id	sid	tid	token	lemma	pos
ap-8497	1	1	acta	acta	PROPN
ap-8497	1	2	polytechnica	polytechnica	PROPN
ap-8497	1	3	https://doi.org/10.14311/ap.2023.63.0171	https://doi.org/10.14311/ap.2023.63.0171	PROPN
ap-8497	1	4	acta	acta	PROPN
ap-8497	1	5	polytechnica	polytechnica	PROPN
ap-8497	1	6	63(3):171–178	63(3):171–178	PROPN
ap-8497	1	7	,	,	PUNCT
ap-8497	1	8	2023	2023	NUM
ap-8497	1	9	©	©	ADP
ap-8497	1	10	2023	2023	NUM
ap-8497	1	11	the	the	DET
ap-8497	1	12	author(s	author(s	NOUN
ap-8497	1	13	)	)	PUNCT
ap-8497	1	14	.	.	PUNCT
ap-8497	2	1	licensed	license	VERB
ap-8497	2	2	under	under	ADP
ap-8497	2	3	a	a	DET
ap-8497	2	4	cc	cc	NOUN
ap-8497	2	5	-	-	PUNCT
ap-8497	2	6	by	by	ADP
ap-8497	2	7	4.0	4.0	NUM
ap-8497	2	8	licence	licence	NOUN
ap-8497	2	9	published	publish	VERB
ap-8497	2	10	by	by	ADP
ap-8497	2	11	the	the	DET
ap-8497	2	12	czech	czech	PROPN
ap-8497	2	13	technical	technical	PROPN
ap-8497	2	14	university	university	PROPN
ap-8497	2	15	in	in	ADP
ap-8497	2	16	prague	prague	PROPN
ap-8497	2	17	qualitative	qualitative	NOUN
ap-8497	2	18	sign	sign	VERB
ap-8497	2	19	stability	stability	NOUN
ap-8497	2	20	of	of	ADP
ap-8497	2	21	linear	linear	ADJ
ap-8497	2	22	time	time	NOUN
ap-8497	2	23	invariant	invariant	ADJ
ap-8497	2	24	descriptor	descriptor	NOUN
ap-8497	2	25	systems	systems	PROPN
ap-8497	2	26	madhusmita	madhusmita	PROPN
ap-8497	2	27	chanda	chanda	PROPN
ap-8497	2	28	,	,	PUNCT
ap-8497	2	29	mamoni	mamoni	PROPN
ap-8497	2	30	paitandia	paitandia	PROPN
ap-8497	2	31	,	,	PUNCT
ap-8497	2	32	mahendra	mahendra	PROPN
ap-8497	2	33	kumar	kumar	PROPN
ap-8497	2	34	guptaa	guptaa	PROPN
ap-8497	2	35	,	,	PUNCT
ap-8497	2	36	b,∗	b,∗	PROPN
ap-8497	2	37	a	a	DET
ap-8497	2	38	national	national	PROPN
ap-8497	2	39	institute	institute	PROPN
ap-8497	2	40	of	of	ADP
ap-8497	2	41	technology	technology	PROPN
ap-8497	2	42	jamshedpur	jamshedpur	PROPN
ap-8497	2	43	,	,	PUNCT
ap-8497	2	44	department	department	PROPN
ap-8497	2	45	of	of	ADP
ap-8497	2	46	mathematics	mathematic	NOUN
ap-8497	2	47	,	,	PUNCT
ap-8497	2	48	831014	831014	NUM
ap-8497	2	49	jamshedpur	jamshedpur	PROPN
ap-8497	2	50	,	,	PUNCT
ap-8497	2	51	india	india	PROPN
ap-8497	2	52	b	b	PROPN
ap-8497	2	53	indian	indian	PROPN
ap-8497	2	54	institute	institute	PROPN
ap-8497	2	55	of	of	ADP
ap-8497	2	56	technology	technology	PROPN
ap-8497	2	57	bhubaneswar	bhubaneswar	NOUN
ap-8497	2	58	,	,	PUNCT
ap-8497	2	59	school	school	NOUN
ap-8497	2	60	of	of	ADP
ap-8497	2	61	basic	basic	ADJ
ap-8497	2	62	sciences	science	NOUN
ap-8497	2	63	,	,	PUNCT
ap-8497	2	64	khordha	khordha	PROPN
ap-8497	2	65	,	,	PUNCT
ap-8497	2	66	752050	752050	NUM
ap-8497	2	67	odisha	odisha	PROPN
ap-8497	2	68	,	,	PUNCT
ap-8497	2	69	india	india	PROPN
ap-8497	2	70	∗	∗	NOUN
ap-8497	2	71	corresponding	correspond	VERB
ap-8497	2	72	author	author	NOUN
ap-8497	2	73	:	:	PUNCT
ap-8497	2	74	mkgupta@iitbbs.ac.in	mkgupta@iitbbs.ac.in	PUNCT
ap-8497	2	75	abstract	abstract	ADJ
ap-8497	2	76	.	.	PUNCT
ap-8497	3	1	this	this	DET
ap-8497	3	2	article	article	NOUN
ap-8497	3	3	discusses	discuss	VERB
ap-8497	3	4	assessing	assess	VERB
ap-8497	3	5	the	the	DET
ap-8497	3	6	instability	instability	NOUN
ap-8497	3	7	of	of	ADP
ap-8497	3	8	a	a	DET
ap-8497	3	9	continuous	continuous	ADJ
ap-8497	3	10	linear	linear	ADJ
ap-8497	3	11	homogeneous	homogeneous	ADJ
ap-8497	3	12	timeinvariant	timeinvariant	NOUN
ap-8497	3	13	descriptor	descriptor	NOUN
ap-8497	3	14	system	system	NOUN
ap-8497	3	15	.	.	PUNCT
ap-8497	4	1	some	some	DET
ap-8497	4	2	necessary	necessary	ADJ
ap-8497	4	3	conditions	condition	NOUN
ap-8497	4	4	and	and	CCONJ
ap-8497	4	5	sufficient	sufficient	ADJ
ap-8497	4	6	conditions	condition	NOUN
ap-8497	4	7	are	be	AUX
ap-8497	4	8	derived	derive	VERB
ap-8497	4	9	to	to	PART
ap-8497	4	10	establish	establish	VERB
ap-8497	4	11	the	the	DET
ap-8497	4	12	stability	stability	NOUN
ap-8497	4	13	of	of	ADP
ap-8497	4	14	a	a	DET
ap-8497	4	15	matrix	matrix	NOUN
ap-8497	4	16	pair	pair	NOUN
ap-8497	4	17	by	by	ADP
ap-8497	4	18	the	the	DET
ap-8497	4	19	fundamentals	fundamental	NOUN
ap-8497	4	20	of	of	ADP
ap-8497	4	21	qualitative	qualitative	ADJ
ap-8497	4	22	ecological	ecological	ADJ
ap-8497	4	23	principles	principle	NOUN
ap-8497	4	24	.	.	PUNCT
ap-8497	5	1	the	the	DET
ap-8497	5	2	proposed	propose	VERB
ap-8497	5	3	conditions	condition	NOUN
ap-8497	5	4	are	be	AUX
ap-8497	5	5	derived	derive	VERB
ap-8497	5	6	using	use	VERB
ap-8497	5	7	only	only	ADV
ap-8497	5	8	the	the	DET
ap-8497	5	9	qualitative	qualitative	NOUN
ap-8497	5	10	(	(	PUNCT
ap-8497	5	11	sign	sign	NOUN
ap-8497	5	12	)	)	PUNCT
ap-8497	5	13	information	information	NOUN
ap-8497	5	14	of	of	ADP
ap-8497	5	15	the	the	DET
ap-8497	5	16	matrix	matrix	NOUN
ap-8497	5	17	pair	pair	NOUN
ap-8497	5	18	elements	element	NOUN
ap-8497	5	19	.	.	PUNCT
ap-8497	6	1	based	base	VERB
ap-8497	6	2	on	on	ADP
ap-8497	6	3	these	these	DET
ap-8497	6	4	conditions	condition	NOUN
ap-8497	6	5	,	,	PUNCT
ap-8497	6	6	the	the	DET
ap-8497	6	7	instability	instability	NOUN
ap-8497	6	8	of	of	ADP
ap-8497	6	9	a	a	DET
ap-8497	6	10	matrix	matrix	NOUN
ap-8497	6	11	pair	pair	NOUN
ap-8497	6	12	can	can	AUX
ap-8497	6	13	easily	easily	ADV
ap-8497	6	14	be	be	AUX
ap-8497	6	15	determined	determine	VERB
ap-8497	6	16	,	,	PUNCT
ap-8497	6	17	without	without	ADP
ap-8497	6	18	any	any	DET
ap-8497	6	19	magnitude	magnitude	NOUN
ap-8497	6	20	information	information	NOUN
ap-8497	6	21	of	of	ADP
ap-8497	6	22	the	the	DET
ap-8497	6	23	matrix	matrix	NOUN
ap-8497	6	24	pair	pair	NOUN
ap-8497	6	25	elements	element	NOUN
ap-8497	6	26	and	and	CCONJ
ap-8497	6	27	without	without	ADP
ap-8497	6	28	numerical	numerical	PROPN
ap-8497	6	29	eigenvalues	eigenvalues	PROPN
ap-8497	6	30	calculations	calculation	NOUN
ap-8497	6	31	.	.	PUNCT
ap-8497	7	1	with	with	ADP
ap-8497	7	2	the	the	DET
ap-8497	7	3	proposed	propose	VERB
ap-8497	7	4	theory	theory	NOUN
ap-8497	7	5	,	,	PUNCT
ap-8497	7	6	magnitude	magnitude	NOUN
ap-8497	7	7	dependent	dependent	ADJ
ap-8497	7	8	stable	stable	ADJ
ap-8497	7	9	,	,	PUNCT
ap-8497	7	10	magnitude	magnitude	NOUN
ap-8497	7	11	dependent	dependent	ADJ
ap-8497	7	12	unstable	unstable	ADJ
ap-8497	7	13	,	,	PUNCT
ap-8497	7	14	and	and	CCONJ
ap-8497	7	15	qualitative	qualitative	ADJ
ap-8497	7	16	sign	sign	NOUN
ap-8497	7	17	stable	stable	ADJ
ap-8497	7	18	matrix	matrix	NOUN
ap-8497	7	19	pairs	pair	NOUN
ap-8497	7	20	can	can	AUX
ap-8497	7	21	be	be	AUX
ap-8497	7	22	distinguished	distinguish	VERB
ap-8497	7	23	.	.	PUNCT
ap-8497	8	1	the	the	DET
ap-8497	8	2	consequences	consequence	NOUN
ap-8497	8	3	of	of	ADP
ap-8497	8	4	the	the	DET
ap-8497	8	5	proposed	propose	VERB
ap-8497	8	6	conditions	condition	NOUN
ap-8497	8	7	and	and	CCONJ
ap-8497	8	8	some	some	DET
ap-8497	8	9	illustrative	illustrative	ADJ
ap-8497	8	10	examples	example	NOUN
ap-8497	8	11	are	be	AUX
ap-8497	8	12	discussed	discuss	VERB
ap-8497	8	13	.	.	PUNCT
ap-8497	9	1	keywords	keyword	NOUN
ap-8497	9	2	:	:	PUNCT
ap-8497	9	3	descriptor	descriptor	NOUN
ap-8497	9	4	systems	system	NOUN
ap-8497	9	5	,	,	PUNCT
ap-8497	9	6	stability	stability	NOUN
ap-8497	9	7	of	of	ADP
ap-8497	9	8	a	a	DET
ap-8497	9	9	matrix	matrix	NOUN
ap-8497	9	10	pair	pair	NOUN
ap-8497	9	11	,	,	PUNCT
ap-8497	9	12	qualitative	qualitative	ADJ
ap-8497	9	13	sign	sign	NOUN
ap-8497	9	14	instability	instability	NOUN
ap-8497	9	15	,	,	PUNCT
ap-8497	9	16	interactions	interaction	NOUN
ap-8497	9	17	and	and	CCONJ
ap-8497	9	18	interconnections	interconnection	NOUN
ap-8497	9	19	,	,	PUNCT
ap-8497	9	20	characteristic	characteristic	ADJ
ap-8497	9	21	polynomial	polynomial	NOUN
ap-8497	9	22	.	.	PUNCT
ap-8497	10	1	1	1	X
ap-8497	10	2	.	.	X
ap-8497	10	3	introduction	introduction	NOUN
ap-8497	10	4	the	the	DET
ap-8497	10	5	concept	concept	NOUN
ap-8497	10	6	of	of	ADP
ap-8497	10	7	stability	stability	NOUN
ap-8497	10	8	of	of	ADP
ap-8497	10	9	a	a	DET
ap-8497	10	10	matrix	matrix	NOUN
ap-8497	10	11	and	and	CCONJ
ap-8497	10	12	a	a	DET
ap-8497	10	13	matrix	matrix	NOUN
ap-8497	10	14	pair	pair	NOUN
ap-8497	10	15	is	be	AUX
ap-8497	10	16	very	very	ADV
ap-8497	10	17	fundamental	fundamental	ADJ
ap-8497	10	18	to	to	ADP
ap-8497	10	19	the	the	DET
ap-8497	10	20	control	control	NOUN
ap-8497	10	21	theory	theory	NOUN
ap-8497	10	22	,	,	PUNCT
ap-8497	10	23	and	and	CCONJ
ap-8497	10	24	it	it	PRON
ap-8497	10	25	is	be	AUX
ap-8497	10	26	an	an	DET
ap-8497	10	27	important	important	ADJ
ap-8497	10	28	property	property	NOUN
ap-8497	10	29	to	to	PART
ap-8497	10	30	be	be	AUX
ap-8497	10	31	analysed	analyse	VERB
ap-8497	10	32	for	for	ADP
ap-8497	10	33	all	all	DET
ap-8497	10	34	practical	practical	ADJ
ap-8497	10	35	control	control	NOUN
ap-8497	10	36	systems	system	NOUN
ap-8497	10	37	.	.	PUNCT
ap-8497	11	1	a	a	DET
ap-8497	11	2	continuous	continuous	ADJ
ap-8497	11	3	homogeneous	homogeneous	ADJ
ap-8497	11	4	linear	linear	ADJ
ap-8497	11	5	time	time	NOUN
ap-8497	11	6	-	-	PUNCT
ap-8497	11	7	invariant	invariant	ADJ
ap-8497	11	8	descriptor	descriptor	NOUN
ap-8497	11	9	system	system	NOUN
ap-8497	11	10	,	,	PUNCT
ap-8497	11	11	i.e.	i.e.	X
ap-8497	11	12	differential	differential	ADJ
ap-8497	11	13	algebraic	algebraic	ADJ
ap-8497	11	14	equations	equation	NOUN
ap-8497	11	15	(	(	PUNCT
ap-8497	11	16	daes	daes	PROPN
ap-8497	11	17	)	)	PUNCT
ap-8497	11	18	can	can	AUX
ap-8497	11	19	be	be	AUX
ap-8497	11	20	written	write	VERB
ap-8497	11	21	as	as	ADP
ap-8497	11	22	:	:	PUNCT
ap-8497	11	23	eẋ(t	eẋ(t	NUM
ap-8497	11	24	)	)	PUNCT
ap-8497	11	25	=	=	SYM
ap-8497	11	26	ax(t	ax(t	NUM
ap-8497	11	27	)	)	PUNCT
ap-8497	11	28	,	,	PUNCT
ap-8497	11	29	(	(	PUNCT
ap-8497	11	30	1	1	X
ap-8497	11	31	)	)	PUNCT
ap-8497	11	32	where	where	SCONJ
ap-8497	11	33	x(t	x(t	PROPN
ap-8497	11	34	)	)	PUNCT
ap-8497	11	35	∈	∈	PROPN
ap-8497	11	36	rn	rn	PROPN
ap-8497	11	37	is	be	AUX
ap-8497	11	38	the	the	DET
ap-8497	11	39	state	state	NOUN
ap-8497	11	40	vector	vector	NOUN
ap-8497	11	41	and	and	CCONJ
ap-8497	11	42	e	e	NOUN
ap-8497	11	43	,	,	PUNCT
ap-8497	11	44	a	a	DET
ap-8497	11	45	∈	∈	ADJ
ap-8497	11	46	rn×n	rn×n	NOUN
ap-8497	11	47	are	be	AUX
ap-8497	11	48	the	the	DET
ap-8497	11	49	constant	constant	ADJ
ap-8497	11	50	matrices	matrix	NOUN
ap-8497	11	51	[	[	X
ap-8497	11	52	1	1	NUM
ap-8497	11	53	]	]	PUNCT
ap-8497	11	54	.	.	PUNCT
ap-8497	12	1	when	when	SCONJ
ap-8497	12	2	e	e	X
ap-8497	12	3	=	=	SYM
ap-8497	12	4	i	i	PROPN
ap-8497	12	5	(	(	PUNCT
ap-8497	12	6	identity	identity	NOUN
ap-8497	12	7	matrix	matrix	NOUN
ap-8497	12	8	)	)	PUNCT
ap-8497	12	9	,	,	PUNCT
ap-8497	12	10	system	system	NOUN
ap-8497	12	11	(	(	PUNCT
ap-8497	12	12	1	1	X
ap-8497	12	13	)	)	PUNCT
ap-8497	12	14	is	be	AUX
ap-8497	12	15	well	well	ADV
ap-8497	12	16	known	know	VERB
ap-8497	12	17	as	as	ADP
ap-8497	12	18	a	a	DET
ap-8497	12	19	state	state	NOUN
ap-8497	12	20	space	space	NOUN
ap-8497	12	21	system	system	NOUN
ap-8497	12	22	.	.	PUNCT
ap-8497	13	1	system	system	NOUN
ap-8497	13	2	(	(	PUNCT
ap-8497	13	3	1	1	X
ap-8497	13	4	)	)	PUNCT
ap-8497	13	5	is	be	AUX
ap-8497	13	6	called	call	VERB
ap-8497	13	7	regular	regular	ADJ
ap-8497	13	8	if	if	SCONJ
ap-8497	13	9	det(λe	det(λe	NUM
ap-8497	13	10	−	−	PROPN
ap-8497	13	11	a	a	X
ap-8497	13	12	)	)	PUNCT
ap-8497	13	13	is	be	AUX
ap-8497	13	14	not	not	PART
ap-8497	13	15	identically	identically	ADV
ap-8497	13	16	zero	zero	NUM
ap-8497	13	17	as	as	ADP
ap-8497	13	18	a	a	DET
ap-8497	13	19	polynomial	polynomial	NOUN
ap-8497	13	20	of	of	ADP
ap-8497	13	21	λ	λ	PROPN
ap-8497	14	1	[	[	X
ap-8497	14	2	2	2	NUM
ap-8497	14	3	,	,	PUNCT
ap-8497	14	4	3	3	NUM
ap-8497	14	5	]	]	PUNCT
ap-8497	14	6	.	.	PUNCT
ap-8497	15	1	a	a	DET
ap-8497	15	2	regular	regular	ADJ
ap-8497	15	3	system	system	NOUN
ap-8497	15	4	(	(	PUNCT
ap-8497	15	5	1	1	X
ap-8497	15	6	)	)	PUNCT
ap-8497	15	7	is	be	AUX
ap-8497	15	8	said	say	VERB
ap-8497	15	9	to	to	PART
ap-8497	15	10	be	be	AUX
ap-8497	15	11	stable	stable	ADJ
ap-8497	15	12	if	if	SCONJ
ap-8497	15	13	and	and	CCONJ
ap-8497	15	14	only	only	ADV
ap-8497	15	15	if	if	SCONJ
ap-8497	15	16	the	the	DET
ap-8497	15	17	matrix	matrix	NOUN
ap-8497	15	18	pair	pair	NOUN
ap-8497	15	19	(	(	PUNCT
ap-8497	15	20	e	e	NOUN
ap-8497	15	21	,	,	PUNCT
ap-8497	15	22	a	a	PRON
ap-8497	15	23	)	)	PUNCT
ap-8497	15	24	is	be	AUX
ap-8497	15	25	a	a	DET
ap-8497	15	26	stable	stable	ADJ
ap-8497	15	27	matrix	matrix	NOUN
ap-8497	15	28	pair	pair	NOUN
ap-8497	15	29	,	,	PUNCT
ap-8497	15	30	i.e.	i.e.	X
ap-8497	15	31	all	all	PRON
ap-8497	15	32	of	of	ADP
ap-8497	15	33	its	its	PRON
ap-8497	15	34	eigenvalues	eigenvalue	NOUN
ap-8497	15	35	have	have	VERB
ap-8497	15	36	negative	negative	ADJ
ap-8497	15	37	real	real	ADJ
ap-8497	15	38	parts	part	NOUN
ap-8497	15	39	.	.	PUNCT
ap-8497	16	1	in	in	ADP
ap-8497	16	2	order	order	NOUN
ap-8497	16	3	to	to	PART
ap-8497	16	4	find	find	VERB
ap-8497	16	5	the	the	DET
ap-8497	16	6	eigenvalues	eigenvalue	NOUN
ap-8497	16	7	of	of	ADP
ap-8497	16	8	the	the	DET
ap-8497	16	9	matrix	matrix	NOUN
ap-8497	16	10	pair	pair	NOUN
ap-8497	16	11	(	(	PUNCT
ap-8497	16	12	e	e	NOUN
ap-8497	16	13	,	,	PUNCT
ap-8497	16	14	a	a	PRON
ap-8497	16	15	)	)	PUNCT
ap-8497	16	16	,	,	PUNCT
ap-8497	16	17	we	we	PRON
ap-8497	16	18	have	have	VERB
ap-8497	16	19	to	to	PART
ap-8497	16	20	determine	determine	VERB
ap-8497	16	21	the	the	DET
ap-8497	16	22	roots	root	NOUN
ap-8497	16	23	of	of	ADP
ap-8497	16	24	the	the	DET
ap-8497	16	25	characteristic	characteristic	ADJ
ap-8497	16	26	equation	equation	NOUN
ap-8497	16	27	det(λe	det(λe	ADP
ap-8497	16	28	−	−	PROPN
ap-8497	16	29	a	a	X
ap-8497	16	30	)	)	PUNCT
ap-8497	16	31	=	=	SYM
ap-8497	17	1	0	0	X
ap-8497	17	2	.	.	PUNCT
ap-8497	18	1	it	it	PRON
ap-8497	18	2	is	be	AUX
ap-8497	18	3	remarkable	remarkable	ADJ
ap-8497	18	4	that	that	SCONJ
ap-8497	18	5	when	when	SCONJ
ap-8497	18	6	matrix	matrix	NOUN
ap-8497	18	7	e	e	NOUN
ap-8497	18	8	is	be	AUX
ap-8497	18	9	singular	singular	ADJ
ap-8497	18	10	,	,	PUNCT
ap-8497	18	11	the	the	DET
ap-8497	18	12	number	number	NOUN
ap-8497	18	13	of	of	ADP
ap-8497	18	14	eigenvalues	eigenvalue	NOUN
ap-8497	18	15	of	of	ADP
ap-8497	18	16	the	the	DET
ap-8497	18	17	matrix	matrix	NOUN
ap-8497	18	18	pair	pair	NOUN
ap-8497	18	19	(	(	PUNCT
ap-8497	18	20	e	e	NOUN
ap-8497	18	21	,	,	PUNCT
ap-8497	18	22	a	a	PRON
ap-8497	18	23	)	)	PUNCT
ap-8497	18	24	is	be	AUX
ap-8497	18	25	less	less	ADJ
ap-8497	18	26	than	than	SCONJ
ap-8497	18	27	n.	n.	VERB
ap-8497	18	28	this	this	DET
ap-8497	18	29	numerical	numerical	PROPN
ap-8497	18	30	eigenvalue	eigenvalue	PROPN
ap-8497	18	31	calculation	calculation	NOUN
ap-8497	18	32	of	of	ADP
ap-8497	18	33	a	a	DET
ap-8497	18	34	matrix	matrix	NOUN
ap-8497	18	35	pair	pair	NOUN
ap-8497	18	36	of	of	ADP
ap-8497	18	37	a	a	DET
ap-8497	18	38	higher	high	ADJ
ap-8497	18	39	order	order	NOUN
ap-8497	18	40	is	be	AUX
ap-8497	18	41	a	a	DET
ap-8497	18	42	computationally	computationally	ADV
ap-8497	18	43	intensive	intensive	ADJ
ap-8497	18	44	effort	effort	NOUN
ap-8497	18	45	.	.	PUNCT
ap-8497	19	1	to	to	PART
ap-8497	19	2	overcome	overcome	VERB
ap-8497	19	3	this	this	DET
ap-8497	19	4	drawback	drawback	NOUN
ap-8497	19	5	,	,	PUNCT
ap-8497	19	6	economists	economist	NOUN
ap-8497	19	7	have	have	AUX
ap-8497	19	8	introduced	introduce	VERB
ap-8497	19	9	the	the	DET
ap-8497	19	10	concept	concept	NOUN
ap-8497	19	11	of	of	ADP
ap-8497	19	12	‘	'	PUNCT
ap-8497	19	13	qualitative	qualitative	ADJ
ap-8497	19	14	stability	stability	NOUN
ap-8497	19	15	’	'	PUNCT
ap-8497	19	16	and	and	CCONJ
ap-8497	19	17	ecologists	ecologist	NOUN
ap-8497	19	18	have	have	AUX
ap-8497	19	19	derived	derive	VERB
ap-8497	19	20	some	some	DET
ap-8497	19	21	necessary	necessary	ADJ
ap-8497	19	22	and	and	CCONJ
ap-8497	19	23	sufficient	sufficient	ADJ
ap-8497	19	24	conditions	condition	NOUN
ap-8497	19	25	for	for	ADP
ap-8497	19	26	the	the	DET
ap-8497	19	27	stability	stability	NOUN
ap-8497	19	28	of	of	ADP
ap-8497	19	29	a	a	DET
ap-8497	19	30	matrix	matrix	NOUN
ap-8497	19	31	using	use	VERB
ap-8497	19	32	only	only	ADV
ap-8497	19	33	the	the	DET
ap-8497	19	34	sign	sign	NOUN
ap-8497	19	35	information	information	NOUN
ap-8497	19	36	of	of	ADP
ap-8497	19	37	matrix	matrix	NOUN
ap-8497	19	38	elements	element	NOUN
ap-8497	19	39	.	.	PUNCT
ap-8497	20	1	nonetheless	nonetheless	ADV
ap-8497	20	2	,	,	PUNCT
ap-8497	20	3	in	in	ADP
ap-8497	20	4	the	the	DET
ap-8497	20	5	literature	literature	NOUN
ap-8497	20	6	,	,	PUNCT
ap-8497	20	7	this	this	DET
ap-8497	20	8	problem	problem	NOUN
ap-8497	20	9	is	be	AUX
ap-8497	20	10	addressed	address	VERB
ap-8497	20	11	only	only	ADV
ap-8497	20	12	for	for	ADP
ap-8497	20	13	state	state	NOUN
ap-8497	20	14	space	space	NOUN
ap-8497	20	15	systems	system	NOUN
ap-8497	20	16	,	,	PUNCT
ap-8497	20	17	i.e.	i.e.	X
ap-8497	20	18	when	when	SCONJ
ap-8497	20	19	e	e	PROPN
ap-8497	20	20	=	=	SYM
ap-8497	20	21	i	i	PROPN
ap-8497	20	22	,	,	PUNCT
ap-8497	20	23	where	where	SCONJ
ap-8497	20	24	eigenvalues	eigenvalue	VERB
ap-8497	20	25	of	of	ADP
ap-8497	20	26	only	only	ADJ
ap-8497	20	27	matrix	matrix	NOUN
ap-8497	20	28	a	a	PRON
ap-8497	20	29	are	be	AUX
ap-8497	20	30	checked	check	VERB
ap-8497	20	31	.	.	PUNCT
ap-8497	21	1	this	this	DET
ap-8497	21	2	paper	paper	NOUN
ap-8497	21	3	extends	extend	VERB
ap-8497	21	4	these	these	DET
ap-8497	21	5	results	result	NOUN
ap-8497	21	6	for	for	ADP
ap-8497	21	7	checking	check	VERB
ap-8497	21	8	the	the	DET
ap-8497	21	9	eigenvalues	eigenvalue	NOUN
ap-8497	21	10	of	of	ADP
ap-8497	21	11	matrix	matrix	NOUN
ap-8497	21	12	pair	pair	NOUN
ap-8497	21	13	(	(	PUNCT
ap-8497	21	14	e	e	NOUN
ap-8497	21	15	,	,	PUNCT
ap-8497	21	16	a	a	PRON
ap-8497	21	17	)	)	PUNCT
ap-8497	21	18	.	.	PUNCT
ap-8497	22	1	in	in	ADP
ap-8497	22	2	this	this	DET
ap-8497	22	3	paper	paper	NOUN
ap-8497	22	4	,	,	PUNCT
ap-8497	22	5	the	the	DET
ap-8497	22	6	word	word	NOUN
ap-8497	22	7	‘	'	PUNCT
ap-8497	22	8	quantitative	quantitative	ADJ
ap-8497	22	9	’	'	PUNCT
ap-8497	22	10	is	be	AUX
ap-8497	22	11	used	use	VERB
ap-8497	22	12	for	for	ADP
ap-8497	22	13	both	both	DET
ap-8497	22	14	magnitude	magnitude	NOUN
ap-8497	22	15	and	and	CCONJ
ap-8497	22	16	sign	sign	VERB
ap-8497	22	17	information	information	NOUN
ap-8497	22	18	,	,	PUNCT
ap-8497	22	19	and	and	CCONJ
ap-8497	22	20	the	the	DET
ap-8497	22	21	word	word	NOUN
ap-8497	22	22	‘	'	PUNCT
ap-8497	22	23	qualitative	qualitative	NOUN
ap-8497	22	24	’	'	PUNCT
ap-8497	22	25	strictly	strictly	ADV
ap-8497	22	26	for	for	ADP
ap-8497	22	27	the	the	DET
ap-8497	22	28	sign	sign	NOUN
ap-8497	22	29	information	information	NOUN
ap-8497	22	30	with	with	ADP
ap-8497	22	31	no	no	DET
ap-8497	22	32	magnitude	magnitude	NOUN
ap-8497	22	33	information	information	NOUN
ap-8497	22	34	of	of	ADP
ap-8497	22	35	matrix	matrix	NOUN
ap-8497	22	36	elements	element	NOUN
ap-8497	22	37	.	.	PUNCT
ap-8497	23	1	matrix	matrix	NOUN
ap-8497	23	2	pairs	pair	NOUN
ap-8497	23	3	which	which	PRON
ap-8497	23	4	are	be	AUX
ap-8497	23	5	stable	stable	ADJ
ap-8497	23	6	,	,	PUNCT
ap-8497	23	7	independent	independent	ADJ
ap-8497	23	8	of	of	ADP
ap-8497	23	9	their	their	PRON
ap-8497	23	10	magnitudes	magnitude	NOUN
ap-8497	23	11	with	with	ADP
ap-8497	23	12	only	only	ADJ
ap-8497	23	13	sign	sign	VERB
ap-8497	23	14	information	information	NOUN
ap-8497	23	15	are	be	AUX
ap-8497	23	16	denoted	denote	VERB
ap-8497	23	17	as	as	SCONJ
ap-8497	23	18	qualitative	qualitative	ADJ
ap-8497	23	19	sign	sign	NOUN
ap-8497	23	20	stable	stable	ADJ
ap-8497	23	21	(	(	PUNCT
ap-8497	23	22	qlss	qlss	NUM
ap-8497	23	23	)	)	PUNCT
ap-8497	23	24	matrix	matrix	NOUN
ap-8497	23	25	pairs	pair	NOUN
ap-8497	23	26	and	and	CCONJ
ap-8497	23	27	qualitative	qualitative	ADJ
ap-8497	23	28	sign	sign	NOUN
ap-8497	23	29	unstable	unstable	ADJ
ap-8497	23	30	are	be	AUX
ap-8497	23	31	denoted	denote	VERB
ap-8497	23	32	as	as	ADP
ap-8497	23	33	‘	'	PUNCT
ap-8497	23	34	qlsu	qlsu	NOUN
ap-8497	23	35	’	'	PUNCT
ap-8497	23	36	matrix	matrix	NOUN
ap-8497	23	37	pairs	pair	NOUN
ap-8497	23	38	.	.	PUNCT
ap-8497	24	1	matrix	matrix	NOUN
ap-8497	24	2	pairs	pair	NOUN
ap-8497	24	3	,	,	PUNCT
ap-8497	24	4	whose	whose	DET
ap-8497	24	5	stability	stability	NOUN
ap-8497	24	6	/	/	SYM
ap-8497	24	7	instability	instability	NOUN
ap-8497	24	8	depend	depend	VERB
ap-8497	24	9	upon	upon	SCONJ
ap-8497	24	10	the	the	DET
ap-8497	24	11	magnitude	magnitude	NOUN
ap-8497	24	12	information	information	NOUN
ap-8497	24	13	of	of	ADP
ap-8497	24	14	the	the	DET
ap-8497	24	15	matrix	matrix	NOUN
ap-8497	24	16	pair	pair	NOUN
ap-8497	24	17	elements	element	NOUN
ap-8497	24	18	,	,	PUNCT
ap-8497	24	19	are	be	AUX
ap-8497	24	20	denoted	denote	VERB
ap-8497	24	21	as	as	ADP
ap-8497	24	22	magnitude	magnitude	NOUN
ap-8497	24	23	dependent	dependent	ADJ
ap-8497	24	24	stable	stable	ADJ
ap-8497	24	25	/	/	SYM
ap-8497	24	26	unstable	unstable	ADJ
ap-8497	24	27	(	(	PUNCT
ap-8497	24	28	mds	mds	PROPN
ap-8497	24	29	/	/	SYM
ap-8497	24	30	u	u	NOUN
ap-8497	24	31	)	)	PUNCT
ap-8497	24	32	matrix	matrix	NOUN
ap-8497	24	33	pairs	pair	NOUN
ap-8497	24	34	.	.	PUNCT
ap-8497	25	1	with	with	ADP
ap-8497	25	2	the	the	DET
ap-8497	25	3	knowledge	knowledge	NOUN
ap-8497	25	4	of	of	ADP
ap-8497	25	5	qualitative	qualitative	ADJ
ap-8497	25	6	sign	sign	NOUN
ap-8497	25	7	structure	structure	NOUN
ap-8497	25	8	,	,	PUNCT
ap-8497	25	9	we	we	PRON
ap-8497	25	10	can	can	AUX
ap-8497	25	11	now	now	ADV
ap-8497	25	12	discuss	discuss	VERB
ap-8497	25	13	the	the	DET
ap-8497	25	14	stability	stability	NOUN
ap-8497	25	15	of	of	ADP
ap-8497	25	16	a	a	DET
ap-8497	25	17	matrix	matrix	NOUN
ap-8497	25	18	pair	pair	NOUN
ap-8497	25	19	.	.	PUNCT
ap-8497	26	1	the	the	DET
ap-8497	26	2	analysis	analysis	NOUN
ap-8497	26	3	of	of	ADP
ap-8497	26	4	stability	stability	NOUN
ap-8497	26	5	of	of	ADP
ap-8497	26	6	matrices	matrix	NOUN
ap-8497	26	7	has	have	AUX
ap-8497	26	8	evoked	evoke	VERB
ap-8497	26	9	various	various	ADJ
ap-8497	26	10	research	research	NOUN
ap-8497	26	11	directions	direction	NOUN
ap-8497	26	12	.	.	PUNCT
ap-8497	27	1	the	the	DET
ap-8497	27	2	way	way	NOUN
ap-8497	27	3	non	non	NOUN
ap-8497	27	4	-	-	NOUN
ap-8497	27	5	engineers	engineer	NOUN
ap-8497	27	6	,	,	PUNCT
ap-8497	27	7	such	such	ADJ
ap-8497	27	8	as	as	ADP
ap-8497	27	9	ecologists	ecologist	NOUN
ap-8497	27	10	and	and	CCONJ
ap-8497	27	11	economists	economist	NOUN
ap-8497	27	12	,	,	PUNCT
ap-8497	27	13	have	have	AUX
ap-8497	27	14	tackled	tackle	VERB
ap-8497	27	15	this	this	DET
ap-8497	27	16	problem	problem	NOUN
ap-8497	27	17	without	without	ADP
ap-8497	27	18	even	even	ADV
ap-8497	27	19	having	have	VERB
ap-8497	27	20	any	any	DET
ap-8497	27	21	magnitude	magnitude	NOUN
ap-8497	27	22	information	information	NOUN
ap-8497	27	23	is	be	AUX
ap-8497	27	24	fascinating	fascinating	ADJ
ap-8497	27	25	.	.	PUNCT
ap-8497	28	1	in	in	ADP
ap-8497	28	2	[	[	X
ap-8497	28	3	4	4	NUM
ap-8497	28	4	]	]	PUNCT
ap-8497	28	5	,	,	PUNCT
ap-8497	28	6	the	the	DET
ap-8497	28	7	stability	stability	NOUN
ap-8497	28	8	problem	problem	NOUN
ap-8497	28	9	of	of	ADP
ap-8497	28	10	a	a	DET
ap-8497	28	11	matrix	matrix	NOUN
ap-8497	28	12	is	be	AUX
ap-8497	28	13	studied	study	VERB
ap-8497	28	14	in	in	ADP
ap-8497	28	15	a	a	DET
ap-8497	28	16	purely	purely	ADV
ap-8497	28	17	qualitative	qualitative	ADJ
ap-8497	28	18	environment	environment	NOUN
ap-8497	28	19	assuming	assume	VERB
ap-8497	28	20	that	that	SCONJ
ap-8497	28	21	quantitative	quantitative	ADJ
ap-8497	28	22	information	information	NOUN
ap-8497	28	23	is	be	AUX
ap-8497	28	24	unavailable	unavailable	ADJ
ap-8497	28	25	.	.	PUNCT
ap-8497	29	1	article	article	NOUN
ap-8497	29	2	[	[	X
ap-8497	29	3	5	5	X
ap-8497	29	4	]	]	PUNCT
ap-8497	29	5	provides	provide	VERB
ap-8497	29	6	some	some	DET
ap-8497	29	7	sufficient	sufficient	ADJ
ap-8497	29	8	conditions	condition	NOUN
ap-8497	29	9	for	for	ADP
ap-8497	29	10	the	the	DET
ap-8497	29	11	qualitative	qualitative	ADJ
ap-8497	29	12	stability	stability	NOUN
ap-8497	29	13	of	of	ADP
ap-8497	29	14	an	an	DET
ap-8497	29	15	ecosystem	ecosystem	NOUN
ap-8497	29	16	by	by	ADP
ap-8497	29	17	simply	simply	ADV
ap-8497	29	18	concluding	conclude	VERB
ap-8497	29	19	the	the	DET
ap-8497	29	20	mutual	mutual	ADJ
ap-8497	29	21	qualitative	qualitative	ADJ
ap-8497	29	22	effects	effect	NOUN
ap-8497	29	23	on	on	ADP
ap-8497	29	24	member	member	NOUN
ap-8497	29	25	species	specie	NOUN
ap-8497	29	26	via	via	ADP
ap-8497	29	27	signed	sign	VERB
ap-8497	29	28	digraphs	digraph	NOUN
ap-8497	29	29	,	,	PUNCT
ap-8497	29	30	whereas	whereas	SCONJ
ap-8497	29	31	necessary	necessary	ADJ
ap-8497	29	32	conditions	condition	NOUN
ap-8497	29	33	for	for	ADP
ap-8497	29	34	the	the	DET
ap-8497	29	35	qualitative	qualitative	ADJ
ap-8497	29	36	stability	stability	NOUN
ap-8497	29	37	are	be	AUX
ap-8497	29	38	presented	present	VERB
ap-8497	29	39	in	in	ADP
ap-8497	29	40	[	[	X
ap-8497	29	41	6	6	NUM
ap-8497	29	42	]	]	PUNCT
ap-8497	29	43	.	.	PUNCT
ap-8497	30	1	in	in	ADP
ap-8497	30	2	[	[	X
ap-8497	30	3	7	7	NUM
ap-8497	30	4	]	]	PUNCT
ap-8497	30	5	,	,	PUNCT
ap-8497	30	6	linear	linear	PROPN
ap-8497	30	7	systems	system	NOUN
ap-8497	30	8	are	be	AUX
ap-8497	30	9	studied	study	VERB
ap-8497	30	10	based	base	VERB
ap-8497	30	11	on	on	ADP
ap-8497	30	12	the	the	DET
ap-8497	30	13	qualitative	qualitative	ADJ
ap-8497	30	14	theory	theory	NOUN
ap-8497	30	15	.	.	PUNCT
ap-8497	31	1	some	some	DET
ap-8497	31	2	conditions	condition	NOUN
ap-8497	31	3	concerning	concern	VERB
ap-8497	31	4	the	the	DET
ap-8497	31	5	structural	structural	ADJ
ap-8497	31	6	qualitative	qualitative	ADJ
ap-8497	31	7	stability	stability	NOUN
ap-8497	31	8	of	of	ADP
ap-8497	31	9	a	a	DET
ap-8497	31	10	system	system	NOUN
ap-8497	31	11	are	be	AUX
ap-8497	31	12	proposed	propose	VERB
ap-8497	31	13	in	in	ADP
ap-8497	31	14	[	[	X
ap-8497	31	15	8	8	NUM
ap-8497	31	16	]	]	PUNCT
ap-8497	31	17	.	.	PUNCT
ap-8497	32	1	a	a	DET
ap-8497	32	2	graph	graph	NOUN
ap-8497	32	3	-	-	PUNCT
ap-8497	32	4	theoretic	theoretic	NOUN
ap-8497	32	5	analysis	analysis	NOUN
ap-8497	32	6	based	base	VERB
ap-8497	32	7	on	on	ADP
ap-8497	32	8	sign	sign	NOUN
ap-8497	32	9	patterns	pattern	NOUN
ap-8497	32	10	of	of	ADP
ap-8497	32	11	a	a	DET
ap-8497	32	12	real	real	ADJ
ap-8497	32	13	square	square	ADJ
ap-8497	32	14	matrix	matrix	NOUN
ap-8497	32	15	is	be	AUX
ap-8497	32	16	used	use	VERB
ap-8497	32	17	to	to	PART
ap-8497	32	18	conclude	conclude	VERB
ap-8497	32	19	the	the	DET
ap-8497	32	20	stability	stability	NOUN
ap-8497	32	21	of	of	ADP
ap-8497	32	22	a	a	DET
ap-8497	32	23	linear	linear	ADJ
ap-8497	32	24	system	system	NOUN
ap-8497	32	25	in	in	ADP
ap-8497	32	26	[	[	X
ap-8497	32	27	9	9	NUM
ap-8497	32	28	]	]	PUNCT
ap-8497	32	29	.	.	PUNCT
ap-8497	33	1	in	in	ADP
ap-8497	33	2	[	[	X
ap-8497	33	3	10	10	NUM
ap-8497	33	4	]	]	PUNCT
ap-8497	33	5	,	,	PUNCT
ap-8497	33	6	it	it	PRON
ap-8497	33	7	has	have	AUX
ap-8497	33	8	been	be	AUX
ap-8497	33	9	shown	show	VERB
ap-8497	33	10	that	that	SCONJ
ap-8497	33	11	in	in	ADP
ap-8497	33	12	a	a	DET
ap-8497	33	13	complex	complex	ADJ
ap-8497	33	14	ecological	ecological	ADJ
ap-8497	33	15	system	system	NOUN
ap-8497	33	16	,	,	PUNCT
ap-8497	33	17	when	when	SCONJ
ap-8497	33	18	species	specie	NOUN
ap-8497	33	19	interact	interact	VERB
ap-8497	33	20	as	as	ADP
ap-8497	33	21	predator	predator	NOUN
ap-8497	33	22	-	-	PUNCT
ap-8497	33	23	prey	prey	NOUN
ap-8497	33	24	,	,	PUNCT
ap-8497	33	25	the	the	DET
ap-8497	33	26	system	system	NOUN
ap-8497	33	27	can	can	AUX
ap-8497	33	28	still	still	ADV
ap-8497	33	29	be	be	AUX
ap-8497	33	30	stable	stable	ADJ
ap-8497	33	31	.	.	PUNCT
ap-8497	34	1	in	in	ADP
ap-8497	34	2	[	[	X
ap-8497	34	3	11	11	NUM
ap-8497	34	4	,	,	PUNCT
ap-8497	34	5	12	12	NUM
ap-8497	34	6	]	]	PUNCT
ap-8497	34	7	,	,	PUNCT
ap-8497	34	8	ecological	ecological	ADJ
ap-8497	34	9	-	-	PUNCT
ap-8497	34	10	sign	sign	NOUN
ap-8497	34	11	stability	stability	NOUN
ap-8497	34	12	pricnciples	pricnciple	NOUN
ap-8497	34	13	of	of	ADP
ap-8497	34	14	a	a	DET
ap-8497	34	15	matrix	matrix	NOUN
ap-8497	34	16	are	be	AUX
ap-8497	34	17	transformed	transform	VERB
ap-8497	34	18	into	into	ADP
ap-8497	34	19	mathematical	mathematical	ADJ
ap-8497	34	20	principles	principle	NOUN
ap-8497	34	21	171	171	NUM
ap-8497	34	22	https://doi.org/10.14311/ap.2023.63.0171	https://doi.org/10.14311/ap.2023.63.0171	PROPN
ap-8497	34	23	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-8497	34	24	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-8497	34	25	m.	m.	PROPN
ap-8497	34	26	chand	chand	PROPN
ap-8497	34	27	,	,	PUNCT
ap-8497	34	28	m.	m.	NOUN
ap-8497	34	29	paitandi	paitandi	PROPN
ap-8497	34	30	,	,	PUNCT
ap-8497	34	31	m.	m.	PROPN
ap-8497	34	32	k.	k.	PROPN
ap-8497	34	33	gupta	gupta	PROPN
ap-8497	34	34	acta	acta	PROPN
ap-8497	34	35	polytechnica	polytechnica	PROPN
ap-8497	34	36	to	to	PART
ap-8497	34	37	encounter	encounter	VERB
ap-8497	34	38	stability	stability	NOUN
ap-8497	34	39	problems	problem	NOUN
ap-8497	34	40	in	in	ADP
ap-8497	34	41	engineering	engineering	NOUN
ap-8497	34	42	control	control	NOUN
ap-8497	34	43	systems	system	NOUN
ap-8497	34	44	.	.	PUNCT
ap-8497	35	1	the	the	DET
ap-8497	35	2	qualitative	qualitative	ADJ
ap-8497	35	3	analysis	analysis	NOUN
ap-8497	35	4	of	of	ADP
ap-8497	35	5	control	control	NOUN
ap-8497	35	6	systems	system	NOUN
ap-8497	35	7	is	be	AUX
ap-8497	35	8	explained	explain	VERB
ap-8497	35	9	in	in	ADP
ap-8497	35	10	[	[	PUNCT
ap-8497	35	11	13	13	NUM
ap-8497	35	12	]	]	PUNCT
ap-8497	35	13	.	.	PUNCT
ap-8497	36	1	the	the	DET
ap-8497	36	2	stability	stability	NOUN
ap-8497	36	3	of	of	ADP
ap-8497	36	4	the	the	DET
ap-8497	36	5	continuous	continuous	ADJ
ap-8497	36	6	-	-	PUNCT
ap-8497	36	7	time	time	NOUN
ap-8497	36	8	linear	linear	PROPN
ap-8497	36	9	state	state	NOUN
ap-8497	36	10	space	space	NOUN
ap-8497	36	11	system	system	NOUN
ap-8497	36	12	is	be	AUX
ap-8497	36	13	explained	explain	VERB
ap-8497	36	14	in	in	ADP
ap-8497	36	15	[	[	X
ap-8497	36	16	14	14	NUM
ap-8497	36	17	]	]	PUNCT
ap-8497	36	18	and	and	CCONJ
ap-8497	36	19	the	the	DET
ap-8497	36	20	stability	stability	NOUN
ap-8497	36	21	of	of	ADP
ap-8497	36	22	discrete	discrete	ADJ
ap-8497	36	23	-	-	PUNCT
ap-8497	36	24	time	time	NOUN
ap-8497	36	25	system	system	NOUN
ap-8497	36	26	is	be	AUX
ap-8497	36	27	explained	explain	VERB
ap-8497	36	28	in	in	ADP
ap-8497	36	29	[	[	X
ap-8497	36	30	15	15	NUM
ap-8497	36	31	]	]	PUNCT
ap-8497	36	32	.	.	PUNCT
ap-8497	37	1	the	the	DET
ap-8497	37	2	series	series	NOUN
ap-8497	37	3	of	of	ADP
ap-8497	37	4	papers	paper	NOUN
ap-8497	37	5	[	[	X
ap-8497	37	6	16	16	NUM
ap-8497	37	7	]	]	PUNCT
ap-8497	37	8	,	,	PUNCT
ap-8497	37	9	[	[	X
ap-8497	37	10	17	17	NUM
ap-8497	37	11	]	]	PUNCT
ap-8497	37	12	,	,	PUNCT
ap-8497	37	13	and	and	CCONJ
ap-8497	37	14	[	[	X
ap-8497	37	15	18	18	NUM
ap-8497	37	16	]	]	PUNCT
ap-8497	37	17	were	be	AUX
ap-8497	37	18	attempts	attempt	NOUN
ap-8497	37	19	to	to	PART
ap-8497	37	20	find	find	VERB
ap-8497	37	21	the	the	DET
ap-8497	37	22	conditions	condition	NOUN
ap-8497	37	23	for	for	ADP
ap-8497	37	24	stability	stability	NOUN
ap-8497	37	25	/	/	SYM
ap-8497	37	26	instability	instability	NOUN
ap-8497	37	27	of	of	ADP
ap-8497	37	28	real	real	ADJ
ap-8497	37	29	matrices	matrix	NOUN
ap-8497	37	30	using	use	VERB
ap-8497	37	31	qualitative	qualitative	ADJ
ap-8497	37	32	reasoning	reasoning	NOUN
ap-8497	37	33	.	.	PUNCT
ap-8497	38	1	in	in	ADP
ap-8497	38	2	[	[	X
ap-8497	38	3	16	16	NUM
ap-8497	38	4	]	]	X
ap-8497	38	5	,	,	PUNCT
ap-8497	38	6	few	few	ADJ
ap-8497	38	7	conditions	condition	NOUN
ap-8497	38	8	for	for	ADP
ap-8497	38	9	qualitative	qualitative	ADJ
ap-8497	38	10	sign	sign	NOUN
ap-8497	38	11	instability	instability	NOUN
ap-8497	38	12	of	of	ADP
ap-8497	38	13	a	a	DET
ap-8497	38	14	matrix	matrix	NOUN
ap-8497	38	15	are	be	AUX
ap-8497	38	16	derived	derive	VERB
ap-8497	38	17	in	in	ADP
ap-8497	38	18	terms	term	NOUN
ap-8497	38	19	of	of	ADP
ap-8497	38	20	the	the	DET
ap-8497	38	21	nature	nature	NOUN
ap-8497	38	22	of	of	ADP
ap-8497	38	23	interactions	interaction	NOUN
ap-8497	38	24	and	and	CCONJ
ap-8497	38	25	interconnections	interconnection	NOUN
ap-8497	38	26	,	,	PUNCT
ap-8497	38	27	taken	take	VERB
ap-8497	38	28	from	from	ADP
ap-8497	38	29	ecological	ecological	ADJ
ap-8497	38	30	principles	principle	NOUN
ap-8497	38	31	.	.	PUNCT
ap-8497	39	1	the	the	DET
ap-8497	39	2	stability	stability	NOUN
ap-8497	39	3	analysis	analysis	NOUN
ap-8497	39	4	of	of	ADP
ap-8497	39	5	a	a	DET
ap-8497	39	6	matrix	matrix	NOUN
ap-8497	39	7	using	use	VERB
ap-8497	39	8	these	these	DET
ap-8497	39	9	conditions	condition	NOUN
ap-8497	39	10	requires	require	VERB
ap-8497	39	11	only	only	ADV
ap-8497	39	12	the	the	DET
ap-8497	39	13	qualitative	qualitative	NOUN
ap-8497	39	14	(	(	PUNCT
ap-8497	39	15	sign	sign	NOUN
ap-8497	39	16	)	)	PUNCT
ap-8497	39	17	information	information	NOUN
ap-8497	39	18	of	of	ADP
ap-8497	39	19	the	the	DET
ap-8497	39	20	matrix	matrix	NOUN
ap-8497	39	21	elements	element	NOUN
ap-8497	39	22	(	(	PUNCT
ap-8497	39	23	no	no	DET
ap-8497	39	24	need	need	NOUN
ap-8497	39	25	for	for	ADP
ap-8497	39	26	any	any	DET
ap-8497	39	27	quantitative	quantitative	ADJ
ap-8497	39	28	information	information	NOUN
ap-8497	39	29	)	)	PUNCT
ap-8497	39	30	.	.	PUNCT
ap-8497	40	1	in	in	ADP
ap-8497	40	2	[	[	X
ap-8497	40	3	17	17	NUM
ap-8497	40	4	]	]	X
ap-8497	40	5	,	,	PUNCT
ap-8497	40	6	an	an	DET
ap-8497	40	7	alternative	alternative	ADJ
ap-8497	40	8	sufficient	sufficient	ADJ
ap-8497	40	9	condition	condition	NOUN
ap-8497	40	10	is	be	AUX
ap-8497	40	11	proposed	propose	VERB
ap-8497	40	12	by	by	ADP
ap-8497	40	13	combining	combine	VERB
ap-8497	40	14	the	the	DET
ap-8497	40	15	concepts	concept	NOUN
ap-8497	40	16	of	of	ADP
ap-8497	40	17	both	both	CCONJ
ap-8497	40	18	quantitative	quantitative	ADJ
ap-8497	40	19	(	(	PUNCT
ap-8497	40	20	magnitude	magnitude	NOUN
ap-8497	40	21	and	and	CCONJ
ap-8497	40	22	sign	sign	VERB
ap-8497	40	23	)	)	PUNCT
ap-8497	40	24	as	as	ADV
ap-8497	40	25	well	well	ADV
ap-8497	40	26	as	as	ADP
ap-8497	40	27	the	the	DET
ap-8497	40	28	qualitative	qualitative	NOUN
ap-8497	40	29	(	(	PUNCT
ap-8497	40	30	only	only	ADV
ap-8497	40	31	sign	sign	NOUN
ap-8497	40	32	)	)	PUNCT
ap-8497	40	33	information	information	NOUN
ap-8497	40	34	of	of	ADP
ap-8497	40	35	the	the	DET
ap-8497	40	36	matrix	matrix	NOUN
ap-8497	40	37	elements	element	NOUN
ap-8497	40	38	.	.	PUNCT
ap-8497	41	1	this	this	DET
ap-8497	41	2	condition	condition	NOUN
ap-8497	41	3	possesses	possess	VERB
ap-8497	41	4	a	a	DET
ap-8497	41	5	convexity	convexity	NOUN
ap-8497	41	6	promotion	promotion	NOUN
ap-8497	41	7	property	property	NOUN
ap-8497	41	8	with	with	ADP
ap-8497	41	9	respect	respect	NOUN
ap-8497	41	10	to	to	ADP
ap-8497	41	11	stability	stability	NOUN
ap-8497	41	12	.	.	PUNCT
ap-8497	42	1	a	a	DET
ap-8497	42	2	new	new	ADJ
ap-8497	42	3	necessary	necessary	ADJ
ap-8497	42	4	and	and	CCONJ
ap-8497	42	5	sufficient	sufficient	ADJ
ap-8497	42	6	condition	condition	NOUN
ap-8497	42	7	is	be	AUX
ap-8497	42	8	proposed	propose	VERB
ap-8497	42	9	in	in	ADP
ap-8497	42	10	[	[	X
ap-8497	42	11	18	18	NUM
ap-8497	42	12	]	]	PUNCT
ap-8497	42	13	,	,	PUNCT
ap-8497	42	14	for	for	ADP
ap-8497	42	15	the	the	DET
ap-8497	42	16	stability	stability	NOUN
ap-8497	42	17	of	of	ADP
ap-8497	42	18	any	any	DET
ap-8497	42	19	real	real	ADJ
ap-8497	42	20	matrix	matrix	NOUN
ap-8497	42	21	that	that	PRON
ap-8497	42	22	does	do	AUX
ap-8497	42	23	not	not	PART
ap-8497	42	24	need	need	VERB
ap-8497	42	25	the	the	DET
ap-8497	42	26	information	information	NOUN
ap-8497	42	27	of	of	ADP
ap-8497	42	28	the	the	DET
ap-8497	42	29	characteristic	characteristic	ADJ
ap-8497	42	30	polynomial	polynomial	NOUN
ap-8497	42	31	,	,	PUNCT
ap-8497	42	32	and	and	CCONJ
ap-8497	42	33	it	it	PRON
ap-8497	42	34	is	be	AUX
ap-8497	42	35	based	base	VERB
ap-8497	42	36	on	on	ADP
ap-8497	42	37	matrix	matrix	NOUN
ap-8497	42	38	entries	entry	NOUN
ap-8497	42	39	’	'	PUNCT
ap-8497	42	40	sign	sign	VERB
ap-8497	42	41	information	information	NOUN
ap-8497	42	42	only	only	ADV
ap-8497	42	43	.	.	PUNCT
ap-8497	43	1	article	article	NOUN
ap-8497	43	2	[	[	X
ap-8497	43	3	19	19	NUM
ap-8497	43	4	]	]	X
ap-8497	43	5	studies	study	NOUN
ap-8497	43	6	asymptotic	asymptotic	ADJ
ap-8497	43	7	stability	stability	NOUN
ap-8497	43	8	criteria	criterion	NOUN
ap-8497	43	9	for	for	ADP
ap-8497	43	10	time	time	NOUN
ap-8497	43	11	-	-	PUNCT
ap-8497	43	12	delayed	delay	VERB
ap-8497	43	13	systems	system	NOUN
ap-8497	43	14	.	.	PUNCT
ap-8497	44	1	remarkable	remarkable	ADJ
ap-8497	44	2	works	work	NOUN
ap-8497	44	3	have	have	AUX
ap-8497	44	4	been	be	AUX
ap-8497	44	5	done	do	VERB
ap-8497	44	6	in	in	ADP
ap-8497	44	7	[	[	X
ap-8497	44	8	20	20	NUM
ap-8497	44	9	,	,	PUNCT
ap-8497	44	10	21	21	NUM
ap-8497	44	11	]	]	PUNCT
ap-8497	44	12	on	on	ADP
ap-8497	44	13	matrices	matrix	NOUN
ap-8497	44	14	with	with	ADP
ap-8497	44	15	stable	stable	ADJ
ap-8497	44	16	sign	sign	NOUN
ap-8497	44	17	patterns	pattern	NOUN
ap-8497	44	18	.	.	PUNCT
ap-8497	45	1	however	however	ADV
ap-8497	45	2	,	,	PUNCT
ap-8497	45	3	all	all	DET
ap-8497	45	4	the	the	DET
ap-8497	45	5	existing	exist	VERB
ap-8497	45	6	research	research	NOUN
ap-8497	45	7	is	be	AUX
ap-8497	45	8	focused	focus	VERB
ap-8497	45	9	on	on	ADP
ap-8497	45	10	the	the	DET
ap-8497	45	11	stability	stability	NOUN
ap-8497	45	12	of	of	ADP
ap-8497	45	13	a	a	DET
ap-8497	45	14	matrix	matrix	NOUN
ap-8497	45	15	confining	confine	VERB
ap-8497	45	16	its	its	PRON
ap-8497	45	17	utility	utility	NOUN
ap-8497	45	18	to	to	PART
ap-8497	45	19	only	only	ADV
ap-8497	45	20	linear	linear	VERB
ap-8497	45	21	normal	normal	ADJ
ap-8497	45	22	state	state	NOUN
ap-8497	45	23	space	space	NOUN
ap-8497	45	24	systems	system	NOUN
ap-8497	45	25	,	,	PUNCT
ap-8497	45	26	and	and	CCONJ
ap-8497	45	27	improving	improve	VERB
ap-8497	45	28	on	on	ADP
ap-8497	45	29	these	these	DET
ap-8497	45	30	papers	paper	NOUN
ap-8497	45	31	,	,	PUNCT
ap-8497	45	32	this	this	DET
ap-8497	45	33	paper	paper	NOUN
ap-8497	45	34	generalises	generalise	VERB
ap-8497	45	35	some	some	PRON
ap-8497	45	36	of	of	ADP
ap-8497	45	37	these	these	DET
ap-8497	45	38	conditions	condition	NOUN
ap-8497	45	39	for	for	ADP
ap-8497	45	40	qualitative	qualitative	ADJ
ap-8497	45	41	stability	stability	NOUN
ap-8497	45	42	/	/	SYM
ap-8497	45	43	instability	instability	NOUN
ap-8497	45	44	of	of	ADP
ap-8497	45	45	a	a	DET
ap-8497	45	46	matrix	matrix	NOUN
ap-8497	45	47	pair	pair	NOUN
ap-8497	45	48	that	that	PRON
ap-8497	45	49	have	have	VERB
ap-8497	45	50	a	a	DET
ap-8497	45	51	relatively	relatively	ADV
ap-8497	45	52	broader	broad	ADJ
ap-8497	45	53	scope	scope	NOUN
ap-8497	45	54	in	in	ADP
ap-8497	45	55	the	the	DET
ap-8497	45	56	analysis	analysis	NOUN
ap-8497	45	57	of	of	ADP
ap-8497	45	58	linear	linear	PROPN
ap-8497	45	59	square	square	ADJ
ap-8497	45	60	descriptor	descriptor	NOUN
ap-8497	45	61	systems	system	NOUN
ap-8497	45	62	in	in	ADP
ap-8497	45	63	control	control	NOUN
ap-8497	45	64	engineering	engineering	NOUN
ap-8497	45	65	.	.	PUNCT
ap-8497	46	1	to	to	ADP
ap-8497	46	2	the	the	DET
ap-8497	46	3	best	good	ADJ
ap-8497	46	4	of	of	ADP
ap-8497	46	5	our	our	PRON
ap-8497	46	6	knowledge	knowledge	NOUN
ap-8497	46	7	,	,	PUNCT
ap-8497	46	8	this	this	PRON
ap-8497	46	9	is	be	AUX
ap-8497	46	10	the	the	DET
ap-8497	46	11	first	first	ADJ
ap-8497	46	12	work	work	NOUN
ap-8497	46	13	discussing	discuss	VERB
ap-8497	46	14	the	the	DET
ap-8497	46	15	qualitative	qualitative	ADJ
ap-8497	46	16	sign	sign	NOUN
ap-8497	46	17	stability	stability	NOUN
ap-8497	46	18	for	for	ADP
ap-8497	46	19	a	a	DET
ap-8497	46	20	matrix	matrix	NOUN
ap-8497	46	21	pair	pair	NOUN
ap-8497	46	22	.	.	PUNCT
ap-8497	47	1	for	for	ADP
ap-8497	47	2	a	a	DET
ap-8497	47	3	proper	proper	ADJ
ap-8497	47	4	perspective	perspective	NOUN
ap-8497	47	5	,	,	PUNCT
ap-8497	47	6	let	let	VERB
ap-8497	47	7	us	we	PRON
ap-8497	47	8	consider	consider	VERB
ap-8497	47	9	the	the	DET
ap-8497	47	10	following	follow	VERB
ap-8497	47	11	matrix	matrix	NOUN
ap-8497	47	12	pairs	pair	NOUN
ap-8497	47	13	(	(	PUNCT
ap-8497	47	14	ei	ei	NOUN
ap-8497	47	15	,	,	PUNCT
ap-8497	47	16	ai	ai	NOUN
ap-8497	47	17	)	)	PUNCT
ap-8497	47	18	,	,	PUNCT
ap-8497	47	19	i	i	PRON
ap-8497	47	20	=	=	NOUN
ap-8497	47	21	1	1	NUM
ap-8497	47	22	,	,	PUNCT
ap-8497	47	23	2	2	NUM
ap-8497	47	24	:	:	PUNCT
ap-8497	47	25	e1	e1	NOUN
ap-8497	47	26	=	=	SYM
ap-8497	47	27			NOUN
ap-8497	47	28	−3	−3	NOUN
ap-8497	47	29	−2	−2	NOUN
ap-8497	47	30	0.1	0.1	NUM
ap-8497	47	31	0.4	0.4	NUM
ap-8497	47	32	−1	−1	NOUN
ap-8497	47	33	0.9	0.9	NUM
ap-8497	47	34	−0.3	−0.3	PROPN
ap-8497	48	1	−8	−8	X
ap-8497	49	1	−0.7	−0.7	NOUN
ap-8497	49	2	5	5	NUM
ap-8497	49	3	3	3	NUM
ap-8497	49	4	1	1	NUM
ap-8497	49	5	0.1	0.1	NUM
ap-8497	49	6	2	2	NUM
ap-8497	49	7	1.4	1.4	NUM
ap-8497	49	8	5	5	NUM
ap-8497	49	9			NOUN
ap-8497	49	10	,	,	PUNCT
ap-8497	49	11	a1	a1	NOUN
ap-8497	49	12	=	=	SYM
ap-8497	49	13			NOUN
ap-8497	49	14	2	2	NUM
ap-8497	49	15	−1	−1	NOUN
ap-8497	49	16	−3	−3	NOUN
ap-8497	49	17	0.5	0.5	NUM
ap-8497	49	18	0.3	0.3	NUM
ap-8497	49	19	−1	−1	NOUN
ap-8497	49	20	0.4	0.4	NUM
ap-8497	49	21	−2	−2	NOUN
ap-8497	49	22	−0.1	−0.1	PROPN
ap-8497	49	23	3	3	NUM
ap-8497	49	24	−0.5	−0.5	NUM
ap-8497	49	25	4	4	NUM
ap-8497	49	26	−2	−2	NOUN
ap-8497	49	27	−0.2	−0.2	NOUN
ap-8497	49	28	1	1	NUM
ap-8497	49	29	0.7	0.7	NUM
ap-8497	49	30			NOUN
ap-8497	49	31	,	,	PUNCT
ap-8497	49	32	e2	e2	PROPN
ap-8497	49	33	=	=	PUNCT
ap-8497	49	34			NOUN
ap-8497	49	35	1	1	NUM
ap-8497	49	36	−0.2	−0.2	PROPN
ap-8497	49	37	0.8	0.8	NUM
ap-8497	49	38	−3.5	−3.5	PROPN
ap-8497	49	39	−4.1	−4.1	PROPN
ap-8497	49	40	1.9	1.9	NUM
ap-8497	49	41	−2.7	−2.7	NUM
ap-8497	49	42	−3.3	−3.3	PROPN
ap-8497	49	43	4	4	NUM
ap-8497	49	44	−0.1	−0.1	PROPN
ap-8497	49	45	−1.2	−1.2	PROPN
ap-8497	49	46	−0.4	−0.4	NUM
ap-8497	49	47	2	2	NUM
ap-8497	49	48	−0.5	−0.5	NOUN
ap-8497	49	49	−4.8	−4.8	VERB
ap-8497	49	50	−0.3	−0.3	PROPN
ap-8497	50	1	−1.7	−1.7	PROPN
ap-8497	51	1	−4.3	−4.3	PROPN
ap-8497	51	2	−3.7	−3.7	NOUN
ap-8497	51	3	0.2	0.2	NUM
ap-8497	51	4	0.6	0.6	NUM
ap-8497	51	5	−2.5	−2.5	NUM
ap-8497	51	6	0.9	0.9	NUM
ap-8497	51	7	−5.2	−5.2	NOUN
ap-8497	52	1	−2.3	−2.3	NOUN
ap-8497	52	2			NOUN
ap-8497	52	3	,	,	PUNCT
ap-8497	52	4	a2	a2	PROPN
ap-8497	52	5	=	=	X
ap-8497	52	6			NUM
ap-8497	53	1	−1	−1	NOUN
ap-8497	53	2	0.2	0.2	NUM
ap-8497	53	3	−3	−3	NOUN
ap-8497	54	1	−0.7	−0.7	PROPN
ap-8497	54	2	5	5	NUM
ap-8497	54	3	−0.9	−0.9	NOUN
ap-8497	54	4	1.3	1.3	NUM
ap-8497	54	5	2.4	2.4	NUM
ap-8497	54	6	−1.2	−1.2	NOUN
ap-8497	54	7	−3.1	−3.1	PROPN
ap-8497	54	8	4.8	4.8	NUM
ap-8497	54	9	−1.1	−1.1	NOUN
ap-8497	54	10	−2	−2	NOUN
ap-8497	54	11	−0.4	−0.4	NUM
ap-8497	55	1	4.3	4.3	NUM
ap-8497	55	2	2.7	2.7	NUM
ap-8497	55	3	1	1	NUM
ap-8497	55	4	−1.8	−1.8	PROPN
ap-8497	55	5	1.7	1.7	NUM
ap-8497	55	6	−0.7	−0.7	NOUN
ap-8497	55	7	−5	−5	PUNCT
ap-8497	55	8	−3.2	−3.2	NOUN
ap-8497	55	9	0.3	0.3	NUM
ap-8497	55	10	−2.9	−2.9	NOUN
ap-8497	55	11	−1.5	−1.5	PROPN
ap-8497	55	12			NOUN
ap-8497	55	13	.	.	PUNCT
ap-8497	56	1	it	it	PRON
ap-8497	56	2	is	be	AUX
ap-8497	56	3	very	very	ADV
ap-8497	56	4	much	much	ADV
ap-8497	56	5	difficult	difficult	ADJ
ap-8497	56	6	to	to	PART
ap-8497	56	7	decide	decide	VERB
ap-8497	56	8	the	the	DET
ap-8497	56	9	stability	stability	NOUN
ap-8497	56	10	/	/	SYM
ap-8497	56	11	instability	instability	NOUN
ap-8497	56	12	of	of	ADP
ap-8497	56	13	the	the	DET
ap-8497	56	14	above	above	ADJ
ap-8497	56	15	matrix	matrix	NOUN
ap-8497	56	16	pairs	pair	NOUN
ap-8497	56	17	with	with	ADP
ap-8497	56	18	the	the	DET
ap-8497	56	19	numerical	numerical	PROPN
ap-8497	56	20	eigenvalue	eigenvalue	PROPN
ap-8497	56	21	calculation	calculation	NOUN
ap-8497	56	22	.	.	PUNCT
ap-8497	57	1	but	but	CCONJ
ap-8497	57	2	with	with	ADP
ap-8497	57	3	the	the	DET
ap-8497	57	4	necessary	necessary	ADJ
ap-8497	57	5	and	and	CCONJ
ap-8497	57	6	sufficient	sufficient	ADJ
ap-8497	57	7	conditions	condition	NOUN
ap-8497	57	8	presented	present	VERB
ap-8497	57	9	in	in	ADP
ap-8497	57	10	this	this	DET
ap-8497	57	11	paper	paper	NOUN
ap-8497	57	12	,	,	PUNCT
ap-8497	57	13	we	we	PRON
ap-8497	57	14	can	can	AUX
ap-8497	57	15	conclude	conclude	VERB
ap-8497	57	16	that	that	SCONJ
ap-8497	57	17	the	the	DET
ap-8497	57	18	matrix	matrix	NOUN
ap-8497	57	19	pair	pair	NOUN
ap-8497	57	20	(	(	PUNCT
ap-8497	57	21	e1	e1	NOUN
ap-8497	57	22	,	,	PUNCT
ap-8497	57	23	a1	a1	NOUN
ap-8497	57	24	)	)	PUNCT
ap-8497	57	25	is	be	AUX
ap-8497	57	26	a	a	DET
ap-8497	57	27	qualitative	qualitative	ADJ
ap-8497	57	28	sign	sign	NOUN
ap-8497	57	29	unstable	unstable	ADJ
ap-8497	57	30	(	(	PUNCT
ap-8497	57	31	qlsu	qlsu	NOUN
ap-8497	57	32	)	)	PUNCT
ap-8497	57	33	matrix	matrix	NOUN
ap-8497	57	34	pair	pair	NOUN
ap-8497	57	35	and	and	CCONJ
ap-8497	57	36	the	the	DET
ap-8497	57	37	matrix	matrix	NOUN
ap-8497	57	38	pair	pair	NOUN
ap-8497	57	39	(	(	PUNCT
ap-8497	57	40	e2	e2	PROPN
ap-8497	57	41	,	,	PUNCT
ap-8497	57	42	a2	a2	PROPN
ap-8497	57	43	)	)	PUNCT
ap-8497	57	44	is	be	AUX
ap-8497	57	45	an	an	DET
ap-8497	57	46	mds	mds	PROPN
ap-8497	57	47	/	/	SYM
ap-8497	57	48	u	u	NOUN
ap-8497	57	49	matrix	matrix	NOUN
ap-8497	57	50	pair	pair	NOUN
ap-8497	57	51	.	.	PUNCT
ap-8497	58	1	this	this	PRON
ap-8497	58	2	is	be	AUX
ap-8497	58	3	concluded	conclude	VERB
ap-8497	58	4	just	just	ADV
ap-8497	58	5	by	by	ADP
ap-8497	58	6	a	a	DET
ap-8497	58	7	simple	simple	ADJ
ap-8497	58	8	visualisation	visualisation	NOUN
ap-8497	58	9	of	of	ADP
ap-8497	58	10	the	the	DET
ap-8497	58	11	nature	nature	NOUN
ap-8497	58	12	of	of	ADP
ap-8497	58	13	interactions	interaction	NOUN
ap-8497	58	14	and	and	CCONJ
ap-8497	58	15	interconnections	interconnection	NOUN
ap-8497	58	16	of	of	ADP
ap-8497	58	17	the	the	DET
ap-8497	58	18	matrix	matrix	NOUN
ap-8497	58	19	pair	pair	NOUN
ap-8497	58	20	.	.	PUNCT
ap-8497	59	1	note	note	VERB
ap-8497	59	2	that	that	SCONJ
ap-8497	59	3	,	,	PUNCT
ap-8497	59	4	the	the	DET
ap-8497	59	5	matrix	matrix	NOUN
ap-8497	59	6	pairs	pair	NOUN
ap-8497	59	7	of	of	ADP
ap-8497	59	8	order	order	NOUN
ap-8497	59	9	2	2	NUM
ap-8497	59	10	do	do	AUX
ap-8497	59	11	not	not	PART
ap-8497	59	12	have	have	VERB
ap-8497	59	13	any	any	DET
ap-8497	59	14	interconnection	interconnection	NOUN
ap-8497	59	15	terms	term	NOUN
ap-8497	59	16	and	and	CCONJ
ap-8497	59	17	thus	thus	ADV
ap-8497	59	18	are	be	AUX
ap-8497	59	19	trivial	trivial	ADJ
ap-8497	59	20	for	for	ADP
ap-8497	59	21	our	our	PRON
ap-8497	59	22	studies	study	NOUN
ap-8497	59	23	.	.	PUNCT
ap-8497	60	1	hence	hence	ADV
ap-8497	60	2	,	,	PUNCT
ap-8497	60	3	we	we	PRON
ap-8497	60	4	focus	focus	VERB
ap-8497	60	5	on	on	ADP
ap-8497	60	6	matrix	matrix	NOUN
ap-8497	60	7	pairs	pair	NOUN
ap-8497	60	8	of	of	ADP
ap-8497	60	9	order	order	NOUN
ap-8497	60	10	3	3	NUM
ap-8497	60	11	and	and	CCONJ
ap-8497	60	12	higher	high	ADJ
ap-8497	60	13	.	.	PUNCT
ap-8497	61	1	in	in	ADP
ap-8497	61	2	the	the	DET
ap-8497	61	3	next	next	ADJ
ap-8497	61	4	section	section	NOUN
ap-8497	61	5	,	,	PUNCT
ap-8497	61	6	the	the	DET
ap-8497	61	7	matrix	matrix	NOUN
ap-8497	61	8	pair	pair	NOUN
ap-8497	61	9	elemental	elemental	ADJ
ap-8497	61	10	sign	sign	NOUN
ap-8497	61	11	structures	structure	NOUN
ap-8497	61	12	are	be	AUX
ap-8497	61	13	briefly	briefly	ADV
ap-8497	61	14	reviewed	review	VERB
ap-8497	61	15	and	and	CCONJ
ap-8497	61	16	few	few	ADJ
ap-8497	61	17	basic	basic	ADJ
ap-8497	61	18	‘	'	PUNCT
ap-8497	61	19	qualitative	qualitative	ADJ
ap-8497	61	20	sign	sign	NOUN
ap-8497	61	21	matrix	matrix	NOUN
ap-8497	61	22	pair	pair	NOUN
ap-8497	61	23	indices	index	NOUN
ap-8497	61	24	’	'	PUNCT
ap-8497	61	25	are	be	AUX
ap-8497	61	26	developed	develop	VERB
ap-8497	61	27	for	for	ADP
ap-8497	61	28	formulating	formulate	VERB
ap-8497	61	29	the	the	DET
ap-8497	61	30	conditions	condition	NOUN
ap-8497	61	31	for	for	ADP
ap-8497	61	32	qualitative	qualitative	ADJ
ap-8497	61	33	sign	sign	NOUN
ap-8497	61	34	instability	instability	NOUN
ap-8497	61	35	.	.	PUNCT
ap-8497	62	1	in	in	ADP
ap-8497	62	2	section	section	NOUN
ap-8497	62	3	3	3	NUM
ap-8497	62	4	,	,	PUNCT
ap-8497	62	5	the	the	DET
ap-8497	62	6	necessary	necessary	ADJ
ap-8497	62	7	and	and	CCONJ
ap-8497	62	8	sufficient	sufficient	ADJ
ap-8497	62	9	conditions	condition	NOUN
ap-8497	62	10	for	for	ADP
ap-8497	62	11	qualitative	qualitative	ADJ
ap-8497	62	12	instability	instability	NOUN
ap-8497	62	13	are	be	AUX
ap-8497	62	14	proposed	propose	VERB
ap-8497	62	15	,	,	PUNCT
ap-8497	62	16	which	which	PRON
ap-8497	62	17	is	be	AUX
ap-8497	62	18	the	the	DET
ap-8497	62	19	main	main	ADJ
ap-8497	62	20	result	result	NOUN
ap-8497	62	21	of	of	ADP
ap-8497	62	22	this	this	DET
ap-8497	62	23	paper	paper	NOUN
ap-8497	62	24	.	.	PUNCT
ap-8497	63	1	section	section	NOUN
ap-8497	63	2	4	4	NUM
ap-8497	63	3	discusses	discuss	VERB
ap-8497	63	4	the	the	DET
ap-8497	63	5	implications	implication	NOUN
ap-8497	63	6	of	of	ADP
ap-8497	63	7	these	these	DET
ap-8497	63	8	conditions	condition	NOUN
ap-8497	63	9	and	and	CCONJ
ap-8497	63	10	illustrates	illustrate	VERB
ap-8497	63	11	few	few	ADJ
ap-8497	63	12	examples	example	NOUN
ap-8497	63	13	for	for	ADP
ap-8497	63	14	a	a	DET
ap-8497	63	15	clear	clear	ADJ
ap-8497	63	16	visualisation	visualisation	NOUN
ap-8497	63	17	of	of	ADP
ap-8497	63	18	the	the	DET
ap-8497	63	19	importance	importance	NOUN
ap-8497	63	20	of	of	ADP
ap-8497	63	21	qualitative	qualitative	ADJ
ap-8497	63	22	stability	stability	NOUN
ap-8497	63	23	.	.	PUNCT
ap-8497	64	1	in	in	ADP
ap-8497	64	2	section	section	NOUN
ap-8497	64	3	5	5	NUM
ap-8497	64	4	,	,	PUNCT
ap-8497	64	5	we	we	PRON
ap-8497	64	6	discuss	discuss	VERB
ap-8497	64	7	the	the	DET
ap-8497	64	8	conclusions	conclusion	NOUN
ap-8497	64	9	drawn	draw	VERB
ap-8497	64	10	from	from	ADP
ap-8497	64	11	this	this	DET
ap-8497	64	12	paper	paper	NOUN
ap-8497	64	13	.	.	PUNCT
ap-8497	65	1	2	2	X
ap-8497	65	2	.	.	X
ap-8497	65	3	qualitative	qualitative	ADJ
ap-8497	65	4	sign	sign	NOUN
ap-8497	65	5	matrix	matrix	NOUN
ap-8497	65	6	pair	pair	NOUN
ap-8497	65	7	indices	index	NOUN
ap-8497	65	8	for	for	ADP
ap-8497	65	9	assessing	assess	VERB
ap-8497	65	10	the	the	DET
ap-8497	65	11	stability	stability	NOUN
ap-8497	65	12	,	,	PUNCT
ap-8497	65	13	first	first	ADV
ap-8497	65	14	,	,	PUNCT
ap-8497	65	15	we	we	PRON
ap-8497	65	16	have	have	VERB
ap-8497	65	17	to	to	PART
ap-8497	65	18	visualise	visualise	VERB
ap-8497	65	19	an	an	DET
ap-8497	65	20	n×n	n×n	PROPN
ap-8497	65	21	matrix	matrix	NOUN
ap-8497	65	22	pair	pair	NOUN
ap-8497	65	23	in	in	ADP
ap-8497	65	24	the	the	DET
ap-8497	65	25	following	following	ADJ
ap-8497	65	26	structured	structure	VERB
ap-8497	65	27	way	way	NOUN
ap-8497	65	28	.	.	PUNCT
ap-8497	66	1	just	just	ADV
ap-8497	66	2	for	for	ADP
ap-8497	66	3	a	a	DET
ap-8497	66	4	simplified	simplified	ADJ
ap-8497	66	5	view	view	NOUN
ap-8497	66	6	,	,	PUNCT
ap-8497	66	7	let	let	VERB
ap-8497	66	8	us	we	PRON
ap-8497	66	9	illustrate	illustrate	VERB
ap-8497	66	10	the	the	DET
ap-8497	66	11	structure	structure	NOUN
ap-8497	66	12	using	use	VERB
ap-8497	66	13	a	a	DET
ap-8497	66	14	4	4	NUM
ap-8497	66	15	×	×	NOUN
ap-8497	66	16	4	4	NUM
ap-8497	66	17	matrix	matrix	NOUN
ap-8497	66	18	pair	pair	NOUN
ap-8497	66	19	:	:	PUNCT
ap-8497	66	20	e	e	X
ap-8497	66	21	=	=	SYM
ap-8497	66	22			NOUN
ap-8497	66	23	e11	e11	X
ap-8497	66	24	e12	e12	NOUN
ap-8497	66	25	e13	e13	PROPN
ap-8497	66	26	e14	e14	PROPN
ap-8497	66	27	e21	e21	PROPN
ap-8497	66	28	e22	e22	X
ap-8497	66	29	e23	e23	PROPN
ap-8497	66	30	e24	e24	PROPN
ap-8497	66	31	e31	e31	PROPN
ap-8497	66	32	e32	e32	PROPN
ap-8497	66	33	e33	e33	PROPN
ap-8497	66	34	e34	e34	PROPN
ap-8497	66	35	e41	e41	VERB
ap-8497	66	36	e42	e42	PRON
ap-8497	66	37	e43	e43	NOUN
ap-8497	66	38	e44	e44	NOUN
ap-8497	66	39			PROPN
ap-8497	66	40	and	and	CCONJ
ap-8497	66	41	a	a	DET
ap-8497	66	42	=	=	NOUN
ap-8497	66	43			NOUN
ap-8497	66	44	a11	a11	PROPN
ap-8497	66	45	a12	a12	PROPN
ap-8497	66	46	a13	a13	PROPN
ap-8497	66	47	a14	a14	PROPN
ap-8497	66	48	a21	a21	PROPN
ap-8497	66	49	a22	a22	PROPN
ap-8497	66	50	a23	a23	PROPN
ap-8497	66	51	a24	a24	PROPN
ap-8497	66	52	a31	a31	PROPN
ap-8497	66	53	a32	a32	PROPN
ap-8497	66	54	a33	a33	PROPN
ap-8497	66	55	a34	a34	PROPN
ap-8497	66	56	a41	a41	PROPN
ap-8497	66	57	a42	a42	PROPN
ap-8497	66	58	a43	a43	PROPN
ap-8497	66	59	a44	a44	PROPN
ap-8497	66	60			PROPN
ap-8497	66	61	.	.	PUNCT
ap-8497	67	1	the	the	DET
ap-8497	67	2	entire	entire	ADJ
ap-8497	67	3	matrix	matrix	NOUN
ap-8497	67	4	pair	pair	NOUN
ap-8497	67	5	sign	sign	NOUN
ap-8497	67	6	structure	structure	NOUN
ap-8497	67	7	is	be	AUX
ap-8497	67	8	completely	completely	ADV
ap-8497	67	9	specified	specify	VERB
ap-8497	67	10	by	by	ADP
ap-8497	67	11	the	the	DET
ap-8497	67	12	diagonal	diagonal	ADJ
ap-8497	67	13	elements	element	NOUN
ap-8497	67	14	and	and	CCONJ
ap-8497	67	15	the	the	DET
ap-8497	67	16	off	off	ADV
ap-8497	67	17	-	-	PUNCT
ap-8497	67	18	diagonal	diagonal	ADJ
ap-8497	67	19	link	link	NOUN
ap-8497	67	20	structures	structure	NOUN
ap-8497	67	21	(	(	PUNCT
ap-8497	67	22	interactions	interaction	NOUN
ap-8497	67	23	and	and	CCONJ
ap-8497	67	24	interconnections	interconnection	NOUN
ap-8497	67	25	)	)	PUNCT
ap-8497	67	26	.	.	PUNCT
ap-8497	68	1	this	this	DET
ap-8497	68	2	matrix	matrix	NOUN
ap-8497	68	3	pair	pair	NOUN
ap-8497	68	4	consists	consist	VERB
ap-8497	68	5	of	of	ADP
ap-8497	68	6	:	:	PUNCT
ap-8497	68	7	•	•	ADP
ap-8497	68	8	diagonal	diagonal	ADJ
ap-8497	68	9	elements	element	NOUN
ap-8497	68	10	:	:	PUNCT
ap-8497	68	11	eii	eii	PROPN
ap-8497	68	12	and	and	CCONJ
ap-8497	68	13	aii	aii	PROPN
ap-8497	68	14	,	,	PUNCT
ap-8497	68	15	•	•	NUM
ap-8497	68	16	interactions	interaction	NOUN
ap-8497	68	17	of	of	ADP
ap-8497	68	18	the	the	DET
ap-8497	68	19	form	form	NOUN
ap-8497	68	20	eijeji	eijeji	NOUN
ap-8497	68	21	and	and	CCONJ
ap-8497	68	22	aijaji	aijaji	NOUN
ap-8497	68	23	,	,	PUNCT
ap-8497	68	24	•	•	ADJ
ap-8497	68	25	interactions	interaction	NOUN
ap-8497	68	26	of	of	ADP
ap-8497	68	27	the	the	DET
ap-8497	68	28	form	form	NOUN
ap-8497	68	29	eijaji	eijaji	NOUN
ap-8497	68	30	,	,	PUNCT
ap-8497	68	31	•	•	NUM
ap-8497	68	32	interconnections	interconnection	NOUN
ap-8497	68	33	of	of	ADP
ap-8497	68	34	the	the	DET
ap-8497	68	35	form	form	NOUN
ap-8497	68	36	bijbjk	bijbjk	NOUN
ap-8497	68	37	.	.	PUNCT
ap-8497	68	38	.	.	PUNCT
ap-8497	68	39	.	.	PUNCT
ap-8497	69	1	bmi	bmi	PROPN
ap-8497	69	2	,	,	PUNCT
ap-8497	69	3	where	where	SCONJ
ap-8497	69	4	bij	bij	NOUN
ap-8497	69	5	=	=	SYM
ap-8497	69	6	eij	eij	PROPN
ap-8497	69	7	or	or	CCONJ
ap-8497	69	8	aij	aij	PROPN
ap-8497	69	9	.	.	PUNCT
ap-8497	70	1	now	now	ADV
ap-8497	70	2	,	,	PUNCT
ap-8497	70	3	we	we	PRON
ap-8497	70	4	look	look	VERB
ap-8497	70	5	at	at	ADP
ap-8497	70	6	the	the	DET
ap-8497	70	7	signs	sign	NOUN
ap-8497	70	8	of	of	ADP
ap-8497	70	9	the	the	DET
ap-8497	70	10	entries	entry	NOUN
ap-8497	70	11	and	and	CCONJ
ap-8497	70	12	use	use	VERB
ap-8497	70	13	the	the	DET
ap-8497	70	14	following	follow	VERB
ap-8497	70	15	sign	sign	NOUN
ap-8497	70	16	convention	convention	NOUN
ap-8497	70	17	in	in	ADP
ap-8497	70	18	the	the	DET
ap-8497	70	19	rest	rest	NOUN
ap-8497	70	20	of	of	ADP
ap-8497	70	21	this	this	DET
ap-8497	70	22	paper	paper	NOUN
ap-8497	70	23	.	.	PUNCT
ap-8497	71	1	we	we	PRON
ap-8497	71	2	use	use	VERB
ap-8497	71	3	the	the	DET
ap-8497	71	4	letter	letter	NOUN
ap-8497	71	5	‘	'	PUNCT
ap-8497	71	6	p	p	NOUN
ap-8497	71	7	’	'	PUNCT
ap-8497	71	8	for	for	ADP
ap-8497	71	9	the	the	DET
ap-8497	71	10	‘	'	PUNCT
ap-8497	71	11	+	+	NOUN
ap-8497	71	12	’	'	PUNCT
ap-8497	71	13	(	(	PUNCT
ap-8497	71	14	positive	positive	ADJ
ap-8497	71	15	)	)	PUNCT
ap-8497	71	16	sign	sign	NOUN
ap-8497	71	17	,	,	PUNCT
ap-8497	71	18	the	the	DET
ap-8497	71	19	letter	letter	NOUN
ap-8497	71	20	‘	'	PUNCT
ap-8497	71	21	n	n	CCONJ
ap-8497	71	22	’	'	PUNCT
ap-8497	71	23	for	for	ADP
ap-8497	71	24	the	the	DET
ap-8497	71	25	‘	'	PUNCT
ap-8497	71	26	−	−	NOUN
ap-8497	71	27	’	'	PUNCT
ap-8497	71	28	(	(	PUNCT
ap-8497	71	29	negative	negative	ADJ
ap-8497	71	30	)	)	PUNCT
ap-8497	71	31	sign	sign	NOUN
ap-8497	71	32	,	,	PUNCT
ap-8497	71	33	and	and	CCONJ
ap-8497	71	34	‘	'	PUNCT
ap-8497	71	35	0	0	NUM
ap-8497	71	36	’	'	PUNCT
ap-8497	71	37	for	for	ADP
ap-8497	71	38	the	the	DET
ap-8497	71	39	zero	zero	NUM
ap-8497	71	40	entry	entry	NOUN
ap-8497	71	41	.	.	PUNCT
ap-8497	72	1	we	we	PRON
ap-8497	72	2	label	label	VERB
ap-8497	72	3	the	the	DET
ap-8497	72	4	interactions	interaction	NOUN
ap-8497	72	5	of	of	ADP
ap-8497	72	6	the	the	DET
ap-8497	72	7	matrix	matrix	NOUN
ap-8497	72	8	pair	pair	NOUN
ap-8497	72	9	172	172	NUM
ap-8497	72	10	vol	vol	NOUN
ap-8497	72	11	.	.	PUNCT
ap-8497	73	1	63	63	NUM
ap-8497	74	1	no	no	NOUN
ap-8497	74	2	.	.	PUNCT
ap-8497	75	1	3/2023	3/2023	NUM
ap-8497	75	2	qualitative	qualitative	NOUN
ap-8497	75	3	sign	sign	NOUN
ap-8497	75	4	stability	stability	NOUN
ap-8497	75	5	of	of	ADP
ap-8497	75	6	linear	linear	ADJ
ap-8497	75	7	time	time	NOUN
ap-8497	75	8	invariant	invariant	ADJ
ap-8497	75	9	descriptor	descriptor	NOUN
ap-8497	75	10	systems	system	NOUN
ap-8497	75	11	notations	notation	NOUN
ap-8497	75	12	np	np	PRON
ap-8497	75	13	number	number	NOUN
ap-8497	75	14	of	of	ADP
ap-8497	75	15	positive	positive	ADJ
ap-8497	75	16	diagonal	diagonal	ADJ
ap-8497	75	17	elements	element	NOUN
ap-8497	75	18	nz	nz	NOUN
ap-8497	75	19	number	number	NOUN
ap-8497	75	20	of	of	ADP
ap-8497	75	21	zero	zero	NUM
ap-8497	75	22	diagonal	diagonal	ADJ
ap-8497	75	23	elements	element	NOUN
ap-8497	75	24	nng	nng	NOUN
ap-8497	75	25	number	number	NOUN
ap-8497	75	26	of	of	ADP
ap-8497	75	27	negative	negative	ADJ
ap-8497	75	28	diagonal	diagonal	ADJ
ap-8497	75	29	elements	element	NOUN
ap-8497	75	30	npz	npz	ADJ
ap-8497	75	31	number	number	NOUN
ap-8497	75	32	of	of	ADP
ap-8497	75	33	non	non	ADJ
ap-8497	75	34	-	-	ADJ
ap-8497	75	35	negative	negative	ADJ
ap-8497	75	36	diagonal	diagonal	ADJ
ap-8497	75	37	elements	element	NOUN
ap-8497	75	38	table	table	NOUN
ap-8497	75	39	1	1	NUM
ap-8497	75	40	.	.	PUNCT
ap-8497	75	41	notations	notation	NOUN
ap-8497	75	42	for	for	ADP
ap-8497	75	43	number	number	NOUN
ap-8497	75	44	of	of	ADP
ap-8497	75	45	diagonal	diagonal	ADJ
ap-8497	75	46	elements	element	NOUN
ap-8497	75	47	.	.	PUNCT
ap-8497	76	1	using	use	VERB
ap-8497	76	2	this	this	DET
ap-8497	76	3	sign	sign	NOUN
ap-8497	76	4	convention	convention	PROPN
ap-8497	76	5	.	.	PUNCT
ap-8497	77	1	the	the	DET
ap-8497	77	2	possible	possible	ADJ
ap-8497	77	3	off	off	ADP
ap-8497	77	4	-	-	PUNCT
ap-8497	77	5	diagonal	diagonal	ADJ
ap-8497	77	6	links	link	NOUN
ap-8497	77	7	or	or	CCONJ
ap-8497	77	8	interactions	interaction	NOUN
ap-8497	77	9	of	of	ADP
ap-8497	77	10	a	a	DET
ap-8497	77	11	matrix	matrix	NOUN
ap-8497	77	12	pair	pair	NOUN
ap-8497	77	13	are	be	AUX
ap-8497	77	14	:	:	PUNCT
ap-8497	77	15	•	•	NUM
ap-8497	77	16	mutualism	mutualism	NOUN
ap-8497	77	17	link	link	NOUN
ap-8497	77	18	:	:	PUNCT
ap-8497	77	19	(	(	PUNCT
ap-8497	77	20	pp	pp	ADJ
ap-8497	77	21	)	)	PUNCT
ap-8497	77	22	link	link	NOUN
ap-8497	77	23	,	,	PUNCT
ap-8497	77	24	•	•	NUM
ap-8497	77	25	competition	competition	NOUN
ap-8497	77	26	link	link	NOUN
ap-8497	77	27	:	:	PUNCT
ap-8497	77	28	(	(	PUNCT
ap-8497	77	29	nn	nn	ADJ
ap-8497	77	30	)	)	PUNCT
ap-8497	77	31	link	link	NOUN
ap-8497	77	32	,	,	PUNCT
ap-8497	77	33	•	•	NUM
ap-8497	77	34	predation	predation	NOUN
ap-8497	77	35	-	-	PUNCT
ap-8497	77	36	prey	prey	NOUN
ap-8497	77	37	,	,	PUNCT
ap-8497	77	38	prey	prey	NOUN
ap-8497	77	39	-	-	PUNCT
ap-8497	77	40	predation	predation	NOUN
ap-8497	77	41	links	link	NOUN
ap-8497	77	42	:	:	PUNCT
ap-8497	77	43	(	(	PUNCT
ap-8497	77	44	pn	pn	NOUN
ap-8497	77	45	)	)	PUNCT
ap-8497	77	46	link	link	NOUN
ap-8497	77	47	and	and	CCONJ
ap-8497	77	48	(	(	PUNCT
ap-8497	77	49	np	np	INTJ
ap-8497	77	50	)	)	PUNCT
ap-8497	77	51	link	link	NOUN
ap-8497	77	52	,	,	PUNCT
ap-8497	77	53	•	•	ADJ
ap-8497	77	54	ammensalism	ammensalism	NOUN
ap-8497	77	55	link	link	NOUN
ap-8497	77	56	:	:	PUNCT
ap-8497	77	57	(	(	PUNCT
ap-8497	77	58	n0	n0	ADJ
ap-8497	77	59	)	)	PUNCT
ap-8497	77	60	link	link	NOUN
ap-8497	77	61	and	and	CCONJ
ap-8497	77	62	(	(	PUNCT
ap-8497	77	63	0n	0n	NUM
ap-8497	77	64	)	)	PUNCT
ap-8497	77	65	link	link	NOUN
ap-8497	77	66	,	,	PUNCT
ap-8497	77	67	•	•	NUM
ap-8497	77	68	commensalism	commensalism	NOUN
ap-8497	77	69	link	link	PROPN
ap-8497	77	70	:	:	PUNCT
ap-8497	77	71	(	(	PUNCT
ap-8497	77	72	p0	p0	NOUN
ap-8497	77	73	)	)	PUNCT
ap-8497	77	74	link	link	NOUN
ap-8497	77	75	and	and	CCONJ
ap-8497	77	76	(	(	PUNCT
ap-8497	77	77	0p	0p	NUM
ap-8497	77	78	)	)	PUNCT
ap-8497	77	79	link	link	NOUN
ap-8497	77	80	,	,	PUNCT
ap-8497	77	81	•	•	NUM
ap-8497	77	82	null	null	PROPN
ap-8497	77	83	link	link	NOUN
ap-8497	77	84	:	:	PUNCT
ap-8497	77	85	(	(	PUNCT
ap-8497	77	86	00	00	NUM
ap-8497	77	87	)	)	PUNCT
ap-8497	77	88	link	link	NOUN
ap-8497	77	89	.	.	PUNCT
ap-8497	78	1	we	we	PRON
ap-8497	78	2	further	far	ADV
ap-8497	78	3	categorise	categorise	VERB
ap-8497	78	4	these	these	DET
ap-8497	78	5	links	link	NOUN
ap-8497	78	6	in	in	ADP
ap-8497	78	7	the	the	DET
ap-8497	78	8	following	following	ADJ
ap-8497	78	9	way	way	NOUN
ap-8497	78	10	.	.	PUNCT
ap-8497	79	1	all	all	DET
ap-8497	79	2	the	the	DET
ap-8497	79	3	mutualism	mutualism	NOUN
ap-8497	79	4	(	(	PUNCT
ap-8497	79	5	pp	pp	ADJ
ap-8497	79	6	)	)	PUNCT
ap-8497	79	7	links	link	NOUN
ap-8497	79	8	and	and	CCONJ
ap-8497	79	9	the	the	DET
ap-8497	79	10	competition	competition	NOUN
ap-8497	79	11	(	(	PUNCT
ap-8497	79	12	nn	nn	X
ap-8497	79	13	)	)	PUNCT
ap-8497	79	14	links	link	NOUN
ap-8497	79	15	are	be	AUX
ap-8497	79	16	collectively	collectively	ADV
ap-8497	79	17	labeled	label	VERB
ap-8497	79	18	as	as	ADP
ap-8497	79	19	‘	'	PUNCT
ap-8497	79	20	same	same	ADJ
ap-8497	79	21	sign	sign	NOUN
ap-8497	79	22	(	(	PUNCT
ap-8497	79	23	ss	ss	NOUN
ap-8497	79	24	)	)	PUNCT
ap-8497	79	25	links	link	NOUN
ap-8497	79	26	’	'	PUNCT
ap-8497	79	27	.	.	PUNCT
ap-8497	80	1	all	all	DET
ap-8497	80	2	the	the	DET
ap-8497	80	3	predation	predation	NOUN
ap-8497	80	4	-	-	PUNCT
ap-8497	80	5	prey	prey	NOUN
ap-8497	80	6	(	(	PUNCT
ap-8497	80	7	pn	pn	NOUN
ap-8497	80	8	)	)	PUNCT
ap-8497	80	9	links	link	NOUN
ap-8497	80	10	and	and	CCONJ
ap-8497	80	11	the	the	DET
ap-8497	80	12	prey	prey	NOUN
ap-8497	80	13	-	-	PUNCT
ap-8497	80	14	predation	predation	NOUN
ap-8497	80	15	(	(	PUNCT
ap-8497	80	16	np	np	INTJ
ap-8497	80	17	)	)	PUNCT
ap-8497	80	18	links	link	NOUN
ap-8497	80	19	are	be	AUX
ap-8497	80	20	collectively	collectively	ADV
ap-8497	80	21	labeled	label	VERB
ap-8497	80	22	as	as	ADP
ap-8497	80	23	‘	'	PUNCT
ap-8497	80	24	opposite	opposite	ADJ
ap-8497	80	25	sign	sign	NOUN
ap-8497	80	26	(	(	PUNCT
ap-8497	80	27	os	os	NOUN
ap-8497	80	28	)	)	PUNCT
ap-8497	80	29	links	link	NOUN
ap-8497	80	30	’	'	PUNCT
ap-8497	80	31	.	.	PUNCT
ap-8497	81	1	similarly	similarly	ADV
ap-8497	81	2	,	,	PUNCT
ap-8497	81	3	all	all	DET
ap-8497	81	4	the	the	DET
ap-8497	81	5	ammensalism	ammensalism	NOUN
ap-8497	81	6	(	(	PUNCT
ap-8497	81	7	n0	n0	NOUN
ap-8497	81	8	and	and	CCONJ
ap-8497	81	9	0n	0n	NUM
ap-8497	81	10	)	)	PUNCT
ap-8497	81	11	links	link	NOUN
ap-8497	81	12	and	and	CCONJ
ap-8497	81	13	the	the	DET
ap-8497	81	14	commensalism	commensalism	NOUN
ap-8497	81	15	(	(	PUNCT
ap-8497	81	16	p0	p0	NOUN
ap-8497	81	17	and	and	CCONJ
ap-8497	81	18	0p	0p	NOUN
ap-8497	81	19	)	)	PUNCT
ap-8497	81	20	links	link	NOUN
ap-8497	81	21	are	be	AUX
ap-8497	81	22	collectively	collectively	ADV
ap-8497	81	23	labeled	label	VERB
ap-8497	81	24	as	as	ADP
ap-8497	81	25	‘	'	PUNCT
ap-8497	81	26	zero	zero	NUM
ap-8497	81	27	sign	sign	NOUN
ap-8497	81	28	(	(	PUNCT
ap-8497	81	29	zs	zs	NOUN
ap-8497	81	30	)	)	PUNCT
ap-8497	81	31	links	link	NOUN
ap-8497	81	32	’	'	PUNCT
ap-8497	81	33	.	.	PUNCT
ap-8497	82	1	finally	finally	ADV
ap-8497	82	2	,	,	PUNCT
ap-8497	82	3	the	the	DET
ap-8497	82	4	null	null	NOUN
ap-8497	82	5	(	(	PUNCT
ap-8497	82	6	00	00	NUM
ap-8497	82	7	)	)	PUNCT
ap-8497	82	8	links	link	NOUN
ap-8497	82	9	are	be	AUX
ap-8497	82	10	labeled	label	VERB
ap-8497	82	11	as	as	ADP
ap-8497	82	12	‘	'	PUNCT
ap-8497	82	13	zero	zero	NUM
ap-8497	82	14	zero	zero	NUM
ap-8497	82	15	’	'	PUNCT
ap-8497	82	16	(	(	PUNCT
ap-8497	82	17	zz	zz	NOUN
ap-8497	82	18	)	)	PUNCT
ap-8497	82	19	links	link	NOUN
ap-8497	82	20	.	.	PUNCT
ap-8497	83	1	for	for	ADP
ap-8497	83	2	a	a	DET
ap-8497	83	3	‘	'	PUNCT
ap-8497	83	4	structural	structural	ADJ
ap-8497	83	5	zero	zero	NUM
ap-8497	83	6	link	link	NOUN
ap-8497	83	7	’	'	PUNCT
ap-8497	83	8	,	,	PUNCT
ap-8497	83	9	we	we	PRON
ap-8497	83	10	label	label	VERB
ap-8497	83	11	them	they	PRON
ap-8497	83	12	as	as	ADP
ap-8497	83	13	szz	szz	NOUN
ap-8497	83	14	links	link	NOUN
ap-8497	83	15	and	and	CCONJ
ap-8497	83	16	for	for	ADP
ap-8497	83	17	elemental	elemental	ADJ
ap-8497	83	18	zero	zero	NUM
ap-8497	83	19	links	link	NOUN
ap-8497	83	20	,	,	PUNCT
ap-8497	83	21	we	we	PRON
ap-8497	83	22	label	label	VERB
ap-8497	83	23	them	they	PRON
ap-8497	83	24	as	as	ADP
ap-8497	83	25	ezz	ezz	ADJ
ap-8497	83	26	links	link	NOUN
ap-8497	83	27	.	.	PUNCT
ap-8497	84	1	•	•	NUM
ap-8497	84	2	same	same	ADJ
ap-8497	84	3	sign	sign	NOUN
ap-8497	84	4	(	(	PUNCT
ap-8497	84	5	ss	ss	NOUN
ap-8497	84	6	)	)	PUNCT
ap-8497	84	7	links	link	NOUN
ap-8497	84	8	:	:	PUNCT
ap-8497	84	9	pp	pp	PROPN
ap-8497	84	10	(	(	PUNCT
ap-8497	84	11	+	+	ADJ
ap-8497	84	12	+	+	NOUN
ap-8497	84	13	)	)	PUNCT
ap-8497	84	14	links	link	NOUN
ap-8497	84	15	and	and	CCONJ
ap-8497	84	16	nn	nn	PROPN
ap-8497	84	17	(	(	PUNCT
ap-8497	84	18	−−	−−	NOUN
ap-8497	84	19	)	)	PUNCT
ap-8497	84	20	links	link	NOUN
ap-8497	84	21	,	,	PUNCT
ap-8497	84	22	•	•	ADV
ap-8497	84	23	opposite	opposite	ADJ
ap-8497	84	24	sign	sign	NOUN
ap-8497	84	25	(	(	PUNCT
ap-8497	84	26	os	os	NOUN
ap-8497	84	27	)	)	PUNCT
ap-8497	84	28	links	link	NOUN
ap-8497	84	29	:	:	PUNCT
ap-8497	84	30	pn	pn	PROPN
ap-8497	84	31	(	(	PUNCT
ap-8497	84	32	+	+	NOUN
ap-8497	84	33	−	−	NOUN
ap-8497	84	34	)	)	PUNCT
ap-8497	84	35	links	link	NOUN
ap-8497	84	36	and	and	CCONJ
ap-8497	84	37	np	np	INTJ
ap-8497	84	38	(	(	PUNCT
ap-8497	84	39	−+	−+	PROPN
ap-8497	84	40	)	)	PUNCT
ap-8497	84	41	links	link	NOUN
ap-8497	84	42	,	,	PUNCT
ap-8497	84	43	•	•	NOUN
ap-8497	84	44	zero	zero	NUM
ap-8497	84	45	sign	sign	NOUN
ap-8497	84	46	(	(	PUNCT
ap-8497	84	47	zs	zs	NOUN
ap-8497	84	48	)	)	PUNCT
ap-8497	84	49	links	link	NOUN
ap-8497	84	50	:	:	PUNCT
ap-8497	84	51	n0	n0	ADJ
ap-8497	84	52	links	link	NOUN
ap-8497	84	53	,	,	PUNCT
ap-8497	84	54	0n	0n	NOUN
ap-8497	84	55	links	link	NOUN
ap-8497	84	56	,	,	PUNCT
ap-8497	84	57	p0	p0	NOUN
ap-8497	84	58	links	link	NOUN
ap-8497	84	59	,	,	PUNCT
ap-8497	84	60	and	and	CCONJ
ap-8497	84	61	0p	0p	NUM
ap-8497	84	62	links	link	NOUN
ap-8497	84	63	,	,	PUNCT
ap-8497	84	64	•	•	NOUN
ap-8497	84	65	zero	zero	NUM
ap-8497	84	66	zero	zero	NUM
ap-8497	84	67	(	(	PUNCT
ap-8497	84	68	zz	zz	NOUN
ap-8497	84	69	)	)	PUNCT
ap-8497	84	70	links	link	NOUN
ap-8497	84	71	:	:	PUNCT
ap-8497	84	72	00	00	NUM
ap-8497	84	73	links	link	NOUN
ap-8497	84	74	.	.	PUNCT
ap-8497	85	1	based	base	VERB
ap-8497	85	2	on	on	ADP
ap-8497	85	3	this	this	DET
ap-8497	85	4	sign	sign	NOUN
ap-8497	85	5	convention	convention	PROPN
ap-8497	85	6	,	,	PUNCT
ap-8497	85	7	the	the	DET
ap-8497	85	8	matrix	matrix	NOUN
ap-8497	85	9	pair	pair	NOUN
ap-8497	85	10	elemental	elemental	ADJ
ap-8497	85	11	sign	sign	NOUN
ap-8497	85	12	structure	structure	NOUN
ap-8497	85	13	of	of	ADP
ap-8497	85	14	an	an	DET
ap-8497	85	15	n	n	NUM
ap-8497	85	16	×	×	NOUN
ap-8497	85	17	n	n	CCONJ
ap-8497	85	18	matrix	matrix	NOUN
ap-8497	85	19	pair	pair	NOUN
ap-8497	85	20	are	be	AUX
ap-8497	85	21	elaborated	elaborate	VERB
ap-8497	85	22	in	in	ADP
ap-8497	85	23	the	the	DET
ap-8497	85	24	following	following	ADJ
ap-8497	85	25	ways	way	NOUN
ap-8497	85	26	:	:	PUNCT
ap-8497	85	27	2.1	2.1	NUM
ap-8497	85	28	.	.	PUNCT
ap-8497	86	1	diagonal	diagonal	ADJ
ap-8497	86	2	elements	element	NOUN
ap-8497	86	3	eii	eii	PROPN
ap-8497	86	4	and	and	CCONJ
ap-8497	86	5	aii	aii	NOUN
ap-8497	86	6	the	the	DET
ap-8497	86	7	number	number	NOUN
ap-8497	86	8	of	of	ADP
ap-8497	86	9	diagonal	diagonal	ADJ
ap-8497	86	10	elements	element	NOUN
ap-8497	86	11	of	of	ADP
ap-8497	86	12	different	different	ADJ
ap-8497	86	13	signs	sign	NOUN
ap-8497	86	14	is	be	AUX
ap-8497	86	15	mentioned	mention	VERB
ap-8497	86	16	in	in	ADP
ap-8497	86	17	table	table	NOUN
ap-8497	86	18	1	1	NUM
ap-8497	86	19	.	.	PUNCT
ap-8497	87	1	the	the	DET
ap-8497	87	2	total	total	ADJ
ap-8497	87	3	number	number	NOUN
ap-8497	87	4	of	of	ADP
ap-8497	87	5	diagonal	diagonal	ADJ
ap-8497	87	6	elements	element	NOUN
ap-8497	87	7	of	of	ADP
ap-8497	87	8	the	the	DET
ap-8497	87	9	matrix	matrix	NOUN
ap-8497	87	10	pair	pair	NOUN
ap-8497	87	11	is	be	AUX
ap-8497	87	12	2n	2n	NUM
ap-8497	87	13	.	.	PUNCT
ap-8497	88	1	the	the	DET
ap-8497	88	2	number	number	NOUN
ap-8497	88	3	of	of	ADP
ap-8497	88	4	non	non	ADJ
ap-8497	88	5	-	-	ADJ
ap-8497	88	6	negative	negative	ADJ
ap-8497	88	7	diagonal	diagonal	ADJ
ap-8497	88	8	elements	element	NOUN
ap-8497	88	9	can	can	AUX
ap-8497	88	10	be	be	AUX
ap-8497	88	11	written	write	VERB
ap-8497	88	12	as	as	ADP
ap-8497	88	13	:	:	PUNCT
ap-8497	88	14	npz	npz	ADJ
ap-8497	88	15	=	=	PUNCT
ap-8497	88	16	np	np	INTJ
ap-8497	88	17	+	+	X
ap-8497	88	18	nz	nz	PROPN
ap-8497	88	19	.	.	PUNCT
ap-8497	89	1	let	let	VERB
ap-8497	89	2	us	we	PRON
ap-8497	89	3	assume	assume	VERB
ap-8497	89	4	that	that	SCONJ
ap-8497	89	5	npz	npz	ADJ
ap-8497	89	6	is	be	AUX
ap-8497	89	7	not	not	PART
ap-8497	89	8	zero	zero	NUM
ap-8497	89	9	and	and	CCONJ
ap-8497	89	10	define	define	VERB
ap-8497	89	11	:	:	PUNCT
ap-8497	89	12	ηpz	ηpz	NOUN
ap-8497	89	13	=	=	SYM
ap-8497	89	14	npz	npz	X
ap-8497	89	15	2n	2n	NUM
ap-8497	89	16	,	,	PUNCT
ap-8497	89	17	ηng	ηng	NOUN
ap-8497	89	18	=	=	SYM
ap-8497	89	19	nng	nng	PROPN
ap-8497	89	20	2n	2n	NUM
ap-8497	89	21	.	.	PUNCT
ap-8497	90	1	notations	notation	NOUN
ap-8497	90	2	ntl	ntl	PROPN
ap-8497	90	3	total	total	ADJ
ap-8497	90	4	number	number	NOUN
ap-8497	90	5	of	of	ADP
ap-8497	90	6	links	link	NOUN
ap-8497	90	7	of	of	ADP
ap-8497	90	8	e	e	PROPN
ap-8497	90	9	and	and	CCONJ
ap-8497	90	10	a	a	DET
ap-8497	90	11	nss	nss	NOUN
ap-8497	90	12	total	total	ADJ
ap-8497	90	13	number	number	NOUN
ap-8497	90	14	of	of	ADP
ap-8497	90	15	ss	ss	NOUN
ap-8497	90	16	links	link	NOUN
ap-8497	90	17	of	of	ADP
ap-8497	90	18	e	e	PROPN
ap-8497	90	19	and	and	CCONJ
ap-8497	90	20	a	a	DET
ap-8497	90	21	nzs	nzs	NOUN
ap-8497	90	22	total	total	ADJ
ap-8497	90	23	number	number	NOUN
ap-8497	90	24	of	of	ADP
ap-8497	90	25	zs	zs	NOUN
ap-8497	90	26	links	link	NOUN
ap-8497	90	27	of	of	ADP
ap-8497	90	28	e	e	PROPN
ap-8497	90	29	and	and	CCONJ
ap-8497	90	30	a	a	DET
ap-8497	90	31	nos	nos	ADJ
ap-8497	90	32	total	total	ADJ
ap-8497	90	33	number	number	NOUN
ap-8497	90	34	of	of	ADP
ap-8497	90	35	os	os	NOUN
ap-8497	90	36	links	link	NOUN
ap-8497	90	37	of	of	ADP
ap-8497	90	38	e	e	PROPN
ap-8497	90	39	and	and	CCONJ
ap-8497	90	40	a	a	DET
ap-8497	90	41	nszz	nszz	ADJ
ap-8497	90	42	total	total	ADJ
ap-8497	90	43	number	number	NOUN
ap-8497	90	44	of	of	ADP
ap-8497	90	45	szz	szz	NOUN
ap-8497	90	46	links	link	NOUN
ap-8497	90	47	of	of	ADP
ap-8497	90	48	e	e	PROPN
ap-8497	90	49	and	and	CCONJ
ap-8497	90	50	a	a	DET
ap-8497	90	51	nezz	nezz	NOUN
ap-8497	90	52	total	total	ADJ
ap-8497	90	53	number	number	NOUN
ap-8497	90	54	of	of	ADP
ap-8497	90	55	ezz	ezz	ADJ
ap-8497	90	56	links	link	NOUN
ap-8497	90	57	of	of	ADP
ap-8497	90	58	e	e	PROPN
ap-8497	90	59	and	and	CCONJ
ap-8497	90	60	a	a	DET
ap-8497	90	61	nlc	nlc	PROPN
ap-8497	90	62	total	total	ADJ
ap-8497	90	63	number	number	NOUN
ap-8497	90	64	of	of	ADP
ap-8497	90	65	active	active	ADJ
ap-8497	90	66	links	link	NOUN
ap-8497	90	67	of	of	ADP
ap-8497	90	68	e	e	PROPN
ap-8497	90	69	and	and	CCONJ
ap-8497	90	70	a	a	DET
ap-8497	90	71	ngood	ngood	NOUN
ap-8497	90	72	number	number	NOUN
ap-8497	90	73	of	of	ADP
ap-8497	90	74	‘	'	PUNCT
ap-8497	90	75	good	good	ADJ
ap-8497	90	76	’	'	PUNCT
ap-8497	90	77	links	link	NOUN
ap-8497	90	78	of	of	ADP
ap-8497	90	79	e	e	PROPN
ap-8497	90	80	and	and	CCONJ
ap-8497	90	81	a	a	DET
ap-8497	90	82	nbad	nbad	ADJ
ap-8497	90	83	number	number	NOUN
ap-8497	90	84	of	of	ADP
ap-8497	90	85	‘	'	PUNCT
ap-8497	90	86	bad	bad	ADJ
ap-8497	90	87	’	'	PUNCT
ap-8497	90	88	links	link	NOUN
ap-8497	90	89	of	of	ADP
ap-8497	90	90	e	e	NOUN
ap-8497	90	91	and	and	CCONJ
ap-8497	90	92	a	a	DET
ap-8497	90	93	table	table	NOUN
ap-8497	90	94	2	2	NUM
ap-8497	90	95	.	.	PUNCT
ap-8497	90	96	notations	notation	NOUN
ap-8497	90	97	for	for	ADP
ap-8497	90	98	number	number	NOUN
ap-8497	90	99	of	of	ADP
ap-8497	90	100	links	link	NOUN
ap-8497	90	101	of	of	ADP
ap-8497	90	102	matrices	matrix	NOUN
ap-8497	90	103	e	e	NOUN
ap-8497	90	104	and	and	CCONJ
ap-8497	90	105	a.	a.	NOUN
ap-8497	90	106	∴	∴	PROPN
ap-8497	90	107	ηpz	ηpz	NOUN
ap-8497	90	108	+	+	CCONJ
ap-8497	90	109	ηng	ηng	NOUN
ap-8497	90	110	=	=	SYM
ap-8497	90	111	1	1	NUM
ap-8497	90	112	.	.	PUNCT
ap-8497	91	1	from	from	ADP
ap-8497	91	2	an	an	DET
ap-8497	91	3	ecological	ecological	ADJ
ap-8497	91	4	perspective	perspective	NOUN
ap-8497	91	5	,	,	PUNCT
ap-8497	91	6	the	the	DET
ap-8497	91	7	information	information	NOUN
ap-8497	91	8	about	about	ADP
ap-8497	91	9	how	how	SCONJ
ap-8497	91	10	a	a	DET
ap-8497	91	11	species	species	NOUN
ap-8497	91	12	affects	affect	VERB
ap-8497	91	13	itself	itself	PRON
ap-8497	91	14	is	be	AUX
ap-8497	91	15	provided	provide	VERB
ap-8497	91	16	by	by	ADP
ap-8497	91	17	the	the	DET
ap-8497	91	18	diagonal	diagonal	ADJ
ap-8497	91	19	elements	element	NOUN
ap-8497	91	20	.	.	PUNCT
ap-8497	92	1	the	the	DET
ap-8497	92	2	positive	positive	ADJ
ap-8497	92	3	sign	sign	NOUN
ap-8497	92	4	signifies	signify	VERB
ap-8497	92	5	that	that	SCONJ
ap-8497	92	6	the	the	DET
ap-8497	92	7	species	specie	NOUN
ap-8497	92	8	helps	help	VERB
ap-8497	92	9	to	to	PART
ap-8497	92	10	increase	increase	VERB
ap-8497	92	11	its	its	PRON
ap-8497	92	12	own	own	ADJ
ap-8497	92	13	population	population	NOUN
ap-8497	92	14	,	,	PUNCT
ap-8497	92	15	zero	zero	NUM
ap-8497	92	16	signifies	signify	VERB
ap-8497	92	17	that	that	SCONJ
ap-8497	92	18	the	the	DET
ap-8497	92	19	species	specie	NOUN
ap-8497	92	20	has	have	VERB
ap-8497	92	21	no	no	DET
ap-8497	92	22	effect	effect	NOUN
ap-8497	92	23	on	on	ADP
ap-8497	92	24	itself	itself	PRON
ap-8497	92	25	,	,	PUNCT
ap-8497	92	26	and	and	CCONJ
ap-8497	92	27	the	the	DET
ap-8497	92	28	negative	negative	ADJ
ap-8497	92	29	sign	sign	NOUN
ap-8497	92	30	signifies	signify	VERB
ap-8497	92	31	that	that	SCONJ
ap-8497	92	32	it	it	PRON
ap-8497	92	33	is	be	AUX
ap-8497	92	34	self	self	NOUN
ap-8497	92	35	-	-	PUNCT
ap-8497	92	36	regulatory	regulatory	ADJ
ap-8497	92	37	.	.	PUNCT
ap-8497	93	1	that	that	PRON
ap-8497	93	2	is	be	AUX
ap-8497	93	3	why	why	SCONJ
ap-8497	93	4	elemental	elemental	ADJ
ap-8497	93	5	+	+	CCONJ
ap-8497	93	6	(	(	PUNCT
ap-8497	93	7	positive	positive	ADJ
ap-8497	93	8	)	)	PUNCT
ap-8497	93	9	and	and	CCONJ
ap-8497	93	10	0	0	NUM
ap-8497	93	11	(	(	PUNCT
ap-8497	93	12	zero	zero	NUM
ap-8497	93	13	)	)	PUNCT
ap-8497	93	14	signs	sign	NOUN
ap-8497	93	15	are	be	AUX
ap-8497	93	16	considered	consider	VERB
ap-8497	93	17	as	as	ADP
ap-8497	93	18	‘	'	PUNCT
ap-8497	93	19	bad	bad	ADJ
ap-8497	93	20	’	'	PUNCT
ap-8497	93	21	signs	sign	NOUN
ap-8497	93	22	and	and	CCONJ
ap-8497	93	23	elemental	elemental	ADJ
ap-8497	93	24	−	−	PROPN
ap-8497	93	25	(	(	PUNCT
ap-8497	93	26	negative	negative	ADJ
ap-8497	93	27	)	)	PUNCT
ap-8497	93	28	signs	sign	NOUN
ap-8497	93	29	are	be	AUX
ap-8497	93	30	considered	consider	VERB
ap-8497	93	31	as	as	ADP
ap-8497	93	32	‘	'	PUNCT
ap-8497	93	33	good	good	ADJ
ap-8497	93	34	’	'	PUNCT
ap-8497	93	35	signs	sign	NOUN
ap-8497	93	36	in	in	ADP
ap-8497	93	37	a	a	DET
ap-8497	93	38	row	row	NOUN
ap-8497	93	39	or	or	CCONJ
ap-8497	93	40	column	column	NOUN
ap-8497	93	41	of	of	ADP
ap-8497	93	42	a	a	DET
ap-8497	93	43	matrix	matrix	NOUN
ap-8497	93	44	pair	pair	NOUN
ap-8497	94	1	[	[	X
ap-8497	94	2	11	11	NUM
ap-8497	94	3	]	]	PUNCT
ap-8497	94	4	.	.	PUNCT
ap-8497	95	1	2.2	2.2	NUM
ap-8497	95	2	.	.	PUNCT
ap-8497	95	3	interactions	interaction	NOUN
ap-8497	95	4	of	of	ADP
ap-8497	95	5	the	the	DET
ap-8497	95	6	form	form	NOUN
ap-8497	95	7	eijeji	eijeji	NOUN
ap-8497	95	8	and	and	CCONJ
ap-8497	95	9	aijaji	aijaji	NOUN
ap-8497	95	10	all	all	DET
ap-8497	95	11	the	the	DET
ap-8497	95	12	products	product	NOUN
ap-8497	95	13	of	of	ADP
ap-8497	95	14	off	off	ADP
ap-8497	95	15	-	-	PUNCT
ap-8497	95	16	diagonal	diagonal	ADJ
ap-8497	95	17	elements	element	NOUN
ap-8497	95	18	of	of	ADP
ap-8497	95	19	the	the	DET
ap-8497	95	20	form	form	NOUN
ap-8497	95	21	eijeji	eijeji	NOUN
ap-8497	95	22	connecting	connect	VERB
ap-8497	95	23	only	only	ADV
ap-8497	95	24	two	two	NUM
ap-8497	95	25	distinct	distinct	ADJ
ap-8497	95	26	nodes	node	NOUN
ap-8497	95	27	(	(	PUNCT
ap-8497	95	28	indices	index	NOUN
ap-8497	95	29	)	)	PUNCT
ap-8497	95	30	of	of	ADP
ap-8497	95	31	matrix	matrix	NOUN
ap-8497	95	32	e	e	NOUN
ap-8497	95	33	are	be	AUX
ap-8497	95	34	known	know	VERB
ap-8497	95	35	as	as	ADP
ap-8497	95	36	interactions	interaction	NOUN
ap-8497	95	37	of	of	ADP
ap-8497	95	38	matrix	matrix	NOUN
ap-8497	95	39	e.	e.	PROPN
ap-8497	95	40	similarly	similarly	ADV
ap-8497	95	41	,	,	PUNCT
ap-8497	95	42	all	all	DET
ap-8497	95	43	the	the	DET
ap-8497	95	44	products	product	NOUN
ap-8497	95	45	of	of	ADP
ap-8497	95	46	off	off	ADP
ap-8497	95	47	-	-	PUNCT
ap-8497	95	48	diagonal	diagonal	ADJ
ap-8497	95	49	elements	element	NOUN
ap-8497	95	50	of	of	ADP
ap-8497	95	51	the	the	DET
ap-8497	95	52	form	form	NOUN
ap-8497	95	53	aijaji	aijaji	NOUN
ap-8497	95	54	connecting	connect	VERB
ap-8497	95	55	only	only	ADV
ap-8497	95	56	two	two	NUM
ap-8497	95	57	distinct	distinct	ADJ
ap-8497	95	58	nodes	node	NOUN
ap-8497	95	59	(	(	PUNCT
ap-8497	95	60	indices	index	NOUN
ap-8497	95	61	)	)	PUNCT
ap-8497	95	62	of	of	ADP
ap-8497	95	63	matrix	matrix	NOUN
ap-8497	95	64	a	a	PRON
ap-8497	95	65	are	be	AUX
ap-8497	95	66	known	know	VERB
ap-8497	95	67	as	as	ADP
ap-8497	95	68	interactions	interaction	NOUN
ap-8497	95	69	of	of	ADP
ap-8497	95	70	matrix	matrix	NOUN
ap-8497	95	71	a.	a.	NOUN
ap-8497	95	72	table	table	NOUN
ap-8497	95	73	2	2	NUM
ap-8497	95	74	includes	include	VERB
ap-8497	95	75	information	information	NOUN
ap-8497	95	76	on	on	ADP
ap-8497	95	77	the	the	DET
ap-8497	95	78	number	number	NOUN
ap-8497	95	79	of	of	ADP
ap-8497	95	80	different	different	ADJ
ap-8497	95	81	links	link	NOUN
ap-8497	95	82	of	of	ADP
ap-8497	95	83	matrices	matrix	NOUN
ap-8497	95	84	e	e	NOUN
ap-8497	95	85	and	and	CCONJ
ap-8497	95	86	a.	a.	NOUN
ap-8497	95	87	the	the	DET
ap-8497	95	88	total	total	ADJ
ap-8497	95	89	number	number	NOUN
ap-8497	95	90	of	of	ADP
ap-8497	95	91	links	link	NOUN
ap-8497	95	92	(	(	PUNCT
ap-8497	95	93	interactions	interaction	NOUN
ap-8497	95	94	)	)	PUNCT
ap-8497	95	95	of	of	ADP
ap-8497	95	96	this	this	DET
ap-8497	95	97	form	form	NOUN
ap-8497	95	98	is	be	AUX
ap-8497	95	99	:	:	PUNCT
ap-8497	95	100	ntl	ntl	PROPN
ap-8497	95	101	=	=	SYM
ap-8497	96	1	[	[	X
ap-8497	96	2	1	1	NUM
ap-8497	96	3	+	+	NUM
ap-8497	96	4	2	2	NUM
ap-8497	96	5	+	+	NUM
ap-8497	96	6	3	3	NUM
ap-8497	96	7	+	+	NUM
ap-8497	96	8	.	.	PUNCT
ap-8497	96	9	.	.	PUNCT
ap-8497	96	10	.	.	PUNCT
ap-8497	97	1	+	+	CCONJ
ap-8497	97	2	(	(	PUNCT
ap-8497	97	3	n	n	CCONJ
ap-8497	97	4	−	−	PROPN
ap-8497	97	5	1	1	NUM
ap-8497	97	6	)	)	PUNCT
ap-8497	97	7	]	]	PUNCT
ap-8497	98	1	×	×	NOUN
ap-8497	98	2	2	2	NUM
ap-8497	98	3	=	=	SYM
ap-8497	98	4	n(n	n(n	X
ap-8497	98	5	−	−	NOUN
ap-8497	98	6	1	1	NUM
ap-8497	98	7	)	)	PUNCT
ap-8497	98	8	and	and	CCONJ
ap-8497	98	9	it	it	PRON
ap-8497	98	10	can	can	AUX
ap-8497	98	11	be	be	AUX
ap-8497	98	12	expressed	express	VERB
ap-8497	98	13	as	as	ADP
ap-8497	98	14	:	:	PUNCT
ap-8497	98	15	ntl	ntl	PROPN
ap-8497	98	16	=	=	PROPN
ap-8497	98	17	nss	nss	PROPN
ap-8497	98	18	+	+	CCONJ
ap-8497	98	19	nzs	nzs	NOUN
ap-8497	98	20	+	+	CCONJ
ap-8497	98	21	nos	nos	X
ap-8497	98	22	+	+	NUM
ap-8497	98	23	nszz	nszz	VERB
ap-8497	98	24	+	+	X
ap-8497	98	25	nezz	nezz	NOUN
ap-8497	98	26	.	.	PUNCT
ap-8497	99	1	(	(	PUNCT
ap-8497	99	2	2	2	X
ap-8497	99	3	)	)	PUNCT
ap-8497	99	4	we	we	PRON
ap-8497	99	5	now	now	ADV
ap-8497	99	6	take	take	VERB
ap-8497	99	7	out	out	ADP
ap-8497	99	8	the	the	DET
ap-8497	99	9	structural	structural	ADJ
ap-8497	99	10	zero	zero	NUM
ap-8497	99	11	links	link	NOUN
ap-8497	99	12	from	from	ADP
ap-8497	99	13	any	any	DET
ap-8497	99	14	further	further	ADJ
ap-8497	99	15	discussion	discussion	NOUN
ap-8497	99	16	[	[	X
ap-8497	99	17	16	16	NUM
ap-8497	99	18	]	]	PUNCT
ap-8497	99	19	and	and	CCONJ
ap-8497	99	20	denote	denote	VERB
ap-8497	99	21	the	the	DET
ap-8497	99	22	total	total	ADJ
ap-8497	99	23	number	number	NOUN
ap-8497	99	24	of	of	ADP
ap-8497	99	25	‘	'	PUNCT
ap-8497	99	26	active	active	ADJ
ap-8497	99	27	links	link	NOUN
ap-8497	99	28	’	'	PUNCT
ap-8497	99	29	as	as	ADP
ap-8497	99	30	nlc	nlc	PROPN
ap-8497	99	31	.	.	PUNCT
ap-8497	100	1	thus	thus	ADV
ap-8497	100	2	:	:	PUNCT
ap-8497	100	3	nlc	nlc	PROPN
ap-8497	100	4	=	=	PROPN
ap-8497	100	5	nss	nss	PROPN
ap-8497	100	6	+	+	CCONJ
ap-8497	100	7	nzs	nzs	NOUN
ap-8497	100	8	+	+	CCONJ
ap-8497	100	9	nos	nos	X
ap-8497	100	10	+	+	CCONJ
ap-8497	100	11	nezz	nezz	NOUN
ap-8497	100	12	.	.	PUNCT
ap-8497	101	1	(	(	PUNCT
ap-8497	101	2	3	3	X
ap-8497	101	3	)	)	PUNCT
ap-8497	101	4	from	from	ADP
ap-8497	101	5	an	an	DET
ap-8497	101	6	ecological	ecological	ADJ
ap-8497	101	7	viewpoint	viewpoint	NOUN
ap-8497	101	8	,	,	PUNCT
ap-8497	101	9	it	it	PRON
ap-8497	101	10	is	be	AUX
ap-8497	101	11	noted	note	VERB
ap-8497	101	12	that	that	SCONJ
ap-8497	101	13	same	same	ADJ
ap-8497	101	14	sign	sign	NOUN
ap-8497	101	15	(	(	PUNCT
ap-8497	101	16	ss	ss	NOUN
ap-8497	101	17	)	)	PUNCT
ap-8497	101	18	links	link	NOUN
ap-8497	101	19	(	(	PUNCT
ap-8497	101	20	i.e.	i.e.	X
ap-8497	101	21	pp	pp	CCONJ
ap-8497	101	22	and	and	CCONJ
ap-8497	101	23	nn	nn	NUM
ap-8497	101	24	links	link	NOUN
ap-8497	101	25	)	)	PUNCT
ap-8497	101	26	of	of	ADP
ap-8497	101	27	this	this	DET
ap-8497	101	28	form	form	NOUN
ap-8497	101	29	are	be	AUX
ap-8497	101	30	highly	highly	ADV
ap-8497	101	31	detrimental	detrimental	ADJ
ap-8497	101	32	to	to	ADP
ap-8497	101	33	stability	stability	NOUN
ap-8497	101	34	whereas	whereas	SCONJ
ap-8497	101	35	,	,	PUNCT
ap-8497	101	36	opposite	opposite	ADJ
ap-8497	101	37	sign	sign	NOUN
ap-8497	101	38	(	(	PUNCT
ap-8497	101	39	os	os	NOUN
ap-8497	101	40	)	)	PUNCT
ap-8497	101	41	links	link	NOUN
ap-8497	101	42	(	(	PUNCT
ap-8497	101	43	i.e.	i.e.	X
ap-8497	101	44	pn	pn	X
ap-8497	101	45	and	and	CCONJ
ap-8497	101	46	np	np	ADP
ap-8497	101	47	links	link	NOUN
ap-8497	101	48	)	)	PUNCT
ap-8497	101	49	of	of	ADP
ap-8497	101	50	this	this	DET
ap-8497	101	51	form	form	NOUN
ap-8497	101	52	are	be	AUX
ap-8497	101	53	conducive	conducive	ADJ
ap-8497	101	54	to	to	ADP
ap-8497	101	55	stability	stability	NOUN
ap-8497	101	56	[	[	X
ap-8497	101	57	10	10	NUM
ap-8497	101	58	,	,	PUNCT
ap-8497	101	59	22	22	NUM
ap-8497	101	60	]	]	PUNCT
ap-8497	101	61	.	.	PUNCT
ap-8497	102	1	so	so	ADV
ap-8497	102	2	,	,	PUNCT
ap-8497	102	3	from	from	ADP
ap-8497	102	4	the	the	DET
ap-8497	102	5	stability	stability	NOUN
ap-8497	102	6	173	173	NUM
ap-8497	102	7	m.	m.	NOUN
ap-8497	102	8	chand	chand	PROPN
ap-8497	102	9	,	,	PUNCT
ap-8497	102	10	m.	m.	NOUN
ap-8497	102	11	paitandi	paitandi	PROPN
ap-8497	102	12	,	,	PUNCT
ap-8497	102	13	m.	m.	PROPN
ap-8497	102	14	k.	k.	PROPN
ap-8497	102	15	gupta	gupta	PROPN
ap-8497	102	16	acta	acta	PROPN
ap-8497	102	17	polytechnica	polytechnica	PROPN
ap-8497	102	18	notations	notation	NOUN
ap-8497	102	19	n	n	DET
ap-8497	102	20	′	′	NUM
ap-8497	102	21	tl	tl	PROPN
ap-8497	102	22	total	total	ADJ
ap-8497	102	23	number	number	NOUN
ap-8497	102	24	of	of	ADP
ap-8497	102	25	links	link	NOUN
ap-8497	102	26	of	of	ADP
ap-8497	102	27	(	(	PUNCT
ap-8497	102	28	e	e	NOUN
ap-8497	102	29	,	,	PUNCT
ap-8497	102	30	a	a	PRON
ap-8497	102	31	)	)	PUNCT
ap-8497	102	32	n	n	NOUN
ap-8497	103	1	′	′	NUM
ap-8497	104	1	ss	ss	INTJ
ap-8497	104	2	total	total	ADJ
ap-8497	104	3	number	number	NOUN
ap-8497	104	4	of	of	ADP
ap-8497	104	5	ss	ss	NOUN
ap-8497	104	6	links	link	NOUN
ap-8497	104	7	of	of	ADP
ap-8497	104	8	(	(	PUNCT
ap-8497	104	9	e	e	NOUN
ap-8497	104	10	,	,	PUNCT
ap-8497	104	11	a	a	PRON
ap-8497	104	12	)	)	PUNCT
ap-8497	104	13	n	n	NOUN
ap-8497	104	14	′	′	NUM
ap-8497	105	1	zs	zs	NOUN
ap-8497	105	2	total	total	ADJ
ap-8497	105	3	number	number	NOUN
ap-8497	105	4	of	of	ADP
ap-8497	105	5	zs	zs	NOUN
ap-8497	105	6	links	link	NOUN
ap-8497	105	7	of	of	ADP
ap-8497	105	8	(	(	PUNCT
ap-8497	105	9	e	e	NOUN
ap-8497	105	10	,	,	PUNCT
ap-8497	105	11	a	a	PRON
ap-8497	105	12	)	)	PUNCT
ap-8497	105	13	n	n	NOUN
ap-8497	105	14	′	′	NUM
ap-8497	105	15	os	os	INTJ
ap-8497	105	16	total	total	ADJ
ap-8497	105	17	number	number	NOUN
ap-8497	105	18	of	of	ADP
ap-8497	105	19	os	os	NOUN
ap-8497	105	20	links	link	NOUN
ap-8497	105	21	of	of	ADP
ap-8497	105	22	(	(	PUNCT
ap-8497	105	23	e	e	NOUN
ap-8497	105	24	,	,	PUNCT
ap-8497	105	25	a	a	PRON
ap-8497	105	26	)	)	PUNCT
ap-8497	105	27	n	n	NOUN
ap-8497	105	28	′	′	NUM
ap-8497	105	29	szz	szz	NOUN
ap-8497	105	30	total	total	ADJ
ap-8497	105	31	number	number	NOUN
ap-8497	105	32	of	of	ADP
ap-8497	105	33	szz	szz	NOUN
ap-8497	105	34	links	link	NOUN
ap-8497	105	35	of	of	ADP
ap-8497	105	36	(	(	PUNCT
ap-8497	105	37	e	e	NOUN
ap-8497	105	38	,	,	PUNCT
ap-8497	105	39	a	a	PRON
ap-8497	105	40	)	)	PUNCT
ap-8497	105	41	n	n	NOUN
ap-8497	105	42	′	′	NUM
ap-8497	105	43	ezz	ezz	PROPN
ap-8497	105	44	total	total	ADJ
ap-8497	105	45	number	number	NOUN
ap-8497	105	46	of	of	ADP
ap-8497	105	47	ezz	ezz	ADJ
ap-8497	105	48	links	link	NOUN
ap-8497	105	49	of	of	ADP
ap-8497	105	50	(	(	PUNCT
ap-8497	105	51	e	e	NOUN
ap-8497	105	52	,	,	PUNCT
ap-8497	105	53	a	a	PRON
ap-8497	105	54	)	)	PUNCT
ap-8497	105	55	n	n	NOUN
ap-8497	105	56	′	′	NUM
ap-8497	105	57	lc	lc	NOUN
ap-8497	105	58	total	total	ADJ
ap-8497	105	59	number	number	NOUN
ap-8497	105	60	of	of	ADP
ap-8497	105	61	active	active	ADJ
ap-8497	105	62	links	link	NOUN
ap-8497	105	63	of	of	ADP
ap-8497	105	64	(	(	PUNCT
ap-8497	105	65	e	e	NOUN
ap-8497	105	66	,	,	PUNCT
ap-8497	105	67	a	a	PRON
ap-8497	105	68	)	)	PUNCT
ap-8497	105	69	n	n	NOUN
ap-8497	105	70	′	′	NUM
ap-8497	105	71	good	good	ADJ
ap-8497	105	72	number	number	NOUN
ap-8497	105	73	of	of	ADP
ap-8497	105	74	‘	'	PUNCT
ap-8497	105	75	good	good	ADJ
ap-8497	105	76	’	'	PUNCT
ap-8497	105	77	links	link	NOUN
ap-8497	105	78	of	of	ADP
ap-8497	105	79	(	(	PUNCT
ap-8497	105	80	e	e	NOUN
ap-8497	105	81	,	,	PUNCT
ap-8497	105	82	a	a	PRON
ap-8497	105	83	)	)	PUNCT
ap-8497	105	84	n	n	NOUN
ap-8497	106	1	′	′	NUM
ap-8497	106	2	bad	bad	ADJ
ap-8497	106	3	number	number	NOUN
ap-8497	106	4	of	of	ADP
ap-8497	106	5	‘	'	PUNCT
ap-8497	106	6	bad	bad	ADJ
ap-8497	106	7	’	'	PUNCT
ap-8497	106	8	links	link	NOUN
ap-8497	106	9	of	of	ADP
ap-8497	106	10	(	(	PUNCT
ap-8497	106	11	e	e	NOUN
ap-8497	106	12	,	,	PUNCT
ap-8497	106	13	a	a	PRON
ap-8497	106	14	)	)	PUNCT
ap-8497	106	15	table	table	NOUN
ap-8497	106	16	3	3	NUM
ap-8497	106	17	.	.	PUNCT
ap-8497	106	18	notations	notation	NOUN
ap-8497	106	19	for	for	ADP
ap-8497	106	20	number	number	NOUN
ap-8497	106	21	of	of	ADP
ap-8497	106	22	links	link	NOUN
ap-8497	106	23	of	of	ADP
ap-8497	106	24	matrix	matrix	NOUN
ap-8497	106	25	pair	pair	NOUN
ap-8497	106	26	(	(	PUNCT
ap-8497	106	27	e	e	NOUN
ap-8497	106	28	,	,	PUNCT
ap-8497	106	29	a	a	PRON
ap-8497	106	30	)	)	PUNCT
ap-8497	106	31	.	.	PUNCT
ap-8497	107	1	point	point	NOUN
ap-8497	107	2	of	of	ADP
ap-8497	107	3	view	view	NOUN
ap-8497	107	4	,	,	PUNCT
ap-8497	107	5	ss	ss	NOUN
ap-8497	107	6	links	link	NOUN
ap-8497	107	7	,	,	PUNCT
ap-8497	107	8	zs	zs	NOUN
ap-8497	107	9	links	link	NOUN
ap-8497	107	10	,	,	PUNCT
ap-8497	107	11	and	and	CCONJ
ap-8497	107	12	zz	zz	NUM
ap-8497	107	13	links	link	NOUN
ap-8497	107	14	of	of	ADP
ap-8497	107	15	this	this	DET
ap-8497	107	16	form	form	NOUN
ap-8497	107	17	are	be	AUX
ap-8497	107	18	considered	consider	VERB
ap-8497	107	19	as	as	ADP
ap-8497	107	20	‘	'	PUNCT
ap-8497	107	21	bad	bad	ADJ
ap-8497	107	22	’	'	PUNCT
ap-8497	107	23	links	link	NOUN
ap-8497	107	24	,	,	PUNCT
ap-8497	107	25	and	and	CCONJ
ap-8497	107	26	os	os	VERB
ap-8497	107	27	links	link	NOUN
ap-8497	107	28	of	of	ADP
ap-8497	107	29	this	this	DET
ap-8497	107	30	form	form	NOUN
ap-8497	107	31	are	be	AUX
ap-8497	107	32	considered	consider	VERB
ap-8497	107	33	as	as	ADP
ap-8497	107	34	‘	'	PUNCT
ap-8497	107	35	good	good	ADJ
ap-8497	107	36	’	'	PUNCT
ap-8497	107	37	links	link	NOUN
ap-8497	107	38	.	.	PUNCT
ap-8497	108	1	hence	hence	ADV
ap-8497	108	2	:	:	PUNCT
ap-8497	108	3	ngood	ngood	PROPN
ap-8497	108	4	=	=	SYM
ap-8497	108	5	nos	nos	X
ap-8497	108	6	,	,	PUNCT
ap-8497	108	7	(	(	PUNCT
ap-8497	108	8	4	4	X
ap-8497	108	9	)	)	PUNCT
ap-8497	108	10	nbad	nbad	ADJ
ap-8497	108	11	=	=	SYM
ap-8497	108	12	nss	nss	NOUN
ap-8497	108	13	+	+	CCONJ
ap-8497	108	14	nzs	nzs	NOUN
ap-8497	108	15	+	+	CCONJ
ap-8497	108	16	nezz	nezz	NOUN
ap-8497	108	17	.	.	PUNCT
ap-8497	109	1	(	(	PUNCT
ap-8497	109	2	5	5	X
ap-8497	109	3	)	)	PUNCT
ap-8497	109	4	let	let	VERB
ap-8497	109	5	us	we	PRON
ap-8497	109	6	define	define	VERB
ap-8497	109	7	:	:	PUNCT
ap-8497	109	8	ηbad	ηbad	NOUN
ap-8497	109	9	=	=	SYM
ap-8497	110	1	nbad	nbad	ADJ
ap-8497	110	2	nlc	nlc	PROPN
ap-8497	110	3	ηgood	ηgood	PROPN
ap-8497	110	4	=	=	SYM
ap-8497	110	5	ngood	ngood	PROPN
ap-8497	110	6	nlc	nlc	PROPN
ap-8497	110	7	∴	∴	PROPN
ap-8497	110	8	ηbad	ηbad	PROPN
ap-8497	110	9	+	+	CCONJ
ap-8497	110	10	ηgood	ηgood	NOUN
ap-8497	110	11	=	=	SYM
ap-8497	110	12	1	1	X
ap-8497	110	13	.	.	PUNCT
ap-8497	111	1	remark	remark	PROPN
ap-8497	111	2	1	1	NUM
ap-8497	111	3	.	.	PUNCT
ap-8497	112	1	the	the	DET
ap-8497	112	2	above	above	ADJ
ap-8497	112	3	indices	index	NOUN
ap-8497	112	4	are	be	AUX
ap-8497	112	5	already	already	ADV
ap-8497	112	6	defined	define	VERB
ap-8497	112	7	for	for	ADP
ap-8497	112	8	matrices	matrix	NOUN
ap-8497	112	9	.	.	PUNCT
ap-8497	113	1	now	now	ADV
ap-8497	113	2	we	we	PRON
ap-8497	113	3	are	be	AUX
ap-8497	113	4	,	,	PUNCT
ap-8497	113	5	for	for	ADP
ap-8497	113	6	the	the	DET
ap-8497	113	7	first	first	ADJ
ap-8497	113	8	time	time	NOUN
ap-8497	113	9	,	,	PUNCT
ap-8497	113	10	going	go	VERB
ap-8497	113	11	to	to	PART
ap-8497	113	12	define	define	VERB
ap-8497	113	13	another	another	DET
ap-8497	113	14	form	form	NOUN
ap-8497	113	15	of	of	ADP
ap-8497	113	16	interaction	interaction	NOUN
ap-8497	113	17	and	and	CCONJ
ap-8497	113	18	chain	chain	NOUN
ap-8497	113	19	for	for	ADP
ap-8497	113	20	matrix	matrix	NOUN
ap-8497	113	21	pairs	pair	NOUN
ap-8497	113	22	.	.	PUNCT
ap-8497	114	1	2.3	2.3	NUM
ap-8497	114	2	.	.	PUNCT
ap-8497	114	3	interactions	interaction	NOUN
ap-8497	114	4	of	of	ADP
ap-8497	114	5	the	the	DET
ap-8497	114	6	form	form	NOUN
ap-8497	114	7	eijaji	eijaji	NOUN
ap-8497	114	8	all	all	DET
ap-8497	114	9	the	the	DET
ap-8497	114	10	products	product	NOUN
ap-8497	114	11	of	of	ADP
ap-8497	114	12	off	off	ADP
ap-8497	114	13	-	-	PUNCT
ap-8497	114	14	diagonal	diagonal	ADJ
ap-8497	114	15	elements	element	NOUN
ap-8497	114	16	of	of	ADP
ap-8497	114	17	the	the	DET
ap-8497	114	18	form	form	NOUN
ap-8497	114	19	eijaji	eijaji	NOUN
ap-8497	114	20	connecting	connect	VERB
ap-8497	114	21	one	one	NUM
ap-8497	114	22	node	node	NOUN
ap-8497	114	23	of	of	ADP
ap-8497	114	24	matrix	matrix	NOUN
ap-8497	114	25	e	e	NOUN
ap-8497	114	26	and	and	CCONJ
ap-8497	114	27	the	the	DET
ap-8497	114	28	corresponding	corresponding	ADJ
ap-8497	114	29	node	node	NOUN
ap-8497	114	30	of	of	ADP
ap-8497	114	31	matrix	matrix	NOUN
ap-8497	114	32	a	a	PRON
ap-8497	114	33	are	be	AUX
ap-8497	114	34	known	know	VERB
ap-8497	114	35	as	as	ADP
ap-8497	114	36	interactions	interaction	NOUN
ap-8497	114	37	of	of	ADP
ap-8497	114	38	the	the	DET
ap-8497	114	39	matrix	matrix	NOUN
ap-8497	114	40	pair	pair	NOUN
ap-8497	114	41	(	(	PUNCT
ap-8497	114	42	e	e	NOUN
ap-8497	114	43	,	,	PUNCT
ap-8497	114	44	a	a	PRON
ap-8497	114	45	)	)	PUNCT
ap-8497	114	46	.	.	PUNCT
ap-8497	115	1	table	table	NOUN
ap-8497	115	2	3	3	NUM
ap-8497	115	3	lists	list	VERB
ap-8497	115	4	the	the	DET
ap-8497	115	5	number	number	NOUN
ap-8497	115	6	of	of	ADP
ap-8497	115	7	different	different	ADJ
ap-8497	115	8	links	link	NOUN
ap-8497	115	9	of	of	ADP
ap-8497	115	10	matrix	matrix	NOUN
ap-8497	115	11	pair	pair	NOUN
ap-8497	115	12	(	(	PUNCT
ap-8497	115	13	e	e	NOUN
ap-8497	115	14	,	,	PUNCT
ap-8497	115	15	a	a	PRON
ap-8497	115	16	)	)	PUNCT
ap-8497	115	17	.	.	PUNCT
ap-8497	116	1	the	the	DET
ap-8497	116	2	total	total	ADJ
ap-8497	116	3	number	number	NOUN
ap-8497	116	4	of	of	ADP
ap-8497	116	5	links	link	NOUN
ap-8497	116	6	(	(	PUNCT
ap-8497	116	7	interactions	interaction	NOUN
ap-8497	116	8	)	)	PUNCT
ap-8497	116	9	of	of	ADP
ap-8497	116	10	this	this	DET
ap-8497	116	11	form	form	NOUN
ap-8497	116	12	is	be	AUX
ap-8497	116	13	:	:	PUNCT
ap-8497	116	14	n	n	X
ap-8497	116	15	′	′	NUM
ap-8497	116	16	tl	tl	PROPN
ap-8497	117	1	=	=	PUNCT
ap-8497	117	2	n(n	n(n	X
ap-8497	117	3	−	−	NOUN
ap-8497	117	4	1	1	NUM
ap-8497	117	5	)	)	PUNCT
ap-8497	118	1	and	and	CCONJ
ap-8497	118	2	it	it	PRON
ap-8497	118	3	can	can	AUX
ap-8497	118	4	be	be	AUX
ap-8497	118	5	expressed	express	VERB
ap-8497	118	6	as	as	ADP
ap-8497	118	7	:	:	PUNCT
ap-8497	118	8	n	n	NUM
ap-8497	118	9	′	′	NUM
ap-8497	119	1	tl	tl	PROPN
ap-8497	119	2	=	=	SYM
ap-8497	120	1	n	n	PROPN
ap-8497	121	1	′	′	NUM
ap-8497	121	2	ss	ss	INTJ
ap-8497	122	1	+	+	CCONJ
ap-8497	122	2	n	n	NUM
ap-8497	123	1	′	′	NUM
ap-8497	123	2	zs	zs	NOUN
ap-8497	124	1	+	+	CCONJ
ap-8497	124	2	n	n	ADV
ap-8497	124	3	′	′	NUM
ap-8497	124	4	os	os	NOUN
ap-8497	125	1	+	+	CCONJ
ap-8497	125	2	n	n	CCONJ
ap-8497	125	3	′	′	NUM
ap-8497	125	4	szz	szz	NOUN
ap-8497	126	1	+	+	CCONJ
ap-8497	126	2	n	n	CCONJ
ap-8497	126	3	′	′	NUM
ap-8497	126	4	ezz	ezz	NOUN
ap-8497	126	5	.	.	PUNCT
ap-8497	127	1	(	(	PUNCT
ap-8497	127	2	6	6	X
ap-8497	127	3	)	)	PUNCT
ap-8497	127	4	we	we	PRON
ap-8497	127	5	now	now	ADV
ap-8497	127	6	take	take	VERB
ap-8497	127	7	out	out	ADP
ap-8497	127	8	the	the	DET
ap-8497	127	9	structural	structural	ADJ
ap-8497	127	10	zero	zero	NUM
ap-8497	127	11	links	link	NOUN
ap-8497	127	12	from	from	ADP
ap-8497	127	13	any	any	DET
ap-8497	127	14	further	further	ADJ
ap-8497	127	15	discussion	discussion	NOUN
ap-8497	127	16	and	and	CCONJ
ap-8497	127	17	denote	denote	VERB
ap-8497	127	18	the	the	DET
ap-8497	127	19	total	total	ADJ
ap-8497	127	20	number	number	NOUN
ap-8497	127	21	of	of	ADP
ap-8497	127	22	‘	'	PUNCT
ap-8497	127	23	active	active	ADJ
ap-8497	127	24	links	link	NOUN
ap-8497	127	25	’	'	PUNCT
ap-8497	127	26	as	as	ADP
ap-8497	127	27	n	n	PROPN
ap-8497	127	28	′	′	NUM
ap-8497	127	29	lc	lc	NOUN
ap-8497	127	30	.	.	PUNCT
ap-8497	128	1	thus	thus	ADV
ap-8497	128	2	:	:	PUNCT
ap-8497	128	3	n	n	PRON
ap-8497	128	4	′	′	NUM
ap-8497	128	5	lc	lc	NOUN
ap-8497	129	1	=	=	SYM
ap-8497	130	1	n	n	PROPN
ap-8497	131	1	′	′	NUM
ap-8497	131	2	ss	ss	INTJ
ap-8497	132	1	+	+	CCONJ
ap-8497	132	2	n	n	NUM
ap-8497	133	1	′	′	NUM
ap-8497	133	2	zs	zs	NOUN
ap-8497	134	1	+	+	CCONJ
ap-8497	134	2	n	n	ADV
ap-8497	134	3	′	′	NUM
ap-8497	134	4	os	os	NOUN
ap-8497	135	1	+	+	CCONJ
ap-8497	135	2	n	n	CCONJ
ap-8497	135	3	′	′	NUM
ap-8497	135	4	ezz	ezz	NOUN
ap-8497	135	5	.	.	PUNCT
ap-8497	136	1	(	(	PUNCT
ap-8497	136	2	7	7	X
ap-8497	136	3	)	)	PUNCT
ap-8497	136	4	in	in	ADP
ap-8497	136	5	ecological	ecological	ADJ
ap-8497	136	6	literature	literature	NOUN
ap-8497	136	7	,	,	PUNCT
ap-8497	136	8	it	it	PRON
ap-8497	136	9	is	be	AUX
ap-8497	136	10	realised	realise	VERB
ap-8497	136	11	that	that	DET
ap-8497	136	12	same	same	ADJ
ap-8497	136	13	sign	sign	NOUN
ap-8497	136	14	(	(	PUNCT
ap-8497	136	15	ss	ss	NOUN
ap-8497	136	16	)	)	PUNCT
ap-8497	136	17	links	link	NOUN
ap-8497	136	18	(	(	PUNCT
ap-8497	136	19	i.e.	i.e.	X
ap-8497	136	20	pp	pp	CCONJ
ap-8497	136	21	and	and	CCONJ
ap-8497	136	22	nn	nn	NUM
ap-8497	136	23	links	link	NOUN
ap-8497	136	24	)	)	PUNCT
ap-8497	136	25	of	of	ADP
ap-8497	136	26	this	this	DET
ap-8497	136	27	form	form	NOUN
ap-8497	136	28	are	be	AUX
ap-8497	136	29	conducive	conducive	ADJ
ap-8497	136	30	to	to	ADP
ap-8497	136	31	stability	stability	NOUN
ap-8497	136	32	whereas	whereas	SCONJ
ap-8497	136	33	opposite	opposite	ADJ
ap-8497	136	34	sign	sign	NOUN
ap-8497	136	35	(	(	PUNCT
ap-8497	136	36	os	os	NOUN
ap-8497	136	37	)	)	PUNCT
ap-8497	136	38	links	link	NOUN
ap-8497	136	39	(	(	PUNCT
ap-8497	136	40	i.e.	i.e.	X
ap-8497	136	41	pn	pn	X
ap-8497	136	42	and	and	CCONJ
ap-8497	136	43	np	np	ADP
ap-8497	136	44	links	link	NOUN
ap-8497	136	45	)	)	PUNCT
ap-8497	136	46	of	of	ADP
ap-8497	136	47	this	this	DET
ap-8497	136	48	form	form	NOUN
ap-8497	136	49	are	be	AUX
ap-8497	136	50	detrimental	detrimental	ADJ
ap-8497	136	51	to	to	ADP
ap-8497	136	52	stability	stability	NOUN
ap-8497	136	53	.	.	PUNCT
ap-8497	137	1	so	so	ADV
ap-8497	137	2	,	,	PUNCT
ap-8497	137	3	ss	ss	NOUN
ap-8497	137	4	links	link	NOUN
ap-8497	137	5	and	and	CCONJ
ap-8497	137	6	zs	zs	NOUN
ap-8497	137	7	links	link	NOUN
ap-8497	137	8	of	of	ADP
ap-8497	137	9	this	this	DET
ap-8497	137	10	form	form	NOUN
ap-8497	137	11	are	be	AUX
ap-8497	137	12	considered	consider	VERB
ap-8497	137	13	as	as	ADP
ap-8497	137	14	‘	'	PUNCT
ap-8497	137	15	good	good	ADJ
ap-8497	137	16	’	'	PUNCT
ap-8497	137	17	links	link	NOUN
ap-8497	137	18	,	,	PUNCT
ap-8497	137	19	and	and	CCONJ
ap-8497	137	20	os	os	VERB
ap-8497	137	21	links	link	NOUN
ap-8497	137	22	of	of	ADP
ap-8497	137	23	this	this	DET
ap-8497	137	24	form	form	NOUN
ap-8497	137	25	are	be	AUX
ap-8497	137	26	considered	consider	VERB
ap-8497	137	27	as	as	ADP
ap-8497	137	28	‘	'	PUNCT
ap-8497	137	29	bad	bad	ADJ
ap-8497	137	30	’	'	PUNCT
ap-8497	137	31	links	link	NOUN
ap-8497	137	32	.	.	PUNCT
ap-8497	138	1	hence	hence	ADV
ap-8497	138	2	:	:	PUNCT
ap-8497	139	1	n	n	DET
ap-8497	139	2	′	′	NUM
ap-8497	140	1	good	good	ADJ
ap-8497	141	1	=	=	PUNCT
ap-8497	141	2	n	n	NOUN
ap-8497	141	3	′	′	NUM
ap-8497	141	4	ss	ss	INTJ
ap-8497	142	1	+	+	CCONJ
ap-8497	142	2	n	n	NUM
ap-8497	143	1	′	′	NUM
ap-8497	143	2	zs	zs	NOUN
ap-8497	144	1	+	+	CCONJ
ap-8497	144	2	n	n	CCONJ
ap-8497	144	3	′	′	NUM
ap-8497	144	4	ezz	ezz	NOUN
ap-8497	144	5	,	,	PUNCT
ap-8497	144	6	(	(	PUNCT
ap-8497	144	7	8)	8)	NUM
ap-8497	144	8	n	n	NOUN
ap-8497	144	9	′	′	NUM
ap-8497	144	10	bad	bad	ADJ
ap-8497	144	11	=	=	PUNCT
ap-8497	145	1	n	n	NOUN
ap-8497	145	2	′	′	NOUN
ap-8497	145	3	os	os	NOUN
ap-8497	145	4	.	.	PUNCT
ap-8497	146	1	(	(	PUNCT
ap-8497	146	2	9	9	X
ap-8497	146	3	)	)	PUNCT
ap-8497	146	4	let	let	VERB
ap-8497	146	5	us	we	PRON
ap-8497	146	6	define	define	VERB
ap-8497	146	7	:	:	PUNCT
ap-8497	146	8	η	η	PROPN
ap-8497	146	9	′	′	NOUN
ap-8497	146	10	bad	bad	ADJ
ap-8497	147	1	=	=	SYM
ap-8497	147	2	n	n	CCONJ
ap-8497	147	3	′	′	NUM
ap-8497	147	4	bad	bad	ADJ
ap-8497	148	1	n	n	NOUN
ap-8497	148	2	′	′	NUM
ap-8497	148	3	lc	lc	PROPN
ap-8497	148	4	η	η	PROPN
ap-8497	148	5	′	′	PROPN
ap-8497	148	6	good	good	NOUN
ap-8497	149	1	=	=	PUNCT
ap-8497	149	2	n	n	NOUN
ap-8497	149	3	′	′	NUM
ap-8497	149	4	good	good	ADJ
ap-8497	150	1	n	n	PRON
ap-8497	150	2	′	′	NUM
ap-8497	150	3	lc	lc	PROPN
ap-8497	150	4	∴	∴	PROPN
ap-8497	150	5	η	η	PROPN
ap-8497	151	1	′	′	NUM
ap-8497	151	2	bad	bad	ADJ
ap-8497	152	1	+	+	CCONJ
ap-8497	152	2	η	η	X
ap-8497	152	3	′	′	ADJ
ap-8497	152	4	good	good	NOUN
ap-8497	152	5	=	=	NOUN
ap-8497	152	6	1	1	X
ap-8497	152	7	.	.	PUNCT
ap-8497	153	1	let	let	VERB
ap-8497	153	2	us	we	PRON
ap-8497	153	3	define	define	VERB
ap-8497	153	4	ζbad	ζbad	NOUN
ap-8497	153	5	as	as	ADP
ap-8497	153	6	potentially	potentially	ADV
ap-8497	153	7	destabilising	destabilising	ADJ
ap-8497	153	8	sign	sign	NOUN
ap-8497	153	9	matrix	matrix	NOUN
ap-8497	153	10	pair	pair	NOUN
ap-8497	153	11	index	index	NOUN
ap-8497	153	12	and	and	CCONJ
ap-8497	153	13	ζgood	ζgood	NOUN
ap-8497	153	14	as	as	ADP
ap-8497	153	15	the	the	DET
ap-8497	153	16	potentially	potentially	ADV
ap-8497	153	17	stabilising	stabilising	ADJ
ap-8497	153	18	sign	sign	NOUN
ap-8497	153	19	matrix	matrix	NOUN
ap-8497	153	20	pair	pair	NOUN
ap-8497	153	21	index	index	NOUN
ap-8497	153	22	.	.	PUNCT
ap-8497	154	1	so	so	ADV
ap-8497	154	2	:	:	PUNCT
ap-8497	154	3	ζgood	ζgood	NOUN
ap-8497	154	4	=	=	PUNCT
ap-8497	154	5	ηng	ηng	NOUN
ap-8497	154	6	+	+	CCONJ
ap-8497	154	7	ηgood	ηgood	NOUN
ap-8497	154	8	+	+	CCONJ
ap-8497	154	9	η	η	PROPN
ap-8497	154	10	′	′	NOUN
ap-8497	154	11	good	good	ADJ
ap-8497	154	12	,	,	PUNCT
ap-8497	154	13	(	(	PUNCT
ap-8497	154	14	10	10	NUM
ap-8497	154	15	)	)	PUNCT
ap-8497	154	16	ζbad	ζbad	ADJ
ap-8497	154	17	=	=	NOUN
ap-8497	154	18	ηpz	ηpz	NOUN
ap-8497	154	19	+	+	CCONJ
ap-8497	154	20	ηbad	ηbad	NOUN
ap-8497	154	21	+	+	CCONJ
ap-8497	154	22	η	η	NOUN
ap-8497	154	23	′	′	NOUN
ap-8497	154	24	bad	bad	ADJ
ap-8497	154	25	.	.	PUNCT
ap-8497	155	1	(	(	PUNCT
ap-8497	155	2	11	11	NUM
ap-8497	155	3	)	)	PUNCT
ap-8497	155	4	also	also	ADV
ap-8497	155	5	define	define	VERB
ap-8497	155	6	ζnet	ζnet	NOUN
ap-8497	155	7	as	as	ADP
ap-8497	155	8	the	the	DET
ap-8497	155	9	net	net	ADJ
ap-8497	155	10	matrix	matrix	NOUN
ap-8497	155	11	pair	pair	NOUN
ap-8497	155	12	stabilisation	stabilisation	NOUN
ap-8497	155	13	index	index	NOUN
ap-8497	155	14	given	give	VERB
ap-8497	155	15	by	by	ADP
ap-8497	155	16	ζnet	ζnet	NOUN
ap-8497	155	17	=	=	PUNCT
ap-8497	155	18	ζgood	ζgood	NOUN
ap-8497	155	19	−	−	PROPN
ap-8497	155	20	ζbad	ζbad	PROPN
ap-8497	155	21	.	.	PUNCT
ap-8497	156	1	(	(	PUNCT
ap-8497	156	2	12	12	NUM
ap-8497	156	3	)	)	PUNCT
ap-8497	156	4	let	let	VERB
ap-8497	156	5	us	we	PRON
ap-8497	156	6	define	define	VERB
ap-8497	156	7	the	the	DET
ap-8497	156	8	index	index	NOUN
ap-8497	156	9	,	,	PUNCT
ap-8497	156	10	known	know	VERB
ap-8497	156	11	as	as	ADP
ap-8497	156	12	‘	'	PUNCT
ap-8497	156	13	chain	chain	NOUN
ap-8497	156	14	’	'	PUNCT
ap-8497	156	15	.	.	PUNCT
ap-8497	157	1	the	the	DET
ap-8497	157	2	elemental	elemental	ADJ
ap-8497	157	3	structure	structure	NOUN
ap-8497	157	4	of	of	ADP
ap-8497	157	5	the	the	DET
ap-8497	157	6	form	form	NOUN
ap-8497	157	7	eijejiaijaji	eijejiaijaji	NOUN
ap-8497	157	8	is	be	AUX
ap-8497	157	9	called	call	VERB
ap-8497	157	10	a	a	DET
ap-8497	157	11	‘	'	PUNCT
ap-8497	157	12	chain	chain	NOUN
ap-8497	157	13	’	'	PUNCT
ap-8497	157	14	.	.	PUNCT
ap-8497	158	1	the	the	DET
ap-8497	158	2	chain	chain	NOUN
ap-8497	158	3	containing	contain	VERB
ap-8497	158	4	at	at	ADV
ap-8497	158	5	least	least	ADV
ap-8497	158	6	three	three	NUM
ap-8497	158	7	‘	'	PUNCT
ap-8497	158	8	+	+	ADJ
ap-8497	158	9	’	'	PUNCT
ap-8497	158	10	sign	sign	NOUN
ap-8497	158	11	is	be	AUX
ap-8497	158	12	known	know	VERB
ap-8497	158	13	as	as	ADP
ap-8497	158	14	‘	'	PUNCT
ap-8497	158	15	+	+	NUM
ap-8497	158	16	chain	chain	NOUN
ap-8497	158	17	’	'	PUNCT
ap-8497	158	18	and	and	CCONJ
ap-8497	158	19	the	the	DET
ap-8497	158	20	chain	chain	NOUN
ap-8497	158	21	containing	contain	VERB
ap-8497	158	22	at	at	ADV
ap-8497	158	23	least	least	ADV
ap-8497	158	24	three	three	NUM
ap-8497	158	25	‘	'	PUNCT
ap-8497	158	26	−	−	NOUN
ap-8497	158	27	’	'	PUNCT
ap-8497	158	28	sign	sign	NOUN
ap-8497	158	29	is	be	AUX
ap-8497	158	30	known	know	VERB
ap-8497	158	31	as	as	ADP
ap-8497	158	32	‘	'	PUNCT
ap-8497	158	33	−	−	NOUN
ap-8497	158	34	chain	chain	NOUN
ap-8497	158	35	’	'	PUNCT
ap-8497	158	36	.	.	PUNCT
ap-8497	159	1	using	use	VERB
ap-8497	159	2	these	these	DET
ap-8497	159	3	‘	'	PUNCT
ap-8497	159	4	qualitative	qualitative	ADJ
ap-8497	159	5	sign	sign	NOUN
ap-8497	159	6	matrix	matrix	NOUN
ap-8497	159	7	pair	pair	NOUN
ap-8497	159	8	indices	index	NOUN
ap-8497	159	9	’	'	PUNCT
ap-8497	159	10	,	,	PUNCT
ap-8497	159	11	we	we	PRON
ap-8497	159	12	discuss	discuss	VERB
ap-8497	159	13	the	the	DET
ap-8497	159	14	qualitative	qualitative	ADJ
ap-8497	159	15	stability	stability	NOUN
ap-8497	159	16	of	of	ADP
ap-8497	159	17	a	a	DET
ap-8497	159	18	matrix	matrix	NOUN
ap-8497	159	19	pair	pair	NOUN
ap-8497	159	20	and	and	CCONJ
ap-8497	159	21	derive	derive	VERB
ap-8497	159	22	few	few	ADJ
ap-8497	159	23	conditions	condition	NOUN
ap-8497	159	24	for	for	ADP
ap-8497	159	25	the	the	DET
ap-8497	159	26	qualitative	qualitative	ADJ
ap-8497	159	27	sign	sign	NOUN
ap-8497	159	28	instability	instability	NOUN
ap-8497	159	29	.	.	PUNCT
ap-8497	160	1	3	3	X
ap-8497	160	2	.	.	X
ap-8497	160	3	conditions	condition	NOUN
ap-8497	160	4	for	for	ADP
ap-8497	160	5	qualitative	qualitative	ADJ
ap-8497	160	6	sign	sign	NOUN
ap-8497	160	7	stability	stability	NOUN
ap-8497	160	8	and	and	CCONJ
ap-8497	160	9	instability	instability	NOUN
ap-8497	160	10	in	in	ADP
ap-8497	160	11	this	this	DET
ap-8497	160	12	section	section	NOUN
ap-8497	160	13	,	,	PUNCT
ap-8497	160	14	the	the	DET
ap-8497	160	15	main	main	ADJ
ap-8497	160	16	results	result	NOUN
ap-8497	160	17	are	be	AUX
ap-8497	160	18	presented	present	VERB
ap-8497	160	19	.	.	PUNCT
ap-8497	161	1	here	here	ADV
ap-8497	161	2	we	we	PRON
ap-8497	161	3	focus	focus	VERB
ap-8497	161	4	on	on	ADP
ap-8497	161	5	the	the	DET
ap-8497	161	6	case	case	NOUN
ap-8497	161	7	of	of	ADP
ap-8497	161	8	matrix	matrix	NOUN
ap-8497	161	9	pairs	pair	NOUN
ap-8497	161	10	with	with	ADP
ap-8497	161	11	diagonal	diagonal	ADJ
ap-8497	161	12	elements	element	NOUN
ap-8497	161	13	containing	contain	VERB
ap-8497	161	14	only	only	ADV
ap-8497	161	15	a	a	DET
ap-8497	161	16	mixture	mixture	NOUN
ap-8497	161	17	of	of	ADP
ap-8497	161	18	positive	positive	ADJ
ap-8497	161	19	and	and	CCONJ
ap-8497	161	20	negative	negative	ADJ
ap-8497	161	21	elements	element	NOUN
ap-8497	161	22	,	,	PUNCT
ap-8497	161	23	i.e.	i.e.	X
ap-8497	161	24	with	with	ADP
ap-8497	161	25	npz	npz	NOUN
ap-8497	161	26	=	=	SYM
ap-8497	161	27	np	np	INTJ
ap-8497	161	28	.	.	PUNCT
ap-8497	162	1	also	also	ADV
ap-8497	162	2	,	,	PUNCT
ap-8497	162	3	we	we	PRON
ap-8497	162	4	assume	assume	VERB
ap-8497	162	5	that	that	SCONJ
ap-8497	162	6	nbad	nbad	ADJ
ap-8497	162	7	=	=	SYM
ap-8497	162	8	nss	nss	NOUN
ap-8497	162	9	and	and	CCONJ
ap-8497	162	10	n	n	NOUN
ap-8497	162	11	′	′	NUM
ap-8497	162	12	good	good	ADJ
ap-8497	163	1	=	=	PUNCT
ap-8497	163	2	n	n	NOUN
ap-8497	163	3	′	′	NUM
ap-8497	163	4	ss	ss	PROPN
ap-8497	163	5	.	.	PUNCT
ap-8497	164	1	a	a	DET
ap-8497	164	2	series	series	NOUN
ap-8497	164	3	of	of	ADP
ap-8497	164	4	necessary	necessary	ADJ
ap-8497	164	5	and	and	CCONJ
ap-8497	164	6	sufficient	sufficient	ADJ
ap-8497	164	7	conditions	condition	NOUN
ap-8497	164	8	for	for	ADP
ap-8497	164	9	stability	stability	NOUN
ap-8497	164	10	/	/	SYM
ap-8497	164	11	instability	instability	NOUN
ap-8497	164	12	of	of	ADP
ap-8497	164	13	a	a	DET
ap-8497	164	14	matrix	matrix	NOUN
ap-8497	164	15	pair	pair	NOUN
ap-8497	164	16	are	be	AUX
ap-8497	164	17	presented	present	VERB
ap-8497	164	18	here	here	ADV
ap-8497	164	19	.	.	PUNCT
ap-8497	165	1	174	174	NUM
ap-8497	165	2	vol	vol	NOUN
ap-8497	165	3	.	.	PUNCT
ap-8497	165	4	63	63	NUM
ap-8497	165	5	no	no	NOUN
ap-8497	165	6	.	.	PUNCT
ap-8497	166	1	3/2023	3/2023	NUM
ap-8497	166	2	qualitative	qualitative	NOUN
ap-8497	166	3	sign	sign	NOUN
ap-8497	166	4	stability	stability	NOUN
ap-8497	166	5	of	of	ADP
ap-8497	166	6	linear	linear	ADJ
ap-8497	166	7	time	time	NOUN
ap-8497	166	8	invariant	invariant	ADJ
ap-8497	166	9	descriptor	descriptor	NOUN
ap-8497	166	10	systems	system	NOUN
ap-8497	166	11	3.1	3.1	NUM
ap-8497	166	12	.	.	PUNCT
ap-8497	166	13	necessary	necessary	ADJ
ap-8497	166	14	conditions	condition	NOUN
ap-8497	166	15	for	for	ADP
ap-8497	166	16	qualitative	qualitative	ADJ
ap-8497	166	17	stability	stability	NOUN
ap-8497	166	18	of	of	ADP
ap-8497	166	19	matrix	matrix	NOUN
ap-8497	166	20	pair	pair	NOUN
ap-8497	166	21	for	for	ADP
ap-8497	166	22	qualitative	qualitative	ADJ
ap-8497	166	23	reasoning	reasoning	NOUN
ap-8497	166	24	,	,	PUNCT
ap-8497	166	25	we	we	PRON
ap-8497	166	26	need	need	VERB
ap-8497	166	27	to	to	PART
ap-8497	166	28	know	know	VERB
ap-8497	166	29	the	the	DET
ap-8497	166	30	number	number	NOUN
ap-8497	166	31	and	and	CCONJ
ap-8497	166	32	nature	nature	NOUN
ap-8497	166	33	of	of	ADP
ap-8497	166	34	the	the	DET
ap-8497	166	35	above	above	ADV
ap-8497	166	36	-	-	PUNCT
ap-8497	166	37	defined	define	VERB
ap-8497	166	38	interactions	interaction	NOUN
ap-8497	166	39	and	and	CCONJ
ap-8497	166	40	interconnections	interconnection	NOUN
ap-8497	166	41	.	.	PUNCT
ap-8497	167	1	but	but	CCONJ
ap-8497	167	2	it	it	PRON
ap-8497	167	3	is	be	AUX
ap-8497	167	4	not	not	PART
ap-8497	167	5	possible	possible	ADJ
ap-8497	167	6	to	to	PART
ap-8497	167	7	find	find	VERB
ap-8497	167	8	the	the	DET
ap-8497	167	9	number	number	NOUN
ap-8497	167	10	and	and	CCONJ
ap-8497	167	11	nature	nature	NOUN
ap-8497	167	12	of	of	ADP
ap-8497	167	13	all	all	DET
ap-8497	167	14	the	the	DET
ap-8497	167	15	interconnection	interconnection	NOUN
ap-8497	167	16	terms	term	NOUN
ap-8497	167	17	of	of	ADP
ap-8497	167	18	a	a	DET
ap-8497	167	19	matrix	matrix	NOUN
ap-8497	167	20	pair	pair	NOUN
ap-8497	167	21	.	.	PUNCT
ap-8497	168	1	so	so	ADV
ap-8497	168	2	,	,	PUNCT
ap-8497	168	3	for	for	ADP
ap-8497	168	4	the	the	DET
ap-8497	168	5	qualitative	qualitative	ADJ
ap-8497	168	6	sign	sign	NOUN
ap-8497	168	7	stability	stability	NOUN
ap-8497	168	8	,	,	PUNCT
ap-8497	168	9	all	all	DET
ap-8497	168	10	the	the	DET
ap-8497	168	11	interconnection	interconnection	NOUN
ap-8497	168	12	terms	term	NOUN
ap-8497	168	13	of	of	ADP
ap-8497	168	14	a	a	DET
ap-8497	168	15	matrix	matrix	NOUN
ap-8497	168	16	pair	pair	NOUN
ap-8497	168	17	need	need	VERB
ap-8497	168	18	to	to	PART
ap-8497	168	19	be	be	AUX
ap-8497	168	20	zero	zero	NUM
ap-8497	168	21	.	.	PUNCT
ap-8497	169	1	furthermore	furthermore	ADV
ap-8497	169	2	,	,	PUNCT
ap-8497	169	3	any	any	DET
ap-8497	169	4	matrix	matrix	NOUN
ap-8497	169	5	pair	pair	NOUN
ap-8497	169	6	(	(	PUNCT
ap-8497	169	7	e	e	NOUN
ap-8497	169	8	,	,	PUNCT
ap-8497	169	9	a	a	PRON
ap-8497	169	10	)	)	PUNCT
ap-8497	169	11	with	with	ADP
ap-8497	169	12	det(a	det(a	PROPN
ap-8497	169	13	)	)	PUNCT
ap-8497	169	14	=	=	SYM
ap-8497	169	15	0	0	PUNCT
ap-8497	169	16	has	have	VERB
ap-8497	169	17	always	always	ADV
ap-8497	169	18	at	at	ADV
ap-8497	169	19	least	least	ADJ
ap-8497	169	20	one	one	NUM
ap-8497	169	21	zero	zero	NUM
ap-8497	169	22	eigenvalue	eigenvalue	NOUN
ap-8497	169	23	,	,	PUNCT
ap-8497	169	24	that	that	PRON
ap-8497	169	25	makes	make	VERB
ap-8497	169	26	the	the	DET
ap-8497	169	27	matrix	matrix	NOUN
ap-8497	169	28	pair	pair	NOUN
ap-8497	169	29	unstable	unstable	ADJ
ap-8497	169	30	.	.	PUNCT
ap-8497	170	1	hence	hence	ADV
ap-8497	170	2	,	,	PUNCT
ap-8497	170	3	the	the	DET
ap-8497	170	4	nonsingularity	nonsingularity	NOUN
ap-8497	170	5	of	of	ADP
ap-8497	170	6	matrix	matrix	NOUN
ap-8497	170	7	a	a	PRON
ap-8497	170	8	is	be	AUX
ap-8497	170	9	also	also	ADV
ap-8497	170	10	necessarily	necessarily	ADV
ap-8497	170	11	required	require	VERB
ap-8497	170	12	for	for	ADP
ap-8497	170	13	qlss	qlss	ADJ
ap-8497	170	14	matrix	matrix	NOUN
ap-8497	170	15	pair	pair	NOUN
ap-8497	170	16	.	.	PUNCT
ap-8497	171	1	let	let	VERB
ap-8497	171	2	us	we	PRON
ap-8497	171	3	consider	consider	VERB
ap-8497	171	4	a	a	DET
ap-8497	171	5	matrix	matrix	NOUN
ap-8497	171	6	pair	pair	NOUN
ap-8497	171	7	(	(	PUNCT
ap-8497	171	8	e	e	NOUN
ap-8497	171	9	,	,	PUNCT
ap-8497	171	10	a	a	PRON
ap-8497	171	11	)	)	PUNCT
ap-8497	171	12	with	with	ADP
ap-8497	171	13	entries	entry	NOUN
ap-8497	171	14	eij	eij	PROPN
ap-8497	171	15	and	and	CCONJ
ap-8497	171	16	aij	aij	PROPN
ap-8497	171	17	,	,	PUNCT
ap-8497	171	18	respectively	respectively	ADV
ap-8497	171	19	.	.	PUNCT
ap-8497	172	1	based	base	VERB
ap-8497	172	2	on	on	ADP
ap-8497	172	3	the	the	DET
ap-8497	172	4	above	above	ADJ
ap-8497	172	5	discussion	discussion	NOUN
ap-8497	172	6	,	,	PUNCT
ap-8497	172	7	we	we	PRON
ap-8497	172	8	are	be	AUX
ap-8497	172	9	enlisting	enlist	VERB
ap-8497	172	10	the	the	DET
ap-8497	172	11	two	two	NUM
ap-8497	172	12	important	important	ADJ
ap-8497	172	13	‘	'	PUNCT
ap-8497	172	14	necessary	necessary	ADJ
ap-8497	172	15	’	'	PUNCT
ap-8497	172	16	conditions	condition	NOUN
ap-8497	172	17	for	for	ADP
ap-8497	172	18	‘	'	PUNCT
ap-8497	172	19	qualitative	qualitative	ADJ
ap-8497	172	20	sign	sign	NOUN
ap-8497	172	21	stability	stability	NOUN
ap-8497	172	22	’	'	PUNCT
ap-8497	172	23	:	:	PUNCT
ap-8497	172	24	•	•	NUM
ap-8497	172	25	c1	c1	NOUN
ap-8497	172	26	:	:	PUNCT
ap-8497	172	27	bijbjk	bijbjk	PROPN
ap-8497	172	28	.	.	PUNCT
ap-8497	172	29	.	.	PUNCT
ap-8497	172	30	.	.	PUNCT
ap-8497	173	1	bqrbri	bqrbri	NOUN
ap-8497	173	2	=	=	PUNCT
ap-8497	173	3	0	0	PROPN
ap-8497	173	4	,	,	PUNCT
ap-8497	173	5	where	where	SCONJ
ap-8497	173	6	bij	bij	NOUN
ap-8497	173	7	=	=	SYM
ap-8497	173	8	eij	eij	PROPN
ap-8497	173	9	or	or	CCONJ
ap-8497	173	10	aij	aij	PROPN
ap-8497	173	11	for	for	ADP
ap-8497	173	12	any	any	DET
ap-8497	173	13	sequences	sequence	NOUN
ap-8497	173	14	of	of	ADP
ap-8497	173	15	three	three	NUM
ap-8497	173	16	or	or	CCONJ
ap-8497	173	17	more	more	ADV
ap-8497	173	18	distinct	distinct	ADJ
ap-8497	173	19	indices	index	NOUN
ap-8497	173	20	i	i	PRON
ap-8497	173	21	,	,	PUNCT
ap-8497	173	22	j	j	PROPN
ap-8497	173	23	,	,	PUNCT
ap-8497	173	24	k	k	PROPN
ap-8497	173	25	,	,	PUNCT
ap-8497	173	26	.	.	PUNCT
ap-8497	173	27	.	.	PUNCT
ap-8497	174	1	.	.	PUNCT
ap-8497	175	1	,	,	PUNCT
ap-8497	175	2	q	q	X
ap-8497	175	3	,	,	PUNCT
ap-8497	175	4	r.	r.	PROPN
ap-8497	175	5	•	•	PROPN
ap-8497	175	6	c2	c2	PROPN
ap-8497	175	7	:	:	PUNCT
ap-8497	175	8	det(a	det(a	ADJ
ap-8497	175	9	)	)	PUNCT
ap-8497	175	10	̸=	̸=	PROPN
ap-8497	175	11	0	0	NUM
ap-8497	175	12	.	.	PUNCT
ap-8497	176	1	here	here	ADV
ap-8497	176	2	,	,	PUNCT
ap-8497	176	3	c1	c1	PROPN
ap-8497	176	4	is	be	AUX
ap-8497	176	5	the	the	DET
ap-8497	176	6	necessarily	necessarily	ADV
ap-8497	176	7	required	require	VERB
ap-8497	176	8	condition	condition	NOUN
ap-8497	176	9	for	for	ADP
ap-8497	176	10	qualitative	qualitative	ADJ
ap-8497	176	11	sign	sign	NOUN
ap-8497	176	12	stability	stability	NOUN
ap-8497	176	13	,	,	PUNCT
ap-8497	176	14	i.e.	i.e.	X
ap-8497	176	15	the	the	DET
ap-8497	176	16	condition	condition	NOUN
ap-8497	176	17	which	which	PRON
ap-8497	176	18	makes	make	VERB
ap-8497	176	19	the	the	DET
ap-8497	176	20	matrix	matrix	NOUN
ap-8497	176	21	pair	pair	NOUN
ap-8497	176	22	stable	stable	ADJ
ap-8497	176	23	,	,	PUNCT
ap-8497	176	24	independent	independent	ADJ
ap-8497	176	25	of	of	ADP
ap-8497	176	26	magnitudes	magnitude	NOUN
ap-8497	176	27	,	,	PUNCT
ap-8497	176	28	and	and	CCONJ
ap-8497	176	29	c2	c2	PROPN
ap-8497	176	30	is	be	AUX
ap-8497	176	31	the	the	DET
ap-8497	176	32	necessarily	necessarily	ADV
ap-8497	176	33	required	require	VERB
ap-8497	176	34	condition	condition	NOUN
ap-8497	176	35	for	for	ADP
ap-8497	176	36	the	the	DET
ap-8497	176	37	stability	stability	NOUN
ap-8497	176	38	of	of	ADP
ap-8497	176	39	the	the	DET
ap-8497	176	40	matrix	matrix	NOUN
ap-8497	176	41	pair	pair	NOUN
ap-8497	176	42	(	(	PUNCT
ap-8497	176	43	e	e	NOUN
ap-8497	176	44	,	,	PUNCT
ap-8497	176	45	a	a	PRON
ap-8497	176	46	)	)	PUNCT
ap-8497	176	47	,	,	PUNCT
ap-8497	176	48	independent	independent	ADJ
ap-8497	176	49	of	of	ADP
ap-8497	176	50	any	any	DET
ap-8497	176	51	qualitative	qualitative	ADJ
ap-8497	176	52	or	or	CCONJ
ap-8497	176	53	quantitative	quantitative	ADJ
ap-8497	176	54	information	information	NOUN
ap-8497	176	55	of	of	ADP
ap-8497	176	56	the	the	DET
ap-8497	176	57	matrix	matrix	NOUN
ap-8497	176	58	pair	pair	NOUN
ap-8497	176	59	elements	element	NOUN
ap-8497	176	60	.	.	PUNCT
ap-8497	177	1	more	more	ADJ
ap-8497	177	2	details	detail	NOUN
ap-8497	177	3	about	about	ADP
ap-8497	177	4	the	the	DET
ap-8497	177	5	concept	concept	NOUN
ap-8497	177	6	of	of	ADP
ap-8497	177	7	qualitative	qualitative	ADJ
ap-8497	177	8	sign	sign	NOUN
ap-8497	177	9	stability	stability	NOUN
ap-8497	177	10	is	be	AUX
ap-8497	177	11	discussed	discuss	VERB
ap-8497	177	12	in	in	ADP
ap-8497	177	13	[	[	X
ap-8497	177	14	11	11	NUM
ap-8497	177	15	,	,	PUNCT
ap-8497	177	16	14	14	NUM
ap-8497	177	17	]	]	PUNCT
ap-8497	177	18	.	.	PUNCT
ap-8497	178	1	the	the	DET
ap-8497	178	2	net	net	ADJ
ap-8497	178	3	matrix	matrix	NOUN
ap-8497	178	4	pair	pair	NOUN
ap-8497	178	5	stabilisation	stabilisation	NOUN
ap-8497	178	6	index	index	NOUN
ap-8497	178	7	ζnet	ζnet	PROPN
ap-8497	178	8	serves	serve	VERB
ap-8497	178	9	as	as	ADP
ap-8497	178	10	an	an	DET
ap-8497	178	11	index	index	NOUN
ap-8497	178	12	to	to	PART
ap-8497	178	13	indicate	indicate	VERB
ap-8497	178	14	the	the	DET
ap-8497	178	15	likelihood	likelihood	NOUN
ap-8497	178	16	of	of	ADP
ap-8497	178	17	matrix	matrix	NOUN
ap-8497	178	18	pair	pair	NOUN
ap-8497	178	19	being	be	AUX
ap-8497	178	20	stable	stable	ADJ
ap-8497	178	21	or	or	CCONJ
ap-8497	178	22	unstable	unstable	ADJ
ap-8497	178	23	in	in	ADP
ap-8497	178	24	a	a	DET
ap-8497	178	25	qualitative	qualitative	ADJ
ap-8497	178	26	way	way	NOUN
ap-8497	178	27	.	.	PUNCT
ap-8497	179	1	negative	negative	ADJ
ap-8497	179	2	values	value	NOUN
ap-8497	179	3	indicate	indicate	VERB
ap-8497	179	4	that	that	SCONJ
ap-8497	179	5	the	the	DET
ap-8497	179	6	matrix	matrix	NOUN
ap-8497	179	7	pair	pair	NOUN
ap-8497	179	8	is	be	AUX
ap-8497	179	9	more	more	ADV
ap-8497	179	10	likely	likely	ADJ
ap-8497	179	11	to	to	PART
ap-8497	179	12	be	be	AUX
ap-8497	179	13	unstable	unstable	ADJ
ap-8497	179	14	,	,	PUNCT
ap-8497	179	15	and	and	CCONJ
ap-8497	179	16	positive	positive	ADJ
ap-8497	179	17	values	value	NOUN
ap-8497	179	18	indicate	indicate	VERB
ap-8497	179	19	that	that	SCONJ
ap-8497	179	20	the	the	DET
ap-8497	179	21	matrix	matrix	NOUN
ap-8497	179	22	pair	pair	NOUN
ap-8497	179	23	is	be	AUX
ap-8497	179	24	more	more	ADV
ap-8497	179	25	likely	likely	ADJ
ap-8497	179	26	to	to	PART
ap-8497	179	27	be	be	AUX
ap-8497	179	28	stable	stable	ADJ
ap-8497	179	29	.	.	PUNCT
ap-8497	180	1	the	the	PRON
ap-8497	180	2	higher	high	ADJ
ap-8497	180	3	the	the	DET
ap-8497	180	4	value	value	NOUN
ap-8497	180	5	,	,	PUNCT
ap-8497	180	6	the	the	PRON
ap-8497	180	7	higher	high	ADJ
ap-8497	180	8	the	the	DET
ap-8497	180	9	probability	probability	NOUN
ap-8497	180	10	,	,	PUNCT
ap-8497	180	11	see	see	VERB
ap-8497	180	12	[	[	X
ap-8497	180	13	16	16	NUM
ap-8497	180	14	]	]	PUNCT
ap-8497	180	15	.	.	PUNCT
ap-8497	181	1	the	the	DET
ap-8497	181	2	qualitative	qualitative	ADJ
ap-8497	181	3	sign	sign	NOUN
ap-8497	181	4	stability	stability	NOUN
ap-8497	181	5	of	of	ADP
ap-8497	181	6	a	a	DET
ap-8497	181	7	matrix	matrix	NOUN
ap-8497	181	8	pair	pair	NOUN
ap-8497	181	9	depends	depend	VERB
ap-8497	181	10	upon	upon	SCONJ
ap-8497	181	11	the	the	DET
ap-8497	181	12	stabilising	stabilise	VERB
ap-8497	181	13	strength	strength	NOUN
ap-8497	181	14	of	of	ADP
ap-8497	181	15	the	the	DET
ap-8497	181	16	matrix	matrix	NOUN
ap-8497	181	17	pair	pair	NOUN
ap-8497	181	18	.	.	PUNCT
ap-8497	182	1	when	when	SCONJ
ap-8497	182	2	the	the	DET
ap-8497	182	3	matrix	matrix	NOUN
ap-8497	182	4	pair	pair	NOUN
ap-8497	182	5	is	be	AUX
ap-8497	182	6	more	more	ADV
ap-8497	182	7	potentially	potentially	ADV
ap-8497	182	8	stabilised	stabilise	VERB
ap-8497	182	9	,	,	PUNCT
ap-8497	182	10	then	then	ADV
ap-8497	182	11	ζnet	ζnet	PROPN
ap-8497	182	12	is	be	AUX
ap-8497	182	13	non	non	ADJ
ap-8497	182	14	-	-	ADJ
ap-8497	182	15	negative	negative	ADJ
ap-8497	182	16	,	,	PUNCT
ap-8497	182	17	and	and	CCONJ
ap-8497	182	18	when	when	SCONJ
ap-8497	182	19	it	it	PRON
ap-8497	182	20	is	be	AUX
ap-8497	182	21	more	more	ADV
ap-8497	182	22	potentially	potentially	ADV
ap-8497	182	23	destabilised	destabilise	VERB
ap-8497	182	24	,	,	PUNCT
ap-8497	182	25	then	then	ADV
ap-8497	182	26	ζnet	ζnet	PROPN
ap-8497	182	27	is	be	AUX
ap-8497	182	28	negative	negative	ADJ
ap-8497	182	29	.	.	PUNCT
ap-8497	183	1	so	so	ADV
ap-8497	183	2	,	,	PUNCT
ap-8497	183	3	the	the	DET
ap-8497	183	4	qualitative	qualitative	ADJ
ap-8497	183	5	stability	stability	NOUN
ap-8497	183	6	is	be	AUX
ap-8497	183	7	connected	connect	VERB
ap-8497	183	8	with	with	ADP
ap-8497	183	9	the	the	DET
ap-8497	183	10	value	value	NOUN
ap-8497	183	11	of	of	ADP
ap-8497	183	12	ζnet	ζnet	NOUN
ap-8497	183	13	.	.	PUNCT
ap-8497	184	1	with	with	ADP
ap-8497	184	2	this	this	DET
ap-8497	184	3	observation	observation	NOUN
ap-8497	184	4	,	,	PUNCT
ap-8497	184	5	we	we	PRON
ap-8497	184	6	have	have	VERB
ap-8497	184	7	the	the	DET
ap-8497	184	8	following	follow	VERB
ap-8497	184	9	conditions	condition	NOUN
ap-8497	184	10	:	:	PUNCT
ap-8497	184	11	•	•	NUM
ap-8497	184	12	ζnet	ζnet	NOUN
ap-8497	184	13	varies	vary	VERB
ap-8497	184	14	in	in	ADP
ap-8497	184	15	an	an	DET
ap-8497	184	16	interval	interval	NOUN
ap-8497	184	17	given	give	VERB
ap-8497	184	18	by	by	ADP
ap-8497	184	19	−3	−3	PROPN
ap-8497	184	20	≤	≤	PROPN
ap-8497	184	21	ζnet	ζnet	NOUN
ap-8497	184	22	≤	≤	ADV
ap-8497	184	23	3	3	NUM
ap-8497	184	24	.	.	SYM
ap-8497	184	25	•	•	NUM
ap-8497	185	1	ζnet	ζnet	NOUN
ap-8497	185	2	<	<	X
ap-8497	185	3	0	0	NUM
ap-8497	185	4	specifies	specifie	NOUN
ap-8497	185	5	that	that	SCONJ
ap-8497	185	6	the	the	DET
ap-8497	185	7	matrix	matrix	NOUN
ap-8497	185	8	pair	pair	NOUN
ap-8497	185	9	is	be	AUX
ap-8497	185	10	mdu	mdu	PROPN
ap-8497	185	11	,	,	PUNCT
ap-8497	185	12	that	that	PRON
ap-8497	185	13	means	mean	VERB
ap-8497	185	14	for	for	ADP
ap-8497	185	15	these	these	DET
ap-8497	185	16	mdu	mdu	PROPN
ap-8497	185	17	matrix	matrix	NOUN
ap-8497	185	18	pairs	pair	NOUN
ap-8497	185	19	,	,	PUNCT
ap-8497	185	20	there	there	PRON
ap-8497	185	21	always	always	ADV
ap-8497	185	22	exist	exist	VERB
ap-8497	185	23	magnitudes	magnitude	NOUN
ap-8497	185	24	that	that	PRON
ap-8497	185	25	make	make	VERB
ap-8497	185	26	this	this	DET
ap-8497	185	27	matrix	matrix	NOUN
ap-8497	185	28	pair	pair	NOUN
ap-8497	185	29	unstable	unstable	ADJ
ap-8497	185	30	.	.	PUNCT
ap-8497	186	1	•	•	NUM
ap-8497	186	2	ζnet	ζnet	PROPN
ap-8497	186	3	≥	≥	NOUN
ap-8497	186	4	0	0	NUM
ap-8497	186	5	specifies	specifie	NOUN
ap-8497	186	6	that	that	SCONJ
ap-8497	186	7	the	the	DET
ap-8497	186	8	matrix	matrix	NOUN
ap-8497	186	9	pair	pair	NOUN
ap-8497	186	10	is	be	AUX
ap-8497	186	11	mds	mds	PROPN
ap-8497	186	12	,	,	PUNCT
ap-8497	186	13	that	that	PRON
ap-8497	186	14	means	mean	VERB
ap-8497	186	15	for	for	ADP
ap-8497	186	16	these	these	DET
ap-8497	186	17	mds	mds	NOUN
ap-8497	186	18	matrix	matrix	NOUN
ap-8497	186	19	pairs	pair	NOUN
ap-8497	186	20	,	,	PUNCT
ap-8497	186	21	there	there	PRON
ap-8497	186	22	always	always	ADV
ap-8497	186	23	exist	exist	VERB
ap-8497	186	24	magnitudes	magnitude	NOUN
ap-8497	186	25	that	that	PRON
ap-8497	186	26	make	make	VERB
ap-8497	186	27	this	this	DET
ap-8497	186	28	matrix	matrix	NOUN
ap-8497	186	29	pair	pair	NOUN
ap-8497	186	30	stable	stable	ADJ
ap-8497	186	31	.	.	PUNCT
ap-8497	187	1	•	•	NUM
ap-8497	187	2	a	a	DET
ap-8497	187	3	given	give	VERB
ap-8497	187	4	(	(	PUNCT
ap-8497	187	5	non	non	ADJ
ap-8497	187	6	-	-	ADJ
ap-8497	187	7	qlss	qlss	ADJ
ap-8497	187	8	)	)	PUNCT
ap-8497	187	9	matrix	matrix	NOUN
ap-8497	187	10	pair	pair	NOUN
ap-8497	187	11	is	be	AUX
ap-8497	187	12	qlsu	qlsu	NOUN
ap-8497	187	13	only	only	ADV
ap-8497	187	14	if	if	SCONJ
ap-8497	187	15	−3	−3	PROPN
ap-8497	187	16	≤	≤	PROPN
ap-8497	187	17	ζnet	ζnet	NOUN
ap-8497	187	18	<	<	X
ap-8497	187	19	0	0	PUNCT
ap-8497	188	1	(	(	PUNCT
ap-8497	188	2	necessary	necessary	ADJ
ap-8497	188	3	condition	condition	NOUN
ap-8497	188	4	for	for	ADP
ap-8497	188	5	qlsu	qlsu	NOUN
ap-8497	188	6	)	)	PUNCT
ap-8497	188	7	.	.	PUNCT
ap-8497	189	1	a	a	DET
ap-8497	189	2	matrix	matrix	NOUN
ap-8497	189	3	pair	pair	NOUN
ap-8497	189	4	,	,	PUNCT
ap-8497	189	5	which	which	PRON
ap-8497	189	6	is	be	AUX
ap-8497	189	7	not	not	PART
ap-8497	189	8	qualitative	qualitative	ADJ
ap-8497	189	9	sign	sign	NOUN
ap-8497	189	10	stable	stable	ADJ
ap-8497	189	11	(	(	PUNCT
ap-8497	189	12	qlss	qlss	PROPN
ap-8497	189	13	)	)	PUNCT
ap-8497	189	14	,	,	PUNCT
ap-8497	189	15	is	be	AUX
ap-8497	189	16	said	say	VERB
ap-8497	189	17	to	to	PART
ap-8497	189	18	be	be	AUX
ap-8497	189	19	a	a	DET
ap-8497	189	20	non	non	ADJ
ap-8497	189	21	-	-	ADJ
ap-8497	189	22	qlss	qlss	ADJ
ap-8497	189	23	matrix	matrix	NOUN
ap-8497	189	24	pair	pair	NOUN
ap-8497	189	25	.	.	PUNCT
ap-8497	190	1	3.2	3.2	NUM
ap-8497	190	2	.	.	PUNCT
ap-8497	191	1	a	a	DET
ap-8497	191	2	necessary	necessary	ADJ
ap-8497	191	3	condition	condition	NOUN
ap-8497	191	4	for	for	ADP
ap-8497	191	5	instability	instability	NOUN
ap-8497	191	6	of	of	ADP
ap-8497	191	7	a	a	DET
ap-8497	191	8	matrix	matrix	NOUN
ap-8497	191	9	in	in	ADP
ap-8497	191	10	a	a	DET
ap-8497	191	11	matrix	matrix	NOUN
ap-8497	191	12	pair	pair	NOUN
ap-8497	191	13	(	(	PUNCT
ap-8497	191	14	e	e	NOUN
ap-8497	191	15	,	,	PUNCT
ap-8497	191	16	a	a	NOUN
ap-8497	191	17	)	)	PUNCT
ap-8497	191	18	,	,	PUNCT
ap-8497	191	19	if	if	SCONJ
ap-8497	191	20	we	we	PRON
ap-8497	191	21	substitute	substitute	VERB
ap-8497	191	22	e	e	X
ap-8497	191	23	by	by	ADP
ap-8497	191	24	the	the	DET
ap-8497	191	25	identity	identity	NOUN
ap-8497	191	26	matrix	matrix	NOUN
ap-8497	191	27	i	i	PRON
ap-8497	191	28	,	,	PUNCT
ap-8497	191	29	then	then	ADV
ap-8497	191	30	the	the	DET
ap-8497	191	31	above	above	ADJ
ap-8497	191	32	necessary	necessary	ADJ
ap-8497	191	33	condition	condition	NOUN
ap-8497	191	34	for	for	ADP
ap-8497	191	35	qlsu	qlsu	NOUN
ap-8497	191	36	will	will	AUX
ap-8497	191	37	be	be	AUX
ap-8497	191	38	the	the	DET
ap-8497	191	39	same	same	ADJ
ap-8497	191	40	as	as	ADP
ap-8497	191	41	that	that	PRON
ap-8497	191	42	of	of	ADP
ap-8497	191	43	the	the	DET
ap-8497	191	44	matrix	matrix	NOUN
ap-8497	191	45	a.	a.	NOUN
ap-8497	191	46	with	with	ADP
ap-8497	191	47	the	the	DET
ap-8497	191	48	fundamentals	fundamental	NOUN
ap-8497	191	49	of	of	ADP
ap-8497	191	50	ecological	ecological	ADJ
ap-8497	191	51	principles	principle	NOUN
ap-8497	191	52	,	,	PUNCT
ap-8497	191	53	the	the	DET
ap-8497	191	54	matrix	matrix	NOUN
ap-8497	191	55	pair	pair	NOUN
ap-8497	191	56	(	(	PUNCT
ap-8497	191	57	i	i	NOUN
ap-8497	191	58	,	,	PUNCT
ap-8497	191	59	a	a	PRON
ap-8497	191	60	)	)	PUNCT
ap-8497	191	61	is	be	AUX
ap-8497	191	62	visualised	visualise	VERB
ap-8497	191	63	in	in	ADP
ap-8497	191	64	the	the	DET
ap-8497	191	65	following	following	ADJ
ap-8497	191	66	structured	structure	VERB
ap-8497	191	67	way	way	NOUN
ap-8497	191	68	.	.	PUNCT
ap-8497	192	1	let	let	VERB
ap-8497	192	2	us	we	PRON
ap-8497	192	3	illustrate	illustrate	VERB
ap-8497	192	4	the	the	DET
ap-8497	192	5	structure	structure	NOUN
ap-8497	192	6	by	by	ADP
ap-8497	192	7	using	use	VERB
ap-8497	192	8	a	a	DET
ap-8497	192	9	4	4	NUM
ap-8497	192	10	×	×	NOUN
ap-8497	192	11	4	4	NUM
ap-8497	192	12	matrix	matrix	NOUN
ap-8497	192	13	pair	pair	NOUN
ap-8497	192	14	.	.	PUNCT
ap-8497	193	1	i	i	PRON
ap-8497	193	2	=	=	PUNCT
ap-8497	193	3			NOUN
ap-8497	193	4	1	1	NUM
ap-8497	193	5	0	0	NUM
ap-8497	193	6	0	0	NUM
ap-8497	193	7	0	0	NUM
ap-8497	193	8	0	0	NUM
ap-8497	193	9	1	1	NUM
ap-8497	193	10	0	0	NUM
ap-8497	193	11	0	0	NUM
ap-8497	193	12	0	0	NUM
ap-8497	193	13	0	0	NUM
ap-8497	193	14	1	1	NUM
ap-8497	193	15	0	0	NUM
ap-8497	193	16	0	0	NUM
ap-8497	193	17	0	0	NUM
ap-8497	193	18	0	0	NUM
ap-8497	193	19	1	1	NUM
ap-8497	193	20			NOUN
ap-8497	193	21	,	,	PUNCT
ap-8497	193	22	a	a	DET
ap-8497	193	23	=	=	NOUN
ap-8497	193	24			NOUN
ap-8497	193	25	a11	a11	PROPN
ap-8497	193	26	a12	a12	PROPN
ap-8497	193	27	a13	a13	PROPN
ap-8497	193	28	a14	a14	PROPN
ap-8497	193	29	a21	a21	PROPN
ap-8497	193	30	a22	a22	PROPN
ap-8497	193	31	a23	a23	PROPN
ap-8497	193	32	a24	a24	PROPN
ap-8497	193	33	a31	a31	PROPN
ap-8497	193	34	a32	a32	PROPN
ap-8497	193	35	a33	a33	PROPN
ap-8497	193	36	a34	a34	PROPN
ap-8497	193	37	a41	a41	PROPN
ap-8497	193	38	a42	a42	PROPN
ap-8497	193	39	a43	a43	PROPN
ap-8497	193	40	a44	a44	PROPN
ap-8497	193	41			PROPN
ap-8497	193	42	according	accord	VERB
ap-8497	193	43	to	to	ADP
ap-8497	193	44	the	the	DET
ap-8497	193	45	qualitative	qualitative	ADJ
ap-8497	193	46	stability	stability	NOUN
ap-8497	193	47	concept	concept	NOUN
ap-8497	193	48	of	of	ADP
ap-8497	193	49	matrix	matrix	NOUN
ap-8497	193	50	pair	pair	NOUN
ap-8497	193	51	:	:	PUNCT
ap-8497	193	52	ηpz	ηpz	NOUN
ap-8497	193	53	=	=	SYM
ap-8497	193	54	n	n	PROPN
ap-8497	193	55	+	+	NUM
ap-8497	193	56	npz(a	npz(a	PROPN
ap-8497	193	57	)	)	PUNCT
ap-8497	193	58	2n	2n	NUM
ap-8497	193	59	=	=	SYM
ap-8497	193	60	1	1	NUM
ap-8497	193	61	2	2	NUM
ap-8497	193	62	+	+	NUM
ap-8497	193	63	npz(a	npz(a	PROPN
ap-8497	193	64	)	)	PUNCT
ap-8497	193	65	2n	2n	NUM
ap-8497	193	66	ηng	ηng	NOUN
ap-8497	193	67	=	=	SYM
ap-8497	193	68	nng(a	nng(a	PROPN
ap-8497	193	69	)	)	PUNCT
ap-8497	193	70	2n	2n	NUM
ap-8497	193	71	ηbad	ηbad	NOUN
ap-8497	193	72	=	=	SYM
ap-8497	193	73	nlc(i	nlc(i	PROPN
ap-8497	193	74	)	)	PUNCT
ap-8497	193	75	+	+	CCONJ
ap-8497	193	76	nbad(a	nbad(a	PROPN
ap-8497	193	77	)	)	PUNCT
ap-8497	193	78	nlc	nlc	PROPN
ap-8497	193	79	=	=	NOUN
ap-8497	193	80	1	1	NUM
ap-8497	193	81	2	2	NUM
ap-8497	193	82	+	+	CCONJ
ap-8497	193	83	nbad(a	nbad(a	PROPN
ap-8497	193	84	)	)	PUNCT
ap-8497	193	85	nlc	nlc	PROPN
ap-8497	193	86	ηgood	ηgood	PROPN
ap-8497	193	87	=	=	SYM
ap-8497	193	88	ngood(a	ngood(a	PROPN
ap-8497	193	89	)	)	PUNCT
ap-8497	193	90	nlc	nlc	PROPN
ap-8497	193	91	η	η	PROPN
ap-8497	193	92	′	′	PROPN
ap-8497	193	93	bad	bad	ADJ
ap-8497	193	94	=	=	SYM
ap-8497	193	95	0	0	NUM
ap-8497	193	96	η	η	PROPN
ap-8497	193	97	′	′	NOUN
ap-8497	193	98	good	good	NOUN
ap-8497	193	99	=	=	NOUN
ap-8497	193	100	1	1	NUM
ap-8497	193	101	∴	∴	PROPN
ap-8497	193	102	ζnet	ζnet	NOUN
ap-8497	193	103	=	=	PUNCT
ap-8497	193	104	ζgood	ζgood	NOUN
ap-8497	193	105	−	−	PROPN
ap-8497	193	106	ζbad	ζbad	NOUN
ap-8497	193	107	=	=	NOUN
ap-8497	193	108	1	1	NUM
ap-8497	193	109	2	2	NUM
ap-8497	193	110	[	[	X
ap-8497	193	111	nng(a	nng(a	NOUN
ap-8497	193	112	)	)	PUNCT
ap-8497	193	113	n	n	PROPN
ap-8497	193	114	+	+	CCONJ
ap-8497	193	115	ngood(a	ngood(a	PROPN
ap-8497	193	116	)	)	PUNCT
ap-8497	193	117	nlc(a	nlc(a	PROPN
ap-8497	193	118	)	)	PUNCT
ap-8497	193	119	−	−	PROPN
ap-8497	193	120	npz(a	npz(a	PROPN
ap-8497	193	121	)	)	PUNCT
ap-8497	193	122	n	n	CCONJ
ap-8497	193	123	−	−	PROPN
ap-8497	193	124	nbad(a	nbad(a	PROPN
ap-8497	193	125	)	)	PUNCT
ap-8497	193	126	nlc(a	nlc(a	PROPN
ap-8497	193	127	)	)	PUNCT
ap-8497	193	128	]	]	PUNCT
ap-8497	194	1	=	=	SYM
ap-8497	194	2	1	1	NUM
ap-8497	194	3	2	2	NUM
ap-8497	194	4	[	[	X
ap-8497	194	5	ζgood(a	ζgood(a	NOUN
ap-8497	194	6	)	)	PUNCT
ap-8497	194	7	−	−	PROPN
ap-8497	195	1	ζbad(a	ζbad(a	PROPN
ap-8497	195	2	)	)	PUNCT
ap-8497	195	3	]	]	PUNCT
ap-8497	196	1	=	=	PUNCT
ap-8497	196	2	1	1	NUM
ap-8497	196	3	2ζnet(a	2ζnet(a	NUM
ap-8497	196	4	)	)	PUNCT
ap-8497	196	5	.	.	PUNCT
ap-8497	197	1	since	since	SCONJ
ap-8497	197	2	the	the	DET
ap-8497	197	3	matrix	matrix	NOUN
ap-8497	197	4	pair	pair	NOUN
ap-8497	197	5	(	(	PUNCT
ap-8497	197	6	i	i	NOUN
ap-8497	197	7	,	,	PUNCT
ap-8497	197	8	a	a	PRON
ap-8497	197	9	)	)	PUNCT
ap-8497	197	10	is	be	AUX
ap-8497	197	11	qlsu	qlsu	NOUN
ap-8497	197	12	only	only	ADV
ap-8497	197	13	if	if	SCONJ
ap-8497	197	14	ζnet	ζnet	PROPN
ap-8497	197	15	<	<	X
ap-8497	197	16	0	0	PROPN
ap-8497	197	17	,	,	PUNCT
ap-8497	197	18	therefore	therefore	ADV
ap-8497	197	19	,	,	PUNCT
ap-8497	197	20	the	the	DET
ap-8497	197	21	matrix	matrix	NOUN
ap-8497	197	22	a	a	PRON
ap-8497	197	23	is	be	AUX
ap-8497	197	24	qlsu	qlsu	NOUN
ap-8497	197	25	only	only	ADV
ap-8497	197	26	if	if	SCONJ
ap-8497	197	27	ζnet(a	ζnet(a	NOUN
ap-8497	197	28	)	)	PUNCT
ap-8497	197	29	<	<	X
ap-8497	197	30	0	0	X
ap-8497	197	31	.	.	PUNCT
ap-8497	198	1	this	this	PRON
ap-8497	198	2	is	be	AUX
ap-8497	198	3	the	the	DET
ap-8497	198	4	necessary	necessary	ADJ
ap-8497	198	5	condition	condition	NOUN
ap-8497	198	6	for	for	ADP
ap-8497	198	7	a	a	DET
ap-8497	198	8	matrix	matrix	NOUN
ap-8497	198	9	to	to	PART
ap-8497	198	10	be	be	AUX
ap-8497	198	11	qlsu	qlsu	NOUN
ap-8497	198	12	,	,	PUNCT
ap-8497	198	13	which	which	PRON
ap-8497	198	14	is	be	AUX
ap-8497	198	15	a	a	DET
ap-8497	198	16	particular	particular	ADJ
ap-8497	198	17	case	case	NOUN
ap-8497	198	18	of	of	ADP
ap-8497	198	19	a	a	DET
ap-8497	198	20	matrix	matrix	NOUN
ap-8497	198	21	pair	pair	NOUN
ap-8497	198	22	.	.	PUNCT
ap-8497	199	1	the	the	DET
ap-8497	199	2	necessary	necessary	ADJ
ap-8497	199	3	and	and	CCONJ
ap-8497	199	4	sufficient	sufficient	ADJ
ap-8497	199	5	conditions	condition	NOUN
ap-8497	199	6	of	of	ADP
ap-8497	199	7	a	a	DET
ap-8497	199	8	matrix	matrix	NOUN
ap-8497	199	9	to	to	PART
ap-8497	199	10	be	be	AUX
ap-8497	199	11	qlsu	qlsu	NOUN
ap-8497	199	12	are	be	AUX
ap-8497	199	13	discussed	discuss	VERB
ap-8497	199	14	extensively	extensively	ADV
ap-8497	199	15	in	in	ADP
ap-8497	199	16	[	[	X
ap-8497	199	17	16	16	NUM
ap-8497	199	18	]	]	PUNCT
ap-8497	199	19	.	.	PUNCT
ap-8497	200	1	in	in	ADP
ap-8497	200	2	this	this	DET
ap-8497	200	3	paper	paper	NOUN
ap-8497	200	4	,	,	PUNCT
ap-8497	200	5	we	we	PRON
ap-8497	200	6	generalise	generalise	VERB
ap-8497	200	7	the	the	DET
ap-8497	200	8	identity	identity	NOUN
ap-8497	200	9	matrix	matrix	NOUN
ap-8497	200	10	i	i	PRON
ap-8497	200	11	to	to	ADP
ap-8497	200	12	any	any	DET
ap-8497	200	13	matrix	matrix	NOUN
ap-8497	200	14	e	e	NOUN
ap-8497	200	15	and	and	CCONJ
ap-8497	200	16	propose	propose	VERB
ap-8497	200	17	few	few	ADJ
ap-8497	200	18	necessary	necessary	ADJ
ap-8497	200	19	and	and	CCONJ
ap-8497	200	20	sufficient	sufficient	ADJ
ap-8497	200	21	conditions	condition	NOUN
ap-8497	200	22	for	for	ADP
ap-8497	200	23	the	the	DET
ap-8497	200	24	qualitative	qualitative	ADJ
ap-8497	200	25	sign	sign	NOUN
ap-8497	200	26	instability	instability	NOUN
ap-8497	200	27	for	for	ADP
ap-8497	200	28	a	a	DET
ap-8497	200	29	matrix	matrix	NOUN
ap-8497	200	30	pair	pair	NOUN
ap-8497	200	31	.	.	PUNCT
ap-8497	201	1	3.3	3.3	NUM
ap-8497	201	2	.	.	PUNCT
ap-8497	202	1	a	a	DET
ap-8497	202	2	necessary	necessary	ADJ
ap-8497	202	3	condition	condition	NOUN
ap-8497	202	4	for	for	ADP
ap-8497	202	5	a	a	DET
ap-8497	202	6	matrix	matrix	NOUN
ap-8497	202	7	pair	pair	NOUN
ap-8497	202	8	to	to	PART
ap-8497	202	9	be	be	AUX
ap-8497	202	10	qlsu	qlsu	NOUN
ap-8497	202	11	we	we	PRON
ap-8497	202	12	know	know	VERB
ap-8497	202	13	that	that	SCONJ
ap-8497	202	14	ζnet	ζnet	PROPN
ap-8497	202	15	is	be	AUX
ap-8497	202	16	a	a	DET
ap-8497	202	17	real	real	ADJ
ap-8497	202	18	function	function	NOUN
ap-8497	202	19	and	and	CCONJ
ap-8497	202	20	it	it	PRON
ap-8497	202	21	takes	take	VERB
ap-8497	202	22	on	on	ADP
ap-8497	202	23	discrete	discrete	ADJ
ap-8497	202	24	values	value	NOUN
ap-8497	202	25	.	.	PUNCT
ap-8497	203	1	so	so	ADV
ap-8497	203	2	there	there	PRON
ap-8497	203	3	may	may	AUX
ap-8497	203	4	be	be	AUX
ap-8497	203	5	a	a	DET
ap-8497	203	6	situation	situation	NOUN
ap-8497	203	7	that	that	SCONJ
ap-8497	203	8	not	not	PART
ap-8497	203	9	all	all	DET
ap-8497	203	10	the	the	DET
ap-8497	203	11	diagonal	diagonal	ADJ
ap-8497	203	12	elements	element	NOUN
ap-8497	203	13	have	have	VERB
ap-8497	203	14	to	to	PART
ap-8497	203	15	be	be	AUX
ap-8497	203	16	positive	positive	ADJ
ap-8497	203	17	and	and	CCONJ
ap-8497	203	18	not	not	PART
ap-8497	203	19	all	all	DET
ap-8497	203	20	the	the	DET
ap-8497	203	21	links	link	NOUN
ap-8497	203	22	have	have	VERB
ap-8497	203	23	to	to	PART
ap-8497	203	24	be	be	AUX
ap-8497	203	25	‘	'	PUNCT
ap-8497	203	26	bad	bad	ADJ
ap-8497	203	27	’	'	PUNCT
ap-8497	203	28	links	link	NOUN
ap-8497	203	29	to	to	PART
ap-8497	203	30	make	make	VERB
ap-8497	203	31	the	the	DET
ap-8497	203	32	matrix	matrix	NOUN
ap-8497	203	33	pair	pair	NOUN
ap-8497	203	34	qlsu	qlsu	NOUN
ap-8497	203	35	.	.	PUNCT
ap-8497	204	1	that	that	PRON
ap-8497	204	2	means	mean	VERB
ap-8497	204	3	,	,	PUNCT
ap-8497	204	4	for	for	SCONJ
ap-8497	204	5	a	a	DET
ap-8497	204	6	matrix	matrix	NOUN
ap-8497	204	7	pair	pair	NOUN
ap-8497	204	8	to	to	PART
ap-8497	204	9	be	be	AUX
ap-8497	204	10	qlsu	qlsu	NOUN
ap-8497	204	11	,	,	PUNCT
ap-8497	204	12	the	the	DET
ap-8497	204	13	number	number	NOUN
ap-8497	204	14	of	of	ADP
ap-8497	204	15	positive	positive	ADJ
ap-8497	204	16	diagonal	diagonal	ADJ
ap-8497	204	17	elements	element	NOUN
ap-8497	204	18	can	can	AUX
ap-8497	204	19	be	be	AUX
ap-8497	204	20	less	less	ADJ
ap-8497	204	21	than	than	ADP
ap-8497	204	22	2n	2n	NUM
ap-8497	204	23	and	and	CCONJ
ap-8497	204	24	the	the	DET
ap-8497	204	25	number	number	NOUN
ap-8497	204	26	of	of	ADP
ap-8497	204	27	bad	bad	ADJ
ap-8497	204	28	links	link	NOUN
ap-8497	204	29	in	in	ADP
ap-8497	204	30	the	the	DET
ap-8497	204	31	matrix	matrix	NOUN
ap-8497	204	32	pair	pair	NOUN
ap-8497	204	33	can	can	AUX
ap-8497	204	34	be	be	AUX
ap-8497	204	35	less	less	ADJ
ap-8497	204	36	than	than	ADP
ap-8497	204	37	nlc	nlc	PROPN
ap-8497	204	38	,	,	PUNCT
ap-8497	204	39	not	not	PART
ap-8497	204	40	necessarily	necessarily	ADV
ap-8497	204	41	equal	equal	ADJ
ap-8497	204	42	to	to	ADP
ap-8497	204	43	nlc	nlc	PROPN
ap-8497	204	44	.	.	PUNCT
ap-8497	205	1	now	now	ADV
ap-8497	205	2	,	,	PUNCT
ap-8497	205	3	we	we	PRON
ap-8497	205	4	calculate	calculate	VERB
ap-8497	205	5	the	the	DET
ap-8497	205	6	minimum	minimum	ADJ
ap-8497	205	7	number	number	NOUN
ap-8497	205	8	of	of	ADP
ap-8497	205	9	bad	bad	ADJ
ap-8497	205	10	links	link	NOUN
ap-8497	205	11	needed	need	VERB
ap-8497	205	12	to	to	PART
ap-8497	205	13	make	make	VERB
ap-8497	205	14	a	a	DET
ap-8497	205	15	matrix	matrix	NOUN
ap-8497	205	16	pair	pair	NOUN
ap-8497	205	17	unstable	unstable	ADJ
ap-8497	205	18	and	and	CCONJ
ap-8497	205	19	denote	denote	VERB
ap-8497	205	20	it	it	PRON
ap-8497	205	21	as	as	ADP
ap-8497	205	22	n∗	n∗	PROPN
ap-8497	205	23	u	u	PROPN
ap-8497	205	24	.	.	PUNCT
ap-8497	206	1	for	for	ADP
ap-8497	206	2	a	a	DET
ap-8497	206	3	matrix	matrix	NOUN
ap-8497	206	4	pair	pair	NOUN
ap-8497	206	5	with	with	ADP
ap-8497	206	6	np	np	NOUN
ap-8497	206	7	̸=	̸=	PROPN
ap-8497	206	8	0	0	NUM
ap-8497	206	9	,	,	PUNCT
ap-8497	206	10	let	let	VERB
ap-8497	206	11	us	we	PRON
ap-8497	206	12	define	define	VERB
ap-8497	206	13	n∗	n∗	PROPN
ap-8497	206	14	u	u	NOUN
ap-8497	206	15	as	as	SCONJ
ap-8497	206	16	follows	follow	VERB
ap-8497	206	17	:	:	PUNCT
ap-8497	206	18	175	175	NUM
ap-8497	206	19	m.	m.	NOUN
ap-8497	206	20	chand	chand	PROPN
ap-8497	206	21	,	,	PUNCT
ap-8497	206	22	m.	m.	NOUN
ap-8497	206	23	paitandi	paitandi	PROPN
ap-8497	206	24	,	,	PUNCT
ap-8497	206	25	m.	m.	PROPN
ap-8497	206	26	k.	k.	PROPN
ap-8497	206	27	gupta	gupta	PROPN
ap-8497	206	28	acta	acta	PROPN
ap-8497	206	29	polytechnica	polytechnica	PROPN
ap-8497	206	30	n∗	n∗	VERB
ap-8497	206	31	u	u	PROPN
ap-8497	206	32	=	=	NOUN
ap-8497	206	33	the	the	DET
ap-8497	206	34	closest	close	ADV
ap-8497	206	35	higher	high	ADJ
ap-8497	206	36	upper	upper	ADJ
ap-8497	206	37	integer	integer	NOUN
ap-8497	206	38	of	of	ADP
ap-8497	206	39	(	(	PUNCT
ap-8497	206	40	ηng	ηng	NOUN
ap-8497	206	41	+	+	CCONJ
ap-8497	206	42	1	1	NUM
ap-8497	206	43	2	2	NUM
ap-8497	206	44	)	)	PUNCT
ap-8497	206	45	times	times	PROPN
ap-8497	206	46	nlc	nlc	PROPN
ap-8497	206	47	,	,	PUNCT
ap-8497	206	48	including	include	VERB
ap-8497	206	49	when	when	SCONJ
ap-8497	206	50	that	that	PRON
ap-8497	206	51	is	be	AUX
ap-8497	206	52	itself	itself	PRON
ap-8497	206	53	an	an	DET
ap-8497	206	54	integer	integer	NOUN
ap-8497	206	55	.	.	PUNCT
ap-8497	207	1	let	let	VERB
ap-8497	207	2	us	we	PRON
ap-8497	207	3	state	state	VERB
ap-8497	207	4	a	a	DET
ap-8497	207	5	theorem	theorem	VERB
ap-8497	207	6	.	.	PUNCT
ap-8497	207	7	theorem	theorem	PROPN
ap-8497	207	8	.	.	PUNCT
ap-8497	208	1	a	a	DET
ap-8497	208	2	matrix	matrix	NOUN
ap-8497	208	3	pair	pair	NOUN
ap-8497	208	4	is	be	AUX
ap-8497	208	5	qlsu	qlsu	NOUN
ap-8497	208	6	only	only	ADV
ap-8497	208	7	if	if	SCONJ
ap-8497	208	8	the	the	DET
ap-8497	208	9	total	total	ADJ
ap-8497	208	10	number	number	NOUN
ap-8497	208	11	of	of	ADP
ap-8497	208	12	bad	bad	ADJ
ap-8497	208	13	links	link	NOUN
ap-8497	208	14	in	in	ADP
ap-8497	208	15	it	it	PRON
ap-8497	208	16	is	be	AUX
ap-8497	208	17	≥	≥	NUM
ap-8497	208	18	n∗	n∗	VERB
ap-8497	208	19	u	u	NOUN
ap-8497	208	20	i.e.	i.e.	X
ap-8497	208	21	nbad	nbad	ADJ
ap-8497	208	22	+	+	CCONJ
ap-8497	208	23	n	n	NUM
ap-8497	209	1	′	′	NUM
ap-8497	209	2	bad	bad	ADJ
ap-8497	209	3	≥	≥	NOUN
ap-8497	209	4	n∗	n∗	VERB
ap-8497	209	5	u	u	NOUN
ap-8497	209	6	.	.	PUNCT
ap-8497	210	1	proof	proof	NOUN
ap-8497	210	2	.	.	PUNCT
ap-8497	211	1	for	for	ADP
ap-8497	211	2	a	a	DET
ap-8497	211	3	qlsu	qlsu	NOUN
ap-8497	211	4	matrix	matrix	NOUN
ap-8497	211	5	pair	pair	NOUN
ap-8497	211	6	,	,	PUNCT
ap-8497	211	7	ζnet	ζnet	NOUN
ap-8497	211	8	<	<	X
ap-8497	211	9	0	0	PUNCT
ap-8497	212	1	=	=	AUX
ap-8497	212	2	⇒	⇒	NOUN
ap-8497	212	3	ηng	ηng	NOUN
ap-8497	212	4	+	+	CCONJ
ap-8497	212	5	ηgood	ηgood	NOUN
ap-8497	212	6	+	+	CCONJ
ap-8497	212	7	η	η	PROPN
ap-8497	212	8	′	′	ADJ
ap-8497	212	9	good	good	ADJ
ap-8497	212	10	<	<	X
ap-8497	212	11	ηpz	ηpz	NOUN
ap-8497	212	12	+	+	CCONJ
ap-8497	212	13	ηbad	ηbad	NOUN
ap-8497	212	14	+	+	CCONJ
ap-8497	212	15	η	η	NOUN
ap-8497	212	16	′	′	ADJ
ap-8497	212	17	bad	bad	ADJ
ap-8497	212	18	=	=	NOUN
ap-8497	212	19	⇒	⇒	VERB
ap-8497	212	20	ηng	ηng	NOUN
ap-8497	212	21	+	+	CCONJ
ap-8497	212	22	1	1	NUM
ap-8497	212	23	−	−	NOUN
ap-8497	212	24	ηbad	ηbad	NOUN
ap-8497	212	25	+	+	CCONJ
ap-8497	212	26	1	1	NUM
ap-8497	212	27	−	−	PROPN
ap-8497	212	28	η	η	NOUN
ap-8497	212	29	′	′	NUM
ap-8497	212	30	bad	bad	ADJ
ap-8497	212	31	<	<	X
ap-8497	212	32	1	1	NUM
ap-8497	212	33	−	−	NOUN
ap-8497	212	34	ηng	ηng	NOUN
ap-8497	212	35	+	+	CCONJ
ap-8497	212	36	ηbad	ηbad	NOUN
ap-8497	212	37	+	+	CCONJ
ap-8497	212	38	η	η	NOUN
ap-8497	212	39	′	′	ADJ
ap-8497	212	40	bad	bad	ADJ
ap-8497	213	1	=	=	NOUN
ap-8497	213	2	⇒	⇒	VERB
ap-8497	213	3	ηng	ηng	NOUN
ap-8497	213	4	+	+	CCONJ
ap-8497	213	5	1	1	NUM
ap-8497	213	6	2	2	NUM
ap-8497	213	7	<	<	X
ap-8497	213	8	ηbad	ηbad	NOUN
ap-8497	213	9	+	+	CCONJ
ap-8497	213	10	η	η	X
ap-8497	213	11	′	′	ADJ
ap-8497	213	12	bad	bad	ADJ
ap-8497	214	1	=	=	NOUN
ap-8497	214	2	⇒	⇒	VERB
ap-8497	214	3	ηng	ηng	NOUN
ap-8497	214	4	+	+	CCONJ
ap-8497	214	5	1	1	NUM
ap-8497	214	6	2	2	NUM
ap-8497	214	7	<	<	X
ap-8497	214	8	nbad	nbad	ADJ
ap-8497	214	9	+	+	CCONJ
ap-8497	214	10	n	n	CCONJ
ap-8497	214	11	′	′	NUM
ap-8497	214	12	bad	bad	ADJ
ap-8497	214	13	nlc	nlc	PROPN
ap-8497	214	14	=	=	PRON
ap-8497	214	15	⇒	⇒	X
ap-8497	214	16	[	[	X
ap-8497	214	17	ηng	ηng	NOUN
ap-8497	214	18	+	+	NUM
ap-8497	214	19	1	1	NUM
ap-8497	214	20	2	2	NUM
ap-8497	214	21	]	]	PUNCT
ap-8497	214	22	×	×	PROPN
ap-8497	214	23	nlc	nlc	PROPN
ap-8497	214	24	<	<	X
ap-8497	214	25	nbad	nbad	ADJ
ap-8497	214	26	+	+	CCONJ
ap-8497	214	27	n	n	CCONJ
ap-8497	214	28	′	′	NUM
ap-8497	214	29	bad	bad	ADJ
ap-8497	214	30	.	.	PUNCT
ap-8497	215	1	thus	thus	ADV
ap-8497	215	2	,	,	PUNCT
ap-8497	215	3	the	the	DET
ap-8497	215	4	total	total	ADJ
ap-8497	215	5	number	number	NOUN
ap-8497	215	6	of	of	ADP
ap-8497	215	7	bad	bad	ADJ
ap-8497	215	8	links	link	NOUN
ap-8497	215	9	needed	need	VERB
ap-8497	215	10	to	to	PART
ap-8497	215	11	make	make	VERB
ap-8497	215	12	a	a	DET
ap-8497	215	13	matrix	matrix	NOUN
ap-8497	215	14	pair	pair	NOUN
ap-8497	215	15	qlsu	qlsu	NOUN
ap-8497	215	16	is	be	AUX
ap-8497	215	17	greater	great	ADJ
ap-8497	215	18	than	than	ADP
ap-8497	215	19	or	or	CCONJ
ap-8497	215	20	equal	equal	ADJ
ap-8497	215	21	to	to	ADP
ap-8497	215	22	n∗	n∗	PROPN
ap-8497	215	23	u	u	PROPN
ap-8497	215	24	.	.	PUNCT
ap-8497	216	1	this	this	PRON
ap-8497	216	2	is	be	AUX
ap-8497	216	3	a	a	DET
ap-8497	216	4	necessary	necessary	ADJ
ap-8497	216	5	condition	condition	NOUN
ap-8497	216	6	for	for	SCONJ
ap-8497	216	7	a	a	DET
ap-8497	216	8	matrix	matrix	NOUN
ap-8497	216	9	pair	pair	NOUN
ap-8497	216	10	to	to	PART
ap-8497	216	11	be	be	AUX
ap-8497	216	12	qlsu	qlsu	NOUN
ap-8497	216	13	.	.	PUNCT
ap-8497	217	1	3.4	3.4	NUM
ap-8497	217	2	.	.	PUNCT
ap-8497	218	1	sufficiency	sufficiency	NOUN
ap-8497	218	2	guidelines	guideline	NOUN
ap-8497	218	3	for	for	ADP
ap-8497	218	4	qlsu	qlsu	NOUN
ap-8497	218	5	matrix	matrix	NOUN
ap-8497	218	6	pair	pair	NOUN
ap-8497	218	7	while	while	SCONJ
ap-8497	218	8	observing	observe	VERB
ap-8497	218	9	the	the	DET
ap-8497	218	10	expression	expression	NOUN
ap-8497	218	11	for	for	ADP
ap-8497	218	12	the	the	DET
ap-8497	218	13	determinant	determinant	NOUN
ap-8497	218	14	of	of	ADP
ap-8497	218	15	a	a	DET
ap-8497	218	16	matrix	matrix	NOUN
ap-8497	218	17	pair	pair	NOUN
ap-8497	218	18	,	,	PUNCT
ap-8497	218	19	we	we	PRON
ap-8497	218	20	find	find	VERB
ap-8497	218	21	that	that	SCONJ
ap-8497	218	22	a	a	DET
ap-8497	218	23	diagonal	diagonal	ADJ
ap-8497	218	24	element	element	NOUN
ap-8497	218	25	is	be	AUX
ap-8497	218	26	always	always	ADV
ap-8497	218	27	multiplied	multiply	VERB
ap-8497	218	28	by	by	ADP
ap-8497	218	29	the	the	DET
ap-8497	218	30	link	link	NOUN
ap-8497	218	31	elements	element	NOUN
ap-8497	218	32	surrounded	surround	VERB
ap-8497	218	33	by	by	ADP
ap-8497	218	34	it	it	PRON
ap-8497	218	35	.	.	PUNCT
ap-8497	219	1	that	that	PRON
ap-8497	219	2	means	mean	VERB
ap-8497	219	3	the	the	DET
ap-8497	219	4	row	row	NOUN
ap-8497	219	5	and	and	CCONJ
ap-8497	219	6	column	column	NOUN
ap-8497	219	7	elements	element	NOUN
ap-8497	219	8	associated	associate	VERB
ap-8497	219	9	with	with	ADP
ap-8497	219	10	a	a	DET
ap-8497	219	11	diagonal	diagonal	ADJ
ap-8497	219	12	element	element	NOUN
ap-8497	219	13	play	play	VERB
ap-8497	219	14	a	a	DET
ap-8497	219	15	vital	vital	ADJ
ap-8497	219	16	role	role	NOUN
ap-8497	219	17	to	to	PART
ap-8497	219	18	assess	assess	VERB
ap-8497	219	19	the	the	DET
ap-8497	219	20	stability	stability	NOUN
ap-8497	219	21	/	/	SYM
ap-8497	219	22	instability	instability	NOUN
ap-8497	219	23	.	.	PUNCT
ap-8497	220	1	these	these	DET
ap-8497	220	2	observations	observation	NOUN
ap-8497	220	3	provide	provide	VERB
ap-8497	220	4	us	we	PRON
ap-8497	220	5	with	with	ADP
ap-8497	220	6	some	some	DET
ap-8497	220	7	‘	'	PUNCT
ap-8497	220	8	guidelines	guideline	NOUN
ap-8497	220	9	’	'	PUNCT
ap-8497	220	10	for	for	ADP
ap-8497	220	11	sufficiency	sufficiency	NOUN
ap-8497	220	12	for	for	ADP
ap-8497	220	13	qlsu	qlsu	NOUN
ap-8497	220	14	[	[	X
ap-8497	220	15	16	16	NUM
ap-8497	220	16	]	]	PUNCT
ap-8497	220	17	.	.	PUNCT
ap-8497	221	1	•	•	NUM
ap-8497	221	2	guideline	guideline	NOUN
ap-8497	221	3	1	1	NUM
ap-8497	221	4	:	:	PUNCT
ap-8497	221	5	a	a	DET
ap-8497	221	6	matrix	matrix	NOUN
ap-8497	221	7	pair	pair	NOUN
ap-8497	221	8	with	with	ADP
ap-8497	221	9	ζnet	ζnet	PROPN
ap-8497	221	10	<	<	X
ap-8497	221	11	0	0	PROPN
ap-8497	221	12	,	,	PUNCT
ap-8497	221	13	is	be	AUX
ap-8497	221	14	likely	likely	ADJ
ap-8497	221	15	qlsu	qlsu	NOUN
ap-8497	221	16	if	if	SCONJ
ap-8497	221	17	a	a	DET
ap-8497	221	18	positive	positive	ADJ
ap-8497	221	19	diagonal	diagonal	ADJ
ap-8497	221	20	element	element	NOUN
ap-8497	221	21	eii	eii	PROPN
ap-8497	221	22	or	or	CCONJ
ap-8497	221	23	aii	aii	PROPN
ap-8497	221	24	is	be	AUX
ap-8497	221	25	surrounded	surround	VERB
ap-8497	221	26	by	by	ADP
ap-8497	221	27	+	+	X
ap-8497	221	28	chains	chain	NOUN
ap-8497	221	29	.	.	PUNCT
ap-8497	222	1	(	(	PUNCT
ap-8497	222	2	the	the	DET
ap-8497	222	3	above	above	ADJ
ap-8497	222	4	guideline	guideline	NOUN
ap-8497	222	5	is	be	AUX
ap-8497	222	6	the	the	DET
ap-8497	222	7	result	result	NOUN
ap-8497	222	8	of	of	ADP
ap-8497	222	9	the	the	DET
ap-8497	222	10	idea	idea	NOUN
ap-8497	222	11	that	that	SCONJ
ap-8497	222	12	positive	positive	ADJ
ap-8497	222	13	diagonal	diagonal	ADJ
ap-8497	222	14	elements	element	NOUN
ap-8497	222	15	along	along	ADP
ap-8497	222	16	with	with	ADP
ap-8497	222	17	+	+	CCONJ
ap-8497	222	18	chains	chain	NOUN
ap-8497	222	19	promote	promote	VERB
ap-8497	222	20	instability	instability	NOUN
ap-8497	222	21	.	.	PUNCT
ap-8497	222	22	)	)	PUNCT
ap-8497	223	1	•	•	NUM
ap-8497	223	2	guideline	guideline	NOUN
ap-8497	223	3	2	2	NUM
ap-8497	223	4	:	:	PUNCT
ap-8497	223	5	a	a	DET
ap-8497	223	6	matrix	matrix	NOUN
ap-8497	223	7	pair	pair	NOUN
ap-8497	223	8	with	with	ADP
ap-8497	223	9	ζnet	ζnet	PROPN
ap-8497	223	10	<	<	X
ap-8497	223	11	0	0	PROPN
ap-8497	223	12	,	,	PUNCT
ap-8497	223	13	is	be	AUX
ap-8497	223	14	likely	likely	ADJ
ap-8497	223	15	qlsu	qlsu	NOUN
ap-8497	223	16	if	if	SCONJ
ap-8497	223	17	a	a	DET
ap-8497	223	18	negative	negative	ADJ
ap-8497	223	19	diagonal	diagonal	ADJ
ap-8497	223	20	element	element	NOUN
ap-8497	223	21	eii	eii	PROPN
ap-8497	223	22	or	or	CCONJ
ap-8497	223	23	aii	aii	PROPN
ap-8497	223	24	is	be	AUX
ap-8497	223	25	surrounded	surround	VERB
ap-8497	223	26	by	by	ADP
ap-8497	223	27	−	−	PROPN
ap-8497	223	28	chains	chain	NOUN
ap-8497	223	29	.	.	PUNCT
ap-8497	224	1	(	(	PUNCT
ap-8497	224	2	the	the	DET
ap-8497	224	3	above	above	ADJ
ap-8497	224	4	guideline	guideline	NOUN
ap-8497	224	5	is	be	AUX
ap-8497	224	6	the	the	DET
ap-8497	224	7	result	result	NOUN
ap-8497	224	8	of	of	ADP
ap-8497	224	9	the	the	DET
ap-8497	224	10	idea	idea	NOUN
ap-8497	224	11	that	that	SCONJ
ap-8497	224	12	negative	negative	ADJ
ap-8497	224	13	diagonal	diagonal	ADJ
ap-8497	224	14	elements	element	NOUN
ap-8497	224	15	along	along	ADP
ap-8497	224	16	with	with	ADP
ap-8497	224	17	−	−	PROPN
ap-8497	224	18	chains	chain	NOUN
ap-8497	224	19	promote	promote	VERB
ap-8497	224	20	instability	instability	NOUN
ap-8497	224	21	.	.	PUNCT
ap-8497	224	22	)	)	PUNCT
ap-8497	225	1	4	4	X
ap-8497	225	2	.	.	X
ap-8497	225	3	illustrative	illustrative	ADJ
ap-8497	225	4	examples	example	NOUN
ap-8497	225	5	for	for	ADP
ap-8497	225	6	instability	instability	NOUN
ap-8497	225	7	of	of	ADP
ap-8497	225	8	a	a	DET
ap-8497	225	9	matrix	matrix	NOUN
ap-8497	225	10	pair	pair	NOUN
ap-8497	225	11	by	by	ADP
ap-8497	225	12	now	now	ADV
ap-8497	225	13	,	,	PUNCT
ap-8497	225	14	we	we	PRON
ap-8497	225	15	have	have	VERB
ap-8497	225	16	few	few	ADJ
ap-8497	225	17	necessary	necessary	ADJ
ap-8497	225	18	conditions	condition	NOUN
ap-8497	225	19	for	for	ADP
ap-8497	225	20	qlsu	qlsu	NOUN
ap-8497	225	21	and	and	CCONJ
ap-8497	225	22	few	few	ADJ
ap-8497	225	23	guidelines	guideline	NOUN
ap-8497	225	24	for	for	ADP
ap-8497	225	25	sufficiency	sufficiency	NOUN
ap-8497	225	26	for	for	ADP
ap-8497	225	27	qlsu	qlsu	NOUN
ap-8497	225	28	.	.	PUNCT
ap-8497	226	1	once	once	ADV
ap-8497	226	2	the	the	DET
ap-8497	226	3	necessary	necessary	ADJ
ap-8497	226	4	condition	condition	NOUN
ap-8497	226	5	ζnet	ζnet	NOUN
ap-8497	226	6	<	<	X
ap-8497	226	7	0	0	X
ap-8497	226	8	is	be	AUX
ap-8497	226	9	satisfied	satisfied	ADJ
ap-8497	226	10	,	,	PUNCT
ap-8497	226	11	we	we	PRON
ap-8497	226	12	can	can	AUX
ap-8497	226	13	make	make	VERB
ap-8497	226	14	a	a	DET
ap-8497	226	15	qlsu	qlsu	NOUN
ap-8497	226	16	matrix	matrix	NOUN
ap-8497	226	17	pair	pair	NOUN
ap-8497	226	18	,	,	PUNCT
ap-8497	226	19	with	with	ADP
ap-8497	226	20	the	the	DET
ap-8497	226	21	appropriate	appropriate	ADJ
ap-8497	226	22	placement	placement	NOUN
ap-8497	226	23	of	of	ADP
ap-8497	226	24	the	the	DET
ap-8497	226	25	‘	'	PUNCT
ap-8497	226	26	bad	bad	ADJ
ap-8497	226	27	’	'	PUNCT
ap-8497	226	28	and	and	CCONJ
ap-8497	226	29	‘	'	PUNCT
ap-8497	226	30	good	good	ADJ
ap-8497	226	31	’	'	PUNCT
ap-8497	226	32	links	link	NOUN
ap-8497	226	33	in	in	ADP
ap-8497	226	34	it	it	PRON
ap-8497	226	35	.	.	PUNCT
ap-8497	227	1	let	let	VERB
ap-8497	227	2	us	we	PRON
ap-8497	227	3	consider	consider	VERB
ap-8497	227	4	some	some	DET
ap-8497	227	5	examples	example	NOUN
ap-8497	227	6	.	.	PUNCT
ap-8497	228	1	example	example	NOUN
ap-8497	228	2	1	1	NUM
ap-8497	228	3	.	.	X
ap-8497	229	1	consider	consider	VERB
ap-8497	229	2	a	a	DET
ap-8497	229	3	4	4	NUM
ap-8497	229	4	×	×	NOUN
ap-8497	229	5	4	4	NUM
ap-8497	229	6	matrix	matrix	NOUN
ap-8497	229	7	pair	pair	NOUN
ap-8497	229	8	with	with	ADP
ap-8497	229	9	diagonal	diagonal	ADJ
ap-8497	229	10	elements	element	NOUN
ap-8497	229	11	as	as	SCONJ
ap-8497	229	12	shown	show	VERB
ap-8497	229	13	below	below	ADV
ap-8497	229	14	:	:	PUNCT
ap-8497	229	15	e	e	X
ap-8497	229	16	=	=	SYM
ap-8497	229	17	−	−	PROPN
ap-8497	229	18	∗	∗	NOUN
ap-8497	229	19	∗	∗	NOUN
ap-8497	229	20	∗	∗	NOUN
ap-8497	229	21	∗	∗	NOUN
ap-8497	229	22	+	+	NUM
ap-8497	229	23	∗	∗	NOUN
ap-8497	229	24	∗	∗	NOUN
ap-8497	229	25	∗	∗	NOUN
ap-8497	229	26	∗	∗	NOUN
ap-8497	229	27	+	+	NUM
ap-8497	229	28	∗	∗	NOUN
ap-8497	229	29	∗	∗	NOUN
ap-8497	229	30	∗	∗	NOUN
ap-8497	229	31	∗	∗	NOUN
ap-8497	229	32	+	+	X
ap-8497	229	33			NUM
ap-8497	229	34	and	and	CCONJ
ap-8497	229	35	a	a	DET
ap-8497	229	36	=	=	X
ap-8497	229	37	+	+	PROPN
ap-8497	229	38	∗	∗	NOUN
ap-8497	229	39	∗	∗	NOUN
ap-8497	229	40	∗	∗	NOUN
ap-8497	229	41	∗	∗	NOUN
ap-8497	229	42	−	−	NOUN
ap-8497	229	43	∗	∗	NOUN
ap-8497	229	44	∗	∗	NOUN
ap-8497	229	45	∗	∗	NOUN
ap-8497	229	46	∗	∗	NOUN
ap-8497	229	47	−	−	NOUN
ap-8497	229	48	∗	∗	NOUN
ap-8497	229	49	∗	∗	NOUN
ap-8497	229	50	∗	∗	NOUN
ap-8497	229	51	∗	∗	NOUN
ap-8497	229	52	+	+	X
ap-8497	229	53			NOUN
ap-8497	229	54	suppose	suppose	VERB
ap-8497	229	55	there	there	PRON
ap-8497	229	56	is	be	VERB
ap-8497	229	57	no	no	DET
ap-8497	229	58	zz	zz	PROPN
ap-8497	229	59	link	link	NOUN
ap-8497	229	60	in	in	ADP
ap-8497	229	61	the	the	DET
ap-8497	229	62	matrix	matrix	NOUN
ap-8497	229	63	pair	pair	NOUN
ap-8497	229	64	.	.	PUNCT
ap-8497	230	1	for	for	ADP
ap-8497	230	2	the	the	DET
ap-8497	230	3	given	give	VERB
ap-8497	230	4	matrix	matrix	NOUN
ap-8497	230	5	pair	pair	NOUN
ap-8497	230	6	(	(	PUNCT
ap-8497	230	7	e	e	NOUN
ap-8497	230	8	,	,	PUNCT
ap-8497	230	9	a	a	PRON
ap-8497	230	10	)	)	PUNCT
ap-8497	230	11	,	,	PUNCT
ap-8497	230	12	ηng	ηng	NOUN
ap-8497	230	13	=3	=3	VERB
ap-8497	230	14	8	8	NUM
ap-8497	230	15	,	,	PUNCT
ap-8497	230	16	ηpz	ηpz	NOUN
ap-8497	230	17	=	=	SYM
ap-8497	230	18	5	5	NUM
ap-8497	230	19	8	8	NUM
ap-8497	230	20	nlc	nlc	PROPN
ap-8497	230	21	=	=	PROPN
ap-8497	230	22	12	12	NUM
ap-8497	230	23	n∗	n∗	PROPN
ap-8497	230	24	u	u	NOUN
ap-8497	230	25	=	=	NOUN
ap-8497	230	26	11	11	NUM
ap-8497	230	27	thus	thus	ADV
ap-8497	230	28	,	,	PUNCT
ap-8497	230	29	nbad	nbad	ADJ
ap-8497	230	30	+	+	CCONJ
ap-8497	230	31	n	n	CCONJ
ap-8497	230	32	′	′	NUM
ap-8497	230	33	bad	bad	ADJ
ap-8497	230	34	≥	≥	NOUN
ap-8497	230	35	11	11	NUM
ap-8497	230	36	.	.	PUNCT
ap-8497	231	1	any	any	DET
ap-8497	231	2	matrix	matrix	NOUN
ap-8497	231	3	pair	pair	NOUN
ap-8497	231	4	with	with	ADP
ap-8497	231	5	the	the	DET
ap-8497	231	6	given	give	VERB
ap-8497	231	7	diagonal	diagonal	ADJ
ap-8497	231	8	element	element	NOUN
ap-8497	231	9	structure	structure	NOUN
ap-8497	231	10	and	and	CCONJ
ap-8497	231	11	satisfying	satisfy	VERB
ap-8497	231	12	the	the	DET
ap-8497	231	13	above	above	ADJ
ap-8497	231	14	condition	condition	NOUN
ap-8497	231	15	have	have	AUX
ap-8497	231	16	ζnet	ζnet	VERB
ap-8497	231	17	<	<	X
ap-8497	231	18	0	0	NUM
ap-8497	231	19	,	,	PUNCT
ap-8497	231	20	and	and	CCONJ
ap-8497	231	21	thus	thus	ADV
ap-8497	231	22	the	the	DET
ap-8497	231	23	matrix	matrix	NOUN
ap-8497	231	24	pair	pair	NOUN
ap-8497	231	25	is	be	AUX
ap-8497	231	26	an	an	DET
ap-8497	231	27	mdu	mdu	PROPN
ap-8497	231	28	matrix	matrix	NOUN
ap-8497	231	29	pair	pair	NOUN
ap-8497	231	30	.	.	PUNCT
ap-8497	232	1	example	example	NOUN
ap-8497	233	1	2	2	NUM
ap-8497	233	2	.	.	PUNCT
ap-8497	233	3	let	let	VERB
ap-8497	233	4	us	we	PRON
ap-8497	233	5	consider	consider	VERB
ap-8497	233	6	a	a	DET
ap-8497	233	7	matrix	matrix	NOUN
ap-8497	233	8	pair	pair	NOUN
ap-8497	233	9	with	with	ADP
ap-8497	233	10	the	the	DET
ap-8497	233	11	conditions	condition	NOUN
ap-8497	233	12	given	give	VERB
ap-8497	233	13	in	in	ADP
ap-8497	233	14	example	example	NOUN
ap-8497	233	15	1	1	NUM
ap-8497	233	16	:	:	PUNCT
ap-8497	233	17	e	e	X
ap-8497	233	18	=	=	PUNCT
ap-8497	233	19	−	−	PROPN
ap-8497	233	20	−	−	PROPN
ap-8497	234	1	+	+	CCONJ
ap-8497	235	1	+	+	CCONJ
ap-8497	235	2	−	−	X
ap-8497	236	1	+	+	CCONJ
ap-8497	236	2	−	−	PROPN
ap-8497	236	3	−	−	NOUN
ap-8497	236	4	−	−	PROPN
ap-8497	237	1	+	+	CCONJ
ap-8497	237	2	+	+	PUNCT
ap-8497	238	1	+	+	PUNCT
ap-8497	238	2	+	+	PUNCT
ap-8497	238	3	+	+	PUNCT
ap-8497	238	4	+	+	PUNCT
ap-8497	238	5	+	+	NOUN
ap-8497	238	6			NUM
ap-8497	238	7	and	and	CCONJ
ap-8497	238	8	a	a	DET
ap-8497	238	9	=	=	X
ap-8497	238	10	+	+	PROPN
ap-8497	238	11	−	−	NOUN
ap-8497	239	1	−	−	PROPN
ap-8497	240	1	+	+	CCONJ
ap-8497	241	1	+	+	CCONJ
ap-8497	241	2	−	−	X
ap-8497	242	1	+	+	CCONJ
ap-8497	242	2	−	−	PROPN
ap-8497	242	3	−	−	PROPN
ap-8497	243	1	+	+	CCONJ
ap-8497	243	2	−	−	PROPN
ap-8497	244	1	+	+	CCONJ
ap-8497	244	2	−	−	PROPN
ap-8497	244	3	−	−	PROPN
ap-8497	245	1	+	+	CCONJ
ap-8497	245	2	+	+	CCONJ
ap-8497	245	3			NUM
ap-8497	245	4	here	here	ADV
ap-8497	245	5	nbad	nbad	ADJ
ap-8497	245	6	=	=	SYM
ap-8497	245	7	7	7	NUM
ap-8497	245	8	,	,	PUNCT
ap-8497	245	9	ngood	ngood	NOUN
ap-8497	245	10	=	=	SYM
ap-8497	245	11	5	5	NUM
ap-8497	245	12	n	n	NOUN
ap-8497	245	13	′	′	NUM
ap-8497	245	14	bad	bad	ADJ
ap-8497	245	15	=	=	SYM
ap-8497	245	16	5	5	NUM
ap-8497	245	17	,	,	PUNCT
ap-8497	245	18	n	n	NOUN
ap-8497	245	19	′	′	NUM
ap-8497	246	1	good	good	ADJ
ap-8497	247	1	=	=	NOUN
ap-8497	247	2	7	7	NUM
ap-8497	247	3	∴	∴	NOUN
ap-8497	247	4	nbad	nbad	ADJ
ap-8497	247	5	+	+	CCONJ
ap-8497	247	6	n	n	CCONJ
ap-8497	247	7	′	′	NUM
ap-8497	247	8	bad	bad	ADJ
ap-8497	247	9	=	=	PUNCT
ap-8497	247	10	7	7	NUM
ap-8497	247	11	+	+	SYM
ap-8497	247	12	5	5	NUM
ap-8497	247	13	=	=	SYM
ap-8497	247	14	12	12	NUM
ap-8497	247	15	>	>	SYM
ap-8497	247	16	11	11	NUM
ap-8497	247	17	=	=	SYM
ap-8497	247	18	n∗	n∗	VERB
ap-8497	247	19	u	u	NOUN
ap-8497	247	20	.	.	PUNCT
ap-8497	248	1	hence	hence	ADV
ap-8497	248	2	,	,	PUNCT
ap-8497	248	3	the	the	DET
ap-8497	248	4	necessary	necessary	ADJ
ap-8497	248	5	condition	condition	NOUN
ap-8497	248	6	is	be	AUX
ap-8497	248	7	satisfied	satisfied	ADJ
ap-8497	248	8	,	,	PUNCT
ap-8497	248	9	and	and	CCONJ
ap-8497	248	10	now	now	ADV
ap-8497	248	11	we	we	PRON
ap-8497	248	12	check	check	VERB
ap-8497	248	13	the	the	DET
ap-8497	248	14	sufficiency	sufficiency	NOUN
ap-8497	248	15	guidelines	guideline	NOUN
ap-8497	248	16	required	require	VERB
ap-8497	248	17	for	for	ADP
ap-8497	248	18	qlsu	qlsu	NOUN
ap-8497	248	19	.	.	PUNCT
ap-8497	249	1	here	here	ADV
ap-8497	249	2	,	,	PUNCT
ap-8497	249	3	all	all	DET
ap-8497	249	4	the	the	DET
ap-8497	249	5	negative	negative	ADJ
ap-8497	249	6	diagonal	diagonal	ADJ
ap-8497	249	7	elements	element	NOUN
ap-8497	249	8	are	be	AUX
ap-8497	249	9	surrounded	surround	VERB
ap-8497	249	10	by	by	ADP
ap-8497	249	11	−	−	PROPN
ap-8497	249	12	chains	chain	NOUN
ap-8497	249	13	.	.	PUNCT
ap-8497	250	1	therefore	therefore	ADV
ap-8497	250	2	,	,	PUNCT
ap-8497	250	3	this	this	PRON
ap-8497	250	4	is	be	AUX
ap-8497	250	5	a	a	DET
ap-8497	250	6	qlsu	qlsu	NOUN
ap-8497	250	7	matrix	matrix	NOUN
ap-8497	250	8	pair	pair	NOUN
ap-8497	250	9	.	.	PUNCT
ap-8497	251	1	it	it	PRON
ap-8497	251	2	is	be	AUX
ap-8497	251	3	noted	note	VERB
ap-8497	251	4	that	that	SCONJ
ap-8497	251	5	once	once	SCONJ
ap-8497	251	6	there	there	PRON
ap-8497	251	7	is	be	VERB
ap-8497	251	8	at	at	ADV
ap-8497	251	9	least	least	ADJ
ap-8497	251	10	one	one	NUM
ap-8497	251	11	positive	positive	ADJ
ap-8497	251	12	diagonal	diagonal	ADJ
ap-8497	251	13	element	element	NOUN
ap-8497	251	14	,	,	PUNCT
ap-8497	251	15	we	we	PRON
ap-8497	251	16	can	can	AUX
ap-8497	251	17	assess	assess	VERB
ap-8497	251	18	the	the	DET
ap-8497	251	19	qualitative	qualitative	ADJ
ap-8497	251	20	sign	sign	NOUN
ap-8497	251	21	instability	instability	NOUN
ap-8497	251	22	by	by	ADP
ap-8497	251	23	computing	compute	VERB
ap-8497	251	24	the	the	DET
ap-8497	251	25	relative	relative	ADJ
ap-8497	251	26	distribution	distribution	NOUN
ap-8497	251	27	of	of	ADP
ap-8497	251	28	the	the	DET
ap-8497	251	29	bad	bad	ADJ
ap-8497	251	30	links	link	NOUN
ap-8497	251	31	together	together	ADV
ap-8497	251	32	with	with	ADP
ap-8497	251	33	the	the	DET
ap-8497	251	34	good	good	ADJ
ap-8497	251	35	links	link	NOUN
ap-8497	251	36	.	.	PUNCT
ap-8497	252	1	example	example	NOUN
ap-8497	253	1	3	3	X
ap-8497	253	2	.	.	PUNCT
ap-8497	253	3	let	let	VERB
ap-8497	253	4	us	we	PRON
ap-8497	253	5	discuss	discuss	VERB
ap-8497	253	6	the	the	DET
ap-8497	253	7	stability	stability	NOUN
ap-8497	253	8	of	of	ADP
ap-8497	253	9	the	the	DET
ap-8497	253	10	matrix	matrix	NOUN
ap-8497	253	11	pair	pair	NOUN
ap-8497	253	12	given	give	VERB
ap-8497	253	13	below	below	ADV
ap-8497	253	14	:	:	PUNCT
ap-8497	253	15	e	e	X
ap-8497	253	16	=	=	SYM
ap-8497	253	17			PROPN
ap-8497	253	18	−	−	PROPN
ap-8497	254	1	−	−	NOUN
ap-8497	254	2	−	−	PROPN
ap-8497	255	1	+	+	CCONJ
ap-8497	255	2	−	−	PROPN
ap-8497	255	3	−	−	PROPN
ap-8497	256	1	+	+	CCONJ
ap-8497	256	2	+	+	PUNCT
ap-8497	256	3	+	+	PUNCT
ap-8497	256	4	+	+	PUNCT
ap-8497	256	5	+	+	PUNCT
ap-8497	256	6	+	+	PUNCT
ap-8497	256	7	+	+	PUNCT
ap-8497	256	8	+	+	NUM
ap-8497	256	9	−	−	ADP
ap-8497	256	10	−	−	NOUN
ap-8497	256	11	−	−	PROPN
ap-8497	257	1	+	+	CCONJ
ap-8497	257	2	+	+	PUNCT
ap-8497	258	1	+	+	PUNCT
ap-8497	258	2	+	+	PUNCT
ap-8497	258	3	+	+	PUNCT
ap-8497	258	4	+	+	CCONJ
ap-8497	258	5	−	−	PROPN
ap-8497	258	6	−	−	PROPN
ap-8497	258	7			ADJ
ap-8497	258	8	and	and	CCONJ
ap-8497	258	9	a	a	DET
ap-8497	258	10	=	=	SYM
ap-8497	258	11			NOUN
ap-8497	258	12	−	−	PROPN
ap-8497	259	1	+	+	CCONJ
ap-8497	260	1	+	+	CCONJ
ap-8497	260	2	−	−	X
ap-8497	261	1	+	+	CCONJ
ap-8497	261	2	+	+	PUNCT
ap-8497	261	3	+	+	PUNCT
ap-8497	261	4	+	+	PUNCT
ap-8497	261	5	+	+	PUNCT
ap-8497	261	6	+	+	PUNCT
ap-8497	261	7	+	+	CCONJ
ap-8497	261	8	−	−	X
ap-8497	262	1	+	+	SYM
ap-8497	262	2	+	+	PUNCT
ap-8497	262	3	+	+	CCONJ
ap-8497	262	4	−	−	X
ap-8497	263	1	+	+	CCONJ
ap-8497	263	2	−	−	PROPN
ap-8497	264	1	+	+	CCONJ
ap-8497	264	2	−	−	PROPN
ap-8497	265	1	+	+	CCONJ
ap-8497	265	2	+	+	PUNCT
ap-8497	266	1	+	+	CCONJ
ap-8497	266	2	−	−	PROPN
ap-8497	266	3	−	−	PROPN
ap-8497	266	4			ADJ
ap-8497	266	5	for	for	ADP
ap-8497	266	6	the	the	DET
ap-8497	266	7	given	give	VERB
ap-8497	266	8	matrix	matrix	NOUN
ap-8497	266	9	pair	pair	NOUN
ap-8497	266	10	(	(	PUNCT
ap-8497	266	11	e	e	NOUN
ap-8497	266	12	,	,	PUNCT
ap-8497	266	13	a	a	PRON
ap-8497	266	14	)	)	PUNCT
ap-8497	266	15	,	,	PUNCT
ap-8497	266	16	ηpz	ηpz	NOUN
ap-8497	266	17	=	=	NOUN
ap-8497	266	18	6	6	NUM
ap-8497	266	19	10	10	NUM
ap-8497	266	20	,	,	PUNCT
ap-8497	266	21	ηng	ηng	NOUN
ap-8497	266	22	=	=	SYM
ap-8497	266	23	4	4	NUM
ap-8497	266	24	10	10	NUM
ap-8497	266	25	ηbad	ηbad	NOUN
ap-8497	266	26	=	=	NOUN
ap-8497	266	27	3	3	NUM
ap-8497	266	28	5	5	NUM
ap-8497	266	29	,	,	PUNCT
ap-8497	266	30	ηgood	ηgood	NOUN
ap-8497	266	31	=	=	SYM
ap-8497	266	32	2	2	NUM
ap-8497	266	33	5	5	NUM
ap-8497	266	34	η	η	NOUN
ap-8497	266	35	′	′	NUM
ap-8497	266	36	bad	bad	ADJ
ap-8497	266	37	=	=	NOUN
ap-8497	266	38	1	1	NUM
ap-8497	266	39	2	2	NUM
ap-8497	266	40	,	,	PUNCT
ap-8497	266	41	η	η	NOUN
ap-8497	266	42	′	′	NOUN
ap-8497	266	43	good	good	NOUN
ap-8497	267	1	=	=	NOUN
ap-8497	267	2	1	1	NUM
ap-8497	267	3	2	2	NUM
ap-8497	267	4	∴	∴	NOUN
ap-8497	267	5	ζnet	ζnet	NOUN
ap-8497	267	6	=	=	PUNCT
ap-8497	267	7	−2	−2	NOUN
ap-8497	267	8	5	5	NUM
ap-8497	267	9	<	<	X
ap-8497	267	10	0	0	NUM
ap-8497	267	11	.	.	PUNCT
ap-8497	268	1	here	here	ADV
ap-8497	268	2	all	all	DET
ap-8497	268	3	the	the	DET
ap-8497	268	4	positive	positive	ADJ
ap-8497	268	5	diagonal	diagonal	ADJ
ap-8497	268	6	elements	element	NOUN
ap-8497	268	7	are	be	AUX
ap-8497	268	8	surrounded	surround	VERB
ap-8497	268	9	by	by	ADP
ap-8497	268	10	+	+	X
ap-8497	268	11	chains	chain	NOUN
ap-8497	268	12	.	.	PUNCT
ap-8497	269	1	hence	hence	ADV
ap-8497	269	2	,	,	PUNCT
ap-8497	269	3	as	as	ADP
ap-8497	269	4	per	per	ADP
ap-8497	269	5	the	the	DET
ap-8497	269	6	sufficiency	sufficiency	NOUN
ap-8497	269	7	guidelines	guideline	NOUN
ap-8497	269	8	for	for	ADP
ap-8497	269	9	qlsu	qlsu	NOUN
ap-8497	269	10	,	,	PUNCT
ap-8497	269	11	the	the	DET
ap-8497	269	12	given	give	VERB
ap-8497	269	13	matrix	matrix	NOUN
ap-8497	269	14	pair	pair	NOUN
ap-8497	269	15	is	be	AUX
ap-8497	269	16	qlsu	qlsu	NOUN
ap-8497	269	17	.	.	PUNCT
ap-8497	270	1	thus	thus	ADV
ap-8497	270	2	,	,	PUNCT
ap-8497	270	3	this	this	DET
ap-8497	270	4	particular	particular	ADJ
ap-8497	270	5	quantitative	quantitative	ADJ
ap-8497	270	6	matrix	matrix	NOUN
ap-8497	270	7	pair	pair	NOUN
ap-8497	270	8	is	be	AUX
ap-8497	270	9	unstable	unstable	ADJ
ap-8497	270	10	without	without	ADP
ap-8497	270	11	any	any	DET
ap-8497	270	12	need	need	NOUN
ap-8497	270	13	of	of	ADP
ap-8497	270	14	eigenvalue	eigenvalue	NOUN
ap-8497	270	15	calculations	calculation	NOUN
ap-8497	270	16	.	.	PUNCT
ap-8497	271	1	176	176	NUM
ap-8497	271	2	vol	vol	NOUN
ap-8497	271	3	.	.	PUNCT
ap-8497	271	4	63	63	NUM
ap-8497	271	5	no	no	NOUN
ap-8497	271	6	.	.	PUNCT
ap-8497	272	1	3/2023	3/2023	NUM
ap-8497	272	2	qualitative	qualitative	NOUN
ap-8497	272	3	sign	sign	NOUN
ap-8497	272	4	stability	stability	NOUN
ap-8497	272	5	of	of	ADP
ap-8497	272	6	linear	linear	ADJ
ap-8497	272	7	time	time	NOUN
ap-8497	272	8	invariant	invariant	ADJ
ap-8497	272	9	descriptor	descriptor	NOUN
ap-8497	272	10	systems	system	NOUN
ap-8497	272	11	example	example	NOUN
ap-8497	272	12	4	4	NUM
ap-8497	272	13	.	.	PUNCT
ap-8497	273	1	consider	consider	VERB
ap-8497	273	2	the	the	DET
ap-8497	273	3	sign	sign	NOUN
ap-8497	273	4	pattern	pattern	NOUN
ap-8497	273	5	of	of	ADP
ap-8497	273	6	the	the	DET
ap-8497	273	7	matrix	matrix	NOUN
ap-8497	273	8	pair	pair	NOUN
ap-8497	273	9	given	give	VERB
ap-8497	273	10	below	below	ADV
ap-8497	273	11	:	:	PUNCT
ap-8497	274	1	e	e	X
ap-8497	274	2	=	=	PUNCT
ap-8497	275	1	[	[	X
ap-8497	275	2	−	−	X
ap-8497	275	3	+	+	CCONJ
ap-8497	275	4	−	−	PROPN
ap-8497	275	5	−	−	PROPN
ap-8497	276	1	+	+	CCONJ
ap-8497	276	2	+	+	PUNCT
ap-8497	276	3	+	+	CCONJ
ap-8497	276	4	−	−	PROPN
ap-8497	277	1	+	+	CCONJ
ap-8497	277	2	]	]	PUNCT
ap-8497	277	3	and	and	CCONJ
ap-8497	277	4	a	a	PRON
ap-8497	277	5	=	=	X
ap-8497	278	1	[	[	X
ap-8497	278	2	+	+	X
ap-8497	278	3	+	+	NUM
ap-8497	278	4	−	−	ADP
ap-8497	278	5	−	−	PROPN
ap-8497	279	1	+	+	CCONJ
ap-8497	279	2	+	+	PUNCT
ap-8497	280	1	+	+	CCONJ
ap-8497	280	2	−	−	PROPN
ap-8497	280	3	−	−	NOUN
ap-8497	280	4	]	]	PUNCT
ap-8497	280	5	this	this	DET
ap-8497	280	6	matrix	matrix	NOUN
ap-8497	280	7	pair	pair	NOUN
ap-8497	280	8	(	(	PUNCT
ap-8497	280	9	e	e	NOUN
ap-8497	280	10	,	,	PUNCT
ap-8497	280	11	a	a	PRON
ap-8497	280	12	)	)	PUNCT
ap-8497	280	13	has	have	VERB
ap-8497	280	14	ηpz	ηpz	NOUN
ap-8497	280	15	=	=	SYM
ap-8497	280	16	4	4	NUM
ap-8497	280	17	6	6	NUM
ap-8497	280	18	,	,	PUNCT
ap-8497	280	19	ηng	ηng	NOUN
ap-8497	280	20	=	=	SYM
ap-8497	280	21	2	2	NUM
ap-8497	280	22	6	6	NUM
ap-8497	280	23	ηbad	ηbad	NOUN
ap-8497	280	24	=	=	SYM
ap-8497	280	25	0	0	NUM
ap-8497	280	26	,	,	PUNCT
ap-8497	280	27	ηgood	ηgood	NOUN
ap-8497	280	28	=	=	SYM
ap-8497	280	29	1	1	NUM
ap-8497	280	30	η	η	NOUN
ap-8497	280	31	′	′	NUM
ap-8497	280	32	bad	bad	ADJ
ap-8497	280	33	=	=	SYM
ap-8497	280	34	1	1	NUM
ap-8497	280	35	,	,	PUNCT
ap-8497	280	36	η	η	NOUN
ap-8497	280	37	′	′	NOUN
ap-8497	280	38	good	good	NOUN
ap-8497	281	1	=	=	NOUN
ap-8497	281	2	0	0	NUM
ap-8497	281	3	making	make	VERB
ap-8497	281	4	ζnet	ζnet	NOUN
ap-8497	281	5	=	=	PUNCT
ap-8497	281	6	−1	−1	NOUN
ap-8497	281	7	3	3	NUM
ap-8497	281	8	<	<	X
ap-8497	281	9	0	0	NUM
ap-8497	281	10	.	.	PUNCT
ap-8497	282	1	since	since	ADV
ap-8497	282	2	,	,	PUNCT
ap-8497	282	3	ζnet	ζnet	PROPN
ap-8497	282	4	<	<	X
ap-8497	282	5	0	0	PROPN
ap-8497	282	6	,	,	PUNCT
ap-8497	282	7	the	the	DET
ap-8497	282	8	necessary	necessary	ADJ
ap-8497	282	9	condition	condition	NOUN
ap-8497	282	10	is	be	AUX
ap-8497	282	11	satisfied	satisfied	ADJ
ap-8497	282	12	.	.	PUNCT
ap-8497	283	1	but	but	CCONJ
ap-8497	283	2	the	the	DET
ap-8497	283	3	sufficient	sufficient	ADJ
ap-8497	283	4	conditions	condition	NOUN
ap-8497	283	5	are	be	AUX
ap-8497	283	6	not	not	PART
ap-8497	283	7	satisfied	satisfied	ADJ
ap-8497	283	8	.	.	PUNCT
ap-8497	284	1	hence	hence	ADV
ap-8497	284	2	,	,	PUNCT
ap-8497	284	3	it	it	PRON
ap-8497	284	4	is	be	AUX
ap-8497	284	5	an	an	DET
ap-8497	284	6	mdu	mdu	NOUN
ap-8497	284	7	(	(	PUNCT
ap-8497	284	8	not	not	PART
ap-8497	284	9	a	a	DET
ap-8497	284	10	qlsu	qlsu	NOUN
ap-8497	284	11	)	)	PUNCT
ap-8497	284	12	matrix	matrix	NOUN
ap-8497	284	13	pair	pair	NOUN
ap-8497	284	14	.	.	PUNCT
ap-8497	285	1	it	it	PRON
ap-8497	285	2	should	should	AUX
ap-8497	285	3	be	be	AUX
ap-8497	285	4	noted	note	VERB
ap-8497	285	5	that	that	SCONJ
ap-8497	285	6	we	we	PRON
ap-8497	285	7	are	be	AUX
ap-8497	285	8	not	not	PART
ap-8497	285	9	stating	state	VERB
ap-8497	285	10	that	that	SCONJ
ap-8497	285	11	the	the	DET
ap-8497	285	12	matrix	matrix	NOUN
ap-8497	285	13	pair	pair	NOUN
ap-8497	285	14	with	with	ADP
ap-8497	285	15	this	this	DET
ap-8497	285	16	elemental	elemental	ADJ
ap-8497	285	17	sign	sign	NOUN
ap-8497	285	18	structure	structure	NOUN
ap-8497	285	19	is	be	AUX
ap-8497	285	20	always	always	ADV
ap-8497	285	21	unstable	unstable	ADJ
ap-8497	285	22	.	.	PUNCT
ap-8497	286	1	we	we	PRON
ap-8497	286	2	are	be	AUX
ap-8497	286	3	simply	simply	ADV
ap-8497	286	4	stating	state	VERB
ap-8497	286	5	that	that	SCONJ
ap-8497	286	6	the	the	DET
ap-8497	286	7	elemental	elemental	ADJ
ap-8497	286	8	sign	sign	NOUN
ap-8497	286	9	structure	structure	NOUN
ap-8497	286	10	of	of	ADP
ap-8497	286	11	the	the	DET
ap-8497	286	12	above	above	ADJ
ap-8497	286	13	matrix	matrix	NOUN
ap-8497	286	14	pair	pair	NOUN
ap-8497	286	15	guarantees	guarantee	VERB
ap-8497	286	16	that	that	SCONJ
ap-8497	286	17	there	there	PRON
ap-8497	286	18	exist	exist	VERB
ap-8497	286	19	magnitudes	magnitude	NOUN
ap-8497	286	20	which	which	PRON
ap-8497	286	21	would	would	AUX
ap-8497	286	22	definitely	definitely	ADV
ap-8497	286	23	make	make	VERB
ap-8497	286	24	this	this	DET
ap-8497	286	25	matrix	matrix	NOUN
ap-8497	286	26	unstable	unstable	ADJ
ap-8497	286	27	.	.	PUNCT
ap-8497	287	1	for	for	ADP
ap-8497	287	2	example	example	NOUN
ap-8497	287	3	,	,	PUNCT
ap-8497	287	4	the	the	DET
ap-8497	287	5	following	follow	VERB
ap-8497	287	6	matrix	matrix	NOUN
ap-8497	287	7	pair	pair	NOUN
ap-8497	287	8	(	(	PUNCT
ap-8497	287	9	e1	e1	NOUN
ap-8497	287	10	,	,	PUNCT
ap-8497	287	11	a1	a1	NOUN
ap-8497	287	12	)	)	PUNCT
ap-8497	287	13	with	with	ADP
ap-8497	287	14	the	the	DET
ap-8497	287	15	above	above	ADJ
ap-8497	287	16	sign	sign	NOUN
ap-8497	287	17	structure	structure	NOUN
ap-8497	287	18	is	be	AUX
ap-8497	287	19	unstable	unstable	ADJ
ap-8497	287	20	,	,	PUNCT
ap-8497	287	21	e1	e1	NOUN
ap-8497	287	22	=	=	PUNCT
ap-8497	288	1	[	[	PUNCT
ap-8497	288	2	−1.6132	−1.6132	NOUN
ap-8497	288	3	2.0118	2.0118	NUM
ap-8497	288	4	−1.6806	−1.6806	X
ap-8497	288	5	−0.0021	−0.0021	NOUN
ap-8497	288	6	0.5791	0.5791	NUM
ap-8497	288	7	0.2139	0.2139	NUM
ap-8497	288	8	0.2017	0.2017	NUM
ap-8497	288	9	−2.1852	−2.1852	SYM
ap-8497	288	10	1.7419	1.7419	NUM
ap-8497	288	11	]	]	PUNCT
ap-8497	288	12	,	,	PUNCT
ap-8497	288	13	a1	a1	NOUN
ap-8497	288	14	=	=	PUNCT
ap-8497	288	15	[	[	PUNCT
ap-8497	288	16	0.2462	0.2462	NUM
ap-8497	288	17	1.8614	1.8614	NUM
ap-8497	288	18	−0.7201	−0.7201	X
ap-8497	288	19	−1.8764	−1.8764	NOUN
ap-8497	288	20	1.4531	1.4531	NUM
ap-8497	288	21	1.9056	1.9056	NUM
ap-8497	288	22	3.4318	3.4318	NUM
ap-8497	288	23	−0.1567	−0.1567	NUM
ap-8497	288	24	−1.7543	−1.7543	NUM
ap-8497	288	25	]	]	PUNCT
ap-8497	288	26	,	,	PUNCT
ap-8497	288	27	while	while	SCONJ
ap-8497	288	28	the	the	DET
ap-8497	288	29	following	follow	VERB
ap-8497	288	30	matrix	matrix	NOUN
ap-8497	288	31	pair	pair	NOUN
ap-8497	288	32	(	(	PUNCT
ap-8497	288	33	e2	e2	PROPN
ap-8497	288	34	,	,	PUNCT
ap-8497	288	35	a2	a2	PROPN
ap-8497	288	36	)	)	PUNCT
ap-8497	288	37	having	have	VERB
ap-8497	288	38	the	the	DET
ap-8497	288	39	same	same	ADJ
ap-8497	288	40	sign	sign	NOUN
ap-8497	288	41	structure	structure	NOUN
ap-8497	288	42	is	be	AUX
ap-8497	288	43	stable	stable	ADJ
ap-8497	288	44	.	.	PUNCT
ap-8497	289	1	e2	e2	PROPN
ap-8497	289	2	=	=	PUNCT
ap-8497	290	1	[	[	X
ap-8497	290	2	−1.0132	−1.0132	X
ap-8497	290	3	0.0118	0.0118	NUM
ap-8497	290	4	−1.0006	−1.0006	X
ap-8497	290	5	−1.0021	−1.0021	NOUN
ap-8497	290	6	0.4001	0.4001	NUM
ap-8497	290	7	0.2110	0.2110	NUM
ap-8497	290	8	0.0213	0.0213	NUM
ap-8497	290	9	−0.0411	−0.0411	PROPN
ap-8497	290	10	0.2015	0.2015	NUM
ap-8497	290	11	]	]	PUNCT
ap-8497	290	12	,	,	PUNCT
ap-8497	290	13	a2	a2	PROPN
ap-8497	290	14	=	=	PUNCT
ap-8497	291	1	[	[	PUNCT
ap-8497	291	2	1.8112	1.8112	NUM
ap-8497	291	3	21.5624	21.5624	NUM
ap-8497	291	4	−1.0207	−1.0207	NOUN
ap-8497	291	5	−0.9016	−0.9016	PROPN
ap-8497	291	6	1.0172	1.0172	NUM
ap-8497	291	7	1.0061	1.0061	NUM
ap-8497	291	8	9.6512	9.6512	NUM
ap-8497	291	9	−0.0600	−0.0600	X
ap-8497	291	10	−5.0234	−5.0234	PRON
ap-8497	291	11	]	]	PUNCT
ap-8497	291	12	.	.	PUNCT
ap-8497	292	1	example	example	NOUN
ap-8497	292	2	5	5	NUM
ap-8497	292	3	.	.	PUNCT
ap-8497	293	1	consider	consider	VERB
ap-8497	293	2	the	the	DET
ap-8497	293	3	matrix	matrix	NOUN
ap-8497	293	4	pair	pair	NOUN
ap-8497	293	5	(	(	PUNCT
ap-8497	293	6	e	e	NOUN
ap-8497	293	7	,	,	PUNCT
ap-8497	293	8	a	a	PRON
ap-8497	293	9	)	)	PUNCT
ap-8497	293	10	with	with	ADP
ap-8497	293	11	a	a	DET
ap-8497	293	12	sign	sign	NOUN
ap-8497	293	13	structure	structure	NOUN
ap-8497	293	14	given	give	VERB
ap-8497	293	15	by	by	ADP
ap-8497	293	16	:	:	PUNCT
ap-8497	293	17	e	e	X
ap-8497	293	18	=	=	SYM
ap-8497	293	19			PROPN
ap-8497	293	20	+	+	PUNCT
ap-8497	293	21	−	−	PROPN
ap-8497	294	1	+	+	CCONJ
ap-8497	294	2	−	−	PROPN
ap-8497	294	3	−	−	PROPN
ap-8497	295	1	+	+	CCONJ
ap-8497	295	2	−	−	PROPN
ap-8497	295	3	−	−	PROPN
ap-8497	296	1	+	+	CCONJ
ap-8497	296	2	−	−	PROPN
ap-8497	296	3	−	−	NUM
ap-8497	297	1	−	−	PROPN
ap-8497	298	1	+	+	CCONJ
ap-8497	298	2	−	−	PROPN
ap-8497	298	3	−	−	NUM
ap-8497	298	4	−	−	PROPN
ap-8497	298	5	−	−	PROPN
ap-8497	298	6	−	−	NOUN
ap-8497	298	7	−	−	PROPN
ap-8497	299	1	+	+	CCONJ
ap-8497	300	1	+	+	CCONJ
ap-8497	300	2	−	−	X
ap-8497	301	1	+	+	CCONJ
ap-8497	301	2	−	−	PROPN
ap-8497	302	1	−	−	PROPN
ap-8497	302	2			ADJ
ap-8497	302	3	and	and	CCONJ
ap-8497	302	4	a	a	DET
ap-8497	302	5	=	=	SYM
ap-8497	302	6			NOUN
ap-8497	302	7	−	−	PROPN
ap-8497	303	1	+	+	CCONJ
ap-8497	303	2	−	−	PROPN
ap-8497	303	3	−	−	PROPN
ap-8497	304	1	+	+	CCONJ
ap-8497	304	2	−	−	PROPN
ap-8497	305	1	+	+	CCONJ
ap-8497	306	1	+	+	NUM
ap-8497	306	2	−	−	ADP
ap-8497	306	3	−	−	PROPN
ap-8497	307	1	+	+	CCONJ
ap-8497	307	2	−	−	PROPN
ap-8497	307	3	−	−	NOUN
ap-8497	307	4	−	−	PROPN
ap-8497	308	1	+	+	CCONJ
ap-8497	308	2	+	+	PUNCT
ap-8497	309	1	+	+	CCONJ
ap-8497	309	2	−	−	X
ap-8497	309	3	+	+	CCONJ
ap-8497	309	4	−	−	PROPN
ap-8497	310	1	−	−	NUM
ap-8497	310	2	−	−	PROPN
ap-8497	311	1	+	+	CCONJ
ap-8497	311	2	−	−	PROPN
ap-8497	312	1	−	−	PROPN
ap-8497	312	2			VERB
ap-8497	312	3	this	this	DET
ap-8497	312	4	matrix	matrix	NOUN
ap-8497	312	5	pair	pair	NOUN
ap-8497	312	6	(	(	PUNCT
ap-8497	312	7	e	e	NOUN
ap-8497	312	8	,	,	PUNCT
ap-8497	312	9	a	a	PRON
ap-8497	312	10	)	)	PUNCT
ap-8497	312	11	has	have	VERB
ap-8497	312	12	ηpz	ηpz	NOUN
ap-8497	312	13	=	=	SYM
ap-8497	312	14	2	2	NUM
ap-8497	312	15	5	5	NUM
ap-8497	312	16	,	,	PUNCT
ap-8497	312	17	ηng	ηng	NOUN
ap-8497	312	18	=	=	SYM
ap-8497	312	19	3	3	NUM
ap-8497	312	20	5	5	NUM
ap-8497	312	21	ηbad	ηbad	NOUN
ap-8497	312	22	=	=	SYM
ap-8497	312	23	2	2	NUM
ap-8497	312	24	5	5	NUM
ap-8497	312	25	,	,	PUNCT
ap-8497	312	26	ηgood	ηgood	NOUN
ap-8497	312	27	=	=	SYM
ap-8497	312	28	3	3	NUM
ap-8497	312	29	5	5	NUM
ap-8497	312	30	η	η	NOUN
ap-8497	312	31	′	′	NUM
ap-8497	312	32	bad	bad	ADJ
ap-8497	312	33	=	=	NOUN
ap-8497	312	34	1	1	NUM
ap-8497	312	35	5	5	NUM
ap-8497	312	36	,	,	PUNCT
ap-8497	312	37	η	η	NOUN
ap-8497	312	38	′	′	NOUN
ap-8497	312	39	good	good	NOUN
ap-8497	313	1	=	=	NOUN
ap-8497	313	2	4	4	NUM
ap-8497	313	3	5	5	NUM
ap-8497	313	4	∴	∴	NOUN
ap-8497	313	5	ζnet	ζnet	NOUN
ap-8497	313	6	=	=	NOUN
ap-8497	313	7	1	1	NUM
ap-8497	313	8	>	>	X
ap-8497	313	9	0	0	NUM
ap-8497	313	10	.	.	PUNCT
ap-8497	314	1	here	here	ADV
ap-8497	314	2	,	,	PUNCT
ap-8497	314	3	ζnet	ζnet	PROPN
ap-8497	314	4	>	>	X
ap-8497	314	5	0	0	PROPN
ap-8497	314	6	,	,	PUNCT
ap-8497	314	7	but	but	CCONJ
ap-8497	314	8	the	the	DET
ap-8497	314	9	necessary	necessary	ADJ
ap-8497	314	10	condition	condition	NOUN
ap-8497	314	11	for	for	ADP
ap-8497	314	12	qualitative	qualitative	ADJ
ap-8497	314	13	sign	sign	NOUN
ap-8497	314	14	stability	stability	NOUN
ap-8497	314	15	c1	c1	PROPN
ap-8497	314	16	is	be	AUX
ap-8497	314	17	not	not	PART
ap-8497	314	18	satisfied	satisfied	ADJ
ap-8497	314	19	.	.	PUNCT
ap-8497	315	1	hence	hence	ADV
ap-8497	315	2	,	,	PUNCT
ap-8497	315	3	it	it	PRON
ap-8497	315	4	is	be	AUX
ap-8497	315	5	an	an	DET
ap-8497	315	6	mds	mds	PROPN
ap-8497	315	7	/	/	SYM
ap-8497	315	8	u	u	NOUN
ap-8497	315	9	matrix	matrix	NOUN
ap-8497	315	10	pair	pair	NOUN
ap-8497	315	11	and	and	CCONJ
ap-8497	315	12	is	be	AUX
ap-8497	315	13	a	a	DET
ap-8497	315	14	non	non	ADJ
ap-8497	315	15	-	-	ADJ
ap-8497	315	16	qlss	qlss	ADJ
ap-8497	315	17	matrix	matrix	NOUN
ap-8497	315	18	pair	pair	NOUN
ap-8497	315	19	.	.	PUNCT
ap-8497	316	1	5	5	X
ap-8497	316	2	.	.	X
ap-8497	316	3	conclusion	conclusion	NOUN
ap-8497	316	4	this	this	DET
ap-8497	316	5	paper	paper	NOUN
ap-8497	316	6	addresses	address	VERB
ap-8497	316	7	the	the	DET
ap-8497	316	8	issue	issue	NOUN
ap-8497	316	9	of	of	ADP
ap-8497	316	10	determining	determine	VERB
ap-8497	316	11	the	the	DET
ap-8497	316	12	stability	stability	NOUN
ap-8497	316	13	/	/	SYM
ap-8497	316	14	instability	instability	NOUN
ap-8497	316	15	of	of	ADP
ap-8497	316	16	a	a	DET
ap-8497	316	17	matrix	matrix	NOUN
ap-8497	316	18	pair	pair	NOUN
ap-8497	316	19	that	that	PRON
ap-8497	316	20	arises	arise	VERB
ap-8497	316	21	in	in	ADP
ap-8497	316	22	a	a	DET
ap-8497	316	23	continuous	continuous	ADJ
ap-8497	316	24	linear	linear	ADJ
ap-8497	316	25	homogeneous	homogeneous	ADJ
ap-8497	316	26	time	time	NOUN
ap-8497	316	27	-	-	PUNCT
ap-8497	316	28	invariant	invariant	ADJ
ap-8497	316	29	system	system	NOUN
ap-8497	316	30	.	.	PUNCT
ap-8497	317	1	the	the	DET
ap-8497	317	2	conditions	condition	NOUN
ap-8497	317	3	for	for	ADP
ap-8497	317	4	a	a	DET
ap-8497	317	5	matrix	matrix	NOUN
ap-8497	317	6	to	to	PART
ap-8497	317	7	be	be	AUX
ap-8497	317	8	qlsu	qlsu	NOUN
ap-8497	317	9	have	have	AUX
ap-8497	317	10	already	already	ADV
ap-8497	317	11	been	be	AUX
ap-8497	317	12	discussed	discuss	VERB
ap-8497	317	13	in	in	ADP
ap-8497	317	14	the	the	DET
ap-8497	317	15	earlier	early	ADJ
ap-8497	317	16	works	work	NOUN
ap-8497	317	17	.	.	PUNCT
ap-8497	318	1	in	in	ADP
ap-8497	318	2	this	this	DET
ap-8497	318	3	research	research	NOUN
ap-8497	318	4	,	,	PUNCT
ap-8497	318	5	we	we	PRON
ap-8497	318	6	generalise	generalise	VERB
ap-8497	318	7	the	the	DET
ap-8497	318	8	identity	identity	NOUN
ap-8497	318	9	matrix	matrix	NOUN
ap-8497	318	10	i	i	PRON
ap-8497	318	11	to	to	ADP
ap-8497	318	12	any	any	DET
ap-8497	318	13	matrix	matrix	NOUN
ap-8497	318	14	e	e	NOUN
ap-8497	318	15	and	and	CCONJ
ap-8497	318	16	propose	propose	VERB
ap-8497	318	17	few	few	ADJ
ap-8497	318	18	necessary	necessary	ADJ
ap-8497	318	19	conditions	condition	NOUN
ap-8497	318	20	and	and	CCONJ
ap-8497	318	21	sufficient	sufficient	ADJ
ap-8497	318	22	conditions	condition	NOUN
ap-8497	318	23	for	for	ADP
ap-8497	318	24	qualitative	qualitative	ADJ
ap-8497	318	25	sign	sign	NOUN
ap-8497	318	26	instability	instability	NOUN
ap-8497	318	27	of	of	ADP
ap-8497	318	28	a	a	DET
ap-8497	318	29	matrix	matrix	NOUN
ap-8497	318	30	pair	pair	NOUN
ap-8497	318	31	.	.	PUNCT
ap-8497	319	1	the	the	DET
ap-8497	319	2	proposed	propose	VERB
ap-8497	319	3	conditions	condition	NOUN
ap-8497	319	4	are	be	AUX
ap-8497	319	5	very	very	ADV
ap-8497	319	6	simple	simple	ADJ
ap-8497	319	7	and	and	CCONJ
ap-8497	319	8	are	be	AUX
ap-8497	319	9	based	base	VERB
ap-8497	319	10	on	on	ADP
ap-8497	319	11	the	the	DET
ap-8497	319	12	number	number	NOUN
ap-8497	319	13	and	and	CCONJ
ap-8497	319	14	nature	nature	NOUN
ap-8497	319	15	of	of	ADP
ap-8497	319	16	the	the	DET
ap-8497	319	17	diagonal	diagonal	ADJ
ap-8497	319	18	elements	element	NOUN
ap-8497	319	19	and	and	CCONJ
ap-8497	319	20	the	the	DET
ap-8497	319	21	number	number	NOUN
ap-8497	319	22	and	and	CCONJ
ap-8497	319	23	nature	nature	NOUN
ap-8497	319	24	of	of	ADP
ap-8497	319	25	the	the	DET
ap-8497	319	26	off	off	ADV
ap-8497	319	27	-	-	PUNCT
ap-8497	319	28	diagonal	diagonal	ADJ
ap-8497	319	29	element	element	NOUN
ap-8497	319	30	pairs	pair	NOUN
ap-8497	319	31	(	(	PUNCT
ap-8497	319	32	links	link	NOUN
ap-8497	319	33	)	)	PUNCT
ap-8497	319	34	.	.	PUNCT
ap-8497	320	1	this	this	PRON
ap-8497	320	2	reflects	reflect	VERB
ap-8497	320	3	that	that	SCONJ
ap-8497	320	4	the	the	DET
ap-8497	320	5	elemental	elemental	ADJ
ap-8497	320	6	sign	sign	NOUN
ap-8497	320	7	structure	structure	NOUN
ap-8497	320	8	of	of	ADP
ap-8497	320	9	a	a	DET
ap-8497	320	10	matrix	matrix	NOUN
ap-8497	320	11	pair	pair	NOUN
ap-8497	320	12	is	be	AUX
ap-8497	320	13	an	an	DET
ap-8497	320	14	important	important	ADJ
ap-8497	320	15	contributor	contributor	NOUN
ap-8497	320	16	to	to	ADP
ap-8497	320	17	the	the	DET
ap-8497	320	18	stability	stability	NOUN
ap-8497	320	19	/	/	SYM
ap-8497	320	20	instability	instability	NOUN
ap-8497	320	21	.	.	PUNCT
ap-8497	321	1	these	these	DET
ap-8497	321	2	conditions	condition	NOUN
ap-8497	321	3	are	be	AUX
ap-8497	321	4	extremely	extremely	ADV
ap-8497	321	5	helpful	helpful	ADJ
ap-8497	321	6	for	for	ADP
ap-8497	321	7	engineers	engineer	NOUN
ap-8497	321	8	and	and	CCONJ
ap-8497	321	9	ecologists	ecologist	NOUN
ap-8497	321	10	,	,	PUNCT
ap-8497	321	11	in	in	ADP
ap-8497	321	12	solving	solve	VERB
ap-8497	321	13	stability	stability	NOUN
ap-8497	321	14	-	-	PUNCT
ap-8497	321	15	related	relate	VERB
ap-8497	321	16	problems	problem	NOUN
ap-8497	321	17	.	.	PUNCT
ap-8497	322	1	acknowledgements	acknowledgement	VERB
ap-8497	322	2	the	the	DET
ap-8497	322	3	research	research	NOUN
ap-8497	322	4	work	work	NOUN
ap-8497	322	5	is	be	AUX
ap-8497	322	6	supported	support	VERB
ap-8497	322	7	by	by	ADP
ap-8497	322	8	serb	serb	PROPN
ap-8497	322	9	,	,	PUNCT
ap-8497	322	10	dst	dst	PROPN
ap-8497	322	11	under	under	ADP
ap-8497	322	12	grant	grant	NOUN
ap-8497	322	13	no	no	INTJ
ap-8497	322	14	.	.	PUNCT
ap-8497	323	1	srg/2019/000451	srg/2019/000451	PROPN
ap-8497	323	2	.	.	PUNCT
ap-8497	324	1	references	reference	NOUN
ap-8497	324	2	[	[	X
ap-8497	324	3	1	1	X
ap-8497	324	4	]	]	PUNCT
ap-8497	324	5	v.	v.	PROPN
ap-8497	324	6	k.	k.	PROPN
ap-8497	324	7	mishra	mishra	PROPN
ap-8497	324	8	,	,	PUNCT
ap-8497	324	9	n.	n.	PROPN
ap-8497	324	10	k.	k.	PROPN
ap-8497	324	11	tomar	tomar	PROPN
ap-8497	324	12	,	,	PUNCT
ap-8497	324	13	m.	m.	PROPN
ap-8497	324	14	k.	k.	PROPN
ap-8497	324	15	gupta	gupta	PROPN
ap-8497	324	16	.	.	PUNCT
ap-8497	325	1	regularization	regularization	NOUN
ap-8497	325	2	and	and	CCONJ
ap-8497	325	3	index	index	NOUN
ap-8497	325	4	reduction	reduction	NOUN
ap-8497	325	5	for	for	ADP
ap-8497	325	6	linear	linear	PROPN
ap-8497	325	7	differential	differential	ADJ
ap-8497	325	8	–	–	PUNCT
ap-8497	325	9	algebraic	algebraic	ADJ
ap-8497	325	10	systems	system	NOUN
ap-8497	325	11	.	.	PUNCT
ap-8497	326	1	computational	computational	ADJ
ap-8497	326	2	and	and	CCONJ
ap-8497	326	3	applied	apply	VERB
ap-8497	326	4	mathematics	mathematic	NOUN
ap-8497	326	5	volume	volume	NOUN
ap-8497	326	6	37(4):4587–4598	37(4):4587–4598	NUM
ap-8497	326	7	,	,	PUNCT
ap-8497	326	8	2018	2018	NUM
ap-8497	326	9	.	.	PUNCT
ap-8497	327	1	https://doi.org/10.1007/s40314-018-0589-3	https://doi.org/10.1007/s40314-018-0589-3	NOUN
ap-8497	328	1	[	[	X
ap-8497	328	2	2	2	NUM
ap-8497	328	3	]	]	PUNCT
ap-8497	328	4	m.	m.	NOUN
ap-8497	328	5	k.	k.	PROPN
ap-8497	328	6	gupta	gupta	PROPN
ap-8497	328	7	,	,	PUNCT
ap-8497	328	8	n.	n.	PROPN
ap-8497	328	9	k.	k.	PROPN
ap-8497	328	10	tomar	tomar	PROPN
ap-8497	328	11	,	,	PUNCT
ap-8497	328	12	s.	s.	PROPN
ap-8497	328	13	bhaumik	bhaumik	PROPN
ap-8497	328	14	.	.	PUNCT
ap-8497	329	1	on	on	ADP
ap-8497	329	2	detectability	detectability	NOUN
ap-8497	329	3	and	and	CCONJ
ap-8497	329	4	observer	observer	NOUN
ap-8497	329	5	design	design	NOUN
ap-8497	329	6	for	for	ADP
ap-8497	329	7	rectangular	rectangular	ADJ
ap-8497	329	8	linear	linear	ADJ
ap-8497	329	9	descriptor	descriptor	NOUN
ap-8497	329	10	system	system	NOUN
ap-8497	329	11	.	.	PUNCT
ap-8497	330	1	international	international	ADJ
ap-8497	330	2	journal	journal	PROPN
ap-8497	330	3	of	of	ADP
ap-8497	330	4	dynamics	dynamic	NOUN
ap-8497	330	5	and	and	CCONJ
ap-8497	330	6	control	control	NOUN
ap-8497	330	7	4(4):438–446	4(4):438–446	NUM
ap-8497	330	8	,	,	PUNCT
ap-8497	330	9	2016	2016	NUM
ap-8497	330	10	.	.	PUNCT
ap-8497	331	1	https://doi.org/10.1007/s40435-014-0146-x	https://doi.org/10.1007/s40435-014-0146-x	PROPN
ap-8497	331	2	[	[	X
ap-8497	331	3	3	3	NUM
ap-8497	331	4	]	]	PUNCT
ap-8497	331	5	m.	m.	NOUN
ap-8497	331	6	k.	k.	PROPN
ap-8497	331	7	gupta	gupta	PROPN
ap-8497	331	8	,	,	PUNCT
ap-8497	331	9	n.	n.	PROPN
ap-8497	331	10	k.	k.	PROPN
ap-8497	331	11	tomar	tomar	PROPN
ap-8497	331	12	,	,	PUNCT
ap-8497	331	13	s.	s.	PROPN
ap-8497	331	14	bhaumik	bhaumik	PROPN
ap-8497	331	15	.	.	PUNCT
ap-8497	332	1	on	on	ADP
ap-8497	332	2	observability	observability	NOUN
ap-8497	332	3	of	of	ADP
ap-8497	332	4	irregular	irregular	ADJ
ap-8497	332	5	descriptor	descriptor	NOUN
ap-8497	332	6	systems	system	NOUN
ap-8497	332	7	.	.	PUNCT
ap-8497	333	1	international	international	ADJ
ap-8497	333	2	conference	conference	NOUN
ap-8497	333	3	on	on	ADP
ap-8497	333	4	advances	advance	NOUN
ap-8497	333	5	in	in	ADP
ap-8497	333	6	control	control	NOUN
ap-8497	333	7	and	and	CCONJ
ap-8497	333	8	optimization	optimization	NOUN
ap-8497	333	9	of	of	ADP
ap-8497	333	10	dynamical	dynamical	ADJ
ap-8497	333	11	systems	system	NOUN
ap-8497	333	12	3(1):376–379	3(1):376–379	NUM
ap-8497	333	13	,	,	PUNCT
ap-8497	333	14	2014	2014	NUM
ap-8497	333	15	.	.	PUNCT
ap-8497	334	1	https	https	NOUN
ap-8497	334	2	:	:	PUNCT
ap-8497	334	3	//doi.org/10.3182/20140313	//doi.org/10.3182/20140313	PROPN
ap-8497	334	4	-	-	PUNCT
ap-8497	334	5	3	3	NUM
ap-8497	334	6	-	-	PUNCT
ap-8497	334	7	in-3024.00089	in-3024.00089	NOUN
ap-8497	334	8	[	[	X
ap-8497	334	9	4	4	NUM
ap-8497	334	10	]	]	PUNCT
ap-8497	334	11	j.	j.	PROPN
ap-8497	334	12	quirk	quirk	PROPN
ap-8497	334	13	,	,	PUNCT
ap-8497	334	14	r.	r.	PROPN
ap-8497	334	15	ruppert	ruppert	PROPN
ap-8497	334	16	.	.	PUNCT
ap-8497	335	1	qualitative	qualitative	ADJ
ap-8497	335	2	economics	economic	NOUN
ap-8497	335	3	and	and	CCONJ
ap-8497	335	4	the	the	DET
ap-8497	335	5	stability	stability	NOUN
ap-8497	335	6	of	of	ADP
ap-8497	335	7	equilibrium	equilibrium	NOUN
ap-8497	335	8	.	.	PUNCT
ap-8497	336	1	the	the	DET
ap-8497	336	2	review	review	NOUN
ap-8497	336	3	of	of	ADP
ap-8497	336	4	economic	economic	ADJ
ap-8497	336	5	studies	study	NOUN
ap-8497	336	6	32(4):311–326	32(4):311–326	NUM
ap-8497	336	7	,	,	PUNCT
ap-8497	336	8	1965	1965	NUM
ap-8497	336	9	.	.	PUNCT
ap-8497	337	1	https://doi.org/10.2307/2295838	https://doi.org/10.2307/2295838	PRON
ap-8497	338	1	[	[	X
ap-8497	338	2	5	5	NUM
ap-8497	338	3	]	]	PUNCT
ap-8497	338	4	c.	c.	PROPN
ap-8497	338	5	jeffries	jeffrie	NOUN
ap-8497	338	6	.	.	PUNCT
ap-8497	339	1	qualitative	qualitative	ADJ
ap-8497	339	2	stability	stability	NOUN
ap-8497	339	3	and	and	CCONJ
ap-8497	339	4	digraphs	digraph	VERB
ap-8497	339	5	in	in	ADP
ap-8497	339	6	model	model	NOUN
ap-8497	339	7	ecosystems	ecosystem	NOUN
ap-8497	339	8	.	.	PUNCT
ap-8497	340	1	ecology	ecology	NOUN
ap-8497	340	2	55(6):1415–1419	55(6):1415–1419	NUM
ap-8497	340	3	,	,	PUNCT
ap-8497	340	4	1974	1974	NUM
ap-8497	340	5	.	.	PUNCT
ap-8497	341	1	https://doi.org/10.2307/1935470	https://doi.org/10.2307/1935470	PUNCT
ap-8497	342	1	[	[	X
ap-8497	342	2	6	6	NUM
ap-8497	342	3	]	]	X
ap-8497	342	4	r.	r.	PROPN
ap-8497	342	5	m.	m.	PROPN
ap-8497	342	6	may	may	AUX
ap-8497	342	7	.	.	PUNCT
ap-8497	343	1	stability	stability	NOUN
ap-8497	343	2	and	and	CCONJ
ap-8497	343	3	complexity	complexity	NOUN
ap-8497	343	4	in	in	ADP
ap-8497	343	5	model	model	NOUN
ap-8497	343	6	ecosystems	ecosystem	NOUN
ap-8497	343	7	.	.	PUNCT
ap-8497	344	1	princeton	princeton	PROPN
ap-8497	344	2	university	university	PROPN
ap-8497	344	3	press	press	NOUN
ap-8497	344	4	,	,	PUNCT
ap-8497	344	5	new	new	PROPN
ap-8497	344	6	jersey	jersey	PROPN
ap-8497	344	7	,	,	PUNCT
ap-8497	344	8	1st	1st	ADJ
ap-8497	344	9	edn	edn	PROPN
ap-8497	344	10	.	.	PUNCT
ap-8497	344	11	,	,	PUNCT
ap-8497	344	12	2019	2019	NUM
ap-8497	344	13	.	.	PUNCT
ap-8497	345	1	https://doi.org/10.1515/9780691206912	https://doi.org/10.1515/9780691206912	VERB
ap-8497	346	1	[	[	X
ap-8497	346	2	7	7	NUM
ap-8497	346	3	]	]	X
ap-8497	346	4	k.	k.	PROPN
ap-8497	346	5	lancaster	lancaster	PROPN
ap-8497	346	6	.	.	PUNCT
ap-8497	347	1	the	the	DET
ap-8497	347	2	theory	theory	NOUN
ap-8497	347	3	of	of	ADP
ap-8497	347	4	qualitative	qualitative	ADJ
ap-8497	347	5	linear	linear	PROPN
ap-8497	347	6	systems	system	NOUN
ap-8497	347	7	.	.	PUNCT
ap-8497	348	1	econometrica	econometrica	PROPN
ap-8497	348	2	:	:	PUNCT
ap-8497	348	3	journal	journal	NOUN
ap-8497	348	4	of	of	ADP
ap-8497	348	5	the	the	DET
ap-8497	348	6	econometric	econometric	ADJ
ap-8497	348	7	society	society	NOUN
ap-8497	348	8	33(2):395–408	33(2):395–408	PROPN
ap-8497	348	9	,	,	PUNCT
ap-8497	348	10	1965	1965	NUM
ap-8497	348	11	.	.	PUNCT
ap-8497	349	1	https://doi.org/10.2307/1909797	https://doi.org/10.2307/1909797	X
ap-8497	350	1	[	[	X
ap-8497	350	2	8	8	X
ap-8497	350	3	]	]	X
ap-8497	350	4	g.	g.	PROPN
ap-8497	350	5	lunghini	lunghini	PROPN
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ap-8497	351	7	.	.	PUNCT
ap-8497	352	1	quality	quality	NOUN
ap-8497	352	2	and	and	CCONJ
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ap-8497	352	5	,	,	PUNCT
ap-8497	352	6	1970	1970	NUM
ap-8497	352	7	.	.	PUNCT
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ap-8497	354	2	9	9	NUM
ap-8497	354	3	]	]	PUNCT
ap-8497	354	4	c.	c.	NOUN
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ap-8497	354	6	,	,	PUNCT
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ap-8497	354	9	,	,	PUNCT
ap-8497	354	10	p.	p.	PROPN
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ap-8497	354	14	.	.	PUNCT
ap-8497	355	1	qualitative	qualitative	ADJ
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ap-8497	355	6	.	.	PUNCT
ap-8497	356	1	linear	linear	ADJ
ap-8497	356	2	algebra	algebra	NOUN
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ap-8497	356	6	87:1–48	87:1–48	NUM
ap-8497	356	7	,	,	PUNCT
ap-8497	356	8	1987	1987	NUM
ap-8497	356	9	.	.	PUNCT
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ap-8497	357	19	m.	m.	PROPN
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ap-8497	358	2	10	10	NUM
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ap-8497	358	8	pascual	pascual	PROPN
ap-8497	358	9	.	.	PUNCT
ap-8497	359	1	network	network	NOUN
ap-8497	359	2	structure	structure	NOUN
ap-8497	359	3	,	,	PUNCT
ap-8497	359	4	predator	predator	NOUN
ap-8497	359	5	–	–	PUNCT
ap-8497	359	6	prey	prey	NOUN
ap-8497	359	7	modules	module	NOUN
ap-8497	359	8	,	,	PUNCT
ap-8497	359	9	and	and	CCONJ
ap-8497	359	10	stability	stability	NOUN
ap-8497	359	11	in	in	ADP
ap-8497	359	12	large	large	ADJ
ap-8497	359	13	food	food	NOUN
ap-8497	359	14	webs	webs	NOUN
ap-8497	359	15	.	.	PUNCT
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ap-8497	360	2	ecology	ecology	NOUN
ap-8497	360	3	1:55–64	1:55–64	PROPN
ap-8497	360	4	,	,	PUNCT
ap-8497	360	5	2008	2008	NUM
ap-8497	360	6	.	.	PUNCT
ap-8497	361	1	https://doi.org/10.1007/s12080-007-0007-8	https://doi.org/10.1007/s12080-007-0007-8	NUM
ap-8497	362	1	[	[	X
ap-8497	362	2	11	11	NUM
ap-8497	362	3	]	]	PUNCT
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ap-8497	362	5	k.	k.	PROPN
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ap-8497	362	7	,	,	PUNCT
ap-8497	362	8	n.	n.	PROPN
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ap-8497	362	10	.	.	PUNCT
ap-8497	363	1	sign	sign	NOUN
ap-8497	363	2	-	-	PUNCT
ap-8497	363	3	stability	stability	NOUN
ap-8497	363	4	concept	concept	NOUN
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ap-8497	363	6	ecology	ecology	NOUN
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ap-8497	363	9	design	design	NOUN
ap-8497	363	10	with	with	ADP
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ap-8497	363	12	applications	application	NOUN
ap-8497	363	13	.	.	PUNCT
ap-8497	364	1	journal	journal	NOUN
ap-8497	364	2	of	of	ADP
ap-8497	364	3	guidance	guidance	NOUN
ap-8497	364	4	,	,	PUNCT
ap-8497	364	5	control	control	NOUN
ap-8497	364	6	,	,	PUNCT
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ap-8497	364	10	,	,	PUNCT
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ap-8497	364	12	.	.	PUNCT
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ap-8497	366	2	12	12	NUM
ap-8497	366	3	]	]	X
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ap-8497	366	6	,	,	PUNCT
ap-8497	366	7	r.	r.	PROPN
ap-8497	366	8	k.	k.	PROPN
ap-8497	366	9	yedavalli	yedavalli	PROPN
ap-8497	366	10	.	.	PUNCT
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ap-8497	367	8	its	its	PRON
ap-8497	367	9	application	application	NOUN
ap-8497	367	10	in	in	ADP
ap-8497	367	11	control	control	NOUN
ap-8497	367	12	design	design	NOUN
ap-8497	367	13	.	.	PUNCT
ap-8497	368	1	in	in	ADP
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ap-8497	368	9	,	,	PUNCT
ap-8497	368	10	pp	pp	ADP
ap-8497	368	11	.	.	PUNCT
ap-8497	369	1	5062–5067	5062–5067	NUM
ap-8497	369	2	.	.	PUNCT
ap-8497	370	1	2010	2010	NUM
ap-8497	370	2	.	.	PUNCT
ap-8497	371	1	https://doi.org/10.1109/acc.2010.5530716	https://doi.org/10.1109/acc.2010.5530716	NOUN
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ap-8497	371	4	]	]	PUNCT
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ap-8497	371	7	,	,	PUNCT
ap-8497	371	8	d.	d.	PROPN
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ap-8497	371	10	,	,	PUNCT
ap-8497	371	11	c.	c.	PROPN
ap-8497	371	12	vargas	vargas	PROPN
ap-8497	371	13	-	-	PUNCT
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ap-8497	371	15	-	-	NOUN
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ap-8497	371	17	.	.	PUNCT
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ap-8497	372	2	analysis	analysis	NOUN
ap-8497	372	3	and	and	CCONJ
ap-8497	372	4	optimal	optimal	ADJ
ap-8497	372	5	control	control	NOUN
ap-8497	372	6	of	of	ADP
ap-8497	372	7	an	an	DET
ap-8497	372	8	epidemic	epidemic	NOUN
ap-8497	372	9	model	model	NOUN
ap-8497	372	10	with	with	ADP
ap-8497	372	11	vaccination	vaccination	NOUN
ap-8497	372	12	and	and	CCONJ
ap-8497	372	13	treatment	treatment	NOUN
ap-8497	372	14	.	.	PUNCT
ap-8497	373	1	mathematics	mathematic	NOUN
ap-8497	373	2	and	and	CCONJ
ap-8497	373	3	computers	computer	NOUN
ap-8497	373	4	in	in	ADP
ap-8497	373	5	simulation	simulation	NOUN
ap-8497	373	6	100:88–102	100:88–102	NUM
ap-8497	373	7	,	,	PUNCT
ap-8497	373	8	2014	2014	NUM
ap-8497	373	9	.	.	PUNCT
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ap-8497	375	2	14	14	NUM
ap-8497	375	3	]	]	X
ap-8497	375	4	e.	e.	PROPN
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ap-8497	375	6	,	,	PUNCT
ap-8497	375	7	a.	a.	PROPN
ap-8497	375	8	bhaya	bhaya	NOUN
ap-8497	375	9	.	.	PUNCT
ap-8497	376	1	matrix	matrix	NOUN
ap-8497	376	2	diagonal	diagonal	ADJ
ap-8497	376	3	and	and	CCONJ
ap-8497	376	4	d	d	NOUN
ap-8497	376	5	-	-	NOUN
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ap-8497	376	7	.	.	PUNCT
ap-8497	377	1	in	in	ADP
ap-8497	377	2	matrix	matrix	NOUN
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ap-8497	377	4	stability	stability	NOUN
ap-8497	377	5	in	in	ADP
ap-8497	377	6	systems	system	NOUN
ap-8497	377	7	and	and	CCONJ
ap-8497	377	8	computation	computation	NOUN
ap-8497	377	9	,	,	PUNCT
ap-8497	377	10	pp	pp	ADJ
ap-8497	377	11	.	.	PUNCT
ap-8497	378	1	25–89	25–89	NUM
ap-8497	378	2	.	.	X
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ap-8497	378	4	.	.	PUNCT
ap-8497	379	1	https://doi.org/10.1007/978-1-4612-1346-8_2	https://doi.org/10.1007/978-1-4612-1346-8_2	PROPN
ap-8497	380	1	[	[	X
ap-8497	380	2	15	15	NUM
ap-8497	380	3	]	]	X
ap-8497	380	4	e.	e.	PROPN
ap-8497	380	5	kaszkurewicz	kaszkurewicz	PROPN
ap-8497	380	6	,	,	PUNCT
ap-8497	380	7	a.	a.	PROPN
ap-8497	380	8	bhaya	bhaya	NOUN
ap-8497	380	9	.	.	PUNCT
ap-8497	381	1	qualitative	qualitative	ADJ
ap-8497	381	2	stability	stability	NOUN
ap-8497	381	3	of	of	ADP
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ap-8497	381	5	-	-	PUNCT
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ap-8497	381	7	systems	system	NOUN
ap-8497	381	8	.	.	PUNCT
ap-8497	382	1	linear	linear	ADJ
ap-8497	382	2	algebra	algebra	NOUN
ap-8497	382	3	and	and	CCONJ
ap-8497	382	4	its	its	PRON
ap-8497	382	5	applications	application	NOUN
ap-8497	382	6	117:65–71	117:65–71	NUM
ap-8497	382	7	,	,	PUNCT
ap-8497	382	8	1989	1989	NUM
ap-8497	382	9	.	.	PUNCT
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ap-8497	384	8	n.	n.	PROPN
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ap-8497	384	10	.	.	PUNCT
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ap-8497	385	2	sign	sign	NOUN
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ap-8497	385	7	space	space	NOUN
ap-8497	385	8	systems	system	NOUN
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ap-8497	385	12	.	.	PUNCT
ap-8497	386	1	in	in	ADP
ap-8497	386	2	proceedings	proceeding	NOUN
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ap-8497	386	8	,	,	PUNCT
ap-8497	386	9	pp	pp	X
ap-8497	386	10	.	.	PUNCT
ap-8497	386	11	85–90	85–90	NUM
ap-8497	386	12	.	.	PUNCT
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ap-8497	386	14	.	.	PUNCT
ap-8497	387	1	[	[	X
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ap-8497	388	5	condition	condition	NOUN
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ap-8497	388	9	stability	stability	NOUN
ap-8497	388	10	of	of	ADP
ap-8497	388	11	a	a	DET
ap-8497	388	12	matrix	matrix	NOUN
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ap-8497	388	16	principles	principle	NOUN
ap-8497	388	17	.	.	PUNCT
ap-8497	389	1	in	in	ADP
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ap-8497	389	8	,	,	PUNCT
ap-8497	389	9	pp	pp	X
ap-8497	389	10	.	.	PUNCT
ap-8497	390	1	500–505	500–505	NUM
ap-8497	390	2	.	.	NOUN
ap-8497	390	3	2015	2015	NUM
ap-8497	390	4	.	.	PUNCT
ap-8497	391	1	[	[	X
ap-8497	391	2	18	18	NUM
ap-8497	391	3	]	]	PUNCT
ap-8497	391	4	r.	r.	PROPN
ap-8497	391	5	k.	k.	PROPN
ap-8497	391	6	yedavalli	yedavalli	PROPN
ap-8497	391	7	.	.	PUNCT
ap-8497	392	1	a	a	DET
ap-8497	392	2	new	new	ADJ
ap-8497	392	3	,	,	PUNCT
ap-8497	392	4	necessary	necessary	ADJ
ap-8497	392	5	and	and	CCONJ
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ap-8497	392	12	a	a	DET
ap-8497	392	13	real	real	ADJ
ap-8497	392	14	matrix	matrix	NOUN
ap-8497	392	15	without	without	ADP
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ap-8497	392	17	polynomial	polynomial	NOUN
ap-8497	392	18	,	,	PUNCT
ap-8497	392	19	using	use	VERB
ap-8497	392	20	qualitative	qualitative	ADJ
ap-8497	392	21	reasoning	reasoning	NOUN
ap-8497	392	22	.	.	PUNCT
ap-8497	393	1	in	in	ADP
ap-8497	393	2	2018	2018	NUM
ap-8497	393	3	annual	annual	ADJ
ap-8497	393	4	american	american	PROPN
ap-8497	393	5	control	control	PROPN
ap-8497	393	6	conference	conference	PROPN
ap-8497	393	7	(	(	PUNCT
ap-8497	393	8	acc	acc	PROPN
ap-8497	393	9	)	)	PUNCT
ap-8497	393	10	,	,	PUNCT
ap-8497	393	11	pp	pp	ADP
ap-8497	393	12	.	.	PUNCT
ap-8497	394	1	2851–2856	2851–2856	NUM
ap-8497	394	2	.	.	NOUN
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ap-8497	394	4	.	.	PUNCT
ap-8497	395	1	https://doi.org/10.23919/acc.2018.8431691	https://doi.org/10.23919/acc.2018.8431691	PROPN
ap-8497	396	1	[	[	X
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ap-8497	396	4	s.	s.	PROPN
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ap-8497	396	7	p.	p.	PROPN
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ap-8497	396	9	.	.	PUNCT
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ap-8497	397	2	asymptotic	asymptotic	ADJ
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ap-8497	397	4	criteria	criterion	NOUN
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ap-8497	397	6	time	time	NOUN
ap-8497	397	7	-	-	PUNCT
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ap-8497	397	10	systems	system	NOUN
ap-8497	397	11	with	with	ADP
ap-8497	397	12	applications	application	NOUN
ap-8497	397	13	in	in	ADP
ap-8497	397	14	control	control	NOUN
ap-8497	397	15	models	model	NOUN
ap-8497	397	16	.	.	PUNCT
ap-8497	398	1	results	result	NOUN
ap-8497	398	2	in	in	ADP
ap-8497	398	3	control	control	NOUN
ap-8497	398	4	and	and	CCONJ
ap-8497	398	5	optimization	optimization	NOUN
ap-8497	398	6	3:100014	3:100014	NUM
ap-8497	398	7	,	,	PUNCT
ap-8497	398	8	2021	2021	NUM
ap-8497	398	9	.	.	PUNCT
ap-8497	399	1	https://doi.org/10.1016/j.rico.2021.100014	https://doi.org/10.1016/j.rico.2021.100014	PROPN
ap-8497	400	1	[	[	X
ap-8497	400	2	20	20	NUM
ap-8497	400	3	]	]	X
ap-8497	400	4	d.	d.	PROPN
ap-8497	400	5	grundy	grundy	PROPN
ap-8497	400	6	,	,	PUNCT
ap-8497	400	7	d.	d.	PROPN
ap-8497	400	8	olesky	olesky	PROPN
ap-8497	400	9	,	,	PUNCT
ap-8497	400	10	p.	p.	PROPN
ap-8497	400	11	van	van	PROPN
ap-8497	400	12	den	den	PROPN
ap-8497	400	13	driessche	driessche	PROPN
ap-8497	400	14	.	.	PUNCT
ap-8497	401	1	constructions	construction	NOUN
ap-8497	401	2	for	for	ADP
ap-8497	401	3	potentially	potentially	ADV
ap-8497	401	4	stable	stable	ADJ
ap-8497	401	5	sign	sign	NOUN
ap-8497	401	6	patterns	pattern	NOUN
ap-8497	401	7	.	.	PUNCT
ap-8497	402	1	linear	linear	ADJ
ap-8497	402	2	algebra	algebra	NOUN
ap-8497	402	3	and	and	CCONJ
ap-8497	402	4	its	its	PRON
ap-8497	402	5	applications	application	NOUN
ap-8497	402	6	436(12):4473–4488	436(12):4473–4488	NUM
ap-8497	402	7	,	,	PUNCT
ap-8497	402	8	2012	2012	NUM
ap-8497	402	9	.	.	PUNCT
ap-8497	403	1	https://doi.org/10.1016/j.laa.2011.08.011	https://doi.org/10.1016/j.laa.2011.08.011	PROPN
ap-8497	404	1	[	[	X
ap-8497	404	2	21	21	NUM
ap-8497	404	3	]	]	PUNCT
ap-8497	404	4	a.	a.	NOUN
ap-8497	404	5	berliner	berliner	PROPN
ap-8497	404	6	,	,	PUNCT
ap-8497	404	7	d.	d.	PROPN
ap-8497	404	8	d.	d.	PROPN
ap-8497	404	9	olesky	olesky	PROPN
ap-8497	404	10	,	,	PUNCT
ap-8497	404	11	p.	p.	PROPN
ap-8497	404	12	van	van	PROPN
ap-8497	404	13	den	den	PROPN
ap-8497	404	14	driessche	driessche	PROPN
ap-8497	404	15	.	.	PUNCT
ap-8497	405	1	relations	relation	NOUN
ap-8497	405	2	between	between	ADP
ap-8497	405	3	classes	class	NOUN
ap-8497	405	4	of	of	ADP
ap-8497	405	5	potentially	potentially	ADV
ap-8497	405	6	stable	stable	ADJ
ap-8497	405	7	sign	sign	NOUN
ap-8497	405	8	patterns	pattern	NOUN
ap-8497	405	9	.	.	PUNCT
ap-8497	406	1	the	the	DET
ap-8497	406	2	electronic	electronic	ADJ
ap-8497	406	3	journal	journal	NOUN
ap-8497	406	4	of	of	ADP
ap-8497	406	5	linear	linear	PROPN
ap-8497	406	6	algebra	algebra	PROPN
ap-8497	406	7	36:561–569	36:561–569	PROPN
ap-8497	406	8	,	,	PUNCT
ap-8497	406	9	2020	2020	NUM
ap-8497	406	10	.	.	PUNCT
ap-8497	407	1	https://doi.org/10.13001/ela.2020.4929	https://doi.org/10.13001/ela.2020.4929	NOUN
ap-8497	407	2	[	[	X
ap-8497	407	3	22	22	NUM
ap-8497	407	4	]	]	X
ap-8497	407	5	s.	s.	PROPN
ap-8497	407	6	allesina	allesina	PROPN
ap-8497	407	7	,	,	PUNCT
ap-8497	407	8	s.	s.	PROPN
ap-8497	407	9	tang	tang	PROPN
ap-8497	407	10	.	.	PUNCT
ap-8497	408	1	stability	stability	NOUN
ap-8497	408	2	criteria	criterion	NOUN
ap-8497	408	3	for	for	ADP
ap-8497	408	4	complex	complex	ADJ
ap-8497	408	5	ecosystems	ecosystem	NOUN
ap-8497	408	6	.	.	PUNCT
ap-8497	409	1	nature	nature	NOUN
ap-8497	409	2	483(7388):205–208	483(7388):205–208	NUM
ap-8497	409	3	,	,	PUNCT
ap-8497	409	4	2012	2012	NUM
ap-8497	409	5	.	.	PUNCT
ap-8497	410	1	https://doi.org/10.1038/nature10832	https://doi.org/10.1038/nature10832	PROPN
ap-8497	410	2	178	178	NUM
ap-8497	410	3	https://doi.org/10.1007/s12080-007-0007-8	https://doi.org/10.1007/s12080-007-0007-8	NUM
ap-8497	410	4	https://doi.org/10.2514/1.46196	https://doi.org/10.2514/1.46196	PROPN
ap-8497	410	5	https://doi.org/10.1109/acc.2010.5530716	https://doi.org/10.1109/acc.2010.5530716	NOUN
ap-8497	410	6	https://doi.org/10.1016/j.matcom.2013.11.005	https://doi.org/10.1016/j.matcom.2013.11.005	VERB
ap-8497	410	7	https://doi.org/10.1007/978-1-4612-1346-8_2	https://doi.org/10.1007/978-1-4612-1346-8_2	PROPN
ap-8497	411	1	https://doi.org/10.1016/0024-3795(89)90547-8	https://doi.org/10.1016/0024-3795(89)90547-8	ADJ
ap-8497	411	2	https://doi.org/10.23919/acc.2018.8431691	https://doi.org/10.23919/acc.2018.8431691	ADJ
ap-8497	411	3	https://doi.org/10.1016/j.rico.2021.100014	https://doi.org/10.1016/j.rico.2021.100014	PROPN
ap-8497	411	4	https://doi.org/10.1016/j.laa.2011.08.011	https://doi.org/10.1016/j.laa.2011.08.011	PROPN
ap-8497	411	5	https://doi.org/10.13001/ela.2020.4929	https://doi.org/10.13001/ela.2020.4929	NOUN
ap-8497	411	6	https://doi.org/10.1038/nature10832	https://doi.org/10.1038/nature10832	PROPN
ap-8497	411	7	acta	acta	PROPN
ap-8497	411	8	polytechnica	polytechnica	PROPN
ap-8497	411	9	63(3):171–178	63(3):171–178	PROPN
ap-8497	411	10	,	,	PUNCT
ap-8497	411	11	2023	2023	NUM
ap-8497	411	12	1	1	NUM
ap-8497	411	13	introduction	introduction	NOUN
ap-8497	411	14	2	2	NUM
ap-8497	411	15	qualitative	qualitative	NOUN
ap-8497	411	16	sign	sign	NOUN
ap-8497	411	17	matrix	matrix	NOUN
ap-8497	411	18	pair	pair	NOUN
ap-8497	411	19	indices	indice	VERB
ap-8497	411	20	2.1	2.1	NUM
ap-8497	411	21	diagonal	diagonal	ADJ
ap-8497	411	22	elements	element	NOUN
ap-8497	411	23	eii	eii	PROPN
ap-8497	411	24	and	and	CCONJ
ap-8497	411	25	aii	aii	PROPN
ap-8497	411	26	2.2	2.2	NUM
ap-8497	411	27	interactions	interaction	NOUN
ap-8497	411	28	of	of	ADP
ap-8497	411	29	the	the	DET
ap-8497	411	30	form	form	NOUN
ap-8497	411	31	eijeji	eijeji	NOUN
ap-8497	411	32	and	and	CCONJ
ap-8497	411	33	aijaji	aijaji	VERB
ap-8497	411	34	2.3	2.3	NUM
ap-8497	411	35	interactions	interaction	NOUN
ap-8497	411	36	of	of	ADP
ap-8497	411	37	the	the	DET
ap-8497	411	38	form	form	NOUN
ap-8497	411	39	eijaji	eijaji	NOUN
ap-8497	411	40	3	3	NUM
ap-8497	411	41	conditions	condition	NOUN
ap-8497	411	42	for	for	ADP
ap-8497	411	43	qualitative	qualitative	ADJ
ap-8497	411	44	sign	sign	NOUN
ap-8497	411	45	stability	stability	NOUN
ap-8497	411	46	and	and	CCONJ
ap-8497	411	47	instability	instability	NOUN
ap-8497	411	48	3.1	3.1	NUM
ap-8497	411	49	necessary	necessary	ADJ
ap-8497	411	50	conditions	condition	NOUN
ap-8497	411	51	for	for	ADP
ap-8497	411	52	qualitative	qualitative	ADJ
ap-8497	411	53	stability	stability	NOUN
ap-8497	411	54	of	of	ADP
ap-8497	411	55	matrix	matrix	NOUN
ap-8497	411	56	pair	pair	NOUN
ap-8497	411	57	3.2	3.2	NUM
ap-8497	411	58	a	a	DET
ap-8497	411	59	necessary	necessary	ADJ
ap-8497	411	60	condition	condition	NOUN
ap-8497	411	61	for	for	ADP
ap-8497	411	62	instability	instability	NOUN
ap-8497	411	63	of	of	ADP
ap-8497	411	64	a	a	DET
ap-8497	411	65	matrix	matrix	NOUN
ap-8497	411	66	3.3	3.3	NUM
ap-8497	411	67	a	a	DET
ap-8497	411	68	necessary	necessary	ADJ
ap-8497	411	69	condition	condition	NOUN
ap-8497	411	70	for	for	ADP
ap-8497	411	71	a	a	DET
ap-8497	411	72	matrix	matrix	NOUN
ap-8497	411	73	pair	pair	NOUN
ap-8497	411	74	to	to	PART
ap-8497	411	75	be	be	AUX
ap-8497	411	76	qlsu	qlsu	NOUN
ap-8497	411	77	3.4	3.4	NUM
ap-8497	411	78	sufficiency	sufficiency	NOUN
ap-8497	411	79	guidelines	guideline	NOUN
ap-8497	411	80	for	for	ADP
ap-8497	411	81	qlsu	qlsu	NOUN
ap-8497	411	82	matrix	matrix	NOUN
ap-8497	411	83	pair	pair	NOUN
ap-8497	411	84	4	4	NUM
ap-8497	411	85	illustrative	illustrative	ADJ
ap-8497	411	86	examples	example	NOUN
ap-8497	411	87	for	for	ADP
ap-8497	411	88	instability	instability	NOUN
ap-8497	411	89	of	of	ADP
ap-8497	411	90	a	a	DET
ap-8497	411	91	matrix	matrix	NOUN
ap-8497	411	92	pair	pair	NOUN
ap-8497	411	93	5	5	NUM
ap-8497	411	94	conclusion	conclusion	NOUN
ap-8497	411	95	acknowledgements	acknowledgement	NOUN
ap-8497	411	96	references	reference	NOUN