id	sid	tid	token	lemma	pos
ejpam-5755	1	1	european	european	PROPN
ejpam-5755	1	2	journal	journal	PROPN
ejpam-5755	1	3	of	of	ADP
ejpam-5755	1	4	pure	pure	ADJ
ejpam-5755	1	5	and	and	CCONJ
ejpam-5755	1	6	applied	applied	ADJ
ejpam-5755	1	7	mathematics	mathematic	NOUN
ejpam-5755	1	8	2025	2025	NUM
ejpam-5755	1	9	,	,	PUNCT
ejpam-5755	1	10	vol	vol	NOUN
ejpam-5755	1	11	.	.	PROPN
ejpam-5755	1	12	18	18	NUM
ejpam-5755	1	13	,	,	PUNCT
ejpam-5755	1	14	issue	issue	NOUN
ejpam-5755	1	15	1	1	NUM
ejpam-5755	1	16	,	,	PUNCT
ejpam-5755	1	17	article	article	NOUN
ejpam-5755	1	18	number	number	NOUN
ejpam-5755	1	19	5755	5755	NUM
ejpam-5755	1	20	issn	issn	PROPN
ejpam-5755	1	21	1307	1307	NUM
ejpam-5755	1	22	-	-	SYM
ejpam-5755	1	23	5543	5543	NUM
ejpam-5755	1	24	–	–	PUNCT
ejpam-5755	1	25	ejpam.com	ejpam.com	X
ejpam-5755	1	26	published	publish	VERB
ejpam-5755	1	27	by	by	ADP
ejpam-5755	1	28	new	new	PROPN
ejpam-5755	1	29	york	york	PROPN
ejpam-5755	1	30	business	business	PROPN
ejpam-5755	1	31	global	global	ADJ
ejpam-5755	1	32	impulsive	impulsive	ADJ
ejpam-5755	1	33	protocols	protocol	NOUN
ejpam-5755	1	34	for	for	ADP
ejpam-5755	1	35	scaled	scale	VERB
ejpam-5755	1	36	consensus	consensus	NOUN
ejpam-5755	1	37	in	in	ADP
ejpam-5755	1	38	edge	edge	NOUN
ejpam-5755	1	39	-	-	PUNCT
ejpam-5755	1	40	dynamic	dynamic	ADJ
ejpam-5755	1	41	multi	multi	ADJ
ejpam-5755	1	42	-	-	ADJ
ejpam-5755	1	43	agent	agent	ADJ
ejpam-5755	1	44	systems	system	NOUN
ejpam-5755	1	45	siriluk	siriluk	NOUN
ejpam-5755	1	46	donganont1	donganont1	NOUN
ejpam-5755	1	47	,	,	PUNCT
ejpam-5755	1	48	uamporn	uamporn	ADJ
ejpam-5755	1	49	witthayarat1	witthayarat1	NOUN
ejpam-5755	1	50	,	,	PUNCT
ejpam-5755	1	51	mana	mana	PROPN
ejpam-5755	1	52	donganont1,∗	donganont1,∗	NOUN
ejpam-5755	1	53	1	1	NUM
ejpam-5755	1	54	school	school	NOUN
ejpam-5755	1	55	of	of	ADP
ejpam-5755	1	56	science	science	NOUN
ejpam-5755	1	57	,	,	PUNCT
ejpam-5755	1	58	university	university	NOUN
ejpam-5755	1	59	of	of	ADP
ejpam-5755	1	60	phayao	phayao	NOUN
ejpam-5755	1	61	,	,	PUNCT
ejpam-5755	1	62	phayao	phayao	NOUN
ejpam-5755	1	63	56000	56000	NUM
ejpam-5755	1	64	,	,	PUNCT
ejpam-5755	1	65	thailand	thailand	PROPN
ejpam-5755	1	66	abstract	abstract	NOUN
ejpam-5755	1	67	.	.	PUNCT
ejpam-5755	2	1	this	this	DET
ejpam-5755	2	2	study	study	NOUN
ejpam-5755	2	3	addresses	address	VERB
ejpam-5755	2	4	the	the	DET
ejpam-5755	2	5	challenge	challenge	NOUN
ejpam-5755	2	6	of	of	ADP
ejpam-5755	2	7	achieving	achieve	VERB
ejpam-5755	2	8	scaled	scaled	ADJ
ejpam-5755	2	9	consensus	consensus	NOUN
ejpam-5755	2	10	in	in	ADP
ejpam-5755	2	11	multi	multi	ADJ
ejpam-5755	2	12	-	-	ADJ
ejpam-5755	2	13	agent	agent	ADJ
ejpam-5755	2	14	systems	system	NOUN
ejpam-5755	2	15	with	with	ADP
ejpam-5755	2	16	edge	edge	NOUN
ejpam-5755	2	17	dynamics	dynamic	NOUN
ejpam-5755	2	18	,	,	PUNCT
ejpam-5755	2	19	a	a	DET
ejpam-5755	2	20	critical	critical	ADJ
ejpam-5755	2	21	aspect	aspect	NOUN
ejpam-5755	2	22	for	for	ADP
ejpam-5755	2	23	practical	practical	ADJ
ejpam-5755	2	24	applications	application	NOUN
ejpam-5755	2	25	such	such	ADJ
ejpam-5755	2	26	as	as	ADP
ejpam-5755	2	27	traffic	traffic	NOUN
ejpam-5755	2	28	networks	network	NOUN
ejpam-5755	2	29	and	and	CCONJ
ejpam-5755	2	30	distributed	distribute	VERB
ejpam-5755	2	31	energy	energy	NOUN
ejpam-5755	2	32	systems	system	NOUN
ejpam-5755	2	33	.	.	PUNCT
ejpam-5755	3	1	utilizing	utilize	VERB
ejpam-5755	3	2	graph	graph	NOUN
ejpam-5755	3	3	theory	theory	NOUN
ejpam-5755	3	4	,	,	PUNCT
ejpam-5755	3	5	matrix	matrix	NOUN
ejpam-5755	3	6	analysis	analysis	NOUN
ejpam-5755	3	7	,	,	PUNCT
ejpam-5755	3	8	and	and	CCONJ
ejpam-5755	3	9	lyapunov	lyapunov	ADJ
ejpam-5755	3	10	stability	stability	NOUN
ejpam-5755	3	11	,	,	PUNCT
ejpam-5755	3	12	we	we	PRON
ejpam-5755	3	13	propose	propose	VERB
ejpam-5755	3	14	impulsive	impulsive	ADJ
ejpam-5755	3	15	consensus	consensus	NOUN
ejpam-5755	3	16	protocols	protocol	NOUN
ejpam-5755	3	17	designed	design	VERB
ejpam-5755	3	18	for	for	ADP
ejpam-5755	3	19	both	both	CCONJ
ejpam-5755	3	20	directed	direct	VERB
ejpam-5755	3	21	and	and	CCONJ
ejpam-5755	3	22	undirected	undirected	ADJ
ejpam-5755	3	23	topologies	topology	NOUN
ejpam-5755	3	24	.	.	PUNCT
ejpam-5755	4	1	these	these	DET
ejpam-5755	4	2	protocols	protocol	NOUN
ejpam-5755	4	3	enable	enable	VERB
ejpam-5755	4	4	agents	agent	NOUN
ejpam-5755	4	5	to	to	PART
ejpam-5755	4	6	converge	converge	VERB
ejpam-5755	4	7	proportionally	proportionally	ADV
ejpam-5755	4	8	to	to	ADP
ejpam-5755	4	9	desired	desire	VERB
ejpam-5755	4	10	ratios	ratio	NOUN
ejpam-5755	4	11	among	among	ADP
ejpam-5755	4	12	states	state	NOUN
ejpam-5755	4	13	,	,	PUNCT
ejpam-5755	4	14	generalizing	generalize	VERB
ejpam-5755	4	15	classical	classical	ADJ
ejpam-5755	4	16	consensus	consensus	NOUN
ejpam-5755	4	17	approaches	approach	NOUN
ejpam-5755	4	18	while	while	SCONJ
ejpam-5755	4	19	significantly	significantly	ADV
ejpam-5755	4	20	reducing	reduce	VERB
ejpam-5755	4	21	communication	communication	NOUN
ejpam-5755	4	22	and	and	CCONJ
ejpam-5755	4	23	control	control	NOUN
ejpam-5755	4	24	costs	cost	NOUN
ejpam-5755	4	25	.	.	PUNCT
ejpam-5755	5	1	we	we	PRON
ejpam-5755	5	2	establish	establish	VERB
ejpam-5755	5	3	sufficient	sufficient	ADJ
ejpam-5755	5	4	conditions	condition	NOUN
ejpam-5755	5	5	for	for	ADP
ejpam-5755	5	6	achieving	achieve	VERB
ejpam-5755	5	7	scaled	scaled	ADJ
ejpam-5755	5	8	consensus	consensus	NOUN
ejpam-5755	5	9	,	,	PUNCT
ejpam-5755	5	10	demonstrating	demonstrate	VERB
ejpam-5755	5	11	that	that	SCONJ
ejpam-5755	5	12	it	it	PRON
ejpam-5755	5	13	requires	require	VERB
ejpam-5755	5	14	the	the	DET
ejpam-5755	5	15	line	line	NOUN
ejpam-5755	5	16	graph	graph	NOUN
ejpam-5755	5	17	of	of	ADP
ejpam-5755	5	18	the	the	DET
ejpam-5755	5	19	communication	communication	NOUN
ejpam-5755	5	20	network	network	NOUN
ejpam-5755	5	21	to	to	PART
ejpam-5755	5	22	be	be	AUX
ejpam-5755	5	23	connected	connect	VERB
ejpam-5755	5	24	and	and	CCONJ
ejpam-5755	5	25	contain	contain	VERB
ejpam-5755	5	26	a	a	DET
ejpam-5755	5	27	spanning	span	VERB
ejpam-5755	5	28	tree	tree	NOUN
ejpam-5755	5	29	.	.	PUNCT
ejpam-5755	6	1	numerical	numerical	ADJ
ejpam-5755	6	2	simulations	simulation	NOUN
ejpam-5755	6	3	validate	validate	VERB
ejpam-5755	6	4	the	the	DET
ejpam-5755	6	5	robustness	robustness	NOUN
ejpam-5755	6	6	and	and	CCONJ
ejpam-5755	6	7	efficiency	efficiency	NOUN
ejpam-5755	6	8	of	of	ADP
ejpam-5755	6	9	the	the	DET
ejpam-5755	6	10	proposed	propose	VERB
ejpam-5755	6	11	protocols	protocol	NOUN
ejpam-5755	6	12	,	,	PUNCT
ejpam-5755	6	13	highlighting	highlight	VERB
ejpam-5755	6	14	their	their	PRON
ejpam-5755	6	15	scalability	scalability	NOUN
ejpam-5755	6	16	and	and	CCONJ
ejpam-5755	6	17	adaptability	adaptability	NOUN
ejpam-5755	6	18	in	in	ADP
ejpam-5755	6	19	dynamic	dynamic	ADJ
ejpam-5755	6	20	and	and	CCONJ
ejpam-5755	6	21	resource	resource	NOUN
ejpam-5755	6	22	-	-	PUNCT
ejpam-5755	6	23	constrained	constrain	VERB
ejpam-5755	6	24	environments	environment	NOUN
ejpam-5755	6	25	.	.	PUNCT
ejpam-5755	7	1	the	the	DET
ejpam-5755	7	2	findings	finding	NOUN
ejpam-5755	7	3	provide	provide	VERB
ejpam-5755	7	4	a	a	DET
ejpam-5755	7	5	solid	solid	ADJ
ejpam-5755	7	6	foundation	foundation	NOUN
ejpam-5755	7	7	for	for	ADP
ejpam-5755	7	8	real	real	ADJ
ejpam-5755	7	9	-	-	PUNCT
ejpam-5755	7	10	world	world	NOUN
ejpam-5755	7	11	applications	application	NOUN
ejpam-5755	7	12	,	,	PUNCT
ejpam-5755	7	13	including	include	VERB
ejpam-5755	7	14	autonomous	autonomous	ADJ
ejpam-5755	7	15	vehicles	vehicle	NOUN
ejpam-5755	7	16	,	,	PUNCT
ejpam-5755	7	17	distributed	distribute	VERB
ejpam-5755	7	18	energy	energy	NOUN
ejpam-5755	7	19	systems	system	NOUN
ejpam-5755	7	20	,	,	PUNCT
ejpam-5755	7	21	and	and	CCONJ
ejpam-5755	7	22	robotic	robotic	ADJ
ejpam-5755	7	23	coordination	coordination	NOUN
ejpam-5755	7	24	,	,	PUNCT
ejpam-5755	7	25	where	where	SCONJ
ejpam-5755	7	26	proportional	proportional	ADJ
ejpam-5755	7	27	state	state	NOUN
ejpam-5755	7	28	alignment	alignment	NOUN
ejpam-5755	7	29	is	be	AUX
ejpam-5755	7	30	essential	essential	ADJ
ejpam-5755	7	31	.	.	PUNCT
ejpam-5755	8	1	2020	2020	NUM
ejpam-5755	8	2	mathematics	mathematic	NOUN
ejpam-5755	8	3	subject	subject	NOUN
ejpam-5755	8	4	classifications	classification	NOUN
ejpam-5755	8	5	:	:	PUNCT
ejpam-5755	8	6	93a16	93a16	NUM
ejpam-5755	8	7	,	,	PUNCT
ejpam-5755	8	8	93b70	93b70	NUM
ejpam-5755	8	9	,	,	PUNCT
ejpam-5755	8	10	93c27	93c27	NUM
ejpam-5755	8	11	,	,	PUNCT
ejpam-5755	8	12	93d50	93d50	NUM
ejpam-5755	8	13	key	key	ADJ
ejpam-5755	8	14	words	word	NOUN
ejpam-5755	8	15	and	and	CCONJ
ejpam-5755	8	16	phrases	phrase	NOUN
ejpam-5755	8	17	:	:	PUNCT
ejpam-5755	8	18	multi	multi	ADJ
ejpam-5755	8	19	-	-	ADJ
ejpam-5755	8	20	agent	agent	ADJ
ejpam-5755	8	21	systems	system	NOUN
ejpam-5755	8	22	,	,	PUNCT
ejpam-5755	8	23	scaled	scale	VERB
ejpam-5755	8	24	consensus	consensus	NOUN
ejpam-5755	8	25	,	,	PUNCT
ejpam-5755	8	26	edge	edge	VERB
ejpam-5755	8	27	consensus	consensus	NOUN
ejpam-5755	8	28	problem	problem	NOUN
ejpam-5755	8	29	,	,	PUNCT
ejpam-5755	8	30	spanning	span	VERB
ejpam-5755	8	31	tree	tree	NOUN
ejpam-5755	8	32	,	,	PUNCT
ejpam-5755	9	1	impulsive	impulsive	ADJ
ejpam-5755	9	2	control	control	NOUN
ejpam-5755	9	3	1	1	NUM
ejpam-5755	9	4	.	.	PUNCT
ejpam-5755	9	5	introduction	introduction	NOUN
ejpam-5755	9	6	and	and	CCONJ
ejpam-5755	9	7	preliminaries	preliminary	NOUN
ejpam-5755	9	8	the	the	DET
ejpam-5755	9	9	consensus	consensus	NOUN
ejpam-5755	9	10	problem	problem	NOUN
ejpam-5755	9	11	in	in	ADP
ejpam-5755	9	12	multi	multi	ADJ
ejpam-5755	9	13	-	-	ADJ
ejpam-5755	9	14	agent	agent	ADJ
ejpam-5755	9	15	systems	system	NOUN
ejpam-5755	9	16	has	have	AUX
ejpam-5755	9	17	been	be	AUX
ejpam-5755	9	18	a	a	DET
ejpam-5755	9	19	cornerstone	cornerstone	NOUN
ejpam-5755	9	20	of	of	ADP
ejpam-5755	9	21	research	research	NOUN
ejpam-5755	9	22	in	in	ADP
ejpam-5755	9	23	networked	networked	ADJ
ejpam-5755	9	24	control	control	NOUN
ejpam-5755	9	25	systems	system	NOUN
ejpam-5755	9	26	,	,	PUNCT
ejpam-5755	9	27	particularly	particularly	ADV
ejpam-5755	9	28	over	over	ADP
ejpam-5755	9	29	the	the	DET
ejpam-5755	9	30	last	last	ADJ
ejpam-5755	9	31	decade	decade	NOUN
ejpam-5755	9	32	.	.	PUNCT
ejpam-5755	10	1	traditional	traditional	ADJ
ejpam-5755	10	2	investigations	investigation	NOUN
ejpam-5755	10	3	have	have	AUX
ejpam-5755	10	4	predominantly	predominantly	ADV
ejpam-5755	10	5	focused	focus	VERB
ejpam-5755	10	6	on	on	ADP
ejpam-5755	10	7	achieving	achieve	VERB
ejpam-5755	10	8	agreement	agreement	NOUN
ejpam-5755	10	9	among	among	ADP
ejpam-5755	10	10	node	node	ADJ
ejpam-5755	10	11	states	state	NOUN
ejpam-5755	10	12	,	,	PUNCT
ejpam-5755	10	13	using	use	VERB
ejpam-5755	10	14	nodal	nodal	NOUN
ejpam-5755	10	15	dynamics	dynamic	NOUN
ejpam-5755	10	16	to	to	PART
ejpam-5755	10	17	model	model	VERB
ejpam-5755	10	18	interactions	interaction	NOUN
ejpam-5755	10	19	.	.	PUNCT
ejpam-5755	11	1	seminal	seminal	ADJ
ejpam-5755	11	2	works	work	NOUN
ejpam-5755	11	3	,	,	PUNCT
ejpam-5755	11	4	such	such	ADJ
ejpam-5755	11	5	as	as	ADP
ejpam-5755	11	6	those	those	PRON
ejpam-5755	11	7	by	by	ADP
ejpam-5755	11	8	olfati	olfati	NOUN
ejpam-5755	11	9	-	-	NOUN
ejpam-5755	11	10	saber	saber	NOUN
ejpam-5755	11	11	et	et	NOUN
ejpam-5755	11	12	al	al	PROPN
ejpam-5755	11	13	.	.	PUNCT
ejpam-5755	12	1	[	[	X
ejpam-5755	12	2	8	8	NUM
ejpam-5755	12	3	,	,	PUNCT
ejpam-5755	12	4	9	9	NUM
ejpam-5755	12	5	]	]	PUNCT
ejpam-5755	12	6	,	,	PUNCT
ejpam-5755	12	7	developed	develop	VERB
ejpam-5755	12	8	integrator	integrator	NOUN
ejpam-5755	12	9	and	and	CCONJ
ejpam-5755	12	10	linear	linear	NOUN
ejpam-5755	12	11	models	model	NOUN
ejpam-5755	12	12	for	for	ADP
ejpam-5755	12	13	consensus	consensus	NOUN
ejpam-5755	12	14	,	,	PUNCT
ejpam-5755	12	15	which	which	PRON
ejpam-5755	12	16	have	have	AUX
ejpam-5755	12	17	since	since	ADV
ejpam-5755	12	18	been	be	AUX
ejpam-5755	12	19	extended	extend	VERB
ejpam-5755	12	20	to	to	PART
ejpam-5755	12	21	nonlinear	nonlinear	NOUN
ejpam-5755	12	22	[	[	X
ejpam-5755	12	23	23	23	NUM
ejpam-5755	12	24	]	]	PUNCT
ejpam-5755	12	25	,	,	PUNCT
ejpam-5755	12	26	second	second	ADJ
ejpam-5755	12	27	order	order	NOUN
ejpam-5755	13	1	[	[	X
ejpam-5755	13	2	21	21	NUM
ejpam-5755	13	3	]	]	PUNCT
ejpam-5755	13	4	,	,	PUNCT
ejpam-5755	13	5	and	and	CCONJ
ejpam-5755	13	6	higher	high	ADJ
ejpam-5755	13	7	order	order	NOUN
ejpam-5755	13	8	systems	system	NOUN
ejpam-5755	13	9	[	[	X
ejpam-5755	13	10	5	5	NUM
ejpam-5755	13	11	]	]	PUNCT
ejpam-5755	13	12	.	.	PUNCT
ejpam-5755	14	1	these	these	DET
ejpam-5755	14	2	studies	study	NOUN
ejpam-5755	14	3	laid	lay	VERB
ejpam-5755	14	4	the	the	DET
ejpam-5755	14	5	groundwork	groundwork	NOUN
ejpam-5755	14	6	for	for	ADP
ejpam-5755	14	7	a	a	DET
ejpam-5755	14	8	variety	variety	NOUN
ejpam-5755	14	9	of	of	ADP
ejpam-5755	14	10	applications	application	NOUN
ejpam-5755	14	11	,	,	PUNCT
ejpam-5755	14	12	from	from	ADP
ejpam-5755	14	13	sensor	sensor	NOUN
ejpam-5755	14	14	networks	network	NOUN
ejpam-5755	14	15	to	to	ADP
ejpam-5755	14	16	robotics	robotic	NOUN
ejpam-5755	14	17	.	.	PUNCT
ejpam-5755	15	1	however	however	ADV
ejpam-5755	15	2	,	,	PUNCT
ejpam-5755	15	3	practical	practical	ADJ
ejpam-5755	15	4	scenarios	scenario	NOUN
ejpam-5755	15	5	often	often	ADV
ejpam-5755	15	6	reveal	reveal	VERB
ejpam-5755	15	7	the	the	DET
ejpam-5755	15	8	limitations	limitation	NOUN
ejpam-5755	15	9	of	of	ADP
ejpam-5755	15	10	the	the	DET
ejpam-5755	15	11	nodal	nodal	NOUN
ejpam-5755	15	12	dynamics	dynamic	NOUN
ejpam-5755	15	13	in	in	ADP
ejpam-5755	15	14	capturing	capture	VERB
ejpam-5755	15	15	real	real	ADJ
ejpam-5755	15	16	-	-	PUNCT
ejpam-5755	15	17	world	world	NOUN
ejpam-5755	15	18	complexities	complexity	NOUN
ejpam-5755	15	19	.	.	PUNCT
ejpam-5755	16	1	for	for	ADP
ejpam-5755	16	2	instance	instance	NOUN
ejpam-5755	16	3	,	,	PUNCT
ejpam-5755	16	4	in	in	ADP
ejpam-5755	16	5	transportation	transportation	NOUN
ejpam-5755	16	6	systems	system	NOUN
ejpam-5755	16	7	or	or	CCONJ
ejpam-5755	16	8	energy	energy	NOUN
ejpam-5755	16	9	networks	network	NOUN
ejpam-5755	16	10	,	,	PUNCT
ejpam-5755	16	11	∗corresponding	∗corresponde	VERB
ejpam-5755	16	12	author	author	NOUN
ejpam-5755	16	13	.	.	PUNCT
ejpam-5755	17	1	doi	doi	NOUN
ejpam-5755	17	2	:	:	PUNCT
ejpam-5755	17	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5755	https://doi.org/10.29020/nybg.ejpam.v18i1.5755	ADJ
ejpam-5755	17	4	email	email	NOUN
ejpam-5755	17	5	addresses	address	VERB
ejpam-5755	17	6	:	:	PUNCT
ejpam-5755	17	7	siriluk.pa@up.ac.th	siriluk.pa@up.ac.th	PROPN
ejpam-5755	17	8	(	(	PUNCT
ejpam-5755	17	9	s.	s.	PROPN
ejpam-5755	17	10	donganont	donganont	PROPN
ejpam-5755	17	11	)	)	PUNCT
ejpam-5755	17	12	,	,	PUNCT
ejpam-5755	17	13	uamporn.wi@up.ac.th	uamporn.wi@up.ac.th	PROPN
ejpam-5755	17	14	(	(	PUNCT
ejpam-5755	17	15	u.	u.	NOUN
ejpam-5755	17	16	witthayarat	witthayarat	NOUN
ejpam-5755	17	17	)	)	PUNCT
ejpam-5755	17	18	,	,	PUNCT
ejpam-5755	17	19	mana.do@up.ac.th	mana.do@up.ac.th	PROPN
ejpam-5755	17	20	(	(	PUNCT
ejpam-5755	17	21	m.	m.	NOUN
ejpam-5755	17	22	donganont	donganont	PROPN
ejpam-5755	17	23	)	)	PUNCT
ejpam-5755	17	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5755	18	1	1	1	NUM
ejpam-5755	18	2	copyright	copyright	NOUN
ejpam-5755	18	3	:	:	PUNCT
ejpam-5755	18	4	©	©	PROPN
ejpam-5755	18	5	2025	2025	NUM
ejpam-5755	18	6	the	the	DET
ejpam-5755	18	7	author(s	author(s	NOUN
ejpam-5755	18	8	)	)	PUNCT
ejpam-5755	18	9	.	.	PUNCT
ejpam-5755	19	1	(	(	PUNCT
ejpam-5755	19	2	cc	cc	NOUN
ejpam-5755	19	3	by	by	ADP
ejpam-5755	19	4	-	-	PUNCT
ejpam-5755	19	5	nc	nc	PROPN
ejpam-5755	19	6	4.0	4.0	NUM
ejpam-5755	19	7	)	)	PUNCT
ejpam-5755	19	8	s.	s.	PROPN
ejpam-5755	19	9	donganont	donganont	PROPN
ejpam-5755	19	10	,	,	PUNCT
ejpam-5755	19	11	u.	u.	NOUN
ejpam-5755	19	12	witthayarat	witthayarat	NOUN
ejpam-5755	19	13	,	,	PUNCT
ejpam-5755	19	14	m.	m.	NOUN
ejpam-5755	19	15	donganont	donganont	PROPN
ejpam-5755	19	16	/	/	SYM
ejpam-5755	19	17	eur	eur	PROPN
ejpam-5755	19	18	.	.	PUNCT
ejpam-5755	20	1	j.	j.	PROPN
ejpam-5755	20	2	pure	pure	PROPN
ejpam-5755	20	3	appl	appl	PROPN
ejpam-5755	20	4	.	.	PROPN
ejpam-5755	20	5	math	math	PROPN
ejpam-5755	20	6	,	,	PUNCT
ejpam-5755	20	7	18	18	NUM
ejpam-5755	20	8	(	(	PUNCT
ejpam-5755	20	9	1	1	NUM
ejpam-5755	20	10	)	)	PUNCT
ejpam-5755	20	11	(	(	PUNCT
ejpam-5755	20	12	2025	2025	NUM
ejpam-5755	20	13	)	)	PUNCT
ejpam-5755	20	14	,	,	PUNCT
ejpam-5755	20	15	5755	5755	NUM
ejpam-5755	20	16	2	2	NUM
ejpam-5755	20	17	of	of	ADP
ejpam-5755	20	18	17	17	NUM
ejpam-5755	20	19	edge	edge	NOUN
ejpam-5755	20	20	dynamics	dynamic	NOUN
ejpam-5755	20	21	representing	represent	VERB
ejpam-5755	20	22	interactions	interaction	NOUN
ejpam-5755	20	23	rather	rather	ADV
ejpam-5755	20	24	than	than	ADP
ejpam-5755	20	25	individual	individual	ADJ
ejpam-5755	20	26	states	state	NOUN
ejpam-5755	20	27	offer	offer	VERB
ejpam-5755	20	28	a	a	DET
ejpam-5755	20	29	more	more	ADV
ejpam-5755	20	30	accurate	accurate	ADJ
ejpam-5755	20	31	framework	framework	NOUN
ejpam-5755	20	32	.	.	PUNCT
ejpam-5755	21	1	edge	edge	NOUN
ejpam-5755	21	2	-	-	PUNCT
ejpam-5755	21	3	based	base	VERB
ejpam-5755	21	4	modeling	modeling	NOUN
ejpam-5755	21	5	has	have	AUX
ejpam-5755	21	6	been	be	AUX
ejpam-5755	21	7	particularly	particularly	ADV
ejpam-5755	21	8	relevant	relevant	ADJ
ejpam-5755	21	9	in	in	ADP
ejpam-5755	21	10	scenarios	scenario	NOUN
ejpam-5755	21	11	such	such	ADJ
ejpam-5755	21	12	as	as	ADP
ejpam-5755	21	13	traffic	traffic	NOUN
ejpam-5755	21	14	systems	system	NOUN
ejpam-5755	21	15	,	,	PUNCT
ejpam-5755	21	16	where	where	SCONJ
ejpam-5755	21	17	road	road	NOUN
ejpam-5755	21	18	conditions	condition	NOUN
ejpam-5755	21	19	(	(	PUNCT
ejpam-5755	21	20	edges	edge	NOUN
ejpam-5755	21	21	)	)	PUNCT
ejpam-5755	21	22	rather	rather	ADV
ejpam-5755	21	23	than	than	ADP
ejpam-5755	21	24	junction	junction	NOUN
ejpam-5755	21	25	states	state	NOUN
ejpam-5755	21	26	(	(	PUNCT
ejpam-5755	21	27	nodes	node	NOUN
ejpam-5755	21	28	)	)	PUNCT
ejpam-5755	21	29	dictate	dictate	VERB
ejpam-5755	21	30	flow	flow	NOUN
ejpam-5755	21	31	efficiency	efficiency	NOUN
ejpam-5755	21	32	[	[	X
ejpam-5755	21	33	6	6	NUM
ejpam-5755	21	34	,	,	PUNCT
ejpam-5755	21	35	14	14	NUM
ejpam-5755	21	36	,	,	PUNCT
ejpam-5755	21	37	18	18	NUM
ejpam-5755	21	38	]	]	PUNCT
ejpam-5755	21	39	.	.	PUNCT
ejpam-5755	22	1	the	the	DET
ejpam-5755	22	2	burgeoning	burgeon	VERB
ejpam-5755	22	3	interest	interest	NOUN
ejpam-5755	22	4	in	in	ADP
ejpam-5755	22	5	edge	edge	NOUN
ejpam-5755	22	6	dynamics	dynamic	NOUN
ejpam-5755	22	7	has	have	AUX
ejpam-5755	22	8	inspired	inspire	VERB
ejpam-5755	22	9	a	a	DET
ejpam-5755	22	10	new	new	ADJ
ejpam-5755	22	11	wave	wave	NOUN
ejpam-5755	22	12	of	of	ADP
ejpam-5755	22	13	research	research	NOUN
ejpam-5755	22	14	aimed	aim	VERB
ejpam-5755	22	15	at	at	ADP
ejpam-5755	22	16	solving	solve	VERB
ejpam-5755	22	17	edge	edge	NOUN
ejpam-5755	22	18	consensus	consensus	NOUN
ejpam-5755	22	19	problems	problem	NOUN
ejpam-5755	22	20	under	under	ADP
ejpam-5755	22	21	dynamic	dynamic	ADJ
ejpam-5755	22	22	topologies	topology	NOUN
ejpam-5755	22	23	.	.	PUNCT
ejpam-5755	23	1	a	a	DET
ejpam-5755	23	2	pressing	press	VERB
ejpam-5755	23	3	challenge	challenge	NOUN
ejpam-5755	23	4	in	in	ADP
ejpam-5755	23	5	multi	multi	ADJ
ejpam-5755	23	6	-	-	ADJ
ejpam-5755	23	7	agent	agent	ADJ
ejpam-5755	23	8	systems	system	NOUN
ejpam-5755	23	9	is	be	AUX
ejpam-5755	23	10	the	the	DET
ejpam-5755	23	11	coordination	coordination	NOUN
ejpam-5755	23	12	of	of	ADP
ejpam-5755	23	13	agents	agent	NOUN
ejpam-5755	23	14	in	in	ADP
ejpam-5755	23	15	discrete	discrete	ADJ
ejpam-5755	23	16	time	time	NOUN
ejpam-5755	23	17	intervals	interval	NOUN
ejpam-5755	23	18	,	,	PUNCT
ejpam-5755	23	19	a	a	DET
ejpam-5755	23	20	scenario	scenario	NOUN
ejpam-5755	23	21	where	where	SCONJ
ejpam-5755	23	22	continuous	continuous	ADJ
ejpam-5755	23	23	-	-	PUNCT
ejpam-5755	23	24	time	time	NOUN
ejpam-5755	23	25	protocols	protocol	NOUN
ejpam-5755	23	26	falter	falter	VERB
ejpam-5755	23	27	.	.	PUNCT
ejpam-5755	24	1	this	this	PRON
ejpam-5755	24	2	has	have	AUX
ejpam-5755	24	3	motivated	motivate	VERB
ejpam-5755	24	4	the	the	DET
ejpam-5755	24	5	adoption	adoption	NOUN
ejpam-5755	24	6	of	of	ADP
ejpam-5755	24	7	impulsive	impulsive	ADJ
ejpam-5755	24	8	consensus	consensus	NOUN
ejpam-5755	24	9	protocols	protocol	NOUN
ejpam-5755	24	10	,	,	PUNCT
ejpam-5755	24	11	which	which	PRON
ejpam-5755	24	12	leverage	leverage	VERB
ejpam-5755	24	13	impulsive	impulsive	ADJ
ejpam-5755	24	14	control	control	NOUN
ejpam-5755	24	15	strategies	strategy	NOUN
ejpam-5755	24	16	to	to	PART
ejpam-5755	24	17	enable	enable	VERB
ejpam-5755	24	18	abrupt	abrupt	ADJ
ejpam-5755	24	19	state	state	NOUN
ejpam-5755	24	20	adjustments	adjustment	NOUN
ejpam-5755	24	21	at	at	ADP
ejpam-5755	24	22	specified	specify	VERB
ejpam-5755	24	23	time	time	NOUN
ejpam-5755	24	24	instances	instance	NOUN
ejpam-5755	24	25	.	.	PUNCT
ejpam-5755	25	1	these	these	DET
ejpam-5755	25	2	protocols	protocol	NOUN
ejpam-5755	25	3	,	,	PUNCT
ejpam-5755	25	4	as	as	SCONJ
ejpam-5755	25	5	highlighted	highlight	VERB
ejpam-5755	25	6	in	in	ADP
ejpam-5755	25	7	studies	study	NOUN
ejpam-5755	25	8	such	such	ADJ
ejpam-5755	25	9	as	as	ADP
ejpam-5755	25	10	wang	wang	PROPN
ejpam-5755	25	11	et	et	PROPN
ejpam-5755	25	12	al	al	PROPN
ejpam-5755	25	13	.	.	PUNCT
ejpam-5755	26	1	[	[	X
ejpam-5755	26	2	14	14	NUM
ejpam-5755	26	3	]	]	PUNCT
ejpam-5755	26	4	and	and	CCONJ
ejpam-5755	26	5	liu	liu	PROPN
ejpam-5755	26	6	et	et	PROPN
ejpam-5755	26	7	al	al	PROPN
ejpam-5755	26	8	.	.	PUNCT
ejpam-5755	27	1	[	[	X
ejpam-5755	27	2	16	16	NUM
ejpam-5755	27	3	,	,	PUNCT
ejpam-5755	27	4	17	17	NUM
ejpam-5755	27	5	]	]	PUNCT
ejpam-5755	27	6	,	,	PUNCT
ejpam-5755	27	7	significantly	significantly	ADV
ejpam-5755	27	8	reduce	reduce	VERB
ejpam-5755	27	9	communication	communication	NOUN
ejpam-5755	27	10	overhead	overhead	ADV
ejpam-5755	27	11	while	while	SCONJ
ejpam-5755	27	12	maintaining	maintain	VERB
ejpam-5755	27	13	robust	robust	ADJ
ejpam-5755	27	14	system	system	NOUN
ejpam-5755	27	15	performance	performance	NOUN
ejpam-5755	27	16	.	.	PUNCT
ejpam-5755	28	1	applications	application	NOUN
ejpam-5755	28	2	span	span	VERB
ejpam-5755	28	3	autonomous	autonomous	ADJ
ejpam-5755	28	4	systems	system	NOUN
ejpam-5755	29	1	[	[	X
ejpam-5755	29	2	12	12	NUM
ejpam-5755	29	3	]	]	X
ejpam-5755	29	4	,	,	PUNCT
ejpam-5755	29	5	deep	deep	ADJ
ejpam-5755	29	6	-	-	PUNCT
ejpam-5755	29	7	space	space	NOUN
ejpam-5755	29	8	missions	mission	NOUN
ejpam-5755	29	9	,	,	PUNCT
ejpam-5755	29	10	and	and	CCONJ
ejpam-5755	29	11	energy	energy	NOUN
ejpam-5755	29	12	-	-	PUNCT
ejpam-5755	29	13	efficient	efficient	ADJ
ejpam-5755	29	14	wireless	wireless	ADJ
ejpam-5755	29	15	sensor	sensor	NOUN
ejpam-5755	29	16	networks	network	NOUN
ejpam-5755	29	17	,	,	PUNCT
ejpam-5755	29	18	where	where	SCONJ
ejpam-5755	29	19	communication	communication	NOUN
ejpam-5755	29	20	constraints	constraint	NOUN
ejpam-5755	29	21	are	be	AUX
ejpam-5755	29	22	a	a	DET
ejpam-5755	29	23	critical	critical	ADJ
ejpam-5755	29	24	consideration	consideration	NOUN
ejpam-5755	29	25	(	(	PUNCT
ejpam-5755	29	26	see	see	VERB
ejpam-5755	29	27	more	more	ADJ
ejpam-5755	29	28	examples	example	NOUN
ejpam-5755	29	29	in	in	ADP
ejpam-5755	29	30	[	[	X
ejpam-5755	29	31	1	1	NUM
ejpam-5755	29	32	,	,	PUNCT
ejpam-5755	29	33	15	15	NUM
ejpam-5755	29	34	,	,	PUNCT
ejpam-5755	29	35	19	19	NUM
ejpam-5755	29	36	,	,	PUNCT
ejpam-5755	29	37	20	20	NUM
ejpam-5755	29	38	,	,	PUNCT
ejpam-5755	29	39	22	22	NUM
ejpam-5755	29	40	]	]	PUNCT
ejpam-5755	29	41	)	)	PUNCT
ejpam-5755	29	42	.	.	PUNCT
ejpam-5755	30	1	a	a	DET
ejpam-5755	30	2	particularly	particularly	ADV
ejpam-5755	30	3	intriguing	intriguing	ADJ
ejpam-5755	30	4	domain	domain	NOUN
ejpam-5755	30	5	within	within	ADP
ejpam-5755	30	6	consensus	consensus	NOUN
ejpam-5755	30	7	research	research	NOUN
ejpam-5755	30	8	is	be	AUX
ejpam-5755	30	9	the	the	DET
ejpam-5755	30	10	scaled	scale	VERB
ejpam-5755	30	11	consensus	consensus	NOUN
ejpam-5755	30	12	problem	problem	NOUN
ejpam-5755	30	13	.	.	PUNCT
ejpam-5755	31	1	unlike	unlike	ADP
ejpam-5755	31	2	traditional	traditional	ADJ
ejpam-5755	31	3	consensus	consensus	NOUN
ejpam-5755	31	4	,	,	PUNCT
ejpam-5755	31	5	which	which	PRON
ejpam-5755	31	6	focuses	focus	VERB
ejpam-5755	31	7	on	on	ADP
ejpam-5755	31	8	convergence	convergence	NOUN
ejpam-5755	31	9	to	to	ADP
ejpam-5755	31	10	a	a	DET
ejpam-5755	31	11	single	single	ADJ
ejpam-5755	31	12	shared	shared	ADJ
ejpam-5755	31	13	state	state	NOUN
ejpam-5755	31	14	,	,	PUNCT
ejpam-5755	31	15	scaled	scale	VERB
ejpam-5755	31	16	consensus	consensus	NOUN
ejpam-5755	31	17	aims	aim	VERB
ejpam-5755	31	18	to	to	PART
ejpam-5755	31	19	achieve	achieve	VERB
ejpam-5755	31	20	predefined	predefine	VERB
ejpam-5755	31	21	proportional	proportional	ADJ
ejpam-5755	31	22	relationships	relationship	NOUN
ejpam-5755	31	23	among	among	ADP
ejpam-5755	31	24	agent	agent	NOUN
ejpam-5755	31	25	states	state	NOUN
ejpam-5755	31	26	.	.	PUNCT
ejpam-5755	32	1	this	this	DET
ejpam-5755	32	2	paradigm	paradigm	NOUN
ejpam-5755	32	3	finds	find	VERB
ejpam-5755	32	4	practical	practical	ADJ
ejpam-5755	32	5	utility	utility	NOUN
ejpam-5755	32	6	in	in	ADP
ejpam-5755	32	7	biological	biological	ADJ
ejpam-5755	32	8	systems	system	NOUN
ejpam-5755	32	9	,	,	PUNCT
ejpam-5755	32	10	multi	multi	ADJ
ejpam-5755	32	11	-	-	ADJ
ejpam-5755	32	12	robot	robot	ADJ
ejpam-5755	32	13	coordination	coordination	NOUN
ejpam-5755	32	14	,	,	PUNCT
ejpam-5755	32	15	and	and	CCONJ
ejpam-5755	32	16	distributed	distribute	VERB
ejpam-5755	32	17	energy	energy	NOUN
ejpam-5755	32	18	systems	system	NOUN
ejpam-5755	32	19	[	[	X
ejpam-5755	32	20	11	11	NUM
ejpam-5755	32	21	]	]	PUNCT
ejpam-5755	32	22	.	.	PUNCT
ejpam-5755	33	1	despite	despite	SCONJ
ejpam-5755	33	2	its	its	PRON
ejpam-5755	33	3	potential	potential	NOUN
ejpam-5755	33	4	,	,	PUNCT
ejpam-5755	33	5	scaled	scale	VERB
ejpam-5755	33	6	consensus	consensus	NOUN
ejpam-5755	33	7	has	have	AUX
ejpam-5755	33	8	remained	remain	VERB
ejpam-5755	33	9	relatively	relatively	ADV
ejpam-5755	33	10	under	under	ADP
ejpam-5755	33	11	explored	explore	VERB
ejpam-5755	33	12	,	,	PUNCT
ejpam-5755	33	13	especially	especially	ADV
ejpam-5755	33	14	concerning	concern	VERB
ejpam-5755	33	15	edge	edge	NOUN
ejpam-5755	33	16	dynamics	dynamic	NOUN
ejpam-5755	33	17	and	and	CCONJ
ejpam-5755	33	18	the	the	DET
ejpam-5755	33	19	impulsive	impulsive	ADJ
ejpam-5755	33	20	protocols	protocol	NOUN
ejpam-5755	33	21	necessary	necessary	ADJ
ejpam-5755	33	22	to	to	PART
ejpam-5755	33	23	regulate	regulate	VERB
ejpam-5755	33	24	them	they	PRON
ejpam-5755	33	25	under	under	ADP
ejpam-5755	33	26	complex	complex	ADJ
ejpam-5755	33	27	topologies	topology	NOUN
ejpam-5755	33	28	.	.	PUNCT
ejpam-5755	34	1	this	this	DET
ejpam-5755	34	2	paper	paper	NOUN
ejpam-5755	34	3	aims	aim	VERB
ejpam-5755	34	4	to	to	PART
ejpam-5755	34	5	fill	fill	VERB
ejpam-5755	34	6	this	this	DET
ejpam-5755	34	7	gap	gap	NOUN
ejpam-5755	34	8	by	by	ADP
ejpam-5755	34	9	addressing	address	VERB
ejpam-5755	34	10	the	the	DET
ejpam-5755	34	11	scaled	scale	VERB
ejpam-5755	34	12	consensus	consensus	NOUN
ejpam-5755	34	13	problem	problem	NOUN
ejpam-5755	34	14	for	for	ADP
ejpam-5755	34	15	edgedynamic	edgedynamic	ADJ
ejpam-5755	34	16	multi	multi	ADJ
ejpam-5755	34	17	-	-	ADJ
ejpam-5755	34	18	agent	agent	ADJ
ejpam-5755	34	19	systems	system	NOUN
ejpam-5755	34	20	under	under	ADP
ejpam-5755	34	21	both	both	CCONJ
ejpam-5755	34	22	directed	direct	VERB
ejpam-5755	34	23	and	and	CCONJ
ejpam-5755	34	24	undirected	undirected	ADJ
ejpam-5755	34	25	topologies	topology	NOUN
ejpam-5755	34	26	.	.	PUNCT
ejpam-5755	35	1	inspired	inspire	VERB
ejpam-5755	35	2	by	by	ADP
ejpam-5755	35	3	foundational	foundational	ADJ
ejpam-5755	35	4	works	work	NOUN
ejpam-5755	35	5	[	[	X
ejpam-5755	35	6	7	7	NUM
ejpam-5755	35	7	,	,	PUNCT
ejpam-5755	35	8	11	11	NUM
ejpam-5755	35	9	,	,	PUNCT
ejpam-5755	35	10	14	14	NUM
ejpam-5755	35	11	]	]	PUNCT
ejpam-5755	35	12	,	,	PUNCT
ejpam-5755	35	13	we	we	PRON
ejpam-5755	35	14	introduce	introduce	VERB
ejpam-5755	35	15	novel	novel	ADJ
ejpam-5755	35	16	impulsive	impulsive	ADJ
ejpam-5755	35	17	control	control	NOUN
ejpam-5755	35	18	protocols	protocol	NOUN
ejpam-5755	35	19	,	,	PUNCT
ejpam-5755	35	20	extending	extend	VERB
ejpam-5755	35	21	their	their	PRON
ejpam-5755	35	22	applicability	applicability	NOUN
ejpam-5755	35	23	to	to	ADP
ejpam-5755	35	24	scenarios	scenario	NOUN
ejpam-5755	35	25	characterized	characterize	VERB
ejpam-5755	35	26	by	by	ADP
ejpam-5755	35	27	heterogeneous	heterogeneous	ADJ
ejpam-5755	35	28	agent	agent	NOUN
ejpam-5755	35	29	dynamics	dynamic	NOUN
ejpam-5755	35	30	.	.	PUNCT
ejpam-5755	36	1	specifically	specifically	ADV
ejpam-5755	36	2	,	,	PUNCT
ejpam-5755	36	3	our	our	PRON
ejpam-5755	36	4	contributions	contribution	NOUN
ejpam-5755	36	5	include	include	VERB
ejpam-5755	36	6	:	:	PUNCT
ejpam-5755	36	7	(	(	PUNCT
ejpam-5755	36	8	1	1	X
ejpam-5755	36	9	)	)	PUNCT
ejpam-5755	36	10	a	a	DET
ejpam-5755	36	11	rigorous	rigorous	ADJ
ejpam-5755	36	12	exploration	exploration	NOUN
ejpam-5755	36	13	of	of	ADP
ejpam-5755	36	14	scaled	scaled	ADJ
ejpam-5755	36	15	consensus	consensus	NOUN
ejpam-5755	36	16	under	under	ADP
ejpam-5755	36	17	impulsive	impulsive	ADJ
ejpam-5755	36	18	protocols	protocol	NOUN
ejpam-5755	36	19	for	for	ADP
ejpam-5755	36	20	edge	edge	NOUN
ejpam-5755	36	21	dynamics	dynamic	NOUN
ejpam-5755	36	22	,	,	PUNCT
ejpam-5755	36	23	expanding	expand	VERB
ejpam-5755	36	24	on	on	ADP
ejpam-5755	36	25	prior	prior	ADJ
ejpam-5755	36	26	analyses	analysis	NOUN
ejpam-5755	36	27	of	of	ADP
ejpam-5755	36	28	nodal	nodal	NOUN
ejpam-5755	36	29	dynamics	dynamic	NOUN
ejpam-5755	36	30	[	[	X
ejpam-5755	36	31	1	1	NUM
ejpam-5755	36	32	,	,	PUNCT
ejpam-5755	36	33	2	2	NUM
ejpam-5755	36	34	]	]	PUNCT
ejpam-5755	36	35	.	.	PUNCT
ejpam-5755	37	1	(	(	PUNCT
ejpam-5755	37	2	2	2	X
ejpam-5755	37	3	)	)	PUNCT
ejpam-5755	37	4	the	the	DET
ejpam-5755	37	5	establishment	establishment	NOUN
ejpam-5755	37	6	of	of	ADP
ejpam-5755	37	7	sufficient	sufficient	ADJ
ejpam-5755	37	8	conditions	condition	NOUN
ejpam-5755	37	9	for	for	ADP
ejpam-5755	37	10	achieving	achieve	VERB
ejpam-5755	37	11	scaled	scaled	ADJ
ejpam-5755	37	12	consensus	consensus	NOUN
ejpam-5755	37	13	,	,	PUNCT
ejpam-5755	37	14	leveraging	leverage	VERB
ejpam-5755	37	15	graph	graph	NOUN
ejpam-5755	37	16	theory	theory	NOUN
ejpam-5755	37	17	and	and	CCONJ
ejpam-5755	37	18	lyapunov	lyapunov	NOUN
ejpam-5755	37	19	-	-	PUNCT
ejpam-5755	37	20	based	base	VERB
ejpam-5755	37	21	stability	stability	NOUN
ejpam-5755	37	22	criteria	criterion	NOUN
ejpam-5755	37	23	.	.	PUNCT
ejpam-5755	38	1	the	the	DET
ejpam-5755	38	2	rest	rest	NOUN
ejpam-5755	38	3	of	of	ADP
ejpam-5755	38	4	the	the	DET
ejpam-5755	38	5	paper	paper	NOUN
ejpam-5755	38	6	is	be	AUX
ejpam-5755	38	7	organized	organize	VERB
ejpam-5755	38	8	as	as	SCONJ
ejpam-5755	38	9	follows	follow	VERB
ejpam-5755	38	10	.	.	PUNCT
ejpam-5755	39	1	section	section	NOUN
ejpam-5755	39	2	2	2	NUM
ejpam-5755	39	3	reviews	review	NOUN
ejpam-5755	39	4	foundational	foundational	ADJ
ejpam-5755	39	5	concepts	concept	NOUN
ejpam-5755	39	6	and	and	CCONJ
ejpam-5755	39	7	frames	frame	VERB
ejpam-5755	39	8	the	the	DET
ejpam-5755	39	9	problem	problem	NOUN
ejpam-5755	39	10	.	.	PUNCT
ejpam-5755	40	1	section	section	NOUN
ejpam-5755	40	2	3	3	NUM
ejpam-5755	40	3	presents	present	VERB
ejpam-5755	40	4	the	the	DET
ejpam-5755	40	5	main	main	ADJ
ejpam-5755	40	6	results	result	NOUN
ejpam-5755	40	7	,	,	PUNCT
ejpam-5755	40	8	deriving	derive	VERB
ejpam-5755	40	9	conditions	condition	NOUN
ejpam-5755	40	10	for	for	ADP
ejpam-5755	40	11	scaled	scale	VERB
ejpam-5755	40	12	consensus	consensus	NOUN
ejpam-5755	40	13	in	in	ADP
ejpam-5755	40	14	undirected	undirected	ADJ
ejpam-5755	40	15	and	and	CCONJ
ejpam-5755	40	16	directed	direct	VERB
ejpam-5755	40	17	topologies	topology	NOUN
ejpam-5755	40	18	.	.	PUNCT
ejpam-5755	41	1	numerical	numerical	ADJ
ejpam-5755	41	2	simulations	simulation	NOUN
ejpam-5755	41	3	,	,	PUNCT
ejpam-5755	41	4	illustrating	illustrate	VERB
ejpam-5755	41	5	the	the	DET
ejpam-5755	41	6	efficacy	efficacy	NOUN
ejpam-5755	41	7	of	of	ADP
ejpam-5755	41	8	the	the	DET
ejpam-5755	41	9	proposed	propose	VERB
ejpam-5755	41	10	methods	method	NOUN
ejpam-5755	41	11	,	,	PUNCT
ejpam-5755	41	12	are	be	AUX
ejpam-5755	41	13	provided	provide	VERB
ejpam-5755	41	14	in	in	ADP
ejpam-5755	41	15	section	section	NOUN
ejpam-5755	41	16	4	4	NUM
ejpam-5755	41	17	.	.	PUNCT
ejpam-5755	42	1	finally	finally	ADV
ejpam-5755	42	2	,	,	PUNCT
ejpam-5755	42	3	section	section	NOUN
ejpam-5755	42	4	5	5	NUM
ejpam-5755	42	5	concludes	conclude	VERB
ejpam-5755	42	6	the	the	DET
ejpam-5755	42	7	paper	paper	NOUN
ejpam-5755	42	8	with	with	ADP
ejpam-5755	42	9	a	a	DET
ejpam-5755	42	10	discussion	discussion	NOUN
ejpam-5755	42	11	of	of	ADP
ejpam-5755	42	12	future	future	ADJ
ejpam-5755	42	13	research	research	NOUN
ejpam-5755	42	14	directions	direction	NOUN
ejpam-5755	42	15	.	.	PUNCT
ejpam-5755	43	1	2	2	X
ejpam-5755	43	2	.	.	NUM
ejpam-5755	43	3	preliminaries	preliminary	NOUN
ejpam-5755	43	4	and	and	CCONJ
ejpam-5755	43	5	problem	problem	NOUN
ejpam-5755	43	6	formulations	formulation	NOUN
ejpam-5755	43	7	2.1	2.1	NUM
ejpam-5755	43	8	.	.	PUNCT
ejpam-5755	44	1	preliminaries	preliminary	NOUN
ejpam-5755	44	2	in	in	ADP
ejpam-5755	44	3	this	this	DET
ejpam-5755	44	4	section	section	NOUN
ejpam-5755	44	5	,	,	PUNCT
ejpam-5755	44	6	we	we	PRON
ejpam-5755	44	7	introduce	introduce	VERB
ejpam-5755	44	8	essential	essential	ADJ
ejpam-5755	44	9	concepts	concept	NOUN
ejpam-5755	44	10	from	from	ADP
ejpam-5755	44	11	graph	graph	NOUN
ejpam-5755	44	12	theory	theory	NOUN
ejpam-5755	44	13	and	and	CCONJ
ejpam-5755	44	14	matrix	matrix	NOUN
ejpam-5755	44	15	theory	theory	NOUN
ejpam-5755	44	16	(	(	PUNCT
ejpam-5755	44	17	for	for	ADP
ejpam-5755	44	18	further	further	ADJ
ejpam-5755	44	19	details	detail	NOUN
ejpam-5755	44	20	,	,	PUNCT
ejpam-5755	44	21	see	see	VERB
ejpam-5755	44	22	[	[	X
ejpam-5755	44	23	3	3	NUM
ejpam-5755	44	24	,	,	PUNCT
ejpam-5755	44	25	4	4	NUM
ejpam-5755	44	26	]	]	NUM
ejpam-5755	44	27	)	)	PUNCT
ejpam-5755	44	28	.	.	PUNCT
ejpam-5755	45	1	throughout	throughout	ADP
ejpam-5755	45	2	the	the	DET
ejpam-5755	45	3	paper	paper	NOUN
ejpam-5755	45	4	,	,	PUNCT
ejpam-5755	45	5	interactions	interaction	NOUN
ejpam-5755	45	6	among	among	ADP
ejpam-5755	45	7	n	n	PRON
ejpam-5755	45	8	agents	agent	NOUN
ejpam-5755	45	9	are	be	AUX
ejpam-5755	45	10	represented	represent	VERB
ejpam-5755	45	11	as	as	ADP
ejpam-5755	45	12	a	a	DET
ejpam-5755	45	13	weighted	weight	VERB
ejpam-5755	45	14	directed	direct	VERB
ejpam-5755	45	15	graph	graph	NOUN
ejpam-5755	45	16	g	g	PROPN
ejpam-5755	45	17	=	=	SYM
ejpam-5755	45	18	(	(	PUNCT
ejpam-5755	45	19	v	v	NOUN
ejpam-5755	45	20	,	,	PUNCT
ejpam-5755	45	21	e	e	NOUN
ejpam-5755	45	22	,	,	PUNCT
ejpam-5755	45	23	a	a	PRON
ejpam-5755	45	24	)	)	PUNCT
ejpam-5755	45	25	,	,	PUNCT
ejpam-5755	45	26	where	where	SCONJ
ejpam-5755	45	27	v	v	NOUN
ejpam-5755	45	28	=	=	SYM
ejpam-5755	45	29	{	{	PUNCT
ejpam-5755	45	30	v1	v1	PROPN
ejpam-5755	45	31	,	,	PUNCT
ejpam-5755	45	32	v2	v2	PROPN
ejpam-5755	45	33	,	,	PUNCT
ejpam-5755	45	34	...	...	PUNCT
ejpam-5755	45	35	,	,	PUNCT
ejpam-5755	45	36	vn	vn	PROPN
ejpam-5755	45	37	}	}	PUNCT
ejpam-5755	45	38	denotes	denote	NOUN
ejpam-5755	45	39	s.	s.	PROPN
ejpam-5755	45	40	donganont	donganont	PROPN
ejpam-5755	45	41	,	,	PUNCT
ejpam-5755	45	42	u.	u.	NOUN
ejpam-5755	45	43	witthayarat	witthayarat	NOUN
ejpam-5755	45	44	,	,	PUNCT
ejpam-5755	45	45	m.	m.	NOUN
ejpam-5755	45	46	donganont	donganont	PROPN
ejpam-5755	45	47	/	/	SYM
ejpam-5755	45	48	eur	eur	PROPN
ejpam-5755	45	49	.	.	PUNCT
ejpam-5755	46	1	j.	j.	PROPN
ejpam-5755	46	2	pure	pure	PROPN
ejpam-5755	46	3	appl	appl	PROPN
ejpam-5755	46	4	.	.	PROPN
ejpam-5755	46	5	math	math	PROPN
ejpam-5755	46	6	,	,	PUNCT
ejpam-5755	46	7	18	18	NUM
ejpam-5755	46	8	(	(	PUNCT
ejpam-5755	46	9	1	1	NUM
ejpam-5755	46	10	)	)	PUNCT
ejpam-5755	46	11	(	(	PUNCT
ejpam-5755	46	12	2025	2025	NUM
ejpam-5755	46	13	)	)	PUNCT
ejpam-5755	46	14	,	,	PUNCT
ejpam-5755	46	15	5755	5755	NUM
ejpam-5755	46	16	3	3	NUM
ejpam-5755	46	17	of	of	ADP
ejpam-5755	46	18	17	17	NUM
ejpam-5755	46	19	the	the	DET
ejpam-5755	46	20	set	set	NOUN
ejpam-5755	46	21	of	of	ADP
ejpam-5755	46	22	nodes	node	NOUN
ejpam-5755	46	23	,	,	PUNCT
ejpam-5755	46	24	e	e	X
ejpam-5755	46	25	=	=	SYM
ejpam-5755	46	26	{	{	PUNCT
ejpam-5755	46	27	eij	eij	PROPN
ejpam-5755	46	28	=	=	SYM
ejpam-5755	46	29	(	(	PUNCT
ejpam-5755	46	30	vi	vi	PROPN
ejpam-5755	46	31	,	,	PUNCT
ejpam-5755	46	32	vj	vj	NOUN
ejpam-5755	46	33	)	)	PUNCT
ejpam-5755	46	34	}	}	PUNCT
ejpam-5755	46	35	⊆	⊆	NUM
ejpam-5755	46	36	v	v	ADP
ejpam-5755	46	37	×v	×v	NOUN
ejpam-5755	46	38	represents	represent	VERB
ejpam-5755	46	39	the	the	DET
ejpam-5755	46	40	set	set	NOUN
ejpam-5755	46	41	of	of	ADP
ejpam-5755	46	42	edges	edge	NOUN
ejpam-5755	46	43	,	,	PUNCT
ejpam-5755	46	44	and	and	CCONJ
ejpam-5755	46	45	a	a	PRON
ejpam-5755	46	46	=	=	X
ejpam-5755	47	1	[	[	X
ejpam-5755	47	2	aij	aij	X
ejpam-5755	47	3	]	]	PUNCT
ejpam-5755	47	4	n×n	n×n	PROPN
ejpam-5755	47	5	is	be	AUX
ejpam-5755	47	6	a	a	DET
ejpam-5755	47	7	nonnegative	nonnegative	ADJ
ejpam-5755	47	8	matrix	matrix	NOUN
ejpam-5755	47	9	.	.	PUNCT
ejpam-5755	48	1	the	the	DET
ejpam-5755	48	2	neighbors	neighbor	NOUN
ejpam-5755	48	3	of	of	ADP
ejpam-5755	48	4	agent	agent	NOUN
ejpam-5755	48	5	i	i	PRON
ejpam-5755	48	6	are	be	AUX
ejpam-5755	48	7	indicated	indicate	VERB
ejpam-5755	48	8	by	by	ADP
ejpam-5755	48	9	ni	ni	PROPN
ejpam-5755	48	10	=	=	PROPN
ejpam-5755	48	11	{	{	PUNCT
ejpam-5755	48	12	j	j	PROPN
ejpam-5755	48	13	:	:	PUNCT
ejpam-5755	48	14	aij	aij	PROPN
ejpam-5755	48	15	>	>	X
ejpam-5755	48	16	0	0	NUM
ejpam-5755	48	17	}	}	PUNCT
ejpam-5755	48	18	.	.	PUNCT
ejpam-5755	49	1	the	the	DET
ejpam-5755	49	2	out	out	ADJ
ejpam-5755	49	3	-	-	PUNCT
ejpam-5755	49	4	degree	degree	NOUN
ejpam-5755	49	5	and	and	CCONJ
ejpam-5755	49	6	in	in	ADP
ejpam-5755	49	7	-	-	PUNCT
ejpam-5755	49	8	degree	degree	NOUN
ejpam-5755	49	9	of	of	ADP
ejpam-5755	49	10	node	node	PROPN
ejpam-5755	49	11	vi	vi	PROPN
ejpam-5755	49	12	are	be	AUX
ejpam-5755	49	13	represented	represent	VERB
ejpam-5755	49	14	as	as	ADP
ejpam-5755	49	15	degout(vi	degout(vi	PROPN
ejpam-5755	49	16	)	)	PUNCT
ejpam-5755	49	17	and	and	CCONJ
ejpam-5755	49	18	degin(vi	degin(vi	PROPN
ejpam-5755	49	19	)	)	PUNCT
ejpam-5755	49	20	,	,	PUNCT
ejpam-5755	49	21	corresponding	correspond	VERB
ejpam-5755	49	22	to	to	ADP
ejpam-5755	49	23	the	the	DET
ejpam-5755	49	24	number	number	NOUN
ejpam-5755	49	25	of	of	ADP
ejpam-5755	49	26	edges	edge	NOUN
ejpam-5755	49	27	eij	eij	PROPN
ejpam-5755	49	28	=	=	SYM
ejpam-5755	49	29	(	(	PUNCT
ejpam-5755	49	30	vi	vi	PROPN
ejpam-5755	49	31	,	,	PUNCT
ejpam-5755	49	32	vj	vj	NOUN
ejpam-5755	49	33	)	)	PUNCT
ejpam-5755	49	34	and	and	CCONJ
ejpam-5755	49	35	eki	eki	NOUN
ejpam-5755	50	1	=	=	SYM
ejpam-5755	50	2	(	(	PUNCT
ejpam-5755	50	3	vk	vk	PROPN
ejpam-5755	50	4	,	,	PUNCT
ejpam-5755	50	5	vi	vi	NOUN
ejpam-5755	50	6	)	)	PUNCT
ejpam-5755	50	7	,	,	PUNCT
ejpam-5755	50	8	respectively	respectively	ADV
ejpam-5755	50	9	.	.	PUNCT
ejpam-5755	51	1	a	a	DET
ejpam-5755	51	2	graph	graph	NOUN
ejpam-5755	51	3	is	be	AUX
ejpam-5755	51	4	considered	consider	VERB
ejpam-5755	51	5	balanced	balanced	ADJ
ejpam-5755	51	6	if	if	SCONJ
ejpam-5755	51	7	each	each	DET
ejpam-5755	51	8	node	node	NOUN
ejpam-5755	51	9	’s	’s	PART
ejpam-5755	51	10	out	out	ADJ
ejpam-5755	51	11	-	-	PUNCT
ejpam-5755	51	12	degree	degree	NOUN
ejpam-5755	51	13	equals	equal	VERB
ejpam-5755	51	14	its	its	PRON
ejpam-5755	51	15	in	in	NOUN
ejpam-5755	51	16	-	-	PUNCT
ejpam-5755	51	17	degree	degree	NOUN
ejpam-5755	51	18	.	.	PUNCT
ejpam-5755	52	1	a	a	DET
ejpam-5755	52	2	directed	direct	VERB
ejpam-5755	52	3	path	path	NOUN
ejpam-5755	52	4	in	in	ADP
ejpam-5755	52	5	g	g	NOUN
ejpam-5755	52	6	consists	consist	VERB
ejpam-5755	52	7	of	of	ADP
ejpam-5755	52	8	a	a	DET
ejpam-5755	52	9	sequence	sequence	NOUN
ejpam-5755	52	10	of	of	ADP
ejpam-5755	52	11	edges	edge	NOUN
ejpam-5755	52	12	(	(	PUNCT
ejpam-5755	52	13	vi1	vi1	NOUN
ejpam-5755	52	14	,	,	PUNCT
ejpam-5755	52	15	vi2	vi2	NOUN
ejpam-5755	52	16	)	)	PUNCT
ejpam-5755	52	17	,	,	PUNCT
ejpam-5755	52	18	(	(	PUNCT
ejpam-5755	52	19	vi2	vi2	INTJ
ejpam-5755	52	20	,	,	PUNCT
ejpam-5755	52	21	vi3	vi3	PROPN
ejpam-5755	52	22	)	)	PUNCT
ejpam-5755	52	23	,	,	PUNCT
ejpam-5755	52	24	(	(	PUNCT
ejpam-5755	52	25	vi3	vi3	VERB
ejpam-5755	52	26	,	,	PUNCT
ejpam-5755	52	27	vi4	vi4	PROPN
ejpam-5755	52	28	)	)	PUNCT
ejpam-5755	52	29	,	,	PUNCT
ejpam-5755	52	30	...	...	PUNCT
ejpam-5755	52	31	,	,	PUNCT
ejpam-5755	52	32	and	and	CCONJ
ejpam-5755	52	33	so	so	ADV
ejpam-5755	52	34	on	on	ADV
ejpam-5755	52	35	.	.	PUNCT
ejpam-5755	53	1	a	a	DET
ejpam-5755	53	2	digraph	digraph	NOUN
ejpam-5755	53	3	g	g	NOUN
ejpam-5755	53	4	is	be	AUX
ejpam-5755	53	5	termed	term	VERB
ejpam-5755	53	6	strongly	strongly	ADV
ejpam-5755	53	7	connected	connect	VERB
ejpam-5755	53	8	if	if	SCONJ
ejpam-5755	53	9	there	there	PRON
ejpam-5755	53	10	exists	exist	VERB
ejpam-5755	53	11	a	a	DET
ejpam-5755	53	12	directed	direct	VERB
ejpam-5755	53	13	path	path	NOUN
ejpam-5755	53	14	between	between	ADP
ejpam-5755	53	15	any	any	DET
ejpam-5755	53	16	two	two	NUM
ejpam-5755	53	17	nodes	node	NOUN
ejpam-5755	53	18	in	in	ADP
ejpam-5755	53	19	g.	g.	PROPN
ejpam-5755	53	20	a	a	DET
ejpam-5755	53	21	directed	direct	VERB
ejpam-5755	53	22	tree	tree	NOUN
ejpam-5755	53	23	is	be	AUX
ejpam-5755	53	24	a	a	DET
ejpam-5755	53	25	digraph	digraph	NOUN
ejpam-5755	53	26	with	with	ADP
ejpam-5755	53	27	a	a	DET
ejpam-5755	53	28	single	single	ADJ
ejpam-5755	53	29	root	root	NOUN
ejpam-5755	53	30	(	(	PUNCT
ejpam-5755	53	31	no	no	DET
ejpam-5755	53	32	edges	edge	NOUN
ejpam-5755	53	33	pointing	point	VERB
ejpam-5755	53	34	to	to	ADP
ejpam-5755	53	35	this	this	DET
ejpam-5755	53	36	node	node	NOUN
ejpam-5755	53	37	)	)	PUNCT
ejpam-5755	53	38	,	,	PUNCT
ejpam-5755	53	39	where	where	SCONJ
ejpam-5755	53	40	every	every	DET
ejpam-5755	53	41	node	node	NOUN
ejpam-5755	53	42	except	except	SCONJ
ejpam-5755	53	43	the	the	DET
ejpam-5755	53	44	root	root	NOUN
ejpam-5755	53	45	has	have	VERB
ejpam-5755	53	46	exactly	exactly	ADV
ejpam-5755	53	47	one	one	NUM
ejpam-5755	53	48	parent	parent	NOUN
ejpam-5755	53	49	.	.	PUNCT
ejpam-5755	54	1	a	a	DET
ejpam-5755	54	2	spanning	span	VERB
ejpam-5755	54	3	tree	tree	NOUN
ejpam-5755	54	4	of	of	ADP
ejpam-5755	54	5	g	g	PROPN
ejpam-5755	54	6	is	be	AUX
ejpam-5755	54	7	a	a	DET
ejpam-5755	54	8	directed	direct	VERB
ejpam-5755	54	9	tree	tree	NOUN
ejpam-5755	54	10	that	that	PRON
ejpam-5755	54	11	connects	connect	VERB
ejpam-5755	54	12	all	all	DET
ejpam-5755	54	13	nodes	node	NOUN
ejpam-5755	54	14	in	in	ADP
ejpam-5755	54	15	g.	g.	PROPN
ejpam-5755	54	16	additionally	additionally	ADV
ejpam-5755	54	17	,	,	PUNCT
ejpam-5755	54	18	we	we	PRON
ejpam-5755	54	19	denote	denote	VERB
ejpam-5755	54	20	r	r	NOUN
ejpam-5755	54	21	as	as	ADP
ejpam-5755	54	22	the	the	DET
ejpam-5755	54	23	set	set	NOUN
ejpam-5755	54	24	of	of	ADP
ejpam-5755	54	25	real	real	ADJ
ejpam-5755	54	26	numbers	number	NOUN
ejpam-5755	54	27	,	,	PUNCT
ejpam-5755	54	28	n	n	CCONJ
ejpam-5755	54	29	as	as	ADP
ejpam-5755	54	30	the	the	DET
ejpam-5755	54	31	set	set	NOUN
ejpam-5755	54	32	of	of	ADP
ejpam-5755	54	33	positive	positive	ADJ
ejpam-5755	54	34	integers	integer	NOUN
ejpam-5755	54	35	,	,	PUNCT
ejpam-5755	54	36	and	and	CCONJ
ejpam-5755	54	37	rn	rn	PROPN
ejpam-5755	54	38	as	as	ADP
ejpam-5755	54	39	the	the	DET
ejpam-5755	54	40	n	n	ADV
ejpam-5755	54	41	-	-	PUNCT
ejpam-5755	54	42	dimensional	dimensional	ADJ
ejpam-5755	54	43	real	real	ADJ
ejpam-5755	54	44	vector	vector	NOUN
ejpam-5755	54	45	space	space	NOUN
ejpam-5755	54	46	.	.	PUNCT
ejpam-5755	55	1	for	for	ADP
ejpam-5755	55	2	a	a	DET
ejpam-5755	55	3	vector	vector	NOUN
ejpam-5755	55	4	or	or	CCONJ
ejpam-5755	55	5	matrix	matrix	NOUN
ejpam-5755	55	6	b	b	NOUN
ejpam-5755	55	7	,	,	PUNCT
ejpam-5755	55	8	bt	bt	PROPN
ejpam-5755	55	9	represents	represent	VERB
ejpam-5755	55	10	its	its	PRON
ejpam-5755	55	11	transpose	transpose	NOUN
ejpam-5755	55	12	,	,	PUNCT
ejpam-5755	55	13	and	and	CCONJ
ejpam-5755	55	14	∥x∥	∥x∥	NOUN
ejpam-5755	55	15	indicates	indicate	VERB
ejpam-5755	55	16	the	the	DET
ejpam-5755	55	17	euclidean	euclidean	ADJ
ejpam-5755	55	18	norm	norm	NOUN
ejpam-5755	55	19	of	of	ADP
ejpam-5755	55	20	vector	vector	NOUN
ejpam-5755	55	21	x.	x.	NOUN
ejpam-5755	56	1	a	a	DET
ejpam-5755	56	2	vector	vector	NOUN
ejpam-5755	56	3	is	be	AUX
ejpam-5755	56	4	nonnegative	nonnegative	ADJ
ejpam-5755	56	5	if	if	SCONJ
ejpam-5755	56	6	all	all	DET
ejpam-5755	56	7	its	its	PRON
ejpam-5755	56	8	components	component	NOUN
ejpam-5755	56	9	are	be	AUX
ejpam-5755	56	10	nonnegative	nonnegative	ADJ
ejpam-5755	56	11	,	,	PUNCT
ejpam-5755	56	12	while	while	SCONJ
ejpam-5755	56	13	the	the	DET
ejpam-5755	56	14	column	column	NOUN
ejpam-5755	56	15	vector	vector	NOUN
ejpam-5755	56	16	with	with	ADP
ejpam-5755	56	17	all	all	DET
ejpam-5755	56	18	entries	entry	NOUN
ejpam-5755	56	19	equal	equal	ADJ
ejpam-5755	56	20	to	to	ADP
ejpam-5755	56	21	one	one	NUM
ejpam-5755	56	22	or	or	CCONJ
ejpam-5755	56	23	zero	zero	NUM
ejpam-5755	56	24	is	be	AUX
ejpam-5755	56	25	denoted	denote	VERB
ejpam-5755	56	26	by	by	ADP
ejpam-5755	56	27	1n	1n	PROPN
ejpam-5755	56	28	and	and	CCONJ
ejpam-5755	56	29	0n	0n	NUM
ejpam-5755	56	30	,	,	PUNCT
ejpam-5755	56	31	respectively	respectively	ADV
ejpam-5755	56	32	.	.	PUNCT
ejpam-5755	57	1	in	in	ADP
ejpam-5755	57	2	is	be	AUX
ejpam-5755	57	3	the	the	DET
ejpam-5755	57	4	n	n	ADV
ejpam-5755	57	5	-	-	PUNCT
ejpam-5755	57	6	dimensional	dimensional	ADJ
ejpam-5755	57	7	identity	identity	NOUN
ejpam-5755	57	8	matrix	matrix	NOUN
ejpam-5755	57	9	,	,	PUNCT
ejpam-5755	57	10	and	and	CCONJ
ejpam-5755	57	11	a	a	DET
ejpam-5755	57	12	diagonal	diagonal	ADJ
ejpam-5755	57	13	matrix	matrix	NOUN
ejpam-5755	57	14	with	with	ADP
ejpam-5755	57	15	diagonal	diagonal	ADJ
ejpam-5755	57	16	elements	element	NOUN
ejpam-5755	57	17	a1	a1	NOUN
ejpam-5755	57	18	,	,	PUNCT
ejpam-5755	57	19	a2	a2	PROPN
ejpam-5755	57	20	,	,	PUNCT
ejpam-5755	57	21	...	...	PUNCT
ejpam-5755	57	22	,	,	PUNCT
ejpam-5755	57	23	an	an	PRON
ejpam-5755	57	24	is	be	AUX
ejpam-5755	57	25	represented	represent	VERB
ejpam-5755	57	26	as	as	ADP
ejpam-5755	57	27	diaga1	diaga1	NOUN
ejpam-5755	57	28	,	,	PUNCT
ejpam-5755	57	29	a2	a2	PROPN
ejpam-5755	57	30	,	,	PUNCT
ejpam-5755	57	31	...	...	PUNCT
ejpam-5755	57	32	,	,	PUNCT
ejpam-5755	57	33	an	an	X
ejpam-5755	57	34	.	.	PUNCT
ejpam-5755	58	1	furthermore	furthermore	ADV
ejpam-5755	58	2	,	,	PUNCT
ejpam-5755	58	3	[	[	X
ejpam-5755	58	4	aij	aij	PROPN
ejpam-5755	58	5	]	]	PUNCT
ejpam-5755	58	6	nn	nn	X
ejpam-5755	58	7	is	be	AUX
ejpam-5755	58	8	an	an	DET
ejpam-5755	58	9	n	n	NOUN
ejpam-5755	58	10	by	by	ADP
ejpam-5755	58	11	n	n	NOUN
ejpam-5755	58	12	matrix	matrix	NOUN
ejpam-5755	58	13	with	with	ADP
ejpam-5755	58	14	aij	aij	PROPN
ejpam-5755	58	15	as	as	ADP
ejpam-5755	58	16	its	its	PRON
ejpam-5755	58	17	(	(	PUNCT
ejpam-5755	58	18	i	i	NOUN
ejpam-5755	58	19	,	,	PUNCT
ejpam-5755	58	20	j)th	j)th	PROPN
ejpam-5755	58	21	entry	entry	NOUN
ejpam-5755	58	22	.	.	PUNCT
ejpam-5755	59	1	a	a	DET
ejpam-5755	59	2	matrix	matrix	NOUN
ejpam-5755	59	3	b	b	NOUN
ejpam-5755	59	4	=	=	PUNCT
ejpam-5755	60	1	[	[	X
ejpam-5755	60	2	bij	bij	NOUN
ejpam-5755	60	3	]	]	X
ejpam-5755	60	4	nn	nn	X
ejpam-5755	60	5	is	be	AUX
ejpam-5755	60	6	classified	classify	VERB
ejpam-5755	60	7	as	as	ADP
ejpam-5755	60	8	nonnegative	nonnegative	ADJ
ejpam-5755	60	9	,	,	PUNCT
ejpam-5755	60	10	denoted	denote	VERB
ejpam-5755	60	11	by	by	ADP
ejpam-5755	60	12	b	b	PROPN
ejpam-5755	60	13	≥	≥	NUM
ejpam-5755	60	14	0	0	NUM
ejpam-5755	60	15	,	,	PUNCT
ejpam-5755	60	16	if	if	SCONJ
ejpam-5755	60	17	all	all	DET
ejpam-5755	60	18	its	its	PRON
ejpam-5755	60	19	entries	entry	NOUN
ejpam-5755	60	20	are	be	AUX
ejpam-5755	60	21	nonnegative	nonnegative	ADJ
ejpam-5755	60	22	.	.	PUNCT
ejpam-5755	61	1	for	for	ADP
ejpam-5755	61	2	nonnegative	nonnegative	ADJ
ejpam-5755	61	3	matrices	matrix	NOUN
ejpam-5755	61	4	,	,	PUNCT
ejpam-5755	61	5	we	we	PRON
ejpam-5755	61	6	define	define	VERB
ejpam-5755	61	7	an	an	DET
ejpam-5755	61	8	order	order	NOUN
ejpam-5755	61	9	such	such	ADJ
ejpam-5755	61	10	that	that	SCONJ
ejpam-5755	61	11	if	if	SCONJ
ejpam-5755	61	12	a	a	PRON
ejpam-5755	61	13	and	and	CCONJ
ejpam-5755	61	14	b	b	NOUN
ejpam-5755	61	15	are	be	AUX
ejpam-5755	61	16	nonnegative	nonnegative	ADJ
ejpam-5755	61	17	,	,	PUNCT
ejpam-5755	61	18	then	then	ADV
ejpam-5755	61	19	a	a	DET
ejpam-5755	61	20	≥	≥	NOUN
ejpam-5755	61	21	b	b	PROPN
ejpam-5755	61	22	implies	imply	VERB
ejpam-5755	61	23	a	a	DET
ejpam-5755	61	24	−	−	PROPN
ejpam-5755	61	25	b	b	NOUN
ejpam-5755	61	26	is	be	AUX
ejpam-5755	61	27	also	also	ADV
ejpam-5755	61	28	a	a	DET
ejpam-5755	61	29	nonnegative	nonnegative	ADJ
ejpam-5755	61	30	matrix	matrix	NOUN
ejpam-5755	61	31	.	.	PUNCT
ejpam-5755	62	1	a	a	PRON
ejpam-5755	62	2	is	be	AUX
ejpam-5755	62	3	termed	term	VERB
ejpam-5755	62	4	a	a	DET
ejpam-5755	62	5	stochastic	stochastic	ADJ
ejpam-5755	62	6	matrix	matrix	NOUN
ejpam-5755	62	7	if	if	SCONJ
ejpam-5755	62	8	it	it	PRON
ejpam-5755	62	9	is	be	AUX
ejpam-5755	62	10	nonnegative	nonnegative	ADJ
ejpam-5755	62	11	and	and	CCONJ
ejpam-5755	62	12	the	the	DET
ejpam-5755	62	13	sum	sum	NOUN
ejpam-5755	62	14	of	of	ADP
ejpam-5755	62	15	each	each	DET
ejpam-5755	62	16	row	row	NOUN
ejpam-5755	62	17	equals	equal	VERB
ejpam-5755	62	18	1	1	NUM
ejpam-5755	62	19	.	.	PUNCT
ejpam-5755	63	1	a	a	DET
ejpam-5755	63	2	stochastic	stochastic	ADJ
ejpam-5755	63	3	matrix	matrix	NOUN
ejpam-5755	63	4	a	a	PRON
ejpam-5755	63	5	is	be	AUX
ejpam-5755	63	6	called	call	VERB
ejpam-5755	63	7	indecomposable	indecomposable	ADJ
ejpam-5755	63	8	and	and	CCONJ
ejpam-5755	63	9	aperiodic	aperiodic	ADJ
ejpam-5755	63	10	(	(	PUNCT
ejpam-5755	63	11	sia	sia	PROPN
ejpam-5755	63	12	)	)	PUNCT
ejpam-5755	63	13	if	if	SCONJ
ejpam-5755	63	14	there	there	PRON
ejpam-5755	63	15	exists	exist	VERB
ejpam-5755	63	16	a	a	DET
ejpam-5755	63	17	column	column	NOUN
ejpam-5755	63	18	vector	vector	NOUN
ejpam-5755	63	19	v	v	ADP
ejpam-5755	63	20	such	such	ADJ
ejpam-5755	64	1	that	that	DET
ejpam-5755	64	2	limn→∞an	limn→∞an	ADJ
ejpam-5755	64	3	=	=	SYM
ejpam-5755	64	4	1nv	1nv	ADJ
ejpam-5755	64	5	t	t	NOUN
ejpam-5755	64	6	,	,	PUNCT
ejpam-5755	64	7	where	where	SCONJ
ejpam-5755	64	8	1n	1n	NOUN
ejpam-5755	64	9	=	=	SYM
ejpam-5755	64	10	(	(	PUNCT
ejpam-5755	64	11	1	1	NUM
ejpam-5755	64	12	,	,	PUNCT
ejpam-5755	64	13	1	1	NUM
ejpam-5755	64	14	,	,	PUNCT
ejpam-5755	64	15	...	...	PUNCT
ejpam-5755	64	16	,	,	PUNCT
ejpam-5755	64	17	1)t	1)t	PROPN
ejpam-5755	64	18	is	be	AUX
ejpam-5755	64	19	a	a	DET
ejpam-5755	64	20	n×	n×	PROPN
ejpam-5755	64	21	1	1	NUM
ejpam-5755	64	22	vector	vector	NOUN
ejpam-5755	64	23	.	.	PUNCT
ejpam-5755	65	1	additionally	additionally	ADV
ejpam-5755	65	2	,	,	PUNCT
ejpam-5755	65	3	we	we	PRON
ejpam-5755	65	4	provide	provide	VERB
ejpam-5755	65	5	some	some	DET
ejpam-5755	65	6	useful	useful	ADJ
ejpam-5755	65	7	definitions	definition	NOUN
ejpam-5755	65	8	,	,	PUNCT
ejpam-5755	65	9	lemmas	lemmas	ADJ
ejpam-5755	65	10	,	,	PUNCT
ejpam-5755	65	11	and	and	CCONJ
ejpam-5755	65	12	properties	property	NOUN
ejpam-5755	65	13	.	.	PUNCT
ejpam-5755	66	1	definition	definition	NOUN
ejpam-5755	66	2	1	1	NUM
ejpam-5755	66	3	.	.	PUNCT
ejpam-5755	67	1	[	[	X
ejpam-5755	67	2	3	3	X
ejpam-5755	67	3	]	]	PUNCT
ejpam-5755	67	4	for	for	ADP
ejpam-5755	67	5	an	an	DET
ejpam-5755	67	6	undirected	undirected	ADJ
ejpam-5755	67	7	graph	graph	NOUN
ejpam-5755	67	8	g	g	NOUN
ejpam-5755	67	9	with	with	ADP
ejpam-5755	67	10	the	the	DET
ejpam-5755	67	11	laplacian	laplacian	ADJ
ejpam-5755	67	12	matrix	matrix	NOUN
ejpam-5755	67	13	l	l	NOUN
ejpam-5755	67	14	the	the	DET
ejpam-5755	67	15	algebraic	algebraic	ADJ
ejpam-5755	67	16	connectivity	connectivity	NOUN
ejpam-5755	67	17	is	be	AUX
ejpam-5755	67	18	defined	define	VERB
ejpam-5755	67	19	as	as	ADP
ejpam-5755	67	20	λ2(l	λ2(l	NOUN
ejpam-5755	67	21	)	)	PUNCT
ejpam-5755	67	22	,	,	PUNCT
ejpam-5755	67	23	the	the	DET
ejpam-5755	67	24	second	second	ADJ
ejpam-5755	67	25	smallest	small	ADJ
ejpam-5755	67	26	eigenvalue	eigenvalue	NOUN
ejpam-5755	67	27	of	of	ADP
ejpam-5755	67	28	l	l	NOUN
ejpam-5755	67	29	:	:	PUNCT
ejpam-5755	68	1	λ2(l	λ2(l	X
ejpam-5755	68	2	)	)	PUNCT
ejpam-5755	68	3	=	=	SYM
ejpam-5755	68	4	min	min	NOUN
ejpam-5755	68	5	x	x	INTJ
ejpam-5755	68	6	̸=0	̸=0	ADV
ejpam-5755	68	7	,	,	PUNCT
ejpam-5755	68	8	1	1	NUM
ejpam-5755	68	9	t	t	NOUN
ejpam-5755	68	10	x=0	x=0	PROPN
ejpam-5755	68	11	xtlx	xtlx	PROPN
ejpam-5755	68	12	xtx	xtx	PROPN
ejpam-5755	68	13	.	.	PUNCT
ejpam-5755	69	1	lemma	lemma	PROPN
ejpam-5755	69	2	1	1	NUM
ejpam-5755	69	3	.	.	PUNCT
ejpam-5755	70	1	[	[	X
ejpam-5755	70	2	10	10	NUM
ejpam-5755	70	3	]	]	PUNCT
ejpam-5755	70	4	let	let	VERB
ejpam-5755	70	5	g	g	PRON
ejpam-5755	70	6	be	be	AUX
ejpam-5755	70	7	a	a	DET
ejpam-5755	70	8	digraph	digraph	NOUN
ejpam-5755	70	9	with	with	ADP
ejpam-5755	70	10	adjacency	adjacency	PROPN
ejpam-5755	70	11	matrix	matrix	NOUN
ejpam-5755	70	12	a	a	DET
ejpam-5755	70	13	and	and	CCONJ
ejpam-5755	70	14	laplacian	laplacian	PROPN
ejpam-5755	70	15	l.	l.	PROPN
ejpam-5755	70	16	then	then	ADV
ejpam-5755	70	17	l̂	l̂	PROPN
ejpam-5755	70	18	=	=	SYM
ejpam-5755	70	19	sym(l	sym(l	PROPN
ejpam-5755	70	20	)	)	PUNCT
ejpam-5755	70	21	=	=	PUNCT
ejpam-5755	70	22	(	(	PUNCT
ejpam-5755	70	23	l+	l+	X
ejpam-5755	70	24	lt	lt	X
ejpam-5755	70	25	)	)	PUNCT
ejpam-5755	70	26	/2	/2	PROPN
ejpam-5755	70	27	is	be	AUX
ejpam-5755	70	28	a	a	DET
ejpam-5755	70	29	valid	valid	ADJ
ejpam-5755	70	30	laplacian	laplacian	ADJ
ejpam-5755	70	31	matrix	matrix	NOUN
ejpam-5755	70	32	for	for	ADP
ejpam-5755	70	33	ĝ	ĝ	NOUN
ejpam-5755	70	34	if	if	SCONJ
ejpam-5755	70	35	g	g	PROPN
ejpam-5755	70	36	is	be	AUX
ejpam-5755	70	37	balanced	balanced	ADJ
ejpam-5755	70	38	.	.	PUNCT
ejpam-5755	71	1	lemma	lemma	PROPN
ejpam-5755	71	2	2	2	NUM
ejpam-5755	71	3	.	.	PUNCT
ejpam-5755	72	1	[	[	X
ejpam-5755	72	2	13	13	NUM
ejpam-5755	72	3	]	]	PUNCT
ejpam-5755	72	4	a	a	DET
ejpam-5755	72	5	stochastic	stochastic	ADJ
ejpam-5755	72	6	matrix	matrix	NOUN
ejpam-5755	72	7	has	have	VERB
ejpam-5755	72	8	algebraic	algebraic	ADJ
ejpam-5755	72	9	multiplicity	multiplicity	NOUN
ejpam-5755	72	10	equal	equal	ADJ
ejpam-5755	72	11	to	to	ADP
ejpam-5755	72	12	one	one	NUM
ejpam-5755	72	13	for	for	ADP
ejpam-5755	72	14	eigenvalue	eigenvalue	PROPN
ejpam-5755	72	15	λ	λ	X
ejpam-5755	72	16	=	=	SYM
ejpam-5755	72	17	1	1	NUM
ejpam-5755	72	18	if	if	SCONJ
ejpam-5755	72	19	and	and	CCONJ
ejpam-5755	72	20	only	only	ADV
ejpam-5755	72	21	if	if	SCONJ
ejpam-5755	72	22	the	the	DET
ejpam-5755	72	23	graph	graph	NOUN
ejpam-5755	72	24	associated	associate	VERB
ejpam-5755	72	25	with	with	ADP
ejpam-5755	72	26	matrix	matrix	NOUN
ejpam-5755	72	27	has	have	VERB
ejpam-5755	72	28	a	a	DET
ejpam-5755	72	29	spanning	span	VERB
ejpam-5755	72	30	tree	tree	NOUN
ejpam-5755	72	31	.	.	PUNCT
ejpam-5755	73	1	furthermore	furthermore	ADV
ejpam-5755	73	2	,	,	PUNCT
ejpam-5755	73	3	a	a	DET
ejpam-5755	73	4	stochastic	stochastic	ADJ
ejpam-5755	73	5	matrix	matrix	NOUN
ejpam-5755	73	6	with	with	ADP
ejpam-5755	73	7	positive	positive	ADJ
ejpam-5755	73	8	diagonal	diagonal	ADJ
ejpam-5755	73	9	elements	element	NOUN
ejpam-5755	73	10	has	have	VERB
ejpam-5755	73	11	the	the	DET
ejpam-5755	73	12	property	property	NOUN
ejpam-5755	73	13	that	that	PRON
ejpam-5755	73	14	|λ|	|λ|	VERB
ejpam-5755	73	15	<	<	X
ejpam-5755	73	16	1	1	NUM
ejpam-5755	73	17	for	for	ADP
ejpam-5755	73	18	every	every	DET
ejpam-5755	73	19	eigenvalue	eigenvalue	NOUN
ejpam-5755	73	20	not	not	PART
ejpam-5755	73	21	equal	equal	ADJ
ejpam-5755	73	22	to	to	ADP
ejpam-5755	73	23	one	one	NUM
ejpam-5755	73	24	.	.	PUNCT
ejpam-5755	74	1	lemma	lemma	PROPN
ejpam-5755	74	2	3	3	X
ejpam-5755	74	3	.	.	PUNCT
ejpam-5755	75	1	[	[	X
ejpam-5755	75	2	13	13	NUM
ejpam-5755	75	3	]	]	PUNCT
ejpam-5755	75	4	let	let	VERB
ejpam-5755	75	5	a	a	PRON
ejpam-5755	75	6	=	=	PUNCT
ejpam-5755	76	1	[	[	X
ejpam-5755	76	2	aij	aij	X
ejpam-5755	76	3	]	]	PUNCT
ejpam-5755	76	4	n×n	n×n	PROPN
ejpam-5755	76	5	be	be	AUX
ejpam-5755	76	6	a	a	DET
ejpam-5755	76	7	stochastic	stochastic	ADJ
ejpam-5755	76	8	matrix	matrix	NOUN
ejpam-5755	76	9	.	.	PUNCT
ejpam-5755	77	1	if	if	SCONJ
ejpam-5755	77	2	a	a	PRON
ejpam-5755	77	3	has	have	VERB
ejpam-5755	77	4	an	an	DET
ejpam-5755	77	5	eigenvalue	eigenvalue	ADJ
ejpam-5755	77	6	λ	λ	NOUN
ejpam-5755	77	7	=	=	NOUN
ejpam-5755	77	8	1	1	NUM
ejpam-5755	77	9	with	with	ADP
ejpam-5755	77	10	algebraic	algebraic	ADJ
ejpam-5755	77	11	multiplicity	multiplicity	NOUN
ejpam-5755	77	12	equal	equal	ADJ
ejpam-5755	77	13	to	to	ADP
ejpam-5755	77	14	one	one	NUM
ejpam-5755	77	15	,	,	PUNCT
ejpam-5755	77	16	and	and	CCONJ
ejpam-5755	77	17	all	all	DET
ejpam-5755	77	18	the	the	DET
ejpam-5755	77	19	other	other	ADJ
ejpam-5755	77	20	eigenvalues	eigenvalue	VERB
ejpam-5755	77	21	satisfy	satisfy	PROPN
ejpam-5755	77	22	|λ|	|λ|	PROPN
ejpam-5755	77	23	<	<	X
ejpam-5755	77	24	1	1	NUM
ejpam-5755	77	25	,	,	PUNCT
ejpam-5755	77	26	then	then	ADV
ejpam-5755	77	27	a	a	PRON
ejpam-5755	77	28	is	be	AUX
ejpam-5755	77	29	sia	sia	PROPN
ejpam-5755	77	30	,	,	PUNCT
ejpam-5755	77	31	that	that	ADV
ejpam-5755	77	32	is	is	ADV
ejpam-5755	77	33	,	,	PUNCT
ejpam-5755	77	34	limk→∞ak	limk→∞ak	PROPN
ejpam-5755	77	35	=	=	PUNCT
ejpam-5755	77	36	1ny	1ny	ADJ
ejpam-5755	77	37	t	t	NOUN
ejpam-5755	77	38	,	,	PUNCT
ejpam-5755	77	39	where	where	SCONJ
ejpam-5755	77	40	y	y	PROPN
ejpam-5755	77	41	is	be	AUX
ejpam-5755	77	42	nonnegative	nonnegative	ADJ
ejpam-5755	77	43	and	and	CCONJ
ejpam-5755	77	44	satisfies	satisfie	NOUN
ejpam-5755	77	45	at	at	ADP
ejpam-5755	77	46	y	y	PROPN
ejpam-5755	77	47	=	=	SYM
ejpam-5755	77	48	y	y	PROPN
ejpam-5755	77	49	,	,	PUNCT
ejpam-5755	77	50	1tny	1tny	NUM
ejpam-5755	77	51	=	=	SYM
ejpam-5755	77	52	1	1	NUM
ejpam-5755	77	53	.	.	X
ejpam-5755	77	54	2.2	2.2	NUM
ejpam-5755	77	55	.	.	PUNCT
ejpam-5755	78	1	problem	problem	NOUN
ejpam-5755	78	2	formulation	formulation	NOUN
ejpam-5755	78	3	consider	consider	VERB
ejpam-5755	78	4	an	an	DET
ejpam-5755	78	5	undirected	undirected	ADJ
ejpam-5755	78	6	network	network	NOUN
ejpam-5755	78	7	g	g	NOUN
ejpam-5755	78	8	=	=	SYM
ejpam-5755	78	9	(	(	PUNCT
ejpam-5755	78	10	v	v	NOUN
ejpam-5755	78	11	,	,	PUNCT
ejpam-5755	78	12	e	e	NOUN
ejpam-5755	78	13	)	)	PUNCT
ejpam-5755	78	14	,	,	PUNCT
ejpam-5755	78	15	with	with	ADP
ejpam-5755	78	16	a	a	DET
ejpam-5755	78	17	set	set	NOUN
ejpam-5755	78	18	of	of	ADP
ejpam-5755	78	19	n	n	PRON
ejpam-5755	78	20	nodes	node	NOUN
ejpam-5755	78	21	and	and	CCONJ
ejpam-5755	78	22	m	m	PRON
ejpam-5755	78	23	edges	edge	NOUN
ejpam-5755	78	24	,	,	PUNCT
ejpam-5755	78	25	where	where	SCONJ
ejpam-5755	78	26	e	e	NOUN
ejpam-5755	78	27	=	=	PRON
ejpam-5755	78	28	{	{	PUNCT
ejpam-5755	78	29	(	(	PUNCT
ejpam-5755	78	30	i	i	PROPN
ejpam-5755	78	31	,	,	PUNCT
ejpam-5755	78	32	j	j	PROPN
ejpam-5755	78	33	)	)	PUNCT
ejpam-5755	78	34	:	:	PUNCT
ejpam-5755	78	35	if	if	SCONJ
ejpam-5755	78	36	there	there	PRON
ejpam-5755	78	37	is	be	VERB
ejpam-5755	78	38	an	an	DET
ejpam-5755	78	39	edge	edge	NOUN
ejpam-5755	78	40	between	between	ADP
ejpam-5755	78	41	node	node	NOUN
ejpam-5755	78	42	i	i	PROPN
ejpam-5755	78	43	and	and	CCONJ
ejpam-5755	78	44	node	node	VERB
ejpam-5755	78	45	j	j	PROPN
ejpam-5755	78	46	}	}	PUNCT
ejpam-5755	78	47	and	and	CCONJ
ejpam-5755	78	48	v	v	NOUN
ejpam-5755	78	49	=	=	SYM
ejpam-5755	78	50	{	{	PUNCT
ejpam-5755	78	51	1	1	NUM
ejpam-5755	78	52	,	,	PUNCT
ejpam-5755	78	53	2	2	NUM
ejpam-5755	78	54	,	,	PUNCT
ejpam-5755	78	55	...	...	PUNCT
ejpam-5755	78	56	,	,	PUNCT
ejpam-5755	78	57	n	n	CCONJ
ejpam-5755	78	58	}	}	PUNCT
ejpam-5755	78	59	.	.	PUNCT
ejpam-5755	79	1	s.	s.	PROPN
ejpam-5755	79	2	donganont	donganont	PROPN
ejpam-5755	79	3	,	,	PUNCT
ejpam-5755	79	4	u.	u.	NOUN
ejpam-5755	79	5	witthayarat	witthayarat	NOUN
ejpam-5755	79	6	,	,	PUNCT
ejpam-5755	79	7	m.	m.	NOUN
ejpam-5755	79	8	donganont	donganont	PROPN
ejpam-5755	79	9	/	/	SYM
ejpam-5755	79	10	eur	eur	PROPN
ejpam-5755	79	11	.	.	PUNCT
ejpam-5755	80	1	j.	j.	PROPN
ejpam-5755	80	2	pure	pure	PROPN
ejpam-5755	80	3	appl	appl	PROPN
ejpam-5755	80	4	.	.	PROPN
ejpam-5755	80	5	math	math	PROPN
ejpam-5755	80	6	,	,	PUNCT
ejpam-5755	80	7	18	18	NUM
ejpam-5755	80	8	(	(	PUNCT
ejpam-5755	80	9	1	1	NUM
ejpam-5755	80	10	)	)	PUNCT
ejpam-5755	80	11	(	(	PUNCT
ejpam-5755	80	12	2025	2025	NUM
ejpam-5755	80	13	)	)	PUNCT
ejpam-5755	80	14	,	,	PUNCT
ejpam-5755	80	15	5755	5755	NUM
ejpam-5755	80	16	4	4	NUM
ejpam-5755	80	17	of	of	ADP
ejpam-5755	80	18	17	17	NUM
ejpam-5755	80	19	the	the	DET
ejpam-5755	80	20	topology	topology	NOUN
ejpam-5755	80	21	of	of	ADP
ejpam-5755	80	22	the	the	DET
ejpam-5755	80	23	network	network	NOUN
ejpam-5755	80	24	is	be	AUX
ejpam-5755	80	25	described	describe	VERB
ejpam-5755	80	26	by	by	ADP
ejpam-5755	80	27	the	the	DET
ejpam-5755	80	28	adjacency	adjacency	NOUN
ejpam-5755	80	29	matrix	matrix	NOUN
ejpam-5755	80	30	a	a	PRON
ejpam-5755	81	1	=	=	X
ejpam-5755	82	1	[	[	X
ejpam-5755	82	2	aij	aij	X
ejpam-5755	82	3	]	]	X
ejpam-5755	82	4	n×n	n×n	PROPN
ejpam-5755	82	5	,	,	PUNCT
ejpam-5755	82	6	where	where	SCONJ
ejpam-5755	82	7	aji	aji	NOUN
ejpam-5755	82	8	=	=	SYM
ejpam-5755	82	9	aij	aij	PROPN
ejpam-5755	82	10	=	=	SYM
ejpam-5755	82	11	{	{	PUNCT
ejpam-5755	82	12	1	1	NUM
ejpam-5755	82	13	,	,	PUNCT
ejpam-5755	82	14	if	if	SCONJ
ejpam-5755	82	15	(	(	PUNCT
ejpam-5755	82	16	i	i	NOUN
ejpam-5755	82	17	,	,	PUNCT
ejpam-5755	82	18	j	j	PROPN
ejpam-5755	82	19	)	)	PUNCT
ejpam-5755	82	20	∈	∈	PROPN
ejpam-5755	82	21	e	e	X
ejpam-5755	82	22	;	;	PUNCT
ejpam-5755	82	23	0	0	NUM
ejpam-5755	82	24	,	,	PUNCT
ejpam-5755	82	25	otherwise	otherwise	ADV
ejpam-5755	82	26	.	.	PUNCT
ejpam-5755	83	1	different	different	ADJ
ejpam-5755	83	2	from	from	ADP
ejpam-5755	83	3	the	the	DET
ejpam-5755	83	4	undirected	undirected	ADJ
ejpam-5755	83	5	network	network	NOUN
ejpam-5755	83	6	,	,	PUNCT
ejpam-5755	83	7	the	the	DET
ejpam-5755	83	8	directed	direct	VERB
ejpam-5755	83	9	network	network	NOUN
ejpam-5755	83	10	can	can	AUX
ejpam-5755	83	11	be	be	AUX
ejpam-5755	83	12	denoted	denote	VERB
ejpam-5755	83	13	by	by	ADP
ejpam-5755	83	14	g	g	PROPN
ejpam-5755	83	15	=	=	SYM
ejpam-5755	83	16	(	(	PUNCT
ejpam-5755	83	17	v	v	NOUN
ejpam-5755	83	18	,	,	PUNCT
ejpam-5755	83	19	e	e	NOUN
ejpam-5755	83	20	)	)	PUNCT
ejpam-5755	83	21	,	,	PUNCT
ejpam-5755	83	22	where	where	SCONJ
ejpam-5755	83	23	e	e	NOUN
ejpam-5755	83	24	=	=	PRON
ejpam-5755	83	25	{	{	PUNCT
ejpam-5755	83	26	(	(	PUNCT
ejpam-5755	83	27	i	i	PROPN
ejpam-5755	83	28	,	,	PUNCT
ejpam-5755	83	29	j	j	PROPN
ejpam-5755	83	30	)	)	PUNCT
ejpam-5755	83	31	;	;	PUNCT
ejpam-5755	83	32	if	if	SCONJ
ejpam-5755	83	33	node	node	NOUN
ejpam-5755	83	34	i	i	PRON
ejpam-5755	83	35	can	can	AUX
ejpam-5755	83	36	receive	receive	VERB
ejpam-5755	83	37	information	information	NOUN
ejpam-5755	83	38	from	from	ADP
ejpam-5755	83	39	node	node	PROPN
ejpam-5755	83	40	j	j	PROPN
ejpam-5755	83	41	}	}	PUNCT
ejpam-5755	83	42	.	.	PUNCT
ejpam-5755	84	1	the	the	DET
ejpam-5755	84	2	topology	topology	NOUN
ejpam-5755	84	3	of	of	ADP
ejpam-5755	84	4	the	the	DET
ejpam-5755	84	5	network	network	NOUN
ejpam-5755	84	6	is	be	AUX
ejpam-5755	84	7	described	describe	VERB
ejpam-5755	84	8	by	by	ADP
ejpam-5755	84	9	the	the	DET
ejpam-5755	84	10	adjacency	adjacency	NOUN
ejpam-5755	84	11	matrix	matrix	NOUN
ejpam-5755	84	12	a	a	PRON
ejpam-5755	85	1	=	=	X
ejpam-5755	86	1	[	[	X
ejpam-5755	86	2	aij	aij	X
ejpam-5755	86	3	]	]	X
ejpam-5755	86	4	n×n	n×n	PROPN
ejpam-5755	86	5	,	,	PUNCT
ejpam-5755	86	6	where	where	SCONJ
ejpam-5755	86	7	aij	aij	PROPN
ejpam-5755	86	8	=	=	SYM
ejpam-5755	86	9	{	{	PUNCT
ejpam-5755	86	10	1	1	NUM
ejpam-5755	86	11	,	,	PUNCT
ejpam-5755	86	12	if	if	SCONJ
ejpam-5755	86	13	(	(	PUNCT
ejpam-5755	86	14	i	i	NOUN
ejpam-5755	86	15	,	,	PUNCT
ejpam-5755	86	16	j	j	PROPN
ejpam-5755	86	17	)	)	PUNCT
ejpam-5755	86	18	∈	∈	PROPN
ejpam-5755	86	19	e	e	X
ejpam-5755	86	20	;	;	PUNCT
ejpam-5755	86	21	0	0	NUM
ejpam-5755	86	22	,	,	PUNCT
ejpam-5755	86	23	otherwise	otherwise	ADV
ejpam-5755	86	24	.	.	PUNCT
ejpam-5755	87	1	for	for	ADP
ejpam-5755	87	2	any	any	DET
ejpam-5755	87	3	node	node	PROPN
ejpam-5755	87	4	i	i	PRON
ejpam-5755	87	5	,	,	PUNCT
ejpam-5755	87	6	its	its	PRON
ejpam-5755	87	7	inbound	inbound	ADJ
ejpam-5755	87	8	edge	edge	NOUN
ejpam-5755	87	9	(	(	PUNCT
ejpam-5755	87	10	i	i	PRON
ejpam-5755	87	11	,	,	PUNCT
ejpam-5755	87	12	k	k	NOUN
ejpam-5755	87	13	)	)	PUNCT
ejpam-5755	87	14	is	be	AUX
ejpam-5755	87	15	adjacent	adjacent	ADJ
ejpam-5755	87	16	to	to	ADP
ejpam-5755	87	17	its	its	PRON
ejpam-5755	87	18	outbound	outbound	ADJ
ejpam-5755	87	19	edge	edge	NOUN
ejpam-5755	87	20	(	(	PUNCT
ejpam-5755	87	21	j	j	NOUN
ejpam-5755	87	22	,	,	PUNCT
ejpam-5755	87	23	i	i	PROPN
ejpam-5755	87	24	)	)	PUNCT
ejpam-5755	87	25	while	while	SCONJ
ejpam-5755	87	26	its	its	PRON
ejpam-5755	87	27	outbound	outbound	ADJ
ejpam-5755	87	28	edge	edge	NOUN
ejpam-5755	87	29	(	(	PUNCT
ejpam-5755	87	30	j	j	NOUN
ejpam-5755	87	31	,	,	PUNCT
ejpam-5755	87	32	i	i	PROPN
ejpam-5755	87	33	)	)	PUNCT
ejpam-5755	87	34	is	be	AUX
ejpam-5755	87	35	adjacent	adjacent	ADJ
ejpam-5755	87	36	from	from	ADP
ejpam-5755	87	37	its	its	PRON
ejpam-5755	87	38	inbound	inbound	ADJ
ejpam-5755	87	39	edge	edge	NOUN
ejpam-5755	87	40	(	(	PUNCT
ejpam-5755	87	41	i	i	NOUN
ejpam-5755	87	42	,	,	PUNCT
ejpam-5755	87	43	k	k	PROPN
ejpam-5755	87	44	)	)	PUNCT
ejpam-5755	87	45	.	.	PUNCT
ejpam-5755	88	1	for	for	ADP
ejpam-5755	88	2	better	well	ADJ
ejpam-5755	88	3	description	description	NOUN
ejpam-5755	88	4	and	and	CCONJ
ejpam-5755	88	5	understanding	understanding	NOUN
ejpam-5755	88	6	,	,	PUNCT
ejpam-5755	88	7	we	we	PRON
ejpam-5755	88	8	say	say	VERB
ejpam-5755	88	9	that	that	SCONJ
ejpam-5755	88	10	the	the	DET
ejpam-5755	88	11	inbound	inbound	ADJ
ejpam-5755	88	12	edge	edge	NOUN
ejpam-5755	88	13	(	(	PUNCT
ejpam-5755	88	14	i	i	PRON
ejpam-5755	88	15	,	,	PUNCT
ejpam-5755	88	16	k	k	PROPN
ejpam-5755	88	17	)	)	PUNCT
ejpam-5755	88	18	is	be	AUX
ejpam-5755	88	19	the	the	DET
ejpam-5755	88	20	valid	valid	ADJ
ejpam-5755	88	21	neighbor	neighbor	NOUN
ejpam-5755	88	22	of	of	ADP
ejpam-5755	88	23	the	the	DET
ejpam-5755	88	24	outbound	outbound	ADJ
ejpam-5755	88	25	edge	edge	NOUN
ejpam-5755	88	26	(	(	PUNCT
ejpam-5755	88	27	j	j	NOUN
ejpam-5755	88	28	,	,	PUNCT
ejpam-5755	88	29	i	i	PROPN
ejpam-5755	88	30	)	)	PUNCT
ejpam-5755	88	31	.	.	PUNCT
ejpam-5755	89	1	let	let	VERB
ejpam-5755	89	2	xij(t	xij(t	PRON
ejpam-5755	89	3	)	)	PUNCT
ejpam-5755	89	4	and	and	CCONJ
ejpam-5755	89	5	βij	βij	PROPN
ejpam-5755	89	6	̸=	̸=	PROPN
ejpam-5755	89	7	0	0	NUM
ejpam-5755	89	8	be	be	AUX
ejpam-5755	89	9	the	the	DET
ejpam-5755	89	10	state	state	NOUN
ejpam-5755	89	11	and	and	CCONJ
ejpam-5755	89	12	scalar	scalar	ADJ
ejpam-5755	89	13	scale	scale	NOUN
ejpam-5755	89	14	of	of	ADP
ejpam-5755	89	15	edge	edge	NOUN
ejpam-5755	89	16	(	(	PUNCT
ejpam-5755	89	17	i	i	PROPN
ejpam-5755	89	18	,	,	PUNCT
ejpam-5755	89	19	j	j	PROPN
ejpam-5755	89	20	)	)	PUNCT
ejpam-5755	89	21	at	at	ADP
ejpam-5755	89	22	time	time	NOUN
ejpam-5755	89	23	t	t	PROPN
ejpam-5755	89	24	,	,	PUNCT
ejpam-5755	89	25	respectively	respectively	ADV
ejpam-5755	89	26	.	.	PUNCT
ejpam-5755	90	1	thus	thus	ADV
ejpam-5755	90	2	,	,	PUNCT
ejpam-5755	90	3	the	the	DET
ejpam-5755	90	4	edge	edge	NOUN
ejpam-5755	90	5	dynamics	dynamic	NOUN
ejpam-5755	90	6	of	of	ADP
ejpam-5755	90	7	each	each	DET
ejpam-5755	90	8	edge	edge	NOUN
ejpam-5755	90	9	can	can	AUX
ejpam-5755	90	10	be	be	AUX
ejpam-5755	90	11	designed	design	VERB
ejpam-5755	90	12	as	as	SCONJ
ejpam-5755	90	13	follows	follow	VERB
ejpam-5755	90	14	:	:	PUNCT
ejpam-5755	90	15	βij	βij	PROPN
ejpam-5755	90	16	ẋij(t	ẋij(t	PROPN
ejpam-5755	90	17	)	)	PUNCT
ejpam-5755	91	1	=	=	SYM
ejpam-5755	91	2	uij(t	uij(t	PROPN
ejpam-5755	91	3	)	)	PUNCT
ejpam-5755	91	4	,	,	PUNCT
ejpam-5755	91	5	for	for	ADP
ejpam-5755	91	6	(	(	PUNCT
ejpam-5755	91	7	i	i	PROPN
ejpam-5755	91	8	,	,	PUNCT
ejpam-5755	91	9	j	j	PROPN
ejpam-5755	91	10	)	)	PUNCT
ejpam-5755	91	11	∈	∈	PROPN
ejpam-5755	91	12	e	e	X
ejpam-5755	91	13	,	,	PUNCT
ejpam-5755	91	14	(	(	PUNCT
ejpam-5755	91	15	2.1	2.1	NUM
ejpam-5755	91	16	)	)	PUNCT
ejpam-5755	91	17	where	where	SCONJ
ejpam-5755	91	18	uij	uij	PRON
ejpam-5755	91	19	∈	∈	PROPN
ejpam-5755	91	20	r	r	NOUN
ejpam-5755	91	21	is	be	AUX
ejpam-5755	91	22	a	a	DET
ejpam-5755	91	23	consensus	consensus	NOUN
ejpam-5755	91	24	protocol	protocol	NOUN
ejpam-5755	91	25	.	.	PUNCT
ejpam-5755	92	1	in	in	ADP
ejpam-5755	92	2	general	general	ADJ
ejpam-5755	92	3	,	,	PUNCT
ejpam-5755	92	4	one	one	PRON
ejpam-5755	92	5	says	say	VERB
ejpam-5755	92	6	that	that	SCONJ
ejpam-5755	92	7	the	the	DET
ejpam-5755	92	8	protocol	protocol	NOUN
ejpam-5755	92	9	uij	uij	PRON
ejpam-5755	92	10	in	in	ADP
ejpam-5755	92	11	(	(	PUNCT
ejpam-5755	92	12	2.1	2.1	NUM
ejpam-5755	92	13	)	)	PUNCT
ejpam-5755	92	14	solves	solve	VERB
ejpam-5755	92	15	the	the	DET
ejpam-5755	92	16	edge	edge	NOUN
ejpam-5755	92	17	consensus	consensus	NOUN
ejpam-5755	92	18	problems	problem	NOUN
ejpam-5755	92	19	if	if	SCONJ
ejpam-5755	92	20	the	the	DET
ejpam-5755	92	21	following	follow	VERB
ejpam-5755	92	22	definition	definition	NOUN
ejpam-5755	92	23	is	be	AUX
ejpam-5755	92	24	satisfied	satisfied	ADJ
ejpam-5755	92	25	:	:	PUNCT
ejpam-5755	92	26	definition	definition	NOUN
ejpam-5755	92	27	2	2	NUM
ejpam-5755	92	28	.	.	PUNCT
ejpam-5755	93	1	the	the	DET
ejpam-5755	93	2	multi	multi	ADJ
ejpam-5755	93	3	agent	agent	NOUN
ejpam-5755	93	4	system	system	NOUN
ejpam-5755	93	5	(	(	PUNCT
ejpam-5755	93	6	2.1	2.1	NUM
ejpam-5755	93	7	)	)	PUNCT
ejpam-5755	93	8	is	be	AUX
ejpam-5755	93	9	said	say	VERB
ejpam-5755	93	10	to	to	PART
ejpam-5755	93	11	reach	reach	VERB
ejpam-5755	93	12	scaled	scale	VERB
ejpam-5755	93	13	consensus	consensus	NOUN
ejpam-5755	93	14	in	in	ADP
ejpam-5755	93	15	edge	edge	NOUN
ejpam-5755	93	16	dynamics	dynamic	NOUN
ejpam-5755	93	17	if	if	SCONJ
ejpam-5755	93	18	for	for	ADP
ejpam-5755	93	19	any	any	DET
ejpam-5755	93	20	initial	initial	ADJ
ejpam-5755	93	21	conditions	condition	NOUN
ejpam-5755	93	22	,	,	PUNCT
ejpam-5755	93	23	lim	lim	PROPN
ejpam-5755	93	24	tk→∞	tk→∞	PROPN
ejpam-5755	93	25	∥βijxij(tk)−	∥βijxij(tk)−	PROPN
ejpam-5755	93	26	βksxks(tk)∥	βksxks(tk)∥	NOUN
ejpam-5755	93	27	=	=	SYM
ejpam-5755	93	28	0	0	NUM
ejpam-5755	93	29	,	,	PUNCT
ejpam-5755	93	30	for	for	ADP
ejpam-5755	93	31	all	all	PRON
ejpam-5755	93	32	(	(	PUNCT
ejpam-5755	93	33	i	i	PROPN
ejpam-5755	93	34	,	,	PUNCT
ejpam-5755	93	35	j	j	PROPN
ejpam-5755	93	36	)	)	PUNCT
ejpam-5755	93	37	,	,	PUNCT
ejpam-5755	93	38	(	(	PUNCT
ejpam-5755	93	39	k	k	X
ejpam-5755	93	40	,	,	PUNCT
ejpam-5755	93	41	s	s	X
ejpam-5755	93	42	)	)	PUNCT
ejpam-5755	93	43	∈	∈	PROPN
ejpam-5755	93	44	e	e	X
ejpam-5755	93	45	.	.	PUNCT
ejpam-5755	94	1	(	(	PUNCT
ejpam-5755	94	2	2.2	2.2	NUM
ejpam-5755	94	3	)	)	PUNCT
ejpam-5755	94	4	3	3	NUM
ejpam-5755	94	5	.	.	PUNCT
ejpam-5755	94	6	scaled	scale	VERB
ejpam-5755	94	7	consensus	consensus	NOUN
ejpam-5755	94	8	results	result	NOUN
ejpam-5755	94	9	on	on	ADP
ejpam-5755	94	10	edge	edge	NOUN
ejpam-5755	94	11	dynamics	dynamic	NOUN
ejpam-5755	94	12	3.1	3.1	NUM
ejpam-5755	94	13	.	.	PUNCT
ejpam-5755	94	14	undirected	undirected	ADJ
ejpam-5755	94	15	communication	communication	NOUN
ejpam-5755	94	16	networks	network	NOUN
ejpam-5755	94	17	in	in	ADP
ejpam-5755	94	18	this	this	DET
ejpam-5755	94	19	section	section	NOUN
ejpam-5755	94	20	,	,	PUNCT
ejpam-5755	94	21	we	we	PRON
ejpam-5755	94	22	solve	solve	VERB
ejpam-5755	94	23	scaled	scale	VERB
ejpam-5755	94	24	consensus	consensus	NOUN
ejpam-5755	94	25	problem	problem	NOUN
ejpam-5755	94	26	of	of	ADP
ejpam-5755	94	27	edge	edge	NOUN
ejpam-5755	94	28	dynamics	dynamic	NOUN
ejpam-5755	94	29	in	in	ADP
ejpam-5755	94	30	mass	mass	NOUN
ejpam-5755	94	31	by	by	ADP
ejpam-5755	94	32	designing	design	VERB
ejpam-5755	94	33	the	the	DET
ejpam-5755	94	34	consensus	consensus	NOUN
ejpam-5755	94	35	protocol	protocol	NOUN
ejpam-5755	94	36	,	,	PUNCT
ejpam-5755	94	37	denoted	denote	VERB
ejpam-5755	94	38	by	by	ADP
ejpam-5755	94	39	uij	uij	PRON
ejpam-5755	94	40	,	,	PUNCT
ejpam-5755	94	41	which	which	PRON
ejpam-5755	94	42	depends	depend	VERB
ejpam-5755	94	43	on	on	ADP
ejpam-5755	94	44	the	the	DET
ejpam-5755	94	45	states	state	NOUN
ejpam-5755	94	46	of	of	ADP
ejpam-5755	94	47	the	the	DET
ejpam-5755	94	48	edge	edge	NOUN
ejpam-5755	94	49	(	(	PUNCT
ejpam-5755	94	50	i	i	PROPN
ejpam-5755	94	51	,	,	PUNCT
ejpam-5755	94	52	j	j	PROPN
ejpam-5755	94	53	)	)	PUNCT
ejpam-5755	94	54	and	and	CCONJ
ejpam-5755	94	55	its	its	PRON
ejpam-5755	94	56	neighboring	neighboring	NOUN
ejpam-5755	94	57	edges	edge	NOUN
ejpam-5755	94	58	.	.	PUNCT
ejpam-5755	95	1	in	in	ADP
ejpam-5755	95	2	addition	addition	NOUN
ejpam-5755	95	3	,	,	PUNCT
ejpam-5755	95	4	two	two	NUM
ejpam-5755	95	5	edges	edge	NOUN
ejpam-5755	95	6	are	be	AUX
ejpam-5755	95	7	neighboring	neighbor	VERB
ejpam-5755	95	8	edges	edge	NOUN
ejpam-5755	95	9	if	if	SCONJ
ejpam-5755	95	10	they	they	PRON
ejpam-5755	95	11	share	share	VERB
ejpam-5755	95	12	exactly	exactly	ADV
ejpam-5755	95	13	a	a	DET
ejpam-5755	95	14	common	common	ADJ
ejpam-5755	95	15	ending	end	VERB
ejpam-5755	95	16	vertex	vertex	NOUN
ejpam-5755	95	17	.	.	PUNCT
ejpam-5755	96	1	assuming	assume	VERB
ejpam-5755	96	2	that	that	SCONJ
ejpam-5755	96	3	the	the	DET
ejpam-5755	96	4	multi	multi	ADJ
ejpam-5755	96	5	-	-	ADJ
ejpam-5755	96	6	agent	agent	ADJ
ejpam-5755	96	7	system	system	NOUN
ejpam-5755	96	8	(	(	PUNCT
ejpam-5755	96	9	2.1	2.1	NUM
ejpam-5755	96	10	)	)	PUNCT
ejpam-5755	96	11	has	have	AUX
ejpam-5755	96	12	been	be	AUX
ejpam-5755	96	13	modelled	model	VERB
ejpam-5755	96	14	as	as	ADP
ejpam-5755	96	15	a	a	DET
ejpam-5755	96	16	connected	connected	ADJ
ejpam-5755	96	17	digraph	digraph	NOUN
ejpam-5755	96	18	,	,	PUNCT
ejpam-5755	96	19	where	where	SCONJ
ejpam-5755	96	20	g	g	NOUN
ejpam-5755	96	21	=	=	SYM
ejpam-5755	96	22	(	(	PUNCT
ejpam-5755	96	23	v	v	NOUN
ejpam-5755	96	24	,	,	PUNCT
ejpam-5755	96	25	e	e	NOUN
ejpam-5755	96	26	,	,	PUNCT
ejpam-5755	96	27	a	a	PRON
ejpam-5755	96	28	)	)	PUNCT
ejpam-5755	96	29	and	and	CCONJ
ejpam-5755	96	30	g′	g′	NOUN
ejpam-5755	96	31	=	=	SYM
ejpam-5755	96	32	(	(	PUNCT
ejpam-5755	96	33	v	v	NOUN
ejpam-5755	96	34	,	,	PUNCT
ejpam-5755	96	35	e	e	NOUN
ejpam-5755	96	36	′,a′	′,a′	NOUN
ejpam-5755	96	37	)	)	PUNCT
ejpam-5755	96	38	,	,	PUNCT
ejpam-5755	96	39	are	be	AUX
ejpam-5755	96	40	the	the	DET
ejpam-5755	96	41	communication	communication	NOUN
ejpam-5755	96	42	networks	network	NOUN
ejpam-5755	96	43	of	of	ADP
ejpam-5755	96	44	system	system	NOUN
ejpam-5755	96	45	(	(	PUNCT
ejpam-5755	96	46	2.1	2.1	NUM
ejpam-5755	96	47	)	)	PUNCT
ejpam-5755	96	48	at	at	ADP
ejpam-5755	96	49	time	time	NOUN
ejpam-5755	96	50	t	t	PROPN
ejpam-5755	96	51	and	and	CCONJ
ejpam-5755	96	52	at	at	ADP
ejpam-5755	96	53	the	the	DET
ejpam-5755	96	54	impulsive	impulsive	ADJ
ejpam-5755	96	55	time	time	NOUN
ejpam-5755	96	56	tk	tk	PROPN
ejpam-5755	96	57	,	,	PUNCT
ejpam-5755	96	58	respectively	respectively	ADV
ejpam-5755	96	59	.	.	PUNCT
ejpam-5755	97	1	given	give	VERB
ejpam-5755	97	2	any	any	DET
ejpam-5755	97	3	scalar	scalar	ADJ
ejpam-5755	97	4	scales	scale	NOUN
ejpam-5755	97	5	βij	βij	NOUN
ejpam-5755	97	6	̸=	̸=	PROPN
ejpam-5755	97	7	0	0	NUM
ejpam-5755	97	8	for	for	SCONJ
ejpam-5755	97	9	all	all	DET
ejpam-5755	97	10	i	i	PROPN
ejpam-5755	97	11	,	,	PUNCT
ejpam-5755	97	12	j	j	PROPN
ejpam-5755	97	13	,	,	PUNCT
ejpam-5755	97	14	the	the	DET
ejpam-5755	97	15	scaled	scale	VERB
ejpam-5755	97	16	consensus	consensus	NOUN
ejpam-5755	97	17	protocol	protocol	NOUN
ejpam-5755	97	18	of	of	ADP
ejpam-5755	97	19	multi	multi	ADJ
ejpam-5755	97	20	-	-	ADJ
ejpam-5755	97	21	agent	agent	ADJ
ejpam-5755	97	22	system	system	NOUN
ejpam-5755	97	23	(	(	PUNCT
ejpam-5755	97	24	2.1	2.1	NUM
ejpam-5755	97	25	)	)	PUNCT
ejpam-5755	97	26	based	base	VERB
ejpam-5755	97	27	on	on	ADP
ejpam-5755	97	28	the	the	DET
ejpam-5755	97	29	state	state	NOUN
ejpam-5755	97	30	of	of	ADP
ejpam-5755	97	31	edges	edge	NOUN
ejpam-5755	97	32	in	in	ADP
ejpam-5755	97	33	a	a	DET
ejpam-5755	97	34	communication	communication	NOUN
ejpam-5755	97	35	network	network	NOUN
ejpam-5755	97	36	g∪g′	g∪g′	NOUN
ejpam-5755	97	37	and	and	CCONJ
ejpam-5755	97	38	its	its	PRON
ejpam-5755	97	39	line	line	NOUN
ejpam-5755	97	40	graph	graph	NOUN
ejpam-5755	97	41	is	be	AUX
ejpam-5755	97	42	defined	define	VERB
ejpam-5755	97	43	as	as	SCONJ
ejpam-5755	97	44	follows	follow	VERB
ejpam-5755	97	45	:	:	PUNCT
ejpam-5755	97	46	for	for	ADP
ejpam-5755	97	47	t	t	PROPN
ejpam-5755	97	48	∈	∈	PROPN
ejpam-5755	97	49	(	(	PUNCT
ejpam-5755	97	50	tk−1	tk−1	PROPN
ejpam-5755	97	51	,	,	PUNCT
ejpam-5755	97	52	tk	tk	PROPN
ejpam-5755	97	53	]	]	X
ejpam-5755	97	54	,	,	PUNCT
ejpam-5755	97	55	uij(t	uij(t	PROPN
ejpam-5755	97	56	)	)	PUNCT
ejpam-5755	97	57	=	=	SYM
ejpam-5755	98	1	|βij	|βij	NOUN
ejpam-5755	98	2	|	|	ADV
ejpam-5755	98	3	[	[	PUNCT
ejpam-5755	98	4	∑	∑	PUNCT
ejpam-5755	98	5	s∈ni	s∈ni	PROPN
ejpam-5755	98	6	ais[βisxis(t)−	ais[βisxis(t)−	PROPN
ejpam-5755	98	7	βijxij(t	βijxij(t	PROPN
ejpam-5755	98	8	)	)	PUNCT
ejpam-5755	98	9	]	]	PUNCT
ejpam-5755	99	1	+	+	CCONJ
ejpam-5755	99	2	∑	∑	PUNCT
ejpam-5755	99	3	s∈nj	s∈nj	PROPN
ejpam-5755	99	4	ajs[βjsxjs(t)−	ajs[βjsxjs(t)−	PROPN
ejpam-5755	99	5	βijxij(t	βijxij(t	PROPN
ejpam-5755	99	6	)	)	PUNCT
ejpam-5755	99	7	]	]	PUNCT
ejpam-5755	99	8	]	]	PUNCT
ejpam-5755	99	9	s.	s.	PROPN
ejpam-5755	99	10	donganont	donganont	PROPN
ejpam-5755	99	11	,	,	PUNCT
ejpam-5755	99	12	u.	u.	NOUN
ejpam-5755	99	13	witthayarat	witthayarat	NOUN
ejpam-5755	99	14	,	,	PUNCT
ejpam-5755	99	15	m.	m.	NOUN
ejpam-5755	99	16	donganont	donganont	PROPN
ejpam-5755	99	17	/	/	SYM
ejpam-5755	99	18	eur	eur	PROPN
ejpam-5755	99	19	.	.	PUNCT
ejpam-5755	100	1	j.	j.	PROPN
ejpam-5755	100	2	pure	pure	PROPN
ejpam-5755	100	3	appl	appl	PROPN
ejpam-5755	100	4	.	.	PROPN
ejpam-5755	100	5	math	math	PROPN
ejpam-5755	100	6	,	,	PUNCT
ejpam-5755	100	7	18	18	NUM
ejpam-5755	100	8	(	(	PUNCT
ejpam-5755	100	9	1	1	NUM
ejpam-5755	100	10	)	)	PUNCT
ejpam-5755	100	11	(	(	PUNCT
ejpam-5755	100	12	2025	2025	NUM
ejpam-5755	100	13	)	)	PUNCT
ejpam-5755	100	14	,	,	PUNCT
ejpam-5755	100	15	5755	5755	NUM
ejpam-5755	100	16	5	5	NUM
ejpam-5755	100	17	of	of	ADP
ejpam-5755	100	18	17	17	NUM
ejpam-5755	100	19	+	+	CCONJ
ejpam-5755	100	20	h	h	NOUN
ejpam-5755	100	21	·	·	PUNCT
ejpam-5755	100	22	|βi|	|βi|	PROPN
ejpam-5755	101	1	∞∑	∞∑	NUM
ejpam-5755	101	2	k=1	k=1	PUNCT
ejpam-5755	102	1	[	[	PUNCT
ejpam-5755	102	2	∑	∑	PUNCT
ejpam-5755	102	3	s∈n	s∈n	NOUN
ejpam-5755	102	4	′	′	NUM
ejpam-5755	103	1	i	i	PRON
ejpam-5755	103	2	a′is[βisxis(t)−	a′is[βisxis(t)−	PROPN
ejpam-5755	103	3	βijxij(t	βijxij(t	PROPN
ejpam-5755	103	4	)	)	PUNCT
ejpam-5755	103	5	]	]	PUNCT
ejpam-5755	104	1	+	+	CCONJ
ejpam-5755	104	2	∑	∑	ADP
ejpam-5755	104	3	s∈n	s∈n	NOUN
ejpam-5755	104	4	′	′	NUM
ejpam-5755	104	5	j	j	PROPN
ejpam-5755	105	1	a′js[βjsxjs(t)−	a′js[βjsxjs(t)−	PROPN
ejpam-5755	105	2	βijxij(t	βijxij(t	PROPN
ejpam-5755	105	3	)	)	PUNCT
ejpam-5755	105	4	]	]	PUNCT
ejpam-5755	105	5	]	]	PUNCT
ejpam-5755	105	6	δ(t−	δ(t−	PROPN
ejpam-5755	105	7	tk	tk	PROPN
ejpam-5755	105	8	)	)	PUNCT
ejpam-5755	105	9	,	,	PUNCT
ejpam-5755	105	10	for	for	ADP
ejpam-5755	105	11	(	(	PUNCT
ejpam-5755	105	12	i	i	PROPN
ejpam-5755	105	13	,	,	PUNCT
ejpam-5755	105	14	j	j	PROPN
ejpam-5755	105	15	)	)	PUNCT
ejpam-5755	105	16	∈	∈	PROPN
ejpam-5755	105	17	e	e	X
ejpam-5755	105	18	,	,	PUNCT
ejpam-5755	105	19	(	(	PUNCT
ejpam-5755	105	20	3.1	3.1	NUM
ejpam-5755	105	21	)	)	PUNCT
ejpam-5755	105	22	where	where	SCONJ
ejpam-5755	105	23	βij	βij	NOUN
ejpam-5755	105	24	is	be	AUX
ejpam-5755	105	25	the	the	DET
ejpam-5755	105	26	scalar	scalar	ADJ
ejpam-5755	105	27	scale	scale	NOUN
ejpam-5755	105	28	of	of	ADP
ejpam-5755	105	29	an	an	DET
ejpam-5755	105	30	edge	edge	NOUN
ejpam-5755	105	31	(	(	PUNCT
ejpam-5755	105	32	i	i	PROPN
ejpam-5755	105	33	,	,	PUNCT
ejpam-5755	105	34	j	j	PROPN
ejpam-5755	105	35	)	)	PUNCT
ejpam-5755	105	36	;	;	PUNCT
ejpam-5755	105	37	h	h	NOUN
ejpam-5755	105	38	=	=	NOUN
ejpam-5755	105	39	tk	tk	PROPN
ejpam-5755	105	40	−	−	PROPN
ejpam-5755	105	41	tk−1	tk−1	PROPN
ejpam-5755	105	42	is	be	AUX
ejpam-5755	105	43	a	a	DET
ejpam-5755	105	44	sampling	sampling	NOUN
ejpam-5755	105	45	period	period	NOUN
ejpam-5755	105	46	;	;	PUNCT
ejpam-5755	105	47	ni	ni	PROPN
ejpam-5755	105	48	and	and	CCONJ
ejpam-5755	105	49	n	n	NUM
ejpam-5755	105	50	′	′	NOUN
ejpam-5755	106	1	i	i	PRON
ejpam-5755	106	2	are	be	AUX
ejpam-5755	106	3	the	the	DET
ejpam-5755	106	4	neighboring	neighboring	NOUN
ejpam-5755	106	5	sets	set	NOUN
ejpam-5755	106	6	of	of	ADP
ejpam-5755	106	7	node	node	NOUN
ejpam-5755	106	8	i	i	PRON
ejpam-5755	106	9	at	at	ADP
ejpam-5755	106	10	time	time	NOUN
ejpam-5755	106	11	t	t	NOUN
ejpam-5755	106	12	and	and	CCONJ
ejpam-5755	106	13	impulsive	impulsive	ADJ
ejpam-5755	106	14	time	time	NOUN
ejpam-5755	106	15	tk	tk	PROPN
ejpam-5755	106	16	,	,	PUNCT
ejpam-5755	106	17	respectively	respectively	ADV
ejpam-5755	106	18	.	.	PUNCT
ejpam-5755	107	1	remark	remark	PROPN
ejpam-5755	107	2	1	1	NUM
ejpam-5755	107	3	.	.	PUNCT
ejpam-5755	108	1	it	it	PRON
ejpam-5755	108	2	can	can	AUX
ejpam-5755	108	3	be	be	AUX
ejpam-5755	108	4	seen	see	VERB
ejpam-5755	108	5	that	that	SCONJ
ejpam-5755	108	6	if	if	SCONJ
ejpam-5755	108	7	βij	βij	NOUN
ejpam-5755	108	8	=	=	SYM
ejpam-5755	108	9	1	1	NUM
ejpam-5755	108	10	for	for	ADP
ejpam-5755	108	11	all	all	PRON
ejpam-5755	108	12	i	i	PROPN
ejpam-5755	108	13	,	,	PUNCT
ejpam-5755	108	14	j	j	PROPN
ejpam-5755	108	15	,	,	PUNCT
ejpam-5755	108	16	the	the	DET
ejpam-5755	108	17	consensus	consensus	NOUN
ejpam-5755	108	18	protocol	protocol	NOUN
ejpam-5755	108	19	(	(	PUNCT
ejpam-5755	108	20	3.1	3.1	NUM
ejpam-5755	108	21	)	)	PUNCT
ejpam-5755	108	22	will	will	AUX
ejpam-5755	108	23	reduce	reduce	VERB
ejpam-5755	108	24	to	to	ADP
ejpam-5755	108	25	the	the	DET
ejpam-5755	108	26	following	follow	VERB
ejpam-5755	108	27	consensus	consensus	NOUN
ejpam-5755	108	28	protocol	protocol	NOUN
ejpam-5755	108	29	uij(t	uij(t	PROPN
ejpam-5755	108	30	)	)	PUNCT
ejpam-5755	108	31	=	=	PUNCT
ejpam-5755	109	1	[	[	PUNCT
ejpam-5755	109	2	∑	∑	PUNCT
ejpam-5755	109	3	s∈ni	s∈ni	PROPN
ejpam-5755	109	4	ais[xis(t)−	ais[xis(t)−	PROPN
ejpam-5755	109	5	xij(t	xij(t	PROPN
ejpam-5755	109	6	)	)	PUNCT
ejpam-5755	109	7	]	]	PUNCT
ejpam-5755	110	1	+	+	CCONJ
ejpam-5755	110	2	∑	∑	PUNCT
ejpam-5755	110	3	s∈nj	s∈nj	PROPN
ejpam-5755	110	4	ajs[xjs(t)−	ajs[xjs(t)−	PROPN
ejpam-5755	110	5	xij(t	xij(t	PROPN
ejpam-5755	110	6	)	)	PUNCT
ejpam-5755	110	7	]	]	PUNCT
ejpam-5755	110	8	]	]	PUNCT
ejpam-5755	111	1	+	+	CCONJ
ejpam-5755	111	2	h	h	NOUN
ejpam-5755	111	3	·	·	PUNCT
ejpam-5755	111	4	∞∑	∞∑	NUM
ejpam-5755	111	5	k=1	k=1	PUNCT
ejpam-5755	111	6	[	[	PUNCT
ejpam-5755	111	7	∑	∑	PUNCT
ejpam-5755	111	8	s∈n	s∈n	NOUN
ejpam-5755	111	9	′	′	NUM
ejpam-5755	112	1	i	i	PRON
ejpam-5755	112	2	a′is[xis(t)−	a′is[xis(t)−	PUNCT
ejpam-5755	112	3	xij(t	xij(t	PROPN
ejpam-5755	112	4	)	)	PUNCT
ejpam-5755	112	5	]	]	PUNCT
ejpam-5755	113	1	+	+	CCONJ
ejpam-5755	113	2	∑	∑	ADP
ejpam-5755	113	3	s∈n	s∈n	NOUN
ejpam-5755	113	4	′	′	NUM
ejpam-5755	113	5	j	j	PROPN
ejpam-5755	113	6	a′js[xjs(t)−	a′js[xjs(t)−	PROPN
ejpam-5755	113	7	xij(t	xij(t	PROPN
ejpam-5755	113	8	)	)	PUNCT
ejpam-5755	113	9	]	]	PUNCT
ejpam-5755	113	10	]	]	PUNCT
ejpam-5755	113	11	δ(t−	δ(t−	PROPN
ejpam-5755	113	12	tk	tk	PROPN
ejpam-5755	113	13	)	)	PUNCT
ejpam-5755	113	14	,	,	PUNCT
ejpam-5755	113	15	for	for	ADP
ejpam-5755	113	16	(	(	PUNCT
ejpam-5755	113	17	i	i	PROPN
ejpam-5755	113	18	,	,	PUNCT
ejpam-5755	113	19	j	j	PROPN
ejpam-5755	113	20	)	)	PUNCT
ejpam-5755	113	21	∈	∈	PROPN
ejpam-5755	113	22	e	e	X
ejpam-5755	113	23	.	.	PUNCT
ejpam-5755	114	1	(	(	PUNCT
ejpam-5755	114	2	3.2	3.2	NUM
ejpam-5755	114	3	)	)	PUNCT
ejpam-5755	114	4	remark	remark	NOUN
ejpam-5755	114	5	2	2	NUM
ejpam-5755	114	6	.	.	PUNCT
ejpam-5755	115	1	if	if	SCONJ
ejpam-5755	115	2	there	there	PRON
ejpam-5755	115	3	is	be	VERB
ejpam-5755	115	4	no	no	DET
ejpam-5755	115	5	instantaneous	instantaneous	ADJ
ejpam-5755	115	6	contact	contact	NOUN
ejpam-5755	115	7	or	or	CCONJ
ejpam-5755	115	8	update	update	NOUN
ejpam-5755	115	9	at	at	ADP
ejpam-5755	115	10	the	the	DET
ejpam-5755	115	11	impulsive	impulsive	ADJ
ejpam-5755	115	12	time	time	NOUN
ejpam-5755	115	13	tk	tk	PROPN
ejpam-5755	115	14	and	and	CCONJ
ejpam-5755	115	15	βij	βij	NOUN
ejpam-5755	115	16	=	=	NOUN
ejpam-5755	115	17	1	1	NUM
ejpam-5755	115	18	for	for	ADP
ejpam-5755	115	19	all	all	PRON
ejpam-5755	115	20	i	i	PROPN
ejpam-5755	115	21	,	,	PUNCT
ejpam-5755	115	22	j	j	PROPN
ejpam-5755	115	23	,	,	PUNCT
ejpam-5755	115	24	the	the	DET
ejpam-5755	115	25	consensus	consensus	NOUN
ejpam-5755	115	26	protocol	protocol	NOUN
ejpam-5755	115	27	(	(	PUNCT
ejpam-5755	115	28	3.1	3.1	NUM
ejpam-5755	115	29	)	)	PUNCT
ejpam-5755	115	30	is	be	AUX
ejpam-5755	115	31	described	describe	VERB
ejpam-5755	115	32	as	as	ADP
ejpam-5755	115	33	in	in	ADP
ejpam-5755	115	34	the	the	DET
ejpam-5755	115	35	following	follow	VERB
ejpam-5755	115	36	consensus	consensus	NOUN
ejpam-5755	115	37	protocol	protocol	NOUN
ejpam-5755	115	38	uij(t	uij(t	PROPN
ejpam-5755	115	39	)	)	PUNCT
ejpam-5755	115	40	=	=	PUNCT
ejpam-5755	116	1	[	[	PUNCT
ejpam-5755	116	2	∑	∑	PUNCT
ejpam-5755	116	3	s∈ni	s∈ni	PROPN
ejpam-5755	116	4	ais[xis(t)−	ais[xis(t)−	PROPN
ejpam-5755	116	5	xij(t	xij(t	PROPN
ejpam-5755	116	6	)	)	PUNCT
ejpam-5755	116	7	]	]	PUNCT
ejpam-5755	117	1	+	+	CCONJ
ejpam-5755	117	2	∑	∑	PUNCT
ejpam-5755	117	3	s∈nj	s∈nj	PROPN
ejpam-5755	117	4	ajs[xjs(t)−	ajs[xjs(t)−	PROPN
ejpam-5755	117	5	xij(t	xij(t	PROPN
ejpam-5755	117	6	)	)	PUNCT
ejpam-5755	117	7	]	]	PUNCT
ejpam-5755	117	8	]	]	PUNCT
ejpam-5755	117	9	,	,	PUNCT
ejpam-5755	117	10	for	for	ADP
ejpam-5755	117	11	(	(	PUNCT
ejpam-5755	117	12	i	i	PROPN
ejpam-5755	117	13	,	,	PUNCT
ejpam-5755	117	14	j	j	PROPN
ejpam-5755	117	15	)	)	PUNCT
ejpam-5755	117	16	∈	∈	PROPN
ejpam-5755	117	17	e	e	X
ejpam-5755	117	18	,	,	PUNCT
ejpam-5755	117	19	(	(	PUNCT
ejpam-5755	117	20	3.3	3.3	NUM
ejpam-5755	117	21	)	)	PUNCT
ejpam-5755	117	22	which	which	PRON
ejpam-5755	117	23	was	be	AUX
ejpam-5755	117	24	investigated	investigate	VERB
ejpam-5755	117	25	by	by	ADP
ejpam-5755	117	26	wang	wang	PROPN
ejpam-5755	117	27	et	et	PROPN
ejpam-5755	117	28	al	al	PROPN
ejpam-5755	117	29	.	.	PROPN
ejpam-5755	117	30	,	,	PUNCT
ejpam-5755	117	31	[	[	X
ejpam-5755	117	32	14	14	NUM
ejpam-5755	117	33	]	]	PUNCT
ejpam-5755	117	34	.	.	PUNCT
ejpam-5755	118	1	this	this	PRON
ejpam-5755	118	2	shows	show	VERB
ejpam-5755	118	3	the	the	DET
ejpam-5755	118	4	generalization	generalization	NOUN
ejpam-5755	118	5	of	of	ADP
ejpam-5755	118	6	our	our	PRON
ejpam-5755	118	7	protocol	protocol	NOUN
ejpam-5755	118	8	.	.	PUNCT
ejpam-5755	119	1	by	by	ADP
ejpam-5755	119	2	the	the	DET
ejpam-5755	119	3	definition	definition	NOUN
ejpam-5755	119	4	of	of	ADP
ejpam-5755	119	5	the	the	DET
ejpam-5755	119	6	dirac	dirac	PROPN
ejpam-5755	119	7	delta	delta	PROPN
ejpam-5755	119	8	function	function	NOUN
ejpam-5755	119	9	,	,	PUNCT
ejpam-5755	119	10	the	the	DET
ejpam-5755	119	11	system	system	NOUN
ejpam-5755	119	12	(	(	PUNCT
ejpam-5755	119	13	2.1	2.1	NUM
ejpam-5755	119	14	)	)	PUNCT
ejpam-5755	119	15	and	and	CCONJ
ejpam-5755	119	16	protocol	protocol	NOUN
ejpam-5755	119	17	(	(	PUNCT
ejpam-5755	119	18	3.1	3.1	NUM
ejpam-5755	119	19	)	)	PUNCT
ejpam-5755	119	20	can	can	AUX
ejpam-5755	119	21	be	be	AUX
ejpam-5755	119	22	described	describe	VERB
ejpam-5755	119	23	as	as	ADP
ejpam-5755	119	24	the	the	DET
ejpam-5755	119	25	impulsive	impulsive	ADJ
ejpam-5755	119	26	system:	system:	PROPN
ejpam-5755	119	27	βij	βij	PROPN
ejpam-5755	119	28	ẋij(t	ẋij(t	PROPN
ejpam-5755	119	29	)	)	PUNCT
ejpam-5755	120	1	=	=	SYM
ejpam-5755	120	2	|βij	|βij	NOUN
ejpam-5755	121	1	|	|	ADV
ejpam-5755	122	1	[	[	X
ejpam-5755	122	2	∑	∑	PUNCT
ejpam-5755	122	3	s∈ni	s∈ni	PROPN
ejpam-5755	122	4	ais[βisxis(t)−	ais[βisxis(t)−	PROPN
ejpam-5755	122	5	βijxij(t	βijxij(t	PROPN
ejpam-5755	122	6	)	)	PUNCT
ejpam-5755	122	7	]	]	PUNCT
ejpam-5755	123	1	+	+	CCONJ
ejpam-5755	123	2	∑	∑	PUNCT
ejpam-5755	123	3	s∈nj	s∈nj	PROPN
ejpam-5755	123	4	ajs[xjs(t)−	ajs[xjs(t)−	PROPN
ejpam-5755	123	5	xij(t	xij(t	PROPN
ejpam-5755	123	6	)	)	PUNCT
ejpam-5755	123	7	]	]	PUNCT
ejpam-5755	123	8	]	]	PUNCT
ejpam-5755	123	9	,	,	PUNCT
ejpam-5755	123	10	t	t	PROPN
ejpam-5755	123	11	∈	∈	PROPN
ejpam-5755	123	12	(	(	PUNCT
ejpam-5755	123	13	tk−1	tk−1	PROPN
ejpam-5755	123	14	,	,	PUNCT
ejpam-5755	123	15	tk	tk	PROPN
ejpam-5755	123	16	)	)	PUNCT
ejpam-5755	123	17	,	,	PUNCT
ejpam-5755	123	18	∆βijxij(tk	∆βijxij(tk	PROPN
ejpam-5755	123	19	)	)	PUNCT
ejpam-5755	123	20	=	=	SYM
ejpam-5755	123	21	h|βi|	h|βi|	PROPN
ejpam-5755	123	22	∑	∑	PUNCT
ejpam-5755	123	23	l∈n	l∈n	ADJ
ejpam-5755	123	24	′	′	INTJ
ejpam-5755	124	1	i	i	PRON
ejpam-5755	124	2	a′il	a′il	VERB
ejpam-5755	124	3	[	[	PUNCT
ejpam-5755	124	4	∑	∑	PUNCT
ejpam-5755	124	5	s∈ni	s∈ni	NOUN
ejpam-5755	124	6	ais[βisxis(tk)−	ais[βisxis(tk)−	NOUN
ejpam-5755	124	7	βijxij(tk	βijxij(tk	NOUN
ejpam-5755	124	8	)	)	PUNCT
ejpam-5755	124	9	]	]	PUNCT
ejpam-5755	125	1	+	+	CCONJ
ejpam-5755	125	2	∑	∑	PUNCT
ejpam-5755	125	3	s∈nj	s∈nj	PROPN
ejpam-5755	125	4	ajs[xjs(tk)−	ajs[xjs(tk)−	PROPN
ejpam-5755	125	5	xij(tk	xij(tk	PROPN
ejpam-5755	125	6	)	)	PUNCT
ejpam-5755	125	7	]	]	PUNCT
ejpam-5755	125	8	]	]	PUNCT
ejpam-5755	125	9	,	,	PUNCT
ejpam-5755	125	10	(	(	PUNCT
ejpam-5755	125	11	3.4	3.4	NUM
ejpam-5755	125	12	)	)	PUNCT
ejpam-5755	125	13	where	where	SCONJ
ejpam-5755	125	14	∆βijxij(tk	∆βijxij(tk	NOUN
ejpam-5755	125	15	)	)	PUNCT
ejpam-5755	125	16	=	=	PUNCT
ejpam-5755	126	1	βijxij(t	βijxij(t	PROPN
ejpam-5755	127	1	+	+	CCONJ
ejpam-5755	127	2	k	k	X
ejpam-5755	127	3	)	)	PUNCT
ejpam-5755	128	1	−βijxij(t	−βijxij(t	PRON
ejpam-5755	128	2	−	−	PROPN
ejpam-5755	129	1	k	k	PROPN
ejpam-5755	129	2	)	)	PUNCT
ejpam-5755	129	3	;	;	PUNCT
ejpam-5755	129	4	βijxij(t	βijxij(t	PRON
ejpam-5755	129	5	+	+	SYM
ejpam-5755	129	6	k	k	X
ejpam-5755	129	7	)	)	PUNCT
ejpam-5755	130	1	=	=	VERB
ejpam-5755	130	2	lim	lim	PROPN
ejpam-5755	130	3	h→0	h→0	PROPN
ejpam-5755	130	4	+	+	X
ejpam-5755	130	5	βijxij(tk+h	βijxij(tk+h	NUM
ejpam-5755	130	6	)	)	PUNCT
ejpam-5755	130	7	and	and	CCONJ
ejpam-5755	130	8	βijxij(t	βijxij(t	PRON
ejpam-5755	130	9	−	−	PROPN
ejpam-5755	130	10	k	k	NOUN
ejpam-5755	130	11	)	)	PUNCT
ejpam-5755	131	1	=	=	SYM
ejpam-5755	131	2	lim	lim	PROPN
ejpam-5755	131	3	h→0	h→0	NOUN
ejpam-5755	132	1	+	+	NUM
ejpam-5755	133	1	βijxij(tk	βijxij(tk	NOUN
ejpam-5755	134	1	−	−	PROPN
ejpam-5755	135	1	h	h	NOUN
ejpam-5755	135	2	)	)	PUNCT
ejpam-5755	135	3	.	.	PUNCT
ejpam-5755	136	1	s.	s.	PROPN
ejpam-5755	136	2	donganont	donganont	PROPN
ejpam-5755	136	3	,	,	PUNCT
ejpam-5755	136	4	u.	u.	NOUN
ejpam-5755	136	5	witthayarat	witthayarat	NOUN
ejpam-5755	136	6	,	,	PUNCT
ejpam-5755	136	7	m.	m.	NOUN
ejpam-5755	136	8	donganont	donganont	PROPN
ejpam-5755	136	9	/	/	SYM
ejpam-5755	136	10	eur	eur	PROPN
ejpam-5755	136	11	.	.	PUNCT
ejpam-5755	137	1	j.	j.	PROPN
ejpam-5755	137	2	pure	pure	PROPN
ejpam-5755	137	3	appl	appl	PROPN
ejpam-5755	137	4	.	.	PROPN
ejpam-5755	137	5	math	math	PROPN
ejpam-5755	137	6	,	,	PUNCT
ejpam-5755	137	7	18	18	NUM
ejpam-5755	137	8	(	(	PUNCT
ejpam-5755	137	9	1	1	NUM
ejpam-5755	137	10	)	)	PUNCT
ejpam-5755	137	11	(	(	PUNCT
ejpam-5755	137	12	2025	2025	NUM
ejpam-5755	137	13	)	)	PUNCT
ejpam-5755	137	14	,	,	PUNCT
ejpam-5755	137	15	5755	5755	NUM
ejpam-5755	137	16	6	6	NUM
ejpam-5755	137	17	of	of	ADP
ejpam-5755	137	18	17	17	NUM
ejpam-5755	137	19	with	with	ADP
ejpam-5755	137	20	out	out	ADP
ejpam-5755	137	21	loss	loss	NOUN
ejpam-5755	137	22	of	of	ADP
ejpam-5755	137	23	generality	generality	NOUN
ejpam-5755	138	1	,	,	PUNCT
ejpam-5755	138	2	we	we	PRON
ejpam-5755	138	3	assume	assume	VERB
ejpam-5755	138	4	that	that	SCONJ
ejpam-5755	138	5	the	the	DET
ejpam-5755	138	6	solution	solution	NOUN
ejpam-5755	138	7	of	of	ADP
ejpam-5755	138	8	system	system	NOUN
ejpam-5755	138	9	(	(	PUNCT
ejpam-5755	138	10	3.4	3.4	NUM
ejpam-5755	138	11	)	)	PUNCT
ejpam-5755	138	12	is	be	AUX
ejpam-5755	138	13	left	leave	VERB
ejpam-5755	138	14	continuous	continuous	ADJ
ejpam-5755	138	15	,	,	PUNCT
ejpam-5755	138	16	that	that	ADV
ejpam-5755	138	17	is	is	ADV
ejpam-5755	138	18	,	,	PUNCT
ejpam-5755	138	19	βijxij(t	βijxij(t	PRON
ejpam-5755	138	20	−	−	PROPN
ejpam-5755	138	21	k	k	NOUN
ejpam-5755	138	22	)	)	PUNCT
ejpam-5755	138	23	=	=	SYM
ejpam-5755	138	24	βijxij(tk	βijxij(tk	NOUN
ejpam-5755	138	25	)	)	PUNCT
ejpam-5755	138	26	and	and	CCONJ
ejpam-5755	138	27	let	let	VERB
ejpam-5755	138	28	y	y	PROPN
ejpam-5755	138	29	(	(	PUNCT
ejpam-5755	138	30	t	t	PROPN
ejpam-5755	138	31	)	)	PUNCT
ejpam-5755	138	32	=	=	PUNCT
ejpam-5755	138	33	(	(	PUNCT
ejpam-5755	138	34	βijxij(t	βijxij(t	NOUN
ejpam-5755	138	35	)	)	PUNCT
ejpam-5755	138	36	)	)	PUNCT
ejpam-5755	139	1	t	t	PROPN
ejpam-5755	139	2	∈	∈	PROPN
ejpam-5755	139	3	rm	rm	PROPN
ejpam-5755	139	4	,	,	PUNCT
ejpam-5755	139	5	i	i	PRON
ejpam-5755	139	6	=	=	NOUN
ejpam-5755	139	7	1	1	NUM
ejpam-5755	139	8	,	,	PUNCT
ejpam-5755	139	9	2	2	NUM
ejpam-5755	139	10	,	,	PUNCT
ejpam-5755	139	11	.	.	PUNCT
ejpam-5755	139	12	.	.	PUNCT
ejpam-5755	139	13	.	.	PUNCT
ejpam-5755	140	1	,	,	PUNCT
ejpam-5755	140	2	n	n	CCONJ
ejpam-5755	140	3	,	,	PUNCT
ejpam-5755	140	4	i	i	PRON
ejpam-5755	140	5	<	<	X
ejpam-5755	140	6	j	j	PROPN
ejpam-5755	140	7	;	;	PUNCT
ejpam-5755	140	8	yij	yij	NOUN
ejpam-5755	140	9	=	=	PUNCT
ejpam-5755	140	10	βijxij	βijxij	NOUN
ejpam-5755	140	11	;	;	PUNCT
ejpam-5755	140	12	βij	βij	PROPN
ejpam-5755	140	13	̸=	̸=	PROPN
ejpam-5755	140	14	0	0	NUM
ejpam-5755	140	15	,	,	PUNCT
ejpam-5755	140	16	b	b	X
ejpam-5755	140	17	=	=	SYM
ejpam-5755	140	18	diag(βij	diag(βij	PROPN
ejpam-5755	140	19	)	)	PUNCT
ejpam-5755	140	20	∈	∈	PROPN
ejpam-5755	140	21	rm×m	rm×m	NOUN
ejpam-5755	140	22	,	,	PUNCT
ejpam-5755	140	23	h	h	NOUN
ejpam-5755	140	24	∈	∈	PROPN
ejpam-5755	140	25	r+	r+	X
ejpam-5755	140	26	.	.	PUNCT
ejpam-5755	141	1	then	then	ADV
ejpam-5755	141	2	,	,	PUNCT
ejpam-5755	141	3	the	the	DET
ejpam-5755	141	4	system	system	NOUN
ejpam-5755	141	5	(	(	PUNCT
ejpam-5755	141	6	3.4	3.4	NUM
ejpam-5755	141	7	)	)	PUNCT
ejpam-5755	141	8	can	can	AUX
ejpam-5755	141	9	be	be	AUX
ejpam-5755	141	10	written	write	VERB
ejpam-5755	141	11	as	as	ADP
ejpam-5755	141	12	the	the	DET
ejpam-5755	141	13	form	form	NOUN
ejpam-5755	141	14	:	:	PUNCT
ejpam-5755	141	15	{	{	PUNCT
ejpam-5755	141	16	ẏ	ẏ	PROPN
ejpam-5755	141	17	(	(	PUNCT
ejpam-5755	141	18	t	t	PROPN
ejpam-5755	141	19	)	)	PUNCT
ejpam-5755	141	20	=	=	VERB
ejpam-5755	142	1	h|b|qy	h|b|qy	PROPN
ejpam-5755	142	2	(	(	PUNCT
ejpam-5755	142	3	t	t	PROPN
ejpam-5755	142	4	)	)	PUNCT
ejpam-5755	142	5	,	,	PUNCT
ejpam-5755	142	6	t	t	PROPN
ejpam-5755	142	7	̸=	̸=	PROPN
ejpam-5755	142	8	tk	tk	PROPN
ejpam-5755	142	9	,	,	PUNCT
ejpam-5755	142	10	y	y	PROPN
ejpam-5755	142	11	(	(	PUNCT
ejpam-5755	142	12	t+k	t+k	NUM
ejpam-5755	142	13	)	)	PUNCT
ejpam-5755	142	14	=	=	PUNCT
ejpam-5755	143	1	[	[	X
ejpam-5755	143	2	i	i	PRON
ejpam-5755	143	3	m	m	VERB
ejpam-5755	143	4	+	+	X
ejpam-5755	143	5	h|b|q′]y	h|b|q′]y	X
ejpam-5755	143	6	(	(	PUNCT
ejpam-5755	143	7	tk	tk	PROPN
ejpam-5755	143	8	)	)	PUNCT
ejpam-5755	143	9	,	,	PUNCT
ejpam-5755	143	10	k	k	PROPN
ejpam-5755	143	11	∈	∈	PROPN
ejpam-5755	143	12	n	n	CCONJ
ejpam-5755	143	13	,	,	PUNCT
ejpam-5755	143	14	(	(	PUNCT
ejpam-5755	143	15	3.5	3.5	NUM
ejpam-5755	143	16	)	)	PUNCT
ejpam-5755	143	17	where	where	SCONJ
ejpam-5755	143	18	h	h	NOUN
ejpam-5755	143	19	is	be	AUX
ejpam-5755	143	20	a	a	DET
ejpam-5755	143	21	step	step	NOUN
ejpam-5755	143	22	size	size	NOUN
ejpam-5755	143	23	,	,	PUNCT
ejpam-5755	143	24	i	i	PRON
ejpam-5755	143	25	m	m	VERB
ejpam-5755	143	26	is	be	AUX
ejpam-5755	143	27	an	an	DET
ejpam-5755	143	28	identity	identity	NOUN
ejpam-5755	143	29	matrix	matrix	NOUN
ejpam-5755	143	30	,	,	PUNCT
ejpam-5755	143	31	|b|	|b|	PROPN
ejpam-5755	143	32	=	=	AUX
ejpam-5755	143	33	diag(|βij	diag(|βij	VERB
ejpam-5755	143	34	|	|	ADV
ejpam-5755	143	35	)	)	PUNCT
ejpam-5755	143	36	,	,	PUNCT
ejpam-5755	143	37	q	q	PUNCT
ejpam-5755	143	38	and	and	CCONJ
ejpam-5755	143	39	q′	q′	NOUN
ejpam-5755	143	40	are	be	AUX
ejpam-5755	143	41	the	the	DET
ejpam-5755	143	42	zero	zero	NUM
ejpam-5755	143	43	-	-	PUNCT
ejpam-5755	143	44	row	row	NOUN
ejpam-5755	143	45	-	-	PUNCT
ejpam-5755	143	46	sum	sum	NOUN
ejpam-5755	143	47	symmetric	symmetric	ADJ
ejpam-5755	143	48	matrices	matrix	NOUN
ejpam-5755	143	49	with	with	ADP
ejpam-5755	143	50	nonnegative	nonnegative	ADJ
ejpam-5755	143	51	off	off	ADP
ejpam-5755	143	52	-	-	PUNCT
ejpam-5755	143	53	diagonal	diagonal	ADJ
ejpam-5755	143	54	elements	element	NOUN
ejpam-5755	143	55	and	and	CCONJ
ejpam-5755	143	56	the	the	DET
ejpam-5755	143	57	diagonal	diagonal	ADJ
ejpam-5755	143	58	elements	element	NOUN
ejpam-5755	143	59	are−	are−	NOUN
ejpam-5755	143	60	{	{	PUNCT
ejpam-5755	143	61	∑	∑	ADV
ejpam-5755	143	62	s∈ni	s∈ni	NOUN
ejpam-5755	143	63	,	,	PUNCT
ejpam-5755	143	64	s	s	PART
ejpam-5755	143	65	̸=j	̸=j	NOUN
ejpam-5755	143	66	ais+	ais+	PUNCT
ejpam-5755	143	67	∑	∑	ADV
ejpam-5755	143	68	s∈nj	s∈nj	PROPN
ejpam-5755	143	69	,	,	PUNCT
ejpam-5755	143	70	s	s	PART
ejpam-5755	143	71	̸=i	̸=i	PROPN
ejpam-5755	143	72	ajs	ajs	PROPN
ejpam-5755	143	73	}	}	PUNCT
ejpam-5755	143	74	at	at	ADP
ejpam-5755	143	75	time	time	NOUN
ejpam-5755	143	76	t	t	NOUN
ejpam-5755	143	77	and	and	CCONJ
ejpam-5755	143	78	impulsive	impulsive	ADJ
ejpam-5755	143	79	time	time	NOUN
ejpam-5755	143	80	tk	tk	PROPN
ejpam-5755	143	81	,	,	PUNCT
ejpam-5755	143	82	respectively	respectively	ADV
ejpam-5755	143	83	.	.	PUNCT
ejpam-5755	144	1	let	let	VERB
ejpam-5755	144	2	βmax	βmax	NOUN
ejpam-5755	144	3	=	=	PUNCT
ejpam-5755	144	4	max{|βij	max{|βij	NOUN
ejpam-5755	144	5	|	|	ADV
ejpam-5755	144	6	}	}	PUNCT
ejpam-5755	144	7	,	,	PUNCT
ejpam-5755	144	8	for	for	ADP
ejpam-5755	144	9	i	i	PRON
ejpam-5755	144	10	,	,	PUNCT
ejpam-5755	144	11	j	j	PROPN
ejpam-5755	144	12	∈	∈	PROPN
ejpam-5755	144	13	in	in	ADP
ejpam-5755	144	14	and	and	CCONJ
ejpam-5755	144	15	∆	∆	PROPN
ejpam-5755	144	16	=	=	SYM
ejpam-5755	144	17	βmax·max	βmax·max	PROPN
ejpam-5755	144	18	{	{	PUNCT
ejpam-5755	144	19	∑	∑	ADV
ejpam-5755	144	20	s∈ni	s∈ni	NOUN
ejpam-5755	144	21	,	,	PUNCT
ejpam-5755	144	22	s	s	PART
ejpam-5755	144	23	̸=j	̸=j	NOUN
ejpam-5755	144	24	ais+	ais+	PUNCT
ejpam-5755	144	25	∑	∑	ADV
ejpam-5755	144	26	s∈nj	s∈nj	PROPN
ejpam-5755	144	27	,	,	PUNCT
ejpam-5755	144	28	s	s	PART
ejpam-5755	144	29	̸=i	̸=i	PROPN
ejpam-5755	144	30	ajs	ajs	PROPN
ejpam-5755	144	31	}	}	PUNCT
ejpam-5755	144	32	.	.	PUNCT
ejpam-5755	145	1	the	the	DET
ejpam-5755	145	2	following	follow	VERB
ejpam-5755	145	3	assumptions	assumption	NOUN
ejpam-5755	145	4	and	and	CCONJ
ejpam-5755	145	5	lemma	lemma	PROPN
ejpam-5755	145	6	are	be	AUX
ejpam-5755	145	7	provided	provide	VERB
ejpam-5755	145	8	in	in	ADP
ejpam-5755	145	9	order	order	NOUN
ejpam-5755	145	10	to	to	PART
ejpam-5755	145	11	obtain	obtain	VERB
ejpam-5755	145	12	our	our	PRON
ejpam-5755	145	13	main	main	ADJ
ejpam-5755	145	14	results	result	NOUN
ejpam-5755	145	15	:	:	PUNCT
ejpam-5755	145	16	(	(	PUNCT
ejpam-5755	145	17	a1	a1	NOUN
ejpam-5755	145	18	)	)	PUNCT
ejpam-5755	145	19	0	0	PUNCT
ejpam-5755	145	20	<	<	X
ejpam-5755	145	21	h	h	X
ejpam-5755	145	22	<	<	X
ejpam-5755	145	23	1	1	NUM
ejpam-5755	145	24	∆	∆	X
ejpam-5755	145	25	,	,	PUNCT
ejpam-5755	145	26	(	(	PUNCT
ejpam-5755	145	27	a2	a2	PROPN
ejpam-5755	145	28	)	)	PUNCT
ejpam-5755	145	29	there	there	PRON
ejpam-5755	145	30	exists	exist	VERB
ejpam-5755	145	31	a	a	DET
ejpam-5755	145	32	constant	constant	ADJ
ejpam-5755	145	33	0	0	NUM
ejpam-5755	145	34	<	<	X
ejpam-5755	145	35	α	α	PROPN
ejpam-5755	145	36	≤	≤	NUM
ejpam-5755	145	37	1	1	NUM
ejpam-5755	146	1	such	such	ADJ
ejpam-5755	146	2	that	that	PRON
ejpam-5755	146	3	(	(	PUNCT
ejpam-5755	146	4	1−	1−	NUM
ejpam-5755	146	5	α)im	α)im	NOUN
ejpam-5755	146	6	+	+	NUM
ejpam-5755	146	7	h|b|q′	h|b|q′	NOUN
ejpam-5755	146	8	+	+	CCONJ
ejpam-5755	146	9	h|b|q′t	h|b|q′t	NOUN
ejpam-5755	146	10	+	+	CCONJ
ejpam-5755	146	11	(	(	PUNCT
ejpam-5755	146	12	h|b|)2q′tq′	h|b|)2q′tq′	NOUN
ejpam-5755	146	13	≤	≤	NOUN
ejpam-5755	146	14	0	0	NUM
ejpam-5755	146	15	.	.	PUNCT
ejpam-5755	147	1	the	the	DET
ejpam-5755	147	2	conditions	condition	NOUN
ejpam-5755	147	3	(	(	PUNCT
ejpam-5755	147	4	a1	a1	NOUN
ejpam-5755	147	5	)	)	PUNCT
ejpam-5755	147	6	and	and	CCONJ
ejpam-5755	147	7	(	(	PUNCT
ejpam-5755	147	8	a2	a2	PROPN
ejpam-5755	147	9	)	)	PUNCT
ejpam-5755	147	10	are	be	AUX
ejpam-5755	147	11	critical	critical	ADJ
ejpam-5755	147	12	to	to	ADP
ejpam-5755	147	13	the	the	DET
ejpam-5755	147	14	results	result	NOUN
ejpam-5755	147	15	as	as	SCONJ
ejpam-5755	147	16	they	they	PRON
ejpam-5755	147	17	ensure	ensure	VERB
ejpam-5755	147	18	stability	stability	NOUN
ejpam-5755	147	19	and	and	CCONJ
ejpam-5755	147	20	convergence	convergence	NOUN
ejpam-5755	147	21	of	of	ADP
ejpam-5755	147	22	the	the	DET
ejpam-5755	147	23	scaled	scaled	ADJ
ejpam-5755	147	24	consensus	consensus	NOUN
ejpam-5755	147	25	protocols	protocol	NOUN
ejpam-5755	147	26	.	.	PUNCT
ejpam-5755	148	1	however	however	ADV
ejpam-5755	148	2	,	,	PUNCT
ejpam-5755	148	3	satisfying	satisfy	VERB
ejpam-5755	148	4	these	these	DET
ejpam-5755	148	5	conditions	condition	NOUN
ejpam-5755	148	6	in	in	ADP
ejpam-5755	148	7	real	real	ADJ
ejpam-5755	148	8	-	-	PUNCT
ejpam-5755	148	9	world	world	NOUN
ejpam-5755	148	10	applications	application	NOUN
ejpam-5755	148	11	presents	present	VERB
ejpam-5755	148	12	several	several	ADJ
ejpam-5755	148	13	practical	practical	ADJ
ejpam-5755	148	14	challenges	challenge	NOUN
ejpam-5755	148	15	and	and	CCONJ
ejpam-5755	148	16	limitations	limitation	NOUN
ejpam-5755	148	17	.	.	PUNCT
ejpam-5755	149	1	1	1	X
ejpam-5755	149	2	.	.	X
ejpam-5755	149	3	condition	condition	NOUN
ejpam-5755	149	4	(	(	PUNCT
ejpam-5755	149	5	a1	a1	PROPN
ejpam-5755	149	6	)	)	PUNCT
ejpam-5755	149	7	imposes	impose	VERB
ejpam-5755	149	8	an	an	DET
ejpam-5755	149	9	upper	upper	ADJ
ejpam-5755	149	10	bound	bind	VERB
ejpam-5755	149	11	on	on	ADP
ejpam-5755	149	12	the	the	DET
ejpam-5755	149	13	step	step	NOUN
ejpam-5755	149	14	size	size	NOUN
ejpam-5755	149	15	h	h	NOUN
ejpam-5755	149	16	,	,	PUNCT
ejpam-5755	149	17	which	which	PRON
ejpam-5755	149	18	depends	depend	VERB
ejpam-5755	149	19	on	on	ADP
ejpam-5755	149	20	the	the	DET
ejpam-5755	149	21	maximum	maximum	ADJ
ejpam-5755	149	22	scaling	scale	VERB
ejpam-5755	149	23	factor	factor	NOUN
ejpam-5755	149	24	βij	βij	NOUN
ejpam-5755	149	25	and	and	CCONJ
ejpam-5755	149	26	the	the	DET
ejpam-5755	149	27	graph	graph	NOUN
ejpam-5755	149	28	topology	topology	NOUN
ejpam-5755	149	29	(	(	PUNCT
ejpam-5755	149	30	e.g.	e.g.	ADV
ejpam-5755	149	31	,	,	PUNCT
ejpam-5755	149	32	adjacency	adjacency	NOUN
ejpam-5755	149	33	matrix	matrix	NOUN
ejpam-5755	149	34	and	and	CCONJ
ejpam-5755	149	35	degree	degree	NOUN
ejpam-5755	149	36	distribution	distribution	NOUN
ejpam-5755	149	37	)	)	PUNCT
ejpam-5755	149	38	.	.	PUNCT
ejpam-5755	150	1	in	in	ADP
ejpam-5755	150	2	dense	dense	ADJ
ejpam-5755	150	3	or	or	CCONJ
ejpam-5755	150	4	highly	highly	ADV
ejpam-5755	150	5	connected	connected	ADJ
ejpam-5755	150	6	networks	network	NOUN
ejpam-5755	150	7	,	,	PUNCT
ejpam-5755	150	8	the	the	DET
ejpam-5755	150	9	maximum	maximum	ADJ
ejpam-5755	150	10	degree	degree	NOUN
ejpam-5755	150	11	can	can	AUX
ejpam-5755	150	12	be	be	AUX
ejpam-5755	150	13	large	large	ADJ
ejpam-5755	150	14	,	,	PUNCT
ejpam-5755	150	15	significantly	significantly	ADV
ejpam-5755	150	16	reducing	reduce	VERB
ejpam-5755	150	17	the	the	DET
ejpam-5755	150	18	permissible	permissible	ADJ
ejpam-5755	150	19	step	step	NOUN
ejpam-5755	150	20	size	size	NOUN
ejpam-5755	150	21	h.	h.	PROPN
ejpam-5755	150	22	this	this	PRON
ejpam-5755	150	23	can	can	AUX
ejpam-5755	150	24	lead	lead	VERB
ejpam-5755	150	25	to	to	ADP
ejpam-5755	150	26	slower	slow	ADJ
ejpam-5755	150	27	convergence	convergence	NOUN
ejpam-5755	150	28	and	and	CCONJ
ejpam-5755	150	29	may	may	AUX
ejpam-5755	150	30	necessitate	necessitate	VERB
ejpam-5755	150	31	frequent	frequent	ADJ
ejpam-5755	150	32	impulsive	impulsive	ADJ
ejpam-5755	150	33	updates	update	NOUN
ejpam-5755	150	34	,	,	PUNCT
ejpam-5755	150	35	which	which	PRON
ejpam-5755	150	36	increase	increase	VERB
ejpam-5755	150	37	communication	communication	NOUN
ejpam-5755	150	38	and	and	CCONJ
ejpam-5755	150	39	computational	computational	ADJ
ejpam-5755	150	40	overhead	overhead	NOUN
ejpam-5755	150	41	.	.	PUNCT
ejpam-5755	151	1	2	2	X
ejpam-5755	151	2	.	.	X
ejpam-5755	151	3	condition	condition	NOUN
ejpam-5755	151	4	(	(	PUNCT
ejpam-5755	151	5	a2	a2	PROPN
ejpam-5755	151	6	)	)	PUNCT
ejpam-5755	151	7	involves	involve	VERB
ejpam-5755	151	8	matrix	matrix	NOUN
ejpam-5755	151	9	inequalities	inequality	NOUN
ejpam-5755	151	10	that	that	PRON
ejpam-5755	151	11	depend	depend	VERB
ejpam-5755	151	12	on	on	ADP
ejpam-5755	151	13	the	the	DET
ejpam-5755	151	14	eigenvalues	eigenvalue	NOUN
ejpam-5755	151	15	of	of	ADP
ejpam-5755	151	16	the	the	DET
ejpam-5755	151	17	system	system	NOUN
ejpam-5755	151	18	’s	’s	PART
ejpam-5755	151	19	laplacian	laplacian	ADJ
ejpam-5755	151	20	matrix	matrix	NOUN
ejpam-5755	151	21	.	.	PUNCT
ejpam-5755	152	1	computing	computing	NOUN
ejpam-5755	152	2	and	and	CCONJ
ejpam-5755	152	3	verifying	verify	VERB
ejpam-5755	152	4	these	these	DET
ejpam-5755	152	5	conditions	condition	NOUN
ejpam-5755	152	6	require	require	VERB
ejpam-5755	152	7	precise	precise	ADJ
ejpam-5755	152	8	knowledge	knowledge	NOUN
ejpam-5755	152	9	of	of	ADP
ejpam-5755	152	10	the	the	DET
ejpam-5755	152	11	network	network	NOUN
ejpam-5755	152	12	’s	’s	PART
ejpam-5755	152	13	topology	topology	NOUN
ejpam-5755	152	14	and	and	CCONJ
ejpam-5755	152	15	weights	weight	NOUN
ejpam-5755	152	16	,	,	PUNCT
ejpam-5755	152	17	which	which	PRON
ejpam-5755	152	18	may	may	AUX
ejpam-5755	152	19	not	not	PART
ejpam-5755	152	20	always	always	ADV
ejpam-5755	152	21	be	be	AUX
ejpam-5755	152	22	available	available	ADJ
ejpam-5755	152	23	or	or	CCONJ
ejpam-5755	152	24	feasible	feasible	ADJ
ejpam-5755	152	25	in	in	ADP
ejpam-5755	152	26	large	large	ADJ
ejpam-5755	152	27	-	-	PUNCT
ejpam-5755	152	28	scale	scale	NOUN
ejpam-5755	152	29	or	or	CCONJ
ejpam-5755	152	30	dynamically	dynamically	ADV
ejpam-5755	152	31	changing	change	VERB
ejpam-5755	152	32	networks	network	NOUN
ejpam-5755	152	33	.	.	PUNCT
ejpam-5755	153	1	furthermore	furthermore	ADV
ejpam-5755	153	2	,	,	PUNCT
ejpam-5755	153	3	satisfying	satisfy	VERB
ejpam-5755	153	4	(	(	PUNCT
ejpam-5755	153	5	1−α)i+	1−α)i+	NUM
ejpam-5755	153	6	h|b|q′	h|b|q′	NOUN
ejpam-5755	153	7	≤	≤	NOUN
ejpam-5755	153	8	0	0	NUM
ejpam-5755	153	9	can	can	AUX
ejpam-5755	153	10	be	be	AUX
ejpam-5755	153	11	restrictive	restrictive	ADJ
ejpam-5755	153	12	in	in	ADP
ejpam-5755	153	13	heterogeneous	heterogeneous	ADJ
ejpam-5755	153	14	networks	network	NOUN
ejpam-5755	153	15	where	where	SCONJ
ejpam-5755	153	16	βij	βij	PROPN
ejpam-5755	153	17	varies	vary	VERB
ejpam-5755	153	18	significantly	significantly	ADV
ejpam-5755	153	19	.	.	PUNCT
ejpam-5755	154	1	in	in	ADP
ejpam-5755	154	2	real	real	ADJ
ejpam-5755	154	3	-	-	PUNCT
ejpam-5755	154	4	world	world	NOUN
ejpam-5755	154	5	applications	application	NOUN
ejpam-5755	154	6	,	,	PUNCT
ejpam-5755	154	7	such	such	ADJ
ejpam-5755	154	8	as	as	ADP
ejpam-5755	154	9	wireless	wireless	ADJ
ejpam-5755	154	10	sensor	sensor	NOUN
ejpam-5755	154	11	networks	network	NOUN
ejpam-5755	154	12	or	or	CCONJ
ejpam-5755	154	13	distributed	distribute	VERB
ejpam-5755	154	14	control	control	NOUN
ejpam-5755	154	15	systems	system	NOUN
ejpam-5755	154	16	,	,	PUNCT
ejpam-5755	154	17	communication	communication	NOUN
ejpam-5755	154	18	delays	delay	NOUN
ejpam-5755	154	19	,	,	PUNCT
ejpam-5755	154	20	packet	packet	NOUN
ejpam-5755	154	21	losses	loss	NOUN
ejpam-5755	154	22	,	,	PUNCT
ejpam-5755	154	23	and	and	CCONJ
ejpam-5755	154	24	resource	resource	NOUN
ejpam-5755	154	25	constraints	constraint	NOUN
ejpam-5755	154	26	add	add	VERB
ejpam-5755	154	27	complexity	complexity	NOUN
ejpam-5755	154	28	.	.	PUNCT
ejpam-5755	155	1	for	for	ADP
ejpam-5755	155	2	example	example	NOUN
ejpam-5755	155	3	:	:	PUNCT
ejpam-5755	155	4	•	•	NUM
ejpam-5755	155	5	delays	delay	NOUN
ejpam-5755	155	6	and	and	CCONJ
ejpam-5755	155	7	losses	loss	NOUN
ejpam-5755	155	8	:	:	PUNCT
ejpam-5755	155	9	even	even	ADV
ejpam-5755	155	10	if	if	SCONJ
ejpam-5755	155	11	h	h	NOUN
ejpam-5755	155	12	is	be	AUX
ejpam-5755	155	13	chosen	choose	VERB
ejpam-5755	155	14	appropriately	appropriately	ADV
ejpam-5755	155	15	,	,	PUNCT
ejpam-5755	155	16	delays	delay	NOUN
ejpam-5755	155	17	in	in	ADP
ejpam-5755	155	18	receiving	receive	VERB
ejpam-5755	155	19	updates	update	NOUN
ejpam-5755	155	20	can	can	AUX
ejpam-5755	155	21	violate	violate	VERB
ejpam-5755	155	22	stability	stability	NOUN
ejpam-5755	155	23	.	.	PUNCT
ejpam-5755	156	1	•	•	NUM
ejpam-5755	156	2	dynamic	dynamic	ADJ
ejpam-5755	156	3	topologies	topology	NOUN
ejpam-5755	156	4	:	:	PUNCT
ejpam-5755	156	5	changes	change	NOUN
ejpam-5755	156	6	in	in	ADP
ejpam-5755	156	7	the	the	DET
ejpam-5755	156	8	network	network	NOUN
ejpam-5755	156	9	structure	structure	NOUN
ejpam-5755	156	10	(	(	PUNCT
ejpam-5755	156	11	e.g.	e.g.	ADV
ejpam-5755	156	12	,	,	PUNCT
ejpam-5755	156	13	node	node	NOUN
ejpam-5755	156	14	or	or	CCONJ
ejpam-5755	156	15	edge	edge	NOUN
ejpam-5755	156	16	failures	failure	NOUN
ejpam-5755	156	17	)	)	PUNCT
ejpam-5755	156	18	can	can	AUX
ejpam-5755	156	19	render	render	VERB
ejpam-5755	156	20	the	the	DET
ejpam-5755	156	21	pre	pre	ADJ
ejpam-5755	156	22	-	-	ADJ
ejpam-5755	156	23	computed	computed	ADJ
ejpam-5755	156	24	conditions	condition	NOUN
ejpam-5755	156	25	invalid	invalid	ADJ
ejpam-5755	156	26	.	.	PUNCT
ejpam-5755	157	1	to	to	PART
ejpam-5755	157	2	address	address	VERB
ejpam-5755	157	3	these	these	DET
ejpam-5755	157	4	challenges	challenge	NOUN
ejpam-5755	157	5	,	,	PUNCT
ejpam-5755	157	6	adaptive	adaptive	ADJ
ejpam-5755	157	7	protocols	protocol	NOUN
ejpam-5755	157	8	that	that	PRON
ejpam-5755	157	9	dynamically	dynamically	ADV
ejpam-5755	157	10	adjust	adjust	VERB
ejpam-5755	157	11	h	h	NOUN
ejpam-5755	157	12	and	and	CCONJ
ejpam-5755	157	13	βij	βij	NOUN
ejpam-5755	157	14	based	base	VERB
ejpam-5755	157	15	on	on	ADP
ejpam-5755	157	16	real	real	ADJ
ejpam-5755	157	17	-	-	PUNCT
ejpam-5755	157	18	time	time	NOUN
ejpam-5755	157	19	network	network	NOUN
ejpam-5755	157	20	conditions	condition	NOUN
ejpam-5755	157	21	could	could	AUX
ejpam-5755	157	22	be	be	AUX
ejpam-5755	157	23	explored	explore	VERB
ejpam-5755	157	24	.	.	PUNCT
ejpam-5755	158	1	additionally	additionally	ADV
ejpam-5755	158	2	,	,	PUNCT
ejpam-5755	158	3	decentralized	decentralized	ADJ
ejpam-5755	158	4	methods	method	NOUN
ejpam-5755	158	5	that	that	PRON
ejpam-5755	158	6	rely	rely	VERB
ejpam-5755	158	7	on	on	ADP
ejpam-5755	158	8	local	local	ADJ
ejpam-5755	158	9	information	information	NOUN
ejpam-5755	158	10	rather	rather	ADV
ejpam-5755	158	11	than	than	ADP
ejpam-5755	158	12	global	global	ADJ
ejpam-5755	158	13	connectivity	connectivity	NOUN
ejpam-5755	158	14	can	can	AUX
ejpam-5755	158	15	improve	improve	VERB
ejpam-5755	158	16	scalability	scalability	NOUN
ejpam-5755	158	17	and	and	CCONJ
ejpam-5755	158	18	robustness	robustness	NOUN
ejpam-5755	158	19	.	.	PUNCT
ejpam-5755	159	1	s.	s.	PROPN
ejpam-5755	159	2	donganont	donganont	PROPN
ejpam-5755	159	3	,	,	PUNCT
ejpam-5755	159	4	u.	u.	NOUN
ejpam-5755	159	5	witthayarat	witthayarat	NOUN
ejpam-5755	159	6	,	,	PUNCT
ejpam-5755	159	7	m.	m.	NOUN
ejpam-5755	159	8	donganont	donganont	PROPN
ejpam-5755	159	9	/	/	SYM
ejpam-5755	159	10	eur	eur	PROPN
ejpam-5755	159	11	.	.	PUNCT
ejpam-5755	160	1	j.	j.	PROPN
ejpam-5755	160	2	pure	pure	PROPN
ejpam-5755	160	3	appl	appl	PROPN
ejpam-5755	160	4	.	.	PROPN
ejpam-5755	160	5	math	math	PROPN
ejpam-5755	160	6	,	,	PUNCT
ejpam-5755	160	7	18	18	NUM
ejpam-5755	160	8	(	(	PUNCT
ejpam-5755	160	9	1	1	NUM
ejpam-5755	160	10	)	)	PUNCT
ejpam-5755	160	11	(	(	PUNCT
ejpam-5755	160	12	2025	2025	NUM
ejpam-5755	160	13	)	)	PUNCT
ejpam-5755	160	14	,	,	PUNCT
ejpam-5755	160	15	5755	5755	NUM
ejpam-5755	160	16	7	7	NUM
ejpam-5755	160	17	of	of	ADP
ejpam-5755	160	18	17	17	NUM
ejpam-5755	160	19	lemma	lemma	PROPN
ejpam-5755	160	20	4	4	NUM
ejpam-5755	160	21	.	.	PUNCT
ejpam-5755	161	1	let	let	VERB
ejpam-5755	161	2	l	l	NOUN
ejpam-5755	161	3	be	be	AUX
ejpam-5755	161	4	the	the	DET
ejpam-5755	161	5	laplacian	laplacian	ADJ
ejpam-5755	161	6	matrix	matrix	NOUN
ejpam-5755	161	7	of	of	ADP
ejpam-5755	161	8	a	a	DET
ejpam-5755	161	9	communication	communication	NOUN
ejpam-5755	161	10	network	network	NOUN
ejpam-5755	161	11	l(g	l(g	PROPN
ejpam-5755	161	12	∪	∪	PROPN
ejpam-5755	161	13	g′	g′	NOUN
ejpam-5755	161	14	)	)	PUNCT
ejpam-5755	161	15	with	with	ADP
ejpam-5755	161	16	m	m	PROPN
ejpam-5755	161	17	nodes	node	NOUN
ejpam-5755	161	18	.	.	PUNCT
ejpam-5755	162	1	define	define	VERB
ejpam-5755	162	2	βmax	βmax	NOUN
ejpam-5755	162	3	=	=	SYM
ejpam-5755	162	4	max	max	PROPN
ejpam-5755	162	5	|βij	|βij	PROPN
ejpam-5755	162	6	|	|	NOUN
ejpam-5755	162	7	,	,	PUNCT
ejpam-5755	162	8	where	where	SCONJ
ejpam-5755	162	9	βij	βij	NOUN
ejpam-5755	162	10	be	be	AUX
ejpam-5755	162	11	a	a	DET
ejpam-5755	162	12	nonzero	nonzero	ADJ
ejpam-5755	162	13	scalar	scalar	ADJ
ejpam-5755	162	14	scale	scale	NOUN
ejpam-5755	162	15	of	of	ADP
ejpam-5755	162	16	edge	edge	NOUN
ejpam-5755	162	17	(	(	PUNCT
ejpam-5755	162	18	i	i	PROPN
ejpam-5755	162	19	,	,	PUNCT
ejpam-5755	162	20	j	j	PROPN
ejpam-5755	162	21	)	)	PUNCT
ejpam-5755	162	22	.	.	PUNCT
ejpam-5755	163	1	assume	assume	VERB
ejpam-5755	163	2	the	the	DET
ejpam-5755	163	3	step	step	NOUN
ejpam-5755	163	4	size	size	NOUN
ejpam-5755	163	5	h	h	NOUN
ejpam-5755	163	6	satisfies	satisfie	NOUN
ejpam-5755	163	7	(	(	PUNCT
ejpam-5755	163	8	a1	a1	NOUN
ejpam-5755	163	9	)	)	PUNCT
ejpam-5755	163	10	and	and	CCONJ
ejpam-5755	163	11	|b|	|b|	PROPN
ejpam-5755	163	12	=	=	PUNCT
ejpam-5755	163	13	diag(|βij	diag(|βij	VERB
ejpam-5755	163	14	|	|	ADV
ejpam-5755	163	15	)	)	PUNCT
ejpam-5755	163	16	,	,	PUNCT
ejpam-5755	163	17	(	(	PUNCT
ejpam-5755	163	18	βij	βij	NOUN
ejpam-5755	163	19	)	)	PUNCT
ejpam-5755	163	20	∈	∈	PROPN
ejpam-5755	163	21	rm	rm	NOUN
ejpam-5755	163	22	.	.	PUNCT
ejpam-5755	164	1	then	then	ADV
ejpam-5755	164	2	,	,	PUNCT
ejpam-5755	164	3	i	i	PRON
ejpam-5755	164	4	m	m	VERB
ejpam-5755	164	5	+	+	PUNCT
ejpam-5755	164	6	h|b|q	h|b|q	ADJ
ejpam-5755	164	7	is	be	AUX
ejpam-5755	164	8	sia	sia	PROPN
ejpam-5755	164	9	,	,	PUNCT
ejpam-5755	164	10	i.e.	i.e.	X
ejpam-5755	164	11	,	,	PUNCT
ejpam-5755	164	12	lim	lim	PROPN
ejpam-5755	164	13	k→∞	k→∞	NOUN
ejpam-5755	165	1	[	[	X
ejpam-5755	165	2	i	i	PRON
ejpam-5755	165	3	m	m	VERB
ejpam-5755	165	4	+	+	CCONJ
ejpam-5755	165	5	h|b|q]k	h|b|q]k	PROPN
ejpam-5755	165	6	=	=	SYM
ejpam-5755	165	7	1myt	1myt	PROPN
ejpam-5755	165	8	if	if	SCONJ
ejpam-5755	165	9	and	and	CCONJ
ejpam-5755	165	10	only	only	ADV
ejpam-5755	165	11	if	if	SCONJ
ejpam-5755	165	12	l(g	l(g	NOUN
ejpam-5755	165	13	∪	∪	ADP
ejpam-5755	165	14	g′	g′	NOUN
ejpam-5755	165	15	)	)	PUNCT
ejpam-5755	165	16	contains	contain	VERB
ejpam-5755	165	17	a	a	DET
ejpam-5755	165	18	spanning	span	VERB
ejpam-5755	165	19	tree	tree	NOUN
ejpam-5755	165	20	.	.	PUNCT
ejpam-5755	166	1	furthermore	furthermore	ADV
ejpam-5755	166	2	,	,	PUNCT
ejpam-5755	166	3	[	[	X
ejpam-5755	166	4	i	i	PRON
ejpam-5755	166	5	m	m	VERB
ejpam-5755	166	6	+	+	CCONJ
ejpam-5755	166	7	h|b|q]t	h|b|q]t	ADJ
ejpam-5755	166	8	y	y	PROPN
ejpam-5755	166	9	=	=	SYM
ejpam-5755	166	10	y	y	PROPN
ejpam-5755	166	11	,	,	PUNCT
ejpam-5755	166	12	1tmy	1tmy	NUM
ejpam-5755	166	13	=	=	SYM
ejpam-5755	166	14	1	1	NUM
ejpam-5755	166	15	,	,	PUNCT
ejpam-5755	166	16	where	where	SCONJ
ejpam-5755	166	17	each	each	DET
ejpam-5755	166	18	element	element	NOUN
ejpam-5755	166	19	of	of	ADP
ejpam-5755	166	20	y	y	PROPN
ejpam-5755	166	21	is	be	AUX
ejpam-5755	166	22	nonnegative	nonnegative	ADJ
ejpam-5755	166	23	.	.	PUNCT
ejpam-5755	167	1	proof	proof	NOUN
ejpam-5755	167	2	.	.	PUNCT
ejpam-5755	168	1	(	(	PUNCT
ejpam-5755	168	2	sufficiency	sufficiency	NOUN
ejpam-5755	168	3	)	)	PUNCT
ejpam-5755	168	4	since	since	SCONJ
ejpam-5755	168	5	0	0	NUM
ejpam-5755	168	6	<	<	X
ejpam-5755	168	7	h	h	X
ejpam-5755	168	8	<	<	X
ejpam-5755	168	9	(	(	PUNCT
ejpam-5755	168	10	∆)−1	∆)−1	PROPN
ejpam-5755	168	11	and	and	CCONJ
ejpam-5755	168	12	using	use	VERB
ejpam-5755	168	13	the	the	DET
ejpam-5755	168	14	fact	fact	NOUN
ejpam-5755	168	15	that	that	SCONJ
ejpam-5755	168	16	l	l	NOUN
ejpam-5755	168	17	=	=	SYM
ejpam-5755	168	18	−q	−q	NOUN
ejpam-5755	168	19	,	,	PUNCT
ejpam-5755	168	20	one	one	NUM
ejpam-5755	168	21	obtains	obtain	VERB
ejpam-5755	168	22	i	i	PRON
ejpam-5755	168	23	m	m	VERB
ejpam-5755	168	24	+	+	ADV
ejpam-5755	168	25	h|b|q	h|b|q	PRON
ejpam-5755	168	26	=	=	PUNCT
ejpam-5755	169	1	i	i	NOUN
ejpam-5755	169	2	m	m	VERB
ejpam-5755	169	3	−	−	NOUN
ejpam-5755	169	4	h|b|l	h|b|l	PROPN
ejpam-5755	169	5	=	=	SYM
ejpam-5755	169	6	(	(	PUNCT
ejpam-5755	169	7	i	i	NOUN
ejpam-5755	169	8	m	m	VERB
ejpam-5755	169	9	−	−	NOUN
ejpam-5755	169	10	h|b|d	h|b|d	NOUN
ejpam-5755	169	11	)	)	PUNCT
ejpam-5755	170	1	+	+	CCONJ
ejpam-5755	170	2	h|b|a	h|b|a	NOUN
ejpam-5755	170	3	is	be	AUX
ejpam-5755	170	4	a	a	DET
ejpam-5755	170	5	stochastic	stochastic	ADJ
ejpam-5755	170	6	matrix	matrix	NOUN
ejpam-5755	170	7	with	with	ADP
ejpam-5755	170	8	positive	positive	ADJ
ejpam-5755	170	9	diagonal	diagonal	ADJ
ejpam-5755	170	10	entries	entry	NOUN
ejpam-5755	170	11	,	,	PUNCT
ejpam-5755	170	12	where	where	SCONJ
ejpam-5755	170	13	d	d	NOUN
ejpam-5755	170	14	=	=	PUNCT
ejpam-5755	170	15	diag(d1	diag(d1	NOUN
ejpam-5755	170	16	,	,	PUNCT
ejpam-5755	170	17	.	.	PUNCT
ejpam-5755	170	18	.	.	PUNCT
ejpam-5755	171	1	.	.	PUNCT
ejpam-5755	172	1	,	,	PUNCT
ejpam-5755	172	2	dm	dm	PROPN
ejpam-5755	172	3	)	)	PUNCT
ejpam-5755	172	4	and	and	CCONJ
ejpam-5755	172	5	a	a	PRON
ejpam-5755	172	6	are	be	AUX
ejpam-5755	172	7	the	the	DET
ejpam-5755	172	8	degree	degree	NOUN
ejpam-5755	172	9	matrix	matrix	NOUN
ejpam-5755	172	10	and	and	CCONJ
ejpam-5755	172	11	adjacency	adjacency	NOUN
ejpam-5755	172	12	matrix	matrix	NOUN
ejpam-5755	172	13	of	of	ADP
ejpam-5755	172	14	l(g	l(g	PROPN
ejpam-5755	172	15	∪	∪	ADJ
ejpam-5755	172	16	g′	g′	NOUN
ejpam-5755	172	17	)	)	PUNCT
ejpam-5755	172	18	,	,	PUNCT
ejpam-5755	172	19	respectively	respectively	ADV
ejpam-5755	172	20	.	.	PUNCT
ejpam-5755	173	1	obviously	obviously	ADV
ejpam-5755	173	2	,	,	PUNCT
ejpam-5755	173	3	for	for	ADP
ejpam-5755	173	4	all	all	DET
ejpam-5755	173	5	r	r	NOUN
ejpam-5755	173	6	,	,	PUNCT
ejpam-5755	173	7	s	s	VERB
ejpam-5755	173	8	∈	∈	PROPN
ejpam-5755	174	1	i	i	PRON
ejpam-5755	174	2	m	m	VERB
ejpam-5755	174	3	;	;	PUNCT
ejpam-5755	174	4	r	r	NOUN
ejpam-5755	174	5	̸=	̸=	PROPN
ejpam-5755	174	6	s	s	NUM
ejpam-5755	174	7	,	,	PUNCT
ejpam-5755	174	8	the	the	DET
ejpam-5755	174	9	(	(	PUNCT
ejpam-5755	174	10	r	r	NOUN
ejpam-5755	174	11	,	,	PUNCT
ejpam-5755	174	12	s)th	s)th	PROPN
ejpam-5755	174	13	entry	entry	NOUN
ejpam-5755	174	14	of	of	ADP
ejpam-5755	174	15	i	i	PRON
ejpam-5755	174	16	m	m	PROPN
ejpam-5755	174	17	−h|b|l	−h|b|l	NOUN
ejpam-5755	174	18	is	be	AUX
ejpam-5755	174	19	positive	positive	ADJ
ejpam-5755	174	20	if	if	SCONJ
ejpam-5755	175	1	and	and	CCONJ
ejpam-5755	175	2	only	only	ADV
ejpam-5755	175	3	if	if	SCONJ
ejpam-5755	175	4	ars	ar	NOUN
ejpam-5755	175	5	>	>	X
ejpam-5755	175	6	0	0	X
ejpam-5755	175	7	.	.	PUNCT
ejpam-5755	176	1	then	then	ADV
ejpam-5755	176	2	,	,	PUNCT
ejpam-5755	176	3	l(g	l(g	NOUN
ejpam-5755	176	4	∪	∪	ADP
ejpam-5755	176	5	g′	g′	NOUN
ejpam-5755	176	6	)	)	PUNCT
ejpam-5755	176	7	is	be	AUX
ejpam-5755	176	8	the	the	DET
ejpam-5755	176	9	graph	graph	NOUN
ejpam-5755	176	10	associated	associate	VERB
ejpam-5755	176	11	with	with	ADP
ejpam-5755	176	12	im−h|b|l	im−h|b|l	NOUN
ejpam-5755	176	13	.	.	PUNCT
ejpam-5755	177	1	combining	combine	VERB
ejpam-5755	177	2	lemma	lemma	PROPN
ejpam-5755	177	3	2	2	PROPN
ejpam-5755	177	4	and	and	CCONJ
ejpam-5755	177	5	lemma	lemma	PROPN
ejpam-5755	177	6	3	3	NUM
ejpam-5755	177	7	,	,	PUNCT
ejpam-5755	177	8	gives	give	VERB
ejpam-5755	177	9	lim	lim	PROPN
ejpam-5755	177	10	k→∞	k→∞	NOUN
ejpam-5755	178	1	[	[	X
ejpam-5755	178	2	im−h|b|l]k	im−h|b|l]k	NOUN
ejpam-5755	178	3	=	=	SYM
ejpam-5755	178	4	lim	lim	PROPN
ejpam-5755	178	5	k→∞	k→∞	NOUN
ejpam-5755	179	1	[	[	X
ejpam-5755	179	2	i	i	PRON
ejpam-5755	179	3	m	m	VERB
ejpam-5755	179	4	+	+	CCONJ
ejpam-5755	179	5	h|b|q]k	h|b|q]k	PROPN
ejpam-5755	179	6	=	=	SYM
ejpam-5755	179	7	1myt	1myt	PROPN
ejpam-5755	179	8	,	,	PUNCT
ejpam-5755	179	9	when	when	SCONJ
ejpam-5755	179	10	g	g	PROPN
ejpam-5755	179	11	has	have	VERB
ejpam-5755	179	12	a	a	DET
ejpam-5755	179	13	spanning	span	VERB
ejpam-5755	179	14	tree	tree	NOUN
ejpam-5755	179	15	,	,	PUNCT
ejpam-5755	179	16	where	where	SCONJ
ejpam-5755	179	17	y	y	PROPN
ejpam-5755	179	18	is	be	AUX
ejpam-5755	179	19	nonnegative	nonnegative	ADJ
ejpam-5755	179	20	vector	vector	NOUN
ejpam-5755	179	21	.	.	PUNCT
ejpam-5755	180	1	moreover	moreover	ADV
ejpam-5755	180	2	,	,	PUNCT
ejpam-5755	180	3	y	y	PROPN
ejpam-5755	180	4	satisfies	satisfy	VERB
ejpam-5755	180	5	[	[	X
ejpam-5755	180	6	i	i	PRON
ejpam-5755	180	7	m	m	VERB
ejpam-5755	180	8	+	+	CCONJ
ejpam-5755	180	9	h|b|q]t	h|b|q]t	ADJ
ejpam-5755	180	10	y	y	PROPN
ejpam-5755	180	11	=	=	SYM
ejpam-5755	180	12	y	y	PROPN
ejpam-5755	180	13	,	,	PUNCT
ejpam-5755	180	14	1tmy	1tmy	NUM
ejpam-5755	180	15	=	=	SYM
ejpam-5755	180	16	1	1	NUM
ejpam-5755	180	17	.	.	PUNCT
ejpam-5755	181	1	(	(	PUNCT
ejpam-5755	181	2	necessary	necessary	ADJ
ejpam-5755	181	3	)	)	PUNCT
ejpam-5755	181	4	from	from	ADP
ejpam-5755	181	5	lemma	lemma	PROPN
ejpam-5755	181	6	2	2	NUM
ejpam-5755	181	7	,	,	PUNCT
ejpam-5755	181	8	if	if	SCONJ
ejpam-5755	181	9	l(g	l(g	NOUN
ejpam-5755	181	10	∪	∪	ADP
ejpam-5755	181	11	g′	g′	NOUN
ejpam-5755	181	12	)	)	PUNCT
ejpam-5755	181	13	does	do	AUX
ejpam-5755	181	14	not	not	PART
ejpam-5755	181	15	contain	contain	VERB
ejpam-5755	181	16	a	a	DET
ejpam-5755	181	17	spanning	span	VERB
ejpam-5755	181	18	tree	tree	NOUN
ejpam-5755	181	19	,	,	PUNCT
ejpam-5755	181	20	the	the	DET
ejpam-5755	181	21	algebraic	algebraic	ADJ
ejpam-5755	181	22	multiplicity	multiplicity	NOUN
ejpam-5755	181	23	of	of	ADP
ejpam-5755	181	24	eigenvalue	eigenvalue	PROPN
ejpam-5755	181	25	λ	λ	PROPN
ejpam-5755	181	26	=	=	SYM
ejpam-5755	181	27	1	1	NUM
ejpam-5755	181	28	of	of	ADP
ejpam-5755	181	29	im−h|b|l	im−h|b|l	ADJ
ejpam-5755	181	30	ism	ism	NOUN
ejpam-5755	181	31	>	>	X
ejpam-5755	181	32	1	1	NUM
ejpam-5755	181	33	.	.	PUNCT
ejpam-5755	182	1	then	then	ADV
ejpam-5755	182	2	,	,	PUNCT
ejpam-5755	182	3	the	the	DET
ejpam-5755	182	4	rank	rank	NOUN
ejpam-5755	182	5	of	of	ADP
ejpam-5755	182	6	lim	lim	PROPN
ejpam-5755	182	7	k→∞	k→∞	NOUN
ejpam-5755	183	1	[	[	X
ejpam-5755	183	2	im−h|b|l]k	im−h|b|l]k	NOUN
ejpam-5755	183	3	is	be	AUX
ejpam-5755	183	4	not	not	PART
ejpam-5755	183	5	equal	equal	ADJ
ejpam-5755	183	6	to	to	ADP
ejpam-5755	183	7	1	1	NUM
ejpam-5755	183	8	.	.	PUNCT
ejpam-5755	184	1	this	this	PRON
ejpam-5755	184	2	implies	imply	VERB
ejpam-5755	184	3	that	that	SCONJ
ejpam-5755	184	4	lim	lim	PROPN
ejpam-5755	184	5	k→∞	k→∞	NOUN
ejpam-5755	185	1	[	[	X
ejpam-5755	185	2	i	i	PRON
ejpam-5755	185	3	m	m	VERB
ejpam-5755	185	4	+	+	CCONJ
ejpam-5755	185	5	h|b|q]k	h|b|q]k	PROPN
ejpam-5755	185	6	=	=	SYM
ejpam-5755	185	7	lim	lim	PROPN
ejpam-5755	185	8	k→∞	k→∞	NOUN
ejpam-5755	186	1	[	[	X
ejpam-5755	186	2	i	i	NOUN
ejpam-5755	186	3	m	m	VERB
ejpam-5755	186	4	−	−	NOUN
ejpam-5755	186	5	h|b|l]k	h|b|l]k	NOUN
ejpam-5755	186	6	̸=	̸=	PROPN
ejpam-5755	186	7	1myt	1myt	NUM
ejpam-5755	186	8	.	.	PUNCT
ejpam-5755	187	1	therefore	therefore	ADV
ejpam-5755	187	2	,	,	PUNCT
ejpam-5755	187	3	i	i	PRON
ejpam-5755	187	4	m	m	VERB
ejpam-5755	187	5	+	+	PUNCT
ejpam-5755	187	6	h|b|q	h|b|q	ADJ
ejpam-5755	187	7	is	be	AUX
ejpam-5755	187	8	not	not	PART
ejpam-5755	187	9	sia	sia	PROPN
ejpam-5755	187	10	.	.	PUNCT
ejpam-5755	188	1	the	the	DET
ejpam-5755	188	2	following	follow	VERB
ejpam-5755	188	3	theorem	theorem	NOUN
ejpam-5755	188	4	is	be	AUX
ejpam-5755	188	5	the	the	DET
ejpam-5755	188	6	scaled	scale	VERB
ejpam-5755	188	7	consensus	consensus	NOUN
ejpam-5755	188	8	results	result	NOUN
ejpam-5755	188	9	based	base	VERB
ejpam-5755	188	10	on	on	ADP
ejpam-5755	188	11	the	the	DET
ejpam-5755	188	12	undirected	undirected	ADJ
ejpam-5755	188	13	network	network	NOUN
ejpam-5755	188	14	.	.	PUNCT
ejpam-5755	189	1	theorem	theorem	NOUN
ejpam-5755	189	2	1	1	NUM
ejpam-5755	189	3	.	.	PUNCT
ejpam-5755	190	1	let	let	VERB
ejpam-5755	190	2	g	g	PRON
ejpam-5755	190	3	be	be	AUX
ejpam-5755	190	4	a	a	DET
ejpam-5755	190	5	communication	communication	NOUN
ejpam-5755	190	6	network	network	NOUN
ejpam-5755	190	7	of	of	ADP
ejpam-5755	190	8	the	the	DET
ejpam-5755	190	9	multi	multi	ADJ
ejpam-5755	190	10	-	-	ADJ
ejpam-5755	190	11	agent	agent	ADJ
ejpam-5755	190	12	system	system	NOUN
ejpam-5755	190	13	(	(	PUNCT
ejpam-5755	190	14	2.1	2.1	NUM
ejpam-5755	190	15	)	)	PUNCT
ejpam-5755	190	16	and	and	CCONJ
ejpam-5755	190	17	βij	βij	PROPN
ejpam-5755	190	18	̸=	̸=	PROPN
ejpam-5755	190	19	0	0	NUM
ejpam-5755	190	20	be	be	AUX
ejpam-5755	190	21	a	a	DET
ejpam-5755	190	22	scalar	scalar	ADJ
ejpam-5755	190	23	scale	scale	NOUN
ejpam-5755	190	24	of	of	ADP
ejpam-5755	190	25	edge	edge	NOUN
ejpam-5755	190	26	(	(	PUNCT
ejpam-5755	190	27	i	i	PROPN
ejpam-5755	190	28	,	,	PUNCT
ejpam-5755	190	29	j	j	PROPN
ejpam-5755	190	30	)	)	PUNCT
ejpam-5755	190	31	.	.	PUNCT
ejpam-5755	191	1	assume	assume	VERB
ejpam-5755	191	2	that	that	SCONJ
ejpam-5755	191	3	the	the	DET
ejpam-5755	191	4	assumptions	assumption	NOUN
ejpam-5755	191	5	(	(	PUNCT
ejpam-5755	191	6	a1	a1	NOUN
ejpam-5755	191	7	)	)	PUNCT
ejpam-5755	191	8	and	and	CCONJ
ejpam-5755	191	9	(	(	PUNCT
ejpam-5755	191	10	a2	a2	NOUN
ejpam-5755	191	11	)	)	PUNCT
ejpam-5755	191	12	hold	hold	NOUN
ejpam-5755	191	13	.	.	PUNCT
ejpam-5755	192	1	then	then	ADV
ejpam-5755	192	2	,	,	PUNCT
ejpam-5755	192	3	the	the	DET
ejpam-5755	192	4	multi	multi	ADJ
ejpam-5755	192	5	-	-	ADJ
ejpam-5755	192	6	agent	agent	ADJ
ejpam-5755	192	7	system	system	NOUN
ejpam-5755	192	8	(	(	PUNCT
ejpam-5755	192	9	2.1	2.1	NUM
ejpam-5755	192	10	)	)	PUNCT
ejpam-5755	192	11	with	with	ADP
ejpam-5755	192	12	the	the	DET
ejpam-5755	192	13	protocol	protocol	NOUN
ejpam-5755	192	14	(	(	PUNCT
ejpam-5755	192	15	3.1	3.1	NUM
ejpam-5755	192	16	)	)	PUNCT
ejpam-5755	192	17	reaches	reach	VERB
ejpam-5755	192	18	scaled	scale	VERB
ejpam-5755	192	19	consensus	consensus	NOUN
ejpam-5755	192	20	on	on	ADP
ejpam-5755	192	21	edge	edge	NOUN
ejpam-5755	192	22	dynamics	dynamic	NOUN
ejpam-5755	192	23	if	if	SCONJ
ejpam-5755	192	24	and	and	CCONJ
ejpam-5755	192	25	only	only	ADV
ejpam-5755	192	26	if	if	SCONJ
ejpam-5755	192	27	the	the	DET
ejpam-5755	192	28	line	line	NOUN
ejpam-5755	192	29	graph	graph	NOUN
ejpam-5755	192	30	l(g	l(g	PROPN
ejpam-5755	192	31	∪	∪	ADJ
ejpam-5755	192	32	g′	g′	NOUN
ejpam-5755	192	33	)	)	PUNCT
ejpam-5755	192	34	is	be	AUX
ejpam-5755	192	35	connected	connect	VERB
ejpam-5755	192	36	.	.	PUNCT
ejpam-5755	193	1	proof	proof	NOUN
ejpam-5755	193	2	.	.	PUNCT
ejpam-5755	194	1	(	(	PUNCT
ejpam-5755	194	2	sufficiency	sufficiency	NOUN
ejpam-5755	194	3	)	)	PUNCT
ejpam-5755	194	4	let	let	VERB
ejpam-5755	194	5	y	y	PROPN
ejpam-5755	194	6	=	=	SYM
ejpam-5755	194	7	(	(	PUNCT
ejpam-5755	194	8	βijxij	βijxij	NOUN
ejpam-5755	194	9	)	)	PUNCT
ejpam-5755	194	10	∈	∈	PROPN
ejpam-5755	194	11	rm	rm	PROPN
ejpam-5755	194	12	,	,	PUNCT
ejpam-5755	194	13	where	where	SCONJ
ejpam-5755	194	14	yij	yij	NOUN
ejpam-5755	194	15	=	=	PUNCT
ejpam-5755	194	16	βijxij	βijxij	NOUN
ejpam-5755	194	17	∈	∈	PROPN
ejpam-5755	194	18	r	r	NOUN
ejpam-5755	194	19	for	for	ADP
ejpam-5755	194	20	all	all	PRON
ejpam-5755	194	21	(	(	PUNCT
ejpam-5755	194	22	i	i	PROPN
ejpam-5755	194	23	,	,	PUNCT
ejpam-5755	194	24	j	j	PROPN
ejpam-5755	194	25	)	)	PUNCT
ejpam-5755	194	26	∈	∈	PROPN
ejpam-5755	194	27	e	e	X
ejpam-5755	194	28	.	.	PUNCT
ejpam-5755	195	1	since	since	SCONJ
ejpam-5755	195	2	l(g	l(g	NOUN
ejpam-5755	195	3	∪	∪	ADP
ejpam-5755	195	4	g′	g′	NOUN
ejpam-5755	195	5	)	)	PUNCT
ejpam-5755	195	6	is	be	AUX
ejpam-5755	195	7	connected	connect	VERB
ejpam-5755	195	8	,	,	PUNCT
ejpam-5755	195	9	one	one	NUM
ejpam-5755	195	10	obtains	obtain	VERB
ejpam-5755	195	11	that	that	DET
ejpam-5755	195	12	ȳ	ȳ	NOUN
ejpam-5755	195	13	=	=	PUNCT
ejpam-5755	195	14	ave(y	ave(y	ADJ
ejpam-5755	195	15	)	)	PUNCT
ejpam-5755	195	16	=	=	SYM
ejpam-5755	195	17	1	1	NUM
ejpam-5755	195	18	m	m	NOUN
ejpam-5755	195	19	∑	∑	PUNCT
ejpam-5755	195	20	(	(	PUNCT
ejpam-5755	195	21	i	i	PROPN
ejpam-5755	195	22	,	,	PUNCT
ejpam-5755	195	23	j)∈e	j)∈e	PROPN
ejpam-5755	195	24	yij	yij	NOUN
ejpam-5755	195	25	is	be	AUX
ejpam-5755	195	26	invariant	invariant	ADJ
ejpam-5755	195	27	quantity	quantity	NOUN
ejpam-5755	195	28	i.e.	i.e.	X
ejpam-5755	195	29	,	,	PUNCT
ejpam-5755	195	30	ȳ(t	ȳ(t	NOUN
ejpam-5755	195	31	)	)	PUNCT
ejpam-5755	195	32	=	=	SYM
ejpam-5755	195	33	ȳ(0	ȳ(0	NOUN
ejpam-5755	195	34	)	)	PUNCT
ejpam-5755	195	35	=	=	SYM
ejpam-5755	195	36	1	1	NUM
ejpam-5755	195	37	m	m	NOUN
ejpam-5755	195	38	∑	∑	PUNCT
ejpam-5755	195	39	(	(	PUNCT
ejpam-5755	195	40	i	i	PROPN
ejpam-5755	195	41	,	,	PUNCT
ejpam-5755	195	42	j)∈e	j)∈e	PROPN
ejpam-5755	195	43	yij(0	yij(0	NOUN
ejpam-5755	195	44	)	)	PUNCT
ejpam-5755	195	45	.	.	PUNCT
ejpam-5755	196	1	the	the	DET
ejpam-5755	196	2	invariant	invariant	PROPN
ejpam-5755	196	3	of	of	ADP
ejpam-5755	196	4	ȳ	ȳ	PROPN
ejpam-5755	196	5	allows	allow	VERB
ejpam-5755	196	6	decomposition	decomposition	NOUN
ejpam-5755	196	7	of	of	ADP
ejpam-5755	196	8	yij	yij	NOUN
ejpam-5755	196	9	for	for	ADP
ejpam-5755	196	10	(	(	PUNCT
ejpam-5755	196	11	i	i	PROPN
ejpam-5755	196	12	,	,	PUNCT
ejpam-5755	196	13	j	j	PROPN
ejpam-5755	196	14	)	)	PUNCT
ejpam-5755	196	15	∈	∈	PROPN
ejpam-5755	196	16	e	e	NOUN
ejpam-5755	196	17	as	as	ADP
ejpam-5755	196	18	in	in	ADP
ejpam-5755	196	19	the	the	DET
ejpam-5755	196	20	following	follow	VERB
ejpam-5755	196	21	equation	equation	NOUN
ejpam-5755	196	22	:	:	PUNCT
ejpam-5755	196	23	ξij(t	ξij(t	PROPN
ejpam-5755	196	24	)	)	PUNCT
ejpam-5755	196	25	=	=	SYM
ejpam-5755	196	26	yij(t)−	yij(t)−	PROPN
ejpam-5755	196	27	ȳ	ȳ	PROPN
ejpam-5755	196	28	,	,	PUNCT
ejpam-5755	196	29	t	t	PROPN
ejpam-5755	196	30	∈	∈	PROPN
ejpam-5755	196	31	(	(	PUNCT
ejpam-5755	196	32	tk−1	tk−1	PROPN
ejpam-5755	196	33	,	,	PUNCT
ejpam-5755	196	34	tk	tk	PROPN
ejpam-5755	196	35	]	]	X
ejpam-5755	196	36	,	,	PUNCT
ejpam-5755	196	37	ξij(t	ξij(t	PROPN
ejpam-5755	196	38	+	+	NUM
ejpam-5755	196	39	k	k	PROPN
ejpam-5755	196	40	)	)	PUNCT
ejpam-5755	197	1	=	=	SYM
ejpam-5755	197	2	yij(t	yij(t	PROPN
ejpam-5755	198	1	+	+	CCONJ
ejpam-5755	198	2	k	k	PROPN
ejpam-5755	198	3	)	)	PUNCT
ejpam-5755	199	1	−	−	PROPN
ejpam-5755	199	2	ȳ	ȳ	PROPN
ejpam-5755	199	3	and	and	CCONJ
ejpam-5755	199	4	ξij(t	ξij(t	PROPN
ejpam-5755	199	5	−	−	PROPN
ejpam-5755	199	6	k	k	PROPN
ejpam-5755	199	7	)	)	PUNCT
ejpam-5755	200	1	=	=	SYM
ejpam-5755	200	2	ξij(tk	ξij(tk	NOUN
ejpam-5755	200	3	)	)	PUNCT
ejpam-5755	200	4	,	,	PUNCT
ejpam-5755	200	5	for	for	ADP
ejpam-5755	200	6	all	all	PRON
ejpam-5755	200	7	(	(	PUNCT
ejpam-5755	200	8	i	i	PROPN
ejpam-5755	200	9	,	,	PUNCT
ejpam-5755	200	10	j	j	PROPN
ejpam-5755	200	11	)	)	PUNCT
ejpam-5755	200	12	∈	∈	PROPN
ejpam-5755	200	13	e	e	NOUN
ejpam-5755	200	14	,	,	PUNCT
ejpam-5755	200	15	with	with	ADP
ejpam-5755	200	16	initial	initial	ADJ
ejpam-5755	200	17	conditions	condition	NOUN
ejpam-5755	200	18	y(t0	y(t0	NOUN
ejpam-5755	200	19	)	)	PUNCT
ejpam-5755	201	1	=	=	SYM
ejpam-5755	201	2	y(0	y(0	PROPN
ejpam-5755	201	3	)	)	PUNCT
ejpam-5755	201	4	=	=	PUNCT
ejpam-5755	201	5	(	(	PUNCT
ejpam-5755	201	6	yij(0	yij(0	PROPN
ejpam-5755	201	7	)	)	PUNCT
ejpam-5755	201	8	)	)	PUNCT
ejpam-5755	202	1	t	t	NOUN
ejpam-5755	202	2	,	,	PUNCT
ejpam-5755	202	3	where	where	SCONJ
ejpam-5755	202	4	ξ	ξ	X
ejpam-5755	202	5	=	=	SYM
ejpam-5755	202	6	(	(	PUNCT
ejpam-5755	202	7	ξij	ξij	NOUN
ejpam-5755	202	8	)	)	PUNCT
ejpam-5755	202	9	t	t	PROPN
ejpam-5755	202	10	,	,	PUNCT
ejpam-5755	202	11	(	(	PUNCT
ejpam-5755	202	12	i	i	PROPN
ejpam-5755	202	13	,	,	PUNCT
ejpam-5755	202	14	j	j	PROPN
ejpam-5755	202	15	)	)	PUNCT
ejpam-5755	202	16	∈	∈	PROPN
ejpam-5755	202	17	e	e	NOUN
ejpam-5755	202	18	is	be	AUX
ejpam-5755	202	19	the	the	DET
ejpam-5755	202	20	error	error	NOUN
ejpam-5755	202	21	vector	vector	NOUN
ejpam-5755	202	22	or	or	CCONJ
ejpam-5755	202	23	disagreement	disagreement	NOUN
ejpam-5755	202	24	s.	s.	PROPN
ejpam-5755	202	25	donganont	donganont	PROPN
ejpam-5755	202	26	,	,	PUNCT
ejpam-5755	202	27	u.	u.	NOUN
ejpam-5755	202	28	witthayarat	witthayarat	NOUN
ejpam-5755	202	29	,	,	PUNCT
ejpam-5755	202	30	m.	m.	NOUN
ejpam-5755	202	31	donganont	donganont	PROPN
ejpam-5755	202	32	/	/	SYM
ejpam-5755	202	33	eur	eur	PROPN
ejpam-5755	202	34	.	.	PUNCT
ejpam-5755	203	1	j.	j.	PROPN
ejpam-5755	203	2	pure	pure	PROPN
ejpam-5755	203	3	appl	appl	PROPN
ejpam-5755	203	4	.	.	PROPN
ejpam-5755	203	5	math	math	PROPN
ejpam-5755	203	6	,	,	PUNCT
ejpam-5755	203	7	18	18	NUM
ejpam-5755	203	8	(	(	PUNCT
ejpam-5755	203	9	1	1	NUM
ejpam-5755	203	10	)	)	PUNCT
ejpam-5755	203	11	(	(	PUNCT
ejpam-5755	203	12	2025	2025	NUM
ejpam-5755	203	13	)	)	PUNCT
ejpam-5755	203	14	,	,	PUNCT
ejpam-5755	203	15	5755	5755	NUM
ejpam-5755	203	16	8	8	NUM
ejpam-5755	203	17	of	of	ADP
ejpam-5755	203	18	17	17	NUM
ejpam-5755	203	19	vector	vector	NOUN
ejpam-5755	203	20	.	.	PUNCT
ejpam-5755	204	1	thus	thus	ADV
ejpam-5755	204	2	,	,	PUNCT
ejpam-5755	204	3	{	{	PUNCT
ejpam-5755	204	4	ξ̇(t	ξ̇(t	X
ejpam-5755	204	5	)	)	PUNCT
ejpam-5755	204	6	=	=	PUNCT
ejpam-5755	204	7	|b|qξ(t	|b|qξ(t	PROPN
ejpam-5755	204	8	)	)	PUNCT
ejpam-5755	204	9	,	,	PUNCT
ejpam-5755	204	10	t	t	PROPN
ejpam-5755	204	11	̸=	̸=	PROPN
ejpam-5755	204	12	tk	tk	PROPN
ejpam-5755	204	13	ξ(t+k	ξ(t+k	PROPN
ejpam-5755	204	14	)	)	PUNCT
ejpam-5755	204	15	=	=	PUNCT
ejpam-5755	205	1	[	[	X
ejpam-5755	205	2	i	i	PRON
ejpam-5755	205	3	m	m	VERB
ejpam-5755	205	4	+	+	X
ejpam-5755	205	5	h|b|q′]ξ(tk	h|b|q′]ξ(tk	NOUN
ejpam-5755	205	6	)	)	PUNCT
ejpam-5755	205	7	,	,	PUNCT
ejpam-5755	205	8	t	t	PROPN
ejpam-5755	205	9	=	=	SYM
ejpam-5755	205	10	tk	tk	PROPN
ejpam-5755	205	11	,	,	PUNCT
ejpam-5755	205	12	k	k	PROPN
ejpam-5755	205	13	∈	∈	PROPN
ejpam-5755	205	14	n.	n.	NOUN
ejpam-5755	205	15	(	(	PUNCT
ejpam-5755	205	16	3.6	3.6	NUM
ejpam-5755	205	17	)	)	PUNCT
ejpam-5755	205	18	consider	consider	VERB
ejpam-5755	205	19	the	the	DET
ejpam-5755	205	20	lyapunov	lyapunov	ADJ
ejpam-5755	205	21	function	function	NOUN
ejpam-5755	205	22	candidate	candidate	NOUN
ejpam-5755	205	23	as	as	SCONJ
ejpam-5755	205	24	follows	follow	VERB
ejpam-5755	205	25	:	:	PUNCT
ejpam-5755	205	26	v	v	X
ejpam-5755	205	27	(	(	PUNCT
ejpam-5755	205	28	ξ	ξ	NOUN
ejpam-5755	205	29	)	)	PUNCT
ejpam-5755	205	30	=	=	SYM
ejpam-5755	205	31	ξt	ξt	X
ejpam-5755	206	1	ξ	ξ	X
ejpam-5755	206	2	.	.	PUNCT
ejpam-5755	207	1	let	let	VERB
ejpam-5755	207	2	v	v	NOUN
ejpam-5755	207	3	(	(	PUNCT
ejpam-5755	207	4	ξ	ξ	NOUN
ejpam-5755	207	5	)	)	PUNCT
ejpam-5755	208	1	=	=	NOUN
ejpam-5755	208	2	:	:	PUNCT
ejpam-5755	208	3	v	v	NUM
ejpam-5755	208	4	(	(	PUNCT
ejpam-5755	208	5	ξ(t	ξ(t	NOUN
ejpam-5755	208	6	)	)	PUNCT
ejpam-5755	208	7	)	)	PUNCT
ejpam-5755	208	8	.	.	PUNCT
ejpam-5755	209	1	since	since	SCONJ
ejpam-5755	209	2	l(g	l(g	NOUN
ejpam-5755	209	3	∪	∪	ADP
ejpam-5755	209	4	g′	g′	NOUN
ejpam-5755	209	5	)	)	PUNCT
ejpam-5755	209	6	is	be	AUX
ejpam-5755	209	7	connected	connect	VERB
ejpam-5755	209	8	,	,	PUNCT
ejpam-5755	209	9	by	by	ADP
ejpam-5755	209	10	lemma	lemma	PROPN
ejpam-5755	209	11	1	1	NUM
ejpam-5755	209	12	[	[	X
ejpam-5755	209	13	10	10	NUM
ejpam-5755	209	14	]	]	PUNCT
ejpam-5755	209	15	,	,	PUNCT
ejpam-5755	209	16	we	we	PRON
ejpam-5755	209	17	have	have	VERB
ejpam-5755	209	18	l̂	l̂	VERB
ejpam-5755	209	19	=	=	SYM
ejpam-5755	209	20	sym(l	sym(l	PROPN
ejpam-5755	209	21	)	)	PUNCT
ejpam-5755	209	22	=	=	SYM
ejpam-5755	210	1	(	(	PUNCT
ejpam-5755	210	2	l	l	NOUN
ejpam-5755	210	3	+	+	CCONJ
ejpam-5755	210	4	lt	lt	NOUN
ejpam-5755	210	5	)	)	PUNCT
ejpam-5755	210	6	/2	/2	PROPN
ejpam-5755	210	7	,	,	PUNCT
ejpam-5755	210	8	where	where	SCONJ
ejpam-5755	210	9	l	l	NOUN
ejpam-5755	210	10	=	=	SYM
ejpam-5755	211	1	−q	−q	NOUN
ejpam-5755	211	2	is	be	AUX
ejpam-5755	211	3	the	the	DET
ejpam-5755	211	4	laplacian	laplacian	ADJ
ejpam-5755	211	5	matrix	matrix	NOUN
ejpam-5755	211	6	of	of	ADP
ejpam-5755	211	7	l(g	l(g	PROPN
ejpam-5755	211	8	∪	∪	ADJ
ejpam-5755	211	9	g′	g′	NOUN
ejpam-5755	211	10	)	)	PUNCT
ejpam-5755	211	11	.	.	PUNCT
ejpam-5755	212	1	hence	hence	ADV
ejpam-5755	212	2	,	,	PUNCT
ejpam-5755	212	3	by	by	ADP
ejpam-5755	212	4	the	the	DET
ejpam-5755	212	5	definition	definition	NOUN
ejpam-5755	212	6	1	1	NUM
ejpam-5755	212	7	,	,	PUNCT
ejpam-5755	212	8	the	the	DET
ejpam-5755	212	9	total	total	ADJ
ejpam-5755	212	10	derivation	derivation	NOUN
ejpam-5755	212	11	of	of	ADP
ejpam-5755	212	12	v	v	NOUN
ejpam-5755	212	13	(	(	PUNCT
ejpam-5755	212	14	ξ	ξ	NOUN
ejpam-5755	212	15	)	)	PUNCT
ejpam-5755	212	16	with	with	ADP
ejpam-5755	212	17	respect	respect	NOUN
ejpam-5755	212	18	to	to	ADP
ejpam-5755	212	19	(	(	PUNCT
ejpam-5755	212	20	3.6	3.6	NUM
ejpam-5755	212	21	)	)	PUNCT
ejpam-5755	212	22	is	be	AUX
ejpam-5755	212	23	v̇	v̇	PROPN
ejpam-5755	212	24	(	(	PUNCT
ejpam-5755	212	25	t	t	NOUN
ejpam-5755	212	26	)	)	PUNCT
ejpam-5755	212	27	=	=	PUNCT
ejpam-5755	213	1	ξ̇t	ξ̇t	PROPN
ejpam-5755	213	2	ξ	ξ	X
ejpam-5755	213	3	+	+	CCONJ
ejpam-5755	213	4	ξt	ξt	X
ejpam-5755	213	5	ξ̇	ξ̇	NOUN
ejpam-5755	213	6	=	=	PUNCT
ejpam-5755	213	7	ξt	ξt	X
ejpam-5755	213	8	(	(	PUNCT
ejpam-5755	213	9	(	(	PUNCT
ejpam-5755	213	10	|b|q)t	|b|q)t	ADJ
ejpam-5755	213	11	+	+	NUM
ejpam-5755	213	12	|b|q)ξ	|b|q)ξ	X
ejpam-5755	213	13	=	=	SYM
ejpam-5755	213	14	−2ξt	−2ξt	NOUN
ejpam-5755	213	15	(	(	PUNCT
ejpam-5755	213	16	|b|l̂)ξ	|b|l̂)ξ	X
ejpam-5755	213	17	≤	≤	NUM
ejpam-5755	213	18	−2λ2(|b|l̂)v	−2λ2(|b|l̂)v	PROPN
ejpam-5755	213	19	(	(	PUNCT
ejpam-5755	213	20	t	t	PROPN
ejpam-5755	213	21	)	)	PUNCT
ejpam-5755	213	22	.	.	PUNCT
ejpam-5755	214	1	this	this	PRON
ejpam-5755	214	2	implies	imply	VERB
ejpam-5755	214	3	that	that	SCONJ
ejpam-5755	214	4	,	,	PUNCT
ejpam-5755	214	5	for	for	ADP
ejpam-5755	214	6	t	t	PROPN
ejpam-5755	214	7	∈	∈	PROPN
ejpam-5755	214	8	(	(	PUNCT
ejpam-5755	214	9	tk−1	tk−1	PROPN
ejpam-5755	214	10	,	,	PUNCT
ejpam-5755	214	11	tk	tk	PROPN
ejpam-5755	214	12	]	]	X
ejpam-5755	214	13	,	,	PUNCT
ejpam-5755	214	14	v	v	PROPN
ejpam-5755	214	15	(	(	PUNCT
ejpam-5755	214	16	t	t	NOUN
ejpam-5755	214	17	)	)	PUNCT
ejpam-5755	214	18	≤	≤	NUM
ejpam-5755	214	19	e−2λ2(|b|l̂)(t−tk−1)v	e−2λ2(|b|l̂)(t−tk−1)v	NOUN
ejpam-5755	214	20	(	(	PUNCT
ejpam-5755	214	21	t+k−1	t+k−1	NOUN
ejpam-5755	214	22	)	)	PUNCT
ejpam-5755	214	23	.	.	PUNCT
ejpam-5755	215	1	on	on	ADP
ejpam-5755	215	2	the	the	DET
ejpam-5755	215	3	other	other	ADJ
ejpam-5755	215	4	hand	hand	NOUN
ejpam-5755	215	5	,	,	PUNCT
ejpam-5755	215	6	when	when	SCONJ
ejpam-5755	215	7	t	t	PROPN
ejpam-5755	215	8	=	=	SYM
ejpam-5755	215	9	tk−1	tk−1	PROPN
ejpam-5755	215	10	,	,	PUNCT
ejpam-5755	215	11	using	use	VERB
ejpam-5755	215	12	(	(	PUNCT
ejpam-5755	215	13	1−α)im	1−α)im	NUM
ejpam-5755	215	14	+	+	NOUN
ejpam-5755	215	15	h|b|q′+h|b|q′t	h|b|q′+h|b|q′t	ADJ
ejpam-5755	215	16	+	+	ADJ
ejpam-5755	215	17	(	(	PUNCT
ejpam-5755	215	18	h|b|)2q′tq′	h|b|)2q′tq′	ADV
ejpam-5755	215	19	≤	≤	NOUN
ejpam-5755	215	20	0	0	NUM
ejpam-5755	215	21	,	,	PUNCT
ejpam-5755	215	22	for	for	ADP
ejpam-5755	215	23	0	0	NUM
ejpam-5755	215	24	<	<	X
ejpam-5755	215	25	α	α	PROPN
ejpam-5755	215	26	≤	≤	NUM
ejpam-5755	215	27	1	1	NUM
ejpam-5755	215	28	,	,	PUNCT
ejpam-5755	215	29	gives	give	VERB
ejpam-5755	215	30	v	v	NOUN
ejpam-5755	215	31	(	(	PUNCT
ejpam-5755	215	32	t+k−1	t+k−1	NOUN
ejpam-5755	215	33	)	)	PUNCT
ejpam-5755	215	34	=	=	SYM
ejpam-5755	215	35	ξt	ξt	X
ejpam-5755	215	36	(	(	PUNCT
ejpam-5755	215	37	tk−1)(im	tk−1)(im	PROPN
ejpam-5755	215	38	+	+	NUM
ejpam-5755	215	39	h|b|q′)t	h|b|q′)t	PROPN
ejpam-5755	215	40	(	(	PUNCT
ejpam-5755	215	41	i	i	NOUN
ejpam-5755	215	42	m	m	VERB
ejpam-5755	215	43	+	+	NUM
ejpam-5755	215	44	h|b|q′)ξ(tk−1	h|b|q′)ξ(tk−1	NUM
ejpam-5755	215	45	)	)	PUNCT
ejpam-5755	215	46	=	=	SYM
ejpam-5755	215	47	ξt	ξt	X
ejpam-5755	215	48	(	(	PUNCT
ejpam-5755	215	49	tk−1)[im	tk−1)[im	NOUN
ejpam-5755	215	50	+	+	CCONJ
ejpam-5755	215	51	h|b|q′t	h|b|q′t	NOUN
ejpam-5755	215	52	+	+	NUM
ejpam-5755	215	53	h|b|q′	h|b|q′	NOUN
ejpam-5755	215	54	+	+	CCONJ
ejpam-5755	215	55	(	(	PUNCT
ejpam-5755	215	56	h|b|)2q′tq′	h|b|)2q′tq′	PROPN
ejpam-5755	215	57	−	−	PROPN
ejpam-5755	215	58	αim	αim	NOUN
ejpam-5755	215	59	+	+	CCONJ
ejpam-5755	215	60	αim	αim	NOUN
ejpam-5755	215	61	]	]	X
ejpam-5755	215	62	ξ(tk−1	ξ(tk−1	X
ejpam-5755	215	63	)	)	PUNCT
ejpam-5755	215	64	=	=	SYM
ejpam-5755	215	65	ξt	ξt	X
ejpam-5755	215	66	(	(	PUNCT
ejpam-5755	215	67	tk−1)[(1−	tk−1)[(1−	PROPN
ejpam-5755	215	68	α)im	α)im	PROPN
ejpam-5755	215	69	+	+	CCONJ
ejpam-5755	215	70	h|b|q′t	h|b|q′t	NOUN
ejpam-5755	215	71	+	+	NUM
ejpam-5755	215	72	h|b|q′	h|b|q′	NOUN
ejpam-5755	215	73	+	+	CCONJ
ejpam-5755	215	74	(	(	PUNCT
ejpam-5755	215	75	h|b|)2q′tq′]ξ(tk−1	h|b|)2q′tq′]ξ(tk−1	NUM
ejpam-5755	215	76	)	)	PUNCT
ejpam-5755	216	1	+	+	CCONJ
ejpam-5755	216	2	αξt	αξt	NOUN
ejpam-5755	216	3	(	(	PUNCT
ejpam-5755	216	4	tk−1)ξ(tk−1	tk−1)ξ(tk−1	NOUN
ejpam-5755	216	5	)	)	PUNCT
ejpam-5755	216	6	≤	≤	NUM
ejpam-5755	216	7	αξt	αξt	NOUN
ejpam-5755	216	8	(	(	PUNCT
ejpam-5755	216	9	tk−1)ξ(tk−1	tk−1)ξ(tk−1	NOUN
ejpam-5755	216	10	)	)	PUNCT
ejpam-5755	216	11	=	=	SYM
ejpam-5755	216	12	αv	αv	ADP
ejpam-5755	216	13	(	(	PUNCT
ejpam-5755	216	14	tk−1	tk−1	PROPN
ejpam-5755	216	15	)	)	PUNCT
ejpam-5755	216	16	.	.	PUNCT
ejpam-5755	217	1	in	in	ADP
ejpam-5755	217	2	general	general	ADJ
ejpam-5755	217	3	,	,	PUNCT
ejpam-5755	217	4	for	for	ADP
ejpam-5755	217	5	t	t	PROPN
ejpam-5755	217	6	∈	∈	PROPN
ejpam-5755	217	7	(	(	PUNCT
ejpam-5755	217	8	tk−1	tk−1	PROPN
ejpam-5755	217	9	,	,	PUNCT
ejpam-5755	217	10	tk	tk	PROPN
ejpam-5755	217	11	]	]	X
ejpam-5755	217	12	,	,	PUNCT
ejpam-5755	217	13	we	we	PRON
ejpam-5755	217	14	have	have	VERB
ejpam-5755	217	15	v	v	NUM
ejpam-5755	217	16	(	(	PUNCT
ejpam-5755	217	17	t	t	NOUN
ejpam-5755	217	18	)	)	PUNCT
ejpam-5755	217	19	≤	≤	PROPN
ejpam-5755	217	20	αk−1e−2λ2(|b|l̂)(t−t+0	αk−1e−2λ2(|b|l̂)(t−t+0	PROPN
ejpam-5755	217	21	)	)	PUNCT
ejpam-5755	217	22	v	v	NOUN
ejpam-5755	217	23	(	(	PUNCT
ejpam-5755	217	24	t+0	t+0	NUM
ejpam-5755	217	25	)	)	PUNCT
ejpam-5755	217	26	.	.	PUNCT
ejpam-5755	218	1	hence	hence	ADV
ejpam-5755	218	2	,	,	PUNCT
ejpam-5755	218	3	|ξ(t)|	|ξ(t)|	ADJ
ejpam-5755	218	4	≤	≤	NUM
ejpam-5755	218	5	α(k−1)/2e−λ2(|b|l̂)(t−t0)|ξ(t+0	α(k−1)/2e−λ2(|b|l̂)(t−t0)|ξ(t+0	NUM
ejpam-5755	218	6	)	)	PUNCT
ejpam-5755	219	1	|	|	ADV
ejpam-5755	219	2	,	,	PUNCT
ejpam-5755	219	3	t	t	PROPN
ejpam-5755	219	4	∈	∈	PROPN
ejpam-5755	219	5	(	(	PUNCT
ejpam-5755	219	6	tk−1	tk−1	PROPN
ejpam-5755	219	7	,	,	PUNCT
ejpam-5755	219	8	tk	tk	PROPN
ejpam-5755	219	9	]	]	X
ejpam-5755	219	10	.	.	PUNCT
ejpam-5755	220	1	therefore	therefore	ADV
ejpam-5755	220	2	,	,	PUNCT
ejpam-5755	220	3	∥yij(t)−	∥yij(t)−	PROPN
ejpam-5755	220	4	ȳ∥	ȳ∥	PUNCT
ejpam-5755	220	5	→	→	SYM
ejpam-5755	220	6	0	0	NUM
ejpam-5755	220	7	as	as	ADP
ejpam-5755	220	8	t	t	PROPN
ejpam-5755	220	9	→	→	SYM
ejpam-5755	220	10	∞	∞	PROPN
ejpam-5755	220	11	or	or	CCONJ
ejpam-5755	220	12	lim	lim	PROPN
ejpam-5755	220	13	t→∞	t→∞	X
ejpam-5755	220	14	βijxij(t	βijxij(t	PROPN
ejpam-5755	220	15	)	)	PUNCT
ejpam-5755	220	16	=	=	SYM
ejpam-5755	220	17	ȳ	ȳ	PROPN
ejpam-5755	220	18	,	,	PUNCT
ejpam-5755	220	19	∀	∀	X
ejpam-5755	220	20	(	(	PUNCT
ejpam-5755	220	21	i	i	PROPN
ejpam-5755	220	22	,	,	PUNCT
ejpam-5755	220	23	j	j	PROPN
ejpam-5755	220	24	)	)	PUNCT
ejpam-5755	220	25	∈	∈	PROPN
ejpam-5755	220	26	e	e	X
ejpam-5755	220	27	.	.	PUNCT
ejpam-5755	221	1	this	this	PRON
ejpam-5755	221	2	implies	imply	VERB
ejpam-5755	221	3	that	that	SCONJ
ejpam-5755	221	4	,	,	PUNCT
ejpam-5755	221	5	for	for	ADP
ejpam-5755	221	6	t	t	PROPN
ejpam-5755	221	7	∈	∈	PROPN
ejpam-5755	221	8	(	(	PUNCT
ejpam-5755	221	9	tk−1	tk−1	PROPN
ejpam-5755	221	10	,	,	PUNCT
ejpam-5755	221	11	tk	tk	PROPN
ejpam-5755	221	12	]	]	PROPN
ejpam-5755	221	13	,	,	PUNCT
ejpam-5755	221	14	lim	lim	PROPN
ejpam-5755	221	15	t→∞	t→∞	ADP
ejpam-5755	221	16	∥βijxij(t)−	∥βijxij(t)−	PROPN
ejpam-5755	221	17	βklxkl(t)∥	βklxkl(t)∥	PROPN
ejpam-5755	221	18	=	=	NOUN
ejpam-5755	221	19	0	0	NUM
ejpam-5755	221	20	for	for	ADP
ejpam-5755	221	21	all	all	PRON
ejpam-5755	221	22	(	(	PUNCT
ejpam-5755	221	23	i	i	PROPN
ejpam-5755	221	24	,	,	PUNCT
ejpam-5755	221	25	j	j	PROPN
ejpam-5755	221	26	)	)	PUNCT
ejpam-5755	221	27	,	,	PUNCT
ejpam-5755	221	28	(	(	PUNCT
ejpam-5755	221	29	k	k	X
ejpam-5755	221	30	,	,	PUNCT
ejpam-5755	221	31	l	l	NOUN
ejpam-5755	221	32	)	)	PUNCT
ejpam-5755	221	33	∈	∈	PROPN
ejpam-5755	221	34	e	e	NOUN
ejpam-5755	221	35	.	.	PUNCT
ejpam-5755	222	1	s.	s.	PROPN
ejpam-5755	222	2	donganont	donganont	PROPN
ejpam-5755	222	3	,	,	PUNCT
ejpam-5755	222	4	u.	u.	NOUN
ejpam-5755	222	5	witthayarat	witthayarat	NOUN
ejpam-5755	222	6	,	,	PUNCT
ejpam-5755	222	7	m.	m.	NOUN
ejpam-5755	222	8	donganont	donganont	PROPN
ejpam-5755	222	9	/	/	SYM
ejpam-5755	222	10	eur	eur	PROPN
ejpam-5755	222	11	.	.	PUNCT
ejpam-5755	223	1	j.	j.	PROPN
ejpam-5755	223	2	pure	pure	PROPN
ejpam-5755	223	3	appl	appl	PROPN
ejpam-5755	223	4	.	.	PROPN
ejpam-5755	223	5	math	math	PROPN
ejpam-5755	223	6	,	,	PUNCT
ejpam-5755	223	7	18	18	NUM
ejpam-5755	223	8	(	(	PUNCT
ejpam-5755	223	9	1	1	NUM
ejpam-5755	223	10	)	)	PUNCT
ejpam-5755	223	11	(	(	PUNCT
ejpam-5755	223	12	2025	2025	NUM
ejpam-5755	223	13	)	)	PUNCT
ejpam-5755	223	14	,	,	PUNCT
ejpam-5755	223	15	5755	5755	NUM
ejpam-5755	223	16	9	9	NUM
ejpam-5755	223	17	of	of	ADP
ejpam-5755	223	18	17	17	NUM
ejpam-5755	223	19	(	(	PUNCT
ejpam-5755	223	20	necessity	necessity	NOUN
ejpam-5755	223	21	)	)	PUNCT
ejpam-5755	223	22	suppose	suppose	VERB
ejpam-5755	223	23	that	that	SCONJ
ejpam-5755	223	24	l(g	l(g	NOUN
ejpam-5755	223	25	∪	∪	ADP
ejpam-5755	223	26	g′	g′	NOUN
ejpam-5755	223	27	)	)	PUNCT
ejpam-5755	223	28	is	be	AUX
ejpam-5755	223	29	not	not	PART
ejpam-5755	223	30	connected	connect	VERB
ejpam-5755	223	31	.	.	PUNCT
ejpam-5755	224	1	thus	thus	ADV
ejpam-5755	224	2	,	,	PUNCT
ejpam-5755	224	3	it	it	PRON
ejpam-5755	224	4	does	do	AUX
ejpam-5755	224	5	not	not	PART
ejpam-5755	224	6	contain	contain	VERB
ejpam-5755	224	7	a	a	DET
ejpam-5755	224	8	spanning	span	VERB
ejpam-5755	224	9	tree	tree	NOUN
ejpam-5755	224	10	.	.	PUNCT
ejpam-5755	225	1	then	then	ADV
ejpam-5755	225	2	,	,	PUNCT
ejpam-5755	225	3	by	by	ADP
ejpam-5755	225	4	lemma	lemma	PROPN
ejpam-5755	225	5	4	4	NUM
ejpam-5755	225	6	,	,	PUNCT
ejpam-5755	225	7	we	we	PRON
ejpam-5755	225	8	have	have	VERB
ejpam-5755	225	9	lim	lim	PROPN
ejpam-5755	225	10	k→∞	k→∞	NOUN
ejpam-5755	226	1	[	[	X
ejpam-5755	226	2	i	i	PRON
ejpam-5755	226	3	m	m	VERB
ejpam-5755	226	4	+	+	PUNCT
ejpam-5755	226	5	h|b|q′]k	h|b|q′]k	VERB
ejpam-5755	226	6	̸=	̸=	PROPN
ejpam-5755	226	7	1ny	1ny	ADJ
ejpam-5755	226	8	t	t	NOUN
ejpam-5755	226	9	.	.	PUNCT
ejpam-5755	227	1	hence	hence	ADV
ejpam-5755	227	2	,	,	PUNCT
ejpam-5755	227	3	lim	lim	PROPN
ejpam-5755	227	4	tk→∞	tk→∞	PROPN
ejpam-5755	227	5	∥βijxij(t)−	∥βijxij(t)−	PROPN
ejpam-5755	228	1	βklxkl(t)∥	βklxkl(t)∥	PROPN
ejpam-5755	228	2	=	=	NOUN
ejpam-5755	228	3	̸	̸	NUM
ejpam-5755	228	4	0	0	NUM
ejpam-5755	228	5	,	,	PUNCT
ejpam-5755	228	6	for	for	ADP
ejpam-5755	228	7	some	some	DET
ejpam-5755	228	8	(	(	PUNCT
ejpam-5755	228	9	i	i	PROPN
ejpam-5755	228	10	,	,	PUNCT
ejpam-5755	228	11	j	j	PROPN
ejpam-5755	228	12	)	)	PUNCT
ejpam-5755	228	13	,	,	PUNCT
ejpam-5755	228	14	(	(	PUNCT
ejpam-5755	228	15	k	k	X
ejpam-5755	228	16	,	,	PUNCT
ejpam-5755	228	17	l	l	NOUN
ejpam-5755	228	18	)	)	PUNCT
ejpam-5755	228	19	∈	∈	PROPN
ejpam-5755	228	20	e	e	X
ejpam-5755	228	21	.	.	PUNCT
ejpam-5755	229	1	this	this	PRON
ejpam-5755	229	2	implies	imply	VERB
ejpam-5755	229	3	that	that	SCONJ
ejpam-5755	229	4	the	the	DET
ejpam-5755	229	5	multi	multi	ADJ
ejpam-5755	229	6	-	-	ADJ
ejpam-5755	229	7	agent	agent	ADJ
ejpam-5755	229	8	system	system	NOUN
ejpam-5755	229	9	(	(	PUNCT
ejpam-5755	229	10	2.1	2.1	NUM
ejpam-5755	229	11	)	)	PUNCT
ejpam-5755	229	12	under	under	ADP
ejpam-5755	229	13	the	the	DET
ejpam-5755	229	14	protocol	protocol	NOUN
ejpam-5755	229	15	(	(	PUNCT
ejpam-5755	229	16	3.1	3.1	NUM
ejpam-5755	229	17	)	)	PUNCT
ejpam-5755	229	18	can	can	AUX
ejpam-5755	229	19	not	not	PART
ejpam-5755	229	20	achieve	achieve	VERB
ejpam-5755	229	21	scaled	scaled	ADJ
ejpam-5755	229	22	consensus	consensus	NOUN
ejpam-5755	229	23	.	.	PUNCT
ejpam-5755	230	1	if	if	SCONJ
ejpam-5755	230	2	the	the	DET
ejpam-5755	230	3	scalar	scalar	ADJ
ejpam-5755	230	4	scales	scale	NOUN
ejpam-5755	230	5	of	of	ADP
ejpam-5755	230	6	all	all	DET
ejpam-5755	230	7	edge	edge	NOUN
ejpam-5755	230	8	are	be	AUX
ejpam-5755	230	9	equal	equal	ADJ
ejpam-5755	230	10	to	to	ADP
ejpam-5755	230	11	one	one	NUM
ejpam-5755	230	12	,	,	PUNCT
ejpam-5755	230	13	the	the	DET
ejpam-5755	230	14	consensus	consensus	NOUN
ejpam-5755	230	15	problem	problem	NOUN
ejpam-5755	230	16	can	can	AUX
ejpam-5755	230	17	be	be	AUX
ejpam-5755	230	18	solved	solve	VERB
ejpam-5755	230	19	as	as	ADP
ejpam-5755	230	20	in	in	ADP
ejpam-5755	230	21	following	follow	VERB
ejpam-5755	230	22	corollary	corollary	ADJ
ejpam-5755	230	23	.	.	PUNCT
ejpam-5755	231	1	corollary	corollary	ADJ
ejpam-5755	231	2	1	1	NUM
ejpam-5755	231	3	.	.	PUNCT
ejpam-5755	232	1	let	let	VERB
ejpam-5755	232	2	g	g	PRON
ejpam-5755	232	3	be	be	AUX
ejpam-5755	232	4	a	a	DET
ejpam-5755	232	5	communication	communication	NOUN
ejpam-5755	232	6	network	network	NOUN
ejpam-5755	232	7	of	of	ADP
ejpam-5755	232	8	the	the	DET
ejpam-5755	232	9	multi	multi	ADJ
ejpam-5755	232	10	-	-	ADJ
ejpam-5755	232	11	agent	agent	ADJ
ejpam-5755	232	12	system	system	NOUN
ejpam-5755	232	13	(	(	PUNCT
ejpam-5755	232	14	2.1	2.1	NUM
ejpam-5755	232	15	)	)	PUNCT
ejpam-5755	232	16	.	.	PUNCT
ejpam-5755	233	1	assume	assume	VERB
ejpam-5755	233	2	that	that	SCONJ
ejpam-5755	233	3	the	the	DET
ejpam-5755	233	4	following	follow	VERB
ejpam-5755	233	5	assumptions	assumption	NOUN
ejpam-5755	233	6	are	be	AUX
ejpam-5755	233	7	satisfied	satisfied	ADJ
ejpam-5755	233	8	:	:	PUNCT
ejpam-5755	233	9	(	(	PUNCT
ejpam-5755	233	10	i	i	NOUN
ejpam-5755	233	11	)	)	PUNCT
ejpam-5755	233	12	0	0	PUNCT
ejpam-5755	234	1	<	<	X
ejpam-5755	234	2	h	h	X
ejpam-5755	234	3	<	<	X
ejpam-5755	234	4	1	1	NUM
ejpam-5755	234	5	max	max	PROPN
ejpam-5755	234	6	{	{	PUNCT
ejpam-5755	234	7	∑	∑	PROPN
ejpam-5755	234	8	s∈ni	s∈ni	NOUN
ejpam-5755	234	9	,	,	PUNCT
ejpam-5755	234	10	s	s	PART
ejpam-5755	234	11	̸=j	̸=j	PROPN
ejpam-5755	234	12	ais	ais	X
ejpam-5755	234	13	+	+	CCONJ
ejpam-5755	234	14	∑	∑	PROPN
ejpam-5755	234	15	s∈nj	s∈nj	PROPN
ejpam-5755	234	16	,	,	PUNCT
ejpam-5755	234	17	s	s	PART
ejpam-5755	234	18	̸=i	̸=i	PROPN
ejpam-5755	234	19	ajs	ajs	PROPN
ejpam-5755	234	20	,	,	PUNCT
ejpam-5755	234	21	(	(	PUNCT
ejpam-5755	234	22	ii	ii	NOUN
ejpam-5755	234	23	)	)	PUNCT
ejpam-5755	234	24	there	there	PRON
ejpam-5755	234	25	exists	exist	VERB
ejpam-5755	234	26	a	a	DET
ejpam-5755	234	27	constant	constant	ADJ
ejpam-5755	234	28	0	0	NUM
ejpam-5755	234	29	<	<	X
ejpam-5755	234	30	α	α	PROPN
ejpam-5755	234	31	≤	≤	NUM
ejpam-5755	234	32	1	1	NUM
ejpam-5755	234	33	such	such	ADJ
ejpam-5755	234	34	that	that	PRON
ejpam-5755	234	35	(	(	PUNCT
ejpam-5755	234	36	1−	1−	NUM
ejpam-5755	234	37	α)im	α)im	NOUN
ejpam-5755	234	38	+	+	CCONJ
ejpam-5755	234	39	hq′	hq′	ADJ
ejpam-5755	234	40	+	+	CCONJ
ejpam-5755	234	41	hq′t	hq′t	NOUN
ejpam-5755	234	42	+	+	NUM
ejpam-5755	234	43	h2q′tq′	h2q′tq′	NOUN
ejpam-5755	234	44	≤	≤	NOUN
ejpam-5755	234	45	0	0	NUM
ejpam-5755	234	46	.	.	PUNCT
ejpam-5755	235	1	then	then	ADV
ejpam-5755	235	2	,	,	PUNCT
ejpam-5755	235	3	the	the	DET
ejpam-5755	235	4	multi	multi	ADJ
ejpam-5755	235	5	-	-	ADJ
ejpam-5755	235	6	agent	agent	ADJ
ejpam-5755	235	7	system	system	NOUN
ejpam-5755	235	8	(	(	PUNCT
ejpam-5755	235	9	2.1	2.1	NUM
ejpam-5755	235	10	)	)	PUNCT
ejpam-5755	235	11	with	with	ADP
ejpam-5755	235	12	the	the	DET
ejpam-5755	235	13	protocol	protocol	NOUN
ejpam-5755	235	14	(	(	PUNCT
ejpam-5755	235	15	3.2	3.2	NUM
ejpam-5755	235	16	)	)	PUNCT
ejpam-5755	235	17	reaches	reach	VERB
ejpam-5755	235	18	consensus	consensus	NOUN
ejpam-5755	235	19	on	on	ADP
ejpam-5755	235	20	edge	edge	NOUN
ejpam-5755	235	21	dynamics	dynamic	NOUN
ejpam-5755	235	22	if	if	SCONJ
ejpam-5755	235	23	and	and	CCONJ
ejpam-5755	235	24	only	only	ADV
ejpam-5755	235	25	if	if	SCONJ
ejpam-5755	235	26	the	the	DET
ejpam-5755	235	27	line	line	NOUN
ejpam-5755	235	28	graph	graph	NOUN
ejpam-5755	235	29	l(g	l(g	PROPN
ejpam-5755	235	30	∪	∪	ADJ
ejpam-5755	235	31	g′	g′	NOUN
ejpam-5755	235	32	)	)	PUNCT
ejpam-5755	235	33	is	be	AUX
ejpam-5755	235	34	connected	connect	VERB
ejpam-5755	235	35	.	.	PUNCT
ejpam-5755	236	1	3.2	3.2	NUM
ejpam-5755	236	2	.	.	PUNCT
ejpam-5755	236	3	directed	direct	VERB
ejpam-5755	236	4	topology	topology	NOUN
ejpam-5755	236	5	in	in	ADP
ejpam-5755	236	6	this	this	DET
ejpam-5755	236	7	section	section	NOUN
ejpam-5755	236	8	,	,	PUNCT
ejpam-5755	236	9	scaled	scale	VERB
ejpam-5755	236	10	consensus	consensus	NOUN
ejpam-5755	236	11	problems	problem	NOUN
ejpam-5755	236	12	of	of	ADP
ejpam-5755	236	13	edge	edge	NOUN
ejpam-5755	236	14	dynamics	dynamic	NOUN
ejpam-5755	236	15	via	via	ADP
ejpam-5755	236	16	directed	direct	VERB
ejpam-5755	236	17	networks	network	NOUN
ejpam-5755	236	18	are	be	AUX
ejpam-5755	236	19	investigated	investigate	VERB
ejpam-5755	236	20	.	.	PUNCT
ejpam-5755	237	1	similar	similar	ADJ
ejpam-5755	237	2	to	to	ADP
ejpam-5755	237	3	undirected	undirected	ADJ
ejpam-5755	237	4	network	network	NOUN
ejpam-5755	237	5	,	,	PUNCT
ejpam-5755	237	6	we	we	PRON
ejpam-5755	237	7	transform	transform	VERB
ejpam-5755	237	8	the	the	DET
ejpam-5755	237	9	original	original	ADJ
ejpam-5755	237	10	nodal	nodal	NOUN
ejpam-5755	237	11	graph	graph	NOUN
ejpam-5755	237	12	into	into	ADP
ejpam-5755	237	13	its	its	PRON
ejpam-5755	237	14	corresponding	corresponding	ADJ
ejpam-5755	237	15	line	line	NOUN
ejpam-5755	237	16	graph	graph	NOUN
ejpam-5755	237	17	.	.	PUNCT
ejpam-5755	238	1	obviously	obviously	ADV
ejpam-5755	238	2	,	,	PUNCT
ejpam-5755	238	3	the	the	DET
ejpam-5755	238	4	line	line	NOUN
ejpam-5755	238	5	graph	graph	NOUN
ejpam-5755	238	6	l(g	l(g	NOUN
ejpam-5755	238	7	)	)	PUNCT
ejpam-5755	238	8	of	of	ADP
ejpam-5755	238	9	a	a	DET
ejpam-5755	238	10	digraph	digraph	NOUN
ejpam-5755	238	11	g	g	NOUN
ejpam-5755	238	12	is	be	AUX
ejpam-5755	238	13	a	a	DET
ejpam-5755	238	14	directed	direct	VERB
ejpam-5755	238	15	graph	graph	NOUN
ejpam-5755	238	16	,	,	PUNCT
ejpam-5755	238	17	and	and	CCONJ
ejpam-5755	238	18	there	there	PRON
ejpam-5755	238	19	are	be	VERB
ejpam-5755	238	20	∑n	∑n	PROPN
ejpam-5755	238	21	i=1	i=1	PROPN
ejpam-5755	238	22	d(in)i	d(in)i	PROPN
ejpam-5755	238	23	vertices	vertex	NOUN
ejpam-5755	238	24	and	and	CCONJ
ejpam-5755	238	25	∑n	∑n	PROPN
ejpam-5755	238	26	i=1	i=1	PROPN
ejpam-5755	238	27	d(in)id(out)i	d(in)id(out)i	PROPN
ejpam-5755	238	28	edges	edge	NOUN
ejpam-5755	238	29	in	in	ADP
ejpam-5755	238	30	l(g	l(g	NOUN
ejpam-5755	238	31	)	)	PUNCT
ejpam-5755	238	32	,	,	PUNCT
ejpam-5755	238	33	where	where	SCONJ
ejpam-5755	238	34	d(in)i	d(in)i	PROPN
ejpam-5755	238	35	and	and	CCONJ
ejpam-5755	238	36	d(out)i	d(out)i	NOUN
ejpam-5755	238	37	is	be	AUX
ejpam-5755	238	38	the	the	DET
ejpam-5755	238	39	in	in	ADP
ejpam-5755	238	40	-	-	PUNCT
ejpam-5755	238	41	degree	degree	NOUN
ejpam-5755	238	42	and	and	CCONJ
ejpam-5755	238	43	out	out	NOUN
ejpam-5755	238	44	-	-	PUNCT
ejpam-5755	238	45	degree	degree	NOUN
ejpam-5755	238	46	of	of	ADP
ejpam-5755	238	47	node	node	PROPN
ejpam-5755	238	48	i	i	PROPN
ejpam-5755	238	49	,	,	PUNCT
ejpam-5755	238	50	respectively	respectively	ADV
ejpam-5755	238	51	.	.	PUNCT
ejpam-5755	239	1	in	in	ADP
ejpam-5755	239	2	addition	addition	NOUN
ejpam-5755	239	3	,	,	PUNCT
ejpam-5755	239	4	the	the	DET
ejpam-5755	239	5	order	order	NOUN
ejpam-5755	239	6	pair	pair	NOUN
ejpam-5755	239	7	(	(	PUNCT
ejpam-5755	239	8	i	i	PROPN
ejpam-5755	239	9	,	,	PUNCT
ejpam-5755	239	10	j	j	PROPN
ejpam-5755	239	11	)	)	PUNCT
ejpam-5755	239	12	refers	refer	VERB
ejpam-5755	239	13	to	to	ADP
ejpam-5755	239	14	the	the	DET
ejpam-5755	239	15	directed	direct	VERB
ejpam-5755	239	16	edge	edge	NOUN
ejpam-5755	239	17	from	from	ADP
ejpam-5755	239	18	node	node	PROPN
ejpam-5755	239	19	j	j	PROPN
ejpam-5755	239	20	to	to	PART
ejpam-5755	239	21	node	node	VERB
ejpam-5755	239	22	i	i	PRON
ejpam-5755	239	23	,	,	PUNCT
ejpam-5755	239	24	and	and	CCONJ
ejpam-5755	239	25	if	if	SCONJ
ejpam-5755	239	26	the	the	DET
ejpam-5755	239	27	direct	direct	ADJ
ejpam-5755	239	28	edge	edge	NOUN
ejpam-5755	239	29	(	(	PUNCT
ejpam-5755	239	30	i1	i1	PROPN
ejpam-5755	239	31	,	,	PUNCT
ejpam-5755	239	32	ji	ji	PROPN
ejpam-5755	239	33	)	)	PUNCT
ejpam-5755	239	34	is	be	AUX
ejpam-5755	239	35	the	the	DET
ejpam-5755	239	36	valid	valid	ADJ
ejpam-5755	239	37	neighbor	neighbor	NOUN
ejpam-5755	239	38	of	of	ADP
ejpam-5755	239	39	the	the	DET
ejpam-5755	239	40	directed	direct	VERB
ejpam-5755	239	41	edge	edge	NOUN
ejpam-5755	239	42	(	(	PUNCT
ejpam-5755	239	43	i2	i2	PROPN
ejpam-5755	239	44	,	,	PUNCT
ejpam-5755	239	45	j2	j2	PROPN
ejpam-5755	239	46	)	)	PUNCT
ejpam-5755	239	47	in	in	ADP
ejpam-5755	239	48	the	the	DET
ejpam-5755	239	49	original	original	ADJ
ejpam-5755	239	50	nodal	nodal	NOUN
ejpam-5755	239	51	graph	graph	NOUN
ejpam-5755	239	52	,	,	PUNCT
ejpam-5755	239	53	add	add	VERB
ejpam-5755	239	54	a	a	DET
ejpam-5755	239	55	new	new	ADJ
ejpam-5755	239	56	directed	direct	VERB
ejpam-5755	239	57	edge	edge	NOUN
ejpam-5755	239	58	between	between	ADP
ejpam-5755	239	59	the	the	DET
ejpam-5755	239	60	generated	generate	VERB
ejpam-5755	239	61	nodes	node	NOUN
ejpam-5755	239	62	i1	i1	PROPN
ejpam-5755	239	63	,	,	PUNCT
ejpam-5755	239	64	ji	ji	PROPN
ejpam-5755	239	65	and	and	CCONJ
ejpam-5755	239	66	i2	i2	PROPN
ejpam-5755	239	67	,	,	PUNCT
ejpam-5755	239	68	j2	j2	PROPN
ejpam-5755	239	69	,	,	PUNCT
ejpam-5755	239	70	and	and	CCONJ
ejpam-5755	239	71	(	(	PUNCT
ejpam-5755	239	72	i1	i1	PROPN
ejpam-5755	239	73	,	,	PUNCT
ejpam-5755	239	74	ji	ji	PROPN
ejpam-5755	239	75	)	)	PUNCT
ejpam-5755	239	76	is	be	AUX
ejpam-5755	239	77	the	the	DET
ejpam-5755	239	78	initial	initial	ADJ
ejpam-5755	239	79	node	node	NOUN
ejpam-5755	239	80	of	of	ADP
ejpam-5755	239	81	the	the	DET
ejpam-5755	239	82	new	new	ADJ
ejpam-5755	239	83	directed	direct	VERB
ejpam-5755	239	84	edge	edge	NOUN
ejpam-5755	239	85	while	while	SCONJ
ejpam-5755	239	86	(	(	PUNCT
ejpam-5755	239	87	i2	i2	PROPN
ejpam-5755	239	88	,	,	PUNCT
ejpam-5755	239	89	j2	j2	PROPN
ejpam-5755	239	90	)	)	PUNCT
ejpam-5755	239	91	is	be	AUX
ejpam-5755	239	92	its	its	PRON
ejpam-5755	239	93	terminal	terminal	ADJ
ejpam-5755	239	94	node	node	NOUN
ejpam-5755	239	95	.	.	PUNCT
ejpam-5755	240	1	the	the	DET
ejpam-5755	240	2	detailed	detailed	ADJ
ejpam-5755	240	3	evolution	evolution	NOUN
ejpam-5755	240	4	of	of	ADP
ejpam-5755	240	5	a	a	DET
ejpam-5755	240	6	digraph	digraph	NOUN
ejpam-5755	240	7	to	to	ADP
ejpam-5755	240	8	its	its	PRON
ejpam-5755	240	9	line	line	NOUN
ejpam-5755	240	10	digraph	digraph	NOUN
ejpam-5755	240	11	can	can	AUX
ejpam-5755	240	12	be	be	AUX
ejpam-5755	240	13	seen	see	VERB
ejpam-5755	240	14	in	in	ADP
ejpam-5755	240	15	[	[	X
ejpam-5755	240	16	18	18	NUM
ejpam-5755	240	17	]	]	PUNCT
ejpam-5755	240	18	.	.	PUNCT
ejpam-5755	241	1	the	the	DET
ejpam-5755	241	2	edge	edge	NOUN
ejpam-5755	241	3	consensus	consensus	NOUN
ejpam-5755	241	4	protocol	protocol	NOUN
ejpam-5755	241	5	for	for	ADP
ejpam-5755	241	6	directed	direct	VERB
ejpam-5755	241	7	topology	topology	NOUN
ejpam-5755	241	8	can	can	AUX
ejpam-5755	241	9	be	be	AUX
ejpam-5755	241	10	designed	design	VERB
ejpam-5755	241	11	as	as	ADP
ejpam-5755	241	12	uij(t	uij(t	PROPN
ejpam-5755	241	13	)	)	PUNCT
ejpam-5755	241	14	=	=	SYM
ejpam-5755	242	1	|βij	|βij	NOUN
ejpam-5755	242	2	|	|	ADV
ejpam-5755	242	3	[	[	PUNCT
ejpam-5755	242	4	∑	∑	INTJ
ejpam-5755	242	5	s∈nj	s∈nj	PROPN
ejpam-5755	242	6	ajs[βisxis(t)−	ajs[βisxis(t)−	PROPN
ejpam-5755	242	7	βijxij(t	βijxij(t	PROPN
ejpam-5755	242	8	)	)	PUNCT
ejpam-5755	242	9	]	]	PUNCT
ejpam-5755	242	10	]	]	PUNCT
ejpam-5755	243	1	+	+	CCONJ
ejpam-5755	243	2	h	h	NOUN
ejpam-5755	243	3	·	·	PUNCT
ejpam-5755	243	4	|βi|	|βi|	PROPN
ejpam-5755	243	5	∞∑	∞∑	NOUN
ejpam-5755	243	6	k=1	k=1	PUNCT
ejpam-5755	243	7	∑	∑	PUNCT
ejpam-5755	243	8	(	(	PUNCT
ejpam-5755	243	9	i	i	PRON
ejpam-5755	243	10	,	,	PUNCT
ejpam-5755	243	11	s)∈e	s)∈e	PROPN
ejpam-5755	243	12	′	′	NUM
ejpam-5755	244	1	a′is[βisxis(t)−	a′is[βisxis(t)−	PROPN
ejpam-5755	244	2	βijxij(t)]δ(t−	βijxij(t)]δ(t−	PROPN
ejpam-5755	244	3	tk),∀(i	tk),∀(i	PROPN
ejpam-5755	244	4	,	,	PUNCT
ejpam-5755	244	5	j	j	NOUN
ejpam-5755	244	6	)	)	PUNCT
ejpam-5755	244	7	∈	∈	PROPN
ejpam-5755	244	8	e	e	X
ejpam-5755	244	9	,	,	PUNCT
ejpam-5755	244	10	(	(	PUNCT
ejpam-5755	244	11	3.7	3.7	NUM
ejpam-5755	244	12	)	)	PUNCT
ejpam-5755	244	13	where	where	SCONJ
ejpam-5755	244	14	all	all	DET
ejpam-5755	244	15	variables	variable	NOUN
ejpam-5755	244	16	are	be	AUX
ejpam-5755	244	17	defined	define	VERB
ejpam-5755	244	18	as	as	ADP
ejpam-5755	244	19	in	in	ADP
ejpam-5755	244	20	the	the	DET
ejpam-5755	244	21	previous	previous	ADJ
ejpam-5755	244	22	section	section	NOUN
ejpam-5755	244	23	.	.	PUNCT
ejpam-5755	245	1	s.	s.	PROPN
ejpam-5755	245	2	donganont	donganont	PROPN
ejpam-5755	245	3	,	,	PUNCT
ejpam-5755	245	4	u.	u.	NOUN
ejpam-5755	245	5	witthayarat	witthayarat	NOUN
ejpam-5755	245	6	,	,	PUNCT
ejpam-5755	245	7	m.	m.	NOUN
ejpam-5755	245	8	donganont	donganont	PROPN
ejpam-5755	245	9	/	/	SYM
ejpam-5755	245	10	eur	eur	PROPN
ejpam-5755	245	11	.	.	PUNCT
ejpam-5755	246	1	j.	j.	PROPN
ejpam-5755	246	2	pure	pure	PROPN
ejpam-5755	246	3	appl	appl	PROPN
ejpam-5755	246	4	.	.	PROPN
ejpam-5755	246	5	math	math	PROPN
ejpam-5755	246	6	,	,	PUNCT
ejpam-5755	246	7	18	18	NUM
ejpam-5755	246	8	(	(	PUNCT
ejpam-5755	246	9	1	1	NUM
ejpam-5755	246	10	)	)	PUNCT
ejpam-5755	246	11	(	(	PUNCT
ejpam-5755	246	12	2025	2025	NUM
ejpam-5755	246	13	)	)	PUNCT
ejpam-5755	246	14	,	,	PUNCT
ejpam-5755	246	15	5755	5755	NUM
ejpam-5755	246	16	10	10	NUM
ejpam-5755	246	17	of	of	ADP
ejpam-5755	246	18	17	17	NUM
ejpam-5755	246	19	remark	remark	NOUN
ejpam-5755	246	20	3	3	NUM
ejpam-5755	246	21	.	.	PUNCT
ejpam-5755	247	1	if	if	SCONJ
ejpam-5755	247	2	βij	βij	NOUN
ejpam-5755	247	3	=	=	NOUN
ejpam-5755	247	4	1	1	NUM
ejpam-5755	247	5	for	for	ADP
ejpam-5755	247	6	all	all	DET
ejpam-5755	247	7	edge	edge	NOUN
ejpam-5755	247	8	(	(	PUNCT
ejpam-5755	247	9	i	i	PROPN
ejpam-5755	247	10	,	,	PUNCT
ejpam-5755	247	11	j	j	PROPN
ejpam-5755	247	12	)	)	PUNCT
ejpam-5755	247	13	,	,	PUNCT
ejpam-5755	247	14	the	the	DET
ejpam-5755	247	15	protocol	protocol	NOUN
ejpam-5755	247	16	(	(	PUNCT
ejpam-5755	247	17	3.7	3.7	NUM
ejpam-5755	247	18	)	)	PUNCT
ejpam-5755	247	19	can	can	AUX
ejpam-5755	247	20	be	be	AUX
ejpam-5755	247	21	written	write	VERB
ejpam-5755	247	22	as	as	ADP
ejpam-5755	247	23	uij(t	uij(t	PROPN
ejpam-5755	247	24	)	)	PUNCT
ejpam-5755	247	25	=	=	SYM
ejpam-5755	247	26	∑	∑	PUNCT
ejpam-5755	247	27	s∈nj	s∈nj	PROPN
ejpam-5755	247	28	ajs[xis(t)−	ajs[xis(t)−	PROPN
ejpam-5755	247	29	xij(t	xij(t	PROPN
ejpam-5755	247	30	)	)	PUNCT
ejpam-5755	247	31	]	]	PUNCT
ejpam-5755	248	1	+	+	CCONJ
ejpam-5755	248	2	h	h	NOUN
ejpam-5755	248	3	·	·	PUNCT
ejpam-5755	249	1	∞∑	∞∑	NUM
ejpam-5755	249	2	k=1	k=1	PUNCT
ejpam-5755	249	3	∑	∑	PUNCT
ejpam-5755	249	4	(	(	PUNCT
ejpam-5755	249	5	i	i	PRON
ejpam-5755	249	6	,	,	PUNCT
ejpam-5755	249	7	s)∈e	s)∈e	PROPN
ejpam-5755	249	8	′	′	NUM
ejpam-5755	249	9	a′is[xis(t)−	a′is[xis(t)−	X
ejpam-5755	250	1	xij(t)]δ(t−	xij(t)]δ(t−	PUNCT
ejpam-5755	250	2	tk	tk	PROPN
ejpam-5755	250	3	)	)	PUNCT
ejpam-5755	250	4	,	,	PUNCT
ejpam-5755	250	5	∀(i	∀(i	PROPN
ejpam-5755	250	6	,	,	PUNCT
ejpam-5755	250	7	j	j	NOUN
ejpam-5755	250	8	)	)	PUNCT
ejpam-5755	250	9	∈	∈	PROPN
ejpam-5755	250	10	e	e	X
ejpam-5755	250	11	,	,	PUNCT
ejpam-5755	250	12	(	(	PUNCT
ejpam-5755	250	13	3.8	3.8	NUM
ejpam-5755	250	14	)	)	PUNCT
ejpam-5755	250	15	which	which	PRON
ejpam-5755	250	16	can	can	AUX
ejpam-5755	250	17	be	be	AUX
ejpam-5755	250	18	called	call	VERB
ejpam-5755	250	19	as	as	ADP
ejpam-5755	250	20	an	an	DET
ejpam-5755	250	21	impulsive	impulsive	ADJ
ejpam-5755	250	22	protocol	protocol	NOUN
ejpam-5755	251	1	and	and	CCONJ
ejpam-5755	251	2	if	if	SCONJ
ejpam-5755	251	3	e	e	ADP
ejpam-5755	251	4	′	′	NOUN
ejpam-5755	251	5	=	=	NOUN
ejpam-5755	251	6	∅	∅	NOUN
ejpam-5755	252	1	or	or	CCONJ
ejpam-5755	252	2	there	there	PRON
ejpam-5755	252	3	is	be	VERB
ejpam-5755	252	4	no	no	DET
ejpam-5755	252	5	instantaneous	instantaneous	ADJ
ejpam-5755	252	6	contact	contact	NOUN
ejpam-5755	252	7	at	at	ADP
ejpam-5755	252	8	the	the	DET
ejpam-5755	252	9	sampling	sampling	NOUN
ejpam-5755	252	10	time	time	NOUN
ejpam-5755	252	11	tk	tk	PROPN
ejpam-5755	252	12	and	and	CCONJ
ejpam-5755	252	13	βij	βij	NOUN
ejpam-5755	252	14	=	=	NOUN
ejpam-5755	252	15	1	1	NUM
ejpam-5755	252	16	for	for	ADP
ejpam-5755	252	17	all	all	DET
ejpam-5755	252	18	edge	edge	NOUN
ejpam-5755	252	19	(	(	PUNCT
ejpam-5755	252	20	i	i	PROPN
ejpam-5755	252	21	,	,	PUNCT
ejpam-5755	252	22	j	j	PROPN
ejpam-5755	252	23	)	)	PUNCT
ejpam-5755	252	24	,	,	PUNCT
ejpam-5755	252	25	one	one	PRON
ejpam-5755	252	26	obtains	obtain	VERB
ejpam-5755	252	27	uij(t	uij(t	PROPN
ejpam-5755	252	28	)	)	PUNCT
ejpam-5755	252	29	=	=	PUNCT
ejpam-5755	252	30	∑	∑	PUNCT
ejpam-5755	252	31	s∈nj	s∈nj	PROPN
ejpam-5755	252	32	ajs[xis(tk)−	ajs[xis(tk)−	PROPN
ejpam-5755	252	33	xij(tk	xij(tk	NOUN
ejpam-5755	252	34	)	)	PUNCT
ejpam-5755	252	35	]	]	PUNCT
ejpam-5755	252	36	,	,	PUNCT
ejpam-5755	252	37	∀(i	∀(i	PROPN
ejpam-5755	252	38	,	,	PUNCT
ejpam-5755	252	39	j	j	NOUN
ejpam-5755	252	40	)	)	PUNCT
ejpam-5755	252	41	∈	∈	PROPN
ejpam-5755	252	42	e	e	X
ejpam-5755	252	43	,	,	PUNCT
ejpam-5755	252	44	(	(	PUNCT
ejpam-5755	252	45	3.9	3.9	NUM
ejpam-5755	252	46	)	)	PUNCT
ejpam-5755	252	47	which	which	PRON
ejpam-5755	252	48	were	be	AUX
ejpam-5755	252	49	studied	study	VERB
ejpam-5755	252	50	in	in	ADP
ejpam-5755	252	51	[	[	X
ejpam-5755	252	52	18	18	NUM
ejpam-5755	252	53	]	]	PUNCT
ejpam-5755	252	54	.	.	PUNCT
ejpam-5755	253	1	theorem	theorem	NOUN
ejpam-5755	253	2	2	2	NUM
ejpam-5755	253	3	.	.	X
ejpam-5755	253	4	consider	consider	VERB
ejpam-5755	253	5	a	a	DET
ejpam-5755	253	6	directed	direct	VERB
ejpam-5755	253	7	communication	communication	NOUN
ejpam-5755	253	8	network	network	NOUN
ejpam-5755	253	9	g	g	NOUN
ejpam-5755	253	10	with	with	ADP
ejpam-5755	253	11	n	n	ADP
ejpam-5755	253	12	nodes	node	NOUN
ejpam-5755	253	13	and	and	CCONJ
ejpam-5755	253	14	m	m	PRON
ejpam-5755	253	15	edges	edge	NOUN
ejpam-5755	253	16	,	,	PUNCT
ejpam-5755	254	1	where	where	SCONJ
ejpam-5755	254	2	the	the	DET
ejpam-5755	254	3	edge	edge	NOUN
ejpam-5755	254	4	dynamics	dynamic	NOUN
ejpam-5755	254	5	described	describe	VERB
ejpam-5755	254	6	as	as	ADP
ejpam-5755	254	7	in	in	ADP
ejpam-5755	254	8	(	(	PUNCT
ejpam-5755	254	9	2.1	2.1	NUM
ejpam-5755	254	10	)	)	PUNCT
ejpam-5755	254	11	.	.	PUNCT
ejpam-5755	255	1	then	then	ADV
ejpam-5755	255	2	,	,	PUNCT
ejpam-5755	255	3	the	the	DET
ejpam-5755	255	4	consensus	consensus	NOUN
ejpam-5755	255	5	protocol	protocol	NOUN
ejpam-5755	255	6	(	(	PUNCT
ejpam-5755	255	7	3.7	3.7	NUM
ejpam-5755	255	8	)	)	PUNCT
ejpam-5755	255	9	solves	solve	NOUN
ejpam-5755	255	10	scaled	scale	VERB
ejpam-5755	255	11	consensus	consensus	NOUN
ejpam-5755	255	12	of	of	ADP
ejpam-5755	255	13	edge	edge	NOUN
ejpam-5755	255	14	dynamics	dynamic	NOUN
ejpam-5755	255	15	if	if	SCONJ
ejpam-5755	255	16	and	and	CCONJ
ejpam-5755	255	17	only	only	ADV
ejpam-5755	255	18	if	if	SCONJ
ejpam-5755	255	19	,	,	PUNCT
ejpam-5755	255	20	for	for	ADP
ejpam-5755	255	21	any	any	DET
ejpam-5755	255	22	initial	initial	ADJ
ejpam-5755	255	23	state	state	NOUN
ejpam-5755	255	24	,	,	PUNCT
ejpam-5755	255	25	the	the	DET
ejpam-5755	255	26	following	follow	VERB
ejpam-5755	255	27	conditions	condition	NOUN
ejpam-5755	255	28	are	be	AUX
ejpam-5755	255	29	satisfied	satisfied	ADJ
ejpam-5755	255	30	:	:	PUNCT
ejpam-5755	255	31	(	(	PUNCT
ejpam-5755	255	32	i	i	NOUN
ejpam-5755	255	33	)	)	PUNCT
ejpam-5755	255	34	the	the	DET
ejpam-5755	255	35	step	step	NOUN
ejpam-5755	255	36	size	size	NOUN
ejpam-5755	256	1	h	h	NOUN
ejpam-5755	256	2	is	be	AUX
ejpam-5755	256	3	satisfies	satisfie	NOUN
ejpam-5755	256	4	0	0	PUNCT
ejpam-5755	256	5	<	<	X
ejpam-5755	256	6	h	h	X
ejpam-5755	256	7	<	<	X
ejpam-5755	256	8	1	1	NUM
ejpam-5755	256	9	maxi	maxi	NOUN
ejpam-5755	256	10	,	,	PUNCT
ejpam-5755	256	11	j	j	PROPN
ejpam-5755	256	12	{	{	PUNCT
ejpam-5755	256	13	∑	∑	PROPN
ejpam-5755	256	14	j∈nj	j∈nj	PROPN
ejpam-5755	256	15	,	,	PUNCT
ejpam-5755	256	16	s	s	PART
ejpam-5755	256	17	̸=i	̸=i	PROPN
ejpam-5755	256	18	ajs}βmax	ajs}βmax	PROPN
ejpam-5755	256	19	;	;	PUNCT
ejpam-5755	256	20	(	(	PUNCT
ejpam-5755	256	21	3.10	3.10	NUM
ejpam-5755	256	22	)	)	PUNCT
ejpam-5755	256	23	(	(	PUNCT
ejpam-5755	256	24	ii	ii	NOUN
ejpam-5755	256	25	)	)	PUNCT
ejpam-5755	256	26	there	there	PRON
ejpam-5755	256	27	exists	exist	VERB
ejpam-5755	256	28	a	a	DET
ejpam-5755	256	29	constant	constant	ADJ
ejpam-5755	256	30	0	0	NUM
ejpam-5755	256	31	<	<	X
ejpam-5755	256	32	α	α	PROPN
ejpam-5755	256	33	≤	≤	NUM
ejpam-5755	256	34	1	1	NUM
ejpam-5755	256	35	such	such	ADJ
ejpam-5755	256	36	that	that	PRON
ejpam-5755	256	37	(	(	PUNCT
ejpam-5755	256	38	1−	1−	NUM
ejpam-5755	256	39	α)im	α)im	NOUN
ejpam-5755	256	40	+	+	NUM
ejpam-5755	256	41	h|b|w	h|b|w	NOUN
ejpam-5755	256	42	′	′	VERB
ejpam-5755	257	1	+	+	CCONJ
ejpam-5755	257	2	h|b|w	h|b|w	NOUN
ejpam-5755	257	3	′t	′t	X
ejpam-5755	257	4	+	+	X
ejpam-5755	257	5	(	(	PUNCT
ejpam-5755	257	6	h|b|)2w	h|b|)2w	PROPN
ejpam-5755	257	7	′tw	′tw	NOUN
ejpam-5755	257	8	′	′	NOUN
ejpam-5755	257	9	≤	≤	NUM
ejpam-5755	257	10	0	0	NUM
ejpam-5755	257	11	;	;	PUNCT
ejpam-5755	257	12	(	(	PUNCT
ejpam-5755	257	13	iii	iii	X
ejpam-5755	257	14	)	)	PUNCT
ejpam-5755	257	15	the	the	DET
ejpam-5755	257	16	line	line	NOUN
ejpam-5755	257	17	digraph	digraph	VERB
ejpam-5755	257	18	l(g	l(g	PROPN
ejpam-5755	257	19	∪	∪	PROPN
ejpam-5755	257	20	g′	g′	NOUN
ejpam-5755	257	21	)	)	PUNCT
ejpam-5755	257	22	is	be	AUX
ejpam-5755	257	23	balanced	balance	VERB
ejpam-5755	257	24	and	and	CCONJ
ejpam-5755	257	25	contains	contain	VERB
ejpam-5755	257	26	a	a	DET
ejpam-5755	257	27	spanning	span	VERB
ejpam-5755	257	28	tree	tree	NOUN
ejpam-5755	257	29	.	.	PUNCT
ejpam-5755	258	1	proof	proof	NOUN
ejpam-5755	258	2	.	.	PUNCT
ejpam-5755	259	1	(	(	PUNCT
ejpam-5755	259	2	sufficiency	sufficiency	NOUN
ejpam-5755	259	3	)	)	PUNCT
ejpam-5755	259	4	assume	assume	VERB
ejpam-5755	259	5	that	that	SCONJ
ejpam-5755	259	6	the	the	DET
ejpam-5755	259	7	conditions	condition	NOUN
ejpam-5755	259	8	(	(	PUNCT
ejpam-5755	259	9	i	i	NOUN
ejpam-5755	259	10	)	)	PUNCT
ejpam-5755	259	11	,	,	PUNCT
ejpam-5755	259	12	(	(	PUNCT
ejpam-5755	259	13	ii	ii	NOUN
ejpam-5755	259	14	)	)	PUNCT
ejpam-5755	259	15	and	and	CCONJ
ejpam-5755	259	16	(	(	PUNCT
ejpam-5755	259	17	iii	iii	X
ejpam-5755	259	18	)	)	PUNCT
ejpam-5755	259	19	are	be	AUX
ejpam-5755	259	20	satisfied	satisfied	ADJ
ejpam-5755	259	21	.	.	PUNCT
ejpam-5755	260	1	according	accord	VERB
ejpam-5755	260	2	to	to	ADP
ejpam-5755	260	3	the	the	DET
ejpam-5755	260	4	definition	definition	NOUN
ejpam-5755	260	5	of	of	ADP
ejpam-5755	260	6	the	the	DET
ejpam-5755	260	7	dirac	dirac	PROPN
ejpam-5755	260	8	delta	delta	PROPN
ejpam-5755	260	9	function	function	NOUN
ejpam-5755	260	10	,	,	PUNCT
ejpam-5755	260	11	the	the	DET
ejpam-5755	260	12	system	system	NOUN
ejpam-5755	260	13	(	(	PUNCT
ejpam-5755	260	14	2.1	2.1	NUM
ejpam-5755	260	15	)	)	PUNCT
ejpam-5755	260	16	under	under	ADP
ejpam-5755	260	17	protocol	protocol	NOUN
ejpam-5755	260	18	(	(	PUNCT
ejpam-5755	260	19	3.7	3.7	NUM
ejpam-5755	260	20	)	)	PUNCT
ejpam-5755	260	21	can	can	AUX
ejpam-5755	260	22	be	be	AUX
ejpam-5755	260	23	written	write	VERB
ejpam-5755	260	24	as	as	PRON
ejpam-5755	260	25	βij	βij	PROPN
ejpam-5755	260	26	ẋij(t	ẋij(t	PROPN
ejpam-5755	260	27	)	)	PUNCT
ejpam-5755	261	1	=	=	SYM
ejpam-5755	261	2	|βij	|βij	NOUN
ejpam-5755	262	1	|	|	ADV
ejpam-5755	262	2	∑	∑	PUNCT
ejpam-5755	262	3	s∈ni	s∈ni	PROPN
ejpam-5755	262	4	ais[βisxis(t)−	ais[βisxis(t)−	PROPN
ejpam-5755	262	5	βijxij(t	βijxij(t	PROPN
ejpam-5755	262	6	)	)	PUNCT
ejpam-5755	262	7	]	]	PUNCT
ejpam-5755	262	8	,	,	PUNCT
ejpam-5755	262	9	t	t	PROPN
ejpam-5755	262	10	∈	∈	PROPN
ejpam-5755	262	11	(	(	PUNCT
ejpam-5755	262	12	tk−1	tk−1	PROPN
ejpam-5755	262	13	,	,	PUNCT
ejpam-5755	262	14	tk	tk	PROPN
ejpam-5755	262	15	)	)	PUNCT
ejpam-5755	262	16	,	,	PUNCT
ejpam-5755	262	17	∆βijxij(tk	∆βijxij(tk	PROPN
ejpam-5755	262	18	)	)	PUNCT
ejpam-5755	262	19	=	=	PUNCT
ejpam-5755	263	1	h|βi|	h|βi|	PROPN
ejpam-5755	263	2	∑	∑	PUNCT
ejpam-5755	263	3	s∈n	s∈n	NOUN
ejpam-5755	263	4	′	′	NUM
ejpam-5755	264	1	i	i	PRON
ejpam-5755	264	2	a′js[βisxis(tk)−	a′js[βisxis(tk)−	VERB
ejpam-5755	264	3	βijxij(tk	βijxij(tk	NOUN
ejpam-5755	264	4	)	)	PUNCT
ejpam-5755	264	5	]	]	PUNCT
ejpam-5755	264	6	,	,	PUNCT
ejpam-5755	264	7	(	(	PUNCT
ejpam-5755	264	8	3.11	3.11	NUM
ejpam-5755	264	9	)	)	PUNCT
ejpam-5755	265	1	where	where	SCONJ
ejpam-5755	265	2	∆βijxij(tk	∆βijxij(tk	NOUN
ejpam-5755	265	3	)	)	PUNCT
ejpam-5755	265	4	=	=	PUNCT
ejpam-5755	266	1	βijxij(t	βijxij(t	PROPN
ejpam-5755	267	1	+	+	CCONJ
ejpam-5755	267	2	k	k	X
ejpam-5755	267	3	)	)	PUNCT
ejpam-5755	268	1	−βijxij(t	−βijxij(t	PRON
ejpam-5755	268	2	−	−	PROPN
ejpam-5755	269	1	k	k	PROPN
ejpam-5755	269	2	)	)	PUNCT
ejpam-5755	269	3	;	;	PUNCT
ejpam-5755	269	4	βijxij(t	βijxij(t	PRON
ejpam-5755	269	5	+	+	SYM
ejpam-5755	269	6	k	k	X
ejpam-5755	269	7	)	)	PUNCT
ejpam-5755	270	1	=	=	VERB
ejpam-5755	270	2	lim	lim	PROPN
ejpam-5755	270	3	h→0	h→0	PROPN
ejpam-5755	270	4	+	+	X
ejpam-5755	270	5	βijxij(tk+h	βijxij(tk+h	NUM
ejpam-5755	270	6	)	)	PUNCT
ejpam-5755	270	7	and	and	CCONJ
ejpam-5755	270	8	βijxij(t	βijxij(t	PRON
ejpam-5755	270	9	−	−	PROPN
ejpam-5755	270	10	k	k	NOUN
ejpam-5755	270	11	)	)	PUNCT
ejpam-5755	271	1	=	=	SYM
ejpam-5755	271	2	lim	lim	PROPN
ejpam-5755	271	3	h→0	h→0	NOUN
ejpam-5755	272	1	+	+	NUM
ejpam-5755	273	1	βijxij(tk	βijxij(tk	NOUN
ejpam-5755	274	1	−	−	PROPN
ejpam-5755	275	1	h	h	NOUN
ejpam-5755	275	2	)	)	PUNCT
ejpam-5755	275	3	.	.	PUNCT
ejpam-5755	276	1	with	with	ADP
ejpam-5755	276	2	out	out	ADP
ejpam-5755	276	3	loss	loss	NOUN
ejpam-5755	276	4	of	of	ADP
ejpam-5755	276	5	generality	generality	NOUN
ejpam-5755	276	6	,	,	PUNCT
ejpam-5755	276	7	we	we	PRON
ejpam-5755	276	8	assume	assume	VERB
ejpam-5755	276	9	that	that	SCONJ
ejpam-5755	276	10	the	the	DET
ejpam-5755	276	11	solution	solution	NOUN
ejpam-5755	276	12	of	of	ADP
ejpam-5755	276	13	system	system	NOUN
ejpam-5755	276	14	(	(	PUNCT
ejpam-5755	276	15	3.11	3.11	NUM
ejpam-5755	276	16	)	)	PUNCT
ejpam-5755	276	17	is	be	AUX
ejpam-5755	276	18	left	leave	VERB
ejpam-5755	276	19	continuous	continuous	ADJ
ejpam-5755	276	20	,	,	PUNCT
ejpam-5755	276	21	that	that	ADV
ejpam-5755	276	22	is	is	ADV
ejpam-5755	276	23	,	,	PUNCT
ejpam-5755	276	24	βijxij(t	βijxij(t	PRON
ejpam-5755	276	25	−	−	PROPN
ejpam-5755	276	26	k	k	NOUN
ejpam-5755	276	27	)	)	PUNCT
ejpam-5755	276	28	=	=	SYM
ejpam-5755	276	29	βijxij(tk	βijxij(tk	NOUN
ejpam-5755	276	30	)	)	PUNCT
ejpam-5755	276	31	and	and	CCONJ
ejpam-5755	276	32	let	let	VERB
ejpam-5755	276	33	y	y	PROPN
ejpam-5755	276	34	(	(	PUNCT
ejpam-5755	276	35	t	t	PROPN
ejpam-5755	276	36	)	)	PUNCT
ejpam-5755	276	37	=	=	PUNCT
ejpam-5755	276	38	(	(	PUNCT
ejpam-5755	276	39	βijxij(t	βijxij(t	NOUN
ejpam-5755	276	40	)	)	PUNCT
ejpam-5755	276	41	)	)	PUNCT
ejpam-5755	277	1	t	t	PROPN
ejpam-5755	277	2	∈	∈	PROPN
ejpam-5755	277	3	rm	rm	PROPN
ejpam-5755	277	4	,	,	PUNCT
ejpam-5755	277	5	i	i	PRON
ejpam-5755	277	6	,	,	PUNCT
ejpam-5755	277	7	j	j	PROPN
ejpam-5755	277	8	=	=	SYM
ejpam-5755	277	9	1	1	NUM
ejpam-5755	277	10	,	,	PUNCT
ejpam-5755	277	11	2	2	NUM
ejpam-5755	277	12	,	,	PUNCT
ejpam-5755	277	13	.	.	PUNCT
ejpam-5755	277	14	.	.	PUNCT
ejpam-5755	277	15	.	.	PUNCT
ejpam-5755	278	1	,	,	PUNCT
ejpam-5755	278	2	n	n	CCONJ
ejpam-5755	278	3	,	,	PUNCT
ejpam-5755	278	4	i	i	PRON
ejpam-5755	278	5	<	<	X
ejpam-5755	278	6	j	j	PROPN
ejpam-5755	278	7	;	;	PUNCT
ejpam-5755	278	8	yij	yij	NOUN
ejpam-5755	278	9	=	=	PUNCT
ejpam-5755	278	10	βijxij	βijxij	NOUN
ejpam-5755	278	11	;	;	PUNCT
ejpam-5755	278	12	βij	βij	PROPN
ejpam-5755	278	13	̸=	̸=	PROPN
ejpam-5755	278	14	0	0	NUM
ejpam-5755	278	15	,	,	PUNCT
ejpam-5755	278	16	b	b	X
ejpam-5755	278	17	=	=	SYM
ejpam-5755	278	18	diag(βij	diag(βij	PROPN
ejpam-5755	278	19	)	)	PUNCT
ejpam-5755	278	20	∈	∈	PROPN
ejpam-5755	278	21	rm×m	rm×m	NOUN
ejpam-5755	278	22	,	,	PUNCT
ejpam-5755	278	23	h	h	NOUN
ejpam-5755	278	24	∈	∈	PROPN
ejpam-5755	278	25	r+	r+	X
ejpam-5755	278	26	.	.	PUNCT
ejpam-5755	279	1	then	then	ADV
ejpam-5755	279	2	,	,	PUNCT
ejpam-5755	279	3	the	the	DET
ejpam-5755	279	4	system	system	NOUN
ejpam-5755	279	5	(	(	PUNCT
ejpam-5755	279	6	3.11	3.11	NUM
ejpam-5755	279	7	)	)	PUNCT
ejpam-5755	279	8	can	can	AUX
ejpam-5755	279	9	be	be	AUX
ejpam-5755	279	10	written	write	VERB
ejpam-5755	279	11	as	as	ADP
ejpam-5755	279	12	the	the	DET
ejpam-5755	279	13	form	form	NOUN
ejpam-5755	279	14	:	:	PUNCT
ejpam-5755	279	15	{	{	PUNCT
ejpam-5755	279	16	ẏ	ẏ	PROPN
ejpam-5755	279	17	(	(	PUNCT
ejpam-5755	279	18	t	t	PROPN
ejpam-5755	279	19	)	)	PUNCT
ejpam-5755	279	20	=	=	SYM
ejpam-5755	279	21	h|b|wy	h|b|wy	NOUN
ejpam-5755	279	22	(	(	PUNCT
ejpam-5755	279	23	t	t	PROPN
ejpam-5755	279	24	)	)	PUNCT
ejpam-5755	279	25	,	,	PUNCT
ejpam-5755	279	26	t	t	PROPN
ejpam-5755	279	27	̸=	̸=	PROPN
ejpam-5755	279	28	tk	tk	PROPN
ejpam-5755	279	29	,	,	PUNCT
ejpam-5755	279	30	y	y	PROPN
ejpam-5755	279	31	(	(	PUNCT
ejpam-5755	279	32	t+k	t+k	NUM
ejpam-5755	279	33	)	)	PUNCT
ejpam-5755	280	1	=	=	PUNCT
ejpam-5755	281	1	[	[	X
ejpam-5755	281	2	i	i	PRON
ejpam-5755	281	3	m	m	VERB
ejpam-5755	281	4	+	+	X
ejpam-5755	281	5	h|b|w	h|b|w	PROPN
ejpam-5755	281	6	′]y	′]y	X
ejpam-5755	281	7	(	(	PUNCT
ejpam-5755	281	8	tk	tk	PROPN
ejpam-5755	281	9	)	)	PUNCT
ejpam-5755	281	10	,	,	PUNCT
ejpam-5755	281	11	k	k	PROPN
ejpam-5755	281	12	∈	∈	PROPN
ejpam-5755	281	13	n	n	CCONJ
ejpam-5755	281	14	,	,	PUNCT
ejpam-5755	281	15	(	(	PUNCT
ejpam-5755	281	16	3.12	3.12	NUM
ejpam-5755	281	17	)	)	PUNCT
ejpam-5755	281	18	s.	s.	PROPN
ejpam-5755	281	19	donganont	donganont	PROPN
ejpam-5755	281	20	,	,	PUNCT
ejpam-5755	281	21	u.	u.	NOUN
ejpam-5755	281	22	witthayarat	witthayarat	NOUN
ejpam-5755	281	23	,	,	PUNCT
ejpam-5755	281	24	m.	m.	NOUN
ejpam-5755	281	25	donganont	donganont	PROPN
ejpam-5755	281	26	/	/	SYM
ejpam-5755	281	27	eur	eur	PROPN
ejpam-5755	281	28	.	.	PUNCT
ejpam-5755	282	1	j.	j.	PROPN
ejpam-5755	282	2	pure	pure	PROPN
ejpam-5755	282	3	appl	appl	PROPN
ejpam-5755	282	4	.	.	PROPN
ejpam-5755	282	5	math	math	PROPN
ejpam-5755	282	6	,	,	PUNCT
ejpam-5755	282	7	18	18	NUM
ejpam-5755	282	8	(	(	PUNCT
ejpam-5755	282	9	1	1	NUM
ejpam-5755	282	10	)	)	PUNCT
ejpam-5755	282	11	(	(	PUNCT
ejpam-5755	282	12	2025	2025	NUM
ejpam-5755	282	13	)	)	PUNCT
ejpam-5755	282	14	,	,	PUNCT
ejpam-5755	282	15	5755	5755	NUM
ejpam-5755	282	16	11	11	NUM
ejpam-5755	282	17	of	of	ADP
ejpam-5755	282	18	17	17	NUM
ejpam-5755	282	19	where	where	SCONJ
ejpam-5755	282	20	h	h	NOUN
ejpam-5755	282	21	is	be	AUX
ejpam-5755	282	22	a	a	DET
ejpam-5755	282	23	step	step	NOUN
ejpam-5755	282	24	size	size	NOUN
ejpam-5755	282	25	,	,	PUNCT
ejpam-5755	282	26	i	i	PRON
ejpam-5755	282	27	m	m	VERB
ejpam-5755	282	28	is	be	AUX
ejpam-5755	282	29	an	an	DET
ejpam-5755	282	30	identity	identity	NOUN
ejpam-5755	282	31	matrix	matrix	NOUN
ejpam-5755	282	32	,	,	PUNCT
ejpam-5755	282	33	|b|	|b|	PROPN
ejpam-5755	282	34	=	=	AUX
ejpam-5755	282	35	diag(|βij	diag(|βij	VERB
ejpam-5755	282	36	|	|	ADV
ejpam-5755	282	37	)	)	PUNCT
ejpam-5755	282	38	,	,	PUNCT
ejpam-5755	282	39	w	w	NOUN
ejpam-5755	282	40	and	and	CCONJ
ejpam-5755	282	41	w	w	PROPN
ejpam-5755	282	42	′	′	NUM
ejpam-5755	282	43	are	be	AUX
ejpam-5755	282	44	the	the	DET
ejpam-5755	282	45	zerorow	zerorow	NOUN
ejpam-5755	282	46	-	-	PUNCT
ejpam-5755	282	47	sum	sum	NOUN
ejpam-5755	282	48	symmetric	symmetric	ADJ
ejpam-5755	282	49	matrices	matrix	NOUN
ejpam-5755	282	50	with	with	ADP
ejpam-5755	282	51	nonnegative	nonnegative	ADJ
ejpam-5755	282	52	off	off	ADP
ejpam-5755	282	53	-	-	PUNCT
ejpam-5755	282	54	diagonal	diagonal	ADJ
ejpam-5755	282	55	elements	element	NOUN
ejpam-5755	282	56	and	and	CCONJ
ejpam-5755	282	57	the	the	DET
ejpam-5755	282	58	diagonal	diagonal	ADJ
ejpam-5755	282	59	elements	element	NOUN
ejpam-5755	282	60	are	be	AUX
ejpam-5755	282	61	−	−	NOUN
ejpam-5755	282	62	∑	∑	ADV
ejpam-5755	282	63	s∈nj	s∈nj	PROPN
ejpam-5755	282	64	,	,	PUNCT
ejpam-5755	282	65	s	s	PART
ejpam-5755	282	66	̸=i	̸=i	PROPN
ejpam-5755	282	67	ajs	ajs	PROPN
ejpam-5755	282	68	at	at	ADP
ejpam-5755	282	69	time	time	NOUN
ejpam-5755	282	70	t	t	PROPN
ejpam-5755	282	71	and	and	CCONJ
ejpam-5755	282	72	impulsive	impulsive	ADJ
ejpam-5755	282	73	time	time	NOUN
ejpam-5755	282	74	tk	tk	PROPN
ejpam-5755	282	75	,	,	PUNCT
ejpam-5755	282	76	respectively	respectively	ADV
ejpam-5755	282	77	.	.	PUNCT
ejpam-5755	283	1	since	since	SCONJ
ejpam-5755	283	2	l(g	l(g	NOUN
ejpam-5755	283	3	∪	∪	ADP
ejpam-5755	283	4	g′	g′	NOUN
ejpam-5755	283	5	)	)	PUNCT
ejpam-5755	283	6	is	be	AUX
ejpam-5755	283	7	balanced	balance	VERB
ejpam-5755	283	8	and	and	CCONJ
ejpam-5755	283	9	contains	contain	VERB
ejpam-5755	283	10	a	a	DET
ejpam-5755	283	11	spanning	span	VERB
ejpam-5755	283	12	tree	tree	NOUN
ejpam-5755	283	13	,	,	PUNCT
ejpam-5755	283	14	one	one	PRON
ejpam-5755	283	15	obtains	obtain	VERB
ejpam-5755	283	16	that	that	PRON
ejpam-5755	283	17	µ̄	µ̄	PROPN
ejpam-5755	283	18	=	=	PUNCT
ejpam-5755	283	19	1	1	NUM
ejpam-5755	283	20	m	m	VERB
ejpam-5755	283	21	∑	∑	PUNCT
ejpam-5755	283	22	(	(	PUNCT
ejpam-5755	283	23	i	i	PROPN
ejpam-5755	283	24	,	,	PUNCT
ejpam-5755	283	25	j)∈e	j)∈e	PROPN
ejpam-5755	283	26	yij	yij	NOUN
ejpam-5755	283	27	is	be	AUX
ejpam-5755	283	28	invariant	invariant	ADJ
ejpam-5755	283	29	quantity	quantity	NOUN
ejpam-5755	283	30	.	.	PUNCT
ejpam-5755	284	1	therefore	therefore	ADV
ejpam-5755	284	2	,	,	PUNCT
ejpam-5755	284	3	ηij(t	ηij(t	PROPN
ejpam-5755	284	4	)	)	PUNCT
ejpam-5755	284	5	=	=	SYM
ejpam-5755	284	6	yij(t)−	yij(t)−	PROPN
ejpam-5755	284	7	µ̄	µ̄	PROPN
ejpam-5755	284	8	,	,	PUNCT
ejpam-5755	284	9	t	t	PROPN
ejpam-5755	284	10	∈	∈	PROPN
ejpam-5755	284	11	(	(	PUNCT
ejpam-5755	284	12	tk−1	tk−1	PROPN
ejpam-5755	284	13	,	,	PUNCT
ejpam-5755	284	14	tk	tk	PROPN
ejpam-5755	284	15	]	]	X
ejpam-5755	284	16	,	,	PUNCT
ejpam-5755	284	17	ηij(t	ηij(t	PROPN
ejpam-5755	284	18	+	+	CCONJ
ejpam-5755	284	19	k	k	PROPN
ejpam-5755	284	20	)	)	PUNCT
ejpam-5755	285	1	=	=	SYM
ejpam-5755	285	2	yij(t	yij(t	PROPN
ejpam-5755	286	1	+	+	CCONJ
ejpam-5755	286	2	k	k	PROPN
ejpam-5755	286	3	)	)	PUNCT
ejpam-5755	287	1	−	−	PROPN
ejpam-5755	287	2	µ̄	µ̄	PROPN
ejpam-5755	287	3	and	and	CCONJ
ejpam-5755	287	4	ηij(t	ηij(t	PROPN
ejpam-5755	287	5	−	−	PROPN
ejpam-5755	287	6	k	k	PROPN
ejpam-5755	287	7	)	)	PUNCT
ejpam-5755	287	8	=	=	SYM
ejpam-5755	287	9	ηij(tk	ηij(tk	NOUN
ejpam-5755	287	10	)	)	PUNCT
ejpam-5755	287	11	,	,	PUNCT
ejpam-5755	287	12	for	for	ADP
ejpam-5755	287	13	all	all	PRON
ejpam-5755	287	14	(	(	PUNCT
ejpam-5755	287	15	i	i	PROPN
ejpam-5755	287	16	,	,	PUNCT
ejpam-5755	287	17	j	j	PROPN
ejpam-5755	287	18	)	)	PUNCT
ejpam-5755	287	19	∈	∈	PROPN
ejpam-5755	287	20	e	e	NOUN
ejpam-5755	287	21	,	,	PUNCT
ejpam-5755	287	22	with	with	ADP
ejpam-5755	287	23	initial	initial	ADJ
ejpam-5755	287	24	conditions	condition	NOUN
ejpam-5755	287	25	y(t0	y(t0	NOUN
ejpam-5755	287	26	)	)	PUNCT
ejpam-5755	287	27	=	=	SYM
ejpam-5755	287	28	y(0	y(0	PROPN
ejpam-5755	287	29	)	)	PUNCT
ejpam-5755	287	30	=	=	PUNCT
ejpam-5755	287	31	(	(	PUNCT
ejpam-5755	287	32	yij(0	yij(0	PROPN
ejpam-5755	287	33	)	)	PUNCT
ejpam-5755	287	34	)	)	PUNCT
ejpam-5755	288	1	t	t	NOUN
ejpam-5755	288	2	,	,	PUNCT
ejpam-5755	288	3	where	where	SCONJ
ejpam-5755	288	4	η	η	PROPN
ejpam-5755	288	5	=	=	PROPN
ejpam-5755	288	6	(	(	PUNCT
ejpam-5755	288	7	ηij	ηij	NOUN
ejpam-5755	288	8	)	)	PUNCT
ejpam-5755	288	9	t	t	PROPN
ejpam-5755	288	10	,	,	PUNCT
ejpam-5755	288	11	(	(	PUNCT
ejpam-5755	288	12	i	i	PROPN
ejpam-5755	288	13	,	,	PUNCT
ejpam-5755	288	14	j	j	PROPN
ejpam-5755	288	15	)	)	PUNCT
ejpam-5755	288	16	∈	∈	PROPN
ejpam-5755	288	17	e	e	NOUN
ejpam-5755	288	18	is	be	AUX
ejpam-5755	288	19	an	an	DET
ejpam-5755	288	20	error	error	NOUN
ejpam-5755	288	21	vector	vector	NOUN
ejpam-5755	288	22	.	.	PUNCT
ejpam-5755	289	1	thus	thus	ADV
ejpam-5755	289	2	,	,	PUNCT
ejpam-5755	289	3	{	{	PUNCT
ejpam-5755	289	4	η̇(t	η̇(t	INTJ
ejpam-5755	289	5	)	)	PUNCT
ejpam-5755	289	6	=	=	SYM
ejpam-5755	289	7	|b|wη(t	|b|wη(t	NOUN
ejpam-5755	289	8	)	)	PUNCT
ejpam-5755	289	9	,	,	PUNCT
ejpam-5755	289	10	t	t	PROPN
ejpam-5755	289	11	̸=	̸=	PROPN
ejpam-5755	289	12	tk	tk	PROPN
ejpam-5755	289	13	η(t+k	η(t+k	PROPN
ejpam-5755	289	14	)	)	PUNCT
ejpam-5755	289	15	=	=	PUNCT
ejpam-5755	290	1	[	[	X
ejpam-5755	290	2	i	i	PRON
ejpam-5755	290	3	m	m	VERB
ejpam-5755	290	4	+	+	NUM
ejpam-5755	290	5	h|b|w	h|b|w	PROPN
ejpam-5755	290	6	′]η(tk	′]η(tk	NOUN
ejpam-5755	290	7	)	)	PUNCT
ejpam-5755	290	8	,	,	PUNCT
ejpam-5755	290	9	t	t	PROPN
ejpam-5755	290	10	=	=	SYM
ejpam-5755	290	11	tk	tk	PROPN
ejpam-5755	290	12	,	,	PUNCT
ejpam-5755	290	13	k	k	PROPN
ejpam-5755	290	14	∈	∈	PROPN
ejpam-5755	290	15	n.	n.	NOUN
ejpam-5755	290	16	(	(	PUNCT
ejpam-5755	290	17	3.13	3.13	NUM
ejpam-5755	290	18	)	)	PUNCT
ejpam-5755	290	19	consider	consider	VERB
ejpam-5755	290	20	the	the	DET
ejpam-5755	290	21	lyapunov	lyapunov	ADJ
ejpam-5755	290	22	function	function	NOUN
ejpam-5755	290	23	candidate	candidate	NOUN
ejpam-5755	290	24	as	as	SCONJ
ejpam-5755	290	25	follows	follow	VERB
ejpam-5755	290	26	:	:	PUNCT
ejpam-5755	290	27	v	v	X
ejpam-5755	290	28	(	(	PUNCT
ejpam-5755	290	29	η	η	NOUN
ejpam-5755	290	30	)	)	PUNCT
ejpam-5755	290	31	=	=	PROPN
ejpam-5755	290	32	ηt	ηt	ADP
ejpam-5755	290	33	η	η	PROPN
ejpam-5755	290	34	.	.	PROPN
ejpam-5755	290	35	similar	similar	ADJ
ejpam-5755	290	36	to	to	ADP
ejpam-5755	290	37	the	the	DET
ejpam-5755	290	38	proof	proof	NOUN
ejpam-5755	290	39	of	of	ADP
ejpam-5755	290	40	theorem	theorem	NOUN
ejpam-5755	290	41	1	1	NUM
ejpam-5755	290	42	,	,	PUNCT
ejpam-5755	290	43	by	by	ADP
ejpam-5755	290	44	using	use	VERB
ejpam-5755	290	45	the	the	DET
ejpam-5755	290	46	fact	fact	NOUN
ejpam-5755	290	47	that	that	SCONJ
ejpam-5755	290	48	l(g	l(g	NOUN
ejpam-5755	290	49	∪	∪	ADP
ejpam-5755	290	50	g′	g′	NOUN
ejpam-5755	290	51	)	)	PUNCT
ejpam-5755	290	52	is	be	AUX
ejpam-5755	290	53	balanced	balance	VERB
ejpam-5755	290	54	and	and	CCONJ
ejpam-5755	290	55	contains	contain	VERB
ejpam-5755	290	56	a	a	DET
ejpam-5755	290	57	spanning	span	VERB
ejpam-5755	290	58	tree	tree	NOUN
ejpam-5755	290	59	together	together	ADV
ejpam-5755	290	60	with	with	ADP
ejpam-5755	290	61	condition	condition	NOUN
ejpam-5755	290	62	(	(	PUNCT
ejpam-5755	290	63	i	i	NOUN
ejpam-5755	290	64	)	)	PUNCT
ejpam-5755	290	65	,	,	PUNCT
ejpam-5755	290	66	(	(	PUNCT
ejpam-5755	290	67	ii	ii	NOUN
ejpam-5755	290	68	)	)	PUNCT
ejpam-5755	290	69	and	and	CCONJ
ejpam-5755	290	70	lemmas	lemmas	PROPN
ejpam-5755	290	71	,	,	PUNCT
ejpam-5755	290	72	we	we	PRON
ejpam-5755	290	73	can	can	AUX
ejpam-5755	290	74	prove	prove	VERB
ejpam-5755	290	75	that	that	SCONJ
ejpam-5755	290	76	∥yij(t)−	∥yij(t)−	PROPN
ejpam-5755	290	77	µ̄∥	µ̄∥	PUNCT
ejpam-5755	290	78	→	→	SYM
ejpam-5755	290	79	0	0	NUM
ejpam-5755	290	80	as	as	ADP
ejpam-5755	290	81	t	t	PROPN
ejpam-5755	290	82	→	→	SYM
ejpam-5755	290	83	∞	∞	PROPN
ejpam-5755	290	84	or	or	CCONJ
ejpam-5755	290	85	lim	lim	PROPN
ejpam-5755	290	86	t→∞	t→∞	X
ejpam-5755	290	87	βijxij(t	βijxij(t	PROPN
ejpam-5755	290	88	)	)	PUNCT
ejpam-5755	290	89	=	=	SYM
ejpam-5755	290	90	µ̄	µ̄	PROPN
ejpam-5755	290	91	,	,	PUNCT
ejpam-5755	290	92	∀	∀	X
ejpam-5755	290	93	(	(	PUNCT
ejpam-5755	290	94	i	i	PROPN
ejpam-5755	290	95	,	,	PUNCT
ejpam-5755	290	96	j	j	PROPN
ejpam-5755	290	97	)	)	PUNCT
ejpam-5755	290	98	∈	∈	PROPN
ejpam-5755	290	99	e	e	X
ejpam-5755	290	100	.	.	PUNCT
ejpam-5755	291	1	this	this	PRON
ejpam-5755	291	2	implies	imply	VERB
ejpam-5755	291	3	that	that	SCONJ
ejpam-5755	291	4	,	,	PUNCT
ejpam-5755	291	5	for	for	ADP
ejpam-5755	291	6	t	t	PROPN
ejpam-5755	291	7	∈	∈	PROPN
ejpam-5755	291	8	(	(	PUNCT
ejpam-5755	291	9	tk−1	tk−1	PROPN
ejpam-5755	291	10	,	,	PUNCT
ejpam-5755	291	11	tk	tk	PROPN
ejpam-5755	291	12	]	]	PROPN
ejpam-5755	291	13	,	,	PUNCT
ejpam-5755	291	14	lim	lim	PROPN
ejpam-5755	291	15	t→∞	t→∞	ADP
ejpam-5755	291	16	∥βijxij(t)−	∥βijxij(t)−	PROPN
ejpam-5755	291	17	βklxkl(t)∥	βklxkl(t)∥	PROPN
ejpam-5755	291	18	=	=	NOUN
ejpam-5755	291	19	0	0	NUM
ejpam-5755	291	20	for	for	ADP
ejpam-5755	291	21	all	all	PRON
ejpam-5755	291	22	(	(	PUNCT
ejpam-5755	291	23	i	i	PROPN
ejpam-5755	291	24	,	,	PUNCT
ejpam-5755	291	25	j	j	PROPN
ejpam-5755	291	26	)	)	PUNCT
ejpam-5755	291	27	,	,	PUNCT
ejpam-5755	291	28	(	(	PUNCT
ejpam-5755	291	29	k	k	X
ejpam-5755	291	30	,	,	PUNCT
ejpam-5755	291	31	l	l	NOUN
ejpam-5755	291	32	)	)	PUNCT
ejpam-5755	291	33	∈	∈	PROPN
ejpam-5755	291	34	e	e	X
ejpam-5755	291	35	.	.	PUNCT
ejpam-5755	292	1	(	(	PUNCT
ejpam-5755	292	2	necessity	necessity	NOUN
ejpam-5755	292	3	)	)	PUNCT
ejpam-5755	292	4	suppose	suppose	VERB
ejpam-5755	292	5	that	that	SCONJ
ejpam-5755	292	6	l(g	l(g	NOUN
ejpam-5755	292	7	∪	∪	ADP
ejpam-5755	292	8	g′	g′	NOUN
ejpam-5755	292	9	)	)	PUNCT
ejpam-5755	292	10	does	do	AUX
ejpam-5755	292	11	not	not	PART
ejpam-5755	292	12	contain	contain	VERB
ejpam-5755	292	13	a	a	DET
ejpam-5755	292	14	spanning	span	VERB
ejpam-5755	292	15	tree	tree	NOUN
ejpam-5755	292	16	.	.	PUNCT
ejpam-5755	293	1	then	then	ADV
ejpam-5755	293	2	,	,	PUNCT
ejpam-5755	293	3	by	by	ADP
ejpam-5755	293	4	lemma	lemma	PROPN
ejpam-5755	293	5	4	4	NUM
ejpam-5755	293	6	,	,	PUNCT
ejpam-5755	293	7	we	we	PRON
ejpam-5755	293	8	have	have	VERB
ejpam-5755	293	9	lim	lim	PROPN
ejpam-5755	293	10	k→∞	k→∞	NOUN
ejpam-5755	294	1	[	[	X
ejpam-5755	294	2	i	i	PRON
ejpam-5755	294	3	m	m	VERB
ejpam-5755	294	4	+	+	X
ejpam-5755	294	5	h|b|w	h|b|w	PROPN
ejpam-5755	294	6	′]k	′]k	PROPN
ejpam-5755	294	7	̸=	̸=	PROPN
ejpam-5755	294	8	1ny	1ny	ADJ
ejpam-5755	294	9	t	t	NOUN
ejpam-5755	294	10	.	.	PUNCT
ejpam-5755	295	1	hence	hence	ADV
ejpam-5755	295	2	,	,	PUNCT
ejpam-5755	295	3	lim	lim	PROPN
ejpam-5755	295	4	tk→∞	tk→∞	PROPN
ejpam-5755	295	5	∥βijxij(t)−	∥βijxij(t)−	PROPN
ejpam-5755	296	1	βklxkl(t)∥	βklxkl(t)∥	PROPN
ejpam-5755	296	2	=	=	NOUN
ejpam-5755	296	3	̸	̸	NUM
ejpam-5755	296	4	0	0	NUM
ejpam-5755	296	5	,	,	PUNCT
ejpam-5755	296	6	for	for	ADP
ejpam-5755	296	7	some	some	PRON
ejpam-5755	296	8	(	(	PUNCT
ejpam-5755	296	9	i	i	PROPN
ejpam-5755	296	10	,	,	PUNCT
ejpam-5755	296	11	j	j	PROPN
ejpam-5755	296	12	)	)	PUNCT
ejpam-5755	296	13	,	,	PUNCT
ejpam-5755	296	14	(	(	PUNCT
ejpam-5755	296	15	k	k	X
ejpam-5755	296	16	,	,	PUNCT
ejpam-5755	296	17	l	l	NOUN
ejpam-5755	296	18	)	)	PUNCT
ejpam-5755	296	19	∈	∈	PROPN
ejpam-5755	296	20	e.	e.	PROPN
ejpam-5755	296	21	this	this	PRON
ejpam-5755	296	22	implies	imply	VERB
ejpam-5755	296	23	that	that	SCONJ
ejpam-5755	296	24	the	the	DET
ejpam-5755	296	25	multi	multi	ADJ
ejpam-5755	296	26	-	-	ADJ
ejpam-5755	296	27	agent	agent	ADJ
ejpam-5755	296	28	system	system	NOUN
ejpam-5755	296	29	(	(	PUNCT
ejpam-5755	296	30	2.1	2.1	NUM
ejpam-5755	296	31	)	)	PUNCT
ejpam-5755	296	32	under	under	ADP
ejpam-5755	296	33	the	the	DET
ejpam-5755	296	34	protocol	protocol	NOUN
ejpam-5755	296	35	(	(	PUNCT
ejpam-5755	296	36	3.7	3.7	NUM
ejpam-5755	296	37	)	)	PUNCT
ejpam-5755	296	38	can	can	AUX
ejpam-5755	296	39	not	not	PART
ejpam-5755	296	40	achieve	achieve	VERB
ejpam-5755	296	41	scaled	scaled	ADJ
ejpam-5755	296	42	consensus	consensus	NOUN
ejpam-5755	296	43	.	.	PUNCT
ejpam-5755	297	1	if	if	SCONJ
ejpam-5755	297	2	the	the	DET
ejpam-5755	297	3	scalar	scalar	ADJ
ejpam-5755	297	4	scales	scale	NOUN
ejpam-5755	297	5	of	of	ADP
ejpam-5755	297	6	all	all	DET
ejpam-5755	297	7	edges	edge	NOUN
ejpam-5755	297	8	are	be	AUX
ejpam-5755	297	9	equal	equal	ADJ
ejpam-5755	297	10	to	to	ADP
ejpam-5755	297	11	one	one	NUM
ejpam-5755	297	12	,	,	PUNCT
ejpam-5755	297	13	then	then	ADV
ejpam-5755	297	14	the	the	DET
ejpam-5755	297	15	consensus	consensus	NOUN
ejpam-5755	297	16	problem	problem	NOUN
ejpam-5755	297	17	is	be	AUX
ejpam-5755	297	18	solved	solve	VERB
ejpam-5755	297	19	as	as	ADP
ejpam-5755	297	20	in	in	ADP
ejpam-5755	297	21	following	follow	VERB
ejpam-5755	297	22	corollary	corollary	ADJ
ejpam-5755	297	23	.	.	PUNCT
ejpam-5755	298	1	corollary	corollary	ADJ
ejpam-5755	298	2	2	2	NUM
ejpam-5755	298	3	.	.	PUNCT
ejpam-5755	298	4	consider	consider	VERB
ejpam-5755	298	5	a	a	DET
ejpam-5755	298	6	directed	direct	VERB
ejpam-5755	298	7	communication	communication	NOUN
ejpam-5755	298	8	network	network	NOUN
ejpam-5755	298	9	g	g	NOUN
ejpam-5755	298	10	with	with	ADP
ejpam-5755	298	11	n	n	ADP
ejpam-5755	298	12	nodes	node	NOUN
ejpam-5755	298	13	and	and	CCONJ
ejpam-5755	298	14	m	m	PRON
ejpam-5755	298	15	edges	edge	NOUN
ejpam-5755	298	16	,	,	PUNCT
ejpam-5755	298	17	where	where	SCONJ
ejpam-5755	298	18	the	the	DET
ejpam-5755	298	19	edge	edge	NOUN
ejpam-5755	298	20	dynamics	dynamic	NOUN
ejpam-5755	298	21	described	describe	VERB
ejpam-5755	298	22	as	as	ADP
ejpam-5755	298	23	in	in	ADP
ejpam-5755	298	24	(	(	PUNCT
ejpam-5755	298	25	2.1	2.1	NUM
ejpam-5755	298	26	)	)	PUNCT
ejpam-5755	298	27	.	.	PUNCT
ejpam-5755	299	1	then	then	ADV
ejpam-5755	299	2	,	,	PUNCT
ejpam-5755	299	3	the	the	DET
ejpam-5755	299	4	consensus	consensus	NOUN
ejpam-5755	299	5	protocol	protocol	NOUN
ejpam-5755	299	6	(	(	PUNCT
ejpam-5755	299	7	3.8	3.8	NUM
ejpam-5755	299	8	)	)	PUNCT
ejpam-5755	299	9	solves	solve	VERB
ejpam-5755	299	10	consensus	consensus	NOUN
ejpam-5755	299	11	of	of	ADP
ejpam-5755	299	12	edge	edge	NOUN
ejpam-5755	299	13	dynamics	dynamic	NOUN
ejpam-5755	299	14	if	if	SCONJ
ejpam-5755	299	15	and	and	CCONJ
ejpam-5755	299	16	only	only	ADV
ejpam-5755	299	17	if	if	SCONJ
ejpam-5755	299	18	,	,	PUNCT
ejpam-5755	299	19	for	for	ADP
ejpam-5755	299	20	any	any	DET
ejpam-5755	299	21	initial	initial	ADJ
ejpam-5755	299	22	state	state	NOUN
ejpam-5755	299	23	,	,	PUNCT
ejpam-5755	299	24	the	the	DET
ejpam-5755	299	25	following	follow	VERB
ejpam-5755	299	26	conditions	condition	NOUN
ejpam-5755	299	27	are	be	AUX
ejpam-5755	299	28	satisfied	satisfied	ADJ
ejpam-5755	299	29	:	:	PUNCT
ejpam-5755	299	30	(	(	PUNCT
ejpam-5755	299	31	i	i	NOUN
ejpam-5755	299	32	)	)	PUNCT
ejpam-5755	299	33	the	the	DET
ejpam-5755	299	34	step	step	NOUN
ejpam-5755	299	35	size	size	NOUN
ejpam-5755	299	36	h	h	NOUN
ejpam-5755	299	37	satisfies	satisfy	VERB
ejpam-5755	299	38	0	0	PUNCT
ejpam-5755	299	39	<	<	X
ejpam-5755	299	40	h	h	X
ejpam-5755	299	41	<	<	X
ejpam-5755	299	42	1	1	NUM
ejpam-5755	299	43	maxi	maxi	NOUN
ejpam-5755	299	44	,	,	PUNCT
ejpam-5755	299	45	j	j	PROPN
ejpam-5755	299	46	{	{	PUNCT
ejpam-5755	299	47	∑	∑	PROPN
ejpam-5755	299	48	j∈nj	j∈nj	PROPN
ejpam-5755	299	49	,	,	PUNCT
ejpam-5755	299	50	s	s	PART
ejpam-5755	299	51	̸=i	̸=i	PROPN
ejpam-5755	299	52	ajs	ajs	PROPN
ejpam-5755	299	53	}	}	PUNCT
ejpam-5755	299	54	;	;	PUNCT
ejpam-5755	299	55	(	(	PUNCT
ejpam-5755	299	56	3.10	3.10	NUM
ejpam-5755	299	57	)	)	PUNCT
ejpam-5755	299	58	(	(	PUNCT
ejpam-5755	299	59	ii	ii	NOUN
ejpam-5755	299	60	)	)	PUNCT
ejpam-5755	299	61	there	there	PRON
ejpam-5755	299	62	exists	exist	VERB
ejpam-5755	299	63	a	a	DET
ejpam-5755	299	64	constant	constant	ADJ
ejpam-5755	299	65	0	0	NUM
ejpam-5755	299	66	<	<	X
ejpam-5755	299	67	α	α	PROPN
ejpam-5755	299	68	≤	≤	NUM
ejpam-5755	299	69	1	1	NUM
ejpam-5755	299	70	such	such	ADJ
ejpam-5755	299	71	that	that	PRON
ejpam-5755	299	72	(	(	PUNCT
ejpam-5755	299	73	1−	1−	NUM
ejpam-5755	299	74	α)im	α)im	NOUN
ejpam-5755	299	75	+	+	CCONJ
ejpam-5755	299	76	hw	hw	PRON
ejpam-5755	299	77	′	′	VERB
ejpam-5755	300	1	+	+	CCONJ
ejpam-5755	300	2	hw	hw	VERB
ejpam-5755	300	3	′t	′t	NOUN
ejpam-5755	300	4	+	+	CCONJ
ejpam-5755	300	5	h2w	h2w	VERB
ejpam-5755	300	6	′tw	′tw	VERB
ejpam-5755	300	7	′	′	NUM
ejpam-5755	300	8	≤	≤	NUM
ejpam-5755	300	9	0	0	NUM
ejpam-5755	300	10	;	;	PUNCT
ejpam-5755	300	11	(	(	PUNCT
ejpam-5755	300	12	iii	iii	X
ejpam-5755	300	13	)	)	PUNCT
ejpam-5755	300	14	the	the	DET
ejpam-5755	300	15	line	line	NOUN
ejpam-5755	300	16	digraph	digraph	VERB
ejpam-5755	300	17	l(g	l(g	PROPN
ejpam-5755	300	18	∪	∪	PROPN
ejpam-5755	300	19	g′	g′	NOUN
ejpam-5755	300	20	)	)	PUNCT
ejpam-5755	300	21	is	be	AUX
ejpam-5755	300	22	balanced	balance	VERB
ejpam-5755	300	23	and	and	CCONJ
ejpam-5755	300	24	contains	contain	VERB
ejpam-5755	300	25	a	a	DET
ejpam-5755	300	26	spanning	span	VERB
ejpam-5755	300	27	tree	tree	NOUN
ejpam-5755	300	28	.	.	PUNCT
ejpam-5755	301	1	s.	s.	PROPN
ejpam-5755	301	2	donganont	donganont	PROPN
ejpam-5755	301	3	,	,	PUNCT
ejpam-5755	301	4	u.	u.	NOUN
ejpam-5755	301	5	witthayarat	witthayarat	NOUN
ejpam-5755	301	6	,	,	PUNCT
ejpam-5755	301	7	m.	m.	NOUN
ejpam-5755	301	8	donganont	donganont	PROPN
ejpam-5755	301	9	/	/	SYM
ejpam-5755	301	10	eur	eur	PROPN
ejpam-5755	301	11	.	.	PUNCT
ejpam-5755	302	1	j.	j.	PROPN
ejpam-5755	302	2	pure	pure	PROPN
ejpam-5755	302	3	appl	appl	PROPN
ejpam-5755	302	4	.	.	PROPN
ejpam-5755	302	5	math	math	PROPN
ejpam-5755	302	6	,	,	PUNCT
ejpam-5755	302	7	18	18	NUM
ejpam-5755	302	8	(	(	PUNCT
ejpam-5755	302	9	1	1	NUM
ejpam-5755	302	10	)	)	PUNCT
ejpam-5755	302	11	(	(	PUNCT
ejpam-5755	302	12	2025	2025	NUM
ejpam-5755	302	13	)	)	PUNCT
ejpam-5755	302	14	,	,	PUNCT
ejpam-5755	302	15	5755	5755	NUM
ejpam-5755	302	16	12	12	NUM
ejpam-5755	302	17	of	of	ADP
ejpam-5755	302	18	17	17	NUM
ejpam-5755	302	19	4	4	NUM
ejpam-5755	302	20	.	.	PUNCT
ejpam-5755	302	21	simulations	simulation	NOUN
ejpam-5755	302	22	and	and	CCONJ
ejpam-5755	302	23	discussion	discussion	NOUN
ejpam-5755	302	24	in	in	ADP
ejpam-5755	302	25	order	order	NOUN
ejpam-5755	302	26	to	to	PART
ejpam-5755	302	27	demonstrate	demonstrate	VERB
ejpam-5755	302	28	the	the	DET
ejpam-5755	302	29	effectiveness	effectiveness	NOUN
ejpam-5755	302	30	of	of	ADP
ejpam-5755	302	31	the	the	DET
ejpam-5755	302	32	theoretical	theoretical	ADJ
ejpam-5755	302	33	results	result	NOUN
ejpam-5755	302	34	in	in	ADP
ejpam-5755	302	35	this	this	DET
ejpam-5755	302	36	work	work	NOUN
ejpam-5755	302	37	,	,	PUNCT
ejpam-5755	302	38	the	the	DET
ejpam-5755	302	39	following	follow	VERB
ejpam-5755	302	40	example	example	NOUN
ejpam-5755	302	41	is	be	AUX
ejpam-5755	302	42	provided	provide	VERB
ejpam-5755	302	43	.	.	PUNCT
ejpam-5755	303	1	example	example	NOUN
ejpam-5755	303	2	1	1	NUM
ejpam-5755	303	3	.	.	X
ejpam-5755	304	1	consider	consider	VERB
ejpam-5755	304	2	a	a	DET
ejpam-5755	304	3	communication	communication	NOUN
ejpam-5755	304	4	network	network	NOUN
ejpam-5755	304	5	of	of	ADP
ejpam-5755	304	6	8	8	NUM
ejpam-5755	304	7	agents	agent	NOUN
ejpam-5755	304	8	denoted	denote	VERB
ejpam-5755	304	9	by	by	ADP
ejpam-5755	304	10	1−	1−	NUM
ejpam-5755	304	11	8	8	NUM
ejpam-5755	304	12	,	,	PUNCT
ejpam-5755	304	13	where	where	SCONJ
ejpam-5755	304	14	the	the	DET
ejpam-5755	304	15	dashed	dash	VERB
ejpam-5755	304	16	line	line	NOUN
ejpam-5755	304	17	refers	refer	VERB
ejpam-5755	304	18	to	to	ADP
ejpam-5755	304	19	a	a	DET
ejpam-5755	304	20	communication	communication	NOUN
ejpam-5755	304	21	at	at	ADP
ejpam-5755	304	22	the	the	DET
ejpam-5755	304	23	impulsive	impulsive	ADJ
ejpam-5755	304	24	time	time	NOUN
ejpam-5755	304	25	tk	tk	PROPN
ejpam-5755	304	26	.	.	PROPN
ejpam-5755	305	1	then	then	ADV
ejpam-5755	305	2	,	,	PUNCT
ejpam-5755	305	3	the	the	DET
ejpam-5755	305	4	communications	communication	NOUN
ejpam-5755	305	5	g	g	NOUN
ejpam-5755	305	6	∪	∪	NOUN
ejpam-5755	305	7	g′	g′	NOUN
ejpam-5755	305	8	can	can	AUX
ejpam-5755	305	9	be	be	AUX
ejpam-5755	305	10	described	describe	VERB
ejpam-5755	305	11	as	as	ADP
ejpam-5755	305	12	in	in	ADP
ejpam-5755	305	13	figure	figure	NOUN
ejpam-5755	305	14	1	1	NUM
ejpam-5755	305	15	.	.	PUNCT
ejpam-5755	306	1	figure	figure	NOUN
ejpam-5755	306	2	1	1	NUM
ejpam-5755	306	3	:	:	PUNCT
ejpam-5755	306	4	the	the	DET
ejpam-5755	306	5	communication	communication	NOUN
ejpam-5755	306	6	net	net	ADJ
ejpam-5755	306	7	work	work	NOUN
ejpam-5755	306	8	g	g	NOUN
ejpam-5755	306	9	∪	∪	ADV
ejpam-5755	306	10	g′.	g′.	NOUN
ejpam-5755	306	11	in	in	ADP
ejpam-5755	306	12	order	order	NOUN
ejpam-5755	306	13	to	to	PART
ejpam-5755	306	14	solve	solve	VERB
ejpam-5755	306	15	edge	edge	NOUN
ejpam-5755	306	16	consensus	consensus	NOUN
ejpam-5755	306	17	problems	problem	NOUN
ejpam-5755	306	18	,	,	PUNCT
ejpam-5755	306	19	we	we	PRON
ejpam-5755	306	20	first	first	ADV
ejpam-5755	306	21	transform	transform	VERB
ejpam-5755	306	22	the	the	DET
ejpam-5755	306	23	graph	graph	NOUN
ejpam-5755	306	24	g∪g′	g∪g′	NOUN
ejpam-5755	306	25	to	to	ADP
ejpam-5755	306	26	its	its	PRON
ejpam-5755	306	27	line	line	NOUN
ejpam-5755	306	28	graph	graph	NOUN
ejpam-5755	306	29	,	,	PUNCT
ejpam-5755	306	30	using	use	VERB
ejpam-5755	306	31	the	the	DET
ejpam-5755	306	32	same	same	ADJ
ejpam-5755	306	33	methodology	methodology	NOUN
ejpam-5755	306	34	as	as	ADP
ejpam-5755	306	35	[	[	X
ejpam-5755	306	36	14	14	NUM
ejpam-5755	306	37	]	]	PUNCT
ejpam-5755	306	38	,	,	PUNCT
ejpam-5755	306	39	denoted	denote	VERB
ejpam-5755	306	40	by	by	ADP
ejpam-5755	306	41	l(g	l(g	NOUN
ejpam-5755	306	42	∪	∪	ADJ
ejpam-5755	306	43	g′	g′	NOUN
ejpam-5755	306	44	)	)	PUNCT
ejpam-5755	306	45	,	,	PUNCT
ejpam-5755	306	46	as	as	SCONJ
ejpam-5755	306	47	shown	show	VERB
ejpam-5755	306	48	in	in	ADP
ejpam-5755	306	49	figure	figure	NOUN
ejpam-5755	306	50	2	2	NUM
ejpam-5755	306	51	.	.	PUNCT
ejpam-5755	307	1	it	it	PRON
ejpam-5755	307	2	can	can	AUX
ejpam-5755	307	3	be	be	AUX
ejpam-5755	307	4	seen	see	VERB
ejpam-5755	307	5	that	that	SCONJ
ejpam-5755	307	6	l(g	l(g	NOUN
ejpam-5755	307	7	∪g′	∪g′	NOUN
ejpam-5755	307	8	)	)	PUNCT
ejpam-5755	307	9	has	have	VERB
ejpam-5755	307	10	9	9	NUM
ejpam-5755	307	11	nodes	node	NOUN
ejpam-5755	307	12	,	,	PUNCT
ejpam-5755	307	13	which	which	PRON
ejpam-5755	307	14	are	be	AUX
ejpam-5755	307	15	x12	x12	NUM
ejpam-5755	307	16	,	,	PUNCT
ejpam-5755	307	17	x16	x16	PROPN
ejpam-5755	307	18	,	,	PUNCT
ejpam-5755	307	19	x23	x23	NUM
ejpam-5755	307	20	,	,	PUNCT
ejpam-5755	307	21	x34	x34	NUM
ejpam-5755	307	22	,	,	PUNCT
ejpam-5755	307	23	x38	x38	NOUN
ejpam-5755	307	24	,	,	PUNCT
ejpam-5755	307	25	x45	x45	PROPN
ejpam-5755	307	26	,	,	PUNCT
ejpam-5755	307	27	x47	x47	PROPN
ejpam-5755	307	28	,	,	PUNCT
ejpam-5755	307	29	x56	x56	PROPN
ejpam-5755	307	30	,	,	PUNCT
ejpam-5755	307	31	x78	x78	NOUN
ejpam-5755	307	32	and	and	CCONJ
ejpam-5755	307	33	12	12	NUM
ejpam-5755	307	34	edges	edge	NOUN
ejpam-5755	307	35	.	.	PUNCT
ejpam-5755	308	1	figure	figure	NOUN
ejpam-5755	308	2	2	2	NUM
ejpam-5755	308	3	:	:	PUNCT
ejpam-5755	308	4	the	the	DET
ejpam-5755	308	5	communication	communication	NOUN
ejpam-5755	308	6	network	network	NOUN
ejpam-5755	308	7	of	of	ADP
ejpam-5755	308	8	l(g	l(g	PROPN
ejpam-5755	308	9	∪	∪	ADP
ejpam-5755	308	10	g′	g′	NOUN
ejpam-5755	308	11	)	)	PUNCT
ejpam-5755	308	12	.	.	PUNCT
ejpam-5755	309	1	s.	s.	PROPN
ejpam-5755	309	2	donganont	donganont	PROPN
ejpam-5755	309	3	,	,	PUNCT
ejpam-5755	309	4	u.	u.	NOUN
ejpam-5755	309	5	witthayarat	witthayarat	NOUN
ejpam-5755	309	6	,	,	PUNCT
ejpam-5755	309	7	m.	m.	NOUN
ejpam-5755	309	8	donganont	donganont	PROPN
ejpam-5755	309	9	/	/	SYM
ejpam-5755	309	10	eur	eur	PROPN
ejpam-5755	309	11	.	.	PUNCT
ejpam-5755	310	1	j.	j.	PROPN
ejpam-5755	310	2	pure	pure	PROPN
ejpam-5755	310	3	appl	appl	PROPN
ejpam-5755	310	4	.	.	PROPN
ejpam-5755	310	5	math	math	PROPN
ejpam-5755	310	6	,	,	PUNCT
ejpam-5755	310	7	18	18	NUM
ejpam-5755	310	8	(	(	PUNCT
ejpam-5755	310	9	1	1	NUM
ejpam-5755	310	10	)	)	PUNCT
ejpam-5755	310	11	(	(	PUNCT
ejpam-5755	310	12	2025	2025	NUM
ejpam-5755	310	13	)	)	PUNCT
ejpam-5755	310	14	,	,	PUNCT
ejpam-5755	310	15	5755	5755	NUM
ejpam-5755	310	16	13	13	NUM
ejpam-5755	310	17	of	of	ADP
ejpam-5755	310	18	17	17	NUM
ejpam-5755	310	19	according	accord	VERB
ejpam-5755	310	20	to	to	ADP
ejpam-5755	310	21	the	the	DET
ejpam-5755	310	22	communication	communication	NOUN
ejpam-5755	310	23	network	network	NOUN
ejpam-5755	310	24	g	g	PROPN
ejpam-5755	310	25	∪	∪	PROPN
ejpam-5755	310	26	g′	g′	NOUN
ejpam-5755	310	27	,	,	PUNCT
ejpam-5755	310	28	the	the	DET
ejpam-5755	310	29	adjacency	adjacency	NOUN
ejpam-5755	310	30	matrix	matrix	NOUN
ejpam-5755	310	31	of	of	ADP
ejpam-5755	310	32	g	g	PROPN
ejpam-5755	310	33	∪	∪	ADJ
ejpam-5755	310	34	g′	g′	NOUN
ejpam-5755	310	35	is	be	AUX
ejpam-5755	310	36	denoted	denote	VERB
ejpam-5755	310	37	by	by	ADP
ejpam-5755	310	38	a	a	PRON
ejpam-5755	310	39	and	and	CCONJ
ejpam-5755	310	40	the	the	DET
ejpam-5755	310	41	laplacian	laplacian	ADJ
ejpam-5755	310	42	matrix	matrix	NOUN
ejpam-5755	310	43	of	of	ADP
ejpam-5755	310	44	its	its	PRON
ejpam-5755	310	45	line	line	NOUN
ejpam-5755	310	46	graph	graph	NOUN
ejpam-5755	310	47	is	be	AUX
ejpam-5755	310	48	−q	−q	ADJ
ejpam-5755	310	49	,	,	PUNCT
ejpam-5755	310	50	where	where	SCONJ
ejpam-5755	310	51	a	a	DET
ejpam-5755	310	52	=	=	NOUN
ejpam-5755	310	53			NOUN
ejpam-5755	310	54	0	0	NUM
ejpam-5755	310	55	1	1	NUM
ejpam-5755	310	56	0	0	NUM
ejpam-5755	310	57	0	0	NUM
ejpam-5755	310	58	0	0	NUM
ejpam-5755	310	59	1	1	NUM
ejpam-5755	310	60	0	0	NUM
ejpam-5755	310	61	0	0	NUM
ejpam-5755	310	62	1	1	NUM
ejpam-5755	310	63	0	0	NUM
ejpam-5755	310	64	1	1	NUM
ejpam-5755	310	65	0	0	NUM
ejpam-5755	310	66	0	0	NUM
ejpam-5755	310	67	0	0	NUM
ejpam-5755	310	68	0	0	NUM
ejpam-5755	310	69	0	0	NUM
ejpam-5755	310	70	0	0	NUM
ejpam-5755	310	71	1	1	NUM
ejpam-5755	310	72	0	0	NUM
ejpam-5755	310	73	1	1	NUM
ejpam-5755	310	74	0	0	NUM
ejpam-5755	310	75	0	0	NUM
ejpam-5755	310	76	0	0	NUM
ejpam-5755	310	77	1	1	NUM
ejpam-5755	310	78	0	0	NUM
ejpam-5755	310	79	0	0	NUM
ejpam-5755	310	80	1	1	NUM
ejpam-5755	310	81	0	0	NUM
ejpam-5755	310	82	1	1	NUM
ejpam-5755	310	83	0	0	NUM
ejpam-5755	310	84	1	1	NUM
ejpam-5755	310	85	0	0	NUM
ejpam-5755	310	86	0	0	NUM
ejpam-5755	310	87	0	0	NUM
ejpam-5755	310	88	0	0	NUM
ejpam-5755	310	89	1	1	NUM
ejpam-5755	310	90	0	0	NUM
ejpam-5755	310	91	1	1	NUM
ejpam-5755	310	92	0	0	NUM
ejpam-5755	310	93	0	0	NUM
ejpam-5755	310	94	1	1	NUM
ejpam-5755	310	95	0	0	NUM
ejpam-5755	310	96	0	0	NUM
ejpam-5755	310	97	0	0	NUM
ejpam-5755	310	98	1	1	NUM
ejpam-5755	310	99	0	0	NUM
ejpam-5755	310	100	0	0	NUM
ejpam-5755	310	101	0	0	NUM
ejpam-5755	310	102	0	0	NUM
ejpam-5755	310	103	0	0	NUM
ejpam-5755	310	104	0	0	NUM
ejpam-5755	310	105	1	1	NUM
ejpam-5755	310	106	0	0	NUM
ejpam-5755	310	107	0	0	NUM
ejpam-5755	310	108	0	0	NUM
ejpam-5755	310	109	1	1	NUM
ejpam-5755	310	110	0	0	NUM
ejpam-5755	310	111	0	0	NUM
ejpam-5755	310	112	1	1	NUM
ejpam-5755	310	113	0	0	NUM
ejpam-5755	310	114	0	0	NUM
ejpam-5755	310	115	0	0	NUM
ejpam-5755	310	116	1	1	NUM
ejpam-5755	310	117	0	0	NUM
ejpam-5755	310	118			NUM
ejpam-5755	310	119	and	and	CCONJ
ejpam-5755	310	120	q	q	NOUN
ejpam-5755	310	121	=	=	SYM
ejpam-5755	310	122			ADJ
ejpam-5755	310	123	−2	−2	NOUN
ejpam-5755	310	124	1	1	NUM
ejpam-5755	310	125	1	1	NUM
ejpam-5755	310	126	0	0	NUM
ejpam-5755	310	127	0	0	NUM
ejpam-5755	310	128	0	0	NUM
ejpam-5755	310	129	0	0	NUM
ejpam-5755	310	130	0	0	NUM
ejpam-5755	310	131	0	0	NUM
ejpam-5755	310	132	1	1	NUM
ejpam-5755	310	133	−2	−2	NOUN
ejpam-5755	310	134	0	0	NUM
ejpam-5755	310	135	0	0	NUM
ejpam-5755	310	136	0	0	NUM
ejpam-5755	310	137	0	0	NUM
ejpam-5755	310	138	0	0	NUM
ejpam-5755	310	139	1	1	NUM
ejpam-5755	310	140	0	0	NUM
ejpam-5755	310	141	1	1	NUM
ejpam-5755	310	142	0	0	NUM
ejpam-5755	311	1	−3	−3	NOUN
ejpam-5755	311	2	1	1	NUM
ejpam-5755	311	3	1	1	NUM
ejpam-5755	311	4	0	0	NUM
ejpam-5755	311	5	0	0	NUM
ejpam-5755	311	6	0	0	NUM
ejpam-5755	311	7	0	0	NUM
ejpam-5755	311	8	0	0	NUM
ejpam-5755	311	9	0	0	NUM
ejpam-5755	311	10	1	1	NUM
ejpam-5755	311	11	−4	−4	SYM
ejpam-5755	311	12	1	1	NUM
ejpam-5755	311	13	1	1	NUM
ejpam-5755	311	14	1	1	NUM
ejpam-5755	311	15	0	0	NUM
ejpam-5755	311	16	0	0	NUM
ejpam-5755	311	17	0	0	NUM
ejpam-5755	311	18	0	0	NUM
ejpam-5755	311	19	1	1	NUM
ejpam-5755	311	20	1	1	NUM
ejpam-5755	311	21	−3	−3	NOUN
ejpam-5755	311	22	0	0	NUM
ejpam-5755	311	23	0	0	NUM
ejpam-5755	311	24	0	0	NUM
ejpam-5755	311	25	1	1	NUM
ejpam-5755	311	26	0	0	NUM
ejpam-5755	311	27	0	0	NUM
ejpam-5755	311	28	0	0	NUM
ejpam-5755	311	29	1	1	NUM
ejpam-5755	311	30	0	0	NUM
ejpam-5755	311	31	−3	−3	NOUN
ejpam-5755	311	32	1	1	NUM
ejpam-5755	311	33	1	1	NUM
ejpam-5755	311	34	0	0	NUM
ejpam-5755	311	35	0	0	NUM
ejpam-5755	311	36	0	0	NUM
ejpam-5755	311	37	0	0	NUM
ejpam-5755	311	38	1	1	NUM
ejpam-5755	311	39	0	0	NUM
ejpam-5755	311	40	1	1	NUM
ejpam-5755	311	41	−3	−3	NOUN
ejpam-5755	311	42	0	0	NUM
ejpam-5755	311	43	1	1	NUM
ejpam-5755	311	44	0	0	NUM
ejpam-5755	311	45	1	1	NUM
ejpam-5755	311	46	0	0	NUM
ejpam-5755	311	47	0	0	NUM
ejpam-5755	311	48	0	0	NUM
ejpam-5755	311	49	1	1	NUM
ejpam-5755	311	50	0	0	NUM
ejpam-5755	311	51	−2	−2	NOUN
ejpam-5755	311	52	0	0	NUM
ejpam-5755	311	53	0	0	NUM
ejpam-5755	311	54	0	0	NUM
ejpam-5755	311	55	0	0	NUM
ejpam-5755	311	56	0	0	NUM
ejpam-5755	311	57	1	1	NUM
ejpam-5755	311	58	0	0	NUM
ejpam-5755	311	59	1	1	NUM
ejpam-5755	311	60	0	0	NUM
ejpam-5755	311	61	−2	−2	NOUN
ejpam-5755	311	62			NOUN
ejpam-5755	311	63	.	.	PUNCT
ejpam-5755	312	1	let	let	VERB
ejpam-5755	312	2	(	(	PUNCT
ejpam-5755	312	3	βij	βij	ADJ
ejpam-5755	312	4	)	)	PUNCT
ejpam-5755	312	5	=	=	SYM
ejpam-5755	313	1	(	(	PUNCT
ejpam-5755	313	2	0.75	0.75	NUM
ejpam-5755	313	3	,	,	PUNCT
ejpam-5755	313	4	2,−2	2,−2	NUM
ejpam-5755	313	5	,	,	PUNCT
ejpam-5755	313	6	1,−1	1,−1	NUM
ejpam-5755	313	7	,	,	PUNCT
ejpam-5755	313	8	1.5,−1.5	1.5,−1.5	NUM
ejpam-5755	313	9	,	,	PUNCT
ejpam-5755	313	10	0.5,−0.5)t	0.5,−0.5)t	NUM
ejpam-5755	313	11	∈	∈	PROPN
ejpam-5755	313	12	r9	r9	NOUN
ejpam-5755	313	13	be	be	VERB
ejpam-5755	313	14	the	the	DET
ejpam-5755	313	15	scalar	scalar	ADJ
ejpam-5755	313	16	scales	scale	NOUN
ejpam-5755	313	17	of	of	ADP
ejpam-5755	313	18	edges	edge	NOUN
ejpam-5755	313	19	and	and	CCONJ
ejpam-5755	313	20	(	(	PUNCT
ejpam-5755	313	21	xij(t0	xij(t0	PROPN
ejpam-5755	313	22	)	)	PUNCT
ejpam-5755	313	23	)	)	PUNCT
ejpam-5755	314	1	=	=	PUNCT
ejpam-5755	314	2	(	(	PUNCT
ejpam-5755	314	3	2.5	2.5	NUM
ejpam-5755	314	4	,	,	PUNCT
ejpam-5755	314	5	1,−1	1,−1	NUM
ejpam-5755	314	6	,	,	PUNCT
ejpam-5755	314	7	0.5,−0.5	0.5,−0.5	NUM
ejpam-5755	314	8	,	,	PUNCT
ejpam-5755	314	9	1.5,−1.5,−2	1.5,−1.5,−2	NUM
ejpam-5755	314	10	,	,	PUNCT
ejpam-5755	314	11	2)t	2)t	NUM
ejpam-5755	314	12	∈	∈	PROPN
ejpam-5755	314	13	r9	r9	NOUN
ejpam-5755	314	14	be	be	VERB
ejpam-5755	314	15	the	the	DET
ejpam-5755	314	16	initial	initial	ADJ
ejpam-5755	314	17	values	value	NOUN
ejpam-5755	314	18	of	of	ADP
ejpam-5755	314	19	edges	edge	NOUN
ejpam-5755	314	20	.	.	PUNCT
ejpam-5755	315	1	by	by	ADP
ejpam-5755	315	2	choosing	choose	VERB
ejpam-5755	315	3	h	h	NOUN
ejpam-5755	315	4	=	=	NOUN
ejpam-5755	315	5	0.125	0.125	NUM
ejpam-5755	315	6	,	,	PUNCT
ejpam-5755	315	7	one	one	PRON
ejpam-5755	315	8	obtains	obtain	VERB
ejpam-5755	315	9	that	that	SCONJ
ejpam-5755	315	10	the	the	DET
ejpam-5755	315	11	condition	condition	NOUN
ejpam-5755	315	12	(	(	PUNCT
ejpam-5755	315	13	a1	a1	NOUN
ejpam-5755	315	14	)	)	PUNCT
ejpam-5755	315	15	holds	hold	NOUN
ejpam-5755	315	16	.	.	PUNCT
ejpam-5755	316	1	moreover	moreover	ADV
ejpam-5755	316	2	,	,	PUNCT
ejpam-5755	316	3	by	by	ADP
ejpam-5755	316	4	using	use	VERB
ejpam-5755	316	5	matlab	matlab	PROPN
ejpam-5755	316	6	,	,	PUNCT
ejpam-5755	316	7	it	it	PRON
ejpam-5755	316	8	can	can	AUX
ejpam-5755	316	9	be	be	AUX
ejpam-5755	316	10	seen	see	VERB
ejpam-5755	316	11	that	that	SCONJ
ejpam-5755	316	12	the	the	DET
ejpam-5755	316	13	condition	condition	NOUN
ejpam-5755	316	14	(	(	PUNCT
ejpam-5755	316	15	a2	a2	PROPN
ejpam-5755	316	16	)	)	PUNCT
ejpam-5755	316	17	is	be	AUX
ejpam-5755	316	18	satisfied	satisfied	ADJ
ejpam-5755	316	19	.	.	PUNCT
ejpam-5755	317	1	since	since	SCONJ
ejpam-5755	317	2	the	the	DET
ejpam-5755	317	3	line	line	NOUN
ejpam-5755	317	4	graph	graph	NOUN
ejpam-5755	317	5	l(g	l(g	PROPN
ejpam-5755	317	6	∪	∪	ADJ
ejpam-5755	317	7	g′	g′	NOUN
ejpam-5755	317	8	)	)	PUNCT
ejpam-5755	317	9	is	be	AUX
ejpam-5755	317	10	connected	connect	VERB
ejpam-5755	317	11	,	,	PUNCT
ejpam-5755	317	12	theorem	theorem	VERB
ejpam-5755	317	13	1	1	NUM
ejpam-5755	317	14	can	can	AUX
ejpam-5755	317	15	guarantee	guarantee	VERB
ejpam-5755	317	16	reaching	reach	VERB
ejpam-5755	317	17	scaled	scale	VERB
ejpam-5755	317	18	consensus	consensus	NOUN
ejpam-5755	317	19	of	of	ADP
ejpam-5755	317	20	edge	edge	NOUN
ejpam-5755	317	21	dynamics	dynamic	NOUN
ejpam-5755	317	22	under	under	ADP
ejpam-5755	317	23	protocol	protocol	NOUN
ejpam-5755	317	24	(	(	PUNCT
ejpam-5755	317	25	3.1	3.1	NUM
ejpam-5755	317	26	)	)	PUNCT
ejpam-5755	317	27	and	and	CCONJ
ejpam-5755	317	28	the	the	DET
ejpam-5755	317	29	state	state	NOUN
ejpam-5755	317	30	trajectories	trajectory	NOUN
ejpam-5755	317	31	of	of	ADP
ejpam-5755	317	32	all	all	DET
ejpam-5755	317	33	edge	edge	NOUN
ejpam-5755	317	34	can	can	AUX
ejpam-5755	317	35	be	be	AUX
ejpam-5755	317	36	described	describe	VERB
ejpam-5755	317	37	as	as	ADP
ejpam-5755	317	38	in	in	ADP
ejpam-5755	317	39	figure	figure	NOUN
ejpam-5755	317	40	3	3	NUM
ejpam-5755	317	41	.	.	PUNCT
ejpam-5755	317	42	figure	figure	VERB
ejpam-5755	317	43	3	3	NUM
ejpam-5755	317	44	:	:	PUNCT
ejpam-5755	317	45	the	the	DET
ejpam-5755	317	46	state	state	NOUN
ejpam-5755	317	47	trajectory	trajectory	NOUN
ejpam-5755	317	48	of	of	ADP
ejpam-5755	317	49	each	each	DET
ejpam-5755	317	50	edge	edge	NOUN
ejpam-5755	317	51	using	use	VERB
ejpam-5755	317	52	protocol(3.1	protocol(3.1	NOUN
ejpam-5755	317	53	)	)	PUNCT
ejpam-5755	317	54	with	with	ADP
ejpam-5755	317	55	h	h	NOUN
ejpam-5755	317	56	=	=	NOUN
ejpam-5755	317	57	0.125	0.125	NUM
ejpam-5755	317	58	and	and	CCONJ
ejpam-5755	317	59	(	(	PUNCT
ejpam-5755	317	60	βij	βij	NOUN
ejpam-5755	317	61	)	)	PUNCT
ejpam-5755	317	62	=	=	SYM
ejpam-5755	317	63	(	(	PUNCT
ejpam-5755	317	64	0.75	0.75	NUM
ejpam-5755	317	65	,	,	PUNCT
ejpam-5755	317	66	2,−2	2,−2	NUM
ejpam-5755	317	67	,	,	PUNCT
ejpam-5755	317	68	1,−1	1,−1	NUM
ejpam-5755	317	69	,	,	PUNCT
ejpam-5755	317	70	1.5,−1.5	1.5,−1.5	NUM
ejpam-5755	317	71	,	,	PUNCT
ejpam-5755	317	72	0.5,−0.5)t	0.5,−0.5)t	NUM
ejpam-5755	317	73	.	.	PUNCT
ejpam-5755	318	1	s.	s.	PROPN
ejpam-5755	318	2	donganont	donganont	PROPN
ejpam-5755	318	3	,	,	PUNCT
ejpam-5755	318	4	u.	u.	NOUN
ejpam-5755	318	5	witthayarat	witthayarat	NOUN
ejpam-5755	318	6	,	,	PUNCT
ejpam-5755	318	7	m.	m.	NOUN
ejpam-5755	318	8	donganont	donganont	PROPN
ejpam-5755	318	9	/	/	SYM
ejpam-5755	318	10	eur	eur	PROPN
ejpam-5755	318	11	.	.	PUNCT
ejpam-5755	319	1	j.	j.	PROPN
ejpam-5755	319	2	pure	pure	PROPN
ejpam-5755	319	3	appl	appl	PROPN
ejpam-5755	319	4	.	.	PROPN
ejpam-5755	319	5	math	math	PROPN
ejpam-5755	319	6	,	,	PUNCT
ejpam-5755	319	7	18	18	NUM
ejpam-5755	319	8	(	(	PUNCT
ejpam-5755	319	9	1	1	NUM
ejpam-5755	319	10	)	)	PUNCT
ejpam-5755	319	11	(	(	PUNCT
ejpam-5755	319	12	2025	2025	NUM
ejpam-5755	319	13	)	)	PUNCT
ejpam-5755	319	14	,	,	PUNCT
ejpam-5755	319	15	5755	5755	NUM
ejpam-5755	319	16	14	14	NUM
ejpam-5755	319	17	of	of	ADP
ejpam-5755	319	18	17	17	NUM
ejpam-5755	319	19	in	in	ADP
ejpam-5755	319	20	addition	addition	NOUN
ejpam-5755	319	21	,	,	PUNCT
ejpam-5755	319	22	when	when	SCONJ
ejpam-5755	319	23	(	(	PUNCT
ejpam-5755	319	24	βij	βij	NOUN
ejpam-5755	319	25	)	)	PUNCT
ejpam-5755	319	26	=	=	PUNCT
ejpam-5755	319	27	(	(	PUNCT
ejpam-5755	319	28	1	1	NUM
ejpam-5755	319	29	,	,	PUNCT
ejpam-5755	319	30	1	1	NUM
ejpam-5755	319	31	,	,	PUNCT
ejpam-5755	319	32	1	1	NUM
ejpam-5755	319	33	,	,	PUNCT
ejpam-5755	319	34	1	1	NUM
ejpam-5755	319	35	,	,	PUNCT
ejpam-5755	319	36	1	1	NUM
ejpam-5755	319	37	,	,	PUNCT
ejpam-5755	319	38	1	1	NUM
ejpam-5755	319	39	,	,	PUNCT
ejpam-5755	319	40	1	1	NUM
ejpam-5755	319	41	,	,	PUNCT
ejpam-5755	319	42	1)t	1)t	NUM
ejpam-5755	319	43	the	the	DET
ejpam-5755	319	44	scaled	scale	VERB
ejpam-5755	319	45	consensus	consensus	NOUN
ejpam-5755	319	46	problems	problem	NOUN
ejpam-5755	319	47	are	be	AUX
ejpam-5755	319	48	the	the	DET
ejpam-5755	319	49	usual	usual	ADJ
ejpam-5755	319	50	consensus	consensus	NOUN
ejpam-5755	319	51	problems	problem	NOUN
ejpam-5755	319	52	(	(	PUNCT
ejpam-5755	319	53	see	see	VERB
ejpam-5755	319	54	figure	figure	NOUN
ejpam-5755	319	55	4	4	NUM
ejpam-5755	319	56	)	)	PUNCT
ejpam-5755	319	57	.	.	PUNCT
ejpam-5755	320	1	figure	figure	VERB
ejpam-5755	320	2	4	4	NUM
ejpam-5755	320	3	:	:	PUNCT
ejpam-5755	320	4	the	the	DET
ejpam-5755	320	5	state	state	NOUN
ejpam-5755	320	6	of	of	ADP
ejpam-5755	320	7	each	each	DET
ejpam-5755	320	8	edge	edge	NOUN
ejpam-5755	320	9	under	under	ADP
ejpam-5755	320	10	protocol	protocol	NOUN
ejpam-5755	320	11	(	(	PUNCT
ejpam-5755	320	12	3.1	3.1	NUM
ejpam-5755	320	13	)	)	PUNCT
ejpam-5755	320	14	with	with	ADP
ejpam-5755	320	15	(	(	PUNCT
ejpam-5755	320	16	βij	βij	NOUN
ejpam-5755	320	17	)	)	PUNCT
ejpam-5755	320	18	=	=	PUNCT
ejpam-5755	321	1	(	(	PUNCT
ejpam-5755	321	2	1	1	NUM
ejpam-5755	321	3	,	,	PUNCT
ejpam-5755	321	4	1	1	NUM
ejpam-5755	321	5	,	,	PUNCT
ejpam-5755	321	6	1	1	NUM
ejpam-5755	321	7	,	,	PUNCT
ejpam-5755	321	8	1	1	NUM
ejpam-5755	321	9	,	,	PUNCT
ejpam-5755	321	10	1	1	NUM
ejpam-5755	321	11	,	,	PUNCT
ejpam-5755	321	12	1	1	NUM
ejpam-5755	321	13	,	,	PUNCT
ejpam-5755	321	14	1	1	NUM
ejpam-5755	321	15	,	,	PUNCT
ejpam-5755	321	16	1	1	NUM
ejpam-5755	321	17	,	,	PUNCT
ejpam-5755	321	18	1)t	1)t	NUM
ejpam-5755	321	19	and	and	CCONJ
ejpam-5755	321	20	h	h	NOUN
ejpam-5755	322	1	=	=	NOUN
ejpam-5755	322	2	0.125	0.125	NUM
ejpam-5755	322	3	.	.	PUNCT
ejpam-5755	323	1	however	however	ADV
ejpam-5755	323	2	,	,	PUNCT
ejpam-5755	323	3	if	if	SCONJ
ejpam-5755	323	4	h	h	NOUN
ejpam-5755	323	5	is	be	AUX
ejpam-5755	323	6	not	not	PART
ejpam-5755	323	7	satisfied	satisfy	VERB
ejpam-5755	323	8	the	the	DET
ejpam-5755	323	9	condition	condition	NOUN
ejpam-5755	323	10	(	(	PUNCT
ejpam-5755	323	11	a1	a1	NOUN
ejpam-5755	323	12	)	)	PUNCT
ejpam-5755	323	13	,	,	PUNCT
ejpam-5755	323	14	the	the	DET
ejpam-5755	323	15	protocol	protocol	NOUN
ejpam-5755	323	16	(	(	PUNCT
ejpam-5755	323	17	3.1	3.1	NUM
ejpam-5755	323	18	)	)	PUNCT
ejpam-5755	323	19	can	can	AUX
ejpam-5755	323	20	not	not	PART
ejpam-5755	323	21	guarantee	guarantee	VERB
ejpam-5755	323	22	reaching	reach	VERB
ejpam-5755	323	23	scaled	scale	VERB
ejpam-5755	323	24	consensus	consensus	NOUN
ejpam-5755	323	25	problem	problem	NOUN
ejpam-5755	323	26	as	as	SCONJ
ejpam-5755	323	27	shown	show	VERB
ejpam-5755	323	28	in	in	ADP
ejpam-5755	323	29	figure	figure	NOUN
ejpam-5755	323	30	5	5	NUM
ejpam-5755	323	31	.	.	PUNCT
ejpam-5755	324	1	it	it	PRON
ejpam-5755	324	2	can	can	AUX
ejpam-5755	324	3	be	be	AUX
ejpam-5755	324	4	seen	see	VERB
ejpam-5755	324	5	that	that	SCONJ
ejpam-5755	324	6	protocols	protocol	NOUN
ejpam-5755	324	7	(	(	PUNCT
ejpam-5755	324	8	3.1	3.1	NUM
ejpam-5755	324	9	)	)	PUNCT
ejpam-5755	324	10	and	and	CCONJ
ejpam-5755	324	11	(	(	PUNCT
ejpam-5755	324	12	3.7	3.7	NUM
ejpam-5755	324	13	)	)	PUNCT
ejpam-5755	324	14	can	can	AUX
ejpam-5755	324	15	solve	solve	VERB
ejpam-5755	324	16	scaled	scale	VERB
ejpam-5755	324	17	consensus	consensus	NOUN
ejpam-5755	324	18	problems	problem	NOUN
ejpam-5755	324	19	if	if	SCONJ
ejpam-5755	324	20	the	the	DET
ejpam-5755	324	21	step	step	NOUN
ejpam-5755	324	22	size	size	NOUN
ejpam-5755	324	23	is	be	AUX
ejpam-5755	324	24	small	small	ADJ
ejpam-5755	324	25	enough	enough	ADV
ejpam-5755	324	26	satisfying	satisfy	VERB
ejpam-5755	324	27	(	(	PUNCT
ejpam-5755	324	28	a1	a1	NOUN
ejpam-5755	324	29	)	)	PUNCT
ejpam-5755	324	30	.	.	PUNCT
ejpam-5755	325	1	in	in	ADP
ejpam-5755	325	2	addition	addition	NOUN
ejpam-5755	325	3	,	,	PUNCT
ejpam-5755	325	4	our	our	PRON
ejpam-5755	325	5	results	result	NOUN
ejpam-5755	325	6	demonstrate	demonstrate	VERB
ejpam-5755	325	7	that	that	SCONJ
ejpam-5755	325	8	the	the	DET
ejpam-5755	325	9	scaled	scale	VERB
ejpam-5755	325	10	consensus	consensus	NOUN
ejpam-5755	325	11	problems	problem	NOUN
ejpam-5755	325	12	on	on	ADP
ejpam-5755	325	13	edge	edge	NOUN
ejpam-5755	325	14	dynamics	dynamic	NOUN
ejpam-5755	325	15	are	be	AUX
ejpam-5755	325	16	solved	solve	VERB
ejpam-5755	325	17	if	if	SCONJ
ejpam-5755	325	18	the	the	DET
ejpam-5755	325	19	communication	communication	NOUN
ejpam-5755	325	20	network	network	NOUN
ejpam-5755	325	21	l(g	l(g	PROPN
ejpam-5755	325	22	∪	∪	PROPN
ejpam-5755	325	23	g′	g′	NOUN
ejpam-5755	325	24	)	)	PUNCT
ejpam-5755	325	25	is	be	AUX
ejpam-5755	325	26	balanced	balance	VERB
ejpam-5755	325	27	and	and	CCONJ
ejpam-5755	325	28	contains	contain	VERB
ejpam-5755	325	29	a	a	DET
ejpam-5755	325	30	spanning	span	VERB
ejpam-5755	325	31	tree	tree	NOUN
ejpam-5755	325	32	(	(	PUNCT
ejpam-5755	325	33	see	see	VERB
ejpam-5755	325	34	figure	figure	NOUN
ejpam-5755	325	35	3	3	NUM
ejpam-5755	325	36	)	)	PUNCT
ejpam-5755	325	37	.	.	PUNCT
ejpam-5755	326	1	on	on	ADP
ejpam-5755	326	2	the	the	DET
ejpam-5755	326	3	other	other	ADJ
ejpam-5755	326	4	hand	hand	NOUN
ejpam-5755	326	5	,	,	PUNCT
ejpam-5755	326	6	if	if	SCONJ
ejpam-5755	326	7	the	the	DET
ejpam-5755	326	8	sampling	sample	VERB
ejpam-5755	326	9	period	period	NOUN
ejpam-5755	326	10	h	h	NOUN
ejpam-5755	326	11	is	be	AUX
ejpam-5755	326	12	not	not	PART
ejpam-5755	326	13	satisfied	satisfy	VERB
ejpam-5755	326	14	the	the	DET
ejpam-5755	326	15	condition	condition	NOUN
ejpam-5755	326	16	(	(	PUNCT
ejpam-5755	326	17	a1	a1	NOUN
ejpam-5755	326	18	)	)	PUNCT
ejpam-5755	326	19	,	,	PUNCT
ejpam-5755	326	20	edge	edge	NOUN
ejpam-5755	326	21	consensus	consensus	NOUN
ejpam-5755	326	22	can	can	AUX
ejpam-5755	326	23	not	not	PART
ejpam-5755	326	24	guarantee	guarantee	VERB
ejpam-5755	326	25	(	(	PUNCT
ejpam-5755	326	26	see	see	VERB
ejpam-5755	326	27	figure	figure	NOUN
ejpam-5755	326	28	5	5	NUM
ejpam-5755	326	29	)	)	PUNCT
ejpam-5755	326	30	.	.	PUNCT
ejpam-5755	327	1	moreover	moreover	ADV
ejpam-5755	327	2	,	,	PUNCT
ejpam-5755	327	3	if	if	SCONJ
ejpam-5755	327	4	the	the	DET
ejpam-5755	327	5	scalar	scalar	ADJ
ejpam-5755	327	6	scale	scale	NOUN
ejpam-5755	327	7	βij	βij	NOUN
ejpam-5755	327	8	=	=	SYM
ejpam-5755	327	9	1	1	NUM
ejpam-5755	327	10	,	,	PUNCT
ejpam-5755	327	11	the	the	DET
ejpam-5755	327	12	simulations	simulation	NOUN
ejpam-5755	327	13	results	result	VERB
ejpam-5755	327	14	(	(	PUNCT
ejpam-5755	327	15	see	see	VERB
ejpam-5755	327	16	figure	figure	NOUN
ejpam-5755	327	17	4	4	NUM
ejpam-5755	327	18	)	)	PUNCT
ejpam-5755	327	19	show	show	VERB
ejpam-5755	327	20	the	the	DET
ejpam-5755	327	21	effectiveness	effectiveness	NOUN
ejpam-5755	327	22	and	and	CCONJ
ejpam-5755	327	23	generalization	generalization	NOUN
ejpam-5755	327	24	of	of	ADP
ejpam-5755	327	25	our	our	PRON
ejpam-5755	327	26	theorems	theorem	NOUN
ejpam-5755	327	27	compared	compare	VERB
ejpam-5755	327	28	to	to	ADP
ejpam-5755	327	29	the	the	DET
ejpam-5755	327	30	results	result	NOUN
ejpam-5755	327	31	of	of	ADP
ejpam-5755	327	32	[	[	X
ejpam-5755	327	33	14	14	NUM
ejpam-5755	327	34	,	,	PUNCT
ejpam-5755	327	35	18	18	NUM
ejpam-5755	327	36	]	]	PUNCT
ejpam-5755	327	37	.	.	PUNCT
ejpam-5755	328	1	the	the	DET
ejpam-5755	328	2	paper	paper	NOUN
ejpam-5755	328	3	’s	’s	PART
ejpam-5755	328	4	theoretical	theoretical	ADJ
ejpam-5755	328	5	contributions	contribution	NOUN
ejpam-5755	328	6	offer	offer	VERB
ejpam-5755	328	7	practical	practical	ADJ
ejpam-5755	328	8	advancements	advancement	NOUN
ejpam-5755	328	9	in	in	ADP
ejpam-5755	328	10	domains	domain	NOUN
ejpam-5755	328	11	such	such	ADJ
ejpam-5755	328	12	as	as	ADP
ejpam-5755	328	13	autonomous	autonomous	ADJ
ejpam-5755	328	14	vehicles	vehicle	NOUN
ejpam-5755	328	15	and	and	CCONJ
ejpam-5755	328	16	distributed	distribute	VERB
ejpam-5755	328	17	energy	energy	NOUN
ejpam-5755	328	18	systems	system	NOUN
ejpam-5755	328	19	,	,	PUNCT
ejpam-5755	328	20	where	where	SCONJ
ejpam-5755	328	21	scaled	scaled	ADJ
ejpam-5755	328	22	consensus	consensus	NOUN
ejpam-5755	328	23	protocols	protocol	NOUN
ejpam-5755	328	24	can	can	AUX
ejpam-5755	328	25	enhance	enhance	VERB
ejpam-5755	328	26	both	both	DET
ejpam-5755	328	27	efficiency	efficiency	NOUN
ejpam-5755	328	28	and	and	CCONJ
ejpam-5755	328	29	reliability	reliability	NOUN
ejpam-5755	328	30	.	.	PUNCT
ejpam-5755	329	1	by	by	ADP
ejpam-5755	329	2	dynamically	dynamically	ADV
ejpam-5755	329	3	adjusting	adjust	VERB
ejpam-5755	329	4	proportional	proportional	ADJ
ejpam-5755	329	5	metrics	metric	NOUN
ejpam-5755	329	6	and	and	CCONJ
ejpam-5755	329	7	reducing	reduce	VERB
ejpam-5755	329	8	communication	communication	NOUN
ejpam-5755	329	9	demands	demand	NOUN
ejpam-5755	329	10	,	,	PUNCT
ejpam-5755	329	11	these	these	DET
ejpam-5755	329	12	protocols	protocol	NOUN
ejpam-5755	329	13	provide	provide	VERB
ejpam-5755	329	14	robust	robust	ADJ
ejpam-5755	329	15	solutions	solution	NOUN
ejpam-5755	329	16	for	for	ADP
ejpam-5755	329	17	complex	complex	ADJ
ejpam-5755	329	18	,	,	PUNCT
ejpam-5755	329	19	dynamic	dynamic	ADJ
ejpam-5755	329	20	,	,	PUNCT
ejpam-5755	329	21	and	and	CCONJ
ejpam-5755	329	22	heterogeneous	heterogeneous	ADJ
ejpam-5755	329	23	environments	environment	NOUN
ejpam-5755	329	24	.	.	PUNCT
ejpam-5755	330	1	in	in	ADP
ejpam-5755	330	2	autonomous	autonomous	ADJ
ejpam-5755	330	3	vehicles	vehicle	NOUN
ejpam-5755	330	4	,	,	PUNCT
ejpam-5755	330	5	scaled	scale	VERB
ejpam-5755	330	6	consensus	consensus	NOUN
ejpam-5755	330	7	enables	enable	VERB
ejpam-5755	330	8	dynamic	dynamic	ADJ
ejpam-5755	330	9	inter	inter	ADJ
ejpam-5755	330	10	-	-	NOUN
ejpam-5755	330	11	vehicle	vehicle	NOUN
ejpam-5755	330	12	distance	distance	NOUN
ejpam-5755	330	13	adjustments	adjustment	NOUN
ejpam-5755	330	14	based	base	VERB
ejpam-5755	330	15	on	on	ADP
ejpam-5755	330	16	individual	individual	ADJ
ejpam-5755	330	17	capabilities	capability	NOUN
ejpam-5755	330	18	like	like	ADP
ejpam-5755	330	19	braking	brake	VERB
ejpam-5755	330	20	power	power	NOUN
ejpam-5755	330	21	or	or	CCONJ
ejpam-5755	330	22	acceleration	acceleration	NOUN
ejpam-5755	330	23	limits	limit	NOUN
ejpam-5755	330	24	,	,	PUNCT
ejpam-5755	330	25	improving	improve	VERB
ejpam-5755	330	26	safety	safety	NOUN
ejpam-5755	330	27	and	and	CCONJ
ejpam-5755	330	28	traffic	traffic	NOUN
ejpam-5755	330	29	efficiency	efficiency	NOUN
ejpam-5755	330	30	.	.	PUNCT
ejpam-5755	331	1	the	the	DET
ejpam-5755	331	2	impulsive	impulsive	ADJ
ejpam-5755	331	3	protocol	protocol	NOUN
ejpam-5755	331	4	’s	’s	PART
ejpam-5755	331	5	ability	ability	NOUN
ejpam-5755	331	6	to	to	PART
ejpam-5755	331	7	minimize	minimize	VERB
ejpam-5755	331	8	communication	communication	NOUN
ejpam-5755	331	9	frequency	frequency	NOUN
ejpam-5755	331	10	proves	prove	VERB
ejpam-5755	331	11	valuable	valuable	ADJ
ejpam-5755	331	12	in	in	ADP
ejpam-5755	331	13	areas	area	NOUN
ejpam-5755	331	14	with	with	ADP
ejpam-5755	331	15	intermittent	intermittent	ADJ
ejpam-5755	331	16	connectivity	connectivity	NOUN
ejpam-5755	331	17	,	,	PUNCT
ejpam-5755	331	18	such	such	ADJ
ejpam-5755	331	19	as	as	ADP
ejpam-5755	331	20	dense	dense	ADJ
ejpam-5755	331	21	urban	urban	ADJ
ejpam-5755	331	22	networks	network	NOUN
ejpam-5755	331	23	or	or	CCONJ
ejpam-5755	331	24	rural	rural	ADJ
ejpam-5755	331	25	highways	highway	NOUN
ejpam-5755	331	26	.	.	PUNCT
ejpam-5755	332	1	similarly	similarly	ADV
ejpam-5755	332	2	,	,	PUNCT
ejpam-5755	332	3	in	in	ADP
ejpam-5755	332	4	distributed	distribute	VERB
ejpam-5755	332	5	energy	energy	NOUN
ejpam-5755	332	6	systems	system	NOUN
ejpam-5755	332	7	,	,	PUNCT
ejpam-5755	332	8	scaled	scaled	ADJ
ejpam-5755	332	9	consens	consen	NOUN
ejpam-5755	332	10	.	.	PUNCT
ejpam-5755	333	1	donganont	donganont	PROPN
ejpam-5755	333	2	,	,	PUNCT
ejpam-5755	333	3	u.	u.	NOUN
ejpam-5755	333	4	witthayarat	witthayarat	NOUN
ejpam-5755	333	5	,	,	PUNCT
ejpam-5755	333	6	m.	m.	NOUN
ejpam-5755	333	7	donganont	donganont	PROPN
ejpam-5755	333	8	/	/	SYM
ejpam-5755	333	9	eur	eur	PROPN
ejpam-5755	333	10	.	.	PUNCT
ejpam-5755	334	1	j.	j.	PROPN
ejpam-5755	334	2	pure	pure	PROPN
ejpam-5755	334	3	appl	appl	PROPN
ejpam-5755	334	4	.	.	PROPN
ejpam-5755	334	5	math	math	PROPN
ejpam-5755	334	6	,	,	PUNCT
ejpam-5755	334	7	18	18	NUM
ejpam-5755	334	8	(	(	PUNCT
ejpam-5755	334	9	1	1	NUM
ejpam-5755	334	10	)	)	PUNCT
ejpam-5755	334	11	(	(	PUNCT
ejpam-5755	334	12	2025	2025	NUM
ejpam-5755	334	13	)	)	PUNCT
ejpam-5755	334	14	,	,	PUNCT
ejpam-5755	334	15	5755	5755	NUM
ejpam-5755	334	16	15	15	NUM
ejpam-5755	334	17	of	of	ADP
ejpam-5755	334	18	17	17	NUM
ejpam-5755	334	19	figure	figure	NOUN
ejpam-5755	334	20	5	5	NUM
ejpam-5755	334	21	:	:	PUNCT
ejpam-5755	334	22	the	the	DET
ejpam-5755	334	23	state	state	NOUN
ejpam-5755	334	24	trajectories	trajectory	NOUN
ejpam-5755	334	25	of	of	ADP
ejpam-5755	334	26	all	all	DET
ejpam-5755	334	27	edges	edge	NOUN
ejpam-5755	334	28	using	use	VERB
ejpam-5755	334	29	the	the	DET
ejpam-5755	334	30	consensus	consensus	NOUN
ejpam-5755	334	31	protocol	protocol	NOUN
ejpam-5755	334	32	(	(	PUNCT
ejpam-5755	334	33	3.1	3.1	NUM
ejpam-5755	334	34	)	)	PUNCT
ejpam-5755	334	35	with	with	ADP
ejpam-5755	334	36	h	h	NOUN
ejpam-5755	334	37	=	=	NOUN
ejpam-5755	334	38	0.3	0.3	NUM
ejpam-5755	334	39	and	and	CCONJ
ejpam-5755	334	40	(	(	PUNCT
ejpam-5755	334	41	βij	βij	NOUN
ejpam-5755	334	42	)	)	PUNCT
ejpam-5755	334	43	=	=	SYM
ejpam-5755	334	44	(	(	PUNCT
ejpam-5755	334	45	0.75	0.75	NUM
ejpam-5755	334	46	,	,	PUNCT
ejpam-5755	334	47	2,−2	2,−2	NUM
ejpam-5755	334	48	,	,	PUNCT
ejpam-5755	334	49	1,−1	1,−1	NUM
ejpam-5755	334	50	,	,	PUNCT
ejpam-5755	334	51	1.5,−1.5	1.5,−1.5	NUM
ejpam-5755	334	52	,	,	PUNCT
ejpam-5755	334	53	0.5,−0.5)t	0.5,−0.5)t	NUM
ejpam-5755	334	54	.	.	PUNCT
ejpam-5755	335	1	sus	sus	PROPN
ejpam-5755	335	2	facilitates	facilitate	VERB
ejpam-5755	335	3	proportional	proportional	ADJ
ejpam-5755	335	4	power	power	NOUN
ejpam-5755	335	5	distribution	distribution	NOUN
ejpam-5755	335	6	among	among	ADP
ejpam-5755	335	7	resources	resource	NOUN
ejpam-5755	335	8	like	like	ADP
ejpam-5755	335	9	solar	solar	ADJ
ejpam-5755	335	10	panels	panel	NOUN
ejpam-5755	335	11	or	or	CCONJ
ejpam-5755	335	12	wind	wind	NOUN
ejpam-5755	335	13	turbines	turbine	NOUN
ejpam-5755	335	14	,	,	PUNCT
ejpam-5755	335	15	optimizing	optimize	VERB
ejpam-5755	335	16	load	load	NOUN
ejpam-5755	335	17	balancing	balancing	NOUN
ejpam-5755	335	18	and	and	CCONJ
ejpam-5755	335	19	efficiency	efficiency	NOUN
ejpam-5755	335	20	.	.	PUNCT
ejpam-5755	336	1	by	by	ADP
ejpam-5755	336	2	reducing	reduce	VERB
ejpam-5755	336	3	communication	communication	NOUN
ejpam-5755	336	4	demands	demand	NOUN
ejpam-5755	336	5	,	,	PUNCT
ejpam-5755	336	6	the	the	DET
ejpam-5755	336	7	approach	approach	NOUN
ejpam-5755	336	8	ensures	ensure	VERB
ejpam-5755	336	9	stable	stable	ADJ
ejpam-5755	336	10	operation	operation	NOUN
ejpam-5755	336	11	even	even	ADV
ejpam-5755	336	12	during	during	ADP
ejpam-5755	336	13	peak	peak	NOUN
ejpam-5755	336	14	loads	load	NOUN
ejpam-5755	336	15	or	or	CCONJ
ejpam-5755	336	16	in	in	ADP
ejpam-5755	336	17	resource	resource	NOUN
ejpam-5755	336	18	-	-	PUNCT
ejpam-5755	336	19	constrained	constrain	VERB
ejpam-5755	336	20	networks	network	NOUN
ejpam-5755	336	21	.	.	PUNCT
ejpam-5755	337	1	these	these	DET
ejpam-5755	337	2	methods	method	NOUN
ejpam-5755	337	3	also	also	ADV
ejpam-5755	337	4	extend	extend	VERB
ejpam-5755	337	5	to	to	ADP
ejpam-5755	337	6	applications	application	NOUN
ejpam-5755	337	7	in	in	ADP
ejpam-5755	337	8	multi	multi	ADJ
ejpam-5755	337	9	-	-	ADJ
ejpam-5755	337	10	robot	robot	ADJ
ejpam-5755	337	11	systems	system	NOUN
ejpam-5755	337	12	and	and	CCONJ
ejpam-5755	337	13	sensor	sensor	NOUN
ejpam-5755	337	14	networks	network	NOUN
ejpam-5755	337	15	,	,	PUNCT
ejpam-5755	337	16	where	where	SCONJ
ejpam-5755	337	17	their	their	PRON
ejpam-5755	337	18	scalability	scalability	NOUN
ejpam-5755	337	19	and	and	CCONJ
ejpam-5755	337	20	adaptability	adaptability	NOUN
ejpam-5755	337	21	support	support	VERB
ejpam-5755	337	22	efficient	efficient	ADJ
ejpam-5755	337	23	task	task	NOUN
ejpam-5755	337	24	allocation	allocation	NOUN
ejpam-5755	337	25	and	and	CCONJ
ejpam-5755	337	26	data	datum	NOUN
ejpam-5755	337	27	aggregation	aggregation	NOUN
ejpam-5755	337	28	.	.	PUNCT
ejpam-5755	338	1	5	5	X
ejpam-5755	338	2	.	.	X
ejpam-5755	338	3	conclusion	conclusion	NOUN
ejpam-5755	338	4	this	this	DET
ejpam-5755	338	5	paper	paper	NOUN
ejpam-5755	338	6	presented	present	VERB
ejpam-5755	338	7	impulsive	impulsive	ADJ
ejpam-5755	338	8	protocols	protocol	NOUN
ejpam-5755	338	9	for	for	ADP
ejpam-5755	338	10	scaled	scale	VERB
ejpam-5755	338	11	consensus	consensus	NOUN
ejpam-5755	338	12	in	in	ADP
ejpam-5755	338	13	edge	edge	NOUN
ejpam-5755	338	14	-	-	PUNCT
ejpam-5755	338	15	dynamic	dynamic	ADJ
ejpam-5755	338	16	multiagent	multiagent	NOUN
ejpam-5755	338	17	systems	system	NOUN
ejpam-5755	338	18	.	.	PUNCT
ejpam-5755	339	1	using	use	VERB
ejpam-5755	339	2	graph	graph	NOUN
ejpam-5755	339	3	theory	theory	NOUN
ejpam-5755	339	4	,	,	PUNCT
ejpam-5755	339	5	matrix	matrix	NOUN
ejpam-5755	339	6	analysis	analysis	NOUN
ejpam-5755	339	7	,	,	PUNCT
ejpam-5755	339	8	and	and	CCONJ
ejpam-5755	339	9	lyapunov	lyapunov	ADJ
ejpam-5755	339	10	stability	stability	NOUN
ejpam-5755	339	11	,	,	PUNCT
ejpam-5755	339	12	we	we	PRON
ejpam-5755	339	13	derived	derive	VERB
ejpam-5755	339	14	sufficient	sufficient	ADJ
ejpam-5755	339	15	conditions	condition	NOUN
ejpam-5755	339	16	for	for	ADP
ejpam-5755	339	17	achieving	achieve	VERB
ejpam-5755	339	18	scaled	scale	VERB
ejpam-5755	339	19	consensus	consensus	NOUN
ejpam-5755	339	20	under	under	ADP
ejpam-5755	339	21	directed	direct	VERB
ejpam-5755	339	22	and	and	CCONJ
ejpam-5755	339	23	undirected	undirected	ADJ
ejpam-5755	339	24	topologies	topology	NOUN
ejpam-5755	339	25	,	,	PUNCT
ejpam-5755	339	26	demonstrating	demonstrate	VERB
ejpam-5755	339	27	robustness	robustness	NOUN
ejpam-5755	339	28	and	and	CCONJ
ejpam-5755	339	29	efficiency	efficiency	NOUN
ejpam-5755	339	30	in	in	ADP
ejpam-5755	339	31	handling	handle	VERB
ejpam-5755	339	32	edge	edge	NOUN
ejpam-5755	339	33	dynamics	dynamic	NOUN
ejpam-5755	339	34	while	while	SCONJ
ejpam-5755	339	35	ensuring	ensure	VERB
ejpam-5755	339	36	convergence	convergence	NOUN
ejpam-5755	339	37	to	to	ADP
ejpam-5755	339	38	desired	desire	VERB
ejpam-5755	339	39	proportional	proportional	ADJ
ejpam-5755	339	40	ratios	ratio	NOUN
ejpam-5755	339	41	.	.	PUNCT
ejpam-5755	340	1	numerical	numerical	ADJ
ejpam-5755	340	2	simulations	simulation	NOUN
ejpam-5755	340	3	validated	validate	VERB
ejpam-5755	340	4	the	the	DET
ejpam-5755	340	5	theoretical	theoretical	ADJ
ejpam-5755	340	6	results	result	NOUN
ejpam-5755	340	7	,	,	PUNCT
ejpam-5755	340	8	showcasing	showcase	VERB
ejpam-5755	340	9	the	the	DET
ejpam-5755	340	10	protocols	protocol	NOUN
ejpam-5755	340	11	’	'	PUNCT
ejpam-5755	340	12	effectiveness	effectiveness	NOUN
ejpam-5755	340	13	in	in	ADP
ejpam-5755	340	14	reducing	reduce	VERB
ejpam-5755	340	15	communication	communication	NOUN
ejpam-5755	340	16	overhead	overhead	ADV
ejpam-5755	340	17	and	and	CCONJ
ejpam-5755	340	18	accelerating	accelerate	VERB
ejpam-5755	340	19	convergence	convergence	NOUN
ejpam-5755	340	20	compared	compare	VERB
ejpam-5755	340	21	to	to	ADP
ejpam-5755	340	22	continuous	continuous	ADJ
ejpam-5755	340	23	-	-	PUNCT
ejpam-5755	340	24	time	time	NOUN
ejpam-5755	340	25	methods	method	NOUN
ejpam-5755	340	26	.	.	PUNCT
ejpam-5755	341	1	these	these	DET
ejpam-5755	341	2	findings	finding	NOUN
ejpam-5755	341	3	underline	underline	VERB
ejpam-5755	341	4	the	the	DET
ejpam-5755	341	5	advantages	advantage	NOUN
ejpam-5755	341	6	of	of	ADP
ejpam-5755	341	7	impulsive	impulsive	ADJ
ejpam-5755	341	8	protocols	protocol	NOUN
ejpam-5755	341	9	in	in	ADP
ejpam-5755	341	10	dynamic	dynamic	ADJ
ejpam-5755	341	11	and	and	CCONJ
ejpam-5755	341	12	heterogeneous	heterogeneous	ADJ
ejpam-5755	341	13	network	network	NOUN
ejpam-5755	341	14	environments	environment	NOUN
ejpam-5755	341	15	.	.	PUNCT
ejpam-5755	342	1	the	the	DET
ejpam-5755	342	2	proposed	propose	VERB
ejpam-5755	342	3	protocols	protocol	NOUN
ejpam-5755	342	4	have	have	VERB
ejpam-5755	342	5	significant	significant	ADJ
ejpam-5755	342	6	real	real	ADJ
ejpam-5755	342	7	-	-	PUNCT
ejpam-5755	342	8	world	world	NOUN
ejpam-5755	342	9	applications	application	NOUN
ejpam-5755	342	10	.	.	PUNCT
ejpam-5755	343	1	in	in	ADP
ejpam-5755	343	2	autonomous	autonomous	ADJ
ejpam-5755	343	3	vehicles	vehicle	NOUN
ejpam-5755	343	4	,	,	PUNCT
ejpam-5755	343	5	they	they	PRON
ejpam-5755	343	6	ensure	ensure	VERB
ejpam-5755	343	7	proportional	proportional	ADJ
ejpam-5755	343	8	inter	inter	ADJ
ejpam-5755	343	9	-	-	NOUN
ejpam-5755	343	10	vehicle	vehicle	NOUN
ejpam-5755	343	11	distances	distance	NOUN
ejpam-5755	343	12	for	for	ADP
ejpam-5755	343	13	safer	safe	ADJ
ejpam-5755	343	14	and	and	CCONJ
ejpam-5755	343	15	more	more	ADV
ejpam-5755	343	16	efficient	efficient	ADJ
ejpam-5755	343	17	traffic	traffic	NOUN
ejpam-5755	343	18	flow	flow	NOUN
ejpam-5755	343	19	.	.	PUNCT
ejpam-5755	344	1	in	in	ADP
ejpam-5755	344	2	distributed	distribute	VERB
ejpam-5755	344	3	energy	energy	NOUN
ejpam-5755	344	4	systems	system	NOUN
ejpam-5755	344	5	,	,	PUNCT
ejpam-5755	344	6	they	they	PRON
ejpam-5755	344	7	balance	balance	VERB
ejpam-5755	344	8	power	power	NOUN
ejpam-5755	344	9	generation	generation	NOUN
ejpam-5755	344	10	and	and	CCONJ
ejpam-5755	344	11	consumption	consumption	NOUN
ejpam-5755	344	12	across	across	ADP
ejpam-5755	344	13	resources	resource	NOUN
ejpam-5755	344	14	proportionally	proportionally	ADV
ejpam-5755	344	15	,	,	PUNCT
ejpam-5755	344	16	optimizing	optimize	VERB
ejpam-5755	344	17	energy	energy	NOUN
ejpam-5755	344	18	utilization	utilization	NOUN
ejpam-5755	344	19	in	in	ADP
ejpam-5755	344	20	smart	smart	ADJ
ejpam-5755	344	21	grids	grid	NOUN
ejpam-5755	344	22	.	.	PUNCT
ejpam-5755	345	1	additional	additional	ADJ
ejpam-5755	345	2	applications	application	NOUN
ejpam-5755	345	3	include	include	VERB
ejpam-5755	345	4	robotics	robotic	NOUN
ejpam-5755	345	5	,	,	PUNCT
ejpam-5755	345	6	sensor	sensor	NOUN
ejpam-5755	345	7	networks	network	NOUN
ejpam-5755	345	8	,	,	PUNCT
ejpam-5755	345	9	and	and	CCONJ
ejpam-5755	345	10	traffic	traffic	NOUN
ejpam-5755	345	11	management	management	NOUN
ejpam-5755	345	12	,	,	PUNCT
ejpam-5755	345	13	where	where	SCONJ
ejpam-5755	345	14	their	their	PRON
ejpam-5755	345	15	scals	scal	NOUN
ejpam-5755	345	16	.	.	PUNCT
ejpam-5755	346	1	donganont	donganont	PROPN
ejpam-5755	346	2	,	,	PUNCT
ejpam-5755	346	3	u.	u.	NOUN
ejpam-5755	346	4	witthayarat	witthayarat	NOUN
ejpam-5755	346	5	,	,	PUNCT
ejpam-5755	346	6	m.	m.	NOUN
ejpam-5755	346	7	donganont	donganont	PROPN
ejpam-5755	346	8	/	/	SYM
ejpam-5755	346	9	eur	eur	PROPN
ejpam-5755	346	10	.	.	PUNCT
ejpam-5755	347	1	j.	j.	PROPN
ejpam-5755	347	2	pure	pure	PROPN
ejpam-5755	347	3	appl	appl	PROPN
ejpam-5755	347	4	.	.	PROPN
ejpam-5755	347	5	math	math	PROPN
ejpam-5755	347	6	,	,	PUNCT
ejpam-5755	347	7	18	18	NUM
ejpam-5755	347	8	(	(	PUNCT
ejpam-5755	347	9	1	1	NUM
ejpam-5755	347	10	)	)	PUNCT
ejpam-5755	347	11	(	(	PUNCT
ejpam-5755	347	12	2025	2025	NUM
ejpam-5755	347	13	)	)	PUNCT
ejpam-5755	347	14	,	,	PUNCT
ejpam-5755	347	15	5755	5755	NUM
ejpam-5755	347	16	16	16	NUM
ejpam-5755	347	17	of	of	ADP
ejpam-5755	347	18	17	17	NUM
ejpam-5755	347	19	ability	ability	NOUN
ejpam-5755	347	20	and	and	CCONJ
ejpam-5755	347	21	adaptability	adaptability	NOUN
ejpam-5755	347	22	provide	provide	VERB
ejpam-5755	347	23	practical	practical	ADJ
ejpam-5755	347	24	advantages	advantage	NOUN
ejpam-5755	347	25	.	.	PUNCT
ejpam-5755	348	1	future	future	ADJ
ejpam-5755	348	2	research	research	NOUN
ejpam-5755	348	3	will	will	AUX
ejpam-5755	348	4	explore	explore	VERB
ejpam-5755	348	5	extensions	extension	NOUN
ejpam-5755	348	6	to	to	ADP
ejpam-5755	348	7	weakly	weakly	ADJ
ejpam-5755	348	8	connected	connected	ADJ
ejpam-5755	348	9	graphs	graph	NOUN
ejpam-5755	348	10	,	,	PUNCT
ejpam-5755	348	11	highly	highly	ADV
ejpam-5755	348	12	dynamic	dynamic	ADJ
ejpam-5755	348	13	topologies	topology	NOUN
ejpam-5755	348	14	,	,	PUNCT
ejpam-5755	348	15	and	and	CCONJ
ejpam-5755	348	16	adaptive	adaptive	ADJ
ejpam-5755	348	17	mechanisms	mechanism	NOUN
ejpam-5755	348	18	for	for	ADP
ejpam-5755	348	19	real	real	ADJ
ejpam-5755	348	20	-	-	PUNCT
ejpam-5755	348	21	time	time	NOUN
ejpam-5755	348	22	parameter	parameter	NOUN
ejpam-5755	348	23	tuning	tuning	NOUN
ejpam-5755	348	24	.	.	PUNCT
ejpam-5755	349	1	real	real	ADJ
ejpam-5755	349	2	-	-	PUNCT
ejpam-5755	349	3	world	world	NOUN
ejpam-5755	349	4	implementations	implementation	NOUN
ejpam-5755	349	5	in	in	ADP
ejpam-5755	349	6	autonomous	autonomous	ADJ
ejpam-5755	349	7	systems	system	NOUN
ejpam-5755	349	8	and	and	CCONJ
ejpam-5755	349	9	smart	smart	ADJ
ejpam-5755	349	10	grids	grid	NOUN
ejpam-5755	349	11	will	will	AUX
ejpam-5755	349	12	further	far	ADV
ejpam-5755	349	13	validate	validate	VERB
ejpam-5755	349	14	their	their	PRON
ejpam-5755	349	15	practicality	practicality	NOUN
ejpam-5755	349	16	and	and	CCONJ
ejpam-5755	349	17	impact	impact	NOUN
ejpam-5755	349	18	,	,	PUNCT
ejpam-5755	349	19	establishing	establish	VERB
ejpam-5755	349	20	a	a	DET
ejpam-5755	349	21	foundation	foundation	NOUN
ejpam-5755	349	22	for	for	ADP
ejpam-5755	349	23	broader	broad	ADJ
ejpam-5755	349	24	adoption	adoption	NOUN
ejpam-5755	349	25	in	in	ADP
ejpam-5755	349	26	complex	complex	ADJ
ejpam-5755	349	27	multi	multi	ADJ
ejpam-5755	349	28	-	-	ADJ
ejpam-5755	349	29	agent	agent	ADJ
ejpam-5755	349	30	systems	system	NOUN
ejpam-5755	349	31	.	.	PUNCT
ejpam-5755	350	1	acknowledgements	acknowledgement	NOUN
ejpam-5755	350	2	the	the	DET
ejpam-5755	350	3	authors	author	NOUN
ejpam-5755	350	4	are	be	AUX
ejpam-5755	350	5	thankful	thankful	ADJ
ejpam-5755	350	6	to	to	ADP
ejpam-5755	350	7	the	the	DET
ejpam-5755	350	8	editors	editor	NOUN
ejpam-5755	350	9	and	and	CCONJ
ejpam-5755	350	10	the	the	DET
ejpam-5755	350	11	anonymous	anonymous	ADJ
ejpam-5755	350	12	reviewers	reviewer	NOUN
ejpam-5755	350	13	for	for	ADP
ejpam-5755	350	14	many	many	ADJ
ejpam-5755	350	15	valuable	valuable	ADJ
ejpam-5755	350	16	suggestions	suggestion	NOUN
ejpam-5755	350	17	to	to	PART
ejpam-5755	350	18	improve	improve	VERB
ejpam-5755	350	19	this	this	DET
ejpam-5755	350	20	paper	paper	NOUN
ejpam-5755	350	21	.	.	PUNCT
ejpam-5755	351	1	funding	fund	VERB
ejpam-5755	351	2	this	this	DET
ejpam-5755	351	3	research	research	NOUN
ejpam-5755	351	4	was	be	AUX
ejpam-5755	351	5	supported	support	VERB
ejpam-5755	351	6	by	by	ADP
ejpam-5755	351	7	the	the	DET
ejpam-5755	351	8	university	university	NOUN
ejpam-5755	351	9	of	of	ADP
ejpam-5755	351	10	phayao	phayao	PROPN
ejpam-5755	351	11	and	and	CCONJ
ejpam-5755	351	12	thailand	thailand	PROPN
ejpam-5755	351	13	science	science	PROPN
ejpam-5755	351	14	research	research	PROPN
ejpam-5755	351	15	and	and	CCONJ
ejpam-5755	351	16	innovation	innovation	NOUN
ejpam-5755	351	17	fund	fund	NOUN
ejpam-5755	351	18	(	(	PUNCT
ejpam-5755	351	19	fundamental	fundamental	ADJ
ejpam-5755	351	20	fund	fund	NOUN
ejpam-5755	351	21	2025	2025	NUM
ejpam-5755	351	22	,	,	PUNCT
ejpam-5755	351	23	grant	grant	VERB
ejpam-5755	351	24	no	no	NOUN
ejpam-5755	351	25	.	.	PUNCT
ejpam-5755	352	1	5020/2567	5020/2567	NUM
ejpam-5755	352	2	)	)	PUNCT
ejpam-5755	352	3	.	.	PUNCT
ejpam-5755	353	1	declarations	declaration	NOUN
ejpam-5755	353	2	the	the	DET
ejpam-5755	353	3	author	author	NOUN
ejpam-5755	353	4	declares	declare	VERB
ejpam-5755	353	5	that	that	SCONJ
ejpam-5755	353	6	they	they	PRON
ejpam-5755	353	7	have	have	VERB
ejpam-5755	353	8	no	no	DET
ejpam-5755	353	9	known	know	VERB
ejpam-5755	353	10	competing	compete	VERB
ejpam-5755	353	11	financial	financial	ADJ
ejpam-5755	353	12	interests	interest	NOUN
ejpam-5755	353	13	or	or	CCONJ
ejpam-5755	353	14	personal	personal	ADJ
ejpam-5755	353	15	relationships	relationship	NOUN
ejpam-5755	353	16	that	that	PRON
ejpam-5755	353	17	could	could	AUX
ejpam-5755	353	18	have	have	AUX
ejpam-5755	353	19	appeared	appear	VERB
ejpam-5755	353	20	to	to	PART
ejpam-5755	353	21	influence	influence	VERB
ejpam-5755	353	22	the	the	DET
ejpam-5755	353	23	work	work	NOUN
ejpam-5755	353	24	reported	report	VERB
ejpam-5755	353	25	in	in	ADP
ejpam-5755	353	26	this	this	DET
ejpam-5755	353	27	paper	paper	NOUN
ejpam-5755	353	28	.	.	PUNCT
ejpam-5755	354	1	conflict	conflict	NOUN
ejpam-5755	354	2	of	of	ADP
ejpam-5755	354	3	interest	interest	NOUN
ejpam-5755	354	4	the	the	DET
ejpam-5755	354	5	authors	author	NOUN
ejpam-5755	354	6	declare	declare	VERB
ejpam-5755	354	7	that	that	SCONJ
ejpam-5755	354	8	they	they	PRON
ejpam-5755	354	9	have	have	VERB
ejpam-5755	354	10	no	no	DET
ejpam-5755	354	11	competing	compete	VERB
ejpam-5755	354	12	interests	interest	NOUN
ejpam-5755	354	13	.	.	PUNCT
ejpam-5755	355	1	references	reference	NOUN
ejpam-5755	355	2	[	[	X
ejpam-5755	355	3	1	1	NUM
ejpam-5755	355	4	]	]	PUNCT
ejpam-5755	355	5	m.	m.	NOUN
ejpam-5755	355	6	donganont	donganont	PROPN
ejpam-5755	355	7	.	.	PUNCT
ejpam-5755	356	1	scaled	scale	VERB
ejpam-5755	356	2	consensus	consensus	NOUN
ejpam-5755	356	3	of	of	ADP
ejpam-5755	356	4	hybrid	hybrid	ADJ
ejpam-5755	356	5	multi	multi	ADJ
ejpam-5755	356	6	-	-	ADJ
ejpam-5755	356	7	agent	agent	ADJ
ejpam-5755	356	8	systems	system	NOUN
ejpam-5755	356	9	via	via	ADP
ejpam-5755	356	10	impulsive	impulsive	ADJ
ejpam-5755	356	11	protocols	protocol	NOUN
ejpam-5755	356	12	.	.	PUNCT
ejpam-5755	357	1	36(3):275–289	36(3):275–289	ADJ
ejpam-5755	357	2	,	,	PUNCT
ejpam-5755	357	3	2025	2025	NUM
ejpam-5755	357	4	.	.	PUNCT
ejpam-5755	358	1	[	[	X
ejpam-5755	358	2	2	2	NUM
ejpam-5755	358	3	]	]	PUNCT
ejpam-5755	358	4	m.	m.	NOUN
ejpam-5755	358	5	donganont	donganont	NOUN
ejpam-5755	358	6	and	and	CCONJ
ejpam-5755	358	7	x.	x.	PROPN
ejpam-5755	358	8	liu	liu	PROPN
ejpam-5755	358	9	.	.	PUNCT
ejpam-5755	359	1	scaled	scale	VERB
ejpam-5755	359	2	consensus	consensus	NOUN
ejpam-5755	359	3	problems	problem	NOUN
ejpam-5755	359	4	of	of	ADP
ejpam-5755	359	5	multi	multi	ADJ
ejpam-5755	359	6	agent	agent	NOUN
ejpam-5755	359	7	systems	system	NOUN
ejpam-5755	359	8	via	via	ADP
ejpam-5755	359	9	impulsive	impulsive	ADJ
ejpam-5755	359	10	protocols	protocol	NOUN
ejpam-5755	359	11	.	.	PUNCT
ejpam-5755	360	1	applied	apply	VERB
ejpam-5755	360	2	mathematical	mathematical	ADJ
ejpam-5755	360	3	modelling	modelling	NOUN
ejpam-5755	360	4	,	,	PUNCT
ejpam-5755	360	5	116:532–546	116:532–546	NUM
ejpam-5755	360	6	,	,	PUNCT
ejpam-5755	360	7	2023	2023	NUM
ejpam-5755	360	8	.	.	PUNCT
ejpam-5755	361	1	[	[	X
ejpam-5755	361	2	3	3	X
ejpam-5755	361	3	]	]	X
ejpam-5755	361	4	c.	c.	NOUN
ejpam-5755	361	5	godsil	godsil	PROPN
ejpam-5755	361	6	and	and	CCONJ
ejpam-5755	361	7	g.	g.	PROPN
ejpam-5755	361	8	royle	royle	PROPN
ejpam-5755	361	9	.	.	PUNCT
ejpam-5755	362	1	algebraic	algebraic	ADJ
ejpam-5755	362	2	graph	graph	NOUN
ejpam-5755	362	3	theory	theory	NOUN
ejpam-5755	362	4	,	,	PUNCT
ejpam-5755	362	5	volume	volume	NOUN
ejpam-5755	362	6	207	207	NUM
ejpam-5755	362	7	.	.	PUNCT
ejpam-5755	363	1	01	01	NUM
ejpam-5755	363	2	2001	2001	NUM
ejpam-5755	363	3	.	.	PUNCT
ejpam-5755	364	1	[	[	X
ejpam-5755	364	2	4	4	X
ejpam-5755	364	3	]	]	X
ejpam-5755	364	4	r.	r.	PROPN
ejpam-5755	364	5	a.	a.	NOUN
ejpam-5755	364	6	horn	horn	PROPN
ejpam-5755	364	7	and	and	CCONJ
ejpam-5755	364	8	c.	c.	PROPN
ejpam-5755	364	9	r.	r.	PROPN
ejpam-5755	364	10	johnson	johnson	PROPN
ejpam-5755	364	11	.	.	PUNCT
ejpam-5755	364	12	matrix	matrix	NOUN
ejpam-5755	364	13	analysis	analysis	NOUN
ejpam-5755	364	14	.	.	PUNCT
ejpam-5755	365	1	cambridge	cambridge	PROPN
ejpam-5755	365	2	university	university	PROPN
ejpam-5755	365	3	press	press	PROPN
ejpam-5755	365	4	,	,	PUNCT
ejpam-5755	365	5	new	new	PROPN
ejpam-5755	365	6	york	york	PROPN
ejpam-5755	365	7	,	,	PUNCT
ejpam-5755	365	8	ny	ny	PROPN
ejpam-5755	365	9	,	,	PUNCT
ejpam-5755	365	10	usa	usa	PROPN
ejpam-5755	365	11	,	,	PUNCT
ejpam-5755	365	12	2nd	2nd	PROPN
ejpam-5755	365	13	edition	edition	NOUN
ejpam-5755	365	14	,	,	PUNCT
ejpam-5755	365	15	2012	2012	NUM
ejpam-5755	365	16	.	.	PUNCT
ejpam-5755	366	1	[	[	X
ejpam-5755	366	2	5	5	X
ejpam-5755	366	3	]	]	PUNCT
ejpam-5755	366	4	f.	f.	PROPN
ejpam-5755	366	5	jiang	jiang	PROPN
ejpam-5755	366	6	and	and	CCONJ
ejpam-5755	366	7	l.	l.	PROPN
ejpam-5755	366	8	wang	wang	PROPN
ejpam-5755	366	9	.	.	PUNCT
ejpam-5755	367	1	consensus	consensus	NOUN
ejpam-5755	367	2	seeking	seeking	NOUN
ejpam-5755	367	3	of	of	ADP
ejpam-5755	367	4	high	high	ADJ
ejpam-5755	367	5	-	-	PUNCT
ejpam-5755	367	6	order	order	NOUN
ejpam-5755	367	7	dynamic	dynamic	ADJ
ejpam-5755	367	8	multi	multi	ADJ
ejpam-5755	367	9	-	-	ADJ
ejpam-5755	367	10	agent	agent	ADJ
ejpam-5755	367	11	systems	system	NOUN
ejpam-5755	367	12	with	with	ADP
ejpam-5755	367	13	fixed	fix	VERB
ejpam-5755	367	14	and	and	CCONJ
ejpam-5755	367	15	switching	switch	VERB
ejpam-5755	367	16	topologies	topology	NOUN
ejpam-5755	367	17	.	.	PUNCT
ejpam-5755	368	1	international	international	ADJ
ejpam-5755	368	2	journal	journal	PROPN
ejpam-5755	368	3	of	of	ADP
ejpam-5755	368	4	control	control	PROPN
ejpam-5755	368	5	,	,	PUNCT
ejpam-5755	368	6	83(2):404–420	83(2):404–420	NUM
ejpam-5755	368	7	,	,	PUNCT
ejpam-5755	368	8	2010	2010	NUM
ejpam-5755	368	9	.	.	PUNCT
ejpam-5755	369	1	[	[	X
ejpam-5755	369	2	6	6	NUM
ejpam-5755	369	3	]	]	PUNCT
ejpam-5755	369	4	z.	z.	PROPN
ejpam-5755	369	5	ji	ji	PROPN
ejpam-5755	369	6	l.	l.	PROPN
ejpam-5755	369	7	tian	tian	PROPN
ejpam-5755	369	8	and	and	CCONJ
ejpam-5755	369	9	t.	t.	PROPN
ejpam-5755	369	10	hou	hou	PROPN
ejpam-5755	369	11	.	.	PUNCT
ejpam-5755	369	12	edge	edge	PROPN
ejpam-5755	369	13	bipartite	bipartite	PROPN
ejpam-5755	369	14	consensus	consensus	NOUN
ejpam-5755	369	15	of	of	ADP
ejpam-5755	369	16	multi	multi	ADJ
ejpam-5755	369	17	-	-	ADJ
ejpam-5755	369	18	agent	agent	ADJ
ejpam-5755	369	19	systems	system	NOUN
ejpam-5755	369	20	*	*	NOUN
ejpam-5755	369	21	.	.	NOUN
ejpam-5755	369	22	2018	2018	NUM
ejpam-5755	369	23	ieee	ieee	NOUN
ejpam-5755	369	24	14th	14th	ADJ
ejpam-5755	369	25	international	international	ADJ
ejpam-5755	369	26	conference	conference	NOUN
ejpam-5755	369	27	on	on	ADP
ejpam-5755	369	28	control	control	NOUN
ejpam-5755	369	29	and	and	CCONJ
ejpam-5755	369	30	automation	automation	NOUN
ejpam-5755	369	31	(	(	PUNCT
ejpam-5755	369	32	icca	icca	PROPN
ejpam-5755	369	33	)	)	PUNCT
ejpam-5755	369	34	,	,	PUNCT
ejpam-5755	369	35	pages	page	NOUN
ejpam-5755	369	36	161	161	NUM
ejpam-5755	369	37	–	–	PUNCT
ejpam-5755	369	38	166	166	NUM
ejpam-5755	369	39	,	,	PUNCT
ejpam-5755	369	40	2018	2018	NUM
ejpam-5755	369	41	.	.	PUNCT
ejpam-5755	370	1	[	[	X
ejpam-5755	370	2	7	7	X
ejpam-5755	370	3	]	]	X
ejpam-5755	370	4	c.	c.	PROPN
ejpam-5755	370	5	liu	liu	PROPN
ejpam-5755	370	6	,	,	PUNCT
ejpam-5755	370	7	h.	h.	PROPN
ejpam-5755	370	8	p.	p.	PROPN
ejpam-5755	370	9	wang	wang	PROPN
ejpam-5755	370	10	,	,	PUNCT
ejpam-5755	370	11	and	and	CCONJ
ejpam-5755	370	12	s.	s.	PROPN
ejpam-5755	370	13	liu	liu	PROPN
ejpam-5755	370	14	.	.	PUNCT
ejpam-5755	371	1	scaled	scale	VERB
ejpam-5755	371	2	consensus	consensus	NOUN
ejpam-5755	371	3	problem	problem	NOUN
ejpam-5755	371	4	of	of	ADP
ejpam-5755	371	5	heterogeneous	heterogeneous	ADJ
ejpam-5755	371	6	firstorder	firstorder	NOUN
ejpam-5755	371	7	multi	multi	ADJ
ejpam-5755	371	8	-	-	ADJ
ejpam-5755	371	9	agent	agent	ADJ
ejpam-5755	371	10	systems	system	NOUN
ejpam-5755	371	11	.	.	PUNCT
ejpam-5755	372	1	2016	2016	NUM
ejpam-5755	372	2	ieee	ieee	PROPN
ejpam-5755	372	3	international	international	ADJ
ejpam-5755	372	4	conference	conference	NOUN
ejpam-5755	372	5	on	on	ADP
ejpam-5755	372	6	information	information	NOUN
ejpam-5755	372	7	and	and	CCONJ
ejpam-5755	372	8	automation	automation	NOUN
ejpam-5755	372	9	(	(	PUNCT
ejpam-5755	372	10	icia	icia	NOUN
ejpam-5755	372	11	)	)	PUNCT
ejpam-5755	372	12	,	,	PUNCT
ejpam-5755	372	13	pages	page	NOUN
ejpam-5755	372	14	1284–1289	1284–1289	NUM
ejpam-5755	372	15	,	,	PUNCT
ejpam-5755	372	16	2016	2016	NUM
ejpam-5755	372	17	.	.	PUNCT
ejpam-5755	373	1	[	[	X
ejpam-5755	373	2	8	8	NUM
ejpam-5755	373	3	]	]	X
ejpam-5755	373	4	r.	r.	PROPN
ejpam-5755	373	5	olfati	olfati	PROPN
ejpam-5755	373	6	-	-	PUNCT
ejpam-5755	373	7	saber	saber	NOUN
ejpam-5755	373	8	.	.	PUNCT
ejpam-5755	374	1	flocking	flock	VERB
ejpam-5755	374	2	for	for	ADP
ejpam-5755	374	3	multi	multi	ADJ
ejpam-5755	374	4	-	-	ADJ
ejpam-5755	374	5	agent	agent	ADJ
ejpam-5755	374	6	dynamic	dynamic	ADJ
ejpam-5755	374	7	systems	system	NOUN
ejpam-5755	374	8	:	:	PUNCT
ejpam-5755	374	9	algorithms	algorithm	NOUN
ejpam-5755	374	10	and	and	CCONJ
ejpam-5755	374	11	theory	theory	NOUN
ejpam-5755	374	12	.	.	PUNCT
ejpam-5755	375	1	ieee	ieee	NOUN
ejpam-5755	375	2	transactions	transaction	NOUN
ejpam-5755	375	3	on	on	ADP
ejpam-5755	375	4	automatic	automatic	ADJ
ejpam-5755	375	5	control	control	NOUN
ejpam-5755	375	6	,	,	PUNCT
ejpam-5755	375	7	51(3):401–420	51(3):401–420	PROPN
ejpam-5755	375	8	,	,	PUNCT
ejpam-5755	375	9	march	march	PROPN
ejpam-5755	375	10	2006	2006	NUM
ejpam-5755	375	11	.	.	PUNCT
ejpam-5755	376	1	s.	s.	PROPN
ejpam-5755	376	2	donganont	donganont	PROPN
ejpam-5755	376	3	,	,	PUNCT
ejpam-5755	376	4	u.	u.	NOUN
ejpam-5755	376	5	witthayarat	witthayarat	NOUN
ejpam-5755	376	6	,	,	PUNCT
ejpam-5755	376	7	m.	m.	NOUN
ejpam-5755	376	8	donganont	donganont	PROPN
ejpam-5755	376	9	/	/	SYM
ejpam-5755	376	10	eur	eur	PROPN
ejpam-5755	376	11	.	.	PUNCT
ejpam-5755	377	1	j.	j.	PROPN
ejpam-5755	377	2	pure	pure	PROPN
ejpam-5755	377	3	appl	appl	PROPN
ejpam-5755	377	4	.	.	PROPN
ejpam-5755	377	5	math	math	PROPN
ejpam-5755	377	6	,	,	PUNCT
ejpam-5755	377	7	18	18	NUM
ejpam-5755	377	8	(	(	PUNCT
ejpam-5755	377	9	1	1	NUM
ejpam-5755	377	10	)	)	PUNCT
ejpam-5755	377	11	(	(	PUNCT
ejpam-5755	377	12	2025	2025	NUM
ejpam-5755	377	13	)	)	PUNCT
ejpam-5755	377	14	,	,	PUNCT
ejpam-5755	377	15	5755	5755	NUM
ejpam-5755	377	16	17	17	NUM
ejpam-5755	377	17	of	of	ADP
ejpam-5755	377	18	17	17	NUM
ejpam-5755	377	19	[	[	SYM
ejpam-5755	377	20	9	9	NUM
ejpam-5755	377	21	]	]	X
ejpam-5755	377	22	r.	r.	PROPN
ejpam-5755	377	23	olfati	olfati	PROPN
ejpam-5755	377	24	-	-	PUNCT
ejpam-5755	377	25	saber	saber	NOUN
ejpam-5755	377	26	,	,	PUNCT
ejpam-5755	377	27	j.	j.	PROPN
ejpam-5755	377	28	a.	a.	PROPN
ejpam-5755	377	29	fax	fax	PROPN
ejpam-5755	377	30	,	,	PUNCT
ejpam-5755	377	31	and	and	CCONJ
ejpam-5755	377	32	r.	r.	PROPN
ejpam-5755	377	33	m.	m.	PROPN
ejpam-5755	377	34	murray	murray	PROPN
ejpam-5755	377	35	.	.	PUNCT
ejpam-5755	378	1	consensus	consensus	NOUN
ejpam-5755	378	2	and	and	CCONJ
ejpam-5755	378	3	cooperation	cooperation	NOUN
ejpam-5755	378	4	in	in	ADP
ejpam-5755	378	5	networked	networked	ADJ
ejpam-5755	378	6	multi	multi	ADJ
ejpam-5755	378	7	-	-	ADJ
ejpam-5755	378	8	agent	agent	ADJ
ejpam-5755	378	9	systems	system	NOUN
ejpam-5755	378	10	.	.	PUNCT
ejpam-5755	379	1	proceedings	proceeding	NOUN
ejpam-5755	379	2	of	of	ADP
ejpam-5755	379	3	the	the	DET
ejpam-5755	379	4	ieee	ieee	NOUN
ejpam-5755	379	5	,	,	PUNCT
ejpam-5755	379	6	95(1):215–233	95(1):215–233	NUM
ejpam-5755	379	7	,	,	PUNCT
ejpam-5755	379	8	jan	jan	PROPN
ejpam-5755	379	9	2007	2007	NUM
ejpam-5755	379	10	.	.	PUNCT
ejpam-5755	380	1	[	[	X
ejpam-5755	380	2	10	10	NUM
ejpam-5755	380	3	]	]	X
ejpam-5755	380	4	r.	r.	PROPN
ejpam-5755	380	5	olfati	olfati	PROPN
ejpam-5755	380	6	-	-	PUNCT
ejpam-5755	380	7	saber	saber	NOUN
ejpam-5755	380	8	and	and	CCONJ
ejpam-5755	380	9	r.	r.	PROPN
ejpam-5755	380	10	m.	m.	PROPN
ejpam-5755	380	11	murray	murray	PROPN
ejpam-5755	380	12	.	.	PUNCT
ejpam-5755	381	1	consensus	consensus	NOUN
ejpam-5755	381	2	problems	problem	NOUN
ejpam-5755	381	3	in	in	ADP
ejpam-5755	381	4	networks	network	NOUN
ejpam-5755	381	5	of	of	ADP
ejpam-5755	381	6	agents	agent	NOUN
ejpam-5755	381	7	with	with	ADP
ejpam-5755	381	8	switching	switch	VERB
ejpam-5755	381	9	topology	topology	NOUN
ejpam-5755	381	10	and	and	CCONJ
ejpam-5755	381	11	time	time	NOUN
ejpam-5755	381	12	-	-	PUNCT
ejpam-5755	381	13	delays	delay	NOUN
ejpam-5755	381	14	.	.	PUNCT
ejpam-5755	382	1	ieee	ieee	NOUN
ejpam-5755	382	2	transactions	transaction	NOUN
ejpam-5755	382	3	on	on	ADP
ejpam-5755	382	4	automatic	automatic	ADJ
ejpam-5755	382	5	control	control	NOUN
ejpam-5755	382	6	,	,	PUNCT
ejpam-5755	382	7	49(9):1520–1533	49(9):1520–1533	NUM
ejpam-5755	382	8	,	,	PUNCT
ejpam-5755	382	9	sep	sep	PROPN
ejpam-5755	382	10	.	.	PROPN
ejpam-5755	382	11	2004	2004	NUM
ejpam-5755	382	12	.	.	PUNCT
ejpam-5755	383	1	[	[	X
ejpam-5755	383	2	11	11	NUM
ejpam-5755	383	3	]	]	PUNCT
ejpam-5755	383	4	s.	s.	PROPN
ejpam-5755	383	5	roy	roy	PROPN
ejpam-5755	383	6	.	.	PROPN
ejpam-5755	383	7	scaled	scaled	PROPN
ejpam-5755	383	8	consensus	consensus	NOUN
ejpam-5755	383	9	.	.	PUNCT
ejpam-5755	384	1	automatica	automatica	PROPN
ejpam-5755	384	2	,	,	PUNCT
ejpam-5755	384	3	51:259–262	51:259–262	PROPN
ejpam-5755	384	4	,	,	PUNCT
ejpam-5755	384	5	2015	2015	NUM
ejpam-5755	384	6	.	.	PUNCT
ejpam-5755	385	1	[	[	X
ejpam-5755	385	2	12	12	NUM
ejpam-5755	385	3	]	]	PUNCT
ejpam-5755	385	4	z.	z.	PROPN
ejpam-5755	385	5	zhang	zhang	PROPN
ejpam-5755	385	6	t.	t.	PROPN
ejpam-5755	385	7	ma	ma	PROPN
ejpam-5755	385	8	and	and	CCONJ
ejpam-5755	385	9	b.	b.	PROPN
ejpam-5755	385	10	cui	cui	PROPN
ejpam-5755	385	11	.	.	PUNCT
ejpam-5755	386	1	variable	variable	ADJ
ejpam-5755	386	2	impulsive	impulsive	ADJ
ejpam-5755	386	3	consensus	consensus	NOUN
ejpam-5755	386	4	of	of	ADP
ejpam-5755	386	5	nonlinear	nonlinear	ADJ
ejpam-5755	386	6	multi	multi	ADJ
ejpam-5755	386	7	-	-	ADJ
ejpam-5755	386	8	agent	agent	ADJ
ejpam-5755	386	9	systems	system	NOUN
ejpam-5755	386	10	.	.	PUNCT
ejpam-5755	387	1	nonlinear	nonlinear	ADJ
ejpam-5755	387	2	analysis	analysis	NOUN
ejpam-5755	387	3	:	:	PUNCT
ejpam-5755	387	4	hybrid	hybrid	ADJ
ejpam-5755	387	5	systems	system	NOUN
ejpam-5755	387	6	,	,	PUNCT
ejpam-5755	387	7	31:1–18	31:1–18	NUM
ejpam-5755	387	8	,	,	PUNCT
ejpam-5755	387	9	2019	2019	NUM
ejpam-5755	387	10	.	.	PUNCT
ejpam-5755	388	1	[	[	X
ejpam-5755	388	2	13	13	NUM
ejpam-5755	388	3	]	]	X
ejpam-5755	388	4	w.	w.	PROPN
ejpam-5755	388	5	ren	ren	PROPN
ejpam-5755	388	6	and	and	CCONJ
ejpam-5755	388	7	r.	r.	PROPN
ejpam-5755	388	8	w.	w.	PROPN
ejpam-5755	388	9	beard	beard	PROPN
ejpam-5755	388	10	.	.	PUNCT
ejpam-5755	389	1	consensus	consensus	NOUN
ejpam-5755	389	2	seeking	seek	VERB
ejpam-5755	389	3	in	in	ADP
ejpam-5755	389	4	multiagent	multiagent	NOUN
ejpam-5755	389	5	systems	system	NOUN
ejpam-5755	389	6	under	under	ADP
ejpam-5755	389	7	dynamically	dynamically	ADV
ejpam-5755	389	8	changing	change	VERB
ejpam-5755	389	9	interaction	interaction	NOUN
ejpam-5755	389	10	topologies	topology	NOUN
ejpam-5755	389	11	.	.	PUNCT
ejpam-5755	390	1	ieee	ieee	NOUN
ejpam-5755	390	2	transactions	transaction	NOUN
ejpam-5755	390	3	on	on	ADP
ejpam-5755	390	4	automatic	automatic	ADJ
ejpam-5755	390	5	control	control	NOUN
ejpam-5755	390	6	,	,	PUNCT
ejpam-5755	390	7	50(5):655	50(5):655	PROPN
ejpam-5755	390	8	–	–	PUNCT
ejpam-5755	390	9	661	661	NUM
ejpam-5755	390	10	,	,	PUNCT
ejpam-5755	390	11	may	may	AUX
ejpam-5755	390	12	2005	2005	NUM
ejpam-5755	390	13	.	.	PUNCT
ejpam-5755	391	1	[	[	X
ejpam-5755	391	2	14	14	NUM
ejpam-5755	391	3	]	]	PUNCT
ejpam-5755	391	4	x.	x.	NOUN
ejpam-5755	391	5	wang	wang	PROPN
ejpam-5755	391	6	and	and	CCONJ
ejpam-5755	391	7	x.	x.	PROPN
ejpam-5755	391	8	wang	wang	PROPN
ejpam-5755	391	9	.	.	PUNCT
ejpam-5755	392	1	consensus	consensus	NOUN
ejpam-5755	392	2	of	of	ADP
ejpam-5755	392	3	edge	edge	NOUN
ejpam-5755	392	4	dynamics	dynamic	NOUN
ejpam-5755	392	5	on	on	ADP
ejpam-5755	392	6	complex	complex	ADJ
ejpam-5755	392	7	networks	network	NOUN
ejpam-5755	392	8	.	.	PUNCT
ejpam-5755	393	1	in	in	ADP
ejpam-5755	393	2	2014	2014	NUM
ejpam-5755	393	3	ieee	ieee	NOUN
ejpam-5755	393	4	international	international	ADJ
ejpam-5755	393	5	symposium	symposium	NOUN
ejpam-5755	393	6	on	on	ADP
ejpam-5755	393	7	circuits	circuit	NOUN
ejpam-5755	393	8	and	and	CCONJ
ejpam-5755	393	9	systems	system	NOUN
ejpam-5755	393	10	(	(	PUNCT
ejpam-5755	393	11	iscas	iscas	PROPN
ejpam-5755	393	12	)	)	PUNCT
ejpam-5755	393	13	,	,	PUNCT
ejpam-5755	393	14	pages	page	NOUN
ejpam-5755	393	15	1271–1274	1271–1274	NUM
ejpam-5755	393	16	,	,	PUNCT
ejpam-5755	393	17	2014	2014	NUM
ejpam-5755	393	18	.	.	PUNCT
ejpam-5755	394	1	[	[	X
ejpam-5755	394	2	15	15	NUM
ejpam-5755	394	3	]	]	X
ejpam-5755	394	4	y.	y.	PROPN
ejpam-5755	394	5	wang	wang	PROPN
ejpam-5755	394	6	and	and	CCONJ
ejpam-5755	394	7	j.	j.	PROPN
ejpam-5755	394	8	lu	lu	PROPN
ejpam-5755	394	9	.	.	PUNCT
ejpam-5755	395	1	some	some	DET
ejpam-5755	395	2	recent	recent	ADJ
ejpam-5755	395	3	results	result	NOUN
ejpam-5755	395	4	of	of	ADP
ejpam-5755	395	5	analysis	analysis	NOUN
ejpam-5755	395	6	and	and	CCONJ
ejpam-5755	395	7	control	control	NOUN
ejpam-5755	395	8	for	for	ADP
ejpam-5755	395	9	impulsive	impulsive	ADJ
ejpam-5755	395	10	systems	system	NOUN
ejpam-5755	395	11	.	.	PUNCT
ejpam-5755	396	1	commun	commun	PROPN
ejpam-5755	396	2	.	.	PUNCT
ejpam-5755	397	1	nonlinear	nonlinear	PROPN
ejpam-5755	397	2	sci	sci	PROPN
ejpam-5755	397	3	.	.	PUNCT
ejpam-5755	397	4	numer	numer	PROPN
ejpam-5755	397	5	.	.	PUNCT
ejpam-5755	398	1	simul	simul	PROPN
ejpam-5755	398	2	.	.	PROPN
ejpam-5755	398	3	,	,	PUNCT
ejpam-5755	398	4	80:104862	80:104862	NUM
ejpam-5755	398	5	,	,	PUNCT
ejpam-5755	398	6	2020	2020	NUM
ejpam-5755	398	7	.	.	PUNCT
ejpam-5755	399	1	[	[	X
ejpam-5755	399	2	16	16	NUM
ejpam-5755	399	3	]	]	PUNCT
ejpam-5755	399	4	k.	k.	PROPN
ejpam-5755	400	1	zhang	zhang	PROPN
ejpam-5755	400	2	x.	x.	PROPN
ejpam-5755	400	3	liu	liu	PROPN
ejpam-5755	400	4	and	and	CCONJ
ejpam-5755	400	5	w.	w.	PROPN
ejpam-5755	400	6	xie	xie	PROPN
ejpam-5755	400	7	.	.	PUNCT
ejpam-5755	401	1	consensus	consensus	NOUN
ejpam-5755	401	2	seeking	seek	VERB
ejpam-5755	401	3	in	in	ADP
ejpam-5755	401	4	multi	multi	ADJ
ejpam-5755	401	5	-	-	ADJ
ejpam-5755	401	6	agent	agent	ADJ
ejpam-5755	401	7	systems	system	NOUN
ejpam-5755	401	8	via	via	ADP
ejpam-5755	401	9	hybrid	hybrid	ADJ
ejpam-5755	401	10	protocols	protocol	NOUN
ejpam-5755	401	11	with	with	ADP
ejpam-5755	401	12	impulse	impulse	ADJ
ejpam-5755	401	13	delays	delay	NOUN
ejpam-5755	401	14	.	.	PUNCT
ejpam-5755	402	1	nonlinear	nonlinear	ADJ
ejpam-5755	402	2	analysis	analysis	NOUN
ejpam-5755	402	3	:	:	PUNCT
ejpam-5755	402	4	hybrid	hybrid	ADJ
ejpam-5755	402	5	systems	system	NOUN
ejpam-5755	402	6	,	,	PUNCT
ejpam-5755	402	7	25:90–98	25:90–98	NUM
ejpam-5755	402	8	,	,	PUNCT
ejpam-5755	402	9	2017	2017	NUM
ejpam-5755	402	10	.	.	PUNCT
ejpam-5755	403	1	[	[	X
ejpam-5755	403	2	17	17	NUM
ejpam-5755	403	3	]	]	PUNCT
ejpam-5755	403	4	k.	k.	PROPN
ejpam-5755	403	5	zhang	zhang	PROPN
ejpam-5755	403	6	x.	x.	PROPN
ejpam-5755	403	7	liu	liu	PROPN
ejpam-5755	403	8	and	and	CCONJ
ejpam-5755	403	9	w.	w.	PROPN
ejpam-5755	403	10	xie	xie	PROPN
ejpam-5755	403	11	.	.	PUNCT
ejpam-5755	404	1	consensus	consensus	NOUN
ejpam-5755	404	2	of	of	ADP
ejpam-5755	404	3	multi	multi	ADJ
ejpam-5755	404	4	-	-	ADJ
ejpam-5755	404	5	agent	agent	ADJ
ejpam-5755	404	6	systems	system	NOUN
ejpam-5755	404	7	via	via	ADP
ejpam-5755	404	8	hybrid	hybrid	ADJ
ejpam-5755	404	9	impulsive	impulsive	ADJ
ejpam-5755	404	10	protocols	protocol	NOUN
ejpam-5755	404	11	with	with	ADP
ejpam-5755	404	12	time	time	NOUN
ejpam-5755	404	13	-	-	PUNCT
ejpam-5755	404	14	delay	delay	NOUN
ejpam-5755	404	15	.	.	PUNCT
ejpam-5755	405	1	nonlinear	nonlinear	ADJ
ejpam-5755	405	2	analysis	analysis	NOUN
ejpam-5755	405	3	:	:	PUNCT
ejpam-5755	405	4	hybrid	hybrid	ADJ
ejpam-5755	405	5	systems	system	NOUN
ejpam-5755	405	6	,	,	PUNCT
ejpam-5755	405	7	30:134–146	30:134–146	NUM
ejpam-5755	405	8	,	,	PUNCT
ejpam-5755	405	9	2018	2018	NUM
ejpam-5755	405	10	.	.	PUNCT
ejpam-5755	406	1	[	[	X
ejpam-5755	406	2	18	18	NUM
ejpam-5755	406	3	]	]	PUNCT
ejpam-5755	406	4	x.	x.	NOUN
ejpam-5755	406	5	wang	wang	PROPN
ejpam-5755	406	6	x.	x.	PROPN
ejpam-5755	406	7	wang	wang	PROPN
ejpam-5755	406	8	and	and	CCONJ
ejpam-5755	406	9	h.	h.	PROPN
ejpam-5755	406	10	su	su	PROPN
ejpam-5755	406	11	.	.	PROPN
ejpam-5755	407	1	consensus	consensus	NOUN
ejpam-5755	407	2	of	of	ADP
ejpam-5755	407	3	edge	edge	NOUN
ejpam-5755	407	4	dynamics	dynamic	NOUN
ejpam-5755	407	5	on	on	ADP
ejpam-5755	407	6	directed	direct	VERB
ejpam-5755	407	7	multi	multi	ADJ
ejpam-5755	407	8	-	-	ADJ
ejpam-5755	407	9	agent	agent	ADJ
ejpam-5755	407	10	systems	system	NOUN
ejpam-5755	407	11	.	.	PUNCT
ejpam-5755	408	1	proceedings	proceeding	NOUN
ejpam-5755	408	2	of	of	ADP
ejpam-5755	408	3	the	the	DET
ejpam-5755	408	4	33rd	33rd	ADJ
ejpam-5755	408	5	chinese	chinese	PROPN
ejpam-5755	408	6	control	control	PROPN
ejpam-5755	408	7	conference	conference	PROPN
ejpam-5755	408	8	,	,	PUNCT
ejpam-5755	408	9	pages	page	NOUN
ejpam-5755	408	10	1372–1376	1372–1376	NUM
ejpam-5755	408	11	,	,	PUNCT
ejpam-5755	408	12	2014	2014	NUM
ejpam-5755	408	13	.	.	PUNCT
ejpam-5755	409	1	[	[	X
ejpam-5755	409	2	19	19	NUM
ejpam-5755	409	3	]	]	PUNCT
ejpam-5755	409	4	t.	t.	PROPN
ejpam-5755	409	5	wei	wei	PROPN
ejpam-5755	409	6	x.	x.	PROPN
ejpam-5755	409	7	xie	xie	PROPN
ejpam-5755	409	8	and	and	CCONJ
ejpam-5755	409	9	x.	x.	PROPN
ejpam-5755	409	10	li	li	PROPN
ejpam-5755	409	11	.	.	PROPN
ejpam-5755	409	12	hybrid	hybrid	ADJ
ejpam-5755	409	13	event	event	NOUN
ejpam-5755	409	14	-	-	PUNCT
ejpam-5755	409	15	triggered	trigger	VERB
ejpam-5755	409	16	approach	approach	NOUN
ejpam-5755	409	17	for	for	ADP
ejpam-5755	409	18	quasi	quasi	NOUN
ejpam-5755	409	19	-	-	NOUN
ejpam-5755	409	20	consensus	consensus	NOUN
ejpam-5755	409	21	of	of	ADP
ejpam-5755	409	22	uncertain	uncertain	ADJ
ejpam-5755	409	23	multi	multi	ADJ
ejpam-5755	409	24	-	-	ADJ
ejpam-5755	409	25	agent	agent	ADJ
ejpam-5755	409	26	systems	system	NOUN
ejpam-5755	409	27	with	with	ADP
ejpam-5755	409	28	impulsive	impulsive	ADJ
ejpam-5755	409	29	protocols	protocol	NOUN
ejpam-5755	409	30	.	.	PUNCT
ejpam-5755	410	1	ieee	ieee	NOUN
ejpam-5755	410	2	transactions	transaction	NOUN
ejpam-5755	410	3	on	on	ADP
ejpam-5755	410	4	circuits	circuit	NOUN
ejpam-5755	410	5	and	and	CCONJ
ejpam-5755	410	6	systems	system	NOUN
ejpam-5755	410	7	i	i	PRON
ejpam-5755	410	8	:	:	PUNCT
ejpam-5755	410	9	regular	regular	ADJ
ejpam-5755	410	10	papers	paper	NOUN
ejpam-5755	410	11	,	,	PUNCT
ejpam-5755	410	12	69(2):872–883	69(2):872–883	PROPN
ejpam-5755	410	13	,	,	PUNCT
ejpam-5755	410	14	2022	2022	NUM
ejpam-5755	410	15	.	.	PUNCT
ejpam-5755	411	1	[	[	X
ejpam-5755	411	2	20	20	NUM
ejpam-5755	411	3	]	]	PUNCT
ejpam-5755	411	4	x.	x.	PROPN
ejpam-5755	411	5	xie	xie	PROPN
ejpam-5755	411	6	,	,	PUNCT
ejpam-5755	411	7	x.	x.	PROPN
ejpam-5755	411	8	li	li	PROPN
ejpam-5755	411	9	,	,	PUNCT
ejpam-5755	411	10	and	and	CCONJ
ejpam-5755	411	11	x.	x.	PROPN
ejpam-5755	411	12	liu	liu	PROPN
ejpam-5755	411	13	.	.	PUNCT
ejpam-5755	412	1	event	event	NOUN
ejpam-5755	412	2	-	-	PUNCT
ejpam-5755	412	3	triggered	trigger	VERB
ejpam-5755	412	4	impulsive	impulsive	ADJ
ejpam-5755	412	5	control	control	NOUN
ejpam-5755	412	6	for	for	ADP
ejpam-5755	412	7	multi	multi	ADJ
ejpam-5755	412	8	-	-	ADJ
ejpam-5755	412	9	agent	agent	ADJ
ejpam-5755	412	10	systems	system	NOUN
ejpam-5755	412	11	with	with	ADP
ejpam-5755	412	12	actuation	actuation	NOUN
ejpam-5755	412	13	delay	delay	NOUN
ejpam-5755	412	14	and	and	CCONJ
ejpam-5755	412	15	continuous	continuous	ADJ
ejpam-5755	412	16	/	/	SYM
ejpam-5755	412	17	periodic	periodic	ADJ
ejpam-5755	412	18	sampling	sampling	NOUN
ejpam-5755	412	19	.	.	PUNCT
ejpam-5755	413	1	chaos	chaos	NOUN
ejpam-5755	413	2	,	,	PUNCT
ejpam-5755	413	3	solitons	soliton	NOUN
ejpam-5755	413	4	&	&	CCONJ
ejpam-5755	413	5	fractals	fractal	NOUN
ejpam-5755	413	6	,	,	PUNCT
ejpam-5755	413	7	175:114067	175:114067	NUM
ejpam-5755	413	8	,	,	PUNCT
ejpam-5755	413	9	2023	2023	NUM
ejpam-5755	413	10	.	.	PUNCT
ejpam-5755	414	1	[	[	X
ejpam-5755	414	2	21	21	NUM
ejpam-5755	414	3	]	]	PUNCT
ejpam-5755	414	4	x.	x.	NOUN
ejpam-5755	414	5	yu	yu	PROPN
ejpam-5755	414	6	y.	y.	PROPN
ejpam-5755	414	7	chen	chen	PROPN
ejpam-5755	414	8	,	,	PUNCT
ejpam-5755	414	9	j.	j.	PROPN
ejpam-5755	414	10	lu	lu	PROPN
ejpam-5755	414	11	and	and	CCONJ
ejpam-5755	414	12	d.	d.	PROPN
ejpam-5755	414	13	j.	j.	PROPN
ejpam-5755	414	14	hill	hill	PROPN
ejpam-5755	414	15	.	.	PUNCT
ejpam-5755	415	1	multi	multi	ADJ
ejpam-5755	415	2	-	-	ADJ
ejpam-5755	415	3	agent	agent	ADJ
ejpam-5755	415	4	systems	system	NOUN
ejpam-5755	415	5	with	with	ADP
ejpam-5755	415	6	dynamical	dynamical	ADJ
ejpam-5755	415	7	topologies	topology	NOUN
ejpam-5755	415	8	:	:	PUNCT
ejpam-5755	415	9	consensus	consensus	NOUN
ejpam-5755	415	10	and	and	CCONJ
ejpam-5755	415	11	applications	application	NOUN
ejpam-5755	415	12	.	.	PUNCT
ejpam-5755	416	1	ieee	ieee	NOUN
ejpam-5755	416	2	circuits	circuit	NOUN
ejpam-5755	416	3	and	and	CCONJ
ejpam-5755	416	4	systems	system	NOUN
ejpam-5755	416	5	magazine	magazine	NOUN
ejpam-5755	416	6	,	,	PUNCT
ejpam-5755	416	7	13(3):21–34	13(3):21–34	NUM
ejpam-5755	416	8	,	,	PUNCT
ejpam-5755	416	9	2013	2013	NUM
ejpam-5755	416	10	.	.	PUNCT
ejpam-5755	417	1	[	[	X
ejpam-5755	417	2	22	22	NUM
ejpam-5755	417	3	]	]	PUNCT
ejpam-5755	417	4	t.	t.	PROPN
ejpam-5755	417	5	chen	chen	PROPN
ejpam-5755	417	6	z.	z.	PROPN
ejpam-5755	417	7	fu	fu	PROPN
ejpam-5755	417	8	,	,	PUNCT
ejpam-5755	417	9	s.	s.	PROPN
ejpam-5755	417	10	peng	peng	PROPN
ejpam-5755	417	11	and	and	CCONJ
ejpam-5755	417	12	z.	z.	PROPN
ejpam-5755	417	13	zheng	zheng	PROPN
ejpam-5755	417	14	.	.	PUNCT
ejpam-5755	418	1	consensus	consensus	NOUN
ejpam-5755	418	2	of	of	ADP
ejpam-5755	418	3	hybrid	hybrid	NOUN
ejpam-5755	418	4	switched	switch	VERB
ejpam-5755	418	5	multi	multi	ADJ
ejpam-5755	418	6	-	-	ADJ
ejpam-5755	418	7	agent	agent	ADJ
ejpam-5755	418	8	systems	system	NOUN
ejpam-5755	418	9	under	under	ADP
ejpam-5755	418	10	different	different	ADJ
ejpam-5755	418	11	topologies	topology	NOUN
ejpam-5755	418	12	via	via	ADP
ejpam-5755	418	13	impulsive	impulsive	ADJ
ejpam-5755	418	14	control	control	NOUN
ejpam-5755	418	15	.	.	PUNCT
ejpam-5755	419	1	ieee	ieee	NOUN
ejpam-5755	419	2	access	access	NOUN
ejpam-5755	419	3	,	,	PUNCT
ejpam-5755	419	4	8:135458	8:135458	NUM
ejpam-5755	419	5	–	–	PUNCT
ejpam-5755	419	6	135467	135467	NUM
ejpam-5755	419	7	,	,	PUNCT
ejpam-5755	419	8	2020	2020	NUM
ejpam-5755	419	9	.	.	PUNCT
ejpam-5755	420	1	[	[	X
ejpam-5755	420	2	23	23	NUM
ejpam-5755	420	3	]	]	X
ejpam-5755	420	4	b.	b.	PROPN
ejpam-5755	420	5	francis	francis	PROPN
ejpam-5755	420	6	z.	z.	PROPN
ejpam-5755	420	7	lin	lin	PROPN
ejpam-5755	420	8	and	and	CCONJ
ejpam-5755	420	9	m.	m.	NOUN
ejpam-5755	420	10	maggiore	maggiore	NOUN
ejpam-5755	420	11	.	.	PUNCT
ejpam-5755	421	1	state	state	NOUN
ejpam-5755	421	2	agreement	agreement	NOUN
ejpam-5755	421	3	for	for	ADP
ejpam-5755	421	4	continuous	continuous	ADJ
ejpam-5755	421	5	-	-	PUNCT
ejpam-5755	421	6	time	time	NOUN
ejpam-5755	421	7	coupled	couple	VERB
ejpam-5755	421	8	nonlinear	nonlinear	ADJ
ejpam-5755	421	9	systems	system	NOUN
ejpam-5755	421	10	.	.	PUNCT
ejpam-5755	422	1	siam	siam	PROPN
ejpam-5755	422	2	journal	journal	PROPN
ejpam-5755	422	3	on	on	ADP
ejpam-5755	422	4	control	control	NOUN
ejpam-5755	422	5	and	and	CCONJ
ejpam-5755	422	6	optimization	optimization	NOUN
ejpam-5755	422	7	,	,	PUNCT
ejpam-5755	422	8	46(1):288–307	46(1):288–307	NOUN
ejpam-5755	422	9	,	,	PUNCT
ejpam-5755	422	10	2007	2007	NUM
ejpam-5755	422	11	.	.	PUNCT