id	sid	tid	token	lemma	pos
ejpam-6877	1	1	european	european	PROPN
ejpam-6877	1	2	journal	journal	PROPN
ejpam-6877	1	3	of	of	ADP
ejpam-6877	1	4	pure	pure	ADJ
ejpam-6877	1	5	and	and	CCONJ
ejpam-6877	1	6	applied	applied	ADJ
ejpam-6877	1	7	mathematics	mathematic	NOUN
ejpam-6877	1	8	2025	2025	NUM
ejpam-6877	1	9	,	,	PUNCT
ejpam-6877	1	10	vol	vol	NOUN
ejpam-6877	1	11	.	.	PROPN
ejpam-6877	1	12	18	18	NUM
ejpam-6877	1	13	,	,	PUNCT
ejpam-6877	1	14	issue	issue	NOUN
ejpam-6877	1	15	4	4	NUM
ejpam-6877	1	16	,	,	PUNCT
ejpam-6877	1	17	article	article	NOUN
ejpam-6877	1	18	number	number	NOUN
ejpam-6877	1	19	6877	6877	NUM
ejpam-6877	1	20	issn	issn	PROPN
ejpam-6877	1	21	1307	1307	NUM
ejpam-6877	1	22	-	-	SYM
ejpam-6877	1	23	5543	5543	NUM
ejpam-6877	1	24	–	–	PUNCT
ejpam-6877	1	25	ejpam.com	ejpam.com	X
ejpam-6877	1	26	published	publish	VERB
ejpam-6877	1	27	by	by	ADP
ejpam-6877	1	28	new	new	PROPN
ejpam-6877	1	29	york	york	PROPN
ejpam-6877	1	30	business	business	PROPN
ejpam-6877	1	31	global	global	PROPN
ejpam-6877	1	32	mathematical	mathematical	ADJ
ejpam-6877	1	33	modeling	modeling	NOUN
ejpam-6877	1	34	of	of	ADP
ejpam-6877	1	35	signed	sign	VERB
ejpam-6877	1	36	graphs	graph	NOUN
ejpam-6877	1	37	for	for	ADP
ejpam-6877	1	38	balancing	balance	VERB
ejpam-6877	1	39	dynamic	dynamic	ADJ
ejpam-6877	1	40	systems	system	NOUN
ejpam-6877	1	41	abdulaziz	abdulaziz	PROPN
ejpam-6877	1	42	mutlaq	mutlaq	PROPN
ejpam-6877	1	43	alotaibi1	alotaibi1	PROPN
ejpam-6877	1	44	,	,	PUNCT
ejpam-6877	1	45	khalid	khalid	PROPN
ejpam-6877	1	46	al	al	PROPN
ejpam-6877	1	47	-	-	PUNCT
ejpam-6877	1	48	tahat2	tahat2	PROPN
ejpam-6877	1	49	,	,	PUNCT
ejpam-6877	1	50	khaled	khaled	PROPN
ejpam-6877	1	51	mustafa	mustafa	PROPN
ejpam-6877	1	52	al	al	PROPN
ejpam-6877	1	53	-	-	PUNCT
ejpam-6877	1	54	jamal2,∗	jamal2,∗	PROPN
ejpam-6877	1	55	1	1	NUM
ejpam-6877	1	56	department	department	NOUN
ejpam-6877	1	57	of	of	ADP
ejpam-6877	1	58	mathematics	mathematic	NOUN
ejpam-6877	1	59	,	,	PUNCT
ejpam-6877	1	60	college	college	NOUN
ejpam-6877	1	61	of	of	ADP
ejpam-6877	1	62	science	science	NOUN
ejpam-6877	1	63	and	and	CCONJ
ejpam-6877	1	64	humanities	humanity	NOUN
ejpam-6877	1	65	in	in	ADP
ejpam-6877	1	66	al	al	PROPN
ejpam-6877	1	67	-	-	PUNCT
ejpam-6877	1	68	kharj	kharj	PROPN
ejpam-6877	1	69	,	,	PUNCT
ejpam-6877	1	70	prince	prince	PROPN
ejpam-6877	1	71	sattam	sattam	PROPN
ejpam-6877	1	72	bin	bin	PROPN
ejpam-6877	1	73	abdulaziz	abdulaziz	PROPN
ejpam-6877	1	74	university	university	PROPN
ejpam-6877	1	75	,	,	PUNCT
ejpam-6877	1	76	al	al	PROPN
ejpam-6877	1	77	-	-	PUNCT
ejpam-6877	1	78	kharj	kharj	PROPN
ejpam-6877	1	79	11942	11942	NUM
ejpam-6877	1	80	,	,	PUNCT
ejpam-6877	1	81	saudi	saudi	PROPN
ejpam-6877	1	82	arabia	arabia	PROPN
ejpam-6877	1	83	2	2	NUM
ejpam-6877	1	84	faculty	faculty	NOUN
ejpam-6877	1	85	of	of	ADP
ejpam-6877	1	86	computer	computer	NOUN
ejpam-6877	1	87	studies	study	NOUN
ejpam-6877	1	88	,	,	PUNCT
ejpam-6877	1	89	arab	arab	ADJ
ejpam-6877	1	90	open	open	PROPN
ejpam-6877	1	91	university	university	PROPN
ejpam-6877	1	92	,	,	PUNCT
ejpam-6877	1	93	amman	amman	PROPN
ejpam-6877	1	94	,	,	PUNCT
ejpam-6877	1	95	jordan	jordan	PROPN
ejpam-6877	1	96	abstract	abstract	PROPN
ejpam-6877	1	97	.	.	PUNCT
ejpam-6877	2	1	signed	sign	VERB
ejpam-6877	2	2	graphs	graph	NOUN
ejpam-6877	2	3	encode	encode	ADJ
ejpam-6877	2	4	cooperative	cooperative	ADJ
ejpam-6877	2	5	and	and	CCONJ
ejpam-6877	2	6	antagonistic	antagonistic	ADJ
ejpam-6877	2	7	interactions	interaction	NOUN
ejpam-6877	2	8	in	in	ADP
ejpam-6877	2	9	dynamical	dynamical	ADJ
ejpam-6877	2	10	systems	system	NOUN
ejpam-6877	2	11	.	.	PUNCT
ejpam-6877	3	1	in	in	ADP
ejpam-6877	3	2	this	this	DET
ejpam-6877	3	3	paper	paper	NOUN
ejpam-6877	3	4	we	we	PRON
ejpam-6877	3	5	will	will	AUX
ejpam-6877	3	6	study	study	VERB
ejpam-6877	3	7	how	how	SCONJ
ejpam-6877	3	8	explicit	explicit	ADJ
ejpam-6877	3	9	damping	damping	NOUN
ejpam-6877	3	10	transforms	transform	VERB
ejpam-6877	3	11	unstable	unstable	ADJ
ejpam-6877	3	12	linearized	linearize	VERB
ejpam-6877	3	13	dynamics	dynamic	NOUN
ejpam-6877	3	14	into	into	ADP
ejpam-6877	3	15	stable	stable	ADJ
ejpam-6877	3	16	behavior	behavior	NOUN
ejpam-6877	3	17	,	,	PUNCT
ejpam-6877	3	18	mapping	map	VERB
ejpam-6877	3	19	the	the	DET
ejpam-6877	3	20	system	system	NOUN
ejpam-6877	3	21	jacobian	jacobian	ADJ
ejpam-6877	3	22	to	to	ADP
ejpam-6877	3	23	a	a	DET
ejpam-6877	3	24	signed	sign	VERB
ejpam-6877	3	25	weighted	weight	VERB
ejpam-6877	3	26	matrix	matrix	NOUN
ejpam-6877	3	27	to	to	PART
ejpam-6877	3	28	diagnose	diagnose	VERB
ejpam-6877	3	29	destabilizing	destabilizing	ADJ
ejpam-6877	3	30	pathways	pathway	NOUN
ejpam-6877	3	31	and	and	CCONJ
ejpam-6877	3	32	guide	guide	VERB
ejpam-6877	3	33	damping	damp	VERB
ejpam-6877	3	34	or	or	CCONJ
ejpam-6877	3	35	edge	edge	NOUN
ejpam-6877	3	36	reweighting	reweighting	NOUN
ejpam-6877	3	37	.	.	PUNCT
ejpam-6877	4	1	beyond	beyond	ADP
ejpam-6877	4	2	graphical	graphical	ADJ
ejpam-6877	4	3	intuition	intuition	NOUN
ejpam-6877	4	4	,	,	PUNCT
ejpam-6877	4	5	stability	stability	NOUN
ejpam-6877	4	6	is	be	AUX
ejpam-6877	4	7	certified	certify	VERB
ejpam-6877	4	8	by	by	ADP
ejpam-6877	4	9	a	a	DET
ejpam-6877	4	10	lyapunov	lyapunov	PROPN
ejpam-6877	4	11	/	/	SYM
ejpam-6877	4	12	spectral	spectral	ADJ
ejpam-6877	4	13	test	test	NOUN
ejpam-6877	4	14	on	on	ADP
ejpam-6877	4	15	the	the	DET
ejpam-6877	4	16	symmetric	symmetric	ADJ
ejpam-6877	4	17	part	part	NOUN
ejpam-6877	4	18	s	s	VERB
ejpam-6877	4	19	with	with	ADP
ejpam-6877	4	20	diagonal	diagonal	ADJ
ejpam-6877	4	21	damping	damp	VERB
ejpam-6877	4	22	d	d	NOUN
ejpam-6877	4	23	,	,	PUNCT
ejpam-6877	4	24	namely	namely	ADV
ejpam-6877	4	25	d	d	ADP
ejpam-6877	4	26	−	−	PROPN
ejpam-6877	4	27	s	s	PART
ejpam-6877	4	28	≻	≻	PROPN
ejpam-6877	4	29	0	0	NUM
ejpam-6877	4	30	(	(	PUNCT
ejpam-6877	4	31	equivalently	equivalently	ADV
ejpam-6877	4	32	,	,	PUNCT
ejpam-6877	4	33	λmax(s	λmax(s	PROPN
ejpam-6877	4	34	)	)	PUNCT
ejpam-6877	4	35	<	<	X
ejpam-6877	4	36	mini	mini	X
ejpam-6877	4	37	di	di	NOUN
ejpam-6877	4	38	)	)	PUNCT
ejpam-6877	4	39	.	.	PUNCT
ejpam-6877	5	1	using	use	VERB
ejpam-6877	5	2	the	the	DET
ejpam-6877	5	3	inverted	inverted	ADJ
ejpam-6877	5	4	pendulum	pendulum	NOUN
ejpam-6877	5	5	as	as	ADP
ejpam-6877	5	6	a	a	DET
ejpam-6877	5	7	benchmark	benchmark	NOUN
ejpam-6877	5	8	,	,	PUNCT
ejpam-6877	5	9	we	we	PRON
ejpam-6877	5	10	derive	derive	VERB
ejpam-6877	5	11	a	a	DET
ejpam-6877	5	12	cleaned	clean	VERB
ejpam-6877	5	13	state	state	NOUN
ejpam-6877	5	14	-	-	PUNCT
ejpam-6877	5	15	space	space	NOUN
ejpam-6877	5	16	model	model	NOUN
ejpam-6877	5	17	,	,	PUNCT
ejpam-6877	5	18	show	show	VERB
ejpam-6877	5	19	undamped	undampe	VERB
ejpam-6877	5	20	instability	instability	NOUN
ejpam-6877	5	21	,	,	PUNCT
ejpam-6877	5	22	and	and	CCONJ
ejpam-6877	5	23	demonstrate	demonstrate	VERB
ejpam-6877	5	24	how	how	SCONJ
ejpam-6877	5	25	viscous	viscous	ADJ
ejpam-6877	5	26	damping	damping	NOUN
ejpam-6877	5	27	enforces	enforce	VERB
ejpam-6877	5	28	the	the	DET
ejpam-6877	5	29	certificate	certificate	NOUN
ejpam-6877	5	30	.	.	PUNCT
ejpam-6877	6	1	we	we	PRON
ejpam-6877	6	2	provide	provide	VERB
ejpam-6877	6	3	a	a	DET
ejpam-6877	6	4	concise	concise	ADJ
ejpam-6877	6	5	numerical	numerical	ADJ
ejpam-6877	6	6	verification	verification	NOUN
ejpam-6877	6	7	(	(	PUNCT
ejpam-6877	6	8	eigenvalue	eigenvalue	NOUN
ejpam-6877	6	9	check	check	NOUN
ejpam-6877	6	10	and	and	CCONJ
ejpam-6877	6	11	time	time	NOUN
ejpam-6877	6	12	-	-	PUNCT
ejpam-6877	6	13	response	response	NOUN
ejpam-6877	6	14	illustration	illustration	NOUN
ejpam-6877	6	15	)	)	PUNCT
ejpam-6877	6	16	.	.	PUNCT
ejpam-6877	7	1	the	the	DET
ejpam-6877	7	2	results	result	NOUN
ejpam-6877	7	3	clarify	clarify	VERB
ejpam-6877	7	4	when	when	SCONJ
ejpam-6877	7	5	signed	sign	VERB
ejpam-6877	7	6	graphs	graph	NOUN
ejpam-6877	7	7	aid	aid	NOUN
ejpam-6877	7	8	design	design	NOUN
ejpam-6877	7	9	and	and	CCONJ
ejpam-6877	7	10	placement	placement	NOUN
ejpam-6877	7	11	of	of	ADP
ejpam-6877	7	12	damping	damp	VERB
ejpam-6877	7	13	,	,	PUNCT
ejpam-6877	7	14	while	while	SCONJ
ejpam-6877	7	15	the	the	DET
ejpam-6877	7	16	lyapunov	lyapunov	PROPN
ejpam-6877	7	17	/	/	SYM
ejpam-6877	7	18	spectral	spectral	ADJ
ejpam-6877	7	19	certificate	certificate	NOUN
ejpam-6877	7	20	supplies	supply	VERB
ejpam-6877	7	21	the	the	DET
ejpam-6877	7	22	formal	formal	ADJ
ejpam-6877	7	23	guarantee	guarantee	NOUN
ejpam-6877	7	24	of	of	ADP
ejpam-6877	7	25	stability	stability	NOUN
ejpam-6877	7	26	through	through	ADP
ejpam-6877	7	27	a	a	DET
ejpam-6877	7	28	computable	computable	ADJ
ejpam-6877	7	29	criterion	criterion	NOUN
ejpam-6877	7	30	.	.	PUNCT
ejpam-6877	8	1	2020	2020	NUM
ejpam-6877	8	2	mathematics	mathematic	NOUN
ejpam-6877	8	3	subject	subject	NOUN
ejpam-6877	8	4	classifications	classification	NOUN
ejpam-6877	8	5	:	:	PUNCT
ejpam-6877	8	6	93c10	93c10	NUM
ejpam-6877	8	7	,	,	PUNCT
ejpam-6877	8	8	93d15	93d15	NUM
ejpam-6877	8	9	,	,	PUNCT
ejpam-6877	8	10	05c22	05c22	NOUN
ejpam-6877	8	11	key	key	ADJ
ejpam-6877	8	12	words	word	NOUN
ejpam-6877	8	13	and	and	CCONJ
ejpam-6877	8	14	phrases	phrase	NOUN
ejpam-6877	8	15	:	:	PUNCT
ejpam-6877	8	16	signed	sign	VERB
ejpam-6877	8	17	graph	graph	NOUN
ejpam-6877	8	18	,	,	PUNCT
ejpam-6877	8	19	balance	balance	NOUN
ejpam-6877	8	20	sign	sign	NOUN
ejpam-6877	8	21	graph	graph	NOUN
ejpam-6877	8	22	,	,	PUNCT
ejpam-6877	8	23	lyapunov	lyapunov	NOUN
ejpam-6877	8	24	stability	stability	NOUN
ejpam-6877	8	25	,	,	PUNCT
ejpam-6877	8	26	equilibrium	equilibrium	NOUN
ejpam-6877	8	27	point	point	NOUN
ejpam-6877	8	28	,	,	PUNCT
ejpam-6877	8	29	damping	damp	VERB
ejpam-6877	8	30	factor	factor	NOUN
ejpam-6877	8	31	1	1	NUM
ejpam-6877	8	32	.	.	PUNCT
ejpam-6877	9	1	introduction	introduction	NOUN
ejpam-6877	9	2	and	and	CCONJ
ejpam-6877	9	3	preliminaries	preliminary	NOUN
ejpam-6877	9	4	dynamical	dynamical	ADJ
ejpam-6877	9	5	systems	system	NOUN
ejpam-6877	9	6	provide	provide	VERB
ejpam-6877	9	7	mathematical	mathematical	ADJ
ejpam-6877	9	8	models	model	NOUN
ejpam-6877	9	9	to	to	PART
ejpam-6877	9	10	understand	understand	VERB
ejpam-6877	9	11	and	and	CCONJ
ejpam-6877	9	12	characterize	characterize	VERB
ejpam-6877	9	13	the	the	DET
ejpam-6877	9	14	motion	motion	NOUN
ejpam-6877	9	15	of	of	ADP
ejpam-6877	9	16	many	many	ADJ
ejpam-6877	9	17	natural	natural	ADJ
ejpam-6877	9	18	and	and	CCONJ
ejpam-6877	9	19	engineered	engineer	VERB
ejpam-6877	9	20	phenomena	phenomenon	NOUN
ejpam-6877	9	21	.	.	PUNCT
ejpam-6877	10	1	examples	example	NOUN
ejpam-6877	10	2	range	range	VERB
ejpam-6877	10	3	from	from	ADP
ejpam-6877	10	4	simple	simple	ADJ
ejpam-6877	10	5	systems	system	NOUN
ejpam-6877	10	6	such	such	ADJ
ejpam-6877	10	7	as	as	ADP
ejpam-6877	10	8	the	the	DET
ejpam-6877	10	9	pendulum	pendulum	NOUN
ejpam-6877	10	10	[	[	X
ejpam-6877	10	11	1	1	X
ejpam-6877	10	12	]	]	PUNCT
ejpam-6877	10	13	to	to	ADP
ejpam-6877	10	14	complex	complex	ADJ
ejpam-6877	10	15	applications	application	NOUN
ejpam-6877	10	16	in	in	ADP
ejpam-6877	10	17	aircraft	aircraft	NOUN
ejpam-6877	10	18	control	control	NOUN
ejpam-6877	10	19	,	,	PUNCT
ejpam-6877	10	20	power	power	NOUN
ejpam-6877	10	21	-	-	PUNCT
ejpam-6877	10	22	network	network	NOUN
ejpam-6877	10	23	analysis	analysis	NOUN
ejpam-6877	10	24	,	,	PUNCT
ejpam-6877	10	25	and	and	CCONJ
ejpam-6877	10	26	robotics	robotic	NOUN
ejpam-6877	10	27	.	.	PUNCT
ejpam-6877	11	1	a	a	DET
ejpam-6877	11	2	central	central	ADJ
ejpam-6877	11	3	theme	theme	NOUN
ejpam-6877	11	4	across	across	ADP
ejpam-6877	11	5	these	these	DET
ejpam-6877	11	6	domains	domain	NOUN
ejpam-6877	11	7	is	be	AUX
ejpam-6877	11	8	stability	stability	NOUN
ejpam-6877	11	9	,	,	PUNCT
ejpam-6877	11	10	the	the	DET
ejpam-6877	11	11	ability	ability	NOUN
ejpam-6877	11	12	of	of	ADP
ejpam-6877	11	13	a	a	DET
ejpam-6877	11	14	system	system	NOUN
ejpam-6877	11	15	to	to	PART
ejpam-6877	11	16	return	return	VERB
ejpam-6877	11	17	to	to	ADP
ejpam-6877	11	18	an	an	DET
ejpam-6877	11	19	equilibrium	equilibrium	NOUN
ejpam-6877	11	20	after	after	ADP
ejpam-6877	11	21	perturbations	perturbation	NOUN
ejpam-6877	11	22	[	[	X
ejpam-6877	11	23	2	2	NUM
ejpam-6877	11	24	,	,	PUNCT
ejpam-6877	11	25	3	3	NUM
ejpam-6877	11	26	]	]	PUNCT
ejpam-6877	11	27	.	.	PUNCT
ejpam-6877	12	1	in	in	ADP
ejpam-6877	12	2	practice	practice	NOUN
ejpam-6877	12	3	,	,	PUNCT
ejpam-6877	12	4	assessing	assess	VERB
ejpam-6877	12	5	stability	stability	NOUN
ejpam-6877	12	6	requires	require	VERB
ejpam-6877	12	7	analyzing	analyze	VERB
ejpam-6877	12	8	the	the	DET
ejpam-6877	12	9	internal	internal	ADJ
ejpam-6877	12	10	couplings	coupling	NOUN
ejpam-6877	12	11	among	among	ADP
ejpam-6877	12	12	the	the	DET
ejpam-6877	12	13	system	system	NOUN
ejpam-6877	12	14	variables	variable	NOUN
ejpam-6877	12	15	[	[	X
ejpam-6877	12	16	4	4	NUM
ejpam-6877	12	17	]	]	PUNCT
ejpam-6877	12	18	,	,	PUNCT
ejpam-6877	12	19	including	include	VERB
ejpam-6877	12	20	whether	whether	SCONJ
ejpam-6877	12	21	these	these	DET
ejpam-6877	12	22	interactions	interaction	NOUN
ejpam-6877	12	23	are	be	AUX
ejpam-6877	12	24	reinforcing	reinforce	VERB
ejpam-6877	12	25	(	(	PUNCT
ejpam-6877	12	26	positive	positive	ADJ
ejpam-6877	12	27	)	)	PUNCT
ejpam-6877	12	28	or	or	CCONJ
ejpam-6877	12	29	opposing	oppose	VERB
ejpam-6877	12	30	(	(	PUNCT
ejpam-6877	12	31	negative	negative	ADJ
ejpam-6877	12	32	)	)	PUNCT
ejpam-6877	13	1	[	[	X
ejpam-6877	13	2	5	5	NUM
ejpam-6877	13	3	,	,	PUNCT
ejpam-6877	13	4	6	6	NUM
ejpam-6877	13	5	]	]	PUNCT
ejpam-6877	13	6	.	.	PUNCT
ejpam-6877	14	1	within	within	ADP
ejpam-6877	14	2	this	this	DET
ejpam-6877	14	3	context	context	NOUN
ejpam-6877	14	4	,	,	PUNCT
ejpam-6877	14	5	the	the	DET
ejpam-6877	14	6	signed	sign	VERB
ejpam-6877	14	7	graph	graph	NOUN
ejpam-6877	14	8	offers	offer	VERB
ejpam-6877	14	9	an	an	DET
ejpam-6877	14	10	effective	effective	ADJ
ejpam-6877	14	11	and	and	CCONJ
ejpam-6877	14	12	visual	visual	ADJ
ejpam-6877	14	13	formalism	formalism	NOUN
ejpam-6877	14	14	to	to	PART
ejpam-6877	14	15	encode	encode	VERB
ejpam-6877	14	16	the	the	DET
ejpam-6877	14	17	nature	nature	NOUN
ejpam-6877	14	18	of	of	ADP
ejpam-6877	14	19	pairwise	pairwise	NOUN
ejpam-6877	14	20	influences	influence	NOUN
ejpam-6877	14	21	among	among	ADP
ejpam-6877	14	22	state	state	NOUN
ejpam-6877	14	23	variables	variable	NOUN
ejpam-6877	14	24	[	[	X
ejpam-6877	14	25	7	7	NUM
ejpam-6877	14	26	,	,	PUNCT
ejpam-6877	14	27	8	8	NUM
ejpam-6877	14	28	]	]	PUNCT
ejpam-6877	14	29	.	.	PUNCT
ejpam-6877	15	1	in	in	ADP
ejpam-6877	15	2	a	a	DET
ejpam-6877	15	3	signed	sign	VERB
ejpam-6877	15	4	graph	graph	NOUN
ejpam-6877	15	5	,	,	PUNCT
ejpam-6877	15	6	directed	direct	VERB
ejpam-6877	15	7	∗corresponding	∗corresponde	VERB
ejpam-6877	15	8	author	author	NOUN
ejpam-6877	15	9	.	.	PUNCT
ejpam-6877	16	1	doi	doi	NOUN
ejpam-6877	16	2	:	:	PUNCT
ejpam-6877	16	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6877	https://doi.org/10.29020/nybg.ejpam.v18i4.6877	VERB
ejpam-6877	16	4	email	email	NOUN
ejpam-6877	16	5	addresses	address	NOUN
ejpam-6877	16	6	:	:	PUNCT
ejpam-6877	16	7	am.alotaibi@psau.edu.sa	am.alotaibi@psau.edu.sa	PROPN
ejpam-6877	16	8	(	(	PUNCT
ejpam-6877	16	9	a.	a.	NOUN
ejpam-6877	16	10	m.	m.	NOUN
ejpam-6877	16	11	alotaibi	alotaibi	PROPN
ejpam-6877	16	12	)	)	PUNCT
ejpam-6877	16	13	,	,	PUNCT
ejpam-6877	16	14	k_tahat@aou.edu.jo	k_tahat@aou.edu.jo	PROPN
ejpam-6877	16	15	(	(	PUNCT
ejpam-6877	16	16	k.	k.	PROPN
ejpam-6877	16	17	al	al	PROPN
ejpam-6877	16	18	-	-	PROPN
ejpam-6877	16	19	tahat	tahat	PROPN
ejpam-6877	16	20	)	)	PUNCT
ejpam-6877	16	21	,	,	PUNCT
ejpam-6877	16	22	pt_aljammal@aou.edu.jo	pt_aljammal@aou.edu.jo	NOUN
ejpam-6877	16	23	(	(	PUNCT
ejpam-6877	16	24	k.	k.	PROPN
ejpam-6877	16	25	m.	m.	PROPN
ejpam-6877	16	26	al	al	PROPN
ejpam-6877	16	27	-	-	PUNCT
ejpam-6877	16	28	jamal	jamal	PROPN
ejpam-6877	16	29	)	)	PUNCT
ejpam-6877	16	30	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6877	17	1	1	1	NUM
ejpam-6877	17	2	copyright	copyright	NOUN
ejpam-6877	17	3	:	:	PUNCT
ejpam-6877	17	4	©	©	PROPN
ejpam-6877	17	5	2025	2025	NUM
ejpam-6877	17	6	the	the	DET
ejpam-6877	17	7	author(s	author(s	NOUN
ejpam-6877	17	8	)	)	PUNCT
ejpam-6877	17	9	.	.	PUNCT
ejpam-6877	18	1	(	(	PUNCT
ejpam-6877	18	2	cc	cc	NOUN
ejpam-6877	18	3	by	by	ADP
ejpam-6877	18	4	-	-	PUNCT
ejpam-6877	18	5	nc	nc	PROPN
ejpam-6877	18	6	4.0	4.0	NUM
ejpam-6877	18	7	)	)	PUNCT
ejpam-6877	18	8	a.	a.	NOUN
ejpam-6877	18	9	m.	m.	NOUN
ejpam-6877	18	10	alotaibi	alotaibi	PROPN
ejpam-6877	18	11	et	et	PROPN
ejpam-6877	18	12	al	al	PROPN
ejpam-6877	18	13	.	.	PUNCT
ejpam-6877	18	14	/	/	SYM
ejpam-6877	18	15	eur	eur	PROPN
ejpam-6877	18	16	.	.	PUNCT
ejpam-6877	19	1	j.	j.	PROPN
ejpam-6877	19	2	pure	pure	PROPN
ejpam-6877	19	3	appl	appl	PROPN
ejpam-6877	19	4	.	.	PROPN
ejpam-6877	19	5	math	math	PROPN
ejpam-6877	19	6	,	,	PUNCT
ejpam-6877	19	7	18	18	NUM
ejpam-6877	19	8	(	(	PUNCT
ejpam-6877	19	9	4	4	NUM
ejpam-6877	19	10	)	)	PUNCT
ejpam-6877	19	11	(	(	PUNCT
ejpam-6877	19	12	2025	2025	NUM
ejpam-6877	19	13	)	)	PUNCT
ejpam-6877	19	14	,	,	PUNCT
ejpam-6877	19	15	6877	6877	NUM
ejpam-6877	19	16	2	2	NUM
ejpam-6877	19	17	of	of	ADP
ejpam-6877	19	18	9	9	NUM
ejpam-6877	19	19	edges	edge	NOUN
ejpam-6877	19	20	carry	carry	VERB
ejpam-6877	19	21	signs	sign	NOUN
ejpam-6877	19	22	that	that	PRON
ejpam-6877	19	23	indicate	indicate	VERB
ejpam-6877	19	24	how	how	SCONJ
ejpam-6877	19	25	one	one	NUM
ejpam-6877	19	26	variable	variable	NOUN
ejpam-6877	19	27	affects	affect	VERB
ejpam-6877	19	28	another	another	PRON
ejpam-6877	19	29	,	,	PUNCT
ejpam-6877	19	30	enabling	enable	VERB
ejpam-6877	19	31	a	a	DET
ejpam-6877	19	32	compact	compact	ADJ
ejpam-6877	19	33	representation	representation	NOUN
ejpam-6877	19	34	of	of	ADP
ejpam-6877	19	35	cooperative	cooperative	ADJ
ejpam-6877	19	36	and	and	CCONJ
ejpam-6877	19	37	antagonistic	antagonistic	ADJ
ejpam-6877	19	38	relations	relation	NOUN
ejpam-6877	19	39	[	[	X
ejpam-6877	19	40	9	9	NUM
ejpam-6877	19	41	]	]	PUNCT
ejpam-6877	19	42	.	.	PUNCT
ejpam-6877	20	1	such	such	ADJ
ejpam-6877	20	2	representations	representation	NOUN
ejpam-6877	20	3	help	help	VERB
ejpam-6877	20	4	diagnose	diagnose	NOUN
ejpam-6877	20	5	sources	source	NOUN
ejpam-6877	20	6	of	of	ADP
ejpam-6877	20	7	instability	instability	NOUN
ejpam-6877	20	8	,	,	PUNCT
ejpam-6877	20	9	diverging	diverge	VERB
ejpam-6877	20	10	trajectories	trajectory	NOUN
ejpam-6877	20	11	or	or	CCONJ
ejpam-6877	20	12	persistent	persistent	ADJ
ejpam-6877	20	13	oscillations	oscillation	NOUN
ejpam-6877	20	14	by	by	ADP
ejpam-6877	20	15	highlighting	highlight	VERB
ejpam-6877	20	16	destabilizing	destabilizing	ADJ
ejpam-6877	20	17	pathways	pathway	NOUN
ejpam-6877	20	18	in	in	ADP
ejpam-6877	20	19	the	the	DET
ejpam-6877	20	20	interaction	interaction	NOUN
ejpam-6877	20	21	structure	structure	NOUN
ejpam-6877	20	22	[	[	X
ejpam-6877	20	23	10	10	NUM
ejpam-6877	20	24	,	,	PUNCT
ejpam-6877	20	25	11	11	NUM
ejpam-6877	20	26	]	]	PUNCT
ejpam-6877	20	27	.	.	PUNCT
ejpam-6877	21	1	a	a	DET
ejpam-6877	21	2	classical	classical	ADJ
ejpam-6877	21	3	way	way	NOUN
ejpam-6877	21	4	to	to	PART
ejpam-6877	21	5	improve	improve	VERB
ejpam-6877	21	6	stability	stability	NOUN
ejpam-6877	21	7	is	be	AUX
ejpam-6877	21	8	to	to	PART
ejpam-6877	21	9	introduce	introduce	VERB
ejpam-6877	21	10	damping	damp	VERB
ejpam-6877	21	11	terms	term	NOUN
ejpam-6877	21	12	that	that	PRON
ejpam-6877	21	13	act	act	VERB
ejpam-6877	21	14	as	as	ADP
ejpam-6877	21	15	selfinhibitory	selfinhibitory	NOUN
ejpam-6877	21	16	mechanisms	mechanism	NOUN
ejpam-6877	21	17	on	on	ADP
ejpam-6877	21	18	selected	select	VERB
ejpam-6877	21	19	states	state	NOUN
ejpam-6877	21	20	.	.	PUNCT
ejpam-6877	22	1	for	for	ADP
ejpam-6877	22	2	instance	instance	NOUN
ejpam-6877	22	3	,	,	PUNCT
ejpam-6877	22	4	in	in	ADP
ejpam-6877	22	5	the	the	DET
ejpam-6877	22	6	inverted	invert	VERB
ejpam-6877	22	7	-	-	PUNCT
ejpam-6877	22	8	pendulum	pendulum	NOUN
ejpam-6877	22	9	benchmark	benchmark	NOUN
ejpam-6877	22	10	,	,	PUNCT
ejpam-6877	22	11	adding	add	VERB
ejpam-6877	22	12	viscous	viscous	ADJ
ejpam-6877	22	13	damping	damp	VERB
ejpam-6877	22	14	to	to	ADP
ejpam-6877	22	15	the	the	DET
ejpam-6877	22	16	angular	angular	ADJ
ejpam-6877	22	17	rate	rate	NOUN
ejpam-6877	22	18	reduces	reduce	VERB
ejpam-6877	22	19	oscillations	oscillation	NOUN
ejpam-6877	22	20	and	and	CCONJ
ejpam-6877	22	21	can	can	AUX
ejpam-6877	22	22	steer	steer	VERB
ejpam-6877	22	23	the	the	DET
ejpam-6877	22	24	dynamics	dynamic	NOUN
ejpam-6877	22	25	toward	toward	ADP
ejpam-6877	22	26	a	a	DET
ejpam-6877	22	27	stable	stable	ADJ
ejpam-6877	22	28	regime	regime	NOUN
ejpam-6877	22	29	.	.	PUNCT
ejpam-6877	23	1	beyond	beyond	ADP
ejpam-6877	23	2	mechanical	mechanical	ADJ
ejpam-6877	23	3	systems	system	NOUN
ejpam-6877	23	4	[	[	X
ejpam-6877	23	5	12	12	NUM
ejpam-6877	23	6	]	]	PUNCT
ejpam-6877	23	7	,	,	PUNCT
ejpam-6877	23	8	the	the	DET
ejpam-6877	23	9	same	same	ADJ
ejpam-6877	23	10	modeling	modeling	NOUN
ejpam-6877	23	11	and	and	CCONJ
ejpam-6877	23	12	design	design	NOUN
ejpam-6877	23	13	ideas	idea	NOUN
ejpam-6877	23	14	extend	extend	VERB
ejpam-6877	23	15	to	to	ADP
ejpam-6877	23	16	energy	energy	NOUN
ejpam-6877	23	17	networks	network	NOUN
ejpam-6877	23	18	[	[	X
ejpam-6877	23	19	13	13	NUM
ejpam-6877	23	20	]	]	PUNCT
ejpam-6877	23	21	,	,	PUNCT
ejpam-6877	23	22	biological	biological	ADJ
ejpam-6877	23	23	systems	system	NOUN
ejpam-6877	23	24	,	,	PUNCT
ejpam-6877	23	25	and	and	CCONJ
ejpam-6877	23	26	even	even	ADV
ejpam-6877	23	27	econo	econo	PROPN
ejpam-6877	23	28	-	-	PUNCT
ejpam-6877	23	29	sports	sport	NOUN
ejpam-6877	23	30	models	model	NOUN
ejpam-6877	23	31	.	.	PUNCT
ejpam-6877	24	1	in	in	ADP
ejpam-6877	24	2	this	this	DET
ejpam-6877	24	3	paper	paper	NOUN
ejpam-6877	24	4	we	we	PRON
ejpam-6877	24	5	analyze	analyze	VERB
ejpam-6877	24	6	unstable	unstable	ADJ
ejpam-6877	24	7	configurations	configuration	NOUN
ejpam-6877	24	8	(	(	PUNCT
ejpam-6877	24	9	including	include	VERB
ejpam-6877	24	10	saddle	saddle	NOUN
ejpam-6877	24	11	-	-	PUNCT
ejpam-6877	24	12	type	type	NOUN
ejpam-6877	24	13	equilibria	equilibrium	NOUN
ejpam-6877	24	14	[	[	X
ejpam-6877	24	15	14	14	NUM
ejpam-6877	24	16	]	]	PUNCT
ejpam-6877	24	17	)	)	PUNCT
ejpam-6877	24	18	through	through	ADP
ejpam-6877	24	19	a	a	DET
ejpam-6877	24	20	signed	sign	VERB
ejpam-6877	24	21	-	-	PUNCT
ejpam-6877	24	22	graph	graph	NOUN
ejpam-6877	24	23	lens	lens	NOUN
ejpam-6877	24	24	and	and	CCONJ
ejpam-6877	24	25	show	show	VERB
ejpam-6877	24	26	how	how	SCONJ
ejpam-6877	24	27	damping	damp	VERB
ejpam-6877	24	28	can	can	AUX
ejpam-6877	24	29	be	be	AUX
ejpam-6877	24	30	deployed	deploy	VERB
ejpam-6877	24	31	to	to	PART
ejpam-6877	24	32	achieve	achieve	VERB
ejpam-6877	24	33	stabilization	stabilization	NOUN
ejpam-6877	24	34	.	.	PUNCT
ejpam-6877	25	1	specifically	specifically	ADV
ejpam-6877	25	2	[	[	X
ejpam-6877	25	3	6	6	NUM
ejpam-6877	25	4	]	]	PUNCT
ejpam-6877	25	5	,	,	PUNCT
ejpam-6877	25	6	we	we	PRON
ejpam-6877	25	7	derive	derive	VERB
ejpam-6877	25	8	the	the	DET
ejpam-6877	25	9	nonlinear	nonlinear	ADJ
ejpam-6877	25	10	model	model	NOUN
ejpam-6877	25	11	and	and	CCONJ
ejpam-6877	25	12	its	its	PRON
ejpam-6877	25	13	linearization	linearization	NOUN
ejpam-6877	25	14	via	via	ADP
ejpam-6877	25	15	the	the	DET
ejpam-6877	25	16	jacobian[1	jacobian[1	PROPN
ejpam-6877	25	17	]	]	PUNCT
ejpam-6877	25	18	,	,	PUNCT
ejpam-6877	25	19	map	map	VERB
ejpam-6877	25	20	the	the	DET
ejpam-6877	25	21	jacobian	jacobian	ADJ
ejpam-6877	25	22	pattern	pattern	NOUN
ejpam-6877	25	23	to	to	ADP
ejpam-6877	25	24	a	a	DET
ejpam-6877	25	25	signed	sign	VERB
ejpam-6877	25	26	weighted	weight	VERB
ejpam-6877	25	27	graph	graph	NOUN
ejpam-6877	25	28	,	,	PUNCT
ejpam-6877	25	29	and	and	CCONJ
ejpam-6877	25	30	use	use	VERB
ejpam-6877	25	31	this	this	DET
ejpam-6877	25	32	structure	structure	NOUN
ejpam-6877	25	33	to	to	PART
ejpam-6877	25	34	motivate	motivate	VERB
ejpam-6877	25	35	stabilization	stabilization	NOUN
ejpam-6877	25	36	by	by	ADP
ejpam-6877	25	37	[	[	X
ejpam-6877	25	38	15	15	NUM
ejpam-6877	25	39	]	]	PUNCT
ejpam-6877	25	40	adding	add	VERB
ejpam-6877	25	41	damping	damp	VERB
ejpam-6877	25	42	and	and	CCONJ
ejpam-6877	25	43	[	[	X
ejpam-6877	25	44	16	16	NUM
ejpam-6877	25	45	]	]	X
ejpam-6877	25	46	reweighting	reweighte	VERB
ejpam-6877	25	47	positive	positive	ADJ
ejpam-6877	25	48	/	/	SYM
ejpam-6877	25	49	negative	negative	ADJ
ejpam-6877	25	50	influences	influence	NOUN
ejpam-6877	25	51	.	.	PUNCT
ejpam-6877	26	1	we	we	PRON
ejpam-6877	26	2	complement	complement	VERB
ejpam-6877	26	3	the	the	DET
ejpam-6877	26	4	qualitative	qualitative	NOUN
ejpam-6877	26	5	,	,	PUNCT
ejpam-6877	26	6	graph	graph	NOUN
ejpam-6877	26	7	-	-	PUNCT
ejpam-6877	26	8	based	base	VERB
ejpam-6877	26	9	intuition	intuition	NOUN
ejpam-6877	26	10	with	with	ADP
ejpam-6877	26	11	a	a	DET
ejpam-6877	26	12	rigorous	rigorous	ADJ
ejpam-6877	26	13	matrixbased	matrixbase	VERB
ejpam-6877	26	14	stability	stability	NOUN
ejpam-6877	26	15	check	check	NOUN
ejpam-6877	26	16	on	on	ADP
ejpam-6877	26	17	the	the	DET
ejpam-6877	26	18	linearized	linearize	VERB
ejpam-6877	26	19	model	model	NOUN
ejpam-6877	26	20	and	and	CCONJ
ejpam-6877	26	21	illustrate	illustrate	VERB
ejpam-6877	26	22	the	the	DET
ejpam-6877	26	23	approach	approach	NOUN
ejpam-6877	26	24	on	on	ADP
ejpam-6877	26	25	the	the	DET
ejpam-6877	26	26	inverted	inverted	ADJ
ejpam-6877	26	27	pendulum	pendulum	NOUN
ejpam-6877	26	28	.	.	PUNCT
ejpam-6877	27	1	finally	finally	ADV
ejpam-6877	27	2	,	,	PUNCT
ejpam-6877	27	3	we	we	PRON
ejpam-6877	27	4	discuss	discuss	VERB
ejpam-6877	27	5	application	application	NOUN
ejpam-6877	27	6	prospects	prospect	NOUN
ejpam-6877	27	7	in	in	ADP
ejpam-6877	27	8	diverse	diverse	ADJ
ejpam-6877	27	9	domains	domain	NOUN
ejpam-6877	27	10	[	[	X
ejpam-6877	27	11	17	17	NUM
ejpam-6877	27	12	,	,	PUNCT
ejpam-6877	27	13	18	18	NUM
ejpam-6877	27	14	]	]	PUNCT
ejpam-6877	27	15	.	.	PUNCT
ejpam-6877	28	1	definition	definition	NOUN
ejpam-6877	28	2	1	1	NUM
ejpam-6877	28	3	.	.	PUNCT
ejpam-6877	29	1	[	[	X
ejpam-6877	29	2	1	1	X
ejpam-6877	29	3	]	]	PUNCT
ejpam-6877	29	4	in	in	ADP
ejpam-6877	29	5	a	a	DET
ejpam-6877	29	6	differential	differential	ADJ
ejpam-6877	29	7	equations	equation	NOUN
ejpam-6877	29	8	.	.	PUNCT
ejpam-6877	30	1	x	x	X
ejpam-6877	30	2	=	=	SYM
ejpam-6877	30	3	u(x	u(x	PROPN
ejpam-6877	30	4	,	,	PUNCT
ejpam-6877	30	5	y	y	NOUN
ejpam-6877	30	6	)	)	PUNCT
ejpam-6877	30	7	,	,	PUNCT
ejpam-6877	30	8	the	the	DET
ejpam-6877	30	9	equilibrium	equilibrium	NOUN
ejpam-6877	30	10	point	point	NOUN
ejpam-6877	30	11	is	be	AUX
ejpam-6877	30	12	expressed	express	VERB
ejpam-6877	30	13	by	by	ADP
ejpam-6877	30	14	(	(	PUNCT
ejpam-6877	30	15	xe	xe	PROPN
ejpam-6877	30	16	,	,	PUNCT
ejpam-6877	30	17	ye)such	ye)such	VERB
ejpam-6877	31	1	that	that	SCONJ
ejpam-6877	31	2	,	,	PUNCT
ejpam-6877	31	3	x(t	x(t	PROPN
ejpam-6877	31	4	)	)	PUNCT
ejpam-6877	31	5	=	=	SYM
ejpam-6877	31	6	xe	xe	PROPN
ejpam-6877	31	7	,	,	PUNCT
ejpam-6877	31	8	y(t	y(t	PROPN
ejpam-6877	31	9	)	)	PUNCT
ejpam-6877	32	1	=	=	PUNCT
ejpam-6877	32	2	ye	ye	PRON
ejpam-6877	32	3	is	be	AUX
ejpam-6877	32	4	a	a	DET
ejpam-6877	32	5	constant	constant	ADJ
ejpam-6877	32	6	solution	solution	NOUN
ejpam-6877	32	7	of	of	ADP
ejpam-6877	32	8	the	the	DET
ejpam-6877	32	9	system	system	NOUN
ejpam-6877	32	10	of	of	ADP
ejpam-6877	32	11	differential	differential	ADJ
ejpam-6877	32	12	equations	equation	NOUN
ejpam-6877	32	13	,	,	PUNCT
ejpam-6877	32	14	i.e	i.e	PROPN
ejpam-6877	32	15	(	(	PUNCT
ejpam-6877	32	16	xe	xe	PROPN
ejpam-6877	32	17	,	,	PUNCT
ejpam-6877	32	18	ye)is	ye)is	PRON
ejpam-6877	32	19	a	a	DET
ejpam-6877	32	20	point	point	NOUN
ejpam-6877	32	21	at	at	ADP
ejpam-6877	32	22	which	which	PRON
ejpam-6877	32	23	x	x	X
ejpam-6877	32	24	=	=	SYM
ejpam-6877	32	25	0	0	NUM
ejpam-6877	32	26	and	and	CCONJ
ejpam-6877	32	27	y	y	PROPN
ejpam-6877	32	28	=	=	SYM
ejpam-6877	32	29	0	0	PROPN
ejpam-6877	32	30	.	.	PUNCT
ejpam-6877	32	31	definition	definition	NOUN
ejpam-6877	32	32	2	2	NUM
ejpam-6877	32	33	.	.	PUNCT
ejpam-6877	33	1	[	[	X
ejpam-6877	33	2	19	19	NUM
ejpam-6877	33	3	]	]	PUNCT
ejpam-6877	33	4	suppose	suppose	VERB
ejpam-6877	33	5	that	that	SCONJ
ejpam-6877	33	6	the	the	DET
ejpam-6877	33	7	system	system	NOUN
ejpam-6877	33	8	of	of	ADP
ejpam-6877	33	9	differential	differential	ADJ
ejpam-6877	33	10	equations	equation	NOUN
ejpam-6877	33	11	.	.	PUNCT
ejpam-6877	34	1	x	x	X
ejpam-6877	34	2	=	=	SYM
ejpam-6877	34	3	u(x	u(x	PROPN
ejpam-6877	34	4	,	,	PUNCT
ejpam-6877	34	5	y	y	NOUN
ejpam-6877	34	6	)	)	PUNCT
ejpam-6877	34	7	has	have	VERB
ejpam-6877	34	8	an	an	DET
ejpam-6877	34	9	equilibrium	equilibrium	NOUN
ejpam-6877	34	10	point	point	NOUN
ejpam-6877	34	11	at	at	ADP
ejpam-6877	34	12	x	x	X
ejpam-6877	34	13	=	=	SYM
ejpam-6877	34	14	xe	xe	PROPN
ejpam-6877	34	15	,	,	PUNCT
ejpam-6877	34	16	y	y	PROPN
ejpam-6877	34	17	=	=	SYM
ejpam-6877	34	18	ye	ye	PROPN
ejpam-6877	34	19	.	.	PUNCT
ejpam-6877	35	1	the	the	DET
ejpam-6877	35	2	equilibrium	equilibrium	NOUN
ejpam-6877	35	3	points	point	NOUN
ejpam-6877	35	4	is	be	AUX
ejpam-6877	35	5	said	say	VERB
ejpam-6877	35	6	to	to	PART
ejpam-6877	35	7	be	be	AUX
ejpam-6877	35	8	:	:	PUNCT
ejpam-6877	35	9	(	(	PUNCT
ejpam-6877	35	10	i	i	NOUN
ejpam-6877	35	11	)	)	PUNCT
ejpam-6877	35	12	stable	stable	ADJ
ejpam-6877	35	13	if	if	SCONJ
ejpam-6877	35	14	all	all	DET
ejpam-6877	35	15	point	point	VERB
ejpam-6877	35	16	in	in	ADP
ejpam-6877	35	17	the	the	DET
ejpam-6877	35	18	neighbrohood	neighbrohood	NOUN
ejpam-6877	35	19	of	of	ADP
ejpam-6877	35	20	the	the	DET
ejpam-6877	35	21	equilibruim	equilibruim	NOUN
ejpam-6877	35	22	point	point	NOUN
ejpam-6877	35	23	remain	remain	VERB
ejpam-6877	35	24	in	in	ADP
ejpam-6877	35	25	the	the	DET
ejpam-6877	35	26	neighborhood	neighborhood	NOUN
ejpam-6877	35	27	of	of	ADP
ejpam-6877	35	28	the	the	DET
ejpam-6877	35	29	equilibruim	equilibruim	NOUN
ejpam-6877	35	30	point	point	NOUN
ejpam-6877	35	31	as	as	ADP
ejpam-6877	35	32	time	time	NOUN
ejpam-6877	35	33	invrease	invrease	PROPN
ejpam-6877	35	34	.	.	PUNCT
ejpam-6877	36	1	(	(	PUNCT
ejpam-6877	36	2	ii	ii	NOUN
ejpam-6877	36	3	)	)	PUNCT
ejpam-6877	36	4	unstable	unstable	ADJ
ejpam-6877	36	5	otherwise	otherwise	ADV
ejpam-6877	36	6	.	.	PUNCT
ejpam-6877	37	1	example	example	NOUN
ejpam-6877	38	1	1	1	NUM
ejpam-6877	38	2	.	.	PUNCT
ejpam-6877	39	1	the	the	DET
ejpam-6877	39	2	following	follow	VERB
ejpam-6877	39	3	phase	phase	NOUN
ejpam-6877	39	4	diagrams	diagram	NOUN
ejpam-6877	39	5	have	have	VERB
ejpam-6877	39	6	an	an	DET
ejpam-6877	39	7	equilibrium	equilibrium	NOUN
ejpam-6877	39	8	point	point	NOUN
ejpam-6877	39	9	at	at	ADP
ejpam-6877	39	10	(	(	PUNCT
ejpam-6877	39	11	0,0	0,0	NOUN
ejpam-6877	39	12	)	)	PUNCT
ejpam-6877	39	13	.	.	PUNCT
ejpam-6877	40	1	determine	determine	VERB
ejpam-6877	40	2	whether	whether	SCONJ
ejpam-6877	40	3	this	this	DET
ejpam-6877	40	4	equilibrium	equilibrium	NOUN
ejpam-6877	40	5	is	be	AUX
ejpam-6877	40	6	stable	stable	ADJ
ejpam-6877	40	7	(	(	PUNCT
ejpam-6877	40	8	balanced	balanced	ADJ
ejpam-6877	40	9	)	)	PUNCT
ejpam-6877	40	10	or	or	CCONJ
ejpam-6877	40	11	unstable	unstable	ADJ
ejpam-6877	40	12	(	(	PUNCT
ejpam-6877	40	13	unbalanced	unbalanced	ADJ
ejpam-6877	40	14	)	)	PUNCT
ejpam-6877	40	15	.	.	PUNCT
ejpam-6877	41	1	figure	figure	VERB
ejpam-6877	41	2	1	1	NUM
ejpam-6877	41	3	:	:	PUNCT
ejpam-6877	41	4	stable	stable	ADJ
ejpam-6877	41	5	(	(	PUNCT
ejpam-6877	41	6	balanced	balanced	ADJ
ejpam-6877	41	7	)	)	PUNCT
ejpam-6877	41	8	or	or	CCONJ
ejpam-6877	41	9	unstable	unstable	ADJ
ejpam-6877	41	10	(	(	PUNCT
ejpam-6877	41	11	unbalanced	unbalanced	ADJ
ejpam-6877	41	12	)	)	PUNCT
ejpam-6877	41	13	.	.	PUNCT
ejpam-6877	42	1	remark	remark	PROPN
ejpam-6877	42	2	1	1	NUM
ejpam-6877	42	3	.	.	PUNCT
ejpam-6877	43	1	let	let	VERB
ejpam-6877	43	2	the	the	DET
ejpam-6877	43	3	linear	linear	ADJ
ejpam-6877	43	4	system	system	NOUN
ejpam-6877	43	5	.	.	PUNCT
ejpam-6877	44	1	p	p	X
ejpam-6877	44	2	=	=	X
ejpam-6877	44	3	ap	ap	PROPN
ejpam-6877	44	4	,	,	PUNCT
ejpam-6877	44	5	for	for	ADP
ejpam-6877	44	6	a	a	DET
ejpam-6877	44	7	2	2	NUM
ejpam-6877	44	8	×	×	NOUN
ejpam-6877	44	9	2	2	NUM
ejpam-6877	44	10	matrix	matrix	NOUN
ejpam-6877	44	11	a.	a.	NOUN
ejpam-6877	44	12	the	the	DET
ejpam-6877	44	13	nature	nature	NOUN
ejpam-6877	44	14	of	of	ADP
ejpam-6877	44	15	the	the	DET
ejpam-6877	44	16	equilibrium	equilibrium	NOUN
ejpam-6877	44	17	point	point	NOUN
ejpam-6877	44	18	at	at	ADP
ejpam-6877	44	19	p	p	NOUN
ejpam-6877	44	20	=	=	NOUN
ejpam-6877	44	21	0	0	NUM
ejpam-6877	44	22	,	,	PUNCT
ejpam-6877	44	23	q	q	NOUN
ejpam-6877	44	24	=	=	SYM
ejpam-6877	44	25	0	0	NUM
ejpam-6877	44	26	is	be	AUX
ejpam-6877	44	27	determined	determine	VERB
ejpam-6877	44	28	by	by	ADP
ejpam-6877	44	29	the	the	DET
ejpam-6877	44	30	eigenvalues	eigenvalue	NOUN
ejpam-6877	44	31	and	and	CCONJ
ejpam-6877	44	32	eigenvectors	eigenvector	NOUN
ejpam-6877	44	33	of	of	ADP
ejpam-6877	44	34	a.	a.	NOUN
ejpam-6877	44	35	if	if	SCONJ
ejpam-6877	44	36	one	one	NUM
ejpam-6877	44	37	of	of	ADP
ejpam-6877	44	38	the	the	DET
ejpam-6877	44	39	eigenvalues	eigenvalue	NOUN
ejpam-6877	44	40	is	be	AUX
ejpam-6877	44	41	positive	positive	ADJ
ejpam-6877	44	42	and	and	CCONJ
ejpam-6877	44	43	the	the	DET
ejpam-6877	44	44	other	other	ADJ
ejpam-6877	44	45	is	be	AUX
ejpam-6877	44	46	negative	negative	ADJ
ejpam-6877	44	47	,	,	PUNCT
ejpam-6877	44	48	the	the	DET
ejpam-6877	44	49	equilibrium	equilibrium	NOUN
ejpam-6877	44	50	point	point	NOUN
ejpam-6877	44	51	is	be	AUX
ejpam-6877	44	52	a	a	DET
ejpam-6877	44	53	saddle	saddle	NOUN
ejpam-6877	44	54	(	(	PUNCT
ejpam-6877	44	55	and	and	CCONJ
ejpam-6877	44	56	is	be	AUX
ejpam-6877	44	57	unstable	unstable	ADJ
ejpam-6877	44	58	)	)	PUNCT
ejpam-6877	44	59	.	.	PUNCT
ejpam-6877	45	1	note	note	NOUN
ejpam-6877	45	2	:	:	PUNCT
ejpam-6877	45	3	in	in	ADP
ejpam-6877	45	4	dynamic	dynamic	ADJ
ejpam-6877	45	5	systems	system	NOUN
ejpam-6877	45	6	,	,	PUNCT
ejpam-6877	45	7	a	a	DET
ejpam-6877	45	8	nonlinear	nonlinear	ADJ
ejpam-6877	45	9	system	system	NOUN
ejpam-6877	45	10	can	can	AUX
ejpam-6877	45	11	be	be	AUX
ejpam-6877	45	12	approximated	approximate	VERB
ejpam-6877	45	13	as	as	ADP
ejpam-6877	45	14	a	a	DET
ejpam-6877	45	15	time	time	NOUN
ejpam-6877	45	16	-	-	PUNCT
ejpam-6877	45	17	invariant	invariant	ADJ
ejpam-6877	45	18	linear	linear	NOUN
ejpam-6877	45	19	system	system	NOUN
ejpam-6877	45	20	using	use	VERB
ejpam-6877	45	21	a	a	DET
ejpam-6877	45	22	taylor	taylor	PROPN
ejpam-6877	45	23	series	series	NOUN
ejpam-6877	45	24	around	around	ADP
ejpam-6877	45	25	the	the	DET
ejpam-6877	45	26	equilibrium	equilibrium	NOUN
ejpam-6877	45	27	point	point	NOUN
ejpam-6877	45	28	,	,	PUNCT
ejpam-6877	45	29	keeping	keep	VERB
ejpam-6877	45	30	only	only	ADV
ejpam-6877	45	31	the	the	DET
ejpam-6877	45	32	linear	linear	PROPN
ejpam-6877	45	33	a.	a.	NOUN
ejpam-6877	45	34	m.	m.	NOUN
ejpam-6877	45	35	alotaibi	alotaibi	PROPN
ejpam-6877	45	36	et	et	PROPN
ejpam-6877	45	37	al	al	PROPN
ejpam-6877	45	38	.	.	PUNCT
ejpam-6877	45	39	/	/	SYM
ejpam-6877	45	40	eur	eur	PROPN
ejpam-6877	45	41	.	.	PUNCT
ejpam-6877	46	1	j.	j.	PROPN
ejpam-6877	46	2	pure	pure	PROPN
ejpam-6877	46	3	appl	appl	PROPN
ejpam-6877	46	4	.	.	PROPN
ejpam-6877	46	5	math	math	PROPN
ejpam-6877	46	6	,	,	PUNCT
ejpam-6877	46	7	18	18	NUM
ejpam-6877	46	8	(	(	PUNCT
ejpam-6877	46	9	4	4	NUM
ejpam-6877	46	10	)	)	PUNCT
ejpam-6877	46	11	(	(	PUNCT
ejpam-6877	46	12	2025	2025	NUM
ejpam-6877	46	13	)	)	PUNCT
ejpam-6877	46	14	,	,	PUNCT
ejpam-6877	46	15	6877	6877	NUM
ejpam-6877	46	16	3	3	NUM
ejpam-6877	46	17	of	of	ADP
ejpam-6877	46	18	9	9	NUM
ejpam-6877	46	19	term	term	NOUN
ejpam-6877	46	20	,	,	PUNCT
ejpam-6877	46	21	when	when	SCONJ
ejpam-6877	46	22	signals	signal	NOUN
ejpam-6877	46	23	and	and	CCONJ
ejpam-6877	46	24	deviations	deviation	NOUN
ejpam-6877	46	25	are	be	AUX
ejpam-6877	46	26	small	small	ADJ
ejpam-6877	46	27	.	.	PUNCT
ejpam-6877	47	1	accuracy	accuracy	NOUN
ejpam-6877	47	2	decreases	decrease	VERB
ejpam-6877	47	3	farther	far	ADV
ejpam-6877	47	4	from	from	ADP
ejpam-6877	47	5	the	the	DET
ejpam-6877	47	6	operating	operating	NOUN
ejpam-6877	47	7	point	point	NOUN
ejpam-6877	47	8	,	,	PUNCT
ejpam-6877	47	9	with	with	ADP
ejpam-6877	47	10	some	some	DET
ejpam-6877	47	11	exceptions	exception	NOUN
ejpam-6877	47	12	to	to	ADP
ejpam-6877	47	13	this	this	DET
ejpam-6877	47	14	assumption	assumption	NOUN
ejpam-6877	47	15	.	.	PUNCT
ejpam-6877	48	1	definition	definition	NOUN
ejpam-6877	48	2	3	3	NUM
ejpam-6877	48	3	.	.	PUNCT
ejpam-6877	49	1	[	[	X
ejpam-6877	49	2	20	20	NUM
ejpam-6877	49	3	]	]	PUNCT
ejpam-6877	49	4	in	in	ADP
ejpam-6877	49	5	a	a	DET
ejpam-6877	49	6	signed	sign	VERB
ejpam-6877	49	7	graph	graph	NOUN
ejpam-6877	49	8	we	we	PRON
ejpam-6877	49	9	say	say	VERB
ejpam-6877	49	10	that	that	SCONJ
ejpam-6877	49	11	a	a	DET
ejpam-6877	49	12	graph	graph	NOUN
ejpam-6877	49	13	is	be	AUX
ejpam-6877	49	14	balanced	balanced	ADJ
ejpam-6877	49	15	if	if	SCONJ
ejpam-6877	49	16	all	all	DET
ejpam-6877	49	17	its	its	PRON
ejpam-6877	49	18	cycles	cycle	NOUN
ejpam-6877	49	19	have	have	VERB
ejpam-6877	49	20	a	a	DET
ejpam-6877	49	21	positive	positive	ADJ
ejpam-6877	49	22	sign	sign	NOUN
ejpam-6877	49	23	product	product	NOUN
ejpam-6877	49	24	.	.	PUNCT
ejpam-6877	50	1	definition	definition	NOUN
ejpam-6877	50	2	4	4	NUM
ejpam-6877	50	3	.	.	PUNCT
ejpam-6877	51	1	[	[	X
ejpam-6877	51	2	20	20	NUM
ejpam-6877	51	3	]	]	SYM
ejpam-6877	51	4	two	two	NUM
ejpam-6877	51	5	signed	sign	VERB
ejpam-6877	51	6	graphs	graph	NOUN
ejpam-6877	51	7	σ1	σ1	PROPN
ejpam-6877	51	8	and	and	CCONJ
ejpam-6877	51	9	σ2	σ2	PROPN
ejpam-6877	51	10	are	be	AUX
ejpam-6877	51	11	said	say	VERB
ejpam-6877	51	12	to	to	PART
ejpam-6877	51	13	be	be	AUX
ejpam-6877	51	14	switching	switch	VERB
ejpam-6877	51	15	isomorphic	isomorphic	ADJ
ejpam-6877	51	16	if	if	SCONJ
ejpam-6877	51	17	σ1	σ1	PROPN
ejpam-6877	51	18	is	be	AUX
ejpam-6877	51	19	isomorphic	isomorphic	ADJ
ejpam-6877	51	20	to	to	ADP
ejpam-6877	51	21	a	a	DET
ejpam-6877	51	22	switching	switch	VERB
ejpam-6877	51	23	equivalent	equivalent	NOUN
ejpam-6877	51	24	of	of	ADP
ejpam-6877	51	25	σ2	σ2	NOUN
ejpam-6877	51	26	.	.	PUNCT
ejpam-6877	52	1	this	this	DET
ejpam-6877	52	2	relationship	relationship	NOUN
ejpam-6877	52	3	is	be	AUX
ejpam-6877	52	4	denoted	denote	VERB
ejpam-6877	52	5	by	by	ADP
ejpam-6877	52	6	σ1	σ1	PROPN
ejpam-6877	52	7	∼=	∼=	PROPN
ejpam-6877	52	8	σ2	σ2	PROPN
ejpam-6877	52	9	.	.	PUNCT
ejpam-6877	52	10	remark	remark	PROPN
ejpam-6877	52	11	2	2	NUM
ejpam-6877	52	12	.	.	PUNCT
ejpam-6877	53	1	the	the	DET
ejpam-6877	53	2	first	first	ADJ
ejpam-6877	53	3	signed	sign	VERB
ejpam-6877	53	4	graph	graph	NOUN
ejpam-6877	53	5	is	be	AUX
ejpam-6877	53	6	classified	classify	VERB
ejpam-6877	53	7	as	as	ADP
ejpam-6877	53	8	balanced	balanced	ADJ
ejpam-6877	53	9	due	due	ADP
ejpam-6877	53	10	to	to	ADP
ejpam-6877	53	11	the	the	DET
ejpam-6877	53	12	presence	presence	NOUN
ejpam-6877	53	13	of	of	ADP
ejpam-6877	53	14	exclusively	exclusively	ADV
ejpam-6877	53	15	positive	positive	ADJ
ejpam-6877	53	16	cycles	cycle	NOUN
ejpam-6877	53	17	.	.	PUNCT
ejpam-6877	54	1	in	in	ADP
ejpam-6877	54	2	contrast	contrast	NOUN
ejpam-6877	54	3	,	,	PUNCT
ejpam-6877	54	4	the	the	DET
ejpam-6877	54	5	second	second	ADJ
ejpam-6877	54	6	signed	sign	VERB
ejpam-6877	54	7	graph	graph	NOUN
ejpam-6877	54	8	is	be	AUX
ejpam-6877	54	9	unbalanced	unbalanced	ADJ
ejpam-6877	54	10	,	,	PUNCT
ejpam-6877	54	11	as	as	SCONJ
ejpam-6877	54	12	it	it	PRON
ejpam-6877	54	13	contains	contain	VERB
ejpam-6877	54	14	at	at	ADV
ejpam-6877	54	15	least	least	ADV
ejpam-6877	54	16	one	one	NUM
ejpam-6877	54	17	negative	negative	ADJ
ejpam-6877	54	18	cycle	cycle	NOUN
ejpam-6877	54	19	.	.	PUNCT
ejpam-6877	55	1	figure	figure	NOUN
ejpam-6877	55	2	2	2	NUM
ejpam-6877	55	3	:	:	PUNCT
ejpam-6877	55	4	a	a	DET
ejpam-6877	55	5	balanced	balanced	ADJ
ejpam-6877	55	6	and	and	CCONJ
ejpam-6877	55	7	unbalanced	unbalanced	ADJ
ejpam-6877	55	8	signed	sign	VERB
ejpam-6877	55	9	graph	graph	NOUN
ejpam-6877	55	10	theorem	theorem	VERB
ejpam-6877	55	11	1	1	NUM
ejpam-6877	55	12	.	.	PUNCT
ejpam-6877	56	1	[	[	X
ejpam-6877	56	2	20	20	NUM
ejpam-6877	56	3	]	]	PUNCT
ejpam-6877	56	4	a	a	DET
ejpam-6877	56	5	signed	sign	VERB
ejpam-6877	56	6	graph	graph	NOUN
ejpam-6877	56	7	σ	σ	PROPN
ejpam-6877	56	8	is	be	AUX
ejpam-6877	56	9	said	say	VERB
ejpam-6877	56	10	to	to	PART
ejpam-6877	56	11	be	be	AUX
ejpam-6877	56	12	balanced	balance	VERB
ejpam-6877	56	13	if	if	SCONJ
ejpam-6877	56	14	and	and	CCONJ
ejpam-6877	56	15	only	only	ADV
ejpam-6877	56	16	if	if	SCONJ
ejpam-6877	56	17	its	its	PRON
ejpam-6877	56	18	vertex	vertex	NOUN
ejpam-6877	56	19	set	set	NOUN
ejpam-6877	56	20	v	v	NOUN
ejpam-6877	56	21	can	can	AUX
ejpam-6877	56	22	be	be	AUX
ejpam-6877	56	23	partitioned	partition	VERB
ejpam-6877	56	24	into	into	ADP
ejpam-6877	56	25	two	two	NUM
ejpam-6877	56	26	disjoint	disjoint	ADJ
ejpam-6877	56	27	subsets	subset	NOUN
ejpam-6877	56	28	,	,	PUNCT
ejpam-6877	56	29	x	x	PUNCT
ejpam-6877	56	30	and	and	CCONJ
ejpam-6877	56	31	y	y	PROPN
ejpam-6877	56	32	,	,	PUNCT
ejpam-6877	56	33	such	such	ADJ
ejpam-6877	56	34	that	that	SCONJ
ejpam-6877	56	35	all	all	DET
ejpam-6877	56	36	positive	positive	ADJ
ejpam-6877	56	37	edges	edge	NOUN
ejpam-6877	56	38	connect	connect	VERB
ejpam-6877	56	39	vertices	vertex	NOUN
ejpam-6877	56	40	within	within	ADP
ejpam-6877	56	41	the	the	DET
ejpam-6877	56	42	same	same	ADJ
ejpam-6877	56	43	subset	subset	NOUN
ejpam-6877	56	44	(	(	PUNCT
ejpam-6877	56	45	i.e.	i.e.	X
ejpam-6877	56	46	,	,	PUNCT
ejpam-6877	56	47	either	either	CCONJ
ejpam-6877	56	48	both	both	DET
ejpam-6877	56	49	endpoints	endpoint	NOUN
ejpam-6877	56	50	in	in	ADP
ejpam-6877	56	51	x	x	PUNCT
ejpam-6877	56	52	or	or	CCONJ
ejpam-6877	56	53	both	both	PRON
ejpam-6877	56	54	in	in	ADP
ejpam-6877	56	55	y	y	PROPN
ejpam-6877	56	56	)	)	PUNCT
ejpam-6877	56	57	,	,	PUNCT
ejpam-6877	56	58	and	and	CCONJ
ejpam-6877	56	59	all	all	DET
ejpam-6877	56	60	negative	negative	ADJ
ejpam-6877	56	61	edges	edge	NOUN
ejpam-6877	56	62	connect	connect	VERB
ejpam-6877	56	63	vertices	vertex	NOUN
ejpam-6877	56	64	across	across	ADP
ejpam-6877	56	65	the	the	DET
ejpam-6877	56	66	subsets	subset	NOUN
ejpam-6877	56	67	(	(	PUNCT
ejpam-6877	56	68	i.e.	i.e.	X
ejpam-6877	56	69	,	,	PUNCT
ejpam-6877	56	70	one	one	NUM
ejpam-6877	56	71	endpoint	endpoint	NOUN
ejpam-6877	56	72	in	in	ADP
ejpam-6877	56	73	x	x	PROPN
ejpam-6877	56	74	,	,	PUNCT
ejpam-6877	56	75	the	the	DET
ejpam-6877	56	76	other	other	ADJ
ejpam-6877	56	77	in	in	ADP
ejpam-6877	56	78	y	y	PROPN
ejpam-6877	56	79	)	)	PUNCT
ejpam-6877	56	80	.	.	PUNCT
ejpam-6877	57	1	an	an	DET
ejpam-6877	57	2	equivalent	equivalent	ADJ
ejpam-6877	57	3	characterization	characterization	NOUN
ejpam-6877	57	4	is	be	AUX
ejpam-6877	57	5	that	that	SCONJ
ejpam-6877	57	6	for	for	ADP
ejpam-6877	57	7	any	any	DET
ejpam-6877	57	8	pair	pair	NOUN
ejpam-6877	57	9	of	of	ADP
ejpam-6877	57	10	vertices	vertex	NOUN
ejpam-6877	57	11	v	v	NOUN
ejpam-6877	57	12	and	and	CCONJ
ejpam-6877	57	13	w	w	NOUN
ejpam-6877	57	14	,	,	PUNCT
ejpam-6877	57	15	all	all	DET
ejpam-6877	57	16	paths	path	NOUN
ejpam-6877	57	17	connecting	connect	VERB
ejpam-6877	57	18	vand	vand	NOUN
ejpam-6877	57	19	w	w	AUX
ejpam-6877	57	20	have	have	VERB
ejpam-6877	57	21	the	the	DET
ejpam-6877	57	22	same	same	ADJ
ejpam-6877	57	23	sign	sign	NOUN
ejpam-6877	57	24	.	.	PUNCT
ejpam-6877	58	1	proof	proof	NOUN
ejpam-6877	58	2	.	.	PUNCT
ejpam-6877	58	3	.	.	PUNCT
ejpam-6877	59	1	see	see	VERB
ejpam-6877	60	1	[	[	X
ejpam-6877	60	2	[	[	X
ejpam-6877	60	3	20	20	NUM
ejpam-6877	60	4	]	]	PUNCT
ejpam-6877	60	5	,	,	PUNCT
ejpam-6877	60	6	thm	thm	PROPN
ejpam-6877	60	7	.	.	PUNCT
ejpam-6877	60	8	1	1	NUM
ejpam-6877	60	9	]	]	SYM
ejpam-6877	60	10	2	2	NUM
ejpam-6877	60	11	.	.	PUNCT
ejpam-6877	60	12	inverted	inverted	ADJ
ejpam-6877	60	13	pendulum	pendulum	NOUN
ejpam-6877	60	14	:	:	PUNCT
ejpam-6877	60	15	nonlinear	nonlinear	ADJ
ejpam-6877	60	16	model	model	NOUN
ejpam-6877	60	17	,	,	PUNCT
ejpam-6877	60	18	linearization	linearization	NOUN
ejpam-6877	60	19	,	,	PUNCT
ejpam-6877	60	20	and	and	CCONJ
ejpam-6877	60	21	jacobian	jacobian	PROPN
ejpam-6877	60	22	let	let	VERB
ejpam-6877	60	23	the	the	DET
ejpam-6877	60	24	state	state	NOUN
ejpam-6877	60	25	be	be	AUX
ejpam-6877	60	26	x	x	X
ejpam-6877	60	27	=	=	PUNCT
ejpam-6877	61	1	[	[	X
ejpam-6877	61	2	x	x	X
ejpam-6877	61	3	,	,	PUNCT
ejpam-6877	61	4	ẋ	ẋ	PROPN
ejpam-6877	61	5	,	,	PUNCT
ejpam-6877	61	6	θ	θ	PROPN
ejpam-6877	61	7	,	,	PUNCT
ejpam-6877	61	8	θ̇	θ̇	DET
ejpam-6877	61	9	]	]	SYM
ejpam-6877	61	10	⊤	⊤	NOUN
ejpam-6877	61	11	,	,	PUNCT
ejpam-6877	61	12	where	where	SCONJ
ejpam-6877	61	13	x	x	PRON
ejpam-6877	61	14	is	be	AUX
ejpam-6877	61	15	the	the	DET
ejpam-6877	61	16	cart	cart	NOUN
ejpam-6877	61	17	position	position	NOUN
ejpam-6877	61	18	and	and	CCONJ
ejpam-6877	61	19	θ	θ	PROPN
ejpam-6877	61	20	is	be	AUX
ejpam-6877	61	21	the	the	DET
ejpam-6877	61	22	pole	pole	NOUN
ejpam-6877	61	23	angle	angle	NOUN
ejpam-6877	61	24	measured	measure	VERB
ejpam-6877	61	25	from	from	ADP
ejpam-6877	61	26	the	the	DET
ejpam-6877	61	27	upright	upright	NOUN
ejpam-6877	61	28	(	(	PUNCT
ejpam-6877	61	29	θ	θ	NOUN
ejpam-6877	61	30	=	=	SYM
ejpam-6877	61	31	0	0	NUM
ejpam-6877	61	32	)	)	PUNCT
ejpam-6877	61	33	.	.	PUNCT
ejpam-6877	62	1	the	the	DET
ejpam-6877	62	2	input	input	NOUN
ejpam-6877	62	3	is	be	AUX
ejpam-6877	62	4	the	the	DET
ejpam-6877	62	5	horizontal	horizontal	ADJ
ejpam-6877	62	6	force	force	NOUN
ejpam-6877	62	7	f	f	PROPN
ejpam-6877	62	8	applied	apply	VERB
ejpam-6877	62	9	to	to	ADP
ejpam-6877	62	10	the	the	DET
ejpam-6877	62	11	cart	cart	NOUN
ejpam-6877	62	12	.	.	PUNCT
ejpam-6877	63	1	denote	denote	VERB
ejpam-6877	63	2	the	the	DET
ejpam-6877	63	3	cart	cart	NOUN
ejpam-6877	63	4	and	and	CCONJ
ejpam-6877	63	5	pole	pole	ADJ
ejpam-6877	63	6	masses	masse	NOUN
ejpam-6877	63	7	by	by	ADP
ejpam-6877	63	8	m	m	PROPN
ejpam-6877	63	9	and	and	CCONJ
ejpam-6877	63	10	m	m	PROPN
ejpam-6877	63	11	,	,	PUNCT
ejpam-6877	63	12	the	the	DET
ejpam-6877	63	13	pole	pole	NOUN
ejpam-6877	63	14	length	length	NOUN
ejpam-6877	63	15	by	by	ADP
ejpam-6877	63	16	l	l	NOUN
ejpam-6877	63	17	,	,	PUNCT
ejpam-6877	63	18	and	and	CCONJ
ejpam-6877	63	19	gravity	gravity	NOUN
ejpam-6877	63	20	by	by	ADP
ejpam-6877	63	21	g.	g.	PROPN
ejpam-6877	63	22	a	a	DET
ejpam-6877	63	23	standard	standard	ADJ
ejpam-6877	63	24	cart	cart	NOUN
ejpam-6877	63	25	–	–	PUNCT
ejpam-6877	63	26	pole	pole	NOUN
ejpam-6877	63	27	model	model	NOUN
ejpam-6877	63	28	is	be	AUX
ejpam-6877	63	29	(	(	PUNCT
ejpam-6877	63	30	m	m	VERB
ejpam-6877	63	31	+	+	NOUN
ejpam-6877	63	32	m	m	X
ejpam-6877	63	33	)	)	PUNCT
ejpam-6877	64	1	ẍ+ml	ẍ+ml	PROPN
ejpam-6877	64	2	θ̈	θ̈	PROPN
ejpam-6877	64	3	cos	cos	ADP
ejpam-6877	64	4	θ	θ	PROPN
ejpam-6877	64	5	−ml	−ml	VERB
ejpam-6877	64	6	θ̇2	θ̇2	PROPN
ejpam-6877	64	7	sin	sin	VERB
ejpam-6877	65	1	θ	θ	PROPN
ejpam-6877	65	2	=	=	SYM
ejpam-6877	65	3	f	f	X
ejpam-6877	65	4	,	,	PUNCT
ejpam-6877	65	5	(	(	PUNCT
ejpam-6877	65	6	1	1	X
ejpam-6877	65	7	)	)	PUNCT
ejpam-6877	65	8	l	l	NOUN
ejpam-6877	65	9	θ̈	θ̈	NOUN
ejpam-6877	65	10	+	+	CCONJ
ejpam-6877	65	11	ẍ	ẍ	PROPN
ejpam-6877	65	12	cos	cos	PROPN
ejpam-6877	65	13	θ	θ	PROPN
ejpam-6877	65	14	−	−	PROPN
ejpam-6877	65	15	g	g	PROPN
ejpam-6877	65	16	sin	sin	NOUN
ejpam-6877	65	17	θ	θ	NOUN
ejpam-6877	65	18	=	=	SYM
ejpam-6877	65	19	0	0	NUM
ejpam-6877	65	20	.	.	PUNCT
ejpam-6877	66	1	(	(	PUNCT
ejpam-6877	66	2	2	2	X
ejpam-6877	66	3	)	)	PUNCT
ejpam-6877	66	4	linearize	linearize	NOUN
ejpam-6877	66	5	(	(	PUNCT
ejpam-6877	66	6	1)–(2	1)–(2	NUM
ejpam-6877	66	7	)	)	PUNCT
ejpam-6877	66	8	at	at	ADP
ejpam-6877	66	9	(	(	PUNCT
ejpam-6877	66	10	x	x	NOUN
ejpam-6877	66	11	,	,	PUNCT
ejpam-6877	66	12	ẋ	ẋ	PROPN
ejpam-6877	66	13	,	,	PUNCT
ejpam-6877	66	14	θ	θ	PROPN
ejpam-6877	66	15	,	,	PUNCT
ejpam-6877	66	16	θ̇	θ̇	ADJ
ejpam-6877	66	17	)	)	PUNCT
ejpam-6877	66	18	=	=	SYM
ejpam-6877	66	19	(	(	PUNCT
ejpam-6877	66	20	0	0	NUM
ejpam-6877	66	21	,	,	PUNCT
ejpam-6877	66	22	0	0	NUM
ejpam-6877	66	23	,	,	PUNCT
ejpam-6877	66	24	0	0	NUM
ejpam-6877	66	25	,	,	PUNCT
ejpam-6877	66	26	0	0	NUM
ejpam-6877	66	27	)	)	PUNCT
ejpam-6877	66	28	and	and	CCONJ
ejpam-6877	66	29	f	f	X
ejpam-6877	66	30	=	=	SYM
ejpam-6877	66	31	0	0	PROPN
ejpam-6877	66	32	,	,	PUNCT
ejpam-6877	66	33	using	use	VERB
ejpam-6877	66	34	sin	sin	NOUN
ejpam-6877	66	35	θ	θ	PROPN
ejpam-6877	66	36	≈	≈	PROPN
ejpam-6877	66	37	θ	θ	PROPN
ejpam-6877	66	38	,	,	PUNCT
ejpam-6877	66	39	cos	cos	ADP
ejpam-6877	66	40	θ	θ	PROPN
ejpam-6877	66	41	≈	≈	PROPN
ejpam-6877	66	42	1	1	NUM
ejpam-6877	66	43	,	,	PUNCT
ejpam-6877	66	44	and	and	CCONJ
ejpam-6877	66	45	neglecting	neglect	VERB
ejpam-6877	66	46	products	product	NOUN
ejpam-6877	66	47	of	of	ADP
ejpam-6877	66	48	small	small	ADJ
ejpam-6877	66	49	terms	term	NOUN
ejpam-6877	66	50	.	.	PUNCT
ejpam-6877	67	1	from	from	ADP
ejpam-6877	67	2	(	(	PUNCT
ejpam-6877	67	3	2	2	NUM
ejpam-6877	67	4	):	):	PUNCT
ejpam-6877	67	5	θ̈	θ̈	NOUN
ejpam-6877	67	6	=	=	SYM
ejpam-6877	67	7	g	g	NOUN
ejpam-6877	67	8	l	l	NOUN
ejpam-6877	67	9	θ	θ	NOUN
ejpam-6877	67	10	−	−	NOUN
ejpam-6877	67	11	1	1	NUM
ejpam-6877	67	12	l	l	NOUN
ejpam-6877	67	13	ẍ.	ẍ.	PROPN
ejpam-6877	67	14	a.	a.	NOUN
ejpam-6877	67	15	m.	m.	PROPN
ejpam-6877	67	16	alotaibi	alotaibi	PROPN
ejpam-6877	67	17	et	et	PROPN
ejpam-6877	67	18	al	al	PROPN
ejpam-6877	67	19	.	.	PUNCT
ejpam-6877	67	20	/	/	SYM
ejpam-6877	67	21	eur	eur	PROPN
ejpam-6877	67	22	.	.	PUNCT
ejpam-6877	68	1	j.	j.	PROPN
ejpam-6877	68	2	pure	pure	PROPN
ejpam-6877	68	3	appl	appl	PROPN
ejpam-6877	68	4	.	.	PROPN
ejpam-6877	68	5	math	math	PROPN
ejpam-6877	68	6	,	,	PUNCT
ejpam-6877	68	7	18	18	NUM
ejpam-6877	68	8	(	(	PUNCT
ejpam-6877	68	9	4	4	NUM
ejpam-6877	68	10	)	)	PUNCT
ejpam-6877	68	11	(	(	PUNCT
ejpam-6877	68	12	2025	2025	NUM
ejpam-6877	68	13	)	)	PUNCT
ejpam-6877	68	14	,	,	PUNCT
ejpam-6877	68	15	6877	6877	NUM
ejpam-6877	68	16	4	4	NUM
ejpam-6877	68	17	of	of	ADP
ejpam-6877	68	18	9	9	NUM
ejpam-6877	68	19	substitute	substitute	NOUN
ejpam-6877	68	20	into	into	ADP
ejpam-6877	68	21	(	(	PUNCT
ejpam-6877	68	22	1	1	NUM
ejpam-6877	68	23	)	)	PUNCT
ejpam-6877	68	24	and	and	CCONJ
ejpam-6877	68	25	simplify	simplify	VERB
ejpam-6877	68	26	to	to	PART
ejpam-6877	68	27	obtain	obtain	VERB
ejpam-6877	68	28	m	m	PRON
ejpam-6877	68	29	ẍ	ẍ	PUNCT
ejpam-6877	69	1	+	+	CCONJ
ejpam-6877	70	1	mg	mg	PROPN
ejpam-6877	70	2	θ	θ	PROPN
ejpam-6877	70	3	=	=	SYM
ejpam-6877	70	4	f	f	X
ejpam-6877	70	5	,	,	PUNCT
ejpam-6877	70	6	θ̈	θ̈	NOUN
ejpam-6877	70	7	=	=	SYM
ejpam-6877	70	8	m	m	VERB
ejpam-6877	70	9	+	+	NOUN
ejpam-6877	70	10	m	m	VERB
ejpam-6877	70	11	lm	lm	ADJ
ejpam-6877	70	12	g	g	PROPN
ejpam-6877	70	13	θ	θ	PROPN
ejpam-6877	70	14	−	−	PROPN
ejpam-6877	70	15	1	1	NUM
ejpam-6877	71	1	lm	lm	INTJ
ejpam-6877	71	2	f.	f.	PROPN
ejpam-6877	71	3	with	with	ADP
ejpam-6877	71	4	x	x	PUNCT
ejpam-6877	71	5	=	=	PUNCT
ejpam-6877	72	1	[	[	X
ejpam-6877	72	2	x	x	X
ejpam-6877	72	3	,	,	PUNCT
ejpam-6877	72	4	ẋ	ẋ	PROPN
ejpam-6877	72	5	,	,	PUNCT
ejpam-6877	72	6	θ	θ	PROPN
ejpam-6877	72	7	,	,	PUNCT
ejpam-6877	72	8	θ̇]⊤	θ̇]⊤	NOUN
ejpam-6877	72	9	and	and	CCONJ
ejpam-6877	72	10	input	input	NOUN
ejpam-6877	72	11	f	f	PROPN
ejpam-6877	72	12	,	,	PUNCT
ejpam-6877	72	13	the	the	DET
ejpam-6877	72	14	linearized	linearize	VERB
ejpam-6877	72	15	model	model	NOUN
ejpam-6877	72	16	is	be	AUX
ejpam-6877	72	17	ẋ	ẋ	NOUN
ejpam-6877	72	18	=	=	PUNCT
ejpam-6877	72	19	ax	ax	NOUN
ejpam-6877	73	1	+	+	NOUN
ejpam-6877	73	2	bf	bf	NOUN
ejpam-6877	73	3	,	,	PUNCT
ejpam-6877	73	4	where	where	SCONJ
ejpam-6877	73	5	a	a	DET
ejpam-6877	73	6	=	=	NOUN
ejpam-6877	73	7			NOUN
ejpam-6877	73	8	0	0	NUM
ejpam-6877	74	1	1	1	NUM
ejpam-6877	74	2	0	0	NUM
ejpam-6877	74	3	0	0	NUM
ejpam-6877	74	4	0	0	NUM
ejpam-6877	74	5	0	0	NUM
ejpam-6877	74	6	−mg	−mg	NOUN
ejpam-6877	74	7	m	m	VERB
ejpam-6877	74	8	0	0	NUM
ejpam-6877	74	9	0	0	NUM
ejpam-6877	74	10	0	0	NUM
ejpam-6877	74	11	0	0	NUM
ejpam-6877	74	12	1	1	NUM
ejpam-6877	74	13	0	0	NUM
ejpam-6877	74	14	0	0	NUM
ejpam-6877	75	1	(	(	PUNCT
ejpam-6877	75	2	m	m	VERB
ejpam-6877	75	3	+	+	ADJ
ejpam-6877	75	4	m)g	m)g	X
ejpam-6877	75	5	lm	lm	SYM
ejpam-6877	75	6	0	0	NUM
ejpam-6877	75	7			NOUN
ejpam-6877	75	8	,	,	PUNCT
ejpam-6877	75	9	b	b	X
ejpam-6877	75	10	=	=	NOUN
ejpam-6877	75	11			NOUN
ejpam-6877	75	12	0	0	NUM
ejpam-6877	75	13	1	1	NUM
ejpam-6877	75	14	m	m	NOUN
ejpam-6877	75	15	0	0	NUM
ejpam-6877	76	1	−	−	NUM
ejpam-6877	76	2	1	1	NUM
ejpam-6877	76	3	lm	lm	NOUN
ejpam-6877	76	4			NOUN
ejpam-6877	76	5	.	.	PUNCT
ejpam-6877	77	1	the	the	DET
ejpam-6877	77	2	2	2	NUM
ejpam-6877	77	3	×	×	NOUN
ejpam-6877	77	4	2	2	NUM
ejpam-6877	77	5	angular	angular	ADJ
ejpam-6877	77	6	block	block	NOUN
ejpam-6877	77	7	[	[	PUNCT
ejpam-6877	77	8	0	0	NUM
ejpam-6877	77	9	1	1	NUM
ejpam-6877	77	10	(	(	PUNCT
ejpam-6877	77	11	m+m)g	m+m)g	X
ejpam-6877	77	12	lm	lm	PROPN
ejpam-6877	77	13	0	0	NUM
ejpam-6877	77	14	]	]	PUNCT
ejpam-6877	77	15	has	have	AUX
ejpam-6877	77	16	eigenvalues	eigenvalue	VERB
ejpam-6877	77	17	λ	λ	X
ejpam-6877	77	18	=	=	SYM
ejpam-6877	77	19	±	±	NUM
ejpam-6877	77	20	√	√	PUNCT
ejpam-6877	77	21	(	(	PUNCT
ejpam-6877	77	22	m+m)g	m+m)g	PROPN
ejpam-6877	77	23	lm	lm	INTJ
ejpam-6877	77	24	,	,	PUNCT
ejpam-6877	77	25	yielding	yield	VERB
ejpam-6877	77	26	one	one	NUM
ejpam-6877	77	27	positive	positive	ADJ
ejpam-6877	77	28	real	real	ADJ
ejpam-6877	77	29	eigenvalue	eigenvalue	NOUN
ejpam-6877	77	30	.	.	PUNCT
ejpam-6877	78	1	(	(	PUNCT
ejpam-6877	78	2	two	two	NUM
ejpam-6877	78	3	additional	additional	ADJ
ejpam-6877	78	4	eigenvalues	eigenvalue	NOUN
ejpam-6877	78	5	are	be	AUX
ejpam-6877	78	6	at	at	ADP
ejpam-6877	78	7	near	near	ADP
ejpam-6877	78	8	the	the	DET
ejpam-6877	78	9	origin	origin	NOUN
ejpam-6877	78	10	due	due	ADP
ejpam-6877	78	11	to	to	ADP
ejpam-6877	78	12	the	the	DET
ejpam-6877	78	13	free	free	ADJ
ejpam-6877	78	14	cart	cart	NOUN
ejpam-6877	78	15	degree	degree	NOUN
ejpam-6877	78	16	of	of	ADP
ejpam-6877	78	17	freedom	freedom	NOUN
ejpam-6877	78	18	)	)	PUNCT
ejpam-6877	78	19	.	.	PUNCT
ejpam-6877	79	1	hence	hence	ADV
ejpam-6877	79	2	,	,	PUNCT
ejpam-6877	79	3	the	the	DET
ejpam-6877	79	4	upright	upright	ADJ
ejpam-6877	79	5	linearization	linearization	NOUN
ejpam-6877	79	6	is	be	AUX
ejpam-6877	79	7	unstable	unstable	ADJ
ejpam-6877	79	8	.	.	PUNCT
ejpam-6877	80	1	a	a	DET
ejpam-6877	80	2	viscous	viscous	ADJ
ejpam-6877	80	3	torque	torque	NOUN
ejpam-6877	80	4	−c	−c	NOUN
ejpam-6877	80	5	θ̇	θ̇	NOUN
ejpam-6877	80	6	about	about	ADP
ejpam-6877	80	7	the	the	DET
ejpam-6877	80	8	pivot	pivot	NOUN
ejpam-6877	80	9	augments	augment	VERB
ejpam-6877	80	10	(	(	PUNCT
ejpam-6877	80	11	2	2	NUM
ejpam-6877	80	12	)	)	PUNCT
ejpam-6877	80	13	and	and	CCONJ
ejpam-6877	80	14	,	,	PUNCT
ejpam-6877	80	15	after	after	ADP
ejpam-6877	80	16	linearization	linearization	NOUN
ejpam-6877	80	17	,	,	PUNCT
ejpam-6877	80	18	adds	add	VERB
ejpam-6877	80	19	−	−	PROPN
ejpam-6877	80	20	c	c	PROPN
ejpam-6877	80	21	ml2	ml2	PROPN
ejpam-6877	80	22	θ̇	θ̇	X
ejpam-6877	80	23	to	to	ADP
ejpam-6877	80	24	θ̈	θ̈	VERB
ejpam-6877	80	25	,	,	PUNCT
ejpam-6877	80	26	so	so	SCONJ
ejpam-6877	80	27	that	that	PRON
ejpam-6877	80	28	adamped	adampe	VERB
ejpam-6877	80	29	=	=	PUNCT
ejpam-6877	80	30			ADJ
ejpam-6877	80	31	0	0	NUM
ejpam-6877	80	32	1	1	NUM
ejpam-6877	80	33	0	0	NUM
ejpam-6877	80	34	0	0	NUM
ejpam-6877	80	35	0	0	NUM
ejpam-6877	80	36	0	0	NUM
ejpam-6877	81	1	−mg	−mg	NOUN
ejpam-6877	81	2	m	m	VERB
ejpam-6877	81	3	0	0	NUM
ejpam-6877	81	4	0	0	NUM
ejpam-6877	81	5	0	0	NUM
ejpam-6877	81	6	0	0	NUM
ejpam-6877	81	7	1	1	NUM
ejpam-6877	81	8	0	0	NUM
ejpam-6877	81	9	0	0	NUM
ejpam-6877	82	1	(	(	PUNCT
ejpam-6877	82	2	m	m	VERB
ejpam-6877	82	3	+	+	NOUN
ejpam-6877	82	4	m)g	m)g	NOUN
ejpam-6877	82	5	lm	lm	INTJ
ejpam-6877	82	6	−	−	PROPN
ejpam-6877	82	7	c	c	PROPN
ejpam-6877	82	8	ml2	ml2	PROPN
ejpam-6877	82	9			NUM
ejpam-6877	82	10	.	.	PUNCT
ejpam-6877	83	1	the	the	DET
ejpam-6877	83	2	reduced	reduce	VERB
ejpam-6877	83	3	angular	angular	ADJ
ejpam-6877	83	4	sub	sub	NOUN
ejpam-6877	83	5	-	-	NOUN
ejpam-6877	83	6	dynamics	dynamic	NOUN
ejpam-6877	83	7	then	then	ADV
ejpam-6877	83	8	have	have	VERB
ejpam-6877	83	9	λ	λ	NOUN
ejpam-6877	83	10	=	=	SYM
ejpam-6877	83	11	−	−	PROPN
ejpam-6877	83	12	c	c	PROPN
ejpam-6877	83	13	2ml2	2ml2	NUM
ejpam-6877	83	14	±	±	NUM
ejpam-6877	83	15	√	√	NOUN
ejpam-6877	83	16	(	(	PUNCT
ejpam-6877	83	17	c	c	PROPN
ejpam-6877	83	18	2ml2	2ml2	NUM
ejpam-6877	83	19	)	)	PUNCT
ejpam-6877	83	20	2	2	NUM
ejpam-6877	83	21	−	−	PROPN
ejpam-6877	83	22	(	(	PUNCT
ejpam-6877	83	23	m	m	VERB
ejpam-6877	83	24	+	+	ADJ
ejpam-6877	83	25	m)g	m)g	X
ejpam-6877	83	26	lm	lm	INTJ
ejpam-6877	83	27	,	,	PUNCT
ejpam-6877	83	28	so	so	ADV
ejpam-6877	83	29	sufficiently	sufficiently	ADV
ejpam-6877	83	30	large	large	ADJ
ejpam-6877	83	31	c	c	NOUN
ejpam-6877	83	32	makes	make	VERB
ejpam-6877	83	33	ℜ(λ	ℜ(λ	PRON
ejpam-6877	83	34	)	)	PUNCT
ejpam-6877	83	35	<	<	X
ejpam-6877	83	36	0	0	NUM
ejpam-6877	83	37	,	,	PUNCT
ejpam-6877	83	38	in	in	ADP
ejpam-6877	83	39	agreement	agreement	NOUN
ejpam-6877	83	40	with	with	ADP
ejpam-6877	83	41	the	the	DET
ejpam-6877	83	42	signed	sign	VERB
ejpam-6877	83	43	-	-	PUNCT
ejpam-6877	83	44	graph	graph	NOUN
ejpam-6877	83	45	intuition	intuition	NOUN
ejpam-6877	83	46	and	and	CCONJ
ejpam-6877	83	47	the	the	DET
ejpam-6877	83	48	matrix	matrix	NOUN
ejpam-6877	83	49	stability	stability	NOUN
ejpam-6877	83	50	certificate	certificate	NOUN
ejpam-6877	83	51	used	use	VERB
ejpam-6877	83	52	in	in	ADP
ejpam-6877	83	53	section	section	NOUN
ejpam-6877	83	54	main	main	ADJ
ejpam-6877	83	55	result	result	NOUN
ejpam-6877	83	56	.	.	PUNCT
ejpam-6877	84	1	the	the	DET
ejpam-6877	84	2	presence	presence	NOUN
ejpam-6877	84	3	of	of	ADP
ejpam-6877	84	4	a	a	DET
ejpam-6877	84	5	positive	positive	ADJ
ejpam-6877	84	6	and	and	CCONJ
ejpam-6877	84	7	negative	negative	ADJ
ejpam-6877	84	8	eigenvalue	eigenvalue	NOUN
ejpam-6877	84	9	confirms	confirm	VERB
ejpam-6877	84	10	that	that	SCONJ
ejpam-6877	84	11	the	the	DET
ejpam-6877	84	12	system	system	NOUN
ejpam-6877	84	13	is	be	AUX
ejpam-6877	84	14	unstable	unstable	ADJ
ejpam-6877	84	15	.	.	PUNCT
ejpam-6877	85	1	the	the	DET
ejpam-6877	85	2	relationships	relationship	NOUN
ejpam-6877	85	3	between	between	ADP
ejpam-6877	85	4	the	the	DET
ejpam-6877	85	5	system	system	NOUN
ejpam-6877	85	6	variables	variable	VERB
ejpam-6877	85	7	in	in	ADP
ejpam-6877	85	8	the	the	DET
ejpam-6877	85	9	unstable	unstable	ADJ
ejpam-6877	85	10	state	state	NOUN
ejpam-6877	85	11	are	be	AUX
ejpam-6877	85	12	represented	represent	VERB
ejpam-6877	85	13	in	in	ADP
ejpam-6877	85	14	the	the	DET
ejpam-6877	85	15	following	follow	VERB
ejpam-6877	85	16	sign	sign	NOUN
ejpam-6877	85	17	graph	graph	NOUN
ejpam-6877	85	18	:	:	PUNCT
ejpam-6877	85	19	figure	figure	NOUN
ejpam-6877	85	20	3	3	NUM
ejpam-6877	85	21	:	:	PUNCT
ejpam-6877	85	22	sign	sign	VERB
ejpam-6877	85	23	graph	graph	NOUN
ejpam-6877	85	24	system	system	NOUN
ejpam-6877	85	25	before	before	ADP
ejpam-6877	85	26	adding	add	VERB
ejpam-6877	85	27	damping	damp	VERB
ejpam-6877	85	28	(	(	PUNCT
ejpam-6877	85	29	unbalanced	unbalanced	ADJ
ejpam-6877	85	30	)	)	PUNCT
ejpam-6877	85	31	a.	a.	NOUN
ejpam-6877	85	32	m.	m.	NOUN
ejpam-6877	85	33	alotaibi	alotaibi	PROPN
ejpam-6877	85	34	et	et	PROPN
ejpam-6877	85	35	al	al	PROPN
ejpam-6877	85	36	.	.	PUNCT
ejpam-6877	85	37	/	/	SYM
ejpam-6877	85	38	eur	eur	PROPN
ejpam-6877	85	39	.	.	PUNCT
ejpam-6877	86	1	j.	j.	PROPN
ejpam-6877	86	2	pure	pure	PROPN
ejpam-6877	86	3	appl	appl	PROPN
ejpam-6877	86	4	.	.	PROPN
ejpam-6877	86	5	math	math	PROPN
ejpam-6877	86	6	,	,	PUNCT
ejpam-6877	86	7	18	18	NUM
ejpam-6877	86	8	(	(	PUNCT
ejpam-6877	86	9	4	4	NUM
ejpam-6877	86	10	)	)	PUNCT
ejpam-6877	86	11	(	(	PUNCT
ejpam-6877	86	12	2025	2025	NUM
ejpam-6877	86	13	)	)	PUNCT
ejpam-6877	86	14	,	,	PUNCT
ejpam-6877	86	15	6877	6877	NUM
ejpam-6877	86	16	5	5	NUM
ejpam-6877	86	17	of	of	ADP
ejpam-6877	86	18	9	9	NUM
ejpam-6877	86	19	figure	figure	NOUN
ejpam-6877	86	20	3	3	NUM
ejpam-6877	86	21	.	.	NOUN
ejpam-6877	86	22	bdepicts	bdepict	VERB
ejpam-6877	86	23	the	the	DET
ejpam-6877	86	24	signed	sign	VERB
ejpam-6877	86	25	-	-	PUNCT
ejpam-6877	86	26	graph	graph	NOUN
ejpam-6877	86	27	of	of	ADP
ejpam-6877	86	28	the	the	DET
ejpam-6877	86	29	linearized	linearize	VERB
ejpam-6877	86	30	cart	cart	NOUN
ejpam-6877	86	31	–	–	PUNCT
ejpam-6877	86	32	pole	pole	NOUN
ejpam-6877	86	33	about	about	ADP
ejpam-6877	86	34	θ	θ	PROPN
ejpam-6877	86	35	=	=	SYM
ejpam-6877	86	36	0	0	NUM
ejpam-6877	86	37	without	without	ADP
ejpam-6877	86	38	damping	damp	VERB
ejpam-6877	86	39	.	.	PUNCT
ejpam-6877	87	1	edge	edge	NOUN
ejpam-6877	87	2	signs	sign	NOUN
ejpam-6877	87	3	/	/	SYM
ejpam-6877	87	4	weights	weight	NOUN
ejpam-6877	87	5	are	be	AUX
ejpam-6877	87	6	induced	induce	VERB
ejpam-6877	87	7	by	by	ADP
ejpam-6877	87	8	the	the	DET
ejpam-6877	87	9	jacobian	jacobian	PROPN
ejpam-6877	87	10	a	a	DET
ejpam-6877	87	11	(	(	PUNCT
ejpam-6877	87	12	e.g.	e.g.	ADV
ejpam-6877	87	13	,	,	PUNCT
ejpam-6877	87	14	θ	θ	PROPN
ejpam-6877	87	15	→	→	SYM
ejpam-6877	87	16	ẋ	ẋ	PROPN
ejpam-6877	88	1	:	:	PUNCT
ejpam-6877	88	2	−mg	−mg	X
ejpam-6877	88	3	m	m	VERB
ejpam-6877	88	4	and	and	CCONJ
ejpam-6877	88	5	θ	θ	PROPN
ejpam-6877	88	6	→	→	SYM
ejpam-6877	88	7	θ̇	θ̇	X
ejpam-6877	88	8	:	:	PUNCT
ejpam-6877	88	9	(	(	PUNCT
ejpam-6877	88	10	m+m)g	m+m)g	PROPN
ejpam-6877	88	11	lm	lm	PROPN
ejpam-6877	88	12	)	)	PUNCT
ejpam-6877	88	13	,	,	PUNCT
ejpam-6877	88	14	which	which	PRON
ejpam-6877	88	15	is	be	AUX
ejpam-6877	88	16	consistent	consistent	ADJ
ejpam-6877	88	17	with	with	ADP
ejpam-6877	88	18	the	the	DET
ejpam-6877	88	19	spectral	spectral	ADJ
ejpam-6877	88	20	analysis	analysis	NOUN
ejpam-6877	88	21	showing	show	VERB
ejpam-6877	88	22	one	one	NUM
ejpam-6877	88	23	positive	positive	ADJ
ejpam-6877	88	24	real	real	ADJ
ejpam-6877	88	25	eigenvalue	eigenvalue	NOUN
ejpam-6877	88	26	and	and	CCONJ
ejpam-6877	88	27	thus	thus	ADV
ejpam-6877	88	28	an	an	DET
ejpam-6877	88	29	unstable	unstable	ADJ
ejpam-6877	88	30	upright	upright	ADJ
ejpam-6877	88	31	equilibrium	equilibrium	NOUN
ejpam-6877	88	32	.	.	PUNCT
ejpam-6877	89	1	the	the	DET
ejpam-6877	89	2	graph	graph	NOUN
ejpam-6877	89	3	provides	provide	VERB
ejpam-6877	89	4	structural	structural	ADJ
ejpam-6877	89	5	intuition	intuition	NOUN
ejpam-6877	89	6	only	only	ADV
ejpam-6877	89	7	;	;	PUNCT
ejpam-6877	89	8	formal	formal	ADJ
ejpam-6877	89	9	stability	stability	NOUN
ejpam-6877	89	10	is	be	AUX
ejpam-6877	89	11	certified	certify	VERB
ejpam-6877	89	12	via	via	ADP
ejpam-6877	89	13	the	the	DET
ejpam-6877	89	14	lyapunov[21	lyapunov[21	PROPN
ejpam-6877	89	15	]	]	X
ejpam-6877	89	16	spectral	spectral	ADJ
ejpam-6877	89	17	matrix	matrix	NOUN
ejpam-6877	89	18	condition	condition	NOUN
ejpam-6877	90	1	d	d	ADP
ejpam-6877	90	2	−	−	PROPN
ejpam-6877	90	3	s	s	PROPN
ejpam-6877	90	4	≻	≻	PROPN
ejpam-6877	90	5	0	0	NUM
ejpam-6877	90	6	(	(	PUNCT
ejpam-6877	90	7	equivalently	equivalently	ADV
ejpam-6877	90	8	,	,	PUNCT
ejpam-6877	90	9	λmax(s	λmax(s	PROPN
ejpam-6877	90	10	)	)	PUNCT
ejpam-6877	90	11	<	<	X
ejpam-6877	90	12	mini	mini	PROPN
ejpam-6877	90	13	di	di	NOUN
ejpam-6877	90	14	)	)	PUNCT
ejpam-6877	90	15	stated	state	VERB
ejpam-6877	90	16	in	in	ADP
ejpam-6877	90	17	section	section	NOUN
ejpam-6877	90	18	main	main	ADJ
ejpam-6877	90	19	result	result	NOUN
ejpam-6877	90	20	.	.	PUNCT
ejpam-6877	91	1	the	the	DET
ejpam-6877	91	2	following	follow	VERB
ejpam-6877	91	3	sign	sign	NOUN
ejpam-6877	91	4	graph	graph	NOUN
ejpam-6877	91	5	illustrates	illustrate	VERB
ejpam-6877	91	6	the	the	DET
ejpam-6877	91	7	relationships	relationship	NOUN
ejpam-6877	91	8	between	between	ADP
ejpam-6877	91	9	system	system	NOUN
ejpam-6877	91	10	variables	variable	NOUN
ejpam-6877	91	11	after	after	ADP
ejpam-6877	91	12	stabilization	stabilization	NOUN
ejpam-6877	91	13	:	:	PUNCT
ejpam-6877	91	14	figure	figure	NOUN
ejpam-6877	91	15	4	4	NUM
ejpam-6877	91	16	.	.	PUNCT
ejpam-6877	91	17	depicts	depict	VERB
ejpam-6877	91	18	the	the	DET
ejpam-6877	91	19	same	same	ADJ
ejpam-6877	91	20	signed	sign	VERB
ejpam-6877	91	21	-	-	PUNCT
ejpam-6877	91	22	graph	graph	NOUN
ejpam-6877	91	23	with	with	ADP
ejpam-6877	91	24	viscous	viscous	ADJ
ejpam-6877	91	25	damping	damping	NOUN
ejpam-6877	91	26	modeled	model	VERB
ejpam-6877	91	27	as	as	ADP
ejpam-6877	91	28	a	a	DET
ejpam-6877	91	29	figure	figure	NOUN
ejpam-6877	91	30	4	4	NUM
ejpam-6877	91	31	:	:	PUNCT
ejpam-6877	91	32	sign	sign	VERB
ejpam-6877	91	33	graph	graph	NOUN
ejpam-6877	91	34	system	system	NOUN
ejpam-6877	91	35	after	after	ADP
ejpam-6877	91	36	adding	add	VERB
ejpam-6877	91	37	damping	damp	VERB
ejpam-6877	91	38	(	(	PUNCT
ejpam-6877	91	39	balanced	balanced	ADJ
ejpam-6877	91	40	)	)	PUNCT
ejpam-6877	91	41	negative	negative	ADJ
ejpam-6877	91	42	self	self	NOUN
ejpam-6877	91	43	-	-	PUNCT
ejpam-6877	91	44	loop	loop	NOUN
ejpam-6877	91	45	on	on	ADP
ejpam-6877	91	46	θ̇	θ̇	NOUN
ejpam-6877	91	47	with	with	ADP
ejpam-6877	91	48	weight	weight	NOUN
ejpam-6877	91	49	−	−	PROPN
ejpam-6877	91	50	c	c	PROPN
ejpam-6877	91	51	ml2	ml2	PROPN
ejpam-6877	91	52	.	.	PUNCT
ejpam-6877	92	1	increasing	increase	VERB
ejpam-6877	92	2	c	c	PROPN
ejpam-6877	92	3	attenuates	attenuate	VERB
ejpam-6877	92	4	destabilizing	destabilizing	ADJ
ejpam-6877	92	5	couplings	coupling	NOUN
ejpam-6877	92	6	and	and	CCONJ
ejpam-6877	92	7	lowers	lower	VERB
ejpam-6877	92	8	the	the	DET
ejpam-6877	92	9	dominant	dominant	ADJ
ejpam-6877	92	10	eigenvalue	eigenvalue	NOUN
ejpam-6877	92	11	of	of	ADP
ejpam-6877	92	12	the	the	DET
ejpam-6877	92	13	symmetric	symmetric	ADJ
ejpam-6877	92	14	part	part	NOUN
ejpam-6877	92	15	,	,	PUNCT
ejpam-6877	92	16	making	make	VERB
ejpam-6877	92	17	it	it	PRON
ejpam-6877	92	18	easier	easy	ADJ
ejpam-6877	92	19	to	to	PART
ejpam-6877	92	20	satisfy	satisfy	VERB
ejpam-6877	92	21	the	the	DET
ejpam-6877	92	22	matrix	matrix	NOUN
ejpam-6877	92	23	stability	stability	NOUN
ejpam-6877	92	24	certificate	certificate	NOUN
ejpam-6877	92	25	d−s	d−s	PROPN
ejpam-6877	92	26	≻	≻	PROPN
ejpam-6877	92	27	0	0	NUM
ejpam-6877	92	28	(	(	PUNCT
ejpam-6877	92	29	equivalently	equivalently	ADV
ejpam-6877	92	30	,	,	PUNCT
ejpam-6877	92	31	λmax(s	λmax(s	PROPN
ejpam-6877	92	32	)	)	PUNCT
ejpam-6877	92	33	<	<	X
ejpam-6877	92	34	mini	mini	X
ejpam-6877	92	35	di	di	PROPN
ejpam-6877	92	36	)	)	PUNCT
ejpam-6877	92	37	.	.	PUNCT
ejpam-6877	93	1	the	the	DET
ejpam-6877	93	2	graph	graph	NOUN
ejpam-6877	93	3	therefore	therefore	ADV
ejpam-6877	93	4	appears	appear	VERB
ejpam-6877	93	5	balanced	balanced	ADJ
ejpam-6877	93	6	after	after	ADP
ejpam-6877	93	7	damping	damp	VERB
ejpam-6877	93	8	,	,	PUNCT
ejpam-6877	93	9	which	which	PRON
ejpam-6877	93	10	is	be	AUX
ejpam-6877	93	11	consistent	consistent	ADJ
ejpam-6877	93	12	with	with	ADP
ejpam-6877	93	13	the	the	DET
ejpam-6877	93	14	lyapunov	lyapunov	NOUN
ejpam-6877	93	15	[	[	X
ejpam-6877	93	16	21]spectral	21]spectral	NUM
ejpam-6877	93	17	result	result	NOUN
ejpam-6877	93	18	.	.	PUNCT
ejpam-6877	94	1	3	3	X
ejpam-6877	94	2	.	.	X
ejpam-6877	94	3	main	main	ADJ
ejpam-6877	94	4	results	result	NOUN
ejpam-6877	94	5	in	in	ADP
ejpam-6877	94	6	this	this	DET
ejpam-6877	94	7	section	section	NOUN
ejpam-6877	94	8	,	,	PUNCT
ejpam-6877	94	9	we	we	PRON
ejpam-6877	94	10	will	will	AUX
ejpam-6877	94	11	discuss	discuss	VERB
ejpam-6877	94	12	how	how	SCONJ
ejpam-6877	94	13	to	to	PART
ejpam-6877	94	14	determine	determine	VERB
ejpam-6877	94	15	the	the	DET
ejpam-6877	94	16	stability	stability	NOUN
ejpam-6877	94	17	of	of	ADP
ejpam-6877	94	18	a	a	DET
ejpam-6877	94	19	system	system	NOUN
ejpam-6877	94	20	at	at	ADP
ejpam-6877	94	21	equilibrium	equilibrium	NOUN
ejpam-6877	94	22	points	point	NOUN
ejpam-6877	94	23	using	use	VERB
ejpam-6877	94	24	signed	sign	VERB
ejpam-6877	94	25	graph	graph	NOUN
ejpam-6877	94	26	theory	theory	NOUN
ejpam-6877	94	27	.	.	PUNCT
ejpam-6877	95	1	we	we	PRON
ejpam-6877	95	2	will	will	AUX
ejpam-6877	95	3	focus	focus	VERB
ejpam-6877	95	4	on	on	ADP
ejpam-6877	95	5	analyzing	analyze	VERB
ejpam-6877	95	6	the	the	DET
ejpam-6877	95	7	causal	causal	ADJ
ejpam-6877	95	8	relationships	relationship	NOUN
ejpam-6877	95	9	between	between	ADP
ejpam-6877	95	10	system	system	NOUN
ejpam-6877	95	11	variables	variable	NOUN
ejpam-6877	95	12	through	through	ADP
ejpam-6877	95	13	positive	positive	ADJ
ejpam-6877	95	14	and	and	CCONJ
ejpam-6877	95	15	negative	negative	ADJ
ejpam-6877	95	16	edges	edge	NOUN
ejpam-6877	95	17	,	,	PUNCT
ejpam-6877	95	18	and	and	CCONJ
ejpam-6877	95	19	determining	determine	VERB
ejpam-6877	95	20	how	how	SCONJ
ejpam-6877	95	21	these	these	DET
ejpam-6877	95	22	edges	edge	NOUN
ejpam-6877	95	23	affect	affect	VERB
ejpam-6877	95	24	the	the	DET
ejpam-6877	95	25	stability	stability	NOUN
ejpam-6877	95	26	of	of	ADP
ejpam-6877	95	27	the	the	DET
ejpam-6877	95	28	system	system	NOUN
ejpam-6877	95	29	.	.	PUNCT
ejpam-6877	96	1	lemma	lemma	PROPN
ejpam-6877	96	2	1	1	X
ejpam-6877	96	3	.	.	PUNCT
ejpam-6877	96	4	consider	consider	VERB
ejpam-6877	96	5	the	the	DET
ejpam-6877	96	6	linearized	linearize	VERB
ejpam-6877	96	7	system	system	NOUN
ejpam-6877	96	8	around	around	ADP
ejpam-6877	96	9	an	an	DET
ejpam-6877	96	10	equilibrium	equilibrium	NOUN
ejpam-6877	96	11	point	point	NOUN
ejpam-6877	96	12	ẋ	ẋ	PUNCT
ejpam-6877	97	1	=	=	NOUN
ejpam-6877	97	2	ax	ax	NOUN
ejpam-6877	97	3	,	,	PUNCT
ejpam-6877	97	4	a	a	DET
ejpam-6877	97	5	∈	∈	NOUN
ejpam-6877	97	6	rn×n	rn×n	NOUN
ejpam-6877	97	7	,	,	PUNCT
ejpam-6877	97	8	and	and	CCONJ
ejpam-6877	97	9	let	let	VERB
ejpam-6877	97	10	σ	σ	NOUN
ejpam-6877	97	11	=	=	SYM
ejpam-6877	97	12	(	(	PUNCT
ejpam-6877	97	13	v	v	NOUN
ejpam-6877	97	14	,	,	PUNCT
ejpam-6877	97	15	e	e	NOUN
ejpam-6877	97	16	,	,	PUNCT
ejpam-6877	97	17	σ	σ	PROPN
ejpam-6877	97	18	)	)	PUNCT
ejpam-6877	97	19	be	be	VERB
ejpam-6877	97	20	the	the	DET
ejpam-6877	97	21	associated	associate	VERB
ejpam-6877	97	22	signed	sign	VERB
ejpam-6877	97	23	graph	graph	NOUN
ejpam-6877	97	24	,	,	PUNCT
ejpam-6877	97	25	where	where	SCONJ
ejpam-6877	97	26	v	v	NOUN
ejpam-6877	97	27	=	=	SYM
ejpam-6877	97	28	{	{	PUNCT
ejpam-6877	97	29	1	1	NUM
ejpam-6877	97	30	,	,	PUNCT
ejpam-6877	97	31	.	.	PUNCT
ejpam-6877	97	32	.	.	PUNCT
ejpam-6877	97	33	.	.	PUNCT
ejpam-6877	97	34	,	,	PUNCT
ejpam-6877	97	35	n	n	CCONJ
ejpam-6877	97	36	}	}	PUNCT
ejpam-6877	97	37	is	be	AUX
ejpam-6877	97	38	the	the	DET
ejpam-6877	97	39	set	set	NOUN
ejpam-6877	97	40	of	of	ADP
ejpam-6877	97	41	vertices	vertex	NOUN
ejpam-6877	97	42	,	,	PUNCT
ejpam-6877	97	43	e	e	PROPN
ejpam-6877	97	44	⊆	⊆	NUM
ejpam-6877	97	45	v	v	ADP
ejpam-6877	97	46	×	×	NOUN
ejpam-6877	97	47	v	v	NOUN
ejpam-6877	97	48	is	be	AUX
ejpam-6877	97	49	the	the	DET
ejpam-6877	97	50	set	set	NOUN
ejpam-6877	97	51	of	of	ADP
ejpam-6877	97	52	directed	direct	VERB
ejpam-6877	97	53	edges	edge	NOUN
ejpam-6877	97	54	,	,	PUNCT
ejpam-6877	97	55	and	and	CCONJ
ejpam-6877	97	56	σ	σ	NOUN
ejpam-6877	97	57	:	:	PUNCT
ejpam-6877	97	58	e	e	X
ejpam-6877	97	59	→	→	PUNCT
ejpam-6877	97	60	{	{	PUNCT
ejpam-6877	97	61	−1,+1	−1,+1	ADJ
ejpam-6877	97	62	}	}	PUNCT
ejpam-6877	97	63	assigns	assign	VERB
ejpam-6877	97	64	a	a	DET
ejpam-6877	97	65	sign	sign	NOUN
ejpam-6877	97	66	to	to	ADP
ejpam-6877	97	67	each	each	DET
ejpam-6877	97	68	edge	edge	NOUN
ejpam-6877	97	69	.	.	PUNCT
ejpam-6877	98	1	for	for	ADP
ejpam-6877	98	2	each	each	DET
ejpam-6877	98	3	(	(	PUNCT
ejpam-6877	98	4	i	i	PROPN
ejpam-6877	98	5	,	,	PUNCT
ejpam-6877	98	6	j	j	PROPN
ejpam-6877	98	7	)	)	PUNCT
ejpam-6877	98	8	∈	∈	PROPN
ejpam-6877	98	9	e	e	NOUN
ejpam-6877	98	10	,	,	PUNCT
ejpam-6877	98	11	let	let	VERB
ejpam-6877	98	12	aij	aij	PROPN
ejpam-6877	98	13	denote	denote	VERB
ejpam-6877	98	14	the	the	DET
ejpam-6877	98	15	(	(	PUNCT
ejpam-6877	98	16	i	i	PROPN
ejpam-6877	98	17	,	,	PUNCT
ejpam-6877	98	18	j)-entry	j)-entry	NOUN
ejpam-6877	98	19	of	of	ADP
ejpam-6877	98	20	a.	a.	NOUN
ejpam-6877	98	21	define	define	VERB
ejpam-6877	98	22	the	the	DET
ejpam-6877	98	23	net	net	ADJ
ejpam-6877	98	24	signed	sign	VERB
ejpam-6877	98	25	a.	a.	NOUN
ejpam-6877	98	26	m.	m.	PROPN
ejpam-6877	98	27	alotaibi	alotaibi	PROPN
ejpam-6877	98	28	et	et	PROPN
ejpam-6877	98	29	al	al	PROPN
ejpam-6877	98	30	.	.	PUNCT
ejpam-6877	98	31	/	/	SYM
ejpam-6877	98	32	eur	eur	PROPN
ejpam-6877	98	33	.	.	PUNCT
ejpam-6877	99	1	j.	j.	PROPN
ejpam-6877	99	2	pure	pure	PROPN
ejpam-6877	99	3	appl	appl	PROPN
ejpam-6877	99	4	.	.	PROPN
ejpam-6877	99	5	math	math	PROPN
ejpam-6877	99	6	,	,	PUNCT
ejpam-6877	99	7	18	18	NUM
ejpam-6877	99	8	(	(	PUNCT
ejpam-6877	99	9	4	4	NUM
ejpam-6877	99	10	)	)	PUNCT
ejpam-6877	99	11	(	(	PUNCT
ejpam-6877	99	12	2025	2025	NUM
ejpam-6877	99	13	)	)	PUNCT
ejpam-6877	99	14	,	,	PUNCT
ejpam-6877	99	15	6877	6877	NUM
ejpam-6877	99	16	6	6	NUM
ejpam-6877	99	17	of	of	ADP
ejpam-6877	99	18	9	9	NUM
ejpam-6877	99	19	influence	influence	NOUN
ejpam-6877	99	20	as	as	ADP
ejpam-6877	99	21	σe	σe	NOUN
ejpam-6877	99	22	=	=	PUNCT
ejpam-6877	99	23	∑	∑	PUNCT
ejpam-6877	99	24	(	(	PUNCT
ejpam-6877	99	25	i	i	PROPN
ejpam-6877	99	26	,	,	PUNCT
ejpam-6877	99	27	j)∈e	j)∈e	PROPN
ejpam-6877	99	28	σ(i	σ(i	PROPN
ejpam-6877	99	29	,	,	PUNCT
ejpam-6877	99	30	j	j	PROPN
ejpam-6877	99	31	)	)	PUNCT
ejpam-6877	99	32	|aij	|aij	PROPN
ejpam-6877	99	33	|	|	NOUN
ejpam-6877	99	34	.	.	PUNCT
ejpam-6877	100	1	then	then	ADV
ejpam-6877	100	2	:	:	PUNCT
ejpam-6877	100	3	(	(	PUNCT
ejpam-6877	100	4	i	i	NOUN
ejpam-6877	100	5	)	)	PUNCT
ejpam-6877	100	6	if	if	SCONJ
ejpam-6877	100	7	σe	σe	VERB
ejpam-6877	100	8	<	<	X
ejpam-6877	100	9	0	0	NUM
ejpam-6877	100	10	,	,	PUNCT
ejpam-6877	100	11	all	all	PRON
ejpam-6877	100	12	eigenvalues	eigenvalue	VERB
ejpam-6877	100	13	of	of	ADP
ejpam-6877	100	14	a	a	PRON
ejpam-6877	100	15	have	have	VERB
ejpam-6877	100	16	strictly	strictly	ADV
ejpam-6877	100	17	negative	negative	ADJ
ejpam-6877	100	18	real	real	ADJ
ejpam-6877	100	19	parts	part	NOUN
ejpam-6877	100	20	,	,	PUNCT
ejpam-6877	100	21	and	and	CCONJ
ejpam-6877	100	22	the	the	DET
ejpam-6877	100	23	equilibrium	equilibrium	NOUN
ejpam-6877	100	24	is	be	AUX
ejpam-6877	100	25	asymptotically	asymptotically	ADV
ejpam-6877	100	26	stable	stable	ADJ
ejpam-6877	100	27	.	.	PUNCT
ejpam-6877	101	1	(	(	PUNCT
ejpam-6877	101	2	ii	ii	NOUN
ejpam-6877	101	3	)	)	PUNCT
ejpam-6877	101	4	if	if	SCONJ
ejpam-6877	101	5	σe	σe	VERB
ejpam-6877	101	6	>	>	X
ejpam-6877	101	7	0	0	NUM
ejpam-6877	101	8	,	,	PUNCT
ejpam-6877	101	9	at	at	ADV
ejpam-6877	101	10	least	least	ADV
ejpam-6877	101	11	one	one	NUM
ejpam-6877	101	12	eigenvalue	eigenvalue	NOUN
ejpam-6877	101	13	of	of	ADP
ejpam-6877	101	14	a	a	PRON
ejpam-6877	101	15	has	have	VERB
ejpam-6877	101	16	a	a	DET
ejpam-6877	101	17	positive	positive	ADJ
ejpam-6877	101	18	real	real	ADJ
ejpam-6877	101	19	part	part	NOUN
ejpam-6877	101	20	,	,	PUNCT
ejpam-6877	101	21	and	and	CCONJ
ejpam-6877	101	22	the	the	DET
ejpam-6877	101	23	equilibrium	equilibrium	NOUN
ejpam-6877	101	24	is	be	AUX
ejpam-6877	101	25	unstable	unstable	ADJ
ejpam-6877	101	26	.	.	PUNCT
ejpam-6877	102	1	proof	proof	NOUN
ejpam-6877	102	2	.	.	PUNCT
ejpam-6877	103	1	stability	stability	NOUN
ejpam-6877	103	2	of	of	ADP
ejpam-6877	103	3	the	the	DET
ejpam-6877	103	4	linear	linear	ADJ
ejpam-6877	103	5	system	system	NOUN
ejpam-6877	103	6	ẋ	ẋ	PUNCT
ejpam-6877	104	1	=	=	PUNCT
ejpam-6877	104	2	ax	ax	NOUN
ejpam-6877	104	3	requires	require	VERB
ejpam-6877	104	4	that	that	SCONJ
ejpam-6877	104	5	ℜ(λi	ℜ(λi	ADV
ejpam-6877	104	6	)	)	PUNCT
ejpam-6877	104	7	<	<	X
ejpam-6877	104	8	0	0	NUM
ejpam-6877	104	9	for	for	ADP
ejpam-6877	104	10	all	all	DET
ejpam-6877	104	11	eigenvalues	eigenvalue	NOUN
ejpam-6877	104	12	λi	λi	ADP
ejpam-6877	104	13	of	of	ADP
ejpam-6877	104	14	a.	a.	NOUN
ejpam-6877	104	15	the	the	DET
ejpam-6877	104	16	signed	sign	VERB
ejpam-6877	104	17	graph	graph	NOUN
ejpam-6877	104	18	σ	σ	NOUN
ejpam-6877	104	19	encodes	encode	NOUN
ejpam-6877	104	20	the	the	DET
ejpam-6877	104	21	interactions	interaction	NOUN
ejpam-6877	104	22	:	:	PUNCT
ejpam-6877	104	23	each	each	DET
ejpam-6877	104	24	entry	entry	NOUN
ejpam-6877	104	25	aij	aij	NOUN
ejpam-6877	104	26	corresponds	correspond	VERB
ejpam-6877	104	27	to	to	ADP
ejpam-6877	104	28	an	an	DET
ejpam-6877	104	29	edge	edge	NOUN
ejpam-6877	104	30	(	(	PUNCT
ejpam-6877	104	31	i	i	PROPN
ejpam-6877	104	32	,	,	PUNCT
ejpam-6877	104	33	j	j	PROPN
ejpam-6877	104	34	)	)	PUNCT
ejpam-6877	104	35	with	with	ADP
ejpam-6877	104	36	sign	sign	PROPN
ejpam-6877	104	37	σ(i	σ(i	PROPN
ejpam-6877	104	38	,	,	PUNCT
ejpam-6877	104	39	j	j	PROPN
ejpam-6877	104	40	)	)	PUNCT
ejpam-6877	104	41	.	.	PUNCT
ejpam-6877	105	1	define	define	VERB
ejpam-6877	105	2	the	the	DET
ejpam-6877	105	3	quadratic	quadratic	ADJ
ejpam-6877	105	4	lyapunov	lyapunov	ADJ
ejpam-6877	105	5	candidate	candidate	NOUN
ejpam-6877	105	6	v	v	NOUN
ejpam-6877	105	7	(	(	PUNCT
ejpam-6877	105	8	x	x	NOUN
ejpam-6877	105	9	)	)	PUNCT
ejpam-6877	105	10	=	=	SYM
ejpam-6877	106	1	x⊤x	x⊤x	X
ejpam-6877	106	2	.	.	PUNCT
ejpam-6877	107	1	its	its	PRON
ejpam-6877	107	2	derivative	derivative	NOUN
ejpam-6877	107	3	along	along	ADP
ejpam-6877	107	4	trajectories	trajectory	NOUN
ejpam-6877	107	5	is	be	AUX
ejpam-6877	107	6	v̇	v̇	NOUN
ejpam-6877	107	7	(	(	PUNCT
ejpam-6877	107	8	x	x	NOUN
ejpam-6877	107	9	)	)	PUNCT
ejpam-6877	107	10	=	=	PUNCT
ejpam-6877	108	1	x⊤(a+a⊤)x	x⊤(a+a⊤)x	PROPN
ejpam-6877	108	2	.	.	PUNCT
ejpam-6877	109	1	if	if	SCONJ
ejpam-6877	109	2	σe	σe	PRON
ejpam-6877	109	3	<	<	X
ejpam-6877	109	4	0	0	PROPN
ejpam-6877	109	5	,	,	PUNCT
ejpam-6877	109	6	the	the	DET
ejpam-6877	109	7	symmetric	symmetric	ADJ
ejpam-6877	109	8	part	part	NOUN
ejpam-6877	109	9	(	(	PUNCT
ejpam-6877	109	10	a	a	DET
ejpam-6877	109	11	+	+	NUM
ejpam-6877	109	12	a⊤	a⊤	NOUN
ejpam-6877	109	13	)	)	PUNCT
ejpam-6877	109	14	is	be	AUX
ejpam-6877	109	15	negative	negative	ADJ
ejpam-6877	109	16	definite	definite	ADJ
ejpam-6877	109	17	,	,	PUNCT
ejpam-6877	109	18	implying	imply	VERB
ejpam-6877	109	19	v̇	v̇	NOUN
ejpam-6877	109	20	(	(	PUNCT
ejpam-6877	109	21	x	x	X
ejpam-6877	109	22	)	)	PUNCT
ejpam-6877	109	23	<	<	X
ejpam-6877	109	24	0	0	NUM
ejpam-6877	109	25	for	for	ADP
ejpam-6877	109	26	all	all	DET
ejpam-6877	109	27	x	x	PUNCT
ejpam-6877	109	28	̸=	̸=	PROPN
ejpam-6877	109	29	0	0	NUM
ejpam-6877	109	30	.	.	PUNCT
ejpam-6877	110	1	hence	hence	ADV
ejpam-6877	110	2	all	all	DET
ejpam-6877	110	3	trajectories	trajectory	NOUN
ejpam-6877	110	4	converge	converge	VERB
ejpam-6877	110	5	to	to	ADP
ejpam-6877	110	6	the	the	DET
ejpam-6877	110	7	origin	origin	NOUN
ejpam-6877	110	8	,	,	PUNCT
ejpam-6877	110	9	so	so	SCONJ
ejpam-6877	110	10	the	the	DET
ejpam-6877	110	11	equilibrium	equilibrium	NOUN
ejpam-6877	110	12	is	be	AUX
ejpam-6877	110	13	asymptotically	asymptotically	ADV
ejpam-6877	110	14	stable	stable	ADJ
ejpam-6877	110	15	.	.	PUNCT
ejpam-6877	111	1	conversely	conversely	ADV
ejpam-6877	111	2	,	,	PUNCT
ejpam-6877	111	3	if	if	SCONJ
ejpam-6877	111	4	σe	σe	VERB
ejpam-6877	111	5	>	>	X
ejpam-6877	111	6	0	0	NUM
ejpam-6877	111	7	,	,	PUNCT
ejpam-6877	111	8	the	the	DET
ejpam-6877	111	9	influence	influence	NOUN
ejpam-6877	111	10	of	of	ADP
ejpam-6877	111	11	positive	positive	ADJ
ejpam-6877	111	12	edges	edge	NOUN
ejpam-6877	111	13	dominates	dominate	VERB
ejpam-6877	111	14	,	,	PUNCT
ejpam-6877	111	15	and	and	CCONJ
ejpam-6877	111	16	(	(	PUNCT
ejpam-6877	111	17	a	a	DET
ejpam-6877	111	18	+	+	NUM
ejpam-6877	111	19	a⊤	a⊤	NOUN
ejpam-6877	111	20	)	)	PUNCT
ejpam-6877	111	21	has	have	VERB
ejpam-6877	111	22	at	at	ADV
ejpam-6877	111	23	least	least	ADV
ejpam-6877	111	24	one	one	NUM
ejpam-6877	111	25	positive	positive	ADJ
ejpam-6877	111	26	eigenvalue	eigenvalue	NOUN
ejpam-6877	111	27	.	.	PUNCT
ejpam-6877	112	1	in	in	ADP
ejpam-6877	112	2	this	this	DET
ejpam-6877	112	3	case	case	NOUN
ejpam-6877	112	4	,	,	PUNCT
ejpam-6877	112	5	v̇	v̇	PROPN
ejpam-6877	112	6	(	(	PUNCT
ejpam-6877	112	7	x	x	NOUN
ejpam-6877	112	8	)	)	PUNCT
ejpam-6877	112	9	>	>	X
ejpam-6877	112	10	0	0	PUNCT
ejpam-6877	112	11	along	along	ADP
ejpam-6877	112	12	some	some	DET
ejpam-6877	112	13	directions	direction	NOUN
ejpam-6877	112	14	in	in	ADP
ejpam-6877	112	15	state	state	NOUN
ejpam-6877	112	16	space	space	NOUN
ejpam-6877	112	17	,	,	PUNCT
ejpam-6877	112	18	which	which	PRON
ejpam-6877	112	19	implies	imply	VERB
ejpam-6877	112	20	that	that	SCONJ
ejpam-6877	112	21	a	a	PRON
ejpam-6877	112	22	has	have	AUX
ejpam-6877	112	23	at	at	ADV
ejpam-6877	112	24	least	least	ADV
ejpam-6877	112	25	one	one	NUM
ejpam-6877	112	26	eigenvalue	eigenvalue	NOUN
ejpam-6877	112	27	with	with	ADP
ejpam-6877	112	28	positive	positive	ADJ
ejpam-6877	112	29	real	real	ADJ
ejpam-6877	112	30	part	part	NOUN
ejpam-6877	112	31	,	,	PUNCT
ejpam-6877	112	32	leading	lead	VERB
ejpam-6877	112	33	to	to	ADP
ejpam-6877	112	34	instability	instability	NOUN
ejpam-6877	112	35	.	.	PUNCT
ejpam-6877	113	1	therefore	therefore	ADV
ejpam-6877	113	2	,	,	PUNCT
ejpam-6877	113	3	the	the	DET
ejpam-6877	113	4	equilibrium	equilibrium	NOUN
ejpam-6877	113	5	is	be	AUX
ejpam-6877	113	6	asymptotically	asymptotically	ADV
ejpam-6877	113	7	stable	stable	ADJ
ejpam-6877	113	8	if	if	SCONJ
ejpam-6877	113	9	and	and	CCONJ
ejpam-6877	113	10	only	only	ADV
ejpam-6877	113	11	if	if	SCONJ
ejpam-6877	113	12	σe	σe	PRON
ejpam-6877	113	13	<	<	X
ejpam-6877	113	14	0	0	X
ejpam-6877	113	15	.	.	PROPN
ejpam-6877	113	16	remark	remark	PROPN
ejpam-6877	113	17	3	3	NUM
ejpam-6877	113	18	.	.	PUNCT
ejpam-6877	114	1	let	let	VERB
ejpam-6877	114	2	aσ	aσ	NOUN
ejpam-6877	114	3	=	=	PUNCT
ejpam-6877	115	1	[	[	X
ejpam-6877	115	2	aijσij	aijσij	X
ejpam-6877	115	3	]	]	PUNCT
ejpam-6877	115	4	be	be	VERB
ejpam-6877	115	5	the	the	DET
ejpam-6877	115	6	signed	sign	VERB
ejpam-6877	115	7	weighted	weight	VERB
ejpam-6877	115	8	adjacency	adjacency	NOUN
ejpam-6877	115	9	induced	induce	VERB
ejpam-6877	115	10	by	by	ADP
ejpam-6877	115	11	the	the	DET
ejpam-6877	115	12	jacobian	jacobian	ADJ
ejpam-6877	115	13	pattern	pattern	NOUN
ejpam-6877	115	14	,	,	PUNCT
ejpam-6877	115	15	and	and	CCONJ
ejpam-6877	115	16	let	let	VERB
ejpam-6877	115	17	s	s	PRON
ejpam-6877	115	18	=	=	NOUN
ejpam-6877	115	19	1	1	NUM
ejpam-6877	115	20	2(aσ	2(aσ	NUM
ejpam-6877	115	21	+	+	PROPN
ejpam-6877	115	22	a⊤	a⊤	PROPN
ejpam-6877	115	23	σ	σ	PROPN
ejpam-6877	115	24	)	)	PUNCT
ejpam-6877	115	25	be	be	AUX
ejpam-6877	115	26	its	its	PRON
ejpam-6877	115	27	symmetric	symmetric	ADJ
ejpam-6877	115	28	part	part	NOUN
ejpam-6877	115	29	.	.	PUNCT
ejpam-6877	116	1	consider	consider	VERB
ejpam-6877	116	2	the	the	DET
ejpam-6877	116	3	linearized	linearize	VERB
ejpam-6877	116	4	dynamics	dynamic	NOUN
ejpam-6877	116	5	ẋ	ẋ	PUNCT
ejpam-6877	117	1	=	=	PUNCT
ejpam-6877	117	2	(	(	PUNCT
ejpam-6877	117	3	aσ	aσ	NOUN
ejpam-6877	117	4	−	−	PROPN
ejpam-6877	117	5	d)x	d)x	NOUN
ejpam-6877	117	6	with	with	ADP
ejpam-6877	117	7	diagonal	diagonal	ADJ
ejpam-6877	117	8	damping	damp	VERB
ejpam-6877	117	9	d	d	PROPN
ejpam-6877	117	10	≻	≻	PROPN
ejpam-6877	117	11	0	0	NUM
ejpam-6877	117	12	.	.	PUNCT
ejpam-6877	118	1	using	use	VERB
ejpam-6877	118	2	lyapunov	lyapunov	NOUN
ejpam-6877	118	3	’s	’s	PART
ejpam-6877	118	4	direct	direct	ADJ
ejpam-6877	118	5	method	method	NOUN
ejpam-6877	118	6	with	with	ADP
ejpam-6877	118	7	v	v	NOUN
ejpam-6877	118	8	(	(	PUNCT
ejpam-6877	118	9	x	x	NOUN
ejpam-6877	118	10	)	)	PUNCT
ejpam-6877	118	11	=	=	SYM
ejpam-6877	118	12	1	1	NUM
ejpam-6877	118	13	2x	2x	NUM
ejpam-6877	118	14	⊤x	⊤x	NOUN
ejpam-6877	118	15	,	,	PUNCT
ejpam-6877	118	16	we	we	PRON
ejpam-6877	118	17	obtain	obtain	VERB
ejpam-6877	118	18	v̇	v̇	NOUN
ejpam-6877	118	19	(	(	PUNCT
ejpam-6877	118	20	x	x	NOUN
ejpam-6877	118	21	)	)	PUNCT
ejpam-6877	118	22	=	=	SYM
ejpam-6877	118	23	x⊤(s	x⊤(s	PROPN
ejpam-6877	118	24	−d)x	−d)x	NOUN
ejpam-6877	118	25	.	.	PUNCT
ejpam-6877	119	1	thus	thus	ADV
ejpam-6877	119	2	asymptotic	asymptotic	ADJ
ejpam-6877	119	3	stability	stability	NOUN
ejpam-6877	119	4	is	be	AUX
ejpam-6877	119	5	ensured	ensure	VERB
ejpam-6877	119	6	whenever	whenever	SCONJ
ejpam-6877	119	7	d	d	PROPN
ejpam-6877	119	8	−	−	PROPN
ejpam-6877	119	9	s	s	PART
ejpam-6877	119	10	≻	≻	PROPN
ejpam-6877	119	11	0	0	NUM
ejpam-6877	119	12	.	.	PUNCT
ejpam-6877	120	1	the	the	DET
ejpam-6877	120	2	qualitative	qualitative	ADJ
ejpam-6877	120	3	rule	rule	NOUN
ejpam-6877	120	4	σe	σe	ADP
ejpam-6877	120	5	<	<	X
ejpam-6877	120	6	0	0	NUM
ejpam-6877	120	7	becomes	become	VERB
ejpam-6877	120	8	operational	operational	ADJ
ejpam-6877	120	9	via	via	ADP
ejpam-6877	120	10	spectral	spectral	ADJ
ejpam-6877	120	11	bounds	bound	NOUN
ejpam-6877	120	12	:	:	PUNCT
ejpam-6877	120	13	λmax(s	λmax(s	NUM
ejpam-6877	120	14	)	)	PUNCT
ejpam-6877	120	15	≤	≤	NUM
ejpam-6877	120	16	ρ(|s|	ρ(|s|	PROPN
ejpam-6877	120	17	)	)	PUNCT
ejpam-6877	120	18	≤	≤	NUM
ejpam-6877	121	1	max	max	PROPN
ejpam-6877	122	1	i	i	PRON
ejpam-6877	122	2	∑	∑	PROPN
ejpam-6877	122	3	j	j	PROPN
ejpam-6877	122	4	|sij	|sij	PRON
ejpam-6877	122	5	|	|	ADV
ejpam-6877	122	6	,	,	PUNCT
ejpam-6877	122	7	so	so	CCONJ
ejpam-6877	122	8	any	any	DET
ejpam-6877	122	9	uniform	uniform	NOUN
ejpam-6877	122	10	damping	damp	VERB
ejpam-6877	122	11	d	d	X
ejpam-6877	122	12	=	=	SYM
ejpam-6877	122	13	di	di	NOUN
ejpam-6877	122	14	with	with	ADP
ejpam-6877	122	15	d	d	X
ejpam-6877	122	16	>	>	X
ejpam-6877	122	17	maxi	maxi	NOUN
ejpam-6877	122	18	∑	∑	PUNCT
ejpam-6877	122	19	j	j	PROPN
ejpam-6877	122	20	|sij	|sij	NUM
ejpam-6877	122	21	|	|	ADV
ejpam-6877	122	22	guarantees	guarantee	VERB
ejpam-6877	122	23	d−s	d−s	PROPN
ejpam-6877	122	24	≻	≻	PROPN
ejpam-6877	122	25	0	0	NUM
ejpam-6877	122	26	.	.	PUNCT
ejpam-6877	123	1	practically	practically	ADV
ejpam-6877	123	2	,	,	PUNCT
ejpam-6877	123	3	strengthening	strengthen	VERB
ejpam-6877	123	4	negative	negative	ADJ
ejpam-6877	123	5	edges	edge	NOUN
ejpam-6877	123	6	(	(	PUNCT
ejpam-6877	123	7	or	or	CCONJ
ejpam-6877	123	8	weakening	weaken	VERB
ejpam-6877	123	9	positive	positive	ADJ
ejpam-6877	123	10	ones	one	NOUN
ejpam-6877	123	11	)	)	PUNCT
ejpam-6877	123	12	reduces	reduce	VERB
ejpam-6877	123	13	λmax(s	λmax(s	PROPN
ejpam-6877	123	14	)	)	PUNCT
ejpam-6877	123	15	,	,	PUNCT
ejpam-6877	123	16	while	while	SCONJ
ejpam-6877	123	17	increasing	increase	VERB
ejpam-6877	123	18	d	d	PROPN
ejpam-6877	123	19	raises	raise	VERB
ejpam-6877	123	20	the	the	DET
ejpam-6877	123	21	damping	damp	VERB
ejpam-6877	123	22	margin	margin	NOUN
ejpam-6877	123	23	;	;	PUNCT
ejpam-6877	123	24	together	together	ADV
ejpam-6877	123	25	they	they	PRON
ejpam-6877	123	26	enforce	enforce	VERB
ejpam-6877	123	27	the	the	DET
ejpam-6877	123	28	matrix	matrix	NOUN
ejpam-6877	123	29	condition	condition	NOUN
ejpam-6877	123	30	for	for	ADP
ejpam-6877	123	31	stability	stability	NOUN
ejpam-6877	123	32	.	.	PUNCT
ejpam-6877	124	1	this	this	PRON
ejpam-6877	124	2	motivates	motivate	VERB
ejpam-6877	124	3	the	the	DET
ejpam-6877	124	4	following	follow	VERB
ejpam-6877	124	5	theorem	theorem	PROPN
ejpam-6877	124	6	.	.	PUNCT
ejpam-6877	124	7	theorem	theorem	NOUN
ejpam-6877	124	8	2	2	NUM
ejpam-6877	124	9	.	.	X
ejpam-6877	124	10	consider	consider	VERB
ejpam-6877	124	11	the	the	DET
ejpam-6877	124	12	linear	linear	ADJ
ejpam-6877	124	13	time	time	NOUN
ejpam-6877	124	14	-	-	PUNCT
ejpam-6877	124	15	invariant	invariant	ADJ
ejpam-6877	124	16	system	system	NOUN
ejpam-6877	124	17	ẋ	ẋ	PROPN
ejpam-6877	125	1	=	=	PUNCT
ejpam-6877	125	2	(	(	PUNCT
ejpam-6877	125	3	aσ	aσ	ADV
ejpam-6877	125	4	−d)x	−d)x	VERB
ejpam-6877	125	5	,	,	PUNCT
ejpam-6877	125	6	x	x	PROPN
ejpam-6877	125	7	∈	∈	PROPN
ejpam-6877	125	8	rn	rn	PROPN
ejpam-6877	125	9	,	,	PUNCT
ejpam-6877	125	10	a.	a.	NOUN
ejpam-6877	125	11	m.	m.	NOUN
ejpam-6877	125	12	alotaibi	alotaibi	PROPN
ejpam-6877	125	13	et	et	PROPN
ejpam-6877	125	14	al	al	PROPN
ejpam-6877	125	15	.	.	PUNCT
ejpam-6877	125	16	/	/	SYM
ejpam-6877	125	17	eur	eur	PROPN
ejpam-6877	125	18	.	.	PUNCT
ejpam-6877	126	1	j.	j.	PROPN
ejpam-6877	126	2	pure	pure	PROPN
ejpam-6877	126	3	appl	appl	PROPN
ejpam-6877	126	4	.	.	PROPN
ejpam-6877	126	5	math	math	PROPN
ejpam-6877	126	6	,	,	PUNCT
ejpam-6877	126	7	18	18	NUM
ejpam-6877	126	8	(	(	PUNCT
ejpam-6877	126	9	4	4	NUM
ejpam-6877	126	10	)	)	PUNCT
ejpam-6877	126	11	(	(	PUNCT
ejpam-6877	126	12	2025	2025	NUM
ejpam-6877	126	13	)	)	PUNCT
ejpam-6877	126	14	,	,	PUNCT
ejpam-6877	126	15	6877	6877	NUM
ejpam-6877	126	16	7	7	NUM
ejpam-6877	126	17	of	of	ADP
ejpam-6877	126	18	9	9	NUM
ejpam-6877	126	19	where	where	SCONJ
ejpam-6877	126	20	aσ	aσ	ADV
ejpam-6877	126	21	=	=	PUNCT
ejpam-6877	127	1	[	[	X
ejpam-6877	127	2	aijσij	aijσij	X
ejpam-6877	127	3	]	]	PUNCT
ejpam-6877	127	4	is	be	AUX
ejpam-6877	127	5	a	a	DET
ejpam-6877	127	6	(	(	PUNCT
ejpam-6877	127	7	possibly	possibly	ADV
ejpam-6877	127	8	signed	sign	VERB
ejpam-6877	127	9	)	)	PUNCT
ejpam-6877	127	10	weighted	weight	VERB
ejpam-6877	127	11	adjacency	adjacency	NOUN
ejpam-6877	127	12	matrix	matrix	NOUN
ejpam-6877	127	13	associated	associate	VERB
ejpam-6877	127	14	with	with	ADP
ejpam-6877	127	15	a	a	DET
ejpam-6877	127	16	signed	sign	VERB
ejpam-6877	127	17	graph	graph	NOUN
ejpam-6877	127	18	σ	σ	NOUN
ejpam-6877	127	19	=	=	SYM
ejpam-6877	127	20	(	(	PUNCT
ejpam-6877	127	21	v	v	NOUN
ejpam-6877	127	22	,	,	PUNCT
ejpam-6877	127	23	e	e	NOUN
ejpam-6877	127	24	,	,	PUNCT
ejpam-6877	127	25	σ	σ	PROPN
ejpam-6877	127	26	)	)	PUNCT
ejpam-6877	127	27	,	,	PUNCT
ejpam-6877	127	28	and	and	CCONJ
ejpam-6877	127	29	d	d	X
ejpam-6877	127	30	=	=	PUNCT
ejpam-6877	127	31	diag(d1	diag(d1	NOUN
ejpam-6877	127	32	,	,	PUNCT
ejpam-6877	127	33	.	.	PUNCT
ejpam-6877	127	34	.	.	PUNCT
ejpam-6877	128	1	.	.	PUNCT
ejpam-6877	129	1	,	,	PUNCT
ejpam-6877	129	2	dn	dn	PROPN
ejpam-6877	129	3	)	)	PUNCT
ejpam-6877	129	4	≻	≻	X
ejpam-6877	130	1	0	0	NUM
ejpam-6877	130	2	is	be	AUX
ejpam-6877	130	3	a	a	DET
ejpam-6877	130	4	diagonal	diagonal	ADJ
ejpam-6877	130	5	damping	damp	VERB
ejpam-6877	130	6	matrix	matrix	NOUN
ejpam-6877	130	7	.	.	PUNCT
ejpam-6877	131	1	let	let	VERB
ejpam-6877	131	2	s	s	PRON
ejpam-6877	131	3	=	=	VERB
ejpam-6877	131	4	aσ	aσ	ADP
ejpam-6877	131	5	+	+	PROPN
ejpam-6877	131	6	a⊤	a⊤	PROPN
ejpam-6877	131	7	σ	σ	PROPN
ejpam-6877	131	8	2	2	PROPN
ejpam-6877	131	9	denote	denote	VERB
ejpam-6877	131	10	the	the	DET
ejpam-6877	131	11	symmetric	symmetric	ADJ
ejpam-6877	131	12	part	part	NOUN
ejpam-6877	131	13	of	of	ADP
ejpam-6877	131	14	aσ	aσ	NOUN
ejpam-6877	131	15	.	.	PUNCT
ejpam-6877	132	1	then	then	ADV
ejpam-6877	132	2	:	:	PUNCT
ejpam-6877	132	3	(	(	PUNCT
ejpam-6877	132	4	i	i	NOUN
ejpam-6877	132	5	)	)	PUNCT
ejpam-6877	132	6	if	if	SCONJ
ejpam-6877	132	7	the	the	DET
ejpam-6877	132	8	matrix	matrix	NOUN
ejpam-6877	132	9	q	q	NOUN
ejpam-6877	132	10	:	:	PUNCT
ejpam-6877	132	11	=	=	SYM
ejpam-6877	133	1	d	d	X
ejpam-6877	133	2	−	−	NOUN
ejpam-6877	133	3	s	s	VERB
ejpam-6877	133	4	is	be	AUX
ejpam-6877	133	5	positive	positive	ADJ
ejpam-6877	133	6	definite	definite	ADJ
ejpam-6877	133	7	,	,	PUNCT
ejpam-6877	133	8	i.e.	i.e.	X
ejpam-6877	133	9	q	q	X
ejpam-6877	133	10	≻	≻	PROPN
ejpam-6877	133	11	0	0	NUM
ejpam-6877	133	12	,	,	PUNCT
ejpam-6877	133	13	then	then	ADV
ejpam-6877	133	14	the	the	DET
ejpam-6877	133	15	equilibrium	equilibrium	NOUN
ejpam-6877	133	16	x	x	PUNCT
ejpam-6877	134	1	=	=	SYM
ejpam-6877	134	2	0	0	NUM
ejpam-6877	134	3	is	be	AUX
ejpam-6877	134	4	asymptotically	asymptotically	ADV
ejpam-6877	134	5	stable	stable	ADJ
ejpam-6877	134	6	.	.	PUNCT
ejpam-6877	135	1	(	(	PUNCT
ejpam-6877	135	2	ii	ii	NOUN
ejpam-6877	135	3	)	)	PUNCT
ejpam-6877	135	4	if	if	SCONJ
ejpam-6877	135	5	the	the	DET
ejpam-6877	135	6	largest	large	ADJ
ejpam-6877	135	7	eigenvalue	eigenvalue	NOUN
ejpam-6877	135	8	of	of	ADP
ejpam-6877	135	9	s	s	PROPN
ejpam-6877	135	10	satisfies	satisfie	NOUN
ejpam-6877	135	11	λmax(s	λmax(s	PROPN
ejpam-6877	135	12	)	)	PUNCT
ejpam-6877	135	13	>	>	X
ejpam-6877	135	14	mini	mini	PROPN
ejpam-6877	135	15	di	di	PROPN
ejpam-6877	135	16	,	,	PUNCT
ejpam-6877	135	17	then	then	ADV
ejpam-6877	135	18	the	the	DET
ejpam-6877	135	19	equilibrium	equilibrium	NOUN
ejpam-6877	135	20	x	x	PUNCT
ejpam-6877	136	1	=	=	SYM
ejpam-6877	136	2	0	0	NUM
ejpam-6877	136	3	is	be	AUX
ejpam-6877	136	4	unstable	unstable	ADJ
ejpam-6877	136	5	.	.	PUNCT
ejpam-6877	137	1	proof	proof	NOUN
ejpam-6877	137	2	.	.	PUNCT
ejpam-6877	138	1	we	we	PRON
ejpam-6877	138	2	use	use	VERB
ejpam-6877	138	3	lyapunov	lyapunov	NOUN
ejpam-6877	138	4	’s	’s	PART
ejpam-6877	138	5	direct	direct	ADJ
ejpam-6877	138	6	method	method	NOUN
ejpam-6877	138	7	see	see	VERB
ejpam-6877	138	8	[	[	X
ejpam-6877	138	9	21	21	NUM
ejpam-6877	138	10	]	]	PUNCT
ejpam-6877	138	11	consider	consider	VERB
ejpam-6877	138	12	the	the	DET
ejpam-6877	138	13	quadratic	quadratic	ADJ
ejpam-6877	138	14	lyapunov	lyapunov	ADJ
ejpam-6877	138	15	candidate	candidate	NOUN
ejpam-6877	138	16	v	v	NOUN
ejpam-6877	138	17	(	(	PUNCT
ejpam-6877	138	18	x	x	NOUN
ejpam-6877	138	19	)	)	PUNCT
ejpam-6877	138	20	=	=	SYM
ejpam-6877	138	21	1	1	NUM
ejpam-6877	138	22	2x	2x	NUM
ejpam-6877	138	23	⊤x	⊤x	NOUN
ejpam-6877	138	24	.	.	PUNCT
ejpam-6877	139	1	along	along	ADP
ejpam-6877	139	2	trajectories	trajectory	NOUN
ejpam-6877	139	3	,	,	PUNCT
ejpam-6877	139	4	v̇	v̇	PROPN
ejpam-6877	139	5	(	(	PUNCT
ejpam-6877	139	6	x	x	X
ejpam-6877	139	7	)	)	PUNCT
ejpam-6877	139	8	=	=	SYM
ejpam-6877	139	9	1	1	NUM
ejpam-6877	139	10	2	2	NUM
ejpam-6877	139	11	x	x	SYM
ejpam-6877	139	12	⊤((aσ	⊤((aσ	NOUN
ejpam-6877	139	13	−d	−d	ADJ
ejpam-6877	139	14	)	)	PUNCT
ejpam-6877	140	1	+	+	CCONJ
ejpam-6877	140	2	(	(	PUNCT
ejpam-6877	140	3	aσ	aσ	NOUN
ejpam-6877	140	4	−d)⊤	−d)⊤	ADJ
ejpam-6877	140	5	)	)	PUNCT
ejpam-6877	140	6	x	x	X
ejpam-6877	141	1	=	=	PUNCT
ejpam-6877	141	2	x⊤(s	x⊤(s	PROPN
ejpam-6877	141	3	−d)x	−d)x	NOUN
ejpam-6877	141	4	=	=	SYM
ejpam-6877	141	5	−x⊤qx	−x⊤qx	PROPN
ejpam-6877	141	6	.	.	PUNCT
ejpam-6877	142	1	(	(	PUNCT
ejpam-6877	142	2	i	i	NOUN
ejpam-6877	142	3	)	)	PUNCT
ejpam-6877	142	4	if	if	SCONJ
ejpam-6877	142	5	q	q	PROPN
ejpam-6877	142	6	≻	≻	PROPN
ejpam-6877	142	7	0	0	NUM
ejpam-6877	142	8	,	,	PUNCT
ejpam-6877	142	9	then	then	ADV
ejpam-6877	142	10	v̇	v̇	NOUN
ejpam-6877	142	11	(	(	PUNCT
ejpam-6877	142	12	x	x	X
ejpam-6877	142	13	)	)	PUNCT
ejpam-6877	142	14	=	=	PUNCT
ejpam-6877	143	1	−x⊤qx	−x⊤qx	X
ejpam-6877	143	2	<	<	X
ejpam-6877	143	3	0	0	PUNCT
ejpam-6877	143	4	for	for	ADP
ejpam-6877	143	5	all	all	DET
ejpam-6877	143	6	x	x	PUNCT
ejpam-6877	143	7	̸=	̸=	PROPN
ejpam-6877	143	8	0	0	NUM
ejpam-6877	143	9	,	,	PUNCT
ejpam-6877	143	10	hence	hence	ADV
ejpam-6877	143	11	x	x	PUNCT
ejpam-6877	143	12	=	=	SYM
ejpam-6877	143	13	0	0	NUM
ejpam-6877	143	14	is	be	AUX
ejpam-6877	143	15	asymptotically	asymptotically	ADV
ejpam-6877	143	16	stable	stable	ADJ
ejpam-6877	143	17	by	by	ADP
ejpam-6877	143	18	lyapunov	lyapunov	PROPN
ejpam-6877	143	19	’s	’s	PART
ejpam-6877	143	20	[	[	X
ejpam-6877	143	21	21	21	NUM
ejpam-6877	143	22	]	]	X
ejpam-6877	143	23	direct	direct	ADJ
ejpam-6877	143	24	method	method	NOUN
ejpam-6877	143	25	.	.	PUNCT
ejpam-6877	144	1	(	(	PUNCT
ejpam-6877	144	2	ii	ii	NOUN
ejpam-6877	144	3	)	)	PUNCT
ejpam-6877	144	4	suppose	suppose	VERB
ejpam-6877	144	5	λmax(s	λmax(s	NUM
ejpam-6877	144	6	)	)	PUNCT
ejpam-6877	144	7	>	>	X
ejpam-6877	144	8	mini	mini	PROPN
ejpam-6877	144	9	di	di	PROPN
ejpam-6877	144	10	.	.	PUNCT
ejpam-6877	145	1	let	let	VERB
ejpam-6877	145	2	v	v	AUX
ejpam-6877	145	3	̸=	̸=	PROPN
ejpam-6877	145	4	0	0	NUM
ejpam-6877	145	5	be	be	AUX
ejpam-6877	145	6	a	a	DET
ejpam-6877	145	7	unit	unit	NOUN
ejpam-6877	145	8	eigenvector	eigenvector	NOUN
ejpam-6877	145	9	of	of	ADP
ejpam-6877	145	10	s	s	PRON
ejpam-6877	145	11	associated	associate	VERB
ejpam-6877	145	12	with	with	ADP
ejpam-6877	145	13	λmax(s	λmax(s	PROPN
ejpam-6877	145	14	)	)	PUNCT
ejpam-6877	145	15	.	.	PUNCT
ejpam-6877	146	1	then	then	ADV
ejpam-6877	146	2	v⊤(s	v⊤(s	PROPN
ejpam-6877	146	3	−d)v	−d)v	NOUN
ejpam-6877	146	4	≥	≥	NOUN
ejpam-6877	146	5	λmax(s)−min	λmax(s)−min	X
ejpam-6877	146	6	i	i	PRON
ejpam-6877	146	7	di	di	VERB
ejpam-6877	146	8	>	>	X
ejpam-6877	146	9	0	0	PROPN
ejpam-6877	146	10	.	.	PUNCT
ejpam-6877	147	1	hence	hence	ADV
ejpam-6877	147	2	,	,	PUNCT
ejpam-6877	147	3	there	there	PRON
ejpam-6877	147	4	exists	exist	VERB
ejpam-6877	147	5	a	a	DET
ejpam-6877	147	6	direction	direction	NOUN
ejpam-6877	147	7	v	v	NOUN
ejpam-6877	147	8	with	with	ADP
ejpam-6877	147	9	v⊤(s	v⊤(s	NOUN
ejpam-6877	147	10	−d)v	−d)v	NOUN
ejpam-6877	147	11	>	>	X
ejpam-6877	147	12	0	0	NUM
ejpam-6877	147	13	,	,	PUNCT
ejpam-6877	147	14	implying	imply	VERB
ejpam-6877	147	15	that	that	SCONJ
ejpam-6877	147	16	the	the	DET
ejpam-6877	147	17	symmetric	symmetric	ADJ
ejpam-6877	147	18	part	part	NOUN
ejpam-6877	147	19	of	of	ADP
ejpam-6877	147	20	(	(	PUNCT
ejpam-6877	147	21	aσ	aσ	ADV
ejpam-6877	147	22	−d	−d	ADJ
ejpam-6877	147	23	)	)	PUNCT
ejpam-6877	147	24	has	have	VERB
ejpam-6877	147	25	a	a	DET
ejpam-6877	147	26	positive	positive	ADJ
ejpam-6877	147	27	rayleigh	rayleigh	NOUN
ejpam-6877	147	28	quotient	quotient	NOUN
ejpam-6877	147	29	;	;	PUNCT
ejpam-6877	147	30	therefore	therefore	ADV
ejpam-6877	147	31	(	(	PUNCT
ejpam-6877	147	32	aσ	aσ	ADV
ejpam-6877	147	33	−d	−d	ADJ
ejpam-6877	147	34	)	)	PUNCT
ejpam-6877	147	35	has	have	VERB
ejpam-6877	147	36	an	an	DET
ejpam-6877	147	37	eigenvalue	eigenvalue	NOUN
ejpam-6877	147	38	with	with	ADP
ejpam-6877	147	39	positive	positive	ADJ
ejpam-6877	147	40	real	real	ADJ
ejpam-6877	147	41	part	part	NOUN
ejpam-6877	147	42	,	,	PUNCT
ejpam-6877	147	43	and	and	CCONJ
ejpam-6877	147	44	the	the	DET
ejpam-6877	147	45	equilibrium	equilibrium	NOUN
ejpam-6877	147	46	is	be	AUX
ejpam-6877	147	47	unstable	unstable	ADJ
ejpam-6877	147	48	.	.	PUNCT
ejpam-6877	148	1	corollary	corollary	ADJ
ejpam-6877	148	2	1	1	NUM
ejpam-6877	148	3	.	.	PUNCT
ejpam-6877	148	4	consider	consider	VERB
ejpam-6877	148	5	the	the	DET
ejpam-6877	148	6	linear	linear	ADJ
ejpam-6877	148	7	time	time	NOUN
ejpam-6877	148	8	-	-	PUNCT
ejpam-6877	148	9	invariant	invariant	ADJ
ejpam-6877	148	10	system	system	NOUN
ejpam-6877	148	11	ẋ	ẋ	PROPN
ejpam-6877	149	1	=	=	PUNCT
ejpam-6877	149	2	(	(	PUNCT
ejpam-6877	149	3	aσ	aσ	ADV
ejpam-6877	149	4	−d)x	−d)x	VERB
ejpam-6877	149	5	,	,	PUNCT
ejpam-6877	149	6	aσ	aσ	ADV
ejpam-6877	149	7	=	=	PUNCT
ejpam-6877	150	1	[	[	X
ejpam-6877	150	2	aijσij	aijσij	X
ejpam-6877	150	3	]	]	X
ejpam-6877	150	4	,	,	PUNCT
ejpam-6877	150	5	d	d	X
ejpam-6877	150	6	=	=	PUNCT
ejpam-6877	150	7	diag(d1	diag(d1	NOUN
ejpam-6877	150	8	,	,	PUNCT
ejpam-6877	150	9	.	.	PUNCT
ejpam-6877	150	10	.	.	PUNCT
ejpam-6877	150	11	.	.	PUNCT
ejpam-6877	151	1	,	,	PUNCT
ejpam-6877	151	2	dn	dn	PROPN
ejpam-6877	151	3	)	)	PUNCT
ejpam-6877	151	4	≻	≻	NOUN
ejpam-6877	151	5	0	0	NUM
ejpam-6877	151	6	,	,	PUNCT
ejpam-6877	151	7	and	and	CCONJ
ejpam-6877	151	8	let	let	VERB
ejpam-6877	151	9	s	s	PRON
ejpam-6877	151	10	=	=	VERB
ejpam-6877	151	11	aσ	aσ	ADP
ejpam-6877	151	12	+	+	PROPN
ejpam-6877	151	13	a⊤	a⊤	PROPN
ejpam-6877	151	14	σ	σ	PROPN
ejpam-6877	151	15	2	2	PROPN
ejpam-6877	151	16	.	.	PUNCT
ejpam-6877	152	1	then	then	ADV
ejpam-6877	152	2	the	the	DET
ejpam-6877	152	3	origin	origin	NOUN
ejpam-6877	152	4	x	x	PUNCT
ejpam-6877	153	1	=	=	SYM
ejpam-6877	153	2	0	0	NUM
ejpam-6877	153	3	is	be	AUX
ejpam-6877	153	4	asymptotically	asymptotically	ADV
ejpam-6877	153	5	stable	stable	ADJ
ejpam-6877	153	6	under	under	ADP
ejpam-6877	153	7	either	either	PRON
ejpam-6877	153	8	of	of	ADP
ejpam-6877	153	9	the	the	DET
ejpam-6877	153	10	following	follow	VERB
ejpam-6877	153	11	design	design	NOUN
ejpam-6877	153	12	rules	rule	NOUN
ejpam-6877	153	13	:	:	PUNCT
ejpam-6877	153	14	(	(	PUNCT
ejpam-6877	153	15	i)(damping	i)(dampe	VERB
ejpam-6877	153	16	design	design	NOUN
ejpam-6877	153	17	)	)	PUNCT
ejpam-6877	153	18	choose	choose	VERB
ejpam-6877	153	19	d	d	NOUN
ejpam-6877	154	1	such	such	ADJ
ejpam-6877	154	2	that	that	SCONJ
ejpam-6877	154	3	d	d	PROPN
ejpam-6877	154	4	−	−	PROPN
ejpam-6877	154	5	s	s	PART
ejpam-6877	154	6	≻	≻	PROPN
ejpam-6877	154	7	0	0	X
ejpam-6877	154	8	.	.	PUNCT
ejpam-6877	155	1	in	in	ADP
ejpam-6877	155	2	particular	particular	ADJ
ejpam-6877	155	3	,	,	PUNCT
ejpam-6877	155	4	it	it	PRON
ejpam-6877	155	5	suffices	suffice	VERB
ejpam-6877	155	6	to	to	PART
ejpam-6877	155	7	take	take	VERB
ejpam-6877	155	8	a	a	DET
ejpam-6877	155	9	uniform	uniform	ADJ
ejpam-6877	155	10	damping	damp	VERB
ejpam-6877	155	11	d	d	X
ejpam-6877	155	12	=	=	SYM
ejpam-6877	155	13	di	di	NOUN
ejpam-6877	155	14	with	with	ADP
ejpam-6877	155	15	d	d	PROPN
ejpam-6877	155	16	>	>	X
ejpam-6877	155	17	λmax(s	λmax(s	PROPN
ejpam-6877	155	18	)	)	PUNCT
ejpam-6877	155	19	.	.	PUNCT
ejpam-6877	156	1	(	(	PUNCT
ejpam-6877	156	2	ii)(edge	ii)(edge	NOUN
ejpam-6877	156	3	reweighting	reweighting	NOUN
ejpam-6877	156	4	)	)	PUNCT
ejpam-6877	156	5	modify	modify	VERB
ejpam-6877	156	6	the	the	DET
ejpam-6877	156	7	signed	sign	VERB
ejpam-6877	156	8	weights	weight	NOUN
ejpam-6877	156	9	{	{	PUNCT
ejpam-6877	156	10	aijσij	aijσij	PROPN
ejpam-6877	156	11	}	}	PUNCT
ejpam-6877	156	12	to	to	PART
ejpam-6877	156	13	obtain	obtain	VERB
ejpam-6877	156	14	a	a	DET
ejpam-6877	156	15	new	new	ADJ
ejpam-6877	156	16	symmetric	symmetric	ADJ
ejpam-6877	156	17	part	part	NOUN
ejpam-6877	156	18	s̃	s̃	PROPN
ejpam-6877	156	19	satisfying	satisfy	VERB
ejpam-6877	156	20	λmax(s̃	λmax(s̃	NOUN
ejpam-6877	156	21	)	)	PUNCT
ejpam-6877	156	22	<	<	X
ejpam-6877	156	23	mini	mini	NOUN
ejpam-6877	156	24	di	di	NOUN
ejpam-6877	156	25	for	for	ADP
ejpam-6877	156	26	the	the	DET
ejpam-6877	156	27	chosen	choose	VERB
ejpam-6877	156	28	d.	d.	PROPN
ejpam-6877	156	29	proof	proof	PROPN
ejpam-6877	156	30	.	.	PUNCT
ejpam-6877	157	1	immediate	immediate	ADJ
ejpam-6877	157	2	from	from	ADP
ejpam-6877	157	3	theorem	theorem	ADJ
ejpam-6877	157	4	2	2	NUM
ejpam-6877	157	5	:	:	PUNCT
ejpam-6877	157	6	item	item	NOUN
ejpam-6877	157	7	(	(	PUNCT
ejpam-6877	157	8	i	i	NOUN
ejpam-6877	157	9	)	)	PUNCT
ejpam-6877	157	10	gives	gives	AUX
ejpam-6877	157	11	asymptotic	asymptotic	ADJ
ejpam-6877	157	12	stability	stability	NOUN
ejpam-6877	157	13	when	when	SCONJ
ejpam-6877	157	14	d−s	d−s	PROPN
ejpam-6877	157	15	≻	≻	PROPN
ejpam-6877	157	16	0	0	NUM
ejpam-6877	157	17	via	via	ADP
ejpam-6877	157	18	lyapunov	lyapunov	PROPN
ejpam-6877	157	19	’s	’s	PART
ejpam-6877	157	20	direct	direct	ADJ
ejpam-6877	157	21	method	method	NOUN
ejpam-6877	157	22	;	;	PUNCT
ejpam-6877	157	23	item	item	NOUN
ejpam-6877	157	24	(	(	PUNCT
ejpam-6877	157	25	ii	ii	NOUN
ejpam-6877	157	26	)	)	PUNCT
ejpam-6877	157	27	shows	show	VERB
ejpam-6877	157	28	instability	instability	NOUN
ejpam-6877	157	29	whenever	whenever	SCONJ
ejpam-6877	157	30	λmax(s	λmax(s	NOUN
ejpam-6877	157	31	)	)	PUNCT
ejpam-6877	157	32	>	>	X
ejpam-6877	157	33	mini	mini	PROPN
ejpam-6877	157	34	di	di	NOUN
ejpam-6877	157	35	.	.	PUNCT
ejpam-6877	157	36	thus	thus	ADV
ejpam-6877	157	37	enforcing	enforce	VERB
ejpam-6877	157	38	either	either	CCONJ
ejpam-6877	157	39	(	(	PUNCT
ejpam-6877	157	40	i	i	NOUN
ejpam-6877	157	41	)	)	PUNCT
ejpam-6877	157	42	or	or	CCONJ
ejpam-6877	157	43	(	(	PUNCT
ejpam-6877	157	44	ii	ii	NOUN
ejpam-6877	157	45	)	)	PUNCT
ejpam-6877	157	46	(	(	PUNCT
ejpam-6877	157	47	with	with	ADP
ejpam-6877	157	48	s̃	s̃	NOUN
ejpam-6877	157	49	)	)	PUNCT
ejpam-6877	157	50	guarantees	guarantee	VERB
ejpam-6877	157	51	stability	stability	NOUN
ejpam-6877	157	52	.	.	PUNCT
ejpam-6877	158	1	a.	a.	PROPN
ejpam-6877	158	2	m.	m.	PROPN
ejpam-6877	158	3	alotaibi	alotaibi	PROPN
ejpam-6877	158	4	et	et	PROPN
ejpam-6877	158	5	al	al	PROPN
ejpam-6877	158	6	.	.	PUNCT
ejpam-6877	158	7	/	/	SYM
ejpam-6877	158	8	eur	eur	PROPN
ejpam-6877	158	9	.	.	PUNCT
ejpam-6877	159	1	j.	j.	PROPN
ejpam-6877	159	2	pure	pure	PROPN
ejpam-6877	159	3	appl	appl	PROPN
ejpam-6877	159	4	.	.	PROPN
ejpam-6877	159	5	math	math	PROPN
ejpam-6877	159	6	,	,	PUNCT
ejpam-6877	159	7	18	18	NUM
ejpam-6877	159	8	(	(	PUNCT
ejpam-6877	159	9	4	4	NUM
ejpam-6877	159	10	)	)	PUNCT
ejpam-6877	159	11	(	(	PUNCT
ejpam-6877	159	12	2025	2025	NUM
ejpam-6877	159	13	)	)	PUNCT
ejpam-6877	159	14	,	,	PUNCT
ejpam-6877	159	15	6877	6877	NUM
ejpam-6877	159	16	8	8	NUM
ejpam-6877	159	17	of	of	ADP
ejpam-6877	159	18	9	9	NUM
ejpam-6877	159	19	remark	remark	NOUN
ejpam-6877	159	20	4	4	NUM
ejpam-6877	159	21	.	.	PUNCT
ejpam-6877	160	1	the	the	DET
ejpam-6877	160	2	qualitative	qualitative	ADJ
ejpam-6877	160	3	condition	condition	NOUN
ejpam-6877	160	4	σe	σe	ADP
ejpam-6877	160	5	<	<	X
ejpam-6877	160	6	0	0	NUM
ejpam-6877	160	7	can	can	AUX
ejpam-6877	160	8	be	be	AUX
ejpam-6877	160	9	interpreted	interpret	VERB
ejpam-6877	160	10	as	as	ADP
ejpam-6877	160	11	promoting	promote	VERB
ejpam-6877	160	12	a	a	DET
ejpam-6877	160	13	decrease	decrease	NOUN
ejpam-6877	160	14	of	of	ADP
ejpam-6877	160	15	λmax(s	λmax(s	NOUN
ejpam-6877	160	16	)	)	PUNCT
ejpam-6877	160	17	relative	relative	ADJ
ejpam-6877	160	18	to	to	ADP
ejpam-6877	160	19	the	the	DET
ejpam-6877	160	20	damping	damp	VERB
ejpam-6877	160	21	level	level	NOUN
ejpam-6877	160	22	.	.	PUNCT
ejpam-6877	161	1	increasing	increase	VERB
ejpam-6877	161	2	the	the	DET
ejpam-6877	161	3	magnitude	magnitude	NOUN
ejpam-6877	161	4	of	of	ADP
ejpam-6877	161	5	negative	negative	ADJ
ejpam-6877	161	6	edges	edge	NOUN
ejpam-6877	161	7	(	(	PUNCT
ejpam-6877	161	8	or	or	CCONJ
ejpam-6877	161	9	decreasing	decrease	VERB
ejpam-6877	161	10	positive	positive	ADJ
ejpam-6877	161	11	ones	one	NOUN
ejpam-6877	161	12	)	)	PUNCT
ejpam-6877	161	13	tends	tend	VERB
ejpam-6877	161	14	to	to	PART
ejpam-6877	161	15	reduce	reduce	VERB
ejpam-6877	161	16	the	the	DET
ejpam-6877	161	17	largest	large	ADJ
ejpam-6877	161	18	eigenvalue	eigenvalue	NOUN
ejpam-6877	161	19	of	of	ADP
ejpam-6877	161	20	s	s	NOUN
ejpam-6877	161	21	;	;	PUNCT
ejpam-6877	161	22	together	together	ADV
ejpam-6877	161	23	with	with	ADP
ejpam-6877	161	24	larger	large	ADJ
ejpam-6877	161	25	d	d	NOUN
ejpam-6877	161	26	,	,	PUNCT
ejpam-6877	161	27	this	this	PRON
ejpam-6877	161	28	enforces	enforce	VERB
ejpam-6877	161	29	d	d	X
ejpam-6877	161	30	−	−	PROPN
ejpam-6877	161	31	s	s	PART
ejpam-6877	161	32	≻	≻	PROPN
ejpam-6877	161	33	0	0	NUM
ejpam-6877	161	34	,	,	PUNCT
ejpam-6877	161	35	which	which	PRON
ejpam-6877	161	36	is	be	AUX
ejpam-6877	161	37	a	a	DET
ejpam-6877	161	38	rigorous	rigorous	ADJ
ejpam-6877	161	39	matrix	matrix	NOUN
ejpam-6877	161	40	condition	condition	NOUN
ejpam-6877	161	41	for	for	ADP
ejpam-6877	161	42	stability	stability	NOUN
ejpam-6877	161	43	.	.	PUNCT
ejpam-6877	162	1	remark	remark	NOUN
ejpam-6877	162	2	5	5	NUM
ejpam-6877	162	3	.	.	PUNCT
ejpam-6877	163	1	for	for	ADP
ejpam-6877	163	2	the	the	DET
ejpam-6877	163	3	linearized	linearize	VERB
ejpam-6877	163	4	cart	cart	NOUN
ejpam-6877	163	5	–	–	PUNCT
ejpam-6877	163	6	pole	pole	NOUN
ejpam-6877	163	7	about	about	ADP
ejpam-6877	163	8	θ	θ	PROPN
ejpam-6877	163	9	=	=	SYM
ejpam-6877	163	10	0	0	NUM
ejpam-6877	163	11	with	with	ADP
ejpam-6877	163	12	m	m	PROPN
ejpam-6877	163	13	=	=	SYM
ejpam-6877	163	14	1	1	NUM
ejpam-6877	163	15	,	,	PUNCT
ejpam-6877	163	16	m	m	VERB
ejpam-6877	163	17	=	=	NOUN
ejpam-6877	163	18	0.1	0.1	NUM
ejpam-6877	163	19	,	,	PUNCT
ejpam-6877	163	20	l	l	NOUN
ejpam-6877	163	21	=	=	SYM
ejpam-6877	163	22	0.5	0.5	NUM
ejpam-6877	163	23	,	,	PUNCT
ejpam-6877	163	24	g	g	NOUN
ejpam-6877	163	25	=	=	SYM
ejpam-6877	163	26	9.81	9.81	NUM
ejpam-6877	163	27	and	and	CCONJ
ejpam-6877	163	28	f	f	PROPN
ejpam-6877	163	29	≡	≡	PROPN
ejpam-6877	163	30	0	0	NUM
ejpam-6877	163	31	,	,	PUNCT
ejpam-6877	163	32	we	we	PRON
ejpam-6877	163	33	evaluate	evaluate	VERB
ejpam-6877	163	34	the	the	DET
ejpam-6877	163	35	spectrum	spectrum	NOUN
ejpam-6877	163	36	of	of	ADP
ejpam-6877	163	37	a	a	PRON
ejpam-6877	163	38	and	and	CCONJ
ejpam-6877	163	39	of	of	ADP
ejpam-6877	163	40	the	the	DET
ejpam-6877	163	41	damped	damped	NOUN
ejpam-6877	163	42	model	model	NOUN
ejpam-6877	163	43	adamped	adamped	X
ejpam-6877	163	44	(	(	PUNCT
ejpam-6877	163	45	viscous	viscous	ADJ
ejpam-6877	163	46	torque	torque	NOUN
ejpam-6877	163	47	on	on	ADP
ejpam-6877	163	48	θ̇	θ̇	PRON
ejpam-6877	163	49	only	only	ADV
ejpam-6877	163	50	)	)	PUNCT
ejpam-6877	163	51	.	.	PUNCT
ejpam-6877	164	1	consistently	consistently	ADV
ejpam-6877	164	2	with	with	ADP
ejpam-6877	164	3	theorem	theorem	NOUN
ejpam-6877	164	4	2	2	NUM
ejpam-6877	164	5	,	,	PUNCT
ejpam-6877	164	6	the	the	DET
ejpam-6877	164	7	undamped	undamped	ADJ
ejpam-6877	164	8	model	model	NOUN
ejpam-6877	164	9	has	have	VERB
ejpam-6877	164	10	one	one	NUM
ejpam-6877	164	11	positive	positive	ADJ
ejpam-6877	164	12	real	real	ADJ
ejpam-6877	164	13	eigenvalue	eigenvalue	NOUN
ejpam-6877	164	14	(	(	PUNCT
ejpam-6877	164	15	upright	upright	ADJ
ejpam-6877	164	16	is	be	AUX
ejpam-6877	164	17	unstable	unstable	ADJ
ejpam-6877	164	18	)	)	PUNCT
ejpam-6877	164	19	.	.	PUNCT
ejpam-6877	165	1	introducing	introduce	VERB
ejpam-6877	165	2	viscous	viscous	ADJ
ejpam-6877	165	3	damping	damping	NOUN
ejpam-6877	165	4	at	at	ADP
ejpam-6877	165	5	the	the	DET
ejpam-6877	165	6	pivot	pivot	NOUN
ejpam-6877	165	7	decreases	decrease	VERB
ejpam-6877	165	8	the	the	DET
ejpam-6877	165	9	growth	growth	NOUN
ejpam-6877	165	10	rate	rate	NOUN
ejpam-6877	165	11	of	of	ADP
ejpam-6877	165	12	this	this	DET
ejpam-6877	165	13	unstable	unstable	ADJ
ejpam-6877	165	14	mode	mode	NOUN
ejpam-6877	165	15	but	but	CCONJ
ejpam-6877	165	16	does	do	AUX
ejpam-6877	165	17	not	not	PART
ejpam-6877	165	18	render	render	VERB
ejpam-6877	165	19	all	all	PRON
ejpam-6877	165	20	eigenvalues	eigenvalue	VERB
ejpam-6877	165	21	’	'	PUNCT
ejpam-6877	165	22	real	real	ADJ
ejpam-6877	165	23	parts	part	NOUN
ejpam-6877	165	24	negative	negative	ADJ
ejpam-6877	165	25	;	;	PUNCT
ejpam-6877	165	26	full	full	ADJ
ejpam-6877	165	27	asymptotic	asymptotic	ADJ
ejpam-6877	165	28	stability	stability	NOUN
ejpam-6877	165	29	of	of	ADP
ejpam-6877	165	30	the	the	DET
ejpam-6877	165	31	full	full	ADJ
ejpam-6877	165	32	state	state	NOUN
ejpam-6877	165	33	requires	require	VERB
ejpam-6877	165	34	either	either	CCONJ
ejpam-6877	165	35	additional	additional	ADJ
ejpam-6877	165	36	damping	damp	VERB
ejpam-6877	165	37	(	(	PUNCT
ejpam-6877	165	38	e.g.	e.g.	ADV
ejpam-6877	165	39	,	,	PUNCT
ejpam-6877	165	40	on	on	ADP
ejpam-6877	165	41	the	the	DET
ejpam-6877	165	42	cart	cart	NOUN
ejpam-6877	165	43	)	)	PUNCT
ejpam-6877	165	44	or	or	CCONJ
ejpam-6877	165	45	state	state	NOUN
ejpam-6877	165	46	feedback	feedback	NOUN
ejpam-6877	165	47	f	f	NOUN
ejpam-6877	166	1	=	=	PUNCT
ejpam-6877	166	2	−kx	−kx	ADJ
ejpam-6877	166	3	so	so	SCONJ
ejpam-6877	166	4	that	that	SCONJ
ejpam-6877	166	5	the	the	DET
ejpam-6877	166	6	matrix	matrix	NOUN
ejpam-6877	166	7	certificate	certificate	NOUN
ejpam-6877	166	8	holds	hold	VERB
ejpam-6877	166	9	,	,	PUNCT
ejpam-6877	166	10	i.e.	i.e.	X
ejpam-6877	166	11	,	,	PUNCT
ejpam-6877	166	12	d−s	d−s	PROPN
ejpam-6877	166	13	≻	≻	PROPN
ejpam-6877	166	14	0	0	NUM
ejpam-6877	167	1	(	(	PUNCT
ejpam-6877	167	2	equivalently	equivalently	ADV
ejpam-6877	167	3	,	,	PUNCT
ejpam-6877	167	4	λmax(s	λmax(s	PROPN
ejpam-6877	167	5	)	)	PUNCT
ejpam-6877	167	6	<	<	X
ejpam-6877	167	7	mini	mini	X
ejpam-6877	167	8	di	di	PROPN
ejpam-6877	167	9	)	)	PUNCT
ejpam-6877	167	10	.	.	PUNCT
ejpam-6877	168	1	this	this	DET
ejpam-6877	168	2	text	text	NOUN
ejpam-6877	168	3	-	-	PUNCT
ejpam-6877	168	4	only	only	ADJ
ejpam-6877	168	5	check	check	NOUN
ejpam-6877	168	6	corroborates	corroborate	VERB
ejpam-6877	168	7	the	the	DET
ejpam-6877	168	8	signedgraph	signedgraph	NOUN
ejpam-6877	168	9	intuition	intuition	NOUN
ejpam-6877	168	10	while	while	SCONJ
ejpam-6877	168	11	using	use	VERB
ejpam-6877	168	12	a	a	DET
ejpam-6877	168	13	computable	computable	ADJ
ejpam-6877	168	14	lyapunov	lyapunov	NOUN
ejpam-6877	168	15	[	[	X
ejpam-6877	168	16	21	21	NUM
ejpam-6877	168	17	]	]	X
ejpam-6877	168	18	spectral	spectral	ADJ
ejpam-6877	168	19	test	test	NOUN
ejpam-6877	168	20	rather	rather	ADV
ejpam-6877	168	21	than	than	ADP
ejpam-6877	168	22	graphical	graphical	ADJ
ejpam-6877	168	23	balance	balance	NOUN
ejpam-6877	168	24	alone	alone	ADV
ejpam-6877	168	25	.	.	PUNCT
ejpam-6877	169	1	4	4	X
ejpam-6877	169	2	.	.	X
ejpam-6877	169	3	conclusion	conclusion	NOUN
ejpam-6877	169	4	this	this	DET
ejpam-6877	169	5	work	work	NOUN
ejpam-6877	169	6	demonstrated	demonstrate	VERB
ejpam-6877	169	7	how	how	SCONJ
ejpam-6877	169	8	explicit	explicit	ADJ
ejpam-6877	169	9	damping	damping	NOUN
ejpam-6877	169	10	can	can	AUX
ejpam-6877	169	11	transform	transform	VERB
ejpam-6877	169	12	an	an	DET
ejpam-6877	169	13	unstable	unstable	ADJ
ejpam-6877	169	14	linearized	linearize	VERB
ejpam-6877	169	15	system	system	NOUN
ejpam-6877	169	16	into	into	ADP
ejpam-6877	169	17	a	a	DET
ejpam-6877	169	18	stable	stable	ADJ
ejpam-6877	169	19	one	one	NOUN
ejpam-6877	169	20	and	and	CCONJ
ejpam-6877	169	21	aligned	align	VERB
ejpam-6877	169	22	the	the	DET
ejpam-6877	169	23	signed	sign	VERB
ejpam-6877	169	24	-	-	PUNCT
ejpam-6877	169	25	graph	graph	NOUN
ejpam-6877	169	26	intuition	intuition	NOUN
ejpam-6877	169	27	with	with	ADP
ejpam-6877	169	28	a	a	DET
ejpam-6877	169	29	rigorous	rigorous	ADJ
ejpam-6877	169	30	lyapunov	lyapunov	NOUN
ejpam-6877	169	31	/	/	SYM
ejpam-6877	169	32	spectral	spectral	ADJ
ejpam-6877	169	33	certificate	certificate	NOUN
ejpam-6877	169	34	.	.	PUNCT
ejpam-6877	170	1	in	in	ADP
ejpam-6877	170	2	the	the	DET
ejpam-6877	170	3	inverted	inverted	ADJ
ejpam-6877	170	4	pendulum	pendulum	NOUN
ejpam-6877	170	5	,	,	PUNCT
ejpam-6877	170	6	the	the	DET
ejpam-6877	170	7	undamped	undamped	ADJ
ejpam-6877	170	8	linearization	linearization	NOUN
ejpam-6877	170	9	is	be	AUX
ejpam-6877	170	10	unstable	unstable	ADJ
ejpam-6877	170	11	,	,	PUNCT
ejpam-6877	170	12	whereas	whereas	SCONJ
ejpam-6877	170	13	adding	add	VERB
ejpam-6877	170	14	viscous	viscous	ADJ
ejpam-6877	170	15	damping	damp	VERB
ejpam-6877	170	16	yields	yield	NOUN
ejpam-6877	170	17	eigenvalues	eigenvalue	VERB
ejpam-6877	170	18	λ	λ	NOUN
ejpam-6877	170	19	=	=	SYM
ejpam-6877	171	1	−	−	PROPN
ejpam-6877	171	2	c	c	NOUN
ejpam-6877	172	1	2±	2±	NUM
ejpam-6877	172	2	√	√	NOUN
ejpam-6877	172	3	c2	c2	PROPN
ejpam-6877	172	4	4	4	NUM
ejpam-6877	172	5	−	−	NOUN
ejpam-6877	172	6	g	g	PROPN
ejpam-6877	172	7	l	l	NOUN
ejpam-6877	172	8	,	,	PUNCT
ejpam-6877	172	9	so	so	ADV
ejpam-6877	172	10	ℜ(λ	ℜ(λ	CCONJ
ejpam-6877	172	11	)	)	PUNCT
ejpam-6877	172	12	<	<	X
ejpam-6877	172	13	0	0	PUNCT
ejpam-6877	173	1	whenever	whenever	SCONJ
ejpam-6877	173	2	c2	c2	PROPN
ejpam-6877	173	3	>	>	X
ejpam-6877	173	4	4	4	NUM
ejpam-6877	173	5	g	g	NOUN
ejpam-6877	173	6	l	l	NOUN
ejpam-6877	173	7	.	.	PUNCT
ejpam-6877	174	1	at	at	ADP
ejpam-6877	174	2	the	the	DET
ejpam-6877	174	3	network	network	NOUN
ejpam-6877	174	4	level	level	NOUN
ejpam-6877	174	5	,	,	PUNCT
ejpam-6877	174	6	modeling	model	VERB
ejpam-6877	174	7	interactions	interaction	NOUN
ejpam-6877	174	8	by	by	ADP
ejpam-6877	174	9	a	a	DET
ejpam-6877	174	10	signed	sign	VERB
ejpam-6877	174	11	weighted	weight	VERB
ejpam-6877	174	12	matrix	matrix	NOUN
ejpam-6877	174	13	aσ	aσ	NOUN
ejpam-6877	174	14	with	with	ADP
ejpam-6877	174	15	symmetric	symmetric	ADJ
ejpam-6877	174	16	part	part	NOUN
ejpam-6877	174	17	s	s	PART
ejpam-6877	174	18	=	=	NOUN
ejpam-6877	174	19	1	1	NUM
ejpam-6877	174	20	2(aσ	2(aσ	NUM
ejpam-6877	174	21	+	+	CCONJ
ejpam-6877	174	22	a⊤	a⊤	PROPN
ejpam-6877	174	23	σ	σ	PROPN
ejpam-6877	174	24	)	)	PUNCT
ejpam-6877	174	25	and	and	CCONJ
ejpam-6877	174	26	diagonal	diagonal	ADJ
ejpam-6877	174	27	damping	damp	VERB
ejpam-6877	174	28	d	d	PROPN
ejpam-6877	174	29	≻	≻	PROPN
ejpam-6877	174	30	0	0	NUM
ejpam-6877	174	31	,	,	PUNCT
ejpam-6877	174	32	we	we	PRON
ejpam-6877	174	33	established	establish	VERB
ejpam-6877	174	34	a	a	DET
ejpam-6877	174	35	computable	computable	ADJ
ejpam-6877	174	36	matrix	matrix	NOUN
ejpam-6877	174	37	certificate	certificate	NOUN
ejpam-6877	174	38	:	:	PUNCT
ejpam-6877	174	39	the	the	DET
ejpam-6877	174	40	origin	origin	NOUN
ejpam-6877	174	41	is	be	AUX
ejpam-6877	174	42	asymptotically	asymptotically	ADV
ejpam-6877	174	43	stable	stable	ADJ
ejpam-6877	175	1	whenever	whenever	SCONJ
ejpam-6877	175	2	d	d	PROPN
ejpam-6877	175	3	−	−	PROPN
ejpam-6877	175	4	s	s	PART
ejpam-6877	175	5	≻	≻	PROPN
ejpam-6877	175	6	0	0	NUM
ejpam-6877	175	7	(	(	PUNCT
ejpam-6877	175	8	equivalently	equivalently	ADV
ejpam-6877	175	9	,	,	PUNCT
ejpam-6877	175	10	λmax(s	λmax(s	PROPN
ejpam-6877	175	11	)	)	PUNCT
ejpam-6877	175	12	<	<	X
ejpam-6877	175	13	mini	mini	X
ejpam-6877	175	14	di	di	PROPN
ejpam-6877	175	15	)	)	PUNCT
ejpam-6877	175	16	.	.	PUNCT
ejpam-6877	176	1	this	this	DET
ejpam-6877	176	2	formal	formal	ADJ
ejpam-6877	176	3	result	result	NOUN
ejpam-6877	176	4	clarifies	clarify	VERB
ejpam-6877	176	5	the	the	DET
ejpam-6877	176	6	qualitative	qualitative	ADJ
ejpam-6877	176	7	rule	rule	NOUN
ejpam-6877	176	8	“	"	PUNCT
ejpam-6877	176	9	σe	σe	X
ejpam-6877	176	10	<	<	X
ejpam-6877	176	11	0	0	NUM
ejpam-6877	176	12	”	"	PUNCT
ejpam-6877	176	13	and	and	CCONJ
ejpam-6877	176	14	is	be	AUX
ejpam-6877	176	15	operationalized	operationalize	VERB
ejpam-6877	176	16	in	in	ADP
ejpam-6877	176	17	corollary	corollary	ADJ
ejpam-6877	176	18	1	1	NUM
ejpam-6877	176	19	via	via	ADP
ejpam-6877	176	20	damping	damp	VERB
ejpam-6877	176	21	and	and	CCONJ
ejpam-6877	176	22	signed	sign	VERB
ejpam-6877	176	23	-	-	PUNCT
ejpam-6877	176	24	edge	edge	NOUN
ejpam-6877	176	25	reweighting	reweighting	NOUN
ejpam-6877	176	26	.	.	PUNCT
ejpam-6877	177	1	looking	look	VERB
ejpam-6877	177	2	ahead	ahead	ADV
ejpam-6877	177	3	,	,	PUNCT
ejpam-6877	177	4	we	we	PRON
ejpam-6877	177	5	will	will	AUX
ejpam-6877	177	6	provide	provide	VERB
ejpam-6877	177	7	full	full	ADJ
ejpam-6877	177	8	time	time	NOUN
ejpam-6877	177	9	-	-	PUNCT
ejpam-6877	177	10	domain	domain	NOUN
ejpam-6877	177	11	simulations	simulation	NOUN
ejpam-6877	177	12	and	and	CCONJ
ejpam-6877	177	13	eigenvalue	eigenvalue	NOUN
ejpam-6877	177	14	-	-	PUNCT
ejpam-6877	177	15	migration	migration	NOUN
ejpam-6877	177	16	plots	plot	NOUN
ejpam-6877	177	17	to	to	PART
ejpam-6877	177	18	corroborate	corroborate	VERB
ejpam-6877	177	19	the	the	DET
ejpam-6877	177	20	certificate	certificate	NOUN
ejpam-6877	177	21	,	,	PUNCT
ejpam-6877	177	22	benchmark	benchmark	VERB
ejpam-6877	177	23	the	the	DET
ejpam-6877	177	24	proposed	propose	VERB
ejpam-6877	177	25	criterion	criterion	NOUN
ejpam-6877	177	26	against	against	ADP
ejpam-6877	177	27	classical	classical	ADJ
ejpam-6877	177	28	tools	tool	NOUN
ejpam-6877	177	29	(	(	PUNCT
ejpam-6877	177	30	direct	direct	ADJ
ejpam-6877	177	31	lyapunov	lyapunov	NOUN
ejpam-6877	177	32	,	,	PUNCT
ejpam-6877	177	33	nyquist	nyquist	NOUN
ejpam-6877	177	34	/	/	SYM
ejpam-6877	177	35	root	root	NOUN
ejpam-6877	177	36	-	-	PUNCT
ejpam-6877	177	37	locus	locus	NOUN
ejpam-6877	177	38	,	,	PUNCT
ejpam-6877	177	39	and	and	CCONJ
ejpam-6877	177	40	lqr	lqr	PROPN
ejpam-6877	177	41	)	)	PUNCT
ejpam-6877	177	42	to	to	PART
ejpam-6877	177	43	quantify	quantify	VERB
ejpam-6877	177	44	stability	stability	NOUN
ejpam-6877	177	45	margins	margin	NOUN
ejpam-6877	177	46	and	and	CCONJ
ejpam-6877	177	47	control	control	NOUN
ejpam-6877	177	48	effort	effort	NOUN
ejpam-6877	177	49	,	,	PUNCT
ejpam-6877	177	50	and	and	CCONJ
ejpam-6877	177	51	validate	validate	VERB
ejpam-6877	177	52	the	the	DET
ejpam-6877	177	53	approach	approach	NOUN
ejpam-6877	177	54	on	on	ADP
ejpam-6877	177	55	real	real	ADJ
ejpam-6877	177	56	datasets	dataset	NOUN
ejpam-6877	177	57	(	(	PUNCT
ejpam-6877	177	58	e.g.	e.g.	ADV
ejpam-6877	177	59	,	,	PUNCT
ejpam-6877	177	60	small	small	ADJ
ejpam-6877	177	61	-	-	PUNCT
ejpam-6877	177	62	signal	signal	NOUN
ejpam-6877	177	63	power	power	NOUN
ejpam-6877	177	64	models	model	NOUN
ejpam-6877	177	65	or	or	CCONJ
ejpam-6877	177	66	networks	network	NOUN
ejpam-6877	177	67	with	with	ADP
ejpam-6877	177	68	antagonistic	antagonistic	ADJ
ejpam-6877	177	69	ties	tie	NOUN
ejpam-6877	177	70	)	)	PUNCT
ejpam-6877	177	71	by	by	ADP
ejpam-6877	177	72	constructing	construct	VERB
ejpam-6877	177	73	aσ	aσ	PRON
ejpam-6877	177	74	and	and	CCONJ
ejpam-6877	177	75	reporting	report	VERB
ejpam-6877	177	76	pre	pre	ADJ
ejpam-6877	177	77	/	/	SYM
ejpam-6877	177	78	post	post	ADJ
ejpam-6877	177	79	damping	damp	VERB
ejpam-6877	177	80	–	–	PUNCT
ejpam-6877	177	81	reweighting	reweighte	VERB
ejpam-6877	177	82	stability	stability	NOUN
ejpam-6877	177	83	certificates	certificate	NOUN
ejpam-6877	177	84	.	.	PUNCT
ejpam-6877	178	1	5	5	X
ejpam-6877	178	2	.	.	X
ejpam-6877	178	3	acknowledgements	acknowledgement	NOUN
ejpam-6877	178	4	this	this	DET
ejpam-6877	178	5	study	study	NOUN
ejpam-6877	178	6	is	be	AUX
ejpam-6877	178	7	supported	support	VERB
ejpam-6877	178	8	via	via	ADP
ejpam-6877	178	9	funding	funding	NOUN
ejpam-6877	178	10	from	from	ADP
ejpam-6877	178	11	prince	prince	PROPN
ejpam-6877	178	12	sattam	sattam	PROPN
ejpam-6877	178	13	bin	bin	PROPN
ejpam-6877	178	14	abdulaziz	abdulaziz	PROPN
ejpam-6877	178	15	university	university	PROPN
ejpam-6877	178	16	project	project	NOUN
ejpam-6877	178	17	number	number	NOUN
ejpam-6877	178	18	(	(	PUNCT
ejpam-6877	178	19	psau/2025	psau/2025	NOUN
ejpam-6877	178	20	/	/	SYM
ejpam-6877	178	21	r/1446	r/1446	PROPN
ejpam-6877	178	22	)	)	PUNCT
ejpam-6877	178	23	.	.	PUNCT
ejpam-6877	179	1	references	reference	NOUN
ejpam-6877	179	2	[	[	X
ejpam-6877	179	3	1	1	NUM
ejpam-6877	179	4	]	]	PUNCT
ejpam-6877	179	5	k.	k.	PROPN
ejpam-6877	179	6	ogata	ogata	PROPN
ejpam-6877	179	7	.	.	PUNCT
ejpam-6877	180	1	modern	modern	ADJ
ejpam-6877	180	2	control	control	PROPN
ejpam-6877	180	3	engineering	engineering	NOUN
ejpam-6877	180	4	.	.	PUNCT
ejpam-6877	181	1	prentice	prentice	PROPN
ejpam-6877	181	2	hall	hall	PROPN
ejpam-6877	181	3	,	,	PUNCT
ejpam-6877	181	4	2010	2010	NUM
ejpam-6877	181	5	.	.	PUNCT
ejpam-6877	182	1	a.	a.	NOUN
ejpam-6877	182	2	m.	m.	PROPN
ejpam-6877	182	3	alotaibi	alotaibi	PROPN
ejpam-6877	182	4	et	et	PROPN
ejpam-6877	182	5	al	al	PROPN
ejpam-6877	182	6	.	.	PUNCT
ejpam-6877	182	7	/	/	SYM
ejpam-6877	182	8	eur	eur	PROPN
ejpam-6877	182	9	.	.	PUNCT
ejpam-6877	183	1	j.	j.	PROPN
ejpam-6877	183	2	pure	pure	PROPN
ejpam-6877	183	3	appl	appl	PROPN
ejpam-6877	183	4	.	.	PROPN
ejpam-6877	183	5	math	math	PROPN
ejpam-6877	183	6	,	,	PUNCT
ejpam-6877	183	7	18	18	NUM
ejpam-6877	183	8	(	(	PUNCT
ejpam-6877	183	9	4	4	NUM
ejpam-6877	183	10	)	)	PUNCT
ejpam-6877	183	11	(	(	PUNCT
ejpam-6877	183	12	2025	2025	NUM
ejpam-6877	183	13	)	)	PUNCT
ejpam-6877	183	14	,	,	PUNCT
ejpam-6877	183	15	6877	6877	NUM
ejpam-6877	183	16	9	9	NUM
ejpam-6877	183	17	of	of	ADP
ejpam-6877	183	18	9	9	NUM
ejpam-6877	183	19	[	[	SYM
ejpam-6877	183	20	2	2	NUM
ejpam-6877	183	21	]	]	X
ejpam-6877	183	22	y.	y.	PROPN
ejpam-6877	183	23	kuang	kuang	PROPN
ejpam-6877	183	24	.	.	PUNCT
ejpam-6877	184	1	delay	delay	VERB
ejpam-6877	184	2	differential	differential	ADJ
ejpam-6877	184	3	equations	equation	NOUN
ejpam-6877	184	4	with	with	ADP
ejpam-6877	184	5	applications	application	NOUN
ejpam-6877	184	6	in	in	ADP
ejpam-6877	184	7	population	population	NOUN
ejpam-6877	184	8	dynamics	dynamic	NOUN
ejpam-6877	184	9	.	.	PUNCT
ejpam-6877	185	1	academic	academic	ADJ
ejpam-6877	185	2	press	press	NOUN
ejpam-6877	185	3	,	,	PUNCT
ejpam-6877	185	4	1993	1993	NUM
ejpam-6877	185	5	.	.	PUNCT
ejpam-6877	186	1	[	[	X
ejpam-6877	186	2	3	3	X
ejpam-6877	186	3	]	]	X
ejpam-6877	186	4	j.-j	j.-j	PROPN
ejpam-6877	186	5	.	.	PUNCT
ejpam-6877	187	1	e.	e.	PROPN
ejpam-6877	187	2	slotine	slotine	PROPN
ejpam-6877	187	3	and	and	CCONJ
ejpam-6877	187	4	w.	w.	PROPN
ejpam-6877	187	5	li	li	PROPN
ejpam-6877	187	6	.	.	PROPN
ejpam-6877	187	7	applied	apply	VERB
ejpam-6877	187	8	nonlinear	nonlinear	ADJ
ejpam-6877	187	9	control	control	NOUN
ejpam-6877	187	10	.	.	PUNCT
ejpam-6877	188	1	prentice	prentice	PROPN
ejpam-6877	188	2	hall	hall	PROPN
ejpam-6877	188	3	,	,	PUNCT
ejpam-6877	188	4	1991	1991	NUM
ejpam-6877	188	5	.	.	PUNCT
ejpam-6877	189	1	[	[	X
ejpam-6877	189	2	4	4	NUM
ejpam-6877	189	3	]	]	X
ejpam-6877	189	4	r.	r.	PROPN
ejpam-6877	189	5	m.	m.	PROPN
ejpam-6877	189	6	murray	murray	PROPN
ejpam-6877	189	7	.	.	PUNCT
ejpam-6877	190	1	control	control	NOUN
ejpam-6877	190	2	in	in	ADP
ejpam-6877	190	3	an	an	DET
ejpam-6877	190	4	information	information	NOUN
ejpam-6877	190	5	rich	rich	ADJ
ejpam-6877	190	6	world	world	NOUN
ejpam-6877	190	7	:	:	PUNCT
ejpam-6877	190	8	report	report	NOUN
ejpam-6877	190	9	of	of	ADP
ejpam-6877	190	10	the	the	DET
ejpam-6877	190	11	panel	panel	NOUN
ejpam-6877	190	12	on	on	ADP
ejpam-6877	190	13	future	future	ADJ
ejpam-6877	190	14	directions	direction	NOUN
ejpam-6877	190	15	in	in	ADP
ejpam-6877	190	16	control	control	NOUN
ejpam-6877	190	17	,	,	PUNCT
ejpam-6877	190	18	dynamics	dynamic	NOUN
ejpam-6877	190	19	,	,	PUNCT
ejpam-6877	190	20	and	and	CCONJ
ejpam-6877	190	21	systems	system	NOUN
ejpam-6877	190	22	.	.	PUNCT
ejpam-6877	191	1	siam	siam	PROPN
ejpam-6877	191	2	,	,	PUNCT
ejpam-6877	191	3	2009	2009	NUM
ejpam-6877	191	4	.	.	PUNCT
ejpam-6877	192	1	[	[	X
ejpam-6877	192	2	5	5	NUM
ejpam-6877	192	3	]	]	PUNCT
ejpam-6877	192	4	a.	a.	NOUN
ejpam-6877	192	5	m.	m.	NOUN
ejpam-6877	192	6	alotaibi	alotaibi	PROPN
ejpam-6877	192	7	and	and	CCONJ
ejpam-6877	192	8	k.	k.	PROPN
ejpam-6877	192	9	m.	m.	PROPN
ejpam-6877	192	10	aljamal	aljamal	PROPN
ejpam-6877	192	11	.	.	PUNCT
ejpam-6877	193	1	exploring	explore	VERB
ejpam-6877	193	2	the	the	DET
ejpam-6877	193	3	associated	associated	ADJ
ejpam-6877	193	4	groups	group	NOUN
ejpam-6877	193	5	of	of	ADP
ejpam-6877	193	6	quasi	quasi	ADJ
ejpam-6877	193	7	-	-	ADJ
ejpam-6877	193	8	free	free	ADJ
ejpam-6877	193	9	groups	group	NOUN
ejpam-6877	193	10	.	.	PUNCT
ejpam-6877	194	1	european	european	ADJ
ejpam-6877	194	2	journal	journal	PROPN
ejpam-6877	194	3	of	of	ADP
ejpam-6877	194	4	pure	pure	ADJ
ejpam-6877	194	5	and	and	CCONJ
ejpam-6877	194	6	applied	applied	ADJ
ejpam-6877	194	7	mathematics	mathematic	NOUN
ejpam-6877	194	8	,	,	PUNCT
ejpam-6877	194	9	17(3):2329–2335	17(3):2329–2335	NUM
ejpam-6877	194	10	,	,	PUNCT
ejpam-6877	194	11	2024	2024	NUM
ejpam-6877	194	12	.	.	PUNCT
ejpam-6877	195	1	[	[	X
ejpam-6877	195	2	6	6	NUM
ejpam-6877	195	3	]	]	PUNCT
ejpam-6877	195	4	k.	k.	PROPN
ejpam-6877	195	5	mustafa	mustafa	PROPN
ejpam-6877	195	6	al	al	PROPN
ejpam-6877	195	7	-	-	PROPN
ejpam-6877	195	8	jamal	jamal	PROPN
ejpam-6877	195	9	and	and	CCONJ
ejpam-6877	195	10	a.	a.	NOUN
ejpam-6877	195	11	t.	t.	PROPN
ejpam-6877	195	12	ab	ab	PROPN
ejpam-6877	195	13	ghani	ghani	PROPN
ejpam-6877	195	14	.	.	PUNCT
ejpam-6877	196	1	on	on	ADP
ejpam-6877	196	2	the	the	DET
ejpam-6877	196	3	relation	relation	NOUN
ejpam-6877	196	4	between	between	ADP
ejpam-6877	196	5	ct	ct	NOUN
ejpam-6877	196	6	-	-	PUNCT
ejpam-6877	196	7	groups	group	NOUN
ejpam-6877	196	8	and	and	CCONJ
ejpam-6877	196	9	nsp	nsp	NOUN
ejpam-6877	196	10	-	-	PUNCT
ejpam-6877	196	11	groups	group	NOUN
ejpam-6877	196	12	on	on	ADP
ejpam-6877	196	13	finite	finite	ADJ
ejpam-6877	196	14	groups	group	NOUN
ejpam-6877	196	15	.	.	PUNCT
ejpam-6877	197	1	in	in	ADP
ejpam-6877	197	2	journal	journal	PROPN
ejpam-6877	197	3	of	of	ADP
ejpam-6877	197	4	physics	physics	PROPN
ejpam-6877	197	5	:	:	PUNCT
ejpam-6877	197	6	conference	conference	NOUN
ejpam-6877	197	7	series	series	NOUN
ejpam-6877	197	8	,	,	PUNCT
ejpam-6877	197	9	volume	volume	NOUN
ejpam-6877	197	10	1366	1366	NUM
ejpam-6877	197	11	,	,	PUNCT
ejpam-6877	197	12	page	page	NOUN
ejpam-6877	197	13	012069	012069	NUM
ejpam-6877	197	14	.	.	PUNCT
ejpam-6877	198	1	iop	iop	NOUN
ejpam-6877	198	2	publishing	publishing	NOUN
ejpam-6877	198	3	,	,	PUNCT
ejpam-6877	198	4	2019	2019	NUM
ejpam-6877	198	5	.	.	PUNCT
ejpam-6877	199	1	[	[	X
ejpam-6877	199	2	7	7	X
ejpam-6877	199	3	]	]	X
ejpam-6877	199	4	b.	b.	PROPN
ejpam-6877	199	5	bollobás	bollobás	PROPN
ejpam-6877	199	6	.	.	PUNCT
ejpam-6877	200	1	modern	modern	ADJ
ejpam-6877	200	2	graph	graph	NOUN
ejpam-6877	200	3	theory	theory	NOUN
ejpam-6877	200	4	.	.	PUNCT
ejpam-6877	201	1	springer	springer	NOUN
ejpam-6877	201	2	,	,	PUNCT
ejpam-6877	201	3	1998	1998	NUM
ejpam-6877	201	4	.	.	PUNCT
ejpam-6877	202	1	[	[	X
ejpam-6877	202	2	8	8	NUM
ejpam-6877	202	3	]	]	X
ejpam-6877	202	4	d.	d.	PROPN
ejpam-6877	202	5	cartwright	cartwright	PROPN
ejpam-6877	202	6	and	and	CCONJ
ejpam-6877	202	7	f.	f.	PROPN
ejpam-6877	202	8	harary	harary	PROPN
ejpam-6877	202	9	.	.	PUNCT
ejpam-6877	203	1	structural	structural	ADJ
ejpam-6877	203	2	balance	balance	NOUN
ejpam-6877	203	3	:	:	PUNCT
ejpam-6877	203	4	a	a	DET
ejpam-6877	203	5	generalization	generalization	NOUN
ejpam-6877	203	6	of	of	ADP
ejpam-6877	203	7	heider	heider	NOUN
ejpam-6877	203	8	’s	’s	PART
ejpam-6877	203	9	theory	theory	NOUN
ejpam-6877	203	10	.	.	PUNCT
ejpam-6877	204	1	psychological	psychological	ADJ
ejpam-6877	204	2	review	review	NOUN
ejpam-6877	204	3	,	,	PUNCT
ejpam-6877	204	4	63(5):277–293	63(5):277–293	PROPN
ejpam-6877	204	5	,	,	PUNCT
ejpam-6877	204	6	1956	1956	NUM
ejpam-6877	204	7	.	.	PUNCT
ejpam-6877	205	1	[	[	X
ejpam-6877	205	2	9	9	NUM
ejpam-6877	205	3	]	]	PUNCT
ejpam-6877	205	4	s.	s.	PROPN
ejpam-6877	205	5	h.	h.	PROPN
ejpam-6877	205	6	strogatz	strogatz	PROPN
ejpam-6877	205	7	.	.	PUNCT
ejpam-6877	206	1	nonlinear	nonlinear	ADJ
ejpam-6877	206	2	dynamics	dynamic	NOUN
ejpam-6877	206	3	and	and	CCONJ
ejpam-6877	206	4	chaos	chaos	NOUN
ejpam-6877	206	5	:	:	PUNCT
ejpam-6877	206	6	with	with	ADP
ejpam-6877	206	7	applications	application	NOUN
ejpam-6877	206	8	to	to	ADP
ejpam-6877	206	9	physics	physics	NOUN
ejpam-6877	206	10	,	,	PUNCT
ejpam-6877	206	11	biology	biology	NOUN
ejpam-6877	206	12	,	,	PUNCT
ejpam-6877	206	13	chemistry	chemistry	NOUN
ejpam-6877	206	14	,	,	PUNCT
ejpam-6877	206	15	and	and	CCONJ
ejpam-6877	206	16	engineering	engineering	NOUN
ejpam-6877	206	17	.	.	PUNCT
ejpam-6877	207	1	westview	westview	PROPN
ejpam-6877	207	2	press	press	PROPN
ejpam-6877	207	3	,	,	PUNCT
ejpam-6877	207	4	2014	2014	NUM
ejpam-6877	207	5	.	.	PUNCT
ejpam-6877	208	1	[	[	X
ejpam-6877	208	2	10	10	NUM
ejpam-6877	208	3	]	]	PUNCT
ejpam-6877	208	4	a.	a.	NOUN
ejpam-6877	208	5	m.	m.	NOUN
ejpam-6877	208	6	alotaibi	alotaibi	PROPN
ejpam-6877	208	7	,	,	PUNCT
ejpam-6877	208	8	k.	k.	PROPN
ejpam-6877	208	9	al	al	PROPN
ejpam-6877	208	10	-	-	PROPN
ejpam-6877	208	11	tahat	tahat	PROPN
ejpam-6877	208	12	,	,	PUNCT
ejpam-6877	208	13	and	and	CCONJ
ejpam-6877	208	14	k.	k.	PROPN
ejpam-6877	208	15	m.	m.	PROPN
ejpam-6877	208	16	aljamal	aljamal	PROPN
ejpam-6877	208	17	.	.	PUNCT
ejpam-6877	209	1	notes	note	NOUN
ejpam-6877	209	2	on	on	ADP
ejpam-6877	209	3	finite	finite	ADJ
ejpam-6877	209	4	groups	group	NOUN
ejpam-6877	209	5	with	with	ADP
ejpam-6877	209	6	nearly	nearly	ADV
ejpam-6877	209	7	spermutable	spermutable	NOUN
ejpam-6877	209	8	and	and	CCONJ
ejpam-6877	209	9	nearly	nearly	ADV
ejpam-6877	209	10	s	s	NOUN
ejpam-6877	209	11	-	-	PUNCT
ejpam-6877	209	12	permutable	permutable	ADJ
ejpam-6877	209	13	-	-	PUNCT
ejpam-6877	209	14	transitive	transitive	ADJ
ejpam-6877	209	15	subgroups	subgroup	NOUN
ejpam-6877	209	16	.	.	PUNCT
ejpam-6877	210	1	european	european	ADJ
ejpam-6877	210	2	journal	journal	PROPN
ejpam-6877	210	3	of	of	ADP
ejpam-6877	210	4	pure	pure	ADJ
ejpam-6877	210	5	and	and	CCONJ
ejpam-6877	210	6	applied	applied	ADJ
ejpam-6877	210	7	mathematics	mathematic	NOUN
ejpam-6877	210	8	,	,	PUNCT
ejpam-6877	210	9	18(3):6033–6033	18(3):6033–6033	NUM
ejpam-6877	210	10	,	,	PUNCT
ejpam-6877	210	11	2025	2025	NUM
ejpam-6877	210	12	.	.	PUNCT
ejpam-6877	211	1	[	[	X
ejpam-6877	211	2	11	11	NUM
ejpam-6877	211	3	]	]	PUNCT
ejpam-6877	211	4	k.	k.	PROPN
ejpam-6877	211	5	al	al	PROPN
ejpam-6877	211	6	-	-	PROPN
ejpam-6877	211	7	tahat	tahat	PROPN
ejpam-6877	211	8	.	.	PUNCT
ejpam-6877	212	1	an	an	DET
ejpam-6877	212	2	innovative	innovative	ADJ
ejpam-6877	212	3	instructional	instructional	ADJ
ejpam-6877	212	4	method	method	NOUN
ejpam-6877	212	5	for	for	ADP
ejpam-6877	212	6	teaching	teach	VERB
ejpam-6877	212	7	object	object	NOUN
ejpam-6877	212	8	-	-	PUNCT
ejpam-6877	212	9	oriented	orient	VERB
ejpam-6877	212	10	modelling	modelling	NOUN
ejpam-6877	212	11	.	.	PUNCT
ejpam-6877	213	1	international	international	ADJ
ejpam-6877	213	2	arab	arab	PROPN
ejpam-6877	213	3	journal	journal	PROPN
ejpam-6877	213	4	of	of	ADP
ejpam-6877	213	5	information	information	NOUN
ejpam-6877	213	6	technology	technology	NOUN
ejpam-6877	213	7	(	(	PUNCT
ejpam-6877	213	8	iajit	iajit	NOUN
ejpam-6877	213	9	)	)	PUNCT
ejpam-6877	213	10	,	,	PUNCT
ejpam-6877	213	11	11(6	11(6	NUM
ejpam-6877	213	12	)	)	PUNCT
ejpam-6877	213	13	,	,	PUNCT
ejpam-6877	213	14	2014	2014	NUM
ejpam-6877	213	15	.	.	PUNCT
ejpam-6877	214	1	[	[	X
ejpam-6877	214	2	12	12	NUM
ejpam-6877	214	3	]	]	X
ejpam-6877	214	4	e.	e.	PROPN
ejpam-6877	214	5	estrada	estrada	PROPN
ejpam-6877	214	6	and	and	CCONJ
ejpam-6877	214	7	n.	n.	PROPN
ejpam-6877	214	8	hatano	hatano	PROPN
ejpam-6877	214	9	.	.	PUNCT
ejpam-6877	215	1	communicability	communicability	PROPN
ejpam-6877	215	2	in	in	ADP
ejpam-6877	215	3	complex	complex	ADJ
ejpam-6877	215	4	networks	network	NOUN
ejpam-6877	215	5	.	.	PUNCT
ejpam-6877	216	1	physical	physical	ADJ
ejpam-6877	216	2	review	review	PROPN
ejpam-6877	216	3	e	e	NOUN
ejpam-6877	216	4	,	,	PUNCT
ejpam-6877	216	5	77(3):036111	77(3):036111	NUM
ejpam-6877	216	6	,	,	PUNCT
ejpam-6877	216	7	2008	2008	NUM
ejpam-6877	216	8	.	.	PUNCT
ejpam-6877	217	1	[	[	X
ejpam-6877	217	2	13	13	NUM
ejpam-6877	217	3	]	]	X
ejpam-6877	217	4	d.	d.	PROPN
ejpam-6877	217	5	m.	m.	PROPN
ejpam-6877	217	6	cvetković	cvetković	PROPN
ejpam-6877	217	7	,	,	PUNCT
ejpam-6877	217	8	p.	p.	PROPN
ejpam-6877	217	9	rowlinson	rowlinson	PROPN
ejpam-6877	217	10	,	,	PUNCT
ejpam-6877	217	11	and	and	CCONJ
ejpam-6877	217	12	s.	s.	PROPN
ejpam-6877	217	13	k.	k.	PROPN
ejpam-6877	217	14	simić	simić	PROPN
ejpam-6877	217	15	.	.	PUNCT
ejpam-6877	218	1	eigenspaces	eigenspace	NOUN
ejpam-6877	218	2	of	of	ADP
ejpam-6877	218	3	graphs	graph	NOUN
ejpam-6877	218	4	.	.	PUNCT
ejpam-6877	219	1	cambridge	cambridge	PROPN
ejpam-6877	219	2	university	university	PROPN
ejpam-6877	219	3	press	press	NOUN
ejpam-6877	219	4	,	,	PUNCT
ejpam-6877	219	5	1995	1995	NUM
ejpam-6877	219	6	.	.	PUNCT
ejpam-6877	220	1	[	[	X
ejpam-6877	220	2	14	14	NUM
ejpam-6877	220	3	]	]	X
ejpam-6877	220	4	r.	r.	PROPN
ejpam-6877	220	5	p.	p.	PROPN
ejpam-6877	220	6	stanley	stanley	PROPN
ejpam-6877	220	7	.	.	PUNCT
ejpam-6877	221	1	enumerative	enumerative	ADJ
ejpam-6877	221	2	combinatorics	combinatoric	NOUN
ejpam-6877	221	3	:	:	PUNCT
ejpam-6877	221	4	volume	volume	NOUN
ejpam-6877	221	5	1	1	NUM
ejpam-6877	221	6	.	.	PUNCT
ejpam-6877	221	7	cambridge	cambridge	PROPN
ejpam-6877	221	8	university	university	PROPN
ejpam-6877	221	9	press	press	NOUN
ejpam-6877	221	10	,	,	PUNCT
ejpam-6877	221	11	1997	1997	NUM
ejpam-6877	221	12	.	.	PUNCT
ejpam-6877	222	1	[	[	X
ejpam-6877	222	2	15	15	NUM
ejpam-6877	222	3	]	]	X
ejpam-6877	222	4	s.	s.	PROPN
ejpam-6877	222	5	boyd	boyd	PROPN
ejpam-6877	222	6	and	and	CCONJ
ejpam-6877	222	7	l.	l.	PROPN
ejpam-6877	222	8	vandenberghe	vandenberghe	PROPN
ejpam-6877	222	9	.	.	PUNCT
ejpam-6877	223	1	convex	convex	PROPN
ejpam-6877	223	2	optimization	optimization	NOUN
ejpam-6877	223	3	.	.	PUNCT
ejpam-6877	224	1	cambridge	cambridge	PROPN
ejpam-6877	224	2	university	university	PROPN
ejpam-6877	224	3	press	press	NOUN
ejpam-6877	224	4	,	,	PUNCT
ejpam-6877	224	5	2004	2004	NUM
ejpam-6877	224	6	.	.	PUNCT
ejpam-6877	225	1	[	[	X
ejpam-6877	225	2	16	16	NUM
ejpam-6877	225	3	]	]	X
ejpam-6877	225	4	g.	g.	PROPN
ejpam-6877	225	5	chen	chen	PROPN
ejpam-6877	225	6	.	.	PUNCT
ejpam-6877	226	1	introduction	introduction	NOUN
ejpam-6877	226	2	to	to	AUX
ejpam-6877	226	3	graph	graph	NOUN
ejpam-6877	226	4	theory	theory	NOUN
ejpam-6877	226	5	and	and	CCONJ
ejpam-6877	226	6	its	its	PRON
ejpam-6877	226	7	applications	application	NOUN
ejpam-6877	226	8	.	.	PUNCT
ejpam-6877	227	1	springer	springer	NOUN
ejpam-6877	227	2	,	,	PUNCT
ejpam-6877	227	3	2013	2013	NUM
ejpam-6877	227	4	.	.	PUNCT
ejpam-6877	228	1	[	[	X
ejpam-6877	228	2	17	17	NUM
ejpam-6877	228	3	]	]	PUNCT
ejpam-6877	228	4	k.	k.	PROPN
ejpam-6877	228	5	m.	m.	PROPN
ejpam-6877	228	6	aljamal	aljamal	PROPN
ejpam-6877	228	7	,	,	PUNCT
ejpam-6877	228	8	a.	a.	NOUN
ejpam-6877	228	9	t.	t.	PROPN
ejpam-6877	228	10	ab	ab	PROPN
ejpam-6877	228	11	ghani	ghani	PROPN
ejpam-6877	228	12	,	,	PUNCT
ejpam-6877	228	13	and	and	CCONJ
ejpam-6877	228	14	r.	r.	PROPN
ejpam-6877	228	15	m.	m.	PROPN
ejpam-6877	228	16	saleh	saleh	PROPN
ejpam-6877	228	17	.	.	PUNCT
ejpam-6877	229	1	on	on	ADP
ejpam-6877	229	2	preimages	preimage	NOUN
ejpam-6877	229	3	of	of	ADP
ejpam-6877	229	4	technology	technology	NOUN
ejpam-6877	229	5	.	.	PUNCT
ejpam-6877	230	1	in	in	ADP
ejpam-6877	230	2	proceedings	proceeding	NOUN
ejpam-6877	230	3	of	of	ADP
ejpam-6877	230	4	the	the	DET
ejpam-6877	230	5	international	international	ADJ
ejpam-6877	230	6	conference	conference	NOUN
ejpam-6877	230	7	on	on	ADP
ejpam-6877	230	8	information	information	NOUN
ejpam-6877	230	9	technology	technology	NOUN
ejpam-6877	230	10	(	(	PUNCT
ejpam-6877	230	11	icit	icit	PROPN
ejpam-6877	230	12	)	)	PUNCT
ejpam-6877	230	13	,	,	PUNCT
ejpam-6877	230	14	pages	page	VERB
ejpam-6877	230	15	340–343	340–343	NUM
ejpam-6877	230	16	.	.	PUNCT
ejpam-6877	231	1	ieee	ieee	PROPN
ejpam-6877	231	2	,	,	PUNCT
ejpam-6877	231	3	2021	2021	NUM
ejpam-6877	231	4	.	.	PUNCT
ejpam-6877	232	1	[	[	X
ejpam-6877	232	2	18	18	NUM
ejpam-6877	232	3	]	]	PUNCT
ejpam-6877	232	4	a.	a.	NOUN
ejpam-6877	232	5	alotaibi	alotaibi	NOUN
ejpam-6877	232	6	.	.	PUNCT
ejpam-6877	233	1	sign	sign	NOUN
ejpam-6877	233	2	-	-	PUNCT
ejpam-6877	233	3	symmetry	symmetry	NOUN
ejpam-6877	233	4	and	and	CCONJ
ejpam-6877	233	5	frustration	frustration	NOUN
ejpam-6877	233	6	index	index	NOUN
ejpam-6877	233	7	in	in	ADP
ejpam-6877	233	8	signed	sign	VERB
ejpam-6877	233	9	graphs	graph	NOUN
ejpam-6877	233	10	.	.	PUNCT
ejpam-6877	234	1	phd	phd	NOUN
ejpam-6877	234	2	thesis	thesis	PROPN
ejpam-6877	234	3	,	,	PUNCT
ejpam-6877	234	4	mississippi	mississippi	PROPN
ejpam-6877	234	5	state	state	PROPN
ejpam-6877	234	6	university	university	PROPN
ejpam-6877	234	7	,	,	PUNCT
ejpam-6877	234	8	2023	2023	NUM
ejpam-6877	234	9	.	.	PUNCT
ejpam-6877	235	1	[	[	X
ejpam-6877	235	2	19	19	NUM
ejpam-6877	235	3	]	]	PUNCT
ejpam-6877	235	4	h.	h.	PROPN
ejpam-6877	235	5	k.	k.	PROPN
ejpam-6877	235	6	khalil	khalil	PROPN
ejpam-6877	235	7	and	and	CCONJ
ejpam-6877	235	8	j.	j.	PROPN
ejpam-6877	235	9	w.	w.	PROPN
ejpam-6877	235	10	grizzle	grizzle	PROPN
ejpam-6877	235	11	.	.	PUNCT
ejpam-6877	236	1	nonlinear	nonlinear	ADJ
ejpam-6877	236	2	systems	system	NOUN
ejpam-6877	236	3	,	,	PUNCT
ejpam-6877	236	4	volume	volume	NOUN
ejpam-6877	236	5	3	3	NUM
ejpam-6877	236	6	.	.	PUNCT
ejpam-6877	236	7	prentice	prentice	PROPN
ejpam-6877	236	8	hall	hall	PROPN
ejpam-6877	236	9	,	,	PUNCT
ejpam-6877	236	10	upper	upper	ADJ
ejpam-6877	236	11	saddle	saddle	NOUN
ejpam-6877	236	12	river	river	PROPN
ejpam-6877	236	13	,	,	PUNCT
ejpam-6877	236	14	nj	nj	PROPN
ejpam-6877	236	15	,	,	PUNCT
ejpam-6877	236	16	2002	2002	NUM
ejpam-6877	236	17	.	.	PUNCT
ejpam-6877	237	1	[	[	X
ejpam-6877	237	2	20	20	NUM
ejpam-6877	237	3	]	]	PUNCT
ejpam-6877	237	4	f.	f.	PROPN
ejpam-6877	237	5	harary	harary	PROPN
ejpam-6877	237	6	.	.	PUNCT
ejpam-6877	238	1	on	on	ADP
ejpam-6877	238	2	the	the	DET
ejpam-6877	238	3	notion	notion	NOUN
ejpam-6877	238	4	of	of	ADP
ejpam-6877	238	5	balance	balance	NOUN
ejpam-6877	238	6	of	of	ADP
ejpam-6877	238	7	a	a	DET
ejpam-6877	238	8	signed	sign	VERB
ejpam-6877	238	9	graph	graph	NOUN
ejpam-6877	238	10	.	.	PUNCT
ejpam-6877	238	11	michigan	michigan	PROPN
ejpam-6877	238	12	mathematical	mathematical	PROPN
ejpam-6877	238	13	journal	journal	PROPN
ejpam-6877	238	14	,	,	PUNCT
ejpam-6877	238	15	2(2):143–146	2(2):143–146	NUM
ejpam-6877	238	16	,	,	PUNCT
ejpam-6877	238	17	1953	1953	NUM
ejpam-6877	238	18	.	.	PUNCT
ejpam-6877	239	1	[	[	X
ejpam-6877	239	2	21	21	NUM
ejpam-6877	239	3	]	]	PUNCT
ejpam-6877	239	4	a.	a.	NOUN
ejpam-6877	239	5	m.	m.	NOUN
ejpam-6877	239	6	lyapunov	lyapunov	PROPN
ejpam-6877	239	7	.	.	PUNCT
ejpam-6877	240	1	the	the	DET
ejpam-6877	240	2	general	general	ADJ
ejpam-6877	240	3	problem	problem	NOUN
ejpam-6877	240	4	of	of	ADP
ejpam-6877	240	5	the	the	DET
ejpam-6877	240	6	stability	stability	NOUN
ejpam-6877	240	7	of	of	ADP
ejpam-6877	240	8	motion	motion	NOUN
ejpam-6877	240	9	.	.	PUNCT
ejpam-6877	241	1	taylor	taylor	PROPN
ejpam-6877	241	2	&	&	CCONJ
ejpam-6877	241	3	francis	francis	PROPN
ejpam-6877	241	4	,	,	PUNCT
ejpam-6877	241	5	1992	1992	NUM
ejpam-6877	241	6	.	.	PUNCT
ejpam-6877	242	1	a.	a.	NOUN
ejpam-6877	242	2	t.	t.	PROPN
ejpam-6877	242	3	fuller	fuller	NOUN
ejpam-6877	242	4	,	,	PUNCT
ejpam-6877	242	5	trans	trans	PROPN
ejpam-6877	242	6	.	.	PROPN
ejpam-6877	242	7	;	;	PUNCT
ejpam-6877	242	8	original	original	ADJ
ejpam-6877	242	9	work	work	NOUN
ejpam-6877	242	10	published	publish	VERB
ejpam-6877	242	11	1892	1892	NUM
ejpam-6877	242	12	.	.	PUNCT