id	sid	tid	token	lemma	pos
ejpam-5384	1	1	european	european	PROPN
ejpam-5384	1	2	journal	journal	PROPN
ejpam-5384	1	3	of	of	ADP
ejpam-5384	1	4	pure	pure	ADJ
ejpam-5384	1	5	and	and	CCONJ
ejpam-5384	1	6	applied	apply	VERB
ejpam-5384	1	7	mathematics	mathematic	NOUN
ejpam-5384	1	8	vol	vol	NOUN
ejpam-5384	1	9	.	.	PROPN
ejpam-5384	2	1	17	17	NUM
ejpam-5384	2	2	,	,	PUNCT
ejpam-5384	2	3	no	no	INTJ
ejpam-5384	2	4	.	.	NOUN
ejpam-5384	2	5	4	4	NUM
ejpam-5384	2	6	,	,	PUNCT
ejpam-5384	2	7	2024	2024	NUM
ejpam-5384	2	8	,	,	PUNCT
ejpam-5384	2	9	2448	2448	NUM
ejpam-5384	2	10	-	-	SYM
ejpam-5384	2	11	2466	2466	NUM
ejpam-5384	2	12	issn	issn	PROPN
ejpam-5384	2	13	1307	1307	NUM
ejpam-5384	2	14	-	-	SYM
ejpam-5384	2	15	5543	5543	NUM
ejpam-5384	2	16	–	–	PUNCT
ejpam-5384	2	17	ejpam.com	ejpam.com	X
ejpam-5384	2	18	published	publish	VERB
ejpam-5384	2	19	by	by	ADP
ejpam-5384	2	20	new	new	PROPN
ejpam-5384	2	21	york	york	PROPN
ejpam-5384	2	22	business	business	PROPN
ejpam-5384	2	23	global	global	ADJ
ejpam-5384	2	24	wardrop	wardrop	NOUN
ejpam-5384	2	25	optimal	optimal	ADJ
ejpam-5384	2	26	networks	network	NOUN
ejpam-5384	2	27	antonios	antonios	PROPN
ejpam-5384	2	28	kalampakas	kalampakas	PROPN
ejpam-5384	2	29	college	college	PROPN
ejpam-5384	2	30	of	of	ADP
ejpam-5384	2	31	engineering	engineering	NOUN
ejpam-5384	2	32	and	and	CCONJ
ejpam-5384	2	33	technology	technology	NOUN
ejpam-5384	2	34	,	,	PUNCT
ejpam-5384	2	35	american	american	PROPN
ejpam-5384	2	36	university	university	PROPN
ejpam-5384	2	37	of	of	ADP
ejpam-5384	2	38	the	the	DET
ejpam-5384	2	39	middle	middle	PROPN
ejpam-5384	2	40	east	east	PROPN
ejpam-5384	2	41	,	,	PUNCT
ejpam-5384	2	42	egaila	egaila	PROPN
ejpam-5384	2	43	,	,	PUNCT
ejpam-5384	2	44	54200	54200	NUM
ejpam-5384	2	45	,	,	PUNCT
ejpam-5384	2	46	kuwait	kuwait	PROPN
ejpam-5384	2	47	abstract	abstract	NOUN
ejpam-5384	2	48	.	.	PUNCT
ejpam-5384	3	1	optimal	optimal	ADJ
ejpam-5384	3	2	flow	flow	NOUN
ejpam-5384	3	3	allocation	allocation	NOUN
ejpam-5384	3	4	in	in	ADP
ejpam-5384	3	5	directed	direct	VERB
ejpam-5384	3	6	networks	network	NOUN
ejpam-5384	3	7	is	be	AUX
ejpam-5384	3	8	often	often	ADV
ejpam-5384	3	9	analyzed	analyze	VERB
ejpam-5384	3	10	through	through	ADP
ejpam-5384	3	11	two	two	NUM
ejpam-5384	3	12	types	type	NOUN
ejpam-5384	3	13	of	of	ADP
ejpam-5384	3	14	equilibria	equilibrium	NOUN
ejpam-5384	3	15	.	.	PUNCT
ejpam-5384	4	1	the	the	DET
ejpam-5384	4	2	first	first	ADJ
ejpam-5384	4	3	,	,	PUNCT
ejpam-5384	4	4	called	call	VERB
ejpam-5384	4	5	user	user	NOUN
ejpam-5384	4	6	equilibrium	equilibrium	NOUN
ejpam-5384	4	7	,	,	PUNCT
ejpam-5384	4	8	occurs	occur	VERB
ejpam-5384	4	9	when	when	SCONJ
ejpam-5384	4	10	the	the	DET
ejpam-5384	4	11	travel	travel	NOUN
ejpam-5384	4	12	times	time	NOUN
ejpam-5384	4	13	on	on	ADP
ejpam-5384	4	14	all	all	DET
ejpam-5384	4	15	utilized	utilize	VERB
ejpam-5384	4	16	routes	route	NOUN
ejpam-5384	4	17	are	be	AUX
ejpam-5384	4	18	the	the	DET
ejpam-5384	4	19	same	same	ADJ
ejpam-5384	4	20	and	and	CCONJ
ejpam-5384	4	21	shorter	short	ADJ
ejpam-5384	4	22	than	than	ADP
ejpam-5384	4	23	every	every	DET
ejpam-5384	4	24	unused	unused	ADJ
ejpam-5384	4	25	route	route	NOUN
ejpam-5384	4	26	.	.	PUNCT
ejpam-5384	5	1	the	the	DET
ejpam-5384	5	2	second	second	ADJ
ejpam-5384	5	3	,	,	PUNCT
ejpam-5384	5	4	called	call	VERB
ejpam-5384	5	5	system	system	NOUN
ejpam-5384	5	6	optimum	optimum	NOUN
ejpam-5384	5	7	,	,	PUNCT
ejpam-5384	5	8	minimizes	minimize	VERB
ejpam-5384	5	9	the	the	DET
ejpam-5384	5	10	average	average	ADJ
ejpam-5384	5	11	travel	travel	NOUN
ejpam-5384	5	12	time	time	NOUN
ejpam-5384	5	13	across	across	ADP
ejpam-5384	5	14	all	all	DET
ejpam-5384	5	15	routes	route	NOUN
ejpam-5384	5	16	.	.	PUNCT
ejpam-5384	6	1	these	these	DET
ejpam-5384	6	2	two	two	NUM
ejpam-5384	6	3	concepts	concept	NOUN
ejpam-5384	6	4	represent	represent	VERB
ejpam-5384	6	5	the	the	DET
ejpam-5384	6	6	optimality	optimality	NOUN
ejpam-5384	6	7	for	for	ADP
ejpam-5384	6	8	individual	individual	ADJ
ejpam-5384	6	9	users	user	NOUN
ejpam-5384	6	10	and	and	CCONJ
ejpam-5384	6	11	for	for	ADP
ejpam-5384	6	12	the	the	DET
ejpam-5384	6	13	network	network	NOUN
ejpam-5384	6	14	as	as	ADP
ejpam-5384	6	15	a	a	DET
ejpam-5384	6	16	whole	whole	NOUN
ejpam-5384	6	17	,	,	PUNCT
ejpam-5384	6	18	respectively	respectively	ADV
ejpam-5384	6	19	,	,	PUNCT
ejpam-5384	6	20	and	and	CCONJ
ejpam-5384	6	21	generally	generally	ADV
ejpam-5384	6	22	do	do	AUX
ejpam-5384	6	23	not	not	PART
ejpam-5384	6	24	coincide	coincide	VERB
ejpam-5384	6	25	.	.	PUNCT
ejpam-5384	7	1	our	our	PRON
ejpam-5384	7	2	main	main	ADJ
ejpam-5384	7	3	objective	objective	NOUN
ejpam-5384	7	4	in	in	ADP
ejpam-5384	7	5	this	this	DET
ejpam-5384	7	6	paper	paper	NOUN
ejpam-5384	7	7	is	be	AUX
ejpam-5384	7	8	to	to	PART
ejpam-5384	7	9	introduce	introduce	VERB
ejpam-5384	7	10	and	and	CCONJ
ejpam-5384	7	11	examine	examine	VERB
ejpam-5384	7	12	the	the	DET
ejpam-5384	7	13	properties	property	NOUN
ejpam-5384	7	14	of	of	ADP
ejpam-5384	7	15	networks	network	NOUN
ejpam-5384	7	16	where	where	SCONJ
ejpam-5384	7	17	the	the	DET
ejpam-5384	7	18	user	user	NOUN
ejpam-5384	7	19	equilibrium	equilibrium	NOUN
ejpam-5384	7	20	and	and	CCONJ
ejpam-5384	7	21	the	the	DET
ejpam-5384	7	22	system	system	NOUN
ejpam-5384	7	23	optimum	optimum	NOUN
ejpam-5384	7	24	are	be	AUX
ejpam-5384	7	25	identical	identical	ADJ
ejpam-5384	7	26	,	,	PUNCT
ejpam-5384	7	27	termed	term	VERB
ejpam-5384	7	28	wardrop	wardrop	VERB
ejpam-5384	7	29	optimal	optimal	ADJ
ejpam-5384	7	30	networks	network	NOUN
ejpam-5384	7	31	.	.	PUNCT
ejpam-5384	8	1	we	we	PRON
ejpam-5384	8	2	achieve	achieve	VERB
ejpam-5384	8	3	this	this	PRON
ejpam-5384	8	4	by	by	ADP
ejpam-5384	8	5	providing	provide	VERB
ejpam-5384	8	6	a	a	DET
ejpam-5384	8	7	set	set	NOUN
ejpam-5384	8	8	of	of	ADP
ejpam-5384	8	9	necessary	necessary	ADJ
ejpam-5384	8	10	and	and	CCONJ
ejpam-5384	8	11	sufficient	sufficient	ADJ
ejpam-5384	8	12	conditions	condition	NOUN
ejpam-5384	8	13	for	for	ADP
ejpam-5384	8	14	wardrop	wardrop	NOUN
ejpam-5384	8	15	optimal	optimal	ADJ
ejpam-5384	8	16	flows	flow	NOUN
ejpam-5384	8	17	and	and	CCONJ
ejpam-5384	8	18	using	use	VERB
ejpam-5384	8	19	this	this	DET
ejpam-5384	8	20	characterization	characterization	NOUN
ejpam-5384	8	21	we	we	PRON
ejpam-5384	8	22	investigate	investigate	VERB
ejpam-5384	8	23	the	the	DET
ejpam-5384	8	24	main	main	ADJ
ejpam-5384	8	25	properties	property	NOUN
ejpam-5384	8	26	of	of	ADP
ejpam-5384	8	27	wardrop	wardrop	NOUN
ejpam-5384	8	28	optimal	optimal	ADJ
ejpam-5384	8	29	networks	network	NOUN
ejpam-5384	8	30	.	.	PUNCT
ejpam-5384	9	1	moreover	moreover	ADV
ejpam-5384	9	2	,	,	PUNCT
ejpam-5384	9	3	we	we	PRON
ejpam-5384	9	4	illustrate	illustrate	VERB
ejpam-5384	9	5	that	that	SCONJ
ejpam-5384	9	6	these	these	DET
ejpam-5384	9	7	flows	flow	NOUN
ejpam-5384	9	8	remain	remain	VERB
ejpam-5384	9	9	consistent	consistent	ADJ
ejpam-5384	9	10	under	under	ADP
ejpam-5384	9	11	several	several	ADJ
ejpam-5384	9	12	important	important	ADJ
ejpam-5384	9	13	transformations	transformation	NOUN
ejpam-5384	9	14	as	as	ADV
ejpam-5384	9	15	well	well	ADV
ejpam-5384	9	16	as	as	ADP
ejpam-5384	9	17	under	under	ADP
ejpam-5384	9	18	uniform	uniform	ADJ
ejpam-5384	9	19	changes	change	NOUN
ejpam-5384	9	20	in	in	ADP
ejpam-5384	9	21	their	their	PRON
ejpam-5384	9	22	latency	latency	NOUN
ejpam-5384	9	23	functions	function	NOUN
ejpam-5384	9	24	.	.	PUNCT
ejpam-5384	10	1	2020	2020	NUM
ejpam-5384	10	2	mathematics	mathematic	NOUN
ejpam-5384	10	3	subject	subject	NOUN
ejpam-5384	10	4	classifications	classification	NOUN
ejpam-5384	10	5	:	:	PUNCT
ejpam-5384	10	6	05c20,05c21,49q22	05c20,05c21,49q22	NOUN
ejpam-5384	10	7	key	key	ADJ
ejpam-5384	10	8	words	word	NOUN
ejpam-5384	10	9	and	and	CCONJ
ejpam-5384	10	10	phrases	phrase	NOUN
ejpam-5384	10	11	:	:	PUNCT
ejpam-5384	10	12	optimal	optimal	ADJ
ejpam-5384	10	13	flow	flow	NOUN
ejpam-5384	10	14	allocation	allocation	NOUN
ejpam-5384	10	15	,	,	PUNCT
ejpam-5384	10	16	resource	resource	NOUN
ejpam-5384	10	17	management	management	NOUN
ejpam-5384	10	18	,	,	PUNCT
ejpam-5384	10	19	wardrop	wardrop	NOUN
ejpam-5384	10	20	equilibrium	equilibrium	NOUN
ejpam-5384	10	21	,	,	PUNCT
ejpam-5384	10	22	user	user	NOUN
ejpam-5384	10	23	and	and	CCONJ
ejpam-5384	10	24	system	system	NOUN
ejpam-5384	10	25	optimum	optimum	ADJ
ejpam-5384	10	26	1	1	NUM
ejpam-5384	10	27	.	.	PUNCT
ejpam-5384	11	1	introduction	introduction	NOUN
ejpam-5384	11	2	the	the	DET
ejpam-5384	11	3	efficient	efficient	ADJ
ejpam-5384	11	4	distribution	distribution	NOUN
ejpam-5384	11	5	of	of	ADP
ejpam-5384	11	6	flow	flow	NOUN
ejpam-5384	11	7	in	in	ADP
ejpam-5384	11	8	directed	direct	VERB
ejpam-5384	11	9	networks	network	NOUN
ejpam-5384	11	10	is	be	AUX
ejpam-5384	11	11	often	often	ADV
ejpam-5384	11	12	examined	examine	VERB
ejpam-5384	11	13	through	through	ADP
ejpam-5384	11	14	two	two	NUM
ejpam-5384	11	15	different	different	ADJ
ejpam-5384	11	16	key	key	ADJ
ejpam-5384	11	17	concepts	concept	NOUN
ejpam-5384	11	18	,	,	PUNCT
ejpam-5384	11	19	known	know	VERB
ejpam-5384	11	20	as	as	ADP
ejpam-5384	11	21	wardrop	wardrop	NOUN
ejpam-5384	11	22	’s	’s	PART
ejpam-5384	11	23	principles	principle	NOUN
ejpam-5384	11	24	:	:	PUNCT
ejpam-5384	11	25	user	user	NOUN
ejpam-5384	11	26	equilibrium	equilibrium	NOUN
ejpam-5384	11	27	and	and	CCONJ
ejpam-5384	11	28	system	system	NOUN
ejpam-5384	11	29	optimum	optimum	NOUN
ejpam-5384	12	1	[	[	X
ejpam-5384	12	2	30	30	NUM
ejpam-5384	12	3	]	]	PUNCT
ejpam-5384	12	4	.	.	PUNCT
ejpam-5384	13	1	wardrop	wardrop	NOUN
ejpam-5384	13	2	’s	’s	PART
ejpam-5384	13	3	principles	principle	NOUN
ejpam-5384	13	4	are	be	AUX
ejpam-5384	13	5	fundamental	fundamental	ADJ
ejpam-5384	13	6	concepts	concept	NOUN
ejpam-5384	13	7	in	in	ADP
ejpam-5384	13	8	transportation	transportation	NOUN
ejpam-5384	13	9	and	and	CCONJ
ejpam-5384	13	10	network	network	NOUN
ejpam-5384	13	11	theory	theory	NOUN
ejpam-5384	13	12	,	,	PUNCT
ejpam-5384	13	13	providing	provide	VERB
ejpam-5384	13	14	a	a	DET
ejpam-5384	13	15	basis	basis	NOUN
ejpam-5384	13	16	for	for	ADP
ejpam-5384	13	17	understanding	understand	VERB
ejpam-5384	13	18	traffic	traffic	NOUN
ejpam-5384	13	19	flow	flow	NOUN
ejpam-5384	13	20	and	and	CCONJ
ejpam-5384	13	21	congestion	congestion	NOUN
ejpam-5384	13	22	management	management	NOUN
ejpam-5384	13	23	.	.	PUNCT
ejpam-5384	14	1	according	accord	VERB
ejpam-5384	14	2	to	to	ADP
ejpam-5384	14	3	wardrop	wardrop	NOUN
ejpam-5384	14	4	’s	’s	PART
ejpam-5384	14	5	first	first	ADJ
ejpam-5384	14	6	principle	principle	NOUN
ejpam-5384	14	7	,	,	PUNCT
ejpam-5384	14	8	user	user	NOUN
ejpam-5384	14	9	equilibrium	equilibrium	NOUN
ejpam-5384	14	10	is	be	AUX
ejpam-5384	14	11	reached	reach	VERB
ejpam-5384	14	12	when	when	SCONJ
ejpam-5384	14	13	travel	travel	NOUN
ejpam-5384	14	14	times	time	NOUN
ejpam-5384	14	15	on	on	ADP
ejpam-5384	14	16	all	all	DET
ejpam-5384	14	17	routes	route	NOUN
ejpam-5384	14	18	in	in	ADP
ejpam-5384	14	19	use	use	NOUN
ejpam-5384	14	20	are	be	AUX
ejpam-5384	14	21	the	the	DET
ejpam-5384	14	22	same	same	ADJ
ejpam-5384	14	23	,	,	PUNCT
ejpam-5384	14	24	and	and	CCONJ
ejpam-5384	14	25	no	no	DET
ejpam-5384	14	26	traveler	traveler	NOUN
ejpam-5384	14	27	can	can	AUX
ejpam-5384	14	28	reduce	reduce	VERB
ejpam-5384	14	29	their	their	PRON
ejpam-5384	14	30	travel	travel	NOUN
ejpam-5384	14	31	time	time	NOUN
ejpam-5384	14	32	by	by	ADP
ejpam-5384	14	33	switching	switch	VERB
ejpam-5384	14	34	routes	route	NOUN
ejpam-5384	14	35	;	;	PUNCT
ejpam-5384	14	36	this	this	DET
ejpam-5384	14	37	state	state	NOUN
ejpam-5384	14	38	is	be	AUX
ejpam-5384	14	39	also	also	ADV
ejpam-5384	14	40	referred	refer	VERB
ejpam-5384	14	41	to	to	ADP
ejpam-5384	14	42	as	as	ADP
ejpam-5384	14	43	a	a	DET
ejpam-5384	14	44	wardrop	wardrop	NOUN
ejpam-5384	14	45	equilibrium	equilibrium	NOUN
ejpam-5384	15	1	[	[	X
ejpam-5384	15	2	7	7	NUM
ejpam-5384	15	3	,	,	PUNCT
ejpam-5384	15	4	19	19	NUM
ejpam-5384	15	5	]	]	PUNCT
ejpam-5384	15	6	.	.	PUNCT
ejpam-5384	16	1	the	the	DET
ejpam-5384	16	2	second	second	ADJ
ejpam-5384	16	3	principle	principle	NOUN
ejpam-5384	16	4	asserts	assert	VERB
ejpam-5384	16	5	that	that	SCONJ
ejpam-5384	16	6	the	the	DET
ejpam-5384	16	7	network	network	NOUN
ejpam-5384	16	8	flow	flow	NOUN
ejpam-5384	16	9	configuration	configuration	NOUN
ejpam-5384	16	10	minimizes	minimize	VERB
ejpam-5384	16	11	the	the	DET
ejpam-5384	16	12	total	total	ADJ
ejpam-5384	16	13	travel	travel	NOUN
ejpam-5384	16	14	time	time	NOUN
ejpam-5384	16	15	for	for	ADP
ejpam-5384	16	16	all	all	DET
ejpam-5384	16	17	users	user	NOUN
ejpam-5384	16	18	,	,	PUNCT
ejpam-5384	16	19	representing	represent	VERB
ejpam-5384	16	20	an	an	DET
ejpam-5384	16	21	optimal	optimal	ADJ
ejpam-5384	16	22	state	state	NOUN
ejpam-5384	16	23	from	from	ADP
ejpam-5384	16	24	the	the	DET
ejpam-5384	16	25	perspective	perspective	NOUN
ejpam-5384	16	26	of	of	ADP
ejpam-5384	16	27	the	the	DET
ejpam-5384	16	28	network	network	NOUN
ejpam-5384	16	29	as	as	ADP
ejpam-5384	16	30	a	a	DET
ejpam-5384	16	31	whole	whole	NOUN
ejpam-5384	16	32	.	.	PUNCT
ejpam-5384	17	1	in	in	ADP
ejpam-5384	17	2	practice	practice	NOUN
ejpam-5384	17	3	,	,	PUNCT
ejpam-5384	17	4	user	user	NOUN
ejpam-5384	17	5	equilibrium	equilibrium	NOUN
ejpam-5384	17	6	and	and	CCONJ
ejpam-5384	17	7	system	system	NOUN
ejpam-5384	17	8	optimum	optimum	NOUN
ejpam-5384	17	9	typically	typically	ADV
ejpam-5384	17	10	differ	differ	VERB
ejpam-5384	17	11	,	,	PUNCT
ejpam-5384	17	12	leading	lead	VERB
ejpam-5384	17	13	to	to	ADP
ejpam-5384	17	14	inefficiencies	inefficiency	NOUN
ejpam-5384	17	15	in	in	ADP
ejpam-5384	17	16	network	network	NOUN
ejpam-5384	17	17	usage	usage	NOUN
ejpam-5384	17	18	.	.	PUNCT
ejpam-5384	18	1	achieving	achieve	VERB
ejpam-5384	18	2	the	the	DET
ejpam-5384	18	3	system	system	NOUN
ejpam-5384	18	4	optimum	optimum	NOUN
ejpam-5384	18	5	typically	typically	ADV
ejpam-5384	18	6	requires	require	VERB
ejpam-5384	18	7	a	a	DET
ejpam-5384	18	8	form	form	NOUN
ejpam-5384	18	9	of	of	ADP
ejpam-5384	18	10	central	central	ADJ
ejpam-5384	18	11	doi	doi	NOUN
ejpam-5384	18	12	:	:	PUNCT
ejpam-5384	18	13	https://doi.org/10.29020/nybg.ejpam.v17i4.5384	https://doi.org/10.29020/nybg.ejpam.v17i4.5384	PROPN
ejpam-5384	18	14	email	email	NOUN
ejpam-5384	18	15	address	address	NOUN
ejpam-5384	18	16	:	:	PUNCT
ejpam-5384	18	17	antonios.kalampakas@aum.edu.kw	antonios.kalampakas@aum.edu.kw	PROPN
ejpam-5384	18	18	(	(	PUNCT
ejpam-5384	18	19	a.	a.	PROPN
ejpam-5384	18	20	kalampakas	kalampakas	PROPN
ejpam-5384	18	21	)	)	PUNCT
ejpam-5384	18	22	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5384	18	23	2448	2448	NUM
ejpam-5384	19	1	copyright	copyright	NOUN
ejpam-5384	19	2	:	:	PUNCT
ejpam-5384	19	3	©	©	PROPN
ejpam-5384	19	4	2024	2024	NUM
ejpam-5384	19	5	the	the	DET
ejpam-5384	19	6	author(s	author(s	NOUN
ejpam-5384	19	7	)	)	PUNCT
ejpam-5384	19	8	.	.	PUNCT
ejpam-5384	20	1	(	(	PUNCT
ejpam-5384	20	2	cc	cc	NOUN
ejpam-5384	20	3	by	by	ADP
ejpam-5384	20	4	-	-	PUNCT
ejpam-5384	20	5	nc	nc	PROPN
ejpam-5384	20	6	4.0	4.0	NUM
ejpam-5384	20	7	)	)	PUNCT
ejpam-5384	20	8	a.	a.	NOUN
ejpam-5384	20	9	kalampakas	kalampakas	PROPN
ejpam-5384	20	10	/	/	SYM
ejpam-5384	20	11	eur	eur	PROPN
ejpam-5384	20	12	.	.	PUNCT
ejpam-5384	21	1	j.	j.	PROPN
ejpam-5384	21	2	pure	pure	PROPN
ejpam-5384	21	3	appl	appl	PROPN
ejpam-5384	21	4	.	.	PROPN
ejpam-5384	21	5	math	math	PROPN
ejpam-5384	21	6	,	,	PUNCT
ejpam-5384	21	7	17	17	NUM
ejpam-5384	21	8	(	(	PUNCT
ejpam-5384	21	9	4	4	NUM
ejpam-5384	21	10	)	)	PUNCT
ejpam-5384	21	11	(	(	PUNCT
ejpam-5384	21	12	2024	2024	NUM
ejpam-5384	21	13	)	)	PUNCT
ejpam-5384	21	14	,	,	PUNCT
ejpam-5384	21	15	2448	2448	NUM
ejpam-5384	21	16	-	-	SYM
ejpam-5384	21	17	2466	2466	NUM
ejpam-5384	21	18	2449	2449	NUM
ejpam-5384	21	19	control	control	NOUN
ejpam-5384	21	20	or	or	CCONJ
ejpam-5384	21	21	coordination	coordination	NOUN
ejpam-5384	21	22	because	because	SCONJ
ejpam-5384	21	23	individual	individual	ADJ
ejpam-5384	21	24	users	user	NOUN
ejpam-5384	21	25	acting	act	VERB
ejpam-5384	21	26	in	in	ADP
ejpam-5384	21	27	their	their	PRON
ejpam-5384	21	28	self	self	NOUN
ejpam-5384	21	29	-	-	PUNCT
ejpam-5384	21	30	interest	interest	NOUN
ejpam-5384	21	31	do	do	AUX
ejpam-5384	21	32	not	not	PART
ejpam-5384	21	33	naturally	naturally	ADV
ejpam-5384	21	34	lead	lead	VERB
ejpam-5384	21	35	to	to	PART
ejpam-5384	21	36	system	system	VERB
ejpam-5384	21	37	optimal	optimal	ADJ
ejpam-5384	21	38	flows	flow	NOUN
ejpam-5384	21	39	.	.	PUNCT
ejpam-5384	22	1	to	to	PART
ejpam-5384	22	2	achieve	achieve	VERB
ejpam-5384	22	3	the	the	DET
ejpam-5384	22	4	system	system	NOUN
ejpam-5384	22	5	optimum	optimum	NOUN
ejpam-5384	22	6	,	,	PUNCT
ejpam-5384	22	7	traffic	traffic	NOUN
ejpam-5384	22	8	may	may	AUX
ejpam-5384	22	9	need	need	VERB
ejpam-5384	22	10	to	to	PART
ejpam-5384	22	11	be	be	AUX
ejpam-5384	22	12	redistributed	redistribute	VERB
ejpam-5384	22	13	by	by	ADP
ejpam-5384	22	14	encouraging	encourage	VERB
ejpam-5384	22	15	or	or	CCONJ
ejpam-5384	22	16	forcing	force	VERB
ejpam-5384	22	17	users	user	NOUN
ejpam-5384	22	18	to	to	PART
ejpam-5384	22	19	follow	follow	VERB
ejpam-5384	22	20	less	less	ADV
ejpam-5384	22	21	congested	congested	ADJ
ejpam-5384	22	22	routes	route	NOUN
ejpam-5384	22	23	,	,	PUNCT
ejpam-5384	22	24	even	even	ADV
ejpam-5384	22	25	if	if	SCONJ
ejpam-5384	22	26	their	their	PRON
ejpam-5384	22	27	travel	travel	NOUN
ejpam-5384	22	28	time	time	NOUN
ejpam-5384	22	29	increases	increase	NOUN
ejpam-5384	22	30	.	.	PUNCT
ejpam-5384	23	1	this	this	DET
ejpam-5384	23	2	redistribution	redistribution	NOUN
ejpam-5384	23	3	reduces	reduce	VERB
ejpam-5384	23	4	the	the	DET
ejpam-5384	23	5	overall	overall	ADJ
ejpam-5384	23	6	congestion	congestion	NOUN
ejpam-5384	23	7	and	and	CCONJ
ejpam-5384	23	8	minimizes	minimize	VERB
ejpam-5384	23	9	the	the	DET
ejpam-5384	23	10	total	total	ADJ
ejpam-5384	23	11	travel	travel	NOUN
ejpam-5384	23	12	time	time	NOUN
ejpam-5384	23	13	or	or	CCONJ
ejpam-5384	23	14	cost	cost	VERB
ejpam-5384	23	15	for	for	ADP
ejpam-5384	23	16	all	all	DET
ejpam-5384	23	17	users	user	NOUN
ejpam-5384	23	18	combined	combine	VERB
ejpam-5384	23	19	.	.	PUNCT
ejpam-5384	24	1	at	at	ADP
ejpam-5384	24	2	user	user	NOUN
ejpam-5384	24	3	equilibrium	equilibrium	NOUN
ejpam-5384	24	4	,	,	PUNCT
ejpam-5384	24	5	the	the	DET
ejpam-5384	24	6	total	total	ADJ
ejpam-5384	24	7	travel	travel	NOUN
ejpam-5384	24	8	time	time	NOUN
ejpam-5384	24	9	is	be	AUX
ejpam-5384	24	10	generally	generally	ADV
ejpam-5384	24	11	higher	high	ADJ
ejpam-5384	24	12	than	than	ADP
ejpam-5384	24	13	at	at	ADP
ejpam-5384	24	14	system	system	NOUN
ejpam-5384	24	15	optimum	optimum	ADJ
ejpam-5384	24	16	because	because	SCONJ
ejpam-5384	24	17	individuals	individual	NOUN
ejpam-5384	24	18	are	be	AUX
ejpam-5384	24	19	not	not	PART
ejpam-5384	24	20	incentivized	incentivize	VERB
ejpam-5384	24	21	to	to	PART
ejpam-5384	24	22	consider	consider	VERB
ejpam-5384	24	23	the	the	DET
ejpam-5384	24	24	overall	overall	ADJ
ejpam-5384	24	25	system	system	NOUN
ejpam-5384	24	26	performance	performance	NOUN
ejpam-5384	24	27	.	.	PUNCT
ejpam-5384	25	1	in	in	ADP
ejpam-5384	25	2	many	many	ADJ
ejpam-5384	25	3	networks	network	NOUN
ejpam-5384	25	4	,	,	PUNCT
ejpam-5384	25	5	user	user	NOUN
ejpam-5384	25	6	equilibrium	equilibrium	NOUN
ejpam-5384	25	7	represents	represent	VERB
ejpam-5384	25	8	a	a	DET
ejpam-5384	25	9	”	"	PUNCT
ejpam-5384	25	10	selfish	selfish	ADJ
ejpam-5384	25	11	”	"	PUNCT
ejpam-5384	25	12	solution	solution	NOUN
ejpam-5384	25	13	,	,	PUNCT
ejpam-5384	25	14	whereas	whereas	SCONJ
ejpam-5384	25	15	the	the	DET
ejpam-5384	25	16	system	system	NOUN
ejpam-5384	25	17	optimum	optimum	NOUN
ejpam-5384	25	18	represents	represent	VERB
ejpam-5384	25	19	a	a	DET
ejpam-5384	25	20	”	"	PUNCT
ejpam-5384	25	21	cooperative	cooperative	ADJ
ejpam-5384	25	22	”	"	PUNCT
ejpam-5384	25	23	solution	solution	NOUN
ejpam-5384	25	24	.	.	PUNCT
ejpam-5384	26	1	the	the	DET
ejpam-5384	26	2	ratio	ratio	NOUN
ejpam-5384	26	3	of	of	ADP
ejpam-5384	26	4	the	the	DET
ejpam-5384	26	5	total	total	ADJ
ejpam-5384	26	6	travel	travel	NOUN
ejpam-5384	26	7	time	time	NOUN
ejpam-5384	26	8	at	at	ADP
ejpam-5384	26	9	user	user	NOUN
ejpam-5384	26	10	equilibrium	equilibrium	NOUN
ejpam-5384	26	11	to	to	ADP
ejpam-5384	26	12	that	that	PRON
ejpam-5384	26	13	at	at	ADP
ejpam-5384	26	14	system	system	NOUN
ejpam-5384	26	15	optimum	optimum	NOUN
ejpam-5384	26	16	is	be	AUX
ejpam-5384	26	17	known	know	VERB
ejpam-5384	26	18	as	as	ADP
ejpam-5384	26	19	the	the	DET
ejpam-5384	26	20	price	price	NOUN
ejpam-5384	26	21	of	of	ADP
ejpam-5384	26	22	anarchy	anarchy	NOUN
ejpam-5384	26	23	.	.	PUNCT
ejpam-5384	27	1	a	a	DET
ejpam-5384	27	2	flow	flow	NOUN
ejpam-5384	27	3	that	that	PRON
ejpam-5384	27	4	is	be	AUX
ejpam-5384	27	5	both	both	DET
ejpam-5384	27	6	system	system	NOUN
ejpam-5384	27	7	optimum	optimum	ADJ
ejpam-5384	27	8	and	and	CCONJ
ejpam-5384	27	9	user	user	NOUN
ejpam-5384	27	10	equilibrium	equilibrium	NOUN
ejpam-5384	27	11	is	be	AUX
ejpam-5384	27	12	called	call	VERB
ejpam-5384	27	13	wardrop	wardrop	NOUN
ejpam-5384	27	14	optimal	optimal	ADJ
ejpam-5384	27	15	flow	flow	NOUN
ejpam-5384	27	16	and	and	CCONJ
ejpam-5384	27	17	networks	network	NOUN
ejpam-5384	27	18	that	that	PRON
ejpam-5384	27	19	admit	admit	VERB
ejpam-5384	27	20	such	such	ADJ
ejpam-5384	27	21	flows	flow	NOUN
ejpam-5384	27	22	are	be	AUX
ejpam-5384	27	23	termed	term	VERB
ejpam-5384	27	24	wardrop	wardrop	NOUN
ejpam-5384	27	25	optimal	optimal	ADJ
ejpam-5384	27	26	networks	network	NOUN
ejpam-5384	27	27	[	[	X
ejpam-5384	27	28	4	4	NUM
ejpam-5384	27	29	,	,	PUNCT
ejpam-5384	27	30	13	13	NUM
ejpam-5384	27	31	]	]	PUNCT
ejpam-5384	27	32	(	(	PUNCT
ejpam-5384	27	33	see	see	VERB
ejpam-5384	27	34	also	also	ADV
ejpam-5384	27	35	[	[	X
ejpam-5384	27	36	2	2	NUM
ejpam-5384	27	37	,	,	PUNCT
ejpam-5384	27	38	3	3	NUM
ejpam-5384	27	39	,	,	PUNCT
ejpam-5384	27	40	5	5	NUM
ejpam-5384	27	41	]	]	PUNCT
ejpam-5384	27	42	where	where	SCONJ
ejpam-5384	27	43	wardrop	wardrop	VERB
ejpam-5384	27	44	optimal	optimal	ADJ
ejpam-5384	27	45	networks	network	NOUN
ejpam-5384	27	46	with	with	ADP
ejpam-5384	27	47	dynamic	dynamic	ADJ
ejpam-5384	27	48	flow	flow	NOUN
ejpam-5384	27	49	assignment	assignment	NOUN
ejpam-5384	27	50	are	be	AUX
ejpam-5384	27	51	examined	examine	VERB
ejpam-5384	27	52	and	and	CCONJ
ejpam-5384	27	53	[	[	X
ejpam-5384	27	54	14	14	NUM
ejpam-5384	27	55	]	]	PUNCT
ejpam-5384	27	56	presenting	presenting	NOUN
ejpam-5384	27	57	,	,	PUNCT
ejpam-5384	27	58	without	without	ADP
ejpam-5384	27	59	proofs	proof	NOUN
ejpam-5384	27	60	,	,	PUNCT
ejpam-5384	27	61	some	some	PRON
ejpam-5384	27	62	of	of	ADP
ejpam-5384	27	63	the	the	DET
ejpam-5384	27	64	main	main	ADJ
ejpam-5384	27	65	properties	property	NOUN
ejpam-5384	27	66	of	of	ADP
ejpam-5384	27	67	wardrop	wardrop	NOUN
ejpam-5384	27	68	optimal	optimal	ADJ
ejpam-5384	27	69	networks	network	NOUN
ejpam-5384	27	70	we	we	PRON
ejpam-5384	27	71	establish	establish	VERB
ejpam-5384	27	72	in	in	ADP
ejpam-5384	27	73	this	this	DET
ejpam-5384	27	74	paper	paper	NOUN
ejpam-5384	27	75	)	)	PUNCT
ejpam-5384	27	76	.	.	PUNCT
ejpam-5384	28	1	by	by	ADP
ejpam-5384	28	2	construction	construction	NOUN
ejpam-5384	28	3	,	,	PUNCT
ejpam-5384	28	4	the	the	DET
ejpam-5384	28	5	price	price	NOUN
ejpam-5384	28	6	of	of	ADP
ejpam-5384	28	7	anarchy	anarchy	NOUN
ejpam-5384	28	8	of	of	ADP
ejpam-5384	28	9	such	such	ADJ
ejpam-5384	28	10	networks	network	NOUN
ejpam-5384	28	11	is	be	AUX
ejpam-5384	28	12	optimal	optimal	ADJ
ejpam-5384	28	13	,	,	PUNCT
ejpam-5384	28	14	i.e.	i.e.	X
ejpam-5384	28	15	,	,	PUNCT
ejpam-5384	28	16	equal	equal	ADJ
ejpam-5384	28	17	to	to	ADP
ejpam-5384	28	18	1	1	NUM
ejpam-5384	28	19	,	,	PUNCT
ejpam-5384	28	20	a	a	DET
ejpam-5384	28	21	desirable	desirable	ADJ
ejpam-5384	28	22	property	property	NOUN
ejpam-5384	28	23	in	in	ADP
ejpam-5384	28	24	network	network	NOUN
ejpam-5384	28	25	theory	theory	NOUN
ejpam-5384	28	26	with	with	ADP
ejpam-5384	28	27	applications	application	NOUN
ejpam-5384	28	28	in	in	ADP
ejpam-5384	28	29	fields	field	NOUN
ejpam-5384	28	30	such	such	ADJ
ejpam-5384	28	31	as	as	ADP
ejpam-5384	28	32	economics	economic	NOUN
ejpam-5384	28	33	[	[	X
ejpam-5384	28	34	26	26	NUM
ejpam-5384	28	35	,	,	PUNCT
ejpam-5384	28	36	28	28	NUM
ejpam-5384	28	37	]	]	PUNCT
ejpam-5384	28	38	,	,	PUNCT
ejpam-5384	28	39	transportation	transportation	NOUN
ejpam-5384	28	40	[	[	X
ejpam-5384	28	41	6	6	NUM
ejpam-5384	28	42	,	,	PUNCT
ejpam-5384	28	43	23	23	NUM
ejpam-5384	28	44	,	,	PUNCT
ejpam-5384	28	45	25	25	NUM
ejpam-5384	28	46	,	,	PUNCT
ejpam-5384	28	47	29	29	NUM
ejpam-5384	28	48	,	,	PUNCT
ejpam-5384	28	49	30	30	NUM
ejpam-5384	28	50	]	]	PUNCT
ejpam-5384	28	51	,	,	PUNCT
ejpam-5384	28	52	and	and	CCONJ
ejpam-5384	28	53	communications	communication	NOUN
ejpam-5384	28	54	[	[	X
ejpam-5384	28	55	18	18	NUM
ejpam-5384	28	56	,	,	PUNCT
ejpam-5384	28	57	20	20	NUM
ejpam-5384	28	58	,	,	PUNCT
ejpam-5384	28	59	21	21	NUM
ejpam-5384	28	60	,	,	PUNCT
ejpam-5384	28	61	24	24	NUM
ejpam-5384	28	62	]	]	PUNCT
ejpam-5384	28	63	,	,	PUNCT
ejpam-5384	28	64	and	and	CCONJ
ejpam-5384	28	65	can	can	AUX
ejpam-5384	28	66	be	be	AUX
ejpam-5384	28	67	also	also	ADV
ejpam-5384	28	68	applied	apply	VERB
ejpam-5384	28	69	to	to	ADP
ejpam-5384	28	70	areas	area	NOUN
ejpam-5384	28	71	like	like	ADP
ejpam-5384	28	72	multiprocessor	multiprocessor	NOUN
ejpam-5384	28	73	task	task	NOUN
ejpam-5384	28	74	scheduling	scheduling	NOUN
ejpam-5384	28	75	[	[	X
ejpam-5384	28	76	8	8	NUM
ejpam-5384	28	77	]	]	PUNCT
ejpam-5384	28	78	and	and	CCONJ
ejpam-5384	28	79	media	medium	NOUN
ejpam-5384	28	80	flow	flow	NOUN
ejpam-5384	28	81	with	with	ADP
ejpam-5384	28	82	double	double	ADJ
ejpam-5384	28	83	diffusion	diffusion	NOUN
ejpam-5384	28	84	[	[	X
ejpam-5384	28	85	12	12	NUM
ejpam-5384	28	86	]	]	PUNCT
ejpam-5384	28	87	.	.	PUNCT
ejpam-5384	29	1	for	for	ADP
ejpam-5384	29	2	a	a	DET
ejpam-5384	29	3	comprehensive	comprehensive	ADJ
ejpam-5384	29	4	review	review	NOUN
ejpam-5384	29	5	of	of	ADP
ejpam-5384	29	6	the	the	DET
ejpam-5384	29	7	literature	literature	NOUN
ejpam-5384	29	8	in	in	ADP
ejpam-5384	29	9	approaches	approach	NOUN
ejpam-5384	29	10	bridging	bridge	VERB
ejpam-5384	29	11	user	user	NOUN
ejpam-5384	29	12	equilibrium	equilibrium	NOUN
ejpam-5384	29	13	and	and	CCONJ
ejpam-5384	29	14	system	system	NOUN
ejpam-5384	29	15	optimum	optimum	ADV
ejpam-5384	29	16	see	see	VERB
ejpam-5384	29	17	[	[	X
ejpam-5384	29	18	22	22	NUM
ejpam-5384	29	19	]	]	PUNCT
ejpam-5384	29	20	.	.	PUNCT
ejpam-5384	30	1	this	this	DET
ejpam-5384	30	2	paper	paper	NOUN
ejpam-5384	30	3	focuses	focus	VERB
ejpam-5384	30	4	on	on	ADP
ejpam-5384	30	5	analyzing	analyze	VERB
ejpam-5384	30	6	these	these	DET
ejpam-5384	30	7	flows	flow	NOUN
ejpam-5384	30	8	and	and	CCONJ
ejpam-5384	30	9	their	their	PRON
ejpam-5384	30	10	corresponding	corresponding	ADJ
ejpam-5384	30	11	networks	network	NOUN
ejpam-5384	30	12	.	.	PUNCT
ejpam-5384	31	1	a	a	DET
ejpam-5384	31	2	flow	flow	NOUN
ejpam-5384	31	3	travelling	travel	VERB
ejpam-5384	31	4	from	from	ADP
ejpam-5384	31	5	initial	initial	ADJ
ejpam-5384	31	6	to	to	PART
ejpam-5384	31	7	target	target	VERB
ejpam-5384	31	8	node	node	NOUN
ejpam-5384	31	9	is	be	AUX
ejpam-5384	31	10	allocated	allocate	VERB
ejpam-5384	31	11	across	across	ADP
ejpam-5384	31	12	multiple	multiple	ADJ
ejpam-5384	31	13	links	link	NOUN
ejpam-5384	31	14	,	,	PUNCT
ejpam-5384	31	15	causing	cause	VERB
ejpam-5384	31	16	congestion	congestion	NOUN
ejpam-5384	31	17	,	,	PUNCT
ejpam-5384	31	18	which	which	PRON
ejpam-5384	31	19	in	in	ADP
ejpam-5384	31	20	turn	turn	NOUN
ejpam-5384	31	21	increases	increase	VERB
ejpam-5384	31	22	travel	travel	NOUN
ejpam-5384	31	23	times	time	NOUN
ejpam-5384	31	24	,	,	PUNCT
ejpam-5384	31	25	captured	capture	VERB
ejpam-5384	31	26	by	by	ADP
ejpam-5384	31	27	link	link	NOUN
ejpam-5384	31	28	-	-	PUNCT
ejpam-5384	31	29	specific	specific	ADJ
ejpam-5384	31	30	latency	latency	NOUN
ejpam-5384	31	31	functions	function	NOUN
ejpam-5384	31	32	that	that	PRON
ejpam-5384	31	33	are	be	AUX
ejpam-5384	31	34	strictly	strictly	ADV
ejpam-5384	31	35	increasing	increase	VERB
ejpam-5384	31	36	.	.	PUNCT
ejpam-5384	32	1	we	we	PRON
ejpam-5384	32	2	establish	establish	VERB
ejpam-5384	32	3	a	a	DET
ejpam-5384	32	4	connection	connection	NOUN
ejpam-5384	32	5	between	between	ADP
ejpam-5384	32	6	the	the	DET
ejpam-5384	32	7	user	user	NOUN
ejpam-5384	32	8	equilibrium	equilibrium	NOUN
ejpam-5384	32	9	and	and	CCONJ
ejpam-5384	32	10	system	system	NOUN
ejpam-5384	32	11	optimum	optimum	NOUN
ejpam-5384	32	12	through	through	ADP
ejpam-5384	32	13	the	the	DET
ejpam-5384	32	14	associated	associated	ADJ
ejpam-5384	32	15	pigovian	pigovian	ADJ
ejpam-5384	32	16	network	network	NOUN
ejpam-5384	32	17	and	and	CCONJ
ejpam-5384	32	18	derive	derive	ADJ
ejpam-5384	32	19	conditions	condition	NOUN
ejpam-5384	32	20	for	for	ADP
ejpam-5384	32	21	the	the	DET
ejpam-5384	32	22	existence	existence	NOUN
ejpam-5384	32	23	and	and	CCONJ
ejpam-5384	32	24	uniqueness	uniqueness	NOUN
ejpam-5384	32	25	of	of	ADP
ejpam-5384	32	26	optimal	optimal	ADJ
ejpam-5384	32	27	flows	flow	NOUN
ejpam-5384	32	28	in	in	ADP
ejpam-5384	32	29	convex	convex	NOUN
ejpam-5384	32	30	networks	network	NOUN
ejpam-5384	32	31	.	.	PUNCT
ejpam-5384	33	1	the	the	DET
ejpam-5384	33	2	paper	paper	NOUN
ejpam-5384	33	3	is	be	AUX
ejpam-5384	33	4	organized	organize	VERB
ejpam-5384	33	5	in	in	ADP
ejpam-5384	33	6	the	the	DET
ejpam-5384	33	7	following	following	ADJ
ejpam-5384	33	8	way	way	NOUN
ejpam-5384	33	9	.	.	PUNCT
ejpam-5384	34	1	in	in	ADP
ejpam-5384	34	2	section	section	NOUN
ejpam-5384	34	3	2	2	NUM
ejpam-5384	34	4	we	we	PRON
ejpam-5384	34	5	outline	outline	VERB
ejpam-5384	34	6	the	the	DET
ejpam-5384	34	7	basic	basic	ADJ
ejpam-5384	34	8	definitions	definition	NOUN
ejpam-5384	34	9	we	we	PRON
ejpam-5384	34	10	use	use	VERB
ejpam-5384	34	11	throughout	throughout	ADP
ejpam-5384	34	12	the	the	DET
ejpam-5384	34	13	paper	paper	NOUN
ejpam-5384	34	14	.	.	PUNCT
ejpam-5384	35	1	section	section	NOUN
ejpam-5384	35	2	3	3	NUM
ejpam-5384	35	3	examines	examine	NOUN
ejpam-5384	35	4	in	in	ADP
ejpam-5384	35	5	detail	detail	NOUN
ejpam-5384	35	6	the	the	DET
ejpam-5384	35	7	user	user	NOUN
ejpam-5384	35	8	equilibrium	equilibrium	NOUN
ejpam-5384	35	9	and	and	CCONJ
ejpam-5384	35	10	introduces	introduce	VERB
ejpam-5384	35	11	the	the	DET
ejpam-5384	35	12	discrete	discrete	ADJ
ejpam-5384	35	13	user	user	NOUN
ejpam-5384	35	14	equilibrium	equilibrium	NOUN
ejpam-5384	35	15	.	.	PUNCT
ejpam-5384	36	1	section	section	NOUN
ejpam-5384	36	2	4	4	NUM
ejpam-5384	36	3	explores	explore	VERB
ejpam-5384	36	4	the	the	DET
ejpam-5384	36	5	system	system	NOUN
ejpam-5384	36	6	optimum	optimum	NOUN
ejpam-5384	36	7	,	,	PUNCT
ejpam-5384	36	8	presenting	present	VERB
ejpam-5384	36	9	necessary	necessary	ADJ
ejpam-5384	36	10	and	and	CCONJ
ejpam-5384	36	11	sufficient	sufficient	ADJ
ejpam-5384	36	12	conditions	condition	NOUN
ejpam-5384	36	13	for	for	ADP
ejpam-5384	36	14	its	its	PRON
ejpam-5384	36	15	characterization	characterization	NOUN
ejpam-5384	36	16	.	.	PUNCT
ejpam-5384	37	1	in	in	ADP
ejpam-5384	37	2	section	section	NOUN
ejpam-5384	37	3	5	5	NUM
ejpam-5384	37	4	we	we	PRON
ejpam-5384	37	5	introduce	introduce	VERB
ejpam-5384	37	6	wardrop	wardrop	NOUN
ejpam-5384	37	7	optimal	optimal	ADJ
ejpam-5384	37	8	networks	network	NOUN
ejpam-5384	37	9	and	and	CCONJ
ejpam-5384	37	10	provide	provide	VERB
ejpam-5384	37	11	a	a	DET
ejpam-5384	37	12	characterization	characterization	NOUN
ejpam-5384	37	13	for	for	ADP
ejpam-5384	37	14	differentiable	differentiable	ADJ
ejpam-5384	37	15	convex	convex	NOUN
ejpam-5384	37	16	networks	network	NOUN
ejpam-5384	37	17	which	which	PRON
ejpam-5384	37	18	demonstrates	demonstrate	VERB
ejpam-5384	37	19	that	that	SCONJ
ejpam-5384	37	20	these	these	DET
ejpam-5384	37	21	flows	flow	NOUN
ejpam-5384	37	22	are	be	AUX
ejpam-5384	37	23	maintained	maintain	VERB
ejpam-5384	37	24	under	under	ADP
ejpam-5384	37	25	specific	specific	ADJ
ejpam-5384	37	26	transformations	transformation	NOUN
ejpam-5384	37	27	.	.	PUNCT
ejpam-5384	38	1	2	2	X
ejpam-5384	38	2	.	.	X
ejpam-5384	38	3	preliminaries	preliminary	NOUN
ejpam-5384	38	4	the	the	DET
ejpam-5384	38	5	networks	network	NOUN
ejpam-5384	38	6	we	we	PRON
ejpam-5384	38	7	will	will	AUX
ejpam-5384	38	8	examine	examine	VERB
ejpam-5384	38	9	have	have	VERB
ejpam-5384	38	10	n	n	NUM
ejpam-5384	38	11	links	link	NOUN
ejpam-5384	38	12	in	in	ADP
ejpam-5384	38	13	=	=	PUNCT
ejpam-5384	38	14	{	{	PUNCT
ejpam-5384	38	15	1	1	NUM
ejpam-5384	38	16	,	,	PUNCT
ejpam-5384	38	17	2	2	NUM
ejpam-5384	38	18	,	,	PUNCT
ejpam-5384	38	19	.	.	PUNCT
ejpam-5384	38	20	.	.	PUNCT
ejpam-5384	39	1	.	.	PUNCT
ejpam-5384	40	1	,	,	PUNCT
ejpam-5384	40	2	n	n	CCONJ
ejpam-5384	40	3	}	}	PUNCT
ejpam-5384	40	4	connecting	connect	VERB
ejpam-5384	40	5	the	the	DET
ejpam-5384	40	6	origin	origin	NOUN
ejpam-5384	40	7	with	with	ADP
ejpam-5384	40	8	the	the	DET
ejpam-5384	40	9	destination	destination	NOUN
ejpam-5384	40	10	node	node	NOUN
ejpam-5384	40	11	[	[	X
ejpam-5384	40	12	1	1	NUM
ejpam-5384	40	13	]	]	PUNCT
ejpam-5384	40	14	.	.	PUNCT
ejpam-5384	41	1	let	let	VERB
ejpam-5384	41	2	ϕi	ϕi	ADP
ejpam-5384	41	3	≥	≥	NOUN
ejpam-5384	41	4	0	0	NUM
ejpam-5384	41	5	denote	denote	VERB
ejpam-5384	41	6	the	the	DET
ejpam-5384	41	7	flow	flow	NOUN
ejpam-5384	41	8	via	via	ADP
ejpam-5384	41	9	link	link	PROPN
ejpam-5384	41	10	i	i	PRON
ejpam-5384	41	11	,	,	PUNCT
ejpam-5384	41	12	for	for	ADP
ejpam-5384	41	13	every	every	DET
ejpam-5384	41	14	i	i	NOUN
ejpam-5384	41	15	∈	∈	PROPN
ejpam-5384	41	16	in	in	ADP
ejpam-5384	41	17	.	.	PUNCT
ejpam-5384	42	1	the	the	DET
ejpam-5384	42	2	total	total	ADJ
ejpam-5384	42	3	flow	flow	NOUN
ejpam-5384	42	4	is	be	AUX
ejpam-5384	42	5	distributed	distribute	VERB
ejpam-5384	42	6	among	among	ADP
ejpam-5384	42	7	the	the	DET
ejpam-5384	42	8	links	link	NOUN
ejpam-5384	42	9	such	such	ADJ
ejpam-5384	42	10	that	that	SCONJ
ejpam-5384	42	11	n∑	n∑	NOUN
ejpam-5384	42	12	i=1	i=1	X
ejpam-5384	43	1	ϕi	ϕi	ADP
ejpam-5384	43	2	=	=	ADJ
ejpam-5384	43	3	1	1	X
ejpam-5384	43	4	.	.	PUNCT
ejpam-5384	44	1	the	the	DET
ejpam-5384	44	2	support	support	NOUN
ejpam-5384	44	3	of	of	ADP
ejpam-5384	44	4	a	a	DET
ejpam-5384	44	5	flow	flow	NOUN
ejpam-5384	44	6	ϕ	ϕ	NOUN
ejpam-5384	44	7	is	be	AUX
ejpam-5384	44	8	denoted	denote	VERB
ejpam-5384	44	9	by	by	ADP
ejpam-5384	44	10	supp(ϕ	supp(ϕ	NOUN
ejpam-5384	44	11	)	)	PUNCT
ejpam-5384	44	12	=	=	SYM
ejpam-5384	45	1	{	{	PUNCT
ejpam-5384	45	2	k	k	X
ejpam-5384	45	3	∈	∈	PROPN
ejpam-5384	45	4	in	in	ADP
ejpam-5384	45	5	|	|	ADV
ejpam-5384	45	6	ϕk	ϕk	ADV
ejpam-5384	45	7	̸=	̸=	PROPN
ejpam-5384	45	8	0	0	NUM
ejpam-5384	45	9	}	}	PUNCT
ejpam-5384	45	10	.	.	PUNCT
ejpam-5384	46	1	additionally	additionally	ADV
ejpam-5384	46	2	,	,	PUNCT
ejpam-5384	46	3	we	we	PRON
ejpam-5384	46	4	a.	a.	PROPN
ejpam-5384	46	5	kalampakas	kalampakas	PROPN
ejpam-5384	46	6	/	/	SYM
ejpam-5384	46	7	eur	eur	PROPN
ejpam-5384	46	8	.	.	PUNCT
ejpam-5384	47	1	j.	j.	PROPN
ejpam-5384	47	2	pure	pure	PROPN
ejpam-5384	47	3	appl	appl	PROPN
ejpam-5384	47	4	.	.	PROPN
ejpam-5384	47	5	math	math	PROPN
ejpam-5384	47	6	,	,	PUNCT
ejpam-5384	47	7	17	17	NUM
ejpam-5384	47	8	(	(	PUNCT
ejpam-5384	47	9	4	4	NUM
ejpam-5384	47	10	)	)	PUNCT
ejpam-5384	47	11	(	(	PUNCT
ejpam-5384	47	12	2024	2024	NUM
ejpam-5384	47	13	)	)	PUNCT
ejpam-5384	47	14	,	,	PUNCT
ejpam-5384	47	15	2448	2448	NUM
ejpam-5384	47	16	-	-	SYM
ejpam-5384	47	17	2466	2466	NUM
ejpam-5384	47	18	2450	2450	NUM
ejpam-5384	47	19	set	set	VERB
ejpam-5384	47	20	sn−1	sn−1	PROPN
ejpam-5384	47	21	=	=	PUNCT
ejpam-5384	47	22	{	{	PUNCT
ejpam-5384	47	23	ϕ	ϕ	PROPN
ejpam-5384	47	24	∈	∈	PROPN
ejpam-5384	47	25	rn	rn	PROPN
ejpam-5384	48	1	+	+	NOUN
ejpam-5384	48	2	:	:	PUNCT
ejpam-5384	48	3	n∑	n∑	INTJ
ejpam-5384	48	4	i=1	i=1	X
ejpam-5384	49	1	ϕi	ϕi	ADP
ejpam-5384	49	2	=	=	ADJ
ejpam-5384	49	3	1	1	NUM
ejpam-5384	49	4	}	}	PUNCT
ejpam-5384	49	5	and	and	CCONJ
ejpam-5384	49	6	int(sn−1	int(sn−1	NOUN
ejpam-5384	49	7	)	)	PUNCT
ejpam-5384	49	8	=	=	PRON
ejpam-5384	49	9	{	{	PUNCT
ejpam-5384	49	10	ϕ	ϕ	NOUN
ejpam-5384	49	11	∈	∈	PROPN
ejpam-5384	49	12	sn−1	sn−1	PROPN
ejpam-5384	49	13	:	:	PUNCT
ejpam-5384	49	14	supp(ϕ	supp(ϕ	NOUN
ejpam-5384	49	15	)	)	PUNCT
ejpam-5384	49	16	=	=	PUNCT
ejpam-5384	49	17	in	in	ADP
ejpam-5384	49	18	}	}	PUNCT
ejpam-5384	49	19	.	.	PUNCT
ejpam-5384	50	1	on	on	ADP
ejpam-5384	50	2	each	each	DET
ejpam-5384	50	3	link	link	NOUN
ejpam-5384	50	4	,	,	PUNCT
ejpam-5384	50	5	the	the	DET
ejpam-5384	50	6	flow	flow	NOUN
ejpam-5384	50	7	induces	induce	VERB
ejpam-5384	50	8	congestion	congestion	NOUN
ejpam-5384	50	9	,	,	PUNCT
ejpam-5384	50	10	increasing	increase	VERB
ejpam-5384	50	11	the	the	DET
ejpam-5384	50	12	traversal	traversal	NOUN
ejpam-5384	50	13	delay	delay	NOUN
ejpam-5384	50	14	[	[	X
ejpam-5384	50	15	30	30	NUM
ejpam-5384	50	16	]	]	PUNCT
ejpam-5384	50	17	.	.	PUNCT
ejpam-5384	51	1	this	this	DET
ejpam-5384	51	2	delay	delay	NOUN
ejpam-5384	51	3	is	be	AUX
ejpam-5384	51	4	captured	capture	VERB
ejpam-5384	51	5	by	by	ADP
ejpam-5384	51	6	continuous	continuous	ADJ
ejpam-5384	51	7	and	and	CCONJ
ejpam-5384	51	8	strictly	strictly	ADV
ejpam-5384	51	9	increasing	increase	VERB
ejpam-5384	51	10	latency	latency	NOUN
ejpam-5384	51	11	functions	function	NOUN
ejpam-5384	51	12	li(x	li(x	NUM
ejpam-5384	51	13	)	)	PUNCT
ejpam-5384	51	14	:	:	PUNCT
ejpam-5384	52	1	[	[	X
ejpam-5384	52	2	0	0	NUM
ejpam-5384	52	3	,	,	PUNCT
ejpam-5384	52	4	1	1	NUM
ejpam-5384	52	5	]	]	PUNCT
ejpam-5384	52	6	→	→	SYM
ejpam-5384	52	7	r	r	X
ejpam-5384	52	8	,	,	PUNCT
ejpam-5384	52	9	i	i	PRON
ejpam-5384	52	10	∈	∈	VERB
ejpam-5384	52	11	in	in	ADP
ejpam-5384	52	12	.	.	PUNCT
ejpam-5384	53	1	such	such	DET
ejpam-5384	53	2	a	a	DET
ejpam-5384	53	3	network	network	NOUN
ejpam-5384	53	4	of	of	ADP
ejpam-5384	53	5	can	can	AUX
ejpam-5384	53	6	thus	thus	ADV
ejpam-5384	53	7	be	be	AUX
ejpam-5384	53	8	characterized	characterize	VERB
ejpam-5384	53	9	by	by	ADP
ejpam-5384	53	10	the	the	DET
ejpam-5384	53	11	vector	vector	NOUN
ejpam-5384	53	12	of	of	ADP
ejpam-5384	53	13	latency	latency	NOUN
ejpam-5384	53	14	functions	function	NOUN
ejpam-5384	53	15	nn	nn	X
ejpam-5384	54	1	=	=	SYM
ejpam-5384	54	2	(	(	PUNCT
ejpam-5384	54	3	l1(x	l1(x	NOUN
ejpam-5384	54	4	)	)	PUNCT
ejpam-5384	54	5	,	,	PUNCT
ejpam-5384	54	6	.	.	PUNCT
ejpam-5384	54	7	.	.	PUNCT
ejpam-5384	54	8	.	.	PUNCT
ejpam-5384	55	1	,	,	PUNCT
ejpam-5384	55	2	ln(x	ln(x	X
ejpam-5384	55	3	)	)	PUNCT
ejpam-5384	55	4	)	)	PUNCT
ejpam-5384	55	5	.	.	PUNCT
ejpam-5384	56	1	if	if	SCONJ
ejpam-5384	56	2	all	all	DET
ejpam-5384	56	3	latency	latency	NOUN
ejpam-5384	56	4	functions	function	NOUN
ejpam-5384	56	5	li(x	li(x	NOUN
ejpam-5384	56	6	)	)	PUNCT
ejpam-5384	56	7	are	be	AUX
ejpam-5384	56	8	differentiable	differentiable	ADJ
ejpam-5384	56	9	,	,	PUNCT
ejpam-5384	56	10	the	the	DET
ejpam-5384	56	11	network	network	NOUN
ejpam-5384	56	12	is	be	AUX
ejpam-5384	56	13	called	call	VERB
ejpam-5384	56	14	a	a	DET
ejpam-5384	56	15	differentiable	differentiable	ADJ
ejpam-5384	56	16	network	network	NOUN
ejpam-5384	56	17	;	;	PUNCT
ejpam-5384	56	18	if	if	SCONJ
ejpam-5384	56	19	they	they	PRON
ejpam-5384	56	20	are	be	AUX
ejpam-5384	56	21	convex	convex	ADJ
ejpam-5384	56	22	,	,	PUNCT
ejpam-5384	56	23	it	it	PRON
ejpam-5384	56	24	is	be	AUX
ejpam-5384	56	25	termed	term	VERB
ejpam-5384	56	26	a	a	DET
ejpam-5384	56	27	convex	convex	ADJ
ejpam-5384	56	28	network	network	NOUN
ejpam-5384	56	29	.	.	PUNCT
ejpam-5384	57	1	a	a	DET
ejpam-5384	57	2	user	user	NOUN
ejpam-5384	57	3	equilibrium	equilibrium	NOUN
ejpam-5384	57	4	or	or	CCONJ
ejpam-5384	57	5	wardrop	wardrop	NOUN
ejpam-5384	57	6	equilibrium	equilibrium	NOUN
ejpam-5384	57	7	of	of	ADP
ejpam-5384	57	8	a	a	DET
ejpam-5384	57	9	network	network	NOUN
ejpam-5384	57	10	nn	nn	X
ejpam-5384	57	11	=	=	SYM
ejpam-5384	57	12	(	(	PUNCT
ejpam-5384	57	13	l1(x	l1(x	NOUN
ejpam-5384	57	14	)	)	PUNCT
ejpam-5384	57	15	,	,	PUNCT
ejpam-5384	57	16	.	.	PUNCT
ejpam-5384	57	17	.	.	PUNCT
ejpam-5384	58	1	.	.	PUNCT
ejpam-5384	59	1	,	,	PUNCT
ejpam-5384	59	2	ln(x	ln(x	X
ejpam-5384	59	3	)	)	PUNCT
ejpam-5384	59	4	)	)	PUNCT
ejpam-5384	59	5	is	be	AUX
ejpam-5384	59	6	a	a	DET
ejpam-5384	59	7	flow	flow	NOUN
ejpam-5384	59	8	ϕ	ϕ	NOUN
ejpam-5384	59	9	=	=	PUNCT
ejpam-5384	59	10	(	(	PUNCT
ejpam-5384	59	11	ϕ1	ϕ1	NOUN
ejpam-5384	59	12	,	,	PUNCT
ejpam-5384	59	13	.	.	PUNCT
ejpam-5384	59	14	.	.	PUNCT
ejpam-5384	60	1	.	.	PUNCT
ejpam-5384	61	1	,	,	PUNCT
ejpam-5384	61	2	ϕn	ϕn	X
ejpam-5384	61	3	)	)	PUNCT
ejpam-5384	61	4	∈	∈	PROPN
ejpam-5384	61	5	sn−1	sn−1	PROPN
ejpam-5384	61	6	such	such	ADJ
ejpam-5384	61	7	that	that	DET
ejpam-5384	61	8	lk(ϕk	lk(ϕk	NOUN
ejpam-5384	61	9	)	)	PUNCT
ejpam-5384	62	1	=	=	SYM
ejpam-5384	62	2	min	min	PROPN
ejpam-5384	62	3	i∈in	i∈in	PROPN
ejpam-5384	62	4	{	{	PUNCT
ejpam-5384	62	5	li(ϕi	li(ϕi	NOUN
ejpam-5384	62	6	)	)	PUNCT
ejpam-5384	62	7	}	}	PUNCT
ejpam-5384	62	8	,	,	PUNCT
ejpam-5384	62	9	∀k	∀k	NOUN
ejpam-5384	62	10	∈	∈	PROPN
ejpam-5384	62	11	in	in	ADP
ejpam-5384	62	12	with	with	ADP
ejpam-5384	62	13	ϕk	ϕk	NUM
ejpam-5384	62	14	>	>	SYM
ejpam-5384	62	15	0	0	NUM
ejpam-5384	62	16	,	,	PUNCT
ejpam-5384	62	17	i.e.	i.e.	X
ejpam-5384	62	18	,	,	PUNCT
ejpam-5384	62	19	the	the	DET
ejpam-5384	62	20	delay	delay	NOUN
ejpam-5384	62	21	is	be	AUX
ejpam-5384	62	22	equal	equal	ADJ
ejpam-5384	62	23	among	among	ADP
ejpam-5384	62	24	all	all	DET
ejpam-5384	62	25	used	use	VERB
ejpam-5384	62	26	links	link	NOUN
ejpam-5384	62	27	and	and	CCONJ
ejpam-5384	62	28	less	less	ADJ
ejpam-5384	62	29	than	than	ADP
ejpam-5384	62	30	that	that	PRON
ejpam-5384	62	31	of	of	ADP
ejpam-5384	62	32	any	any	DET
ejpam-5384	62	33	unused	unused	ADJ
ejpam-5384	62	34	link	link	NOUN
ejpam-5384	62	35	[	[	X
ejpam-5384	62	36	6	6	NUM
ejpam-5384	62	37	]	]	PUNCT
ejpam-5384	62	38	.	.	PUNCT
ejpam-5384	63	1	the	the	DET
ejpam-5384	63	2	overall	overall	ADJ
ejpam-5384	63	3	delay	delay	NOUN
ejpam-5384	63	4	of	of	ADP
ejpam-5384	63	5	a	a	DET
ejpam-5384	63	6	network	network	NOUN
ejpam-5384	63	7	nn	nn	X
ejpam-5384	63	8	=	=	SYM
ejpam-5384	63	9	(	(	PUNCT
ejpam-5384	63	10	l1(x	l1(x	NOUN
ejpam-5384	63	11	)	)	PUNCT
ejpam-5384	63	12	,	,	PUNCT
ejpam-5384	63	13	.	.	PUNCT
ejpam-5384	63	14	.	.	PUNCT
ejpam-5384	63	15	.	.	PUNCT
ejpam-5384	64	1	,	,	PUNCT
ejpam-5384	64	2	ln(x	ln(x	X
ejpam-5384	64	3	)	)	PUNCT
ejpam-5384	64	4	)	)	PUNCT
ejpam-5384	65	1	for	for	ADP
ejpam-5384	65	2	ϕ	ϕ	NOUN
ejpam-5384	65	3	=	=	SYM
ejpam-5384	65	4	(	(	PUNCT
ejpam-5384	65	5	ϕ1	ϕ1	NOUN
ejpam-5384	65	6	,	,	PUNCT
ejpam-5384	65	7	.	.	PUNCT
ejpam-5384	65	8	.	.	PUNCT
ejpam-5384	65	9	.	.	PUNCT
ejpam-5384	66	1	,	,	PUNCT
ejpam-5384	66	2	ϕn	ϕn	X
ejpam-5384	66	3	)	)	PUNCT
ejpam-5384	66	4	∈	∈	PROPN
ejpam-5384	66	5	sn−1	sn−1	PROPN
ejpam-5384	66	6	is	be	AUX
ejpam-5384	66	7	given	give	VERB
ejpam-5384	66	8	by	by	ADP
ejpam-5384	66	9	n∑	n∑	PROPN
ejpam-5384	66	10	i=1	i=1	PROPN
ejpam-5384	66	11	ϕili(ϕi	ϕili(ϕi	PROPN
ejpam-5384	66	12	)	)	PUNCT
ejpam-5384	66	13	.	.	PUNCT
ejpam-5384	67	1	a	a	DET
ejpam-5384	67	2	system	system	NOUN
ejpam-5384	67	3	optimum	optimum	NOUN
ejpam-5384	67	4	of	of	ADP
ejpam-5384	67	5	a	a	DET
ejpam-5384	67	6	network	network	NOUN
ejpam-5384	67	7	nn	nn	X
ejpam-5384	67	8	=	=	SYM
ejpam-5384	67	9	(	(	PUNCT
ejpam-5384	67	10	l1(x	l1(x	NOUN
ejpam-5384	67	11	)	)	PUNCT
ejpam-5384	67	12	,	,	PUNCT
ejpam-5384	67	13	.	.	PUNCT
ejpam-5384	67	14	.	.	PUNCT
ejpam-5384	67	15	.	.	PUNCT
ejpam-5384	68	1	,	,	PUNCT
ejpam-5384	68	2	ln(x	ln(x	X
ejpam-5384	68	3	)	)	PUNCT
ejpam-5384	68	4	)	)	PUNCT
ejpam-5384	68	5	is	be	AUX
ejpam-5384	68	6	a	a	DET
ejpam-5384	68	7	flow	flow	NOUN
ejpam-5384	68	8	(	(	PUNCT
ejpam-5384	68	9	ϕ1	ϕ1	NOUN
ejpam-5384	68	10	,	,	PUNCT
ejpam-5384	68	11	.	.	PUNCT
ejpam-5384	68	12	.	.	PUNCT
ejpam-5384	69	1	.	.	PUNCT
ejpam-5384	70	1	,	,	PUNCT
ejpam-5384	70	2	ϕn	ϕn	X
ejpam-5384	70	3	)	)	PUNCT
ejpam-5384	70	4	∈	∈	PROPN
ejpam-5384	70	5	sn−1	sn−1	PROPN
ejpam-5384	70	6	that	that	PRON
ejpam-5384	70	7	minimizes	minimize	VERB
ejpam-5384	70	8	this	this	DET
ejpam-5384	70	9	average	average	ADJ
ejpam-5384	70	10	delay	delay	NOUN
ejpam-5384	71	1	[	[	X
ejpam-5384	71	2	6	6	NUM
ejpam-5384	71	3	]	]	PUNCT
ejpam-5384	71	4	.	.	PUNCT
ejpam-5384	72	1	3	3	X
ejpam-5384	72	2	.	.	X
ejpam-5384	72	3	user	user	NOUN
ejpam-5384	72	4	equilibrium	equilibrium	NOUN
ejpam-5384	72	5	in	in	ADP
ejpam-5384	72	6	what	what	PRON
ejpam-5384	72	7	follows	follow	VERB
ejpam-5384	72	8	,	,	PUNCT
ejpam-5384	72	9	we	we	PRON
ejpam-5384	72	10	explore	explore	VERB
ejpam-5384	72	11	several	several	ADJ
ejpam-5384	72	12	properties	property	NOUN
ejpam-5384	72	13	that	that	PRON
ejpam-5384	72	14	will	will	AUX
ejpam-5384	72	15	be	be	AUX
ejpam-5384	72	16	essential	essential	ADJ
ejpam-5384	72	17	throughout	throughout	ADV
ejpam-5384	72	18	.	.	PUNCT
ejpam-5384	73	1	the	the	DET
ejpam-5384	73	2	next	next	ADJ
ejpam-5384	73	3	lemma	lemma	PROPN
ejpam-5384	73	4	demonstrates	demonstrate	VERB
ejpam-5384	73	5	that	that	SCONJ
ejpam-5384	73	6	user	user	NOUN
ejpam-5384	73	7	equilibrium	equilibrium	NOUN
ejpam-5384	73	8	remains	remain	VERB
ejpam-5384	73	9	unchanged	unchanged	ADJ
ejpam-5384	73	10	under	under	ADP
ejpam-5384	73	11	mappings	mapping	NOUN
ejpam-5384	73	12	which	which	PRON
ejpam-5384	73	13	are	be	AUX
ejpam-5384	73	14	strictly	strictly	ADV
ejpam-5384	73	15	increasing	increase	VERB
ejpam-5384	73	16	.	.	PUNCT
ejpam-5384	74	1	this	this	PRON
ejpam-5384	74	2	is	be	AUX
ejpam-5384	74	3	because	because	SCONJ
ejpam-5384	74	4	the	the	DET
ejpam-5384	74	5	minimum	minimum	ADJ
ejpam-5384	74	6	value	value	NOUN
ejpam-5384	74	7	in	in	ADP
ejpam-5384	74	8	a	a	DET
ejpam-5384	74	9	set	set	NOUN
ejpam-5384	74	10	is	be	AUX
ejpam-5384	74	11	preserved	preserve	VERB
ejpam-5384	74	12	when	when	SCONJ
ejpam-5384	74	13	a	a	DET
ejpam-5384	74	14	strictly	strictly	ADV
ejpam-5384	74	15	increasing	increase	VERB
ejpam-5384	74	16	function	function	NOUN
ejpam-5384	74	17	is	be	AUX
ejpam-5384	74	18	applied	apply	VERB
ejpam-5384	74	19	.	.	PUNCT
ejpam-5384	75	1	lemma	lemma	PROPN
ejpam-5384	75	2	1	1	X
ejpam-5384	75	3	.	.	PUNCT
ejpam-5384	76	1	consider	consider	VERB
ejpam-5384	76	2	a	a	DET
ejpam-5384	76	3	network	network	NOUN
ejpam-5384	76	4	nn	nn	X
ejpam-5384	76	5	=	=	SYM
ejpam-5384	76	6	(	(	PUNCT
ejpam-5384	76	7	l1(x	l1(x	NOUN
ejpam-5384	76	8	)	)	PUNCT
ejpam-5384	76	9	,	,	PUNCT
ejpam-5384	76	10	.	.	PUNCT
ejpam-5384	76	11	.	.	PUNCT
ejpam-5384	77	1	.	.	PUNCT
ejpam-5384	78	1	,	,	PUNCT
ejpam-5384	78	2	ln(x	ln(x	X
ejpam-5384	78	3	)	)	PUNCT
ejpam-5384	78	4	)	)	PUNCT
ejpam-5384	79	1	and	and	CCONJ
ejpam-5384	79	2	a	a	DET
ejpam-5384	79	3	strictly	strictly	ADV
ejpam-5384	79	4	increasing	increase	VERB
ejpam-5384	79	5	and	and	CCONJ
ejpam-5384	79	6	continuous	continuous	ADJ
ejpam-5384	79	7	function	function	NOUN
ejpam-5384	79	8	f(x	f(x	PROPN
ejpam-5384	79	9	)	)	PUNCT
ejpam-5384	79	10	:	:	PUNCT
ejpam-5384	80	1	r	r	NOUN
ejpam-5384	80	2	→	→	SYM
ejpam-5384	80	3	r	r	NOUN
ejpam-5384	80	4	,	,	PUNCT
ejpam-5384	80	5	if	if	SCONJ
ejpam-5384	80	6	a	a	DET
ejpam-5384	80	7	flow	flow	NOUN
ejpam-5384	80	8	(	(	PUNCT
ejpam-5384	80	9	ϕ1	ϕ1	NOUN
ejpam-5384	80	10	,	,	PUNCT
ejpam-5384	80	11	.	.	PUNCT
ejpam-5384	80	12	.	.	PUNCT
ejpam-5384	80	13	.	.	PUNCT
ejpam-5384	81	1	,	,	PUNCT
ejpam-5384	81	2	ϕn	ϕn	X
ejpam-5384	81	3	)	)	PUNCT
ejpam-5384	81	4	∈	∈	PROPN
ejpam-5384	81	5	sn−1	sn−1	PROPN
ejpam-5384	81	6	is	be	AUX
ejpam-5384	81	7	user	user	NOUN
ejpam-5384	81	8	equilibrium	equilibrium	NOUN
ejpam-5384	81	9	of	of	ADP
ejpam-5384	81	10	nn	nn	PROPN
ejpam-5384	81	11	then	then	ADV
ejpam-5384	81	12	it	it	PRON
ejpam-5384	81	13	is	be	AUX
ejpam-5384	81	14	also	also	ADV
ejpam-5384	81	15	user	user	NOUN
ejpam-5384	81	16	equilibrium	equilibrium	NOUN
ejpam-5384	81	17	of	of	ADP
ejpam-5384	81	18	f(nn	f(nn	NOUN
ejpam-5384	81	19	)	)	PUNCT
ejpam-5384	81	20	=	=	SYM
ejpam-5384	81	21	(	(	PUNCT
ejpam-5384	81	22	f(l1(x	f(l1(x	NOUN
ejpam-5384	81	23	)	)	PUNCT
ejpam-5384	81	24	)	)	PUNCT
ejpam-5384	81	25	,	,	PUNCT
ejpam-5384	81	26	.	.	PUNCT
ejpam-5384	81	27	.	.	PUNCT
ejpam-5384	82	1	.	.	PUNCT
ejpam-5384	83	1	,	,	PUNCT
ejpam-5384	83	2	f(ln(x	f(ln(x	PROPN
ejpam-5384	83	3	)	)	PUNCT
ejpam-5384	83	4	)	)	PUNCT
ejpam-5384	83	5	)	)	PUNCT
ejpam-5384	83	6	.	.	PUNCT
ejpam-5384	84	1	on	on	ADP
ejpam-5384	84	2	the	the	DET
ejpam-5384	84	3	other	other	ADJ
ejpam-5384	84	4	hand	hand	NOUN
ejpam-5384	84	5	,	,	PUNCT
ejpam-5384	84	6	the	the	DET
ejpam-5384	84	7	above	above	ADJ
ejpam-5384	84	8	property	property	NOUN
ejpam-5384	84	9	does	do	AUX
ejpam-5384	84	10	n’t	not	PART
ejpam-5384	84	11	hold	hold	VERB
ejpam-5384	84	12	for	for	ADP
ejpam-5384	84	13	system	system	NOUN
ejpam-5384	84	14	optimums	optimum	NOUN
ejpam-5384	84	15	as	as	SCONJ
ejpam-5384	84	16	it	it	PRON
ejpam-5384	84	17	is	be	AUX
ejpam-5384	84	18	illustrated	illustrate	VERB
ejpam-5384	84	19	in	in	ADP
ejpam-5384	84	20	the	the	DET
ejpam-5384	84	21	following	follow	VERB
ejpam-5384	84	22	example	example	NOUN
ejpam-5384	84	23	.	.	PUNCT
ejpam-5384	85	1	a.	a.	PROPN
ejpam-5384	85	2	kalampakas	kalampakas	PROPN
ejpam-5384	85	3	/	/	SYM
ejpam-5384	85	4	eur	eur	PROPN
ejpam-5384	85	5	.	.	PUNCT
ejpam-5384	86	1	j.	j.	PROPN
ejpam-5384	86	2	pure	pure	PROPN
ejpam-5384	86	3	appl	appl	PROPN
ejpam-5384	86	4	.	.	PROPN
ejpam-5384	86	5	math	math	PROPN
ejpam-5384	86	6	,	,	PUNCT
ejpam-5384	86	7	17	17	NUM
ejpam-5384	86	8	(	(	PUNCT
ejpam-5384	86	9	4	4	NUM
ejpam-5384	86	10	)	)	PUNCT
ejpam-5384	86	11	(	(	PUNCT
ejpam-5384	86	12	2024	2024	NUM
ejpam-5384	86	13	)	)	PUNCT
ejpam-5384	86	14	,	,	PUNCT
ejpam-5384	86	15	2448	2448	NUM
ejpam-5384	86	16	-	-	SYM
ejpam-5384	86	17	2466	2466	NUM
ejpam-5384	86	18	2451	2451	NUM
ejpam-5384	86	19	l1(x	l1(x	NOUN
ejpam-5384	86	20	)	)	PUNCT
ejpam-5384	86	21	=	=	SYM
ejpam-5384	87	1	x2/3	x2/3	PROPN
ejpam-5384	87	2	l2(x	l2(x	NOUN
ejpam-5384	87	3	)	)	PUNCT
ejpam-5384	87	4	=	=	SYM
ejpam-5384	88	1	2x/3	2x/3	NUM
ejpam-5384	88	2	figure	figure	NOUN
ejpam-5384	88	3	1	1	NUM
ejpam-5384	88	4	:	:	PUNCT
ejpam-5384	88	5	a	a	DET
ejpam-5384	88	6	network	network	NOUN
ejpam-5384	88	7	n	n	X
ejpam-5384	88	8	with	with	ADP
ejpam-5384	88	9	two	two	NUM
ejpam-5384	88	10	parallel	parallel	ADJ
ejpam-5384	88	11	links	link	NOUN
ejpam-5384	88	12	example	example	NOUN
ejpam-5384	88	13	1	1	X
ejpam-5384	88	14	.	.	X
ejpam-5384	89	1	we	we	PRON
ejpam-5384	89	2	examine	examine	VERB
ejpam-5384	89	3	the	the	DET
ejpam-5384	89	4	network	network	NOUN
ejpam-5384	89	5	n	n	NOUN
ejpam-5384	89	6	=	=	SYM
ejpam-5384	89	7	{	{	PUNCT
ejpam-5384	89	8	x2	x2	NOUN
ejpam-5384	89	9	3	3	NUM
ejpam-5384	89	10	,	,	PUNCT
ejpam-5384	89	11	2x	2x	NUM
ejpam-5384	89	12	3	3	NUM
ejpam-5384	89	13	}	}	PUNCT
ejpam-5384	89	14	presented	present	VERB
ejpam-5384	89	15	in	in	ADP
ejpam-5384	89	16	fig	fig	NOUN
ejpam-5384	89	17	.	.	PUNCT
ejpam-5384	90	1	1	1	NUM
ejpam-5384	90	2	which	which	PRON
ejpam-5384	90	3	was	be	AUX
ejpam-5384	90	4	utilized	utilize	VERB
ejpam-5384	90	5	in	in	ADP
ejpam-5384	90	6	[	[	X
ejpam-5384	90	7	1	1	NUM
ejpam-5384	90	8	]	]	PUNCT
ejpam-5384	90	9	to	to	PART
ejpam-5384	90	10	highlight	highlight	VERB
ejpam-5384	90	11	the	the	DET
ejpam-5384	90	12	inefficiency	inefficiency	NOUN
ejpam-5384	90	13	due	due	ADP
ejpam-5384	90	14	to	to	ADP
ejpam-5384	90	15	congestion	congestion	NOUN
ejpam-5384	90	16	externalities	externality	NOUN
ejpam-5384	90	17	.	.	PUNCT
ejpam-5384	91	1	the	the	DET
ejpam-5384	91	2	system	system	NOUN
ejpam-5384	91	3	optimum	optimum	NOUN
ejpam-5384	91	4	that	that	PRON
ejpam-5384	91	5	minimizes	minimize	VERB
ejpam-5384	91	6	the	the	DET
ejpam-5384	91	7	average	average	ADJ
ejpam-5384	91	8	delay	delay	NOUN
ejpam-5384	91	9	of	of	ADP
ejpam-5384	91	10	the	the	DET
ejpam-5384	91	11	network	network	NOUN
ejpam-5384	91	12	is	be	AUX
ejpam-5384	91	13	ϕso	ϕso	NOUN
ejpam-5384	91	14	=	=	SYM
ejpam-5384	91	15	(	(	PUNCT
ejpam-5384	91	16	23	23	NUM
ejpam-5384	91	17	,	,	PUNCT
ejpam-5384	91	18	1	1	NUM
ejpam-5384	91	19	3	3	NUM
ejpam-5384	91	20	)	)	PUNCT
ejpam-5384	91	21	and	and	CCONJ
ejpam-5384	91	22	the	the	DET
ejpam-5384	91	23	user	user	NOUN
ejpam-5384	91	24	equilibrium	equilibrium	NOUN
ejpam-5384	91	25	that	that	PRON
ejpam-5384	91	26	equates	equate	VERB
ejpam-5384	91	27	delay	delay	NOUN
ejpam-5384	91	28	on	on	ADP
ejpam-5384	91	29	the	the	DET
ejpam-5384	91	30	two	two	NUM
ejpam-5384	91	31	links	link	NOUN
ejpam-5384	91	32	is	be	AUX
ejpam-5384	91	33	ϕwe	ϕwe	ADJ
ejpam-5384	92	1	≈	≈	PROPN
ejpam-5384	92	2	(	(	PUNCT
ejpam-5384	92	3	0.73	0.73	NUM
ejpam-5384	92	4	,	,	PUNCT
ejpam-5384	92	5	0.27	0.27	NUM
ejpam-5384	92	6	)	)	PUNCT
ejpam-5384	92	7	.	.	PUNCT
ejpam-5384	93	1	the	the	DET
ejpam-5384	93	2	network	network	NOUN
ejpam-5384	93	3	obtained	obtain	VERB
ejpam-5384	93	4	by	by	ADP
ejpam-5384	93	5	taking	take	VERB
ejpam-5384	93	6	the	the	DET
ejpam-5384	93	7	image	image	NOUN
ejpam-5384	93	8	of	of	ADP
ejpam-5384	93	9	n	n	NUM
ejpam-5384	93	10	via	via	ADP
ejpam-5384	93	11	the	the	DET
ejpam-5384	93	12	continuous	continuous	ADJ
ejpam-5384	93	13	and	and	CCONJ
ejpam-5384	93	14	strictly	strictly	ADV
ejpam-5384	93	15	increasing	increase	VERB
ejpam-5384	93	16	function	function	NOUN
ejpam-5384	93	17	f(x	f(x	PROPN
ejpam-5384	93	18	)	)	PUNCT
ejpam-5384	94	1	=	=	PUNCT
ejpam-5384	94	2	x2	x2	PROPN
ejpam-5384	94	3	is	be	AUX
ejpam-5384	94	4	f(n	f(n	PROPN
ejpam-5384	94	5	)	)	PUNCT
ejpam-5384	95	1	=	=	PRON
ejpam-5384	95	2	{	{	PUNCT
ejpam-5384	95	3	x4	x4	PROPN
ejpam-5384	95	4	9	9	NUM
ejpam-5384	95	5	,	,	PUNCT
ejpam-5384	95	6	4x2	4x2	NUM
ejpam-5384	95	7	9	9	NUM
ejpam-5384	95	8	}	}	PUNCT
ejpam-5384	95	9	.	.	PUNCT
ejpam-5384	96	1	it	it	PRON
ejpam-5384	96	2	is	be	AUX
ejpam-5384	96	3	straightforward	straightforward	ADJ
ejpam-5384	96	4	to	to	PART
ejpam-5384	96	5	see	see	VERB
ejpam-5384	96	6	that	that	SCONJ
ejpam-5384	96	7	the	the	DET
ejpam-5384	96	8	user	user	NOUN
ejpam-5384	96	9	equilibrium	equilibrium	NOUN
ejpam-5384	96	10	of	of	ADP
ejpam-5384	96	11	f(n	f(n	PROPN
ejpam-5384	96	12	)	)	PUNCT
ejpam-5384	96	13	is	be	AUX
ejpam-5384	96	14	the	the	DET
ejpam-5384	96	15	same	same	ADJ
ejpam-5384	96	16	but	but	CCONJ
ejpam-5384	96	17	the	the	DET
ejpam-5384	96	18	new	new	ADJ
ejpam-5384	96	19	system	system	NOUN
ejpam-5384	96	20	optimum	optimum	NOUN
ejpam-5384	96	21	is	be	AUX
ejpam-5384	96	22	ϕso′	ϕso′	PROPN
ejpam-5384	96	23	≈	≈	PROPN
ejpam-5384	96	24	{	{	PUNCT
ejpam-5384	96	25	0.69	0.69	NUM
ejpam-5384	96	26	,	,	PUNCT
ejpam-5384	96	27	0.31	0.31	NUM
ejpam-5384	96	28	}	}	PUNCT
ejpam-5384	96	29	.	.	PUNCT
ejpam-5384	97	1	the	the	DET
ejpam-5384	97	2	example	example	NOUN
ejpam-5384	97	3	demonstrates	demonstrate	VERB
ejpam-5384	97	4	that	that	SCONJ
ejpam-5384	97	5	,	,	PUNCT
ejpam-5384	97	6	the	the	DET
ejpam-5384	97	7	system	system	NOUN
ejpam-5384	97	8	optimum	optimum	ADJ
ejpam-5384	97	9	unlike	unlike	ADP
ejpam-5384	97	10	the	the	DET
ejpam-5384	97	11	user	user	NOUN
ejpam-5384	97	12	equilibrium	equilibrium	NOUN
ejpam-5384	97	13	is	be	AUX
ejpam-5384	97	14	not	not	PART
ejpam-5384	97	15	generally	generally	ADV
ejpam-5384	97	16	maintained	maintain	VERB
ejpam-5384	97	17	by	by	ADP
ejpam-5384	97	18	the	the	DET
ejpam-5384	97	19	type	type	NOUN
ejpam-5384	97	20	of	of	ADP
ejpam-5384	97	21	latency	latency	NOUN
ejpam-5384	97	22	function	function	NOUN
ejpam-5384	97	23	we	we	PRON
ejpam-5384	97	24	consider	consider	VERB
ejpam-5384	97	25	i.e.	i.e.	X
ejpam-5384	97	26	,	,	PUNCT
ejpam-5384	97	27	continuous	continuous	ADJ
ejpam-5384	97	28	,	,	PUNCT
ejpam-5384	97	29	convex	convex	ADJ
ejpam-5384	97	30	and	and	CCONJ
ejpam-5384	97	31	strictly	strictly	ADV
ejpam-5384	97	32	increasing	increase	VERB
ejpam-5384	97	33	.	.	PUNCT
ejpam-5384	98	1	this	this	PRON
ejpam-5384	98	2	raises	raise	VERB
ejpam-5384	98	3	the	the	DET
ejpam-5384	98	4	following	follow	VERB
ejpam-5384	98	5	question	question	NOUN
ejpam-5384	98	6	:	:	PUNCT
ejpam-5384	98	7	do	do	AUX
ejpam-5384	98	8	wardrop	wardrop	VERB
ejpam-5384	98	9	optimal	optimal	ADJ
ejpam-5384	98	10	flows	flow	NOUN
ejpam-5384	98	11	remain	remain	VERB
ejpam-5384	98	12	consistent	consistent	ADJ
ejpam-5384	98	13	under	under	ADP
ejpam-5384	98	14	such	such	ADJ
ejpam-5384	98	15	transformations	transformation	NOUN
ejpam-5384	98	16	?	?	PUNCT
ejpam-5384	99	1	we	we	PRON
ejpam-5384	99	2	will	will	AUX
ejpam-5384	99	3	address	address	VERB
ejpam-5384	99	4	this	this	DET
ejpam-5384	99	5	question	question	NOUN
ejpam-5384	99	6	in	in	ADP
ejpam-5384	99	7	section	section	NOUN
ejpam-5384	99	8	5	5	NUM
ejpam-5384	99	9	.	.	PUNCT
ejpam-5384	100	1	the	the	DET
ejpam-5384	100	2	below	below	ADJ
ejpam-5384	100	3	property	property	NOUN
ejpam-5384	100	4	will	will	AUX
ejpam-5384	100	5	be	be	AUX
ejpam-5384	100	6	very	very	ADV
ejpam-5384	100	7	useful	useful	ADJ
ejpam-5384	100	8	in	in	ADP
ejpam-5384	100	9	our	our	PRON
ejpam-5384	100	10	subsequent	subsequent	ADJ
ejpam-5384	100	11	constructions	construction	NOUN
ejpam-5384	100	12	.	.	PUNCT
ejpam-5384	101	1	it	it	PRON
ejpam-5384	101	2	can	can	AUX
ejpam-5384	101	3	be	be	AUX
ejpam-5384	101	4	easily	easily	ADV
ejpam-5384	101	5	proved	prove	VERB
ejpam-5384	101	6	by	by	ADP
ejpam-5384	101	7	a	a	DET
ejpam-5384	101	8	simple	simple	ADJ
ejpam-5384	101	9	geometric	geometric	ADJ
ejpam-5384	101	10	inspection	inspection	NOUN
ejpam-5384	101	11	of	of	ADP
ejpam-5384	101	12	the	the	DET
ejpam-5384	101	13	curves	curve	NOUN
ejpam-5384	101	14	of	of	ADP
ejpam-5384	101	15	the	the	DET
ejpam-5384	101	16	strictly	strictly	ADV
ejpam-5384	101	17	increasing	increase	VERB
ejpam-5384	101	18	latency	latency	NOUN
ejpam-5384	101	19	functions	function	NOUN
ejpam-5384	101	20	on	on	ADP
ejpam-5384	101	21	the	the	DET
ejpam-5384	101	22	same	same	ADJ
ejpam-5384	101	23	coordinate	coordinate	NOUN
ejpam-5384	101	24	system	system	NOUN
ejpam-5384	101	25	.	.	PUNCT
ejpam-5384	102	1	below	below	ADP
ejpam-5384	102	2	we	we	PRON
ejpam-5384	102	3	provide	provide	VERB
ejpam-5384	102	4	a	a	DET
ejpam-5384	102	5	more	more	ADV
ejpam-5384	102	6	detailed	detailed	ADJ
ejpam-5384	102	7	algebraic	algebraic	ADJ
ejpam-5384	102	8	proof	proof	NOUN
ejpam-5384	102	9	(	(	PUNCT
ejpam-5384	102	10	similar	similar	ADJ
ejpam-5384	102	11	constructions	construction	NOUN
ejpam-5384	102	12	exist	exist	VERB
ejpam-5384	102	13	in	in	ADP
ejpam-5384	102	14	the	the	DET
ejpam-5384	102	15	literature	literature	NOUN
ejpam-5384	102	16	for	for	ADP
ejpam-5384	102	17	the	the	DET
ejpam-5384	102	18	user	user	NOUN
ejpam-5384	102	19	equilibrium	equilibrium	NOUN
ejpam-5384	102	20	,	,	PUNCT
ejpam-5384	102	21	see	see	VERB
ejpam-5384	103	1	e.g.	e.g.	ADV
ejpam-5384	103	2	[	[	X
ejpam-5384	103	3	27	27	NUM
ejpam-5384	103	4	]	]	NUM
ejpam-5384	103	5	)	)	PUNCT
ejpam-5384	103	6	.	.	PUNCT
ejpam-5384	104	1	proposition	proposition	NOUN
ejpam-5384	104	2	1	1	NUM
ejpam-5384	104	3	.	.	PUNCT
ejpam-5384	105	1	there	there	PRON
ejpam-5384	105	2	exists	exist	VERB
ejpam-5384	105	3	a	a	DET
ejpam-5384	105	4	unique	unique	ADJ
ejpam-5384	105	5	user	user	NOUN
ejpam-5384	105	6	equilibrium	equilibrium	NOUN
ejpam-5384	105	7	for	for	ADP
ejpam-5384	105	8	any	any	DET
ejpam-5384	105	9	network	network	NOUN
ejpam-5384	105	10	nn	nn	PROPN
ejpam-5384	105	11	.	.	PROPN
ejpam-5384	105	12	proof	proof	NOUN
ejpam-5384	105	13	.	.	PUNCT
ejpam-5384	106	1	let	let	VERB
ejpam-5384	106	2	nn	nn	X
ejpam-5384	106	3	=	=	SYM
ejpam-5384	106	4	(	(	PUNCT
ejpam-5384	106	5	l1(x	l1(x	NOUN
ejpam-5384	106	6	)	)	PUNCT
ejpam-5384	106	7	,	,	PUNCT
ejpam-5384	106	8	·	·	PUNCT
ejpam-5384	106	9	·	·	PUNCT
ejpam-5384	106	10	·	·	PUNCT
ejpam-5384	106	11	,	,	PUNCT
ejpam-5384	106	12	ln(x	ln(x	X
ejpam-5384	106	13	)	)	PUNCT
ejpam-5384	106	14	)	)	PUNCT
ejpam-5384	106	15	.	.	PUNCT
ejpam-5384	107	1	for	for	ADP
ejpam-5384	107	2	each	each	DET
ejpam-5384	107	3	i	i	PRON
ejpam-5384	107	4	∈	∈	PROPN
ejpam-5384	107	5	in	in	ADP
ejpam-5384	107	6	,	,	PUNCT
ejpam-5384	107	7	we	we	PRON
ejpam-5384	107	8	set	set	VERB
ejpam-5384	107	9	ai	ai	PROPN
ejpam-5384	107	10	=	=	PROPN
ejpam-5384	107	11	li(0	li(0	PROPN
ejpam-5384	107	12	)	)	PUNCT
ejpam-5384	107	13	,	,	PUNCT
ejpam-5384	107	14	bi	bi	NOUN
ejpam-5384	107	15	=	=	PROPN
ejpam-5384	107	16	li(1	li(1	PROPN
ejpam-5384	107	17	)	)	PUNCT
ejpam-5384	107	18	and	and	CCONJ
ejpam-5384	107	19	consider	consider	VERB
ejpam-5384	107	20	the	the	DET
ejpam-5384	107	21	inverse	inverse	NOUN
ejpam-5384	107	22	(	(	PUNCT
ejpam-5384	107	23	again	again	ADV
ejpam-5384	107	24	continuous	continuous	ADJ
ejpam-5384	107	25	,	,	PUNCT
ejpam-5384	107	26	strictly	strictly	ADV
ejpam-5384	107	27	increasing	increase	VERB
ejpam-5384	107	28	)	)	PUNCT
ejpam-5384	107	29	function	function	NOUN
ejpam-5384	107	30	l−1	l−1	PROPN
ejpam-5384	108	1	i	i	PRON
ejpam-5384	108	2	:	:	PUNCT
ejpam-5384	109	1	[	[	X
ejpam-5384	109	2	ai	ai	ADP
ejpam-5384	109	3	,	,	PUNCT
ejpam-5384	109	4	bi	bi	NOUN
ejpam-5384	109	5	]	]	X
ejpam-5384	109	6	→	→	X
ejpam-5384	110	1	[	[	X
ejpam-5384	110	2	0	0	NUM
ejpam-5384	110	3	,	,	PUNCT
ejpam-5384	110	4	1	1	NUM
ejpam-5384	110	5	]	]	PUNCT
ejpam-5384	110	6	of	of	ADP
ejpam-5384	110	7	each	each	DET
ejpam-5384	110	8	latency	latency	NOUN
ejpam-5384	110	9	function	function	NOUN
ejpam-5384	110	10	li	li	PROPN
ejpam-5384	110	11	:	:	PUNCT
ejpam-5384	111	1	[	[	X
ejpam-5384	111	2	0	0	NUM
ejpam-5384	111	3	,	,	PUNCT
ejpam-5384	111	4	1	1	NUM
ejpam-5384	111	5	]	]	PUNCT
ejpam-5384	111	6	→	→	X
ejpam-5384	111	7	[	[	X
ejpam-5384	111	8	ai	ai	NOUN
ejpam-5384	111	9	,	,	PUNCT
ejpam-5384	111	10	bi	bi	NOUN
ejpam-5384	111	11	]	]	X
ejpam-5384	111	12	.	.	PUNCT
ejpam-5384	112	1	we	we	PRON
ejpam-5384	112	2	define	define	VERB
ejpam-5384	112	3	a	a	DET
ejpam-5384	112	4	continuous	continuous	ADJ
ejpam-5384	112	5	and	and	CCONJ
ejpam-5384	112	6	increasing	increase	VERB
ejpam-5384	112	7	function	function	NOUN
ejpam-5384	112	8	l−1	l−1	PROPN
ejpam-5384	113	1	i	i	PRON
ejpam-5384	113	2	:	:	PUNCT
ejpam-5384	114	1	r	r	X
ejpam-5384	114	2	→	→	SYM
ejpam-5384	114	3	[	[	X
ejpam-5384	114	4	0	0	NUM
ejpam-5384	114	5	,	,	PUNCT
ejpam-5384	114	6	1	1	NUM
ejpam-5384	114	7	]	]	PUNCT
ejpam-5384	114	8	by	by	ADP
ejpam-5384	114	9	l−1	l−1	PROPN
ejpam-5384	114	10	i	i	PRON
ejpam-5384	114	11	(	(	PUNCT
ejpam-5384	114	12	y	y	NOUN
ejpam-5384	114	13	)	)	PUNCT
ejpam-5384	114	14	:	:	PUNCT
ejpam-5384	115	1	=	=	SYM
ejpam-5384	115	2			NOUN
ejpam-5384	115	3	0	0	NUM
ejpam-5384	115	4	,	,	PUNCT
ejpam-5384	115	5	if	if	SCONJ
ejpam-5384	115	6	y	y	PROPN
ejpam-5384	115	7	<	<	X
ejpam-5384	115	8	ai	ai	VERB
ejpam-5384	115	9	l−1	l−1	PROPN
ejpam-5384	115	10	i	i	PRON
ejpam-5384	115	11	(	(	PUNCT
ejpam-5384	115	12	y	y	NOUN
ejpam-5384	115	13	)	)	PUNCT
ejpam-5384	115	14	,	,	PUNCT
ejpam-5384	115	15	if	if	SCONJ
ejpam-5384	115	16	ai	ai	VERB
ejpam-5384	115	17	≤	≤	NUM
ejpam-5384	115	18	y	y	PROPN
ejpam-5384	115	19	≤	≤	NUM
ejpam-5384	115	20	bi	bi	NOUN
ejpam-5384	115	21	1	1	NUM
ejpam-5384	115	22	,	,	PUNCT
ejpam-5384	115	23	if	if	SCONJ
ejpam-5384	115	24	y	y	PROPN
ejpam-5384	115	25	>	>	X
ejpam-5384	115	26	bi	bi	NOUN
ejpam-5384	115	27	as	as	ADV
ejpam-5384	115	28	well	well	ADV
ejpam-5384	115	29	as	as	ADP
ejpam-5384	115	30	a	a	DET
ejpam-5384	115	31	function	function	NOUN
ejpam-5384	115	32	l−1	l−1	NOUN
ejpam-5384	115	33	:	:	PUNCT
ejpam-5384	115	34	r	r	NOUN
ejpam-5384	115	35	→	→	SYM
ejpam-5384	115	36	[	[	X
ejpam-5384	115	37	0	0	NUM
ejpam-5384	115	38	,	,	PUNCT
ejpam-5384	115	39	n	n	CCONJ
ejpam-5384	115	40	]	]	PUNCT
ejpam-5384	115	41	by	by	ADP
ejpam-5384	115	42	l−1(y	l−1(y	PROPN
ejpam-5384	115	43	)	)	PUNCT
ejpam-5384	115	44	:	:	PUNCT
ejpam-5384	116	1	=	=	PUNCT
ejpam-5384	116	2	∑	∑	PUNCT
ejpam-5384	116	3	i∈in	i∈in	PROPN
ejpam-5384	116	4	l−1	l−1	PROPN
ejpam-5384	116	5	i	i	PRON
ejpam-5384	116	6	(	(	PUNCT
ejpam-5384	116	7	y	y	NOUN
ejpam-5384	116	8	)	)	PUNCT
ejpam-5384	116	9	.	.	PUNCT
ejpam-5384	117	1	a.	a.	PROPN
ejpam-5384	117	2	kalampakas	kalampakas	PROPN
ejpam-5384	117	3	/	/	SYM
ejpam-5384	117	4	eur	eur	PROPN
ejpam-5384	117	5	.	.	PUNCT
ejpam-5384	118	1	j.	j.	PROPN
ejpam-5384	118	2	pure	pure	PROPN
ejpam-5384	118	3	appl	appl	PROPN
ejpam-5384	118	4	.	.	PROPN
ejpam-5384	118	5	math	math	PROPN
ejpam-5384	118	6	,	,	PUNCT
ejpam-5384	118	7	17	17	NUM
ejpam-5384	118	8	(	(	PUNCT
ejpam-5384	118	9	4	4	NUM
ejpam-5384	118	10	)	)	PUNCT
ejpam-5384	118	11	(	(	PUNCT
ejpam-5384	118	12	2024	2024	NUM
ejpam-5384	118	13	)	)	PUNCT
ejpam-5384	118	14	,	,	PUNCT
ejpam-5384	118	15	2448	2448	NUM
ejpam-5384	118	16	-	-	SYM
ejpam-5384	118	17	2466	2466	NUM
ejpam-5384	118	18	2452	2452	NUM
ejpam-5384	118	19	then	then	ADV
ejpam-5384	118	20	l−1	l−1	PROPN
ejpam-5384	118	21	:	:	PUNCT
ejpam-5384	119	1	r	r	NOUN
ejpam-5384	119	2	→	→	SYM
ejpam-5384	119	3	[	[	X
ejpam-5384	119	4	0	0	NUM
ejpam-5384	119	5	,	,	PUNCT
ejpam-5384	119	6	n	n	CCONJ
ejpam-5384	119	7	]	]	PUNCT
ejpam-5384	119	8	is	be	AUX
ejpam-5384	119	9	also	also	ADV
ejpam-5384	119	10	a	a	DET
ejpam-5384	119	11	continuous	continuous	ADJ
ejpam-5384	119	12	and	and	CCONJ
ejpam-5384	119	13	increasing	increase	VERB
ejpam-5384	119	14	function	function	NOUN
ejpam-5384	119	15	such	such	ADJ
ejpam-5384	119	16	that	that	PRON
ejpam-5384	119	17	l−1(y	l−1(y	PROPN
ejpam-5384	119	18	)	)	PUNCT
ejpam-5384	120	1	=	=	SYM
ejpam-5384	120	2	0	0	NUM
ejpam-5384	121	1	for	for	SCONJ
ejpam-5384	121	2	any	any	DET
ejpam-5384	121	3	0	0	NUM
ejpam-5384	121	4	≤	≤	NUM
ejpam-5384	121	5	y	y	PROPN
ejpam-5384	121	6	≤	≤	NUM
ejpam-5384	121	7	min	min	NOUN
ejpam-5384	121	8	i∈in	i∈in	PROPN
ejpam-5384	121	9	{	{	PUNCT
ejpam-5384	121	10	ai	ai	VERB
ejpam-5384	121	11	}	}	PUNCT
ejpam-5384	121	12	and	and	CCONJ
ejpam-5384	121	13	l−1(y	l−1(y	PROPN
ejpam-5384	121	14	)	)	PUNCT
ejpam-5384	122	1	=	=	SYM
ejpam-5384	122	2	n	n	PROPN
ejpam-5384	122	3	for	for	ADP
ejpam-5384	122	4	any	any	DET
ejpam-5384	122	5	y	y	PROPN
ejpam-5384	122	6	≥	≥	NOUN
ejpam-5384	122	7	max	max	PROPN
ejpam-5384	122	8	i∈in	i∈in	PROPN
ejpam-5384	122	9	{	{	PUNCT
ejpam-5384	122	10	bi	bi	NOUN
ejpam-5384	122	11	}	}	PUNCT
ejpam-5384	122	12	.	.	PUNCT
ejpam-5384	123	1	since	since	SCONJ
ejpam-5384	123	2	l−1	l−1	PROPN
ejpam-5384	123	3	j	j	NOUN
ejpam-5384	123	4	:	:	PUNCT
ejpam-5384	123	5	[	[	X
ejpam-5384	123	6	aj	aj	PROPN
ejpam-5384	123	7	,	,	PUNCT
ejpam-5384	123	8	bj	bj	VERB
ejpam-5384	123	9	]	]	PUNCT
ejpam-5384	123	10	→	→	PUNCT
ejpam-5384	124	1	[	[	X
ejpam-5384	124	2	0	0	NUM
ejpam-5384	124	3	,	,	PUNCT
ejpam-5384	124	4	1	1	NUM
ejpam-5384	124	5	]	]	PUNCT
ejpam-5384	124	6	is	be	AUX
ejpam-5384	124	7	the	the	DET
ejpam-5384	124	8	strictly	strictly	ADV
ejpam-5384	124	9	increasing	increase	VERB
ejpam-5384	124	10	function	function	NOUN
ejpam-5384	124	11	on	on	ADP
ejpam-5384	124	12	the	the	DET
ejpam-5384	124	13	interval	interval	NOUN
ejpam-5384	124	14	[	[	X
ejpam-5384	124	15	aj	aj	PROPN
ejpam-5384	124	16	,	,	PUNCT
ejpam-5384	124	17	bj	bj	VERB
ejpam-5384	124	18	]	]	PUNCT
ejpam-5384	124	19	where	where	SCONJ
ejpam-5384	124	20	aj	aj	PROPN
ejpam-5384	124	21	=	=	PROPN
ejpam-5384	124	22	min	min	PROPN
ejpam-5384	124	23	i∈in	i∈in	PROPN
ejpam-5384	124	24	{	{	PUNCT
ejpam-5384	124	25	ai	ai	NOUN
ejpam-5384	124	26	}	}	PUNCT
ejpam-5384	124	27	,	,	PUNCT
ejpam-5384	124	28	therefore	therefore	ADV
ejpam-5384	124	29	the	the	DET
ejpam-5384	124	30	function	function	NOUN
ejpam-5384	124	31	l−1	l−1	PROPN
ejpam-5384	124	32	:	:	PUNCT
ejpam-5384	125	1	[	[	X
ejpam-5384	125	2	aj	aj	PROPN
ejpam-5384	125	3	,	,	PUNCT
ejpam-5384	125	4	bj	bj	VERB
ejpam-5384	125	5	]	]	PUNCT
ejpam-5384	125	6	→	→	PUNCT
ejpam-5384	126	1	[	[	X
ejpam-5384	126	2	0	0	NUM
ejpam-5384	126	3	,	,	PUNCT
ejpam-5384	126	4	n	n	CCONJ
ejpam-5384	126	5	]	]	PUNCT
ejpam-5384	126	6	is	be	AUX
ejpam-5384	126	7	also	also	ADV
ejpam-5384	126	8	strictly	strictly	ADV
ejpam-5384	126	9	increasing	increase	VERB
ejpam-5384	126	10	on	on	ADP
ejpam-5384	126	11	the	the	DET
ejpam-5384	126	12	same	same	ADJ
ejpam-5384	126	13	interval	interval	NOUN
ejpam-5384	126	14	[	[	X
ejpam-5384	126	15	aj	aj	PROPN
ejpam-5384	126	16	,	,	PUNCT
ejpam-5384	126	17	bj	bj	VERB
ejpam-5384	126	18	]	]	PUNCT
ejpam-5384	126	19	where	where	SCONJ
ejpam-5384	126	20	aj	aj	PROPN
ejpam-5384	126	21	=	=	PROPN
ejpam-5384	126	22	min	min	PROPN
ejpam-5384	126	23	i∈in	i∈in	PROPN
ejpam-5384	126	24	{	{	PUNCT
ejpam-5384	126	25	ai	ai	NOUN
ejpam-5384	126	26	}	}	PUNCT
ejpam-5384	126	27	.	.	PUNCT
ejpam-5384	127	1	it	it	PRON
ejpam-5384	127	2	can	can	AUX
ejpam-5384	127	3	be	be	AUX
ejpam-5384	127	4	easily	easily	ADV
ejpam-5384	127	5	seen	see	VERB
ejpam-5384	127	6	that	that	SCONJ
ejpam-5384	127	7	l−1(aj	l−1(aj	PROPN
ejpam-5384	127	8	)	)	PUNCT
ejpam-5384	128	1	=	=	SYM
ejpam-5384	128	2	0	0	NUM
ejpam-5384	128	3	and	and	CCONJ
ejpam-5384	128	4	l−1(bj	l−1(bj	PROPN
ejpam-5384	128	5	)	)	PUNCT
ejpam-5384	128	6	≥	≥	NOUN
ejpam-5384	128	7	l−1	l−1	PROPN
ejpam-5384	128	8	j	j	PROPN
ejpam-5384	128	9	(	(	PUNCT
ejpam-5384	128	10	bj	bj	PROPN
ejpam-5384	128	11	)	)	PUNCT
ejpam-5384	128	12	=	=	SYM
ejpam-5384	129	1	1	1	X
ejpam-5384	129	2	.	.	PUNCT
ejpam-5384	129	3	let	let	VERB
ejpam-5384	129	4	l−1(bj	l−1(bj	NOUN
ejpam-5384	129	5	)	)	PUNCT
ejpam-5384	129	6	=	=	SYM
ejpam-5384	130	1	1	1	X
ejpam-5384	130	2	.	.	PUNCT
ejpam-5384	130	3	then	then	ADV
ejpam-5384	130	4	the	the	DET
ejpam-5384	130	5	unique	unique	ADJ
ejpam-5384	130	6	user	user	NOUN
ejpam-5384	130	7	equilibrium	equilibrium	NOUN
ejpam-5384	130	8	is	be	AUX
ejpam-5384	130	9	ϕ	ϕ	NOUN
ejpam-5384	130	10	=	=	PUNCT
ejpam-5384	130	11	(	(	PUNCT
ejpam-5384	130	12	0	0	NUM
ejpam-5384	130	13	,	,	PUNCT
ejpam-5384	130	14	0	0	NUM
ejpam-5384	130	15	·	·	PUNCT
ejpam-5384	130	16	·	·	PUNCT
ejpam-5384	130	17	·	·	PUNCT
ejpam-5384	130	18	,	,	PUNCT
ejpam-5384	130	19	0	0	NUM
ejpam-5384	130	20	,	,	PUNCT
ejpam-5384	130	21	1︸︷︷︸	1︸︷︷︸	NUM
ejpam-5384	130	22	j	j	PROPN
ejpam-5384	130	23	,	,	PUNCT
ejpam-5384	130	24	0	0	NUM
ejpam-5384	130	25	,	,	PUNCT
ejpam-5384	130	26	·	·	PUNCT
ejpam-5384	130	27	·	·	PUNCT
ejpam-5384	130	28	·	·	PUNCT
ejpam-5384	130	29	0	0	X
ejpam-5384	130	30	)	)	PUNCT
ejpam-5384	130	31	with	with	ADP
ejpam-5384	130	32	supp(ϕ	supp(ϕ	NOUN
ejpam-5384	130	33	)	)	PUNCT
ejpam-5384	130	34	=	=	SYM
ejpam-5384	130	35	{	{	PUNCT
ejpam-5384	130	36	j	j	NOUN
ejpam-5384	130	37	}	}	PUNCT
ejpam-5384	130	38	.	.	PUNCT
ejpam-5384	131	1	indeed	indeed	ADV
ejpam-5384	131	2	,	,	PUNCT
ejpam-5384	131	3	since	since	SCONJ
ejpam-5384	131	4	l−1(bj	l−1(bj	PROPN
ejpam-5384	131	5	)	)	PUNCT
ejpam-5384	131	6	=	=	SYM
ejpam-5384	132	1	∑	∑	PUNCT
ejpam-5384	132	2	i∈in	i∈in	PROPN
ejpam-5384	132	3	l−1	l−1	PROPN
ejpam-5384	132	4	i	i	PRON
ejpam-5384	132	5	(	(	PUNCT
ejpam-5384	132	6	bj	bj	NOUN
ejpam-5384	132	7	)	)	PUNCT
ejpam-5384	132	8	=	=	SYM
ejpam-5384	132	9	1	1	NUM
ejpam-5384	132	10	,	,	PUNCT
ejpam-5384	132	11	it	it	PRON
ejpam-5384	132	12	is	be	AUX
ejpam-5384	132	13	easy	easy	ADJ
ejpam-5384	132	14	to	to	PART
ejpam-5384	132	15	see	see	VERB
ejpam-5384	132	16	that	that	SCONJ
ejpam-5384	132	17	l−1	l−1	PROPN
ejpam-5384	132	18	j	j	PROPN
ejpam-5384	132	19	(	(	PUNCT
ejpam-5384	132	20	bj	bj	PROPN
ejpam-5384	132	21	)	)	PUNCT
ejpam-5384	132	22	=	=	PUNCT
ejpam-5384	133	1	l−1	l−1	PROPN
ejpam-5384	133	2	j	j	PROPN
ejpam-5384	133	3	(	(	PUNCT
ejpam-5384	133	4	bj	bj	PROPN
ejpam-5384	133	5	)	)	PUNCT
ejpam-5384	133	6	=	=	SYM
ejpam-5384	133	7	1	1	NUM
ejpam-5384	133	8	or	or	CCONJ
ejpam-5384	133	9	equivalently	equivalently	ADV
ejpam-5384	133	10	lj(1	lj(1	PROPN
ejpam-5384	133	11	)	)	PUNCT
ejpam-5384	133	12	=	=	PUNCT
ejpam-5384	133	13	bj	bj	NOUN
ejpam-5384	133	14	and	and	CCONJ
ejpam-5384	133	15	meanwhile	meanwhile	ADV
ejpam-5384	133	16	l−1	l−1	PROPN
ejpam-5384	133	17	i	i	PRON
ejpam-5384	133	18	(	(	PUNCT
ejpam-5384	133	19	bj	bj	NOUN
ejpam-5384	133	20	)	)	PUNCT
ejpam-5384	133	21	=	=	SYM
ejpam-5384	133	22	0	0	NUM
ejpam-5384	133	23	for	for	ADP
ejpam-5384	133	24	every	every	DET
ejpam-5384	133	25	i	i	PROPN
ejpam-5384	133	26	∈	∈	PROPN
ejpam-5384	133	27	in	in	ADP
ejpam-5384	133	28	with	with	ADP
ejpam-5384	133	29	i	i	PRON
ejpam-5384	133	30	̸=	̸=	PROPN
ejpam-5384	133	31	j	j	PROPN
ejpam-5384	133	32	or	or	CCONJ
ejpam-5384	133	33	equivalently	equivalently	ADV
ejpam-5384	133	34	bj	bj	VERB
ejpam-5384	133	35	≤	≤	NOUN
ejpam-5384	133	36	ai	ai	VERB
ejpam-5384	133	37	for	for	ADP
ejpam-5384	133	38	every	every	DET
ejpam-5384	133	39	i	i	PROPN
ejpam-5384	133	40	∈	∈	PROPN
ejpam-5384	133	41	in	in	ADP
ejpam-5384	133	42	with	with	ADP
ejpam-5384	133	43	i	i	PROPN
ejpam-5384	133	44	̸=	̸=	PROPN
ejpam-5384	133	45	j.	j.	PROPN
ejpam-5384	133	46	the	the	DET
ejpam-5384	133	47	last	last	ADJ
ejpam-5384	133	48	inequality	inequality	NOUN
ejpam-5384	133	49	means	mean	VERB
ejpam-5384	133	50	that	that	SCONJ
ejpam-5384	133	51	li(0	li(0	PROPN
ejpam-5384	133	52	)	)	PUNCT
ejpam-5384	133	53	=	=	PUNCT
ejpam-5384	133	54	ai	ai	VERB
ejpam-5384	133	55	≥	≥	NOUN
ejpam-5384	133	56	bj	bj	ADP
ejpam-5384	133	57	=	=	PUNCT
ejpam-5384	133	58	lj(1	lj(1	PROPN
ejpam-5384	133	59	)	)	PUNCT
ejpam-5384	133	60	for	for	ADP
ejpam-5384	133	61	every	every	DET
ejpam-5384	133	62	i	i	PROPN
ejpam-5384	133	63	∈	∈	PROPN
ejpam-5384	133	64	in	in	ADP
ejpam-5384	133	65	with	with	ADP
ejpam-5384	133	66	i	i	PROPN
ejpam-5384	133	67	̸=	̸=	PROPN
ejpam-5384	133	68	j.	j.	PROPN
ejpam-5384	133	69	let	let	VERB
ejpam-5384	133	70	l−1(bj	l−1(bj	PROPN
ejpam-5384	133	71	)	)	PUNCT
ejpam-5384	133	72	>	>	X
ejpam-5384	134	1	1	1	X
ejpam-5384	134	2	.	.	PUNCT
ejpam-5384	134	3	since	since	SCONJ
ejpam-5384	134	4	l−1([0	l−1([0	PROPN
ejpam-5384	134	5	,	,	PUNCT
ejpam-5384	134	6	aj	aj	PROPN
ejpam-5384	134	7	]	]	X
ejpam-5384	134	8	)	)	PUNCT
ejpam-5384	134	9	=	=	SYM
ejpam-5384	134	10	0	0	NUM
ejpam-5384	134	11	,	,	PUNCT
ejpam-5384	134	12	the	the	DET
ejpam-5384	134	13	function	function	NOUN
ejpam-5384	134	14	l−1	l−1	PROPN
ejpam-5384	134	15	is	be	AUX
ejpam-5384	134	16	strictly	strictly	ADV
ejpam-5384	134	17	increasing	increase	VERB
ejpam-5384	134	18	on	on	ADP
ejpam-5384	134	19	the	the	DET
ejpam-5384	134	20	interval	interval	NOUN
ejpam-5384	134	21	[	[	X
ejpam-5384	134	22	aj	aj	PROPN
ejpam-5384	134	23	,	,	PUNCT
ejpam-5384	134	24	bj	bj	ADP
ejpam-5384	134	25	]	]	PUNCT
ejpam-5384	134	26	,	,	PUNCT
ejpam-5384	134	27	and	and	CCONJ
ejpam-5384	134	28	l−1(bj	l−1(bj	PROPN
ejpam-5384	134	29	)	)	PUNCT
ejpam-5384	134	30	>	>	X
ejpam-5384	135	1	1	1	X
ejpam-5384	135	2	.	.	PUNCT
ejpam-5384	135	3	then	then	ADV
ejpam-5384	135	4	there	there	PRON
ejpam-5384	135	5	always	always	ADV
ejpam-5384	135	6	exists	exist	VERB
ejpam-5384	135	7	a	a	DET
ejpam-5384	135	8	unique	unique	ADJ
ejpam-5384	135	9	c	c	NOUN
ejpam-5384	135	10	∈	∈	PROPN
ejpam-5384	135	11	(	(	PUNCT
ejpam-5384	135	12	aj	aj	PROPN
ejpam-5384	135	13	,	,	PUNCT
ejpam-5384	135	14	bj	bj	VERB
ejpam-5384	135	15	)	)	PUNCT
ejpam-5384	135	16	such	such	ADJ
ejpam-5384	135	17	that	that	SCONJ
ejpam-5384	135	18	l−1(c	l−1(c	PROPN
ejpam-5384	135	19	)	)	PUNCT
ejpam-5384	136	1	=	=	SYM
ejpam-5384	136	2	1	1	X
ejpam-5384	136	3	.	.	PUNCT
ejpam-5384	136	4	let	let	VERB
ejpam-5384	136	5	us	we	PRON
ejpam-5384	136	6	define	define	VERB
ejpam-5384	136	7	the	the	DET
ejpam-5384	136	8	following	follow	VERB
ejpam-5384	136	9	sets	set	NOUN
ejpam-5384	136	10	α	α	NOUN
ejpam-5384	136	11	:	:	PUNCT
ejpam-5384	136	12	=	=	SYM
ejpam-5384	136	13	{	{	PUNCT
ejpam-5384	136	14	k	k	X
ejpam-5384	136	15	∈	∈	PROPN
ejpam-5384	136	16	in	in	ADP
ejpam-5384	136	17	:	:	PUNCT
ejpam-5384	136	18	c	c	PROPN
ejpam-5384	136	19	∈	∈	PROPN
ejpam-5384	136	20	(	(	PUNCT
ejpam-5384	136	21	ak	ak	PROPN
ejpam-5384	136	22	,	,	PUNCT
ejpam-5384	136	23	bk	bk	PROPN
ejpam-5384	136	24	)	)	PUNCT
ejpam-5384	136	25	}	}	PUNCT
ejpam-5384	136	26	and	and	CCONJ
ejpam-5384	136	27	β	β	X
ejpam-5384	136	28	:	:	PUNCT
ejpam-5384	136	29	=	=	X
ejpam-5384	136	30	{	{	PUNCT
ejpam-5384	136	31	s	s	NOUN
ejpam-5384	136	32	∈	∈	NOUN
ejpam-5384	136	33	in	in	ADP
ejpam-5384	136	34	:	:	PUNCT
ejpam-5384	136	35	c	c	PROPN
ejpam-5384	136	36	̸∈	̸∈	PROPN
ejpam-5384	136	37	(	(	PUNCT
ejpam-5384	136	38	as	as	ADP
ejpam-5384	136	39	,	,	PUNCT
ejpam-5384	136	40	bs	bs	NOUN
ejpam-5384	136	41	)	)	PUNCT
ejpam-5384	136	42	}	}	PUNCT
ejpam-5384	136	43	.	.	PUNCT
ejpam-5384	137	1	obviously	obviously	ADV
ejpam-5384	137	2	,	,	PUNCT
ejpam-5384	137	3	due	due	ADP
ejpam-5384	137	4	to	to	ADP
ejpam-5384	137	5	the	the	DET
ejpam-5384	137	6	construction	construction	NOUN
ejpam-5384	137	7	,	,	PUNCT
ejpam-5384	137	8	we	we	PRON
ejpam-5384	137	9	have	have	VERB
ejpam-5384	137	10	that	that	DET
ejpam-5384	137	11	j	j	PROPN
ejpam-5384	137	12	∈	∈	PROPN
ejpam-5384	137	13	α	α	PROPN
ejpam-5384	137	14	̸=	̸=	PROPN
ejpam-5384	137	15	∅	∅	NOUN
ejpam-5384	137	16	,	,	PUNCT
ejpam-5384	137	17	α	α	PROPN
ejpam-5384	137	18	∪	∪	NOUN
ejpam-5384	137	19	β	β	X
ejpam-5384	137	20	=	=	SYM
ejpam-5384	137	21	in	in	ADP
ejpam-5384	137	22	,	,	PUNCT
ejpam-5384	137	23	and	and	CCONJ
ejpam-5384	137	24	α	α	PROPN
ejpam-5384	137	25	∩	∩	ADJ
ejpam-5384	137	26	β	β	X
ejpam-5384	137	27	=	=	VERB
ejpam-5384	137	28	∅.	∅.	ADV
ejpam-5384	137	29	let	let	VERB
ejpam-5384	137	30	us	we	PRON
ejpam-5384	137	31	define	define	VERB
ejpam-5384	138	1	ϕk	ϕk	INTJ
ejpam-5384	138	2	:	:	PUNCT
ejpam-5384	138	3	=	=	SYM
ejpam-5384	138	4	l−1	l−1	PROPN
ejpam-5384	138	5	k	k	X
ejpam-5384	138	6	(	(	PUNCT
ejpam-5384	138	7	c	c	NOUN
ejpam-5384	138	8	)	)	PUNCT
ejpam-5384	138	9	for	for	ADP
ejpam-5384	138	10	every	every	DET
ejpam-5384	138	11	k	k	PROPN
ejpam-5384	138	12	∈	∈	PROPN
ejpam-5384	138	13	α	α	NOUN
ejpam-5384	138	14	.	.	PUNCT
ejpam-5384	139	1	it	it	PRON
ejpam-5384	139	2	is	be	AUX
ejpam-5384	139	3	obvious	obvious	ADJ
ejpam-5384	139	4	that	that	SCONJ
ejpam-5384	139	5	0	0	X
ejpam-5384	139	6	=	=	SYM
ejpam-5384	139	7	l−1	l−1	PROPN
ejpam-5384	139	8	k	k	PROPN
ejpam-5384	139	9	(	(	PUNCT
ejpam-5384	139	10	ak	ak	PROPN
ejpam-5384	139	11	)	)	PUNCT
ejpam-5384	139	12	<	<	X
ejpam-5384	140	1	ϕk	ϕk	NOUN
ejpam-5384	140	2	=	=	SYM
ejpam-5384	140	3	l−1	l−1	PROPN
ejpam-5384	140	4	k	k	NOUN
ejpam-5384	140	5	(	(	PUNCT
ejpam-5384	140	6	c	c	X
ejpam-5384	140	7	)	)	PUNCT
ejpam-5384	140	8	<	<	X
ejpam-5384	141	1	l−1	l−1	PROPN
ejpam-5384	141	2	k	k	PROPN
ejpam-5384	141	3	(	(	PUNCT
ejpam-5384	141	4	bk	bk	PROPN
ejpam-5384	141	5	)	)	PUNCT
ejpam-5384	141	6	=	=	SYM
ejpam-5384	141	7	1	1	NUM
ejpam-5384	141	8	,	,	PUNCT
ejpam-5384	141	9	∀	∀	PUNCT
ejpam-5384	141	10	k	k	NOUN
ejpam-5384	141	11	∈	∈	PROPN
ejpam-5384	142	1	α	α	X
ejpam-5384	142	2	.	.	PUNCT
ejpam-5384	143	1	we	we	PRON
ejpam-5384	143	2	then	then	ADV
ejpam-5384	143	3	obtain	obtain	VERB
ejpam-5384	143	4	that	that	DET
ejpam-5384	143	5	1	1	NUM
ejpam-5384	143	6	=	=	SYM
ejpam-5384	143	7	l−1(c	l−1(c	PROPN
ejpam-5384	143	8	)	)	PUNCT
ejpam-5384	144	1	=	=	PUNCT
ejpam-5384	144	2	∑	∑	PUNCT
ejpam-5384	145	1	i∈in	i∈in	PROPN
ejpam-5384	145	2	l−1	l−1	PROPN
ejpam-5384	145	3	i	i	PRON
ejpam-5384	145	4	(	(	PUNCT
ejpam-5384	145	5	c	c	NOUN
ejpam-5384	145	6	)	)	PUNCT
ejpam-5384	145	7	=	=	SYM
ejpam-5384	145	8	∑	∑	PUNCT
ejpam-5384	145	9	k∈α	k∈α	NOUN
ejpam-5384	145	10	l−1	l−1	PROPN
ejpam-5384	145	11	k	k	PROPN
ejpam-5384	145	12	(	(	PUNCT
ejpam-5384	145	13	c	c	NOUN
ejpam-5384	145	14	)	)	PUNCT
ejpam-5384	145	15	+	+	CCONJ
ejpam-5384	145	16	∑	∑	PUNCT
ejpam-5384	145	17	s∈β	s∈β	VERB
ejpam-5384	145	18	l−1	l−1	PROPN
ejpam-5384	145	19	s	s	PART
ejpam-5384	145	20	(	(	PUNCT
ejpam-5384	145	21	c	c	NOUN
ejpam-5384	145	22	)	)	PUNCT
ejpam-5384	145	23	=	=	SYM
ejpam-5384	145	24	∑	∑	PUNCT
ejpam-5384	145	25	k∈α	k∈α	NOUN
ejpam-5384	145	26	l−1	l−1	PROPN
ejpam-5384	145	27	k	k	PROPN
ejpam-5384	145	28	(	(	PUNCT
ejpam-5384	145	29	c)︸	c)︸	PROPN
ejpam-5384	145	30	︷︷	︷︷	PROPN
ejpam-5384	145	31	︸	︸	ADP
ejpam-5384	145	32	positive	positive	ADJ
ejpam-5384	145	33	term	term	NOUN
ejpam-5384	145	34	+	+	CCONJ
ejpam-5384	145	35	∑	∑	PUNCT
ejpam-5384	145	36	s∈β	s∈β	VERB
ejpam-5384	145	37	l−1	l−1	PROPN
ejpam-5384	145	38	s	s	PART
ejpam-5384	145	39	(	(	PUNCT
ejpam-5384	145	40	c	c	NOUN
ejpam-5384	145	41	)	)	PUNCT
ejpam-5384	145	42	>	>	PUNCT
ejpam-5384	145	43	∑	∑	PUNCT
ejpam-5384	145	44	s∈β	s∈β	PROPN
ejpam-5384	145	45	l−1	l−1	PROPN
ejpam-5384	145	46	s	s	PART
ejpam-5384	145	47	(	(	PUNCT
ejpam-5384	145	48	c	c	NOUN
ejpam-5384	145	49	)	)	PUNCT
ejpam-5384	145	50	.	.	PUNCT
ejpam-5384	146	1	(	(	PUNCT
ejpam-5384	146	2	1	1	X
ejpam-5384	146	3	)	)	PUNCT
ejpam-5384	146	4	a.	a.	NOUN
ejpam-5384	146	5	kalampakas	kalampakas	PROPN
ejpam-5384	146	6	/	/	SYM
ejpam-5384	146	7	eur	eur	PROPN
ejpam-5384	146	8	.	.	PUNCT
ejpam-5384	147	1	j.	j.	PROPN
ejpam-5384	147	2	pure	pure	PROPN
ejpam-5384	147	3	appl	appl	PROPN
ejpam-5384	147	4	.	.	PROPN
ejpam-5384	147	5	math	math	PROPN
ejpam-5384	147	6	,	,	PUNCT
ejpam-5384	147	7	17	17	NUM
ejpam-5384	147	8	(	(	PUNCT
ejpam-5384	147	9	4	4	NUM
ejpam-5384	147	10	)	)	PUNCT
ejpam-5384	147	11	(	(	PUNCT
ejpam-5384	147	12	2024	2024	NUM
ejpam-5384	147	13	)	)	PUNCT
ejpam-5384	147	14	,	,	PUNCT
ejpam-5384	147	15	2448	2448	NUM
ejpam-5384	147	16	-	-	SYM
ejpam-5384	147	17	2466	2466	NUM
ejpam-5384	147	18	2453	2453	NUM
ejpam-5384	147	19	consequently	consequently	ADV
ejpam-5384	147	20	,	,	PUNCT
ejpam-5384	147	21	we	we	PRON
ejpam-5384	147	22	derive	derive	VERB
ejpam-5384	147	23	that	that	SCONJ
ejpam-5384	147	24	l−1	l−1	PROPN
ejpam-5384	147	25	s	s	PART
ejpam-5384	147	26	(	(	PUNCT
ejpam-5384	147	27	c	c	NOUN
ejpam-5384	147	28	)	)	PUNCT
ejpam-5384	147	29	<	<	X
ejpam-5384	147	30	1	1	NUM
ejpam-5384	147	31	for	for	ADP
ejpam-5384	147	32	any	any	DET
ejpam-5384	147	33	s	s	X
ejpam-5384	147	34	∈	∈	NOUN
ejpam-5384	147	35	β	β	NOUN
ejpam-5384	147	36	.	.	PUNCT
ejpam-5384	148	1	since	since	SCONJ
ejpam-5384	148	2	c	c	PROPN
ejpam-5384	148	3	̸∈	̸∈	PROPN
ejpam-5384	148	4	(	(	PUNCT
ejpam-5384	148	5	as	as	ADP
ejpam-5384	148	6	,	,	PUNCT
ejpam-5384	148	7	bs	bs	NOUN
ejpam-5384	148	8	)	)	PUNCT
ejpam-5384	148	9	for	for	ADP
ejpam-5384	148	10	any	any	DET
ejpam-5384	148	11	s	s	X
ejpam-5384	148	12	∈	∈	PROPN
ejpam-5384	148	13	β	β	X
ejpam-5384	148	14	and	and	CCONJ
ejpam-5384	148	15	l−1	l−1	PROPN
ejpam-5384	148	16	s	s	PART
ejpam-5384	148	17	(	(	PUNCT
ejpam-5384	148	18	c	c	NOUN
ejpam-5384	148	19	)	)	PUNCT
ejpam-5384	148	20	<	<	X
ejpam-5384	148	21	1	1	NUM
ejpam-5384	148	22	,	,	PUNCT
ejpam-5384	148	23	due	due	ADP
ejpam-5384	148	24	to	to	ADP
ejpam-5384	148	25	the	the	DET
ejpam-5384	148	26	definition	definition	NOUN
ejpam-5384	148	27	of	of	ADP
ejpam-5384	148	28	the	the	DET
ejpam-5384	148	29	function	function	NOUN
ejpam-5384	148	30	l−1	l−1	PROPN
ejpam-5384	148	31	s	s	PART
ejpam-5384	148	32	(	(	PUNCT
ejpam-5384	148	33	y	y	NOUN
ejpam-5384	148	34	)	)	PUNCT
ejpam-5384	148	35	,	,	PUNCT
ejpam-5384	148	36	we	we	PRON
ejpam-5384	148	37	must	must	AUX
ejpam-5384	148	38	have	have	VERB
ejpam-5384	148	39	that	that	PRON
ejpam-5384	148	40	l−1	l−1	PROPN
ejpam-5384	148	41	s	s	PART
ejpam-5384	148	42	(	(	PUNCT
ejpam-5384	148	43	c	c	NOUN
ejpam-5384	148	44	)	)	PUNCT
ejpam-5384	148	45	=	=	SYM
ejpam-5384	148	46	0	0	NUM
ejpam-5384	148	47	for	for	ADP
ejpam-5384	148	48	any	any	DET
ejpam-5384	148	49	s	s	X
ejpam-5384	148	50	∈	∈	PROPN
ejpam-5384	148	51	β	β	NOUN
ejpam-5384	148	52	.	.	PUNCT
ejpam-5384	149	1	equivalently	equivalently	ADV
ejpam-5384	149	2	,	,	PUNCT
ejpam-5384	149	3	this	this	PRON
ejpam-5384	149	4	means	mean	VERB
ejpam-5384	149	5	that	that	SCONJ
ejpam-5384	149	6	lk(ϕk	lk(ϕk	NOUN
ejpam-5384	149	7	)	)	PUNCT
ejpam-5384	150	1	=	=	PUNCT
ejpam-5384	150	2	c	c	NOUN
ejpam-5384	150	3	≤	≤	NOUN
ejpam-5384	150	4	as	as	ADP
ejpam-5384	150	5	=	=	PROPN
ejpam-5384	150	6	ls(0	ls(0	PROPN
ejpam-5384	150	7	)	)	PUNCT
ejpam-5384	150	8	,	,	PUNCT
ejpam-5384	150	9	∀	∀	PUNCT
ejpam-5384	150	10	k	k	PROPN
ejpam-5384	150	11	∈	∈	PROPN
ejpam-5384	150	12	α	α	NOUN
ejpam-5384	150	13	and	and	CCONJ
ejpam-5384	150	14	∀	∀	NOUN
ejpam-5384	150	15	s	s	NOUN
ejpam-5384	150	16	∈	∈	NOUN
ejpam-5384	150	17	β	β	X
ejpam-5384	150	18	.	.	PUNCT
ejpam-5384	151	1	moreover	moreover	ADV
ejpam-5384	151	2	,	,	PUNCT
ejpam-5384	151	3	since	since	SCONJ
ejpam-5384	151	4	∑	∑	PART
ejpam-5384	151	5	s∈β	s∈β	VERB
ejpam-5384	151	6	l−1	l−1	PROPN
ejpam-5384	151	7	s	s	PART
ejpam-5384	151	8	(	(	PUNCT
ejpam-5384	151	9	c	c	NOUN
ejpam-5384	151	10	)	)	PUNCT
ejpam-5384	151	11	=	=	SYM
ejpam-5384	151	12	0	0	NUM
ejpam-5384	151	13	,	,	PUNCT
ejpam-5384	151	14	it	it	PRON
ejpam-5384	151	15	follows	follow	VERB
ejpam-5384	151	16	from	from	ADP
ejpam-5384	151	17	(	(	PUNCT
ejpam-5384	151	18	1	1	NUM
ejpam-5384	151	19	)	)	PUNCT
ejpam-5384	151	20	that	that	SCONJ
ejpam-5384	151	21	l−1(c	l−1(c	ADJ
ejpam-5384	151	22	)	)	PUNCT
ejpam-5384	152	1	=	=	PUNCT
ejpam-5384	152	2	∑	∑	PUNCT
ejpam-5384	153	1	i∈in	i∈in	PROPN
ejpam-5384	153	2	l−1	l−1	PROPN
ejpam-5384	153	3	i	i	PRON
ejpam-5384	153	4	(	(	PUNCT
ejpam-5384	153	5	c	c	NOUN
ejpam-5384	153	6	)	)	PUNCT
ejpam-5384	153	7	=	=	SYM
ejpam-5384	153	8	∑	∑	PUNCT
ejpam-5384	153	9	k∈α	k∈α	NOUN
ejpam-5384	153	10	l−1	l−1	PROPN
ejpam-5384	153	11	k	k	PROPN
ejpam-5384	153	12	(	(	PUNCT
ejpam-5384	153	13	c	c	NOUN
ejpam-5384	153	14	)	)	PUNCT
ejpam-5384	153	15	+	+	CCONJ
ejpam-5384	153	16	∑	∑	PUNCT
ejpam-5384	153	17	s∈β	s∈β	VERB
ejpam-5384	153	18	l−1	l−1	PROPN
ejpam-5384	153	19	s	s	PART
ejpam-5384	153	20	(	(	PUNCT
ejpam-5384	153	21	c)︸	c)︸	PROPN
ejpam-5384	153	22	︷︷	︷︷	PROPN
ejpam-5384	153	23	︸	︸	ADP
ejpam-5384	153	24	zero	zero	NUM
ejpam-5384	153	25	terms	term	NOUN
ejpam-5384	153	26	=	=	SYM
ejpam-5384	153	27	∑	∑	PUNCT
ejpam-5384	153	28	k∈α	k∈α	ADJ
ejpam-5384	153	29	l−1	l−1	PROPN
ejpam-5384	153	30	k	k	PROPN
ejpam-5384	153	31	(	(	PUNCT
ejpam-5384	153	32	c	c	NOUN
ejpam-5384	153	33	)	)	PUNCT
ejpam-5384	153	34	=	=	PUNCT
ejpam-5384	153	35	∑	∑	PUNCT
ejpam-5384	153	36	k∈α	k∈α	NOUN
ejpam-5384	153	37	ϕk	ϕk	NOUN
ejpam-5384	153	38	=	=	SYM
ejpam-5384	153	39	1	1	X
ejpam-5384	153	40	.	.	PUNCT
ejpam-5384	154	1	hence	hence	ADV
ejpam-5384	154	2	,	,	PUNCT
ejpam-5384	154	3	the	the	DET
ejpam-5384	154	4	flow	flow	NOUN
ejpam-5384	154	5	ϕ	ϕ	NOUN
ejpam-5384	154	6	=	=	PUNCT
ejpam-5384	154	7	(	(	PUNCT
ejpam-5384	154	8	ϕ1	ϕ1	NOUN
ejpam-5384	154	9	,	,	PUNCT
ejpam-5384	154	10	ϕ2	ϕ2	ADV
ejpam-5384	154	11	,	,	PUNCT
ejpam-5384	154	12	·	·	PUNCT
ejpam-5384	154	13	·	·	PUNCT
ejpam-5384	154	14	·	·	PUNCT
ejpam-5384	154	15	,	,	PUNCT
ejpam-5384	154	16	ϕn	ϕn	X
ejpam-5384	154	17	)	)	PUNCT
ejpam-5384	154	18	which	which	PRON
ejpam-5384	154	19	is	be	AUX
ejpam-5384	154	20	defined	define	VERB
ejpam-5384	154	21	as	as	SCONJ
ejpam-5384	154	22	follows	follow	VERB
ejpam-5384	154	23	ϕk	ϕk	ADV
ejpam-5384	154	24	:	:	PUNCT
ejpam-5384	154	25	=	=	SYM
ejpam-5384	154	26	l−1	l−1	PROPN
ejpam-5384	154	27	k	k	X
ejpam-5384	154	28	(	(	PUNCT
ejpam-5384	154	29	c	c	NOUN
ejpam-5384	154	30	)	)	PUNCT
ejpam-5384	154	31	for	for	ADP
ejpam-5384	154	32	every	every	DET
ejpam-5384	154	33	k	k	PROPN
ejpam-5384	154	34	∈	∈	PROPN
ejpam-5384	154	35	α	α	NOUN
ejpam-5384	154	36	and	and	CCONJ
ejpam-5384	154	37	ϕk	ϕk	NOUN
ejpam-5384	154	38	:	:	PUNCT
ejpam-5384	154	39	=	=	SYM
ejpam-5384	154	40	0	0	NUM
ejpam-5384	154	41	for	for	ADP
ejpam-5384	154	42	every	every	DET
ejpam-5384	154	43	k	k	PROPN
ejpam-5384	154	44	∈	∈	PROPN
ejpam-5384	154	45	β	β	X
ejpam-5384	154	46	=	=	NOUN
ejpam-5384	154	47	in	in	ADP
ejpam-5384	154	48	\	\	PROPN
ejpam-5384	154	49	α	α	PROPN
ejpam-5384	154	50	is	be	AUX
ejpam-5384	154	51	user	user	NOUN
ejpam-5384	154	52	equilibrium	equilibrium	NOUN
ejpam-5384	154	53	and	and	CCONJ
ejpam-5384	154	54	it	it	PRON
ejpam-5384	154	55	is	be	AUX
ejpam-5384	154	56	unique	unique	ADJ
ejpam-5384	154	57	due	due	ADP
ejpam-5384	154	58	to	to	ADP
ejpam-5384	154	59	the	the	DET
ejpam-5384	154	60	uniqueness	uniqueness	NOUN
ejpam-5384	154	61	of	of	ADP
ejpam-5384	154	62	the	the	DET
ejpam-5384	154	63	point	point	NOUN
ejpam-5384	154	64	c.	c.	PROPN
ejpam-5384	154	65	this	this	PRON
ejpam-5384	154	66	completes	complete	VERB
ejpam-5384	154	67	the	the	DET
ejpam-5384	154	68	proof	proof	NOUN
ejpam-5384	154	69	.	.	PUNCT
ejpam-5384	155	1	3.1	3.1	NUM
ejpam-5384	155	2	.	.	PUNCT
ejpam-5384	155	3	discrete	discrete	ADJ
ejpam-5384	155	4	user	user	NOUN
ejpam-5384	155	5	equilibrium	equilibrium	NOUN
ejpam-5384	155	6	the	the	DET
ejpam-5384	155	7	definition	definition	NOUN
ejpam-5384	155	8	of	of	ADP
ejpam-5384	155	9	user	user	NOUN
ejpam-5384	155	10	equilibrium	equilibrium	NOUN
ejpam-5384	155	11	,	,	PUNCT
ejpam-5384	155	12	as	as	SCONJ
ejpam-5384	155	13	it	it	PRON
ejpam-5384	155	14	was	be	AUX
ejpam-5384	155	15	introduced	introduce	VERB
ejpam-5384	155	16	[	[	PUNCT
ejpam-5384	155	17	6	6	NUM
ejpam-5384	155	18	,	,	PUNCT
ejpam-5384	155	19	7	7	NUM
ejpam-5384	155	20	,	,	PUNCT
ejpam-5384	155	21	30	30	NUM
ejpam-5384	155	22	]	]	PUNCT
ejpam-5384	155	23	and	and	CCONJ
ejpam-5384	155	24	studied	study	VERB
ejpam-5384	155	25	in	in	ADP
ejpam-5384	155	26	the	the	DET
ejpam-5384	155	27	literature	literature	NOUN
ejpam-5384	155	28	since	since	SCONJ
ejpam-5384	155	29	then	then	ADV
ejpam-5384	155	30	,	,	PUNCT
ejpam-5384	155	31	assumes	assume	VERB
ejpam-5384	155	32	that	that	SCONJ
ejpam-5384	155	33	the	the	DET
ejpam-5384	155	34	traffic	traffic	NOUN
ejpam-5384	155	35	flow	flow	NOUN
ejpam-5384	155	36	can	can	AUX
ejpam-5384	155	37	be	be	AUX
ejpam-5384	155	38	represented	represent	VERB
ejpam-5384	155	39	as	as	ADP
ejpam-5384	155	40	a	a	DET
ejpam-5384	155	41	positive	positive	ADJ
ejpam-5384	155	42	real	real	ADJ
ejpam-5384	155	43	number	number	NOUN
ejpam-5384	155	44	.	.	PUNCT
ejpam-5384	156	1	the	the	DET
ejpam-5384	156	2	advantage	advantage	NOUN
ejpam-5384	156	3	of	of	ADP
ejpam-5384	156	4	this	this	DET
ejpam-5384	156	5	representation	representation	NOUN
ejpam-5384	156	6	is	be	AUX
ejpam-5384	156	7	that	that	SCONJ
ejpam-5384	156	8	it	it	PRON
ejpam-5384	156	9	can	can	AUX
ejpam-5384	156	10	be	be	AUX
ejpam-5384	156	11	infinitely	infinitely	ADV
ejpam-5384	156	12	divided	divide	VERB
ejpam-5384	156	13	into	into	ADP
ejpam-5384	156	14	smaller	small	ADJ
ejpam-5384	156	15	flows	flow	NOUN
ejpam-5384	156	16	and	and	CCONJ
ejpam-5384	156	17	thus	thus	ADV
ejpam-5384	156	18	we	we	PRON
ejpam-5384	156	19	can	can	AUX
ejpam-5384	156	20	always	always	ADV
ejpam-5384	156	21	obtain	obtain	VERB
ejpam-5384	156	22	the	the	DET
ejpam-5384	156	23	exact	exact	ADJ
ejpam-5384	156	24	value	value	NOUN
ejpam-5384	156	25	of	of	ADP
ejpam-5384	156	26	flow	flow	NOUN
ejpam-5384	156	27	distribution	distribution	NOUN
ejpam-5384	156	28	that	that	PRON
ejpam-5384	156	29	creates	create	VERB
ejpam-5384	156	30	the	the	DET
ejpam-5384	156	31	user	user	NOUN
ejpam-5384	156	32	optimum	optimum	NOUN
ejpam-5384	156	33	.	.	PUNCT
ejpam-5384	157	1	on	on	ADP
ejpam-5384	157	2	the	the	DET
ejpam-5384	157	3	other	other	ADJ
ejpam-5384	157	4	hand	hand	NOUN
ejpam-5384	157	5	this	this	PRON
ejpam-5384	157	6	is	be	AUX
ejpam-5384	157	7	just	just	ADV
ejpam-5384	157	8	an	an	DET
ejpam-5384	157	9	approximation	approximation	NOUN
ejpam-5384	157	10	of	of	ADP
ejpam-5384	157	11	the	the	DET
ejpam-5384	157	12	situation	situation	NOUN
ejpam-5384	157	13	in	in	ADP
ejpam-5384	157	14	real	real	ADJ
ejpam-5384	157	15	life	life	NOUN
ejpam-5384	157	16	scenarios	scenario	NOUN
ejpam-5384	157	17	,	,	PUNCT
ejpam-5384	157	18	where	where	SCONJ
ejpam-5384	157	19	for	for	ADP
ejpam-5384	157	20	transportation	transportation	NOUN
ejpam-5384	157	21	networks	network	NOUN
ejpam-5384	157	22	individual	individual	ADJ
ejpam-5384	157	23	vehicles	vehicle	NOUN
ejpam-5384	157	24	can	can	AUX
ejpam-5384	157	25	not	not	PART
ejpam-5384	157	26	be	be	AUX
ejpam-5384	157	27	split	split	VERB
ejpam-5384	157	28	and	and	CCONJ
ejpam-5384	157	29	more	more	ADJ
ejpam-5384	157	30	over	over	ADP
ejpam-5384	157	31	they	they	PRON
ejpam-5384	157	32	can	can	AUX
ejpam-5384	157	33	have	have	VERB
ejpam-5384	157	34	varying	vary	VERB
ejpam-5384	157	35	sizes	size	NOUN
ejpam-5384	157	36	.	.	PUNCT
ejpam-5384	158	1	the	the	DET
ejpam-5384	158	2	same	same	ADJ
ejpam-5384	158	3	can	can	AUX
ejpam-5384	158	4	be	be	AUX
ejpam-5384	158	5	said	say	VERB
ejpam-5384	158	6	for	for	ADP
ejpam-5384	158	7	information	information	NOUN
ejpam-5384	158	8	networks	network	NOUN
ejpam-5384	158	9	and	and	CCONJ
ejpam-5384	158	10	parallel	parallel	ADJ
ejpam-5384	158	11	processing	processing	NOUN
ejpam-5384	158	12	in	in	ADP
ejpam-5384	158	13	relation	relation	NOUN
ejpam-5384	158	14	respectively	respectively	ADV
ejpam-5384	158	15	to	to	ADP
ejpam-5384	158	16	the	the	DET
ejpam-5384	158	17	packages	package	NOUN
ejpam-5384	158	18	and	and	CCONJ
ejpam-5384	158	19	the	the	DET
ejpam-5384	158	20	processes	process	NOUN
ejpam-5384	158	21	that	that	PRON
ejpam-5384	158	22	run	run	VERB
ejpam-5384	158	23	in	in	ADP
ejpam-5384	158	24	parallel	parallel	NOUN
ejpam-5384	158	25	.	.	PUNCT
ejpam-5384	159	1	to	to	PART
ejpam-5384	159	2	address	address	VERB
ejpam-5384	159	3	these	these	DET
ejpam-5384	159	4	situations	situation	NOUN
ejpam-5384	159	5	,	,	PUNCT
ejpam-5384	159	6	in	in	ADP
ejpam-5384	159	7	what	what	PRON
ejpam-5384	159	8	follows	follow	VERB
ejpam-5384	159	9	,	,	PUNCT
ejpam-5384	159	10	we	we	PRON
ejpam-5384	159	11	will	will	AUX
ejpam-5384	159	12	introduce	introduce	VERB
ejpam-5384	159	13	a	a	DET
ejpam-5384	159	14	notion	notion	NOUN
ejpam-5384	159	15	of	of	ADP
ejpam-5384	159	16	user	user	NOUN
ejpam-5384	159	17	equilibrium	equilibrium	NOUN
ejpam-5384	159	18	for	for	ADP
ejpam-5384	159	19	discrete	discrete	ADJ
ejpam-5384	159	20	multi	multi	ADJ
ejpam-5384	159	21	-	-	ADJ
ejpam-5384	159	22	type	type	ADJ
ejpam-5384	159	23	flow	flow	NOUN
ejpam-5384	159	24	.	.	PUNCT
ejpam-5384	160	1	an	an	DET
ejpam-5384	160	2	additional	additional	ADJ
ejpam-5384	160	3	advantage	advantage	NOUN
ejpam-5384	160	4	of	of	ADP
ejpam-5384	160	5	this	this	DET
ejpam-5384	160	6	representation	representation	NOUN
ejpam-5384	160	7	is	be	AUX
ejpam-5384	160	8	that	that	SCONJ
ejpam-5384	160	9	the	the	DET
ejpam-5384	160	10	resulting	result	VERB
ejpam-5384	160	11	discrete	discrete	ADJ
ejpam-5384	160	12	structures	structure	NOUN
ejpam-5384	160	13	could	could	AUX
ejpam-5384	160	14	be	be	AUX
ejpam-5384	160	15	algebraically	algebraically	ADV
ejpam-5384	160	16	recognized	recognize	VERB
ejpam-5384	160	17	in	in	ADP
ejpam-5384	160	18	a	a	DET
ejpam-5384	160	19	manner	manner	NOUN
ejpam-5384	160	20	similar	similar	ADJ
ejpam-5384	160	21	to	to	ADP
ejpam-5384	160	22	[	[	X
ejpam-5384	160	23	10	10	NUM
ejpam-5384	160	24	]	]	PUNCT
ejpam-5384	160	25	for	for	ADP
ejpam-5384	160	26	crisp	crisp	ADJ
ejpam-5384	160	27	graphs	graph	NOUN
ejpam-5384	160	28	and	and	CCONJ
ejpam-5384	160	29	[	[	X
ejpam-5384	160	30	17	17	NUM
ejpam-5384	160	31	]	]	PUNCT
ejpam-5384	160	32	,	,	PUNCT
ejpam-5384	161	1	[	[	X
ejpam-5384	161	2	16	16	NUM
ejpam-5384	161	3	]	]	PUNCT
ejpam-5384	161	4	for	for	ADP
ejpam-5384	161	5	fuzzy	fuzzy	ADJ
ejpam-5384	161	6	structures	structure	NOUN
ejpam-5384	161	7	.	.	PUNCT
ejpam-5384	162	1	we	we	PRON
ejpam-5384	162	2	will	will	AUX
ejpam-5384	162	3	consider	consider	VERB
ejpam-5384	162	4	again	again	ADV
ejpam-5384	162	5	a	a	DET
ejpam-5384	162	6	network	network	NOUN
ejpam-5384	162	7	with	with	ADP
ejpam-5384	162	8	n	n	CCONJ
ejpam-5384	162	9	parallel	parallel	ADJ
ejpam-5384	162	10	links	link	NOUN
ejpam-5384	162	11	,	,	PUNCT
ejpam-5384	162	12	in	in	ADP
ejpam-5384	162	13	=	=	PUNCT
ejpam-5384	162	14	{	{	PUNCT
ejpam-5384	162	15	1	1	NUM
ejpam-5384	162	16	,	,	PUNCT
ejpam-5384	162	17	2	2	NUM
ejpam-5384	162	18	,	,	PUNCT
ejpam-5384	162	19	.	.	PUNCT
ejpam-5384	162	20	.	.	PUNCT
ejpam-5384	163	1	.	.	PUNCT
ejpam-5384	164	1	,	,	PUNCT
ejpam-5384	164	2	n	n	CCONJ
ejpam-5384	164	3	}	}	PUNCT
ejpam-5384	164	4	,	,	PUNCT
ejpam-5384	164	5	where	where	SCONJ
ejpam-5384	164	6	constants	constant	VERB
ejpam-5384	164	7	c1	c1	PROPN
ejpam-5384	164	8	,	,	PUNCT
ejpam-5384	164	9	.	.	PUNCT
ejpam-5384	164	10	.	.	PUNCT
ejpam-5384	164	11	.	.	PUNCT
ejpam-5384	165	1	,	,	PUNCT
ejpam-5384	165	2	cn	cn	PROPN
ejpam-5384	165	3	,	,	PUNCT
ejpam-5384	165	4	represent	represent	VERB
ejpam-5384	165	5	the	the	DET
ejpam-5384	165	6	cost	cost	NOUN
ejpam-5384	165	7	of	of	ADP
ejpam-5384	165	8	using	use	VERB
ejpam-5384	165	9	the	the	DET
ejpam-5384	165	10	link	link	NOUN
ejpam-5384	165	11	i	i	PRON
ejpam-5384	165	12	,	,	PUNCT
ejpam-5384	165	13	for	for	ADP
ejpam-5384	165	14	i	i	PROPN
ejpam-5384	165	15	=	=	NOUN
ejpam-5384	165	16	1	1	NUM
ejpam-5384	165	17	,	,	PUNCT
ejpam-5384	165	18	.	.	PUNCT
ejpam-5384	165	19	.	.	PUNCT
ejpam-5384	166	1	.	.	PUNCT
ejpam-5384	167	1	,	,	PUNCT
ejpam-5384	167	2	n	n	CCONJ
ejpam-5384	167	3	,	,	PUNCT
ejpam-5384	167	4	for	for	ADP
ejpam-5384	167	5	a	a	DET
ejpam-5384	167	6	transportation	transportation	NOUN
ejpam-5384	167	7	network	network	NOUN
ejpam-5384	167	8	this	this	PRON
ejpam-5384	167	9	can	can	AUX
ejpam-5384	167	10	be	be	AUX
ejpam-5384	167	11	for	for	ADP
ejpam-5384	167	12	example	example	NOUN
ejpam-5384	167	13	,	,	PUNCT
ejpam-5384	167	14	the	the	DET
ejpam-5384	167	15	transit	transit	NOUN
ejpam-5384	167	16	time	time	NOUN
ejpam-5384	167	17	of	of	ADP
ejpam-5384	167	18	a	a	DET
ejpam-5384	167	19	unit	unit	NOUN
ejpam-5384	167	20	traffic	traffic	NOUN
ejpam-5384	167	21	through	through	ADP
ejpam-5384	167	22	the	the	DET
ejpam-5384	167	23	link	link	NOUN
ejpam-5384	167	24	i.	i.	NOUN
ejpam-5384	167	25	the	the	DET
ejpam-5384	167	26	flow	flow	NOUN
ejpam-5384	167	27	is	be	AUX
ejpam-5384	167	28	given	give	VERB
ejpam-5384	167	29	by	by	ADP
ejpam-5384	167	30	a	a	DET
ejpam-5384	167	31	flow	flow	NOUN
ejpam-5384	167	32	-	-	PUNCT
ejpam-5384	167	33	vector	vector	NOUN
ejpam-5384	167	34	ϕ	ϕ	NOUN
ejpam-5384	167	35	=	=	PUNCT
ejpam-5384	167	36	(	(	PUNCT
ejpam-5384	167	37	ϕ1	ϕ1	NOUN
ejpam-5384	167	38	,	,	PUNCT
ejpam-5384	167	39	ϕ2	ϕ2	ADV
ejpam-5384	167	40	,	,	PUNCT
ejpam-5384	167	41	.	.	PUNCT
ejpam-5384	167	42	.	.	PUNCT
ejpam-5384	168	1	.	.	PUNCT
ejpam-5384	169	1	,	,	PUNCT
ejpam-5384	169	2	ϕn	ϕn	PROPN
ejpam-5384	169	3	)	)	PUNCT
ejpam-5384	169	4	,	,	PUNCT
ejpam-5384	169	5	ϕi	ϕi	ADP
ejpam-5384	169	6	>	>	X
ejpam-5384	169	7	0	0	NUM
ejpam-5384	169	8	,	,	PUNCT
ejpam-5384	169	9	n	n	PRON
ejpam-5384	169	10	≥	≥	NOUN
ejpam-5384	169	11	n	n	CCONJ
ejpam-5384	169	12	,	,	PUNCT
ejpam-5384	169	13	where	where	SCONJ
ejpam-5384	169	14	ϕi	ϕi	ADV
ejpam-5384	169	15	is	be	AUX
ejpam-5384	169	16	the	the	DET
ejpam-5384	169	17	size	size	NOUN
ejpam-5384	169	18	of	of	ADP
ejpam-5384	169	19	the	the	DET
ejpam-5384	169	20	packet	packet	NOUN
ejpam-5384	169	21	or	or	CCONJ
ejpam-5384	169	22	vehicle	vehicle	NOUN
ejpam-5384	169	23	i.	i.	NOUN
ejpam-5384	169	24	we	we	PRON
ejpam-5384	169	25	assume	assume	VERB
ejpam-5384	169	26	that	that	SCONJ
ejpam-5384	169	27	all	all	DET
ejpam-5384	169	28	flow	flow	NOUN
ejpam-5384	169	29	is	be	AUX
ejpam-5384	169	30	distributed	distribute	VERB
ejpam-5384	169	31	among	among	ADP
ejpam-5384	169	32	all	all	DET
ejpam-5384	169	33	n	n	PRON
ejpam-5384	169	34	links	link	NOUN
ejpam-5384	169	35	and	and	CCONJ
ejpam-5384	169	36	denote	denote	VERB
ejpam-5384	169	37	the	the	DET
ejpam-5384	169	38	total	total	ADJ
ejpam-5384	169	39	flow	flow	NOUN
ejpam-5384	169	40	size	size	NOUN
ejpam-5384	169	41	by	by	ADP
ejpam-5384	169	42	x	x	PROPN
ejpam-5384	169	43	=	=	SYM
ejpam-5384	169	44	n∑	n∑	PROPN
ejpam-5384	169	45	i=1	i=1	X
ejpam-5384	169	46	ϕi	ϕi	PROPN
ejpam-5384	169	47	.	.	PUNCT
ejpam-5384	169	48	a.	a.	PROPN
ejpam-5384	169	49	kalampakas	kalampakas	PROPN
ejpam-5384	169	50	/	/	SYM
ejpam-5384	169	51	eur	eur	PROPN
ejpam-5384	169	52	.	.	PUNCT
ejpam-5384	170	1	j.	j.	PROPN
ejpam-5384	170	2	pure	pure	PROPN
ejpam-5384	170	3	appl	appl	PROPN
ejpam-5384	170	4	.	.	PROPN
ejpam-5384	170	5	math	math	PROPN
ejpam-5384	170	6	,	,	PUNCT
ejpam-5384	170	7	17	17	NUM
ejpam-5384	170	8	(	(	PUNCT
ejpam-5384	170	9	4	4	NUM
ejpam-5384	170	10	)	)	PUNCT
ejpam-5384	170	11	(	(	PUNCT
ejpam-5384	170	12	2024	2024	NUM
ejpam-5384	170	13	)	)	PUNCT
ejpam-5384	170	14	,	,	PUNCT
ejpam-5384	170	15	2448	2448	NUM
ejpam-5384	170	16	-	-	SYM
ejpam-5384	170	17	2466	2466	NUM
ejpam-5384	170	18	2454	2454	NUM
ejpam-5384	170	19	the	the	DET
ejpam-5384	170	20	elementary	elementary	ADJ
ejpam-5384	170	21	flow	flow	NOUN
ejpam-5384	170	22	of	of	ADP
ejpam-5384	170	23	each	each	DET
ejpam-5384	170	24	type	type	NOUN
ejpam-5384	170	25	is	be	AUX
ejpam-5384	170	26	unsplittable	unsplittable	ADJ
ejpam-5384	170	27	in	in	ADP
ejpam-5384	170	28	the	the	DET
ejpam-5384	170	29	sense	sense	NOUN
ejpam-5384	170	30	that	that	SCONJ
ejpam-5384	170	31	a	a	DET
ejpam-5384	170	32	vehicle	vehicle	NOUN
ejpam-5384	170	33	or	or	CCONJ
ejpam-5384	170	34	a	a	DET
ejpam-5384	170	35	packet	packet	NOUN
ejpam-5384	170	36	ϕk	ϕk	NOUN
ejpam-5384	170	37	is	be	AUX
ejpam-5384	170	38	routed	route	VERB
ejpam-5384	170	39	in	in	ADP
ejpam-5384	170	40	whole	whole	NOUN
ejpam-5384	170	41	along	along	ADP
ejpam-5384	170	42	one	one	NUM
ejpam-5384	170	43	and	and	CCONJ
ejpam-5384	170	44	only	only	ADV
ejpam-5384	170	45	one	one	NUM
ejpam-5384	170	46	link	link	NOUN
ejpam-5384	170	47	i	i	NOUN
ejpam-5384	170	48	=	=	NOUN
ejpam-5384	170	49	1	1	NUM
ejpam-5384	170	50	,	,	PUNCT
ejpam-5384	170	51	2	2	NUM
ejpam-5384	170	52	,	,	PUNCT
ejpam-5384	170	53	.	.	PUNCT
ejpam-5384	170	54	.	.	PUNCT
ejpam-5384	171	1	.	.	PUNCT
ejpam-5384	172	1	,	,	PUNCT
ejpam-5384	172	2	n.	n.	PROPN
ejpam-5384	172	3	hence	hence	ADV
ejpam-5384	172	4	it	it	PRON
ejpam-5384	172	5	holds	hold	VERB
ejpam-5384	172	6	n∑	n∑	NOUN
ejpam-5384	172	7	k=1	k=1	PROPN
ejpam-5384	172	8	n∑	n∑	PROPN
ejpam-5384	173	1	i=1	i=1	PROPN
ejpam-5384	173	2	δikϕ	δikϕ	NOUN
ejpam-5384	173	3	(	(	PUNCT
ejpam-5384	173	4	k	k	X
ejpam-5384	173	5	)	)	PUNCT
ejpam-5384	173	6	i	i	NOUN
ejpam-5384	174	1	=	=	PUNCT
ejpam-5384	174	2	x	x	INTJ
ejpam-5384	174	3	,	,	PUNCT
ejpam-5384	174	4	where	where	SCONJ
ejpam-5384	174	5	δik	δik	PROPN
ejpam-5384	174	6	=	=	PUNCT
ejpam-5384	174	7	{	{	PUNCT
ejpam-5384	174	8	1	1	NUM
ejpam-5384	174	9	,	,	PUNCT
ejpam-5384	174	10	if	if	SCONJ
ejpam-5384	174	11	ϕi	ϕi	ADV
ejpam-5384	174	12	is	be	AUX
ejpam-5384	174	13	routed	route	VERB
ejpam-5384	174	14	along	along	ADP
ejpam-5384	174	15	the	the	DET
ejpam-5384	174	16	link	link	NOUN
ejpam-5384	174	17	k	k	PROPN
ejpam-5384	174	18	0	0	PROPN
ejpam-5384	174	19	,	,	PUNCT
ejpam-5384	174	20	otherwise	otherwise	ADV
ejpam-5384	174	21	.	.	PUNCT
ejpam-5384	175	1	in	in	ADP
ejpam-5384	175	2	order	order	NOUN
ejpam-5384	175	3	to	to	PART
ejpam-5384	175	4	introduce	introduce	VERB
ejpam-5384	175	5	the	the	DET
ejpam-5384	175	6	user	user	NOUN
ejpam-5384	175	7	equilibrium	equilibrium	NOUN
ejpam-5384	175	8	from	from	ADP
ejpam-5384	175	9	the	the	DET
ejpam-5384	175	10	discrete	discrete	ADJ
ejpam-5384	175	11	case	case	NOUN
ejpam-5384	175	12	we	we	PRON
ejpam-5384	175	13	will	will	AUX
ejpam-5384	175	14	consider	consider	VERB
ejpam-5384	175	15	the	the	DET
ejpam-5384	175	16	particular	particular	ADJ
ejpam-5384	175	17	case	case	NOUN
ejpam-5384	175	18	of	of	ADP
ejpam-5384	175	19	two	two	NUM
ejpam-5384	175	20	links	link	NOUN
ejpam-5384	175	21	,	,	PUNCT
ejpam-5384	175	22	i2	i2	NOUN
ejpam-5384	175	23	=	=	PUNCT
ejpam-5384	175	24	{	{	PUNCT
ejpam-5384	175	25	1	1	NUM
ejpam-5384	175	26	,	,	PUNCT
ejpam-5384	175	27	2	2	NUM
ejpam-5384	175	28	}	}	PUNCT
ejpam-5384	175	29	.	.	PUNCT
ejpam-5384	176	1	let	let	VERB
ejpam-5384	176	2	x	x	PUNCT
ejpam-5384	176	3	=	=	PRON
ejpam-5384	176	4	{	{	PUNCT
ejpam-5384	176	5	ϕ1	ϕ1	NOUN
ejpam-5384	176	6	,	,	PUNCT
ejpam-5384	176	7	ϕ2	ϕ2	ADV
ejpam-5384	176	8	,	,	PUNCT
ejpam-5384	176	9	.	.	PUNCT
ejpam-5384	176	10	.	.	PUNCT
ejpam-5384	177	1	.	.	PUNCT
ejpam-5384	178	1	,	,	PUNCT
ejpam-5384	178	2	ϕn	ϕn	AUX
ejpam-5384	178	3	}	}	PUNCT
ejpam-5384	178	4	be	be	AUX
ejpam-5384	178	5	a	a	DET
ejpam-5384	178	6	flow	flow	NOUN
ejpam-5384	178	7	-	-	PUNCT
ejpam-5384	178	8	set	set	NOUN
ejpam-5384	178	9	,	,	PUNCT
ejpam-5384	178	10	ϕi	ϕi	ADP
ejpam-5384	178	11	∈	∈	PROPN
ejpam-5384	178	12	r+	r+	X
ejpam-5384	178	13	.	.	PUNCT
ejpam-5384	179	1	let	let	VERB
ejpam-5384	179	2	px	px	PROPN
ejpam-5384	179	3	2	2	NUM
ejpam-5384	179	4	be	be	AUX
ejpam-5384	179	5	a	a	DET
ejpam-5384	179	6	partition	partition	NOUN
ejpam-5384	179	7	of	of	ADP
ejpam-5384	179	8	x	x	PUNCT
ejpam-5384	179	9	into	into	ADP
ejpam-5384	179	10	two	two	NUM
ejpam-5384	179	11	subsets	subset	NOUN
ejpam-5384	179	12	x	x	PUNCT
ejpam-5384	179	13	′	′	NUM
ejpam-5384	180	1	and	and	CCONJ
ejpam-5384	180	2	x	x	PART
ejpam-5384	180	3	′′	′′	PROPN
ejpam-5384	180	4	,	,	PUNCT
ejpam-5384	180	5	where	where	SCONJ
ejpam-5384	180	6	x	x	PUNCT
ejpam-5384	180	7	′	′	NUM
ejpam-5384	180	8	̸=	̸=	PROPN
ejpam-5384	180	9	∅	∅	NOUN
ejpam-5384	180	10	,	,	PUNCT
ejpam-5384	180	11	x	x	PUNCT
ejpam-5384	180	12	′′	′′	PROPN
ejpam-5384	180	13	̸=	̸=	PROPN
ejpam-5384	180	14	∅	∅	NOUN
ejpam-5384	180	15	,	,	PUNCT
ejpam-5384	180	16	x	x	NOUN
ejpam-5384	180	17	′	′	NOUN
ejpam-5384	180	18	∪x	∪x	NOUN
ejpam-5384	181	1	′′	′′	PROPN
ejpam-5384	181	2	=	=	SYM
ejpam-5384	181	3	x	x	PROPN
ejpam-5384	181	4	,	,	PUNCT
ejpam-5384	181	5	x	x	NOUN
ejpam-5384	181	6	′	′	NOUN
ejpam-5384	181	7	∩x	∩x	PUNCT
ejpam-5384	182	1	′′	′′	NOUN
ejpam-5384	182	2	=	=	NOUN
ejpam-5384	182	3	∅	∅	NOUN
ejpam-5384	182	4	,	,	PUNCT
ejpam-5384	182	5	and	and	CCONJ
ejpam-5384	182	6	x	x	X
ejpam-5384	182	7	′′	′′	NOUN
ejpam-5384	182	8	=	=	NOUN
ejpam-5384	182	9	x	x	SYM
ejpam-5384	182	10	\x	\x	NOUN
ejpam-5384	182	11	′.	′.	NOUN
ejpam-5384	182	12	to	to	PART
ejpam-5384	182	13	further	far	ADV
ejpam-5384	182	14	simplify	simplify	VERB
ejpam-5384	182	15	,	,	PUNCT
ejpam-5384	182	16	we	we	PRON
ejpam-5384	182	17	assume	assume	VERB
ejpam-5384	182	18	that	that	SCONJ
ejpam-5384	182	19	the	the	DET
ejpam-5384	182	20	latency	latency	NOUN
ejpam-5384	182	21	functions	function	NOUN
ejpam-5384	182	22	lk(x	lk(x	NOUN
ejpam-5384	182	23	)	)	PUNCT
ejpam-5384	182	24	:	:	PUNCT
ejpam-5384	183	1	[	[	X
ejpam-5384	183	2	0	0	NUM
ejpam-5384	183	3	,	,	PUNCT
ejpam-5384	183	4	t	t	X
ejpam-5384	183	5	]	]	PUNCT
ejpam-5384	183	6	→	→	SYM
ejpam-5384	183	7	r	r	X
ejpam-5384	183	8	,	,	PUNCT
ejpam-5384	183	9	k	k	PROPN
ejpam-5384	183	10	∈	∈	PROPN
ejpam-5384	183	11	in	in	ADP
ejpam-5384	183	12	,	,	PUNCT
ejpam-5384	183	13	t	t	PROPN
ejpam-5384	183	14	=	=	PUNCT
ejpam-5384	183	15	∑n	∑n	PROPN
ejpam-5384	183	16	i=1	i=1	X
ejpam-5384	184	1	ϕi	ϕi	ADP
ejpam-5384	184	2	of	of	ADP
ejpam-5384	184	3	the	the	DET
ejpam-5384	184	4	two	two	NUM
ejpam-5384	184	5	links	link	NOUN
ejpam-5384	184	6	,	,	PUNCT
ejpam-5384	184	7	are	be	AUX
ejpam-5384	184	8	given	give	VERB
ejpam-5384	184	9	by	by	ADP
ejpam-5384	184	10	lk(x	lk(x	NOUN
ejpam-5384	184	11	)	)	PUNCT
ejpam-5384	184	12	=	=	SYM
ejpam-5384	184	13	cix	cix	PROPN
ejpam-5384	184	14	,	,	PUNCT
ejpam-5384	184	15	k	k	PROPN
ejpam-5384	184	16	=	=	SYM
ejpam-5384	184	17	1	1	NUM
ejpam-5384	184	18	,	,	PUNCT
ejpam-5384	184	19	2	2	NUM
ejpam-5384	184	20	.	.	PUNCT
ejpam-5384	184	21	hence	hence	ADV
ejpam-5384	184	22	,	,	PUNCT
ejpam-5384	184	23	according	accord	VERB
ejpam-5384	184	24	to	to	ADP
ejpam-5384	184	25	this	this	DET
ejpam-5384	184	26	setup	setup	NOUN
ejpam-5384	184	27	,	,	PUNCT
ejpam-5384	184	28	the	the	DET
ejpam-5384	184	29	user	user	NOUN
ejpam-5384	184	30	equilibrium	equilibrium	NOUN
ejpam-5384	184	31	can	can	AUX
ejpam-5384	184	32	be	be	AUX
ejpam-5384	184	33	described	describe	VERB
ejpam-5384	184	34	as	as	ADP
ejpam-5384	184	35	the	the	DET
ejpam-5384	184	36	partition	partition	NOUN
ejpam-5384	184	37	px	px	PROPN
ejpam-5384	184	38	2	2	NUM
ejpam-5384	184	39	that	that	PRON
ejpam-5384	184	40	minimizes	minimize	VERB
ejpam-5384	184	41	the	the	DET
ejpam-5384	184	42	difference	difference	NOUN
ejpam-5384	184	43	between	between	ADP
ejpam-5384	184	44	the	the	DET
ejpam-5384	184	45	time	time	NOUN
ejpam-5384	184	46	needed	need	VERB
ejpam-5384	184	47	for	for	ADP
ejpam-5384	184	48	each	each	PRON
ejpam-5384	184	49	of	of	ADP
ejpam-5384	184	50	the	the	DET
ejpam-5384	184	51	two	two	NUM
ejpam-5384	184	52	flow	flow	NOUN
ejpam-5384	184	53	subsets	subset	NOUN
ejpam-5384	184	54	x	x	PUNCT
ejpam-5384	184	55	′	′	NUM
ejpam-5384	184	56	and	and	CCONJ
ejpam-5384	184	57	x	x	X
ejpam-5384	184	58	′′	′′	PROPN
ejpam-5384	184	59	to	to	PART
ejpam-5384	184	60	travel	travel	VERB
ejpam-5384	184	61	across	across	ADP
ejpam-5384	184	62	the	the	DET
ejpam-5384	184	63	two	two	NUM
ejpam-5384	184	64	links	link	NOUN
ejpam-5384	184	65	.	.	PUNCT
ejpam-5384	185	1	in	in	ADP
ejpam-5384	185	2	other	other	ADJ
ejpam-5384	185	3	words	word	NOUN
ejpam-5384	185	4	,	,	PUNCT
ejpam-5384	185	5	to	to	PART
ejpam-5384	185	6	find	find	VERB
ejpam-5384	185	7	the	the	DET
ejpam-5384	185	8	user	user	NOUN
ejpam-5384	185	9	equilibrium	equilibrium	NOUN
ejpam-5384	185	10	one	one	PRON
ejpam-5384	185	11	must	must	AUX
ejpam-5384	185	12	solve	solve	VERB
ejpam-5384	185	13	the	the	DET
ejpam-5384	185	14	optimization	optimization	NOUN
ejpam-5384	185	15	problem	problem	NOUN
ejpam-5384	185	16	min	min	PROPN
ejpam-5384	185	17	px	px	PROPN
ejpam-5384	185	18	2	2	NUM
ejpam-5384	185	19			PUNCT
ejpam-5384	185	20	∣∣∣∣∣ck	∣∣∣∣∣ck	NOUN
ejpam-5384	185	21	∑	∑	PROPN
ejpam-5384	185	22	ϕi∈x′	ϕi∈x′	PROPN
ejpam-5384	185	23	δikϕi	δikϕi	NOUN
ejpam-5384	185	24	−	−	PROPN
ejpam-5384	185	25	ck	ck	INTJ
ejpam-5384	185	26	∑	∑	PUNCT
ejpam-5384	185	27	ϕi∈x′′	ϕi∈x′′	PROPN
ejpam-5384	185	28	δikϕi	δikϕi	PROPN
ejpam-5384	185	29	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5384	186	1			PROPN
ejpam-5384	186	2	,	,	PUNCT
ejpam-5384	186	3	k	k	PROPN
ejpam-5384	186	4	=	=	SYM
ejpam-5384	186	5	1	1	NUM
ejpam-5384	186	6	,	,	PUNCT
ejpam-5384	186	7	2	2	NUM
ejpam-5384	186	8	with	with	ADP
ejpam-5384	186	9	ϕi	ϕi	ADP
ejpam-5384	186	10	>	>	X
ejpam-5384	186	11	0	0	X
ejpam-5384	186	12	.	.	PUNCT
ejpam-5384	187	1	consequently	consequently	ADV
ejpam-5384	187	2	,	,	PUNCT
ejpam-5384	187	3	the	the	DET
ejpam-5384	187	4	discrete	discrete	ADJ
ejpam-5384	187	5	user	user	NOUN
ejpam-5384	187	6	equilibrium	equilibrium	NOUN
ejpam-5384	187	7	does	do	AUX
ejpam-5384	187	8	not	not	PART
ejpam-5384	187	9	equalize	equalize	VERB
ejpam-5384	187	10	the	the	DET
ejpam-5384	187	11	link	link	NOUN
ejpam-5384	187	12	delays	delay	NOUN
ejpam-5384	187	13	as	as	ADP
ejpam-5384	187	14	in	in	ADP
ejpam-5384	187	15	the	the	DET
ejpam-5384	187	16	continuous	continuous	ADJ
ejpam-5384	187	17	case	case	NOUN
ejpam-5384	187	18	,	,	PUNCT
ejpam-5384	187	19	rather	rather	ADV
ejpam-5384	187	20	than	than	ADP
ejpam-5384	187	21	minimize	minimize	VERB
ejpam-5384	187	22	the	the	DET
ejpam-5384	187	23	absolute	absolute	ADJ
ejpam-5384	187	24	difference	difference	NOUN
ejpam-5384	187	25	between	between	ADP
ejpam-5384	187	26	them	they	PRON
ejpam-5384	187	27	.	.	PUNCT
ejpam-5384	188	1	this	this	PRON
ejpam-5384	188	2	can	can	AUX
ejpam-5384	188	3	be	be	AUX
ejpam-5384	188	4	further	far	ADV
ejpam-5384	188	5	generalized	generalize	VERB
ejpam-5384	188	6	for	for	ADP
ejpam-5384	188	7	more	more	ADJ
ejpam-5384	188	8	than	than	ADP
ejpam-5384	188	9	two	two	NUM
ejpam-5384	188	10	parallel	parallel	ADJ
ejpam-5384	188	11	links	link	NOUN
ejpam-5384	188	12	by	by	ADP
ejpam-5384	188	13	minimizing	minimize	VERB
ejpam-5384	188	14	the	the	DET
ejpam-5384	188	15	sum	sum	NOUN
ejpam-5384	188	16	of	of	ADP
ejpam-5384	188	17	absolute	absolute	ADJ
ejpam-5384	188	18	differences	difference	NOUN
ejpam-5384	188	19	between	between	ADP
ejpam-5384	188	20	all	all	DET
ejpam-5384	188	21	pairs	pair	NOUN
ejpam-5384	188	22	of	of	ADP
ejpam-5384	188	23	links	link	NOUN
ejpam-5384	188	24	delays	delay	NOUN
ejpam-5384	188	25	.	.	PUNCT
ejpam-5384	189	1	moreover	moreover	ADV
ejpam-5384	189	2	,	,	PUNCT
ejpam-5384	189	3	the	the	DET
ejpam-5384	189	4	link	link	NOUN
ejpam-5384	189	5	latency	latency	NOUN
ejpam-5384	189	6	function	function	NOUN
ejpam-5384	189	7	can	can	AUX
ejpam-5384	189	8	be	be	AUX
ejpam-5384	189	9	further	far	ADV
ejpam-5384	189	10	enhanced	enhance	VERB
ejpam-5384	189	11	by	by	ADP
ejpam-5384	189	12	adding	add	VERB
ejpam-5384	189	13	a	a	DET
ejpam-5384	189	14	maximum	maximum	ADJ
ejpam-5384	189	15	capacity	capacity	NOUN
ejpam-5384	189	16	and	and	CCONJ
ejpam-5384	189	17	a	a	DET
ejpam-5384	189	18	constant	constant	ADJ
ejpam-5384	189	19	toll	toll	NOUN
ejpam-5384	189	20	price	price	NOUN
ejpam-5384	189	21	.	.	PUNCT
ejpam-5384	190	1	hence	hence	ADV
ejpam-5384	190	2	,	,	PUNCT
ejpam-5384	190	3	if	if	SCONJ
ejpam-5384	190	4	we	we	PRON
ejpam-5384	190	5	denote	denote	VERB
ejpam-5384	190	6	by	by	ADP
ejpam-5384	190	7	ri	ri	PROPN
ejpam-5384	190	8	,	,	PUNCT
ejpam-5384	190	9	i	i	PRON
ejpam-5384	190	10	∈	∈	VERB
ejpam-5384	190	11	in	in	ADP
ejpam-5384	190	12	,	,	PUNCT
ejpam-5384	190	13	the	the	DET
ejpam-5384	190	14	capacity	capacity	NOUN
ejpam-5384	190	15	of	of	ADP
ejpam-5384	190	16	the	the	DET
ejpam-5384	190	17	link	link	NOUN
ejpam-5384	190	18	i	i	PRON
ejpam-5384	190	19	,	,	PUNCT
ejpam-5384	190	20	it	it	PRON
ejpam-5384	190	21	can	can	AUX
ejpam-5384	190	22	be	be	AUX
ejpam-5384	190	23	assumed	assume	VERB
ejpam-5384	190	24	that	that	SCONJ
ejpam-5384	190	25	the	the	DET
ejpam-5384	190	26	flow	flow	NOUN
ejpam-5384	190	27	on	on	ADP
ejpam-5384	190	28	the	the	DET
ejpam-5384	190	29	link	link	NOUN
ejpam-5384	190	30	i	i	PRON
ejpam-5384	190	31	can	can	AUX
ejpam-5384	190	32	not	not	PART
ejpam-5384	190	33	exceed	exceed	VERB
ejpam-5384	190	34	ri	ri	NOUN
ejpam-5384	190	35	,	,	PUNCT
ejpam-5384	190	36	that	that	PRON
ejpam-5384	190	37	is	be	AUX
ejpam-5384	190	38	n∑	n∑	PROPN
ejpam-5384	190	39	i=1	i=1	PROPN
ejpam-5384	190	40	δikϕ	δikϕ	PROPN
ejpam-5384	190	41	(	(	PUNCT
ejpam-5384	190	42	k	k	X
ejpam-5384	190	43	)	)	PUNCT
ejpam-5384	190	44	i	i	PROPN
ejpam-5384	190	45	≤	≤	PROPN
ejpam-5384	190	46	ri	ri	PROPN
ejpam-5384	190	47	,	,	PUNCT
ejpam-5384	190	48	k	k	PROPN
ejpam-5384	190	49	=	=	SYM
ejpam-5384	190	50	1	1	NUM
ejpam-5384	190	51	,	,	PUNCT
ejpam-5384	190	52	2	2	NUM
ejpam-5384	190	53	,	,	PUNCT
ejpam-5384	190	54	.	.	PUNCT
ejpam-5384	190	55	.	.	PUNCT
ejpam-5384	191	1	.	.	PUNCT
ejpam-5384	192	1	,	,	PUNCT
ejpam-5384	192	2	n.	n.	NOUN
ejpam-5384	192	3	if	if	SCONJ
ejpam-5384	192	4	we	we	PRON
ejpam-5384	192	5	additionally	additionally	ADV
ejpam-5384	192	6	assume	assume	VERB
ejpam-5384	192	7	that	that	SCONJ
ejpam-5384	192	8	the	the	DET
ejpam-5384	192	9	price	price	NOUN
ejpam-5384	192	10	of	of	ADP
ejpam-5384	192	11	sending	send	VERB
ejpam-5384	192	12	the	the	DET
ejpam-5384	192	13	flow	flow	NOUN
ejpam-5384	192	14	through	through	ADP
ejpam-5384	192	15	a	a	DET
ejpam-5384	192	16	link	link	NOUN
ejpam-5384	192	17	i	i	NOUN
ejpam-5384	192	18	=	=	NOUN
ejpam-5384	192	19	1	1	NUM
ejpam-5384	192	20	,	,	PUNCT
ejpam-5384	192	21	2	2	NUM
ejpam-5384	192	22	,	,	PUNCT
ejpam-5384	192	23	.	.	PUNCT
ejpam-5384	192	24	.	.	PUNCT
ejpam-5384	193	1	.	.	PUNCT
ejpam-5384	194	1	,	,	PUNCT
ejpam-5384	194	2	n	n	PRON
ejpam-5384	194	3	is	be	AUX
ejpam-5384	194	4	increased	increase	VERB
ejpam-5384	194	5	by	by	ADP
ejpam-5384	194	6	a	a	DET
ejpam-5384	194	7	constant	constant	ADJ
ejpam-5384	194	8	toll	toll	NOUN
ejpam-5384	194	9	price	price	NOUN
ejpam-5384	194	10	pi	pi	NOUN
ejpam-5384	194	11	,	,	PUNCT
ejpam-5384	194	12	i	i	PRON
ejpam-5384	194	13	=	=	NOUN
ejpam-5384	194	14	1	1	NUM
ejpam-5384	194	15	,	,	PUNCT
ejpam-5384	194	16	2	2	NUM
ejpam-5384	194	17	,	,	PUNCT
ejpam-5384	194	18	.	.	PUNCT
ejpam-5384	194	19	.	.	PUNCT
ejpam-5384	195	1	.	.	PUNCT
ejpam-5384	196	1	,	,	PUNCT
ejpam-5384	196	2	n.	n.	PROPN
ejpam-5384	196	3	then	then	ADV
ejpam-5384	196	4	the	the	DET
ejpam-5384	196	5	delay	delay	NOUN
ejpam-5384	196	6	on	on	ADP
ejpam-5384	196	7	each	each	DET
ejpam-5384	196	8	link	link	NOUN
ejpam-5384	196	9	is	be	AUX
ejpam-5384	196	10	given	give	VERB
ejpam-5384	196	11	by	by	ADP
ejpam-5384	196	12	ck	ck	PROPN
ejpam-5384	196	13	n∑	n∑	PROPN
ejpam-5384	196	14	i=1	i=1	PROPN
ejpam-5384	196	15	δikϕi	δikϕi	PROPN
ejpam-5384	196	16	+	+	CCONJ
ejpam-5384	196	17	pk	pk	PROPN
ejpam-5384	196	18	,	,	PUNCT
ejpam-5384	196	19	k	k	NOUN
ejpam-5384	196	20	=	=	SYM
ejpam-5384	196	21	1	1	NUM
ejpam-5384	196	22	,	,	PUNCT
ejpam-5384	196	23	2	2	NUM
ejpam-5384	196	24	,	,	PUNCT
ejpam-5384	196	25	.	.	PUNCT
ejpam-5384	196	26	.	.	PUNCT
ejpam-5384	196	27	.	.	PUNCT
ejpam-5384	197	1	,	,	PUNCT
ejpam-5384	197	2	n.	n.	PROPN
ejpam-5384	197	3	a.	a.	PROPN
ejpam-5384	197	4	kalampakas	kalampakas	PROPN
ejpam-5384	197	5	/	/	SYM
ejpam-5384	197	6	eur	eur	PROPN
ejpam-5384	197	7	.	.	PUNCT
ejpam-5384	198	1	j.	j.	PROPN
ejpam-5384	198	2	pure	pure	PROPN
ejpam-5384	198	3	appl	appl	PROPN
ejpam-5384	198	4	.	.	PROPN
ejpam-5384	198	5	math	math	PROPN
ejpam-5384	198	6	,	,	PUNCT
ejpam-5384	198	7	17	17	NUM
ejpam-5384	198	8	(	(	PUNCT
ejpam-5384	198	9	4	4	NUM
ejpam-5384	198	10	)	)	PUNCT
ejpam-5384	198	11	(	(	PUNCT
ejpam-5384	198	12	2024	2024	NUM
ejpam-5384	198	13	)	)	PUNCT
ejpam-5384	198	14	,	,	PUNCT
ejpam-5384	198	15	2448	2448	NUM
ejpam-5384	198	16	-	-	SYM
ejpam-5384	198	17	2466	2466	NUM
ejpam-5384	198	18	2455	2455	NUM
ejpam-5384	198	19	4	4	NUM
ejpam-5384	198	20	.	.	PUNCT
ejpam-5384	199	1	system	system	NOUN
ejpam-5384	199	2	optimum	optimum	ADV
ejpam-5384	199	3	our	our	PRON
ejpam-5384	199	4	next	next	ADJ
ejpam-5384	199	5	step	step	NOUN
ejpam-5384	199	6	is	be	AUX
ejpam-5384	199	7	to	to	PART
ejpam-5384	199	8	investigate	investigate	VERB
ejpam-5384	199	9	the	the	DET
ejpam-5384	199	10	properties	property	NOUN
ejpam-5384	199	11	of	of	ADP
ejpam-5384	199	12	the	the	DET
ejpam-5384	199	13	system	system	NOUN
ejpam-5384	199	14	optimum	optimum	NOUN
ejpam-5384	199	15	.	.	PUNCT
ejpam-5384	200	1	the	the	DET
ejpam-5384	200	2	networks	network	NOUN
ejpam-5384	200	3	we	we	PRON
ejpam-5384	200	4	will	will	AUX
ejpam-5384	200	5	examine	examine	VERB
ejpam-5384	200	6	from	from	ADP
ejpam-5384	200	7	now	now	ADV
ejpam-5384	200	8	on	on	ADV
ejpam-5384	200	9	are	be	AUX
ejpam-5384	200	10	assumed	assume	VERB
ejpam-5384	200	11	to	to	PART
ejpam-5384	200	12	be	be	AUX
ejpam-5384	200	13	differentiable	differentiable	ADJ
ejpam-5384	200	14	.	.	PUNCT
ejpam-5384	201	1	we	we	PRON
ejpam-5384	201	2	start	start	VERB
ejpam-5384	201	3	with	with	ADP
ejpam-5384	201	4	the	the	DET
ejpam-5384	201	5	following	follow	VERB
ejpam-5384	201	6	important	important	ADJ
ejpam-5384	201	7	result	result	NOUN
ejpam-5384	201	8	.	.	PUNCT
ejpam-5384	202	1	proposition	proposition	NOUN
ejpam-5384	202	2	2	2	NUM
ejpam-5384	202	3	.	.	PUNCT
ejpam-5384	202	4	consider	consider	VERB
ejpam-5384	202	5	a	a	DET
ejpam-5384	202	6	network	network	NOUN
ejpam-5384	202	7	nn	nn	X
ejpam-5384	202	8	=	=	SYM
ejpam-5384	202	9	(	(	PUNCT
ejpam-5384	202	10	l1(x	l1(x	NOUN
ejpam-5384	202	11	)	)	PUNCT
ejpam-5384	202	12	,	,	PUNCT
ejpam-5384	202	13	.	.	PUNCT
ejpam-5384	202	14	.	.	PUNCT
ejpam-5384	203	1	.	.	PUNCT
ejpam-5384	204	1	,	,	PUNCT
ejpam-5384	204	2	ln(x	ln(x	X
ejpam-5384	204	3	)	)	PUNCT
ejpam-5384	204	4	)	)	PUNCT
ejpam-5384	204	5	,	,	PUNCT
ejpam-5384	204	6	then	then	ADV
ejpam-5384	204	7	for	for	ADP
ejpam-5384	204	8	every	every	DET
ejpam-5384	204	9	i	i	PROPN
ejpam-5384	204	10	,	,	PUNCT
ejpam-5384	204	11	j	j	PROPN
ejpam-5384	204	12	∈	∈	PROPN
ejpam-5384	204	13	in	in	ADP
ejpam-5384	204	14	we	we	PRON
ejpam-5384	204	15	have	have	AUX
ejpam-5384	204	16	li(ϕi	li(ϕi	VERB
ejpam-5384	204	17	)	)	PUNCT
ejpam-5384	205	1	+	+	CCONJ
ejpam-5384	205	2	ϕil	ϕil	INTJ
ejpam-5384	205	3	′	′	NUM
ejpam-5384	205	4	i(ϕi	i(ϕi	ADJ
ejpam-5384	205	5	)	)	PUNCT
ejpam-5384	205	6	=	=	SYM
ejpam-5384	205	7	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	205	8	)	)	PUNCT
ejpam-5384	206	1	+	+	CCONJ
ejpam-5384	206	2	ϕjl	ϕjl	NOUN
ejpam-5384	206	3	′	′	NUM
ejpam-5384	206	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	206	5	)	)	PUNCT
ejpam-5384	206	6	.	.	PUNCT
ejpam-5384	206	7	provided	provide	VERB
ejpam-5384	206	8	that	that	DET
ejpam-5384	206	9	ϕ	ϕ	NOUN
ejpam-5384	206	10	=	=	PUNCT
ejpam-5384	206	11	(	(	PUNCT
ejpam-5384	206	12	ϕ1	ϕ1	NOUN
ejpam-5384	206	13	,	,	PUNCT
ejpam-5384	206	14	.	.	PUNCT
ejpam-5384	206	15	.	.	PUNCT
ejpam-5384	207	1	.	.	PUNCT
ejpam-5384	208	1	,	,	PUNCT
ejpam-5384	208	2	ϕn	ϕn	X
ejpam-5384	208	3	)	)	PUNCT
ejpam-5384	208	4	∈	∈	PROPN
ejpam-5384	208	5	int(sn−1	int(sn−1	PROPN
ejpam-5384	208	6	)	)	PUNCT
ejpam-5384	208	7	is	be	AUX
ejpam-5384	208	8	system	system	NOUN
ejpam-5384	208	9	optimum	optimum	ADJ
ejpam-5384	208	10	of	of	ADP
ejpam-5384	208	11	the	the	DET
ejpam-5384	208	12	network	network	NOUN
ejpam-5384	208	13	.	.	PUNCT
ejpam-5384	209	1	proof	proof	NOUN
ejpam-5384	209	2	.	.	PUNCT
ejpam-5384	210	1	let	let	VERB
ejpam-5384	210	2	(	(	PUNCT
ejpam-5384	210	3	ϕ1	ϕ1	NOUN
ejpam-5384	210	4	,	,	PUNCT
ejpam-5384	210	5	·	·	PUNCT
ejpam-5384	210	6	·	·	PUNCT
ejpam-5384	210	7	·	·	PUNCT
ejpam-5384	210	8	,	,	PUNCT
ejpam-5384	210	9	ϕi	ϕi	ADP
ejpam-5384	210	10	,	,	PUNCT
ejpam-5384	210	11	·	·	PUNCT
ejpam-5384	210	12	·	·	PUNCT
ejpam-5384	210	13	·	·	PUNCT
ejpam-5384	210	14	,	,	PUNCT
ejpam-5384	210	15	ϕj	ϕj	INTJ
ejpam-5384	210	16	,	,	PUNCT
ejpam-5384	210	17	·	·	PUNCT
ejpam-5384	210	18	·	·	PUNCT
ejpam-5384	210	19	·	·	PUNCT
ejpam-5384	210	20	ϕn	ϕn	X
ejpam-5384	210	21	)	)	PUNCT
ejpam-5384	210	22	∈	∈	PROPN
ejpam-5384	211	1	intsn−1	intsn−1	PROPN
ejpam-5384	211	2	.	.	PUNCT
ejpam-5384	212	1	the	the	DET
ejpam-5384	212	2	total	total	ADJ
ejpam-5384	212	3	delay	delay	NOUN
ejpam-5384	212	4	of	of	ADP
ejpam-5384	212	5	the	the	DET
ejpam-5384	212	6	network	network	NOUN
ejpam-5384	212	7	at	at	ADP
ejpam-5384	212	8	this	this	DET
ejpam-5384	212	9	flow	flow	NOUN
ejpam-5384	212	10	is	be	AUX
ejpam-5384	212	11	t	t	NOUN
ejpam-5384	212	12	=	=	PUNCT
ejpam-5384	212	13	ϕ1l1(ϕ1	ϕ1l1(ϕ1	X
ejpam-5384	212	14	)	)	PUNCT
ejpam-5384	213	1	+	+	CCONJ
ejpam-5384	213	2	·	·	PUNCT
ejpam-5384	213	3	·	·	PUNCT
ejpam-5384	213	4	·	·	PUNCT
ejpam-5384	213	5	+	+	NUM
ejpam-5384	213	6	ϕili(ϕi	ϕili(ϕi	X
ejpam-5384	213	7	)	)	PUNCT
ejpam-5384	213	8	+	+	CCONJ
ejpam-5384	213	9	·	·	PUNCT
ejpam-5384	213	10	·	·	PUNCT
ejpam-5384	213	11	·	·	PUNCT
ejpam-5384	213	12	+	+	NUM
ejpam-5384	213	13	ϕjlj(ϕj	ϕjlj(ϕj	NOUN
ejpam-5384	213	14	)	)	PUNCT
ejpam-5384	213	15	+	+	CCONJ
ejpam-5384	213	16	ϕnln(ϕn	ϕnln(ϕn	NOUN
ejpam-5384	213	17	)	)	PUNCT
ejpam-5384	213	18	.	.	PUNCT
ejpam-5384	214	1	for	for	ADP
ejpam-5384	214	2	0	0	NUM
ejpam-5384	214	3	<	<	X
ejpam-5384	214	4	ϵ	ϵ	X
ejpam-5384	214	5	<	<	X
ejpam-5384	214	6	1	1	NUM
ejpam-5384	214	7	,	,	PUNCT
ejpam-5384	214	8	the	the	DET
ejpam-5384	214	9	total	total	ADJ
ejpam-5384	214	10	delay	delay	NOUN
ejpam-5384	214	11	of	of	ADP
ejpam-5384	214	12	the	the	DET
ejpam-5384	214	13	network	network	NOUN
ejpam-5384	214	14	at	at	ADP
ejpam-5384	214	15	the	the	DET
ejpam-5384	214	16	flow	flow	NOUN
ejpam-5384	214	17	x+ϵ,−ϵ	x+ϵ,−ϵ	PRON
ejpam-5384	214	18	{	{	PUNCT
ejpam-5384	214	19	i	i	PROPN
ejpam-5384	214	20	,	,	PUNCT
ejpam-5384	214	21	j	j	PROPN
ejpam-5384	214	22	}	}	PUNCT
ejpam-5384	214	23	=	=	SYM
ejpam-5384	214	24	(	(	PUNCT
ejpam-5384	214	25	ϕ1	ϕ1	PROPN
ejpam-5384	214	26	,	,	PUNCT
ejpam-5384	214	27	·	·	PUNCT
ejpam-5384	214	28	·	·	PUNCT
ejpam-5384	214	29	·	·	PUNCT
ejpam-5384	214	30	,	,	PUNCT
ejpam-5384	214	31	ϕi	ϕi	ADP
ejpam-5384	214	32	+	+	CCONJ
ejpam-5384	214	33	ϵ	ϵ	NUM
ejpam-5384	214	34	,	,	PUNCT
ejpam-5384	214	35	·	·	PUNCT
ejpam-5384	214	36	·	·	PUNCT
ejpam-5384	214	37	·	·	PUNCT
ejpam-5384	214	38	,	,	PUNCT
ejpam-5384	214	39	ϕj	ϕj	ADP
ejpam-5384	214	40	−	−	PROPN
ejpam-5384	214	41	ϵ	ϵ	X
ejpam-5384	214	42	,	,	PUNCT
ejpam-5384	214	43	·	·	PUNCT
ejpam-5384	214	44	·	·	PUNCT
ejpam-5384	214	45	·	·	PUNCT
ejpam-5384	214	46	ϕn	ϕn	X
ejpam-5384	214	47	)	)	PUNCT
ejpam-5384	214	48	∈	∈	PROPN
ejpam-5384	214	49	intsn−1	intsn−1	PROPN
ejpam-5384	214	50	is	be	AUX
ejpam-5384	214	51	t+ϵ	t+ϵ	NOUN
ejpam-5384	214	52	=	=	NOUN
ejpam-5384	214	53	ϕ1l1(ϕ1	ϕ1l1(ϕ1	X
ejpam-5384	214	54	)	)	PUNCT
ejpam-5384	214	55	+	+	CCONJ
ejpam-5384	214	56	·	·	PUNCT
ejpam-5384	214	57	·	·	PUNCT
ejpam-5384	214	58	·	·	PUNCT
ejpam-5384	214	59	+	+	CCONJ
ejpam-5384	214	60	(	(	PUNCT
ejpam-5384	214	61	ϕi	ϕi	ADP
ejpam-5384	214	62	+	+	CCONJ
ejpam-5384	214	63	ϵ)li(ϕi	ϵ)li(ϕi	ADJ
ejpam-5384	214	64	+	+	CCONJ
ejpam-5384	214	65	ϵ	ϵ	X
ejpam-5384	214	66	)	)	PUNCT
ejpam-5384	214	67	+	+	CCONJ
ejpam-5384	214	68	·	·	PUNCT
ejpam-5384	214	69	·	·	PUNCT
ejpam-5384	214	70	·	·	PUNCT
ejpam-5384	214	71	+	+	CCONJ
ejpam-5384	214	72	(	(	PUNCT
ejpam-5384	214	73	ϕj	ϕj	INTJ
ejpam-5384	214	74	−	−	PROPN
ejpam-5384	214	75	ϵ)lj(ϕj	ϵ)lj(ϕj	NUM
ejpam-5384	214	76	−	−	PROPN
ejpam-5384	214	77	ϵ	ϵ	X
ejpam-5384	214	78	)	)	PUNCT
ejpam-5384	214	79	+	+	CCONJ
ejpam-5384	214	80	·	·	PUNCT
ejpam-5384	214	81	·	·	PUNCT
ejpam-5384	214	82	·	·	PUNCT
ejpam-5384	214	83	+	+	NUM
ejpam-5384	214	84	ϕnln(ϕn	ϕnln(ϕn	NOUN
ejpam-5384	214	85	)	)	PUNCT
ejpam-5384	214	86	.	.	PUNCT
ejpam-5384	215	1	the	the	DET
ejpam-5384	215	2	delay	delay	NOUN
ejpam-5384	215	3	t+ϵ	t+ϵ	ADP
ejpam-5384	215	4	is	be	AUX
ejpam-5384	215	5	less	less	ADJ
ejpam-5384	215	6	than	than	ADP
ejpam-5384	215	7	the	the	DET
ejpam-5384	215	8	delay	delay	NOUN
ejpam-5384	215	9	t	t	PROPN
ejpam-5384	216	1	if	if	SCONJ
ejpam-5384	216	2	the	the	DET
ejpam-5384	216	3	difference	difference	NOUN
ejpam-5384	216	4	t+ϵ	t+ϵ	ADP
ejpam-5384	216	5	−	−	PROPN
ejpam-5384	216	6	t	t	NOUN
ejpam-5384	216	7	=	=	SYM
ejpam-5384	216	8	(	(	PUNCT
ejpam-5384	216	9	ϕi	ϕi	ADP
ejpam-5384	217	1	+	+	CCONJ
ejpam-5384	217	2	ϵ)li(ϕi	ϵ)li(ϕi	ADJ
ejpam-5384	217	3	+	+	CCONJ
ejpam-5384	217	4	ϵ)−	ϵ)−	ADJ
ejpam-5384	217	5	ϕili(ϕi	ϕili(ϕi	ADJ
ejpam-5384	217	6	)	)	PUNCT
ejpam-5384	218	1	+	+	CCONJ
ejpam-5384	218	2	(	(	PUNCT
ejpam-5384	218	3	ϕj	ϕj	INTJ
ejpam-5384	218	4	−	−	PROPN
ejpam-5384	218	5	ϵ)lj(ϕj	ϵ)lj(ϕj	PUNCT
ejpam-5384	219	1	−	−	PROPN
ejpam-5384	219	2	ϵ)−	ϵ)−	ADJ
ejpam-5384	219	3	ϕjlj(ϕj	ϕjlj(ϕj	PROPN
ejpam-5384	219	4	)	)	PUNCT
ejpam-5384	219	5	=	=	SYM
ejpam-5384	219	6	(	(	PUNCT
ejpam-5384	219	7	ϕi	ϕi	ADP
ejpam-5384	220	1	+	+	CCONJ
ejpam-5384	220	2	ϵ)li(ϕi	ϵ)li(ϕi	ADJ
ejpam-5384	221	1	+	+	CCONJ
ejpam-5384	222	1	ϵ)−	ϵ)−	ADJ
ejpam-5384	222	2	(	(	PUNCT
ejpam-5384	222	3	ϕi	ϕi	ADP
ejpam-5384	222	4	+	+	CCONJ
ejpam-5384	222	5	ϵ)li(ϕi	ϵ)li(ϕi	NUM
ejpam-5384	222	6	)	)	PUNCT
ejpam-5384	222	7	+	+	NOUN
ejpam-5384	222	8	ϵli(ϕi	ϵli(ϕi	NUM
ejpam-5384	222	9	)	)	PUNCT
ejpam-5384	222	10	+	+	CCONJ
ejpam-5384	222	11	(	(	PUNCT
ejpam-5384	222	12	ϕj	ϕj	INTJ
ejpam-5384	222	13	−	−	PROPN
ejpam-5384	222	14	ϵ)lj(ϕj	ϵ)lj(ϕj	PUNCT
ejpam-5384	223	1	−	−	PROPN
ejpam-5384	223	2	ϵ)−	ϵ)−	PROPN
ejpam-5384	223	3	(	(	PUNCT
ejpam-5384	223	4	ϕj	ϕj	INTJ
ejpam-5384	223	5	−	−	PROPN
ejpam-5384	223	6	ϵ)lj(ϕj)−	ϵ)lj(ϕj)−	PROPN
ejpam-5384	223	7	ϵlj(ϕj	ϵlj(ϕj	PROPN
ejpam-5384	223	8	)	)	PUNCT
ejpam-5384	223	9	=	=	SYM
ejpam-5384	223	10	(	(	PUNCT
ejpam-5384	223	11	ϕi	ϕi	ADP
ejpam-5384	223	12	+	+	NOUN
ejpam-5384	223	13	ϵ)[li(ϕi	ϵ)[li(ϕi	NUM
ejpam-5384	223	14	+	+	CCONJ
ejpam-5384	223	15	ϵ)−	ϵ)−	ADJ
ejpam-5384	223	16	li(ϕi	li(ϕi	NOUN
ejpam-5384	223	17	)	)	PUNCT
ejpam-5384	223	18	]	]	PUNCT
ejpam-5384	224	1	+	+	PUNCT
ejpam-5384	224	2	ϵli(ϕi	ϵli(ϕi	NUM
ejpam-5384	224	3	)	)	PUNCT
ejpam-5384	224	4	−	−	PROPN
ejpam-5384	224	5	(	(	PUNCT
ejpam-5384	224	6	ϕj	ϕj	INTJ
ejpam-5384	224	7	−	−	PROPN
ejpam-5384	224	8	ϵ	ϵ	X
ejpam-5384	224	9	)	)	PUNCT
ejpam-5384	225	1	[	[	X
ejpam-5384	225	2	lj(ϕj)−	lj(ϕj)−	X
ejpam-5384	225	3	lj(ϕj	lj(ϕj	NOUN
ejpam-5384	225	4	−	−	PROPN
ejpam-5384	225	5	ϵ)]−	ϵ)]−	NUM
ejpam-5384	225	6	ϵlj(ϕj	ϵlj(ϕj	X
ejpam-5384	225	7	)	)	PUNCT
ejpam-5384	225	8	is	be	AUX
ejpam-5384	225	9	negative	negative	ADJ
ejpam-5384	225	10	.	.	PUNCT
ejpam-5384	226	1	by	by	ADP
ejpam-5384	226	2	dividing	divide	VERB
ejpam-5384	226	3	with	with	ADP
ejpam-5384	226	4	ϵ	ϵ	NOUN
ejpam-5384	226	5	and	and	CCONJ
ejpam-5384	226	6	taking	take	VERB
ejpam-5384	226	7	the	the	DET
ejpam-5384	226	8	limit	limit	NOUN
ejpam-5384	226	9	with	with	ADP
ejpam-5384	226	10	ϵ	ϵ	PROPN
ejpam-5384	226	11	→	→	SYM
ejpam-5384	226	12	0	0	NUM
ejpam-5384	226	13	,	,	PUNCT
ejpam-5384	226	14	the	the	DET
ejpam-5384	226	15	above	above	ADJ
ejpam-5384	226	16	quantity	quantity	NOUN
ejpam-5384	226	17	becomes	become	VERB
ejpam-5384	226	18	li(ϕi	li(ϕi	ADJ
ejpam-5384	226	19	)	)	PUNCT
ejpam-5384	227	1	+	+	CCONJ
ejpam-5384	228	1	ϕil	ϕil	INTJ
ejpam-5384	228	2	′	′	NUM
ejpam-5384	228	3	i(ϕi)−	i(ϕi)−	NOUN
ejpam-5384	228	4	lj(ϕj)−	lj(ϕj)−	PUNCT
ejpam-5384	229	1	ϕjl	ϕjl	NOUN
ejpam-5384	229	2	′	′	NUM
ejpam-5384	229	3	j(ϕj	j(ϕj	NOUN
ejpam-5384	229	4	)	)	PUNCT
ejpam-5384	229	5	.	.	PUNCT
ejpam-5384	230	1	if	if	SCONJ
ejpam-5384	230	2	this	this	PRON
ejpam-5384	230	3	is	be	AUX
ejpam-5384	230	4	negative	negative	ADJ
ejpam-5384	230	5	,	,	PUNCT
ejpam-5384	230	6	the	the	DET
ejpam-5384	230	7	marginal	marginal	ADJ
ejpam-5384	230	8	difference	difference	NOUN
ejpam-5384	230	9	t+ϵ−t	t+ϵ−t	PROPN
ejpam-5384	230	10	is	be	AUX
ejpam-5384	230	11	negative	negative	ADJ
ejpam-5384	230	12	,	,	PUNCT
ejpam-5384	230	13	and	and	CCONJ
ejpam-5384	230	14	therefore	therefore	ADV
ejpam-5384	230	15	we	we	PRON
ejpam-5384	230	16	will	will	AUX
ejpam-5384	230	17	obtain	obtain	VERB
ejpam-5384	230	18	a	a	DET
ejpam-5384	230	19	better	well	ADJ
ejpam-5384	230	20	total	total	ADJ
ejpam-5384	230	21	latency	latency	NOUN
ejpam-5384	230	22	by	by	ADP
ejpam-5384	230	23	removing	remove	VERB
ejpam-5384	230	24	flow	flow	NOUN
ejpam-5384	230	25	from	from	ADP
ejpam-5384	230	26	ϕj	ϕj	ADV
ejpam-5384	230	27	and	and	CCONJ
ejpam-5384	230	28	adding	add	VERB
ejpam-5384	230	29	it	it	PRON
ejpam-5384	230	30	to	to	ADP
ejpam-5384	230	31	ϕi	ϕi	ADP
ejpam-5384	230	32	.	.	PUNCT
ejpam-5384	231	1	hence	hence	ADV
ejpam-5384	231	2	,	,	PUNCT
ejpam-5384	231	3	at	at	ADP
ejpam-5384	231	4	any	any	DET
ejpam-5384	231	5	given	give	VERB
ejpam-5384	231	6	flow	flow	NOUN
ejpam-5384	231	7	as	as	ADP
ejpam-5384	231	8	above	above	ADV
ejpam-5384	231	9	,	,	PUNCT
ejpam-5384	231	10	if	if	SCONJ
ejpam-5384	231	11	we	we	PRON
ejpam-5384	231	12	reduce	reduce	VERB
ejpam-5384	231	13	the	the	DET
ejpam-5384	231	14	flow	flow	NOUN
ejpam-5384	231	15	ϕj	ϕj	INTJ
ejpam-5384	231	16	by	by	ADP
ejpam-5384	231	17	ϵ	ϵ	X
ejpam-5384	231	18	while	while	SCONJ
ejpam-5384	231	19	at	at	ADP
ejpam-5384	231	20	the	the	DET
ejpam-5384	231	21	same	same	ADJ
ejpam-5384	231	22	time	time	NOUN
ejpam-5384	231	23	increase	increase	VERB
ejpam-5384	231	24	the	the	DET
ejpam-5384	231	25	flow	flow	NOUN
ejpam-5384	231	26	ϕi	ϕi	ADP
ejpam-5384	231	27	by	by	ADP
ejpam-5384	231	28	the	the	DET
ejpam-5384	231	29	same	same	ADJ
ejpam-5384	231	30	amount	amount	NOUN
ejpam-5384	231	31	we	we	PRON
ejpam-5384	231	32	will	will	AUX
ejpam-5384	231	33	obtain	obtain	VERB
ejpam-5384	231	34	a	a	DET
ejpam-5384	231	35	better	well	ADJ
ejpam-5384	231	36	total	total	ADJ
ejpam-5384	231	37	delay	delay	NOUN
ejpam-5384	231	38	if	if	SCONJ
ejpam-5384	231	39	li(ϕi	li(ϕi	ADJ
ejpam-5384	231	40	)	)	PUNCT
ejpam-5384	232	1	+	+	CCONJ
ejpam-5384	232	2	ϕil	ϕil	INTJ
ejpam-5384	232	3	′	′	NUM
ejpam-5384	232	4	i(ϕi	i(ϕi	ADJ
ejpam-5384	232	5	)	)	PUNCT
ejpam-5384	232	6	<	<	X
ejpam-5384	232	7	lj(ϕj	lj(ϕj	NOUN
ejpam-5384	232	8	)	)	PUNCT
ejpam-5384	232	9	+	+	CCONJ
ejpam-5384	232	10	ϕjl	ϕjl	NOUN
ejpam-5384	232	11	′	′	NUM
ejpam-5384	232	12	j(ϕj	j(ϕj	NOUN
ejpam-5384	232	13	)	)	PUNCT
ejpam-5384	232	14	.	.	PUNCT
ejpam-5384	233	1	(	(	PUNCT
ejpam-5384	233	2	2	2	X
ejpam-5384	233	3	)	)	PUNCT
ejpam-5384	233	4	similarly	similarly	ADV
ejpam-5384	233	5	we	we	PRON
ejpam-5384	233	6	can	can	AUX
ejpam-5384	233	7	consider	consider	VERB
ejpam-5384	233	8	the	the	DET
ejpam-5384	233	9	total	total	ADJ
ejpam-5384	233	10	delay	delay	NOUN
ejpam-5384	233	11	of	of	ADP
ejpam-5384	233	12	the	the	DET
ejpam-5384	233	13	flow	flow	NOUN
ejpam-5384	233	14	x−ϵ	x−ϵ	PUNCT
ejpam-5384	234	1	=	=	PUNCT
ejpam-5384	234	2	(	(	PUNCT
ejpam-5384	234	3	ϕi	ϕi	ADP
ejpam-5384	234	4	−	−	PROPN
ejpam-5384	234	5	ϵ	ϵ	NOUN
ejpam-5384	234	6	,	,	PUNCT
ejpam-5384	234	7	ϕj	ϕj	PROPN
ejpam-5384	234	8	+	+	CCONJ
ejpam-5384	234	9	ϵ	ϵ	X
ejpam-5384	234	10	)	)	PUNCT
ejpam-5384	234	11	∈	∈	PROPN
ejpam-5384	234	12	s1	s1	PROPN
ejpam-5384	234	13	a.	a.	PROPN
ejpam-5384	234	14	kalampakas	kalampakas	PROPN
ejpam-5384	234	15	/	/	SYM
ejpam-5384	234	16	eur	eur	PROPN
ejpam-5384	234	17	.	.	PUNCT
ejpam-5384	235	1	j.	j.	PROPN
ejpam-5384	235	2	pure	pure	PROPN
ejpam-5384	235	3	appl	appl	PROPN
ejpam-5384	235	4	.	.	PROPN
ejpam-5384	235	5	math	math	PROPN
ejpam-5384	235	6	,	,	PUNCT
ejpam-5384	235	7	17	17	NUM
ejpam-5384	235	8	(	(	PUNCT
ejpam-5384	235	9	4	4	NUM
ejpam-5384	235	10	)	)	PUNCT
ejpam-5384	235	11	(	(	PUNCT
ejpam-5384	235	12	2024	2024	NUM
ejpam-5384	235	13	)	)	PUNCT
ejpam-5384	235	14	,	,	PUNCT
ejpam-5384	235	15	2448	2448	NUM
ejpam-5384	235	16	-	-	SYM
ejpam-5384	235	17	2466	2466	NUM
ejpam-5384	235	18	2456	2456	NUM
ejpam-5384	235	19	as	as	SCONJ
ejpam-5384	235	20	follows	follow	VERB
ejpam-5384	235	21	t−ϵ	t−ϵ	ADV
ejpam-5384	235	22	=	=	SYM
ejpam-5384	235	23	(	(	PUNCT
ejpam-5384	235	24	ϕi	ϕi	ADP
ejpam-5384	235	25	−	−	PROPN
ejpam-5384	235	26	ϵ)li(ϕi	ϵ)li(ϕi	ADJ
ejpam-5384	235	27	−	−	PROPN
ejpam-5384	235	28	ϵ	ϵ	X
ejpam-5384	235	29	)	)	PUNCT
ejpam-5384	236	1	+	+	CCONJ
ejpam-5384	236	2	(	(	PUNCT
ejpam-5384	236	3	ϕj	ϕj	INTJ
ejpam-5384	236	4	+	+	NUM
ejpam-5384	236	5	ϵ)lj(ϕj	ϵ)lj(ϕj	NUM
ejpam-5384	236	6	+	+	CCONJ
ejpam-5384	236	7	ϵ	ϵ	X
ejpam-5384	236	8	)	)	PUNCT
ejpam-5384	236	9	.	.	PUNCT
ejpam-5384	237	1	in	in	ADP
ejpam-5384	237	2	this	this	DET
ejpam-5384	237	3	case	case	NOUN
ejpam-5384	237	4	for	for	ADP
ejpam-5384	237	5	the	the	DET
ejpam-5384	237	6	new	new	ADJ
ejpam-5384	237	7	delay	delay	NOUN
ejpam-5384	237	8	t−ϵ	t−ϵ	ADV
ejpam-5384	237	9	to	to	PART
ejpam-5384	237	10	be	be	AUX
ejpam-5384	237	11	less	less	ADJ
ejpam-5384	237	12	than	than	ADP
ejpam-5384	237	13	t	t	PROPN
ejpam-5384	237	14	,	,	PUNCT
ejpam-5384	237	15	the	the	DET
ejpam-5384	237	16	difference	difference	NOUN
ejpam-5384	237	17	t−ϵ	t−ϵ	ADP
ejpam-5384	237	18	−	−	PROPN
ejpam-5384	237	19	t	t	NOUN
ejpam-5384	237	20	must	must	AUX
ejpam-5384	237	21	be	be	AUX
ejpam-5384	237	22	negative	negative	ADJ
ejpam-5384	237	23	and	and	CCONJ
ejpam-5384	237	24	using	use	VERB
ejpam-5384	237	25	the	the	DET
ejpam-5384	237	26	same	same	ADJ
ejpam-5384	237	27	syllogism	syllogism	NOUN
ejpam-5384	237	28	it	it	PRON
ejpam-5384	237	29	turns	turn	VERB
ejpam-5384	237	30	out	out	ADP
ejpam-5384	237	31	that	that	SCONJ
ejpam-5384	237	32	the	the	DET
ejpam-5384	237	33	new	new	ADJ
ejpam-5384	237	34	total	total	ADJ
ejpam-5384	237	35	delay	delay	NOUN
ejpam-5384	237	36	t−ϵ	t−ϵ	ADP
ejpam-5384	237	37	−	−	PROPN
ejpam-5384	237	38	t	t	PROPN
ejpam-5384	237	39	is	be	AUX
ejpam-5384	237	40	lower	low	ADJ
ejpam-5384	237	41	than	than	ADP
ejpam-5384	237	42	t	t	PROPN
ejpam-5384	237	43	if	if	SCONJ
ejpam-5384	237	44	the	the	DET
ejpam-5384	237	45	quantity	quantity	NOUN
ejpam-5384	237	46	−li(ϕi)−	−li(ϕi)−	VERB
ejpam-5384	237	47	ϕil	ϕil	ADV
ejpam-5384	237	48	′	′	NUM
ejpam-5384	237	49	i(ϕi	i(ϕi	ADJ
ejpam-5384	237	50	)	)	PUNCT
ejpam-5384	237	51	+	+	NUM
ejpam-5384	237	52	lj(ϕj	lj(ϕj	NOUN
ejpam-5384	237	53	)	)	PUNCT
ejpam-5384	238	1	+	+	CCONJ
ejpam-5384	238	2	ϕjl	ϕjl	NOUN
ejpam-5384	238	3	′	′	NUM
ejpam-5384	238	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	238	5	)	)	PUNCT
ejpam-5384	238	6	is	be	AUX
ejpam-5384	238	7	negative	negative	ADJ
ejpam-5384	238	8	.	.	PUNCT
ejpam-5384	239	1	therefore	therefore	ADV
ejpam-5384	239	2	,	,	PUNCT
ejpam-5384	239	3	if	if	SCONJ
ejpam-5384	239	4	we	we	PRON
ejpam-5384	239	5	reduce	reduce	VERB
ejpam-5384	239	6	the	the	DET
ejpam-5384	239	7	flow	flow	NOUN
ejpam-5384	239	8	ϕi	ϕi	ADP
ejpam-5384	239	9	by	by	ADP
ejpam-5384	239	10	ϵ	ϵ	X
ejpam-5384	239	11	while	while	SCONJ
ejpam-5384	239	12	at	at	ADP
ejpam-5384	239	13	the	the	DET
ejpam-5384	239	14	same	same	ADJ
ejpam-5384	239	15	time	time	NOUN
ejpam-5384	239	16	increase	increase	VERB
ejpam-5384	239	17	the	the	DET
ejpam-5384	239	18	flow	flow	NOUN
ejpam-5384	239	19	ϕj	ϕj	INTJ
ejpam-5384	239	20	by	by	ADP
ejpam-5384	239	21	the	the	DET
ejpam-5384	239	22	same	same	ADJ
ejpam-5384	239	23	amount	amount	NOUN
ejpam-5384	239	24	we	we	PRON
ejpam-5384	239	25	will	will	AUX
ejpam-5384	239	26	obtain	obtain	VERB
ejpam-5384	239	27	a	a	DET
ejpam-5384	239	28	better	well	ADJ
ejpam-5384	239	29	total	total	ADJ
ejpam-5384	239	30	delay	delay	NOUN
ejpam-5384	239	31	if	if	SCONJ
ejpam-5384	239	32	li(ϕi	li(ϕi	ADJ
ejpam-5384	239	33	)	)	PUNCT
ejpam-5384	240	1	+	+	CCONJ
ejpam-5384	240	2	ϕil	ϕil	INTJ
ejpam-5384	240	3	′	′	NUM
ejpam-5384	240	4	i(ϕi	i(ϕi	ADJ
ejpam-5384	240	5	)	)	PUNCT
ejpam-5384	240	6	>	>	X
ejpam-5384	240	7	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	240	8	)	)	PUNCT
ejpam-5384	241	1	+	+	CCONJ
ejpam-5384	241	2	ϕjl	ϕjl	NOUN
ejpam-5384	241	3	′	′	NUM
ejpam-5384	241	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	241	5	)	)	PUNCT
ejpam-5384	241	6	.	.	PUNCT
ejpam-5384	242	1	(	(	PUNCT
ejpam-5384	242	2	3	3	X
ejpam-5384	242	3	)	)	PUNCT
ejpam-5384	242	4	by	by	AUX
ejpam-5384	242	5	consider	consider	VERB
ejpam-5384	242	6	both	both	DET
ejpam-5384	242	7	equations	equation	NOUN
ejpam-5384	242	8	2	2	NUM
ejpam-5384	242	9	and	and	CCONJ
ejpam-5384	242	10	3	3	NUM
ejpam-5384	242	11	we	we	PRON
ejpam-5384	242	12	deduce	deduce	VERB
ejpam-5384	242	13	that	that	SCONJ
ejpam-5384	242	14	an	an	DET
ejpam-5384	242	15	optimal	optimal	ADJ
ejpam-5384	242	16	flow	flow	NOUN
ejpam-5384	242	17	(	(	PUNCT
ejpam-5384	242	18	ϕi	ϕi	PROPN
ejpam-5384	242	19	,	,	PUNCT
ejpam-5384	242	20	ϕj	ϕj	INTJ
ejpam-5384	242	21	)	)	PUNCT
ejpam-5384	242	22	∈	∈	PROPN
ejpam-5384	242	23	ints1	ints1	NOUN
ejpam-5384	242	24	implies	imply	VERB
ejpam-5384	242	25	li(ϕi	li(ϕi	ADJ
ejpam-5384	242	26	)	)	PUNCT
ejpam-5384	243	1	+	+	CCONJ
ejpam-5384	243	2	ϕil	ϕil	INTJ
ejpam-5384	243	3	′	′	NUM
ejpam-5384	243	4	i(ϕi	i(ϕi	ADJ
ejpam-5384	243	5	)	)	PUNCT
ejpam-5384	243	6	=	=	SYM
ejpam-5384	243	7	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	243	8	)	)	PUNCT
ejpam-5384	244	1	+	+	CCONJ
ejpam-5384	244	2	ϕjl	ϕjl	NOUN
ejpam-5384	244	3	′	′	NUM
ejpam-5384	244	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	244	5	)	)	PUNCT
ejpam-5384	244	6	,	,	PUNCT
ejpam-5384	244	7	(	(	PUNCT
ejpam-5384	244	8	4	4	X
ejpam-5384	244	9	)	)	PUNCT
ejpam-5384	244	10	which	which	PRON
ejpam-5384	244	11	completes	complete	VERB
ejpam-5384	244	12	the	the	DET
ejpam-5384	244	13	proof	proof	NOUN
ejpam-5384	244	14	.	.	PUNCT
ejpam-5384	245	1	we	we	PRON
ejpam-5384	245	2	can	can	AUX
ejpam-5384	245	3	generalize	generalize	VERB
ejpam-5384	245	4	the	the	DET
ejpam-5384	245	5	above	above	ADV
ejpam-5384	245	6	as	as	SCONJ
ejpam-5384	245	7	follows	follow	VERB
ejpam-5384	245	8	.	.	PUNCT
ejpam-5384	246	1	theorem	theorem	NOUN
ejpam-5384	246	2	1	1	X
ejpam-5384	246	3	.	.	X
ejpam-5384	246	4	consider	consider	VERB
ejpam-5384	246	5	a	a	DET
ejpam-5384	246	6	network	network	NOUN
ejpam-5384	246	7	nn	nn	X
ejpam-5384	246	8	=	=	SYM
ejpam-5384	246	9	(	(	PUNCT
ejpam-5384	246	10	l1(x	l1(x	NOUN
ejpam-5384	246	11	)	)	PUNCT
ejpam-5384	246	12	,	,	PUNCT
ejpam-5384	246	13	.	.	PUNCT
ejpam-5384	246	14	.	.	PUNCT
ejpam-5384	247	1	.	.	PUNCT
ejpam-5384	248	1	,	,	PUNCT
ejpam-5384	248	2	ln(x	ln(x	X
ejpam-5384	248	3	)	)	PUNCT
ejpam-5384	248	4	)	)	PUNCT
ejpam-5384	248	5	,	,	PUNCT
ejpam-5384	248	6	then	then	ADV
ejpam-5384	248	7	it	it	PRON
ejpam-5384	248	8	holds	hold	VERB
ejpam-5384	248	9	li(ϕi	li(ϕi	ADJ
ejpam-5384	248	10	)	)	PUNCT
ejpam-5384	249	1	+	+	CCONJ
ejpam-5384	249	2	ϕil	ϕil	INTJ
ejpam-5384	249	3	′	′	NUM
ejpam-5384	249	4	i(ϕi	i(ϕi	ADJ
ejpam-5384	249	5	)	)	PUNCT
ejpam-5384	249	6	=	=	SYM
ejpam-5384	249	7	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	249	8	)	)	PUNCT
ejpam-5384	250	1	+	+	CCONJ
ejpam-5384	250	2	ϕjl	ϕjl	NOUN
ejpam-5384	250	3	′	′	NUM
ejpam-5384	250	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	250	5	)	)	PUNCT
ejpam-5384	250	6	,	,	PUNCT
ejpam-5384	250	7	for	for	ADP
ejpam-5384	250	8	every	every	DET
ejpam-5384	250	9	i	i	PROPN
ejpam-5384	250	10	,	,	PUNCT
ejpam-5384	250	11	j	j	PROPN
ejpam-5384	250	12	∈	∈	PROPN
ejpam-5384	250	13	in	in	ADP
ejpam-5384	250	14	with	with	ADP
ejpam-5384	250	15	ϕi	ϕi	ADP
ejpam-5384	250	16	,	,	PUNCT
ejpam-5384	250	17	ϕj	ϕj	INTJ
ejpam-5384	250	18	>	>	X
ejpam-5384	250	19	0	0	PUNCT
ejpam-5384	250	20	and	and	CCONJ
ejpam-5384	250	21	li(0	li(0	PROPN
ejpam-5384	250	22	)	)	PUNCT
ejpam-5384	250	23	≥	≥	NOUN
ejpam-5384	250	24	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	250	25	)	)	PUNCT
ejpam-5384	251	1	+	+	CCONJ
ejpam-5384	251	2	ϕjl	ϕjl	NOUN
ejpam-5384	251	3	′	′	NUM
ejpam-5384	251	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	251	5	)	)	PUNCT
ejpam-5384	251	6	,	,	PUNCT
ejpam-5384	251	7	for	for	ADP
ejpam-5384	251	8	every	every	DET
ejpam-5384	251	9	i	i	PROPN
ejpam-5384	251	10	,	,	PUNCT
ejpam-5384	251	11	j	j	PROPN
ejpam-5384	251	12	∈	∈	PROPN
ejpam-5384	251	13	in	in	ADP
ejpam-5384	251	14	with	with	ADP
ejpam-5384	251	15	ϕi	ϕi	ADP
ejpam-5384	251	16	=	=	SYM
ejpam-5384	251	17	0	0	PROPN
ejpam-5384	251	18	,	,	PUNCT
ejpam-5384	251	19	ϕj	ϕj	ADP
ejpam-5384	251	20	>	>	X
ejpam-5384	251	21	0	0	NUM
ejpam-5384	251	22	,	,	PUNCT
ejpam-5384	251	23	provided	provide	VERB
ejpam-5384	251	24	that	that	PRON
ejpam-5384	251	25	ϕ	ϕ	NOUN
ejpam-5384	251	26	=	=	PUNCT
ejpam-5384	251	27	(	(	PUNCT
ejpam-5384	251	28	ϕ1	ϕ1	NOUN
ejpam-5384	251	29	,	,	PUNCT
ejpam-5384	251	30	.	.	PUNCT
ejpam-5384	251	31	.	.	PUNCT
ejpam-5384	252	1	.	.	PUNCT
ejpam-5384	253	1	,	,	PUNCT
ejpam-5384	253	2	ϕn	ϕn	X
ejpam-5384	253	3	)	)	PUNCT
ejpam-5384	253	4	∈	∈	PROPN
ejpam-5384	253	5	sn−1	sn−1	PROPN
ejpam-5384	253	6	is	be	AUX
ejpam-5384	253	7	system	system	NOUN
ejpam-5384	253	8	optimum	optimum	ADJ
ejpam-5384	253	9	of	of	ADP
ejpam-5384	253	10	the	the	DET
ejpam-5384	253	11	network	network	NOUN
ejpam-5384	253	12	.	.	PUNCT
ejpam-5384	254	1	proof	proof	NOUN
ejpam-5384	254	2	.	.	PUNCT
ejpam-5384	255	1	we	we	PRON
ejpam-5384	255	2	only	only	ADV
ejpam-5384	255	3	have	have	VERB
ejpam-5384	255	4	to	to	PART
ejpam-5384	255	5	consider	consider	VERB
ejpam-5384	255	6	the	the	DET
ejpam-5384	255	7	case	case	NOUN
ejpam-5384	255	8	of	of	ADP
ejpam-5384	255	9	a	a	DET
ejpam-5384	255	10	system	system	NOUN
ejpam-5384	255	11	optimum	optimum	NOUN
ejpam-5384	255	12	ϕ	ϕ	X
ejpam-5384	255	13	=	=	PUNCT
ejpam-5384	255	14	(	(	PUNCT
ejpam-5384	255	15	ϕ1	ϕ1	NOUN
ejpam-5384	255	16	,	,	PUNCT
ejpam-5384	255	17	.	.	PUNCT
ejpam-5384	255	18	.	.	PUNCT
ejpam-5384	256	1	.	.	PUNCT
ejpam-5384	257	1	,	,	PUNCT
ejpam-5384	257	2	ϕn	ϕn	X
ejpam-5384	257	3	)	)	PUNCT
ejpam-5384	257	4	∈	∈	PROPN
ejpam-5384	257	5	sn−1	sn−1	PROPN
ejpam-5384	257	6	on	on	ADP
ejpam-5384	257	7	nn	nn	INTJ
ejpam-5384	257	8	such	such	ADJ
ejpam-5384	257	9	that	that	SCONJ
ejpam-5384	257	10	there	there	PRON
ejpam-5384	257	11	exists	exist	VERB
ejpam-5384	257	12	an	an	DET
ejpam-5384	257	13	i	i	PROPN
ejpam-5384	257	14	∈	∈	PROPN
ejpam-5384	257	15	in	in	ADP
ejpam-5384	257	16	with	with	ADP
ejpam-5384	257	17	ϕi	ϕi	ADP
ejpam-5384	257	18	=	=	NOUN
ejpam-5384	257	19	0	0	PROPN
ejpam-5384	257	20	.	.	PUNCT
ejpam-5384	258	1	using	use	VERB
ejpam-5384	258	2	a	a	DET
ejpam-5384	258	3	similar	similar	ADJ
ejpam-5384	258	4	argument	argument	NOUN
ejpam-5384	258	5	as	as	ADP
ejpam-5384	258	6	in	in	ADP
ejpam-5384	258	7	the	the	DET
ejpam-5384	258	8	previous	previous	ADJ
ejpam-5384	258	9	proposition	proposition	NOUN
ejpam-5384	258	10	we	we	PRON
ejpam-5384	258	11	get	get	VERB
ejpam-5384	258	12	that	that	SCONJ
ejpam-5384	258	13	if	if	SCONJ
ejpam-5384	258	14	there	there	PRON
ejpam-5384	258	15	exists	exist	VERB
ejpam-5384	258	16	any	any	DET
ejpam-5384	258	17	j	j	PROPN
ejpam-5384	258	18	∈	∈	PROPN
ejpam-5384	258	19	in	in	ADP
ejpam-5384	258	20	such	such	ADJ
ejpam-5384	258	21	that	that	DET
ejpam-5384	258	22	li(ϕi	li(ϕi	NOUN
ejpam-5384	258	23	)	)	PUNCT
ejpam-5384	259	1	+	+	CCONJ
ejpam-5384	259	2	ϕil	ϕil	INTJ
ejpam-5384	259	3	′	′	NUM
ejpam-5384	259	4	i(ϕi	i(ϕi	ADJ
ejpam-5384	259	5	)	)	PUNCT
ejpam-5384	259	6	<	<	X
ejpam-5384	259	7	lj(ϕj	lj(ϕj	NOUN
ejpam-5384	259	8	)	)	PUNCT
ejpam-5384	259	9	+	+	CCONJ
ejpam-5384	259	10	ϕjl	ϕjl	NOUN
ejpam-5384	259	11	′	′	NUM
ejpam-5384	259	12	j(ϕj	j(ϕj	NOUN
ejpam-5384	259	13	)	)	PUNCT
ejpam-5384	259	14	,	,	PUNCT
ejpam-5384	259	15	(	(	PUNCT
ejpam-5384	259	16	5	5	X
ejpam-5384	259	17	)	)	PUNCT
ejpam-5384	259	18	then	then	ADV
ejpam-5384	259	19	we	we	PRON
ejpam-5384	259	20	will	will	AUX
ejpam-5384	259	21	achieve	achieve	VERB
ejpam-5384	259	22	lower	low	ADJ
ejpam-5384	259	23	total	total	ADJ
ejpam-5384	259	24	delay	delay	NOUN
ejpam-5384	259	25	by	by	ADP
ejpam-5384	259	26	ϵ-reducing	ϵ-reduce	VERB
ejpam-5384	259	27	ϕj	ϕj	ADP
ejpam-5384	259	28	while	while	SCONJ
ejpam-5384	259	29	at	at	ADP
ejpam-5384	259	30	the	the	DET
ejpam-5384	259	31	same	same	ADJ
ejpam-5384	259	32	time	time	NOUN
ejpam-5384	259	33	ϵ-increasing	ϵ-increase	VERB
ejpam-5384	259	34	ϕi	ϕi	ADP
ejpam-5384	259	35	.	.	PUNCT
ejpam-5384	260	1	since	since	SCONJ
ejpam-5384	260	2	x	x	PROPN
ejpam-5384	260	3	∈	∈	PROPN
ejpam-5384	260	4	sn−1	sn−1	PROPN
ejpam-5384	260	5	is	be	AUX
ejpam-5384	260	6	system	system	NOUN
ejpam-5384	260	7	optimum	optimum	NOUN
ejpam-5384	260	8	this	this	PRON
ejpam-5384	260	9	is	be	AUX
ejpam-5384	260	10	not	not	PART
ejpam-5384	260	11	possible	possible	ADJ
ejpam-5384	260	12	.	.	PUNCT
ejpam-5384	261	1	thus	thus	ADV
ejpam-5384	261	2	,	,	PUNCT
ejpam-5384	261	3	taking	take	VERB
ejpam-5384	261	4	also	also	ADV
ejpam-5384	261	5	into	into	ADP
ejpam-5384	261	6	account	account	NOUN
ejpam-5384	261	7	that	that	SCONJ
ejpam-5384	261	8	ϕi	ϕi	ADP
ejpam-5384	261	9	=	=	SYM
ejpam-5384	261	10	0	0	NUM
ejpam-5384	261	11	,	,	PUNCT
ejpam-5384	261	12	it	it	PRON
ejpam-5384	261	13	must	must	AUX
ejpam-5384	261	14	hold	hold	VERB
ejpam-5384	261	15	li(0	li(0	PROPN
ejpam-5384	261	16	)	)	PUNCT
ejpam-5384	261	17	≥	≥	NOUN
ejpam-5384	261	18	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	261	19	)	)	PUNCT
ejpam-5384	262	1	+	+	CCONJ
ejpam-5384	262	2	ϕjl	ϕjl	NOUN
ejpam-5384	262	3	′	′	NUM
ejpam-5384	262	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	262	5	)	)	PUNCT
ejpam-5384	262	6	,	,	PUNCT
ejpam-5384	262	7	for	for	ADP
ejpam-5384	262	8	every	every	DET
ejpam-5384	262	9	i	i	PROPN
ejpam-5384	262	10	,	,	PUNCT
ejpam-5384	262	11	j	j	PROPN
ejpam-5384	262	12	∈	∈	PROPN
ejpam-5384	262	13	in	in	ADP
ejpam-5384	262	14	with	with	ADP
ejpam-5384	262	15	ϕi	ϕi	ADP
ejpam-5384	262	16	=	=	SYM
ejpam-5384	262	17	0	0	NUM
ejpam-5384	262	18	and	and	CCONJ
ejpam-5384	262	19	ϕj	ϕj	INTJ
ejpam-5384	262	20	>	>	X
ejpam-5384	262	21	0	0	X
ejpam-5384	262	22	.	.	PUNCT
ejpam-5384	263	1	now	now	ADV
ejpam-5384	263	2	,	,	PUNCT
ejpam-5384	263	3	for	for	ADP
ejpam-5384	263	4	differentiable	differentiable	ADJ
ejpam-5384	263	5	latency	latency	NOUN
ejpam-5384	263	6	functions	function	NOUN
ejpam-5384	263	7	li(x	li(x	NOUN
ejpam-5384	263	8	)	)	PUNCT
ejpam-5384	263	9	,	,	PUNCT
ejpam-5384	263	10	we	we	PRON
ejpam-5384	263	11	construct	construct	VERB
ejpam-5384	263	12	the	the	DET
ejpam-5384	263	13	following	follow	VERB
ejpam-5384	263	14	functions	function	NOUN
ejpam-5384	263	15	pi(x	pi(x	NOUN
ejpam-5384	263	16	)	)	PUNCT
ejpam-5384	263	17	=	=	SYM
ejpam-5384	264	1	li(x	li(x	X
ejpam-5384	264	2	)	)	PUNCT
ejpam-5384	265	1	+	+	CCONJ
ejpam-5384	265	2	xl′i(x	xl′i(x	ADJ
ejpam-5384	265	3	)	)	PUNCT
ejpam-5384	265	4	.	.	PUNCT
ejpam-5384	266	1	in	in	ADP
ejpam-5384	266	2	this	this	DET
ejpam-5384	266	3	way	way	NOUN
ejpam-5384	266	4	,	,	PUNCT
ejpam-5384	266	5	for	for	ADP
ejpam-5384	266	6	every	every	DET
ejpam-5384	266	7	network	network	NOUN
ejpam-5384	266	8	nn	nn	PROPN
ejpam-5384	266	9	=	=	SYM
ejpam-5384	266	10	(	(	PUNCT
ejpam-5384	266	11	l1(x	l1(x	NOUN
ejpam-5384	266	12	)	)	PUNCT
ejpam-5384	266	13	,	,	PUNCT
ejpam-5384	266	14	.	.	PUNCT
ejpam-5384	266	15	.	.	PUNCT
ejpam-5384	266	16	.	.	PUNCT
ejpam-5384	267	1	,	,	PUNCT
ejpam-5384	267	2	ln(x	ln(x	X
ejpam-5384	267	3	)	)	PUNCT
ejpam-5384	267	4	)	)	PUNCT
ejpam-5384	267	5	,	,	PUNCT
ejpam-5384	267	6	we	we	PRON
ejpam-5384	267	7	construct	construct	VERB
ejpam-5384	267	8	a	a	DET
ejpam-5384	267	9	corresponding	corresponding	ADJ
ejpam-5384	267	10	(	(	PUNCT
ejpam-5384	267	11	pigovian	pigovian	NOUN
ejpam-5384	267	12	)	)	PUNCT
ejpam-5384	267	13	network	network	NOUN
ejpam-5384	267	14	pnn	pnn	PROPN
ejpam-5384	267	15	=	=	PROPN
ejpam-5384	267	16	(	(	PUNCT
ejpam-5384	267	17	p1(x	p1(x	NOUN
ejpam-5384	267	18	)	)	PUNCT
ejpam-5384	267	19	,	,	PUNCT
ejpam-5384	267	20	.	.	PUNCT
ejpam-5384	267	21	.	.	PUNCT
ejpam-5384	268	1	.	.	PUNCT
ejpam-5384	269	1	,	,	PUNCT
ejpam-5384	269	2	pn(x	pn(x	ADJ
ejpam-5384	269	3	)	)	PUNCT
ejpam-5384	269	4	)	)	PUNCT
ejpam-5384	269	5	.	.	PUNCT
ejpam-5384	270	1	theorem	theorem	NOUN
ejpam-5384	270	2	1	1	NUM
ejpam-5384	270	3	is	be	AUX
ejpam-5384	270	4	then	then	ADV
ejpam-5384	270	5	reformulated	reformulate	VERB
ejpam-5384	270	6	to	to	PART
ejpam-5384	270	7	describe	describe	VERB
ejpam-5384	270	8	the	the	DET
ejpam-5384	270	9	relationship	relationship	NOUN
ejpam-5384	270	10	between	between	ADP
ejpam-5384	270	11	the	the	DET
ejpam-5384	270	12	two	two	NUM
ejpam-5384	270	13	networks	network	NOUN
ejpam-5384	270	14	.	.	PUNCT
ejpam-5384	271	1	a.	a.	PROPN
ejpam-5384	271	2	kalampakas	kalampakas	PROPN
ejpam-5384	271	3	/	/	SYM
ejpam-5384	271	4	eur	eur	PROPN
ejpam-5384	271	5	.	.	PUNCT
ejpam-5384	272	1	j.	j.	PROPN
ejpam-5384	272	2	pure	pure	PROPN
ejpam-5384	272	3	appl	appl	PROPN
ejpam-5384	272	4	.	.	PROPN
ejpam-5384	272	5	math	math	PROPN
ejpam-5384	272	6	,	,	PUNCT
ejpam-5384	272	7	17	17	NUM
ejpam-5384	272	8	(	(	PUNCT
ejpam-5384	272	9	4	4	NUM
ejpam-5384	272	10	)	)	PUNCT
ejpam-5384	272	11	(	(	PUNCT
ejpam-5384	272	12	2024	2024	NUM
ejpam-5384	272	13	)	)	PUNCT
ejpam-5384	272	14	,	,	PUNCT
ejpam-5384	272	15	2448	2448	NUM
ejpam-5384	272	16	-	-	SYM
ejpam-5384	272	17	2466	2466	NUM
ejpam-5384	272	18	2457	2457	NUM
ejpam-5384	272	19	theorem	theorem	NOUN
ejpam-5384	272	20	2	2	NUM
ejpam-5384	272	21	.	.	X
ejpam-5384	272	22	consider	consider	VERB
ejpam-5384	272	23	a	a	DET
ejpam-5384	272	24	network	network	NOUN
ejpam-5384	272	25	nn	nn	X
ejpam-5384	273	1	=	=	SYM
ejpam-5384	274	1	(	(	PUNCT
ejpam-5384	274	2	l1(x	l1(x	NOUN
ejpam-5384	274	3	)	)	PUNCT
ejpam-5384	274	4	,	,	PUNCT
ejpam-5384	274	5	.	.	PUNCT
ejpam-5384	274	6	.	.	PUNCT
ejpam-5384	275	1	.	.	PUNCT
ejpam-5384	276	1	,	,	PUNCT
ejpam-5384	276	2	ln(x	ln(x	X
ejpam-5384	276	3	)	)	PUNCT
ejpam-5384	276	4	)	)	PUNCT
ejpam-5384	277	1	and	and	CCONJ
ejpam-5384	277	2	a	a	DET
ejpam-5384	277	3	flow	flow	NOUN
ejpam-5384	277	4	ϕ	ϕ	NOUN
ejpam-5384	277	5	=	=	PUNCT
ejpam-5384	277	6	(	(	PUNCT
ejpam-5384	277	7	ϕ1	ϕ1	NOUN
ejpam-5384	277	8	,	,	PUNCT
ejpam-5384	277	9	.	.	PUNCT
ejpam-5384	277	10	.	.	PUNCT
ejpam-5384	278	1	.	.	PUNCT
ejpam-5384	279	1	,	,	PUNCT
ejpam-5384	279	2	ϕn	ϕn	X
ejpam-5384	279	3	)	)	PUNCT
ejpam-5384	279	4	∈	∈	PROPN
ejpam-5384	279	5	sn−1	sn−1	PROPN
ejpam-5384	279	6	,	,	PUNCT
ejpam-5384	279	7	then	then	ADV
ejpam-5384	279	8	if	if	SCONJ
ejpam-5384	279	9	ϕ	ϕ	NOUN
ejpam-5384	279	10	is	be	AUX
ejpam-5384	279	11	system	system	NOUN
ejpam-5384	279	12	optimum	optimum	ADJ
ejpam-5384	279	13	of	of	ADP
ejpam-5384	279	14	nn	nn	INTJ
ejpam-5384	279	15	it	it	PRON
ejpam-5384	279	16	is	be	AUX
ejpam-5384	279	17	also	also	ADV
ejpam-5384	279	18	user	user	NOUN
ejpam-5384	279	19	equilibrium	equilibrium	NOUN
ejpam-5384	279	20	of	of	ADP
ejpam-5384	279	21	pnn	pnn	PROPN
ejpam-5384	279	22	=	=	PUNCT
ejpam-5384	279	23	(	(	PUNCT
ejpam-5384	279	24	p1(x	p1(x	NOUN
ejpam-5384	279	25	)	)	PUNCT
ejpam-5384	279	26	,	,	PUNCT
ejpam-5384	279	27	.	.	PUNCT
ejpam-5384	279	28	.	.	PUNCT
ejpam-5384	279	29	.	.	PUNCT
ejpam-5384	280	1	,	,	PUNCT
ejpam-5384	280	2	pn(x	pn(x	ADJ
ejpam-5384	280	3	)	)	PUNCT
ejpam-5384	280	4	)	)	PUNCT
ejpam-5384	280	5	.	.	PUNCT
ejpam-5384	281	1	proposition	proposition	NOUN
ejpam-5384	281	2	1	1	NUM
ejpam-5384	281	3	allows	allow	VERB
ejpam-5384	281	4	us	we	PRON
ejpam-5384	281	5	now	now	ADV
ejpam-5384	281	6	the	the	DET
ejpam-5384	281	7	achieve	achieve	VERB
ejpam-5384	281	8	the	the	DET
ejpam-5384	281	9	following	follow	VERB
ejpam-5384	281	10	uniqueness	uniqueness	NOUN
ejpam-5384	281	11	result	result	NOUN
ejpam-5384	281	12	.	.	PUNCT
ejpam-5384	282	1	proposition	proposition	NOUN
ejpam-5384	282	2	3	3	NUM
ejpam-5384	282	3	.	.	PUNCT
ejpam-5384	282	4	a	a	DET
ejpam-5384	282	5	convex	convex	PROPN
ejpam-5384	282	6	network	network	NOUN
ejpam-5384	282	7	nn	nn	X
ejpam-5384	282	8	=	=	SYM
ejpam-5384	282	9	(	(	PUNCT
ejpam-5384	282	10	l1(x	l1(x	NOUN
ejpam-5384	282	11	)	)	PUNCT
ejpam-5384	282	12	,	,	PUNCT
ejpam-5384	282	13	.	.	PUNCT
ejpam-5384	282	14	.	.	PUNCT
ejpam-5384	283	1	.	.	PUNCT
ejpam-5384	284	1	,	,	PUNCT
ejpam-5384	284	2	ln(x	ln(x	X
ejpam-5384	284	3	)	)	PUNCT
ejpam-5384	284	4	)	)	PUNCT
ejpam-5384	285	1	has	have	VERB
ejpam-5384	285	2	a	a	DET
ejpam-5384	285	3	unique	unique	ADJ
ejpam-5384	285	4	system	system	NOUN
ejpam-5384	285	5	optimum	optimum	NOUN
ejpam-5384	285	6	.	.	PUNCT
ejpam-5384	286	1	proof	proof	NOUN
ejpam-5384	286	2	.	.	PUNCT
ejpam-5384	287	1	all	all	DET
ejpam-5384	287	2	the	the	DET
ejpam-5384	287	3	latency	latency	NOUN
ejpam-5384	287	4	functions	function	NOUN
ejpam-5384	287	5	are	be	AUX
ejpam-5384	287	6	differentiable	differentiable	ADJ
ejpam-5384	287	7	in	in	ADP
ejpam-5384	287	8	[	[	X
ejpam-5384	287	9	0	0	NUM
ejpam-5384	287	10	,	,	PUNCT
ejpam-5384	287	11	1	1	NUM
ejpam-5384	287	12	]	]	PUNCT
ejpam-5384	287	13	,	,	PUNCT
ejpam-5384	287	14	hence	hence	ADV
ejpam-5384	287	15	the	the	DET
ejpam-5384	287	16	total	total	ADJ
ejpam-5384	287	17	delay	delay	NOUN
ejpam-5384	287	18	n∑	n∑	PROPN
ejpam-5384	287	19	i=1	i=1	PROPN
ejpam-5384	287	20	ϕili(ϕi	ϕili(ϕi	PROPN
ejpam-5384	287	21	)	)	PUNCT
ejpam-5384	287	22	has	have	VERB
ejpam-5384	287	23	at	at	ADV
ejpam-5384	287	24	least	least	ADJ
ejpam-5384	287	25	one	one	NUM
ejpam-5384	287	26	minimum	minimum	NOUN
ejpam-5384	287	27	.	.	PUNCT
ejpam-5384	288	1	therefore	therefore	ADV
ejpam-5384	288	2	,	,	PUNCT
ejpam-5384	288	3	there	there	PRON
ejpam-5384	288	4	is	be	VERB
ejpam-5384	288	5	at	at	ADV
ejpam-5384	288	6	least	least	ADJ
ejpam-5384	288	7	one	one	NUM
ejpam-5384	288	8	system	system	NOUN
ejpam-5384	288	9	optimum	optimum	NOUN
ejpam-5384	288	10	of	of	ADP
ejpam-5384	288	11	nn	nn	PROPN
ejpam-5384	288	12	.	.	PROPN
ejpam-5384	288	13	moreover	moreover	ADV
ejpam-5384	288	14	,	,	PUNCT
ejpam-5384	288	15	we	we	PRON
ejpam-5384	288	16	know	know	VERB
ejpam-5384	288	17	that	that	SCONJ
ejpam-5384	288	18	the	the	DET
ejpam-5384	288	19	latency	latency	NOUN
ejpam-5384	288	20	functions	function	NOUN
ejpam-5384	288	21	are	be	AUX
ejpam-5384	288	22	differentiable	differentiable	ADJ
ejpam-5384	288	23	and	and	CCONJ
ejpam-5384	288	24	convex	convex	ADJ
ejpam-5384	288	25	and	and	CCONJ
ejpam-5384	288	26	so	so	ADV
ejpam-5384	288	27	pi(x	pi(x	NUM
ejpam-5384	288	28	)	)	PUNCT
ejpam-5384	288	29	will	will	AUX
ejpam-5384	288	30	be	be	AUX
ejpam-5384	288	31	strictly	strictly	ADV
ejpam-5384	288	32	increasing	increase	VERB
ejpam-5384	288	33	and	and	CCONJ
ejpam-5384	288	34	continuous	continuous	ADJ
ejpam-5384	288	35	.	.	PUNCT
ejpam-5384	289	1	thus	thus	ADV
ejpam-5384	289	2	,	,	PUNCT
ejpam-5384	289	3	according	accord	VERB
ejpam-5384	289	4	to	to	ADP
ejpam-5384	289	5	proposition	proposition	NOUN
ejpam-5384	289	6	1	1	NUM
ejpam-5384	289	7	there	there	PRON
ejpam-5384	289	8	is	be	VERB
ejpam-5384	289	9	a	a	DET
ejpam-5384	289	10	unique	unique	ADJ
ejpam-5384	289	11	user	user	NOUN
ejpam-5384	289	12	equilibrium	equilibrium	NOUN
ejpam-5384	289	13	of	of	ADP
ejpam-5384	289	14	pnn	pnn	PROPN
ejpam-5384	289	15	=	=	PUNCT
ejpam-5384	289	16	(	(	PUNCT
ejpam-5384	289	17	p1(x	p1(x	NOUN
ejpam-5384	289	18	)	)	PUNCT
ejpam-5384	289	19	,	,	PUNCT
ejpam-5384	289	20	.	.	PUNCT
ejpam-5384	289	21	.	.	PUNCT
ejpam-5384	290	1	.	.	PUNCT
ejpam-5384	291	1	,	,	PUNCT
ejpam-5384	291	2	pn(x	pn(x	ADJ
ejpam-5384	291	3	)	)	PUNCT
ejpam-5384	291	4	)	)	PUNCT
ejpam-5384	291	5	.	.	PUNCT
ejpam-5384	292	1	ther	ther	PROPN
ejpam-5384	292	2	result	result	NOUN
ejpam-5384	292	3	follows	follow	VERB
ejpam-5384	292	4	by	by	ADP
ejpam-5384	292	5	applying	apply	VERB
ejpam-5384	292	6	theorem	theorem	NOUN
ejpam-5384	292	7	2	2	NUM
ejpam-5384	292	8	.	.	PUNCT
ejpam-5384	293	1	the	the	DET
ejpam-5384	293	2	following	follow	VERB
ejpam-5384	293	3	characterization	characterization	NOUN
ejpam-5384	293	4	of	of	ADP
ejpam-5384	293	5	system	system	NOUN
ejpam-5384	293	6	optimums	optimum	NOUN
ejpam-5384	293	7	is	be	AUX
ejpam-5384	293	8	achieved	achieve	VERB
ejpam-5384	293	9	by	by	ADP
ejpam-5384	293	10	combining	combine	VERB
ejpam-5384	293	11	the	the	DET
ejpam-5384	293	12	previous	previous	ADJ
ejpam-5384	293	13	results	result	NOUN
ejpam-5384	293	14	.	.	PUNCT
ejpam-5384	294	1	theorem	theorem	NOUN
ejpam-5384	294	2	3	3	NUM
ejpam-5384	294	3	.	.	PUNCT
ejpam-5384	294	4	given	give	VERB
ejpam-5384	294	5	a	a	DET
ejpam-5384	294	6	convex	convex	NOUN
ejpam-5384	294	7	network	network	NOUN
ejpam-5384	294	8	nn	nn	X
ejpam-5384	294	9	=	=	SYM
ejpam-5384	294	10	(	(	PUNCT
ejpam-5384	294	11	l1(x	l1(x	NOUN
ejpam-5384	294	12	)	)	PUNCT
ejpam-5384	294	13	,	,	PUNCT
ejpam-5384	294	14	.	.	PUNCT
ejpam-5384	294	15	.	.	PUNCT
ejpam-5384	295	1	.	.	PUNCT
ejpam-5384	296	1	,	,	PUNCT
ejpam-5384	296	2	ln(x	ln(x	X
ejpam-5384	296	3	)	)	PUNCT
ejpam-5384	296	4	)	)	PUNCT
ejpam-5384	297	1	and	and	CCONJ
ejpam-5384	297	2	a	a	DET
ejpam-5384	297	3	flow	flow	NOUN
ejpam-5384	297	4	ϕ	ϕ	NOUN
ejpam-5384	297	5	=	=	PUNCT
ejpam-5384	297	6	(	(	PUNCT
ejpam-5384	297	7	ϕ1	ϕ1	NOUN
ejpam-5384	297	8	,	,	PUNCT
ejpam-5384	297	9	.	.	PUNCT
ejpam-5384	297	10	.	.	PUNCT
ejpam-5384	298	1	.	.	PUNCT
ejpam-5384	299	1	,	,	PUNCT
ejpam-5384	299	2	ϕn	ϕn	X
ejpam-5384	299	3	)	)	PUNCT
ejpam-5384	299	4	∈	∈	PROPN
ejpam-5384	299	5	sn−1	sn−1	PROPN
ejpam-5384	299	6	the	the	DET
ejpam-5384	299	7	following	follow	VERB
ejpam-5384	299	8	conditions	condition	NOUN
ejpam-5384	299	9	are	be	AUX
ejpam-5384	299	10	equivalent	equivalent	ADJ
ejpam-5384	299	11	.	.	PUNCT
ejpam-5384	300	1	i	i	PRON
ejpam-5384	300	2	)	)	PUNCT
ejpam-5384	300	3	the	the	DET
ejpam-5384	300	4	flow	flow	NOUN
ejpam-5384	300	5	ϕ	ϕ	NOUN
ejpam-5384	300	6	is	be	AUX
ejpam-5384	300	7	the	the	DET
ejpam-5384	300	8	system	system	NOUN
ejpam-5384	300	9	optimum	optimum	NOUN
ejpam-5384	300	10	of	of	ADP
ejpam-5384	300	11	nn	nn	PROPN
ejpam-5384	300	12	.	.	PROPN
ejpam-5384	300	13	ii	ii	PROPN
ejpam-5384	300	14	)	)	PUNCT
ejpam-5384	300	15	the	the	DET
ejpam-5384	300	16	flow	flow	NOUN
ejpam-5384	300	17	ϕ	ϕ	NOUN
ejpam-5384	300	18	is	be	AUX
ejpam-5384	300	19	the	the	DET
ejpam-5384	300	20	user	user	NOUN
ejpam-5384	300	21	equilibrium	equilibrium	NOUN
ejpam-5384	300	22	of	of	ADP
ejpam-5384	300	23	pnn	pnn	PROPN
ejpam-5384	300	24	=	=	PUNCT
ejpam-5384	300	25	(	(	PUNCT
ejpam-5384	300	26	p1(x	p1(x	NOUN
ejpam-5384	300	27	)	)	PUNCT
ejpam-5384	300	28	,	,	PUNCT
ejpam-5384	300	29	.	.	PUNCT
ejpam-5384	300	30	.	.	PUNCT
ejpam-5384	301	1	.	.	PUNCT
ejpam-5384	302	1	,	,	PUNCT
ejpam-5384	302	2	pn(x	pn(x	ADJ
ejpam-5384	302	3	)	)	PUNCT
ejpam-5384	302	4	)	)	PUNCT
ejpam-5384	302	5	.	.	PUNCT
ejpam-5384	303	1	iii	iii	X
ejpam-5384	303	2	)	)	PUNCT
ejpam-5384	303	3	it	it	PRON
ejpam-5384	303	4	holds	hold	VERB
ejpam-5384	303	5	li(ϕi	li(ϕi	ADJ
ejpam-5384	303	6	)	)	PUNCT
ejpam-5384	304	1	+	+	CCONJ
ejpam-5384	304	2	ϕil	ϕil	INTJ
ejpam-5384	304	3	′	′	NUM
ejpam-5384	304	4	i(ϕi	i(ϕi	ADJ
ejpam-5384	304	5	)	)	PUNCT
ejpam-5384	304	6	=	=	SYM
ejpam-5384	304	7	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	304	8	)	)	PUNCT
ejpam-5384	305	1	+	+	CCONJ
ejpam-5384	305	2	ϕjl	ϕjl	NOUN
ejpam-5384	305	3	′	′	NUM
ejpam-5384	305	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	305	5	)	)	PUNCT
ejpam-5384	305	6	,	,	PUNCT
ejpam-5384	305	7	for	for	ADP
ejpam-5384	305	8	every	every	DET
ejpam-5384	305	9	i	i	PROPN
ejpam-5384	305	10	,	,	PUNCT
ejpam-5384	305	11	j	j	PROPN
ejpam-5384	305	12	∈	∈	PROPN
ejpam-5384	305	13	in	in	ADP
ejpam-5384	305	14	with	with	ADP
ejpam-5384	305	15	ϕi	ϕi	ADP
ejpam-5384	305	16	,	,	PUNCT
ejpam-5384	305	17	ϕj	ϕj	INTJ
ejpam-5384	305	18	>	>	X
ejpam-5384	305	19	0	0	PUNCT
ejpam-5384	305	20	and	and	CCONJ
ejpam-5384	305	21	li(0	li(0	PROPN
ejpam-5384	305	22	)	)	PUNCT
ejpam-5384	305	23	≥	≥	NOUN
ejpam-5384	305	24	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	305	25	)	)	PUNCT
ejpam-5384	306	1	+	+	CCONJ
ejpam-5384	306	2	ϕjl	ϕjl	NOUN
ejpam-5384	306	3	′	′	NUM
ejpam-5384	306	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	306	5	)	)	PUNCT
ejpam-5384	306	6	,	,	PUNCT
ejpam-5384	306	7	for	for	ADP
ejpam-5384	306	8	every	every	DET
ejpam-5384	306	9	i	i	PROPN
ejpam-5384	306	10	,	,	PUNCT
ejpam-5384	306	11	j	j	PROPN
ejpam-5384	306	12	∈	∈	PROPN
ejpam-5384	306	13	in	in	ADP
ejpam-5384	306	14	,	,	PUNCT
ejpam-5384	306	15	with	with	ADP
ejpam-5384	306	16	ϕi	ϕi	ADP
ejpam-5384	306	17	=	=	SYM
ejpam-5384	306	18	0	0	NUM
ejpam-5384	306	19	,	,	PUNCT
ejpam-5384	306	20	and	and	CCONJ
ejpam-5384	306	21	ϕj	ϕj	ADP
ejpam-5384	306	22	>	>	X
ejpam-5384	306	23	0	0	X
ejpam-5384	306	24	.	.	NUM
ejpam-5384	307	1	iv	iv	X
ejpam-5384	307	2	)	)	PUNCT
ejpam-5384	307	3	it	it	PRON
ejpam-5384	307	4	holds	hold	VERB
ejpam-5384	307	5	lk(ϕk	lk(ϕk	NOUN
ejpam-5384	307	6	)	)	PUNCT
ejpam-5384	308	1	+	+	NUM
ejpam-5384	308	2	ϕkl	ϕkl	X
ejpam-5384	308	3	′(ϕk	′(ϕk	NOUN
ejpam-5384	308	4	)	)	PUNCT
ejpam-5384	309	1	=	=	SYM
ejpam-5384	309	2	min	min	PROPN
ejpam-5384	309	3	i∈in	i∈in	PROPN
ejpam-5384	309	4	{	{	PUNCT
ejpam-5384	309	5	li(ϕi	li(ϕi	NOUN
ejpam-5384	309	6	)	)	PUNCT
ejpam-5384	310	1	+	+	CCONJ
ejpam-5384	310	2	ϕil	ϕil	INTJ
ejpam-5384	310	3	′	′	NUM
ejpam-5384	310	4	i(ϕi	i(ϕi	ADJ
ejpam-5384	310	5	)	)	PUNCT
ejpam-5384	310	6	}	}	PUNCT
ejpam-5384	310	7	,	,	PUNCT
ejpam-5384	310	8	for	for	ADP
ejpam-5384	310	9	every	every	DET
ejpam-5384	310	10	ϕk	ϕk	NOUN
ejpam-5384	310	11	>	>	X
ejpam-5384	310	12	0	0	X
ejpam-5384	310	13	.	.	PUNCT
ejpam-5384	310	14	a.	a.	PROPN
ejpam-5384	310	15	kalampakas	kalampakas	PROPN
ejpam-5384	310	16	/	/	SYM
ejpam-5384	310	17	eur	eur	PROPN
ejpam-5384	310	18	.	.	PUNCT
ejpam-5384	311	1	j.	j.	PROPN
ejpam-5384	311	2	pure	pure	PROPN
ejpam-5384	311	3	appl	appl	PROPN
ejpam-5384	311	4	.	.	PROPN
ejpam-5384	311	5	math	math	PROPN
ejpam-5384	311	6	,	,	PUNCT
ejpam-5384	311	7	17	17	NUM
ejpam-5384	311	8	(	(	PUNCT
ejpam-5384	311	9	4	4	NUM
ejpam-5384	311	10	)	)	PUNCT
ejpam-5384	311	11	(	(	PUNCT
ejpam-5384	311	12	2024	2024	NUM
ejpam-5384	311	13	)	)	PUNCT
ejpam-5384	311	14	,	,	PUNCT
ejpam-5384	311	15	2448	2448	NUM
ejpam-5384	311	16	-	-	SYM
ejpam-5384	311	17	2466	2466	NUM
ejpam-5384	311	18	2458	2458	NUM
ejpam-5384	311	19	5	5	NUM
ejpam-5384	311	20	.	.	PUNCT
ejpam-5384	312	1	wardrop	wardrop	VERB
ejpam-5384	312	2	optimal	optimal	ADJ
ejpam-5384	312	3	networks	network	NOUN
ejpam-5384	312	4	flows	flow	NOUN
ejpam-5384	312	5	that	that	PRON
ejpam-5384	312	6	are	be	AUX
ejpam-5384	312	7	at	at	ADP
ejpam-5384	312	8	the	the	DET
ejpam-5384	312	9	same	same	ADJ
ejpam-5384	312	10	time	time	NOUN
ejpam-5384	312	11	system	system	NOUN
ejpam-5384	312	12	optimum	optimum	NOUN
ejpam-5384	312	13	and	and	CCONJ
ejpam-5384	312	14	user	user	NOUN
ejpam-5384	312	15	equilibrium	equilibrium	NOUN
ejpam-5384	313	1	are	be	AUX
ejpam-5384	313	2	called	call	VERB
ejpam-5384	313	3	wardrop	wardrop	NOUN
ejpam-5384	313	4	optimal	optimal	ADJ
ejpam-5384	313	5	flows	flow	NOUN
ejpam-5384	313	6	(	(	PUNCT
ejpam-5384	313	7	wofs	wof	NOUN
ejpam-5384	313	8	)	)	PUNCT
ejpam-5384	313	9	.	.	PUNCT
ejpam-5384	314	1	in	in	ADP
ejpam-5384	314	2	this	this	DET
ejpam-5384	314	3	section	section	NOUN
ejpam-5384	314	4	we	we	PRON
ejpam-5384	314	5	will	will	AUX
ejpam-5384	314	6	investigate	investigate	VERB
ejpam-5384	314	7	networks	network	NOUN
ejpam-5384	314	8	admitting	admit	VERB
ejpam-5384	314	9	such	such	ADJ
ejpam-5384	314	10	flows	flow	NOUN
ejpam-5384	314	11	i.e.	i.e.	X
ejpam-5384	314	12	,	,	PUNCT
ejpam-5384	314	13	wardrop	wardrop	VERB
ejpam-5384	314	14	optimal	optimal	ADJ
ejpam-5384	314	15	networks	network	NOUN
ejpam-5384	314	16	(	(	PUNCT
ejpam-5384	314	17	wons	won	NOUN
ejpam-5384	314	18	)	)	PUNCT
ejpam-5384	314	19	.	.	PUNCT
ejpam-5384	315	1	first	first	ADV
ejpam-5384	315	2	we	we	PRON
ejpam-5384	315	3	need	need	VERB
ejpam-5384	315	4	to	to	PART
ejpam-5384	315	5	identify	identify	VERB
ejpam-5384	315	6	some	some	DET
ejpam-5384	315	7	necessary	necessary	ADJ
ejpam-5384	315	8	conditions	condition	NOUN
ejpam-5384	315	9	for	for	ADP
ejpam-5384	315	10	system	system	NOUN
ejpam-5384	315	11	optimums	optimum	NOUN
ejpam-5384	315	12	.	.	PUNCT
ejpam-5384	316	1	by	by	ADP
ejpam-5384	316	2	applying	apply	VERB
ejpam-5384	316	3	theorem	theorem	NOUN
ejpam-5384	316	4	3	3	NUM
ejpam-5384	316	5	we	we	PRON
ejpam-5384	316	6	get	get	VERB
ejpam-5384	316	7	the	the	DET
ejpam-5384	316	8	following	follow	VERB
ejpam-5384	316	9	two	two	NUM
ejpam-5384	316	10	propositions	proposition	NOUN
ejpam-5384	316	11	.	.	PUNCT
ejpam-5384	317	1	proposition	proposition	NOUN
ejpam-5384	317	2	4	4	NUM
ejpam-5384	317	3	.	.	PUNCT
ejpam-5384	318	1	if	if	SCONJ
ejpam-5384	318	2	the	the	DET
ejpam-5384	318	3	flow	flow	NOUN
ejpam-5384	318	4	ϕ	ϕ	NOUN
ejpam-5384	318	5	=	=	PUNCT
ejpam-5384	318	6	(	(	PUNCT
ejpam-5384	318	7	ϕ1	ϕ1	NOUN
ejpam-5384	318	8	,	,	PUNCT
ejpam-5384	318	9	.	.	PUNCT
ejpam-5384	318	10	.	.	PUNCT
ejpam-5384	319	1	.	.	PUNCT
ejpam-5384	320	1	,	,	PUNCT
ejpam-5384	320	2	ϕn	ϕn	X
ejpam-5384	320	3	)	)	PUNCT
ejpam-5384	320	4	∈	∈	PROPN
ejpam-5384	320	5	sn−1	sn−1	PROPN
ejpam-5384	320	6	is	be	AUX
ejpam-5384	320	7	wof	wof	NOUN
ejpam-5384	320	8	of	of	ADP
ejpam-5384	320	9	the	the	DET
ejpam-5384	320	10	network	network	NOUN
ejpam-5384	320	11	nn	nn	PROPN
ejpam-5384	320	12	=	=	SYM
ejpam-5384	320	13	(	(	PUNCT
ejpam-5384	320	14	l1(x	l1(x	NOUN
ejpam-5384	320	15	)	)	PUNCT
ejpam-5384	320	16	,	,	PUNCT
ejpam-5384	320	17	.	.	PUNCT
ejpam-5384	320	18	.	.	PUNCT
ejpam-5384	320	19	.	.	PUNCT
ejpam-5384	321	1	,	,	PUNCT
ejpam-5384	321	2	ln(x	ln(x	X
ejpam-5384	321	3	)	)	PUNCT
ejpam-5384	321	4	)	)	PUNCT
ejpam-5384	322	1	then	then	ADV
ejpam-5384	322	2	it	it	PRON
ejpam-5384	322	3	holds	hold	VERB
ejpam-5384	322	4	i	i	PRON
ejpam-5384	322	5	)	)	PUNCT
ejpam-5384	322	6	ϕil	ϕil	ADP
ejpam-5384	322	7	′	′	NUM
ejpam-5384	322	8	i(ϕi	i(ϕi	ADJ
ejpam-5384	322	9	)	)	PUNCT
ejpam-5384	322	10	=	=	SYM
ejpam-5384	322	11	ϕjl	ϕjl	NOUN
ejpam-5384	322	12	′	′	NUM
ejpam-5384	322	13	j(ϕj	j(ϕj	NOUN
ejpam-5384	322	14	)	)	PUNCT
ejpam-5384	322	15	,	,	PUNCT
ejpam-5384	322	16	for	for	ADP
ejpam-5384	322	17	every	every	DET
ejpam-5384	322	18	i	i	PROPN
ejpam-5384	322	19	,	,	PUNCT
ejpam-5384	322	20	j	j	PROPN
ejpam-5384	322	21	∈	∈	PROPN
ejpam-5384	322	22	in	in	ADP
ejpam-5384	322	23	,	,	PUNCT
ejpam-5384	322	24	with	with	ADP
ejpam-5384	322	25	ϕi	ϕi	ADP
ejpam-5384	322	26	,	,	PUNCT
ejpam-5384	322	27	ϕj	ϕj	INTJ
ejpam-5384	322	28	>	>	X
ejpam-5384	322	29	0	0	PROPN
ejpam-5384	322	30	,	,	PUNCT
ejpam-5384	322	31	ii	ii	NOUN
ejpam-5384	322	32	)	)	PUNCT
ejpam-5384	322	33	li(0	li(0	PROPN
ejpam-5384	322	34	)	)	PUNCT
ejpam-5384	322	35	≥	≥	NOUN
ejpam-5384	322	36	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	322	37	)	)	PUNCT
ejpam-5384	323	1	+	+	CCONJ
ejpam-5384	323	2	ϕjl	ϕjl	NOUN
ejpam-5384	323	3	′	′	NUM
ejpam-5384	323	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	323	5	)	)	PUNCT
ejpam-5384	323	6	,	,	PUNCT
ejpam-5384	323	7	for	for	ADP
ejpam-5384	323	8	every	every	DET
ejpam-5384	323	9	i	i	PROPN
ejpam-5384	323	10	,	,	PUNCT
ejpam-5384	323	11	j	j	PROPN
ejpam-5384	323	12	∈	∈	PROPN
ejpam-5384	323	13	in	in	ADP
ejpam-5384	323	14	,	,	PUNCT
ejpam-5384	323	15	with	with	ADP
ejpam-5384	323	16	ϕi	ϕi	ADP
ejpam-5384	323	17	=	=	SYM
ejpam-5384	323	18	0	0	NUM
ejpam-5384	323	19	and	and	CCONJ
ejpam-5384	323	20	ϕj	ϕj	ADP
ejpam-5384	323	21	>	>	X
ejpam-5384	323	22	0	0	X
ejpam-5384	323	23	.	.	PUNCT
ejpam-5384	324	1	proposition	proposition	NOUN
ejpam-5384	324	2	5	5	NUM
ejpam-5384	324	3	.	.	PUNCT
ejpam-5384	325	1	if	if	SCONJ
ejpam-5384	325	2	the	the	DET
ejpam-5384	325	3	flow	flow	NOUN
ejpam-5384	325	4	ϕ	ϕ	NOUN
ejpam-5384	325	5	=	=	PUNCT
ejpam-5384	325	6	(	(	PUNCT
ejpam-5384	325	7	ϕ1	ϕ1	NOUN
ejpam-5384	325	8	,	,	PUNCT
ejpam-5384	325	9	.	.	PUNCT
ejpam-5384	325	10	.	.	PUNCT
ejpam-5384	326	1	.	.	PUNCT
ejpam-5384	327	1	,	,	PUNCT
ejpam-5384	327	2	ϕn	ϕn	X
ejpam-5384	327	3	)	)	PUNCT
ejpam-5384	327	4	∈	∈	PROPN
ejpam-5384	327	5	sn−1	sn−1	PROPN
ejpam-5384	327	6	is	be	AUX
ejpam-5384	327	7	user	user	NOUN
ejpam-5384	327	8	equilibrium	equilibrium	NOUN
ejpam-5384	327	9	of	of	ADP
ejpam-5384	327	10	the	the	DET
ejpam-5384	327	11	convex	convex	PROPN
ejpam-5384	327	12	network	network	NOUN
ejpam-5384	327	13	nn	nn	PROPN
ejpam-5384	327	14	=	=	SYM
ejpam-5384	327	15	(	(	PUNCT
ejpam-5384	327	16	l1(x	l1(x	NOUN
ejpam-5384	327	17	)	)	PUNCT
ejpam-5384	327	18	,	,	PUNCT
ejpam-5384	327	19	.	.	PUNCT
ejpam-5384	327	20	.	.	PUNCT
ejpam-5384	328	1	.	.	PUNCT
ejpam-5384	329	1	,	,	PUNCT
ejpam-5384	329	2	ln(x	ln(x	X
ejpam-5384	329	3	)	)	PUNCT
ejpam-5384	329	4	)	)	PUNCT
ejpam-5384	330	1	and	and	CCONJ
ejpam-5384	330	2	the	the	DET
ejpam-5384	330	3	following	follow	VERB
ejpam-5384	330	4	conditions	condition	NOUN
ejpam-5384	330	5	hold	hold	VERB
ejpam-5384	330	6	i	i	PRON
ejpam-5384	330	7	)	)	PUNCT
ejpam-5384	330	8	ϕil	ϕil	ADP
ejpam-5384	330	9	′	′	NUM
ejpam-5384	330	10	i(ϕi	i(ϕi	ADJ
ejpam-5384	330	11	)	)	PUNCT
ejpam-5384	330	12	=	=	SYM
ejpam-5384	330	13	ϕjl	ϕjl	NOUN
ejpam-5384	330	14	′	′	NUM
ejpam-5384	330	15	j(ϕj	j(ϕj	NOUN
ejpam-5384	330	16	)	)	PUNCT
ejpam-5384	330	17	,	,	PUNCT
ejpam-5384	330	18	for	for	ADP
ejpam-5384	330	19	every	every	DET
ejpam-5384	330	20	i	i	PROPN
ejpam-5384	330	21	,	,	PUNCT
ejpam-5384	330	22	j	j	PROPN
ejpam-5384	330	23	∈	∈	PROPN
ejpam-5384	330	24	in	in	ADP
ejpam-5384	330	25	,	,	PUNCT
ejpam-5384	330	26	with	with	ADP
ejpam-5384	330	27	ϕi	ϕi	ADP
ejpam-5384	330	28	,	,	PUNCT
ejpam-5384	330	29	ϕj	ϕj	INTJ
ejpam-5384	330	30	>	>	X
ejpam-5384	330	31	0	0	PROPN
ejpam-5384	330	32	,	,	PUNCT
ejpam-5384	330	33	ii	ii	NOUN
ejpam-5384	330	34	)	)	PUNCT
ejpam-5384	330	35	li(0	li(0	PROPN
ejpam-5384	330	36	)	)	PUNCT
ejpam-5384	330	37	≥	≥	NOUN
ejpam-5384	330	38	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	330	39	)	)	PUNCT
ejpam-5384	331	1	+	+	CCONJ
ejpam-5384	331	2	ϕjl	ϕjl	NOUN
ejpam-5384	331	3	′	′	NUM
ejpam-5384	331	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	331	5	)	)	PUNCT
ejpam-5384	331	6	,	,	PUNCT
ejpam-5384	331	7	for	for	ADP
ejpam-5384	331	8	every	every	DET
ejpam-5384	331	9	i	i	PROPN
ejpam-5384	331	10	,	,	PUNCT
ejpam-5384	331	11	j	j	PROPN
ejpam-5384	331	12	∈	∈	PROPN
ejpam-5384	331	13	in	in	ADP
ejpam-5384	331	14	,	,	PUNCT
ejpam-5384	331	15	with	with	ADP
ejpam-5384	331	16	ϕi	ϕi	ADP
ejpam-5384	331	17	=	=	SYM
ejpam-5384	331	18	0	0	NUM
ejpam-5384	331	19	and	and	CCONJ
ejpam-5384	331	20	ϕj	ϕj	ADP
ejpam-5384	331	21	>	>	X
ejpam-5384	331	22	0	0	PROPN
ejpam-5384	331	23	,	,	PUNCT
ejpam-5384	331	24	then	then	ADV
ejpam-5384	331	25	the	the	DET
ejpam-5384	331	26	flow	flow	NOUN
ejpam-5384	331	27	ϕ	ϕ	NOUN
ejpam-5384	331	28	is	be	AUX
ejpam-5384	331	29	also	also	ADV
ejpam-5384	331	30	system	system	NOUN
ejpam-5384	331	31	optimum	optimum	NOUN
ejpam-5384	331	32	.	.	PUNCT
ejpam-5384	332	1	combining	combine	VERB
ejpam-5384	332	2	the	the	DET
ejpam-5384	332	3	above	above	ADJ
ejpam-5384	332	4	propositions	proposition	NOUN
ejpam-5384	332	5	we	we	PRON
ejpam-5384	332	6	arrive	arrive	VERB
ejpam-5384	332	7	at	at	ADP
ejpam-5384	332	8	the	the	DET
ejpam-5384	332	9	following	following	ADJ
ejpam-5384	332	10	result	result	NOUN
ejpam-5384	332	11	.	.	PUNCT
ejpam-5384	333	1	theorem	theorem	ADJ
ejpam-5384	333	2	4	4	NUM
ejpam-5384	333	3	.	.	PUNCT
ejpam-5384	334	1	if	if	SCONJ
ejpam-5384	334	2	the	the	DET
ejpam-5384	334	3	flow	flow	NOUN
ejpam-5384	334	4	(	(	PUNCT
ejpam-5384	334	5	ϕ1	ϕ1	NOUN
ejpam-5384	334	6	,	,	PUNCT
ejpam-5384	334	7	.	.	PUNCT
ejpam-5384	334	8	.	.	PUNCT
ejpam-5384	334	9	.	.	PUNCT
ejpam-5384	335	1	,	,	PUNCT
ejpam-5384	335	2	ϕn	ϕn	X
ejpam-5384	335	3	)	)	PUNCT
ejpam-5384	335	4	∈	∈	PROPN
ejpam-5384	335	5	sn−1	sn−1	PROPN
ejpam-5384	335	6	is	be	AUX
ejpam-5384	335	7	a	a	DET
ejpam-5384	335	8	user	user	NOUN
ejpam-5384	335	9	equilibrium	equilibrium	NOUN
ejpam-5384	335	10	of	of	ADP
ejpam-5384	335	11	a	a	DET
ejpam-5384	335	12	convex	convex	NOUN
ejpam-5384	335	13	network	network	NOUN
ejpam-5384	335	14	nn	nn	X
ejpam-5384	335	15	=	=	SYM
ejpam-5384	335	16	(	(	PUNCT
ejpam-5384	335	17	l1(x	l1(x	NOUN
ejpam-5384	335	18	)	)	PUNCT
ejpam-5384	335	19	,	,	PUNCT
ejpam-5384	335	20	.	.	PUNCT
ejpam-5384	335	21	.	.	PUNCT
ejpam-5384	335	22	.	.	PUNCT
ejpam-5384	336	1	,	,	PUNCT
ejpam-5384	336	2	ln(x	ln(x	X
ejpam-5384	336	3	)	)	PUNCT
ejpam-5384	336	4	)	)	PUNCT
ejpam-5384	337	1	,	,	PUNCT
ejpam-5384	337	2	then	then	ADV
ejpam-5384	337	3	the	the	DET
ejpam-5384	337	4	following	follow	VERB
ejpam-5384	337	5	conditions	condition	NOUN
ejpam-5384	337	6	are	be	AUX
ejpam-5384	337	7	equivalent	equivalent	ADJ
ejpam-5384	337	8	i	i	X
ejpam-5384	337	9	)	)	PUNCT
ejpam-5384	337	10	it	it	PRON
ejpam-5384	337	11	holds	hold	VERB
ejpam-5384	337	12	ϕil	ϕil	ADJ
ejpam-5384	337	13	′	′	NUM
ejpam-5384	337	14	i(ϕi	i(ϕi	ADJ
ejpam-5384	337	15	)	)	PUNCT
ejpam-5384	337	16	=	=	SYM
ejpam-5384	337	17	ϕjl	ϕjl	NOUN
ejpam-5384	337	18	′	′	NUM
ejpam-5384	337	19	j(ϕj	j(ϕj	NOUN
ejpam-5384	337	20	)	)	PUNCT
ejpam-5384	337	21	,	,	PUNCT
ejpam-5384	337	22	for	for	ADP
ejpam-5384	337	23	every	every	DET
ejpam-5384	337	24	i	i	PROPN
ejpam-5384	337	25	,	,	PUNCT
ejpam-5384	337	26	j	j	PROPN
ejpam-5384	337	27	∈	∈	PROPN
ejpam-5384	337	28	in	in	ADP
ejpam-5384	337	29	with	with	ADP
ejpam-5384	337	30	ϕi	ϕi	ADP
ejpam-5384	337	31	,	,	PUNCT
ejpam-5384	337	32	ϕj	ϕj	INTJ
ejpam-5384	337	33	>	>	X
ejpam-5384	337	34	0	0	NUM
ejpam-5384	337	35	,	,	PUNCT
ejpam-5384	337	36	and	and	CCONJ
ejpam-5384	337	37	li(0	li(0	PROPN
ejpam-5384	337	38	)	)	PUNCT
ejpam-5384	337	39	≥	≥	NOUN
ejpam-5384	337	40	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	337	41	)	)	PUNCT
ejpam-5384	338	1	+	+	CCONJ
ejpam-5384	338	2	ϕjl	ϕjl	NOUN
ejpam-5384	338	3	′	′	NUM
ejpam-5384	338	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	338	5	)	)	PUNCT
ejpam-5384	338	6	,	,	PUNCT
ejpam-5384	338	7	for	for	ADP
ejpam-5384	338	8	every	every	DET
ejpam-5384	338	9	i	i	PROPN
ejpam-5384	338	10	,	,	PUNCT
ejpam-5384	338	11	j	j	PROPN
ejpam-5384	338	12	∈	∈	PROPN
ejpam-5384	338	13	in	in	ADP
ejpam-5384	338	14	with	with	ADP
ejpam-5384	338	15	ϕi	ϕi	ADP
ejpam-5384	338	16	=	=	SYM
ejpam-5384	338	17	0	0	NUM
ejpam-5384	338	18	,	,	PUNCT
ejpam-5384	338	19	and	and	CCONJ
ejpam-5384	338	20	ϕj	ϕj	ADP
ejpam-5384	338	21	>	>	X
ejpam-5384	338	22	0	0	PROPN
ejpam-5384	338	23	.	.	PUNCT
ejpam-5384	338	24	ii	ii	PROPN
ejpam-5384	338	25	)	)	PUNCT
ejpam-5384	338	26	the	the	DET
ejpam-5384	338	27	flow	flow	NOUN
ejpam-5384	338	28	ϕ	ϕ	NOUN
ejpam-5384	338	29	is	be	AUX
ejpam-5384	338	30	a	a	DET
ejpam-5384	338	31	system	system	NOUN
ejpam-5384	338	32	optimum	optimum	NOUN
ejpam-5384	338	33	.	.	PUNCT
ejpam-5384	339	1	on	on	ADP
ejpam-5384	339	2	the	the	DET
ejpam-5384	339	3	other	other	ADJ
ejpam-5384	339	4	hand	hand	NOUN
ejpam-5384	339	5	,	,	PUNCT
ejpam-5384	339	6	we	we	PRON
ejpam-5384	339	7	get	get	VERB
ejpam-5384	339	8	the	the	DET
ejpam-5384	339	9	following	follow	VERB
ejpam-5384	339	10	requirements	requirement	NOUN
ejpam-5384	339	11	for	for	ADP
ejpam-5384	339	12	a	a	DET
ejpam-5384	339	13	flow	flow	NOUN
ejpam-5384	339	14	that	that	PRON
ejpam-5384	339	15	is	be	AUX
ejpam-5384	339	16	a	a	DET
ejpam-5384	339	17	system	system	NOUN
ejpam-5384	339	18	optimum	optimum	NOUN
ejpam-5384	339	19	.	.	PUNCT
ejpam-5384	340	1	proposition	proposition	NOUN
ejpam-5384	340	2	6	6	NUM
ejpam-5384	340	3	.	.	PUNCT
ejpam-5384	341	1	if	if	SCONJ
ejpam-5384	341	2	the	the	DET
ejpam-5384	341	3	flow	flow	NOUN
ejpam-5384	341	4	ϕ	ϕ	NOUN
ejpam-5384	341	5	=	=	PUNCT
ejpam-5384	341	6	(	(	PUNCT
ejpam-5384	341	7	ϕ1	ϕ1	NOUN
ejpam-5384	341	8	,	,	PUNCT
ejpam-5384	341	9	.	.	PUNCT
ejpam-5384	341	10	.	.	PUNCT
ejpam-5384	342	1	.	.	PUNCT
ejpam-5384	343	1	,	,	PUNCT
ejpam-5384	343	2	ϕn	ϕn	X
ejpam-5384	343	3	)	)	PUNCT
ejpam-5384	343	4	∈	∈	PROPN
ejpam-5384	343	5	sn−1	sn−1	PROPN
ejpam-5384	343	6	is	be	AUX
ejpam-5384	343	7	system	system	NOUN
ejpam-5384	343	8	optimum	optimum	ADJ
ejpam-5384	343	9	of	of	ADP
ejpam-5384	343	10	a	a	DET
ejpam-5384	343	11	network	network	NOUN
ejpam-5384	343	12	nn	nn	X
ejpam-5384	343	13	=	=	SYM
ejpam-5384	343	14	(	(	PUNCT
ejpam-5384	343	15	l1(x	l1(x	NOUN
ejpam-5384	343	16	)	)	PUNCT
ejpam-5384	343	17	,	,	PUNCT
ejpam-5384	343	18	.	.	PUNCT
ejpam-5384	343	19	.	.	PUNCT
ejpam-5384	343	20	.	.	PUNCT
ejpam-5384	344	1	,	,	PUNCT
ejpam-5384	344	2	ln(x	ln(x	X
ejpam-5384	344	3	)	)	PUNCT
ejpam-5384	344	4	)	)	PUNCT
ejpam-5384	345	1	and	and	CCONJ
ejpam-5384	345	2	it	it	PRON
ejpam-5384	345	3	holds	hold	VERB
ejpam-5384	345	4	li(ϕi	li(ϕi	ADJ
ejpam-5384	345	5	)	)	PUNCT
ejpam-5384	345	6	=	=	SYM
ejpam-5384	345	7	lj(ϕj	lj(ϕj	NOUN
ejpam-5384	345	8	)	)	PUNCT
ejpam-5384	345	9	,	,	PUNCT
ejpam-5384	345	10	for	for	ADP
ejpam-5384	345	11	every	every	DET
ejpam-5384	345	12	i	i	PROPN
ejpam-5384	345	13	,	,	PUNCT
ejpam-5384	345	14	j	j	PROPN
ejpam-5384	345	15	∈	∈	PROPN
ejpam-5384	345	16	in	in	ADP
ejpam-5384	345	17	with	with	ADP
ejpam-5384	345	18	ϕi	ϕi	ADP
ejpam-5384	345	19	,	,	PUNCT
ejpam-5384	345	20	ϕj	ϕj	INTJ
ejpam-5384	345	21	>	>	X
ejpam-5384	345	22	0	0	PROPN
ejpam-5384	345	23	,	,	PUNCT
ejpam-5384	345	24	then	then	ADV
ejpam-5384	345	25	it	it	PRON
ejpam-5384	345	26	is	be	AUX
ejpam-5384	345	27	also	also	ADV
ejpam-5384	345	28	a	a	DET
ejpam-5384	345	29	user	user	NOUN
ejpam-5384	345	30	equilibrium	equilibrium	NOUN
ejpam-5384	345	31	.	.	PUNCT
ejpam-5384	346	1	a.	a.	PROPN
ejpam-5384	346	2	kalampakas	kalampakas	PROPN
ejpam-5384	346	3	/	/	SYM
ejpam-5384	346	4	eur	eur	PROPN
ejpam-5384	346	5	.	.	PUNCT
ejpam-5384	347	1	j.	j.	PROPN
ejpam-5384	347	2	pure	pure	PROPN
ejpam-5384	347	3	appl	appl	PROPN
ejpam-5384	347	4	.	.	PROPN
ejpam-5384	347	5	math	math	PROPN
ejpam-5384	347	6	,	,	PUNCT
ejpam-5384	347	7	17	17	NUM
ejpam-5384	347	8	(	(	PUNCT
ejpam-5384	347	9	4	4	NUM
ejpam-5384	347	10	)	)	PUNCT
ejpam-5384	347	11	(	(	PUNCT
ejpam-5384	347	12	2024	2024	NUM
ejpam-5384	347	13	)	)	PUNCT
ejpam-5384	347	14	,	,	PUNCT
ejpam-5384	347	15	2448	2448	NUM
ejpam-5384	347	16	-	-	SYM
ejpam-5384	347	17	2466	2466	NUM
ejpam-5384	347	18	2459	2459	NUM
ejpam-5384	347	19	hence	hence	ADV
ejpam-5384	347	20	we	we	PRON
ejpam-5384	347	21	can	can	AUX
ejpam-5384	347	22	arrive	arrive	VERB
ejpam-5384	347	23	at	at	ADP
ejpam-5384	347	24	the	the	DET
ejpam-5384	347	25	next	next	ADJ
ejpam-5384	347	26	theorem	theorem	PROPN
ejpam-5384	347	27	.	.	PUNCT
ejpam-5384	348	1	theorem	theorem	PROPN
ejpam-5384	348	2	5	5	NUM
ejpam-5384	348	3	.	.	PUNCT
ejpam-5384	348	4	given	give	VERB
ejpam-5384	348	5	a	a	DET
ejpam-5384	348	6	flow	flow	NOUN
ejpam-5384	348	7	ϕ	ϕ	NOUN
ejpam-5384	348	8	=	=	PUNCT
ejpam-5384	348	9	(	(	PUNCT
ejpam-5384	348	10	ϕ1	ϕ1	NOUN
ejpam-5384	348	11	,	,	PUNCT
ejpam-5384	348	12	.	.	PUNCT
ejpam-5384	348	13	.	.	PUNCT
ejpam-5384	349	1	.	.	PUNCT
ejpam-5384	350	1	,	,	PUNCT
ejpam-5384	350	2	ϕn	ϕn	X
ejpam-5384	350	3	)	)	PUNCT
ejpam-5384	350	4	∈	∈	PROPN
ejpam-5384	350	5	sn−1	sn−1	PROPN
ejpam-5384	350	6	of	of	ADP
ejpam-5384	350	7	a	a	DET
ejpam-5384	350	8	convex	convex	NOUN
ejpam-5384	350	9	network	network	NOUN
ejpam-5384	350	10	nn	nn	X
ejpam-5384	350	11	=	=	SYM
ejpam-5384	350	12	(	(	PUNCT
ejpam-5384	350	13	l1(x	l1(x	NOUN
ejpam-5384	350	14	)	)	PUNCT
ejpam-5384	350	15	,	,	PUNCT
ejpam-5384	350	16	.	.	PUNCT
ejpam-5384	350	17	.	.	PUNCT
ejpam-5384	351	1	.	.	PUNCT
ejpam-5384	352	1	,	,	PUNCT
ejpam-5384	352	2	ln(x	ln(x	X
ejpam-5384	352	3	)	)	PUNCT
ejpam-5384	352	4	)	)	PUNCT
ejpam-5384	352	5	,	,	PUNCT
ejpam-5384	352	6	the	the	DET
ejpam-5384	352	7	following	follow	VERB
ejpam-5384	352	8	conditions	condition	NOUN
ejpam-5384	352	9	are	be	AUX
ejpam-5384	352	10	equivalent	equivalent	ADJ
ejpam-5384	352	11	:	:	PUNCT
ejpam-5384	352	12	i	i	X
ejpam-5384	352	13	)	)	PUNCT
ejpam-5384	352	14	the	the	DET
ejpam-5384	352	15	flow	flow	NOUN
ejpam-5384	352	16	ϕ	ϕ	PROPN
ejpam-5384	352	17	wardrop	wardrop	NOUN
ejpam-5384	352	18	optimal	optimal	ADJ
ejpam-5384	352	19	.	.	PUNCT
ejpam-5384	353	1	ii	ii	X
ejpam-5384	353	2	)	)	PUNCT
ejpam-5384	353	3	it	it	PRON
ejpam-5384	353	4	holds	hold	VERB
ejpam-5384	353	5	:	:	PUNCT
ejpam-5384	353	6	li(ϕi	li(ϕi	ADJ
ejpam-5384	353	7	)	)	PUNCT
ejpam-5384	353	8	=	=	SYM
ejpam-5384	353	9	lj(ϕj	lj(ϕj	NOUN
ejpam-5384	353	10	)	)	PUNCT
ejpam-5384	353	11	,	,	PUNCT
ejpam-5384	353	12	for	for	ADP
ejpam-5384	353	13	every	every	DET
ejpam-5384	353	14	i	i	PROPN
ejpam-5384	353	15	,	,	PUNCT
ejpam-5384	353	16	j	j	PROPN
ejpam-5384	353	17	∈	∈	PROPN
ejpam-5384	353	18	in	in	ADP
ejpam-5384	353	19	with	with	ADP
ejpam-5384	353	20	ϕi	ϕi	ADP
ejpam-5384	353	21	,	,	PUNCT
ejpam-5384	353	22	ϕj	ϕj	INTJ
ejpam-5384	353	23	>	>	X
ejpam-5384	353	24	0	0	PROPN
ejpam-5384	353	25	,	,	PUNCT
ejpam-5384	353	26	ϕil	ϕil	ADV
ejpam-5384	353	27	′	′	NUM
ejpam-5384	353	28	i(ϕi	i(ϕi	ADJ
ejpam-5384	353	29	)	)	PUNCT
ejpam-5384	353	30	=	=	SYM
ejpam-5384	353	31	ϕjl	ϕjl	NOUN
ejpam-5384	353	32	′	′	NUM
ejpam-5384	353	33	j(ϕj	j(ϕj	NOUN
ejpam-5384	353	34	)	)	PUNCT
ejpam-5384	353	35	,	,	PUNCT
ejpam-5384	353	36	for	for	ADP
ejpam-5384	353	37	every	every	DET
ejpam-5384	353	38	i	i	PROPN
ejpam-5384	353	39	,	,	PUNCT
ejpam-5384	353	40	j	j	PROPN
ejpam-5384	353	41	∈	∈	PROPN
ejpam-5384	353	42	in	in	ADP
ejpam-5384	353	43	with	with	ADP
ejpam-5384	353	44	ϕi	ϕi	ADP
ejpam-5384	353	45	,	,	PUNCT
ejpam-5384	353	46	ϕj	ϕj	INTJ
ejpam-5384	353	47	>	>	X
ejpam-5384	353	48	0	0	PROPN
ejpam-5384	353	49	,	,	PUNCT
ejpam-5384	353	50	li(0	li(0	PROPN
ejpam-5384	353	51	)	)	PUNCT
ejpam-5384	353	52	≥	≥	NOUN
ejpam-5384	353	53	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	353	54	)	)	PUNCT
ejpam-5384	354	1	+	+	CCONJ
ejpam-5384	354	2	ϕjl	ϕjl	NOUN
ejpam-5384	354	3	′	′	NUM
ejpam-5384	354	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	354	5	)	)	PUNCT
ejpam-5384	354	6	,	,	PUNCT
ejpam-5384	354	7	for	for	ADP
ejpam-5384	354	8	every	every	DET
ejpam-5384	354	9	i	i	PROPN
ejpam-5384	354	10	,	,	PUNCT
ejpam-5384	354	11	j	j	PROPN
ejpam-5384	354	12	∈	∈	PROPN
ejpam-5384	354	13	in	in	ADP
ejpam-5384	354	14	with	with	ADP
ejpam-5384	354	15	ϕi	ϕi	ADP
ejpam-5384	354	16	=	=	SYM
ejpam-5384	354	17	0	0	NUM
ejpam-5384	354	18	,	,	PUNCT
ejpam-5384	354	19	and	and	CCONJ
ejpam-5384	354	20	ϕj	ϕj	ADP
ejpam-5384	354	21	>	>	X
ejpam-5384	354	22	0	0	X
ejpam-5384	354	23	.	.	PUNCT
ejpam-5384	355	1	if	if	SCONJ
ejpam-5384	355	2	we	we	PRON
ejpam-5384	355	3	only	only	ADV
ejpam-5384	355	4	consider	consider	VERB
ejpam-5384	355	5	internal	internal	ADJ
ejpam-5384	355	6	flows	flow	NOUN
ejpam-5384	355	7	,	,	PUNCT
ejpam-5384	355	8	then	then	ADV
ejpam-5384	355	9	we	we	PRON
ejpam-5384	355	10	get	get	VERB
ejpam-5384	355	11	the	the	DET
ejpam-5384	355	12	following	following	NOUN
ejpam-5384	355	13	corollary	corollary	NOUN
ejpam-5384	355	14	as	as	ADP
ejpam-5384	355	15	a	a	DET
ejpam-5384	355	16	particular	particular	ADJ
ejpam-5384	355	17	case	case	NOUN
ejpam-5384	355	18	of	of	ADP
ejpam-5384	355	19	the	the	DET
ejpam-5384	355	20	above	above	ADJ
ejpam-5384	355	21	result	result	NOUN
ejpam-5384	355	22	.	.	PUNCT
ejpam-5384	356	1	corollary	corollary	ADJ
ejpam-5384	356	2	1	1	NUM
ejpam-5384	356	3	.	.	PUNCT
ejpam-5384	357	1	given	give	VERB
ejpam-5384	357	2	a	a	DET
ejpam-5384	357	3	flow	flow	NOUN
ejpam-5384	357	4	ϕ	ϕ	NOUN
ejpam-5384	357	5	=	=	PUNCT
ejpam-5384	357	6	(	(	PUNCT
ejpam-5384	357	7	ϕ1	ϕ1	NOUN
ejpam-5384	357	8	,	,	PUNCT
ejpam-5384	357	9	.	.	PUNCT
ejpam-5384	357	10	.	.	PUNCT
ejpam-5384	357	11	.	.	PUNCT
ejpam-5384	358	1	,	,	PUNCT
ejpam-5384	358	2	ϕn	ϕn	X
ejpam-5384	358	3	)	)	PUNCT
ejpam-5384	358	4	∈	∈	PROPN
ejpam-5384	358	5	int(sn−1	int(sn−1	PROPN
ejpam-5384	358	6	)	)	PUNCT
ejpam-5384	358	7	of	of	ADP
ejpam-5384	358	8	a	a	DET
ejpam-5384	358	9	convex	convex	NOUN
ejpam-5384	358	10	network	network	NOUN
ejpam-5384	358	11	nn	nn	X
ejpam-5384	358	12	=	=	SYM
ejpam-5384	358	13	(	(	PUNCT
ejpam-5384	358	14	l1(x	l1(x	NOUN
ejpam-5384	358	15	)	)	PUNCT
ejpam-5384	358	16	,	,	PUNCT
ejpam-5384	358	17	.	.	PUNCT
ejpam-5384	358	18	.	.	PUNCT
ejpam-5384	358	19	.	.	PUNCT
ejpam-5384	359	1	,	,	PUNCT
ejpam-5384	359	2	ln(x	ln(x	X
ejpam-5384	359	3	)	)	PUNCT
ejpam-5384	359	4	)	)	PUNCT
ejpam-5384	359	5	,	,	PUNCT
ejpam-5384	359	6	the	the	DET
ejpam-5384	359	7	following	follow	VERB
ejpam-5384	359	8	conditions	condition	NOUN
ejpam-5384	359	9	are	be	AUX
ejpam-5384	359	10	equivalent	equivalent	ADJ
ejpam-5384	359	11	:	:	PUNCT
ejpam-5384	359	12	i	i	X
ejpam-5384	359	13	)	)	PUNCT
ejpam-5384	359	14	the	the	DET
ejpam-5384	359	15	flow	flow	NOUN
ejpam-5384	359	16	ϕ	ϕ	PROPN
ejpam-5384	359	17	wardrop	wardrop	NOUN
ejpam-5384	359	18	optimal	optimal	ADJ
ejpam-5384	359	19	.	.	PUNCT
ejpam-5384	360	1	ii	ii	X
ejpam-5384	360	2	)	)	PUNCT
ejpam-5384	360	3	it	it	PRON
ejpam-5384	360	4	holds	hold	VERB
ejpam-5384	360	5	:	:	PUNCT
ejpam-5384	360	6	li(ϕi	li(ϕi	ADJ
ejpam-5384	360	7	)	)	PUNCT
ejpam-5384	360	8	=	=	SYM
ejpam-5384	360	9	lj(ϕj	lj(ϕj	NOUN
ejpam-5384	360	10	)	)	PUNCT
ejpam-5384	360	11	,	,	PUNCT
ejpam-5384	360	12	for	for	ADP
ejpam-5384	360	13	every	every	DET
ejpam-5384	360	14	i	i	PROPN
ejpam-5384	360	15	,	,	PUNCT
ejpam-5384	360	16	j	j	PROPN
ejpam-5384	360	17	∈	∈	PROPN
ejpam-5384	360	18	in	in	ADP
ejpam-5384	360	19	with	with	ADP
ejpam-5384	360	20	ϕi	ϕi	ADP
ejpam-5384	360	21	,	,	PUNCT
ejpam-5384	360	22	ϕj	ϕj	INTJ
ejpam-5384	360	23	>	>	X
ejpam-5384	360	24	0	0	PROPN
ejpam-5384	360	25	,	,	PUNCT
ejpam-5384	360	26	ϕil	ϕil	ADV
ejpam-5384	360	27	′	′	NUM
ejpam-5384	360	28	i(ϕi	i(ϕi	ADJ
ejpam-5384	360	29	)	)	PUNCT
ejpam-5384	360	30	=	=	SYM
ejpam-5384	360	31	ϕjl	ϕjl	NOUN
ejpam-5384	360	32	′	′	NUM
ejpam-5384	360	33	j(ϕj	j(ϕj	NOUN
ejpam-5384	360	34	)	)	PUNCT
ejpam-5384	360	35	,	,	PUNCT
ejpam-5384	360	36	for	for	ADP
ejpam-5384	360	37	every	every	DET
ejpam-5384	360	38	i	i	PROPN
ejpam-5384	360	39	,	,	PUNCT
ejpam-5384	360	40	j	j	PROPN
ejpam-5384	360	41	∈	∈	PROPN
ejpam-5384	360	42	in	in	ADP
ejpam-5384	360	43	with	with	ADP
ejpam-5384	360	44	ϕi	ϕi	ADP
ejpam-5384	360	45	,	,	PUNCT
ejpam-5384	360	46	ϕj	ϕj	INTJ
ejpam-5384	360	47	>	>	X
ejpam-5384	360	48	0	0	X
ejpam-5384	360	49	.	.	PUNCT
ejpam-5384	361	1	the	the	DET
ejpam-5384	361	2	next	next	ADJ
ejpam-5384	361	3	result	result	NOUN
ejpam-5384	361	4	provides	provide	VERB
ejpam-5384	361	5	some	some	DET
ejpam-5384	361	6	insight	insight	NOUN
ejpam-5384	361	7	on	on	ADP
ejpam-5384	361	8	the	the	DET
ejpam-5384	361	9	effect	effect	NOUN
ejpam-5384	361	10	of	of	ADP
ejpam-5384	361	11	appropriate	appropriate	ADJ
ejpam-5384	361	12	transformations	transformation	NOUN
ejpam-5384	361	13	on	on	ADP
ejpam-5384	361	14	the	the	DET
ejpam-5384	361	15	latency	latency	NOUN
ejpam-5384	361	16	functions	function	NOUN
ejpam-5384	361	17	of	of	ADP
ejpam-5384	361	18	our	our	PRON
ejpam-5384	361	19	networks	network	NOUN
ejpam-5384	361	20	.	.	PUNCT
ejpam-5384	362	1	theorem	theorem	VERB
ejpam-5384	362	2	6	6	NUM
ejpam-5384	362	3	.	.	PUNCT
ejpam-5384	363	1	if	if	SCONJ
ejpam-5384	363	2	the	the	DET
ejpam-5384	363	3	flow	flow	NOUN
ejpam-5384	363	4	ϕ	ϕ	NOUN
ejpam-5384	363	5	=	=	PUNCT
ejpam-5384	363	6	(	(	PUNCT
ejpam-5384	363	7	ϕ1	ϕ1	NOUN
ejpam-5384	363	8	,	,	PUNCT
ejpam-5384	363	9	.	.	PUNCT
ejpam-5384	363	10	.	.	PUNCT
ejpam-5384	364	1	.	.	PUNCT
ejpam-5384	365	1	,	,	PUNCT
ejpam-5384	365	2	ϕn	ϕn	X
ejpam-5384	365	3	)	)	PUNCT
ejpam-5384	365	4	∈	∈	PROPN
ejpam-5384	365	5	sn−1	sn−1	PROPN
ejpam-5384	365	6	is	be	AUX
ejpam-5384	365	7	the	the	DET
ejpam-5384	365	8	wof	wof	X
ejpam-5384	365	9	of	of	ADP
ejpam-5384	365	10	a	a	DET
ejpam-5384	365	11	convex	convex	NOUN
ejpam-5384	365	12	network	network	NOUN
ejpam-5384	365	13	nn	nn	X
ejpam-5384	365	14	=	=	SYM
ejpam-5384	365	15	(	(	PUNCT
ejpam-5384	365	16	l1(x	l1(x	NOUN
ejpam-5384	365	17	)	)	PUNCT
ejpam-5384	365	18	,	,	PUNCT
ejpam-5384	365	19	.	.	PUNCT
ejpam-5384	365	20	.	.	PUNCT
ejpam-5384	365	21	.	.	PUNCT
ejpam-5384	366	1	,	,	PUNCT
ejpam-5384	366	2	ln(x	ln(x	X
ejpam-5384	366	3	)	)	PUNCT
ejpam-5384	366	4	)	)	PUNCT
ejpam-5384	366	5	,	,	PUNCT
ejpam-5384	366	6	then	then	ADV
ejpam-5384	366	7	it	it	PRON
ejpam-5384	366	8	is	be	AUX
ejpam-5384	366	9	also	also	ADV
ejpam-5384	366	10	wof	wof	X
ejpam-5384	366	11	of	of	ADP
ejpam-5384	366	12	the	the	DET
ejpam-5384	366	13	network	network	NOUN
ejpam-5384	366	14	f(nn	f(nn	NOUN
ejpam-5384	366	15	)	)	PUNCT
ejpam-5384	366	16	=	=	SYM
ejpam-5384	366	17	(	(	PUNCT
ejpam-5384	366	18	f(l1(x	f(l1(x	NOUN
ejpam-5384	366	19	)	)	PUNCT
ejpam-5384	366	20	)	)	PUNCT
ejpam-5384	366	21	,	,	PUNCT
ejpam-5384	366	22	.	.	PUNCT
ejpam-5384	366	23	.	.	PUNCT
ejpam-5384	367	1	.	.	PUNCT
ejpam-5384	368	1	,	,	PUNCT
ejpam-5384	368	2	f(ln(x	f(ln(x	PROPN
ejpam-5384	368	3	)	)	PUNCT
ejpam-5384	368	4	)	)	PUNCT
ejpam-5384	368	5	)	)	PUNCT
ejpam-5384	368	6	,	,	PUNCT
ejpam-5384	368	7	where	where	SCONJ
ejpam-5384	368	8	f(x	f(x	PROPN
ejpam-5384	368	9	)	)	PUNCT
ejpam-5384	368	10	:	:	PUNCT
ejpam-5384	369	1	r	r	NOUN
ejpam-5384	369	2	→	→	SYM
ejpam-5384	369	3	r	r	NOUN
ejpam-5384	369	4	is	be	AUX
ejpam-5384	369	5	a	a	DET
ejpam-5384	369	6	a	a	PRON
ejpam-5384	369	7	continuous	continuous	ADJ
ejpam-5384	369	8	,	,	PUNCT
ejpam-5384	369	9	strictly	strictly	ADV
ejpam-5384	369	10	increasing	increase	VERB
ejpam-5384	369	11	and	and	CCONJ
ejpam-5384	369	12	convex	convex	ADJ
ejpam-5384	369	13	function	function	NOUN
ejpam-5384	369	14	.	.	PUNCT
ejpam-5384	370	1	a.	a.	PROPN
ejpam-5384	370	2	kalampakas	kalampakas	PROPN
ejpam-5384	370	3	/	/	SYM
ejpam-5384	370	4	eur	eur	PROPN
ejpam-5384	370	5	.	.	PUNCT
ejpam-5384	371	1	j.	j.	PROPN
ejpam-5384	371	2	pure	pure	PROPN
ejpam-5384	371	3	appl	appl	PROPN
ejpam-5384	371	4	.	.	PROPN
ejpam-5384	371	5	math	math	PROPN
ejpam-5384	371	6	,	,	PUNCT
ejpam-5384	371	7	17	17	NUM
ejpam-5384	371	8	(	(	PUNCT
ejpam-5384	371	9	4	4	NUM
ejpam-5384	371	10	)	)	PUNCT
ejpam-5384	371	11	(	(	PUNCT
ejpam-5384	371	12	2024	2024	NUM
ejpam-5384	371	13	)	)	PUNCT
ejpam-5384	371	14	,	,	PUNCT
ejpam-5384	371	15	2448	2448	NUM
ejpam-5384	371	16	-	-	SYM
ejpam-5384	371	17	2466	2466	NUM
ejpam-5384	371	18	2460	2460	NUM
ejpam-5384	371	19	proof	proof	NOUN
ejpam-5384	371	20	.	.	PUNCT
ejpam-5384	372	1	since	since	SCONJ
ejpam-5384	372	2	ϕ	ϕ	PROPN
ejpam-5384	372	3	is	be	AUX
ejpam-5384	372	4	wof	wof	NOUN
ejpam-5384	372	5	of	of	ADP
ejpam-5384	372	6	nn	nn	INTJ
ejpam-5384	372	7	we	we	PRON
ejpam-5384	372	8	get	get	VERB
ejpam-5384	372	9	li(ϕi	li(ϕi	ADJ
ejpam-5384	372	10	)	)	PUNCT
ejpam-5384	372	11	=	=	SYM
ejpam-5384	372	12	lj(ϕj	lj(ϕj	NOUN
ejpam-5384	372	13	)	)	PUNCT
ejpam-5384	372	14	,	,	PUNCT
ejpam-5384	372	15	for	for	ADP
ejpam-5384	372	16	every	every	DET
ejpam-5384	372	17	i	i	PROPN
ejpam-5384	372	18	,	,	PUNCT
ejpam-5384	372	19	j	j	PROPN
ejpam-5384	372	20	∈	∈	PROPN
ejpam-5384	372	21	in	in	ADP
ejpam-5384	372	22	with	with	ADP
ejpam-5384	372	23	ϕi	ϕi	ADP
ejpam-5384	372	24	,	,	PUNCT
ejpam-5384	372	25	ϕj	ϕj	INTJ
ejpam-5384	372	26	>	>	X
ejpam-5384	372	27	0	0	PROPN
ejpam-5384	372	28	,	,	PUNCT
ejpam-5384	372	29	(	(	PUNCT
ejpam-5384	372	30	6	6	NUM
ejpam-5384	372	31	)	)	PUNCT
ejpam-5384	372	32	from	from	ADP
ejpam-5384	372	33	where	where	SCONJ
ejpam-5384	372	34	we	we	PRON
ejpam-5384	372	35	can	can	AUX
ejpam-5384	372	36	derive	derive	VERB
ejpam-5384	372	37	the	the	DET
ejpam-5384	372	38	first	first	ADJ
ejpam-5384	372	39	item	item	NOUN
ejpam-5384	372	40	of	of	ADP
ejpam-5384	372	41	theorem	theorem	NOUN
ejpam-5384	372	42	5	5	NUM
ejpam-5384	372	43	for	for	ADP
ejpam-5384	372	44	the	the	DET
ejpam-5384	372	45	set	set	NOUN
ejpam-5384	372	46	f(nn	f(nn	NOUN
ejpam-5384	372	47	):	):	PUNCT
ejpam-5384	372	48	f(li(ϕi	f(li(ϕi	ADJ
ejpam-5384	372	49	)	)	PUNCT
ejpam-5384	372	50	=	=	SYM
ejpam-5384	372	51	f(lj(ϕj	f(lj(ϕj	NOUN
ejpam-5384	372	52	)	)	PUNCT
ejpam-5384	372	53	)	)	PUNCT
ejpam-5384	372	54	,	,	PUNCT
ejpam-5384	372	55	for	for	ADP
ejpam-5384	372	56	every	every	DET
ejpam-5384	372	57	i	i	PROPN
ejpam-5384	372	58	,	,	PUNCT
ejpam-5384	372	59	j	j	PROPN
ejpam-5384	372	60	∈	∈	PROPN
ejpam-5384	372	61	in	in	ADP
ejpam-5384	372	62	with	with	ADP
ejpam-5384	372	63	ϕi	ϕi	ADP
ejpam-5384	372	64	,	,	PUNCT
ejpam-5384	372	65	ϕj	ϕj	INTJ
ejpam-5384	372	66	>	>	X
ejpam-5384	372	67	0	0	X
ejpam-5384	372	68	.	.	PUNCT
ejpam-5384	373	1	since	since	SCONJ
ejpam-5384	373	2	ϕ	ϕ	PROPN
ejpam-5384	373	3	is	be	AUX
ejpam-5384	373	4	also	also	ADV
ejpam-5384	373	5	optimal	optimal	ADJ
ejpam-5384	373	6	flow	flow	NOUN
ejpam-5384	373	7	of	of	ADP
ejpam-5384	373	8	ln	ln	ADJ
ejpam-5384	373	9	,	,	PUNCT
ejpam-5384	373	10	we	we	PRON
ejpam-5384	373	11	have	have	VERB
ejpam-5384	373	12	ϕil	ϕil	INTJ
ejpam-5384	373	13	′	′	NUM
ejpam-5384	373	14	i(ϕi	i(ϕi	ADJ
ejpam-5384	373	15	)	)	PUNCT
ejpam-5384	373	16	=	=	SYM
ejpam-5384	373	17	ϕjl	ϕjl	NOUN
ejpam-5384	373	18	′	′	NUM
ejpam-5384	373	19	j(ϕj	j(ϕj	NOUN
ejpam-5384	373	20	)	)	PUNCT
ejpam-5384	373	21	,	,	PUNCT
ejpam-5384	373	22	for	for	ADP
ejpam-5384	373	23	every	every	DET
ejpam-5384	373	24	i	i	PROPN
ejpam-5384	373	25	,	,	PUNCT
ejpam-5384	373	26	j	j	PROPN
ejpam-5384	373	27	∈	∈	PROPN
ejpam-5384	373	28	in	in	ADP
ejpam-5384	373	29	with	with	ADP
ejpam-5384	373	30	ϕi	ϕi	ADP
ejpam-5384	373	31	,	,	PUNCT
ejpam-5384	373	32	ϕj	ϕj	INTJ
ejpam-5384	373	33	>	>	X
ejpam-5384	373	34	0	0	PROPN
ejpam-5384	373	35	,	,	PUNCT
ejpam-5384	373	36	(	(	PUNCT
ejpam-5384	373	37	7	7	NUM
ejpam-5384	373	38	)	)	PUNCT
ejpam-5384	373	39	and	and	CCONJ
ejpam-5384	373	40	li(0	li(0	PROPN
ejpam-5384	373	41	)	)	PUNCT
ejpam-5384	373	42	≥	≥	NOUN
ejpam-5384	373	43	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	373	44	)	)	PUNCT
ejpam-5384	374	1	+	+	CCONJ
ejpam-5384	374	2	ϕjl	ϕjl	NOUN
ejpam-5384	374	3	′	′	NUM
ejpam-5384	374	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	374	5	)	)	PUNCT
ejpam-5384	374	6	,	,	PUNCT
ejpam-5384	374	7	for	for	ADP
ejpam-5384	374	8	every	every	DET
ejpam-5384	374	9	i	i	PROPN
ejpam-5384	374	10	,	,	PUNCT
ejpam-5384	374	11	j	j	PROPN
ejpam-5384	374	12	∈	∈	PROPN
ejpam-5384	374	13	in	in	ADP
ejpam-5384	374	14	with	with	ADP
ejpam-5384	374	15	ϕi	ϕi	ADP
ejpam-5384	374	16	=	=	SYM
ejpam-5384	374	17	0	0	NUM
ejpam-5384	374	18	,	,	PUNCT
ejpam-5384	374	19	and	and	CCONJ
ejpam-5384	374	20	ϕj	ϕj	ADP
ejpam-5384	374	21	>	>	X
ejpam-5384	374	22	0	0	PROPN
ejpam-5384	374	23	.	.	PUNCT
ejpam-5384	375	1	(	(	PUNCT
ejpam-5384	375	2	8)	8)	NUM
ejpam-5384	375	3	for	for	ADP
ejpam-5384	375	4	ϕi	ϕi	ADP
ejpam-5384	375	5	,	,	PUNCT
ejpam-5384	375	6	ϕj	ϕj	INTJ
ejpam-5384	375	7	>	>	X
ejpam-5384	375	8	0	0	PROPN
ejpam-5384	375	9	,	,	PUNCT
ejpam-5384	375	10	it	it	PRON
ejpam-5384	375	11	holds	hold	VERB
ejpam-5384	375	12	ϕi(f(li(ϕi	ϕi(f(li(ϕi	ADV
ejpam-5384	375	13	)	)	PUNCT
ejpam-5384	375	14	)	)	PUNCT
ejpam-5384	375	15	)	)	PUNCT
ejpam-5384	376	1	′	′	NUM
ejpam-5384	377	1	=	=	PUNCT
ejpam-5384	377	2	ϕif	ϕif	PROPN
ejpam-5384	377	3	′(li(ϕi))l	′(li(ϕi))l	NOUN
ejpam-5384	377	4	′	′	NUM
ejpam-5384	377	5	i(ϕi	i(ϕi	ADJ
ejpam-5384	377	6	)	)	PUNCT
ejpam-5384	377	7	(	(	PUNCT
ejpam-5384	377	8	6),(7	6),(7	NOUN
ejpam-5384	377	9	)	)	PUNCT
ejpam-5384	377	10	=	=	SYM
ejpam-5384	377	11	ϕjf	ϕjf	NOUN
ejpam-5384	377	12	′(lj(ϕj))l	′(lj(ϕj))l	PROPN
ejpam-5384	377	13	′	′	NUM
ejpam-5384	377	14	j(ϕj	j(ϕj	NOUN
ejpam-5384	377	15	)	)	PUNCT
ejpam-5384	377	16	=	=	SYM
ejpam-5384	377	17	ϕj(f(lj(ϕj	ϕj(f(lj(ϕj	PROPN
ejpam-5384	377	18	)	)	PUNCT
ejpam-5384	377	19	)	)	PUNCT
ejpam-5384	377	20	)	)	PUNCT
ejpam-5384	378	1	′.	′.	NOUN
ejpam-5384	378	2	(	(	PUNCT
ejpam-5384	378	3	9	9	NUM
ejpam-5384	378	4	)	)	PUNCT
ejpam-5384	378	5	hence	hence	ADV
ejpam-5384	378	6	the	the	DET
ejpam-5384	378	7	second	second	ADJ
ejpam-5384	378	8	condition	condition	NOUN
ejpam-5384	378	9	of	of	ADP
ejpam-5384	378	10	theorem	theorem	ADJ
ejpam-5384	378	11	5	5	NUM
ejpam-5384	378	12	is	be	AUX
ejpam-5384	378	13	satisfied	satisfied	ADJ
ejpam-5384	378	14	by	by	ADP
ejpam-5384	378	15	ϕ.	ϕ.	PROPN
ejpam-5384	378	16	now	now	ADV
ejpam-5384	378	17	let	let	VERB
ejpam-5384	378	18	ϕi	ϕi	ADP
ejpam-5384	378	19	=	=	PUNCT
ejpam-5384	378	20	0	0	PUNCT
ejpam-5384	378	21	and	and	CCONJ
ejpam-5384	378	22	ϕj	ϕj	INTJ
ejpam-5384	378	23	>	>	X
ejpam-5384	378	24	0	0	X
ejpam-5384	378	25	.	.	PUNCT
ejpam-5384	379	1	since	since	SCONJ
ejpam-5384	379	2	f	f	PROPN
ejpam-5384	379	3	is	be	AUX
ejpam-5384	379	4	increasing	increase	VERB
ejpam-5384	379	5	,	,	PUNCT
ejpam-5384	379	6	from	from	ADP
ejpam-5384	379	7	equation	equation	NOUN
ejpam-5384	379	8	8	8	NUM
ejpam-5384	379	9	we	we	PRON
ejpam-5384	379	10	obtain	obtain	VERB
ejpam-5384	379	11	f(li(0	f(li(0	NOUN
ejpam-5384	379	12	)	)	PUNCT
ejpam-5384	379	13	)	)	PUNCT
ejpam-5384	379	14	≥	≥	NOUN
ejpam-5384	379	15	f(lj(ϕj	f(lj(ϕj	NOUN
ejpam-5384	379	16	)	)	PUNCT
ejpam-5384	380	1	+	+	CCONJ
ejpam-5384	380	2	ϕjl	ϕjl	NOUN
ejpam-5384	380	3	′	′	NUM
ejpam-5384	380	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	380	5	)	)	PUNCT
ejpam-5384	380	6	)	)	PUNCT
ejpam-5384	380	7	.	.	PUNCT
ejpam-5384	381	1	we	we	PRON
ejpam-5384	381	2	need	need	VERB
ejpam-5384	381	3	to	to	PART
ejpam-5384	381	4	prove	prove	VERB
ejpam-5384	381	5	the	the	DET
ejpam-5384	381	6	third	third	ADJ
ejpam-5384	381	7	condition	condition	NOUN
ejpam-5384	381	8	of	of	ADP
ejpam-5384	381	9	theorem	theorem	NOUN
ejpam-5384	381	10	5	5	NUM
ejpam-5384	381	11	which	which	PRON
ejpam-5384	381	12	is	be	AUX
ejpam-5384	381	13	f(li(0	f(li(0	ADJ
ejpam-5384	381	14	)	)	PUNCT
ejpam-5384	381	15	)	)	PUNCT
ejpam-5384	381	16	≥	≥	NOUN
ejpam-5384	381	17	f(lj(ϕj	f(lj(ϕj	NOUN
ejpam-5384	381	18	)	)	PUNCT
ejpam-5384	381	19	)	)	PUNCT
ejpam-5384	382	1	+	+	CCONJ
ejpam-5384	382	2	ϕj	ϕj	INTJ
ejpam-5384	382	3	(	(	PUNCT
ejpam-5384	382	4	f(lj(ϕj	f(lj(ϕj	NOUN
ejpam-5384	382	5	)	)	PUNCT
ejpam-5384	382	6	)	)	PUNCT
ejpam-5384	382	7	)	)	PUNCT
ejpam-5384	382	8	′	′	NOUN
ejpam-5384	382	9	,	,	PUNCT
ejpam-5384	382	10	for	for	ADP
ejpam-5384	382	11	every	every	DET
ejpam-5384	382	12	i	i	PROPN
ejpam-5384	382	13	,	,	PUNCT
ejpam-5384	382	14	j	j	PROPN
ejpam-5384	382	15	∈	∈	PROPN
ejpam-5384	382	16	in	in	ADP
ejpam-5384	382	17	with	with	ADP
ejpam-5384	382	18	ϕi	ϕi	ADP
ejpam-5384	382	19	=	=	SYM
ejpam-5384	382	20	0	0	NUM
ejpam-5384	382	21	,	,	PUNCT
ejpam-5384	382	22	and	and	CCONJ
ejpam-5384	382	23	ϕj	ϕj	ADP
ejpam-5384	382	24	>	>	X
ejpam-5384	382	25	0	0	X
ejpam-5384	382	26	.	.	PUNCT
ejpam-5384	383	1	therefore	therefore	ADV
ejpam-5384	383	2	,	,	PUNCT
ejpam-5384	383	3	it	it	PRON
ejpam-5384	383	4	suffices	suffice	VERB
ejpam-5384	383	5	to	to	PART
ejpam-5384	383	6	show	show	VERB
ejpam-5384	383	7	that	that	SCONJ
ejpam-5384	383	8	f(lj(ϕj	f(lj(ϕj	NOUN
ejpam-5384	383	9	)	)	PUNCT
ejpam-5384	383	10	+	+	CCONJ
ejpam-5384	383	11	ϕjl	ϕjl	NOUN
ejpam-5384	383	12	′	′	NUM
ejpam-5384	383	13	j(ϕj	j(ϕj	NOUN
ejpam-5384	383	14	)	)	PUNCT
ejpam-5384	383	15	)	)	PUNCT
ejpam-5384	383	16	≥	≥	NOUN
ejpam-5384	383	17	f(lj(ϕj	f(lj(ϕj	NOUN
ejpam-5384	383	18	)	)	PUNCT
ejpam-5384	383	19	)	)	PUNCT
ejpam-5384	384	1	+	+	CCONJ
ejpam-5384	384	2	ϕj	ϕj	INTJ
ejpam-5384	384	3	(	(	PUNCT
ejpam-5384	384	4	f(lj(ϕj	f(lj(ϕj	NOUN
ejpam-5384	384	5	)	)	PUNCT
ejpam-5384	384	6	)	)	PUNCT
ejpam-5384	384	7	)	)	PUNCT
ejpam-5384	385	1	′	′	NUM
ejpam-5384	385	2	⇒	⇒	NOUN
ejpam-5384	385	3	f(lj(ϕj	f(lj(ϕj	NOUN
ejpam-5384	385	4	)	)	PUNCT
ejpam-5384	385	5	+	+	CCONJ
ejpam-5384	385	6	ϕjl	ϕjl	NOUN
ejpam-5384	385	7	′	′	NUM
ejpam-5384	385	8	j(ϕj))−	j(ϕj))−	NOUN
ejpam-5384	385	9	f(lj(ϕj	f(lj(ϕj	NOUN
ejpam-5384	385	10	)	)	PUNCT
ejpam-5384	385	11	)	)	PUNCT
ejpam-5384	385	12	≥	≥	PROPN
ejpam-5384	385	13	ϕjf	ϕjf	NOUN
ejpam-5384	385	14	′(lj(ϕj	′(lj(ϕj	NOUN
ejpam-5384	385	15	)	)	PUNCT
ejpam-5384	385	16	)	)	PUNCT
ejpam-5384	386	1	l	l	NOUN
ejpam-5384	386	2	′	′	NUM
ejpam-5384	386	3	j(ϕj	j(ϕj	NOUN
ejpam-5384	386	4	)	)	PUNCT
ejpam-5384	386	5	⇒	⇒	VERB
ejpam-5384	386	6	f(lj(ϕj	f(lj(ϕj	NOUN
ejpam-5384	386	7	)	)	PUNCT
ejpam-5384	387	1	+	+	NUM
ejpam-5384	387	2	ϕjl	ϕjl	NOUN
ejpam-5384	387	3	′	′	NUM
ejpam-5384	388	1	j(ϕj))−	j(ϕj))−	NOUN
ejpam-5384	388	2	f(lj(ϕj	f(lj(ϕj	NOUN
ejpam-5384	388	3	)	)	PUNCT
ejpam-5384	388	4	)	)	PUNCT
ejpam-5384	388	5	ϕjl′j(ϕj	ϕjl′j(ϕj	PROPN
ejpam-5384	388	6	)	)	PUNCT
ejpam-5384	388	7	≥	≥	PROPN
ejpam-5384	388	8	f	f	PROPN
ejpam-5384	388	9	′(lj(ϕj	′(lj(ϕj	NOUN
ejpam-5384	388	10	)	)	PUNCT
ejpam-5384	388	11	)	)	PUNCT
ejpam-5384	388	12	.	.	PUNCT
ejpam-5384	389	1	if	if	SCONJ
ejpam-5384	389	2	we	we	PRON
ejpam-5384	389	3	set	set	VERB
ejpam-5384	389	4	a	a	DET
ejpam-5384	389	5	=	=	NOUN
ejpam-5384	389	6	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	389	7	)	)	PUNCT
ejpam-5384	389	8	and	and	CCONJ
ejpam-5384	389	9	b	b	X
ejpam-5384	389	10	=	=	SYM
ejpam-5384	389	11	ϕjl	ϕjl	PROPN
ejpam-5384	389	12	′	′	NUM
ejpam-5384	389	13	j(ϕj	j(ϕj	NOUN
ejpam-5384	389	14	)	)	PUNCT
ejpam-5384	389	15	,	,	PUNCT
ejpam-5384	389	16	the	the	DET
ejpam-5384	389	17	last	last	ADJ
ejpam-5384	389	18	inequality	inequality	NOUN
ejpam-5384	389	19	can	can	AUX
ejpam-5384	389	20	be	be	AUX
ejpam-5384	389	21	rewritten	rewrite	VERB
ejpam-5384	389	22	as	as	ADP
ejpam-5384	389	23	f(a+	f(a+	PROPN
ejpam-5384	389	24	b)−	b)−	PROPN
ejpam-5384	389	25	f(a	f(a	PROPN
ejpam-5384	389	26	)	)	PUNCT
ejpam-5384	389	27	b	b	PROPN
ejpam-5384	389	28	≥	≥	NOUN
ejpam-5384	389	29	f	f	NOUN
ejpam-5384	389	30	′(a	′(a	ADJ
ejpam-5384	389	31	)	)	PUNCT
ejpam-5384	389	32	.	.	PUNCT
ejpam-5384	390	1	since	since	SCONJ
ejpam-5384	390	2	b	b	PROPN
ejpam-5384	390	3	>	>	X
ejpam-5384	390	4	0	0	PROPN
ejpam-5384	390	5	,	,	PUNCT
ejpam-5384	390	6	the	the	DET
ejpam-5384	390	7	left	left	ADJ
ejpam-5384	390	8	hand	hand	NOUN
ejpam-5384	390	9	side	side	NOUN
ejpam-5384	390	10	of	of	ADP
ejpam-5384	390	11	the	the	DET
ejpam-5384	390	12	above	above	ADJ
ejpam-5384	390	13	inequality	inequality	NOUN
ejpam-5384	390	14	is	be	AUX
ejpam-5384	390	15	the	the	DET
ejpam-5384	390	16	average	average	ADJ
ejpam-5384	390	17	increase	increase	NOUN
ejpam-5384	390	18	of	of	ADP
ejpam-5384	390	19	f(x	f(x	PROPN
ejpam-5384	390	20	)	)	PUNCT
ejpam-5384	390	21	at	at	ADP
ejpam-5384	390	22	the	the	DET
ejpam-5384	390	23	interval	interval	NOUN
ejpam-5384	390	24	[	[	X
ejpam-5384	390	25	a	a	X
ejpam-5384	390	26	,	,	PUNCT
ejpam-5384	390	27	a+b	a+b	NUM
ejpam-5384	390	28	]	]	PUNCT
ejpam-5384	390	29	and	and	CCONJ
ejpam-5384	390	30	the	the	DET
ejpam-5384	390	31	right	right	ADJ
ejpam-5384	390	32	hand	hand	NOUN
ejpam-5384	390	33	side	side	NOUN
ejpam-5384	390	34	is	be	AUX
ejpam-5384	390	35	the	the	DET
ejpam-5384	390	36	rate	rate	NOUN
ejpam-5384	390	37	of	of	ADP
ejpam-5384	390	38	change	change	NOUN
ejpam-5384	390	39	of	of	ADP
ejpam-5384	390	40	f(x	f(x	PROPN
ejpam-5384	390	41	)	)	PUNCT
ejpam-5384	390	42	at	at	ADP
ejpam-5384	390	43	a.	a.	NOUN
ejpam-5384	390	44	therefore	therefore	ADV
ejpam-5384	390	45	,	,	PUNCT
ejpam-5384	390	46	from	from	ADP
ejpam-5384	390	47	the	the	DET
ejpam-5384	390	48	convexity	convexity	NOUN
ejpam-5384	390	49	of	of	ADP
ejpam-5384	390	50	f(x	f(x	PROPN
ejpam-5384	390	51	)	)	PUNCT
ejpam-5384	390	52	,	,	PUNCT
ejpam-5384	390	53	we	we	PRON
ejpam-5384	390	54	deduce	deduce	VERB
ejpam-5384	390	55	that	that	SCONJ
ejpam-5384	390	56	the	the	DET
ejpam-5384	390	57	inequality	inequality	NOUN
ejpam-5384	390	58	holds	hold	VERB
ejpam-5384	390	59	true	true	ADJ
ejpam-5384	390	60	.	.	PUNCT
ejpam-5384	391	1	the	the	DET
ejpam-5384	391	2	proof	proof	NOUN
ejpam-5384	391	3	is	be	AUX
ejpam-5384	391	4	completed	complete	VERB
ejpam-5384	391	5	.	.	PUNCT
ejpam-5384	392	1	the	the	DET
ejpam-5384	392	2	above	above	ADJ
ejpam-5384	392	3	theorem	theorem	NOUN
ejpam-5384	392	4	shows	show	VERB
ejpam-5384	392	5	that	that	SCONJ
ejpam-5384	392	6	wofs	wof	NOUN
ejpam-5384	392	7	are	be	AUX
ejpam-5384	392	8	preserved	preserve	VERB
ejpam-5384	392	9	by	by	ADP
ejpam-5384	392	10	continuous	continuous	ADJ
ejpam-5384	392	11	,	,	PUNCT
ejpam-5384	392	12	strictly	strictly	ADV
ejpam-5384	392	13	increasing	increase	VERB
ejpam-5384	392	14	and	and	CCONJ
ejpam-5384	392	15	convex	convex	NOUN
ejpam-5384	392	16	functions	function	NOUN
ejpam-5384	392	17	.	.	PUNCT
ejpam-5384	393	1	nevertheless	nevertheless	ADV
ejpam-5384	393	2	,	,	PUNCT
ejpam-5384	393	3	this	this	PRON
ejpam-5384	393	4	does	do	AUX
ejpam-5384	393	5	not	not	PART
ejpam-5384	393	6	hold	hold	VERB
ejpam-5384	393	7	for	for	ADP
ejpam-5384	393	8	a	a	DET
ejpam-5384	393	9	system	system	NOUN
ejpam-5384	393	10	optimum	optimum	NOUN
ejpam-5384	393	11	which	which	PRON
ejpam-5384	393	12	is	be	AUX
ejpam-5384	393	13	not	not	PART
ejpam-5384	393	14	user	user	NOUN
ejpam-5384	393	15	equilibrium	equilibrium	NOUN
ejpam-5384	393	16	.	.	PUNCT
ejpam-5384	394	1	indeed	indeed	ADV
ejpam-5384	394	2	,	,	PUNCT
ejpam-5384	394	3	as	as	SCONJ
ejpam-5384	394	4	it	it	PRON
ejpam-5384	394	5	shown	show	VERB
ejpam-5384	394	6	in	in	ADP
ejpam-5384	394	7	example	example	NOUN
ejpam-5384	394	8	1	1	NUM
ejpam-5384	394	9	the	the	DET
ejpam-5384	394	10	system	system	NOUN
ejpam-5384	394	11	optimum	optimum	NOUN
ejpam-5384	394	12	of	of	ADP
ejpam-5384	394	13	the	the	DET
ejpam-5384	394	14	network	network	NOUN
ejpam-5384	394	15	of	of	ADP
ejpam-5384	394	16	figure	figure	NOUN
ejpam-5384	394	17	1	1	NUM
ejpam-5384	394	18	does	do	AUX
ejpam-5384	394	19	not	not	PART
ejpam-5384	394	20	remain	remain	VERB
ejpam-5384	394	21	the	the	DET
ejpam-5384	394	22	same	same	ADJ
ejpam-5384	394	23	after	after	ADP
ejpam-5384	394	24	taking	take	VERB
ejpam-5384	394	25	the	the	DET
ejpam-5384	394	26	image	image	NOUN
ejpam-5384	394	27	of	of	ADP
ejpam-5384	394	28	n	n	NUM
ejpam-5384	394	29	via	via	ADP
ejpam-5384	394	30	the	the	DET
ejpam-5384	394	31	continuous	continuous	ADJ
ejpam-5384	394	32	,	,	PUNCT
ejpam-5384	394	33	strictly	strictly	ADV
ejpam-5384	394	34	increasing	increase	VERB
ejpam-5384	394	35	and	and	CCONJ
ejpam-5384	394	36	convex	convex	VERB
ejpam-5384	394	37	function	function	NOUN
ejpam-5384	394	38	f(x	f(x	PROPN
ejpam-5384	394	39	)	)	PUNCT
ejpam-5384	395	1	=	=	SYM
ejpam-5384	395	2	x2	x2	PROPN
ejpam-5384	395	3	.	.	PUNCT
ejpam-5384	395	4	a.	a.	PROPN
ejpam-5384	395	5	kalampakas	kalampakas	PROPN
ejpam-5384	395	6	/	/	SYM
ejpam-5384	395	7	eur	eur	PROPN
ejpam-5384	395	8	.	.	PUNCT
ejpam-5384	396	1	j.	j.	PROPN
ejpam-5384	396	2	pure	pure	PROPN
ejpam-5384	396	3	appl	appl	PROPN
ejpam-5384	396	4	.	.	PROPN
ejpam-5384	396	5	math	math	PROPN
ejpam-5384	396	6	,	,	PUNCT
ejpam-5384	396	7	17	17	NUM
ejpam-5384	396	8	(	(	PUNCT
ejpam-5384	396	9	4	4	NUM
ejpam-5384	396	10	)	)	PUNCT
ejpam-5384	396	11	(	(	PUNCT
ejpam-5384	396	12	2024	2024	NUM
ejpam-5384	396	13	)	)	PUNCT
ejpam-5384	396	14	,	,	PUNCT
ejpam-5384	396	15	2448	2448	NUM
ejpam-5384	396	16	-	-	SYM
ejpam-5384	396	17	2466	2466	NUM
ejpam-5384	396	18	2461	2461	NUM
ejpam-5384	396	19	example	example	NOUN
ejpam-5384	396	20	2	2	NUM
ejpam-5384	396	21	.	.	PUNCT
ejpam-5384	397	1	let	let	VERB
ejpam-5384	397	2	us	we	PRON
ejpam-5384	397	3	examine	examine	VERB
ejpam-5384	397	4	the	the	DET
ejpam-5384	397	5	linear	linear	PROPN
ejpam-5384	397	6	network	network	NOUN
ejpam-5384	397	7	w1	w1	NOUN
ejpam-5384	397	8	=	=	SYM
ejpam-5384	397	9	{	{	PUNCT
ejpam-5384	397	10	x	x	PROPN
ejpam-5384	397	11	2	2	NUM
ejpam-5384	397	12	,	,	PUNCT
ejpam-5384	397	13	x	x	NOUN
ejpam-5384	397	14	3	3	X
ejpam-5384	397	15	}	}	PUNCT
ejpam-5384	397	16	shown	show	VERB
ejpam-5384	397	17	in	in	ADP
ejpam-5384	397	18	fig	fig	NOUN
ejpam-5384	397	19	.	.	PUNCT
ejpam-5384	398	1	2a	2a	NUM
ejpam-5384	398	2	.	.	PUNCT
ejpam-5384	399	1	the	the	DET
ejpam-5384	399	2	system	system	NOUN
ejpam-5384	399	3	optimum	optimum	NOUN
ejpam-5384	399	4	that	that	PRON
ejpam-5384	399	5	minimizes	minimize	VERB
ejpam-5384	399	6	the	the	DET
ejpam-5384	399	7	average	average	ADJ
ejpam-5384	399	8	delay	delay	NOUN
ejpam-5384	399	9	of	of	ADP
ejpam-5384	399	10	the	the	DET
ejpam-5384	399	11	network	network	NOUN
ejpam-5384	399	12	and	and	CCONJ
ejpam-5384	399	13	the	the	DET
ejpam-5384	399	14	user	user	NOUN
ejpam-5384	399	15	equilibrium	equilibrium	NOUN
ejpam-5384	399	16	that	that	PRON
ejpam-5384	399	17	equates	equate	VERB
ejpam-5384	399	18	delay	delay	NOUN
ejpam-5384	399	19	on	on	ADP
ejpam-5384	399	20	the	the	DET
ejpam-5384	399	21	two	two	NUM
ejpam-5384	399	22	links	link	NOUN
ejpam-5384	399	23	are	be	AUX
ejpam-5384	399	24	identical	identical	ADJ
ejpam-5384	399	25	and	and	CCONJ
ejpam-5384	399	26	equal	equal	ADJ
ejpam-5384	399	27	with	with	ADP
ejpam-5384	399	28	ϕ	ϕ	NOUN
ejpam-5384	399	29	=	=	PUNCT
ejpam-5384	399	30	(	(	PUNCT
ejpam-5384	399	31	0.4	0.4	NUM
ejpam-5384	399	32	,	,	PUNCT
ejpam-5384	399	33	0.6	0.6	NUM
ejpam-5384	399	34	)	)	PUNCT
ejpam-5384	399	35	.	.	PUNCT
ejpam-5384	400	1	similarly	similarly	ADV
ejpam-5384	400	2	for	for	ADP
ejpam-5384	400	3	the	the	DET
ejpam-5384	400	4	quadratic	quadratic	ADJ
ejpam-5384	400	5	network	network	NOUN
ejpam-5384	400	6	w2	w2	NOUN
ejpam-5384	400	7	=	=	SYM
ejpam-5384	400	8	{	{	PUNCT
ejpam-5384	400	9	4x2	4x2	NUM
ejpam-5384	400	10	,	,	PUNCT
ejpam-5384	400	11	x2	x2	PROPN
ejpam-5384	400	12	}	}	PUNCT
ejpam-5384	400	13	of	of	ADP
ejpam-5384	400	14	fig	fig	NOUN
ejpam-5384	400	15	.	.	PUNCT
ejpam-5384	400	16	2b	2b	NOUN
ejpam-5384	400	17	,	,	PUNCT
ejpam-5384	400	18	it	it	PRON
ejpam-5384	400	19	can	can	AUX
ejpam-5384	400	20	easily	easily	ADV
ejpam-5384	400	21	be	be	AUX
ejpam-5384	400	22	verified	verify	VERB
ejpam-5384	400	23	that	that	SCONJ
ejpam-5384	400	24	the	the	DET
ejpam-5384	400	25	system	system	NOUN
ejpam-5384	400	26	optimum	optimum	ADJ
ejpam-5384	400	27	and	and	CCONJ
ejpam-5384	400	28	the	the	DET
ejpam-5384	400	29	user	user	NOUN
ejpam-5384	400	30	equilibrium	equilibrium	NOUN
ejpam-5384	400	31	are	be	AUX
ejpam-5384	400	32	identical	identical	ADJ
ejpam-5384	400	33	and	and	CCONJ
ejpam-5384	400	34	equal	equal	ADJ
ejpam-5384	400	35	with	with	ADP
ejpam-5384	400	36	ϕ	ϕ	NOUN
ejpam-5384	400	37	=	=	PUNCT
ejpam-5384	400	38	(	(	PUNCT
ejpam-5384	400	39	1/3	1/3	NUM
ejpam-5384	400	40	,	,	PUNCT
ejpam-5384	400	41	2/3	2/3	NUM
ejpam-5384	400	42	)	)	PUNCT
ejpam-5384	400	43	.	.	PUNCT
ejpam-5384	401	1	l1(x	l1(x	X
ejpam-5384	401	2	)	)	PUNCT
ejpam-5384	402	1	=	=	X
ejpam-5384	402	2	x/2	x/2	X
ejpam-5384	402	3	l2(x	l2(x	PROPN
ejpam-5384	402	4	)	)	PUNCT
ejpam-5384	402	5	=	=	SYM
ejpam-5384	402	6	x/3	x/3	X
ejpam-5384	402	7	(	(	PUNCT
ejpam-5384	402	8	a	a	NOUN
ejpam-5384	402	9	)	)	PUNCT
ejpam-5384	402	10	w1	w1	NOUN
ejpam-5384	402	11	:	:	PUNCT
ejpam-5384	402	12	linear	linear	ADJ
ejpam-5384	402	13	wardrop	wardrop	NOUN
ejpam-5384	402	14	optimal	optimal	ADJ
ejpam-5384	402	15	network	network	NOUN
ejpam-5384	402	16	l1(x	l1(x	NOUN
ejpam-5384	402	17	)	)	PUNCT
ejpam-5384	402	18	=	=	SYM
ejpam-5384	402	19	4x2	4x2	NUM
ejpam-5384	402	20	l2(x	l2(x	NOUN
ejpam-5384	402	21	)	)	PUNCT
ejpam-5384	402	22	=	=	SYM
ejpam-5384	403	1	x2	x2	PROPN
ejpam-5384	403	2	(	(	PUNCT
ejpam-5384	403	3	b	b	NOUN
ejpam-5384	403	4	)	)	PUNCT
ejpam-5384	403	5	w2	w2	NOUN
ejpam-5384	403	6	:	:	PUNCT
ejpam-5384	403	7	quadratic	quadratic	ADJ
ejpam-5384	403	8	wardrop	wardrop	NOUN
ejpam-5384	403	9	optimal	optimal	ADJ
ejpam-5384	403	10	network	network	NOUN
ejpam-5384	403	11	figure	figure	NOUN
ejpam-5384	403	12	2	2	NUM
ejpam-5384	403	13	:	:	PUNCT
ejpam-5384	403	14	two	two	NUM
ejpam-5384	403	15	wardrop	wardrop	NOUN
ejpam-5384	403	16	optimal	optimal	ADJ
ejpam-5384	403	17	networks	network	NOUN
ejpam-5384	403	18	the	the	DET
ejpam-5384	403	19	next	next	ADJ
ejpam-5384	403	20	corollaries	corollary	NOUN
ejpam-5384	403	21	illustrate	illustrate	VERB
ejpam-5384	403	22	the	the	DET
ejpam-5384	403	23	effect	effect	NOUN
ejpam-5384	403	24	of	of	ADP
ejpam-5384	403	25	some	some	DET
ejpam-5384	403	26	fundamental	fundamental	ADJ
ejpam-5384	403	27	transformations	transformation	NOUN
ejpam-5384	403	28	onwofs	onwof	NOUN
ejpam-5384	403	29	.	.	PUNCT
ejpam-5384	404	1	corollary	corollary	ADJ
ejpam-5384	404	2	2	2	NUM
ejpam-5384	404	3	.	.	PUNCT
ejpam-5384	405	1	if	if	SCONJ
ejpam-5384	405	2	a	a	DET
ejpam-5384	405	3	flow	flow	NOUN
ejpam-5384	405	4	ϕ	ϕ	NOUN
ejpam-5384	405	5	∈	∈	PROPN
ejpam-5384	405	6	sn−1	sn−1	PROPN
ejpam-5384	405	7	is	be	AUX
ejpam-5384	405	8	wof	wof	NOUN
ejpam-5384	405	9	of	of	ADP
ejpam-5384	405	10	a	a	DET
ejpam-5384	405	11	convex	convex	NOUN
ejpam-5384	405	12	network	network	NOUN
ejpam-5384	405	13	nn	nn	X
ejpam-5384	405	14	=	=	SYM
ejpam-5384	405	15	(	(	PUNCT
ejpam-5384	405	16	l1(x	l1(x	NOUN
ejpam-5384	405	17	)	)	PUNCT
ejpam-5384	405	18	,	,	PUNCT
ejpam-5384	405	19	.	.	PUNCT
ejpam-5384	405	20	.	.	PUNCT
ejpam-5384	406	1	.	.	PUNCT
ejpam-5384	407	1	,	,	PUNCT
ejpam-5384	407	2	ln(x	ln(x	X
ejpam-5384	407	3	)	)	PUNCT
ejpam-5384	407	4	)	)	PUNCT
ejpam-5384	408	1	then	then	ADV
ejpam-5384	408	2	it	it	PRON
ejpam-5384	408	3	is	be	AUX
ejpam-5384	408	4	also	also	ADV
ejpam-5384	408	5	a	a	DET
ejpam-5384	408	6	wof	wof	NOUN
ejpam-5384	408	7	of	of	ADP
ejpam-5384	408	8	the	the	DET
ejpam-5384	408	9	following	follow	VERB
ejpam-5384	408	10	networks	network	NOUN
ejpam-5384	408	11	.	.	PUNCT
ejpam-5384	409	1	i	i	PRON
ejpam-5384	409	2	)	)	PUNCT
ejpam-5384	409	3	nn	nn	PROPN
ejpam-5384	410	1	+	+	NUM
ejpam-5384	410	2	b	b	X
ejpam-5384	410	3	=	=	SYM
ejpam-5384	410	4	(	(	PUNCT
ejpam-5384	410	5	l1(x	l1(x	NOUN
ejpam-5384	410	6	)	)	PUNCT
ejpam-5384	410	7	+	+	NUM
ejpam-5384	410	8	b	b	NOUN
ejpam-5384	410	9	,	,	PUNCT
ejpam-5384	410	10	.	.	PUNCT
ejpam-5384	410	11	.	.	PUNCT
ejpam-5384	410	12	.	.	PUNCT
ejpam-5384	411	1	,	,	PUNCT
ejpam-5384	411	2	ln(x	ln(x	X
ejpam-5384	411	3	)	)	PUNCT
ejpam-5384	412	1	+	+	NUM
ejpam-5384	412	2	b	b	X
ejpam-5384	412	3	)	)	PUNCT
ejpam-5384	412	4	,	,	PUNCT
ejpam-5384	412	5	for	for	ADP
ejpam-5384	412	6	every	every	DET
ejpam-5384	412	7	b	b	PROPN
ejpam-5384	412	8	>	>	X
ejpam-5384	412	9	0	0	NUM
ejpam-5384	412	10	.	.	PUNCT
ejpam-5384	412	11	ii	ii	PROPN
ejpam-5384	412	12	)	)	PUNCT
ejpam-5384	412	13	ann	ann	PROPN
ejpam-5384	413	1	=	=	PUNCT
ejpam-5384	413	2	(	(	PUNCT
ejpam-5384	413	3	al1(x	al1(x	NOUN
ejpam-5384	413	4	)	)	PUNCT
ejpam-5384	413	5	,	,	PUNCT
ejpam-5384	413	6	.	.	PUNCT
ejpam-5384	413	7	.	.	PUNCT
ejpam-5384	413	8	.	.	PUNCT
ejpam-5384	414	1	,	,	PUNCT
ejpam-5384	414	2	aln(x	aln(x	PROPN
ejpam-5384	414	3	)	)	PUNCT
ejpam-5384	414	4	)	)	PUNCT
ejpam-5384	414	5	,	,	PUNCT
ejpam-5384	414	6	for	for	ADP
ejpam-5384	414	7	every	every	DET
ejpam-5384	414	8	a	a	DET
ejpam-5384	414	9	>	>	X
ejpam-5384	414	10	0	0	NUM
ejpam-5384	414	11	.	.	PUNCT
ejpam-5384	415	1	for	for	ADP
ejpam-5384	415	2	the	the	DET
ejpam-5384	415	3	particular	particular	ADJ
ejpam-5384	415	4	case	case	NOUN
ejpam-5384	415	5	of	of	ADP
ejpam-5384	415	6	internal	internal	ADJ
ejpam-5384	415	7	flows	flow	NOUN
ejpam-5384	415	8	,	,	PUNCT
ejpam-5384	415	9	we	we	PRON
ejpam-5384	415	10	can	can	AUX
ejpam-5384	415	11	also	also	ADV
ejpam-5384	415	12	state	state	VERB
ejpam-5384	415	13	the	the	DET
ejpam-5384	415	14	following	following	NOUN
ejpam-5384	415	15	.	.	PUNCT
ejpam-5384	416	1	corollary	corollary	ADJ
ejpam-5384	416	2	3	3	NUM
ejpam-5384	416	3	.	.	PUNCT
ejpam-5384	417	1	if	if	SCONJ
ejpam-5384	417	2	the	the	DET
ejpam-5384	417	3	flow	flow	NOUN
ejpam-5384	417	4	ϕ	ϕ	NOUN
ejpam-5384	417	5	=	=	PUNCT
ejpam-5384	417	6	(	(	PUNCT
ejpam-5384	417	7	ϕ1	ϕ1	NOUN
ejpam-5384	417	8	,	,	PUNCT
ejpam-5384	417	9	.	.	PUNCT
ejpam-5384	417	10	.	.	PUNCT
ejpam-5384	418	1	.	.	PUNCT
ejpam-5384	419	1	,	,	PUNCT
ejpam-5384	419	2	ϕn	ϕn	X
ejpam-5384	419	3	)	)	PUNCT
ejpam-5384	419	4	∈	∈	PROPN
ejpam-5384	419	5	intsn−1	intsn−1	PROPN
ejpam-5384	419	6	is	be	AUX
ejpam-5384	419	7	the	the	DET
ejpam-5384	419	8	wof	wof	X
ejpam-5384	419	9	of	of	ADP
ejpam-5384	419	10	a	a	DET
ejpam-5384	419	11	convex	convex	NOUN
ejpam-5384	419	12	network	network	NOUN
ejpam-5384	419	13	nn	nn	X
ejpam-5384	419	14	=	=	SYM
ejpam-5384	419	15	(	(	PUNCT
ejpam-5384	419	16	l1(x	l1(x	NOUN
ejpam-5384	419	17	)	)	PUNCT
ejpam-5384	419	18	,	,	PUNCT
ejpam-5384	419	19	.	.	PUNCT
ejpam-5384	419	20	.	.	PUNCT
ejpam-5384	419	21	.	.	PUNCT
ejpam-5384	420	1	,	,	PUNCT
ejpam-5384	420	2	ln(x	ln(x	X
ejpam-5384	420	3	)	)	PUNCT
ejpam-5384	420	4	)	)	PUNCT
ejpam-5384	420	5	,	,	PUNCT
ejpam-5384	420	6	then	then	ADV
ejpam-5384	420	7	it	it	PRON
ejpam-5384	420	8	is	be	AUX
ejpam-5384	420	9	also	also	ADV
ejpam-5384	420	10	wof	wof	NOUN
ejpam-5384	420	11	of	of	ADP
ejpam-5384	420	12	f(nn	f(nn	NOUN
ejpam-5384	420	13	)	)	PUNCT
ejpam-5384	420	14	=	=	SYM
ejpam-5384	420	15	(	(	PUNCT
ejpam-5384	420	16	f(l1(x	f(l1(x	NOUN
ejpam-5384	420	17	)	)	PUNCT
ejpam-5384	420	18	)	)	PUNCT
ejpam-5384	420	19	,	,	PUNCT
ejpam-5384	420	20	.	.	PUNCT
ejpam-5384	420	21	.	.	PUNCT
ejpam-5384	421	1	.	.	PUNCT
ejpam-5384	422	1	,	,	PUNCT
ejpam-5384	422	2	f(ln(x	f(ln(x	PROPN
ejpam-5384	422	3	)	)	PUNCT
ejpam-5384	422	4	)	)	PUNCT
ejpam-5384	422	5	)	)	PUNCT
ejpam-5384	422	6	,	,	PUNCT
ejpam-5384	422	7	where	where	SCONJ
ejpam-5384	422	8	f(x	f(x	PROPN
ejpam-5384	422	9	)	)	PUNCT
ejpam-5384	422	10	:	:	PUNCT
ejpam-5384	423	1	r	r	NOUN
ejpam-5384	423	2	→	→	SYM
ejpam-5384	423	3	r	r	NOUN
ejpam-5384	423	4	is	be	AUX
ejpam-5384	423	5	a	a	DET
ejpam-5384	423	6	continuous	continuous	ADJ
ejpam-5384	423	7	,	,	PUNCT
ejpam-5384	423	8	strictly	strictly	ADV
ejpam-5384	423	9	increasing	increase	VERB
ejpam-5384	423	10	function	function	NOUN
ejpam-5384	423	11	.	.	PUNCT
ejpam-5384	424	1	next	next	ADV
ejpam-5384	424	2	we	we	PRON
ejpam-5384	424	3	examine	examine	VERB
ejpam-5384	424	4	networks	network	NOUN
ejpam-5384	424	5	with	with	ADP
ejpam-5384	424	6	identical	identical	ADJ
ejpam-5384	424	7	latency	latency	NOUN
ejpam-5384	424	8	functions	function	NOUN
ejpam-5384	424	9	.	.	PUNCT
ejpam-5384	425	1	proposition	proposition	NOUN
ejpam-5384	425	2	7	7	NUM
ejpam-5384	425	3	.	.	PUNCT
ejpam-5384	426	1	if	if	SCONJ
ejpam-5384	426	2	the	the	DET
ejpam-5384	426	3	latency	latency	NOUN
ejpam-5384	426	4	functions	function	NOUN
ejpam-5384	426	5	across	across	ADP
ejpam-5384	426	6	all	all	DET
ejpam-5384	426	7	links	link	NOUN
ejpam-5384	426	8	of	of	ADP
ejpam-5384	426	9	a	a	DET
ejpam-5384	426	10	network	network	NOUN
ejpam-5384	426	11	are	be	AUX
ejpam-5384	426	12	identical	identical	ADJ
ejpam-5384	426	13	then	then	ADV
ejpam-5384	426	14	the	the	DET
ejpam-5384	426	15	wof	wof	X
ejpam-5384	426	16	is	be	AUX
ejpam-5384	426	17	uniformly	uniformly	ADV
ejpam-5384	426	18	distributed	distribute	VERB
ejpam-5384	426	19	.	.	PUNCT
ejpam-5384	427	1	proof	proof	NOUN
ejpam-5384	427	2	.	.	PUNCT
ejpam-5384	428	1	it	it	PRON
ejpam-5384	428	2	suffices	suffice	VERB
ejpam-5384	428	3	to	to	PART
ejpam-5384	428	4	observe	observe	VERB
ejpam-5384	428	5	that	that	PRON
ejpam-5384	428	6	ϕ	ϕ	NOUN
ejpam-5384	428	7	=	=	PUNCT
ejpam-5384	428	8	(	(	PUNCT
ejpam-5384	428	9	1n	1n	NUM
ejpam-5384	428	10	,	,	PUNCT
ejpam-5384	428	11	.	.	PUNCT
ejpam-5384	428	12	.	.	PUNCT
ejpam-5384	429	1	.	.	PUNCT
ejpam-5384	430	1	,	,	PUNCT
ejpam-5384	430	2	1	1	NUM
ejpam-5384	430	3	n	n	CCONJ
ejpam-5384	430	4	)	)	PUNCT
ejpam-5384	430	5	is	be	AUX
ejpam-5384	430	6	the	the	DET
ejpam-5384	430	7	wof	wof	X
ejpam-5384	430	8	of	of	ADP
ejpam-5384	430	9	nn	nn	PROPN
ejpam-5384	430	10	.	.	PROPN
ejpam-5384	431	1	similarly	similarly	ADV
ejpam-5384	431	2	we	we	PRON
ejpam-5384	431	3	have	have	VERB
ejpam-5384	431	4	proposition	proposition	NOUN
ejpam-5384	431	5	8	8	NUM
ejpam-5384	431	6	.	.	PUNCT
ejpam-5384	432	1	any	any	DET
ejpam-5384	432	2	internal	internal	ADJ
ejpam-5384	432	3	flow	flow	NOUN
ejpam-5384	432	4	p	p	NOUN
ejpam-5384	432	5	=	=	SYM
ejpam-5384	432	6	(	(	PUNCT
ejpam-5384	432	7	p1	p1	PROPN
ejpam-5384	432	8	,	,	PUNCT
ejpam-5384	432	9	·	·	PUNCT
ejpam-5384	432	10	·	·	PUNCT
ejpam-5384	432	11	·	·	PUNCT
ejpam-5384	432	12	,	,	PUNCT
ejpam-5384	432	13	pn	pn	PROPN
ejpam-5384	432	14	)	)	PUNCT
ejpam-5384	432	15	∈	∈	PROPN
ejpam-5384	432	16	intsn−1	intsn−1	PROPN
ejpam-5384	432	17	is	be	AUX
ejpam-5384	432	18	the	the	DET
ejpam-5384	432	19	wof	wof	X
ejpam-5384	432	20	of	of	ADP
ejpam-5384	432	21	nn	nn	X
ejpam-5384	432	22	=	=	SYM
ejpam-5384	432	23	(	(	PUNCT
ejpam-5384	432	24	ϕ1	ϕ1	PROPN
ejpam-5384	432	25	p1	p1	PROPN
ejpam-5384	432	26	,	,	PUNCT
ejpam-5384	432	27	.	.	PUNCT
ejpam-5384	432	28	.	.	PUNCT
ejpam-5384	433	1	.	.	PUNCT
ejpam-5384	434	1	,	,	PUNCT
ejpam-5384	434	2	ϕn	ϕn	INTJ
ejpam-5384	434	3	pn	pn	PROPN
ejpam-5384	434	4	)	)	PUNCT
ejpam-5384	434	5	.	.	PUNCT
ejpam-5384	435	1	this	this	PRON
ejpam-5384	435	2	result	result	VERB
ejpam-5384	435	3	together	together	ADV
ejpam-5384	435	4	with	with	ADP
ejpam-5384	435	5	corollary	corollary	ADJ
ejpam-5384	435	6	3	3	NUM
ejpam-5384	435	7	,	,	PUNCT
ejpam-5384	435	8	gives	give	VERB
ejpam-5384	435	9	the	the	DET
ejpam-5384	435	10	following	follow	VERB
ejpam-5384	435	11	proposition	proposition	NOUN
ejpam-5384	435	12	.	.	PUNCT
ejpam-5384	436	1	a.	a.	PROPN
ejpam-5384	436	2	kalampakas	kalampakas	PROPN
ejpam-5384	436	3	/	/	SYM
ejpam-5384	436	4	eur	eur	PROPN
ejpam-5384	436	5	.	.	PUNCT
ejpam-5384	437	1	j.	j.	PROPN
ejpam-5384	437	2	pure	pure	PROPN
ejpam-5384	437	3	appl	appl	PROPN
ejpam-5384	437	4	.	.	PROPN
ejpam-5384	437	5	math	math	PROPN
ejpam-5384	437	6	,	,	PUNCT
ejpam-5384	437	7	17	17	NUM
ejpam-5384	437	8	(	(	PUNCT
ejpam-5384	437	9	4	4	NUM
ejpam-5384	437	10	)	)	PUNCT
ejpam-5384	437	11	(	(	PUNCT
ejpam-5384	437	12	2024	2024	NUM
ejpam-5384	437	13	)	)	PUNCT
ejpam-5384	437	14	,	,	PUNCT
ejpam-5384	437	15	2448	2448	NUM
ejpam-5384	437	16	-	-	SYM
ejpam-5384	437	17	2466	2466	NUM
ejpam-5384	437	18	2462	2462	NUM
ejpam-5384	437	19	proposition	proposition	NOUN
ejpam-5384	437	20	9	9	NUM
ejpam-5384	437	21	.	.	PUNCT
ejpam-5384	438	1	an	an	DET
ejpam-5384	438	2	internal	internal	ADJ
ejpam-5384	438	3	flow	flow	NOUN
ejpam-5384	438	4	p	p	NOUN
ejpam-5384	438	5	=	=	SYM
ejpam-5384	438	6	(	(	PUNCT
ejpam-5384	438	7	p1	p1	PROPN
ejpam-5384	438	8	,	,	PUNCT
ejpam-5384	438	9	·	·	PUNCT
ejpam-5384	438	10	·	·	PUNCT
ejpam-5384	438	11	·	·	PUNCT
ejpam-5384	438	12	,	,	PUNCT
ejpam-5384	438	13	pn	pn	PROPN
ejpam-5384	438	14	)	)	PUNCT
ejpam-5384	438	15	∈	∈	PROPN
ejpam-5384	438	16	intsn−1	intsn−1	PROPN
ejpam-5384	438	17	is	be	AUX
ejpam-5384	438	18	the	the	DET
ejpam-5384	438	19	wof	wof	X
ejpam-5384	438	20	of	of	ADP
ejpam-5384	438	21	nn	nn	X
ejpam-5384	439	1	=	=	X
ejpam-5384	439	2	(	(	PUNCT
ejpam-5384	439	3	f(ϕ1	f(ϕ1	ADJ
ejpam-5384	439	4	p1	p1	PROPN
ejpam-5384	439	5	)	)	PUNCT
ejpam-5384	439	6	,	,	PUNCT
ejpam-5384	439	7	.	.	PUNCT
ejpam-5384	439	8	.	.	PUNCT
ejpam-5384	439	9	.	.	PUNCT
ejpam-5384	440	1	,	,	PUNCT
ejpam-5384	440	2	f(ϕn	f(ϕn	NOUN
ejpam-5384	440	3	pn	pn	PROPN
ejpam-5384	440	4	)	)	PUNCT
ejpam-5384	440	5	)	)	PUNCT
ejpam-5384	441	1	,	,	PUNCT
ejpam-5384	441	2	where	where	SCONJ
ejpam-5384	441	3	f(x	f(x	PROPN
ejpam-5384	441	4	)	)	PUNCT
ejpam-5384	441	5	is	be	AUX
ejpam-5384	441	6	any	any	DET
ejpam-5384	441	7	continuous	continuous	ADJ
ejpam-5384	441	8	,	,	PUNCT
ejpam-5384	441	9	strictly	strictly	ADV
ejpam-5384	441	10	increasing	increase	VERB
ejpam-5384	441	11	function	function	NOUN
ejpam-5384	441	12	.	.	PUNCT
ejpam-5384	442	1	by	by	ADP
ejpam-5384	442	2	using	use	VERB
ejpam-5384	442	3	theorem	theorem	NOUN
ejpam-5384	442	4	5	5	NUM
ejpam-5384	442	5	we	we	PRON
ejpam-5384	442	6	obtain	obtain	VERB
ejpam-5384	442	7	the	the	DET
ejpam-5384	442	8	next	next	ADJ
ejpam-5384	442	9	proposition	proposition	NOUN
ejpam-5384	442	10	.	.	PUNCT
ejpam-5384	443	1	proposition	proposition	NOUN
ejpam-5384	443	2	10	10	NUM
ejpam-5384	443	3	.	.	PUNCT
ejpam-5384	444	1	if	if	SCONJ
ejpam-5384	444	2	a	a	DET
ejpam-5384	444	3	flow	flow	NOUN
ejpam-5384	444	4	ϕ	ϕ	NOUN
ejpam-5384	444	5	=	=	PUNCT
ejpam-5384	444	6	(	(	PUNCT
ejpam-5384	444	7	ϕ1	ϕ1	NOUN
ejpam-5384	444	8	,	,	PUNCT
ejpam-5384	444	9	.	.	PUNCT
ejpam-5384	444	10	.	.	PUNCT
ejpam-5384	445	1	.	.	PUNCT
ejpam-5384	446	1	,	,	PUNCT
ejpam-5384	446	2	ϕn	ϕn	X
ejpam-5384	446	3	)	)	PUNCT
ejpam-5384	446	4	∈	∈	PROPN
ejpam-5384	446	5	sn−1	sn−1	PROPN
ejpam-5384	446	6	is	be	AUX
ejpam-5384	446	7	at	at	ADP
ejpam-5384	446	8	the	the	DET
ejpam-5384	446	9	same	same	ADJ
ejpam-5384	446	10	time	time	NOUN
ejpam-5384	446	11	,	,	PUNCT
ejpam-5384	446	12	wof	wof	X
ejpam-5384	446	13	of	of	ADP
ejpam-5384	446	14	the	the	DET
ejpam-5384	446	15	convex	convex	PROPN
ejpam-5384	446	16	networks	network	NOUN
ejpam-5384	446	17	nn	nn	PROPN
ejpam-5384	447	1	=	=	SYM
ejpam-5384	447	2	(	(	PUNCT
ejpam-5384	447	3	l1(x	l1(x	NOUN
ejpam-5384	447	4	)	)	PUNCT
ejpam-5384	447	5	,	,	PUNCT
ejpam-5384	447	6	.	.	PUNCT
ejpam-5384	447	7	.	.	PUNCT
ejpam-5384	448	1	.	.	PUNCT
ejpam-5384	449	1	,	,	PUNCT
ejpam-5384	449	2	ln(x	ln(x	X
ejpam-5384	449	3	)	)	PUNCT
ejpam-5384	449	4	)	)	PUNCT
ejpam-5384	450	1	and	and	CCONJ
ejpam-5384	450	2	nn	nn	X
ejpam-5384	450	3	=	=	SYM
ejpam-5384	450	4	(	(	PUNCT
ejpam-5384	450	5	l1(x	l1(x	NOUN
ejpam-5384	450	6	)	)	PUNCT
ejpam-5384	450	7	,	,	PUNCT
ejpam-5384	450	8	.	.	PUNCT
ejpam-5384	450	9	.	.	PUNCT
ejpam-5384	450	10	.	.	PUNCT
ejpam-5384	451	1	,	,	PUNCT
ejpam-5384	451	2	ln(x	ln(x	X
ejpam-5384	451	3	)	)	PUNCT
ejpam-5384	451	4	)	)	PUNCT
ejpam-5384	452	1	then	then	ADV
ejpam-5384	452	2	it	it	PRON
ejpam-5384	452	3	is	be	AUX
ejpam-5384	452	4	also	also	ADV
ejpam-5384	452	5	wof	wof	X
ejpam-5384	452	6	of	of	ADP
ejpam-5384	452	7	nnnn	nnnn	NOUN
ejpam-5384	452	8	=	=	SYM
ejpam-5384	452	9	(	(	PUNCT
ejpam-5384	452	10	l1(x)l1(x	l1(x)l1(x	NOUN
ejpam-5384	452	11	)	)	PUNCT
ejpam-5384	452	12	,	,	PUNCT
ejpam-5384	452	13	.	.	PUNCT
ejpam-5384	452	14	.	.	PUNCT
ejpam-5384	452	15	.	.	PUNCT
ejpam-5384	453	1	,	,	PUNCT
ejpam-5384	453	2	ln(x)ln(x	ln(x)ln(x	PROPN
ejpam-5384	453	3	)	)	PUNCT
ejpam-5384	453	4	)	)	PUNCT
ejpam-5384	453	5	.	.	PUNCT
ejpam-5384	454	1	proof	proof	NOUN
ejpam-5384	454	2	.	.	PUNCT
ejpam-5384	455	1	since	since	SCONJ
ejpam-5384	455	2	ϕ	ϕ	PROPN
ejpam-5384	455	3	is	be	AUX
ejpam-5384	455	4	wof	wof	NOUN
ejpam-5384	455	5	of	of	ADP
ejpam-5384	455	6	the	the	DET
ejpam-5384	455	7	networksnn	networksnn	PROPN
ejpam-5384	455	8	andnn	andnn	PROPN
ejpam-5384	455	9	,	,	PUNCT
ejpam-5384	455	10	from	from	ADP
ejpam-5384	455	11	the	the	DET
ejpam-5384	455	12	first	first	ADJ
ejpam-5384	455	13	condition	condition	NOUN
ejpam-5384	455	14	of	of	ADP
ejpam-5384	455	15	theorem	theorem	NOUN
ejpam-5384	455	16	5	5	NUM
ejpam-5384	455	17	for	for	ADP
ejpam-5384	455	18	the	the	DET
ejpam-5384	455	19	two	two	NUM
ejpam-5384	455	20	networks	network	NOUN
ejpam-5384	455	21	we	we	PRON
ejpam-5384	455	22	have	have	AUX
ejpam-5384	455	23	li(ϕi	li(ϕi	VERB
ejpam-5384	455	24	)	)	PUNCT
ejpam-5384	455	25	=	=	SYM
ejpam-5384	455	26	lj(ϕj	lj(ϕj	NOUN
ejpam-5384	455	27	)	)	PUNCT
ejpam-5384	455	28	,	,	PUNCT
ejpam-5384	455	29	for	for	ADP
ejpam-5384	455	30	every	every	DET
ejpam-5384	455	31	i	i	PROPN
ejpam-5384	455	32	,	,	PUNCT
ejpam-5384	455	33	j	j	PROPN
ejpam-5384	455	34	∈	∈	PROPN
ejpam-5384	455	35	in	in	ADP
ejpam-5384	455	36	with	with	ADP
ejpam-5384	455	37	ϕi	ϕi	ADP
ejpam-5384	455	38	,	,	PUNCT
ejpam-5384	455	39	ϕj	ϕj	INTJ
ejpam-5384	455	40	>	>	X
ejpam-5384	455	41	0	0	PROPN
ejpam-5384	455	42	,	,	PUNCT
ejpam-5384	455	43	(	(	PUNCT
ejpam-5384	455	44	10	10	NUM
ejpam-5384	455	45	)	)	PUNCT
ejpam-5384	455	46	and	and	CCONJ
ejpam-5384	455	47	li(ϕi	li(ϕi	ADJ
ejpam-5384	455	48	)	)	PUNCT
ejpam-5384	455	49	=	=	SYM
ejpam-5384	455	50	lj(ϕj	lj(ϕj	NOUN
ejpam-5384	455	51	)	)	PUNCT
ejpam-5384	455	52	,	,	PUNCT
ejpam-5384	455	53	for	for	ADP
ejpam-5384	455	54	every	every	DET
ejpam-5384	455	55	i	i	PROPN
ejpam-5384	455	56	,	,	PUNCT
ejpam-5384	455	57	j	j	PROPN
ejpam-5384	455	58	∈	∈	PROPN
ejpam-5384	455	59	in	in	ADP
ejpam-5384	455	60	with	with	ADP
ejpam-5384	455	61	ϕi	ϕi	ADP
ejpam-5384	455	62	,	,	PUNCT
ejpam-5384	455	63	ϕj	ϕj	INTJ
ejpam-5384	455	64	>	>	X
ejpam-5384	455	65	0	0	X
ejpam-5384	455	66	.	.	PUNCT
ejpam-5384	456	1	(	(	PUNCT
ejpam-5384	456	2	11	11	NUM
ejpam-5384	456	3	)	)	PUNCT
ejpam-5384	456	4	by	by	ADP
ejpam-5384	456	5	multiplication	multiplication	NOUN
ejpam-5384	456	6	of	of	ADP
ejpam-5384	456	7	the	the	DET
ejpam-5384	456	8	two	two	NUM
ejpam-5384	456	9	we	we	PRON
ejpam-5384	456	10	get	get	VERB
ejpam-5384	456	11	the	the	DET
ejpam-5384	456	12	first	first	ADJ
ejpam-5384	456	13	condition	condition	NOUN
ejpam-5384	456	14	for	for	ADP
ejpam-5384	456	15	the	the	DET
ejpam-5384	456	16	network	network	NOUN
ejpam-5384	456	17	nnnn	nnnn	PROPN
ejpam-5384	456	18	:	:	PUNCT
ejpam-5384	456	19	li(ϕi)li(x	li(ϕi)li(x	NUM
ejpam-5384	456	20	)	)	PUNCT
ejpam-5384	456	21	=	=	SYM
ejpam-5384	457	1	lj(ϕj)lj(x	lj(ϕj)lj(x	PROPN
ejpam-5384	457	2	)	)	PUNCT
ejpam-5384	457	3	,	,	PUNCT
ejpam-5384	457	4	for	for	ADP
ejpam-5384	457	5	every	every	DET
ejpam-5384	457	6	i	i	PROPN
ejpam-5384	457	7	,	,	PUNCT
ejpam-5384	457	8	j	j	PROPN
ejpam-5384	457	9	∈	∈	PROPN
ejpam-5384	457	10	in	in	ADP
ejpam-5384	457	11	with	with	ADP
ejpam-5384	457	12	ϕi	ϕi	ADP
ejpam-5384	457	13	,	,	PUNCT
ejpam-5384	457	14	ϕj	ϕj	INTJ
ejpam-5384	457	15	>	>	X
ejpam-5384	457	16	0	0	PROPN
ejpam-5384	457	17	,	,	PUNCT
ejpam-5384	457	18	(	(	PUNCT
ejpam-5384	457	19	12	12	NUM
ejpam-5384	457	20	)	)	PUNCT
ejpam-5384	457	21	which	which	PRON
ejpam-5384	457	22	establishes	establish	VERB
ejpam-5384	457	23	the	the	DET
ejpam-5384	457	24	first	first	ADJ
ejpam-5384	457	25	condition	condition	NOUN
ejpam-5384	457	26	of	of	ADP
ejpam-5384	457	27	theorem	theorem	NOUN
ejpam-5384	457	28	5	5	NUM
ejpam-5384	457	29	for	for	ADP
ejpam-5384	457	30	nnnn	nnnn	NOUN
ejpam-5384	457	31	.	.	PUNCT
ejpam-5384	458	1	from	from	ADP
ejpam-5384	458	2	the	the	DET
ejpam-5384	458	3	second	second	ADJ
ejpam-5384	458	4	condition	condition	NOUN
ejpam-5384	458	5	of	of	ADP
ejpam-5384	458	6	theorem	theorem	NOUN
ejpam-5384	458	7	5	5	NUM
ejpam-5384	458	8	for	for	ADP
ejpam-5384	458	9	the	the	DET
ejpam-5384	458	10	networks	network	NOUN
ejpam-5384	458	11	nn	nn	PROPN
ejpam-5384	458	12	and	and	CCONJ
ejpam-5384	458	13	nn	nn	INTJ
ejpam-5384	458	14	we	we	PRON
ejpam-5384	458	15	have	have	VERB
ejpam-5384	458	16	ϕil	ϕil	INTJ
ejpam-5384	458	17	′	′	NUM
ejpam-5384	458	18	i(ϕi	i(ϕi	ADJ
ejpam-5384	458	19	)	)	PUNCT
ejpam-5384	458	20	=	=	SYM
ejpam-5384	458	21	ϕjl	ϕjl	NOUN
ejpam-5384	458	22	′	′	NUM
ejpam-5384	458	23	j(ϕj	j(ϕj	NOUN
ejpam-5384	458	24	)	)	PUNCT
ejpam-5384	458	25	,	,	PUNCT
ejpam-5384	458	26	for	for	ADP
ejpam-5384	458	27	every	every	DET
ejpam-5384	458	28	i	i	PROPN
ejpam-5384	458	29	,	,	PUNCT
ejpam-5384	458	30	j	j	PROPN
ejpam-5384	458	31	∈	∈	PROPN
ejpam-5384	458	32	in	in	ADP
ejpam-5384	458	33	with	with	ADP
ejpam-5384	458	34	ϕi	ϕi	ADP
ejpam-5384	458	35	,	,	PUNCT
ejpam-5384	458	36	ϕj	ϕj	INTJ
ejpam-5384	458	37	>	>	X
ejpam-5384	458	38	0	0	PROPN
ejpam-5384	458	39	,	,	PUNCT
ejpam-5384	458	40	(	(	PUNCT
ejpam-5384	458	41	13	13	NUM
ejpam-5384	458	42	)	)	PUNCT
ejpam-5384	458	43	and	and	CCONJ
ejpam-5384	458	44	ϕil	ϕil	INTJ
ejpam-5384	458	45	′	′	NUM
ejpam-5384	458	46	i(ϕi	i(ϕi	ADJ
ejpam-5384	458	47	)	)	PUNCT
ejpam-5384	458	48	=	=	SYM
ejpam-5384	458	49	ϕjl	ϕjl	NOUN
ejpam-5384	458	50	′	′	NUM
ejpam-5384	458	51	j(ϕj	j(ϕj	NOUN
ejpam-5384	458	52	)	)	PUNCT
ejpam-5384	458	53	,	,	PUNCT
ejpam-5384	458	54	for	for	ADP
ejpam-5384	458	55	every	every	DET
ejpam-5384	458	56	i	i	PROPN
ejpam-5384	458	57	,	,	PUNCT
ejpam-5384	458	58	j	j	PROPN
ejpam-5384	458	59	∈	∈	PROPN
ejpam-5384	458	60	in	in	ADP
ejpam-5384	458	61	with	with	ADP
ejpam-5384	458	62	ϕi	ϕi	ADP
ejpam-5384	458	63	,	,	PUNCT
ejpam-5384	458	64	ϕj	ϕj	INTJ
ejpam-5384	458	65	>	>	X
ejpam-5384	458	66	0	0	X
ejpam-5384	458	67	.	.	PUNCT
ejpam-5384	459	1	(	(	PUNCT
ejpam-5384	459	2	14	14	NUM
ejpam-5384	459	3	)	)	PUNCT
ejpam-5384	459	4	to	to	PART
ejpam-5384	459	5	prove	prove	VERB
ejpam-5384	459	6	the	the	DET
ejpam-5384	459	7	second	second	ADJ
ejpam-5384	459	8	condition	condition	NOUN
ejpam-5384	459	9	for	for	ADP
ejpam-5384	459	10	nnnn	nnnn	NOUN
ejpam-5384	459	11	we	we	PRON
ejpam-5384	459	12	need	need	VERB
ejpam-5384	459	13	to	to	PART
ejpam-5384	459	14	prove	prove	VERB
ejpam-5384	459	15	that	that	SCONJ
ejpam-5384	459	16	for	for	ADP
ejpam-5384	459	17	every	every	DET
ejpam-5384	459	18	ϕi	ϕi	NOUN
ejpam-5384	459	19	,	,	PUNCT
ejpam-5384	459	20	ϕj	ϕj	INTJ
ejpam-5384	459	21	>	>	X
ejpam-5384	459	22	0	0	NUM
ejpam-5384	460	1	it	it	PRON
ejpam-5384	460	2	holds	hold	VERB
ejpam-5384	460	3	that	that	DET
ejpam-5384	460	4	ϕi(li(ϕi)li(ϕi	ϕi(li(ϕi)li(ϕi	VERB
ejpam-5384	460	5	)	)	PUNCT
ejpam-5384	460	6	)	)	PUNCT
ejpam-5384	461	1	′	′	NUM
ejpam-5384	462	1	=	=	PUNCT
ejpam-5384	462	2	ϕj(lj(ϕj)lj(ϕj	ϕj(lj(ϕj)lj(ϕj	NOUN
ejpam-5384	462	3	)	)	PUNCT
ejpam-5384	462	4	)	)	PUNCT
ejpam-5384	463	1	′	′	NOUN
ejpam-5384	463	2	,	,	PUNCT
ejpam-5384	463	3	(	(	PUNCT
ejpam-5384	463	4	15	15	NUM
ejpam-5384	463	5	)	)	PUNCT
ejpam-5384	463	6	or	or	CCONJ
ejpam-5384	463	7	equivalently	equivalently	ADV
ejpam-5384	463	8	ϕil	ϕil	ADJ
ejpam-5384	463	9	′	′	NUM
ejpam-5384	463	10	i(ϕi)li(ϕi	i(ϕi)li(ϕi	NOUN
ejpam-5384	463	11	)	)	PUNCT
ejpam-5384	463	12	+	+	NUM
ejpam-5384	463	13	ϕili(ϕi)l	ϕili(ϕi)l	NOUN
ejpam-5384	463	14	′	′	NUM
ejpam-5384	463	15	i(ϕi	i(ϕi	ADJ
ejpam-5384	463	16	)	)	PUNCT
ejpam-5384	463	17	=	=	SYM
ejpam-5384	463	18	ϕjl	ϕjl	NOUN
ejpam-5384	463	19	′	′	NUM
ejpam-5384	463	20	j(ϕj)lj(ϕj	j(ϕj)lj(ϕj	PROPN
ejpam-5384	463	21	)	)	PUNCT
ejpam-5384	464	1	+	+	NUM
ejpam-5384	464	2	ϕjlj(ϕj)l	ϕjlj(ϕj)l	NOUN
ejpam-5384	464	3	′	′	NUM
ejpam-5384	464	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	464	5	)	)	PUNCT
ejpam-5384	464	6	.	.	PUNCT
ejpam-5384	465	1	(	(	PUNCT
ejpam-5384	465	2	16	16	NUM
ejpam-5384	465	3	)	)	PUNCT
ejpam-5384	465	4	by	by	ADP
ejpam-5384	465	5	multiplying	multiply	VERB
ejpam-5384	465	6	equations	equation	NOUN
ejpam-5384	465	7	11	11	NUM
ejpam-5384	465	8	and	and	CCONJ
ejpam-5384	465	9	13	13	NUM
ejpam-5384	465	10	we	we	PRON
ejpam-5384	465	11	get	get	VERB
ejpam-5384	465	12	ϕil	ϕil	INTJ
ejpam-5384	465	13	′	′	NUM
ejpam-5384	465	14	i(ϕi)li(ϕi	i(ϕi)li(ϕi	NOUN
ejpam-5384	465	15	)	)	PUNCT
ejpam-5384	466	1	=	=	SYM
ejpam-5384	466	2	ϕjl	ϕjl	NOUN
ejpam-5384	466	3	′	′	NUM
ejpam-5384	466	4	j(ϕj)lj(ϕj	j(ϕj)lj(ϕj	NOUN
ejpam-5384	466	5	)	)	PUNCT
ejpam-5384	466	6	,	,	PUNCT
ejpam-5384	466	7	for	for	ADP
ejpam-5384	466	8	every	every	DET
ejpam-5384	466	9	i	i	PROPN
ejpam-5384	466	10	,	,	PUNCT
ejpam-5384	466	11	j	j	PROPN
ejpam-5384	466	12	∈	∈	PROPN
ejpam-5384	466	13	in	in	ADP
ejpam-5384	466	14	with	with	ADP
ejpam-5384	466	15	ϕi	ϕi	ADP
ejpam-5384	466	16	,	,	PUNCT
ejpam-5384	466	17	ϕj	ϕj	INTJ
ejpam-5384	466	18	>	>	X
ejpam-5384	466	19	0	0	X
ejpam-5384	466	20	.	.	PUNCT
ejpam-5384	467	1	(	(	PUNCT
ejpam-5384	467	2	17	17	NUM
ejpam-5384	467	3	)	)	PUNCT
ejpam-5384	467	4	by	by	ADP
ejpam-5384	467	5	multiplying	multiply	VERB
ejpam-5384	467	6	equations	equation	NOUN
ejpam-5384	467	7	10	10	NUM
ejpam-5384	467	8	and	and	CCONJ
ejpam-5384	467	9	14	14	NUM
ejpam-5384	467	10	we	we	PRON
ejpam-5384	467	11	get	get	VERB
ejpam-5384	467	12	ϕili(ϕi)l	ϕili(ϕi)l	NOUN
ejpam-5384	467	13	′	′	NUM
ejpam-5384	467	14	i(ϕi	i(ϕi	ADJ
ejpam-5384	467	15	)	)	PUNCT
ejpam-5384	467	16	=	=	SYM
ejpam-5384	468	1	ϕjlj(ϕj)l	ϕjlj(ϕj)l	ADP
ejpam-5384	469	1	′	′	NUM
ejpam-5384	469	2	j(ϕj	j(ϕj	NOUN
ejpam-5384	469	3	)	)	PUNCT
ejpam-5384	469	4	,	,	PUNCT
ejpam-5384	469	5	for	for	ADP
ejpam-5384	469	6	every	every	DET
ejpam-5384	469	7	i	i	PROPN
ejpam-5384	469	8	,	,	PUNCT
ejpam-5384	469	9	j	j	PROPN
ejpam-5384	469	10	∈	∈	PROPN
ejpam-5384	469	11	in	in	ADP
ejpam-5384	469	12	with	with	ADP
ejpam-5384	469	13	ϕi	ϕi	ADP
ejpam-5384	469	14	,	,	PUNCT
ejpam-5384	469	15	ϕj	ϕj	INTJ
ejpam-5384	469	16	>	>	X
ejpam-5384	469	17	0	0	X
ejpam-5384	469	18	.	.	PUNCT
ejpam-5384	470	1	(	(	PUNCT
ejpam-5384	470	2	18	18	NUM
ejpam-5384	470	3	)	)	PUNCT
ejpam-5384	470	4	equation	equation	NOUN
ejpam-5384	470	5	16	16	NUM
ejpam-5384	470	6	is	be	AUX
ejpam-5384	470	7	now	now	ADV
ejpam-5384	470	8	obtained	obtain	VERB
ejpam-5384	470	9	by	by	ADP
ejpam-5384	470	10	adding	add	VERB
ejpam-5384	470	11	equations	equation	NOUN
ejpam-5384	470	12	17	17	NUM
ejpam-5384	470	13	and	and	CCONJ
ejpam-5384	470	14	18	18	NUM
ejpam-5384	470	15	.	.	PUNCT
ejpam-5384	470	16	a.	a.	PROPN
ejpam-5384	470	17	kalampakas	kalampakas	PROPN
ejpam-5384	470	18	/	/	SYM
ejpam-5384	470	19	eur	eur	PROPN
ejpam-5384	470	20	.	.	PUNCT
ejpam-5384	471	1	j.	j.	PROPN
ejpam-5384	471	2	pure	pure	PROPN
ejpam-5384	471	3	appl	appl	PROPN
ejpam-5384	471	4	.	.	PROPN
ejpam-5384	471	5	math	math	PROPN
ejpam-5384	471	6	,	,	PUNCT
ejpam-5384	471	7	17	17	NUM
ejpam-5384	471	8	(	(	PUNCT
ejpam-5384	471	9	4	4	NUM
ejpam-5384	471	10	)	)	PUNCT
ejpam-5384	471	11	(	(	PUNCT
ejpam-5384	471	12	2024	2024	NUM
ejpam-5384	471	13	)	)	PUNCT
ejpam-5384	471	14	,	,	PUNCT
ejpam-5384	471	15	2448	2448	NUM
ejpam-5384	471	16	-	-	SYM
ejpam-5384	471	17	2466	2466	NUM
ejpam-5384	471	18	2463	2463	NUM
ejpam-5384	471	19	now	now	ADV
ejpam-5384	471	20	,	,	PUNCT
ejpam-5384	471	21	for	for	ADP
ejpam-5384	471	22	the	the	DET
ejpam-5384	471	23	remaining	remain	VERB
ejpam-5384	471	24	part	part	NOUN
ejpam-5384	471	25	of	of	ADP
ejpam-5384	471	26	the	the	DET
ejpam-5384	471	27	proof	proof	NOUN
ejpam-5384	471	28	,	,	PUNCT
ejpam-5384	471	29	from	from	ADP
ejpam-5384	471	30	the	the	DET
ejpam-5384	471	31	last	last	ADJ
ejpam-5384	471	32	condition	condition	NOUN
ejpam-5384	471	33	of	of	ADP
ejpam-5384	471	34	theorem	theorem	NOUN
ejpam-5384	471	35	5	5	NUM
ejpam-5384	471	36	for	for	ADP
ejpam-5384	471	37	nn	nn	PROPN
ejpam-5384	471	38	and	and	CCONJ
ejpam-5384	471	39	nn	nn	PROPN
ejpam-5384	471	40	,	,	PUNCT
ejpam-5384	471	41	it	it	PRON
ejpam-5384	471	42	holds	hold	VERB
ejpam-5384	471	43	that	that	SCONJ
ejpam-5384	471	44	for	for	ADP
ejpam-5384	471	45	every	every	DET
ejpam-5384	471	46	i	i	PROPN
ejpam-5384	471	47	,	,	PUNCT
ejpam-5384	471	48	j	j	PROPN
ejpam-5384	471	49	∈	∈	PROPN
ejpam-5384	471	50	in	in	ADP
ejpam-5384	471	51	,	,	PUNCT
ejpam-5384	471	52	with	with	ADP
ejpam-5384	471	53	ϕi	ϕi	ADP
ejpam-5384	471	54	=	=	SYM
ejpam-5384	471	55	0	0	NUM
ejpam-5384	471	56	and	and	CCONJ
ejpam-5384	471	57	ϕj	ϕj	ADP
ejpam-5384	471	58	>	>	X
ejpam-5384	471	59	0	0	PUNCT
ejpam-5384	472	1	li(0	li(0	PROPN
ejpam-5384	472	2	)	)	PUNCT
ejpam-5384	472	3	≥	≥	NOUN
ejpam-5384	472	4	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	472	5	)	)	PUNCT
ejpam-5384	473	1	+	+	CCONJ
ejpam-5384	473	2	ϕj	ϕj	ADP
ejpam-5384	473	3	l	l	NOUN
ejpam-5384	473	4	′	′	NUM
ejpam-5384	473	5	j(ϕj	j(ϕj	NOUN
ejpam-5384	473	6	)	)	PUNCT
ejpam-5384	473	7	and	and	CCONJ
ejpam-5384	473	8	li(0	li(0	PROPN
ejpam-5384	473	9	)	)	PUNCT
ejpam-5384	473	10	≥	≥	NOUN
ejpam-5384	473	11	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	473	12	)	)	PUNCT
ejpam-5384	474	1	+	+	CCONJ
ejpam-5384	474	2	ϕj	ϕj	ADP
ejpam-5384	474	3	l	l	NOUN
ejpam-5384	474	4	′	′	NUM
ejpam-5384	474	5	j(ϕj	j(ϕj	NOUN
ejpam-5384	474	6	)	)	PUNCT
ejpam-5384	474	7	.	.	PUNCT
ejpam-5384	475	1	by	by	ADP
ejpam-5384	475	2	multiplying	multiply	VERB
ejpam-5384	475	3	the	the	DET
ejpam-5384	475	4	above	above	ADJ
ejpam-5384	475	5	inequalities	inequality	NOUN
ejpam-5384	475	6	we	we	PRON
ejpam-5384	475	7	get	get	VERB
ejpam-5384	475	8	li(0)li(0	li(0)li(0	PROPN
ejpam-5384	475	9	)	)	PUNCT
ejpam-5384	475	10	≥	≥	NOUN
ejpam-5384	475	11	lj(ϕj)lj(ϕj	lj(ϕj)lj(ϕj	NOUN
ejpam-5384	475	12	)	)	PUNCT
ejpam-5384	475	13	+	+	CCONJ
ejpam-5384	475	14	lj(ϕj)ϕj	lj(ϕj)ϕj	PROPN
ejpam-5384	475	15	l	l	NOUN
ejpam-5384	475	16	′	′	NUM
ejpam-5384	475	17	j(ϕj	j(ϕj	NOUN
ejpam-5384	475	18	)	)	PUNCT
ejpam-5384	476	1	+	+	CCONJ
ejpam-5384	476	2	lj(ϕj)ϕj	lj(ϕj)ϕj	PROPN
ejpam-5384	477	1	l	l	NOUN
ejpam-5384	477	2	′	′	NUM
ejpam-5384	477	3	j(ϕj	j(ϕj	NOUN
ejpam-5384	477	4	)	)	PUNCT
ejpam-5384	478	1	+	+	CCONJ
ejpam-5384	478	2	ϕj	ϕj	ADP
ejpam-5384	478	3	l	l	NOUN
ejpam-5384	478	4	′	′	NUM
ejpam-5384	479	1	j(ϕj)ϕj	j(ϕj)ϕj	PROPN
ejpam-5384	479	2	l	l	NOUN
ejpam-5384	479	3	′	′	NUM
ejpam-5384	479	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	479	5	)	)	PUNCT
ejpam-5384	479	6	.	.	PUNCT
ejpam-5384	480	1	(	(	PUNCT
ejpam-5384	480	2	19	19	NUM
ejpam-5384	480	3	)	)	PUNCT
ejpam-5384	480	4	from	from	ADP
ejpam-5384	480	5	this	this	PRON
ejpam-5384	480	6	,	,	PUNCT
ejpam-5384	480	7	we	we	PRON
ejpam-5384	480	8	get	get	VERB
ejpam-5384	480	9	the	the	DET
ejpam-5384	480	10	third	third	ADJ
ejpam-5384	480	11	condition	condition	NOUN
ejpam-5384	480	12	of	of	ADP
ejpam-5384	480	13	theorem	theorem	NOUN
ejpam-5384	480	14	5	5	NUM
ejpam-5384	480	15	for	for	ADP
ejpam-5384	480	16	the	the	DET
ejpam-5384	480	17	network	network	NOUN
ejpam-5384	480	18	nnnn	nnnn	PROPN
ejpam-5384	480	19	,	,	PUNCT
ejpam-5384	480	20	which	which	PRON
ejpam-5384	480	21	is	be	AUX
ejpam-5384	480	22	:	:	PUNCT
ejpam-5384	480	23	li(0)li(0	li(0)li(0	PROPN
ejpam-5384	480	24	)	)	PUNCT
ejpam-5384	480	25	≥	≥	NOUN
ejpam-5384	480	26	lj(ϕj)lj(ϕj	lj(ϕj)lj(ϕj	NOUN
ejpam-5384	480	27	)	)	PUNCT
ejpam-5384	481	1	+	+	CCONJ
ejpam-5384	481	2	ϕj	ϕj	INTJ
ejpam-5384	481	3	(	(	PUNCT
ejpam-5384	481	4	lj(ϕj)lj(ϕj	lj(ϕj)lj(ϕj	NOUN
ejpam-5384	481	5	)	)	PUNCT
ejpam-5384	481	6	)	)	PUNCT
ejpam-5384	481	7	′	′	NUM
ejpam-5384	481	8	,	,	PUNCT
ejpam-5384	481	9	(	(	PUNCT
ejpam-5384	481	10	20	20	NUM
ejpam-5384	481	11	)	)	PUNCT
ejpam-5384	481	12	or	or	CCONJ
ejpam-5384	481	13	equivalently	equivalently	ADV
ejpam-5384	481	14	li(0)li(0	li(0)li(0	PROPN
ejpam-5384	481	15	)	)	PUNCT
ejpam-5384	481	16	≥	≥	NOUN
ejpam-5384	481	17	lj(ϕj)lj(ϕj	lj(ϕj)lj(ϕj	NOUN
ejpam-5384	481	18	)	)	PUNCT
ejpam-5384	481	19	+	+	CCONJ
ejpam-5384	481	20	ϕjl	ϕjl	NOUN
ejpam-5384	481	21	′	′	NUM
ejpam-5384	481	22	j(ϕj)lj(ϕj	j(ϕj)lj(ϕj	PROPN
ejpam-5384	481	23	)	)	PUNCT
ejpam-5384	482	1	+	+	CCONJ
ejpam-5384	482	2	ϕj	ϕj	ADP
ejpam-5384	482	3	lj(ϕj)ϕjl	lj(ϕj)ϕjl	PROPN
ejpam-5384	482	4	′	′	NUM
ejpam-5384	482	5	j(ϕj	j(ϕj	NOUN
ejpam-5384	482	6	)	)	PUNCT
ejpam-5384	482	7	.	.	PUNCT
ejpam-5384	483	1	(	(	PUNCT
ejpam-5384	483	2	21	21	NUM
ejpam-5384	483	3	)	)	PUNCT
ejpam-5384	483	4	in	in	ADP
ejpam-5384	483	5	a	a	DET
ejpam-5384	483	6	similar	similar	ADJ
ejpam-5384	483	7	way	way	NOUN
ejpam-5384	483	8	,	,	PUNCT
ejpam-5384	483	9	we	we	PRON
ejpam-5384	483	10	will	will	AUX
ejpam-5384	483	11	establish	establish	VERB
ejpam-5384	483	12	the	the	DET
ejpam-5384	483	13	next	next	ADJ
ejpam-5384	483	14	proposition	proposition	NOUN
ejpam-5384	483	15	.	.	PUNCT
ejpam-5384	484	1	proposition	proposition	NOUN
ejpam-5384	484	2	11	11	NUM
ejpam-5384	484	3	.	.	PUNCT
ejpam-5384	485	1	if	if	SCONJ
ejpam-5384	485	2	the	the	DET
ejpam-5384	485	3	flow	flow	NOUN
ejpam-5384	485	4	ϕ	ϕ	NOUN
ejpam-5384	485	5	=	=	PUNCT
ejpam-5384	485	6	(	(	PUNCT
ejpam-5384	485	7	ϕ1	ϕ1	NOUN
ejpam-5384	485	8	,	,	PUNCT
ejpam-5384	485	9	.	.	PUNCT
ejpam-5384	485	10	.	.	PUNCT
ejpam-5384	486	1	.	.	PUNCT
ejpam-5384	487	1	,	,	PUNCT
ejpam-5384	487	2	ϕn	ϕn	X
ejpam-5384	487	3	)	)	PUNCT
ejpam-5384	487	4	∈	∈	PROPN
ejpam-5384	487	5	sn−1	sn−1	PROPN
ejpam-5384	487	6	is	be	AUX
ejpam-5384	487	7	wof	wof	NOUN
ejpam-5384	487	8	of	of	ADP
ejpam-5384	487	9	the	the	DET
ejpam-5384	487	10	convex	convex	PROPN
ejpam-5384	487	11	networks	network	NOUN
ejpam-5384	487	12	nn	nn	PROPN
ejpam-5384	488	1	=	=	SYM
ejpam-5384	488	2	(	(	PUNCT
ejpam-5384	488	3	l1(x	l1(x	NOUN
ejpam-5384	488	4	)	)	PUNCT
ejpam-5384	488	5	,	,	PUNCT
ejpam-5384	488	6	.	.	PUNCT
ejpam-5384	488	7	.	.	PUNCT
ejpam-5384	489	1	.	.	PUNCT
ejpam-5384	490	1	,	,	PUNCT
ejpam-5384	490	2	ln(x	ln(x	X
ejpam-5384	490	3	)	)	PUNCT
ejpam-5384	490	4	)	)	PUNCT
ejpam-5384	491	1	and	and	CCONJ
ejpam-5384	491	2	nn	nn	X
ejpam-5384	491	3	=	=	SYM
ejpam-5384	491	4	(	(	PUNCT
ejpam-5384	491	5	l1(x	l1(x	NOUN
ejpam-5384	491	6	)	)	PUNCT
ejpam-5384	491	7	,	,	PUNCT
ejpam-5384	491	8	.	.	PUNCT
ejpam-5384	491	9	.	.	PUNCT
ejpam-5384	491	10	.	.	PUNCT
ejpam-5384	492	1	,	,	PUNCT
ejpam-5384	492	2	ln(x	ln(x	X
ejpam-5384	492	3	)	)	PUNCT
ejpam-5384	492	4	)	)	PUNCT
ejpam-5384	492	5	,	,	PUNCT
ejpam-5384	492	6	then	then	ADV
ejpam-5384	492	7	it	it	PRON
ejpam-5384	492	8	is	be	AUX
ejpam-5384	492	9	also	also	ADV
ejpam-5384	492	10	wof	wof	X
ejpam-5384	492	11	of	of	ADP
ejpam-5384	493	1	nn	nn	PROPN
ejpam-5384	493	2	+	+	PROPN
ejpam-5384	493	3	nn	nn	X
ejpam-5384	493	4	=	=	SYM
ejpam-5384	493	5	(	(	PUNCT
ejpam-5384	493	6	l1(x	l1(x	NOUN
ejpam-5384	493	7	)	)	PUNCT
ejpam-5384	494	1	+	+	NUM
ejpam-5384	494	2	l1(x	l1(x	NOUN
ejpam-5384	494	3	)	)	PUNCT
ejpam-5384	494	4	,	,	PUNCT
ejpam-5384	494	5	.	.	PUNCT
ejpam-5384	494	6	.	.	PUNCT
ejpam-5384	495	1	.	.	PUNCT
ejpam-5384	496	1	,	,	PUNCT
ejpam-5384	496	2	ln(x	ln(x	X
ejpam-5384	496	3	)	)	PUNCT
ejpam-5384	497	1	+	+	CCONJ
ejpam-5384	497	2	ln(x	ln(x	X
ejpam-5384	497	3	)	)	PUNCT
ejpam-5384	497	4	)	)	PUNCT
ejpam-5384	497	5	.	.	PUNCT
ejpam-5384	498	1	proof	proof	NOUN
ejpam-5384	498	2	.	.	PUNCT
ejpam-5384	499	1	since	since	SCONJ
ejpam-5384	499	2	ϕ	ϕ	PROPN
ejpam-5384	499	3	is	be	AUX
ejpam-5384	499	4	wof	wof	NOUN
ejpam-5384	499	5	of	of	ADP
ejpam-5384	499	6	the	the	DET
ejpam-5384	499	7	networksnn	networksnn	PROPN
ejpam-5384	499	8	andnn	andnn	PROPN
ejpam-5384	499	9	,	,	PUNCT
ejpam-5384	499	10	from	from	ADP
ejpam-5384	499	11	the	the	DET
ejpam-5384	499	12	first	first	ADJ
ejpam-5384	499	13	condition	condition	NOUN
ejpam-5384	499	14	of	of	ADP
ejpam-5384	499	15	theorem	theorem	NOUN
ejpam-5384	499	16	5	5	NUM
ejpam-5384	499	17	,	,	PUNCT
ejpam-5384	499	18	we	we	PRON
ejpam-5384	499	19	have	have	VERB
ejpam-5384	499	20	that	that	PRON
ejpam-5384	499	21	for	for	ADP
ejpam-5384	499	22	the	the	DET
ejpam-5384	499	23	two	two	NUM
ejpam-5384	499	24	networks	network	NOUN
ejpam-5384	499	25	it	it	PRON
ejpam-5384	499	26	holds	hold	VERB
ejpam-5384	499	27	li(ϕi	li(ϕi	ADJ
ejpam-5384	499	28	)	)	PUNCT
ejpam-5384	499	29	=	=	SYM
ejpam-5384	499	30	lj(ϕj	lj(ϕj	NOUN
ejpam-5384	499	31	)	)	PUNCT
ejpam-5384	499	32	,	,	PUNCT
ejpam-5384	499	33	for	for	ADP
ejpam-5384	499	34	every	every	DET
ejpam-5384	499	35	i	i	PROPN
ejpam-5384	499	36	,	,	PUNCT
ejpam-5384	499	37	j	j	PROPN
ejpam-5384	499	38	∈	∈	PROPN
ejpam-5384	499	39	in	in	ADP
ejpam-5384	499	40	with	with	ADP
ejpam-5384	499	41	ϕi	ϕi	ADP
ejpam-5384	499	42	,	,	PUNCT
ejpam-5384	499	43	ϕj	ϕj	INTJ
ejpam-5384	499	44	>	>	X
ejpam-5384	499	45	0	0	PROPN
ejpam-5384	499	46	,	,	PUNCT
ejpam-5384	499	47	(	(	PUNCT
ejpam-5384	499	48	22	22	NUM
ejpam-5384	499	49	)	)	PUNCT
ejpam-5384	499	50	and	and	CCONJ
ejpam-5384	499	51	li(ϕi	li(ϕi	ADJ
ejpam-5384	499	52	)	)	PUNCT
ejpam-5384	499	53	=	=	SYM
ejpam-5384	499	54	lj(ϕj	lj(ϕj	NOUN
ejpam-5384	499	55	)	)	PUNCT
ejpam-5384	499	56	,	,	PUNCT
ejpam-5384	499	57	for	for	ADP
ejpam-5384	499	58	every	every	DET
ejpam-5384	499	59	i	i	PROPN
ejpam-5384	499	60	,	,	PUNCT
ejpam-5384	499	61	j	j	PROPN
ejpam-5384	499	62	∈	∈	PROPN
ejpam-5384	499	63	in	in	ADP
ejpam-5384	499	64	with	with	ADP
ejpam-5384	499	65	ϕi	ϕi	ADP
ejpam-5384	499	66	,	,	PUNCT
ejpam-5384	499	67	ϕj	ϕj	INTJ
ejpam-5384	499	68	>	>	X
ejpam-5384	499	69	0	0	X
ejpam-5384	499	70	.	.	PUNCT
ejpam-5384	500	1	(	(	PUNCT
ejpam-5384	500	2	23	23	NUM
ejpam-5384	500	3	)	)	PUNCT
ejpam-5384	500	4	by	by	ADP
ejpam-5384	500	5	adding	add	VERB
ejpam-5384	500	6	the	the	DET
ejpam-5384	500	7	two	two	NUM
ejpam-5384	500	8	we	we	PRON
ejpam-5384	500	9	get	get	VERB
ejpam-5384	500	10	the	the	DET
ejpam-5384	500	11	first	first	ADJ
ejpam-5384	500	12	condition	condition	NOUN
ejpam-5384	500	13	for	for	ADP
ejpam-5384	500	14	the	the	DET
ejpam-5384	500	15	network	network	NOUN
ejpam-5384	500	16	nn	nn	PROPN
ejpam-5384	500	17	+	+	PROPN
ejpam-5384	500	18	nn	nn	X
ejpam-5384	500	19	li(ϕi	li(ϕi	NOUN
ejpam-5384	500	20	)	)	PUNCT
ejpam-5384	501	1	+	+	NUM
ejpam-5384	501	2	li(x	li(x	X
ejpam-5384	501	3	)	)	PUNCT
ejpam-5384	501	4	=	=	SYM
ejpam-5384	501	5	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	501	6	)	)	PUNCT
ejpam-5384	501	7	+	+	NUM
ejpam-5384	501	8	lj(x	lj(x	NUM
ejpam-5384	501	9	)	)	PUNCT
ejpam-5384	501	10	,	,	PUNCT
ejpam-5384	501	11	for	for	ADP
ejpam-5384	501	12	every	every	DET
ejpam-5384	501	13	i	i	PROPN
ejpam-5384	501	14	,	,	PUNCT
ejpam-5384	501	15	j	j	PROPN
ejpam-5384	501	16	∈	∈	PROPN
ejpam-5384	501	17	in	in	ADP
ejpam-5384	501	18	with	with	ADP
ejpam-5384	501	19	ϕi	ϕi	ADP
ejpam-5384	501	20	,	,	PUNCT
ejpam-5384	501	21	ϕj	ϕj	INTJ
ejpam-5384	501	22	>	>	X
ejpam-5384	501	23	0	0	PROPN
ejpam-5384	501	24	,	,	PUNCT
ejpam-5384	501	25	(	(	PUNCT
ejpam-5384	501	26	24	24	NUM
ejpam-5384	501	27	)	)	PUNCT
ejpam-5384	501	28	which	which	PRON
ejpam-5384	501	29	settles	settle	VERB
ejpam-5384	501	30	the	the	DET
ejpam-5384	501	31	first	first	ADJ
ejpam-5384	501	32	condition	condition	NOUN
ejpam-5384	501	33	of	of	ADP
ejpam-5384	501	34	theorem	theorem	NOUN
ejpam-5384	501	35	5	5	NUM
ejpam-5384	501	36	for	for	ADP
ejpam-5384	501	37	nn	nn	PROPN
ejpam-5384	501	38	+	+	PROPN
ejpam-5384	501	39	nn	nn	PROPN
ejpam-5384	501	40	.	.	PROPN
ejpam-5384	501	41	for	for	ADP
ejpam-5384	501	42	the	the	DET
ejpam-5384	501	43	next	next	ADJ
ejpam-5384	501	44	condition	condition	NOUN
ejpam-5384	501	45	of	of	ADP
ejpam-5384	501	46	theorem	theorem	NOUN
ejpam-5384	501	47	5	5	NUM
ejpam-5384	501	48	,	,	PUNCT
ejpam-5384	501	49	assume	assume	VERB
ejpam-5384	501	50	that	that	SCONJ
ejpam-5384	501	51	for	for	ADP
ejpam-5384	501	52	the	the	DET
ejpam-5384	501	53	networks	network	NOUN
ejpam-5384	501	54	nn	nn	PROPN
ejpam-5384	501	55	and	and	CCONJ
ejpam-5384	501	56	nn	nn	INTJ
ejpam-5384	501	57	we	we	PRON
ejpam-5384	501	58	have	have	VERB
ejpam-5384	501	59	ϕil	ϕil	INTJ
ejpam-5384	501	60	′	′	NUM
ejpam-5384	501	61	i(ϕi	i(ϕi	ADJ
ejpam-5384	501	62	)	)	PUNCT
ejpam-5384	501	63	=	=	SYM
ejpam-5384	501	64	ϕjl	ϕjl	NOUN
ejpam-5384	501	65	′	′	NUM
ejpam-5384	501	66	j(ϕj	j(ϕj	NOUN
ejpam-5384	501	67	)	)	PUNCT
ejpam-5384	501	68	,	,	PUNCT
ejpam-5384	501	69	for	for	SCONJ
ejpam-5384	501	70	every	every	DET
ejpam-5384	501	71	i	i	PROPN
ejpam-5384	501	72	,	,	PUNCT
ejpam-5384	501	73	j	j	PROPN
ejpam-5384	501	74	∈	∈	PROPN
ejpam-5384	501	75	in	in	ADP
ejpam-5384	501	76	with	with	ADP
ejpam-5384	501	77	ϕi	ϕi	ADP
ejpam-5384	501	78	,	,	PUNCT
ejpam-5384	501	79	ϕj	ϕj	INTJ
ejpam-5384	501	80	>	>	X
ejpam-5384	501	81	0	0	X
ejpam-5384	501	82	.	.	PUNCT
ejpam-5384	502	1	(	(	PUNCT
ejpam-5384	502	2	25	25	NUM
ejpam-5384	502	3	)	)	PUNCT
ejpam-5384	502	4	and	and	CCONJ
ejpam-5384	502	5	ϕil	ϕil	INTJ
ejpam-5384	502	6	′	′	NUM
ejpam-5384	502	7	i(ϕi	i(ϕi	ADJ
ejpam-5384	502	8	)	)	PUNCT
ejpam-5384	502	9	=	=	SYM
ejpam-5384	502	10	ϕjl	ϕjl	NOUN
ejpam-5384	502	11	′	′	NUM
ejpam-5384	502	12	j(ϕj	j(ϕj	NOUN
ejpam-5384	502	13	)	)	PUNCT
ejpam-5384	502	14	,	,	PUNCT
ejpam-5384	502	15	for	for	ADP
ejpam-5384	502	16	every	every	DET
ejpam-5384	502	17	i	i	PROPN
ejpam-5384	502	18	,	,	PUNCT
ejpam-5384	502	19	j	j	PROPN
ejpam-5384	502	20	∈	∈	PROPN
ejpam-5384	502	21	in	in	ADP
ejpam-5384	502	22	with	with	ADP
ejpam-5384	502	23	ϕi	ϕi	ADP
ejpam-5384	502	24	,	,	PUNCT
ejpam-5384	502	25	ϕj	ϕj	INTJ
ejpam-5384	502	26	>	>	X
ejpam-5384	502	27	0	0	X
ejpam-5384	502	28	.	.	PUNCT
ejpam-5384	503	1	(	(	PUNCT
ejpam-5384	503	2	26	26	NUM
ejpam-5384	503	3	)	)	PUNCT
ejpam-5384	503	4	by	by	ADP
ejpam-5384	503	5	adding	add	VERB
ejpam-5384	503	6	equations	equation	NOUN
ejpam-5384	503	7	25	25	NUM
ejpam-5384	503	8	and	and	CCONJ
ejpam-5384	503	9	26	26	NUM
ejpam-5384	503	10	we	we	PRON
ejpam-5384	503	11	get	get	VERB
ejpam-5384	503	12	ϕil	ϕil	INTJ
ejpam-5384	503	13	′	′	NUM
ejpam-5384	503	14	i(ϕi	i(ϕi	ADJ
ejpam-5384	503	15	)	)	PUNCT
ejpam-5384	504	1	+	+	CCONJ
ejpam-5384	504	2	ϕil	ϕil	ADJ
ejpam-5384	504	3	′	′	NUM
ejpam-5384	504	4	i(ϕi	i(ϕi	ADJ
ejpam-5384	504	5	)	)	PUNCT
ejpam-5384	504	6	=	=	SYM
ejpam-5384	504	7	ϕjl	ϕjl	NOUN
ejpam-5384	504	8	′	′	NUM
ejpam-5384	504	9	j(ϕj	j(ϕj	NOUN
ejpam-5384	504	10	)	)	PUNCT
ejpam-5384	505	1	+	+	CCONJ
ejpam-5384	505	2	ϕjl	ϕjl	NOUN
ejpam-5384	505	3	′	′	NUM
ejpam-5384	505	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	505	5	)	)	PUNCT
ejpam-5384	505	6	,	,	PUNCT
ejpam-5384	505	7	(	(	PUNCT
ejpam-5384	505	8	27	27	NUM
ejpam-5384	505	9	)	)	PUNCT
ejpam-5384	505	10	bibliography	bibliography	NOUN
ejpam-5384	505	11	2464	2464	NUM
ejpam-5384	505	12	or	or	CCONJ
ejpam-5384	505	13	equivalently	equivalently	ADV
ejpam-5384	505	14	ϕi(li(ϕi	ϕi(li(ϕi	NUM
ejpam-5384	505	15	)	)	PUNCT
ejpam-5384	505	16	+	+	CCONJ
ejpam-5384	505	17	li(ϕi	li(ϕi	ADJ
ejpam-5384	505	18	)	)	PUNCT
ejpam-5384	505	19	)	)	PUNCT
ejpam-5384	505	20	′	′	NUM
ejpam-5384	506	1	=	=	PUNCT
ejpam-5384	506	2	ϕj(lj(ϕj	ϕj(lj(ϕj	X
ejpam-5384	506	3	)	)	PUNCT
ejpam-5384	506	4	+	+	NUM
ejpam-5384	506	5	lj(ϕj	lj(ϕj	NOUN
ejpam-5384	506	6	)	)	PUNCT
ejpam-5384	506	7	)	)	PUNCT
ejpam-5384	506	8	′	′	NOUN
ejpam-5384	506	9	,	,	PUNCT
ejpam-5384	506	10	(	(	PUNCT
ejpam-5384	506	11	28	28	NUM
ejpam-5384	506	12	)	)	PUNCT
ejpam-5384	506	13	as	as	SCONJ
ejpam-5384	506	14	desired	desire	VERB
ejpam-5384	506	15	.	.	PUNCT
ejpam-5384	507	1	now	now	ADV
ejpam-5384	507	2	for	for	ADP
ejpam-5384	507	3	the	the	DET
ejpam-5384	507	4	remaining	remain	VERB
ejpam-5384	507	5	part	part	NOUN
ejpam-5384	507	6	of	of	ADP
ejpam-5384	507	7	the	the	DET
ejpam-5384	507	8	proof	proof	NOUN
ejpam-5384	507	9	,	,	PUNCT
ejpam-5384	507	10	if	if	SCONJ
ejpam-5384	507	11	for	for	ADP
ejpam-5384	507	12	nn	nn	PROPN
ejpam-5384	507	13	and	and	CCONJ
ejpam-5384	507	14	nn	nn	PROPN
ejpam-5384	507	15	it	it	PRON
ejpam-5384	507	16	holds	hold	VERB
ejpam-5384	507	17	li(0	li(0	PROPN
ejpam-5384	507	18	)	)	PUNCT
ejpam-5384	507	19	≥	≥	NOUN
ejpam-5384	507	20	lj(ϕj	lj(ϕj	NOUN
ejpam-5384	507	21	)	)	PUNCT
ejpam-5384	508	1	+	+	CCONJ
ejpam-5384	508	2	ϕj	ϕj	ADP
ejpam-5384	508	3	l	l	NOUN
ejpam-5384	508	4	′	′	NUM
ejpam-5384	508	5	j(ϕj	j(ϕj	NOUN
ejpam-5384	508	6	)	)	PUNCT
ejpam-5384	508	7	and	and	CCONJ
ejpam-5384	508	8	li(0	li(0	PROPN
ejpam-5384	508	9	)	)	PUNCT
ejpam-5384	508	10	≥	≥	NOUN
ejpam-5384	508	11	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	508	12	)	)	PUNCT
ejpam-5384	509	1	+	+	CCONJ
ejpam-5384	509	2	ϕj	ϕj	ADP
ejpam-5384	509	3	l	l	NOUN
ejpam-5384	509	4	′	′	NUM
ejpam-5384	509	5	j(ϕj	j(ϕj	NOUN
ejpam-5384	509	6	)	)	PUNCT
ejpam-5384	509	7	,	,	PUNCT
ejpam-5384	509	8	for	for	ADP
ejpam-5384	509	9	every	every	DET
ejpam-5384	509	10	i	i	PROPN
ejpam-5384	509	11	,	,	PUNCT
ejpam-5384	509	12	j	j	PROPN
ejpam-5384	509	13	∈	∈	PROPN
ejpam-5384	509	14	in	in	ADP
ejpam-5384	509	15	with	with	ADP
ejpam-5384	509	16	ϕi	ϕi	ADP
ejpam-5384	509	17	=	=	SYM
ejpam-5384	509	18	0	0	NUM
ejpam-5384	509	19	and	and	CCONJ
ejpam-5384	509	20	ϕj	ϕj	ADP
ejpam-5384	509	21	>	>	X
ejpam-5384	509	22	0	0	PROPN
ejpam-5384	509	23	,	,	PUNCT
ejpam-5384	509	24	then	then	ADV
ejpam-5384	509	25	by	by	ADP
ejpam-5384	509	26	adding	add	VERB
ejpam-5384	509	27	the	the	DET
ejpam-5384	509	28	above	above	ADJ
ejpam-5384	509	29	inequalities	inequality	NOUN
ejpam-5384	509	30	we	we	PRON
ejpam-5384	509	31	get	get	VERB
ejpam-5384	509	32	li(0	li(0	PROPN
ejpam-5384	509	33	)	)	PUNCT
ejpam-5384	509	34	+	+	SYM
ejpam-5384	509	35	li(0	li(0	PROPN
ejpam-5384	509	36	)	)	PUNCT
ejpam-5384	509	37	≥	≥	NOUN
ejpam-5384	509	38	lj(ϕj	lj(ϕj	PROPN
ejpam-5384	509	39	)	)	PUNCT
ejpam-5384	509	40	+	+	NUM
ejpam-5384	509	41	lj(ϕj	lj(ϕj	NOUN
ejpam-5384	509	42	)	)	PUNCT
ejpam-5384	510	1	+	+	NUM
ejpam-5384	510	2	ϕj(l	ϕj(l	NUM
ejpam-5384	510	3	′	′	NUM
ejpam-5384	510	4	j(ϕj	j(ϕj	NOUN
ejpam-5384	510	5	)	)	PUNCT
ejpam-5384	510	6	+	+	NUM
ejpam-5384	510	7	l	l	NOUN
ejpam-5384	510	8	′	′	NUM
ejpam-5384	510	9	j(ϕj	j(ϕj	NOUN
ejpam-5384	510	10	)	)	PUNCT
ejpam-5384	510	11	)	)	PUNCT
ejpam-5384	510	12	.	.	PUNCT
ejpam-5384	511	1	(	(	PUNCT
ejpam-5384	511	2	29	29	NUM
ejpam-5384	511	3	)	)	PUNCT
ejpam-5384	511	4	from	from	ADP
ejpam-5384	511	5	the	the	DET
ejpam-5384	511	6	above	above	NOUN
ejpam-5384	511	7	,	,	PUNCT
ejpam-5384	511	8	the	the	DET
ejpam-5384	511	9	last	last	ADJ
ejpam-5384	511	10	condition	condition	NOUN
ejpam-5384	511	11	of	of	ADP
ejpam-5384	511	12	theorem	theorem	NOUN
ejpam-5384	511	13	5	5	NUM
ejpam-5384	511	14	for	for	ADP
ejpam-5384	511	15	the	the	DET
ejpam-5384	511	16	network	network	NOUN
ejpam-5384	511	17	nn	nn	PROPN
ejpam-5384	511	18	+	+	PROPN
ejpam-5384	511	19	nn	nn	PROPN
ejpam-5384	511	20	follows	follow	VERB
ejpam-5384	511	21	.	.	PUNCT
ejpam-5384	512	1	6	6	X
ejpam-5384	512	2	.	.	X
ejpam-5384	512	3	conclusion	conclusion	NOUN
ejpam-5384	512	4	and	and	CCONJ
ejpam-5384	512	5	future	future	ADJ
ejpam-5384	512	6	work	work	NOUN
ejpam-5384	512	7	we	we	PRON
ejpam-5384	512	8	have	have	AUX
ejpam-5384	512	9	investigated	investigate	VERB
ejpam-5384	512	10	directed	direct	VERB
ejpam-5384	512	11	,	,	PUNCT
ejpam-5384	512	12	parallel	parallel	ADJ
ejpam-5384	512	13	networks	network	NOUN
ejpam-5384	512	14	with	with	ADP
ejpam-5384	512	15	congestion	congestion	NOUN
ejpam-5384	512	16	externalities	externality	NOUN
ejpam-5384	512	17	and	and	CCONJ
ejpam-5384	512	18	their	their	PRON
ejpam-5384	512	19	equilibriums	equilibrium	NOUN
ejpam-5384	512	20	.	.	PUNCT
ejpam-5384	513	1	we	we	PRON
ejpam-5384	513	2	identified	identify	VERB
ejpam-5384	513	3	necessary	necessary	ADJ
ejpam-5384	513	4	and	and	CCONJ
ejpam-5384	513	5	sufficient	sufficient	ADJ
ejpam-5384	513	6	conditions	condition	NOUN
ejpam-5384	513	7	for	for	ADP
ejpam-5384	513	8	achieving	achieve	VERB
ejpam-5384	513	9	the	the	DET
ejpam-5384	513	10	system	system	NOUN
ejpam-5384	513	11	optimum	optimum	ADJ
ejpam-5384	513	12	and	and	CCONJ
ejpam-5384	513	13	we	we	PRON
ejpam-5384	513	14	introduced	introduce	VERB
ejpam-5384	513	15	wardrop	wardrop	NOUN
ejpam-5384	513	16	optimal	optimal	ADJ
ejpam-5384	513	17	networks	network	NOUN
ejpam-5384	513	18	admitting	admit	VERB
ejpam-5384	513	19	the	the	DET
ejpam-5384	513	20	same	same	ADJ
ejpam-5384	513	21	user	user	NOUN
ejpam-5384	513	22	and	and	CCONJ
ejpam-5384	513	23	system	system	NOUN
ejpam-5384	513	24	equilibrium	equilibrium	NOUN
ejpam-5384	513	25	.	.	PUNCT
ejpam-5384	514	1	in	in	ADP
ejpam-5384	514	2	addition	addition	NOUN
ejpam-5384	514	3	we	we	PRON
ejpam-5384	514	4	establish	establish	VERB
ejpam-5384	514	5	a	a	DET
ejpam-5384	514	6	characterization	characterization	NOUN
ejpam-5384	514	7	of	of	ADP
ejpam-5384	514	8	wardrop	wardrop	NOUN
ejpam-5384	514	9	optimal	optimal	ADJ
ejpam-5384	514	10	networks	network	NOUN
ejpam-5384	514	11	which	which	PRON
ejpam-5384	514	12	allows	allow	VERB
ejpam-5384	514	13	us	we	PRON
ejpam-5384	514	14	to	to	PART
ejpam-5384	514	15	identify	identify	VERB
ejpam-5384	514	16	important	important	ADJ
ejpam-5384	514	17	closure	closure	NOUN
ejpam-5384	514	18	properties	property	NOUN
ejpam-5384	514	19	of	of	ADP
ejpam-5384	514	20	the	the	DET
ejpam-5384	514	21	related	related	ADJ
ejpam-5384	514	22	class	class	NOUN
ejpam-5384	514	23	of	of	ADP
ejpam-5384	514	24	networks	network	NOUN
ejpam-5384	514	25	.	.	PUNCT
ejpam-5384	515	1	future	future	ADJ
ejpam-5384	515	2	research	research	NOUN
ejpam-5384	515	3	directions	direction	NOUN
ejpam-5384	515	4	deriving	derive	VERB
ejpam-5384	515	5	from	from	ADP
ejpam-5384	515	6	the	the	DET
ejpam-5384	515	7	results	result	NOUN
ejpam-5384	515	8	presented	present	VERB
ejpam-5384	515	9	in	in	ADP
ejpam-5384	515	10	this	this	DET
ejpam-5384	515	11	paper	paper	NOUN
ejpam-5384	515	12	include	include	VERB
ejpam-5384	515	13	the	the	DET
ejpam-5384	515	14	investigation	investigation	NOUN
ejpam-5384	515	15	of	of	ADP
ejpam-5384	515	16	wardrop	wardrop	NOUN
ejpam-5384	515	17	optimal	optimal	ADJ
ejpam-5384	515	18	flows	flow	NOUN
ejpam-5384	515	19	in	in	ADP
ejpam-5384	515	20	networks	network	NOUN
ejpam-5384	515	21	with	with	ADP
ejpam-5384	515	22	more	more	ADV
ejpam-5384	515	23	general	general	ADJ
ejpam-5384	515	24	underlying	underlie	VERB
ejpam-5384	515	25	graph	graph	NOUN
ejpam-5384	515	26	structures	structure	NOUN
ejpam-5384	515	27	by	by	ADP
ejpam-5384	515	28	analyzing	analyze	VERB
ejpam-5384	515	29	all	all	DET
ejpam-5384	515	30	potential	potential	ADJ
ejpam-5384	515	31	paths	path	NOUN
ejpam-5384	515	32	from	from	ADP
ejpam-5384	515	33	the	the	DET
ejpam-5384	515	34	origin	origin	NOUN
ejpam-5384	515	35	to	to	ADP
ejpam-5384	515	36	the	the	DET
ejpam-5384	515	37	destination	destination	NOUN
ejpam-5384	515	38	,	,	PUNCT
ejpam-5384	515	39	similarly	similarly	ADV
ejpam-5384	515	40	to	to	ADP
ejpam-5384	515	41	the	the	DET
ejpam-5384	515	42	approach	approach	NOUN
ejpam-5384	515	43	introduced	introduce	VERB
ejpam-5384	515	44	in	in	ADP
ejpam-5384	515	45	[	[	X
ejpam-5384	515	46	15	15	NUM
ejpam-5384	515	47	]	]	PUNCT
ejpam-5384	515	48	.	.	PUNCT
ejpam-5384	516	1	additionally	additionally	ADV
ejpam-5384	516	2	,	,	PUNCT
ejpam-5384	516	3	this	this	DET
ejpam-5384	516	4	framework	framework	NOUN
ejpam-5384	516	5	could	could	AUX
ejpam-5384	516	6	be	be	AUX
ejpam-5384	516	7	utilized	utilize	VERB
ejpam-5384	516	8	for	for	ADP
ejpam-5384	516	9	the	the	DET
ejpam-5384	516	10	algebraic	algebraic	ADJ
ejpam-5384	516	11	recognition	recognition	NOUN
ejpam-5384	516	12	of	of	ADP
ejpam-5384	516	13	such	such	ADJ
ejpam-5384	516	14	networks	network	NOUN
ejpam-5384	516	15	,	,	PUNCT
ejpam-5384	516	16	thereby	thereby	ADV
ejpam-5384	516	17	enabling	enable	VERB
ejpam-5384	516	18	the	the	DET
ejpam-5384	516	19	use	use	NOUN
ejpam-5384	516	20	of	of	ADP
ejpam-5384	516	21	graph	graph	NOUN
ejpam-5384	516	22	recognizability	recognizability	NOUN
ejpam-5384	516	23	to	to	PART
ejpam-5384	516	24	identify	identify	VERB
ejpam-5384	516	25	graph	graph	NOUN
ejpam-5384	516	26	properties	property	NOUN
ejpam-5384	516	27	,	,	PUNCT
ejpam-5384	516	28	such	such	ADJ
ejpam-5384	516	29	as	as	ADP
ejpam-5384	516	30	determining	determine	VERB
ejpam-5384	516	31	if	if	SCONJ
ejpam-5384	516	32	a	a	DET
ejpam-5384	516	33	graph	graph	NOUN
ejpam-5384	516	34	is	be	AUX
ejpam-5384	516	35	eulerian	eulerian	ADJ
ejpam-5384	517	1	[	[	X
ejpam-5384	517	2	9	9	NUM
ejpam-5384	517	3	]	]	PUNCT
ejpam-5384	517	4	and	and	CCONJ
ejpam-5384	517	5	k	k	ADJ
ejpam-5384	517	6	-	-	ADJ
ejpam-5384	517	7	colorable	colorable	ADJ
ejpam-5384	517	8	[	[	X
ejpam-5384	517	9	11	11	NUM
ejpam-5384	517	10	]	]	PUNCT
ejpam-5384	517	11	.	.	PUNCT
ejpam-5384	518	1	bibliography	bibliography	NOUN
ejpam-5384	519	1	[	[	X
ejpam-5384	519	2	1	1	X
ejpam-5384	519	3	]	]	X
ejpam-5384	519	4	d.	d.	PROPN
ejpam-5384	519	5	acemoglu	acemoglu	PROPN
ejpam-5384	519	6	and	and	CCONJ
ejpam-5384	519	7	a.	a.	NOUN
ejpam-5384	519	8	ozdaglar	ozdaglar	NOUN
ejpam-5384	519	9	.	.	PUNCT
ejpam-5384	520	1	competition	competition	NOUN
ejpam-5384	520	2	and	and	CCONJ
ejpam-5384	520	3	efficiency	efficiency	NOUN
ejpam-5384	520	4	in	in	ADP
ejpam-5384	520	5	congested	congested	ADJ
ejpam-5384	520	6	markets	market	NOUN
ejpam-5384	520	7	.	.	PUNCT
ejpam-5384	521	1	mathematics	mathematic	NOUN
ejpam-5384	521	2	of	of	ADP
ejpam-5384	521	3	operations	operation	NOUN
ejpam-5384	521	4	research	research	NOUN
ejpam-5384	521	5	,	,	PUNCT
ejpam-5384	521	6	32(1):1	32(1):1	PROPN
ejpam-5384	521	7	–	–	PUNCT
ejpam-5384	521	8	31	31	NUM
ejpam-5384	521	9	,	,	PUNCT
ejpam-5384	521	10	2007	2007	NUM
ejpam-5384	521	11	.	.	PUNCT
ejpam-5384	522	1	[	[	X
ejpam-5384	522	2	2	2	NUM
ejpam-5384	522	3	]	]	PUNCT
ejpam-5384	522	4	a.	a.	NOUN
ejpam-5384	522	5	bagdasaryan	bagdasaryan	PROPN
ejpam-5384	522	6	,	,	PUNCT
ejpam-5384	522	7	a.	a.	NOUN
ejpam-5384	522	8	kalampakas	kalampakas	PROPN
ejpam-5384	522	9	,	,	PUNCT
ejpam-5384	522	10	and	and	CCONJ
ejpam-5384	522	11	m.	m.	NOUN
ejpam-5384	522	12	saburov	saburov	NOUN
ejpam-5384	522	13	.	.	PUNCT
ejpam-5384	523	1	dynamic	dynamic	ADJ
ejpam-5384	523	2	traffic	traffic	NOUN
ejpam-5384	523	3	flow	flow	NOUN
ejpam-5384	523	4	assignment	assignment	NOUN
ejpam-5384	523	5	on	on	ADP
ejpam-5384	523	6	parallel	parallel	ADJ
ejpam-5384	523	7	networks	network	NOUN
ejpam-5384	523	8	.	.	PUNCT
ejpam-5384	524	1	in	in	ADP
ejpam-5384	524	2	new	new	ADJ
ejpam-5384	524	3	technologies	technology	NOUN
ejpam-5384	524	4	,	,	PUNCT
ejpam-5384	524	5	development	development	NOUN
ejpam-5384	524	6	and	and	CCONJ
ejpam-5384	524	7	application	application	NOUN
ejpam-5384	524	8	vi	vi	PROPN
ejpam-5384	524	9	,	,	PUNCT
ejpam-5384	524	10	pages	page	NOUN
ejpam-5384	524	11	702–711	702–711	NUM
ejpam-5384	524	12	.	.	PUNCT
ejpam-5384	524	13	springer	springer	PROPN
ejpam-5384	524	14	nature	nature	PROPN
ejpam-5384	524	15	switzerland	switzerland	PROPN
ejpam-5384	524	16	,	,	PUNCT
ejpam-5384	524	17	2023	2023	NUM
ejpam-5384	524	18	.	.	PUNCT
ejpam-5384	525	1	[	[	X
ejpam-5384	525	2	3	3	NUM
ejpam-5384	525	3	]	]	PUNCT
ejpam-5384	525	4	a.	a.	NOUN
ejpam-5384	525	5	bagdasaryan	bagdasaryan	PROPN
ejpam-5384	525	6	,	,	PUNCT
ejpam-5384	525	7	a.	a.	NOUN
ejpam-5384	525	8	kalampakas	kalampakas	PROPN
ejpam-5384	525	9	,	,	PUNCT
ejpam-5384	525	10	and	and	CCONJ
ejpam-5384	525	11	m.	m.	NOUN
ejpam-5384	525	12	saburov	saburov	NOUN
ejpam-5384	525	13	.	.	PUNCT
ejpam-5384	526	1	discrete	discrete	ADJ
ejpam-5384	526	2	-	-	PUNCT
ejpam-5384	526	3	time	time	NOUN
ejpam-5384	526	4	replicator	replicator	NOUN
ejpam-5384	526	5	equations	equation	NOUN
ejpam-5384	526	6	on	on	ADP
ejpam-5384	526	7	parallel	parallel	ADJ
ejpam-5384	526	8	neural	neural	ADJ
ejpam-5384	526	9	networks	network	NOUN
ejpam-5384	526	10	.	.	PUNCT
ejpam-5384	527	1	in	in	ADP
ejpam-5384	527	2	engineering	engineering	NOUN
ejpam-5384	527	3	applications	application	NOUN
ejpam-5384	527	4	of	of	ADP
ejpam-5384	527	5	neural	neural	ADJ
ejpam-5384	527	6	networks	network	NOUN
ejpam-5384	527	7	,	,	PUNCT
ejpam-5384	527	8	pages	page	NOUN
ejpam-5384	527	9	492–503	492–503	NUM
ejpam-5384	527	10	.	.	PUNCT
ejpam-5384	528	1	springer	springer	PROPN
ejpam-5384	528	2	nature	nature	PROPN
ejpam-5384	528	3	switzerland	switzerland	PROPN
ejpam-5384	528	4	,	,	PUNCT
ejpam-5384	528	5	2024	2024	NUM
ejpam-5384	528	6	.	.	PUNCT
ejpam-5384	529	1	[	[	X
ejpam-5384	529	2	4	4	NUM
ejpam-5384	529	3	]	]	PUNCT
ejpam-5384	529	4	a.	a.	NOUN
ejpam-5384	529	5	bagdasaryan	bagdasaryan	PROPN
ejpam-5384	529	6	,	,	PUNCT
ejpam-5384	529	7	a.	a.	NOUN
ejpam-5384	529	8	kalampakas	kalampakas	PROPN
ejpam-5384	529	9	,	,	PUNCT
ejpam-5384	529	10	and	and	CCONJ
ejpam-5384	529	11	m.	m.	NOUN
ejpam-5384	529	12	saburov	saburov	NOUN
ejpam-5384	529	13	.	.	PUNCT
ejpam-5384	530	1	dynamics	dynamic	NOUN
ejpam-5384	530	2	of	of	ADP
ejpam-5384	530	3	replicator	replicator	NOUN
ejpam-5384	530	4	equations	equation	NOUN
ejpam-5384	530	5	on	on	ADP
ejpam-5384	530	6	wardrop	wardrop	NOUN
ejpam-5384	530	7	optimal	optimal	ADJ
ejpam-5384	530	8	networks	network	NOUN
ejpam-5384	530	9	.	.	PUNCT
ejpam-5384	531	1	russian	russian	ADJ
ejpam-5384	531	2	mathematical	mathematical	ADJ
ejpam-5384	531	3	surveys	survey	NOUN
ejpam-5384	531	4	,	,	PUNCT
ejpam-5384	531	5	79:176–178	79:176–178	NUM
ejpam-5384	531	6	,	,	PUNCT
ejpam-5384	531	7	2024	2024	NUM
ejpam-5384	531	8	.	.	PUNCT
ejpam-5384	532	1	bibliography	bibliography	NOUN
ejpam-5384	532	2	2465	2465	NUM
ejpam-5384	533	1	[	[	X
ejpam-5384	533	2	5	5	NUM
ejpam-5384	533	3	]	]	PUNCT
ejpam-5384	533	4	a.	a.	NOUN
ejpam-5384	533	5	bagdasaryan	bagdasaryan	PROPN
ejpam-5384	533	6	,	,	PUNCT
ejpam-5384	533	7	a.	a.	PROPN
ejpam-5384	533	8	kalampakas	kalampakas	PROPN
ejpam-5384	533	9	,	,	PUNCT
ejpam-5384	533	10	m.	m.	NOUN
ejpam-5384	533	11	saburov	saburov	NOUN
ejpam-5384	533	12	,	,	PUNCT
ejpam-5384	533	13	and	and	CCONJ
ejpam-5384	533	14	s.	s.	PROPN
ejpam-5384	533	15	spartalis	spartalis	PROPN
ejpam-5384	533	16	.	.	PUNCT
ejpam-5384	534	1	optimal	optimal	ADJ
ejpam-5384	534	2	traffic	traffic	NOUN
ejpam-5384	534	3	flow	flow	NOUN
ejpam-5384	534	4	distributions	distribution	NOUN
ejpam-5384	534	5	on	on	ADP
ejpam-5384	534	6	dynamic	dynamic	ADJ
ejpam-5384	534	7	networks	network	NOUN
ejpam-5384	534	8	.	.	PUNCT
ejpam-5384	535	1	in	in	ADP
ejpam-5384	535	2	engineering	engineering	NOUN
ejpam-5384	535	3	applications	application	NOUN
ejpam-5384	535	4	of	of	ADP
ejpam-5384	535	5	neural	neural	ADJ
ejpam-5384	535	6	networks	network	NOUN
ejpam-5384	535	7	,	,	PUNCT
ejpam-5384	535	8	pages	page	NOUN
ejpam-5384	535	9	178–190	178–190	NUM
ejpam-5384	535	10	.	.	PUNCT
ejpam-5384	535	11	springer	springer	PROPN
ejpam-5384	535	12	nature	nature	PROPN
ejpam-5384	535	13	switzerland	switzerland	PROPN
ejpam-5384	535	14	,	,	PUNCT
ejpam-5384	535	15	2023	2023	NUM
ejpam-5384	535	16	.	.	PUNCT
ejpam-5384	536	1	[	[	X
ejpam-5384	536	2	6	6	NUM
ejpam-5384	536	3	]	]	PUNCT
ejpam-5384	536	4	m.	m.	NOUN
ejpam-5384	536	5	j.	j.	PROPN
ejpam-5384	536	6	beckmann	beckmann	PROPN
ejpam-5384	536	7	,	,	PUNCT
ejpam-5384	536	8	c.	c.	PROPN
ejpam-5384	536	9	b.	b.	PROPN
ejpam-5384	536	10	mcguire	mcguire	PROPN
ejpam-5384	536	11	,	,	PUNCT
ejpam-5384	536	12	and	and	CCONJ
ejpam-5384	536	13	c.	c.	PROPN
ejpam-5384	536	14	b.	b.	PROPN
ejpam-5384	536	15	winsten	winsten	PROPN
ejpam-5384	536	16	.	.	PUNCT
ejpam-5384	537	1	studies	study	NOUN
ejpam-5384	537	2	in	in	ADP
ejpam-5384	537	3	the	the	DET
ejpam-5384	537	4	economics	economic	NOUN
ejpam-5384	537	5	of	of	ADP
ejpam-5384	537	6	transportation	transportation	NOUN
ejpam-5384	537	7	.	.	PUNCT
ejpam-5384	538	1	rand	rand	NOUN
ejpam-5384	538	2	corporation	corporation	NOUN
ejpam-5384	538	3	,	,	PUNCT
ejpam-5384	538	4	1955	1955	NUM
ejpam-5384	538	5	.	.	PUNCT
ejpam-5384	539	1	[	[	X
ejpam-5384	539	2	7	7	X
ejpam-5384	539	3	]	]	X
ejpam-5384	539	4	s.	s.	PROPN
ejpam-5384	539	5	dafermos	dafermos	PROPN
ejpam-5384	539	6	and	and	CCONJ
ejpam-5384	539	7	f.	f.	PROPN
ejpam-5384	539	8	sparrow	sparrow	PROPN
ejpam-5384	539	9	.	.	PUNCT
ejpam-5384	540	1	the	the	DET
ejpam-5384	540	2	traffic	traffic	NOUN
ejpam-5384	540	3	assignment	assignment	NOUN
ejpam-5384	540	4	problem	problem	NOUN
ejpam-5384	540	5	for	for	ADP
ejpam-5384	540	6	a	a	DET
ejpam-5384	540	7	general	general	ADJ
ejpam-5384	540	8	network	network	NOUN
ejpam-5384	540	9	.	.	PUNCT
ejpam-5384	541	1	journal	journal	PROPN
ejpam-5384	541	2	of	of	ADP
ejpam-5384	541	3	research	research	NOUN
ejpam-5384	541	4	of	of	ADP
ejpam-5384	541	5	the	the	DET
ejpam-5384	541	6	national	national	PROPN
ejpam-5384	541	7	bureau	bureau	PROPN
ejpam-5384	541	8	of	of	ADP
ejpam-5384	541	9	standards	standards	PROPN
ejpam-5384	541	10	-	-	PUNCT
ejpam-5384	541	11	b.	b.	PROPN
ejpam-5384	541	12	mathematical	mathematical	PROPN
ejpam-5384	541	13	sciences	sciences	PROPN
ejpam-5384	541	14	,	,	PUNCT
ejpam-5384	541	15	73(2):91	73(2):91	NUM
ejpam-5384	541	16	–	–	PUNCT
ejpam-5384	541	17	118	118	NUM
ejpam-5384	541	18	,	,	PUNCT
ejpam-5384	541	19	1969	1969	NUM
ejpam-5384	541	20	.	.	PUNCT
ejpam-5384	542	1	[	[	X
ejpam-5384	542	2	8	8	NUM
ejpam-5384	542	3	]	]	X
ejpam-5384	542	4	r.	r.	PROPN
ejpam-5384	542	5	hwang	hwang	PROPN
ejpam-5384	542	6	,	,	PUNCT
ejpam-5384	542	7	m.	m.	PROPN
ejpam-5384	542	8	gen	gen	PROPN
ejpam-5384	542	9	,	,	PUNCT
ejpam-5384	542	10	and	and	CCONJ
ejpam-5384	542	11	h.	h.	PROPN
ejpam-5384	542	12	katayama	katayama	PROPN
ejpam-5384	542	13	.	.	PUNCT
ejpam-5384	543	1	a	a	DET
ejpam-5384	543	2	comparison	comparison	NOUN
ejpam-5384	543	3	of	of	ADP
ejpam-5384	543	4	multiprocessor	multiprocessor	NOUN
ejpam-5384	543	5	task	task	NOUN
ejpam-5384	543	6	scheduling	scheduling	NOUN
ejpam-5384	543	7	algorithms	algorithm	NOUN
ejpam-5384	543	8	with	with	ADP
ejpam-5384	543	9	communication	communication	NOUN
ejpam-5384	543	10	costs	cost	NOUN
ejpam-5384	543	11	.	.	PUNCT
ejpam-5384	544	1	computers	computer	NOUN
ejpam-5384	544	2	and	and	CCONJ
ejpam-5384	544	3	operations	operation	NOUN
ejpam-5384	544	4	research	research	NOUN
ejpam-5384	544	5	,	,	PUNCT
ejpam-5384	544	6	35(3):976–993	35(3):976–993	PROPN
ejpam-5384	544	7	,	,	PUNCT
ejpam-5384	544	8	2008	2008	NUM
ejpam-5384	544	9	.	.	PUNCT
ejpam-5384	545	1	part	part	NOUN
ejpam-5384	545	2	special	special	ADJ
ejpam-5384	545	3	issue	issue	NOUN
ejpam-5384	545	4	:	:	PUNCT
ejpam-5384	545	5	new	new	ADJ
ejpam-5384	545	6	trends	trend	NOUN
ejpam-5384	545	7	in	in	ADP
ejpam-5384	545	8	locational	locational	ADJ
ejpam-5384	545	9	analysis	analysis	NOUN
ejpam-5384	545	10	.	.	PUNCT
ejpam-5384	546	1	[	[	X
ejpam-5384	546	2	9	9	NUM
ejpam-5384	546	3	]	]	PUNCT
ejpam-5384	546	4	a.	a.	NOUN
ejpam-5384	546	5	kalampakas	kalampakas	PROPN
ejpam-5384	546	6	.	.	PUNCT
ejpam-5384	547	1	the	the	DET
ejpam-5384	547	2	syntactic	syntactic	ADJ
ejpam-5384	547	3	complexity	complexity	NOUN
ejpam-5384	547	4	of	of	ADP
ejpam-5384	547	5	eulerian	eulerian	ADJ
ejpam-5384	547	6	graphs	graph	NOUN
ejpam-5384	547	7	.	.	PUNCT
ejpam-5384	548	1	lecture	lecture	NOUN
ejpam-5384	548	2	notes	note	NOUN
ejpam-5384	548	3	in	in	ADP
ejpam-5384	548	4	computer	computer	NOUN
ejpam-5384	548	5	science	science	NOUN
ejpam-5384	548	6	(	(	PUNCT
ejpam-5384	548	7	including	include	VERB
ejpam-5384	548	8	subseries	subserie	NOUN
ejpam-5384	548	9	lecture	lecture	VERB
ejpam-5384	548	10	notes	note	NOUN
ejpam-5384	548	11	in	in	ADP
ejpam-5384	548	12	artificial	artificial	ADJ
ejpam-5384	548	13	intelligence	intelligence	NOUN
ejpam-5384	548	14	and	and	CCONJ
ejpam-5384	548	15	lecture	lecture	NOUN
ejpam-5384	548	16	notes	note	NOUN
ejpam-5384	548	17	in	in	ADP
ejpam-5384	548	18	bioinformatics	bioinformatics	NOUN
ejpam-5384	548	19	)	)	PUNCT
ejpam-5384	548	20	,	,	PUNCT
ejpam-5384	548	21	4728	4728	NUM
ejpam-5384	548	22	lncs:208	lncs:208	VERB
ejpam-5384	548	23	–	–	PUNCT
ejpam-5384	548	24	217	217	NUM
ejpam-5384	548	25	,	,	PUNCT
ejpam-5384	548	26	2007	2007	NUM
ejpam-5384	548	27	.	.	PUNCT
ejpam-5384	549	1	[	[	X
ejpam-5384	549	2	10	10	NUM
ejpam-5384	549	3	]	]	PUNCT
ejpam-5384	549	4	a.	a.	NOUN
ejpam-5384	549	5	kalampakas	kalampakas	PROPN
ejpam-5384	549	6	.	.	PUNCT
ejpam-5384	550	1	graph	graph	NOUN
ejpam-5384	550	2	automata	automata	PROPN
ejpam-5384	550	3	:	:	PUNCT
ejpam-5384	550	4	the	the	DET
ejpam-5384	550	5	algebraic	algebraic	ADJ
ejpam-5384	550	6	properties	property	NOUN
ejpam-5384	550	7	of	of	ADP
ejpam-5384	550	8	abelian	abelian	ADJ
ejpam-5384	550	9	relational	relational	ADJ
ejpam-5384	550	10	graphoids	graphoid	NOUN
ejpam-5384	550	11	.	.	PUNCT
ejpam-5384	551	1	lecture	lecture	NOUN
ejpam-5384	551	2	notes	note	NOUN
ejpam-5384	551	3	in	in	ADP
ejpam-5384	551	4	computer	computer	NOUN
ejpam-5384	551	5	science	science	NOUN
ejpam-5384	551	6	(	(	PUNCT
ejpam-5384	551	7	including	include	VERB
ejpam-5384	551	8	subseries	subserie	NOUN
ejpam-5384	551	9	lecture	lecture	VERB
ejpam-5384	551	10	notes	note	NOUN
ejpam-5384	551	11	in	in	ADP
ejpam-5384	551	12	artificial	artificial	ADJ
ejpam-5384	551	13	intelligence	intelligence	NOUN
ejpam-5384	551	14	and	and	CCONJ
ejpam-5384	551	15	lecture	lecture	NOUN
ejpam-5384	551	16	notes	note	NOUN
ejpam-5384	551	17	in	in	ADP
ejpam-5384	551	18	bioinformatics	bioinformatics	NOUN
ejpam-5384	551	19	)	)	PUNCT
ejpam-5384	551	20	,	,	PUNCT
ejpam-5384	551	21	7020	7020	NUM
ejpam-5384	551	22	lncs:168	lncs:168	NOUN
ejpam-5384	551	23	–	–	PUNCT
ejpam-5384	551	24	182	182	NUM
ejpam-5384	551	25	,	,	PUNCT
ejpam-5384	551	26	2011	2011	NUM
ejpam-5384	551	27	.	.	PUNCT
ejpam-5384	552	1	[	[	X
ejpam-5384	552	2	11	11	NUM
ejpam-5384	552	3	]	]	PUNCT
ejpam-5384	552	4	a.	a.	NOUN
ejpam-5384	552	5	kalampakas	kalampakas	PROPN
ejpam-5384	552	6	.	.	PUNCT
ejpam-5384	553	1	graph	graph	NOUN
ejpam-5384	553	2	automata	automata	NOUN
ejpam-5384	553	3	and	and	CCONJ
ejpam-5384	553	4	graph	graph	NOUN
ejpam-5384	553	5	colorability	colorability	NOUN
ejpam-5384	553	6	.	.	PUNCT
ejpam-5384	554	1	european	european	PROPN
ejpam-5384	554	2	journal	journal	PROPN
ejpam-5384	554	3	of	of	ADP
ejpam-5384	554	4	pure	pure	ADJ
ejpam-5384	554	5	and	and	CCONJ
ejpam-5384	554	6	applied	applied	ADJ
ejpam-5384	554	7	mathematics	mathematic	NOUN
ejpam-5384	554	8	,	,	PUNCT
ejpam-5384	554	9	16(1):112–120	16(1):112–120	PROPN
ejpam-5384	554	10	,	,	PUNCT
ejpam-5384	554	11	jan	jan	PROPN
ejpam-5384	554	12	.	.	PROPN
ejpam-5384	554	13	2023	2023	NUM
ejpam-5384	554	14	.	.	PUNCT
ejpam-5384	555	1	[	[	X
ejpam-5384	555	2	12	12	NUM
ejpam-5384	555	3	]	]	PUNCT
ejpam-5384	555	4	a.	a.	NOUN
ejpam-5384	555	5	kalampakas	kalampakas	PROPN
ejpam-5384	555	6	and	and	CCONJ
ejpam-5384	555	7	e.	e.	PROPN
ejpam-5384	555	8	aifantis	aifantis	PROPN
ejpam-5384	555	9	.	.	PUNCT
ejpam-5384	556	1	random	random	ADJ
ejpam-5384	556	2	walk	walk	NOUN
ejpam-5384	556	3	on	on	ADP
ejpam-5384	556	4	graphs	graph	NOUN
ejpam-5384	556	5	:	:	PUNCT
ejpam-5384	556	6	an	an	DET
ejpam-5384	556	7	application	application	NOUN
ejpam-5384	556	8	to	to	ADP
ejpam-5384	556	9	the	the	DET
ejpam-5384	556	10	double	double	ADJ
ejpam-5384	556	11	diffusivity	diffusivity	NOUN
ejpam-5384	556	12	model	model	NOUN
ejpam-5384	556	13	.	.	PUNCT
ejpam-5384	557	1	mechanics	mechanic	NOUN
ejpam-5384	557	2	research	research	NOUN
ejpam-5384	557	3	communications	communication	NOUN
ejpam-5384	557	4	,	,	PUNCT
ejpam-5384	557	5	43:101	43:101	NUM
ejpam-5384	557	6	–	–	PUNCT
ejpam-5384	557	7	104	104	NUM
ejpam-5384	557	8	,	,	PUNCT
ejpam-5384	557	9	2012	2012	NUM
ejpam-5384	557	10	.	.	PUNCT
ejpam-5384	558	1	[	[	X
ejpam-5384	558	2	13	13	NUM
ejpam-5384	558	3	]	]	PUNCT
ejpam-5384	558	4	a.	a.	NOUN
ejpam-5384	558	5	kalampakas	kalampakas	PROPN
ejpam-5384	558	6	,	,	PUNCT
ejpam-5384	558	7	a.	a.	NOUN
ejpam-5384	558	8	bagdasaryan	bagdasaryan	PROPN
ejpam-5384	558	9	,	,	PUNCT
ejpam-5384	558	10	m.	m.	NOUN
ejpam-5384	558	11	saburov	saburov	NOUN
ejpam-5384	558	12	,	,	PUNCT
ejpam-5384	558	13	and	and	CCONJ
ejpam-5384	558	14	s.	s.	PROPN
ejpam-5384	558	15	spartalis	spartalis	PROPN
ejpam-5384	558	16	.	.	PUNCT
ejpam-5384	559	1	user	user	NOUN
ejpam-5384	559	2	equilibrium	equilibrium	NOUN
ejpam-5384	559	3	and	and	CCONJ
ejpam-5384	559	4	system	system	NOUN
ejpam-5384	559	5	optimality	optimality	NOUN
ejpam-5384	559	6	conditions	condition	NOUN
ejpam-5384	559	7	for	for	ADP
ejpam-5384	559	8	flow	flow	NOUN
ejpam-5384	559	9	distributions	distribution	NOUN
ejpam-5384	559	10	on	on	ADP
ejpam-5384	559	11	congested	congested	ADJ
ejpam-5384	559	12	networks	network	NOUN
ejpam-5384	559	13	.	.	PUNCT
ejpam-5384	560	1	in	in	ADP
ejpam-5384	560	2	engineering	engineering	NOUN
ejpam-5384	560	3	applications	application	NOUN
ejpam-5384	560	4	of	of	ADP
ejpam-5384	560	5	neural	neural	ADJ
ejpam-5384	560	6	networks	network	NOUN
ejpam-5384	560	7	,	,	PUNCT
ejpam-5384	560	8	pages	page	NOUN
ejpam-5384	560	9	203–214	203–214	NUM
ejpam-5384	560	10	.	.	PUNCT
ejpam-5384	561	1	springer	springer	NOUN
ejpam-5384	561	2	nature	nature	PROPN
ejpam-5384	561	3	switzerland	switzerland	PROPN
ejpam-5384	561	4	,	,	PUNCT
ejpam-5384	561	5	2023	2023	NUM
ejpam-5384	561	6	.	.	PUNCT
ejpam-5384	562	1	[	[	X
ejpam-5384	562	2	14	14	NUM
ejpam-5384	562	3	]	]	PUNCT
ejpam-5384	562	4	a.	a.	NOUN
ejpam-5384	562	5	kalampakas	kalampakas	PROPN
ejpam-5384	562	6	,	,	PUNCT
ejpam-5384	562	7	a.	a.	NOUN
ejpam-5384	562	8	bagdasaryan	bagdasaryan	PROPN
ejpam-5384	562	9	,	,	PUNCT
ejpam-5384	562	10	m.	m.	NOUN
ejpam-5384	562	11	saburov	saburov	NOUN
ejpam-5384	562	12	,	,	PUNCT
ejpam-5384	562	13	and	and	CCONJ
ejpam-5384	562	14	s.	s.	PROPN
ejpam-5384	562	15	spartalis	spartalis	PROPN
ejpam-5384	562	16	.	.	PUNCT
ejpam-5384	563	1	user	user	NOUN
ejpam-5384	563	2	equilibrium	equilibrium	NOUN
ejpam-5384	563	3	and	and	CCONJ
ejpam-5384	563	4	system	system	NOUN
ejpam-5384	563	5	optimality	optimality	NOUN
ejpam-5384	563	6	conditions	condition	NOUN
ejpam-5384	563	7	for	for	ADP
ejpam-5384	563	8	flow	flow	NOUN
ejpam-5384	563	9	distributions	distribution	NOUN
ejpam-5384	563	10	on	on	ADP
ejpam-5384	563	11	congested	congested	ADJ
ejpam-5384	563	12	networks	network	NOUN
ejpam-5384	563	13	.	.	PUNCT
ejpam-5384	564	1	in	in	ADP
ejpam-5384	564	2	engineering	engineering	NOUN
ejpam-5384	564	3	applications	application	NOUN
ejpam-5384	564	4	of	of	ADP
ejpam-5384	564	5	neural	neural	ADJ
ejpam-5384	564	6	networks	network	NOUN
ejpam-5384	564	7	,	,	PUNCT
ejpam-5384	564	8	pages	page	NOUN
ejpam-5384	564	9	203	203	NUM
ejpam-5384	564	10	–	–	PUNCT
ejpam-5384	564	11	214	214	NUM
ejpam-5384	564	12	.	.	PUNCT
ejpam-5384	565	1	springer	springer	NOUN
ejpam-5384	565	2	nature	nature	PROPN
ejpam-5384	565	3	switzerland	switzerland	PROPN
ejpam-5384	565	4	,	,	PUNCT
ejpam-5384	565	5	2023	2023	NUM
ejpam-5384	565	6	.	.	PUNCT
ejpam-5384	566	1	[	[	X
ejpam-5384	566	2	15	15	NUM
ejpam-5384	566	3	]	]	X
ejpam-5384	566	4	a.	a.	NOUN
ejpam-5384	566	5	kalampakas	kalampakas	PROPN
ejpam-5384	566	6	and	and	CCONJ
ejpam-5384	566	7	s.	s.	PROPN
ejpam-5384	566	8	spartalis	spartalis	PROPN
ejpam-5384	566	9	.	.	PUNCT
ejpam-5384	567	1	hyperoperations	hyperoperation	NOUN
ejpam-5384	567	2	on	on	ADP
ejpam-5384	567	3	directed	direct	VERB
ejpam-5384	567	4	graphs	graph	NOUN
ejpam-5384	567	5	.	.	PUNCT
ejpam-5384	568	1	journal	journal	NOUN
ejpam-5384	568	2	of	of	ADP
ejpam-5384	568	3	discrete	discrete	ADJ
ejpam-5384	568	4	mathematical	mathematical	ADJ
ejpam-5384	568	5	sciences	science	NOUN
ejpam-5384	568	6	and	and	CCONJ
ejpam-5384	568	7	cryptography	cryptography	NOUN
ejpam-5384	568	8	,	,	PUNCT
ejpam-5384	568	9	27(3):1011–1025	27(3):1011–1025	NUM
ejpam-5384	568	10	,	,	PUNCT
ejpam-5384	568	11	2024	2024	NUM
ejpam-5384	568	12	.	.	PUNCT
ejpam-5384	569	1	[	[	X
ejpam-5384	569	2	16	16	NUM
ejpam-5384	569	3	]	]	PUNCT
ejpam-5384	569	4	a.	a.	NOUN
ejpam-5384	569	5	kalampakas	kalampakas	PROPN
ejpam-5384	569	6	,	,	PUNCT
ejpam-5384	569	7	s.	s.	PROPN
ejpam-5384	569	8	spartalis	spartalis	PROPN
ejpam-5384	569	9	,	,	PUNCT
ejpam-5384	569	10	and	and	CCONJ
ejpam-5384	569	11	l.	l.	PROPN
ejpam-5384	569	12	iliadis	iliadis	PROPN
ejpam-5384	569	13	.	.	PUNCT
ejpam-5384	570	1	syntactic	syntactic	ADJ
ejpam-5384	570	2	recognizability	recognizability	NOUN
ejpam-5384	570	3	of	of	ADP
ejpam-5384	570	4	graphs	graph	NOUN
ejpam-5384	570	5	with	with	ADP
ejpam-5384	570	6	fuzzy	fuzzy	ADJ
ejpam-5384	570	7	attributes	attribute	NOUN
ejpam-5384	570	8	.	.	PUNCT
ejpam-5384	571	1	fuzzy	fuzzy	ADJ
ejpam-5384	571	2	sets	set	NOUN
ejpam-5384	571	3	and	and	CCONJ
ejpam-5384	571	4	systems	system	NOUN
ejpam-5384	571	5	,	,	PUNCT
ejpam-5384	571	6	229:91	229:91	NUM
ejpam-5384	571	7	–	–	PUNCT
ejpam-5384	571	8	100	100	NUM
ejpam-5384	571	9	,	,	PUNCT
ejpam-5384	571	10	2013	2013	NUM
ejpam-5384	571	11	.	.	PUNCT
ejpam-5384	572	1	bibliography	bibliography	NOUN
ejpam-5384	572	2	2466	2466	NUM
ejpam-5384	572	3	[	[	X
ejpam-5384	572	4	17	17	NUM
ejpam-5384	572	5	]	]	PUNCT
ejpam-5384	572	6	a.	a.	NOUN
ejpam-5384	572	7	kalampakas	kalampakas	PROPN
ejpam-5384	572	8	,	,	PUNCT
ejpam-5384	572	9	s.	s.	PROPN
ejpam-5384	572	10	spartalis	spartalis	PROPN
ejpam-5384	572	11	,	,	PUNCT
ejpam-5384	572	12	l.	l.	PROPN
ejpam-5384	572	13	iliadis	iliadis	PROPN
ejpam-5384	572	14	,	,	PUNCT
ejpam-5384	572	15	and	and	CCONJ
ejpam-5384	572	16	e.	e.	PROPN
ejpam-5384	572	17	pimenidis	pimenidis	PROPN
ejpam-5384	572	18	.	.	PUNCT
ejpam-5384	573	1	fuzzy	fuzzy	ADJ
ejpam-5384	573	2	graphs	graph	NOUN
ejpam-5384	573	3	:	:	PUNCT
ejpam-5384	573	4	algebraic	algebraic	ADJ
ejpam-5384	573	5	structure	structure	NOUN
ejpam-5384	573	6	and	and	CCONJ
ejpam-5384	573	7	syntactic	syntactic	ADJ
ejpam-5384	573	8	recognition	recognition	NOUN
ejpam-5384	573	9	.	.	PUNCT
ejpam-5384	574	1	artificial	artificial	ADJ
ejpam-5384	574	2	intelligence	intelligence	NOUN
ejpam-5384	574	3	review	review	NOUN
ejpam-5384	574	4	,	,	PUNCT
ejpam-5384	574	5	42(3):479	42(3):479	NUM
ejpam-5384	574	6	–	–	PUNCT
ejpam-5384	574	7	490	490	NUM
ejpam-5384	574	8	,	,	PUNCT
ejpam-5384	574	9	2014	2014	NUM
ejpam-5384	574	10	.	.	PUNCT
ejpam-5384	575	1	[	[	X
ejpam-5384	575	2	18	18	NUM
ejpam-5384	575	3	]	]	PUNCT
ejpam-5384	575	4	f.	f.	PROPN
ejpam-5384	575	5	p.	p.	PROPN
ejpam-5384	575	6	kelly	kelly	PROPN
ejpam-5384	575	7	,	,	PUNCT
ejpam-5384	575	8	a.	a.	PROPN
ejpam-5384	575	9	k.	k.	PROPN
ejpam-5384	575	10	maulloo	maulloo	PROPN
ejpam-5384	575	11	,	,	PUNCT
ejpam-5384	575	12	and	and	CCONJ
ejpam-5384	575	13	d.	d.	PROPN
ejpam-5384	575	14	k.	k.	PROPN
ejpam-5384	576	1	h.	h.	PROPN
ejpam-5384	576	2	tan	tan	PROPN
ejpam-5384	576	3	.	.	PUNCT
ejpam-5384	577	1	rate	rate	NOUN
ejpam-5384	577	2	control	control	NOUN
ejpam-5384	577	3	for	for	ADP
ejpam-5384	577	4	communication	communication	NOUN
ejpam-5384	577	5	networks	network	NOUN
ejpam-5384	577	6	:	:	PUNCT
ejpam-5384	577	7	shadow	shadow	NOUN
ejpam-5384	577	8	prices	price	NOUN
ejpam-5384	577	9	,	,	PUNCT
ejpam-5384	577	10	proportional	proportional	ADJ
ejpam-5384	577	11	fairness	fairness	NOUN
ejpam-5384	577	12	and	and	CCONJ
ejpam-5384	577	13	stability	stability	NOUN
ejpam-5384	577	14	.	.	PUNCT
ejpam-5384	578	1	journal	journal	NOUN
ejpam-5384	578	2	of	of	ADP
ejpam-5384	578	3	the	the	DET
ejpam-5384	578	4	operational	operational	ADJ
ejpam-5384	578	5	research	research	NOUN
ejpam-5384	578	6	society	society	NOUN
ejpam-5384	578	7	,	,	PUNCT
ejpam-5384	578	8	49(3):237–252	49(3):237–252	NOUN
ejpam-5384	578	9	,	,	PUNCT
ejpam-5384	578	10	1998	1998	NUM
ejpam-5384	578	11	.	.	PUNCT
ejpam-5384	579	1	[	[	X
ejpam-5384	579	2	19	19	NUM
ejpam-5384	579	3	]	]	X
ejpam-5384	579	4	f.	f.	PROPN
ejpam-5384	579	5	h.	h.	PROPN
ejpam-5384	579	6	knight	knight	PROPN
ejpam-5384	579	7	.	.	PUNCT
ejpam-5384	580	1	some	some	DET
ejpam-5384	580	2	fallacies	fallacy	NOUN
ejpam-5384	580	3	in	in	ADP
ejpam-5384	580	4	the	the	DET
ejpam-5384	580	5	interpretation	interpretation	NOUN
ejpam-5384	580	6	of	of	ADP
ejpam-5384	580	7	social	social	ADJ
ejpam-5384	580	8	cost	cost	NOUN
ejpam-5384	580	9	.	.	PUNCT
ejpam-5384	581	1	the	the	DET
ejpam-5384	581	2	quarterly	quarterly	ADJ
ejpam-5384	581	3	journal	journal	NOUN
ejpam-5384	581	4	of	of	ADP
ejpam-5384	581	5	economics	economic	NOUN
ejpam-5384	581	6	,	,	PUNCT
ejpam-5384	581	7	38(4):582–606	38(4):582–606	PROPN
ejpam-5384	581	8	,	,	PUNCT
ejpam-5384	581	9	1924	1924	NUM
ejpam-5384	581	10	.	.	PUNCT
ejpam-5384	582	1	[	[	X
ejpam-5384	582	2	20	20	NUM
ejpam-5384	582	3	]	]	X
ejpam-5384	582	4	y.a	y.a	PROPN
ejpam-5384	582	5	.	.	PROPN
ejpam-5384	582	6	korilis	korilis	PROPN
ejpam-5384	582	7	,	,	PUNCT
ejpam-5384	582	8	a.a	a.a	PROPN
ejpam-5384	582	9	.	.	PROPN
ejpam-5384	582	10	lazar	lazar	PROPN
ejpam-5384	582	11	,	,	PUNCT
ejpam-5384	582	12	and	and	CCONJ
ejpam-5384	582	13	a.	a.	NOUN
ejpam-5384	582	14	orda	orda	PROPN
ejpam-5384	582	15	.	.	PUNCT
ejpam-5384	583	1	achieving	achieve	VERB
ejpam-5384	583	2	network	network	NOUN
ejpam-5384	583	3	optima	optima	PROPN
ejpam-5384	583	4	using	use	VERB
ejpam-5384	583	5	stackelberg	stackelberg	PROPN
ejpam-5384	583	6	routing	routing	NOUN
ejpam-5384	583	7	strategies	strategy	NOUN
ejpam-5384	583	8	.	.	PUNCT
ejpam-5384	584	1	ieee	ieee	PROPN
ejpam-5384	584	2	/	/	SYM
ejpam-5384	584	3	acm	acm	PROPN
ejpam-5384	584	4	transactions	transaction	NOUN
ejpam-5384	584	5	on	on	ADP
ejpam-5384	584	6	networking	networking	NOUN
ejpam-5384	584	7	,	,	PUNCT
ejpam-5384	584	8	5(1):161–173	5(1):161–173	NUM
ejpam-5384	584	9	,	,	PUNCT
ejpam-5384	584	10	1997	1997	NUM
ejpam-5384	584	11	.	.	PUNCT
ejpam-5384	585	1	[	[	X
ejpam-5384	585	2	21	21	NUM
ejpam-5384	585	3	]	]	X
ejpam-5384	585	4	s.h	s.h	PROPN
ejpam-5384	585	5	.	.	PROPN
ejpam-5384	585	6	low	low	PROPN
ejpam-5384	585	7	and	and	CCONJ
ejpam-5384	585	8	d.e	d.e	PROPN
ejpam-5384	585	9	.	.	PROPN
ejpam-5384	585	10	lapsley	lapsley	PROPN
ejpam-5384	585	11	.	.	PUNCT
ejpam-5384	586	1	optimization	optimization	NOUN
ejpam-5384	586	2	flow	flow	NOUN
ejpam-5384	586	3	control	control	NOUN
ejpam-5384	586	4	.	.	PUNCT
ejpam-5384	587	1	i.	i.	PROPN
ejpam-5384	587	2	basic	basic	ADJ
ejpam-5384	587	3	algorithm	algorithm	NOUN
ejpam-5384	587	4	and	and	CCONJ
ejpam-5384	587	5	convergence	convergence	NOUN
ejpam-5384	587	6	.	.	PUNCT
ejpam-5384	588	1	ieee	ieee	PROPN
ejpam-5384	588	2	/	/	SYM
ejpam-5384	588	3	acm	acm	PROPN
ejpam-5384	588	4	transactions	transaction	NOUN
ejpam-5384	588	5	on	on	ADP
ejpam-5384	588	6	networking	network	VERB
ejpam-5384	588	7	,	,	PUNCT
ejpam-5384	588	8	7(6):861–874	7(6):861–874	NOUN
ejpam-5384	588	9	,	,	PUNCT
ejpam-5384	588	10	1999	1999	NUM
ejpam-5384	588	11	.	.	PUNCT
ejpam-5384	589	1	[	[	X
ejpam-5384	589	2	22	22	NUM
ejpam-5384	589	3	]	]	X
ejpam-5384	589	4	v.	v.	X
ejpam-5384	589	5	morandi	morandi	PROPN
ejpam-5384	589	6	.	.	PUNCT
ejpam-5384	590	1	bridging	bridge	VERB
ejpam-5384	590	2	the	the	DET
ejpam-5384	590	3	user	user	NOUN
ejpam-5384	590	4	equilibrium	equilibrium	NOUN
ejpam-5384	590	5	and	and	CCONJ
ejpam-5384	590	6	the	the	DET
ejpam-5384	590	7	system	system	NOUN
ejpam-5384	590	8	optimum	optimum	NOUN
ejpam-5384	590	9	in	in	ADP
ejpam-5384	590	10	static	static	ADJ
ejpam-5384	590	11	traffic	traffic	NOUN
ejpam-5384	590	12	assignment	assignment	NOUN
ejpam-5384	590	13	:	:	PUNCT
ejpam-5384	590	14	a	a	DET
ejpam-5384	590	15	review	review	NOUN
ejpam-5384	590	16	.	.	PUNCT
ejpam-5384	591	1	4or	4or	ADJ
ejpam-5384	591	2	,	,	PUNCT
ejpam-5384	591	3	22(1):89	22(1):89	NUM
ejpam-5384	591	4	–	–	PUNCT
ejpam-5384	591	5	119	119	NUM
ejpam-5384	591	6	,	,	PUNCT
ejpam-5384	591	7	2024	2024	NUM
ejpam-5384	591	8	.	.	PUNCT
ejpam-5384	592	1	[	[	X
ejpam-5384	592	2	23	23	NUM
ejpam-5384	592	3	]	]	PUNCT
ejpam-5384	592	4	a.	a.	NOUN
ejpam-5384	592	5	nagurney	nagurney	NOUN
ejpam-5384	592	6	.	.	PUNCT
ejpam-5384	593	1	spatial	spatial	ADJ
ejpam-5384	593	2	price	price	NOUN
ejpam-5384	593	3	equilibrium	equilibrium	NOUN
ejpam-5384	593	4	,	,	PUNCT
ejpam-5384	593	5	pages	page	NOUN
ejpam-5384	593	6	3646	3646	NUM
ejpam-5384	593	7	–	–	PUNCT
ejpam-5384	593	8	3652	3652	NUM
ejpam-5384	593	9	.	.	PUNCT
ejpam-5384	594	1	springer	springer	PROPN
ejpam-5384	594	2	us	us	PROPN
ejpam-5384	594	3	,	,	PUNCT
ejpam-5384	594	4	boston	boston	PROPN
ejpam-5384	594	5	,	,	PUNCT
ejpam-5384	594	6	ma	ma	PROPN
ejpam-5384	594	7	,	,	PUNCT
ejpam-5384	594	8	2009	2009	NUM
ejpam-5384	594	9	.	.	PUNCT
ejpam-5384	595	1	[	[	X
ejpam-5384	595	2	24	24	NUM
ejpam-5384	595	3	]	]	PUNCT
ejpam-5384	595	4	a.	a.	NOUN
ejpam-5384	595	5	orda	orda	PROPN
ejpam-5384	595	6	,	,	PUNCT
ejpam-5384	595	7	r.	r.	PROPN
ejpam-5384	595	8	rom	rom	PROPN
ejpam-5384	595	9	,	,	PUNCT
ejpam-5384	595	10	and	and	CCONJ
ejpam-5384	595	11	n.	n.	PROPN
ejpam-5384	595	12	shimkin	shimkin	PROPN
ejpam-5384	595	13	.	.	PUNCT
ejpam-5384	596	1	competitive	competitive	ADJ
ejpam-5384	596	2	routing	routing	NOUN
ejpam-5384	596	3	in	in	ADP
ejpam-5384	596	4	multiuser	multiuser	NOUN
ejpam-5384	596	5	communication	communication	NOUN
ejpam-5384	596	6	networks	network	NOUN
ejpam-5384	596	7	.	.	PUNCT
ejpam-5384	597	1	ieee	ieee	PROPN
ejpam-5384	597	2	/	/	SYM
ejpam-5384	597	3	acm	acm	PROPN
ejpam-5384	597	4	transactions	transaction	NOUN
ejpam-5384	597	5	on	on	ADP
ejpam-5384	597	6	networking	networking	NOUN
ejpam-5384	597	7	,	,	PUNCT
ejpam-5384	597	8	1(5):510–521	1(5):510–521	NUM
ejpam-5384	597	9	,	,	PUNCT
ejpam-5384	597	10	1993	1993	NUM
ejpam-5384	597	11	.	.	PUNCT
ejpam-5384	598	1	[	[	X
ejpam-5384	598	2	25	25	NUM
ejpam-5384	598	3	]	]	PUNCT
ejpam-5384	598	4	m.	m.	NOUN
ejpam-5384	598	5	patriksson	patriksson	NOUN
ejpam-5384	598	6	.	.	PUNCT
ejpam-5384	599	1	the	the	DET
ejpam-5384	599	2	traffic	traffic	NOUN
ejpam-5384	599	3	assignment	assignment	NOUN
ejpam-5384	599	4	problem	problem	NOUN
ejpam-5384	599	5	:	:	PUNCT
ejpam-5384	599	6	models	model	NOUN
ejpam-5384	599	7	and	and	CCONJ
ejpam-5384	599	8	methods	method	NOUN
ejpam-5384	599	9	.	.	PUNCT
ejpam-5384	600	1	vsp	vsp	PROPN
ejpam-5384	600	2	,	,	PUNCT
ejpam-5384	600	3	utrecht	utrecht	PROPN
ejpam-5384	600	4	,	,	PUNCT
ejpam-5384	600	5	the	the	DET
ejpam-5384	600	6	netherlands	netherlands	PROPN
ejpam-5384	600	7	,	,	PUNCT
ejpam-5384	600	8	1994	1994	NUM
ejpam-5384	600	9	.	.	PUNCT
ejpam-5384	601	1	[	[	X
ejpam-5384	601	2	26	26	NUM
ejpam-5384	601	3	]	]	PUNCT
ejpam-5384	601	4	a.	a.	NOUN
ejpam-5384	601	5	c.	c.	PROPN
ejpam-5384	601	6	pigou	pigou	PROPN
ejpam-5384	601	7	.	.	PUNCT
ejpam-5384	602	1	the	the	DET
ejpam-5384	602	2	economics	economic	NOUN
ejpam-5384	602	3	of	of	ADP
ejpam-5384	602	4	welfare	welfare	NOUN
ejpam-5384	602	5	.	.	PUNCT
ejpam-5384	603	1	macmillan	macmillan	PROPN
ejpam-5384	603	2	,	,	PUNCT
ejpam-5384	603	3	london	london	PROPN
ejpam-5384	603	4	,	,	PUNCT
ejpam-5384	603	5	1920	1920	NUM
ejpam-5384	603	6	.	.	PUNCT
ejpam-5384	604	1	[	[	X
ejpam-5384	604	2	27	27	NUM
ejpam-5384	604	3	]	]	PUNCT
ejpam-5384	604	4	m.	m.	NOUN
ejpam-5384	604	5	saburov	saburov	NOUN
ejpam-5384	604	6	.	.	PUNCT
ejpam-5384	605	1	on	on	ADP
ejpam-5384	605	2	replicator	replicator	NOUN
ejpam-5384	605	3	equations	equation	NOUN
ejpam-5384	605	4	with	with	ADP
ejpam-5384	605	5	nonlinear	nonlinear	ADJ
ejpam-5384	605	6	payoff	payoff	NOUN
ejpam-5384	605	7	functions	function	NOUN
ejpam-5384	605	8	defined	define	VERB
ejpam-5384	605	9	by	by	ADP
ejpam-5384	605	10	the	the	DET
ejpam-5384	605	11	ricker	ricker	NOUN
ejpam-5384	605	12	models	model	NOUN
ejpam-5384	605	13	.	.	PUNCT
ejpam-5384	606	1	adv	adv	PROPN
ejpam-5384	606	2	.	.	PUNCT
ejpam-5384	607	1	pure	pure	ADJ
ejpam-5384	607	2	appl	appl	PROPN
ejpam-5384	607	3	.	.	PUNCT
ejpam-5384	607	4	math	math	PROPN
ejpam-5384	607	5	.	.	PUNCT
ejpam-5384	607	6	,	,	PUNCT
ejpam-5384	607	7	12:39–156	12:39–156	NUM
ejpam-5384	607	8	,	,	PUNCT
ejpam-5384	607	9	2021	2021	NUM
ejpam-5384	607	10	.	.	PUNCT
ejpam-5384	608	1	[	[	X
ejpam-5384	608	2	28	28	NUM
ejpam-5384	608	3	]	]	X
ejpam-5384	608	4	s.	s.	PROPN
ejpam-5384	608	5	sanghavi	sanghavi	PROPN
ejpam-5384	608	6	and	and	CCONJ
ejpam-5384	608	7	b.	b.	PROPN
ejpam-5384	608	8	hajek	hajek	PROPN
ejpam-5384	608	9	.	.	PUNCT
ejpam-5384	609	1	optimal	optimal	ADJ
ejpam-5384	609	2	allocation	allocation	NOUN
ejpam-5384	609	3	of	of	ADP
ejpam-5384	609	4	a	a	DET
ejpam-5384	609	5	divisible	divisible	ADJ
ejpam-5384	609	6	good	good	NOUN
ejpam-5384	609	7	to	to	ADP
ejpam-5384	609	8	strategic	strategic	ADJ
ejpam-5384	609	9	buyers	buyer	NOUN
ejpam-5384	609	10	.	.	PUNCT
ejpam-5384	610	1	in	in	ADP
ejpam-5384	610	2	2004	2004	NUM
ejpam-5384	610	3	43rd	43rd	NOUN
ejpam-5384	610	4	ieee	ieee	NOUN
ejpam-5384	610	5	conference	conference	NOUN
ejpam-5384	610	6	on	on	ADP
ejpam-5384	610	7	decision	decision	NOUN
ejpam-5384	610	8	and	and	CCONJ
ejpam-5384	610	9	control	control	NOUN
ejpam-5384	610	10	(	(	PUNCT
ejpam-5384	610	11	cdc	cdc	PROPN
ejpam-5384	610	12	)	)	PUNCT
ejpam-5384	610	13	(	(	PUNCT
ejpam-5384	610	14	ieee	ieee	NOUN
ejpam-5384	610	15	cat	cat	NOUN
ejpam-5384	610	16	.	.	PUNCT
ejpam-5384	610	17	no.04ch37601	no.04ch37601	X
ejpam-5384	610	18	)	)	PUNCT
ejpam-5384	610	19	,	,	PUNCT
ejpam-5384	610	20	volume	volume	NOUN
ejpam-5384	610	21	3	3	NUM
ejpam-5384	610	22	,	,	PUNCT
ejpam-5384	610	23	pages	page	NOUN
ejpam-5384	610	24	2748–2753	2748–2753	NUM
ejpam-5384	610	25	vol.3	vol.3	NOUN
ejpam-5384	610	26	,	,	PUNCT
ejpam-5384	610	27	2004	2004	NUM
ejpam-5384	610	28	.	.	PUNCT
ejpam-5384	611	1	[	[	X
ejpam-5384	611	2	29	29	NUM
ejpam-5384	611	3	]	]	X
ejpam-5384	611	4	m.k	m.k	PROPN
ejpam-5384	611	5	.	.	PROPN
ejpam-5384	611	6	sharma	sharma	PROPN
ejpam-5384	611	7	,	,	PUNCT
ejpam-5384	611	8	sadhna	sadhna	NOUN
ejpam-5384	611	9	,	,	PUNCT
ejpam-5384	611	10	a.k	a.k	PROPN
ejpam-5384	611	11	.	.	PROPN
ejpam-5384	611	12	bhargava	bhargava	PROPN
ejpam-5384	611	13	,	,	PUNCT
ejpam-5384	611	14	s.	s.	PROPN
ejpam-5384	611	15	kumar	kumar	PROPN
ejpam-5384	611	16	,	,	PUNCT
ejpam-5384	611	17	l.	l.	PROPN
ejpam-5384	611	18	rathour	rathour	PROPN
ejpam-5384	611	19	,	,	PUNCT
ejpam-5384	611	20	l.n	l.n	PROPN
ejpam-5384	611	21	.	.	PROPN
ejpam-5384	611	22	mishra	mishra	PROPN
ejpam-5384	611	23	,	,	PUNCT
ejpam-5384	611	24	and	and	CCONJ
ejpam-5384	611	25	s.	s.	PROPN
ejpam-5384	611	26	pandey	pandey	PROPN
ejpam-5384	611	27	.	.	PUNCT
ejpam-5384	612	1	a	a	DET
ejpam-5384	612	2	fermatean	fermatean	ADJ
ejpam-5384	612	3	fuzzy	fuzzy	ADJ
ejpam-5384	612	4	ranking	ranking	NOUN
ejpam-5384	612	5	function	function	NOUN
ejpam-5384	612	6	in	in	ADP
ejpam-5384	612	7	optimization	optimization	NOUN
ejpam-5384	612	8	of	of	ADP
ejpam-5384	612	9	intuitionistic	intuitionistic	ADJ
ejpam-5384	612	10	fuzzy	fuzzy	ADJ
ejpam-5384	612	11	transportation	transportation	NOUN
ejpam-5384	612	12	problems	problem	NOUN
ejpam-5384	612	13	.	.	PUNCT
ejpam-5384	613	1	advanced	advanced	ADJ
ejpam-5384	613	2	mathematical	mathematical	ADJ
ejpam-5384	613	3	models	model	NOUN
ejpam-5384	613	4	and	and	CCONJ
ejpam-5384	613	5	applications	application	NOUN
ejpam-5384	613	6	,	,	PUNCT
ejpam-5384	613	7	7(2):191	7(2):191	NUM
ejpam-5384	613	8	–	–	PUNCT
ejpam-5384	613	9	204	204	NUM
ejpam-5384	613	10	,	,	PUNCT
ejpam-5384	613	11	2022	2022	NUM
ejpam-5384	613	12	.	.	PUNCT
ejpam-5384	614	1	[	[	X
ejpam-5384	614	2	30	30	NUM
ejpam-5384	614	3	]	]	X
ejpam-5384	614	4	j.	j.	PROPN
ejpam-5384	614	5	g.	g.	PROPN
ejpam-5384	614	6	wardrop	wardrop	PROPN
ejpam-5384	614	7	.	.	PUNCT
ejpam-5384	615	1	some	some	DET
ejpam-5384	615	2	theoretical	theoretical	ADJ
ejpam-5384	615	3	aspects	aspect	NOUN
ejpam-5384	615	4	of	of	ADP
ejpam-5384	615	5	road	road	NOUN
ejpam-5384	615	6	traffic	traffic	NOUN
ejpam-5384	615	7	research	research	NOUN
ejpam-5384	615	8	.	.	PUNCT
ejpam-5384	616	1	proceedings	proceeding	NOUN
ejpam-5384	616	2	of	of	ADP
ejpam-5384	616	3	the	the	DET
ejpam-5384	616	4	institute	institute	NOUN
ejpam-5384	616	5	of	of	ADP
ejpam-5384	616	6	civil	civil	ADJ
ejpam-5384	616	7	engineers	engineer	NOUN
ejpam-5384	616	8	,	,	PUNCT
ejpam-5384	616	9	part	part	PROPN
ejpam-5384	616	10	ii	ii	PROPN
ejpam-5384	616	11	,	,	PUNCT
ejpam-5384	616	12	1	1	NUM
ejpam-5384	616	13	,	,	PUNCT
ejpam-5384	616	14	325	325	NUM
ejpam-5384	616	15	-	-	SYM
ejpam-5384	616	16	378	378	NUM
ejpam-5384	616	17	,	,	PUNCT
ejpam-5384	616	18	3:325–362	3:325–362	NUM
ejpam-5384	616	19	,	,	PUNCT
ejpam-5384	616	20	1952	1952	NUM
ejpam-5384	616	21	.	.	PUNCT