id	sid	tid	token	lemma	pos
ejpam-4859	1	1	european	european	PROPN
ejpam-4859	1	2	journal	journal	PROPN
ejpam-4859	1	3	of	of	ADP
ejpam-4859	1	4	pure	pure	ADJ
ejpam-4859	1	5	and	and	CCONJ
ejpam-4859	1	6	applied	apply	VERB
ejpam-4859	1	7	mathematics	mathematic	NOUN
ejpam-4859	1	8	vol	vol	NOUN
ejpam-4859	1	9	.	.	PUNCT
ejpam-4859	2	1	16	16	NUM
ejpam-4859	2	2	,	,	PUNCT
ejpam-4859	2	3	no	no	INTJ
ejpam-4859	2	4	.	.	NOUN
ejpam-4859	2	5	4	4	NUM
ejpam-4859	2	6	,	,	PUNCT
ejpam-4859	2	7	2023	2023	NUM
ejpam-4859	2	8	,	,	PUNCT
ejpam-4859	2	9	2557	2557	NUM
ejpam-4859	2	10	-	-	SYM
ejpam-4859	2	11	2580	2580	NUM
ejpam-4859	2	12	issn	issn	PROPN
ejpam-4859	2	13	1307	1307	NUM
ejpam-4859	2	14	-	-	SYM
ejpam-4859	2	15	5543	5543	NUM
ejpam-4859	2	16	–	–	PUNCT
ejpam-4859	2	17	ejpam.com	ejpam.com	X
ejpam-4859	2	18	published	publish	VERB
ejpam-4859	2	19	by	by	ADP
ejpam-4859	2	20	new	new	PROPN
ejpam-4859	2	21	york	york	PROPN
ejpam-4859	2	22	business	business	PROPN
ejpam-4859	2	23	global	global	PROPN
ejpam-4859	2	24	s	s	NOUN
ejpam-4859	2	25	-	-	PUNCT
ejpam-4859	2	26	invariant	invariant	ADJ
ejpam-4859	2	27	termwise	termwise	NOUN
ejpam-4859	2	28	addition	addition	NOUN
ejpam-4859	2	29	of	of	ADP
ejpam-4859	2	30	reactions	reaction	NOUN
ejpam-4859	2	31	via	via	ADP
ejpam-4859	2	32	reaction	reaction	NOUN
ejpam-4859	2	33	vector	vector	NOUN
ejpam-4859	2	34	multiples	multiple	NOUN
ejpam-4859	2	35	(	(	PUNCT
ejpam-4859	2	36	star	star	NOUN
ejpam-4859	2	37	-	-	PUNCT
ejpam-4859	2	38	rvm	rvm	PROPN
ejpam-4859	2	39	)	)	PUNCT
ejpam-4859	2	40	transformation	transformation	NOUN
ejpam-4859	2	41	daryl	daryl	PROPN
ejpam-4859	2	42	m.	m.	PROPN
ejpam-4859	2	43	magpantay	magpantay	PROPN
ejpam-4859	2	44	college	college	PROPN
ejpam-4859	2	45	of	of	ADP
ejpam-4859	2	46	arts	art	NOUN
ejpam-4859	2	47	and	and	CCONJ
ejpam-4859	2	48	sciences	sciences	PROPN
ejpam-4859	2	49	,	,	PUNCT
ejpam-4859	2	50	batangas	batangas	PROPN
ejpam-4859	2	51	state	state	PROPN
ejpam-4859	2	52	university	university	PROPN
ejpam-4859	2	53	the	the	DET
ejpam-4859	2	54	national	national	PROPN
ejpam-4859	2	55	engineering	engineering	PROPN
ejpam-4859	2	56	university	university	PROPN
ejpam-4859	2	57	,	,	PUNCT
ejpam-4859	2	58	batangas	batangas	PROPN
ejpam-4859	2	59	city	city	PROPN
ejpam-4859	2	60	,	,	PUNCT
ejpam-4859	2	61	batangas	batangas	PROPN
ejpam-4859	2	62	,	,	PUNCT
ejpam-4859	2	63	philippines	philippine	NOUN
ejpam-4859	2	64	abstract	abstract	ADJ
ejpam-4859	2	65	.	.	PUNCT
ejpam-4859	3	1	interest	interest	NOUN
ejpam-4859	3	2	in	in	ADP
ejpam-4859	3	3	connecting	connect	VERB
ejpam-4859	3	4	chemical	chemical	ADJ
ejpam-4859	3	5	reactions	reaction	NOUN
ejpam-4859	3	6	network	network	NOUN
ejpam-4859	3	7	theory	theory	NOUN
ejpam-4859	3	8	(	(	PUNCT
ejpam-4859	3	9	crnt	crnt	PROPN
ejpam-4859	3	10	)	)	PUNCT
ejpam-4859	3	11	and	and	CCONJ
ejpam-4859	3	12	evolutionary	evolutionary	ADJ
ejpam-4859	3	13	game	game	NOUN
ejpam-4859	3	14	theory	theory	NOUN
ejpam-4859	3	15	(	(	PUNCT
ejpam-4859	3	16	egt	egt	PROPN
ejpam-4859	3	17	)	)	PUNCT
ejpam-4859	3	18	arise	arise	NOUN
ejpam-4859	3	19	viewing	view	VERB
ejpam-4859	3	20	the	the	DET
ejpam-4859	3	21	tools	tool	NOUN
ejpam-4859	3	22	of	of	ADP
ejpam-4859	3	23	network	network	NOUN
ejpam-4859	3	24	in	in	ADP
ejpam-4859	3	25	the	the	DET
ejpam-4859	3	26	analysis	analysis	NOUN
ejpam-4859	3	27	of	of	ADP
ejpam-4859	3	28	evolutionary	evolutionary	ADJ
ejpam-4859	3	29	games	game	NOUN
ejpam-4859	3	30	.	.	PUNCT
ejpam-4859	4	1	here	here	ADV
ejpam-4859	4	2	,	,	PUNCT
ejpam-4859	4	3	the	the	DET
ejpam-4859	4	4	evolution	evolution	NOUN
ejpam-4859	4	5	of	of	ADP
ejpam-4859	4	6	population	population	NOUN
ejpam-4859	4	7	species	specie	NOUN
ejpam-4859	4	8	is	be	AUX
ejpam-4859	4	9	studied	study	VERB
ejpam-4859	4	10	as	as	ADP
ejpam-4859	4	11	a	a	DET
ejpam-4859	4	12	biological	biological	ADJ
ejpam-4859	4	13	phenomenon	phenomenon	NOUN
ejpam-4859	4	14	and	and	CCONJ
ejpam-4859	4	15	describing	describe	VERB
ejpam-4859	4	16	the	the	DET
ejpam-4859	4	17	rate	rate	NOUN
ejpam-4859	4	18	of	of	ADP
ejpam-4859	4	19	such	such	ADJ
ejpam-4859	4	20	changes	change	NOUN
ejpam-4859	4	21	through	through	ADP
ejpam-4859	4	22	a	a	DET
ejpam-4859	4	23	replicator	replicator	NOUN
ejpam-4859	4	24	system	system	NOUN
ejpam-4859	4	25	becomes	become	VERB
ejpam-4859	4	26	a	a	DET
ejpam-4859	4	27	focus	focus	NOUN
ejpam-4859	4	28	.	.	PUNCT
ejpam-4859	5	1	a	a	DET
ejpam-4859	5	2	set	set	NOUN
ejpam-4859	5	3	of	of	ADP
ejpam-4859	5	4	polynomial	polynomial	ADJ
ejpam-4859	5	5	kinetics	kinetic	NOUN
ejpam-4859	5	6	(	(	PUNCT
ejpam-4859	5	7	pok	pok	NOUN
ejpam-4859	5	8	)	)	PUNCT
ejpam-4859	5	9	may	may	AUX
ejpam-4859	5	10	then	then	ADV
ejpam-4859	5	11	be	be	AUX
ejpam-4859	5	12	introduced	introduce	VERB
ejpam-4859	5	13	for	for	ADP
ejpam-4859	5	14	the	the	DET
ejpam-4859	5	15	realization	realization	NOUN
ejpam-4859	5	16	of	of	ADP
ejpam-4859	5	17	this	this	DET
ejpam-4859	5	18	replicator	replicator	NOUN
ejpam-4859	5	19	system	system	NOUN
ejpam-4859	5	20	and	and	CCONJ
ejpam-4859	5	21	this	this	PRON
ejpam-4859	5	22	is	be	AUX
ejpam-4859	5	23	based	base	VERB
ejpam-4859	5	24	on	on	ADP
ejpam-4859	5	25	the	the	DET
ejpam-4859	5	26	polynomial	polynomial	ADJ
ejpam-4859	5	27	payoff	payoff	NOUN
ejpam-4859	5	28	functions	function	NOUN
ejpam-4859	5	29	defined	define	VERB
ejpam-4859	5	30	in	in	ADP
ejpam-4859	5	31	the	the	DET
ejpam-4859	5	32	game	game	NOUN
ejpam-4859	5	33	.	.	PUNCT
ejpam-4859	6	1	these	these	DET
ejpam-4859	6	2	polynomial	polynomial	ADJ
ejpam-4859	6	3	kinetics	kinetic	NOUN
ejpam-4859	6	4	result	result	VERB
ejpam-4859	6	5	in	in	ADP
ejpam-4859	6	6	polynomial	polynomial	ADJ
ejpam-4859	6	7	dynamical	dynamical	ADJ
ejpam-4859	6	8	systems	system	NOUN
ejpam-4859	6	9	of	of	ADP
ejpam-4859	6	10	ordinary	ordinary	ADJ
ejpam-4859	6	11	differential	differential	ADJ
ejpam-4859	6	12	equations	equation	NOUN
ejpam-4859	6	13	,	,	PUNCT
ejpam-4859	6	14	which	which	PRON
ejpam-4859	6	15	are	be	AUX
ejpam-4859	6	16	used	use	VERB
ejpam-4859	6	17	in	in	ADP
ejpam-4859	6	18	analyzing	analyze	VERB
ejpam-4859	6	19	strategies	strategy	NOUN
ejpam-4859	6	20	that	that	PRON
ejpam-4859	6	21	prove	prove	VERB
ejpam-4859	6	22	beneficial	beneficial	ADJ
ejpam-4859	6	23	under	under	ADP
ejpam-4859	6	24	certain	certain	ADJ
ejpam-4859	6	25	conditions	condition	NOUN
ejpam-4859	6	26	.	.	PUNCT
ejpam-4859	7	1	from	from	ADP
ejpam-4859	7	2	the	the	DET
ejpam-4859	7	3	crnt	crnt	ADJ
ejpam-4859	7	4	point	point	NOUN
ejpam-4859	7	5	of	of	ADP
ejpam-4859	7	6	view	view	NOUN
ejpam-4859	7	7	,	,	PUNCT
ejpam-4859	7	8	it	it	PRON
ejpam-4859	7	9	now	now	ADV
ejpam-4859	7	10	becomes	become	VERB
ejpam-4859	7	11	interesting	interesting	ADJ
ejpam-4859	7	12	to	to	PART
ejpam-4859	7	13	study	study	VERB
ejpam-4859	7	14	a	a	DET
ejpam-4859	7	15	superset	superset	NOUN
ejpam-4859	7	16	of	of	ADP
ejpam-4859	7	17	pok	pok	NOUN
ejpam-4859	7	18	,	,	PUNCT
ejpam-4859	7	19	which	which	PRON
ejpam-4859	7	20	we	we	PRON
ejpam-4859	7	21	call	call	VERB
ejpam-4859	7	22	poly	poly	ADJ
ejpam-4859	7	23	-	-	PUNCT
ejpam-4859	7	24	pl	pl	NOUN
ejpam-4859	7	25	kinetics	kinetic	NOUN
ejpam-4859	7	26	(	(	PUNCT
ejpam-4859	7	27	pyk	pyk	PROPN
ejpam-4859	7	28	)	)	PUNCT
ejpam-4859	7	29	.	.	PUNCT
ejpam-4859	8	1	this	this	DET
ejpam-4859	8	2	set	set	NOUN
ejpam-4859	8	3	is	be	AUX
ejpam-4859	8	4	formed	form	VERB
ejpam-4859	8	5	by	by	ADP
ejpam-4859	8	6	getting	get	VERB
ejpam-4859	8	7	nonnegative	nonnegative	ADJ
ejpam-4859	8	8	linear	linear	ADJ
ejpam-4859	8	9	combinations	combination	NOUN
ejpam-4859	8	10	of	of	ADP
ejpam-4859	8	11	power	power	NOUN
ejpam-4859	8	12	law	law	NOUN
ejpam-4859	8	13	functions	function	NOUN
ejpam-4859	8	14	.	.	PUNCT
ejpam-4859	9	1	thus	thus	ADV
ejpam-4859	9	2	,	,	PUNCT
ejpam-4859	9	3	pyk	pyk	PROPN
ejpam-4859	9	4	contains	contain	VERB
ejpam-4859	9	5	the	the	DET
ejpam-4859	9	6	set	set	VERB
ejpam-4859	9	7	plk	plk	NOUN
ejpam-4859	9	8	of	of	ADP
ejpam-4859	9	9	power	power	NOUN
ejpam-4859	9	10	law	law	NOUN
ejpam-4859	9	11	kinetics	kinetic	NOUN
ejpam-4859	9	12	as	as	ADP
ejpam-4859	9	13	mono	mono	NOUN
ejpam-4859	9	14	-	-	PUNCT
ejpam-4859	9	15	pl	pl	NOUN
ejpam-4859	9	16	kinetics	kinetic	NOUN
ejpam-4859	9	17	with	with	ADP
ejpam-4859	9	18	coefficient	coefficient	NOUN
ejpam-4859	9	19	1	1	X
ejpam-4859	9	20	.	.	PUNCT
ejpam-4859	9	21	seeing	see	VERB
ejpam-4859	9	22	this	this	DET
ejpam-4859	9	23	connection	connection	NOUN
ejpam-4859	9	24	between	between	ADP
ejpam-4859	9	25	crnt	crnt	PROPN
ejpam-4859	9	26	and	and	CCONJ
ejpam-4859	9	27	egt	egt	PROPN
ejpam-4859	9	28	and	and	CCONJ
ejpam-4859	9	29	what	what	PRON
ejpam-4859	9	30	are	be	AUX
ejpam-4859	9	31	known	know	VERB
ejpam-4859	9	32	about	about	ADP
ejpam-4859	9	33	power	power	NOUN
ejpam-4859	9	34	law	law	NOUN
ejpam-4859	9	35	kinetics	kinetic	NOUN
ejpam-4859	9	36	,	,	PUNCT
ejpam-4859	9	37	we	we	PRON
ejpam-4859	9	38	take	take	VERB
ejpam-4859	9	39	an	an	DET
ejpam-4859	9	40	interest	interest	NOUN
ejpam-4859	9	41	in	in	ADP
ejpam-4859	9	42	studying	study	VERB
ejpam-4859	9	43	pyk	pyk	PROPN
ejpam-4859	9	44	systems	system	NOUN
ejpam-4859	9	45	.	.	PUNCT
ejpam-4859	10	1	this	this	DET
ejpam-4859	10	2	paper	paper	NOUN
ejpam-4859	10	3	aims	aim	VERB
ejpam-4859	10	4	to	to	PART
ejpam-4859	10	5	analyze	analyze	VERB
ejpam-4859	10	6	different	different	ADJ
ejpam-4859	10	7	ways	way	NOUN
ejpam-4859	10	8	of	of	ADP
ejpam-4859	10	9	transforming	transform	VERB
ejpam-4859	10	10	pyk	pyk	NOUN
ejpam-4859	10	11	to	to	ADP
ejpam-4859	10	12	plk	plk	VERB
ejpam-4859	10	13	in	in	ADP
ejpam-4859	10	14	order	order	NOUN
ejpam-4859	10	15	to	to	PART
ejpam-4859	10	16	explore	explore	VERB
ejpam-4859	10	17	some	some	DET
ejpam-4859	10	18	approaches	approach	NOUN
ejpam-4859	10	19	for	for	ADP
ejpam-4859	10	20	crnt	crnt	ADJ
ejpam-4859	10	21	analysis	analysis	NOUN
ejpam-4859	10	22	of	of	ADP
ejpam-4859	10	23	pyk	pyk	PROPN
ejpam-4859	10	24	systems	system	NOUN
ejpam-4859	10	25	.	.	PUNCT
ejpam-4859	11	1	specifically	specifically	ADV
ejpam-4859	11	2	,	,	PUNCT
ejpam-4859	11	3	we	we	PRON
ejpam-4859	11	4	study	study	VERB
ejpam-4859	11	5	a	a	DET
ejpam-4859	11	6	network	network	NOUN
ejpam-4859	11	7	structure	structure	NOUN
ejpam-4859	11	8	-	-	PUNCT
ejpam-4859	11	9	oriented	orient	VERB
ejpam-4859	11	10	transformations	transformation	NOUN
ejpam-4859	11	11	using	use	VERB
ejpam-4859	11	12	the	the	DET
ejpam-4859	11	13	s	s	NOUN
ejpam-4859	11	14	-	-	PUNCT
ejpam-4859	11	15	invariant	invariant	ADJ
ejpam-4859	11	16	term	term	NOUN
ejpam-4859	11	17	-	-	PUNCT
ejpam-4859	11	18	wise	wise	ADJ
ejpam-4859	11	19	addition	addition	NOUN
ejpam-4859	11	20	of	of	ADP
ejpam-4859	11	21	reactions	reaction	NOUN
ejpam-4859	11	22	(	(	PUNCT
ejpam-4859	11	23	star	star	NOUN
ejpam-4859	11	24	)	)	PUNCT
ejpam-4859	11	25	via	via	ADP
ejpam-4859	11	26	reaction	reaction	NOUN
ejpam-4859	11	27	vector	vector	NOUN
ejpam-4859	11	28	multiples	multiple	NOUN
ejpam-4859	11	29	(	(	PUNCT
ejpam-4859	11	30	rvm	rvm	NOUN
ejpam-4859	11	31	)	)	PUNCT
ejpam-4859	11	32	that	that	PRON
ejpam-4859	11	33	transform	transform	VERB
ejpam-4859	11	34	pyk	pyk	NOUN
ejpam-4859	11	35	to	to	ADP
ejpam-4859	11	36	plk	plk	PROPN
ejpam-4859	11	37	systems	system	NOUN
ejpam-4859	11	38	.	.	PUNCT
ejpam-4859	12	1	2020	2020	NUM
ejpam-4859	12	2	mathematics	mathematics	PROPN
ejpam-4859	12	3	subject	subject	NOUN
ejpam-4859	12	4	classifications	classification	NOUN
ejpam-4859	12	5	:	:	PUNCT
ejpam-4859	12	6	92	92	NUM
ejpam-4859	12	7	key	key	ADJ
ejpam-4859	12	8	words	word	NOUN
ejpam-4859	12	9	and	and	CCONJ
ejpam-4859	12	10	phrases	phrase	NOUN
ejpam-4859	12	11	:	:	PUNCT
ejpam-4859	12	12	chemical	chemical	ADJ
ejpam-4859	12	13	reactions	reaction	NOUN
ejpam-4859	12	14	network	network	NOUN
ejpam-4859	12	15	theory	theory	NOUN
ejpam-4859	12	16	,	,	PUNCT
ejpam-4859	12	17	power	power	NOUN
ejpam-4859	12	18	law	law	NOUN
ejpam-4859	12	19	kinetics	kinetic	NOUN
ejpam-4859	12	20	,	,	PUNCT
ejpam-4859	12	21	reaction	reaction	NOUN
ejpam-4859	12	22	vector	vector	NOUN
ejpam-4859	12	23	multiples	multiple	NOUN
ejpam-4859	12	24	,	,	PUNCT
ejpam-4859	12	25	mono	mono	NOUN
ejpam-4859	12	26	-	-	PUNCT
ejpam-4859	12	27	pl	pl	NOUN
ejpam-4859	12	28	kinetics	kinetic	NOUN
ejpam-4859	12	29	1	1	NUM
ejpam-4859	12	30	.	.	PUNCT
ejpam-4859	13	1	introduction	introduction	NOUN
ejpam-4859	13	2	the	the	DET
ejpam-4859	13	3	study	study	NOUN
ejpam-4859	13	4	of	of	ADP
ejpam-4859	13	5	evolutionary	evolutionary	ADJ
ejpam-4859	13	6	game	game	NOUN
ejpam-4859	13	7	theory	theory	NOUN
ejpam-4859	13	8	(	(	PUNCT
ejpam-4859	13	9	egt	egt	PROPN
ejpam-4859	13	10	)	)	PUNCT
ejpam-4859	13	11	revolves	revolve	VERB
ejpam-4859	13	12	around	around	ADP
ejpam-4859	13	13	dynamics	dynamic	NOUN
ejpam-4859	13	14	that	that	PRON
ejpam-4859	13	15	describe	describe	VERB
ejpam-4859	13	16	the	the	DET
ejpam-4859	13	17	spread	spread	NOUN
ejpam-4859	13	18	of	of	ADP
ejpam-4859	13	19	successful	successful	ADJ
ejpam-4859	13	20	strategies	strategy	NOUN
ejpam-4859	13	21	in	in	ADP
ejpam-4859	13	22	a	a	DET
ejpam-4859	13	23	population	population	NOUN
ejpam-4859	13	24	of	of	ADP
ejpam-4859	13	25	various	various	ADJ
ejpam-4859	13	26	species	specie	NOUN
ejpam-4859	13	27	.	.	PUNCT
ejpam-4859	14	1	egt	egt	PROPN
ejpam-4859	14	2	models	model	VERB
ejpam-4859	14	3	how	how	SCONJ
ejpam-4859	14	4	individuals	individual	NOUN
ejpam-4859	14	5	or	or	CCONJ
ejpam-4859	14	6	populations	population	NOUN
ejpam-4859	14	7	change	change	VERB
ejpam-4859	14	8	their	their	PRON
ejpam-4859	14	9	strategy	strategy	NOUN
ejpam-4859	14	10	over	over	ADP
ejpam-4859	14	11	time	time	NOUN
ejpam-4859	14	12	based	base	VERB
ejpam-4859	14	13	on	on	ADP
ejpam-4859	14	14	payoff	payoff	NOUN
ejpam-4859	14	15	comparisons	comparison	NOUN
ejpam-4859	14	16	.	.	PUNCT
ejpam-4859	15	1	one	one	NUM
ejpam-4859	15	2	important	important	ADJ
ejpam-4859	15	3	game	game	NOUN
ejpam-4859	15	4	dynamics	dynamic	NOUN
ejpam-4859	15	5	that	that	PRON
ejpam-4859	15	6	is	be	AUX
ejpam-4859	15	7	mostly	mostly	ADV
ejpam-4859	15	8	studied	study	VERB
ejpam-4859	15	9	is	be	AUX
ejpam-4859	15	10	the	the	DET
ejpam-4859	15	11	replicator	replicator	NOUN
ejpam-4859	15	12	equation	equation	NOUN
ejpam-4859	15	13	.	.	PUNCT
ejpam-4859	16	1	this	this	DET
ejpam-4859	16	2	doi	doi	NOUN
ejpam-4859	16	3	:	:	PUNCT
ejpam-4859	16	4	https://doi.org/10.29020/nybg.ejpam.v16i4.4859	https://doi.org/10.29020/nybg.ejpam.v16i4.4859	PROPN
ejpam-4859	16	5	email	email	NOUN
ejpam-4859	16	6	address	address	NOUN
ejpam-4859	16	7	:	:	PUNCT
ejpam-4859	16	8	daryl.magpantay@g.batstate-u.edu.ph	daryl.magpantay@g.batstate-u.edu.ph	PROPN
ejpam-4859	16	9	(	(	PUNCT
ejpam-4859	16	10	d.	d.	PROPN
ejpam-4859	16	11	magpantay	magpantay	PROPN
ejpam-4859	16	12	)	)	PUNCT
ejpam-4859	16	13	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4859	16	14	2557	2557	NUM
ejpam-4859	17	1	©	©	ADP
ejpam-4859	17	2	2023	2023	NUM
ejpam-4859	17	3	ejpam	ejpam	NOUN
ejpam-4859	17	4	all	all	DET
ejpam-4859	17	5	rights	right	NOUN
ejpam-4859	17	6	reserved	reserve	VERB
ejpam-4859	17	7	.	.	PUNCT
ejpam-4859	18	1	d.	d.	PROPN
ejpam-4859	18	2	magpantay	magpantay	PROPN
ejpam-4859	18	3	/	/	SYM
ejpam-4859	18	4	eur	eur	PROPN
ejpam-4859	18	5	.	.	PUNCT
ejpam-4859	19	1	j.	j.	PROPN
ejpam-4859	19	2	pure	pure	PROPN
ejpam-4859	19	3	appl	appl	PROPN
ejpam-4859	19	4	.	.	PROPN
ejpam-4859	19	5	math	math	PROPN
ejpam-4859	19	6	,	,	PUNCT
ejpam-4859	19	7	16	16	NUM
ejpam-4859	19	8	(	(	PUNCT
ejpam-4859	19	9	4	4	NUM
ejpam-4859	19	10	)	)	PUNCT
ejpam-4859	19	11	(	(	PUNCT
ejpam-4859	19	12	2023	2023	NUM
ejpam-4859	19	13	)	)	PUNCT
ejpam-4859	19	14	,	,	PUNCT
ejpam-4859	19	15	2557	2557	NUM
ejpam-4859	19	16	-	-	SYM
ejpam-4859	19	17	2580	2580	NUM
ejpam-4859	19	18	2558	2558	NUM
ejpam-4859	19	19	equation	equation	NOUN
ejpam-4859	19	20	allows	allow	VERB
ejpam-4859	19	21	the	the	DET
ejpam-4859	19	22	reproduction	reproduction	NOUN
ejpam-4859	19	23	success	success	NOUN
ejpam-4859	19	24	technically	technically	ADV
ejpam-4859	19	25	known	know	VERB
ejpam-4859	19	26	as	as	ADP
ejpam-4859	19	27	fitness	fitness	NOUN
ejpam-4859	19	28	function	function	NOUN
ejpam-4859	19	29	to	to	PART
ejpam-4859	19	30	incorporate	incorporate	VERB
ejpam-4859	19	31	the	the	DET
ejpam-4859	19	32	distribution	distribution	NOUN
ejpam-4859	19	33	of	of	ADP
ejpam-4859	19	34	the	the	DET
ejpam-4859	19	35	finitely	finitely	ADV
ejpam-4859	19	36	many	many	ADJ
ejpam-4859	19	37	species	specie	NOUN
ejpam-4859	19	38	in	in	ADP
ejpam-4859	19	39	the	the	DET
ejpam-4859	19	40	population	population	NOUN
ejpam-4859	19	41	.	.	PUNCT
ejpam-4859	20	1	with	with	ADP
ejpam-4859	20	2	this	this	DET
ejpam-4859	20	3	property	property	NOUN
ejpam-4859	20	4	,	,	PUNCT
ejpam-4859	20	5	a	a	DET
ejpam-4859	20	6	replicator	replicator	NOUN
ejpam-4859	20	7	equation	equation	NOUN
ejpam-4859	20	8	captures	capture	VERB
ejpam-4859	20	9	the	the	DET
ejpam-4859	20	10	essence	essence	NOUN
ejpam-4859	20	11	of	of	ADP
ejpam-4859	20	12	natural	natural	ADJ
ejpam-4859	20	13	selection	selection	NOUN
ejpam-4859	20	14	so	so	SCONJ
ejpam-4859	20	15	that	that	SCONJ
ejpam-4859	20	16	traits	trait	NOUN
ejpam-4859	20	17	that	that	PRON
ejpam-4859	20	18	favor	favor	VERB
ejpam-4859	20	19	survival	survival	NOUN
ejpam-4859	20	20	and	and	CCONJ
ejpam-4859	20	21	reproduction	reproduction	NOUN
ejpam-4859	20	22	(	(	PUNCT
ejpam-4859	20	23	i.e.	i.e.	X
ejpam-4859	20	24	,	,	PUNCT
ejpam-4859	20	25	having	have	VERB
ejpam-4859	20	26	higher	high	ADJ
ejpam-4859	20	27	fitness	fitness	NOUN
ejpam-4859	20	28	or	or	CCONJ
ejpam-4859	20	29	reproductive	reproductive	ADJ
ejpam-4859	20	30	success	success	NOUN
ejpam-4859	20	31	)	)	PUNCT
ejpam-4859	20	32	contribute	contribute	VERB
ejpam-4859	20	33	to	to	PART
ejpam-4859	20	34	increase	increase	VERB
ejpam-4859	20	35	in	in	ADP
ejpam-4859	20	36	size	size	NOUN
ejpam-4859	20	37	over	over	ADP
ejpam-4859	20	38	generations	generation	NOUN
ejpam-4859	20	39	.	.	PUNCT
ejpam-4859	21	1	payoffs	payoff	NOUN
ejpam-4859	21	2	are	be	AUX
ejpam-4859	21	3	translated	translate	VERB
ejpam-4859	21	4	as	as	ADP
ejpam-4859	21	5	fitness	fitness	NOUN
ejpam-4859	21	6	so	so	SCONJ
ejpam-4859	21	7	that	that	SCONJ
ejpam-4859	21	8	over	over	ADP
ejpam-4859	21	9	time	time	NOUN
ejpam-4859	21	10	the	the	DET
ejpam-4859	21	11	change	change	NOUN
ejpam-4859	21	12	in	in	ADP
ejpam-4859	21	13	the	the	DET
ejpam-4859	21	14	frequency	frequency	NOUN
ejpam-4859	21	15	of	of	ADP
ejpam-4859	21	16	a	a	DET
ejpam-4859	21	17	strategy	strategy	NOUN
ejpam-4859	21	18	in	in	ADP
ejpam-4859	21	19	a	a	DET
ejpam-4859	21	20	large	large	ADJ
ejpam-4859	21	21	,	,	PUNCT
ejpam-4859	21	22	well	well	ADV
ejpam-4859	21	23	-	-	PUNCT
ejpam-4859	21	24	mixed	mix	VERB
ejpam-4859	21	25	population	population	NOUN
ejpam-4859	21	26	is	be	AUX
ejpam-4859	21	27	described	describe	VERB
ejpam-4859	21	28	through	through	ADP
ejpam-4859	21	29	the	the	DET
ejpam-4859	21	30	replicator	replicator	NOUN
ejpam-4859	21	31	equation	equation	NOUN
ejpam-4859	21	32	.	.	PUNCT
ejpam-4859	22	1	this	this	DET
ejpam-4859	22	2	rate	rate	NOUN
ejpam-4859	22	3	is	be	AUX
ejpam-4859	22	4	described	describe	VERB
ejpam-4859	22	5	as	as	ADP
ejpam-4859	22	6	the	the	DET
ejpam-4859	22	7	product	product	NOUN
ejpam-4859	22	8	of	of	ADP
ejpam-4859	22	9	the	the	DET
ejpam-4859	22	10	proportion	proportion	NOUN
ejpam-4859	22	11	of	of	ADP
ejpam-4859	22	12	this	this	DET
ejpam-4859	22	13	species	specie	NOUN
ejpam-4859	22	14	and	and	CCONJ
ejpam-4859	22	15	the	the	DET
ejpam-4859	22	16	difference	difference	NOUN
ejpam-4859	22	17	between	between	ADP
ejpam-4859	22	18	its	its	PRON
ejpam-4859	22	19	expected	expect	VERB
ejpam-4859	22	20	payoff	payoff	NOUN
ejpam-4859	22	21	and	and	CCONJ
ejpam-4859	22	22	the	the	DET
ejpam-4859	22	23	average	average	ADJ
ejpam-4859	22	24	payoff	payoff	NOUN
ejpam-4859	22	25	of	of	ADP
ejpam-4859	22	26	the	the	DET
ejpam-4859	22	27	population	population	NOUN
ejpam-4859	22	28	[	[	X
ejpam-4859	22	29	3	3	NUM
ejpam-4859	22	30	]	]	PUNCT
ejpam-4859	22	31	.	.	PUNCT
ejpam-4859	23	1	veloz	veloz	PROPN
ejpam-4859	23	2	et	et	PROPN
ejpam-4859	23	3	al	al	PROPN
ejpam-4859	23	4	.	.	PUNCT
ejpam-4859	24	1	[	[	X
ejpam-4859	24	2	9	9	NUM
ejpam-4859	24	3	]	]	PUNCT
ejpam-4859	24	4	proposed	propose	VERB
ejpam-4859	24	5	a	a	DET
ejpam-4859	24	6	manner	manner	NOUN
ejpam-4859	24	7	of	of	ADP
ejpam-4859	24	8	analyzing	analyze	VERB
ejpam-4859	24	9	the	the	DET
ejpam-4859	24	10	dynamics	dynamic	NOUN
ejpam-4859	24	11	of	of	ADP
ejpam-4859	24	12	egt	egt	PROPN
ejpam-4859	24	13	games	game	NOUN
ejpam-4859	24	14	using	use	VERB
ejpam-4859	24	15	chemical	chemical	NOUN
ejpam-4859	24	16	reaction	reaction	NOUN
ejpam-4859	24	17	network	network	NOUN
ejpam-4859	24	18	.	.	PUNCT
ejpam-4859	25	1	from	from	ADP
ejpam-4859	25	2	this	this	DET
ejpam-4859	25	3	vantage	vantage	NOUN
ejpam-4859	25	4	point	point	NOUN
ejpam-4859	25	5	,	,	PUNCT
ejpam-4859	25	6	an	an	DET
ejpam-4859	25	7	encounter	encounter	NOUN
ejpam-4859	25	8	between	between	ADP
ejpam-4859	25	9	two	two	NUM
ejpam-4859	25	10	species	specie	NOUN
ejpam-4859	25	11	is	be	AUX
ejpam-4859	25	12	treated	treat	VERB
ejpam-4859	25	13	as	as	ADP
ejpam-4859	25	14	a	a	DET
ejpam-4859	25	15	reaction	reaction	NOUN
ejpam-4859	25	16	that	that	PRON
ejpam-4859	25	17	results	result	VERB
ejpam-4859	25	18	in	in	ADP
ejpam-4859	25	19	a	a	DET
ejpam-4859	25	20	gain	gain	NOUN
ejpam-4859	25	21	or	or	CCONJ
ejpam-4859	25	22	loss	loss	NOUN
ejpam-4859	25	23	(	(	PUNCT
ejpam-4859	25	24	i.e.	i.e.	X
ejpam-4859	25	25	payoff	payoff	NOUN
ejpam-4859	25	26	)	)	PUNCT
ejpam-4859	25	27	for	for	ADP
ejpam-4859	25	28	each	each	DET
ejpam-4859	25	29	species	specie	NOUN
ejpam-4859	25	30	.	.	PUNCT
ejpam-4859	26	1	they	they	PRON
ejpam-4859	26	2	introduced	introduce	VERB
ejpam-4859	26	3	a	a	DET
ejpam-4859	26	4	set	set	NOUN
ejpam-4859	26	5	of	of	ADP
ejpam-4859	26	6	polynomial	polynomial	ADJ
ejpam-4859	26	7	kinetics	kinetic	NOUN
ejpam-4859	26	8	for	for	ADP
ejpam-4859	26	9	the	the	DET
ejpam-4859	26	10	realization	realization	NOUN
ejpam-4859	26	11	of	of	ADP
ejpam-4859	26	12	replicator	replicator	NOUN
ejpam-4859	26	13	system	system	NOUN
ejpam-4859	26	14	-	-	PUNCT
ejpam-4859	26	15	based	base	VERB
ejpam-4859	26	16	evolutionary	evolutionary	ADJ
ejpam-4859	26	17	games	game	NOUN
ejpam-4859	26	18	with	with	ADP
ejpam-4859	26	19	polynomial	polynomial	ADJ
ejpam-4859	26	20	payoff	payoff	NOUN
ejpam-4859	26	21	functions	function	NOUN
ejpam-4859	26	22	(	(	PUNCT
ejpam-4859	26	23	mostly	mostly	ADV
ejpam-4859	26	24	linear	linear	ADJ
ejpam-4859	26	25	functions	function	NOUN
ejpam-4859	26	26	)	)	PUNCT
ejpam-4859	26	27	.	.	PUNCT
ejpam-4859	27	1	the	the	DET
ejpam-4859	27	2	proposed	propose	VERB
ejpam-4859	27	3	analysis	analysis	NOUN
ejpam-4859	27	4	allows	allow	VERB
ejpam-4859	27	5	for	for	ADP
ejpam-4859	27	6	the	the	DET
ejpam-4859	27	7	application	application	NOUN
ejpam-4859	27	8	of	of	ADP
ejpam-4859	27	9	chemical	chemical	ADJ
ejpam-4859	27	10	reactions	reaction	NOUN
ejpam-4859	27	11	network	network	NOUN
ejpam-4859	27	12	theory	theory	NOUN
ejpam-4859	27	13	(	(	PUNCT
ejpam-4859	27	14	crnt	crnt	PROPN
ejpam-4859	27	15	)	)	PUNCT
ejpam-4859	27	16	.	.	PUNCT
ejpam-4859	28	1	crnt	crnt	PROPN
ejpam-4859	28	2	is	be	AUX
ejpam-4859	28	3	an	an	DET
ejpam-4859	28	4	area	area	NOUN
ejpam-4859	28	5	of	of	ADP
ejpam-4859	28	6	applied	apply	VERB
ejpam-4859	28	7	mathematics	mathematic	NOUN
ejpam-4859	28	8	that	that	PRON
ejpam-4859	28	9	attempts	attempt	VERB
ejpam-4859	28	10	to	to	PART
ejpam-4859	28	11	model	model	VERB
ejpam-4859	28	12	the	the	DET
ejpam-4859	28	13	behavior	behavior	NOUN
ejpam-4859	28	14	of	of	ADP
ejpam-4859	28	15	real	real	ADJ
ejpam-4859	28	16	world	world	NOUN
ejpam-4859	28	17	chemical	chemical	NOUN
ejpam-4859	28	18	systems	system	NOUN
ejpam-4859	28	19	.	.	PUNCT
ejpam-4859	29	1	it	it	PRON
ejpam-4859	29	2	aims	aim	VERB
ejpam-4859	29	3	to	to	PART
ejpam-4859	29	4	understand	understand	VERB
ejpam-4859	29	5	connections	connection	NOUN
ejpam-4859	29	6	between	between	ADP
ejpam-4859	29	7	network	network	NOUN
ejpam-4859	29	8	structure	structure	NOUN
ejpam-4859	29	9	and	and	CCONJ
ejpam-4859	29	10	system	system	NOUN
ejpam-4859	29	11	dynamics	dynamic	NOUN
ejpam-4859	29	12	with	with	ADP
ejpam-4859	29	13	mathematical	mathematical	ADJ
ejpam-4859	29	14	methods	method	NOUN
ejpam-4859	29	15	from	from	ADP
ejpam-4859	29	16	graph	graph	NOUN
ejpam-4859	29	17	theory	theory	NOUN
ejpam-4859	29	18	,	,	PUNCT
ejpam-4859	29	19	linear	linear	PROPN
ejpam-4859	29	20	algebra	algebra	PROPN
ejpam-4859	29	21	,	,	PUNCT
ejpam-4859	29	22	group	group	NOUN
ejpam-4859	29	23	theory	theory	NOUN
ejpam-4859	29	24	and	and	CCONJ
ejpam-4859	29	25	the	the	DET
ejpam-4859	29	26	theory	theory	NOUN
ejpam-4859	29	27	of	of	ADP
ejpam-4859	29	28	ordinary	ordinary	ADJ
ejpam-4859	29	29	differential	differential	ADJ
ejpam-4859	29	30	equations	equation	NOUN
ejpam-4859	29	31	.	.	PUNCT
ejpam-4859	30	1	results	result	NOUN
ejpam-4859	30	2	from	from	ADP
ejpam-4859	30	3	mendoza	mendoza	PROPN
ejpam-4859	30	4	et	et	PROPN
ejpam-4859	30	5	al	al	PROPN
ejpam-4859	30	6	.	.	PUNCT
ejpam-4859	31	1	[	[	X
ejpam-4859	31	2	7	7	NUM
ejpam-4859	31	3	]	]	PUNCT
ejpam-4859	31	4	included	include	VERB
ejpam-4859	31	5	the	the	DET
ejpam-4859	31	6	subset	subset	NOUN
ejpam-4859	31	7	of	of	ADP
ejpam-4859	31	8	sums	sum	NOUN
ejpam-4859	31	9	of	of	ADP
ejpam-4859	31	10	power	power	NOUN
ejpam-4859	31	11	law	law	NOUN
ejpam-4859	31	12	kinetics	kinetic	NOUN
ejpam-4859	31	13	.	.	PUNCT
ejpam-4859	32	1	a	a	DET
ejpam-4859	32	2	particular	particular	ADJ
ejpam-4859	32	3	interesting	interesting	ADJ
ejpam-4859	32	4	family	family	NOUN
ejpam-4859	32	5	of	of	ADP
ejpam-4859	32	6	kinetics	kinetic	NOUN
ejpam-4859	32	7	of	of	ADP
ejpam-4859	32	8	this	this	DET
ejpam-4859	32	9	type	type	NOUN
ejpam-4859	32	10	is	be	AUX
ejpam-4859	32	11	the	the	DET
ejpam-4859	32	12	polynomial	polynomial	ADJ
ejpam-4859	32	13	kinetic	kinetic	ADJ
ejpam-4859	32	14	system	system	NOUN
ejpam-4859	32	15	where	where	SCONJ
ejpam-4859	32	16	all	all	DET
ejpam-4859	32	17	exponents	exponent	NOUN
ejpam-4859	32	18	are	be	AUX
ejpam-4859	32	19	non	non	ADJ
ejpam-4859	32	20	-	-	ADJ
ejpam-4859	32	21	negative	negative	ADJ
ejpam-4859	32	22	integers	integer	NOUN
ejpam-4859	32	23	,	,	PUNCT
ejpam-4859	32	24	which	which	PRON
ejpam-4859	32	25	is	be	AUX
ejpam-4859	32	26	a	a	DET
ejpam-4859	32	27	sum	sum	NOUN
ejpam-4859	32	28	of	of	ADP
ejpam-4859	32	29	monomials	monomial	NOUN
ejpam-4859	32	30	with	with	ADP
ejpam-4859	32	31	real	real	ADJ
ejpam-4859	32	32	coefficients	coefficient	NOUN
ejpam-4859	32	33	.	.	PUNCT
ejpam-4859	33	1	the	the	DET
ejpam-4859	33	2	consideration	consideration	NOUN
ejpam-4859	33	3	of	of	ADP
ejpam-4859	33	4	the	the	DET
ejpam-4859	33	5	superset	superset	NOUN
ejpam-4859	33	6	called	call	VERB
ejpam-4859	33	7	poly	poly	ADJ
ejpam-4859	33	8	-	-	PUNCT
ejpam-4859	33	9	pl	pl	NOUN
ejpam-4859	33	10	kinetics	kinetic	NOUN
ejpam-4859	33	11	(	(	PUNCT
ejpam-4859	33	12	pyk	pyk	PROPN
ejpam-4859	33	13	)	)	PUNCT
ejpam-4859	33	14	,	,	PUNCT
ejpam-4859	33	15	i.e.	i.e.	X
ejpam-4859	33	16	of	of	ADP
ejpam-4859	33	17	real	real	ADJ
ejpam-4859	33	18	exponents	exponent	NOUN
ejpam-4859	33	19	instead	instead	ADV
ejpam-4859	33	20	of	of	ADP
ejpam-4859	33	21	just	just	ADV
ejpam-4859	33	22	non	non	ADJ
ejpam-4859	33	23	-	-	ADJ
ejpam-4859	33	24	negative	negative	ADJ
ejpam-4859	33	25	integers	integer	NOUN
ejpam-4859	33	26	,	,	PUNCT
ejpam-4859	33	27	came	come	VERB
ejpam-4859	33	28	from	from	ADP
ejpam-4859	33	29	the	the	DET
ejpam-4859	33	30	observation	observation	NOUN
ejpam-4859	33	31	that	that	SCONJ
ejpam-4859	33	32	“	"	PUNCT
ejpam-4859	33	33	sums	sum	NOUN
ejpam-4859	33	34	of	of	ADP
ejpam-4859	33	35	power	power	NOUN
ejpam-4859	33	36	law	law	NOUN
ejpam-4859	33	37	functions	function	NOUN
ejpam-4859	33	38	”	"	PUNCT
ejpam-4859	33	39	occurred	occur	VERB
ejpam-4859	33	40	in	in	ADP
ejpam-4859	33	41	power	power	NOUN
ejpam-4859	33	42	law	law	NOUN
ejpam-4859	33	43	approximations	approximation	NOUN
ejpam-4859	33	44	of	of	ADP
ejpam-4859	33	45	some	some	DET
ejpam-4859	33	46	carbon	carbon	NOUN
ejpam-4859	33	47	cycle	cycle	NOUN
ejpam-4859	33	48	models	model	NOUN
ejpam-4859	33	49	in	in	ADP
ejpam-4859	33	50	[	[	X
ejpam-4859	33	51	6	6	NUM
ejpam-4859	33	52	]	]	PUNCT
ejpam-4859	33	53	.	.	PUNCT
ejpam-4859	34	1	thus	thus	ADV
ejpam-4859	34	2	,	,	PUNCT
ejpam-4859	34	3	pyk	pyk	PROPN
ejpam-4859	34	4	contains	contain	VERB
ejpam-4859	34	5	the	the	DET
ejpam-4859	34	6	set	set	VERB
ejpam-4859	34	7	plk	plk	NOUN
ejpam-4859	34	8	of	of	ADP
ejpam-4859	34	9	power	power	NOUN
ejpam-4859	34	10	law	law	NOUN
ejpam-4859	34	11	kinetics	kinetic	NOUN
ejpam-4859	34	12	as	as	ADP
ejpam-4859	34	13	mono	mono	NOUN
ejpam-4859	34	14	-	-	PUNCT
ejpam-4859	34	15	pl	pl	NOUN
ejpam-4859	34	16	kinetics	kinetic	NOUN
ejpam-4859	34	17	with	with	ADP
ejpam-4859	34	18	coefficient	coefficient	NOUN
ejpam-4859	34	19	1	1	X
ejpam-4859	34	20	.	.	PUNCT
ejpam-4859	34	21	with	with	ADP
ejpam-4859	34	22	this	this	DET
ejpam-4859	34	23	relationship	relationship	NOUN
ejpam-4859	34	24	and	and	CCONJ
ejpam-4859	34	25	available	available	ADJ
ejpam-4859	34	26	results	result	NOUN
ejpam-4859	34	27	in	in	ADP
ejpam-4859	34	28	plk	plk	PROPN
ejpam-4859	34	29	,	,	PUNCT
ejpam-4859	34	30	we	we	PRON
ejpam-4859	34	31	are	be	AUX
ejpam-4859	34	32	motivated	motivated	ADJ
ejpam-4859	34	33	to	to	PART
ejpam-4859	34	34	analyze	analyze	VERB
ejpam-4859	34	35	pyk	pyk	PROPN
ejpam-4859	34	36	systems	system	NOUN
ejpam-4859	34	37	in	in	ADP
ejpam-4859	34	38	crnt	crnt	PROPN
ejpam-4859	34	39	setting	setting	NOUN
ejpam-4859	34	40	.	.	PUNCT
ejpam-4859	35	1	this	this	PRON
ejpam-4859	35	2	leads	lead	VERB
ejpam-4859	35	3	us	we	PRON
ejpam-4859	35	4	to	to	ADP
ejpam-4859	35	5	an	an	DET
ejpam-4859	35	6	interest	interest	NOUN
ejpam-4859	35	7	in	in	ADP
ejpam-4859	35	8	finding	find	VERB
ejpam-4859	35	9	different	different	ADJ
ejpam-4859	35	10	ways	way	NOUN
ejpam-4859	35	11	to	to	PART
ejpam-4859	35	12	transform	transform	VERB
ejpam-4859	35	13	pyk	pyk	PROPN
ejpam-4859	35	14	to	to	ADP
ejpam-4859	35	15	plk	plk	PROPN
ejpam-4859	35	16	.	.	PUNCT
ejpam-4859	36	1	the	the	DET
ejpam-4859	36	2	contribution	contribution	NOUN
ejpam-4859	36	3	of	of	ADP
ejpam-4859	36	4	this	this	DET
ejpam-4859	36	5	paper	paper	NOUN
ejpam-4859	36	6	is	be	AUX
ejpam-4859	36	7	to	to	PART
ejpam-4859	36	8	explore	explore	VERB
ejpam-4859	36	9	some	some	DET
ejpam-4859	36	10	approaches	approach	NOUN
ejpam-4859	36	11	for	for	ADP
ejpam-4859	36	12	crnt	crnt	ADJ
ejpam-4859	36	13	analysis	analysis	NOUN
ejpam-4859	36	14	of	of	ADP
ejpam-4859	36	15	pyk	pyk	PROPN
ejpam-4859	36	16	systems	system	NOUN
ejpam-4859	36	17	specifically	specifically	ADV
ejpam-4859	36	18	via	via	ADP
ejpam-4859	36	19	dynamic	dynamic	ADJ
ejpam-4859	36	20	equivalence	equivalence	NOUN
ejpam-4859	36	21	to	to	ADP
ejpam-4859	36	22	power	power	NOUN
ejpam-4859	36	23	kinetic	kinetic	NOUN
ejpam-4859	36	24	systems	system	NOUN
ejpam-4859	36	25	using	use	VERB
ejpam-4859	36	26	s	s	PART
ejpam-4859	36	27	-	-	PUNCT
ejpam-4859	36	28	invariant	invariant	ADJ
ejpam-4859	36	29	term	term	NOUN
ejpam-4859	36	30	-	-	PUNCT
ejpam-4859	36	31	wise	wise	ADJ
ejpam-4859	36	32	addition	addition	NOUN
ejpam-4859	36	33	of	of	ADP
ejpam-4859	36	34	reactions	reaction	NOUN
ejpam-4859	36	35	(	(	PUNCT
ejpam-4859	36	36	star	star	NOUN
ejpam-4859	36	37	)	)	PUNCT
ejpam-4859	36	38	approach	approach	NOUN
ejpam-4859	36	39	.	.	PUNCT
ejpam-4859	37	1	a	a	DET
ejpam-4859	37	2	star	star	NOUN
ejpam-4859	37	3	method	method	NOUN
ejpam-4859	37	4	introduces	introduce	VERB
ejpam-4859	37	5	additional	additional	ADJ
ejpam-4859	37	6	different	different	ADJ
ejpam-4859	37	7	reaction(s	reaction(s	NOUN
ejpam-4859	37	8	)	)	PUNCT
ejpam-4859	37	9	for	for	ADP
ejpam-4859	37	10	each	each	PRON
ejpam-4859	37	11	of	of	ADP
ejpam-4859	37	12	the	the	DET
ejpam-4859	37	13	identical	identical	ADJ
ejpam-4859	37	14	reaction	reaction	NOUN
ejpam-4859	37	15	vectors	vector	NOUN
ejpam-4859	37	16	in	in	ADP
ejpam-4859	37	17	the	the	DET
ejpam-4859	37	18	sum	sum	NOUN
ejpam-4859	37	19	.	.	PUNCT
ejpam-4859	38	1	2	2	X
ejpam-4859	38	2	.	.	NUM
ejpam-4859	38	3	preliminaries	preliminary	NOUN
ejpam-4859	38	4	2.1	2.1	NUM
ejpam-4859	38	5	.	.	PUNCT
ejpam-4859	38	6	basic	basic	ADJ
ejpam-4859	38	7	concepts	concept	NOUN
ejpam-4859	38	8	on	on	ADP
ejpam-4859	38	9	chemical	chemical	ADJ
ejpam-4859	38	10	reaction	reaction	NOUN
ejpam-4859	38	11	network	network	NOUN
ejpam-4859	38	12	theory	theory	NOUN
ejpam-4859	38	13	(	(	PUNCT
ejpam-4859	38	14	crnt	crnt	PROPN
ejpam-4859	38	15	)	)	PUNCT
ejpam-4859	38	16	we	we	PRON
ejpam-4859	38	17	begin	begin	VERB
ejpam-4859	38	18	by	by	ADP
ejpam-4859	38	19	defining	define	VERB
ejpam-4859	38	20	concepts	concept	NOUN
ejpam-4859	38	21	related	relate	VERB
ejpam-4859	38	22	to	to	ADP
ejpam-4859	38	23	chemical	chemical	ADJ
ejpam-4859	38	24	reaction	reaction	NOUN
ejpam-4859	38	25	network	network	NOUN
ejpam-4859	38	26	.	.	PUNCT
ejpam-4859	39	1	these	these	PRON
ejpam-4859	39	2	were	be	AUX
ejpam-4859	39	3	taken	take	VERB
ejpam-4859	39	4	from	from	ADP
ejpam-4859	39	5	the	the	DET
ejpam-4859	39	6	phd	phd	NOUN
ejpam-4859	39	7	thesis	thesis	NOUN
ejpam-4859	39	8	of	of	ADP
ejpam-4859	39	9	boros	boro	NOUN
ejpam-4859	39	10	[	[	X
ejpam-4859	39	11	2	2	NUM
ejpam-4859	39	12	]	]	PUNCT
ejpam-4859	39	13	.	.	PUNCT
ejpam-4859	40	1	definition	definition	NOUN
ejpam-4859	40	2	1	1	NUM
ejpam-4859	40	3	.	.	PUNCT
ejpam-4859	41	1	let	let	VERB
ejpam-4859	41	2	s	s	PRON
ejpam-4859	41	3	be	be	AUX
ejpam-4859	41	4	a	a	DET
ejpam-4859	41	5	non	non	ADJ
ejpam-4859	41	6	-	-	ADJ
ejpam-4859	41	7	empty	empty	ADJ
ejpam-4859	41	8	finite	finite	NOUN
ejpam-4859	41	9	set	set	NOUN
ejpam-4859	41	10	of	of	ADP
ejpam-4859	41	11	chemical	chemical	ADJ
ejpam-4859	41	12	species	specie	NOUN
ejpam-4859	41	13	.	.	PUNCT
ejpam-4859	42	1	a	a	DET
ejpam-4859	42	2	chemical	chemical	NOUN
ejpam-4859	42	3	complex	complex	NOUN
ejpam-4859	42	4	is	be	AUX
ejpam-4859	42	5	a	a	DET
ejpam-4859	42	6	linear	linear	ADJ
ejpam-4859	42	7	combination	combination	NOUN
ejpam-4859	42	8	of	of	ADP
ejpam-4859	42	9	the	the	DET
ejpam-4859	42	10	species	specie	NOUN
ejpam-4859	42	11	with	with	ADP
ejpam-4859	42	12	non	non	ADJ
ejpam-4859	42	13	-	-	ADJ
ejpam-4859	42	14	negative	negative	ADJ
ejpam-4859	42	15	integer	integer	NOUN
ejpam-4859	42	16	coefficients	coefficient	NOUN
ejpam-4859	42	17	called	call	VERB
ejpam-4859	42	18	d.	d.	PROPN
ejpam-4859	42	19	magpantay	magpantay	PROPN
ejpam-4859	42	20	/	/	SYM
ejpam-4859	42	21	eur	eur	PROPN
ejpam-4859	42	22	.	.	PUNCT
ejpam-4859	43	1	j.	j.	PROPN
ejpam-4859	43	2	pure	pure	PROPN
ejpam-4859	43	3	appl	appl	PROPN
ejpam-4859	43	4	.	.	PROPN
ejpam-4859	43	5	math	math	PROPN
ejpam-4859	43	6	,	,	PUNCT
ejpam-4859	43	7	16	16	NUM
ejpam-4859	43	8	(	(	PUNCT
ejpam-4859	43	9	4	4	NUM
ejpam-4859	43	10	)	)	PUNCT
ejpam-4859	43	11	(	(	PUNCT
ejpam-4859	43	12	2023	2023	NUM
ejpam-4859	43	13	)	)	PUNCT
ejpam-4859	43	14	,	,	PUNCT
ejpam-4859	43	15	2557	2557	NUM
ejpam-4859	43	16	-	-	SYM
ejpam-4859	43	17	2580	2580	NUM
ejpam-4859	43	18	2559	2559	NUM
ejpam-4859	43	19	stoichiometric	stoichiometric	ADJ
ejpam-4859	43	20	coefficients	coefficient	NOUN
ejpam-4859	43	21	.	.	PUNCT
ejpam-4859	44	1	the	the	DET
ejpam-4859	44	2	set	set	NOUN
ejpam-4859	44	3	of	of	ADP
ejpam-4859	44	4	complexes	complex	NOUN
ejpam-4859	44	5	is	be	AUX
ejpam-4859	44	6	denoted	denote	VERB
ejpam-4859	44	7	by	by	ADP
ejpam-4859	44	8	c	c	PROPN
ejpam-4859	44	9	.	.	PUNCT
ejpam-4859	45	1	we	we	PRON
ejpam-4859	45	2	reserve	reserve	VERB
ejpam-4859	45	3	m	m	VERB
ejpam-4859	45	4	to	to	PART
ejpam-4859	45	5	denote	denote	VERB
ejpam-4859	45	6	the	the	DET
ejpam-4859	45	7	number	number	NOUN
ejpam-4859	45	8	of	of	ADP
ejpam-4859	45	9	species	specie	NOUN
ejpam-4859	45	10	and	and	CCONJ
ejpam-4859	45	11	n	n	NOUN
ejpam-4859	45	12	to	to	PART
ejpam-4859	45	13	denote	denote	VERB
ejpam-4859	45	14	the	the	DET
ejpam-4859	45	15	number	number	NOUN
ejpam-4859	45	16	of	of	ADP
ejpam-4859	45	17	complexes	complex	NOUN
ejpam-4859	45	18	.	.	PUNCT
ejpam-4859	46	1	a	a	DET
ejpam-4859	46	2	complex	complex	NOUN
ejpam-4859	46	3	is	be	AUX
ejpam-4859	46	4	called	call	VERB
ejpam-4859	46	5	monospecies	monospecie	NOUN
ejpam-4859	46	6	if	if	SCONJ
ejpam-4859	46	7	it	it	PRON
ejpam-4859	46	8	consists	consist	VERB
ejpam-4859	46	9	of	of	ADP
ejpam-4859	46	10	only	only	ADV
ejpam-4859	46	11	one	one	NUM
ejpam-4859	46	12	species	specie	NOUN
ejpam-4859	46	13	,	,	PUNCT
ejpam-4859	46	14	i.e.	i.e.	X
ejpam-4859	46	15	of	of	ADP
ejpam-4859	46	16	the	the	DET
ejpam-4859	46	17	form	form	NOUN
ejpam-4859	46	18	kai	kai	PROPN
ejpam-4859	46	19	,	,	PUNCT
ejpam-4859	46	20	k	k	PROPN
ejpam-4859	46	21	a	a	DET
ejpam-4859	46	22	non	non	ADJ
ejpam-4859	46	23	-	-	ADJ
ejpam-4859	46	24	negative	negative	ADJ
ejpam-4859	46	25	integer	integer	NOUN
ejpam-4859	46	26	and	and	CCONJ
ejpam-4859	46	27	ai	ai	VERB
ejpam-4859	46	28	a	a	DET
ejpam-4859	46	29	species	specie	NOUN
ejpam-4859	46	30	.	.	PUNCT
ejpam-4859	47	1	it	it	PRON
ejpam-4859	47	2	is	be	AUX
ejpam-4859	47	3	called	call	VERB
ejpam-4859	47	4	monomolecular	monomolecular	ADJ
ejpam-4859	47	5	if	if	SCONJ
ejpam-4859	47	6	k	k	PROPN
ejpam-4859	47	7	=	=	SYM
ejpam-4859	47	8	1	1	NUM
ejpam-4859	47	9	,	,	PUNCT
ejpam-4859	47	10	and	and	CCONJ
ejpam-4859	47	11	is	be	AUX
ejpam-4859	47	12	identified	identify	VERB
ejpam-4859	47	13	with	with	ADP
ejpam-4859	47	14	the	the	DET
ejpam-4859	47	15	zero	zero	NUM
ejpam-4859	47	16	complex	complex	NOUN
ejpam-4859	47	17	for	for	ADP
ejpam-4859	47	18	k	k	PROPN
ejpam-4859	47	19	=	=	PUNCT
ejpam-4859	47	20	0	0	PROPN
ejpam-4859	47	21	.	.	PUNCT
ejpam-4859	48	1	a	a	DET
ejpam-4859	48	2	zero	zero	NUM
ejpam-4859	48	3	complex	complex	NOUN
ejpam-4859	48	4	represents	represent	VERB
ejpam-4859	48	5	the	the	DET
ejpam-4859	48	6	”	"	PUNCT
ejpam-4859	48	7	outside	outside	NOUN
ejpam-4859	48	8	”	"	PUNCT
ejpam-4859	48	9	of	of	ADP
ejpam-4859	48	10	the	the	DET
ejpam-4859	48	11	system	system	NOUN
ejpam-4859	48	12	studied	study	VERB
ejpam-4859	48	13	,	,	PUNCT
ejpam-4859	48	14	from	from	ADP
ejpam-4859	48	15	which	which	PRON
ejpam-4859	48	16	chemicals	chemical	NOUN
ejpam-4859	48	17	can	can	AUX
ejpam-4859	48	18	flow	flow	VERB
ejpam-4859	48	19	into	into	ADP
ejpam-4859	48	20	the	the	DET
ejpam-4859	48	21	system	system	NOUN
ejpam-4859	48	22	at	at	ADP
ejpam-4859	48	23	a	a	DET
ejpam-4859	48	24	constant	constant	ADJ
ejpam-4859	48	25	rate	rate	NOUN
ejpam-4859	48	26	and	and	CCONJ
ejpam-4859	48	27	to	to	ADP
ejpam-4859	48	28	which	which	PRON
ejpam-4859	48	29	they	they	PRON
ejpam-4859	48	30	can	can	AUX
ejpam-4859	48	31	flow	flow	VERB
ejpam-4859	48	32	out	out	ADP
ejpam-4859	48	33	at	at	ADP
ejpam-4859	48	34	a	a	DET
ejpam-4859	48	35	linear	linear	ADJ
ejpam-4859	48	36	rate	rate	NOUN
ejpam-4859	48	37	(	(	PUNCT
ejpam-4859	48	38	proportional	proportional	ADJ
ejpam-4859	48	39	to	to	ADP
ejpam-4859	48	40	the	the	DET
ejpam-4859	48	41	concentration	concentration	NOUN
ejpam-4859	48	42	of	of	ADP
ejpam-4859	48	43	the	the	DET
ejpam-4859	48	44	species	specie	NOUN
ejpam-4859	48	45	)	)	PUNCT
ejpam-4859	48	46	.	.	PUNCT
ejpam-4859	49	1	in	in	ADP
ejpam-4859	49	2	biological	biological	ADJ
ejpam-4859	49	3	systems	system	NOUN
ejpam-4859	49	4	,	,	PUNCT
ejpam-4859	49	5	the	the	DET
ejpam-4859	49	6	”	"	PUNCT
ejpam-4859	49	7	outside	outside	NOUN
ejpam-4859	49	8	”	"	PUNCT
ejpam-4859	49	9	also	also	ADV
ejpam-4859	49	10	stands	stand	VERB
ejpam-4859	49	11	for	for	ADP
ejpam-4859	49	12	the	the	DET
ejpam-4859	49	13	degradation	degradation	NOUN
ejpam-4859	49	14	of	of	ADP
ejpam-4859	49	15	a	a	DET
ejpam-4859	49	16	species	specie	NOUN
ejpam-4859	49	17	.	.	PUNCT
ejpam-4859	50	1	an	an	DET
ejpam-4859	50	2	inflow	inflow	NOUN
ejpam-4859	50	3	reaction	reaction	NOUN
ejpam-4859	50	4	is	be	AUX
ejpam-4859	50	5	a	a	DET
ejpam-4859	50	6	reaction	reaction	NOUN
ejpam-4859	50	7	with	with	ADP
ejpam-4859	50	8	source	source	NOUN
ejpam-4859	50	9	“	"	PUNCT
ejpam-4859	50	10	0	0	NUM
ejpam-4859	50	11	”	"	PUNCT
ejpam-4859	50	12	and	and	CCONJ
ejpam-4859	50	13	an	an	DET
ejpam-4859	50	14	outflow	outflow	ADJ
ejpam-4859	50	15	reaction	reaction	NOUN
ejpam-4859	50	16	is	be	AUX
ejpam-4859	50	17	a	a	DET
ejpam-4859	50	18	reaction	reaction	NOUN
ejpam-4859	50	19	with	with	ADP
ejpam-4859	50	20	a	a	DET
ejpam-4859	50	21	monomolecular	monomolecular	ADJ
ejpam-4859	50	22	complex	complex	NOUN
ejpam-4859	50	23	as	as	ADP
ejpam-4859	50	24	source	source	NOUN
ejpam-4859	50	25	and	and	CCONJ
ejpam-4859	50	26	the	the	DET
ejpam-4859	50	27	zero	zero	NUM
ejpam-4859	50	28	complex	complex	NOUN
ejpam-4859	50	29	as	as	ADP
ejpam-4859	50	30	target	target	NOUN
ejpam-4859	50	31	.	.	PUNCT
ejpam-4859	51	1	definition	definition	NOUN
ejpam-4859	51	2	2	2	NUM
ejpam-4859	51	3	.	.	PUNCT
ejpam-4859	52	1	the	the	DET
ejpam-4859	52	2	set	set	NOUN
ejpam-4859	52	3	of	of	ADP
ejpam-4859	52	4	reactions	reaction	NOUN
ejpam-4859	52	5	r	r	NOUN
ejpam-4859	52	6	is	be	AUX
ejpam-4859	52	7	a	a	DET
ejpam-4859	52	8	non	non	ADJ
ejpam-4859	52	9	-	-	ADJ
ejpam-4859	52	10	empty	empty	ADJ
ejpam-4859	52	11	subset	subset	NOUN
ejpam-4859	52	12	of	of	ADP
ejpam-4859	52	13	c	c	PROPN
ejpam-4859	52	14	×	×	PROPN
ejpam-4859	52	15	c	c	NOUN
ejpam-4859	52	16	such	such	ADJ
ejpam-4859	52	17	that	that	SCONJ
ejpam-4859	52	18	(	(	PUNCT
ejpam-4859	52	19	a	a	NOUN
ejpam-4859	52	20	)	)	PUNCT
ejpam-4859	52	21	(	(	PUNCT
ejpam-4859	52	22	y	y	PROPN
ejpam-4859	52	23	,	,	PUNCT
ejpam-4859	52	24	y	y	PROPN
ejpam-4859	52	25	)	)	PUNCT
ejpam-4859	52	26	/∈	/∈	PUNCT
ejpam-4859	53	1	r	r	NOUN
ejpam-4859	53	2	,	,	PUNCT
ejpam-4859	53	3	for	for	ADP
ejpam-4859	53	4	all	all	DET
ejpam-4859	53	5	y	y	PROPN
ejpam-4859	53	6	∈	∈	PROPN
ejpam-4859	53	7	c	c	NOUN
ejpam-4859	53	8	;	;	PUNCT
ejpam-4859	53	9	and	and	CCONJ
ejpam-4859	53	10	(	(	PUNCT
ejpam-4859	53	11	b	b	NOUN
ejpam-4859	53	12	)	)	PUNCT
ejpam-4859	53	13	for	for	ADP
ejpam-4859	53	14	each	each	DET
ejpam-4859	53	15	y	y	PROPN
ejpam-4859	53	16	∈	∈	PROPN
ejpam-4859	53	17	c	c	NOUN
ejpam-4859	53	18	,	,	PUNCT
ejpam-4859	53	19	there	there	PRON
ejpam-4859	53	20	exists	exist	VERB
ejpam-4859	53	21	a	a	DET
ejpam-4859	53	22	y′	y′	NOUN
ejpam-4859	53	23	∈	∈	NOUN
ejpam-4859	53	24	c	c	NOUN
ejpam-4859	53	25	such	such	ADJ
ejpam-4859	53	26	that	that	PRON
ejpam-4859	53	27	(	(	PUNCT
ejpam-4859	53	28	y′	y′	NUM
ejpam-4859	53	29	,	,	PUNCT
ejpam-4859	53	30	y	y	NOUN
ejpam-4859	53	31	)	)	PUNCT
ejpam-4859	53	32	∈	∈	PROPN
ejpam-4859	53	33	r	r	NOUN
ejpam-4859	53	34	or	or	CCONJ
ejpam-4859	53	35	such	such	ADJ
ejpam-4859	53	36	that	that	SCONJ
ejpam-4859	53	37	(	(	PUNCT
ejpam-4859	53	38	y	y	NOUN
ejpam-4859	53	39	,	,	PUNCT
ejpam-4859	53	40	y′	y′	NUM
ejpam-4859	53	41	)	)	PUNCT
ejpam-4859	54	1	∈	∈	PROPN
ejpam-4859	54	2	r.	r.	NOUN
ejpam-4859	54	3	we	we	PRON
ejpam-4859	54	4	denote	denote	VERB
ejpam-4859	54	5	r	r	NOUN
ejpam-4859	54	6	as	as	ADP
ejpam-4859	54	7	|r|	|r|	NOUN
ejpam-4859	54	8	or	or	CCONJ
ejpam-4859	54	9	the	the	DET
ejpam-4859	54	10	number	number	NOUN
ejpam-4859	54	11	of	of	ADP
ejpam-4859	54	12	reactions	reaction	NOUN
ejpam-4859	54	13	.	.	PUNCT
ejpam-4859	55	1	for	for	ADP
ejpam-4859	55	2	each	each	PRON
ejpam-4859	55	3	(	(	PUNCT
ejpam-4859	55	4	y	y	PROPN
ejpam-4859	55	5	,	,	PUNCT
ejpam-4859	55	6	y′	y′	NUM
ejpam-4859	55	7	)	)	PUNCT
ejpam-4859	55	8	∈	∈	NOUN
ejpam-4859	55	9	r	r	NOUN
ejpam-4859	55	10	we	we	PRON
ejpam-4859	55	11	say	say	VERB
ejpam-4859	55	12	that	that	SCONJ
ejpam-4859	55	13	a	a	DET
ejpam-4859	55	14	complex	complex	ADJ
ejpam-4859	55	15	y	y	NOUN
ejpam-4859	55	16	reacts	react	VERB
ejpam-4859	55	17	to	to	PART
ejpam-4859	55	18	complex	complex	VERB
ejpam-4859	55	19	y′.	y′.	NOUN
ejpam-4859	55	20	also	also	ADV
ejpam-4859	55	21	,	,	PUNCT
ejpam-4859	55	22	we	we	PRON
ejpam-4859	55	23	can	can	AUX
ejpam-4859	55	24	write	write	VERB
ejpam-4859	55	25	y	y	PROPN
ejpam-4859	55	26	→	→	SYM
ejpam-4859	55	27	y′	y′	NOUN
ejpam-4859	55	28	in	in	ADP
ejpam-4859	55	29	place	place	NOUN
ejpam-4859	55	30	of	of	ADP
ejpam-4859	55	31	(	(	PUNCT
ejpam-4859	55	32	y	y	PROPN
ejpam-4859	55	33	,	,	PUNCT
ejpam-4859	55	34	y′	y′	NUM
ejpam-4859	55	35	)	)	PUNCT
ejpam-4859	55	36	.	.	PUNCT
ejpam-4859	56	1	in	in	ADP
ejpam-4859	56	2	this	this	DET
ejpam-4859	56	3	paper	paper	NOUN
ejpam-4859	56	4	,	,	PUNCT
ejpam-4859	56	5	the	the	DET
ejpam-4859	56	6	notations	notation	NOUN
ejpam-4859	56	7	(	(	PUNCT
ejpam-4859	56	8	y	y	NOUN
ejpam-4859	56	9	,	,	PUNCT
ejpam-4859	56	10	y′	y′	NUM
ejpam-4859	56	11	)	)	PUNCT
ejpam-4859	56	12	or	or	CCONJ
ejpam-4859	56	13	y	y	PROPN
ejpam-4859	56	14	→	→	SYM
ejpam-4859	56	15	y′	y′	NOUN
ejpam-4859	56	16	are	be	AUX
ejpam-4859	56	17	used	use	VERB
ejpam-4859	56	18	interchangeably	interchangeably	ADV
ejpam-4859	56	19	and	and	CCONJ
ejpam-4859	56	20	we	we	PRON
ejpam-4859	56	21	say	say	VERB
ejpam-4859	56	22	that	that	SCONJ
ejpam-4859	56	23	y	y	PROPN
ejpam-4859	56	24	is	be	AUX
ejpam-4859	56	25	the	the	DET
ejpam-4859	56	26	reactant	reactant	NOUN
ejpam-4859	56	27	complex	complex	NOUN
ejpam-4859	56	28	and	and	CCONJ
ejpam-4859	56	29	y′	y′	NOUN
ejpam-4859	56	30	is	be	AUX
ejpam-4859	56	31	the	the	DET
ejpam-4859	56	32	product	product	NOUN
ejpam-4859	56	33	complex	complex	NOUN
ejpam-4859	56	34	of	of	ADP
ejpam-4859	56	35	the	the	DET
ejpam-4859	56	36	reaction	reaction	NOUN
ejpam-4859	56	37	.	.	PUNCT
ejpam-4859	57	1	we	we	PRON
ejpam-4859	57	2	now	now	ADV
ejpam-4859	57	3	formally	formally	ADV
ejpam-4859	57	4	define	define	VERB
ejpam-4859	57	5	a	a	DET
ejpam-4859	57	6	chemical	chemical	ADJ
ejpam-4859	57	7	reaction	reaction	NOUN
ejpam-4859	57	8	network	network	NOUN
ejpam-4859	57	9	.	.	PUNCT
ejpam-4859	58	1	definition	definition	NOUN
ejpam-4859	58	2	3	3	NUM
ejpam-4859	58	3	.	.	PUNCT
ejpam-4859	59	1	a	a	DET
ejpam-4859	59	2	chemical	chemical	NOUN
ejpam-4859	59	3	reaction	reaction	NOUN
ejpam-4859	59	4	network	network	NOUN
ejpam-4859	59	5	(	(	PUNCT
ejpam-4859	59	6	crn	crn	PROPN
ejpam-4859	59	7	)	)	PUNCT
ejpam-4859	59	8	is	be	AUX
ejpam-4859	59	9	a	a	DET
ejpam-4859	59	10	triple	triple	ADJ
ejpam-4859	59	11	n	n	NOUN
ejpam-4859	59	12	=	=	SYM
ejpam-4859	59	13	(	(	PUNCT
ejpam-4859	59	14	s	s	NOUN
ejpam-4859	59	15	,	,	PUNCT
ejpam-4859	59	16	c	c	NOUN
ejpam-4859	59	17	,	,	PUNCT
ejpam-4859	59	18	r	r	NOUN
ejpam-4859	59	19	)	)	PUNCT
ejpam-4859	59	20	of	of	ADP
ejpam-4859	59	21	three	three	NUM
ejpam-4859	59	22	non	non	ADJ
ejpam-4859	59	23	-	-	ADJ
ejpam-4859	59	24	empty	empty	ADJ
ejpam-4859	59	25	finite	finite	ADJ
ejpam-4859	59	26	sets	set	NOUN
ejpam-4859	59	27	,	,	PUNCT
ejpam-4859	59	28	where	where	SCONJ
ejpam-4859	59	29	s	s	NOUN
ejpam-4859	59	30	is	be	AUX
ejpam-4859	59	31	the	the	DET
ejpam-4859	59	32	set	set	NOUN
ejpam-4859	59	33	of	of	ADP
ejpam-4859	59	34	chemical	chemical	NOUN
ejpam-4859	59	35	species	specie	NOUN
ejpam-4859	59	36	,	,	PUNCT
ejpam-4859	59	37	c	c	PROPN
ejpam-4859	59	38	is	be	AUX
ejpam-4859	59	39	the	the	DET
ejpam-4859	59	40	set	set	NOUN
ejpam-4859	59	41	of	of	ADP
ejpam-4859	59	42	chemical	chemical	ADJ
ejpam-4859	59	43	complexes	complex	NOUN
ejpam-4859	59	44	,	,	PUNCT
ejpam-4859	59	45	and	and	CCONJ
ejpam-4859	59	46	r	r	NOUN
ejpam-4859	59	47	is	be	AUX
ejpam-4859	59	48	the	the	DET
ejpam-4859	59	49	set	set	NOUN
ejpam-4859	59	50	of	of	ADP
ejpam-4859	59	51	reactions	reaction	NOUN
ejpam-4859	59	52	.	.	PUNCT
ejpam-4859	60	1	example	example	NOUN
ejpam-4859	61	1	1	1	NUM
ejpam-4859	61	2	.	.	PUNCT
ejpam-4859	61	3	let	let	VERB
ejpam-4859	61	4	n	n	NOUN
ejpam-4859	61	5	=	=	SYM
ejpam-4859	61	6	(	(	PUNCT
ejpam-4859	61	7	s	s	NOUN
ejpam-4859	61	8	,	,	PUNCT
ejpam-4859	61	9	c	c	NOUN
ejpam-4859	61	10	,	,	PUNCT
ejpam-4859	61	11	r	r	NOUN
ejpam-4859	61	12	)	)	PUNCT
ejpam-4859	61	13	be	be	AUX
ejpam-4859	61	14	a	a	DET
ejpam-4859	61	15	chemical	chemical	ADJ
ejpam-4859	61	16	reaction	reaction	NOUN
ejpam-4859	61	17	network	network	NOUN
ejpam-4859	61	18	such	such	ADJ
ejpam-4859	61	19	that	that	PRON
ejpam-4859	61	20	s	s	PART
ejpam-4859	61	21	=	=	NOUN
ejpam-4859	61	22	{	{	PUNCT
ejpam-4859	61	23	a1	a1	PROPN
ejpam-4859	61	24	,	,	PUNCT
ejpam-4859	61	25	a2	a2	PROPN
ejpam-4859	61	26	,	,	PUNCT
ejpam-4859	61	27	a3	a3	NOUN
ejpam-4859	61	28	,	,	PUNCT
ejpam-4859	61	29	a4	a4	NOUN
ejpam-4859	61	30	}	}	PUNCT
ejpam-4859	61	31	c	c	NOUN
ejpam-4859	61	32	=	=	PUNCT
ejpam-4859	61	33	{	{	PUNCT
ejpam-4859	61	34	2a1	2a1	NUM
ejpam-4859	61	35	,	,	PUNCT
ejpam-4859	61	36	a2	a2	PROPN
ejpam-4859	61	37	+	+	PROPN
ejpam-4859	61	38	a3	a3	NOUN
ejpam-4859	61	39	,	,	PUNCT
ejpam-4859	61	40	a3	a3	NOUN
ejpam-4859	61	41	,	,	PUNCT
ejpam-4859	61	42	3a4	3a4	NUM
ejpam-4859	61	43	}	}	PUNCT
ejpam-4859	61	44	r	r	NOUN
ejpam-4859	61	45	=	=	SYM
ejpam-4859	61	46	{	{	PUNCT
ejpam-4859	61	47	2a1	2a1	PROPN
ejpam-4859	61	48	→	→	SYM
ejpam-4859	61	49	a3	a3	NOUN
ejpam-4859	61	50	,	,	PUNCT
ejpam-4859	61	51	a2	a2	PROPN
ejpam-4859	61	52	+	+	PROPN
ejpam-4859	61	53	a3	a3	NOUN
ejpam-4859	61	54	→	→	SYM
ejpam-4859	61	55	a3	a3	NOUN
ejpam-4859	61	56	,	,	PUNCT
ejpam-4859	61	57	a3	a3	NOUN
ejpam-4859	61	58	→	→	SYM
ejpam-4859	61	59	a2	a2	PROPN
ejpam-4859	61	60	+	+	PROPN
ejpam-4859	61	61	a3	a3	NOUN
ejpam-4859	61	62	,	,	PUNCT
ejpam-4859	61	63	3a4	3a4	NUM
ejpam-4859	61	64	→	→	SYM
ejpam-4859	61	65	a2	a2	PROPN
ejpam-4859	61	66	+	+	PROPN
ejpam-4859	61	67	a3	a3	NOUN
ejpam-4859	61	68	,	,	PUNCT
ejpam-4859	61	69	2a1	2a1	NUM
ejpam-4859	61	70	→	→	SYM
ejpam-4859	61	71	3a4	3a4	NUM
ejpam-4859	61	72	}	}	PUNCT
ejpam-4859	61	73	or	or	CCONJ
ejpam-4859	61	74	r	r	NOUN
ejpam-4859	61	75	=	=	SYM
ejpam-4859	61	76	{	{	PUNCT
ejpam-4859	61	77	(	(	PUNCT
ejpam-4859	61	78	2a1	2a1	NUM
ejpam-4859	61	79	,	,	PUNCT
ejpam-4859	61	80	a3	a3	NOUN
ejpam-4859	61	81	)	)	PUNCT
ejpam-4859	61	82	,	,	PUNCT
ejpam-4859	61	83	(	(	PUNCT
ejpam-4859	61	84	a2	a2	PROPN
ejpam-4859	61	85	+	+	NOUN
ejpam-4859	61	86	a3	a3	NOUN
ejpam-4859	61	87	,	,	PUNCT
ejpam-4859	61	88	a3	a3	NOUN
ejpam-4859	61	89	)	)	PUNCT
ejpam-4859	61	90	,	,	PUNCT
ejpam-4859	61	91	(	(	PUNCT
ejpam-4859	61	92	a3	a3	NOUN
ejpam-4859	61	93	,	,	PUNCT
ejpam-4859	61	94	a2	a2	PROPN
ejpam-4859	61	95	+	+	NOUN
ejpam-4859	61	96	a3	a3	NOUN
ejpam-4859	61	97	)	)	PUNCT
ejpam-4859	61	98	,	,	PUNCT
ejpam-4859	61	99	(	(	PUNCT
ejpam-4859	61	100	3a4	3a4	NUM
ejpam-4859	61	101	,	,	PUNCT
ejpam-4859	61	102	a2	a2	PROPN
ejpam-4859	61	103	+	+	NOUN
ejpam-4859	61	104	a3	a3	NOUN
ejpam-4859	61	105	)	)	PUNCT
ejpam-4859	61	106	,	,	PUNCT
ejpam-4859	61	107	(	(	PUNCT
ejpam-4859	61	108	2a1	2a1	NUM
ejpam-4859	61	109	,	,	PUNCT
ejpam-4859	61	110	3a4	3a4	NUM
ejpam-4859	61	111	)	)	PUNCT
ejpam-4859	61	112	}	}	PUNCT
ejpam-4859	61	113	as	as	SCONJ
ejpam-4859	61	114	observed	observe	VERB
ejpam-4859	61	115	,	,	PUNCT
ejpam-4859	61	116	m	m	VERB
ejpam-4859	61	117	=	=	NOUN
ejpam-4859	61	118	4	4	NUM
ejpam-4859	61	119	,	,	PUNCT
ejpam-4859	61	120	n	n	NOUN
ejpam-4859	61	121	=	=	SYM
ejpam-4859	61	122	4	4	NUM
ejpam-4859	61	123	and	and	CCONJ
ejpam-4859	61	124	r	r	NOUN
ejpam-4859	61	125	=	=	SYM
ejpam-4859	61	126	5	5	X
ejpam-4859	61	127	.	.	PUNCT
ejpam-4859	61	128	d.	d.	PROPN
ejpam-4859	61	129	magpantay	magpantay	PROPN
ejpam-4859	61	130	/	/	SYM
ejpam-4859	61	131	eur	eur	PROPN
ejpam-4859	61	132	.	.	PUNCT
ejpam-4859	62	1	j.	j.	PROPN
ejpam-4859	62	2	pure	pure	PROPN
ejpam-4859	62	3	appl	appl	PROPN
ejpam-4859	62	4	.	.	PROPN
ejpam-4859	62	5	math	math	PROPN
ejpam-4859	62	6	,	,	PUNCT
ejpam-4859	62	7	16	16	NUM
ejpam-4859	62	8	(	(	PUNCT
ejpam-4859	62	9	4	4	NUM
ejpam-4859	62	10	)	)	PUNCT
ejpam-4859	62	11	(	(	PUNCT
ejpam-4859	62	12	2023	2023	NUM
ejpam-4859	62	13	)	)	PUNCT
ejpam-4859	62	14	,	,	PUNCT
ejpam-4859	62	15	2557	2557	NUM
ejpam-4859	62	16	-	-	SYM
ejpam-4859	62	17	2580	2580	NUM
ejpam-4859	62	18	2560	2560	NUM
ejpam-4859	62	19	2.2	2.2	NUM
ejpam-4859	62	20	.	.	PUNCT
ejpam-4859	63	1	connectivity	connectivity	NOUN
ejpam-4859	63	2	in	in	ADP
ejpam-4859	63	3	a	a	DET
ejpam-4859	63	4	crn	crn	NOUN
ejpam-4859	63	5	we	we	PRON
ejpam-4859	63	6	first	first	ADV
ejpam-4859	63	7	recall	recall	VERB
ejpam-4859	63	8	some	some	DET
ejpam-4859	63	9	basic	basic	ADJ
ejpam-4859	63	10	concepts	concept	NOUN
ejpam-4859	63	11	of	of	ADP
ejpam-4859	63	12	graph	graph	NOUN
ejpam-4859	63	13	theory	theory	NOUN
ejpam-4859	63	14	.	.	PUNCT
ejpam-4859	64	1	two	two	NUM
ejpam-4859	64	2	vertices	vertice	VERB
ejpam-4859	64	3	y	y	PROPN
ejpam-4859	64	4	and	and	CCONJ
ejpam-4859	64	5	y′	y′	NOUN
ejpam-4859	64	6	are	be	AUX
ejpam-4859	64	7	connected	connect	VERB
ejpam-4859	64	8	if	if	SCONJ
ejpam-4859	64	9	there	there	PRON
ejpam-4859	64	10	is	be	VERB
ejpam-4859	64	11	a	a	DET
ejpam-4859	64	12	path	path	NOUN
ejpam-4859	64	13	between	between	ADP
ejpam-4859	64	14	them	they	PRON
ejpam-4859	64	15	,	,	PUNCT
ejpam-4859	64	16	i.e.	i.e.	X
ejpam-4859	64	17	a	a	DET
ejpam-4859	64	18	sequence	sequence	NOUN
ejpam-4859	64	19	of	of	ADP
ejpam-4859	64	20	adjacent	adjacent	ADJ
ejpam-4859	64	21	vertices	vertex	NOUN
ejpam-4859	64	22	y	y	PROPN
ejpam-4859	64	23	=	=	SYM
ejpam-4859	64	24	y1	y1	PROPN
ejpam-4859	64	25	,	,	PUNCT
ejpam-4859	64	26	y2	y2	PROPN
ejpam-4859	64	27	,	,	PUNCT
ejpam-4859	64	28	·	·	PUNCT
ejpam-4859	64	29	·	·	PUNCT
ejpam-4859	64	30	·	·	PUNCT
ejpam-4859	65	1	yn	yn	X
ejpam-4859	65	2	=	=	PUNCT
ejpam-4859	66	1	y′.	y′.	PROPN
ejpam-4859	66	2	they	they	PRON
ejpam-4859	66	3	are	be	AUX
ejpam-4859	66	4	strongly	strongly	ADV
ejpam-4859	66	5	connected	connect	VERB
ejpam-4859	66	6	if	if	SCONJ
ejpam-4859	66	7	there	there	PRON
ejpam-4859	66	8	is	be	VERB
ejpam-4859	66	9	a	a	DET
ejpam-4859	66	10	directed	direct	VERB
ejpam-4859	66	11	path	path	NOUN
ejpam-4859	66	12	between	between	ADP
ejpam-4859	66	13	y	y	PROPN
ejpam-4859	66	14	and	and	CCONJ
ejpam-4859	66	15	y′	y′	PROPN
ejpam-4859	66	16	and	and	CCONJ
ejpam-4859	66	17	vice	vice	ADV
ejpam-4859	66	18	versa	versa	ADV
ejpam-4859	66	19	.	.	PUNCT
ejpam-4859	67	1	connected	connect	VERB
ejpam-4859	67	2	and	and	CCONJ
ejpam-4859	67	3	strongly	strongly	ADV
ejpam-4859	67	4	connected	connect	VERB
ejpam-4859	67	5	are	be	AUX
ejpam-4859	67	6	equivalence	equivalence	NOUN
ejpam-4859	67	7	relations	relation	NOUN
ejpam-4859	67	8	,	,	PUNCT
ejpam-4859	67	9	and	and	CCONJ
ejpam-4859	67	10	the	the	DET
ejpam-4859	67	11	equivalence	equivalence	NOUN
ejpam-4859	67	12	classes	class	NOUN
ejpam-4859	67	13	are	be	AUX
ejpam-4859	67	14	called	call	VERB
ejpam-4859	67	15	connected	connected	ADJ
ejpam-4859	67	16	components	component	NOUN
ejpam-4859	67	17	and	and	CCONJ
ejpam-4859	67	18	strong	strong	ADJ
ejpam-4859	67	19	connected	connected	ADJ
ejpam-4859	67	20	components	component	NOUN
ejpam-4859	67	21	,	,	PUNCT
ejpam-4859	67	22	respectively	respectively	ADV
ejpam-4859	67	23	.	.	PUNCT
ejpam-4859	68	1	each	each	DET
ejpam-4859	68	2	connected	connected	ADJ
ejpam-4859	68	3	component	component	NOUN
ejpam-4859	68	4	is	be	AUX
ejpam-4859	68	5	clearly	clearly	ADV
ejpam-4859	68	6	the	the	DET
ejpam-4859	68	7	disjoint	disjoint	PROPN
ejpam-4859	68	8	union	union	NOUN
ejpam-4859	68	9	of	of	ADP
ejpam-4859	68	10	strong	strong	ADJ
ejpam-4859	68	11	connected	connected	ADJ
ejpam-4859	68	12	components	component	NOUN
ejpam-4859	68	13	.	.	PUNCT
ejpam-4859	69	1	connectivity	connectivity	NOUN
ejpam-4859	69	2	in	in	ADP
ejpam-4859	69	3	a	a	DET
ejpam-4859	69	4	digraph	digraph	NOUN
ejpam-4859	69	5	that	that	PRON
ejpam-4859	69	6	is	be	AUX
ejpam-4859	69	7	applied	apply	VERB
ejpam-4859	69	8	to	to	ADP
ejpam-4859	69	9	crns	crn	NOUN
ejpam-4859	69	10	is	be	AUX
ejpam-4859	69	11	traditionally	traditionally	ADV
ejpam-4859	69	12	called	call	VERB
ejpam-4859	69	13	a	a	DET
ejpam-4859	69	14	linkage	linkage	NOUN
ejpam-4859	69	15	class	class	NOUN
ejpam-4859	69	16	in	in	ADP
ejpam-4859	69	17	crnt	crnt	PROPN
ejpam-4859	69	18	.	.	PUNCT
ejpam-4859	70	1	we	we	PRON
ejpam-4859	70	2	formally	formally	ADV
ejpam-4859	70	3	define	define	VERB
ejpam-4859	70	4	it	it	PRON
ejpam-4859	70	5	as	as	SCONJ
ejpam-4859	70	6	follows	follow	VERB
ejpam-4859	70	7	:	:	PUNCT
ejpam-4859	70	8	definition	definition	NOUN
ejpam-4859	70	9	4	4	NUM
ejpam-4859	70	10	.	.	PUNCT
ejpam-4859	71	1	a	a	DET
ejpam-4859	71	2	linkage	linkage	NOUN
ejpam-4859	71	3	class	class	NOUN
ejpam-4859	71	4	of	of	ADP
ejpam-4859	71	5	a	a	DET
ejpam-4859	71	6	crn	crn	NOUN
ejpam-4859	71	7	is	be	AUX
ejpam-4859	71	8	a	a	DET
ejpam-4859	71	9	maximal	maximal	ADJ
ejpam-4859	71	10	weakly	weakly	ADJ
ejpam-4859	71	11	connected	connected	ADJ
ejpam-4859	71	12	subgraph	subgraph	NOUN
ejpam-4859	71	13	of	of	ADP
ejpam-4859	71	14	its	its	PRON
ejpam-4859	71	15	reaction	reaction	NOUN
ejpam-4859	71	16	graph	graph	NOUN
ejpam-4859	71	17	.	.	PUNCT
ejpam-4859	72	1	a	a	DET
ejpam-4859	72	2	strong	strong	ADJ
ejpam-4859	72	3	linkage	linkage	NOUN
ejpam-4859	72	4	class	class	NOUN
ejpam-4859	72	5	is	be	AUX
ejpam-4859	72	6	a	a	DET
ejpam-4859	72	7	maximal	maximal	ADJ
ejpam-4859	72	8	strongly	strongly	ADV
ejpam-4859	72	9	connected	connect	VERB
ejpam-4859	72	10	subgraph	subgraph	NOUN
ejpam-4859	72	11	of	of	ADP
ejpam-4859	72	12	the	the	DET
ejpam-4859	72	13	reaction	reaction	NOUN
ejpam-4859	72	14	graph	graph	NOUN
ejpam-4859	72	15	.	.	PUNCT
ejpam-4859	73	1	a	a	DET
ejpam-4859	73	2	terminal	terminal	ADJ
ejpam-4859	73	3	strong	strong	ADJ
ejpam-4859	73	4	linkage	linkage	NOUN
ejpam-4859	73	5	class	class	NOUN
ejpam-4859	73	6	is	be	AUX
ejpam-4859	73	7	a	a	DET
ejpam-4859	73	8	strong	strong	ADJ
ejpam-4859	73	9	linkage	linkage	NOUN
ejpam-4859	73	10	class	class	NOUN
ejpam-4859	73	11	containing	contain	VERB
ejpam-4859	73	12	no	no	DET
ejpam-4859	73	13	complex	complex	NOUN
ejpam-4859	73	14	that	that	PRON
ejpam-4859	73	15	reacts	react	VERB
ejpam-4859	73	16	to	to	ADP
ejpam-4859	73	17	a	a	DET
ejpam-4859	73	18	complex	complex	NOUN
ejpam-4859	73	19	belonging	belong	VERB
ejpam-4859	73	20	to	to	ADP
ejpam-4859	73	21	a	a	DET
ejpam-4859	73	22	different	different	ADJ
ejpam-4859	73	23	strong	strong	ADJ
ejpam-4859	73	24	linkage	linkage	NOUN
ejpam-4859	73	25	class	class	NOUN
ejpam-4859	73	26	.	.	PUNCT
ejpam-4859	73	27	example	example	NOUN
ejpam-4859	74	1	2	2	NUM
ejpam-4859	74	2	.	.	X
ejpam-4859	74	3	note	note	VERB
ejpam-4859	74	4	that	that	SCONJ
ejpam-4859	74	5	for	for	ADP
ejpam-4859	74	6	example	example	NOUN
ejpam-4859	74	7	1	1	NUM
ejpam-4859	74	8	we	we	PRON
ejpam-4859	74	9	have	have	VERB
ejpam-4859	74	10	:	:	PUNCT
ejpam-4859	74	11	1	1	NUM
ejpam-4859	74	12	linkage	linkage	NOUN
ejpam-4859	74	13	class	class	NOUN
ejpam-4859	74	14	:	:	PUNCT
ejpam-4859	74	15	{	{	PUNCT
ejpam-4859	74	16	2a1	2a1	NUM
ejpam-4859	74	17	,	,	PUNCT
ejpam-4859	74	18	a3	a3	NOUN
ejpam-4859	74	19	,	,	PUNCT
ejpam-4859	74	20	a2	a2	PROPN
ejpam-4859	74	21	+	+	PROPN
ejpam-4859	74	22	a3	a3	NOUN
ejpam-4859	74	23	,	,	PUNCT
ejpam-4859	74	24	3a4	3a4	NUM
ejpam-4859	74	25	}	}	PUNCT
ejpam-4859	74	26	;	;	PUNCT
ejpam-4859	74	27	3	3	NUM
ejpam-4859	74	28	strong	strong	ADJ
ejpam-4859	74	29	linkage	linkage	NOUN
ejpam-4859	74	30	classes	class	NOUN
ejpam-4859	74	31	:	:	PUNCT
ejpam-4859	74	32	{	{	PUNCT
ejpam-4859	74	33	a3	a3	NOUN
ejpam-4859	74	34	,	,	PUNCT
ejpam-4859	74	35	a2	a2	PROPN
ejpam-4859	74	36	+	+	NOUN
ejpam-4859	74	37	a3	a3	NOUN
ejpam-4859	74	38	}	}	PUNCT
ejpam-4859	74	39	,	,	PUNCT
ejpam-4859	74	40	{	{	PUNCT
ejpam-4859	74	41	2a1	2a1	NOUN
ejpam-4859	74	42	}	}	PUNCT
ejpam-4859	74	43	and	and	CCONJ
ejpam-4859	74	44	{	{	PUNCT
ejpam-4859	74	45	3a4	3a4	NUM
ejpam-4859	74	46	}	}	PUNCT
ejpam-4859	74	47	;	;	PUNCT
ejpam-4859	74	48	and	and	CCONJ
ejpam-4859	74	49	1	1	NUM
ejpam-4859	74	50	terminal	terminal	ADJ
ejpam-4859	74	51	strong	strong	ADJ
ejpam-4859	74	52	linkage	linkage	NOUN
ejpam-4859	74	53	class	class	NOUN
ejpam-4859	74	54	:	:	PUNCT
ejpam-4859	74	55	{	{	PUNCT
ejpam-4859	74	56	a3	a3	NOUN
ejpam-4859	74	57	,	,	PUNCT
ejpam-4859	74	58	a2	a2	PROPN
ejpam-4859	74	59	+	+	NOUN
ejpam-4859	74	60	a3	a3	NOUN
ejpam-4859	74	61	}	}	PUNCT
ejpam-4859	74	62	.	.	PUNCT
ejpam-4859	75	1	we	we	PRON
ejpam-4859	75	2	denote	denote	VERB
ejpam-4859	75	3	the	the	DET
ejpam-4859	75	4	number	number	NOUN
ejpam-4859	75	5	of	of	ADP
ejpam-4859	75	6	linkage	linkage	NOUN
ejpam-4859	75	7	classes	class	NOUN
ejpam-4859	75	8	with	with	ADP
ejpam-4859	75	9	ℓ	ℓ	PROPN
ejpam-4859	75	10	,	,	PUNCT
ejpam-4859	75	11	that	that	PRON
ejpam-4859	75	12	of	of	ADP
ejpam-4859	75	13	the	the	DET
ejpam-4859	75	14	strong	strong	ADJ
ejpam-4859	75	15	linkage	linkage	NOUN
ejpam-4859	75	16	classes	class	NOUN
ejpam-4859	75	17	with	with	ADP
ejpam-4859	75	18	sℓ	sℓ	NOUN
ejpam-4859	75	19	,	,	PUNCT
ejpam-4859	75	20	and	and	CCONJ
ejpam-4859	75	21	that	that	PRON
ejpam-4859	75	22	of	of	ADP
ejpam-4859	75	23	terminal	terminal	ADJ
ejpam-4859	75	24	strong	strong	ADJ
ejpam-4859	75	25	linkage	linkage	NOUN
ejpam-4859	75	26	classes	class	NOUN
ejpam-4859	75	27	with	with	ADP
ejpam-4859	75	28	t.	t.	PROPN
ejpam-4859	75	29	clearly	clearly	ADV
ejpam-4859	75	30	,	,	PUNCT
ejpam-4859	75	31	ℓ	ℓ	PROPN
ejpam-4859	75	32	≤	≤	PROPN
ejpam-4859	75	33	t	t	PROPN
ejpam-4859	75	34	≤	≤	NUM
ejpam-4859	75	35	sℓ.	sℓ.	PROPN
ejpam-4859	75	36	there	there	PRON
ejpam-4859	75	37	are	be	VERB
ejpam-4859	75	38	two	two	NUM
ejpam-4859	75	39	types	type	NOUN
ejpam-4859	75	40	of	of	ADP
ejpam-4859	75	41	terminal	terminal	ADJ
ejpam-4859	75	42	strong	strong	ADJ
ejpam-4859	75	43	linkage	linkage	NOUN
ejpam-4859	75	44	classes	class	NOUN
ejpam-4859	75	45	in	in	ADP
ejpam-4859	75	46	a	a	DET
ejpam-4859	75	47	crn	crn	NOUN
ejpam-4859	75	48	:	:	PUNCT
ejpam-4859	75	49	cycles	cycle	NOUN
ejpam-4859	75	50	and	and	CCONJ
ejpam-4859	75	51	singletons	singleton	NOUN
ejpam-4859	75	52	(	(	PUNCT
ejpam-4859	75	53	which	which	PRON
ejpam-4859	75	54	are	be	AUX
ejpam-4859	75	55	called	call	VERB
ejpam-4859	75	56	terminal	terminal	ADJ
ejpam-4859	75	57	points	point	NOUN
ejpam-4859	75	58	)	)	PUNCT
ejpam-4859	75	59	.	.	PUNCT
ejpam-4859	76	1	definition	definition	NOUN
ejpam-4859	76	2	5	5	NUM
ejpam-4859	76	3	.	.	PUNCT
ejpam-4859	77	1	a	a	DET
ejpam-4859	77	2	crn	crn	NOUN
ejpam-4859	77	3	is	be	AUX
ejpam-4859	77	4	called	call	VERB
ejpam-4859	77	5	:	:	PUNCT
ejpam-4859	77	6	i	i	NOUN
ejpam-4859	77	7	)	)	PUNCT
ejpam-4859	77	8	point	point	NOUN
ejpam-4859	77	9	terminal	terminal	NOUN
ejpam-4859	77	10	if	if	SCONJ
ejpam-4859	77	11	t	t	NOUN
ejpam-4859	77	12	=	=	SYM
ejpam-4859	77	13	n−	n−	PROPN
ejpam-4859	77	14	nr	nr	PROPN
ejpam-4859	77	15	;	;	PUNCT
ejpam-4859	77	16	ii	ii	NOUN
ejpam-4859	77	17	)	)	PUNCT
ejpam-4859	77	18	weakly	weakly	ADV
ejpam-4859	77	19	reversible	reversible	ADJ
ejpam-4859	77	20	if	if	SCONJ
ejpam-4859	77	21	sℓ	sℓ	ADP
ejpam-4859	77	22	=	=	NOUN
ejpam-4859	77	23	ℓ	ℓ	PROPN
ejpam-4859	77	24	,	,	PUNCT
ejpam-4859	77	25	i.e.	i.e.	X
ejpam-4859	77	26	every	every	DET
ejpam-4859	77	27	linkage	linkage	NOUN
ejpam-4859	77	28	class	class	NOUN
ejpam-4859	77	29	is	be	AUX
ejpam-4859	77	30	a	a	DET
ejpam-4859	77	31	strong	strong	ADJ
ejpam-4859	77	32	linkage	linkage	NOUN
ejpam-4859	77	33	class	class	NOUN
ejpam-4859	77	34	;	;	PUNCT
ejpam-4859	77	35	and	and	CCONJ
ejpam-4859	77	36	iii	iii	X
ejpam-4859	77	37	)	)	PUNCT
ejpam-4859	77	38	t	t	PROPN
ejpam-4859	77	39	-	-	PUNCT
ejpam-4859	77	40	minimal	minimal	ADJ
ejpam-4859	77	41	if	if	SCONJ
ejpam-4859	77	42	t	t	NOUN
ejpam-4859	77	43	=	=	SYM
ejpam-4859	77	44	ℓ	ℓ	PROPN
ejpam-4859	77	45	,	,	PUNCT
ejpam-4859	77	46	i.e.	i.e.	X
ejpam-4859	77	47	every	every	DET
ejpam-4859	77	48	linkage	linkage	NOUN
ejpam-4859	77	49	class	class	NOUN
ejpam-4859	77	50	contains	contain	VERB
ejpam-4859	77	51	exactly	exactly	ADV
ejpam-4859	77	52	one	one	NUM
ejpam-4859	77	53	terminal	terminal	ADJ
ejpam-4859	77	54	strong	strong	ADJ
ejpam-4859	77	55	linkage	linkage	NOUN
ejpam-4859	77	56	class	class	NOUN
ejpam-4859	77	57	.	.	PUNCT
ejpam-4859	78	1	remark	remark	NOUN
ejpam-4859	78	2	1	1	NUM
ejpam-4859	78	3	.	.	PUNCT
ejpam-4859	79	1	we	we	PRON
ejpam-4859	79	2	denote	denote	VERB
ejpam-4859	79	3	by	by	ADP
ejpam-4859	79	4	tc	tc	ADP
ejpam-4859	79	5	the	the	DET
ejpam-4859	79	6	number	number	NOUN
ejpam-4859	79	7	of	of	ADP
ejpam-4859	79	8	cycle	cycle	NOUN
ejpam-4859	79	9	-	-	PUNCT
ejpam-4859	79	10	terminal	terminal	NOUN
ejpam-4859	79	11	classes	class	NOUN
ejpam-4859	79	12	and	and	CCONJ
ejpam-4859	79	13	tp	tp	ADP
ejpam-4859	79	14	the	the	DET
ejpam-4859	79	15	number	number	NOUN
ejpam-4859	79	16	of	of	ADP
ejpam-4859	79	17	point	point	NOUN
ejpam-4859	79	18	-	-	PUNCT
ejpam-4859	79	19	terminal	terminal	ADJ
ejpam-4859	79	20	classes	class	NOUN
ejpam-4859	79	21	.	.	PUNCT
ejpam-4859	80	1	then	then	ADV
ejpam-4859	80	2	t	t	PROPN
ejpam-4859	80	3	=	=	PUNCT
ejpam-4859	80	4	tc	tc	PROPN
ejpam-4859	80	5	+	+	NUM
ejpam-4859	81	1	tp	tp	NOUN
ejpam-4859	81	2	.	.	PUNCT
ejpam-4859	81	3	note	note	NOUN
ejpam-4859	81	4	also	also	ADV
ejpam-4859	81	5	that	that	SCONJ
ejpam-4859	81	6	n	n	CCONJ
ejpam-4859	81	7	−	−	PROPN
ejpam-4859	81	8	nr	nr	NOUN
ejpam-4859	81	9	=	=	PROPN
ejpam-4859	81	10	tp	tp	PROPN
ejpam-4859	81	11	=	=	PUNCT
ejpam-4859	81	12	t	t	PROPN
ejpam-4859	81	13	−	−	PROPN
ejpam-4859	81	14	tc	tc	NOUN
ejpam-4859	81	15	.	.	PUNCT
ejpam-4859	82	1	a	a	DET
ejpam-4859	82	2	crn	crn	NOUN
ejpam-4859	82	3	is	be	AUX
ejpam-4859	82	4	cycle	cycle	NOUN
ejpam-4859	82	5	-	-	PUNCT
ejpam-4859	82	6	terminal	terminal	NOUN
ejpam-4859	82	7	if	if	SCONJ
ejpam-4859	82	8	tp	tp	VERB
ejpam-4859	82	9	=	=	SYM
ejpam-4859	82	10	0	0	PUNCT
ejpam-4859	83	1	(	(	PUNCT
ejpam-4859	83	2	i.e.	i.e.	X
ejpam-4859	83	3	n	n	CCONJ
ejpam-4859	83	4	=	=	PROPN
ejpam-4859	83	5	nr	nr	PROPN
ejpam-4859	83	6	)	)	PUNCT
ejpam-4859	83	7	,	,	PUNCT
ejpam-4859	83	8	point	point	NOUN
ejpam-4859	83	9	-	-	PUNCT
ejpam-4859	83	10	terminal	terminal	NOUN
ejpam-4859	83	11	if	if	SCONJ
ejpam-4859	83	12	tc	tc	NUM
ejpam-4859	83	13	=	=	SYM
ejpam-4859	83	14	0	0	PUNCT
ejpam-4859	84	1	(	(	PUNCT
ejpam-4859	84	2	i.e.	i.e.	X
ejpam-4859	84	3	t	t	X
ejpam-4859	84	4	=	=	SYM
ejpam-4859	84	5	n	n	CCONJ
ejpam-4859	84	6	−	−	PROPN
ejpam-4859	84	7	nr	nr	PROPN
ejpam-4859	84	8	)	)	PUNCT
ejpam-4859	84	9	and	and	CCONJ
ejpam-4859	84	10	pointand	pointand	VERB
ejpam-4859	84	11	cycle	cycle	NOUN
ejpam-4859	84	12	-	-	PUNCT
ejpam-4859	84	13	terminal	terminal	NOUN
ejpam-4859	84	14	otherwise	otherwise	ADV
ejpam-4859	84	15	(	(	PUNCT
ejpam-4859	84	16	i.e.	i.e.	X
ejpam-4859	84	17	tp	tp	ADP
ejpam-4859	84	18	>	>	X
ejpam-4859	84	19	0	0	PUNCT
ejpam-4859	85	1	and	and	CCONJ
ejpam-4859	85	2	tc	tc	X
ejpam-4859	85	3	>	>	X
ejpam-4859	85	4	0	0	NUM
ejpam-4859	85	5	or	or	CCONJ
ejpam-4859	85	6	equivalently	equivalently	ADV
ejpam-4859	85	7	,	,	PUNCT
ejpam-4859	85	8	t	t	PROPN
ejpam-4859	85	9	>	>	X
ejpam-4859	85	10	n−	n−	PROPN
ejpam-4859	85	11	nr	nr	PROPN
ejpam-4859	85	12	)	)	PUNCT
ejpam-4859	85	13	.	.	PUNCT
ejpam-4859	86	1	example	example	NOUN
ejpam-4859	87	1	3	3	NUM
ejpam-4859	87	2	.	.	PUNCT
ejpam-4859	87	3	as	as	SCONJ
ejpam-4859	87	4	observed	observe	VERB
ejpam-4859	87	5	in	in	ADP
ejpam-4859	87	6	example	example	NOUN
ejpam-4859	87	7	1	1	NUM
ejpam-4859	87	8	,	,	PUNCT
ejpam-4859	87	9	t	t	NOUN
ejpam-4859	87	10	=	=	SYM
ejpam-4859	87	11	1	1	NUM
ejpam-4859	87	12	and	and	CCONJ
ejpam-4859	87	13	n−	n−	NOUN
ejpam-4859	87	14	nr	nr	NOUN
ejpam-4859	87	15	=	=	NOUN
ejpam-4859	87	16	4−	4−	PROPN
ejpam-4859	87	17	4	4	NUM
ejpam-4859	87	18	=	=	SYM
ejpam-4859	87	19	0	0	NUM
ejpam-4859	87	20	.	.	PUNCT
ejpam-4859	88	1	this	this	PRON
ejpam-4859	88	2	implies	imply	VERB
ejpam-4859	88	3	that	that	SCONJ
ejpam-4859	88	4	the	the	DET
ejpam-4859	88	5	network	network	NOUN
ejpam-4859	88	6	is	be	AUX
ejpam-4859	88	7	not	not	PART
ejpam-4859	88	8	point	point	NOUN
ejpam-4859	88	9	terminal	terminal	NOUN
ejpam-4859	88	10	.	.	PUNCT
ejpam-4859	89	1	also	also	ADV
ejpam-4859	89	2	,	,	PUNCT
ejpam-4859	89	3	sℓ	sℓ	NOUN
ejpam-4859	89	4	=	=	NOUN
ejpam-4859	89	5	3	3	NUM
ejpam-4859	89	6	̸=	̸=	PROPN
ejpam-4859	89	7	1	1	NUM
ejpam-4859	89	8	=	=	NOUN
ejpam-4859	89	9	ℓ.	ℓ.	NOUN
ejpam-4859	89	10	hence	hence	ADV
ejpam-4859	89	11	,	,	PUNCT
ejpam-4859	89	12	the	the	DET
ejpam-4859	89	13	network	network	NOUN
ejpam-4859	89	14	is	be	AUX
ejpam-4859	89	15	not	not	PART
ejpam-4859	89	16	weakly	weakly	ADV
ejpam-4859	89	17	reversible	reversible	ADJ
ejpam-4859	89	18	.	.	PUNCT
ejpam-4859	90	1	but	but	CCONJ
ejpam-4859	90	2	,	,	PUNCT
ejpam-4859	90	3	t	t	PROPN
ejpam-4859	90	4	=	=	SYM
ejpam-4859	90	5	1	1	NUM
ejpam-4859	90	6	=	=	NOUN
ejpam-4859	90	7	ℓ.	ℓ.	NOUN
ejpam-4859	90	8	thus	thus	ADV
ejpam-4859	90	9	,	,	PUNCT
ejpam-4859	90	10	the	the	DET
ejpam-4859	90	11	network	network	NOUN
ejpam-4859	90	12	is	be	AUX
ejpam-4859	90	13	t	t	PROPN
ejpam-4859	90	14	-	-	PUNCT
ejpam-4859	90	15	minimal	minimal	NOUN
ejpam-4859	90	16	.	.	PUNCT
ejpam-4859	91	1	d.	d.	PROPN
ejpam-4859	91	2	magpantay	magpantay	PROPN
ejpam-4859	91	3	/	/	SYM
ejpam-4859	91	4	eur	eur	PROPN
ejpam-4859	91	5	.	.	PUNCT
ejpam-4859	92	1	j.	j.	PROPN
ejpam-4859	92	2	pure	pure	PROPN
ejpam-4859	92	3	appl	appl	PROPN
ejpam-4859	92	4	.	.	PROPN
ejpam-4859	92	5	math	math	PROPN
ejpam-4859	92	6	,	,	PUNCT
ejpam-4859	92	7	16	16	NUM
ejpam-4859	92	8	(	(	PUNCT
ejpam-4859	92	9	4	4	NUM
ejpam-4859	92	10	)	)	PUNCT
ejpam-4859	92	11	(	(	PUNCT
ejpam-4859	92	12	2023	2023	NUM
ejpam-4859	92	13	)	)	PUNCT
ejpam-4859	92	14	,	,	PUNCT
ejpam-4859	92	15	2557	2557	NUM
ejpam-4859	92	16	-	-	SYM
ejpam-4859	92	17	2580	2580	NUM
ejpam-4859	92	18	2561	2561	NUM
ejpam-4859	92	19	a	a	DET
ejpam-4859	92	20	network	network	NOUN
ejpam-4859	92	21	in	in	ADP
ejpam-4859	92	22	the	the	DET
ejpam-4859	92	23	form	form	NOUN
ejpam-4859	92	24	of	of	ADP
ejpam-4859	92	25	a	a	DET
ejpam-4859	92	26	simple	simple	ADJ
ejpam-4859	92	27	cycle	cycle	NOUN
ejpam-4859	92	28	is	be	AUX
ejpam-4859	92	29	an	an	DET
ejpam-4859	92	30	example	example	NOUN
ejpam-4859	92	31	of	of	ADP
ejpam-4859	92	32	a	a	DET
ejpam-4859	92	33	weakly	weakly	ADJ
ejpam-4859	92	34	reversible	reversible	ADJ
ejpam-4859	92	35	network	network	NOUN
ejpam-4859	92	36	.	.	PUNCT
ejpam-4859	93	1	the	the	DET
ejpam-4859	93	2	next	next	ADJ
ejpam-4859	93	3	proposition	proposition	NOUN
ejpam-4859	93	4	shows	show	VERB
ejpam-4859	93	5	that	that	SCONJ
ejpam-4859	93	6	the	the	DET
ejpam-4859	93	7	set	set	NOUN
ejpam-4859	93	8	of	of	ADP
ejpam-4859	93	9	nonbranching	nonbranching	NOUN
ejpam-4859	93	10	digraphs	digraphs	ADJ
ejpam-4859	93	11	is	be	AUX
ejpam-4859	93	12	a	a	DET
ejpam-4859	93	13	subset	subset	NOUN
ejpam-4859	93	14	of	of	ADP
ejpam-4859	93	15	the	the	DET
ejpam-4859	93	16	set	set	NOUN
ejpam-4859	93	17	of	of	ADP
ejpam-4859	93	18	t	t	PROPN
ejpam-4859	93	19	-	-	PUNCT
ejpam-4859	93	20	minimal	minimal	ADJ
ejpam-4859	93	21	digraphs	digraph	NOUN
ejpam-4859	93	22	.	.	PUNCT
ejpam-4859	94	1	proposition	proposition	NOUN
ejpam-4859	94	2	1	1	NUM
ejpam-4859	94	3	.	.	PUNCT
ejpam-4859	95	1	if	if	SCONJ
ejpam-4859	95	2	a	a	DET
ejpam-4859	95	3	digraph	digraph	NOUN
ejpam-4859	95	4	is	be	AUX
ejpam-4859	95	5	nonbranching	nonbranching	NOUN
ejpam-4859	95	6	,	,	PUNCT
ejpam-4859	95	7	then	then	ADV
ejpam-4859	95	8	it	it	PRON
ejpam-4859	95	9	is	be	AUX
ejpam-4859	95	10	t	t	PROPN
ejpam-4859	95	11	-	-	PUNCT
ejpam-4859	95	12	minimal	minimal	ADJ
ejpam-4859	95	13	.	.	PUNCT
ejpam-4859	96	1	proof	proof	NOUN
ejpam-4859	96	2	.	.	PUNCT
ejpam-4859	97	1	suppose	suppose	VERB
ejpam-4859	97	2	a	a	DET
ejpam-4859	97	3	digraph	digraph	NOUN
ejpam-4859	97	4	is	be	AUX
ejpam-4859	97	5	not	not	PART
ejpam-4859	97	6	t	t	NOUN
ejpam-4859	97	7	-	-	PUNCT
ejpam-4859	97	8	minimal	minimal	ADJ
ejpam-4859	97	9	.	.	PUNCT
ejpam-4859	98	1	that	that	PRON
ejpam-4859	98	2	is	be	AUX
ejpam-4859	98	3	,	,	PUNCT
ejpam-4859	98	4	there	there	PRON
ejpam-4859	98	5	is	be	VERB
ejpam-4859	98	6	a	a	DET
ejpam-4859	98	7	connected	connected	ADJ
ejpam-4859	98	8	component	component	NOUN
ejpam-4859	98	9	with	with	ADP
ejpam-4859	98	10	at	at	ADV
ejpam-4859	98	11	least	least	ADV
ejpam-4859	98	12	two	two	NUM
ejpam-4859	98	13	terminal	terminal	ADJ
ejpam-4859	98	14	strong	strong	ADJ
ejpam-4859	98	15	components	component	NOUN
ejpam-4859	98	16	t	t	PROPN
ejpam-4859	98	17	,	,	PUNCT
ejpam-4859	98	18	t	t	PROPN
ejpam-4859	98	19	′.	′.	NOUN
ejpam-4859	98	20	if	if	SCONJ
ejpam-4859	98	21	y	y	PROPN
ejpam-4859	98	22	is	be	AUX
ejpam-4859	98	23	in	in	ADP
ejpam-4859	98	24	t	t	PROPN
ejpam-4859	98	25	and	and	CCONJ
ejpam-4859	98	26	y′	y′	NOUN
ejpam-4859	98	27	in	in	ADP
ejpam-4859	98	28	t	t	PROPN
ejpam-4859	98	29	′	′	NOUN
ejpam-4859	98	30	,	,	PUNCT
ejpam-4859	98	31	then	then	ADV
ejpam-4859	98	32	there	there	PRON
ejpam-4859	98	33	is	be	VERB
ejpam-4859	98	34	an	an	DET
ejpam-4859	98	35	(	(	PUNCT
ejpam-4859	98	36	undirected	undirected	ADJ
ejpam-4859	98	37	)	)	PUNCT
ejpam-4859	98	38	path	path	NOUN
ejpam-4859	98	39	from	from	ADP
ejpam-4859	98	40	y	y	PRON
ejpam-4859	98	41	to	to	ADP
ejpam-4859	98	42	y′	y′	NUM
ejpam-4859	98	43	,	,	PUNCT
ejpam-4859	98	44	with	with	ADP
ejpam-4859	98	45	the	the	DET
ejpam-4859	98	46	first	first	ADJ
ejpam-4859	98	47	arc	arc	NOUN
ejpam-4859	98	48	pointing	pointing	NOUN
ejpam-4859	98	49	into	into	ADP
ejpam-4859	98	50	t	t	PROPN
ejpam-4859	98	51	and	and	CCONJ
ejpam-4859	98	52	the	the	DET
ejpam-4859	98	53	last	last	ADJ
ejpam-4859	98	54	arc	arc	NOUN
ejpam-4859	98	55	pointing	point	VERB
ejpam-4859	98	56	into	into	ADP
ejpam-4859	98	57	t	t	PROPN
ejpam-4859	98	58	′.	′.	NOUN
ejpam-4859	98	59	clearly	clearly	ADV
ejpam-4859	98	60	,	,	PUNCT
ejpam-4859	98	61	there	there	PRON
ejpam-4859	98	62	must	must	AUX
ejpam-4859	98	63	at	at	ADV
ejpam-4859	98	64	least	least	ADV
ejpam-4859	98	65	one	one	NUM
ejpam-4859	98	66	vertex	vertex	NOUN
ejpam-4859	98	67	v	v	NOUN
ejpam-4859	98	68	with	with	ADP
ejpam-4859	98	69	d+(v	d+(v	NOUN
ejpam-4859	98	70	)	)	PUNCT
ejpam-4859	98	71	≥	≥	NOUN
ejpam-4859	98	72	2	2	NUM
ejpam-4859	98	73	,	,	PUNCT
ejpam-4859	98	74	contradicting	contradict	VERB
ejpam-4859	98	75	the	the	DET
ejpam-4859	98	76	nonbranching	nonbranching	NOUN
ejpam-4859	98	77	hypothesis	hypothesis	NOUN
ejpam-4859	98	78	.	.	PUNCT
ejpam-4859	99	1	2.3	2.3	NUM
ejpam-4859	99	2	.	.	PUNCT
ejpam-4859	99	3	deficiency	deficiency	NOUN
ejpam-4859	99	4	of	of	ADP
ejpam-4859	99	5	a	a	DET
ejpam-4859	99	6	crn	crn	NOUN
ejpam-4859	99	7	a	a	DET
ejpam-4859	99	8	central	central	ADJ
ejpam-4859	99	9	concept	concept	NOUN
ejpam-4859	99	10	of	of	ADP
ejpam-4859	99	11	the	the	DET
ejpam-4859	99	12	theory	theory	NOUN
ejpam-4859	99	13	of	of	ADP
ejpam-4859	99	14	chemical	chemical	ADJ
ejpam-4859	99	15	reaction	reaction	NOUN
ejpam-4859	99	16	networks	network	NOUN
ejpam-4859	99	17	is	be	AUX
ejpam-4859	99	18	the	the	DET
ejpam-4859	99	19	deficiency	deficiency	NOUN
ejpam-4859	99	20	of	of	ADP
ejpam-4859	99	21	the	the	DET
ejpam-4859	99	22	crn	crn	NOUN
ejpam-4859	99	23	.	.	PUNCT
ejpam-4859	100	1	shinar	shinar	NOUN
ejpam-4859	100	2	and	and	CCONJ
ejpam-4859	100	3	feinberg	feinberg	PROPN
ejpam-4859	101	1	[	[	X
ejpam-4859	101	2	8	8	NUM
ejpam-4859	101	3	]	]	PUNCT
ejpam-4859	101	4	describe	describe	VERB
ejpam-4859	101	5	the	the	DET
ejpam-4859	101	6	“	"	PUNCT
ejpam-4859	101	7	deficiency	deficiency	NOUN
ejpam-4859	101	8	philosophy	philosophy	NOUN
ejpam-4859	101	9	”	"	PUNCT
ejpam-4859	101	10	as	as	SCONJ
ejpam-4859	101	11	follows	follow	VERB
ejpam-4859	101	12	:	:	PUNCT
ejpam-4859	101	13	the	the	DET
ejpam-4859	101	14	deficiency	deficiency	NOUN
ejpam-4859	101	15	of	of	ADP
ejpam-4859	101	16	a	a	DET
ejpam-4859	101	17	reaction	reaction	NOUN
ejpam-4859	101	18	network	network	NOUN
ejpam-4859	101	19	is	be	AUX
ejpam-4859	101	20	an	an	DET
ejpam-4859	101	21	integer	integer	NOUN
ejpam-4859	101	22	index	index	NOUN
ejpam-4859	101	23	that	that	PRON
ejpam-4859	101	24	assumes	assume	VERB
ejpam-4859	101	25	a	a	DET
ejpam-4859	101	26	non	non	ADJ
ejpam-4859	101	27	-	-	ADJ
ejpam-4859	101	28	negative	negative	ADJ
ejpam-4859	101	29	value	value	NOUN
ejpam-4859	101	30	.	.	PUNCT
ejpam-4859	102	1	loosely	loosely	ADV
ejpam-4859	102	2	speaking	speak	VERB
ejpam-4859	102	3	,	,	PUNCT
ejpam-4859	102	4	the	the	DET
ejpam-4859	102	5	deficiency	deficiency	NOUN
ejpam-4859	102	6	measures	measure	VERB
ejpam-4859	102	7	the	the	DET
ejpam-4859	102	8	amount	amount	NOUN
ejpam-4859	102	9	of	of	ADP
ejpam-4859	102	10	linear	linear	ADJ
ejpam-4859	102	11	independence	independence	NOUN
ejpam-4859	102	12	among	among	ADP
ejpam-4859	102	13	the	the	DET
ejpam-4859	102	14	reactions	reaction	NOUN
ejpam-4859	102	15	of	of	ADP
ejpam-4859	102	16	the	the	DET
ejpam-4859	102	17	network	network	NOUN
ejpam-4859	102	18	.	.	PUNCT
ejpam-4859	103	1	the	the	DET
ejpam-4859	103	2	lowest	low	ADJ
ejpam-4859	103	3	value	value	NOUN
ejpam-4859	103	4	that	that	PRON
ejpam-4859	103	5	the	the	DET
ejpam-4859	103	6	deficiency	deficiency	NOUN
ejpam-4859	103	7	can	can	AUX
ejpam-4859	103	8	assume	assume	VERB
ejpam-4859	103	9	,	,	PUNCT
ejpam-4859	103	10	which	which	PRON
ejpam-4859	103	11	is	be	AUX
ejpam-4859	103	12	zero	zero	NUM
ejpam-4859	103	13	,	,	PUNCT
ejpam-4859	103	14	is	be	AUX
ejpam-4859	103	15	associated	associate	VERB
ejpam-4859	103	16	with	with	ADP
ejpam-4859	103	17	the	the	DET
ejpam-4859	103	18	highest	high	ADJ
ejpam-4859	103	19	possible	possible	ADJ
ejpam-4859	103	20	extent	extent	NOUN
ejpam-4859	103	21	of	of	ADP
ejpam-4859	103	22	linear	linear	ADJ
ejpam-4859	103	23	independence	independence	NOUN
ejpam-4859	103	24	among	among	ADP
ejpam-4859	103	25	the	the	DET
ejpam-4859	103	26	individual	individual	ADJ
ejpam-4859	103	27	reactions	reaction	NOUN
ejpam-4859	103	28	,	,	PUNCT
ejpam-4859	103	29	consistent	consistent	ADJ
ejpam-4859	103	30	with	with	ADP
ejpam-4859	103	31	the	the	DET
ejpam-4859	103	32	network	network	NOUN
ejpam-4859	103	33	’s	’s	PART
ejpam-4859	103	34	structure	structure	NOUN
ejpam-4859	103	35	as	as	ADP
ejpam-4859	103	36	a	a	DET
ejpam-4859	103	37	directed	direct	VERB
ejpam-4859	103	38	graph	graph	NOUN
ejpam-4859	103	39	.	.	PUNCT
ejpam-4859	104	1	the	the	PRON
ejpam-4859	104	2	higher	high	ADJ
ejpam-4859	104	3	the	the	DET
ejpam-4859	104	4	deficiency	deficiency	NOUN
ejpam-4859	104	5	,	,	PUNCT
ejpam-4859	104	6	the	the	PRON
ejpam-4859	104	7	lower	low	ADJ
ejpam-4859	104	8	the	the	DET
ejpam-4859	104	9	extent	extent	NOUN
ejpam-4859	104	10	of	of	ADP
ejpam-4859	104	11	linear	linear	ADJ
ejpam-4859	104	12	independence	independence	NOUN
ejpam-4859	104	13	.	.	PUNCT
ejpam-4859	105	1	we	we	PRON
ejpam-4859	105	2	formally	formally	ADV
ejpam-4859	105	3	define	define	VERB
ejpam-4859	105	4	the	the	DET
ejpam-4859	105	5	deficiency	deficiency	NOUN
ejpam-4859	105	6	of	of	ADP
ejpam-4859	105	7	a	a	DET
ejpam-4859	105	8	crn	crn	NOUN
ejpam-4859	105	9	as	as	SCONJ
ejpam-4859	105	10	follows	follow	VERB
ejpam-4859	105	11	:	:	PUNCT
ejpam-4859	105	12	definition	definition	NOUN
ejpam-4859	105	13	6	6	NUM
ejpam-4859	105	14	.	.	PUNCT
ejpam-4859	106	1	the	the	DET
ejpam-4859	106	2	deficiency	deficiency	NOUN
ejpam-4859	106	3	of	of	ADP
ejpam-4859	106	4	a	a	DET
ejpam-4859	106	5	crn	crn	NOUN
ejpam-4859	106	6	is	be	AUX
ejpam-4859	106	7	the	the	DET
ejpam-4859	106	8	integer	integer	NOUN
ejpam-4859	106	9	δ	δ	NOUN
ejpam-4859	106	10	=	=	SYM
ejpam-4859	106	11	n−	n−	PROPN
ejpam-4859	106	12	ℓ−	ℓ−	PROPN
ejpam-4859	106	13	s.	s.	PROPN
ejpam-4859	106	14	example	example	NOUN
ejpam-4859	106	15	4	4	NUM
ejpam-4859	106	16	.	.	PUNCT
ejpam-4859	107	1	in	in	ADP
ejpam-4859	107	2	example	example	NOUN
ejpam-4859	107	3	1	1	NUM
ejpam-4859	107	4	,	,	PUNCT
ejpam-4859	107	5	observe	observe	VERB
ejpam-4859	107	6	that	that	SCONJ
ejpam-4859	107	7	n	n	NOUN
ejpam-4859	107	8	=	=	SYM
ejpam-4859	107	9	4	4	NUM
ejpam-4859	107	10	,	,	PUNCT
ejpam-4859	107	11	ℓ	ℓ	NOUN
ejpam-4859	107	12	=	=	SYM
ejpam-4859	107	13	1	1	NUM
ejpam-4859	107	14	and	and	CCONJ
ejpam-4859	107	15	s	s	NOUN
ejpam-4859	107	16	=	=	ADJ
ejpam-4859	107	17	3	3	X
ejpam-4859	107	18	.	.	PUNCT
ejpam-4859	107	19	with	with	ADP
ejpam-4859	107	20	this	this	PRON
ejpam-4859	107	21	,	,	PUNCT
ejpam-4859	107	22	the	the	DET
ejpam-4859	107	23	deficiency	deficiency	NOUN
ejpam-4859	107	24	of	of	ADP
ejpam-4859	107	25	the	the	DET
ejpam-4859	107	26	network	network	NOUN
ejpam-4859	107	27	δ	δ	NOUN
ejpam-4859	107	28	=	=	SYM
ejpam-4859	107	29	n−	n−	PROPN
ejpam-4859	107	30	ℓ−	ℓ−	PROPN
ejpam-4859	107	31	s	s	NOUN
ejpam-4859	107	32	=	=	SYM
ejpam-4859	107	33	4−	4−	PROPN
ejpam-4859	107	34	1−	1−	NUM
ejpam-4859	107	35	3	3	NUM
ejpam-4859	107	36	=	=	SYM
ejpam-4859	107	37	0	0	NUM
ejpam-4859	107	38	.	.	PUNCT
ejpam-4859	108	1	by	by	ADP
ejpam-4859	108	2	relating	relate	VERB
ejpam-4859	108	3	deficiency	deficiency	NOUN
ejpam-4859	108	4	to	to	ADP
ejpam-4859	108	5	linear	linear	PROPN
ejpam-4859	108	6	maps	map	NOUN
ejpam-4859	108	7	defined	define	VERB
ejpam-4859	108	8	from	from	ADP
ejpam-4859	108	9	a	a	DET
ejpam-4859	108	10	crn	crn	NOUN
ejpam-4859	108	11	,	,	PUNCT
ejpam-4859	108	12	we	we	PRON
ejpam-4859	108	13	have	have	VERB
ejpam-4859	108	14	the	the	DET
ejpam-4859	108	15	following	follow	VERB
ejpam-4859	108	16	proposition	proposition	NOUN
ejpam-4859	108	17	which	which	PRON
ejpam-4859	108	18	is	be	AUX
ejpam-4859	108	19	a	a	DET
ejpam-4859	108	20	classical	classical	ADJ
ejpam-4859	108	21	result	result	NOUN
ejpam-4859	108	22	.	.	PUNCT
ejpam-4859	109	1	one	one	PRON
ejpam-4859	109	2	can	can	AUX
ejpam-4859	109	3	refer	refer	VERB
ejpam-4859	109	4	to	to	ADP
ejpam-4859	109	5	[	[	X
ejpam-4859	109	6	4	4	NUM
ejpam-4859	109	7	]	]	PUNCT
ejpam-4859	109	8	but	but	CCONJ
ejpam-4859	109	9	we	we	PRON
ejpam-4859	109	10	provide	provide	VERB
ejpam-4859	109	11	its	its	PRON
ejpam-4859	109	12	proof	proof	NOUN
ejpam-4859	109	13	for	for	ADP
ejpam-4859	109	14	the	the	DET
ejpam-4859	109	15	convenience	convenience	NOUN
ejpam-4859	109	16	of	of	ADP
ejpam-4859	109	17	the	the	DET
ejpam-4859	109	18	reader	reader	NOUN
ejpam-4859	109	19	.	.	PUNCT
ejpam-4859	110	1	proposition	proposition	NOUN
ejpam-4859	110	2	2	2	NUM
ejpam-4859	110	3	.	.	PUNCT
ejpam-4859	111	1	the	the	DET
ejpam-4859	111	2	deficiency	deficiency	NOUN
ejpam-4859	111	3	δ	δ	PROPN
ejpam-4859	111	4	is	be	AUX
ejpam-4859	111	5	equal	equal	ADJ
ejpam-4859	111	6	to	to	ADP
ejpam-4859	111	7	dim(kery	dim(kery	NUM
ejpam-4859	111	8	∩	∩	NOUN
ejpam-4859	112	1	i	i	PROPN
ejpam-4859	112	2	m	m	PROPN
ejpam-4859	112	3	ia	ia	PROPN
ejpam-4859	112	4	)	)	PUNCT
ejpam-4859	112	5	.	.	PUNCT
ejpam-4859	113	1	proof	proof	NOUN
ejpam-4859	113	2	.	.	PUNCT
ejpam-4859	114	1	it	it	PRON
ejpam-4859	114	2	follows	follow	VERB
ejpam-4859	114	3	from	from	ADP
ejpam-4859	114	4	basic	basic	ADJ
ejpam-4859	114	5	dimensional	dimensional	ADJ
ejpam-4859	114	6	considerations	consideration	NOUN
ejpam-4859	114	7	that	that	PRON
ejpam-4859	114	8	dim(ker(y	dim(ker(y	PROPN
ejpam-4859	114	9	ia	ia	PROPN
ejpam-4859	114	10	)	)	PUNCT
ejpam-4859	114	11	)	)	PUNCT
ejpam-4859	115	1	=	=	PUNCT
ejpam-4859	115	2	dim(ker(ia	dim(ker(ia	PROPN
ejpam-4859	115	3	)	)	PUNCT
ejpam-4859	115	4	)	)	PUNCT
ejpam-4859	116	1	+	+	CCONJ
ejpam-4859	116	2	dim(ker(y	dim(ker(y	ADJ
ejpam-4859	116	3	)	)	PUNCT
ejpam-4859	116	4	∩	∩	NOUN
ejpam-4859	116	5	im(ia	im(ia	PROPN
ejpam-4859	116	6	)	)	PUNCT
ejpam-4859	116	7	)	)	PUNCT
ejpam-4859	116	8	.	.	PUNCT
ejpam-4859	117	1	from	from	ADP
ejpam-4859	117	2	the	the	DET
ejpam-4859	117	3	rank	rank	NOUN
ejpam-4859	117	4	-	-	PUNCT
ejpam-4859	117	5	nullity	nullity	NOUN
ejpam-4859	117	6	theorem	theorem	NOUN
ejpam-4859	117	7	,	,	PUNCT
ejpam-4859	117	8	we	we	PRON
ejpam-4859	117	9	have	have	AUX
ejpam-4859	117	10	dim(ker(y	dim(ker(y	VERB
ejpam-4859	117	11	ia	ia	PROPN
ejpam-4859	117	12	)	)	PUNCT
ejpam-4859	117	13	)	)	PUNCT
ejpam-4859	118	1	=	=	PUNCT
ejpam-4859	118	2	r	r	NOUN
ejpam-4859	118	3	−	−	PROPN
ejpam-4859	118	4	dim(im(y	dim(im(y	PROPN
ejpam-4859	118	5	ia	ia	PROPN
ejpam-4859	118	6	)	)	PUNCT
ejpam-4859	118	7	)	)	PUNCT
ejpam-4859	119	1	=	=	PUNCT
ejpam-4859	120	1	r	r	NOUN
ejpam-4859	120	2	−	−	PROPN
ejpam-4859	120	3	s.	s.	PROPN
ejpam-4859	120	4	the	the	DET
ejpam-4859	120	5	rank	rank	NOUN
ejpam-4859	120	6	of	of	ADP
ejpam-4859	120	7	ia	ia	PROPN
ejpam-4859	120	8	corresponds	correspond	VERB
ejpam-4859	120	9	to	to	ADP
ejpam-4859	120	10	the	the	DET
ejpam-4859	120	11	number	number	NOUN
ejpam-4859	120	12	of	of	ADP
ejpam-4859	120	13	complexes	complex	NOUN
ejpam-4859	120	14	minus	minus	ADP
ejpam-4859	120	15	the	the	DET
ejpam-4859	120	16	number	number	NOUN
ejpam-4859	120	17	of	of	ADP
ejpam-4859	120	18	linkage	linkage	NOUN
ejpam-4859	120	19	classes	class	NOUN
ejpam-4859	120	20	,	,	PUNCT
ejpam-4859	120	21	so	so	SCONJ
ejpam-4859	120	22	that	that	SCONJ
ejpam-4859	120	23	dim(im(ia	dim(im(ia	PROPN
ejpam-4859	120	24	)	)	PUNCT
ejpam-4859	120	25	)	)	PUNCT
ejpam-4859	121	1	=	=	PUNCT
ejpam-4859	121	2	n−	n−	PROPN
ejpam-4859	121	3	ℓ.	ℓ.	NOUN
ejpam-4859	121	4	d.	d.	PROPN
ejpam-4859	121	5	magpantay	magpantay	PROPN
ejpam-4859	121	6	/	/	SYM
ejpam-4859	121	7	eur	eur	PROPN
ejpam-4859	121	8	.	.	PUNCT
ejpam-4859	122	1	j.	j.	PROPN
ejpam-4859	122	2	pure	pure	PROPN
ejpam-4859	122	3	appl	appl	PROPN
ejpam-4859	122	4	.	.	PROPN
ejpam-4859	122	5	math	math	PROPN
ejpam-4859	122	6	,	,	PUNCT
ejpam-4859	122	7	16	16	NUM
ejpam-4859	122	8	(	(	PUNCT
ejpam-4859	122	9	4	4	NUM
ejpam-4859	122	10	)	)	PUNCT
ejpam-4859	122	11	(	(	PUNCT
ejpam-4859	122	12	2023	2023	NUM
ejpam-4859	122	13	)	)	PUNCT
ejpam-4859	122	14	,	,	PUNCT
ejpam-4859	122	15	2557	2557	NUM
ejpam-4859	122	16	-	-	SYM
ejpam-4859	122	17	2580	2580	NUM
ejpam-4859	122	18	2562	2562	NUM
ejpam-4859	122	19	it	it	PRON
ejpam-4859	122	20	follows	follow	VERB
ejpam-4859	122	21	that	that	SCONJ
ejpam-4859	122	22	dim(ker(ia	dim(ker(ia	PROPN
ejpam-4859	122	23	)	)	PUNCT
ejpam-4859	122	24	)	)	PUNCT
ejpam-4859	123	1	=	=	PUNCT
ejpam-4859	123	2	r	r	NOUN
ejpam-4859	123	3	−	−	PROPN
ejpam-4859	123	4	(	(	PUNCT
ejpam-4859	123	5	n−	n−	NOUN
ejpam-4859	123	6	ℓ	ℓ	NUM
ejpam-4859	123	7	)	)	PUNCT
ejpam-4859	124	1	=	=	SYM
ejpam-4859	124	2	r	r	NOUN
ejpam-4859	124	3	+	+	CCONJ
ejpam-4859	124	4	ℓ−	ℓ−	PROPN
ejpam-4859	124	5	n	n	PRON
ejpam-4859	124	6	it	it	PRON
ejpam-4859	124	7	implies	imply	VERB
ejpam-4859	124	8	that	that	SCONJ
ejpam-4859	124	9	dim(ker(y	dim(ker(y	ADJ
ejpam-4859	124	10	)	)	PUNCT
ejpam-4859	124	11	∩	∩	NOUN
ejpam-4859	124	12	im(ia	im(ia	NOUN
ejpam-4859	124	13	)	)	PUNCT
ejpam-4859	124	14	)	)	PUNCT
ejpam-4859	125	1	=	=	SYM
ejpam-4859	125	2	dim(ker(y	dim(ker(y	PROPN
ejpam-4859	125	3	ia))−	ia))−	NOUN
ejpam-4859	125	4	dim(ker(ia	dim(ker(ia	PROPN
ejpam-4859	125	5	)	)	PUNCT
ejpam-4859	125	6	)	)	PUNCT
ejpam-4859	126	1	=	=	PRON
ejpam-4859	126	2	(	(	PUNCT
ejpam-4859	126	3	r	r	NOUN
ejpam-4859	126	4	−	−	PROPN
ejpam-4859	126	5	s)−	s)−	PROPN
ejpam-4859	126	6	(	(	PUNCT
ejpam-4859	126	7	r	r	NOUN
ejpam-4859	126	8	+	+	CCONJ
ejpam-4859	126	9	ℓ−	ℓ−	PROPN
ejpam-4859	126	10	n	n	CCONJ
ejpam-4859	126	11	)	)	PUNCT
ejpam-4859	127	1	=	=	PUNCT
ejpam-4859	127	2	n−	n−	NOUN
ejpam-4859	127	3	ℓ−	ℓ−	PROPN
ejpam-4859	127	4	s	s	NOUN
ejpam-4859	127	5	=	=	PROPN
ejpam-4859	127	6	δ	δ	PROPN
ejpam-4859	127	7	.	.	PUNCT
ejpam-4859	128	1	2.3.1	2.3.1	NUM
ejpam-4859	128	2	.	.	PUNCT
ejpam-4859	128	3	terminality	terminality	NOUN
ejpam-4859	128	4	and	and	CCONJ
ejpam-4859	128	5	reactant	reactant	NOUN
ejpam-4859	128	6	diversity	diversity	NOUN
ejpam-4859	128	7	the	the	DET
ejpam-4859	128	8	terminality	terminality	NOUN
ejpam-4859	128	9	of	of	ADP
ejpam-4859	128	10	a	a	DET
ejpam-4859	128	11	network	network	NOUN
ejpam-4859	128	12	is	be	AUX
ejpam-4859	128	13	the	the	DET
ejpam-4859	128	14	non	non	ADJ
ejpam-4859	128	15	-	-	ADJ
ejpam-4859	128	16	negative	negative	ADJ
ejpam-4859	128	17	integer	integer	NOUN
ejpam-4859	128	18	τ(n	τ(n	NOUN
ejpam-4859	128	19	)	)	PUNCT
ejpam-4859	129	1	=	=	SYM
ejpam-4859	129	2	t−	t−	PRON
ejpam-4859	129	3	ℓ.	ℓ.	NOUN
ejpam-4859	129	4	we	we	PRON
ejpam-4859	129	5	now	now	ADV
ejpam-4859	129	6	introduce	introduce	VERB
ejpam-4859	129	7	useful	useful	ADJ
ejpam-4859	129	8	partition	partition	NOUN
ejpam-4859	129	9	of	of	ADP
ejpam-4859	129	10	networks	network	NOUN
ejpam-4859	129	11	with	with	ADP
ejpam-4859	129	12	respect	respect	NOUN
ejpam-4859	129	13	to	to	ADP
ejpam-4859	129	14	terminality	terminality	NOUN
ejpam-4859	129	15	:	:	PUNCT
ejpam-4859	129	16	definition	definition	NOUN
ejpam-4859	129	17	7	7	NUM
ejpam-4859	129	18	.	.	PUNCT
ejpam-4859	130	1	a	a	DET
ejpam-4859	130	2	crn	crn	NOUN
ejpam-4859	130	3	is	be	AUX
ejpam-4859	130	4	of	of	ADP
ejpam-4859	130	5	type	type	NOUN
ejpam-4859	130	6	terminality	terminality	NOUN
ejpam-4859	130	7	bounded	bound	VERB
ejpam-4859	130	8	by	by	ADP
ejpam-4859	130	9	deficiency	deficiency	NOUN
ejpam-4859	130	10	(	(	PUNCT
ejpam-4859	130	11	tbd	tbd	NOUN
ejpam-4859	130	12	)	)	PUNCT
ejpam-4859	131	1	if	if	SCONJ
ejpam-4859	131	2	t−ℓ	t−ℓ	NOUN
ejpam-4859	131	3	≤	≤	PROPN
ejpam-4859	131	4	δ	δ	PROPN
ejpam-4859	131	5	.	.	PUNCT
ejpam-4859	132	1	otherwise	otherwise	ADV
ejpam-4859	132	2	,	,	PUNCT
ejpam-4859	132	3	it	it	PRON
ejpam-4859	132	4	is	be	AUX
ejpam-4859	132	5	of	of	ADP
ejpam-4859	132	6	type	type	NOUN
ejpam-4859	132	7	terminality	terminality	NOUN
ejpam-4859	132	8	not	not	PART
ejpam-4859	132	9	deficiency	deficiency	NOUN
ejpam-4859	132	10	-	-	PUNCT
ejpam-4859	132	11	bounded	bound	VERB
ejpam-4859	132	12	(	(	PUNCT
ejpam-4859	132	13	tnd	tnd	NOUN
ejpam-4859	132	14	)	)	PUNCT
ejpam-4859	132	15	,	,	PUNCT
ejpam-4859	132	16	i.e.	i.e.	X
ejpam-4859	132	17	t−	t−	PROPN
ejpam-4859	132	18	ℓ	ℓ	PROPN
ejpam-4859	132	19	>	>	X
ejpam-4859	132	20	δ	δ	PROPN
ejpam-4859	132	21	.	.	PUNCT
ejpam-4859	133	1	definition	definition	NOUN
ejpam-4859	133	2	8	8	NUM
ejpam-4859	133	3	.	.	PUNCT
ejpam-4859	134	1	a	a	DET
ejpam-4859	134	2	crn	crn	NOUN
ejpam-4859	134	3	has	have	VERB
ejpam-4859	134	4	low	low	ADJ
ejpam-4859	134	5	reactant	reactant	NOUN
ejpam-4859	134	6	diversity	diversity	NOUN
ejpam-4859	134	7	(	(	PUNCT
ejpam-4859	134	8	lrd	lrd	PROPN
ejpam-4859	134	9	)	)	PUNCT
ejpam-4859	134	10	if	if	SCONJ
ejpam-4859	134	11	nr	nr	PRON
ejpam-4859	134	12	<	<	X
ejpam-4859	134	13	s	s	PROPN
ejpam-4859	134	14	,	,	PUNCT
ejpam-4859	134	15	.	.	PUNCT
ejpam-4859	135	1	otherwise	otherwise	ADV
ejpam-4859	135	2	it	it	PRON
ejpam-4859	135	3	has	have	VERB
ejpam-4859	135	4	sufficient	sufficient	ADJ
ejpam-4859	135	5	reactant	reactant	NOUN
ejpam-4859	135	6	diversity	diversity	NOUN
ejpam-4859	135	7	(	(	PUNCT
ejpam-4859	135	8	srd	srd	NOUN
ejpam-4859	135	9	)	)	PUNCT
ejpam-4859	135	10	.	.	PUNCT
ejpam-4859	136	1	an	an	DET
ejpam-4859	136	2	srd	srd	NOUN
ejpam-4859	136	3	network	network	NOUN
ejpam-4859	136	4	has	have	VERB
ejpam-4859	136	5	high	high	ADJ
ejpam-4859	136	6	reactant	reactant	NOUN
ejpam-4859	136	7	diversity	diversity	NOUN
ejpam-4859	136	8	(	(	PUNCT
ejpam-4859	136	9	hrd	hrd	NOUN
ejpam-4859	136	10	)	)	PUNCT
ejpam-4859	136	11	or	or	CCONJ
ejpam-4859	136	12	medium	medium	ADJ
ejpam-4859	136	13	reactant	reactant	NOUN
ejpam-4859	136	14	diversity	diversity	NOUN
ejpam-4859	136	15	(	(	PUNCT
ejpam-4859	136	16	mrd	mrd	PROPN
ejpam-4859	136	17	)	)	PUNCT
ejpam-4859	136	18	if	if	SCONJ
ejpam-4859	136	19	nr	nr	PRON
ejpam-4859	136	20	>	>	X
ejpam-4859	136	21	s	s	X
ejpam-4859	136	22	or	or	CCONJ
ejpam-4859	136	23	nr	nr	PROPN
ejpam-4859	136	24	=	=	SYM
ejpam-4859	136	25	s	s	PROPN
ejpam-4859	136	26	,	,	PUNCT
ejpam-4859	136	27	respectively	respectively	ADV
ejpam-4859	136	28	.	.	PUNCT
ejpam-4859	136	29	example	example	NOUN
ejpam-4859	136	30	5	5	NUM
ejpam-4859	136	31	.	.	PUNCT
ejpam-4859	137	1	going	go	VERB
ejpam-4859	137	2	back	back	ADV
ejpam-4859	137	3	to	to	ADP
ejpam-4859	137	4	the	the	DET
ejpam-4859	137	5	example	example	NOUN
ejpam-4859	137	6	1	1	NUM
ejpam-4859	137	7	,	,	PUNCT
ejpam-4859	137	8	we	we	PRON
ejpam-4859	137	9	have	have	VERB
ejpam-4859	137	10	t	t	NOUN
ejpam-4859	137	11	−	−	PROPN
ejpam-4859	137	12	ℓ	ℓ	X
ejpam-4859	137	13	=	=	SYM
ejpam-4859	138	1	1	1	NUM
ejpam-4859	138	2	−	−	NUM
ejpam-4859	138	3	1	1	NUM
ejpam-4859	138	4	=	=	SYM
ejpam-4859	138	5	0	0	PUNCT
ejpam-4859	138	6	=	=	SYM
ejpam-4859	138	7	δ	δ	PROPN
ejpam-4859	138	8	and	and	CCONJ
ejpam-4859	138	9	nr	nr	NOUN
ejpam-4859	138	10	=	=	NOUN
ejpam-4859	138	11	4	4	NUM
ejpam-4859	138	12	>	>	SYM
ejpam-4859	138	13	3	3	NUM
ejpam-4859	138	14	=	=	SYM
ejpam-4859	138	15	s.	s.	PROPN
ejpam-4859	138	16	hence	hence	ADV
ejpam-4859	138	17	,	,	PUNCT
ejpam-4859	138	18	the	the	DET
ejpam-4859	138	19	crn	crn	NOUN
ejpam-4859	138	20	is	be	AUX
ejpam-4859	138	21	of	of	ADP
ejpam-4859	138	22	type	type	NOUN
ejpam-4859	138	23	terminality	terminality	NOUN
ejpam-4859	138	24	bounded	bound	VERB
ejpam-4859	138	25	by	by	ADP
ejpam-4859	138	26	deficiency	deficiency	NOUN
ejpam-4859	138	27	(	(	PUNCT
ejpam-4859	138	28	tbd	tbd	NOUN
ejpam-4859	138	29	)	)	PUNCT
ejpam-4859	138	30	and	and	CCONJ
ejpam-4859	138	31	has	have	VERB
ejpam-4859	138	32	sufficient	sufficient	ADJ
ejpam-4859	138	33	reactant	reactant	NOUN
ejpam-4859	138	34	diversity	diversity	NOUN
ejpam-4859	138	35	(	(	PUNCT
ejpam-4859	138	36	srd	srd	NOUN
ejpam-4859	138	37	)	)	PUNCT
ejpam-4859	138	38	.	.	PUNCT
ejpam-4859	139	1	the	the	DET
ejpam-4859	139	2	next	next	ADJ
ejpam-4859	139	3	proposition	proposition	NOUN
ejpam-4859	139	4	provides	provide	VERB
ejpam-4859	139	5	the	the	DET
ejpam-4859	139	6	initial	initial	ADJ
ejpam-4859	139	7	positioning	positioning	NOUN
ejpam-4859	139	8	of	of	ADP
ejpam-4859	139	9	reactant	reactant	NOUN
ejpam-4859	139	10	diversity	diversity	NOUN
ejpam-4859	139	11	in	in	ADP
ejpam-4859	139	12	the	the	DET
ejpam-4859	139	13	crn	crn	NOUN
ejpam-4859	139	14	landscape	landscape	NOUN
ejpam-4859	139	15	:	:	PUNCT
ejpam-4859	139	16	proposition	proposition	NOUN
ejpam-4859	139	17	3	3	NUM
ejpam-4859	139	18	.	.	PUNCT
ejpam-4859	140	1	a	a	DET
ejpam-4859	140	2	tbd	tbd	NOUN
ejpam-4859	140	3	network	network	NOUN
ejpam-4859	140	4	is	be	AUX
ejpam-4859	140	5	an	an	DET
ejpam-4859	140	6	srd	srd	NOUN
ejpam-4859	140	7	network	network	NOUN
ejpam-4859	140	8	.	.	PUNCT
ejpam-4859	141	1	proof	proof	NOUN
ejpam-4859	141	2	.	.	PUNCT
ejpam-4859	142	1	since	since	SCONJ
ejpam-4859	142	2	the	the	DET
ejpam-4859	142	3	network	network	NOUN
ejpam-4859	142	4	is	be	AUX
ejpam-4859	142	5	tbd	tbd	NOUN
ejpam-4859	142	6	,	,	PUNCT
ejpam-4859	142	7	t−	t−	PROPN
ejpam-4859	142	8	ℓ	ℓ	PROPN
ejpam-4859	142	9	≤	≤	PROPN
ejpam-4859	142	10	δ	δ	PROPN
ejpam-4859	142	11	.	.	PUNCT
ejpam-4859	143	1	this	this	PRON
ejpam-4859	143	2	implies	imply	VERB
ejpam-4859	143	3	that	that	SCONJ
ejpam-4859	143	4	(	(	PUNCT
ejpam-4859	143	5	n−nr)−	n−nr)−	PROPN
ejpam-4859	143	6	ℓ	ℓ	PROPN
ejpam-4859	143	7	≤	≤	PROPN
ejpam-4859	143	8	n−	n−	NOUN
ejpam-4859	143	9	s−	s−	PROPN
ejpam-4859	143	10	ℓ.	ℓ.	NOUN
ejpam-4859	143	11	hence	hence	ADV
ejpam-4859	143	12	,	,	PUNCT
ejpam-4859	143	13	n−	n−	PROPN
ejpam-4859	143	14	nr	nr	NOUN
ejpam-4859	143	15	≤	≤	NUM
ejpam-4859	143	16	n−	n−	PROPN
ejpam-4859	143	17	s	s	PART
ejpam-4859	143	18	and	and	CCONJ
ejpam-4859	143	19	so	so	ADV
ejpam-4859	143	20	nr	nr	PROPN
ejpam-4859	143	21	≥	≥	PROPN
ejpam-4859	143	22	s.	s.	PROPN
ejpam-4859	143	23	corollary	corollary	PROPN
ejpam-4859	143	24	1	1	PROPN
ejpam-4859	143	25	.	.	PUNCT
ejpam-4859	143	26	a	a	DET
ejpam-4859	143	27	t	t	PROPN
ejpam-4859	143	28	-	-	PUNCT
ejpam-4859	143	29	minimal	minimal	ADJ
ejpam-4859	143	30	network	network	NOUN
ejpam-4859	143	31	is	be	AUX
ejpam-4859	143	32	an	an	DET
ejpam-4859	143	33	srd	srd	NOUN
ejpam-4859	143	34	network	network	NOUN
ejpam-4859	143	35	.	.	PUNCT
ejpam-4859	144	1	for	for	ADP
ejpam-4859	144	2	a	a	DET
ejpam-4859	144	3	point	point	NOUN
ejpam-4859	144	4	terminal	terminal	ADJ
ejpam-4859	144	5	networks	network	NOUN
ejpam-4859	144	6	,	,	PUNCT
ejpam-4859	144	7	we	we	PRON
ejpam-4859	144	8	obtain	obtain	VERB
ejpam-4859	144	9	the	the	DET
ejpam-4859	144	10	following	follow	VERB
ejpam-4859	144	11	equivalences	equivalence	NOUN
ejpam-4859	144	12	:	:	PUNCT
ejpam-4859	144	13	proposition	proposition	NOUN
ejpam-4859	144	14	4	4	NUM
ejpam-4859	144	15	.	.	PUNCT
ejpam-4859	145	1	for	for	ADP
ejpam-4859	145	2	a	a	DET
ejpam-4859	145	3	point	point	NOUN
ejpam-4859	145	4	terminal	terminal	ADJ
ejpam-4859	145	5	crn	crn	NOUN
ejpam-4859	145	6	,	,	PUNCT
ejpam-4859	145	7	a	a	DET
ejpam-4859	145	8	network	network	NOUN
ejpam-4859	145	9	is	be	AUX
ejpam-4859	145	10	srd	srd	NOUN
ejpam-4859	145	11	if	if	SCONJ
ejpam-4859	146	1	and	and	CCONJ
ejpam-4859	146	2	only	only	ADV
ejpam-4859	146	3	if	if	SCONJ
ejpam-4859	146	4	it	it	PRON
ejpam-4859	146	5	istbd	istbd	VERB
ejpam-4859	146	6	.	.	PUNCT
ejpam-4859	147	1	proof	proof	NOUN
ejpam-4859	147	2	.	.	PUNCT
ejpam-4859	148	1	since	since	SCONJ
ejpam-4859	148	2	the	the	DET
ejpam-4859	148	3	network	network	NOUN
ejpam-4859	148	4	is	be	AUX
ejpam-4859	148	5	srd	srd	NOUN
ejpam-4859	148	6	,	,	PUNCT
ejpam-4859	148	7	nr	nr	PROPN
ejpam-4859	148	8	≥	≥	PROPN
ejpam-4859	148	9	s.	s.	PROPN
ejpam-4859	148	10	with	with	ADP
ejpam-4859	148	11	this	this	PRON
ejpam-4859	148	12	,	,	PUNCT
ejpam-4859	148	13	(	(	PUNCT
ejpam-4859	148	14	n−	n−	NOUN
ejpam-4859	148	15	nr)−	nr)−	NOUN
ejpam-4859	148	16	ℓ	ℓ	NOUN
ejpam-4859	148	17	≤	≤	PROPN
ejpam-4859	148	18	n−	n−	NOUN
ejpam-4859	148	19	s−	s−	PROPN
ejpam-4859	148	20	ℓ.	ℓ.	NOUN
ejpam-4859	148	21	thus	thus	ADV
ejpam-4859	148	22	,	,	PUNCT
ejpam-4859	149	1	t−	t−	PROPN
ejpam-4859	149	2	ℓ	ℓ	PROPN
ejpam-4859	149	3	≤	≤	PROPN
ejpam-4859	149	4	δ	δ	PROPN
ejpam-4859	149	5	.	.	PUNCT
ejpam-4859	150	1	d.	d.	PROPN
ejpam-4859	150	2	magpantay	magpantay	PROPN
ejpam-4859	150	3	/	/	SYM
ejpam-4859	150	4	eur	eur	PROPN
ejpam-4859	150	5	.	.	PUNCT
ejpam-4859	151	1	j.	j.	PROPN
ejpam-4859	151	2	pure	pure	PROPN
ejpam-4859	151	3	appl	appl	PROPN
ejpam-4859	151	4	.	.	PROPN
ejpam-4859	151	5	math	math	PROPN
ejpam-4859	151	6	,	,	PUNCT
ejpam-4859	151	7	16	16	NUM
ejpam-4859	151	8	(	(	PUNCT
ejpam-4859	151	9	4	4	NUM
ejpam-4859	151	10	)	)	PUNCT
ejpam-4859	151	11	(	(	PUNCT
ejpam-4859	151	12	2023	2023	NUM
ejpam-4859	151	13	)	)	PUNCT
ejpam-4859	151	14	,	,	PUNCT
ejpam-4859	151	15	2557	2557	NUM
ejpam-4859	151	16	-	-	SYM
ejpam-4859	151	17	2580	2580	NUM
ejpam-4859	151	18	2563	2563	NUM
ejpam-4859	151	19	2.4	2.4	NUM
ejpam-4859	151	20	.	.	PUNCT
ejpam-4859	151	21	reactant	reactant	NOUN
ejpam-4859	151	22	subspace	subspace	NOUN
ejpam-4859	151	23	in	in	ADP
ejpam-4859	151	24	this	this	DET
ejpam-4859	151	25	section	section	NOUN
ejpam-4859	151	26	,	,	PUNCT
ejpam-4859	151	27	our	our	PRON
ejpam-4859	151	28	focus	focus	NOUN
ejpam-4859	151	29	was	be	AUX
ejpam-4859	151	30	on	on	ADP
ejpam-4859	151	31	the	the	DET
ejpam-4859	151	32	set	set	NOUN
ejpam-4859	151	33	of	of	ADP
ejpam-4859	151	34	reactant	reactant	NOUN
ejpam-4859	151	35	complexes	complexe	VERB
ejpam-4859	151	36	ρ(r	ρ(r	NOUN
ejpam-4859	151	37	)	)	PUNCT
ejpam-4859	151	38	and	and	CCONJ
ejpam-4859	151	39	its	its	PRON
ejpam-4859	151	40	cardinality	cardinality	PROPN
ejpam-4859	151	41	nr	nr	PROPN
ejpam-4859	151	42	.	.	PUNCT
ejpam-4859	152	1	the	the	DET
ejpam-4859	152	2	following	follow	VERB
ejpam-4859	152	3	was	be	AUX
ejpam-4859	152	4	the	the	DET
ejpam-4859	152	5	linear	linear	ADJ
ejpam-4859	152	6	space	space	NOUN
ejpam-4859	152	7	generated	generate	VERB
ejpam-4859	152	8	by	by	ADP
ejpam-4859	152	9	ρ(r	ρ(r	PROPN
ejpam-4859	152	10	)	)	PUNCT
ejpam-4859	152	11	.	.	PUNCT
ejpam-4859	153	1	definition	definition	NOUN
ejpam-4859	153	2	9	9	NUM
ejpam-4859	153	3	.	.	PUNCT
ejpam-4859	154	1	the	the	DET
ejpam-4859	154	2	reactant	reactant	NOUN
ejpam-4859	154	3	subspace	subspace	NOUN
ejpam-4859	154	4	r	r	NOUN
ejpam-4859	154	5	is	be	AUX
ejpam-4859	154	6	the	the	DET
ejpam-4859	154	7	linear	linear	ADJ
ejpam-4859	154	8	space	space	NOUN
ejpam-4859	154	9	in	in	ADP
ejpam-4859	154	10	rs	r	NOUN
ejpam-4859	154	11	generated	generate	VERB
ejpam-4859	154	12	by	by	ADP
ejpam-4859	154	13	the	the	DET
ejpam-4859	154	14	reactant	reactant	NOUN
ejpam-4859	154	15	complexes	complex	NOUN
ejpam-4859	154	16	,	,	PUNCT
ejpam-4859	154	17	i.e.	i.e.	X
ejpam-4859	154	18	⟨ρ(r)⟩.	⟨ρ(r)⟩.	VERB
ejpam-4859	154	19	the	the	DET
ejpam-4859	154	20	value	value	NOUN
ejpam-4859	154	21	q	q	NOUN
ejpam-4859	154	22	:	:	PUNCT
ejpam-4859	154	23	=	=	SYM
ejpam-4859	154	24	dim	dim	ADJ
ejpam-4859	154	25	r	r	NOUN
ejpam-4859	154	26	is	be	AUX
ejpam-4859	154	27	called	call	VERB
ejpam-4859	154	28	the	the	DET
ejpam-4859	154	29	reactant	reactant	NOUN
ejpam-4859	154	30	rank	rank	NOUN
ejpam-4859	154	31	of	of	ADP
ejpam-4859	154	32	the	the	DET
ejpam-4859	154	33	network	network	NOUN
ejpam-4859	154	34	.	.	PUNCT
ejpam-4859	155	1	remark	remark	PROPN
ejpam-4859	155	2	2	2	NUM
ejpam-4859	155	3	.	.	PUNCT
ejpam-4859	156	1	we	we	PRON
ejpam-4859	156	2	denote	denote	VERB
ejpam-4859	156	3	dim	dim	ADJ
ejpam-4859	156	4	r	r	NOUN
ejpam-4859	156	5	by	by	ADP
ejpam-4859	156	6	“	"	PUNCT
ejpam-4859	156	7	q	q	NOUN
ejpam-4859	156	8	”	"	PUNCT
ejpam-4859	156	9	(	(	PUNCT
ejpam-4859	156	10	since	since	SCONJ
ejpam-4859	156	11	“	"	PUNCT
ejpam-4859	156	12	r	r	NOUN
ejpam-4859	156	13	”	"	PUNCT
ejpam-4859	156	14	is	be	AUX
ejpam-4859	156	15	already	already	ADV
ejpam-4859	156	16	reserved	reserve	VERB
ejpam-4859	156	17	for	for	ADP
ejpam-4859	156	18	the	the	DET
ejpam-4859	156	19	number	number	NOUN
ejpam-4859	156	20	of	of	ADP
ejpam-4859	156	21	reactions	reaction	NOUN
ejpam-4859	156	22	)	)	PUNCT
ejpam-4859	156	23	.	.	PUNCT
ejpam-4859	157	1	we	we	PRON
ejpam-4859	157	2	also	also	ADV
ejpam-4859	157	3	denote	denote	VERB
ejpam-4859	157	4	dim	dim	ADJ
ejpam-4859	158	1	i	i	PRON
ejpam-4859	158	2	m	m	VERB
ejpam-4859	158	3	y	y	NOUN
ejpam-4859	158	4	by	by	ADP
ejpam-4859	158	5	“	"	PUNCT
ejpam-4859	158	6	c	c	NOUN
ejpam-4859	158	7	”	"	PUNCT
ejpam-4859	158	8	(	(	PUNCT
ejpam-4859	158	9	since	since	SCONJ
ejpam-4859	158	10	i	i	PRON
ejpam-4859	158	11	m	m	VERB
ejpam-4859	158	12	y	y	VERB
ejpam-4859	158	13	consists	consist	VERB
ejpam-4859	158	14	precisely	precisely	ADV
ejpam-4859	158	15	of	of	ADP
ejpam-4859	158	16	the	the	DET
ejpam-4859	158	17	network	network	NOUN
ejpam-4859	158	18	’s	’s	PART
ejpam-4859	158	19	complexes	complex	NOUN
ejpam-4859	158	20	embedded	embed	VERB
ejpam-4859	158	21	in	in	ADP
ejpam-4859	158	22	rs	rs	PROPN
ejpam-4859	158	23	)	)	PUNCT
ejpam-4859	158	24	.	.	PUNCT
ejpam-4859	159	1	example	example	NOUN
ejpam-4859	160	1	6	6	NUM
ejpam-4859	160	2	.	.	PUNCT
ejpam-4859	161	1	as	as	ADP
ejpam-4859	161	2	per	per	ADP
ejpam-4859	161	3	example	example	NOUN
ejpam-4859	161	4	1	1	NUM
ejpam-4859	161	5	,	,	PUNCT
ejpam-4859	161	6	the	the	DET
ejpam-4859	161	7	reactant	reactant	NOUN
ejpam-4859	161	8	subspace	subspace	NOUN
ejpam-4859	161	9	r	r	NOUN
ejpam-4859	161	10	=	=	PUNCT
ejpam-4859	161	11	⟨{2a1	⟨{2a1	NOUN
ejpam-4859	161	12	,	,	PUNCT
ejpam-4859	161	13	a2	a2	PROPN
ejpam-4859	161	14	+	+	CCONJ
ejpam-4859	161	15	a3	a3	NOUN
ejpam-4859	161	16	,	,	PUNCT
ejpam-4859	161	17	a3	a3	NOUN
ejpam-4859	161	18	,	,	PUNCT
ejpam-4859	161	19	3a4}⟩.	3a4}⟩.	NUM
ejpam-4859	161	20	with	with	ADP
ejpam-4859	161	21	this	this	PRON
ejpam-4859	161	22	,	,	PUNCT
ejpam-4859	161	23	the	the	DET
ejpam-4859	161	24	reactant	reactant	NOUN
ejpam-4859	161	25	rank	rank	NOUN
ejpam-4859	161	26	is	be	AUX
ejpam-4859	161	27	q	q	NOUN
ejpam-4859	161	28	=	=	ADJ
ejpam-4859	161	29	4	4	NUM
ejpam-4859	161	30	.	.	PUNCT
ejpam-4859	162	1	the	the	DET
ejpam-4859	162	2	relationship	relationship	NOUN
ejpam-4859	162	3	of	of	ADP
ejpam-4859	162	4	the	the	DET
ejpam-4859	162	5	reactant	reactant	NOUN
ejpam-4859	162	6	rank	rank	NOUN
ejpam-4859	162	7	to	to	ADP
ejpam-4859	162	8	the	the	DET
ejpam-4859	162	9	network	network	NOUN
ejpam-4859	162	10	’s	’s	PART
ejpam-4859	162	11	rank	rank	NOUN
ejpam-4859	162	12	is	be	AUX
ejpam-4859	162	13	important	important	ADJ
ejpam-4859	162	14	in	in	ADP
ejpam-4859	162	15	the	the	DET
ejpam-4859	162	16	study	study	NOUN
ejpam-4859	162	17	of	of	ADP
ejpam-4859	162	18	the	the	DET
ejpam-4859	162	19	reactant	reactant	NOUN
ejpam-4859	162	20	subspace	subspace	NOUN
ejpam-4859	162	21	and	and	CCONJ
ejpam-4859	162	22	we	we	PRON
ejpam-4859	162	23	introduce	introduce	VERB
ejpam-4859	162	24	some	some	DET
ejpam-4859	162	25	relevant	relevant	ADJ
ejpam-4859	162	26	concepts	concept	NOUN
ejpam-4859	162	27	here	here	ADV
ejpam-4859	162	28	.	.	PUNCT
ejpam-4859	163	1	definition	definition	NOUN
ejpam-4859	163	2	10	10	NUM
ejpam-4859	163	3	.	.	PUNCT
ejpam-4859	164	1	the	the	DET
ejpam-4859	164	2	rank	rank	NOUN
ejpam-4859	164	3	difference	difference	NOUN
ejpam-4859	164	4	∆(n	∆(n	NOUN
ejpam-4859	164	5	)	)	PUNCT
ejpam-4859	164	6	is	be	AUX
ejpam-4859	164	7	equal	equal	ADJ
ejpam-4859	164	8	to	to	ADP
ejpam-4859	164	9	s	s	PROPN
ejpam-4859	164	10	−	−	PROPN
ejpam-4859	164	11	q.	q.	NOUN
ejpam-4859	165	1	the	the	DET
ejpam-4859	165	2	network	network	NOUN
ejpam-4859	165	3	has	have	VERB
ejpam-4859	165	4	high	high	ADJ
ejpam-4859	165	5	reactant	reactant	NOUN
ejpam-4859	165	6	rank	rank	NOUN
ejpam-4859	165	7	(	(	PUNCT
ejpam-4859	165	8	hrr	hrr	PROPN
ejpam-4859	165	9	)	)	PUNCT
ejpam-4859	165	10	if	if	SCONJ
ejpam-4859	165	11	∆(n	∆(n	NOUN
ejpam-4859	165	12	)	)	PUNCT
ejpam-4859	165	13	is	be	AUX
ejpam-4859	165	14	negative	negative	ADJ
ejpam-4859	165	15	,	,	PUNCT
ejpam-4859	165	16	medium	medium	ADJ
ejpam-4859	165	17	reactant	reactant	NOUN
ejpam-4859	165	18	rank	rank	NOUN
ejpam-4859	165	19	(	(	PUNCT
ejpam-4859	165	20	mrr	mrr	PROPN
ejpam-4859	165	21	)	)	PUNCT
ejpam-4859	165	22	if	if	SCONJ
ejpam-4859	165	23	it	it	PRON
ejpam-4859	165	24	is	be	AUX
ejpam-4859	165	25	zero	zero	NUM
ejpam-4859	165	26	and	and	CCONJ
ejpam-4859	165	27	low	low	ADJ
ejpam-4859	165	28	reactant	reactant	NOUN
ejpam-4859	165	29	rank	rank	NOUN
ejpam-4859	165	30	(	(	PUNCT
ejpam-4859	165	31	lrr	lrr	ADJ
ejpam-4859	165	32	)	)	PUNCT
ejpam-4859	165	33	if	if	SCONJ
ejpam-4859	165	34	it	it	PRON
ejpam-4859	165	35	is	be	AUX
ejpam-4859	165	36	positive	positive	ADJ
ejpam-4859	165	37	.	.	PUNCT
ejpam-4859	165	38	example	example	NOUN
ejpam-4859	166	1	7	7	NUM
ejpam-4859	166	2	.	.	PUNCT
ejpam-4859	166	3	referring	refer	VERB
ejpam-4859	166	4	to	to	ADP
ejpam-4859	166	5	example	example	NOUN
ejpam-4859	166	6	1	1	NUM
ejpam-4859	166	7	,	,	PUNCT
ejpam-4859	166	8	observe	observe	VERB
ejpam-4859	166	9	that	that	SCONJ
ejpam-4859	166	10	the	the	DET
ejpam-4859	166	11	rank	rank	NOUN
ejpam-4859	166	12	difference	difference	NOUN
ejpam-4859	166	13	∆(n	∆(n	NOUN
ejpam-4859	166	14	)	)	PUNCT
ejpam-4859	167	1	=	=	SYM
ejpam-4859	167	2	s	s	PART
ejpam-4859	167	3	−	−	NOUN
ejpam-4859	167	4	q	q	NOUN
ejpam-4859	168	1	=	=	NOUN
ejpam-4859	168	2	3−	3−	NUM
ejpam-4859	168	3	4	4	NUM
ejpam-4859	168	4	=	=	SYM
ejpam-4859	168	5	−1	−1	NOUN
ejpam-4859	168	6	.	.	PUNCT
ejpam-4859	169	1	thus	thus	ADV
ejpam-4859	169	2	,	,	PUNCT
ejpam-4859	169	3	the	the	DET
ejpam-4859	169	4	network	network	NOUN
ejpam-4859	169	5	has	have	VERB
ejpam-4859	169	6	high	high	ADJ
ejpam-4859	169	7	reactant	reactant	NOUN
ejpam-4859	169	8	rank	rank	NOUN
ejpam-4859	169	9	(	(	PUNCT
ejpam-4859	169	10	hrr	hrr	PROPN
ejpam-4859	169	11	)	)	PUNCT
ejpam-4859	169	12	.	.	PUNCT
ejpam-4859	170	1	in	in	ADP
ejpam-4859	170	2	the	the	DET
ejpam-4859	170	3	previous	previous	ADJ
ejpam-4859	170	4	discussion	discussion	NOUN
ejpam-4859	170	5	,	,	PUNCT
ejpam-4859	170	6	we	we	PRON
ejpam-4859	170	7	introduce	introduce	VERB
ejpam-4859	170	8	the	the	DET
ejpam-4859	170	9	deficiency	deficiency	NOUN
ejpam-4859	170	10	of	of	ADP
ejpam-4859	170	11	the	the	DET
ejpam-4859	170	12	network	network	NOUN
ejpam-4859	170	13	.	.	PUNCT
ejpam-4859	171	1	we	we	PRON
ejpam-4859	171	2	now	now	ADV
ejpam-4859	171	3	introduce	introduce	VERB
ejpam-4859	171	4	deficiency	deficiency	NOUN
ejpam-4859	171	5	focusing	focus	VERB
ejpam-4859	171	6	on	on	ADP
ejpam-4859	171	7	the	the	DET
ejpam-4859	171	8	reactant	reactant	NOUN
ejpam-4859	171	9	complexes	complex	NOUN
ejpam-4859	171	10	.	.	PUNCT
ejpam-4859	172	1	this	this	DET
ejpam-4859	172	2	concept	concept	NOUN
ejpam-4859	172	3	was	be	AUX
ejpam-4859	172	4	introduced	introduce	VERB
ejpam-4859	172	5	by	by	ADP
ejpam-4859	172	6	arceo	arceo	PROPN
ejpam-4859	172	7	et	et	PROPN
ejpam-4859	172	8	al	al	PROPN
ejpam-4859	173	1	[	[	X
ejpam-4859	173	2	1	1	NUM
ejpam-4859	173	3	]	]	PUNCT
ejpam-4859	173	4	.	.	PUNCT
ejpam-4859	174	1	definition	definition	NOUN
ejpam-4859	174	2	11	11	NUM
ejpam-4859	174	3	.	.	PUNCT
ejpam-4859	175	1	the	the	DET
ejpam-4859	175	2	reactant	reactant	NOUN
ejpam-4859	175	3	deficiency	deficiency	NOUN
ejpam-4859	175	4	δρ	δρ	NOUN
ejpam-4859	175	5	:	:	PUNCT
ejpam-4859	175	6	=	=	NOUN
ejpam-4859	175	7	nr	nr	PROPN
ejpam-4859	175	8	−	−	PROPN
ejpam-4859	175	9	q	q	ADJ
ejpam-4859	175	10	,	,	PUNCT
ejpam-4859	175	11	i.e.	i.e.	X
ejpam-4859	175	12	,	,	PUNCT
ejpam-4859	175	13	the	the	DET
ejpam-4859	175	14	difference	difference	NOUN
ejpam-4859	175	15	between	between	ADP
ejpam-4859	175	16	the	the	DET
ejpam-4859	175	17	number	number	NOUN
ejpam-4859	175	18	of	of	ADP
ejpam-4859	175	19	reactant	reactant	NOUN
ejpam-4859	175	20	complexes	complex	NOUN
ejpam-4859	175	21	and	and	CCONJ
ejpam-4859	175	22	the	the	DET
ejpam-4859	175	23	reactant	reactant	NOUN
ejpam-4859	175	24	rank	rank	PROPN
ejpam-4859	175	25	q.	q.	PROPN
ejpam-4859	175	26	example	example	PROPN
ejpam-4859	175	27	8	8	NUM
ejpam-4859	175	28	.	.	PUNCT
ejpam-4859	176	1	the	the	DET
ejpam-4859	176	2	reactant	reactant	NOUN
ejpam-4859	176	3	deficiency	deficiency	NOUN
ejpam-4859	176	4	of	of	ADP
ejpam-4859	176	5	the	the	DET
ejpam-4859	176	6	network	network	NOUN
ejpam-4859	176	7	in	in	ADP
ejpam-4859	176	8	example	example	NOUN
ejpam-4859	176	9	1	1	NUM
ejpam-4859	176	10	is	be	AUX
ejpam-4859	176	11	δρ	δρ	ADP
ejpam-4859	176	12	:	:	PUNCT
ejpam-4859	176	13	=	=	SYM
ejpam-4859	176	14	nr−q	nr−q	NOUN
ejpam-4859	176	15	=	=	PUNCT
ejpam-4859	177	1	4−4	4−4	NUM
ejpam-4859	177	2	=	=	SYM
ejpam-4859	177	3	0	0	NUM
ejpam-4859	177	4	.	.	NOUN
ejpam-4859	177	5	2.5	2.5	NUM
ejpam-4859	177	6	.	.	PUNCT
ejpam-4859	178	1	poly	poly	ADJ
ejpam-4859	178	2	-	-	PUNCT
ejpam-4859	178	3	pl	pl	NOUN
ejpam-4859	178	4	kinetic	kinetic	NOUN
ejpam-4859	178	5	systems	system	NOUN
ejpam-4859	178	6	in	in	ADP
ejpam-4859	178	7	this	this	DET
ejpam-4859	178	8	section	section	NOUN
ejpam-4859	178	9	,	,	PUNCT
ejpam-4859	178	10	we	we	PRON
ejpam-4859	178	11	introduce	introduce	VERB
ejpam-4859	178	12	a	a	DET
ejpam-4859	178	13	more	more	ADV
ejpam-4859	178	14	general	general	ADJ
ejpam-4859	178	15	definition	definition	NOUN
ejpam-4859	178	16	of	of	ADP
ejpam-4859	178	17	a	a	DET
ejpam-4859	178	18	kinetics	kinetic	NOUN
ejpam-4859	178	19	.	.	PUNCT
ejpam-4859	179	1	we	we	PRON
ejpam-4859	179	2	begin	begin	VERB
ejpam-4859	179	3	with	with	ADP
ejpam-4859	179	4	the	the	DET
ejpam-4859	179	5	definition	definition	NOUN
ejpam-4859	179	6	and	and	CCONJ
ejpam-4859	179	7	basic	basic	ADJ
ejpam-4859	179	8	properties	property	NOUN
ejpam-4859	179	9	of	of	ADP
ejpam-4859	179	10	a	a	DET
ejpam-4859	179	11	chemical	chemical	NOUN
ejpam-4859	179	12	kinetic	kinetic	NOUN
ejpam-4859	179	13	system	system	NOUN
ejpam-4859	179	14	(	(	PUNCT
ejpam-4859	179	15	cks	ck	NOUN
ejpam-4859	179	16	)	)	PUNCT
ejpam-4859	179	17	.	.	PUNCT
ejpam-4859	180	1	a	a	DET
ejpam-4859	180	2	kinetics	kinetic	NOUN
ejpam-4859	180	3	for	for	ADP
ejpam-4859	180	4	a	a	DET
ejpam-4859	180	5	crn	crn	NOUN
ejpam-4859	180	6	is	be	AUX
ejpam-4859	180	7	an	an	DET
ejpam-4859	180	8	assignment	assignment	NOUN
ejpam-4859	180	9	of	of	ADP
ejpam-4859	180	10	a	a	DET
ejpam-4859	180	11	rate	rate	NOUN
ejpam-4859	180	12	function	function	NOUN
ejpam-4859	180	13	to	to	ADP
ejpam-4859	180	14	each	each	DET
ejpam-4859	180	15	reaction	reaction	NOUN
ejpam-4859	180	16	in	in	ADP
ejpam-4859	180	17	the	the	DET
ejpam-4859	180	18	network	network	NOUN
ejpam-4859	180	19	.	.	PUNCT
ejpam-4859	181	1	this	this	PRON
ejpam-4859	181	2	is	be	AUX
ejpam-4859	181	3	defined	define	VERB
ejpam-4859	181	4	formally	formally	ADV
ejpam-4859	181	5	below	below	ADV
ejpam-4859	181	6	.	.	PUNCT
ejpam-4859	182	1	definition	definition	NOUN
ejpam-4859	182	2	12	12	NUM
ejpam-4859	182	3	.	.	PUNCT
ejpam-4859	183	1	a	a	DET
ejpam-4859	183	2	kinetics	kinetic	NOUN
ejpam-4859	183	3	of	of	ADP
ejpam-4859	183	4	a	a	DET
ejpam-4859	183	5	crn	crn	NOUN
ejpam-4859	183	6	n	n	NOUN
ejpam-4859	183	7	=	=	SYM
ejpam-4859	183	8	(	(	PUNCT
ejpam-4859	183	9	s	s	NOUN
ejpam-4859	183	10	,	,	PUNCT
ejpam-4859	183	11	c	c	NOUN
ejpam-4859	183	12	,	,	PUNCT
ejpam-4859	183	13	r	r	NOUN
ejpam-4859	183	14	)	)	PUNCT
ejpam-4859	183	15	is	be	AUX
ejpam-4859	183	16	an	an	DET
ejpam-4859	183	17	assignment	assignment	NOUN
ejpam-4859	183	18	of	of	ADP
ejpam-4859	183	19	a	a	DET
ejpam-4859	183	20	rate	rate	NOUN
ejpam-4859	183	21	function	function	NOUN
ejpam-4859	183	22	kij	kij	PROPN
ejpam-4859	183	23	:	:	PUNCT
ejpam-4859	183	24	ωk	ωk	ADP
ejpam-4859	183	25	→	→	PUNCT
ejpam-4859	183	26	r≥	r≥	PROPN
ejpam-4859	183	27	to	to	ADP
ejpam-4859	183	28	each	each	DET
ejpam-4859	183	29	reaction	reaction	NOUN
ejpam-4859	183	30	(	(	PUNCT
ejpam-4859	183	31	i	i	PROPN
ejpam-4859	183	32	,	,	PUNCT
ejpam-4859	183	33	j	j	PROPN
ejpam-4859	183	34	)	)	PUNCT
ejpam-4859	183	35	∈	∈	PROPN
ejpam-4859	183	36	r	r	NOUN
ejpam-4859	183	37	,	,	PUNCT
ejpam-4859	183	38	where	where	SCONJ
ejpam-4859	183	39	ωk	ωk	ADP
ejpam-4859	183	40	is	be	AUX
ejpam-4859	183	41	a	a	DET
ejpam-4859	183	42	set	set	NOUN
ejpam-4859	183	43	such	such	ADJ
ejpam-4859	183	44	that	that	DET
ejpam-4859	183	45	rs	rs	NOUN
ejpam-4859	183	46	>	>	X
ejpam-4859	183	47	⊆	⊆	NUM
ejpam-4859	183	48	ωk	ωk	ADP
ejpam-4859	183	49	⊆	⊆	NUM
ejpam-4859	183	50	rs	rs	ADJ
ejpam-4859	183	51	≥	≥	NOUN
ejpam-4859	183	52	,	,	PUNCT
ejpam-4859	183	53	and	and	CCONJ
ejpam-4859	183	54	kij(c	kij(c	X
ejpam-4859	183	55	)	)	PUNCT
ejpam-4859	183	56	≥	≥	NOUN
ejpam-4859	183	57	0	0	NUM
ejpam-4859	183	58	,	,	PUNCT
ejpam-4859	183	59	for	for	ADP
ejpam-4859	183	60	all	all	DET
ejpam-4859	183	61	c	c	NOUN
ejpam-4859	183	62	∈	∈	NOUN
ejpam-4859	183	63	ωk	ωk	ADP
ejpam-4859	183	64	.	.	PUNCT
ejpam-4859	184	1	a	a	DET
ejpam-4859	184	2	kinetics	kinetic	NOUN
ejpam-4859	184	3	for	for	ADP
ejpam-4859	184	4	a	a	DET
ejpam-4859	184	5	network	network	NOUN
ejpam-4859	184	6	n	n	PRON
ejpam-4859	184	7	is	be	AUX
ejpam-4859	184	8	denoted	denote	VERB
ejpam-4859	184	9	by	by	ADP
ejpam-4859	184	10	k	k	PROPN
ejpam-4859	184	11	=	=	PUNCT
ejpam-4859	185	1	[	[	X
ejpam-4859	185	2	k1,k2	k1,k2	PROPN
ejpam-4859	185	3	,	,	PUNCT
ejpam-4859	185	4	.	.	PUNCT
ejpam-4859	185	5	.	.	PUNCT
ejpam-4859	186	1	.	.	PUNCT
ejpam-4859	187	1	,	,	PUNCT
ejpam-4859	187	2	kr	kr	PROPN
ejpam-4859	187	3	]	]	X
ejpam-4859	187	4	t	t	NOUN
ejpam-4859	187	5	:	:	PUNCT
ejpam-4859	187	6	ωk	ωk	ADP
ejpam-4859	187	7	→	→	SYM
ejpam-4859	187	8	rs	rs	ADJ
ejpam-4859	187	9	≥	≥	NOUN
ejpam-4859	187	10	.	.	PUNCT
ejpam-4859	188	1	the	the	DET
ejpam-4859	188	2	pair	pair	NOUN
ejpam-4859	188	3	(	(	PUNCT
ejpam-4859	188	4	n	n	NOUN
ejpam-4859	188	5	,	,	PUNCT
ejpam-4859	188	6	k	k	NOUN
ejpam-4859	188	7	)	)	PUNCT
ejpam-4859	188	8	is	be	AUX
ejpam-4859	188	9	called	call	VERB
ejpam-4859	188	10	the	the	DET
ejpam-4859	188	11	chemical	chemical	NOUN
ejpam-4859	188	12	kinetic	kinetic	NOUN
ejpam-4859	188	13	system	system	NOUN
ejpam-4859	188	14	(	(	PUNCT
ejpam-4859	188	15	cks	ck	NOUN
ejpam-4859	188	16	)	)	PUNCT
ejpam-4859	188	17	.	.	PUNCT
ejpam-4859	189	1	d.	d.	PROPN
ejpam-4859	189	2	magpantay	magpantay	PROPN
ejpam-4859	189	3	/	/	SYM
ejpam-4859	189	4	eur	eur	PROPN
ejpam-4859	189	5	.	.	PUNCT
ejpam-4859	190	1	j.	j.	PROPN
ejpam-4859	190	2	pure	pure	PROPN
ejpam-4859	190	3	appl	appl	PROPN
ejpam-4859	190	4	.	.	PROPN
ejpam-4859	190	5	math	math	PROPN
ejpam-4859	190	6	,	,	PUNCT
ejpam-4859	190	7	16	16	NUM
ejpam-4859	190	8	(	(	PUNCT
ejpam-4859	190	9	4	4	NUM
ejpam-4859	190	10	)	)	PUNCT
ejpam-4859	190	11	(	(	PUNCT
ejpam-4859	190	12	2023	2023	NUM
ejpam-4859	190	13	)	)	PUNCT
ejpam-4859	190	14	,	,	PUNCT
ejpam-4859	190	15	2557	2557	NUM
ejpam-4859	190	16	-	-	SYM
ejpam-4859	190	17	2580	2580	NUM
ejpam-4859	190	18	2564	2564	NUM
ejpam-4859	190	19	the	the	DET
ejpam-4859	190	20	above	above	ADJ
ejpam-4859	190	21	definition	definition	NOUN
ejpam-4859	190	22	is	be	AUX
ejpam-4859	190	23	adopted	adopt	VERB
ejpam-4859	190	24	from	from	ADP
ejpam-4859	190	25	the	the	DET
ejpam-4859	190	26	paper	paper	NOUN
ejpam-4859	190	27	of	of	ADP
ejpam-4859	190	28	wiuf	wiuf	NOUN
ejpam-4859	190	29	&	&	CCONJ
ejpam-4859	190	30	feliu	feliu	PROPN
ejpam-4859	191	1	[	[	X
ejpam-4859	191	2	10	10	NUM
ejpam-4859	191	3	]	]	PUNCT
ejpam-4859	191	4	.	.	PUNCT
ejpam-4859	192	1	however	however	ADV
ejpam-4859	192	2	,	,	PUNCT
ejpam-4859	192	3	in	in	ADP
ejpam-4859	192	4	this	this	DET
ejpam-4859	192	5	paper	paper	NOUN
ejpam-4859	192	6	,	,	PUNCT
ejpam-4859	192	7	we	we	PRON
ejpam-4859	192	8	use	use	VERB
ejpam-4859	192	9	simpler	simple	ADJ
ejpam-4859	192	10	definition	definition	NOUN
ejpam-4859	192	11	of	of	ADP
ejpam-4859	192	12	cks	ck	NOUN
ejpam-4859	192	13	as	as	SCONJ
ejpam-4859	192	14	follows	follow	VERB
ejpam-4859	192	15	:	:	PUNCT
ejpam-4859	192	16	definition	definition	NOUN
ejpam-4859	192	17	13	13	NUM
ejpam-4859	192	18	.	.	PUNCT
ejpam-4859	193	1	a	a	DET
ejpam-4859	193	2	chemical	chemical	NOUN
ejpam-4859	193	3	kinetics	kinetic	NOUN
ejpam-4859	193	4	is	be	AUX
ejpam-4859	193	5	a	a	DET
ejpam-4859	193	6	kinetics	kinetic	NOUN
ejpam-4859	193	7	satisfying	satisfy	VERB
ejpam-4859	193	8	the	the	DET
ejpam-4859	193	9	positivity	positivity	NOUN
ejpam-4859	193	10	condition	condition	NOUN
ejpam-4859	193	11	:	:	PUNCT
ejpam-4859	193	12	for	for	ADP
ejpam-4859	193	13	each	each	DET
ejpam-4859	193	14	reaction	reaction	NOUN
ejpam-4859	193	15	(	(	PUNCT
ejpam-4859	193	16	i	i	PROPN
ejpam-4859	193	17	,	,	PUNCT
ejpam-4859	193	18	j	j	PROPN
ejpam-4859	193	19	)	)	PUNCT
ejpam-4859	193	20	∈	∈	PROPN
ejpam-4859	193	21	r	r	NOUN
ejpam-4859	193	22	,	,	PUNCT
ejpam-4859	193	23	kij(c	kij(c	PROPN
ejpam-4859	193	24	)	)	PUNCT
ejpam-4859	193	25	>	>	X
ejpam-4859	193	26	0	0	PUNCT
ejpam-4859	194	1	if	if	SCONJ
ejpam-4859	194	2	and	and	CCONJ
ejpam-4859	194	3	only	only	ADV
ejpam-4859	194	4	if	if	SCONJ
ejpam-4859	194	5	supp	supp	PROPN
ejpam-4859	194	6	i	i	PROPN
ejpam-4859	194	7	⊂	⊂	PROPN
ejpam-4859	194	8	supp	supp	PROPN
ejpam-4859	194	9	c	c	PROPN
ejpam-4859	194	10	,	,	PUNCT
ejpam-4859	194	11	where	where	SCONJ
ejpam-4859	194	12	c	c	PROPN
ejpam-4859	194	13	∈	∈	PROPN
ejpam-4859	194	14	ωk	ωk	ADP
ejpam-4859	194	15	.	.	PUNCT
ejpam-4859	194	16	remark	remark	PROPN
ejpam-4859	194	17	3	3	NUM
ejpam-4859	194	18	.	.	PUNCT
ejpam-4859	194	19	(	(	PUNCT
ejpam-4859	194	20	feinberg	feinberg	PROPN
ejpam-4859	194	21	,	,	PUNCT
ejpam-4859	194	22	1987	1987	NUM
ejpam-4859	194	23	)	)	PUNCT
ejpam-4859	194	24	the	the	DET
ejpam-4859	194	25	“	"	PUNCT
ejpam-4859	194	26	positivity	positivity	NOUN
ejpam-4859	194	27	condition	condition	NOUN
ejpam-4859	194	28	”	"	PUNCT
ejpam-4859	194	29	requires	require	VERB
ejpam-4859	194	30	that	that	SCONJ
ejpam-4859	194	31	the	the	DET
ejpam-4859	194	32	rate	rate	NOUN
ejpam-4859	194	33	function	function	VERB
ejpam-4859	194	34	kij	kij	PROPN
ejpam-4859	194	35	of	of	ADP
ejpam-4859	194	36	the	the	DET
ejpam-4859	194	37	reaction	reaction	NOUN
ejpam-4859	195	1	i	i	PRON
ejpam-4859	195	2	→	→	SYM
ejpam-4859	195	3	j	j	PROPN
ejpam-4859	195	4	proceeds	proceed	VERB
ejpam-4859	195	5	at	at	ADP
ejpam-4859	195	6	a	a	DET
ejpam-4859	195	7	nonzero	nonzero	NOUN
ejpam-4859	195	8	rate	rate	NOUN
ejpam-4859	195	9	at	at	ADP
ejpam-4859	195	10	a	a	DET
ejpam-4859	195	11	specified	specified	ADJ
ejpam-4859	195	12	composition	composition	NOUN
ejpam-4859	195	13	precisely	precisely	ADV
ejpam-4859	195	14	when	when	SCONJ
ejpam-4859	195	15	all	all	DET
ejpam-4859	195	16	species	specie	NOUN
ejpam-4859	195	17	in	in	ADP
ejpam-4859	195	18	the	the	DET
ejpam-4859	195	19	reactant	reactant	NOUN
ejpam-4859	195	20	complex	complex	NOUN
ejpam-4859	195	21	i	i	PRON
ejpam-4859	195	22	are	be	AUX
ejpam-4859	195	23	present	present	ADJ
ejpam-4859	195	24	in	in	ADP
ejpam-4859	195	25	this	this	DET
ejpam-4859	195	26	composition	composition	NOUN
ejpam-4859	195	27	.	.	PUNCT
ejpam-4859	196	1	note	note	VERB
ejpam-4859	196	2	that	that	SCONJ
ejpam-4859	196	3	the	the	DET
ejpam-4859	196	4	notation	notation	NOUN
ejpam-4859	196	5	supp	supp	PROPN
ejpam-4859	196	6	c	c	PROPN
ejpam-4859	196	7	refers	refer	VERB
ejpam-4859	196	8	to	to	ADP
ejpam-4859	196	9	the	the	DET
ejpam-4859	196	10	set	set	NOUN
ejpam-4859	196	11	of	of	ADP
ejpam-4859	196	12	species	specie	NOUN
ejpam-4859	196	13	in	in	ADP
ejpam-4859	196	14	the	the	DET
ejpam-4859	196	15	crn	crn	NOUN
ejpam-4859	196	16	that	that	PRON
ejpam-4859	196	17	have	have	VERB
ejpam-4859	196	18	nonzero	nonzero	NOUN
ejpam-4859	196	19	concentrations	concentration	NOUN
ejpam-4859	196	20	at	at	ADP
ejpam-4859	196	21	composition	composition	NOUN
ejpam-4859	196	22	c.	c.	NOUN
ejpam-4859	196	23	on	on	ADP
ejpam-4859	196	24	the	the	DET
ejpam-4859	196	25	other	other	ADJ
ejpam-4859	196	26	hand	hand	NOUN
ejpam-4859	196	27	,	,	PUNCT
ejpam-4859	196	28	supp	supp	PROPN
ejpam-4859	196	29	i	i	PRON
ejpam-4859	196	30	pertains	pertain	VERB
ejpam-4859	196	31	to	to	ADP
ejpam-4859	196	32	the	the	DET
ejpam-4859	196	33	set	set	NOUN
ejpam-4859	196	34	of	of	ADP
ejpam-4859	196	35	species	specie	NOUN
ejpam-4859	196	36	in	in	ADP
ejpam-4859	196	37	the	the	DET
ejpam-4859	196	38	complex	complex	NOUN
ejpam-4859	196	39	i	i	PRON
ejpam-4859	196	40	i.e.	i.e.	X
ejpam-4859	196	41	,	,	PUNCT
ejpam-4859	196	42	these	these	PRON
ejpam-4859	196	43	are	be	AUX
ejpam-4859	196	44	the	the	DET
ejpam-4859	196	45	“	"	PUNCT
ejpam-4859	196	46	ingredients	ingredient	NOUN
ejpam-4859	196	47	”	"	PUNCT
ejpam-4859	196	48	required	require	VERB
ejpam-4859	196	49	for	for	ADP
ejpam-4859	196	50	the	the	DET
ejpam-4859	196	51	reaction	reaction	NOUN
ejpam-4859	196	52	i	i	PRON
ejpam-4859	196	53	→	→	SYM
ejpam-4859	196	54	j	j	PROPN
ejpam-4859	196	55	to	to	PART
ejpam-4859	196	56	happen	happen	VERB
ejpam-4859	196	57	.	.	PUNCT
ejpam-4859	197	1	hence	hence	ADV
ejpam-4859	197	2	,	,	PUNCT
ejpam-4859	197	3	by	by	ADP
ejpam-4859	197	4	supp	supp	PROPN
ejpam-4859	197	5	i	i	PROPN
ejpam-4859	197	6	⊂	⊂	PROPN
ejpam-4859	197	7	supp	supp	PROPN
ejpam-4859	198	1	c	c	AUX
ejpam-4859	198	2	,	,	PUNCT
ejpam-4859	198	3	we	we	PRON
ejpam-4859	198	4	mean	mean	VERB
ejpam-4859	198	5	that	that	SCONJ
ejpam-4859	198	6	at	at	ADP
ejpam-4859	198	7	composition	composition	NOUN
ejpam-4859	198	8	c	c	NOUN
ejpam-4859	198	9	,	,	PUNCT
ejpam-4859	198	10	all	all	DET
ejpam-4859	198	11	ingredients	ingredient	NOUN
ejpam-4859	198	12	needed	need	VERB
ejpam-4859	198	13	for	for	ADP
ejpam-4859	198	14	the	the	DET
ejpam-4859	198	15	occurrence	occurrence	NOUN
ejpam-4859	198	16	of	of	ADP
ejpam-4859	198	17	the	the	DET
ejpam-4859	198	18	reaction	reaction	NOUN
ejpam-4859	198	19	i	i	PRON
ejpam-4859	198	20	→	→	SYM
ejpam-4859	198	21	j	j	PROPN
ejpam-4859	198	22	are	be	AUX
ejpam-4859	198	23	available	available	ADJ
ejpam-4859	198	24	.	.	PUNCT
ejpam-4859	199	1	a	a	DET
ejpam-4859	199	2	chemical	chemical	NOUN
ejpam-4859	199	3	kinetics	kinetic	NOUN
ejpam-4859	199	4	gives	give	VERB
ejpam-4859	199	5	rise	rise	NOUN
ejpam-4859	199	6	to	to	ADP
ejpam-4859	199	7	two	two	NUM
ejpam-4859	199	8	closely	closely	ADV
ejpam-4859	199	9	related	relate	VERB
ejpam-4859	199	10	objects	object	NOUN
ejpam-4859	199	11	:	:	PUNCT
ejpam-4859	199	12	the	the	DET
ejpam-4859	199	13	species	species	NOUN
ejpam-4859	199	14	formation	formation	NOUN
ejpam-4859	199	15	rate	rate	NOUN
ejpam-4859	199	16	function	function	NOUN
ejpam-4859	199	17	(	(	PUNCT
ejpam-4859	199	18	sfrf	sfrf	NOUN
ejpam-4859	199	19	)	)	PUNCT
ejpam-4859	199	20	and	and	CCONJ
ejpam-4859	199	21	the	the	DET
ejpam-4859	199	22	associated	associated	ADJ
ejpam-4859	199	23	ode	ode	PROPN
ejpam-4859	199	24	systems	system	NOUN
ejpam-4859	199	25	:	:	PUNCT
ejpam-4859	199	26	definition	definition	NOUN
ejpam-4859	199	27	14	14	NUM
ejpam-4859	199	28	.	.	PUNCT
ejpam-4859	200	1	the	the	DET
ejpam-4859	200	2	species	species	NOUN
ejpam-4859	200	3	formation	formation	NOUN
ejpam-4859	200	4	rate	rate	NOUN
ejpam-4859	200	5	function	function	NOUN
ejpam-4859	200	6	(	(	PUNCT
ejpam-4859	200	7	sfrf	sfrf	NOUN
ejpam-4859	200	8	)	)	PUNCT
ejpam-4859	200	9	of	of	ADP
ejpam-4859	200	10	cks	cks	PROPN
ejpam-4859	200	11	is	be	AUX
ejpam-4859	200	12	the	the	DET
ejpam-4859	200	13	vector	vector	NOUN
ejpam-4859	200	14	field	field	NOUN
ejpam-4859	200	15	f(x	f(x	PROPN
ejpam-4859	200	16	)	)	PUNCT
ejpam-4859	200	17	=	=	PUNCT
ejpam-4859	200	18	nk(x	nk(x	X
ejpam-4859	200	19	)	)	PUNCT
ejpam-4859	200	20	=	=	PUNCT
ejpam-4859	201	1	∑	∑	PUNCT
ejpam-4859	201	2	y→y′	y→y′	PROPN
ejpam-4859	201	3	ky→y′(x)(y	ky→y′(x)(y	PROPN
ejpam-4859	201	4	′	′	VERB
ejpam-4859	202	1	−	−	PROPN
ejpam-4859	202	2	y	y	PROPN
ejpam-4859	202	3	)	)	PUNCT
ejpam-4859	202	4	.	.	PUNCT
ejpam-4859	203	1	where	where	SCONJ
ejpam-4859	203	2	n	n	PRON
ejpam-4859	203	3	is	be	AUX
ejpam-4859	203	4	the	the	DET
ejpam-4859	203	5	stoichiometric	stoichiometric	ADJ
ejpam-4859	203	6	matrix	matrix	NOUN
ejpam-4859	203	7	.	.	PUNCT
ejpam-4859	204	1	the	the	DET
ejpam-4859	204	2	equation	equation	NOUN
ejpam-4859	204	3	ċ	ċ	X
ejpam-4859	204	4	=	=	SYM
ejpam-4859	204	5	f(c	f(c	PROPN
ejpam-4859	204	6	)	)	PUNCT
ejpam-4859	204	7	is	be	AUX
ejpam-4859	204	8	the	the	DET
ejpam-4859	204	9	ode	ode	ADJ
ejpam-4859	204	10	or	or	CCONJ
ejpam-4859	204	11	dynamical	dynamical	ADJ
ejpam-4859	204	12	system	system	NOUN
ejpam-4859	204	13	of	of	ADP
ejpam-4859	204	14	the	the	DET
ejpam-4859	204	15	cks	ck	NOUN
ejpam-4859	204	16	.	.	PUNCT
ejpam-4859	204	17	example	example	NOUN
ejpam-4859	204	18	9	9	NUM
ejpam-4859	204	19	.	.	X
ejpam-4859	204	20	refering	refer	VERB
ejpam-4859	204	21	to	to	ADP
ejpam-4859	204	22	example	example	NOUN
ejpam-4859	204	23	1	1	NUM
ejpam-4859	204	24	,	,	PUNCT
ejpam-4859	204	25	the	the	DET
ejpam-4859	204	26	dynamical	dynamical	ADJ
ejpam-4859	204	27	system	system	NOUN
ejpam-4859	204	28	of	of	ADP
ejpam-4859	204	29	the	the	DET
ejpam-4859	204	30	cks	ck	NOUN
ejpam-4859	204	31	is	be	AUX
ejpam-4859	204	32	ċ	ċ	PROPN
ejpam-4859	204	33	=	=	SYM
ejpam-4859	204	34	nk(c	nk(c	PROPN
ejpam-4859	204	35	)	)	PUNCT
ejpam-4859	205	1	=	=	SYM
ejpam-4859	205	2			NOUN
ejpam-4859	206	1	−2	−2	NOUN
ejpam-4859	206	2	0	0	NUM
ejpam-4859	206	3	0	0	NUM
ejpam-4859	206	4	0	0	NUM
ejpam-4859	206	5	−2	−2	NOUN
ejpam-4859	206	6	0	0	NUM
ejpam-4859	206	7	−1	−1	NOUN
ejpam-4859	206	8	1	1	NUM
ejpam-4859	206	9	1	1	NUM
ejpam-4859	206	10	0	0	NUM
ejpam-4859	206	11	1	1	NUM
ejpam-4859	206	12	0	0	NUM
ejpam-4859	206	13	0	0	NUM
ejpam-4859	206	14	1	1	NUM
ejpam-4859	206	15	0	0	NUM
ejpam-4859	206	16	0	0	NUM
ejpam-4859	206	17	0	0	NUM
ejpam-4859	206	18	0	0	NUM
ejpam-4859	207	1	−3	−3	NOUN
ejpam-4859	207	2	3	3	NUM
ejpam-4859	207	3			NOUN
ejpam-4859	207	4			NOUN
ejpam-4859	207	5	k2a1→a3	k2a1→a3	PUNCT
ejpam-4859	208	1	ka2+a3→a3	ka2+a3→a3	PROPN
ejpam-4859	208	2	ka3→a2+a3	ka3→a2+a3	PROPN
ejpam-4859	208	3	k3a4→a2+a3	k3a4→a2+a3	PROPN
ejpam-4859	208	4	k2a1→3a4	k2a1→3a4	PROPN
ejpam-4859	208	5			PROPN
ejpam-4859	208	6	.	.	PUNCT
ejpam-4859	209	1	here	here	ADV
ejpam-4859	209	2	,	,	PUNCT
ejpam-4859	209	3	k(x	k(x	PROPN
ejpam-4859	209	4	)	)	PUNCT
ejpam-4859	209	5	is	be	AUX
ejpam-4859	209	6	called	call	VERB
ejpam-4859	209	7	the	the	DET
ejpam-4859	209	8	kinetic	kinetic	ADJ
ejpam-4859	209	9	vector	vector	NOUN
ejpam-4859	209	10	.	.	PUNCT
ejpam-4859	210	1	we	we	PRON
ejpam-4859	210	2	will	will	AUX
ejpam-4859	210	3	assume	assume	VERB
ejpam-4859	210	4	that	that	SCONJ
ejpam-4859	210	5	the	the	DET
ejpam-4859	210	6	ode	ode	ADJ
ejpam-4859	210	7	system	system	NOUN
ejpam-4859	210	8	above	above	ADV
ejpam-4859	210	9	is	be	AUX
ejpam-4859	210	10	under	under	ADP
ejpam-4859	210	11	power	power	NOUN
ejpam-4859	210	12	law	law	NOUN
ejpam-4859	210	13	kinetics	kinetic	NOUN
ejpam-4859	210	14	(	(	PUNCT
ejpam-4859	210	15	plk	plk	PROPN
ejpam-4859	210	16	)	)	PUNCT
ejpam-4859	210	17	which	which	PRON
ejpam-4859	210	18	have	have	VERB
ejpam-4859	210	19	the	the	DET
ejpam-4859	210	20	form	form	NOUN
ejpam-4859	210	21	ki(x	ki(x	PUNCT
ejpam-4859	210	22	)	)	PUNCT
ejpam-4859	211	1	=	=	PRON
ejpam-4859	211	2	ki	ki	PROPN
ejpam-4859	211	3	m∏	m∏	PROPN
ejpam-4859	211	4	j=1	j=1	PROPN
ejpam-4859	212	1	xfij	xfij	PROPN
ejpam-4859	212	2	where	where	SCONJ
ejpam-4859	212	3	1	1	NUM
ejpam-4859	212	4	≤	≤	NUM
ejpam-4859	212	5	i	i	NOUN
ejpam-4859	212	6	≤	≤	ADJ
ejpam-4859	212	7	r	r	NOUN
ejpam-4859	212	8	with	with	ADP
ejpam-4859	212	9	ki	ki	PROPN
ejpam-4859	212	10	∈	∈	PROPN
ejpam-4859	212	11	r+	r+	PUNCT
ejpam-4859	212	12	and	and	CCONJ
ejpam-4859	212	13	fij	fij	PROPN
ejpam-4859	212	14	∈	∈	PROPN
ejpam-4859	212	15	r.	r.	PROPN
ejpam-4859	212	16	power	power	PROPN
ejpam-4859	212	17	law	law	NOUN
ejpam-4859	212	18	kinetics	kinetic	NOUN
ejpam-4859	212	19	is	be	AUX
ejpam-4859	212	20	defined	define	VERB
ejpam-4859	212	21	by	by	ADP
ejpam-4859	212	22	an	an	DET
ejpam-4859	212	23	r	r	NOUN
ejpam-4859	212	24	×m	×m	NOUN
ejpam-4859	212	25	matrix	matrix	NOUN
ejpam-4859	212	26	f	f	NOUN
ejpam-4859	213	1	=	=	PUNCT
ejpam-4859	214	1	[	[	X
ejpam-4859	214	2	fij	fij	PROPN
ejpam-4859	214	3	]	]	PUNCT
ejpam-4859	214	4	,	,	PUNCT
ejpam-4859	214	5	called	call	VERB
ejpam-4859	214	6	the	the	DET
ejpam-4859	214	7	kinetic	kinetic	ADJ
ejpam-4859	214	8	order	order	NOUN
ejpam-4859	214	9	matrix	matrix	NOUN
ejpam-4859	214	10	,	,	PUNCT
ejpam-4859	214	11	and	and	CCONJ
ejpam-4859	214	12	vector	vector	NOUN
ejpam-4859	214	13	k	k	PROPN
ejpam-4859	214	14	∈	∈	PROPN
ejpam-4859	214	15	rr	rr	PROPN
ejpam-4859	214	16	,	,	PUNCT
ejpam-4859	214	17	called	call	VERB
ejpam-4859	214	18	the	the	DET
ejpam-4859	214	19	rate	rate	NOUN
ejpam-4859	214	20	vector	vector	NOUN
ejpam-4859	214	21	.	.	PUNCT
ejpam-4859	215	1	a	a	DET
ejpam-4859	215	2	particular	particular	ADJ
ejpam-4859	215	3	example	example	NOUN
ejpam-4859	215	4	of	of	ADP
ejpam-4859	215	5	power	power	NOUN
ejpam-4859	215	6	law	law	NOUN
ejpam-4859	215	7	kinetics	kinetic	NOUN
ejpam-4859	215	8	is	be	AUX
ejpam-4859	215	9	the	the	DET
ejpam-4859	215	10	well	well	ADV
ejpam-4859	215	11	-	-	PUNCT
ejpam-4859	215	12	known	know	VERB
ejpam-4859	215	13	mass	mass	NOUN
ejpam-4859	215	14	action	action	NOUN
ejpam-4859	215	15	kinetics	kinetic	NOUN
ejpam-4859	215	16	where	where	SCONJ
ejpam-4859	215	17	the	the	DET
ejpam-4859	215	18	kinetic	kinetic	ADJ
ejpam-4859	215	19	order	order	NOUN
ejpam-4859	215	20	matrix	matrix	NOUN
ejpam-4859	215	21	consists	consist	VERB
ejpam-4859	215	22	of	of	ADP
ejpam-4859	215	23	stoichiometric	stoichiometric	ADJ
ejpam-4859	215	24	coefficients	coefficient	NOUN
ejpam-4859	215	25	of	of	ADP
ejpam-4859	215	26	the	the	DET
ejpam-4859	215	27	reactants	reactant	NOUN
ejpam-4859	215	28	.	.	PUNCT
ejpam-4859	216	1	in	in	ADP
ejpam-4859	216	2	example	example	NOUN
ejpam-4859	216	3	1	1	NUM
ejpam-4859	216	4	,	,	PUNCT
ejpam-4859	216	5	we	we	PRON
ejpam-4859	216	6	assume	assume	VERB
ejpam-4859	216	7	power	power	NOUN
ejpam-4859	216	8	law	law	NOUN
ejpam-4859	216	9	kinetics	kinetic	VERB
ejpam-4859	216	10	so	so	SCONJ
ejpam-4859	216	11	that	that	SCONJ
ejpam-4859	216	12	the	the	DET
ejpam-4859	216	13	kinetic	kinetic	ADJ
ejpam-4859	216	14	order	order	NOUN
ejpam-4859	216	15	matrix	matrix	NOUN
ejpam-4859	216	16	is	be	AUX
ejpam-4859	216	17	d.	d.	PROPN
ejpam-4859	216	18	magpantay	magpantay	PROPN
ejpam-4859	216	19	/	/	SYM
ejpam-4859	216	20	eur	eur	PROPN
ejpam-4859	216	21	.	.	PUNCT
ejpam-4859	217	1	j.	j.	PROPN
ejpam-4859	217	2	pure	pure	PROPN
ejpam-4859	217	3	appl	appl	PROPN
ejpam-4859	217	4	.	.	PROPN
ejpam-4859	217	5	math	math	PROPN
ejpam-4859	217	6	,	,	PUNCT
ejpam-4859	217	7	16	16	NUM
ejpam-4859	217	8	(	(	PUNCT
ejpam-4859	217	9	4	4	NUM
ejpam-4859	217	10	)	)	PUNCT
ejpam-4859	217	11	(	(	PUNCT
ejpam-4859	217	12	2023	2023	NUM
ejpam-4859	217	13	)	)	PUNCT
ejpam-4859	217	14	,	,	PUNCT
ejpam-4859	217	15	2557	2557	NUM
ejpam-4859	217	16	-	-	SYM
ejpam-4859	217	17	2580	2580	NUM
ejpam-4859	217	18	2565	2565	NUM
ejpam-4859	217	19	a1	a1	NOUN
ejpam-4859	217	20	a2	a2	PROPN
ejpam-4859	217	21	a3	a3	NOUN
ejpam-4859	217	22	a4	a4	PROPN
ejpam-4859	217	23	f	f	NOUN
ejpam-4859	217	24	=	=	PUNCT
ejpam-4859	217	25			NOUN
ejpam-4859	217	26	f11	f11	VERB
ejpam-4859	217	27	0	0	NUM
ejpam-4859	217	28	0	0	NUM
ejpam-4859	217	29	0	0	NUM
ejpam-4859	217	30	0	0	NUM
ejpam-4859	217	31	f22	f22	NOUN
ejpam-4859	217	32	f32	f32	NOUN
ejpam-4859	217	33	0	0	NUM
ejpam-4859	217	34	0	0	NUM
ejpam-4859	217	35	0	0	NUM
ejpam-4859	218	1	f33	f33	NOUN
ejpam-4859	218	2	0	0	NUM
ejpam-4859	218	3	0	0	NUM
ejpam-4859	218	4	0	0	NUM
ejpam-4859	218	5	0	0	NUM
ejpam-4859	218	6	f44	f44	NOUN
ejpam-4859	218	7	f15	f15	PROPN
ejpam-4859	218	8	0	0	NUM
ejpam-4859	218	9	0	0	NUM
ejpam-4859	218	10	0	0	NUM
ejpam-4859	218	11			NOUN
ejpam-4859	218	12	r1	r1	NOUN
ejpam-4859	218	13	r2	r2	PROPN
ejpam-4859	218	14	r3	r3	PROPN
ejpam-4859	218	15	r4	r4	PROPN
ejpam-4859	218	16	r5	r5	PROPN
ejpam-4859	218	17	where	where	SCONJ
ejpam-4859	218	18	fij	fij	PROPN
ejpam-4859	218	19	∈	∈	PROPN
ejpam-4859	218	20	r.	r.	PROPN
ejpam-4859	218	21	poly	poly	PROPN
ejpam-4859	218	22	-	-	PUNCT
ejpam-4859	218	23	pl	pl	NOUN
ejpam-4859	218	24	kinetics	kinetic	NOUN
ejpam-4859	218	25	(	(	PUNCT
ejpam-4859	218	26	pyk	pyk	NOUN
ejpam-4859	218	27	)	)	PUNCT
ejpam-4859	218	28	are	be	AUX
ejpam-4859	218	29	kinetic	kinetic	ADJ
ejpam-4859	218	30	systems	system	NOUN
ejpam-4859	218	31	consisting	consist	VERB
ejpam-4859	218	32	of	of	ADP
ejpam-4859	218	33	non	non	ADJ
ejpam-4859	218	34	-	-	ADJ
ejpam-4859	218	35	negative	negative	ADJ
ejpam-4859	218	36	linear	linear	ADJ
ejpam-4859	218	37	combinations	combination	NOUN
ejpam-4859	218	38	of	of	ADP
ejpam-4859	218	39	power	power	NOUN
ejpam-4859	218	40	law	law	NOUN
ejpam-4859	218	41	functions	function	NOUN
ejpam-4859	218	42	.	.	PUNCT
ejpam-4859	219	1	this	this	DET
ejpam-4859	219	2	set	set	NOUN
ejpam-4859	219	3	contains	contain	VERB
ejpam-4859	219	4	the	the	DET
ejpam-4859	219	5	set	set	VERB
ejpam-4859	219	6	plk	plk	NOUN
ejpam-4859	219	7	of	of	ADP
ejpam-4859	219	8	power	power	NOUN
ejpam-4859	219	9	law	law	NOUN
ejpam-4859	219	10	kinetics	kinetic	NOUN
ejpam-4859	219	11	as	as	ADP
ejpam-4859	219	12	“	"	PUNCT
ejpam-4859	219	13	mono	mono	NOUN
ejpam-4859	219	14	-	-	PUNCT
ejpam-4859	219	15	pl	pl	NOUN
ejpam-4859	219	16	kinetics	kinetic	NOUN
ejpam-4859	219	17	with	with	ADP
ejpam-4859	219	18	coefficient	coefficient	NOUN
ejpam-4859	219	19	1	1	NUM
ejpam-4859	219	20	”	"	PUNCT
ejpam-4859	219	21	.	.	PUNCT
ejpam-4859	220	1	like	like	ADP
ejpam-4859	220	2	plk	plk	PROPN
ejpam-4859	220	3	,	,	PUNCT
ejpam-4859	220	4	the	the	DET
ejpam-4859	220	5	definition	definition	NOUN
ejpam-4859	220	6	domain	domain	NOUN
ejpam-4859	220	7	of	of	ADP
ejpam-4859	220	8	pyk	pyk	PROPN
ejpam-4859	220	9	is	be	AUX
ejpam-4859	220	10	the	the	DET
ejpam-4859	220	11	positive	positive	ADJ
ejpam-4859	220	12	orthant	orthant	NOUN
ejpam-4859	220	13	rm	rm	PROPN
ejpam-4859	220	14	>	>	X
ejpam-4859	220	15	.	.	PUNCT
ejpam-4859	221	1	however	however	ADV
ejpam-4859	221	2	,	,	PUNCT
ejpam-4859	221	3	for	for	ADP
ejpam-4859	221	4	subsets	subset	NOUN
ejpam-4859	221	5	,	,	PUNCT
ejpam-4859	221	6	this	this	PRON
ejpam-4859	221	7	may	may	AUX
ejpam-4859	221	8	be	be	AUX
ejpam-4859	221	9	extended	extend	VERB
ejpam-4859	221	10	to	to	ADP
ejpam-4859	221	11	the	the	DET
ejpam-4859	221	12	whole	whole	ADJ
ejpam-4859	221	13	nonnegative	nonnegative	ADJ
ejpam-4859	221	14	orthant	orthant	PROPN
ejpam-4859	221	15	rm	rm	PROPN
ejpam-4859	221	16	≥	≥	PROPN
ejpam-4859	221	17	.	.	PUNCT
ejpam-4859	222	1	clearly	clearly	ADV
ejpam-4859	222	2	,	,	PUNCT
ejpam-4859	222	3	pyk	pyk	PROPN
ejpam-4859	222	4	and	and	CCONJ
ejpam-4859	222	5	plk	plk	PROPN
ejpam-4859	222	6	generate	generate	VERB
ejpam-4859	222	7	the	the	DET
ejpam-4859	222	8	same	same	ADJ
ejpam-4859	222	9	sets	set	NOUN
ejpam-4859	222	10	of	of	ADP
ejpam-4859	222	11	sfrfs	sfrfs	NOUN
ejpam-4859	222	12	,	,	PUNCT
ejpam-4859	222	13	the	the	DET
ejpam-4859	222	14	power	power	NOUN
ejpam-4859	222	15	law	law	NOUN
ejpam-4859	222	16	dynamical	dynamical	ADJ
ejpam-4859	222	17	systems	system	NOUN
ejpam-4859	222	18	(	(	PUNCT
ejpam-4859	222	19	or	or	CCONJ
ejpam-4859	222	20	gma	gma	NOUN
ejpam-4859	222	21	systems	system	NOUN
ejpam-4859	222	22	in	in	ADP
ejpam-4859	222	23	bst	bst	PROPN
ejpam-4859	222	24	terminology	terminology	NOUN
ejpam-4859	222	25	)	)	PUNCT
ejpam-4859	222	26	.	.	PUNCT
ejpam-4859	223	1	after	after	ADP
ejpam-4859	223	2	setting	set	VERB
ejpam-4859	223	3	the	the	DET
ejpam-4859	223	4	standard	standard	ADJ
ejpam-4859	223	5	ordering	ordering	NOUN
ejpam-4859	223	6	of	of	ADP
ejpam-4859	223	7	species	specie	NOUN
ejpam-4859	223	8	x1	x1	PROPN
ejpam-4859	223	9	,	,	PUNCT
ejpam-4859	223	10	.	.	PUNCT
ejpam-4859	223	11	.	.	PUNCT
ejpam-4859	223	12	.	.	PUNCT
ejpam-4859	224	1	,	,	PUNCT
ejpam-4859	224	2	xm	xm	PROPN
ejpam-4859	224	3	,	,	PUNCT
ejpam-4859	224	4	we	we	PRON
ejpam-4859	224	5	have	have	VERB
ejpam-4859	224	6	the	the	DET
ejpam-4859	224	7	following	follow	VERB
ejpam-4859	224	8	definition	definition	NOUN
ejpam-4859	224	9	:	:	PUNCT
ejpam-4859	224	10	definition	definition	NOUN
ejpam-4859	224	11	15	15	NUM
ejpam-4859	224	12	.	.	PUNCT
ejpam-4859	225	1	a	a	DET
ejpam-4859	225	2	kinetics	kinetic	NOUN
ejpam-4859	225	3	k	k	NOUN
ejpam-4859	225	4	:	:	PUNCT
ejpam-4859	225	5	rm	rm	PROPN
ejpam-4859	225	6	>	>	X
ejpam-4859	225	7	→	→	PUNCT
ejpam-4859	225	8	rr	rr	PROPN
ejpam-4859	225	9	is	be	AUX
ejpam-4859	225	10	a	a	DET
ejpam-4859	225	11	poly	poly	ADJ
ejpam-4859	225	12	-	-	PUNCT
ejpam-4859	225	13	pl	pl	NOUN
ejpam-4859	225	14	kinetics	kinetic	NOUN
ejpam-4859	225	15	if	if	SCONJ
ejpam-4859	225	16	ki(x	ki(x	NUM
ejpam-4859	225	17	)	)	PUNCT
ejpam-4859	225	18	=	=	SYM
ejpam-4859	225	19	ki(ai,1x	ki(ai,1x	PROPN
ejpam-4859	225	20	fi,1	fi,1	PROPN
ejpam-4859	225	21	+	+	PUNCT
ejpam-4859	225	22	.	.	PUNCT
ejpam-4859	225	23	.	.	PUNCT
ejpam-4859	226	1	.+	.+	NOUN
ejpam-4859	226	2	ai	ai	VERB
ejpam-4859	226	3	,	,	PUNCT
ejpam-4859	226	4	jx	jx	PROPN
ejpam-4859	226	5	fi	fi	PROPN
ejpam-4859	226	6	,	,	PUNCT
ejpam-4859	226	7	j	j	PROPN
ejpam-4859	226	8	)	)	PUNCT
ejpam-4859	226	9	where	where	SCONJ
ejpam-4859	226	10	1	1	NUM
ejpam-4859	226	11	≤	≤	NUM
ejpam-4859	226	12	i	i	NOUN
ejpam-4859	226	13	≤	≤	ADJ
ejpam-4859	226	14	r	r	NOUN
ejpam-4859	226	15	(	(	PUNCT
ejpam-4859	226	16	1	1	X
ejpam-4859	226	17	)	)	PUNCT
ejpam-4859	226	18	written	write	VERB
ejpam-4859	226	19	in	in	ADP
ejpam-4859	226	20	lexicographic	lexicographic	ADJ
ejpam-4859	226	21	order	order	NOUN
ejpam-4859	226	22	with	with	ADP
ejpam-4859	226	23	ki	ki	PROPN
ejpam-4859	226	24	∈	∈	PROPN
ejpam-4859	226	25	r+	r+	X
ejpam-4859	226	26	,	,	PUNCT
ejpam-4859	226	27	fi	fi	NOUN
ejpam-4859	226	28	,	,	PUNCT
ejpam-4859	226	29	j	j	PROPN
ejpam-4859	226	30	,	,	PUNCT
ejpam-4859	226	31	ai	ai	VERB
ejpam-4859	226	32	,	,	PUNCT
ejpam-4859	226	33	j	j	PROPN
ejpam-4859	226	34	∈	∈	PROPN
ejpam-4859	226	35	rm	rm	PROPN
ejpam-4859	226	36	and	and	CCONJ
ejpam-4859	226	37	1	1	NUM
ejpam-4859	226	38	≤	≤	NUM
ejpam-4859	226	39	j	j	PROPN
ejpam-4859	226	40	≤	≤	PROPN
ejpam-4859	227	1	hi	hi	INTJ
ejpam-4859	227	2	(	(	PUNCT
ejpam-4859	227	3	where	where	SCONJ
ejpam-4859	227	4	hi	hi	INTJ
ejpam-4859	227	5	is	be	AUX
ejpam-4859	227	6	the	the	DET
ejpam-4859	227	7	number	number	NOUN
ejpam-4859	227	8	of	of	ADP
ejpam-4859	227	9	terms	term	NOUN
ejpam-4859	227	10	in	in	ADP
ejpam-4859	227	11	reaction	reaction	NOUN
ejpam-4859	227	12	i	i	PROPN
ejpam-4859	227	13	)	)	PUNCT
ejpam-4859	227	14	.	.	PUNCT
ejpam-4859	228	1	power	power	NOUN
ejpam-4859	228	2	-	-	PUNCT
ejpam-4859	228	3	law	law	NOUN
ejpam-4859	228	4	kinetics	kinetic	NOUN
ejpam-4859	228	5	is	be	AUX
ejpam-4859	228	6	defined	define	VERB
ejpam-4859	228	7	by	by	ADP
ejpam-4859	228	8	r	r	PROPN
ejpam-4859	228	9	×	×	PROPN
ejpam-4859	228	10	m	m	NOUN
ejpam-4859	228	11	matrices	matrix	NOUN
ejpam-4859	228	12	fi	fi	NOUN
ejpam-4859	228	13	,	,	PUNCT
ejpam-4859	228	14	k	k	PROPN
ejpam-4859	229	1	=	=	PUNCT
ejpam-4859	230	1	[	[	X
ejpam-4859	230	2	fij	fij	PROPN
ejpam-4859	230	3	]	]	PUNCT
ejpam-4859	230	4	,	,	PUNCT
ejpam-4859	230	5	called	call	VERB
ejpam-4859	230	6	the	the	DET
ejpam-4859	230	7	kinetic	kinetic	ADJ
ejpam-4859	230	8	order	order	NOUN
ejpam-4859	230	9	matrices	matrix	NOUN
ejpam-4859	230	10	,	,	PUNCT
ejpam-4859	230	11	vectors	vector	NOUN
ejpam-4859	230	12	k	k	NOUN
ejpam-4859	231	1	=	=	PUNCT
ejpam-4859	232	1	[	[	X
ejpam-4859	232	2	ki	ki	X
ejpam-4859	232	3	]	]	X
ejpam-4859	232	4	called	call	VERB
ejpam-4859	232	5	the	the	DET
ejpam-4859	232	6	rate	rate	NOUN
ejpam-4859	232	7	vector	vector	NOUN
ejpam-4859	232	8	and	and	CCONJ
ejpam-4859	232	9	ai	ai	VERB
ejpam-4859	232	10	,	,	PUNCT
ejpam-4859	232	11	j	j	PROPN
ejpam-4859	232	12	∈	∈	PROPN
ejpam-4859	232	13	rr	rr	PROPN
ejpam-4859	232	14	>	>	X
ejpam-4859	232	15	called	call	VERB
ejpam-4859	232	16	the	the	DET
ejpam-4859	232	17	poly	poly	ADJ
ejpam-4859	232	18	-	-	PUNCT
ejpam-4859	232	19	rate	rate	NOUN
ejpam-4859	232	20	vectors	vector	NOUN
ejpam-4859	232	21	.	.	PUNCT
ejpam-4859	233	1	example	example	NOUN
ejpam-4859	233	2	10	10	NUM
ejpam-4859	233	3	.	.	PUNCT
ejpam-4859	234	1	for	for	ADP
ejpam-4859	234	2	(	(	PUNCT
ejpam-4859	234	3	n	n	X
ejpam-4859	234	4	,	,	PUNCT
ejpam-4859	234	5	k	k	NOUN
ejpam-4859	234	6	)	)	PUNCT
ejpam-4859	234	7	with	with	ADP
ejpam-4859	234	8	s	s	NOUN
ejpam-4859	234	9	=	=	SYM
ejpam-4859	234	10	{	{	PUNCT
ejpam-4859	234	11	x	x	PROPN
ejpam-4859	234	12	,	,	PUNCT
ejpam-4859	234	13	y	y	PROPN
ejpam-4859	234	14	}	}	PUNCT
ejpam-4859	234	15	and	and	CCONJ
ejpam-4859	234	16	r	r	NOUN
ejpam-4859	234	17	=	=	SYM
ejpam-4859	234	18	{	{	PUNCT
ejpam-4859	234	19	r	r	NOUN
ejpam-4859	234	20	:	:	PUNCT
ejpam-4859	234	21	x	x	X
ejpam-4859	234	22	→	→	SYM
ejpam-4859	234	23	2x	2x	NUM
ejpam-4859	234	24	,	,	PUNCT
ejpam-4859	234	25	r′	r′	NUM
ejpam-4859	234	26	:	:	PUNCT
ejpam-4859	234	27	2x	2x	NUM
ejpam-4859	234	28	→	→	SYM
ejpam-4859	234	29	5x+y	5x+y	NUM
ejpam-4859	234	30	}	}	PUNCT
ejpam-4859	234	31	,	,	PUNCT
ejpam-4859	234	32	let	let	VERB
ejpam-4859	234	33	the	the	DET
ejpam-4859	234	34	poly	poly	ADJ
ejpam-4859	234	35	-	-	PUNCT
ejpam-4859	234	36	pl	pl	NOUN
ejpam-4859	234	37	kinetics	kinetic	NOUN
ejpam-4859	234	38	be	be	AUX
ejpam-4859	234	39	given	give	VERB
ejpam-4859	234	40	by	by	ADP
ejpam-4859	234	41	:	:	PUNCT
ejpam-4859	234	42	k1(x	k1(x	PROPN
ejpam-4859	234	43	,	,	PUNCT
ejpam-4859	234	44	y	y	PROPN
ejpam-4859	234	45	)	)	PUNCT
ejpam-4859	235	1	=	=	SYM
ejpam-4859	235	2	k1(2xy	k1(2xy	NOUN
ejpam-4859	236	1	+	+	CCONJ
ejpam-4859	236	2	0.5y	0.5y	PROPN
ejpam-4859	236	3	2	2	NUM
ejpam-4859	236	4	)	)	PUNCT
ejpam-4859	236	5	and	and	CCONJ
ejpam-4859	236	6	k2(x	k2(x	PROPN
ejpam-4859	236	7	,	,	PUNCT
ejpam-4859	236	8	y	y	PROPN
ejpam-4859	236	9	)	)	PUNCT
ejpam-4859	237	1	=	=	PUNCT
ejpam-4859	237	2	k2(0.75x	k2(0.75x	X
ejpam-4859	237	3	2y	2y	PROPN
ejpam-4859	238	1	+	+	ADJ
ejpam-4859	238	2	x3	x3	ADJ
ejpam-4859	238	3	)	)	PUNCT
ejpam-4859	238	4	where	where	SCONJ
ejpam-4859	238	5	k1	k1	NOUN
ejpam-4859	238	6	,	,	PUNCT
ejpam-4859	238	7	k2	k2	PROPN
ejpam-4859	238	8	are	be	AUX
ejpam-4859	238	9	rate	rate	NOUN
ejpam-4859	238	10	constants	constant	NOUN
ejpam-4859	238	11	.	.	PUNCT
ejpam-4859	239	1	the	the	DET
ejpam-4859	239	2	kinetic	kinetic	ADJ
ejpam-4859	239	3	order	order	NOUN
ejpam-4859	239	4	matrices	matrix	NOUN
ejpam-4859	239	5	are	be	AUX
ejpam-4859	239	6	f1,k	f1,k	PROPN
ejpam-4859	239	7	=	=	PUNCT
ejpam-4859	240	1	[	[	PUNCT
ejpam-4859	240	2	1	1	NUM
ejpam-4859	240	3	1	1	NUM
ejpam-4859	240	4	0	0	NUM
ejpam-4859	240	5	2	2	NUM
ejpam-4859	240	6	]	]	PUNCT
ejpam-4859	240	7	;	;	PUNCT
ejpam-4859	240	8	and	and	CCONJ
ejpam-4859	240	9	f2,k	f2,k	PROPN
ejpam-4859	241	1	=	=	PRON
ejpam-4859	241	2	[	[	PUNCT
ejpam-4859	241	3	2	2	NUM
ejpam-4859	241	4	1	1	NUM
ejpam-4859	241	5	3	3	NUM
ejpam-4859	241	6	0	0	NUM
ejpam-4859	241	7	]	]	PUNCT
ejpam-4859	241	8	with	with	ADP
ejpam-4859	241	9	the	the	DET
ejpam-4859	241	10	kinetic	kinetic	ADJ
ejpam-4859	241	11	order	order	NOUN
ejpam-4859	241	12	vector	vector	NOUN
ejpam-4859	241	13	k	k	NOUN
ejpam-4859	242	1	=	=	PUNCT
ejpam-4859	243	1	[	[	PUNCT
ejpam-4859	243	2	k1	k1	NOUN
ejpam-4859	243	3	k2	k2	NOUN
ejpam-4859	243	4	]	]	PUNCT
ejpam-4859	243	5	.	.	PUNCT
ejpam-4859	244	1	d.	d.	PROPN
ejpam-4859	244	2	magpantay	magpantay	PROPN
ejpam-4859	244	3	/	/	SYM
ejpam-4859	244	4	eur	eur	PROPN
ejpam-4859	244	5	.	.	PUNCT
ejpam-4859	245	1	j.	j.	PROPN
ejpam-4859	245	2	pure	pure	PROPN
ejpam-4859	245	3	appl	appl	PROPN
ejpam-4859	245	4	.	.	PROPN
ejpam-4859	245	5	math	math	PROPN
ejpam-4859	245	6	,	,	PUNCT
ejpam-4859	245	7	16	16	NUM
ejpam-4859	245	8	(	(	PUNCT
ejpam-4859	245	9	4	4	NUM
ejpam-4859	245	10	)	)	PUNCT
ejpam-4859	245	11	(	(	PUNCT
ejpam-4859	245	12	2023	2023	NUM
ejpam-4859	245	13	)	)	PUNCT
ejpam-4859	245	14	,	,	PUNCT
ejpam-4859	245	15	2557	2557	NUM
ejpam-4859	245	16	-	-	SYM
ejpam-4859	245	17	2580	2580	NUM
ejpam-4859	245	18	2566	2566	NUM
ejpam-4859	245	19	2.6	2.6	NUM
ejpam-4859	245	20	.	.	PUNCT
ejpam-4859	246	1	star	star	NOUN
ejpam-4859	246	2	transformations	transformation	NOUN
ejpam-4859	246	3	of	of	ADP
ejpam-4859	246	4	chemical	chemical	ADJ
ejpam-4859	246	5	kinetic	kinetic	NOUN
ejpam-4859	246	6	systems	system	NOUN
ejpam-4859	246	7	now	now	ADV
ejpam-4859	246	8	,	,	PUNCT
ejpam-4859	246	9	we	we	PRON
ejpam-4859	246	10	introduce	introduce	VERB
ejpam-4859	246	11	the	the	DET
ejpam-4859	246	12	concept	concept	NOUN
ejpam-4859	246	13	of	of	ADP
ejpam-4859	246	14	transformation	transformation	NOUN
ejpam-4859	246	15	of	of	ADP
ejpam-4859	246	16	chemical	chemical	ADJ
ejpam-4859	246	17	kinetic	kinetic	ADJ
ejpam-4859	246	18	system	system	NOUN
ejpam-4859	246	19	as	as	ADP
ejpam-4859	246	20	a	a	DET
ejpam-4859	246	21	special	special	ADJ
ejpam-4859	246	22	kind	kind	NOUN
ejpam-4859	246	23	of	of	ADP
ejpam-4859	246	24	dynamic	dynamic	ADJ
ejpam-4859	246	25	equivalence	equivalence	NOUN
ejpam-4859	246	26	.	.	PUNCT
ejpam-4859	247	1	we	we	PRON
ejpam-4859	247	2	begin	begin	VERB
ejpam-4859	247	3	with	with	ADP
ejpam-4859	247	4	a	a	DET
ejpam-4859	247	5	formal	formal	ADJ
ejpam-4859	247	6	definition	definition	NOUN
ejpam-4859	247	7	of	of	ADP
ejpam-4859	247	8	dynamic	dynamic	ADJ
ejpam-4859	247	9	equivalence	equivalence	NOUN
ejpam-4859	247	10	of	of	ADP
ejpam-4859	247	11	chemical	chemical	ADJ
ejpam-4859	247	12	kinetic	kinetic	NOUN
ejpam-4859	247	13	systems	system	NOUN
ejpam-4859	247	14	.	.	PUNCT
ejpam-4859	248	1	definition	definition	NOUN
ejpam-4859	248	2	16	16	NUM
ejpam-4859	248	3	.	.	PUNCT
ejpam-4859	249	1	a	a	DET
ejpam-4859	249	2	chemical	chemical	ADJ
ejpam-4859	249	3	kinetic	kinetic	NOUN
ejpam-4859	249	4	system	system	NOUN
ejpam-4859	249	5	(	(	PUNCT
ejpam-4859	249	6	n	n	CCONJ
ejpam-4859	249	7	∗,k∗	∗,k∗	ADJ
ejpam-4859	249	8	)	)	PUNCT
ejpam-4859	249	9	is	be	AUX
ejpam-4859	249	10	dynamically	dynamically	ADV
ejpam-4859	249	11	equivalent	equivalent	ADJ
ejpam-4859	249	12	to	to	ADP
ejpam-4859	249	13	(	(	PUNCT
ejpam-4859	249	14	n	n	CCONJ
ejpam-4859	249	15	,	,	PUNCT
ejpam-4859	249	16	k	k	NOUN
ejpam-4859	249	17	)	)	PUNCT
ejpam-4859	249	18	if	if	SCONJ
ejpam-4859	249	19	:	:	PUNCT
ejpam-4859	249	20	(	(	PUNCT
ejpam-4859	249	21	i	i	NOUN
ejpam-4859	249	22	)	)	PUNCT
ejpam-4859	249	23	n	n	CCONJ
ejpam-4859	249	24	∗	∗	NOUN
ejpam-4859	249	25	and	and	CCONJ
ejpam-4859	249	26	n	n	CCONJ
ejpam-4859	249	27	have	have	VERB
ejpam-4859	249	28	the	the	DET
ejpam-4859	249	29	same	same	ADJ
ejpam-4859	249	30	set	set	NOUN
ejpam-4859	249	31	of	of	ADP
ejpam-4859	249	32	species	specie	NOUN
ejpam-4859	249	33	,	,	PUNCT
ejpam-4859	249	34	i.e.	i.e.	X
ejpam-4859	249	35	n	n	X
ejpam-4859	249	36	=	=	SYM
ejpam-4859	249	37	(	(	PUNCT
ejpam-4859	249	38	s	s	NOUN
ejpam-4859	249	39	,	,	PUNCT
ejpam-4859	249	40	c	c	NOUN
ejpam-4859	249	41	,	,	PUNCT
ejpam-4859	249	42	r	r	NOUN
ejpam-4859	249	43	)	)	PUNCT
ejpam-4859	249	44	and	and	CCONJ
ejpam-4859	249	45	n	n	PRON
ejpam-4859	249	46	∗	∗	NOUN
ejpam-4859	249	47	=	=	PUNCT
ejpam-4859	249	48	(	(	PUNCT
ejpam-4859	249	49	s	s	NOUN
ejpam-4859	249	50	,	,	PUNCT
ejpam-4859	249	51	c	c	NOUN
ejpam-4859	249	52	∗,r∗	∗,r∗	VERB
ejpam-4859	249	53	)	)	PUNCT
ejpam-4859	249	54	(	(	PUNCT
ejpam-4859	249	55	ii	ii	NOUN
ejpam-4859	249	56	)	)	PUNCT
ejpam-4859	249	57	n∗	n∗	PROPN
ejpam-4859	249	58	and	and	CCONJ
ejpam-4859	249	59	n	n	PRON
ejpam-4859	249	60	are	be	AUX
ejpam-4859	249	61	their	their	PRON
ejpam-4859	249	62	respective	respective	ADJ
ejpam-4859	249	63	stoichiometric	stoichiometric	ADJ
ejpam-4859	249	64	matrices	matrix	NOUN
ejpam-4859	249	65	,	,	PUNCT
ejpam-4859	249	66	then	then	ADV
ejpam-4859	249	67	their	their	PRON
ejpam-4859	249	68	sfrf´s	sfrf´s	PROPN
ejpam-4859	249	69	(	(	PUNCT
ejpam-4859	249	70	vector	vector	NOUN
ejpam-4859	249	71	fields	field	NOUN
ejpam-4859	249	72	)	)	PUNCT
ejpam-4859	249	73	coincide	coincide	NOUN
ejpam-4859	249	74	,	,	PUNCT
ejpam-4859	249	75	i.e.	i.e.	X
ejpam-4859	249	76	f∗	f∗	X
ejpam-4859	249	77	=	=	SYM
ejpam-4859	249	78	n∗k∗	n∗k∗	NOUN
ejpam-4859	250	1	=	=	NOUN
ejpam-4859	250	2	nk	nk	PROPN
ejpam-4859	250	3	=	=	PROPN
ejpam-4859	250	4	f	f	PROPN
ejpam-4859	250	5	.	.	PUNCT
ejpam-4859	251	1	condition	condition	NOUN
ejpam-4859	251	2	(	(	PUNCT
ejpam-4859	251	3	i	i	NOUN
ejpam-4859	251	4	)	)	PUNCT
ejpam-4859	251	5	implies	imply	VERB
ejpam-4859	251	6	that	that	SCONJ
ejpam-4859	251	7	additional	additional	ADJ
ejpam-4859	251	8	complexes	complex	NOUN
ejpam-4859	251	9	and	and	CCONJ
ejpam-4859	251	10	reactions	reaction	NOUN
ejpam-4859	251	11	do	do	AUX
ejpam-4859	251	12	not	not	PART
ejpam-4859	251	13	affect	affect	VERB
ejpam-4859	251	14	the	the	DET
ejpam-4859	251	15	said	say	VERB
ejpam-4859	251	16	equivalence	equivalence	NOUN
ejpam-4859	251	17	.	.	PUNCT
ejpam-4859	252	1	as	as	ADP
ejpam-4859	252	2	for	for	ADP
ejpam-4859	252	3	condition	condition	NOUN
ejpam-4859	252	4	(	(	PUNCT
ejpam-4859	252	5	ii	ii	NOUN
ejpam-4859	252	6	)	)	PUNCT
ejpam-4859	252	7	,	,	PUNCT
ejpam-4859	252	8	an	an	DET
ejpam-4859	252	9	immediate	immediate	ADJ
ejpam-4859	252	10	necessary	necessary	ADJ
ejpam-4859	252	11	condition	condition	NOUN
ejpam-4859	252	12	for	for	ADP
ejpam-4859	252	13	dynamic	dynamic	ADJ
ejpam-4859	252	14	equivalence	equivalence	NOUN
ejpam-4859	252	15	is	be	AUX
ejpam-4859	252	16	the	the	DET
ejpam-4859	252	17	coincidence	coincidence	NOUN
ejpam-4859	252	18	of	of	ADP
ejpam-4859	252	19	their	their	PRON
ejpam-4859	252	20	kinetic	kinetic	ADJ
ejpam-4859	252	21	subspaces	subspace	NOUN
ejpam-4859	252	22	as	as	SCONJ
ejpam-4859	252	23	shown	show	VERB
ejpam-4859	252	24	in	in	ADP
ejpam-4859	252	25	the	the	DET
ejpam-4859	252	26	following	follow	VERB
ejpam-4859	252	27	proposition	proposition	NOUN
ejpam-4859	252	28	:	:	PUNCT
ejpam-4859	252	29	proposition	proposition	NOUN
ejpam-4859	252	30	5	5	NUM
ejpam-4859	252	31	.	.	PUNCT
ejpam-4859	253	1	if	if	SCONJ
ejpam-4859	253	2	(	(	PUNCT
ejpam-4859	253	3	n	n	CCONJ
ejpam-4859	253	4	∗,k∗	∗,k∗	ADJ
ejpam-4859	253	5	)	)	PUNCT
ejpam-4859	253	6	is	be	AUX
ejpam-4859	253	7	dynamically	dynamically	ADV
ejpam-4859	253	8	equivalent	equivalent	ADJ
ejpam-4859	253	9	to	to	ADP
ejpam-4859	253	10	(	(	PUNCT
ejpam-4859	253	11	n	n	CCONJ
ejpam-4859	253	12	,	,	PUNCT
ejpam-4859	253	13	k	k	PROPN
ejpam-4859	253	14	)	)	PUNCT
ejpam-4859	253	15	,	,	PUNCT
ejpam-4859	253	16	then	then	ADV
ejpam-4859	253	17	their	their	PRON
ejpam-4859	253	18	kinetic	kinetic	ADJ
ejpam-4859	253	19	subspaces	subspace	NOUN
ejpam-4859	253	20	k∗	k∗	VERB
ejpam-4859	253	21	and	and	CCONJ
ejpam-4859	253	22	k	k	PROPN
ejpam-4859	253	23	are	be	AUX
ejpam-4859	253	24	equal	equal	ADJ
ejpam-4859	253	25	.	.	PUNCT
ejpam-4859	254	1	proof	proof	NOUN
ejpam-4859	254	2	.	.	PUNCT
ejpam-4859	255	1	since	since	SCONJ
ejpam-4859	255	2	(	(	PUNCT
ejpam-4859	255	3	n	n	CCONJ
ejpam-4859	255	4	∗,k∗	∗,k∗	ADJ
ejpam-4859	255	5	)	)	PUNCT
ejpam-4859	255	6	is	be	AUX
ejpam-4859	255	7	dynamically	dynamically	ADV
ejpam-4859	255	8	equivalent	equivalent	ADJ
ejpam-4859	255	9	to	to	ADP
ejpam-4859	255	10	(	(	PUNCT
ejpam-4859	255	11	n	n	CCONJ
ejpam-4859	255	12	,	,	PUNCT
ejpam-4859	255	13	k	k	NOUN
ejpam-4859	255	14	)	)	PUNCT
ejpam-4859	255	15	,	,	PUNCT
ejpam-4859	255	16	f∗	f∗	NOUN
ejpam-4859	255	17	=	=	SYM
ejpam-4859	255	18	f	f	PROPN
ejpam-4859	255	19	.	.	PUNCT
ejpam-4859	256	1	hence	hence	ADV
ejpam-4859	256	2	,	,	PUNCT
ejpam-4859	256	3	i	i	PRON
ejpam-4859	256	4	m	m	VERB
ejpam-4859	256	5	f∗	f∗	NOUN
ejpam-4859	256	6	=	=	PUNCT
ejpam-4859	257	1	i	i	PRON
ejpam-4859	257	2	m	m	PROPN
ejpam-4859	257	3	f	f	PROPN
ejpam-4859	257	4	span(im	span(im	PROPN
ejpam-4859	257	5	f∗	f∗	PROPN
ejpam-4859	257	6	)	)	PUNCT
ejpam-4859	257	7	=	=	PUNCT
ejpam-4859	257	8	span(im	span(im	PROPN
ejpam-4859	257	9	f	f	PROPN
ejpam-4859	257	10	)	)	PUNCT
ejpam-4859	257	11	k∗	k∗	NOUN
ejpam-4859	258	1	=	=	PUNCT
ejpam-4859	258	2	k.	k.	PROPN
ejpam-4859	259	1	we	we	PRON
ejpam-4859	259	2	tolerate	tolerate	VERB
ejpam-4859	259	3	the	the	DET
ejpam-4859	259	4	use	use	NOUN
ejpam-4859	259	5	of	of	ADP
ejpam-4859	259	6	k	k	PROPN
ejpam-4859	259	7	and	and	CCONJ
ejpam-4859	259	8	k∗	k∗	VERB
ejpam-4859	259	9	for	for	ADP
ejpam-4859	259	10	two	two	NUM
ejpam-4859	259	11	different	different	ADJ
ejpam-4859	259	12	meanings	meaning	NOUN
ejpam-4859	259	13	(	(	PUNCT
ejpam-4859	259	14	kinetics	kinetic	NOUN
ejpam-4859	259	15	and	and	CCONJ
ejpam-4859	259	16	kinetic	kinetic	ADJ
ejpam-4859	259	17	subspace	subspace	NOUN
ejpam-4859	259	18	)	)	PUNCT
ejpam-4859	259	19	since	since	SCONJ
ejpam-4859	259	20	it	it	PRON
ejpam-4859	259	21	is	be	AUX
ejpam-4859	259	22	usually	usually	ADV
ejpam-4859	259	23	clear	clear	ADJ
ejpam-4859	259	24	from	from	ADP
ejpam-4859	259	25	the	the	DET
ejpam-4859	259	26	context	context	NOUN
ejpam-4859	259	27	which	which	DET
ejpam-4859	259	28	one	one	NOUN
ejpam-4859	259	29	is	be	AUX
ejpam-4859	259	30	referred	refer	VERB
ejpam-4859	259	31	to	to	ADP
ejpam-4859	259	32	.	.	PUNCT
ejpam-4859	260	1	we	we	PRON
ejpam-4859	260	2	know	know	VERB
ejpam-4859	260	3	the	the	DET
ejpam-4859	260	4	fact	fact	NOUN
ejpam-4859	260	5	that	that	SCONJ
ejpam-4859	260	6	the	the	DET
ejpam-4859	260	7	kinetic	kinetic	ADJ
ejpam-4859	260	8	subspace	subspace	NOUN
ejpam-4859	260	9	is	be	AUX
ejpam-4859	260	10	contained	contain	VERB
ejpam-4859	260	11	in	in	ADP
ejpam-4859	260	12	the	the	DET
ejpam-4859	260	13	stoichiometric	stoichiometric	NOUN
ejpam-4859	260	14	subspace	subspace	NOUN
ejpam-4859	260	15	s	s	PART
ejpam-4859	260	16	for	for	ADP
ejpam-4859	260	17	any	any	DET
ejpam-4859	260	18	chemical	chemical	NOUN
ejpam-4859	260	19	kinetic	kinetic	NOUN
ejpam-4859	260	20	system	system	NOUN
ejpam-4859	260	21	but	but	CCONJ
ejpam-4859	260	22	in	in	ADP
ejpam-4859	260	23	general	general	ADJ
ejpam-4859	260	24	,	,	PUNCT
ejpam-4859	260	25	they	they	PRON
ejpam-4859	260	26	may	may	AUX
ejpam-4859	260	27	not	not	PART
ejpam-4859	260	28	coincide	coincide	VERB
ejpam-4859	260	29	(	(	PUNCT
ejpam-4859	260	30	for	for	ADP
ejpam-4859	260	31	example	example	NOUN
ejpam-4859	260	32	,	,	PUNCT
ejpam-4859	260	33	for	for	ADP
ejpam-4859	260	34	mak	mak	PROPN
ejpam-4859	260	35	systems	system	NOUN
ejpam-4859	260	36	with	with	ADP
ejpam-4859	260	37	t	t	PROPN
ejpam-4859	260	38	−	−	PROPN
ejpam-4859	260	39	ℓ	ℓ	PROPN
ejpam-4859	260	40	>	>	X
ejpam-4859	260	41	δ	δ	PROPN
ejpam-4859	260	42	)	)	PUNCT
ejpam-4859	260	43	.	.	PUNCT
ejpam-4859	261	1	our	our	PRON
ejpam-4859	261	2	new	new	ADJ
ejpam-4859	261	3	concept	concept	NOUN
ejpam-4859	261	4	requires	require	VERB
ejpam-4859	261	5	that	that	SCONJ
ejpam-4859	261	6	this	this	DET
ejpam-4859	261	7	structural	structural	ADJ
ejpam-4859	261	8	property	property	NOUN
ejpam-4859	261	9	holds	hold	VERB
ejpam-4859	261	10	:	:	PUNCT
ejpam-4859	261	11	definition	definition	NOUN
ejpam-4859	261	12	17	17	NUM
ejpam-4859	261	13	.	.	PUNCT
ejpam-4859	262	1	a	a	DET
ejpam-4859	262	2	chemical	chemical	ADJ
ejpam-4859	262	3	kinetic	kinetic	NOUN
ejpam-4859	262	4	system	system	NOUN
ejpam-4859	262	5	(	(	PUNCT
ejpam-4859	262	6	n	n	CCONJ
ejpam-4859	262	7	∗,k∗	∗,k∗	ADJ
ejpam-4859	262	8	)	)	PUNCT
ejpam-4859	262	9	is	be	AUX
ejpam-4859	262	10	a	a	DET
ejpam-4859	262	11	transformation	transformation	NOUN
ejpam-4859	262	12	of	of	ADP
ejpam-4859	262	13	(	(	PUNCT
ejpam-4859	262	14	n	n	X
ejpam-4859	262	15	,	,	PUNCT
ejpam-4859	262	16	k	k	NOUN
ejpam-4859	262	17	)	)	PUNCT
ejpam-4859	262	18	if	if	SCONJ
ejpam-4859	262	19	:	:	PUNCT
ejpam-4859	262	20	i	i	NOUN
ejpam-4859	262	21	)	)	PUNCT
ejpam-4859	262	22	(	(	PUNCT
ejpam-4859	262	23	n	n	CCONJ
ejpam-4859	262	24	∗,k∗	∗,k∗	ADJ
ejpam-4859	262	25	)	)	PUNCT
ejpam-4859	262	26	is	be	AUX
ejpam-4859	262	27	dynamically	dynamically	ADV
ejpam-4859	262	28	equivalent	equivalent	ADJ
ejpam-4859	262	29	to	to	ADP
ejpam-4859	262	30	(	(	PUNCT
ejpam-4859	262	31	n	n	CCONJ
ejpam-4859	262	32	,	,	PUNCT
ejpam-4859	262	33	k	k	NOUN
ejpam-4859	262	34	)	)	PUNCT
ejpam-4859	262	35	and	and	CCONJ
ejpam-4859	262	36	ii	ii	NOUN
ejpam-4859	262	37	)	)	PUNCT
ejpam-4859	262	38	s∗	s∗	PROPN
ejpam-4859	262	39	=	=	PUNCT
ejpam-4859	262	40	s.	s.	PROPN
ejpam-4859	262	41	this	this	PRON
ejpam-4859	262	42	will	will	AUX
ejpam-4859	262	43	be	be	AUX
ejpam-4859	262	44	the	the	DET
ejpam-4859	262	45	basis	basis	NOUN
ejpam-4859	262	46	of	of	ADP
ejpam-4859	262	47	the	the	DET
ejpam-4859	262	48	transformations	transformation	NOUN
ejpam-4859	262	49	that	that	PRON
ejpam-4859	262	50	are	be	AUX
ejpam-4859	262	51	introduced	introduce	VERB
ejpam-4859	262	52	throughout	throughout	ADP
ejpam-4859	262	53	this	this	DET
ejpam-4859	262	54	chapter	chapter	NOUN
ejpam-4859	262	55	.	.	PUNCT
ejpam-4859	263	1	d.	d.	PROPN
ejpam-4859	263	2	magpantay	magpantay	PROPN
ejpam-4859	263	3	/	/	SYM
ejpam-4859	263	4	eur	eur	PROPN
ejpam-4859	263	5	.	.	PUNCT
ejpam-4859	264	1	j.	j.	PROPN
ejpam-4859	264	2	pure	pure	PROPN
ejpam-4859	264	3	appl	appl	PROPN
ejpam-4859	264	4	.	.	PROPN
ejpam-4859	264	5	math	math	PROPN
ejpam-4859	264	6	,	,	PUNCT
ejpam-4859	264	7	16	16	NUM
ejpam-4859	264	8	(	(	PUNCT
ejpam-4859	264	9	4	4	NUM
ejpam-4859	264	10	)	)	PUNCT
ejpam-4859	264	11	(	(	PUNCT
ejpam-4859	264	12	2023	2023	NUM
ejpam-4859	264	13	)	)	PUNCT
ejpam-4859	264	14	,	,	PUNCT
ejpam-4859	264	15	2557	2557	NUM
ejpam-4859	264	16	-	-	SYM
ejpam-4859	264	17	2580	2580	NUM
ejpam-4859	264	18	2567	2567	NUM
ejpam-4859	264	19	2.7	2.7	NUM
ejpam-4859	264	20	.	.	PUNCT
ejpam-4859	265	1	star	star	NOUN
ejpam-4859	265	2	transformation	transformation	NOUN
ejpam-4859	265	3	:	:	PUNCT
ejpam-4859	265	4	definition	definition	NOUN
ejpam-4859	265	5	and	and	CCONJ
ejpam-4859	265	6	basic	basic	ADJ
ejpam-4859	265	7	properties	property	NOUN
ejpam-4859	265	8	star	star	NOUN
ejpam-4859	265	9	(	(	PUNCT
ejpam-4859	265	10	s	s	NOUN
ejpam-4859	265	11	-	-	PUNCT
ejpam-4859	265	12	invariant	invariant	ADJ
ejpam-4859	265	13	termwise	termwise	NOUN
ejpam-4859	265	14	addition	addition	NOUN
ejpam-4859	265	15	of	of	ADP
ejpam-4859	265	16	reactions	reaction	NOUN
ejpam-4859	265	17	)	)	PUNCT
ejpam-4859	265	18	is	be	AUX
ejpam-4859	265	19	a	a	DET
ejpam-4859	265	20	network	network	NOUN
ejpam-4859	265	21	structure	structure	NOUN
ejpam-4859	265	22	-	-	PUNCT
ejpam-4859	265	23	oriented	orient	VERB
ejpam-4859	265	24	approach	approach	NOUN
ejpam-4859	265	25	to	to	ADP
ejpam-4859	265	26	poly	poly	ADJ
ejpam-4859	265	27	-	-	PUNCT
ejpam-4859	265	28	pl	pl	NOUN
ejpam-4859	265	29	kinetics	kinetic	NOUN
ejpam-4859	265	30	based	base	VERB
ejpam-4859	265	31	on	on	ADP
ejpam-4859	265	32	the	the	DET
ejpam-4859	265	33	following	follow	VERB
ejpam-4859	265	34	basic	basic	ADJ
ejpam-4859	265	35	observation	observation	NOUN
ejpam-4859	265	36	:	:	PUNCT
ejpam-4859	265	37	for	for	ADP
ejpam-4859	265	38	the	the	DET
ejpam-4859	265	39	rate	rate	NOUN
ejpam-4859	265	40	function	function	NOUN
ejpam-4859	265	41	ki(x	ki(x	NUM
ejpam-4859	265	42	)	)	PUNCT
ejpam-4859	265	43	and	and	CCONJ
ejpam-4859	265	44	for	for	ADP
ejpam-4859	265	45	a	a	DET
ejpam-4859	265	46	reaction	reaction	NOUN
ejpam-4859	265	47	ri	ri	NOUN
ejpam-4859	265	48	:	:	PUNCT
ejpam-4859	265	49	yi	yi	PROPN
ejpam-4859	265	50	→	→	SYM
ejpam-4859	265	51	y′i	y′i	NOUN
ejpam-4859	265	52	in	in	ADP
ejpam-4859	265	53	a	a	DET
ejpam-4859	265	54	pyk	pyk	NOUN
ejpam-4859	265	55	system	system	NOUN
ejpam-4859	265	56	(	(	PUNCT
ejpam-4859	265	57	n	n	X
ejpam-4859	265	58	,	,	PUNCT
ejpam-4859	265	59	k	k	NOUN
ejpam-4859	265	60	)	)	PUNCT
ejpam-4859	265	61	with	with	ADP
ejpam-4859	265	62	n	n	NOUN
ejpam-4859	265	63	=	=	SYM
ejpam-4859	265	64	(	(	PUNCT
ejpam-4859	265	65	s	s	NOUN
ejpam-4859	265	66	,	,	PUNCT
ejpam-4859	265	67	c	c	NOUN
ejpam-4859	265	68	,	,	PUNCT
ejpam-4859	265	69	r	r	X
ejpam-4859	265	70	)	)	PUNCT
ejpam-4859	265	71	we	we	PRON
ejpam-4859	265	72	have	have	VERB
ejpam-4859	265	73	ki(x	ki(x	NUM
ejpam-4859	265	74	)	)	PUNCT
ejpam-4859	266	1	=	=	PUNCT
ejpam-4859	266	2	ki(ai1mi1	ki(ai1mi1	PROPN
ejpam-4859	266	3	+	+	NOUN
ejpam-4859	266	4	.	.	PUNCT
ejpam-4859	266	5	.	.	PUNCT
ejpam-4859	267	1	.+aihmih)(y	.+aihmih)(y	PUNCT
ejpam-4859	267	2	′	′	NUM
ejpam-4859	267	3	i−yi	i−yi	ADJ
ejpam-4859	267	4	)	)	PUNCT
ejpam-4859	268	1	=	=	PUNCT
ejpam-4859	268	2	kiai1mi1(y	kiai1mi1(y	PROPN
ejpam-4859	268	3	′	′	NUM
ejpam-4859	268	4	i−yi)+	i−yi)+	NOUN
ejpam-4859	268	5	.	.	PUNCT
ejpam-4859	268	6	.	.	PUNCT
ejpam-4859	269	1	.+kiaihmih(y	.+kiaihmih(y	PUNCT
ejpam-4859	270	1	′	′	NUM
ejpam-4859	270	2	i−yi	i−yi	ADJ
ejpam-4859	270	3	)	)	PUNCT
ejpam-4859	270	4	(	(	PUNCT
ejpam-4859	270	5	2	2	X
ejpam-4859	270	6	)	)	PUNCT
ejpam-4859	270	7	where	where	SCONJ
ejpam-4859	270	8	mij	mij	NOUN
ejpam-4859	270	9	are	be	AUX
ejpam-4859	270	10	the	the	DET
ejpam-4859	270	11	h	h	PROPN
ejpam-4859	270	12	power	power	NOUN
ejpam-4859	270	13	law	law	NOUN
ejpam-4859	270	14	functions	function	NOUN
ejpam-4859	270	15	for	for	ADP
ejpam-4859	270	16	the	the	DET
ejpam-4859	270	17	i	i	PROPN
ejpam-4859	270	18	-	-	PUNCT
ejpam-4859	270	19	th	th	NOUN
ejpam-4859	270	20	reaction	reaction	NOUN
ejpam-4859	270	21	.	.	PUNCT
ejpam-4859	271	1	a	a	DET
ejpam-4859	271	2	star	star	NOUN
ejpam-4859	271	3	method	method	NOUN
ejpam-4859	271	4	introduces	introduce	VERB
ejpam-4859	271	5	additional	additional	ADJ
ejpam-4859	271	6	different	different	ADJ
ejpam-4859	271	7	reaction(s	reaction(s	NOUN
ejpam-4859	271	8	)	)	PUNCT
ejpam-4859	271	9	for	for	ADP
ejpam-4859	271	10	each	each	PRON
ejpam-4859	271	11	of	of	ADP
ejpam-4859	271	12	the	the	DET
ejpam-4859	271	13	h	h	PROPN
ejpam-4859	271	14	identical	identical	ADJ
ejpam-4859	271	15	reaction	reaction	NOUN
ejpam-4859	271	16	vectors	vector	NOUN
ejpam-4859	271	17	y′i	y′i	NOUN
ejpam-4859	271	18	−	−	PROPN
ejpam-4859	271	19	yi	yi	PROPN
ejpam-4859	271	20	in	in	ADP
ejpam-4859	271	21	the	the	DET
ejpam-4859	271	22	sum	sum	NOUN
ejpam-4859	271	23	.	.	PUNCT
ejpam-4859	272	1	this	this	PRON
ejpam-4859	272	2	enlarges	enlarge	VERB
ejpam-4859	272	3	the	the	DET
ejpam-4859	272	4	sets	set	NOUN
ejpam-4859	272	5	of	of	ADP
ejpam-4859	272	6	reactions	reaction	NOUN
ejpam-4859	272	7	and	and	CCONJ
ejpam-4859	272	8	complexes	complex	NOUN
ejpam-4859	272	9	,	,	PUNCT
ejpam-4859	272	10	so	so	SCONJ
ejpam-4859	272	11	the	the	DET
ejpam-4859	272	12	new	new	ADJ
ejpam-4859	272	13	crn	crn	NOUN
ejpam-4859	272	14	n	n	PRON
ejpam-4859	272	15	∗	∗	NOUN
ejpam-4859	272	16	=	=	PUNCT
ejpam-4859	272	17	(	(	PUNCT
ejpam-4859	272	18	s	s	NOUN
ejpam-4859	272	19	,	,	PUNCT
ejpam-4859	272	20	c	c	NOUN
ejpam-4859	272	21	∗,r∗	∗,r∗	VERB
ejpam-4859	272	22	)	)	PUNCT
ejpam-4859	272	23	and	and	CCONJ
ejpam-4859	272	24	new	new	ADJ
ejpam-4859	272	25	kinetics	kinetic	NOUN
ejpam-4859	272	26	k∗	k∗	NOUN
ejpam-4859	272	27	:	:	PUNCT
ejpam-4859	272	28	rs	rs	INTJ
ejpam-4859	272	29	>	>	X
ejpam-4859	272	30	→	→	PUNCT
ejpam-4859	272	31	rr∗	rr∗	NOUN
ejpam-4859	272	32	are	be	AUX
ejpam-4859	272	33	constructed	construct	VERB
ejpam-4859	272	34	.	.	PUNCT
ejpam-4859	273	1	remark	remark	NOUN
ejpam-4859	273	2	4	4	NUM
ejpam-4859	273	3	.	.	PUNCT
ejpam-4859	274	1	when	when	SCONJ
ejpam-4859	274	2	the	the	DET
ejpam-4859	274	3	poly	poly	ADJ
ejpam-4859	274	4	-	-	PUNCT
ejpam-4859	274	5	pl	pl	NOUN
ejpam-4859	274	6	kinetics	kinetic	NOUN
ejpam-4859	274	7	do	do	AUX
ejpam-4859	274	8	not	not	PART
ejpam-4859	274	9	have	have	VERB
ejpam-4859	274	10	the	the	DET
ejpam-4859	274	11	same	same	ADJ
ejpam-4859	274	12	number	number	NOUN
ejpam-4859	274	13	of	of	ADP
ejpam-4859	274	14	terms	term	NOUN
ejpam-4859	274	15	,	,	PUNCT
ejpam-4859	274	16	one	one	PRON
ejpam-4859	274	17	simply	simply	ADV
ejpam-4859	274	18	uses	use	VERB
ejpam-4859	274	19	the	the	DET
ejpam-4859	274	20	same	same	ADJ
ejpam-4859	274	21	“	"	PUNCT
ejpam-4859	274	22	trick	trick	NOUN
ejpam-4859	274	23	”	"	PUNCT
ejpam-4859	274	24	of	of	ADP
ejpam-4859	274	25	replacing	replace	VERB
ejpam-4859	274	26	the	the	DET
ejpam-4859	274	27	last	last	ADJ
ejpam-4859	274	28	term	term	NOUN
ejpam-4859	274	29	of	of	ADP
ejpam-4859	274	30	the	the	DET
ejpam-4859	274	31	shorter	short	ADJ
ejpam-4859	274	32	function	function	NOUN
ejpam-4859	274	33	with	with	ADP
ejpam-4859	274	34	(	(	PUNCT
ejpam-4859	274	35	h	h	NOUN
ejpam-4859	274	36	−	−	PROPN
ejpam-4859	274	37	h′	h′	PROPN
ejpam-4859	274	38	+	+	CCONJ
ejpam-4859	274	39	1	1	X
ejpam-4859	274	40	)	)	PUNCT
ejpam-4859	274	41	copies	copy	NOUN
ejpam-4859	274	42	of	of	ADP
ejpam-4859	274	43	1	1	NUM
ejpam-4859	274	44	h−h′+1	h−h′+1	PROPN
ejpam-4859	274	45	of	of	ADP
ejpam-4859	274	46	that	that	DET
ejpam-4859	274	47	term	term	NOUN
ejpam-4859	274	48	.	.	PUNCT
ejpam-4859	275	1	illustration	illustration	NOUN
ejpam-4859	275	2	1	1	NUM
ejpam-4859	275	3	.	.	PUNCT
ejpam-4859	275	4	suppose	suppose	VERB
ejpam-4859	275	5	the	the	DET
ejpam-4859	275	6	following	following	NOUN
ejpam-4859	275	7	are	be	AUX
ejpam-4859	275	8	the	the	DET
ejpam-4859	275	9	poly	poly	ADJ
ejpam-4859	275	10	-	-	PUNCT
ejpam-4859	275	11	pl	pl	NOUN
ejpam-4859	275	12	kinetics	kinetic	NOUN
ejpam-4859	275	13	of	of	ADP
ejpam-4859	275	14	a	a	DET
ejpam-4859	275	15	network	network	NOUN
ejpam-4859	275	16	:	:	PUNCT
ejpam-4859	275	17	k1(x	k1(x	NOUN
ejpam-4859	275	18	,	,	PUNCT
ejpam-4859	275	19	y	y	PROPN
ejpam-4859	275	20	)	)	PUNCT
ejpam-4859	276	1	=	=	PRON
ejpam-4859	276	2	k1(2x	k1(2x	VERB
ejpam-4859	276	3	3y	3y	NUM
ejpam-4859	276	4	+	+	ADJ
ejpam-4859	276	5	x2y	x2y	X
ejpam-4859	276	6	2	2	NUM
ejpam-4859	277	1	+	+	NUM
ejpam-4859	277	2	4xy	4xy	ADJ
ejpam-4859	277	3	2	2	NUM
ejpam-4859	277	4	+	+	CCONJ
ejpam-4859	277	5	0.5y	0.5y	NUM
ejpam-4859	277	6	3	3	NUM
ejpam-4859	277	7	)	)	PUNCT
ejpam-4859	277	8	k2(x	k2(x	PROPN
ejpam-4859	277	9	,	,	PUNCT
ejpam-4859	277	10	y	y	PROPN
ejpam-4859	277	11	)	)	PUNCT
ejpam-4859	278	1	=	=	PUNCT
ejpam-4859	278	2	k2(5x	k2(5x	PROPN
ejpam-4859	278	3	4y	4y	NOUN
ejpam-4859	278	4	2	2	NUM
ejpam-4859	278	5	+	+	CCONJ
ejpam-4859	278	6	6xy	6xy	ADJ
ejpam-4859	278	7	3	3	NUM
ejpam-4859	278	8	)	)	PUNCT
ejpam-4859	278	9	.	.	PUNCT
ejpam-4859	279	1	it	it	PRON
ejpam-4859	279	2	is	be	AUX
ejpam-4859	279	3	equvalent	equvalent	ADJ
ejpam-4859	279	4	to	to	ADP
ejpam-4859	279	5	k1(x	k1(x	PROPN
ejpam-4859	279	6	,	,	PUNCT
ejpam-4859	279	7	y	y	PROPN
ejpam-4859	279	8	)	)	PUNCT
ejpam-4859	280	1	=	=	PRON
ejpam-4859	280	2	k1(2x	k1(2x	VERB
ejpam-4859	280	3	3y	3y	NUM
ejpam-4859	280	4	+	+	ADJ
ejpam-4859	280	5	x2y	x2y	X
ejpam-4859	280	6	2	2	NUM
ejpam-4859	281	1	+	+	NUM
ejpam-4859	281	2	4xy	4xy	ADJ
ejpam-4859	281	3	2	2	NUM
ejpam-4859	281	4	+	+	CCONJ
ejpam-4859	281	5	0.5y	0.5y	NUM
ejpam-4859	281	6	3	3	NUM
ejpam-4859	281	7	)	)	PUNCT
ejpam-4859	281	8	k2(x	k2(x	PROPN
ejpam-4859	281	9	,	,	PUNCT
ejpam-4859	281	10	y	y	PROPN
ejpam-4859	281	11	)	)	PUNCT
ejpam-4859	282	1	=	=	PUNCT
ejpam-4859	282	2	k2(5x	k2(5x	PROPN
ejpam-4859	282	3	4y	4y	NOUN
ejpam-4859	282	4	2	2	NUM
ejpam-4859	282	5	+	+	CCONJ
ejpam-4859	282	6	2xy	2xy	ADJ
ejpam-4859	282	7	3	3	NUM
ejpam-4859	283	1	+	+	CCONJ
ejpam-4859	283	2	2xy	2xy	ADJ
ejpam-4859	283	3	3	3	NUM
ejpam-4859	284	1	+	+	CCONJ
ejpam-4859	284	2	2xy	2xy	ADJ
ejpam-4859	284	3	3	3	NUM
ejpam-4859	284	4	)	)	PUNCT
ejpam-4859	284	5	.	.	PUNCT
ejpam-4859	285	1	notice	notice	VERB
ejpam-4859	285	2	that	that	SCONJ
ejpam-4859	285	3	n	n	PROPN
ejpam-4859	285	4	and	and	CCONJ
ejpam-4859	285	5	n	n	PRON
ejpam-4859	285	6	∗	∗	NOUN
ejpam-4859	285	7	have	have	VERB
ejpam-4859	285	8	the	the	DET
ejpam-4859	285	9	same	same	ADJ
ejpam-4859	285	10	set	set	NOUN
ejpam-4859	285	11	of	of	ADP
ejpam-4859	285	12	species	specie	NOUN
ejpam-4859	285	13	as	as	ADP
ejpam-4859	285	14	one	one	NUM
ejpam-4859	285	15	of	of	ADP
ejpam-4859	285	16	requirements	requirement	NOUN
ejpam-4859	285	17	to	to	PART
ejpam-4859	285	18	be	be	AUX
ejpam-4859	285	19	dynamically	dynamically	ADV
ejpam-4859	285	20	equivalent	equivalent	ADJ
ejpam-4859	285	21	.	.	PUNCT
ejpam-4859	286	1	since	since	SCONJ
ejpam-4859	286	2	it	it	PRON
ejpam-4859	286	3	is	be	AUX
ejpam-4859	286	4	s	s	NOUN
ejpam-4859	286	5	-	-	PUNCT
ejpam-4859	286	6	invariant	invariant	ADJ
ejpam-4859	286	7	and	and	CCONJ
ejpam-4859	286	8	it	it	PRON
ejpam-4859	286	9	is	be	AUX
ejpam-4859	286	10	a	a	DET
ejpam-4859	286	11	transformation	transformation	NOUN
ejpam-4859	286	12	,	,	PUNCT
ejpam-4859	286	13	this	this	PRON
ejpam-4859	286	14	assures	assure	VERB
ejpam-4859	286	15	the	the	DET
ejpam-4859	286	16	equality	equality	NOUN
ejpam-4859	286	17	of	of	ADP
ejpam-4859	286	18	the	the	DET
ejpam-4859	286	19	stoichiometric	stoichiometric	NOUN
ejpam-4859	286	20	subspace	subspace	NOUN
ejpam-4859	286	21	s	s	PROPN
ejpam-4859	286	22	of	of	ADP
ejpam-4859	286	23	the	the	DET
ejpam-4859	286	24	original	original	ADJ
ejpam-4859	286	25	network	network	NOUN
ejpam-4859	286	26	to	to	ADP
ejpam-4859	286	27	the	the	DET
ejpam-4859	286	28	stoichiometric	stoichiometric	NOUN
ejpam-4859	286	29	subspace	subspace	NOUN
ejpam-4859	286	30	s∗	s∗	PROPN
ejpam-4859	286	31	of	of	ADP
ejpam-4859	286	32	the	the	DET
ejpam-4859	286	33	network	network	NOUN
ejpam-4859	286	34	produced	produce	VERB
ejpam-4859	286	35	by	by	ADP
ejpam-4859	286	36	adding	add	VERB
ejpam-4859	286	37	complexes	complex	NOUN
ejpam-4859	286	38	and	and	CCONJ
ejpam-4859	286	39	reactions	reaction	NOUN
ejpam-4859	286	40	.	.	PUNCT
ejpam-4859	287	1	this	this	PRON
ejpam-4859	287	2	implies	imply	VERB
ejpam-4859	287	3	s	s	PART
ejpam-4859	287	4	=	=	NOUN
ejpam-4859	287	5	dim	dim	NOUN
ejpam-4859	287	6	s	s	PART
ejpam-4859	287	7	=	=	NOUN
ejpam-4859	287	8	dim	dim	ADJ
ejpam-4859	287	9	s∗	s∗	NOUN
ejpam-4859	287	10	=	=	PUNCT
ejpam-4859	287	11	s∗.	s∗.	ADJ
ejpam-4859	287	12	aside	aside	ADV
ejpam-4859	287	13	from	from	ADP
ejpam-4859	287	14	these	these	DET
ejpam-4859	287	15	observations	observation	NOUN
ejpam-4859	287	16	,	,	PUNCT
ejpam-4859	287	17	we	we	PRON
ejpam-4859	287	18	have	have	VERB
ejpam-4859	287	19	the	the	DET
ejpam-4859	287	20	following	follow	VERB
ejpam-4859	287	21	properties	property	NOUN
ejpam-4859	287	22	for	for	ADP
ejpam-4859	287	23	any	any	DET
ejpam-4859	287	24	star	star	NOUN
ejpam-4859	287	25	method	method	NOUN
ejpam-4859	287	26	:	:	PUNCT
ejpam-4859	287	27	proposition	proposition	NOUN
ejpam-4859	287	28	6	6	NUM
ejpam-4859	287	29	.	.	PUNCT
ejpam-4859	288	1	let	let	VERB
ejpam-4859	288	2	n	n	PRON
ejpam-4859	288	3	∗	∗	NOUN
ejpam-4859	288	4	=	=	PUNCT
ejpam-4859	288	5	(	(	PUNCT
ejpam-4859	288	6	s	s	NOUN
ejpam-4859	288	7	,	,	PUNCT
ejpam-4859	288	8	c	c	PROPN
ejpam-4859	288	9	∗,r∗	∗,r∗	VERB
ejpam-4859	288	10	)	)	PUNCT
ejpam-4859	288	11	be	be	AUX
ejpam-4859	288	12	a	a	DET
ejpam-4859	288	13	star	star	NOUN
ejpam-4859	288	14	transform	transform	NOUN
ejpam-4859	288	15	of	of	ADP
ejpam-4859	288	16	n	n	NOUN
ejpam-4859	288	17	=	=	SYM
ejpam-4859	288	18	(	(	PUNCT
ejpam-4859	288	19	s	s	NOUN
ejpam-4859	288	20	,	,	PUNCT
ejpam-4859	288	21	c	c	NOUN
ejpam-4859	288	22	,	,	PUNCT
ejpam-4859	288	23	r	r	NOUN
ejpam-4859	288	24	)	)	PUNCT
ejpam-4859	288	25	.	.	PUNCT
ejpam-4859	289	1	then	then	ADV
ejpam-4859	289	2	|r∗|	|r∗|	PRON
ejpam-4859	289	3	=	=	SYM
ejpam-4859	289	4	hr	hr	NOUN
ejpam-4859	289	5	and	and	CCONJ
ejpam-4859	289	6	|c	|c	PUNCT
ejpam-4859	289	7	∗|	∗|	PROPN
ejpam-4859	289	8	≤	≤	PUNCT
ejpam-4859	289	9	hn	hn	PROPN
ejpam-4859	289	10	.	.	PUNCT
ejpam-4859	290	1	proof	proof	NOUN
ejpam-4859	290	2	.	.	PUNCT
ejpam-4859	291	1	for	for	ADP
ejpam-4859	291	2	the	the	DET
ejpam-4859	291	3	first	first	ADJ
ejpam-4859	291	4	part	part	NOUN
ejpam-4859	291	5	,	,	PUNCT
ejpam-4859	291	6	since	since	SCONJ
ejpam-4859	291	7	starmethod	starmethod	NOUN
ejpam-4859	291	8	introduces	introduce	NOUN
ejpam-4859	291	9	an	an	DET
ejpam-4859	291	10	additional	additional	ADJ
ejpam-4859	291	11	different	different	ADJ
ejpam-4859	291	12	reaction	reaction	NOUN
ejpam-4859	291	13	for	for	ADP
ejpam-4859	291	14	each	each	PRON
ejpam-4859	291	15	of	of	ADP
ejpam-4859	291	16	the	the	DET
ejpam-4859	291	17	h	h	PROPN
ejpam-4859	291	18	identical	identical	ADJ
ejpam-4859	291	19	reaction	reaction	NOUN
ejpam-4859	291	20	vectors	vector	NOUN
ejpam-4859	291	21	y′i−yi	y′i−yi	ADV
ejpam-4859	291	22	in	in	ADP
ejpam-4859	291	23	the	the	DET
ejpam-4859	291	24	sum	sum	NOUN
ejpam-4859	291	25	,	,	PUNCT
ejpam-4859	291	26	the	the	DET
ejpam-4859	291	27	claim	claim	NOUN
ejpam-4859	291	28	follows	follow	VERB
ejpam-4859	291	29	immediately	immediately	ADV
ejpam-4859	291	30	from	from	ADP
ejpam-4859	291	31	(	(	PUNCT
ejpam-4859	291	32	2	2	NUM
ejpam-4859	291	33	)	)	PUNCT
ejpam-4859	291	34	and	and	CCONJ
ejpam-4859	291	35	from	from	ADP
ejpam-4859	291	36	the	the	DET
ejpam-4859	291	37	fact	fact	NOUN
ejpam-4859	291	38	that	that	SCONJ
ejpam-4859	291	39	hn	hn	PROPN
ejpam-4859	291	40	is	be	AUX
ejpam-4859	291	41	the	the	DET
ejpam-4859	291	42	maximum	maximum	ADJ
ejpam-4859	291	43	number	number	NOUN
ejpam-4859	291	44	of	of	ADP
ejpam-4859	291	45	complexes	complex	NOUN
ejpam-4859	291	46	(	(	PUNCT
ejpam-4859	291	47	i.e.	i.e.	X
ejpam-4859	291	48	when	when	SCONJ
ejpam-4859	291	49	these	these	PRON
ejpam-4859	291	50	are	be	AUX
ejpam-4859	291	51	all	all	ADV
ejpam-4859	291	52	different	different	ADJ
ejpam-4859	291	53	)	)	PUNCT
ejpam-4859	291	54	for	for	ADP
ejpam-4859	291	55	hr	hr	NOUN
ejpam-4859	291	56	reactions	reaction	NOUN
ejpam-4859	291	57	.	.	PUNCT
ejpam-4859	292	1	remark	remark	PROPN
ejpam-4859	292	2	5	5	NUM
ejpam-4859	292	3	.	.	PUNCT
ejpam-4859	293	1	observe	observe	VERB
ejpam-4859	293	2	that	that	SCONJ
ejpam-4859	293	3	k∗	k∗	NOUN
ejpam-4859	293	4	ij	ij	INTJ
ejpam-4859	293	5	=	=	SYM
ejpam-4859	293	6	k∗ijmij	k∗ijmij	PROPN
ejpam-4859	293	7	,	,	PUNCT
ejpam-4859	293	8	with	with	ADP
ejpam-4859	293	9	k∗ij	k∗ij	PROPN
ejpam-4859	293	10	=	=	SYM
ejpam-4859	293	11	kiaij	kiaij	PROPN
ejpam-4859	293	12	,	,	PUNCT
ejpam-4859	293	13	is	be	AUX
ejpam-4859	293	14	the	the	DET
ejpam-4859	293	15	kinetic	kinetic	ADJ
ejpam-4859	293	16	function	function	NOUN
ejpam-4859	293	17	of	of	ADP
ejpam-4859	293	18	the	the	DET
ejpam-4859	293	19	reaction	reaction	NOUN
ejpam-4859	293	20	rij	rij	PROPN
ejpam-4859	293	21	corresponding	correspond	VERB
ejpam-4859	293	22	to	to	ADP
ejpam-4859	293	23	the	the	DET
ejpam-4859	293	24	reaction	reaction	NOUN
ejpam-4859	293	25	vector	vector	NOUN
ejpam-4859	293	26	(	(	PUNCT
ejpam-4859	293	27	y′i	y′i	NOUN
ejpam-4859	293	28	−	−	PROPN
ejpam-4859	293	29	yi	yi	NOUN
ejpam-4859	293	30	)	)	PUNCT
ejpam-4859	293	31	.	.	PUNCT
ejpam-4859	294	1	the	the	DET
ejpam-4859	294	2	stoichiometric	stoichiometric	ADJ
ejpam-4859	294	3	matrix	matrix	NOUN
ejpam-4859	294	4	n∗	n∗	VERB
ejpam-4859	294	5	d.	d.	PROPN
ejpam-4859	294	6	magpantay	magpantay	PROPN
ejpam-4859	294	7	/	/	SYM
ejpam-4859	294	8	eur	eur	PROPN
ejpam-4859	294	9	.	.	PUNCT
ejpam-4859	295	1	j.	j.	PROPN
ejpam-4859	295	2	pure	pure	PROPN
ejpam-4859	295	3	appl	appl	PROPN
ejpam-4859	295	4	.	.	PROPN
ejpam-4859	295	5	math	math	PROPN
ejpam-4859	295	6	,	,	PUNCT
ejpam-4859	295	7	16	16	NUM
ejpam-4859	295	8	(	(	PUNCT
ejpam-4859	295	9	4	4	NUM
ejpam-4859	295	10	)	)	PUNCT
ejpam-4859	295	11	(	(	PUNCT
ejpam-4859	295	12	2023	2023	NUM
ejpam-4859	295	13	)	)	PUNCT
ejpam-4859	295	14	,	,	PUNCT
ejpam-4859	295	15	2557	2557	NUM
ejpam-4859	295	16	-	-	SYM
ejpam-4859	295	17	2580	2580	NUM
ejpam-4859	295	18	2568	2568	NUM
ejpam-4859	295	19	becomes	become	VERB
ejpam-4859	295	20	an	an	DET
ejpam-4859	295	21	m	m	NOUN
ejpam-4859	295	22	×	×	NOUN
ejpam-4859	295	23	hr	hr	NOUN
ejpam-4859	295	24	matrix	matrix	NOUN
ejpam-4859	295	25	,	,	PUNCT
ejpam-4859	295	26	and	and	CCONJ
ejpam-4859	295	27	usually	usually	ADV
ejpam-4859	295	28	the	the	DET
ejpam-4859	295	29	reaction	reaction	NOUN
ejpam-4859	295	30	vector	vector	NOUN
ejpam-4859	295	31	of	of	ADP
ejpam-4859	295	32	the	the	DET
ejpam-4859	295	33	reaction	reaction	NOUN
ejpam-4859	295	34	ri	ri	PROPN
ejpam-4859	295	35	are	be	AUX
ejpam-4859	295	36	just	just	ADV
ejpam-4859	295	37	replicated	replicate	VERB
ejpam-4859	295	38	h	h	PROPN
ejpam-4859	295	39	times	time	NOUN
ejpam-4859	295	40	.	.	PUNCT
ejpam-4859	296	1	let	let	VERB
ejpam-4859	296	2	the	the	DET
ejpam-4859	296	3	reaction	reaction	NOUN
ejpam-4859	296	4	vector	vector	NOUN
ejpam-4859	296	5	y′i	y′i	NOUN
ejpam-4859	296	6	−	−	PROPN
ejpam-4859	296	7	yi	yi	NOUN
ejpam-4859	296	8	=	=	SYM
ejpam-4859	296	9	(	(	PUNCT
ejpam-4859	296	10	ci1	ci1	PROPN
ejpam-4859	296	11	,	,	PUNCT
ejpam-4859	296	12	ci2	ci2	PROPN
ejpam-4859	296	13	,	,	PUNCT
ejpam-4859	296	14	.	.	PUNCT
ejpam-4859	296	15	.	.	PUNCT
ejpam-4859	297	1	.	.	PUNCT
ejpam-4859	298	1	,	,	PUNCT
ejpam-4859	298	2	cim	cim	PROPN
ejpam-4859	298	3	)	)	PUNCT
ejpam-4859	298	4	.	.	PUNCT
ejpam-4859	299	1	by	by	ADP
ejpam-4859	299	2	the	the	DET
ejpam-4859	299	3	remark	remark	NOUN
ejpam-4859	299	4	above	above	ADV
ejpam-4859	299	5	,	,	PUNCT
ejpam-4859	299	6	we	we	PRON
ejpam-4859	299	7	have	have	VERB
ejpam-4859	299	8	r11	r11	NOUN
ejpam-4859	299	9	r12	r12	NOUN
ejpam-4859	299	10	.	.	PUNCT
ejpam-4859	299	11	.	.	PUNCT
ejpam-4859	299	12	.	.	PUNCT
ejpam-4859	300	1	r1h	r1h	NOUN
ejpam-4859	300	2	r21	r21	NOUN
ejpam-4859	300	3	r22	r22	NOUN
ejpam-4859	300	4	.	.	PUNCT
ejpam-4859	300	5	.	.	PUNCT
ejpam-4859	300	6	.	.	PUNCT
ejpam-4859	301	1	r2h	r2h	NOUN
ejpam-4859	301	2	.	.	PUNCT
ejpam-4859	301	3	.	.	PUNCT
ejpam-4859	301	4	.	.	PUNCT
ejpam-4859	302	1	rr1	rr1	NOUN
ejpam-4859	302	2	rr2	rr2	PROPN
ejpam-4859	302	3	.	.	PUNCT
ejpam-4859	302	4	.	.	PUNCT
ejpam-4859	302	5	.	.	PUNCT
ejpam-4859	303	1	rrh	rrh	PROPN
ejpam-4859	303	2	n∗	n∗	PROPN
ejpam-4859	304	1	=	=	SYM
ejpam-4859	304	2			PROPN
ejpam-4859	304	3	c11	c11	NOUN
ejpam-4859	304	4	c11	c11	NOUN
ejpam-4859	304	5	.	.	PUNCT
ejpam-4859	304	6	.	.	PUNCT
ejpam-4859	305	1	.	.	PUNCT
ejpam-4859	306	1	c11	c11	NOUN
ejpam-4859	306	2	c21	c21	PROPN
ejpam-4859	306	3	c21	c21	PROPN
ejpam-4859	306	4	.	.	PUNCT
ejpam-4859	306	5	.	.	PUNCT
ejpam-4859	306	6	.	.	PUNCT
ejpam-4859	307	1	c21	c21	PROPN
ejpam-4859	307	2	.	.	PUNCT
ejpam-4859	307	3	.	.	PUNCT
ejpam-4859	307	4	.	.	PUNCT
ejpam-4859	308	1	cr1	cr1	PROPN
ejpam-4859	308	2	cr1	cr1	PROPN
ejpam-4859	308	3	.	.	PUNCT
ejpam-4859	308	4	.	.	PUNCT
ejpam-4859	308	5	.	.	PUNCT
ejpam-4859	309	1	cr1	cr1	PROPN
ejpam-4859	309	2	c12	c12	PROPN
ejpam-4859	309	3	c12	c12	PROPN
ejpam-4859	309	4	.	.	PUNCT
ejpam-4859	309	5	.	.	PUNCT
ejpam-4859	309	6	.	.	PUNCT
ejpam-4859	310	1	c12	c12	PROPN
ejpam-4859	310	2	c22	c22	PROPN
ejpam-4859	310	3	c22	c22	PROPN
ejpam-4859	310	4	.	.	PUNCT
ejpam-4859	310	5	.	.	PUNCT
ejpam-4859	310	6	.	.	PUNCT
ejpam-4859	311	1	c22	c22	PROPN
ejpam-4859	311	2	.	.	PUNCT
ejpam-4859	311	3	.	.	PUNCT
ejpam-4859	311	4	.	.	PUNCT
ejpam-4859	312	1	cr2	cr2	PROPN
ejpam-4859	312	2	cr2	cr2	PROPN
ejpam-4859	312	3	.	.	PUNCT
ejpam-4859	312	4	.	.	PUNCT
ejpam-4859	312	5	.	.	PUNCT
ejpam-4859	313	1	cr2	cr2	PROPN
ejpam-4859	313	2	...	...	PUNCT
ejpam-4859	313	3	...	...	PUNCT
ejpam-4859	313	4	.	.	PUNCT
ejpam-4859	313	5	.	.	PUNCT
ejpam-4859	313	6	.	.	PUNCT
ejpam-4859	314	1	...	...	PUNCT
ejpam-4859	314	2	...	...	PUNCT
ejpam-4859	314	3	...	...	PUNCT
ejpam-4859	314	4	.	.	PUNCT
ejpam-4859	314	5	.	.	PUNCT
ejpam-4859	315	1	.	.	PUNCT
ejpam-4859	315	2	...	...	PUNCT
ejpam-4859	315	3	.	.	PUNCT
ejpam-4859	316	1	.	.	PUNCT
ejpam-4859	316	2	.	.	PUNCT
ejpam-4859	317	1	...	...	PUNCT
ejpam-4859	317	2	...	...	PUNCT
ejpam-4859	317	3	.	.	PUNCT
ejpam-4859	317	4	.	.	PUNCT
ejpam-4859	318	1	.	.	PUNCT
ejpam-4859	319	1	...	...	PUNCT
ejpam-4859	320	1	c1	c1	PROPN
ejpam-4859	320	2	m	m	PROPN
ejpam-4859	320	3	c1	c1	PROPN
ejpam-4859	320	4	m	m	PROPN
ejpam-4859	320	5	.	.	PUNCT
ejpam-4859	320	6	.	.	PUNCT
ejpam-4859	320	7	.	.	PUNCT
ejpam-4859	321	1	c1	c1	PROPN
ejpam-4859	321	2	m	m	PROPN
ejpam-4859	321	3	c2	c2	PROPN
ejpam-4859	321	4	m	m	PROPN
ejpam-4859	321	5	c2	c2	PROPN
ejpam-4859	321	6	m	m	PROPN
ejpam-4859	321	7	.	.	PUNCT
ejpam-4859	321	8	.	.	PUNCT
ejpam-4859	321	9	.	.	PUNCT
ejpam-4859	322	1	c2	c2	PROPN
ejpam-4859	322	2	m	m	PROPN
ejpam-4859	322	3	.	.	PUNCT
ejpam-4859	322	4	.	.	PUNCT
ejpam-4859	322	5	.	.	PUNCT
ejpam-4859	323	1	crm	crm	PROPN
ejpam-4859	323	2	crm	crm	PROPN
ejpam-4859	323	3	.	.	PUNCT
ejpam-4859	323	4	.	.	PUNCT
ejpam-4859	323	5	.	.	PUNCT
ejpam-4859	324	1	crm	crm	PROPN
ejpam-4859	324	2			PROPN
ejpam-4859	324	3	a1	a1	PROPN
ejpam-4859	324	4	a2	a2	PROPN
ejpam-4859	324	5	...	...	PUNCT
ejpam-4859	324	6	am	be	AUX
ejpam-4859	324	7	and	and	CCONJ
ejpam-4859	324	8	k∗	k∗	ADJ
ejpam-4859	324	9	=	=	SYM
ejpam-4859	324	10			NOUN
ejpam-4859	324	11	k∗	k∗	VERB
ejpam-4859	324	12	11	11	NUM
ejpam-4859	324	13	k∗	k∗	NOUN
ejpam-4859	324	14	12	12	NUM
ejpam-4859	324	15	...	...	PUNCT
ejpam-4859	325	1	k∗	k∗	PROPN
ejpam-4859	325	2	1h	1h	NUM
ejpam-4859	325	3	k∗	k∗	PROPN
ejpam-4859	325	4	21	21	NUM
ejpam-4859	325	5	k∗	k∗	NOUN
ejpam-4859	325	6	22	22	NUM
ejpam-4859	325	7	...	...	PUNCT
ejpam-4859	326	1	k∗	k∗	PROPN
ejpam-4859	326	2	2h	2h	NUM
ejpam-4859	326	3	...	...	PUNCT
ejpam-4859	327	1	k∗	k∗	PROPN
ejpam-4859	327	2	r1	r1	PROPN
ejpam-4859	327	3	k∗	k∗	PROPN
ejpam-4859	327	4	r2	r2	PROPN
ejpam-4859	327	5	...	...	PUNCT
ejpam-4859	328	1	k∗	k∗	PROPN
ejpam-4859	328	2	rh	rh	PROPN
ejpam-4859	328	3			PROPN
ejpam-4859	328	4	.	.	PUNCT
ejpam-4859	329	1	hence	hence	ADV
ejpam-4859	329	2	,	,	PUNCT
ejpam-4859	329	3	n∗k∗	n∗k∗	PUNCT
ejpam-4859	330	1	=	=	NOUN
ejpam-4859	330	2			NOUN
ejpam-4859	331	1	c11k∗	c11k∗	NUM
ejpam-4859	331	2	11	11	NUM
ejpam-4859	331	3	+	+	CCONJ
ejpam-4859	331	4	c11k∗	c11k∗	NUM
ejpam-4859	331	5	12	12	NUM
ejpam-4859	331	6	+	+	CCONJ
ejpam-4859	331	7	.	.	PUNCT
ejpam-4859	331	8	.	.	PUNCT
ejpam-4859	332	1	.+	.+	NOUN
ejpam-4859	332	2	c11k∗	c11k∗	NUM
ejpam-4859	332	3	1h	1h	NUM
ejpam-4859	332	4	+	+	CCONJ
ejpam-4859	332	5	c21k∗	c21k∗	NUM
ejpam-4859	332	6	21	21	NUM
ejpam-4859	332	7	+	+	CCONJ
ejpam-4859	332	8	c21k∗	c21k∗	NUM
ejpam-4859	332	9	22	22	NUM
ejpam-4859	333	1	+	+	CCONJ
ejpam-4859	333	2	.	.	PUNCT
ejpam-4859	333	3	.	.	PUNCT
ejpam-4859	334	1	.+	.+	NOUN
ejpam-4859	334	2	c21k∗	c21k∗	NUM
ejpam-4859	334	3	2h	2h	NUM
ejpam-4859	334	4	+	+	PUNCT
ejpam-4859	334	5	.	.	PUNCT
ejpam-4859	334	6	.	.	PUNCT
ejpam-4859	335	1	.+	.+	NOUN
ejpam-4859	335	2	cr1k∗	cr1k∗	VERB
ejpam-4859	335	3	r1	r1	NOUN
ejpam-4859	335	4	+	+	CCONJ
ejpam-4859	335	5	cr1k∗	cr1k∗	NOUN
ejpam-4859	335	6	r2	r2	NOUN
ejpam-4859	335	7	+	+	X
ejpam-4859	335	8	.	.	PUNCT
ejpam-4859	335	9	.	.	PUNCT
ejpam-4859	336	1	.+	.+	NOUN
ejpam-4859	336	2	cr1k∗	cr1k∗	VERB
ejpam-4859	336	3	rh	rh	NOUN
ejpam-4859	336	4	c12k∗	c12k∗	NUM
ejpam-4859	336	5	11	11	NUM
ejpam-4859	336	6	+	+	NUM
ejpam-4859	336	7	c12k∗	c12k∗	NUM
ejpam-4859	336	8	12	12	NUM
ejpam-4859	336	9	+	+	CCONJ
ejpam-4859	336	10	.	.	PUNCT
ejpam-4859	336	11	.	.	PUNCT
ejpam-4859	337	1	.+	.+	NOUN
ejpam-4859	337	2	c12k∗	c12k∗	NUM
ejpam-4859	337	3	1h	1h	NUM
ejpam-4859	337	4	+	+	NUM
ejpam-4859	337	5	c22k∗	c22k∗	NUM
ejpam-4859	337	6	21	21	NUM
ejpam-4859	337	7	+	+	NUM
ejpam-4859	337	8	c22k∗	c22k∗	NUM
ejpam-4859	337	9	22	22	NUM
ejpam-4859	337	10	+	+	CCONJ
ejpam-4859	337	11	.	.	PUNCT
ejpam-4859	337	12	.	.	PUNCT
ejpam-4859	338	1	.+	.+	NOUN
ejpam-4859	338	2	c22k∗	c22k∗	NUM
ejpam-4859	338	3	2h	2h	NUM
ejpam-4859	338	4	+	+	PUNCT
ejpam-4859	338	5	.	.	PUNCT
ejpam-4859	338	6	.	.	PUNCT
ejpam-4859	339	1	.+	.+	NOUN
ejpam-4859	339	2	cr2k∗	cr2k∗	VERB
ejpam-4859	339	3	r1	r1	PROPN
ejpam-4859	339	4	+	+	NUM
ejpam-4859	339	5	cr2k∗	cr2k∗	NOUN
ejpam-4859	339	6	r2	r2	PROPN
ejpam-4859	339	7	+	+	X
ejpam-4859	339	8	.	.	PUNCT
ejpam-4859	339	9	.	.	PUNCT
ejpam-4859	340	1	.+	.+	NOUN
ejpam-4859	340	2	cr2k∗	cr2k∗	VERB
ejpam-4859	340	3	rh	rh	PROPN
ejpam-4859	340	4	...	...	PUNCT
ejpam-4859	340	5	c1mk∗	c1mk∗	PROPN
ejpam-4859	340	6	11	11	NUM
ejpam-4859	340	7	+	+	CCONJ
ejpam-4859	340	8	c1mk∗	c1mk∗	NOUN
ejpam-4859	340	9	12	12	NUM
ejpam-4859	340	10	+	+	CCONJ
ejpam-4859	340	11	.	.	PUNCT
ejpam-4859	340	12	.	.	PUNCT
ejpam-4859	341	1	.+	.+	NOUN
ejpam-4859	341	2	c1mk∗	c1mk∗	VERB
ejpam-4859	341	3	1h	1h	NUM
ejpam-4859	341	4	+	+	CCONJ
ejpam-4859	341	5	c2mk∗	c2mk∗	PROPN
ejpam-4859	341	6	21	21	NUM
ejpam-4859	341	7	+	+	CCONJ
ejpam-4859	341	8	c2mk∗	c2mk∗	PROPN
ejpam-4859	341	9	22	22	NUM
ejpam-4859	341	10	+	+	CCONJ
ejpam-4859	341	11	.	.	PUNCT
ejpam-4859	341	12	.	.	PUNCT
ejpam-4859	342	1	.+	.+	NOUN
ejpam-4859	342	2	c2mk∗	c2mk∗	VERB
ejpam-4859	342	3	2h	2h	NUM
ejpam-4859	342	4	+	+	PUNCT
ejpam-4859	342	5	.	.	PUNCT
ejpam-4859	342	6	.	.	PUNCT
ejpam-4859	343	1	.+	.+	NOUN
ejpam-4859	343	2	crmk∗	crmk∗	VERB
ejpam-4859	343	3	r1	r1	PROPN
ejpam-4859	343	4	+	+	CCONJ
ejpam-4859	343	5	crmk∗	crmk∗	ADJ
ejpam-4859	343	6	r2	r2	NOUN
ejpam-4859	343	7	+	+	X
ejpam-4859	343	8	.	.	PUNCT
ejpam-4859	343	9	.	.	PUNCT
ejpam-4859	344	1	.+	.+	NOUN
ejpam-4859	344	2	crmk∗	crmk∗	VERB
ejpam-4859	344	3	rh	rh	NOUN
ejpam-4859	344	4			NOUN
ejpam-4859	344	5	=	=	NOUN
ejpam-4859	344	6			NOUN
ejpam-4859	344	7	c11(k	c11(k	NOUN
ejpam-4859	344	8	∗	∗	VERB
ejpam-4859	344	9	11	11	NUM
ejpam-4859	345	1	+	+	NOUN
ejpam-4859	345	2	k∗	k∗	NOUN
ejpam-4859	345	3	12	12	NUM
ejpam-4859	345	4	+	+	NOUN
ejpam-4859	345	5	.	.	PUNCT
ejpam-4859	345	6	.	.	PUNCT
ejpam-4859	346	1	.+k∗	.+k∗	PROPN
ejpam-4859	346	2	1h	1h	NUM
ejpam-4859	346	3	)	)	PUNCT
ejpam-4859	347	1	+	+	NUM
ejpam-4859	347	2	c21(k	c21(k	NOUN
ejpam-4859	347	3	∗	∗	NOUN
ejpam-4859	347	4	21	21	NUM
ejpam-4859	348	1	+	+	NOUN
ejpam-4859	348	2	k∗	k∗	NOUN
ejpam-4859	348	3	22	22	NUM
ejpam-4859	348	4	+	+	CCONJ
ejpam-4859	348	5	.	.	PUNCT
ejpam-4859	348	6	.	.	PUNCT
ejpam-4859	349	1	.+k∗	.+k∗	NUM
ejpam-4859	349	2	2h	2h	NUM
ejpam-4859	349	3	)	)	PUNCT
ejpam-4859	350	1	+	+	CCONJ
ejpam-4859	350	2	.	.	PUNCT
ejpam-4859	350	3	.	.	PUNCT
ejpam-4859	351	1	.+	.+	NOUN
ejpam-4859	352	1	cr1(k	cr1(k	NOUN
ejpam-4859	352	2	∗	∗	VERB
ejpam-4859	352	3	r1	r1	NOUN
ejpam-4859	352	4	+	+	PROPN
ejpam-4859	352	5	k∗	k∗	NOUN
ejpam-4859	352	6	r2	r2	NOUN
ejpam-4859	352	7	+	+	X
ejpam-4859	352	8	.	.	PUNCT
ejpam-4859	352	9	.	.	PUNCT
ejpam-4859	353	1	.+k∗	.+k∗	PROPN
ejpam-4859	353	2	rh	rh	PROPN
ejpam-4859	353	3	)	)	PUNCT
ejpam-4859	353	4	c12(k	c12(k	NOUN
ejpam-4859	353	5	∗	∗	NOUN
ejpam-4859	353	6	11	11	NUM
ejpam-4859	354	1	+	+	NOUN
ejpam-4859	354	2	k∗	k∗	NOUN
ejpam-4859	354	3	12	12	NUM
ejpam-4859	354	4	+	+	NOUN
ejpam-4859	354	5	.	.	PUNCT
ejpam-4859	354	6	.	.	PUNCT
ejpam-4859	355	1	.+k∗	.+k∗	PROPN
ejpam-4859	355	2	1h	1h	NUM
ejpam-4859	355	3	)	)	PUNCT
ejpam-4859	356	1	+	+	CCONJ
ejpam-4859	356	2	c22(k	c22(k	NOUN
ejpam-4859	356	3	∗	∗	NOUN
ejpam-4859	356	4	21	21	NUM
ejpam-4859	357	1	+	+	NOUN
ejpam-4859	357	2	k∗	k∗	NOUN
ejpam-4859	357	3	22	22	NUM
ejpam-4859	357	4	+	+	CCONJ
ejpam-4859	357	5	.	.	PUNCT
ejpam-4859	357	6	.	.	PUNCT
ejpam-4859	358	1	.+k∗	.+k∗	NUM
ejpam-4859	358	2	2h	2h	NUM
ejpam-4859	358	3	)	)	PUNCT
ejpam-4859	359	1	+	+	CCONJ
ejpam-4859	359	2	.	.	PUNCT
ejpam-4859	359	3	.	.	PUNCT
ejpam-4859	360	1	.+	.+	NOUN
ejpam-4859	360	2	cr2(k	cr2(k	PROPN
ejpam-4859	360	3	∗	∗	VERB
ejpam-4859	360	4	r1	r1	PROPN
ejpam-4859	360	5	+	+	PROPN
ejpam-4859	360	6	k∗	k∗	NOUN
ejpam-4859	360	7	r2	r2	NOUN
ejpam-4859	360	8	+	+	X
ejpam-4859	360	9	.	.	PUNCT
ejpam-4859	360	10	.	.	PUNCT
ejpam-4859	361	1	.+k∗	.+k∗	PROPN
ejpam-4859	361	2	rh	rh	PROPN
ejpam-4859	361	3	)	)	PUNCT
ejpam-4859	361	4	...	...	PUNCT
ejpam-4859	362	1	c1m(k∗	c1m(k∗	VERB
ejpam-4859	362	2	11	11	NUM
ejpam-4859	363	1	+	+	NOUN
ejpam-4859	363	2	k∗	k∗	PROPN
ejpam-4859	363	3	12	12	NUM
ejpam-4859	363	4	+	+	NOUN
ejpam-4859	363	5	.	.	PUNCT
ejpam-4859	363	6	.	.	PUNCT
ejpam-4859	364	1	.+k∗	.+k∗	PROPN
ejpam-4859	364	2	1h	1h	NUM
ejpam-4859	364	3	)	)	PUNCT
ejpam-4859	365	1	+	+	CCONJ
ejpam-4859	365	2	c2m(k∗	c2m(k∗	NOUN
ejpam-4859	365	3	21	21	NUM
ejpam-4859	365	4	+	+	NOUN
ejpam-4859	365	5	k∗	k∗	PROPN
ejpam-4859	365	6	22	22	NUM
ejpam-4859	366	1	+	+	CCONJ
ejpam-4859	366	2	.	.	PUNCT
ejpam-4859	366	3	.	.	PUNCT
ejpam-4859	367	1	.+k∗	.+k∗	NUM
ejpam-4859	367	2	2h	2h	NUM
ejpam-4859	367	3	)	)	PUNCT
ejpam-4859	368	1	+	+	CCONJ
ejpam-4859	368	2	.	.	PUNCT
ejpam-4859	368	3	.	.	PUNCT
ejpam-4859	369	1	.+	.+	NOUN
ejpam-4859	369	2	crm(k∗	crm(k∗	PROPN
ejpam-4859	369	3	r1	r1	PROPN
ejpam-4859	369	4	+	+	PROPN
ejpam-4859	369	5	k∗	k∗	NOUN
ejpam-4859	369	6	r2	r2	NOUN
ejpam-4859	369	7	+	+	X
ejpam-4859	369	8	.	.	PUNCT
ejpam-4859	369	9	.	.	PUNCT
ejpam-4859	370	1	.+k∗	.+k∗	PROPN
ejpam-4859	370	2	rh	rh	PROPN
ejpam-4859	370	3	)	)	PUNCT
ejpam-4859	370	4			NOUN
ejpam-4859	370	5	=	=	SYM
ejpam-4859	370	6			NOUN
ejpam-4859	370	7	c11k1	c11k1	NOUN
ejpam-4859	370	8	+	+	CCONJ
ejpam-4859	370	9	c21k2	c21k2	NOUN
ejpam-4859	370	10	+	+	X
ejpam-4859	370	11	.	.	PUNCT
ejpam-4859	370	12	.	.	PUNCT
ejpam-4859	371	1	.+	.+	NOUN
ejpam-4859	371	2	cr1kr	cr1kr	ADJ
ejpam-4859	371	3	c12k1	c12k1	NOUN
ejpam-4859	371	4	+	+	CCONJ
ejpam-4859	371	5	c22k2	c22k2	NOUN
ejpam-4859	371	6	+	+	NOUN
ejpam-4859	371	7	.	.	PUNCT
ejpam-4859	371	8	.	.	PUNCT
ejpam-4859	372	1	.+	.+	NOUN
ejpam-4859	372	2	cr2kr	cr2kr	PROPN
ejpam-4859	372	3	...	...	PUNCT
ejpam-4859	372	4	c1mk1	c1mk1	X
ejpam-4859	372	5	+	+	NUM
ejpam-4859	372	6	c2mk2	c2mk2	NOUN
ejpam-4859	372	7	+	+	X
ejpam-4859	372	8	.	.	PUNCT
ejpam-4859	372	9	.	.	PUNCT
ejpam-4859	373	1	.+	.+	NOUN
ejpam-4859	373	2	crmkr	crmkr	VERB
ejpam-4859	373	3			PROPN
ejpam-4859	373	4	d.	d.	PROPN
ejpam-4859	373	5	magpantay	magpantay	PROPN
ejpam-4859	373	6	/	/	SYM
ejpam-4859	373	7	eur	eur	PROPN
ejpam-4859	373	8	.	.	PUNCT
ejpam-4859	374	1	j.	j.	PROPN
ejpam-4859	374	2	pure	pure	PROPN
ejpam-4859	374	3	appl	appl	PROPN
ejpam-4859	374	4	.	.	PROPN
ejpam-4859	374	5	math	math	PROPN
ejpam-4859	374	6	,	,	PUNCT
ejpam-4859	374	7	16	16	NUM
ejpam-4859	374	8	(	(	PUNCT
ejpam-4859	374	9	4	4	NUM
ejpam-4859	374	10	)	)	PUNCT
ejpam-4859	374	11	(	(	PUNCT
ejpam-4859	374	12	2023	2023	NUM
ejpam-4859	374	13	)	)	PUNCT
ejpam-4859	374	14	,	,	PUNCT
ejpam-4859	374	15	2557	2557	NUM
ejpam-4859	374	16	-	-	SYM
ejpam-4859	374	17	2580	2580	NUM
ejpam-4859	374	18	2569	2569	NUM
ejpam-4859	374	19	=	=	SYM
ejpam-4859	374	20			PROPN
ejpam-4859	374	21	c11	c11	NOUN
ejpam-4859	374	22	c21	c21	NOUN
ejpam-4859	374	23	.	.	PUNCT
ejpam-4859	374	24	.	.	PUNCT
ejpam-4859	374	25	.	.	PUNCT
ejpam-4859	375	1	cr1	cr1	PROPN
ejpam-4859	375	2	c12	c12	PROPN
ejpam-4859	375	3	c22	c22	PROPN
ejpam-4859	375	4	.	.	PUNCT
ejpam-4859	375	5	.	.	PUNCT
ejpam-4859	375	6	.	.	PUNCT
ejpam-4859	376	1	cr2	cr2	PROPN
ejpam-4859	376	2	...	...	PUNCT
ejpam-4859	377	1	c1	c1	PROPN
ejpam-4859	377	2	m	m	PROPN
ejpam-4859	377	3	c2	c2	PROPN
ejpam-4859	377	4	m	m	PROPN
ejpam-4859	377	5	.	.	PUNCT
ejpam-4859	377	6	.	.	PUNCT
ejpam-4859	377	7	.	.	PUNCT
ejpam-4859	378	1	crm	crm	PROPN
ejpam-4859	378	2			PROPN
ejpam-4859	378	3			PROPN
ejpam-4859	378	4	k1	k1	PROPN
ejpam-4859	378	5	k2	k2	PROPN
ejpam-4859	378	6	...	...	PUNCT
ejpam-4859	379	1	kr	kr	PROPN
ejpam-4859	379	2			PROPN
ejpam-4859	380	1	=	=	SYM
ejpam-4859	381	1	nk	nk	PROPN
ejpam-4859	382	1	thus	thus	ADV
ejpam-4859	382	2	,	,	PUNCT
ejpam-4859	382	3	f∗	f∗	NOUN
ejpam-4859	382	4	=	=	SYM
ejpam-4859	382	5	n∗k∗	n∗k∗	NOUN
ejpam-4859	383	1	=	=	NOUN
ejpam-4859	383	2	nk	nk	PROPN
ejpam-4859	383	3	=	=	SYM
ejpam-4859	383	4	f	f	PROPN
ejpam-4859	384	1	and	and	CCONJ
ejpam-4859	384	2	so	so	ADV
ejpam-4859	384	3	(	(	PUNCT
ejpam-4859	384	4	n	n	CCONJ
ejpam-4859	384	5	∗,k∗	∗,k∗	ADJ
ejpam-4859	384	6	)	)	PUNCT
ejpam-4859	384	7	is	be	AUX
ejpam-4859	384	8	dynamically	dynamically	ADV
ejpam-4859	384	9	equivalent	equivalent	ADJ
ejpam-4859	384	10	to	to	ADP
ejpam-4859	384	11	(	(	PUNCT
ejpam-4859	384	12	n	n	CCONJ
ejpam-4859	384	13	,	,	PUNCT
ejpam-4859	384	14	k	k	NOUN
ejpam-4859	384	15	)	)	PUNCT
ejpam-4859	384	16	under	under	ADP
ejpam-4859	384	17	star	star	NOUN
ejpam-4859	384	18	transformation	transformation	NOUN
ejpam-4859	384	19	.	.	PUNCT
ejpam-4859	385	1	3	3	X
ejpam-4859	385	2	.	.	X
ejpam-4859	385	3	the	the	DET
ejpam-4859	385	4	s	s	NOUN
ejpam-4859	385	5	-	-	PUNCT
ejpam-4859	385	6	invariant	invariant	ADJ
ejpam-4859	385	7	termwise	termwise	NOUN
ejpam-4859	385	8	addition	addition	NOUN
ejpam-4859	385	9	of	of	ADP
ejpam-4859	385	10	reactions	reaction	NOUN
ejpam-4859	385	11	via	via	ADP
ejpam-4859	385	12	reaction	reaction	NOUN
ejpam-4859	385	13	vector	vector	NOUN
ejpam-4859	385	14	multiples	multiple	NOUN
ejpam-4859	385	15	(	(	PUNCT
ejpam-4859	385	16	star	star	NOUN
ejpam-4859	385	17	-	-	PUNCT
ejpam-4859	385	18	rvm	rvm	NOUN
ejpam-4859	385	19	)	)	PUNCT
ejpam-4859	385	20	transformation	transformation	NOUN
ejpam-4859	385	21	in	in	ADP
ejpam-4859	385	22	this	this	DET
ejpam-4859	385	23	section	section	NOUN
ejpam-4859	385	24	,	,	PUNCT
ejpam-4859	385	25	we	we	PRON
ejpam-4859	385	26	introduce	introduce	VERB
ejpam-4859	385	27	the	the	DET
ejpam-4859	385	28	first	first	ADJ
ejpam-4859	385	29	method	method	NOUN
ejpam-4859	385	30	of	of	ADP
ejpam-4859	385	31	star	star	NOUN
ejpam-4859	385	32	transformation	transformation	NOUN
ejpam-4859	385	33	.	.	PUNCT
ejpam-4859	386	1	also	also	ADV
ejpam-4859	386	2	,	,	PUNCT
ejpam-4859	386	3	we	we	PRON
ejpam-4859	386	4	identify	identify	VERB
ejpam-4859	386	5	and	and	CCONJ
ejpam-4859	386	6	compare	compare	VERB
ejpam-4859	386	7	the	the	DET
ejpam-4859	386	8	network	network	NOUN
ejpam-4859	386	9	numbers	number	NOUN
ejpam-4859	386	10	and	and	CCONJ
ejpam-4859	386	11	discuss	discuss	VERB
ejpam-4859	386	12	the	the	DET
ejpam-4859	386	13	variant	variant	NOUN
ejpam-4859	386	14	and	and	CCONJ
ejpam-4859	386	15	invariant	invariant	ADJ
ejpam-4859	386	16	crn	crn	NOUN
ejpam-4859	386	17	properties	property	NOUN
ejpam-4859	386	18	.	.	PUNCT
ejpam-4859	387	1	3.1	3.1	NUM
ejpam-4859	387	2	.	.	PUNCT
ejpam-4859	387	3	definition	definition	NOUN
ejpam-4859	387	4	and	and	CCONJ
ejpam-4859	387	5	some	some	DET
ejpam-4859	387	6	illustrative	illustrative	ADJ
ejpam-4859	387	7	examples	example	NOUN
ejpam-4859	387	8	in	in	ADP
ejpam-4859	387	9	star	star	NOUN
ejpam-4859	387	10	transformations	transformation	NOUN
ejpam-4859	387	11	,	,	PUNCT
ejpam-4859	387	12	new	new	ADJ
ejpam-4859	387	13	reactions	reaction	NOUN
ejpam-4859	387	14	and	and	CCONJ
ejpam-4859	387	15	complexes	complex	NOUN
ejpam-4859	387	16	are	be	AUX
ejpam-4859	387	17	added	add	VERB
ejpam-4859	387	18	.	.	PUNCT
ejpam-4859	388	1	there	there	PRON
ejpam-4859	388	2	are	be	VERB
ejpam-4859	388	3	various	various	ADJ
ejpam-4859	388	4	ways	way	NOUN
ejpam-4859	388	5	of	of	ADP
ejpam-4859	388	6	constructing	construct	VERB
ejpam-4859	388	7	a	a	DET
ejpam-4859	388	8	crn	crn	NOUN
ejpam-4859	388	9	from	from	ADP
ejpam-4859	388	10	these	these	PRON
ejpam-4859	388	11	.	.	PUNCT
ejpam-4859	389	1	one	one	NUM
ejpam-4859	389	2	method	method	NOUN
ejpam-4859	389	3	is	be	AUX
ejpam-4859	389	4	by	by	ADP
ejpam-4859	389	5	using	use	VERB
ejpam-4859	389	6	reaction	reaction	NOUN
ejpam-4859	389	7	vector	vector	NOUN
ejpam-4859	389	8	multiples	multiple	NOUN
ejpam-4859	389	9	described	describe	VERB
ejpam-4859	389	10	as	as	ADP
ejpam-4859	389	11	follows	follow	VERB
ejpam-4859	389	12	:	:	PUNCT
ejpam-4859	389	13	definition	definition	NOUN
ejpam-4859	389	14	18	18	NUM
ejpam-4859	389	15	.	.	PUNCT
ejpam-4859	390	1	let	let	VERB
ejpam-4859	390	2	n	n	NOUN
ejpam-4859	390	3	=	=	SYM
ejpam-4859	390	4	(	(	PUNCT
ejpam-4859	390	5	s	s	NOUN
ejpam-4859	390	6	,	,	PUNCT
ejpam-4859	390	7	c	c	NOUN
ejpam-4859	390	8	,	,	PUNCT
ejpam-4859	390	9	r	r	NOUN
ejpam-4859	390	10	)	)	PUNCT
ejpam-4859	390	11	be	be	AUX
ejpam-4859	390	12	a	a	DET
ejpam-4859	390	13	crn	crn	NOUN
ejpam-4859	390	14	and	and	CCONJ
ejpam-4859	390	15	y	y	PROPN
ejpam-4859	390	16	→	→	SYM
ejpam-4859	390	17	y′	y′	NOUN
ejpam-4859	390	18	∈	∈	NOUN
ejpam-4859	390	19	r	r	NOUN
ejpam-4859	390	20	with	with	ADP
ejpam-4859	390	21	y′	y′	NUM
ejpam-4859	390	22	−	−	PROPN
ejpam-4859	390	23	y	y	PROPN
ejpam-4859	390	24	=	=	SYM
ejpam-4859	390	25	(	(	PUNCT
ejpam-4859	390	26	c1	c1	PROPN
ejpam-4859	390	27	,	,	PUNCT
ejpam-4859	390	28	.	.	PUNCT
ejpam-4859	390	29	.	.	PUNCT
ejpam-4859	391	1	.	.	PUNCT
ejpam-4859	392	1	,	,	PUNCT
ejpam-4859	392	2	ck	ck	X
ejpam-4859	392	3	)	)	PUNCT
ejpam-4859	392	4	satisfying	satisfy	VERB
ejpam-4859	392	5	the	the	DET
ejpam-4859	392	6	condition	condition	NOUN
ejpam-4859	392	7	that	that	SCONJ
ejpam-4859	392	8	either	either	CCONJ
ejpam-4859	392	9	ci	ci	PROPN
ejpam-4859	392	10	≥	≥	PROPN
ejpam-4859	392	11	0	0	NUM
ejpam-4859	392	12	or	or	CCONJ
ejpam-4859	392	13	ci	ci	NOUN
ejpam-4859	392	14	≤	≤	NOUN
ejpam-4859	392	15	0	0	NUM
ejpam-4859	392	16	for	for	ADP
ejpam-4859	392	17	all	all	DET
ejpam-4859	392	18	i	i	PRON
ejpam-4859	392	19	=	=	NOUN
ejpam-4859	392	20	1	1	NUM
ejpam-4859	392	21	,	,	PUNCT
ejpam-4859	392	22	.	.	PUNCT
ejpam-4859	392	23	.	.	PUNCT
ejpam-4859	393	1	.	.	PUNCT
ejpam-4859	394	1	,	,	PUNCT
ejpam-4859	394	2	k.	k.	PROPN
ejpam-4859	395	1	the	the	DET
ejpam-4859	395	2	s	s	NOUN
ejpam-4859	395	3	-	-	PUNCT
ejpam-4859	395	4	invariant	invariant	ADJ
ejpam-4859	395	5	termwise	termwise	NOUN
ejpam-4859	395	6	addition	addition	NOUN
ejpam-4859	395	7	of	of	ADP
ejpam-4859	395	8	reactions	reaction	NOUN
ejpam-4859	395	9	via	via	ADP
ejpam-4859	395	10	reaction	reaction	NOUN
ejpam-4859	395	11	vector	vector	NOUN
ejpam-4859	395	12	multiples	multiple	NOUN
ejpam-4859	395	13	(	(	PUNCT
ejpam-4859	395	14	star	star	NOUN
ejpam-4859	395	15	-	-	PUNCT
ejpam-4859	395	16	rvm	rvm	NOUN
ejpam-4859	395	17	)	)	PUNCT
ejpam-4859	395	18	transform	transform	NOUN
ejpam-4859	395	19	,	,	PUNCT
ejpam-4859	395	20	(	(	PUNCT
ejpam-4859	395	21	n	n	CCONJ
ejpam-4859	395	22	∗,k∗	∗,k∗	ADJ
ejpam-4859	395	23	)	)	PUNCT
ejpam-4859	395	24	,	,	PUNCT
ejpam-4859	395	25	for	for	ADP
ejpam-4859	395	26	each	each	DET
ejpam-4859	395	27	reaction	reaction	NOUN
ejpam-4859	395	28	y	y	PROPN
ejpam-4859	395	29	→	→	PUNCT
ejpam-4859	395	30	y′	y′	ADV
ejpam-4859	395	31	having	have	VERB
ejpam-4859	395	32	poly	poly	ADJ
ejpam-4859	395	33	-	-	PUNCT
ejpam-4859	395	34	pl	pl	NOUN
ejpam-4859	395	35	kinetics	kinetic	NOUN
ejpam-4859	395	36	k(x	k(x	PROPN
ejpam-4859	395	37	)	)	PUNCT
ejpam-4859	396	1	=	=	PUNCT
ejpam-4859	396	2	h∑	h∑	ADP
ejpam-4859	396	3	j=1	j=1	ADJ
ejpam-4859	396	4	ajpj	ajpj	NOUN
ejpam-4859	396	5	proceeds	proceed	VERB
ejpam-4859	396	6	as	as	SCONJ
ejpam-4859	396	7	follows	follow	VERB
ejpam-4859	396	8	:	:	PUNCT
ejpam-4859	396	9	(	(	PUNCT
ejpam-4859	396	10	i	i	NOUN
ejpam-4859	396	11	)	)	PUNCT
ejpam-4859	396	12	when	when	SCONJ
ejpam-4859	396	13	ci	ci	PROPN
ejpam-4859	396	14	≥	≥	NOUN
ejpam-4859	396	15	0	0	NUM
ejpam-4859	396	16	for	for	ADP
ejpam-4859	396	17	all	all	DET
ejpam-4859	396	18	i	i	PRON
ejpam-4859	396	19	=	=	NOUN
ejpam-4859	396	20	1	1	NUM
ejpam-4859	396	21	,	,	PUNCT
ejpam-4859	396	22	.	.	PUNCT
ejpam-4859	396	23	.	.	PUNCT
ejpam-4859	396	24	.	.	PUNCT
ejpam-4859	397	1	,	,	PUNCT
ejpam-4859	397	2	k	k	NOUN
ejpam-4859	397	3	,	,	PUNCT
ejpam-4859	397	4	define	define	VERB
ejpam-4859	397	5	the	the	DET
ejpam-4859	397	6	additional	additional	ADJ
ejpam-4859	397	7	complexes	complex	NOUN
ejpam-4859	397	8	and	and	CCONJ
ejpam-4859	397	9	reactions	reaction	NOUN
ejpam-4859	397	10	y	y	PROPN
ejpam-4859	397	11	→	→	SYM
ejpam-4859	397	12	y′	y′	NOUN
ejpam-4859	397	13	→	→	SYM
ejpam-4859	397	14	y′	y′	NOUN
ejpam-4859	397	15	+	+	CCONJ
ejpam-4859	397	16	(	(	PUNCT
ejpam-4859	397	17	y′	y′	NUM
ejpam-4859	397	18	−	−	PROPN
ejpam-4859	397	19	y	y	PROPN
ejpam-4859	397	20	)	)	PUNCT
ejpam-4859	397	21	→	→	SYM
ejpam-4859	397	22	y′	y′	NOUN
ejpam-4859	398	1	+	+	SYM
ejpam-4859	398	2	2(y′	2(y′	NUM
ejpam-4859	398	3	−	−	PROPN
ejpam-4859	398	4	y	y	NOUN
ejpam-4859	398	5	)	)	PUNCT
ejpam-4859	398	6	→	→	PUNCT
ejpam-4859	398	7	·	·	PUNCT
ejpam-4859	398	8	·	·	PUNCT
ejpam-4859	398	9	·	·	PUNCT
ejpam-4859	398	10	y′	y′	PUNCT
ejpam-4859	399	1	+	+	CCONJ
ejpam-4859	399	2	(	(	PUNCT
ejpam-4859	399	3	h−	h−	PROPN
ejpam-4859	399	4	1)(y′	1)(y′	NUM
ejpam-4859	399	5	−	−	PROPN
ejpam-4859	399	6	y	y	PROPN
ejpam-4859	399	7	)	)	PUNCT
ejpam-4859	399	8	with	with	ADP
ejpam-4859	399	9	corresponding	correspond	VERB
ejpam-4859	399	10	kinetics	kinetic	NOUN
ejpam-4859	399	11	p	p	PROPN
ejpam-4859	399	12	∗	∗	NOUN
ejpam-4859	399	13	1	1	NUM
ejpam-4859	399	14	,	,	PUNCT
ejpam-4859	399	15	p	p	NOUN
ejpam-4859	399	16	∗	∗	NOUN
ejpam-4859	399	17	2	2	NUM
ejpam-4859	399	18	,	,	PUNCT
ejpam-4859	399	19	.	.	PUNCT
ejpam-4859	399	20	.	.	PUNCT
ejpam-4859	399	21	.	.	PUNCT
ejpam-4859	399	22	,	,	PUNCT
ejpam-4859	399	23	p	p	NOUN
ejpam-4859	399	24	∗	∗	NOUN
ejpam-4859	399	25	h	h	NOUN
ejpam-4859	399	26	;	;	PUNCT
ejpam-4859	399	27	(	(	PUNCT
ejpam-4859	399	28	ii	ii	NOUN
ejpam-4859	399	29	)	)	PUNCT
ejpam-4859	399	30	when	when	SCONJ
ejpam-4859	399	31	ci	ci	PROPN
ejpam-4859	399	32	≤	≤	NOUN
ejpam-4859	399	33	0	0	NUM
ejpam-4859	399	34	for	for	ADP
ejpam-4859	399	35	all	all	DET
ejpam-4859	399	36	i	i	PRON
ejpam-4859	399	37	=	=	NOUN
ejpam-4859	399	38	1	1	NUM
ejpam-4859	399	39	,	,	PUNCT
ejpam-4859	399	40	.	.	PUNCT
ejpam-4859	399	41	.	.	PUNCT
ejpam-4859	399	42	.	.	PUNCT
ejpam-4859	400	1	,	,	PUNCT
ejpam-4859	400	2	k	k	NOUN
ejpam-4859	400	3	,	,	PUNCT
ejpam-4859	400	4	define	define	VERB
ejpam-4859	400	5	the	the	DET
ejpam-4859	400	6	additional	additional	ADJ
ejpam-4859	400	7	complexes	complex	NOUN
ejpam-4859	400	8	and	and	CCONJ
ejpam-4859	400	9	reactions	reaction	NOUN
ejpam-4859	400	10	y	y	PROPN
ejpam-4859	401	1	+	+	CCONJ
ejpam-4859	401	2	(	(	PUNCT
ejpam-4859	401	3	h−	h−	PROPN
ejpam-4859	401	4	1)(y	1)(y	NUM
ejpam-4859	401	5	−	−	NUM
ejpam-4859	401	6	y′	y′	NUM
ejpam-4859	401	7	)	)	PUNCT
ejpam-4859	401	8	→	→	SYM
ejpam-4859	401	9	·	·	PUNCT
ejpam-4859	401	10	·	·	PUNCT
ejpam-4859	401	11	·	·	PUNCT
ejpam-4859	401	12	→	→	PUNCT
ejpam-4859	401	13	y	y	PROPN
ejpam-4859	402	1	+	+	CCONJ
ejpam-4859	402	2	2(y	2(y	NUM
ejpam-4859	402	3	−	−	NUM
ejpam-4859	402	4	y′	y′	NUM
ejpam-4859	402	5	)	)	PUNCT
ejpam-4859	402	6	→	→	SYM
ejpam-4859	402	7	y	y	PROPN
ejpam-4859	403	1	+	+	CCONJ
ejpam-4859	403	2	(	(	PUNCT
ejpam-4859	403	3	y	y	PROPN
ejpam-4859	403	4	−	−	NOUN
ejpam-4859	403	5	y′	y′	NUM
ejpam-4859	403	6	)	)	PUNCT
ejpam-4859	403	7	→	→	SYM
ejpam-4859	403	8	y	y	PROPN
ejpam-4859	403	9	→	→	SYM
ejpam-4859	403	10	y′	y′	NOUN
ejpam-4859	403	11	with	with	ADP
ejpam-4859	403	12	corresponding	correspond	VERB
ejpam-4859	403	13	kinetics	kinetic	NOUN
ejpam-4859	403	14	p	p	NOUN
ejpam-4859	403	15	∗	∗	NOUN
ejpam-4859	403	16	h	h	NOUN
ejpam-4859	403	17	,	,	PUNCT
ejpam-4859	403	18	.	.	PUNCT
ejpam-4859	403	19	.	.	PUNCT
ejpam-4859	404	1	.	.	PUNCT
ejpam-4859	405	1	,	,	PUNCT
ejpam-4859	406	1	p	p	NOUN
ejpam-4859	406	2	∗	∗	NOUN
ejpam-4859	406	3	2	2	NUM
ejpam-4859	406	4	,	,	PUNCT
ejpam-4859	406	5	p	p	NOUN
ejpam-4859	406	6	∗	∗	NOUN
ejpam-4859	406	7	1	1	NUM
ejpam-4859	406	8	where	where	SCONJ
ejpam-4859	406	9	p	p	NOUN
ejpam-4859	406	10	∗	∗	X
ejpam-4859	406	11	j	j	NOUN
ejpam-4859	406	12	=	=	PUNCT
ejpam-4859	406	13	ajpj	ajpj	NOUN
ejpam-4859	406	14	,	,	PUNCT
ejpam-4859	406	15	1	1	NUM
ejpam-4859	406	16	≤	≤	NUM
ejpam-4859	406	17	j	j	PROPN
ejpam-4859	406	18	≤	≤	PROPN
ejpam-4859	406	19	h.	h.	PROPN
ejpam-4859	406	20	example	example	NOUN
ejpam-4859	406	21	11	11	NUM
ejpam-4859	406	22	.	.	PUNCT
ejpam-4859	407	1	for	for	ADP
ejpam-4859	407	2	(	(	PUNCT
ejpam-4859	407	3	n	n	X
ejpam-4859	407	4	,	,	PUNCT
ejpam-4859	407	5	k	k	NOUN
ejpam-4859	407	6	)	)	PUNCT
ejpam-4859	407	7	with	with	ADP
ejpam-4859	407	8	s	s	NOUN
ejpam-4859	407	9	=	=	SYM
ejpam-4859	407	10	{	{	PUNCT
ejpam-4859	407	11	x	x	PROPN
ejpam-4859	407	12	,	,	PUNCT
ejpam-4859	407	13	y	y	PROPN
ejpam-4859	407	14	}	}	PUNCT
ejpam-4859	407	15	and	and	CCONJ
ejpam-4859	407	16	r	r	NOUN
ejpam-4859	407	17	=	=	SYM
ejpam-4859	407	18	{	{	PUNCT
ejpam-4859	407	19	r	r	NOUN
ejpam-4859	407	20	:	:	PUNCT
ejpam-4859	407	21	x	x	X
ejpam-4859	407	22	→	→	SYM
ejpam-4859	407	23	2x	2x	NUM
ejpam-4859	407	24	,	,	PUNCT
ejpam-4859	407	25	r′	r′	NUM
ejpam-4859	407	26	:	:	PUNCT
ejpam-4859	407	27	2x	2x	NUM
ejpam-4859	407	28	→	→	SYM
ejpam-4859	407	29	5x	5x	NUM
ejpam-4859	407	30	+	+	ADJ
ejpam-4859	407	31	y	y	NOUN
ejpam-4859	407	32	}	}	PUNCT
ejpam-4859	407	33	,	,	PUNCT
ejpam-4859	407	34	let	let	VERB
ejpam-4859	407	35	the	the	DET
ejpam-4859	407	36	poly	poly	ADJ
ejpam-4859	407	37	-	-	PUNCT
ejpam-4859	407	38	pl	pl	NOUN
ejpam-4859	407	39	kinetics	kinetic	NOUN
ejpam-4859	407	40	be	be	AUX
ejpam-4859	407	41	given	give	VERB
ejpam-4859	407	42	by	by	ADP
ejpam-4859	407	43	:	:	PUNCT
ejpam-4859	407	44	kr(x	kr(x	PROPN
ejpam-4859	407	45	,	,	PUNCT
ejpam-4859	407	46	y	y	NOUN
ejpam-4859	407	47	)	)	PUNCT
ejpam-4859	408	1	=	=	VERB
ejpam-4859	408	2	k(2xy	k(2xy	NOUN
ejpam-4859	408	3	+	+	CCONJ
ejpam-4859	408	4	0.5y	0.5y	PROPN
ejpam-4859	408	5	2	2	NUM
ejpam-4859	408	6	)	)	PUNCT
ejpam-4859	408	7	kr′(x	kr′(x	PROPN
ejpam-4859	408	8	,	,	PUNCT
ejpam-4859	408	9	y	y	PROPN
ejpam-4859	408	10	)	)	PUNCT
ejpam-4859	408	11	=	=	SYM
ejpam-4859	409	1	k′(0.75x2y	k′(0.75x2y	X
ejpam-4859	410	1	+	+	NOUN
ejpam-4859	410	2	x3	x3	ADJ
ejpam-4859	410	3	)	)	PUNCT
ejpam-4859	410	4	d.	d.	PROPN
ejpam-4859	410	5	magpantay	magpantay	PROPN
ejpam-4859	410	6	/	/	SYM
ejpam-4859	410	7	eur	eur	PROPN
ejpam-4859	410	8	.	.	PUNCT
ejpam-4859	411	1	j.	j.	PROPN
ejpam-4859	411	2	pure	pure	PROPN
ejpam-4859	411	3	appl	appl	PROPN
ejpam-4859	411	4	.	.	PROPN
ejpam-4859	411	5	math	math	PROPN
ejpam-4859	411	6	,	,	PUNCT
ejpam-4859	411	7	16	16	NUM
ejpam-4859	411	8	(	(	PUNCT
ejpam-4859	411	9	4	4	NUM
ejpam-4859	411	10	)	)	PUNCT
ejpam-4859	411	11	(	(	PUNCT
ejpam-4859	411	12	2023	2023	NUM
ejpam-4859	411	13	)	)	PUNCT
ejpam-4859	411	14	,	,	PUNCT
ejpam-4859	411	15	2557	2557	NUM
ejpam-4859	411	16	-	-	SYM
ejpam-4859	411	17	2580	2580	NUM
ejpam-4859	411	18	2570	2570	NUM
ejpam-4859	411	19	where	where	SCONJ
ejpam-4859	411	20	k	k	PROPN
ejpam-4859	411	21	,	,	PUNCT
ejpam-4859	411	22	k′	k′	PROPN
ejpam-4859	411	23	are	be	AUX
ejpam-4859	411	24	rate	rate	NOUN
ejpam-4859	411	25	constants	constant	NOUN
ejpam-4859	411	26	.	.	PUNCT
ejpam-4859	412	1	the	the	DET
ejpam-4859	412	2	reaction	reaction	NOUN
ejpam-4859	412	3	vector	vector	NOUN
ejpam-4859	412	4	for	for	ADP
ejpam-4859	412	5	reaction	reaction	NOUN
ejpam-4859	412	6	r	r	NOUN
ejpam-4859	412	7	is	be	AUX
ejpam-4859	412	8	2x−x	2x−x	NOUN
ejpam-4859	412	9	=	=	SYM
ejpam-4859	412	10	x	x	X
ejpam-4859	412	11	and	and	CCONJ
ejpam-4859	412	12	for	for	ADP
ejpam-4859	412	13	reaction	reaction	NOUN
ejpam-4859	412	14	r′	r′	NOUN
ejpam-4859	412	15	is	be	AUX
ejpam-4859	412	16	5x+y	5x+y	NUM
ejpam-4859	412	17	−2x	−2x	NOUN
ejpam-4859	412	18	=	=	PUNCT
ejpam-4859	413	1	3x	3x	PROPN
ejpam-4859	414	1	+	+	CCONJ
ejpam-4859	414	2	y	y	PROPN
ejpam-4859	414	3	.	.	PUNCT
ejpam-4859	415	1	generating	generate	VERB
ejpam-4859	415	2	star	star	NOUN
ejpam-4859	415	3	-	-	PUNCT
ejpam-4859	415	4	rvm	rvm	PROPN
ejpam-4859	415	5	transform	transform	NOUN
ejpam-4859	415	6	,	,	PUNCT
ejpam-4859	415	7	we	we	PRON
ejpam-4859	415	8	have	have	VERB
ejpam-4859	415	9	(	(	PUNCT
ejpam-4859	415	10	n	n	CCONJ
ejpam-4859	415	11	∗,k∗	∗,k∗	ADJ
ejpam-4859	415	12	)	)	PUNCT
ejpam-4859	415	13	where	where	SCONJ
ejpam-4859	415	14	s	s	VERB
ejpam-4859	415	15	=	=	PRON
ejpam-4859	415	16	{	{	PUNCT
ejpam-4859	415	17	x	x	PROPN
ejpam-4859	415	18	,	,	PUNCT
ejpam-4859	415	19	y	y	PROPN
ejpam-4859	415	20	}	}	PUNCT
ejpam-4859	415	21	and	and	CCONJ
ejpam-4859	415	22	r∗	r∗	VERB
ejpam-4859	415	23	=	=	PUNCT
ejpam-4859	415	24	{	{	PUNCT
ejpam-4859	415	25	r	r	NOUN
ejpam-4859	415	26	:	:	PUNCT
ejpam-4859	415	27	x	x	X
ejpam-4859	415	28	→	→	SYM
ejpam-4859	415	29	2x	2x	NUM
ejpam-4859	415	30	,	,	PUNCT
ejpam-4859	415	31	r∗	r∗	VERB
ejpam-4859	415	32	:	:	PUNCT
ejpam-4859	415	33	2x	2x	NUM
ejpam-4859	415	34	→	→	SYM
ejpam-4859	415	35	3x	3x	NUM
ejpam-4859	415	36	,	,	PUNCT
ejpam-4859	415	37	r′	r′	PUNCT
ejpam-4859	415	38	:	:	PUNCT
ejpam-4859	416	1	2x	2x	NUM
ejpam-4859	416	2	→	→	SYM
ejpam-4859	416	3	5x	5x	NUM
ejpam-4859	416	4	+	+	NOUN
ejpam-4859	416	5	y	y	NOUN
ejpam-4859	416	6	,	,	PUNCT
ejpam-4859	416	7	r′∗	r′∗	NOUN
ejpam-4859	416	8	:	:	PUNCT
ejpam-4859	416	9	5x	5x	NOUN
ejpam-4859	416	10	+	+	CCONJ
ejpam-4859	416	11	y	y	PROPN
ejpam-4859	416	12	→	→	SYM
ejpam-4859	416	13	8x	8x	PROPN
ejpam-4859	416	14	+	+	CCONJ
ejpam-4859	416	15	2y	2y	NUM
ejpam-4859	416	16	}	}	PUNCT
ejpam-4859	416	17	.	.	PUNCT
ejpam-4859	417	1	the	the	DET
ejpam-4859	417	2	kinetic	kinetic	ADJ
ejpam-4859	417	3	functions	function	NOUN
ejpam-4859	417	4	are	be	AUX
ejpam-4859	417	5	as	as	ADP
ejpam-4859	417	6	folows	folow	NOUN
ejpam-4859	417	7	:	:	PUNCT
ejpam-4859	417	8	k∗	k∗	PROPN
ejpam-4859	417	9	r	r	PROPN
ejpam-4859	417	10	(	(	PUNCT
ejpam-4859	417	11	x	x	X
ejpam-4859	417	12	,	,	PUNCT
ejpam-4859	417	13	y	y	PROPN
ejpam-4859	417	14	)	)	PUNCT
ejpam-4859	418	1	=	=	PUNCT
ejpam-4859	419	1	2kxy	2kxy	NUM
ejpam-4859	419	2	=	=	SYM
ejpam-4859	419	3	k∗xy	k∗xy	PROPN
ejpam-4859	419	4	k∗	k∗	PROPN
ejpam-4859	419	5	r∗(x	r∗(x	PROPN
ejpam-4859	419	6	,	,	PUNCT
ejpam-4859	419	7	y	y	PROPN
ejpam-4859	419	8	)	)	PUNCT
ejpam-4859	419	9	=	=	PUNCT
ejpam-4859	420	1	0.5ky	0.5ky	NUM
ejpam-4859	420	2	2	2	NUM
ejpam-4859	420	3	=	=	SYM
ejpam-4859	420	4	k∗∗y	k∗∗y	VERB
ejpam-4859	420	5	2	2	NUM
ejpam-4859	420	6	k∗	k∗	PROPN
ejpam-4859	420	7	r′(x	r′(x	PROPN
ejpam-4859	420	8	,	,	PUNCT
ejpam-4859	420	9	y	y	PROPN
ejpam-4859	420	10	)	)	PUNCT
ejpam-4859	421	1	=	=	SYM
ejpam-4859	421	2	0.75k′x2y	0.75k′x2y	X
ejpam-4859	421	3	=	=	SYM
ejpam-4859	421	4	k′∗x2y	k′∗x2y	PROPN
ejpam-4859	421	5	k∗	k∗	NOUN
ejpam-4859	421	6	r′∗(x	r′∗(x	PROPN
ejpam-4859	421	7	,	,	PUNCT
ejpam-4859	421	8	y	y	PROPN
ejpam-4859	421	9	)	)	PUNCT
ejpam-4859	422	1	=	=	PUNCT
ejpam-4859	422	2	k′x3	k′x3	NOUN
ejpam-4859	423	1	=	=	SYM
ejpam-4859	424	1	k′∗∗x3	k′∗∗x3	PROPN
ejpam-4859	424	2	example	example	NOUN
ejpam-4859	424	3	12	12	NUM
ejpam-4859	424	4	.	.	PUNCT
ejpam-4859	425	1	for	for	ADP
ejpam-4859	425	2	(	(	PUNCT
ejpam-4859	425	3	n	n	X
ejpam-4859	425	4	,	,	PUNCT
ejpam-4859	425	5	k	k	PROPN
ejpam-4859	425	6	)	)	PUNCT
ejpam-4859	425	7	,	,	PUNCT
ejpam-4859	425	8	with	with	ADP
ejpam-4859	425	9	s	s	NOUN
ejpam-4859	425	10	=	=	PUNCT
ejpam-4859	425	11	{	{	PUNCT
ejpam-4859	425	12	x	x	PROPN
ejpam-4859	425	13	,	,	PUNCT
ejpam-4859	425	14	y	y	PROPN
ejpam-4859	425	15	}	}	PUNCT
ejpam-4859	425	16	and	and	CCONJ
ejpam-4859	425	17	r	r	NOUN
ejpam-4859	425	18	=	=	SYM
ejpam-4859	425	19	{	{	PUNCT
ejpam-4859	425	20	r1	r1	NOUN
ejpam-4859	425	21	:	:	PUNCT
ejpam-4859	425	22	2x	2x	NUM
ejpam-4859	425	23	+	+	CCONJ
ejpam-4859	425	24	2y	2y	NUM
ejpam-4859	425	25	→	→	SYM
ejpam-4859	425	26	x	x	SYM
ejpam-4859	425	27	+	+	NUM
ejpam-4859	425	28	y	y	PROPN
ejpam-4859	425	29	,	,	PUNCT
ejpam-4859	425	30	r2	r2	PROPN
ejpam-4859	425	31	:	:	PUNCT
ejpam-4859	425	32	x+y	x+y	NUM
ejpam-4859	425	33	→	→	SYM
ejpam-4859	425	34	2x+y	2x+y	NUM
ejpam-4859	425	35	,	,	PUNCT
ejpam-4859	425	36	r3	r3	PROPN
ejpam-4859	425	37	:	:	PUNCT
ejpam-4859	425	38	2x+y	2x+y	NUM
ejpam-4859	425	39	→	→	SYM
ejpam-4859	425	40	2x+2y	2x+2y	NUM
ejpam-4859	425	41	}	}	PUNCT
ejpam-4859	425	42	.	.	PUNCT
ejpam-4859	426	1	let	let	VERB
ejpam-4859	426	2	the	the	DET
ejpam-4859	426	3	poly	poly	ADJ
ejpam-4859	426	4	-	-	PUNCT
ejpam-4859	426	5	pl	pl	NOUN
ejpam-4859	426	6	kinetics	kinetic	NOUN
ejpam-4859	426	7	be	be	AUX
ejpam-4859	426	8	given	give	VERB
ejpam-4859	426	9	by	by	ADP
ejpam-4859	426	10	(	(	PUNCT
ejpam-4859	426	11	k1	k1	PROPN
ejpam-4859	426	12	,	,	PUNCT
ejpam-4859	426	13	k2	k2	NOUN
ejpam-4859	426	14	,	,	PUNCT
ejpam-4859	426	15	k3	k3	NOUN
ejpam-4859	426	16	are	be	AUX
ejpam-4859	426	17	as	as	ADV
ejpam-4859	426	18	usual	usual	ADJ
ejpam-4859	426	19	the	the	DET
ejpam-4859	426	20	rate	rate	NOUN
ejpam-4859	426	21	constants	constant	NOUN
ejpam-4859	426	22	):	):	PUNCT
ejpam-4859	426	23	kr1(x	kr1(x	PROPN
ejpam-4859	426	24	,	,	PUNCT
ejpam-4859	426	25	y	y	PROPN
ejpam-4859	426	26	)	)	PUNCT
ejpam-4859	427	1	=	=	SYM
ejpam-4859	427	2	k1(0.2xy	k1(0.2xy	NOUN
ejpam-4859	427	3	+	+	CCONJ
ejpam-4859	427	4	5y	5y	NUM
ejpam-4859	427	5	2	2	NUM
ejpam-4859	427	6	)	)	PUNCT
ejpam-4859	427	7	kr2(x	kr2(x	PROPN
ejpam-4859	427	8	,	,	PUNCT
ejpam-4859	427	9	y	y	PROPN
ejpam-4859	427	10	)	)	PUNCT
ejpam-4859	428	1	=	=	PUNCT
ejpam-4859	428	2	k2(0.3x	k2(0.3x	PROPN
ejpam-4859	428	3	2	2	NUM
ejpam-4859	428	4	+	+	CCONJ
ejpam-4859	428	5	2x3y	2x3y	ADJ
ejpam-4859	428	6	)	)	PUNCT
ejpam-4859	428	7	kr3(x	kr3(x	PROPN
ejpam-4859	428	8	,	,	PUNCT
ejpam-4859	428	9	y	y	PROPN
ejpam-4859	428	10	)	)	PUNCT
ejpam-4859	429	1	=	=	PUNCT
ejpam-4859	430	1	k3(2.5x	k3(2.5x	NOUN
ejpam-4859	430	2	+	+	NOUN
ejpam-4859	430	3	3y	3y	NUM
ejpam-4859	430	4	3	3	X
ejpam-4859	430	5	)	)	PUNCT
ejpam-4859	430	6	generating	generate	VERB
ejpam-4859	430	7	star	star	NOUN
ejpam-4859	430	8	-	-	PUNCT
ejpam-4859	430	9	rvm	rvm	PROPN
ejpam-4859	430	10	transform	transform	NOUN
ejpam-4859	430	11	,	,	PUNCT
ejpam-4859	430	12	we	we	PRON
ejpam-4859	430	13	have	have	VERB
ejpam-4859	430	14	(	(	PUNCT
ejpam-4859	430	15	n	n	CCONJ
ejpam-4859	430	16	∗,k∗	∗,k∗	ADJ
ejpam-4859	430	17	)	)	PUNCT
ejpam-4859	430	18	where	where	SCONJ
ejpam-4859	430	19	s	s	VERB
ejpam-4859	430	20	=	=	PRON
ejpam-4859	430	21	{	{	PUNCT
ejpam-4859	430	22	x	x	PROPN
ejpam-4859	430	23	,	,	PUNCT
ejpam-4859	430	24	y	y	PROPN
ejpam-4859	430	25	}	}	PUNCT
ejpam-4859	430	26	and	and	CCONJ
ejpam-4859	430	27	r∗	r∗	PROPN
ejpam-4859	430	28	=	=	SYM
ejpam-4859	430	29	{	{	PUNCT
ejpam-4859	430	30	r1	r1	NOUN
ejpam-4859	430	31	:	:	PUNCT
ejpam-4859	430	32	2x	2x	NUM
ejpam-4859	430	33	+	+	CCONJ
ejpam-4859	430	34	2y	2y	NUM
ejpam-4859	430	35	→	→	SYM
ejpam-4859	430	36	x	x	SYM
ejpam-4859	431	1	+	+	NUM
ejpam-4859	431	2	y	y	NOUN
ejpam-4859	431	3	,	,	PUNCT
ejpam-4859	431	4	r∗1	r∗1	VERB
ejpam-4859	431	5	:	:	PUNCT
ejpam-4859	432	1	3x	3x	NUM
ejpam-4859	432	2	+	+	CCONJ
ejpam-4859	432	3	3y	3y	NUM
ejpam-4859	432	4	→	→	SYM
ejpam-4859	432	5	2x	2x	NUM
ejpam-4859	432	6	+	+	CCONJ
ejpam-4859	432	7	2y	2y	NUM
ejpam-4859	432	8	,	,	PUNCT
ejpam-4859	432	9	r2	r2	PROPN
ejpam-4859	432	10	:	:	PUNCT
ejpam-4859	433	1	x	x	X
ejpam-4859	433	2	+	+	PUNCT
ejpam-4859	433	3	y	y	PROPN
ejpam-4859	433	4	→	→	SYM
ejpam-4859	433	5	2x	2x	NUM
ejpam-4859	434	1	+	+	CCONJ
ejpam-4859	434	2	y	y	NOUN
ejpam-4859	434	3	,	,	PUNCT
ejpam-4859	434	4	r∗2	r∗2	ADJ
ejpam-4859	434	5	:	:	PUNCT
ejpam-4859	435	1	2x	2x	NUM
ejpam-4859	435	2	+	+	CCONJ
ejpam-4859	435	3	y	y	PROPN
ejpam-4859	435	4	→	→	SYM
ejpam-4859	435	5	3x+	3x+	NUM
ejpam-4859	435	6	y	y	PROPN
ejpam-4859	435	7	,	,	PUNCT
ejpam-4859	435	8	r3	r3	PROPN
ejpam-4859	435	9	:	:	PUNCT
ejpam-4859	435	10	2x	2x	NUM
ejpam-4859	435	11	+	+	CCONJ
ejpam-4859	435	12	y	y	PROPN
ejpam-4859	435	13	→	→	SYM
ejpam-4859	435	14	2x	2x	NUM
ejpam-4859	435	15	+	+	CCONJ
ejpam-4859	435	16	2y	2y	NUM
ejpam-4859	435	17	,	,	PUNCT
ejpam-4859	435	18	r∗3	r∗3	NOUN
ejpam-4859	435	19	:	:	PUNCT
ejpam-4859	435	20	2x	2x	NUM
ejpam-4859	435	21	+	+	CCONJ
ejpam-4859	435	22	2y	2y	NUM
ejpam-4859	435	23	→	→	SYM
ejpam-4859	435	24	2x	2x	NUM
ejpam-4859	435	25	+	+	X
ejpam-4859	435	26	3y	3y	NUM
ejpam-4859	435	27	}	}	PUNCT
ejpam-4859	435	28	.	.	PUNCT
ejpam-4859	436	1	the	the	DET
ejpam-4859	436	2	kinetic	kinetic	ADJ
ejpam-4859	436	3	functions	function	NOUN
ejpam-4859	436	4	are	be	AUX
ejpam-4859	436	5	as	as	ADP
ejpam-4859	436	6	folows	folow	NOUN
ejpam-4859	436	7	:	:	PUNCT
ejpam-4859	436	8	k∗	k∗	PROPN
ejpam-4859	436	9	r1(x	r1(x	PRON
ejpam-4859	436	10	,	,	PUNCT
ejpam-4859	436	11	y	y	PROPN
ejpam-4859	436	12	)	)	PUNCT
ejpam-4859	436	13	=	=	PUNCT
ejpam-4859	437	1	0.2k1xy	0.2k1xy	NOUN
ejpam-4859	437	2	=	=	PUNCT
ejpam-4859	438	1	k∗1xy	k∗1xy	NOUN
ejpam-4859	438	2	k∗	k∗	PROPN
ejpam-4859	438	3	r∗1	r∗1	PROPN
ejpam-4859	438	4	(	(	PUNCT
ejpam-4859	438	5	x	x	X
ejpam-4859	438	6	,	,	PUNCT
ejpam-4859	438	7	y	y	PROPN
ejpam-4859	438	8	)	)	PUNCT
ejpam-4859	438	9	=	=	PUNCT
ejpam-4859	438	10	5k1y	5k1y	NOUN
ejpam-4859	438	11	2	2	NUM
ejpam-4859	438	12	=	=	SYM
ejpam-4859	438	13	k∗∗1	k∗∗1	ADJ
ejpam-4859	438	14	y	y	PROPN
ejpam-4859	438	15	2	2	NUM
ejpam-4859	438	16	k∗	k∗	NOUN
ejpam-4859	438	17	r2(x	r2(x	PROPN
ejpam-4859	438	18	,	,	PUNCT
ejpam-4859	438	19	y	y	PROPN
ejpam-4859	438	20	)	)	PUNCT
ejpam-4859	438	21	=	=	PUNCT
ejpam-4859	439	1	0.3k2x	0.3k2x	NUM
ejpam-4859	439	2	2	2	NUM
ejpam-4859	439	3	=	=	SYM
ejpam-4859	439	4	k∗2x	k∗2x	NOUN
ejpam-4859	439	5	2	2	NUM
ejpam-4859	439	6	k∗	k∗	NOUN
ejpam-4859	439	7	r∗2	r∗2	NOUN
ejpam-4859	439	8	(	(	PUNCT
ejpam-4859	439	9	x	x	X
ejpam-4859	439	10	,	,	PUNCT
ejpam-4859	439	11	y	y	PROPN
ejpam-4859	439	12	)	)	PUNCT
ejpam-4859	439	13	=	=	PUNCT
ejpam-4859	440	1	2k2x	2k2x	NUM
ejpam-4859	440	2	3y	3y	NOUN
ejpam-4859	440	3	=	=	SYM
ejpam-4859	440	4	k∗∗2	k∗∗2	PROPN
ejpam-4859	440	5	x3y	x3y	PROPN
ejpam-4859	440	6	k∗	k∗	PROPN
ejpam-4859	440	7	r3(x	r3(x	PROPN
ejpam-4859	440	8	,	,	PUNCT
ejpam-4859	440	9	y	y	PROPN
ejpam-4859	440	10	)	)	PUNCT
ejpam-4859	440	11	=	=	PUNCT
ejpam-4859	441	1	2.5k3x	2.5k3x	NUM
ejpam-4859	441	2	=	=	SYM
ejpam-4859	441	3	k∗3x	k∗3x	PROPN
ejpam-4859	441	4	k∗	k∗	PROPN
ejpam-4859	441	5	r∗3	r∗3	NOUN
ejpam-4859	441	6	(	(	PUNCT
ejpam-4859	441	7	x	x	X
ejpam-4859	441	8	,	,	PUNCT
ejpam-4859	441	9	y	y	PROPN
ejpam-4859	441	10	)	)	PUNCT
ejpam-4859	441	11	=	=	PUNCT
ejpam-4859	442	1	3k3y	3k3y	NOUN
ejpam-4859	442	2	3	3	X
ejpam-4859	442	3	=	=	SYM
ejpam-4859	442	4	k∗∗3	k∗∗3	NOUN
ejpam-4859	442	5	y	y	PROPN
ejpam-4859	442	6	3	3	NUM
ejpam-4859	442	7	3.2	3.2	NUM
ejpam-4859	442	8	.	.	PUNCT
ejpam-4859	443	1	a	a	DET
ejpam-4859	443	2	comparison	comparison	NOUN
ejpam-4859	443	3	of	of	ADP
ejpam-4859	443	4	network	network	NOUN
ejpam-4859	443	5	numbers	number	NOUN
ejpam-4859	443	6	the	the	DET
ejpam-4859	443	7	network	network	NOUN
ejpam-4859	443	8	numbers	number	NOUN
ejpam-4859	443	9	of	of	ADP
ejpam-4859	443	10	a	a	DET
ejpam-4859	443	11	crn	crn	NOUN
ejpam-4859	443	12	refers	refer	VERB
ejpam-4859	443	13	to	to	ADP
ejpam-4859	443	14	the	the	DET
ejpam-4859	443	15	number	number	NOUN
ejpam-4859	443	16	of	of	ADP
ejpam-4859	443	17	species	specie	NOUN
ejpam-4859	443	18	,	,	PUNCT
ejpam-4859	443	19	complexes	complex	NOUN
ejpam-4859	443	20	,	,	PUNCT
ejpam-4859	443	21	reactant	reactant	NOUN
ejpam-4859	443	22	complexes	complex	NOUN
ejpam-4859	443	23	,	,	PUNCT
ejpam-4859	443	24	reactions	reaction	NOUN
ejpam-4859	443	25	,	,	PUNCT
ejpam-4859	443	26	linkage	linkage	NOUN
ejpam-4859	443	27	classes	class	NOUN
ejpam-4859	443	28	,	,	PUNCT
ejpam-4859	443	29	strong	strong	ADJ
ejpam-4859	443	30	linkage	linkage	NOUN
ejpam-4859	443	31	classes	class	NOUN
ejpam-4859	443	32	and	and	CCONJ
ejpam-4859	443	33	terminal	terminal	ADJ
ejpam-4859	443	34	strong	strong	ADJ
ejpam-4859	443	35	lingkage	lingkage	NOUN
ejpam-4859	443	36	classes	class	NOUN
ejpam-4859	443	37	.	.	PUNCT
ejpam-4859	444	1	it	it	PRON
ejpam-4859	444	2	also	also	ADV
ejpam-4859	444	3	includes	include	VERB
ejpam-4859	444	4	the	the	DET
ejpam-4859	444	5	rank	rank	NOUN
ejpam-4859	444	6	,	,	PUNCT
ejpam-4859	444	7	reactant	reactant	NOUN
ejpam-4859	444	8	rank	rank	NOUN
ejpam-4859	444	9	,	,	PUNCT
ejpam-4859	444	10	rank	rank	NOUN
ejpam-4859	444	11	difference	difference	NOUN
ejpam-4859	444	12	,	,	PUNCT
ejpam-4859	444	13	deficiency	deficiency	NOUN
ejpam-4859	444	14	and	and	CCONJ
ejpam-4859	444	15	reactant	reactant	NOUN
ejpam-4859	444	16	deficiency	deficiency	NOUN
ejpam-4859	444	17	of	of	ADP
ejpam-4859	444	18	the	the	DET
ejpam-4859	444	19	network	network	NOUN
ejpam-4859	444	20	.	.	PUNCT
ejpam-4859	445	1	it	it	PRON
ejpam-4859	445	2	provides	provide	VERB
ejpam-4859	445	3	different	different	ADJ
ejpam-4859	445	4	descriptions	description	NOUN
ejpam-4859	445	5	of	of	ADP
ejpam-4859	445	6	a	a	DET
ejpam-4859	445	7	network	network	NOUN
ejpam-4859	445	8	and	and	CCONJ
ejpam-4859	445	9	basis	basis	NOUN
ejpam-4859	445	10	of	of	ADP
ejpam-4859	445	11	comparison	comparison	NOUN
ejpam-4859	445	12	to	to	ADP
ejpam-4859	445	13	the	the	DET
ejpam-4859	445	14	other	other	ADJ
ejpam-4859	445	15	networks	network	NOUN
ejpam-4859	445	16	.	.	PUNCT
ejpam-4859	446	1	for	for	ADP
ejpam-4859	446	2	the	the	DET
ejpam-4859	446	3	star	star	NOUN
ejpam-4859	446	4	-	-	PUNCT
ejpam-4859	446	5	rvm	rvm	PROPN
ejpam-4859	446	6	method	method	NOUN
ejpam-4859	446	7	,	,	PUNCT
ejpam-4859	446	8	we	we	PRON
ejpam-4859	446	9	compare	compare	VERB
ejpam-4859	446	10	the	the	DET
ejpam-4859	446	11	network	network	NOUN
ejpam-4859	446	12	numbers	number	NOUN
ejpam-4859	446	13	of	of	ADP
ejpam-4859	446	14	the	the	DET
ejpam-4859	446	15	original	original	ADJ
ejpam-4859	446	16	and	and	CCONJ
ejpam-4859	446	17	the	the	DET
ejpam-4859	446	18	transformed	transform	VERB
ejpam-4859	446	19	network	network	NOUN
ejpam-4859	446	20	.	.	PUNCT
ejpam-4859	447	1	these	these	PRON
ejpam-4859	447	2	are	be	AUX
ejpam-4859	447	3	reflected	reflect	VERB
ejpam-4859	447	4	on	on	ADP
ejpam-4859	447	5	table	table	NOUN
ejpam-4859	447	6	3.1	3.1	NUM
ejpam-4859	447	7	.	.	PUNCT
ejpam-4859	448	1	since	since	SCONJ
ejpam-4859	448	2	we	we	PRON
ejpam-4859	448	3	have	have	VERB
ejpam-4859	448	4	the	the	DET
ejpam-4859	448	5	same	same	ADJ
ejpam-4859	448	6	set	set	NOUN
ejpam-4859	448	7	of	of	ADP
ejpam-4859	448	8	species	specie	NOUN
ejpam-4859	448	9	,	,	PUNCT
ejpam-4859	448	10	m∗	m∗	NOUN
ejpam-4859	448	11	=	=	SYM
ejpam-4859	448	12	m.	m.	NOUN
ejpam-4859	448	13	note	note	VERB
ejpam-4859	448	14	that	that	SCONJ
ejpam-4859	448	15	the	the	DET
ejpam-4859	448	16	number	number	NOUN
ejpam-4859	448	17	of	of	ADP
ejpam-4859	448	18	possible	possible	ADJ
ejpam-4859	448	19	additional	additional	ADJ
ejpam-4859	448	20	complexes	complex	NOUN
ejpam-4859	448	21	is	be	AUX
ejpam-4859	448	22	r(h−	r(h−	NOUN
ejpam-4859	448	23	1	1	NUM
ejpam-4859	448	24	)	)	PUNCT
ejpam-4859	448	25	.	.	PUNCT
ejpam-4859	449	1	this	this	PRON
ejpam-4859	449	2	means	mean	VERB
ejpam-4859	449	3	that	that	SCONJ
ejpam-4859	449	4	the	the	DET
ejpam-4859	449	5	maximum	maximum	ADJ
ejpam-4859	449	6	number	number	NOUN
ejpam-4859	449	7	of	of	ADP
ejpam-4859	449	8	complexes	complex	NOUN
ejpam-4859	449	9	in	in	ADP
ejpam-4859	449	10	n	n	ADP
ejpam-4859	449	11	∗	∗	NOUN
ejpam-4859	449	12	is	be	AUX
ejpam-4859	449	13	r(h	r(h	PROPN
ejpam-4859	449	14	−	−	NOUN
ejpam-4859	449	15	1	1	NUM
ejpam-4859	449	16	)	)	PUNCT
ejpam-4859	450	1	+	+	CCONJ
ejpam-4859	450	2	n	n	CCONJ
ejpam-4859	450	3	since	since	SCONJ
ejpam-4859	450	4	it	it	PRON
ejpam-4859	450	5	will	will	AUX
ejpam-4859	450	6	depends	depend	VERB
ejpam-4859	450	7	on	on	ADP
ejpam-4859	450	8	whether	whether	SCONJ
ejpam-4859	450	9	all	all	DET
ejpam-4859	450	10	additional	additional	ADJ
ejpam-4859	450	11	complexes	complex	NOUN
ejpam-4859	450	12	are	be	AUX
ejpam-4859	450	13	unique	unique	ADJ
ejpam-4859	450	14	compared	compare	VERB
ejpam-4859	450	15	to	to	ADP
ejpam-4859	450	16	the	the	DET
ejpam-4859	450	17	original	original	ADJ
ejpam-4859	450	18	complexes	complex	NOUN
ejpam-4859	450	19	and	and	CCONJ
ejpam-4859	450	20	within	within	ADP
ejpam-4859	450	21	the	the	DET
ejpam-4859	450	22	set	set	NOUN
ejpam-4859	450	23	.	.	PUNCT
ejpam-4859	451	1	the	the	DET
ejpam-4859	451	2	same	same	ADJ
ejpam-4859	451	3	may	may	AUX
ejpam-4859	451	4	be	be	AUX
ejpam-4859	451	5	said	say	VERB
ejpam-4859	451	6	about	about	ADP
ejpam-4859	451	7	the	the	DET
ejpam-4859	451	8	reactant	reactant	NOUN
ejpam-4859	451	9	complexes	complex	NOUN
ejpam-4859	451	10	of	of	ADP
ejpam-4859	451	11	the	the	DET
ejpam-4859	451	12	two	two	NUM
ejpam-4859	451	13	networks	network	NOUN
ejpam-4859	451	14	.	.	PUNCT
ejpam-4859	452	1	as	as	ADP
ejpam-4859	452	2	part	part	NOUN
ejpam-4859	452	3	of	of	ADP
ejpam-4859	452	4	the	the	DET
ejpam-4859	452	5	properties	property	NOUN
ejpam-4859	452	6	of	of	ADP
ejpam-4859	452	7	star	star	NOUN
ejpam-4859	452	8	transformation	transformation	NOUN
ejpam-4859	452	9	shown	show	VERB
ejpam-4859	452	10	in	in	ADP
ejpam-4859	452	11	table	table	NOUN
ejpam-4859	452	12	3.1	3.1	NUM
ejpam-4859	452	13	,	,	PUNCT
ejpam-4859	452	14	we	we	PRON
ejpam-4859	452	15	have	have	VERB
ejpam-4859	452	16	|r∗|	|r∗|	NUM
ejpam-4859	452	17	=	=	SYM
ejpam-4859	452	18	r∗	r∗	NOUN
ejpam-4859	452	19	=	=	SYM
ejpam-4859	452	20	hr	hr	NOUN
ejpam-4859	452	21	and	and	CCONJ
ejpam-4859	452	22	s∗	s∗	PROPN
ejpam-4859	452	23	=	=	PUNCT
ejpam-4859	452	24	s.	s.	PROPN
ejpam-4859	452	25	observe	observe	VERB
ejpam-4859	452	26	that	that	SCONJ
ejpam-4859	452	27	on	on	ADP
ejpam-4859	452	28	the	the	DET
ejpam-4859	452	29	construction	construction	NOUN
ejpam-4859	452	30	using	use	VERB
ejpam-4859	452	31	star	star	NOUN
ejpam-4859	452	32	-	-	PUNCT
ejpam-4859	452	33	rvm	rvm	PROPN
ejpam-4859	452	34	method	method	NOUN
ejpam-4859	452	35	,	,	PUNCT
ejpam-4859	452	36	no	no	DET
ejpam-4859	452	37	additional	additional	ADJ
ejpam-4859	452	38	linkage	linkage	NOUN
ejpam-4859	452	39	class	class	NOUN
ejpam-4859	452	40	is	be	AUX
ejpam-4859	452	41	produced	produce	VERB
ejpam-4859	452	42	.	.	PUNCT
ejpam-4859	453	1	however	however	ADV
ejpam-4859	453	2	,	,	PUNCT
ejpam-4859	453	3	it	it	PRON
ejpam-4859	453	4	is	be	AUX
ejpam-4859	453	5	possible	possible	ADJ
ejpam-4859	453	6	that	that	SCONJ
ejpam-4859	453	7	original	original	ADJ
ejpam-4859	453	8	number	number	NOUN
ejpam-4859	453	9	of	of	ADP
ejpam-4859	453	10	linkage	linkage	NOUN
ejpam-4859	453	11	d.	d.	PROPN
ejpam-4859	453	12	magpantay	magpantay	PROPN
ejpam-4859	453	13	/	/	SYM
ejpam-4859	453	14	eur	eur	PROPN
ejpam-4859	453	15	.	.	PUNCT
ejpam-4859	454	1	j.	j.	PROPN
ejpam-4859	454	2	pure	pure	PROPN
ejpam-4859	454	3	appl	appl	PROPN
ejpam-4859	454	4	.	.	PROPN
ejpam-4859	454	5	math	math	PROPN
ejpam-4859	454	6	,	,	PUNCT
ejpam-4859	454	7	16	16	NUM
ejpam-4859	454	8	(	(	PUNCT
ejpam-4859	454	9	4	4	NUM
ejpam-4859	454	10	)	)	PUNCT
ejpam-4859	454	11	(	(	PUNCT
ejpam-4859	454	12	2023	2023	NUM
ejpam-4859	454	13	)	)	PUNCT
ejpam-4859	454	14	,	,	PUNCT
ejpam-4859	454	15	2557	2557	NUM
ejpam-4859	454	16	-	-	SYM
ejpam-4859	454	17	2580	2580	NUM
ejpam-4859	454	18	2571	2571	NUM
ejpam-4859	454	19	table	table	NOUN
ejpam-4859	454	20	1	1	NUM
ejpam-4859	454	21	:	:	PUNCT
ejpam-4859	454	22	network	network	NOUN
ejpam-4859	454	23	numbers	number	NOUN
ejpam-4859	454	24	of	of	ADP
ejpam-4859	454	25	star	star	NOUN
ejpam-4859	454	26	-	-	PUNCT
ejpam-4859	454	27	rvm	rvm	PROPN
ejpam-4859	454	28	transform	transform	NOUN
ejpam-4859	454	29	network	network	NOUN
ejpam-4859	454	30	number	number	NOUN
ejpam-4859	454	31	value	value	NOUN
ejpam-4859	454	32	/	/	SYM
ejpam-4859	454	33	bounds	bound	NOUN
ejpam-4859	454	34	number	number	NOUN
ejpam-4859	454	35	of	of	ADP
ejpam-4859	454	36	species	specie	NOUN
ejpam-4859	454	37	m∗	m∗	NOUN
ejpam-4859	454	38	=	=	SYM
ejpam-4859	454	39	m	m	PRON
ejpam-4859	454	40	number	number	NOUN
ejpam-4859	454	41	of	of	ADP
ejpam-4859	454	42	complexes	complex	NOUN
ejpam-4859	454	43	n	n	PRON
ejpam-4859	454	44	≤	≤	NUM
ejpam-4859	454	45	n∗	n∗	PROPN
ejpam-4859	454	46	≤	≤	NUM
ejpam-4859	454	47	r(h−	r(h−	PROPN
ejpam-4859	454	48	1	1	NUM
ejpam-4859	454	49	)	)	PUNCT
ejpam-4859	454	50	+	+	CCONJ
ejpam-4859	455	1	n	n	DET
ejpam-4859	455	2	number	number	NOUN
ejpam-4859	455	3	of	of	ADP
ejpam-4859	455	4	reactant	reactant	NOUN
ejpam-4859	455	5	complexes	complexe	VERB
ejpam-4859	455	6	nr	nr	NOUN
ejpam-4859	455	7	≤	≤	NUM
ejpam-4859	455	8	n∗	n∗	PROPN
ejpam-4859	455	9	r	r	NOUN
ejpam-4859	455	10	≤	≤	NUM
ejpam-4859	455	11	r(h−	r(h−	NOUN
ejpam-4859	455	12	1	1	NUM
ejpam-4859	455	13	)	)	PUNCT
ejpam-4859	455	14	+	+	CCONJ
ejpam-4859	455	15	nr	nr	PRON
ejpam-4859	455	16	number	number	NOUN
ejpam-4859	455	17	of	of	ADP
ejpam-4859	455	18	reactions	reaction	NOUN
ejpam-4859	455	19	r∗	r∗	VERB
ejpam-4859	455	20	=	=	PUNCT
ejpam-4859	455	21	hr	hr	NOUN
ejpam-4859	455	22	number	number	NOUN
ejpam-4859	455	23	of	of	ADP
ejpam-4859	455	24	linkage	linkage	NOUN
ejpam-4859	455	25	classes	class	NOUN
ejpam-4859	455	26	ℓ∗	ℓ∗	PROPN
ejpam-4859	455	27	≤	≤	PROPN
ejpam-4859	455	28	ℓ	ℓ	PROPN
ejpam-4859	455	29	rank	rank	NOUN
ejpam-4859	455	30	of	of	ADP
ejpam-4859	455	31	network	network	NOUN
ejpam-4859	456	1	s∗	s∗	PROPN
ejpam-4859	457	1	=	=	SYM
ejpam-4859	458	1	s	s	PART
ejpam-4859	458	2	reactant	reactant	NOUN
ejpam-4859	458	3	rank	rank	NOUN
ejpam-4859	458	4	of	of	ADP
ejpam-4859	458	5	the	the	DET
ejpam-4859	458	6	network	network	NOUN
ejpam-4859	458	7	q∗	q∗	NOUN
ejpam-4859	458	8	=	=	PUNCT
ejpam-4859	458	9	c	c	NOUN
ejpam-4859	458	10	rank	rank	NOUN
ejpam-4859	458	11	difference	difference	NOUN
ejpam-4859	458	12	∆(n	∆(n	NOUN
ejpam-4859	458	13	)	)	PUNCT
ejpam-4859	458	14	∗	∗	NOUN
ejpam-4859	458	15	=	=	PUNCT
ejpam-4859	458	16	s−	s−	NOUN
ejpam-4859	458	17	c	c	NOUN
ejpam-4859	458	18	deficiency	deficiency	NOUN
ejpam-4859	458	19	of	of	ADP
ejpam-4859	458	20	the	the	DET
ejpam-4859	458	21	network	network	NOUN
ejpam-4859	458	22	δ	δ	PROPN
ejpam-4859	458	23	≤	≤	NUM
ejpam-4859	458	24	δ∗	δ∗	PROPN
ejpam-4859	458	25	≤	≤	NUM
ejpam-4859	458	26	n+	n+	PART
ejpam-4859	458	27	r(h−	r(h−	PROPN
ejpam-4859	458	28	1)−	1)−	NUM
ejpam-4859	458	29	s−	s−	PROPN
ejpam-4859	458	30	1	1	NUM
ejpam-4859	458	31	classses	classse	NOUN
ejpam-4859	458	32	may	may	AUX
ejpam-4859	458	33	be	be	AUX
ejpam-4859	458	34	reduced	reduce	VERB
ejpam-4859	458	35	.	.	PUNCT
ejpam-4859	459	1	this	this	PRON
ejpam-4859	459	2	happens	happen	VERB
ejpam-4859	459	3	when	when	SCONJ
ejpam-4859	459	4	there	there	PRON
ejpam-4859	459	5	exists	exist	VERB
ejpam-4859	459	6	additional	additional	ADJ
ejpam-4859	459	7	complex	complex	NOUN
ejpam-4859	459	8	that	that	PRON
ejpam-4859	459	9	is	be	AUX
ejpam-4859	459	10	equal	equal	ADJ
ejpam-4859	459	11	to	to	ADP
ejpam-4859	459	12	an	an	DET
ejpam-4859	459	13	original	original	ADJ
ejpam-4859	459	14	complex	complex	NOUN
ejpam-4859	459	15	or	or	CCONJ
ejpam-4859	459	16	another	another	DET
ejpam-4859	459	17	additional	additional	ADJ
ejpam-4859	459	18	complex	complex	NOUN
ejpam-4859	459	19	.	.	PUNCT
ejpam-4859	460	1	hence	hence	ADV
ejpam-4859	460	2	,	,	PUNCT
ejpam-4859	460	3	ℓ∗	ℓ∗	PROPN
ejpam-4859	460	4	≤	≤	PROPN
ejpam-4859	460	5	ℓ	ℓ	PROPN
ejpam-4859	460	6	(	(	PUNCT
ejpam-4859	460	7	as	as	SCONJ
ejpam-4859	460	8	shown	show	VERB
ejpam-4859	460	9	in	in	ADP
ejpam-4859	460	10	table	table	NOUN
ejpam-4859	460	11	3.1	3.1	NUM
ejpam-4859	460	12	)	)	PUNCT
ejpam-4859	460	13	.	.	PUNCT
ejpam-4859	461	1	moreover	moreover	ADV
ejpam-4859	461	2	,	,	PUNCT
ejpam-4859	461	3	the	the	DET
ejpam-4859	461	4	number	number	NOUN
ejpam-4859	461	5	of	of	ADP
ejpam-4859	461	6	terminal	terminal	ADJ
ejpam-4859	461	7	linkage	linkage	NOUN
ejpam-4859	461	8	class	class	NOUN
ejpam-4859	461	9	is	be	AUX
ejpam-4859	461	10	impossible	impossible	ADJ
ejpam-4859	461	11	to	to	PART
ejpam-4859	461	12	decrease	decrease	VERB
ejpam-4859	461	13	after	after	ADP
ejpam-4859	461	14	the	the	DET
ejpam-4859	461	15	transformation	transformation	NOUN
ejpam-4859	461	16	.	.	PUNCT
ejpam-4859	462	1	with	with	ADP
ejpam-4859	462	2	this	this	PRON
ejpam-4859	462	3	,	,	PUNCT
ejpam-4859	462	4	t∗	t∗	NOUN
ejpam-4859	462	5	≤	≤	PROPN
ejpam-4859	462	6	t	t	NOUN
ejpam-4859	462	7	(	(	PUNCT
ejpam-4859	462	8	see	see	VERB
ejpam-4859	462	9	table	table	NOUN
ejpam-4859	462	10	3.1	3.1	NUM
ejpam-4859	462	11	)	)	PUNCT
ejpam-4859	462	12	.	.	PUNCT
ejpam-4859	463	1	for	for	ADP
ejpam-4859	463	2	the	the	DET
ejpam-4859	463	3	deficiency	deficiency	NOUN
ejpam-4859	463	4	of	of	ADP
ejpam-4859	463	5	the	the	DET
ejpam-4859	463	6	network	network	NOUN
ejpam-4859	463	7	and	and	CCONJ
ejpam-4859	463	8	reactant	reactant	NOUN
ejpam-4859	463	9	rank	rank	NOUN
ejpam-4859	463	10	of	of	ADP
ejpam-4859	463	11	the	the	DET
ejpam-4859	463	12	network	network	NOUN
ejpam-4859	463	13	,	,	PUNCT
ejpam-4859	463	14	we	we	PRON
ejpam-4859	463	15	refer	refer	VERB
ejpam-4859	463	16	to	to	ADP
ejpam-4859	463	17	the	the	DET
ejpam-4859	463	18	next	next	ADJ
ejpam-4859	463	19	section	section	NOUN
ejpam-4859	463	20	of	of	ADP
ejpam-4859	463	21	this	this	DET
ejpam-4859	463	22	paper	paper	NOUN
ejpam-4859	463	23	.	.	PUNCT
ejpam-4859	464	1	3.3	3.3	NUM
ejpam-4859	464	2	.	.	PUNCT
ejpam-4859	465	1	invariance	invariance	NOUN
ejpam-4859	465	2	of	of	ADP
ejpam-4859	465	3	crn	crn	NOUN
ejpam-4859	465	4	properties	property	NOUN
ejpam-4859	465	5	under	under	ADP
ejpam-4859	465	6	star	star	NOUN
ejpam-4859	465	7	-	-	PUNCT
ejpam-4859	465	8	rvm	rvm	NOUN
ejpam-4859	465	9	transformation	transformation	NOUN
ejpam-4859	465	10	at	at	ADP
ejpam-4859	465	11	this	this	DET
ejpam-4859	465	12	point	point	NOUN
ejpam-4859	465	13	,	,	PUNCT
ejpam-4859	465	14	we	we	PRON
ejpam-4859	465	15	explore	explore	VERB
ejpam-4859	465	16	the	the	DET
ejpam-4859	465	17	different	different	ADJ
ejpam-4859	465	18	crn	crn	NOUN
ejpam-4859	465	19	properties	property	NOUN
ejpam-4859	465	20	that	that	PRON
ejpam-4859	465	21	are	be	AUX
ejpam-4859	465	22	invariant	invariant	ADJ
ejpam-4859	465	23	under	under	ADP
ejpam-4859	465	24	the	the	DET
ejpam-4859	465	25	star	star	NOUN
ejpam-4859	465	26	-	-	PUNCT
ejpam-4859	465	27	rvm	rvm	NOUN
ejpam-4859	465	28	transformation	transformation	NOUN
ejpam-4859	465	29	.	.	PUNCT
ejpam-4859	466	1	we	we	PRON
ejpam-4859	466	2	study	study	VERB
ejpam-4859	466	3	necessary	necessary	ADJ
ejpam-4859	466	4	and/or	and/or	CCONJ
ejpam-4859	466	5	sufficient	sufficient	ADJ
ejpam-4859	466	6	conditions	condition	NOUN
ejpam-4859	466	7	that	that	PRON
ejpam-4859	466	8	are	be	AUX
ejpam-4859	466	9	required	require	VERB
ejpam-4859	466	10	for	for	SCONJ
ejpam-4859	466	11	these	these	DET
ejpam-4859	466	12	properties	property	NOUN
ejpam-4859	466	13	to	to	PART
ejpam-4859	466	14	be	be	AUX
ejpam-4859	466	15	invariant	invariant	ADJ
ejpam-4859	466	16	under	under	ADP
ejpam-4859	466	17	the	the	DET
ejpam-4859	466	18	transformation	transformation	NOUN
ejpam-4859	466	19	.	.	PUNCT
ejpam-4859	467	1	3.3.1	3.3.1	NUM
ejpam-4859	467	2	.	.	X
ejpam-4859	467	3	t	t	NOUN
ejpam-4859	467	4	-	-	PUNCT
ejpam-4859	467	5	minimality	minimality	NOUN
ejpam-4859	467	6	we	we	PRON
ejpam-4859	467	7	observe	observe	VERB
ejpam-4859	467	8	from	from	ADP
ejpam-4859	467	9	example	example	NOUN
ejpam-4859	467	10	11	11	NUM
ejpam-4859	467	11	that	that	SCONJ
ejpam-4859	467	12	the	the	DET
ejpam-4859	467	13	number	number	NOUN
ejpam-4859	467	14	of	of	ADP
ejpam-4859	467	15	linkage	linkage	NOUN
ejpam-4859	467	16	classes	class	NOUN
ejpam-4859	467	17	ℓ	ℓ	X
ejpam-4859	467	18	is	be	AUX
ejpam-4859	467	19	1	1	NUM
ejpam-4859	467	20	and	and	CCONJ
ejpam-4859	467	21	the	the	DET
ejpam-4859	467	22	number	number	NOUN
ejpam-4859	467	23	of	of	ADP
ejpam-4859	467	24	terminal	terminal	ADJ
ejpam-4859	467	25	strong	strong	ADJ
ejpam-4859	467	26	linkage	linkage	NOUN
ejpam-4859	467	27	classes	class	NOUN
ejpam-4859	467	28	t	t	PROPN
ejpam-4859	467	29	is	be	AUX
ejpam-4859	467	30	also	also	ADV
ejpam-4859	467	31	1	1	NUM
ejpam-4859	467	32	.	.	PUNCT
ejpam-4859	468	1	since	since	SCONJ
ejpam-4859	468	2	ℓ	ℓ	PROPN
ejpam-4859	468	3	=	=	SYM
ejpam-4859	468	4	t	t	PROPN
ejpam-4859	468	5	,	,	PUNCT
ejpam-4859	468	6	n	n	X
ejpam-4859	468	7	is	be	AUX
ejpam-4859	468	8	t	t	PROPN
ejpam-4859	468	9	-	-	PUNCT
ejpam-4859	468	10	minimal	minimal	NOUN
ejpam-4859	468	11	.	.	PUNCT
ejpam-4859	469	1	note	note	VERB
ejpam-4859	469	2	that	that	SCONJ
ejpam-4859	469	3	we	we	PRON
ejpam-4859	469	4	have	have	VERB
ejpam-4859	469	5	ℓ∗	ℓ∗	NOUN
ejpam-4859	469	6	=	=	SYM
ejpam-4859	469	7	1	1	NUM
ejpam-4859	469	8	and	and	CCONJ
ejpam-4859	469	9	t∗	t∗	NOUN
ejpam-4859	469	10	=	=	SYM
ejpam-4859	469	11	2	2	NUM
ejpam-4859	470	1	and	and	CCONJ
ejpam-4859	470	2	so	so	ADV
ejpam-4859	470	3	n	n	NOUN
ejpam-4859	470	4	∗	∗	NOUN
ejpam-4859	470	5	is	be	AUX
ejpam-4859	470	6	not	not	PART
ejpam-4859	470	7	t	t	NOUN
ejpam-4859	470	8	-	-	PUNCT
ejpam-4859	470	9	minimal	minimal	ADJ
ejpam-4859	470	10	.	.	PUNCT
ejpam-4859	471	1	this	this	PRON
ejpam-4859	471	2	tells	tell	VERB
ejpam-4859	471	3	us	we	PRON
ejpam-4859	471	4	that	that	SCONJ
ejpam-4859	471	5	if	if	SCONJ
ejpam-4859	471	6	n	n	NOUN
ejpam-4859	471	7	is	be	AUX
ejpam-4859	471	8	t	t	NOUN
ejpam-4859	471	9	-	-	PUNCT
ejpam-4859	471	10	minimal	minimal	ADJ
ejpam-4859	471	11	then	then	ADV
ejpam-4859	471	12	n	n	PRON
ejpam-4859	471	13	∗	∗	NOUN
ejpam-4859	471	14	is	be	AUX
ejpam-4859	471	15	not	not	PART
ejpam-4859	471	16	necessarily	necessarily	ADV
ejpam-4859	471	17	t	t	NOUN
ejpam-4859	471	18	-	-	PUNCT
ejpam-4859	471	19	minimal	minimal	ADJ
ejpam-4859	471	20	.	.	PUNCT
ejpam-4859	472	1	with	with	ADP
ejpam-4859	472	2	this	this	PRON
ejpam-4859	472	3	,	,	PUNCT
ejpam-4859	472	4	we	we	PRON
ejpam-4859	472	5	will	will	AUX
ejpam-4859	472	6	inject	inject	VERB
ejpam-4859	472	7	conditions	condition	NOUN
ejpam-4859	472	8	on	on	ADP
ejpam-4859	472	9	a	a	DET
ejpam-4859	472	10	t	t	NOUN
ejpam-4859	472	11	-	-	PUNCT
ejpam-4859	472	12	minimal	minimal	ADJ
ejpam-4859	472	13	network	network	NOUN
ejpam-4859	472	14	in	in	ADP
ejpam-4859	472	15	order	order	NOUN
ejpam-4859	472	16	to	to	PART
ejpam-4859	472	17	have	have	AUX
ejpam-4859	472	18	a	a	DET
ejpam-4859	472	19	t	t	NOUN
ejpam-4859	472	20	-	-	PUNCT
ejpam-4859	472	21	minimal	minimal	NOUN
ejpam-4859	472	22	star	star	NOUN
ejpam-4859	472	23	-	-	PUNCT
ejpam-4859	472	24	rvm	rvm	PROPN
ejpam-4859	472	25	transform	transform	NOUN
ejpam-4859	472	26	network	network	NOUN
ejpam-4859	472	27	stated	state	VERB
ejpam-4859	472	28	as	as	SCONJ
ejpam-4859	472	29	follows	follow	VERB
ejpam-4859	472	30	:	:	PUNCT
ejpam-4859	472	31	proposition	proposition	NOUN
ejpam-4859	472	32	7	7	NUM
ejpam-4859	472	33	.	.	PUNCT
ejpam-4859	473	1	let	let	VERB
ejpam-4859	473	2	n	n	PRON
ejpam-4859	473	3	be	be	AUX
ejpam-4859	473	4	a	a	DET
ejpam-4859	473	5	poly	poly	ADJ
ejpam-4859	473	6	-	-	PUNCT
ejpam-4859	473	7	pl	pl	NOUN
ejpam-4859	473	8	system	system	NOUN
ejpam-4859	473	9	with	with	ADP
ejpam-4859	473	10	a	a	DET
ejpam-4859	473	11	poly	poly	ADJ
ejpam-4859	473	12	-	-	PUNCT
ejpam-4859	473	13	pl	pl	NOUN
ejpam-4859	473	14	kinetics	kinetic	NOUN
ejpam-4859	473	15	of	of	ADP
ejpam-4859	473	16	h	h	NOUN
ejpam-4859	473	17	=	=	SYM
ejpam-4859	473	18	2	2	NUM
ejpam-4859	473	19	and	and	CCONJ
ejpam-4859	473	20	n	n	PROPN
ejpam-4859	473	21	∗	∗	NOUN
ejpam-4859	473	22	be	be	VERB
ejpam-4859	473	23	the	the	DET
ejpam-4859	473	24	star	star	NOUN
ejpam-4859	473	25	-	-	PUNCT
ejpam-4859	473	26	rvm	rvm	PROPN
ejpam-4859	473	27	transform	transform	NOUN
ejpam-4859	473	28	of	of	ADP
ejpam-4859	473	29	n	n	NOUN
ejpam-4859	473	30	.	.	PUNCT
ejpam-4859	474	1	if	if	SCONJ
ejpam-4859	474	2	n	n	PRON
ejpam-4859	474	3	is	be	AUX
ejpam-4859	474	4	t	t	NOUN
ejpam-4859	474	5	-	-	PUNCT
ejpam-4859	474	6	minimal	minimal	ADJ
ejpam-4859	474	7	and	and	CCONJ
ejpam-4859	474	8	for	for	ADP
ejpam-4859	474	9	every	every	DET
ejpam-4859	474	10	complex	complex	ADJ
ejpam-4859	474	11	y	y	NOUN
ejpam-4859	474	12	of	of	ADP
ejpam-4859	474	13	n	n	PROPN
ejpam-4859	474	14	,	,	PUNCT
ejpam-4859	474	15	d−(y	d−(y	NOUN
ejpam-4859	474	16	)	)	PUNCT
ejpam-4859	475	1	+	+	PUNCT
ejpam-4859	475	2	d+(y	d+(y	NOUN
ejpam-4859	475	3	)	)	PUNCT
ejpam-4859	475	4	=	=	PUNCT
ejpam-4859	476	1	1	1	NUM
ejpam-4859	476	2	then	then	ADV
ejpam-4859	476	3	n	n	PRON
ejpam-4859	476	4	∗	∗	NOUN
ejpam-4859	476	5	is	be	AUX
ejpam-4859	476	6	t	t	NOUN
ejpam-4859	476	7	-	-	PUNCT
ejpam-4859	476	8	minimal	minimal	ADJ
ejpam-4859	476	9	.	.	PUNCT
ejpam-4859	477	1	proof	proof	NOUN
ejpam-4859	477	2	.	.	PUNCT
ejpam-4859	478	1	let	let	VERB
ejpam-4859	478	2	n	n	PRON
ejpam-4859	478	3	be	be	AUX
ejpam-4859	478	4	a	a	DET
ejpam-4859	478	5	poly	poly	ADJ
ejpam-4859	478	6	-	-	PUNCT
ejpam-4859	478	7	pl	pl	NOUN
ejpam-4859	478	8	systems	system	NOUN
ejpam-4859	478	9	with	with	ADP
ejpam-4859	478	10	a	a	DET
ejpam-4859	478	11	poly	poly	ADJ
ejpam-4859	478	12	-	-	PUNCT
ejpam-4859	478	13	pl	pl	NOUN
ejpam-4859	478	14	kinetics	kinetic	NOUN
ejpam-4859	478	15	of	of	ADP
ejpam-4859	478	16	h	h	NOUN
ejpam-4859	478	17	=	=	SYM
ejpam-4859	478	18	2	2	NUM
ejpam-4859	478	19	and	and	CCONJ
ejpam-4859	478	20	n	n	PROPN
ejpam-4859	478	21	∗	∗	NOUN
ejpam-4859	478	22	be	be	VERB
ejpam-4859	478	23	the	the	DET
ejpam-4859	478	24	star	star	NOUN
ejpam-4859	478	25	-	-	PUNCT
ejpam-4859	478	26	rvm	rvm	PROPN
ejpam-4859	478	27	transform	transform	NOUN
ejpam-4859	478	28	of	of	ADP
ejpam-4859	478	29	n	n	PROPN
ejpam-4859	478	30	.	.	PUNCT
ejpam-4859	479	1	suppose	suppose	VERB
ejpam-4859	479	2	n	n	PRON
ejpam-4859	479	3	is	be	AUX
ejpam-4859	479	4	t	t	NOUN
ejpam-4859	479	5	-	-	PUNCT
ejpam-4859	479	6	minimal	minimal	ADJ
ejpam-4859	479	7	and	and	CCONJ
ejpam-4859	479	8	for	for	ADP
ejpam-4859	479	9	every	every	DET
ejpam-4859	479	10	complex	complex	ADJ
ejpam-4859	479	11	y	y	NOUN
ejpam-4859	479	12	,	,	PUNCT
ejpam-4859	479	13	d−(y	d−(y	NOUN
ejpam-4859	479	14	)	)	PUNCT
ejpam-4859	480	1	+	+	PUNCT
ejpam-4859	480	2	d+(y	d+(y	NOUN
ejpam-4859	480	3	)	)	PUNCT
ejpam-4859	480	4	=	=	PUNCT
ejpam-4859	481	1	1	1	X
ejpam-4859	481	2	.	.	PUNCT
ejpam-4859	481	3	since	since	SCONJ
ejpam-4859	481	4	n	n	NUM
ejpam-4859	481	5	is	be	AUX
ejpam-4859	481	6	t	t	PROPN
ejpam-4859	481	7	-	-	PUNCT
ejpam-4859	481	8	minimal	minimal	ADJ
ejpam-4859	481	9	,	,	PUNCT
ejpam-4859	481	10	the	the	DET
ejpam-4859	481	11	number	number	NOUN
ejpam-4859	481	12	of	of	ADP
ejpam-4859	481	13	linkage	linkage	NOUN
ejpam-4859	481	14	classes	class	NOUN
ejpam-4859	481	15	l	l	NOUN
ejpam-4859	481	16	is	be	AUX
ejpam-4859	481	17	equal	equal	ADJ
ejpam-4859	481	18	to	to	ADP
ejpam-4859	481	19	the	the	DET
ejpam-4859	481	20	number	number	NOUN
ejpam-4859	481	21	of	of	ADP
ejpam-4859	481	22	terminal	terminal	ADJ
ejpam-4859	481	23	strong	strong	ADJ
ejpam-4859	481	24	linkage	linkage	NOUN
ejpam-4859	481	25	classes	class	NOUN
ejpam-4859	481	26	t.	t.	NOUN
ejpam-4859	482	1	this	this	PRON
ejpam-4859	482	2	assures	assure	VERB
ejpam-4859	482	3	that	that	SCONJ
ejpam-4859	482	4	no	no	DET
ejpam-4859	482	5	original	original	ADJ
ejpam-4859	482	6	complex	complex	NOUN
ejpam-4859	482	7	reacts	react	NOUN
ejpam-4859	482	8	to	to	ADP
ejpam-4859	482	9	a	a	DET
ejpam-4859	482	10	complex	complex	NOUN
ejpam-4859	482	11	belonging	belong	VERB
ejpam-4859	482	12	to	to	ADP
ejpam-4859	482	13	a	a	DET
ejpam-4859	482	14	different	different	ADJ
ejpam-4859	482	15	strong	strong	ADJ
ejpam-4859	482	16	linkage	linkage	NOUN
ejpam-4859	482	17	class	class	NOUN
ejpam-4859	482	18	.	.	PUNCT
ejpam-4859	483	1	d.	d.	PROPN
ejpam-4859	483	2	magpantay	magpantay	PROPN
ejpam-4859	483	3	/	/	SYM
ejpam-4859	483	4	eur	eur	PROPN
ejpam-4859	483	5	.	.	PUNCT
ejpam-4859	484	1	j.	j.	PROPN
ejpam-4859	484	2	pure	pure	PROPN
ejpam-4859	484	3	appl	appl	PROPN
ejpam-4859	484	4	.	.	PROPN
ejpam-4859	484	5	math	math	PROPN
ejpam-4859	484	6	,	,	PUNCT
ejpam-4859	484	7	16	16	NUM
ejpam-4859	484	8	(	(	PUNCT
ejpam-4859	484	9	4	4	NUM
ejpam-4859	484	10	)	)	PUNCT
ejpam-4859	484	11	(	(	PUNCT
ejpam-4859	484	12	2023	2023	NUM
ejpam-4859	484	13	)	)	PUNCT
ejpam-4859	484	14	,	,	PUNCT
ejpam-4859	484	15	2557	2557	NUM
ejpam-4859	484	16	-	-	SYM
ejpam-4859	484	17	2580	2580	NUM
ejpam-4859	484	18	2572	2572	NUM
ejpam-4859	484	19	since	since	SCONJ
ejpam-4859	484	20	for	for	ADP
ejpam-4859	484	21	every	every	DET
ejpam-4859	484	22	complex	complex	ADJ
ejpam-4859	484	23	y	y	NOUN
ejpam-4859	484	24	,	,	PUNCT
ejpam-4859	484	25	d−(y	d−(y	NOUN
ejpam-4859	484	26	)	)	PUNCT
ejpam-4859	484	27	+	+	PUNCT
ejpam-4859	484	28	d+(y	d+(y	NOUN
ejpam-4859	484	29	)	)	PUNCT
ejpam-4859	484	30	=	=	SYM
ejpam-4859	485	1	1	1	NUM
ejpam-4859	485	2	,	,	PUNCT
ejpam-4859	485	3	we	we	PRON
ejpam-4859	485	4	can	can	AUX
ejpam-4859	485	5	partition	partition	VERB
ejpam-4859	485	6	the	the	DET
ejpam-4859	485	7	set	set	NOUN
ejpam-4859	485	8	of	of	ADP
ejpam-4859	485	9	complexes	complex	NOUN
ejpam-4859	485	10	to	to	ADP
ejpam-4859	485	11	pairs	pair	NOUN
ejpam-4859	485	12	where	where	SCONJ
ejpam-4859	485	13	each	each	DET
ejpam-4859	485	14	equivalence	equivalence	NOUN
ejpam-4859	485	15	class	class	NOUN
ejpam-4859	485	16	is	be	AUX
ejpam-4859	485	17	given	give	VERB
ejpam-4859	485	18	by	by	ADP
ejpam-4859	485	19	{	{	PUNCT
ejpam-4859	485	20	y	y	PROPN
ejpam-4859	485	21	,	,	PUNCT
ejpam-4859	485	22	y′	y′	NUM
ejpam-4859	485	23	}	}	PUNCT
ejpam-4859	485	24	such	such	ADJ
ejpam-4859	485	25	that	that	SCONJ
ejpam-4859	485	26	y	y	PROPN
ejpam-4859	485	27	→	→	PUNCT
ejpam-4859	485	28	y′.	y′.	PROPN
ejpam-4859	485	29	constructing	construct	VERB
ejpam-4859	485	30	n	n	DET
ejpam-4859	485	31	∗	∗	NOUN
ejpam-4859	485	32	,	,	PUNCT
ejpam-4859	485	33	note	note	VERB
ejpam-4859	485	34	that	that	SCONJ
ejpam-4859	485	35	since	since	SCONJ
ejpam-4859	485	36	h	h	NOUN
ejpam-4859	485	37	=	=	NOUN
ejpam-4859	485	38	2	2	NUM
ejpam-4859	485	39	we	we	PRON
ejpam-4859	485	40	will	will	AUX
ejpam-4859	485	41	add	add	VERB
ejpam-4859	485	42	one	one	NUM
ejpam-4859	485	43	complex	complex	ADJ
ejpam-4859	485	44	y∗	y∗	ADJ
ejpam-4859	485	45	and	and	CCONJ
ejpam-4859	485	46	reaction	reaction	NOUN
ejpam-4859	485	47	y′	y′	NOUN
ejpam-4859	485	48	→	→	SYM
ejpam-4859	485	49	y∗	y∗	ADV
ejpam-4859	485	50	or	or	CCONJ
ejpam-4859	485	51	y∗	y∗	PROPN
ejpam-4859	485	52	→	→	PUNCT
ejpam-4859	485	53	y.	y.	PROPN
ejpam-4859	485	54	now	now	ADV
ejpam-4859	485	55	,	,	PUNCT
ejpam-4859	485	56	if	if	SCONJ
ejpam-4859	485	57	each	each	DET
ejpam-4859	485	58	y∗	y∗	NOUN
ejpam-4859	485	59	is	be	AUX
ejpam-4859	485	60	not	not	PART
ejpam-4859	485	61	equal	equal	ADJ
ejpam-4859	485	62	to	to	ADP
ejpam-4859	485	63	any	any	PRON
ejpam-4859	485	64	of	of	ADP
ejpam-4859	485	65	the	the	DET
ejpam-4859	485	66	original	original	ADJ
ejpam-4859	485	67	complexes	complex	NOUN
ejpam-4859	485	68	or	or	CCONJ
ejpam-4859	485	69	any	any	DET
ejpam-4859	485	70	additional	additional	ADJ
ejpam-4859	485	71	complexes	complex	NOUN
ejpam-4859	485	72	then	then	ADV
ejpam-4859	485	73	there	there	PRON
ejpam-4859	485	74	will	will	AUX
ejpam-4859	485	75	be	be	AUX
ejpam-4859	485	76	no	no	DET
ejpam-4859	485	77	changes	change	NOUN
ejpam-4859	485	78	in	in	ADP
ejpam-4859	485	79	the	the	DET
ejpam-4859	485	80	number	number	NOUN
ejpam-4859	485	81	of	of	ADP
ejpam-4859	485	82	linkage	linkage	NOUN
ejpam-4859	485	83	classes	class	NOUN
ejpam-4859	485	84	and	and	CCONJ
ejpam-4859	485	85	terminal	terminal	VERB
ejpam-4859	485	86	strong	strong	ADJ
ejpam-4859	485	87	linkage	linkage	NOUN
ejpam-4859	485	88	classes	class	NOUN
ejpam-4859	485	89	.	.	PUNCT
ejpam-4859	486	1	hence	hence	ADV
ejpam-4859	486	2	,	,	PUNCT
ejpam-4859	486	3	the	the	DET
ejpam-4859	486	4	equality	equality	NOUN
ejpam-4859	486	5	of	of	ADP
ejpam-4859	486	6	l	l	PROPN
ejpam-4859	486	7	and	and	CCONJ
ejpam-4859	486	8	t	t	PROPN
ejpam-4859	486	9	still	still	ADV
ejpam-4859	486	10	holds	hold	VERB
ejpam-4859	486	11	.	.	PUNCT
ejpam-4859	487	1	thus	thus	ADV
ejpam-4859	487	2	,	,	PUNCT
ejpam-4859	487	3	n	n	PRON
ejpam-4859	487	4	∗	∗	NOUN
ejpam-4859	487	5	is	be	AUX
ejpam-4859	487	6	t	t	NOUN
ejpam-4859	487	7	-	-	PUNCT
ejpam-4859	487	8	minimal	minimal	NOUN
ejpam-4859	487	9	.	.	PUNCT
ejpam-4859	488	1	on	on	ADP
ejpam-4859	488	2	the	the	DET
ejpam-4859	488	3	other	other	ADJ
ejpam-4859	488	4	hand	hand	NOUN
ejpam-4859	488	5	,	,	PUNCT
ejpam-4859	488	6	suppose	suppose	VERB
ejpam-4859	488	7	a	a	DET
ejpam-4859	488	8	particular	particular	ADJ
ejpam-4859	488	9	additional	additional	ADJ
ejpam-4859	488	10	complex	complex	ADJ
ejpam-4859	488	11	y∗1	y∗1	NOUN
ejpam-4859	488	12	∈	∈	PROPN
ejpam-4859	488	13	{	{	PUNCT
ejpam-4859	488	14	y2	y2	PROPN
ejpam-4859	488	15	,	,	PUNCT
ejpam-4859	488	16	y′2	y′2	NOUN
ejpam-4859	488	17	,	,	PUNCT
ejpam-4859	488	18	y∗2	y∗2	NOUN
ejpam-4859	488	19	}	}	PUNCT
ejpam-4859	488	20	of	of	ADP
ejpam-4859	488	21	the	the	DET
ejpam-4859	488	22	reactions	reaction	NOUN
ejpam-4859	488	23	y2	y2	INTJ
ejpam-4859	488	24	→	→	SYM
ejpam-4859	488	25	y′2	y′2	ADJ
ejpam-4859	488	26	→	→	SYM
ejpam-4859	488	27	y∗2	y∗2	NOUN
ejpam-4859	488	28	or	or	CCONJ
ejpam-4859	488	29	y∗2	y∗2	NOUN
ejpam-4859	488	30	→	→	PUNCT
ejpam-4859	488	31	y2	y2	PROPN
ejpam-4859	488	32	→	→	SYM
ejpam-4859	488	33	y′2	y′2	X
ejpam-4859	488	34	.	.	PUNCT
ejpam-4859	489	1	with	with	ADP
ejpam-4859	489	2	this	this	PRON
ejpam-4859	489	3	,	,	PUNCT
ejpam-4859	489	4	the	the	DET
ejpam-4859	489	5	linkage	linkage	NOUN
ejpam-4859	489	6	class	class	NOUN
ejpam-4859	489	7	where	where	SCONJ
ejpam-4859	489	8	y∗1	y∗1	PROPN
ejpam-4859	489	9	belongs	belong	VERB
ejpam-4859	489	10	and	and	CCONJ
ejpam-4859	489	11	the	the	DET
ejpam-4859	489	12	linkage	linkage	NOUN
ejpam-4859	489	13	class	class	NOUN
ejpam-4859	489	14	of	of	ADP
ejpam-4859	489	15	{	{	PUNCT
ejpam-4859	489	16	y2	y2	PROPN
ejpam-4859	489	17	,	,	PUNCT
ejpam-4859	489	18	y′2	y′2	NOUN
ejpam-4859	489	19	,	,	PUNCT
ejpam-4859	489	20	y∗2	y∗2	PROPN
ejpam-4859	489	21	}	}	PUNCT
ejpam-4859	489	22	will	will	AUX
ejpam-4859	489	23	be	be	AUX
ejpam-4859	489	24	merged	merge	VERB
ejpam-4859	489	25	.	.	PUNCT
ejpam-4859	490	1	hence	hence	ADV
ejpam-4859	490	2	,	,	PUNCT
ejpam-4859	490	3	the	the	DET
ejpam-4859	490	4	number	number	NOUN
ejpam-4859	490	5	linkage	linkage	NOUN
ejpam-4859	490	6	of	of	ADP
ejpam-4859	490	7	classes	class	NOUN
ejpam-4859	490	8	and	and	CCONJ
ejpam-4859	490	9	terminal	terminal	ADJ
ejpam-4859	490	10	strong	strong	ADJ
ejpam-4859	490	11	linkage	linkage	NOUN
ejpam-4859	490	12	classes	class	NOUN
ejpam-4859	490	13	will	will	AUX
ejpam-4859	490	14	be	be	AUX
ejpam-4859	490	15	both	both	PRON
ejpam-4859	490	16	decreased	decrease	VERB
ejpam-4859	490	17	by	by	ADP
ejpam-4859	490	18	one	one	NUM
ejpam-4859	490	19	.	.	PUNCT
ejpam-4859	491	1	thus	thus	ADV
ejpam-4859	491	2	,	,	PUNCT
ejpam-4859	491	3	the	the	DET
ejpam-4859	491	4	equality	equality	NOUN
ejpam-4859	491	5	of	of	ADP
ejpam-4859	491	6	l	l	NOUN
ejpam-4859	491	7	and	and	CCONJ
ejpam-4859	491	8	t	t	PROPN
ejpam-4859	491	9	still	still	ADV
ejpam-4859	491	10	holds	hold	VERB
ejpam-4859	491	11	and	and	CCONJ
ejpam-4859	491	12	therefore	therefore	ADV
ejpam-4859	491	13	n	n	PRON
ejpam-4859	491	14	∗	∗	NOUN
ejpam-4859	491	15	is	be	AUX
ejpam-4859	491	16	t	t	NOUN
ejpam-4859	491	17	-	-	PUNCT
ejpam-4859	491	18	minimal	minimal	NOUN
ejpam-4859	491	19	.	.	PUNCT
ejpam-4859	492	1	for	for	ADP
ejpam-4859	492	2	the	the	DET
ejpam-4859	492	3	next	next	ADJ
ejpam-4859	492	4	property	property	NOUN
ejpam-4859	492	5	,	,	PUNCT
ejpam-4859	492	6	we	we	PRON
ejpam-4859	492	7	will	will	AUX
ejpam-4859	492	8	explore	explore	VERB
ejpam-4859	492	9	the	the	DET
ejpam-4859	492	10	weakly	weakly	ADJ
ejpam-4859	492	11	reversibility	reversibility	NOUN
ejpam-4859	492	12	of	of	ADP
ejpam-4859	492	13	star	star	NOUN
ejpam-4859	492	14	-	-	PUNCT
ejpam-4859	492	15	rvm	rvm	NOUN
ejpam-4859	492	16	transform	transform	NOUN
ejpam-4859	492	17	.	.	PUNCT
ejpam-4859	493	1	3.3.2	3.3.2	X
ejpam-4859	493	2	.	.	X
ejpam-4859	493	3	weakly	weakly	ADJ
ejpam-4859	493	4	reversibility	reversibility	NOUN
ejpam-4859	493	5	example	example	NOUN
ejpam-4859	493	6	12	12	NUM
ejpam-4859	493	7	shows	show	VERB
ejpam-4859	493	8	that	that	SCONJ
ejpam-4859	493	9	if	if	SCONJ
ejpam-4859	493	10	n	n	NOUN
ejpam-4859	493	11	is	be	AUX
ejpam-4859	493	12	weakly	weakly	ADV
ejpam-4859	493	13	reversible	reversible	ADJ
ejpam-4859	493	14	,	,	PUNCT
ejpam-4859	493	15	n	n	PRON
ejpam-4859	493	16	∗	∗	NOUN
ejpam-4859	493	17	is	be	AUX
ejpam-4859	493	18	not	not	PART
ejpam-4859	493	19	always	always	ADV
ejpam-4859	493	20	weakly	weakly	ADV
ejpam-4859	493	21	reversible	reversible	ADJ
ejpam-4859	493	22	.	.	PUNCT
ejpam-4859	494	1	notice	notice	VERB
ejpam-4859	494	2	that	that	SCONJ
ejpam-4859	494	3	the	the	DET
ejpam-4859	494	4	network	network	NOUN
ejpam-4859	494	5	n	n	PART
ejpam-4859	494	6	is	be	AUX
ejpam-4859	494	7	a	a	DET
ejpam-4859	494	8	cycle	cycle	NOUN
ejpam-4859	494	9	.	.	PUNCT
ejpam-4859	495	1	hence	hence	ADV
ejpam-4859	495	2	,	,	PUNCT
ejpam-4859	495	3	n	n	PRON
ejpam-4859	495	4	is	be	AUX
ejpam-4859	495	5	weakly	weakly	ADV
ejpam-4859	495	6	reversible	reversible	ADJ
ejpam-4859	495	7	.	.	PUNCT
ejpam-4859	496	1	with	with	ADP
ejpam-4859	496	2	the	the	DET
ejpam-4859	496	3	corresponding	corresponding	ADJ
ejpam-4859	496	4	star	star	NOUN
ejpam-4859	496	5	-	-	PUNCT
ejpam-4859	496	6	rvm	rvm	PROPN
ejpam-4859	496	7	transform	transform	NOUN
ejpam-4859	496	8	,	,	PUNCT
ejpam-4859	496	9	we	we	PRON
ejpam-4859	496	10	note	note	VERB
ejpam-4859	496	11	that	that	SCONJ
ejpam-4859	496	12	the	the	DET
ejpam-4859	496	13	additional	additional	ADJ
ejpam-4859	496	14	reactions	reaction	NOUN
ejpam-4859	496	15	r∗1	r∗1	NOUN
ejpam-4859	496	16	,	,	PUNCT
ejpam-4859	496	17	r	r	NOUN
ejpam-4859	496	18	∗	∗	NOUN
ejpam-4859	496	19	2	2	NUM
ejpam-4859	496	20	and	and	CCONJ
ejpam-4859	496	21	r∗3	r∗3	NOUN
ejpam-4859	496	22	do	do	AUX
ejpam-4859	496	23	not	not	PART
ejpam-4859	496	24	belong	belong	VERB
ejpam-4859	496	25	to	to	ADP
ejpam-4859	496	26	any	any	DET
ejpam-4859	496	27	cycle	cycle	NOUN
ejpam-4859	496	28	.	.	PUNCT
ejpam-4859	497	1	thus	thus	ADV
ejpam-4859	497	2	,	,	PUNCT
ejpam-4859	497	3	n	n	PRON
ejpam-4859	497	4	∗	∗	NOUN
ejpam-4859	497	5	is	be	AUX
ejpam-4859	497	6	not	not	PART
ejpam-4859	497	7	weakly	weakly	ADV
ejpam-4859	497	8	reversible	reversible	ADJ
ejpam-4859	497	9	.	.	PUNCT
ejpam-4859	498	1	hence	hence	ADV
ejpam-4859	498	2	,	,	PUNCT
ejpam-4859	498	3	the	the	DET
ejpam-4859	498	4	following	follow	VERB
ejpam-4859	498	5	states	state	VERB
ejpam-4859	498	6	the	the	DET
ejpam-4859	498	7	sufficient	sufficient	ADJ
ejpam-4859	498	8	condition	condition	NOUN
ejpam-4859	498	9	for	for	ADP
ejpam-4859	498	10	a	a	DET
ejpam-4859	498	11	weakly	weakly	ADJ
ejpam-4859	498	12	reversible	reversible	ADJ
ejpam-4859	498	13	network	network	NOUN
ejpam-4859	498	14	to	to	PART
ejpam-4859	498	15	have	have	VERB
ejpam-4859	498	16	a	a	DET
ejpam-4859	498	17	weakly	weakly	ADJ
ejpam-4859	498	18	reversible	reversible	ADJ
ejpam-4859	498	19	star	star	NOUN
ejpam-4859	498	20	-	-	PUNCT
ejpam-4859	498	21	rvm	rvm	PROPN
ejpam-4859	498	22	transform	transform	NOUN
ejpam-4859	498	23	netwok	netwok	NOUN
ejpam-4859	498	24	:	:	PUNCT
ejpam-4859	498	25	proposition	proposition	NOUN
ejpam-4859	498	26	8	8	NUM
ejpam-4859	498	27	.	.	PUNCT
ejpam-4859	499	1	if	if	SCONJ
ejpam-4859	499	2	for	for	ADP
ejpam-4859	499	3	every	every	DET
ejpam-4859	499	4	reaction	reaction	NOUN
ejpam-4859	499	5	y	y	PROPN
ejpam-4859	499	6	→	→	PUNCT
ejpam-4859	499	7	y′	y′	NUM
ejpam-4859	499	8	of	of	ADP
ejpam-4859	499	9	a	a	DET
ejpam-4859	499	10	weakly	weakly	ADJ
ejpam-4859	499	11	reversible	reversible	ADJ
ejpam-4859	499	12	network	network	NOUN
ejpam-4859	499	13	n	n	CCONJ
ejpam-4859	499	14	the	the	DET
ejpam-4859	499	15	last	last	ADJ
ejpam-4859	499	16	additional	additional	ADJ
ejpam-4859	499	17	complex	complex	ADJ
ejpam-4859	499	18	y∗	y∗	ADV
ejpam-4859	499	19	in	in	ADP
ejpam-4859	499	20	star	star	NOUN
ejpam-4859	499	21	-	-	PUNCT
ejpam-4859	499	22	rvm	rvm	NOUN
ejpam-4859	499	23	transform	transform	NOUN
ejpam-4859	499	24	n∗	n∗	PROPN
ejpam-4859	499	25	is	be	AUX
ejpam-4859	499	26	equal	equal	ADJ
ejpam-4859	499	27	to	to	ADP
ejpam-4859	499	28	any	any	PRON
ejpam-4859	499	29	of	of	ADP
ejpam-4859	499	30	the	the	DET
ejpam-4859	499	31	original	original	ADJ
ejpam-4859	499	32	complex	complex	NOUN
ejpam-4859	499	33	of	of	ADP
ejpam-4859	499	34	n	n	PROPN
ejpam-4859	499	35	,	,	PUNCT
ejpam-4859	499	36	then	then	ADV
ejpam-4859	499	37	n	n	DET
ejpam-4859	499	38	∗	∗	NOUN
ejpam-4859	499	39	is	be	AUX
ejpam-4859	499	40	weakly	weakly	ADV
ejpam-4859	499	41	reversible	reversible	ADJ
ejpam-4859	499	42	.	.	PUNCT
ejpam-4859	500	1	proof	proof	NOUN
ejpam-4859	500	2	.	.	PUNCT
ejpam-4859	501	1	let	let	VERB
ejpam-4859	501	2	n	n	PRON
ejpam-4859	501	3	be	be	AUX
ejpam-4859	501	4	a	a	DET
ejpam-4859	501	5	weakly	weakly	ADV
ejpam-4859	501	6	reversible	reversible	ADJ
ejpam-4859	501	7	network	network	NOUN
ejpam-4859	501	8	and	and	CCONJ
ejpam-4859	501	9	n	n	PROPN
ejpam-4859	501	10	∗	∗	NOUN
ejpam-4859	501	11	be	be	VERB
ejpam-4859	501	12	the	the	DET
ejpam-4859	501	13	star	star	NOUN
ejpam-4859	501	14	-	-	PUNCT
ejpam-4859	501	15	rvm	rvm	PROPN
ejpam-4859	501	16	transform	transform	NOUN
ejpam-4859	501	17	of	of	ADP
ejpam-4859	501	18	n	n	PROPN
ejpam-4859	501	19	.	.	PUNCT
ejpam-4859	502	1	recall	recall	VERB
ejpam-4859	502	2	that	that	SCONJ
ejpam-4859	502	3	the	the	DET
ejpam-4859	502	4	original	original	ADJ
ejpam-4859	502	5	complexes	complex	NOUN
ejpam-4859	502	6	are	be	AUX
ejpam-4859	502	7	part	part	NOUN
ejpam-4859	502	8	of	of	ADP
ejpam-4859	502	9	the	the	DET
ejpam-4859	502	10	complexes	complex	NOUN
ejpam-4859	502	11	of	of	ADP
ejpam-4859	502	12	n	n	PRON
ejpam-4859	502	13	∗.	∗.	PROPN
ejpam-4859	502	14	thus	thus	ADV
ejpam-4859	502	15	,	,	PUNCT
ejpam-4859	502	16	the	the	DET
ejpam-4859	502	17	symmetry	symmetry	NOUN
ejpam-4859	502	18	property	property	NOUN
ejpam-4859	502	19	of	of	ADP
ejpam-4859	502	20	directed	direct	VERB
ejpam-4859	502	21	path	path	NOUN
ejpam-4859	502	22	in	in	ADP
ejpam-4859	502	23	the	the	DET
ejpam-4859	502	24	said	say	VERB
ejpam-4859	502	25	complexes	complex	NOUN
ejpam-4859	502	26	still	still	ADV
ejpam-4859	502	27	holds	hold	VERB
ejpam-4859	502	28	.	.	PUNCT
ejpam-4859	503	1	suppose	suppose	VERB
ejpam-4859	503	2	y	y	PROPN
ejpam-4859	503	3	→	→	SYM
ejpam-4859	503	4	y′	y′	NOUN
ejpam-4859	503	5	is	be	AUX
ejpam-4859	503	6	an	an	DET
ejpam-4859	503	7	arbitrary	arbitrary	ADJ
ejpam-4859	503	8	reaction	reaction	NOUN
ejpam-4859	503	9	in	in	ADP
ejpam-4859	503	10	n	n	CCONJ
ejpam-4859	503	11	and	and	CCONJ
ejpam-4859	503	12	y∗	y∗	ADV
ejpam-4859	503	13	is	be	AUX
ejpam-4859	503	14	the	the	DET
ejpam-4859	503	15	last	last	ADJ
ejpam-4859	503	16	additional	additional	ADJ
ejpam-4859	503	17	complex	complex	NOUN
ejpam-4859	503	18	in	in	ADP
ejpam-4859	503	19	the	the	DET
ejpam-4859	503	20	said	say	VERB
ejpam-4859	503	21	reaction	reaction	NOUN
ejpam-4859	503	22	that	that	PRON
ejpam-4859	503	23	is	be	AUX
ejpam-4859	503	24	equal	equal	ADJ
ejpam-4859	503	25	to	to	ADP
ejpam-4859	503	26	any	any	DET
ejpam-4859	503	27	original	original	ADJ
ejpam-4859	503	28	complex	complex	NOUN
ejpam-4859	503	29	.	.	PUNCT
ejpam-4859	504	1	on	on	ADP
ejpam-4859	504	2	the	the	DET
ejpam-4859	504	3	same	same	ADJ
ejpam-4859	504	4	linkage	linkage	NOUN
ejpam-4859	504	5	class	class	NOUN
ejpam-4859	504	6	,	,	PUNCT
ejpam-4859	504	7	let	let	VERB
ejpam-4859	504	8	ŷ	ŷ	AUX
ejpam-4859	504	9	be	be	AUX
ejpam-4859	504	10	any	any	DET
ejpam-4859	504	11	additional	additional	ADJ
ejpam-4859	504	12	complex	complex	NOUN
ejpam-4859	504	13	in	in	ADP
ejpam-4859	504	14	the	the	DET
ejpam-4859	504	15	reaction	reaction	NOUN
ejpam-4859	504	16	.	.	PUNCT
ejpam-4859	505	1	if	if	SCONJ
ejpam-4859	505	2	ŷ	ŷ	NUM
ejpam-4859	505	3	is	be	AUX
ejpam-4859	505	4	an	an	DET
ejpam-4859	505	5	original	original	ADJ
ejpam-4859	505	6	complex	complex	NOUN
ejpam-4859	505	7	then	then	ADV
ejpam-4859	505	8	the	the	DET
ejpam-4859	505	9	symmetry	symmetry	NOUN
ejpam-4859	505	10	property	property	NOUN
ejpam-4859	505	11	of	of	ADP
ejpam-4859	505	12	directed	direct	VERB
ejpam-4859	505	13	path	path	NOUN
ejpam-4859	505	14	(	(	PUNCT
ejpam-4859	505	15	there	there	PRON
ejpam-4859	505	16	is	be	VERB
ejpam-4859	505	17	directed	direct	VERB
ejpam-4859	505	18	path	path	NOUN
ejpam-4859	505	19	from	from	ADP
ejpam-4859	505	20	one	one	NUM
ejpam-4859	505	21	complex	complex	NOUN
ejpam-4859	505	22	to	to	ADP
ejpam-4859	505	23	another	another	PRON
ejpam-4859	505	24	and	and	CCONJ
ejpam-4859	505	25	vice	vice	ADV
ejpam-4859	505	26	versa	versa	ADV
ejpam-4859	505	27	)	)	PUNCT
ejpam-4859	505	28	holds	hold	VERB
ejpam-4859	505	29	in	in	ADP
ejpam-4859	505	30	this	this	DET
ejpam-4859	505	31	case	case	NOUN
ejpam-4859	505	32	.	.	PUNCT
ejpam-4859	506	1	now	now	ADV
ejpam-4859	506	2	,	,	PUNCT
ejpam-4859	506	3	for	for	ADP
ejpam-4859	506	4	the	the	DET
ejpam-4859	506	5	case	case	NOUN
ejpam-4859	506	6	that	that	PRON
ejpam-4859	506	7	ŷ	ŷ	NUM
ejpam-4859	506	8	is	be	AUX
ejpam-4859	506	9	not	not	PART
ejpam-4859	506	10	equal	equal	ADJ
ejpam-4859	506	11	to	to	ADP
ejpam-4859	506	12	any	any	DET
ejpam-4859	506	13	original	original	ADJ
ejpam-4859	506	14	complex	complex	NOUN
ejpam-4859	506	15	.	.	PUNCT
ejpam-4859	507	1	by	by	ADP
ejpam-4859	507	2	the	the	DET
ejpam-4859	507	3	construction	construction	NOUN
ejpam-4859	507	4	of	of	ADP
ejpam-4859	507	5	star	star	NOUN
ejpam-4859	507	6	-	-	PUNCT
ejpam-4859	507	7	rvm	rvm	NOUN
ejpam-4859	507	8	,	,	PUNCT
ejpam-4859	507	9	there	there	PRON
ejpam-4859	507	10	is	be	VERB
ejpam-4859	507	11	a	a	DET
ejpam-4859	507	12	directed	direct	VERB
ejpam-4859	507	13	path	path	NOUN
ejpam-4859	507	14	from	from	ADP
ejpam-4859	507	15	y	y	PROPN
ejpam-4859	507	16	to	to	ADP
ejpam-4859	507	17	ŷ	ŷ	NUM
ejpam-4859	507	18	,	,	PUNCT
ejpam-4859	507	19	y	y	PROPN
ejpam-4859	507	20	⇒	⇒	PROPN
ejpam-4859	507	21	ŷ	ŷ	NUM
ejpam-4859	507	22	(	(	PUNCT
ejpam-4859	507	23	or	or	CCONJ
ejpam-4859	507	24	for	for	ADP
ejpam-4859	507	25	the	the	DET
ejpam-4859	507	26	other	other	ADJ
ejpam-4859	507	27	case	case	NOUN
ejpam-4859	507	28	of	of	ADP
ejpam-4859	507	29	star	star	NOUN
ejpam-4859	507	30	-	-	PUNCT
ejpam-4859	507	31	rvm	rvm	NOUN
ejpam-4859	507	32	,	,	PUNCT
ejpam-4859	507	33	ŷ	ŷ	X
ejpam-4859	507	34	⇒	⇒	PROPN
ejpam-4859	507	35	y	y	PROPN
ejpam-4859	507	36	)	)	PUNCT
ejpam-4859	507	37	.	.	PUNCT
ejpam-4859	508	1	we	we	PRON
ejpam-4859	508	2	have	have	VERB
ejpam-4859	508	3	to	to	PART
ejpam-4859	508	4	show	show	VERB
ejpam-4859	508	5	that	that	SCONJ
ejpam-4859	508	6	there	there	PRON
ejpam-4859	508	7	exist	exist	VERB
ejpam-4859	508	8	ŷ	ŷ	X
ejpam-4859	508	9	⇒	⇒	PROPN
ejpam-4859	508	10	y	y	PROPN
ejpam-4859	508	11	(	(	PUNCT
ejpam-4859	508	12	y	y	PROPN
ejpam-4859	508	13	⇒	⇒	PROPN
ejpam-4859	508	14	ŷ	ŷ	NUM
ejpam-4859	508	15	)	)	PUNCT
ejpam-4859	508	16	,	,	PUNCT
ejpam-4859	508	17	respectively	respectively	ADV
ejpam-4859	508	18	.	.	PUNCT
ejpam-4859	509	1	since	since	SCONJ
ejpam-4859	509	2	ŷ	ŷ	NUM
ejpam-4859	509	3	̸=	̸=	PROPN
ejpam-4859	509	4	y∗	y∗	ADV
ejpam-4859	509	5	and	and	CCONJ
ejpam-4859	509	6	by	by	ADP
ejpam-4859	509	7	the	the	DET
ejpam-4859	509	8	fact	fact	NOUN
ejpam-4859	509	9	that	that	SCONJ
ejpam-4859	509	10	ŷ	ŷ	ADJ
ejpam-4859	509	11	and	and	CCONJ
ejpam-4859	509	12	y∗	y∗	ADV
ejpam-4859	509	13	are	be	AUX
ejpam-4859	509	14	both	both	PRON
ejpam-4859	509	15	additional	additional	ADJ
ejpam-4859	509	16	complexes	complex	NOUN
ejpam-4859	509	17	on	on	ADP
ejpam-4859	509	18	the	the	DET
ejpam-4859	509	19	same	same	ADJ
ejpam-4859	509	20	reaction	reaction	NOUN
ejpam-4859	509	21	,	,	PUNCT
ejpam-4859	509	22	there	there	PRON
ejpam-4859	509	23	exist	exist	VERB
ejpam-4859	509	24	ŷ	ŷ	X
ejpam-4859	509	25	⇒	⇒	PROPN
ejpam-4859	509	26	y∗	y∗	PROPN
ejpam-4859	509	27	(	(	PUNCT
ejpam-4859	509	28	y∗	y∗	ADV
ejpam-4859	509	29	⇒	⇒	NOUN
ejpam-4859	509	30	ŷ	ŷ	NUM
ejpam-4859	509	31	)	)	PUNCT
ejpam-4859	509	32	,	,	PUNCT
ejpam-4859	509	33	respectively	respectively	ADV
ejpam-4859	509	34	.	.	PUNCT
ejpam-4859	510	1	and	and	CCONJ
ejpam-4859	510	2	by	by	ADP
ejpam-4859	510	3	the	the	DET
ejpam-4859	510	4	fact	fact	NOUN
ejpam-4859	510	5	that	that	SCONJ
ejpam-4859	510	6	y∗	y∗	PROPN
ejpam-4859	510	7	is	be	AUX
ejpam-4859	510	8	equal	equal	ADJ
ejpam-4859	510	9	d.	d.	PROPN
ejpam-4859	510	10	magpantay	magpantay	PROPN
ejpam-4859	510	11	/	/	SYM
ejpam-4859	510	12	eur	eur	PROPN
ejpam-4859	510	13	.	.	PUNCT
ejpam-4859	511	1	j.	j.	PROPN
ejpam-4859	511	2	pure	pure	PROPN
ejpam-4859	511	3	appl	appl	PROPN
ejpam-4859	511	4	.	.	PROPN
ejpam-4859	511	5	math	math	PROPN
ejpam-4859	511	6	,	,	PUNCT
ejpam-4859	511	7	16	16	NUM
ejpam-4859	511	8	(	(	PUNCT
ejpam-4859	511	9	4	4	NUM
ejpam-4859	511	10	)	)	PUNCT
ejpam-4859	511	11	(	(	PUNCT
ejpam-4859	511	12	2023	2023	NUM
ejpam-4859	511	13	)	)	PUNCT
ejpam-4859	511	14	,	,	PUNCT
ejpam-4859	511	15	2557	2557	NUM
ejpam-4859	511	16	-	-	SYM
ejpam-4859	511	17	2580	2580	NUM
ejpam-4859	511	18	2573	2573	NUM
ejpam-4859	511	19	to	to	ADP
ejpam-4859	511	20	an	an	DET
ejpam-4859	511	21	original	original	ADJ
ejpam-4859	511	22	complex	complex	NOUN
ejpam-4859	511	23	of	of	ADP
ejpam-4859	511	24	a	a	DET
ejpam-4859	511	25	weakly	weakly	ADJ
ejpam-4859	511	26	reversible	reversible	ADJ
ejpam-4859	511	27	network	network	NOUN
ejpam-4859	511	28	n	n	NOUN
ejpam-4859	511	29	,	,	PUNCT
ejpam-4859	511	30	there	there	PRON
ejpam-4859	511	31	exists	exist	VERB
ejpam-4859	511	32	y∗	y∗	PROPN
ejpam-4859	511	33	⇒	⇒	VERB
ejpam-4859	511	34	y	y	PROPN
ejpam-4859	511	35	(	(	PUNCT
ejpam-4859	511	36	y	y	PROPN
ejpam-4859	511	37	⇒	⇒	PROPN
ejpam-4859	511	38	y∗	y∗	ADV
ejpam-4859	511	39	)	)	PUNCT
ejpam-4859	511	40	,	,	PUNCT
ejpam-4859	511	41	respectively	respectively	ADV
ejpam-4859	511	42	.	.	PUNCT
ejpam-4859	512	1	hence	hence	ADV
ejpam-4859	512	2	,	,	PUNCT
ejpam-4859	512	3	there	there	PRON
ejpam-4859	512	4	exists	exist	VERB
ejpam-4859	512	5	ŷ	ŷ	X
ejpam-4859	512	6	⇒	⇒	PROPN
ejpam-4859	512	7	y	y	PROPN
ejpam-4859	512	8	(	(	PUNCT
ejpam-4859	512	9	y∗	y∗	ADV
ejpam-4859	512	10	⇒	⇒	NOUN
ejpam-4859	512	11	ŷ	ŷ	NUM
ejpam-4859	512	12	)	)	PUNCT
ejpam-4859	512	13	,	,	PUNCT
ejpam-4859	512	14	respectively	respectively	ADV
ejpam-4859	512	15	.	.	PUNCT
ejpam-4859	513	1	thus	thus	ADV
ejpam-4859	513	2	,	,	PUNCT
ejpam-4859	513	3	in	in	ADP
ejpam-4859	513	4	n	n	DET
ejpam-4859	513	5	∗	∗	NOUN
ejpam-4859	513	6	,	,	PUNCT
ejpam-4859	513	7	whenever	whenever	SCONJ
ejpam-4859	513	8	there	there	PRON
ejpam-4859	513	9	is	be	VERB
ejpam-4859	513	10	ya	ya	PROPN
ejpam-4859	513	11	⇒	⇒	NOUN
ejpam-4859	513	12	yb	yb	INTJ
ejpam-4859	513	13	we	we	PRON
ejpam-4859	513	14	also	also	ADV
ejpam-4859	513	15	have	have	VERB
ejpam-4859	513	16	yb	yb	PROPN
ejpam-4859	513	17	⇒	⇒	NOUN
ejpam-4859	513	18	ya	ya	PRON
ejpam-4859	514	1	and	and	CCONJ
ejpam-4859	514	2	so	so	ADV
ejpam-4859	514	3	n	n	NOUN
ejpam-4859	514	4	∗	∗	NOUN
ejpam-4859	514	5	is	be	AUX
ejpam-4859	514	6	weakly	weakly	ADV
ejpam-4859	514	7	reversible	reversible	ADJ
ejpam-4859	514	8	.	.	PUNCT
ejpam-4859	515	1	similar	similar	ADJ
ejpam-4859	515	2	with	with	ADP
ejpam-4859	515	3	weakly	weakly	ADJ
ejpam-4859	515	4	reversibility	reversibility	NOUN
ejpam-4859	515	5	,	,	PUNCT
ejpam-4859	515	6	cycle	cycle	NOUN
ejpam-4859	515	7	terminal	terminal	NOUN
ejpam-4859	515	8	property	property	NOUN
ejpam-4859	515	9	is	be	AUX
ejpam-4859	515	10	not	not	PART
ejpam-4859	515	11	conserved	conserve	VERB
ejpam-4859	515	12	in	in	ADP
ejpam-4859	515	13	the	the	DET
ejpam-4859	515	14	starrvm	starrvm	NOUN
ejpam-4859	515	15	transform	transform	NOUN
ejpam-4859	515	16	as	as	SCONJ
ejpam-4859	515	17	dicussed	dicusse	VERB
ejpam-4859	515	18	in	in	ADP
ejpam-4859	515	19	the	the	DET
ejpam-4859	515	20	next	next	ADJ
ejpam-4859	515	21	section	section	NOUN
ejpam-4859	515	22	.	.	PUNCT
ejpam-4859	516	1	3.3.3	3.3.3	NUM
ejpam-4859	516	2	.	.	PUNCT
ejpam-4859	516	3	cycle	cycle	NOUN
ejpam-4859	516	4	terminal	terminal	NOUN
ejpam-4859	516	5	property	property	NOUN
ejpam-4859	516	6	in	in	ADP
ejpam-4859	516	7	example	example	NOUN
ejpam-4859	516	8	12	12	NUM
ejpam-4859	516	9	,	,	PUNCT
ejpam-4859	516	10	observe	observe	VERB
ejpam-4859	516	11	that	that	SCONJ
ejpam-4859	516	12	n	n	NOUN
ejpam-4859	516	13	=	=	SYM
ejpam-4859	516	14	nr	nr	PROPN
ejpam-4859	516	15	.	.	PUNCT
ejpam-4859	517	1	this	this	PRON
ejpam-4859	517	2	implies	imply	VERB
ejpam-4859	517	3	that	that	SCONJ
ejpam-4859	517	4	n	n	PRON
ejpam-4859	517	5	is	be	AUX
ejpam-4859	517	6	cycle	cycle	NOUN
ejpam-4859	517	7	terminal	terminal	NOUN
ejpam-4859	517	8	.	.	PUNCT
ejpam-4859	518	1	but	but	CCONJ
ejpam-4859	518	2	after	after	ADP
ejpam-4859	518	3	finding	find	VERB
ejpam-4859	518	4	the	the	DET
ejpam-4859	518	5	star	star	NOUN
ejpam-4859	518	6	-	-	PUNCT
ejpam-4859	518	7	rvm	rvm	PROPN
ejpam-4859	518	8	transform	transform	NOUN
ejpam-4859	518	9	,	,	PUNCT
ejpam-4859	518	10	n∗	n∗	PROPN
ejpam-4859	518	11	=	=	NOUN
ejpam-4859	518	12	6	6	NUM
ejpam-4859	518	13	̸=	̸=	PROPN
ejpam-4859	518	14	3	3	NUM
ejpam-4859	518	15	=	=	SYM
ejpam-4859	518	16	n∗	n∗	PROPN
ejpam-4859	518	17	r	r	NOUN
ejpam-4859	518	18	indicating	indicate	VERB
ejpam-4859	518	19	that	that	SCONJ
ejpam-4859	518	20	n	n	NOUN
ejpam-4859	518	21	∗	∗	NOUN
ejpam-4859	518	22	is	be	AUX
ejpam-4859	518	23	not	not	PART
ejpam-4859	518	24	cycle	cycle	NOUN
ejpam-4859	518	25	terminal	terminal	NOUN
ejpam-4859	518	26	.	.	PUNCT
ejpam-4859	519	1	thus	thus	ADV
ejpam-4859	519	2	,	,	PUNCT
ejpam-4859	519	3	the	the	DET
ejpam-4859	519	4	cycle	cycle	NOUN
ejpam-4859	519	5	terminal	terminal	NOUN
ejpam-4859	519	6	property	property	NOUN
ejpam-4859	519	7	is	be	AUX
ejpam-4859	519	8	not	not	PART
ejpam-4859	519	9	invariant	invariant	ADJ
ejpam-4859	519	10	under	under	ADP
ejpam-4859	519	11	the	the	DET
ejpam-4859	519	12	star	star	NOUN
ejpam-4859	519	13	-	-	PUNCT
ejpam-4859	519	14	rvm	rvm	NOUN
ejpam-4859	519	15	transformation	transformation	NOUN
ejpam-4859	519	16	.	.	PUNCT
ejpam-4859	520	1	hence	hence	ADV
ejpam-4859	520	2	,	,	PUNCT
ejpam-4859	520	3	we	we	PRON
ejpam-4859	520	4	have	have	VERB
ejpam-4859	520	5	the	the	DET
ejpam-4859	520	6	following	follow	VERB
ejpam-4859	520	7	sufficient	sufficient	ADJ
ejpam-4859	520	8	condition	condition	NOUN
ejpam-4859	520	9	.	.	PUNCT
ejpam-4859	521	1	proposition	proposition	NOUN
ejpam-4859	521	2	9	9	NUM
ejpam-4859	521	3	.	.	PUNCT
ejpam-4859	522	1	if	if	SCONJ
ejpam-4859	522	2	for	for	ADP
ejpam-4859	522	3	every	every	DET
ejpam-4859	522	4	reaction	reaction	NOUN
ejpam-4859	522	5	y	y	PROPN
ejpam-4859	522	6	→	→	PUNCT
ejpam-4859	522	7	y′	y′	NUM
ejpam-4859	522	8	of	of	ADP
ejpam-4859	522	9	a	a	DET
ejpam-4859	522	10	cycle	cycle	NOUN
ejpam-4859	522	11	terminal	terminal	NOUN
ejpam-4859	522	12	network	network	NOUN
ejpam-4859	522	13	n	n	CCONJ
ejpam-4859	522	14	the	the	DET
ejpam-4859	522	15	last	last	ADJ
ejpam-4859	522	16	additional	additional	ADJ
ejpam-4859	522	17	complex	complex	ADJ
ejpam-4859	522	18	y∗	y∗	ADV
ejpam-4859	522	19	in	in	ADP
ejpam-4859	522	20	star	star	NOUN
ejpam-4859	522	21	-	-	PUNCT
ejpam-4859	522	22	rvm	rvm	PROPN
ejpam-4859	522	23	transform	transform	NOUN
ejpam-4859	522	24	n	n	PRON
ejpam-4859	522	25	∗	∗	NOUN
ejpam-4859	522	26	is	be	AUX
ejpam-4859	522	27	equal	equal	ADJ
ejpam-4859	522	28	to	to	ADP
ejpam-4859	522	29	any	any	DET
ejpam-4859	522	30	original	original	ADJ
ejpam-4859	522	31	complex	complex	NOUN
ejpam-4859	522	32	or	or	CCONJ
ejpam-4859	522	33	additional	additional	ADJ
ejpam-4859	522	34	complex	complex	NOUN
ejpam-4859	522	35	,	,	PUNCT
ejpam-4859	522	36	then	then	ADV
ejpam-4859	522	37	n	n	PRON
ejpam-4859	522	38	∗	∗	NOUN
ejpam-4859	522	39	is	be	AUX
ejpam-4859	522	40	cycle	cycle	NOUN
ejpam-4859	522	41	terminal	terminal	NOUN
ejpam-4859	522	42	.	.	PUNCT
ejpam-4859	523	1	proof	proof	NOUN
ejpam-4859	523	2	.	.	PUNCT
ejpam-4859	524	1	let	let	VERB
ejpam-4859	524	2	n	n	PRON
ejpam-4859	524	3	be	be	AUX
ejpam-4859	524	4	a	a	DET
ejpam-4859	524	5	cycle	cycle	NOUN
ejpam-4859	524	6	terminal	terminal	ADJ
ejpam-4859	524	7	network	network	NOUN
ejpam-4859	524	8	where	where	SCONJ
ejpam-4859	524	9	n	n	X
ejpam-4859	524	10	is	be	AUX
ejpam-4859	524	11	the	the	DET
ejpam-4859	524	12	number	number	NOUN
ejpam-4859	524	13	of	of	ADP
ejpam-4859	524	14	complexes	complex	NOUN
ejpam-4859	524	15	and	and	CCONJ
ejpam-4859	524	16	nr	nr	PRON
ejpam-4859	524	17	is	be	AUX
ejpam-4859	524	18	the	the	DET
ejpam-4859	524	19	number	number	NOUN
ejpam-4859	524	20	of	of	ADP
ejpam-4859	524	21	reactant	reactant	NOUN
ejpam-4859	524	22	complexes	complex	NOUN
ejpam-4859	524	23	.	.	PUNCT
ejpam-4859	525	1	this	this	PRON
ejpam-4859	525	2	means	mean	VERB
ejpam-4859	525	3	that	that	SCONJ
ejpam-4859	525	4	n	n	PROPN
ejpam-4859	525	5	=	=	SYM
ejpam-4859	525	6	nr	nr	PROPN
ejpam-4859	525	7	.	.	PUNCT
ejpam-4859	525	8	constructing	construct	VERB
ejpam-4859	525	9	n	n	DET
ejpam-4859	525	10	∗	∗	NOUN
ejpam-4859	525	11	by	by	ADP
ejpam-4859	525	12	star	star	NOUN
ejpam-4859	525	13	-	-	PUNCT
ejpam-4859	525	14	rvm	rvm	PROPN
ejpam-4859	525	15	method	method	NOUN
ejpam-4859	525	16	,	,	PUNCT
ejpam-4859	525	17	let	let	VERB
ejpam-4859	525	18	n∗	n∗	NOUN
ejpam-4859	525	19	be	be	AUX
ejpam-4859	525	20	the	the	DET
ejpam-4859	525	21	number	number	NOUN
ejpam-4859	525	22	of	of	ADP
ejpam-4859	525	23	complexes	complex	NOUN
ejpam-4859	525	24	and	and	CCONJ
ejpam-4859	525	25	n∗	n∗	PROPN
ejpam-4859	525	26	r	r	NOUN
ejpam-4859	525	27	be	be	VERB
ejpam-4859	525	28	the	the	DET
ejpam-4859	525	29	number	number	NOUN
ejpam-4859	525	30	of	of	ADP
ejpam-4859	525	31	reactant	reactant	NOUN
ejpam-4859	525	32	complexes	complex	NOUN
ejpam-4859	525	33	of	of	ADP
ejpam-4859	525	34	n	n	PRON
ejpam-4859	525	35	∗.	∗.	PROPN
ejpam-4859	525	36	we	we	PRON
ejpam-4859	525	37	have	have	VERB
ejpam-4859	525	38	to	to	PART
ejpam-4859	525	39	show	show	VERB
ejpam-4859	525	40	that	that	SCONJ
ejpam-4859	525	41	n∗	n∗	PROPN
ejpam-4859	526	1	=	=	PUNCT
ejpam-4859	526	2	n∗	n∗	PROPN
ejpam-4859	526	3	r	r	NOUN
ejpam-4859	526	4	let	let	VERB
ejpam-4859	526	5	x	x	PRON
ejpam-4859	526	6	be	be	AUX
ejpam-4859	526	7	the	the	DET
ejpam-4859	526	8	number	number	NOUN
ejpam-4859	526	9	of	of	ADP
ejpam-4859	526	10	additional	additional	ADJ
ejpam-4859	526	11	complexes	complex	NOUN
ejpam-4859	526	12	.	.	PUNCT
ejpam-4859	527	1	suppose	suppose	VERB
ejpam-4859	527	2	that	that	SCONJ
ejpam-4859	527	3	for	for	ADP
ejpam-4859	527	4	every	every	DET
ejpam-4859	527	5	reaction	reaction	NOUN
ejpam-4859	527	6	y	y	PROPN
ejpam-4859	527	7	→	→	PUNCT
ejpam-4859	527	8	y′	y′	NOUN
ejpam-4859	527	9	of	of	ADP
ejpam-4859	527	10	n	n	PROPN
ejpam-4859	527	11	,	,	PUNCT
ejpam-4859	527	12	the	the	DET
ejpam-4859	527	13	last	last	ADJ
ejpam-4859	527	14	additional	additional	ADJ
ejpam-4859	527	15	complex	complex	ADJ
ejpam-4859	527	16	y∗	y∗	ADV
ejpam-4859	527	17	in	in	ADP
ejpam-4859	527	18	n	n	PROPN
ejpam-4859	527	19	∗	∗	NOUN
ejpam-4859	527	20	is	be	AUX
ejpam-4859	527	21	equal	equal	ADJ
ejpam-4859	527	22	to	to	ADP
ejpam-4859	527	23	any	any	DET
ejpam-4859	527	24	original	original	ADJ
ejpam-4859	527	25	complex	complex	NOUN
ejpam-4859	527	26	or	or	CCONJ
ejpam-4859	527	27	additional	additional	ADJ
ejpam-4859	527	28	complex	complex	NOUN
ejpam-4859	527	29	.	.	PUNCT
ejpam-4859	528	1	this	this	PRON
ejpam-4859	528	2	implies	imply	VERB
ejpam-4859	528	3	that	that	SCONJ
ejpam-4859	528	4	all	all	DET
ejpam-4859	528	5	additional	additional	ADJ
ejpam-4859	528	6	complexes	complex	NOUN
ejpam-4859	528	7	are	be	AUX
ejpam-4859	528	8	source	source	NOUN
ejpam-4859	528	9	vertices	vertex	NOUN
ejpam-4859	528	10	.	.	PUNCT
ejpam-4859	529	1	hence	hence	ADV
ejpam-4859	529	2	,	,	PUNCT
ejpam-4859	529	3	n∗	n∗	PROPN
ejpam-4859	529	4	=	=	SYM
ejpam-4859	529	5	n+x	n+x	PROPN
ejpam-4859	529	6	and	and	CCONJ
ejpam-4859	529	7	n∗	n∗	VERB
ejpam-4859	529	8	r	r	NOUN
ejpam-4859	529	9	=	=	PROPN
ejpam-4859	529	10	nr	nr	PROPN
ejpam-4859	529	11	+	+	NOUN
ejpam-4859	529	12	x.	x.	NOUN
ejpam-4859	530	1	thus	thus	ADV
ejpam-4859	530	2	,	,	PUNCT
ejpam-4859	530	3	n∗	n∗	PROPN
ejpam-4859	531	1	−	−	PROPN
ejpam-4859	532	1	n∗	n∗	PROPN
ejpam-4859	532	2	r	r	NOUN
ejpam-4859	532	3	=	=	SYM
ejpam-4859	532	4	(	(	PUNCT
ejpam-4859	532	5	n+	n+	X
ejpam-4859	532	6	x)−	x)−	PROPN
ejpam-4859	532	7	(	(	PUNCT
ejpam-4859	532	8	nr	nr	PROPN
ejpam-4859	532	9	+	+	NOUN
ejpam-4859	532	10	x	x	X
ejpam-4859	532	11	)	)	PUNCT
ejpam-4859	532	12	=	=	VERB
ejpam-4859	533	1	n−	n−	NOUN
ejpam-4859	533	2	nr	nr	NOUN
ejpam-4859	533	3	=	=	NOUN
ejpam-4859	533	4	0	0	PROPN
ejpam-4859	533	5	.	.	PUNCT
ejpam-4859	534	1	therefore	therefore	ADV
ejpam-4859	534	2	,	,	PUNCT
ejpam-4859	534	3	n∗	n∗	PROPN
ejpam-4859	534	4	=	=	SYM
ejpam-4859	534	5	n∗	n∗	PROPN
ejpam-4859	534	6	r	r	NOUN
ejpam-4859	534	7	and	and	CCONJ
ejpam-4859	534	8	n	n	PROPN
ejpam-4859	534	9	∗	∗	NOUN
ejpam-4859	534	10	is	be	AUX
ejpam-4859	534	11	cycle	cycle	NOUN
ejpam-4859	534	12	terminal	terminal	NOUN
ejpam-4859	534	13	.	.	PUNCT
ejpam-4859	535	1	in	in	ADP
ejpam-4859	535	2	the	the	DET
ejpam-4859	535	3	next	next	ADJ
ejpam-4859	535	4	section	section	NOUN
ejpam-4859	535	5	,	,	PUNCT
ejpam-4859	535	6	we	we	PRON
ejpam-4859	535	7	discuss	discuss	VERB
ejpam-4859	535	8	the	the	DET
ejpam-4859	535	9	first	first	ADJ
ejpam-4859	535	10	property	property	NOUN
ejpam-4859	535	11	that	that	PRON
ejpam-4859	535	12	is	be	AUX
ejpam-4859	535	13	invariant	invariant	ADJ
ejpam-4859	535	14	under	under	ADP
ejpam-4859	535	15	the	the	DET
ejpam-4859	535	16	star	star	NOUN
ejpam-4859	535	17	-	-	PUNCT
ejpam-4859	535	18	rvm	rvm	NOUN
ejpam-4859	535	19	transformation	transformation	NOUN
ejpam-4859	535	20	.	.	PUNCT
ejpam-4859	536	1	3.3.4	3.3.4	X
ejpam-4859	536	2	.	.	PUNCT
ejpam-4859	536	3	point	point	NOUN
ejpam-4859	536	4	terminal	terminal	ADJ
ejpam-4859	536	5	property	property	NOUN
ejpam-4859	536	6	on	on	ADP
ejpam-4859	536	7	the	the	DET
ejpam-4859	536	8	next	next	ADJ
ejpam-4859	536	9	proposition	proposition	NOUN
ejpam-4859	536	10	,	,	PUNCT
ejpam-4859	536	11	we	we	PRON
ejpam-4859	536	12	show	show	VERB
ejpam-4859	536	13	that	that	SCONJ
ejpam-4859	536	14	the	the	DET
ejpam-4859	536	15	star	star	NOUN
ejpam-4859	536	16	-	-	PUNCT
ejpam-4859	536	17	rvm	rvm	PROPN
ejpam-4859	536	18	transform	transform	NOUN
ejpam-4859	536	19	of	of	ADP
ejpam-4859	536	20	a	a	DET
ejpam-4859	536	21	point	point	NOUN
ejpam-4859	536	22	terminal	terminal	ADJ
ejpam-4859	536	23	network	network	NOUN
ejpam-4859	536	24	is	be	AUX
ejpam-4859	536	25	also	also	ADV
ejpam-4859	536	26	point	point	NOUN
ejpam-4859	536	27	terminal	terminal	NOUN
ejpam-4859	536	28	.	.	PUNCT
ejpam-4859	537	1	proposition	proposition	NOUN
ejpam-4859	537	2	10	10	NUM
ejpam-4859	537	3	.	.	PUNCT
ejpam-4859	538	1	if	if	SCONJ
ejpam-4859	538	2	a	a	DET
ejpam-4859	538	3	poly	poly	ADJ
ejpam-4859	538	4	-	-	PUNCT
ejpam-4859	538	5	pl	pl	NOUN
ejpam-4859	538	6	system	system	NOUN
ejpam-4859	538	7	(	(	PUNCT
ejpam-4859	538	8	n	n	X
ejpam-4859	538	9	,	,	PUNCT
ejpam-4859	538	10	k	k	NOUN
ejpam-4859	538	11	)	)	PUNCT
ejpam-4859	538	12	is	be	AUX
ejpam-4859	538	13	point	point	NOUN
ejpam-4859	538	14	terminal	terminal	NOUN
ejpam-4859	538	15	,	,	PUNCT
ejpam-4859	538	16	its	its	PRON
ejpam-4859	538	17	star	star	NOUN
ejpam-4859	538	18	-	-	PUNCT
ejpam-4859	538	19	rvm	rvm	PROPN
ejpam-4859	538	20	transform	transform	NOUN
ejpam-4859	538	21	(	(	PUNCT
ejpam-4859	538	22	n	n	CCONJ
ejpam-4859	538	23	∗,k∗	∗,k∗	ADJ
ejpam-4859	538	24	)	)	PUNCT
ejpam-4859	538	25	is	be	AUX
ejpam-4859	538	26	also	also	ADV
ejpam-4859	538	27	point	point	NOUN
ejpam-4859	538	28	terminal	terminal	NOUN
ejpam-4859	538	29	.	.	PUNCT
ejpam-4859	539	1	proof	proof	NOUN
ejpam-4859	539	2	.	.	PUNCT
ejpam-4859	540	1	let	let	AUX
ejpam-4859	540	2	(	(	PUNCT
ejpam-4859	540	3	n	n	X
ejpam-4859	540	4	,	,	PUNCT
ejpam-4859	540	5	k	k	NOUN
ejpam-4859	540	6	)	)	PUNCT
ejpam-4859	540	7	be	be	AUX
ejpam-4859	540	8	a	a	DET
ejpam-4859	540	9	poly	poly	ADJ
ejpam-4859	540	10	-	-	PUNCT
ejpam-4859	540	11	pl	pl	NOUN
ejpam-4859	540	12	systems	system	NOUN
ejpam-4859	540	13	and	and	CCONJ
ejpam-4859	540	14	(	(	PUNCT
ejpam-4859	540	15	n	n	CCONJ
ejpam-4859	540	16	∗,k∗	∗,k∗	ADJ
ejpam-4859	540	17	)	)	PUNCT
ejpam-4859	540	18	be	be	AUX
ejpam-4859	540	19	the	the	DET
ejpam-4859	540	20	its	its	PRON
ejpam-4859	540	21	star	star	NOUN
ejpam-4859	540	22	-	-	PUNCT
ejpam-4859	540	23	rvm	rvm	PROPN
ejpam-4859	540	24	transform	transform	NOUN
ejpam-4859	540	25	.	.	PUNCT
ejpam-4859	541	1	suppose	suppose	VERB
ejpam-4859	541	2	n	n	PRON
ejpam-4859	541	3	is	be	AUX
ejpam-4859	541	4	point	point	NOUN
ejpam-4859	541	5	terminal	terminal	ADJ
ejpam-4859	541	6	.	.	PUNCT
ejpam-4859	542	1	this	this	PRON
ejpam-4859	542	2	means	mean	VERB
ejpam-4859	542	3	that	that	SCONJ
ejpam-4859	542	4	t	t	NOUN
ejpam-4859	542	5	=	=	SYM
ejpam-4859	542	6	n	n	PROPN
ejpam-4859	542	7	−	−	PROPN
ejpam-4859	542	8	nr	nr	INTJ
ejpam-4859	542	9	where	where	SCONJ
ejpam-4859	542	10	t	t	PROPN
ejpam-4859	542	11	is	be	AUX
ejpam-4859	542	12	the	the	DET
ejpam-4859	542	13	number	number	NOUN
ejpam-4859	542	14	d.	d.	PROPN
ejpam-4859	542	15	magpantay	magpantay	PROPN
ejpam-4859	542	16	/	/	SYM
ejpam-4859	542	17	eur	eur	PROPN
ejpam-4859	542	18	.	.	PUNCT
ejpam-4859	543	1	j.	j.	PROPN
ejpam-4859	543	2	pure	pure	PROPN
ejpam-4859	543	3	appl	appl	PROPN
ejpam-4859	543	4	.	.	PROPN
ejpam-4859	543	5	math	math	PROPN
ejpam-4859	543	6	,	,	PUNCT
ejpam-4859	543	7	16	16	NUM
ejpam-4859	543	8	(	(	PUNCT
ejpam-4859	543	9	4	4	NUM
ejpam-4859	543	10	)	)	PUNCT
ejpam-4859	543	11	(	(	PUNCT
ejpam-4859	543	12	2023	2023	NUM
ejpam-4859	543	13	)	)	PUNCT
ejpam-4859	543	14	,	,	PUNCT
ejpam-4859	543	15	2557	2557	NUM
ejpam-4859	543	16	-	-	SYM
ejpam-4859	543	17	2580	2580	NUM
ejpam-4859	543	18	2574	2574	NUM
ejpam-4859	543	19	of	of	ADP
ejpam-4859	543	20	terminal	terminal	ADJ
ejpam-4859	543	21	strong	strong	ADJ
ejpam-4859	543	22	linkage	linkage	NOUN
ejpam-4859	543	23	classes	class	NOUN
ejpam-4859	543	24	,	,	PUNCT
ejpam-4859	543	25	n	n	X
ejpam-4859	543	26	is	be	AUX
ejpam-4859	543	27	the	the	DET
ejpam-4859	543	28	number	number	NOUN
ejpam-4859	543	29	of	of	ADP
ejpam-4859	543	30	complexes	complex	NOUN
ejpam-4859	543	31	and	and	CCONJ
ejpam-4859	543	32	nr	nr	PRON
ejpam-4859	543	33	be	be	AUX
ejpam-4859	543	34	the	the	DET
ejpam-4859	543	35	number	number	NOUN
ejpam-4859	543	36	of	of	ADP
ejpam-4859	543	37	reactant	reactant	NOUN
ejpam-4859	543	38	complexes	complex	NOUN
ejpam-4859	543	39	.	.	PUNCT
ejpam-4859	544	1	let	let	VERB
ejpam-4859	544	2	t	t	NOUN
ejpam-4859	544	3	=	=	PRON
ejpam-4859	544	4	{	{	PUNCT
ejpam-4859	544	5	{	{	PUNCT
ejpam-4859	544	6	y}|y	y}|y	PROPN
ejpam-4859	544	7	is	be	AUX
ejpam-4859	544	8	a	a	DET
ejpam-4859	544	9	complex	complex	ADJ
ejpam-4859	544	10	such	such	ADJ
ejpam-4859	544	11	that	that	DET
ejpam-4859	544	12	d+(y	d+(y	NOUN
ejpam-4859	544	13	)	)	PUNCT
ejpam-4859	544	14	=	=	PUNCT
ejpam-4859	545	1	0	0	NUM
ejpam-4859	545	2	}	}	PUNCT
ejpam-4859	545	3	.	.	PUNCT
ejpam-4859	546	1	hence	hence	ADV
ejpam-4859	546	2	,	,	PUNCT
ejpam-4859	546	3	t	t	PROPN
ejpam-4859	546	4	=	=	PUNCT
ejpam-4859	546	5	|t	|t	NOUN
ejpam-4859	546	6	|	|	ADV
ejpam-4859	546	7	.	.	PUNCT
ejpam-4859	547	1	constructing	construct	VERB
ejpam-4859	547	2	n	n	DET
ejpam-4859	547	3	∗	∗	NOUN
ejpam-4859	547	4	by	by	ADP
ejpam-4859	547	5	star	star	NOUN
ejpam-4859	547	6	-	-	PUNCT
ejpam-4859	547	7	rvm	rvm	PROPN
ejpam-4859	547	8	method	method	NOUN
ejpam-4859	547	9	,	,	PUNCT
ejpam-4859	547	10	we	we	PRON
ejpam-4859	547	11	let	let	VERB
ejpam-4859	547	12	t∗	t∗	NOUN
ejpam-4859	547	13	be	be	AUX
ejpam-4859	547	14	the	the	DET
ejpam-4859	547	15	number	number	NOUN
ejpam-4859	547	16	of	of	ADP
ejpam-4859	547	17	terminal	terminal	ADJ
ejpam-4859	547	18	strong	strong	ADJ
ejpam-4859	547	19	linkage	linkage	NOUN
ejpam-4859	547	20	classes	class	NOUN
ejpam-4859	547	21	,	,	PUNCT
ejpam-4859	547	22	n∗	n∗	VERB
ejpam-4859	547	23	the	the	DET
ejpam-4859	547	24	number	number	NOUN
ejpam-4859	547	25	of	of	ADP
ejpam-4859	547	26	complexes	complex	NOUN
ejpam-4859	547	27	and	and	CCONJ
ejpam-4859	547	28	n∗	n∗	PROPN
ejpam-4859	547	29	r	r	NOUN
ejpam-4859	547	30	the	the	DET
ejpam-4859	547	31	number	number	NOUN
ejpam-4859	547	32	of	of	ADP
ejpam-4859	547	33	reactant	reactant	NOUN
ejpam-4859	547	34	complexes	complex	NOUN
ejpam-4859	547	35	.	.	PUNCT
ejpam-4859	548	1	we	we	PRON
ejpam-4859	548	2	have	have	VERB
ejpam-4859	548	3	to	to	PART
ejpam-4859	548	4	show	show	VERB
ejpam-4859	548	5	t∗	t∗	NOUN
ejpam-4859	548	6	=	=	PUNCT
ejpam-4859	548	7	n∗	n∗	PROPN
ejpam-4859	548	8	−	−	PROPN
ejpam-4859	548	9	n∗	n∗	PROPN
ejpam-4859	548	10	r	r	NOUN
ejpam-4859	548	11	.	.	PUNCT
ejpam-4859	549	1	we	we	PRON
ejpam-4859	549	2	divide	divide	VERB
ejpam-4859	549	3	our	our	PRON
ejpam-4859	549	4	proof	proof	NOUN
ejpam-4859	549	5	into	into	ADP
ejpam-4859	549	6	two	two	NUM
ejpam-4859	549	7	parts	part	NOUN
ejpam-4859	549	8	corresponding	correspond	VERB
ejpam-4859	549	9	to	to	ADP
ejpam-4859	549	10	the	the	DET
ejpam-4859	549	11	cases	case	NOUN
ejpam-4859	549	12	defined	define	VERB
ejpam-4859	549	13	on	on	ADP
ejpam-4859	549	14	of	of	ADP
ejpam-4859	549	15	star	star	NOUN
ejpam-4859	549	16	-	-	PUNCT
ejpam-4859	549	17	rvm	rvm	NOUN
ejpam-4859	549	18	.	.	PUNCT
ejpam-4859	550	1	case	case	NOUN
ejpam-4859	550	2	1	1	NUM
ejpam-4859	550	3	(	(	PUNCT
ejpam-4859	550	4	for	for	ADP
ejpam-4859	550	5	case	case	NOUN
ejpam-4859	550	6	(	(	PUNCT
ejpam-4859	550	7	i	i	NOUN
ejpam-4859	550	8	)	)	PUNCT
ejpam-4859	550	9	in	in	ADP
ejpam-4859	550	10	star	star	NOUN
ejpam-4859	550	11	-	-	PUNCT
ejpam-4859	550	12	rvm	rvm	NOUN
ejpam-4859	550	13	):	):	PUNCT
ejpam-4859	550	14	let	let	VERB
ejpam-4859	550	15	t	t	NOUN
ejpam-4859	550	16	∗	∗	VERB
ejpam-4859	550	17	=	=	SYM
ejpam-4859	550	18	{	{	PUNCT
ejpam-4859	550	19	{	{	PUNCT
ejpam-4859	550	20	y∗}|y∗	y∗}|y∗	NOUN
ejpam-4859	550	21	is	be	AUX
ejpam-4859	550	22	an	an	DET
ejpam-4859	550	23	additional	additional	ADJ
ejpam-4859	550	24	complex	complex	NOUN
ejpam-4859	550	25	such	such	ADJ
ejpam-4859	550	26	that	that	SCONJ
ejpam-4859	550	27	d+(y∗	d+(y∗	NOUN
ejpam-4859	550	28	)	)	PUNCT
ejpam-4859	551	1	=	=	PUNCT
ejpam-4859	551	2	0	0	NUM
ejpam-4859	551	3	}	}	PUNCT
ejpam-4859	551	4	.	.	PUNCT
ejpam-4859	552	1	observe	observe	VERB
ejpam-4859	552	2	that	that	DET
ejpam-4859	552	3	t∗	t∗	NOUN
ejpam-4859	552	4	=	=	SYM
ejpam-4859	552	5	|t	|t	NOUN
ejpam-4859	552	6	∗|	∗|	NOUN
ejpam-4859	552	7	since	since	ADV
ejpam-4859	552	8	,	,	PUNCT
ejpam-4859	552	9	by	by	ADP
ejpam-4859	552	10	the	the	DET
ejpam-4859	552	11	construction	construction	NOUN
ejpam-4859	552	12	,	,	PUNCT
ejpam-4859	552	13	t∗	t∗	PROPN
ejpam-4859	552	14	is	be	AUX
ejpam-4859	552	15	the	the	DET
ejpam-4859	552	16	number	number	NOUN
ejpam-4859	552	17	of	of	ADP
ejpam-4859	552	18	additional	additional	ADJ
ejpam-4859	552	19	complexes	complex	NOUN
ejpam-4859	552	20	that	that	PRON
ejpam-4859	552	21	serves	serve	VERB
ejpam-4859	552	22	as	as	ADP
ejpam-4859	552	23	target	target	NOUN
ejpam-4859	552	24	only	only	ADV
ejpam-4859	552	25	vertices	vertex	NOUN
ejpam-4859	552	26	.	.	PUNCT
ejpam-4859	553	1	let	let	VERB
ejpam-4859	553	2	x	x	PRON
ejpam-4859	553	3	be	be	AUX
ejpam-4859	553	4	the	the	DET
ejpam-4859	553	5	number	number	NOUN
ejpam-4859	553	6	of	of	ADP
ejpam-4859	553	7	additional	additional	ADJ
ejpam-4859	553	8	complex	complex	ADJ
ejpam-4859	553	9	y′∗	y′∗	NOUN
ejpam-4859	553	10	such	such	ADJ
ejpam-4859	553	11	that	that	DET
ejpam-4859	553	12	d+(y′∗	d+(y′∗	NOUN
ejpam-4859	553	13	)	)	PUNCT
ejpam-4859	553	14	̸=	̸=	PROPN
ejpam-4859	553	15	0	0	NUM
ejpam-4859	553	16	.	.	PUNCT
ejpam-4859	554	1	this	this	PRON
ejpam-4859	554	2	implies	imply	VERB
ejpam-4859	554	3	that	that	SCONJ
ejpam-4859	554	4	the	the	DET
ejpam-4859	554	5	number	number	NOUN
ejpam-4859	554	6	of	of	ADP
ejpam-4859	554	7	additional	additional	ADJ
ejpam-4859	554	8	complexes	complex	NOUN
ejpam-4859	554	9	is	be	AUX
ejpam-4859	554	10	x+	x+	ADJ
ejpam-4859	554	11	t∗	t∗	NOUN
ejpam-4859	554	12	and	and	CCONJ
ejpam-4859	554	13	n∗	n∗	PROPN
ejpam-4859	554	14	=	=	SYM
ejpam-4859	554	15	n+	n+	NUM
ejpam-4859	554	16	x+	x+	PROPN
ejpam-4859	554	17	t∗.	t∗.	PROPN
ejpam-4859	554	18	also	also	ADV
ejpam-4859	554	19	,	,	PUNCT
ejpam-4859	554	20	observe	observe	VERB
ejpam-4859	554	21	that	that	SCONJ
ejpam-4859	554	22	by	by	ADP
ejpam-4859	554	23	the	the	DET
ejpam-4859	554	24	definition	definition	NOUN
ejpam-4859	554	25	of	of	ADP
ejpam-4859	554	26	star	star	NOUN
ejpam-4859	554	27	-	-	PUNCT
ejpam-4859	554	28	rvm	rvm	PROPN
ejpam-4859	554	29	transform	transform	NOUN
ejpam-4859	554	30	,	,	PUNCT
ejpam-4859	554	31	n∗	n∗	PROPN
ejpam-4859	554	32	r	r	NOUN
ejpam-4859	554	33	=	=	PUNCT
ejpam-4859	554	34	nr	nr	PROPN
ejpam-4859	554	35	+	+	CCONJ
ejpam-4859	554	36	t+	t+	NOUN
ejpam-4859	554	37	x.	x.	NOUN
ejpam-4859	554	38	now	now	ADV
ejpam-4859	554	39	,	,	PUNCT
ejpam-4859	554	40	n∗	n∗	PROPN
ejpam-4859	555	1	−	−	PROPN
ejpam-4859	556	1	n∗	n∗	PROPN
ejpam-4859	556	2	r	r	NOUN
ejpam-4859	556	3	=	=	SYM
ejpam-4859	556	4	(	(	PUNCT
ejpam-4859	556	5	n+	n+	X
ejpam-4859	556	6	x+	x+	ADJ
ejpam-4859	556	7	t∗)−	t∗)−	PROPN
ejpam-4859	556	8	(	(	PUNCT
ejpam-4859	556	9	nr	nr	PROPN
ejpam-4859	556	10	+	+	CCONJ
ejpam-4859	556	11	t+	t+	NOUN
ejpam-4859	556	12	x	x	NOUN
ejpam-4859	556	13	)	)	PUNCT
ejpam-4859	556	14	=	=	SYM
ejpam-4859	556	15	n+	n+	X
ejpam-4859	556	16	x+	x+	X
ejpam-4859	556	17	t∗	t∗	NOUN
ejpam-4859	556	18	−	−	PROPN
ejpam-4859	556	19	nr	nr	NOUN
ejpam-4859	556	20	−	−	PROPN
ejpam-4859	556	21	t−	t−	PROPN
ejpam-4859	556	22	x	x	NOUN
ejpam-4859	556	23	)	)	PUNCT
ejpam-4859	556	24	=	=	SYM
ejpam-4859	557	1	[	[	X
ejpam-4859	557	2	(	(	PUNCT
ejpam-4859	557	3	n−	n−	NOUN
ejpam-4859	557	4	nr)−	nr)−	NOUN
ejpam-4859	557	5	t	t	X
ejpam-4859	557	6	]	]	X
ejpam-4859	557	7	+	+	NUM
ejpam-4859	557	8	t∗	t∗	NOUN
ejpam-4859	557	9	=	=	SYM
ejpam-4859	557	10	t∗.	t∗.	NOUN
ejpam-4859	557	11	case	case	NOUN
ejpam-4859	557	12	2	2	NUM
ejpam-4859	557	13	(	(	PUNCT
ejpam-4859	557	14	for	for	ADP
ejpam-4859	557	15	case	case	NOUN
ejpam-4859	557	16	(	(	PUNCT
ejpam-4859	557	17	ii	ii	NOUN
ejpam-4859	557	18	)	)	PUNCT
ejpam-4859	557	19	in	in	ADP
ejpam-4859	557	20	star	star	NOUN
ejpam-4859	557	21	-	-	PUNCT
ejpam-4859	557	22	rvm	rvm	NOUN
ejpam-4859	557	23	):	):	PUNCT
ejpam-4859	557	24	note	note	VERB
ejpam-4859	557	25	that	that	SCONJ
ejpam-4859	557	26	if	if	SCONJ
ejpam-4859	557	27	each	each	DET
ejpam-4859	557	28	additional	additional	ADJ
ejpam-4859	557	29	complex	complex	NOUN
ejpam-4859	557	30	is	be	AUX
ejpam-4859	557	31	not	not	PART
ejpam-4859	557	32	equal	equal	ADJ
ejpam-4859	557	33	to	to	ADP
ejpam-4859	557	34	any	any	DET
ejpam-4859	557	35	element	element	NOUN
ejpam-4859	557	36	of	of	ADP
ejpam-4859	557	37	t	t	PROPN
ejpam-4859	557	38	,	,	PUNCT
ejpam-4859	557	39	we	we	PRON
ejpam-4859	557	40	have	have	AUX
ejpam-4859	557	41	t∗	t∗	NOUN
ejpam-4859	557	42	=	=	SYM
ejpam-4859	557	43	n∗−n∗	n∗−n∗	NOUN
ejpam-4859	557	44	r	r	NOUN
ejpam-4859	557	45	in	in	ADP
ejpam-4859	557	46	star	star	NOUN
ejpam-4859	557	47	-	-	PUNCT
ejpam-4859	557	48	rvm	rvm	PROPN
ejpam-4859	557	49	transform	transform	NOUN
ejpam-4859	557	50	.	.	PUNCT
ejpam-4859	557	51	suppose	suppose	VERB
ejpam-4859	557	52	there	there	PRON
ejpam-4859	557	53	exists	exist	VERB
ejpam-4859	557	54	an	an	DET
ejpam-4859	557	55	additional	additional	ADJ
ejpam-4859	557	56	complex	complex	NOUN
ejpam-4859	557	57	that	that	PRON
ejpam-4859	557	58	is	be	AUX
ejpam-4859	557	59	equal	equal	ADJ
ejpam-4859	557	60	to	to	ADP
ejpam-4859	557	61	an	an	DET
ejpam-4859	557	62	element	element	NOUN
ejpam-4859	557	63	of	of	ADP
ejpam-4859	557	64	t	t	PROPN
ejpam-4859	557	65	.	.	PUNCT
ejpam-4859	558	1	let	let	VERB
ejpam-4859	558	2	y	y	PRON
ejpam-4859	558	3	be	be	AUX
ejpam-4859	558	4	the	the	DET
ejpam-4859	558	5	number	number	NOUN
ejpam-4859	558	6	additional	additional	ADJ
ejpam-4859	558	7	complexes	complex	NOUN
ejpam-4859	558	8	in	in	ADP
ejpam-4859	558	9	this	this	DET
ejpam-4859	558	10	case	case	NOUN
ejpam-4859	558	11	that	that	PRON
ejpam-4859	558	12	is	be	AUX
ejpam-4859	558	13	equal	equal	ADJ
ejpam-4859	558	14	to	to	ADP
ejpam-4859	558	15	any	any	DET
ejpam-4859	558	16	element	element	NOUN
ejpam-4859	558	17	of	of	ADP
ejpam-4859	558	18	t	t	PROPN
ejpam-4859	558	19	and	and	CCONJ
ejpam-4859	558	20	z	z	PROPN
ejpam-4859	558	21	is	be	AUX
ejpam-4859	558	22	the	the	DET
ejpam-4859	558	23	number	number	NOUN
ejpam-4859	558	24	of	of	ADP
ejpam-4859	558	25	other	other	ADJ
ejpam-4859	558	26	additional	additional	ADJ
ejpam-4859	558	27	complexes	complex	NOUN
ejpam-4859	558	28	.	.	PUNCT
ejpam-4859	559	1	this	this	PRON
ejpam-4859	559	2	implies	imply	VERB
ejpam-4859	559	3	that	that	SCONJ
ejpam-4859	559	4	n∗	n∗	PROPN
ejpam-4859	559	5	=	=	SYM
ejpam-4859	559	6	n+	n+	PROPN
ejpam-4859	559	7	z	z	NUM
ejpam-4859	559	8	,	,	PUNCT
ejpam-4859	559	9	n∗	n∗	PROPN
ejpam-4859	559	10	r	r	NOUN
ejpam-4859	559	11	=	=	PUNCT
ejpam-4859	559	12	nr	nr	PROPN
ejpam-4859	559	13	+	+	NOUN
ejpam-4859	559	14	z	z	PROPN
ejpam-4859	560	1	+	+	CCONJ
ejpam-4859	560	2	y	y	PROPN
ejpam-4859	560	3	and	and	CCONJ
ejpam-4859	560	4	t∗	t∗	NOUN
ejpam-4859	560	5	=	=	PUNCT
ejpam-4859	561	1	t−	t−	PROPN
ejpam-4859	561	2	y.	y.	NOUN
ejpam-4859	561	3	now	now	ADV
ejpam-4859	561	4	,	,	PUNCT
ejpam-4859	561	5	n∗	n∗	PROPN
ejpam-4859	561	6	−	−	PROPN
ejpam-4859	562	1	n∗	n∗	PROPN
ejpam-4859	562	2	r	r	NOUN
ejpam-4859	562	3	=	=	SYM
ejpam-4859	562	4	(	(	PUNCT
ejpam-4859	562	5	n+	n+	X
ejpam-4859	562	6	z)−	z)−	PROPN
ejpam-4859	562	7	(	(	PUNCT
ejpam-4859	562	8	nr	nr	PROPN
ejpam-4859	562	9	+	+	NOUN
ejpam-4859	562	10	z	z	PROPN
ejpam-4859	562	11	+	+	NUM
ejpam-4859	562	12	y	y	NOUN
ejpam-4859	562	13	)	)	PUNCT
ejpam-4859	562	14	=	=	PUNCT
ejpam-4859	563	1	n−	n−	NOUN
ejpam-4859	563	2	nr	nr	NOUN
ejpam-4859	563	3	−	−	PROPN
ejpam-4859	564	1	y	y	NOUN
ejpam-4859	564	2	=	=	PUNCT
ejpam-4859	565	1	[	[	X
ejpam-4859	565	2	(	(	PUNCT
ejpam-4859	565	3	n−	n−	NOUN
ejpam-4859	565	4	nr)−	nr)−	NOUN
ejpam-4859	565	5	t	t	X
ejpam-4859	565	6	]	]	X
ejpam-4859	565	7	+	+	CCONJ
ejpam-4859	565	8	t−	t−	PROPN
ejpam-4859	565	9	y	y	PROPN
ejpam-4859	565	10	=	=	SYM
ejpam-4859	565	11	t∗.	t∗.	PROPN
ejpam-4859	565	12	3.3.5	3.3.5	PROPN
ejpam-4859	565	13	.	.	PUNCT
ejpam-4859	566	1	equality	equality	NOUN
ejpam-4859	566	2	of	of	ADP
ejpam-4859	566	3	rank	rank	NOUN
ejpam-4859	566	4	we	we	PRON
ejpam-4859	566	5	show	show	VERB
ejpam-4859	566	6	that	that	SCONJ
ejpam-4859	566	7	the	the	DET
ejpam-4859	566	8	dimension	dimension	NOUN
ejpam-4859	566	9	of	of	ADP
ejpam-4859	566	10	the	the	DET
ejpam-4859	566	11	stoichiometric	stoichiometric	ADJ
ejpam-4859	566	12	subspace	subspace	NOUN
ejpam-4859	566	13	of	of	ADP
ejpam-4859	566	14	the	the	DET
ejpam-4859	566	15	original	original	ADJ
ejpam-4859	566	16	network	network	NOUN
ejpam-4859	566	17	and	and	CCONJ
ejpam-4859	566	18	its	its	PRON
ejpam-4859	566	19	star	star	NOUN
ejpam-4859	566	20	-	-	PUNCT
ejpam-4859	566	21	rvm	rvm	PROPN
ejpam-4859	566	22	transform	transform	NOUN
ejpam-4859	566	23	are	be	AUX
ejpam-4859	566	24	equal	equal	ADJ
ejpam-4859	566	25	.	.	PUNCT
ejpam-4859	567	1	d.	d.	PROPN
ejpam-4859	567	2	magpantay	magpantay	PROPN
ejpam-4859	567	3	/	/	SYM
ejpam-4859	567	4	eur	eur	PROPN
ejpam-4859	567	5	.	.	PUNCT
ejpam-4859	568	1	j.	j.	PROPN
ejpam-4859	568	2	pure	pure	PROPN
ejpam-4859	568	3	appl	appl	PROPN
ejpam-4859	568	4	.	.	PROPN
ejpam-4859	568	5	math	math	PROPN
ejpam-4859	568	6	,	,	PUNCT
ejpam-4859	568	7	16	16	NUM
ejpam-4859	568	8	(	(	PUNCT
ejpam-4859	568	9	4	4	NUM
ejpam-4859	568	10	)	)	PUNCT
ejpam-4859	568	11	(	(	PUNCT
ejpam-4859	568	12	2023	2023	NUM
ejpam-4859	568	13	)	)	PUNCT
ejpam-4859	568	14	,	,	PUNCT
ejpam-4859	568	15	2557	2557	NUM
ejpam-4859	568	16	-	-	SYM
ejpam-4859	568	17	2580	2580	NUM
ejpam-4859	568	18	2575	2575	NUM
ejpam-4859	568	19	proposition	proposition	NOUN
ejpam-4859	568	20	11	11	NUM
ejpam-4859	568	21	.	.	PUNCT
ejpam-4859	569	1	if	if	SCONJ
ejpam-4859	569	2	(	(	PUNCT
ejpam-4859	569	3	n	n	X
ejpam-4859	569	4	,	,	PUNCT
ejpam-4859	569	5	k	k	NOUN
ejpam-4859	569	6	)	)	PUNCT
ejpam-4859	569	7	is	be	AUX
ejpam-4859	569	8	a	a	DET
ejpam-4859	569	9	poly	poly	ADJ
ejpam-4859	569	10	-	-	PUNCT
ejpam-4859	569	11	pl	pl	NOUN
ejpam-4859	569	12	system	system	NOUN
ejpam-4859	569	13	and	and	CCONJ
ejpam-4859	569	14	(	(	PUNCT
ejpam-4859	569	15	n	n	CCONJ
ejpam-4859	569	16	∗,k∗	∗,k∗	ADJ
ejpam-4859	569	17	)	)	PUNCT
ejpam-4859	569	18	its	its	PRON
ejpam-4859	569	19	star	star	NOUN
ejpam-4859	569	20	-	-	PUNCT
ejpam-4859	569	21	rvm	rvm	PROPN
ejpam-4859	569	22	transform	transform	NOUN
ejpam-4859	569	23	then	then	ADV
ejpam-4859	569	24	s	s	VERB
ejpam-4859	569	25	=	=	PUNCT
ejpam-4859	569	26	s∗.	s∗.	ADJ
ejpam-4859	569	27	proof	proof	NOUN
ejpam-4859	569	28	.	.	PUNCT
ejpam-4859	570	1	recall	recall	VERB
ejpam-4859	570	2	that	that	PRON
ejpam-4859	570	3	s	s	VERB
ejpam-4859	571	1	=	=	PUNCT
ejpam-4859	571	2	span{y′−y	span{y′−y	NOUN
ejpam-4859	571	3	∈	∈	NOUN
ejpam-4859	571	4	rs	rs	NOUN
ejpam-4859	571	5	:	:	PUNCT
ejpam-4859	571	6	y	y	PROPN
ejpam-4859	571	7	→	→	SYM
ejpam-4859	571	8	y′	y′	NOUN
ejpam-4859	571	9	∈	∈	PROPN
ejpam-4859	571	10	r	r	NOUN
ejpam-4859	571	11	}	}	PUNCT
ejpam-4859	571	12	is	be	AUX
ejpam-4859	571	13	the	the	DET
ejpam-4859	571	14	stoichiometric	stoichiometric	ADJ
ejpam-4859	571	15	subspace	subspace	NOUN
ejpam-4859	571	16	of	of	ADP
ejpam-4859	571	17	n	n	PROPN
ejpam-4859	571	18	and	and	CCONJ
ejpam-4859	571	19	s	s	NOUN
ejpam-4859	571	20	=	=	NOUN
ejpam-4859	571	21	dim	dim	ADJ
ejpam-4859	571	22	s.	s.	PROPN
ejpam-4859	571	23	observe	observe	VERB
ejpam-4859	571	24	that	that	SCONJ
ejpam-4859	571	25	for	for	ADP
ejpam-4859	571	26	a	a	DET
ejpam-4859	571	27	reaction	reaction	NOUN
ejpam-4859	571	28	y	y	PROPN
ejpam-4859	571	29	→	→	SYM
ejpam-4859	571	30	y′	y′	NOUN
ejpam-4859	571	31	in	in	ADP
ejpam-4859	571	32	n	n	PROPN
ejpam-4859	571	33	,	,	PUNCT
ejpam-4859	571	34	each	each	DET
ejpam-4859	571	35	reaction	reaction	NOUN
ejpam-4859	571	36	or	or	CCONJ
ejpam-4859	571	37	complex	complex	NOUN
ejpam-4859	571	38	in	in	ADP
ejpam-4859	571	39	n	n	ADP
ejpam-4859	571	40	∗	∗	NOUN
ejpam-4859	571	41	by	by	ADP
ejpam-4859	571	42	star	star	NOUN
ejpam-4859	571	43	-	-	PUNCT
ejpam-4859	571	44	rvm	rvm	PROPN
ejpam-4859	571	45	method	method	NOUN
ejpam-4859	571	46	is	be	AUX
ejpam-4859	571	47	in	in	ADP
ejpam-4859	571	48	the	the	DET
ejpam-4859	571	49	form	form	NOUN
ejpam-4859	571	50	:	:	PUNCT
ejpam-4859	571	51	y	y	PROPN
ejpam-4859	571	52	→	→	SYM
ejpam-4859	571	53	y′	y′	NOUN
ejpam-4859	571	54	→	→	SYM
ejpam-4859	571	55	y′	y′	NOUN
ejpam-4859	572	1	+	+	CCONJ
ejpam-4859	572	2	(	(	PUNCT
ejpam-4859	572	3	y′	y′	NUM
ejpam-4859	572	4	−	−	PROPN
ejpam-4859	572	5	y	y	PROPN
ejpam-4859	572	6	)	)	PUNCT
ejpam-4859	572	7	→	→	SYM
ejpam-4859	572	8	y′	y′	NOUN
ejpam-4859	572	9	+	+	SYM
ejpam-4859	572	10	2(y′	2(y′	NUM
ejpam-4859	572	11	−	−	PROPN
ejpam-4859	572	12	y	y	NOUN
ejpam-4859	572	13	)	)	PUNCT
ejpam-4859	572	14	→	→	PUNCT
ejpam-4859	572	15	.	.	PUNCT
ejpam-4859	572	16	.	.	PUNCT
ejpam-4859	572	17	.	.	PUNCT
ejpam-4859	573	1	or	or	CCONJ
ejpam-4859	573	2	·	·	PUNCT
ejpam-4859	573	3	·	·	PUNCT
ejpam-4859	573	4	·	·	PUNCT
ejpam-4859	573	5	→	→	PUNCT
ejpam-4859	573	6	y	y	PROPN
ejpam-4859	573	7	+	+	CCONJ
ejpam-4859	573	8	2(y	2(y	NUM
ejpam-4859	573	9	−	−	NUM
ejpam-4859	573	10	y′	y′	NUM
ejpam-4859	573	11	)	)	PUNCT
ejpam-4859	573	12	→	→	SYM
ejpam-4859	573	13	y	y	PROPN
ejpam-4859	574	1	+	+	CCONJ
ejpam-4859	574	2	(	(	PUNCT
ejpam-4859	574	3	y	y	PROPN
ejpam-4859	574	4	−	−	NOUN
ejpam-4859	574	5	y′	y′	NUM
ejpam-4859	574	6	)	)	PUNCT
ejpam-4859	574	7	→	→	SYM
ejpam-4859	574	8	y	y	PROPN
ejpam-4859	574	9	→	→	SYM
ejpam-4859	574	10	y′	y′	NOUN
ejpam-4859	574	11	with	with	ADP
ejpam-4859	574	12	this	this	PRON
ejpam-4859	574	13	,	,	PUNCT
ejpam-4859	574	14	a	a	DET
ejpam-4859	574	15	reaction	reaction	NOUN
ejpam-4859	574	16	vector	vector	NOUN
ejpam-4859	574	17	of	of	ADP
ejpam-4859	574	18	n	n	PROPN
ejpam-4859	574	19	∗	∗	NOUN
ejpam-4859	574	20	is	be	AUX
ejpam-4859	574	21	in	in	ADP
ejpam-4859	574	22	the	the	DET
ejpam-4859	574	23	form	form	NOUN
ejpam-4859	574	24	y′	y′	ADV
ejpam-4859	574	25	−	−	PROPN
ejpam-4859	575	1	y.	y.	NOUN
ejpam-4859	575	2	this	this	PRON
ejpam-4859	575	3	implies	imply	VERB
ejpam-4859	575	4	that	that	SCONJ
ejpam-4859	575	5	the	the	DET
ejpam-4859	575	6	stoichiometric	stoichiometric	ADJ
ejpam-4859	575	7	subspace	subspace	NOUN
ejpam-4859	575	8	of	of	ADP
ejpam-4859	575	9	n	n	PROPN
ejpam-4859	575	10	∗	∗	NOUN
ejpam-4859	575	11	is	be	AUX
ejpam-4859	576	1	s∗	s∗	PROPN
ejpam-4859	576	2	=	=	PUNCT
ejpam-4859	576	3	span{y′	span{y′	PROPN
ejpam-4859	576	4	−	−	PROPN
ejpam-4859	576	5	y	y	PROPN
ejpam-4859	576	6	∈	∈	PROPN
ejpam-4859	576	7	rs	rs	NOUN
ejpam-4859	576	8	:	:	PUNCT
ejpam-4859	576	9	y	y	PROPN
ejpam-4859	576	10	→	→	SYM
ejpam-4859	576	11	y′	y′	NOUN
ejpam-4859	576	12	∈	∈	PROPN
ejpam-4859	576	13	r	r	NOUN
ejpam-4859	576	14	}	}	PUNCT
ejpam-4859	576	15	.	.	PUNCT
ejpam-4859	577	1	hence	hence	ADV
ejpam-4859	577	2	,	,	PUNCT
ejpam-4859	577	3	s∗	s∗	PROPN
ejpam-4859	577	4	=	=	SYM
ejpam-4859	577	5	s	s	PROPN
ejpam-4859	577	6	and	and	CCONJ
ejpam-4859	577	7	s∗	s∗	PROPN
ejpam-4859	577	8	=	=	PUNCT
ejpam-4859	577	9	s.	s.	PROPN
ejpam-4859	577	10	3.3.6	3.3.6	PROPN
ejpam-4859	577	11	.	.	PUNCT
ejpam-4859	578	1	terminality	terminality	NOUN
ejpam-4859	578	2	bounded	bound	VERB
ejpam-4859	578	3	by	by	ADP
ejpam-4859	578	4	deficiency	deficiency	NOUN
ejpam-4859	578	5	(	(	PUNCT
ejpam-4859	578	6	tbd	tbd	NOUN
ejpam-4859	578	7	)	)	PUNCT
ejpam-4859	578	8	and	and	CCONJ
ejpam-4859	578	9	sufficient	sufficient	ADJ
ejpam-4859	578	10	reactant	reactant	NOUN
ejpam-4859	578	11	deficiency	deficiency	NOUN
ejpam-4859	578	12	(	(	PUNCT
ejpam-4859	578	13	srd	srd	NOUN
ejpam-4859	578	14	)	)	PUNCT
ejpam-4859	578	15	another	another	DET
ejpam-4859	578	16	two	two	NUM
ejpam-4859	578	17	properties	property	NOUN
ejpam-4859	578	18	conserved	conserve	VERB
ejpam-4859	578	19	under	under	ADP
ejpam-4859	578	20	star	star	NOUN
ejpam-4859	578	21	-	-	PUNCT
ejpam-4859	578	22	rvm	rvm	PROPN
ejpam-4859	578	23	method	method	NOUN
ejpam-4859	578	24	are	be	AUX
ejpam-4859	578	25	the	the	DET
ejpam-4859	578	26	tbd	tbd	NOUN
ejpam-4859	578	27	and	and	CCONJ
ejpam-4859	578	28	srd	srd	NOUN
ejpam-4859	578	29	as	as	SCONJ
ejpam-4859	578	30	discussed	discuss	VERB
ejpam-4859	578	31	in	in	ADP
ejpam-4859	578	32	the	the	DET
ejpam-4859	578	33	next	next	ADJ
ejpam-4859	578	34	propositions	proposition	NOUN
ejpam-4859	578	35	and	and	CCONJ
ejpam-4859	578	36	corollaries	corollary	NOUN
ejpam-4859	578	37	.	.	PUNCT
ejpam-4859	579	1	proposition	proposition	NOUN
ejpam-4859	579	2	12	12	NUM
ejpam-4859	579	3	.	.	PUNCT
ejpam-4859	580	1	let	let	AUX
ejpam-4859	580	2	(	(	PUNCT
ejpam-4859	580	3	n	n	X
ejpam-4859	580	4	,	,	PUNCT
ejpam-4859	580	5	k	k	NOUN
ejpam-4859	580	6	)	)	PUNCT
ejpam-4859	580	7	be	be	AUX
ejpam-4859	580	8	a	a	DET
ejpam-4859	580	9	poly	poly	ADJ
ejpam-4859	580	10	-	-	PUNCT
ejpam-4859	580	11	pl	pl	NOUN
ejpam-4859	580	12	system	system	NOUN
ejpam-4859	580	13	and	and	CCONJ
ejpam-4859	580	14	(	(	PUNCT
ejpam-4859	580	15	n	n	CCONJ
ejpam-4859	580	16	∗,k∗	∗,k∗	ADJ
ejpam-4859	580	17	)	)	PUNCT
ejpam-4859	580	18	be	be	AUX
ejpam-4859	580	19	its	its	PRON
ejpam-4859	580	20	star	star	NOUN
ejpam-4859	580	21	-	-	PUNCT
ejpam-4859	580	22	rvm	rvm	NOUN
ejpam-4859	580	23	transform	transform	NOUN
ejpam-4859	580	24	.	.	PUNCT
ejpam-4859	581	1	if	if	SCONJ
ejpam-4859	581	2	n	n	NOUN
ejpam-4859	581	3	is	be	AUX
ejpam-4859	581	4	of	of	ADP
ejpam-4859	581	5	tbd	tbd	NOUN
ejpam-4859	581	6	type	type	NOUN
ejpam-4859	581	7	so	so	ADV
ejpam-4859	581	8	is	be	AUX
ejpam-4859	581	9	n	n	PRON
ejpam-4859	581	10	∗.	∗.	ADJ
ejpam-4859	581	11	proof	proof	NOUN
ejpam-4859	581	12	.	.	PUNCT
ejpam-4859	582	1	let	let	AUX
ejpam-4859	582	2	(	(	PUNCT
ejpam-4859	582	3	n	n	X
ejpam-4859	582	4	,	,	PUNCT
ejpam-4859	582	5	k	k	NOUN
ejpam-4859	582	6	)	)	PUNCT
ejpam-4859	582	7	be	be	AUX
ejpam-4859	582	8	a	a	DET
ejpam-4859	582	9	poly	poly	ADJ
ejpam-4859	582	10	-	-	PUNCT
ejpam-4859	582	11	pl	pl	NOUN
ejpam-4859	582	12	systems	system	NOUN
ejpam-4859	582	13	and	and	CCONJ
ejpam-4859	582	14	(	(	PUNCT
ejpam-4859	582	15	n	n	CCONJ
ejpam-4859	582	16	∗,k∗	∗,k∗	ADJ
ejpam-4859	582	17	)	)	PUNCT
ejpam-4859	582	18	be	be	AUX
ejpam-4859	582	19	its	its	PRON
ejpam-4859	582	20	star	star	NOUN
ejpam-4859	582	21	-	-	PUNCT
ejpam-4859	582	22	rvm	rvm	PROPN
ejpam-4859	582	23	transform	transform	NOUN
ejpam-4859	582	24	.	.	PUNCT
ejpam-4859	583	1	suppose	suppose	VERB
ejpam-4859	583	2	n	n	PRON
ejpam-4859	583	3	is	be	AUX
ejpam-4859	583	4	of	of	ADP
ejpam-4859	583	5	tbd	tbd	NOUN
ejpam-4859	583	6	type	type	NOUN
ejpam-4859	583	7	.	.	PUNCT
ejpam-4859	584	1	this	this	PRON
ejpam-4859	584	2	means	mean	VERB
ejpam-4859	584	3	that	that	SCONJ
ejpam-4859	584	4	t−	t−	PROPN
ejpam-4859	584	5	ℓ	ℓ	PROPN
ejpam-4859	584	6	≤	≤	PROPN
ejpam-4859	584	7	δ	δ	PROPN
ejpam-4859	584	8	=	=	SYM
ejpam-4859	584	9	n−	n−	PROPN
ejpam-4859	584	10	ℓ−	ℓ−	PROPN
ejpam-4859	584	11	s.	s.	PROPN
ejpam-4859	584	12	hence	hence	ADV
ejpam-4859	584	13	,	,	PUNCT
ejpam-4859	584	14	t	t	PROPN
ejpam-4859	584	15	≤	≤	NUM
ejpam-4859	584	16	n−	n−	NOUN
ejpam-4859	584	17	s.	s.	PROPN
ejpam-4859	584	18	with	with	ADP
ejpam-4859	584	19	this	this	PRON
ejpam-4859	584	20	,	,	PUNCT
ejpam-4859	584	21	we	we	PRON
ejpam-4859	584	22	have	have	VERB
ejpam-4859	584	23	to	to	PART
ejpam-4859	584	24	show	show	VERB
ejpam-4859	584	25	that	that	DET
ejpam-4859	584	26	t∗	t∗	NOUN
ejpam-4859	584	27	≤	≤	PUNCT
ejpam-4859	584	28	n∗	n∗	NOUN
ejpam-4859	584	29	−	−	PROPN
ejpam-4859	585	1	s∗.	s∗.	ADJ
ejpam-4859	585	2	we	we	PRON
ejpam-4859	585	3	present	present	VERB
ejpam-4859	585	4	the	the	DET
ejpam-4859	585	5	proof	proof	NOUN
ejpam-4859	585	6	in	in	ADP
ejpam-4859	585	7	two	two	NUM
ejpam-4859	585	8	parts	part	NOUN
ejpam-4859	585	9	.	.	PUNCT
ejpam-4859	586	1	i.	i.	PROPN
ejpam-4859	586	2	suppose	suppose	VERB
ejpam-4859	586	3	t∗	t∗	NOUN
ejpam-4859	586	4	≤	≤	ADJ
ejpam-4859	586	5	t.	t.	NOUN
ejpam-4859	586	6	recall	recall	NOUN
ejpam-4859	586	7	that	that	DET
ejpam-4859	586	8	,	,	PUNCT
ejpam-4859	586	9	n	n	PRON
ejpam-4859	586	10	≤	≤	NOUN
ejpam-4859	586	11	n∗	n∗	NOUN
ejpam-4859	586	12	and	and	CCONJ
ejpam-4859	586	13	s	s	NOUN
ejpam-4859	586	14	=	=	NOUN
ejpam-4859	586	15	s∗.	s∗.	INTJ
ejpam-4859	586	16	this	this	PRON
ejpam-4859	586	17	implies	imply	VERB
ejpam-4859	586	18	that	that	SCONJ
ejpam-4859	586	19	n−	n−	PROPN
ejpam-4859	586	20	s	s	PART
ejpam-4859	586	21	≤	≤	NUM
ejpam-4859	586	22	n∗	n∗	NOUN
ejpam-4859	586	23	−	−	PROPN
ejpam-4859	586	24	s∗.	s∗.	ADJ
ejpam-4859	586	25	hence	hence	ADV
ejpam-4859	586	26	t∗	t∗	VERB
ejpam-4859	586	27	≤	≤	NUM
ejpam-4859	586	28	t	t	NOUN
ejpam-4859	586	29	≤	≤	NUM
ejpam-4859	586	30	n−	n−	PROPN
ejpam-4859	586	31	s	s	PART
ejpam-4859	586	32	≤	≤	NUM
ejpam-4859	586	33	n∗	n∗	PROPN
ejpam-4859	586	34	−	−	PROPN
ejpam-4859	586	35	s∗.	s∗.	PROPN
ejpam-4859	586	36	ii	ii	PROPN
ejpam-4859	586	37	.	.	PUNCT
ejpam-4859	586	38	suppose	suppose	VERB
ejpam-4859	586	39	t∗	t∗	NOUN
ejpam-4859	586	40	>	>	PUNCT
ejpam-4859	586	41	t.	t.	PROPN
ejpam-4859	587	1	this	this	PRON
ejpam-4859	587	2	means	mean	VERB
ejpam-4859	587	3	that	that	SCONJ
ejpam-4859	587	4	n∗	n∗	PROPN
ejpam-4859	587	5	>	>	X
ejpam-4859	587	6	n	n	PROPN
ejpam-4859	587	7	and	and	CCONJ
ejpam-4859	587	8	(	(	PUNCT
ejpam-4859	587	9	t∗	t∗	PROPN
ejpam-4859	587	10	−	−	PROPN
ejpam-4859	587	11	t	t	PROPN
ejpam-4859	587	12	)	)	PUNCT
ejpam-4859	587	13	,	,	PUNCT
ejpam-4859	587	14	(	(	PUNCT
ejpam-4859	587	15	n∗	n∗	PROPN
ejpam-4859	587	16	−	−	PROPN
ejpam-4859	587	17	n	n	CCONJ
ejpam-4859	587	18	)	)	PUNCT
ejpam-4859	587	19	∈	∈	PROPN
ejpam-4859	587	20	z+	z+	NUM
ejpam-4859	587	21	.	.	PUNCT
ejpam-4859	588	1	d.	d.	PROPN
ejpam-4859	588	2	magpantay	magpantay	PROPN
ejpam-4859	588	3	/	/	SYM
ejpam-4859	588	4	eur	eur	PROPN
ejpam-4859	588	5	.	.	PUNCT
ejpam-4859	589	1	j.	j.	PROPN
ejpam-4859	589	2	pure	pure	PROPN
ejpam-4859	589	3	appl	appl	PROPN
ejpam-4859	589	4	.	.	PROPN
ejpam-4859	589	5	math	math	PROPN
ejpam-4859	589	6	,	,	PUNCT
ejpam-4859	589	7	16	16	NUM
ejpam-4859	589	8	(	(	PUNCT
ejpam-4859	589	9	4	4	NUM
ejpam-4859	589	10	)	)	PUNCT
ejpam-4859	589	11	(	(	PUNCT
ejpam-4859	589	12	2023	2023	NUM
ejpam-4859	589	13	)	)	PUNCT
ejpam-4859	589	14	,	,	PUNCT
ejpam-4859	589	15	2557	2557	NUM
ejpam-4859	589	16	-	-	SYM
ejpam-4859	589	17	2580	2580	NUM
ejpam-4859	589	18	2576	2576	NUM
ejpam-4859	589	19	by	by	ADP
ejpam-4859	589	20	the	the	DET
ejpam-4859	589	21	construction	construction	NOUN
ejpam-4859	589	22	of	of	ADP
ejpam-4859	589	23	n∗	n∗	PROPN
ejpam-4859	589	24	using	use	VERB
ejpam-4859	589	25	star	star	NOUN
ejpam-4859	589	26	-	-	PUNCT
ejpam-4859	589	27	rvm	rvm	PROPN
ejpam-4859	589	28	method	method	NOUN
ejpam-4859	589	29	,	,	PUNCT
ejpam-4859	589	30	observe	observe	VERB
ejpam-4859	589	31	that	that	SCONJ
ejpam-4859	589	32	t∗−t	t∗−t	NOUN
ejpam-4859	589	33	=	=	PUNCT
ejpam-4859	589	34	|{{y∗	|{{y∗	NUM
ejpam-4859	589	35	}	}	PUNCT
ejpam-4859	589	36	:	:	PUNCT
ejpam-4859	589	37	y∗	y∗	ADV
ejpam-4859	589	38	is	be	AUX
ejpam-4859	589	39	an	an	DET
ejpam-4859	589	40	additional	additional	ADJ
ejpam-4859	589	41	complex	complex	NOUN
ejpam-4859	589	42	such	such	ADJ
ejpam-4859	589	43	that	that	SCONJ
ejpam-4859	589	44	d+(y∗	d+(y∗	PROPN
ejpam-4859	589	45	)	)	PUNCT
ejpam-4859	590	1	=	=	SYM
ejpam-4859	590	2	0}|	0}|	NUM
ejpam-4859	590	3	and	and	CCONJ
ejpam-4859	590	4	n∗−n	n∗−n	X
ejpam-4859	590	5	is	be	AUX
ejpam-4859	590	6	the	the	DET
ejpam-4859	590	7	number	number	NOUN
ejpam-4859	590	8	of	of	ADP
ejpam-4859	590	9	additional	additional	ADJ
ejpam-4859	590	10	complexes	complex	NOUN
ejpam-4859	590	11	not	not	PART
ejpam-4859	590	12	equal	equal	ADJ
ejpam-4859	590	13	to	to	ADP
ejpam-4859	590	14	any	any	DET
ejpam-4859	590	15	original	original	ADJ
ejpam-4859	590	16	or	or	CCONJ
ejpam-4859	590	17	other	other	ADJ
ejpam-4859	590	18	additional	additional	ADJ
ejpam-4859	590	19	complex	complex	NOUN
ejpam-4859	590	20	.	.	PUNCT
ejpam-4859	591	1	note	note	VERB
ejpam-4859	591	2	that	that	SCONJ
ejpam-4859	591	3	,	,	PUNCT
ejpam-4859	591	4	by	by	ADP
ejpam-4859	591	5	the	the	DET
ejpam-4859	591	6	fact	fact	NOUN
ejpam-4859	591	7	that	that	SCONJ
ejpam-4859	591	8	y∗	y∗	PROPN
ejpam-4859	591	9	is	be	AUX
ejpam-4859	591	10	an	an	DET
ejpam-4859	591	11	additional	additional	ADJ
ejpam-4859	591	12	complex	complex	NOUN
ejpam-4859	591	13	such	such	ADJ
ejpam-4859	591	14	that	that	SCONJ
ejpam-4859	591	15	d+(y∗	d+(y∗	PROPN
ejpam-4859	591	16	)	)	PUNCT
ejpam-4859	592	1	=	=	SYM
ejpam-4859	592	2	0	0	NUM
ejpam-4859	592	3	,	,	PUNCT
ejpam-4859	592	4	all	all	DET
ejpam-4859	592	5	such	such	ADJ
ejpam-4859	592	6	v∗	v∗	PROPN
ejpam-4859	592	7	’s	’s	PART
ejpam-4859	592	8	are	be	AUX
ejpam-4859	592	9	unique	unique	ADJ
ejpam-4859	592	10	.	.	PUNCT
ejpam-4859	593	1	hence	hence	ADV
ejpam-4859	593	2	,	,	PUNCT
ejpam-4859	593	3	t∗	t∗	NOUN
ejpam-4859	593	4	−	−	NOUN
ejpam-4859	593	5	t	t	NOUN
ejpam-4859	593	6	≤	≤	NUM
ejpam-4859	593	7	n∗	n∗	PROPN
ejpam-4859	593	8	−	−	PROPN
ejpam-4859	593	9	n.	n.	PROPN
ejpam-4859	593	10	thus	thus	ADV
ejpam-4859	593	11	,	,	PUNCT
ejpam-4859	593	12	t	t	PROPN
ejpam-4859	593	13	≤	≤	NUM
ejpam-4859	593	14	n−	n−	PROPN
ejpam-4859	593	15	s	s	PART
ejpam-4859	593	16	t+	t+	PUNCT
ejpam-4859	593	17	(	(	PUNCT
ejpam-4859	593	18	t∗	t∗	NOUN
ejpam-4859	593	19	−	−	PROPN
ejpam-4859	593	20	t	t	PROPN
ejpam-4859	593	21	)	)	PUNCT
ejpam-4859	593	22	≤	≤	NOUN
ejpam-4859	593	23	n−	n−	NOUN
ejpam-4859	593	24	s+	s+	PUNCT
ejpam-4859	593	25	(	(	PUNCT
ejpam-4859	593	26	n∗	n∗	PROPN
ejpam-4859	593	27	−	−	PROPN
ejpam-4859	593	28	n	n	CCONJ
ejpam-4859	593	29	)	)	PUNCT
ejpam-4859	593	30	t∗	t∗	NOUN
ejpam-4859	593	31	≤	≤	PUNCT
ejpam-4859	593	32	n∗	n∗	PROPN
ejpam-4859	593	33	−	−	PROPN
ejpam-4859	593	34	s	s	PART
ejpam-4859	593	35	t∗	t∗	NOUN
ejpam-4859	593	36	≤	≤	PUNCT
ejpam-4859	593	37	n∗	n∗	NOUN
ejpam-4859	593	38	−	−	PROPN
ejpam-4859	594	1	s∗.	s∗.	ADJ
ejpam-4859	594	2	therefore	therefore	ADV
ejpam-4859	594	3	,	,	PUNCT
ejpam-4859	594	4	t∗	t∗	NOUN
ejpam-4859	594	5	−	−	NOUN
ejpam-4859	594	6	ℓ∗	ℓ∗	PROPN
ejpam-4859	594	7	≤	≤	PUNCT
ejpam-4859	594	8	n∗	n∗	PROPN
ejpam-4859	594	9	−	−	PROPN
ejpam-4859	595	1	ℓ∗	ℓ∗	PROPN
ejpam-4859	596	1	−	−	PROPN
ejpam-4859	596	2	s∗	s∗	PROPN
ejpam-4859	596	3	=	=	SYM
ejpam-4859	596	4	δ∗	δ∗	NOUN
ejpam-4859	596	5	implying	imply	VERB
ejpam-4859	596	6	that	that	SCONJ
ejpam-4859	596	7	n	n	NOUN
ejpam-4859	596	8	∗	∗	NOUN
ejpam-4859	596	9	is	be	AUX
ejpam-4859	596	10	also	also	ADV
ejpam-4859	596	11	of	of	ADP
ejpam-4859	596	12	tbd	tbd	NOUN
ejpam-4859	596	13	type	type	NOUN
ejpam-4859	596	14	.	.	PUNCT
ejpam-4859	597	1	we	we	PRON
ejpam-4859	597	2	recall	recall	VERB
ejpam-4859	597	3	that	that	SCONJ
ejpam-4859	597	4	a	a	DET
ejpam-4859	597	5	tbd	tbd	NOUN
ejpam-4859	597	6	network	network	NOUN
ejpam-4859	597	7	is	be	AUX
ejpam-4859	597	8	srd	srd	NOUN
ejpam-4859	597	9	.	.	PUNCT
ejpam-4859	598	1	this	this	PRON
ejpam-4859	598	2	means	mean	VERB
ejpam-4859	598	3	that	that	SCONJ
ejpam-4859	598	4	srd	srd	NOUN
ejpam-4859	598	5	property	property	NOUN
ejpam-4859	598	6	should	should	AUX
ejpam-4859	598	7	also	also	ADV
ejpam-4859	598	8	be	be	AUX
ejpam-4859	598	9	conserved	conserve	VERB
ejpam-4859	598	10	after	after	ADP
ejpam-4859	598	11	the	the	DET
ejpam-4859	598	12	method	method	NOUN
ejpam-4859	598	13	.	.	PUNCT
ejpam-4859	599	1	this	this	PRON
ejpam-4859	599	2	was	be	AUX
ejpam-4859	599	3	reflected	reflect	VERB
ejpam-4859	599	4	on	on	ADP
ejpam-4859	599	5	the	the	DET
ejpam-4859	599	6	following	follow	VERB
ejpam-4859	599	7	proposition	proposition	NOUN
ejpam-4859	599	8	.	.	PUNCT
ejpam-4859	600	1	proposition	proposition	NOUN
ejpam-4859	600	2	13	13	NUM
ejpam-4859	600	3	.	.	PUNCT
ejpam-4859	601	1	let	let	AUX
ejpam-4859	601	2	(	(	PUNCT
ejpam-4859	601	3	n	n	X
ejpam-4859	601	4	,	,	PUNCT
ejpam-4859	601	5	k	k	NOUN
ejpam-4859	601	6	)	)	PUNCT
ejpam-4859	601	7	be	be	AUX
ejpam-4859	601	8	a	a	DET
ejpam-4859	601	9	poly	poly	ADJ
ejpam-4859	601	10	-	-	PUNCT
ejpam-4859	601	11	pl	pl	NOUN
ejpam-4859	601	12	system	system	NOUN
ejpam-4859	601	13	and	and	CCONJ
ejpam-4859	601	14	(	(	PUNCT
ejpam-4859	601	15	n	n	CCONJ
ejpam-4859	601	16	∗,k∗	∗,k∗	ADJ
ejpam-4859	601	17	)	)	PUNCT
ejpam-4859	601	18	be	be	AUX
ejpam-4859	601	19	its	its	PRON
ejpam-4859	601	20	star	star	NOUN
ejpam-4859	601	21	-	-	PUNCT
ejpam-4859	601	22	rvm	rvm	NOUN
ejpam-4859	601	23	transform	transform	NOUN
ejpam-4859	601	24	.	.	PUNCT
ejpam-4859	602	1	if	if	SCONJ
ejpam-4859	602	2	n	n	PRON
ejpam-4859	602	3	has	have	VERB
ejpam-4859	602	4	sufficient	sufficient	ADJ
ejpam-4859	602	5	reactant	reactant	NOUN
ejpam-4859	602	6	diversity	diversity	NOUN
ejpam-4859	602	7	(	(	PUNCT
ejpam-4859	602	8	srd	srd	NOUN
ejpam-4859	602	9	)	)	PUNCT
ejpam-4859	602	10	then	then	ADV
ejpam-4859	602	11	n	n	PRON
ejpam-4859	602	12	∗	∗	NOUN
ejpam-4859	602	13	has	have	VERB
ejpam-4859	602	14	also	also	ADV
ejpam-4859	602	15	sufficient	sufficient	ADJ
ejpam-4859	602	16	reactant	reactant	NOUN
ejpam-4859	602	17	diversity	diversity	NOUN
ejpam-4859	602	18	(	(	PUNCT
ejpam-4859	602	19	srd	srd	NOUN
ejpam-4859	602	20	)	)	PUNCT
ejpam-4859	602	21	.	.	PUNCT
ejpam-4859	603	1	proof	proof	NOUN
ejpam-4859	603	2	.	.	PUNCT
ejpam-4859	604	1	let	let	VERB
ejpam-4859	604	2	n	n	PRON
ejpam-4859	604	3	be	be	AUX
ejpam-4859	604	4	a	a	DET
ejpam-4859	604	5	poly	poly	ADJ
ejpam-4859	604	6	-	-	PUNCT
ejpam-4859	604	7	pl	pl	NOUN
ejpam-4859	604	8	system	system	NOUN
ejpam-4859	604	9	and	and	CCONJ
ejpam-4859	604	10	n	n	PROPN
ejpam-4859	604	11	∗	∗	NOUN
ejpam-4859	604	12	be	be	VERB
ejpam-4859	604	13	the	the	DET
ejpam-4859	604	14	star	star	NOUN
ejpam-4859	604	15	-	-	PUNCT
ejpam-4859	604	16	rvm	rvm	PROPN
ejpam-4859	604	17	transform	transform	NOUN
ejpam-4859	604	18	of	of	ADP
ejpam-4859	604	19	n	n	PROPN
ejpam-4859	604	20	.	.	PUNCT
ejpam-4859	605	1	suppose	suppose	VERB
ejpam-4859	605	2	n	n	PRON
ejpam-4859	605	3	has	have	VERB
ejpam-4859	605	4	srd	srd	NOUN
ejpam-4859	605	5	.	.	PUNCT
ejpam-4859	606	1	this	this	PRON
ejpam-4859	606	2	means	mean	VERB
ejpam-4859	606	3	that	that	SCONJ
ejpam-4859	606	4	nr	nr	PRON
ejpam-4859	606	5	≥	≥	PROPN
ejpam-4859	606	6	s.	s.	PROPN
ejpam-4859	606	7	recall	recall	VERB
ejpam-4859	606	8	that	that	PRON
ejpam-4859	606	9	,	,	PUNCT
ejpam-4859	606	10	n∗	n∗	PROPN
ejpam-4859	606	11	r	r	PROPN
ejpam-4859	606	12	≥	≥	NOUN
ejpam-4859	606	13	nr	nr	NOUN
ejpam-4859	606	14	and	and	CCONJ
ejpam-4859	606	15	s∗	s∗	PROPN
ejpam-4859	606	16	=	=	PUNCT
ejpam-4859	606	17	s.	s.	PROPN
ejpam-4859	606	18	thus	thus	ADV
ejpam-4859	606	19	,	,	PUNCT
ejpam-4859	606	20	n∗	n∗	PROPN
ejpam-4859	606	21	r	r	PROPN
ejpam-4859	606	22	≥	≥	PROPN
ejpam-4859	606	23	nr	nr	PRON
ejpam-4859	606	24	≥	≥	NOUN
ejpam-4859	606	25	s	s	PART
ejpam-4859	606	26	=	=	NOUN
ejpam-4859	606	27	s∗.	s∗.	INTJ
ejpam-4859	606	28	therefore	therefore	ADV
ejpam-4859	606	29	,	,	PUNCT
ejpam-4859	606	30	n∗	n∗	PROPN
ejpam-4859	606	31	has	have	VERB
ejpam-4859	606	32	also	also	ADV
ejpam-4859	606	33	srd	srd	NOUN
ejpam-4859	606	34	)	)	PUNCT
ejpam-4859	606	35	.	.	PUNCT
ejpam-4859	607	1	corollary	corollary	ADJ
ejpam-4859	607	2	2	2	NUM
ejpam-4859	607	3	.	.	PUNCT
ejpam-4859	607	4	:	:	PUNCT
ejpam-4859	607	5	let	let	VERB
ejpam-4859	607	6	n	n	PRON
ejpam-4859	607	7	be	be	AUX
ejpam-4859	607	8	a	a	DET
ejpam-4859	607	9	poly	poly	ADJ
ejpam-4859	607	10	-	-	PUNCT
ejpam-4859	607	11	pl	pl	NOUN
ejpam-4859	607	12	systems	system	NOUN
ejpam-4859	607	13	with	with	ADP
ejpam-4859	607	14	a	a	DET
ejpam-4859	607	15	poly	poly	ADJ
ejpam-4859	607	16	-	-	PUNCT
ejpam-4859	607	17	pl	pl	NOUN
ejpam-4859	607	18	kinetics	kinetic	NOUN
ejpam-4859	607	19	of	of	ADP
ejpam-4859	607	20	h	h	NOUN
ejpam-4859	607	21	=	=	SYM
ejpam-4859	607	22	2	2	NUM
ejpam-4859	607	23	and	and	CCONJ
ejpam-4859	607	24	n∗	n∗	PROPN
ejpam-4859	607	25	be	be	VERB
ejpam-4859	607	26	the	the	DET
ejpam-4859	607	27	star	star	NOUN
ejpam-4859	607	28	-	-	PUNCT
ejpam-4859	607	29	rvm	rvm	PROPN
ejpam-4859	607	30	transform	transform	NOUN
ejpam-4859	607	31	of	of	ADP
ejpam-4859	607	32	n	n	NOUN
ejpam-4859	607	33	.	.	PUNCT
ejpam-4859	608	1	if	if	SCONJ
ejpam-4859	608	2	n	n	PRON
ejpam-4859	608	3	is	be	AUX
ejpam-4859	608	4	t	t	NOUN
ejpam-4859	608	5	-	-	PUNCT
ejpam-4859	608	6	minimal	minimal	ADJ
ejpam-4859	608	7	and	and	CCONJ
ejpam-4859	608	8	for	for	ADP
ejpam-4859	608	9	every	every	DET
ejpam-4859	608	10	complex	complex	ADJ
ejpam-4859	608	11	v	v	NOUN
ejpam-4859	608	12	,	,	PUNCT
ejpam-4859	608	13	d−(v)+d+(v	d−(v)+d+(v	PROPN
ejpam-4859	608	14	)	)	PUNCT
ejpam-4859	608	15	=	=	SYM
ejpam-4859	608	16	1	1	NUM
ejpam-4859	608	17	then	then	ADV
ejpam-4859	608	18	n∗	n∗	PROPN
ejpam-4859	608	19	is	be	AUX
ejpam-4859	608	20	srd	srd	NOUN
ejpam-4859	608	21	network	network	NOUN
ejpam-4859	608	22	d.	d.	PROPN
ejpam-4859	608	23	magpantay	magpantay	PROPN
ejpam-4859	608	24	/	/	SYM
ejpam-4859	608	25	eur	eur	PROPN
ejpam-4859	608	26	.	.	PUNCT
ejpam-4859	609	1	j.	j.	PROPN
ejpam-4859	609	2	pure	pure	PROPN
ejpam-4859	609	3	appl	appl	PROPN
ejpam-4859	609	4	.	.	PROPN
ejpam-4859	609	5	math	math	PROPN
ejpam-4859	609	6	,	,	PUNCT
ejpam-4859	609	7	16	16	NUM
ejpam-4859	609	8	(	(	PUNCT
ejpam-4859	609	9	4	4	NUM
ejpam-4859	609	10	)	)	PUNCT
ejpam-4859	609	11	(	(	PUNCT
ejpam-4859	609	12	2023	2023	NUM
ejpam-4859	609	13	)	)	PUNCT
ejpam-4859	609	14	,	,	PUNCT
ejpam-4859	609	15	2557	2557	NUM
ejpam-4859	609	16	-	-	SYM
ejpam-4859	609	17	2580	2580	NUM
ejpam-4859	609	18	2577	2577	NUM
ejpam-4859	609	19	3.3.7	3.3.7	PROPN
ejpam-4859	609	20	.	.	PUNCT
ejpam-4859	610	1	complex	complex	ADJ
ejpam-4859	610	2	factorizability	factorizability	NOUN
ejpam-4859	610	3	one	one	NUM
ejpam-4859	610	4	of	of	ADP
ejpam-4859	610	5	the	the	DET
ejpam-4859	610	6	most	most	ADV
ejpam-4859	610	7	important	important	ADJ
ejpam-4859	610	8	kinetic	kinetic	ADJ
ejpam-4859	610	9	properties	property	NOUN
ejpam-4859	610	10	is	be	AUX
ejpam-4859	610	11	complex	complex	ADJ
ejpam-4859	610	12	factorizability	factorizability	NOUN
ejpam-4859	610	13	.	.	PUNCT
ejpam-4859	611	1	to	to	PART
ejpam-4859	611	2	explore	explore	VERB
ejpam-4859	611	3	the	the	DET
ejpam-4859	611	4	said	say	VERB
ejpam-4859	611	5	property	property	NOUN
ejpam-4859	611	6	with	with	ADP
ejpam-4859	611	7	regards	regard	NOUN
ejpam-4859	611	8	to	to	ADP
ejpam-4859	611	9	star	star	NOUN
ejpam-4859	611	10	-	-	PUNCT
ejpam-4859	611	11	rvm	rvm	PROPN
ejpam-4859	611	12	method	method	NOUN
ejpam-4859	611	13	,	,	PUNCT
ejpam-4859	611	14	we	we	PRON
ejpam-4859	611	15	consider	consider	VERB
ejpam-4859	611	16	the	the	DET
ejpam-4859	611	17	following	follow	VERB
ejpam-4859	611	18	example	example	NOUN
ejpam-4859	611	19	.	.	PUNCT
ejpam-4859	612	1	example	example	NOUN
ejpam-4859	612	2	13	13	NUM
ejpam-4859	612	3	.	.	PUNCT
ejpam-4859	613	1	for	for	ADP
ejpam-4859	613	2	(	(	PUNCT
ejpam-4859	613	3	n	n	X
ejpam-4859	613	4	,	,	PUNCT
ejpam-4859	613	5	k	k	PROPN
ejpam-4859	613	6	)	)	PUNCT
ejpam-4859	613	7	,	,	PUNCT
ejpam-4859	613	8	suppose	suppose	VERB
ejpam-4859	613	9	s	s	VERB
ejpam-4859	613	10	=	=	PUNCT
ejpam-4859	613	11	{	{	PUNCT
ejpam-4859	613	12	x	x	PROPN
ejpam-4859	613	13	,	,	PUNCT
ejpam-4859	613	14	y	y	PROPN
ejpam-4859	613	15	}	}	PUNCT
ejpam-4859	613	16	and	and	CCONJ
ejpam-4859	613	17	r	r	NOUN
ejpam-4859	613	18	=	=	SYM
ejpam-4859	613	19	{	{	PUNCT
ejpam-4859	613	20	r	r	NOUN
ejpam-4859	613	21	:1	:1	PUNCT
ejpam-4859	613	22	x	x	PROPN
ejpam-4859	614	1	+	+	NUM
ejpam-4859	614	2	y	y	PROPN
ejpam-4859	614	3	→	→	SYM
ejpam-4859	614	4	x	x	PROPN
ejpam-4859	615	1	+	+	PUNCT
ejpam-4859	615	2	2y	2y	NUM
ejpam-4859	615	3	,	,	PUNCT
ejpam-4859	615	4	r2	r2	PROPN
ejpam-4859	615	5	:	:	PUNCT
ejpam-4859	615	6	x	x	X
ejpam-4859	616	1	+	+	PUNCT
ejpam-4859	616	2	2y	2y	NUM
ejpam-4859	616	3	→	→	SYM
ejpam-4859	616	4	2x	2x	NUM
ejpam-4859	616	5	+	+	X
ejpam-4859	616	6	2y	2y	NUM
ejpam-4859	616	7	.	.	PUNCT
ejpam-4859	617	1	let	let	VERB
ejpam-4859	617	2	the	the	DET
ejpam-4859	617	3	poly	poly	ADJ
ejpam-4859	617	4	-	-	PUNCT
ejpam-4859	617	5	pl	pl	NOUN
ejpam-4859	617	6	kinetics	kinetic	NOUN
ejpam-4859	617	7	be	be	AUX
ejpam-4859	617	8	given	give	VERB
ejpam-4859	617	9	by	by	ADP
ejpam-4859	617	10	:	:	PUNCT
ejpam-4859	617	11	kr1(x	kr1(x	PROPN
ejpam-4859	617	12	,	,	PUNCT
ejpam-4859	617	13	y	y	PROPN
ejpam-4859	617	14	)	)	PUNCT
ejpam-4859	618	1	=	=	PUNCT
ejpam-4859	619	1	k2(x	k2(x	PROPN
ejpam-4859	619	2	2y	2y	PROPN
ejpam-4859	620	1	+	+	ADJ
ejpam-4859	620	2	xy	xy	NOUN
ejpam-4859	620	3	2	2	NUM
ejpam-4859	620	4	)	)	PUNCT
ejpam-4859	620	5	kr2(x	kr2(x	PROPN
ejpam-4859	620	6	,	,	PUNCT
ejpam-4859	620	7	y	y	PROPN
ejpam-4859	620	8	)	)	PUNCT
ejpam-4859	621	1	=	=	PUNCT
ejpam-4859	622	1	k3(x	k3(x	PROPN
ejpam-4859	622	2	+	+	ADJ
ejpam-4859	622	3	x2y	x2y	NOUN
ejpam-4859	622	4	2	2	NUM
ejpam-4859	622	5	)	)	PUNCT
ejpam-4859	622	6	where	where	SCONJ
ejpam-4859	622	7	k1	k1	NOUN
ejpam-4859	622	8	and	and	CCONJ
ejpam-4859	622	9	k2	k2	PROPN
ejpam-4859	622	10	are	be	AUX
ejpam-4859	622	11	rate	rate	NOUN
ejpam-4859	622	12	constants	constant	NOUN
ejpam-4859	622	13	.	.	PUNCT
ejpam-4859	623	1	note	note	VERB
ejpam-4859	623	2	that	that	SCONJ
ejpam-4859	623	3	the	the	DET
ejpam-4859	623	4	given	give	VERB
ejpam-4859	623	5	(	(	PUNCT
ejpam-4859	623	6	n	n	CCONJ
ejpam-4859	623	7	,	,	PUNCT
ejpam-4859	623	8	k	k	NOUN
ejpam-4859	623	9	)	)	PUNCT
ejpam-4859	623	10	is	be	AUX
ejpam-4859	623	11	complex	complex	ADJ
ejpam-4859	623	12	factorizable	factorizable	NOUN
ejpam-4859	623	13	(	(	PUNCT
ejpam-4859	623	14	plk−rdk	plk−rdk	NUM
ejpam-4859	623	15	)	)	PUNCT
ejpam-4859	623	16	.	.	PUNCT
ejpam-4859	624	1	generating	generate	VERB
ejpam-4859	624	2	starrvm	starrvm	NOUN
ejpam-4859	624	3	transform	transform	NOUN
ejpam-4859	624	4	,	,	PUNCT
ejpam-4859	624	5	we	we	PRON
ejpam-4859	624	6	have	have	VERB
ejpam-4859	624	7	(	(	PUNCT
ejpam-4859	624	8	n	n	CCONJ
ejpam-4859	624	9	∗,k∗	∗,k∗	ADJ
ejpam-4859	624	10	)	)	PUNCT
ejpam-4859	624	11	where	where	SCONJ
ejpam-4859	624	12	s	s	VERB
ejpam-4859	624	13	=	=	PRON
ejpam-4859	624	14	{	{	PUNCT
ejpam-4859	624	15	x	x	PROPN
ejpam-4859	624	16	,	,	PUNCT
ejpam-4859	624	17	y	y	PROPN
ejpam-4859	624	18	}	}	PUNCT
ejpam-4859	624	19	and	and	CCONJ
ejpam-4859	624	20	r∗	r∗	PROPN
ejpam-4859	624	21	=	=	SYM
ejpam-4859	624	22	{	{	PUNCT
ejpam-4859	624	23	r1	r1	NOUN
ejpam-4859	624	24	:	:	PUNCT
ejpam-4859	624	25	x	x	X
ejpam-4859	625	1	+	+	PUNCT
ejpam-4859	625	2	y	y	PROPN
ejpam-4859	625	3	→	→	SYM
ejpam-4859	625	4	x	x	SYM
ejpam-4859	625	5	+2y	+2y	ADJ
ejpam-4859	625	6	,	,	PUNCT
ejpam-4859	625	7	r∗1	r∗1	NOUN
ejpam-4859	625	8	=	=	PUNCT
ejpam-4859	625	9	x	x	PUNCT
ejpam-4859	625	10	+2y	+2y	NUM
ejpam-4859	625	11	→	→	SYM
ejpam-4859	625	12	x	x	SYM
ejpam-4859	625	13	+3y	+3y	ADJ
ejpam-4859	625	14	,	,	PUNCT
ejpam-4859	625	15	r2	r2	PROPN
ejpam-4859	625	16	:	:	PUNCT
ejpam-4859	625	17	x	x	X
ejpam-4859	625	18	+2y	+2y	NUM
ejpam-4859	625	19	→	→	SYM
ejpam-4859	625	20	2x	2x	NUM
ejpam-4859	625	21	+2y	+2y	ADJ
ejpam-4859	625	22	,	,	PUNCT
ejpam-4859	625	23	r∗2	r∗2	ADJ
ejpam-4859	625	24	:	:	PUNCT
ejpam-4859	625	25	2x	2x	NUM
ejpam-4859	625	26	+2y	+2y	NUM
ejpam-4859	625	27	→	→	SYM
ejpam-4859	625	28	3x	3x	NUM
ejpam-4859	625	29	+2y	+2y	NUM
ejpam-4859	625	30	}	}	PUNCT
ejpam-4859	625	31	.	.	PUNCT
ejpam-4859	626	1	the	the	DET
ejpam-4859	626	2	kinetic	kinetic	ADJ
ejpam-4859	626	3	functions	function	NOUN
ejpam-4859	626	4	are	be	AUX
ejpam-4859	626	5	as	as	SCONJ
ejpam-4859	626	6	follows	follow	VERB
ejpam-4859	626	7	:	:	PUNCT
ejpam-4859	626	8	k∗	k∗	VERB
ejpam-4859	626	9	r1(x	r1(x	PRON
ejpam-4859	626	10	,	,	PUNCT
ejpam-4859	626	11	y	y	PROPN
ejpam-4859	626	12	)	)	PUNCT
ejpam-4859	627	1	=	=	SYM
ejpam-4859	627	2	k∗2x	k∗2x	ADJ
ejpam-4859	627	3	2y	2y	NOUN
ejpam-4859	627	4	k∗	k∗	NOUN
ejpam-4859	627	5	r1∗(x	r1∗(x	PROPN
ejpam-4859	627	6	,	,	PUNCT
ejpam-4859	627	7	y	y	PROPN
ejpam-4859	627	8	)	)	PUNCT
ejpam-4859	628	1	=	=	PUNCT
ejpam-4859	629	1	k∗∗2	k∗∗2	NOUN
ejpam-4859	629	2	xy	xy	PROPN
ejpam-4859	629	3	2	2	NUM
ejpam-4859	629	4	k∗	k∗	PROPN
ejpam-4859	629	5	r2(x	r2(x	PROPN
ejpam-4859	629	6	,	,	PUNCT
ejpam-4859	629	7	y	y	PROPN
ejpam-4859	629	8	)	)	PUNCT
ejpam-4859	629	9	=	=	SYM
ejpam-4859	630	1	k∗3x	k∗3x	PROPN
ejpam-4859	630	2	k∗	k∗	PROPN
ejpam-4859	630	3	r2∗(x	r2∗(x	PROPN
ejpam-4859	630	4	,	,	PUNCT
ejpam-4859	630	5	y	y	PROPN
ejpam-4859	630	6	)	)	PUNCT
ejpam-4859	631	1	=	=	SYM
ejpam-4859	631	2	k∗∗3	k∗∗3	NOUN
ejpam-4859	631	3	x2y	x2y	NOUN
ejpam-4859	631	4	2	2	X
ejpam-4859	631	5	.	.	X
ejpam-4859	631	6	observe	observe	VERB
ejpam-4859	631	7	that	that	SCONJ
ejpam-4859	631	8	the	the	DET
ejpam-4859	631	9	kinetic	kinetic	ADJ
ejpam-4859	631	10	order	order	NOUN
ejpam-4859	631	11	of	of	ADP
ejpam-4859	631	12	the	the	DET
ejpam-4859	631	13	reactant	reactant	NOUN
ejpam-4859	631	14	x	x	PUNCT
ejpam-4859	632	1	+	+	PUNCT
ejpam-4859	632	2	2y	2y	NOUN
ejpam-4859	632	3	for	for	SCONJ
ejpam-4859	632	4	the	the	DET
ejpam-4859	632	5	reactions	reaction	NOUN
ejpam-4859	632	6	r∗1	r∗1	VERB
ejpam-4859	632	7	and	and	CCONJ
ejpam-4859	632	8	r2	r2	PROPN
ejpam-4859	632	9	are	be	AUX
ejpam-4859	632	10	not	not	PART
ejpam-4859	632	11	equal	equal	ADJ
ejpam-4859	632	12	.	.	PUNCT
ejpam-4859	633	1	thus	thus	ADV
ejpam-4859	633	2	,	,	PUNCT
ejpam-4859	633	3	(	(	PUNCT
ejpam-4859	633	4	n	n	CCONJ
ejpam-4859	633	5	∗,k∗	∗,k∗	ADJ
ejpam-4859	633	6	)	)	PUNCT
ejpam-4859	633	7	is	be	AUX
ejpam-4859	633	8	not	not	PART
ejpam-4859	633	9	plk	plk	PROPN
ejpam-4859	633	10	−rdk	−rdk	NOUN
ejpam-4859	633	11	and	and	CCONJ
ejpam-4859	633	12	so	so	ADV
ejpam-4859	633	13	is	be	AUX
ejpam-4859	633	14	not	not	PART
ejpam-4859	633	15	complex	complex	ADJ
ejpam-4859	633	16	factorizable	factorizable	NOUN
ejpam-4859	633	17	.	.	PUNCT
ejpam-4859	634	1	with	with	ADP
ejpam-4859	634	2	this	this	PRON
ejpam-4859	634	3	,	,	PUNCT
ejpam-4859	634	4	we	we	PRON
ejpam-4859	634	5	have	have	VERB
ejpam-4859	634	6	the	the	DET
ejpam-4859	634	7	following	follow	VERB
ejpam-4859	634	8	proposition	proposition	NOUN
ejpam-4859	634	9	stating	state	VERB
ejpam-4859	634	10	conditions	condition	NOUN
ejpam-4859	634	11	that	that	PRON
ejpam-4859	634	12	assure	assure	VERB
ejpam-4859	634	13	complex	complex	ADJ
ejpam-4859	634	14	factorizability	factorizability	NOUN
ejpam-4859	634	15	of	of	ADP
ejpam-4859	634	16	n	n	DET
ejpam-4859	634	17	∗	∗	NOUN
ejpam-4859	634	18	given	give	VERB
ejpam-4859	634	19	that	that	SCONJ
ejpam-4859	634	20	n	n	PRON
ejpam-4859	634	21	is	be	AUX
ejpam-4859	634	22	.	.	PUNCT
ejpam-4859	635	1	proposition	proposition	NOUN
ejpam-4859	635	2	14	14	NUM
ejpam-4859	635	3	.	.	PUNCT
ejpam-4859	636	1	let	let	AUX
ejpam-4859	636	2	(	(	PUNCT
ejpam-4859	636	3	n	n	X
ejpam-4859	636	4	,	,	PUNCT
ejpam-4859	636	5	k	k	NOUN
ejpam-4859	636	6	)	)	PUNCT
ejpam-4859	636	7	be	be	AUX
ejpam-4859	636	8	a	a	DET
ejpam-4859	636	9	poly	poly	ADJ
ejpam-4859	636	10	-	-	PUNCT
ejpam-4859	636	11	pl	pl	NOUN
ejpam-4859	636	12	system	system	NOUN
ejpam-4859	636	13	of	of	ADP
ejpam-4859	636	14	h	h	NOUN
ejpam-4859	636	15	=	=	SYM
ejpam-4859	636	16	2	2	NUM
ejpam-4859	636	17	and	and	CCONJ
ejpam-4859	636	18	(	(	PUNCT
ejpam-4859	636	19	n	n	CCONJ
ejpam-4859	636	20	∗,k∗	∗,k∗	ADJ
ejpam-4859	636	21	)	)	PUNCT
ejpam-4859	636	22	be	be	VERB
ejpam-4859	636	23	the	the	DET
ejpam-4859	636	24	starrvm	starrvm	NOUN
ejpam-4859	636	25	transform	transform	NOUN
ejpam-4859	636	26	.	.	PUNCT
ejpam-4859	637	1	if	if	SCONJ
ejpam-4859	637	2	(	(	PUNCT
ejpam-4859	637	3	n	n	X
ejpam-4859	637	4	,	,	PUNCT
ejpam-4859	637	5	k	k	NOUN
ejpam-4859	637	6	)	)	PUNCT
ejpam-4859	637	7	is	be	AUX
ejpam-4859	637	8	complex	complex	ADJ
ejpam-4859	637	9	factorizable	factorizable	NOUN
ejpam-4859	637	10	satisfying	satisfy	VERB
ejpam-4859	637	11	the	the	DET
ejpam-4859	637	12	following	following	NOUN
ejpam-4859	637	13	:	:	PUNCT
ejpam-4859	637	14	i.	i.	NOUN
ejpam-4859	637	15	for	for	ADP
ejpam-4859	637	16	every	every	DET
ejpam-4859	637	17	complex	complex	ADJ
ejpam-4859	637	18	y	y	NOUN
ejpam-4859	637	19	,	,	PUNCT
ejpam-4859	637	20	either	either	CCONJ
ejpam-4859	637	21	d−(y	d−(y	ADJ
ejpam-4859	637	22	)	)	PUNCT
ejpam-4859	637	23	=	=	SYM
ejpam-4859	637	24	0	0	NUM
ejpam-4859	637	25	or	or	CCONJ
ejpam-4859	637	26	d+(y	d+(y	PROPN
ejpam-4859	637	27	)	)	PUNCT
ejpam-4859	638	1	=	=	SYM
ejpam-4859	638	2	0	0	PUNCT
ejpam-4859	639	1	(	(	PUNCT
ejpam-4859	639	2	but	but	CCONJ
ejpam-4859	639	3	not	not	PART
ejpam-4859	639	4	both	both	PRON
ejpam-4859	639	5	)	)	PUNCT
ejpam-4859	639	6	,	,	PUNCT
ejpam-4859	639	7	ii	ii	PROPN
ejpam-4859	639	8	.	.	PUNCT
ejpam-4859	640	1	the	the	DET
ejpam-4859	640	2	components	component	NOUN
ejpam-4859	640	3	of	of	ADP
ejpam-4859	640	4	the	the	DET
ejpam-4859	640	5	reaction	reaction	NOUN
ejpam-4859	640	6	vectors	vector	NOUN
ejpam-4859	640	7	in	in	ADP
ejpam-4859	640	8	n	n	CCONJ
ejpam-4859	640	9	are	be	AUX
ejpam-4859	640	10	all	all	ADV
ejpam-4859	640	11	positive	positive	ADJ
ejpam-4859	640	12	or	or	CCONJ
ejpam-4859	640	13	equal	equal	ADJ
ejpam-4859	640	14	to	to	ADP
ejpam-4859	640	15	zero	zero	NUM
ejpam-4859	640	16	then	then	ADV
ejpam-4859	640	17	(	(	PUNCT
ejpam-4859	640	18	n	n	CCONJ
ejpam-4859	640	19	∗,k∗	∗,k∗	ADJ
ejpam-4859	640	20	)	)	PUNCT
ejpam-4859	640	21	is	be	AUX
ejpam-4859	640	22	complex	complex	ADJ
ejpam-4859	640	23	factorizable	factorizable	NOUN
ejpam-4859	640	24	.	.	PUNCT
ejpam-4859	641	1	proof	proof	NOUN
ejpam-4859	641	2	.	.	PUNCT
ejpam-4859	642	1	let	let	AUX
ejpam-4859	642	2	(	(	PUNCT
ejpam-4859	642	3	n	n	X
ejpam-4859	642	4	,	,	PUNCT
ejpam-4859	642	5	k	k	NOUN
ejpam-4859	642	6	)	)	PUNCT
ejpam-4859	642	7	be	be	AUX
ejpam-4859	642	8	a	a	DET
ejpam-4859	642	9	poly	poly	ADJ
ejpam-4859	642	10	-	-	PUNCT
ejpam-4859	642	11	pl	pl	NOUN
ejpam-4859	642	12	kinetic	kinetic	ADJ
ejpam-4859	642	13	system	system	NOUN
ejpam-4859	642	14	with	with	ADP
ejpam-4859	642	15	a	a	DET
ejpam-4859	642	16	poly	poly	ADJ
ejpam-4859	642	17	-	-	PUNCT
ejpam-4859	642	18	pl	pl	NOUN
ejpam-4859	642	19	kinetics	kinetic	NOUN
ejpam-4859	642	20	of	of	ADP
ejpam-4859	642	21	h	h	NOUN
ejpam-4859	642	22	=	=	SYM
ejpam-4859	642	23	2	2	NUM
ejpam-4859	642	24	and	and	CCONJ
ejpam-4859	642	25	(	(	PUNCT
ejpam-4859	642	26	n	n	CCONJ
ejpam-4859	642	27	∗,k∗	∗,k∗	ADJ
ejpam-4859	642	28	)	)	PUNCT
ejpam-4859	642	29	be	be	VERB
ejpam-4859	642	30	the	the	DET
ejpam-4859	642	31	star	star	NOUN
ejpam-4859	642	32	-	-	PUNCT
ejpam-4859	642	33	rvm	rvm	PROPN
ejpam-4859	642	34	transform	transform	NOUN
ejpam-4859	642	35	.	.	PUNCT
ejpam-4859	643	1	since	since	SCONJ
ejpam-4859	643	2	(	(	PUNCT
ejpam-4859	643	3	n	n	X
ejpam-4859	643	4	,	,	PUNCT
ejpam-4859	643	5	k	k	NOUN
ejpam-4859	643	6	)	)	PUNCT
ejpam-4859	643	7	is	be	AUX
ejpam-4859	643	8	complex	complex	ADJ
ejpam-4859	643	9	factorizable	factorizable	NOUN
ejpam-4859	643	10	,	,	PUNCT
ejpam-4859	643	11	it	it	PRON
ejpam-4859	643	12	is	be	AUX
ejpam-4859	643	13	plk	plk	PROPN
ejpam-4859	643	14	−	−	PROPN
ejpam-4859	643	15	rdk	rdk	PROPN
ejpam-4859	643	16	.	.	PUNCT
ejpam-4859	644	1	this	this	PRON
ejpam-4859	644	2	implies	imply	VERB
ejpam-4859	644	3	that	that	SCONJ
ejpam-4859	644	4	if	if	SCONJ
ejpam-4859	644	5	there	there	PRON
ejpam-4859	644	6	are	be	VERB
ejpam-4859	644	7	reactions	reaction	NOUN
ejpam-4859	644	8	with	with	ADP
ejpam-4859	644	9	the	the	DET
ejpam-4859	644	10	same	same	ADJ
ejpam-4859	644	11	reactant	reactant	NOUN
ejpam-4859	644	12	complexes	complex	NOUN
ejpam-4859	644	13	,	,	PUNCT
ejpam-4859	644	14	they	they	PRON
ejpam-4859	644	15	have	have	VERB
ejpam-4859	644	16	equal	equal	ADJ
ejpam-4859	644	17	kinetic	kinetic	ADJ
ejpam-4859	644	18	orders	order	NOUN
ejpam-4859	644	19	.	.	PUNCT
ejpam-4859	645	1	also	also	ADV
ejpam-4859	645	2	,	,	PUNCT
ejpam-4859	645	3	since	since	SCONJ
ejpam-4859	645	4	the	the	DET
ejpam-4859	645	5	components	component	NOUN
ejpam-4859	645	6	of	of	ADP
ejpam-4859	645	7	the	the	DET
ejpam-4859	645	8	reaction	reaction	NOUN
ejpam-4859	645	9	vectors	vector	NOUN
ejpam-4859	645	10	in	in	ADP
ejpam-4859	645	11	n	n	CCONJ
ejpam-4859	645	12	are	be	AUX
ejpam-4859	645	13	all	all	PRON
ejpam-4859	645	14	nonnegative	nonnegative	ADJ
ejpam-4859	645	15	then	then	ADV
ejpam-4859	645	16	only	only	ADV
ejpam-4859	645	17	case	case	NOUN
ejpam-4859	645	18	(	(	PUNCT
ejpam-4859	645	19	i	i	NOUN
ejpam-4859	645	20	)	)	PUNCT
ejpam-4859	645	21	of	of	ADP
ejpam-4859	645	22	star	star	NOUN
ejpam-4859	645	23	-	-	PUNCT
ejpam-4859	645	24	rvm	rvm	NOUN
ejpam-4859	645	25	applies	apply	VERB
ejpam-4859	645	26	.	.	PUNCT
ejpam-4859	646	1	now	now	ADV
ejpam-4859	646	2	,	,	PUNCT
ejpam-4859	646	3	take	take	VERB
ejpam-4859	646	4	note	note	NOUN
ejpam-4859	646	5	of	of	ADP
ejpam-4859	646	6	the	the	DET
ejpam-4859	646	7	following	following	NOUN
ejpam-4859	646	8	on	on	ADP
ejpam-4859	646	9	star	star	NOUN
ejpam-4859	646	10	-	-	PUNCT
ejpam-4859	646	11	rvm	rvm	PROPN
ejpam-4859	646	12	transform	transform	NOUN
ejpam-4859	646	13	(	(	PUNCT
ejpam-4859	646	14	n	n	CCONJ
ejpam-4859	646	15	∗,k∗	∗,k∗	ADJ
ejpam-4859	646	16	)	)	PUNCT
ejpam-4859	646	17	:	:	PUNCT
ejpam-4859	646	18	d.	d.	PROPN
ejpam-4859	646	19	magpantay	magpantay	PROPN
ejpam-4859	646	20	/	/	SYM
ejpam-4859	646	21	eur	eur	PROPN
ejpam-4859	646	22	.	.	PUNCT
ejpam-4859	647	1	j.	j.	PROPN
ejpam-4859	647	2	pure	pure	PROPN
ejpam-4859	647	3	appl	appl	PROPN
ejpam-4859	647	4	.	.	PROPN
ejpam-4859	647	5	math	math	PROPN
ejpam-4859	647	6	,	,	PUNCT
ejpam-4859	647	7	16	16	NUM
ejpam-4859	647	8	(	(	PUNCT
ejpam-4859	647	9	4	4	NUM
ejpam-4859	647	10	)	)	PUNCT
ejpam-4859	647	11	(	(	PUNCT
ejpam-4859	647	12	2023	2023	NUM
ejpam-4859	647	13	)	)	PUNCT
ejpam-4859	647	14	,	,	PUNCT
ejpam-4859	647	15	2557	2557	NUM
ejpam-4859	647	16	-	-	SYM
ejpam-4859	647	17	2580	2580	NUM
ejpam-4859	647	18	2578	2578	NUM
ejpam-4859	647	19	(	(	PUNCT
ejpam-4859	647	20	a	a	X
ejpam-4859	647	21	)	)	PUNCT
ejpam-4859	647	22	since	since	SCONJ
ejpam-4859	647	23	for	for	ADP
ejpam-4859	647	24	every	every	DET
ejpam-4859	647	25	complex	complex	ADJ
ejpam-4859	647	26	y	y	NOUN
ejpam-4859	647	27	,	,	PUNCT
ejpam-4859	647	28	either	either	CCONJ
ejpam-4859	647	29	d−(y	d−(y	ADJ
ejpam-4859	647	30	)	)	PUNCT
ejpam-4859	647	31	=	=	SYM
ejpam-4859	647	32	0	0	NUM
ejpam-4859	647	33	or	or	CCONJ
ejpam-4859	647	34	d+(y	d+(y	PROPN
ejpam-4859	647	35	)	)	PUNCT
ejpam-4859	647	36	=	=	SYM
ejpam-4859	647	37	0	0	PUNCT
ejpam-4859	647	38	(	(	PUNCT
ejpam-4859	647	39	but	but	CCONJ
ejpam-4859	647	40	not	not	PART
ejpam-4859	647	41	both	both	PRON
ejpam-4859	647	42	)	)	PUNCT
ejpam-4859	647	43	,	,	PUNCT
ejpam-4859	647	44	then	then	ADV
ejpam-4859	647	45	a	a	DET
ejpam-4859	647	46	complex	complex	NOUN
ejpam-4859	647	47	is	be	AUX
ejpam-4859	647	48	either	either	CCONJ
ejpam-4859	647	49	a	a	DET
ejpam-4859	647	50	reactant	reactant	NOUN
ejpam-4859	647	51	complex	complex	NOUN
ejpam-4859	647	52	or	or	CCONJ
ejpam-4859	647	53	a	a	DET
ejpam-4859	647	54	product	product	NOUN
ejpam-4859	647	55	complex	complex	NOUN
ejpam-4859	647	56	.	.	PUNCT
ejpam-4859	648	1	this	this	PRON
ejpam-4859	648	2	assures	assure	VERB
ejpam-4859	648	3	us	we	PRON
ejpam-4859	648	4	that	that	SCONJ
ejpam-4859	648	5	the	the	DET
ejpam-4859	648	6	reactant	reactant	NOUN
ejpam-4859	648	7	complexes	complexe	VERB
ejpam-4859	648	8	on	on	ADP
ejpam-4859	648	9	additional	additional	ADJ
ejpam-4859	648	10	reactions	reaction	NOUN
ejpam-4859	648	11	on	on	ADP
ejpam-4859	648	12	n∗	n∗	PROPN
ejpam-4859	648	13	are	be	AUX
ejpam-4859	648	14	original	original	ADJ
ejpam-4859	648	15	product	product	NOUN
ejpam-4859	648	16	complexes	complex	NOUN
ejpam-4859	648	17	which	which	PRON
ejpam-4859	648	18	are	be	AUX
ejpam-4859	648	19	different	different	ADJ
ejpam-4859	648	20	from	from	ADP
ejpam-4859	648	21	the	the	DET
ejpam-4859	648	22	original	original	ADJ
ejpam-4859	648	23	reactant	reactant	NOUN
ejpam-4859	648	24	complexes	complex	NOUN
ejpam-4859	648	25	.	.	PUNCT
ejpam-4859	649	1	(	(	PUNCT
ejpam-4859	649	2	b	b	X
ejpam-4859	649	3	)	)	PUNCT
ejpam-4859	649	4	since	since	SCONJ
ejpam-4859	649	5	h	h	NOUN
ejpam-4859	649	6	=	=	SYM
ejpam-4859	649	7	2	2	NUM
ejpam-4859	649	8	,	,	PUNCT
ejpam-4859	649	9	we	we	PRON
ejpam-4859	649	10	are	be	AUX
ejpam-4859	649	11	sure	sure	ADJ
ejpam-4859	649	12	that	that	SCONJ
ejpam-4859	649	13	the	the	DET
ejpam-4859	649	14	additional	additional	ADJ
ejpam-4859	649	15	complexes	complex	NOUN
ejpam-4859	649	16	on	on	ADP
ejpam-4859	649	17	the	the	DET
ejpam-4859	649	18	additional	additional	ADJ
ejpam-4859	649	19	reactions	reaction	NOUN
ejpam-4859	649	20	are	be	AUX
ejpam-4859	649	21	all	all	PRON
ejpam-4859	649	22	product	product	NOUN
ejpam-4859	649	23	complexes	complex	NOUN
ejpam-4859	649	24	.	.	PUNCT
ejpam-4859	650	1	by	by	ADP
ejpam-4859	650	2	(	(	PUNCT
ejpam-4859	650	3	a	a	X
ejpam-4859	650	4	)	)	PUNCT
ejpam-4859	650	5	and	and	CCONJ
ejpam-4859	650	6	(	(	PUNCT
ejpam-4859	650	7	b	b	NOUN
ejpam-4859	650	8	)	)	PUNCT
ejpam-4859	650	9	,	,	PUNCT
ejpam-4859	650	10	the	the	DET
ejpam-4859	650	11	state	state	NOUN
ejpam-4859	650	12	where	where	SCONJ
ejpam-4859	650	13	the	the	DET
ejpam-4859	650	14	reactions	reaction	NOUN
ejpam-4859	650	15	with	with	ADP
ejpam-4859	650	16	the	the	DET
ejpam-4859	650	17	same	same	ADJ
ejpam-4859	650	18	reactant	reactant	NOUN
ejpam-4859	650	19	complexes	complex	NOUN
ejpam-4859	650	20	,	,	PUNCT
ejpam-4859	650	21	have	have	VERB
ejpam-4859	650	22	equal	equal	ADJ
ejpam-4859	650	23	kinetic	kinetic	ADJ
ejpam-4859	650	24	order	order	NOUN
ejpam-4859	650	25	was	be	AUX
ejpam-4859	650	26	maintained	maintain	VERB
ejpam-4859	650	27	.	.	PUNCT
ejpam-4859	651	1	hence	hence	ADV
ejpam-4859	651	2	,	,	PUNCT
ejpam-4859	651	3	(	(	PUNCT
ejpam-4859	651	4	n	n	CCONJ
ejpam-4859	651	5	∗,k∗	∗,k∗	ADJ
ejpam-4859	651	6	)	)	PUNCT
ejpam-4859	651	7	is	be	AUX
ejpam-4859	651	8	plk	plk	PROPN
ejpam-4859	651	9	−	−	PROPN
ejpam-4859	651	10	rdk	rdk	NOUN
ejpam-4859	651	11	and	and	CCONJ
ejpam-4859	651	12	complex	complex	ADJ
ejpam-4859	651	13	factorizable	factorizable	NOUN
ejpam-4859	651	14	.	.	PUNCT
ejpam-4859	652	1	in	in	ADP
ejpam-4859	652	2	the	the	DET
ejpam-4859	652	3	next	next	ADJ
ejpam-4859	652	4	section	section	NOUN
ejpam-4859	652	5	,	,	PUNCT
ejpam-4859	652	6	we	we	PRON
ejpam-4859	652	7	identify	identify	VERB
ejpam-4859	652	8	the	the	DET
ejpam-4859	652	9	bounds	bound	NOUN
ejpam-4859	652	10	on	on	ADP
ejpam-4859	652	11	n	n	DET
ejpam-4859	652	12	∗	∗	NOUN
ejpam-4859	652	13	of	of	ADP
ejpam-4859	652	14	one	one	NUM
ejpam-4859	652	15	important	important	ADJ
ejpam-4859	652	16	property	property	NOUN
ejpam-4859	652	17	of	of	ADP
ejpam-4859	652	18	crn	crn	NOUN
ejpam-4859	652	19	which	which	PRON
ejpam-4859	652	20	is	be	AUX
ejpam-4859	652	21	the	the	DET
ejpam-4859	652	22	deficiency	deficiency	NOUN
ejpam-4859	652	23	of	of	ADP
ejpam-4859	652	24	the	the	DET
ejpam-4859	652	25	network	network	NOUN
ejpam-4859	652	26	δ∗.	δ∗.	ADP
ejpam-4859	652	27	3.3.8	3.3.8	NUM
ejpam-4859	652	28	.	.	PUNCT
ejpam-4859	653	1	deficiency	deficiency	NOUN
ejpam-4859	653	2	of	of	ADP
ejpam-4859	653	3	the	the	DET
ejpam-4859	653	4	network	network	NOUN
ejpam-4859	653	5	by	by	ADP
ejpam-4859	653	6	the	the	DET
ejpam-4859	653	7	construction	construction	NOUN
ejpam-4859	653	8	of	of	ADP
ejpam-4859	653	9	star	star	NOUN
ejpam-4859	653	10	-	-	PUNCT
ejpam-4859	653	11	rvm	rvm	NOUN
ejpam-4859	653	12	,	,	PUNCT
ejpam-4859	653	13	the	the	DET
ejpam-4859	653	14	number	number	NOUN
ejpam-4859	653	15	of	of	ADP
ejpam-4859	653	16	complexes	complex	NOUN
ejpam-4859	653	17	is	be	AUX
ejpam-4859	653	18	most	most	ADV
ejpam-4859	653	19	likely	likely	ADV
ejpam-4859	653	20	increased	increase	VERB
ejpam-4859	653	21	but	but	CCONJ
ejpam-4859	653	22	the	the	DET
ejpam-4859	653	23	number	number	NOUN
ejpam-4859	653	24	of	of	ADP
ejpam-4859	653	25	linkage	linkage	NOUN
ejpam-4859	653	26	classes	class	NOUN
ejpam-4859	653	27	is	be	AUX
ejpam-4859	653	28	most	most	ADV
ejpam-4859	653	29	likely	likely	ADV
ejpam-4859	653	30	decreased	decrease	VERB
ejpam-4859	653	31	.	.	PUNCT
ejpam-4859	654	1	these	these	DET
ejpam-4859	654	2	cases	case	NOUN
ejpam-4859	654	3	are	be	AUX
ejpam-4859	654	4	important	important	ADJ
ejpam-4859	654	5	to	to	PART
ejpam-4859	654	6	consider	consider	VERB
ejpam-4859	654	7	on	on	ADP
ejpam-4859	654	8	how	how	SCONJ
ejpam-4859	654	9	the	the	DET
ejpam-4859	654	10	deficiency	deficiency	NOUN
ejpam-4859	654	11	of	of	ADP
ejpam-4859	654	12	the	the	DET
ejpam-4859	654	13	network	network	NOUN
ejpam-4859	654	14	in	in	ADP
ejpam-4859	654	15	star	star	NOUN
ejpam-4859	654	16	-	-	PUNCT
ejpam-4859	654	17	rvm	rvm	NOUN
ejpam-4859	654	18	transform	transform	NOUN
ejpam-4859	654	19	changes	change	NOUN
ejpam-4859	654	20	.	.	PUNCT
ejpam-4859	655	1	in	in	ADP
ejpam-4859	655	2	the	the	DET
ejpam-4859	655	3	next	next	ADJ
ejpam-4859	655	4	proposition	proposition	NOUN
ejpam-4859	655	5	,	,	PUNCT
ejpam-4859	655	6	we	we	PRON
ejpam-4859	655	7	present	present	VERB
ejpam-4859	655	8	the	the	DET
ejpam-4859	655	9	bounds	bound	NOUN
ejpam-4859	655	10	for	for	ADP
ejpam-4859	655	11	the	the	DET
ejpam-4859	655	12	said	say	VERB
ejpam-4859	655	13	property	property	NOUN
ejpam-4859	655	14	:	:	PUNCT
ejpam-4859	655	15	proposition	proposition	NOUN
ejpam-4859	655	16	15	15	NUM
ejpam-4859	655	17	.	.	PUNCT
ejpam-4859	656	1	let	let	AUX
ejpam-4859	656	2	(	(	PUNCT
ejpam-4859	656	3	n	n	X
ejpam-4859	656	4	,	,	PUNCT
ejpam-4859	656	5	k	k	NOUN
ejpam-4859	656	6	)	)	PUNCT
ejpam-4859	656	7	be	be	AUX
ejpam-4859	656	8	a	a	DET
ejpam-4859	656	9	poly	poly	ADJ
ejpam-4859	656	10	-	-	PUNCT
ejpam-4859	656	11	pl	pl	NOUN
ejpam-4859	656	12	system	system	NOUN
ejpam-4859	656	13	and	and	CCONJ
ejpam-4859	656	14	(	(	PUNCT
ejpam-4859	656	15	n	n	CCONJ
ejpam-4859	656	16	∗,k∗	∗,k∗	ADJ
ejpam-4859	656	17	)	)	PUNCT
ejpam-4859	656	18	be	be	VERB
ejpam-4859	656	19	the	the	DET
ejpam-4859	656	20	star	star	NOUN
ejpam-4859	656	21	-	-	PUNCT
ejpam-4859	656	22	rvm	rvm	PROPN
ejpam-4859	656	23	transform	transform	NOUN
ejpam-4859	656	24	.	.	PUNCT
ejpam-4859	657	1	given	give	VERB
ejpam-4859	657	2	the	the	DET
ejpam-4859	657	3	deficiency	deficiency	NOUN
ejpam-4859	657	4	δ	δ	PROPN
ejpam-4859	657	5	of	of	ADP
ejpam-4859	657	6	the	the	DET
ejpam-4859	657	7	network	network	NOUN
ejpam-4859	657	8	n	n	CCONJ
ejpam-4859	657	9	,	,	PUNCT
ejpam-4859	657	10	then	then	ADV
ejpam-4859	657	11	the	the	DET
ejpam-4859	657	12	deficiency	deficiency	NOUN
ejpam-4859	657	13	δ∗	δ∗	NOUN
ejpam-4859	657	14	of	of	ADP
ejpam-4859	657	15	the	the	DET
ejpam-4859	657	16	network	network	NOUN
ejpam-4859	657	17	n	n	PRON
ejpam-4859	657	18	∗	∗	NOUN
ejpam-4859	657	19	,	,	PUNCT
ejpam-4859	657	20	is	be	AUX
ejpam-4859	657	21	given	give	VERB
ejpam-4859	657	22	by	by	ADP
ejpam-4859	657	23	δ	δ	PROPN
ejpam-4859	657	24	≤	≤	PROPN
ejpam-4859	657	25	δ∗	δ∗	PROPN
ejpam-4859	657	26	≤	≤	NUM
ejpam-4859	657	27	n+	n+	PUNCT
ejpam-4859	657	28	r(m−	r(m−	PROPN
ejpam-4859	657	29	1)−	1)−	PROPN
ejpam-4859	657	30	s−	s−	PROPN
ejpam-4859	657	31	1	1	NUM
ejpam-4859	657	32	.	.	PUNCT
ejpam-4859	657	33	where	where	SCONJ
ejpam-4859	657	34	n	n	PRON
ejpam-4859	657	35	is	be	AUX
ejpam-4859	657	36	the	the	DET
ejpam-4859	657	37	number	number	NOUN
ejpam-4859	657	38	of	of	ADP
ejpam-4859	657	39	complexes	complex	NOUN
ejpam-4859	657	40	,	,	PUNCT
ejpam-4859	657	41	ℓ	ℓ	PROPN
ejpam-4859	657	42	is	be	AUX
ejpam-4859	657	43	the	the	DET
ejpam-4859	657	44	number	number	NOUN
ejpam-4859	657	45	of	of	ADP
ejpam-4859	657	46	linkage	linkage	NOUN
ejpam-4859	657	47	classes	class	NOUN
ejpam-4859	657	48	and	and	CCONJ
ejpam-4859	657	49	s	s	VERB
ejpam-4859	657	50	is	be	AUX
ejpam-4859	657	51	the	the	DET
ejpam-4859	657	52	dimension	dimension	NOUN
ejpam-4859	657	53	of	of	ADP
ejpam-4859	657	54	the	the	DET
ejpam-4859	657	55	stoichiometric	stoichiometric	ADJ
ejpam-4859	657	56	subspace	subspace	NOUN
ejpam-4859	657	57	of	of	ADP
ejpam-4859	657	58	the	the	DET
ejpam-4859	657	59	network	network	NOUN
ejpam-4859	657	60	n	n	NOUN
ejpam-4859	657	61	.	.	PUNCT
ejpam-4859	658	1	proof	proof	NOUN
ejpam-4859	658	2	.	.	PUNCT
ejpam-4859	659	1	observe	observe	VERB
ejpam-4859	659	2	that	that	PRON
ejpam-4859	659	3	:	:	PUNCT
ejpam-4859	659	4	i.	i.	PROPN
ejpam-4859	659	5	n	n	CCONJ
ejpam-4859	659	6	≤	≤	NOUN
ejpam-4859	659	7	n∗	n∗	NOUN
ejpam-4859	659	8	because	because	SCONJ
ejpam-4859	659	9	of	of	ADP
ejpam-4859	659	10	the	the	DET
ejpam-4859	659	11	possible	possible	ADJ
ejpam-4859	659	12	additional	additional	ADJ
ejpam-4859	659	13	complexes	complex	NOUN
ejpam-4859	659	14	ii	ii	NOUN
ejpam-4859	659	15	.	.	PUNCT
ejpam-4859	660	1	ℓ∗	ℓ∗	PROPN
ejpam-4859	660	2	≤	≤	PROPN
ejpam-4859	660	3	ℓ	ℓ	PROPN
ejpam-4859	660	4	since	since	SCONJ
ejpam-4859	660	5	star	star	NOUN
ejpam-4859	660	6	-	-	PUNCT
ejpam-4859	660	7	rvm	rvm	PROPN
ejpam-4859	660	8	method	method	NOUN
ejpam-4859	660	9	does	do	AUX
ejpam-4859	660	10	not	not	PART
ejpam-4859	660	11	produce	produce	VERB
ejpam-4859	660	12	additional	additional	ADJ
ejpam-4859	660	13	linkage	linkage	NOUN
ejpam-4859	660	14	class	class	NOUN
ejpam-4859	660	15	but	but	CCONJ
ejpam-4859	660	16	rather	rather	ADV
ejpam-4859	660	17	it	it	PRON
ejpam-4859	660	18	can	can	AUX
ejpam-4859	660	19	lessen	lessen	VERB
ejpam-4859	660	20	the	the	DET
ejpam-4859	660	21	number	number	NOUN
ejpam-4859	660	22	of	of	ADP
ejpam-4859	660	23	original	original	ADJ
ejpam-4859	660	24	linkage	linkage	NOUN
ejpam-4859	660	25	classes	class	NOUN
ejpam-4859	660	26	which	which	PRON
ejpam-4859	660	27	happens	happen	VERB
ejpam-4859	660	28	when	when	SCONJ
ejpam-4859	660	29	there	there	PRON
ejpam-4859	660	30	exist	exist	VERB
ejpam-4859	660	31	additional	additional	ADJ
ejpam-4859	660	32	complexes	complex	NOUN
ejpam-4859	660	33	which	which	PRON
ejpam-4859	660	34	are	be	AUX
ejpam-4859	660	35	equal	equal	ADJ
ejpam-4859	660	36	to	to	ADP
ejpam-4859	660	37	some	some	DET
ejpam-4859	660	38	original	original	ADJ
ejpam-4859	660	39	complexes	complex	NOUN
ejpam-4859	660	40	.	.	PUNCT
ejpam-4859	661	1	with	with	ADP
ejpam-4859	661	2	the	the	DET
ejpam-4859	661	3	two	two	NUM
ejpam-4859	661	4	observations	observation	NOUN
ejpam-4859	661	5	,	,	PUNCT
ejpam-4859	661	6	we	we	PRON
ejpam-4859	661	7	can	can	AUX
ejpam-4859	661	8	say	say	VERB
ejpam-4859	661	9	that	that	SCONJ
ejpam-4859	661	10	n−	n−	PROPN
ejpam-4859	661	11	ℓ	ℓ	PROPN
ejpam-4859	661	12	≤	≤	NOUN
ejpam-4859	661	13	n∗	n∗	PROPN
ejpam-4859	661	14	−	−	PROPN
ejpam-4859	661	15	ℓ∗.	ℓ∗.	NOUN
ejpam-4859	661	16	(	(	PUNCT
ejpam-4859	661	17	3	3	X
ejpam-4859	661	18	)	)	PUNCT
ejpam-4859	661	19	recall	recall	VERB
ejpam-4859	661	20	that	that	SCONJ
ejpam-4859	661	21	from	from	ADP
ejpam-4859	661	22	proposition	proposition	NOUN
ejpam-4859	661	23	11	11	NUM
ejpam-4859	661	24	,	,	PUNCT
ejpam-4859	661	25	that	that	PRON
ejpam-4859	661	26	s∗	s∗	PROPN
ejpam-4859	661	27	=	=	PUNCT
ejpam-4859	661	28	s.	s.	PROPN
ejpam-4859	661	29	by	by	ADP
ejpam-4859	661	30	(	(	PUNCT
ejpam-4859	661	31	3	3	NUM
ejpam-4859	661	32	)	)	PUNCT
ejpam-4859	661	33	,	,	PUNCT
ejpam-4859	661	34	n−	n−	PROPN
ejpam-4859	661	35	ℓ−	ℓ−	PROPN
ejpam-4859	661	36	s	s	PART
ejpam-4859	661	37	≤	≤	NUM
ejpam-4859	661	38	n∗	n∗	PROPN
ejpam-4859	661	39	−	−	PROPN
ejpam-4859	661	40	ℓ∗	ℓ∗	PROPN
ejpam-4859	661	41	−	−	PROPN
ejpam-4859	661	42	s∗	s∗	PROPN
ejpam-4859	661	43	δ	δ	PROPN
ejpam-4859	661	44	≤	≤	NOUN
ejpam-4859	661	45	δ∗.	δ∗.	ADP
ejpam-4859	661	46	references	reference	NOUN
ejpam-4859	661	47	2579	2579	NUM
ejpam-4859	661	48	given	give	VERB
ejpam-4859	661	49	the	the	DET
ejpam-4859	661	50	number	number	NOUN
ejpam-4859	661	51	of	of	ADP
ejpam-4859	661	52	terms	term	NOUN
ejpam-4859	661	53	in	in	ADP
ejpam-4859	661	54	k	k	PROPN
ejpam-4859	661	55	,	,	PUNCT
ejpam-4859	661	56	h	h	NOUN
ejpam-4859	661	57	and	and	CCONJ
ejpam-4859	661	58	number	number	NOUN
ejpam-4859	661	59	of	of	ADP
ejpam-4859	661	60	reactions	reaction	NOUN
ejpam-4859	661	61	r	r	NOUN
ejpam-4859	661	62	in	in	ADP
ejpam-4859	661	63	n	n	PROPN
ejpam-4859	661	64	,	,	PUNCT
ejpam-4859	661	65	it	it	PRON
ejpam-4859	661	66	can	can	AUX
ejpam-4859	661	67	be	be	AUX
ejpam-4859	661	68	observed	observe	VERB
ejpam-4859	661	69	that	that	SCONJ
ejpam-4859	661	70	the	the	DET
ejpam-4859	661	71	maximum	maximum	ADJ
ejpam-4859	661	72	number	number	NOUN
ejpam-4859	661	73	of	of	ADP
ejpam-4859	661	74	additional	additional	ADJ
ejpam-4859	661	75	complexes	complex	NOUN
ejpam-4859	661	76	in	in	ADP
ejpam-4859	661	77	n	n	ADP
ejpam-4859	661	78	∗	∗	NOUN
ejpam-4859	661	79	is	be	AUX
ejpam-4859	661	80	(	(	PUNCT
ejpam-4859	661	81	h−	h−	PROPN
ejpam-4859	661	82	1)r	1)r	NUM
ejpam-4859	661	83	.	.	PUNCT
ejpam-4859	662	1	thus	thus	ADV
ejpam-4859	662	2	,	,	PUNCT
ejpam-4859	662	3	δ	δ	PROPN
ejpam-4859	662	4	≤	≤	PROPN
ejpam-4859	662	5	δ∗	δ∗	PROPN
ejpam-4859	662	6	≤	≤	NUM
ejpam-4859	662	7	n+	n+	PART
ejpam-4859	663	1	r(h−	r(h−	PROPN
ejpam-4859	663	2	1)−	1)−	NUM
ejpam-4859	663	3	ℓ∗	ℓ∗	PROPN
ejpam-4859	663	4	−	−	PROPN
ejpam-4859	663	5	s.	s.	PROPN
ejpam-4859	663	6	since	since	SCONJ
ejpam-4859	663	7	ℓ	ℓ	PROPN
ejpam-4859	663	8	≥	≥	NUM
ejpam-4859	663	9	1	1	NUM
ejpam-4859	663	10	,	,	PUNCT
ejpam-4859	663	11	δ	δ	PROPN
ejpam-4859	663	12	≤	≤	PROPN
ejpam-4859	663	13	δ∗	δ∗	PROPN
ejpam-4859	663	14	≤	≤	NUM
ejpam-4859	663	15	n+	n+	PART
ejpam-4859	663	16	r(h−	r(h−	PROPN
ejpam-4859	663	17	1)−	1)−	NUM
ejpam-4859	663	18	s−	s−	PROPN
ejpam-4859	663	19	1	1	NUM
ejpam-4859	663	20	.	.	PUNCT
ejpam-4859	663	21	3.3.9	3.3.9	NUM
ejpam-4859	663	22	.	.	PUNCT
ejpam-4859	663	23	reactant	reactant	NOUN
ejpam-4859	663	24	rank	rank	VERB
ejpam-4859	663	25	the	the	DET
ejpam-4859	663	26	following	follow	VERB
ejpam-4859	663	27	proposition	proposition	NOUN
ejpam-4859	663	28	tells	tell	VERB
ejpam-4859	663	29	about	about	ADP
ejpam-4859	663	30	the	the	DET
ejpam-4859	663	31	effect	effect	NOUN
ejpam-4859	663	32	of	of	ADP
ejpam-4859	663	33	the	the	DET
ejpam-4859	663	34	star	star	NOUN
ejpam-4859	663	35	-	-	PUNCT
ejpam-4859	663	36	rvm	rvm	PROPN
ejpam-4859	663	37	transformation	transformation	NOUN
ejpam-4859	663	38	on	on	ADP
ejpam-4859	663	39	the	the	DET
ejpam-4859	663	40	reactant	reactant	NOUN
ejpam-4859	663	41	rank	rank	NOUN
ejpam-4859	663	42	of	of	ADP
ejpam-4859	663	43	the	the	DET
ejpam-4859	663	44	network	network	NOUN
ejpam-4859	663	45	.	.	PUNCT
ejpam-4859	664	1	proposition	proposition	NOUN
ejpam-4859	664	2	16	16	NUM
ejpam-4859	664	3	.	.	PUNCT
ejpam-4859	665	1	let	let	AUX
ejpam-4859	665	2	(	(	PUNCT
ejpam-4859	665	3	n	n	X
ejpam-4859	665	4	,	,	PUNCT
ejpam-4859	665	5	k	k	NOUN
ejpam-4859	665	6	)	)	PUNCT
ejpam-4859	665	7	be	be	AUX
ejpam-4859	665	8	a	a	DET
ejpam-4859	665	9	poly	poly	ADJ
ejpam-4859	665	10	-	-	PUNCT
ejpam-4859	665	11	pl	pl	NOUN
ejpam-4859	665	12	system	system	NOUN
ejpam-4859	665	13	and	and	CCONJ
ejpam-4859	665	14	(	(	PUNCT
ejpam-4859	665	15	n	n	CCONJ
ejpam-4859	665	16	∗,k∗	∗,k∗	ADJ
ejpam-4859	665	17	)	)	PUNCT
ejpam-4859	665	18	be	be	VERB
ejpam-4859	665	19	the	the	DET
ejpam-4859	665	20	star	star	NOUN
ejpam-4859	665	21	-	-	PUNCT
ejpam-4859	665	22	rvm	rvm	PROPN
ejpam-4859	665	23	transform	transform	NOUN
ejpam-4859	665	24	.	.	PUNCT
ejpam-4859	666	1	the	the	DET
ejpam-4859	666	2	reactant	reactant	NOUN
ejpam-4859	666	3	rank	rank	NOUN
ejpam-4859	666	4	of	of	ADP
ejpam-4859	666	5	n	n	PROPN
ejpam-4859	666	6	∗	∗	NOUN
ejpam-4859	666	7	is	be	AUX
ejpam-4859	666	8	q∗	q∗	NOUN
ejpam-4859	666	9	=	=	SYM
ejpam-4859	666	10	c	c	NOUN
ejpam-4859	666	11	,	,	PUNCT
ejpam-4859	666	12	where	where	SCONJ
ejpam-4859	666	13	c	c	PROPN
ejpam-4859	666	14	is	be	AUX
ejpam-4859	666	15	the	the	DET
ejpam-4859	666	16	rank	rank	NOUN
ejpam-4859	666	17	of	of	ADP
ejpam-4859	666	18	the	the	DET
ejpam-4859	666	19	linear	linear	PROPN
ejpam-4859	666	20	subspace	subspace	NOUN
ejpam-4859	666	21	generated	generate	VERB
ejpam-4859	666	22	by	by	ADP
ejpam-4859	666	23	the	the	DET
ejpam-4859	666	24	all	all	DET
ejpam-4859	666	25	the	the	DET
ejpam-4859	666	26	complexes	complex	NOUN
ejpam-4859	666	27	.	.	PUNCT
ejpam-4859	667	1	proof	proof	NOUN
ejpam-4859	667	2	.	.	PUNCT
ejpam-4859	668	1	let	let	AUX
ejpam-4859	668	2	(	(	PUNCT
ejpam-4859	668	3	n	n	X
ejpam-4859	668	4	,	,	PUNCT
ejpam-4859	668	5	k	k	NOUN
ejpam-4859	668	6	)	)	PUNCT
ejpam-4859	668	7	be	be	AUX
ejpam-4859	668	8	a	a	DET
ejpam-4859	668	9	poly	poly	ADJ
ejpam-4859	668	10	-	-	PUNCT
ejpam-4859	668	11	pl	pl	NOUN
ejpam-4859	668	12	systems	system	NOUN
ejpam-4859	668	13	and	and	CCONJ
ejpam-4859	668	14	(	(	PUNCT
ejpam-4859	668	15	n	n	CCONJ
ejpam-4859	668	16	∗,k∗	∗,k∗	ADJ
ejpam-4859	668	17	)	)	PUNCT
ejpam-4859	668	18	be	be	VERB
ejpam-4859	668	19	the	the	DET
ejpam-4859	668	20	star	star	NOUN
ejpam-4859	668	21	-	-	PUNCT
ejpam-4859	668	22	rvm	rvm	PROPN
ejpam-4859	668	23	transform	transform	NOUN
ejpam-4859	668	24	.	.	PUNCT
ejpam-4859	669	1	also	also	ADV
ejpam-4859	669	2	,	,	PUNCT
ejpam-4859	669	3	let	let	VERB
ejpam-4859	669	4	q∗	q∗	NOUN
ejpam-4859	669	5	be	be	AUX
ejpam-4859	669	6	the	the	DET
ejpam-4859	669	7	reactant	reactant	NOUN
ejpam-4859	669	8	rank	rank	NOUN
ejpam-4859	669	9	of	of	ADP
ejpam-4859	669	10	n∗.	n∗.	PROPN
ejpam-4859	669	11	note	note	VERB
ejpam-4859	669	12	that	that	SCONJ
ejpam-4859	669	13	for	for	ADP
ejpam-4859	669	14	a	a	DET
ejpam-4859	669	15	reaction	reaction	NOUN
ejpam-4859	669	16	y	y	PROPN
ejpam-4859	669	17	→	→	SYM
ejpam-4859	669	18	y′	y′	NOUN
ejpam-4859	669	19	in	in	ADP
ejpam-4859	669	20	n	n	PROPN
ejpam-4859	669	21	,	,	PUNCT
ejpam-4859	669	22	the	the	DET
ejpam-4859	669	23	reactions	reaction	NOUN
ejpam-4859	669	24	and	and	CCONJ
ejpam-4859	669	25	complexes	complex	NOUN
ejpam-4859	669	26	in	in	ADP
ejpam-4859	669	27	n	n	ADP
ejpam-4859	669	28	∗	∗	NOUN
ejpam-4859	669	29	by	by	ADP
ejpam-4859	669	30	starrvm	starrvm	NOUN
ejpam-4859	669	31	method	method	NOUN
ejpam-4859	669	32	is	be	AUX
ejpam-4859	669	33	in	in	ADP
ejpam-4859	669	34	the	the	DET
ejpam-4859	669	35	form	form	NOUN
ejpam-4859	669	36	:	:	PUNCT
ejpam-4859	669	37	y	y	PROPN
ejpam-4859	669	38	→	→	SYM
ejpam-4859	669	39	y′	y′	NOUN
ejpam-4859	669	40	→	→	SYM
ejpam-4859	669	41	y′	y′	NOUN
ejpam-4859	669	42	+	+	CCONJ
ejpam-4859	669	43	(	(	PUNCT
ejpam-4859	669	44	y′	y′	NUM
ejpam-4859	669	45	−	−	PROPN
ejpam-4859	669	46	y	y	PROPN
ejpam-4859	669	47	)	)	PUNCT
ejpam-4859	669	48	→	→	SYM
ejpam-4859	669	49	y′	y′	NOUN
ejpam-4859	670	1	+	+	SYM
ejpam-4859	670	2	2(y′	2(y′	NUM
ejpam-4859	670	3	−	−	PROPN
ejpam-4859	670	4	y	y	NOUN
ejpam-4859	670	5	)	)	PUNCT
ejpam-4859	670	6	→	→	PUNCT
ejpam-4859	670	7	.	.	PUNCT
ejpam-4859	670	8	.	.	PUNCT
ejpam-4859	670	9	.	.	PUNCT
ejpam-4859	671	1	or	or	CCONJ
ejpam-4859	671	2	y	y	PROPN
ejpam-4859	672	1	+	+	CCONJ
ejpam-4859	672	2	(	(	PUNCT
ejpam-4859	672	3	h−	h−	PROPN
ejpam-4859	672	4	1)(y	1)(y	NUM
ejpam-4859	672	5	−	−	NUM
ejpam-4859	672	6	y′	y′	NUM
ejpam-4859	672	7	)	)	PUNCT
ejpam-4859	672	8	→	→	SYM
ejpam-4859	672	9	·	·	PUNCT
ejpam-4859	672	10	·	·	PUNCT
ejpam-4859	672	11	·	·	PUNCT
ejpam-4859	673	1	→	→	PUNCT
ejpam-4859	673	2	y	y	PROPN
ejpam-4859	673	3	+	+	CCONJ
ejpam-4859	673	4	2(y	2(y	NUM
ejpam-4859	673	5	−	−	NUM
ejpam-4859	673	6	y′	y′	NUM
ejpam-4859	673	7	)	)	PUNCT
ejpam-4859	673	8	→	→	SYM
ejpam-4859	673	9	y	y	PROPN
ejpam-4859	674	1	+	+	CCONJ
ejpam-4859	674	2	(	(	PUNCT
ejpam-4859	674	3	y	y	PROPN
ejpam-4859	674	4	−	−	NOUN
ejpam-4859	674	5	y′	y′	NUM
ejpam-4859	674	6	)	)	PUNCT
ejpam-4859	674	7	→	→	SYM
ejpam-4859	674	8	y	y	X
ejpam-4859	674	9	→	→	SYM
ejpam-4859	674	10	y′	y′	NOUN
ejpam-4859	674	11	observe	observe	VERB
ejpam-4859	674	12	that	that	SCONJ
ejpam-4859	674	13	all	all	DET
ejpam-4859	674	14	additional	additional	ADJ
ejpam-4859	674	15	reactant	reactant	NOUN
ejpam-4859	674	16	complexes	complex	NOUN
ejpam-4859	674	17	from	from	ADP
ejpam-4859	674	18	every	every	DET
ejpam-4859	674	19	reaction	reaction	NOUN
ejpam-4859	674	20	y	y	PROPN
ejpam-4859	674	21	→	→	SYM
ejpam-4859	674	22	y′	y′	NOUN
ejpam-4859	674	23	in	in	ADP
ejpam-4859	674	24	this	this	DET
ejpam-4859	674	25	transformed	transform	VERB
ejpam-4859	674	26	network	network	NOUN
ejpam-4859	674	27	are	be	AUX
ejpam-4859	674	28	linear	linear	ADJ
ejpam-4859	674	29	combinations	combination	NOUN
ejpam-4859	674	30	of	of	ADP
ejpam-4859	674	31	y	y	PROPN
ejpam-4859	674	32	and	and	CCONJ
ejpam-4859	674	33	y′.	y′.	PROPN
ejpam-4859	674	34	this	this	PRON
ejpam-4859	674	35	implies	imply	VERB
ejpam-4859	674	36	that	that	SCONJ
ejpam-4859	674	37	all	all	DET
ejpam-4859	674	38	reactant	reactant	NOUN
ejpam-4859	674	39	complexes	complex	NOUN
ejpam-4859	674	40	of	of	ADP
ejpam-4859	674	41	n	n	PROPN
ejpam-4859	674	42	∗	∗	NOUN
ejpam-4859	674	43	are	be	AUX
ejpam-4859	674	44	linear	linear	ADJ
ejpam-4859	674	45	combinations	combination	NOUN
ejpam-4859	674	46	of	of	ADP
ejpam-4859	674	47	the	the	DET
ejpam-4859	674	48	complexes	complex	NOUN
ejpam-4859	674	49	in	in	ADP
ejpam-4859	674	50	n	n	PROPN
ejpam-4859	674	51	.	.	PUNCT
ejpam-4859	675	1	hence	hence	ADV
ejpam-4859	675	2	,	,	PUNCT
ejpam-4859	675	3	the	the	DET
ejpam-4859	675	4	reactant	reactant	NOUN
ejpam-4859	675	5	rank	rank	NOUN
ejpam-4859	675	6	q∗	q∗	NOUN
ejpam-4859	675	7	=	=	SYM
ejpam-4859	675	8	c.	c.	PROPN
ejpam-4859	675	9	4	4	NUM
ejpam-4859	675	10	.	.	PUNCT
ejpam-4859	676	1	conclusion	conclusion	NOUN
ejpam-4859	676	2	star	star	NOUN
ejpam-4859	676	3	transformations	transformation	NOUN
ejpam-4859	676	4	from	from	ADP
ejpam-4859	676	5	pyk	pyk	PROPN
ejpam-4859	676	6	to	to	ADP
ejpam-4859	676	7	plk	plk	PROPN
ejpam-4859	676	8	is	be	AUX
ejpam-4859	676	9	introduced	introduce	VERB
ejpam-4859	676	10	leading	lead	VERB
ejpam-4859	676	11	to	to	ADP
ejpam-4859	676	12	analyses	analysis	NOUN
ejpam-4859	676	13	of	of	ADP
ejpam-4859	676	14	power	power	NOUN
ejpam-4859	676	15	law	law	NOUN
ejpam-4859	676	16	kinetics	kinetic	NOUN
ejpam-4859	676	17	and	and	CCONJ
ejpam-4859	676	18	their	their	PRON
ejpam-4859	676	19	invariant	invariant	ADJ
ejpam-4859	676	20	properties	property	NOUN
ejpam-4859	676	21	.	.	PUNCT
ejpam-4859	677	1	the	the	DET
ejpam-4859	677	2	transformation	transformation	NOUN
ejpam-4859	677	3	is	be	AUX
ejpam-4859	677	4	defined	define	VERB
ejpam-4859	677	5	by	by	ADP
ejpam-4859	677	6	constructing	construct	VERB
ejpam-4859	677	7	crn	crn	NOUN
ejpam-4859	677	8	using	use	VERB
ejpam-4859	677	9	additional	additional	ADJ
ejpam-4859	677	10	complexes	complex	NOUN
ejpam-4859	677	11	and	and	CCONJ
ejpam-4859	677	12	reactions	reaction	NOUN
ejpam-4859	677	13	using	use	VERB
ejpam-4859	677	14	multiple	multiple	ADJ
ejpam-4859	677	15	reaction	reaction	NOUN
ejpam-4859	677	16	vectors	vector	NOUN
ejpam-4859	677	17	.	.	PUNCT
ejpam-4859	678	1	a	a	DET
ejpam-4859	678	2	comparison	comparison	NOUN
ejpam-4859	678	3	of	of	ADP
ejpam-4859	678	4	the	the	DET
ejpam-4859	678	5	network	network	NOUN
ejpam-4859	678	6	numbers	number	NOUN
ejpam-4859	678	7	of	of	ADP
ejpam-4859	678	8	the	the	DET
ejpam-4859	678	9	original	original	ADJ
ejpam-4859	678	10	network	network	NOUN
ejpam-4859	678	11	and	and	CCONJ
ejpam-4859	678	12	its	its	PRON
ejpam-4859	678	13	transformed	transform	VERB
ejpam-4859	678	14	network	network	NOUN
ejpam-4859	678	15	lead	lead	VERB
ejpam-4859	678	16	us	we	PRON
ejpam-4859	678	17	to	to	ADP
ejpam-4859	678	18	the	the	DET
ejpam-4859	678	19	identification	identification	NOUN
ejpam-4859	678	20	variant	variant	NOUN
ejpam-4859	678	21	and	and	CCONJ
ejpam-4859	678	22	invariant	invariant	ADJ
ejpam-4859	678	23	properties	property	NOUN
ejpam-4859	678	24	brought	bring	VERB
ejpam-4859	678	25	about	about	ADP
ejpam-4859	678	26	by	by	ADP
ejpam-4859	678	27	these	these	DET
ejpam-4859	678	28	transformations	transformation	NOUN
ejpam-4859	678	29	.	.	PUNCT
ejpam-4859	679	1	references	reference	NOUN
ejpam-4859	679	2	[	[	X
ejpam-4859	679	3	1	1	NUM
ejpam-4859	679	4	]	]	PUNCT
ejpam-4859	679	5	arceo	arceo	PROPN
ejpam-4859	679	6	cp	cp	PROPN
ejpam-4859	679	7	,	,	PUNCT
ejpam-4859	679	8	jose	jose	PROPN
ejpam-4859	679	9	ec	ec	PROPN
ejpam-4859	679	10	,	,	PUNCT
ejpam-4859	679	11	lao	lao	PROPN
ejpam-4859	679	12	ar	ar	PROPN
ejpam-4859	679	13	,	,	PUNCT
ejpam-4859	679	14	mendoza	mendoza	PROPN
ejpam-4859	679	15	er	er	INTJ
ejpam-4859	679	16	.	.	PUNCT
ejpam-4859	679	17	reactant	reactant	NOUN
ejpam-4859	679	18	subspaces	subspace	NOUN
ejpam-4859	679	19	and	and	CCONJ
ejpam-4859	679	20	kinetics	kinetic	NOUN
ejpam-4859	679	21	of	of	ADP
ejpam-4859	679	22	chemical	chemical	ADJ
ejpam-4859	679	23	reaction	reaction	NOUN
ejpam-4859	679	24	networks	network	NOUN
ejpam-4859	679	25	.	.	PUNCT
ejpam-4859	680	1	journal	journal	PROPN
ejpam-4859	680	2	of	of	ADP
ejpam-4859	680	3	mathematical	mathematical	ADJ
ejpam-4859	680	4	chemistry	chemistry	NOUN
ejpam-4859	680	5	.	.	PUNCT
ejpam-4859	681	1	56(2):395–422	56(2):395–422	NUM
ejpam-4859	681	2	,	,	PUNCT
ejpam-4859	681	3	2018	2018	NUM
ejpam-4859	681	4	references	reference	NOUN
ejpam-4859	681	5	2580	2580	NUM
ejpam-4859	681	6	[	[	X
ejpam-4859	681	7	2	2	NUM
ejpam-4859	681	8	]	]	X
ejpam-4859	681	9	boros	boro	NOUN
ejpam-4859	681	10	,	,	PUNCT
ejpam-4859	681	11	b.	b.	PROPN
ejpam-4859	681	12	on	on	ADP
ejpam-4859	681	13	the	the	DET
ejpam-4859	681	14	positive	positive	ADJ
ejpam-4859	681	15	steady	steady	ADJ
ejpam-4859	681	16	states	state	NOUN
ejpam-4859	681	17	of	of	ADP
ejpam-4859	681	18	deficiency	deficiency	NOUN
ejpam-4859	681	19	one	one	NUM
ejpam-4859	681	20	mass	mass	NOUN
ejpam-4859	681	21	action	action	NOUN
ejpam-4859	681	22	systems	system	NOUN
ejpam-4859	681	23	.	.	PUNCT
ejpam-4859	682	1	phd	phd	NOUN
ejpam-4859	682	2	thesis	thesis	PROPN
ejpam-4859	682	3	,	,	PUNCT
ejpam-4859	682	4	eotvos	eotvos	PROPN
ejpam-4859	682	5	lorand	lorand	PROPN
ejpam-4859	682	6	university	university	NOUN
ejpam-4859	682	7	.	.	PUNCT
ejpam-4859	683	1	[	[	X
ejpam-4859	683	2	3	3	X
ejpam-4859	683	3	]	]	X
ejpam-4859	683	4	cressman	cressman	ADJ
ejpam-4859	683	5	r	r	NOUN
ejpam-4859	683	6	,	,	PUNCT
ejpam-4859	683	7	tao	tao	PROPN
ejpam-4859	683	8	y.	y.	PROPN
ejpam-4859	683	9	the	the	DET
ejpam-4859	683	10	replicator	replicator	NOUN
ejpam-4859	683	11	equation	equation	NOUN
ejpam-4859	683	12	and	and	CCONJ
ejpam-4859	683	13	other	other	ADJ
ejpam-4859	683	14	game	game	NOUN
ejpam-4859	683	15	dynamics	dynamic	NOUN
ejpam-4859	683	16	.	.	PUNCT
ejpam-4859	684	1	proceedings	proceeding	NOUN
ejpam-4859	684	2	of	of	ADP
ejpam-4859	684	3	thenational	thenational	ADJ
ejpam-4859	684	4	academy	academy	NOUN
ejpam-4859	684	5	of	of	ADP
ejpam-4859	684	6	sciences	sciences	PROPN
ejpam-4859	684	7	.	.	PUNCT
ejpam-4859	684	8	111	111	NUM
ejpam-4859	684	9	,	,	PUNCT
ejpam-4859	684	10	10810–10817	10810–10817	NUM
ejpam-4859	684	11	,	,	PUNCT
ejpam-4859	684	12	2018	2018	NUM
ejpam-4859	684	13	[	[	X
ejpam-4859	684	14	4	4	NUM
ejpam-4859	684	15	]	]	X
ejpam-4859	684	16	feinberg	feinberg	PROPN
ejpam-4859	684	17	m.	m.	NOUN
ejpam-4859	684	18	lectures	lecture	VERB
ejpam-4859	684	19	on	on	ADP
ejpam-4859	684	20	chemical	chemical	ADJ
ejpam-4859	684	21	reaction	reaction	NOUN
ejpam-4859	684	22	networks	network	NOUN
ejpam-4859	684	23	.	.	PUNCT
ejpam-4859	685	1	notes	note	NOUN
ejpam-4859	685	2	of	of	ADP
ejpam-4859	685	3	lectures	lecture	NOUN
ejpam-4859	685	4	given	give	VERB
ejpam-4859	685	5	at	at	ADP
ejpam-4859	685	6	the	the	DET
ejpam-4859	685	7	mathematics	mathematics	PROPN
ejpam-4859	685	8	research	research	NOUN
ejpam-4859	685	9	center	center	NOUN
ejpam-4859	685	10	of	of	ADP
ejpam-4859	685	11	the	the	DET
ejpam-4859	685	12	university	university	PROPN
ejpam-4859	685	13	of	of	ADP
ejpam-4859	685	14	wisconsin	wisconsin	PROPN
ejpam-4859	685	15	.	.	PUNCT
ejpam-4859	686	1	1979	1979	NUM
ejpam-4859	687	1	[	[	X
ejpam-4859	687	2	5	5	NUM
ejpam-4859	687	3	]	]	X
ejpam-4859	687	4	feinberg	feinberg	PROPN
ejpam-4859	687	5	m.	m.	PROPN
ejpam-4859	687	6	chemical	chemical	PROPN
ejpam-4859	687	7	reaction	reaction	NOUN
ejpam-4859	687	8	network	network	NOUN
ejpam-4859	687	9	structure	structure	NOUN
ejpam-4859	687	10	and	and	CCONJ
ejpam-4859	687	11	the	the	DET
ejpam-4859	687	12	stability	stability	NOUN
ejpam-4859	687	13	of	of	ADP
ejpam-4859	687	14	complex	complex	ADJ
ejpam-4859	687	15	isothermal	isothermal	ADJ
ejpam-4859	687	16	reactors	reactor	NOUN
ejpam-4859	687	17	:	:	PUNCT
ejpam-4859	687	18	i.the	i.the	DET
ejpam-4859	687	19	deficiency	deficiency	NOUN
ejpam-4859	687	20	zero	zero	NUM
ejpam-4859	687	21	and	and	CCONJ
ejpam-4859	687	22	deficiency	deficiency	NOUN
ejpam-4859	687	23	one	one	NUM
ejpam-4859	687	24	theorems	theorem	NOUN
ejpam-4859	687	25	.	.	PUNCT
ejpam-4859	688	1	chemical	chemical	NOUN
ejpam-4859	688	2	engineering	engineering	NOUN
ejpam-4859	688	3	science	science	NOUN
ejpam-4859	688	4	.	.	PUNCT
ejpam-4859	689	1	42	42	NUM
ejpam-4859	689	2	2229	2229	NUM
ejpam-4859	689	3	-	-	SYM
ejpam-4859	689	4	2268,1987	2268,1987	NUM
ejpam-4859	690	1	[	[	X
ejpam-4859	690	2	6	6	NUM
ejpam-4859	690	3	]	]	X
ejpam-4859	690	4	fortun	fortun	NOUN
ejpam-4859	690	5	nt	not	PART
ejpam-4859	690	6	,	,	PUNCT
ejpam-4859	690	7	lao	lao	PROPN
ejpam-4859	690	8	ar	ar	PROPN
ejpam-4859	690	9	,	,	PUNCT
ejpam-4859	690	10	razon	razon	PROPN
ejpam-4859	690	11	lf	lf	PROPN
ejpam-4859	690	12	and	and	CCONJ
ejpam-4859	690	13	mendoza	mendoza	PROPN
ejpam-4859	690	14	er	er	INTJ
ejpam-4859	690	15	.	.	PUNCT
ejpam-4859	690	16	multistationarity	multistationarity	NOUN
ejpam-4859	690	17	in	in	ADP
ejpam-4859	690	18	earth´s	earth´s	PROPN
ejpam-4859	690	19	preindustrial	preindustrial	ADJ
ejpam-4859	690	20	carbon	carbon	NOUN
ejpam-4859	690	21	cycle	cycle	NOUN
ejpam-4859	690	22	models	model	NOUN
ejpam-4859	690	23	.	.	PUNCT
ejpam-4859	691	1	manila	manila	PROPN
ejpam-4859	691	2	j.	j.	PROPN
ejpam-4859	691	3	science	science	PROPN
ejpam-4859	691	4	11	11	NUM
ejpam-4859	691	5	,	,	PUNCT
ejpam-4859	691	6	81	81	NUM
ejpam-4859	691	7	-	-	SYM
ejpam-4859	691	8	96	96	NUM
ejpam-4859	691	9	,	,	PUNCT
ejpam-4859	691	10	2018	2018	NUM
ejpam-4859	691	11	[	[	X
ejpam-4859	691	12	7	7	X
ejpam-4859	691	13	]	]	X
ejpam-4859	691	14	mendoza	mendoza	PROPN
ejpam-4859	691	15	er	er	INTJ
ejpam-4859	691	16	,	,	PUNCT
ejpam-4859	691	17	talabis	talabis	NOUN
ejpam-4859	691	18	dasj	dasj	NOUN
ejpam-4859	691	19	and	and	CCONJ
ejpam-4859	691	20	jose	jose	PROPN
ejpam-4859	691	21	ec	ec	PROPN
ejpam-4859	691	22	.	.	PUNCT
ejpam-4859	692	1	positive	positive	ADJ
ejpam-4859	692	2	equilibria	equilibrium	NOUN
ejpam-4859	692	3	of	of	ADP
ejpam-4859	692	4	weakly	weakly	ADJ
ejpam-4859	692	5	reversible	reversible	ADJ
ejpam-4859	692	6	power	power	NOUN
ejpam-4859	692	7	law	law	NOUN
ejpam-4859	692	8	kinetic	kinetic	NOUN
ejpam-4859	692	9	systems	system	NOUN
ejpam-4859	692	10	with	with	ADP
ejpam-4859	692	11	linear	linear	ADJ
ejpam-4859	692	12	independent	independent	ADJ
ejpam-4859	692	13	interactions	interaction	NOUN
ejpam-4859	692	14	.	.	PUNCT
ejpam-4859	693	1	j.	j.	PROPN
ejpam-4859	693	2	math	math	PROPN
ejpam-4859	693	3	chem	chem	PROPN
ejpam-4859	693	4	.	.	PUNCT
ejpam-4859	694	1	10910018	10910018	NUM
ejpam-4859	694	2	-	-	SYM
ejpam-4859	694	3	0909	0909	NUM
ejpam-4859	694	4	-	-	PUNCT
ejpam-4859	694	5	2	2	NUM
ejpam-4859	694	6	,	,	PUNCT
ejpam-4859	694	7	2018	2018	NUM
ejpam-4859	695	1	[	[	SYM
ejpam-4859	695	2	8	8	NUM
ejpam-4859	695	3	]	]	SYM
ejpam-4859	695	4	shinar	shinar	NOUN
ejpam-4859	695	5	g	g	PROPN
ejpam-4859	695	6	and	and	CCONJ
ejpam-4859	695	7	feinberg	feinberg	PROPN
ejpam-4859	695	8	m.	m.	NOUN
ejpam-4859	695	9	design	design	NOUN
ejpam-4859	695	10	principles	principle	NOUN
ejpam-4859	695	11	for	for	ADP
ejpam-4859	695	12	robust	robust	ADJ
ejpam-4859	695	13	biochemical	biochemical	ADJ
ejpam-4859	695	14	reaction	reaction	NOUN
ejpam-4859	695	15	networks	network	NOUN
ejpam-4859	695	16	:	:	PUNCT
ejpam-4859	695	17	what	what	PRON
ejpam-4859	695	18	works	work	VERB
ejpam-4859	695	19	,	,	PUNCT
ejpam-4859	695	20	what	what	PRON
ejpam-4859	695	21	can	can	AUX
ejpam-4859	695	22	not	not	PART
ejpam-4859	695	23	work	work	VERB
ejpam-4859	695	24	,	,	PUNCT
ejpam-4859	695	25	and	and	CCONJ
ejpam-4859	695	26	what	what	PRON
ejpam-4859	695	27	might	might	AUX
ejpam-4859	695	28	almost	almost	ADV
ejpam-4859	695	29	work	work	VERB
ejpam-4859	695	30	.	.	PUNCT
ejpam-4859	696	1	mathematical	mathematical	ADJ
ejpam-4859	696	2	biosciences	bioscience	NOUN
ejpam-4859	696	3	,	,	PUNCT
ejpam-4859	696	4	231	231	NUM
ejpam-4859	696	5	1:39–48	1:39–48	NUM
ejpam-4859	696	6	,	,	PUNCT
ejpam-4859	696	7	2011	2011	NUM
ejpam-4859	697	1	[	[	X
ejpam-4859	697	2	9	9	NUM
ejpam-4859	697	3	]	]	PUNCT
ejpam-4859	697	4	veloz	veloz	PROPN
ejpam-4859	697	5	t	t	PROPN
ejpam-4859	697	6	,	,	PUNCT
ejpam-4859	697	7	razeto	razeto	NOUN
ejpam-4859	697	8	-	-	PUNCT
ejpam-4859	697	9	barry	barry	NOUN
ejpam-4859	697	10	p	p	NOUN
ejpam-4859	697	11	,	,	PUNCT
ejpam-4859	697	12	dittrich	dittrich	VERB
ejpam-4859	697	13	p	p	NOUN
ejpam-4859	697	14	and	and	CCONJ
ejpam-4859	697	15	fajardo	fajardo	PROPN
ejpam-4859	697	16	a.	a.	NOUN
ejpam-4859	697	17	reaction	reaction	PROPN
ejpam-4859	697	18	networks	network	NOUN
ejpam-4859	697	19	and	and	CCONJ
ejpam-4859	697	20	evolutionary	evolutionary	ADJ
ejpam-4859	697	21	game	game	NOUN
ejpam-4859	697	22	theory	theory	NOUN
ejpam-4859	697	23	.	.	PUNCT
ejpam-4859	698	1	j.math	j.math	NOUN
ejpam-4859	698	2	.	.	PUNCT
ejpam-4859	699	1	biol	biol	PROPN
ejpam-4859	699	2	.	.	PUNCT
ejpam-4859	700	1	68	68	NUM
ejpam-4859	700	2	:	:	PUNCT
ejpam-4859	700	3	181	181	NUM
ejpam-4859	700	4	-	-	SYM
ejpam-4859	700	5	206	206	NUM
ejpam-4859	700	6	,	,	PUNCT
ejpam-4859	700	7	2014	2014	NUM
ejpam-4859	701	1	[	[	X
ejpam-4859	701	2	10	10	NUM
ejpam-4859	701	3	]	]	PUNCT
ejpam-4859	701	4	wiuf	wiuf	NOUN
ejpam-4859	701	5	c	c	PROPN
ejpam-4859	701	6	and	and	CCONJ
ejpam-4859	701	7	feliu	feliu	PROPN
ejpam-4859	701	8	e.	e.	PROPN
ejpam-4859	701	9	power	power	PROPN
ejpam-4859	701	10	-	-	PUNCT
ejpam-4859	701	11	law	law	NOUN
ejpam-4859	701	12	kinetics	kinetic	NOUN
ejpam-4859	701	13	and	and	CCONJ
ejpam-4859	701	14	determinant	determinant	ADJ
ejpam-4859	701	15	criteria	criterion	NOUN
ejpam-4859	701	16	for	for	ADP
ejpam-4859	701	17	the	the	DET
ejpam-4859	701	18	preclusion	preclusion	NOUN
ejpam-4859	701	19	of	of	ADP
ejpam-4859	701	20	multistationarity	multistationarity	NOUN
ejpam-4859	701	21	in	in	ADP
ejpam-4859	701	22	networks	network	NOUN
ejpam-4859	701	23	of	of	ADP
ejpam-4859	701	24	interacting	interact	VERB
ejpam-4859	701	25	species	specie	NOUN
ejpam-4859	701	26	.	.	PUNCT
ejpam-4859	702	1	iam	iam	PROPN
ejpam-4859	702	2	j	j	PROPN
ejpam-4859	702	3	appl	appl	PROPN
ejpam-4859	702	4	dyn	dyn	PROPN
ejpam-4859	702	5	syst	syst	PROPN
ejpam-4859	702	6	.	.	PUNCT
ejpam-4859	703	1	12	12	NUM
ejpam-4859	703	2	:	:	PUNCT
ejpam-4859	703	3	1685	1685	NUM
ejpam-4859	703	4	-	-	SYM
ejpam-4859	703	5	1721	1721	NUM
ejpam-4859	703	6	,	,	PUNCT
ejpam-4859	703	7	2013	2013	NUM