329276-tfrjw743	268	34	also	also	RB
cord-329276-tfrjw743	268	35	with	with	IN
cord-329276-tfrjw743	268	36	respect	respect	NN
cord-329276-tfrjw743	268	37	to	to	IN
cord-329276-tfrjw743	268	38	other	other	JJ
cord-329276-tfrjw743	268	39	criteria	criterion	NNS
cord-329276-tfrjw743	268	40	which	which	WDT
cord-329276-tfrjw743	268	41	were	be	VBD
cord-329276-tfrjw743	268	42	not	not	RB
cord-329276-tfrjw743	268	43	included	include	VBN
cord-329276-tfrjw743	268	44	in	in	IN
cord-329276-tfrjw743	268	45	the	the	DT
cord-329276-tfrjw743	268	46	mathematical	mathematical	JJ
cord-329276-tfrjw743	268	47	model	model	NN
cord-329276-tfrjw743	268	48	.	.	.
cord-329276-tfrjw743	269	1	The	the	DT
cord-329276-tfrjw743	269	2	choice	choice	NN
cord-329276-tfrjw743	269	3	of	of	IN
cord-329276-tfrjw743	269	4	taking	take	VBG
cord-329276-tfrjw743	269	5	an	an	DT
cord-329276-tfrjw743	269	6	L	l	NN
cord-329276-tfrjw743	269	7	1	1	CD
cord-329276-tfrjw743	269	8	-or	-or	NN
cord-329276-tfrjw743	269	9	L	l	NN
cord-329276-tfrjw743	269	10	2	2	CD
cord-329276-tfrjw743	269	11	-norm	-norm	NN
cord-329276-tfrjw743	269	12	,	,	,
cord-329276-tfrjw743	269	13	however	however	RB
cord-329276-tfrjw743	269	14	,	,	,
cord-329276-tfrjw743	269	15	is	be	VBZ
cord-329276-tfrjw743	269	16	not	not	RB
cord-329276-tfrjw743	269	17	irrelevant	irrelevant	JJ
cord-329276-tfrjw743	269	18	.	.	.
cord-329276-tfrjw743	270	1	Generally	generally	RB
cord-329276-tfrjw743	270	2	speaking	speak	VBG
cord-329276-tfrjw743	270	3	,	,	,
cord-329276-tfrjw743	270	4	an	an	DT
cord-329276-tfrjw743	270	5	L	l	NN
cord-329276-tfrjw743	270	6	1	1	CD
cord-329276-tfrjw743	270	7	-formulation	-formulation	NN
cord-329276-tfrjw743	270	8	is	be	VBZ
cord-329276-tfrjw743	270	9	to	to	TO
cord-329276-tfrjw743	270	10	be	be	VB
cord-329276-tfrjw743	270	11	preferred	prefer	VBN
cord-329276-tfrjw743	270	12	from	from	IN
cord-329276-tfrjw743	270	13	a	a	DT
cord-329276-tfrjw743	270	14	modeling	modeling	NN
cord-329276-tfrjw743	270	15	perspective	perspective	NN
cord-329276-tfrjw743	270	16	while	while	IN
cord-329276-tfrjw743	270	17	the	the	DT
cord-329276-tfrjw743	270	18	L	l	NN
cord-329276-tfrjw743	270	19	2	2	CD
cord-329276-tfrjw743	270	20	-formulation	-formulation	NN
cord-329276-tfrjw743	270	21	offers	offer	VBZ
cord-329276-tfrjw743	270	22	significant	significant	JJ
cord-329276-tfrjw743	270	23	mathematical	mathematical	JJ
cord-329276-tfrjw743	270	24	and	and	CC
cord-329276-tfrjw743	270	25	numerical	numerical	JJ
cord-329276-tfrjw743	270	26	advantages	advantage	NNS
cord-329276-tfrjw743	270	27	.	.	.
cord-329276-tfrjw743	271	1	In	in	IN
cord-329276-tfrjw743	271	2	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	271	3	,	,	,
cord-329276-tfrjw743	271	4	there	there	EX
cord-329276-tfrjw743	271	5	exists	exist	VBZ
cord-329276-tfrjw743	271	6	a	a	DT
cord-329276-tfrjw743	271	7	clear	clear	JJ
cord-329276-tfrjw743	271	8	interpretation	interpretation	NN
cord-329276-tfrjw743	271	9	for	for	IN
cord-329276-tfrjw743	271	10	the	the	DT
cord-329276-tfrjw743	271	11	integral	integral	JJ
cord-329276-tfrjw743	271	12	T	T	NNP
cord-329276-tfrjw743	271	13	0	0	CD
cord-329276-tfrjw743	271	14	u(t)dt	u(t)dt	,
cord-329276-tfrjw743	271	15	related	relate	VBN
cord-329276-tfrjw743	271	16	to	to	IN
cord-329276-tfrjw743	271	17	the	the	DT
cord-329276-tfrjw743	271	18	total	total	JJ
cord-329276-tfrjw743	271	19	dose	dose	NN
cord-329276-tfrjw743	271	20	given	give	VBN
cord-329276-tfrjw743	271	21	regardless	regardless	RB
cord-329276-tfrjw743	271	22	of	of	IN
cord-329276-tfrjw743	271	23	whether	whether	IN
cord-329276-tfrjw743	271	24	u	u	NNP
cord-329276-tfrjw743	271	25	represents	represent	VBZ
cord-329276-tfrjw743	271	26	the	the	DT
cord-329276-tfrjw743	271	27	dose	dose	JJ
cord-329276-tfrjw743	271	28	rate	rate	NN
cord-329276-tfrjw743	271	29	of	of	IN
cord-329276-tfrjw743	271	30	the	the	DT
cord-329276-tfrjw743	271	31	drug	drug	NN
cord-329276-tfrjw743	271	32	or	or	CC
cord-329276-tfrjw743	271	33	its	-PRON-	PRP$
cord-329276-tfrjw743	271	34	concentration	concentration	NN
cord-329276-tfrjw743	271	35	.	.	.
cord-329276-tfrjw743	272	1	This	this	DT
cord-329276-tfrjw743	272	2	is	be	VBZ
cord-329276-tfrjw743	272	3	an	an	DT
cord-329276-tfrjw743	272	4	essential	essential	JJ
cord-329276-tfrjw743	272	5	pharmacological	pharmacological	JJ
cord-329276-tfrjw743	272	6	quantity	quantity	NN
cord-329276-tfrjw743	272	7	also	also	RB
cord-329276-tfrjw743	272	8	referred	refer	VBD
cord-329276-tfrjw743	272	9	to	to	IN
cord-329276-tfrjw743	272	10	as	as	IN
cord-329276-tfrjw743	272	11	the	the	DT
cord-329276-tfrjw743	272	12	AUC	AUC	NNP
cord-329276-tfrjw743	272	13	(	(	-LRB-
cord-329276-tfrjw743	272	14	area	area	NN
cord-329276-tfrjw743	272	15	under	under	IN
cord-329276-tfrjw743	272	16	the	the	DT
cord-329276-tfrjw743	272	17	curve	curve	NN
cord-329276-tfrjw743	272	18	)	)	-RRB-
cord-329276-tfrjw743	272	19	,	,	,
cord-329276-tfrjw743	272	20	and	and	CC
cord-329276-tfrjw743	272	21	it	-PRON-	PRP
cord-329276-tfrjw743	272	22	plays	play	VBZ
cord-329276-tfrjw743	272	23	a	a	DT
cord-329276-tfrjw743	272	24	major	major	JJ
cord-329276-tfrjw743	272	25	role	role	NN
cord-329276-tfrjw743	272	26	in	in	IN
cord-329276-tfrjw743	272	27	interpreting	interpret	VBG
cord-329276-tfrjw743	272	28	the	the	DT
cord-329276-tfrjw743	272	29	overall	overall	JJ
cord-329276-tfrjw743	272	30	efficacy	efficacy	NN
cord-329276-tfrjw743	272	31	and	and	CC
cord-329276-tfrjw743	272	32	side	side	NN
cord-329276-tfrjw743	272	33	effects	effect	NNS
cord-329276-tfrjw743	272	34	of	of	IN
cord-329276-tfrjw743	272	35	a	a	DT
cord-329276-tfrjw743	272	36	drug	drug	NN
cord-329276-tfrjw743	272	37	.	.	.
cord-329276-tfrjw743	273	1	Thus	thus	RB
cord-329276-tfrjw743	273	2	,	,	,
cord-329276-tfrjw743	273	3	making	make	VBG
cord-329276-tfrjw743	273	4	the	the	DT
cord-329276-tfrjw743	273	5	choice	choice	NN
cord-329276-tfrjw743	273	6	of	of	IN
cord-329276-tfrjw743	273	7	an	an	DT
cord-329276-tfrjw743	273	8	L	l	NN
cord-329276-tfrjw743	273	9	1	1	CD
cord-329276-tfrjw743	273	10	-formulation	-formulation	NN
cord-329276-tfrjw743	273	11	as	as	IN
cord-329276-tfrjw743	273	12	the	the	DT
cord-329276-tfrjw743	273	13	penalty	penalty	NN
cord-329276-tfrjw743	273	14	of	of	IN
cord-329276-tfrjw743	273	15	the	the	DT
cord-329276-tfrjw743	273	16	control	control	NN
cord-329276-tfrjw743	273	17	leads	lead	VBZ
cord-329276-tfrjw743	273	18	to	to	IN
cord-329276-tfrjw743	273	19	a	a	DT
cord-329276-tfrjw743	273	20	realistic	realistic	JJ
cord-329276-tfrjw743	273	21	modeling	modeling	NN
cord-329276-tfrjw743	273	22	.	.	.
cord-329276-tfrjw743	274	1	The	the	DT
cord-329276-tfrjw743	274	2	handicap	handicap	NN
cord-329276-tfrjw743	274	3	of	of	IN
cord-329276-tfrjw743	274	4	an	an	DT
cord-329276-tfrjw743	274	5	L	l	NN
cord-329276-tfrjw743	274	6	1	1	CD
cord-329276-tfrjw743	274	7	-type	-type	NN
cord-329276-tfrjw743	274	8	approach	approach	NN
cord-329276-tfrjw743	274	9	lies	lie	VBZ
cord-329276-tfrjw743	274	10	with	with	IN
cord-329276-tfrjw743	274	11	the	the	DT
cord-329276-tfrjw743	274	12	fact	fact	NN
cord-329276-tfrjw743	274	13	that	that	IN
cord-329276-tfrjw743	274	14	the	the	DT
cord-329276-tfrjw743	274	15	mathematical	mathematical	JJ
cord-329276-tfrjw743	274	16	analysis	analysis	NN
cord-329276-tfrjw743	274	17	generally	generally	RB
cord-329276-tfrjw743	274	18	becomes	become	VBZ
cord-329276-tfrjw743	274	19	difficult	difficult	JJ
cord-329276-tfrjw743	274	20	.	.	.
cord-329276-tfrjw743	275	1	Optimal	optimal	JJ
cord-329276-tfrjw743	275	2	solutions	solution	NNS
cord-329276-tfrjw743	275	3	need	need	VBP
cord-329276-tfrjw743	275	4	to	to	TO
cord-329276-tfrjw743	275	5	be	be	VB
cord-329276-tfrjw743	275	6	synthesized	synthesize	VBN
cord-329276-tfrjw743	275	7	from	from	IN
cord-329276-tfrjw743	275	8	concatenations	concatenation	NNS
cord-329276-tfrjw743	275	9	of	of	IN
cord-329276-tfrjw743	275	10	bang	bang	NN
cord-329276-tfrjw743	275	11	and	and	CC
cord-329276-tfrjw743	275	12	singular	singular	JJ
cord-329276-tfrjw743	275	13	controls	control	NNS
cord-329276-tfrjw743	275	14	(	(	-LRB-
cord-329276-tfrjw743	275	15	and	and	CC
cord-329276-tfrjw743	275	16	we	-PRON-	PRP
cord-329276-tfrjw743	275	17	shall	shall	MD
cord-329276-tfrjw743	275	18	discuss	discuss	VB
cord-329276-tfrjw743	275	19	this	this	DT
cord-329276-tfrjw743	275	20	more	more	JJR
cord-329276-tfrjw743	275	21	in	in	IN
cord-329276-tfrjw743	275	22	the	the	DT
cord-329276-tfrjw743	275	23	next	next	JJ
cord-329276-tfrjw743	275	24	section	section	NN
cord-329276-tfrjw743	275	25	)	)	-RRB-
cord-329276-tfrjw743	275	26	and	and	CC
cord-329276-tfrjw743	275	27	reliable	reliable	JJ
cord-329276-tfrjw743	275	28	numerical	numerical	JJ
cord-329276-tfrjw743	275	29	methods	method	NNS
cord-329276-tfrjw743	275	30	to	to	TO
cord-329276-tfrjw743	275	31	solve	solve	VB
cord-329276-tfrjw743	275	32	such	such	JJ
cord-329276-tfrjw743	275	33	problems	problem	NNS
cord-329276-tfrjw743	275	34	do	do	VBP
cord-329276-tfrjw743	275	35	not	not	RB
cord-329276-tfrjw743	275	36	exist	exist	VB
cord-329276-tfrjw743	275	37	.	.	.
cord-329276-tfrjw743	276	1	It	-PRON-	PRP
cord-329276-tfrjw743	276	2	is	be	VBZ
cord-329276-tfrjw743	276	3	for	for	IN
cord-329276-tfrjw743	276	4	this	this	DT
cord-329276-tfrjw743	276	5	reason	reason	NN
cord-329276-tfrjw743	276	6	-	-	:
cord-329276-tfrjw743	276	7	and	and	CC
cord-329276-tfrjw743	276	8	in	in	IN
cord-329276-tfrjw743	276	9	our	-PRON-	PRP$
cord-329276-tfrjw743	276	10	opinion	opinion	NN
cord-329276-tfrjw743	276	11	,	,	,
cord-329276-tfrjw743	276	12	for	for	IN
cord-329276-tfrjw743	276	13	this	this	DT
cord-329276-tfrjw743	276	14	reason	reason	NN
cord-329276-tfrjw743	276	15	only	only	RB
cord-329276-tfrjw743	276	16	-	-	:
cord-329276-tfrjw743	276	17	that	that	IN
cord-329276-tfrjw743	276	18	the	the	DT
cord-329276-tfrjw743	276	19	use	use	NN
cord-329276-tfrjw743	276	20	of	of	IN
cord-329276-tfrjw743	276	21	an	an	DT
cord-329276-tfrjw743	276	22	L	l	NN
cord-329276-tfrjw743	276	23	2	2	CD
cord-329276-tfrjw743	276	24	-criterion	-criterion	NN
cord-329276-tfrjw743	276	25	in	in	IN
cord-329276-tfrjw743	276	26	the	the	DT
cord-329276-tfrjw743	276	27	literature	literature	NN
cord-329276-tfrjw743	276	28	is	be	VBZ
cord-329276-tfrjw743	276	29	wide	wide	JJ
cord-329276-tfrjw743	276	30	-	-	HYPH
cord-329276-tfrjw743	276	31	spread	spread	NN
cord-329276-tfrjw743	276	32	.	.	.
cord-329276-tfrjw743	277	1	For	for	IN
cord-329276-tfrjw743	277	2	,	,	,
cord-329276-tfrjw743	277	3	in	in	IN
cord-329276-tfrjw743	277	4	this	this	DT
cord-329276-tfrjw743	277	5	case	case	NN
cord-329276-tfrjw743	277	6	,	,	,
cord-329276-tfrjw743	277	7	the	the	DT
cord-329276-tfrjw743	277	8	application	application	NN
cord-329276-tfrjw743	277	9	of	of	IN
cord-329276-tfrjw743	277	10	the	the	DT
cord-329276-tfrjw743	277	11	necessary	necessary	JJ
cord-329276-tfrjw743	277	12	conditions	condition	NNS
cord-329276-tfrjw743	277	13	for	for	IN
cord-329276-tfrjw743	277	14	optimality	optimality	NN
cord-329276-tfrjw743	277	15	of	of	IN
cord-329276-tfrjw743	277	16	the	the	DT
cord-329276-tfrjw743	277	17	Pontryagin	Pontryagin	NNP
cord-329276-tfrjw743	277	18	maximum	maximum	NN
cord-329276-tfrjw743	277	19	principle	principle	NN
cord-329276-tfrjw743	277	20	[	[	-LRB-
cord-329276-tfrjw743	277	21	33	33	CD
cord-329276-tfrjw743	277	22	]	]	-RRB-
cord-329276-tfrjw743	277	23	[	[	-LRB-
cord-329276-tfrjw743	277	24	34	34	CD
cord-329276-tfrjw743	277	25	]	]	-RRB-
cord-329276-tfrjw743	277	26	[	[	-LRB-
cord-329276-tfrjw743	277	27	35	35	CD
cord-329276-tfrjw743	277	28	]	]	-RRB-
cord-329276-tfrjw743	277	29	[	[	-LRB-
cord-329276-tfrjw743	277	30	36	36	CD
cord-329276-tfrjw743	277	31	]	]	-RRB-
cord-329276-tfrjw743	277	32	leads	lead	VBZ
cord-329276-tfrjw743	277	33	to	to	IN
cord-329276-tfrjw743	277	34	a	a	DT
cord-329276-tfrjw743	277	35	closed	closed	JJ
cord-329276-tfrjw743	277	36	form	form	NN
cord-329276-tfrjw743	277	37	formula	formula	NN
cord-329276-tfrjw743	277	38	for	for	IN
cord-329276-tfrjw743	277	39	the	the	DT
cord-329276-tfrjw743	277	40	control	control	NN
cord-329276-tfrjw743	277	41	as	as	IN
cord-329276-tfrjw743	277	42	a	a	DT
cord-329276-tfrjw743	277	43	function	function	NN
cord-329276-tfrjw743	277	44	of	of	IN
cord-329276-tfrjw743	277	45	state	state	NN
cord-329276-tfrjw743	277	46	and	and	CC
cord-329276-tfrjw743	277	47	multiplier	multiplier	NN
cord-329276-tfrjw743	277	48	that	that	WDT
cord-329276-tfrjw743	277	49	can	can	MD
cord-329276-tfrjw743	277	50	easily	easily	RB
cord-329276-tfrjw743	277	51	be	be	VB
cord-329276-tfrjw743	277	52	solved	solve	VBN
cord-329276-tfrjw743	277	53	numerically	numerically	RB
cord-329276-tfrjw743	277	54	.	.	.
cord-329276-tfrjw743	278	1	This	this	DT
cord-329276-tfrjw743	278	2	,	,	,
cord-329276-tfrjw743	278	3	however	however	RB
cord-329276-tfrjw743	278	4	,	,	,
cord-329276-tfrjw743	278	5	does	do	VBZ
cord-329276-tfrjw743	278	6	not	not	RB
cord-329276-tfrjw743	278	7	guarantee	guarantee	VB
cord-329276-tfrjw743	278	8	that	that	IN
cord-329276-tfrjw743	278	9	a	a	DT
cord-329276-tfrjw743	278	10	numerically	numerically	RB
cord-329276-tfrjw743	278	11	computed	compute	VBN
cord-329276-tfrjw743	278	12	solution	solution	NN
cord-329276-tfrjw743	278	13	is	be	VBZ
cord-329276-tfrjw743	278	14	optimal	optimal	JJ
cord-329276-tfrjw743	278	15	as	as	IN
cord-329276-tfrjw743	278	16	only	only	JJ
cord-329276-tfrjw743	278	17	extremals	extremal	NNS
cord-329276-tfrjw743	278	18	(	(	-LRB-
cord-329276-tfrjw743	278	19	pairs	pair	NNS
cord-329276-tfrjw743	278	20	of	of	IN
cord-329276-tfrjw743	278	21	controlled	control	VBN
cord-329276-tfrjw743	278	22	trajectories	trajectory	NNS
cord-329276-tfrjw743	278	23	and	and	CC
cord-329276-tfrjw743	278	24	multipliers	multiplier	NNS
cord-329276-tfrjw743	278	25	which	which	WDT
cord-329276-tfrjw743	278	26	satisfy	satisfy	VBP
cord-329276-tfrjw743	278	27	the	the	DT
cord-329276-tfrjw743	278	28	first	first	JJ
cord-329276-tfrjw743	278	29	-	-	HYPH
cord-329276-tfrjw743	278	30	order	order	NN
cord-329276-tfrjw743	278	31	necessary	necessary	JJ
cord-329276-tfrjw743	278	32	conditions	condition	NNS
cord-329276-tfrjw743	278	33	for	for	IN
cord-329276-tfrjw743	278	34	optimality	optimality	NN
cord-329276-tfrjw743	278	35	)	)	-RRB-
cord-329276-tfrjw743	278	36	are	be	VBP
cord-329276-tfrjw743	278	37	obtained	obtain	VBN
cord-329276-tfrjw743	278	38	,	,	,
cord-329276-tfrjw743	278	39	a	a	DT
cord-329276-tfrjw743	278	40	fact	fact	NN
cord-329276-tfrjw743	278	41	often	often	RB
cord-329276-tfrjw743	278	42	understated	understate	VBN
cord-329276-tfrjw743	278	43	by	by	IN
cord-329276-tfrjw743	278	44	many	many	JJ
cord-329276-tfrjw743	278	45	researchers	researcher	NNS
cord-329276-tfrjw743	278	46	.	.	.
cord-329276-tfrjw743	279	1	Indeed	indeed	RB
cord-329276-tfrjw743	279	2	,	,	,
cord-329276-tfrjw743	279	3	the	the	DT
cord-329276-tfrjw743	279	4	projection	projection	NN
cord-329276-tfrjw743	279	5	from	from	IN
cord-329276-tfrjw743	279	6	the	the	DT
cord-329276-tfrjw743	279	7	space	space	NN
cord-329276-tfrjw743	279	8	of	of	IN
cord-329276-tfrjw743	279	9	extremals	extremal	NNS
cord-329276-tfrjw743	279	10	into	into	IN
cord-329276-tfrjw743	279	11	the	the	DT
cord-329276-tfrjw743	279	12	state	state	NN
cord-329276-tfrjw743	279	13	space	space	NN
cord-329276-tfrjw743	279	14	(	(	-LRB-
cord-329276-tfrjw743	279	15	i.e.	i.e.	FW
cord-329276-tfrjw743	279	16	,	,	,
cord-329276-tfrjw743	279	17	projecting	project	VBG
cord-329276-tfrjw743	279	18	out	out	RP
cord-329276-tfrjw743	279	19	the	the	DT
cord-329276-tfrjw743	279	20	multiplier	multiplier	NN
cord-329276-tfrjw743	279	21	)	)	-RRB-
cord-329276-tfrjw743	279	22	can	can	MD
cord-329276-tfrjw743	279	23	haveand	haveand	NN
cord-329276-tfrjw743	279	24	often	often	RB
cord-329276-tfrjw743	279	25	does	do	VBZ
cord-329276-tfrjw743	279	26	have	have	VB
cord-329276-tfrjw743	279	27	-	-	HYPH
cord-329276-tfrjw743	279	28	singularities	singularity	NNS
cord-329276-tfrjw743	279	29	,	,	,
cord-329276-tfrjw743	279	30	the	the	DT
cord-329276-tfrjw743	279	31	equivalent	equivalent	NN
cord-329276-tfrjw743	279	32	of	of	IN
cord-329276-tfrjw743	279	33	the	the	DT
cord-329276-tfrjw743	279	34	well	well	RB
cord-329276-tfrjw743	279	35	-	-	HYPH
cord-329276-tfrjw743	279	36	known	know	VBN
cord-329276-tfrjw743	279	37	conjugate	conjugate	NN
cord-329276-tfrjw743	279	38	points	point	NNS
cord-329276-tfrjw743	279	39	from	from	IN
cord-329276-tfrjw743	279	40	the	the	DT
cord-329276-tfrjw743	279	41	calculus	calculus	NN
cord-329276-tfrjw743	279	42	of	of	IN
cord-329276-tfrjw743	279	43	variations	variation	NNS
cord-329276-tfrjw743	279	44	.	.	.
cord-329276-tfrjw743	280	1	For	for	IN
cord-329276-tfrjw743	280	2	problems	problem	NNS
cord-329276-tfrjw743	280	3	employing	employ	VBG
cord-329276-tfrjw743	280	4	an	an	DT
cord-329276-tfrjw743	280	5	L	l	NN
cord-329276-tfrjw743	280	6	2	2	CD
cord-329276-tfrjw743	280	7	-type	-type	CD
cord-329276-tfrjw743	280	8	objective	objective	NN
cord-329276-tfrjw743	280	9	,	,	,
cord-329276-tfrjw743	280	10	higherorder	higherorder	NN
cord-329276-tfrjw743	280	11	tests	test	NNS
cord-329276-tfrjw743	280	12	for	for	IN
cord-329276-tfrjw743	280	13	local	local	JJ
cord-329276-tfrjw743	280	14	optimality	optimality	NN
cord-329276-tfrjw743	280	15	are	be	VBP
cord-329276-tfrjw743	280	16	given	give	VBN
cord-329276-tfrjw743	280	17	in	in	IN
cord-329276-tfrjw743	280	18	[	[	-LRB-
cord-329276-tfrjw743	280	19	15	15	CD
cord-329276-tfrjw743	280	20	,	,	,
cord-329276-tfrjw743	280	21	Chapter	chapter	NN
cord-329276-tfrjw743	280	22	4	4	CD
cord-329276-tfrjw743	280	23	]	]	-RRB-
cord-329276-tfrjw743	280	24	or	or	CC
cord-329276-tfrjw743	280	25	[	[	-LRB-
cord-329276-tfrjw743	280	26	37	37	CD
cord-329276-tfrjw743	280	27	]	]	-RRB-
cord-329276-tfrjw743	280	28	and	and	CC
cord-329276-tfrjw743	280	29	are	be	VBP
cord-329276-tfrjw743	280	30	not	not	RB
cord-329276-tfrjw743	280	31	difficult	difficult	JJ
cord-329276-tfrjw743	280	32	to	to	TO
cord-329276-tfrjw743	280	33	apply	apply	VB
cord-329276-tfrjw743	280	34	,	,	,
cord-329276-tfrjw743	280	35	but	but	CC
cord-329276-tfrjw743	280	36	generally	generally	RB
cord-329276-tfrjw743	280	37	this	this	DT
cord-329276-tfrjw743	280	38	is	be	VBZ
cord-329276-tfrjw743	280	39	not	not	RB
cord-329276-tfrjw743	280	40	done	do	VBN
cord-329276-tfrjw743	280	41	in	in	IN
cord-329276-tfrjw743	280	42	the	the	DT
cord-329276-tfrjw743	280	43	literature	literature	NN
cord-329276-tfrjw743	280	44	.	.	.
cord-329276-tfrjw743	281	1	Our	-PRON-	PRP$
cord-329276-tfrjw743	281	2	main	main	JJ
cord-329276-tfrjw743	281	3	objection	objection	NN
cord-329276-tfrjw743	281	4	to	to	IN
cord-329276-tfrjw743	281	5	the	the	DT
cord-329276-tfrjw743	281	6	use	use	NN
cord-329276-tfrjw743	281	7	of	of	IN
cord-329276-tfrjw743	281	8	an	an	DT
cord-329276-tfrjw743	281	9	L	l	NN
cord-329276-tfrjw743	281	10	2	2	CD
cord-329276-tfrjw743	281	11	-criterion	-criterion	NN
cord-329276-tfrjw743	281	12	in	in	IN
cord-329276-tfrjw743	281	13	the	the	DT
cord-329276-tfrjw743	281	14	controls	control	NNS
cord-329276-tfrjw743	281	15	,	,	,
cord-329276-tfrjw743	281	16	however	however	RB
cord-329276-tfrjw743	281	17	,	,	,
cord-329276-tfrjw743	281	18	does	do	VBZ
cord-329276-tfrjw743	281	19	not	not	RB
cord-329276-tfrjw743	281	20	lie	lie	VB
cord-329276-tfrjw743	281	21	with	with	IN
cord-329276-tfrjw743	281	22	this	this	DT
cord-329276-tfrjw743	281	23	mathematical	mathematical	JJ
cord-329276-tfrjw743	281	24	aspect	aspect	NN
cord-329276-tfrjw743	281	25	,	,	,
cord-329276-tfrjw743	281	26	but	but	CC
cord-329276-tfrjw743	281	27	simply	simply	RB
cord-329276-tfrjw743	281	28	with	with	IN
cord-329276-tfrjw743	281	29	the	the	DT
cord-329276-tfrjw743	281	30	fact	fact	NN
cord-329276-tfrjw743	281	31	that	that	IN
cord-329276-tfrjw743	281	32	for	for	IN
cord-329276-tfrjw743	281	33	biomedical	biomedical	JJ
cord-329276-tfrjw743	281	34	problems	problem	NNS
cord-329276-tfrjw743	281	35	it	-PRON-	PRP
cord-329276-tfrjw743	281	36	seems	seem	VBZ
cord-329276-tfrjw743	281	37	rather	rather	RB
cord-329276-tfrjw743	281	38	impossible	impossible	JJ
cord-329276-tfrjw743	281	39	to	to	TO
cord-329276-tfrjw743	281	40	give	give	VB
cord-329276-tfrjw743	281	41	a	a	DT
cord-329276-tfrjw743	281	42	satisfactory	satisfactory	JJ
cord-329276-tfrjw743	281	43	justification	justification	NN
cord-329276-tfrjw743	281	44	for	for	IN
cord-329276-tfrjw743	281	45	such	such	PDT
cord-329276-tfrjw743	281	46	a	a	DT
cord-329276-tfrjw743	281	47	functional	functional	JJ
cord-329276-tfrjw743	281	48	form	form	NN
cord-329276-tfrjw743	281	49	as	as	IN
cord-329276-tfrjw743	281	50	the	the	DT
cord-329276-tfrjw743	281	51	meaning	meaning	NN
cord-329276-tfrjw743	281	52	of	of	IN
cord-329276-tfrjw743	281	53	the	the	DT
cord-329276-tfrjw743	281	54	phrase	phrase	NN
cord-329276-tfrjw743	281	55	"	"	``
cord-329276-tfrjw743	281	56	systemic	systemic	JJ
cord-329276-tfrjw743	281	57	cost	cost	NN
cord-329276-tfrjw743	281	58	"	"	''
cord-329276-tfrjw743	281	59	employed	employ	VBN
cord-329276-tfrjw743	281	60	in	in	IN
cord-329276-tfrjw743	281	61	the	the	DT
cord-329276-tfrjw743	281	62	vast	vast	JJ
cord-329276-tfrjw743	281	63	literature	literature	NN
cord-329276-tfrjw743	281	64	is	be	VBZ
cord-329276-tfrjw743	281	65	hard	hard	JJ
cord-329276-tfrjw743	281	66	to	to	TO
cord-329276-tfrjw743	281	67	capture	capture	VB
cord-329276-tfrjw743	281	68	.	.	.
cord-329276-tfrjw743	282	1	In	in	IN
cord-329276-tfrjw743	282	2	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	282	3	,	,	,
cord-329276-tfrjw743	282	4	for	for	IN
cord-329276-tfrjw743	282	5	example	example	NN
cord-329276-tfrjw743	282	6	,	,	,
cord-329276-tfrjw743	282	7	not	not	RB
cord-329276-tfrjw743	282	8	only	only	RB
cord-329276-tfrjw743	282	9	does	do	VBZ
cord-329276-tfrjw743	282	10	the	the	DT
cord-329276-tfrjw743	282	11	quantity	quantity	NN
cord-329276-tfrjw743	282	12	T	t	NN
cord-329276-tfrjw743	282	13	0	0	CD
cord-329276-tfrjw743	282	14	u(t	u(t	NN
cord-329276-tfrjw743	282	15	)	)	-RRB-
cord-329276-tfrjw743	283	1	2	2	CD
cord-329276-tfrjw743	283	2	dt	dt	NNS
cord-329276-tfrjw743	283	3	not	not	RB
cord-329276-tfrjw743	283	4	represent	represent	VBP
cord-329276-tfrjw743	283	5	any	any	DT
cord-329276-tfrjw743	283	6	pharmacologically	pharmacologically	RB
cord-329276-tfrjw743	283	7	meaningful	meaningful	JJ
cord-329276-tfrjw743	283	8	quantity	quantity	NN
cord-329276-tfrjw743	283	9	,	,	,
cord-329276-tfrjw743	283	10	but	but	CC
cord-329276-tfrjw743	283	11	in	in	IN
cord-329276-tfrjw743	283	12	addition	addition	NN
cord-329276-tfrjw743	283	13	,	,	,
cord-329276-tfrjw743	283	14	if	if	IN
cord-329276-tfrjw743	283	15	one	one	PRP
cord-329276-tfrjw743	283	16	normalizes	normalize	VBZ
cord-329276-tfrjw743	283	17	the	the	DT
cord-329276-tfrjw743	283	18	controls	control	NNS
cord-329276-tfrjw743	283	19	to	to	TO
cord-329276-tfrjw743	283	20	satisfy	satisfy	VB
cord-329276-tfrjw743	283	21	0	0	CD
cord-329276-tfrjw743	283	22	≤	≤	NN
cord-329276-tfrjw743	283	23	u	u	NN
cord-329276-tfrjw743	283	24	i	i	NN
cord-329276-tfrjw743	283	25	≤	≤	NNP
cord-329276-tfrjw743	283	26	1	1	CD
cord-329276-tfrjw743	283	27	,	,	,
cord-329276-tfrjw743	283	28	as	as	IN
cord-329276-tfrjw743	283	29	it	-PRON-	PRP
cord-329276-tfrjw743	283	30	is	be	VBZ
cord-329276-tfrjw743	283	31	often	often	RB
cord-329276-tfrjw743	283	32	done	do	VBN
cord-329276-tfrjw743	283	33	,	,	,
cord-329276-tfrjw743	283	34	then	then	RB
cord-329276-tfrjw743	283	35	his	-PRON-	PRP$
cord-329276-tfrjw743	283	36	strongly	strongly	RB
cord-329276-tfrjw743	283	37	favors	favor	VBZ
cord-329276-tfrjw743	283	38	smaller	small	JJR
cord-329276-tfrjw743	283	39	partial	partial	JJ
cord-329276-tfrjw743	283	40	doses	dose	NNS
cord-329276-tfrjw743	283	41	over	over	IN
cord-329276-tfrjw743	283	42	the	the	DT
cord-329276-tfrjw743	283	43	higher	high	JJR
cord-329276-tfrjw743	283	44	full	full	JJ
cord-329276-tfrjw743	283	45	doses	dose	NNS
cord-329276-tfrjw743	283	46	as	as	IN
cord-329276-tfrjw743	283	47	half	half	PDT
cord-329276-tfrjw743	283	48	the	the	DT
cord-329276-tfrjw743	283	49	maximum	maximum	JJ
cord-329276-tfrjw743	283	50	dose	dose	NN
cord-329276-tfrjw743	283	51	is	be	VBZ
cord-329276-tfrjw743	283	52	only	only	RB
cord-329276-tfrjw743	283	53	given	give	VBN
cord-329276-tfrjw743	283	54	a	a	DT
cord-329276-tfrjw743	283	55	quarter	quarter	NN
cord-329276-tfrjw743	283	56	of	of	IN
cord-329276-tfrjw743	283	57	the	the	DT
cord-329276-tfrjw743	283	58	weight	weight	NN
cord-329276-tfrjw743	283	59	of	of	IN
cord-329276-tfrjw743	283	60	the	the	DT
cord-329276-tfrjw743	283	61	maximum	maximum	JJ
cord-329276-tfrjw743	283	62	dose	dose	NN
cord-329276-tfrjw743	283	63	.	.	.
cord-329276-tfrjw743	284	1	Thus	thus	RB
cord-329276-tfrjw743	284	2	,	,	,
cord-329276-tfrjw743	284	3	from	from	IN
cord-329276-tfrjw743	284	4	the	the	DT
cord-329276-tfrjw743	284	5	very	very	JJ
cord-329276-tfrjw743	284	6	setup	setup	NN
cord-329276-tfrjw743	284	7	,	,	,
cord-329276-tfrjw743	284	8	a	a	DT
cord-329276-tfrjw743	284	9	bias	bias	NN
cord-329276-tfrjw743	284	10	is	be	VBZ
cord-329276-tfrjw743	284	11	built	build	VBN
cord-329276-tfrjw743	284	12	into	into	IN
cord-329276-tfrjw743	284	13	the	the	DT
cord-329276-tfrjw743	284	14	optimal	optimal	JJ
cord-329276-tfrjw743	284	15	solutions	solution	NNS
cord-329276-tfrjw743	284	16	to	to	TO
cord-329276-tfrjw743	284	17	be	be	VB
cord-329276-tfrjw743	284	18	computed	compute	VBN
cord-329276-tfrjw743	284	19	which	which	WDT
cord-329276-tfrjw743	284	20	the	the	DT
cord-329276-tfrjw743	284	21	underlying	underlie	VBG
cord-329276-tfrjw743	284	22	system	system	NN
cord-329276-tfrjw743	284	23	does	do	VBZ
cord-329276-tfrjw743	284	24	not	not	RB
cord-329276-tfrjw743	284	25	have	have	VB
cord-329276-tfrjw743	284	26	.	.	.
cord-329276-tfrjw743	285	1	Cost	cost	NN
cord-329276-tfrjw743	285	2	is	be	VBZ
cord-329276-tfrjw743	285	3	another	another	DT
cord-329276-tfrjw743	285	4	questionable	questionable	JJ
cord-329276-tfrjw743	285	5	justification	justification	NN
cord-329276-tfrjw743	285	6	for	for	IN
cord-329276-tfrjw743	285	7	an	an	DT
cord-329276-tfrjw743	285	8	L	l	NN
cord-329276-tfrjw743	285	9	2	2	CD
cord-329276-tfrjw743	285	10	-type	-type	CD
cord-329276-tfrjw743	285	11	objective	objective	NN
cord-329276-tfrjw743	285	12	as	as	IN
cord-329276-tfrjw743	285	13	$	$	$
cord-329276-tfrjw743	285	14	2	2	CD
cord-329276-tfrjw743	285	15	just	just	RB
cord-329276-tfrjw743	285	16	is	be	VBZ
cord-329276-tfrjw743	285	17	not	not	RB
cord-329276-tfrjw743	285	18	a	a	DT
cord-329276-tfrjw743	285	19	very	very	RB
cord-329276-tfrjw743	285	20	meaningful	meaningful	JJ
cord-329276-tfrjw743	285	21	quantity	quantity	NN
cord-329276-tfrjw743	285	22	.	.	.
cord-329276-tfrjw743	286	1	It	-PRON-	PRP
cord-329276-tfrjw743	286	2	is	be	VBZ
cord-329276-tfrjw743	286	3	certainly	certainly	RB
cord-329276-tfrjw743	286	4	true	true	JJ
cord-329276-tfrjw743	286	5	that	that	IN
cord-329276-tfrjw743	286	6	the	the	DT
cord-329276-tfrjw743	286	7	cost	cost	NN
cord-329276-tfrjw743	286	8	need	nee	MD
cord-329276-tfrjw743	286	9	not	not	RB
cord-329276-tfrjw743	286	10	be	be	VB
cord-329276-tfrjw743	286	11	linear	linear	JJ
cord-329276-tfrjw743	286	12	in	in	IN
cord-329276-tfrjw743	287	1	u.	u.	NNP
cord-329276-tfrjw743	287	2	This	this	DT
cord-329276-tfrjw743	287	3	particularly	particularly	RB
cord-329276-tfrjw743	287	4	holds	hold	VBZ
cord-329276-tfrjw743	287	5	in	in	IN
cord-329276-tfrjw743	287	6	epidemiological	epidemiological	JJ
cord-329276-tfrjw743	287	7	models	model	NNS
cord-329276-tfrjw743	287	8	where	where	WRB
cord-329276-tfrjw743	287	9	the	the	DT
cord-329276-tfrjw743	287	10	cost	cost	NN
cord-329276-tfrjw743	287	11	of	of	IN
cord-329276-tfrjw743	287	12	vaccinating	vaccinate	VBG
cord-329276-tfrjw743	287	13	the	the	DT
cord-329276-tfrjw743	287	14	first	first	JJ
cord-329276-tfrjw743	287	15	10	10	CD
cord-329276-tfrjw743	287	16	%	%	NN
cord-329276-tfrjw743	287	17	of	of	IN
cord-329276-tfrjw743	287	18	a	a	DT
cord-329276-tfrjw743	287	19	population	population	NN
cord-329276-tfrjw743	287	20	clearly	clearly	RB
cord-329276-tfrjw743	287	21	is	be	VBZ
cord-329276-tfrjw743	287	22	much	much	RB
cord-329276-tfrjw743	287	23	smaller	small	JJR
cord-329276-tfrjw743	287	24	than	than	IN
cord-329276-tfrjw743	287	25	the	the	DT
cord-329276-tfrjw743	287	26	cost	cost	NN
cord-329276-tfrjw743	287	27	of	of	IN
cord-329276-tfrjw743	287	28	vaccinating	vaccinate	VBG
cord-329276-tfrjw743	287	29	the	the	DT
cord-329276-tfrjw743	287	30	last	last	JJ
cord-329276-tfrjw743	287	31	10	10	CD
cord-329276-tfrjw743	287	32	%	%	NN
cord-329276-tfrjw743	287	33	of	of	IN
cord-329276-tfrjw743	287	34	this	this	DT
cord-329276-tfrjw743	287	35	population	population	NN
cord-329276-tfrjw743	287	36	as	as	IN
cord-329276-tfrjw743	287	37	much	much	RB
cord-329276-tfrjw743	287	38	greater	great	JJR
cord-329276-tfrjw743	287	39	efforts	effort	NNS
cord-329276-tfrjw743	287	40	will	will	MD
cord-329276-tfrjw743	287	41	be	be	VB
cord-329276-tfrjw743	287	42	needed	need	VBN
cord-329276-tfrjw743	287	43	to	to	TO
cord-329276-tfrjw743	287	44	reach	reach	VB
cord-329276-tfrjw743	287	45	the	the	DT
cord-329276-tfrjw743	287	46	tail	tail	NN
cord-329276-tfrjw743	287	47	end	end	NN
cord-329276-tfrjw743	287	48	of	of	IN
cord-329276-tfrjw743	287	49	the	the	DT
cord-329276-tfrjw743	287	50	population	population	NN
cord-329276-tfrjw743	287	51	.	.	.
cord-329276-tfrjw743	288	1	Yet	yet	RB
cord-329276-tfrjw743	288	2	,	,	,
cord-329276-tfrjw743	288	3	while	while	IN
cord-329276-tfrjw743	288	4	this	this	DT
cord-329276-tfrjw743	288	5	clearly	clearly	RB
cord-329276-tfrjw743	288	6	makes	make	VBZ
cord-329276-tfrjw743	288	7	a	a	DT
cord-329276-tfrjw743	288	8	point	point	NN
cord-329276-tfrjw743	288	9	for	for	IN
cord-329276-tfrjw743	288	10	some	some	DT
cord-329276-tfrjw743	288	11	nonlinear	nonlinear	JJ
cord-329276-tfrjw743	288	12	relation	relation	NN
cord-329276-tfrjw743	288	13	,	,	,
cord-329276-tfrjw743	288	14	a	a	DT
cord-329276-tfrjw743	288	15	quadratic	quadratic	JJ
cord-329276-tfrjw743	288	16	term	term	NN
cord-329276-tfrjw743	288	17	does	do	VBZ
cord-329276-tfrjw743	288	18	not	not	RB
cord-329276-tfrjw743	288	19	seem	seem	VB
cord-329276-tfrjw743	288	20	to	to	TO
cord-329276-tfrjw743	288	21	be	be	VB
cord-329276-tfrjw743	288	22	the	the	DT
cord-329276-tfrjw743	288	23	answer	answer	NN
cord-329276-tfrjw743	288	24	to	to	IN
cord-329276-tfrjw743	288	25	this	this	DT
cord-329276-tfrjw743	288	26	.	.	.
cord-329276-tfrjw743	289	1	We	-PRON-	PRP
cord-329276-tfrjw743	289	2	still	still	RB
cord-329276-tfrjw743	289	3	remark	remark	VBP
cord-329276-tfrjw743	289	4	that	that	IN
cord-329276-tfrjw743	289	5	it	-PRON-	PRP
cord-329276-tfrjw743	289	6	is	be	VBZ
cord-329276-tfrjw743	289	7	often	often	RB
cord-329276-tfrjw743	289	8	the	the	DT
cord-329276-tfrjw743	289	9	typical	typical	JJ
cord-329276-tfrjw743	289	10	scenario	scenario	NN
cord-329276-tfrjw743	289	11	that	that	IN
cord-329276-tfrjw743	289	12	optimal	optimal	JJ
cord-329276-tfrjw743	289	13	solutions	solution	NNS
cord-329276-tfrjw743	289	14	for	for	IN
cord-329276-tfrjw743	289	15	the	the	DT
cord-329276-tfrjw743	289	16	L	L	NNP
cord-329276-tfrjw743	289	17	2	2	CD
cord-329276-tfrjw743	289	18	-type	-type	CD
cord-329276-tfrjw743	289	19	term	term	NN
cord-329276-tfrjw743	289	20	(	(	-LRB-
cord-329276-tfrjw743	289	21	which	which	WDT
cord-329276-tfrjw743	289	22	necessarily	necessarily	RB
cord-329276-tfrjw743	289	23	are	be	VBP
cord-329276-tfrjw743	289	24	continuous	continuous	JJ
cord-329276-tfrjw743	289	25	)	)	-RRB-
cord-329276-tfrjw743	289	26	exhibit	exhibit	VBP
cord-329276-tfrjw743	289	27	sharp	sharp	JJ
cord-329276-tfrjw743	289	28	rises	rise	NNS
cord-329276-tfrjw743	289	29	from	from	IN
cord-329276-tfrjw743	289	30	the	the	DT
cord-329276-tfrjw743	289	31	lower	low	JJR
cord-329276-tfrjw743	289	32	control	control	NN
cord-329276-tfrjw743	289	33	value	value	NN
cord-329276-tfrjw743	290	1	u	u	NN
cord-329276-tfrjw743	290	2	=	=	SYM
cord-329276-tfrjw743	290	3	0	0	NFP
cord-329276-tfrjw743	290	4	to	to	IN
cord-329276-tfrjw743	290	5	its	-PRON-	PRP$
cord-329276-tfrjw743	290	6	maximum	maximum	JJ
cord-329276-tfrjw743	290	7	value	value	NN
cord-329276-tfrjw743	290	8	u	u	NN
cord-329276-tfrjw743	290	9	=	=	SYM
cord-329276-tfrjw743	290	10	u	u	NNP
cord-329276-tfrjw743	290	11	max	max	NNP
cord-329276-tfrjw743	290	12	mimicking	mimic	VBG
cord-329276-tfrjw743	290	13	optimal	optimal	JJ
cord-329276-tfrjw743	290	14	bang	bang	NNP
cord-329276-tfrjw743	290	15	-	-	HYPH
cord-329276-tfrjw743	290	16	bang	bang	NNP
cord-329276-tfrjw743	290	17	controls	control	NNS
cord-329276-tfrjw743	290	18	which	which	WDT
cord-329276-tfrjw743	290	19	would	would	MD
cord-329276-tfrjw743	290	20	be	be	VB
cord-329276-tfrjw743	290	21	obtained	obtain	VBN
cord-329276-tfrjw743	290	22	by	by	IN
cord-329276-tfrjw743	290	23	using	use	VBG
cord-329276-tfrjw743	290	24	an	an	DT
cord-329276-tfrjw743	290	25	L	L	NNP
cord-329276-tfrjw743	290	26	1	1	CD
cord-329276-tfrjw743	290	27	-type	-type	CD
cord-329276-tfrjw743	290	28	term	term	NN
cord-329276-tfrjw743	290	29	.	.	.
cord-329276-tfrjw743	291	1	Indeed	indeed	RB
cord-329276-tfrjw743	291	2	,	,	,
cord-329276-tfrjw743	291	3	from	from	IN
cord-329276-tfrjw743	291	4	a	a	DT
cord-329276-tfrjw743	291	5	numerical	numerical	JJ
cord-329276-tfrjw743	291	6	perspective	perspective	NN
cord-329276-tfrjw743	291	7	,	,	,
cord-329276-tfrjw743	291	8	it	-PRON-	PRP
cord-329276-tfrjw743	291	9	makes	make	VBZ
cord-329276-tfrjw743	291	10	sense	sense	NN
cord-329276-tfrjw743	291	11	to	to	TO
cord-329276-tfrjw743	291	12	consider	consider	VB
cord-329276-tfrjw743	291	13	the	the	DT
cord-329276-tfrjw743	291	14	problem	problem	NN
cord-329276-tfrjw743	291	15	when	when	WRB
cord-329276-tfrjw743	291	16	the	the	DT
cord-329276-tfrjw743	291	17	control	control	NN
cord-329276-tfrjw743	291	18	terms	term	NNS
cord-329276-tfrjw743	291	19	are	be	VBP
cord-329276-tfrjw743	291	20	taken	take	VBN
cord-329276-tfrjw743	291	21	in	in	IN
cord-329276-tfrjw743	291	22	the	the	DT
cord-329276-tfrjw743	291	23	form	form	NN
cord-329276-tfrjw743	292	1	u	u	NNP
cord-329276-tfrjw743	292	2	+	+	CC
cord-329276-tfrjw743	292	3	εu	εu	VBZ
cord-329276-tfrjw743	292	4	2	2	CD
cord-329276-tfrjw743	293	1	and	and	CC
cord-329276-tfrjw743	293	2	then	then	RB
cord-329276-tfrjw743	293	3	the	the	DT
cord-329276-tfrjw743	293	4	limit	limit	NN
cord-329276-tfrjw743	293	5	as	as	IN
cord-329276-tfrjw743	293	6	ε	ε	NNP
cord-329276-tfrjw743	293	7	→	→	WDT
cord-329276-tfrjw743	293	8	0	0	NFP
cord-329276-tfrjw743	293	9	is	be	VBZ
cord-329276-tfrjw743	293	10	taken	take	VBN
cord-329276-tfrjw743	293	11	(	(	-LRB-
cord-329276-tfrjw743	293	12	if	if	IN
cord-329276-tfrjw743	293	13	it	-PRON-	PRP
cord-329276-tfrjw743	293	14	exists	exist	VBZ
cord-329276-tfrjw743	293	15	)	)	-RRB-
cord-329276-tfrjw743	293	16	.	.	.
cord-329276-tfrjw743	294	1	We	-PRON-	PRP
cord-329276-tfrjw743	294	2	note	note	VBP
cord-329276-tfrjw743	294	3	,	,	,
cord-329276-tfrjw743	294	4	however	however	RB
cord-329276-tfrjw743	294	5	,	,	,
cord-329276-tfrjw743	294	6	that	that	IN
cord-329276-tfrjw743	294	7	our	-PRON-	PRP$
cord-329276-tfrjw743	294	8	interest	interest	NN
cord-329276-tfrjw743	294	9	in	in	IN
cord-329276-tfrjw743	294	10	solving	solve	VBG
cord-329276-tfrjw743	294	11	the	the	DT
cord-329276-tfrjw743	294	12	optimal	optimal	JJ
cord-329276-tfrjw743	294	13	control	control	NN
cord-329276-tfrjw743	294	14	problems	problem	NNS
cord-329276-tfrjw743	294	15	is	be	VBZ
cord-329276-tfrjw743	294	16	more	more	JJR
cord-329276-tfrjw743	294	17	in	in	IN
cord-329276-tfrjw743	294	18	trying	try	VBG
cord-329276-tfrjw743	294	19	to	to	TO
cord-329276-tfrjw743	294	20	obtain	obtain	VB
cord-329276-tfrjw743	294	21	a	a	DT
cord-329276-tfrjw743	294	22	better	well	JJR
cord-329276-tfrjw743	294	23	global	global	JJ
cord-329276-tfrjw743	294	24	understanding	understanding	NN
cord-329276-tfrjw743	294	25	of	of	IN
cord-329276-tfrjw743	294	26	the	the	DT
cord-329276-tfrjw743	294	27	dynamics	dynamic	NNS
cord-329276-tfrjw743	294	28	,	,	,
cord-329276-tfrjw743	294	29	i.e.	i.e.	FW
cord-329276-tfrjw743	294	30	,	,	,
cord-329276-tfrjw743	294	31	the	the	DT
cord-329276-tfrjw743	294	32	underlying	underlying	JJ
cord-329276-tfrjw743	294	33	problem	problem	NN
cord-329276-tfrjw743	294	34	,	,	,
cord-329276-tfrjw743	294	35	than	than	IN
cord-329276-tfrjw743	294	36	to	to	TO
cord-329276-tfrjw743	294	37	obtain	obtain	VB
cord-329276-tfrjw743	294	38	one	one	CD
cord-329276-tfrjw743	294	39	particular	particular	JJ
cord-329276-tfrjw743	294	40	numerical	numerical	JJ
cord-329276-tfrjw743	294	41	solution	solution	NN
cord-329276-tfrjw743	294	42	(	(	-LRB-
cord-329276-tfrjw743	294	43	which	which	WDT
cord-329276-tfrjw743	294	44	is	be	VBZ
cord-329276-tfrjw743	294	45	a	a	DT
cord-329276-tfrjw743	294	46	much	much	RB
cord-329276-tfrjw743	294	47	easier	easy	JJR
cord-329276-tfrjw743	294	48	problem	problem	NN
cord-329276-tfrjw743	294	49	)	)	-RRB-
cord-329276-tfrjw743	294	50	.	.	.
cord-329276-tfrjw743	295	1	As	as	IN
cord-329276-tfrjw743	295	2	a	a	DT
cord-329276-tfrjw743	295	3	rule	rule	NN
cord-329276-tfrjw743	295	4	,	,	,
cord-329276-tfrjw743	295	5	the	the	DT
cord-329276-tfrjw743	295	6	parameter	parameter	NN
cord-329276-tfrjw743	295	7	values	value	NNS
cord-329276-tfrjw743	295	8	in	in	IN
cord-329276-tfrjw743	295	9	the	the	DT
cord-329276-tfrjw743	295	10	model	model	NN
cord-329276-tfrjw743	295	11	are	be	VBP
cord-329276-tfrjw743	295	12	uncertain	uncertain	JJ
cord-329276-tfrjw743	295	13	and	and	CC
cord-329276-tfrjw743	295	14	the	the	DT
cord-329276-tfrjw743	295	15	solutions	solution	NNS
cord-329276-tfrjw743	295	16	can	can	MD
cord-329276-tfrjw743	295	17	be	be	VB
cord-329276-tfrjw743	295	18	quite	quite	RB
cord-329276-tfrjw743	295	19	sensitive	sensitive	JJ
cord-329276-tfrjw743	295	20	to	to	IN
cord-329276-tfrjw743	295	21	these	these	DT
cord-329276-tfrjw743	295	22	values	value	NNS
cord-329276-tfrjw743	295	23	(	(	-LRB-
cord-329276-tfrjw743	295	24	e.g.	e.g.	RB
cord-329276-tfrjw743	295	25	,	,	,
cord-329276-tfrjw743	295	26	for	for	IN
cord-329276-tfrjw743	295	27	Stepanova	Stepanova	NNP
cord-329276-tfrjw743	295	28	's	's	POS
cord-329276-tfrjw743	295	29	model	model	NN
cord-329276-tfrjw743	295	30	)	)	-RRB-
cord-329276-tfrjw743	295	31	which	which	WDT
cord-329276-tfrjw743	295	32	limits	limit	VBZ
cord-329276-tfrjw743	295	33	the	the	DT
cord-329276-tfrjw743	295	34	practical	practical	JJ
cord-329276-tfrjw743	295	35	use	use	NN
cord-329276-tfrjw743	295	36	of	of	IN
cord-329276-tfrjw743	295	37	small	small	JJ
cord-329276-tfrjw743	295	38	numerical	numerical	JJ
cord-329276-tfrjw743	295	39	studies	study	NNS
cord-329276-tfrjw743	295	40	.	.	.
cord-329276-tfrjw743	296	1	We	-PRON-	PRP
cord-329276-tfrjw743	296	2	illustrate	illustrate	VBP
cord-329276-tfrjw743	296	3	some	some	DT
cord-329276-tfrjw743	296	4	of	of	IN
cord-329276-tfrjw743	296	5	these	these	DT
cord-329276-tfrjw743	296	6	effects	effect	NNS
cord-329276-tfrjw743	296	7	with	with	IN
cord-329276-tfrjw743	296	8	locally	locally	RB
cord-329276-tfrjw743	296	9	optimal	optimal	JJ
cord-329276-tfrjw743	296	10	solutions	solution	NNS
cord-329276-tfrjw743	296	11	for	for	IN
cord-329276-tfrjw743	296	12	a	a	DT
cord-329276-tfrjw743	296	13	cell	cell	NN
cord-329276-tfrjw743	296	14	-	-	HYPH
cord-329276-tfrjw743	296	15	cycle	cycle	NN
cord-329276-tfrjw743	296	16	specific	specific	JJ
cord-329276-tfrjw743	296	17	model	model	NN
cord-329276-tfrjw743	296	18	for	for	IN
cord-329276-tfrjw743	296	19	cancer	cancer	NN
cord-329276-tfrjw743	296	20	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	296	21	due	due	IN
cord-329276-tfrjw743	296	22	to	to	IN
cord-329276-tfrjw743	296	23	Swierniak	Swierniak	NNP
cord-329276-tfrjw743	296	24	[	[	-LRB-
cord-329276-tfrjw743	296	25	8	8	CD
cord-329276-tfrjw743	296	26	,	,	,
cord-329276-tfrjw743	296	27	12	12	CD
cord-329276-tfrjw743	296	28	]	]	-RRB-
cord-329276-tfrjw743	296	29	.	.	.
cord-329276-tfrjw743	297	1	In	in	IN
cord-329276-tfrjw743	297	2	such	such	JJ
cord-329276-tfrjw743	297	3	models	model	NNS
cord-329276-tfrjw743	297	4	,	,	,
cord-329276-tfrjw743	297	5	the	the	DT
cord-329276-tfrjw743	297	6	various	various	JJ
cord-329276-tfrjw743	297	7	phases	phase	NNS
cord-329276-tfrjw743	297	8	of	of	IN
cord-329276-tfrjw743	297	9	the	the	DT
cord-329276-tfrjw743	297	10	cell	cell	NN
cord-329276-tfrjw743	297	11	-	-	HYPH
cord-329276-tfrjw743	297	12	cycle	cycle	NN
cord-329276-tfrjw743	297	13	-	-	:
cord-329276-tfrjw743	297	14	a	a	DT
cord-329276-tfrjw743	297	15	quiescent	quiescent	JJ
cord-329276-tfrjw743	297	16	phase	phase	NN
cord-329276-tfrjw743	297	17	G	g	NN
cord-329276-tfrjw743	297	18	0	0	CD
cord-329276-tfrjw743	297	19	,	,	,
cord-329276-tfrjw743	297	20	a	a	DT
cord-329276-tfrjw743	297	21	first	first	JJ
cord-329276-tfrjw743	297	22	growth	growth	NN
cord-329276-tfrjw743	297	23	phase	phase	NN
cord-329276-tfrjw743	297	24	G	g	NN
cord-329276-tfrjw743	297	25	1	1	CD
cord-329276-tfrjw743	297	26	,	,	,
cord-329276-tfrjw743	297	27	synthesis	synthesis	NN
cord-329276-tfrjw743	297	28	S	S	NNP
cord-329276-tfrjw743	297	29	,	,	,
cord-329276-tfrjw743	297	30	a	a	DT
cord-329276-tfrjw743	297	31	second	second	JJ
cord-329276-tfrjw743	297	32	growth	growth	NN
cord-329276-tfrjw743	297	33	phase	phase	NN
cord-329276-tfrjw743	297	34	G	G	NNP
cord-329276-tfrjw743	297	35	2	2	CD
cord-329276-tfrjw743	297	36	,	,	,
cord-329276-tfrjw743	297	37	and	and	CC
cord-329276-tfrjw743	297	38	mitosis	mitosis	NN
cord-329276-tfrjw743	297	39	M	M	NNP
cord-329276-tfrjw743	297	40	-	-	,
cord-329276-tfrjw743	297	41	are	be	VBP
cord-329276-tfrjw743	297	42	clustered	cluster	VBN
cord-329276-tfrjw743	297	43	into	into	IN
cord-329276-tfrjw743	297	44	compartments	compartment	NNS
cord-329276-tfrjw743	297	45	and	and	CC
cord-329276-tfrjw743	297	46	the	the	DT
cord-329276-tfrjw743	297	47	dynamics	dynamic	NNS
cord-329276-tfrjw743	297	48	describes	describe	VBZ
cord-329276-tfrjw743	297	49	the	the	DT
cord-329276-tfrjw743	297	50	transitions	transition	NNS
cord-329276-tfrjw743	297	51	,	,	,
cord-329276-tfrjw743	297	52	i.e.	i.e.	FW
cord-329276-tfrjw743	297	53	,	,	,
cord-329276-tfrjw743	297	54	the	the	DT
cord-329276-tfrjw743	297	55	flow	flow	NN
cord-329276-tfrjw743	297	56	between	between	IN
cord-329276-tfrjw743	297	57	these	these	DT
cord-329276-tfrjw743	297	58	compartments	compartment	NNS
cord-329276-tfrjw743	297	59	.	.	.
cord-329276-tfrjw743	298	1	Mathematically	mathematically	RB
cord-329276-tfrjw743	298	2	,	,	,
cord-329276-tfrjw743	298	3	the	the	DT
cord-329276-tfrjw743	298	4	dynamics	dynamic	NNS
cord-329276-tfrjw743	298	5	becomes	become	VBZ
cord-329276-tfrjw743	298	6	a	a	DT
cord-329276-tfrjw743	298	7	bilinear	bilinear	JJ
cord-329276-tfrjw743	298	8	system	system	NN
cord-329276-tfrjw743	298	9	of	of	IN
cord-329276-tfrjw743	298	10	the	the	DT
cord-329276-tfrjw743	298	11	forṁ	forṁ	NN
cord-329276-tfrjw743	298	12	with	with	IN
cord-329276-tfrjw743	298	13	the	the	DT
cord-329276-tfrjw743	298	14	state	state	NN
cord-329276-tfrjw743	299	1	N	N	NNP
cord-329276-tfrjw743	300	1	i	i	PRP
cord-329276-tfrjw743	300	2	representing	represent	VBG
cord-329276-tfrjw743	300	3	the	the	DT
cord-329276-tfrjw743	300	4	average	average	JJ
cord-329276-tfrjw743	300	5	number	number	NN
cord-329276-tfrjw743	300	6	of	of	IN
cord-329276-tfrjw743	300	7	cells	cell	NNS
cord-329276-tfrjw743	300	8	in	in	IN
cord-329276-tfrjw743	300	9	the	the	DT
cord-329276-tfrjw743	300	10	respective	respective	JJ
cord-329276-tfrjw743	300	11	compartments	compartment	NNS
cord-329276-tfrjw743	300	12	and	and	CC
cord-329276-tfrjw743	300	13	the	the	DT
cord-329276-tfrjw743	300	14	matrices	matrix	NNS
cord-329276-tfrjw743	300	15	A	A	NNP
cord-329276-tfrjw743	300	16	and	and	CC
cord-329276-tfrjw743	300	17	B	B	NNP
cord-329276-tfrjw743	300	18	j	j	NNP
cord-329276-tfrjw743	300	19	modeling	model	VBG
cord-329276-tfrjw743	300	20	the	the	DT
cord-329276-tfrjw743	300	21	flow	flow	NN
cord-329276-tfrjw743	300	22	rates	rate	NNS
cord-329276-tfrjw743	300	23	between	between	IN
cord-329276-tfrjw743	300	24	the	the	DT
cord-329276-tfrjw743	300	25	compartments	compartment	NNS
cord-329276-tfrjw743	300	26	.	.	.
cord-329276-tfrjw743	301	1	The	the	DT
cord-329276-tfrjw743	301	2	controls	control	NNS
cord-329276-tfrjw743	301	3	represent	represent	VBP
cord-329276-tfrjw743	301	4	cytotoxic	cytotoxic	JJ
cord-329276-tfrjw743	301	5	agents	agent	NNS
cord-329276-tfrjw743	301	6	which	which	WDT
cord-329276-tfrjw743	301	7	indiscriminately	indiscriminately	RB
cord-329276-tfrjw743	301	8	kill	kill	VBP
cord-329276-tfrjw743	301	9	cells	cell	NNS
cord-329276-tfrjw743	301	10	,	,	,
cord-329276-tfrjw743	301	11	cytostatic	cytostatic	JJ
cord-329276-tfrjw743	301	12	agents	agent	NNS
cord-329276-tfrjw743	301	13	which	which	WDT
cord-329276-tfrjw743	301	14	block	block	VBP
cord-329276-tfrjw743	301	15	the	the	DT
cord-329276-tfrjw743	301	16	transitions	transition	NNS
cord-329276-tfrjw743	301	17	of	of	IN
cord-329276-tfrjw743	301	18	cells	cell	NNS
cord-329276-tfrjw743	301	19	through	through	IN
cord-329276-tfrjw743	301	20	the	the	DT
cord-329276-tfrjw743	301	21	cell	cell	NN
cord-329276-tfrjw743	301	22	-	-	HYPH
cord-329276-tfrjw743	301	23	cycle	cycle	NN
cord-329276-tfrjw743	301	24	and	and	CC
cord-329276-tfrjw743	301	25	recruiting	recruit	VBG
cord-329276-tfrjw743	301	26	agents	agent	NNS
cord-329276-tfrjw743	301	27	which	which	WDT
cord-329276-tfrjw743	301	28	entice	entice	VBP
cord-329276-tfrjw743	301	29	cells	cell	NNS
cord-329276-tfrjw743	301	30	to	to	TO
cord-329276-tfrjw743	301	31	leave	leave	VB
cord-329276-tfrjw743	301	32	the	the	DT
cord-329276-tfrjw743	301	33	quiescent	quiescent	JJ
cord-329276-tfrjw743	301	34	phase	phase	NN
cord-329276-tfrjw743	301	35	and	and	CC
cord-329276-tfrjw743	301	36	become	become	VB
cord-329276-tfrjw743	301	37	active	active	JJ
cord-329276-tfrjw743	301	38	again	again	RB
cord-329276-tfrjw743	301	39	so	so	IN
cord-329276-tfrjw743	301	40	that	that	IN
cord-329276-tfrjw743	301	41	it	-PRON-	PRP
cord-329276-tfrjw743	301	42	is	be	VBZ
cord-329276-tfrjw743	301	43	possible	possible	JJ
cord-329276-tfrjw743	301	44	to	to	TO
cord-329276-tfrjw743	301	45	kill	kill	VB
cord-329276-tfrjw743	301	46	them	-PRON-	PRP
cord-329276-tfrjw743	301	47	.	.	.
cord-329276-tfrjw743	302	1	A	a	DT
cord-329276-tfrjw743	302	2	typical	typical	JJ
cord-329276-tfrjw743	302	3	form	form	NN
cord-329276-tfrjw743	302	4	of	of	IN
cord-329276-tfrjw743	302	5	the	the	DT
cord-329276-tfrjw743	302	6	objective	objective	NN
cord-329276-tfrjw743	302	7	is	be	VBZ
cord-329276-tfrjw743	302	8	given	give	VBN
cord-329276-tfrjw743	302	9	by	by	IN
cord-329276-tfrjw743	302	10	 	 	_SP
cord-329276-tfrjw743	302	11	with	with	IN
cord-329276-tfrjw743	302	12	the	the	DT
cord-329276-tfrjw743	302	13	coefficients	coefficient	NNS
cord-329276-tfrjw743	302	14	nonnegative	nonnegative	JJ
cord-329276-tfrjw743	302	15	weights	weight	NNS
cord-329276-tfrjw743	302	16	.	.	.
cord-329276-tfrjw743	303	1	Figure	figure	NN
cord-329276-tfrjw743	303	2	3	3	CD
cord-329276-tfrjw743	303	3	compares	compare	VBZ
cord-329276-tfrjw743	303	4	locally	locally	RB
cord-329276-tfrjw743	303	5	optimal	optimal	JJ
cord-329276-tfrjw743	303	6	solutions	solution	NNS
cord-329276-tfrjw743	303	7	for	for	IN
cord-329276-tfrjw743	303	8	a	a	DT
cord-329276-tfrjw743	303	9	3-compartment	3-compartment	CD
cord-329276-tfrjw743	303	10	model	model	NN
cord-329276-tfrjw743	303	11	with	with	IN
cord-329276-tfrjw743	303	12	the	the	DT
cord-329276-tfrjw743	303	13	compartments	compartment	NNS
cord-329276-tfrjw743	303	14	N	n	CD
cord-329276-tfrjw743	303	15	1	1	CD
cord-329276-tfrjw743	303	16	∼	∼	NNP
cord-329276-tfrjw743	303	17	G0	G0	NNP
cord-329276-tfrjw743	303	18	/	/	SYM
cord-329276-tfrjw743	303	19	G	G	NNP
cord-329276-tfrjw743	303	20	1	1	CD
cord-329276-tfrjw743	303	21	,	,	,
cord-329276-tfrjw743	303	22	N	n	CD
cord-329276-tfrjw743	303	23	2	2	CD
cord-329276-tfrjw743	303	24	∼	∼	NNP
cord-329276-tfrjw743	303	25	S	S	NNP
cord-329276-tfrjw743	303	26	and	and	CC
cord-329276-tfrjw743	303	27	N	N	NNP
cord-329276-tfrjw743	303	28	3	3	CD
cord-329276-tfrjw743	303	29	∼	∼	NN
cord-329276-tfrjw743	303	30	G	G	NNP
cord-329276-tfrjw743	303	31	2	2	CD
cord-329276-tfrjw743	303	32	/M	/M	.
cord-329276-tfrjw743	303	33	for	for	IN
cord-329276-tfrjw743	303	34	L	l	NN
cord-329276-tfrjw743	303	35	1	1	CD
cord-329276-tfrjw743	304	1	-and	-and	:
cord-329276-tfrjw743	305	1	L	l	NN
cord-329276-tfrjw743	305	2	2	2	CD
cord-329276-tfrjw743	305	3	-type	-type	CD
cord-329276-tfrjw743	305	4	functional	functional	JJ
cord-329276-tfrjw743	305	5	terms	term	NNS
cord-329276-tfrjw743	305	6	on	on	IN
cord-329276-tfrjw743	305	7	the	the	DT
cord-329276-tfrjw743	305	8	controls	control	NNS
cord-329276-tfrjw743	305	9	which	which	WDT
cord-329276-tfrjw743	305	10	represent	represent	VBP
cord-329276-tfrjw743	305	11	a	a	DT
cord-329276-tfrjw743	305	12	cytotoxic	cytotoxic	JJ
cord-329276-tfrjw743	305	13	agent	agent	NN
cord-329276-tfrjw743	305	14	u	u	NN
cord-329276-tfrjw743	305	15	and	and	CC
cord-329276-tfrjw743	305	16	a	a	DT
cord-329276-tfrjw743	305	17	cytostatic	cytostatic	JJ
cord-329276-tfrjw743	305	18	agent	agent	NN
cord-329276-tfrjw743	305	19	v	v	NN
cord-329276-tfrjw743	305	20	[	[	-LRB-
cord-329276-tfrjw743	305	21	11	11	CD
cord-329276-tfrjw743	305	22	,	,	,
cord-329276-tfrjw743	305	23	15	15	CD
cord-329276-tfrjw743	305	24	,	,	,
cord-329276-tfrjw743	305	25	37	37	CD
cord-329276-tfrjw743	305	26	]	]	-RRB-
cord-329276-tfrjw743	305	27	.	.	.
cord-329276-tfrjw743	306	1	Optimal	optimal	JJ
cord-329276-tfrjw743	306	2	controls	control	NNS
cord-329276-tfrjw743	306	3	for	for	IN
cord-329276-tfrjw743	306	4	the	the	DT
cord-329276-tfrjw743	306	5	L	L	NNP
cord-329276-tfrjw743	306	6	1	1	CD
cord-329276-tfrjw743	306	7	-type	-type	CD
cord-329276-tfrjw743	306	8	objective	objective	NN
cord-329276-tfrjw743	306	9	are	be	VBP
cord-329276-tfrjw743	306	10	bang	bang	NNP
cord-329276-tfrjw743	306	11	-	-	HYPH
cord-329276-tfrjw743	306	12	bang	bang	NNP
cord-329276-tfrjw743	306	13	,	,	,
cord-329276-tfrjw743	306	14	i.e.	i.e.	FW
cord-329276-tfrjw743	306	15	,	,	,
cord-329276-tfrjw743	306	16	switch	switch	VB
cord-329276-tfrjw743	306	17	between	between	IN
cord-329276-tfrjw743	306	18	full	full	JJ
cord-329276-tfrjw743	306	19	dose	dose	NN
cord-329276-tfrjw743	306	20	therapies	therapy	NNS
cord-329276-tfrjw743	306	21	and	and	CC
cord-329276-tfrjw743	306	22	rest	rest	NN
cord-329276-tfrjw743	306	23	-	-	HYPH
cord-329276-tfrjw743	306	24	periods	period	NNS
cord-329276-tfrjw743	306	25	while	while	IN
cord-329276-tfrjw743	306	26	optimal	optimal	JJ
cord-329276-tfrjw743	306	27	controls	control	NNS
cord-329276-tfrjw743	306	28	for	for	IN
cord-329276-tfrjw743	306	29	the	the	DT
cord-329276-tfrjw743	306	30	L	L	NNP
cord-329276-tfrjw743	306	31	2	2	CD
cord-329276-tfrjw743	306	32	-type	-type	CD
cord-329276-tfrjw743	306	33	objective	objective	NN
cord-329276-tfrjw743	306	34	are	be	VBP
cord-329276-tfrjw743	306	35	necessarily	necessarily	RB
cord-329276-tfrjw743	306	36	continuous	continuous	JJ
cord-329276-tfrjw743	306	37	.	.	.
cord-329276-tfrjw743	307	1	For	for	IN
cord-329276-tfrjw743	307	2	an	an	DT
cord-329276-tfrjw743	307	3	L	l	NN
cord-329276-tfrjw743	307	4	1	1	CD
cord-329276-tfrjw743	307	5	-type	-type	CD
cord-329276-tfrjw743	307	6	objective	objective	NN
cord-329276-tfrjw743	307	7	,	,	,
cord-329276-tfrjw743	307	8	the	the	DT
cord-329276-tfrjw743	307	9	optimal	optimal	JJ
cord-329276-tfrjw743	307	10	administration	administration	NN
cord-329276-tfrjw743	307	11	of	of	IN
cord-329276-tfrjw743	307	12	the	the	DT
cord-329276-tfrjw743	307	13	killing	killing	NN
cord-329276-tfrjw743	307	14	agent	agent	NN
cord-329276-tfrjw743	307	15	u	u	NNP
cord-329276-tfrjw743	307	16	is	be	VBZ
cord-329276-tfrjw743	307	17	full	full	JJ
cord-329276-tfrjw743	307	18	dose	dose	NN
cord-329276-tfrjw743	307	19	initially	initially	RB
cord-329276-tfrjw743	307	20	followed	follow	VBD
cord-329276-tfrjw743	307	21	with	with	IN
cord-329276-tfrjw743	307	22	a	a	DT
cord-329276-tfrjw743	307	23	rest	rest	NN
cord-329276-tfrjw743	307	24	period	period	NN
cord-329276-tfrjw743	307	25	(	(	-LRB-
cord-329276-tfrjw743	307	26	and	and	CC
cord-329276-tfrjw743	307	27	this	this	DT
cord-329276-tfrjw743	307	28	is	be	VBZ
cord-329276-tfrjw743	307	29	what	what	WP
cord-329276-tfrjw743	307	30	medically	medically	RB
cord-329276-tfrjw743	307	31	makes	make	VBZ
cord-329276-tfrjw743	307	32	most	most	JJS
cord-329276-tfrjw743	307	33	sense	sense	NN
cord-329276-tfrjw743	307	34	here	here	RB
cord-329276-tfrjw743	307	35	)	)	-RRB-
cord-329276-tfrjw743	307	36	,	,	,
cord-329276-tfrjw743	307	37	whereas	whereas	IN
cord-329276-tfrjw743	307	38	for	for	IN
cord-329276-tfrjw743	307	39	the	the	DT
cord-329276-tfrjw743	307	40	L	L	NNP
cord-329276-tfrjw743	307	41	2	2	CD
cord-329276-tfrjw743	307	42	-type	-type	CD
cord-329276-tfrjw743	307	43	objective	objective	VBP
cord-329276-tfrjw743	307	44	the	the	DT
cord-329276-tfrjw743	307	45	continuity	continuity	NN
cord-329276-tfrjw743	307	46	of	of	IN
cord-329276-tfrjw743	307	47	the	the	DT
cord-329276-tfrjw743	307	48	control	control	NN
cord-329276-tfrjw743	307	49	generates	generate	VBZ
cord-329276-tfrjw743	307	50	decreasing	decrease	VBG
cord-329276-tfrjw743	307	51	lower	low	JJR
cord-329276-tfrjw743	307	52	dose	dose	JJ
cord-329276-tfrjw743	307	53	administrations	administration	NNS
cord-329276-tfrjw743	307	54	of	of	IN
cord-329276-tfrjw743	307	55	the	the	DT
cord-329276-tfrjw743	307	56	cytotoxic	cytotoxic	JJ
cord-329276-tfrjw743	307	57	agent	agent	NN
cord-329276-tfrjw743	307	58	toward	toward	IN
cord-329276-tfrjw743	307	59	the	the	DT
cord-329276-tfrjw743	307	60	end	end	NN
cord-329276-tfrjw743	307	61	of	of	IN
cord-329276-tfrjw743	307	62	the	the	DT
cord-329276-tfrjw743	307	63	therapy	therapy	NN
cord-329276-tfrjw743	307	64	interval	interval	NN
cord-329276-tfrjw743	307	65	.	.	.
cord-329276-tfrjw743	308	1	The	the	DT
cord-329276-tfrjw743	308	2	total	total	JJ
cord-329276-tfrjw743	308	3	doses	dose	NNS
cord-329276-tfrjw743	308	4	given	give	VBN
cord-329276-tfrjw743	308	5	in	in	IN
cord-329276-tfrjw743	308	6	both	both	DT
cord-329276-tfrjw743	308	7	cases	case	NNS
cord-329276-tfrjw743	308	8	are	be	VBP
cord-329276-tfrjw743	308	9	similar	similar	JJ
cord-329276-tfrjw743	308	10	.	.	.
cord-329276-tfrjw743	309	1	For	for	IN
cord-329276-tfrjw743	309	2	the	the	DT
cord-329276-tfrjw743	309	3	blocking	block	VBG
cord-329276-tfrjw743	309	4	agent	agent	NN
cord-329276-tfrjw743	309	5	v	v	NN
cord-329276-tfrjw743	309	6	,	,	,
cord-329276-tfrjw743	309	7	the	the	DT
cord-329276-tfrjw743	309	8	optimal	optimal	JJ
cord-329276-tfrjw743	309	9	L	l	NN
cord-329276-tfrjw743	309	10	2	2	CD
cord-329276-tfrjw743	309	11	-control	-control	CD
cord-329276-tfrjw743	309	12	clearly	clearly	RB
cord-329276-tfrjw743	309	13	mimics	mimic	VBZ
cord-329276-tfrjw743	309	14	the	the	DT
cord-329276-tfrjw743	309	15	optimal	optimal	NN
cord-329276-tfrjw743	310	1	L	L	NNP
cord-329276-tfrjw743	310	2	1	1	CD
cord-329276-tfrjw743	310	3	-control	-control	.
cord-329276-tfrjw743	311	1	with	with	IN
cord-329276-tfrjw743	311	2	steep	steep	JJ
cord-329276-tfrjw743	311	3	continuous	continuous	JJ
cord-329276-tfrjw743	311	4	intermediate	intermediate	JJ
cord-329276-tfrjw743	311	5	segments	segment	NNS
cord-329276-tfrjw743	311	6	.	.	.
cord-329276-tfrjw743	312	1	The	the	DT
cord-329276-tfrjw743	312	2	behavior	behavior	NN
cord-329276-tfrjw743	312	3	of	of	IN
cord-329276-tfrjw743	312	4	the	the	DT
cord-329276-tfrjw743	312	5	controlled	control	VBN
cord-329276-tfrjw743	312	6	trajectories	trajectory	NNS
cord-329276-tfrjw743	312	7	for	for	IN
cord-329276-tfrjw743	312	8	both	both	DT
cord-329276-tfrjw743	312	9	objectives	objective	NNS
cord-329276-tfrjw743	312	10	is	be	VBZ
cord-329276-tfrjw743	312	11	very	very	RB
cord-329276-tfrjw743	312	12	much	much	RB
cord-329276-tfrjw743	312	13	the	the	DT
cord-329276-tfrjw743	312	14	same	same	JJ
cord-329276-tfrjw743	312	15	.	.	.
cord-329276-tfrjw743	313	1	The	the	DT
cord-329276-tfrjw743	313	2	terminal	terminal	JJ
cord-329276-tfrjw743	313	3	values	value	NNS
cord-329276-tfrjw743	313	4	for	for	IN
cord-329276-tfrjw743	313	5	the	the	DT
cord-329276-tfrjw743	313	6	states	state	NNS
cord-329276-tfrjw743	313	7	corresponding	correspond	VBG
cord-329276-tfrjw743	313	8	to	to	IN
cord-329276-tfrjw743	313	9	the	the	DT
cord-329276-tfrjw743	313	10	L	l	NN
cord-329276-tfrjw743	313	11	1	1	CD
cord-329276-tfrjw743	314	1	-and	-and	:
cord-329276-tfrjw743	315	1	L	l	NN
cord-329276-tfrjw743	315	2	2	2	CD
cord-329276-tfrjw743	315	3	-type	-type	CD
cord-329276-tfrjw743	315	4	objectives	objective	NNS
cord-329276-tfrjw743	315	5	are	be	VBP
cord-329276-tfrjw743	315	6	close	close	JJ
cord-329276-tfrjw743	315	7	,	,	,
cord-329276-tfrjw743	315	8	and	and	CC
cord-329276-tfrjw743	315	9	the	the	DT
cord-329276-tfrjw743	315	10	reduction	reduction	NN
cord-329276-tfrjw743	315	11	in	in	IN
cord-329276-tfrjw743	315	12	the	the	DT
cord-329276-tfrjw743	315	13	total	total	JJ
cord-329276-tfrjw743	315	14	cancer	cancer	NN
cord-329276-tfrjw743	315	15	burden	burden	NN
cord-329276-tfrjw743	315	16	is	be	VBZ
cord-329276-tfrjw743	315	17	from	from	IN
cord-329276-tfrjw743	315	18	the	the	DT
cord-329276-tfrjw743	315	19	initial	initial	JJ
cord-329276-tfrjw743	315	20	normalization	normalization	NN
cord-329276-tfrjw743	315	21	of	of	IN
cord-329276-tfrjw743	315	22	C(0	C(0	NNP
cord-329276-tfrjw743	315	23	)	)	-RRB-
cord-329276-tfrjw743	316	1	=	=	NFP
cord-329276-tfrjw743	317	1	1	1	CD
cord-329276-tfrjw743	317	2	to	to	IN
cord-329276-tfrjw743	317	3	C(21	C(21	NNP
cord-329276-tfrjw743	317	4	)	)	-RRB-
cord-329276-tfrjw743	318	1	=	=	LS
cord-329276-tfrjw743	318	2	0.8673	0.8673	CD
cord-329276-tfrjw743	318	3	for	for	IN
cord-329276-tfrjw743	318	4	minimizing	minimize	VBG
cord-329276-tfrjw743	318	5	J	J	NNP
cord-329276-tfrjw743	318	6	1	1	CD
cord-329276-tfrjw743	318	7	and	and	CC
cord-329276-tfrjw743	318	8	to	to	IN
cord-329276-tfrjw743	318	9	C(21	C(21	NNP
cord-329276-tfrjw743	318	10	)	)	-RRB-
cord-329276-tfrjw743	318	11	=	=	NFP
cord-329276-tfrjw743	319	1	0.8314	0.8314	CD
cord-329276-tfrjw743	319	2	for	for	IN
cord-329276-tfrjw743	319	3	minimizing	minimize	VBG
cord-329276-tfrjw743	319	4	J	J	NNP
cord-329276-tfrjw743	319	5	2	2	CD
cord-329276-tfrjw743	319	6	.	.	.
cord-329276-tfrjw743	320	1	In	in	IN
cord-329276-tfrjw743	320	2	both	both	DT
cord-329276-tfrjw743	320	3	cases	case	NNS
cord-329276-tfrjw743	320	4	,	,	,
cord-329276-tfrjw743	320	5	the	the	DT
cord-329276-tfrjw743	320	6	initial	initial	JJ
cord-329276-tfrjw743	320	7	condition	condition	NN
cord-329276-tfrjw743	320	8	was	be	VBD
cord-329276-tfrjw743	320	9	chosen	choose	VBN
cord-329276-tfrjw743	320	10	as	as	IN
cord-329276-tfrjw743	320	11	the	the	DT
cord-329276-tfrjw743	320	12	normalized	normalized	JJ
cord-329276-tfrjw743	320	13	steadystate	steadystate	NN
cord-329276-tfrjw743	320	14	of	of	IN
cord-329276-tfrjw743	320	15	the	the	DT
cord-329276-tfrjw743	320	16	uncontrolled	uncontrolled	JJ
cord-329276-tfrjw743	320	17	dynamics	dynamic	NNS
cord-329276-tfrjw743	320	18	(	(	-LRB-
cord-329276-tfrjw743	320	19	i.e.	i.e.	FW
cord-329276-tfrjw743	320	20	,	,	,
cord-329276-tfrjw743	320	21	assuming	assume	VBG
cord-329276-tfrjw743	320	22	no	no	DT
cord-329276-tfrjw743	320	23	earlier	early	JJR
cord-329276-tfrjw743	320	24	treatment	treatment	NN
cord-329276-tfrjw743	320	25	)	)	-RRB-
cord-329276-tfrjw743	320	26	.	.	.
cord-329276-tfrjw743	321	1	Computing	compute	VBG
cord-329276-tfrjw743	321	2	the	the	DT
cord-329276-tfrjw743	321	3	total	total	JJ
cord-329276-tfrjw743	321	4	dose	dose	NN
cord-329276-tfrjw743	321	5	of	of	IN
cord-329276-tfrjw743	321	6	the	the	DT
cord-329276-tfrjw743	321	7	drugs	drug	NNS
cord-329276-tfrjw743	321	8	given	give	VBN
cord-329276-tfrjw743	321	9	for	for	IN
cord-329276-tfrjw743	321	10	the	the	DT
cord-329276-tfrjw743	321	11	L	L	NNP
cord-329276-tfrjw743	321	12	2	2	CD
cord-329276-tfrjw743	321	13	-optimal	-optimal	JJS
cord-329276-tfrjw743	321	14	control	control	NN
cord-329276-tfrjw743	321	15	,	,	,
cord-329276-tfrjw743	321	16	one	one	NN
cord-329276-tfrjw743	321	17	sees	see	VBZ
cord-329276-tfrjw743	321	18	,	,	,
cord-329276-tfrjw743	321	19	however	however	RB
cord-329276-tfrjw743	321	20	,	,	,
cord-329276-tfrjw743	321	21	that	that	IN
cord-329276-tfrjw743	321	22	while	while	IN
cord-329276-tfrjw743	321	23	minimizing	minimize	VBG
cord-329276-tfrjw743	321	24	the	the	DT
cord-329276-tfrjw743	321	25	quadratic	quadratic	JJ
cord-329276-tfrjw743	321	26	objective	objective	NN
cord-329276-tfrjw743	321	27	leads	lead	VBZ
cord-329276-tfrjw743	321	28	to	to	IN
cord-329276-tfrjw743	321	29	about	about	RB
cord-329276-tfrjw743	321	30	a	a	DT
cord-329276-tfrjw743	321	31	3	3	CD
cord-329276-tfrjw743	321	32	%	%	NN
cord-329276-tfrjw743	321	33	improvement	improvement	NN
cord-329276-tfrjw743	321	34	in	in	IN
cord-329276-tfrjw743	321	35	the	the	DT
cord-329276-tfrjw743	321	36	reduction	reduction	NN
cord-329276-tfrjw743	321	37	of	of	IN
cord-329276-tfrjw743	321	38	the	the	DT
cord-329276-tfrjw743	321	39	tumor	tumor	NN
cord-329276-tfrjw743	321	40	,	,	,
cord-329276-tfrjw743	321	41	this	this	DT
cord-329276-tfrjw743	321	42	is	be	VBZ
cord-329276-tfrjw743	321	43	at	at	IN
cord-329276-tfrjw743	321	44	the	the	DT
cord-329276-tfrjw743	321	45	expense	expense	NN
cord-329276-tfrjw743	321	46	of	of	IN
cord-329276-tfrjw743	321	47	increasing	increase	VBG
cord-329276-tfrjw743	321	48	the	the	DT
cord-329276-tfrjw743	321	49	amounts	amount	NNS
cord-329276-tfrjw743	321	50	of	of	IN
cord-329276-tfrjw743	321	51	both	both	CC
cord-329276-tfrjw743	321	52	the	the	DT
cord-329276-tfrjw743	321	53	cytotoxic	cytotoxic	JJ
cord-329276-tfrjw743	321	54	and	and	CC
cord-329276-tfrjw743	321	55	cytostatic	cytostatic	JJ
cord-329276-tfrjw743	321	56	agents	agent	NNS
cord-329276-tfrjw743	321	57	by	by	IN
cord-329276-tfrjw743	321	58	about	about	RB
cord-329276-tfrjw743	321	59	20	20	CD
cord-329276-tfrjw743	321	60	%	%	NN
cord-329276-tfrjw743	321	61	.	.	.
cord-329276-tfrjw743	322	1	Thus	thus	RB
cord-329276-tfrjw743	322	2	,	,	,
cord-329276-tfrjw743	322	3	higher	high	JJR
cord-329276-tfrjw743	322	4	side	side	NN
cord-329276-tfrjw743	322	5	-	-	HYPH
cord-329276-tfrjw743	322	6	effects	effect	NNS
cord-329276-tfrjw743	322	7	are	be	VBP
cord-329276-tfrjw743	322	8	encountered	encounter	VBN
cord-329276-tfrjw743	322	9	.	.	.
cord-329276-tfrjw743	323	1	Minimizing	minimize	VBG
cord-329276-tfrjw743	323	2	J	J	NNP
cord-329276-tfrjw743	323	3	1	1	CD
cord-329276-tfrjw743	323	4	would	would	MD
cord-329276-tfrjw743	323	5	appear	appear	VB
cord-329276-tfrjw743	323	6	to	to	TO
cord-329276-tfrjw743	323	7	be	be	VB
cord-329276-tfrjw743	323	8	the	the	DT
cord-329276-tfrjw743	323	9	preferred	preferred	JJ
cord-329276-tfrjw743	323	10	strategy	strategy	NN
cord-329276-tfrjw743	323	11	.	.	.
cord-329276-tfrjw743	324	1	An	an	DT
cord-329276-tfrjw743	324	2	alternative	alternative	JJ
cord-329276-tfrjw743	324	3	approach	approach	NN
cord-329276-tfrjw743	324	4	-	-	:
cord-329276-tfrjw743	324	5	and	and	CC
cord-329276-tfrjw743	324	6	the	the	DT
cord-329276-tfrjw743	324	7	one	one	NN
cord-329276-tfrjw743	324	8	which	which	WDT
cord-329276-tfrjw743	324	9	seems	seem	VBZ
cord-329276-tfrjw743	324	10	to	to	TO
cord-329276-tfrjw743	324	11	be	be	VB
cord-329276-tfrjw743	324	12	preferred	prefer	VBN
cord-329276-tfrjw743	324	13	by	by	IN
cord-329276-tfrjw743	324	14	medical	medical	JJ
cord-329276-tfrjw743	324	15	practitioners	practitioner	NNS
cord-329276-tfrjw743	324	16	-	-	,
cord-329276-tfrjw743	324	17	is	be	VBZ
cord-329276-tfrjw743	324	18	to	to	TO
cord-329276-tfrjw743	324	19	impose	impose	VB
cord-329276-tfrjw743	324	20	the	the	DT
cord-329276-tfrjw743	324	21	total	total	JJ
cord-329276-tfrjw743	324	22	amount	amount	NN
cord-329276-tfrjw743	324	23	of	of	IN
cord-329276-tfrjw743	324	24	drug	drug	NN
cord-329276-tfrjw743	324	25	(	(	-LRB-
cord-329276-tfrjw743	324	26	or	or	CC
cord-329276-tfrjw743	324	27	radio	radio	NN
cord-329276-tfrjw743	324	28	therapy	therapy	NN
cord-329276-tfrjw743	324	29	dose	dose	NN
cord-329276-tfrjw743	324	30	etc	etc	FW
cord-329276-tfrjw743	324	31	.	.	.
cord-329276-tfrjw743	324	32	)	)	-RRB-
cord-329276-tfrjw743	325	1	given	give	VBN
cord-329276-tfrjw743	325	2	a	a	DT
cord-329276-tfrjw743	325	3	priori	priori	FW
cord-329276-tfrjw743	325	4	.	.	.
cord-329276-tfrjw743	326	1	The	the	DT
cord-329276-tfrjw743	326	2	argument	argument	NN
cord-329276-tfrjw743	326	3	is	be	VBZ
cord-329276-tfrjw743	326	4	that	that	IN
cord-329276-tfrjw743	326	5	,	,	,
cord-329276-tfrjw743	326	6	to	to	TO
cord-329276-tfrjw743	326	7	begin	begin	VB
cord-329276-tfrjw743	326	8	with	with	IN
cord-329276-tfrjw743	326	9	,	,	,
cord-329276-tfrjw743	326	10	any	any	DT
cord-329276-tfrjw743	326	11	mathematical	mathematical	JJ
cord-329276-tfrjw743	326	12	model	model	NN
cord-329276-tfrjw743	326	13	represents	represent	VBZ
cord-329276-tfrjw743	326	14	only	only	RB
cord-329276-tfrjw743	326	15	a	a	DT
cord-329276-tfrjw743	326	16	small	small	JJ
cord-329276-tfrjw743	326	17	view	view	NN
cord-329276-tfrjw743	326	18	of	of	IN
cord-329276-tfrjw743	326	19	the	the	DT
cord-329276-tfrjw743	326	20	underlying	underlying	JJ
cord-329276-tfrjw743	326	21	problem	problem	NN
cord-329276-tfrjw743	326	22	and	and	CC
cord-329276-tfrjw743	326	23	that	that	IN
cord-329276-tfrjw743	326	24	,	,	,
cord-329276-tfrjw743	326	25	by	by	IN
cord-329276-tfrjw743	326	26	sheer	sheer	JJ
cord-329276-tfrjw743	326	27	necessity	necessity	NN
cord-329276-tfrjw743	326	28	of	of	IN
cord-329276-tfrjw743	326	29	the	the	DT
cord-329276-tfrjw743	326	30	complexity	complexity	NN
cord-329276-tfrjw743	326	31	which	which	WDT
cord-329276-tfrjw743	326	32	,	,	,
cord-329276-tfrjw743	326	33	for	for	IN
cord-329276-tfrjw743	326	34	example	example	NN
cord-329276-tfrjw743	326	35	,	,	,
cord-329276-tfrjw743	326	36	cancer	cancer	NN
cord-329276-tfrjw743	326	37	therapy	therapy	NN
cord-329276-tfrjw743	326	38	is	be	VBZ
cord-329276-tfrjw743	326	39	,	,	,
cord-329276-tfrjw743	326	40	many	many	JJ
cord-329276-tfrjw743	326	41	aspects	aspect	NNS
cord-329276-tfrjw743	326	42	need	need	VBP
cord-329276-tfrjw743	326	43	to	to	TO
cord-329276-tfrjw743	326	44	be	be	VB
cord-329276-tfrjw743	326	45	neglected	neglect	VBN
cord-329276-tfrjw743	326	46	.	.	.
cord-329276-tfrjw743	327	1	Thus	thus	RB
cord-329276-tfrjw743	327	2	,	,	,
cord-329276-tfrjw743	327	3	the	the	DT
cord-329276-tfrjw743	327	4	point	point	NN
cord-329276-tfrjw743	327	5	of	of	IN
cord-329276-tfrjw743	327	6	view	view	NN
cord-329276-tfrjw743	327	7	is	be	VBZ
cord-329276-tfrjw743	327	8	taken	take	VBN
cord-329276-tfrjw743	327	9	that	that	DT
cord-329276-tfrjw743	327	10	,	,	,
cord-329276-tfrjw743	327	11	based	base	VBN
cord-329276-tfrjw743	327	12	on	on	IN
cord-329276-tfrjw743	327	13	other	other	JJ
cord-329276-tfrjw743	327	14	assessments	assessment	NNS
cord-329276-tfrjw743	327	15	such	such	JJ
cord-329276-tfrjw743	327	16	as	as	IN
cord-329276-tfrjw743	327	17	the	the	DT
cord-329276-tfrjw743	327	18	side	side	NN
cord-329276-tfrjw743	327	19	effects	effect	NNS
cord-329276-tfrjw743	327	20	of	of	IN
cord-329276-tfrjw743	327	21	the	the	DT
cord-329276-tfrjw743	327	22	therapy	therapy	NN
cord-329276-tfrjw743	327	23	,	,	,
cord-329276-tfrjw743	327	24	the	the	DT
cord-329276-tfrjw743	327	25	total	total	JJ
cord-329276-tfrjw743	327	26	amount	amount	NN
cord-329276-tfrjw743	327	27	of	of	IN
cord-329276-tfrjw743	327	28	drug	drug	NN
cord-329276-tfrjw743	327	29	to	to	TO
cord-329276-tfrjw743	327	30	be	be	VB
cord-329276-tfrjw743	327	31	given	give	VBN
cord-329276-tfrjw743	327	32	has	have	VBZ
cord-329276-tfrjw743	327	33	been	be	VBN
cord-329276-tfrjw743	327	34	determined	determine	VBN
cord-329276-tfrjw743	327	35	a	a	DT
cord-329276-tfrjw743	327	36	priori	priori	FW
cord-329276-tfrjw743	327	37	,	,	,
cord-329276-tfrjw743	327	38	Here	here	RB
cord-329276-tfrjw743	327	39	,	,	,
cord-329276-tfrjw743	327	40	then	then	RB
cord-329276-tfrjw743	327	41	the	the	DT
cord-329276-tfrjw743	327	42	question	question	NN
cord-329276-tfrjw743	327	43	simply	simply	RB
cord-329276-tfrjw743	327	44	becomes	become	VBZ
cord-329276-tfrjw743	327	45	the	the	DT
cord-329276-tfrjw743	327	46	following	follow	VBG
cord-329276-tfrjw743	327	47	one	one	CD
cord-329276-tfrjw743	327	48	:	:	:
cord-329276-tfrjw743	327	49	given	give	VBN
cord-329276-tfrjw743	327	50	this	this	DT
cord-329276-tfrjw743	327	51	amount	amount	NN
cord-329276-tfrjw743	327	52	of	of	IN
cord-329276-tfrjw743	327	53	drug	drug	NN
cord-329276-tfrjw743	327	54	,	,	,
cord-329276-tfrjw743	327	55	how	how	WRB
cord-329276-tfrjw743	327	56	can	can	MD
cord-329276-tfrjw743	327	57	it	-PRON-	PRP
cord-329276-tfrjw743	327	58	be	be	VB
cord-329276-tfrjw743	327	59	administered	administer	VBN
cord-329276-tfrjw743	327	60	in	in	IN
cord-329276-tfrjw743	327	61	the	the	DT
cord-329276-tfrjw743	327	62	best	good	JJS
cord-329276-tfrjw743	327	63	possible	possible	JJ
cord-329276-tfrjw743	327	64	way	way	NN
cord-329276-tfrjw743	327	65	?	?	.
cord-329276-tfrjw743	328	1	Mathematically	mathematically	RB
cord-329276-tfrjw743	328	2	,	,	,
cord-329276-tfrjw743	328	3	this	this	DT
cord-329276-tfrjw743	328	4	amounts	amount	VBZ
cord-329276-tfrjw743	328	5	to	to	IN
cord-329276-tfrjw743	328	6	adding	add	VBG
cord-329276-tfrjw743	328	7	the	the	DT
cord-329276-tfrjw743	328	8	trivial	trivial	JJ
cord-329276-tfrjw743	328	9	equationẏ	equationẏ	NN
cord-329276-tfrjw743	329	1	=	=	SYM
cord-329276-tfrjw743	329	2	u	u	NNP
cord-329276-tfrjw743	329	3	,	,	,
cord-329276-tfrjw743	329	4	y(0	y(0	NNP
cord-329276-tfrjw743	329	5	)	)	-RRB-
cord-329276-tfrjw743	329	6	=	=	SYM
cord-329276-tfrjw743	329	7	0	0	NFP
cord-329276-tfrjw743	329	8	,	,	,
cord-329276-tfrjw743	329	9	to	to	IN
cord-329276-tfrjw743	329	10	the	the	DT
cord-329276-tfrjw743	329	11	dynamics	dynamic	NNS
cord-329276-tfrjw743	329	12	and	and	CC
cord-329276-tfrjw743	329	13	the	the	DT
cord-329276-tfrjw743	329	14	terminal	terminal	JJ
cord-329276-tfrjw743	329	15	condition	condition	NN
cord-329276-tfrjw743	329	16	y(T	y(t	NN
cord-329276-tfrjw743	329	17	)	)	-RRB-
cord-329276-tfrjw743	330	1	≤	≤	NNP
cord-329276-tfrjw743	330	2	A	A	NNP
cord-329276-tfrjw743	330	3	is	be	VBZ
cord-329276-tfrjw743	330	4	imposed	impose	VBN
cord-329276-tfrjw743	330	5	as	as	IN
cord-329276-tfrjw743	330	6	an	an	DT
cord-329276-tfrjw743	330	7	isoperimetric	isoperimetric	JJ
cord-329276-tfrjw743	330	8	constraint	constraint	NN
cord-329276-tfrjw743	330	9	.	.	.
cord-329276-tfrjw743	331	1	This	this	DT
cord-329276-tfrjw743	331	2	approach	approach	NN
cord-329276-tfrjw743	331	3	,	,	,
cord-329276-tfrjw743	331	4	for	for	IN
cord-329276-tfrjw743	331	5	example	example	NN
cord-329276-tfrjw743	331	6	,	,	,
cord-329276-tfrjw743	331	7	was	be	VBD
cord-329276-tfrjw743	331	8	taken	take	VBN
cord-329276-tfrjw743	331	9	in	in	IN
cord-329276-tfrjw743	331	10	solving	solve	VBG
cord-329276-tfrjw743	331	11	Hahnfeldt	Hahnfeldt	NNP
cord-329276-tfrjw743	331	12	's	's	POS
cord-329276-tfrjw743	331	13	model	model	NN
cord-329276-tfrjw743	331	14	for	for	IN
cord-329276-tfrjw743	331	15	antiangiogenic	antiangiogenic	NNP
cord-329276-tfrjw743	331	16	therapy	therapy	NN
cord-329276-tfrjw743	331	17	as	as	IN
cord-329276-tfrjw743	331	18	an	an	DT
cord-329276-tfrjw743	331	19	optimal	optimal	JJ
cord-329276-tfrjw743	331	20	control	control	NN
cord-329276-tfrjw743	331	21	problem	problem	NN
cord-329276-tfrjw743	331	22	[	[	-LRB-
cord-329276-tfrjw743	331	23	13	13	CD
cord-329276-tfrjw743	331	24	,	,	,
cord-329276-tfrjw743	331	25	15	15	CD
cord-329276-tfrjw743	331	26	]	]	-RRB-
cord-329276-tfrjw743	331	27	.	.	.
cord-329276-tfrjw743	332	1	In	in	IN
cord-329276-tfrjw743	332	2	such	such	PDT
cord-329276-tfrjw743	332	3	a	a	DT
cord-329276-tfrjw743	332	4	case	case	NN
cord-329276-tfrjw743	332	5	,	,	,
cord-329276-tfrjw743	332	6	no	no	DT
cord-329276-tfrjw743	332	7	control	control	NN
cord-329276-tfrjw743	332	8	related	related	JJ
cord-329276-tfrjw743	332	9	term	term	NN
cord-329276-tfrjw743	332	10	will	will	MD
cord-329276-tfrjw743	332	11	be	be	VB
cord-329276-tfrjw743	332	12	included	include	VBN
cord-329276-tfrjw743	332	13	in	in	IN
cord-329276-tfrjw743	332	14	the	the	DT
cord-329276-tfrjw743	332	15	objective	objective	NN
cord-329276-tfrjw743	332	16	.	.	.
cord-329276-tfrjw743	333	1	From	from	IN
cord-329276-tfrjw743	333	2	a	a	DT
cord-329276-tfrjw743	333	3	modeling	modeling	NN
cord-329276-tfrjw743	333	4	perspective	perspective	NN
cord-329276-tfrjw743	333	5	,	,	,
cord-329276-tfrjw743	333	6	the	the	DT
cord-329276-tfrjw743	333	7	use	use	NN
cord-329276-tfrjw743	333	8	of	of	IN
cord-329276-tfrjw743	333	9	a	a	DT
cord-329276-tfrjw743	333	10	hard	hard	JJ
cord-329276-tfrjw743	333	11	constraint	constraint	NN
cord-329276-tfrjw743	333	12	on	on	IN
cord-329276-tfrjw743	333	13	the	the	DT
cord-329276-tfrjw743	333	14	controls	control	NNS
cord-329276-tfrjw743	333	15	seems	seem	VBZ
cord-329276-tfrjw743	333	16	to	to	TO
cord-329276-tfrjw743	333	17	be	be	VB
cord-329276-tfrjw743	333	18	more	more	RBR
cord-329276-tfrjw743	333	19	adequate	adequate	JJ
cord-329276-tfrjw743	333	20	.	.	.
cord-329276-tfrjw743	334	1	Mathematically	mathematically	RB
cord-329276-tfrjw743	334	2	,	,	,
cord-329276-tfrjw743	334	3	however	however	RB
cord-329276-tfrjw743	334	4	,	,	,
cord-329276-tfrjw743	334	5	there	there	EX
cord-329276-tfrjw743	334	6	are	be	VBP
cord-329276-tfrjw743	334	7	close	close	JJ
cord-329276-tfrjw743	334	8	relations	relation	NNS
cord-329276-tfrjw743	334	9	between	between	IN
cord-329276-tfrjw743	334	10	the	the	DT
cord-329276-tfrjw743	334	11	necessary	necessary	JJ
cord-329276-tfrjw743	334	12	conditions	condition	NNS
cord-329276-tfrjw743	334	13	for	for	IN
cord-329276-tfrjw743	334	14	optimality	optimality	NN
cord-329276-tfrjw743	334	15	for	for	IN
cord-329276-tfrjw743	334	16	both	both	DT
cord-329276-tfrjw743	334	17	formulations	formulation	NNS
cord-329276-tfrjw743	334	18	(	(	-LRB-
cord-329276-tfrjw743	334	19	either	either	CC
cord-329276-tfrjw743	334	20	as	as	IN
cord-329276-tfrjw743	334	21	a	a	DT
cord-329276-tfrjw743	334	22	soft	soft	JJ
cord-329276-tfrjw743	334	23	or	or	CC
cord-329276-tfrjw743	334	24	hard	hard	JJ
cord-329276-tfrjw743	334	25	constraint	constraint	NN
cord-329276-tfrjw743	334	26	)	)	-RRB-
cord-329276-tfrjw743	334	27	and	and	CC
cord-329276-tfrjw743	334	28	it	-PRON-	PRP
cord-329276-tfrjw743	334	29	makes	make	VBZ
cord-329276-tfrjw743	334	30	little	little	JJ
cord-329276-tfrjw743	334	31	difference	difference	NN
cord-329276-tfrjw743	334	32	if	if	IN
cord-329276-tfrjw743	334	33	one	one	CD
cord-329276-tfrjw743	334	34	or	or	CC
cord-329276-tfrjw743	334	35	the	the	DT
cord-329276-tfrjw743	334	36	other	other	JJ
cord-329276-tfrjw743	334	37	formulation	formulation	NN
cord-329276-tfrjw743	334	38	is	be	VBZ
cord-329276-tfrjw743	334	39	chosen	choose	VBN
cord-329276-tfrjw743	334	40	.	.	.
cord-329276-tfrjw743	335	1	The	the	DT
cord-329276-tfrjw743	335	2	Lagrangian	Lagrangian	NNP
cord-329276-tfrjw743	335	3	L	L	NNP
cord-329276-tfrjw743	335	4	and	and	CC
cord-329276-tfrjw743	335	5	the	the	DT
cord-329276-tfrjw743	335	6	penalty	penalty	NN
cord-329276-tfrjw743	335	7	term	term	NN
cord-329276-tfrjw743	335	8	ϕ	ϕ	RB
cord-329276-tfrjw743	335	9	allow	allow	VB
cord-329276-tfrjw743	335	10	to	to	TO
cord-329276-tfrjw743	335	11	judge	judge	VB
cord-329276-tfrjw743	335	12	the	the	DT
cord-329276-tfrjw743	335	13	impact	impact	NN
cord-329276-tfrjw743	335	14	of	of	IN
cord-329276-tfrjw743	335	15	the	the	DT
cord-329276-tfrjw743	335	16	therapy	therapy	NN
cord-329276-tfrjw743	335	17	on	on	IN
cord-329276-tfrjw743	335	18	the	the	DT
cord-329276-tfrjw743	335	19	state	state	NN
cord-329276-tfrjw743	335	20	.	.	.
cord-329276-tfrjw743	336	1	Including	include	VBG
cord-329276-tfrjw743	336	2	the	the	DT
cord-329276-tfrjw743	336	3	Lagrangian	Lagrangian	NNP
cord-329276-tfrjw743	336	4	L	L	NNP
cord-329276-tfrjw743	336	5	in	in	IN
cord-329276-tfrjw743	336	6	the	the	DT
cord-329276-tfrjw743	336	7	objective	objective	NN
cord-329276-tfrjw743	336	8	can	can	MD
cord-329276-tfrjw743	336	9	also	also	RB
cord-329276-tfrjw743	336	10	be	be	VB
cord-329276-tfrjw743	336	11	viewed	view	VBN
cord-329276-tfrjw743	336	12	as	as	IN
cord-329276-tfrjw743	336	13	incorporating	incorporate	VBG
cord-329276-tfrjw743	336	14	a	a	DT
cord-329276-tfrjw743	336	15	soft	soft	JJ
cord-329276-tfrjw743	336	16	constraint	constraint	NN
cord-329276-tfrjw743	336	17	on	on	IN
cord-329276-tfrjw743	336	18	the	the	DT
cord-329276-tfrjw743	336	19	state	state	NN
cord-329276-tfrjw743	336	20	.	.	.
cord-329276-tfrjw743	337	1	For	for	IN
cord-329276-tfrjw743	337	2	example	example	NN
cord-329276-tfrjw743	337	3	,	,	,
cord-329276-tfrjw743	337	4	in	in	IN
cord-329276-tfrjw743	337	5	cancer	cancer	NN
cord-329276-tfrjw743	337	6	therapies	therapy	NNS
cord-329276-tfrjw743	337	7	,	,	,
cord-329276-tfrjw743	337	8	it	-PRON-	PRP
cord-329276-tfrjw743	337	9	is	be	VBZ
cord-329276-tfrjw743	337	10	clearly	clearly	RB
cord-329276-tfrjw743	337	11	important	important	JJ
cord-329276-tfrjw743	337	12	to	to	TO
cord-329276-tfrjw743	337	13	limit	limit	VB
cord-329276-tfrjw743	337	14	the	the	DT
cord-329276-tfrjw743	337	15	size	size	NN
cord-329276-tfrjw743	337	16	of	of	IN
cord-329276-tfrjw743	337	17	the	the	DT
cord-329276-tfrjw743	337	18	tumor	tumor	NN
cord-329276-tfrjw743	337	19	,	,	,
cord-329276-tfrjw743	337	20	or	or	CC
cord-329276-tfrjw743	337	21	,	,	,
cord-329276-tfrjw743	337	22	in	in	IN
cord-329276-tfrjw743	337	23	another	another	DT
cord-329276-tfrjw743	337	24	indirect	indirect	JJ
cord-329276-tfrjw743	337	25	measurement	measurement	NN
cord-329276-tfrjw743	337	26	of	of	IN
cord-329276-tfrjw743	337	27	the	the	DT
cord-329276-tfrjw743	337	28	side	side	NN
cord-329276-tfrjw743	337	29	effects	effect	NNS
cord-329276-tfrjw743	337	30	,	,	,
cord-329276-tfrjw743	337	31	prevent	prevent	VBP
cord-329276-tfrjw743	337	32	that	that	IN
cord-329276-tfrjw743	337	33	the	the	DT
cord-329276-tfrjw743	337	34	level	level	NN
cord-329276-tfrjw743	337	35	of	of	IN
cord-329276-tfrjw743	337	36	the	the	DT
cord-329276-tfrjw743	337	37	bone	bone	NN
cord-329276-tfrjw743	337	38	marrow	marrow	NN
cord-329276-tfrjw743	337	39	becomes	become	VBZ
cord-329276-tfrjw743	337	40	too	too	RB
cord-329276-tfrjw743	337	41	small	small	JJ
cord-329276-tfrjw743	337	42	.	.	.
cord-329276-tfrjw743	338	1	Clearly	clearly	RB
cord-329276-tfrjw743	338	2	,	,	,
cord-329276-tfrjw743	338	3	such	such	JJ
cord-329276-tfrjw743	338	4	restrictions	restriction	NNS
cord-329276-tfrjw743	338	5	could	could	MD
cord-329276-tfrjw743	338	6	be	be	VB
cord-329276-tfrjw743	338	7	modeled	model	VBN
cord-329276-tfrjw743	338	8	as	as	IN
cord-329276-tfrjw743	338	9	state	state	NN
cord-329276-tfrjw743	338	10	-	-	HYPH
cord-329276-tfrjw743	338	11	space	space	NN
cord-329276-tfrjw743	338	12	constraints	constraint	NNS
cord-329276-tfrjw743	338	13	imposing	impose	VBG
cord-329276-tfrjw743	338	14	upper	upper	JJ
cord-329276-tfrjw743	338	15	or	or	CC
cord-329276-tfrjw743	338	16	lower	low	JJR
cord-329276-tfrjw743	338	17	bounds	bound	NNS
cord-329276-tfrjw743	338	18	on	on	IN
cord-329276-tfrjw743	338	19	some	some	DT
cord-329276-tfrjw743	338	20	of	of	IN
cord-329276-tfrjw743	338	21	the	the	DT
cord-329276-tfrjw743	338	22	variables	variable	NNS
cord-329276-tfrjw743	338	23	.	.	.
cord-329276-tfrjw743	339	1	For	for	IN
cord-329276-tfrjw743	339	2	example	example	NN
cord-329276-tfrjw743	339	3	,	,	,
cord-329276-tfrjw743	339	4	in	in	IN
cord-329276-tfrjw743	339	5	[	[	-LRB-
cord-329276-tfrjw743	339	6	38	38	CD
cord-329276-tfrjw743	339	7	]	]	-RRB-
cord-329276-tfrjw743	339	8	an	an	DT
cord-329276-tfrjw743	339	9	explicit	explicit	JJ
cord-329276-tfrjw743	339	10	upper	upper	NN
cord-329276-tfrjw743	339	11	bound	bind	VBN
cord-329276-tfrjw743	339	12	in	in	IN
cord-329276-tfrjw743	339	13	the	the	DT
cord-329276-tfrjw743	339	14	form	form	NN
cord-329276-tfrjw743	339	15	Fig	Fig	NNP
cord-329276-tfrjw743	339	16	.	.	.
cord-329276-tfrjw743	339	17	4	4	CD
cord-329276-tfrjw743	339	18	Examples	example	NNS
cord-329276-tfrjw743	339	19	of	of	IN
cord-329276-tfrjw743	339	20	locally	locally	RB
cord-329276-tfrjw743	339	21	optimal	optimal	JJ
cord-329276-tfrjw743	339	22	controls	control	NNS
cord-329276-tfrjw743	339	23	(	(	-LRB-
cord-329276-tfrjw743	339	24	left	left	RB
cord-329276-tfrjw743	339	25	)	)	-RRB-
cord-329276-tfrjw743	339	26	and	and	CC
cord-329276-tfrjw743	339	27	their	-PRON-	PRP$
cord-329276-tfrjw743	339	28	corresponding	correspond	VBG
cord-329276-tfrjw743	339	29	trajectories	trajectory	NNS
cord-329276-tfrjw743	339	30	(	(	-LRB-
cord-329276-tfrjw743	339	31	right	right	RB
cord-329276-tfrjw743	339	32	)	)	-RRB-
cord-329276-tfrjw743	339	33	for	for	IN
cord-329276-tfrjw743	339	34	a	a	DT
cord-329276-tfrjw743	339	35	cellcycle	cellcycle	NNP
cord-329276-tfrjw743	339	36	specific	specific	JJ
cord-329276-tfrjw743	339	37	2-compartment	2-compartment	CD
cord-329276-tfrjw743	339	38	model	model	NN
cord-329276-tfrjw743	339	39	for	for	IN
cord-329276-tfrjw743	339	40	cancer	cancer	NN
cord-329276-tfrjw743	339	41	therapy	therapy	NN
cord-329276-tfrjw743	339	42	over	over	IN
cord-329276-tfrjw743	339	43	a	a	DT
cord-329276-tfrjw743	339	44	fixed	fix	VBN
cord-329276-tfrjw743	339	45	therapy	therapy	NN
cord-329276-tfrjw743	339	46	horizon	horizon	NN
cord-329276-tfrjw743	339	47	(	(	-LRB-
cord-329276-tfrjw743	339	48	T	T	NNP
cord-329276-tfrjw743	339	49	=	=	SYM
cord-329276-tfrjw743	339	50	21	21	CD
cord-329276-tfrjw743	339	51	days	day	NNS
cord-329276-tfrjw743	339	52	)	)	-RRB-
cord-329276-tfrjw743	339	53	with	with	IN
cord-329276-tfrjw743	339	54	Lagrangian	lagrangian	JJ
cord-329276-tfrjw743	339	55	term	term	NN
cord-329276-tfrjw743	339	56	L	l	NN
cord-329276-tfrjw743	339	57	in	in	IN
cord-329276-tfrjw743	339	58	the	the	DT
cord-329276-tfrjw743	339	59	objective	objective	NN
cord-329276-tfrjw743	339	60	(	(	-LRB-
cord-329276-tfrjw743	339	61	top	top	JJ
cord-329276-tfrjw743	339	62	row	row	NN
cord-329276-tfrjw743	339	63	,	,	,
cord-329276-tfrjw743	339	64	q	q	NN
cord-329276-tfrjw743	339	65	=	=	NN
cord-329276-tfrjw743	339	66	0.1	0.1	CD
cord-329276-tfrjw743	339	67	)	)	-RRB-
cord-329276-tfrjw743	339	68	and	and	CC
cord-329276-tfrjw743	339	69	without	without	IN
cord-329276-tfrjw743	339	70	Lagrangian	lagrangian	JJ
cord-329276-tfrjw743	339	71	term	term	NN
cord-329276-tfrjw743	339	72	in	in	IN
cord-329276-tfrjw743	339	73	the	the	DT
cord-329276-tfrjw743	339	74	objective	objective	JJ
cord-329276-tfrjw743	339	75	(	(	-LRB-
cord-329276-tfrjw743	339	76	bottom	bottom	NN
cord-329276-tfrjw743	339	77	row	row	NN
cord-329276-tfrjw743	339	78	,	,	,
cord-329276-tfrjw743	339	79	q	q	NN
cord-329276-tfrjw743	339	80	=	=	SYM
cord-329276-tfrjw743	339	81	0	0	CD
cord-329276-tfrjw743	339	82	)	)	-RRB-
cord-329276-tfrjw743	339	83	.	.	.
cord-329276-tfrjw743	340	1	The	the	DT
cord-329276-tfrjw743	340	2	initial	initial	JJ
cord-329276-tfrjw743	340	3	condition	condition	NN
cord-329276-tfrjw743	340	4	is	be	VBZ
cord-329276-tfrjw743	340	5	the	the	DT
cord-329276-tfrjw743	340	6	normalized	normalized	JJ
cord-329276-tfrjw743	340	7	value	value	NN
cord-329276-tfrjw743	340	8	of	of	IN
cord-329276-tfrjw743	340	9	the	the	DT
cord-329276-tfrjw743	340	10	steady	steady	JJ
cord-329276-tfrjw743	340	11	-	-	HYPH
cord-329276-tfrjw743	340	12	state	state	NN
cord-329276-tfrjw743	340	13	solution	solution	NN
cord-329276-tfrjw743	340	14	for	for	IN
cord-329276-tfrjw743	340	15	the	the	DT
cord-329276-tfrjw743	340	16	uncontrolled	uncontrolled	JJ
cord-329276-tfrjw743	340	17	system	system	NN
cord-329276-tfrjw743	340	18	is	be	VBZ
cord-329276-tfrjw743	340	19	imposed	impose	VBN
cord-329276-tfrjw743	340	20	on	on	IN
cord-329276-tfrjw743	340	21	the	the	DT
cord-329276-tfrjw743	340	22	total	total	JJ
cord-329276-tfrjw743	340	23	number	number	NN
cord-329276-tfrjw743	340	24	of	of	IN
cord-329276-tfrjw743	340	25	cancer	cancer	NN
cord-329276-tfrjw743	340	26	cells	cell	NNS
cord-329276-tfrjw743	340	27	N	n	CD
cord-329276-tfrjw743	340	28	(	(	-LRB-
cord-329276-tfrjw743	340	29	t	t	NN
cord-329276-tfrjw743	340	30	)	)	-RRB-
cord-329276-tfrjw743	340	31	in	in	IN
cord-329276-tfrjw743	340	32	a	a	DT
cord-329276-tfrjw743	340	33	cell	cell	NN
cord-329276-tfrjw743	340	34	-	-	HYPH
cord-329276-tfrjw743	340	35	cycle	cycle	NN
cord-329276-tfrjw743	340	36	specific	specific	JJ
cord-329276-tfrjw743	340	37	model	model	NN
cord-329276-tfrjw743	340	38	for	for	IN
cord-329276-tfrjw743	340	39	cancer	cancer	NN
cord-329276-tfrjw743	340	40	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	340	41	.	.	.
cord-329276-tfrjw743	341	1	Here	here	RB
cord-329276-tfrjw743	341	2	,	,	,
cord-329276-tfrjw743	341	3	however	however	RB
cord-329276-tfrjw743	341	4	,	,	,
cord-329276-tfrjw743	341	5	a	a	DT
cord-329276-tfrjw743	341	6	modeling	modeling	NN
cord-329276-tfrjw743	341	7	approach	approach	NN
cord-329276-tfrjw743	341	8	of	of	IN
cord-329276-tfrjw743	341	9	using	use	VBG
cord-329276-tfrjw743	341	10	soft	soft	JJ
cord-329276-tfrjw743	341	11	constraints	constraint	NNS
cord-329276-tfrjw743	341	12	is	be	VBZ
cord-329276-tfrjw743	341	13	preferred	prefer	VBN
cord-329276-tfrjw743	341	14	as	as	IN
cord-329276-tfrjw743	341	15	the	the	DT
cord-329276-tfrjw743	341	16	necessary	necessary	JJ
cord-329276-tfrjw743	341	17	conditions	condition	NNS
cord-329276-tfrjw743	341	18	for	for	IN
cord-329276-tfrjw743	341	19	optimality	optimality	NN
cord-329276-tfrjw743	341	20	become	become	VBP
cord-329276-tfrjw743	341	21	more	more	RBR
cord-329276-tfrjw743	341	22	involved	involved	JJ
cord-329276-tfrjw743	341	23	if	if	IN
cord-329276-tfrjw743	341	24	statespace	statespace	NN
cord-329276-tfrjw743	341	25	constraints	constraint	NNS
cord-329276-tfrjw743	341	26	are	be	VBP
cord-329276-tfrjw743	341	27	present	present	JJ
cord-329276-tfrjw743	341	28	.	.	.
cord-329276-tfrjw743	342	1	If	if	IN
cord-329276-tfrjw743	342	2	explicit	explicit	JJ
cord-329276-tfrjw743	342	3	state	state	NN
cord-329276-tfrjw743	342	4	-	-	HYPH
cord-329276-tfrjw743	342	5	space	space	NN
cord-329276-tfrjw743	342	6	constraints	constraint	NNS
cord-329276-tfrjw743	342	7	are	be	VBP
cord-329276-tfrjw743	342	8	included	include	VBN
cord-329276-tfrjw743	342	9	in	in	IN
cord-329276-tfrjw743	342	10	the	the	DT
cord-329276-tfrjw743	342	11	modeling	modeling	NN
cord-329276-tfrjw743	342	12	,	,	,
cord-329276-tfrjw743	342	13	then	then	RB
cord-329276-tfrjw743	342	14	,	,	,
cord-329276-tfrjw743	342	15	a	a	FW
cord-329276-tfrjw743	342	16	priori	priori	FW
cord-329276-tfrjw743	342	17	,	,	,
cord-329276-tfrjw743	342	18	the	the	DT
cord-329276-tfrjw743	342	19	associated	associated	JJ
cord-329276-tfrjw743	342	20	multiplier	multiplier	NN
cord-329276-tfrjw743	342	21	is	be	VBZ
cord-329276-tfrjw743	342	22	only	only	RB
cord-329276-tfrjw743	342	23	known	know	VBN
cord-329276-tfrjw743	342	24	to	to	TO
cord-329276-tfrjw743	342	25	be	be	VB
cord-329276-tfrjw743	342	26	a	a	DT
cord-329276-tfrjw743	342	27	positive	positive	JJ
cord-329276-tfrjw743	342	28	Radon	radon	NN
cord-329276-tfrjw743	342	29	-	-	HYPH
cord-329276-tfrjw743	342	30	measure	measure	NN
cord-329276-tfrjw743	342	31	.	.	.
cord-329276-tfrjw743	343	1	Although	although	IN
cord-329276-tfrjw743	343	2	it	-PRON-	PRP
cord-329276-tfrjw743	343	3	can	can	MD
cord-329276-tfrjw743	343	4	be	be	VB
cord-329276-tfrjw743	343	5	shown	show	VBN
cord-329276-tfrjw743	343	6	that	that	IN
cord-329276-tfrjw743	343	7	this	this	DT
cord-329276-tfrjw743	343	8	measure	measure	NN
cord-329276-tfrjw743	343	9	is	be	VBZ
cord-329276-tfrjw743	343	10	absolutely	absolutely	RB
cord-329276-tfrjw743	343	11	continuous	continuous	JJ
cord-329276-tfrjw743	343	12	with	with	IN
cord-329276-tfrjw743	343	13	respect	respect	NN
cord-329276-tfrjw743	343	14	to	to	IN
cord-329276-tfrjw743	343	15	Lebesgue	Lebesgue	NNP
cord-329276-tfrjw743	343	16	measure	measure	NN
cord-329276-tfrjw743	343	17	if	if	IN
cord-329276-tfrjw743	343	18	the	the	DT
cord-329276-tfrjw743	343	19	constraint	constraint	NN
cord-329276-tfrjw743	343	20	is	be	VBZ
cord-329276-tfrjw743	343	21	an	an	DT
cord-329276-tfrjw743	343	22	embedded	embedded	JJ
cord-329276-tfrjw743	343	23	hypersurface	hypersurface	NN
cord-329276-tfrjw743	343	24	(	(	-LRB-
cord-329276-tfrjw743	343	25	e.g.	e.g.	RB
cord-329276-tfrjw743	343	26	,	,	,
cord-329276-tfrjw743	343	27	see	see	VB
cord-329276-tfrjw743	343	28	[	[	-LRB-
cord-329276-tfrjw743	343	29	39	39	CD
cord-329276-tfrjw743	343	30	]	]	-RRB-
cord-329276-tfrjw743	343	31	)	)	-RRB-
cord-329276-tfrjw743	343	32	,	,	,
cord-329276-tfrjw743	343	33	the	the	DT
cord-329276-tfrjw743	343	34	effort	effort	NN
cord-329276-tfrjw743	343	35	of	of	IN
cord-329276-tfrjw743	343	36	dealing	deal	VBG
cord-329276-tfrjw743	343	37	with	with	IN
cord-329276-tfrjw743	343	38	a	a	DT
cord-329276-tfrjw743	343	39	state	state	NN
cord-329276-tfrjw743	343	40	-	-	HYPH
cord-329276-tfrjw743	343	41	space	space	NN
cord-329276-tfrjw743	343	42	constraint	constraint	NN
cord-329276-tfrjw743	343	43	is	be	VBZ
cord-329276-tfrjw743	343	44	much	much	RB
cord-329276-tfrjw743	343	45	more	more	RBR
cord-329276-tfrjw743	343	46	involved	involved	JJ
cord-329276-tfrjw743	343	47	than	than	IN
cord-329276-tfrjw743	343	48	having	have	VBG
cord-329276-tfrjw743	343	49	a	a	DT
cord-329276-tfrjw743	343	50	Lagrangian	lagrangian	JJ
cord-329276-tfrjw743	343	51	present	present	NN
cord-329276-tfrjw743	343	52	in	in	IN
cord-329276-tfrjw743	343	53	the	the	DT
cord-329276-tfrjw743	343	54	objective	objective	NN
cord-329276-tfrjw743	343	55	.	.	.
cord-329276-tfrjw743	344	1	A	a	DT
cord-329276-tfrjw743	344	2	common	common	JJ
cord-329276-tfrjw743	344	3	pitfall	pitfall	NN
cord-329276-tfrjw743	344	4	in	in	IN
cord-329276-tfrjw743	344	5	the	the	DT
cord-329276-tfrjw743	344	6	modeling	modeling	NN
cord-329276-tfrjw743	344	7	is	be	VBZ
cord-329276-tfrjw743	344	8	not	not	RB
cord-329276-tfrjw743	344	9	to	to	TO
cord-329276-tfrjw743	344	10	include	include	VB
cord-329276-tfrjw743	344	11	such	such	PDT
cord-329276-tfrjw743	344	12	a	a	DT
cord-329276-tfrjw743	344	13	term	term	NN
cord-329276-tfrjw743	344	14	.	.	.
cord-329276-tfrjw743	345	1	Then	then	RB
cord-329276-tfrjw743	345	2	,	,	,
cord-329276-tfrjw743	345	3	naturally	naturally	RB
cord-329276-tfrjw743	345	4	,	,	,
cord-329276-tfrjw743	345	5	the	the	DT
cord-329276-tfrjw743	345	6	emphasis	emphasis	NN
cord-329276-tfrjw743	345	7	of	of	IN
cord-329276-tfrjw743	345	8	the	the	DT
cord-329276-tfrjw743	345	9	minimization	minimization	NN
cord-329276-tfrjw743	345	10	is	be	VBZ
cord-329276-tfrjw743	345	11	put	put	VBN
cord-329276-tfrjw743	345	12	on	on	IN
cord-329276-tfrjw743	345	13	the	the	DT
cord-329276-tfrjw743	345	14	terminal	terminal	JJ
cord-329276-tfrjw743	345	15	time	time	NN
cord-329276-tfrjw743	345	16	and	and	CC
cord-329276-tfrjw743	345	17	quite	quite	RB
cord-329276-tfrjw743	345	18	often	often	RB
cord-329276-tfrjw743	345	19	control	control	NN
cord-329276-tfrjw743	345	20	actions	action	NNS
cord-329276-tfrjw743	345	21	will	will	MD
cord-329276-tfrjw743	345	22	be	be	VB
cord-329276-tfrjw743	345	23	delayed	delay	VBN
cord-329276-tfrjw743	345	24	initially	initially	RB
cord-329276-tfrjw743	345	25	and	and	CC
cord-329276-tfrjw743	345	26	be	be	VB
cord-329276-tfrjw743	345	27	concentrated	concentrate	VBN
cord-329276-tfrjw743	345	28	near	near	IN
cord-329276-tfrjw743	345	29	the	the	DT
cord-329276-tfrjw743	345	30	terminal	terminal	JJ
cord-329276-tfrjw743	345	31	time	time	NN
cord-329276-tfrjw743	345	32	.	.	.
cord-329276-tfrjw743	346	1	Once	once	RB
cord-329276-tfrjw743	346	2	again	again	RB
cord-329276-tfrjw743	346	3	,	,	,
cord-329276-tfrjw743	346	4	however	however	RB
cord-329276-tfrjw743	346	5	,	,	,
cord-329276-tfrjw743	346	6	this	this	DT
cord-329276-tfrjw743	346	7	is	be	VBZ
cord-329276-tfrjw743	346	8	then	then	RB
cord-329276-tfrjw743	346	9	not	not	RB
cord-329276-tfrjw743	346	10	a	a	DT
cord-329276-tfrjw743	346	11	feature	feature	NN
cord-329276-tfrjw743	346	12	of	of	IN
cord-329276-tfrjw743	346	13	the	the	DT
cord-329276-tfrjw743	346	14	underlying	underlying	JJ
cord-329276-tfrjw743	346	15	problem	problem	NN
cord-329276-tfrjw743	346	16	,	,	,
cord-329276-tfrjw743	346	17	but	but	CC
cord-329276-tfrjw743	346	18	it	-PRON-	PRP
cord-329276-tfrjw743	346	19	has	have	VBZ
cord-329276-tfrjw743	346	20	been	be	VBN
cord-329276-tfrjw743	346	21	imposed	impose	VBN
cord-329276-tfrjw743	346	22	,	,	,
cord-329276-tfrjw743	346	23	possibly	possibly	RB
cord-329276-tfrjw743	346	24	unwillingly	unwillingly	RB
cord-329276-tfrjw743	346	25	,	,	,
cord-329276-tfrjw743	346	26	by	by	IN
cord-329276-tfrjw743	346	27	the	the	DT
cord-329276-tfrjw743	346	28	particular	particular	JJ
cord-329276-tfrjw743	346	29	form	form	NN
cord-329276-tfrjw743	346	30	of	of	IN
cord-329276-tfrjw743	346	31	the	the	DT
cord-329276-tfrjw743	346	32	objective	objective	NN
cord-329276-tfrjw743	346	33	that	that	WDT
cord-329276-tfrjw743	346	34	was	be	VBD
cord-329276-tfrjw743	346	35	chosen	choose	VBN
cord-329276-tfrjw743	346	36	.	.	.
cord-329276-tfrjw743	347	1	Figure	figure	NN
cord-329276-tfrjw743	347	2	4	4	CD
cord-329276-tfrjw743	347	3	illustrates	illustrate	VBZ
cord-329276-tfrjw743	347	4	this	this	DT
cord-329276-tfrjw743	347	5	feature	feature	NN
cord-329276-tfrjw743	347	6	by	by	IN
cord-329276-tfrjw743	347	7	comparing	compare	VBG
cord-329276-tfrjw743	347	8	the	the	DT
cord-329276-tfrjw743	347	9	optimal	optimal	JJ
cord-329276-tfrjw743	347	10	solutions	solution	NNS
cord-329276-tfrjw743	347	11	for	for	IN
cord-329276-tfrjw743	347	12	a	a	DT
cord-329276-tfrjw743	347	13	2-compartment	2-compartment	CD
cord-329276-tfrjw743	347	14	cell	cell	NN
cord-329276-tfrjw743	347	15	-	-	HYPH
cord-329276-tfrjw743	347	16	cycle	cycle	NN
cord-329276-tfrjw743	347	17	specific	specific	JJ
cord-329276-tfrjw743	347	18	model	model	NN
cord-329276-tfrjw743	347	19	for	for	IN
cord-329276-tfrjw743	347	20	cancer	cancer	NN
cord-329276-tfrjw743	347	21	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	347	22	[	[	-LRB-
cord-329276-tfrjw743	347	23	8	8	CD
cord-329276-tfrjw743	347	24	,	,	,
cord-329276-tfrjw743	347	25	10	10	CD
cord-329276-tfrjw743	347	26	,	,	,
cord-329276-tfrjw743	347	27	15	15	CD
cord-329276-tfrjw743	347	28	]	]	-RRB-
cord-329276-tfrjw743	347	29	.	.	.
cord-329276-tfrjw743	348	1	The	the	DT
cord-329276-tfrjw743	348	2	two	two	CD
cord-329276-tfrjw743	348	3	compartments	compartment	NNS
cord-329276-tfrjw743	348	4	represent	represent	VBP
cord-329276-tfrjw743	348	5	the	the	DT
cord-329276-tfrjw743	348	6	clustered	clustered	JJ
cord-329276-tfrjw743	348	7	phase	phase	NN
cord-329276-tfrjw743	348	8	N	n	CD
cord-329276-tfrjw743	348	9	1	1	CD
cord-329276-tfrjw743	348	10	∼	∼	NN
cord-329276-tfrjw743	348	11	G	g	NN
cord-329276-tfrjw743	348	12	1	1	CD
cord-329276-tfrjw743	348	13	/G	/g	SYM
cord-329276-tfrjw743	348	14	0	0	CD
cord-329276-tfrjw743	348	15	+	+	CD
cord-329276-tfrjw743	349	1	S	S	NNP
cord-329276-tfrjw743	349	2	and	and	CC
cord-329276-tfrjw743	349	3	N	n	CD
cord-329276-tfrjw743	349	4	2	2	CD
cord-329276-tfrjw743	349	5	∼	∼	NN
cord-329276-tfrjw743	349	6	G	g	NN
cord-329276-tfrjw743	349	7	2	2	CD
cord-329276-tfrjw743	349	8	/M	/M	:
cord-329276-tfrjw743	349	9	of	of	IN
cord-329276-tfrjw743	349	10	the	the	DT
cord-329276-tfrjw743	349	11	cell	cell	NN
cord-329276-tfrjw743	349	12	cycle	cycle	NN
cord-329276-tfrjw743	349	13	and	and	CC
cord-329276-tfrjw743	349	14	the	the	DT
cord-329276-tfrjw743	349	15	drug	drug	NN
cord-329276-tfrjw743	349	16	is	be	VBZ
cord-329276-tfrjw743	349	17	a	a	DT
cord-329276-tfrjw743	349	18	G	g	NN
cord-329276-tfrjw743	349	19	2	2	CD
cord-329276-tfrjw743	349	20	/M	/M	.
cord-329276-tfrjw743	349	21	-	-	HYPH
cord-329276-tfrjw743	349	22	specific	specific	JJ
cord-329276-tfrjw743	349	23	cytotoxic	cytotoxic	JJ
cord-329276-tfrjw743	349	24	agent	agent	NN
cord-329276-tfrjw743	349	25	.	.	.
cord-329276-tfrjw743	350	1	The	the	DT
cord-329276-tfrjw743	350	2	objective	objective	NN
cord-329276-tfrjw743	350	3	was	be	VBD
cord-329276-tfrjw743	350	4	chosen	choose	VBN
cord-329276-tfrjw743	350	5	in	in	IN
cord-329276-tfrjw743	350	6	the	the	DT
cord-329276-tfrjw743	350	7	form	form	NN
cord-329276-tfrjw743	350	8	for	for	IN
cord-329276-tfrjw743	350	9	q	q	NN
cord-329276-tfrjw743	350	10	=	=	NN
cord-329276-tfrjw743	350	11	0.1	0.1	CD
cord-329276-tfrjw743	351	1	and	and	CC
cord-329276-tfrjw743	351	2	q	q	NNP
cord-329276-tfrjw743	351	3	=	=	SYM
cord-329276-tfrjw743	351	4	0	0	NFP
cord-329276-tfrjw743	351	5	over	over	IN
cord-329276-tfrjw743	351	6	a	a	DT
cord-329276-tfrjw743	351	7	fixed	fix	VBN
cord-329276-tfrjw743	351	8	3	3	CD
cord-329276-tfrjw743	351	9	week	week	NN
cord-329276-tfrjw743	351	10	therapy	therapy	NN
cord-329276-tfrjw743	351	11	period	period	NN
cord-329276-tfrjw743	351	12	.	.	.
cord-329276-tfrjw743	352	1	Optimal	optimal	JJ
cord-329276-tfrjw743	352	2	controls	control	NNS
cord-329276-tfrjw743	352	3	are	be	VBP
cord-329276-tfrjw743	352	4	bangbang	bangbang	JJ
cord-329276-tfrjw743	352	5	with	with	IN
cord-329276-tfrjw743	352	6	one	one	CD
cord-329276-tfrjw743	352	7	switching	switching	NN
cord-329276-tfrjw743	352	8	.	.	.
cord-329276-tfrjw743	353	1	If	if	IN
cord-329276-tfrjw743	353	2	only	only	RB
cord-329276-tfrjw743	353	3	a	a	DT
cord-329276-tfrjw743	353	4	penalty	penalty	NN
cord-329276-tfrjw743	353	5	term	term	NN
cord-329276-tfrjw743	353	6	is	be	VBZ
cord-329276-tfrjw743	353	7	used	use	VBN
cord-329276-tfrjw743	353	8	,	,	,
cord-329276-tfrjw743	353	9	then	then	RB
cord-329276-tfrjw743	353	10	the	the	DT
cord-329276-tfrjw743	353	11	drug	drug	NN
cord-329276-tfrjw743	353	12	administration	administration	NN
cord-329276-tfrjw743	353	13	is	be	VBZ
cord-329276-tfrjw743	353	14	all	all	DT
cord-329276-tfrjw743	353	15	put	put	VBN
cord-329276-tfrjw743	353	16	to	to	IN
cord-329276-tfrjw743	353	17	the	the	DT
cord-329276-tfrjw743	353	18	end	end	NN
cord-329276-tfrjw743	353	19	of	of	IN
cord-329276-tfrjw743	353	20	therapy	therapy	NN
cord-329276-tfrjw743	353	21	with	with	IN
cord-329276-tfrjw743	353	22	an	an	DT
cord-329276-tfrjw743	353	23	unacceptable	unacceptable	JJ
cord-329276-tfrjw743	353	24	spike	spike	NN
cord-329276-tfrjw743	353	25	in	in	IN
cord-329276-tfrjw743	353	26	the	the	DT
cord-329276-tfrjw743	353	27	tumor	tumor	NN
cord-329276-tfrjw743	353	28	cells	cell	NNS
cord-329276-tfrjw743	353	29	in	in	IN
cord-329276-tfrjw743	353	30	between	between	IN
cord-329276-tfrjw743	353	31	.	.	.
cord-329276-tfrjw743	354	1	The	the	DT
cord-329276-tfrjw743	354	2	choice	choice	NN
cord-329276-tfrjw743	354	3	of	of	IN
cord-329276-tfrjw743	354	4	the	the	DT
cord-329276-tfrjw743	354	5	objective	objective	NN
cord-329276-tfrjw743	354	6	is	be	VBZ
cord-329276-tfrjw743	354	7	often	often	RB
cord-329276-tfrjw743	354	8	made	make	VBN
cord-329276-tfrjw743	354	9	in	in	IN
cord-329276-tfrjw743	354	10	an	an	DT
cord-329276-tfrjw743	354	11	heuristic	heuristic	JJ
cord-329276-tfrjw743	354	12	ad	ad	FW
cord-329276-tfrjw743	354	13	hoc	hoc	FW
cord-329276-tfrjw743	354	14	manner	manner	NN
cord-329276-tfrjw743	354	15	.	.	.
cord-329276-tfrjw743	355	1	Sometimes	sometimes	RB
cord-329276-tfrjw743	355	2	,	,	,
cord-329276-tfrjw743	355	3	however	however	RB
cord-329276-tfrjw743	355	4	,	,	,
cord-329276-tfrjw743	355	5	the	the	DT
cord-329276-tfrjw743	355	6	underlying	underlie	VBG
cord-329276-tfrjw743	355	7	biology	biology	NN
cord-329276-tfrjw743	355	8	can	can	MD
cord-329276-tfrjw743	355	9	be	be	VB
cord-329276-tfrjw743	355	10	used	use	VBN
cord-329276-tfrjw743	355	11	as	as	IN
cord-329276-tfrjw743	355	12	a	a	DT
cord-329276-tfrjw743	355	13	guide	guide	NN
cord-329276-tfrjw743	355	14	.	.	.
cord-329276-tfrjw743	356	1	Stepanova	Stepanova	NNP
cord-329276-tfrjw743	356	2	's	's	POS
cord-329276-tfrjw743	356	3	model	model	NN
cord-329276-tfrjw743	356	4	provides	provide	VBZ
cord-329276-tfrjw743	356	5	a	a	DT
cord-329276-tfrjw743	356	6	beautiful	beautiful	JJ
cord-329276-tfrjw743	356	7	illustration	illustration	NN
cord-329276-tfrjw743	356	8	how	how	WRB
cord-329276-tfrjw743	356	9	this	this	DT
cord-329276-tfrjw743	356	10	can	can	MD
cord-329276-tfrjw743	356	11	be	be	VB
cord-329276-tfrjw743	356	12	achieved	achieve	VBN
cord-329276-tfrjw743	356	13	.	.	.
cord-329276-tfrjw743	357	1	Assuming	assume	VBG
cord-329276-tfrjw743	357	2	that	that	IN
cord-329276-tfrjw743	357	3	the	the	DT
cord-329276-tfrjw743	357	4	parameter	parameter	NN
cord-329276-tfrjw743	357	5	values	value	NNS
cord-329276-tfrjw743	357	6	are	be	VBP
cord-329276-tfrjw743	357	7	such	such	JJ
cord-329276-tfrjw743	357	8	that	that	IN
cord-329276-tfrjw743	357	9	the	the	DT
cord-329276-tfrjw743	357	10	dynamics	dynamic	NNS
cord-329276-tfrjw743	357	11	is	be	VBZ
cord-329276-tfrjw743	357	12	bi	bi	JJ
cord-329276-tfrjw743	357	13	-	-	JJ
cord-329276-tfrjw743	357	14	stable	stable	JJ
cord-329276-tfrjw743	357	15	with	with	IN
cord-329276-tfrjw743	357	16	a	a	DT
cord-329276-tfrjw743	357	17	benign	benign	JJ
cord-329276-tfrjw743	357	18	and	and	CC
cord-329276-tfrjw743	357	19	a	a	DT
cord-329276-tfrjw743	357	20	malignant	malignant	JJ
cord-329276-tfrjw743	357	21	region	region	NN
cord-329276-tfrjw743	357	22	,	,	,
cord-329276-tfrjw743	357	23	the	the	DT
cord-329276-tfrjw743	357	24	practical	practical	JJ
cord-329276-tfrjw743	357	25	aim	aim	NN
cord-329276-tfrjw743	357	26	of	of	IN
cord-329276-tfrjw743	357	27	therapy	therapy	NN
cord-329276-tfrjw743	357	28	then	then	RB
cord-329276-tfrjw743	357	29	can	can	MD
cord-329276-tfrjw743	357	30	be	be	VB
cord-329276-tfrjw743	357	31	formulated	formulate	VBN
cord-329276-tfrjw743	357	32	as	as	IN
cord-329276-tfrjw743	357	33	moving	move	VBG
cord-329276-tfrjw743	357	34	the	the	DT
cord-329276-tfrjw743	357	35	state	state	NN
cord-329276-tfrjw743	357	36	of	of	IN
cord-329276-tfrjw743	357	37	the	the	DT
cord-329276-tfrjw743	357	38	system	system	NN
cord-329276-tfrjw743	357	39	from	from	IN
cord-329276-tfrjw743	357	40	the	the	DT
cord-329276-tfrjw743	357	41	malignant	malignant	JJ
cord-329276-tfrjw743	357	42	region	region	NN
cord-329276-tfrjw743	357	43	into	into	IN
cord-329276-tfrjw743	357	44	the	the	DT
cord-329276-tfrjw743	357	45	region	region	NN
cord-329276-tfrjw743	357	46	of	of	IN
cord-329276-tfrjw743	357	47	attraction	attraction	NN
cord-329276-tfrjw743	357	48	of	of	IN
cord-329276-tfrjw743	357	49	the	the	DT
cord-329276-tfrjw743	357	50	stable	stable	JJ
cord-329276-tfrjw743	357	51	,	,	,
cord-329276-tfrjw743	357	52	benign	benign	JJ
cord-329276-tfrjw743	357	53	equilibrium	equilibrium	NN
cord-329276-tfrjw743	357	54	point	point	NN
cord-329276-tfrjw743	357	55	while	while	IN
cord-329276-tfrjw743	357	56	keeping	keep	VBG
cord-329276-tfrjw743	357	57	side	side	NN
cord-329276-tfrjw743	357	58	effects	effect	NNS
cord-329276-tfrjw743	357	59	tolerable	tolerable	JJ
cord-329276-tfrjw743	357	60	.	.	.
cord-329276-tfrjw743	358	1	Assuming	assume	VBG
cord-329276-tfrjw743	358	2	the	the	DT
cord-329276-tfrjw743	358	3	controls	control	NNS
cord-329276-tfrjw743	358	4	are	be	VBP
cord-329276-tfrjw743	358	5	a	a	DT
cord-329276-tfrjw743	358	6	strongly	strongly	RB
cord-329276-tfrjw743	358	7	targeted	target	VBN
cord-329276-tfrjw743	358	8	cytotoxic	cytotoxic	JJ
cord-329276-tfrjw743	358	9	agent	agent	NN
cord-329276-tfrjw743	358	10	u	u	NN
cord-329276-tfrjw743	358	11	and	and	CC
cord-329276-tfrjw743	358	12	an	an	DT
cord-329276-tfrjw743	358	13	immuno	immuno	JJ
cord-329276-tfrjw743	358	14	-	-	HYPH
cord-329276-tfrjw743	358	15	stimulatory	stimulatory	JJ
cord-329276-tfrjw743	358	16	agent	agent	NN
cord-329276-tfrjw743	358	17	v	v	NN
cord-329276-tfrjw743	358	18	,	,	,
cord-329276-tfrjw743	358	19	this	this	DT
cord-329276-tfrjw743	358	20	can	can	MD
cord-329276-tfrjw743	358	21	be	be	VB
cord-329276-tfrjw743	358	22	achieved	achieve	VBN
cord-329276-tfrjw743	358	23	using	use	VBG
cord-329276-tfrjw743	358	24	an	an	DT
cord-329276-tfrjw743	358	25	objective	objective	JJ
cord-329276-tfrjw743	358	26	functional	functional	NN
cord-329276-tfrjw743	358	27	of	of	IN
cord-329276-tfrjw743	358	28	the	the	DT
cord-329276-tfrjw743	358	29	following	follow	VBG
cord-329276-tfrjw743	358	30	form	form	NN
cord-329276-tfrjw743	358	31	:	:	:
cord-329276-tfrjw743	358	32	All	all	DT
cord-329276-tfrjw743	358	33	coefficients	coefficient	NNS
cord-329276-tfrjw743	358	34	are	be	VBP
cord-329276-tfrjw743	358	35	positive	positive	JJ
cord-329276-tfrjw743	358	36	and	and	CC
cord-329276-tfrjw743	358	37	the	the	DT
cord-329276-tfrjw743	358	38	choice	choice	NN
cord-329276-tfrjw743	358	39	of	of	IN
cord-329276-tfrjw743	358	40	the	the	DT
cord-329276-tfrjw743	358	41	weights	weight	NNS
cord-329276-tfrjw743	358	42	aims	aim	VBZ
cord-329276-tfrjw743	358	43	at	at	IN
cord-329276-tfrjw743	358	44	striking	strike	VBG
cord-329276-tfrjw743	358	45	a	a	DT
cord-329276-tfrjw743	358	46	balance	balance	NN
cord-329276-tfrjw743	358	47	between	between	IN
cord-329276-tfrjw743	358	48	the	the	DT
cord-329276-tfrjw743	358	49	benefit	benefit	NN
cord-329276-tfrjw743	358	50	at	at	IN
cord-329276-tfrjw743	358	51	the	the	DT
cord-329276-tfrjw743	358	52	terminal	terminal	JJ
cord-329276-tfrjw743	358	53	time	time	NN
cord-329276-tfrjw743	358	54	and	and	CC
cord-329276-tfrjw743	358	55	the	the	DT
cord-329276-tfrjw743	358	56	side	side	NN
cord-329276-tfrjw743	358	57	effects	effect	NNS
cord-329276-tfrjw743	358	58	measured	measure	VBN
cord-329276-tfrjw743	358	59	by	by	IN
cord-329276-tfrjw743	358	60	the	the	DT
cord-329276-tfrjw743	358	61	total	total	JJ
cord-329276-tfrjw743	358	62	amount	amount	NN
cord-329276-tfrjw743	358	63	of	of	IN
cord-329276-tfrjw743	358	64	drugs	drug	NNS
cord-329276-tfrjw743	358	65	given	give	VBN
cord-329276-tfrjw743	358	66	while	while	IN
cord-329276-tfrjw743	358	67	it	-PRON-	PRP
cord-329276-tfrjw743	358	68	also	also	RB
cord-329276-tfrjw743	358	69	guarantees	guarantee	VBZ
cord-329276-tfrjw743	358	70	the	the	DT
cord-329276-tfrjw743	358	71	existence	existence	NN
cord-329276-tfrjw743	358	72	of	of	IN
cord-329276-tfrjw743	358	73	an	an	DT
cord-329276-tfrjw743	358	74	optimal	optimal	JJ
cord-329276-tfrjw743	358	75	solution	solution	NN
cord-329276-tfrjw743	358	76	by	by	IN
cord-329276-tfrjw743	358	77	penalizing	penalize	VBG
cord-329276-tfrjw743	358	78	the	the	DT
cord-329276-tfrjw743	358	79	free	free	JJ
cord-329276-tfrjw743	358	80	terminal	terminal	JJ
cord-329276-tfrjw743	358	81	time	time	NN
cord-329276-tfrjw743	358	82	T	T	NNP
cord-329276-tfrjw743	358	83	[	[	-LRB-
cord-329276-tfrjw743	358	84	15	15	CD
cord-329276-tfrjw743	358	85	,	,	,
cord-329276-tfrjw743	358	86	40	40	CD
cord-329276-tfrjw743	358	87	,	,	,
cord-329276-tfrjw743	358	88	41	41	CD
cord-329276-tfrjw743	358	89	]	]	-RRB-
cord-329276-tfrjw743	358	90	.	.	.
cord-329276-tfrjw743	359	1	We	-PRON-	PRP
cord-329276-tfrjw743	359	2	discuss	discuss	VBP
cord-329276-tfrjw743	359	3	the	the	DT
cord-329276-tfrjw743	359	4	significance	significance	NN
cord-329276-tfrjw743	359	5	of	of	IN
cord-329276-tfrjw743	359	6	each	each	DT
cord-329276-tfrjw743	359	7	penalty	penalty	NN
cord-329276-tfrjw743	359	8	term	term	NN
cord-329276-tfrjw743	359	9	in	in	IN
cord-329276-tfrjw743	359	10	(	(	-LRB-
cord-329276-tfrjw743	359	11	17	17	CD
cord-329276-tfrjw743	359	12	)	)	-RRB-
cord-329276-tfrjw743	359	13	in	in	IN
cord-329276-tfrjw743	359	14	detail	detail	NN
cord-329276-tfrjw743	359	15	:	:	:
cord-329276-tfrjw743	360	1	(	(	-LRB-
cord-329276-tfrjw743	360	2	i	i	NN
cord-329276-tfrjw743	360	3	)	)	-RRB-
cord-329276-tfrjw743	361	1	The	the	DT
cord-329276-tfrjw743	361	2	term	term	NN
cord-329276-tfrjw743	361	3	Ap(T	Ap(T	NNP
cord-329276-tfrjw743	361	4	)	)	-RRB-
cord-329276-tfrjw743	362	1	−	−	NNP
cord-329276-tfrjw743	362	2	Br(T	Br(T	NNP
cord-329276-tfrjw743	362	3	)	)	-RRB-
cord-329276-tfrjw743	362	4	at	at	IN
cord-329276-tfrjw743	362	5	the	the	DT
cord-329276-tfrjw743	362	6	terminal	terminal	JJ
cord-329276-tfrjw743	362	7	time	time	NN
cord-329276-tfrjw743	362	8	is	be	VBZ
cord-329276-tfrjw743	362	9	designed	design	VBN
cord-329276-tfrjw743	362	10	to	to	TO
cord-329276-tfrjw743	362	11	induce	induce	VB
cord-329276-tfrjw743	362	12	a	a	DT
cord-329276-tfrjw743	362	13	transfer	transfer	NN
cord-329276-tfrjw743	362	14	of	of	IN
cord-329276-tfrjw743	362	15	the	the	DT
cord-329276-tfrjw743	362	16	system	system	NN
cord-329276-tfrjw743	362	17	from	from	IN
cord-329276-tfrjw743	362	18	the	the	DT
cord-329276-tfrjw743	362	19	malignant	malignant	JJ
cord-329276-tfrjw743	362	20	into	into	IN
cord-329276-tfrjw743	362	21	the	the	DT
cord-329276-tfrjw743	362	22	benign	benign	JJ
cord-329276-tfrjw743	362	23	region	region	NN
cord-329276-tfrjw743	362	24	of	of	IN
cord-329276-tfrjw743	362	25	the	the	DT
cord-329276-tfrjw743	362	26	state	state	NN
cord-329276-tfrjw743	362	27	space	space	NN
cord-329276-tfrjw743	362	28	.	.	.
cord-329276-tfrjw743	363	1	As	as	IN
cord-329276-tfrjw743	363	2	is	be	VBZ
cord-329276-tfrjw743	363	3	seen	see	VBN
cord-329276-tfrjw743	363	4	in	in	IN
cord-329276-tfrjw743	363	5	Fig	Fig	NNP
cord-329276-tfrjw743	363	6	.	.	NNP
cord-329276-tfrjw743	363	7	2	2	CD
cord-329276-tfrjw743	363	8	,	,	,
cord-329276-tfrjw743	363	9	points	point	NNS
cord-329276-tfrjw743	363	10	with	with	IN
cord-329276-tfrjw743	363	11	small	small	JJ
cord-329276-tfrjw743	363	12	tumor	tumor	NN
cord-329276-tfrjw743	363	13	volumes	volume	NNS
cord-329276-tfrjw743	363	14	and	and	CC
cord-329276-tfrjw743	363	15	depressed	depressed	JJ
cord-329276-tfrjw743	363	16	immunocompetent	immunocompetent	JJ
cord-329276-tfrjw743	363	17	cell	cell	NN
cord-329276-tfrjw743	363	18	densities	density	NNS
cord-329276-tfrjw743	363	19	lie	lie	VBP
cord-329276-tfrjw743	363	20	in	in	IN
cord-329276-tfrjw743	363	21	the	the	DT
cord-329276-tfrjw743	363	22	malignant	malignant	JJ
cord-329276-tfrjw743	363	23	region	region	NN
cord-329276-tfrjw743	363	24	and	and	CC
cord-329276-tfrjw743	363	25	it	-PRON-	PRP
cord-329276-tfrjw743	363	26	may	may	MD
cord-329276-tfrjw743	363	27	not	not	RB
cord-329276-tfrjw743	363	28	suffice	suffice	VB
cord-329276-tfrjw743	363	29	to	to	TO
cord-329276-tfrjw743	363	30	simply	simply	RB
cord-329276-tfrjw743	363	31	minimize	minimize	VB
cord-329276-tfrjw743	363	32	the	the	DT
cord-329276-tfrjw743	363	33	tumor	tumor	NN
cord-329276-tfrjw743	363	34	volume	volume	NN
cord-329276-tfrjw743	363	35	.	.	.
cord-329276-tfrjw743	364	1	Rather	rather	RB
cord-329276-tfrjw743	364	2	,	,	,
cord-329276-tfrjw743	364	3	it	-PRON-	PRP
cord-329276-tfrjw743	364	4	is	be	VBZ
cord-329276-tfrjw743	364	5	the	the	DT
cord-329276-tfrjw743	364	6	geometric	geometric	JJ
cord-329276-tfrjw743	364	7	shape	shape	NN
cord-329276-tfrjw743	364	8	of	of	IN
cord-329276-tfrjw743	364	9	the	the	DT
cord-329276-tfrjw743	364	10	stability	stability	NN
cord-329276-tfrjw743	364	11	boundary	boundary	NN
cord-329276-tfrjw743	364	12	between	between	IN
cord-329276-tfrjw743	364	13	the	the	DT
cord-329276-tfrjw743	364	14	benign	benign	JJ
cord-329276-tfrjw743	364	15	and	and	CC
cord-329276-tfrjw743	364	16	malignant	malignant	JJ
cord-329276-tfrjw743	364	17	region	region	NN
cord-329276-tfrjw743	364	18	that	that	WDT
cord-329276-tfrjw743	364	19	matters	matter	VBZ
cord-329276-tfrjw743	364	20	.	.	.
cord-329276-tfrjw743	365	1	Even	even	RB
cord-329276-tfrjw743	365	2	for	for	IN
cord-329276-tfrjw743	365	3	a	a	DT
cord-329276-tfrjw743	365	4	low	low	JJ
cord-329276-tfrjw743	365	5	-	-	HYPH
cord-329276-tfrjw743	365	6	dimensional	dimensional	JJ
cord-329276-tfrjw743	365	7	dynamical	dynamical	JJ
cord-329276-tfrjw743	365	8	system	system	NN
cord-329276-tfrjw743	365	9	like	like	IN
cord-329276-tfrjw743	365	10	Stepanova	Stepanova	NNP
cord-329276-tfrjw743	365	11	's	's	POS
cord-329276-tfrjw743	365	12	model	model	NN
cord-329276-tfrjw743	365	13	,	,	,
cord-329276-tfrjw743	365	14	it	-PRON-	PRP
cord-329276-tfrjw743	365	15	is	be	VBZ
cord-329276-tfrjw743	365	16	generally	generally	RB
cord-329276-tfrjw743	365	17	not	not	RB
cord-329276-tfrjw743	365	18	possible	possible	JJ
cord-329276-tfrjw743	365	19	to	to	TO
cord-329276-tfrjw743	365	20	give	give	VB
cord-329276-tfrjw743	365	21	a	a	DT
cord-329276-tfrjw743	365	22	functional	functional	JJ
cord-329276-tfrjw743	365	23	description	description	NN
cord-329276-tfrjw743	365	24	of	of	IN
cord-329276-tfrjw743	365	25	the	the	DT
cord-329276-tfrjw743	365	26	separatrix	separatrix	NN
cord-329276-tfrjw743	365	27	which	which	WDT
cord-329276-tfrjw743	365	28	is	be	VBZ
cord-329276-tfrjw743	365	29	the	the	DT
cord-329276-tfrjw743	365	30	stable	stable	JJ
cord-329276-tfrjw743	365	31	manifold	manifold	NN
cord-329276-tfrjw743	365	32	of	of	IN
cord-329276-tfrjw743	365	33	the	the	DT
cord-329276-tfrjw743	365	34	unstable	unstable	JJ
cord-329276-tfrjw743	365	35	equilibrium	equilibrium	NN
cord-329276-tfrjw743	365	36	point	point	NN
cord-329276-tfrjw743	365	37	of	of	IN
cord-329276-tfrjw743	365	38	the	the	DT
cord-329276-tfrjw743	365	39	system	system	NN
cord-329276-tfrjw743	365	40	.	.	.
cord-329276-tfrjw743	366	1	Its	-PRON-	PRP$
cord-329276-tfrjw743	366	2	tangent	tangent	JJ
cord-329276-tfrjw743	366	3	space	space	NN
cord-329276-tfrjw743	366	4	,	,	,
cord-329276-tfrjw743	366	5	however	however	RB
cord-329276-tfrjw743	366	6	,	,	,
cord-329276-tfrjw743	366	7	is	be	VBZ
cord-329276-tfrjw743	366	8	easily	easily	RB
cord-329276-tfrjw743	366	9	computed	compute	VBN
cord-329276-tfrjw743	366	10	,	,	,
cord-329276-tfrjw743	366	11	and	and	CC
cord-329276-tfrjw743	366	12	it	-PRON-	PRP
cord-329276-tfrjw743	366	13	thus	thus	RB
cord-329276-tfrjw743	366	14	becomes	become	VBZ
cord-329276-tfrjw743	366	15	a	a	DT
cord-329276-tfrjw743	366	16	good	good	JJ
cord-329276-tfrjw743	366	17	heuristic	heuristic	NN
cord-329276-tfrjw743	366	18	to	to	TO
cord-329276-tfrjw743	366	19	choose	choose	VB
cord-329276-tfrjw743	366	20	the	the	DT
cord-329276-tfrjw743	366	21	coefficients	coefficient	NNS
cord-329276-tfrjw743	366	22	A	A	NNP
cord-329276-tfrjw743	366	23	and	and	CC
cord-329276-tfrjw743	366	24	B	b	NN
cord-329276-tfrjw743	366	25	in	in	IN
cord-329276-tfrjw743	366	26	the	the	DT
cord-329276-tfrjw743	366	27	penalty	penalty	NN
cord-329276-tfrjw743	366	28	term	term	NN
cord-329276-tfrjw743	366	29	such	such	JJ
cord-329276-tfrjw743	366	30	that	that	IN
cord-329276-tfrjw743	366	31	the	the	DT
cord-329276-tfrjw743	366	32	minimization	minimization	NN
cord-329276-tfrjw743	366	33	of	of	IN
cord-329276-tfrjw743	366	34	this	this	DT
cord-329276-tfrjw743	366	35	term	term	NN
cord-329276-tfrjw743	366	36	corresponds	correspond	VBZ
cord-329276-tfrjw743	366	37	to	to	IN
cord-329276-tfrjw743	366	38	moving	move	VBG
cord-329276-tfrjw743	366	39	in	in	IN
cord-329276-tfrjw743	366	40	the	the	DT
cord-329276-tfrjw743	366	41	normal	normal	JJ
cord-329276-tfrjw743	366	42	direction	direction	NN
cord-329276-tfrjw743	366	43	to	to	IN
cord-329276-tfrjw743	366	44	this	this	DT
cord-329276-tfrjw743	366	45	stable	stable	JJ
cord-329276-tfrjw743	366	46	manifold	manifold	NN
cord-329276-tfrjw743	366	47	from	from	IN
cord-329276-tfrjw743	366	48	the	the	DT
cord-329276-tfrjw743	366	49	malignant	malignant	JJ
cord-329276-tfrjw743	366	50	toward	toward	IN
cord-329276-tfrjw743	366	51	the	the	DT
cord-329276-tfrjw743	366	52	benign	benign	JJ
cord-329276-tfrjw743	366	53	region	region	NN
cord-329276-tfrjw743	366	54	.	.	.
cord-329276-tfrjw743	367	1	Alternatively	alternatively	RB
cord-329276-tfrjw743	367	2	,	,	,
cord-329276-tfrjw743	367	3	one	one	PRP
cord-329276-tfrjw743	367	4	could	could	MD
cord-329276-tfrjw743	367	5	also	also	RB
cord-329276-tfrjw743	367	6	choose	choose	VB
cord-329276-tfrjw743	367	7	these	these	DT
cord-329276-tfrjw743	367	8	coefficients	coefficient	NNS
cord-329276-tfrjw743	367	9	to	to	TO
cord-329276-tfrjw743	367	10	move	move	VB
cord-329276-tfrjw743	367	11	into	into	IN
cord-329276-tfrjw743	367	12	the	the	DT
cord-329276-tfrjw743	367	13	direction	direction	NN
cord-329276-tfrjw743	367	14	of	of	IN
cord-329276-tfrjw743	367	15	the	the	DT
cord-329276-tfrjw743	367	16	unstable	unstable	JJ
cord-329276-tfrjw743	367	17	eigenvector	eigenvector	NN
cord-329276-tfrjw743	367	18	at	at	IN
cord-329276-tfrjw743	367	19	the	the	DT
cord-329276-tfrjw743	367	20	saddle	saddle	NN
cord-329276-tfrjw743	367	21	point	point	NN
cord-329276-tfrjw743	367	22	.	.	.
cord-329276-tfrjw743	368	1	For	for	IN
cord-329276-tfrjw743	368	2	,	,	,
cord-329276-tfrjw743	368	3	this	this	DT
cord-329276-tfrjw743	368	4	is	be	VBZ
cord-329276-tfrjw743	368	5	the	the	DT
cord-329276-tfrjw743	368	6	tangent	tangent	JJ
cord-329276-tfrjw743	368	7	vector	vector	NN
cord-329276-tfrjw743	368	8	to	to	IN
cord-329276-tfrjw743	368	9	the	the	DT
cord-329276-tfrjw743	368	10	path	path	NN
cord-329276-tfrjw743	369	1	which	which	WDT
cord-329276-tfrjw743	369	2	uncontrolled	uncontrolled	JJ
cord-329276-tfrjw743	369	3	trajectories	trajectory	NNS
cord-329276-tfrjw743	369	4	will	will	MD
cord-329276-tfrjw743	369	5	closely	closely	RB
cord-329276-tfrjw743	369	6	when	when	WRB
cord-329276-tfrjw743	369	7	in	in	IN
cord-329276-tfrjw743	369	8	the	the	DT
cord-329276-tfrjw743	369	9	benign	benign	JJ
cord-329276-tfrjw743	369	10	region	region	NN
cord-329276-tfrjw743	369	11	.	.	.
cord-329276-tfrjw743	370	1	In	in	IN
cord-329276-tfrjw743	370	2	the	the	DT
cord-329276-tfrjw743	370	3	formulation	formulation	NN
cord-329276-tfrjw743	370	4	(	(	-LRB-
cord-329276-tfrjw743	370	5	17	17	CD
cord-329276-tfrjw743	370	6	)	)	-RRB-
cord-329276-tfrjw743	370	7	we	-PRON-	PRP
cord-329276-tfrjw743	370	8	have	have	VBP
cord-329276-tfrjw743	370	9	followed	follow	VBN
cord-329276-tfrjw743	370	10	the	the	DT
cord-329276-tfrjw743	370	11	first	first	JJ
cord-329276-tfrjw743	370	12	approach	approach	NN
cord-329276-tfrjw743	370	13	and	and	CC
cord-329276-tfrjw743	370	14	v	v	NN
cord-329276-tfrjw743	370	15	=	=	NN
cord-329276-tfrjw743	371	1	(	(	-LRB-
cord-329276-tfrjw743	371	2	B	b	NN
cord-329276-tfrjw743	371	3	,	,	,
cord-329276-tfrjw743	371	4	A	a	NN
cord-329276-tfrjw743	371	5	)	)	-RRB-
cord-329276-tfrjw743	371	6	T	t	NN
cord-329276-tfrjw743	371	7	is	be	VBZ
cord-329276-tfrjw743	371	8	the	the	DT
cord-329276-tfrjw743	371	9	stable	stable	JJ
cord-329276-tfrjw743	371	10	eigenvector	eigenvector	NN
cord-329276-tfrjw743	371	11	of	of	IN
cord-329276-tfrjw743	371	12	the	the	DT
cord-329276-tfrjw743	371	13	saddle	saddle	NN
cord-329276-tfrjw743	371	14	point	point	NN
cord-329276-tfrjw743	371	15	oriented	orient	VBN
cord-329276-tfrjw743	371	16	so	so	IN
cord-329276-tfrjw743	371	17	that	that	IN
cord-329276-tfrjw743	371	18	both	both	CC
cord-329276-tfrjw743	371	19	A	A	NNP
cord-329276-tfrjw743	371	20	and	and	CC
cord-329276-tfrjw743	371	21	B	b	NN
cord-329276-tfrjw743	371	22	are	be	VBP
cord-329276-tfrjw743	371	23	positive	positive	JJ
cord-329276-tfrjw743	371	24	numbers	number	NNS
cord-329276-tfrjw743	371	25	(	(	-LRB-
cord-329276-tfrjw743	371	26	see	see	VB
cord-329276-tfrjw743	371	27	Fig	Fig	NNP
cord-329276-tfrjw743	371	28	.	.	NNP
cord-329276-tfrjw743	371	29	5	5	CD
cord-329276-tfrjw743	371	30	)	)	-RRB-
cord-329276-tfrjw743	371	31	.	.	.
cord-329276-tfrjw743	372	1	It	-PRON-	PRP
cord-329276-tfrjw743	372	2	follows	follow	VBZ
cord-329276-tfrjw743	372	3	from	from	IN
cord-329276-tfrjw743	372	4	the	the	DT
cord-329276-tfrjw743	372	5	geometry	geometry	NN
cord-329276-tfrjw743	372	6	of	of	IN
cord-329276-tfrjw743	372	7	the	the	DT
cord-329276-tfrjw743	372	8	stable	stable	JJ
cord-329276-tfrjw743	372	9	manifold	manifold	NN
cord-329276-tfrjw743	372	10	that	that	WDT
cord-329276-tfrjw743	372	11	A	a	NN
cord-329276-tfrjw743	372	12	and	and	CC
cord-329276-tfrjw743	372	13	B	B	NNP
cord-329276-tfrjw743	372	14	will	will	MD
cord-329276-tfrjw743	372	15	have	have	VB
cord-329276-tfrjw743	372	16	the	the	DT
cord-329276-tfrjw743	372	17	same	same	JJ
cord-329276-tfrjw743	372	18	sign	sign	NN
cord-329276-tfrjw743	372	19	and	and	CC
cord-329276-tfrjw743	372	20	including	include	VBG
cord-329276-tfrjw743	372	21	in	in	IN
cord-329276-tfrjw743	372	22	the	the	DT
cord-329276-tfrjw743	372	23	objective	objective	NN
cord-329276-tfrjw743	372	24	a	a	DT
cord-329276-tfrjw743	372	25	term	term	NN
cord-329276-tfrjw743	372	26	of	of	IN
cord-329276-tfrjw743	372	27	the	the	DT
cord-329276-tfrjw743	372	28	form	form	NN
cord-329276-tfrjw743	372	29	Ap(T	Ap(T	NNP
cord-329276-tfrjw743	372	30	)	)	-RRB-
cord-329276-tfrjw743	372	31	−	−	NNP
cord-329276-tfrjw743	372	32	Br(T	Br(T	NNP
cord-329276-tfrjw743	372	33	)	)	-RRB-
cord-329276-tfrjw743	372	34	gives	give	VBZ
cord-329276-tfrjw743	372	35	the	the	DT
cord-329276-tfrjw743	372	36	correct	correct	JJ
cord-329276-tfrjw743	372	37	direction	direction	NN
cord-329276-tfrjw743	372	38	to	to	TO
cord-329276-tfrjw743	372	39	minimize	minimize	VB
cord-329276-tfrjw743	372	40	in	in	IN
cord-329276-tfrjw743	372	41	the	the	DT
cord-329276-tfrjw743	372	42	objective	objective	NN
cord-329276-tfrjw743	372	43	.	.	.
cord-329276-tfrjw743	373	1	The	the	DT
cord-329276-tfrjw743	373	2	level	level	NN
cord-329276-tfrjw743	373	3	sets	set	NNS
cord-329276-tfrjw743	373	4	of	of	IN
cord-329276-tfrjw743	373	5	this	this	DT
cord-329276-tfrjw743	373	6	quantity	quantity	NN
cord-329276-tfrjw743	373	7	are	be	VBP
cord-329276-tfrjw743	373	8	lines	line	NNS
cord-329276-tfrjw743	373	9	parallel	parallel	JJ
cord-329276-tfrjw743	373	10	to	to	IN
cord-329276-tfrjw743	373	11	the	the	DT
cord-329276-tfrjw743	373	12	tangent	tangent	JJ
cord-329276-tfrjw743	373	13	space	space	NN
cord-329276-tfrjw743	373	14	of	of	IN
cord-329276-tfrjw743	373	15	the	the	DT
cord-329276-tfrjw743	373	16	stable	stable	JJ
cord-329276-tfrjw743	373	17	manifold	manifold	JJ
cord-329276-tfrjw743	373	18	6	6	CD
cord-329276-tfrjw743	373	19	)	)	-RRB-
cord-329276-tfrjw743	373	20	with	with	IN
cord-329276-tfrjw743	373	21	some	some	DT
cord-329276-tfrjw743	373	22	sample	sample	NN
cord-329276-tfrjw743	373	23	trajectories	trajectory	NNS
cord-329276-tfrjw743	373	24	shown	show	VBN
cord-329276-tfrjw743	373	25	in	in	IN
cord-329276-tfrjw743	373	26	blue	blue	JJ
cord-329276-tfrjw743	373	27	.	.	.
cord-329276-tfrjw743	374	1	The	the	DT
cord-329276-tfrjw743	374	2	dynamics	dynamic	NNS
cord-329276-tfrjw743	374	3	has	have	VBZ
cord-329276-tfrjw743	374	4	three	three	CD
cord-329276-tfrjw743	374	5	equilibria	equilibrium	NNS
cord-329276-tfrjw743	374	6	:	:	:
cord-329276-tfrjw743	374	7	a	a	DT
cord-329276-tfrjw743	374	8	locally	locally	RB
cord-329276-tfrjw743	374	9	asymptotically	asymptotically	RB
cord-329276-tfrjw743	374	10	stable	stable	JJ
cord-329276-tfrjw743	374	11	focus	focus	NN
cord-329276-tfrjw743	374	12	which	which	WDT
cord-329276-tfrjw743	374	13	is	be	VBZ
cord-329276-tfrjw743	374	14	benign	benign	JJ
cord-329276-tfrjw743	374	15	(	(	-LRB-
cord-329276-tfrjw743	374	16	shown	show	VBN
cord-329276-tfrjw743	374	17	as	as	IN
cord-329276-tfrjw743	374	18	a	a	DT
cord-329276-tfrjw743	374	19	small	small	JJ
cord-329276-tfrjw743	374	20	green	green	JJ
cord-329276-tfrjw743	374	21	circle	circle	NN
cord-329276-tfrjw743	374	22	)	)	-RRB-
cord-329276-tfrjw743	374	23	,	,	,
cord-329276-tfrjw743	374	24	a	a	DT
cord-329276-tfrjw743	374	25	saddle	saddle	NN
cord-329276-tfrjw743	374	26	point	point	NN
cord-329276-tfrjw743	374	27	(	(	-LRB-
cord-329276-tfrjw743	374	28	shown	show	VBN
cord-329276-tfrjw743	374	29	as	as	IN
cord-329276-tfrjw743	374	30	a	a	DT
cord-329276-tfrjw743	374	31	small	small	JJ
cord-329276-tfrjw743	374	32	grey	grey	JJ
cord-329276-tfrjw743	374	33	circle	circle	NN
cord-329276-tfrjw743	374	34	)	)	-RRB-
cord-329276-tfrjw743	374	35	and	and	CC
cord-329276-tfrjw743	374	36	a	a	DT
cord-329276-tfrjw743	374	37	locally	locally	RB
cord-329276-tfrjw743	374	38	asymptotically	asymptotically	RB
cord-329276-tfrjw743	374	39	stable	stable	JJ
cord-329276-tfrjw743	374	40	node	node	NN
cord-329276-tfrjw743	374	41	which	which	WDT
cord-329276-tfrjw743	374	42	is	be	VBZ
cord-329276-tfrjw743	374	43	malignant	malignant	JJ
cord-329276-tfrjw743	374	44	(	(	-LRB-
cord-329276-tfrjw743	374	45	shown	show	VBN
cord-329276-tfrjw743	374	46	as	as	IN
cord-329276-tfrjw743	374	47	a	a	DT
cord-329276-tfrjw743	374	48	small	small	JJ
cord-329276-tfrjw743	374	49	red	red	JJ
cord-329276-tfrjw743	374	50	circle	circle	NN
cord-329276-tfrjw743	374	51	)	)	-RRB-
cord-329276-tfrjw743	374	52	.	.	.
cord-329276-tfrjw743	375	1	The	the	DT
cord-329276-tfrjw743	375	2	stable	stable	JJ
cord-329276-tfrjw743	375	3	and	and	CC
cord-329276-tfrjw743	375	4	unstable	unstable	JJ
cord-329276-tfrjw743	375	5	manifolds	manifold	NNS
cord-329276-tfrjw743	375	6	of	of	IN
cord-329276-tfrjw743	375	7	the	the	DT
cord-329276-tfrjw743	375	8	saddle	saddle	NN
cord-329276-tfrjw743	375	9	point	point	NN
cord-329276-tfrjw743	375	10	are	be	VBP
cord-329276-tfrjw743	375	11	shown	show	VBN
cord-329276-tfrjw743	375	12	as	as	IN
cord-329276-tfrjw743	375	13	solid	solid	JJ
cord-329276-tfrjw743	375	14	black	black	JJ
cord-329276-tfrjw743	375	15	curves	curve	NNS
cord-329276-tfrjw743	375	16	.	.	.
cord-329276-tfrjw743	376	1	The	the	DT
cord-329276-tfrjw743	376	2	tangent	tangent	JJ
cord-329276-tfrjw743	376	3	vector	vector	NN
cord-329276-tfrjw743	376	4	to	to	IN
cord-329276-tfrjw743	376	5	the	the	DT
cord-329276-tfrjw743	376	6	stable	stable	JJ
cord-329276-tfrjw743	376	7	manifold	manifold	NN
cord-329276-tfrjw743	376	8	of	of	IN
cord-329276-tfrjw743	376	9	the	the	DT
cord-329276-tfrjw743	376	10	saddle	saddle	NN
cord-329276-tfrjw743	376	11	at	at	IN
cord-329276-tfrjw743	376	12	the	the	DT
cord-329276-tfrjw743	376	13	equilibrium	equilibrium	NN
cord-329276-tfrjw743	376	14	point	point	NN
cord-329276-tfrjw743	376	15	is	be	VBZ
cord-329276-tfrjw743	376	16	labeled	label	VBN
cord-329276-tfrjw743	376	17	v	v	IN
cord-329276-tfrjw743	376	18	=	=	NN
cord-329276-tfrjw743	376	19	(	(	-LRB-
cord-329276-tfrjw743	376	20	B	b	NN
cord-329276-tfrjw743	376	21	,	,	,
cord-329276-tfrjw743	376	22	A	a	NN
cord-329276-tfrjw743	376	23	)	)	-RRB-
cord-329276-tfrjw743	376	24	T	t	NN
cord-329276-tfrjw743	376	25	oriented	orient	VBD
cord-329276-tfrjw743	376	26	so	so	IN
cord-329276-tfrjw743	376	27	that	that	IN
cord-329276-tfrjw743	376	28	both	both	DT
cord-329276-tfrjw743	376	29	entries	entry	NNS
cord-329276-tfrjw743	376	30	are	be	VBP
cord-329276-tfrjw743	376	31	positive	positive	JJ
cord-329276-tfrjw743	376	32	of	of	IN
cord-329276-tfrjw743	376	33	the	the	DT
cord-329276-tfrjw743	376	34	saddle	saddle	NN
cord-329276-tfrjw743	376	35	,	,	,
cord-329276-tfrjw743	376	36	and	and	CC
cord-329276-tfrjw743	376	37	minimizing	minimize	VBG
cord-329276-tfrjw743	376	38	this	this	DT
cord-329276-tfrjw743	376	39	quantity	quantity	NN
cord-329276-tfrjw743	376	40	thus	thus	RB
cord-329276-tfrjw743	376	41	creates	create	VBZ
cord-329276-tfrjw743	376	42	an	an	DT
cord-329276-tfrjw743	376	43	incentive	incentive	NN
cord-329276-tfrjw743	376	44	for	for	IN
cord-329276-tfrjw743	376	45	the	the	DT
cord-329276-tfrjw743	376	46	system	system	NN
cord-329276-tfrjw743	376	47	to	to	TO
cord-329276-tfrjw743	376	48	move	move	VB
cord-329276-tfrjw743	376	49	into	into	IN
cord-329276-tfrjw743	376	50	the	the	DT
cord-329276-tfrjw743	376	51	benign	benign	JJ
cord-329276-tfrjw743	376	52	region	region	NN
cord-329276-tfrjw743	376	53	.	.	.
cord-329276-tfrjw743	377	1	(	(	-LRB-
cord-329276-tfrjw743	377	2	ii	ii	NN
cord-329276-tfrjw743	377	3	)	)	-RRB-
cord-329276-tfrjw743	378	1	The	the	DT
cord-329276-tfrjw743	378	2	integrals	integral	NNS
cord-329276-tfrjw743	378	3	of	of	IN
cord-329276-tfrjw743	378	4	the	the	DT
cord-329276-tfrjw743	378	5	controls	control	NNS
cord-329276-tfrjw743	378	6	,	,	,
cord-329276-tfrjw743	378	7	T	T	NNP
cord-329276-tfrjw743	378	8	0	0	CD
cord-329276-tfrjw743	378	9	u(t)dt	u(t)dt	,
cord-329276-tfrjw743	378	10	and	and	CC
cord-329276-tfrjw743	378	11	T	t	NN
cord-329276-tfrjw743	378	12	0	0	CD
cord-329276-tfrjw743	378	13	v(t)dt	v(t)dt	NN
cord-329276-tfrjw743	378	14	,	,	,
cord-329276-tfrjw743	378	15	measure	measure	VB
cord-329276-tfrjw743	378	16	the	the	DT
cord-329276-tfrjw743	378	17	total	total	JJ
cord-329276-tfrjw743	378	18	amounts	amount	NNS
cord-329276-tfrjw743	378	19	of	of	IN
cord-329276-tfrjw743	378	20	drugs	drug	NNS
cord-329276-tfrjw743	378	21	given	give	VBN
cord-329276-tfrjw743	378	22	and	and	CC
cord-329276-tfrjw743	378	23	,	,	,
cord-329276-tfrjw743	378	24	once	once	RB
cord-329276-tfrjw743	378	25	again	again	RB
cord-329276-tfrjw743	378	26	,	,	,
cord-329276-tfrjw743	378	27	represent	represent	VBP
cord-329276-tfrjw743	378	28	a	a	DT
cord-329276-tfrjw743	378	29	soft	soft	JJ
cord-329276-tfrjw743	378	30	modeling	modeling	NN
cord-329276-tfrjw743	378	31	of	of	IN
cord-329276-tfrjw743	378	32	the	the	DT
cord-329276-tfrjw743	378	33	side	side	NN
cord-329276-tfrjw743	378	34	effects	effect	NNS
cord-329276-tfrjw743	378	35	of	of	IN
cord-329276-tfrjw743	378	36	the	the	DT
cord-329276-tfrjw743	378	37	drugs	drug	NNS
cord-329276-tfrjw743	378	38	.	.	.
cord-329276-tfrjw743	379	1	Clinical	clinical	JJ
cord-329276-tfrjw743	379	2	data	datum	NNS
cord-329276-tfrjw743	379	3	as	as	IN
cord-329276-tfrjw743	379	4	to	to	IN
cord-329276-tfrjw743	379	5	the	the	DT
cord-329276-tfrjw743	379	6	severity	severity	NN
cord-329276-tfrjw743	379	7	of	of	IN
cord-329276-tfrjw743	379	8	the	the	DT
cord-329276-tfrjw743	379	9	drugs	drug	NNS
cord-329276-tfrjw743	379	10	should	should	MD
cord-329276-tfrjw743	379	11	be	be	VB
cord-329276-tfrjw743	379	12	reflected	reflect	VBN
cord-329276-tfrjw743	379	13	in	in	IN
cord-329276-tfrjw743	379	14	the	the	DT
cord-329276-tfrjw743	379	15	choices	choice	NNS
cord-329276-tfrjw743	379	16	for	for	IN
cord-329276-tfrjw743	379	17	C	C	NNP
cord-329276-tfrjw743	379	18	and	and	CC
cord-329276-tfrjw743	379	19	D.	D.	NNP
cord-329276-tfrjw743	379	20	Naturally	naturally	RB
cord-329276-tfrjw743	379	21	,	,	,
cord-329276-tfrjw743	379	22	the	the	DT
cord-329276-tfrjw743	379	23	specific	specific	JJ
cord-329276-tfrjw743	379	24	type	type	NN
cord-329276-tfrjw743	379	25	of	of	IN
cord-329276-tfrjw743	379	26	tumor	tumor	NN
cord-329276-tfrjw743	379	27	and	and	CC
cord-329276-tfrjw743	379	28	stage	stage	NN
cord-329276-tfrjw743	379	29	of	of	IN
cord-329276-tfrjw743	379	30	cancer	cancer	NN
cord-329276-tfrjw743	379	31	will	will	MD
cord-329276-tfrjw743	379	32	need	need	VB
cord-329276-tfrjw743	379	33	to	to	TO
cord-329276-tfrjw743	379	34	enter	enter	VB
cord-329276-tfrjw743	379	35	into	into	IN
cord-329276-tfrjw743	379	36	the	the	DT
cord-329276-tfrjw743	379	37	calibration	calibration	NN
cord-329276-tfrjw743	379	38	of	of	IN
cord-329276-tfrjw743	379	39	these	these	DT
cord-329276-tfrjw743	379	40	coefficients	coefficient	NNS
cord-329276-tfrjw743	379	41	.	.	.
cord-329276-tfrjw743	380	1	In	in	IN
cord-329276-tfrjw743	380	2	a	a	DT
cord-329276-tfrjw743	380	3	more	more	RBR
cord-329276-tfrjw743	380	4	advanced	advanced	JJ
cord-329276-tfrjw743	380	5	stage	stage	NN
cord-329276-tfrjw743	380	6	,	,	,
cord-329276-tfrjw743	380	7	higher	high	JJR
cord-329276-tfrjw743	380	8	side	side	NN
cord-329276-tfrjw743	380	9	effects	effect	NNS
cord-329276-tfrjw743	380	10	need	need	VBP
cord-329276-tfrjw743	380	11	to	to	TO
cord-329276-tfrjw743	380	12	be	be	VB
cord-329276-tfrjw743	380	13	tolerated	tolerate	VBN
cord-329276-tfrjw743	380	14	and	and	CC
cord-329276-tfrjw743	380	15	thus	thus	RB
cord-329276-tfrjw743	380	16	smaller	small	JJR
cord-329276-tfrjw743	380	17	values	value	NNS
cord-329276-tfrjw743	380	18	of	of	IN
cord-329276-tfrjw743	380	19	C	C	NNP
cord-329276-tfrjw743	380	20	would	would	MD
cord-329276-tfrjw743	380	21	be	be	VB
cord-329276-tfrjw743	380	22	taken	take	VBN
cord-329276-tfrjw743	380	23	.	.	.
cord-329276-tfrjw743	381	1	(	(	-LRB-
cord-329276-tfrjw743	381	2	iii	iii	NN
cord-329276-tfrjw743	381	3	)	)	-RRB-
cord-329276-tfrjw743	382	1	The	the	DT
cord-329276-tfrjw743	382	2	penalty	penalty	NN
cord-329276-tfrjw743	382	3	term	term	NN
cord-329276-tfrjw743	382	4	ST	ST	NNP
cord-329276-tfrjw743	382	5	on	on	IN
cord-329276-tfrjw743	382	6	the	the	DT
cord-329276-tfrjw743	382	7	terminal	terminal	JJ
cord-329276-tfrjw743	382	8	time	time	NN
cord-329276-tfrjw743	382	9	makes	make	VBZ
cord-329276-tfrjw743	382	10	the	the	DT
cord-329276-tfrjw743	382	11	mathematical	mathematical	JJ
cord-329276-tfrjw743	382	12	problem	problem	NN
cord-329276-tfrjw743	382	13	well	well	RB
cord-329276-tfrjw743	382	14	-	-	HYPH
cord-329276-tfrjw743	382	15	posed	pose	VBN
cord-329276-tfrjw743	382	16	.	.	.
cord-329276-tfrjw743	383	1	This	this	DT
cord-329276-tfrjw743	383	2	term	term	NN
cord-329276-tfrjw743	383	3	,	,	,
cord-329276-tfrjw743	383	4	which	which	WDT
cord-329276-tfrjw743	383	5	can	can	MD
cord-329276-tfrjw743	383	6	be	be	VB
cord-329276-tfrjw743	383	7	written	write	VBN
cord-329276-tfrjw743	383	8	either	either	CC
cord-329276-tfrjw743	383	9	under	under	IN
cord-329276-tfrjw743	383	10	the	the	DT
cord-329276-tfrjw743	383	11	integral	integral	JJ
cord-329276-tfrjw743	383	12	or	or	CC
cord-329276-tfrjw743	383	13	as	as	IN
cord-329276-tfrjw743	383	14	a	a	DT
cord-329276-tfrjw743	383	15	separate	separate	JJ
cord-329276-tfrjw743	383	16	penalty	penalty	NN
cord-329276-tfrjw743	383	17	term	term	NN
cord-329276-tfrjw743	383	18	ST	ST	NNP
cord-329276-tfrjw743	383	19	,	,	,
cord-329276-tfrjw743	383	20	is	be	VBZ
cord-329276-tfrjw743	383	21	somewhat	somewhat	RB
cord-329276-tfrjw743	383	22	unusual	unusual	JJ
cord-329276-tfrjw743	383	23	.	.	.
cord-329276-tfrjw743	384	1	It	-PRON-	PRP
cord-329276-tfrjw743	384	2	has	have	VBZ
cord-329276-tfrjw743	384	3	to	to	TO
cord-329276-tfrjw743	384	4	do	do	VB
cord-329276-tfrjw743	384	5	with	with	IN
cord-329276-tfrjw743	384	6	the	the	DT
cord-329276-tfrjw743	384	7	nature	nature	NN
cord-329276-tfrjw743	384	8	of	of	IN
cord-329276-tfrjw743	384	9	the	the	DT
cord-329276-tfrjw743	384	10	underlying	underlying	JJ
cord-329276-tfrjw743	384	11	problem	problem	NN
cord-329276-tfrjw743	384	12	and	and	CC
cord-329276-tfrjw743	384	13	the	the	DT
cord-329276-tfrjw743	384	14	emphasis	emphasis	NN
cord-329276-tfrjw743	384	15	on	on	IN
cord-329276-tfrjw743	384	16	the	the	DT
cord-329276-tfrjw743	384	17	regions	region	NNS
cord-329276-tfrjw743	384	18	of	of	IN
cord-329276-tfrjw743	384	19	attraction	attraction	NN
cord-329276-tfrjw743	384	20	.	.	.
cord-329276-tfrjw743	385	1	The	the	DT
cord-329276-tfrjw743	385	2	existence	existence	NN
cord-329276-tfrjw743	385	3	of	of	IN
cord-329276-tfrjw743	385	4	the	the	DT
cord-329276-tfrjw743	385	5	asymptotically	asymptotically	RB
cord-329276-tfrjw743	385	6	stable	stable	JJ
cord-329276-tfrjw743	385	7	,	,	,
cord-329276-tfrjw743	385	8	benign	benign	JJ
cord-329276-tfrjw743	385	9	equilibrium	equilibrium	NN
cord-329276-tfrjw743	385	10	point	point	NN
cord-329276-tfrjw743	385	11	generates	generate	VBZ
cord-329276-tfrjw743	385	12	controlled	control	VBN
cord-329276-tfrjw743	385	13	trajectories	trajectory	NNS
cord-329276-tfrjw743	385	14	that	that	WDT
cord-329276-tfrjw743	385	15	improve	improve	VBP
cord-329276-tfrjw743	385	16	the	the	DT
cord-329276-tfrjw743	385	17	value	value	NN
cord-329276-tfrjw743	385	18	Ap(T	Ap(T	NNP
cord-329276-tfrjw743	385	19	)	)	-RRB-
cord-329276-tfrjw743	385	20	−	−	NNP
cord-329276-tfrjw743	385	21	Br(T	Br(T	NNP
cord-329276-tfrjw743	385	22	)	)	-RRB-
cord-329276-tfrjw743	385	23	of	of	IN
cord-329276-tfrjw743	385	24	the	the	DT
cord-329276-tfrjw743	385	25	objective	objective	NN
cord-329276-tfrjw743	385	26	along	along	IN
cord-329276-tfrjw743	385	27	the	the	DT
cord-329276-tfrjw743	385	28	trivial	trivial	JJ
cord-329276-tfrjw743	385	29	controls	control	NNS
cord-329276-tfrjw743	386	1	u	u	NNP
cord-329276-tfrjw743	386	2	=	=	SYM
cord-329276-tfrjw743	386	3	0	0	CD
cord-329276-tfrjw743	386	4	and	and	CC
cord-329276-tfrjw743	386	5	v	v	NN
cord-329276-tfrjw743	386	6	=	=	SYM
cord-329276-tfrjw743	386	7	0	0	CD
cord-329276-tfrjw743	386	8	.	.	.
cord-329276-tfrjw743	387	1	If	if	IN
cord-329276-tfrjw743	387	2	no	no	DT
cord-329276-tfrjw743	387	3	penalty	penalty	NN
cord-329276-tfrjw743	387	4	is	be	VBZ
cord-329276-tfrjw743	387	5	imposed	impose	VBN
cord-329276-tfrjw743	387	6	on	on	IN
cord-329276-tfrjw743	387	7	the	the	DT
cord-329276-tfrjw743	387	8	free	free	JJ
cord-329276-tfrjw743	387	9	terminal	terminal	JJ
cord-329276-tfrjw743	387	10	time	time	NN
cord-329276-tfrjw743	387	11	,	,	,
cord-329276-tfrjw743	387	12	then	then	RB
cord-329276-tfrjw743	387	13	this	this	DT
cord-329276-tfrjw743	387	14	creates	create	VBZ
cord-329276-tfrjw743	387	15	a	a	DT
cord-329276-tfrjw743	387	16	"	"	``
cord-329276-tfrjw743	387	17	free	free	JJ
cord-329276-tfrjw743	387	18	pass	pass	NN
cord-329276-tfrjw743	387	19	"	"	''
cord-329276-tfrjw743	387	20	structure	structure	NN
cord-329276-tfrjw743	387	21	in	in	IN
cord-329276-tfrjw743	387	22	which	which	WDT
cord-329276-tfrjw743	387	23	the	the	DT
cord-329276-tfrjw743	387	24	value	value	NN
cord-329276-tfrjw743	387	25	of	of	IN
cord-329276-tfrjw743	387	26	the	the	DT
cord-329276-tfrjw743	387	27	objective	objective	NN
cord-329276-tfrjw743	387	28	can	can	MD
cord-329276-tfrjw743	387	29	be	be	VB
cord-329276-tfrjw743	387	30	improved	improve	VBN
cord-329276-tfrjw743	387	31	without	without	IN
cord-329276-tfrjw743	387	32	incurring	incur	VBG
cord-329276-tfrjw743	387	33	a	a	DT
cord-329276-tfrjw743	387	34	cost	cost	NN
cord-329276-tfrjw743	387	35	.	.	.
cord-329276-tfrjw743	388	1	As	as	IN
cord-329276-tfrjw743	388	2	a	a	DT
cord-329276-tfrjw743	388	3	result	result	NN
cord-329276-tfrjw743	388	4	,	,	,
cord-329276-tfrjw743	388	5	in	in	IN
cord-329276-tfrjw743	388	6	such	such	PDT
cord-329276-tfrjw743	388	7	a	a	DT
cord-329276-tfrjw743	388	8	situation	situation	NN
cord-329276-tfrjw743	388	9	an	an	DT
cord-329276-tfrjw743	388	10	optimal	optimal	JJ
cord-329276-tfrjw743	388	11	solution	solution	NN
cord-329276-tfrjw743	388	12	may	may	MD
cord-329276-tfrjw743	388	13	not	not	RB
cord-329276-tfrjw743	388	14	exist	exist	VB
cord-329276-tfrjw743	388	15	.	.	.
cord-329276-tfrjw743	389	1	Intuitively	intuitively	RB
cord-329276-tfrjw743	389	2	,	,	,
cord-329276-tfrjw743	389	3	the	the	DT
cord-329276-tfrjw743	389	4	controls	control	NNS
cord-329276-tfrjw743	389	5	can	can	MD
cord-329276-tfrjw743	389	6	switch	switch	VB
cord-329276-tfrjw743	389	7	to	to	IN
cord-329276-tfrjw743	389	8	(	(	-LRB-
cord-329276-tfrjw743	389	9	u	u	NNP
cord-329276-tfrjw743	389	10	,	,	,
cord-329276-tfrjw743	389	11	v	v	LS
cord-329276-tfrjw743	389	12	)	)	-RRB-
cord-329276-tfrjw743	389	13	=	=	.
cord-329276-tfrjw743	390	1	(	(	-LRB-
cord-329276-tfrjw743	390	2	0	0	NFP
cord-329276-tfrjw743	390	3	,	,	,
cord-329276-tfrjw743	390	4	0	0	CD
cord-329276-tfrjw743	390	5	)	)	-RRB-
cord-329276-tfrjw743	390	6	immediately	immediately	RB
cord-329276-tfrjw743	390	7	as	as	IN
cord-329276-tfrjw743	390	8	the	the	DT
cord-329276-tfrjw743	390	9	separatrix	separatrix	NNP
cord-329276-tfrjw743	390	10	is	be	VBZ
cord-329276-tfrjw743	390	11	crossed	cross	VBN
cord-329276-tfrjw743	390	12	and	and	CC
cord-329276-tfrjw743	390	13	then	then	RB
cord-329276-tfrjw743	390	14	take	take	VB
cord-329276-tfrjw743	390	15	an	an	DT
cord-329276-tfrjw743	390	16	increasingly	increasingly	RB
cord-329276-tfrjw743	390	17	longer	long	JJR
cord-329276-tfrjw743	390	18	time	time	NN
cord-329276-tfrjw743	390	19	as	as	IN
cord-329276-tfrjw743	390	20	they	-PRON-	PRP
cord-329276-tfrjw743	390	21	pass	pass	VBP
cord-329276-tfrjw743	390	22	near	near	IN
cord-329276-tfrjw743	390	23	the	the	DT
cord-329276-tfrjw743	390	24	saddle	saddle	NN
cord-329276-tfrjw743	390	25	point	point	NN
cord-329276-tfrjw743	390	26	with	with	IN
cord-329276-tfrjw743	390	27	the	the	DT
cord-329276-tfrjw743	390	28	infimum	infimum	NN
cord-329276-tfrjw743	390	29	arising	arise	VBG
cord-329276-tfrjw743	390	30	in	in	IN
cord-329276-tfrjw743	390	31	the	the	DT
cord-329276-tfrjw743	390	32	limit	limit	NN
cord-329276-tfrjw743	391	1	T	T	NNP
cord-329276-tfrjw743	392	1	→	→	IN
cord-329276-tfrjw743	392	2	∞.	∞.	NNP
cord-329276-tfrjw743	393	1	From	from	IN
cord-329276-tfrjw743	393	2	a	a	DT
cord-329276-tfrjw743	393	3	practical	practical	JJ
cord-329276-tfrjw743	393	4	point	point	NN
cord-329276-tfrjw743	393	5	of	of	IN
cord-329276-tfrjw743	393	6	view	view	NN
cord-329276-tfrjw743	393	7	,	,	,
cord-329276-tfrjw743	393	8	this	this	DT
cord-329276-tfrjw743	393	9	behavior	behavior	NN
cord-329276-tfrjw743	393	10	of	of	IN
cord-329276-tfrjw743	393	11	course	course	NN
cord-329276-tfrjw743	393	12	is	be	VBZ
cord-329276-tfrjw743	393	13	not	not	RB
cord-329276-tfrjw743	393	14	acceptable	acceptable	JJ
cord-329276-tfrjw743	393	15	.	.	.
cord-329276-tfrjw743	394	1	Mathematically	mathematically	RB
cord-329276-tfrjw743	394	2	,	,	,
cord-329276-tfrjw743	394	3	this	this	DT
cord-329276-tfrjw743	394	4	behavior	behavior	NN
cord-329276-tfrjw743	394	5	is	be	VBZ
cord-329276-tfrjw743	394	6	easily	easily	RB
cord-329276-tfrjw743	394	7	eliminated	eliminate	VBN
cord-329276-tfrjw743	394	8	by	by	IN
cord-329276-tfrjw743	394	9	including	include	VBG
cord-329276-tfrjw743	394	10	a	a	DT
cord-329276-tfrjw743	394	11	penalty	penalty	NN
cord-329276-tfrjw743	394	12	term	term	NN
cord-329276-tfrjw743	394	13	on	on	IN
cord-329276-tfrjw743	394	14	the	the	DT
cord-329276-tfrjw743	394	15	final	final	JJ
cord-329276-tfrjw743	394	16	time	time	NN
cord-329276-tfrjw743	394	17	in	in	IN
cord-329276-tfrjw743	394	18	the	the	DT
cord-329276-tfrjw743	394	19	objective	objective	NN
cord-329276-tfrjw743	394	20	.	.	.
cord-329276-tfrjw743	395	1	This	this	DT
cord-329276-tfrjw743	395	2	limits	limit	VBZ
cord-329276-tfrjw743	395	3	the	the	DT
cord-329276-tfrjw743	395	4	size	size	NN
cord-329276-tfrjw743	395	5	of	of	IN
cord-329276-tfrjw743	395	6	the	the	DT
cord-329276-tfrjw743	395	7	therapy	therapy	NN
cord-329276-tfrjw743	395	8	interval	interval	NN
cord-329276-tfrjw743	395	9	and	and	CC
cord-329276-tfrjw743	395	10	creates	create	VBZ
cord-329276-tfrjw743	395	11	a	a	DT
cord-329276-tfrjw743	395	12	mathematically	mathematically	RB
cord-329276-tfrjw743	395	13	well	well	RB
cord-329276-tfrjw743	395	14	-	-	HYPH
cord-329276-tfrjw743	395	15	posed	pose	VBN
cord-329276-tfrjw743	395	16	problem	problem	NN
cord-329276-tfrjw743	395	17	.	.	.
cord-329276-tfrjw743	396	1	We	-PRON-	PRP
cord-329276-tfrjw743	396	2	discuss	discuss	VBP
cord-329276-tfrjw743	396	3	general	general	JJ
cord-329276-tfrjw743	396	4	properties	property	NNS
cord-329276-tfrjw743	396	5	of	of	IN
cord-329276-tfrjw743	396	6	optimal	optimal	JJ
cord-329276-tfrjw743	396	7	controls	control	NNS
cord-329276-tfrjw743	396	8	for	for	IN
cord-329276-tfrjw743	396	9	control	control	NN
cord-329276-tfrjw743	396	10	-	-	HYPH
cord-329276-tfrjw743	396	11	affine	affine	NN
cord-329276-tfrjw743	396	12	systems	system	NNS
cord-329276-tfrjw743	396	13	when	when	WRB
cord-329276-tfrjw743	396	14	the	the	DT
cord-329276-tfrjw743	396	15	L	l	NN
cord-329276-tfrjw743	396	16	1	1	CD
cord-329276-tfrjw743	396	17	-norm	-norm	.
cord-329276-tfrjw743	396	18	(	(	-LRB-
cord-329276-tfrjw743	396	19	k	k	NN
cord-329276-tfrjw743	396	20	=	=	SYM
cord-329276-tfrjw743	396	21	1	1	CD
cord-329276-tfrjw743	396	22	)	)	-RRB-
cord-329276-tfrjw743	396	23	is	be	VBZ
cord-329276-tfrjw743	396	24	used	use	VBN
cord-329276-tfrjw743	396	25	on	on	IN
cord-329276-tfrjw743	396	26	the	the	DT
cord-329276-tfrjw743	396	27	controls	control	NNS
cord-329276-tfrjw743	396	28	and	and	CC
cord-329276-tfrjw743	396	29	give	give	VB
cord-329276-tfrjw743	396	30	examples	example	NNS
cord-329276-tfrjw743	396	31	of	of	IN
cord-329276-tfrjw743	396	32	solutions	solution	NNS
cord-329276-tfrjw743	396	33	for	for	IN
cord-329276-tfrjw743	396	34	some	some	DT
cord-329276-tfrjw743	396	35	of	of	IN
cord-329276-tfrjw743	396	36	the	the	DT
cord-329276-tfrjw743	396	37	problems	problem	NNS
cord-329276-tfrjw743	396	38	mentioned	mention	VBN
cord-329276-tfrjw743	396	39	earlier	early	RBR
cord-329276-tfrjw743	396	40	.	.	.
cord-329276-tfrjw743	397	1	We	-PRON-	PRP
cord-329276-tfrjw743	397	2	consider	consider	VBP
cord-329276-tfrjw743	397	3	the	the	DT
cord-329276-tfrjw743	397	4	optimal	optimal	JJ
cord-329276-tfrjw743	397	5	control	control	NN
cord-329276-tfrjw743	397	6	problem	problem	NN
cord-329276-tfrjw743	397	7	to	to	TO
cord-329276-tfrjw743	397	8	minimize	minimize	VB
cord-329276-tfrjw743	397	9	the	the	DT
cord-329276-tfrjw743	397	10	objective	objective	NN
cord-329276-tfrjw743	397	11	(	(	-LRB-
cord-329276-tfrjw743	397	12	13	13	CD
cord-329276-tfrjw743	397	13	)	)	-RRB-
cord-329276-tfrjw743	397	14	over	over	IN
cord-329276-tfrjw743	397	15	all	all	DT
cord-329276-tfrjw743	397	16	admissible	admissible	JJ
cord-329276-tfrjw743	397	17	controls	control	NNS
cord-329276-tfrjw743	397	18	u	u	NN
cord-329276-tfrjw743	397	19	∈	∈	NN
cord-329276-tfrjw743	397	20	U	u	NN
cord-329276-tfrjw743	397	21	subject	subject	JJ
cord-329276-tfrjw743	397	22	to	to	IN
cord-329276-tfrjw743	397	23	the	the	DT
cord-329276-tfrjw743	397	24	dynamics	dynamic	NNS
cord-329276-tfrjw743	397	25	(	(	-LRB-
cord-329276-tfrjw743	397	26	1	1	CD
cord-329276-tfrjw743	397	27	)	)	-RRB-
cord-329276-tfrjw743	397	28	and	and	CC
cord-329276-tfrjw743	397	29	terminal	terminal	JJ
cord-329276-tfrjw743	397	30	constraints	constraint	NNS
cord-329276-tfrjw743	397	31	.	.	.
cord-329276-tfrjw743	398	1	Necessary	necessary	JJ
cord-329276-tfrjw743	398	2	conditions	condition	NNS
cord-329276-tfrjw743	398	3	for	for	IN
cord-329276-tfrjw743	398	4	optimality	optimality	NN
cord-329276-tfrjw743	398	5	of	of	IN
cord-329276-tfrjw743	398	6	a	a	DT
cord-329276-tfrjw743	398	7	controlled	control	VBN
cord-329276-tfrjw743	398	8	trajectory	trajectory	NN
cord-329276-tfrjw743	399	1	(	(	-LRB-
cord-329276-tfrjw743	399	2	x	x	NFP
cord-329276-tfrjw743	399	3	*	*	NFP
cord-329276-tfrjw743	399	4	,	,	,
cord-329276-tfrjw743	400	1	u	u	NNP
cord-329276-tfrjw743	400	2	*	*	NFP
cord-329276-tfrjw743	400	3	)	)	-RRB-
cord-329276-tfrjw743	400	4	are	be	VBP
cord-329276-tfrjw743	400	5	given	give	VBN
cord-329276-tfrjw743	400	6	by	by	IN
cord-329276-tfrjw743	400	7	the	the	DT
cord-329276-tfrjw743	400	8	Pontryagin	Pontryagin	NNP
cord-329276-tfrjw743	400	9	maximum	maximum	NN
cord-329276-tfrjw743	400	10	principle	principle	NN
cord-329276-tfrjw743	400	11	[	[	-LRB-
cord-329276-tfrjw743	400	12	33	33	CD
cord-329276-tfrjw743	400	13	]	]	-RRB-
cord-329276-tfrjw743	400	14	(	(	-LRB-
cord-329276-tfrjw743	400	15	for	for	IN
cord-329276-tfrjw743	400	16	some	some	DT
cord-329276-tfrjw743	400	17	recent	recent	JJ
cord-329276-tfrjw743	400	18	references	reference	NNS
cord-329276-tfrjw743	400	19	,	,	,
cord-329276-tfrjw743	400	20	see	see	VB
cord-329276-tfrjw743	400	21	[	[	-LRB-
cord-329276-tfrjw743	400	22	34	34	CD
cord-329276-tfrjw743	400	23	]	]	-RRB-
cord-329276-tfrjw743	401	1	[	[	-LRB-
cord-329276-tfrjw743	401	2	35	35	CD
cord-329276-tfrjw743	401	3	]	]	-RRB-
cord-329276-tfrjw743	401	4	[	[	-LRB-
cord-329276-tfrjw743	401	5	36	36	CD
cord-329276-tfrjw743	401	6	]	]	-RRB-
cord-329276-tfrjw743	401	7	)	)	-RRB-
cord-329276-tfrjw743	401	8	.	.	.
cord-329276-tfrjw743	402	1	These	these	DT
cord-329276-tfrjw743	402	2	conditions	condition	NNS
cord-329276-tfrjw743	402	3	are	be	VBP
cord-329276-tfrjw743	402	4	formulated	formulate	VBN
cord-329276-tfrjw743	402	5	in	in	IN
cord-329276-tfrjw743	402	6	terms	term	NNS
cord-329276-tfrjw743	402	7	of	of	IN
cord-329276-tfrjw743	402	8	the	the	DT
cord-329276-tfrjw743	402	9	(	(	-LRB-
cord-329276-tfrjw743	402	10	control	control	NN
cord-329276-tfrjw743	402	11	)	)	-RRB-
cord-329276-tfrjw743	402	12	Hamiltonian	hamiltonian	JJ
cord-329276-tfrjw743	402	13	H	h	NN
cord-329276-tfrjw743	402	14	defined	define	VBN
cord-329276-tfrjw743	402	15	as	as	IN
cord-329276-tfrjw743	402	16	where	where	WRB
cord-329276-tfrjw743	402	17	λ	λ	NN
cord-329276-tfrjw743	402	18	0	0	CD
cord-329276-tfrjw743	402	19	≥	≥	CD
cord-329276-tfrjw743	402	20	0	0	CD
cord-329276-tfrjw743	402	21	and	and	CC
cord-329276-tfrjw743	402	22	λ	λ	NN
cord-329276-tfrjw743	402	23	∈	∈	NN
cord-329276-tfrjw743	402	24	R	r	NN
cord-329276-tfrjw743	402	25	n	n	NN
cord-329276-tfrjw743	402	26	are	be	VBP
cord-329276-tfrjw743	402	27	multipliers	multiplier	NNS
cord-329276-tfrjw743	402	28	which	which	WDT
cord-329276-tfrjw743	402	29	we	-PRON-	PRP
cord-329276-tfrjw743	402	30	write	write	VBP
cord-329276-tfrjw743	402	31	as	as	IN
cord-329276-tfrjw743	402	32	a	a	DT
cord-329276-tfrjw743	402	33	row	row	NN
cord-329276-tfrjw743	402	34	-	-	HYPH
cord-329276-tfrjw743	402	35	vector	vector	NN
cord-329276-tfrjw743	402	36	.	.	.
cord-329276-tfrjw743	403	1	The	the	DT
cord-329276-tfrjw743	403	2	most	most	RBS
cord-329276-tfrjw743	403	3	important	important	JJ
cord-329276-tfrjw743	403	4	of	of	IN
cord-329276-tfrjw743	403	5	the	the	DT
cord-329276-tfrjw743	403	6	conditions	condition	NNS
cord-329276-tfrjw743	403	7	of	of	IN
cord-329276-tfrjw743	403	8	the	the	DT
cord-329276-tfrjw743	403	9	maximum	maximum	JJ
cord-329276-tfrjw743	403	10	principle	principle	JJ
cord-329276-tfrjw743	403	11	states	state	VBZ
cord-329276-tfrjw743	403	12	that	that	IN
cord-329276-tfrjw743	403	13	the	the	DT
cord-329276-tfrjw743	403	14	optimal	optimal	JJ
cord-329276-tfrjw743	403	15	control	control	NN
cord-329276-tfrjw743	404	1	u	u	LS
cord-329276-tfrjw743	404	2	*	*	NFP
cord-329276-tfrjw743	404	3	for	for	IN
cord-329276-tfrjw743	404	4	almost	almost	RB
cord-329276-tfrjw743	404	5	every	every	DT
cord-329276-tfrjw743	404	6	time	time	NN
cord-329276-tfrjw743	404	7	minimizes	minimize	VBZ
cord-329276-tfrjw743	404	8	the	the	DT
cord-329276-tfrjw743	404	9	control	control	NN
cord-329276-tfrjw743	404	10	Hamiltonian	Hamiltonian	NNP
cord-329276-tfrjw743	404	11	H	H	NNP
cord-329276-tfrjw743	404	12	pointwise	pointwise	NN
cord-329276-tfrjw743	404	13	over	over	IN
cord-329276-tfrjw743	404	14	the	the	DT
cord-329276-tfrjw743	404	15	control	control	NN
cord-329276-tfrjw743	404	16	set	set	VBD
cord-329276-tfrjw743	404	17	U	U	NNP
cord-329276-tfrjw743	404	18	along	along	IN
cord-329276-tfrjw743	404	19	the	the	DT
cord-329276-tfrjw743	404	20	optimal	optimal	NN
cord-329276-tfrjw743	404	21	controlled	control	VBN
cord-329276-tfrjw743	404	22	trajectory	trajectory	NN
cord-329276-tfrjw743	405	1	x	x	LS
cord-329276-tfrjw743	405	2	*	*	NFP
cord-329276-tfrjw743	405	3	and	and	CC
cord-329276-tfrjw743	405	4	the	the	DT
cord-329276-tfrjw743	405	5	multipliers	multiplier	NNS
cord-329276-tfrjw743	405	6	λ	λ	XX
cord-329276-tfrjw743	405	7	0	0	CD
cord-329276-tfrjw743	405	8	and	and	CC
cord-329276-tfrjw743	405	9	λ	λ	NN
cord-329276-tfrjw743	405	10	,	,	,
cord-329276-tfrjw743	405	11	i.e.	i.e.	FW
cord-329276-tfrjw743	405	12	,	,	,
cord-329276-tfrjw743	405	13	we	-PRON-	PRP
cord-329276-tfrjw743	405	14	have	have	VBP
cord-329276-tfrjw743	405	15	that	that	DT
cord-329276-tfrjw743	405	16	For	for	IN
cord-329276-tfrjw743	405	17	the	the	DT
cord-329276-tfrjw743	405	18	problems	problem	NNS
cord-329276-tfrjw743	405	19	considered	consider	VBN
cord-329276-tfrjw743	405	20	here	here	RB
cord-329276-tfrjw743	405	21	,	,	,
cord-329276-tfrjw743	405	22	the	the	DT
cord-329276-tfrjw743	405	23	Hamiltonian	Hamiltonian	NNP
cord-329276-tfrjw743	405	24	H	H	NNP
cord-329276-tfrjw743	405	25	is	be	VBZ
cord-329276-tfrjw743	405	26	affine	affine	JJ
cord-329276-tfrjw743	405	27	in	in	IN
cord-329276-tfrjw743	405	28	the	the	DT
cord-329276-tfrjw743	405	29	controls	control	NNS
cord-329276-tfrjw743	405	30	and	and	CC
cord-329276-tfrjw743	405	31	for	for	IN
cord-329276-tfrjw743	405	32	each	each	DT
cord-329276-tfrjw743	405	33	component	component	NN
cord-329276-tfrjw743	405	34	u	u	NN
cord-329276-tfrjw743	405	35	i	i	PRP
cord-329276-tfrjw743	405	36	of	of	IN
cord-329276-tfrjw743	405	37	u	u	NNP
cord-329276-tfrjw743	405	38	the	the	DT
cord-329276-tfrjw743	405	39	control	control	NN
cord-329276-tfrjw743	405	40	set	set	NN
cord-329276-tfrjw743	405	41	is	be	VBZ
cord-329276-tfrjw743	405	42	a	a	DT
cord-329276-tfrjw743	405	43	compact	compact	JJ
cord-329276-tfrjw743	405	44	interval	interval	NN
cord-329276-tfrjw743	405	45	.	.	.
cord-329276-tfrjw743	406	1	Hence	hence	RB
cord-329276-tfrjw743	406	2	,	,	,
cord-329276-tfrjw743	406	3	the	the	DT
cord-329276-tfrjw743	406	4	minimum	minimum	JJ
cord-329276-tfrjw743	406	5	condition	condition	NN
cord-329276-tfrjw743	406	6	splits	split	VBZ
cord-329276-tfrjw743	406	7	into	into	IN
cord-329276-tfrjw743	406	8	m	m	LS
cord-329276-tfrjw743	406	9	separate	separate	JJ
cord-329276-tfrjw743	406	10	scalar	scalar	JJ
cord-329276-tfrjw743	406	11	minimization	minimization	NN
cord-329276-tfrjw743	406	12	problems	problem	NNS
cord-329276-tfrjw743	406	13	that	that	WDT
cord-329276-tfrjw743	406	14	are	be	VBP
cord-329276-tfrjw743	406	15	easily	easily	RB
cord-329276-tfrjw743	406	16	solved	solve	VBN
cord-329276-tfrjw743	406	17	.	.	.
cord-329276-tfrjw743	407	1	Defining	define	VBG
cord-329276-tfrjw743	407	2	the	the	DT
cord-329276-tfrjw743	407	3	functions	function	NNS
cord-329276-tfrjw743	407	4	Φ	φ	NN
cord-329276-tfrjw743	407	5	j	j	NNP
cord-329276-tfrjw743	407	6	:	:	:
cord-329276-tfrjw743	407	7	[	[	-LRB-
cord-329276-tfrjw743	407	8	0	0	NFP
cord-329276-tfrjw743	407	9	,	,	,
cord-329276-tfrjw743	407	10	T	T	NNP
cord-329276-tfrjw743	407	11	]	]	-RRB-
cord-329276-tfrjw743	408	1	→	→	IN
cord-329276-tfrjw743	408	2	R	r	NN
cord-329276-tfrjw743	408	3	,	,	,
cord-329276-tfrjw743	408	4	it	-PRON-	PRP
cord-329276-tfrjw743	408	5	follows	follow	VBZ
cord-329276-tfrjw743	408	6	that	that	IN
cord-329276-tfrjw743	408	7	the	the	DT
cord-329276-tfrjw743	408	8	optimal	optimal	JJ
cord-329276-tfrjw743	408	9	controls	control	NNS
cord-329276-tfrjw743	408	10	satisfy	satisfy	VBP
cord-329276-tfrjw743	408	11	The	the	DT
cord-329276-tfrjw743	408	12	function	function	NN
cord-329276-tfrjw743	408	13	Φ	φ	NN
cord-329276-tfrjw743	408	14	j	j	NNP
cord-329276-tfrjw743	408	15	is	be	VBZ
cord-329276-tfrjw743	408	16	called	call	VBN
cord-329276-tfrjw743	408	17	the	the	DT
cord-329276-tfrjw743	408	18	switching	switching	NN
cord-329276-tfrjw743	408	19	function	function	NN
cord-329276-tfrjw743	408	20	corresponding	correspond	VBG
cord-329276-tfrjw743	408	21	to	to	IN
cord-329276-tfrjw743	408	22	the	the	DT
cord-329276-tfrjw743	408	23	control	control	NN
cord-329276-tfrjw743	408	24	u	u	NNP
cord-329276-tfrjw743	408	25	j	j	NNP
cord-329276-tfrjw743	408	26	.	.	.
cord-329276-tfrjw743	409	1	A	a	DT
cord-329276-tfrjw743	409	2	priori	priori	FW
cord-329276-tfrjw743	409	3	,	,	,
cord-329276-tfrjw743	409	4	the	the	DT
cord-329276-tfrjw743	409	5	control	control	NN
cord-329276-tfrjw743	409	6	u	u	NNP
cord-329276-tfrjw743	409	7	j	j	NNP
cord-329276-tfrjw743	409	8	is	be	VBZ
cord-329276-tfrjw743	409	9	not	not	RB
cord-329276-tfrjw743	409	10	determined	determine	VBN
cord-329276-tfrjw743	409	11	by	by	IN
cord-329276-tfrjw743	409	12	the	the	DT
cord-329276-tfrjw743	409	13	minimum	minimum	JJ
cord-329276-tfrjw743	409	14	condition	condition	NN
cord-329276-tfrjw743	409	15	at	at	IN
cord-329276-tfrjw743	409	16	times	time	NNS
cord-329276-tfrjw743	409	17	when	when	WRB
cord-329276-tfrjw743	409	18	Φ	Φ	NNP
cord-329276-tfrjw743	409	19	j	j	NNP
cord-329276-tfrjw743	409	20	(	(	-LRB-
cord-329276-tfrjw743	409	21	τ	τ	NN
cord-329276-tfrjw743	409	22	)	)	-RRB-
cord-329276-tfrjw743	409	23	=	=	SYM
cord-329276-tfrjw743	409	24	0	0	CD
cord-329276-tfrjw743	409	25	.	.	.
cord-329276-tfrjw743	410	1	In	in	IN
cord-329276-tfrjw743	410	2	such	such	PDT
cord-329276-tfrjw743	410	3	a	a	DT
cord-329276-tfrjw743	410	4	case	case	NN
cord-329276-tfrjw743	410	5	,	,	,
cord-329276-tfrjw743	410	6	all	all	DT
cord-329276-tfrjw743	410	7	control	control	NN
cord-329276-tfrjw743	410	8	values	value	NNS
cord-329276-tfrjw743	410	9	trivially	trivially	RB
cord-329276-tfrjw743	410	10	satisfy	satisfy	VBP
cord-329276-tfrjw743	410	11	the	the	DT
cord-329276-tfrjw743	410	12	minimum	minimum	JJ
cord-329276-tfrjw743	410	13	condition	condition	NN
cord-329276-tfrjw743	410	14	and	and	CC
cord-329276-tfrjw743	410	15	thus	thus	RB
cord-329276-tfrjw743	410	16	,	,	,
cord-329276-tfrjw743	410	17	in	in	IN
cord-329276-tfrjw743	410	18	principle	principle	NN
cord-329276-tfrjw743	410	19	,	,	,
cord-329276-tfrjw743	410	20	all	all	DT
cord-329276-tfrjw743	410	21	are	be	VBP
cord-329276-tfrjw743	410	22	candidates	candidate	NNS
cord-329276-tfrjw743	410	23	for	for	IN
cord-329276-tfrjw743	410	24	optimality	optimality	NN
cord-329276-tfrjw743	410	25	.	.	.
cord-329276-tfrjw743	411	1	However	however	RB
cord-329276-tfrjw743	411	2	,	,	,
cord-329276-tfrjw743	411	3	the	the	DT
cord-329276-tfrjw743	411	4	switching	switching	NN
cord-329276-tfrjw743	411	5	functions	function	NNS
cord-329276-tfrjw743	411	6	are	be	VBP
cord-329276-tfrjw743	411	7	absolutely	absolutely	RB
cord-329276-tfrjw743	411	8	continuous	continuous	JJ
cord-329276-tfrjw743	411	9	and	and	CC
cord-329276-tfrjw743	411	10	if	if	IN
cord-329276-tfrjw743	411	11	the	the	DT
cord-329276-tfrjw743	411	12	derivativeΦ	derivativeΦ	NNP
cord-329276-tfrjw743	411	13	j	j	NNP
cord-329276-tfrjw743	411	14	(	(	-LRB-
cord-329276-tfrjw743	411	15	τ	τ	NN
cord-329276-tfrjw743	411	16	)	)	-RRB-
cord-329276-tfrjw743	411	17	does	do	VBZ
cord-329276-tfrjw743	411	18	not	not	RB
cord-329276-tfrjw743	411	19	vanish	vanish	VB
cord-329276-tfrjw743	411	20	,	,	,
cord-329276-tfrjw743	411	21	then	then	RB
cord-329276-tfrjw743	411	22	the	the	DT
cord-329276-tfrjw743	411	23	control	control	NN
cord-329276-tfrjw743	411	24	switches	switch	VBZ
cord-329276-tfrjw743	411	25	at	at	IN
cord-329276-tfrjw743	411	26	time	time	NN
cord-329276-tfrjw743	411	27	τ	τ	NN
cord-329276-tfrjw743	411	28	between	between	IN
cord-329276-tfrjw743	411	29	u	u	NNP
cord-329276-tfrjw743	411	30	j	j	NNP
cord-329276-tfrjw743	411	31	=	=	SYM
cord-329276-tfrjw743	411	32	0	0	CD
cord-329276-tfrjw743	411	33	to	to	IN
cord-329276-tfrjw743	411	34	u	u	NNP
cord-329276-tfrjw743	411	35	j	j	NNP
cord-329276-tfrjw743	411	36	=	=	SYM
cord-329276-tfrjw743	411	37	u	u	NNP
cord-329276-tfrjw743	411	38	max	max	NNP
cord-329276-tfrjw743	411	39	j	j	NNP
cord-329276-tfrjw743	411	40	ifΦ	ifΦ	NNP
cord-329276-tfrjw743	411	41	j	j	NNP
cord-329276-tfrjw743	411	42	(	(	-LRB-
cord-329276-tfrjw743	411	43	τ	τ	NN
cord-329276-tfrjw743	411	44	)	)	-RRB-
cord-329276-tfrjw743	411	45	=	=	SYM
cord-329276-tfrjw743	411	46	0	0	CD
cord-329276-tfrjw743	411	47	.	.	.
cord-329276-tfrjw743	412	1	Such	such	JJ
cord-329276-tfrjw743	412	2	a	a	DT
cord-329276-tfrjw743	412	3	time	time	NN
cord-329276-tfrjw743	412	4	τ	τ	NN
cord-329276-tfrjw743	412	5	is	be	VBZ
cord-329276-tfrjw743	412	6	called	call	VBN
cord-329276-tfrjw743	412	7	a	a	DT
cord-329276-tfrjw743	412	8	bang	bang	NNP
cord-329276-tfrjw743	412	9	-	-	HYPH
cord-329276-tfrjw743	412	10	bang	bang	NNP
cord-329276-tfrjw743	412	11	switch	switch	NN
cord-329276-tfrjw743	412	12	.	.	.
cord-329276-tfrjw743	413	1	On	on	IN
cord-329276-tfrjw743	413	2	the	the	DT
cord-329276-tfrjw743	413	3	other	other	JJ
cord-329276-tfrjw743	413	4	hand	hand	NN
cord-329276-tfrjw743	413	5	,	,	,
cord-329276-tfrjw743	413	6	if	if	IN
cord-329276-tfrjw743	413	7	Φ	Φ	NNP
cord-329276-tfrjw743	413	8	j	j	NNP
cord-329276-tfrjw743	413	9	(	(	-LRB-
cord-329276-tfrjw743	413	10	t	t	NN
cord-329276-tfrjw743	413	11	)	)	-RRB-
cord-329276-tfrjw743	413	12	were	be	VBD
cord-329276-tfrjw743	413	13	to	to	TO
cord-329276-tfrjw743	413	14	vanish	vanish	VB
cord-329276-tfrjw743	413	15	identically	identically	RB
cord-329276-tfrjw743	413	16	on	on	IN
cord-329276-tfrjw743	413	17	an	an	DT
cord-329276-tfrjw743	413	18	open	open	JJ
cord-329276-tfrjw743	413	19	interval	interval	NN
cord-329276-tfrjw743	414	1	I	-PRON-	PRP
cord-329276-tfrjw743	414	2	,	,	,
cord-329276-tfrjw743	414	3	then	then	RB
cord-329276-tfrjw743	414	4	,	,	,
cord-329276-tfrjw743	414	5	although	although	IN
cord-329276-tfrjw743	414	6	the	the	DT
cord-329276-tfrjw743	414	7	minimization	minimization	NN
cord-329276-tfrjw743	414	8	property	property	NN
cord-329276-tfrjw743	414	9	by	by	IN
cord-329276-tfrjw743	414	10	itself	-PRON-	PRP
cord-329276-tfrjw743	414	11	gives	give	VBZ
cord-329276-tfrjw743	414	12	no	no	DT
cord-329276-tfrjw743	414	13	information	information	NN
cord-329276-tfrjw743	414	14	about	about	IN
cord-329276-tfrjw743	414	15	the	the	DT
cord-329276-tfrjw743	414	16	control	control	NN
cord-329276-tfrjw743	414	17	,	,	,
cord-329276-tfrjw743	414	18	in	in	IN
cord-329276-tfrjw743	414	19	this	this	DT
cord-329276-tfrjw743	414	20	case	case	NN
cord-329276-tfrjw743	414	21	also	also	RB
cord-329276-tfrjw743	414	22	all	all	PDT
cord-329276-tfrjw743	414	23	the	the	DT
cord-329276-tfrjw743	414	24	derivatives	derivative	NNS
cord-329276-tfrjw743	414	25	of	of	IN
cord-329276-tfrjw743	414	26	Φ	Φ	NNP
cord-329276-tfrjw743	414	27	j	j	NNP
cord-329276-tfrjw743	414	28	(	(	-LRB-
cord-329276-tfrjw743	414	29	t	t	NN
cord-329276-tfrjw743	414	30	)	)	-RRB-
cord-329276-tfrjw743	414	31	must	must	MD
cord-329276-tfrjw743	414	32	vanish	vanish	VB
cord-329276-tfrjw743	414	33	and	and	CC
cord-329276-tfrjw743	414	34	this	this	DT
cord-329276-tfrjw743	414	35	condition	condition	NN
cord-329276-tfrjw743	414	36	puts	put	VBZ
cord-329276-tfrjw743	414	37	strong	strong	JJ
cord-329276-tfrjw743	414	38	limitations	limitation	NNS
cord-329276-tfrjw743	414	39	on	on	IN
cord-329276-tfrjw743	414	40	the	the	DT
cord-329276-tfrjw743	414	41	controls	control	NNS
cord-329276-tfrjw743	414	42	.	.	.
cord-329276-tfrjw743	415	1	Extremal	Extremal	NNP
cord-329276-tfrjw743	415	2	controls	control	VBZ
cord-329276-tfrjw743	415	3	for	for	IN
cord-329276-tfrjw743	415	4	which	which	WDT
cord-329276-tfrjw743	415	5	the	the	DT
cord-329276-tfrjw743	415	6	switching	switching	NN
cord-329276-tfrjw743	415	7	function	function	NN
cord-329276-tfrjw743	415	8	vanishes	vanish	VBZ
cord-329276-tfrjw743	415	9	identically	identically	RB
cord-329276-tfrjw743	415	10	over	over	IN
cord-329276-tfrjw743	415	11	an	an	DT
cord-329276-tfrjw743	415	12	open	open	JJ
cord-329276-tfrjw743	415	13	interval	interval	NN
cord-329276-tfrjw743	415	14	I	-PRON-	PRP
cord-329276-tfrjw743	415	15	are	be	VBP
cord-329276-tfrjw743	415	16	called	call	VBN
cord-329276-tfrjw743	415	17	singular	singular	JJ
cord-329276-tfrjw743	415	18	,	,	,
cord-329276-tfrjw743	415	19	while	while	IN
cord-329276-tfrjw743	415	20	the	the	DT
cord-329276-tfrjw743	415	21	constant	constant	JJ
cord-329276-tfrjw743	415	22	controls	control	NNS
cord-329276-tfrjw743	415	23	u	u	NNP
cord-329276-tfrjw743	415	24	j	j	NNP
cord-329276-tfrjw743	415	25	=	=	SYM
cord-329276-tfrjw743	415	26	0	0	NFP
cord-329276-tfrjw743	415	27	and	and	CC
cord-329276-tfrjw743	415	28	u	u	NNP
cord-329276-tfrjw743	415	29	j	j	NNP
cord-329276-tfrjw743	415	30	=	=	SYM
cord-329276-tfrjw743	415	31	u	u	NNP
cord-329276-tfrjw743	415	32	max	max	NNP
cord-329276-tfrjw743	415	33	j	j	NNP
cord-329276-tfrjw743	415	34	are	be	VBP
cord-329276-tfrjw743	415	35	called	call	VBN
cord-329276-tfrjw743	415	36	bang	bang	NNP
cord-329276-tfrjw743	415	37	controls	control	NNS
cord-329276-tfrjw743	415	38	;	;	:
cord-329276-tfrjw743	415	39	controls	control	VBZ
cord-329276-tfrjw743	415	40	that	that	IN
cord-329276-tfrjw743	415	41	only	only	RB
cord-329276-tfrjw743	415	42	switch	switch	VBP
cord-329276-tfrjw743	415	43	between	between	IN
cord-329276-tfrjw743	415	44	0	0	CD
cord-329276-tfrjw743	415	45	and	and	CC
cord-329276-tfrjw743	415	46	the	the	DT
cord-329276-tfrjw743	415	47	maximum	maximum	JJ
cord-329276-tfrjw743	415	48	control	control	NN
cord-329276-tfrjw743	415	49	values	value	NNS
cord-329276-tfrjw743	415	50	are	be	VBP
cord-329276-tfrjw743	415	51	called	call	VBN
cord-329276-tfrjw743	415	52	bang	bang	NNP
cord-329276-tfrjw743	415	53	-	-	HYPH
cord-329276-tfrjw743	415	54	bang	bang	NNP
cord-329276-tfrjw743	415	55	controls	control	NNS
cord-329276-tfrjw743	415	56	.	.	.
cord-329276-tfrjw743	416	1	We	-PRON-	PRP
cord-329276-tfrjw743	416	2	mention	mention	VBP
cord-329276-tfrjw743	416	3	that	that	IN
cord-329276-tfrjw743	416	4	higher	high	JJR
cord-329276-tfrjw743	416	5	-	-	HYPH
cord-329276-tfrjw743	416	6	order	order	NN
cord-329276-tfrjw743	416	7	necessary	necessary	JJ
cord-329276-tfrjw743	416	8	conditions	condition	NNS
cord-329276-tfrjw743	416	9	for	for	IN
cord-329276-tfrjw743	416	10	optimality	optimality	NN
cord-329276-tfrjw743	416	11	of	of	IN
cord-329276-tfrjw743	416	12	singular	singular	JJ
cord-329276-tfrjw743	416	13	controls	control	NNS
cord-329276-tfrjw743	416	14	are	be	VBP
cord-329276-tfrjw743	416	15	available	available	JJ
cord-329276-tfrjw743	416	16	,	,	,
cord-329276-tfrjw743	416	17	the	the	DT
cord-329276-tfrjw743	416	18	so	so	RB
cord-329276-tfrjw743	416	19	-	-	HYPH
cord-329276-tfrjw743	416	20	called	call	VBN
cord-329276-tfrjw743	416	21	generalized	generalized	JJ
cord-329276-tfrjw743	416	22	Legendre	Legendre	NNP
cord-329276-tfrjw743	416	23	-	-	HYPH
cord-329276-tfrjw743	416	24	Clebsch	Clebsch	NNP
cord-329276-tfrjw743	416	25	conditions	condition	NNS
cord-329276-tfrjw743	416	26	(	(	-LRB-
cord-329276-tfrjw743	416	27	e.g.	e.g.	RB
cord-329276-tfrjw743	416	28	,	,	,
cord-329276-tfrjw743	416	29	see	see	VB
cord-329276-tfrjw743	416	30	[	[	-LRB-
cord-329276-tfrjw743	416	31	36	36	CD
cord-329276-tfrjw743	416	32	]	]	-RRB-
cord-329276-tfrjw743	416	33	)	)	-RRB-
cord-329276-tfrjw743	416	34	,	,	,
cord-329276-tfrjw743	416	35	that	that	WDT
cord-329276-tfrjw743	416	36	allow	allow	VBP
cord-329276-tfrjw743	416	37	us	-PRON-	PRP
cord-329276-tfrjw743	416	38	to	to	TO
cord-329276-tfrjw743	416	39	distinguish	distinguish	VB
cord-329276-tfrjw743	416	40	between	between	IN
cord-329276-tfrjw743	416	41	minimizing	minimize	VBG
cord-329276-tfrjw743	416	42	and	and	CC
cord-329276-tfrjw743	416	43	maximizing	maximize	VBG
cord-329276-tfrjw743	416	44	singular	singular	JJ
cord-329276-tfrjw743	416	45	controls	control	NNS
cord-329276-tfrjw743	416	46	.	.	.
cord-329276-tfrjw743	417	1	If	if	IN
cord-329276-tfrjw743	417	2	the	the	DT
cord-329276-tfrjw743	417	3	control	control	NN
cord-329276-tfrjw743	417	4	represents	represent	VBZ
cord-329276-tfrjw743	417	5	dose	dose	NN
cord-329276-tfrjw743	417	6	rates	rate	NNS
cord-329276-tfrjw743	417	7	for	for	IN
cord-329276-tfrjw743	417	8	the	the	DT
cord-329276-tfrjw743	417	9	application	application	NN
cord-329276-tfrjw743	417	10	of	of	IN
cord-329276-tfrjw743	417	11	some	some	DT
cord-329276-tfrjw743	417	12	therapeutic	therapeutic	JJ
cord-329276-tfrjw743	417	13	agent	agent	NN
cord-329276-tfrjw743	417	14	,	,	,
cord-329276-tfrjw743	417	15	then	then	RB
cord-329276-tfrjw743	417	16	bang	bang	NNP
cord-329276-tfrjw743	417	17	-	-	HYPH
cord-329276-tfrjw743	417	18	bang	bang	NNP
cord-329276-tfrjw743	417	19	controls	control	NNS
cord-329276-tfrjw743	417	20	correspond	correspond	VBP
cord-329276-tfrjw743	417	21	to	to	IN
cord-329276-tfrjw743	417	22	treatment	treatment	NN
cord-329276-tfrjw743	417	23	strategies	strategy	NNS
cord-329276-tfrjw743	417	24	that	that	WDT
cord-329276-tfrjw743	417	25	switch	switch	VBP
cord-329276-tfrjw743	417	26	between	between	IN
cord-329276-tfrjw743	417	27	maximum	maximum	JJ
cord-329276-tfrjw743	417	28	dose	dose	NN
cord-329276-tfrjw743	417	29	therapy	therapy	NN
cord-329276-tfrjw743	417	30	sessions	session	NNS
cord-329276-tfrjw743	417	31	and	and	CC
cord-329276-tfrjw743	417	32	rest	rest	NN
cord-329276-tfrjw743	417	33	-	-	HYPH
cord-329276-tfrjw743	417	34	periods	period	NNS
cord-329276-tfrjw743	417	35	,	,	,
cord-329276-tfrjw743	417	36	the	the	DT
cord-329276-tfrjw743	417	37	typical	typical	JJ
cord-329276-tfrjw743	417	38	MTD	MTD	NNP
cord-329276-tfrjw743	417	39	(	(	-LRB-
cord-329276-tfrjw743	417	40	maximum	maximum	JJ
cord-329276-tfrjw743	417	41	tolerated	tolerate	VBN
cord-329276-tfrjw743	417	42	dose	dose	NN
cord-329276-tfrjw743	417	43	)	)	-RRB-
cord-329276-tfrjw743	417	44	type	type	NN
cord-329276-tfrjw743	417	45	applications	application	NNS
cord-329276-tfrjw743	417	46	of	of	IN
cord-329276-tfrjw743	417	47	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	417	48	.	.	.
cord-329276-tfrjw743	418	1	Singular	singular	JJ
cord-329276-tfrjw743	418	2	controls	control	NNS
cord-329276-tfrjw743	418	3	,	,	,
cord-329276-tfrjw743	418	4	on	on	IN
cord-329276-tfrjw743	418	5	the	the	DT
cord-329276-tfrjw743	418	6	other	other	JJ
cord-329276-tfrjw743	418	7	hand	hand	NN
cord-329276-tfrjw743	418	8	,	,	,
cord-329276-tfrjw743	418	9	correspond	correspond	VB
cord-329276-tfrjw743	418	10	to	to	IN
cord-329276-tfrjw743	418	11	time	time	NN
cord-329276-tfrjw743	418	12	-	-	HYPH
cord-329276-tfrjw743	418	13	varying	vary	VBG
cord-329276-tfrjw743	418	14	administrations	administration	NNS
cord-329276-tfrjw743	418	15	of	of	IN
cord-329276-tfrjw743	418	16	the	the	DT
cord-329276-tfrjw743	418	17	agent	agent	NN
cord-329276-tfrjw743	418	18	at	at	IN
cord-329276-tfrjw743	418	19	intermediate	intermediate	JJ
cord-329276-tfrjw743	418	20	and	and	CC
cord-329276-tfrjw743	418	21	often	often	RB
cord-329276-tfrjw743	418	22	significantly	significantly	RB
cord-329276-tfrjw743	418	23	lower	low	JJR
cord-329276-tfrjw743	418	24	dose	dose	NN
cord-329276-tfrjw743	418	25	rates	rate	NNS
cord-329276-tfrjw743	418	26	.	.	.
cord-329276-tfrjw743	419	1	There	there	EX
cord-329276-tfrjw743	419	2	is	be	VBZ
cord-329276-tfrjw743	419	3	growing	grow	VBG
cord-329276-tfrjw743	419	4	interest	interest	NN
cord-329276-tfrjw743	419	5	in	in	IN
cord-329276-tfrjw743	419	6	such	such	JJ
cord-329276-tfrjw743	419	7	structures	structure	NNS
cord-329276-tfrjw743	419	8	in	in	IN
cord-329276-tfrjw743	419	9	the	the	DT
cord-329276-tfrjw743	419	10	medical	medical	JJ
cord-329276-tfrjw743	419	11	community	community	NN
cord-329276-tfrjw743	419	12	because	because	IN
cord-329276-tfrjw743	419	13	of	of	IN
cord-329276-tfrjw743	419	14	mounting	mount	VBG
cord-329276-tfrjw743	419	15	evidence	evidence	NN
cord-329276-tfrjw743	419	16	that	that	IN
cord-329276-tfrjw743	419	17	"	"	``
cord-329276-tfrjw743	419	18	more	more	JJR
cord-329276-tfrjw743	419	19	is	be	VBZ
cord-329276-tfrjw743	419	20	not	not	RB
cord-329276-tfrjw743	419	21	necessarily	necessarily	RB
cord-329276-tfrjw743	419	22	better	well	JJR
cord-329276-tfrjw743	419	23	"	"	''
cord-329276-tfrjw743	419	24	[	[	-LRB-
cord-329276-tfrjw743	419	25	42	42	CD
cord-329276-tfrjw743	419	26	,	,	,
cord-329276-tfrjw743	419	27	43	43	CD
cord-329276-tfrjw743	419	28	]	]	-RRB-
cord-329276-tfrjw743	419	29	and	and	CC
cord-329276-tfrjw743	419	30	that	that	IN
cord-329276-tfrjw743	419	31	a	a	DT
cord-329276-tfrjw743	419	32	biologically	biologically	RB
cord-329276-tfrjw743	419	33	optimal	optimal	JJ
cord-329276-tfrjw743	419	34	dose	dose	NN
cord-329276-tfrjw743	419	35	(	(	-LRB-
cord-329276-tfrjw743	419	36	BOD	bod	NN
cord-329276-tfrjw743	419	37	)	)	-RRB-
cord-329276-tfrjw743	419	38	with	with	IN
cord-329276-tfrjw743	419	39	the	the	DT
cord-329276-tfrjw743	419	40	best	good	JJS
cord-329276-tfrjw743	419	41	overall	overall	JJ
cord-329276-tfrjw743	419	42	response	response	NN
cord-329276-tfrjw743	419	43	should	should	MD
cord-329276-tfrjw743	419	44	be	be	VB
cord-329276-tfrjw743	419	45	sought	seek	VBN
cord-329276-tfrjw743	419	46	.	.	.
cord-329276-tfrjw743	420	1	Hence	hence	RB
cord-329276-tfrjw743	420	2	,	,	,
cord-329276-tfrjw743	420	3	the	the	DT
cord-329276-tfrjw743	420	4	question	question	NN
cord-329276-tfrjw743	420	5	whether	whether	IN
cord-329276-tfrjw743	420	6	optimal	optimal	JJ
cord-329276-tfrjw743	420	7	controls	control	NNS
cord-329276-tfrjw743	420	8	are	be	VBP
cord-329276-tfrjw743	420	9	bang	bang	NNP
cord-329276-tfrjw743	420	10	-	-	HYPH
cord-329276-tfrjw743	420	11	bang	bang	NNP
cord-329276-tfrjw743	420	12	or	or	CC
cord-329276-tfrjw743	420	13	singular	singular	JJ
cord-329276-tfrjw743	420	14	has	have	VBZ
cord-329276-tfrjw743	420	15	a	a	DT
cord-329276-tfrjw743	420	16	rather	rather	RB
cord-329276-tfrjw743	420	17	direct	direct	JJ
cord-329276-tfrjw743	420	18	interpretation	interpretation	NN
cord-329276-tfrjw743	420	19	and	and	CC
cord-329276-tfrjw743	420	20	its	-PRON-	PRP$
cord-329276-tfrjw743	420	21	answer	answer	NN
cord-329276-tfrjw743	420	22	is	be	VBZ
cord-329276-tfrjw743	420	23	of	of	IN
cord-329276-tfrjw743	420	24	practical	practical	JJ
cord-329276-tfrjw743	420	25	relevance	relevance	NN
cord-329276-tfrjw743	420	26	for	for	IN
cord-329276-tfrjw743	420	27	the	the	DT
cord-329276-tfrjw743	420	28	structure	structure	NN
cord-329276-tfrjw743	420	29	of	of	IN
cord-329276-tfrjw743	420	30	optimal	optimal	JJ
cord-329276-tfrjw743	420	31	treatment	treatment	NN
cord-329276-tfrjw743	420	32	protocols	protocol	NNS
cord-329276-tfrjw743	420	33	.	.	.
cord-329276-tfrjw743	421	1	Summarizing	summarize	VBG
cord-329276-tfrjw743	421	2	,	,	,
cord-329276-tfrjw743	421	3	solving	solve	VBG
cord-329276-tfrjw743	421	4	an	an	DT
cord-329276-tfrjw743	421	5	optimal	optimal	JJ
cord-329276-tfrjw743	421	6	control	control	NN
cord-329276-tfrjw743	421	7	is	be	VBZ
cord-329276-tfrjw743	421	8	tantamount	tantamount	JJ
cord-329276-tfrjw743	421	9	to	to	IN
cord-329276-tfrjw743	421	10	determining	determine	VBG
cord-329276-tfrjw743	421	11	the	the	DT
cord-329276-tfrjw743	421	12	correct	correct	JJ
cord-329276-tfrjw743	421	13	sequences	sequence	NNS
cord-329276-tfrjw743	421	14	and	and	CC
cord-329276-tfrjw743	421	15	switching	switch	VBG
cord-329276-tfrjw743	421	16	times	time	NNS
cord-329276-tfrjw743	421	17	for	for	IN
cord-329276-tfrjw743	421	18	the	the	DT
cord-329276-tfrjw743	421	19	controls	control	NNS
cord-329276-tfrjw743	421	20	as	as	IN
cord-329276-tfrjw743	421	21	concatenations	concatenation	NNS
cord-329276-tfrjw743	421	22	of	of	IN
cord-329276-tfrjw743	421	23	bang	bang	NN
cord-329276-tfrjw743	421	24	and	and	CC
cord-329276-tfrjw743	421	25	singular	singular	JJ
cord-329276-tfrjw743	421	26	segments	segment	NNS
cord-329276-tfrjw743	421	27	.	.	.
cord-329276-tfrjw743	422	1	We	-PRON-	PRP
cord-329276-tfrjw743	422	2	close	close	VBP
cord-329276-tfrjw743	422	3	this	this	DT
cord-329276-tfrjw743	422	4	review	review	NN
cord-329276-tfrjw743	422	5	with	with	IN
cord-329276-tfrjw743	422	6	two	two	CD
cord-329276-tfrjw743	422	7	examples	example	NNS
cord-329276-tfrjw743	422	8	of	of	IN
cord-329276-tfrjw743	422	9	optimal	optimal	JJ
cord-329276-tfrjw743	422	10	solutions	solution	NNS
cord-329276-tfrjw743	422	11	and	and	CC
cord-329276-tfrjw743	422	12	interpretations	interpretation	NNS
cord-329276-tfrjw743	422	13	of	of	IN
cord-329276-tfrjw743	422	14	these	these	DT
cord-329276-tfrjw743	422	15	results	result	NNS
cord-329276-tfrjw743	422	16	.	.	.
cord-329276-tfrjw743	423	1	We	-PRON-	PRP
cord-329276-tfrjw743	423	2	consider	consider	VBP
cord-329276-tfrjw743	423	3	the	the	DT
cord-329276-tfrjw743	423	4	model	model	NN
cord-329276-tfrjw743	423	5	(	(	-LRB-
cord-329276-tfrjw743	423	6	2)-(3	2)-(3	CD
cord-329276-tfrjw743	423	7	)	)	-RRB-
cord-329276-tfrjw743	423	8	for	for	IN
cord-329276-tfrjw743	423	9	angiogenic	angiogenic	JJ
cord-329276-tfrjw743	423	10	signaling	signal	VBG
cord-329276-tfrjw743	423	11	with	with	IN
cord-329276-tfrjw743	423	12	an	an	DT
cord-329276-tfrjw743	423	13	antiangiogenic	antiangiogenic	JJ
cord-329276-tfrjw743	423	14	agent	agent	NN
cord-329276-tfrjw743	423	15	u	u	NNP
cord-329276-tfrjw743	423	16	and	and	CC
cord-329276-tfrjw743	423	17	a	a	DT
cord-329276-tfrjw743	423	18	chemotherapeutic	chemotherapeutic	JJ
cord-329276-tfrjw743	423	19	agent	agent	NN
cord-329276-tfrjw743	423	20	v.	v.	IN
cord-329276-tfrjw743	423	21	Modeling	model	VBG
cord-329276-tfrjw743	423	22	the	the	DT
cord-329276-tfrjw743	423	23	effects	effect	NNS
cord-329276-tfrjw743	423	24	of	of	IN
cord-329276-tfrjw743	423	25	these	these	DT
cord-329276-tfrjw743	423	26	controls	control	NNS
cord-329276-tfrjw743	423	27	using	use	VBG
cord-329276-tfrjw743	423	28	Skipper	Skipper	NNP
cord-329276-tfrjw743	423	29	's	's	POS
cord-329276-tfrjw743	423	30	log	log	NN
cord-329276-tfrjw743	423	31	-	-	HYPH
cord-329276-tfrjw743	423	32	linear	linear	JJ
cord-329276-tfrjw743	423	33	model	model	NN
cord-329276-tfrjw743	423	34	and	and	CC
cord-329276-tfrjw743	423	35	treating	treat	VBG
cord-329276-tfrjw743	423	36	the	the	DT
cord-329276-tfrjw743	423	37	concentrations	concentration	NNS
cord-329276-tfrjw743	423	38	of	of	IN
cord-329276-tfrjw743	423	39	the	the	DT
cord-329276-tfrjw743	423	40	agents	agent	NNS
cord-329276-tfrjw743	423	41	as	as	IN
cord-329276-tfrjw743	423	42	the	the	DT
cord-329276-tfrjw743	423	43	controls	control	NNS
cord-329276-tfrjw743	423	44	gives	give	VBZ
cord-329276-tfrjw743	423	45	the	the	DT
cord-329276-tfrjw743	423	46	following	follow	VBG
cord-329276-tfrjw743	423	47	controlled	control	VBN
cord-329276-tfrjw743	423	48	dynamics	dynamic	NNS
cord-329276-tfrjw743	423	49	:	:	:
cord-329276-tfrjw743	423	50	We	-PRON-	PRP
cord-329276-tfrjw743	423	51	are	be	VBP
cord-329276-tfrjw743	423	52	taking	take	VBG
cord-329276-tfrjw743	423	53	the	the	DT
cord-329276-tfrjw743	423	54	point	point	NN
cord-329276-tfrjw743	423	55	of	of	IN
cord-329276-tfrjw743	423	56	view	view	NN
cord-329276-tfrjw743	423	57	that	that	IN
cord-329276-tfrjw743	423	58	the	the	DT
cord-329276-tfrjw743	423	59	available	available	JJ
cord-329276-tfrjw743	423	60	amounts	amount	NNS
cord-329276-tfrjw743	423	61	of	of	IN
cord-329276-tfrjw743	423	62	agents	agent	NNS
cord-329276-tfrjw743	423	63	have	have	VBP
cord-329276-tfrjw743	423	64	been	be	VBN
cord-329276-tfrjw743	423	65	determined	determine	VBN
cord-329276-tfrjw743	423	66	a	a	DT
cord-329276-tfrjw743	423	67	priori	priori	FW
cord-329276-tfrjw743	423	68	.	.	.
cord-329276-tfrjw743	424	1	We	-PRON-	PRP
cord-329276-tfrjw743	424	2	add	add	VBP
cord-329276-tfrjw743	424	3	the	the	DT
cord-329276-tfrjw743	424	4	trivial	trivial	JJ
cord-329276-tfrjw743	424	5	dynamicsẏ	dynamicsẏ	NN
cord-329276-tfrjw743	424	6	=	=	.
cord-329276-tfrjw743	425	1	u	u	NNP
cord-329276-tfrjw743	425	2	andż	andż	NNP
cord-329276-tfrjw743	425	3	=	=	.
cord-329276-tfrjw743	426	1	v	v	LS
cord-329276-tfrjw743	426	2	which	which	WDT
cord-329276-tfrjw743	426	3	keep	keep	VBP
cord-329276-tfrjw743	426	4	track	track	NN
cord-329276-tfrjw743	426	5	of	of	IN
cord-329276-tfrjw743	426	6	the	the	DT
cord-329276-tfrjw743	426	7	amounts	amount	NNS
cord-329276-tfrjw743	426	8	of	of	IN
cord-329276-tfrjw743	426	9	agents	agent	NNS
cord-329276-tfrjw743	426	10	used	use	VBN
cord-329276-tfrjw743	426	11	and	and	CC
cord-329276-tfrjw743	426	12	impose	impose	VB
cord-329276-tfrjw743	426	13	the	the	DT
cord-329276-tfrjw743	426	14	isoperimetric	isoperimetric	JJ
cord-329276-tfrjw743	426	15	constraints	constraint	NNS
cord-329276-tfrjw743	426	16	T	T	NNP
cord-329276-tfrjw743	426	17	0	0	CD
cord-329276-tfrjw743	426	18	u(t)dt	u(t)dt	NNP
cord-329276-tfrjw743	426	19	≤	≤	NNP
cord-329276-tfrjw743	426	20	y	y	NNP
cord-329276-tfrjw743	426	21	max	max	NNP
cord-329276-tfrjw743	426	22	and	and	CC
cord-329276-tfrjw743	426	23	T	T	NNP
cord-329276-tfrjw743	426	24	0	0	CD
cord-329276-tfrjw743	426	25	v(t)dt	v(t)dt	:
cord-329276-tfrjw743	426	26	≤	≤	NN
cord-329276-tfrjw743	426	27	z	z	NNP
cord-329276-tfrjw743	426	28	max	max	NN
cord-329276-tfrjw743	426	29	at	at	IN
cord-329276-tfrjw743	426	30	the	the	DT
cord-329276-tfrjw743	426	31	end	end	NN
cord-329276-tfrjw743	426	32	-	-	HYPH
cord-329276-tfrjw743	426	33	point	point	NN
cord-329276-tfrjw743	426	34	.	.	.
cord-329276-tfrjw743	427	1	The	the	DT
cord-329276-tfrjw743	427	2	terminal	terminal	JJ
cord-329276-tfrjw743	427	3	time	time	NN
cord-329276-tfrjw743	427	4	T	T	NNP
cord-329276-tfrjw743	427	5	is	be	VBZ
cord-329276-tfrjw743	427	6	free	free	JJ
cord-329276-tfrjw743	427	7	.	.	.
cord-329276-tfrjw743	428	1	Once	once	IN
cord-329276-tfrjw743	428	2	side	side	NN
cord-329276-tfrjw743	428	3	effects	effect	NNS
cord-329276-tfrjw743	428	4	have	have	VBP
cord-329276-tfrjw743	428	5	been	be	VBN
cord-329276-tfrjw743	428	6	modeled	model	VBN
cord-329276-tfrjw743	428	7	in	in	IN
cord-329276-tfrjw743	428	8	this	this	DT
cord-329276-tfrjw743	428	9	way	way	NN
cord-329276-tfrjw743	428	10	,	,	,
cord-329276-tfrjw743	428	11	our	-PRON-	PRP$
cord-329276-tfrjw743	428	12	objective	objective	NN
cord-329276-tfrjw743	428	13	simply	simply	RB
cord-329276-tfrjw743	428	14	becomes	become	VBZ
cord-329276-tfrjw743	428	15	to	to	TO
cord-329276-tfrjw743	428	16	minimize	minimize	VB
cord-329276-tfrjw743	428	17	the	the	DT
cord-329276-tfrjw743	428	18	tumor	tumor	NN
cord-329276-tfrjw743	428	19	volume	volume	NN
cord-329276-tfrjw743	428	20	,	,	,
cord-329276-tfrjw743	428	21	i.e.	i.e.	FW
cord-329276-tfrjw743	428	22	,	,	,
cord-329276-tfrjw743	428	23	J	J	NNP
cord-329276-tfrjw743	428	24	(	(	-LRB-
cord-329276-tfrjw743	428	25	u	u	NNP
cord-329276-tfrjw743	428	26	)	)	-RRB-
cord-329276-tfrjw743	428	27	=	=	SYM
cord-329276-tfrjw743	428	28	p(T	p(T	VBN
cord-329276-tfrjw743	428	29	)	)	-RRB-
cord-329276-tfrjw743	428	30	.	.	.
cord-329276-tfrjw743	429	1	From	from	IN
cord-329276-tfrjw743	429	2	a	a	DT
cord-329276-tfrjw743	429	3	practical	practical	JJ
cord-329276-tfrjw743	429	4	point	point	NN
cord-329276-tfrjw743	429	5	of	of	IN
cord-329276-tfrjw743	429	6	view	view	NN
cord-329276-tfrjw743	429	7	,	,	,
cord-329276-tfrjw743	429	8	the	the	DT
cord-329276-tfrjw743	429	9	optimal	optimal	JJ
cord-329276-tfrjw743	429	10	solution	solution	NN
cord-329276-tfrjw743	429	11	then	then	RB
cord-329276-tfrjw743	429	12	simply	simply	RB
cord-329276-tfrjw743	429	13	answers	answer	VBZ
cord-329276-tfrjw743	429	14	the	the	DT
cord-329276-tfrjw743	429	15	following	following	JJ
cord-329276-tfrjw743	429	16	question	question	NN
cord-329276-tfrjw743	429	17	:	:	:
cord-329276-tfrjw743	429	18	given	give	VBN
cord-329276-tfrjw743	429	19	a	a	DT
cord-329276-tfrjw743	429	20	priori	priori	FW
cord-329276-tfrjw743	429	21	determined	determine	VBN
cord-329276-tfrjw743	429	22	amounts	amount	NNS
cord-329276-tfrjw743	429	23	of	of	IN
cord-329276-tfrjw743	429	24	agents	agent	NNS
cord-329276-tfrjw743	429	25	,	,	,
cord-329276-tfrjw743	429	26	how	how	WRB
cord-329276-tfrjw743	429	27	can	can	MD
cord-329276-tfrjw743	429	28	they	-PRON-	PRP
cord-329276-tfrjw743	429	29	best	well	RBS
cord-329276-tfrjw743	429	30	be	be	VB
cord-329276-tfrjw743	429	31	administered	administer	VBN
cord-329276-tfrjw743	429	32	in	in	IN
cord-329276-tfrjw743	429	33	time	time	NN
cord-329276-tfrjw743	429	34	to	to	TO
cord-329276-tfrjw743	429	35	maximize	maximize	VB
cord-329276-tfrjw743	429	36	the	the	DT
cord-329276-tfrjw743	429	37	tumor	tumor	NN
cord-329276-tfrjw743	429	38	reduction	reduction	NN
cord-329276-tfrjw743	429	39	?	?	.
cord-329276-tfrjw743	430	1	For	for	IN
cord-329276-tfrjw743	430	2	the	the	DT
cord-329276-tfrjw743	430	3	monotherapy	monotherapy	JJ
cord-329276-tfrjw743	430	4	problem	problem	NN
cord-329276-tfrjw743	430	5	when	when	WRB
cord-329276-tfrjw743	430	6	z	z	NNP
cord-329276-tfrjw743	430	7	max	max	NNP
cord-329276-tfrjw743	430	8	=	=	SYM
cord-329276-tfrjw743	430	9	0	0	CD
cord-329276-tfrjw743	430	10	,	,	,
cord-329276-tfrjw743	430	11	i.e.	i.e.	FW
cord-329276-tfrjw743	430	12	,	,	,
cord-329276-tfrjw743	430	13	no	no	DT
cord-329276-tfrjw743	430	14	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	430	15	is	be	VBZ
cord-329276-tfrjw743	430	16	given	give	VBN
cord-329276-tfrjw743	430	17	,	,	,
cord-329276-tfrjw743	430	18	we	-PRON-	PRP
cord-329276-tfrjw743	430	19	have	have	VBP
cord-329276-tfrjw743	430	20	given	give	VBN
cord-329276-tfrjw743	430	21	a	a	DT
cord-329276-tfrjw743	430	22	complete	complete	JJ
cord-329276-tfrjw743	430	23	global	global	JJ
cord-329276-tfrjw743	430	24	solution	solution	NN
cord-329276-tfrjw743	430	25	to	to	IN
cord-329276-tfrjw743	430	26	this	this	DT
cord-329276-tfrjw743	430	27	problem	problem	NN
cord-329276-tfrjw743	430	28	in	in	IN
cord-329276-tfrjw743	430	29	form	form	NN
cord-329276-tfrjw743	430	30	of	of	IN
cord-329276-tfrjw743	430	31	a	a	DT
cord-329276-tfrjw743	430	32	regular	regular	JJ
cord-329276-tfrjw743	430	33	synthesis	synthesis	NN
cord-329276-tfrjw743	430	34	of	of	IN
cord-329276-tfrjw743	430	35	optimal	optimal	JJ
cord-329276-tfrjw743	430	36	controls	control	NNS
cord-329276-tfrjw743	430	37	[	[	-LRB-
cord-329276-tfrjw743	430	38	13	13	CD
cord-329276-tfrjw743	430	39	,	,	,
cord-329276-tfrjw743	430	40	15	15	CD
cord-329276-tfrjw743	430	41	]	]	-RRB-
cord-329276-tfrjw743	430	42	.	.	.
cord-329276-tfrjw743	431	1	This	this	DT
cord-329276-tfrjw743	431	2	solution	solution	NN
cord-329276-tfrjw743	431	3	specifies	specify	VBZ
cord-329276-tfrjw743	431	4	the	the	DT
cord-329276-tfrjw743	431	5	optimal	optimal	JJ
cord-329276-tfrjw743	431	6	control	control	NN
cord-329276-tfrjw743	431	7	as	as	IN
cord-329276-tfrjw743	431	8	a	a	DT
cord-329276-tfrjw743	431	9	feedback	feedback	NN
cord-329276-tfrjw743	431	10	function	function	NN
cord-329276-tfrjw743	431	11	of	of	IN
cord-329276-tfrjw743	431	12	the	the	DT
cord-329276-tfrjw743	431	13	state	state	NN
cord-329276-tfrjw743	431	14	(	(	-LRB-
cord-329276-tfrjw743	431	15	p	p	NN
cord-329276-tfrjw743	431	16	,	,	,
cord-329276-tfrjw743	431	17	q	q	NNP
cord-329276-tfrjw743	431	18	,	,	,
cord-329276-tfrjw743	431	19	y	y	NNP
cord-329276-tfrjw743	431	20	)	)	-RRB-
cord-329276-tfrjw743	431	21	for	for	IN
cord-329276-tfrjw743	431	22	arbitrary	arbitrary	JJ
cord-329276-tfrjw743	431	23	initial	initial	JJ
cord-329276-tfrjw743	431	24	conditions	condition	NNS
cord-329276-tfrjw743	431	25	.	.	.
cord-329276-tfrjw743	432	1	Figure	figure	NN
cord-329276-tfrjw743	432	2	6	6	CD
cord-329276-tfrjw743	432	3	gives	give	VBZ
cord-329276-tfrjw743	432	4	a	a	DT
cord-329276-tfrjw743	432	5	twodimensional	twodimensional	JJ
cord-329276-tfrjw743	432	6	representation	representation	NN
cord-329276-tfrjw743	432	7	of	of	IN
cord-329276-tfrjw743	432	8	this	this	DT
cord-329276-tfrjw743	432	9	solution	solution	NN
cord-329276-tfrjw743	432	10	into	into	IN
cord-329276-tfrjw743	432	11	the	the	DT
cord-329276-tfrjw743	432	12	(	(	-LRB-
cord-329276-tfrjw743	432	13	p	p	NN
cord-329276-tfrjw743	432	14	,	,	,
cord-329276-tfrjw743	432	15	q)-space	q)-space	NN
cord-329276-tfrjw743	432	16	with	with	IN
cord-329276-tfrjw743	432	17	p	p	NN
cord-329276-tfrjw743	432	18	shown	show	VBN
cord-329276-tfrjw743	432	19	as	as	IN
cord-329276-tfrjw743	432	20	the	the	DT
cord-329276-tfrjw743	432	21	vertical	vertical	NN
cord-329276-tfrjw743	432	22	and	and	CC
cord-329276-tfrjw743	432	23	q	q	NNP
cord-329276-tfrjw743	432	24	as	as	IN
cord-329276-tfrjw743	432	25	the	the	DT
cord-329276-tfrjw743	432	26	horizontal	horizontal	JJ
cord-329276-tfrjw743	432	27	variable	variable	NN
cord-329276-tfrjw743	432	28	.	.	.
cord-329276-tfrjw743	433	1	For	for	IN
cord-329276-tfrjw743	433	2	a	a	DT
cord-329276-tfrjw743	433	3	medically	medically	RB
cord-329276-tfrjw743	433	4	realistic	realistic	JJ
cord-329276-tfrjw743	433	5	initial	initial	JJ
cord-329276-tfrjw743	433	6	condition	condition	NN
cord-329276-tfrjw743	433	7	(	(	-LRB-
cord-329276-tfrjw743	433	8	with	with	IN
cord-329276-tfrjw743	433	9	the	the	DT
cord-329276-tfrjw743	433	10	carrying	carrying	NN
cord-329276-tfrjw743	433	11	capacity	capacity	NN
cord-329276-tfrjw743	433	12	larger	large	JJR
cord-329276-tfrjw743	433	13	than	than	IN
cord-329276-tfrjw743	433	14	the	the	DT
cord-329276-tfrjw743	433	15	tumor	tumor	NN
cord-329276-tfrjw743	433	16	volume	volume	NN
cord-329276-tfrjw743	433	17	)	)	-RRB-
cord-329276-tfrjw743	433	18	,	,	,
cord-329276-tfrjw743	433	19	optimal	optimal	JJ
cord-329276-tfrjw743	433	20	controls	control	NNS
cord-329276-tfrjw743	433	21	start	start	VBP
cord-329276-tfrjw743	433	22	with	with	IN
cord-329276-tfrjw743	433	23	a	a	DT
cord-329276-tfrjw743	433	24	full	full	JJ
cord-329276-tfrjw743	433	25	-	-	HYPH
cord-329276-tfrjw743	433	26	dose	dose	NN
cord-329276-tfrjw743	433	27	segment	segment	NN
cord-329276-tfrjw743	433	28	(	(	-LRB-
cord-329276-tfrjw743	433	29	shown	show	VBN
cord-329276-tfrjw743	433	30	as	as	IN
cord-329276-tfrjw743	433	31	solid	solid	JJ
cord-329276-tfrjw743	433	32	green	green	JJ
cord-329276-tfrjw743	433	33	curves	curve	NNS
cord-329276-tfrjw743	433	34	in	in	IN
cord-329276-tfrjw743	433	35	the	the	DT
cord-329276-tfrjw743	433	36	figure	figure	NN
cord-329276-tfrjw743	433	37	)	)	-RRB-
cord-329276-tfrjw743	433	38	until	until	IN
cord-329276-tfrjw743	433	39	an	an	DT
cord-329276-tfrjw743	433	40	optimal	optimal	JJ
cord-329276-tfrjw743	433	41	singular	singular	JJ
cord-329276-tfrjw743	433	42	arc	arc	NN
cord-329276-tfrjw743	433	43	S	S	NNP
cord-329276-tfrjw743	433	44	is	be	VBZ
cord-329276-tfrjw743	433	45	reached	reach	VBN
cord-329276-tfrjw743	433	46	.	.	.
cord-329276-tfrjw743	434	1	This	this	DT
cord-329276-tfrjw743	434	2	segment	segment	NN
cord-329276-tfrjw743	434	3	is	be	VBZ
cord-329276-tfrjw743	434	4	short	short	JJ
cord-329276-tfrjw743	434	5	in	in	IN
cord-329276-tfrjw743	434	6	time	time	NN
cord-329276-tfrjw743	434	7	.	.	.
cord-329276-tfrjw743	435	1	Using	use	VBG
cord-329276-tfrjw743	435	2	the	the	DT
cord-329276-tfrjw743	435	3	conditions	condition	NNS
cord-329276-tfrjw743	435	4	of	of	IN
cord-329276-tfrjw743	435	5	the	the	DT
cord-329276-tfrjw743	435	6	maximum	maximum	JJ
cord-329276-tfrjw743	435	7	principle	principle	NN
cord-329276-tfrjw743	435	8	,	,	,
cord-329276-tfrjw743	435	9	the	the	DT
cord-329276-tfrjw743	435	10	curve	curve	NN
cord-329276-tfrjw743	435	11	S	S	NNP
cord-329276-tfrjw743	435	12	can	can	MD
cord-329276-tfrjw743	435	13	be	be	VB
cord-329276-tfrjw743	435	14	described	describe	VBN
cord-329276-tfrjw743	435	15	explicitly	explicitly	RB
cord-329276-tfrjw743	435	16	as	as	IN
cord-329276-tfrjw743	435	17	[	[	-LRB-
cord-329276-tfrjw743	435	18	13	13	CD
cord-329276-tfrjw743	435	19	,	,	,
cord-329276-tfrjw743	435	20	15	15	CD
cord-329276-tfrjw743	435	21	]	]	-RRB-
cord-329276-tfrjw743	436	1	μ	μ	NNP
cord-329276-tfrjw743	436	2	+	+	CC
cord-329276-tfrjw743	436	3	dp	dp	NNP
cord-329276-tfrjw743	437	1	Then	then	RB
cord-329276-tfrjw743	437	2	,	,	,
cord-329276-tfrjw743	437	3	and	and	CC
cord-329276-tfrjw743	437	4	for	for	IN
cord-329276-tfrjw743	437	5	a	a	DT
cord-329276-tfrjw743	437	6	rather	rather	RB
cord-329276-tfrjw743	437	7	long	long	JJ
cord-329276-tfrjw743	437	8	time	time	NN
cord-329276-tfrjw743	437	9	,	,	,
cord-329276-tfrjw743	437	10	the	the	DT
cord-329276-tfrjw743	437	11	optimal	optimal	NN
cord-329276-tfrjw743	437	12	controlled	control	VBN
cord-329276-tfrjw743	437	13	trajectory	trajectory	NN
cord-329276-tfrjw743	437	14	follows	follow	VBZ
cord-329276-tfrjw743	437	15	this	this	DT
cord-329276-tfrjw743	437	16	singular	singular	JJ
cord-329276-tfrjw743	437	17	arc	arc	NN
cord-329276-tfrjw743	437	18	S	S	NNP
cord-329276-tfrjw743	437	19	(	(	-LRB-
cord-329276-tfrjw743	437	20	shown	show	VBN
cord-329276-tfrjw743	437	21	as	as	IN
cord-329276-tfrjw743	437	22	the	the	DT
cord-329276-tfrjw743	437	23	solid	solid	JJ
cord-329276-tfrjw743	437	24	blue	blue	JJ
cord-329276-tfrjw743	437	25	curve	curve	NN
cord-329276-tfrjw743	437	26	)	)	-RRB-
cord-329276-tfrjw743	437	27	until	until	IN
cord-329276-tfrjw743	437	28	all	all	DT
cord-329276-tfrjw743	437	29	antiangiogenic	antiangiogenic	JJ
cord-329276-tfrjw743	437	30	agents	agent	NNS
cord-329276-tfrjw743	437	31	are	be	VBP
cord-329276-tfrjw743	437	32	used	use	VBN
cord-329276-tfrjw743	437	33	up	up	RP
cord-329276-tfrjw743	437	34	.	.	.
cord-329276-tfrjw743	438	1	Because	because	IN
cord-329276-tfrjw743	438	2	of	of	IN
cord-329276-tfrjw743	438	3	after	after	IN
cord-329276-tfrjw743	438	4	effects	effect	NNS
cord-329276-tfrjw743	438	5	there	there	RB
cord-329276-tfrjw743	438	6	still	still	RB
cord-329276-tfrjw743	438	7	exists	exist	VBZ
cord-329276-tfrjw743	438	8	a	a	DT
cord-329276-tfrjw743	438	9	small	small	JJ
cord-329276-tfrjw743	438	10	interval	interval	NN
cord-329276-tfrjw743	438	11	on	on	IN
cord-329276-tfrjw743	438	12	which	which	WDT
cord-329276-tfrjw743	438	13	the	the	DT
cord-329276-tfrjw743	438	14	tumor	tumor	NN
cord-329276-tfrjw743	438	15	volume	volume	NN
cord-329276-tfrjw743	438	16	decreases	decrease	VBZ
cord-329276-tfrjw743	438	17	further	further	RB
cord-329276-tfrjw743	438	18	shown	show	VBN
cord-329276-tfrjw743	438	19	as	as	IN
cord-329276-tfrjw743	438	20	a	a	DT
cord-329276-tfrjw743	438	21	dashed	dash	VBN
cord-329276-tfrjw743	438	22	green	green	JJ
cord-329276-tfrjw743	438	23	curve	curve	NN
cord-329276-tfrjw743	438	24	.	.	.
cord-329276-tfrjw743	439	1	We	-PRON-	PRP
cord-329276-tfrjw743	439	2	note	note	VBP
cord-329276-tfrjw743	439	3	that	that	IN
cord-329276-tfrjw743	439	4	,	,	,
cord-329276-tfrjw743	439	5	and	and	CC
cord-329276-tfrjw743	439	6	different	different	JJ
cord-329276-tfrjw743	439	7	from	from	IN
cord-329276-tfrjw743	439	8	the	the	DT
cord-329276-tfrjw743	439	9	impression	impression	NN
cord-329276-tfrjw743	439	10	given	give	VBN
cord-329276-tfrjw743	439	11	in	in	IN
cord-329276-tfrjw743	439	12	the	the	DT
cord-329276-tfrjw743	439	13	phase	phase	NN
cord-329276-tfrjw743	439	14	portrait	portrait	NN
cord-329276-tfrjw743	439	15	,	,	,
cord-329276-tfrjw743	439	16	the	the	DT
cord-329276-tfrjw743	439	17	times	time	NNS
cord-329276-tfrjw743	439	18	along	along	IN
cord-329276-tfrjw743	439	19	the	the	DT
cord-329276-tfrjw743	439	20	individual	individual	JJ
cord-329276-tfrjw743	439	21	segments	segment	NNS
cord-329276-tfrjw743	439	22	are	be	VBP
cord-329276-tfrjw743	439	23	as	as	IN
cord-329276-tfrjw743	439	24	described	describe	VBN
cord-329276-tfrjw743	439	25	above	above	RB
cord-329276-tfrjw743	439	26	.	.	.
cord-329276-tfrjw743	440	1	The	the	DT
cord-329276-tfrjw743	440	2	system	system	NN
cord-329276-tfrjw743	440	3	has	have	VBZ
cord-329276-tfrjw743	440	4	a	a	DT
cord-329276-tfrjw743	440	5	strong	strong	JJ
cord-329276-tfrjw743	440	6	differential	differential	JJ
cord-329276-tfrjw743	440	7	-	-	HYPH
cord-329276-tfrjw743	440	8	algebraic	algebraic	JJ
cord-329276-tfrjw743	440	9	character	character	NN
cord-329276-tfrjw743	440	10	and	and	CC
cord-329276-tfrjw743	440	11	as	as	IN
cord-329276-tfrjw743	440	12	a	a	DT
cord-329276-tfrjw743	440	13	result	result	NN
cord-329276-tfrjw743	440	14	the	the	DT
cord-329276-tfrjw743	440	15	dynamics	dynamic	NNS
cord-329276-tfrjw743	440	16	along	along	IN
cord-329276-tfrjw743	440	17	the	the	DT
cord-329276-tfrjw743	440	18	full	full	JJ
cord-329276-tfrjw743	440	19	and	and	CC
cord-329276-tfrjw743	440	20	no	no	DT
cord-329276-tfrjw743	440	21	dose	dose	NN
cord-329276-tfrjw743	440	22	segments	segment	NNS
cord-329276-tfrjw743	440	23	occurring	occur	VBG
cord-329276-tfrjw743	440	24	in	in	IN
cord-329276-tfrjw743	440	25	the	the	DT
cord-329276-tfrjw743	440	26	optimal	optimal	JJ
cord-329276-tfrjw743	440	27	synthesis	synthesis	NN
cord-329276-tfrjw743	440	28	is	be	VBZ
cord-329276-tfrjw743	440	29	very	very	RB
cord-329276-tfrjw743	440	30	fast	fast	RB
cord-329276-tfrjw743	440	31	generating	generate	VBG
cord-329276-tfrjw743	440	32	the	the	DT
cord-329276-tfrjw743	440	33	almost	almost	RB
cord-329276-tfrjw743	440	34	horizontal	horizontal	JJ
cord-329276-tfrjw743	440	35	lines	line	NNS
cord-329276-tfrjw743	440	36	seen	see	VBN
cord-329276-tfrjw743	440	37	in	in	IN
cord-329276-tfrjw743	440	38	Fig	Fig	NNP
cord-329276-tfrjw743	440	39	.	.	.
cord-329276-tfrjw743	441	1	6	6	LS
cord-329276-tfrjw743	441	2	.	.	.
cord-329276-tfrjw743	442	1	Optimal	optimal	JJ
cord-329276-tfrjw743	442	2	controls	control	NNS
cord-329276-tfrjw743	442	3	are	be	VBP
cord-329276-tfrjw743	442	4	strongly	strongly	RB
cord-329276-tfrjw743	442	5	characterized	characterize	VBN
cord-329276-tfrjw743	442	6	by	by	IN
cord-329276-tfrjw743	442	7	the	the	DT
cord-329276-tfrjw743	442	8	singular	singular	JJ
cord-329276-tfrjw743	442	9	control	control	NN
cord-329276-tfrjw743	442	10	which	which	WDT
cord-329276-tfrjw743	442	11	follows	follow	VBZ
cord-329276-tfrjw743	442	12	a	a	DT
cord-329276-tfrjw743	442	13	specific	specific	JJ
cord-329276-tfrjw743	442	14	time	time	NN
cord-329276-tfrjw743	442	15	-	-	HYPH
cord-329276-tfrjw743	442	16	varying	vary	VBG
cord-329276-tfrjw743	442	17	concentration	concentration	NN
cord-329276-tfrjw743	442	18	of	of	IN
cord-329276-tfrjw743	442	19	the	the	DT
cord-329276-tfrjw743	442	20	agents	agent	NNS
cord-329276-tfrjw743	442	21	which	which	WDT
cord-329276-tfrjw743	442	22	maintains	maintain	VBZ
cord-329276-tfrjw743	442	23	an	an	DT
cord-329276-tfrjw743	442	24	optimal	optimal	JJ
cord-329276-tfrjw743	442	25	relation	relation	NN
cord-329276-tfrjw743	442	26	between	between	IN
cord-329276-tfrjw743	442	27	the	the	DT
cord-329276-tfrjw743	442	28	tumor	tumor	NN
cord-329276-tfrjw743	442	29	volume	volume	NN
cord-329276-tfrjw743	442	30	p	p	NN
cord-329276-tfrjw743	442	31	and	and	CC
cord-329276-tfrjw743	442	32	its	-PRON-	PRP$
cord-329276-tfrjw743	442	33	carrying	carrying	NN
cord-329276-tfrjw743	442	34	capacity	capacity	NN
cord-329276-tfrjw743	442	35	q.	q.	NN
cord-329276-tfrjw743	443	1	It	-PRON-	PRP
cord-329276-tfrjw743	443	2	is	be	VBZ
cord-329276-tfrjw743	443	3	the	the	DT
cord-329276-tfrjw743	443	4	functional	functional	JJ
cord-329276-tfrjw743	443	5	relation	relation	NN
cord-329276-tfrjw743	443	6	defined	define	VBN
cord-329276-tfrjw743	443	7	by	by	IN
cord-329276-tfrjw743	443	8	the	the	DT
cord-329276-tfrjw743	443	9	singular	singular	JJ
cord-329276-tfrjw743	443	10	arc	arc	NN
cord-329276-tfrjw743	443	11	which	which	WDT
cord-329276-tfrjw743	443	12	provides	provide	VBZ
cord-329276-tfrjw743	443	13	ideal	ideal	JJ
cord-329276-tfrjw743	443	14	conditions	condition	NNS
cord-329276-tfrjw743	443	15	for	for	IN
cord-329276-tfrjw743	443	16	tumor	tumor	NN
cord-329276-tfrjw743	443	17	shrinkage	shrinkage	NN
cord-329276-tfrjw743	443	18	.	.	.
cord-329276-tfrjw743	444	1	The	the	DT
cord-329276-tfrjw743	444	2	optimal	optimal	JJ
cord-329276-tfrjw743	444	3	solution	solution	NN
cord-329276-tfrjw743	444	4	for	for	IN
cord-329276-tfrjw743	444	5	the	the	DT
cord-329276-tfrjw743	444	6	monotherapy	monotherapy	NNP
cord-329276-tfrjw743	444	7	problem	problem	NN
cord-329276-tfrjw743	444	8	provides	provide	VBZ
cord-329276-tfrjw743	444	9	the	the	DT
cord-329276-tfrjw743	444	10	mathematical	mathematical	JJ
cord-329276-tfrjw743	444	11	foundation	foundation	NN
cord-329276-tfrjw743	444	12	on	on	IN
cord-329276-tfrjw743	444	13	which	which	WDT
cord-329276-tfrjw743	444	14	optimal	optimal	JJ
cord-329276-tfrjw743	444	15	controls	control	NNS
cord-329276-tfrjw743	444	16	for	for	IN
cord-329276-tfrjw743	444	17	combination	combination	NN
cord-329276-tfrjw743	444	18	therapies	therapy	NNS
cord-329276-tfrjw743	444	19	with	with	IN
cord-329276-tfrjw743	444	20	antiangiogenic	antiangiogenic	JJ
cord-329276-tfrjw743	444	21	treatments	treatment	NNS
cord-329276-tfrjw743	444	22	can	can	MD
cord-329276-tfrjw743	444	23	be	be	VB
cord-329276-tfrjw743	444	24	computed	compute	VBN
cord-329276-tfrjw743	444	25	.	.	.
cord-329276-tfrjw743	445	1	This	this	DT
cord-329276-tfrjw743	445	2	holds	hold	VBZ
cord-329276-tfrjw743	445	3	both	both	DT
cord-329276-tfrjw743	445	4	for	for	IN
cord-329276-tfrjw743	445	5	combinations	combination	NNS
cord-329276-tfrjw743	445	6	with	with	IN
cord-329276-tfrjw743	445	7	radiotherapy	radiotherapy	NN
cord-329276-tfrjw743	445	8	[	[	-LRB-
cord-329276-tfrjw743	445	9	44	44	CD
cord-329276-tfrjw743	445	10	]	]	-RRB-
cord-329276-tfrjw743	445	11	and	and	CC
cord-329276-tfrjw743	445	12	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	445	13	[	[	-LRB-
cord-329276-tfrjw743	445	14	32	32	CD
cord-329276-tfrjw743	445	15	,	,	,
cord-329276-tfrjw743	445	16	45	45	CD
cord-329276-tfrjw743	445	17	]	]	-RRB-
cord-329276-tfrjw743	445	18	.	.	.
cord-329276-tfrjw743	446	1	Here	here	RB
cord-329276-tfrjw743	446	2	,	,	,
cord-329276-tfrjw743	446	3	we	-PRON-	PRP
cord-329276-tfrjw743	446	4	still	still	RB
cord-329276-tfrjw743	446	5	discuss	discuss	VBP
cord-329276-tfrjw743	446	6	the	the	DT
cord-329276-tfrjw743	446	7	latter	latter	JJ
cord-329276-tfrjw743	446	8	case	case	NN
cord-329276-tfrjw743	446	9	.	.	.
cord-329276-tfrjw743	447	1	Below	below	IN
cord-329276-tfrjw743	447	2	we	-PRON-	PRP
cord-329276-tfrjw743	447	3	state	state	VBP
cord-329276-tfrjw743	447	4	the	the	DT
cord-329276-tfrjw743	447	5	optimal	optimal	JJ
cord-329276-tfrjw743	447	6	concatenation	concatenation	NN
cord-329276-tfrjw743	447	7	structure	structure	NN
cord-329276-tfrjw743	447	8	for	for	IN
cord-329276-tfrjw743	447	9	a	a	DT
cord-329276-tfrjw743	447	10	typical	typical	JJ
cord-329276-tfrjw743	447	11	scenario	scenario	NN
cord-329276-tfrjw743	447	12	which	which	WDT
cord-329276-tfrjw743	447	13	includes	include	VBZ
cord-329276-tfrjw743	447	14	an	an	DT
cord-329276-tfrjw743	447	15	initial	initial	JJ
cord-329276-tfrjw743	447	16	condition	condition	NN
cord-329276-tfrjw743	447	17	when	when	WRB
cord-329276-tfrjw743	447	18	the	the	DT
cord-329276-tfrjw743	447	19	carrying	carry	VBG
cord-329276-tfrjw743	447	20	capacity	capacity	NN
cord-329276-tfrjw743	447	21	significantly	significantly	RB
cord-329276-tfrjw743	447	22	exceeds	exceed	VBZ
cord-329276-tfrjw743	447	23	the	the	DT
cord-329276-tfrjw743	447	24	tumor	tumor	NN
cord-329276-tfrjw743	447	25	volume	volume	NN
cord-329276-tfrjw743	447	26	,	,	,
cord-329276-tfrjw743	447	27	when	when	WRB
cord-329276-tfrjw743	447	28	there	there	EX
cord-329276-tfrjw743	447	29	is	be	VBZ
cord-329276-tfrjw743	447	30	ample	ample	JJ
cord-329276-tfrjw743	447	31	supply	supply	NN
cord-329276-tfrjw743	447	32	of	of	IN
cord-329276-tfrjw743	447	33	antiangiogenic	antiangiogenic	NNP
cord-329276-tfrjw743	447	34	inhibitors	inhibitor	NNS
cord-329276-tfrjw743	447	35	(	(	-LRB-
cord-329276-tfrjw743	447	36	whose	whose	WP$
cord-329276-tfrjw743	447	37	side	side	NN
cord-329276-tfrjw743	447	38	effects	effect	NNS
cord-329276-tfrjw743	447	39	generally	generally	RB
cord-329276-tfrjw743	447	40	are	be	VBP
cord-329276-tfrjw743	447	41	low	low	JJ
cord-329276-tfrjw743	447	42	)	)	-RRB-
cord-329276-tfrjw743	447	43	and	and	CC
cord-329276-tfrjw743	447	44	a	a	DT
cord-329276-tfrjw743	447	45	more	more	RBR
cord-329276-tfrjw743	447	46	limited	limited	JJ
cord-329276-tfrjw743	447	47	total	total	JJ
cord-329276-tfrjw743	447	48	dose	dose	NN
cord-329276-tfrjw743	447	49	of	of	IN
cord-329276-tfrjw743	447	50	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	447	51	(	(	-LRB-
cord-329276-tfrjw743	447	52	which	which	WDT
cord-329276-tfrjw743	447	53	generally	generally	RB
cord-329276-tfrjw743	447	54	has	have	VBZ
cord-329276-tfrjw743	447	55	much	much	RB
cord-329276-tfrjw743	447	56	higher	high	JJR
cord-329276-tfrjw743	447	57	side	side	NN
cord-329276-tfrjw743	447	58	effects	effect	NNS
cord-329276-tfrjw743	447	59	)	)	-RRB-
cord-329276-tfrjw743	447	60	to	to	TO
cord-329276-tfrjw743	447	61	be	be	VB
cord-329276-tfrjw743	447	62	given	give	VBN
cord-329276-tfrjw743	447	63	.	.	.
cord-329276-tfrjw743	448	1	In	in	IN
cord-329276-tfrjw743	448	2	such	such	PDT
cord-329276-tfrjw743	448	3	a	a	DT
cord-329276-tfrjw743	448	4	situation	situation	NN
cord-329276-tfrjw743	448	5	,	,	,
cord-329276-tfrjw743	448	6	optimal	optimal	JJ
cord-329276-tfrjw743	448	7	controls	control	NNS
cord-329276-tfrjw743	448	8	(	(	-LRB-
cord-329276-tfrjw743	448	9	u	u	NNP
cord-329276-tfrjw743	448	10	*	*	NNP
cord-329276-tfrjw743	448	11	,	,	,
cord-329276-tfrjw743	448	12	v	v	LS
cord-329276-tfrjw743	448	13	*	*	NFP
cord-329276-tfrjw743	448	14	)	)	-RRB-
cord-329276-tfrjw743	448	15	consist	consist	VBP
cord-329276-tfrjw743	448	16	of	of	IN
cord-329276-tfrjw743	448	17	concatenations	concatenation	NNS
cord-329276-tfrjw743	448	18	of	of	IN
cord-329276-tfrjw743	448	19	four	four	CD
cord-329276-tfrjw743	448	20	segments	segment	NNS
cord-329276-tfrjw743	448	21	of	of	IN
cord-329276-tfrjw743	448	22	the	the	DT
cord-329276-tfrjw743	448	23	following	follow	VBG
cord-329276-tfrjw743	448	24	form	form	NN
cord-329276-tfrjw743	448	25	:	:	:
cord-329276-tfrjw743	448	26	Initially	initially	RB
cord-329276-tfrjw743	448	27	,	,	,
cord-329276-tfrjw743	448	28	no	no	DT
cord-329276-tfrjw743	448	29	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	448	30	is	be	VBZ
cord-329276-tfrjw743	448	31	given	give	VBN
cord-329276-tfrjw743	448	32	,	,	,
cord-329276-tfrjw743	448	33	while	while	IN
cord-329276-tfrjw743	448	34	antiangiogenic	antiangiogenic	JJ
cord-329276-tfrjw743	448	35	drugs	drug	NNS
cord-329276-tfrjw743	448	36	are	be	VBP
cord-329276-tfrjw743	448	37	given	give	VBN
cord-329276-tfrjw743	448	38	at	at	IN
cord-329276-tfrjw743	448	39	full	full	JJ
cord-329276-tfrjw743	448	40	dose	dose	NN
cord-329276-tfrjw743	448	41	until	until	IN
cord-329276-tfrjw743	448	42	the	the	DT
cord-329276-tfrjw743	448	43	optimal	optimal	JJ
cord-329276-tfrjw743	448	44	singular	singular	JJ
cord-329276-tfrjw743	448	45	arc	arc	NN
cord-329276-tfrjw743	448	46	S	S	NNP
cord-329276-tfrjw743	448	47	for	for	IN
cord-329276-tfrjw743	448	48	the	the	DT
cord-329276-tfrjw743	448	49	monotherapy	monotherapy	JJ
cord-329276-tfrjw743	448	50	problem	problem	NN
cord-329276-tfrjw743	448	51	is	be	VBZ
cord-329276-tfrjw743	448	52	reached	reach	VBN
cord-329276-tfrjw743	448	53	.	.	.
cord-329276-tfrjw743	449	1	At	at	IN
cord-329276-tfrjw743	449	2	this	this	DT
cord-329276-tfrjw743	449	3	point	point	NN
cord-329276-tfrjw743	449	4	,	,	,
cord-329276-tfrjw743	449	5	administration	administration	NN
cord-329276-tfrjw743	449	6	switches	switch	VBZ
cord-329276-tfrjw743	449	7	to	to	IN
cord-329276-tfrjw743	449	8	the	the	DT
cord-329276-tfrjw743	449	9	optimal	optimal	JJ
cord-329276-tfrjw743	449	10	singular	singular	JJ
cord-329276-tfrjw743	449	11	control	control	NN
cord-329276-tfrjw743	449	12	for	for	IN
cord-329276-tfrjw743	449	13	the	the	DT
cord-329276-tfrjw743	449	14	monotherapy	monotherapy	JJ
cord-329276-tfrjw743	449	15	problem	problem	NN
cord-329276-tfrjw743	449	16	until	until	IN
cord-329276-tfrjw743	449	17	a	a	DT
cord-329276-tfrjw743	449	18	specific	specific	JJ
cord-329276-tfrjw743	449	19	time	time	NN
cord-329276-tfrjw743	449	20	τ	τ	NN
cord-329276-tfrjw743	449	21	is	be	VBZ
cord-329276-tfrjw743	449	22	reached	reach	VBN
cord-329276-tfrjw743	449	23	.	.	.
cord-329276-tfrjw743	450	1	At	at	IN
cord-329276-tfrjw743	450	2	this	this	DT
cord-329276-tfrjw743	450	3	time	time	NN
cord-329276-tfrjw743	450	4	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	450	5	commences	commence	VBZ
cord-329276-tfrjw743	450	6	in	in	IN
cord-329276-tfrjw743	450	7	a	a	DT
cord-329276-tfrjw743	450	8	single	single	JJ
cord-329276-tfrjw743	450	9	full	full	JJ
cord-329276-tfrjw743	450	10	dose	dose	NN
cord-329276-tfrjw743	450	11	(	(	-LRB-
cord-329276-tfrjw743	450	12	MTD	MTD	NNP
cord-329276-tfrjw743	450	13	)	)	-RRB-
cord-329276-tfrjw743	450	14	session	session	NN
cord-329276-tfrjw743	450	15	.	.	.
cord-329276-tfrjw743	451	1	In	in	IN
cord-329276-tfrjw743	451	2	the	the	DT
cord-329276-tfrjw743	451	3	medical	medical	JJ
cord-329276-tfrjw743	451	4	literature	literature	NN
cord-329276-tfrjw743	451	5	this	this	DT
cord-329276-tfrjw743	451	6	has	have	VBZ
cord-329276-tfrjw743	451	7	been	be	VBN
cord-329276-tfrjw743	451	8	called	call	VBN
cord-329276-tfrjw743	451	9	the	the	DT
cord-329276-tfrjw743	451	10	'	'	``
cord-329276-tfrjw743	451	11	optimal	optimal	JJ
cord-329276-tfrjw743	451	12	therapeutic	therapeutic	JJ
cord-329276-tfrjw743	451	13	window	window	NN
cord-329276-tfrjw743	451	14	'	'	''
cord-329276-tfrjw743	451	15	[	[	-LRB-
cord-329276-tfrjw743	451	16	30	30	CD
cord-329276-tfrjw743	451	17	]	]	-RRB-
cord-329276-tfrjw743	451	18	.	.	.
cord-329276-tfrjw743	452	1	Also	also	RB
cord-329276-tfrjw743	452	2	,	,	,
cord-329276-tfrjw743	452	3	because	because	IN
cord-329276-tfrjw743	452	4	of	of	IN
cord-329276-tfrjw743	452	5	the	the	DT
cord-329276-tfrjw743	452	6	onset	onset	NN
cord-329276-tfrjw743	452	7	of	of	IN
cord-329276-tfrjw743	452	8	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	452	9	,	,	,
cord-329276-tfrjw743	452	10	the	the	DT
cord-329276-tfrjw743	452	11	formula	formula	NN
cord-329276-tfrjw743	452	12	for	for	IN
cord-329276-tfrjw743	452	13	the	the	DT
cord-329276-tfrjw743	452	14	optimal	optimal	JJ
cord-329276-tfrjw743	452	15	singular	singular	JJ
cord-329276-tfrjw743	452	16	control	control	NN
cord-329276-tfrjw743	452	17	adjusts	adjust	VBZ
cord-329276-tfrjw743	452	18	and	and	CC
cord-329276-tfrjw743	452	19	this	this	DT
cord-329276-tfrjw743	452	20	is	be	VBZ
cord-329276-tfrjw743	452	21	seen	see	VBN
cord-329276-tfrjw743	452	22	as	as	IN
cord-329276-tfrjw743	452	23	a	a	DT
cord-329276-tfrjw743	452	24	small	small	JJ
cord-329276-tfrjw743	452	25	kink	kink	NN
cord-329276-tfrjw743	452	26	in	in	IN
cord-329276-tfrjw743	452	27	Fig	Fig	NNP
cord-329276-tfrjw743	452	28	.	.	.
cord-329276-tfrjw743	452	29	7	7	CD
cord-329276-tfrjw743	452	30	which	which	WDT
cord-329276-tfrjw743	452	31	gives	give	VBZ
cord-329276-tfrjw743	452	32	a	a	DT
cord-329276-tfrjw743	452	33	sample	sample	NN
cord-329276-tfrjw743	452	34	of	of	IN
cord-329276-tfrjw743	452	35	the	the	DT
cord-329276-tfrjw743	452	36	time	time	NN
cord-329276-tfrjw743	452	37	-	-	HYPH
cord-329276-tfrjw743	452	38	evolution	evolution	NN
cord-329276-tfrjw743	452	39	for	for	IN
cord-329276-tfrjw743	452	40	optimal	optimal	JJ
cord-329276-tfrjw743	452	41	controls	control	NNS
cord-329276-tfrjw743	453	1	u	u	NNP
cord-329276-tfrjw743	454	1	*	*	NFP
cord-329276-tfrjw743	454	2	and	and	CC
cord-329276-tfrjw743	454	3	v	v	LS
cord-329276-tfrjw743	454	4	*	*	NFP
cord-329276-tfrjw743	454	5	.	.	.
cord-329276-tfrjw743	455	1	Then	then	RB
cord-329276-tfrjw743	455	2	,	,	,
cord-329276-tfrjw743	455	3	both	both	DT
cord-329276-tfrjw743	455	4	controls	control	NNS
cord-329276-tfrjw743	455	5	are	be	VBP
cord-329276-tfrjw743	455	6	given	give	VBN
cord-329276-tfrjw743	455	7	until	until	IN
cord-329276-tfrjw743	455	8	all	all	DT
cord-329276-tfrjw743	455	9	available	available	JJ
cord-329276-tfrjw743	455	10	drugs	drug	NNS
cord-329276-tfrjw743	455	11	are	be	VBP
cord-329276-tfrjw743	455	12	exhausted	exhausted	JJ
cord-329276-tfrjw743	455	13	.	.	.
cord-329276-tfrjw743	456	1	In	in	IN
cord-329276-tfrjw743	456	2	Eq	Eq	NNP
cord-329276-tfrjw743	456	3	.	.	.
cord-329276-tfrjw743	457	1	(	(	-LRB-
cord-329276-tfrjw743	457	2	25	25	CD
cord-329276-tfrjw743	457	3	)	)	-RRB-
cord-329276-tfrjw743	457	4	we	-PRON-	PRP
cord-329276-tfrjw743	457	5	have	have	VBP
cord-329276-tfrjw743	457	6	formulated	formulate	VBN
cord-329276-tfrjw743	457	7	the	the	DT
cord-329276-tfrjw743	457	8	controls	control	NNS
cord-329276-tfrjw743	457	9	for	for	IN
cord-329276-tfrjw743	457	10	the	the	DT
cord-329276-tfrjw743	457	11	case	case	NN
cord-329276-tfrjw743	457	12	that	that	IN
cord-329276-tfrjw743	457	13	the	the	DT
cord-329276-tfrjw743	457	14	antiangiogenic	antiangiogenic	NNP
cord-329276-tfrjw743	457	15	inhibitors	inhibitor	NNS
cord-329276-tfrjw743	457	16	run	run	VBP
cord-329276-tfrjw743	457	17	out	out	RP
cord-329276-tfrjw743	457	18	first	first	RB
cord-329276-tfrjw743	457	19	,	,	,
cord-329276-tfrjw743	457	20	but	but	CC
cord-329276-tfrjw743	457	21	this	this	DT
cord-329276-tfrjw743	457	22	depends	depend	VBZ
cord-329276-tfrjw743	457	23	on	on	IN
cord-329276-tfrjw743	457	24	the	the	DT
cord-329276-tfrjw743	457	25	total	total	JJ
cord-329276-tfrjw743	457	26	amounts	amount	NNS
cord-329276-tfrjw743	457	27	available	available	JJ
cord-329276-tfrjw743	457	28	and	and	CC
cord-329276-tfrjw743	457	29	could	could	MD
cord-329276-tfrjw743	457	30	also	also	RB
cord-329276-tfrjw743	457	31	be	be	VB
cord-329276-tfrjw743	457	32	reversed	reverse	VBN
cord-329276-tfrjw743	457	33	.	.	.
cord-329276-tfrjw743	458	1	Figure	figure	NN
cord-329276-tfrjw743	458	2	8	8	CD
cord-329276-tfrjw743	458	3	illustrates	illustrate	VBZ
cord-329276-tfrjw743	458	4	the	the	DT
cord-329276-tfrjw743	458	5	shape	shape	NN
cord-329276-tfrjw743	458	6	of	of	IN
cord-329276-tfrjw743	458	7	the	the	DT
cord-329276-tfrjw743	458	8	optimal	optimal	JJ
cord-329276-tfrjw743	458	9	controlled	control	VBN
cord-329276-tfrjw743	458	10	trajectory	trajectory	NN
cord-329276-tfrjw743	458	11	in	in	IN
cord-329276-tfrjw743	458	12	(	(	-LRB-
cord-329276-tfrjw743	458	13	p	p	NN
cord-329276-tfrjw743	458	14	,	,	,
cord-329276-tfrjw743	458	15	q)-space	q)-space	NN
cord-329276-tfrjw743	458	16	.	.	.
cord-329276-tfrjw743	459	1	Mathematical	mathematical	JJ
cord-329276-tfrjw743	459	2	optimization	optimization	NN
cord-329276-tfrjw743	459	3	of	of	IN
cord-329276-tfrjw743	459	4	the	the	DT
cord-329276-tfrjw743	459	5	combined	combine	VBN
cord-329276-tfrjw743	459	6	therapy	therapy	NN
cord-329276-tfrjw743	459	7	strongly	strongly	RB
cord-329276-tfrjw743	459	8	supports	support	VBZ
cord-329276-tfrjw743	459	9	the	the	DT
cord-329276-tfrjw743	459	10	following	following	JJ
cord-329276-tfrjw743	459	11	two	two	CD
cord-329276-tfrjw743	459	12	qualitative	qualitative	JJ
cord-329276-tfrjw743	459	13	conclusions	conclusion	NNS
cord-329276-tfrjw743	459	14	:	:	:
cord-329276-tfrjw743	459	15	(	(	-LRB-
cord-329276-tfrjw743	459	16	i	i	NN
cord-329276-tfrjw743	459	17	)	)	-RRB-
cord-329276-tfrjw743	459	18	there	there	EX
cord-329276-tfrjw743	459	19	is	be	VBZ
cord-329276-tfrjw743	459	20	an	an	DT
cord-329276-tfrjw743	459	21	optimal	optimal	JJ
cord-329276-tfrjw743	459	22	relation	relation	NN
cord-329276-tfrjw743	459	23	between	between	IN
cord-329276-tfrjw743	459	24	the	the	DT
cord-329276-tfrjw743	459	25	tumor	tumor	NN
cord-329276-tfrjw743	459	26	volume	volume	NN
cord-329276-tfrjw743	459	27	p	p	NN
cord-329276-tfrjw743	459	28	and	and	CC
cord-329276-tfrjw743	459	29	its	-PRON-	PRP$
cord-329276-tfrjw743	459	30	carrying	carrying	NN
cord-329276-tfrjw743	459	31	capacity	capacity	NN
cord-329276-tfrjw743	459	32	q	q	NN
cord-329276-tfrjw743	459	33	along	along	IN
cord-329276-tfrjw743	459	34	which	which	WDT
cord-329276-tfrjw743	459	35	the	the	DT
cord-329276-tfrjw743	459	36	tumor	tumor	NN
cord-329276-tfrjw743	459	37	decrease	decrease	NN
cord-329276-tfrjw743	459	38	is	be	VBZ
cord-329276-tfrjw743	459	39	maximized	maximize	VBN
cord-329276-tfrjw743	459	40	.	.	.
cord-329276-tfrjw743	460	1	This	this	DT
cord-329276-tfrjw743	460	2	relation	relation	NN
cord-329276-tfrjw743	460	3	is	be	VBZ
cord-329276-tfrjw743	460	4	given	give	VBN
cord-329276-tfrjw743	460	5	by	by	IN
cord-329276-tfrjw743	460	6	the	the	DT
cord-329276-tfrjw743	460	7	optimal	optimal	JJ
cord-329276-tfrjw743	460	8	singular	singular	JJ
cord-329276-tfrjw743	460	9	arc	arc	NN
cord-329276-tfrjw743	460	10	S	S	NNP
cord-329276-tfrjw743	460	11	of	of	IN
cord-329276-tfrjw743	460	12	the	the	DT
cord-329276-tfrjw743	460	13	monotherapy	monotherapy	NNP
cord-329276-tfrjw743	460	14	problem	problem	NN
cord-329276-tfrjw743	460	15	.	.	.
cord-329276-tfrjw743	461	1	(	(	-LRB-
cord-329276-tfrjw743	461	2	ii	ii	NN
cord-329276-tfrjw743	461	3	)	)	-RRB-
cord-329276-tfrjw743	462	1	Along	along	IN
cord-329276-tfrjw743	462	2	this	this	DT
cord-329276-tfrjw743	462	3	path	path	NN
cord-329276-tfrjw743	462	4	there	there	EX
cord-329276-tfrjw743	462	5	is	be	VBZ
cord-329276-tfrjw743	462	6	an	an	DT
cord-329276-tfrjw743	462	7	optimal	optimal	JJ
cord-329276-tfrjw743	462	8	point	point	NN
cord-329276-tfrjw743	462	9	so	so	IN
cord-329276-tfrjw743	462	10	that	that	IN
cord-329276-tfrjw743	462	11	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	462	12	is	be	VBZ
cord-329276-tfrjw743	462	13	given	give	VBN
cord-329276-tfrjw743	462	14	in	in	IN
cord-329276-tfrjw743	462	15	one	one	CD
cord-329276-tfrjw743	462	16	full	full	JJ
cord-329276-tfrjw743	462	17	dose	dose	NN
cord-329276-tfrjw743	462	18	MTD	MTD	NNP
cord-329276-tfrjw743	462	19	administration	administration	NN
cord-329276-tfrjw743	462	20	as	as	IN
cord-329276-tfrjw743	462	21	this	this	DT
cord-329276-tfrjw743	462	22	point	point	NN
cord-329276-tfrjw743	462	23	is	be	VBZ
cord-329276-tfrjw743	462	24	reached	reach	VBN
cord-329276-tfrjw743	462	25	.	.	.
cord-329276-tfrjw743	463	1	These	these	DT
cord-329276-tfrjw743	463	2	properties	property	NNS
cord-329276-tfrjw743	463	3	reflect	reflect	VBP
cord-329276-tfrjw743	463	4	the	the	DT
cord-329276-tfrjw743	463	5	ideas	idea	NNS
cord-329276-tfrjw743	463	6	of	of	IN
cord-329276-tfrjw743	463	7	'	'	``
cord-329276-tfrjw743	463	8	pruning	prune	VBG
cord-329276-tfrjw743	463	9	'	'	''
cord-329276-tfrjw743	463	10	the	the	DT
cord-329276-tfrjw743	463	11	vasculature	vasculature	NN
cord-329276-tfrjw743	463	12	and	and	CC
cord-329276-tfrjw743	463	13	of	of	IN
cord-329276-tfrjw743	463	14	a	a	DT
cord-329276-tfrjw743	463	15	'	'	``
cord-329276-tfrjw743	463	16	therapeutic	therapeutic	JJ
cord-329276-tfrjw743	463	17	window	window	NN
cord-329276-tfrjw743	463	18	'	'	''
cord-329276-tfrjw743	463	19	[	[	-LRB-
cord-329276-tfrjw743	463	20	30	30	CD
cord-329276-tfrjw743	463	21	,	,	,
cord-329276-tfrjw743	463	22	31	31	CD
cord-329276-tfrjw743	463	23	]	]	-RRB-
cord-329276-tfrjw743	463	24	proposed	propose	VBN
cord-329276-tfrjw743	463	25	in	in	IN
cord-329276-tfrjw743	463	26	the	the	DT
cord-329276-tfrjw743	463	27	medical	medical	JJ
cord-329276-tfrjw743	463	28	literature	literature	NN
cord-329276-tfrjw743	463	29	.	.	.
cord-329276-tfrjw743	464	1	Fig	Fig	NNP
cord-329276-tfrjw743	464	2	.	.	NNP
cord-329276-tfrjw743	464	3	7	7	CD
cord-329276-tfrjw743	464	4	Illustration	illustration	NN
cord-329276-tfrjw743	464	5	of	of	IN
cord-329276-tfrjw743	464	6	the	the	DT
cord-329276-tfrjw743	464	7	qualitative	qualitative	JJ
cord-329276-tfrjw743	464	8	shape	shape	NN
cord-329276-tfrjw743	464	9	of	of	IN
cord-329276-tfrjw743	464	10	optimal	optimal	JJ
cord-329276-tfrjw743	464	11	controls	control	NNS
cord-329276-tfrjw743	465	1	u	u	NNP
cord-329276-tfrjw743	465	2	*	*	NFP
cord-329276-tfrjw743	465	3	(	(	-LRB-
cord-329276-tfrjw743	465	4	left	left	NN
cord-329276-tfrjw743	465	5	)	)	-RRB-
cord-329276-tfrjw743	465	6	and	and	CC
cord-329276-tfrjw743	465	7	v	v	LS
cord-329276-tfrjw743	465	8	*	*	NFP
cord-329276-tfrjw743	465	9	(	(	-LRB-
cord-329276-tfrjw743	465	10	right	right	UH
cord-329276-tfrjw743	465	11	)	)	-RRB-
cord-329276-tfrjw743	465	12	for	for	IN
cord-329276-tfrjw743	465	13	combination	combination	NN
cord-329276-tfrjw743	465	14	treatments	treatment	NNS
cord-329276-tfrjw743	465	15	with	with	IN
cord-329276-tfrjw743	465	16	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	465	17	and	and	CC
cord-329276-tfrjw743	465	18	antiangiogenic	antiangiogenic	NNP
cord-329276-tfrjw743	465	19	inhibitors	inhibitor	NNS
cord-329276-tfrjw743	465	20	for	for	IN
cord-329276-tfrjw743	465	21	medically	medically	RB
cord-329276-tfrjw743	465	22	realistic	realistic	JJ
cord-329276-tfrjw743	465	23	initial	initial	JJ
cord-329276-tfrjw743	465	24	values	value	NNS
cord-329276-tfrjw743	465	25	:	:	:
cord-329276-tfrjw743	465	26	after	after	IN
cord-329276-tfrjw743	465	27	a	a	DT
cord-329276-tfrjw743	465	28	brief	brief	JJ
cord-329276-tfrjw743	465	29	initial	initial	JJ
cord-329276-tfrjw743	465	30	period	period	NN
cord-329276-tfrjw743	465	31	of	of	IN
cord-329276-tfrjw743	465	32	full	full	JJ
cord-329276-tfrjw743	465	33	dose	dose	NN
cord-329276-tfrjw743	465	34	therapy	therapy	NN
cord-329276-tfrjw743	465	35	,	,	,
cord-329276-tfrjw743	465	36	administration	administration	NN
cord-329276-tfrjw743	465	37	of	of	IN
cord-329276-tfrjw743	465	38	the	the	DT
cord-329276-tfrjw743	465	39	antiangiogenic	antiangiogenic	NNP
cord-329276-tfrjw743	465	40	agent	agent	NN
cord-329276-tfrjw743	465	41	follows	follow	VBZ
cord-329276-tfrjw743	465	42	the	the	DT
cord-329276-tfrjw743	465	43	singular	singular	JJ
cord-329276-tfrjw743	465	44	control	control	NN
cord-329276-tfrjw743	465	45	until	until	IN
cord-329276-tfrjw743	465	46	,	,	,
cord-329276-tfrjw743	465	47	at	at	IN
cord-329276-tfrjw743	465	48	a	a	DT
cord-329276-tfrjw743	465	49	specific	specific	JJ
cord-329276-tfrjw743	465	50	time	time	NN
cord-329276-tfrjw743	465	51	τ	τ	NN
cord-329276-tfrjw743	465	52	,	,	,
cord-329276-tfrjw743	465	53	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	465	54	commences	commence	VBZ
cord-329276-tfrjw743	465	55	.	.	.
cord-329276-tfrjw743	466	1	At	at	IN
cord-329276-tfrjw743	466	2	that	that	DT
cord-329276-tfrjw743	466	3	time	time	NN
cord-329276-tfrjw743	466	4	,	,	,
cord-329276-tfrjw743	466	5	the	the	DT
cord-329276-tfrjw743	466	6	dose	dose	NN
cord-329276-tfrjw743	466	7	of	of	IN
cord-329276-tfrjw743	466	8	the	the	DT
cord-329276-tfrjw743	466	9	antiangiogenic	antiangiogenic	JJ
cord-329276-tfrjw743	466	10	agent	agent	NN
cord-329276-tfrjw743	466	11	adjusts	adjust	VBZ
cord-329276-tfrjw743	466	12	to	to	IN
cord-329276-tfrjw743	466	13	the	the	DT
cord-329276-tfrjw743	466	14	presence	presence	NN
cord-329276-tfrjw743	466	15	of	of	IN
cord-329276-tfrjw743	466	16	the	the	DT
cord-329276-tfrjw743	466	17	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	466	18	.	.	.
cord-329276-tfrjw743	467	1	As	as	IN
cord-329276-tfrjw743	467	2	the	the	DT
cord-329276-tfrjw743	467	3	dose	dose	NN
cord-329276-tfrjw743	467	4	of	of	IN
cord-329276-tfrjw743	467	5	the	the	DT
cord-329276-tfrjw743	467	6	antiangiogenic	antiangiogenic	JJ
cord-329276-tfrjw743	467	7	agent	agent	NN
cord-329276-tfrjw743	467	8	intensifies	intensify	VBZ
cord-329276-tfrjw743	467	9	along	along	IN
cord-329276-tfrjw743	467	10	the	the	DT
cord-329276-tfrjw743	467	11	singular	singular	JJ
cord-329276-tfrjw743	467	12	arc	arc	NN
cord-329276-tfrjw743	467	13	for	for	IN
cord-329276-tfrjw743	467	14	the	the	DT
cord-329276-tfrjw743	467	15	monotherapy	monotherapy	NNP
cord-329276-tfrjw743	467	16	problem	problem	NN
cord-329276-tfrjw743	467	17	,	,	,
cord-329276-tfrjw743	467	18	in	in	IN
cord-329276-tfrjw743	467	19	the	the	DT
cord-329276-tfrjw743	467	20	presence	presence	NN
cord-329276-tfrjw743	467	21	of	of	IN
cord-329276-tfrjw743	467	22	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	467	23	which	which	WDT
cord-329276-tfrjw743	467	24	also	also	RB
cord-329276-tfrjw743	467	25	has	have	VBZ
cord-329276-tfrjw743	467	26	antiangiogenic	antiangiogenic	JJ
cord-329276-tfrjw743	467	27	effects	effect	NNS
cord-329276-tfrjw743	467	28	,	,	,
cord-329276-tfrjw743	467	29	the	the	DT
cord-329276-tfrjw743	467	30	dose	dose	NN
cord-329276-tfrjw743	467	31	increases	increase	NNS
cord-329276-tfrjw743	467	32	in	in	IN
cord-329276-tfrjw743	467	33	a	a	DT
cord-329276-tfrjw743	467	34	small	small	JJ
cord-329276-tfrjw743	467	35	jump	jump	NN
cord-329276-tfrjw743	467	36	at	at	IN
cord-329276-tfrjw743	467	37	time	time	NN
cord-329276-tfrjw743	467	38	τ	τ	NN
cord-329276-tfrjw743	467	39	.	.	.
cord-329276-tfrjw743	468	1	The	the	DT
cord-329276-tfrjw743	468	2	control	control	NN
cord-329276-tfrjw743	468	3	follows	follow	VBZ
cord-329276-tfrjw743	468	4	the	the	DT
cord-329276-tfrjw743	468	5	adjusted	adjust	VBN
cord-329276-tfrjw743	468	6	singular	singular	JJ
cord-329276-tfrjw743	468	7	control	control	NN
cord-329276-tfrjw743	468	8	until	until	IN
cord-329276-tfrjw743	468	9	all	all	DT
cord-329276-tfrjw743	468	10	inhibitors	inhibitor	NNS
cord-329276-tfrjw743	468	11	are	be	VBP
cord-329276-tfrjw743	468	12	exhausted	exhausted	JJ
cord-329276-tfrjw743	468	13	.	.	.
cord-329276-tfrjw743	469	1	Chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	469	2	is	be	VBZ
cord-329276-tfrjw743	469	3	given	give	VBN
cord-329276-tfrjw743	469	4	in	in	IN
cord-329276-tfrjw743	469	5	one	one	CD
cord-329276-tfrjw743	469	6	full	full	JJ
cord-329276-tfrjw743	469	7	dose	dose	NN
cord-329276-tfrjw743	469	8	segment	segment	NN
cord-329276-tfrjw743	469	9	commencing	commence	VBG
cord-329276-tfrjw743	469	10	at	at	IN
cord-329276-tfrjw743	469	11	time	time	NN
cord-329276-tfrjw743	469	12	τ	τ	NN
cord-329276-tfrjw743	469	13	Fig	Fig	NNP
cord-329276-tfrjw743	469	14	.	.	.
cord-329276-tfrjw743	469	15	8	8	CD
cord-329276-tfrjw743	470	1	"	"	``
cord-329276-tfrjw743	470	2	Optimal	optimal	JJ
cord-329276-tfrjw743	470	3	therapeutic	therapeutic	JJ
cord-329276-tfrjw743	470	4	window	window	NN
cord-329276-tfrjw743	470	5	"	"	''
cord-329276-tfrjw743	471	1	:	:	:
cord-329276-tfrjw743	471	2	the	the	DT
cord-329276-tfrjw743	471	3	red	red	JJ
cord-329276-tfrjw743	471	4	curve	curve	NN
cord-329276-tfrjw743	471	5	depicts	depict	VBZ
cord-329276-tfrjw743	471	6	the	the	DT
cord-329276-tfrjw743	471	7	optimal	optimal	JJ
cord-329276-tfrjw743	471	8	controlled	control	VBN
cord-329276-tfrjw743	471	9	trajectory	trajectory	NN
cord-329276-tfrjw743	471	10	for	for	IN
cord-329276-tfrjw743	471	11	the	the	DT
cord-329276-tfrjw743	471	12	antiangiogenic	antiangiogenic	NNP
cord-329276-tfrjw743	471	13	monotherapy	monotherapy	IN
cord-329276-tfrjw743	471	14	problem	problem	NN
cord-329276-tfrjw743	471	15	(	(	-LRB-
cord-329276-tfrjw743	471	16	the	the	DT
cord-329276-tfrjw743	471	17	control	control	NN
cord-329276-tfrjw743	471	18	is	be	VBZ
cord-329276-tfrjw743	471	19	given	give	VBN
cord-329276-tfrjw743	471	20	by	by	IN
cord-329276-tfrjw743	471	21	full	full	JJ
cord-329276-tfrjw743	471	22	dose	dose	NN
cord-329276-tfrjw743	471	23	therapy	therapy	NN
cord-329276-tfrjw743	471	24	along	along	IN
cord-329276-tfrjw743	471	25	the	the	DT
cord-329276-tfrjw743	471	26	vertical	vertical	JJ
cord-329276-tfrjw743	471	27	portion	portion	NN
cord-329276-tfrjw743	471	28	and	and	CC
cord-329276-tfrjw743	471	29	then	then	RB
cord-329276-tfrjw743	471	30	follows	follow	VBZ
cord-329276-tfrjw743	471	31	the	the	DT
cord-329276-tfrjw743	471	32	singular	singular	JJ
cord-329276-tfrjw743	471	33	arc	arc	NN
cord-329276-tfrjw743	471	34	where	where	WRB
cord-329276-tfrjw743	471	35	the	the	DT
cord-329276-tfrjw743	471	36	tumor	tumor	NN
cord-329276-tfrjw743	471	37	volume	volume	NN
cord-329276-tfrjw743	471	38	decreases	decrease	NNS
cord-329276-tfrjw743	471	39	)	)	-RRB-
cord-329276-tfrjw743	471	40	.	.	.
cord-329276-tfrjw743	472	1	Chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	472	2	then	then	RB
cord-329276-tfrjw743	472	3	commences	commence	VBZ
cord-329276-tfrjw743	472	4	at	at	IN
cord-329276-tfrjw743	472	5	an	an	DT
cord-329276-tfrjw743	472	6	optimal	optimal	JJ
cord-329276-tfrjw743	472	7	time	time	NN
cord-329276-tfrjw743	472	8	τ	τ	NN
cord-329276-tfrjw743	472	9	and	and	CC
cord-329276-tfrjw743	472	10	the	the	DT
cord-329276-tfrjw743	472	11	optimal	optimal	JJ
cord-329276-tfrjw743	472	12	trajectory	trajectory	NN
cord-329276-tfrjw743	472	13	is	be	VBZ
cord-329276-tfrjw743	472	14	shown	show	VBN
cord-329276-tfrjw743	472	15	as	as	IN
cord-329276-tfrjw743	472	16	solid	solid	JJ
cord-329276-tfrjw743	472	17	blue	blue	JJ
cord-329276-tfrjw743	472	18	curve	curve	NN
cord-329276-tfrjw743	472	19	.	.	.
cord-329276-tfrjw743	473	1	(	(	-LRB-
cord-329276-tfrjw743	473	2	The	the	DT
cord-329276-tfrjw743	473	3	remaining	remain	VBG
cord-329276-tfrjw743	473	4	optimal	optimal	JJ
cord-329276-tfrjw743	473	5	monotherapy	monotherapy	IN
cord-329276-tfrjw743	473	6	trajectory	trajectory	NN
cord-329276-tfrjw743	473	7	is	be	VBZ
cord-329276-tfrjw743	473	8	shown	show	VBN
cord-329276-tfrjw743	473	9	as	as	IN
cord-329276-tfrjw743	473	10	dotted	dotted	JJ
cord-329276-tfrjw743	473	11	red	red	JJ
cord-329276-tfrjw743	473	12	curve	curve	NN
cord-329276-tfrjw743	473	13	.	.	.
cord-329276-tfrjw743	473	14	)	)	-RRB-
cord-329276-tfrjw743	474	1	When	when	WRB
cord-329276-tfrjw743	474	2	all	all	DT
cord-329276-tfrjw743	474	3	antiangiogenic	antiangiogenic	JJ
cord-329276-tfrjw743	474	4	agents	agent	NNS
cord-329276-tfrjw743	474	5	are	be	VBP
cord-329276-tfrjw743	474	6	exhausted	exhausted	JJ
cord-329276-tfrjw743	474	7	,	,	,
cord-329276-tfrjw743	474	8	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	474	9	continues	continue	VBZ
cord-329276-tfrjw743	474	10	until	until	IN
cord-329276-tfrjw743	474	11	all	all	DT
cord-329276-tfrjw743	474	12	drugs	drug	NNS
cord-329276-tfrjw743	474	13	have	have	VBP
cord-329276-tfrjw743	474	14	been	be	VBN
cord-329276-tfrjw743	474	15	administered	administer	VBN
cord-329276-tfrjw743	474	16	.	.	.
cord-329276-tfrjw743	475	1	The	the	DT
cord-329276-tfrjw743	475	2	junction	junction	NN
cord-329276-tfrjw743	475	3	point	point	NN
cord-329276-tfrjw743	475	4	corresponds	correspond	VBZ
cord-329276-tfrjw743	475	5	to	to	IN
cord-329276-tfrjw743	475	6	the	the	DT
cord-329276-tfrjw743	475	7	kink	kink	NN
cord-329276-tfrjw743	475	8	in	in	IN
cord-329276-tfrjw743	475	9	the	the	DT
cord-329276-tfrjw743	475	10	blue	blue	JJ
cord-329276-tfrjw743	475	11	trajectory	trajectory	NN
cord-329276-tfrjw743	475	12	.	.	.
cord-329276-tfrjw743	476	1	Chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	476	2	still	still	RB
cord-329276-tfrjw743	476	3	lowers	lower	VBZ
cord-329276-tfrjw743	476	4	the	the	DT
cord-329276-tfrjw743	476	5	tumor	tumor	NN
cord-329276-tfrjw743	476	6	volume	volume	NN
cord-329276-tfrjw743	476	7	,	,	,
cord-329276-tfrjw743	476	8	but	but	CC
cord-329276-tfrjw743	476	9	as	as	IN
cord-329276-tfrjw743	476	10	there	there	EX
cord-329276-tfrjw743	476	11	are	be	VBP
cord-329276-tfrjw743	476	12	no	no	DT
cord-329276-tfrjw743	476	13	more	more	RBR
cord-329276-tfrjw743	476	14	antiangiogenic	antiangiogenic	JJ
cord-329276-tfrjw743	476	15	agents	agent	NNS
cord-329276-tfrjw743	476	16	given	give	VBN
cord-329276-tfrjw743	476	17	,	,	,
cord-329276-tfrjw743	476	18	the	the	DT
cord-329276-tfrjw743	476	19	vasculature	vasculature	NN
cord-329276-tfrjw743	476	20	increases	increase	VBZ
cord-329276-tfrjw743	476	21	again	again	RB
cord-329276-tfrjw743	477	1	We	-PRON-	PRP
cord-329276-tfrjw743	477	2	remark	remark	VBP
cord-329276-tfrjw743	477	3	that	that	IN
cord-329276-tfrjw743	477	4	the	the	DT
cord-329276-tfrjw743	477	5	optimal	optimal	JJ
cord-329276-tfrjw743	477	6	controls	control	NNS
cord-329276-tfrjw743	477	7	in	in	IN
cord-329276-tfrjw743	477	8	this	this	DT
cord-329276-tfrjw743	477	9	model	model	NN
cord-329276-tfrjw743	477	10	(	(	-LRB-
cord-329276-tfrjw743	477	11	and	and	CC
cord-329276-tfrjw743	477	12	this	this	DT
cord-329276-tfrjw743	477	13	is	be	VBZ
cord-329276-tfrjw743	477	14	also	also	RB
cord-329276-tfrjw743	477	15	the	the	DT
cord-329276-tfrjw743	477	16	case	case	NN
cord-329276-tfrjw743	477	17	in	in	IN
cord-329276-tfrjw743	477	18	many	many	JJ
cord-329276-tfrjw743	477	19	other	other	JJ
cord-329276-tfrjw743	477	20	models	model	NNS
cord-329276-tfrjw743	477	21	where	where	WRB
cord-329276-tfrjw743	477	22	the	the	DT
cord-329276-tfrjw743	477	23	concentration	concentration	NN
cord-329276-tfrjw743	477	24	is	be	VBZ
cord-329276-tfrjw743	477	25	taken	take	VBN
cord-329276-tfrjw743	477	26	as	as	IN
cord-329276-tfrjw743	477	27	the	the	DT
cord-329276-tfrjw743	477	28	control	control	NN
cord-329276-tfrjw743	477	29	)	)	-RRB-
cord-329276-tfrjw743	477	30	are	be	VBP
cord-329276-tfrjw743	477	31	discontinuous	discontinuous	JJ
cord-329276-tfrjw743	477	32	.	.	.
cord-329276-tfrjw743	478	1	Obviously	obviously	RB
cord-329276-tfrjw743	478	2	,	,	,
cord-329276-tfrjw743	478	3	this	this	DT
cord-329276-tfrjw743	478	4	a	a	DT
cord-329276-tfrjw743	478	5	quirk	quirk	NN
cord-329276-tfrjw743	478	6	of	of	IN
cord-329276-tfrjw743	478	7	the	the	DT
cord-329276-tfrjw743	478	8	modeling	modeling	NN
cord-329276-tfrjw743	478	9	as	as	IN
cord-329276-tfrjw743	478	10	concentrations	concentration	NNS
cord-329276-tfrjw743	478	11	are	be	VBP
cord-329276-tfrjw743	478	12	continuous	continuous	JJ
cord-329276-tfrjw743	478	13	functions	function	NNS
cord-329276-tfrjw743	478	14	.	.	.
cord-329276-tfrjw743	479	1	This	this	DT
cord-329276-tfrjw743	479	2	discrepancy	discrepancy	NN
cord-329276-tfrjw743	479	3	,	,	,
cord-329276-tfrjw743	479	4	however	however	RB
cord-329276-tfrjw743	479	5	,	,	,
cord-329276-tfrjw743	479	6	is	be	VBZ
cord-329276-tfrjw743	479	7	easily	easily	RB
cord-329276-tfrjw743	479	8	removed	remove	VBN
cord-329276-tfrjw743	479	9	by	by	IN
cord-329276-tfrjw743	479	10	adding	add	VBG
cord-329276-tfrjw743	479	11	a	a	DT
cord-329276-tfrjw743	479	12	model	model	NN
cord-329276-tfrjw743	479	13	for	for	IN
cord-329276-tfrjw743	479	14	the	the	DT
cord-329276-tfrjw743	479	15	pharmacokinetics	pharmacokinetic	NNS
cord-329276-tfrjw743	479	16	of	of	IN
cord-329276-tfrjw743	479	17	the	the	DT
cord-329276-tfrjw743	479	18	drug	drug	NN
cord-329276-tfrjw743	479	19	which	which	WDT
cord-329276-tfrjw743	479	20	smoothes	smooth	VBZ
cord-329276-tfrjw743	479	21	out	out	RP
cord-329276-tfrjw743	479	22	the	the	DT
cord-329276-tfrjw743	479	23	transitions	transition	NNS
cord-329276-tfrjw743	479	24	between	between	IN
cord-329276-tfrjw743	479	25	the	the	DT
cord-329276-tfrjw743	479	26	segments	segment	NNS
cord-329276-tfrjw743	479	27	while	while	IN
cord-329276-tfrjw743	479	28	following	follow	VBG
cord-329276-tfrjw743	479	29	the	the	DT
cord-329276-tfrjw743	479	30	same	same	JJ
cord-329276-tfrjw743	479	31	structure	structure	NN
cord-329276-tfrjw743	479	32	.	.	.
cord-329276-tfrjw743	480	1	The	the	DT
cord-329276-tfrjw743	480	2	simplified	simplified	JJ
cord-329276-tfrjw743	480	3	modeling	modeling	NN
cord-329276-tfrjw743	480	4	with	with	IN
cord-329276-tfrjw743	480	5	the	the	DT
cord-329276-tfrjw743	480	6	controls	control	NNS
cord-329276-tfrjw743	480	7	representing	represent	VBG
cord-329276-tfrjw743	480	8	concentrations	concentration	NNS
cord-329276-tfrjw743	480	9	has	have	VBZ
cord-329276-tfrjw743	480	10	,	,	,
cord-329276-tfrjw743	480	11	from	from	IN
cord-329276-tfrjw743	480	12	a	a	DT
cord-329276-tfrjw743	480	13	mathematical	mathematical	JJ
cord-329276-tfrjw743	480	14	point	point	NN
cord-329276-tfrjw743	480	15	of	of	IN
cord-329276-tfrjw743	480	16	view	view	NN
cord-329276-tfrjw743	480	17	,	,	,
cord-329276-tfrjw743	480	18	the	the	DT
cord-329276-tfrjw743	480	19	advantage	advantage	NN
cord-329276-tfrjw743	480	20	of	of	IN
cord-329276-tfrjw743	480	21	a	a	DT
cord-329276-tfrjw743	480	22	lower	low	JJR
cord-329276-tfrjw743	480	23	dimensional	dimensional	JJ
cord-329276-tfrjw743	480	24	state	state	NN
cord-329276-tfrjw743	480	25	-	-	HYPH
cord-329276-tfrjw743	480	26	space	space	NN
cord-329276-tfrjw743	480	27	and	and	CC
cord-329276-tfrjw743	480	28	,	,	,
cord-329276-tfrjw743	480	29	more	more	RBR
cord-329276-tfrjw743	480	30	importantly	importantly	RB
cord-329276-tfrjw743	480	31	,	,	,
cord-329276-tfrjw743	480	32	the	the	DT
cord-329276-tfrjw743	480	33	analysis	analysis	NN
cord-329276-tfrjw743	480	34	of	of	IN
cord-329276-tfrjw743	480	35	singular	singular	JJ
cord-329276-tfrjw743	480	36	controls	control	NNS
cord-329276-tfrjw743	480	37	is	be	VBZ
cord-329276-tfrjw743	480	38	simpler	simple	JJR
cord-329276-tfrjw743	480	39	(	(	-LRB-
cord-329276-tfrjw743	480	40	c.f	c.f	NNP
cord-329276-tfrjw743	480	41	.	.	NNP
cord-329276-tfrjw743	480	42	,	,	,
cord-329276-tfrjw743	480	43	[	[	-LRB-
cord-329276-tfrjw743	480	44	46	46	CD
cord-329276-tfrjw743	480	45	,	,	,
cord-329276-tfrjw743	480	46	47	47	CD
cord-329276-tfrjw743	480	47	]	]	-RRB-
cord-329276-tfrjw743	480	48	)	)	-RRB-
cord-329276-tfrjw743	480	49	.	.	.
cord-329276-tfrjw743	481	1	This	this	DT
cord-329276-tfrjw743	481	2	makes	make	VBZ
cord-329276-tfrjw743	481	3	the	the	DT
cord-329276-tfrjw743	481	4	overall	overall	JJ
cord-329276-tfrjw743	481	5	structure	structure	NN
cord-329276-tfrjw743	481	6	of	of	IN
cord-329276-tfrjw743	481	7	solutions	solution	NNS
cord-329276-tfrjw743	481	8	more	more	RBR
cord-329276-tfrjw743	481	9	tractable	tractable	JJ
cord-329276-tfrjw743	481	10	.	.	.
cord-329276-tfrjw743	482	1	Our	-PRON-	PRP$
cord-329276-tfrjw743	482	2	paper	paper	NN
cord-329276-tfrjw743	482	3	[	[	-LRB-
cord-329276-tfrjw743	482	4	48	48	CD
cord-329276-tfrjw743	482	5	]	]	-RRB-
cord-329276-tfrjw743	482	6	gives	give	VBZ
cord-329276-tfrjw743	482	7	an	an	DT
cord-329276-tfrjw743	482	8	in	in	IN
cord-329276-tfrjw743	482	9	depth	depth	NN
cord-329276-tfrjw743	482	10	discussion	discussion	NN
cord-329276-tfrjw743	482	11	of	of	IN
cord-329276-tfrjw743	482	12	these	these	DT
cord-329276-tfrjw743	482	13	aspects	aspect	NNS
cord-329276-tfrjw743	482	14	related	relate	VBN
cord-329276-tfrjw743	482	15	to	to	IN
cord-329276-tfrjw743	482	16	the	the	DT
cord-329276-tfrjw743	482	17	pharmacometrics	pharmacometric	NNS
cord-329276-tfrjw743	482	18	of	of	IN
cord-329276-tfrjw743	482	19	the	the	DT
cord-329276-tfrjw743	482	20	drugs	drug	NNS
cord-329276-tfrjw743	482	21	.	.	.
cord-329276-tfrjw743	483	1	We	-PRON-	PRP
cord-329276-tfrjw743	483	2	conclude	conclude	VBP
cord-329276-tfrjw743	483	3	with	with	IN
cord-329276-tfrjw743	483	4	an	an	DT
cord-329276-tfrjw743	483	5	example	example	NN
cord-329276-tfrjw743	483	6	of	of	IN
cord-329276-tfrjw743	483	7	a	a	DT
cord-329276-tfrjw743	483	8	numerically	numerically	RB
cord-329276-tfrjw743	483	9	computed	compute	VBN
cord-329276-tfrjw743	483	10	optimal	optimal	JJ
cord-329276-tfrjw743	483	11	solution	solution	NN
cord-329276-tfrjw743	483	12	for	for	IN
cord-329276-tfrjw743	483	13	Stepanova	Stepanova	NNP
cord-329276-tfrjw743	483	14	's	's	POS
cord-329276-tfrjw743	483	15	model	model	NN
cord-329276-tfrjw743	483	16	with	with	IN
cord-329276-tfrjw743	483	17	strongly	strongly	RB
cord-329276-tfrjw743	483	18	targeted	target	VBN
cord-329276-tfrjw743	483	19	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	483	20	u	u	NNP
cord-329276-tfrjw743	483	21	[	[	-LRB-
cord-329276-tfrjw743	483	22	15	15	CD
cord-329276-tfrjw743	483	23	,	,	,
cord-329276-tfrjw743	483	24	40	40	CD
cord-329276-tfrjw743	483	25	,	,	,
cord-329276-tfrjw743	483	26	41	41	CD
cord-329276-tfrjw743	483	27	,	,	,
cord-329276-tfrjw743	483	28	49	49	CD
cord-329276-tfrjw743	483	29	]	]	-RRB-
cord-329276-tfrjw743	483	30	.	.	.
cord-329276-tfrjw743	484	1	Again	again	RB
cord-329276-tfrjw743	484	2	we	-PRON-	PRP
cord-329276-tfrjw743	484	3	treat	treat	VBP
cord-329276-tfrjw743	484	4	the	the	DT
cord-329276-tfrjw743	484	5	concentration	concentration	NN
cord-329276-tfrjw743	484	6	of	of	IN
cord-329276-tfrjw743	484	7	the	the	DT
cord-329276-tfrjw743	484	8	agent	agent	NN
cord-329276-tfrjw743	484	9	as	as	IN
cord-329276-tfrjw743	484	10	the	the	DT
cord-329276-tfrjw743	484	11	control	control	NN
cord-329276-tfrjw743	484	12	and	and	CC
cord-329276-tfrjw743	484	13	use	use	NNP
cord-329276-tfrjw743	484	14	Skipper	Skipper	NNP
cord-329276-tfrjw743	484	15	's	's	POS
cord-329276-tfrjw743	484	16	log	log	NN
cord-329276-tfrjw743	484	17	-	-	HYPH
cord-329276-tfrjw743	484	18	linear	linear	JJ
cord-329276-tfrjw743	484	19	model	model	NN
cord-329276-tfrjw743	484	20	to	to	TO
cord-329276-tfrjw743	484	21	describe	describe	VB
cord-329276-tfrjw743	484	22	the	the	DT
cord-329276-tfrjw743	484	23	effect	effect	NN
cord-329276-tfrjw743	484	24	of	of	IN
cord-329276-tfrjw743	484	25	treatment	treatment	NN
cord-329276-tfrjw743	484	26	.	.	.
cord-329276-tfrjw743	485	1	This	this	DT
cord-329276-tfrjw743	485	2	simply	simply	RB
cord-329276-tfrjw743	485	3	adds	add	VBZ
cord-329276-tfrjw743	485	4	a	a	DT
cord-329276-tfrjw743	485	5	term	term	NN
cord-329276-tfrjw743	485	6	−κ	−κ	CD
cord-329276-tfrjw743	485	7	pu	pu	NNP
cord-329276-tfrjw743	485	8	to	to	IN
cord-329276-tfrjw743	485	9	the	the	DT
cord-329276-tfrjw743	485	10	dynamics	dynamic	NNS
cord-329276-tfrjw743	485	11	(	(	-LRB-
cord-329276-tfrjw743	485	12	5	5	CD
cord-329276-tfrjw743	485	13	)	)	-RRB-
cord-329276-tfrjw743	485	14	of	of	IN
cord-329276-tfrjw743	485	15	the	the	DT
cord-329276-tfrjw743	485	16	tumor	tumor	NN
cord-329276-tfrjw743	485	17	volume	volume	NN
cord-329276-tfrjw743	485	18	.	.	.
cord-329276-tfrjw743	486	1	Choosing	choose	VBG
cord-329276-tfrjw743	486	2	the	the	DT
cord-329276-tfrjw743	486	3	objective	objective	JJ
cord-329276-tfrjw743	486	4	functional	functional	JJ
cord-329276-tfrjw743	486	5	in	in	IN
cord-329276-tfrjw743	486	6	the	the	DT
cord-329276-tfrjw743	486	7	form	form	NN
cord-329276-tfrjw743	486	8	(	(	-LRB-
cord-329276-tfrjw743	486	9	17	17	CD
cord-329276-tfrjw743	486	10	)	)	-RRB-
cord-329276-tfrjw743	486	11	with	with	IN
cord-329276-tfrjw743	486	12	N	n	NN
cord-329276-tfrjw743	486	13	=	=	SYM
cord-329276-tfrjw743	486	14	0	0	NFP
cord-329276-tfrjw743	486	15	(	(	-LRB-
cord-329276-tfrjw743	486	16	as	as	IN
cord-329276-tfrjw743	486	17	we	-PRON-	PRP
cord-329276-tfrjw743	486	18	do	do	VBP
cord-329276-tfrjw743	486	19	not	not	RB
cord-329276-tfrjw743	486	20	consider	consider	VB
cord-329276-tfrjw743	486	21	an	an	DT
cord-329276-tfrjw743	486	22	immune	immune	JJ
cord-329276-tfrjw743	486	23	boost	boost	NN
cord-329276-tfrjw743	486	24	)	)	-RRB-
cord-329276-tfrjw743	486	25	,	,	,
cord-329276-tfrjw743	486	26	optimal	optimal	JJ
cord-329276-tfrjw743	486	27	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	486	28	protocols	protocol	NNS
cord-329276-tfrjw743	486	29	follow	follow	VBP
cord-329276-tfrjw743	486	30	the	the	DT
cord-329276-tfrjw743	486	31	concatenation	concatenation	NN
cord-329276-tfrjw743	486	32	structure	structure	NN
cord-329276-tfrjw743	486	33	1s01	1s01	CD
cord-329276-tfrjw743	486	34	with	with	IN
cord-329276-tfrjw743	486	35	1	1	CD
cord-329276-tfrjw743	486	36	representing	represent	VBG
cord-329276-tfrjw743	486	37	a	a	DT
cord-329276-tfrjw743	486	38	full	full	JJ
cord-329276-tfrjw743	486	39	dose	dose	NN
cord-329276-tfrjw743	486	40	segment	segment	NN
cord-329276-tfrjw743	486	41	,	,	,
cord-329276-tfrjw743	487	1	s	s	LS
cord-329276-tfrjw743	487	2	denoting	denote	VBG
cord-329276-tfrjw743	487	3	administration	administration	NN
cord-329276-tfrjw743	487	4	following	follow	VBG
cord-329276-tfrjw743	487	5	a	a	DT
cord-329276-tfrjw743	487	6	singular	singular	JJ
cord-329276-tfrjw743	487	7	control	control	NN
cord-329276-tfrjw743	487	8	and	and	CC
cord-329276-tfrjw743	487	9	0	0	CD
cord-329276-tfrjw743	487	10	standing	standing	NN
cord-329276-tfrjw743	487	11	for	for	IN
cord-329276-tfrjw743	487	12	a	a	DT
cord-329276-tfrjw743	487	13	rest	rest	NN
cord-329276-tfrjw743	487	14	-	-	HYPH
cord-329276-tfrjw743	487	15	period	period	NN
cord-329276-tfrjw743	487	16	of	of	IN
cord-329276-tfrjw743	487	17	the	the	DT
cord-329276-tfrjw743	487	18	treatment	treatment	NN
cord-329276-tfrjw743	487	19	.	.	.
cord-329276-tfrjw743	488	1	Figure	figure	NN
cord-329276-tfrjw743	488	2	9	9	CD
cord-329276-tfrjw743	488	3	gives	give	VBZ
cord-329276-tfrjw743	488	4	a	a	DT
cord-329276-tfrjw743	488	5	characteristic	characteristic	JJ
cord-329276-tfrjw743	488	6	example	example	NN
cord-329276-tfrjw743	488	7	of	of	IN
cord-329276-tfrjw743	488	8	a	a	DT
cord-329276-tfrjw743	488	9	solution	solution	NN
cord-329276-tfrjw743	488	10	:	:	:
cord-329276-tfrjw743	488	11	the	the	DT
cord-329276-tfrjw743	488	12	initial	initial	JJ
cord-329276-tfrjw743	488	13	state	state	NN
cord-329276-tfrjw743	488	14	z	z	NNP
cord-329276-tfrjw743	488	15	0	0	CD
cord-329276-tfrjw743	488	16	=	=	NFP
cord-329276-tfrjw743	489	1	(	(	-LRB-
cord-329276-tfrjw743	489	2	p	p	NN
cord-329276-tfrjw743	489	3	0	0	CD
cord-329276-tfrjw743	489	4	,	,	,
cord-329276-tfrjw743	489	5	r	r	NN
cord-329276-tfrjw743	489	6	0	0	CD
cord-329276-tfrjw743	489	7	)	)	-RRB-
cord-329276-tfrjw743	489	8	is	be	VBZ
cord-329276-tfrjw743	489	9	characterized	characterize	VBN
cord-329276-tfrjw743	489	10	by	by	IN
cord-329276-tfrjw743	489	11	a	a	DT
cord-329276-tfrjw743	489	12	high	high	JJ
cord-329276-tfrjw743	489	13	tumor	tumor	NN
cord-329276-tfrjw743	489	14	volume	volume	NN
cord-329276-tfrjw743	489	15	and	and	CC
cord-329276-tfrjw743	489	16	depressed	depressed	JJ
cord-329276-tfrjw743	489	17	immuno	immuno	JJ
cord-329276-tfrjw743	489	18	-	-	JJ
cord-329276-tfrjw743	489	19	competent	competent	JJ
cord-329276-tfrjw743	489	20	density	density	NN
cord-329276-tfrjw743	489	21	close	close	JJ
cord-329276-tfrjw743	489	22	to	to	IN
cord-329276-tfrjw743	489	23	the	the	DT
cord-329276-tfrjw743	489	24	values	value	NNS
cord-329276-tfrjw743	489	25	of	of	IN
cord-329276-tfrjw743	489	26	the	the	DT
cord-329276-tfrjw743	489	27	malignant	malignant	JJ
cord-329276-tfrjw743	489	28	equilibrium	equilibrium	NN
cord-329276-tfrjw743	489	29	point	point	NN
cord-329276-tfrjw743	489	30	.	.	.
cord-329276-tfrjw743	490	1	In	in	IN
cord-329276-tfrjw743	490	2	the	the	DT
cord-329276-tfrjw743	490	3	figure	figure	NN
cord-329276-tfrjw743	490	4	,	,	,
cord-329276-tfrjw743	490	5	the	the	DT
cord-329276-tfrjw743	490	6	unstable	unstable	JJ
cord-329276-tfrjw743	490	7	equilibrium	equilibrium	NN
cord-329276-tfrjw743	490	8	point	point	NN
cord-329276-tfrjw743	490	9	is	be	VBZ
cord-329276-tfrjw743	490	10	marked	mark	VBN
cord-329276-tfrjw743	490	11	with	with	IN
cord-329276-tfrjw743	490	12	a	a	DT
cord-329276-tfrjw743	490	13	green	green	JJ
cord-329276-tfrjw743	490	14	dot	dot	NN
cord-329276-tfrjw743	490	15	and	and	CC
cord-329276-tfrjw743	490	16	the	the	DT
cord-329276-tfrjw743	490	17	black	black	JJ
cord-329276-tfrjw743	490	18	curves	curve	NNS
cord-329276-tfrjw743	490	19	crossing	cross	VBG
cord-329276-tfrjw743	490	20	in	in	IN
cord-329276-tfrjw743	490	21	it	-PRON-	PRP
cord-329276-tfrjw743	490	22	are	be	VBP
cord-329276-tfrjw743	490	23	its	-PRON-	PRP$
cord-329276-tfrjw743	490	24	stable	stable	JJ
cord-329276-tfrjw743	490	25	and	and	CC
cord-329276-tfrjw743	490	26	unstable	unstable	JJ
cord-329276-tfrjw743	490	27	manifolds	manifold	NNS
cord-329276-tfrjw743	490	28	,	,	,
cord-329276-tfrjw743	490	29	respectively	respectively	RB
cord-329276-tfrjw743	490	30	.	.	.
cord-329276-tfrjw743	491	1	Initially	initially	RB
cord-329276-tfrjw743	491	2	,	,	,
cord-329276-tfrjw743	491	3	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	491	4	is	be	VBZ
cord-329276-tfrjw743	491	5	given	give	VBN
cord-329276-tfrjw743	491	6	at	at	IN
cord-329276-tfrjw743	491	7	full	full	JJ
cord-329276-tfrjw743	491	8	dose	dose	NN
cord-329276-tfrjw743	491	9	until	until	IN
cord-329276-tfrjw743	491	10	the	the	DT
cord-329276-tfrjw743	491	11	state	state	NN
cord-329276-tfrjw743	491	12	of	of	IN
cord-329276-tfrjw743	491	13	system	system	NN
cord-329276-tfrjw743	491	14	has	have	VBZ
cord-329276-tfrjw743	491	15	crossed	cross	VBN
cord-329276-tfrjw743	491	16	over	over	RP
cord-329276-tfrjw743	491	17	into	into	IN
cord-329276-tfrjw743	491	18	the	the	DT
cord-329276-tfrjw743	491	19	benign	benign	JJ
cord-329276-tfrjw743	491	20	region	region	NN
cord-329276-tfrjw743	491	21	.	.	.
cord-329276-tfrjw743	492	1	Then	then	RB
cord-329276-tfrjw743	492	2	it	-PRON-	PRP
cord-329276-tfrjw743	492	3	follows	follow	VBZ
cord-329276-tfrjw743	492	4	a	a	DT
cord-329276-tfrjw743	492	5	singular	singular	JJ
cord-329276-tfrjw743	492	6	arc	arc	NN
cord-329276-tfrjw743	492	7	where	where	WRB
cord-329276-tfrjw743	492	8	the	the	DT
cord-329276-tfrjw743	492	9	concentration	concentration	NN
cord-329276-tfrjw743	492	10	of	of	IN
cord-329276-tfrjw743	492	11	the	the	DT
cord-329276-tfrjw743	492	12	drug	drug	NN
cord-329276-tfrjw743	492	13	is	be	VBZ
cord-329276-tfrjw743	492	14	dropped	drop	VBN
cord-329276-tfrjw743	492	15	significantly	significantly	RB
cord-329276-tfrjw743	492	16	through	through	IN
cord-329276-tfrjw743	492	17	lower	low	JJR
cord-329276-tfrjw743	492	18	dose	dose	NN
cord-329276-tfrjw743	492	19	administrations	administration	NNS
cord-329276-tfrjw743	492	20	.	.	.
cord-329276-tfrjw743	493	1	The	the	DT
cord-329276-tfrjw743	493	2	full	full	JJ
cord-329276-tfrjw743	493	3	singular	singular	JJ
cord-329276-tfrjw743	493	4	curve	curve	NN
cord-329276-tfrjw743	493	5	is	be	VBZ
cord-329276-tfrjw743	493	6	indicated	indicate	VBN
cord-329276-tfrjw743	493	7	by	by	IN
cord-329276-tfrjw743	493	8	a	a	DT
cord-329276-tfrjw743	493	9	dotted	dotted	JJ
cord-329276-tfrjw743	493	10	red	red	JJ
cord-329276-tfrjw743	493	11	curve	curve	NN
cord-329276-tfrjw743	493	12	in	in	IN
cord-329276-tfrjw743	493	13	the	the	DT
cord-329276-tfrjw743	493	14	figure	figure	NN
cord-329276-tfrjw743	493	15	.	.	.
cord-329276-tfrjw743	494	1	Finally	finally	RB
cord-329276-tfrjw743	494	2	,	,	,
cord-329276-tfrjw743	494	3	as	as	IN
cord-329276-tfrjw743	494	4	the	the	DT
cord-329276-tfrjw743	494	5	state	state	NN
cord-329276-tfrjw743	494	6	of	of	IN
cord-329276-tfrjw743	494	7	the	the	DT
cord-329276-tfrjw743	494	8	system	system	NN
cord-329276-tfrjw743	494	9	is	be	VBZ
cord-329276-tfrjw743	494	10	in	in	IN
cord-329276-tfrjw743	494	11	the	the	DT
cord-329276-tfrjw743	494	12	benign	benign	JJ
cord-329276-tfrjw743	494	13	region	region	NN
cord-329276-tfrjw743	494	14	,	,	,
cord-329276-tfrjw743	494	15	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	494	16	is	be	VBZ
cord-329276-tfrjw743	494	17	stopped	stop	VBN
cord-329276-tfrjw743	494	18	and	and	CC
cord-329276-tfrjw743	494	19	the	the	DT
cord-329276-tfrjw743	494	20	uncontrolled	uncontrolled	JJ
cord-329276-tfrjw743	494	21	dynamics	dynamic	NNS
cord-329276-tfrjw743	494	22	(	(	-LRB-
cord-329276-tfrjw743	494	23	i.e.	i.e.	FW
cord-329276-tfrjw743	494	24	,	,	,
cord-329276-tfrjw743	494	25	the	the	DT
cord-329276-tfrjw743	494	26	actions	action	NNS
cord-329276-tfrjw743	494	27	of	of	IN
cord-329276-tfrjw743	494	28	the	the	DT
cord-329276-tfrjw743	494	29	immune	immune	JJ
cord-329276-tfrjw743	494	30	system	system	NN
cord-329276-tfrjw743	494	31	)	)	-RRB-
cord-329276-tfrjw743	494	32	lead	lead	VBP
cord-329276-tfrjw743	494	33	to	to	IN
cord-329276-tfrjw743	494	34	further	further	JJ
cord-329276-tfrjw743	494	35	reductions	reduction	NNS
cord-329276-tfrjw743	494	36	in	in	IN
cord-329276-tfrjw743	494	37	the	the	DT
cord-329276-tfrjw743	494	38	tumor	tumor	NN
cord-329276-tfrjw743	494	39	volume	volume	NN
cord-329276-tfrjw743	494	40	.	.	.
cord-329276-tfrjw743	495	1	Interestingly	interestingly	RB
cord-329276-tfrjw743	495	2	,	,	,
cord-329276-tfrjw743	495	3	toward	toward	IN
cord-329276-tfrjw743	495	4	the	the	DT
cord-329276-tfrjw743	495	5	end	end	NN
cord-329276-tfrjw743	495	6	,	,	,
cord-329276-tfrjw743	495	7	optimal	optimal	JJ
cord-329276-tfrjw743	495	8	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	495	9	protocols	protocol	NNS
cord-329276-tfrjw743	495	10	still	still	RB
cord-329276-tfrjw743	495	11	apply	apply	VBP
cord-329276-tfrjw743	495	12	a	a	DT
cord-329276-tfrjw743	495	13	short	short	JJ
cord-329276-tfrjw743	495	14	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	495	15	segment	segment	NN
cord-329276-tfrjw743	495	16	.	.	.
cord-329276-tfrjw743	496	1	This	this	DT
cord-329276-tfrjw743	496	2	indeed	indeed	RB
cord-329276-tfrjw743	496	3	seems	seem	VBZ
cord-329276-tfrjw743	496	4	to	to	TO
cord-329276-tfrjw743	496	5	be	be	VB
cord-329276-tfrjw743	496	6	mirrored	mirror	VBN
cord-329276-tfrjw743	496	7	by	by	IN
cord-329276-tfrjw743	496	8	what	what	WP
cord-329276-tfrjw743	496	9	has	have	VBZ
cord-329276-tfrjw743	496	10	proven	prove	VBN
cord-329276-tfrjw743	496	11	a	a	DT
cord-329276-tfrjw743	496	12	particularly	particularly	RB
cord-329276-tfrjw743	496	13	effective	effective	JJ
cord-329276-tfrjw743	496	14	administration	administration	NN
cord-329276-tfrjw743	496	15	protocol	protocol	NN
cord-329276-tfrjw743	496	16	also	also	RB
cord-329276-tfrjw743	496	17	in	in	IN
cord-329276-tfrjw743	496	18	medical	medical	JJ
cord-329276-tfrjw743	496	19	practice	practice	NN
cord-329276-tfrjw743	496	20	.	.	.
cord-329276-tfrjw743	497	1	If	if	IN
cord-329276-tfrjw743	497	2	the	the	DT
cord-329276-tfrjw743	497	3	effect	effect	NN
cord-329276-tfrjw743	497	4	of	of	IN
cord-329276-tfrjw743	497	5	an	an	DT
cord-329276-tfrjw743	497	6	immune	immune	JJ
cord-329276-tfrjw743	497	7	boost	boost	NN
cord-329276-tfrjw743	497	8	is	be	VBZ
cord-329276-tfrjw743	497	9	incorporated	incorporate	VBN
cord-329276-tfrjw743	497	10	into	into	IN
cord-329276-tfrjw743	497	11	the	the	DT
cord-329276-tfrjw743	497	12	system	system	NN
cord-329276-tfrjw743	497	13	,	,	,
cord-329276-tfrjw743	497	14	this	this	DT
cord-329276-tfrjw743	497	15	structure	structure	NN
cord-329276-tfrjw743	497	16	is	be	VBZ
cord-329276-tfrjw743	497	17	generally	generally	RB
cord-329276-tfrjw743	497	18	preserved	preserve	VBN
cord-329276-tfrjw743	497	19	.	.	.
cord-329276-tfrjw743	498	1	Figure	figure	NN
cord-329276-tfrjw743	498	2	10	10	CD
cord-329276-tfrjw743	498	3	gives	give	VBZ
cord-329276-tfrjw743	498	4	an	an	DT
cord-329276-tfrjw743	498	5	example	example	NN
cord-329276-tfrjw743	498	6	of	of	IN
cord-329276-tfrjw743	498	7	an	an	DT
cord-329276-tfrjw743	498	8	optimal	optimal	JJ
cord-329276-tfrjw743	498	9	control	control	NN
cord-329276-tfrjw743	498	10	for	for	IN
cord-329276-tfrjw743	498	11	the	the	DT
cord-329276-tfrjw743	498	12	combination	combination	NN
cord-329276-tfrjw743	498	13	therapy	therapy	NN
cord-329276-tfrjw743	498	14	with	with	IN
cord-329276-tfrjw743	498	15	the	the	DT
cord-329276-tfrjw743	498	16	chemotherapeutic	chemotherapeutic	JJ
cord-329276-tfrjw743	498	17	agent	agent	NN
cord-329276-tfrjw743	498	18	shown	show	VBN
cord-329276-tfrjw743	498	19	in	in	IN
cord-329276-tfrjw743	498	20	red	red	JJ
cord-329276-tfrjw743	498	21	and	and	CC
cord-329276-tfrjw743	498	22	the	the	DT
cord-329276-tfrjw743	498	23	immune	immune	JJ
cord-329276-tfrjw743	498	24	boost	boost	NN
cord-329276-tfrjw743	498	25	in	in	IN
cord-329276-tfrjw743	498	26	green	green	JJ
cord-329276-tfrjw743	498	27	.	.	.
cord-329276-tfrjw743	499	1	Essentially	essentially	RB
cord-329276-tfrjw743	499	2	,	,	,
cord-329276-tfrjw743	499	3	the	the	DT
cord-329276-tfrjw743	499	4	immune	immune	JJ
cord-329276-tfrjw743	499	5	boost	boost	NN
cord-329276-tfrjw743	499	6	is	be	VBZ
cord-329276-tfrjw743	499	7	only	only	RB
cord-329276-tfrjw743	499	8	given	give	VBN
cord-329276-tfrjw743	499	9	toward	toward	IN
cord-329276-tfrjw743	499	10	the	the	DT
cord-329276-tfrjw743	499	11	end	end	NN
cord-329276-tfrjw743	499	12	to	to	TO
cord-329276-tfrjw743	499	13	steer	steer	VB
cord-329276-tfrjw743	499	14	the	the	DT
cord-329276-tfrjw743	499	15	system	system	NN
cord-329276-tfrjw743	499	16	into	into	IN
cord-329276-tfrjw743	499	17	a	a	DT
cord-329276-tfrjw743	499	18	better	well	JJR
cord-329276-tfrjw743	499	19	terminal	terminal	NN
cord-329276-tfrjw743	499	20	state	state	NN
cord-329276-tfrjw743	499	21	.	.	.
cord-329276-tfrjw743	500	1	This	this	DT
cord-329276-tfrjw743	500	2	figure	figure	NN
cord-329276-tfrjw743	500	3	also	also	RB
cord-329276-tfrjw743	500	4	clearly	clearly	RB
cord-329276-tfrjw743	500	5	shows	show	VBZ
cord-329276-tfrjw743	500	6	the	the	DT
cord-329276-tfrjw743	500	7	lowering	lowering	NN
cord-329276-tfrjw743	500	8	of	of	IN
cord-329276-tfrjw743	500	9	the	the	DT
cord-329276-tfrjw743	500	10	dose	dose	JJ
cord-329276-tfrjw743	500	11	rate	rate	NN
cord-329276-tfrjw743	500	12	for	for	IN
cord-329276-tfrjw743	500	13	the	the	DT
cord-329276-tfrjw743	500	14	cytotoxic	cytotoxic	JJ
cord-329276-tfrjw743	500	15	drug	drug	NN
cord-329276-tfrjw743	500	16	along	along	IN
cord-329276-tfrjw743	500	17	the	the	DT
cord-329276-tfrjw743	500	18	singular	singular	JJ
cord-329276-tfrjw743	500	19	segment	segment	NN
cord-329276-tfrjw743	500	20	.	.	.
cord-329276-tfrjw743	501	1	It	-PRON-	PRP
cord-329276-tfrjw743	501	2	has	have	VBZ
cord-329276-tfrjw743	501	3	not	not	RB
cord-329276-tfrjw743	501	4	been	be	VBN
cord-329276-tfrjw743	501	5	our	-PRON-	PRP$
cord-329276-tfrjw743	501	6	aim	aim	NN
cord-329276-tfrjw743	501	7	to	to	TO
cord-329276-tfrjw743	501	8	discuss	discuss	VB
cord-329276-tfrjw743	501	9	numerical	numerical	JJ
cord-329276-tfrjw743	501	10	methods	method	NNS
cord-329276-tfrjw743	501	11	in	in	IN
cord-329276-tfrjw743	501	12	optimal	optimal	JJ
cord-329276-tfrjw743	501	13	control	control	NN
cord-329276-tfrjw743	501	14	in	in	IN
cord-329276-tfrjw743	501	15	this	this	DT
cord-329276-tfrjw743	501	16	paper	paper	NN
cord-329276-tfrjw743	501	17	.	.	.
cord-329276-tfrjw743	502	1	For	for	IN
cord-329276-tfrjw743	502	2	completeness	completeness	NN
cord-329276-tfrjw743	502	3	sake	sake	NN
cord-329276-tfrjw743	502	4	,	,	,
cord-329276-tfrjw743	502	5	however	however	RB
cord-329276-tfrjw743	502	6	,	,	,
cord-329276-tfrjw743	502	7	we	-PRON-	PRP
cord-329276-tfrjw743	502	8	include	include	VBP
cord-329276-tfrjw743	502	9	some	some	DT
cord-329276-tfrjw743	502	10	brief	brief	JJ
cord-329276-tfrjw743	502	11	comments	comment	NNS
cord-329276-tfrjw743	502	12	on	on	IN
cord-329276-tfrjw743	502	13	the	the	DT
cord-329276-tfrjw743	502	14	methods	method	NNS
cord-329276-tfrjw743	502	15	that	that	WDT
cord-329276-tfrjw743	502	16	were	be	VBD
cord-329276-tfrjw743	502	17	used	use	VBN
cord-329276-tfrjw743	502	18	by	by	IN
cord-329276-tfrjw743	502	19	us	-PRON-	PRP
cord-329276-tfrjw743	502	20	and	and	CC
cord-329276-tfrjw743	502	21	our	-PRON-	PRP$
cord-329276-tfrjw743	502	22	co	co	NNS
cord-329276-tfrjw743	502	23	-	-	NNS
cord-329276-tfrjw743	502	24	workers	worker	NNS
cord-329276-tfrjw743	502	25	to	to	TO
cord-329276-tfrjw743	502	26	arrive	arrive	VB
cord-329276-tfrjw743	502	27	at	at	IN
cord-329276-tfrjw743	502	28	the	the	DT
cord-329276-tfrjw743	502	29	solutions	solution	NNS
cord-329276-tfrjw743	502	30	shown	show	VBN
cord-329276-tfrjw743	502	31	in	in	IN
cord-329276-tfrjw743	502	32	this	this	DT
cord-329276-tfrjw743	502	33	paper	paper	NN
cord-329276-tfrjw743	502	34	.	.	.
cord-329276-tfrjw743	503	1	The	the	DT
cord-329276-tfrjw743	503	2	initial	initial	JJ
cord-329276-tfrjw743	503	3	point	point	NN
cord-329276-tfrjw743	503	4	,	,	,
cord-329276-tfrjw743	503	5	all	all	DT
cord-329276-tfrjw743	503	6	junctions	junction	NNS
cord-329276-tfrjw743	503	7	(	(	-LRB-
cord-329276-tfrjw743	503	8	where	where	WRB
cord-329276-tfrjw743	503	9	the	the	DT
cord-329276-tfrjw743	503	10	control	control	NN
cord-329276-tfrjw743	503	11	switches	switch	VBZ
cord-329276-tfrjw743	503	12	)	)	-RRB-
cord-329276-tfrjw743	503	13	,	,	,
cord-329276-tfrjw743	503	14	and	and	CC
cord-329276-tfrjw743	503	15	the	the	DT
cord-329276-tfrjw743	503	16	terminal	terminal	JJ
cord-329276-tfrjw743	503	17	point	point	NN
cord-329276-tfrjw743	503	18	of	of	IN
cord-329276-tfrjw743	503	19	the	the	DT
cord-329276-tfrjw743	503	20	optimal	optimal	JJ
cord-329276-tfrjw743	503	21	trajectory	trajectory	NN
cord-329276-tfrjw743	503	22	are	be	VBP
cord-329276-tfrjw743	503	23	marked	mark	VBN
cord-329276-tfrjw743	503	24	by	by	IN
cord-329276-tfrjw743	503	25	black	black	JJ
cord-329276-tfrjw743	503	26	dots	dot	NNS
cord-329276-tfrjw743	503	27	.	.	.
cord-329276-tfrjw743	504	1	Starting	start	VBG
cord-329276-tfrjw743	504	2	at	at	IN
cord-329276-tfrjw743	504	3	z	z	NN
cord-329276-tfrjw743	504	4	0	0	CD
cord-329276-tfrjw743	504	5	=	=	NFP
cord-329276-tfrjw743	505	1	(	(	-LRB-
cord-329276-tfrjw743	505	2	p	p	NN
cord-329276-tfrjw743	505	3	0	0	CD
cord-329276-tfrjw743	505	4	,	,	,
cord-329276-tfrjw743	505	5	r	r	NN
cord-329276-tfrjw743	505	6	0	0	CD
cord-329276-tfrjw743	505	7	)	)	-RRB-
cord-329276-tfrjw743	505	8	,	,	,
cord-329276-tfrjw743	505	9	initially	initially	RB
cord-329276-tfrjw743	505	10	full	full	JJ
cord-329276-tfrjw743	505	11	dose	dose	JJ
cord-329276-tfrjw743	505	12	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	505	13	is	be	VBZ
cord-329276-tfrjw743	505	14	used	use	VBN
cord-329276-tfrjw743	505	15	.	.	.
cord-329276-tfrjw743	506	1	Along	along	IN
cord-329276-tfrjw743	506	2	that	that	DT
cord-329276-tfrjw743	506	3	trajectory	trajectory	NN
cord-329276-tfrjw743	506	4	,	,	,
cord-329276-tfrjw743	506	5	the	the	DT
cord-329276-tfrjw743	506	6	system	system	NN
cord-329276-tfrjw743	506	7	enters	enter	VBZ
cord-329276-tfrjw743	506	8	from	from	IN
cord-329276-tfrjw743	506	9	the	the	DT
cord-329276-tfrjw743	506	10	malignant	malignant	JJ
cord-329276-tfrjw743	506	11	region	region	NN
cord-329276-tfrjw743	506	12	(	(	-LRB-
cord-329276-tfrjw743	506	13	below	below	IN
cord-329276-tfrjw743	506	14	the	the	DT
cord-329276-tfrjw743	506	15	stable	stable	JJ
cord-329276-tfrjw743	506	16	manifold	manifold	NN
cord-329276-tfrjw743	506	17	of	of	IN
cord-329276-tfrjw743	506	18	the	the	DT
cord-329276-tfrjw743	506	19	saddle	saddle	NN
cord-329276-tfrjw743	506	20	point	point	NN
cord-329276-tfrjw743	506	21	)	)	-RRB-
cord-329276-tfrjw743	506	22	into	into	IN
cord-329276-tfrjw743	506	23	the	the	DT
cord-329276-tfrjw743	506	24	benign	benign	JJ
cord-329276-tfrjw743	506	25	region	region	NN
cord-329276-tfrjw743	506	26	(	(	-LRB-
cord-329276-tfrjw743	506	27	above	above	IN
cord-329276-tfrjw743	506	28	the	the	DT
cord-329276-tfrjw743	506	29	stable	stable	JJ
cord-329276-tfrjw743	506	30	manifold	manifold	NN
cord-329276-tfrjw743	506	31	of	of	IN
cord-329276-tfrjw743	506	32	the	the	DT
cord-329276-tfrjw743	506	33	saddle	saddle	NN
cord-329276-tfrjw743	506	34	point	point	NN
cord-329276-tfrjw743	506	35	)	)	-RRB-
cord-329276-tfrjw743	506	36	.	.	.
cord-329276-tfrjw743	507	1	The	the	DT
cord-329276-tfrjw743	507	2	stable	stable	JJ
cord-329276-tfrjw743	507	3	and	and	CC
cord-329276-tfrjw743	507	4	unstable	unstable	JJ
cord-329276-tfrjw743	507	5	manifolds	manifold	NNS
cord-329276-tfrjw743	507	6	of	of	IN
cord-329276-tfrjw743	507	7	the	the	DT
cord-329276-tfrjw743	507	8	saddle	saddle	NN
cord-329276-tfrjw743	507	9	point	point	NN
cord-329276-tfrjw743	507	10	(	(	-LRB-
cord-329276-tfrjw743	507	11	marked	mark	VBN
cord-329276-tfrjw743	507	12	by	by	IN
cord-329276-tfrjw743	507	13	a	a	DT
cord-329276-tfrjw743	507	14	green	green	JJ
cord-329276-tfrjw743	507	15	dot	dot	NN
cord-329276-tfrjw743	507	16	)	)	-RRB-
cord-329276-tfrjw743	507	17	are	be	VBP
cord-329276-tfrjw743	507	18	the	the	DT
cord-329276-tfrjw743	507	19	black	black	JJ
cord-329276-tfrjw743	507	20	curves	curve	NNS
cord-329276-tfrjw743	507	21	which	which	WDT
cord-329276-tfrjw743	507	22	intersect	intersect	VBP
cord-329276-tfrjw743	507	23	transversally	transversally	RB
cord-329276-tfrjw743	507	24	in	in	IN
cord-329276-tfrjw743	507	25	the	the	DT
cord-329276-tfrjw743	507	26	saddle	saddle	NN
cord-329276-tfrjw743	507	27	point	point	NN
cord-329276-tfrjw743	507	28	.	.	.
cord-329276-tfrjw743	508	1	The	the	DT
cord-329276-tfrjw743	508	2	singular	singular	JJ
cord-329276-tfrjw743	508	3	arc	arc	NN
cord-329276-tfrjw743	508	4	is	be	VBZ
cord-329276-tfrjw743	508	5	the	the	DT
cord-329276-tfrjw743	508	6	U	u	NN
cord-329276-tfrjw743	508	7	-	-	HYPH
cord-329276-tfrjw743	508	8	shaped	shape	VBN
cord-329276-tfrjw743	508	9	curve	curve	NN
cord-329276-tfrjw743	508	10	shown	show	VBN
cord-329276-tfrjw743	508	11	as	as	IN
cord-329276-tfrjw743	508	12	solid	solid	JJ
cord-329276-tfrjw743	508	13	green	green	JJ
cord-329276-tfrjw743	508	14	segments	segment	NNS
cord-329276-tfrjw743	508	15	where	where	WRB
cord-329276-tfrjw743	508	16	the	the	DT
cord-329276-tfrjw743	508	17	singular	singular	JJ
cord-329276-tfrjw743	508	18	control	control	NN
cord-329276-tfrjw743	508	19	is	be	VBZ
cord-329276-tfrjw743	508	20	admissible	admissible	JJ
cord-329276-tfrjw743	508	21	and	and	CC
cord-329276-tfrjw743	508	22	as	as	IN
cord-329276-tfrjw743	508	23	dotted	dotted	JJ
cord-329276-tfrjw743	508	24	red	red	JJ
cord-329276-tfrjw743	508	25	segments	segment	NNS
cord-329276-tfrjw743	508	26	where	where	WRB
cord-329276-tfrjw743	508	27	the	the	DT
cord-329276-tfrjw743	508	28	singular	singular	JJ
cord-329276-tfrjw743	508	29	control	control	NN
cord-329276-tfrjw743	508	30	is	be	VBZ
cord-329276-tfrjw743	508	31	inadmissible	inadmissible	JJ
cord-329276-tfrjw743	508	32	.	.	.
cord-329276-tfrjw743	509	1	Once	once	IN
cord-329276-tfrjw743	509	2	the	the	DT
cord-329276-tfrjw743	509	3	optimal	optimal	NN
cord-329276-tfrjw743	509	4	controlled	control	VBN
cord-329276-tfrjw743	509	5	trajectory	trajectory	NN
cord-329276-tfrjw743	509	6	meets	meet	VBZ
cord-329276-tfrjw743	509	7	the	the	DT
cord-329276-tfrjw743	509	8	singular	singular	JJ
cord-329276-tfrjw743	509	9	arc	arc	NN
cord-329276-tfrjw743	509	10	,	,	,
cord-329276-tfrjw743	509	11	the	the	DT
cord-329276-tfrjw743	509	12	control	control	NN
cord-329276-tfrjw743	509	13	switches	switch	VBZ
cord-329276-tfrjw743	509	14	to	to	TO
cord-329276-tfrjw743	509	15	become	become	VB
cord-329276-tfrjw743	509	16	singular	singular	JJ
cord-329276-tfrjw743	509	17	and	and	CC
cord-329276-tfrjw743	509	18	the	the	DT
cord-329276-tfrjw743	509	19	trajectory	trajectory	NN
cord-329276-tfrjw743	509	20	follows	follow	VBZ
cord-329276-tfrjw743	509	21	the	the	DT
cord-329276-tfrjw743	509	22	singular	singular	JJ
cord-329276-tfrjw743	509	23	arc	arc	NN
cord-329276-tfrjw743	509	24	(	(	-LRB-
cord-329276-tfrjw743	509	25	at	at	IN
cord-329276-tfrjw743	509	26	much	much	RB
cord-329276-tfrjw743	509	27	reduced	reduce	VBN
cord-329276-tfrjw743	509	28	dose	dose	NN
cord-329276-tfrjw743	509	29	rates	rate	NNS
cord-329276-tfrjw743	509	30	,	,	,
cord-329276-tfrjw743	509	31	c.f	c.f	NNP
cord-329276-tfrjw743	509	32	.	.	NNP
cord-329276-tfrjw743	509	33	,	,	,
cord-329276-tfrjw743	509	34	Fig	Fig	NNP
cord-329276-tfrjw743	509	35	.	.	NNP
cord-329276-tfrjw743	509	36	10	10	CD
cord-329276-tfrjw743	509	37	)	)	-RRB-
cord-329276-tfrjw743	509	38	.	.	.
cord-329276-tfrjw743	510	1	Then	then	RB
cord-329276-tfrjw743	510	2	,	,	,
cord-329276-tfrjw743	510	3	at	at	IN
cord-329276-tfrjw743	510	4	a	a	DT
cord-329276-tfrjw743	510	5	certain	certain	JJ
cord-329276-tfrjw743	510	6	time	time	NN
cord-329276-tfrjw743	510	7	,	,	,
cord-329276-tfrjw743	510	8	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	510	9	stops	stop	NNS
cord-329276-tfrjw743	510	10	and	and	CC
cord-329276-tfrjw743	510	11	the	the	DT
cord-329276-tfrjw743	510	12	trajectory	trajectory	NN
cord-329276-tfrjw743	510	13	follows	follow	VBZ
cord-329276-tfrjw743	510	14	the	the	DT
cord-329276-tfrjw743	510	15	dynamics	dynamic	NNS
cord-329276-tfrjw743	510	16	of	of	IN
cord-329276-tfrjw743	510	17	the	the	DT
cord-329276-tfrjw743	510	18	uncontrolled	uncontrolled	JJ
cord-329276-tfrjw743	510	19	system	system	NN
cord-329276-tfrjw743	510	20	approaching	approach	VBG
cord-329276-tfrjw743	510	21	,	,	,
cord-329276-tfrjw743	510	22	and	and	CC
cord-329276-tfrjw743	510	23	ultimately	ultimately	RB
cord-329276-tfrjw743	510	24	tracing	trace	VBG
cord-329276-tfrjw743	510	25	,	,	,
cord-329276-tfrjw743	510	26	the	the	DT
cord-329276-tfrjw743	510	27	unstable	unstable	JJ
cord-329276-tfrjw743	510	28	manifold	manifold	NN
cord-329276-tfrjw743	510	29	of	of	IN
cord-329276-tfrjw743	510	30	the	the	DT
cord-329276-tfrjw743	510	31	saddle	saddle	NN
cord-329276-tfrjw743	510	32	point	point	NN
cord-329276-tfrjw743	510	33	.	.	.
cord-329276-tfrjw743	511	1	As	as	IN
cord-329276-tfrjw743	511	2	the	the	DT
cord-329276-tfrjw743	511	3	state	state	NN
cord-329276-tfrjw743	511	4	lies	lie	VBZ
cord-329276-tfrjw743	511	5	in	in	IN
cord-329276-tfrjw743	511	6	the	the	DT
cord-329276-tfrjw743	511	7	benign	benign	JJ
cord-329276-tfrjw743	511	8	region	region	NN
cord-329276-tfrjw743	511	9	,	,	,
cord-329276-tfrjw743	511	10	this	this	DT
cord-329276-tfrjw743	511	11	leads	lead	VBZ
cord-329276-tfrjw743	511	12	to	to	IN
cord-329276-tfrjw743	511	13	an	an	DT
cord-329276-tfrjw743	511	14	overall	overall	JJ
cord-329276-tfrjw743	511	15	improvement	improvement	NN
cord-329276-tfrjw743	511	16	of	of	IN
cord-329276-tfrjw743	511	17	the	the	DT
cord-329276-tfrjw743	511	18	objective	objective	JJ
cord-329276-tfrjw743	511	19	value	value	NN
cord-329276-tfrjw743	511	20	.	.	.
cord-329276-tfrjw743	512	1	The	the	DT
cord-329276-tfrjw743	512	2	optimal	optimal	JJ
cord-329276-tfrjw743	512	3	control	control	NN
cord-329276-tfrjw743	512	4	then	then	RB
cord-329276-tfrjw743	512	5	ends	end	VBZ
cord-329276-tfrjw743	512	6	with	with	IN
cord-329276-tfrjw743	512	7	another	another	DT
cord-329276-tfrjw743	512	8	brief	brief	JJ
cord-329276-tfrjw743	512	9	full	full	JJ
cord-329276-tfrjw743	512	10	dose	dose	NN
cord-329276-tfrjw743	512	11	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	512	12	session	session	NN
cord-329276-tfrjw743	512	13	to	to	TO
cord-329276-tfrjw743	512	14	reach	reach	VB
cord-329276-tfrjw743	512	15	the	the	DT
cord-329276-tfrjw743	512	16	optimal	optimal	JJ
cord-329276-tfrjw743	512	17	terminal	terminal	NN
cord-329276-tfrjw743	512	18	point	point	NN
cord-329276-tfrjw743	513	1	The	the	DT
cord-329276-tfrjw743	513	2	problem	problem	NN
cord-329276-tfrjw743	513	3	is	be	VBZ
cord-329276-tfrjw743	513	4	simpler	simple	JJR
cord-329276-tfrjw743	513	5	if	if	IN
cord-329276-tfrjw743	513	6	an	an	DT
cord-329276-tfrjw743	513	7	L	l	NN
cord-329276-tfrjw743	513	8	2	2	CD
cord-329276-tfrjw743	513	9	-type	-type	CD
cord-329276-tfrjw743	513	10	objective	objective	NN
cord-329276-tfrjw743	513	11	is	be	VBZ
cord-329276-tfrjw743	513	12	employed	employ	VBN
cord-329276-tfrjw743	513	13	in	in	IN
cord-329276-tfrjw743	513	14	the	the	DT
cord-329276-tfrjw743	513	15	control	control	NN
cord-329276-tfrjw743	513	16	as	as	IN
cord-329276-tfrjw743	513	17	this	this	DT
cord-329276-tfrjw743	513	18	makes	make	VBZ
cord-329276-tfrjw743	513	19	the	the	DT
cord-329276-tfrjw743	513	20	Hamiltonian	Hamiltonian	NNP
cord-329276-tfrjw743	513	21	H	H	NNP
cord-329276-tfrjw743	513	22	of	of	IN
cord-329276-tfrjw743	513	23	the	the	DT
cord-329276-tfrjw743	513	24	optimal	optimal	JJ
cord-329276-tfrjw743	513	25	control	control	NN
cord-329276-tfrjw743	513	26	problem	problem	NN
cord-329276-tfrjw743	513	27	strictly	strictly	RB
cord-329276-tfrjw743	513	28	convex	convex	JJ
cord-329276-tfrjw743	513	29	and	and	CC
cord-329276-tfrjw743	513	30	optimal	optimal	JJ
cord-329276-tfrjw743	513	31	controls	control	NNS
cord-329276-tfrjw743	513	32	are	be	VBP
cord-329276-tfrjw743	513	33	continuous	continuous	JJ
cord-329276-tfrjw743	513	34	.	.	.
cord-329276-tfrjw743	514	1	In	in	IN
cord-329276-tfrjw743	514	2	this	this	DT
cord-329276-tfrjw743	514	3	case	case	NN
cord-329276-tfrjw743	514	4	,	,	,
cord-329276-tfrjw743	514	5	standard	standard	JJ
cord-329276-tfrjw743	514	6	shooting	shooting	NN
cord-329276-tfrjw743	514	7	methods	method	NNS
cord-329276-tfrjw743	514	8	can	can	MD
cord-329276-tfrjw743	514	9	be	be	VB
cord-329276-tfrjw743	514	10	applied	apply	VBN
cord-329276-tfrjw743	514	11	to	to	IN
cord-329276-tfrjw743	514	12	the	the	DT
cord-329276-tfrjw743	514	13	combined	combined	JJ
cord-329276-tfrjw743	514	14	system	system	NN
cord-329276-tfrjw743	514	15	of	of	IN
cord-329276-tfrjw743	514	16	dynamics	dynamic	NNS
cord-329276-tfrjw743	514	17	and	and	CC
cord-329276-tfrjw743	514	18	adjoint	adjoint	NN
cord-329276-tfrjw743	514	19	equations	equation	NNS
cord-329276-tfrjw743	514	20	to	to	TO
cord-329276-tfrjw743	514	21	compute	compute	VB
cord-329276-tfrjw743	514	22	numerical	numerical	JJ
cord-329276-tfrjw743	514	23	extremals	extremal	NNS
cord-329276-tfrjw743	514	24	.	.	.
cord-329276-tfrjw743	515	1	Their	-PRON-	PRP$
cord-329276-tfrjw743	515	2	local	local	JJ
cord-329276-tfrjw743	515	3	optimality	optimality	NN
cord-329276-tfrjw743	515	4	is	be	VBZ
cord-329276-tfrjw743	515	5	easily	easily	RB
cord-329276-tfrjw743	515	6	verified	verify	VBN
cord-329276-tfrjw743	515	7	or	or	CC
cord-329276-tfrjw743	515	8	excluded	exclude	VBN
cord-329276-tfrjw743	515	9	by	by	IN
cord-329276-tfrjw743	515	10	computing	compute	VBG
cord-329276-tfrjw743	515	11	conjugate	conjugate	NN
cord-329276-tfrjw743	515	12	points	point	NNS
cord-329276-tfrjw743	515	13	using	use	VBG
cord-329276-tfrjw743	515	14	a	a	DT
cord-329276-tfrjw743	515	15	second	second	JJ
cord-329276-tfrjw743	515	16	-	-	HYPH
cord-329276-tfrjw743	515	17	order	order	NN
cord-329276-tfrjw743	515	18	approach	approach	NN
cord-329276-tfrjw743	515	19	which	which	WDT
cord-329276-tfrjw743	515	20	tests	test	VBZ
cord-329276-tfrjw743	515	21	the	the	DT
cord-329276-tfrjw743	515	22	existence	existence	NN
cord-329276-tfrjw743	515	23	of	of	IN
cord-329276-tfrjw743	515	24	a	a	DT
cord-329276-tfrjw743	515	25	solution	solution	NN
cord-329276-tfrjw743	515	26	of	of	IN
cord-329276-tfrjw743	515	27	the	the	DT
cord-329276-tfrjw743	515	28	associated	associated	JJ
cord-329276-tfrjw743	515	29	matrix	matrix	NN
cord-329276-tfrjw743	515	30	Riccati	Riccati	NNP
cord-329276-tfrjw743	515	31	differential	differential	JJ
cord-329276-tfrjw743	515	32	equation	equation	NN
cord-329276-tfrjw743	515	33	as	as	IN
cord-329276-tfrjw743	515	34	described	describe	VBN
cord-329276-tfrjw743	515	35	in	in	IN
cord-329276-tfrjw743	515	36	[	[	-LRB-
cord-329276-tfrjw743	515	37	37	37	CD
cord-329276-tfrjw743	515	38	]	]	-RRB-
cord-329276-tfrjw743	515	39	.	.	.
cord-329276-tfrjw743	516	1	Other	other	JJ
cord-329276-tfrjw743	516	2	approaches	approach	NNS
cord-329276-tfrjw743	516	3	are	be	VBP
cord-329276-tfrjw743	516	4	based	base	VBN
cord-329276-tfrjw743	516	5	on	on	IN
cord-329276-tfrjw743	516	6	discretizations	discretization	NNS
cord-329276-tfrjw743	516	7	or	or	CC
cord-329276-tfrjw743	516	8	pseudo	pseudo	JJ
cord-329276-tfrjw743	516	9	-	-	JJ
cord-329276-tfrjw743	516	10	spectral	spectral	JJ
cord-329276-tfrjw743	516	11	methods	method	NNS
cord-329276-tfrjw743	516	12	(	(	-LRB-
cord-329276-tfrjw743	516	13	e.g.	e.g.	RB
cord-329276-tfrjw743	516	14	,	,	,
cord-329276-tfrjw743	516	15	see	see	VB
cord-329276-tfrjw743	516	16	[	[	-LRB-
cord-329276-tfrjw743	516	17	50	50	CD
cord-329276-tfrjw743	516	18	]	]	-RRB-
cord-329276-tfrjw743	516	19	[	[	-LRB-
cord-329276-tfrjw743	516	20	51	51	CD
cord-329276-tfrjw743	516	21	]	]	-RRB-
cord-329276-tfrjw743	516	22	[	[	-LRB-
cord-329276-tfrjw743	516	23	52	52	CD
cord-329276-tfrjw743	516	24	]	]	-RRB-
cord-329276-tfrjw743	516	25	)	)	-RRB-
cord-329276-tfrjw743	516	26	.	.	.
cord-329276-tfrjw743	517	1	For	for	IN
cord-329276-tfrjw743	517	2	the	the	DT
cord-329276-tfrjw743	517	3	solutions	solution	NNS
cord-329276-tfrjw743	517	4	shown	show	VBN
cord-329276-tfrjw743	517	5	in	in	IN
cord-329276-tfrjw743	517	6	Sect	Sect	NNP
cord-329276-tfrjw743	517	7	.	.	.
cord-329276-tfrjw743	518	1	4.3	4.3	CD
cord-329276-tfrjw743	518	2	we	-PRON-	PRP
cord-329276-tfrjw743	518	3	used	use	VBD
cord-329276-tfrjw743	518	4	GPOPS	GPOPS	NNP
cord-329276-tfrjw743	518	5	(	(	-LRB-
cord-329276-tfrjw743	518	6	General	General	NNP
cord-329276-tfrjw743	518	7	Pseudo	Pseudo	NNP
cord-329276-tfrjw743	518	8	-	-	HYPH
cord-329276-tfrjw743	518	9	spectral	spectral	JJ
cord-329276-tfrjw743	518	10	OPtimal	OPtimal	NNP
cord-329276-tfrjw743	518	11	control	control	NN
cord-329276-tfrjw743	518	12	Software	Software	NNP
cord-329276-tfrjw743	518	13	)	)	-RRB-
cord-329276-tfrjw743	518	14	,	,	,
cord-329276-tfrjw743	518	15	an	an	DT
cord-329276-tfrjw743	518	16	open	open	JJ
cord-329276-tfrjw743	518	17	-	-	HYPH
cord-329276-tfrjw743	518	18	source	source	NN
cord-329276-tfrjw743	518	19	MATLAB	MATLAB	NNP
cord-329276-tfrjw743	518	20	optimal	optimal	JJ
cord-329276-tfrjw743	518	21	control	control	NN
cord-329276-tfrjw743	518	22	software	software	NN
cord-329276-tfrjw743	518	23	that	that	WDT
cord-329276-tfrjw743	518	24	implements	implement	VBZ
cord-329276-tfrjw743	518	25	the	the	DT
cord-329276-tfrjw743	518	26	Gauss	Gauss	NNP
cord-329276-tfrjw743	518	27	hp	hp	JJ
cord-329276-tfrjw743	518	28	-	-	JJ
cord-329276-tfrjw743	518	29	adaptive	adaptive	JJ
cord-329276-tfrjw743	518	30	pseudospectral	pseudospectral	JJ
cord-329276-tfrjw743	518	31	methods	method	NNS
cord-329276-tfrjw743	518	32	(	(	-LRB-
cord-329276-tfrjw743	518	33	http://www.gpops.org/	http://www.gpops.org/	XX
cord-329276-tfrjw743	518	34	,	,	,
cord-329276-tfrjw743	518	35	[	[	-LRB-
cord-329276-tfrjw743	518	36	53	53	CD
cord-329276-tfrjw743	518	37	]	]	-RRB-
cord-329276-tfrjw743	518	38	)	)	-RRB-
cord-329276-tfrjw743	518	39	.	.	.
cord-329276-tfrjw743	519	1	These	these	DT
cord-329276-tfrjw743	519	2	methods	method	NNS
cord-329276-tfrjw743	519	3	approximate	approximate	VBP
cord-329276-tfrjw743	519	4	the	the	DT
cord-329276-tfrjw743	519	5	state	state	NN
cord-329276-tfrjw743	519	6	using	use	VBG
cord-329276-tfrjw743	519	7	a	a	DT
cord-329276-tfrjw743	519	8	basis	basis	NN
cord-329276-tfrjw743	519	9	of	of	IN
cord-329276-tfrjw743	519	10	Lagrange	Lagrange	NNP
cord-329276-tfrjw743	519	11	polynomials	polynomial	NNS
cord-329276-tfrjw743	519	12	and	and	CC
cord-329276-tfrjw743	519	13	collocate	collocate	VBP
cord-329276-tfrjw743	519	14	the	the	DT
cord-329276-tfrjw743	519	15	dynamics	dynamic	NNS
cord-329276-tfrjw743	519	16	at	at	IN
cord-329276-tfrjw743	519	17	the	the	DT
cord-329276-tfrjw743	519	18	Legendre	Legendre	NNP
cord-329276-tfrjw743	519	19	-	-	HYPH
cord-329276-tfrjw743	519	20	Gauss	Gauss	NNP
cord-329276-tfrjw743	519	21	nodes	node	NNS
cord-329276-tfrjw743	519	22	[	[	-LRB-
cord-329276-tfrjw743	519	23	50	50	CD
cord-329276-tfrjw743	519	24	]	]	-RRB-
cord-329276-tfrjw743	519	25	.	.	.
cord-329276-tfrjw743	520	1	The	the	DT
cord-329276-tfrjw743	520	2	continuous	continuous	JJ
cord-329276-tfrjw743	520	3	-	-	HYPH
cord-329276-tfrjw743	520	4	time	time	NN
cord-329276-tfrjw743	520	5	optimal	optimal	JJ
cord-329276-tfrjw743	520	6	control	control	NN
cord-329276-tfrjw743	520	7	problem	problem	NN
cord-329276-tfrjw743	520	8	is	be	VBZ
cord-329276-tfrjw743	520	9	then	then	RB
cord-329276-tfrjw743	520	10	transformed	transform	VBN
cord-329276-tfrjw743	520	11	into	into	IN
cord-329276-tfrjw743	520	12	a	a	DT
cord-329276-tfrjw743	520	13	finite	finite	JJ
cord-329276-tfrjw743	520	14	-	-	HYPH
cord-329276-tfrjw743	520	15	dimensional	dimensional	JJ
cord-329276-tfrjw743	520	16	nonlinear	nonlinear	JJ
cord-329276-tfrjw743	520	17	programming	programming	NN
cord-329276-tfrjw743	520	18	problem	problem	NN
cord-329276-tfrjw743	520	19	that	that	WDT
cord-329276-tfrjw743	520	20	is	be	VBZ
cord-329276-tfrjw743	520	21	being	be	VBG
cord-329276-tfrjw743	520	22	solved	solve	VBN
cord-329276-tfrjw743	520	23	using	use	VBG
cord-329276-tfrjw743	520	24	well	well	RB
cord-329276-tfrjw743	520	25	-	-	HYPH
cord-329276-tfrjw743	520	26	known	know	VBN
cord-329276-tfrjw743	520	27	and	and	CC
cord-329276-tfrjw743	520	28	standard	standard	JJ
cord-329276-tfrjw743	520	29	algorithms	algorithm	NNS
cord-329276-tfrjw743	520	30	.	.	.
cord-329276-tfrjw743	521	1	Fig	Fig	NNP
cord-329276-tfrjw743	521	2	.	.	.
cord-329276-tfrjw743	522	1	9	9	LS
cord-329276-tfrjw743	522	2	.	.	.
cord-329276-tfrjw743	523	1	The	the	DT
cord-329276-tfrjw743	523	2	maximum	maximum	JJ
cord-329276-tfrjw743	523	3	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	523	4	dose	dose	NN
cord-329276-tfrjw743	523	5	rate	rate	NN
cord-329276-tfrjw743	523	6	(	(	-LRB-
cord-329276-tfrjw743	523	7	vertical	vertical	JJ
cord-329276-tfrjw743	523	8	axis	axis	NN
cord-329276-tfrjw743	523	9	)	)	-RRB-
cord-329276-tfrjw743	523	10	has	have	VBZ
cord-329276-tfrjw743	523	11	been	be	VBN
cord-329276-tfrjw743	523	12	normalized	normalize	VBN
cord-329276-tfrjw743	523	13	to	to	IN
cord-329276-tfrjw743	523	14	1	1	CD
cord-329276-tfrjw743	523	15	.	.	.
cord-329276-tfrjw743	524	1	As	as	IN
cord-329276-tfrjw743	524	2	can	can	MD
cord-329276-tfrjw743	524	3	be	be	VB
cord-329276-tfrjw743	524	4	seen	see	VBN
cord-329276-tfrjw743	524	5	,	,	,
cord-329276-tfrjw743	524	6	the	the	DT
cord-329276-tfrjw743	524	7	time	time	NN
cord-329276-tfrjw743	524	8	-	-	HYPH
cord-329276-tfrjw743	524	9	intervals	interval	NNS
cord-329276-tfrjw743	524	10	when	when	WRB
cord-329276-tfrjw743	524	11	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	524	12	is	be	VBZ
cord-329276-tfrjw743	524	13	at	at	IN
cord-329276-tfrjw743	524	14	full	full	JJ
cord-329276-tfrjw743	524	15	dose	dose	NN
cord-329276-tfrjw743	524	16	are	be	VBP
cord-329276-tfrjw743	524	17	brief	brief	JJ
cord-329276-tfrjw743	524	18	and	and	CC
cord-329276-tfrjw743	524	19	the	the	DT
cord-329276-tfrjw743	524	20	optimal	optimal	JJ
cord-329276-tfrjw743	524	21	dose	dose	NN
cord-329276-tfrjw743	524	22	rates	rate	NNS
cord-329276-tfrjw743	524	23	drop	drop	VBP
cord-329276-tfrjw743	524	24	significantly	significantly	RB
cord-329276-tfrjw743	524	25	along	along	IN
cord-329276-tfrjw743	524	26	the	the	DT
cord-329276-tfrjw743	524	27	much	much	RB
cord-329276-tfrjw743	524	28	longer	long	RBR
cord-329276-tfrjw743	524	29	singular	singular	JJ
cord-329276-tfrjw743	524	30	segment	segment	NN
cord-329276-tfrjw743	524	31	.	.	.
cord-329276-tfrjw743	525	1	The	the	DT
cord-329276-tfrjw743	525	2	rest	rest	NN
cord-329276-tfrjw743	525	3	-	-	HYPH
cord-329276-tfrjw743	525	4	period	period	NN
cord-329276-tfrjw743	525	5	is	be	VBZ
cord-329276-tfrjw743	525	6	the	the	DT
cord-329276-tfrjw743	525	7	most	most	RBS
cord-329276-tfrjw743	525	8	dominant	dominant	JJ
cord-329276-tfrjw743	525	9	time	time	NN
cord-329276-tfrjw743	525	10	-	-	HYPH
cord-329276-tfrjw743	525	11	period	period	NN
cord-329276-tfrjw743	525	12	(	(	-LRB-
cord-329276-tfrjw743	525	13	almost	almost	RB
cord-329276-tfrjw743	525	14	8	8	CD
cord-329276-tfrjw743	525	15	units	unit	NNS
cord-329276-tfrjw743	525	16	out	out	IN
cord-329276-tfrjw743	525	17	of	of	IN
cord-329276-tfrjw743	525	18	T	T	NNP
cord-329276-tfrjw743	525	19	=	=	SYM
cord-329276-tfrjw743	525	20	12	12	CD
cord-329276-tfrjw743	525	21	)	)	-RRB-
cord-329276-tfrjw743	526	1	Problems	problem	NNS
cord-329276-tfrjw743	526	2	with	with	IN
cord-329276-tfrjw743	526	3	an	an	DT
cord-329276-tfrjw743	526	4	L	l	NN
cord-329276-tfrjw743	526	5	1	1	CD
cord-329276-tfrjw743	526	6	-type	-type	CD
cord-329276-tfrjw743	526	7	objective	objective	NN
cord-329276-tfrjw743	526	8	which	which	WDT
cord-329276-tfrjw743	526	9	contain	contain	VBP
cord-329276-tfrjw743	526	10	optimal	optimal	JJ
cord-329276-tfrjw743	526	11	singular	singular	JJ
cord-329276-tfrjw743	526	12	arcs	arc	NNS
cord-329276-tfrjw743	526	13	are	be	VBP
cord-329276-tfrjw743	526	14	more	more	RBR
cord-329276-tfrjw743	526	15	involved	involve	VBN
cord-329276-tfrjw743	526	16	numerically	numerically	RB
cord-329276-tfrjw743	526	17	as	as	IN
cord-329276-tfrjw743	526	18	the	the	DT
cord-329276-tfrjw743	526	19	singular	singular	JJ
cord-329276-tfrjw743	526	20	control	control	NN
cord-329276-tfrjw743	526	21	is	be	VBZ
cord-329276-tfrjw743	526	22	only	only	RB
cord-329276-tfrjw743	526	23	optimal	optimal	JJ
cord-329276-tfrjw743	526	24	on	on	IN
cord-329276-tfrjw743	526	25	an	an	DT
cord-329276-tfrjw743	526	26	embedded	embed	VBN
cord-329276-tfrjw743	526	27	submanifold	submanifold	NN
cord-329276-tfrjw743	526	28	of	of	IN
cord-329276-tfrjw743	526	29	positive	positive	JJ
cord-329276-tfrjw743	526	30	codimension	codimension	NN
cord-329276-tfrjw743	526	31	.	.	.
cord-329276-tfrjw743	527	1	Such	such	JJ
cord-329276-tfrjw743	527	2	a	a	DT
cord-329276-tfrjw743	527	3	structure	structure	NN
cord-329276-tfrjw743	527	4	is	be	VBZ
cord-329276-tfrjw743	527	5	inherently	inherently	RB
cord-329276-tfrjw743	527	6	difficult	difficult	JJ
cord-329276-tfrjw743	527	7	to	to	TO
cord-329276-tfrjw743	527	8	locate	locate	VB
cord-329276-tfrjw743	527	9	numerically	numerically	RB
cord-329276-tfrjw743	527	10	.	.	.
cord-329276-tfrjw743	528	1	Various	various	JJ
cord-329276-tfrjw743	528	2	algorithms	algorithm	NNS
cord-329276-tfrjw743	528	3	,	,	,
cord-329276-tfrjw743	528	4	including	include	VBG
cord-329276-tfrjw743	528	5	commercial	commercial	JJ
cord-329276-tfrjw743	528	6	programs	program	NNS
cord-329276-tfrjw743	528	7	,	,	,
cord-329276-tfrjw743	528	8	we	-PRON-	PRP
cord-329276-tfrjw743	528	9	tried	try	VBD
cord-329276-tfrjw743	528	10	were	be	VBD
cord-329276-tfrjw743	528	11	simply	simply	RB
cord-329276-tfrjw743	528	12	unable	unable	JJ
cord-329276-tfrjw743	528	13	to	to	TO
cord-329276-tfrjw743	528	14	deal	deal	VB
cord-329276-tfrjw743	528	15	with	with	IN
cord-329276-tfrjw743	528	16	this	this	DT
cord-329276-tfrjw743	528	17	situation	situation	NN
cord-329276-tfrjw743	528	18	.	.	.
cord-329276-tfrjw743	529	1	For	for	IN
cord-329276-tfrjw743	529	2	the	the	DT
cord-329276-tfrjw743	529	3	antiangiogenic	antiangiogenic	NNP
cord-329276-tfrjw743	529	4	monotherapy	monotherapy	IN
cord-329276-tfrjw743	529	5	problem	problem	NN
cord-329276-tfrjw743	529	6	(	(	-LRB-
cord-329276-tfrjw743	529	7	see	see	VB
cord-329276-tfrjw743	529	8	Fig	Fig	NNP
cord-329276-tfrjw743	529	9	.	.	.
cord-329276-tfrjw743	529	10	6	6	CD
cord-329276-tfrjw743	529	11	)	)	-RRB-
cord-329276-tfrjw743	530	1	the	the	DT
cord-329276-tfrjw743	530	2	complete	complete	JJ
cord-329276-tfrjw743	530	3	optimal	optimal	JJ
cord-329276-tfrjw743	530	4	synthesis	synthesis	NN
cord-329276-tfrjw743	530	5	was	be	VBD
cord-329276-tfrjw743	530	6	determined	determine	VBN
cord-329276-tfrjw743	530	7	by	by	IN
cord-329276-tfrjw743	530	8	us	-PRON-	PRP
cord-329276-tfrjw743	530	9	theoretically	theoretically	RB
cord-329276-tfrjw743	530	10	by	by	IN
cord-329276-tfrjw743	530	11	analytical	analytical	JJ
cord-329276-tfrjw743	530	12	means	mean	NNS
cord-329276-tfrjw743	530	13	[	[	-LRB-
cord-329276-tfrjw743	530	14	13	13	CD
cord-329276-tfrjw743	530	15	]	]	-RRB-
cord-329276-tfrjw743	530	16	.	.	.
cord-329276-tfrjw743	531	1	The	the	DT
cord-329276-tfrjw743	531	2	computation	computation	NN
cord-329276-tfrjw743	531	3	of	of	IN
cord-329276-tfrjw743	531	4	optimal	optimal	JJ
cord-329276-tfrjw743	531	5	controlled	control	VBN
cord-329276-tfrjw743	531	6	trajectories	trajectory	NNS
cord-329276-tfrjw743	531	7	then	then	RB
cord-329276-tfrjw743	531	8	amounts	amount	VBZ
cord-329276-tfrjw743	531	9	to	to	IN
cord-329276-tfrjw743	531	10	the	the	DT
cord-329276-tfrjw743	531	11	'	'	``
cord-329276-tfrjw743	531	12	evaluation	evaluation	NN
cord-329276-tfrjw743	531	13	of	of	IN
cord-329276-tfrjw743	531	14	a	a	DT
cord-329276-tfrjw743	531	15	function	function	NN
cord-329276-tfrjw743	531	16	'	'	''
cord-329276-tfrjw743	531	17	and	and	CC
cord-329276-tfrjw743	531	18	is	be	VBZ
cord-329276-tfrjw743	531	19	a	a	DT
cord-329276-tfrjw743	531	20	matter	matter	NN
cord-329276-tfrjw743	531	21	of	of	IN
cord-329276-tfrjw743	531	22	seconds	second	NNS
cord-329276-tfrjw743	531	23	(	(	-LRB-
cord-329276-tfrjw743	531	24	c.f	c.f	NNP
cord-329276-tfrjw743	531	25	.	.	NNP
cord-329276-tfrjw743	531	26	,	,	,
cord-329276-tfrjw743	531	27	also	also	RB
cord-329276-tfrjw743	531	28	[	[	-LRB-
cord-329276-tfrjw743	531	29	54	54	CD
cord-329276-tfrjw743	531	30	]	]	-RRB-
cord-329276-tfrjw743	531	31	)	)	-RRB-
cord-329276-tfrjw743	531	32	.	.	.
cord-329276-tfrjw743	532	1	For	for	IN
cord-329276-tfrjw743	532	2	the	the	DT
cord-329276-tfrjw743	532	3	combination	combination	NN
cord-329276-tfrjw743	532	4	therapies	therapy	NNS
cord-329276-tfrjw743	532	5	,	,	,
cord-329276-tfrjw743	532	6	based	base	VBN
cord-329276-tfrjw743	532	7	on	on	IN
cord-329276-tfrjw743	532	8	the	the	DT
cord-329276-tfrjw743	532	9	monotherapy	monotherapy	NN
cord-329276-tfrjw743	532	10	results	result	NNS
cord-329276-tfrjw743	532	11	,	,	,
cord-329276-tfrjw743	532	12	the	the	DT
cord-329276-tfrjw743	532	13	computations	computation	NNS
cord-329276-tfrjw743	532	14	were	be	VBD
cord-329276-tfrjw743	532	15	made	make	VBN
cord-329276-tfrjw743	532	16	by	by	IN
cord-329276-tfrjw743	532	17	Maurer	Maurer	NNP
cord-329276-tfrjw743	532	18	.	.	.
cord-329276-tfrjw743	533	1	States	state	NNS
cord-329276-tfrjw743	533	2	,	,	,
cord-329276-tfrjw743	533	3	controls	control	NNS
cord-329276-tfrjw743	533	4	and	and	CC
cord-329276-tfrjw743	533	5	adjoint	adjoint	NN
cord-329276-tfrjw743	533	6	variables	variable	NNS
cord-329276-tfrjw743	533	7	were	be	VBD
cord-329276-tfrjw743	533	8	computed	compute	VBN
cord-329276-tfrjw743	533	9	using	use	VBG
cord-329276-tfrjw743	533	10	discretization	discretization	NN
cord-329276-tfrjw743	533	11	methods	method	NNS
cord-329276-tfrjw743	533	12	which	which	WDT
cord-329276-tfrjw743	533	13	transcribed	transcribe	VBD
cord-329276-tfrjw743	533	14	the	the	DT
cord-329276-tfrjw743	533	15	optimal	optimal	JJ
cord-329276-tfrjw743	533	16	control	control	NN
cord-329276-tfrjw743	533	17	problem	problem	NN
cord-329276-tfrjw743	533	18	into	into	IN
cord-329276-tfrjw743	533	19	a	a	DT
cord-329276-tfrjw743	533	20	large	large	JJ
cord-329276-tfrjw743	533	21	-	-	HYPH
cord-329276-tfrjw743	533	22	scale	scale	NN
cord-329276-tfrjw743	533	23	nonlinear	nonlinear	JJ
cord-329276-tfrjw743	533	24	programming	programming	NN
cord-329276-tfrjw743	533	25	problem	problem	NN
cord-329276-tfrjw743	533	26	which	which	WDT
cord-329276-tfrjw743	533	27	was	be	VBD
cord-329276-tfrjw743	533	28	implemented	implement	VBN
cord-329276-tfrjw743	533	29	in	in	IN
cord-329276-tfrjw743	533	30	the	the	DT
cord-329276-tfrjw743	533	31	framework	framework	NN
cord-329276-tfrjw743	533	32	of	of	IN
cord-329276-tfrjw743	533	33	the	the	DT
cord-329276-tfrjw743	533	34	Applied	Applied	NNP
cord-329276-tfrjw743	533	35	Mathematical	Mathematical	NNP
cord-329276-tfrjw743	533	36	Modeling	Modeling	NNP
cord-329276-tfrjw743	533	37	Programming	Programming	NNP
cord-329276-tfrjw743	533	38	Language	Language	NNP
cord-329276-tfrjw743	533	39	AMPL	AMPL	NNP
cord-329276-tfrjw743	533	40	and	and	CC
cord-329276-tfrjw743	533	41	is	be	VBZ
cord-329276-tfrjw743	533	42	linked	link	VBN
cord-329276-tfrjw743	533	43	to	to	IN
cord-329276-tfrjw743	533	44	various	various	JJ
cord-329276-tfrjw743	533	45	optimization	optimization	NN
cord-329276-tfrjw743	533	46	codes	code	NNS
cord-329276-tfrjw743	533	47	.	.	.
cord-329276-tfrjw743	534	1	Either	either	CC
cord-329276-tfrjw743	534	2	the	the	DT
cord-329276-tfrjw743	534	3	interior	interior	JJ
cord-329276-tfrjw743	534	4	-	-	HYPH
cord-329276-tfrjw743	534	5	point	point	NN
cord-329276-tfrjw743	534	6	method	method	NN
cord-329276-tfrjw743	534	7	IPOPT	IPOPT	NNP
cord-329276-tfrjw743	534	8	based	base	VBN
cord-329276-tfrjw743	534	9	on	on	IN
cord-329276-tfrjw743	534	10	[	[	-LRB-
cord-329276-tfrjw743	534	11	55	55	CD
cord-329276-tfrjw743	534	12	]	]	-RRB-
cord-329276-tfrjw743	534	13	or	or	CC
cord-329276-tfrjw743	534	14	the	the	DT
cord-329276-tfrjw743	534	15	optimization	optimization	NN
cord-329276-tfrjw743	534	16	code	code	NN
cord-329276-tfrjw743	534	17	NUDOCCCS	NUDOCCCS	NNP
cord-329276-tfrjw743	534	18	developed	develop	VBD
cord-329276-tfrjw743	534	19	in	in	IN
cord-329276-tfrjw743	534	20	[	[	-LRB-
cord-329276-tfrjw743	534	21	56	56	CD
cord-329276-tfrjw743	534	22	]	]	-RRB-
cord-329276-tfrjw743	534	23	in	in	IN
cord-329276-tfrjw743	534	24	conjunction	conjunction	NN
cord-329276-tfrjw743	534	25	with	with	IN
cord-329276-tfrjw743	534	26	the	the	DT
cord-329276-tfrjw743	534	27	arcparametrization	arcparametrization	NN
cord-329276-tfrjw743	534	28	method	method	NN
cord-329276-tfrjw743	534	29	[	[	-LRB-
cord-329276-tfrjw743	534	30	57	57	CD
cord-329276-tfrjw743	534	31	]	]	-RRB-
cord-329276-tfrjw743	534	32	were	be	VBD
cord-329276-tfrjw743	534	33	used	use	VBN
cord-329276-tfrjw743	534	34	.	.	.
cord-329276-tfrjw743	535	1	On	on	IN
cord-329276-tfrjw743	535	2	the	the	DT
cord-329276-tfrjw743	535	3	other	other	JJ
cord-329276-tfrjw743	535	4	hand	hand	NN
cord-329276-tfrjw743	535	5	,	,	,
cord-329276-tfrjw743	535	6	if	if	IN
cord-329276-tfrjw743	535	7	optimal	optimal	JJ
cord-329276-tfrjw743	535	8	controls	control	NNS
cord-329276-tfrjw743	535	9	are	be	VBP
cord-329276-tfrjw743	535	10	bang	bang	NNP
cord-329276-tfrjw743	535	11	-	-	HYPH
cord-329276-tfrjw743	535	12	bang	bang	NNP
cord-329276-tfrjw743	535	13	(	(	-LRB-
cord-329276-tfrjw743	535	14	such	such	JJ
cord-329276-tfrjw743	535	15	as	as	IN
cord-329276-tfrjw743	535	16	for	for	IN
cord-329276-tfrjw743	535	17	the	the	DT
cord-329276-tfrjw743	535	18	cell	cell	NN
cord-329276-tfrjw743	535	19	-	-	HYPH
cord-329276-tfrjw743	535	20	cycle	cycle	NN
cord-329276-tfrjw743	535	21	specific	specific	JJ
cord-329276-tfrjw743	535	22	methods	method	NNS
cord-329276-tfrjw743	535	23	for	for	IN
cord-329276-tfrjw743	535	24	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	535	25	)	)	-RRB-
cord-329276-tfrjw743	535	26	,	,	,
cord-329276-tfrjw743	535	27	the	the	DT
cord-329276-tfrjw743	535	28	numerical	numerical	JJ
cord-329276-tfrjw743	535	29	problem	problem	NN
cord-329276-tfrjw743	535	30	is	be	VBZ
cord-329276-tfrjw743	535	31	simple	simple	JJ
cord-329276-tfrjw743	535	32	and	and	CC
cord-329276-tfrjw743	535	33	basic	basic	JJ
cord-329276-tfrjw743	535	34	algorithms	algorithm	NNS
cord-329276-tfrjw743	535	35	which	which	WDT
cord-329276-tfrjw743	535	36	minimize	minimize	VBP
cord-329276-tfrjw743	535	37	over	over	IN
cord-329276-tfrjw743	535	38	the	the	DT
cord-329276-tfrjw743	535	39	switching	switching	NN
cord-329276-tfrjw743	535	40	times	time	NNS
cord-329276-tfrjw743	535	41	(	(	-LRB-
cord-329276-tfrjw743	535	42	e.g.	e.g.	RB
cord-329276-tfrjw743	535	43	,	,	,
cord-329276-tfrjw743	535	44	gradient	gradient	NN
cord-329276-tfrjw743	535	45	procedures	procedure	NNS
cord-329276-tfrjw743	535	46	[	[	-LRB-
cord-329276-tfrjw743	535	47	58	58	CD
cord-329276-tfrjw743	535	48	]	]	-RRB-
cord-329276-tfrjw743	535	49	)	)	-RRB-
cord-329276-tfrjw743	535	50	can	can	MD
cord-329276-tfrjw743	535	51	be	be	VB
cord-329276-tfrjw743	535	52	used	use	VBN
cord-329276-tfrjw743	535	53	.	.	.
cord-329276-tfrjw743	536	1	A	a	DT
cord-329276-tfrjw743	536	2	verification	verification	NN
cord-329276-tfrjw743	536	3	of	of	IN
cord-329276-tfrjw743	536	4	second	second	JJ
cord-329276-tfrjw743	536	5	-	-	HYPH
cord-329276-tfrjw743	536	6	order	order	NN
cord-329276-tfrjw743	536	7	conditions	condition	NNS
cord-329276-tfrjw743	536	8	for	for	IN
cord-329276-tfrjw743	536	9	optimality	optimality	NN
cord-329276-tfrjw743	536	10	can	can	MD
cord-329276-tfrjw743	536	11	easily	easily	RB
cord-329276-tfrjw743	536	12	be	be	VB
cord-329276-tfrjw743	536	13	built	build	VBN
cord-329276-tfrjw743	536	14	into	into	IN
cord-329276-tfrjw743	536	15	this	this	DT
cord-329276-tfrjw743	536	16	algorithm	algorithm	NN
cord-329276-tfrjw743	536	17	[	[	-LRB-
cord-329276-tfrjw743	536	18	15	15	CD
cord-329276-tfrjw743	536	19	]	]	-RRB-
cord-329276-tfrjw743	536	20	.	.	.
cord-329276-tfrjw743	537	1	In	in	IN
cord-329276-tfrjw743	537	2	his	-PRON-	PRP$
cord-329276-tfrjw743	537	3	paper	paper	NN
cord-329276-tfrjw743	537	4	,	,	,
cord-329276-tfrjw743	537	5	we	-PRON-	PRP
cord-329276-tfrjw743	537	6	formulated	formulate	VBD
cord-329276-tfrjw743	537	7	an	an	DT
cord-329276-tfrjw743	537	8	optimal	optimal	JJ
cord-329276-tfrjw743	537	9	control	control	NN
cord-329276-tfrjw743	537	10	problem	problem	NN
cord-329276-tfrjw743	537	11	for	for	IN
cord-329276-tfrjw743	537	12	a	a	DT
cord-329276-tfrjw743	537	13	general	general	JJ
cord-329276-tfrjw743	537	14	dynamical	dynamical	JJ
cord-329276-tfrjw743	537	15	system	system	NN
cord-329276-tfrjw743	537	16	which	which	WDT
cord-329276-tfrjw743	537	17	is	be	VBZ
cord-329276-tfrjw743	537	18	nonlinear	nonlinear	JJ
cord-329276-tfrjw743	537	19	in	in	IN
cord-329276-tfrjw743	537	20	the	the	DT
cord-329276-tfrjw743	537	21	state	state	NN
cord-329276-tfrjw743	537	22	and	and	CC
cord-329276-tfrjw743	537	23	affine	affine	NN
cord-329276-tfrjw743	537	24	in	in	IN
cord-329276-tfrjw743	537	25	the	the	DT
cord-329276-tfrjw743	537	26	controls	control	NNS
cord-329276-tfrjw743	537	27	.	.	.
cord-329276-tfrjw743	538	1	The	the	DT
cord-329276-tfrjw743	538	2	presented	present	VBN
cord-329276-tfrjw743	538	3	framework	framework	NN
cord-329276-tfrjw743	538	4	encompasses	encompass	VBZ
cord-329276-tfrjw743	538	5	a	a	DT
cord-329276-tfrjw743	538	6	number	number	NN
cord-329276-tfrjw743	538	7	of	of	IN
cord-329276-tfrjw743	538	8	models	model	NNS
cord-329276-tfrjw743	538	9	for	for	IN
cord-329276-tfrjw743	538	10	treatment	treatment	NN
cord-329276-tfrjw743	538	11	of	of	IN
cord-329276-tfrjw743	538	12	biomedical	biomedical	JJ
cord-329276-tfrjw743	538	13	problems	problem	NNS
cord-329276-tfrjw743	538	14	,	,	,
cord-329276-tfrjw743	538	15	especially	especially	RB
cord-329276-tfrjw743	538	16	cancer	cancer	NN
cord-329276-tfrjw743	538	17	therapies	therapy	NNS
cord-329276-tfrjw743	538	18	,	,	,
cord-329276-tfrjw743	538	19	as	as	RB
cord-329276-tfrjw743	538	20	well	well	RB
cord-329276-tfrjw743	538	21	as	as	IN
cord-329276-tfrjw743	538	22	the	the	DT
cord-329276-tfrjw743	538	23	more	more	RBR
cord-329276-tfrjw743	538	24	common	common	JJ
cord-329276-tfrjw743	538	25	models	model	NNS
cord-329276-tfrjw743	538	26	in	in	IN
cord-329276-tfrjw743	538	27	epidemiology	epidemiology	NN
cord-329276-tfrjw743	538	28	.	.	.
cord-329276-tfrjw743	539	1	The	the	DT
cord-329276-tfrjw743	539	2	controls	control	NNS
cord-329276-tfrjw743	539	3	account	account	VBP
cord-329276-tfrjw743	539	4	for	for	IN
cord-329276-tfrjw743	539	5	either	either	CC
cord-329276-tfrjw743	539	6	therapeutic	therapeutic	JJ
cord-329276-tfrjw743	539	7	or	or	CC
cord-329276-tfrjw743	539	8	epidemiological	epidemiological	JJ
cord-329276-tfrjw743	539	9	interventions	intervention	NNS
cord-329276-tfrjw743	539	10	.	.	.
cord-329276-tfrjw743	540	1	The	the	DT
cord-329276-tfrjw743	540	2	terms	term	NNS
cord-329276-tfrjw743	540	3	in	in	IN
cord-329276-tfrjw743	540	4	the	the	DT
cord-329276-tfrjw743	540	5	cost	cost	NN
cord-329276-tfrjw743	540	6	functional	functional	JJ
cord-329276-tfrjw743	540	7	represent	represent	VBP
cord-329276-tfrjw743	540	8	various	various	JJ
cord-329276-tfrjw743	540	9	aspects	aspect	NNS
cord-329276-tfrjw743	540	10	and	and	CC
cord-329276-tfrjw743	540	11	constraints	constraint	NNS
cord-329276-tfrjw743	540	12	that	that	WDT
cord-329276-tfrjw743	540	13	need	need	VBP
cord-329276-tfrjw743	540	14	to	to	TO
cord-329276-tfrjw743	540	15	be	be	VB
cord-329276-tfrjw743	540	16	taken	take	VBN
cord-329276-tfrjw743	540	17	into	into	IN
cord-329276-tfrjw743	540	18	consideration	consideration	NN
cord-329276-tfrjw743	540	19	when	when	WRB
cord-329276-tfrjw743	540	20	the	the	DT
cord-329276-tfrjw743	540	21	dynamics	dynamic	NNS
cord-329276-tfrjw743	540	22	is	be	VBZ
cord-329276-tfrjw743	540	23	considered	consider	VBN
cord-329276-tfrjw743	540	24	as	as	IN
cord-329276-tfrjw743	540	25	an	an	DT
cord-329276-tfrjw743	540	26	optimal	optimal	JJ
cord-329276-tfrjw743	540	27	control	control	NN
cord-329276-tfrjw743	540	28	problem	problem	NN
cord-329276-tfrjw743	540	29	.	.	.
cord-329276-tfrjw743	541	1	We	-PRON-	PRP
cord-329276-tfrjw743	541	2	discussed	discuss	VBD
cord-329276-tfrjw743	541	3	,	,	,
cord-329276-tfrjw743	541	4	and	and	CC
cord-329276-tfrjw743	541	5	using	use	VBG
cord-329276-tfrjw743	541	6	examples	example	NNS
cord-329276-tfrjw743	541	7	from	from	IN
cord-329276-tfrjw743	541	8	our	-PRON-	PRP$
cord-329276-tfrjw743	541	9	own	own	JJ
cord-329276-tfrjw743	541	10	work	work	NN
cord-329276-tfrjw743	541	11	illustrated	illustrate	VBD
cord-329276-tfrjw743	541	12	how	how	WRB
cord-329276-tfrjw743	541	13	the	the	DT
cord-329276-tfrjw743	541	14	solutions	solution	NNS
cord-329276-tfrjw743	541	15	to	to	IN
cord-329276-tfrjw743	541	16	these	these	DT
cord-329276-tfrjw743	541	17	problems	problem	NNS
cord-329276-tfrjw743	541	18	share	share	VBP
cord-329276-tfrjw743	541	19	certain	certain	JJ
cord-329276-tfrjw743	541	20	common	common	JJ
cord-329276-tfrjw743	541	21	characteristics	characteristic	NNS
cord-329276-tfrjw743	541	22	,	,	,
cord-329276-tfrjw743	541	23	what	what	WDT
cord-329276-tfrjw743	541	24	differences	difference	NNS
cord-329276-tfrjw743	541	25	can	can	MD
cord-329276-tfrjw743	541	26	be	be	VB
cord-329276-tfrjw743	541	27	expected	expect	VBN
cord-329276-tfrjw743	541	28	to	to	TO
cord-329276-tfrjw743	541	29	appear	appear	VB
cord-329276-tfrjw743	541	30	and	and	CC
cord-329276-tfrjw743	541	31	,	,	,
cord-329276-tfrjw743	541	32	most	most	RBS
cord-329276-tfrjw743	541	33	importantly	importantly	RB
cord-329276-tfrjw743	541	34	,	,	,
cord-329276-tfrjw743	541	35	how	how	WRB
cord-329276-tfrjw743	541	36	the	the	DT
cord-329276-tfrjw743	541	37	choice	choice	NN
cord-329276-tfrjw743	541	38	of	of	IN
cord-329276-tfrjw743	541	39	the	the	DT
cord-329276-tfrjw743	541	40	objective	objective	NN
cord-329276-tfrjw743	541	41	affects	affect	VBZ
cord-329276-tfrjw743	541	42	the	the	DT
cord-329276-tfrjw743	541	43	form	form	NN
cord-329276-tfrjw743	541	44	of	of	IN
cord-329276-tfrjw743	541	45	the	the	DT
cord-329276-tfrjw743	541	46	solutions	solution	NNS
cord-329276-tfrjw743	541	47	both	both	CC
cord-329276-tfrjw743	541	48	quantitatively	quantitatively	RB
cord-329276-tfrjw743	541	49	and	and	CC
cord-329276-tfrjw743	541	50	qualitatively	qualitatively	RB
cord-329276-tfrjw743	541	51	.	.	.
cord-329276-tfrjw743	542	1	Specifically	specifically	RB
cord-329276-tfrjw743	542	2	,	,	,
cord-329276-tfrjw743	542	3	it	-PRON-	PRP
cord-329276-tfrjw743	542	4	has	have	VBZ
cord-329276-tfrjw743	542	5	been	be	VBN
cord-329276-tfrjw743	542	6	emphasized	emphasize	VBN
cord-329276-tfrjw743	542	7	that	that	IN
cord-329276-tfrjw743	542	8	omitting	omit	VBG
cord-329276-tfrjw743	542	9	some	some	DT
cord-329276-tfrjw743	542	10	important	important	JJ
cord-329276-tfrjw743	542	11	terms	term	NNS
cord-329276-tfrjw743	542	12	in	in	IN
cord-329276-tfrjw743	542	13	the	the	DT
cord-329276-tfrjw743	542	14	objective	objective	NN
cord-329276-tfrjw743	542	15	,	,	,
cord-329276-tfrjw743	542	16	like	like	UH
cord-329276-tfrjw743	542	17	,	,	,
cord-329276-tfrjw743	542	18	for	for	IN
cord-329276-tfrjw743	542	19	example	example	NN
cord-329276-tfrjw743	542	20	,	,	,
cord-329276-tfrjw743	542	21	penalties	penalty	NNS
cord-329276-tfrjw743	542	22	on	on	IN
cord-329276-tfrjw743	542	23	the	the	DT
cord-329276-tfrjw743	542	24	tumor	tumor	NN
cord-329276-tfrjw743	542	25	size	size	NN
cord-329276-tfrjw743	542	26	during	during	IN
cord-329276-tfrjw743	542	27	therapy	therapy	NN
cord-329276-tfrjw743	542	28	-	-	:
cord-329276-tfrjw743	542	29	not	not	RB
cord-329276-tfrjw743	542	30	an	an	DT
cord-329276-tfrjw743	542	31	uncommon	uncommon	JJ
cord-329276-tfrjw743	542	32	procedure	procedure	NN
cord-329276-tfrjw743	542	33	in	in	IN
cord-329276-tfrjw743	542	34	the	the	DT
cord-329276-tfrjw743	542	35	literature	literature	NN
cord-329276-tfrjw743	542	36	-	-	:
cord-329276-tfrjw743	542	37	may	may	MD
cord-329276-tfrjw743	542	38	lead	lead	VB
cord-329276-tfrjw743	542	39	to	to	IN
cord-329276-tfrjw743	542	40	dubious	dubious	JJ
cord-329276-tfrjw743	542	41	solutions	solution	NNS
cord-329276-tfrjw743	542	42	which	which	WDT
cord-329276-tfrjw743	542	43	indicate	indicate	VBP
cord-329276-tfrjw743	542	44	to	to	TO
cord-329276-tfrjw743	542	45	wait	wait	VB
cord-329276-tfrjw743	542	46	and	and	CC
cord-329276-tfrjw743	542	47	administer	administer	VB
cord-329276-tfrjw743	542	48	cancer	cancer	NN
cord-329276-tfrjw743	542	49	treatment	treatment	NN
cord-329276-tfrjw743	542	50	only	only	RB
cord-329276-tfrjw743	542	51	toward	toward	IN
cord-329276-tfrjw743	542	52	the	the	DT
cord-329276-tfrjw743	542	53	end	end	NN
cord-329276-tfrjw743	542	54	of	of	IN
cord-329276-tfrjw743	542	55	the	the	DT
cord-329276-tfrjw743	542	56	therapy	therapy	NN
cord-329276-tfrjw743	542	57	period	period	NN
cord-329276-tfrjw743	542	58	.	.	.
cord-329276-tfrjw743	543	1	Clearly	clearly	RB
cord-329276-tfrjw743	543	2	,	,	,
cord-329276-tfrjw743	543	3	often	often	RB
cord-329276-tfrjw743	543	4	mathematical	mathematical	JJ
cord-329276-tfrjw743	543	5	features	feature	NNS
cord-329276-tfrjw743	543	6	of	of	IN
cord-329276-tfrjw743	543	7	the	the	DT
cord-329276-tfrjw743	543	8	solutions	solution	NNS
cord-329276-tfrjw743	543	9	(	(	-LRB-
cord-329276-tfrjw743	543	10	e.g.	e.g.	RB
cord-329276-tfrjw743	543	11	,	,	,
cord-329276-tfrjw743	543	12	continuous	continuous	JJ
cord-329276-tfrjw743	543	13	versus	versus	IN
cord-329276-tfrjw743	543	14	discontinuous	discontinuous	JJ
cord-329276-tfrjw743	543	15	protocols	protocol	NNS
cord-329276-tfrjw743	543	16	for	for	IN
cord-329276-tfrjw743	543	17	the	the	DT
cord-329276-tfrjw743	543	18	dosage	dosage	NN
cord-329276-tfrjw743	543	19	of	of	IN
cord-329276-tfrjw743	543	20	a	a	DT
cord-329276-tfrjw743	543	21	drug	drug	NN
cord-329276-tfrjw743	543	22	)	)	-RRB-
cord-329276-tfrjw743	543	23	are	be	VBP
cord-329276-tfrjw743	543	24	preprogrammed	preprogramme	VBN
cord-329276-tfrjw743	543	25	through	through	IN
cord-329276-tfrjw743	543	26	the	the	DT
cord-329276-tfrjw743	543	27	choice	choice	NN
cord-329276-tfrjw743	543	28	of	of	IN
cord-329276-tfrjw743	543	29	the	the	DT
cord-329276-tfrjw743	543	30	objective	objective	JJ
cord-329276-tfrjw743	543	31	functional	functional	NN
cord-329276-tfrjw743	543	32	.	.	.
cord-329276-tfrjw743	544	1	This	this	DT
cord-329276-tfrjw743	544	2	is	be	VBZ
cord-329276-tfrjw743	544	3	acceptable	acceptable	JJ
cord-329276-tfrjw743	544	4	,	,	,
cord-329276-tfrjw743	544	5	provided	provide	VBN
cord-329276-tfrjw743	544	6	one	one	CD
cord-329276-tfrjw743	544	7	is	be	VBZ
cord-329276-tfrjw743	544	8	aware	aware	JJ
cord-329276-tfrjw743	544	9	that	that	IN
cord-329276-tfrjw743	544	10	this	this	DT
cord-329276-tfrjw743	544	11	is	be	VBZ
cord-329276-tfrjw743	544	12	an	an	DT
cord-329276-tfrjw743	544	13	outcome	outcome	NN
cord-329276-tfrjw743	544	14	of	of	IN
cord-329276-tfrjw743	544	15	the	the	DT
cord-329276-tfrjw743	544	16	mathematical	mathematical	JJ
cord-329276-tfrjw743	544	17	formulation	formulation	NN
cord-329276-tfrjw743	544	18	and	and	CC
cord-329276-tfrjw743	544	19	not	not	RB
cord-329276-tfrjw743	544	20	an	an	DT
cord-329276-tfrjw743	544	21	indication	indication	NN
cord-329276-tfrjw743	544	22	of	of	IN
cord-329276-tfrjw743	544	23	properties	property	NNS
cord-329276-tfrjw743	544	24	of	of	IN
cord-329276-tfrjw743	544	25	the	the	DT
cord-329276-tfrjw743	544	26	underlying	underlying	JJ
cord-329276-tfrjw743	544	27	dynamical	dynamical	JJ
cord-329276-tfrjw743	544	28	system	system	NN
cord-329276-tfrjw743	544	29	or	or	CC
cord-329276-tfrjw743	544	30	biology	biology	NN
cord-329276-tfrjw743	544	31	.	.	.
cord-329276-tfrjw743	545	1	The	the	DT
cord-329276-tfrjw743	545	2	purpose	purpose	NN
cord-329276-tfrjw743	545	3	of	of	IN
cord-329276-tfrjw743	545	4	this	this	DT
cord-329276-tfrjw743	545	5	article	article	NN
cord-329276-tfrjw743	545	6	was	be	VBD
cord-329276-tfrjw743	545	7	to	to	TO
cord-329276-tfrjw743	545	8	review	review	VB
cord-329276-tfrjw743	545	9	and	and	CC
cord-329276-tfrjw743	545	10	somewhat	somewhat	RB
cord-329276-tfrjw743	545	11	organize	organize	VB
cord-329276-tfrjw743	545	12	and	and	CC
cord-329276-tfrjw743	545	13	illustrate	illustrate	VB
cord-329276-tfrjw743	545	14	work	work	NN
cord-329276-tfrjw743	545	15	done	do	VBN
cord-329276-tfrjw743	545	16	by	by	IN
cord-329276-tfrjw743	545	17	us	-PRON-	PRP
cord-329276-tfrjw743	545	18	on	on	IN
cord-329276-tfrjw743	545	19	this	this	DT
cord-329276-tfrjw743	545	20	topic	topic	NN
cord-329276-tfrjw743	545	21	as	as	RB
cord-329276-tfrjw743	545	22	well	well	RB
cord-329276-tfrjw743	545	23	as	as	IN
cord-329276-tfrjw743	545	24	to	to	TO
cord-329276-tfrjw743	545	25	point	point	VB
cord-329276-tfrjw743	545	26	out	out	RP
cord-329276-tfrjw743	545	27	some	some	DT
cord-329276-tfrjw743	545	28	common	common	JJ
cord-329276-tfrjw743	545	29	pitfalls	pitfall	NNS
cord-329276-tfrjw743	545	30	and	and	CC
cord-329276-tfrjw743	545	31	errors	error	NNS
cord-329276-tfrjw743	545	32	which	which	WDT
cord-329276-tfrjw743	545	33	often	often	RB
cord-329276-tfrjw743	545	34	are	be	VBP
cord-329276-tfrjw743	545	35	made	make	VBN
cord-329276-tfrjw743	545	36	when	when	WRB
cord-329276-tfrjw743	545	37	biological	biological	JJ
cord-329276-tfrjw743	545	38	phenomena	phenomenon	NNS
cord-329276-tfrjw743	545	39	are	be	VBP
cord-329276-tfrjw743	545	40	put	put	VBN
cord-329276-tfrjw743	545	41	into	into	IN
cord-329276-tfrjw743	545	42	the	the	DT
cord-329276-tfrjw743	545	43	mathematical	mathematical	JJ
cord-329276-tfrjw743	545	44	framework	framework	NN
cord-329276-tfrjw743	545	45	of	of	IN
cord-329276-tfrjw743	545	46	optimal	optimal	JJ
cord-329276-tfrjw743	545	47	control	control	NN
cord-329276-tfrjw743	545	48	theory	theory	NN
cord-329276-tfrjw743	545	49	.	.	.
cord-329276-tfrjw743	546	1	Mathematical	Mathematical	NNP
cord-329276-tfrjw743	546	2	Models	Models	NNPS
cord-329276-tfrjw743	546	3	in	in	IN
cord-329276-tfrjw743	546	4	Cell	Cell	NNP
cord-329276-tfrjw743	546	5	Biology	Biology	NNP
cord-329276-tfrjw743	546	6	and	and	CC
cord-329276-tfrjw743	546	7	Cancer	cancer	NN
cord-329276-tfrjw743	547	1	Chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	548	1	An	an	DT
cord-329276-tfrjw743	548	2	optimal	optimal	JJ
cord-329276-tfrjw743	548	3	control	control	NN
cord-329276-tfrjw743	548	4	problem	problem	NN
cord-329276-tfrjw743	548	5	related	relate	VBN
cord-329276-tfrjw743	548	6	to	to	IN
cord-329276-tfrjw743	548	7	leukemia	leukemia	NN
cord-329276-tfrjw743	548	8	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	548	9	Applications	application	NNS
cord-329276-tfrjw743	548	10	of	of	IN
cord-329276-tfrjw743	548	11	Optimal	Optimal	NNP
cord-329276-tfrjw743	548	12	Control	Control	NNP
cord-329276-tfrjw743	548	13	Theory	Theory	NNP
cord-329276-tfrjw743	548	14	in	in	IN
cord-329276-tfrjw743	548	15	Medicine	Medicine	NNP
cord-329276-tfrjw743	548	16	General	General	NNP
cord-329276-tfrjw743	548	17	applications	application	NNS
cord-329276-tfrjw743	548	18	of	of	IN
cord-329276-tfrjw743	548	19	optimal	optimal	JJ
cord-329276-tfrjw743	548	20	control	control	NN
cord-329276-tfrjw743	548	21	theory	theory	NN
cord-329276-tfrjw743	548	22	in	in	IN
cord-329276-tfrjw743	548	23	cancer	cancer	NN
cord-329276-tfrjw743	548	24	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	548	25	Role	role	NN
cord-329276-tfrjw743	548	26	of	of	IN
cord-329276-tfrjw743	548	27	optimal	optimal	JJ
cord-329276-tfrjw743	548	28	control	control	NN
cord-329276-tfrjw743	548	29	in	in	IN
cord-329276-tfrjw743	548	30	cancer	cancer	NN
cord-329276-tfrjw743	549	1	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	549	2	Optimal	Optimal	NNP
cord-329276-tfrjw743	549	3	treatment	treatment	NN
cord-329276-tfrjw743	549	4	protocols	protocol	NNS
cord-329276-tfrjw743	549	5	in	in	IN
cord-329276-tfrjw743	549	6	leukemia	leukemia	NN
cord-329276-tfrjw743	549	7	-	-	HYPH
cord-329276-tfrjw743	549	8	modelling	model	VBG
cord-329276-tfrjw743	549	9	the	the	DT
cord-329276-tfrjw743	549	10	proliferation	proliferation	NN
cord-329276-tfrjw743	549	11	cycle	cycle	NN
cord-329276-tfrjw743	549	12	Optimal	Optimal	NNP
cord-329276-tfrjw743	549	13	Control	Control	NNP
cord-329276-tfrjw743	549	14	of	of	IN
cord-329276-tfrjw743	549	15	Drug	Drug	NNP
cord-329276-tfrjw743	549	16	Administration	Administration	NNP
cord-329276-tfrjw743	549	17	in	in	IN
cord-329276-tfrjw743	549	18	Cancer	Cancer	NNP
cord-329276-tfrjw743	549	19	Chemotherapy	Chemotherapy	NNP
cord-329276-tfrjw743	549	20	Cell	Cell	NNP
cord-329276-tfrjw743	549	21	cycle	cycle	NN
cord-329276-tfrjw743	549	22	as	as	IN
cord-329276-tfrjw743	549	23	an	an	DT
cord-329276-tfrjw743	549	24	object	object	NN
cord-329276-tfrjw743	549	25	of	of	IN
cord-329276-tfrjw743	549	26	control	control	NN
cord-329276-tfrjw743	549	27	A	a	DT
cord-329276-tfrjw743	549	28	mathematical	mathematical	JJ
cord-329276-tfrjw743	549	29	tumor	tumor	NN
cord-329276-tfrjw743	549	30	model	model	NN
cord-329276-tfrjw743	549	31	with	with	IN
cord-329276-tfrjw743	549	32	immune	immune	JJ
cord-329276-tfrjw743	549	33	resistance	resistance	NN
cord-329276-tfrjw743	549	34	and	and	CC
cord-329276-tfrjw743	549	35	drug	drug	NN
cord-329276-tfrjw743	549	36	therapy	therapy	NN
cord-329276-tfrjw743	549	37	:	:	:
cord-329276-tfrjw743	549	38	an	an	DT
cord-329276-tfrjw743	549	39	optimal	optimal	JJ
cord-329276-tfrjw743	549	40	control	control	NN
cord-329276-tfrjw743	549	41	approach	approach	NN
cord-329276-tfrjw743	550	1	Optimal	optimal	JJ
cord-329276-tfrjw743	550	2	bang	bang	NNP
cord-329276-tfrjw743	550	3	-	-	HYPH
cord-329276-tfrjw743	550	4	bang	bang	NNP
cord-329276-tfrjw743	550	5	controls	control	NNS
cord-329276-tfrjw743	550	6	for	for	IN
cord-329276-tfrjw743	550	7	a	a	DT
cord-329276-tfrjw743	550	8	2-compartment	2-compartment	CD
cord-329276-tfrjw743	550	9	model	model	NN
cord-329276-tfrjw743	550	10	in	in	IN
cord-329276-tfrjw743	550	11	cancer	cancer	NN
cord-329276-tfrjw743	550	12	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	550	13	Analysis	Analysis	NNP
cord-329276-tfrjw743	550	14	of	of	IN
cord-329276-tfrjw743	550	15	a	a	DT
cord-329276-tfrjw743	550	16	cell	cell	NN
cord-329276-tfrjw743	550	17	-	-	HYPH
cord-329276-tfrjw743	550	18	cycle	cycle	NN
cord-329276-tfrjw743	550	19	specific	specific	JJ
cord-329276-tfrjw743	550	20	model	model	NN
cord-329276-tfrjw743	550	21	for	for	IN
cord-329276-tfrjw743	550	22	cancer	cancer	NN
cord-329276-tfrjw743	550	23	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	550	24	Optimal	Optimal	NNP
cord-329276-tfrjw743	550	25	control	control	NN
cord-329276-tfrjw743	550	26	for	for	IN
cord-329276-tfrjw743	550	27	a	a	DT
cord-329276-tfrjw743	550	28	class	class	NN
cord-329276-tfrjw743	550	29	of	of	IN
cord-329276-tfrjw743	550	30	compartmental	compartmental	JJ
cord-329276-tfrjw743	550	31	models	model	NNS
cord-329276-tfrjw743	550	32	in	in	IN
cord-329276-tfrjw743	550	33	cancer	cancer	NN
cord-329276-tfrjw743	550	34	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	550	35	Antiangiogenic	Antiangiogenic	NNP
cord-329276-tfrjw743	550	36	therapy	therapy	NN
cord-329276-tfrjw743	550	37	in	in	IN
cord-329276-tfrjw743	550	38	cancer	cancer	NN
cord-329276-tfrjw743	550	39	treatment	treatment	NN
cord-329276-tfrjw743	550	40	as	as	IN
cord-329276-tfrjw743	550	41	an	an	DT
cord-329276-tfrjw743	550	42	optimal	optimal	JJ
cord-329276-tfrjw743	550	43	control	control	NN
cord-329276-tfrjw743	550	44	problem	problem	NN
cord-329276-tfrjw743	550	45	Optimal	Optimal	NNP
cord-329276-tfrjw743	550	46	control	control	NN
cord-329276-tfrjw743	550	47	problems	problem	NNS
cord-329276-tfrjw743	550	48	for	for	IN
cord-329276-tfrjw743	550	49	the	the	DT
cord-329276-tfrjw743	550	50	Gompertz	Gompertz	NNP
cord-329276-tfrjw743	550	51	model	model	NN
cord-329276-tfrjw743	550	52	under	under	IN
cord-329276-tfrjw743	550	53	the	the	DT
cord-329276-tfrjw743	550	54	Norton	Norton	NNP
cord-329276-tfrjw743	550	55	-	-	HYPH
cord-329276-tfrjw743	550	56	Simon	Simon	NNP
cord-329276-tfrjw743	550	57	hypothesis	hypothesis	NN
cord-329276-tfrjw743	550	58	in	in	IN
cord-329276-tfrjw743	550	59	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	550	60	Optimal	Optimal	NNP
cord-329276-tfrjw743	550	61	Control	Control	NNP
cord-329276-tfrjw743	550	62	for	for	IN
cord-329276-tfrjw743	550	63	Mathematical	Mathematical	NNP
cord-329276-tfrjw743	550	64	Models	Models	NNPS
cord-329276-tfrjw743	550	65	of	of	IN
cord-329276-tfrjw743	550	66	Cancer	Cancer	NNP
cord-329276-tfrjw743	550	67	Therapies	Therapies	NNPS
cord-329276-tfrjw743	551	1	A	a	DT
cord-329276-tfrjw743	551	2	Gompertzian	gompertzian	JJ
cord-329276-tfrjw743	551	3	model	model	NN
cord-329276-tfrjw743	551	4	of	of	IN
cord-329276-tfrjw743	551	5	human	human	JJ
cord-329276-tfrjw743	551	6	breast	breast	NN
cord-329276-tfrjw743	551	7	cancer	cancer	NN
cord-329276-tfrjw743	551	8	growth	growth	NN
cord-329276-tfrjw743	551	9	Mathematical	Mathematical	NNP
cord-329276-tfrjw743	551	10	Models	Models	NNPS
cord-329276-tfrjw743	551	11	in	in	IN
cord-329276-tfrjw743	551	12	Cancer	Cancer	NNP
cord-329276-tfrjw743	551	13	Research	Research	NNP
cord-329276-tfrjw743	551	14	Fractal	Fractal	NNP
cord-329276-tfrjw743	551	15	growth	growth	NN
cord-329276-tfrjw743	551	16	of	of	IN
cord-329276-tfrjw743	551	17	tumors	tumor	NNS
cord-329276-tfrjw743	551	18	and	and	CC
cord-329276-tfrjw743	551	19	other	other	JJ
cord-329276-tfrjw743	551	20	cellular	cellular	JJ
cord-329276-tfrjw743	551	21	populations	population	NNS
cord-329276-tfrjw743	551	22	:	:	:
cord-329276-tfrjw743	552	1	linking	link	VBG
cord-329276-tfrjw743	552	2	the	the	DT
cord-329276-tfrjw743	552	3	mechanistic	mechanistic	JJ
cord-329276-tfrjw743	552	4	to	to	IN
cord-329276-tfrjw743	552	5	the	the	DT
cord-329276-tfrjw743	552	6	phenomenological	phenomenological	JJ
cord-329276-tfrjw743	552	7	modeling	modeling	NN
cord-329276-tfrjw743	552	8	and	and	CC
cord-329276-tfrjw743	552	9	vice	vice	NN
cord-329276-tfrjw743	552	10	versa	versa	RB
cord-329276-tfrjw743	552	11	Tumor	tumor	NN
cord-329276-tfrjw743	552	12	development	development	NN
cord-329276-tfrjw743	552	13	under	under	IN
cord-329276-tfrjw743	552	14	angiogenic	angiogenic	JJ
cord-329276-tfrjw743	552	15	signaling	signaling	NN
cord-329276-tfrjw743	552	16	:	:	:
cord-329276-tfrjw743	552	17	a	a	DT
cord-329276-tfrjw743	552	18	dynamical	dynamical	JJ
cord-329276-tfrjw743	552	19	theory	theory	NN
cord-329276-tfrjw743	552	20	of	of	IN
cord-329276-tfrjw743	552	21	tumor	tumor	NN
cord-329276-tfrjw743	552	22	growth	growth	NN
cord-329276-tfrjw743	552	23	,	,	,
cord-329276-tfrjw743	552	24	treatment	treatment	NN
cord-329276-tfrjw743	552	25	response	response	NN
cord-329276-tfrjw743	552	26	,	,	,
cord-329276-tfrjw743	552	27	and	and	CC
cord-329276-tfrjw743	552	28	postvascular	postvascular	JJ
cord-329276-tfrjw743	552	29	dormancy	dormancy	NN
cord-329276-tfrjw743	552	30	Course	course	NN
cord-329276-tfrjw743	552	31	of	of	IN
cord-329276-tfrjw743	552	32	the	the	DT
cord-329276-tfrjw743	552	33	immune	immune	JJ
cord-329276-tfrjw743	552	34	reaction	reaction	NN
cord-329276-tfrjw743	552	35	during	during	IN
cord-329276-tfrjw743	552	36	the	the	DT
cord-329276-tfrjw743	552	37	development	development	NN
cord-329276-tfrjw743	552	38	of	of	IN
cord-329276-tfrjw743	552	39	a	a	DT
cord-329276-tfrjw743	552	40	malignant	malignant	JJ
cord-329276-tfrjw743	552	41	tumour	tumour	NN
cord-329276-tfrjw743	552	42	Optimization	optimization	NN
cord-329276-tfrjw743	552	43	of	of	IN
cord-329276-tfrjw743	552	44	combination	combination	NN
cord-329276-tfrjw743	552	45	therapy	therapy	NN
cord-329276-tfrjw743	552	46	for	for	IN
cord-329276-tfrjw743	552	47	chronic	chronic	JJ
cord-329276-tfrjw743	552	48	myeloid	myeloid	NN
cord-329276-tfrjw743	552	49	leukemia	leukemia	NN
cord-329276-tfrjw743	552	50	with	with	IN
cord-329276-tfrjw743	552	51	dosing	dosing	NN
cord-329276-tfrjw743	552	52	constraints	constraint	NNS
cord-329276-tfrjw743	552	53	Nonlinear	nonlinear	JJ
cord-329276-tfrjw743	552	54	dynamics	dynamic	NNS
cord-329276-tfrjw743	552	55	of	of	IN
cord-329276-tfrjw743	552	56	immunogenic	immunogenic	JJ
cord-329276-tfrjw743	552	57	tumors	tumor	NNS
cord-329276-tfrjw743	552	58	:	:	:
cord-329276-tfrjw743	553	1	parameter	parameter	NN
cord-329276-tfrjw743	553	2	estimation	estimation	NN
cord-329276-tfrjw743	553	3	and	and	CC
cord-329276-tfrjw743	553	4	global	global	JJ
cord-329276-tfrjw743	553	5	bifurcation	bifurcation	NN
cord-329276-tfrjw743	553	6	analysis	analysis	NN
cord-329276-tfrjw743	554	1	Dynamic	dynamic	JJ
cord-329276-tfrjw743	554	2	response	response	NN
cord-329276-tfrjw743	554	3	of	of	IN
cord-329276-tfrjw743	554	4	cancer	cancer	NN
cord-329276-tfrjw743	554	5	under	under	IN
cord-329276-tfrjw743	554	6	the	the	DT
cord-329276-tfrjw743	554	7	influence	influence	NN
cord-329276-tfrjw743	554	8	of	of	IN
cord-329276-tfrjw743	554	9	immunological	immunological	JJ
cord-329276-tfrjw743	554	10	activity	activity	NN
cord-329276-tfrjw743	554	11	and	and	CC
cord-329276-tfrjw743	554	12	therapy	therapy	NN
cord-329276-tfrjw743	554	13	Tumour	tumour	NN
cord-329276-tfrjw743	554	14	eradication	eradication	NN
cord-329276-tfrjw743	554	15	by	by	IN
cord-329276-tfrjw743	554	16	antiangiogenic	antiangiogenic	NNP
cord-329276-tfrjw743	554	17	therapy	therapy	NN
cord-329276-tfrjw743	554	18	:	:	:
cord-329276-tfrjw743	554	19	analysis	analysis	NN
cord-329276-tfrjw743	554	20	and	and	CC
cord-329276-tfrjw743	554	21	extensions	extension	NNS
cord-329276-tfrjw743	554	22	of	of	IN
cord-329276-tfrjw743	554	23	the	the	DT
cord-329276-tfrjw743	554	24	model	model	NN
cord-329276-tfrjw743	554	25	by	by	IN
cord-329276-tfrjw743	554	26	The	the	DT
cord-329276-tfrjw743	554	27	three	three	CD
cord-329276-tfrjw743	554	28	E	e	NN
cord-329276-tfrjw743	554	29	's	's	POS
cord-329276-tfrjw743	554	30	of	of	IN
cord-329276-tfrjw743	554	31	cancer	cancer	NN
cord-329276-tfrjw743	554	32	immunoediting	immunoedite	VBG
cord-329276-tfrjw743	554	33	The	the	DT
cord-329276-tfrjw743	554	34	Molecular	Molecular	NNP
cord-329276-tfrjw743	554	35	Theory	Theory	NNP
cord-329276-tfrjw743	554	36	of	of	IN
cord-329276-tfrjw743	554	37	Radiation	Radiation	NNP
cord-329276-tfrjw743	554	38	Biology	Biology	NNP
cord-329276-tfrjw743	554	39	Dynamic	dynamic	JJ
cord-329276-tfrjw743	554	40	optimization	optimization	NN
cord-329276-tfrjw743	554	41	of	of	IN
cord-329276-tfrjw743	554	42	a	a	DT
cord-329276-tfrjw743	554	43	linear	linear	JJ
cord-329276-tfrjw743	554	44	-	-	HYPH
cord-329276-tfrjw743	554	45	quadratic	quadratic	JJ
cord-329276-tfrjw743	554	46	model	model	NN
cord-329276-tfrjw743	554	47	with	with	IN
cord-329276-tfrjw743	554	48	incomplete	incomplete	JJ
cord-329276-tfrjw743	554	49	repair	repair	NN
cord-329276-tfrjw743	554	50	and	and	CC
cord-329276-tfrjw743	554	51	volume	volume	NN
cord-329276-tfrjw743	554	52	-	-	HYPH
cord-329276-tfrjw743	554	53	dependent	dependent	JJ
cord-329276-tfrjw743	554	54	sensitivity	sensitivity	NN
cord-329276-tfrjw743	554	55	and	and	CC
cord-329276-tfrjw743	554	56	repopulation	repopulation	NN
cord-329276-tfrjw743	555	1	On	on	IN
cord-329276-tfrjw743	555	2	mathematical	mathematical	JJ
cord-329276-tfrjw743	555	3	modeling	modeling	NN
cord-329276-tfrjw743	555	4	of	of	IN
cord-329276-tfrjw743	555	5	critical	critical	JJ
cord-329276-tfrjw743	555	6	variables	variable	NNS
cord-329276-tfrjw743	555	7	in	in	IN
cord-329276-tfrjw743	555	8	cancer	cancer	NN
cord-329276-tfrjw743	555	9	treatment	treatment	NN
cord-329276-tfrjw743	555	10	(	(	-LRB-
cord-329276-tfrjw743	555	11	goals	goal	NNS
cord-329276-tfrjw743	555	12	:	:	:
cord-329276-tfrjw743	555	13	better	well	JJR
cord-329276-tfrjw743	555	14	understanding	understanding	NN
cord-329276-tfrjw743	555	15	of	of	IN
cord-329276-tfrjw743	555	16	the	the	DT
cord-329276-tfrjw743	555	17	past	past	NN
cord-329276-tfrjw743	555	18	and	and	CC
cord-329276-tfrjw743	555	19	better	well	JJR
cord-329276-tfrjw743	555	20	planning	planning	NN
cord-329276-tfrjw743	555	21	in	in	IN
cord-329276-tfrjw743	555	22	the	the	DT
cord-329276-tfrjw743	555	23	future	future	NN
cord-329276-tfrjw743	555	24	)	)	-RRB-
cord-329276-tfrjw743	555	25	Closed	closed	JJ
cord-329276-tfrjw743	555	26	-	-	HYPH
cord-329276-tfrjw743	555	27	loop	loop	NN
cord-329276-tfrjw743	555	28	subcutaneous	subcutaneous	JJ
cord-329276-tfrjw743	555	29	insulin	insulin	NN
cord-329276-tfrjw743	555	30	infusion	infusion	NN
cord-329276-tfrjw743	555	31	algorithm	algorithm	NN
cord-329276-tfrjw743	555	32	with	with	IN
cord-329276-tfrjw743	555	33	a	a	DT
cord-329276-tfrjw743	555	34	short	short	RB
cord-329276-tfrjw743	555	35	-	-	HYPH
cord-329276-tfrjw743	555	36	acting	act	VBG
cord-329276-tfrjw743	555	37	insulin	insulin	NN
cord-329276-tfrjw743	555	38	analog	analog	NN
cord-329276-tfrjw743	555	39	for	for	IN
cord-329276-tfrjw743	555	40	long	long	JJ
cord-329276-tfrjw743	555	41	-	-	HYPH
cord-329276-tfrjw743	555	42	term	term	NN
cord-329276-tfrjw743	555	43	clinical	clinical	JJ
cord-329276-tfrjw743	555	44	application	application	NN
cord-329276-tfrjw743	555	45	of	of	IN
cord-329276-tfrjw743	555	46	a	a	DT
cord-329276-tfrjw743	555	47	wearable	wearable	JJ
cord-329276-tfrjw743	555	48	artificial	artificial	JJ
cord-329276-tfrjw743	555	49	endocrine	endocrine	JJ
cord-329276-tfrjw743	555	50	pancreas	pancreas	NN
cord-329276-tfrjw743	555	51	Normalizing	normalize	VBG
cord-329276-tfrjw743	555	52	tumor	tumor	NN
cord-329276-tfrjw743	555	53	vasculature	vasculature	NN
cord-329276-tfrjw743	555	54	with	with	IN
cord-329276-tfrjw743	555	55	antiangiogenic	antiangiogenic	NNP
cord-329276-tfrjw743	555	56	therapy	therapy	NN
cord-329276-tfrjw743	555	57	:	:	:
cord-329276-tfrjw743	555	58	a	a	DT
cord-329276-tfrjw743	555	59	new	new	JJ
cord-329276-tfrjw743	555	60	paradigm	paradigm	NN
cord-329276-tfrjw743	555	61	for	for	IN
cord-329276-tfrjw743	555	62	combination	combination	NN
cord-329276-tfrjw743	555	63	therapy	therapy	NN
cord-329276-tfrjw743	556	1	Vascular	vascular	JJ
cord-329276-tfrjw743	556	2	normalization	normalization	NN
cord-329276-tfrjw743	556	3	as	as	IN
cord-329276-tfrjw743	556	4	a	a	DT
cord-329276-tfrjw743	556	5	rationale	rationale	NN
cord-329276-tfrjw743	556	6	for	for	IN
cord-329276-tfrjw743	556	7	combining	combine	VBG
cord-329276-tfrjw743	556	8	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	556	9	with	with	IN
cord-329276-tfrjw743	556	10	antiangiogenic	antiangiogenic	JJ
cord-329276-tfrjw743	556	11	agents	agent	NNS
cord-329276-tfrjw743	556	12	On	on	IN
cord-329276-tfrjw743	556	13	optimal	optimal	JJ
cord-329276-tfrjw743	556	14	delivery	delivery	NN
cord-329276-tfrjw743	556	15	of	of	IN
cord-329276-tfrjw743	556	16	combination	combination	NN
cord-329276-tfrjw743	556	17	therapy	therapy	NN
cord-329276-tfrjw743	556	18	for	for	IN
cord-329276-tfrjw743	556	19	tumors	tumor	NNS
cord-329276-tfrjw743	557	1	The	the	DT
cord-329276-tfrjw743	557	2	Mathematical	Mathematical	NNP
cord-329276-tfrjw743	557	3	Theory	Theory	NNP
cord-329276-tfrjw743	557	4	of	of	IN
cord-329276-tfrjw743	557	5	Optimal	Optimal	NNP
cord-329276-tfrjw743	557	6	Processes	process	NNS
cord-329276-tfrjw743	558	1	Singular	singular	JJ
cord-329276-tfrjw743	558	2	Trajectories	trajectory	NNS
cord-329276-tfrjw743	558	3	and	and	CC
cord-329276-tfrjw743	558	4	Their	-PRON-	PRP$
cord-329276-tfrjw743	558	5	Role	role	NN
cord-329276-tfrjw743	558	6	in	in	IN
cord-329276-tfrjw743	558	7	Control	Control	NNP
cord-329276-tfrjw743	558	8	Theory	Theory	NNP
cord-329276-tfrjw743	558	9	.	.	.
cord-329276-tfrjw743	559	1	Mathématiques	Mathématiques	NNP
cord-329276-tfrjw743	559	2	and	and	CC
cord-329276-tfrjw743	559	3	Applications	Applications	NNPS
cord-329276-tfrjw743	559	4	Introduction	Introduction	NNP
cord-329276-tfrjw743	559	5	to	to	IN
cord-329276-tfrjw743	559	6	the	the	DT
cord-329276-tfrjw743	559	7	Mathematical	Mathematical	NNP
cord-329276-tfrjw743	559	8	Theory	Theory	NNP
cord-329276-tfrjw743	559	9	of	of	IN
cord-329276-tfrjw743	560	1	Control	Control	NNP
cord-329276-tfrjw743	560	2	Geometric	Geometric	NNP
cord-329276-tfrjw743	560	3	Optimal	Optimal	NNP
cord-329276-tfrjw743	560	4	Control	Control	NNP
cord-329276-tfrjw743	560	5	Sufficient	sufficient	JJ
cord-329276-tfrjw743	560	6	conditions	condition	NNS
cord-329276-tfrjw743	560	7	for	for	IN
cord-329276-tfrjw743	560	8	strong	strong	JJ
cord-329276-tfrjw743	560	9	local	local	JJ
cord-329276-tfrjw743	560	10	optimality	optimality	NN
cord-329276-tfrjw743	560	11	in	in	IN
cord-329276-tfrjw743	560	12	optimal	optimal	JJ
cord-329276-tfrjw743	560	13	control	control	NN
cord-329276-tfrjw743	560	14	problems	problem	NNS
cord-329276-tfrjw743	560	15	with	with	IN
cord-329276-tfrjw743	560	16	L	L	NNP
cord-329276-tfrjw743	560	17	2	2	CD
cord-329276-tfrjw743	560	18	-type	-type	CD
cord-329276-tfrjw743	560	19	objectives	objective	NNS
cord-329276-tfrjw743	560	20	and	and	CC
cord-329276-tfrjw743	560	21	control	control	NN
cord-329276-tfrjw743	560	22	constraints	constraint	NNS
cord-329276-tfrjw743	561	1	A	a	DT
cord-329276-tfrjw743	561	2	model	model	NN
cord-329276-tfrjw743	561	3	for	for	IN
cord-329276-tfrjw743	561	4	cancer	cancer	NN
cord-329276-tfrjw743	561	5	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	561	6	with	with	IN
cord-329276-tfrjw743	561	7	state	state	NN
cord-329276-tfrjw743	561	8	space	space	NN
cord-329276-tfrjw743	561	9	constraints	constraint	NNS
cord-329276-tfrjw743	562	1	A	a	DT
cord-329276-tfrjw743	562	2	local	local	JJ
cord-329276-tfrjw743	562	3	field	field	NN
cord-329276-tfrjw743	562	4	of	of	IN
cord-329276-tfrjw743	562	5	extremals	extremal	NNS
cord-329276-tfrjw743	562	6	for	for	IN
cord-329276-tfrjw743	562	7	optimal	optimal	JJ
cord-329276-tfrjw743	562	8	control	control	NN
cord-329276-tfrjw743	562	9	problems	problem	NNS
cord-329276-tfrjw743	562	10	with	with	IN
cord-329276-tfrjw743	562	11	state	state	NN
cord-329276-tfrjw743	562	12	constraints	constraint	NNS
cord-329276-tfrjw743	562	13	of	of	IN
cord-329276-tfrjw743	562	14	relative	relative	JJ
cord-329276-tfrjw743	562	15	degree	degree	NN
cord-329276-tfrjw743	562	16	1	1	CD
cord-329276-tfrjw743	562	17	Optimal	Optimal	NNP
cord-329276-tfrjw743	562	18	response	response	NN
cord-329276-tfrjw743	562	19	to	to	IN
cord-329276-tfrjw743	562	20	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	562	21	for	for	IN
cord-329276-tfrjw743	562	22	a	a	DT
cord-329276-tfrjw743	562	23	mathematical	mathematical	JJ
cord-329276-tfrjw743	562	24	model	model	NN
cord-329276-tfrjw743	562	25	of	of	IN
cord-329276-tfrjw743	562	26	tumor	tumor	NN
cord-329276-tfrjw743	562	27	-	-	HYPH
cord-329276-tfrjw743	562	28	immune	immune	JJ
cord-329276-tfrjw743	562	29	dynamics	dynamic	NNS
cord-329276-tfrjw743	562	30	Optimal	Optimal	NNP
cord-329276-tfrjw743	562	31	controls	control	NNS
cord-329276-tfrjw743	562	32	for	for	IN
cord-329276-tfrjw743	562	33	a	a	DT
cord-329276-tfrjw743	562	34	mathematical	mathematical	JJ
cord-329276-tfrjw743	562	35	model	model	NN
cord-329276-tfrjw743	562	36	of	of	IN
cord-329276-tfrjw743	562	37	tumor	tumor	NN
cord-329276-tfrjw743	562	38	-	-	HYPH
cord-329276-tfrjw743	562	39	immune	immune	JJ
cord-329276-tfrjw743	562	40	interactions	interaction	NNS
cord-329276-tfrjw743	562	41	under	under	IN
cord-329276-tfrjw743	562	42	targeted	target	VBN
cord-329276-tfrjw743	562	43	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	562	44	with	with	IN
cord-329276-tfrjw743	562	45	immune	immune	JJ
cord-329276-tfrjw743	562	46	boost	boost	NN
cord-329276-tfrjw743	562	47	Less	Less	JJR
cord-329276-tfrjw743	562	48	is	be	VBZ
cord-329276-tfrjw743	562	49	more	more	JJR
cord-329276-tfrjw743	562	50	,	,	,
cord-329276-tfrjw743	562	51	regularly	regularly	RB
cord-329276-tfrjw743	562	52	:	:	:
cord-329276-tfrjw743	562	53	metronomic	metronomic	JJ
cord-329276-tfrjw743	562	54	dosing	dosing	NN
cord-329276-tfrjw743	562	55	of	of	IN
cord-329276-tfrjw743	562	56	cytotoxic	cytotoxic	JJ
cord-329276-tfrjw743	562	57	drugs	drug	NNS
cord-329276-tfrjw743	562	58	can	can	MD
cord-329276-tfrjw743	562	59	target	target	VB
cord-329276-tfrjw743	562	60	tumor	tumor	NN
cord-329276-tfrjw743	562	61	angiogenesis	angiogenesis	NN
cord-329276-tfrjw743	562	62	in	in	IN
cord-329276-tfrjw743	562	63	mice	mouse	NNS
cord-329276-tfrjw743	562	64	Perspective	perspective	NN
cord-329276-tfrjw743	562	65	on	on	IN
cord-329276-tfrjw743	562	66	"	"	``
cord-329276-tfrjw743	562	67	more	more	JJR
cord-329276-tfrjw743	562	68	is	be	VBZ
cord-329276-tfrjw743	562	69	not	not	RB
cord-329276-tfrjw743	562	70	necessarily	necessarily	RB
cord-329276-tfrjw743	562	71	bette	bette	NNP
cord-329276-tfrjw743	562	72	"	"	''
cord-329276-tfrjw743	562	73	:	:	:
cord-329276-tfrjw743	562	74	metronomic	metronomic	JJ
cord-329276-tfrjw743	562	75	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	562	76	Optimal	Optimal	NNP
cord-329276-tfrjw743	562	77	combined	combined	JJ
cord-329276-tfrjw743	562	78	radio	radio	NN
cord-329276-tfrjw743	562	79	-	-	HYPH
cord-329276-tfrjw743	562	80	and	and	CC
cord-329276-tfrjw743	562	81	antiangiogenic	antiangiogenic	JJ
cord-329276-tfrjw743	562	82	cancer	cancer	NN
cord-329276-tfrjw743	562	83	therapy	therapy	NN
cord-329276-tfrjw743	562	84	Optimal	Optimal	NNP
cord-329276-tfrjw743	562	85	and	and	CC
cord-329276-tfrjw743	562	86	suboptimal	suboptimal	JJ
cord-329276-tfrjw743	562	87	protocols	protocol	NNS
cord-329276-tfrjw743	562	88	for	for	IN
cord-329276-tfrjw743	562	89	a	a	DT
cord-329276-tfrjw743	562	90	mathematical	mathematical	JJ
cord-329276-tfrjw743	562	91	model	model	NN
cord-329276-tfrjw743	562	92	for	for	IN
cord-329276-tfrjw743	562	93	tumor	tumor	NN
cord-329276-tfrjw743	562	94	anti	anti	JJ
cord-329276-tfrjw743	562	95	-	-	JJ
cord-329276-tfrjw743	562	96	angiogenesis	angiogenesis	JJ
cord-329276-tfrjw743	562	97	in	in	IN
cord-329276-tfrjw743	562	98	combination	combination	NN
cord-329276-tfrjw743	562	99	with	with	IN
cord-329276-tfrjw743	562	100	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	562	101	Minimizing	minimize	VBG
cord-329276-tfrjw743	562	102	tumor	tumor	NN
cord-329276-tfrjw743	562	103	volume	volume	NN
cord-329276-tfrjw743	562	104	for	for	IN
cord-329276-tfrjw743	562	105	a	a	DT
cord-329276-tfrjw743	562	106	mathematical	mathematical	JJ
cord-329276-tfrjw743	562	107	model	model	NN
cord-329276-tfrjw743	562	108	of	of	IN
cord-329276-tfrjw743	562	109	anti	anti	JJ
cord-329276-tfrjw743	562	110	-	-	JJ
cord-329276-tfrjw743	562	111	angiogenesis	angiogenesis	JJ
cord-329276-tfrjw743	562	112	with	with	IN
cord-329276-tfrjw743	563	1	linear	linear	NNP
cord-329276-tfrjw743	563	2	pharmacokinetics	pharmacokinetics	NNP
cord-329276-tfrjw743	563	3	Singular	Singular	NNP
cord-329276-tfrjw743	563	4	controls	control	VBZ
cord-329276-tfrjw743	563	5	and	and	CC
cord-329276-tfrjw743	563	6	chattering	chatter	VBG
cord-329276-tfrjw743	563	7	arcs	arc	NNS
cord-329276-tfrjw743	563	8	in	in	IN
cord-329276-tfrjw743	563	9	optimal	optimal	JJ
cord-329276-tfrjw743	563	10	control	control	NN
cord-329276-tfrjw743	563	11	problems	problem	NNS
cord-329276-tfrjw743	563	12	arising	arise	VBG
cord-329276-tfrjw743	563	13	in	in	IN
cord-329276-tfrjw743	563	14	biomedicine	biomedicine	NN
cord-329276-tfrjw743	563	15	On	on	IN
cord-329276-tfrjw743	563	16	the	the	DT
cord-329276-tfrjw743	563	17	role	role	NN
cord-329276-tfrjw743	563	18	of	of	IN
cord-329276-tfrjw743	563	19	pharmacometrics	pharmacometric	NNS
cord-329276-tfrjw743	563	20	in	in	IN
cord-329276-tfrjw743	563	21	mathematical	mathematical	JJ
cord-329276-tfrjw743	563	22	models	model	NNS
cord-329276-tfrjw743	563	23	for	for	IN
cord-329276-tfrjw743	563	24	cancer	cancer	NN
cord-329276-tfrjw743	563	25	treatments	treatment	NNS
cord-329276-tfrjw743	563	26	On	on	IN
cord-329276-tfrjw743	563	27	optimal	optimal	JJ
cord-329276-tfrjw743	563	28	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	563	29	with	with	IN
cord-329276-tfrjw743	563	30	a	a	DT
cord-329276-tfrjw743	563	31	stongly	stongly	RB
cord-329276-tfrjw743	563	32	targeted	target	VBN
cord-329276-tfrjw743	563	33	agent	agent	NN
cord-329276-tfrjw743	563	34	for	for	IN
cord-329276-tfrjw743	563	35	a	a	DT
cord-329276-tfrjw743	563	36	model	model	NN
cord-329276-tfrjw743	563	37	of	of	IN
cord-329276-tfrjw743	563	38	tumor	tumor	NN
cord-329276-tfrjw743	563	39	-	-	HYPH
cord-329276-tfrjw743	563	40	immune	immune	NN
cord-329276-tfrjw743	563	41	system	system	NN
cord-329276-tfrjw743	563	42	interactions	interaction	NNS
cord-329276-tfrjw743	563	43	with	with	IN
cord-329276-tfrjw743	563	44	generalized	generalized	JJ
cord-329276-tfrjw743	563	45	logistic	logistic	JJ
cord-329276-tfrjw743	563	46	growth	growth	NN
cord-329276-tfrjw743	563	47	Direct	direct	JJ
cord-329276-tfrjw743	563	48	trajectory	trajectory	NN
cord-329276-tfrjw743	563	49	optimization	optimization	NN
cord-329276-tfrjw743	563	50	and	and	CC
cord-329276-tfrjw743	563	51	costate	costate	NN
cord-329276-tfrjw743	563	52	estimation	estimation	NN
cord-329276-tfrjw743	563	53	via	via	IN
cord-329276-tfrjw743	563	54	an	an	DT
cord-329276-tfrjw743	563	55	orthogonal	orthogonal	JJ
cord-329276-tfrjw743	563	56	collocation	collocation	NN
cord-329276-tfrjw743	563	57	method	method	NN
cord-329276-tfrjw743	564	1	The	the	DT
cord-329276-tfrjw743	564	2	Chebyshev	Chebyshev	NNP
cord-329276-tfrjw743	564	3	-	-	HYPH
cord-329276-tfrjw743	564	4	Legendre	Legendre	NNP
cord-329276-tfrjw743	564	5	collocation	collocation	NN
cord-329276-tfrjw743	564	6	method	method	NN
cord-329276-tfrjw743	564	7	for	for	IN
cord-329276-tfrjw743	564	8	a	a	DT
cord-329276-tfrjw743	564	9	class	class	NN
cord-329276-tfrjw743	564	10	of	of	IN
cord-329276-tfrjw743	564	11	optimal	optimal	JJ
cord-329276-tfrjw743	564	12	control	control	NN
cord-329276-tfrjw743	564	13	problems	problem	NNS
cord-329276-tfrjw743	565	1	Zero	zero	CD
cord-329276-tfrjw743	565	2	-	-	HYPH
cord-329276-tfrjw743	565	3	propellant	propellant	NN
cord-329276-tfrjw743	565	4	maneuver	maneuver	NN
cord-329276-tfrjw743	565	5	guidance	guidance	NN
cord-329276-tfrjw743	565	6	User	User	NNP
cord-329276-tfrjw743	565	7	's	's	POS
cord-329276-tfrjw743	565	8	Manual	Manual	NNP
cord-329276-tfrjw743	565	9	for	for	IN
cord-329276-tfrjw743	565	10	GPOPS	GPOPS	NNP
cord-329276-tfrjw743	565	11	:	:	:
cord-329276-tfrjw743	566	1	A	a	DT
cord-329276-tfrjw743	566	2	MATLAB	MATLAB	NNP
cord-329276-tfrjw743	566	3	Package	Package	NNP
cord-329276-tfrjw743	566	4	for	for	IN
cord-329276-tfrjw743	566	5	Dynamic	Dynamic	NNP
cord-329276-tfrjw743	566	6	Optimization	Optimization	NNP
cord-329276-tfrjw743	566	7	Using	use	VBG
cord-329276-tfrjw743	566	8	the	the	DT
cord-329276-tfrjw743	566	9	Gauss	Gauss	NNP
cord-329276-tfrjw743	566	10	Pseudospectral	Pseudospectral	NNP
cord-329276-tfrjw743	566	11	Method	Method	NNP
cord-329276-tfrjw743	566	12	Optimal	Optimal	NNP
cord-329276-tfrjw743	566	13	and	and	CC
cord-329276-tfrjw743	566	14	suboptimal	suboptimal	JJ
cord-329276-tfrjw743	566	15	protocols	protocol	NNS
cord-329276-tfrjw743	566	16	for	for	IN
cord-329276-tfrjw743	566	17	a	a	DT
cord-329276-tfrjw743	566	18	class	class	NN
cord-329276-tfrjw743	566	19	of	of	IN
cord-329276-tfrjw743	566	20	mathematical	mathematical	JJ
cord-329276-tfrjw743	566	21	models	model	NNS
cord-329276-tfrjw743	566	22	of	of	IN
cord-329276-tfrjw743	566	23	tumor	tumor	NN
cord-329276-tfrjw743	566	24	anti	anti	JJ
cord-329276-tfrjw743	566	25	-	-	JJ
cord-329276-tfrjw743	566	26	angiogenesis	angiogenesis	JJ
cord-329276-tfrjw743	567	1	On	on	IN
cord-329276-tfrjw743	567	2	the	the	DT
cord-329276-tfrjw743	567	3	implementation	implementation	NN
cord-329276-tfrjw743	567	4	of	of	IN
cord-329276-tfrjw743	567	5	an	an	DT
cord-329276-tfrjw743	567	6	interior	interior	JJ
cord-329276-tfrjw743	567	7	-	-	HYPH
cord-329276-tfrjw743	567	8	point	point	NN
cord-329276-tfrjw743	567	9	filter	filter	NN
cord-329276-tfrjw743	567	10	line	line	NN
cord-329276-tfrjw743	567	11	-	-	HYPH
cord-329276-tfrjw743	567	12	search	search	NN
cord-329276-tfrjw743	567	13	algorithm	algorithm	NN
cord-329276-tfrjw743	567	14	for	for	IN
cord-329276-tfrjw743	567	15	large	large	JJ
cord-329276-tfrjw743	567	16	-	-	HYPH
cord-329276-tfrjw743	567	17	scale	scale	NN
cord-329276-tfrjw743	567	18	nonlinear	nonlinear	JJ
cord-329276-tfrjw743	567	19	programming	programming	NN
cord-329276-tfrjw743	567	20	SQP	sqp	NN
cord-329276-tfrjw743	567	21	-	-	HYPH
cord-329276-tfrjw743	567	22	methods	method	NNS
cord-329276-tfrjw743	567	23	for	for	IN
cord-329276-tfrjw743	567	24	solving	solve	VBG
cord-329276-tfrjw743	567	25	optimal	optimal	JJ
cord-329276-tfrjw743	567	26	control	control	NN
cord-329276-tfrjw743	567	27	problems	problem	NNS
cord-329276-tfrjw743	567	28	with	with	IN
cord-329276-tfrjw743	567	29	control	control	NN
cord-329276-tfrjw743	567	30	and	and	CC
cord-329276-tfrjw743	567	31	state	state	NN
cord-329276-tfrjw743	567	32	constraints	constraint	NNS
cord-329276-tfrjw743	567	33	:	:	:
cord-329276-tfrjw743	567	34	adjoint	adjoint	NN
cord-329276-tfrjw743	567	35	variables	variable	NNS
cord-329276-tfrjw743	567	36	,	,	,
cord-329276-tfrjw743	567	37	sensitivity	sensitivity	NN
cord-329276-tfrjw743	567	38	analysis	analysis	NN
cord-329276-tfrjw743	567	39	and	and	CC
cord-329276-tfrjw743	567	40	real	real	JJ
cord-329276-tfrjw743	567	41	-	-	HYPH
cord-329276-tfrjw743	567	42	time	time	NN
cord-329276-tfrjw743	567	43	control	control	NN
cord-329276-tfrjw743	567	44	Optimization	optimization	NN
cord-329276-tfrjw743	567	45	methods	method	NNS
cord-329276-tfrjw743	567	46	for	for	IN
cord-329276-tfrjw743	567	47	the	the	DT
cord-329276-tfrjw743	567	48	verification	verification	NN
cord-329276-tfrjw743	567	49	of	of	IN
cord-329276-tfrjw743	567	50	secondorder	secondorder	NN
cord-329276-tfrjw743	567	51	sufficient	sufficient	JJ
cord-329276-tfrjw743	567	52	conditions	condition	NNS
cord-329276-tfrjw743	567	53	for	for	IN
cord-329276-tfrjw743	567	54	bang	bang	NNP
cord-329276-tfrjw743	567	55	-	-	HYPH
cord-329276-tfrjw743	567	56	bang	bang	NNP
cord-329276-tfrjw743	567	57	controls	control	VBZ
cord-329276-tfrjw743	567	58	A	a	DT
cord-329276-tfrjw743	567	59	gradient	gradient	NN
cord-329276-tfrjw743	567	60	method	method	NN
cord-329276-tfrjw743	567	61	for	for	IN
cord-329276-tfrjw743	567	62	application	application	NN
cord-329276-tfrjw743	567	63	of	of	IN
cord-329276-tfrjw743	567	64	chemotherapy	chemotherapy	NN
cord-329276-tfrjw743	567	65	models	model	NNS
cord-329276-tfrjw743	568	1	Publisher	publisher	NN
cord-329276-tfrjw743	568	2	's	's	POS
cord-329276-tfrjw743	568	3	Note	Note	NNP
cord-329276-tfrjw743	568	4	Springer	Springer	NNP
cord-329276-tfrjw743	568	5	Nature	Nature	NNP
cord-329276-tfrjw743	568	6	remains	remain	VBZ
cord-329276-tfrjw743	568	7	neutral	neutral	JJ
cord-329276-tfrjw743	568	8	with	with	IN
cord-329276-tfrjw743	568	9	regard	regard	NN
cord-329276-tfrjw743	568	10	to	to	IN
cord-329276-tfrjw743	568	11	jurisdictional	jurisdictional	JJ
cord-329276-tfrjw743	568	12	claims	claim	NNS
cord-329276-tfrjw743	568	13	in	in	IN
cord-329276-tfrjw743	568	14	published	publish	VBN
cord-329276-tfrjw743	568	15	maps	map	NNS
cord-329276-tfrjw743	568	16	and	and	CC
cord-329276-tfrjw743	568	17	institutional	institutional	JJ
cord-329276-tfrjw743	568	18	affiliations	affiliation	NNS
cord-329276-tfrjw743	569	1	We	-PRON-	PRP
cord-329276-tfrjw743	569	2	are	be	VBP
cord-329276-tfrjw743	569	3	grateful	grateful	JJ
cord-329276-tfrjw743	569	4	to	to	IN
cord-329276-tfrjw743	569	5	four	four	CD
cord-329276-tfrjw743	569	6	anonymous	anonymous	JJ
cord-329276-tfrjw743	569	7	referees	referee	NNS
cord-329276-tfrjw743	569	8	of	of	IN
cord-329276-tfrjw743	569	9	this	this	DT
cord-329276-tfrjw743	569	10	paper	paper	NN
cord-329276-tfrjw743	569	11	for	for	IN
cord-329276-tfrjw743	569	12	their	-PRON-	PRP$
cord-329276-tfrjw743	569	13	useful	useful	JJ
cord-329276-tfrjw743	569	14	comments	comment	NNS
cord-329276-tfrjw743	569	15	which	which	WDT
cord-329276-tfrjw743	569	16	helped	help	VBD
cord-329276-tfrjw743	569	17	us	-PRON-	PRP
cord-329276-tfrjw743	569	18	improve	improve	VB
cord-329276-tfrjw743	569	19	our	-PRON-	PRP$
cord-329276-tfrjw743	569	20	presentation	presentation	NN
cord-329276-tfrjw743	569	21	.	.	.
cord-329276-tfrjw743	570	1	All	all	DT
cord-329276-tfrjw743	570	2	data	datum	NNS
cord-329276-tfrjw743	570	3	generated	generate	VBD
cord-329276-tfrjw743	570	4	or	or	CC
cord-329276-tfrjw743	570	5	analyzed	analyze	VBN
cord-329276-tfrjw743	570	6	during	during	IN
cord-329276-tfrjw743	570	7	this	this	DT
cord-329276-tfrjw743	570	8	study	study	NN
cord-329276-tfrjw743	570	9	are	be	VBP
cord-329276-tfrjw743	570	10	included	include	VBN
cord-329276-tfrjw743	570	11	in	in	IN
cord-329276-tfrjw743	570	12	this	this	DT
cord-329276-tfrjw743	570	13	published	publish	VBN
cord-329276-tfrjw743	570	14	article	article	NN
cord-329276-tfrjw743	570	15	.	.	.