id	sid	tid	token	lemma	pos
ejpam-5386	1	1	european	european	PROPN
ejpam-5386	1	2	journal	journal	PROPN
ejpam-5386	1	3	of	of	ADP
ejpam-5386	1	4	pure	pure	ADJ
ejpam-5386	1	5	and	and	CCONJ
ejpam-5386	1	6	applied	apply	VERB
ejpam-5386	1	7	mathematics	mathematic	NOUN
ejpam-5386	1	8	vol	vol	NOUN
ejpam-5386	1	9	.	.	PROPN
ejpam-5386	2	1	17	17	NUM
ejpam-5386	2	2	,	,	PUNCT
ejpam-5386	2	3	no	no	INTJ
ejpam-5386	2	4	.	.	NOUN
ejpam-5386	2	5	4	4	NUM
ejpam-5386	2	6	,	,	PUNCT
ejpam-5386	2	7	2024	2024	NUM
ejpam-5386	2	8	,	,	PUNCT
ejpam-5386	2	9	2651	2651	NUM
ejpam-5386	2	10	-	-	SYM
ejpam-5386	2	11	2675	2675	NUM
ejpam-5386	2	12	issn	issn	PROPN
ejpam-5386	2	13	1307	1307	NUM
ejpam-5386	2	14	-	-	SYM
ejpam-5386	2	15	5543	5543	NUM
ejpam-5386	2	16	–	–	PUNCT
ejpam-5386	2	17	ejpam.com	ejpam.com	X
ejpam-5386	2	18	published	publish	VERB
ejpam-5386	2	19	by	by	ADP
ejpam-5386	2	20	new	new	PROPN
ejpam-5386	2	21	york	york	PROPN
ejpam-5386	2	22	business	business	PROPN
ejpam-5386	2	23	global	global	ADJ
ejpam-5386	2	24	simultaneous	simultaneous	ADJ
ejpam-5386	2	25	identification	identification	NOUN
ejpam-5386	2	26	of	of	ADP
ejpam-5386	2	27	the	the	DET
ejpam-5386	2	28	parameters	parameter	NOUN
ejpam-5386	2	29	in	in	ADP
ejpam-5386	2	30	the	the	DET
ejpam-5386	2	31	mathematical	mathematical	ADJ
ejpam-5386	2	32	model	model	NOUN
ejpam-5386	2	33	of	of	ADP
ejpam-5386	2	34	brain	brain	NOUN
ejpam-5386	2	35	tumor	tumor	NOUN
ejpam-5386	2	36	growth	growth	NOUN
ejpam-5386	2	37	dynamics	dynamic	NOUN
ejpam-5386	2	38	under	under	ADP
ejpam-5386	2	39	treatment	treatment	NOUN
ejpam-5386	2	40	salih	salih	PROPN
ejpam-5386	2	41	tatar1,∗	tatar1,∗	PROPN
ejpam-5386	2	42	,	,	PUNCT
ejpam-5386	2	43	mohamed	mohamed	PROPN
ejpam-5386	2	44	bensalah2	bensalah2	PROPN
ejpam-5386	2	45	,	,	PUNCT
ejpam-5386	2	46	maryam	maryam	PROPN
ejpam-5386	2	47	alamil1	alamil1	PROPN
ejpam-5386	3	1	1	1	NUM
ejpam-5386	3	2	college	college	NOUN
ejpam-5386	3	3	of	of	ADP
ejpam-5386	3	4	science	science	NOUN
ejpam-5386	3	5	and	and	CCONJ
ejpam-5386	3	6	general	general	ADJ
ejpam-5386	3	7	studies	study	NOUN
ejpam-5386	3	8	,	,	PUNCT
ejpam-5386	3	9	alfaisal	alfaisal	NOUN
ejpam-5386	3	10	university	university	NOUN
ejpam-5386	3	11	,	,	PUNCT
ejpam-5386	3	12	riyadh	riyadh	PROPN
ejpam-5386	3	13	11533	11533	NUM
ejpam-5386	3	14	,	,	PUNCT
ejpam-5386	3	15	saudi	saudi	PROPN
ejpam-5386	3	16	arabia	arabia	PROPN
ejpam-5386	3	17	2	2	NUM
ejpam-5386	3	18	department	department	NOUN
ejpam-5386	3	19	of	of	ADP
ejpam-5386	3	20	computer	computer	NOUN
ejpam-5386	3	21	sciences	sciences	PROPN
ejpam-5386	3	22	,	,	PUNCT
ejpam-5386	3	23	higher	high	ADJ
ejpam-5386	3	24	institute	institute	NOUN
ejpam-5386	3	25	of	of	ADP
ejpam-5386	3	26	applied	apply	VERB
ejpam-5386	3	27	science	science	NOUN
ejpam-5386	3	28	and	and	CCONJ
ejpam-5386	3	29	technology	technology	NOUN
ejpam-5386	3	30	of	of	ADP
ejpam-5386	3	31	sousse	sousse	PROPN
ejpam-5386	3	32	,	,	PUNCT
ejpam-5386	3	33	university	university	NOUN
ejpam-5386	3	34	of	of	ADP
ejpam-5386	3	35	sousse	sousse	PROPN
ejpam-5386	3	36	,	,	PUNCT
ejpam-5386	3	37	rue	rue	X
ejpam-5386	3	38	tahar	tahar	PROPN
ejpam-5386	3	39	ben	ben	PROPN
ejpam-5386	3	40	achour	achour	PROPN
ejpam-5386	3	41	,	,	PUNCT
ejpam-5386	3	42	sousse	sousse	PROPN
ejpam-5386	3	43	4003	4003	NUM
ejpam-5386	3	44	,	,	PUNCT
ejpam-5386	3	45	tunisia	tunisia	NOUN
ejpam-5386	3	46	abstract	abstract	NOUN
ejpam-5386	3	47	.	.	PUNCT
ejpam-5386	4	1	this	this	DET
ejpam-5386	4	2	paper	paper	NOUN
ejpam-5386	4	3	is	be	AUX
ejpam-5386	4	4	devoted	devote	VERB
ejpam-5386	4	5	to	to	ADP
ejpam-5386	4	6	an	an	DET
ejpam-5386	4	7	inverse	inverse	NOUN
ejpam-5386	4	8	problem	problem	NOUN
ejpam-5386	4	9	for	for	ADP
ejpam-5386	4	10	a	a	DET
ejpam-5386	4	11	nonlinear	nonlinear	ADJ
ejpam-5386	4	12	parabolic	parabolic	ADJ
ejpam-5386	4	13	equation	equation	NOUN
ejpam-5386	4	14	related	relate	VERB
ejpam-5386	4	15	to	to	AUX
ejpam-5386	4	16	brain	brain	VERB
ejpam-5386	4	17	tumor	tumor	NOUN
ejpam-5386	4	18	dynamics	dynamic	NOUN
ejpam-5386	4	19	.	.	PUNCT
ejpam-5386	5	1	after	after	ADP
ejpam-5386	5	2	reformulating	reformulate	VERB
ejpam-5386	5	3	the	the	DET
ejpam-5386	5	4	inverse	inverse	NOUN
ejpam-5386	5	5	problem	problem	NOUN
ejpam-5386	5	6	as	as	ADP
ejpam-5386	5	7	a	a	DET
ejpam-5386	5	8	minimization	minimization	NOUN
ejpam-5386	5	9	problem	problem	NOUN
ejpam-5386	5	10	,	,	PUNCT
ejpam-5386	5	11	we	we	PRON
ejpam-5386	5	12	prove	prove	VERB
ejpam-5386	5	13	the	the	DET
ejpam-5386	5	14	existence	existence	NOUN
ejpam-5386	5	15	and	and	CCONJ
ejpam-5386	5	16	stability	stability	NOUN
ejpam-5386	5	17	of	of	ADP
ejpam-5386	5	18	the	the	DET
ejpam-5386	5	19	solution	solution	NOUN
ejpam-5386	5	20	to	to	ADP
ejpam-5386	5	21	the	the	DET
ejpam-5386	5	22	minimization	minimization	NOUN
ejpam-5386	5	23	problem	problem	NOUN
ejpam-5386	5	24	.	.	PUNCT
ejpam-5386	6	1	based	base	VERB
ejpam-5386	6	2	on	on	ADP
ejpam-5386	6	3	the	the	DET
ejpam-5386	6	4	fréchet	fréchet	NOUN
ejpam-5386	6	5	differentiability	differentiability	NOUN
ejpam-5386	6	6	of	of	ADP
ejpam-5386	6	7	the	the	DET
ejpam-5386	6	8	objective	objective	NOUN
ejpam-5386	6	9	(	(	PUNCT
ejpam-5386	6	10	cost	cost	NOUN
ejpam-5386	6	11	)	)	PUNCT
ejpam-5386	6	12	functional	functional	ADJ
ejpam-5386	6	13	,	,	PUNCT
ejpam-5386	6	14	we	we	PRON
ejpam-5386	6	15	develop	develop	VERB
ejpam-5386	6	16	an	an	DET
ejpam-5386	6	17	efficient	efficient	ADJ
ejpam-5386	6	18	iterative	iterative	NOUN
ejpam-5386	6	19	procedure	procedure	NOUN
ejpam-5386	6	20	for	for	ADP
ejpam-5386	6	21	the	the	DET
ejpam-5386	6	22	numerical	numerical	ADJ
ejpam-5386	6	23	solution	solution	NOUN
ejpam-5386	6	24	to	to	ADP
ejpam-5386	6	25	the	the	DET
ejpam-5386	6	26	minimization	minimization	NOUN
ejpam-5386	6	27	problem	problem	NOUN
ejpam-5386	6	28	.	.	PUNCT
ejpam-5386	7	1	numerical	numerical	ADJ
ejpam-5386	7	2	examples	example	NOUN
ejpam-5386	7	3	with	with	ADP
ejpam-5386	7	4	noise	noise	NOUN
ejpam-5386	7	5	-	-	PUNCT
ejpam-5386	7	6	free	free	ADJ
ejpam-5386	7	7	and	and	CCONJ
ejpam-5386	7	8	noisy	noisy	ADJ
ejpam-5386	7	9	data	datum	NOUN
ejpam-5386	7	10	illustrate	illustrate	VERB
ejpam-5386	7	11	applicability	applicability	NOUN
ejpam-5386	7	12	and	and	CCONJ
ejpam-5386	7	13	accuracy	accuracy	NOUN
ejpam-5386	7	14	of	of	ADP
ejpam-5386	7	15	the	the	DET
ejpam-5386	7	16	proposed	propose	VERB
ejpam-5386	7	17	method	method	NOUN
ejpam-5386	7	18	to	to	ADP
ejpam-5386	7	19	some	some	DET
ejpam-5386	7	20	extent	extent	NOUN
ejpam-5386	7	21	.	.	PUNCT
ejpam-5386	8	1	2020	2020	NUM
ejpam-5386	8	2	mathematics	mathematic	NOUN
ejpam-5386	8	3	subject	subject	NOUN
ejpam-5386	8	4	classifications	classification	NOUN
ejpam-5386	8	5	:	:	PUNCT
ejpam-5386	8	6	35r30	35r30	NUM
ejpam-5386	8	7	,	,	PUNCT
ejpam-5386	8	8	65n21	65n21	NUM
ejpam-5386	8	9	,	,	PUNCT
ejpam-5386	8	10	35q92	35q92	NUM
ejpam-5386	8	11	,	,	PUNCT
ejpam-5386	8	12	65m32	65m32	NOUN
ejpam-5386	8	13	,	,	PUNCT
ejpam-5386	8	14	35k61	35k61	NUM
ejpam-5386	8	15	key	key	ADJ
ejpam-5386	8	16	words	word	NOUN
ejpam-5386	8	17	and	and	CCONJ
ejpam-5386	8	18	phrases	phrase	NOUN
ejpam-5386	8	19	:	:	PUNCT
ejpam-5386	8	20	brain	brain	NOUN
ejpam-5386	8	21	tumor	tumor	NOUN
ejpam-5386	8	22	,	,	PUNCT
ejpam-5386	8	23	inverse	inverse	NOUN
ejpam-5386	8	24	problem	problem	NOUN
ejpam-5386	8	25	,	,	PUNCT
ejpam-5386	8	26	optimization	optimization	NOUN
ejpam-5386	8	27	problem	problem	NOUN
ejpam-5386	8	28	,	,	PUNCT
ejpam-5386	8	29	fréchet	fréchet	NOUN
ejpam-5386	8	30	differentiability	differentiability	NOUN
ejpam-5386	8	31	nomenclature	nomenclature	ADJ
ejpam-5386	8	32	g(c	g(c	NOUN
ejpam-5386	8	33	)	)	PUNCT
ejpam-5386	8	34	reaction	reaction	NOUN
ejpam-5386	8	35	term	term	NOUN
ejpam-5386	8	36	b	b	PROPN
ejpam-5386	8	37	spatial	spatial	ADJ
ejpam-5386	8	38	domain	domain	NOUN
ejpam-5386	8	39	of	of	ADP
ejpam-5386	8	40	the	the	DET
ejpam-5386	8	41	brain	brain	NOUN
ejpam-5386	8	42	ν	ν	ADP
ejpam-5386	8	43	the	the	DET
ejpam-5386	8	44	outward	outward	ADJ
ejpam-5386	8	45	normal	normal	ADJ
ejpam-5386	8	46	vector	vector	NOUN
ejpam-5386	8	47	on	on	ADP
ejpam-5386	8	48	the	the	DET
ejpam-5386	8	49	boundary	boundary	ADJ
ejpam-5386	8	50	φ	φ	PROPN
ejpam-5386	8	51	initial	initial	ADJ
ejpam-5386	8	52	cell	cell	NOUN
ejpam-5386	8	53	density	density	NOUN
ejpam-5386	8	54	d(x	d(x	NOUN
ejpam-5386	8	55	)	)	PUNCT
ejpam-5386	8	56	diffusion	diffusion	NOUN
ejpam-5386	8	57	coefficient	coefficient	NOUN
ejpam-5386	8	58	c	c	PROPN
ejpam-5386	8	59	cell	cell	NOUN
ejpam-5386	8	60	density	density	NOUN
ejpam-5386	8	61	at	at	ADP
ejpam-5386	8	62	position	position	NOUN
ejpam-5386	8	63	x	x	PUNCT
ejpam-5386	8	64	and	and	CCONJ
ejpam-5386	8	65	time	time	NOUN
ejpam-5386	8	66	t	t	PROPN
ejpam-5386	8	67	div	div	PROPN
ejpam-5386	8	68	divergence	divergence	NOUN
ejpam-5386	8	69	operator	operator	NOUN
ejpam-5386	8	70	∇	∇	X
ejpam-5386	8	71	gradient	gradient	NOUN
ejpam-5386	8	72	operator	operator	NOUN
ejpam-5386	8	73	∂b	∂b	PROPN
ejpam-5386	8	74	boundary	boundary	NOUN
ejpam-5386	8	75	of	of	ADP
ejpam-5386	8	76	b	b	PROPN
ejpam-5386	8	77	h	h	NOUN
ejpam-5386	8	78	mesh	mesh	NOUN
ejpam-5386	8	79	step	step	NOUN
ejpam-5386	8	80	in	in	ADP
ejpam-5386	8	81	x	x	PUNCT
ejpam-5386	8	82	direction	direction	NOUN
ejpam-5386	8	83	τ	τ	PROPN
ejpam-5386	8	84	time	time	NOUN
ejpam-5386	8	85	step	step	NOUN
ejpam-5386	8	86	in	in	ADP
ejpam-5386	8	87	t	t	PROPN
ejpam-5386	8	88	direction	direction	NOUN
ejpam-5386	8	89	t	t	PROPN
ejpam-5386	8	90	final	final	ADJ
ejpam-5386	8	91	time	time	NOUN
ejpam-5386	8	92	ε	ε	PROPN
ejpam-5386	8	93	noise	noise	NOUN
ejpam-5386	8	94	level	level	NOUN
ejpam-5386	8	95	clim	clim	NOUN
ejpam-5386	8	96	carrying	carry	VERB
ejpam-5386	8	97	capacity	capacity	NOUN
ejpam-5386	8	98	ρ	ρ	PROPN
ejpam-5386	8	99	proliferation	proliferation	NOUN
ejpam-5386	8	100	parameter	parameter	PROPN
ejpam-5386	8	101	dw	dw	PROPN
ejpam-5386	8	102	diffusion	diffusion	PROPN
ejpam-5386	8	103	coefficient	coefficient	NOUN
ejpam-5386	8	104	for	for	ADP
ejpam-5386	8	105	white	white	ADJ
ejpam-5386	8	106	matter	matter	NOUN
ejpam-5386	8	107	dg	dg	PROPN
ejpam-5386	8	108	diffusion	diffusion	NOUN
ejpam-5386	8	109	coefficient	coefficient	NOUN
ejpam-5386	8	110	for	for	ADP
ejpam-5386	8	111	gray	gray	ADJ
ejpam-5386	8	112	matter	matter	NOUN
ejpam-5386	8	113	k(x	k(x	PROPN
ejpam-5386	8	114	,	,	PUNCT
ejpam-5386	8	115	t	t	PROPN
ejpam-5386	8	116	)	)	PUNCT
ejpam-5386	8	117	treatment	treatment	NOUN
ejpam-5386	8	118	term	term	NOUN
ejpam-5386	8	119	α	α	PRON
ejpam-5386	8	120	spatial	spatial	ADJ
ejpam-5386	8	121	component	component	NOUN
ejpam-5386	8	122	of	of	ADP
ejpam-5386	8	123	the	the	DET
ejpam-5386	8	124	treatment	treatment	NOUN
ejpam-5386	8	125	profile	profile	NOUN
ejpam-5386	8	126	β	β	X
ejpam-5386	8	127	temporal	temporal	ADJ
ejpam-5386	8	128	component	component	NOUN
ejpam-5386	8	129	of	of	ADP
ejpam-5386	8	130	the	the	DET
ejpam-5386	8	131	treatment	treatment	NOUN
ejpam-5386	8	132	profile	profile	NOUN
ejpam-5386	8	133	aα	aα	NOUN
ejpam-5386	8	134	×aφ	×aφ	NOUN
ejpam-5386	8	135	set	set	NOUN
ejpam-5386	8	136	of	of	ADP
ejpam-5386	8	137	admissible	admissible	ADJ
ejpam-5386	8	138	solutions	solution	NOUN
ejpam-5386	8	139	j(α	j(α	PROPN
ejpam-5386	8	140	,	,	PUNCT
ejpam-5386	8	141	φ	φ	NUM
ejpam-5386	8	142	)	)	PUNCT
ejpam-5386	8	143	objective	objective	ADJ
ejpam-5386	8	144	functional	functional	ADJ
ejpam-5386	8	145	∗corresponding	∗corresponding	NOUN
ejpam-5386	8	146	author	author	NOUN
ejpam-5386	8	147	.	.	PUNCT
ejpam-5386	9	1	doi	doi	NOUN
ejpam-5386	9	2	:	:	PUNCT
ejpam-5386	9	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5386	https://doi.org/10.29020/nybg.ejpam.v17i4.5386	VERB
ejpam-5386	9	4	email	email	NOUN
ejpam-5386	9	5	addresses	address	NOUN
ejpam-5386	9	6	:	:	PUNCT
ejpam-5386	9	7	statar@alfaisal.edu	statar@alfaisal.edu	PROPN
ejpam-5386	9	8	(	(	PUNCT
ejpam-5386	9	9	s.	s.	PROPN
ejpam-5386	9	10	tatar	tatar	PROPN
ejpam-5386	9	11	)	)	PUNCT
ejpam-5386	9	12	,	,	PUNCT
ejpam-5386	9	13	mohamed.bensalah@fsm.rnu.tn	mohamed.bensalah@fsm.rnu.tn	NOUN
ejpam-5386	9	14	(	(	PUNCT
ejpam-5386	9	15	m.	m.	NOUN
ejpam-5386	9	16	bensalah	bensalah	PROPN
ejpam-5386	9	17	)	)	PUNCT
ejpam-5386	9	18	,	,	PUNCT
ejpam-5386	9	19	malamil@alfaisal.edu	malamil@alfaisal.edu	PROPN
ejpam-5386	9	20	(	(	PUNCT
ejpam-5386	9	21	m.	m.	NOUN
ejpam-5386	9	22	alamil	alamil	PROPN
ejpam-5386	9	23	)	)	PUNCT
ejpam-5386	9	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5386	10	1	2651	2651	NUM
ejpam-5386	11	1	copyright	copyright	NOUN
ejpam-5386	11	2	:	:	PUNCT
ejpam-5386	11	3	©	©	PROPN
ejpam-5386	11	4	2024	2024	NUM
ejpam-5386	11	5	the	the	DET
ejpam-5386	11	6	author(s	author(s	NOUN
ejpam-5386	11	7	)	)	PUNCT
ejpam-5386	11	8	.	.	PUNCT
ejpam-5386	12	1	(	(	PUNCT
ejpam-5386	12	2	cc	cc	NOUN
ejpam-5386	12	3	by	by	ADP
ejpam-5386	12	4	-	-	PUNCT
ejpam-5386	12	5	nc	nc	PROPN
ejpam-5386	12	6	4.0	4.0	NUM
ejpam-5386	12	7	)	)	PUNCT
ejpam-5386	12	8	s.	s.	PROPN
ejpam-5386	12	9	tatar	tatar	PROPN
ejpam-5386	12	10	,	,	PUNCT
ejpam-5386	12	11	m.	m.	NOUN
ejpam-5386	12	12	bensalah	bensalah	PROPN
ejpam-5386	12	13	,	,	PUNCT
ejpam-5386	12	14	m.	m.	NOUN
ejpam-5386	12	15	alamil	alamil	PROPN
ejpam-5386	12	16	/	/	SYM
ejpam-5386	12	17	eur	eur	PROPN
ejpam-5386	12	18	.	.	PUNCT
ejpam-5386	13	1	j.	j.	PROPN
ejpam-5386	13	2	pure	pure	PROPN
ejpam-5386	13	3	appl	appl	PROPN
ejpam-5386	13	4	.	.	PROPN
ejpam-5386	13	5	math	math	PROPN
ejpam-5386	13	6	,	,	PUNCT
ejpam-5386	13	7	17	17	NUM
ejpam-5386	13	8	(	(	PUNCT
ejpam-5386	13	9	4	4	NUM
ejpam-5386	13	10	)	)	PUNCT
ejpam-5386	13	11	(	(	PUNCT
ejpam-5386	13	12	2024	2024	NUM
ejpam-5386	13	13	)	)	PUNCT
ejpam-5386	13	14	,	,	PUNCT
ejpam-5386	13	15	2651	2651	NUM
ejpam-5386	13	16	-	-	SYM
ejpam-5386	13	17	2675	2675	NUM
ejpam-5386	13	18	2652	2652	NUM
ejpam-5386	13	19	ζkα	ζkα	NOUN
ejpam-5386	13	20	step	step	NOUN
ejpam-5386	13	21	size	size	NOUN
ejpam-5386	13	22	for	for	ADP
ejpam-5386	13	23	α	α	PROPN
ejpam-5386	13	24	ζkφ	ζkφ	NOUN
ejpam-5386	13	25	step	step	NOUN
ejpam-5386	13	26	size	size	NOUN
ejpam-5386	13	27	for	for	ADP
ejpam-5386	13	28	φ	φ	PROPN
ejpam-5386	13	29	sk	sk	PROPN
ejpam-5386	13	30	α	α	PROPN
ejpam-5386	13	31	search	search	NOUN
ejpam-5386	13	32	direction	direction	NOUN
ejpam-5386	13	33	for	for	ADP
ejpam-5386	13	34	α	α	PROPN
ejpam-5386	13	35	sk	sk	PROPN
ejpam-5386	13	36	φ	φ	PROPN
ejpam-5386	13	37	search	search	NOUN
ejpam-5386	13	38	direction	direction	NOUN
ejpam-5386	13	39	for	for	ADP
ejpam-5386	13	40	φ	φ	PROPN
ejpam-5386	13	41	ε̄	ε̄	ADJ
ejpam-5386	13	42	tolerance	tolerance	NOUN
ejpam-5386	13	43	parameter	parameter	NOUN
ejpam-5386	13	44	ωi	ωi	PUNCT
ejpam-5386	13	45	weight	weight	NOUN
ejpam-5386	13	46	functions	function	NOUN
ejpam-5386	13	47	1	1	NUM
ejpam-5386	13	48	.	.	PUNCT
ejpam-5386	13	49	introduction	introduction	NOUN
ejpam-5386	13	50	in	in	ADP
ejpam-5386	13	51	this	this	DET
ejpam-5386	13	52	paper	paper	NOUN
ejpam-5386	13	53	,	,	PUNCT
ejpam-5386	13	54	we	we	PRON
ejpam-5386	13	55	consider	consider	VERB
ejpam-5386	13	56	an	an	DET
ejpam-5386	13	57	inverse	inverse	NOUN
ejpam-5386	13	58	problem	problem	NOUN
ejpam-5386	13	59	for	for	ADP
ejpam-5386	13	60	the	the	DET
ejpam-5386	13	61	following	follow	VERB
ejpam-5386	13	62	problem:	problem:	ADP
ejpam-5386	13	63	∂tc−	∂tc−	VERB
ejpam-5386	13	64	div(d(x)∇c	div(d(x)∇c	NUM
ejpam-5386	13	65	)	)	PUNCT
ejpam-5386	13	66	+	+	CCONJ
ejpam-5386	14	1	k(x	k(x	PROPN
ejpam-5386	14	2	,	,	PUNCT
ejpam-5386	14	3	t	t	NOUN
ejpam-5386	14	4	)	)	PUNCT
ejpam-5386	14	5	c−	c−	ADJ
ejpam-5386	14	6	g(c	g(c	NOUN
ejpam-5386	14	7	)	)	PUNCT
ejpam-5386	14	8	=	=	SYM
ejpam-5386	14	9	0	0	PUNCT
ejpam-5386	14	10	(	(	PUNCT
ejpam-5386	14	11	x	x	NOUN
ejpam-5386	14	12	,	,	PUNCT
ejpam-5386	14	13	t	t	PROPN
ejpam-5386	14	14	)	)	PUNCT
ejpam-5386	14	15	∈	∈	PROPN
ejpam-5386	14	16	b	b	PROPN
ejpam-5386	14	17	×	×	NOUN
ejpam-5386	14	18	(	(	PUNCT
ejpam-5386	14	19	0	0	NUM
ejpam-5386	14	20	,	,	PUNCT
ejpam-5386	14	21	t	t	NOUN
ejpam-5386	14	22	)	)	PUNCT
ejpam-5386	14	23	,	,	PUNCT
ejpam-5386	14	24	d(x	d(x	PROPN
ejpam-5386	14	25	)	)	PUNCT
ejpam-5386	15	1	∂νc	∂νc	PROPN
ejpam-5386	15	2	=	=	SYM
ejpam-5386	15	3	0	0	PUNCT
ejpam-5386	15	4	(	(	PUNCT
ejpam-5386	15	5	x	x	NOUN
ejpam-5386	15	6	,	,	PUNCT
ejpam-5386	15	7	t	t	PROPN
ejpam-5386	15	8	)	)	PUNCT
ejpam-5386	15	9	∈	∈	PROPN
ejpam-5386	15	10	b	b	PROPN
ejpam-5386	15	11	×	×	NOUN
ejpam-5386	15	12	(	(	PUNCT
ejpam-5386	15	13	0	0	NUM
ejpam-5386	15	14	,	,	PUNCT
ejpam-5386	15	15	t	t	NOUN
ejpam-5386	15	16	)	)	PUNCT
ejpam-5386	15	17	,	,	PUNCT
ejpam-5386	15	18	c(x	c(x	NOUN
ejpam-5386	15	19	,	,	PUNCT
ejpam-5386	15	20	0	0	NUM
ejpam-5386	15	21	)	)	PUNCT
ejpam-5386	15	22	=	=	SYM
ejpam-5386	15	23	φ(x	φ(x	NOUN
ejpam-5386	15	24	)	)	PUNCT
ejpam-5386	15	25	x	x	X
ejpam-5386	15	26	∈	∈	PROPN
ejpam-5386	15	27	b	b	PROPN
ejpam-5386	15	28	,	,	PUNCT
ejpam-5386	15	29	(	(	PUNCT
ejpam-5386	15	30	1	1	X
ejpam-5386	15	31	)	)	PUNCT
ejpam-5386	15	32	where	where	SCONJ
ejpam-5386	15	33	b	b	X
ejpam-5386	15	34	⊂	⊂	PROPN
ejpam-5386	15	35	rd	rd	PROPN
ejpam-5386	16	1	(	(	PUNCT
ejpam-5386	16	2	d	d	NOUN
ejpam-5386	16	3	=	=	SYM
ejpam-5386	16	4	1,2	1,2	NUM
ejpam-5386	16	5	,	,	PUNCT
ejpam-5386	16	6	.	.	PUNCT
ejpam-5386	16	7	.	.	PUNCT
ejpam-5386	16	8	.	.	PUNCT
ejpam-5386	16	9	)	)	PUNCT
ejpam-5386	16	10	be	be	AUX
ejpam-5386	16	11	an	an	DET
ejpam-5386	16	12	open	open	ADJ
ejpam-5386	16	13	bounded	bounded	ADJ
ejpam-5386	16	14	domain	domain	NOUN
ejpam-5386	16	15	with	with	ADP
ejpam-5386	16	16	a	a	DET
ejpam-5386	16	17	sufficiently	sufficiently	ADV
ejpam-5386	16	18	smooth	smooth	ADJ
ejpam-5386	16	19	boundary	boundary	ADJ
ejpam-5386	16	20	∂b	∂b	PROPN
ejpam-5386	16	21	,	,	PUNCT
ejpam-5386	16	22	t	t	PROPN
ejpam-5386	16	23	>	>	X
ejpam-5386	16	24	0	0	PUNCT
ejpam-5386	16	25	is	be	AUX
ejpam-5386	16	26	a	a	DET
ejpam-5386	16	27	final	final	ADJ
ejpam-5386	16	28	time	time	NOUN
ejpam-5386	16	29	,	,	PUNCT
ejpam-5386	16	30	c(x	c(x	NOUN
ejpam-5386	16	31	,	,	PUNCT
ejpam-5386	16	32	t	t	PROPN
ejpam-5386	16	33	)	)	PUNCT
ejpam-5386	16	34	is	be	AUX
ejpam-5386	16	35	the	the	DET
ejpam-5386	16	36	tumor	tumor	NOUN
ejpam-5386	16	37	cell	cell	NOUN
ejpam-5386	16	38	density	density	NOUN
ejpam-5386	16	39	at	at	ADP
ejpam-5386	16	40	the	the	DET
ejpam-5386	16	41	time	time	NOUN
ejpam-5386	16	42	t	t	PROPN
ejpam-5386	16	43	and	and	CCONJ
ejpam-5386	16	44	the	the	DET
ejpam-5386	16	45	spatial	spatial	ADJ
ejpam-5386	16	46	location	location	NOUN
ejpam-5386	16	47	x	x	PUNCT
ejpam-5386	16	48	within	within	ADP
ejpam-5386	16	49	the	the	DET
ejpam-5386	16	50	brain	brain	NOUN
ejpam-5386	16	51	region	region	NOUN
ejpam-5386	16	52	b	b	PROPN
ejpam-5386	16	53	,	,	PUNCT
ejpam-5386	16	54	k(x	k(x	PROPN
ejpam-5386	16	55	,	,	PUNCT
ejpam-5386	16	56	t	t	PROPN
ejpam-5386	16	57	)	)	PUNCT
ejpam-5386	16	58	c(x	c(x	PROPN
ejpam-5386	16	59	,	,	PUNCT
ejpam-5386	16	60	t	t	PROPN
ejpam-5386	16	61	)	)	PUNCT
ejpam-5386	16	62	is	be	AUX
ejpam-5386	16	63	the	the	DET
ejpam-5386	16	64	treatment	treatment	NOUN
ejpam-5386	16	65	term	term	NOUN
ejpam-5386	16	66	describing	describe	VERB
ejpam-5386	16	67	the	the	DET
ejpam-5386	16	68	death	death	NOUN
ejpam-5386	16	69	of	of	ADP
ejpam-5386	16	70	cells	cell	NOUN
ejpam-5386	16	71	due	due	ADJ
ejpam-5386	16	72	to	to	ADP
ejpam-5386	16	73	chemotherapy	chemotherapy	NOUN
ejpam-5386	16	74	or	or	CCONJ
ejpam-5386	16	75	radiation	radiation	NOUN
ejpam-5386	16	76	therapy	therapy	NOUN
ejpam-5386	16	77	,	,	PUNCT
ejpam-5386	16	78	d(x	d(x	PROPN
ejpam-5386	16	79	)	)	PUNCT
ejpam-5386	16	80	is	be	AUX
ejpam-5386	16	81	the	the	DET
ejpam-5386	16	82	diffusion	diffusion	NOUN
ejpam-5386	16	83	coefficient	coefficient	NOUN
ejpam-5386	16	84	of	of	ADP
ejpam-5386	16	85	cells	cell	NOUN
ejpam-5386	16	86	in	in	ADP
ejpam-5386	16	87	the	the	DET
ejpam-5386	16	88	brain	brain	NOUN
ejpam-5386	16	89	tissue	tissue	NOUN
ejpam-5386	16	90	modeling	model	VERB
ejpam-5386	16	91	a	a	DET
ejpam-5386	16	92	random	random	ADJ
ejpam-5386	16	93	tumor	tumor	NOUN
ejpam-5386	16	94	cell	cell	NOUN
ejpam-5386	16	95	movement	movement	NOUN
ejpam-5386	16	96	as	as	ADP
ejpam-5386	16	97	a	a	DET
ejpam-5386	16	98	diffusive	diffusive	ADJ
ejpam-5386	16	99	flux	flux	NOUN
ejpam-5386	16	100	proportional	proportional	ADJ
ejpam-5386	16	101	to	to	ADP
ejpam-5386	16	102	the	the	DET
ejpam-5386	16	103	cell	cell	NOUN
ejpam-5386	16	104	density	density	NOUN
ejpam-5386	16	105	gradient	gradient	NOUN
ejpam-5386	16	106	,	,	PUNCT
ejpam-5386	16	107	div(d(x)∇c	div(d(x)∇c	NUM
ejpam-5386	16	108	)	)	PUNCT
ejpam-5386	16	109	captures	capture	VERB
ejpam-5386	16	110	random	random	ADJ
ejpam-5386	16	111	tumor	tumor	NOUN
ejpam-5386	16	112	cell	cell	NOUN
ejpam-5386	16	113	movement	movement	NOUN
ejpam-5386	16	114	,	,	PUNCT
ejpam-5386	16	115	g(c	g(c	PROPN
ejpam-5386	16	116	)	)	PUNCT
ejpam-5386	16	117	is	be	AUX
ejpam-5386	16	118	the	the	DET
ejpam-5386	16	119	reaction	reaction	NOUN
ejpam-5386	16	120	term	term	NOUN
ejpam-5386	16	121	that	that	PRON
ejpam-5386	16	122	describes	describe	VERB
ejpam-5386	16	123	the	the	DET
ejpam-5386	16	124	growth	growth	NOUN
ejpam-5386	16	125	dynamics	dynamic	NOUN
ejpam-5386	16	126	of	of	ADP
ejpam-5386	16	127	the	the	DET
ejpam-5386	16	128	tumor	tumor	NOUN
ejpam-5386	16	129	and	and	CCONJ
ejpam-5386	16	130	ν	ν	NOUN
ejpam-5386	16	131	is	be	AUX
ejpam-5386	16	132	the	the	DET
ejpam-5386	16	133	outward	outward	ADJ
ejpam-5386	16	134	unit	unit	NOUN
ejpam-5386	16	135	normal	normal	ADJ
ejpam-5386	16	136	.	.	PUNCT
ejpam-5386	17	1	the	the	DET
ejpam-5386	17	2	boundary	boundary	ADJ
ejpam-5386	17	3	condition	condition	NOUN
ejpam-5386	17	4	d(x	d(x	NOUN
ejpam-5386	17	5	)	)	PUNCT
ejpam-5386	18	1	∂νc	∂νc	PROPN
ejpam-5386	18	2	=	=	SYM
ejpam-5386	18	3	0	0	NUM
ejpam-5386	18	4	ensures	ensure	VERB
ejpam-5386	18	5	tumor	tumor	NOUN
ejpam-5386	18	6	cells	cell	NOUN
ejpam-5386	18	7	do	do	AUX
ejpam-5386	18	8	not	not	PART
ejpam-5386	18	9	diffuse	diffuse	VERB
ejpam-5386	18	10	beyond	beyond	ADP
ejpam-5386	18	11	the	the	DET
ejpam-5386	18	12	brain	brain	NOUN
ejpam-5386	18	13	region	region	NOUN
ejpam-5386	18	14	.	.	PUNCT
ejpam-5386	19	1	additionally	additionally	ADV
ejpam-5386	19	2	,	,	PUNCT
ejpam-5386	19	3	the	the	DET
ejpam-5386	19	4	function	function	NOUN
ejpam-5386	19	5	φ(x	φ(x	NOUN
ejpam-5386	19	6	)	)	PUNCT
ejpam-5386	19	7	∈	∈	PROPN
ejpam-5386	19	8	l2(b	l2(b	NOUN
ejpam-5386	19	9	)	)	PUNCT
ejpam-5386	19	10	represents	represent	VERB
ejpam-5386	19	11	the	the	DET
ejpam-5386	19	12	initial	initial	ADJ
ejpam-5386	19	13	tumor	tumor	NOUN
ejpam-5386	19	14	cell	cell	NOUN
ejpam-5386	19	15	density	density	NOUN
ejpam-5386	19	16	at	at	ADP
ejpam-5386	19	17	t	t	PROPN
ejpam-5386	19	18	=	=	SYM
ejpam-5386	19	19	0	0	PROPN
ejpam-5386	19	20	.	.	PUNCT
ejpam-5386	20	1	the	the	DET
ejpam-5386	20	2	problem	problem	NOUN
ejpam-5386	20	3	(	(	PUNCT
ejpam-5386	20	4	1	1	X
ejpam-5386	20	5	)	)	PUNCT
ejpam-5386	20	6	is	be	AUX
ejpam-5386	20	7	a	a	DET
ejpam-5386	20	8	well	well	ADV
ejpam-5386	20	9	-	-	PUNCT
ejpam-5386	20	10	known	know	VERB
ejpam-5386	20	11	model	model	NOUN
ejpam-5386	20	12	related	relate	VERB
ejpam-5386	20	13	to	to	ADP
ejpam-5386	20	14	the	the	DET
ejpam-5386	20	15	growth	growth	NOUN
ejpam-5386	20	16	of	of	ADP
ejpam-5386	20	17	brain	brain	NOUN
ejpam-5386	20	18	tumors	tumor	NOUN
ejpam-5386	20	19	under	under	ADP
ejpam-5386	20	20	treatment	treatment	NOUN
ejpam-5386	20	21	the	the	DET
ejpam-5386	20	22	model	model	NOUN
ejpam-5386	20	23	(	(	PUNCT
ejpam-5386	20	24	1	1	X
ejpam-5386	20	25	)	)	PUNCT
ejpam-5386	20	26	serves	serve	VERB
ejpam-5386	20	27	as	as	ADP
ejpam-5386	20	28	a	a	DET
ejpam-5386	20	29	fundamental	fundamental	ADJ
ejpam-5386	20	30	tool	tool	NOUN
ejpam-5386	20	31	for	for	ADP
ejpam-5386	20	32	understanding	understand	VERB
ejpam-5386	20	33	brain	brain	NOUN
ejpam-5386	20	34	tumor	tumor	NOUN
ejpam-5386	20	35	dynamics	dynamic	NOUN
ejpam-5386	20	36	and	and	CCONJ
ejpam-5386	20	37	optimizing	optimize	VERB
ejpam-5386	20	38	treatment	treatment	NOUN
ejpam-5386	20	39	strategies	strategy	NOUN
ejpam-5386	20	40	through	through	ADP
ejpam-5386	20	41	comprehensive	comprehensive	ADJ
ejpam-5386	20	42	mathematical	mathematical	ADJ
ejpam-5386	20	43	analysis	analysis	NOUN
ejpam-5386	20	44	.	.	PUNCT
ejpam-5386	21	1	for	for	ADP
ejpam-5386	21	2	instance	instance	NOUN
ejpam-5386	21	3	,	,	PUNCT
ejpam-5386	21	4	the	the	DET
ejpam-5386	21	5	authors	author	NOUN
ejpam-5386	21	6	work	work	VERB
ejpam-5386	21	7	the	the	DET
ejpam-5386	21	8	problem	problem	NOUN
ejpam-5386	21	9	(	(	PUNCT
ejpam-5386	21	10	1	1	NUM
ejpam-5386	21	11	)	)	PUNCT
ejpam-5386	21	12	with	with	ADP
ejpam-5386	21	13	a	a	DET
ejpam-5386	21	14	source	source	NOUN
ejpam-5386	21	15	term	term	NOUN
ejpam-5386	21	16	such	such	ADJ
ejpam-5386	21	17	that	that	SCONJ
ejpam-5386	21	18	the	the	DET
ejpam-5386	21	19	model	model	NOUN
ejpam-5386	21	20	has	have	VERB
ejpam-5386	21	21	logistic	logistic	ADJ
ejpam-5386	21	22	growth	growth	NOUN
ejpam-5386	21	23	and	and	CCONJ
ejpam-5386	21	24	accomplish	accomplish	VERB
ejpam-5386	21	25	full	full	ADJ
ejpam-5386	21	26	3	3	NUM
ejpam-5386	21	27	-	-	PUNCT
ejpam-5386	21	28	dimensional	dimensional	ADJ
ejpam-5386	21	29	simulations	simulation	NOUN
ejpam-5386	21	30	of	of	ADP
ejpam-5386	21	31	the	the	DET
ejpam-5386	21	32	tumor	tumor	NOUN
ejpam-5386	21	33	in	in	ADP
ejpam-5386	21	34	time	time	NOUN
ejpam-5386	21	35	on	on	ADP
ejpam-5386	21	36	two	two	NUM
ejpam-5386	21	37	types	type	NOUN
ejpam-5386	21	38	of	of	ADP
ejpam-5386	21	39	imaging	imaging	NOUN
ejpam-5386	21	40	data	datum	NOUN
ejpam-5386	21	41	,	,	PUNCT
ejpam-5386	21	42	the	the	DET
ejpam-5386	21	43	3d	3d	PROPN
ejpam-5386	21	44	shepp	shepp	PROPN
ejpam-5386	21	45	-	-	PUNCT
ejpam-5386	21	46	logan	logan	PROPN
ejpam-5386	21	47	head	head	NOUN
ejpam-5386	21	48	phantom	phantom	NOUN
ejpam-5386	21	49	image	image	NOUN
ejpam-5386	21	50	and	and	CCONJ
ejpam-5386	21	51	an	an	DET
ejpam-5386	21	52	mri	mri	NOUN
ejpam-5386	21	53	t1	t1	NOUN
ejpam-5386	21	54	-	-	PUNCT
ejpam-5386	21	55	weighted	weight	VERB
ejpam-5386	21	56	brain	brain	NOUN
ejpam-5386	21	57	scan	scan	NOUN
ejpam-5386	21	58	from	from	ADP
ejpam-5386	21	59	the	the	DET
ejpam-5386	21	60	internet	internet	NOUN
ejpam-5386	21	61	brain	brain	NOUN
ejpam-5386	21	62	segmentation	segmentation	NOUN
ejpam-5386	21	63	repository	repository	NOUN
ejpam-5386	21	64	in	in	ADP
ejpam-5386	21	65	[	[	X
ejpam-5386	21	66	15	15	NUM
ejpam-5386	21	67	]	]	PUNCT
ejpam-5386	21	68	.	.	PUNCT
ejpam-5386	22	1	in	in	ADP
ejpam-5386	22	2	[	[	X
ejpam-5386	22	3	1	1	NUM
ejpam-5386	22	4	]	]	PUNCT
ejpam-5386	22	5	,	,	PUNCT
ejpam-5386	22	6	the	the	DET
ejpam-5386	22	7	authors	author	NOUN
ejpam-5386	22	8	study	study	VERB
ejpam-5386	22	9	a	a	DET
ejpam-5386	22	10	treatment	treatment	NOUN
ejpam-5386	22	11	parameter	parameter	NOUN
ejpam-5386	22	12	identification	identification	NOUN
ejpam-5386	22	13	problem	problem	NOUN
ejpam-5386	22	14	in	in	ADP
ejpam-5386	22	15	(	(	PUNCT
ejpam-5386	22	16	1	1	NUM
ejpam-5386	22	17	)	)	PUNCT
ejpam-5386	22	18	.	.	PUNCT
ejpam-5386	23	1	they	they	PRON
ejpam-5386	23	2	derive	derive	VERB
ejpam-5386	23	3	a	a	DET
ejpam-5386	23	4	nonlinear	nonlinear	ADJ
ejpam-5386	23	5	conjugate	conjugate	ADJ
ejpam-5386	23	6	gradient	gradient	NOUN
ejpam-5386	23	7	method	method	NOUN
ejpam-5386	23	8	for	for	ADP
ejpam-5386	23	9	the	the	DET
ejpam-5386	23	10	inverse	inverse	NOUN
ejpam-5386	23	11	problem	problem	NOUN
ejpam-5386	23	12	and	and	CCONJ
ejpam-5386	23	13	reconstruct	reconstruct	VERB
ejpam-5386	23	14	the	the	DET
ejpam-5386	23	15	unknown	unknown	ADJ
ejpam-5386	23	16	parameter	parameter	NOUN
ejpam-5386	23	17	from	from	ADP
ejpam-5386	23	18	additional	additional	ADJ
ejpam-5386	23	19	information	information	NOUN
ejpam-5386	23	20	about	about	ADP
ejpam-5386	23	21	the	the	DET
ejpam-5386	23	22	tumor	tumor	NOUN
ejpam-5386	23	23	taken	take	VERB
ejpam-5386	23	24	at	at	ADP
ejpam-5386	23	25	a	a	DET
ejpam-5386	23	26	fixed	fix	VERB
ejpam-5386	23	27	instance	instance	NOUN
ejpam-5386	23	28	of	of	ADP
ejpam-5386	23	29	time	time	NOUN
ejpam-5386	23	30	.	.	PUNCT
ejpam-5386	24	1	in	in	ADP
ejpam-5386	24	2	[	[	X
ejpam-5386	24	3	26	26	NUM
ejpam-5386	24	4	]	]	PUNCT
ejpam-5386	24	5	,	,	PUNCT
ejpam-5386	24	6	the	the	DET
ejpam-5386	24	7	authors	author	NOUN
ejpam-5386	24	8	analyze	analyze	VERB
ejpam-5386	24	9	the	the	DET
ejpam-5386	24	10	behavior	behavior	NOUN
ejpam-5386	24	11	of	of	ADP
ejpam-5386	24	12	gliomas	glioma	NOUN
ejpam-5386	24	13	mechanistically	mechanistically	ADV
ejpam-5386	24	14	,	,	PUNCT
ejpam-5386	24	15	deriving	derive	VERB
ejpam-5386	24	16	their	their	PRON
ejpam-5386	24	17	behavior	behavior	NOUN
ejpam-5386	24	18	from	from	ADP
ejpam-5386	24	19	two	two	NUM
ejpam-5386	24	20	fundamental	fundamental	ADJ
ejpam-5386	24	21	properties	property	NOUN
ejpam-5386	24	22	,	,	PUNCT
ejpam-5386	24	23	the	the	DET
ejpam-5386	24	24	net	net	ADJ
ejpam-5386	24	25	proliferation	proliferation	NOUN
ejpam-5386	24	26	rate	rate	NOUN
ejpam-5386	24	27	and	and	CCONJ
ejpam-5386	24	28	the	the	DET
ejpam-5386	24	29	diffusion	diffusion	NOUN
ejpam-5386	24	30	coefficient	coefficient	NOUN
ejpam-5386	24	31	.	.	PUNCT
ejpam-5386	25	1	they	they	PRON
ejpam-5386	25	2	conclude	conclude	VERB
ejpam-5386	25	3	that	that	SCONJ
ejpam-5386	25	4	although	although	SCONJ
ejpam-5386	25	5	these	these	PRON
ejpam-5386	25	6	clearly	clearly	ADV
ejpam-5386	25	7	determine	determine	VERB
ejpam-5386	25	8	the	the	DET
ejpam-5386	25	9	tumor	tumor	NOUN
ejpam-5386	25	10	’s	’s	PART
ejpam-5386	25	11	growth	growth	NOUN
ejpam-5386	25	12	as	as	ADP
ejpam-5386	25	13	an	an	DET
ejpam-5386	25	14	expansion	expansion	NOUN
ejpam-5386	25	15	of	of	ADP
ejpam-5386	25	16	its	its	PRON
ejpam-5386	25	17	traveling	travel	VERB
ejpam-5386	25	18	wave	wave	NOUN
ejpam-5386	25	19	front	front	NOUN
ejpam-5386	25	20	,	,	PUNCT
ejpam-5386	25	21	other	other	ADJ
ejpam-5386	25	22	factors	factor	NOUN
ejpam-5386	25	23	(	(	PUNCT
ejpam-5386	25	24	such	such	ADJ
ejpam-5386	25	25	as	as	ADP
ejpam-5386	25	26	age	age	NOUN
ejpam-5386	25	27	and	and	CCONJ
ejpam-5386	25	28	karnofsky	karnofsky	ADJ
ejpam-5386	25	29	performance	performance	NOUN
ejpam-5386	25	30	score	score	NOUN
ejpam-5386	25	31	)	)	PUNCT
ejpam-5386	25	32	combine	combine	VERB
ejpam-5386	25	33	to	to	PART
ejpam-5386	25	34	determine	determine	VERB
ejpam-5386	25	35	the	the	DET
ejpam-5386	25	36	patient	patient	NOUN
ejpam-5386	25	37	’s	’s	PART
ejpam-5386	25	38	prognosis	prognosis	NOUN
ejpam-5386	25	39	,	,	PUNCT
ejpam-5386	25	40	the	the	DET
ejpam-5386	25	41	survival	survival	NOUN
ejpam-5386	25	42	time	time	NOUN
ejpam-5386	25	43	.	.	PUNCT
ejpam-5386	26	1	the	the	DET
ejpam-5386	26	2	authors	author	NOUN
ejpam-5386	26	3	extend	extend	VERB
ejpam-5386	26	4	a	a	DET
ejpam-5386	26	5	mathematical	mathematical	ADJ
ejpam-5386	26	6	model	model	NOUN
ejpam-5386	26	7	of	of	ADP
ejpam-5386	26	8	gliomas	glioma	NOUN
ejpam-5386	26	9	based	base	VERB
ejpam-5386	26	10	on	on	ADP
ejpam-5386	26	11	proliferation	proliferation	NOUN
ejpam-5386	26	12	and	and	CCONJ
ejpam-5386	26	13	diffusion	diffusion	NOUN
ejpam-5386	26	14	rates	rate	NOUN
ejpam-5386	26	15	to	to	PART
ejpam-5386	26	16	incorporate	incorporate	VERB
ejpam-5386	26	17	the	the	DET
ejpam-5386	26	18	effects	effect	NOUN
ejpam-5386	26	19	of	of	ADP
ejpam-5386	26	20	augmented	augment	VERB
ejpam-5386	26	21	cell	cell	NOUN
ejpam-5386	26	22	motility	motility	NOUN
ejpam-5386	26	23	in	in	ADP
ejpam-5386	26	24	white	white	ADJ
ejpam-5386	26	25	matter	matter	NOUN
ejpam-5386	26	26	as	as	SCONJ
ejpam-5386	26	27	compared	compare	VERB
ejpam-5386	26	28	to	to	ADP
ejpam-5386	26	29	grey	grey	ADJ
ejpam-5386	26	30	matter	matter	NOUN
ejpam-5386	26	31	and	and	CCONJ
ejpam-5386	26	32	they	they	PRON
ejpam-5386	26	33	simulate	simulate	VERB
ejpam-5386	26	34	model	model	NOUN
ejpam-5386	26	35	tumors	tumor	NOUN
ejpam-5386	26	36	on	on	ADP
ejpam-5386	26	37	an	an	DET
ejpam-5386	26	38	anatomically	anatomically	ADV
ejpam-5386	26	39	accurate	accurate	ADJ
ejpam-5386	26	40	brain	brain	NOUN
ejpam-5386	26	41	domain	domain	NOUN
ejpam-5386	26	42	by	by	ADP
ejpam-5386	26	43	using	use	VERB
ejpam-5386	26	44	a	a	DET
ejpam-5386	26	45	detailed	detailed	ADJ
ejpam-5386	26	46	mapping	mapping	NOUN
ejpam-5386	26	47	of	of	ADP
ejpam-5386	26	48	the	the	DET
ejpam-5386	26	49	white	white	ADJ
ejpam-5386	26	50	and	and	CCONJ
ejpam-5386	26	51	grey	grey	ADJ
ejpam-5386	26	52	matter	matter	NOUN
ejpam-5386	26	53	in	in	ADP
ejpam-5386	26	54	the	the	DET
ejpam-5386	26	55	brain	brain	NOUN
ejpam-5386	26	56	developed	develop	VERB
ejpam-5386	26	57	for	for	ADP
ejpam-5386	26	58	a	a	DET
ejpam-5386	26	59	mri	mri	NOUN
ejpam-5386	26	60	simulator	simulator	NOUN
ejpam-5386	26	61	,	,	PUNCT
ejpam-5386	26	62	s.	s.	PROPN
ejpam-5386	26	63	tatar	tatar	PROPN
ejpam-5386	26	64	,	,	PUNCT
ejpam-5386	26	65	m.	m.	NOUN
ejpam-5386	26	66	bensalah	bensalah	PROPN
ejpam-5386	26	67	,	,	PUNCT
ejpam-5386	26	68	m.	m.	NOUN
ejpam-5386	26	69	alamil	alamil	PROPN
ejpam-5386	26	70	/	/	SYM
ejpam-5386	26	71	eur	eur	PROPN
ejpam-5386	26	72	.	.	PUNCT
ejpam-5386	27	1	j.	j.	PROPN
ejpam-5386	27	2	pure	pure	PROPN
ejpam-5386	27	3	appl	appl	PROPN
ejpam-5386	27	4	.	.	PROPN
ejpam-5386	27	5	math	math	PROPN
ejpam-5386	27	6	,	,	PUNCT
ejpam-5386	27	7	17	17	NUM
ejpam-5386	27	8	(	(	PUNCT
ejpam-5386	27	9	4	4	NUM
ejpam-5386	27	10	)	)	PUNCT
ejpam-5386	27	11	(	(	PUNCT
ejpam-5386	27	12	2024	2024	NUM
ejpam-5386	27	13	)	)	PUNCT
ejpam-5386	27	14	,	,	PUNCT
ejpam-5386	27	15	2651	2651	NUM
ejpam-5386	27	16	-	-	SYM
ejpam-5386	27	17	2675	2675	NUM
ejpam-5386	27	18	2653	2653	NUM
ejpam-5386	27	19	in	in	ADP
ejpam-5386	27	20	[	[	X
ejpam-5386	27	21	24	24	NUM
ejpam-5386	27	22	]	]	PUNCT
ejpam-5386	27	23	.	.	PUNCT
ejpam-5386	28	1	a	a	DET
ejpam-5386	28	2	simple	simple	ADJ
ejpam-5386	28	3	spatio	spatio	ADJ
ejpam-5386	28	4	-	-	PUNCT
ejpam-5386	28	5	temporal	temporal	ADJ
ejpam-5386	28	6	mathematical	mathematical	ADJ
ejpam-5386	28	7	model	model	NOUN
ejpam-5386	28	8	,	,	PUNCT
ejpam-5386	28	9	based	base	VERB
ejpam-5386	28	10	on	on	ADP
ejpam-5386	28	11	proliferation	proliferation	NOUN
ejpam-5386	28	12	and	and	CCONJ
ejpam-5386	28	13	diffusion	diffusion	NOUN
ejpam-5386	28	14	,	,	PUNCT
ejpam-5386	28	15	that	that	PRON
ejpam-5386	28	16	incorporates	incorporate	VERB
ejpam-5386	28	17	the	the	DET
ejpam-5386	28	18	effects	effect	NOUN
ejpam-5386	28	19	of	of	ADP
ejpam-5386	28	20	radiotherapeutic	radiotherapeutic	NOUN
ejpam-5386	28	21	and	and	CCONJ
ejpam-5386	28	22	chemotherapeutic	chemotherapeutic	ADJ
ejpam-5386	28	23	treatments	treatment	NOUN
ejpam-5386	28	24	has	have	AUX
ejpam-5386	28	25	been	be	AUX
ejpam-5386	28	26	studied	study	VERB
ejpam-5386	28	27	in	in	ADP
ejpam-5386	28	28	[	[	X
ejpam-5386	28	29	19	19	NUM
ejpam-5386	28	30	]	]	PUNCT
ejpam-5386	28	31	.	.	PUNCT
ejpam-5386	29	1	moreover	moreover	ADV
ejpam-5386	29	2	,	,	PUNCT
ejpam-5386	29	3	they	they	PRON
ejpam-5386	29	4	study	study	VERB
ejpam-5386	29	5	the	the	DET
ejpam-5386	29	6	effects	effect	NOUN
ejpam-5386	29	7	of	of	ADP
ejpam-5386	29	8	different	different	ADJ
ejpam-5386	29	9	schedules	schedule	NOUN
ejpam-5386	29	10	of	of	ADP
ejpam-5386	29	11	radiation	radiation	NOUN
ejpam-5386	29	12	therapy	therapy	NOUN
ejpam-5386	29	13	,	,	PUNCT
ejpam-5386	29	14	including	include	VERB
ejpam-5386	29	15	fractionated	fractionate	VERB
ejpam-5386	29	16	and	and	CCONJ
ejpam-5386	29	17	hyperfractionated	hyperfractionate	VERB
ejpam-5386	29	18	external	external	ADJ
ejpam-5386	29	19	beam	beam	NOUN
ejpam-5386	29	20	radiotherapy	radiotherapy	NOUN
ejpam-5386	29	21	,	,	PUNCT
ejpam-5386	29	22	using	use	VERB
ejpam-5386	29	23	a	a	DET
ejpam-5386	29	24	generalized	generalized	ADJ
ejpam-5386	29	25	linear	linear	ADJ
ejpam-5386	29	26	quadratic	quadratic	ADJ
ejpam-5386	29	27	model	model	NOUN
ejpam-5386	29	28	.	.	PUNCT
ejpam-5386	30	1	in	in	ADP
ejpam-5386	30	2	[	[	X
ejpam-5386	30	3	23	23	NUM
ejpam-5386	30	4	]	]	PUNCT
ejpam-5386	30	5	,	,	PUNCT
ejpam-5386	30	6	the	the	DET
ejpam-5386	30	7	authors	author	NOUN
ejpam-5386	30	8	present	present	VERB
ejpam-5386	30	9	a	a	DET
ejpam-5386	30	10	novel	novel	ADJ
ejpam-5386	30	11	explicit	explicit	ADJ
ejpam-5386	30	12	triscale	triscale	ADJ
ejpam-5386	30	13	reaction	reaction	NOUN
ejpam-5386	30	14	-	-	PUNCT
ejpam-5386	30	15	diffusion	diffusion	NOUN
ejpam-5386	30	16	numerical	numerical	PROPN
ejpam-5386	30	17	model	model	NOUN
ejpam-5386	30	18	of	of	ADP
ejpam-5386	30	19	glioblastoma	glioblastoma	NOUN
ejpam-5386	30	20	multiforme	multiforme	NOUN
ejpam-5386	30	21	tumor	tumor	NOUN
ejpam-5386	30	22	growth	growth	NOUN
ejpam-5386	30	23	,	,	PUNCT
ejpam-5386	30	24	they	they	PRON
ejpam-5386	30	25	adopt	adopt	VERB
ejpam-5386	30	26	a	a	DET
ejpam-5386	30	27	finite	finite	ADJ
ejpam-5386	30	28	-	-	PUNCT
ejpam-5386	30	29	difference	difference	NOUN
ejpam-5386	30	30	time	time	NOUN
ejpam-5386	30	31	-	-	PUNCT
ejpam-5386	30	32	domain	domain	NOUN
ejpam-5386	30	33	method	method	NOUN
ejpam-5386	30	34	for	for	ADP
ejpam-5386	30	35	the	the	DET
ejpam-5386	30	36	numerical	numerical	ADJ
ejpam-5386	30	37	solution	solution	NOUN
ejpam-5386	30	38	and	and	CCONJ
ejpam-5386	30	39	then	then	ADV
ejpam-5386	30	40	a	a	DET
ejpam-5386	30	41	clinical	clinical	ADJ
ejpam-5386	30	42	scenario	scenario	NOUN
ejpam-5386	30	43	is	be	AUX
ejpam-5386	30	44	addressed	address	VERB
ejpam-5386	30	45	to	to	PART
ejpam-5386	30	46	demonstrate	demonstrate	VERB
ejpam-5386	30	47	the	the	DET
ejpam-5386	30	48	workflow	workflow	NOUN
ejpam-5386	30	49	of	of	ADP
ejpam-5386	30	50	a	a	DET
ejpam-5386	30	51	possible	possible	ADJ
ejpam-5386	30	52	clinical	clinical	ADJ
ejpam-5386	30	53	validation	validation	NOUN
ejpam-5386	30	54	procedure	procedure	NOUN
ejpam-5386	30	55	.	.	PUNCT
ejpam-5386	31	1	other	other	ADJ
ejpam-5386	31	2	researchers	researcher	NOUN
ejpam-5386	31	3	[	[	X
ejpam-5386	31	4	20	20	NUM
ejpam-5386	31	5	]	]	PUNCT
ejpam-5386	31	6	present	present	VERB
ejpam-5386	31	7	an	an	DET
ejpam-5386	31	8	extension	extension	NOUN
ejpam-5386	31	9	of	of	ADP
ejpam-5386	31	10	swanson	swanson	PROPN
ejpam-5386	31	11	’s	’s	PART
ejpam-5386	31	12	reaction	reaction	NOUN
ejpam-5386	31	13	-	-	PUNCT
ejpam-5386	31	14	diffusion	diffusion	NOUN
ejpam-5386	31	15	model	model	NOUN
ejpam-5386	31	16	in	in	ADP
ejpam-5386	31	17	order	order	NOUN
ejpam-5386	31	18	to	to	PART
ejpam-5386	31	19	include	include	VERB
ejpam-5386	31	20	the	the	DET
ejpam-5386	31	21	effects	effect	NOUN
ejpam-5386	31	22	of	of	ADP
ejpam-5386	31	23	radiation	radiation	NOUN
ejpam-5386	31	24	therapy	therapy	NOUN
ejpam-5386	31	25	using	use	VERB
ejpam-5386	31	26	the	the	DET
ejpam-5386	31	27	classic	classic	ADJ
ejpam-5386	31	28	linear	linear	ADJ
ejpam-5386	31	29	-	-	PUNCT
ejpam-5386	31	30	quadratic	quadratic	ADJ
ejpam-5386	31	31	radiobiological	radiobiological	ADJ
ejpam-5386	31	32	model	model	NOUN
ejpam-5386	31	33	for	for	ADP
ejpam-5386	31	34	radiation	radiation	NOUN
ejpam-5386	31	35	efficacy	efficacy	NOUN
ejpam-5386	31	36	,	,	PUNCT
ejpam-5386	31	37	along	along	ADP
ejpam-5386	31	38	with	with	ADP
ejpam-5386	31	39	an	an	DET
ejpam-5386	31	40	investigation	investigation	NOUN
ejpam-5386	31	41	of	of	ADP
ejpam-5386	31	42	response	response	NOUN
ejpam-5386	31	43	to	to	ADP
ejpam-5386	31	44	various	various	ADJ
ejpam-5386	31	45	therapy	therapy	NOUN
ejpam-5386	31	46	schedules	schedule	NOUN
ejpam-5386	31	47	and	and	CCONJ
ejpam-5386	31	48	dose	dose	NOUN
ejpam-5386	31	49	distributions	distribution	NOUN
ejpam-5386	31	50	on	on	ADP
ejpam-5386	31	51	a	a	DET
ejpam-5386	31	52	virtual	virtual	ADJ
ejpam-5386	31	53	tumor	tumor	NOUN
ejpam-5386	31	54	.	.	PUNCT
ejpam-5386	32	1	some	some	PRON
ejpam-5386	32	2	of	of	ADP
ejpam-5386	32	3	the	the	DET
ejpam-5386	32	4	recent	recent	ADJ
ejpam-5386	32	5	developments	development	NOUN
ejpam-5386	32	6	in	in	ADP
ejpam-5386	32	7	mathematical	mathematical	ADJ
ejpam-5386	32	8	modeling	modeling	NOUN
ejpam-5386	32	9	are	be	AUX
ejpam-5386	32	10	reviewed	review	VERB
ejpam-5386	32	11	in	in	ADP
ejpam-5386	32	12	[	[	X
ejpam-5386	32	13	25	25	NUM
ejpam-5386	32	14	]	]	PUNCT
ejpam-5386	32	15	.	.	PUNCT
ejpam-5386	33	1	a	a	DET
ejpam-5386	33	2	model	model	NOUN
ejpam-5386	33	3	of	of	ADP
ejpam-5386	33	4	untreated	untreated	ADJ
ejpam-5386	33	5	gliomas	glioma	NOUN
ejpam-5386	33	6	is	be	AUX
ejpam-5386	33	7	represented	represented	AUX
ejpam-5386	33	8	first	first	ADV
ejpam-5386	33	9	followed	follow	VERB
ejpam-5386	33	10	by	by	ADP
ejpam-5386	33	11	models	model	NOUN
ejpam-5386	33	12	of	of	ADP
ejpam-5386	33	13	polyclonal	polyclonal	ADJ
ejpam-5386	33	14	gliomas	glioma	NOUN
ejpam-5386	33	15	that	that	PRON
ejpam-5386	33	16	follows	follow	VERB
ejpam-5386	33	17	a	a	DET
ejpam-5386	33	18	chemotherapy	chemotherapy	NOUN
ejpam-5386	33	19	or	or	CCONJ
ejpam-5386	33	20	a	a	DET
ejpam-5386	33	21	surgical	surgical	ADJ
ejpam-5386	33	22	resection	resection	NOUN
ejpam-5386	33	23	.	.	PUNCT
ejpam-5386	34	1	such	such	ADJ
ejpam-5386	34	2	reviewed	review	VERB
ejpam-5386	34	3	models	model	NOUN
ejpam-5386	34	4	illustrate	illustrate	VERB
ejpam-5386	34	5	the	the	DET
ejpam-5386	34	6	evolution	evolution	NOUN
ejpam-5386	34	7	of	of	ADP
ejpam-5386	34	8	mathematical	mathematical	ADJ
ejpam-5386	34	9	models	model	NOUN
ejpam-5386	34	10	for	for	ADP
ejpam-5386	34	11	glioma	glioma	NOUN
ejpam-5386	34	12	growth	growth	NOUN
ejpam-5386	34	13	and	and	CCONJ
ejpam-5386	34	14	invasion	invasion	NOUN
ejpam-5386	34	15	beginning	begin	VERB
ejpam-5386	34	16	in	in	ADP
ejpam-5386	34	17	simple	simple	ADJ
ejpam-5386	34	18	homogeneous	homogeneous	ADJ
ejpam-5386	34	19	tissue	tissue	NOUN
ejpam-5386	34	20	,	,	PUNCT
ejpam-5386	34	21	with	with	ADP
ejpam-5386	34	22	or	or	CCONJ
ejpam-5386	34	23	without	without	ADP
ejpam-5386	34	24	gross	gross	ADJ
ejpam-5386	34	25	anatomical	anatomical	ADJ
ejpam-5386	34	26	boundaries	boundary	NOUN
ejpam-5386	34	27	(	(	PUNCT
ejpam-5386	34	28	skull	skull	NOUN
ejpam-5386	34	29	and	and	CCONJ
ejpam-5386	34	30	ventricles	ventricle	NOUN
ejpam-5386	34	31	)	)	PUNCT
ejpam-5386	34	32	,	,	PUNCT
ejpam-5386	34	33	extending	extend	VERB
ejpam-5386	34	34	to	to	ADP
ejpam-5386	34	35	complex	complex	ADJ
ejpam-5386	34	36	heterogeneous	heterogeneous	ADJ
ejpam-5386	34	37	tissue	tissue	NOUN
ejpam-5386	34	38	,	,	PUNCT
ejpam-5386	34	39	with	with	ADP
ejpam-5386	34	40	varying	vary	VERB
ejpam-5386	34	41	proportions	proportion	NOUN
ejpam-5386	34	42	of	of	ADP
ejpam-5386	34	43	grey	grey	PROPN
ejpam-5386	34	44	and	and	CCONJ
ejpam-5386	34	45	white	white	ADJ
ejpam-5386	34	46	matter	matter	NOUN
ejpam-5386	34	47	in	in	ADP
ejpam-5386	34	48	cerebral	cerebral	ADJ
ejpam-5386	34	49	cortex	cortex	NOUN
ejpam-5386	34	50	(	(	PUNCT
ejpam-5386	34	51	including	include	VERB
ejpam-5386	34	52	the	the	DET
ejpam-5386	34	53	sulcal	sulcal	ADJ
ejpam-5386	34	54	pattern	pattern	NOUN
ejpam-5386	34	55	)	)	PUNCT
ejpam-5386	34	56	,	,	PUNCT
ejpam-5386	34	57	deep	deep	ADJ
ejpam-5386	34	58	cerebral	cerebral	ADJ
ejpam-5386	34	59	nuclei	nucleus	NOUN
ejpam-5386	34	60	,	,	PUNCT
ejpam-5386	34	61	brainstem	brainstem	NOUN
ejpam-5386	34	62	and	and	CCONJ
ejpam-5386	34	63	cerebellum	cerebellum	NOUN
ejpam-5386	34	64	.	.	PUNCT
ejpam-5386	35	1	a	a	DET
ejpam-5386	35	2	patient	patient	NOUN
ejpam-5386	35	3	-	-	PUNCT
ejpam-5386	35	4	specific	specific	ADJ
ejpam-5386	35	5	,	,	PUNCT
ejpam-5386	35	6	biologically	biologically	ADV
ejpam-5386	35	7	based	base	VERB
ejpam-5386	35	8	mathematical	mathematical	ADJ
ejpam-5386	35	9	model	model	NOUN
ejpam-5386	35	10	for	for	ADP
ejpam-5386	35	11	glioma	glioma	NOUN
ejpam-5386	35	12	growth	growth	NOUN
ejpam-5386	35	13	that	that	PRON
ejpam-5386	35	14	quantifies	quantify	VERB
ejpam-5386	35	15	response	response	VERB
ejpam-5386	35	16	to	to	ADP
ejpam-5386	35	17	xrt	xrt	PROPN
ejpam-5386	35	18	in	in	ADP
ejpam-5386	35	19	individual	individual	ADJ
ejpam-5386	35	20	patients	patient	NOUN
ejpam-5386	35	21	in	in	ADP
ejpam-5386	35	22	vivo	vivo	NOUN
ejpam-5386	35	23	is	be	AUX
ejpam-5386	35	24	presented	present	VERB
ejpam-5386	35	25	in	in	ADP
ejpam-5386	35	26	[	[	X
ejpam-5386	35	27	21	21	NUM
ejpam-5386	35	28	]	]	PUNCT
ejpam-5386	35	29	.	.	PUNCT
ejpam-5386	36	1	this	this	DET
ejpam-5386	36	2	mathematical	mathematical	ADJ
ejpam-5386	36	3	model	model	NOUN
ejpam-5386	36	4	uses	use	VERB
ejpam-5386	36	5	net	net	ADJ
ejpam-5386	36	6	rates	rate	NOUN
ejpam-5386	36	7	of	of	ADP
ejpam-5386	36	8	proliferation	proliferation	NOUN
ejpam-5386	36	9	and	and	CCONJ
ejpam-5386	36	10	migration	migration	NOUN
ejpam-5386	36	11	of	of	ADP
ejpam-5386	36	12	malignant	malignant	ADJ
ejpam-5386	36	13	tumor	tumor	NOUN
ejpam-5386	36	14	cells	cell	NOUN
ejpam-5386	36	15	to	to	PART
ejpam-5386	36	16	characterize	characterize	VERB
ejpam-5386	36	17	the	the	DET
ejpam-5386	36	18	tumor	tumor	NOUN
ejpam-5386	36	19	’s	’s	PART
ejpam-5386	36	20	growth	growth	NOUN
ejpam-5386	36	21	and	and	CCONJ
ejpam-5386	36	22	invasion	invasion	NOUN
ejpam-5386	36	23	along	along	ADP
ejpam-5386	36	24	with	with	ADP
ejpam-5386	36	25	the	the	DET
ejpam-5386	36	26	linear	linear	ADJ
ejpam-5386	36	27	-	-	PUNCT
ejpam-5386	36	28	quadratic	quadratic	ADJ
ejpam-5386	36	29	model	model	NOUN
ejpam-5386	36	30	for	for	ADP
ejpam-5386	36	31	the	the	DET
ejpam-5386	36	32	response	response	NOUN
ejpam-5386	36	33	to	to	ADP
ejpam-5386	36	34	radiation	radiation	NOUN
ejpam-5386	36	35	therapy	therapy	NOUN
ejpam-5386	36	36	.	.	PUNCT
ejpam-5386	37	1	in	in	ADP
ejpam-5386	37	2	this	this	DET
ejpam-5386	37	3	paper	paper	NOUN
ejpam-5386	37	4	,	,	PUNCT
ejpam-5386	37	5	we	we	PRON
ejpam-5386	37	6	study	study	VERB
ejpam-5386	37	7	an	an	DET
ejpam-5386	37	8	inverse	inverse	NOUN
ejpam-5386	37	9	problem	problem	NOUN
ejpam-5386	37	10	for	for	ADP
ejpam-5386	37	11	the	the	DET
ejpam-5386	37	12	nonlinear	nonlinear	ADJ
ejpam-5386	37	13	parabolic	parabolic	ADJ
ejpam-5386	37	14	problem	problem	NOUN
ejpam-5386	37	15	(	(	PUNCT
ejpam-5386	37	16	1	1	NUM
ejpam-5386	37	17	)	)	PUNCT
ejpam-5386	37	18	.	.	PUNCT
ejpam-5386	38	1	inverse	inverse	NOUN
ejpam-5386	38	2	problems	problem	NOUN
ejpam-5386	38	3	of	of	ADP
ejpam-5386	38	4	finding	find	VERB
ejpam-5386	38	5	coefficients	coefficient	NOUN
ejpam-5386	38	6	,	,	PUNCT
ejpam-5386	38	7	the	the	DET
ejpam-5386	38	8	initial	initial	ADJ
ejpam-5386	38	9	distribution	distribution	NOUN
ejpam-5386	38	10	,	,	PUNCT
ejpam-5386	38	11	sources	source	NOUN
ejpam-5386	38	12	or	or	CCONJ
ejpam-5386	38	13	parameters	parameter	NOUN
ejpam-5386	38	14	are	be	AUX
ejpam-5386	38	15	physically	physically	ADV
ejpam-5386	38	16	and	and	CCONJ
ejpam-5386	38	17	practically	practically	ADV
ejpam-5386	38	18	very	very	ADV
ejpam-5386	38	19	important	important	ADJ
ejpam-5386	38	20	.	.	PUNCT
ejpam-5386	39	1	recently	recently	ADV
ejpam-5386	39	2	,	,	PUNCT
ejpam-5386	39	3	there	there	PRON
ejpam-5386	39	4	has	have	AUX
ejpam-5386	39	5	been	be	AUX
ejpam-5386	39	6	a	a	DET
ejpam-5386	39	7	growing	grow	VERB
ejpam-5386	39	8	interest	interest	NOUN
ejpam-5386	39	9	in	in	ADP
ejpam-5386	39	10	inverse	inverse	NOUN
ejpam-5386	39	11	problems	problem	NOUN
ejpam-5386	39	12	for	for	ADP
ejpam-5386	39	13	nonlinear	nonlinear	ADJ
ejpam-5386	39	14	parabolic	parabolic	ADJ
ejpam-5386	39	15	equations	equation	NOUN
ejpam-5386	39	16	.	.	PUNCT
ejpam-5386	40	1	for	for	ADP
ejpam-5386	40	2	instance	instance	NOUN
ejpam-5386	40	3	,	,	PUNCT
ejpam-5386	40	4	the	the	DET
ejpam-5386	40	5	simultaneous	simultaneous	ADJ
ejpam-5386	40	6	reconstruction	reconstruction	NOUN
ejpam-5386	40	7	of	of	ADP
ejpam-5386	40	8	the	the	DET
ejpam-5386	40	9	initial	initial	ADJ
ejpam-5386	40	10	temperature	temperature	NOUN
ejpam-5386	40	11	and	and	CCONJ
ejpam-5386	40	12	heat	heat	NOUN
ejpam-5386	40	13	radiative	radiative	ADJ
ejpam-5386	40	14	coefficient	coefficient	NOUN
ejpam-5386	40	15	in	in	ADP
ejpam-5386	40	16	a	a	DET
ejpam-5386	40	17	heat	heat	NOUN
ejpam-5386	40	18	conductive	conductive	ADJ
ejpam-5386	40	19	system	system	NOUN
ejpam-5386	40	20	is	be	AUX
ejpam-5386	40	21	studied	study	VERB
ejpam-5386	40	22	in	in	ADP
ejpam-5386	40	23	[	[	X
ejpam-5386	40	24	28	28	NUM
ejpam-5386	40	25	]	]	PUNCT
ejpam-5386	40	26	.	.	PUNCT
ejpam-5386	41	1	they	they	PRON
ejpam-5386	41	2	prove	prove	VERB
ejpam-5386	41	3	the	the	DET
ejpam-5386	41	4	stability	stability	NOUN
ejpam-5386	41	5	of	of	ADP
ejpam-5386	41	6	the	the	DET
ejpam-5386	41	7	inverse	inverse	NOUN
ejpam-5386	41	8	problem	problem	NOUN
ejpam-5386	41	9	and	and	CCONJ
ejpam-5386	41	10	then	then	ADV
ejpam-5386	41	11	the	the	DET
ejpam-5386	41	12	reconstruction	reconstruction	NOUN
ejpam-5386	41	13	process	process	NOUN
ejpam-5386	41	14	is	be	AUX
ejpam-5386	41	15	done	do	VERB
ejpam-5386	41	16	by	by	ADP
ejpam-5386	41	17	tikhonov	tikhonov	NOUN
ejpam-5386	41	18	regularization	regularization	NOUN
ejpam-5386	41	19	.	.	PUNCT
ejpam-5386	42	1	in	in	ADP
ejpam-5386	42	2	[	[	X
ejpam-5386	42	3	3	3	NUM
ejpam-5386	42	4	]	]	PUNCT
ejpam-5386	42	5	,	,	PUNCT
ejpam-5386	42	6	the	the	DET
ejpam-5386	42	7	identification	identification	NOUN
ejpam-5386	42	8	of	of	ADP
ejpam-5386	42	9	the	the	DET
ejpam-5386	42	10	space	space	NOUN
ejpam-5386	42	11	-	-	PUNCT
ejpam-5386	42	12	dependent	dependent	ADJ
ejpam-5386	42	13	reaction	reaction	NOUN
ejpam-5386	42	14	coefficient	coefficient	NOUN
ejpam-5386	42	15	,	,	PUNCT
ejpam-5386	42	16	the	the	DET
ejpam-5386	42	17	initial	initial	ADJ
ejpam-5386	42	18	temperature	temperature	NOUN
ejpam-5386	42	19	and	and	CCONJ
ejpam-5386	42	20	the	the	DET
ejpam-5386	42	21	source	source	NOUN
ejpam-5386	42	22	term	term	NOUN
ejpam-5386	42	23	from	from	ADP
ejpam-5386	42	24	measured	measure	VERB
ejpam-5386	42	25	temperatures	temperature	NOUN
ejpam-5386	42	26	at	at	ADP
ejpam-5386	42	27	two	two	NUM
ejpam-5386	42	28	instants	instant	NOUN
ejpam-5386	42	29	t1	t1	NOUN
ejpam-5386	42	30	,	,	PUNCT
ejpam-5386	42	31	t2	t2	NOUN
ejpam-5386	42	32	and	and	CCONJ
ejpam-5386	42	33	at	at	ADP
ejpam-5386	42	34	the	the	DET
ejpam-5386	42	35	final	final	ADJ
ejpam-5386	42	36	time	time	NOUN
ejpam-5386	42	37	t	t	PROPN
ejpam-5386	42	38	are	be	AUX
ejpam-5386	42	39	investigated	investigate	VERB
ejpam-5386	42	40	.	.	PUNCT
ejpam-5386	43	1	in	in	ADP
ejpam-5386	43	2	[	[	X
ejpam-5386	43	3	4	4	NUM
ejpam-5386	43	4	]	]	PUNCT
ejpam-5386	43	5	,	,	PUNCT
ejpam-5386	43	6	an	an	DET
ejpam-5386	43	7	inverse	inverse	ADJ
ejpam-5386	43	8	problem	problem	NOUN
ejpam-5386	43	9	of	of	ADP
ejpam-5386	43	10	simultaneously	simultaneously	ADV
ejpam-5386	43	11	identifying	identify	VERB
ejpam-5386	43	12	and	and	CCONJ
ejpam-5386	43	13	reconstructing	reconstruct	VERB
ejpam-5386	43	14	the	the	DET
ejpam-5386	43	15	space	space	NOUN
ejpam-5386	43	16	-	-	PUNCT
ejpam-5386	43	17	dependent	dependent	ADJ
ejpam-5386	43	18	reaction	reaction	NOUN
ejpam-5386	43	19	coefficient	coefficient	NOUN
ejpam-5386	43	20	and	and	CCONJ
ejpam-5386	43	21	source	source	NOUN
ejpam-5386	43	22	term	term	NOUN
ejpam-5386	43	23	component	component	NOUN
ejpam-5386	43	24	from	from	ADP
ejpam-5386	43	25	time	time	NOUN
ejpam-5386	43	26	-	-	PUNCT
ejpam-5386	43	27	integral	integral	ADJ
ejpam-5386	43	28	temperature	temperature	NOUN
ejpam-5386	43	29	measurements	measurement	NOUN
ejpam-5386	43	30	is	be	AUX
ejpam-5386	43	31	investigated	investigate	VERB
ejpam-5386	43	32	.	.	PUNCT
ejpam-5386	44	1	after	after	SCONJ
ejpam-5386	44	2	they	they	PRON
ejpam-5386	44	3	prove	prove	VERB
ejpam-5386	44	4	the	the	DET
ejpam-5386	44	5	existence	existence	NOUN
ejpam-5386	44	6	and	and	CCONJ
ejpam-5386	44	7	uniqueness	uniqueness	NOUN
ejpam-5386	44	8	of	of	ADP
ejpam-5386	44	9	the	the	DET
ejpam-5386	44	10	solution	solution	NOUN
ejpam-5386	44	11	,	,	PUNCT
ejpam-5386	44	12	the	the	DET
ejpam-5386	44	13	conjugate	conjugate	ADJ
ejpam-5386	44	14	gradient	gradient	NOUN
ejpam-5386	44	15	method	method	NOUN
ejpam-5386	44	16	to	to	PART
ejpam-5386	44	17	find	find	VERB
ejpam-5386	44	18	the	the	DET
ejpam-5386	44	19	numerical	numerical	ADJ
ejpam-5386	44	20	solution	solution	NOUN
ejpam-5386	44	21	is	be	AUX
ejpam-5386	44	22	developed	develop	VERB
ejpam-5386	44	23	,	,	PUNCT
ejpam-5386	44	24	and	and	CCONJ
ejpam-5386	44	25	its	its	PRON
ejpam-5386	44	26	convergence	convergence	NOUN
ejpam-5386	44	27	is	be	AUX
ejpam-5386	44	28	proved	prove	VERB
ejpam-5386	44	29	from	from	ADP
ejpam-5386	44	30	the	the	DET
ejpam-5386	44	31	lipschitz	lipschitz	ADJ
ejpam-5386	44	32	continuity	continuity	NOUN
ejpam-5386	44	33	of	of	ADP
ejpam-5386	44	34	these	these	DET
ejpam-5386	44	35	gradients	gradient	NOUN
ejpam-5386	44	36	.	.	PUNCT
ejpam-5386	45	1	a	a	DET
ejpam-5386	45	2	novel	novel	ADJ
ejpam-5386	45	3	inverse	inverse	NOUN
ejpam-5386	45	4	problem	problem	NOUN
ejpam-5386	45	5	of	of	ADP
ejpam-5386	45	6	reconstructing	reconstruct	VERB
ejpam-5386	45	7	the	the	DET
ejpam-5386	45	8	unknown	unknown	ADJ
ejpam-5386	45	9	time	time	NOUN
ejpam-5386	45	10	-	-	PUNCT
ejpam-5386	45	11	dependent	dependent	ADJ
ejpam-5386	45	12	source	source	NOUN
ejpam-5386	45	13	term	term	NOUN
ejpam-5386	45	14	entering	enter	VERB
ejpam-5386	45	15	the	the	DET
ejpam-5386	45	16	fourth	fourth	ADJ
ejpam-5386	45	17	-	-	PUNCT
ejpam-5386	45	18	order	order	NOUN
ejpam-5386	45	19	parabolic	parabolic	ADJ
ejpam-5386	45	20	equation	equation	NOUN
ejpam-5386	45	21	of	of	ADP
ejpam-5386	45	22	thermal	thermal	ADJ
ejpam-5386	45	23	grooving	grooving	NOUN
ejpam-5386	45	24	by	by	ADP
ejpam-5386	45	25	surface	surface	NOUN
ejpam-5386	45	26	diffusion	diffusion	NOUN
ejpam-5386	45	27	from	from	ADP
ejpam-5386	45	28	a	a	DET
ejpam-5386	45	29	given	give	VERB
ejpam-5386	45	30	integral	integral	ADJ
ejpam-5386	45	31	observation	observation	NOUN
ejpam-5386	45	32	is	be	AUX
ejpam-5386	45	33	formulated	formulate	VERB
ejpam-5386	45	34	in	in	ADP
ejpam-5386	45	35	[	[	X
ejpam-5386	45	36	5	5	NUM
ejpam-5386	45	37	]	]	PUNCT
ejpam-5386	45	38	.	.	PUNCT
ejpam-5386	46	1	the	the	DET
ejpam-5386	46	2	author	author	NOUN
ejpam-5386	46	3	studies	study	VERB
ejpam-5386	46	4	the	the	DET
ejpam-5386	46	5	determination	determination	NOUN
ejpam-5386	46	6	of	of	ADP
ejpam-5386	46	7	an	an	DET
ejpam-5386	46	8	unknown	unknown	ADJ
ejpam-5386	46	9	time	time	NOUN
ejpam-5386	46	10	-	-	PUNCT
ejpam-5386	46	11	dependent	dependent	ADJ
ejpam-5386	46	12	source	source	NOUN
ejpam-5386	46	13	term	term	NOUN
ejpam-5386	46	14	in	in	ADP
ejpam-5386	46	15	a	a	DET
ejpam-5386	46	16	kuramoto	kuramoto	NOUN
ejpam-5386	46	17	-	-	PUNCT
ejpam-5386	46	18	sivashinsky	sivashinsky	NOUN
ejpam-5386	46	19	equation	equation	NOUN
ejpam-5386	46	20	from	from	ADP
ejpam-5386	46	21	given	give	VERB
ejpam-5386	46	22	additional	additional	ADJ
ejpam-5386	46	23	integral	integral	ADJ
ejpam-5386	46	24	-	-	PUNCT
ejpam-5386	46	25	type	type	NOUN
ejpam-5386	46	26	measurement	measurement	NOUN
ejpam-5386	46	27	in	in	ADP
ejpam-5386	46	28	[	[	X
ejpam-5386	46	29	2	2	NUM
ejpam-5386	46	30	]	]	PUNCT
ejpam-5386	46	31	.	.	PUNCT
ejpam-5386	47	1	in	in	ADP
ejpam-5386	47	2	[	[	X
ejpam-5386	47	3	22	22	NUM
ejpam-5386	47	4	]	]	PUNCT
ejpam-5386	47	5	,	,	PUNCT
ejpam-5386	47	6	some	some	DET
ejpam-5386	47	7	methods	method	NOUN
ejpam-5386	47	8	are	be	AUX
ejpam-5386	47	9	developed	develop	VERB
ejpam-5386	47	10	for	for	ADP
ejpam-5386	47	11	finds	find	NOUN
ejpam-5386	47	12	.	.	PUNCT
ejpam-5386	48	1	tatar	tatar	NOUN
ejpam-5386	48	2	,	,	PUNCT
ejpam-5386	48	3	m.	m.	NOUN
ejpam-5386	48	4	bensalah	bensalah	PROPN
ejpam-5386	48	5	,	,	PUNCT
ejpam-5386	48	6	m.	m.	NOUN
ejpam-5386	48	7	alamil	alamil	PROPN
ejpam-5386	48	8	/	/	SYM
ejpam-5386	48	9	eur	eur	PROPN
ejpam-5386	48	10	.	.	PUNCT
ejpam-5386	49	1	j.	j.	PROPN
ejpam-5386	49	2	pure	pure	PROPN
ejpam-5386	49	3	appl	appl	PROPN
ejpam-5386	49	4	.	.	PROPN
ejpam-5386	49	5	math	math	PROPN
ejpam-5386	49	6	,	,	PUNCT
ejpam-5386	49	7	17	17	NUM
ejpam-5386	49	8	(	(	PUNCT
ejpam-5386	49	9	4	4	NUM
ejpam-5386	49	10	)	)	PUNCT
ejpam-5386	49	11	(	(	PUNCT
ejpam-5386	49	12	2024	2024	NUM
ejpam-5386	49	13	)	)	PUNCT
ejpam-5386	49	14	,	,	PUNCT
ejpam-5386	49	15	2651	2651	NUM
ejpam-5386	49	16	-	-	SYM
ejpam-5386	49	17	2675	2675	NUM
ejpam-5386	49	18	2654	2654	NUM
ejpam-5386	49	19	ing	e	VERB
ejpam-5386	49	20	the	the	DET
ejpam-5386	49	21	thermophysical	thermophysical	ADJ
ejpam-5386	49	22	parameters	parameter	NOUN
ejpam-5386	49	23	of	of	ADP
ejpam-5386	49	24	a	a	DET
ejpam-5386	49	25	two	two	NUM
ejpam-5386	49	26	-	-	PUNCT
ejpam-5386	49	27	layer	layer	NOUN
ejpam-5386	49	28	soil	soil	NOUN
ejpam-5386	49	29	and	and	CCONJ
ejpam-5386	49	30	a	a	DET
ejpam-5386	49	31	rational	rational	ADJ
ejpam-5386	49	32	method	method	NOUN
ejpam-5386	49	33	of	of	ADP
ejpam-5386	49	34	choosing	choose	VERB
ejpam-5386	49	35	the	the	DET
ejpam-5386	49	36	damping	damp	VERB
ejpam-5386	49	37	coefficient	coefficient	NOUN
ejpam-5386	49	38	is	be	AUX
ejpam-5386	49	39	also	also	ADV
ejpam-5386	49	40	proposed	propose	VERB
ejpam-5386	49	41	,	,	PUNCT
ejpam-5386	49	42	which	which	PRON
ejpam-5386	49	43	provides	provide	VERB
ejpam-5386	49	44	an	an	DET
ejpam-5386	49	45	indicative	indicative	ADJ
ejpam-5386	49	46	rate	rate	NOUN
ejpam-5386	49	47	of	of	ADP
ejpam-5386	49	48	convergence	convergence	NOUN
ejpam-5386	49	49	of	of	ADP
ejpam-5386	49	50	the	the	DET
ejpam-5386	49	51	approximate	approximate	ADJ
ejpam-5386	49	52	value	value	NOUN
ejpam-5386	49	53	of	of	ADP
ejpam-5386	49	54	the	the	DET
ejpam-5386	49	55	functional	functional	ADJ
ejpam-5386	49	56	to	to	ADP
ejpam-5386	49	57	zero	zero	NUM
ejpam-5386	49	58	.	.	PUNCT
ejpam-5386	50	1	our	our	PRON
ejpam-5386	50	2	paper	paper	NOUN
ejpam-5386	50	3	can	can	AUX
ejpam-5386	50	4	be	be	AUX
ejpam-5386	50	5	considered	consider	VERB
ejpam-5386	50	6	as	as	ADP
ejpam-5386	50	7	an	an	DET
ejpam-5386	50	8	addition	addition	NOUN
ejpam-5386	50	9	to	to	ADP
ejpam-5386	50	10	these	these	DET
ejpam-5386	50	11	studies	study	NOUN
ejpam-5386	50	12	.	.	PUNCT
ejpam-5386	51	1	this	this	DET
ejpam-5386	51	2	article	article	NOUN
ejpam-5386	51	3	is	be	AUX
ejpam-5386	51	4	organized	organize	VERB
ejpam-5386	51	5	as	as	SCONJ
ejpam-5386	51	6	follows	follow	VERB
ejpam-5386	51	7	:	:	PUNCT
ejpam-5386	51	8	in	in	ADP
ejpam-5386	51	9	the	the	DET
ejpam-5386	51	10	next	next	ADJ
ejpam-5386	51	11	section	section	NOUN
ejpam-5386	51	12	,	,	PUNCT
ejpam-5386	51	13	we	we	PRON
ejpam-5386	51	14	formulate	formulate	VERB
ejpam-5386	51	15	and	and	CCONJ
ejpam-5386	51	16	analyze	analyze	VERB
ejpam-5386	51	17	the	the	DET
ejpam-5386	51	18	direct	direct	ADJ
ejpam-5386	51	19	and	and	CCONJ
ejpam-5386	51	20	the	the	DET
ejpam-5386	51	21	inverse	inverse	NOUN
ejpam-5386	51	22	problems	problem	NOUN
ejpam-5386	51	23	.	.	PUNCT
ejpam-5386	52	1	in	in	ADP
ejpam-5386	52	2	section	section	NOUN
ejpam-5386	52	3	3	3	NUM
ejpam-5386	52	4	,	,	PUNCT
ejpam-5386	52	5	we	we	PRON
ejpam-5386	52	6	present	present	VERB
ejpam-5386	52	7	an	an	DET
ejpam-5386	52	8	iterative	iterative	NOUN
ejpam-5386	52	9	procedure	procedure	NOUN
ejpam-5386	52	10	based	base	VERB
ejpam-5386	52	11	on	on	ADP
ejpam-5386	52	12	the	the	DET
ejpam-5386	52	13	conjugate	conjugate	ADJ
ejpam-5386	52	14	gradient	gradient	NOUN
ejpam-5386	52	15	method	method	NOUN
ejpam-5386	52	16	to	to	PART
ejpam-5386	52	17	solve	solve	VERB
ejpam-5386	52	18	the	the	DET
ejpam-5386	52	19	minimization	minimization	NOUN
ejpam-5386	52	20	problem	problem	NOUN
ejpam-5386	52	21	.	.	PUNCT
ejpam-5386	53	1	some	some	DET
ejpam-5386	53	2	numerical	numerical	ADJ
ejpam-5386	53	3	examples	example	NOUN
ejpam-5386	53	4	with	with	ADP
ejpam-5386	53	5	noise	noise	NOUN
ejpam-5386	53	6	-	-	PUNCT
ejpam-5386	53	7	free	free	ADJ
ejpam-5386	53	8	and	and	CCONJ
ejpam-5386	53	9	noisy	noisy	ADJ
ejpam-5386	53	10	data	datum	NOUN
ejpam-5386	53	11	are	be	AUX
ejpam-5386	53	12	given	give	VERB
ejpam-5386	53	13	to	to	PART
ejpam-5386	53	14	show	show	VERB
ejpam-5386	53	15	the	the	DET
ejpam-5386	53	16	efficiency	efficiency	NOUN
ejpam-5386	53	17	of	of	ADP
ejpam-5386	53	18	the	the	DET
ejpam-5386	53	19	method	method	NOUN
ejpam-5386	53	20	in	in	ADP
ejpam-5386	53	21	section	section	NOUN
ejpam-5386	53	22	4	4	NUM
ejpam-5386	53	23	.	.	PUNCT
ejpam-5386	54	1	the	the	DET
ejpam-5386	54	2	conclusions	conclusion	NOUN
ejpam-5386	54	3	and	and	CCONJ
ejpam-5386	54	4	possible	possible	ADJ
ejpam-5386	54	5	directions	direction	NOUN
ejpam-5386	54	6	on	on	ADP
ejpam-5386	54	7	the	the	DET
ejpam-5386	54	8	problem	problem	NOUN
ejpam-5386	54	9	are	be	AUX
ejpam-5386	54	10	given	give	VERB
ejpam-5386	54	11	in	in	ADP
ejpam-5386	54	12	section	section	NOUN
ejpam-5386	54	13	5	5	NUM
ejpam-5386	54	14	.	.	NOUN
ejpam-5386	54	15	2	2	NUM
ejpam-5386	54	16	.	.	X
ejpam-5386	54	17	formulations	formulation	NOUN
ejpam-5386	54	18	and	and	CCONJ
ejpam-5386	54	19	analyses	analysis	NOUN
ejpam-5386	54	20	of	of	ADP
ejpam-5386	54	21	the	the	DET
ejpam-5386	54	22	direct	direct	ADJ
ejpam-5386	54	23	and	and	CCONJ
ejpam-5386	54	24	the	the	DET
ejpam-5386	54	25	inverse	inverse	NOUN
ejpam-5386	54	26	problems	problem	NOUN
ejpam-5386	54	27	in	in	ADP
ejpam-5386	54	28	this	this	DET
ejpam-5386	54	29	section	section	NOUN
ejpam-5386	54	30	,	,	PUNCT
ejpam-5386	54	31	we	we	PRON
ejpam-5386	54	32	define	define	VERB
ejpam-5386	54	33	the	the	DET
ejpam-5386	54	34	direct	direct	ADJ
ejpam-5386	54	35	and	and	CCONJ
ejpam-5386	54	36	the	the	DET
ejpam-5386	54	37	inverse	inverse	NOUN
ejpam-5386	54	38	problems	problem	NOUN
ejpam-5386	54	39	.	.	PUNCT
ejpam-5386	55	1	throughout	throughout	ADP
ejpam-5386	55	2	this	this	DET
ejpam-5386	55	3	paper	paper	NOUN
ejpam-5386	55	4	,	,	PUNCT
ejpam-5386	55	5	we	we	PRON
ejpam-5386	55	6	define	define	VERB
ejpam-5386	55	7	q	q	NOUN
ejpam-5386	55	8	:	:	PUNCT
ejpam-5386	55	9	=	=	SYM
ejpam-5386	55	10	b×(0	b×(0	PROPN
ejpam-5386	55	11	,	,	PUNCT
ejpam-5386	55	12	t	t	PROPN
ejpam-5386	55	13	)	)	PUNCT
ejpam-5386	55	14	and	and	CCONJ
ejpam-5386	55	15	bt	bt	INTJ
ejpam-5386	55	16	:	:	PUNCT
ejpam-5386	55	17	=	=	SYM
ejpam-5386	55	18	∂b×(0	∂b×(0	PROPN
ejpam-5386	55	19	,	,	PUNCT
ejpam-5386	55	20	t	t	PROPN
ejpam-5386	55	21	)	)	PUNCT
ejpam-5386	55	22	.	.	PUNCT
ejpam-5386	56	1	the	the	DET
ejpam-5386	56	2	diffusion	diffusion	NOUN
ejpam-5386	56	3	coefficient	coefficient	NOUN
ejpam-5386	56	4	d(x	d(x	PROPN
ejpam-5386	56	5	)	)	PUNCT
ejpam-5386	56	6	is	be	AUX
ejpam-5386	56	7	assumed	assume	VERB
ejpam-5386	56	8	to	to	PART
ejpam-5386	56	9	encompass	encompass	VERB
ejpam-5386	56	10	two	two	NUM
ejpam-5386	56	11	regions	region	NOUN
ejpam-5386	56	12	,	,	PUNCT
ejpam-5386	56	13	white	white	ADJ
ejpam-5386	56	14	and	and	CCONJ
ejpam-5386	56	15	grey	grey	ADJ
ejpam-5386	56	16	matter	matter	NOUN
ejpam-5386	56	17	,	,	PUNCT
ejpam-5386	56	18	as	as	ADP
ejpam-5386	56	19	in	in	ADP
ejpam-5386	56	20	the	the	DET
ejpam-5386	56	21	papers	paper	NOUN
ejpam-5386	56	22	[	[	X
ejpam-5386	56	23	10	10	NUM
ejpam-5386	56	24	,	,	PUNCT
ejpam-5386	56	25	24	24	NUM
ejpam-5386	56	26	,	,	PUNCT
ejpam-5386	56	27	25	25	NUM
ejpam-5386	56	28	]	]	PUNCT
ejpam-5386	56	29	,	,	PUNCT
ejpam-5386	56	30	reflecting	reflect	VERB
ejpam-5386	56	31	the	the	DET
ejpam-5386	56	32	spatial	spatial	ADJ
ejpam-5386	56	33	heterogeneity	heterogeneity	NOUN
ejpam-5386	56	34	of	of	ADP
ejpam-5386	56	35	brain	brain	NOUN
ejpam-5386	56	36	tissue	tissue	NOUN
ejpam-5386	56	37	.	.	PUNCT
ejpam-5386	57	1	specifically	specifically	ADV
ejpam-5386	57	2	,	,	PUNCT
ejpam-5386	57	3	we	we	PRON
ejpam-5386	57	4	define	define	VERB
ejpam-5386	57	5	d(x	d(x	NOUN
ejpam-5386	57	6	)	)	PUNCT
ejpam-5386	57	7	as	as	ADP
ejpam-5386	57	8	:	:	PUNCT
ejpam-5386	57	9	d(x	d(x	NOUN
ejpam-5386	57	10	)	)	PUNCT
ejpam-5386	58	1	=	=	PRON
ejpam-5386	58	2	{	{	PUNCT
ejpam-5386	58	3	dw	dw	NOUN
ejpam-5386	58	4	,	,	PUNCT
ejpam-5386	58	5	if	if	SCONJ
ejpam-5386	58	6	x	x	SYM
ejpam-5386	58	7	∈	∈	PROPN
ejpam-5386	58	8	white	white	ADJ
ejpam-5386	58	9	matter	matter	NOUN
ejpam-5386	58	10	,	,	PUNCT
ejpam-5386	58	11	dg	dg	PROPN
ejpam-5386	58	12	,	,	PUNCT
ejpam-5386	58	13	if	if	SCONJ
ejpam-5386	58	14	x	x	SYM
ejpam-5386	58	15	∈	∈	PROPN
ejpam-5386	58	16	grey	grey	NOUN
ejpam-5386	58	17	matter	matter	NOUN
ejpam-5386	58	18	,	,	PUNCT
ejpam-5386	58	19	where	where	SCONJ
ejpam-5386	58	20	dg	dg	NOUN
ejpam-5386	58	21	and	and	CCONJ
ejpam-5386	58	22	dw	dw	PROPN
ejpam-5386	58	23	denote	denote	VERB
ejpam-5386	58	24	the	the	DET
ejpam-5386	58	25	diffusion	diffusion	NOUN
ejpam-5386	58	26	coefficients	coefficient	NOUN
ejpam-5386	58	27	for	for	ADP
ejpam-5386	58	28	grey	grey	ADJ
ejpam-5386	58	29	and	and	CCONJ
ejpam-5386	58	30	white	white	ADJ
ejpam-5386	58	31	matter	matter	NOUN
ejpam-5386	58	32	,	,	PUNCT
ejpam-5386	58	33	respectively	respectively	ADV
ejpam-5386	58	34	,	,	PUNCT
ejpam-5386	58	35	satisfying	satisfy	VERB
ejpam-5386	58	36	0	0	NUM
ejpam-5386	58	37	<	<	X
ejpam-5386	58	38	dg	dg	X
ejpam-5386	58	39	≪	≪	VERB
ejpam-5386	58	40	dw	dw	PROPN
ejpam-5386	58	41	.	.	PROPN
ejpam-5386	58	42	for	for	ADP
ejpam-5386	58	43	the	the	DET
ejpam-5386	58	44	growth	growth	NOUN
ejpam-5386	58	45	function	function	NOUN
ejpam-5386	58	46	g(c	g(c	NOUN
ejpam-5386	58	47	)	)	PUNCT
ejpam-5386	58	48	,	,	PUNCT
ejpam-5386	58	49	we	we	PRON
ejpam-5386	58	50	adopt	adopt	VERB
ejpam-5386	58	51	a	a	DET
ejpam-5386	58	52	logistic	logistic	ADJ
ejpam-5386	58	53	growth	growth	NOUN
ejpam-5386	58	54	model	model	NOUN
ejpam-5386	58	55	to	to	PART
ejpam-5386	58	56	ensure	ensure	VERB
ejpam-5386	58	57	that	that	SCONJ
ejpam-5386	58	58	the	the	DET
ejpam-5386	58	59	growth	growth	NOUN
ejpam-5386	58	60	rate	rate	NOUN
ejpam-5386	58	61	diminishes	diminish	VERB
ejpam-5386	58	62	as	as	SCONJ
ejpam-5386	58	63	the	the	DET
ejpam-5386	58	64	cell	cell	NOUN
ejpam-5386	58	65	density	density	NOUN
ejpam-5386	58	66	approaches	approach	VERB
ejpam-5386	58	67	its	its	PRON
ejpam-5386	58	68	maximum	maximum	ADJ
ejpam-5386	58	69	capacity	capacity	NOUN
ejpam-5386	58	70	.	.	PUNCT
ejpam-5386	59	1	thus	thus	ADV
ejpam-5386	59	2	,	,	PUNCT
ejpam-5386	59	3	g(c	g(c	PROPN
ejpam-5386	59	4	)	)	PUNCT
ejpam-5386	59	5	is	be	AUX
ejpam-5386	59	6	defined	define	VERB
ejpam-5386	59	7	as	as	ADP
ejpam-5386	59	8	:	:	PUNCT
ejpam-5386	59	9	g(c	g(c	NOUN
ejpam-5386	59	10	)	)	PUNCT
ejpam-5386	59	11	=	=	PUNCT
ejpam-5386	59	12	ρ	ρ	X
ejpam-5386	59	13	c	c	X
ejpam-5386	59	14	(	(	PUNCT
ejpam-5386	59	15	1−	1−	NUM
ejpam-5386	59	16	c	c	PROPN
ejpam-5386	59	17	clim	clim	PROPN
ejpam-5386	59	18	)	)	PUNCT
ejpam-5386	59	19	,	,	PUNCT
ejpam-5386	59	20	where	where	SCONJ
ejpam-5386	59	21	ρ	ρ	PROPN
ejpam-5386	59	22	is	be	AUX
ejpam-5386	59	23	the	the	DET
ejpam-5386	59	24	net	net	ADJ
ejpam-5386	59	25	proliferation	proliferation	NOUN
ejpam-5386	59	26	rate	rate	NOUN
ejpam-5386	59	27	and	and	CCONJ
ejpam-5386	59	28	clim	clim	NOUN
ejpam-5386	59	29	represents	represent	VERB
ejpam-5386	59	30	the	the	DET
ejpam-5386	59	31	carrying	carrying	NOUN
ejpam-5386	59	32	capacity	capacity	NOUN
ejpam-5386	59	33	.	.	PUNCT
ejpam-5386	60	1	this	this	DET
ejpam-5386	60	2	formulation	formulation	NOUN
ejpam-5386	60	3	provides	provide	VERB
ejpam-5386	60	4	a	a	DET
ejpam-5386	60	5	more	more	ADV
ejpam-5386	60	6	realistic	realistic	ADJ
ejpam-5386	60	7	representation	representation	NOUN
ejpam-5386	60	8	of	of	ADP
ejpam-5386	60	9	tumor	tumor	NOUN
ejpam-5386	60	10	growth	growth	NOUN
ejpam-5386	60	11	dynamics	dynamic	NOUN
ejpam-5386	60	12	compared	compare	VERB
ejpam-5386	60	13	to	to	ADP
ejpam-5386	60	14	simple	simple	ADJ
ejpam-5386	60	15	exponential	exponential	ADJ
ejpam-5386	60	16	models	model	NOUN
ejpam-5386	60	17	[	[	X
ejpam-5386	60	18	7	7	NUM
ejpam-5386	60	19	,	,	PUNCT
ejpam-5386	60	20	9	9	NUM
ejpam-5386	60	21	,	,	PUNCT
ejpam-5386	60	22	24	24	NUM
ejpam-5386	60	23	,	,	PUNCT
ejpam-5386	60	24	26	26	NUM
ejpam-5386	60	25	,	,	PUNCT
ejpam-5386	60	26	27	27	NUM
ejpam-5386	60	27	]	]	PUNCT
ejpam-5386	60	28	,	,	PUNCT
ejpam-5386	60	29	which	which	PRON
ejpam-5386	60	30	may	may	AUX
ejpam-5386	60	31	result	result	VERB
ejpam-5386	60	32	in	in	ADP
ejpam-5386	60	33	unbounded	unbounded	ADJ
ejpam-5386	60	34	growth	growth	NOUN
ejpam-5386	60	35	over	over	ADP
ejpam-5386	60	36	time	time	NOUN
ejpam-5386	60	37	.	.	PUNCT
ejpam-5386	61	1	definition	definition	NOUN
ejpam-5386	61	2	1	1	NUM
ejpam-5386	61	3	.	.	PUNCT
ejpam-5386	62	1	the	the	DET
ejpam-5386	62	2	weak	weak	ADJ
ejpam-5386	62	3	solution	solution	NOUN
ejpam-5386	62	4	c	c	PROPN
ejpam-5386	62	5	∈	∈	PROPN
ejpam-5386	62	6	l2	l2	NOUN
ejpam-5386	62	7	(	(	PUNCT
ejpam-5386	62	8	0	0	NUM
ejpam-5386	62	9	,	,	PUNCT
ejpam-5386	62	10	t	t	NOUN
ejpam-5386	62	11	;	;	PUNCT
ejpam-5386	62	12	h1(b	h1(b	NUM
ejpam-5386	62	13	)	)	PUNCT
ejpam-5386	62	14	)	)	PUNCT
ejpam-5386	62	15	of	of	ADP
ejpam-5386	62	16	the	the	DET
ejpam-5386	62	17	problem	problem	NOUN
ejpam-5386	62	18	(	(	PUNCT
ejpam-5386	62	19	1	1	X
ejpam-5386	62	20	)	)	PUNCT
ejpam-5386	62	21	is	be	AUX
ejpam-5386	62	22	defined	define	VERB
ejpam-5386	62	23	as	as	ADP
ejpam-5386	62	24	the	the	DET
ejpam-5386	62	25	solution	solution	NOUN
ejpam-5386	62	26	of	of	ADP
ejpam-5386	62	27	the	the	DET
ejpam-5386	62	28	following	follow	VERB
ejpam-5386	62	29	problem:∫	problem:∫	NOUN
ejpam-5386	62	30	t	t	PROPN
ejpam-5386	63	1	0	0	NUM
ejpam-5386	63	2	∫	∫	PROPN
ejpam-5386	63	3	b	b	PROPN
ejpam-5386	63	4	(	(	PUNCT
ejpam-5386	63	5	∂tc(x	∂tc(x	NOUN
ejpam-5386	63	6	,	,	PUNCT
ejpam-5386	63	7	t)ψ+d(x)∇c(x	t)ψ+d(x)∇c(x	NOUN
ejpam-5386	63	8	,	,	PUNCT
ejpam-5386	63	9	t	t	PROPN
ejpam-5386	63	10	)	)	PUNCT
ejpam-5386	63	11	·	·	PUNCT
ejpam-5386	63	12	∇ψ+k(x	∇ψ+k(x	PROPN
ejpam-5386	63	13	,	,	PUNCT
ejpam-5386	63	14	t	t	NOUN
ejpam-5386	63	15	)	)	PUNCT
ejpam-5386	63	16	c(x	c(x	NOUN
ejpam-5386	63	17	,	,	PUNCT
ejpam-5386	63	18	t)ψ	t)ψ	NOUN
ejpam-5386	63	19	)	)	PUNCT
ejpam-5386	63	20	dx	dx	PROPN
ejpam-5386	64	1	dt	dt	X
ejpam-5386	65	1	=	=	SYM
ejpam-5386	65	2	∫	∫	PROPN
ejpam-5386	65	3	t	t	PROPN
ejpam-5386	65	4	0	0	NUM
ejpam-5386	66	1	∫	∫	PROPN
ejpam-5386	66	2	b	b	PROPN
ejpam-5386	66	3	g(c)ψ	g(c)ψ	PROPN
ejpam-5386	66	4	dx	dx	PROPN
ejpam-5386	66	5	dt	dt	PROPN
ejpam-5386	66	6	,	,	PUNCT
ejpam-5386	66	7	(	(	PUNCT
ejpam-5386	66	8	2	2	X
ejpam-5386	66	9	)	)	PUNCT
ejpam-5386	66	10	for	for	ADP
ejpam-5386	66	11	all	all	DET
ejpam-5386	66	12	ψ	ψ	PRON
ejpam-5386	66	13	∈	∈	NOUN
ejpam-5386	66	14	l2	l2	NOUN
ejpam-5386	66	15	(	(	PUNCT
ejpam-5386	66	16	0	0	NUM
ejpam-5386	66	17	,	,	PUNCT
ejpam-5386	66	18	t	t	NOUN
ejpam-5386	66	19	;	;	PUNCT
ejpam-5386	66	20	h1(b	h1(b	NUM
ejpam-5386	66	21	)	)	PUNCT
ejpam-5386	66	22	)	)	PUNCT
ejpam-5386	66	23	.	.	PUNCT
ejpam-5386	67	1	for	for	ADP
ejpam-5386	67	2	given	give	VERB
ejpam-5386	67	3	inputs	input	NOUN
ejpam-5386	67	4	d(x	d(x	PROPN
ejpam-5386	67	5	)	)	PUNCT
ejpam-5386	67	6	,	,	PUNCT
ejpam-5386	67	7	k(x	k(x	PROPN
ejpam-5386	67	8	,	,	PUNCT
ejpam-5386	67	9	t	t	PROPN
ejpam-5386	67	10	)	)	PUNCT
ejpam-5386	67	11	,	,	PUNCT
ejpam-5386	67	12	φ(x	φ(x	PROPN
ejpam-5386	67	13	)	)	PUNCT
ejpam-5386	67	14	and	and	CCONJ
ejpam-5386	67	15	t	t	X
ejpam-5386	67	16	>	>	X
ejpam-5386	67	17	0	0	PROPN
ejpam-5386	67	18	,	,	PUNCT
ejpam-5386	67	19	the	the	DET
ejpam-5386	67	20	problem	problem	NOUN
ejpam-5386	67	21	(	(	PUNCT
ejpam-5386	67	22	1	1	X
ejpam-5386	67	23	)	)	PUNCT
ejpam-5386	67	24	is	be	AUX
ejpam-5386	67	25	called	call	VERB
ejpam-5386	67	26	the	the	DET
ejpam-5386	67	27	direct	direct	ADJ
ejpam-5386	67	28	problem	problem	NOUN
ejpam-5386	67	29	.	.	PUNCT
ejpam-5386	68	1	like	like	ADP
ejpam-5386	68	2	most	most	ADJ
ejpam-5386	68	3	direct	direct	ADJ
ejpam-5386	68	4	problems	problem	NOUN
ejpam-5386	68	5	of	of	ADP
ejpam-5386	68	6	the	the	DET
ejpam-5386	68	7	mathematical	mathematical	ADJ
ejpam-5386	68	8	physics	physics	NOUN
ejpam-5386	68	9	,	,	PUNCT
ejpam-5386	68	10	the	the	DET
ejpam-5386	68	11	problem	problem	NOUN
ejpam-5386	68	12	(	(	PUNCT
ejpam-5386	68	13	1	1	X
ejpam-5386	68	14	)	)	PUNCT
ejpam-5386	68	15	is	be	AUX
ejpam-5386	68	16	well	well	ADV
ejpam-5386	68	17	posed	pose	VERB
ejpam-5386	68	18	,	,	PUNCT
ejpam-5386	68	19	see	see	VERB
ejpam-5386	68	20	[	[	X
ejpam-5386	68	21	1	1	NUM
ejpam-5386	68	22	,	,	PUNCT
ejpam-5386	68	23	16	16	NUM
ejpam-5386	68	24	]	]	PUNCT
ejpam-5386	68	25	for	for	ADP
ejpam-5386	68	26	details	detail	NOUN
ejpam-5386	68	27	.	.	PUNCT
ejpam-5386	69	1	s.	s.	PROPN
ejpam-5386	69	2	tatar	tatar	PROPN
ejpam-5386	69	3	,	,	PUNCT
ejpam-5386	69	4	m.	m.	NOUN
ejpam-5386	69	5	bensalah	bensalah	PROPN
ejpam-5386	69	6	,	,	PUNCT
ejpam-5386	69	7	m.	m.	NOUN
ejpam-5386	69	8	alamil	alamil	PROPN
ejpam-5386	69	9	/	/	SYM
ejpam-5386	69	10	eur	eur	PROPN
ejpam-5386	69	11	.	.	PUNCT
ejpam-5386	70	1	j.	j.	PROPN
ejpam-5386	70	2	pure	pure	PROPN
ejpam-5386	70	3	appl	appl	PROPN
ejpam-5386	70	4	.	.	PROPN
ejpam-5386	70	5	math	math	PROPN
ejpam-5386	70	6	,	,	PUNCT
ejpam-5386	70	7	17	17	NUM
ejpam-5386	70	8	(	(	PUNCT
ejpam-5386	70	9	4	4	NUM
ejpam-5386	70	10	)	)	PUNCT
ejpam-5386	70	11	(	(	PUNCT
ejpam-5386	70	12	2024	2024	NUM
ejpam-5386	70	13	)	)	PUNCT
ejpam-5386	70	14	,	,	PUNCT
ejpam-5386	70	15	2651	2651	NUM
ejpam-5386	70	16	-	-	SYM
ejpam-5386	70	17	2675	2675	NUM
ejpam-5386	70	18	2655	2655	NUM
ejpam-5386	70	19	here	here	ADV
ejpam-5386	70	20	the	the	DET
ejpam-5386	70	21	inverse	inverse	NOUN
ejpam-5386	70	22	problem	problem	NOUN
ejpam-5386	70	23	consists	consist	VERB
ejpam-5386	70	24	of	of	ADP
ejpam-5386	70	25	simultaneously	simultaneously	ADV
ejpam-5386	70	26	determining	determine	VERB
ejpam-5386	70	27	the	the	DET
ejpam-5386	70	28	treatment	treatment	NOUN
ejpam-5386	70	29	profile	profile	NOUN
ejpam-5386	70	30	k(x	k(x	PROPN
ejpam-5386	70	31	,	,	PUNCT
ejpam-5386	70	32	t	t	PROPN
ejpam-5386	70	33	)	)	PUNCT
ejpam-5386	70	34	and	and	CCONJ
ejpam-5386	70	35	the	the	DET
ejpam-5386	70	36	initial	initial	ADJ
ejpam-5386	70	37	tumor	tumor	NOUN
ejpam-5386	70	38	cell	cell	NOUN
ejpam-5386	70	39	density	density	NOUN
ejpam-5386	70	40	φ	φ	PROPN
ejpam-5386	70	41	,	,	PUNCT
ejpam-5386	70	42	by	by	ADP
ejpam-5386	70	43	means	mean	NOUN
ejpam-5386	70	44	of	of	ADP
ejpam-5386	70	45	the	the	DET
ejpam-5386	70	46	time	time	NOUN
ejpam-5386	70	47	-	-	PUNCT
ejpam-5386	70	48	integral	integral	ADJ
ejpam-5386	70	49	measurements	measurement	NOUN
ejpam-5386	70	50	of	of	ADP
ejpam-5386	70	51	tumor	tumor	NOUN
ejpam-5386	70	52	cell	cell	NOUN
ejpam-5386	70	53	density	density	NOUN
ejpam-5386	70	54	(	(	PUNCT
ejpam-5386	70	55	measured	measure	VERB
ejpam-5386	70	56	data	datum	NOUN
ejpam-5386	70	57	)	)	PUNCT
ejpam-5386	70	58	defined	define	VERB
ejpam-5386	70	59	as	as	SCONJ
ejpam-5386	70	60	follows	follow	VERB
ejpam-5386	70	61	:	:	PUNCT
ejpam-5386	70	62	ϕ1	ϕ1	NOUN
ejpam-5386	70	63	:	:	PUNCT
ejpam-5386	70	64	=	=	SYM
ejpam-5386	70	65	∫	∫	PROPN
ejpam-5386	70	66	t	t	PROPN
ejpam-5386	70	67	0	0	NUM
ejpam-5386	70	68	ω1(t	ω1(t	NUM
ejpam-5386	70	69	)	)	PUNCT
ejpam-5386	70	70	c(x	c(x	NOUN
ejpam-5386	70	71	,	,	PUNCT
ejpam-5386	70	72	t	t	PROPN
ejpam-5386	70	73	)	)	PUNCT
ejpam-5386	70	74	dt	dt	NOUN
ejpam-5386	70	75	and	and	CCONJ
ejpam-5386	70	76	ϕ2	ϕ2	ADV
ejpam-5386	70	77	:	:	PUNCT
ejpam-5386	70	78	=	=	SYM
ejpam-5386	70	79	∫	∫	PROPN
ejpam-5386	70	80	t	t	PROPN
ejpam-5386	70	81	0	0	NUM
ejpam-5386	70	82	ω2(t	ω2(t	NOUN
ejpam-5386	70	83	)	)	PUNCT
ejpam-5386	70	84	c(x	c(x	PROPN
ejpam-5386	70	85	,	,	PUNCT
ejpam-5386	70	86	t	t	PROPN
ejpam-5386	70	87	)	)	PUNCT
ejpam-5386	70	88	dt	dt	NOUN
ejpam-5386	70	89	,	,	PUNCT
ejpam-5386	70	90	x	x	PUNCT
ejpam-5386	70	91	∈	∈	PROPN
ejpam-5386	70	92	b	b	PROPN
ejpam-5386	70	93	,	,	PUNCT
ejpam-5386	70	94	(	(	PUNCT
ejpam-5386	70	95	3	3	NUM
ejpam-5386	70	96	)	)	PUNCT
ejpam-5386	70	97	where	where	SCONJ
ejpam-5386	70	98	ω1(t	ω1(t	ADP
ejpam-5386	70	99	)	)	PUNCT
ejpam-5386	70	100	and	and	CCONJ
ejpam-5386	70	101	ω2(t	ω2(t	SYM
ejpam-5386	70	102	)	)	PUNCT
ejpam-5386	70	103	denote	denote	VERB
ejpam-5386	70	104	two	two	NUM
ejpam-5386	70	105	distinct	distinct	ADJ
ejpam-5386	70	106	weight	weight	NOUN
ejpam-5386	70	107	functions	function	NOUN
ejpam-5386	70	108	.	.	PUNCT
ejpam-5386	71	1	we	we	PRON
ejpam-5386	71	2	note	note	VERB
ejpam-5386	71	3	that	that	SCONJ
ejpam-5386	71	4	since	since	SCONJ
ejpam-5386	71	5	timeintegral	timeintegral	ADJ
ejpam-5386	71	6	measurements	measurement	NOUN
ejpam-5386	71	7	of	of	ADP
ejpam-5386	71	8	tumor	tumor	NOUN
ejpam-5386	71	9	cell	cell	NOUN
ejpam-5386	71	10	density	density	NOUN
ejpam-5386	71	11	do	do	AUX
ejpam-5386	71	12	not	not	PART
ejpam-5386	71	13	typically	typically	ADV
ejpam-5386	71	14	reveal	reveal	VERB
ejpam-5386	71	15	time	time	NOUN
ejpam-5386	71	16	-	-	PUNCT
ejpam-5386	71	17	dependent	dependent	ADJ
ejpam-5386	71	18	profiles	profile	NOUN
ejpam-5386	71	19	,	,	PUNCT
ejpam-5386	71	20	we	we	PRON
ejpam-5386	71	21	consider	consider	VERB
ejpam-5386	71	22	the	the	DET
ejpam-5386	71	23	function	function	NOUN
ejpam-5386	71	24	k(x	k(x	PROPN
ejpam-5386	71	25	,	,	PUNCT
ejpam-5386	71	26	t	t	PROPN
ejpam-5386	71	27	)	)	PUNCT
ejpam-5386	71	28	∈	∈	PROPN
ejpam-5386	71	29	l∞(q	l∞(q	NOUN
ejpam-5386	71	30	)	)	PUNCT
ejpam-5386	71	31	in	in	ADP
ejpam-5386	71	32	the	the	DET
ejpam-5386	71	33	following	follow	VERB
ejpam-5386	71	34	separable	separable	ADJ
ejpam-5386	71	35	form	form	NOUN
ejpam-5386	71	36	:	:	PUNCT
ejpam-5386	72	1	k(x	k(x	PROPN
ejpam-5386	72	2	,	,	PUNCT
ejpam-5386	72	3	t	t	PROPN
ejpam-5386	72	4	)	)	PUNCT
ejpam-5386	72	5	=	=	SYM
ejpam-5386	72	6	α(x)β(t	α(x)β(t	NOUN
ejpam-5386	72	7	)	)	PUNCT
ejpam-5386	72	8	,	,	PUNCT
ejpam-5386	72	9	(	(	PUNCT
ejpam-5386	72	10	4	4	X
ejpam-5386	72	11	)	)	PUNCT
ejpam-5386	72	12	where	where	SCONJ
ejpam-5386	72	13	α(x	α(x	NOUN
ejpam-5386	72	14	)	)	PUNCT
ejpam-5386	72	15	∈	∈	PROPN
ejpam-5386	72	16	l∞(b	l∞(b	X
ejpam-5386	72	17	)	)	PUNCT
ejpam-5386	72	18	represents	represent	VERB
ejpam-5386	72	19	the	the	DET
ejpam-5386	72	20	spatial	spatial	ADJ
ejpam-5386	72	21	component	component	NOUN
ejpam-5386	72	22	of	of	ADP
ejpam-5386	72	23	the	the	DET
ejpam-5386	72	24	treatment	treatment	NOUN
ejpam-5386	72	25	profile	profile	NOUN
ejpam-5386	72	26	k(x	k(x	PROPN
ejpam-5386	72	27	,	,	PUNCT
ejpam-5386	72	28	t	t	PROPN
ejpam-5386	72	29	)	)	PUNCT
ejpam-5386	72	30	and	and	CCONJ
ejpam-5386	72	31	describes	describe	VERB
ejpam-5386	72	32	how	how	SCONJ
ejpam-5386	72	33	the	the	DET
ejpam-5386	72	34	treatment	treatment	NOUN
ejpam-5386	72	35	efficacy	efficacy	NOUN
ejpam-5386	72	36	varies	vary	VERB
ejpam-5386	72	37	across	across	ADP
ejpam-5386	72	38	different	different	ADJ
ejpam-5386	72	39	spatial	spatial	ADJ
ejpam-5386	72	40	locations	location	NOUN
ejpam-5386	72	41	within	within	ADP
ejpam-5386	72	42	the	the	DET
ejpam-5386	72	43	brain	brain	NOUN
ejpam-5386	72	44	region	region	NOUN
ejpam-5386	72	45	.	.	PUNCT
ejpam-5386	73	1	on	on	ADP
ejpam-5386	73	2	the	the	DET
ejpam-5386	73	3	other	other	ADJ
ejpam-5386	73	4	hand	hand	NOUN
ejpam-5386	73	5	,	,	PUNCT
ejpam-5386	73	6	β(t	β(t	PROPN
ejpam-5386	73	7	)	)	PUNCT
ejpam-5386	73	8	∈	∈	PROPN
ejpam-5386	73	9	l∞(0	l∞(0	PRON
ejpam-5386	73	10	,	,	PUNCT
ejpam-5386	73	11	t	t	PROPN
ejpam-5386	73	12	)	)	PUNCT
ejpam-5386	73	13	is	be	AUX
ejpam-5386	73	14	the	the	DET
ejpam-5386	73	15	temporal	temporal	ADJ
ejpam-5386	73	16	component	component	NOUN
ejpam-5386	73	17	of	of	ADP
ejpam-5386	73	18	the	the	DET
ejpam-5386	73	19	treatment	treatment	NOUN
ejpam-5386	73	20	profile	profile	NOUN
ejpam-5386	73	21	and	and	CCONJ
ejpam-5386	73	22	captures	capture	VERB
ejpam-5386	73	23	how	how	SCONJ
ejpam-5386	73	24	the	the	DET
ejpam-5386	73	25	treatment	treatment	NOUN
ejpam-5386	73	26	effectiveness	effectiveness	NOUN
ejpam-5386	73	27	evolves	evolve	VERB
ejpam-5386	73	28	over	over	ADP
ejpam-5386	73	29	time	time	NOUN
ejpam-5386	73	30	.	.	PUNCT
ejpam-5386	74	1	in	in	ADP
ejpam-5386	74	2	the	the	DET
ejpam-5386	74	3	inverse	inverse	NOUN
ejpam-5386	74	4	problem	problem	NOUN
ejpam-5386	74	5	considered	consider	VERB
ejpam-5386	74	6	here	here	ADV
ejpam-5386	74	7	,	,	PUNCT
ejpam-5386	74	8	our	our	PRON
ejpam-5386	74	9	focus	focus	NOUN
ejpam-5386	74	10	shifts	shift	NOUN
ejpam-5386	74	11	to	to	ADP
ejpam-5386	74	12	scenarios	scenario	NOUN
ejpam-5386	74	13	where	where	SCONJ
ejpam-5386	74	14	the	the	DET
ejpam-5386	74	15	spatial	spatial	ADJ
ejpam-5386	74	16	component	component	NOUN
ejpam-5386	74	17	α(x	α(x	NOUN
ejpam-5386	74	18	)	)	PUNCT
ejpam-5386	74	19	is	be	AUX
ejpam-5386	74	20	unknown	unknown	ADJ
ejpam-5386	74	21	,	,	PUNCT
ejpam-5386	74	22	while	while	SCONJ
ejpam-5386	74	23	the	the	DET
ejpam-5386	74	24	temporal	temporal	ADJ
ejpam-5386	74	25	component	component	NOUN
ejpam-5386	74	26	β(t	β(t	PROPN
ejpam-5386	74	27	)	)	PUNCT
ejpam-5386	74	28	is	be	AUX
ejpam-5386	74	29	known	know	VERB
ejpam-5386	74	30	.	.	PUNCT
ejpam-5386	75	1	by	by	ADP
ejpam-5386	75	2	taking	take	VERB
ejpam-5386	75	3	(	(	PUNCT
ejpam-5386	75	4	4	4	NUM
ejpam-5386	75	5	)	)	PUNCT
ejpam-5386	75	6	into	into	ADP
ejpam-5386	75	7	account	account	NOUN
ejpam-5386	75	8	in	in	ADP
ejpam-5386	75	9	the	the	DET
ejpam-5386	75	10	problem	problem	NOUN
ejpam-5386	75	11	(	(	PUNCT
ejpam-5386	75	12	1	1	NUM
ejpam-5386	75	13	)	)	PUNCT
ejpam-5386	75	14	,	,	PUNCT
ejpam-5386	75	15	we	we	PRON
ejpam-5386	75	16	have	have	AUX
ejpam-5386	75	17	∂tu−	∂tu−	NUM
ejpam-5386	75	18	div(d(x)∇u	div(d(x)∇u	NOUN
ejpam-5386	75	19	)	)	PUNCT
ejpam-5386	76	1	+	+	PROPN
ejpam-5386	76	2	α⋆(x)β(t)u−	α⋆(x)β(t)u−	PROPN
ejpam-5386	76	3	g(u	g(u	PROPN
ejpam-5386	76	4	)	)	PUNCT
ejpam-5386	76	5	=	=	SYM
ejpam-5386	76	6	0	0	NUM
ejpam-5386	77	1	in	in	ADP
ejpam-5386	77	2	q	q	NOUN
ejpam-5386	77	3	,	,	PUNCT
ejpam-5386	77	4	d(x	d(x	PROPN
ejpam-5386	77	5	)	)	PUNCT
ejpam-5386	77	6	∂νu	∂νu	NOUN
ejpam-5386	77	7	=	=	NOUN
ejpam-5386	77	8	0	0	NUM
ejpam-5386	77	9	on	on	ADP
ejpam-5386	77	10	bt	bt	PROPN
ejpam-5386	77	11	,	,	PUNCT
ejpam-5386	77	12	u(x	u(x	PROPN
ejpam-5386	77	13	,	,	PUNCT
ejpam-5386	77	14	0	0	NUM
ejpam-5386	77	15	)	)	PUNCT
ejpam-5386	77	16	=	=	SYM
ejpam-5386	77	17	φ⋆(x	φ⋆(x	NOUN
ejpam-5386	77	18	)	)	PUNCT
ejpam-5386	77	19	in	in	ADP
ejpam-5386	77	20	b.	b.	PROPN
ejpam-5386	77	21	(	(	PUNCT
ejpam-5386	77	22	5	5	NUM
ejpam-5386	77	23	)	)	PUNCT
ejpam-5386	77	24	the	the	DET
ejpam-5386	77	25	focus	focus	NOUN
ejpam-5386	77	26	of	of	ADP
ejpam-5386	77	27	our	our	PRON
ejpam-5386	77	28	investigation	investigation	NOUN
ejpam-5386	77	29	in	in	ADP
ejpam-5386	77	30	this	this	DET
ejpam-5386	77	31	article	article	NOUN
ejpam-5386	77	32	revolves	revolve	VERB
ejpam-5386	77	33	around	around	ADP
ejpam-5386	77	34	the	the	DET
ejpam-5386	77	35	simultaneous	simultaneous	ADJ
ejpam-5386	77	36	determination	determination	NOUN
ejpam-5386	77	37	of	of	ADP
ejpam-5386	77	38	the	the	DET
ejpam-5386	77	39	response	response	NOUN
ejpam-5386	77	40	treatment	treatment	NOUN
ejpam-5386	77	41	parameter	parameter	NOUN
ejpam-5386	77	42	α⋆(x	α⋆(x	PROPN
ejpam-5386	77	43	)	)	PUNCT
ejpam-5386	77	44	and	and	CCONJ
ejpam-5386	77	45	the	the	DET
ejpam-5386	77	46	initial	initial	ADJ
ejpam-5386	77	47	cell	cell	NOUN
ejpam-5386	77	48	density	density	NOUN
ejpam-5386	77	49	φ⋆(x	φ⋆(x	NOUN
ejpam-5386	77	50	)	)	PUNCT
ejpam-5386	77	51	from	from	ADP
ejpam-5386	77	52	two	two	NUM
ejpam-5386	77	53	time	time	NOUN
ejpam-5386	77	54	-	-	PUNCT
ejpam-5386	77	55	integral	integral	ADJ
ejpam-5386	77	56	measurements	measurement	NOUN
ejpam-5386	77	57	of	of	ADP
ejpam-5386	77	58	u	u	NOUN
ejpam-5386	77	59	defined	define	VERB
ejpam-5386	77	60	by	by	ADP
ejpam-5386	77	61	(	(	PUNCT
ejpam-5386	77	62	3	3	NUM
ejpam-5386	77	63	)	)	PUNCT
ejpam-5386	77	64	.	.	PUNCT
ejpam-5386	78	1	we	we	PRON
ejpam-5386	78	2	first	first	ADV
ejpam-5386	78	3	define	define	VERB
ejpam-5386	78	4	the	the	DET
ejpam-5386	78	5	sets	set	NOUN
ejpam-5386	78	6	of	of	ADP
ejpam-5386	78	7	admissible	admissible	ADJ
ejpam-5386	78	8	solutions	solution	NOUN
ejpam-5386	78	9	to	to	PART
ejpam-5386	78	10	analyze	analyze	VERB
ejpam-5386	78	11	the	the	DET
ejpam-5386	78	12	direct	direct	ADJ
ejpam-5386	78	13	problem	problem	NOUN
ejpam-5386	78	14	(	(	PUNCT
ejpam-5386	78	15	5	5	NUM
ejpam-5386	78	16	)	)	PUNCT
ejpam-5386	78	17	.	.	PUNCT
ejpam-5386	79	1	a	a	DET
ejpam-5386	79	2	set	set	VERB
ejpam-5386	79	3	aα	aα	NOUN
ejpam-5386	79	4	×aφ	×aφ	NOUN
ejpam-5386	79	5	defined	define	VERB
ejpam-5386	79	6	by	by	ADP
ejpam-5386	79	7	aα	aα	NOUN
ejpam-5386	79	8	:	:	PUNCT
ejpam-5386	79	9	=	=	SYM
ejpam-5386	79	10	{	{	PUNCT
ejpam-5386	79	11	α(x	α(x	PROPN
ejpam-5386	79	12	)	)	PUNCT
ejpam-5386	79	13	:	:	PUNCT
ejpam-5386	80	1	α	α	PROPN
ejpam-5386	80	2	∈	∈	PROPN
ejpam-5386	80	3	l∞(ω	l∞(ω	NOUN
ejpam-5386	80	4	)	)	PUNCT
ejpam-5386	80	5	,	,	PUNCT
ejpam-5386	80	6	0	0	NUM
ejpam-5386	80	7	<	<	X
ejpam-5386	80	8	α	α	PROPN
ejpam-5386	80	9	⩽	⩽	PROPN
ejpam-5386	80	10	α(x	α(x	PROPN
ejpam-5386	80	11	)	)	PUNCT
ejpam-5386	80	12	⩽	⩽	NOUN
ejpam-5386	81	1	α	α	X
ejpam-5386	81	2	,	,	PUNCT
ejpam-5386	81	3	a.e	a.e	PROPN
ejpam-5386	81	4	x	x	SYM
ejpam-5386	81	5	∈	∈	PROPN
ejpam-5386	81	6	ω	ω	PROPN
ejpam-5386	81	7	}	}	PUNCT
ejpam-5386	81	8	,	,	PUNCT
ejpam-5386	81	9	aφ	aφ	ADP
ejpam-5386	81	10	:	:	PUNCT
ejpam-5386	81	11	=	=	PRON
ejpam-5386	81	12	{	{	PUNCT
ejpam-5386	81	13	φ(x	φ(x	PROPN
ejpam-5386	81	14	)	)	PUNCT
ejpam-5386	81	15	:	:	PUNCT
ejpam-5386	81	16	φ	φ	PROPN
ejpam-5386	81	17	∈	∈	PROPN
ejpam-5386	81	18	l∞(ω	l∞(ω	NOUN
ejpam-5386	81	19	)	)	PUNCT
ejpam-5386	81	20	,	,	PUNCT
ejpam-5386	81	21	|φ(x)|	|φ(x)|	PROPN
ejpam-5386	81	22	⩽	⩽	PROPN
ejpam-5386	81	23	φ	φ	PROPN
ejpam-5386	81	24	,	,	PUNCT
ejpam-5386	81	25	a.e	a.e	PROPN
ejpam-5386	81	26	x	x	SYM
ejpam-5386	81	27	∈	∈	PROPN
ejpam-5386	81	28	ω	ω	PROPN
ejpam-5386	81	29	}	}	PUNCT
ejpam-5386	81	30	,	,	PUNCT
ejpam-5386	81	31	is	be	AUX
ejpam-5386	81	32	called	call	VERB
ejpam-5386	81	33	the	the	DET
ejpam-5386	81	34	set	set	NOUN
ejpam-5386	81	35	of	of	ADP
ejpam-5386	81	36	admissible	admissible	ADJ
ejpam-5386	81	37	solutions	solution	NOUN
ejpam-5386	81	38	where	where	SCONJ
ejpam-5386	81	39	α	α	X
ejpam-5386	81	40	,	,	PUNCT
ejpam-5386	81	41	α	α	NOUN
ejpam-5386	81	42	,	,	PUNCT
ejpam-5386	81	43	and	and	CCONJ
ejpam-5386	81	44	φ	φ	PROPN
ejpam-5386	81	45	are	be	AUX
ejpam-5386	81	46	predetermined	predetermine	VERB
ejpam-5386	81	47	positive	positive	ADJ
ejpam-5386	81	48	constants	constant	NOUN
ejpam-5386	81	49	.	.	PUNCT
ejpam-5386	82	1	for	for	ADP
ejpam-5386	82	2	each	each	DET
ejpam-5386	82	3	pair	pair	NOUN
ejpam-5386	82	4	(	(	PUNCT
ejpam-5386	82	5	α	α	NOUN
ejpam-5386	82	6	,	,	PUNCT
ejpam-5386	82	7	φ	φ	NOUN
ejpam-5386	82	8	)	)	PUNCT
ejpam-5386	82	9	belonging	belong	VERB
ejpam-5386	82	10	to	to	ADP
ejpam-5386	82	11	aα×aφ	aα×aφ	PROPN
ejpam-5386	82	12	,	,	PUNCT
ejpam-5386	82	13	we	we	PRON
ejpam-5386	82	14	denote	denote	VERB
ejpam-5386	82	15	the	the	DET
ejpam-5386	82	16	solution	solution	NOUN
ejpam-5386	82	17	to	to	ADP
ejpam-5386	82	18	problem	problem	NOUN
ejpam-5386	82	19	(	(	PUNCT
ejpam-5386	82	20	5	5	NUM
ejpam-5386	82	21	)	)	PUNCT
ejpam-5386	82	22	by	by	ADP
ejpam-5386	82	23	c(α	c(α	PROPN
ejpam-5386	82	24	,	,	PUNCT
ejpam-5386	82	25	φ	φ	NOUN
ejpam-5386	82	26	)	)	PUNCT
ejpam-5386	82	27	.	.	PUNCT
ejpam-5386	83	1	in	in	ADP
ejpam-5386	83	2	real	real	ADJ
ejpam-5386	83	3	-	-	PUNCT
ejpam-5386	83	4	world	world	NOUN
ejpam-5386	83	5	scenarios	scenario	NOUN
ejpam-5386	83	6	,	,	PUNCT
ejpam-5386	83	7	observed	observe	VERB
ejpam-5386	83	8	data	datum	NOUN
ejpam-5386	83	9	ϕ1	ϕ1	NOUN
ejpam-5386	83	10	and	and	CCONJ
ejpam-5386	83	11	ϕ2	ϕ2	ADV
ejpam-5386	83	12	are	be	AUX
ejpam-5386	83	13	given	give	VERB
ejpam-5386	83	14	with	with	ADP
ejpam-5386	83	15	some	some	DET
ejpam-5386	83	16	error	error	NOUN
ejpam-5386	83	17	including	include	VERB
ejpam-5386	83	18	measurement	measurement	NOUN
ejpam-5386	83	19	errors	error	NOUN
ejpam-5386	83	20	,	,	PUNCT
ejpam-5386	83	21	biological	biological	ADJ
ejpam-5386	83	22	variability	variability	NOUN
ejpam-5386	83	23	,	,	PUNCT
ejpam-5386	83	24	spatial	spatial	ADJ
ejpam-5386	83	25	heterogeneity	heterogeneity	NOUN
ejpam-5386	83	26	and	and	CCONJ
ejpam-5386	83	27	temporal	temporal	ADJ
ejpam-5386	83	28	dynamics	dynamic	NOUN
ejpam-5386	83	29	inherent	inherent	ADJ
ejpam-5386	83	30	in	in	ADP
ejpam-5386	83	31	tumor	tumor	NOUN
ejpam-5386	83	32	growth	growth	NOUN
ejpam-5386	83	33	and	and	CCONJ
ejpam-5386	83	34	treatment	treatment	NOUN
ejpam-5386	83	35	response	response	NOUN
ejpam-5386	83	36	.	.	PUNCT
ejpam-5386	84	1	to	to	PART
ejpam-5386	84	2	overcome	overcome	VERB
ejpam-5386	84	3	these	these	DET
ejpam-5386	84	4	effects	effect	NOUN
ejpam-5386	84	5	,	,	PUNCT
ejpam-5386	84	6	we	we	PRON
ejpam-5386	84	7	introduce	introduce	VERB
ejpam-5386	84	8	perturbed	perturb	VERB
ejpam-5386	84	9	measurements	measurement	NOUN
ejpam-5386	84	10	ϕε1	ϕε1	PROPN
ejpam-5386	84	11	and	and	CCONJ
ejpam-5386	84	12	ϕε2	ϕε2	NOUN
ejpam-5386	84	13	as	as	SCONJ
ejpam-5386	84	14	follows	follow	VERB
ejpam-5386	84	15	:	:	PUNCT
ejpam-5386	85	1	∥ϕεi	∥ϕεi	VERB
ejpam-5386	85	2	−	−	PROPN
ejpam-5386	85	3	ϕi∥l∞(ω	ϕi∥l∞(ω	NOUN
ejpam-5386	85	4	)	)	PUNCT
ejpam-5386	85	5	⩽	⩽	PROPN
ejpam-5386	85	6	ε	ε	PROPN
ejpam-5386	85	7	,	,	PUNCT
ejpam-5386	85	8	for	for	ADP
ejpam-5386	85	9	i	i	PROPN
ejpam-5386	85	10	=	=	SYM
ejpam-5386	85	11	1	1	NUM
ejpam-5386	85	12	,	,	PUNCT
ejpam-5386	85	13	2	2	NUM
ejpam-5386	85	14	,	,	PUNCT
ejpam-5386	85	15	(	(	PUNCT
ejpam-5386	85	16	6	6	NUM
ejpam-5386	85	17	)	)	PUNCT
ejpam-5386	85	18	s.	s.	PROPN
ejpam-5386	85	19	tatar	tatar	PROPN
ejpam-5386	85	20	,	,	PUNCT
ejpam-5386	85	21	m.	m.	NOUN
ejpam-5386	85	22	bensalah	bensalah	PROPN
ejpam-5386	85	23	,	,	PUNCT
ejpam-5386	85	24	m.	m.	NOUN
ejpam-5386	85	25	alamil	alamil	PROPN
ejpam-5386	85	26	/	/	SYM
ejpam-5386	85	27	eur	eur	PROPN
ejpam-5386	85	28	.	.	PUNCT
ejpam-5386	86	1	j.	j.	PROPN
ejpam-5386	86	2	pure	pure	PROPN
ejpam-5386	86	3	appl	appl	PROPN
ejpam-5386	86	4	.	.	PROPN
ejpam-5386	86	5	math	math	PROPN
ejpam-5386	86	6	,	,	PUNCT
ejpam-5386	86	7	17	17	NUM
ejpam-5386	86	8	(	(	PUNCT
ejpam-5386	86	9	4	4	NUM
ejpam-5386	86	10	)	)	PUNCT
ejpam-5386	86	11	(	(	PUNCT
ejpam-5386	86	12	2024	2024	NUM
ejpam-5386	86	13	)	)	PUNCT
ejpam-5386	86	14	,	,	PUNCT
ejpam-5386	86	15	2651	2651	NUM
ejpam-5386	86	16	-	-	SYM
ejpam-5386	86	17	2675	2675	NUM
ejpam-5386	86	18	2656	2656	NUM
ejpam-5386	86	19	where	where	SCONJ
ejpam-5386	86	20	ε	ε	PROPN
ejpam-5386	86	21	>	>	X
ejpam-5386	86	22	0	0	NUM
ejpam-5386	86	23	represents	represent	VERB
ejpam-5386	86	24	the	the	DET
ejpam-5386	86	25	magnitude	magnitude	NOUN
ejpam-5386	86	26	of	of	ADP
ejpam-5386	86	27	noise	noise	NOUN
ejpam-5386	86	28	in	in	ADP
ejpam-5386	86	29	the	the	DET
ejpam-5386	86	30	data	datum	NOUN
ejpam-5386	86	31	.	.	PUNCT
ejpam-5386	87	1	consequently	consequently	ADV
ejpam-5386	87	2	,	,	PUNCT
ejpam-5386	87	3	the	the	DET
ejpam-5386	87	4	quasisolution	quasisolution	NOUN
ejpam-5386	87	5	,	,	PUNCT
ejpam-5386	87	6	see	see	VERB
ejpam-5386	87	7	[	[	X
ejpam-5386	87	8	14	14	NUM
ejpam-5386	87	9	]	]	X
ejpam-5386	87	10	,	,	PUNCT
ejpam-5386	87	11	of	of	ADP
ejpam-5386	87	12	the	the	DET
ejpam-5386	87	13	inverse	inverse	NOUN
ejpam-5386	87	14	problem	problem	NOUN
ejpam-5386	87	15	under	under	ADP
ejpam-5386	87	16	consideration	consideration	NOUN
ejpam-5386	87	17	is	be	AUX
ejpam-5386	87	18	obtained	obtain	VERB
ejpam-5386	87	19	by	by	ADP
ejpam-5386	87	20	minimizing	minimize	VERB
ejpam-5386	87	21	the	the	DET
ejpam-5386	87	22	following	follow	VERB
ejpam-5386	87	23	least	least	ADJ
ejpam-5386	87	24	-	-	PUNCT
ejpam-5386	87	25	squares	square	NOUN
ejpam-5386	87	26	objective	objective	ADJ
ejpam-5386	87	27	functional	functional	ADJ
ejpam-5386	87	28	:	:	PUNCT
ejpam-5386	87	29	j(α	j(α	PROPN
ejpam-5386	87	30	,	,	PUNCT
ejpam-5386	87	31	φ	φ	NUM
ejpam-5386	87	32	)	)	PUNCT
ejpam-5386	87	33	:	:	PUNCT
ejpam-5386	88	1	=	=	SYM
ejpam-5386	88	2	1	1	NUM
ejpam-5386	88	3	2	2	NUM
ejpam-5386	88	4	∥∥∥∫	∥∥∥∫	NOUN
ejpam-5386	88	5	t	t	NOUN
ejpam-5386	88	6	0	0	NUM
ejpam-5386	88	7	ω1(t	ω1(t	NUM
ejpam-5386	88	8	)	)	PUNCT
ejpam-5386	88	9	c(α	c(α	NOUN
ejpam-5386	88	10	,	,	PUNCT
ejpam-5386	88	11	φ	φ	NUM
ejpam-5386	88	12	)	)	PUNCT
ejpam-5386	88	13	dt−	dt−	PUNCT
ejpam-5386	88	14	ϕε1	ϕε1	X
ejpam-5386	88	15	∥∥∥2	∥∥∥2	X
ejpam-5386	88	16	l2(ω	l2(ω	NOUN
ejpam-5386	88	17	)	)	PUNCT
ejpam-5386	88	18	+	+	CCONJ
ejpam-5386	88	19	1	1	NUM
ejpam-5386	88	20	2	2	NUM
ejpam-5386	88	21	∥∥∥∫	∥∥∥∫	NOUN
ejpam-5386	88	22	t	t	NOUN
ejpam-5386	88	23	0	0	NUM
ejpam-5386	88	24	ω2(t	ω2(t	NOUN
ejpam-5386	88	25	)	)	PUNCT
ejpam-5386	88	26	c(α	c(α	NOUN
ejpam-5386	88	27	,	,	PUNCT
ejpam-5386	88	28	φ	φ	NUM
ejpam-5386	88	29	)	)	PUNCT
ejpam-5386	88	30	dt−	dt−	NUM
ejpam-5386	88	31	ϕε2	ϕε2	X
ejpam-5386	88	32	∥∥∥2	∥∥∥2	NOUN
ejpam-5386	88	33	l2(ω	l2(ω	NOUN
ejpam-5386	88	34	)	)	PUNCT
ejpam-5386	88	35	.	.	PUNCT
ejpam-5386	89	1	(	(	PUNCT
ejpam-5386	89	2	7	7	X
ejpam-5386	89	3	)	)	PUNCT
ejpam-5386	89	4	therefore	therefore	ADV
ejpam-5386	89	5	,	,	PUNCT
ejpam-5386	89	6	the	the	DET
ejpam-5386	89	7	inverse	inverse	NOUN
ejpam-5386	89	8	problem	problem	NOUN
ejpam-5386	89	9	addressed	address	VERB
ejpam-5386	89	10	in	in	ADP
ejpam-5386	89	11	this	this	DET
ejpam-5386	89	12	article	article	NOUN
ejpam-5386	89	13	can	can	AUX
ejpam-5386	89	14	be	be	AUX
ejpam-5386	89	15	reformulated	reformulate	VERB
ejpam-5386	89	16	and	and	CCONJ
ejpam-5386	89	17	modeled	model	VERB
ejpam-5386	89	18	by	by	ADP
ejpam-5386	89	19	the	the	DET
ejpam-5386	89	20	following	follow	VERB
ejpam-5386	89	21	minimization	minimization	NOUN
ejpam-5386	89	22	problem:	problem:	NOUN
ejpam-5386	89	23	find	find	NOUN
ejpam-5386	89	24	(	(	PUNCT
ejpam-5386	89	25	α⋆,φ⋆	α⋆,φ⋆	NOUN
ejpam-5386	89	26	)	)	PUNCT
ejpam-5386	89	27	∈	∈	PROPN
ejpam-5386	89	28	aα	aα	NOUN
ejpam-5386	89	29	×aφ	×aφ	NOUN
ejpam-5386	89	30	such	such	ADJ
ejpam-5386	89	31	that	that	DET
ejpam-5386	89	32	j(α⋆,φ⋆	j(α⋆,φ⋆	PROPN
ejpam-5386	89	33	)	)	PUNCT
ejpam-5386	89	34	⩽	⩽	PROPN
ejpam-5386	89	35	j(α	j(α	PROPN
ejpam-5386	89	36	,	,	PUNCT
ejpam-5386	89	37	φ	φ	NOUN
ejpam-5386	89	38	)	)	PUNCT
ejpam-5386	89	39	,	,	PUNCT
ejpam-5386	89	40	∀(α	∀(α	PROPN
ejpam-5386	89	41	,	,	PUNCT
ejpam-5386	89	42	φ	φ	NUM
ejpam-5386	89	43	)	)	PUNCT
ejpam-5386	89	44	∈	∈	PROPN
ejpam-5386	89	45	aα	aα	NOUN
ejpam-5386	89	46	×aφ	×aφ	PROPN
ejpam-5386	89	47	.	.	PUNCT
ejpam-5386	90	1	(	(	PUNCT
ejpam-5386	90	2	8)	8)	NUM
ejpam-5386	90	3	it	it	PRON
ejpam-5386	90	4	is	be	AUX
ejpam-5386	90	5	worth	worth	ADJ
ejpam-5386	90	6	noting	note	VERB
ejpam-5386	90	7	that	that	SCONJ
ejpam-5386	90	8	in	in	ADP
ejpam-5386	90	9	this	this	DET
ejpam-5386	90	10	paper	paper	NOUN
ejpam-5386	90	11	,	,	PUNCT
ejpam-5386	90	12	we	we	PRON
ejpam-5386	90	13	adopt	adopt	VERB
ejpam-5386	90	14	the	the	DET
ejpam-5386	90	15	regularization	regularization	NOUN
ejpam-5386	90	16	before	before	ADP
ejpam-5386	90	17	discretization	discretization	NOUN
ejpam-5386	90	18	strategy	strategy	NOUN
ejpam-5386	90	19	,	,	PUNCT
ejpam-5386	90	20	as	as	SCONJ
ejpam-5386	90	21	opposed	oppose	VERB
ejpam-5386	90	22	to	to	ADP
ejpam-5386	90	23	the	the	DET
ejpam-5386	90	24	alternative	alternative	ADJ
ejpam-5386	90	25	approach	approach	NOUN
ejpam-5386	90	26	of	of	ADP
ejpam-5386	90	27	discretization	discretization	NOUN
ejpam-5386	90	28	before	before	ADP
ejpam-5386	90	29	regularization	regularization	NOUN
ejpam-5386	90	30	discussed	discuss	VERB
ejpam-5386	90	31	in	in	ADP
ejpam-5386	90	32	[	[	X
ejpam-5386	90	33	3	3	NUM
ejpam-5386	90	34	,	,	PUNCT
ejpam-5386	90	35	11	11	NUM
ejpam-5386	90	36	]	]	PUNCT
ejpam-5386	90	37	.	.	PUNCT
ejpam-5386	91	1	theorem	theorem	NOUN
ejpam-5386	91	2	1	1	NUM
ejpam-5386	91	3	.	.	PUNCT
ejpam-5386	92	1	there	there	PRON
ejpam-5386	92	2	exists	exist	VERB
ejpam-5386	92	3	at	at	ADP
ejpam-5386	92	4	least	least	ADV
ejpam-5386	92	5	one	one	NUM
ejpam-5386	92	6	minimizer	minimizer	NOUN
ejpam-5386	92	7	for	for	ADP
ejpam-5386	92	8	the	the	DET
ejpam-5386	92	9	optimization	optimization	NOUN
ejpam-5386	92	10	problem	problem	NOUN
ejpam-5386	92	11	(	(	PUNCT
ejpam-5386	92	12	8)	8)	NUM
ejpam-5386	92	13	.	.	PUNCT
ejpam-5386	93	1	proof	proof	NOUN
ejpam-5386	93	2	.	.	PUNCT
ejpam-5386	94	1	since	since	SCONJ
ejpam-5386	94	2	j(α	j(α	PROPN
ejpam-5386	94	3	,	,	PUNCT
ejpam-5386	94	4	φ	φ	NUM
ejpam-5386	94	5	)	)	PUNCT
ejpam-5386	94	6	is	be	AUX
ejpam-5386	94	7	nonnegative	nonnegative	ADJ
ejpam-5386	94	8	,	,	PUNCT
ejpam-5386	94	9	we	we	PRON
ejpam-5386	94	10	know	know	VERB
ejpam-5386	94	11	that	that	PRON
ejpam-5386	94	12	inf	inf	PROPN
ejpam-5386	94	13	j(α	j(α	PROPN
ejpam-5386	94	14	,	,	PUNCT
ejpam-5386	94	15	φ	φ	NUM
ejpam-5386	94	16	)	)	PUNCT
ejpam-5386	94	17	is	be	AUX
ejpam-5386	94	18	finite	finite	ADJ
ejpam-5386	94	19	over	over	ADP
ejpam-5386	94	20	aα	aα	NOUN
ejpam-5386	94	21	×aφ	×aφ	PROPN
ejpam-5386	94	22	.	.	PUNCT
ejpam-5386	95	1	thus	thus	ADV
ejpam-5386	95	2	,	,	PUNCT
ejpam-5386	95	3	there	there	PRON
ejpam-5386	95	4	exists	exist	VERB
ejpam-5386	95	5	a	a	DET
ejpam-5386	95	6	minimizing	minimize	VERB
ejpam-5386	95	7	sequence	sequence	NOUN
ejpam-5386	95	8	{	{	PUNCT
ejpam-5386	95	9	αn	αn	NOUN
ejpam-5386	95	10	,	,	PUNCT
ejpam-5386	95	11	φn}n⩾0	φn}n⩾0	PROPN
ejpam-5386	95	12	from	from	ADP
ejpam-5386	95	13	aα	aα	NOUN
ejpam-5386	95	14	×aφ	×aφ	NOUN
ejpam-5386	95	15	such	such	ADJ
ejpam-5386	95	16	that	that	SCONJ
ejpam-5386	95	17	lim	lim	PROPN
ejpam-5386	95	18	n→∞	n→∞	NUM
ejpam-5386	95	19	j(αn	j(αn	PROPN
ejpam-5386	95	20	,	,	PUNCT
ejpam-5386	95	21	φn	φn	NOUN
ejpam-5386	95	22	)	)	PUNCT
ejpam-5386	95	23	=	=	SYM
ejpam-5386	95	24	inf	inf	PROPN
ejpam-5386	95	25	α∈aα	α∈aα	NOUN
ejpam-5386	95	26	φ∈aφ	φ∈aφ	PROPN
ejpam-5386	95	27	j(α	j(α	PROPN
ejpam-5386	95	28	,	,	PUNCT
ejpam-5386	95	29	φ	φ	NUM
ejpam-5386	95	30	)	)	PUNCT
ejpam-5386	95	31	.	.	PUNCT
ejpam-5386	96	1	this	this	PRON
ejpam-5386	96	2	implies	imply	VERB
ejpam-5386	96	3	the	the	DET
ejpam-5386	96	4	boundedness	boundedness	NOUN
ejpam-5386	96	5	of	of	ADP
ejpam-5386	96	6	{	{	PUNCT
ejpam-5386	96	7	αn	αn	NOUN
ejpam-5386	96	8	,	,	PUNCT
ejpam-5386	96	9	φn}n⩾0	φn}n⩾0	PROPN
ejpam-5386	96	10	in	in	ADP
ejpam-5386	96	11	l∞(b	l∞(b	PROPN
ejpam-5386	96	12	)	)	PUNCT
ejpam-5386	96	13	×	×	PROPN
ejpam-5386	96	14	l2(b	l2(b	NUM
ejpam-5386	96	15	)	)	PUNCT
ejpam-5386	96	16	and	and	CCONJ
ejpam-5386	96	17	therefore	therefore	ADV
ejpam-5386	96	18	there	there	PRON
ejpam-5386	96	19	is	be	VERB
ejpam-5386	96	20	a	a	DET
ejpam-5386	96	21	subsequence	subsequence	NOUN
ejpam-5386	96	22	(	(	PUNCT
ejpam-5386	96	23	still	still	ADV
ejpam-5386	96	24	denoted	denote	VERB
ejpam-5386	96	25	as	as	ADP
ejpam-5386	96	26	{	{	PUNCT
ejpam-5386	96	27	αn	αn	NOUN
ejpam-5386	96	28	,	,	PUNCT
ejpam-5386	96	29	φn}n⩾0	φn}n⩾0	PROPN
ejpam-5386	96	30	)	)	PUNCT
ejpam-5386	96	31	such	such	ADJ
ejpam-5386	96	32	that	that	SCONJ
ejpam-5386	96	33	both	both	PRON
ejpam-5386	96	34	{	{	PUNCT
ejpam-5386	96	35	αn}n⩾0	αn}n⩾0	PROPN
ejpam-5386	96	36	and	and	CCONJ
ejpam-5386	96	37	{	{	PUNCT
ejpam-5386	96	38	φn}n⩾0	φn}n⩾0	PROPN
ejpam-5386	96	39	converge	converge	VERB
ejpam-5386	96	40	weakly	weakly	ADV
ejpam-5386	96	41	to	to	ADP
ejpam-5386	96	42	α⋆	α⋆	VERB
ejpam-5386	96	43	∈	∈	PROPN
ejpam-5386	96	44	l∞(b	l∞(b	NOUN
ejpam-5386	96	45	)	)	PUNCT
ejpam-5386	96	46	and	and	CCONJ
ejpam-5386	96	47	φ⋆	φ⋆	NUM
ejpam-5386	96	48	∈	∈	PROPN
ejpam-5386	96	49	l2(b	l2(b	NUM
ejpam-5386	96	50	)	)	PUNCT
ejpam-5386	96	51	,	,	PUNCT
ejpam-5386	96	52	respectively	respectively	ADV
ejpam-5386	96	53	,	,	PUNCT
ejpam-5386	96	54	since	since	SCONJ
ejpam-5386	96	55	the	the	DET
ejpam-5386	96	56	sets	set	NOUN
ejpam-5386	96	57	aα	aα	NOUN
ejpam-5386	96	58	and	and	CCONJ
ejpam-5386	96	59	aφ	aφ	ADJ
ejpam-5386	96	60	are	be	AUX
ejpam-5386	96	61	closed	close	VERB
ejpam-5386	96	62	and	and	CCONJ
ejpam-5386	96	63	convex	convex	NOUN
ejpam-5386	96	64	.	.	PUNCT
ejpam-5386	97	1	we	we	PRON
ejpam-5386	97	2	shall	shall	AUX
ejpam-5386	97	3	prove	prove	VERB
ejpam-5386	97	4	first	first	ADV
ejpam-5386	97	5	that	that	SCONJ
ejpam-5386	97	6	(	(	PUNCT
ejpam-5386	97	7	α⋆,φ⋆	α⋆,φ⋆	NOUN
ejpam-5386	97	8	)	)	PUNCT
ejpam-5386	97	9	is	be	AUX
ejpam-5386	97	10	indeed	indeed	ADV
ejpam-5386	97	11	a	a	DET
ejpam-5386	97	12	minimizer	minimizer	NOUN
ejpam-5386	97	13	of	of	ADP
ejpam-5386	97	14	(	(	PUNCT
ejpam-5386	97	15	8)	8)	NUM
ejpam-5386	97	16	.	.	PUNCT
ejpam-5386	98	1	since	since	SCONJ
ejpam-5386	98	2	each	each	DET
ejpam-5386	98	3	pair	pair	NOUN
ejpam-5386	98	4	(	(	PUNCT
ejpam-5386	98	5	αn	αn	NOUN
ejpam-5386	98	6	,	,	PUNCT
ejpam-5386	98	7	φn	φn	NOUN
ejpam-5386	98	8	)	)	PUNCT
ejpam-5386	98	9	corresponds	correspond	VERB
ejpam-5386	98	10	to	to	ADP
ejpam-5386	98	11	a	a	DET
ejpam-5386	98	12	solution	solution	NOUN
ejpam-5386	98	13	cn	cn	X
ejpam-5386	98	14	:	:	PUNCT
ejpam-5386	98	15	=	=	SYM
ejpam-5386	98	16	c	c	X
ejpam-5386	98	17	(	(	PUNCT
ejpam-5386	98	18	αn	αn	NOUN
ejpam-5386	98	19	,	,	PUNCT
ejpam-5386	98	20	φn	φn	NOUN
ejpam-5386	98	21	)	)	PUNCT
ejpam-5386	98	22	to	to	ADP
ejpam-5386	98	23	(	(	PUNCT
ejpam-5386	98	24	5	5	NUM
ejpam-5386	98	25	)	)	PUNCT
ejpam-5386	98	26	with	with	ADP
ejpam-5386	98	27	α	α	NOUN
ejpam-5386	98	28	=	=	PUNCT
ejpam-5386	98	29	αn	αn	NOUN
ejpam-5386	98	30	and	and	CCONJ
ejpam-5386	98	31	φ	φ	NOUN
ejpam-5386	98	32	=	=	SYM
ejpam-5386	98	33	φn	φn	PROPN
ejpam-5386	98	34	,	,	PUNCT
ejpam-5386	98	35	by	by	ADP
ejpam-5386	98	36	letting	let	VERB
ejpam-5386	98	37	ψ	ψ	X
ejpam-5386	98	38	=	=	X
ejpam-5386	98	39	cn	cn	PROPN
ejpam-5386	98	40	in	in	ADP
ejpam-5386	98	41	(	(	PUNCT
ejpam-5386	98	42	2	2	NUM
ejpam-5386	98	43	)	)	PUNCT
ejpam-5386	98	44	and	and	CCONJ
ejpam-5386	98	45	using	use	VERB
ejpam-5386	98	46	1	1	NUM
ejpam-5386	98	47	2∂tc	2∂tc	NUM
ejpam-5386	98	48	2	2	NUM
ejpam-5386	98	49	=	=	SYM
ejpam-5386	98	50	ctc	ctc	PROPN
ejpam-5386	98	51	,	,	PUNCT
ejpam-5386	98	52	it	it	PRON
ejpam-5386	98	53	follows	follow	VERB
ejpam-5386	98	54	immediately	immediately	ADV
ejpam-5386	98	55	that	that	SCONJ
ejpam-5386	98	56	the	the	DET
ejpam-5386	98	57	sequence	sequence	NOUN
ejpam-5386	98	58	{	{	PUNCT
ejpam-5386	98	59	cn	cn	NOUN
ejpam-5386	98	60	:	:	PUNCT
ejpam-5386	98	61	=	=	SYM
ejpam-5386	98	62	c	c	X
ejpam-5386	98	63	(	(	PUNCT
ejpam-5386	98	64	αn	αn	NOUN
ejpam-5386	98	65	,	,	PUNCT
ejpam-5386	98	66	φn	φn	NOUN
ejpam-5386	98	67	)	)	PUNCT
ejpam-5386	98	68	}	}	PUNCT
ejpam-5386	98	69	is	be	AUX
ejpam-5386	98	70	also	also	ADV
ejpam-5386	98	71	bounded	bound	VERB
ejpam-5386	98	72	in	in	ADP
ejpam-5386	98	73	l2(0	l2(0	PROPN
ejpam-5386	98	74	,	,	PUNCT
ejpam-5386	98	75	t	t	NOUN
ejpam-5386	98	76	;	;	PUNCT
ejpam-5386	98	77	h1(b	h1(b	NUM
ejpam-5386	98	78	)	)	PUNCT
ejpam-5386	98	79	)	)	PUNCT
ejpam-5386	98	80	.	.	PUNCT
ejpam-5386	99	1	this	this	PRON
ejpam-5386	99	2	indicates	indicate	VERB
ejpam-5386	99	3	the	the	DET
ejpam-5386	99	4	existence	existence	NOUN
ejpam-5386	99	5	of	of	ADP
ejpam-5386	99	6	some	some	DET
ejpam-5386	99	7	c⋆	c⋆	X
ejpam-5386	99	8	∈	∈	PROPN
ejpam-5386	99	9	l2(0	l2(0	NOUN
ejpam-5386	99	10	,	,	PUNCT
ejpam-5386	99	11	t	t	NOUN
ejpam-5386	99	12	;	;	PUNCT
ejpam-5386	99	13	h1(b	h1(b	NUM
ejpam-5386	99	14	)	)	PUNCT
ejpam-5386	99	15	)	)	PUNCT
ejpam-5386	99	16	and	and	CCONJ
ejpam-5386	99	17	a	a	DET
ejpam-5386	99	18	subsequence	subsequence	NOUN
ejpam-5386	99	19	of	of	ADP
ejpam-5386	99	20	{	{	PUNCT
ejpam-5386	99	21	cn	cn	PROPN
ejpam-5386	99	22	}	}	PUNCT
ejpam-5386	99	23	,	,	PUNCT
ejpam-5386	99	24	still	still	ADV
ejpam-5386	99	25	denoted	denote	VERB
ejpam-5386	99	26	by	by	ADP
ejpam-5386	99	27	{	{	PUNCT
ejpam-5386	99	28	cn	cn	PROPN
ejpam-5386	99	29	}	}	PUNCT
ejpam-5386	99	30	,	,	PUNCT
ejpam-5386	99	31	such	such	ADJ
ejpam-5386	99	32	that	that	DET
ejpam-5386	99	33	cn	cn	PROPN
ejpam-5386	99	34	:	:	PUNCT
ejpam-5386	99	35	=	=	SYM
ejpam-5386	99	36	c	c	X
ejpam-5386	99	37	(	(	PUNCT
ejpam-5386	99	38	αn	αn	NOUN
ejpam-5386	99	39	,	,	PUNCT
ejpam-5386	99	40	φn	φn	NOUN
ejpam-5386	99	41	)	)	PUNCT
ejpam-5386	99	42	⇀	⇀	NOUN
ejpam-5386	99	43	c⋆	c⋆	NOUN
ejpam-5386	99	44	in	in	ADP
ejpam-5386	99	45	l2(0	l2(0	NOUN
ejpam-5386	99	46	,	,	PUNCT
ejpam-5386	99	47	t	t	NOUN
ejpam-5386	99	48	;	;	PUNCT
ejpam-5386	99	49	h1(b	h1(b	NUM
ejpam-5386	99	50	)	)	PUNCT
ejpam-5386	99	51	)	)	PUNCT
ejpam-5386	99	52	.	.	PUNCT
ejpam-5386	100	1	(	(	PUNCT
ejpam-5386	100	2	9	9	X
ejpam-5386	100	3	)	)	PUNCT
ejpam-5386	100	4	we	we	PRON
ejpam-5386	100	5	claim	claim	VERB
ejpam-5386	100	6	c⋆	c⋆	ADV
ejpam-5386	100	7	=	=	SYM
ejpam-5386	100	8	c	c	X
ejpam-5386	100	9	(	(	PUNCT
ejpam-5386	100	10	α⋆,φ⋆	α⋆,φ⋆	NOUN
ejpam-5386	100	11	)	)	PUNCT
ejpam-5386	100	12	.	.	PUNCT
ejpam-5386	101	1	the	the	DET
ejpam-5386	101	2	continuity	continuity	NOUN
ejpam-5386	101	3	of	of	ADP
ejpam-5386	101	4	g(c	g(c	NOUN
ejpam-5386	101	5	)	)	PUNCT
ejpam-5386	101	6	with	with	ADP
ejpam-5386	101	7	respect	respect	NOUN
ejpam-5386	101	8	to	to	ADP
ejpam-5386	101	9	c	c	PROPN
ejpam-5386	101	10	together	together	ADV
ejpam-5386	101	11	with	with	ADP
ejpam-5386	101	12	(	(	PUNCT
ejpam-5386	101	13	9	9	X
ejpam-5386	101	14	)	)	PUNCT
ejpam-5386	101	15	imply	imply	ADV
ejpam-5386	101	16	∂tc	∂tc	PROPN
ejpam-5386	101	17	(	(	PUNCT
ejpam-5386	101	18	α	α	NOUN
ejpam-5386	101	19	n	n	CCONJ
ejpam-5386	101	20	,	,	PUNCT
ejpam-5386	101	21	φn	φn	NOUN
ejpam-5386	101	22	)	)	PUNCT
ejpam-5386	101	23	⇀	⇀	PROPN
ejpam-5386	101	24	∂tc	∂tc	PROPN
ejpam-5386	101	25	⋆	⋆	NOUN
ejpam-5386	101	26	,	,	PUNCT
ejpam-5386	101	27	∇c	∇c	PROPN
ejpam-5386	101	28	(	(	PUNCT
ejpam-5386	101	29	αn	αn	VERB
ejpam-5386	101	30	,	,	PUNCT
ejpam-5386	101	31	φn	φn	NOUN
ejpam-5386	101	32	)	)	PUNCT
ejpam-5386	101	33	⇀	⇀	PROPN
ejpam-5386	101	34	∇c⋆	∇c⋆	PROPN
ejpam-5386	101	35	in	in	ADP
ejpam-5386	101	36	l2(q	l2(q	PROPN
ejpam-5386	101	37	)	)	PUNCT
ejpam-5386	101	38	.	.	PUNCT
ejpam-5386	102	1	letting	let	VERB
ejpam-5386	102	2	n→	n→	PUNCT
ejpam-5386	102	3	∞	∞	PROPN
ejpam-5386	102	4	in	in	ADP
ejpam-5386	102	5	(	(	PUNCT
ejpam-5386	102	6	2	2	NUM
ejpam-5386	102	7	)	)	PUNCT
ejpam-5386	102	8	with	with	ADP
ejpam-5386	102	9	α	α	NOUN
ejpam-5386	102	10	=	=	PUNCT
ejpam-5386	102	11	αn	αn	NOUN
ejpam-5386	102	12	and	and	CCONJ
ejpam-5386	102	13	φ	φ	NOUN
ejpam-5386	102	14	=	=	VERB
ejpam-5386	102	15	φn	φn	ADP
ejpam-5386	102	16	yields∫	yields∫	PROPN
ejpam-5386	102	17	t	t	PROPN
ejpam-5386	102	18	0	0	NUM
ejpam-5386	102	19	∫	∫	PROPN
ejpam-5386	102	20	b	b	PROPN
ejpam-5386	102	21	(	(	PUNCT
ejpam-5386	102	22	∂tc	∂tc	PROPN
ejpam-5386	102	23	⋆	⋆	PUNCT
ejpam-5386	102	24	ψ	ψ	PROPN
ejpam-5386	102	25	+	+	PROPN
ejpam-5386	102	26	d(x)∇c⋆	d(x)∇c⋆	NOUN
ejpam-5386	102	27	·	·	PUNCT
ejpam-5386	103	1	∇ψ	∇ψ	PROPN
ejpam-5386	103	2	+	+	NOUN
ejpam-5386	103	3	α⋆(x)β(t	α⋆(x)β(t	NOUN
ejpam-5386	103	4	)	)	PUNCT
ejpam-5386	103	5	c⋆	c⋆	ADP
ejpam-5386	103	6	ψ	ψ	X
ejpam-5386	103	7	)	)	PUNCT
ejpam-5386	103	8	dx	dx	PROPN
ejpam-5386	103	9	dt	dt	PROPN
ejpam-5386	104	1	=	=	SYM
ejpam-5386	104	2	∫	∫	PROPN
ejpam-5386	104	3	t	t	PROPN
ejpam-5386	104	4	0	0	NUM
ejpam-5386	105	1	∫	∫	PROPN
ejpam-5386	106	1	b	b	PROPN
ejpam-5386	106	2	g(c⋆)ψ	g(c⋆)ψ	PROPN
ejpam-5386	106	3	dx	dx	PROPN
ejpam-5386	106	4	dt	dt	PROPN
ejpam-5386	106	5	,	,	PUNCT
ejpam-5386	106	6	(	(	PUNCT
ejpam-5386	106	7	10	10	NUM
ejpam-5386	106	8	)	)	PUNCT
ejpam-5386	106	9	s.	s.	PROPN
ejpam-5386	106	10	tatar	tatar	PROPN
ejpam-5386	106	11	,	,	PUNCT
ejpam-5386	106	12	m.	m.	NOUN
ejpam-5386	106	13	bensalah	bensalah	PROPN
ejpam-5386	106	14	,	,	PUNCT
ejpam-5386	106	15	m.	m.	NOUN
ejpam-5386	106	16	alamil	alamil	PROPN
ejpam-5386	106	17	/	/	SYM
ejpam-5386	106	18	eur	eur	PROPN
ejpam-5386	106	19	.	.	PUNCT
ejpam-5386	107	1	j.	j.	PROPN
ejpam-5386	107	2	pure	pure	PROPN
ejpam-5386	107	3	appl	appl	PROPN
ejpam-5386	107	4	.	.	PROPN
ejpam-5386	107	5	math	math	PROPN
ejpam-5386	107	6	,	,	PUNCT
ejpam-5386	107	7	17	17	NUM
ejpam-5386	107	8	(	(	PUNCT
ejpam-5386	107	9	4	4	NUM
ejpam-5386	107	10	)	)	PUNCT
ejpam-5386	107	11	(	(	PUNCT
ejpam-5386	107	12	2024	2024	NUM
ejpam-5386	107	13	)	)	PUNCT
ejpam-5386	107	14	,	,	PUNCT
ejpam-5386	107	15	2651	2651	NUM
ejpam-5386	107	16	-	-	SYM
ejpam-5386	107	17	2675	2675	NUM
ejpam-5386	107	18	2657	2657	NUM
ejpam-5386	107	19	for	for	ADP
ejpam-5386	107	20	all	all	DET
ejpam-5386	107	21	ψ	ψ	PRON
ejpam-5386	107	22	∈	∈	NOUN
ejpam-5386	107	23	l2	l2	NOUN
ejpam-5386	107	24	(	(	PUNCT
ejpam-5386	107	25	0	0	NUM
ejpam-5386	107	26	,	,	PUNCT
ejpam-5386	107	27	t	t	NOUN
ejpam-5386	107	28	;	;	PUNCT
ejpam-5386	107	29	h1(b	h1(b	NUM
ejpam-5386	107	30	)	)	PUNCT
ejpam-5386	107	31	)	)	PUNCT
ejpam-5386	107	32	.	.	PUNCT
ejpam-5386	108	1	next	next	ADV
ejpam-5386	108	2	,	,	PUNCT
ejpam-5386	108	3	we	we	PRON
ejpam-5386	108	4	shall	shall	AUX
ejpam-5386	108	5	prove	prove	VERB
ejpam-5386	108	6	c⋆	c⋆	NOUN
ejpam-5386	108	7	(	(	PUNCT
ejpam-5386	108	8	·	·	PUNCT
ejpam-5386	108	9	,	,	PUNCT
ejpam-5386	108	10	0	0	NUM
ejpam-5386	108	11	)	)	PUNCT
ejpam-5386	108	12	=	=	SYM
ejpam-5386	108	13	φ⋆	φ⋆	PROPN
ejpam-5386	108	14	,	,	PUNCT
ejpam-5386	108	15	which	which	PRON
ejpam-5386	108	16	with	with	ADP
ejpam-5386	108	17	(	(	PUNCT
ejpam-5386	108	18	10	10	NUM
ejpam-5386	108	19	)	)	PUNCT
ejpam-5386	108	20	implies	imply	VERB
ejpam-5386	108	21	c⋆	c⋆	NOUN
ejpam-5386	108	22	=	=	SYM
ejpam-5386	108	23	c(α⋆,φ⋆	c(α⋆,φ⋆	PROPN
ejpam-5386	108	24	)	)	PUNCT
ejpam-5386	108	25	.	.	PUNCT
ejpam-5386	109	1	in	in	ADP
ejpam-5386	109	2	doing	do	VERB
ejpam-5386	109	3	so	so	ADV
ejpam-5386	109	4	,	,	PUNCT
ejpam-5386	109	5	we	we	PRON
ejpam-5386	109	6	take	take	VERB
ejpam-5386	109	7	ϑ	ϑ	NOUN
ejpam-5386	109	8	in	in	ADP
ejpam-5386	109	9	c1[0	c1[0	PROPN
ejpam-5386	109	10	,	,	PUNCT
ejpam-5386	109	11	t	t	X
ejpam-5386	109	12	]	]	PUNCT
ejpam-5386	109	13	,	,	PUNCT
ejpam-5386	109	14	with	with	ADP
ejpam-5386	109	15	ϑ(0	ϑ(0	PROPN
ejpam-5386	109	16	)	)	PUNCT
ejpam-5386	109	17	̸=	̸=	PROPN
ejpam-5386	109	18	0	0	NUM
ejpam-5386	109	19	and	and	CCONJ
ejpam-5386	109	20	ϑ(t	ϑ(t	NOUN
ejpam-5386	109	21	)	)	PUNCT
ejpam-5386	110	1	=	=	SYM
ejpam-5386	110	2	0	0	NUM
ejpam-5386	110	3	and	and	CCONJ
ejpam-5386	110	4	ζ	ζ	NOUN
ejpam-5386	110	5	∈	∈	NOUN
ejpam-5386	110	6	l2(b	l2(b	NUM
ejpam-5386	110	7	)	)	PUNCT
ejpam-5386	110	8	.	.	PUNCT
ejpam-5386	111	1	we	we	PRON
ejpam-5386	111	2	employ	employ	VERB
ejpam-5386	111	3	the	the	DET
ejpam-5386	111	4	classical	classical	ADJ
ejpam-5386	111	5	integration	integration	NOUN
ejpam-5386	111	6	by	by	ADP
ejpam-5386	111	7	parts	part	NOUN
ejpam-5386	111	8	formula	formula	NOUN
ejpam-5386	111	9	to	to	ADP
ejpam-5386	111	10	get∫	get∫	PROPN
ejpam-5386	111	11	t	t	PROPN
ejpam-5386	111	12	0	0	NUM
ejpam-5386	111	13	∫	∫	PROPN
ejpam-5386	111	14	b	b	PROPN
ejpam-5386	111	15	∂tc	∂tc	PROPN
ejpam-5386	111	16	(	(	PUNCT
ejpam-5386	111	17	α	α	NOUN
ejpam-5386	111	18	n	n	CCONJ
ejpam-5386	111	19	,	,	PUNCT
ejpam-5386	111	20	φn	φn	NOUN
ejpam-5386	111	21	)	)	PUNCT
ejpam-5386	111	22	ψ	ψ	NOUN
ejpam-5386	111	23	ζ	ζ	NOUN
ejpam-5386	111	24	dx	dx	PROPN
ejpam-5386	111	25	dt	dt	NOUN
ejpam-5386	112	1	=	=	PUNCT
ejpam-5386	113	1	−	−	PROPN
ejpam-5386	113	2	∫	∫	PROPN
ejpam-5386	113	3	b	b	PROPN
ejpam-5386	113	4	φn	φn	ADP
ejpam-5386	113	5	ψ(0	ψ(0	NOUN
ejpam-5386	113	6	)	)	PUNCT
ejpam-5386	113	7	ζ	ζ	NOUN
ejpam-5386	113	8	dx−	dx−	NUM
ejpam-5386	113	9	∫	∫	PROPN
ejpam-5386	113	10	t	t	PROPN
ejpam-5386	113	11	0	0	NUM
ejpam-5386	113	12	∫	∫	PROPN
ejpam-5386	114	1	b	b	PROPN
ejpam-5386	114	2	c	c	PROPN
ejpam-5386	114	3	(	(	PUNCT
ejpam-5386	114	4	αn	αn	NOUN
ejpam-5386	114	5	,	,	PUNCT
ejpam-5386	114	6	φn	φn	NOUN
ejpam-5386	114	7	)	)	PUNCT
ejpam-5386	114	8	∂tψ	∂tψ	PROPN
ejpam-5386	114	9	ζ	ζ	PROPN
ejpam-5386	114	10	dx	dx	PROPN
ejpam-5386	114	11	dt	dt	PROPN
ejpam-5386	114	12	.	.	PUNCT
ejpam-5386	115	1	(	(	PUNCT
ejpam-5386	115	2	11	11	X
ejpam-5386	115	3	)	)	PUNCT
ejpam-5386	115	4	letting	let	VERB
ejpam-5386	115	5	n→	n→	PUNCT
ejpam-5386	115	6	∞	∞	PROPN
ejpam-5386	115	7	in	in	ADP
ejpam-5386	115	8	(	(	PUNCT
ejpam-5386	115	9	11	11	NUM
ejpam-5386	115	10	)	)	PUNCT
ejpam-5386	115	11	,	,	PUNCT
ejpam-5386	115	12	we	we	PRON
ejpam-5386	115	13	conclude	conclude	VERB
ejpam-5386	115	14	that∫	that∫	PROPN
ejpam-5386	115	15	t	t	PROPN
ejpam-5386	115	16	0	0	NUM
ejpam-5386	116	1	∫	∫	PROPN
ejpam-5386	116	2	b	b	PROPN
ejpam-5386	116	3	∂tc	∂tc	PROPN
ejpam-5386	116	4	⋆	⋆	VERB
ejpam-5386	116	5	ψ	ψ	X
ejpam-5386	116	6	ζ	ζ	NOUN
ejpam-5386	116	7	dx	dx	NOUN
ejpam-5386	116	8	dt	dt	NOUN
ejpam-5386	116	9	=	=	PUNCT
ejpam-5386	117	1	−	−	PROPN
ejpam-5386	117	2	∫	∫	PROPN
ejpam-5386	117	3	b	b	PROPN
ejpam-5386	117	4	φ⋆	φ⋆	X
ejpam-5386	117	5	ψ(0	ψ(0	NOUN
ejpam-5386	117	6	)	)	PUNCT
ejpam-5386	117	7	ζ	ζ	NOUN
ejpam-5386	117	8	dx−	dx−	NUM
ejpam-5386	117	9	∫	∫	PROPN
ejpam-5386	117	10	t	t	PROPN
ejpam-5386	117	11	0	0	NUM
ejpam-5386	118	1	∫	∫	PROPN
ejpam-5386	118	2	b	b	PROPN
ejpam-5386	119	1	c⋆	c⋆	X
ejpam-5386	119	2	∂tψ	∂tψ	PROPN
ejpam-5386	119	3	ζ	ζ	PROPN
ejpam-5386	119	4	dx	dx	PROPN
ejpam-5386	119	5	dt	dt	PROPN
ejpam-5386	119	6	.	.	PUNCT
ejpam-5386	120	1	(	(	PUNCT
ejpam-5386	120	2	12	12	NUM
ejpam-5386	120	3	)	)	PUNCT
ejpam-5386	120	4	on	on	ADP
ejpam-5386	120	5	the	the	DET
ejpam-5386	120	6	other	other	ADJ
ejpam-5386	120	7	hand	hand	NOUN
ejpam-5386	120	8	,	,	PUNCT
ejpam-5386	120	9	we	we	PRON
ejpam-5386	120	10	have:∫	have:∫	VERB
ejpam-5386	121	1	t	t	PROPN
ejpam-5386	121	2	0	0	NUM
ejpam-5386	121	3	∫	∫	PROPN
ejpam-5386	122	1	b	b	PROPN
ejpam-5386	122	2	∂tc	∂tc	PROPN
ejpam-5386	122	3	⋆	⋆	VERB
ejpam-5386	122	4	ψ	ψ	X
ejpam-5386	122	5	ζ	ζ	NOUN
ejpam-5386	122	6	dx	dx	NOUN
ejpam-5386	122	7	dt	dt	NOUN
ejpam-5386	122	8	=	=	PUNCT
ejpam-5386	123	1	−	−	PROPN
ejpam-5386	123	2	∫	∫	PROPN
ejpam-5386	123	3	b	b	X
ejpam-5386	123	4	c⋆	c⋆	X
ejpam-5386	123	5	(	(	PUNCT
ejpam-5386	123	6	·	·	PUNCT
ejpam-5386	123	7	,	,	PUNCT
ejpam-5386	123	8	0)ψ(0	0)ψ(0	ADJ
ejpam-5386	123	9	)	)	PUNCT
ejpam-5386	123	10	ζ	ζ	NOUN
ejpam-5386	123	11	dx−	dx−	NUM
ejpam-5386	123	12	∫	∫	PROPN
ejpam-5386	123	13	t	t	PROPN
ejpam-5386	123	14	0	0	NUM
ejpam-5386	124	1	∫	∫	PROPN
ejpam-5386	124	2	b	b	PROPN
ejpam-5386	125	1	c⋆	c⋆	X
ejpam-5386	125	2	∂tψ	∂tψ	PROPN
ejpam-5386	125	3	ζ	ζ	PROPN
ejpam-5386	125	4	dx	dx	PROPN
ejpam-5386	125	5	dt	dt	PROPN
ejpam-5386	125	6	,	,	PUNCT
ejpam-5386	125	7	(	(	PUNCT
ejpam-5386	125	8	13	13	NUM
ejpam-5386	125	9	)	)	PUNCT
ejpam-5386	125	10	which	which	PRON
ejpam-5386	125	11	,	,	PUNCT
ejpam-5386	125	12	together	together	ADV
ejpam-5386	125	13	with	with	ADP
ejpam-5386	125	14	(	(	PUNCT
ejpam-5386	125	15	12	12	NUM
ejpam-5386	125	16	)	)	PUNCT
ejpam-5386	125	17	,	,	PUNCT
ejpam-5386	125	18	implies	imply	VERB
ejpam-5386	125	19	that	that	SCONJ
ejpam-5386	125	20	c⋆	c⋆	X
ejpam-5386	125	21	(	(	PUNCT
ejpam-5386	125	22	·	·	PUNCT
ejpam-5386	125	23	,	,	PUNCT
ejpam-5386	125	24	0	0	NUM
ejpam-5386	125	25	)	)	PUNCT
ejpam-5386	125	26	=	=	PRON
ejpam-5386	125	27	φ⋆.	φ⋆.	NOUN
ejpam-5386	125	28	therefore	therefore	ADV
ejpam-5386	125	29	,	,	PUNCT
ejpam-5386	125	30	c⋆	c⋆	ADP
ejpam-5386	125	31	:	:	PUNCT
ejpam-5386	125	32	=	=	SYM
ejpam-5386	125	33	c(α⋆,φ⋆	c(α⋆,φ⋆	PROPN
ejpam-5386	125	34	)	)	PUNCT
ejpam-5386	125	35	.	.	PUNCT
ejpam-5386	126	1	by	by	ADP
ejpam-5386	126	2	αn	αn	NOUN
ejpam-5386	126	3	⇀	⇀	PROPN
ejpam-5386	126	4	α⋆	α⋆	NOUN
ejpam-5386	127	1	and	and	CCONJ
ejpam-5386	127	2	φn	φn	ADP
ejpam-5386	127	3	⇀	⇀	X
ejpam-5386	128	1	φ⋆	φ⋆	X
ejpam-5386	129	1	in	in	ADP
ejpam-5386	129	2	l∞(b	l∞(b	PROPN
ejpam-5386	129	3	)	)	PUNCT
ejpam-5386	129	4	⊂	⊂	PROPN
ejpam-5386	129	5	l2(b	l2(b	NUM
ejpam-5386	129	6	)	)	PUNCT
ejpam-5386	129	7	and	and	CCONJ
ejpam-5386	129	8	l2(b	l2(b	NUM
ejpam-5386	129	9	)	)	PUNCT
ejpam-5386	129	10	,	,	PUNCT
ejpam-5386	129	11	respectively	respectively	ADV
ejpam-5386	129	12	,	,	PUNCT
ejpam-5386	129	13	we	we	PRON
ejpam-5386	129	14	use	use	VERB
ejpam-5386	129	15	the	the	DET
ejpam-5386	129	16	lower	low	ADJ
ejpam-5386	129	17	semi	semi	NOUN
ejpam-5386	129	18	-	-	NOUN
ejpam-5386	129	19	continuity	continuity	NOUN
ejpam-5386	129	20	of	of	ADP
ejpam-5386	129	21	the	the	DET
ejpam-5386	129	22	l2	l2	NOUN
ejpam-5386	129	23	-	-	PUNCT
ejpam-5386	129	24	norm	norm	NOUN
ejpam-5386	129	25	to	to	PART
ejpam-5386	129	26	conclude	conclude	VERB
ejpam-5386	129	27	that	that	PRON
ejpam-5386	129	28	j	j	PROPN
ejpam-5386	129	29	(	(	PUNCT
ejpam-5386	129	30	α⋆,φ⋆	α⋆,φ⋆	PROPN
ejpam-5386	129	31	)	)	PUNCT
ejpam-5386	129	32	=	=	SYM
ejpam-5386	129	33	1	1	NUM
ejpam-5386	129	34	2	2	NUM
ejpam-5386	129	35	∥∥∥∫	∥∥∥∫	NOUN
ejpam-5386	129	36	t	t	NOUN
ejpam-5386	129	37	0	0	NUM
ejpam-5386	129	38	ω1(t	ω1(t	NUM
ejpam-5386	129	39	)	)	PUNCT
ejpam-5386	129	40	c(α	c(α	PROPN
ejpam-5386	129	41	⋆,φ⋆	⋆,φ⋆	X
ejpam-5386	129	42	)	)	PUNCT
ejpam-5386	129	43	dt−	dt−	PUNCT
ejpam-5386	129	44	ϕε1	ϕε1	X
ejpam-5386	129	45	∥∥∥2	∥∥∥2	X
ejpam-5386	129	46	l2(b	l2(b	NUM
ejpam-5386	129	47	)	)	PUNCT
ejpam-5386	130	1	+	+	CCONJ
ejpam-5386	130	2	1	1	NUM
ejpam-5386	130	3	2	2	NUM
ejpam-5386	130	4	∥∥∥∫	∥∥∥∫	NOUN
ejpam-5386	130	5	t	t	NOUN
ejpam-5386	130	6	0	0	NUM
ejpam-5386	130	7	ω2(t	ω2(t	NOUN
ejpam-5386	130	8	)	)	PUNCT
ejpam-5386	130	9	c(α	c(α	PROPN
ejpam-5386	130	10	⋆,φ⋆	⋆,φ⋆	X
ejpam-5386	130	11	)	)	PUNCT
ejpam-5386	130	12	dt−	dt−	NUM
ejpam-5386	130	13	ϕε2	ϕε2	X
ejpam-5386	130	14	∥∥∥2	∥∥∥2	NOUN
ejpam-5386	130	15	l2(b	l2(b	NUM
ejpam-5386	130	16	)	)	PUNCT
ejpam-5386	130	17	≤	≤	NOUN
ejpam-5386	130	18	lim	lim	PROPN
ejpam-5386	130	19	inf	inf	PROPN
ejpam-5386	130	20	n→∞	n→∞	NUM
ejpam-5386	130	21	1	1	NUM
ejpam-5386	130	22	2	2	NUM
ejpam-5386	130	23	∥∥∥∫	∥∥∥∫	NOUN
ejpam-5386	130	24	t	t	NOUN
ejpam-5386	130	25	0	0	NUM
ejpam-5386	130	26	ω1(t	ω1(t	NUM
ejpam-5386	130	27	)	)	PUNCT
ejpam-5386	130	28	c(α	c(α	PROPN
ejpam-5386	130	29	n	n	CCONJ
ejpam-5386	130	30	,	,	PUNCT
ejpam-5386	130	31	φn	φn	NOUN
ejpam-5386	130	32	)	)	PUNCT
ejpam-5386	130	33	dt−	dt−	PUNCT
ejpam-5386	130	34	ϕε1	ϕε1	X
ejpam-5386	130	35	∥∥∥2	∥∥∥2	X
ejpam-5386	130	36	l2(b	l2(b	NUM
ejpam-5386	130	37	)	)	PUNCT
ejpam-5386	131	1	+	+	CCONJ
ejpam-5386	131	2	1	1	NUM
ejpam-5386	131	3	2	2	NUM
ejpam-5386	131	4	∥∥∥∫	∥∥∥∫	NOUN
ejpam-5386	131	5	t	t	NOUN
ejpam-5386	131	6	0	0	NUM
ejpam-5386	131	7	ω2(t	ω2(t	NOUN
ejpam-5386	131	8	)	)	PUNCT
ejpam-5386	131	9	c(α	c(α	PROPN
ejpam-5386	131	10	n	n	CCONJ
ejpam-5386	131	11	,	,	PUNCT
ejpam-5386	131	12	φn	φn	NOUN
ejpam-5386	131	13	)	)	PUNCT
ejpam-5386	131	14	dt−	dt−	NUM
ejpam-5386	131	15	ϕε2	ϕε2	X
ejpam-5386	131	16	∥∥∥2	∥∥∥2	NOUN
ejpam-5386	131	17	l2(b	l2(b	NUM
ejpam-5386	131	18	)	)	PUNCT
ejpam-5386	131	19	≤	≤	NOUN
ejpam-5386	131	20	lim	lim	PROPN
ejpam-5386	131	21	inf	inf	PROPN
ejpam-5386	131	22	n→∞	n→∞	X
ejpam-5386	131	23	j	j	PROPN
ejpam-5386	131	24	(	(	PUNCT
ejpam-5386	131	25	αn	αn	NOUN
ejpam-5386	131	26	,	,	PUNCT
ejpam-5386	131	27	φn	φn	NOUN
ejpam-5386	131	28	)	)	PUNCT
ejpam-5386	131	29	=	=	SYM
ejpam-5386	131	30	inf	inf	PROPN
ejpam-5386	131	31	α∈aα	α∈aα	NOUN
ejpam-5386	131	32	φ∈aφ	φ∈aφ	PROPN
ejpam-5386	131	33	j(α	j(α	PROPN
ejpam-5386	131	34	,	,	PUNCT
ejpam-5386	131	35	φ	φ	NUM
ejpam-5386	131	36	)	)	PUNCT
ejpam-5386	131	37	.	.	PUNCT
ejpam-5386	132	1	hence	hence	ADV
ejpam-5386	132	2	,	,	PUNCT
ejpam-5386	132	3	the	the	DET
ejpam-5386	132	4	proof	proof	NOUN
ejpam-5386	132	5	is	be	AUX
ejpam-5386	132	6	complete	complete	ADJ
ejpam-5386	132	7	.	.	PUNCT
ejpam-5386	133	1	after	after	ADP
ejpam-5386	133	2	that	that	PRON
ejpam-5386	133	3	,	,	PUNCT
ejpam-5386	133	4	we	we	PRON
ejpam-5386	133	5	prove	prove	VERB
ejpam-5386	133	6	the	the	DET
ejpam-5386	133	7	stability	stability	NOUN
ejpam-5386	133	8	of	of	ADP
ejpam-5386	133	9	(	(	PUNCT
ejpam-5386	133	10	8)	8)	NUM
ejpam-5386	133	11	in	in	ADP
ejpam-5386	133	12	the	the	DET
ejpam-5386	133	13	sense	sense	NOUN
ejpam-5386	133	14	that	that	SCONJ
ejpam-5386	133	15	the	the	DET
ejpam-5386	133	16	minimization	minimization	NOUN
ejpam-5386	133	17	problem	problem	NOUN
ejpam-5386	133	18	(	(	PUNCT
ejpam-5386	133	19	8)	8)	NUM
ejpam-5386	133	20	effectively	effectively	ADV
ejpam-5386	133	21	stabilizes	stabilize	VERB
ejpam-5386	133	22	the	the	DET
ejpam-5386	133	23	considered	consider	VERB
ejpam-5386	133	24	inverse	inverse	ADJ
ejpam-5386	133	25	problem	problem	NOUN
ejpam-5386	133	26	against	against	ADP
ejpam-5386	133	27	perturbations	perturbation	NOUN
ejpam-5386	133	28	in	in	ADP
ejpam-5386	133	29	the	the	DET
ejpam-5386	133	30	measured	measure	VERB
ejpam-5386	133	31	data	datum	NOUN
ejpam-5386	133	32	.	.	PUNCT
ejpam-5386	134	1	for	for	ADP
ejpam-5386	134	2	this	this	DET
ejpam-5386	134	3	purpose	purpose	NOUN
ejpam-5386	134	4	,	,	PUNCT
ejpam-5386	134	5	let	let	VERB
ejpam-5386	134	6	{	{	PUNCT
ejpam-5386	134	7	ϕε1,ℓ	ϕε1,ℓ	VERB
ejpam-5386	134	8	,	,	PUNCT
ejpam-5386	134	9	ϕε2,ℓ}∞ℓ=0	ϕε2,ℓ}∞ℓ=0	PRON
ejpam-5386	134	10	denote	denote	VERB
ejpam-5386	134	11	a	a	DET
ejpam-5386	134	12	sequence	sequence	NOUN
ejpam-5386	134	13	of	of	ADP
ejpam-5386	134	14	measurements	measurement	NOUN
ejpam-5386	134	15	of	of	ADP
ejpam-5386	134	16	{	{	PUNCT
ejpam-5386	134	17	ϕε1	ϕε1	PROPN
ejpam-5386	134	18	,	,	PUNCT
ejpam-5386	134	19	ϕε2	ϕε2	PROPN
ejpam-5386	134	20	}	}	PUNCT
ejpam-5386	134	21	in	in	ADP
ejpam-5386	134	22	l2(b)×l2(b	l2(b)×l2(b	PROPN
ejpam-5386	134	23	)	)	PUNCT
ejpam-5386	134	24	.	.	PUNCT
ejpam-5386	135	1	for	for	ADP
ejpam-5386	135	2	each	each	DET
ejpam-5386	135	3	ℓ	ℓ	PROPN
ejpam-5386	135	4	∈	∈	PROPN
ejpam-5386	135	5	n	n	CCONJ
ejpam-5386	135	6	,	,	PUNCT
ejpam-5386	135	7	we	we	PRON
ejpam-5386	135	8	denote	denote	VERB
ejpam-5386	135	9	the	the	DET
ejpam-5386	135	10	solution	solution	NOUN
ejpam-5386	135	11	of	of	ADP
ejpam-5386	135	12	the	the	DET
ejpam-5386	135	13	minimization	minimization	NOUN
ejpam-5386	135	14	problem	problem	NOUN
ejpam-5386	135	15	by	by	ADP
ejpam-5386	135	16	(	(	PUNCT
ejpam-5386	135	17	αℓ,φℓ	αℓ,φℓ	PROPN
ejpam-5386	135	18	)	)	PUNCT
ejpam-5386	135	19	.	.	PUNCT
ejpam-5386	136	1	then	then	ADV
ejpam-5386	136	2	,	,	PUNCT
ejpam-5386	136	3	we	we	PRON
ejpam-5386	136	4	have	have	VERB
ejpam-5386	136	5	the	the	DET
ejpam-5386	136	6	following	follow	VERB
ejpam-5386	136	7	minimization	minimization	NOUN
ejpam-5386	136	8	problem	problem	NOUN
ejpam-5386	136	9	:	:	PUNCT
ejpam-5386	136	10	min	min	PROPN
ejpam-5386	136	11	α∈aα	α∈aα	PROPN
ejpam-5386	136	12	φ∈aφ	φ∈aφ	PROPN
ejpam-5386	136	13	jℓ(α	jℓ(α	NUM
ejpam-5386	136	14	,	,	PUNCT
ejpam-5386	136	15	φ	φ	NUM
ejpam-5386	136	16	)	)	PUNCT
ejpam-5386	136	17	,	,	PUNCT
ejpam-5386	136	18	jℓ(α	jℓ(α	PROPN
ejpam-5386	136	19	,	,	PUNCT
ejpam-5386	136	20	φ	φ	NUM
ejpam-5386	136	21	)	)	PUNCT
ejpam-5386	136	22	:	:	PUNCT
ejpam-5386	137	1	=	=	SYM
ejpam-5386	137	2	1	1	NUM
ejpam-5386	137	3	2	2	NUM
ejpam-5386	137	4	2∑	2∑	NOUN
ejpam-5386	137	5	k=1	k=1	PUNCT
ejpam-5386	138	1	∥∥∥∫	∥∥∥∫	VERB
ejpam-5386	138	2	t	t	PROPN
ejpam-5386	138	3	0	0	NUM
ejpam-5386	138	4	ωk(t	ωk(t	NOUN
ejpam-5386	138	5	)	)	PUNCT
ejpam-5386	138	6	c(α	c(α	PROPN
ejpam-5386	138	7	,	,	PUNCT
ejpam-5386	138	8	φ	φ	NUM
ejpam-5386	138	9	)	)	PUNCT
ejpam-5386	138	10	dt−	dt−	VERB
ejpam-5386	138	11	ϕεk,ℓ	ϕεk,ℓ	ADP
ejpam-5386	138	12	∥∥∥2	∥∥∥2	NOUN
ejpam-5386	138	13	l2(b	l2(b	NOUN
ejpam-5386	138	14	)	)	PUNCT
ejpam-5386	138	15	,	,	PUNCT
ejpam-5386	138	16	ℓ	ℓ	X
ejpam-5386	138	17	=	=	SYM
ejpam-5386	138	18	0	0	NUM
ejpam-5386	138	19	,	,	PUNCT
ejpam-5386	138	20	1	1	NUM
ejpam-5386	138	21	,	,	PUNCT
ejpam-5386	138	22	.	.	PUNCT
ejpam-5386	138	23	.	.	PUNCT
ejpam-5386	138	24	.	.	PUNCT
ejpam-5386	139	1	(	(	PUNCT
ejpam-5386	139	2	14	14	NUM
ejpam-5386	139	3	)	)	PUNCT
ejpam-5386	139	4	the	the	DET
ejpam-5386	139	5	following	follow	VERB
ejpam-5386	139	6	theorem	theorem	ADJ
ejpam-5386	139	7	states	state	NOUN
ejpam-5386	139	8	the	the	DET
ejpam-5386	139	9	convergence	convergence	NOUN
ejpam-5386	139	10	of	of	ADP
ejpam-5386	139	11	the	the	DET
ejpam-5386	139	12	sequence	sequence	NOUN
ejpam-5386	139	13	{	{	PUNCT
ejpam-5386	139	14	αℓ,φℓ}ℓ⩾0	αℓ,φℓ}ℓ⩾0	NOUN
ejpam-5386	139	15	when	when	SCONJ
ejpam-5386	139	16	ϕεk,ℓ	ϕεk,ℓ	DET
ejpam-5386	139	17	−→	−→	VERB
ejpam-5386	139	18	ϕεk	ϕεk	NOUN
ejpam-5386	139	19	in	in	ADP
ejpam-5386	139	20	l2(b	l2(b	NOUN
ejpam-5386	139	21	)	)	PUNCT
ejpam-5386	139	22	as	as	ADP
ejpam-5386	139	23	ℓ	ℓ	PROPN
ejpam-5386	139	24	−→	−→	NOUN
ejpam-5386	139	25	∞	∞	PROPN
ejpam-5386	139	26	,	,	PUNCT
ejpam-5386	139	27	for	for	ADP
ejpam-5386	139	28	k	k	PROPN
ejpam-5386	139	29	=	=	SYM
ejpam-5386	139	30	1	1	NUM
ejpam-5386	139	31	,	,	PUNCT
ejpam-5386	139	32	2	2	NUM
ejpam-5386	139	33	.	.	PUNCT
ejpam-5386	139	34	(	(	PUNCT
ejpam-5386	139	35	15	15	NUM
ejpam-5386	139	36	)	)	PUNCT
ejpam-5386	139	37	s.	s.	PROPN
ejpam-5386	139	38	tatar	tatar	PROPN
ejpam-5386	139	39	,	,	PUNCT
ejpam-5386	139	40	m.	m.	NOUN
ejpam-5386	139	41	bensalah	bensalah	PROPN
ejpam-5386	139	42	,	,	PUNCT
ejpam-5386	139	43	m.	m.	NOUN
ejpam-5386	139	44	alamil	alamil	PROPN
ejpam-5386	139	45	/	/	SYM
ejpam-5386	139	46	eur	eur	PROPN
ejpam-5386	139	47	.	.	PUNCT
ejpam-5386	140	1	j.	j.	PROPN
ejpam-5386	140	2	pure	pure	PROPN
ejpam-5386	140	3	appl	appl	PROPN
ejpam-5386	140	4	.	.	PROPN
ejpam-5386	140	5	math	math	PROPN
ejpam-5386	140	6	,	,	PUNCT
ejpam-5386	140	7	17	17	NUM
ejpam-5386	140	8	(	(	PUNCT
ejpam-5386	140	9	4	4	NUM
ejpam-5386	140	10	)	)	PUNCT
ejpam-5386	140	11	(	(	PUNCT
ejpam-5386	140	12	2024	2024	NUM
ejpam-5386	140	13	)	)	PUNCT
ejpam-5386	140	14	,	,	PUNCT
ejpam-5386	140	15	2651	2651	NUM
ejpam-5386	140	16	-	-	SYM
ejpam-5386	140	17	2675	2675	NUM
ejpam-5386	140	18	2658	2658	NUM
ejpam-5386	140	19	theorem	theorem	NOUN
ejpam-5386	140	20	2	2	NUM
ejpam-5386	140	21	.	.	PUNCT
ejpam-5386	141	1	if	if	SCONJ
ejpam-5386	141	2	(	(	PUNCT
ejpam-5386	141	3	15	15	NUM
ejpam-5386	141	4	)	)	PUNCT
ejpam-5386	141	5	holds	hold	VERB
ejpam-5386	141	6	,	,	PUNCT
ejpam-5386	141	7	then	then	ADV
ejpam-5386	141	8	the	the	DET
ejpam-5386	141	9	sequence	sequence	NOUN
ejpam-5386	141	10	{	{	PUNCT
ejpam-5386	141	11	αℓ,φℓ}ℓ⩾0	αℓ,φℓ}ℓ⩾0	PROPN
ejpam-5386	141	12	of	of	ADP
ejpam-5386	141	13	minimizers	minimizer	NOUN
ejpam-5386	141	14	of	of	ADP
ejpam-5386	141	15	the	the	DET
ejpam-5386	141	16	problems	problem	NOUN
ejpam-5386	141	17	(	(	PUNCT
ejpam-5386	141	18	14	14	NUM
ejpam-5386	141	19	)	)	PUNCT
ejpam-5386	141	20	converges	converge	VERB
ejpam-5386	141	21	weakly	weakly	ADJ
ejpam-5386	141	22	in	in	ADP
ejpam-5386	141	23	l∞(b)×l2(b	l∞(b)×l2(b	ADJ
ejpam-5386	141	24	)	)	PUNCT
ejpam-5386	141	25	to	to	ADP
ejpam-5386	141	26	a	a	DET
ejpam-5386	141	27	minimizer	minimizer	NOUN
ejpam-5386	141	28	,	,	PUNCT
ejpam-5386	141	29	associated	associate	VERB
ejpam-5386	141	30	with	with	ADP
ejpam-5386	141	31	the	the	DET
ejpam-5386	141	32	measured	measure	VERB
ejpam-5386	141	33	data	datum	NOUN
ejpam-5386	141	34	{	{	PUNCT
ejpam-5386	141	35	ϕε1	ϕε1	PROPN
ejpam-5386	141	36	,	,	PUNCT
ejpam-5386	141	37	ϕε2	ϕε2	PROPN
ejpam-5386	141	38	}	}	PUNCT
ejpam-5386	141	39	,	,	PUNCT
ejpam-5386	141	40	of	of	ADP
ejpam-5386	141	41	the	the	DET
ejpam-5386	141	42	optimization	optimization	NOUN
ejpam-5386	141	43	problem	problem	NOUN
ejpam-5386	141	44	(	(	PUNCT
ejpam-5386	141	45	8)	8)	NUM
ejpam-5386	141	46	.	.	PUNCT
ejpam-5386	142	1	proof	proof	NOUN
ejpam-5386	142	2	.	.	PUNCT
ejpam-5386	143	1	the	the	DET
ejpam-5386	143	2	existence	existence	NOUN
ejpam-5386	143	3	of	of	ADP
ejpam-5386	143	4	each	each	DET
ejpam-5386	143	5	pair	pair	NOUN
ejpam-5386	143	6	(	(	PUNCT
ejpam-5386	143	7	αℓ,φℓ	αℓ,φℓ	PROPN
ejpam-5386	143	8	)	)	PUNCT
ejpam-5386	143	9	is	be	AUX
ejpam-5386	143	10	guaranteed	guarantee	VERB
ejpam-5386	143	11	by	by	ADP
ejpam-5386	143	12	theorem	theorem	NOUN
ejpam-5386	143	13	1	1	NUM
ejpam-5386	143	14	.	.	PUNCT
ejpam-5386	143	15	by	by	ADP
ejpam-5386	143	16	definition	definition	NOUN
ejpam-5386	143	17	,	,	PUNCT
ejpam-5386	143	18	we	we	PRON
ejpam-5386	143	19	have	have	VERB
ejpam-5386	143	20	:	:	PUNCT
ejpam-5386	143	21	jℓ	jℓ	NOUN
ejpam-5386	143	22	(	(	PUNCT
ejpam-5386	143	23	αℓ,φℓ	αℓ,φℓ	NOUN
ejpam-5386	143	24	)	)	PUNCT
ejpam-5386	143	25	≤	≤	NOUN
ejpam-5386	143	26	jℓ(α	jℓ(α	PUNCT
ejpam-5386	143	27	,	,	PUNCT
ejpam-5386	143	28	φ	φ	NOUN
ejpam-5386	143	29	)	)	PUNCT
ejpam-5386	143	30	,	,	PUNCT
ejpam-5386	143	31	∀(α	∀(α	PROPN
ejpam-5386	143	32	,	,	PUNCT
ejpam-5386	143	33	φ	φ	NUM
ejpam-5386	143	34	)	)	PUNCT
ejpam-5386	143	35	∈	∈	PROPN
ejpam-5386	143	36	aα	aα	NOUN
ejpam-5386	143	37	×aφ	×aφ	PROPN
ejpam-5386	143	38	,	,	PUNCT
ejpam-5386	143	39	that	that	PRON
ejpam-5386	143	40	implies	imply	VERB
ejpam-5386	143	41	the	the	DET
ejpam-5386	143	42	uniform	uniform	ADJ
ejpam-5386	143	43	boundedness	boundedness	NOUN
ejpam-5386	143	44	of	of	ADP
ejpam-5386	143	45	(	(	PUNCT
ejpam-5386	143	46	αℓ,φℓ	αℓ,φℓ	PROPN
ejpam-5386	143	47	)	)	PUNCT
ejpam-5386	143	48	in	in	ADP
ejpam-5386	143	49	l	l	NOUN
ejpam-5386	143	50	∞(b)×l2(b	∞(b)×l2(b	PROPN
ejpam-5386	143	51	)	)	PUNCT
ejpam-5386	143	52	.	.	PUNCT
ejpam-5386	144	1	consequently	consequently	ADV
ejpam-5386	144	2	,	,	PUNCT
ejpam-5386	144	3	there	there	PRON
ejpam-5386	144	4	exist	exist	VERB
ejpam-5386	144	5	α⋆	α⋆	ADP
ejpam-5386	144	6	∈	∈	PROPN
ejpam-5386	144	7	l∞(b	l∞(b	NOUN
ejpam-5386	144	8	)	)	PUNCT
ejpam-5386	144	9	,	,	PUNCT
ejpam-5386	144	10	φ⋆	φ⋆	PUNCT
ejpam-5386	145	1	∈	∈	PROPN
ejpam-5386	145	2	l2(b	l2(b	NUM
ejpam-5386	145	3	)	)	PUNCT
ejpam-5386	145	4	,	,	PUNCT
ejpam-5386	145	5	and	and	CCONJ
ejpam-5386	145	6	a	a	DET
ejpam-5386	145	7	subsequence	subsequence	NOUN
ejpam-5386	145	8	(	(	PUNCT
ejpam-5386	145	9	still	still	ADV
ejpam-5386	145	10	denoted	denote	VERB
ejpam-5386	145	11	as	as	ADP
ejpam-5386	145	12	{	{	PUNCT
ejpam-5386	145	13	αℓ,φℓ}ℓ⩾0	αℓ,φℓ}ℓ⩾0	NOUN
ejpam-5386	145	14	)	)	PUNCT
ejpam-5386	145	15	,	,	PUNCT
ejpam-5386	145	16	such	such	ADJ
ejpam-5386	145	17	that	that	SCONJ
ejpam-5386	145	18	:	:	PUNCT
ejpam-5386	145	19	(	(	PUNCT
ejpam-5386	145	20	αℓ,φℓ	αℓ,φℓ	NOUN
ejpam-5386	145	21	)	)	PUNCT
ejpam-5386	145	22	⇀	⇀	PROPN
ejpam-5386	145	23	(	(	PUNCT
ejpam-5386	145	24	α⋆,φ⋆	α⋆,φ⋆	NOUN
ejpam-5386	145	25	)	)	PUNCT
ejpam-5386	145	26	in	in	ADP
ejpam-5386	145	27	l∞(b)×	l∞(b)×	NOUN
ejpam-5386	145	28	l2(b	l2(b	NUM
ejpam-5386	145	29	)	)	PUNCT
ejpam-5386	145	30	as	as	SCONJ
ejpam-5386	145	31	ℓ→	ℓ→	PROPN
ejpam-5386	145	32	∞.	∞.	PROPN
ejpam-5386	145	33	it	it	PRON
ejpam-5386	145	34	suffices	suffice	VERB
ejpam-5386	145	35	to	to	PART
ejpam-5386	145	36	show	show	VERB
ejpam-5386	145	37	that	that	SCONJ
ejpam-5386	145	38	(	(	PUNCT
ejpam-5386	145	39	α⋆,φ⋆	α⋆,φ⋆	NOUN
ejpam-5386	145	40	)	)	PUNCT
ejpam-5386	145	41	is	be	AUX
ejpam-5386	145	42	indeed	indeed	ADV
ejpam-5386	145	43	a	a	DET
ejpam-5386	145	44	minimizer	minimizer	NOUN
ejpam-5386	145	45	of	of	ADP
ejpam-5386	145	46	(	(	PUNCT
ejpam-5386	145	47	8)	8)	NUM
ejpam-5386	145	48	.	.	PUNCT
ejpam-5386	145	49	repeating	repeat	VERB
ejpam-5386	145	50	the	the	DET
ejpam-5386	145	51	same	same	ADJ
ejpam-5386	145	52	argument	argument	NOUN
ejpam-5386	145	53	as	as	SCONJ
ejpam-5386	145	54	that	that	PRON
ejpam-5386	145	55	in	in	ADP
ejpam-5386	145	56	the	the	DET
ejpam-5386	145	57	proof	proof	NOUN
ejpam-5386	145	58	of	of	ADP
ejpam-5386	145	59	theorem	theorem	NOUN
ejpam-5386	145	60	1	1	NUM
ejpam-5386	145	61	,	,	PUNCT
ejpam-5386	145	62	we	we	PRON
ejpam-5386	145	63	derive	derive	VERB
ejpam-5386	145	64	:	:	PUNCT
ejpam-5386	145	65	c	c	NOUN
ejpam-5386	145	66	(	(	PUNCT
ejpam-5386	145	67	αℓ,φℓ	αℓ,φℓ	NOUN
ejpam-5386	145	68	)	)	PUNCT
ejpam-5386	145	69	⇀	⇀	PROPN
ejpam-5386	145	70	c	c	NOUN
ejpam-5386	145	71	(	(	PUNCT
ejpam-5386	145	72	α⋆,φ⋆	α⋆,φ⋆	NOUN
ejpam-5386	145	73	)	)	PUNCT
ejpam-5386	145	74	in	in	ADP
ejpam-5386	145	75	l2	l2	NOUN
ejpam-5386	145	76	(	(	PUNCT
ejpam-5386	145	77	0	0	NUM
ejpam-5386	145	78	,	,	PUNCT
ejpam-5386	145	79	t	t	NOUN
ejpam-5386	145	80	;	;	PUNCT
ejpam-5386	145	81	h1(b	h1(b	NUM
ejpam-5386	145	82	)	)	PUNCT
ejpam-5386	145	83	)	)	PUNCT
ejpam-5386	145	84	as	as	ADP
ejpam-5386	145	85	ℓ→	ℓ→	PROPN
ejpam-5386	145	86	∞	∞	PROPN
ejpam-5386	145	87	,	,	PUNCT
ejpam-5386	145	88	up	up	ADP
ejpam-5386	145	89	to	to	ADP
ejpam-5386	145	90	taking	take	VERB
ejpam-5386	145	91	a	a	DET
ejpam-5386	145	92	further	further	ADJ
ejpam-5386	145	93	subsequence	subsequence	NOUN
ejpam-5386	145	94	.	.	PUNCT
ejpam-5386	146	1	combining	combine	VERB
ejpam-5386	146	2	this	this	DET
ejpam-5386	146	3	convergence	convergence	NOUN
ejpam-5386	146	4	with	with	ADP
ejpam-5386	146	5	(	(	PUNCT
ejpam-5386	146	6	15	15	NUM
ejpam-5386	146	7	)	)	PUNCT
ejpam-5386	146	8	,	,	PUNCT
ejpam-5386	146	9	we	we	PRON
ejpam-5386	146	10	obtain:∫	obtain:∫	VERB
ejpam-5386	146	11	t	t	PROPN
ejpam-5386	146	12	0	0	NUM
ejpam-5386	146	13	ωk(t	ωk(t	NOUN
ejpam-5386	146	14	)	)	PUNCT
ejpam-5386	146	15	c	c	NOUN
ejpam-5386	146	16	(	(	PUNCT
ejpam-5386	146	17	αℓ,φℓ)−ϕεk,ℓ	αℓ,φℓ)−ϕεk,ℓ	NUM
ejpam-5386	146	18	dt	dt	NOUN
ejpam-5386	147	1	⇀	⇀	PROPN
ejpam-5386	147	2	∫	∫	PROPN
ejpam-5386	147	3	t	t	NOUN
ejpam-5386	147	4	0	0	NUM
ejpam-5386	147	5	ωk(t	ωk(t	NOUN
ejpam-5386	147	6	)	)	PUNCT
ejpam-5386	147	7	c	c	NOUN
ejpam-5386	147	8	(	(	PUNCT
ejpam-5386	147	9	α	α	NOUN
ejpam-5386	147	10	⋆,φ⋆)−ϕεk	⋆,φ⋆)−ϕεk	NOUN
ejpam-5386	147	11	dt	dt	NOUN
ejpam-5386	147	12	in	in	ADP
ejpam-5386	147	13	l2(b	l2(b	NOUN
ejpam-5386	147	14	)	)	PUNCT
ejpam-5386	147	15	as	as	ADP
ejpam-5386	147	16	ℓ→	ℓ→	PROPN
ejpam-5386	147	17	∞	∞	PROPN
ejpam-5386	147	18	,	,	PUNCT
ejpam-5386	147	19	for	for	ADP
ejpam-5386	147	20	k	k	PROPN
ejpam-5386	147	21	=	=	SYM
ejpam-5386	147	22	1	1	NUM
ejpam-5386	147	23	,	,	PUNCT
ejpam-5386	147	24	2	2	NUM
ejpam-5386	147	25	.	.	X
ejpam-5386	148	1	therefore	therefore	ADV
ejpam-5386	148	2	,	,	PUNCT
ejpam-5386	148	3	for	for	ADP
ejpam-5386	148	4	k	k	PROPN
ejpam-5386	148	5	=	=	SYM
ejpam-5386	148	6	1	1	NUM
ejpam-5386	148	7	,	,	PUNCT
ejpam-5386	148	8	2	2	NUM
ejpam-5386	148	9	,	,	PUNCT
ejpam-5386	148	10	we	we	PRON
ejpam-5386	148	11	have:∥∥∥∫	have:∥∥∥∫	VERB
ejpam-5386	148	12	t	t	NOUN
ejpam-5386	148	13	0	0	NUM
ejpam-5386	148	14	ωk(t	ωk(t	NOUN
ejpam-5386	148	15	)	)	PUNCT
ejpam-5386	148	16	c(α	c(α	PROPN
ejpam-5386	148	17	⋆,φ⋆	⋆,φ⋆	X
ejpam-5386	148	18	)	)	PUNCT
ejpam-5386	148	19	dt−	dt−	NUM
ejpam-5386	148	20	ϕεk	ϕεk	NOUN
ejpam-5386	148	21	∥∥∥2	∥∥∥2	NOUN
ejpam-5386	148	22	l2(b	l2(b	NOUN
ejpam-5386	148	23	)	)	PUNCT
ejpam-5386	148	24	≤	≤	NOUN
ejpam-5386	148	25	lim	lim	PROPN
ejpam-5386	148	26	inf	inf	PROPN
ejpam-5386	148	27	ℓ→∞	ℓ→∞	NUM
ejpam-5386	148	28	∥∥∥∫	∥∥∥∫	PROPN
ejpam-5386	148	29	t	t	PROPN
ejpam-5386	148	30	0	0	NUM
ejpam-5386	148	31	ωk(t	ωk(t	NOUN
ejpam-5386	148	32	)	)	PUNCT
ejpam-5386	148	33	c(αℓ,φℓ	c(αℓ,φℓ	NOUN
ejpam-5386	148	34	)	)	PUNCT
ejpam-5386	148	35	dt−	dt−	NUM
ejpam-5386	148	36	ϕεk,ℓ	ϕεk,ℓ	ADP
ejpam-5386	148	37	∥∥∥2	∥∥∥2	NOUN
ejpam-5386	148	38	l2(b	l2(b	NUM
ejpam-5386	148	39	)	)	PUNCT
ejpam-5386	148	40	.	.	PUNCT
ejpam-5386	149	1	by	by	ADP
ejpam-5386	149	2	using	use	VERB
ejpam-5386	149	3	the	the	DET
ejpam-5386	149	4	lower	low	ADJ
ejpam-5386	149	5	semi	semi	NOUN
ejpam-5386	149	6	-	-	NOUN
ejpam-5386	149	7	continuity	continuity	NOUN
ejpam-5386	149	8	of	of	ADP
ejpam-5386	149	9	the	the	DET
ejpam-5386	149	10	l2	l2	NOUN
ejpam-5386	149	11	-	-	PUNCT
ejpam-5386	149	12	norm	norm	NOUN
ejpam-5386	149	13	,	,	PUNCT
ejpam-5386	149	14	we	we	PRON
ejpam-5386	149	15	deduce	deduce	VERB
ejpam-5386	149	16	that	that	SCONJ
ejpam-5386	149	17	:	:	PUNCT
ejpam-5386	149	18	j	j	PROPN
ejpam-5386	149	19	(	(	PUNCT
ejpam-5386	149	20	α⋆,φ⋆	α⋆,φ⋆	PROPN
ejpam-5386	149	21	)	)	PUNCT
ejpam-5386	149	22	=	=	SYM
ejpam-5386	149	23	1	1	NUM
ejpam-5386	149	24	2	2	NUM
ejpam-5386	149	25	2∑	2∑	NOUN
ejpam-5386	149	26	k=1	k=1	PUNCT
ejpam-5386	150	1	∥∥∥∫	∥∥∥∫	VERB
ejpam-5386	150	2	t	t	PROPN
ejpam-5386	150	3	0	0	NUM
ejpam-5386	150	4	ωk(t	ωk(t	NOUN
ejpam-5386	150	5	)	)	PUNCT
ejpam-5386	150	6	c(α	c(α	PROPN
ejpam-5386	150	7	⋆,φ⋆	⋆,φ⋆	X
ejpam-5386	150	8	)	)	PUNCT
ejpam-5386	150	9	dt−	dt−	NUM
ejpam-5386	151	1	ϕεk	ϕεk	NOUN
ejpam-5386	151	2	∥∥∥2	∥∥∥2	NOUN
ejpam-5386	151	3	l2(b	l2(b	NOUN
ejpam-5386	151	4	)	)	PUNCT
ejpam-5386	151	5	≤	≤	NUM
ejpam-5386	151	6	1	1	NUM
ejpam-5386	151	7	2	2	NUM
ejpam-5386	151	8	lim	lim	PROPN
ejpam-5386	151	9	inf	inf	PROPN
ejpam-5386	151	10	ℓ→∞	ℓ→∞	NUM
ejpam-5386	151	11	2∑	2∑	NOUN
ejpam-5386	151	12	k=1	k=1	PUNCT
ejpam-5386	152	1	∥∥∥∫	∥∥∥∫	PROPN
ejpam-5386	152	2	t	t	PROPN
ejpam-5386	152	3	0	0	NUM
ejpam-5386	152	4	ωk(t	ωk(t	NOUN
ejpam-5386	152	5	)	)	PUNCT
ejpam-5386	152	6	c(αℓ,φℓ	c(αℓ,φℓ	NOUN
ejpam-5386	152	7	)	)	PUNCT
ejpam-5386	152	8	dt−	dt−	NUM
ejpam-5386	152	9	ϕεk,ℓ	ϕεk,ℓ	ADP
ejpam-5386	152	10	∥∥∥2	∥∥∥2	NOUN
ejpam-5386	152	11	l2(b	l2(b	NOUN
ejpam-5386	152	12	)	)	PUNCT
ejpam-5386	153	1	≤	≤	NUM
ejpam-5386	153	2	1	1	NUM
ejpam-5386	153	3	2	2	NUM
ejpam-5386	153	4	lim	lim	NOUN
ejpam-5386	153	5	ℓ→∞	ℓ→∞	NUM
ejpam-5386	153	6	2∑	2∑	NOUN
ejpam-5386	153	7	k=1	k=1	PUNCT
ejpam-5386	154	1	∥∥∥∫	∥∥∥∫	PROPN
ejpam-5386	154	2	t	t	PROPN
ejpam-5386	154	3	0	0	NUM
ejpam-5386	154	4	ωk(t	ωk(t	NOUN
ejpam-5386	154	5	)	)	PUNCT
ejpam-5386	154	6	c(α	c(α	PROPN
ejpam-5386	154	7	,	,	PUNCT
ejpam-5386	154	8	φ	φ	NUM
ejpam-5386	154	9	)	)	PUNCT
ejpam-5386	154	10	dt−	dt−	VERB
ejpam-5386	154	11	ϕεk,ℓ	ϕεk,ℓ	ADP
ejpam-5386	154	12	∥∥∥2	∥∥∥2	NOUN
ejpam-5386	154	13	l2(b	l2(b	NOUN
ejpam-5386	154	14	)	)	PUNCT
ejpam-5386	154	15	=	=	SYM
ejpam-5386	154	16	1	1	NUM
ejpam-5386	154	17	2	2	NUM
ejpam-5386	154	18	2∑	2∑	NOUN
ejpam-5386	154	19	k=1	k=1	PUNCT
ejpam-5386	155	1	∥∥∥∫	∥∥∥∫	VERB
ejpam-5386	155	2	t	t	PROPN
ejpam-5386	155	3	0	0	NUM
ejpam-5386	155	4	ωk(t	ωk(t	NOUN
ejpam-5386	155	5	)	)	PUNCT
ejpam-5386	155	6	c(α	c(α	PROPN
ejpam-5386	155	7	,	,	PUNCT
ejpam-5386	155	8	φ	φ	NUM
ejpam-5386	155	9	)	)	PUNCT
ejpam-5386	155	10	dt−	dt−	NUM
ejpam-5386	155	11	ϕεk	ϕεk	NOUN
ejpam-5386	155	12	∥∥∥2	∥∥∥2	NOUN
ejpam-5386	155	13	l2(b	l2(b	NUM
ejpam-5386	155	14	)	)	PUNCT
ejpam-5386	155	15	=	=	PUNCT
ejpam-5386	155	16	j(α	j(α	PROPN
ejpam-5386	155	17	,	,	PUNCT
ejpam-5386	155	18	φ	φ	NOUN
ejpam-5386	155	19	)	)	PUNCT
ejpam-5386	155	20	,	,	PUNCT
ejpam-5386	155	21	∀(α	∀(α	PROPN
ejpam-5386	155	22	,	,	PUNCT
ejpam-5386	155	23	φ	φ	NUM
ejpam-5386	155	24	)	)	PUNCT
ejpam-5386	155	25	∈	∈	PROPN
ejpam-5386	155	26	aα	aα	NOUN
ejpam-5386	155	27	×aφ	×aφ	PROPN
ejpam-5386	155	28	.	.	PUNCT
ejpam-5386	156	1	thus	thus	ADV
ejpam-5386	156	2	,	,	PUNCT
ejpam-5386	156	3	the	the	DET
ejpam-5386	156	4	proof	proof	NOUN
ejpam-5386	156	5	is	be	AUX
ejpam-5386	156	6	complete	complete	ADJ
ejpam-5386	156	7	.	.	PUNCT
ejpam-5386	157	1	s.	s.	PROPN
ejpam-5386	157	2	tatar	tatar	PROPN
ejpam-5386	157	3	,	,	PUNCT
ejpam-5386	157	4	m.	m.	NOUN
ejpam-5386	157	5	bensalah	bensalah	PROPN
ejpam-5386	157	6	,	,	PUNCT
ejpam-5386	157	7	m.	m.	NOUN
ejpam-5386	157	8	alamil	alamil	PROPN
ejpam-5386	157	9	/	/	SYM
ejpam-5386	157	10	eur	eur	PROPN
ejpam-5386	157	11	.	.	PUNCT
ejpam-5386	158	1	j.	j.	PROPN
ejpam-5386	158	2	pure	pure	PROPN
ejpam-5386	158	3	appl	appl	PROPN
ejpam-5386	158	4	.	.	PROPN
ejpam-5386	158	5	math	math	PROPN
ejpam-5386	158	6	,	,	PUNCT
ejpam-5386	158	7	17	17	NUM
ejpam-5386	158	8	(	(	PUNCT
ejpam-5386	158	9	4	4	NUM
ejpam-5386	158	10	)	)	PUNCT
ejpam-5386	158	11	(	(	PUNCT
ejpam-5386	158	12	2024	2024	NUM
ejpam-5386	158	13	)	)	PUNCT
ejpam-5386	158	14	,	,	PUNCT
ejpam-5386	158	15	2651	2651	NUM
ejpam-5386	158	16	-	-	SYM
ejpam-5386	158	17	2675	2675	NUM
ejpam-5386	158	18	2659	2659	NUM
ejpam-5386	158	19	3	3	NUM
ejpam-5386	158	20	.	.	NOUN
ejpam-5386	158	21	conjugate	conjugate	ADJ
ejpam-5386	158	22	gradient	gradient	ADJ
ejpam-5386	158	23	method	method	NOUN
ejpam-5386	158	24	in	in	ADP
ejpam-5386	158	25	this	this	DET
ejpam-5386	158	26	section	section	NOUN
ejpam-5386	158	27	,	,	PUNCT
ejpam-5386	158	28	we	we	PRON
ejpam-5386	158	29	develop	develop	VERB
ejpam-5386	158	30	an	an	DET
ejpam-5386	158	31	efficient	efficient	ADJ
ejpam-5386	158	32	iterative	iterative	NOUN
ejpam-5386	158	33	procedure	procedure	NOUN
ejpam-5386	158	34	based	base	VERB
ejpam-5386	158	35	on	on	ADP
ejpam-5386	158	36	the	the	DET
ejpam-5386	158	37	conjugate	conjugate	ADJ
ejpam-5386	158	38	gradient	gradient	NOUN
ejpam-5386	158	39	method	method	NOUN
ejpam-5386	158	40	to	to	PART
ejpam-5386	158	41	solve	solve	VERB
ejpam-5386	158	42	the	the	DET
ejpam-5386	158	43	minimization	minimization	NOUN
ejpam-5386	158	44	problem	problem	NOUN
ejpam-5386	158	45	(	(	PUNCT
ejpam-5386	158	46	8)	8)	NUM
ejpam-5386	158	47	.	.	PUNCT
ejpam-5386	159	1	like	like	ADP
ejpam-5386	159	2	all	all	DET
ejpam-5386	159	3	effective	effective	ADJ
ejpam-5386	159	4	iterative	iterative	NOUN
ejpam-5386	159	5	methods	method	NOUN
ejpam-5386	159	6	for	for	ADP
ejpam-5386	159	7	optimization	optimization	NOUN
ejpam-5386	159	8	problems	problem	NOUN
ejpam-5386	159	9	,	,	PUNCT
ejpam-5386	159	10	our	our	PRON
ejpam-5386	159	11	approach	approach	NOUN
ejpam-5386	159	12	requires	require	VERB
ejpam-5386	159	13	information	information	NOUN
ejpam-5386	159	14	about	about	ADP
ejpam-5386	159	15	the	the	DET
ejpam-5386	159	16	derivatives	derivative	NOUN
ejpam-5386	159	17	of	of	ADP
ejpam-5386	159	18	the	the	DET
ejpam-5386	159	19	objective	objective	ADJ
ejpam-5386	159	20	function	function	NOUN
ejpam-5386	159	21	.	.	PUNCT
ejpam-5386	160	1	we	we	PRON
ejpam-5386	160	2	start	start	VERB
ejpam-5386	160	3	by	by	ADP
ejpam-5386	160	4	deriving	derive	VERB
ejpam-5386	160	5	the	the	DET
ejpam-5386	160	6	fréchet	fréchet	NOUN
ejpam-5386	160	7	derivatives	derivative	NOUN
ejpam-5386	160	8	j	j	PROPN
ejpam-5386	160	9	′	′	NUM
ejpam-5386	160	10	α(α	α(α	PROPN
ejpam-5386	160	11	,	,	PUNCT
ejpam-5386	160	12	φ	φ	NUM
ejpam-5386	160	13	)	)	PUNCT
ejpam-5386	160	14	and	and	CCONJ
ejpam-5386	160	15	j	j	PROPN
ejpam-5386	160	16	′	′	PROPN
ejpam-5386	160	17	φ(α	φ(α	PROPN
ejpam-5386	160	18	,	,	PUNCT
ejpam-5386	160	19	φ	φ	NUM
ejpam-5386	160	20	)	)	PUNCT
ejpam-5386	160	21	of	of	ADP
ejpam-5386	160	22	the	the	DET
ejpam-5386	160	23	objective	objective	ADJ
ejpam-5386	160	24	functional	functional	ADJ
ejpam-5386	160	25	j(α	j(α	PROPN
ejpam-5386	160	26	,	,	PUNCT
ejpam-5386	160	27	φ	φ	NUM
ejpam-5386	160	28	)	)	PUNCT
ejpam-5386	160	29	with	with	ADP
ejpam-5386	160	30	respect	respect	NOUN
ejpam-5386	160	31	to	to	ADP
ejpam-5386	160	32	the	the	DET
ejpam-5386	160	33	unknown	unknown	ADJ
ejpam-5386	160	34	terms	term	NOUN
ejpam-5386	160	35	α	α	PRON
ejpam-5386	160	36	and	and	CCONJ
ejpam-5386	160	37	φ	φ	NUM
ejpam-5386	160	38	,	,	PUNCT
ejpam-5386	160	39	respectively	respectively	ADV
ejpam-5386	160	40	.	.	PUNCT
ejpam-5386	161	1	subsequently	subsequently	ADV
ejpam-5386	161	2	,	,	PUNCT
ejpam-5386	161	3	we	we	PRON
ejpam-5386	161	4	establish	establish	VERB
ejpam-5386	161	5	the	the	DET
ejpam-5386	161	6	conjugate	conjugate	ADJ
ejpam-5386	161	7	gradient	gradient	NOUN
ejpam-5386	161	8	method	method	NOUN
ejpam-5386	161	9	,	,	PUNCT
ejpam-5386	161	10	which	which	PRON
ejpam-5386	161	11	utilizes	utilize	VERB
ejpam-5386	161	12	these	these	DET
ejpam-5386	161	13	gradients	gradient	NOUN
ejpam-5386	161	14	to	to	PART
ejpam-5386	161	15	reconstruct	reconstruct	VERB
ejpam-5386	161	16	the	the	DET
ejpam-5386	161	17	unknown	unknown	ADJ
ejpam-5386	161	18	coefficients	coefficient	NOUN
ejpam-5386	161	19	simultaneously	simultaneously	ADV
ejpam-5386	161	20	.	.	PUNCT
ejpam-5386	162	1	we	we	PRON
ejpam-5386	162	2	refer	refer	VERB
ejpam-5386	162	3	the	the	DET
ejpam-5386	162	4	readers	reader	NOUN
ejpam-5386	162	5	to	to	ADP
ejpam-5386	162	6	[	[	X
ejpam-5386	162	7	13	13	NUM
ejpam-5386	162	8	]	]	PUNCT
ejpam-5386	162	9	for	for	ADP
ejpam-5386	162	10	convergence	convergence	NOUN
ejpam-5386	162	11	of	of	ADP
ejpam-5386	162	12	this	this	DET
ejpam-5386	162	13	algorithm	algorithm	NOUN
ejpam-5386	162	14	.	.	PUNCT
ejpam-5386	163	1	3.1	3.1	NUM
ejpam-5386	163	2	.	.	PUNCT
ejpam-5386	163	3	fréchet	fréchet	VERB
ejpam-5386	163	4	derivatives	derivative	NOUN
ejpam-5386	163	5	following	follow	VERB
ejpam-5386	163	6	the	the	DET
ejpam-5386	163	7	methodology	methodology	NOUN
ejpam-5386	163	8	in	in	ADP
ejpam-5386	163	9	[	[	X
ejpam-5386	163	10	3	3	NUM
ejpam-5386	163	11	,	,	PUNCT
ejpam-5386	163	12	4	4	NUM
ejpam-5386	163	13	,	,	PUNCT
ejpam-5386	163	14	17	17	NUM
ejpam-5386	163	15	]	]	PUNCT
ejpam-5386	163	16	,	,	PUNCT
ejpam-5386	163	17	we	we	PRON
ejpam-5386	163	18	can	can	AUX
ejpam-5386	163	19	reduce	reduce	VERB
ejpam-5386	163	20	the	the	DET
ejpam-5386	163	21	computational	computational	ADJ
ejpam-5386	163	22	costs	cost	NOUN
ejpam-5386	163	23	for	for	ADP
ejpam-5386	163	24	the	the	DET
ejpam-5386	163	25	fréchet	fréchet	NOUN
ejpam-5386	163	26	derivatives	derivative	NOUN
ejpam-5386	163	27	by	by	ADP
ejpam-5386	163	28	introducing	introduce	VERB
ejpam-5386	163	29	the	the	DET
ejpam-5386	163	30	adjoint	adjoint	NOUN
ejpam-5386	163	31	system	system	NOUN
ejpam-5386	163	32	of	of	ADP
ejpam-5386	163	33	(	(	PUNCT
ejpam-5386	163	34	5	5	NUM
ejpam-5386	163	35	)	)	PUNCT
ejpam-5386	163	36	,	,	PUNCT
ejpam-5386	163	37	which	which	PRON
ejpam-5386	163	38	represents	represent	VERB
ejpam-5386	163	39	a	a	DET
ejpam-5386	163	40	backward	backward	ADJ
ejpam-5386	163	41	time	time	NOUN
ejpam-5386	163	42	diffusion	diffusion	NOUN
ejpam-5386	163	43	equation:	equation:	NOUN
ejpam-5386	163	44	−∂tv	−∂tv	NOUN
ejpam-5386	163	45	−	−	NOUN
ejpam-5386	163	46	div(d(x)∇v	div(d(x)∇v	NUM
ejpam-5386	163	47	)	)	PUNCT
ejpam-5386	164	1	+	+	CCONJ
ejpam-5386	164	2	(	(	PUNCT
ejpam-5386	164	3	α(x)β(t)−	α(x)β(t)−	PROPN
ejpam-5386	164	4	g′c(α	g′c(α	PROPN
ejpam-5386	164	5	,	,	PUNCT
ejpam-5386	164	6	φ	φ	NOUN
ejpam-5386	164	7	)	)	PUNCT
ejpam-5386	164	8	)	)	PUNCT
ejpam-5386	165	1	v	v	NOUN
ejpam-5386	165	2	=	=	SYM
ejpam-5386	165	3	2∑	2∑	NOUN
ejpam-5386	165	4	k=1	k=1	NOUN
ejpam-5386	165	5	ωk(t	ωk(t	NOUN
ejpam-5386	165	6	)	)	PUNCT
ejpam-5386	165	7	(	(	PUNCT
ejpam-5386	165	8	∫	∫	PROPN
ejpam-5386	165	9	t	t	PROPN
ejpam-5386	165	10	0	0	NUM
ejpam-5386	165	11	ωk(τ	ωk(τ	NUM
ejpam-5386	165	12	)	)	PUNCT
ejpam-5386	165	13	c(α	c(α	PROPN
ejpam-5386	165	14	,	,	PUNCT
ejpam-5386	165	15	φ	φ	NOUN
ejpam-5386	165	16	)	)	PUNCT
ejpam-5386	165	17	dτ	dτ	NOUN
ejpam-5386	165	18	−	−	PROPN
ejpam-5386	165	19	ϕεk	ϕεk	NOUN
ejpam-5386	165	20	)	)	PUNCT
ejpam-5386	165	21	in	in	ADP
ejpam-5386	165	22	q	q	NOUN
ejpam-5386	165	23	,	,	PUNCT
ejpam-5386	165	24	d(x	d(x	PROPN
ejpam-5386	165	25	)	)	PUNCT
ejpam-5386	165	26	∂νv	∂νv	NOUN
ejpam-5386	165	27	=	=	NOUN
ejpam-5386	165	28	0	0	NUM
ejpam-5386	165	29	on	on	ADP
ejpam-5386	165	30	bt	bt	PRON
ejpam-5386	165	31	,	,	PUNCT
ejpam-5386	165	32	v(x	v(x	PROPN
ejpam-5386	165	33	,	,	PUNCT
ejpam-5386	165	34	t	t	NOUN
ejpam-5386	165	35	)	)	PUNCT
ejpam-5386	166	1	=	=	SYM
ejpam-5386	166	2	0	0	NUM
ejpam-5386	167	1	in	in	ADP
ejpam-5386	167	2	b	b	PROPN
ejpam-5386	167	3	,	,	PUNCT
ejpam-5386	167	4	(	(	PUNCT
ejpam-5386	167	5	16	16	NUM
ejpam-5386	167	6	)	)	PUNCT
ejpam-5386	167	7	where	where	SCONJ
ejpam-5386	167	8	g′c(α	g′c(α	NOUN
ejpam-5386	167	9	,	,	PUNCT
ejpam-5386	167	10	φ	φ	NUM
ejpam-5386	167	11	)	)	PUNCT
ejpam-5386	167	12	represents	represent	VERB
ejpam-5386	167	13	the	the	DET
ejpam-5386	167	14	fréchet	fréchet	NOUN
ejpam-5386	167	15	derivative	derivative	NOUN
ejpam-5386	167	16	of	of	ADP
ejpam-5386	167	17	g	g	PROPN
ejpam-5386	167	18	at	at	ADP
ejpam-5386	167	19	c(α	c(α	PROPN
ejpam-5386	167	20	,	,	PUNCT
ejpam-5386	167	21	φ	φ	NOUN
ejpam-5386	167	22	)	)	PUNCT
ejpam-5386	167	23	.	.	PUNCT
ejpam-5386	168	1	the	the	DET
ejpam-5386	168	2	system	system	NOUN
ejpam-5386	168	3	(	(	PUNCT
ejpam-5386	168	4	16	16	NUM
ejpam-5386	168	5	)	)	PUNCT
ejpam-5386	168	6	is	be	AUX
ejpam-5386	168	7	linear	linear	ADJ
ejpam-5386	168	8	and	and	CCONJ
ejpam-5386	168	9	it	it	PRON
ejpam-5386	168	10	is	be	AUX
ejpam-5386	168	11	a	a	DET
ejpam-5386	168	12	well	well	ADV
ejpam-5386	168	13	-	-	PUNCT
ejpam-5386	168	14	posed	pose	VERB
ejpam-5386	168	15	problem	problem	NOUN
ejpam-5386	168	16	,	,	PUNCT
ejpam-5386	168	17	see	see	VERB
ejpam-5386	168	18	[	[	X
ejpam-5386	168	19	6	6	NUM
ejpam-5386	168	20	]	]	PUNCT
ejpam-5386	168	21	.	.	PUNCT
ejpam-5386	169	1	for	for	ADP
ejpam-5386	169	2	simplicity	simplicity	NOUN
ejpam-5386	169	3	,	,	PUNCT
ejpam-5386	169	4	we	we	PRON
ejpam-5386	169	5	denote	denote	VERB
ejpam-5386	169	6	c(α	c(α	PROPN
ejpam-5386	169	7	,	,	PUNCT
ejpam-5386	169	8	φ	φ	NUM
ejpam-5386	169	9	)	)	PUNCT
ejpam-5386	169	10	by	by	ADP
ejpam-5386	169	11	c.	c.	PROPN
ejpam-5386	169	12	theorem	theorem	PROPN
ejpam-5386	169	13	3	3	X
ejpam-5386	169	14	.	.	PUNCT
ejpam-5386	170	1	the	the	DET
ejpam-5386	170	2	objective	objective	ADJ
ejpam-5386	170	3	functional	functional	ADJ
ejpam-5386	170	4	j(α	j(α	PROPN
ejpam-5386	170	5	,	,	PUNCT
ejpam-5386	170	6	φ	φ	NUM
ejpam-5386	170	7	)	)	PUNCT
ejpam-5386	170	8	is	be	AUX
ejpam-5386	170	9	fréchet	fréchet	VERB
ejpam-5386	170	10	differentiable	differentiable	ADJ
ejpam-5386	170	11	and	and	CCONJ
ejpam-5386	170	12	the	the	DET
ejpam-5386	170	13	derivatives	derivative	NOUN
ejpam-5386	170	14	j	j	PROPN
ejpam-5386	170	15	′	′	NUM
ejpam-5386	170	16	α(α	α(α	PROPN
ejpam-5386	170	17	,	,	PUNCT
ejpam-5386	170	18	φ	φ	NUM
ejpam-5386	170	19	)	)	PUNCT
ejpam-5386	170	20	and	and	CCONJ
ejpam-5386	170	21	j	j	PROPN
ejpam-5386	170	22	′	′	PROPN
ejpam-5386	170	23	φ(α	φ(α	PROPN
ejpam-5386	170	24	,	,	PUNCT
ejpam-5386	170	25	φ	φ	NUM
ejpam-5386	170	26	)	)	PUNCT
ejpam-5386	170	27	at	at	ADP
ejpam-5386	170	28	(	(	PUNCT
ejpam-5386	170	29	α	α	X
ejpam-5386	170	30	,	,	PUNCT
ejpam-5386	170	31	φ	φ	NOUN
ejpam-5386	170	32	)	)	PUNCT
ejpam-5386	170	33	∈	∈	PROPN
ejpam-5386	170	34	aα	aα	NOUN
ejpam-5386	170	35	×aφ	×aφ	NOUN
ejpam-5386	170	36	are	be	AUX
ejpam-5386	170	37	given	give	VERB
ejpam-5386	170	38	by:j	by:j	PROPN
ejpam-5386	170	39	′	′	NUM
ejpam-5386	171	1	α(α	α(α	PROPN
ejpam-5386	171	2	,	,	PUNCT
ejpam-5386	171	3	φ	φ	NUM
ejpam-5386	171	4	)	)	PUNCT
ejpam-5386	171	5	=	=	PUNCT
ejpam-5386	172	1	−	−	PROPN
ejpam-5386	172	2	∫	∫	PROPN
ejpam-5386	172	3	t	t	PROPN
ejpam-5386	172	4	0	0	NUM
ejpam-5386	172	5	β(t	β(t	PROPN
ejpam-5386	172	6	)	)	PUNCT
ejpam-5386	172	7	c(x	c(x	PROPN
ejpam-5386	172	8	,	,	PUNCT
ejpam-5386	172	9	t	t	PROPN
ejpam-5386	172	10	)	)	PUNCT
ejpam-5386	172	11	v(x	v(x	PROPN
ejpam-5386	172	12	,	,	PUNCT
ejpam-5386	172	13	t	t	PROPN
ejpam-5386	172	14	)	)	PUNCT
ejpam-5386	172	15	dt	dt	PROPN
ejpam-5386	172	16	,	,	PUNCT
ejpam-5386	172	17	j	j	PROPN
ejpam-5386	172	18	′	′	PROPN
ejpam-5386	172	19	φ(α	φ(α	PROPN
ejpam-5386	172	20	,	,	PUNCT
ejpam-5386	172	21	φ	φ	NUM
ejpam-5386	172	22	)	)	PUNCT
ejpam-5386	172	23	=	=	SYM
ejpam-5386	173	1	v(x	v(x	PROPN
ejpam-5386	173	2	,	,	PUNCT
ejpam-5386	173	3	0	0	NUM
ejpam-5386	173	4	)	)	PUNCT
ejpam-5386	173	5	,	,	PUNCT
ejpam-5386	173	6	(	(	PUNCT
ejpam-5386	173	7	17	17	NUM
ejpam-5386	173	8	)	)	PUNCT
ejpam-5386	173	9	where	where	SCONJ
ejpam-5386	173	10	v	v	NOUN
ejpam-5386	173	11	is	be	AUX
ejpam-5386	173	12	the	the	DET
ejpam-5386	173	13	solution	solution	NOUN
ejpam-5386	173	14	to	to	ADP
ejpam-5386	173	15	the	the	DET
ejpam-5386	173	16	adjoint	adjoint	NOUN
ejpam-5386	173	17	problem	problem	NOUN
ejpam-5386	173	18	(	(	PUNCT
ejpam-5386	173	19	16	16	NUM
ejpam-5386	173	20	)	)	PUNCT
ejpam-5386	173	21	.	.	PUNCT
ejpam-5386	174	1	we	we	PRON
ejpam-5386	174	2	need	need	VERB
ejpam-5386	174	3	the	the	DET
ejpam-5386	174	4	following	follow	VERB
ejpam-5386	174	5	two	two	NUM
ejpam-5386	174	6	sensitivity	sensitivity	NOUN
ejpam-5386	174	7	problems	problem	NOUN
ejpam-5386	174	8	to	to	PART
ejpam-5386	174	9	prove	prove	VERB
ejpam-5386	174	10	theorem	theorem	ADJ
ejpam-5386	174	11	3	3	NUM
ejpam-5386	174	12	.	.	NOUN
ejpam-5386	174	13	sensitivity	sensitivity	NOUN
ejpam-5386	174	14	problem	problem	NOUN
ejpam-5386	174	15	associated	associate	VERB
ejpam-5386	174	16	with	with	ADP
ejpam-5386	174	17	the	the	DET
ejpam-5386	174	18	treatment	treatment	NOUN
ejpam-5386	174	19	parameter	parameter	NOUN
ejpam-5386	174	20	.	.	PUNCT
ejpam-5386	175	1	assume	assume	VERB
ejpam-5386	175	2	c(x	c(x	PROPN
ejpam-5386	175	3	,	,	PUNCT
ejpam-5386	175	4	t	t	PROPN
ejpam-5386	175	5	)	)	PUNCT
ejpam-5386	175	6	is	be	AUX
ejpam-5386	175	7	perturbed	perturb	VERB
ejpam-5386	175	8	by	by	ADP
ejpam-5386	175	9	ϵ	ϵ	NOUN
ejpam-5386	175	10	ηα(x	ηα(x	PROPN
ejpam-5386	175	11	,	,	PUNCT
ejpam-5386	175	12	t	t	PROPN
ejpam-5386	175	13	)	)	PUNCT
ejpam-5386	175	14	and	and	CCONJ
ejpam-5386	175	15	the	the	DET
ejpam-5386	175	16	therapy	therapy	NOUN
ejpam-5386	175	17	parameter	parameter	PROPN
ejpam-5386	175	18	α(x	α(x	PROPN
ejpam-5386	175	19	)	)	PUNCT
ejpam-5386	175	20	is	be	AUX
ejpam-5386	175	21	perturbed	perturb	VERB
ejpam-5386	175	22	by	by	ADP
ejpam-5386	175	23	ϵα0(x	ϵα0(x	PROPN
ejpam-5386	175	24	)	)	PUNCT
ejpam-5386	175	25	,	,	PUNCT
ejpam-5386	175	26	where	where	SCONJ
ejpam-5386	175	27	ϵ	ϵ	X
ejpam-5386	175	28	>	>	X
ejpam-5386	175	29	0	0	NUM
ejpam-5386	175	30	is	be	AUX
ejpam-5386	175	31	a	a	DET
ejpam-5386	175	32	small	small	ADJ
ejpam-5386	175	33	number	number	NOUN
ejpam-5386	175	34	and	and	CCONJ
ejpam-5386	175	35	α0	α0	PROPN
ejpam-5386	175	36	∈	∈	PROPN
ejpam-5386	175	37	aα	aα	NOUN
ejpam-5386	175	38	.	.	PUNCT
ejpam-5386	176	1	substituting	substitute	VERB
ejpam-5386	176	2	the	the	DET
ejpam-5386	176	3	perturbed	perturb	VERB
ejpam-5386	176	4	cell	cell	NOUN
ejpam-5386	176	5	density	density	NOUN
ejpam-5386	176	6	c(x	c(x	NOUN
ejpam-5386	176	7	,	,	PUNCT
ejpam-5386	176	8	t)+ϵ	t)+ϵ	PROPN
ejpam-5386	176	9	ηα(x	ηα(x	NOUN
ejpam-5386	176	10	,	,	PUNCT
ejpam-5386	176	11	t	t	PROPN
ejpam-5386	176	12	)	)	PUNCT
ejpam-5386	176	13	and	and	CCONJ
ejpam-5386	176	14	the	the	DET
ejpam-5386	176	15	perturbed	perturb	VERB
ejpam-5386	176	16	therapy	therapy	NOUN
ejpam-5386	176	17	parameter	parameter	NOUN
ejpam-5386	176	18	α(x	α(x	PROPN
ejpam-5386	176	19	)	)	PUNCT
ejpam-5386	177	1	+	+	NUM
ejpam-5386	177	2	ϵα0(x	ϵα0(x	NOUN
ejpam-5386	177	3	)	)	PUNCT
ejpam-5386	177	4	into	into	ADP
ejpam-5386	177	5	the	the	DET
ejpam-5386	177	6	original	original	ADJ
ejpam-5386	177	7	problem	problem	NOUN
ejpam-5386	177	8	(	(	PUNCT
ejpam-5386	177	9	5	5	X
ejpam-5386	177	10	)	)	PUNCT
ejpam-5386	177	11	yields	yield	VERB
ejpam-5386	177	12	a	a	DET
ejpam-5386	177	13	perturbed	perturb	VERB
ejpam-5386	177	14	problem	problem	NOUN
ejpam-5386	177	15	.	.	PUNCT
ejpam-5386	178	1	the	the	DET
ejpam-5386	178	2	resulting	result	VERB
ejpam-5386	178	3	sensitivity	sensitivity	NOUN
ejpam-5386	178	4	problem	problem	NOUN
ejpam-5386	178	5	is	be	AUX
ejpam-5386	178	6	given	give	VERB
ejpam-5386	178	7	by	by	NOUN
ejpam-5386	178	8	∂tηα	∂tηα	NOUN
ejpam-5386	178	9	−	−	PROPN
ejpam-5386	178	10	div(d(x)∇ηα	div(d(x)∇ηα	NOUN
ejpam-5386	178	11	)	)	PUNCT
ejpam-5386	179	1	+	+	NOUN
ejpam-5386	179	2	α(x)β(t	α(x)β(t	NOUN
ejpam-5386	179	3	)	)	PUNCT
ejpam-5386	179	4	ηα	ηα	VERB
ejpam-5386	179	5	−	−	NOUN
ejpam-5386	179	6	g′c	g′c	NOUN
ejpam-5386	179	7	ηα	ηα	NOUN
ejpam-5386	179	8	=	=	PUNCT
ejpam-5386	179	9	−β(t)α0(x	−β(t)α0(x	NOUN
ejpam-5386	179	10	)	)	PUNCT
ejpam-5386	179	11	c	c	NOUN
ejpam-5386	179	12	in	in	ADP
ejpam-5386	179	13	q	q	PROPN
ejpam-5386	179	14	,	,	PUNCT
ejpam-5386	179	15	d	d	X
ejpam-5386	179	16	∂νηα	∂νηα	X
ejpam-5386	179	17	=	=	NOUN
ejpam-5386	179	18	0	0	NUM
ejpam-5386	179	19	on	on	ADP
ejpam-5386	179	20	bt	bt	PRON
ejpam-5386	179	21	,	,	PUNCT
ejpam-5386	179	22	ηα(x	ηα(x	ADJ
ejpam-5386	179	23	,	,	PUNCT
ejpam-5386	179	24	0	0	NUM
ejpam-5386	179	25	)	)	PUNCT
ejpam-5386	179	26	=	=	SYM
ejpam-5386	179	27	0	0	NUM
ejpam-5386	179	28	in	in	ADP
ejpam-5386	179	29	ω	ω	PROPN
ejpam-5386	179	30	.	.	PUNCT
ejpam-5386	180	1	(	(	PUNCT
ejpam-5386	180	2	18	18	NUM
ejpam-5386	180	3	)	)	PUNCT
ejpam-5386	180	4	s.	s.	PROPN
ejpam-5386	180	5	tatar	tatar	PROPN
ejpam-5386	180	6	,	,	PUNCT
ejpam-5386	180	7	m.	m.	NOUN
ejpam-5386	180	8	bensalah	bensalah	PROPN
ejpam-5386	180	9	,	,	PUNCT
ejpam-5386	180	10	m.	m.	NOUN
ejpam-5386	180	11	alamil	alamil	PROPN
ejpam-5386	180	12	/	/	SYM
ejpam-5386	180	13	eur	eur	PROPN
ejpam-5386	180	14	.	.	PUNCT
ejpam-5386	181	1	j.	j.	PROPN
ejpam-5386	181	2	pure	pure	PROPN
ejpam-5386	181	3	appl	appl	PROPN
ejpam-5386	181	4	.	.	PROPN
ejpam-5386	181	5	math	math	PROPN
ejpam-5386	181	6	,	,	PUNCT
ejpam-5386	181	7	17	17	NUM
ejpam-5386	181	8	(	(	PUNCT
ejpam-5386	181	9	4	4	NUM
ejpam-5386	181	10	)	)	PUNCT
ejpam-5386	181	11	(	(	PUNCT
ejpam-5386	181	12	2024	2024	NUM
ejpam-5386	181	13	)	)	PUNCT
ejpam-5386	181	14	,	,	PUNCT
ejpam-5386	181	15	2651	2651	NUM
ejpam-5386	181	16	-	-	SYM
ejpam-5386	181	17	2675	2675	NUM
ejpam-5386	181	18	2660	2660	NUM
ejpam-5386	181	19	sensitivity	sensitivity	NOUN
ejpam-5386	181	20	problem	problem	NOUN
ejpam-5386	181	21	associated	associate	VERB
ejpam-5386	181	22	with	with	ADP
ejpam-5386	181	23	initial	initial	ADJ
ejpam-5386	181	24	activation	activation	NOUN
ejpam-5386	181	25	of	of	ADP
ejpam-5386	181	26	the	the	DET
ejpam-5386	181	27	tissue	tissue	NOUN
ejpam-5386	181	28	.	.	PUNCT
ejpam-5386	182	1	similarly	similarly	ADV
ejpam-5386	182	2	,	,	PUNCT
ejpam-5386	182	3	assume	assume	VERB
ejpam-5386	182	4	c(x	c(x	NOUN
ejpam-5386	182	5	,	,	PUNCT
ejpam-5386	182	6	t	t	PROPN
ejpam-5386	182	7	)	)	PUNCT
ejpam-5386	182	8	is	be	AUX
ejpam-5386	182	9	perturbed	perturb	VERB
ejpam-5386	182	10	by	by	ADP
ejpam-5386	182	11	ϵ	ϵ	NOUN
ejpam-5386	182	12	ηφ(x	ηφ(x	PUNCT
ejpam-5386	182	13	,	,	PUNCT
ejpam-5386	182	14	t	t	PROPN
ejpam-5386	182	15	)	)	PUNCT
ejpam-5386	182	16	and	and	CCONJ
ejpam-5386	182	17	the	the	DET
ejpam-5386	182	18	initial	initial	ADJ
ejpam-5386	182	19	activation	activation	NOUN
ejpam-5386	182	20	of	of	ADP
ejpam-5386	182	21	the	the	DET
ejpam-5386	182	22	tissue	tissue	NOUN
ejpam-5386	182	23	,	,	PUNCT
ejpam-5386	182	24	denoted	denote	VERB
ejpam-5386	182	25	as	as	ADP
ejpam-5386	182	26	φ(x	φ(x	NOUN
ejpam-5386	182	27	)	)	PUNCT
ejpam-5386	182	28	,	,	PUNCT
ejpam-5386	182	29	is	be	AUX
ejpam-5386	182	30	perturbed	perturb	VERB
ejpam-5386	182	31	by	by	ADP
ejpam-5386	182	32	ϵφ0(x	ϵφ0(x	PROPN
ejpam-5386	182	33	)	)	PUNCT
ejpam-5386	182	34	,	,	PUNCT
ejpam-5386	182	35	where	where	SCONJ
ejpam-5386	182	36	ϵ	ϵ	X
ejpam-5386	182	37	>	>	X
ejpam-5386	182	38	0	0	NUM
ejpam-5386	182	39	is	be	AUX
ejpam-5386	182	40	a	a	DET
ejpam-5386	182	41	small	small	ADJ
ejpam-5386	182	42	number	number	NOUN
ejpam-5386	182	43	and	and	CCONJ
ejpam-5386	182	44	φ0	φ0	PROPN
ejpam-5386	182	45	∈	∈	PROPN
ejpam-5386	182	46	aφ	aφ	NOUN
ejpam-5386	182	47	.	.	PUNCT
ejpam-5386	183	1	substituting	substitute	VERB
ejpam-5386	183	2	the	the	DET
ejpam-5386	183	3	perturbed	perturb	VERB
ejpam-5386	183	4	cell	cell	NOUN
ejpam-5386	183	5	density	density	NOUN
ejpam-5386	183	6	c(x	c(x	NOUN
ejpam-5386	183	7	,	,	PUNCT
ejpam-5386	183	8	t	t	PROPN
ejpam-5386	183	9	)	)	PUNCT
ejpam-5386	184	1	+	+	CCONJ
ejpam-5386	184	2	ϵ	ϵ	X
ejpam-5386	184	3	ηφ(x	ηφ(x	NUM
ejpam-5386	184	4	,	,	PUNCT
ejpam-5386	184	5	t	t	PROPN
ejpam-5386	184	6	)	)	PUNCT
ejpam-5386	184	7	and	and	CCONJ
ejpam-5386	184	8	perturbed	perturb	VERB
ejpam-5386	184	9	initial	initial	ADJ
ejpam-5386	184	10	activation	activation	NOUN
ejpam-5386	184	11	of	of	ADP
ejpam-5386	184	12	the	the	DET
ejpam-5386	184	13	tissue	tissue	NOUN
ejpam-5386	184	14	φ(x	φ(x	NOUN
ejpam-5386	184	15	)	)	PUNCT
ejpam-5386	185	1	+	+	SYM
ejpam-5386	185	2	ϵφ0(x	ϵφ0(x	NOUN
ejpam-5386	185	3	)	)	PUNCT
ejpam-5386	185	4	into	into	ADP
ejpam-5386	185	5	the	the	DET
ejpam-5386	185	6	original	original	ADJ
ejpam-5386	185	7	problem	problem	NOUN
ejpam-5386	185	8	(	(	PUNCT
ejpam-5386	185	9	5	5	X
ejpam-5386	185	10	)	)	PUNCT
ejpam-5386	185	11	yields	yield	VERB
ejpam-5386	185	12	a	a	DET
ejpam-5386	185	13	perturbed	perturb	VERB
ejpam-5386	185	14	problem	problem	NOUN
ejpam-5386	185	15	.	.	PUNCT
ejpam-5386	186	1	the	the	DET
ejpam-5386	186	2	resulting	result	VERB
ejpam-5386	186	3	sensitivity	sensitivity	NOUN
ejpam-5386	186	4	problem	problem	NOUN
ejpam-5386	186	5	is	be	AUX
ejpam-5386	186	6	given	give	VERB
ejpam-5386	186	7	by	by	NOUN
ejpam-5386	186	8	∂tηφ	∂tηφ	NUM
ejpam-5386	186	9	−	−	PRON
ejpam-5386	186	10	div(d(x)∇ηφ	div(d(x)∇ηφ	NUM
ejpam-5386	186	11	)	)	PUNCT
ejpam-5386	186	12	+	+	NOUN
ejpam-5386	186	13	α(x)β(t	α(x)β(t	NOUN
ejpam-5386	186	14	)	)	PUNCT
ejpam-5386	186	15	ηφ	ηφ	ADP
ejpam-5386	186	16	−	−	PROPN
ejpam-5386	186	17	g′c	g′c	NOUN
ejpam-5386	186	18	ηφ	ηφ	NOUN
ejpam-5386	186	19	=	=	NOUN
ejpam-5386	186	20	0	0	NUM
ejpam-5386	186	21	in	in	ADP
ejpam-5386	186	22	q	q	PROPN
ejpam-5386	186	23	,	,	PUNCT
ejpam-5386	186	24	d	d	X
ejpam-5386	186	25	∂νηφ	∂νηφ	SYM
ejpam-5386	186	26	=	=	SYM
ejpam-5386	186	27	0	0	NUM
ejpam-5386	186	28	on	on	ADP
ejpam-5386	186	29	bt	bt	PRON
ejpam-5386	186	30	,	,	PUNCT
ejpam-5386	186	31	ηφ(x	ηφ(x	ADV
ejpam-5386	186	32	,	,	PUNCT
ejpam-5386	186	33	0	0	NUM
ejpam-5386	186	34	)	)	PUNCT
ejpam-5386	186	35	=	=	SYM
ejpam-5386	187	1	φ0(x	φ0(x	NOUN
ejpam-5386	187	2	)	)	PUNCT
ejpam-5386	187	3	in	in	ADP
ejpam-5386	187	4	ω	ω	PROPN
ejpam-5386	187	5	.	.	PUNCT
ejpam-5386	188	1	(	(	PUNCT
ejpam-5386	188	2	19	19	NUM
ejpam-5386	188	3	)	)	PUNCT
ejpam-5386	188	4	note	note	NOUN
ejpam-5386	188	5	that	that	SCONJ
ejpam-5386	188	6	the	the	DET
ejpam-5386	188	7	problems	problem	NOUN
ejpam-5386	188	8	(	(	PUNCT
ejpam-5386	188	9	18	18	NUM
ejpam-5386	188	10	)	)	PUNCT
ejpam-5386	188	11	and	and	CCONJ
ejpam-5386	188	12	(	(	PUNCT
ejpam-5386	188	13	19	19	NUM
ejpam-5386	188	14	)	)	PUNCT
ejpam-5386	188	15	are	be	AUX
ejpam-5386	188	16	linear	linear	ADJ
ejpam-5386	188	17	,	,	PUNCT
ejpam-5386	188	18	and	and	CCONJ
ejpam-5386	188	19	their	their	PRON
ejpam-5386	188	20	well	well	ADJ
ejpam-5386	188	21	-	-	PUNCT
ejpam-5386	188	22	posedness	posedness	NOUN
ejpam-5386	188	23	is	be	AUX
ejpam-5386	188	24	classical	classical	ADJ
ejpam-5386	188	25	,	,	PUNCT
ejpam-5386	188	26	see	see	VERB
ejpam-5386	188	27	[	[	X
ejpam-5386	188	28	6	6	NUM
ejpam-5386	188	29	]	]	PUNCT
ejpam-5386	188	30	.	.	PUNCT
ejpam-5386	189	1	these	these	DET
ejpam-5386	189	2	sensitivity	sensitivity	NOUN
ejpam-5386	189	3	problems	problem	NOUN
ejpam-5386	189	4	are	be	AUX
ejpam-5386	189	5	important	important	ADJ
ejpam-5386	189	6	to	to	PART
ejpam-5386	189	7	determine	determine	VERB
ejpam-5386	189	8	the	the	DET
ejpam-5386	189	9	step	step	NOUN
ejpam-5386	189	10	sizes	size	NOUN
ejpam-5386	189	11	in	in	ADP
ejpam-5386	189	12	the	the	DET
ejpam-5386	189	13	descent	descent	NOUN
ejpam-5386	189	14	direction	direction	NOUN
ejpam-5386	189	15	in	in	ADP
ejpam-5386	189	16	the	the	DET
ejpam-5386	189	17	conjugate	conjugate	ADJ
ejpam-5386	189	18	gradient	gradient	NOUN
ejpam-5386	189	19	method	method	NOUN
ejpam-5386	189	20	.	.	PUNCT
ejpam-5386	190	1	proof	proof	NOUN
ejpam-5386	190	2	of	of	ADP
ejpam-5386	190	3	theorem	theorem	NOUN
ejpam-5386	190	4	3	3	X
ejpam-5386	190	5	.	.	PUNCT
ejpam-5386	191	1	let	let	VERB
ejpam-5386	191	2	ϵ	ϵ	PRON
ejpam-5386	191	3	>	>	X
ejpam-5386	191	4	0	0	PUNCT
ejpam-5386	192	1	and	and	CCONJ
ejpam-5386	192	2	α0	α0	PROPN
ejpam-5386	192	3	∈	∈	PROPN
ejpam-5386	192	4	aα	aα	NOUN
ejpam-5386	192	5	be	be	AUX
ejpam-5386	192	6	given	give	VERB
ejpam-5386	192	7	,	,	PUNCT
ejpam-5386	192	8	then	then	ADV
ejpam-5386	192	9	direct	direct	ADJ
ejpam-5386	192	10	calculations	calculation	NOUN
ejpam-5386	192	11	yield	yield	VERB
ejpam-5386	192	12	j(α+	j(α+	PRON
ejpam-5386	192	13	ϵα0,φ)−	ϵα0,φ)−	PROPN
ejpam-5386	192	14	j(α	j(α	PROPN
ejpam-5386	192	15	,	,	PUNCT
ejpam-5386	192	16	φ	φ	NUM
ejpam-5386	192	17	)	)	PUNCT
ejpam-5386	192	18	=	=	SYM
ejpam-5386	192	19	ϵ	ϵ	NOUN
ejpam-5386	192	20	{	{	PUNCT
ejpam-5386	193	1	2∑	2∑	NUM
ejpam-5386	193	2	k=1	k=1	PUNCT
ejpam-5386	193	3	∫	∫	PROPN
ejpam-5386	193	4	q	q	PROPN
ejpam-5386	193	5	ηα(x	ηα(x	PROPN
ejpam-5386	193	6	,	,	PUNCT
ejpam-5386	193	7	t)ωk(t	t)ωk(t	PRON
ejpam-5386	193	8	)	)	PUNCT
ejpam-5386	193	9	(	(	PUNCT
ejpam-5386	193	10	∫	∫	PROPN
ejpam-5386	193	11	t	t	PROPN
ejpam-5386	193	12	0	0	NUM
ejpam-5386	193	13	ωk(τ	ωk(τ	NUM
ejpam-5386	193	14	)	)	PUNCT
ejpam-5386	193	15	c(x	c(x	NOUN
ejpam-5386	193	16	,	,	PUNCT
ejpam-5386	193	17	τ	τ	NOUN
ejpam-5386	193	18	)	)	PUNCT
ejpam-5386	193	19	dτ	dτ	NOUN
ejpam-5386	193	20	−	−	PROPN
ejpam-5386	193	21	ϕεk	ϕεk	NOUN
ejpam-5386	193	22	)	)	PUNCT
ejpam-5386	193	23	dx	dx	PROPN
ejpam-5386	194	1	dt	dt	X
ejpam-5386	195	1	}	}	PUNCT
ejpam-5386	196	1	+	+	CCONJ
ejpam-5386	196	2	ϵ2	ϵ2	PROPN
ejpam-5386	196	3	2	2	NUM
ejpam-5386	196	4	{	{	PUNCT
ejpam-5386	196	5	2∑	2∑	NUM
ejpam-5386	196	6	k=1	k=1	X
ejpam-5386	196	7	(	(	PUNCT
ejpam-5386	196	8	∥∥∥∫	∥∥∥∫	ADJ
ejpam-5386	196	9	t	t	NOUN
ejpam-5386	196	10	0	0	NUM
ejpam-5386	196	11	ωk(t	ωk(t	NOUN
ejpam-5386	196	12	)	)	PUNCT
ejpam-5386	196	13	ηα	ηα	PROPN
ejpam-5386	196	14	dt	dt	NOUN
ejpam-5386	196	15	∥∥∥2	∥∥∥2	NOUN
ejpam-5386	196	16	2	2	NUM
ejpam-5386	196	17	)	)	PUNCT
ejpam-5386	196	18	}	}	PUNCT
ejpam-5386	196	19	.	.	PUNCT
ejpam-5386	197	1	(	(	PUNCT
ejpam-5386	197	2	20	20	NUM
ejpam-5386	197	3	)	)	PUNCT
ejpam-5386	197	4	therefore	therefore	ADV
ejpam-5386	197	5	,	,	PUNCT
ejpam-5386	197	6	the	the	DET
ejpam-5386	197	7	directional	directional	ADJ
ejpam-5386	197	8	derivative	derivative	NOUN
ejpam-5386	197	9	of	of	ADP
ejpam-5386	197	10	j(α	j(α	PROPN
ejpam-5386	197	11	,	,	PUNCT
ejpam-5386	197	12	φ	φ	NUM
ejpam-5386	197	13	)	)	PUNCT
ejpam-5386	197	14	with	with	ADP
ejpam-5386	197	15	respect	respect	NOUN
ejpam-5386	197	16	to	to	ADP
ejpam-5386	197	17	α	α	NOUN
ejpam-5386	197	18	in	in	ADP
ejpam-5386	197	19	the	the	DET
ejpam-5386	197	20	direction	direction	NOUN
ejpam-5386	197	21	α0(x	α0(x	NOUN
ejpam-5386	197	22	)	)	PUNCT
ejpam-5386	197	23	is	be	AUX
ejpam-5386	197	24	given	give	VERB
ejpam-5386	197	25	by	by	ADP
ejpam-5386	197	26	j	j	PROPN
ejpam-5386	197	27	′	′	PROPN
ejpam-5386	197	28	α(α	α(α	PROPN
ejpam-5386	197	29	,	,	PUNCT
ejpam-5386	197	30	φ	φ	NUM
ejpam-5386	197	31	)	)	PUNCT
ejpam-5386	197	32	·	·	PUNCT
ejpam-5386	197	33	α0	α0	PROPN
ejpam-5386	197	34	=	=	SYM
ejpam-5386	197	35	lim	lim	PROPN
ejpam-5386	197	36	ϵ→0	ϵ→0	PROPN
ejpam-5386	197	37	j(α+	j(α+	PROPN
ejpam-5386	197	38	ϵα0,φ)−	ϵα0,φ)−	PROPN
ejpam-5386	197	39	j(α	j(α	PROPN
ejpam-5386	197	40	,	,	PUNCT
ejpam-5386	197	41	φ	φ	NUM
ejpam-5386	197	42	)	)	PUNCT
ejpam-5386	197	43	ϵ	ϵ	X
ejpam-5386	198	1	=	=	SYM
ejpam-5386	198	2	2∑	2∑	NOUN
ejpam-5386	198	3	k=1	k=1	PUNCT
ejpam-5386	198	4	∫	∫	PROPN
ejpam-5386	199	1	q	q	PROPN
ejpam-5386	199	2	ηα(x	ηα(x	PROPN
ejpam-5386	199	3	,	,	PUNCT
ejpam-5386	199	4	t)ωk(t	t)ωk(t	PRON
ejpam-5386	199	5	)	)	PUNCT
ejpam-5386	199	6	(	(	PUNCT
ejpam-5386	200	1	∫	∫	PROPN
ejpam-5386	200	2	t	t	PROPN
ejpam-5386	200	3	0	0	NUM
ejpam-5386	200	4	ωk(τ	ωk(τ	NUM
ejpam-5386	200	5	)	)	PUNCT
ejpam-5386	200	6	c(x	c(x	NOUN
ejpam-5386	200	7	,	,	PUNCT
ejpam-5386	200	8	τ	τ	NOUN
ejpam-5386	200	9	)	)	PUNCT
ejpam-5386	200	10	dτ	dτ	NOUN
ejpam-5386	200	11	−	−	PROPN
ejpam-5386	200	12	ϕεk	ϕεk	NOUN
ejpam-5386	200	13	)	)	PUNCT
ejpam-5386	200	14	dx	dx	PROPN
ejpam-5386	201	1	dt	dt	X
ejpam-5386	201	2	.	.	PUNCT
ejpam-5386	202	1	multiplying	multiply	VERB
ejpam-5386	202	2	both	both	DET
ejpam-5386	202	3	sides	side	NOUN
ejpam-5386	202	4	of	of	ADP
ejpam-5386	202	5	the	the	DET
ejpam-5386	202	6	first	first	ADJ
ejpam-5386	202	7	equation	equation	NOUN
ejpam-5386	202	8	in	in	ADP
ejpam-5386	202	9	(	(	PUNCT
ejpam-5386	202	10	16	16	NUM
ejpam-5386	202	11	)	)	PUNCT
ejpam-5386	202	12	by	by	ADP
ejpam-5386	202	13	ηα	ηα	PROPN
ejpam-5386	202	14	,	,	PUNCT
ejpam-5386	202	15	integrating	integrate	VERB
ejpam-5386	202	16	over	over	ADP
ejpam-5386	202	17	q	q	NOUN
ejpam-5386	202	18	,	,	PUNCT
ejpam-5386	202	19	using	use	VERB
ejpam-5386	202	20	the	the	DET
ejpam-5386	202	21	green	green	ADJ
ejpam-5386	202	22	formula	formula	NOUN
ejpam-5386	202	23	and	and	CCONJ
ejpam-5386	202	24	the	the	DET
ejpam-5386	202	25	fact	fact	NOUN
ejpam-5386	202	26	that	that	SCONJ
ejpam-5386	202	27	d(x	d(x	NOUN
ejpam-5386	202	28	)	)	PUNCT
ejpam-5386	202	29	∂νv	∂νv	NOUN
ejpam-5386	202	30	=	=	NOUN
ejpam-5386	202	31	0	0	NUM
ejpam-5386	202	32	on	on	ADP
ejpam-5386	202	33	bt	bt	PROPN
ejpam-5386	202	34	,	,	PUNCT
ejpam-5386	202	35	we	we	PRON
ejpam-5386	202	36	obtain	obtain	VERB
ejpam-5386	202	37	−	−	PROPN
ejpam-5386	202	38	∫	∫	PROPN
ejpam-5386	202	39	q	q	PROPN
ejpam-5386	203	1	∂tv	∂tv	PROPN
ejpam-5386	203	2	ηα	ηα	NOUN
ejpam-5386	203	3	dx	dx	PROPN
ejpam-5386	203	4	dt+	dt+	NOUN
ejpam-5386	203	5	∫	∫	PROPN
ejpam-5386	203	6	q	q	X
ejpam-5386	203	7	d(x)∇v∇ηα	d(x)∇v∇ηα	ADP
ejpam-5386	203	8	dx	dx	PROPN
ejpam-5386	203	9	dt+	dt+	NOUN
ejpam-5386	203	10	∫	∫	PROPN
ejpam-5386	203	11	q	q	PROPN
ejpam-5386	204	1	(	(	PUNCT
ejpam-5386	204	2	α(x)β(t)−	α(x)β(t)−	PROPN
ejpam-5386	204	3	g′c	g′c	PROPN
ejpam-5386	204	4	)	)	PUNCT
ejpam-5386	204	5	v	v	NOUN
ejpam-5386	204	6	ηα	ηα	NOUN
ejpam-5386	204	7	dx	dx	PROPN
ejpam-5386	204	8	dt	dt	NOUN
ejpam-5386	205	1	=	=	PUNCT
ejpam-5386	205	2	2∑	2∑	X
ejpam-5386	205	3	k=1	k=1	PUNCT
ejpam-5386	205	4	∫	∫	PROPN
ejpam-5386	206	1	q	q	PROPN
ejpam-5386	206	2	ωk(t	ωk(t	NOUN
ejpam-5386	206	3	)	)	PUNCT
ejpam-5386	206	4	ηα	ηα	PROPN
ejpam-5386	206	5	(	(	PUNCT
ejpam-5386	206	6	∫	∫	PROPN
ejpam-5386	206	7	t	t	PROPN
ejpam-5386	206	8	0	0	NUM
ejpam-5386	206	9	ωk(τ	ωk(τ	NUM
ejpam-5386	206	10	)	)	PUNCT
ejpam-5386	206	11	c(x	c(x	NOUN
ejpam-5386	206	12	,	,	PUNCT
ejpam-5386	206	13	τ	τ	NOUN
ejpam-5386	206	14	)	)	PUNCT
ejpam-5386	206	15	dτ	dτ	NOUN
ejpam-5386	206	16	−	−	PROPN
ejpam-5386	206	17	ϕεk	ϕεk	NOUN
ejpam-5386	206	18	)	)	PUNCT
ejpam-5386	206	19	dx	dx	PROPN
ejpam-5386	207	1	dt	dt	X
ejpam-5386	207	2	.	.	PUNCT
ejpam-5386	208	1	applying	apply	VERB
ejpam-5386	208	2	the	the	DET
ejpam-5386	208	3	green	green	NOUN
ejpam-5386	208	4	’s	’s	NOUN
ejpam-5386	208	5	and	and	CCONJ
ejpam-5386	208	6	the	the	DET
ejpam-5386	208	7	integration	integration	NOUN
ejpam-5386	208	8	by	by	ADP
ejpam-5386	208	9	parts	part	NOUN
ejpam-5386	208	10	formulas	formula	NOUN
ejpam-5386	208	11	in	in	ADP
ejpam-5386	208	12	the	the	DET
ejpam-5386	208	13	above	above	ADJ
ejpam-5386	208	14	identity	identity	NOUN
ejpam-5386	208	15	and	and	CCONJ
ejpam-5386	208	16	taking	take	VERB
ejpam-5386	208	17	into	into	ADP
ejpam-5386	208	18	account	account	NOUN
ejpam-5386	208	19	that	that	SCONJ
ejpam-5386	208	20	ηα(x	ηα(x	VERB
ejpam-5386	208	21	,	,	PUNCT
ejpam-5386	208	22	0	0	NUM
ejpam-5386	208	23	)	)	PUNCT
ejpam-5386	208	24	=	=	SYM
ejpam-5386	208	25	0	0	NUM
ejpam-5386	208	26	and	and	CCONJ
ejpam-5386	208	27	v(x	v(x	PROPN
ejpam-5386	208	28	,	,	PUNCT
ejpam-5386	208	29	t	t	NOUN
ejpam-5386	208	30	)	)	PUNCT
ejpam-5386	209	1	=	=	SYM
ejpam-5386	209	2	0	0	NUM
ejpam-5386	209	3	for	for	ADP
ejpam-5386	209	4	all	all	DET
ejpam-5386	209	5	x	x	SYM
ejpam-5386	209	6	∈	∈	PROPN
ejpam-5386	209	7	ω	ω	NOUN
ejpam-5386	209	8	,	,	PUNCT
ejpam-5386	209	9	we	we	PRON
ejpam-5386	209	10	get	get	VERB
ejpam-5386	209	11	s.	s.	PROPN
ejpam-5386	209	12	tatar	tatar	PROPN
ejpam-5386	209	13	,	,	PUNCT
ejpam-5386	209	14	m.	m.	NOUN
ejpam-5386	209	15	bensalah	bensalah	PROPN
ejpam-5386	209	16	,	,	PUNCT
ejpam-5386	209	17	m.	m.	NOUN
ejpam-5386	209	18	alamil	alamil	PROPN
ejpam-5386	209	19	/	/	SYM
ejpam-5386	209	20	eur	eur	PROPN
ejpam-5386	209	21	.	.	PUNCT
ejpam-5386	210	1	j.	j.	PROPN
ejpam-5386	210	2	pure	pure	PROPN
ejpam-5386	210	3	appl	appl	PROPN
ejpam-5386	210	4	.	.	PROPN
ejpam-5386	210	5	math	math	PROPN
ejpam-5386	210	6	,	,	PUNCT
ejpam-5386	210	7	17	17	NUM
ejpam-5386	210	8	(	(	PUNCT
ejpam-5386	210	9	4	4	NUM
ejpam-5386	210	10	)	)	PUNCT
ejpam-5386	210	11	(	(	PUNCT
ejpam-5386	210	12	2024	2024	NUM
ejpam-5386	210	13	)	)	PUNCT
ejpam-5386	210	14	,	,	PUNCT
ejpam-5386	210	15	2651	2651	NUM
ejpam-5386	210	16	-	-	SYM
ejpam-5386	210	17	2675	2675	NUM
ejpam-5386	210	18	2661	2661	NUM
ejpam-5386	210	19	∫	∫	NOUN
ejpam-5386	210	20	q	q	PROPN
ejpam-5386	210	21	(	(	PUNCT
ejpam-5386	210	22	∂tηα	∂tηα	NOUN
ejpam-5386	210	23	−	−	NUM
ejpam-5386	210	24	div(d(x)∇ηα	div(d(x)∇ηα	NOUN
ejpam-5386	210	25	)	)	PUNCT
ejpam-5386	211	1	+	+	NOUN
ejpam-5386	211	2	α(x)β(t	α(x)β(t	NOUN
ejpam-5386	211	3	)	)	PUNCT
ejpam-5386	211	4	ηα	ηα	VERB
ejpam-5386	211	5	−	−	NOUN
ejpam-5386	211	6	g′c	g′c	X
ejpam-5386	211	7	ηα	ηα	PROPN
ejpam-5386	211	8	)	)	PUNCT
ejpam-5386	211	9	v	v	ADP
ejpam-5386	211	10	dx	dx	PROPN
ejpam-5386	212	1	dt	dt	NOUN
ejpam-5386	213	1	=	=	SYM
ejpam-5386	213	2	3∑	3∑	NUM
ejpam-5386	213	3	k=1	k=1	NOUN
ejpam-5386	213	4	∫	∫	PROPN
ejpam-5386	213	5	q	q	PROPN
ejpam-5386	213	6	ωk(t	ωk(t	NOUN
ejpam-5386	213	7	)	)	PUNCT
ejpam-5386	213	8	ηα	ηα	PROPN
ejpam-5386	213	9	(	(	PUNCT
ejpam-5386	213	10	∫	∫	PROPN
ejpam-5386	213	11	t	t	PROPN
ejpam-5386	213	12	0	0	NUM
ejpam-5386	213	13	ωk(τ	ωk(τ	NUM
ejpam-5386	213	14	)	)	PUNCT
ejpam-5386	213	15	c(x	c(x	NOUN
ejpam-5386	213	16	,	,	PUNCT
ejpam-5386	213	17	τ	τ	NOUN
ejpam-5386	213	18	)	)	PUNCT
ejpam-5386	213	19	dτ	dτ	NOUN
ejpam-5386	213	20	−	−	PROPN
ejpam-5386	213	21	ϕεk	ϕεk	NOUN
ejpam-5386	213	22	)	)	PUNCT
ejpam-5386	213	23	dx	dx	PROPN
ejpam-5386	214	1	dt	dt	PROPN
ejpam-5386	214	2	.	.	PUNCT
ejpam-5386	215	1	the	the	DET
ejpam-5386	215	2	first	first	ADJ
ejpam-5386	215	3	equation	equation	NOUN
ejpam-5386	215	4	in	in	ADP
ejpam-5386	215	5	(	(	PUNCT
ejpam-5386	215	6	18	18	NUM
ejpam-5386	215	7	)	)	PUNCT
ejpam-5386	215	8	leads	lead	VERB
ejpam-5386	215	9	to	to	ADP
ejpam-5386	215	10	2∑	2∑	NUM
ejpam-5386	215	11	k=1	k=1	PUNCT
ejpam-5386	215	12	∫	∫	PROPN
ejpam-5386	215	13	q	q	PROPN
ejpam-5386	215	14	ωk(t	ωk(t	NOUN
ejpam-5386	215	15	)	)	PUNCT
ejpam-5386	215	16	ηα	ηα	PROPN
ejpam-5386	215	17	(	(	PUNCT
ejpam-5386	215	18	∫	∫	PROPN
ejpam-5386	215	19	t	t	PROPN
ejpam-5386	215	20	0	0	NUM
ejpam-5386	215	21	ωk(τ	ωk(τ	NUM
ejpam-5386	215	22	)	)	PUNCT
ejpam-5386	215	23	c(x	c(x	NOUN
ejpam-5386	215	24	,	,	PUNCT
ejpam-5386	215	25	τ	τ	NOUN
ejpam-5386	215	26	)	)	PUNCT
ejpam-5386	215	27	dτ	dτ	NOUN
ejpam-5386	215	28	−	−	PROPN
ejpam-5386	215	29	ϕεk	ϕεk	NOUN
ejpam-5386	215	30	)	)	PUNCT
ejpam-5386	215	31	dx	dx	PROPN
ejpam-5386	216	1	dt	dt	NOUN
ejpam-5386	217	1	=	=	PUNCT
ejpam-5386	217	2	−	−	PROPN
ejpam-5386	217	3	∫	∫	PROPN
ejpam-5386	217	4	q	q	PROPN
ejpam-5386	217	5	β(t)α0(x	β(t)α0(x	ADJ
ejpam-5386	217	6	)	)	PUNCT
ejpam-5386	217	7	c(x	c(x	PROPN
ejpam-5386	217	8	,	,	PUNCT
ejpam-5386	217	9	t	t	PROPN
ejpam-5386	217	10	)	)	PUNCT
ejpam-5386	217	11	v(x	v(x	PROPN
ejpam-5386	217	12	,	,	PUNCT
ejpam-5386	217	13	t	t	PROPN
ejpam-5386	217	14	)	)	PUNCT
ejpam-5386	217	15	dx	dx	PROPN
ejpam-5386	218	1	dt	dt	PROPN
ejpam-5386	218	2	.	.	PUNCT
ejpam-5386	219	1	therefore	therefore	ADV
ejpam-5386	219	2	,	,	PUNCT
ejpam-5386	219	3	the	the	DET
ejpam-5386	219	4	directional	directional	ADJ
ejpam-5386	219	5	derivative	derivative	NOUN
ejpam-5386	219	6	of	of	ADP
ejpam-5386	219	7	j(α	j(α	PROPN
ejpam-5386	219	8	,	,	PUNCT
ejpam-5386	219	9	φ	φ	NUM
ejpam-5386	219	10	)	)	PUNCT
ejpam-5386	219	11	with	with	ADP
ejpam-5386	219	12	respect	respect	NOUN
ejpam-5386	219	13	to	to	ADP
ejpam-5386	219	14	α	α	NOUN
ejpam-5386	219	15	in	in	ADP
ejpam-5386	219	16	the	the	DET
ejpam-5386	219	17	direction	direction	NOUN
ejpam-5386	219	18	α0(x	α0(x	NOUN
ejpam-5386	219	19	)	)	PUNCT
ejpam-5386	219	20	is	be	AUX
ejpam-5386	219	21	given	give	VERB
ejpam-5386	219	22	by	by	ADP
ejpam-5386	219	23	j	j	PROPN
ejpam-5386	219	24	′	′	PROPN
ejpam-5386	219	25	α(α	α(α	PROPN
ejpam-5386	219	26	,	,	PUNCT
ejpam-5386	219	27	φ	φ	NUM
ejpam-5386	219	28	)	)	PUNCT
ejpam-5386	219	29	·	·	PUNCT
ejpam-5386	219	30	α0	α0	ADJ
ejpam-5386	219	31	=	=	SYM
ejpam-5386	220	1	−	−	PROPN
ejpam-5386	220	2	∫	∫	PROPN
ejpam-5386	220	3	q	q	PROPN
ejpam-5386	220	4	β(t)α0(x	β(t)α0(x	ADJ
ejpam-5386	220	5	)	)	PUNCT
ejpam-5386	220	6	c(x	c(x	PROPN
ejpam-5386	220	7	,	,	PUNCT
ejpam-5386	220	8	t	t	PROPN
ejpam-5386	220	9	)	)	PUNCT
ejpam-5386	220	10	v(x	v(x	PROPN
ejpam-5386	220	11	,	,	PUNCT
ejpam-5386	220	12	t	t	PROPN
ejpam-5386	220	13	)	)	PUNCT
ejpam-5386	220	14	dx	dx	PROPN
ejpam-5386	221	1	dt	dt	PROPN
ejpam-5386	221	2	.	.	PUNCT
ejpam-5386	222	1	(	(	PUNCT
ejpam-5386	222	2	21	21	NUM
ejpam-5386	222	3	)	)	PUNCT
ejpam-5386	222	4	similarly	similarly	ADV
ejpam-5386	222	5	,	,	PUNCT
ejpam-5386	222	6	by	by	ADP
ejpam-5386	222	7	using	use	VERB
ejpam-5386	222	8	the	the	DET
ejpam-5386	222	9	weak	weak	ADJ
ejpam-5386	222	10	formulations	formulation	NOUN
ejpam-5386	222	11	of	of	ADP
ejpam-5386	222	12	the	the	DET
ejpam-5386	222	13	adjoint	adjoint	PROPN
ejpam-5386	222	14	problem	problem	NOUN
ejpam-5386	222	15	(	(	PUNCT
ejpam-5386	222	16	16	16	NUM
ejpam-5386	222	17	)	)	PUNCT
ejpam-5386	222	18	and	and	CCONJ
ejpam-5386	222	19	the	the	DET
ejpam-5386	222	20	sensitivity	sensitivity	NOUN
ejpam-5386	222	21	problem	problem	NOUN
ejpam-5386	222	22	(	(	PUNCT
ejpam-5386	222	23	19	19	NUM
ejpam-5386	222	24	)	)	PUNCT
ejpam-5386	222	25	,	,	PUNCT
ejpam-5386	222	26	we	we	PRON
ejpam-5386	222	27	can	can	AUX
ejpam-5386	222	28	derive	derive	VERB
ejpam-5386	222	29	j	j	PROPN
ejpam-5386	222	30	′	′	PROPN
ejpam-5386	222	31	φ(α	φ(α	PROPN
ejpam-5386	222	32	,	,	PUNCT
ejpam-5386	222	33	φ	φ	NUM
ejpam-5386	222	34	)	)	PUNCT
ejpam-5386	222	35	·	·	PUNCT
ejpam-5386	222	36	φ0	φ0	PROPN
ejpam-5386	222	37	=	=	SYM
ejpam-5386	222	38	∫	∫	PROPN
ejpam-5386	222	39	ω	ω	PROPN
ejpam-5386	222	40	φ0(x	φ0(x	NOUN
ejpam-5386	222	41	)	)	PUNCT
ejpam-5386	222	42	v(x	v(x	PROPN
ejpam-5386	222	43	,	,	PUNCT
ejpam-5386	222	44	0	0	NUM
ejpam-5386	222	45	)	)	PUNCT
ejpam-5386	222	46	dx	dx	PROPN
ejpam-5386	222	47	.	.	PUNCT
ejpam-5386	223	1	the	the	DET
ejpam-5386	223	2	proof	proof	NOUN
ejpam-5386	223	3	is	be	AUX
ejpam-5386	223	4	complete	complete	ADJ
ejpam-5386	223	5	.	.	PUNCT
ejpam-5386	224	1	3.2	3.2	NUM
ejpam-5386	224	2	.	.	PUNCT
ejpam-5386	224	3	iterative	iterative	ADJ
ejpam-5386	224	4	algorithm	algorithm	NOUN
ejpam-5386	224	5	in	in	ADP
ejpam-5386	224	6	this	this	DET
ejpam-5386	224	7	subsection	subsection	NOUN
ejpam-5386	224	8	,	,	PUNCT
ejpam-5386	224	9	we	we	PRON
ejpam-5386	224	10	employ	employ	VERB
ejpam-5386	224	11	a	a	DET
ejpam-5386	224	12	conjugate	conjugate	ADJ
ejpam-5386	224	13	gradient	gradient	NOUN
ejpam-5386	224	14	method	method	NOUN
ejpam-5386	224	15	to	to	PART
ejpam-5386	224	16	approximate	approximate	VERB
ejpam-5386	224	17	the	the	DET
ejpam-5386	224	18	minimizer	minimizer	NOUN
ejpam-5386	224	19	of	of	ADP
ejpam-5386	224	20	the	the	DET
ejpam-5386	224	21	functional	functional	ADJ
ejpam-5386	224	22	j(α	j(α	PROPN
ejpam-5386	224	23	,	,	PUNCT
ejpam-5386	224	24	φ	φ	NOUN
ejpam-5386	224	25	)	)	PUNCT
ejpam-5386	224	26	defined	define	VERB
ejpam-5386	224	27	by	by	ADP
ejpam-5386	224	28	(	(	PUNCT
ejpam-5386	224	29	7	7	NUM
ejpam-5386	224	30	)	)	PUNCT
ejpam-5386	224	31	.	.	PUNCT
ejpam-5386	225	1	let	let	AUX
ejpam-5386	225	2	(	(	PUNCT
ejpam-5386	225	3	αk	αk	NOUN
ejpam-5386	225	4	,	,	PUNCT
ejpam-5386	225	5	φk	φk	AUX
ejpam-5386	225	6	)	)	PUNCT
ejpam-5386	225	7	be	be	AUX
ejpam-5386	225	8	the	the	DET
ejpam-5386	225	9	kth	kth	PROPN
ejpam-5386	225	10	approximation	approximation	NOUN
ejpam-5386	225	11	of	of	ADP
ejpam-5386	225	12	the	the	DET
ejpam-5386	225	13	solution	solution	NOUN
ejpam-5386	225	14	(	(	PUNCT
ejpam-5386	225	15	α	α	X
ejpam-5386	225	16	,	,	PUNCT
ejpam-5386	225	17	φ	φ	NOUN
ejpam-5386	225	18	)	)	PUNCT
ejpam-5386	225	19	.	.	PUNCT
ejpam-5386	226	1	the	the	DET
ejpam-5386	226	2	iterations	iteration	NOUN
ejpam-5386	226	3	are	be	AUX
ejpam-5386	226	4	given	give	VERB
ejpam-5386	226	5	by	by	ADP
ejpam-5386	226	6	the	the	DET
ejpam-5386	226	7	following	follow	VERB
ejpam-5386	226	8	equations	equation	NOUN
ejpam-5386	226	9	:	:	PUNCT
ejpam-5386	226	10	αk+1	αk+1	NUM
ejpam-5386	226	11	=	=	SYM
ejpam-5386	226	12	αk	αk	ADP
ejpam-5386	226	13	+	+	NOUN
ejpam-5386	226	14	ζkαs	ζkαs	PROPN
ejpam-5386	226	15	k	k	PROPN
ejpam-5386	226	16	α	α	PROPN
ejpam-5386	226	17	and	and	CCONJ
ejpam-5386	226	18	φk+1	φk+1	NUM
ejpam-5386	226	19	=	=	PUNCT
ejpam-5386	226	20	φk	φk	ADP
ejpam-5386	226	21	+	+	X
ejpam-5386	226	22	ζkφs	ζkφs	NOUN
ejpam-5386	226	23	k	k	PROPN
ejpam-5386	226	24	φ	φ	PROPN
ejpam-5386	226	25	,	,	PUNCT
ejpam-5386	226	26	k	k	PROPN
ejpam-5386	226	27	=	=	SYM
ejpam-5386	226	28	0	0	NUM
ejpam-5386	226	29	,	,	PUNCT
ejpam-5386	226	30	1	1	NUM
ejpam-5386	226	31	,	,	PUNCT
ejpam-5386	226	32	2	2	NUM
ejpam-5386	226	33	,	,	PUNCT
ejpam-5386	226	34	·	·	PUNCT
ejpam-5386	226	35	·	·	PUNCT
ejpam-5386	226	36	·	·	PUNCT
ejpam-5386	226	37	.	.	PUNCT
ejpam-5386	227	1	(	(	PUNCT
ejpam-5386	227	2	22	22	NUM
ejpam-5386	227	3	)	)	PUNCT
ejpam-5386	227	4	in	in	ADP
ejpam-5386	227	5	(	(	PUNCT
ejpam-5386	227	6	22	22	NUM
ejpam-5386	227	7	)	)	PUNCT
ejpam-5386	227	8	,	,	PUNCT
ejpam-5386	227	9	the	the	DET
ejpam-5386	227	10	index	index	NOUN
ejpam-5386	227	11	k	k	PROPN
ejpam-5386	227	12	denotes	denote	VERB
ejpam-5386	227	13	the	the	DET
ejpam-5386	227	14	number	number	NOUN
ejpam-5386	227	15	of	of	ADP
ejpam-5386	227	16	iterations	iteration	NOUN
ejpam-5386	227	17	,	,	PUNCT
ejpam-5386	227	18	α0(x	α0(x	NOUN
ejpam-5386	227	19	)	)	PUNCT
ejpam-5386	227	20	and	and	CCONJ
ejpam-5386	227	21	φ0(x	φ0(x	PRON
ejpam-5386	227	22	)	)	PUNCT
ejpam-5386	227	23	are	be	AUX
ejpam-5386	227	24	the	the	DET
ejpam-5386	227	25	initial	initial	ADJ
ejpam-5386	227	26	guesses	guess	NOUN
ejpam-5386	227	27	for	for	ADP
ejpam-5386	227	28	α(x	α(x	NOUN
ejpam-5386	227	29	)	)	PUNCT
ejpam-5386	227	30	and	and	CCONJ
ejpam-5386	227	31	φ(x	φ(x	NOUN
ejpam-5386	227	32	)	)	PUNCT
ejpam-5386	227	33	,	,	PUNCT
ejpam-5386	227	34	respectively	respectively	ADV
ejpam-5386	227	35	.	.	PUNCT
ejpam-5386	228	1	the	the	DET
ejpam-5386	228	2	terms	term	NOUN
ejpam-5386	228	3	ζkα	ζkα	VERB
ejpam-5386	228	4	and	and	CCONJ
ejpam-5386	228	5	ζkφ	ζkφ	NOUN
ejpam-5386	228	6	are	be	AUX
ejpam-5386	228	7	the	the	DET
ejpam-5386	228	8	step	step	NOUN
ejpam-5386	228	9	sizes	size	NOUN
ejpam-5386	228	10	,	,	PUNCT
ejpam-5386	228	11	and	and	CCONJ
ejpam-5386	229	1	sk	sk	AUX
ejpam-5386	229	2	α	α	PROPN
ejpam-5386	229	3	and	and	CCONJ
ejpam-5386	229	4	sk	sk	PROPN
ejpam-5386	229	5	φ	φ	PROPN
ejpam-5386	229	6	represent	represent	VERB
ejpam-5386	229	7	the	the	DET
ejpam-5386	229	8	search	search	NOUN
ejpam-5386	229	9	directions	direction	NOUN
ejpam-5386	229	10	which	which	PRON
ejpam-5386	229	11	are	be	AUX
ejpam-5386	229	12	determined	determine	VERB
ejpam-5386	229	13	by	by	ADP
ejpam-5386	229	14	the	the	DET
ejpam-5386	229	15	following	follow	VERB
ejpam-5386	229	16	equations	equation	NOUN
ejpam-5386	229	17	:	:	PUNCT
ejpam-5386	229	18	sk	sk	PROPN
ejpam-5386	229	19	α	α	PROPN
ejpam-5386	229	20	=	=	X
ejpam-5386	229	21	{	{	PUNCT
ejpam-5386	229	22	−j	−j	NOUN
ejpam-5386	229	23	′0	′0	VERB
ejpam-5386	229	24	α	α	NOUN
ejpam-5386	229	25	,	,	PUNCT
ejpam-5386	229	26	k	k	PROPN
ejpam-5386	229	27	=	=	SYM
ejpam-5386	229	28	0	0	NUM
ejpam-5386	229	29	,	,	PUNCT
ejpam-5386	229	30	−j	−j	VERB
ejpam-5386	229	31	′k	′k	SCONJ
ejpam-5386	229	32	α	α	NOUN
ejpam-5386	229	33	+	+	CCONJ
ejpam-5386	229	34	ϑkα	ϑkα	NOUN
ejpam-5386	229	35	s	s	PART
ejpam-5386	229	36	k−1	k−1	PROPN
ejpam-5386	229	37	α	α	PROPN
ejpam-5386	229	38	,	,	PUNCT
ejpam-5386	229	39	k	k	X
ejpam-5386	229	40	≥	≥	NUM
ejpam-5386	229	41	1	1	NUM
ejpam-5386	229	42	,	,	PUNCT
ejpam-5386	229	43	and	and	CCONJ
ejpam-5386	229	44	sk	sk	VERB
ejpam-5386	229	45	φ	φ	PROPN
ejpam-5386	229	46	=	=	X
ejpam-5386	229	47	{	{	PUNCT
ejpam-5386	229	48	−j	−j	NOUN
ejpam-5386	229	49	′0	′0	PROPN
ejpam-5386	229	50	φ	φ	PROPN
ejpam-5386	229	51	,	,	PUNCT
ejpam-5386	229	52	k	k	PROPN
ejpam-5386	229	53	=	=	SYM
ejpam-5386	229	54	0	0	NUM
ejpam-5386	229	55	,	,	PUNCT
ejpam-5386	229	56	−j	−j	VERB
ejpam-5386	229	57	′k	′k	SCONJ
ejpam-5386	229	58	φ	φ	PROPN
ejpam-5386	229	59	+	+	PROPN
ejpam-5386	229	60	ϑkφ	ϑkφ	NOUN
ejpam-5386	229	61	s	s	PART
ejpam-5386	229	62	k−1	k−1	PROPN
ejpam-5386	229	63	φ	φ	PROPN
ejpam-5386	229	64	,	,	PUNCT
ejpam-5386	229	65	k	k	PROPN
ejpam-5386	229	66	≥	≥	NUM
ejpam-5386	229	67	1	1	NUM
ejpam-5386	229	68	,	,	PUNCT
ejpam-5386	229	69	(	(	PUNCT
ejpam-5386	229	70	23	23	NUM
ejpam-5386	229	71	)	)	PUNCT
ejpam-5386	229	72	where	where	SCONJ
ejpam-5386	229	73	j	j	PROPN
ejpam-5386	229	74	′k	′k	NOUN
ejpam-5386	229	75	α	α	PROPN
ejpam-5386	229	76	=	=	PUNCT
ejpam-5386	229	77	j	j	PROPN
ejpam-5386	230	1	′	′	NUM
ejpam-5386	231	1	α(α	α(α	PROPN
ejpam-5386	231	2	k	k	PROPN
ejpam-5386	231	3	,	,	PUNCT
ejpam-5386	231	4	φk	φk	ADP
ejpam-5386	231	5	)	)	PUNCT
ejpam-5386	231	6	and	and	CCONJ
ejpam-5386	231	7	j	j	PROPN
ejpam-5386	231	8	′k	′k	NOUN
ejpam-5386	231	9	φ	φ	PROPN
ejpam-5386	231	10	=	=	SYM
ejpam-5386	231	11	j	j	PROPN
ejpam-5386	231	12	′	′	NUM
ejpam-5386	231	13	φ(α	φ(α	PROPN
ejpam-5386	231	14	k	k	PROPN
ejpam-5386	231	15	,	,	PUNCT
ejpam-5386	231	16	φk	φk	ADP
ejpam-5386	231	17	)	)	PUNCT
ejpam-5386	231	18	denote	denote	VERB
ejpam-5386	231	19	the	the	DET
ejpam-5386	231	20	derivatives	derivative	NOUN
ejpam-5386	231	21	of	of	ADP
ejpam-5386	231	22	j(α	j(α	PROPN
ejpam-5386	231	23	,	,	PUNCT
ejpam-5386	231	24	φ	φ	NUM
ejpam-5386	231	25	)	)	PUNCT
ejpam-5386	231	26	with	with	ADP
ejpam-5386	231	27	respect	respect	NOUN
ejpam-5386	231	28	to	to	ADP
ejpam-5386	231	29	α	α	PROPN
ejpam-5386	231	30	and	and	CCONJ
ejpam-5386	231	31	φ	φ	NUM
ejpam-5386	231	32	,	,	PUNCT
ejpam-5386	231	33	respectively	respectively	ADV
ejpam-5386	231	34	,	,	PUNCT
ejpam-5386	231	35	at	at	ADP
ejpam-5386	231	36	point	point	NOUN
ejpam-5386	231	37	(	(	PUNCT
ejpam-5386	231	38	αk	αk	NOUN
ejpam-5386	231	39	,	,	PUNCT
ejpam-5386	231	40	φk	φk	ADP
ejpam-5386	231	41	)	)	PUNCT
ejpam-5386	231	42	.	.	PUNCT
ejpam-5386	232	1	the	the	DET
ejpam-5386	232	2	terms	term	NOUN
ejpam-5386	232	3	ϑkα	ϑkα	NOUN
ejpam-5386	232	4	and	and	CCONJ
ejpam-5386	232	5	ϑkφ	ϑkφ	NOUN
ejpam-5386	232	6	are	be	AUX
ejpam-5386	232	7	the	the	DET
ejpam-5386	232	8	conjugate	conjugate	ADJ
ejpam-5386	232	9	coefficients	coefficient	NOUN
ejpam-5386	232	10	obtained	obtain	VERB
ejpam-5386	232	11	using	use	VERB
ejpam-5386	232	12	the	the	DET
ejpam-5386	232	13	fletcher	fletcher	PROPN
ejpam-5386	232	14	-	-	PUNCT
ejpam-5386	232	15	reeves	reeve	NOUN
ejpam-5386	232	16	formula	formula	NOUN
ejpam-5386	232	17	[	[	X
ejpam-5386	232	18	12	12	NUM
ejpam-5386	232	19	]	]	X
ejpam-5386	232	20	ϑkα	ϑkα	NOUN
ejpam-5386	232	21	=	=	SYM
ejpam-5386	232	22	∥∥j	∥∥j	NOUN
ejpam-5386	232	23	′k	′k	ADP
ejpam-5386	232	24	α	α	X
ejpam-5386	232	25	∥∥	∥∥	VERB
ejpam-5386	232	26	2∥∥∥j	2∥∥∥j	NOUN
ejpam-5386	232	27	′k−1	′k−1	VERB
ejpam-5386	232	28	α	α	DET
ejpam-5386	232	29	∥∥∥	∥∥∥	PROPN
ejpam-5386	232	30	2	2	NUM
ejpam-5386	232	31	and	and	CCONJ
ejpam-5386	232	32	ϑkφ	ϑkφ	NOUN
ejpam-5386	232	33	=	=	SYM
ejpam-5386	232	34	∥∥j	∥∥j	NOUN
ejpam-5386	232	35	′k	′k	PROPN
ejpam-5386	232	36	φ	φ	PROPN
ejpam-5386	232	37	∥∥	∥∥	PROPN
ejpam-5386	232	38	2∥∥∥j	2∥∥∥j	PROPN
ejpam-5386	232	39	′k−1	′k−1	PROPN
ejpam-5386	232	40	φ	φ	PROPN
ejpam-5386	232	41	∥∥∥	∥∥∥	PROPN
ejpam-5386	232	42	2	2	NUM
ejpam-5386	232	43	,	,	PUNCT
ejpam-5386	232	44	k	k	NOUN
ejpam-5386	232	45	=	=	SYM
ejpam-5386	232	46	1	1	NUM
ejpam-5386	232	47	,	,	PUNCT
ejpam-5386	232	48	2	2	NUM
ejpam-5386	232	49	,	,	PUNCT
ejpam-5386	232	50	·	·	PUNCT
ejpam-5386	232	51	·	·	PUNCT
ejpam-5386	232	52	·	·	PUNCT
ejpam-5386	232	53	.	.	PUNCT
ejpam-5386	233	1	(	(	PUNCT
ejpam-5386	233	2	24	24	NUM
ejpam-5386	233	3	)	)	PUNCT
ejpam-5386	233	4	s.	s.	PROPN
ejpam-5386	233	5	tatar	tatar	PROPN
ejpam-5386	233	6	,	,	PUNCT
ejpam-5386	233	7	m.	m.	NOUN
ejpam-5386	233	8	bensalah	bensalah	PROPN
ejpam-5386	233	9	,	,	PUNCT
ejpam-5386	233	10	m.	m.	NOUN
ejpam-5386	233	11	alamil	alamil	PROPN
ejpam-5386	233	12	/	/	SYM
ejpam-5386	233	13	eur	eur	PROPN
ejpam-5386	233	14	.	.	PUNCT
ejpam-5386	234	1	j.	j.	PROPN
ejpam-5386	234	2	pure	pure	PROPN
ejpam-5386	234	3	appl	appl	PROPN
ejpam-5386	234	4	.	.	PROPN
ejpam-5386	234	5	math	math	PROPN
ejpam-5386	234	6	,	,	PUNCT
ejpam-5386	234	7	17	17	NUM
ejpam-5386	234	8	(	(	PUNCT
ejpam-5386	234	9	4	4	NUM
ejpam-5386	234	10	)	)	PUNCT
ejpam-5386	234	11	(	(	PUNCT
ejpam-5386	234	12	2024	2024	NUM
ejpam-5386	234	13	)	)	PUNCT
ejpam-5386	234	14	,	,	PUNCT
ejpam-5386	234	15	2651	2651	NUM
ejpam-5386	234	16	-	-	SYM
ejpam-5386	234	17	2675	2675	NUM
ejpam-5386	234	18	2662	2662	NUM
ejpam-5386	234	19	building	build	VERB
ejpam-5386	234	20	upon	upon	SCONJ
ejpam-5386	234	21	the	the	DET
ejpam-5386	234	22	preceding	precede	VERB
ejpam-5386	234	23	discussions	discussion	NOUN
ejpam-5386	234	24	,	,	PUNCT
ejpam-5386	234	25	it	it	PRON
ejpam-5386	234	26	is	be	AUX
ejpam-5386	234	27	noteworthy	noteworthy	ADJ
ejpam-5386	234	28	that	that	SCONJ
ejpam-5386	234	29	all	all	DET
ejpam-5386	234	30	parameters	parameter	NOUN
ejpam-5386	234	31	are	be	AUX
ejpam-5386	234	32	explicitly	explicitly	ADV
ejpam-5386	234	33	expressed	express	VERB
ejpam-5386	234	34	,	,	PUNCT
ejpam-5386	234	35	except	except	SCONJ
ejpam-5386	234	36	the	the	DET
ejpam-5386	234	37	search	search	NOUN
ejpam-5386	234	38	step	step	NOUN
ejpam-5386	234	39	sizes	size	NOUN
ejpam-5386	234	40	ζkα	ζkα	VERB
ejpam-5386	234	41	and	and	CCONJ
ejpam-5386	234	42	ζkφ	ζkφ	VERB
ejpam-5386	234	43	.	.	PUNCT
ejpam-5386	235	1	the	the	DET
ejpam-5386	235	2	determination	determination	NOUN
ejpam-5386	235	3	of	of	ADP
ejpam-5386	235	4	these	these	DET
ejpam-5386	235	5	parameters	parameter	NOUN
ejpam-5386	235	6	is	be	AUX
ejpam-5386	235	7	accomplished	accomplish	VERB
ejpam-5386	235	8	through	through	ADP
ejpam-5386	235	9	the	the	DET
ejpam-5386	235	10	utilization	utilization	NOUN
ejpam-5386	235	11	of	of	ADP
ejpam-5386	235	12	the	the	DET
ejpam-5386	235	13	line	line	NOUN
ejpam-5386	235	14	search	search	NOUN
ejpam-5386	235	15	method	method	NOUN
ejpam-5386	235	16	.	.	PUNCT
ejpam-5386	236	1	specifically	specifically	ADV
ejpam-5386	236	2	,	,	PUNCT
ejpam-5386	236	3	the	the	DET
ejpam-5386	236	4	values	value	NOUN
ejpam-5386	236	5	for	for	ADP
ejpam-5386	236	6	ζkα	ζkα	NOUN
ejpam-5386	236	7	and	and	CCONJ
ejpam-5386	236	8	ζkφ	ζkφ	NOUN
ejpam-5386	236	9	are	be	AUX
ejpam-5386	236	10	obtained	obtain	VERB
ejpam-5386	236	11	by	by	ADP
ejpam-5386	236	12	minimizing	minimize	VERB
ejpam-5386	236	13	the	the	DET
ejpam-5386	236	14	following	follow	VERB
ejpam-5386	236	15	functional	functional	ADJ
ejpam-5386	236	16	:	:	PUNCT
ejpam-5386	236	17	j(αk+1,φk+1	j(αk+1,φk+1	NOUN
ejpam-5386	236	18	)	)	PUNCT
ejpam-5386	236	19	:	:	PUNCT
ejpam-5386	237	1	=	=	SYM
ejpam-5386	237	2	1	1	NUM
ejpam-5386	237	3	2	2	NUM
ejpam-5386	237	4	2∑	2∑	NUM
ejpam-5386	237	5	i=1	i=1	X
ejpam-5386	237	6	(	(	PUNCT
ejpam-5386	237	7	∥∥∥∫	∥∥∥∫	PROPN
ejpam-5386	237	8	t	t	PROPN
ejpam-5386	237	9	0	0	NUM
ejpam-5386	237	10	ωi(t)u(α	ωi(t)u(α	PROPN
ejpam-5386	237	11	k+1,φk+1	k+1,φk+1	PROPN
ejpam-5386	237	12	)	)	PUNCT
ejpam-5386	237	13	dt−	dt−	CCONJ
ejpam-5386	237	14	ϕεi	ϕεi	VERB
ejpam-5386	237	15	∥∥∥2	∥∥∥2	NOUN
ejpam-5386	237	16	2	2	NUM
ejpam-5386	237	17	)	)	PUNCT
ejpam-5386	237	18	.	.	PUNCT
ejpam-5386	238	1	since	since	SCONJ
ejpam-5386	238	2	the	the	DET
ejpam-5386	238	3	search	search	NOUN
ejpam-5386	238	4	step	step	NOUN
ejpam-5386	238	5	sizes	size	NOUN
ejpam-5386	238	6	ζkα	ζkα	VERB
ejpam-5386	238	7	and	and	CCONJ
ejpam-5386	238	8	ζkφ	ζkφ	NOUN
ejpam-5386	238	9	are	be	AUX
ejpam-5386	238	10	implicit	implicit	ADJ
ejpam-5386	238	11	in	in	ADP
ejpam-5386	238	12	the	the	DET
ejpam-5386	238	13	expression	expression	NOUN
ejpam-5386	238	14	of	of	ADP
ejpam-5386	238	15	j(αk+1	j(αk+1	PROPN
ejpam-5386	238	16	,	,	PUNCT
ejpam-5386	238	17	φk+1	φk+1	NOUN
ejpam-5386	238	18	)	)	PUNCT
ejpam-5386	238	19	,	,	PUNCT
ejpam-5386	238	20	we	we	PRON
ejpam-5386	238	21	adopt	adopt	VERB
ejpam-5386	238	22	a	a	DET
ejpam-5386	238	23	similar	similar	ADJ
ejpam-5386	238	24	approach	approach	NOUN
ejpam-5386	238	25	to	to	ADP
ejpam-5386	238	26	[	[	X
ejpam-5386	238	27	3	3	NUM
ejpam-5386	238	28	,	,	PUNCT
ejpam-5386	238	29	4	4	NUM
ejpam-5386	238	30	]	]	PUNCT
ejpam-5386	238	31	and	and	CCONJ
ejpam-5386	238	32	linearize	linearize	VERB
ejpam-5386	238	33	it	it	PRON
ejpam-5386	238	34	such	such	ADJ
ejpam-5386	238	35	that	that	SCONJ
ejpam-5386	238	36	these	these	DET
ejpam-5386	238	37	parameters	parameter	NOUN
ejpam-5386	238	38	become	become	VERB
ejpam-5386	238	39	explicit	explicit	ADJ
ejpam-5386	238	40	in	in	ADP
ejpam-5386	238	41	the	the	DET
ejpam-5386	238	42	new	new	ADJ
ejpam-5386	238	43	formulation	formulation	NOUN
ejpam-5386	238	44	.	.	PUNCT
ejpam-5386	239	1	hence	hence	ADV
ejpam-5386	239	2	c(αk+1,φk+1	c(αk+1,φk+1	NOUN
ejpam-5386	239	3	)	)	PUNCT
ejpam-5386	239	4	becomes	become	VERB
ejpam-5386	239	5	as	as	SCONJ
ejpam-5386	239	6	follows	follow	VERB
ejpam-5386	239	7	:	:	PUNCT
ejpam-5386	239	8	c(αk+1,φk+1	c(αk+1,φk+1	NOUN
ejpam-5386	239	9	)	)	PUNCT
ejpam-5386	239	10	:	:	PUNCT
ejpam-5386	239	11	≈	≈	PROPN
ejpam-5386	239	12	c(αk	c(αk	PROPN
ejpam-5386	239	13	,	,	PUNCT
ejpam-5386	239	14	φk	φk	ADP
ejpam-5386	239	15	)	)	PUNCT
ejpam-5386	239	16	+	+	CCONJ
ejpam-5386	239	17	ζkαη	ζkαη	NOUN
ejpam-5386	239	18	k	k	PROPN
ejpam-5386	239	19	α	α	PROPN
ejpam-5386	239	20	+	+	X
ejpam-5386	239	21	ζkφη	ζkφη	VERB
ejpam-5386	239	22	k	k	PROPN
ejpam-5386	239	23	φ	φ	PROPN
ejpam-5386	239	24	,	,	PUNCT
ejpam-5386	239	25	(	(	PUNCT
ejpam-5386	239	26	25	25	NUM
ejpam-5386	239	27	)	)	PUNCT
ejpam-5386	239	28	where	where	SCONJ
ejpam-5386	239	29	ηkα	ηkα	NOUN
ejpam-5386	239	30	and	and	CCONJ
ejpam-5386	239	31	ηkφ	ηkφ	NOUN
ejpam-5386	239	32	are	be	AUX
ejpam-5386	239	33	obtained	obtain	VERB
ejpam-5386	239	34	by	by	ADP
ejpam-5386	239	35	solving	solve	VERB
ejpam-5386	239	36	the	the	DET
ejpam-5386	239	37	sensitivity	sensitivity	NOUN
ejpam-5386	239	38	problems	problem	NOUN
ejpam-5386	239	39	(	(	PUNCT
ejpam-5386	239	40	18	18	NUM
ejpam-5386	239	41	)	)	PUNCT
ejpam-5386	239	42	and	and	CCONJ
ejpam-5386	239	43	(	(	PUNCT
ejpam-5386	239	44	19	19	NUM
ejpam-5386	239	45	)	)	PUNCT
ejpam-5386	239	46	with	with	ADP
ejpam-5386	239	47	(	(	PUNCT
ejpam-5386	239	48	α	α	X
ejpam-5386	239	49	,	,	PUNCT
ejpam-5386	239	50	φ	φ	NOUN
ejpam-5386	239	51	)	)	PUNCT
ejpam-5386	239	52	=	=	PRON
ejpam-5386	239	53	(	(	PUNCT
ejpam-5386	239	54	αk	αk	NOUN
ejpam-5386	239	55	,	,	PUNCT
ejpam-5386	239	56	φk	φk	ADP
ejpam-5386	239	57	)	)	PUNCT
ejpam-5386	239	58	and	and	CCONJ
ejpam-5386	239	59	(	(	PUNCT
ejpam-5386	239	60	α0,φ0	α0,φ0	PROPN
ejpam-5386	239	61	)	)	PUNCT
ejpam-5386	239	62	=	=	PRON
ejpam-5386	240	1	(	(	PUNCT
ejpam-5386	240	2	sk	sk	PROPN
ejpam-5386	240	3	α	α	PROPN
ejpam-5386	240	4	,	,	PUNCT
ejpam-5386	240	5	s	s	PROPN
ejpam-5386	240	6	k	k	PROPN
ejpam-5386	240	7	φ	φ	PROPN
ejpam-5386	240	8	)	)	PUNCT
ejpam-5386	240	9	.	.	PUNCT
ejpam-5386	241	1	we	we	PRON
ejpam-5386	241	2	now	now	ADV
ejpam-5386	241	3	define	define	VERB
ejpam-5386	241	4	cki	cki	PROPN
ejpam-5386	241	5	=	=	SYM
ejpam-5386	241	6	∫	∫	PROPN
ejpam-5386	241	7	t	t	PROPN
ejpam-5386	241	8	0	0	NUM
ejpam-5386	241	9	ωi	ωi	PROPN
ejpam-5386	241	10	c	c	PROPN
ejpam-5386	241	11	k	k	PROPN
ejpam-5386	241	12	dt	dt	PROPN
ejpam-5386	241	13	,	,	PUNCT
ejpam-5386	241	14	ηkα	ηkα	NOUN
ejpam-5386	241	15	,	,	PUNCT
ejpam-5386	241	16	i	i	PRON
ejpam-5386	241	17	=	=	NOUN
ejpam-5386	242	1	∫	∫	PROPN
ejpam-5386	242	2	t	t	PROPN
ejpam-5386	242	3	0	0	NUM
ejpam-5386	242	4	ωi	ωi	PROPN
ejpam-5386	242	5	η	η	PROPN
ejpam-5386	242	6	k	k	PROPN
ejpam-5386	242	7	α	α	PROPN
ejpam-5386	242	8	dt	dt	X
ejpam-5386	242	9	and	and	CCONJ
ejpam-5386	242	10	ηkφ	ηkφ	PROPN
ejpam-5386	242	11	,	,	PUNCT
ejpam-5386	242	12	i	i	PRON
ejpam-5386	243	1	=	=	NOUN
ejpam-5386	243	2	∫	∫	PROPN
ejpam-5386	243	3	t	t	PROPN
ejpam-5386	243	4	0	0	NUM
ejpam-5386	244	1	ωi	ωi	PROPN
ejpam-5386	244	2	η	η	PROPN
ejpam-5386	244	3	k	k	PROPN
ejpam-5386	244	4	φ	φ	PROPN
ejpam-5386	244	5	dt	dt	PROPN
ejpam-5386	244	6	,	,	PUNCT
ejpam-5386	244	7	for	for	ADP
ejpam-5386	244	8	i	i	PROPN
ejpam-5386	244	9	=	=	SYM
ejpam-5386	244	10	1	1	NUM
ejpam-5386	244	11	,	,	PUNCT
ejpam-5386	244	12	2	2	NUM
ejpam-5386	244	13	,	,	PUNCT
ejpam-5386	244	14	with	with	ADP
ejpam-5386	244	15	ck	ck	NOUN
ejpam-5386	244	16	=	=	SYM
ejpam-5386	244	17	c(αk	c(αk	PROPN
ejpam-5386	244	18	,	,	PUNCT
ejpam-5386	244	19	φk	φk	ADP
ejpam-5386	244	20	)	)	PUNCT
ejpam-5386	244	21	.	.	PUNCT
ejpam-5386	245	1	then	then	ADV
ejpam-5386	245	2	,	,	PUNCT
ejpam-5386	245	3	from	from	ADP
ejpam-5386	245	4	(	(	PUNCT
ejpam-5386	245	5	7	7	NUM
ejpam-5386	245	6	)	)	PUNCT
ejpam-5386	245	7	and	and	CCONJ
ejpam-5386	245	8	(	(	PUNCT
ejpam-5386	245	9	25	25	NUM
ejpam-5386	245	10	)	)	PUNCT
ejpam-5386	245	11	,	,	PUNCT
ejpam-5386	245	12	we	we	PRON
ejpam-5386	245	13	have	have	VERB
ejpam-5386	245	14	j(αk+1,φk+1	j(αk+1,φk+1	NOUN
ejpam-5386	245	15	)	)	PUNCT
ejpam-5386	245	16	=	=	SYM
ejpam-5386	246	1	1	1	NUM
ejpam-5386	246	2	2	2	NUM
ejpam-5386	246	3	2∑	2∑	NUM
ejpam-5386	246	4	i=1	i=1	PROPN
ejpam-5386	246	5	∫	∫	PROPN
ejpam-5386	246	6	ω	ω	PROPN
ejpam-5386	246	7	(	(	PUNCT
ejpam-5386	246	8	cki	cki	PROPN
ejpam-5386	246	9	+	+	PROPN
ejpam-5386	246	10	ζkα	ζkα	PROPN
ejpam-5386	246	11	η	η	PROPN
ejpam-5386	246	12	k	k	PROPN
ejpam-5386	246	13	α	α	PROPN
ejpam-5386	246	14	,	,	PUNCT
ejpam-5386	246	15	i	i	PRON
ejpam-5386	246	16	+	+	CCONJ
ejpam-5386	246	17	ζkφ	ζkφ	VERB
ejpam-5386	246	18	η	η	PROPN
ejpam-5386	246	19	k	k	PROPN
ejpam-5386	246	20	φ	φ	PROPN
ejpam-5386	246	21	,	,	PUNCT
ejpam-5386	246	22	i	i	PRON
ejpam-5386	246	23	−	−	VERB
ejpam-5386	246	24	ϕεi	ϕεi	VERB
ejpam-5386	246	25	)	)	PUNCT
ejpam-5386	246	26	2	2	NUM
ejpam-5386	246	27	dx	dx	PROPN
ejpam-5386	246	28	.	.	PUNCT
ejpam-5386	247	1	(	(	PUNCT
ejpam-5386	247	2	26	26	NUM
ejpam-5386	247	3	)	)	PUNCT
ejpam-5386	247	4	it	it	PRON
ejpam-5386	247	5	follows	follow	VERB
ejpam-5386	247	6	∂j(αk+1,φk+1	∂j(αk+1,φk+1	NOUN
ejpam-5386	247	7	)	)	PUNCT
ejpam-5386	247	8	∂ζkα	∂ζkα	NUM
ejpam-5386	247	9	:	:	PUNCT
ejpam-5386	247	10	=	=	SYM
ejpam-5386	248	1	r1ζ	r1ζ	PROPN
ejpam-5386	248	2	k	k	PROPN
ejpam-5386	249	1	α	α	PROPN
ejpam-5386	249	2	+	+	PROPN
ejpam-5386	249	3	r2ζ	r2ζ	PROPN
ejpam-5386	249	4	k	k	PROPN
ejpam-5386	249	5	φ	φ	PROPN
ejpam-5386	249	6	−	−	PROPN
ejpam-5386	249	7	y1	y1	PROPN
ejpam-5386	249	8	and	and	CCONJ
ejpam-5386	249	9	∂j(αk+1,φk+1	∂j(αk+1,φk+1	NOUN
ejpam-5386	249	10	)	)	PUNCT
ejpam-5386	249	11	∂ζkγ	∂ζkγ	NOUN
ejpam-5386	249	12	:	:	PUNCT
ejpam-5386	250	1	=	=	PUNCT
ejpam-5386	250	2	r2ζ	r2ζ	NOUN
ejpam-5386	250	3	k	k	PROPN
ejpam-5386	250	4	α	α	PROPN
ejpam-5386	250	5	+	+	PROPN
ejpam-5386	250	6	r3ζ	r3ζ	NOUN
ejpam-5386	250	7	k	k	X
ejpam-5386	250	8	φ	φ	PROPN
ejpam-5386	250	9	−	−	PROPN
ejpam-5386	251	1	y2	y2	INTJ
ejpam-5386	251	2	,	,	PUNCT
ejpam-5386	251	3	where	where	SCONJ
ejpam-5386	251	4	r1	r1	PROPN
ejpam-5386	251	5	=	=	PUNCT
ejpam-5386	251	6	2∑	2∑	NUM
ejpam-5386	251	7	i=1	i=1	X
ejpam-5386	251	8	∥ηkα	∥ηkα	PROPN
ejpam-5386	251	9	,	,	PUNCT
ejpam-5386	251	10	i∥22	i∥22	PROPN
ejpam-5386	251	11	,	,	PUNCT
ejpam-5386	251	12	r2	r2	PROPN
ejpam-5386	251	13	=	=	PUNCT
ejpam-5386	252	1	2∑	2∑	NUM
ejpam-5386	252	2	i=1	i=1	PROPN
ejpam-5386	252	3	∫	∫	PROPN
ejpam-5386	253	1	b	b	PROPN
ejpam-5386	253	2	ηkα	ηkα	PROPN
ejpam-5386	253	3	,	,	PUNCT
ejpam-5386	253	4	i	i	PROPN
ejpam-5386	253	5	η	η	PROPN
ejpam-5386	253	6	k	k	PROPN
ejpam-5386	253	7	φ	φ	PROPN
ejpam-5386	253	8	,	,	PUNCT
ejpam-5386	253	9	i	i	PRON
ejpam-5386	253	10	dx	dx	PROPN
ejpam-5386	253	11	,	,	PUNCT
ejpam-5386	253	12	r3	r3	PROPN
ejpam-5386	253	13	=	=	SYM
ejpam-5386	254	1	2∑	2∑	NUM
ejpam-5386	254	2	i=1	i=1	X
ejpam-5386	254	3	∥ηkφ	∥ηkφ	PROPN
ejpam-5386	254	4	,	,	PUNCT
ejpam-5386	254	5	i∥22	i∥22	PROPN
ejpam-5386	254	6	,	,	PUNCT
ejpam-5386	254	7	y1	y1	NOUN
ejpam-5386	254	8	=	=	PUNCT
ejpam-5386	254	9	2∑	2∑	NUM
ejpam-5386	254	10	i=1	i=1	PROPN
ejpam-5386	254	11	∫	∫	PROPN
ejpam-5386	255	1	b	b	PROPN
ejpam-5386	255	2	ηkα	ηkα	NOUN
ejpam-5386	255	3	,	,	PUNCT
ejpam-5386	255	4	i(ϕ	i(ϕ	PROPN
ejpam-5386	255	5	ε	ε	PROPN
ejpam-5386	255	6	i	i	PRON
ejpam-5386	255	7	−	−	PROPN
ejpam-5386	255	8	cki	cki	PROPN
ejpam-5386	255	9	)	)	PUNCT
ejpam-5386	255	10	dx	dx	PROPN
ejpam-5386	255	11	,	,	PUNCT
ejpam-5386	255	12	and	and	CCONJ
ejpam-5386	256	1	y2	y2	NOUN
ejpam-5386	256	2	=	=	SYM
ejpam-5386	257	1	2∑	2∑	NUM
ejpam-5386	257	2	i=1	i=1	PROPN
ejpam-5386	257	3	∫	∫	PROPN
ejpam-5386	257	4	b	b	PROPN
ejpam-5386	257	5	ηkφ	ηkφ	PROPN
ejpam-5386	257	6	,	,	PUNCT
ejpam-5386	257	7	i(ϕ	i(ϕ	PROPN
ejpam-5386	257	8	ε	ε	PROPN
ejpam-5386	257	9	i	i	PRON
ejpam-5386	257	10	−	−	PROPN
ejpam-5386	257	11	cki	cki	PROPN
ejpam-5386	257	12	)	)	PUNCT
ejpam-5386	257	13	dx	dx	PROPN
ejpam-5386	257	14	.	.	PUNCT
ejpam-5386	258	1	by	by	ADP
ejpam-5386	258	2	setting	set	VERB
ejpam-5386	258	3	∂j(αk+1,φk+1	∂j(αk+1,φk+1	NOUN
ejpam-5386	258	4	)	)	PUNCT
ejpam-5386	258	5	∂ζkα	∂ζkα	NUM
ejpam-5386	258	6	=	=	SYM
ejpam-5386	258	7	∂j(αk+1,φk+1	∂j(αk+1,φk+1	PROPN
ejpam-5386	258	8	)	)	PUNCT
ejpam-5386	258	9	∂ζkφ	∂ζkφ	PUNCT
ejpam-5386	258	10	=	=	SYM
ejpam-5386	258	11	0	0	NUM
ejpam-5386	258	12	,	,	PUNCT
ejpam-5386	258	13	one	one	PRON
ejpam-5386	258	14	can	can	AUX
ejpam-5386	258	15	deduce	deduce	VERB
ejpam-5386	258	16	that	that	SCONJ
ejpam-5386	258	17	the	the	DET
ejpam-5386	258	18	search	search	NOUN
ejpam-5386	258	19	step	step	NOUN
ejpam-5386	258	20	sizes	size	NOUN
ejpam-5386	258	21	ζkα	ζkα	VERB
ejpam-5386	258	22	and	and	CCONJ
ejpam-5386	258	23	ζkφ	ζkφ	VERB
ejpam-5386	258	24	satisfy	satisfy	VERB
ejpam-5386	258	25	the	the	DET
ejpam-5386	258	26	following	follow	VERB
ejpam-5386	258	27	linear	linear	ADJ
ejpam-5386	258	28	system	system	NOUN
ejpam-5386	258	29	{	{	PUNCT
ejpam-5386	258	30	r1ζ	r1ζ	NOUN
ejpam-5386	258	31	k	k	PROPN
ejpam-5386	259	1	α	α	PROPN
ejpam-5386	259	2	+	+	PROPN
ejpam-5386	259	3	r2ζ	r2ζ	PROPN
ejpam-5386	259	4	k	k	PROPN
ejpam-5386	259	5	φ	φ	PROPN
ejpam-5386	259	6	=	=	SYM
ejpam-5386	259	7	y1	y1	PROPN
ejpam-5386	259	8	,	,	PUNCT
ejpam-5386	259	9	r2ζ	r2ζ	PROPN
ejpam-5386	259	10	k	k	PROPN
ejpam-5386	259	11	α	α	PROPN
ejpam-5386	260	1	+	+	PROPN
ejpam-5386	260	2	r3ζ	r3ζ	PROPN
ejpam-5386	260	3	k	k	PROPN
ejpam-5386	260	4	φ	φ	PROPN
ejpam-5386	260	5	=	=	SYM
ejpam-5386	260	6	y2	y2	PROPN
ejpam-5386	260	7	.	.	PUNCT
ejpam-5386	261	1	s.	s.	PROPN
ejpam-5386	261	2	tatar	tatar	PROPN
ejpam-5386	261	3	,	,	PUNCT
ejpam-5386	261	4	m.	m.	NOUN
ejpam-5386	261	5	bensalah	bensalah	PROPN
ejpam-5386	261	6	,	,	PUNCT
ejpam-5386	261	7	m.	m.	NOUN
ejpam-5386	261	8	alamil	alamil	PROPN
ejpam-5386	261	9	/	/	SYM
ejpam-5386	261	10	eur	eur	PROPN
ejpam-5386	261	11	.	.	PUNCT
ejpam-5386	262	1	j.	j.	PROPN
ejpam-5386	262	2	pure	pure	PROPN
ejpam-5386	262	3	appl	appl	PROPN
ejpam-5386	262	4	.	.	PROPN
ejpam-5386	262	5	math	math	PROPN
ejpam-5386	262	6	,	,	PUNCT
ejpam-5386	262	7	17	17	NUM
ejpam-5386	262	8	(	(	PUNCT
ejpam-5386	262	9	4	4	NUM
ejpam-5386	262	10	)	)	PUNCT
ejpam-5386	262	11	(	(	PUNCT
ejpam-5386	262	12	2024	2024	NUM
ejpam-5386	262	13	)	)	PUNCT
ejpam-5386	262	14	,	,	PUNCT
ejpam-5386	262	15	2651	2651	NUM
ejpam-5386	262	16	-	-	SYM
ejpam-5386	262	17	2675	2675	NUM
ejpam-5386	262	18	2663	2663	NUM
ejpam-5386	262	19	therefore	therefore	ADV
ejpam-5386	262	20	,	,	PUNCT
ejpam-5386	262	21	direct	direct	ADJ
ejpam-5386	262	22	calculations	calculation	NOUN
ejpam-5386	262	23	yield	yield	VERB
ejpam-5386	262	24	ζkα	ζkα	NOUN
ejpam-5386	262	25	=	=	PUNCT
ejpam-5386	262	26	r3y1	r3y1	PROPN
ejpam-5386	262	27	−r2y2	−r2y2	PROPN
ejpam-5386	262	28	r3r1	r3r1	VERB
ejpam-5386	262	29	−r2	−r2	PROPN
ejpam-5386	262	30	2	2	NUM
ejpam-5386	262	31	and	and	CCONJ
ejpam-5386	262	32	ζkα	ζkα	NOUN
ejpam-5386	262	33	=	=	PUNCT
ejpam-5386	262	34	r1y2	r1y2	PRON
ejpam-5386	262	35	−r2y1	−r2y1	PROPN
ejpam-5386	262	36	r3r1	r3r1	VERB
ejpam-5386	262	37	−r2	−r2	PROPN
ejpam-5386	262	38	2	2	NUM
ejpam-5386	262	39	.	.	PUNCT
ejpam-5386	263	1	(	(	PUNCT
ejpam-5386	263	2	27	27	NUM
ejpam-5386	263	3	)	)	PUNCT
ejpam-5386	263	4	in	in	ADP
ejpam-5386	263	5	the	the	DET
ejpam-5386	263	6	context	context	NOUN
ejpam-5386	263	7	of	of	ADP
ejpam-5386	263	8	iterative	iterative	ADJ
ejpam-5386	263	9	algorithms	algorithm	NOUN
ejpam-5386	263	10	,	,	PUNCT
ejpam-5386	263	11	it	it	PRON
ejpam-5386	263	12	is	be	AUX
ejpam-5386	263	13	widely	widely	ADV
ejpam-5386	263	14	recognized	recognize	VERB
ejpam-5386	263	15	that	that	SCONJ
ejpam-5386	263	16	determining	determine	VERB
ejpam-5386	263	17	a	a	DET
ejpam-5386	263	18	suitable	suitable	ADJ
ejpam-5386	263	19	stopping	stopping	NOUN
ejpam-5386	263	20	criterion	criterion	NOUN
ejpam-5386	263	21	is	be	AUX
ejpam-5386	263	22	crucial	crucial	ADJ
ejpam-5386	263	23	.	.	PUNCT
ejpam-5386	264	1	addressing	address	VERB
ejpam-5386	264	2	this	this	DET
ejpam-5386	264	3	concern	concern	NOUN
ejpam-5386	264	4	,	,	PUNCT
ejpam-5386	264	5	the	the	DET
ejpam-5386	264	6	present	present	ADJ
ejpam-5386	264	7	study	study	NOUN
ejpam-5386	264	8	employs	employ	VERB
ejpam-5386	264	9	the	the	DET
ejpam-5386	264	10	discrepancy	discrepancy	NOUN
ejpam-5386	264	11	principle	principle	NOUN
ejpam-5386	264	12	to	to	PART
ejpam-5386	264	13	conclude	conclude	VERB
ejpam-5386	264	14	the	the	DET
ejpam-5386	264	15	iteration	iteration	NOUN
ejpam-5386	264	16	process	process	NOUN
ejpam-5386	264	17	.	.	PUNCT
ejpam-5386	265	1	according	accord	VERB
ejpam-5386	265	2	to	to	ADP
ejpam-5386	265	3	this	this	DET
ejpam-5386	265	4	principle	principle	NOUN
ejpam-5386	265	5	,	,	PUNCT
ejpam-5386	265	6	the	the	DET
ejpam-5386	265	7	iteration	iteration	NOUN
ejpam-5386	265	8	procedure	procedure	NOUN
ejpam-5386	265	9	if	if	SCONJ
ejpam-5386	265	10	the	the	DET
ejpam-5386	265	11	following	follow	VERB
ejpam-5386	265	12	condition	condition	NOUN
ejpam-5386	265	13	is	be	AUX
ejpam-5386	265	14	fulfilled	fulfil	VERB
ejpam-5386	265	15	:	:	PUNCT
ejpam-5386	265	16	j	j	PROPN
ejpam-5386	265	17	(	(	PUNCT
ejpam-5386	265	18	αk	αk	NOUN
ejpam-5386	265	19	,	,	PUNCT
ejpam-5386	265	20	φk	φk	ADP
ejpam-5386	265	21	)	)	PUNCT
ejpam-5386	265	22	≤	≤	NUM
ejpam-5386	265	23	ε̄	ε̄	NOUN
ejpam-5386	265	24	,	,	PUNCT
ejpam-5386	265	25	(	(	PUNCT
ejpam-5386	265	26	28	28	NUM
ejpam-5386	265	27	)	)	PUNCT
ejpam-5386	265	28	where	where	SCONJ
ejpam-5386	265	29	ε̄	ε̄	NOUN
ejpam-5386	265	30	is	be	AUX
ejpam-5386	265	31	a	a	DET
ejpam-5386	265	32	small	small	ADJ
ejpam-5386	265	33	positive	positive	ADJ
ejpam-5386	265	34	value	value	NOUN
ejpam-5386	265	35	,	,	PUNCT
ejpam-5386	265	36	such	such	ADJ
ejpam-5386	265	37	as	as	ADP
ejpam-5386	265	38	ε̄	ε̄	ADJ
ejpam-5386	265	39	=	=	SYM
ejpam-5386	265	40	10−6	10−6	NUM
ejpam-5386	265	41	for	for	ADP
ejpam-5386	265	42	exact	exact	ADJ
ejpam-5386	265	43	measurements	measurement	NOUN
ejpam-5386	265	44	.	.	PUNCT
ejpam-5386	266	1	in	in	ADP
ejpam-5386	266	2	cases	case	NOUN
ejpam-5386	266	3	where	where	SCONJ
ejpam-5386	266	4	the	the	DET
ejpam-5386	266	5	measurements	measurement	NOUN
ejpam-5386	266	6	exhibit	exhibit	VERB
ejpam-5386	266	7	noise	noise	NOUN
ejpam-5386	266	8	,	,	PUNCT
ejpam-5386	266	9	ε̄	ε̄	ADJ
ejpam-5386	266	10	=	=	SYM
ejpam-5386	266	11	1	1	NUM
ejpam-5386	266	12	2	2	NUM
ejpam-5386	266	13	2∑	2∑	NOUN
ejpam-5386	266	14	i=1	i=1	X
ejpam-5386	267	1	∥ϕεi	∥ϕεi	ADJ
ejpam-5386	267	2	−	−	PROPN
ejpam-5386	267	3	ϕi∥22	ϕi∥22	NOUN
ejpam-5386	267	4	.	.	PUNCT
ejpam-5386	268	1	building	build	VERB
ejpam-5386	268	2	upon	upon	SCONJ
ejpam-5386	268	3	(	(	PUNCT
ejpam-5386	268	4	6	6	NUM
ejpam-5386	268	5	)	)	PUNCT
ejpam-5386	268	6	,	,	PUNCT
ejpam-5386	268	7	it	it	PRON
ejpam-5386	268	8	is	be	AUX
ejpam-5386	268	9	established	establish	VERB
ejpam-5386	268	10	that	that	DET
ejpam-5386	268	11	ε̄	ε̄	ADJ
ejpam-5386	268	12	⩽	⩽	PROPN
ejpam-5386	268	13	ε2	ε2	PROPN
ejpam-5386	268	14	.	.	PUNCT
ejpam-5386	269	1	consequently	consequently	ADV
ejpam-5386	269	2	,	,	PUNCT
ejpam-5386	269	3	the	the	DET
ejpam-5386	269	4	primary	primary	ADJ
ejpam-5386	269	5	steps	step	NOUN
ejpam-5386	269	6	of	of	ADP
ejpam-5386	269	7	our	our	PRON
ejpam-5386	269	8	reconstruction	reconstruction	NOUN
ejpam-5386	269	9	approach	approach	NOUN
ejpam-5386	269	10	are	be	AUX
ejpam-5386	269	11	summarized	summarize	VERB
ejpam-5386	269	12	in	in	ADP
ejpam-5386	269	13	the	the	DET
ejpam-5386	269	14	following	follow	VERB
ejpam-5386	269	15	algorithm	algorithm	NOUN
ejpam-5386	269	16	:	:	PUNCT
ejpam-5386	269	17	algorithm	algorithm	NOUN
ejpam-5386	269	18	1	1	NUM
ejpam-5386	269	19	(	(	PUNCT
ejpam-5386	269	20	h).step	h).step	NOUN
ejpam-5386	269	21	1	1	NUM
ejpam-5386	269	22	.	.	PUNCT
ejpam-5386	270	1	set	set	VERB
ejpam-5386	270	2	k	k	PROPN
ejpam-5386	270	3	=	=	PUNCT
ejpam-5386	270	4	0	0	PUNCT
ejpam-5386	270	5	and	and	CCONJ
ejpam-5386	270	6	choose	choose	VERB
ejpam-5386	270	7	initial	initial	ADJ
ejpam-5386	270	8	guesses	guess	NOUN
ejpam-5386	270	9	α0	α0	ADJ
ejpam-5386	270	10	and	and	CCONJ
ejpam-5386	270	11	φ0	φ0	PROPN
ejpam-5386	270	12	for	for	ADP
ejpam-5386	270	13	the	the	DET
ejpam-5386	270	14	unknown	unknown	ADJ
ejpam-5386	270	15	coefficients	coefficient	NOUN
ejpam-5386	270	16	α	α	PROPN
ejpam-5386	270	17	and	and	CCONJ
ejpam-5386	270	18	φ	φ	NUM
ejpam-5386	270	19	,	,	PUNCT
ejpam-5386	270	20	respectively	respectively	ADV
ejpam-5386	270	21	.	.	PUNCT
ejpam-5386	271	1	step	step	NOUN
ejpam-5386	271	2	2	2	NUM
ejpam-5386	271	3	.	.	PUNCT
ejpam-5386	272	1	solve	solve	VERB
ejpam-5386	272	2	the	the	DET
ejpam-5386	272	3	direct	direct	ADJ
ejpam-5386	272	4	problem	problem	NOUN
ejpam-5386	272	5	(	(	PUNCT
ejpam-5386	272	6	5	5	NUM
ejpam-5386	272	7	)	)	PUNCT
ejpam-5386	272	8	with	with	ADP
ejpam-5386	272	9	(	(	PUNCT
ejpam-5386	272	10	α	α	X
ejpam-5386	272	11	,	,	PUNCT
ejpam-5386	272	12	φ	φ	NOUN
ejpam-5386	272	13	)	)	PUNCT
ejpam-5386	272	14	=	=	PRON
ejpam-5386	272	15	(	(	PUNCT
ejpam-5386	272	16	αk	αk	NOUN
ejpam-5386	272	17	,	,	PUNCT
ejpam-5386	272	18	φk	φk	ADP
ejpam-5386	272	19	)	)	PUNCT
ejpam-5386	272	20	to	to	PART
ejpam-5386	272	21	get	get	VERB
ejpam-5386	272	22	ck	ck	NOUN
ejpam-5386	272	23	=	=	SYM
ejpam-5386	272	24	c(αk	c(αk	PROPN
ejpam-5386	272	25	,	,	PUNCT
ejpam-5386	272	26	φk	φk	ADP
ejpam-5386	272	27	)	)	PUNCT
ejpam-5386	272	28	.	.	PUNCT
ejpam-5386	273	1	step	step	NOUN
ejpam-5386	273	2	3	3	NUM
ejpam-5386	273	3	.	.	PUNCT
ejpam-5386	274	1	solve	solve	VERB
ejpam-5386	274	2	the	the	DET
ejpam-5386	274	3	adjoint	adjoint	NOUN
ejpam-5386	274	4	problem	problem	NOUN
ejpam-5386	274	5	(	(	PUNCT
ejpam-5386	274	6	16	16	NUM
ejpam-5386	274	7	)	)	PUNCT
ejpam-5386	274	8	and	and	CCONJ
ejpam-5386	274	9	evaluate	evaluate	VERB
ejpam-5386	274	10	the	the	DET
ejpam-5386	274	11	gradients	gradient	NOUN
ejpam-5386	274	12	j	j	PROPN
ejpam-5386	274	13	′,k	′,k	NOUN
ejpam-5386	274	14	α	α	NOUN
ejpam-5386	274	15	=	=	SYM
ejpam-5386	274	16	j	j	PROPN
ejpam-5386	274	17	′	′	NUM
ejpam-5386	275	1	α(α	α(α	PROPN
ejpam-5386	275	2	k	k	PROPN
ejpam-5386	275	3	,	,	PUNCT
ejpam-5386	275	4	φk	φk	ADP
ejpam-5386	275	5	)	)	PUNCT
ejpam-5386	275	6	and	and	CCONJ
ejpam-5386	275	7	j	j	PROPN
ejpam-5386	275	8	′,k	′,k	PROPN
ejpam-5386	275	9	φ	φ	PROPN
ejpam-5386	275	10	=	=	SYM
ejpam-5386	275	11	j	j	PROPN
ejpam-5386	275	12	′	′	NUM
ejpam-5386	275	13	φ(α	φ(α	PROPN
ejpam-5386	275	14	k	k	PROPN
ejpam-5386	275	15	,	,	PUNCT
ejpam-5386	275	16	φk	φk	ADP
ejpam-5386	275	17	)	)	PUNCT
ejpam-5386	275	18	given	give	VERB
ejpam-5386	275	19	in	in	ADP
ejpam-5386	275	20	theorem	theorem	ADJ
ejpam-5386	275	21	3	3	NUM
ejpam-5386	275	22	.	.	NOUN
ejpam-5386	275	23	step	step	NOUN
ejpam-5386	275	24	4	4	NUM
ejpam-5386	275	25	.	.	PUNCT
ejpam-5386	275	26	calculate	calculate	VERB
ejpam-5386	275	27	the	the	DET
ejpam-5386	275	28	conjugate	conjugate	ADJ
ejpam-5386	275	29	coefficients	coefficient	NOUN
ejpam-5386	275	30	ϑkα	ϑkα	NOUN
ejpam-5386	275	31	and	and	CCONJ
ejpam-5386	275	32	ϑkφ	ϑkφ	NOUN
ejpam-5386	275	33	by	by	ADP
ejpam-5386	275	34	(	(	PUNCT
ejpam-5386	275	35	24	24	NUM
ejpam-5386	275	36	)	)	PUNCT
ejpam-5386	275	37	and	and	CCONJ
ejpam-5386	275	38	the	the	DET
ejpam-5386	275	39	directions	direction	NOUN
ejpam-5386	275	40	sk	sk	VERB
ejpam-5386	275	41	α	α	PROPN
ejpam-5386	275	42	and	and	CCONJ
ejpam-5386	275	43	sk	sk	PRON
ejpam-5386	275	44	φ	φ	PROPN
ejpam-5386	275	45	by	by	ADP
ejpam-5386	275	46	(	(	PUNCT
ejpam-5386	275	47	23	23	NUM
ejpam-5386	275	48	)	)	PUNCT
ejpam-5386	275	49	.	.	PUNCT
ejpam-5386	276	1	step	step	NOUN
ejpam-5386	276	2	5	5	NUM
ejpam-5386	276	3	.	.	PUNCT
ejpam-5386	276	4	calculate	calculate	VERB
ejpam-5386	276	5	the	the	DET
ejpam-5386	276	6	step	step	NOUN
ejpam-5386	276	7	sizes	size	NOUN
ejpam-5386	276	8	ζkα	ζkα	VERB
ejpam-5386	276	9	and	and	CCONJ
ejpam-5386	276	10	ζkφ	ζkφ	VERB
ejpam-5386	276	11	by	by	ADP
ejpam-5386	276	12	(	(	PUNCT
ejpam-5386	276	13	27	27	NUM
ejpam-5386	276	14	)	)	PUNCT
ejpam-5386	276	15	.	.	PUNCT
ejpam-5386	277	1	step	step	NOUN
ejpam-5386	277	2	6	6	NUM
ejpam-5386	277	3	.	.	PUNCT
ejpam-5386	277	4	update	update	VERB
ejpam-5386	277	5	αk+1	αk+1	NUM
ejpam-5386	277	6	and	and	CCONJ
ejpam-5386	277	7	φk+1	φk+1	VERB
ejpam-5386	277	8	by	by	ADP
ejpam-5386	277	9	(	(	PUNCT
ejpam-5386	277	10	22	22	NUM
ejpam-5386	277	11	)	)	PUNCT
ejpam-5386	277	12	.	.	PUNCT
ejpam-5386	278	1	step	step	NOUN
ejpam-5386	278	2	7	7	NUM
ejpam-5386	278	3	if	if	SCONJ
ejpam-5386	278	4	the	the	DET
ejpam-5386	278	5	condition	condition	NOUN
ejpam-5386	278	6	(	(	PUNCT
ejpam-5386	278	7	28	28	NUM
ejpam-5386	278	8	)	)	PUNCT
ejpam-5386	278	9	is	be	AUX
ejpam-5386	278	10	satisfied	satisfied	ADJ
ejpam-5386	278	11	,	,	PUNCT
ejpam-5386	278	12	then	then	ADV
ejpam-5386	278	13	go	go	VERB
ejpam-5386	278	14	to	to	PART
ejpam-5386	278	15	step	step	VERB
ejpam-5386	278	16	8	8	NUM
ejpam-5386	278	17	.	.	PUNCT
ejpam-5386	279	1	otherwise	otherwise	ADV
ejpam-5386	279	2	set	set	VERB
ejpam-5386	279	3	k	k	PROPN
ejpam-5386	279	4	=	=	PUNCT
ejpam-5386	279	5	k+1	k+1	PROPN
ejpam-5386	279	6	and	and	CCONJ
ejpam-5386	279	7	go	go	VERB
ejpam-5386	279	8	to	to	PART
ejpam-5386	279	9	step	step	VERB
ejpam-5386	279	10	2	2	NUM
ejpam-5386	279	11	.	.	PUNCT
ejpam-5386	279	12	step	step	NOUN
ejpam-5386	279	13	8	8	NUM
ejpam-5386	279	14	end	end	NOUN
ejpam-5386	279	15	.	.	PUNCT
ejpam-5386	280	1	s.	s.	PROPN
ejpam-5386	280	2	tatar	tatar	PROPN
ejpam-5386	280	3	,	,	PUNCT
ejpam-5386	280	4	m.	m.	NOUN
ejpam-5386	280	5	bensalah	bensalah	PROPN
ejpam-5386	280	6	,	,	PUNCT
ejpam-5386	280	7	m.	m.	NOUN
ejpam-5386	280	8	alamil	alamil	PROPN
ejpam-5386	280	9	/	/	SYM
ejpam-5386	280	10	eur	eur	PROPN
ejpam-5386	280	11	.	.	PUNCT
ejpam-5386	281	1	j.	j.	PROPN
ejpam-5386	281	2	pure	pure	PROPN
ejpam-5386	281	3	appl	appl	PROPN
ejpam-5386	281	4	.	.	PROPN
ejpam-5386	281	5	math	math	PROPN
ejpam-5386	281	6	,	,	PUNCT
ejpam-5386	281	7	17	17	NUM
ejpam-5386	281	8	(	(	PUNCT
ejpam-5386	281	9	4	4	NUM
ejpam-5386	281	10	)	)	PUNCT
ejpam-5386	281	11	(	(	PUNCT
ejpam-5386	281	12	2024	2024	NUM
ejpam-5386	281	13	)	)	PUNCT
ejpam-5386	281	14	,	,	PUNCT
ejpam-5386	281	15	2651	2651	NUM
ejpam-5386	281	16	-	-	SYM
ejpam-5386	281	17	2675	2675	NUM
ejpam-5386	281	18	2664	2664	NUM
ejpam-5386	281	19	4	4	NUM
ejpam-5386	281	20	.	.	PUNCT
ejpam-5386	281	21	numerical	numerical	ADJ
ejpam-5386	281	22	experiments	experiment	NOUN
ejpam-5386	281	23	we	we	PRON
ejpam-5386	281	24	set	set	VERB
ejpam-5386	281	25	t	t	NOUN
ejpam-5386	281	26	=	=	SYM
ejpam-5386	281	27	1	1	NUM
ejpam-5386	281	28	and	and	CCONJ
ejpam-5386	281	29	b	b	X
ejpam-5386	281	30	=	=	SYM
ejpam-5386	281	31	(	(	PUNCT
ejpam-5386	281	32	0	0	NUM
ejpam-5386	281	33	,	,	PUNCT
ejpam-5386	281	34	1	1	NUM
ejpam-5386	281	35	)	)	PUNCT
ejpam-5386	281	36	in	in	ADP
ejpam-5386	281	37	all	all	DET
ejpam-5386	281	38	numerical	numerical	ADJ
ejpam-5386	281	39	examples	example	NOUN
ejpam-5386	281	40	.	.	PUNCT
ejpam-5386	282	1	we	we	PRON
ejpam-5386	282	2	rely	rely	VERB
ejpam-5386	282	3	on	on	ADP
ejpam-5386	282	4	the	the	DET
ejpam-5386	282	5	finite	finite	ADJ
ejpam-5386	282	6	difference	difference	NOUN
ejpam-5386	282	7	method	method	NOUN
ejpam-5386	282	8	as	as	SCONJ
ejpam-5386	282	9	our	our	PRON
ejpam-5386	282	10	primary	primary	ADJ
ejpam-5386	282	11	tool	tool	NOUN
ejpam-5386	282	12	to	to	PART
ejpam-5386	282	13	deal	deal	VERB
ejpam-5386	282	14	with	with	ADP
ejpam-5386	282	15	not	not	PART
ejpam-5386	282	16	only	only	ADV
ejpam-5386	282	17	the	the	DET
ejpam-5386	282	18	direct	direct	ADJ
ejpam-5386	282	19	problem	problem	NOUN
ejpam-5386	282	20	but	but	CCONJ
ejpam-5386	282	21	also	also	ADV
ejpam-5386	282	22	its	its	PRON
ejpam-5386	282	23	associated	associated	ADJ
ejpam-5386	282	24	sensitive	sensitive	ADJ
ejpam-5386	282	25	and	and	CCONJ
ejpam-5386	282	26	adjoint	adjoint	NOUN
ejpam-5386	282	27	variants	variant	NOUN
ejpam-5386	282	28	.	.	PUNCT
ejpam-5386	283	1	setting	set	VERB
ejpam-5386	283	2	a	a	DET
ejpam-5386	283	3	structured	structured	ADJ
ejpam-5386	283	4	approach	approach	NOUN
ejpam-5386	283	5	,	,	PUNCT
ejpam-5386	283	6	we	we	PRON
ejpam-5386	283	7	designate	designate	VERB
ejpam-5386	283	8	h	h	NOUN
ejpam-5386	283	9	=	=	NOUN
ejpam-5386	283	10	0.02	0.02	NUM
ejpam-5386	283	11	as	as	ADP
ejpam-5386	283	12	the	the	DET
ejpam-5386	283	13	step	step	NOUN
ejpam-5386	283	14	size	size	NOUN
ejpam-5386	283	15	and	and	CCONJ
ejpam-5386	283	16	τ	τ	X
ejpam-5386	283	17	=	=	NOUN
ejpam-5386	283	18	0.005	0.005	NUM
ejpam-5386	283	19	as	as	ADP
ejpam-5386	283	20	the	the	DET
ejpam-5386	283	21	time	time	NOUN
ejpam-5386	283	22	increment	increment	NOUN
ejpam-5386	283	23	,	,	PUNCT
ejpam-5386	283	24	ensuring	ensure	VERB
ejpam-5386	283	25	a	a	DET
ejpam-5386	283	26	balanced	balanced	ADJ
ejpam-5386	283	27	exploration	exploration	NOUN
ejpam-5386	283	28	of	of	ADP
ejpam-5386	283	29	the	the	DET
ejpam-5386	283	30	problem	problem	NOUN
ejpam-5386	283	31	domain	domain	NOUN
ejpam-5386	283	32	both	both	CCONJ
ejpam-5386	283	33	spatially	spatially	ADV
ejpam-5386	283	34	and	and	CCONJ
ejpam-5386	283	35	temporally	temporally	ADV
ejpam-5386	283	36	.	.	PUNCT
ejpam-5386	284	1	moreover	moreover	ADV
ejpam-5386	284	2	,	,	PUNCT
ejpam-5386	284	3	to	to	PART
ejpam-5386	284	4	handle	handle	VERB
ejpam-5386	284	5	integrals	integral	NOUN
ejpam-5386	284	6	within	within	ADP
ejpam-5386	284	7	our	our	PRON
ejpam-5386	284	8	computations	computation	NOUN
ejpam-5386	284	9	,	,	PUNCT
ejpam-5386	284	10	we	we	PRON
ejpam-5386	284	11	employ	employ	VERB
ejpam-5386	284	12	the	the	DET
ejpam-5386	284	13	trapezoidal	trapezoidal	ADJ
ejpam-5386	284	14	rule	rule	NOUN
ejpam-5386	284	15	,	,	PUNCT
ejpam-5386	284	16	a	a	DET
ejpam-5386	284	17	widely	widely	ADV
ejpam-5386	284	18	recognized	recognize	VERB
ejpam-5386	284	19	numerical	numerical	ADJ
ejpam-5386	284	20	technique	technique	NOUN
ejpam-5386	284	21	that	that	PRON
ejpam-5386	284	22	provides	provide	VERB
ejpam-5386	284	23	reliable	reliable	ADJ
ejpam-5386	284	24	approximations	approximation	NOUN
ejpam-5386	284	25	.	.	PUNCT
ejpam-5386	285	1	all	all	DET
ejpam-5386	285	2	numerical	numerical	ADJ
ejpam-5386	285	3	experiments	experiment	NOUN
ejpam-5386	285	4	are	be	AUX
ejpam-5386	285	5	carried	carry	VERB
ejpam-5386	285	6	out	out	ADP
ejpam-5386	285	7	in	in	ADP
ejpam-5386	285	8	matlab	matlab	PROPN
ejpam-5386	285	9	(	(	PUNCT
ejpam-5386	285	10	version	version	NOUN
ejpam-5386	285	11	r2017a	r2017a	PROPN
ejpam-5386	285	12	)	)	PUNCT
ejpam-5386	285	13	.	.	PUNCT
ejpam-5386	286	1	in	in	ADP
ejpam-5386	286	2	the	the	DET
ejpam-5386	286	3	context	context	NOUN
ejpam-5386	286	4	of	of	ADP
ejpam-5386	286	5	noisy	noisy	ADJ
ejpam-5386	286	6	observations	observation	NOUN
ejpam-5386	286	7	,	,	PUNCT
ejpam-5386	286	8	we	we	PRON
ejpam-5386	286	9	enhance	enhance	VERB
ejpam-5386	286	10	the	the	DET
ejpam-5386	286	11	fidelity	fidelity	NOUN
ejpam-5386	286	12	of	of	ADP
ejpam-5386	286	13	our	our	PRON
ejpam-5386	286	14	simulations	simulation	NOUN
ejpam-5386	286	15	by	by	ADP
ejpam-5386	286	16	incorporating	incorporate	VERB
ejpam-5386	286	17	gaussian	gaussian	ADJ
ejpam-5386	286	18	additive	additive	NOUN
ejpam-5386	286	19	noise	noise	NOUN
ejpam-5386	286	20	to	to	ADP
ejpam-5386	286	21	ϕε1	ϕε1	PROPN
ejpam-5386	286	22	and	and	CCONJ
ejpam-5386	286	23	ϕε2	ϕε2	PROPN
ejpam-5386	286	24	,	,	PUNCT
ejpam-5386	286	25	as	as	SCONJ
ejpam-5386	286	26	detailed	detailed	ADJ
ejpam-5386	286	27	in	in	ADP
ejpam-5386	286	28	(	(	PUNCT
ejpam-5386	286	29	6	6	NUM
ejpam-5386	286	30	)	)	PUNCT
ejpam-5386	286	31	.	.	PUNCT
ejpam-5386	287	1	this	this	DET
ejpam-5386	287	2	noise	noise	NOUN
ejpam-5386	287	3	,	,	PUNCT
ejpam-5386	287	4	with	with	ADP
ejpam-5386	287	5	amplitude	amplitude	NOUN
ejpam-5386	287	6	σ	σ	NOUN
ejpam-5386	287	7	,	,	PUNCT
ejpam-5386	287	8	is	be	AUX
ejpam-5386	287	9	dynamically	dynamically	ADV
ejpam-5386	287	10	adjusted	adjust	VERB
ejpam-5386	287	11	based	base	VERB
ejpam-5386	287	12	on	on	ADP
ejpam-5386	287	13	a	a	DET
ejpam-5386	287	14	specified	specified	ADJ
ejpam-5386	287	15	percentage	percentage	NOUN
ejpam-5386	287	16	p	p	NOUN
ejpam-5386	287	17	representing	represent	VERB
ejpam-5386	287	18	the	the	DET
ejpam-5386	287	19	noise	noise	NOUN
ejpam-5386	287	20	level	level	NOUN
ejpam-5386	287	21	in	in	ADP
ejpam-5386	287	22	the	the	DET
ejpam-5386	287	23	data	datum	NOUN
ejpam-5386	287	24	.	.	PUNCT
ejpam-5386	288	1	utilizing	utilize	VERB
ejpam-5386	288	2	the	the	DET
ejpam-5386	288	3	term	term	NOUN
ejpam-5386	288	4	”	"	PUNCT
ejpam-5386	288	5	random(1	random(1	NOUN
ejpam-5386	288	6	)	)	PUNCT
ejpam-5386	288	7	”	"	PUNCT
ejpam-5386	288	8	,	,	PUNCT
ejpam-5386	288	9	we	we	PRON
ejpam-5386	288	10	introduce	introduce	VERB
ejpam-5386	288	11	variability	variability	NOUN
ejpam-5386	288	12	representative	representative	NOUN
ejpam-5386	288	13	of	of	ADP
ejpam-5386	288	14	real	real	ADJ
ejpam-5386	288	15	-	-	PUNCT
ejpam-5386	288	16	world	world	NOUN
ejpam-5386	288	17	conditions	condition	NOUN
ejpam-5386	288	18	by	by	ADP
ejpam-5386	288	19	generating	generate	VERB
ejpam-5386	288	20	random	random	ADJ
ejpam-5386	288	21	values	value	NOUN
ejpam-5386	288	22	from	from	ADP
ejpam-5386	288	23	a	a	DET
ejpam-5386	288	24	gaussian	gaussian	ADJ
ejpam-5386	288	25	distribution	distribution	NOUN
ejpam-5386	288	26	with	with	ADP
ejpam-5386	288	27	a	a	DET
ejpam-5386	288	28	mean	mean	NOUN
ejpam-5386	288	29	of	of	ADP
ejpam-5386	288	30	zero	zero	NUM
ejpam-5386	288	31	and	and	CCONJ
ejpam-5386	288	32	a	a	DET
ejpam-5386	288	33	standard	standard	ADJ
ejpam-5386	288	34	deviation	deviation	NOUN
ejpam-5386	288	35	of	of	ADP
ejpam-5386	288	36	unity	unity	NOUN
ejpam-5386	288	37	.	.	PUNCT
ejpam-5386	289	1	specifically	specifically	ADV
ejpam-5386	289	2	,	,	PUNCT
ejpam-5386	289	3	the	the	DET
ejpam-5386	289	4	noisy	noisy	ADJ
ejpam-5386	289	5	observations	observation	NOUN
ejpam-5386	289	6	ϕεi	ϕεi	VERB
ejpam-5386	289	7	are	be	AUX
ejpam-5386	289	8	generated	generate	VERB
ejpam-5386	289	9	according	accord	VERB
ejpam-5386	289	10	to	to	ADP
ejpam-5386	289	11	:	:	PUNCT
ejpam-5386	289	12	ϕεi	ϕεi	VERB
ejpam-5386	289	13	=	=	PUNCT
ejpam-5386	289	14	ϕi	ϕi	ADP
ejpam-5386	289	15	+	+	NOUN
ejpam-5386	289	16	σ	σ	NOUN
ejpam-5386	289	17	×	×	NOUN
ejpam-5386	289	18	random(1	random(1	NOUN
ejpam-5386	289	19	)	)	PUNCT
ejpam-5386	289	20	,	,	PUNCT
ejpam-5386	289	21	i	i	PRON
ejpam-5386	289	22	=	=	NOUN
ejpam-5386	289	23	1	1	NUM
ejpam-5386	289	24	,	,	PUNCT
ejpam-5386	289	25	2	2	NUM
ejpam-5386	289	26	,	,	PUNCT
ejpam-5386	289	27	where	where	SCONJ
ejpam-5386	289	28	σ	σ	PROPN
ejpam-5386	289	29	is	be	AUX
ejpam-5386	289	30	calculated	calculate	VERB
ejpam-5386	289	31	as	as	ADP
ejpam-5386	289	32	σ	σ	X
ejpam-5386	289	33	=	=	SYM
ejpam-5386	289	34	p	p	PROPN
ejpam-5386	289	35	100	100	NUM
ejpam-5386	289	36	×	×	NOUN
ejpam-5386	289	37	maxx∈ω{|ϕ1(x)|	maxx∈ω{|ϕ1(x)|	NOUN
ejpam-5386	289	38	,	,	PUNCT
ejpam-5386	289	39	|ϕ2(x)|	|ϕ2(x)|	VERB
ejpam-5386	289	40	}	}	PUNCT
ejpam-5386	289	41	.	.	PUNCT
ejpam-5386	290	1	this	this	DET
ejpam-5386	290	2	approach	approach	NOUN
ejpam-5386	290	3	ensures	ensure	VERB
ejpam-5386	290	4	that	that	SCONJ
ejpam-5386	290	5	our	our	PRON
ejpam-5386	290	6	computational	computational	ADJ
ejpam-5386	290	7	model	model	NOUN
ejpam-5386	290	8	captures	capture	VERB
ejpam-5386	290	9	the	the	DET
ejpam-5386	290	10	inherent	inherent	ADJ
ejpam-5386	290	11	uncertainties	uncertainty	NOUN
ejpam-5386	290	12	present	present	ADJ
ejpam-5386	290	13	in	in	ADP
ejpam-5386	290	14	real	real	ADJ
ejpam-5386	290	15	-	-	PUNCT
ejpam-5386	290	16	world	world	NOUN
ejpam-5386	290	17	measurements	measurement	NOUN
ejpam-5386	290	18	,	,	PUNCT
ejpam-5386	290	19	enhancing	enhance	VERB
ejpam-5386	290	20	the	the	DET
ejpam-5386	290	21	robustness	robustness	NOUN
ejpam-5386	290	22	of	of	ADP
ejpam-5386	290	23	our	our	PRON
ejpam-5386	290	24	simulations	simulation	NOUN
ejpam-5386	290	25	.	.	PUNCT
ejpam-5386	291	1	the	the	DET
ejpam-5386	291	2	accuracy	accuracy	NOUN
ejpam-5386	291	3	errors	error	NOUN
ejpam-5386	291	4	eα(k	eα(k	PUNCT
ejpam-5386	291	5	)	)	PUNCT
ejpam-5386	291	6	and	and	CCONJ
ejpam-5386	291	7	eφ(k	eφ(k	NUM
ejpam-5386	291	8	)	)	PUNCT
ejpam-5386	291	9	,	,	PUNCT
ejpam-5386	291	10	as	as	ADP
ejpam-5386	291	11	functions	function	NOUN
ejpam-5386	291	12	of	of	ADP
ejpam-5386	291	13	the	the	DET
ejpam-5386	291	14	iteration	iteration	NOUN
ejpam-5386	291	15	number	number	NOUN
ejpam-5386	291	16	k	k	PROPN
ejpam-5386	291	17	,	,	PUNCT
ejpam-5386	291	18	for	for	ADP
ejpam-5386	291	19	the	the	DET
ejpam-5386	291	20	treatment	treatment	NOUN
ejpam-5386	291	21	parameter	parameter	NOUN
ejpam-5386	291	22	α(x	α(x	PROPN
ejpam-5386	291	23	)	)	PUNCT
ejpam-5386	291	24	and	and	CCONJ
ejpam-5386	291	25	the	the	DET
ejpam-5386	291	26	initial	initial	ADJ
ejpam-5386	291	27	cell	cell	NOUN
ejpam-5386	291	28	density	density	NOUN
ejpam-5386	291	29	φ(x	φ(x	NOUN
ejpam-5386	291	30	)	)	PUNCT
ejpam-5386	291	31	,	,	PUNCT
ejpam-5386	291	32	respectively	respectively	ADV
ejpam-5386	291	33	,	,	PUNCT
ejpam-5386	291	34	are	be	AUX
ejpam-5386	291	35	defined	define	VERB
ejpam-5386	291	36	as	as	ADP
ejpam-5386	291	37	eα(k	eα(k	NUM
ejpam-5386	291	38	)	)	PUNCT
ejpam-5386	291	39	:	:	PUNCT
ejpam-5386	292	1	=	=	SYM
ejpam-5386	292	2	∥αk	∥αk	PROPN
ejpam-5386	292	3	−α∥2	−α∥2	NOUN
ejpam-5386	292	4	,	,	PUNCT
ejpam-5386	292	5	(	(	PUNCT
ejpam-5386	292	6	29	29	NUM
ejpam-5386	292	7	)	)	PUNCT
ejpam-5386	292	8	eφ(k	eφ(k	NUM
ejpam-5386	292	9	)	)	PUNCT
ejpam-5386	292	10	:	:	PUNCT
ejpam-5386	292	11	=	=	SYM
ejpam-5386	292	12	∥φk	∥φk	PROPN
ejpam-5386	292	13	−φ∥2	−φ∥2	NOUN
ejpam-5386	292	14	,	,	PUNCT
ejpam-5386	292	15	(	(	PUNCT
ejpam-5386	292	16	30	30	NUM
ejpam-5386	292	17	)	)	PUNCT
ejpam-5386	292	18	where	where	SCONJ
ejpam-5386	292	19	αk	αk	NOUN
ejpam-5386	292	20	and	and	CCONJ
ejpam-5386	292	21	φk	φk	AUX
ejpam-5386	292	22	are	be	AUX
ejpam-5386	292	23	the	the	DET
ejpam-5386	292	24	cgm	cgm	PROPN
ejpam-5386	292	25	iterates	iterate	NOUN
ejpam-5386	292	26	,	,	PUNCT
ejpam-5386	292	27	and	and	CCONJ
ejpam-5386	292	28	α	α	PROPN
ejpam-5386	292	29	and	and	CCONJ
ejpam-5386	292	30	φ	φ	PROPN
ejpam-5386	292	31	are	be	AUX
ejpam-5386	292	32	the	the	DET
ejpam-5386	292	33	analytical	analytical	ADJ
ejpam-5386	292	34	expressions	expression	NOUN
ejpam-5386	292	35	of	of	ADP
ejpam-5386	292	36	the	the	DET
ejpam-5386	292	37	treatment	treatment	NOUN
ejpam-5386	292	38	parameter	parameter	NOUN
ejpam-5386	292	39	and	and	CCONJ
ejpam-5386	292	40	the	the	DET
ejpam-5386	292	41	initial	initial	ADJ
ejpam-5386	292	42	cell	cell	NOUN
ejpam-5386	292	43	density	density	NOUN
ejpam-5386	292	44	.	.	PUNCT
ejpam-5386	293	1	throughout	throughout	ADP
ejpam-5386	293	2	this	this	DET
ejpam-5386	293	3	section	section	NOUN
ejpam-5386	293	4	,	,	PUNCT
ejpam-5386	293	5	we	we	PRON
ejpam-5386	293	6	maintain	maintain	VERB
ejpam-5386	293	7	a	a	DET
ejpam-5386	293	8	consistent	consistent	ADJ
ejpam-5386	293	9	temporal	temporal	ADJ
ejpam-5386	293	10	component	component	NOUN
ejpam-5386	293	11	β(t	β(t	PROPN
ejpam-5386	293	12	)	)	PUNCT
ejpam-5386	293	13	within	within	ADP
ejpam-5386	293	14	the	the	DET
ejpam-5386	293	15	treatment	treatment	NOUN
ejpam-5386	293	16	profile	profile	NOUN
ejpam-5386	293	17	,	,	PUNCT
ejpam-5386	293	18	specified	specify	VERB
ejpam-5386	293	19	as	as	ADP
ejpam-5386	293	20	exp	exp	NOUN
ejpam-5386	293	21	(	(	PUNCT
ejpam-5386	293	22	−t	−t	NOUN
ejpam-5386	293	23	)	)	PUNCT
ejpam-5386	293	24	.	.	PUNCT
ejpam-5386	294	1	furthermore	furthermore	ADV
ejpam-5386	294	2	,	,	PUNCT
ejpam-5386	294	3	our	our	PRON
ejpam-5386	294	4	initial	initial	ADJ
ejpam-5386	294	5	guesses	guess	NOUN
ejpam-5386	294	6	for	for	ADP
ejpam-5386	294	7	the	the	DET
ejpam-5386	294	8	treatment	treatment	NOUN
ejpam-5386	294	9	parameter	parameter	NOUN
ejpam-5386	294	10	α0	α0	ADJ
ejpam-5386	294	11	and	and	CCONJ
ejpam-5386	294	12	initial	initial	ADJ
ejpam-5386	294	13	cell	cell	NOUN
ejpam-5386	294	14	density	density	NOUN
ejpam-5386	294	15	φ0	φ0	PROPN
ejpam-5386	294	16	are	be	AUX
ejpam-5386	294	17	both	both	PRON
ejpam-5386	294	18	set	set	VERB
ejpam-5386	294	19	to	to	ADP
ejpam-5386	294	20	1	1	NUM
ejpam-5386	294	21	,	,	PUNCT
ejpam-5386	294	22	establishing	establish	VERB
ejpam-5386	294	23	a	a	DET
ejpam-5386	294	24	standardized	standardized	ADJ
ejpam-5386	294	25	starting	starting	NOUN
ejpam-5386	294	26	point	point	NOUN
ejpam-5386	294	27	for	for	ADP
ejpam-5386	294	28	our	our	PRON
ejpam-5386	294	29	analysis	analysis	NOUN
ejpam-5386	294	30	.	.	PUNCT
ejpam-5386	295	1	expanding	expand	VERB
ejpam-5386	295	2	upon	upon	SCONJ
ejpam-5386	295	3	our	our	PRON
ejpam-5386	295	4	problem	problem	NOUN
ejpam-5386	295	5	configuration	configuration	NOUN
ejpam-5386	295	6	,	,	PUNCT
ejpam-5386	295	7	the	the	DET
ejpam-5386	295	8	parameters	parameter	NOUN
ejpam-5386	295	9	governing	govern	VERB
ejpam-5386	295	10	the	the	DET
ejpam-5386	295	11	logistic	logistic	ADJ
ejpam-5386	295	12	reaction	reaction	NOUN
ejpam-5386	295	13	function	function	NOUN
ejpam-5386	295	14	g(c	g(c	NOUN
ejpam-5386	295	15	)	)	PUNCT
ejpam-5386	295	16	and	and	CCONJ
ejpam-5386	295	17	the	the	DET
ejpam-5386	295	18	diffusion	diffusion	NOUN
ejpam-5386	295	19	term	term	NOUN
ejpam-5386	295	20	are	be	AUX
ejpam-5386	295	21	listed	list	VERB
ejpam-5386	295	22	in	in	ADP
ejpam-5386	295	23	table	table	NOUN
ejpam-5386	295	24	1	1	NUM
ejpam-5386	295	25	.	.	PUNCT
ejpam-5386	295	26	parameter	parameter	NOUN
ejpam-5386	295	27	value	value	NOUN
ejpam-5386	295	28	references	reference	NOUN
ejpam-5386	295	29	growth	growth	NOUN
ejpam-5386	295	30	rate	rate	NOUN
ejpam-5386	295	31	ρ	ρ	PROPN
ejpam-5386	295	32	0.0012	0.0012	NUM
ejpam-5386	295	33	cock	cock	NOUN
ejpam-5386	295	34	et	et	PROPN
ejpam-5386	295	35	al	al	PROPN
ejpam-5386	295	36	.	.	PUNCT
ejpam-5386	296	1	[	[	X
ejpam-5386	296	2	8	8	NUM
ejpam-5386	296	3	]	]	ADJ
ejpam-5386	296	4	diffusion	diffusion	NOUN
ejpam-5386	296	5	coefficient	coefficient	NOUN
ejpam-5386	296	6	dg	dg	VERB
ejpam-5386	296	7	0.0013	0.0013	NUM
ejpam-5386	296	8	tracqui	tracqui	NOUN
ejpam-5386	296	9	et	et	PROPN
ejpam-5386	296	10	al	al	PROPN
ejpam-5386	296	11	.	.	PUNCT
ejpam-5386	297	1	[	[	X
ejpam-5386	297	2	27	27	NUM
ejpam-5386	297	3	]	]	PUNCT
ejpam-5386	297	4	diffusion	diffusion	NOUN
ejpam-5386	297	5	coefficient	coefficient	NOUN
ejpam-5386	297	6	dω	dω	ADP
ejpam-5386	297	7	0.0065	0.0065	NUM
ejpam-5386	297	8	swanson	swanson	PROPN
ejpam-5386	297	9	et	et	PROPN
ejpam-5386	297	10	al	al	PROPN
ejpam-5386	297	11	.	.	PUNCT
ejpam-5386	298	1	[	[	X
ejpam-5386	298	2	24	24	NUM
ejpam-5386	298	3	]	]	PUNCT
ejpam-5386	298	4	carrying	carry	VERB
ejpam-5386	298	5	capacity	capacity	NOUN
ejpam-5386	298	6	clim	clim	NOUN
ejpam-5386	298	7	0.625	0.625	NUM
ejpam-5386	298	8	noviantri	noviantri	PROPN
ejpam-5386	298	9	et	et	PROPN
ejpam-5386	298	10	al	al	PROPN
ejpam-5386	298	11	.	.	PUNCT
ejpam-5386	299	1	[	[	X
ejpam-5386	299	2	18	18	NUM
ejpam-5386	299	3	]	]	SYM
ejpam-5386	299	4	table	table	NOUN
ejpam-5386	299	5	1	1	NUM
ejpam-5386	299	6	:	:	PUNCT
ejpam-5386	299	7	numerical	numerical	ADJ
ejpam-5386	299	8	values	value	NOUN
ejpam-5386	299	9	of	of	ADP
ejpam-5386	299	10	physical	physical	ADJ
ejpam-5386	299	11	coefficients	coefficient	NOUN
ejpam-5386	299	12	.	.	PUNCT
ejpam-5386	300	1	s.	s.	PROPN
ejpam-5386	300	2	tatar	tatar	PROPN
ejpam-5386	300	3	,	,	PUNCT
ejpam-5386	300	4	m.	m.	NOUN
ejpam-5386	300	5	bensalah	bensalah	PROPN
ejpam-5386	300	6	,	,	PUNCT
ejpam-5386	300	7	m.	m.	NOUN
ejpam-5386	300	8	alamil	alamil	PROPN
ejpam-5386	300	9	/	/	SYM
ejpam-5386	300	10	eur	eur	PROPN
ejpam-5386	300	11	.	.	PUNCT
ejpam-5386	301	1	j.	j.	PROPN
ejpam-5386	301	2	pure	pure	PROPN
ejpam-5386	301	3	appl	appl	PROPN
ejpam-5386	301	4	.	.	PROPN
ejpam-5386	301	5	math	math	PROPN
ejpam-5386	301	6	,	,	PUNCT
ejpam-5386	301	7	17	17	NUM
ejpam-5386	301	8	(	(	PUNCT
ejpam-5386	301	9	4	4	NUM
ejpam-5386	301	10	)	)	PUNCT
ejpam-5386	301	11	(	(	PUNCT
ejpam-5386	301	12	2024	2024	NUM
ejpam-5386	301	13	)	)	PUNCT
ejpam-5386	301	14	,	,	PUNCT
ejpam-5386	301	15	2651	2651	NUM
ejpam-5386	301	16	-	-	SYM
ejpam-5386	301	17	2675	2675	NUM
ejpam-5386	301	18	2665	2665	NUM
ejpam-5386	301	19	example	example	NOUN
ejpam-5386	302	1	1	1	NUM
ejpam-5386	302	2	.	.	PUNCT
ejpam-5386	303	1	in	in	ADP
ejpam-5386	303	2	this	this	DET
ejpam-5386	303	3	example	example	NOUN
ejpam-5386	303	4	,	,	PUNCT
ejpam-5386	303	5	we	we	PRON
ejpam-5386	303	6	aim	aim	VERB
ejpam-5386	303	7	to	to	PART
ejpam-5386	303	8	evaluate	evaluate	VERB
ejpam-5386	303	9	the	the	DET
ejpam-5386	303	10	performance	performance	NOUN
ejpam-5386	303	11	of	of	ADP
ejpam-5386	303	12	our	our	PRON
ejpam-5386	303	13	algorithm	algorithm	NOUN
ejpam-5386	303	14	in	in	ADP
ejpam-5386	303	15	identifying	identify	VERB
ejpam-5386	303	16	the	the	DET
ejpam-5386	303	17	treatment	treatment	NOUN
ejpam-5386	303	18	parameter	parameter	NOUN
ejpam-5386	303	19	α	α	NOUN
ejpam-5386	303	20	and	and	CCONJ
ejpam-5386	303	21	initial	initial	ADJ
ejpam-5386	303	22	cell	cell	NOUN
ejpam-5386	303	23	density	density	NOUN
ejpam-5386	303	24	φ	φ	PROPN
ejpam-5386	303	25	within	within	ADP
ejpam-5386	303	26	a	a	DET
ejpam-5386	303	27	controlled	control	VERB
ejpam-5386	303	28	setting	setting	NOUN
ejpam-5386	303	29	.	.	PUNCT
ejpam-5386	304	1	these	these	DET
ejpam-5386	304	2	two	two	NUM
ejpam-5386	304	3	functions	function	NOUN
ejpam-5386	304	4	are	be	AUX
ejpam-5386	304	5	assumed	assume	VERB
ejpam-5386	304	6	to	to	PART
ejpam-5386	304	7	exhibit	exhibit	VERB
ejpam-5386	304	8	smooth	smooth	ADJ
ejpam-5386	304	9	behavior	behavior	NOUN
ejpam-5386	304	10	,	,	PUNCT
ejpam-5386	304	11	reflecting	reflect	VERB
ejpam-5386	304	12	typical	typical	ADJ
ejpam-5386	304	13	characteristics	characteristic	NOUN
ejpam-5386	304	14	observed	observe	VERB
ejpam-5386	304	15	in	in	ADP
ejpam-5386	304	16	many	many	ADJ
ejpam-5386	304	17	practical	practical	ADJ
ejpam-5386	304	18	applications	application	NOUN
ejpam-5386	304	19	.	.	PUNCT
ejpam-5386	305	1	by	by	ADP
ejpam-5386	305	2	selecting	select	VERB
ejpam-5386	305	3	smooth	smooth	ADJ
ejpam-5386	305	4	functions	function	NOUN
ejpam-5386	305	5	for	for	ADP
ejpam-5386	305	6	α	α	PROPN
ejpam-5386	305	7	and	and	CCONJ
ejpam-5386	305	8	φ	φ	NUM
ejpam-5386	305	9	,	,	PUNCT
ejpam-5386	305	10	we	we	PRON
ejpam-5386	305	11	aim	aim	VERB
ejpam-5386	305	12	to	to	PART
ejpam-5386	305	13	establish	establish	VERB
ejpam-5386	305	14	a	a	DET
ejpam-5386	305	15	baseline	baseline	ADJ
ejpam-5386	305	16	assessment	assessment	NOUN
ejpam-5386	305	17	of	of	ADP
ejpam-5386	305	18	the	the	DET
ejpam-5386	305	19	algorithm	algorithm	NOUN
ejpam-5386	305	20	’s	’s	PART
ejpam-5386	305	21	capability	capability	NOUN
ejpam-5386	305	22	to	to	PART
ejpam-5386	305	23	accurately	accurately	ADV
ejpam-5386	305	24	reconstruct	reconstruct	VERB
ejpam-5386	305	25	these	these	DET
ejpam-5386	305	26	essential	essential	ADJ
ejpam-5386	305	27	parameters	parameter	NOUN
ejpam-5386	305	28	under	under	ADP
ejpam-5386	305	29	ideal	ideal	ADJ
ejpam-5386	305	30	conditions	condition	NOUN
ejpam-5386	305	31	.	.	PUNCT
ejpam-5386	306	1	this	this	DET
ejpam-5386	306	2	test	test	NOUN
ejpam-5386	306	3	serves	serve	VERB
ejpam-5386	306	4	as	as	ADP
ejpam-5386	306	5	a	a	DET
ejpam-5386	306	6	crucial	crucial	ADJ
ejpam-5386	306	7	step	step	NOUN
ejpam-5386	306	8	in	in	ADP
ejpam-5386	306	9	validating	validate	VERB
ejpam-5386	306	10	the	the	DET
ejpam-5386	306	11	effectiveness	effectiveness	NOUN
ejpam-5386	306	12	and	and	CCONJ
ejpam-5386	306	13	reliability	reliability	NOUN
ejpam-5386	306	14	of	of	ADP
ejpam-5386	306	15	our	our	PRON
ejpam-5386	306	16	computational	computational	ADJ
ejpam-5386	306	17	approach	approach	NOUN
ejpam-5386	306	18	before	before	ADP
ejpam-5386	306	19	extending	extend	VERB
ejpam-5386	306	20	it	it	PRON
ejpam-5386	306	21	to	to	ADP
ejpam-5386	306	22	more	more	ADV
ejpam-5386	306	23	complex	complex	ADJ
ejpam-5386	306	24	scenarios	scenario	NOUN
ejpam-5386	306	25	.	.	PUNCT
ejpam-5386	307	1	in	in	ADP
ejpam-5386	307	2	doing	do	VERB
ejpam-5386	307	3	so	so	ADV
ejpam-5386	307	4	,	,	PUNCT
ejpam-5386	307	5	we	we	PRON
ejpam-5386	307	6	choose	choose	VERB
ejpam-5386	307	7	the	the	DET
ejpam-5386	307	8	weight	weight	NOUN
ejpam-5386	307	9	functions	function	NOUN
ejpam-5386	307	10	as	as	ADP
ejpam-5386	307	11	ω1(t	ω1(t	NUM
ejpam-5386	307	12	)	)	PUNCT
ejpam-5386	307	13	=	=	SYM
ejpam-5386	307	14	1	1	NUM
ejpam-5386	307	15	and	and	CCONJ
ejpam-5386	307	16	ω2(t	ω2(t	NUM
ejpam-5386	307	17	)	)	PUNCT
ejpam-5386	307	18	=	=	SYM
ejpam-5386	307	19	e−t	e−t	NOUN
ejpam-5386	307	20	,	,	PUNCT
ejpam-5386	307	21	tailoring	tailor	VERB
ejpam-5386	307	22	our	our	PRON
ejpam-5386	307	23	algorithm	algorithm	NOUN
ejpam-5386	307	24	to	to	ADP
ejpam-5386	307	25	specific	specific	ADJ
ejpam-5386	307	26	characteristics	characteristic	NOUN
ejpam-5386	307	27	of	of	ADP
ejpam-5386	307	28	the	the	DET
ejpam-5386	307	29	problem	problem	NOUN
ejpam-5386	307	30	domain	domain	NOUN
ejpam-5386	307	31	.	.	PUNCT
ejpam-5386	308	1	with	with	ADP
ejpam-5386	308	2	these	these	DET
ejpam-5386	308	3	choices	choice	NOUN
ejpam-5386	308	4	,	,	PUNCT
ejpam-5386	308	5	we	we	PRON
ejpam-5386	308	6	proceed	proceed	VERB
ejpam-5386	308	7	to	to	PART
ejpam-5386	308	8	test	test	VERB
ejpam-5386	308	9	our	our	PRON
ejpam-5386	308	10	algorithm	algorithm	NOUN
ejpam-5386	308	11	’s	’s	PART
ejpam-5386	308	12	ability	ability	NOUN
ejpam-5386	308	13	to	to	PART
ejpam-5386	308	14	reconstruct	reconstruct	VERB
ejpam-5386	308	15	a	a	DET
ejpam-5386	308	16	treatment	treatment	NOUN
ejpam-5386	308	17	parameter	parameter	NOUN
ejpam-5386	308	18	α	α	NOUN
ejpam-5386	308	19	and	and	CCONJ
ejpam-5386	308	20	initial	initial	ADJ
ejpam-5386	308	21	cell	cell	NOUN
ejpam-5386	308	22	density	density	NOUN
ejpam-5386	308	23	φ	φ	PROPN
ejpam-5386	308	24	defined	define	VERB
ejpam-5386	308	25	as	as	ADP
ejpam-5386	308	26	α(x	α(x	NOUN
ejpam-5386	308	27	)	)	PUNCT
ejpam-5386	308	28	=	=	SYM
ejpam-5386	308	29	2x+	2x+	NUM
ejpam-5386	308	30	sin(πx	sin(πx	NOUN
ejpam-5386	308	31	)	)	PUNCT
ejpam-5386	309	1	+	+	CCONJ
ejpam-5386	309	2	1	1	NUM
ejpam-5386	309	3	and	and	CCONJ
ejpam-5386	309	4	φ(x	φ(x	NOUN
ejpam-5386	309	5	)	)	PUNCT
ejpam-5386	309	6	=	=	SYM
ejpam-5386	309	7	cos(4πx	cos(4πx	NOUN
ejpam-5386	309	8	)	)	PUNCT
ejpam-5386	309	9	+	+	CCONJ
ejpam-5386	309	10	1	1	NUM
ejpam-5386	309	11	2	2	NUM
ejpam-5386	309	12	.	.	PUNCT
ejpam-5386	310	1	in	in	ADP
ejpam-5386	310	2	figure	figure	NOUN
ejpam-5386	310	3	1	1	NUM
ejpam-5386	310	4	,	,	PUNCT
ejpam-5386	310	5	we	we	PRON
ejpam-5386	310	6	show	show	VERB
ejpam-5386	310	7	the	the	DET
ejpam-5386	310	8	behavior	behavior	NOUN
ejpam-5386	310	9	of	of	ADP
ejpam-5386	310	10	the	the	DET
ejpam-5386	310	11	objective	objective	ADJ
ejpam-5386	310	12	functional	functional	ADJ
ejpam-5386	310	13	j(αk	j(αk	PROPN
ejpam-5386	310	14	,	,	PUNCT
ejpam-5386	310	15	φk	φk	ADP
ejpam-5386	310	16	)	)	PUNCT
ejpam-5386	310	17	,	,	PUNCT
ejpam-5386	310	18	as	as	SCONJ
ejpam-5386	310	19	defined	define	VERB
ejpam-5386	310	20	in	in	ADP
ejpam-5386	310	21	(	(	PUNCT
ejpam-5386	310	22	7	7	NUM
ejpam-5386	310	23	)	)	PUNCT
ejpam-5386	310	24	,	,	PUNCT
ejpam-5386	310	25	with	with	ADP
ejpam-5386	310	26	respect	respect	NOUN
ejpam-5386	310	27	to	to	ADP
ejpam-5386	310	28	the	the	DET
ejpam-5386	310	29	iteration	iteration	NOUN
ejpam-5386	310	30	number	number	NOUN
ejpam-5386	310	31	k.	k.	PROPN
ejpam-5386	311	1	this	this	DET
ejpam-5386	311	2	functional	functional	ADJ
ejpam-5386	311	3	characterizes	characterize	VERB
ejpam-5386	311	4	the	the	DET
ejpam-5386	311	5	simultaneous	simultaneous	ADJ
ejpam-5386	311	6	recovery	recovery	NOUN
ejpam-5386	311	7	of	of	ADP
ejpam-5386	311	8	the	the	DET
ejpam-5386	311	9	two	two	NUM
ejpam-5386	311	10	unknown	unknown	ADJ
ejpam-5386	311	11	parameters	parameter	NOUN
ejpam-5386	311	12	α(x	α(x	PROPN
ejpam-5386	311	13	)	)	PUNCT
ejpam-5386	311	14	and	and	CCONJ
ejpam-5386	311	15	φ(x	φ(x	NOUN
ejpam-5386	311	16	)	)	PUNCT
ejpam-5386	311	17	in	in	ADP
ejpam-5386	311	18	the	the	DET
ejpam-5386	311	19	noise	noise	NOUN
ejpam-5386	311	20	free	free	ADJ
ejpam-5386	311	21	case	case	NOUN
ejpam-5386	311	22	(	(	PUNCT
ejpam-5386	311	23	p	p	NOUN
ejpam-5386	311	24	=	=	NOUN
ejpam-5386	311	25	0	0	NUM
ejpam-5386	311	26	)	)	PUNCT
ejpam-5386	311	27	,	,	PUNCT
ejpam-5386	311	28	as	as	ADV
ejpam-5386	311	29	well	well	ADV
ejpam-5386	311	30	as	as	ADP
ejpam-5386	311	31	with	with	ADP
ejpam-5386	311	32	noise	noise	NOUN
ejpam-5386	311	33	levels	level	NOUN
ejpam-5386	311	34	p	p	X
ejpam-5386	311	35	=	=	SYM
ejpam-5386	311	36	1	1	NUM
ejpam-5386	311	37	and	and	CCONJ
ejpam-5386	311	38	p	p	NOUN
ejpam-5386	311	39	=	=	PROPN
ejpam-5386	311	40	2	2	NUM
ejpam-5386	311	41	.	.	PUNCT
ejpam-5386	311	42	from	from	ADP
ejpam-5386	311	43	this	this	DET
ejpam-5386	311	44	figure	figure	NOUN
ejpam-5386	311	45	,	,	PUNCT
ejpam-5386	311	46	it	it	PRON
ejpam-5386	311	47	can	can	AUX
ejpam-5386	311	48	be	be	AUX
ejpam-5386	311	49	seen	see	VERB
ejpam-5386	311	50	that	that	SCONJ
ejpam-5386	311	51	the	the	DET
ejpam-5386	311	52	objective	objective	ADJ
ejpam-5386	311	53	functional	functional	ADJ
ejpam-5386	311	54	(	(	PUNCT
ejpam-5386	311	55	7	7	NUM
ejpam-5386	311	56	)	)	PUNCT
ejpam-5386	311	57	is	be	AUX
ejpam-5386	311	58	monotonic	monotonic	ADJ
ejpam-5386	311	59	decreasing	decrease	VERB
ejpam-5386	311	60	and	and	CCONJ
ejpam-5386	311	61	convergent	convergent	NOUN
ejpam-5386	311	62	.	.	PUNCT
ejpam-5386	312	1	additionally	additionally	ADV
ejpam-5386	312	2	,	,	PUNCT
ejpam-5386	312	3	we	we	PRON
ejpam-5386	312	4	observe	observe	VERB
ejpam-5386	312	5	rapid	rapid	ADJ
ejpam-5386	312	6	convergence	convergence	NOUN
ejpam-5386	312	7	of	of	ADP
ejpam-5386	312	8	the	the	DET
ejpam-5386	312	9	functional	functional	ADJ
ejpam-5386	312	10	to	to	ADP
ejpam-5386	312	11	a	a	DET
ejpam-5386	312	12	small	small	ADJ
ejpam-5386	312	13	positive	positive	ADJ
ejpam-5386	312	14	value	value	NOUN
ejpam-5386	312	15	,	,	PUNCT
ejpam-5386	312	16	underscoring	underscore	VERB
ejpam-5386	312	17	the	the	DET
ejpam-5386	312	18	algorithm	algorithm	NOUN
ejpam-5386	312	19	’s	’s	PART
ejpam-5386	312	20	efficiency	efficiency	NOUN
ejpam-5386	312	21	in	in	ADP
ejpam-5386	312	22	minimizing	minimize	VERB
ejpam-5386	312	23	the	the	DET
ejpam-5386	312	24	objective	objective	NOUN
ejpam-5386	312	25	and	and	CCONJ
ejpam-5386	312	26	thereby	thereby	ADV
ejpam-5386	312	27	refining	refine	VERB
ejpam-5386	312	28	the	the	DET
ejpam-5386	312	29	parameter	parameter	NOUN
ejpam-5386	312	30	estimates	estimate	NOUN
ejpam-5386	312	31	.	.	PUNCT
ejpam-5386	313	1	figure	figure	VERB
ejpam-5386	313	2	1	1	NUM
ejpam-5386	313	3	:	:	PUNCT
ejpam-5386	313	4	the	the	DET
ejpam-5386	313	5	objective	objective	ADJ
ejpam-5386	313	6	functional	functional	ADJ
ejpam-5386	313	7	j(αk	j(αk	PROPN
ejpam-5386	313	8	,	,	PUNCT
ejpam-5386	313	9	φk	φk	ADP
ejpam-5386	313	10	)	)	PUNCT
ejpam-5386	313	11	,	,	PUNCT
ejpam-5386	313	12	for	for	ADP
ejpam-5386	313	13	different	different	ADJ
ejpam-5386	313	14	noise	noise	NOUN
ejpam-5386	313	15	levels	level	NOUN
ejpam-5386	313	16	p	p	PROPN
ejpam-5386	313	17	∈	∈	PROPN
ejpam-5386	313	18	{	{	PUNCT
ejpam-5386	313	19	0	0	NUM
ejpam-5386	313	20	,	,	PUNCT
ejpam-5386	313	21	1	1	NUM
ejpam-5386	313	22	,	,	PUNCT
ejpam-5386	313	23	2	2	NUM
ejpam-5386	313	24	}	}	PUNCT
ejpam-5386	313	25	,	,	PUNCT
ejpam-5386	313	26	in	in	ADP
ejpam-5386	313	27	example	example	NOUN
ejpam-5386	313	28	1	1	NUM
ejpam-5386	313	29	.	.	PUNCT
ejpam-5386	313	30	based	base	VERB
ejpam-5386	313	31	on	on	ADP
ejpam-5386	313	32	the	the	DET
ejpam-5386	313	33	discrepancy	discrepancy	NOUN
ejpam-5386	313	34	principle	principle	NOUN
ejpam-5386	313	35	(	(	PUNCT
ejpam-5386	313	36	28	28	NUM
ejpam-5386	313	37	)	)	PUNCT
ejpam-5386	313	38	,	,	PUNCT
ejpam-5386	313	39	table	table	NOUN
ejpam-5386	313	40	2	2	NUM
ejpam-5386	313	41	presents	present	VERB
ejpam-5386	313	42	a	a	DET
ejpam-5386	313	43	comprehensive	comprehensive	ADJ
ejpam-5386	313	44	overview	overview	NOUN
ejpam-5386	313	45	of	of	ADP
ejpam-5386	313	46	key	key	ADJ
ejpam-5386	313	47	metrics	metric	NOUN
ejpam-5386	313	48	for	for	ADP
ejpam-5386	313	49	each	each	DET
ejpam-5386	313	50	chosen	choose	VERB
ejpam-5386	313	51	noise	noise	NOUN
ejpam-5386	313	52	level	level	NOUN
ejpam-5386	313	53	p	p	X
ejpam-5386	313	54	∈	∈	PROPN
ejpam-5386	313	55	{	{	PUNCT
ejpam-5386	313	56	0	0	NUM
ejpam-5386	313	57	,	,	PUNCT
ejpam-5386	313	58	1	1	NUM
ejpam-5386	313	59	,	,	PUNCT
ejpam-5386	313	60	2	2	NUM
ejpam-5386	313	61	}	}	PUNCT
ejpam-5386	313	62	.	.	PUNCT
ejpam-5386	314	1	specifically	specifically	ADV
ejpam-5386	314	2	,	,	PUNCT
ejpam-5386	314	3	the	the	DET
ejpam-5386	314	4	table	table	NOUN
ejpam-5386	314	5	lists	list	VERB
ejpam-5386	314	6	the	the	DET
ejpam-5386	314	7	stopping	stop	VERB
ejpam-5386	314	8	iteration	iteration	NOUN
ejpam-5386	314	9	numbers	number	NOUN
ejpam-5386	314	10	k⋆	k⋆	PROPN
ejpam-5386	314	11	,	,	PUNCT
ejpam-5386	314	12	the	the	DET
ejpam-5386	314	13	threshold	threshold	NOUN
ejpam-5386	314	14	ε	ε	PROPN
ejpam-5386	314	15	,	,	PUNCT
ejpam-5386	314	16	the	the	DET
ejpam-5386	314	17	errors	error	NOUN
ejpam-5386	314	18	(	(	PUNCT
ejpam-5386	314	19	29	29	NUM
ejpam-5386	314	20	)	)	PUNCT
ejpam-5386	314	21	associated	associate	VERB
ejpam-5386	314	22	with	with	ADP
ejpam-5386	314	23	the	the	DET
ejpam-5386	314	24	unknowns	unknown	NOUN
ejpam-5386	314	25	α(x	α(x	PROPN
ejpam-5386	314	26	)	)	PUNCT
ejpam-5386	314	27	s.	s.	PROPN
ejpam-5386	314	28	tatar	tatar	PROPN
ejpam-5386	314	29	,	,	PUNCT
ejpam-5386	314	30	m.	m.	NOUN
ejpam-5386	314	31	bensalah	bensalah	PROPN
ejpam-5386	314	32	,	,	PUNCT
ejpam-5386	314	33	m.	m.	NOUN
ejpam-5386	314	34	alamil	alamil	PROPN
ejpam-5386	314	35	/	/	SYM
ejpam-5386	314	36	eur	eur	PROPN
ejpam-5386	314	37	.	.	PUNCT
ejpam-5386	315	1	j.	j.	PROPN
ejpam-5386	315	2	pure	pure	PROPN
ejpam-5386	315	3	appl	appl	PROPN
ejpam-5386	315	4	.	.	PROPN
ejpam-5386	315	5	math	math	PROPN
ejpam-5386	315	6	,	,	PUNCT
ejpam-5386	315	7	17	17	NUM
ejpam-5386	315	8	(	(	PUNCT
ejpam-5386	315	9	4	4	NUM
ejpam-5386	315	10	)	)	PUNCT
ejpam-5386	315	11	(	(	PUNCT
ejpam-5386	315	12	2024	2024	NUM
ejpam-5386	315	13	)	)	PUNCT
ejpam-5386	315	14	,	,	PUNCT
ejpam-5386	315	15	2651	2651	NUM
ejpam-5386	315	16	-	-	SYM
ejpam-5386	315	17	2675	2675	NUM
ejpam-5386	315	18	2666	2666	NUM
ejpam-5386	315	19	and	and	CCONJ
ejpam-5386	315	20	φ(x	φ(x	NOUN
ejpam-5386	315	21	)	)	PUNCT
ejpam-5386	315	22	,	,	PUNCT
ejpam-5386	315	23	as	as	ADV
ejpam-5386	315	24	well	well	ADV
ejpam-5386	315	25	as	as	ADP
ejpam-5386	315	26	the	the	DET
ejpam-5386	315	27	norms	norm	NOUN
ejpam-5386	315	28	of	of	ADP
ejpam-5386	315	29	the	the	DET
ejpam-5386	315	30	fréchet	fréchet	NOUN
ejpam-5386	315	31	gradients	gradient	NOUN
ejpam-5386	315	32	∥j	∥j	ADV
ejpam-5386	315	33	′,k⋆	′,k⋆	PROPN
ejpam-5386	315	34	α	α	NUM
ejpam-5386	315	35	∥2	∥2	NOUN
ejpam-5386	315	36	and	and	CCONJ
ejpam-5386	315	37	∥j	∥j	PROPN
ejpam-5386	315	38	′,k⋆	′,k⋆	PROPN
ejpam-5386	315	39	φ	φ	NUM
ejpam-5386	315	40	∥2	∥2	X
ejpam-5386	315	41	.	.	PUNCT
ejpam-5386	316	1	ε̄	ε̄	PROPN
ejpam-5386	316	2	k⋆	k⋆	NOUN
ejpam-5386	316	3	eα(k	eα(k	PUNCT
ejpam-5386	316	4	⋆	⋆	X
ejpam-5386	316	5	)	)	PUNCT
ejpam-5386	316	6	eφ(k	eφ(k	NUM
ejpam-5386	316	7	⋆	⋆	X
ejpam-5386	316	8	)	)	PUNCT
ejpam-5386	316	9	∥j	∥j	ADV
ejpam-5386	316	10	′,k⋆	′,k⋆	PROPN
ejpam-5386	316	11	α	α	PRON
ejpam-5386	316	12	∥2	∥2	NOUN
ejpam-5386	317	1	∥j	∥j	ADV
ejpam-5386	317	2	′,k⋆	′,k⋆	PROPN
ejpam-5386	317	3	φ	φ	NUM
ejpam-5386	317	4	∥2	∥2	PROPN
ejpam-5386	318	1	p	p	X
ejpam-5386	318	2	=	=	PUNCT
ejpam-5386	318	3	0	0	NUM
ejpam-5386	318	4	1.00e−	1.00e−	NUM
ejpam-5386	318	5	06	06	NUM
ejpam-5386	318	6	161	161	NUM
ejpam-5386	318	7	4.41e−	4.41e−	NUM
ejpam-5386	318	8	02	02	NUM
ejpam-5386	318	9	3.11e−	3.11e−	NUM
ejpam-5386	318	10	02	02	NUM
ejpam-5386	318	11	2.09e−	2.09e−	NUM
ejpam-5386	318	12	04	04	NUM
ejpam-5386	318	13	3.34e−	3.34e−	NUM
ejpam-5386	318	14	04	04	NUM
ejpam-5386	319	1	p	p	NOUN
ejpam-5386	319	2	=	=	NOUN
ejpam-5386	319	3	1	1	NUM
ejpam-5386	319	4	8.54e−	8.54e−	NUM
ejpam-5386	319	5	05	05	NUM
ejpam-5386	319	6	66	66	NUM
ejpam-5386	319	7	1.21e−	1.21e−	NUM
ejpam-5386	319	8	01	01	NUM
ejpam-5386	319	9	1.17e−	1.17e−	NUM
ejpam-5386	319	10	01	01	NUM
ejpam-5386	319	11	3.04e−	3.04e−	NUM
ejpam-5386	319	12	04	04	NUM
ejpam-5386	319	13	3.63e−	3.63e−	NUM
ejpam-5386	319	14	04	04	NUM
ejpam-5386	320	1	p	p	NOUN
ejpam-5386	320	2	=	=	NOUN
ejpam-5386	320	3	2	2	NUM
ejpam-5386	320	4	3.41e−	3.41e−	NUM
ejpam-5386	320	5	04	04	NUM
ejpam-5386	320	6	43	43	NUM
ejpam-5386	320	7	2.21e−	2.21e−	NUM
ejpam-5386	320	8	01	01	NUM
ejpam-5386	320	9	1.56e−	1.56e−	NUM
ejpam-5386	320	10	01	01	NUM
ejpam-5386	320	11	1.24e−	1.24e−	NUM
ejpam-5386	320	12	03	03	NUM
ejpam-5386	320	13	1.45e−	1.45e−	NUM
ejpam-5386	320	14	03	03	NUM
ejpam-5386	320	15	table	table	NOUN
ejpam-5386	320	16	2	2	NUM
ejpam-5386	320	17	:	:	PUNCT
ejpam-5386	320	18	choices	choice	NOUN
ejpam-5386	320	19	of	of	ADP
ejpam-5386	320	20	noise	noise	NOUN
ejpam-5386	320	21	levels	level	NOUN
ejpam-5386	320	22	p	p	NOUN
ejpam-5386	320	23	and	and	CCONJ
ejpam-5386	320	24	their	their	PRON
ejpam-5386	320	25	respective	respective	ADJ
ejpam-5386	320	26	threshold	threshold	NOUN
ejpam-5386	320	27	values	value	NOUN
ejpam-5386	320	28	,	,	PUNCT
ejpam-5386	320	29	the	the	DET
ejpam-5386	320	30	corresponding	corresponding	ADJ
ejpam-5386	320	31	stopping	stopping	NOUN
ejpam-5386	320	32	iteration	iteration	NOUN
ejpam-5386	320	33	numbers	number	NOUN
ejpam-5386	320	34	k⋆	k⋆	NOUN
ejpam-5386	320	35	,	,	PUNCT
ejpam-5386	320	36	l2	l2	NOUN
ejpam-5386	320	37	-	-	PUNCT
ejpam-5386	320	38	errors	error	NOUN
ejpam-5386	320	39	,	,	PUNCT
ejpam-5386	320	40	and	and	CCONJ
ejpam-5386	320	41	norms	norm	NOUN
ejpam-5386	320	42	of	of	ADP
ejpam-5386	320	43	the	the	DET
ejpam-5386	320	44	fréchet	fréchet	NOUN
ejpam-5386	320	45	gradients	gradient	NOUN
ejpam-5386	320	46	in	in	ADP
ejpam-5386	320	47	example	example	NOUN
ejpam-5386	320	48	1	1	NUM
ejpam-5386	320	49	.	.	PUNCT
ejpam-5386	320	50	from	from	ADP
ejpam-5386	320	51	table	table	NOUN
ejpam-5386	320	52	2	2	NUM
ejpam-5386	320	53	,	,	PUNCT
ejpam-5386	320	54	it	it	PRON
ejpam-5386	320	55	is	be	AUX
ejpam-5386	320	56	evident	evident	ADJ
ejpam-5386	320	57	that	that	SCONJ
ejpam-5386	320	58	the	the	DET
ejpam-5386	320	59	numerical	numerical	ADJ
ejpam-5386	320	60	solutions	solution	NOUN
ejpam-5386	320	61	are	be	AUX
ejpam-5386	320	62	reasonably	reasonably	ADV
ejpam-5386	320	63	accurate	accurate	ADJ
ejpam-5386	320	64	for	for	ADP
ejpam-5386	320	65	both	both	DET
ejpam-5386	320	66	α(x	α(x	NOUN
ejpam-5386	320	67	)	)	PUNCT
ejpam-5386	320	68	and	and	CCONJ
ejpam-5386	320	69	φ(x	φ(x	NOUN
ejpam-5386	320	70	)	)	PUNCT
ejpam-5386	320	71	.	.	PUNCT
ejpam-5386	321	1	furthermore	furthermore	ADV
ejpam-5386	321	2	,	,	PUNCT
ejpam-5386	321	3	the	the	DET
ejpam-5386	321	4	norms	norm	NOUN
ejpam-5386	321	5	of	of	ADP
ejpam-5386	321	6	the	the	DET
ejpam-5386	321	7	fréchet	fréchet	NOUN
ejpam-5386	321	8	gradients	gradient	NOUN
ejpam-5386	321	9	indicate	indicate	VERB
ejpam-5386	321	10	that	that	SCONJ
ejpam-5386	321	11	the	the	DET
ejpam-5386	321	12	conjugate	conjugate	ADJ
ejpam-5386	321	13	gradient	gradient	NOUN
ejpam-5386	321	14	method	method	NOUN
ejpam-5386	321	15	(	(	PUNCT
ejpam-5386	321	16	cgm	cgm	PROPN
ejpam-5386	321	17	)	)	PUNCT
ejpam-5386	321	18	,	,	PUNCT
ejpam-5386	321	19	with	with	ADP
ejpam-5386	321	20	iterations	iteration	NOUN
ejpam-5386	321	21	stopped	stop	VERB
ejpam-5386	321	22	by	by	ADP
ejpam-5386	321	23	the	the	DET
ejpam-5386	321	24	discrepancy	discrepancy	NOUN
ejpam-5386	321	25	principle	principle	NOUN
ejpam-5386	321	26	(	(	PUNCT
ejpam-5386	321	27	28	28	NUM
ejpam-5386	321	28	)	)	PUNCT
ejpam-5386	321	29	,	,	PUNCT
ejpam-5386	321	30	serves	serve	VERB
ejpam-5386	321	31	as	as	ADP
ejpam-5386	321	32	a	a	DET
ejpam-5386	321	33	semi	semi	ADJ
ejpam-5386	321	34	-	-	ADJ
ejpam-5386	321	35	convergent	convergent	ADJ
ejpam-5386	321	36	regularization	regularization	NOUN
ejpam-5386	321	37	method	method	NOUN
ejpam-5386	321	38	.	.	PUNCT
ejpam-5386	322	1	in	in	ADP
ejpam-5386	322	2	figure	figure	NOUN
ejpam-5386	322	3	2	2	NUM
ejpam-5386	322	4	,	,	PUNCT
ejpam-5386	322	5	we	we	PRON
ejpam-5386	322	6	illustrate	illustrate	VERB
ejpam-5386	322	7	the	the	DET
ejpam-5386	322	8	numerical	numerical	ADJ
ejpam-5386	322	9	solutions	solution	NOUN
ejpam-5386	322	10	for	for	ADP
ejpam-5386	322	11	the	the	DET
ejpam-5386	322	12	treatment	treatment	NOUN
ejpam-5386	322	13	parameter	parameter	NOUN
ejpam-5386	322	14	α(x	α(x	PROPN
ejpam-5386	322	15	)	)	PUNCT
ejpam-5386	322	16	and	and	CCONJ
ejpam-5386	322	17	the	the	DET
ejpam-5386	322	18	initial	initial	ADJ
ejpam-5386	322	19	cell	cell	NOUN
ejpam-5386	322	20	density	density	NOUN
ejpam-5386	322	21	φ(x	φ(x	NOUN
ejpam-5386	322	22	)	)	PUNCT
ejpam-5386	322	23	at	at	ADP
ejpam-5386	322	24	the	the	DET
ejpam-5386	322	25	stopping	stop	VERB
ejpam-5386	322	26	iteration	iteration	NOUN
ejpam-5386	322	27	numbers	number	NOUN
ejpam-5386	322	28	k⋆	k⋆	X
ejpam-5386	322	29	determined	determine	VERB
ejpam-5386	322	30	from	from	ADP
ejpam-5386	322	31	table	table	NOUN
ejpam-5386	322	32	2	2	NUM
ejpam-5386	322	33	.	.	PUNCT
ejpam-5386	323	1	these	these	DET
ejpam-5386	323	2	solutions	solution	NOUN
ejpam-5386	323	3	are	be	AUX
ejpam-5386	323	4	shown	show	VERB
ejpam-5386	323	5	for	for	ADP
ejpam-5386	323	6	noise	noise	NOUN
ejpam-5386	323	7	levels	level	NOUN
ejpam-5386	323	8	p	p	NOUN
ejpam-5386	323	9	in	in	ADP
ejpam-5386	323	10	{	{	PUNCT
ejpam-5386	323	11	0	0	NUM
ejpam-5386	323	12	,	,	PUNCT
ejpam-5386	323	13	1	1	NUM
ejpam-5386	323	14	,	,	PUNCT
ejpam-5386	323	15	2	2	NUM
ejpam-5386	323	16	}	}	PUNCT
ejpam-5386	323	17	.	.	PUNCT
ejpam-5386	324	1	from	from	ADP
ejpam-5386	324	2	figure	figure	NOUN
ejpam-5386	324	3	2	2	NUM
ejpam-5386	324	4	,	,	PUNCT
ejpam-5386	324	5	it	it	PRON
ejpam-5386	324	6	is	be	AUX
ejpam-5386	324	7	evident	evident	ADJ
ejpam-5386	324	8	that	that	SCONJ
ejpam-5386	324	9	for	for	ADP
ejpam-5386	324	10	noise	noise	NOUN
ejpam-5386	324	11	-	-	PUNCT
ejpam-5386	324	12	free	free	ADJ
ejpam-5386	324	13	data	datum	NOUN
ejpam-5386	324	14	(	(	PUNCT
ejpam-5386	324	15	p	p	NOUN
ejpam-5386	324	16	=	=	NOUN
ejpam-5386	324	17	0	0	NUM
ejpam-5386	324	18	)	)	PUNCT
ejpam-5386	324	19	,	,	PUNCT
ejpam-5386	324	20	the	the	DET
ejpam-5386	324	21	analytical	analytical	ADJ
ejpam-5386	324	22	and	and	CCONJ
ejpam-5386	324	23	numerical	numerical	ADJ
ejpam-5386	324	24	solutions	solution	NOUN
ejpam-5386	324	25	overlap	overlap	NOUN
ejpam-5386	324	26	,	,	PUNCT
ejpam-5386	324	27	making	make	VERB
ejpam-5386	324	28	them	they	PRON
ejpam-5386	324	29	indistinguishable	indistinguishable	ADJ
ejpam-5386	324	30	graphically	graphically	ADV
ejpam-5386	324	31	.	.	PUNCT
ejpam-5386	325	1	however	however	ADV
ejpam-5386	325	2	,	,	PUNCT
ejpam-5386	325	3	as	as	ADP
ejpam-5386	325	4	the	the	DET
ejpam-5386	325	5	level	level	NOUN
ejpam-5386	325	6	of	of	ADP
ejpam-5386	325	7	noise	noise	NOUN
ejpam-5386	325	8	increases	increase	NOUN
ejpam-5386	325	9	,	,	PUNCT
ejpam-5386	325	10	the	the	DET
ejpam-5386	325	11	accuracy	accuracy	NOUN
ejpam-5386	325	12	of	of	ADP
ejpam-5386	325	13	the	the	DET
ejpam-5386	325	14	solutions	solution	NOUN
ejpam-5386	325	15	decreases	decrease	VERB
ejpam-5386	325	16	.	.	PUNCT
ejpam-5386	326	1	overall	overall	ADV
ejpam-5386	326	2	,	,	PUNCT
ejpam-5386	326	3	it	it	PRON
ejpam-5386	326	4	can	can	AUX
ejpam-5386	326	5	be	be	AUX
ejpam-5386	326	6	observed	observe	VERB
ejpam-5386	326	7	that	that	PRON
ejpam-5386	326	8	stable	stable	ADJ
ejpam-5386	326	9	and	and	CCONJ
ejpam-5386	326	10	accurate	accurate	ADJ
ejpam-5386	326	11	solutions	solution	NOUN
ejpam-5386	326	12	are	be	AUX
ejpam-5386	326	13	obtained	obtain	VERB
ejpam-5386	326	14	for	for	ADP
ejpam-5386	326	15	both	both	DET
ejpam-5386	326	16	coefficients	coefficient	NOUN
ejpam-5386	326	17	α(x	α(x	PROPN
ejpam-5386	326	18	)	)	PUNCT
ejpam-5386	326	19	and	and	CCONJ
ejpam-5386	326	20	φ(x	φ(x	NOUN
ejpam-5386	326	21	)	)	PUNCT
ejpam-5386	326	22	.	.	PUNCT
ejpam-5386	327	1	(	(	PUNCT
ejpam-5386	327	2	a	a	X
ejpam-5386	327	3	)	)	PUNCT
ejpam-5386	327	4	the	the	DET
ejpam-5386	327	5	treatment	treatment	NOUN
ejpam-5386	327	6	parameter	parameter	NOUN
ejpam-5386	327	7	α(x	α(x	PROPN
ejpam-5386	327	8	)	)	PUNCT
ejpam-5386	327	9	(	(	PUNCT
ejpam-5386	327	10	b	b	X
ejpam-5386	327	11	)	)	PUNCT
ejpam-5386	327	12	the	the	DET
ejpam-5386	327	13	initial	initial	ADJ
ejpam-5386	327	14	cell	cell	NOUN
ejpam-5386	327	15	density	density	NOUN
ejpam-5386	327	16	φ(x	φ(x	NOUN
ejpam-5386	327	17	)	)	PUNCT
ejpam-5386	327	18	figure	figure	NOUN
ejpam-5386	327	19	2	2	NUM
ejpam-5386	327	20	:	:	PUNCT
ejpam-5386	327	21	the	the	DET
ejpam-5386	327	22	numerical	numerical	ADJ
ejpam-5386	327	23	results	result	NOUN
ejpam-5386	327	24	for	for	ADP
ejpam-5386	327	25	example	example	NOUN
ejpam-5386	327	26	1	1	NUM
ejpam-5386	327	27	for	for	ADP
ejpam-5386	327	28	p	p	PROPN
ejpam-5386	327	29	∈	∈	PROPN
ejpam-5386	327	30	{	{	PUNCT
ejpam-5386	327	31	0	0	NUM
ejpam-5386	327	32	,	,	PUNCT
ejpam-5386	327	33	1	1	NUM
ejpam-5386	327	34	,	,	PUNCT
ejpam-5386	327	35	2	2	NUM
ejpam-5386	327	36	}	}	PUNCT
ejpam-5386	327	37	.	.	PUNCT
ejpam-5386	328	1	left	leave	VERB
ejpam-5386	328	2	:	:	PUNCT
ejpam-5386	328	3	the	the	DET
ejpam-5386	328	4	treatment	treatment	NOUN
ejpam-5386	328	5	parameter	parameter	NOUN
ejpam-5386	328	6	α(x	α(x	PROPN
ejpam-5386	328	7	)	)	PUNCT
ejpam-5386	328	8	.	.	PUNCT
ejpam-5386	329	1	right	right	ADV
ejpam-5386	329	2	:	:	PUNCT
ejpam-5386	329	3	the	the	DET
ejpam-5386	329	4	initial	initial	ADJ
ejpam-5386	329	5	cell	cell	NOUN
ejpam-5386	329	6	density	density	NOUN
ejpam-5386	329	7	φ(x	φ(x	NOUN
ejpam-5386	329	8	)	)	PUNCT
ejpam-5386	329	9	.	.	PUNCT
ejpam-5386	330	1	example	example	NOUN
ejpam-5386	331	1	2	2	NUM
ejpam-5386	331	2	.	.	X
ejpam-5386	331	3	in	in	ADP
ejpam-5386	331	4	this	this	DET
ejpam-5386	331	5	example	example	NOUN
ejpam-5386	331	6	,	,	PUNCT
ejpam-5386	331	7	we	we	PRON
ejpam-5386	331	8	test	test	VERB
ejpam-5386	331	9	our	our	PRON
ejpam-5386	331	10	algorithm	algorithm	NOUN
ejpam-5386	331	11	to	to	PART
ejpam-5386	331	12	recover	recover	VERB
ejpam-5386	331	13	a	a	DET
ejpam-5386	331	14	smooth	smooth	ADJ
ejpam-5386	331	15	treatment	treatment	NOUN
ejpam-5386	331	16	parameter	parameter	NOUN
ejpam-5386	331	17	and	and	CCONJ
ejpam-5386	331	18	a	a	DET
ejpam-5386	331	19	non	non	ADJ
ejpam-5386	331	20	-	-	ADJ
ejpam-5386	331	21	smooth	smooth	ADJ
ejpam-5386	331	22	initial	initial	ADJ
ejpam-5386	331	23	cell	cell	NOUN
ejpam-5386	331	24	density	density	NOUN
ejpam-5386	331	25	,	,	PUNCT
ejpam-5386	331	26	driven	drive	VERB
ejpam-5386	331	27	by	by	ADP
ejpam-5386	331	28	considerations	consideration	NOUN
ejpam-5386	331	29	in	in	ADP
ejpam-5386	331	30	brain	brain	NOUN
ejpam-5386	331	31	tumor	tumor	NOUN
ejpam-5386	331	32	growth	growth	NOUN
ejpam-5386	331	33	dynamics	dynamic	NOUN
ejpam-5386	331	34	.	.	PUNCT
ejpam-5386	332	1	typically	typically	ADV
ejpam-5386	332	2	,	,	PUNCT
ejpam-5386	332	3	treatment	treatment	NOUN
ejpam-5386	332	4	parameters	parameter	NOUN
ejpam-5386	332	5	in	in	ADP
ejpam-5386	332	6	such	such	ADJ
ejpam-5386	332	7	scenarios	scenario	NOUN
ejpam-5386	332	8	exhibit	exhibit	VERB
ejpam-5386	332	9	smooth	smooth	ADJ
ejpam-5386	332	10	variations	variation	NOUN
ejpam-5386	332	11	,	,	PUNCT
ejpam-5386	332	12	while	while	SCONJ
ejpam-5386	332	13	initial	initial	ADJ
ejpam-5386	332	14	cell	cell	NOUN
ejpam-5386	332	15	densities	density	NOUN
ejpam-5386	332	16	may	may	AUX
ejpam-5386	332	17	feature	feature	VERB
ejpam-5386	332	18	sharp	sharp	ADJ
ejpam-5386	332	19	changes	change	NOUN
ejpam-5386	332	20	or	or	CCONJ
ejpam-5386	332	21	irregularities	irregularity	NOUN
ejpam-5386	332	22	.	.	PUNCT
ejpam-5386	333	1	by	by	ADP
ejpam-5386	333	2	addressing	address	VERB
ejpam-5386	333	3	these	these	DET
ejpam-5386	333	4	characteristics	characteristic	NOUN
ejpam-5386	333	5	,	,	PUNCT
ejpam-5386	333	6	we	we	PRON
ejpam-5386	333	7	aim	aim	VERB
ejpam-5386	333	8	to	to	PART
ejpam-5386	333	9	enhance	enhance	VERB
ejpam-5386	333	10	the	the	DET
ejpam-5386	333	11	applicability	applicability	NOUN
ejpam-5386	333	12	of	of	ADP
ejpam-5386	333	13	our	our	PRON
ejpam-5386	333	14	algorithm	algorithm	NOUN
ejpam-5386	333	15	in	in	ADP
ejpam-5386	333	16	real	real	ADJ
ejpam-5386	333	17	-	-	PUNCT
ejpam-5386	333	18	world	world	NOUN
ejpam-5386	333	19	s.	s.	PROPN
ejpam-5386	333	20	tatar	tatar	PROPN
ejpam-5386	333	21	,	,	PUNCT
ejpam-5386	333	22	m.	m.	NOUN
ejpam-5386	333	23	bensalah	bensalah	PROPN
ejpam-5386	333	24	,	,	PUNCT
ejpam-5386	333	25	m.	m.	NOUN
ejpam-5386	333	26	alamil	alamil	PROPN
ejpam-5386	333	27	/	/	SYM
ejpam-5386	333	28	eur	eur	PROPN
ejpam-5386	333	29	.	.	PUNCT
ejpam-5386	334	1	j.	j.	PROPN
ejpam-5386	334	2	pure	pure	PROPN
ejpam-5386	334	3	appl	appl	PROPN
ejpam-5386	334	4	.	.	PROPN
ejpam-5386	334	5	math	math	PROPN
ejpam-5386	334	6	,	,	PUNCT
ejpam-5386	334	7	17	17	NUM
ejpam-5386	334	8	(	(	PUNCT
ejpam-5386	334	9	4	4	NUM
ejpam-5386	334	10	)	)	PUNCT
ejpam-5386	334	11	(	(	PUNCT
ejpam-5386	334	12	2024	2024	NUM
ejpam-5386	334	13	)	)	PUNCT
ejpam-5386	334	14	,	,	PUNCT
ejpam-5386	334	15	2651	2651	NUM
ejpam-5386	334	16	-	-	SYM
ejpam-5386	334	17	2675	2675	NUM
ejpam-5386	334	18	2667	2667	NUM
ejpam-5386	334	19	medical	medical	ADJ
ejpam-5386	334	20	contexts	contexts	NOUN
ejpam-5386	334	21	,	,	PUNCT
ejpam-5386	334	22	where	where	SCONJ
ejpam-5386	334	23	accurate	accurate	ADJ
ejpam-5386	334	24	characterization	characterization	NOUN
ejpam-5386	334	25	of	of	ADP
ejpam-5386	334	26	tumor	tumor	NOUN
ejpam-5386	334	27	growth	growth	NOUN
ejpam-5386	334	28	dynamics	dynamic	NOUN
ejpam-5386	334	29	is	be	AUX
ejpam-5386	334	30	crucial	crucial	ADJ
ejpam-5386	334	31	for	for	ADP
ejpam-5386	334	32	effective	effective	ADJ
ejpam-5386	334	33	treatment	treatment	NOUN
ejpam-5386	334	34	planning	planning	NOUN
ejpam-5386	334	35	and	and	CCONJ
ejpam-5386	334	36	monitoring	monitoring	NOUN
ejpam-5386	334	37	.	.	PUNCT
ejpam-5386	335	1	moreover	moreover	ADV
ejpam-5386	335	2	,	,	PUNCT
ejpam-5386	335	3	investigating	investigate	VERB
ejpam-5386	335	4	the	the	DET
ejpam-5386	335	5	algorithm	algorithm	NOUN
ejpam-5386	335	6	’s	’s	PART
ejpam-5386	335	7	performance	performance	NOUN
ejpam-5386	335	8	in	in	ADP
ejpam-5386	335	9	recovering	recover	VERB
ejpam-5386	335	10	both	both	CCONJ
ejpam-5386	335	11	smooth	smooth	ADJ
ejpam-5386	335	12	and	and	CCONJ
ejpam-5386	335	13	non	non	ADJ
ejpam-5386	335	14	-	-	ADJ
ejpam-5386	335	15	smooth	smooth	ADJ
ejpam-5386	335	16	parameters	parameter	NOUN
ejpam-5386	335	17	provides	provide	VERB
ejpam-5386	335	18	valuable	valuable	ADJ
ejpam-5386	335	19	insights	insight	NOUN
ejpam-5386	335	20	into	into	ADP
ejpam-5386	335	21	its	its	PRON
ejpam-5386	335	22	robustness	robustness	NOUN
ejpam-5386	335	23	and	and	CCONJ
ejpam-5386	335	24	versatility	versatility	NOUN
ejpam-5386	335	25	across	across	ADP
ejpam-5386	335	26	diverse	diverse	ADJ
ejpam-5386	335	27	tumor	tumor	NOUN
ejpam-5386	335	28	growth	growth	NOUN
ejpam-5386	335	29	patterns	pattern	NOUN
ejpam-5386	335	30	.	.	PUNCT
ejpam-5386	336	1	to	to	PART
ejpam-5386	336	2	demonstrate	demonstrate	VERB
ejpam-5386	336	3	the	the	DET
ejpam-5386	336	4	effectiveness	effectiveness	NOUN
ejpam-5386	336	5	of	of	ADP
ejpam-5386	336	6	our	our	PRON
ejpam-5386	336	7	proposed	propose	VERB
ejpam-5386	336	8	iterative	iterative	NOUN
ejpam-5386	336	9	method	method	NOUN
ejpam-5386	336	10	in	in	ADP
ejpam-5386	336	11	this	this	DET
ejpam-5386	336	12	scenario	scenario	NOUN
ejpam-5386	336	13	,	,	PUNCT
ejpam-5386	336	14	we	we	PRON
ejpam-5386	336	15	define	define	VERB
ejpam-5386	336	16	the	the	DET
ejpam-5386	336	17	exact	exact	ADJ
ejpam-5386	336	18	treatment	treatment	NOUN
ejpam-5386	336	19	parameter	parameter	NOUN
ejpam-5386	336	20	α(x	α(x	PROPN
ejpam-5386	336	21	)	)	PUNCT
ejpam-5386	336	22	and	and	CCONJ
ejpam-5386	336	23	initial	initial	ADJ
ejpam-5386	336	24	cell	cell	NOUN
ejpam-5386	336	25	density	density	NOUN
ejpam-5386	336	26	φ(x	φ(x	NOUN
ejpam-5386	336	27	)	)	PUNCT
ejpam-5386	336	28	to	to	PART
ejpam-5386	336	29	be	be	AUX
ejpam-5386	336	30	reconstructed	reconstruct	VERB
ejpam-5386	336	31	as	as	SCONJ
ejpam-5386	336	32	follows	follow	VERB
ejpam-5386	336	33	:	:	PUNCT
ejpam-5386	336	34	α(x	α(x	NUM
ejpam-5386	336	35	)	)	PUNCT
ejpam-5386	336	36	=	=	SYM
ejpam-5386	337	1	1	1	NUM
ejpam-5386	337	2	+	+	NUM
ejpam-5386	337	3	sin(4πx	sin(4πx	X
ejpam-5386	337	4	)	)	PUNCT
ejpam-5386	337	5	2	2	NUM
ejpam-5386	337	6	and	and	CCONJ
ejpam-5386	337	7	φ(x	φ(x	NOUN
ejpam-5386	337	8	)	)	PUNCT
ejpam-5386	337	9	=	=	SYM
ejpam-5386	338	1			NOUN
ejpam-5386	338	2	0	0	NUM
ejpam-5386	338	3	,	,	PUNCT
ejpam-5386	338	4	if	if	SCONJ
ejpam-5386	338	5	x	x	PUNCT
ejpam-5386	338	6	∈	∈	PROPN
ejpam-5386	339	1	[	[	X
ejpam-5386	339	2	0	0	NUM
ejpam-5386	339	3	,	,	PUNCT
ejpam-5386	339	4	0.2	0.2	NUM
ejpam-5386	339	5	]	]	PUNCT
ejpam-5386	339	6	∪	∪	ADP
ejpam-5386	339	7	[	[	X
ejpam-5386	339	8	0.8	0.8	NUM
ejpam-5386	339	9	,	,	PUNCT
ejpam-5386	339	10	0.1	0.1	NUM
ejpam-5386	339	11	]	]	PUNCT
ejpam-5386	339	12	,	,	PUNCT
ejpam-5386	339	13	2	2	NUM
ejpam-5386	339	14	sin(πx)−	sin(πx)−	PROPN
ejpam-5386	339	15	1	1	NUM
ejpam-5386	339	16	,	,	PUNCT
ejpam-5386	339	17	if	if	SCONJ
ejpam-5386	339	18	x	x	PUNCT
ejpam-5386	339	19	∈	∈	PROPN
ejpam-5386	340	1	[	[	X
ejpam-5386	340	2	0.2	0.2	NUM
ejpam-5386	340	3	,	,	PUNCT
ejpam-5386	340	4	0.5	0.5	NUM
ejpam-5386	340	5	]	]	PUNCT
ejpam-5386	340	6	,	,	PUNCT
ejpam-5386	340	7	−10x	−10x	PROPN
ejpam-5386	340	8	3	3	NUM
ejpam-5386	340	9	+	+	NUM
ejpam-5386	340	10	8	8	NUM
ejpam-5386	340	11	3	3	NUM
ejpam-5386	340	12	,	,	PUNCT
ejpam-5386	340	13	otherwise	otherwise	ADV
ejpam-5386	340	14	.	.	PUNCT
ejpam-5386	341	1	the	the	DET
ejpam-5386	341	2	measured	measured	ADJ
ejpam-5386	341	3	data	datum	NOUN
ejpam-5386	341	4	ϕεi	ϕεi	VERB
ejpam-5386	341	5	,	,	PUNCT
ejpam-5386	341	6	for	for	ADP
ejpam-5386	341	7	i	i	PROPN
ejpam-5386	341	8	=	=	SYM
ejpam-5386	341	9	1	1	NUM
ejpam-5386	341	10	,	,	PUNCT
ejpam-5386	341	11	2	2	NUM
ejpam-5386	341	12	,	,	PUNCT
ejpam-5386	341	13	are	be	AUX
ejpam-5386	341	14	generated	generate	VERB
ejpam-5386	341	15	using	use	VERB
ejpam-5386	341	16	the	the	DET
ejpam-5386	341	17	weight	weight	NOUN
ejpam-5386	341	18	functions	function	NOUN
ejpam-5386	341	19	ω1(t	ω1(t	NUM
ejpam-5386	341	20	)	)	PUNCT
ejpam-5386	341	21	=	=	SYM
ejpam-5386	342	1	1	1	NUM
ejpam-5386	342	2	+	+	NUM
ejpam-5386	342	3	t2	t2	NOUN
ejpam-5386	342	4	and	and	CCONJ
ejpam-5386	342	5	ω2(t	ω2(t	NOUN
ejpam-5386	342	6	)	)	PUNCT
ejpam-5386	342	7	=	=	SYM
ejpam-5386	342	8	exp(−2	exp(−2	PROPN
ejpam-5386	342	9	t	t	NOUN
ejpam-5386	342	10	)	)	PUNCT
ejpam-5386	342	11	.	.	PUNCT
ejpam-5386	343	1	figure	figure	NOUN
ejpam-5386	343	2	3	3	NUM
ejpam-5386	343	3	illustrates	illustrate	VERB
ejpam-5386	343	4	the	the	DET
ejpam-5386	343	5	objective	objective	ADJ
ejpam-5386	343	6	functional	functional	ADJ
ejpam-5386	343	7	j(αk	j(αk	PROPN
ejpam-5386	343	8	,	,	PUNCT
ejpam-5386	343	9	φk	φk	ADP
ejpam-5386	343	10	)	)	PUNCT
ejpam-5386	343	11	given	give	VERB
ejpam-5386	343	12	by	by	ADP
ejpam-5386	343	13	(	(	PUNCT
ejpam-5386	343	14	7	7	NUM
ejpam-5386	343	15	)	)	PUNCT
ejpam-5386	343	16	for	for	ADP
ejpam-5386	343	17	the	the	DET
ejpam-5386	343	18	simultaneous	simultaneous	ADJ
ejpam-5386	343	19	reconstruction	reconstruction	NOUN
ejpam-5386	343	20	of	of	ADP
ejpam-5386	343	21	the	the	DET
ejpam-5386	343	22	unknown	unknown	ADJ
ejpam-5386	343	23	coefficients	coefficient	NOUN
ejpam-5386	343	24	with	with	ADP
ejpam-5386	343	25	noise	noise	NOUN
ejpam-5386	343	26	levels	level	NOUN
ejpam-5386	343	27	p	p	PROPN
ejpam-5386	343	28	∈	∈	PROPN
ejpam-5386	343	29	{	{	PUNCT
ejpam-5386	343	30	0	0	NUM
ejpam-5386	343	31	,	,	PUNCT
ejpam-5386	343	32	1	1	NUM
ejpam-5386	343	33	,	,	PUNCT
ejpam-5386	343	34	2	2	NUM
ejpam-5386	343	35	}	}	PUNCT
ejpam-5386	343	36	.	.	PUNCT
ejpam-5386	344	1	from	from	ADP
ejpam-5386	344	2	this	this	DET
ejpam-5386	344	3	figure	figure	NOUN
ejpam-5386	344	4	,	,	PUNCT
ejpam-5386	344	5	it	it	PRON
ejpam-5386	344	6	is	be	AUX
ejpam-5386	344	7	evident	evident	ADJ
ejpam-5386	344	8	that	that	SCONJ
ejpam-5386	344	9	the	the	DET
ejpam-5386	344	10	objective	objective	ADJ
ejpam-5386	344	11	function	function	NOUN
ejpam-5386	344	12	rapidly	rapidly	ADV
ejpam-5386	344	13	decreases	decrease	VERB
ejpam-5386	344	14	monotonically	monotonically	ADV
ejpam-5386	344	15	and	and	CCONJ
ejpam-5386	344	16	thus	thus	ADV
ejpam-5386	344	17	it	it	PRON
ejpam-5386	344	18	is	be	AUX
ejpam-5386	344	19	convergent	convergent	ADJ
ejpam-5386	344	20	.	.	PUNCT
ejpam-5386	345	1	figure	figure	VERB
ejpam-5386	345	2	3	3	NUM
ejpam-5386	345	3	:	:	PUNCT
ejpam-5386	345	4	the	the	DET
ejpam-5386	345	5	objective	objective	ADJ
ejpam-5386	345	6	functional	functional	ADJ
ejpam-5386	345	7	j(αk	j(αk	PROPN
ejpam-5386	345	8	,	,	PUNCT
ejpam-5386	345	9	φk	φk	ADP
ejpam-5386	345	10	)	)	PUNCT
ejpam-5386	345	11	,	,	PUNCT
ejpam-5386	345	12	for	for	ADP
ejpam-5386	345	13	different	different	ADJ
ejpam-5386	345	14	noise	noise	NOUN
ejpam-5386	345	15	levels	level	NOUN
ejpam-5386	345	16	p	p	PROPN
ejpam-5386	345	17	∈	∈	PROPN
ejpam-5386	345	18	{	{	PUNCT
ejpam-5386	345	19	0	0	NUM
ejpam-5386	345	20	,	,	PUNCT
ejpam-5386	345	21	1	1	NUM
ejpam-5386	345	22	,	,	PUNCT
ejpam-5386	345	23	2	2	NUM
ejpam-5386	345	24	}	}	PUNCT
ejpam-5386	345	25	,	,	PUNCT
ejpam-5386	346	1	in	in	ADP
ejpam-5386	346	2	example	example	NOUN
ejpam-5386	346	3	2	2	X
ejpam-5386	346	4	.	.	PUNCT
ejpam-5386	347	1	the	the	DET
ejpam-5386	347	2	choices	choice	NOUN
ejpam-5386	347	3	of	of	ADP
ejpam-5386	347	4	p	p	NOUN
ejpam-5386	347	5	in	in	ADP
ejpam-5386	347	6	the	the	DET
ejpam-5386	347	7	test	test	NOUN
ejpam-5386	347	8	and	and	CCONJ
ejpam-5386	347	9	the	the	DET
ejpam-5386	347	10	corresponding	corresponding	ADJ
ejpam-5386	347	11	numerical	numerical	ADJ
ejpam-5386	347	12	performances	performance	NOUN
ejpam-5386	347	13	are	be	AUX
ejpam-5386	347	14	listed	list	VERB
ejpam-5386	347	15	in	in	ADP
ejpam-5386	347	16	table	table	NOUN
ejpam-5386	347	17	3	3	NUM
ejpam-5386	347	18	.	.	PUNCT
ejpam-5386	347	19	s.	s.	PROPN
ejpam-5386	347	20	tatar	tatar	PROPN
ejpam-5386	347	21	,	,	PUNCT
ejpam-5386	347	22	m.	m.	NOUN
ejpam-5386	347	23	bensalah	bensalah	PROPN
ejpam-5386	347	24	,	,	PUNCT
ejpam-5386	347	25	m.	m.	NOUN
ejpam-5386	347	26	alamil	alamil	PROPN
ejpam-5386	347	27	/	/	SYM
ejpam-5386	347	28	eur	eur	PROPN
ejpam-5386	347	29	.	.	PUNCT
ejpam-5386	348	1	j.	j.	PROPN
ejpam-5386	348	2	pure	pure	PROPN
ejpam-5386	348	3	appl	appl	PROPN
ejpam-5386	348	4	.	.	PROPN
ejpam-5386	348	5	math	math	PROPN
ejpam-5386	348	6	,	,	PUNCT
ejpam-5386	348	7	17	17	NUM
ejpam-5386	348	8	(	(	PUNCT
ejpam-5386	348	9	4	4	NUM
ejpam-5386	348	10	)	)	PUNCT
ejpam-5386	348	11	(	(	PUNCT
ejpam-5386	348	12	2024	2024	NUM
ejpam-5386	348	13	)	)	PUNCT
ejpam-5386	348	14	,	,	PUNCT
ejpam-5386	348	15	2651	2651	NUM
ejpam-5386	348	16	-	-	SYM
ejpam-5386	348	17	2675	2675	NUM
ejpam-5386	348	18	2668	2668	NUM
ejpam-5386	348	19	ε̄	ε̄	ADJ
ejpam-5386	348	20	k⋆	k⋆	NOUN
ejpam-5386	348	21	eα(k	eα(k	PUNCT
ejpam-5386	348	22	⋆	⋆	X
ejpam-5386	348	23	)	)	PUNCT
ejpam-5386	348	24	eφ(k	eφ(k	NUM
ejpam-5386	348	25	⋆	⋆	X
ejpam-5386	348	26	)	)	PUNCT
ejpam-5386	349	1	∥j	∥j	ADV
ejpam-5386	349	2	′,k⋆	′,k⋆	PROPN
ejpam-5386	349	3	α	α	PRON
ejpam-5386	349	4	∥2	∥2	NOUN
ejpam-5386	350	1	∥j	∥j	ADV
ejpam-5386	350	2	′,k⋆	′,k⋆	PROPN
ejpam-5386	350	3	φ	φ	NUM
ejpam-5386	350	4	∥2	∥2	PROPN
ejpam-5386	351	1	p	p	X
ejpam-5386	351	2	=	=	PUNCT
ejpam-5386	351	3	0	0	NUM
ejpam-5386	351	4	1.00e−	1.00e−	NUM
ejpam-5386	351	5	06	06	NUM
ejpam-5386	351	6	167	167	NUM
ejpam-5386	351	7	1.14e−	1.14e−	NUM
ejpam-5386	351	8	02	02	NUM
ejpam-5386	351	9	1.33e−	1.33e−	NUM
ejpam-5386	351	10	01	01	NUM
ejpam-5386	351	11	3.43e−	3.43e−	NUM
ejpam-5386	351	12	04	04	NUM
ejpam-5386	351	13	2.58e−	2.58e−	NOUN
ejpam-5386	351	14	05	05	NUM
ejpam-5386	352	1	p	p	NOUN
ejpam-5386	352	2	=	=	NOUN
ejpam-5386	352	3	1	1	NUM
ejpam-5386	352	4	3.18e−	3.18e−	NUM
ejpam-5386	352	5	02	02	NUM
ejpam-5386	352	6	17	17	NUM
ejpam-5386	352	7	9.05e−	9.05e−	NUM
ejpam-5386	352	8	02	02	NUM
ejpam-5386	352	9	2.16e−	2.16e−	NUM
ejpam-5386	352	10	01	01	NUM
ejpam-5386	352	11	1.17e−	1.17e−	NUM
ejpam-5386	352	12	01	01	NUM
ejpam-5386	352	13	1.01e−	1.01e−	NUM
ejpam-5386	352	14	01	01	NUM
ejpam-5386	353	1	p	p	NOUN
ejpam-5386	353	2	=	=	NOUN
ejpam-5386	353	3	2	2	NUM
ejpam-5386	353	4	1.27e−	1.27e−	NUM
ejpam-5386	353	5	01	01	NUM
ejpam-5386	353	6	9	9	NUM
ejpam-5386	353	7	1.06e−	1.06e−	NUM
ejpam-5386	353	8	01	01	NUM
ejpam-5386	353	9	3.07e−	3.07e−	NUM
ejpam-5386	353	10	01	01	NUM
ejpam-5386	353	11	3.30e−	3.30e−	NUM
ejpam-5386	353	12	01	01	NUM
ejpam-5386	353	13	1.22e−	1.22e−	NUM
ejpam-5386	353	14	01	01	NUM
ejpam-5386	353	15	table	table	NOUN
ejpam-5386	353	16	3	3	NUM
ejpam-5386	353	17	:	:	PUNCT
ejpam-5386	353	18	choices	choice	NOUN
ejpam-5386	353	19	of	of	ADP
ejpam-5386	353	20	noise	noise	NOUN
ejpam-5386	353	21	levels	level	NOUN
ejpam-5386	353	22	p	p	NOUN
ejpam-5386	353	23	alongside	alongside	ADP
ejpam-5386	353	24	their	their	PRON
ejpam-5386	353	25	respective	respective	ADJ
ejpam-5386	353	26	threshold	threshold	NOUN
ejpam-5386	353	27	values	value	NOUN
ejpam-5386	353	28	,	,	PUNCT
ejpam-5386	353	29	the	the	DET
ejpam-5386	353	30	corresponding	corresponding	ADJ
ejpam-5386	353	31	stopping	stopping	NOUN
ejpam-5386	353	32	iteration	iteration	NOUN
ejpam-5386	353	33	numbers	number	NOUN
ejpam-5386	353	34	k⋆	k⋆	NOUN
ejpam-5386	353	35	,	,	PUNCT
ejpam-5386	353	36	l2	l2	NOUN
ejpam-5386	353	37	-	-	PUNCT
ejpam-5386	353	38	errors	error	NOUN
ejpam-5386	353	39	,	,	PUNCT
ejpam-5386	353	40	and	and	CCONJ
ejpam-5386	353	41	norms	norm	NOUN
ejpam-5386	353	42	of	of	ADP
ejpam-5386	353	43	the	the	DET
ejpam-5386	353	44	fréchet	fréchet	NOUN
ejpam-5386	353	45	gradients	gradient	NOUN
ejpam-5386	353	46	in	in	ADP
ejpam-5386	353	47	example	example	NOUN
ejpam-5386	353	48	2	2	NUM
ejpam-5386	353	49	.	.	PUNCT
ejpam-5386	354	1	in	in	ADP
ejpam-5386	354	2	comparison	comparison	NOUN
ejpam-5386	354	3	with	with	ADP
ejpam-5386	354	4	example	example	NOUN
ejpam-5386	354	5	1	1	NUM
ejpam-5386	354	6	,	,	PUNCT
ejpam-5386	354	7	table	table	NOUN
ejpam-5386	354	8	3	3	NUM
ejpam-5386	354	9	highlights	highlight	NOUN
ejpam-5386	354	10	the	the	DET
ejpam-5386	354	11	impact	impact	NOUN
ejpam-5386	354	12	of	of	ADP
ejpam-5386	354	13	the	the	DET
ejpam-5386	354	14	non	non	ADJ
ejpam-5386	354	15	-	-	ADJ
ejpam-5386	354	16	smoothness	smoothness	ADJ
ejpam-5386	354	17	of	of	ADP
ejpam-5386	354	18	the	the	DET
ejpam-5386	354	19	initial	initial	ADJ
ejpam-5386	354	20	cell	cell	NOUN
ejpam-5386	354	21	density	density	NOUN
ejpam-5386	354	22	on	on	ADP
ejpam-5386	354	23	the	the	DET
ejpam-5386	354	24	accuracy	accuracy	NOUN
ejpam-5386	354	25	of	of	ADP
ejpam-5386	354	26	our	our	PRON
ejpam-5386	354	27	method	method	NOUN
ejpam-5386	354	28	.	.	PUNCT
ejpam-5386	355	1	the	the	DET
ejpam-5386	355	2	corresponding	corresponding	ADJ
ejpam-5386	355	3	numerical	numerical	ADJ
ejpam-5386	355	4	solutions	solution	NOUN
ejpam-5386	355	5	for	for	ADP
ejpam-5386	355	6	the	the	DET
ejpam-5386	355	7	treatment	treatment	NOUN
ejpam-5386	355	8	parameter	parameter	NOUN
ejpam-5386	355	9	α(x	α(x	PROPN
ejpam-5386	355	10	)	)	PUNCT
ejpam-5386	355	11	and	and	CCONJ
ejpam-5386	355	12	the	the	DET
ejpam-5386	355	13	initial	initial	ADJ
ejpam-5386	355	14	cell	cell	NOUN
ejpam-5386	355	15	density	density	NOUN
ejpam-5386	355	16	φ(x	φ(x	NOUN
ejpam-5386	355	17	)	)	PUNCT
ejpam-5386	355	18	at	at	ADP
ejpam-5386	355	19	the	the	DET
ejpam-5386	355	20	stopping	stop	VERB
ejpam-5386	355	21	iteration	iteration	NOUN
ejpam-5386	355	22	numbers	number	NOUN
ejpam-5386	355	23	obtained	obtain	VERB
ejpam-5386	355	24	based	base	VERB
ejpam-5386	355	25	on	on	ADP
ejpam-5386	355	26	the	the	DET
ejpam-5386	355	27	discrepancy	discrepancy	NOUN
ejpam-5386	355	28	principle	principle	NOUN
ejpam-5386	355	29	(	(	PUNCT
ejpam-5386	355	30	28	28	NUM
ejpam-5386	355	31	)	)	PUNCT
ejpam-5386	355	32	are	be	AUX
ejpam-5386	355	33	illustrated	illustrate	VERB
ejpam-5386	355	34	in	in	ADP
ejpam-5386	355	35	figure	figure	NOUN
ejpam-5386	355	36	4	4	NUM
ejpam-5386	355	37	.	.	PUNCT
ejpam-5386	356	1	(	(	PUNCT
ejpam-5386	356	2	a	a	X
ejpam-5386	356	3	)	)	PUNCT
ejpam-5386	356	4	the	the	DET
ejpam-5386	356	5	treatment	treatment	NOUN
ejpam-5386	356	6	parameter	parameter	NOUN
ejpam-5386	356	7	α(x	α(x	PROPN
ejpam-5386	356	8	)	)	PUNCT
ejpam-5386	357	1	(	(	PUNCT
ejpam-5386	357	2	b	b	X
ejpam-5386	357	3	)	)	PUNCT
ejpam-5386	357	4	the	the	DET
ejpam-5386	357	5	initial	initial	ADJ
ejpam-5386	357	6	cell	cell	NOUN
ejpam-5386	357	7	density	density	NOUN
ejpam-5386	357	8	φ(x	φ(x	NOUN
ejpam-5386	357	9	)	)	PUNCT
ejpam-5386	357	10	figure	figure	NOUN
ejpam-5386	357	11	4	4	NUM
ejpam-5386	357	12	:	:	PUNCT
ejpam-5386	357	13	the	the	DET
ejpam-5386	357	14	numerical	numerical	ADJ
ejpam-5386	357	15	results	result	NOUN
ejpam-5386	357	16	for	for	ADP
ejpam-5386	357	17	example	example	NOUN
ejpam-5386	357	18	2	2	NUM
ejpam-5386	357	19	for	for	ADP
ejpam-5386	357	20	different	different	ADJ
ejpam-5386	357	21	noise	noise	NOUN
ejpam-5386	357	22	levels	level	NOUN
ejpam-5386	357	23	p	p	PROPN
ejpam-5386	357	24	∈	∈	PROPN
ejpam-5386	357	25	{	{	PUNCT
ejpam-5386	357	26	0	0	NUM
ejpam-5386	357	27	,	,	PUNCT
ejpam-5386	357	28	1	1	NUM
ejpam-5386	357	29	,	,	PUNCT
ejpam-5386	357	30	2	2	NUM
ejpam-5386	357	31	}	}	PUNCT
ejpam-5386	357	32	.	.	PUNCT
ejpam-5386	358	1	left	leave	VERB
ejpam-5386	358	2	:	:	PUNCT
ejpam-5386	358	3	the	the	DET
ejpam-5386	358	4	treatment	treatment	NOUN
ejpam-5386	358	5	parameter	parameter	NOUN
ejpam-5386	358	6	α(x	α(x	PROPN
ejpam-5386	358	7	)	)	PUNCT
ejpam-5386	358	8	.	.	PUNCT
ejpam-5386	359	1	right	right	ADV
ejpam-5386	359	2	:	:	PUNCT
ejpam-5386	359	3	the	the	DET
ejpam-5386	359	4	initial	initial	ADJ
ejpam-5386	359	5	cell	cell	NOUN
ejpam-5386	359	6	density	density	NOUN
ejpam-5386	359	7	φ(x	φ(x	NOUN
ejpam-5386	359	8	)	)	PUNCT
ejpam-5386	359	9	.	.	PUNCT
ejpam-5386	360	1	similar	similar	ADJ
ejpam-5386	360	2	to	to	ADP
ejpam-5386	360	3	the	the	DET
ejpam-5386	360	4	previous	previous	ADJ
ejpam-5386	360	5	test	test	NOUN
ejpam-5386	360	6	,	,	PUNCT
ejpam-5386	360	7	figure	figure	VERB
ejpam-5386	360	8	4	4	NUM
ejpam-5386	360	9	demonstrates	demonstrate	VERB
ejpam-5386	360	10	that	that	SCONJ
ejpam-5386	360	11	the	the	DET
ejpam-5386	360	12	efficiency	efficiency	NOUN
ejpam-5386	360	13	of	of	ADP
ejpam-5386	360	14	our	our	PRON
ejpam-5386	360	15	algorithm	algorithm	NOUN
ejpam-5386	360	16	diminishes	diminish	VERB
ejpam-5386	360	17	with	with	ADP
ejpam-5386	360	18	increasing	increase	VERB
ejpam-5386	360	19	noise	noise	NOUN
ejpam-5386	360	20	level	level	NOUN
ejpam-5386	360	21	p.	p.	NOUN
ejpam-5386	360	22	specifically	specifically	ADV
ejpam-5386	360	23	,	,	PUNCT
ejpam-5386	360	24	the	the	DET
ejpam-5386	360	25	numerical	numerical	ADJ
ejpam-5386	360	26	results	result	NOUN
ejpam-5386	360	27	exhibit	exhibit	VERB
ejpam-5386	360	28	high	high	ADJ
ejpam-5386	360	29	accuracy	accuracy	NOUN
ejpam-5386	360	30	when	when	SCONJ
ejpam-5386	360	31	no	no	DET
ejpam-5386	360	32	noise	noise	NOUN
ejpam-5386	360	33	is	be	AUX
ejpam-5386	360	34	present	present	ADJ
ejpam-5386	360	35	(	(	PUNCT
ejpam-5386	360	36	0	0	NUM
ejpam-5386	360	37	%	%	NOUN
ejpam-5386	360	38	noise	noise	NOUN
ejpam-5386	360	39	added	add	VERB
ejpam-5386	360	40	in	in	ADP
ejpam-5386	360	41	the	the	DET
ejpam-5386	360	42	measured	measured	ADJ
ejpam-5386	360	43	data	datum	NOUN
ejpam-5386	360	44	ϕi	ϕi	ADP
ejpam-5386	360	45	,	,	PUNCT
ejpam-5386	360	46	for	for	ADP
ejpam-5386	360	47	i	i	PROPN
ejpam-5386	360	48	=	=	SYM
ejpam-5386	360	49	1	1	NUM
ejpam-5386	360	50	,	,	PUNCT
ejpam-5386	360	51	2	2	NUM
ejpam-5386	360	52	)	)	PUNCT
ejpam-5386	360	53	.	.	PUNCT
ejpam-5386	361	1	it	it	PRON
ejpam-5386	361	2	is	be	AUX
ejpam-5386	361	3	noteworthy	noteworthy	ADJ
ejpam-5386	361	4	that	that	SCONJ
ejpam-5386	361	5	the	the	DET
ejpam-5386	361	6	reconstruction	reconstruction	NOUN
ejpam-5386	361	7	of	of	ADP
ejpam-5386	361	8	smooth	smooth	ADJ
ejpam-5386	361	9	functions	function	NOUN
ejpam-5386	361	10	displays	display	VERB
ejpam-5386	361	11	higher	high	ADJ
ejpam-5386	361	12	accuracy	accuracy	NOUN
ejpam-5386	361	13	compared	compare	VERB
ejpam-5386	361	14	to	to	ADP
ejpam-5386	361	15	non	non	ADJ
ejpam-5386	361	16	-	-	ADJ
ejpam-5386	361	17	smooth	smooth	ADJ
ejpam-5386	361	18	cases	case	NOUN
ejpam-5386	361	19	.	.	PUNCT
ejpam-5386	362	1	however	however	ADV
ejpam-5386	362	2	,	,	PUNCT
ejpam-5386	362	3	stable	stable	ADJ
ejpam-5386	362	4	and	and	CCONJ
ejpam-5386	362	5	accurate	accurate	ADJ
ejpam-5386	362	6	solutions	solution	NOUN
ejpam-5386	362	7	are	be	AUX
ejpam-5386	362	8	attained	attain	VERB
ejpam-5386	362	9	for	for	ADP
ejpam-5386	362	10	both	both	DET
ejpam-5386	362	11	coefficients	coefficient	NOUN
ejpam-5386	362	12	overall	overall	ADJ
ejpam-5386	362	13	.	.	PUNCT
ejpam-5386	363	1	example	example	NOUN
ejpam-5386	364	1	3	3	NUM
ejpam-5386	364	2	.	.	PUNCT
ejpam-5386	364	3	in	in	ADP
ejpam-5386	364	4	this	this	DET
ejpam-5386	364	5	example	example	NOUN
ejpam-5386	364	6	,	,	PUNCT
ejpam-5386	364	7	we	we	PRON
ejpam-5386	364	8	test	test	VERB
ejpam-5386	364	9	our	our	PRON
ejpam-5386	364	10	algorithm	algorithm	NOUN
ejpam-5386	364	11	to	to	PART
ejpam-5386	364	12	identify	identify	VERB
ejpam-5386	364	13	a	a	DET
ejpam-5386	364	14	non	non	ADJ
ejpam-5386	364	15	-	-	ADJ
ejpam-5386	364	16	smooth	smooth	ADJ
ejpam-5386	364	17	treatment	treatment	NOUN
ejpam-5386	364	18	parameter	parameter	NOUN
ejpam-5386	364	19	and	and	CCONJ
ejpam-5386	364	20	a	a	DET
ejpam-5386	364	21	smooth	smooth	ADJ
ejpam-5386	364	22	initial	initial	ADJ
ejpam-5386	364	23	cell	cell	NOUN
ejpam-5386	364	24	density	density	NOUN
ejpam-5386	364	25	.	.	PUNCT
ejpam-5386	365	1	this	this	DET
ejpam-5386	365	2	experimental	experimental	ADJ
ejpam-5386	365	3	setup	setup	NOUN
ejpam-5386	365	4	stems	stem	VERB
ejpam-5386	365	5	from	from	ADP
ejpam-5386	365	6	insights	insight	NOUN
ejpam-5386	365	7	gained	gain	VERB
ejpam-5386	365	8	in	in	ADP
ejpam-5386	365	9	brain	brain	NOUN
ejpam-5386	365	10	tumor	tumor	NOUN
ejpam-5386	365	11	dynamics	dynamic	NOUN
ejpam-5386	365	12	,	,	PUNCT
ejpam-5386	365	13	where	where	SCONJ
ejpam-5386	365	14	treatments	treatment	NOUN
ejpam-5386	365	15	such	such	ADJ
ejpam-5386	365	16	as	as	ADP
ejpam-5386	365	17	radiation	radiation	NOUN
ejpam-5386	365	18	therapy	therapy	NOUN
ejpam-5386	365	19	or	or	CCONJ
ejpam-5386	365	20	chemotherapy	chemotherapy	NOUN
ejpam-5386	365	21	often	often	ADV
ejpam-5386	365	22	induce	induce	VERB
ejpam-5386	365	23	localized	localized	ADJ
ejpam-5386	365	24	variations	variation	NOUN
ejpam-5386	365	25	in	in	ADP
ejpam-5386	365	26	treatment	treatment	NOUN
ejpam-5386	365	27	effectiveness	effectiveness	NOUN
ejpam-5386	365	28	,	,	PUNCT
ejpam-5386	365	29	resulting	result	VERB
ejpam-5386	365	30	in	in	ADP
ejpam-5386	365	31	non	non	ADJ
ejpam-5386	365	32	-	-	ADJ
ejpam-5386	365	33	smooth	smooth	ADJ
ejpam-5386	365	34	patterns	pattern	NOUN
ejpam-5386	365	35	in	in	ADP
ejpam-5386	365	36	the	the	DET
ejpam-5386	365	37	treatment	treatment	NOUN
ejpam-5386	365	38	parameter	parameter	NOUN
ejpam-5386	365	39	.	.	PUNCT
ejpam-5386	366	1	conversely	conversely	ADV
ejpam-5386	366	2	,	,	PUNCT
ejpam-5386	366	3	the	the	DET
ejpam-5386	366	4	initial	initial	ADJ
ejpam-5386	366	5	distribution	distribution	NOUN
ejpam-5386	366	6	of	of	ADP
ejpam-5386	366	7	healthy	healthy	ADJ
ejpam-5386	366	8	and	and	CCONJ
ejpam-5386	366	9	tumor	tumor	NOUN
ejpam-5386	366	10	cells	cell	NOUN
ejpam-5386	366	11	within	within	ADP
ejpam-5386	366	12	the	the	DET
ejpam-5386	366	13	brain	brain	NOUN
ejpam-5386	366	14	tissue	tissue	NOUN
ejpam-5386	366	15	tends	tend	VERB
ejpam-5386	366	16	to	to	PART
ejpam-5386	366	17	exhibit	exhibit	VERB
ejpam-5386	366	18	a	a	DET
ejpam-5386	366	19	more	more	ADV
ejpam-5386	366	20	uniform	uniform	NOUN
ejpam-5386	366	21	or	or	CCONJ
ejpam-5386	366	22	grads	grad	NOUN
ejpam-5386	366	23	.	.	PUNCT
ejpam-5386	367	1	tatar	tatar	NOUN
ejpam-5386	367	2	,	,	PUNCT
ejpam-5386	367	3	m.	m.	NOUN
ejpam-5386	367	4	bensalah	bensalah	PROPN
ejpam-5386	367	5	,	,	PUNCT
ejpam-5386	367	6	m.	m.	NOUN
ejpam-5386	367	7	alamil	alamil	PROPN
ejpam-5386	367	8	/	/	SYM
ejpam-5386	367	9	eur	eur	PROPN
ejpam-5386	367	10	.	.	PUNCT
ejpam-5386	368	1	j.	j.	PROPN
ejpam-5386	368	2	pure	pure	PROPN
ejpam-5386	368	3	appl	appl	PROPN
ejpam-5386	368	4	.	.	PROPN
ejpam-5386	368	5	math	math	PROPN
ejpam-5386	368	6	,	,	PUNCT
ejpam-5386	368	7	17	17	NUM
ejpam-5386	368	8	(	(	PUNCT
ejpam-5386	368	9	4	4	NUM
ejpam-5386	368	10	)	)	PUNCT
ejpam-5386	368	11	(	(	PUNCT
ejpam-5386	368	12	2024	2024	NUM
ejpam-5386	368	13	)	)	PUNCT
ejpam-5386	368	14	,	,	PUNCT
ejpam-5386	368	15	2651	2651	NUM
ejpam-5386	368	16	-	-	SYM
ejpam-5386	368	17	2675	2675	NUM
ejpam-5386	368	18	2669	2669	NUM
ejpam-5386	368	19	ual	ual	ADJ
ejpam-5386	368	20	pattern	pattern	NOUN
ejpam-5386	368	21	,	,	PUNCT
ejpam-5386	368	22	reflecting	reflect	VERB
ejpam-5386	368	23	the	the	DET
ejpam-5386	368	24	inherent	inherent	ADJ
ejpam-5386	368	25	composition	composition	NOUN
ejpam-5386	368	26	and	and	CCONJ
ejpam-5386	368	27	structure	structure	NOUN
ejpam-5386	368	28	of	of	ADP
ejpam-5386	368	29	the	the	DET
ejpam-5386	368	30	brain	brain	NOUN
ejpam-5386	368	31	.	.	PUNCT
ejpam-5386	369	1	by	by	ADP
ejpam-5386	369	2	exploring	explore	VERB
ejpam-5386	369	3	this	this	DET
ejpam-5386	369	4	contrast	contrast	NOUN
ejpam-5386	369	5	in	in	ADP
ejpam-5386	369	6	parameter	parameter	NOUN
ejpam-5386	369	7	characteristics	characteristic	NOUN
ejpam-5386	369	8	,	,	PUNCT
ejpam-5386	369	9	we	we	PRON
ejpam-5386	369	10	aim	aim	VERB
ejpam-5386	369	11	to	to	PART
ejpam-5386	369	12	further	far	ADV
ejpam-5386	369	13	enhance	enhance	VERB
ejpam-5386	369	14	the	the	DET
ejpam-5386	369	15	adaptability	adaptability	NOUN
ejpam-5386	369	16	and	and	CCONJ
ejpam-5386	369	17	effectiveness	effectiveness	NOUN
ejpam-5386	369	18	of	of	ADP
ejpam-5386	369	19	our	our	PRON
ejpam-5386	369	20	algorithm	algorithm	NOUN
ejpam-5386	369	21	in	in	ADP
ejpam-5386	369	22	diverse	diverse	ADJ
ejpam-5386	369	23	tumor	tumor	NOUN
ejpam-5386	369	24	growth	growth	NOUN
ejpam-5386	369	25	scenarios	scenario	NOUN
ejpam-5386	369	26	.	.	PUNCT
ejpam-5386	370	1	for	for	ADP
ejpam-5386	370	2	this	this	DET
ejpam-5386	370	3	purpose	purpose	NOUN
ejpam-5386	370	4	,	,	PUNCT
ejpam-5386	370	5	we	we	PRON
ejpam-5386	370	6	set	set	VERB
ejpam-5386	370	7	ω1(t	ω1(t	PRON
ejpam-5386	370	8	)	)	PUNCT
ejpam-5386	370	9	=	=	SYM
ejpam-5386	370	10	log(1	log(1	NOUN
ejpam-5386	370	11	+	+	CCONJ
ejpam-5386	370	12	t2	t2	NOUN
ejpam-5386	370	13	)	)	PUNCT
ejpam-5386	370	14	and	and	CCONJ
ejpam-5386	370	15	ω2(t	ω2(t	NUM
ejpam-5386	370	16	)	)	PUNCT
ejpam-5386	370	17	=	=	SYM
ejpam-5386	370	18	2	2	NUM
ejpam-5386	370	19	,	,	PUNCT
ejpam-5386	370	20	and	and	CCONJ
ejpam-5386	370	21	evaluate	evaluate	VERB
ejpam-5386	370	22	the	the	DET
ejpam-5386	370	23	algorithm	algorithm	NOUN
ejpam-5386	370	24	’s	’s	PART
ejpam-5386	370	25	performance	performance	NOUN
ejpam-5386	370	26	in	in	ADP
ejpam-5386	370	27	recovering	recover	VERB
ejpam-5386	370	28	:	:	PUNCT
ejpam-5386	370	29	α(x	α(x	NUM
ejpam-5386	370	30	)	)	PUNCT
ejpam-5386	370	31	=	=	PUNCT
ejpam-5386	370	32	max(1	max(1	NOUN
ejpam-5386	370	33	,	,	PUNCT
ejpam-5386	370	34	1−	1−	NUM
ejpam-5386	370	35	(	(	PUNCT
ejpam-5386	370	36	1−	1−	NUM
ejpam-5386	370	37	x2	x2	NOUN
ejpam-5386	370	38	)	)	PUNCT
ejpam-5386	370	39	cos(5πx	cos(5πx	NOUN
ejpam-5386	370	40	)	)	PUNCT
ejpam-5386	370	41	)	)	PUNCT
ejpam-5386	370	42	and	and	CCONJ
ejpam-5386	370	43	φ(x	φ(x	NOUN
ejpam-5386	370	44	)	)	PUNCT
ejpam-5386	371	1	=	=	SYM
ejpam-5386	371	2	cos(πx)−	cos(πx)−	PROPN
ejpam-5386	371	3	x2	x2	PROPN
ejpam-5386	372	1	+	+	NUM
ejpam-5386	372	2	2x	2x	NUM
ejpam-5386	372	3	2	2	NUM
ejpam-5386	372	4	.	.	PUNCT
ejpam-5386	373	1	the	the	DET
ejpam-5386	373	2	objective	objective	ADJ
ejpam-5386	373	3	functional	functional	ADJ
ejpam-5386	373	4	j(αk	j(αk	PROPN
ejpam-5386	373	5	,	,	PUNCT
ejpam-5386	373	6	φk	φk	ADP
ejpam-5386	373	7	)	)	PUNCT
ejpam-5386	373	8	defined	define	VERB
ejpam-5386	373	9	by	by	ADP
ejpam-5386	373	10	(	(	PUNCT
ejpam-5386	373	11	7	7	X
ejpam-5386	373	12	)	)	PUNCT
ejpam-5386	373	13	is	be	AUX
ejpam-5386	373	14	shown	show	VERB
ejpam-5386	373	15	in	in	ADP
ejpam-5386	373	16	figure	figure	NOUN
ejpam-5386	373	17	5	5	NUM
ejpam-5386	373	18	.	.	PUNCT
ejpam-5386	374	1	it	it	PRON
ejpam-5386	374	2	is	be	AUX
ejpam-5386	374	3	clear	clear	ADJ
ejpam-5386	374	4	that	that	SCONJ
ejpam-5386	374	5	the	the	DET
ejpam-5386	374	6	objective	objective	ADJ
ejpam-5386	374	7	function	function	NOUN
ejpam-5386	374	8	decreases	decrease	VERB
ejpam-5386	374	9	steadily	steadily	ADV
ejpam-5386	374	10	and	and	CCONJ
ejpam-5386	374	11	monotonically	monotonically	ADV
ejpam-5386	374	12	with	with	ADP
ejpam-5386	374	13	the	the	DET
ejpam-5386	374	14	iteration	iteration	NOUN
ejpam-5386	374	15	numbers	number	NOUN
ejpam-5386	374	16	k	k	PROPN
ejpam-5386	374	17	and	and	CCONJ
ejpam-5386	374	18	thus	thus	ADV
ejpam-5386	374	19	it	it	PRON
ejpam-5386	374	20	is	be	AUX
ejpam-5386	374	21	convergent	convergent	ADJ
ejpam-5386	374	22	.	.	PUNCT
ejpam-5386	375	1	figure	figure	NOUN
ejpam-5386	375	2	5	5	NUM
ejpam-5386	375	3	:	:	PUNCT
ejpam-5386	375	4	the	the	DET
ejpam-5386	375	5	objective	objective	ADJ
ejpam-5386	375	6	functional	functional	ADJ
ejpam-5386	375	7	j(αk	j(αk	PROPN
ejpam-5386	375	8	,	,	PUNCT
ejpam-5386	375	9	φk	φk	ADP
ejpam-5386	375	10	)	)	PUNCT
ejpam-5386	375	11	,	,	PUNCT
ejpam-5386	375	12	for	for	ADP
ejpam-5386	375	13	different	different	ADJ
ejpam-5386	375	14	noise	noise	NOUN
ejpam-5386	375	15	levels	level	NOUN
ejpam-5386	375	16	p	p	PROPN
ejpam-5386	375	17	∈	∈	PROPN
ejpam-5386	375	18	{	{	PUNCT
ejpam-5386	375	19	0	0	NUM
ejpam-5386	375	20	,	,	PUNCT
ejpam-5386	375	21	1	1	NUM
ejpam-5386	375	22	,	,	PUNCT
ejpam-5386	375	23	2	2	NUM
ejpam-5386	375	24	}	}	PUNCT
ejpam-5386	375	25	,	,	PUNCT
ejpam-5386	375	26	in	in	ADP
ejpam-5386	375	27	example	example	NOUN
ejpam-5386	376	1	3	3	NUM
ejpam-5386	376	2	.	.	PUNCT
ejpam-5386	376	3	based	base	VERB
ejpam-5386	376	4	on	on	ADP
ejpam-5386	376	5	the	the	DET
ejpam-5386	376	6	discrepancy	discrepancy	NOUN
ejpam-5386	376	7	principle	principle	NOUN
ejpam-5386	376	8	(	(	PUNCT
ejpam-5386	376	9	28	28	NUM
ejpam-5386	376	10	)	)	PUNCT
ejpam-5386	376	11	for	for	ADP
ejpam-5386	376	12	each	each	DET
ejpam-5386	376	13	chosen	choose	VERB
ejpam-5386	376	14	noise	noise	NOUN
ejpam-5386	376	15	level	level	NOUN
ejpam-5386	376	16	p	p	X
ejpam-5386	376	17	∈	∈	PROPN
ejpam-5386	376	18	{	{	PUNCT
ejpam-5386	376	19	0	0	NUM
ejpam-5386	376	20	,	,	PUNCT
ejpam-5386	376	21	1	1	NUM
ejpam-5386	376	22	,	,	PUNCT
ejpam-5386	376	23	2	2	NUM
ejpam-5386	376	24	}	}	PUNCT
ejpam-5386	376	25	,	,	PUNCT
ejpam-5386	376	26	we	we	PRON
ejpam-5386	376	27	present	present	VERB
ejpam-5386	376	28	the	the	DET
ejpam-5386	376	29	choices	choice	NOUN
ejpam-5386	376	30	of	of	ADP
ejpam-5386	376	31	p	p	NOUN
ejpam-5386	376	32	in	in	ADP
ejpam-5386	376	33	this	this	DET
ejpam-5386	376	34	test	test	NOUN
ejpam-5386	376	35	along	along	ADP
ejpam-5386	376	36	with	with	ADP
ejpam-5386	376	37	the	the	DET
ejpam-5386	376	38	corresponding	corresponding	ADJ
ejpam-5386	376	39	numerical	numerical	ADJ
ejpam-5386	376	40	performances	performance	NOUN
ejpam-5386	376	41	in	in	ADP
ejpam-5386	376	42	table	table	NOUN
ejpam-5386	376	43	4	4	NUM
ejpam-5386	376	44	.	.	PUNCT
ejpam-5386	376	45	ε̄	ε̄	PROPN
ejpam-5386	376	46	k⋆	k⋆	NOUN
ejpam-5386	376	47	eα(k	eα(k	PUNCT
ejpam-5386	376	48	⋆	⋆	X
ejpam-5386	376	49	)	)	PUNCT
ejpam-5386	376	50	eφ(k	eφ(k	NUM
ejpam-5386	376	51	⋆	⋆	X
ejpam-5386	376	52	)	)	PUNCT
ejpam-5386	377	1	∥j	∥j	ADV
ejpam-5386	377	2	′,k⋆	′,k⋆	PROPN
ejpam-5386	377	3	α	α	PRON
ejpam-5386	377	4	∥2	∥2	NOUN
ejpam-5386	378	1	∥j	∥j	ADV
ejpam-5386	378	2	′,k⋆	′,k⋆	PROPN
ejpam-5386	378	3	φ	φ	NUM
ejpam-5386	378	4	∥2	∥2	PROPN
ejpam-5386	379	1	p	p	X
ejpam-5386	379	2	=	=	PUNCT
ejpam-5386	379	3	0	0	NUM
ejpam-5386	379	4	1.00e−	1.00e−	NUM
ejpam-5386	379	5	06	06	NUM
ejpam-5386	380	1	162	162	NUM
ejpam-5386	380	2	6.75e−	6.75e−	NUM
ejpam-5386	380	3	02	02	NUM
ejpam-5386	380	4	2.46e−	2.46e−	NUM
ejpam-5386	380	5	02	02	NUM
ejpam-5386	380	6	6.36e−	6.36e−	NUM
ejpam-5386	380	7	05	05	NUM
ejpam-5386	380	8	1.01e−	1.01e−	NUM
ejpam-5386	380	9	04	04	NUM
ejpam-5386	381	1	p	p	NOUN
ejpam-5386	381	2	=	=	NOUN
ejpam-5386	381	3	1	1	NUM
ejpam-5386	381	4	1.83e−	1.83e−	NUM
ejpam-5386	381	5	05	05	NUM
ejpam-5386	381	6	116	116	NUM
ejpam-5386	381	7	7.92e−	7.92e−	NUM
ejpam-5386	381	8	02	02	NUM
ejpam-5386	381	9	5.71e−	5.71e−	NUM
ejpam-5386	381	10	02	02	NUM
ejpam-5386	381	11	6.62e−	6.62e−	NUM
ejpam-5386	381	12	04	04	NUM
ejpam-5386	381	13	6.94e−	6.94e−	NUM
ejpam-5386	381	14	04	04	NUM
ejpam-5386	382	1	p	p	NOUN
ejpam-5386	382	2	=	=	NOUN
ejpam-5386	382	3	2	2	NUM
ejpam-5386	382	4	7.35e−	7.35e−	NUM
ejpam-5386	382	5	05	05	NUM
ejpam-5386	382	6	88	88	NUM
ejpam-5386	382	7	1.08e−	1.08e−	NUM
ejpam-5386	382	8	01	01	NUM
ejpam-5386	382	9	7.27e−	7.27e−	NUM
ejpam-5386	382	10	02	02	NUM
ejpam-5386	382	11	1.06e−	1.06e−	NUM
ejpam-5386	382	12	03	03	NUM
ejpam-5386	382	13	5.77e−	5.77e−	NUM
ejpam-5386	382	14	03	03	NUM
ejpam-5386	382	15	table	table	NOUN
ejpam-5386	382	16	4	4	NUM
ejpam-5386	382	17	:	:	PUNCT
ejpam-5386	382	18	choices	choice	NOUN
ejpam-5386	382	19	of	of	ADP
ejpam-5386	382	20	noise	noise	NOUN
ejpam-5386	382	21	levels	level	NOUN
ejpam-5386	382	22	p	p	NOUN
ejpam-5386	382	23	and	and	CCONJ
ejpam-5386	382	24	their	their	PRON
ejpam-5386	382	25	respective	respective	ADJ
ejpam-5386	382	26	threshold	threshold	NOUN
ejpam-5386	382	27	values	value	NOUN
ejpam-5386	382	28	,	,	PUNCT
ejpam-5386	382	29	the	the	DET
ejpam-5386	382	30	corresponding	corresponding	ADJ
ejpam-5386	382	31	stopping	stopping	NOUN
ejpam-5386	382	32	iteration	iteration	NOUN
ejpam-5386	382	33	numbers	number	NOUN
ejpam-5386	382	34	k⋆	k⋆	NOUN
ejpam-5386	382	35	,	,	PUNCT
ejpam-5386	382	36	l2	l2	NOUN
ejpam-5386	382	37	-	-	PUNCT
ejpam-5386	382	38	errors	error	NOUN
ejpam-5386	382	39	,	,	PUNCT
ejpam-5386	382	40	and	and	CCONJ
ejpam-5386	382	41	norms	norm	NOUN
ejpam-5386	382	42	of	of	ADP
ejpam-5386	382	43	the	the	DET
ejpam-5386	382	44	fréchet	fréchet	NOUN
ejpam-5386	382	45	gradients	gradient	NOUN
ejpam-5386	382	46	in	in	ADP
ejpam-5386	382	47	example	example	NOUN
ejpam-5386	382	48	3	3	NUM
ejpam-5386	382	49	.	.	NOUN
ejpam-5386	382	50	similar	similar	ADJ
ejpam-5386	382	51	to	to	ADP
ejpam-5386	382	52	the	the	DET
ejpam-5386	382	53	previous	previous	ADJ
ejpam-5386	382	54	scenarios	scenario	NOUN
ejpam-5386	382	55	,	,	PUNCT
ejpam-5386	382	56	we	we	PRON
ejpam-5386	382	57	conclude	conclude	VERB
ejpam-5386	382	58	this	this	DET
ejpam-5386	382	59	test	test	NOUN
ejpam-5386	382	60	by	by	ADP
ejpam-5386	382	61	illustrating	illustrate	VERB
ejpam-5386	382	62	the	the	DET
ejpam-5386	382	63	comparisons	comparison	NOUN
ejpam-5386	382	64	of	of	ADP
ejpam-5386	382	65	the	the	DET
ejpam-5386	382	66	recovered	recover	VERB
ejpam-5386	382	67	solutions	solution	NOUN
ejpam-5386	382	68	with	with	ADP
ejpam-5386	382	69	the	the	DET
ejpam-5386	382	70	exact	exact	ADJ
ejpam-5386	382	71	ones	one	NOUN
ejpam-5386	382	72	in	in	ADP
ejpam-5386	382	73	figure	figure	NOUN
ejpam-5386	382	74	6	6	NUM
ejpam-5386	382	75	.	.	PUNCT
ejpam-5386	382	76	s.	s.	PROPN
ejpam-5386	382	77	tatar	tatar	PROPN
ejpam-5386	382	78	,	,	PUNCT
ejpam-5386	382	79	m.	m.	NOUN
ejpam-5386	382	80	bensalah	bensalah	PROPN
ejpam-5386	382	81	,	,	PUNCT
ejpam-5386	382	82	m.	m.	NOUN
ejpam-5386	382	83	alamil	alamil	PROPN
ejpam-5386	382	84	/	/	SYM
ejpam-5386	382	85	eur	eur	PROPN
ejpam-5386	382	86	.	.	PUNCT
ejpam-5386	383	1	j.	j.	PROPN
ejpam-5386	383	2	pure	pure	PROPN
ejpam-5386	383	3	appl	appl	PROPN
ejpam-5386	383	4	.	.	PROPN
ejpam-5386	383	5	math	math	PROPN
ejpam-5386	383	6	,	,	PUNCT
ejpam-5386	383	7	17	17	NUM
ejpam-5386	383	8	(	(	PUNCT
ejpam-5386	383	9	4	4	NUM
ejpam-5386	383	10	)	)	PUNCT
ejpam-5386	383	11	(	(	PUNCT
ejpam-5386	383	12	2024	2024	NUM
ejpam-5386	383	13	)	)	PUNCT
ejpam-5386	383	14	,	,	PUNCT
ejpam-5386	383	15	2651	2651	NUM
ejpam-5386	383	16	-	-	SYM
ejpam-5386	383	17	2675	2675	NUM
ejpam-5386	383	18	2670	2670	NUM
ejpam-5386	383	19	(	(	PUNCT
ejpam-5386	383	20	a	a	X
ejpam-5386	383	21	)	)	PUNCT
ejpam-5386	383	22	the	the	DET
ejpam-5386	383	23	treatment	treatment	NOUN
ejpam-5386	383	24	parameter	parameter	NOUN
ejpam-5386	383	25	α(x	α(x	PROPN
ejpam-5386	383	26	)	)	PUNCT
ejpam-5386	383	27	(	(	PUNCT
ejpam-5386	383	28	b	b	X
ejpam-5386	383	29	)	)	PUNCT
ejpam-5386	383	30	the	the	DET
ejpam-5386	383	31	initial	initial	ADJ
ejpam-5386	383	32	cell	cell	NOUN
ejpam-5386	383	33	density	density	NOUN
ejpam-5386	383	34	φ(x	φ(x	NOUN
ejpam-5386	383	35	)	)	PUNCT
ejpam-5386	383	36	figure	figure	NOUN
ejpam-5386	383	37	6	6	NUM
ejpam-5386	383	38	:	:	PUNCT
ejpam-5386	383	39	the	the	DET
ejpam-5386	383	40	numerical	numerical	ADJ
ejpam-5386	383	41	results	result	NOUN
ejpam-5386	383	42	for	for	ADP
ejpam-5386	383	43	example	example	NOUN
ejpam-5386	383	44	3	3	NUM
ejpam-5386	383	45	for	for	ADP
ejpam-5386	383	46	different	different	ADJ
ejpam-5386	383	47	noise	noise	NOUN
ejpam-5386	383	48	levels	level	NOUN
ejpam-5386	383	49	p	p	PROPN
ejpam-5386	383	50	∈	∈	PROPN
ejpam-5386	383	51	{	{	PUNCT
ejpam-5386	383	52	0	0	NUM
ejpam-5386	383	53	,	,	PUNCT
ejpam-5386	383	54	1	1	NUM
ejpam-5386	383	55	,	,	PUNCT
ejpam-5386	383	56	2	2	NUM
ejpam-5386	383	57	}	}	PUNCT
ejpam-5386	383	58	.	.	PUNCT
ejpam-5386	384	1	left	leave	VERB
ejpam-5386	384	2	:	:	PUNCT
ejpam-5386	384	3	the	the	DET
ejpam-5386	384	4	treatment	treatment	NOUN
ejpam-5386	384	5	parameter	parameter	NOUN
ejpam-5386	384	6	α(x	α(x	PROPN
ejpam-5386	384	7	)	)	PUNCT
ejpam-5386	384	8	.	.	PUNCT
ejpam-5386	385	1	right	right	ADV
ejpam-5386	385	2	:	:	PUNCT
ejpam-5386	385	3	the	the	DET
ejpam-5386	385	4	initial	initial	ADJ
ejpam-5386	385	5	cell	cell	NOUN
ejpam-5386	385	6	density	density	NOUN
ejpam-5386	385	7	φ(x	φ(x	NOUN
ejpam-5386	385	8	)	)	PUNCT
ejpam-5386	385	9	.	.	PUNCT
ejpam-5386	386	1	as	as	SCONJ
ejpam-5386	386	2	it	it	PRON
ejpam-5386	386	3	is	be	AUX
ejpam-5386	386	4	expected	expect	VERB
ejpam-5386	386	5	from	from	ADP
ejpam-5386	386	6	the	the	DET
ejpam-5386	386	7	previous	previous	ADJ
ejpam-5386	386	8	test	test	NOUN
ejpam-5386	386	9	,	,	PUNCT
ejpam-5386	386	10	figure	figure	VERB
ejpam-5386	386	11	6	6	NUM
ejpam-5386	386	12	confirms	confirm	VERB
ejpam-5386	386	13	that	that	SCONJ
ejpam-5386	386	14	the	the	DET
ejpam-5386	386	15	efficiency	efficiency	NOUN
ejpam-5386	386	16	of	of	ADP
ejpam-5386	386	17	our	our	PRON
ejpam-5386	386	18	algorithm	algorithm	NOUN
ejpam-5386	386	19	is	be	AUX
ejpam-5386	386	20	sensitive	sensitive	ADJ
ejpam-5386	386	21	to	to	ADP
ejpam-5386	386	22	both	both	CCONJ
ejpam-5386	386	23	the	the	DET
ejpam-5386	386	24	noise	noise	NOUN
ejpam-5386	386	25	level	level	NOUN
ejpam-5386	386	26	and	and	CCONJ
ejpam-5386	386	27	the	the	DET
ejpam-5386	386	28	smoothness	smoothness	NOUN
ejpam-5386	386	29	of	of	ADP
ejpam-5386	386	30	the	the	DET
ejpam-5386	386	31	coefficient	coefficient	NOUN
ejpam-5386	386	32	being	be	AUX
ejpam-5386	386	33	reconstructed	reconstruct	VERB
ejpam-5386	386	34	.	.	PUNCT
ejpam-5386	387	1	example	example	NOUN
ejpam-5386	388	1	4	4	NUM
ejpam-5386	388	2	.	.	X
ejpam-5386	388	3	in	in	ADP
ejpam-5386	388	4	brain	brain	NOUN
ejpam-5386	388	5	tumor	tumor	NOUN
ejpam-5386	388	6	growth	growth	NOUN
ejpam-5386	388	7	,	,	PUNCT
ejpam-5386	388	8	various	various	ADJ
ejpam-5386	388	9	factors	factor	NOUN
ejpam-5386	388	10	such	such	ADJ
ejpam-5386	388	11	as	as	ADP
ejpam-5386	388	12	genetic	genetic	ADJ
ejpam-5386	388	13	mutations	mutation	NOUN
ejpam-5386	388	14	,	,	PUNCT
ejpam-5386	388	15	cellular	cellular	ADJ
ejpam-5386	388	16	interactions	interaction	NOUN
ejpam-5386	388	17	,	,	PUNCT
ejpam-5386	388	18	and	and	CCONJ
ejpam-5386	388	19	microenvironmental	microenvironmental	ADJ
ejpam-5386	388	20	conditions	condition	NOUN
ejpam-5386	388	21	can	can	AUX
ejpam-5386	388	22	contribute	contribute	VERB
ejpam-5386	388	23	to	to	ADP
ejpam-5386	388	24	the	the	DET
ejpam-5386	388	25	formation	formation	NOUN
ejpam-5386	388	26	of	of	ADP
ejpam-5386	388	27	complex	complex	ADJ
ejpam-5386	388	28	spatial	spatial	ADJ
ejpam-5386	388	29	patterns	pattern	NOUN
ejpam-5386	388	30	in	in	ADP
ejpam-5386	388	31	both	both	CCONJ
ejpam-5386	388	32	the	the	DET
ejpam-5386	388	33	treatment	treatment	NOUN
ejpam-5386	388	34	response	response	NOUN
ejpam-5386	388	35	and	and	CCONJ
ejpam-5386	388	36	the	the	DET
ejpam-5386	388	37	distribution	distribution	NOUN
ejpam-5386	388	38	of	of	ADP
ejpam-5386	388	39	tumor	tumor	NOUN
ejpam-5386	388	40	cells	cell	NOUN
ejpam-5386	388	41	.	.	PUNCT
ejpam-5386	389	1	these	these	DET
ejpam-5386	389	2	patterns	pattern	NOUN
ejpam-5386	389	3	may	may	AUX
ejpam-5386	389	4	include	include	VERB
ejpam-5386	389	5	regions	region	NOUN
ejpam-5386	389	6	of	of	ADP
ejpam-5386	389	7	high	high	ADJ
ejpam-5386	389	8	and	and	CCONJ
ejpam-5386	389	9	low	low	ADJ
ejpam-5386	389	10	treatment	treatment	NOUN
ejpam-5386	389	11	effectiveness	effectiveness	NOUN
ejpam-5386	389	12	,	,	PUNCT
ejpam-5386	389	13	as	as	ADV
ejpam-5386	389	14	well	well	ADV
ejpam-5386	389	15	as	as	ADP
ejpam-5386	389	16	areas	area	NOUN
ejpam-5386	389	17	of	of	ADP
ejpam-5386	389	18	dense	dense	ADJ
ejpam-5386	389	19	and	and	CCONJ
ejpam-5386	389	20	sparse	sparse	ADJ
ejpam-5386	389	21	tumor	tumor	NOUN
ejpam-5386	389	22	cell	cell	NOUN
ejpam-5386	389	23	populations	population	NOUN
ejpam-5386	389	24	,	,	PUNCT
ejpam-5386	389	25	resulting	result	VERB
ejpam-5386	389	26	in	in	ADP
ejpam-5386	389	27	non	non	ADJ
ejpam-5386	389	28	-	-	ADJ
ejpam-5386	389	29	smooth	smooth	ADJ
ejpam-5386	389	30	variations	variation	NOUN
ejpam-5386	389	31	in	in	ADP
ejpam-5386	389	32	these	these	DET
ejpam-5386	389	33	coefficients	coefficient	NOUN
ejpam-5386	389	34	.	.	PUNCT
ejpam-5386	390	1	according	accord	VERB
ejpam-5386	390	2	to	to	ADP
ejpam-5386	390	3	this	this	DET
ejpam-5386	390	4	observation	observation	NOUN
ejpam-5386	390	5	,	,	PUNCT
ejpam-5386	390	6	in	in	ADP
ejpam-5386	390	7	this	this	DET
ejpam-5386	390	8	test	test	NOUN
ejpam-5386	390	9	,	,	PUNCT
ejpam-5386	390	10	we	we	PRON
ejpam-5386	390	11	focus	focus	VERB
ejpam-5386	390	12	on	on	ADP
ejpam-5386	390	13	the	the	DET
ejpam-5386	390	14	identification	identification	NOUN
ejpam-5386	390	15	of	of	ADP
ejpam-5386	390	16	the	the	DET
ejpam-5386	390	17	treatment	treatment	NOUN
ejpam-5386	390	18	parameter	parameter	NOUN
ejpam-5386	390	19	and	and	CCONJ
ejpam-5386	390	20	the	the	DET
ejpam-5386	390	21	initial	initial	ADJ
ejpam-5386	390	22	cell	cell	NOUN
ejpam-5386	390	23	density	density	NOUN
ejpam-5386	390	24	in	in	ADP
ejpam-5386	390	25	more	more	ADJ
ejpam-5386	390	26	complex	complex	ADJ
ejpam-5386	390	27	scenarios	scenario	NOUN
ejpam-5386	390	28	,	,	PUNCT
ejpam-5386	390	29	where	where	SCONJ
ejpam-5386	390	30	both	both	DET
ejpam-5386	390	31	coefficients	coefficient	NOUN
ejpam-5386	390	32	to	to	PART
ejpam-5386	390	33	be	be	AUX
ejpam-5386	390	34	reconstructed	reconstruct	VERB
ejpam-5386	390	35	are	be	AUX
ejpam-5386	390	36	represented	represent	VERB
ejpam-5386	390	37	by	by	ADP
ejpam-5386	390	38	non	non	ADJ
ejpam-5386	390	39	smooth	smooth	ADJ
ejpam-5386	390	40	functions	function	NOUN
ejpam-5386	390	41	.	.	PUNCT
ejpam-5386	391	1	in	in	ADP
ejpam-5386	391	2	doing	do	VERB
ejpam-5386	391	3	so	so	ADV
ejpam-5386	391	4	,	,	PUNCT
ejpam-5386	391	5	we	we	PRON
ejpam-5386	391	6	choose	choose	VERB
ejpam-5386	391	7	the	the	DET
ejpam-5386	391	8	weight	weight	NOUN
ejpam-5386	391	9	functions	function	NOUN
ejpam-5386	391	10	as	as	ADP
ejpam-5386	391	11	ω1(t	ω1(t	NUM
ejpam-5386	391	12	)	)	PUNCT
ejpam-5386	391	13	=	=	SYM
ejpam-5386	392	1	1	1	NUM
ejpam-5386	392	2	+	+	NUM
ejpam-5386	392	3	t	t	NOUN
ejpam-5386	392	4	+	+	CCONJ
ejpam-5386	392	5	t2	t2	PROPN
ejpam-5386	392	6	and	and	CCONJ
ejpam-5386	392	7	ω2(t	ω2(t	NUM
ejpam-5386	392	8	)	)	PUNCT
ejpam-5386	392	9	=	=	SYM
ejpam-5386	392	10	t3	t3	PROPN
ejpam-5386	392	11	,	,	PUNCT
ejpam-5386	392	12	and	and	CCONJ
ejpam-5386	392	13	we	we	PRON
ejpam-5386	392	14	test	test	VERB
ejpam-5386	392	15	our	our	PRON
ejpam-5386	392	16	iterative	iterative	NOUN
ejpam-5386	392	17	procedure	procedure	NOUN
ejpam-5386	392	18	to	to	PART
ejpam-5386	392	19	identify	identify	VERB
ejpam-5386	392	20	the	the	DET
ejpam-5386	392	21	following	follow	VERB
ejpam-5386	392	22	two	two	NUM
ejpam-5386	392	23	coefficients	coefficient	NOUN
ejpam-5386	392	24	:	:	PUNCT
ejpam-5386	392	25	α(x	α(x	NOUN
ejpam-5386	392	26	)	)	PUNCT
ejpam-5386	392	27	=	=	PUNCT
ejpam-5386	392	28	2−	2−	NUM
ejpam-5386	392	29	|1−	|1−	NOUN
ejpam-5386	392	30	2x|	2x|	NUM
ejpam-5386	392	31	and	and	CCONJ
ejpam-5386	392	32	φ(x	φ(x	NOUN
ejpam-5386	392	33	)	)	PUNCT
ejpam-5386	392	34	=	=	SYM
ejpam-5386	393	1			NOUN
ejpam-5386	393	2	0	0	NUM
ejpam-5386	393	3	,	,	PUNCT
ejpam-5386	393	4	if	if	SCONJ
ejpam-5386	393	5	x	x	PUNCT
ejpam-5386	393	6	∈	∈	PROPN
ejpam-5386	394	1	[	[	X
ejpam-5386	394	2	0	0	NUM
ejpam-5386	394	3	,	,	PUNCT
ejpam-5386	394	4	0.2	0.2	NUM
ejpam-5386	394	5	]	]	PUNCT
ejpam-5386	394	6	∪	∪	ADP
ejpam-5386	394	7	[	[	X
ejpam-5386	394	8	0.8	0.8	NUM
ejpam-5386	394	9	,	,	PUNCT
ejpam-5386	394	10	0.1	0.1	NUM
ejpam-5386	394	11	]	]	PUNCT
ejpam-5386	394	12	,	,	PUNCT
ejpam-5386	394	13	10x	10x	X
ejpam-5386	394	14	3	3	NUM
ejpam-5386	394	15	−	−	NUM
ejpam-5386	394	16	2	2	NUM
ejpam-5386	394	17	3	3	NUM
ejpam-5386	394	18	,	,	PUNCT
ejpam-5386	394	19	if	if	SCONJ
ejpam-5386	394	20	x	x	PUNCT
ejpam-5386	394	21	∈	∈	PROPN
ejpam-5386	395	1	[	[	X
ejpam-5386	395	2	0.2	0.2	NUM
ejpam-5386	395	3	,	,	PUNCT
ejpam-5386	395	4	0.5	0.5	NUM
ejpam-5386	395	5	]	]	PUNCT
ejpam-5386	395	6	,	,	PUNCT
ejpam-5386	395	7	−10x	−10x	PROPN
ejpam-5386	395	8	3	3	NUM
ejpam-5386	395	9	+	+	NUM
ejpam-5386	395	10	8	8	NUM
ejpam-5386	395	11	3	3	NUM
ejpam-5386	395	12	,	,	PUNCT
ejpam-5386	395	13	if	if	SCONJ
ejpam-5386	395	14	x	x	PUNCT
ejpam-5386	395	15	∈	∈	PROPN
ejpam-5386	395	16	[	[	X
ejpam-5386	395	17	0.5	0.5	NUM
ejpam-5386	395	18	,	,	PUNCT
ejpam-5386	395	19	0.8	0.8	NUM
ejpam-5386	395	20	]	]	PUNCT
ejpam-5386	395	21	.	.	PUNCT
ejpam-5386	396	1	following	follow	VERB
ejpam-5386	396	2	the	the	DET
ejpam-5386	396	3	same	same	ADJ
ejpam-5386	396	4	steps	step	NOUN
ejpam-5386	396	5	as	as	ADP
ejpam-5386	396	6	in	in	ADP
ejpam-5386	396	7	the	the	DET
ejpam-5386	396	8	previous	previous	ADJ
ejpam-5386	396	9	tests	test	NOUN
ejpam-5386	396	10	,	,	PUNCT
ejpam-5386	396	11	we	we	PRON
ejpam-5386	396	12	start	start	VERB
ejpam-5386	396	13	this	this	DET
ejpam-5386	396	14	analysis	analysis	NOUN
ejpam-5386	396	15	by	by	ADP
ejpam-5386	396	16	illustrating	illustrate	VERB
ejpam-5386	396	17	the	the	DET
ejpam-5386	396	18	evolution	evolution	NOUN
ejpam-5386	396	19	of	of	ADP
ejpam-5386	396	20	the	the	DET
ejpam-5386	396	21	objective	objective	ADJ
ejpam-5386	396	22	functional	functional	ADJ
ejpam-5386	396	23	j(αk	j(αk	PROPN
ejpam-5386	396	24	,	,	PUNCT
ejpam-5386	396	25	φk	φk	ADP
ejpam-5386	396	26	)	)	PUNCT
ejpam-5386	396	27	in	in	ADP
ejpam-5386	396	28	figure	figure	NOUN
ejpam-5386	396	29	7	7	NUM
ejpam-5386	396	30	.	.	PUNCT
ejpam-5386	397	1	this	this	PRON
ejpam-5386	397	2	depicts	depict	VERB
ejpam-5386	397	3	the	the	DET
ejpam-5386	397	4	simultaneous	simultaneous	ADJ
ejpam-5386	397	5	recovery	recovery	NOUN
ejpam-5386	397	6	of	of	ADP
ejpam-5386	397	7	the	the	DET
ejpam-5386	397	8	treatment	treatment	NOUN
ejpam-5386	397	9	parameter	parameter	NOUN
ejpam-5386	397	10	α(x	α(x	PROPN
ejpam-5386	397	11	)	)	PUNCT
ejpam-5386	397	12	and	and	CCONJ
ejpam-5386	397	13	the	the	DET
ejpam-5386	397	14	initial	initial	ADJ
ejpam-5386	397	15	cell	cell	NOUN
ejpam-5386	397	16	density	density	NOUN
ejpam-5386	397	17	φ(x	φ(x	NOUN
ejpam-5386	397	18	)	)	PUNCT
ejpam-5386	397	19	,	,	PUNCT
ejpam-5386	397	20	considering	consider	VERB
ejpam-5386	397	21	noise	noise	NOUN
ejpam-5386	397	22	levels	level	NOUN
ejpam-5386	397	23	p	p	X
ejpam-5386	397	24	=	=	PUNCT
ejpam-5386	397	25	{	{	PUNCT
ejpam-5386	397	26	0	0	NUM
ejpam-5386	397	27	,	,	PUNCT
ejpam-5386	397	28	1	1	NUM
ejpam-5386	397	29	,	,	PUNCT
ejpam-5386	397	30	2	2	NUM
ejpam-5386	397	31	}	}	PUNCT
ejpam-5386	397	32	.	.	PUNCT
ejpam-5386	398	1	notably	notably	ADV
ejpam-5386	398	2	,	,	PUNCT
ejpam-5386	398	3	the	the	DET
ejpam-5386	398	4	objective	objective	ADJ
ejpam-5386	398	5	function	function	NOUN
ejpam-5386	398	6	exhibits	exhibit	VERB
ejpam-5386	398	7	a	a	DET
ejpam-5386	398	8	monotonically	monotonically	ADV
ejpam-5386	398	9	decreasing	decrease	VERB
ejpam-5386	398	10	trend	trend	NOUN
ejpam-5386	398	11	with	with	ADP
ejpam-5386	398	12	k	k	NOUN
ejpam-5386	398	13	,	,	PUNCT
ejpam-5386	398	14	converging	converge	VERB
ejpam-5386	398	15	rapidly	rapidly	ADV
ejpam-5386	398	16	to	to	ADP
ejpam-5386	398	17	a	a	DET
ejpam-5386	398	18	small	small	ADJ
ejpam-5386	398	19	positive	positive	ADJ
ejpam-5386	398	20	value	value	NOUN
ejpam-5386	398	21	,	,	PUNCT
ejpam-5386	398	22	as	as	SCONJ
ejpam-5386	398	23	expected	expect	VERB
ejpam-5386	398	24	.	.	PUNCT
ejpam-5386	399	1	s.	s.	PROPN
ejpam-5386	399	2	tatar	tatar	PROPN
ejpam-5386	399	3	,	,	PUNCT
ejpam-5386	399	4	m.	m.	NOUN
ejpam-5386	399	5	bensalah	bensalah	PROPN
ejpam-5386	399	6	,	,	PUNCT
ejpam-5386	399	7	m.	m.	NOUN
ejpam-5386	399	8	alamil	alamil	PROPN
ejpam-5386	399	9	/	/	SYM
ejpam-5386	399	10	eur	eur	PROPN
ejpam-5386	399	11	.	.	PUNCT
ejpam-5386	400	1	j.	j.	PROPN
ejpam-5386	400	2	pure	pure	PROPN
ejpam-5386	400	3	appl	appl	PROPN
ejpam-5386	400	4	.	.	PROPN
ejpam-5386	400	5	math	math	PROPN
ejpam-5386	400	6	,	,	PUNCT
ejpam-5386	400	7	17	17	NUM
ejpam-5386	400	8	(	(	PUNCT
ejpam-5386	400	9	4	4	NUM
ejpam-5386	400	10	)	)	PUNCT
ejpam-5386	400	11	(	(	PUNCT
ejpam-5386	400	12	2024	2024	NUM
ejpam-5386	400	13	)	)	PUNCT
ejpam-5386	400	14	,	,	PUNCT
ejpam-5386	400	15	2651	2651	NUM
ejpam-5386	400	16	-	-	SYM
ejpam-5386	400	17	2675	2675	NUM
ejpam-5386	400	18	2671	2671	NUM
ejpam-5386	400	19	figure	figure	NOUN
ejpam-5386	400	20	7	7	NUM
ejpam-5386	400	21	:	:	PUNCT
ejpam-5386	400	22	the	the	DET
ejpam-5386	400	23	objective	objective	ADJ
ejpam-5386	400	24	functional	functional	ADJ
ejpam-5386	400	25	j(αk	j(αk	PROPN
ejpam-5386	400	26	,	,	PUNCT
ejpam-5386	400	27	φk	φk	ADP
ejpam-5386	400	28	)	)	PUNCT
ejpam-5386	400	29	,	,	PUNCT
ejpam-5386	400	30	for	for	ADP
ejpam-5386	400	31	different	different	ADJ
ejpam-5386	400	32	noise	noise	NOUN
ejpam-5386	400	33	levels	level	NOUN
ejpam-5386	400	34	p	p	PROPN
ejpam-5386	400	35	∈	∈	PROPN
ejpam-5386	400	36	{	{	PUNCT
ejpam-5386	400	37	0	0	NUM
ejpam-5386	400	38	,	,	PUNCT
ejpam-5386	400	39	1	1	NUM
ejpam-5386	400	40	,	,	PUNCT
ejpam-5386	400	41	2	2	NUM
ejpam-5386	400	42	}	}	PUNCT
ejpam-5386	400	43	,	,	PUNCT
ejpam-5386	400	44	in	in	ADP
ejpam-5386	400	45	example	example	NOUN
ejpam-5386	400	46	4	4	NUM
ejpam-5386	400	47	.	.	PUNCT
ejpam-5386	401	1	the	the	DET
ejpam-5386	401	2	choices	choice	NOUN
ejpam-5386	401	3	of	of	ADP
ejpam-5386	401	4	noise	noise	NOUN
ejpam-5386	401	5	levels	level	NOUN
ejpam-5386	401	6	p	p	NOUN
ejpam-5386	401	7	along	along	ADP
ejpam-5386	401	8	with	with	ADP
ejpam-5386	401	9	their	their	PRON
ejpam-5386	401	10	corresponding	corresponding	ADJ
ejpam-5386	401	11	numerical	numerical	ADJ
ejpam-5386	401	12	performances	performance	NOUN
ejpam-5386	401	13	are	be	AUX
ejpam-5386	401	14	detailed	detail	VERB
ejpam-5386	401	15	in	in	ADP
ejpam-5386	401	16	table	table	NOUN
ejpam-5386	401	17	5	5	NUM
ejpam-5386	401	18	.	.	PUNCT
ejpam-5386	401	19	ε̄	ε̄	PROPN
ejpam-5386	401	20	k⋆	k⋆	NOUN
ejpam-5386	401	21	eα(k	eα(k	PUNCT
ejpam-5386	401	22	⋆	⋆	X
ejpam-5386	401	23	)	)	PUNCT
ejpam-5386	401	24	eφ(k	eφ(k	NUM
ejpam-5386	401	25	⋆	⋆	X
ejpam-5386	401	26	)	)	PUNCT
ejpam-5386	402	1	∥j	∥j	ADV
ejpam-5386	402	2	′,k⋆	′,k⋆	PROPN
ejpam-5386	402	3	α	α	PRON
ejpam-5386	402	4	∥2	∥2	NOUN
ejpam-5386	403	1	∥j	∥j	ADV
ejpam-5386	403	2	′,k⋆	′,k⋆	PROPN
ejpam-5386	403	3	φ	φ	NUM
ejpam-5386	403	4	∥2	∥2	PROPN
ejpam-5386	404	1	p	p	X
ejpam-5386	404	2	=	=	PUNCT
ejpam-5386	404	3	0	0	NUM
ejpam-5386	404	4	1.00e−	1.00e−	NUM
ejpam-5386	404	5	06	06	NUM
ejpam-5386	404	6	207	207	NUM
ejpam-5386	404	7	6.23e−	6.23e−	NUM
ejpam-5386	404	8	02	02	NUM
ejpam-5386	404	9	1.52e−	1.52e−	NUM
ejpam-5386	404	10	02	02	NUM
ejpam-5386	404	11	6.21e−	6.21e−	NUM
ejpam-5386	404	12	04	04	NUM
ejpam-5386	404	13	1.61e−	1.61e−	NUM
ejpam-5386	404	14	04	04	NUM
ejpam-5386	405	1	p	p	NOUN
ejpam-5386	405	2	=	=	NOUN
ejpam-5386	405	3	1	1	NUM
ejpam-5386	405	4	1.15e−	1.15e−	NUM
ejpam-5386	405	5	03	03	NUM
ejpam-5386	405	6	20	20	NUM
ejpam-5386	405	7	1.11e−	1.11e−	NUM
ejpam-5386	405	8	01	01	NUM
ejpam-5386	405	9	4.90e−	4.90e−	NOUN
ejpam-5386	405	10	02	02	NUM
ejpam-5386	405	11	1.01e−	1.01e−	NUM
ejpam-5386	405	12	03	03	NUM
ejpam-5386	406	1	7.27e−	7.27e−	NUM
ejpam-5386	406	2	03	03	NUM
ejpam-5386	407	1	p	p	NOUN
ejpam-5386	407	2	=	=	NOUN
ejpam-5386	407	3	2	2	NUM
ejpam-5386	407	4	4.60e−	4.60e−	NOUN
ejpam-5386	407	5	03	03	NUM
ejpam-5386	407	6	11	11	NUM
ejpam-5386	407	7	1.58e−	1.58e−	NUM
ejpam-5386	407	8	01	01	NUM
ejpam-5386	407	9	7.38e−	7.38e−	NUM
ejpam-5386	407	10	02	02	NUM
ejpam-5386	407	11	1.09e−	1.09e−	NUM
ejpam-5386	407	12	03	03	NUM
ejpam-5386	407	13	6.52e−	6.52e−	NUM
ejpam-5386	407	14	03	03	NUM
ejpam-5386	407	15	table	table	NOUN
ejpam-5386	407	16	5	5	NUM
ejpam-5386	407	17	:	:	PUNCT
ejpam-5386	407	18	choices	choice	NOUN
ejpam-5386	407	19	of	of	ADP
ejpam-5386	407	20	noise	noise	NOUN
ejpam-5386	407	21	levels	level	NOUN
ejpam-5386	407	22	p	p	NOUN
ejpam-5386	407	23	alongside	alongside	ADP
ejpam-5386	407	24	their	their	PRON
ejpam-5386	407	25	respective	respective	ADJ
ejpam-5386	407	26	threshold	threshold	NOUN
ejpam-5386	407	27	values	value	NOUN
ejpam-5386	407	28	,	,	PUNCT
ejpam-5386	407	29	the	the	DET
ejpam-5386	407	30	corresponding	corresponding	ADJ
ejpam-5386	407	31	stopping	stopping	NOUN
ejpam-5386	407	32	iteration	iteration	NOUN
ejpam-5386	407	33	numbers	number	NOUN
ejpam-5386	407	34	k⋆	k⋆	NOUN
ejpam-5386	407	35	,	,	PUNCT
ejpam-5386	407	36	l2	l2	NOUN
ejpam-5386	407	37	-	-	PUNCT
ejpam-5386	407	38	errors	error	NOUN
ejpam-5386	407	39	,	,	PUNCT
ejpam-5386	407	40	and	and	CCONJ
ejpam-5386	407	41	norms	norm	NOUN
ejpam-5386	407	42	of	of	ADP
ejpam-5386	407	43	the	the	DET
ejpam-5386	407	44	fréchet	fréchet	NOUN
ejpam-5386	407	45	gradients	gradient	NOUN
ejpam-5386	407	46	in	in	ADP
ejpam-5386	407	47	example	example	NOUN
ejpam-5386	407	48	4	4	NUM
ejpam-5386	407	49	.	.	X
ejpam-5386	407	50	utilizing	utilize	VERB
ejpam-5386	407	51	the	the	DET
ejpam-5386	407	52	stopping	stop	VERB
ejpam-5386	407	53	iteration	iteration	NOUN
ejpam-5386	407	54	numbers	number	NOUN
ejpam-5386	407	55	k⋆	k⋆	PROPN
ejpam-5386	407	56	,	,	PUNCT
ejpam-5386	407	57	obtained	obtain	VERB
ejpam-5386	407	58	according	accord	VERB
ejpam-5386	407	59	to	to	ADP
ejpam-5386	407	60	the	the	DET
ejpam-5386	407	61	discrepancy	discrepancy	NOUN
ejpam-5386	407	62	principle	principle	NOUN
ejpam-5386	407	63	(	(	PUNCT
ejpam-5386	407	64	28	28	NUM
ejpam-5386	407	65	)	)	PUNCT
ejpam-5386	407	66	,	,	PUNCT
ejpam-5386	407	67	we	we	PRON
ejpam-5386	407	68	present	present	VERB
ejpam-5386	407	69	the	the	DET
ejpam-5386	407	70	comparisons	comparison	NOUN
ejpam-5386	407	71	between	between	ADP
ejpam-5386	407	72	the	the	DET
ejpam-5386	407	73	exact	exact	ADJ
ejpam-5386	407	74	solutions	solution	NOUN
ejpam-5386	407	75	and	and	CCONJ
ejpam-5386	407	76	the	the	DET
ejpam-5386	407	77	recovered	recovered	ADJ
ejpam-5386	407	78	ones	one	NOUN
ejpam-5386	407	79	for	for	ADP
ejpam-5386	407	80	each	each	DET
ejpam-5386	407	81	chosen	choose	VERB
ejpam-5386	407	82	noise	noise	NOUN
ejpam-5386	407	83	level	level	NOUN
ejpam-5386	407	84	p	p	NOUN
ejpam-5386	407	85	in	in	ADP
ejpam-5386	407	86	figure	figure	NOUN
ejpam-5386	407	87	8	8	NUM
ejpam-5386	407	88	.	.	PUNCT
ejpam-5386	408	1	s.	s.	PROPN
ejpam-5386	408	2	tatar	tatar	PROPN
ejpam-5386	408	3	,	,	PUNCT
ejpam-5386	408	4	m.	m.	NOUN
ejpam-5386	408	5	bensalah	bensalah	PROPN
ejpam-5386	408	6	,	,	PUNCT
ejpam-5386	408	7	m.	m.	NOUN
ejpam-5386	408	8	alamil	alamil	PROPN
ejpam-5386	408	9	/	/	SYM
ejpam-5386	408	10	eur	eur	PROPN
ejpam-5386	408	11	.	.	PUNCT
ejpam-5386	409	1	j.	j.	PROPN
ejpam-5386	409	2	pure	pure	PROPN
ejpam-5386	409	3	appl	appl	PROPN
ejpam-5386	409	4	.	.	PROPN
ejpam-5386	409	5	math	math	PROPN
ejpam-5386	409	6	,	,	PUNCT
ejpam-5386	409	7	17	17	NUM
ejpam-5386	409	8	(	(	PUNCT
ejpam-5386	409	9	4	4	NUM
ejpam-5386	409	10	)	)	PUNCT
ejpam-5386	409	11	(	(	PUNCT
ejpam-5386	409	12	2024	2024	NUM
ejpam-5386	409	13	)	)	PUNCT
ejpam-5386	409	14	,	,	PUNCT
ejpam-5386	409	15	2651	2651	NUM
ejpam-5386	409	16	-	-	SYM
ejpam-5386	409	17	2675	2675	NUM
ejpam-5386	409	18	2672	2672	NUM
ejpam-5386	409	19	(	(	PUNCT
ejpam-5386	409	20	a	a	X
ejpam-5386	409	21	)	)	PUNCT
ejpam-5386	409	22	the	the	DET
ejpam-5386	409	23	treatment	treatment	NOUN
ejpam-5386	409	24	parameter	parameter	NOUN
ejpam-5386	409	25	α(x	α(x	PROPN
ejpam-5386	409	26	)	)	PUNCT
ejpam-5386	409	27	(	(	PUNCT
ejpam-5386	409	28	b	b	X
ejpam-5386	409	29	)	)	PUNCT
ejpam-5386	409	30	the	the	DET
ejpam-5386	409	31	initial	initial	ADJ
ejpam-5386	409	32	cell	cell	NOUN
ejpam-5386	409	33	density	density	NOUN
ejpam-5386	409	34	φ(x	φ(x	NOUN
ejpam-5386	409	35	)	)	PUNCT
ejpam-5386	409	36	figure	figure	NOUN
ejpam-5386	409	37	8	8	NUM
ejpam-5386	409	38	:	:	PUNCT
ejpam-5386	409	39	the	the	DET
ejpam-5386	409	40	numerical	numerical	ADJ
ejpam-5386	409	41	results	result	NOUN
ejpam-5386	409	42	for	for	ADP
ejpam-5386	409	43	example	example	NOUN
ejpam-5386	409	44	4	4	NUM
ejpam-5386	409	45	for	for	ADP
ejpam-5386	409	46	different	different	ADJ
ejpam-5386	409	47	noise	noise	NOUN
ejpam-5386	409	48	levels	level	NOUN
ejpam-5386	409	49	p	p	PROPN
ejpam-5386	409	50	∈	∈	PROPN
ejpam-5386	409	51	{	{	PUNCT
ejpam-5386	409	52	0	0	NUM
ejpam-5386	409	53	,	,	PUNCT
ejpam-5386	409	54	1	1	NUM
ejpam-5386	409	55	,	,	PUNCT
ejpam-5386	409	56	2	2	NUM
ejpam-5386	409	57	}	}	PUNCT
ejpam-5386	409	58	.	.	PUNCT
ejpam-5386	410	1	left	leave	VERB
ejpam-5386	410	2	:	:	PUNCT
ejpam-5386	410	3	the	the	DET
ejpam-5386	410	4	treatment	treatment	NOUN
ejpam-5386	410	5	parameter	parameter	NOUN
ejpam-5386	410	6	α(x	α(x	PROPN
ejpam-5386	410	7	)	)	PUNCT
ejpam-5386	410	8	.	.	PUNCT
ejpam-5386	411	1	right	right	ADV
ejpam-5386	411	2	:	:	PUNCT
ejpam-5386	411	3	the	the	DET
ejpam-5386	411	4	initial	initial	ADJ
ejpam-5386	411	5	cell	cell	NOUN
ejpam-5386	411	6	density	density	NOUN
ejpam-5386	411	7	φ(x	φ(x	NOUN
ejpam-5386	411	8	)	)	PUNCT
ejpam-5386	411	9	.	.	PUNCT
ejpam-5386	412	1	in	in	ADP
ejpam-5386	412	2	comparison	comparison	NOUN
ejpam-5386	412	3	with	with	ADP
ejpam-5386	412	4	all	all	DET
ejpam-5386	412	5	previous	previous	ADJ
ejpam-5386	412	6	tests	test	NOUN
ejpam-5386	412	7	,	,	PUNCT
ejpam-5386	412	8	it	it	PRON
ejpam-5386	412	9	is	be	AUX
ejpam-5386	412	10	evident	evident	ADJ
ejpam-5386	412	11	from	from	ADP
ejpam-5386	412	12	figure	figure	NOUN
ejpam-5386	412	13	8	8	NUM
ejpam-5386	412	14	that	that	SCONJ
ejpam-5386	412	15	the	the	DET
ejpam-5386	412	16	accuracy	accuracy	NOUN
ejpam-5386	412	17	and	and	CCONJ
ejpam-5386	412	18	efficiency	efficiency	NOUN
ejpam-5386	412	19	are	be	AUX
ejpam-5386	412	20	reduced	reduce	VERB
ejpam-5386	412	21	in	in	ADP
ejpam-5386	412	22	this	this	DET
ejpam-5386	412	23	scenario	scenario	NOUN
ejpam-5386	412	24	due	due	ADP
ejpam-5386	412	25	to	to	ADP
ejpam-5386	412	26	the	the	DET
ejpam-5386	412	27	non	non	ADJ
ejpam-5386	412	28	-	-	ADJ
ejpam-5386	412	29	smoothness	smoothness	ADJ
ejpam-5386	412	30	of	of	ADP
ejpam-5386	412	31	the	the	DET
ejpam-5386	412	32	functions	function	NOUN
ejpam-5386	412	33	to	to	PART
ejpam-5386	412	34	be	be	AUX
ejpam-5386	412	35	reconstructed	reconstruct	VERB
ejpam-5386	412	36	.	.	PUNCT
ejpam-5386	413	1	however	however	ADV
ejpam-5386	413	2	,	,	PUNCT
ejpam-5386	413	3	overall	overall	ADV
ejpam-5386	413	4	,	,	PUNCT
ejpam-5386	413	5	the	the	DET
ejpam-5386	413	6	obtained	obtain	VERB
ejpam-5386	413	7	results	result	NOUN
ejpam-5386	413	8	are	be	AUX
ejpam-5386	413	9	acceptable	acceptable	ADJ
ejpam-5386	413	10	.	.	PUNCT
ejpam-5386	414	1	5	5	X
ejpam-5386	414	2	.	.	X
ejpam-5386	414	3	conclusions	conclusion	NOUN
ejpam-5386	414	4	in	in	ADP
ejpam-5386	414	5	this	this	DET
ejpam-5386	414	6	paper	paper	NOUN
ejpam-5386	414	7	,	,	PUNCT
ejpam-5386	414	8	we	we	PRON
ejpam-5386	414	9	addressed	address	VERB
ejpam-5386	414	10	an	an	DET
ejpam-5386	414	11	inverse	inverse	NOUN
ejpam-5386	414	12	problem	problem	NOUN
ejpam-5386	414	13	involving	involve	VERB
ejpam-5386	414	14	the	the	DET
ejpam-5386	414	15	simultaneous	simultaneous	ADJ
ejpam-5386	414	16	determination	determination	NOUN
ejpam-5386	414	17	of	of	ADP
ejpam-5386	414	18	the	the	DET
ejpam-5386	414	19	treatment	treatment	NOUN
ejpam-5386	414	20	response	response	NOUN
ejpam-5386	414	21	parameter	parameter	NOUN
ejpam-5386	414	22	and	and	CCONJ
ejpam-5386	414	23	the	the	DET
ejpam-5386	414	24	initial	initial	ADJ
ejpam-5386	414	25	tumor	tumor	NOUN
ejpam-5386	414	26	cell	cell	NOUN
ejpam-5386	414	27	density	density	NOUN
ejpam-5386	414	28	in	in	ADP
ejpam-5386	414	29	a	a	DET
ejpam-5386	414	30	nonlinear	nonlinear	ADJ
ejpam-5386	414	31	parabolic	parabolic	ADJ
ejpam-5386	414	32	problem	problem	NOUN
ejpam-5386	414	33	related	relate	VERB
ejpam-5386	414	34	to	to	AUX
ejpam-5386	414	35	brain	brain	VERB
ejpam-5386	414	36	tumor	tumor	NOUN
ejpam-5386	414	37	dynamics	dynamic	NOUN
ejpam-5386	414	38	.	.	PUNCT
ejpam-5386	415	1	by	by	ADP
ejpam-5386	415	2	reformulating	reformulate	VERB
ejpam-5386	415	3	the	the	DET
ejpam-5386	415	4	inverse	inverse	NOUN
ejpam-5386	415	5	problem	problem	NOUN
ejpam-5386	415	6	as	as	ADP
ejpam-5386	415	7	a	a	DET
ejpam-5386	415	8	minimization	minimization	NOUN
ejpam-5386	415	9	problem	problem	NOUN
ejpam-5386	415	10	,	,	PUNCT
ejpam-5386	415	11	we	we	PRON
ejpam-5386	415	12	established	establish	VERB
ejpam-5386	415	13	the	the	DET
ejpam-5386	415	14	existence	existence	NOUN
ejpam-5386	415	15	and	and	CCONJ
ejpam-5386	415	16	initial	initial	ADJ
ejpam-5386	415	17	stability	stability	NOUN
ejpam-5386	415	18	of	of	ADP
ejpam-5386	415	19	the	the	DET
ejpam-5386	415	20	solution	solution	NOUN
ejpam-5386	415	21	.	.	PUNCT
ejpam-5386	416	1	we	we	PRON
ejpam-5386	416	2	proved	prove	VERB
ejpam-5386	416	3	the	the	DET
ejpam-5386	416	4	fréchet	fréchet	NOUN
ejpam-5386	416	5	differentiability	differentiability	NOUN
ejpam-5386	416	6	of	of	ADP
ejpam-5386	416	7	the	the	DET
ejpam-5386	416	8	objective	objective	NOUN
ejpam-5386	416	9	(	(	PUNCT
ejpam-5386	416	10	cost	cost	NOUN
ejpam-5386	416	11	)	)	PUNCT
ejpam-5386	416	12	functional	functional	ADJ
ejpam-5386	416	13	and	and	CCONJ
ejpam-5386	416	14	presented	present	VERB
ejpam-5386	416	15	explicit	explicit	ADJ
ejpam-5386	416	16	formulas	formula	NOUN
ejpam-5386	416	17	for	for	ADP
ejpam-5386	416	18	the	the	DET
ejpam-5386	416	19	derivatives	derivative	NOUN
ejpam-5386	416	20	by	by	ADP
ejpam-5386	416	21	using	use	VERB
ejpam-5386	416	22	the	the	DET
ejpam-5386	416	23	solution	solution	NOUN
ejpam-5386	416	24	to	to	ADP
ejpam-5386	416	25	related	related	ADJ
ejpam-5386	416	26	adjoint	adjoint	NOUN
ejpam-5386	416	27	problem	problem	NOUN
ejpam-5386	416	28	.	.	PUNCT
ejpam-5386	417	1	based	base	VERB
ejpam-5386	417	2	on	on	ADP
ejpam-5386	417	3	the	the	DET
ejpam-5386	417	4	fréchet	fréchet	NOUN
ejpam-5386	417	5	differentiability	differentiability	NOUN
ejpam-5386	417	6	of	of	ADP
ejpam-5386	417	7	the	the	DET
ejpam-5386	417	8	objective	objective	NOUN
ejpam-5386	417	9	(	(	PUNCT
ejpam-5386	417	10	cost	cost	NOUN
ejpam-5386	417	11	)	)	PUNCT
ejpam-5386	417	12	functional	functional	ADJ
ejpam-5386	417	13	,	,	PUNCT
ejpam-5386	417	14	we	we	PRON
ejpam-5386	417	15	developed	develop	VERB
ejpam-5386	417	16	an	an	DET
ejpam-5386	417	17	efficient	efficient	ADJ
ejpam-5386	417	18	iterative	iterative	NOUN
ejpam-5386	417	19	procedure	procedure	NOUN
ejpam-5386	417	20	using	use	VERB
ejpam-5386	417	21	the	the	DET
ejpam-5386	417	22	conjugate	conjugate	ADJ
ejpam-5386	417	23	gradient	gradient	NOUN
ejpam-5386	417	24	method	method	NOUN
ejpam-5386	417	25	combined	combine	VERB
ejpam-5386	417	26	with	with	ADP
ejpam-5386	417	27	morozov	morozov	PROPN
ejpam-5386	417	28	’s	’s	PART
ejpam-5386	417	29	discrepancy	discrepancy	NOUN
ejpam-5386	417	30	principle	principle	NOUN
ejpam-5386	417	31	to	to	PART
ejpam-5386	417	32	solve	solve	VERB
ejpam-5386	417	33	the	the	DET
ejpam-5386	417	34	variational	variational	ADJ
ejpam-5386	417	35	problem	problem	NOUN
ejpam-5386	417	36	.	.	PUNCT
ejpam-5386	418	1	numerical	numerical	ADJ
ejpam-5386	418	2	examples	example	NOUN
ejpam-5386	418	3	,	,	PUNCT
ejpam-5386	418	4	with	with	ADP
ejpam-5386	418	5	both	both	DET
ejpam-5386	418	6	noise	noise	NOUN
ejpam-5386	418	7	-	-	PUNCT
ejpam-5386	418	8	free	free	ADJ
ejpam-5386	418	9	and	and	CCONJ
ejpam-5386	418	10	noisy	noisy	ADJ
ejpam-5386	418	11	data	datum	NOUN
ejpam-5386	418	12	,	,	PUNCT
ejpam-5386	418	13	demonstrated	demonstrate	VERB
ejpam-5386	418	14	the	the	DET
ejpam-5386	418	15	applicability	applicability	NOUN
ejpam-5386	418	16	and	and	CCONJ
ejpam-5386	418	17	accuracy	accuracy	NOUN
ejpam-5386	418	18	of	of	ADP
ejpam-5386	418	19	the	the	DET
ejpam-5386	418	20	proposed	propose	VERB
ejpam-5386	418	21	method	method	NOUN
ejpam-5386	418	22	.	.	PUNCT
ejpam-5386	419	1	on	on	ADP
ejpam-5386	419	2	the	the	DET
ejpam-5386	419	3	other	other	ADJ
ejpam-5386	419	4	hand	hand	NOUN
ejpam-5386	419	5	,	,	PUNCT
ejpam-5386	419	6	several	several	ADJ
ejpam-5386	419	7	mathematical	mathematical	ADJ
ejpam-5386	419	8	issues	issue	NOUN
ejpam-5386	419	9	of	of	ADP
ejpam-5386	419	10	high	high	ADJ
ejpam-5386	419	11	interest	interest	NOUN
ejpam-5386	419	12	have	have	AUX
ejpam-5386	419	13	not	not	PART
ejpam-5386	419	14	been	be	AUX
ejpam-5386	419	15	discussed	discuss	VERB
ejpam-5386	419	16	in	in	ADP
ejpam-5386	419	17	this	this	DET
ejpam-5386	419	18	paper	paper	NOUN
ejpam-5386	419	19	.	.	PUNCT
ejpam-5386	420	1	the	the	DET
ejpam-5386	420	2	stability	stability	NOUN
ejpam-5386	420	3	problem	problem	NOUN
ejpam-5386	420	4	is	be	AUX
ejpam-5386	420	5	one	one	NUM
ejpam-5386	420	6	of	of	ADP
ejpam-5386	420	7	them	they	PRON
ejpam-5386	420	8	.	.	PUNCT
ejpam-5386	421	1	the	the	DET
ejpam-5386	421	2	full	full	ADJ
ejpam-5386	421	3	stability	stability	NOUN
ejpam-5386	421	4	issue	issue	NOUN
ejpam-5386	421	5	is	be	AUX
ejpam-5386	421	6	,	,	PUNCT
ejpam-5386	421	7	however	however	ADV
ejpam-5386	421	8	,	,	PUNCT
ejpam-5386	421	9	to	to	ADP
ejpam-5386	421	10	the	the	DET
ejpam-5386	421	11	best	good	ADJ
ejpam-5386	421	12	of	of	ADP
ejpam-5386	421	13	our	our	PRON
ejpam-5386	421	14	knowledge	knowledge	NOUN
ejpam-5386	421	15	,	,	PUNCT
ejpam-5386	421	16	still	still	ADV
ejpam-5386	421	17	an	an	DET
ejpam-5386	421	18	open	open	ADJ
ejpam-5386	421	19	problem	problem	NOUN
ejpam-5386	421	20	which	which	PRON
ejpam-5386	421	21	deserves	deserve	VERB
ejpam-5386	421	22	further	further	ADJ
ejpam-5386	421	23	investigation	investigation	NOUN
ejpam-5386	421	24	.	.	PUNCT
ejpam-5386	422	1	additionally	additionally	ADV
ejpam-5386	422	2	,	,	PUNCT
ejpam-5386	422	3	the	the	DET
ejpam-5386	422	4	uniqueness	uniqueness	ADJ
ejpam-5386	422	5	analysis	analysis	NOUN
ejpam-5386	422	6	of	of	ADP
ejpam-5386	422	7	the	the	DET
ejpam-5386	422	8	considered	consider	VERB
ejpam-5386	422	9	inverse	inverse	NOUN
ejpam-5386	422	10	problem	problem	NOUN
ejpam-5386	422	11	remains	remain	VERB
ejpam-5386	422	12	an	an	DET
ejpam-5386	422	13	area	area	NOUN
ejpam-5386	422	14	for	for	ADP
ejpam-5386	422	15	future	future	ADJ
ejpam-5386	422	16	research	research	NOUN
ejpam-5386	422	17	.	.	PUNCT
ejpam-5386	423	1	these	these	DET
ejpam-5386	423	2	aspects	aspect	NOUN
ejpam-5386	423	3	will	will	AUX
ejpam-5386	423	4	be	be	AUX
ejpam-5386	423	5	the	the	DET
ejpam-5386	423	6	focus	focus	NOUN
ejpam-5386	423	7	of	of	ADP
ejpam-5386	423	8	forthcoming	forthcoming	ADJ
ejpam-5386	423	9	studies	study	NOUN
ejpam-5386	423	10	to	to	PART
ejpam-5386	423	11	enhance	enhance	VERB
ejpam-5386	423	12	the	the	DET
ejpam-5386	423	13	robustness	robustness	NOUN
ejpam-5386	423	14	and	and	CCONJ
ejpam-5386	423	15	reliability	reliability	NOUN
ejpam-5386	423	16	of	of	ADP
ejpam-5386	423	17	the	the	DET
ejpam-5386	423	18	proposed	propose	VERB
ejpam-5386	423	19	methods	method	NOUN
ejpam-5386	423	20	in	in	ADP
ejpam-5386	423	21	practical	practical	ADJ
ejpam-5386	423	22	applications	application	NOUN
ejpam-5386	423	23	.	.	PUNCT
ejpam-5386	424	1	acknowledgements	acknowledgement	NOUN
ejpam-5386	424	2	the	the	DET
ejpam-5386	424	3	authors	author	NOUN
ejpam-5386	424	4	thank	thank	VERB
ejpam-5386	424	5	to	to	ADP
ejpam-5386	424	6	anonymous	anonymous	ADJ
ejpam-5386	424	7	referees	referee	NOUN
ejpam-5386	424	8	and	and	CCONJ
ejpam-5386	424	9	editor	editor	NOUN
ejpam-5386	424	10	for	for	ADP
ejpam-5386	424	11	their	their	PRON
ejpam-5386	424	12	valuable	valuable	ADJ
ejpam-5386	424	13	comments	comment	NOUN
ejpam-5386	424	14	and	and	CCONJ
ejpam-5386	424	15	suggestions	suggestion	NOUN
ejpam-5386	424	16	that	that	PRON
ejpam-5386	424	17	have	have	AUX
ejpam-5386	424	18	greatly	greatly	ADV
ejpam-5386	424	19	improved	improve	VERB
ejpam-5386	424	20	the	the	DET
ejpam-5386	424	21	presentation	presentation	NOUN
ejpam-5386	424	22	of	of	ADP
ejpam-5386	424	23	the	the	DET
ejpam-5386	424	24	paper	paper	NOUN
ejpam-5386	424	25	.	.	PUNCT
ejpam-5386	425	1	references	reference	NOUN
ejpam-5386	425	2	2673	2673	NUM
ejpam-5386	425	3	references	reference	NOUN
ejpam-5386	425	4	[	[	X
ejpam-5386	425	5	1	1	NUM
ejpam-5386	425	6	]	]	X
ejpam-5386	425	7	g.	g.	PROPN
ejpam-5386	425	8	baravdish	baravdish	PROPN
ejpam-5386	425	9	,	,	PUNCT
ejpam-5386	425	10	b.	b.	PROPN
ejpam-5386	425	11	t.	t.	PROPN
ejpam-5386	425	12	johansson	johansson	PROPN
ejpam-5386	425	13	,	,	PUNCT
ejpam-5386	425	14	o.	o.	PROPN
ejpam-5386	425	15	svensson	svensson	PROPN
ejpam-5386	425	16	,	,	PUNCT
ejpam-5386	425	17	and	and	CCONJ
ejpam-5386	425	18	w.	w.	PROPN
ejpam-5386	425	19	ssebunjo	ssebunjo	PROPN
ejpam-5386	425	20	.	.	PUNCT
ejpam-5386	426	1	identifying	identify	VERB
ejpam-5386	426	2	a	a	DET
ejpam-5386	426	3	response	response	NOUN
ejpam-5386	426	4	parameter	parameter	NOUN
ejpam-5386	426	5	in	in	ADP
ejpam-5386	426	6	a	a	DET
ejpam-5386	426	7	model	model	NOUN
ejpam-5386	426	8	of	of	ADP
ejpam-5386	426	9	brain	brain	NOUN
ejpam-5386	426	10	tumor	tumor	NOUN
ejpam-5386	426	11	evolution	evolution	NOUN
ejpam-5386	426	12	under	under	ADP
ejpam-5386	426	13	therapy	therapy	NOUN
ejpam-5386	426	14	.	.	PUNCT
ejpam-5386	427	1	i	i	PRON
ejpam-5386	427	2	m	m	VERB
ejpam-5386	427	3	a	a	DET
ejpam-5386	427	4	journal	journal	NOUN
ejpam-5386	427	5	of	of	ADP
ejpam-5386	427	6	applied	apply	VERB
ejpam-5386	427	7	mathematics	mathematic	NOUN
ejpam-5386	427	8	,	,	PUNCT
ejpam-5386	427	9	88(2):378–404	88(2):378–404	PROPN
ejpam-5386	427	10	,	,	PUNCT
ejpam-5386	427	11	2023	2023	NUM
ejpam-5386	427	12	.	.	PUNCT
ejpam-5386	428	1	[	[	X
ejpam-5386	428	2	2	2	NUM
ejpam-5386	428	3	]	]	PUNCT
ejpam-5386	428	4	k.	k.	PROPN
ejpam-5386	428	5	cao	cao	PROPN
ejpam-5386	428	6	.	.	PUNCT
ejpam-5386	429	1	identification	identification	NOUN
ejpam-5386	429	2	of	of	ADP
ejpam-5386	429	3	the	the	DET
ejpam-5386	429	4	time	time	NOUN
ejpam-5386	429	5	-	-	PUNCT
ejpam-5386	429	6	dependent	dependent	ADJ
ejpam-5386	429	7	source	source	NOUN
ejpam-5386	429	8	term	term	NOUN
ejpam-5386	429	9	in	in	ADP
ejpam-5386	429	10	a	a	DET
ejpam-5386	429	11	kuramoto	kuramoto	NOUN
ejpam-5386	429	12	–	–	PUNCT
ejpam-5386	429	13	sivashinsky	sivashinsky	ADJ
ejpam-5386	429	14	equation	equation	NOUN
ejpam-5386	429	15	.	.	PUNCT
ejpam-5386	430	1	journal	journal	PROPN
ejpam-5386	430	2	of	of	ADP
ejpam-5386	430	3	inverse	inverse	NOUN
ejpam-5386	430	4	and	and	CCONJ
ejpam-5386	430	5	ill	ill	ADV
ejpam-5386	430	6	-	-	PUNCT
ejpam-5386	430	7	posed	pose	VERB
ejpam-5386	430	8	problems	problem	NOUN
ejpam-5386	430	9	,	,	PUNCT
ejpam-5386	430	10	32(3):361–387	32(3):361–387	PROPN
ejpam-5386	430	11	,	,	PUNCT
ejpam-5386	430	12	2024	2024	NUM
ejpam-5386	430	13	.	.	PUNCT
ejpam-5386	431	1	[	[	X
ejpam-5386	431	2	3	3	X
ejpam-5386	431	3	]	]	PUNCT
ejpam-5386	431	4	k.	k.	PROPN
ejpam-5386	431	5	cao	cao	PROPN
ejpam-5386	431	6	and	and	CCONJ
ejpam-5386	431	7	d.	d.	PROPN
ejpam-5386	431	8	lesnic	lesnic	PROPN
ejpam-5386	431	9	.	.	PUNCT
ejpam-5386	432	1	simultaneous	simultaneous	ADJ
ejpam-5386	432	2	reconstruction	reconstruction	NOUN
ejpam-5386	432	3	of	of	ADP
ejpam-5386	432	4	the	the	DET
ejpam-5386	432	5	spatially	spatially	ADV
ejpam-5386	432	6	-	-	PUNCT
ejpam-5386	432	7	distributed	distribute	VERB
ejpam-5386	432	8	reaction	reaction	NOUN
ejpam-5386	432	9	coefficient	coefficient	NOUN
ejpam-5386	432	10	,	,	PUNCT
ejpam-5386	432	11	initial	initial	ADJ
ejpam-5386	432	12	temperature	temperature	NOUN
ejpam-5386	432	13	and	and	CCONJ
ejpam-5386	432	14	heat	heat	NOUN
ejpam-5386	432	15	source	source	NOUN
ejpam-5386	432	16	from	from	ADP
ejpam-5386	432	17	temperature	temperature	NOUN
ejpam-5386	432	18	measurements	measurement	NOUN
ejpam-5386	432	19	at	at	ADP
ejpam-5386	432	20	different	different	ADJ
ejpam-5386	432	21	times	time	NOUN
ejpam-5386	432	22	.	.	PUNCT
ejpam-5386	433	1	computers	computer	NOUN
ejpam-5386	433	2	&	&	CCONJ
ejpam-5386	433	3	mathematics	mathematics	PROPN
ejpam-5386	433	4	with	with	ADP
ejpam-5386	433	5	applications	application	NOUN
ejpam-5386	433	6	,	,	PUNCT
ejpam-5386	433	7	78(10):3237–3249	78(10):3237–3249	NUM
ejpam-5386	433	8	,	,	PUNCT
ejpam-5386	433	9	2019	2019	NUM
ejpam-5386	433	10	.	.	PUNCT
ejpam-5386	434	1	[	[	X
ejpam-5386	434	2	4	4	X
ejpam-5386	434	3	]	]	PUNCT
ejpam-5386	434	4	k.	k.	PROPN
ejpam-5386	434	5	cao	cao	PROPN
ejpam-5386	434	6	and	and	CCONJ
ejpam-5386	434	7	d.	d.	PROPN
ejpam-5386	434	8	lesnic	lesnic	PROPN
ejpam-5386	434	9	.	.	PUNCT
ejpam-5386	435	1	simultaneous	simultaneous	ADJ
ejpam-5386	435	2	identification	identification	NOUN
ejpam-5386	435	3	and	and	CCONJ
ejpam-5386	435	4	reconstruction	reconstruction	NOUN
ejpam-5386	435	5	of	of	ADP
ejpam-5386	435	6	the	the	DET
ejpam-5386	435	7	spacedependent	spacedependent	NOUN
ejpam-5386	435	8	reaction	reaction	NOUN
ejpam-5386	435	9	coefficient	coefficient	NOUN
ejpam-5386	435	10	and	and	CCONJ
ejpam-5386	435	11	source	source	NOUN
ejpam-5386	435	12	term	term	NOUN
ejpam-5386	435	13	.	.	PUNCT
ejpam-5386	436	1	journal	journal	NOUN
ejpam-5386	436	2	of	of	ADP
ejpam-5386	436	3	inverse	inverse	NOUN
ejpam-5386	436	4	and	and	CCONJ
ejpam-5386	436	5	ill	ill	ADV
ejpam-5386	436	6	-	-	PUNCT
ejpam-5386	436	7	posed	pose	VERB
ejpam-5386	436	8	problems	problem	NOUN
ejpam-5386	436	9	,	,	PUNCT
ejpam-5386	436	10	29(6):867–894	29(6):867–894	PROPN
ejpam-5386	436	11	,	,	PUNCT
ejpam-5386	436	12	2021	2021	NUM
ejpam-5386	436	13	.	.	PUNCT
ejpam-5386	437	1	[	[	X
ejpam-5386	437	2	5	5	X
ejpam-5386	437	3	]	]	PUNCT
ejpam-5386	437	4	k.	k.	PROPN
ejpam-5386	437	5	cao	cao	PROPN
ejpam-5386	437	6	and	and	CCONJ
ejpam-5386	437	7	d.	d.	PROPN
ejpam-5386	437	8	lesnic	lesnic	PROPN
ejpam-5386	437	9	.	.	PUNCT
ejpam-5386	438	1	reconstruction	reconstruction	NOUN
ejpam-5386	438	2	of	of	ADP
ejpam-5386	438	3	the	the	DET
ejpam-5386	438	4	time	time	NOUN
ejpam-5386	438	5	-	-	PUNCT
ejpam-5386	438	6	dependent	dependent	ADJ
ejpam-5386	438	7	source	source	NOUN
ejpam-5386	438	8	in	in	ADP
ejpam-5386	438	9	thermal	thermal	ADJ
ejpam-5386	438	10	grooving	grooving	NOUN
ejpam-5386	438	11	by	by	ADP
ejpam-5386	438	12	surface	surface	NOUN
ejpam-5386	438	13	diffusion	diffusion	NOUN
ejpam-5386	438	14	.	.	PUNCT
ejpam-5386	439	1	journal	journal	PROPN
ejpam-5386	439	2	of	of	ADP
ejpam-5386	439	3	computational	computational	ADJ
ejpam-5386	439	4	and	and	CCONJ
ejpam-5386	439	5	applied	applied	ADJ
ejpam-5386	439	6	mathematics	mathematic	NOUN
ejpam-5386	439	7	,	,	PUNCT
ejpam-5386	439	8	444:115789	444:115789	NUM
ejpam-5386	439	9	,	,	PUNCT
ejpam-5386	439	10	2024	2024	NUM
ejpam-5386	439	11	.	.	PUNCT
ejpam-5386	440	1	[	[	X
ejpam-5386	440	2	6	6	NUM
ejpam-5386	440	3	]	]	PUNCT
ejpam-5386	440	4	m.	m.	NOUN
ejpam-5386	440	5	choulli	choulli	PROPN
ejpam-5386	440	6	.	.	PUNCT
ejpam-5386	441	1	une	une	PROPN
ejpam-5386	441	2	introduction	introduction	NOUN
ejpam-5386	441	3	aux	aux	PROPN
ejpam-5386	441	4	problèmes	problèmes	PROPN
ejpam-5386	441	5	inverses	inverses	PROPN
ejpam-5386	441	6	elliptiques	elliptique	NOUN
ejpam-5386	441	7	et	et	PROPN
ejpam-5386	441	8	paraboliques	parabolique	NOUN
ejpam-5386	441	9	.	.	PUNCT
ejpam-5386	442	1	springer	springer	NOUN
ejpam-5386	442	2	,	,	PUNCT
ejpam-5386	442	3	2009	2009	NUM
ejpam-5386	442	4	.	.	PUNCT
ejpam-5386	443	1	[	[	X
ejpam-5386	443	2	7	7	X
ejpam-5386	443	3	]	]	X
ejpam-5386	443	4	o.	o.	PROPN
ejpam-5386	443	5	clatz	clatz	PROPN
ejpam-5386	443	6	,	,	PUNCT
ejpam-5386	443	7	m.	m.	NOUN
ejpam-5386	443	8	sermesant	sermesant	PROPN
ejpam-5386	443	9	,	,	PUNCT
ejpam-5386	443	10	p.	p.	NOUN
ejpam-5386	443	11	y.	y.	PROPN
ejpam-5386	443	12	bondiau	bondiau	PROPN
ejpam-5386	443	13	,	,	PUNCT
ejpam-5386	443	14	h.	h.	PROPN
ejpam-5386	443	15	delingette	delingette	PROPN
ejpam-5386	443	16	,	,	PUNCT
ejpam-5386	443	17	s.	s.	PROPN
ejpam-5386	443	18	k.	k.	PROPN
ejpam-5386	443	19	warfield	warfield	PROPN
ejpam-5386	443	20	,	,	PUNCT
ejpam-5386	443	21	g.	g.	PROPN
ejpam-5386	443	22	malandain	malandain	PROPN
ejpam-5386	443	23	,	,	PUNCT
ejpam-5386	443	24	and	and	CCONJ
ejpam-5386	443	25	n.	n.	PROPN
ejpam-5386	443	26	ayache	ayache	PROPN
ejpam-5386	443	27	.	.	PUNCT
ejpam-5386	444	1	realistic	realistic	ADJ
ejpam-5386	444	2	simulation	simulation	NOUN
ejpam-5386	444	3	of	of	ADP
ejpam-5386	444	4	the	the	DET
ejpam-5386	444	5	3	3	NUM
ejpam-5386	444	6	-	-	PUNCT
ejpam-5386	444	7	d	d	NOUN
ejpam-5386	444	8	growth	growth	NOUN
ejpam-5386	444	9	of	of	ADP
ejpam-5386	444	10	brain	brain	NOUN
ejpam-5386	444	11	tumors	tumor	NOUN
ejpam-5386	444	12	in	in	ADP
ejpam-5386	444	13	mr	mr	PROPN
ejpam-5386	444	14	images	image	NOUN
ejpam-5386	444	15	coupling	couple	VERB
ejpam-5386	444	16	diffusion	diffusion	NOUN
ejpam-5386	444	17	with	with	ADP
ejpam-5386	444	18	biomechanical	biomechanical	ADJ
ejpam-5386	444	19	deformation	deformation	NOUN
ejpam-5386	444	20	.	.	PUNCT
ejpam-5386	445	1	ieee	ieee	NOUN
ejpam-5386	445	2	transactions	transaction	NOUN
ejpam-5386	445	3	on	on	ADP
ejpam-5386	445	4	medical	medical	ADJ
ejpam-5386	445	5	imaging	imaging	NOUN
ejpam-5386	445	6	,	,	PUNCT
ejpam-5386	445	7	24(10):1334–1346	24(10):1334–1346	NUM
ejpam-5386	445	8	,	,	PUNCT
ejpam-5386	445	9	2005	2005	NUM
ejpam-5386	445	10	.	.	PUNCT
ejpam-5386	446	1	[	[	X
ejpam-5386	446	2	8	8	X
ejpam-5386	446	3	]	]	X
ejpam-5386	446	4	j.	j.	PROPN
ejpam-5386	446	5	cook	cook	PROPN
ejpam-5386	446	6	,	,	PUNCT
ejpam-5386	446	7	d.	d.	PROPN
ejpam-5386	446	8	e.	e.	PROPN
ejpam-5386	446	9	woodward	woodward	PROPN
ejpam-5386	446	10	,	,	PUNCT
ejpam-5386	446	11	p.	p.	NOUN
ejpam-5386	446	12	tracqui	tracqui	NOUN
ejpam-5386	446	13	,	,	PUNCT
ejpam-5386	446	14	and	and	CCONJ
ejpam-5386	446	15	j.	j.	PROPN
ejpam-5386	446	16	d.	d.	PROPN
ejpam-5386	446	17	murray	murray	PROPN
ejpam-5386	446	18	.	.	PUNCT
ejpam-5386	447	1	resection	resection	NOUN
ejpam-5386	447	2	of	of	ADP
ejpam-5386	447	3	gliomas	glioma	NOUN
ejpam-5386	447	4	and	and	CCONJ
ejpam-5386	447	5	life	life	NOUN
ejpam-5386	447	6	expectancy	expectancy	NOUN
ejpam-5386	447	7	.	.	PUNCT
ejpam-5386	448	1	journal	journal	PROPN
ejpam-5386	448	2	of	of	ADP
ejpam-5386	448	3	neuro	neuro	NOUN
ejpam-5386	448	4	-	-	PUNCT
ejpam-5386	448	5	oncology	oncology	NOUN
ejpam-5386	448	6	,	,	PUNCT
ejpam-5386	448	7	24(4):131–135	24(4):131–135	PROPN
ejpam-5386	448	8	,	,	PUNCT
ejpam-5386	448	9	1995	1995	NUM
ejpam-5386	448	10	.	.	PUNCT
ejpam-5386	449	1	[	[	X
ejpam-5386	449	2	9	9	NUM
ejpam-5386	449	3	]	]	X
ejpam-5386	449	4	g.	g.	PROPN
ejpam-5386	449	5	c.	c.	PROPN
ejpam-5386	449	6	cruywagen	cruywagen	PROPN
ejpam-5386	449	7	,	,	PUNCT
ejpam-5386	449	8	d.	d.	PROPN
ejpam-5386	449	9	e.	e.	PROPN
ejpam-5386	449	10	woodward	woodward	PROPN
ejpam-5386	449	11	,	,	PUNCT
ejpam-5386	449	12	p.	p.	PROPN
ejpam-5386	449	13	tracqui	tracqui	NOUN
ejpam-5386	449	14	,	,	PUNCT
ejpam-5386	449	15	g.	g.	PROPN
ejpam-5386	449	16	t.	t.	PROPN
ejpam-5386	449	17	bartoo	bartoo	ADV
ejpam-5386	449	18	,	,	PUNCT
ejpam-5386	449	19	j.	j.	PROPN
ejpam-5386	449	20	d.	d.	PROPN
ejpam-5386	449	21	murray	murray	PROPN
ejpam-5386	449	22	,	,	PUNCT
ejpam-5386	449	23	and	and	CCONJ
ejpam-5386	449	24	ec	ec	PROPN
ejpam-5386	449	25	alvord	alvord	PROPN
ejpam-5386	449	26	.	.	PUNCT
ejpam-5386	450	1	the	the	DET
ejpam-5386	450	2	modelling	modelling	NOUN
ejpam-5386	450	3	of	of	ADP
ejpam-5386	450	4	diffusive	diffusive	ADJ
ejpam-5386	450	5	tumours	tumour	NOUN
ejpam-5386	450	6	.	.	PUNCT
ejpam-5386	451	1	journal	journal	NOUN
ejpam-5386	451	2	of	of	ADP
ejpam-5386	451	3	biological	biological	ADJ
ejpam-5386	451	4	systems	system	NOUN
ejpam-5386	451	5	,	,	PUNCT
ejpam-5386	451	6	3(4):937–945	3(4):937–945	NUM
ejpam-5386	451	7	,	,	PUNCT
ejpam-5386	451	8	1995	1995	NUM
ejpam-5386	451	9	.	.	PUNCT
ejpam-5386	452	1	[	[	X
ejpam-5386	452	2	10	10	NUM
ejpam-5386	452	3	]	]	PUNCT
ejpam-5386	452	4	m.	m.	NOUN
ejpam-5386	452	5	dolgushin	dolgushin	PROPN
ejpam-5386	452	6	,	,	PUNCT
ejpam-5386	452	7	v.	v.	ADP
ejpam-5386	452	8	kornienko	kornienko	PROPN
ejpam-5386	452	9	,	,	PUNCT
ejpam-5386	452	10	and	and	CCONJ
ejpam-5386	452	11	i.	i.	PROPN
ejpam-5386	452	12	pronin	pronin	PROPN
ejpam-5386	452	13	.	.	PUNCT
ejpam-5386	453	1	brain	brain	NOUN
ejpam-5386	453	2	metastases	metastasis	NOUN
ejpam-5386	453	3	:	:	PUNCT
ejpam-5386	453	4	advanced	advanced	ADJ
ejpam-5386	453	5	neuroimaging	neuroimaging	NOUN
ejpam-5386	453	6	.	.	PUNCT
ejpam-5386	454	1	springer	springer	NOUN
ejpam-5386	454	2	,	,	PUNCT
ejpam-5386	454	3	2018	2018	NUM
ejpam-5386	454	4	.	.	PUNCT
ejpam-5386	455	1	[	[	X
ejpam-5386	455	2	11	11	NUM
ejpam-5386	455	3	]	]	PUNCT
ejpam-5386	455	4	h.	h.	PROPN
ejpam-5386	455	5	w.	w.	PROPN
ejpam-5386	455	6	engl	engl	PROPN
ejpam-5386	455	7	and	and	CCONJ
ejpam-5386	455	8	c.	c.	PROPN
ejpam-5386	455	9	w.	w.	PROPN
ejpam-5386	455	10	groetsch	groetsch	PROPN
ejpam-5386	455	11	.	.	PUNCT
ejpam-5386	456	1	projection	projection	NOUN
ejpam-5386	456	2	-	-	PUNCT
ejpam-5386	456	3	regularization	regularization	NOUN
ejpam-5386	456	4	methods	method	NOUN
ejpam-5386	456	5	for	for	ADP
ejpam-5386	456	6	linear	linear	ADJ
ejpam-5386	456	7	operator	operator	NOUN
ejpam-5386	456	8	equations	equation	NOUN
ejpam-5386	456	9	of	of	ADP
ejpam-5386	456	10	the	the	DET
ejpam-5386	456	11	first	first	ADJ
ejpam-5386	456	12	kind	kind	NOUN
ejpam-5386	456	13	.	.	PUNCT
ejpam-5386	457	1	australian	australian	ADJ
ejpam-5386	457	2	national	national	PROPN
ejpam-5386	457	3	university	university	PROPN
ejpam-5386	457	4	,	,	PUNCT
ejpam-5386	457	5	mathematical	mathematical	ADJ
ejpam-5386	457	6	sciences	sciences	PROPN
ejpam-5386	457	7	institute	institute	PROPN
ejpam-5386	457	8	,	,	PUNCT
ejpam-5386	457	9	17:17–31	17:17–31	NUM
ejpam-5386	457	10	,	,	PUNCT
ejpam-5386	457	11	1988	1988	NUM
ejpam-5386	457	12	.	.	PUNCT
ejpam-5386	458	1	[	[	X
ejpam-5386	458	2	12	12	NUM
ejpam-5386	458	3	]	]	PUNCT
ejpam-5386	458	4	r.	r.	PROPN
ejpam-5386	458	5	fletcher	fletcher	PROPN
ejpam-5386	458	6	and	and	CCONJ
ejpam-5386	458	7	c.	c.	PROPN
ejpam-5386	458	8	m.	m.	PROPN
ejpam-5386	458	9	reeves	reeves	PROPN
ejpam-5386	458	10	.	.	PUNCT
ejpam-5386	459	1	function	function	NOUN
ejpam-5386	459	2	minimization	minimization	NOUN
ejpam-5386	459	3	by	by	ADP
ejpam-5386	459	4	conjugate	conjugate	ADJ
ejpam-5386	459	5	gradients	gradient	NOUN
ejpam-5386	459	6	.	.	PUNCT
ejpam-5386	460	1	the	the	DET
ejpam-5386	460	2	computer	computer	NOUN
ejpam-5386	460	3	journal	journal	NOUN
ejpam-5386	460	4	,	,	PUNCT
ejpam-5386	460	5	7(2):149–154	7(2):149–154	NUM
ejpam-5386	460	6	,	,	PUNCT
ejpam-5386	460	7	1964	1964	NUM
ejpam-5386	460	8	.	.	PUNCT
ejpam-5386	461	1	references	reference	NOUN
ejpam-5386	461	2	2674	2674	NUM
ejpam-5386	461	3	[	[	X
ejpam-5386	461	4	13	13	NUM
ejpam-5386	461	5	]	]	PUNCT
ejpam-5386	461	6	j.	j.	PROPN
ejpam-5386	461	7	c.	c.	PROPN
ejpam-5386	461	8	gilbert	gilbert	PROPN
ejpam-5386	461	9	and	and	CCONJ
ejpam-5386	461	10	j.	j.	PROPN
ejpam-5386	461	11	nocedal	nocedal	PROPN
ejpam-5386	461	12	.	.	PUNCT
ejpam-5386	462	1	global	global	ADJ
ejpam-5386	462	2	convergence	convergence	NOUN
ejpam-5386	462	3	properties	property	NOUN
ejpam-5386	462	4	of	of	ADP
ejpam-5386	462	5	conjugate	conjugate	ADJ
ejpam-5386	462	6	gradient	gradient	ADJ
ejpam-5386	462	7	methods	method	NOUN
ejpam-5386	462	8	for	for	ADP
ejpam-5386	462	9	optimization	optimization	NOUN
ejpam-5386	462	10	.	.	PUNCT
ejpam-5386	463	1	siam	siam	PROPN
ejpam-5386	463	2	journal	journal	PROPN
ejpam-5386	463	3	on	on	ADP
ejpam-5386	463	4	optimization	optimization	NOUN
ejpam-5386	463	5	,	,	PUNCT
ejpam-5386	463	6	2:21–42	2:21–42	NUM
ejpam-5386	463	7	,	,	PUNCT
ejpam-5386	463	8	1992	1992	NUM
ejpam-5386	463	9	.	.	PUNCT
ejpam-5386	464	1	[	[	X
ejpam-5386	464	2	14	14	NUM
ejpam-5386	464	3	]	]	X
ejpam-5386	464	4	v.	v.	PROPN
ejpam-5386	464	5	k.	k.	PROPN
ejpam-5386	464	6	ivanov	ivanov	PROPN
ejpam-5386	464	7	,	,	PUNCT
ejpam-5386	464	8	v.	v.	ADP
ejpam-5386	464	9	v.	v.	ADP
ejpam-5386	464	10	vasin	vasin	NOUN
ejpam-5386	464	11	,	,	PUNCT
ejpam-5386	464	12	and	and	CCONJ
ejpam-5386	464	13	v.	v.	ADP
ejpam-5386	464	14	p.	p.	PROPN
ejpam-5386	464	15	tanana	tanana	PROPN
ejpam-5386	464	16	.	.	PUNCT
ejpam-5386	465	1	theory	theory	NOUN
ejpam-5386	465	2	of	of	ADP
ejpam-5386	465	3	linear	linear	PROPN
ejpam-5386	465	4	ill	ill	ADV
ejpam-5386	465	5	-	-	PUNCT
ejpam-5386	465	6	posed	pose	VERB
ejpam-5386	465	7	problems	problem	NOUN
ejpam-5386	465	8	and	and	CCONJ
ejpam-5386	465	9	its	its	PRON
ejpam-5386	465	10	applications	application	NOUN
ejpam-5386	465	11	.	.	PUNCT
ejpam-5386	466	1	2022	2022	NUM
ejpam-5386	466	2	.	.	PUNCT
ejpam-5386	467	1	[	[	X
ejpam-5386	467	2	15	15	NUM
ejpam-5386	467	3	]	]	X
ejpam-5386	467	4	r.	r.	PROPN
ejpam-5386	467	5	jaroudi	jaroudi	PROPN
ejpam-5386	467	6	,	,	PUNCT
ejpam-5386	467	7	f.	f.	PROPN
ejpam-5386	467	8	aström	aström	PROPN
ejpam-5386	467	9	,	,	PUNCT
ejpam-5386	467	10	b.	b.	PROPN
ejpam-5386	467	11	t.	t.	PROPN
ejpam-5386	467	12	johansson	johansson	PROPN
ejpam-5386	467	13	,	,	PUNCT
ejpam-5386	467	14	and	and	CCONJ
ejpam-5386	467	15	g.	g.	PROPN
ejpam-5386	467	16	baravdish	baravdish	PROPN
ejpam-5386	467	17	.	.	PUNCT
ejpam-5386	468	1	numerical	numerical	ADJ
ejpam-5386	468	2	simulations	simulation	NOUN
ejpam-5386	468	3	in	in	ADP
ejpam-5386	468	4	3	3	NUM
ejpam-5386	468	5	-	-	PUNCT
ejpam-5386	468	6	dimensions	dimension	NOUN
ejpam-5386	468	7	of	of	ADP
ejpam-5386	468	8	reaction	reaction	NOUN
ejpam-5386	468	9	–	–	PUNCT
ejpam-5386	468	10	diffusion	diffusion	NOUN
ejpam-5386	468	11	models	model	NOUN
ejpam-5386	468	12	for	for	ADP
ejpam-5386	468	13	brain	brain	NOUN
ejpam-5386	468	14	tumor	tumor	NOUN
ejpam-5386	468	15	growth	growth	NOUN
ejpam-5386	468	16	.	.	PUNCT
ejpam-5386	469	1	international	international	ADJ
ejpam-5386	469	2	journal	journal	PROPN
ejpam-5386	469	3	of	of	ADP
ejpam-5386	469	4	computer	computer	NOUN
ejpam-5386	469	5	mathematics	mathematic	NOUN
ejpam-5386	469	6	,	,	PUNCT
ejpam-5386	469	7	2019	2019	NUM
ejpam-5386	469	8	.	.	PUNCT
ejpam-5386	470	1	[	[	X
ejpam-5386	470	2	16	16	NUM
ejpam-5386	470	3	]	]	X
ejpam-5386	470	4	b.	b.	PROPN
ejpam-5386	470	5	kaltenbacher	kaltenbacher	PROPN
ejpam-5386	470	6	and	and	CCONJ
ejpam-5386	470	7	w.	w.	PROPN
ejpam-5386	470	8	rundell	rundell	PROPN
ejpam-5386	470	9	.	.	PUNCT
ejpam-5386	471	1	on	on	ADP
ejpam-5386	471	2	the	the	DET
ejpam-5386	471	3	simultaneous	simultaneous	ADJ
ejpam-5386	471	4	recovery	recovery	NOUN
ejpam-5386	471	5	of	of	ADP
ejpam-5386	471	6	the	the	DET
ejpam-5386	471	7	conductivity	conductivity	NOUN
ejpam-5386	471	8	and	and	CCONJ
ejpam-5386	471	9	the	the	DET
ejpam-5386	471	10	nonlinear	nonlinear	ADJ
ejpam-5386	471	11	reaction	reaction	NOUN
ejpam-5386	471	12	term	term	NOUN
ejpam-5386	471	13	in	in	ADP
ejpam-5386	471	14	a	a	DET
ejpam-5386	471	15	parabolic	parabolic	ADJ
ejpam-5386	471	16	equation	equation	NOUN
ejpam-5386	471	17	.	.	PUNCT
ejpam-5386	472	1	inverse	inverse	NOUN
ejpam-5386	472	2	problems	problem	NOUN
ejpam-5386	472	3	and	and	CCONJ
ejpam-5386	472	4	imaging	imaging	NOUN
ejpam-5386	472	5	,	,	PUNCT
ejpam-5386	472	6	14(5):939–966	14(5):939–966	PROPN
ejpam-5386	472	7	,	,	PUNCT
ejpam-5386	472	8	2020	2020	NUM
ejpam-5386	472	9	.	.	PUNCT
ejpam-5386	473	1	[	[	X
ejpam-5386	473	2	17	17	NUM
ejpam-5386	473	3	]	]	X
ejpam-5386	473	4	y.	y.	PROPN
ejpam-5386	473	5	liu	liu	PROPN
ejpam-5386	473	6	,	,	PUNCT
ejpam-5386	473	7	d.	d.	PROPN
ejpam-5386	473	8	jiang	jiang	PROPN
ejpam-5386	473	9	,	,	PUNCT
ejpam-5386	473	10	and	and	CCONJ
ejpam-5386	473	11	m.	m.	PROPN
ejpam-5386	473	12	yamamoto	yamamoto	PROPN
ejpam-5386	473	13	.	.	PUNCT
ejpam-5386	474	1	inverse	inverse	PROPN
ejpam-5386	474	2	source	source	NOUN
ejpam-5386	474	3	problem	problem	NOUN
ejpam-5386	474	4	for	for	ADP
ejpam-5386	474	5	a	a	DET
ejpam-5386	474	6	double	double	ADJ
ejpam-5386	474	7	hyperbolic	hyperbolic	ADJ
ejpam-5386	474	8	equation	equation	NOUN
ejpam-5386	474	9	describing	describe	VERB
ejpam-5386	474	10	the	the	DET
ejpam-5386	474	11	three	three	NUM
ejpam-5386	474	12	-	-	PUNCT
ejpam-5386	474	13	dimensional	dimensional	ADJ
ejpam-5386	474	14	time	time	NOUN
ejpam-5386	474	15	cone	cone	NOUN
ejpam-5386	474	16	model	model	NOUN
ejpam-5386	474	17	.	.	PUNCT
ejpam-5386	475	1	siam	siam	PROPN
ejpam-5386	475	2	journal	journal	PROPN
ejpam-5386	475	3	on	on	ADP
ejpam-5386	475	4	applied	apply	VERB
ejpam-5386	475	5	mathematics	mathematic	NOUN
ejpam-5386	475	6	,	,	PUNCT
ejpam-5386	475	7	75(6):2610–2635	75(6):2610–2635	NOUN
ejpam-5386	475	8	,	,	PUNCT
ejpam-5386	475	9	2015	2015	NUM
ejpam-5386	475	10	.	.	PUNCT
ejpam-5386	476	1	[	[	X
ejpam-5386	476	2	18	18	NUM
ejpam-5386	476	3	]	]	X
ejpam-5386	476	4	v.	v.	CCONJ
ejpam-5386	476	5	noviantri	noviantri	ADJ
ejpam-5386	476	6	,	,	PUNCT
ejpam-5386	476	7	t.	t.	NOUN
ejpam-5386	476	8	tomy	tomy	NOUN
ejpam-5386	476	9	,	,	PUNCT
ejpam-5386	476	10	and	and	CCONJ
ejpam-5386	476	11	a.	a.	NOUN
ejpam-5386	476	12	chowanda	chowanda	PROPN
ejpam-5386	476	13	.	.	PUNCT
ejpam-5386	477	1	linear	linear	ADJ
ejpam-5386	477	2	and	and	CCONJ
ejpam-5386	477	3	nonlinear	nonlinear	ADJ
ejpam-5386	477	4	model	model	NOUN
ejpam-5386	477	5	of	of	ADP
ejpam-5386	477	6	brain	brain	NOUN
ejpam-5386	477	7	tumor	tumor	NOUN
ejpam-5386	477	8	growth	growth	NOUN
ejpam-5386	477	9	simulation	simulation	NOUN
ejpam-5386	477	10	using	use	VERB
ejpam-5386	477	11	finite	finite	ADJ
ejpam-5386	477	12	difference	difference	NOUN
ejpam-5386	477	13	method	method	NOUN
ejpam-5386	477	14	.	.	PUNCT
ejpam-5386	478	1	procedia	procedia	PROPN
ejpam-5386	478	2	computer	computer	NOUN
ejpam-5386	478	3	science	science	NOUN
ejpam-5386	478	4	,	,	PUNCT
ejpam-5386	478	5	179:297–304	179:297–304	NUM
ejpam-5386	478	6	,	,	PUNCT
ejpam-5386	478	7	2021	2021	NUM
ejpam-5386	478	8	.	.	PUNCT
ejpam-5386	479	1	[	[	X
ejpam-5386	479	2	19	19	NUM
ejpam-5386	479	3	]	]	X
ejpam-5386	479	4	g.	g.	PROPN
ejpam-5386	479	5	powathil	powathil	PROPN
ejpam-5386	479	6	,	,	PUNCT
ejpam-5386	479	7	m.	m.	PROPN
ejpam-5386	479	8	kohandel	kohandel	PROPN
ejpam-5386	479	9	,	,	PUNCT
ejpam-5386	479	10	s.	s.	PROPN
ejpam-5386	479	11	sivaloganathan	sivaloganathan	PROPN
ejpam-5386	479	12	,	,	PUNCT
ejpam-5386	479	13	a.	a.	PROPN
ejpam-5386	479	14	oza	oza	PROPN
ejpam-5386	479	15	,	,	PUNCT
ejpam-5386	479	16	and	and	CCONJ
ejpam-5386	479	17	m.	m.	PROPN
ejpam-5386	479	18	milosevic	milosevic	PROPN
ejpam-5386	479	19	.	.	PUNCT
ejpam-5386	480	1	mathematical	mathematical	ADJ
ejpam-5386	480	2	modeling	modeling	NOUN
ejpam-5386	480	3	of	of	ADP
ejpam-5386	480	4	brain	brain	NOUN
ejpam-5386	480	5	tumors	tumor	NOUN
ejpam-5386	480	6	:	:	PUNCT
ejpam-5386	480	7	effects	effect	NOUN
ejpam-5386	480	8	of	of	ADP
ejpam-5386	480	9	radiotherapy	radiotherapy	NOUN
ejpam-5386	480	10	and	and	CCONJ
ejpam-5386	480	11	chemotherapy	chemotherapy	NOUN
ejpam-5386	480	12	.	.	PUNCT
ejpam-5386	481	1	physics	physics	PROPN
ejpam-5386	481	2	in	in	ADP
ejpam-5386	481	3	medicine	medicine	PROPN
ejpam-5386	481	4	&	&	CCONJ
ejpam-5386	481	5	biology	biology	NOUN
ejpam-5386	481	6	,	,	PUNCT
ejpam-5386	481	7	52(11):3291	52(11):3291	NUM
ejpam-5386	481	8	,	,	PUNCT
ejpam-5386	481	9	2007	2007	NUM
ejpam-5386	481	10	.	.	PUNCT
ejpam-5386	482	1	[	[	X
ejpam-5386	482	2	20	20	NUM
ejpam-5386	482	3	]	]	PUNCT
ejpam-5386	482	4	r.	r.	PROPN
ejpam-5386	482	5	rockne	rockne	PROPN
ejpam-5386	482	6	,	,	PUNCT
ejpam-5386	482	7	ec	ec	PROPN
ejpam-5386	482	8	alvord	alvord	PROPN
ejpam-5386	482	9	jr	jr	PROPN
ejpam-5386	482	10	,	,	PUNCT
ejpam-5386	482	11	j.	j.	PROPN
ejpam-5386	482	12	k.	k.	PROPN
ejpam-5386	482	13	rockhill	rockhill	PROPN
ejpam-5386	482	14	,	,	PUNCT
ejpam-5386	482	15	and	and	CCONJ
ejpam-5386	482	16	k.	k.	PROPN
ejpam-5386	482	17	r.	r.	PROPN
ejpam-5386	482	18	swanson	swanson	PROPN
ejpam-5386	482	19	.	.	PUNCT
ejpam-5386	483	1	a	a	DET
ejpam-5386	483	2	mathematical	mathematical	ADJ
ejpam-5386	483	3	model	model	NOUN
ejpam-5386	483	4	for	for	ADP
ejpam-5386	483	5	brain	brain	NOUN
ejpam-5386	483	6	tumor	tumor	NOUN
ejpam-5386	483	7	response	response	NOUN
ejpam-5386	483	8	to	to	ADP
ejpam-5386	483	9	radiation	radiation	NOUN
ejpam-5386	483	10	therapy	therapy	NOUN
ejpam-5386	483	11	.	.	PUNCT
ejpam-5386	484	1	journal	journal	PROPN
ejpam-5386	484	2	of	of	ADP
ejpam-5386	484	3	mathematical	mathematical	ADJ
ejpam-5386	484	4	biology	biology	NOUN
ejpam-5386	484	5	,	,	PUNCT
ejpam-5386	484	6	58:561–578	58:561–578	PROPN
ejpam-5386	484	7	,	,	PUNCT
ejpam-5386	484	8	2009	2009	NUM
ejpam-5386	484	9	.	.	PUNCT
ejpam-5386	485	1	[	[	X
ejpam-5386	485	2	21	21	NUM
ejpam-5386	485	3	]	]	X
ejpam-5386	485	4	r.	r.	PROPN
ejpam-5386	485	5	rockne	rockne	PROPN
ejpam-5386	485	6	,	,	PUNCT
ejpam-5386	485	7	j.	j.	PROPN
ejpam-5386	485	8	k.	k.	PROPN
ejpam-5386	485	9	rockhill	rockhill	PROPN
ejpam-5386	485	10	,	,	PUNCT
ejpam-5386	485	11	m.	m.	NOUN
ejpam-5386	485	12	mrugala	mrugala	PROPN
ejpam-5386	485	13	,	,	PUNCT
ejpam-5386	485	14	a.	a.	PROPN
ejpam-5386	485	15	m.	m.	PROPN
ejpam-5386	485	16	spence	spence	PROPN
ejpam-5386	485	17	,	,	PUNCT
ejpam-5386	485	18	i.	i.	PROPN
ejpam-5386	485	19	kalet	kalet	PROPN
ejpam-5386	485	20	,	,	PUNCT
ejpam-5386	485	21	k.	k.	PROPN
ejpam-5386	485	22	hendrickson	hendrickson	PROPN
ejpam-5386	485	23	,	,	PUNCT
ejpam-5386	485	24	a.	a.	PROPN
ejpam-5386	485	25	lai	lai	PROPN
ejpam-5386	485	26	,	,	PUNCT
ejpam-5386	485	27	t.	t.	PROPN
ejpam-5386	485	28	cloughesy	cloughesy	PROPN
ejpam-5386	485	29	,	,	PUNCT
ejpam-5386	485	30	ec	ec	PROPN
ejpam-5386	485	31	alvord	alvord	PROPN
ejpam-5386	485	32	jr	jr	PROPN
ejpam-5386	485	33	,	,	PUNCT
ejpam-5386	485	34	and	and	CCONJ
ejpam-5386	485	35	k.	k.	PROPN
ejpam-5386	485	36	r.	r.	PROPN
ejpam-5386	485	37	swanson	swanson	PROPN
ejpam-5386	485	38	.	.	PUNCT
ejpam-5386	486	1	predicting	predict	VERB
ejpam-5386	486	2	the	the	DET
ejpam-5386	486	3	efficacy	efficacy	NOUN
ejpam-5386	486	4	of	of	ADP
ejpam-5386	486	5	radiotherapy	radiotherapy	NOUN
ejpam-5386	486	6	in	in	ADP
ejpam-5386	486	7	individual	individual	ADJ
ejpam-5386	486	8	glioblastoma	glioblastoma	NOUN
ejpam-5386	486	9	patients	patient	NOUN
ejpam-5386	486	10	in	in	ADP
ejpam-5386	486	11	vivo	vivo	NOUN
ejpam-5386	486	12	:	:	PUNCT
ejpam-5386	486	13	a	a	DET
ejpam-5386	486	14	mathematical	mathematical	ADJ
ejpam-5386	486	15	modeling	modeling	NOUN
ejpam-5386	486	16	approach	approach	NOUN
ejpam-5386	486	17	.	.	PUNCT
ejpam-5386	487	1	physics	physics	NOUN
ejpam-5386	487	2	in	in	ADP
ejpam-5386	487	3	medicine	medicine	PROPN
ejpam-5386	487	4	&	&	CCONJ
ejpam-5386	487	5	biology	biology	NOUN
ejpam-5386	487	6	,	,	PUNCT
ejpam-5386	487	7	55(12):3271–3285	55(12):3271–3285	NUM
ejpam-5386	487	8	,	,	PUNCT
ejpam-5386	487	9	2010	2010	NUM
ejpam-5386	487	10	.	.	PUNCT
ejpam-5386	488	1	[	[	X
ejpam-5386	488	2	22	22	NUM
ejpam-5386	488	3	]	]	X
ejpam-5386	488	4	b.	b.	PROPN
ejpam-5386	488	5	rysbaiuly	rysbaiuly	PROPN
ejpam-5386	488	6	and	and	CCONJ
ejpam-5386	488	7	n.	n.	PROPN
ejpam-5386	488	8	e.	e.	PROPN
ejpam-5386	488	9	mukhametkaliyeva	mukhametkaliyeva	PROPN
ejpam-5386	488	10	.	.	PUNCT
ejpam-5386	488	11	iterative	iterative	NOUN
ejpam-5386	488	12	method	method	NOUN
ejpam-5386	488	13	of	of	ADP
ejpam-5386	488	14	finding	find	VERB
ejpam-5386	488	15	all	all	DET
ejpam-5386	488	16	thermophysical	thermophysical	ADJ
ejpam-5386	488	17	parameters	parameter	NOUN
ejpam-5386	488	18	of	of	ADP
ejpam-5386	488	19	a	a	DET
ejpam-5386	488	20	two	two	NUM
ejpam-5386	488	21	-	-	PUNCT
ejpam-5386	488	22	layer	layer	NOUN
ejpam-5386	488	23	soil	soil	NOUN
ejpam-5386	488	24	.	.	PUNCT
ejpam-5386	489	1	in	in	ADP
ejpam-5386	489	2	journal	journal	PROPN
ejpam-5386	489	3	of	of	ADP
ejpam-5386	489	4	physics	physics	PROPN
ejpam-5386	489	5	:	:	PUNCT
ejpam-5386	489	6	conference	conference	NOUN
ejpam-5386	489	7	series	series	NOUN
ejpam-5386	489	8	,	,	PUNCT
ejpam-5386	489	9	volume	volume	NOUN
ejpam-5386	489	10	2224	2224	NUM
ejpam-5386	489	11	,	,	PUNCT
ejpam-5386	489	12	page	page	NOUN
ejpam-5386	489	13	012041	012041	NUM
ejpam-5386	489	14	,	,	PUNCT
ejpam-5386	489	15	2022	2022	NUM
ejpam-5386	489	16	.	.	PUNCT
ejpam-5386	490	1	[	[	X
ejpam-5386	490	2	23	23	NUM
ejpam-5386	490	3	]	]	X
ejpam-5386	490	4	g.	g.	PROPN
ejpam-5386	490	5	s.	s.	PROPN
ejpam-5386	490	6	stamatakos	stamatakos	PROPN
ejpam-5386	490	7	and	and	CCONJ
ejpam-5386	490	8	s.	s.	PROPN
ejpam-5386	490	9	g.	g.	PROPN
ejpam-5386	490	10	giatili	giatili	PROPN
ejpam-5386	490	11	.	.	PUNCT
ejpam-5386	491	1	a	a	DET
ejpam-5386	491	2	numerical	numerical	ADJ
ejpam-5386	491	3	handling	handling	NOUN
ejpam-5386	491	4	of	of	ADP
ejpam-5386	491	5	the	the	DET
ejpam-5386	491	6	boundary	boundary	ADJ
ejpam-5386	491	7	conditions	condition	NOUN
ejpam-5386	491	8	imposed	impose	VERB
ejpam-5386	491	9	by	by	ADP
ejpam-5386	491	10	the	the	DET
ejpam-5386	491	11	skull	skull	NOUN
ejpam-5386	491	12	on	on	ADP
ejpam-5386	491	13	an	an	DET
ejpam-5386	491	14	inhomogeneous	inhomogeneous	ADJ
ejpam-5386	491	15	diffusion	diffusion	NOUN
ejpam-5386	491	16	-	-	PUNCT
ejpam-5386	491	17	reaction	reaction	NOUN
ejpam-5386	491	18	model	model	NOUN
ejpam-5386	491	19	of	of	ADP
ejpam-5386	491	20	glioblastoma	glioblastoma	NOUN
ejpam-5386	491	21	invasion	invasion	NOUN
ejpam-5386	491	22	into	into	ADP
ejpam-5386	491	23	the	the	DET
ejpam-5386	491	24	brain	brain	NOUN
ejpam-5386	491	25	:	:	PUNCT
ejpam-5386	491	26	clinical	clinical	ADJ
ejpam-5386	491	27	validation	validation	NOUN
ejpam-5386	491	28	aspects	aspect	NOUN
ejpam-5386	491	29	.	.	PUNCT
ejpam-5386	492	1	cancer	cancer	NOUN
ejpam-5386	492	2	informatics	informatic	NOUN
ejpam-5386	492	3	,	,	PUNCT
ejpam-5386	492	4	pages	page	NOUN
ejpam-5386	492	5	1–16	1–16	PROPN
ejpam-5386	492	6	,	,	PUNCT
ejpam-5386	492	7	2017	2017	NUM
ejpam-5386	492	8	.	.	PUNCT
ejpam-5386	493	1	[	[	X
ejpam-5386	493	2	24	24	NUM
ejpam-5386	493	3	]	]	PUNCT
ejpam-5386	493	4	k.	k.	PROPN
ejpam-5386	493	5	r.	r.	PROPN
ejpam-5386	493	6	swanson	swanson	PROPN
ejpam-5386	493	7	,	,	PUNCT
ejpam-5386	493	8	ec	ec	PROPN
ejpam-5386	493	9	alvord	alvord	PROPN
ejpam-5386	493	10	jr	jr	PROPN
ejpam-5386	493	11	,	,	PUNCT
ejpam-5386	493	12	and	and	CCONJ
ejpam-5386	493	13	j.	j.	PROPN
ejpam-5386	493	14	d.	d.	PROPN
ejpam-5386	493	15	murray	murray	PROPN
ejpam-5386	493	16	.	.	PUNCT
ejpam-5386	494	1	a	a	DET
ejpam-5386	494	2	quantitative	quantitative	ADJ
ejpam-5386	494	3	model	model	NOUN
ejpam-5386	494	4	for	for	ADP
ejpam-5386	494	5	differential	differential	ADJ
ejpam-5386	494	6	motility	motility	NOUN
ejpam-5386	494	7	of	of	ADP
ejpam-5386	494	8	gliomas	glioma	NOUN
ejpam-5386	494	9	in	in	ADP
ejpam-5386	494	10	grey	grey	PROPN
ejpam-5386	494	11	and	and	CCONJ
ejpam-5386	494	12	white	white	ADJ
ejpam-5386	494	13	matter	matter	NOUN
ejpam-5386	494	14	.	.	PUNCT
ejpam-5386	495	1	cell	cell	NOUN
ejpam-5386	495	2	proliferation	proliferation	NOUN
ejpam-5386	495	3	,	,	PUNCT
ejpam-5386	495	4	33(5):317–329	33(5):317–329	PROPN
ejpam-5386	495	5	,	,	PUNCT
ejpam-5386	495	6	2000	2000	NUM
ejpam-5386	495	7	.	.	PUNCT
ejpam-5386	496	1	references	reference	NOUN
ejpam-5386	496	2	2675	2675	NUM
ejpam-5386	497	1	[	[	X
ejpam-5386	497	2	25	25	NUM
ejpam-5386	497	3	]	]	PUNCT
ejpam-5386	497	4	k.	k.	PROPN
ejpam-5386	497	5	r.	r.	PROPN
ejpam-5386	497	6	swanson	swanson	PROPN
ejpam-5386	497	7	,	,	PUNCT
ejpam-5386	497	8	ec	ec	PROPN
ejpam-5386	497	9	alvord	alvord	PROPN
ejpam-5386	497	10	jr	jr	PROPN
ejpam-5386	497	11	,	,	PUNCT
ejpam-5386	497	12	and	and	CCONJ
ejpam-5386	497	13	j.	j.	PROPN
ejpam-5386	497	14	d.	d.	PROPN
ejpam-5386	497	15	murray	murray	PROPN
ejpam-5386	497	16	.	.	PUNCT
ejpam-5386	498	1	virtual	virtual	ADJ
ejpam-5386	498	2	brain	brain	NOUN
ejpam-5386	498	3	tumours	tumour	NOUN
ejpam-5386	498	4	(	(	PUNCT
ejpam-5386	498	5	gliomas	glioma	NOUN
ejpam-5386	498	6	)	)	PUNCT
ejpam-5386	498	7	enhance	enhance	VERB
ejpam-5386	498	8	the	the	DET
ejpam-5386	498	9	reality	reality	NOUN
ejpam-5386	498	10	of	of	ADP
ejpam-5386	498	11	medical	medical	ADJ
ejpam-5386	498	12	imaging	imaging	NOUN
ejpam-5386	498	13	and	and	CCONJ
ejpam-5386	498	14	highlight	highlight	VERB
ejpam-5386	498	15	inadequacies	inadequacy	NOUN
ejpam-5386	498	16	of	of	ADP
ejpam-5386	498	17	current	current	ADJ
ejpam-5386	498	18	therapy	therapy	NOUN
ejpam-5386	498	19	.	.	PUNCT
ejpam-5386	499	1	british	british	ADJ
ejpam-5386	499	2	journal	journal	PROPN
ejpam-5386	499	3	of	of	ADP
ejpam-5386	499	4	cancer	cancer	NOUN
ejpam-5386	499	5	,	,	PUNCT
ejpam-5386	499	6	86(1):14–18	86(1):14–18	NUM
ejpam-5386	499	7	,	,	PUNCT
ejpam-5386	499	8	2002	2002	NUM
ejpam-5386	499	9	.	.	PUNCT
ejpam-5386	500	1	[	[	X
ejpam-5386	500	2	26	26	NUM
ejpam-5386	500	3	]	]	PUNCT
ejpam-5386	500	4	k.	k.	PROPN
ejpam-5386	500	5	r.	r.	PROPN
ejpam-5386	500	6	swanson	swanson	PROPN
ejpam-5386	500	7	,	,	PUNCT
ejpam-5386	500	8	c.	c.	PROPN
ejpam-5386	500	9	bridge	bridge	PROPN
ejpam-5386	500	10	,	,	PUNCT
ejpam-5386	500	11	j.	j.	PROPN
ejpam-5386	500	12	d.	d.	PROPN
ejpam-5386	500	13	murray	murray	PROPN
ejpam-5386	500	14	,	,	PUNCT
ejpam-5386	500	15	and	and	CCONJ
ejpam-5386	500	16	ec	ec	PROPN
ejpam-5386	500	17	alvord	alvord	PROPN
ejpam-5386	500	18	jr	jr	PROPN
ejpam-5386	500	19	.	.	PROPN
ejpam-5386	500	20	virtual	virtual	ADJ
ejpam-5386	500	21	and	and	CCONJ
ejpam-5386	500	22	real	real	ADJ
ejpam-5386	500	23	brain	brain	NOUN
ejpam-5386	500	24	tumors	tumor	NOUN
ejpam-5386	500	25	:	:	PUNCT
ejpam-5386	500	26	using	use	VERB
ejpam-5386	500	27	mathematical	mathematical	ADJ
ejpam-5386	500	28	modeling	modeling	NOUN
ejpam-5386	500	29	to	to	PART
ejpam-5386	500	30	quantify	quantify	VERB
ejpam-5386	500	31	glioma	glioma	NOUN
ejpam-5386	500	32	growth	growth	NOUN
ejpam-5386	500	33	and	and	CCONJ
ejpam-5386	500	34	invasion	invasion	NOUN
ejpam-5386	500	35	.	.	PUNCT
ejpam-5386	501	1	journal	journal	NOUN
ejpam-5386	501	2	of	of	ADP
ejpam-5386	501	3	the	the	DET
ejpam-5386	501	4	neurological	neurological	ADJ
ejpam-5386	501	5	sciences	science	NOUN
ejpam-5386	501	6	,	,	PUNCT
ejpam-5386	501	7	216(1):1–10	216(1):1–10	NUM
ejpam-5386	501	8	,	,	PUNCT
ejpam-5386	501	9	2003	2003	NUM
ejpam-5386	501	10	.	.	PUNCT
ejpam-5386	502	1	[	[	X
ejpam-5386	502	2	27	27	NUM
ejpam-5386	502	3	]	]	X
ejpam-5386	502	4	p.	p.	NOUN
ejpam-5386	502	5	tracqui	tracqui	NOUN
ejpam-5386	502	6	,	,	PUNCT
ejpam-5386	502	7	g.	g.	PROPN
ejpam-5386	502	8	c.	c.	PROPN
ejpam-5386	502	9	cruywagen	cruywagen	PROPN
ejpam-5386	502	10	,	,	PUNCT
ejpam-5386	502	11	d.	d.	PROPN
ejpam-5386	502	12	e.	e.	PROPN
ejpam-5386	502	13	woodward	woodward	PROPN
ejpam-5386	502	14	,	,	PUNCT
ejpam-5386	502	15	g.	g.	PROPN
ejpam-5386	502	16	t.	t.	PROPN
ejpam-5386	502	17	bartoo	bartoo	ADV
ejpam-5386	502	18	,	,	PUNCT
ejpam-5386	502	19	j.	j.	PROPN
ejpam-5386	502	20	d.	d.	PROPN
ejpam-5386	502	21	murray	murray	PROPN
ejpam-5386	502	22	,	,	PUNCT
ejpam-5386	502	23	and	and	CCONJ
ejpam-5386	502	24	ec	ec	PROPN
ejpam-5386	502	25	alvord	alvord	PROPN
ejpam-5386	502	26	.	.	PUNCT
ejpam-5386	503	1	a	a	DET
ejpam-5386	503	2	mathematical	mathematical	ADJ
ejpam-5386	503	3	model	model	NOUN
ejpam-5386	503	4	of	of	ADP
ejpam-5386	503	5	glioma	glioma	NOUN
ejpam-5386	503	6	growth	growth	NOUN
ejpam-5386	503	7	:	:	PUNCT
ejpam-5386	503	8	the	the	DET
ejpam-5386	503	9	effect	effect	NOUN
ejpam-5386	503	10	of	of	ADP
ejpam-5386	503	11	chemotherapy	chemotherapy	NOUN
ejpam-5386	503	12	on	on	ADP
ejpam-5386	503	13	spatio	spatio	PROPN
ejpam-5386	503	14	-	-	PUNCT
ejpam-5386	503	15	temporal	temporal	ADJ
ejpam-5386	503	16	growth	growth	NOUN
ejpam-5386	503	17	.	.	PUNCT
ejpam-5386	504	1	cell	cell	NOUN
ejpam-5386	504	2	proliferation	proliferation	NOUN
ejpam-5386	504	3	,	,	PUNCT
ejpam-5386	504	4	28(1):17–31	28(1):17–31	NUM
ejpam-5386	504	5	,	,	PUNCT
ejpam-5386	504	6	1995	1995	NUM
ejpam-5386	504	7	.	.	PUNCT
ejpam-5386	505	1	[	[	X
ejpam-5386	505	2	28	28	NUM
ejpam-5386	505	3	]	]	X
ejpam-5386	505	4	m.	m.	NOUN
ejpam-5386	505	5	yamamoto	yamamoto	PROPN
ejpam-5386	505	6	and	and	CCONJ
ejpam-5386	505	7	j.	j.	PROPN
ejpam-5386	505	8	zou	zou	PROPN
ejpam-5386	505	9	.	.	PUNCT
ejpam-5386	506	1	simultaneous	simultaneous	ADJ
ejpam-5386	506	2	reconstruction	reconstruction	NOUN
ejpam-5386	506	3	of	of	ADP
ejpam-5386	506	4	the	the	DET
ejpam-5386	506	5	initial	initial	ADJ
ejpam-5386	506	6	temperature	temperature	NOUN
ejpam-5386	506	7	and	and	CCONJ
ejpam-5386	506	8	heat	heat	NOUN
ejpam-5386	506	9	radiative	radiative	ADJ
ejpam-5386	506	10	coefficient	coefficient	NOUN
ejpam-5386	506	11	.	.	PUNCT
ejpam-5386	507	1	inverse	inverse	NOUN
ejpam-5386	507	2	problems	problem	NOUN
ejpam-5386	507	3	,	,	PUNCT
ejpam-5386	507	4	17(4):1181	17(4):1181	NUM
ejpam-5386	507	5	,	,	PUNCT
ejpam-5386	507	6	2001	2001	NUM
ejpam-5386	507	7	.	.	PUNCT