id	sid	tid	token	lemma	pos
ejpam-3712	1	1	european	european	PROPN
ejpam-3712	1	2	journal	journal	PROPN
ejpam-3712	1	3	of	of	ADP
ejpam-3712	1	4	pure	pure	ADJ
ejpam-3712	1	5	and	and	CCONJ
ejpam-3712	1	6	applied	apply	VERB
ejpam-3712	1	7	mathematics	mathematic	NOUN
ejpam-3712	1	8	vol	vol	NOUN
ejpam-3712	1	9	.	.	PROPN
ejpam-3712	2	1	13	13	NUM
ejpam-3712	2	2	,	,	PUNCT
ejpam-3712	2	3	no	no	INTJ
ejpam-3712	2	4	.	.	NOUN
ejpam-3712	2	5	5	5	NUM
ejpam-3712	2	6	,	,	PUNCT
ejpam-3712	2	7	2020	2020	NUM
ejpam-3712	2	8	,	,	PUNCT
ejpam-3712	2	9	1149	1149	NUM
ejpam-3712	2	10	-	-	PUNCT
ejpam-3712	2	11	1161	1161	NUM
ejpam-3712	2	12	issn	issn	PROPN
ejpam-3712	2	13	1307	1307	NUM
ejpam-3712	2	14	-	-	SYM
ejpam-3712	2	15	5543	5543	NUM
ejpam-3712	2	16	–	–	PUNCT
ejpam-3712	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3712	2	18	published	publish	VERB
ejpam-3712	2	19	by	by	ADP
ejpam-3712	2	20	new	new	PROPN
ejpam-3712	2	21	york	york	PROPN
ejpam-3712	2	22	business	business	PROPN
ejpam-3712	2	23	global	global	ADJ
ejpam-3712	2	24	special	special	ADJ
ejpam-3712	2	25	issue	issue	NOUN
ejpam-3712	2	26	dedicated	dedicate	VERB
ejpam-3712	2	27	to	to	ADP
ejpam-3712	2	28	professor	professor	NOUN
ejpam-3712	2	29	hari	hari	PROPN
ejpam-3712	2	30	m.	m.	PROPN
ejpam-3712	2	31	srivastava	srivastava	PROPN
ejpam-3712	2	32	on	on	ADP
ejpam-3712	2	33	the	the	DET
ejpam-3712	2	34	occasion	occasion	NOUN
ejpam-3712	2	35	of	of	ADP
ejpam-3712	2	36	his	his	PRON
ejpam-3712	2	37	80th	80th	ADJ
ejpam-3712	2	38	birthday	birthday	NOUN
ejpam-3712	2	39	computing	compute	VERB
ejpam-3712	2	40	discrete	discrete	ADJ
ejpam-3712	2	41	adriatic	adriatic	ADJ
ejpam-3712	2	42	indices	index	NOUN
ejpam-3712	2	43	of	of	ADP
ejpam-3712	2	44	probabilistic	probabilistic	ADJ
ejpam-3712	2	45	neural	neural	ADJ
ejpam-3712	2	46	network	network	NOUN
ejpam-3712	2	47	t.	t.	PROPN
ejpam-3712	2	48	deepika1,∗	deepika1,∗	NOUN
ejpam-3712	2	49	,	,	PUNCT
ejpam-3712	2	50	v.	v.	ADP
ejpam-3712	2	51	lokesha2	lokesha2	PROPN
ejpam-3712	2	52	1	1	NUM
ejpam-3712	2	53	department	department	NOUN
ejpam-3712	2	54	of	of	ADP
ejpam-3712	2	55	mathematics	mathematic	NOUN
ejpam-3712	2	56	,	,	PUNCT
ejpam-3712	2	57	dayananda	dayananda	PROPN
ejpam-3712	2	58	sagar	sagar	PROPN
ejpam-3712	2	59	university	university	PROPN
ejpam-3712	2	60	,	,	PUNCT
ejpam-3712	2	61	bengaluru	bengaluru	PROPN
ejpam-3712	2	62	,	,	PUNCT
ejpam-3712	2	63	karnataka	karnataka	PROPN
ejpam-3712	2	64	,	,	PUNCT
ejpam-3712	2	65	india	india	PROPN
ejpam-3712	2	66	.	.	PROPN
ejpam-3712	2	67	2	2	NUM
ejpam-3712	2	68	department	department	NOUN
ejpam-3712	2	69	of	of	ADP
ejpam-3712	2	70	mathematics	mathematic	NOUN
ejpam-3712	2	71	,	,	PUNCT
ejpam-3712	2	72	vijayanagara	vijayanagara	PROPN
ejpam-3712	2	73	sri	sri	PROPN
ejpam-3712	2	74	krishnadevaraya	krishnadevaraya	PROPN
ejpam-3712	2	75	university	university	PROPN
ejpam-3712	2	76	,	,	PUNCT
ejpam-3712	2	77	ballari	ballari	NOUN
ejpam-3712	2	78	,	,	PUNCT
ejpam-3712	2	79	karnataka	karnataka	PROPN
ejpam-3712	2	80	,	,	PUNCT
ejpam-3712	2	81	india	india	PROPN
ejpam-3712	2	82	.	.	PUNCT
ejpam-3712	2	83	abstract	abstract	PROPN
ejpam-3712	2	84	.	.	PUNCT
ejpam-3712	3	1	a	a	DET
ejpam-3712	3	2	topological	topological	ADJ
ejpam-3712	3	3	index	index	NOUN
ejpam-3712	3	4	is	be	AUX
ejpam-3712	3	5	a	a	DET
ejpam-3712	3	6	numeric	numeric	ADJ
ejpam-3712	3	7	quantity	quantity	NOUN
ejpam-3712	3	8	which	which	PRON
ejpam-3712	3	9	characterizes	characterize	VERB
ejpam-3712	3	10	the	the	DET
ejpam-3712	3	11	whole	whole	ADJ
ejpam-3712	3	12	structure	structure	NOUN
ejpam-3712	3	13	of	of	ADP
ejpam-3712	3	14	a	a	DET
ejpam-3712	3	15	graph	graph	NOUN
ejpam-3712	3	16	.	.	PUNCT
ejpam-3712	4	1	adriatic	adriatic	ADJ
ejpam-3712	4	2	indices	index	NOUN
ejpam-3712	4	3	are	be	AUX
ejpam-3712	4	4	also	also	ADV
ejpam-3712	4	5	part	part	NOUN
ejpam-3712	4	6	of	of	ADP
ejpam-3712	4	7	topological	topological	ADJ
ejpam-3712	4	8	indices	index	NOUN
ejpam-3712	4	9	,	,	PUNCT
ejpam-3712	4	10	mainly	mainly	ADV
ejpam-3712	4	11	it	it	PRON
ejpam-3712	4	12	is	be	AUX
ejpam-3712	4	13	classified	classify	VERB
ejpam-3712	4	14	into	into	ADP
ejpam-3712	4	15	two	two	NUM
ejpam-3712	4	16	namely	namely	ADV
ejpam-3712	4	17	extended	extended	ADJ
ejpam-3712	4	18	variables	variable	NOUN
ejpam-3712	4	19	and	and	CCONJ
ejpam-3712	4	20	discrete	discrete	ADJ
ejpam-3712	4	21	adriatic	adriatic	ADJ
ejpam-3712	4	22	indices	index	NOUN
ejpam-3712	4	23	,	,	PUNCT
ejpam-3712	4	24	especially	especially	ADV
ejpam-3712	4	25	,	,	PUNCT
ejpam-3712	4	26	discrete	discrete	ADJ
ejpam-3712	4	27	adriatic	adriatic	ADJ
ejpam-3712	4	28	indices	index	NOUN
ejpam-3712	4	29	are	be	AUX
ejpam-3712	4	30	analyzed	analyze	VERB
ejpam-3712	4	31	on	on	ADP
ejpam-3712	4	32	the	the	DET
ejpam-3712	4	33	testing	testing	NOUN
ejpam-3712	4	34	sets	set	NOUN
ejpam-3712	4	35	provided	provide	VERB
ejpam-3712	4	36	by	by	ADP
ejpam-3712	4	37	the	the	DET
ejpam-3712	4	38	international	international	PROPN
ejpam-3712	4	39	academy	academy	PROPN
ejpam-3712	4	40	of	of	ADP
ejpam-3712	4	41	mathematical	mathematical	ADJ
ejpam-3712	4	42	chemistry	chemistry	NOUN
ejpam-3712	4	43	(	(	PUNCT
ejpam-3712	4	44	iamc	iamc	NOUN
ejpam-3712	4	45	)	)	PUNCT
ejpam-3712	4	46	and	and	CCONJ
ejpam-3712	4	47	it	it	PRON
ejpam-3712	4	48	has	have	AUX
ejpam-3712	4	49	been	be	AUX
ejpam-3712	4	50	shown	show	VERB
ejpam-3712	4	51	that	that	SCONJ
ejpam-3712	4	52	they	they	PRON
ejpam-3712	4	53	have	have	VERB
ejpam-3712	4	54	good	good	ADJ
ejpam-3712	4	55	presaging	presage	VERB
ejpam-3712	4	56	substances	substance	NOUN
ejpam-3712	4	57	in	in	ADP
ejpam-3712	4	58	many	many	ADJ
ejpam-3712	4	59	compacts	compact	NOUN
ejpam-3712	4	60	.	.	PUNCT
ejpam-3712	5	1	this	this	PRON
ejpam-3712	5	2	contrived	contrive	VERB
ejpam-3712	5	3	attention	attention	NOUN
ejpam-3712	5	4	to	to	PART
ejpam-3712	5	5	compute	compute	VERB
ejpam-3712	5	6	some	some	DET
ejpam-3712	5	7	discrete	discrete	ADJ
ejpam-3712	5	8	adriatic	adriatic	ADJ
ejpam-3712	5	9	indices	index	NOUN
ejpam-3712	5	10	of	of	ADP
ejpam-3712	5	11	probabilistic	probabilistic	ADJ
ejpam-3712	5	12	neural	neural	ADJ
ejpam-3712	5	13	network	network	NOUN
ejpam-3712	5	14	.	.	PUNCT
ejpam-3712	6	1	2020	2020	NUM
ejpam-3712	6	2	mathematics	mathematic	NOUN
ejpam-3712	6	3	subject	subject	NOUN
ejpam-3712	6	4	classifications	classification	NOUN
ejpam-3712	6	5	:	:	PUNCT
ejpam-3712	6	6	05c09,05c30	05c09,05c30	NOUN
ejpam-3712	6	7	key	key	ADJ
ejpam-3712	6	8	words	word	NOUN
ejpam-3712	6	9	and	and	CCONJ
ejpam-3712	6	10	phrases	phrase	NOUN
ejpam-3712	6	11	:	:	PUNCT
ejpam-3712	6	12	topological	topological	ADJ
ejpam-3712	6	13	indices	index	NOUN
ejpam-3712	6	14	,	,	PUNCT
ejpam-3712	6	15	probabilistic	probabilistic	ADJ
ejpam-3712	6	16	neural	neural	ADJ
ejpam-3712	6	17	network	network	NOUN
ejpam-3712	6	18	,	,	PUNCT
ejpam-3712	6	19	degree	degree	NOUN
ejpam-3712	6	20	vertex	vertex	NOUN
ejpam-3712	6	21	.	.	PUNCT
ejpam-3712	7	1	1	1	X
ejpam-3712	7	2	.	.	X
ejpam-3712	7	3	prologue	prologue	NOUN
ejpam-3712	7	4	and	and	CCONJ
ejpam-3712	7	5	provocation	provocation	NOUN
ejpam-3712	7	6	in	in	ADP
ejpam-3712	7	7	this	this	DET
ejpam-3712	7	8	work	work	NOUN
ejpam-3712	7	9	peculiar	peculiar	ADJ
ejpam-3712	7	10	attention	attention	NOUN
ejpam-3712	7	11	is	be	AUX
ejpam-3712	7	12	compensated	compensate	VERB
ejpam-3712	7	13	to	to	ADP
ejpam-3712	7	14	adriatic	adriatic	ADJ
ejpam-3712	7	15	indices	index	NOUN
ejpam-3712	7	16	that	that	PRON
ejpam-3712	7	17	have	have	AUX
ejpam-3712	7	18	been	be	AUX
ejpam-3712	7	19	defined	define	VERB
ejpam-3712	7	20	by	by	ADP
ejpam-3712	7	21	d.	d.	PROPN
ejpam-3712	7	22	vukičević	vukičević	PROPN
ejpam-3712	7	23	and	and	CCONJ
ejpam-3712	7	24	m.	m.	NOUN
ejpam-3712	7	25	gasperov	gasperov	PROPN
ejpam-3712	7	26	.	.	PUNCT
ejpam-3712	8	1	discrete	discrete	ADJ
ejpam-3712	8	2	adriatic	adriatic	ADJ
ejpam-3712	8	3	indices	index	NOUN
ejpam-3712	8	4	are	be	AUX
ejpam-3712	8	5	the	the	DET
ejpam-3712	8	6	family	family	NOUN
ejpam-3712	8	7	of	of	ADP
ejpam-3712	8	8	148	148	NUM
ejpam-3712	8	9	bond	bond	NOUN
ejpam-3712	8	10	-	-	PUNCT
ejpam-3712	8	11	additive	additive	ADJ
ejpam-3712	8	12	topological	topological	ADJ
ejpam-3712	8	13	indices	index	NOUN
ejpam-3712	8	14	defined	define	VERB
ejpam-3712	8	15	as	as	ADP
ejpam-3712	8	16	follows	follow	VERB
ejpam-3712	8	17	.	.	PUNCT
ejpam-3712	9	1	adr(g	adr(g	X
ejpam-3712	9	2	)	)	PUNCT
ejpam-3712	9	3	=	=	SYM
ejpam-3712	9	4	∑	∑	PUNCT
ejpam-3712	9	5	uv∈e(g	uv∈e(g	NUM
ejpam-3712	9	6	)	)	PUNCT
ejpam-3712	9	7	γj(ϕi	γj(ϕi	PROPN
ejpam-3712	9	8	,	,	PUNCT
ejpam-3712	9	9	a(tu	a(tu	PROPN
ejpam-3712	9	10	)	)	PUNCT
ejpam-3712	9	11	,	,	PUNCT
ejpam-3712	9	12	ϕi	ϕi	ADP
ejpam-3712	9	13	,	,	PUNCT
ejpam-3712	9	14	a(tv	a(tv	NOUN
ejpam-3712	9	15	)	)	PUNCT
ejpam-3712	9	16	)	)	PUNCT
ejpam-3712	9	17	where	where	SCONJ
ejpam-3712	9	18	the	the	DET
ejpam-3712	9	19	variables	variable	NOUN
ejpam-3712	9	20	and	and	CCONJ
ejpam-3712	9	21	functions	function	NOUN
ejpam-3712	9	22	can	can	AUX
ejpam-3712	9	23	take	take	VERB
ejpam-3712	9	24	the	the	DET
ejpam-3712	9	25	following	follow	VERB
ejpam-3712	9	26	values	value	NOUN
ejpam-3712	9	27	:	:	PUNCT
ejpam-3712	9	28	∗corresponding	∗corresponde	VERB
ejpam-3712	9	29	author	author	NOUN
ejpam-3712	9	30	.	.	PUNCT
ejpam-3712	10	1	doi	doi	NOUN
ejpam-3712	10	2	:	:	PUNCT
ejpam-3712	10	3	https://doi.org/10.29020/nybg.ejpam.v13i5.3712	https://doi.org/10.29020/nybg.ejpam.v13i5.3712	NOUN
ejpam-3712	10	4	email	email	NOUN
ejpam-3712	10	5	addresses	address	NOUN
ejpam-3712	10	6	:	:	PUNCT
ejpam-3712	10	7	v.lokesha@gmail.com	v.lokesha@gmail.com	X
ejpam-3712	10	8	(	(	PUNCT
ejpam-3712	10	9	v.	v.	ADP
ejpam-3712	10	10	lokesha	lokesha	PROPN
ejpam-3712	10	11	)	)	PUNCT
ejpam-3712	10	12	,	,	PUNCT
ejpam-3712	10	13	sastry.deepi@gmail.com	sastry.deepi@gmail.com	X
ejpam-3712	10	14	(	(	PUNCT
ejpam-3712	10	15	t.	t.	PROPN
ejpam-3712	10	16	deepika	deepika	PROPN
ejpam-3712	10	17	)	)	PUNCT
ejpam-3712	10	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-3712	10	19	1149	1149	NUM
ejpam-3712	11	1	c	c	NOUN
ejpam-3712	11	2	©	©	NOUN
ejpam-3712	11	3	2020	2020	NUM
ejpam-3712	11	4	ejpam	ejpam	VERB
ejpam-3712	11	5	all	all	DET
ejpam-3712	11	6	rights	right	NOUN
ejpam-3712	11	7	reserved	reserve	VERB
ejpam-3712	11	8	.	.	PUNCT
ejpam-3712	12	1	t.	t.	PROPN
ejpam-3712	12	2	deepika	deepika	PROPN
ejpam-3712	12	3	,	,	PUNCT
ejpam-3712	12	4	v.	v.	ADP
ejpam-3712	12	5	lokesha	lokesha	PROPN
ejpam-3712	12	6	/	/	SYM
ejpam-3712	12	7	eur	eur	PROPN
ejpam-3712	12	8	.	.	PUNCT
ejpam-3712	13	1	j.	j.	PROPN
ejpam-3712	13	2	pure	pure	PROPN
ejpam-3712	13	3	appl	appl	PROPN
ejpam-3712	13	4	.	.	PROPN
ejpam-3712	13	5	math	math	PROPN
ejpam-3712	13	6	,	,	PUNCT
ejpam-3712	13	7	13	13	NUM
ejpam-3712	13	8	(	(	PUNCT
ejpam-3712	13	9	5	5	NUM
ejpam-3712	13	10	)	)	PUNCT
ejpam-3712	13	11	(	(	PUNCT
ejpam-3712	13	12	2020	2020	NUM
ejpam-3712	13	13	)	)	PUNCT
ejpam-3712	13	14	,	,	PUNCT
ejpam-3712	13	15	1149	1149	NUM
ejpam-3712	13	16	-	-	SYM
ejpam-3712	13	17	1161	1161	NUM
ejpam-3712	13	18	1150	1150	NUM
ejpam-3712	13	19	tu	tu	PROPN
ejpam-3712	13	20	∈	∈	PROPN
ejpam-3712	13	21	{	{	PUNCT
ejpam-3712	13	22	du	du	PROPN
ejpam-3712	13	23	,	,	PUNCT
ejpam-3712	13	24	du	du	NOUN
ejpam-3712	13	25	}	}	PUNCT
ejpam-3712	13	26	i	i	PRON
ejpam-3712	13	27	∈	∈	PROPN
ejpam-3712	13	28	{	{	PUNCT
ejpam-3712	13	29	1	1	NUM
ejpam-3712	13	30	,	,	PUNCT
ejpam-3712	13	31	2	2	NUM
ejpam-3712	13	32	,	,	PUNCT
ejpam-3712	13	33	3	3	NUM
ejpam-3712	13	34	}	}	PUNCT
ejpam-3712	13	35	j	j	PROPN
ejpam-3712	13	36	∈	∈	PROPN
ejpam-3712	13	37	{	{	PUNCT
ejpam-3712	13	38	1	1	NUM
ejpam-3712	13	39	,	,	PUNCT
ejpam-3712	13	40	2	2	NUM
ejpam-3712	13	41	,	,	PUNCT
ejpam-3712	13	42	.....	.....	PUNCT
ejpam-3712	13	43	,	,	PUNCT
ejpam-3712	13	44	8	8	X
ejpam-3712	13	45	}	}	PUNCT
ejpam-3712	13	46	a	a	PRON
ejpam-3712	13	47	=	=	X
ejpam-3712	13	48			NOUN
ejpam-3712	13	49	(	(	PUNCT
ejpam-3712	13	50	−1,−1	−1,−1	ADV
ejpam-3712	13	51	2	2	NUM
ejpam-3712	13	52	,	,	PUNCT
ejpam-3712	13	53	1	1	NUM
ejpam-3712	13	54	2	2	NUM
ejpam-3712	13	55	,	,	PUNCT
ejpam-3712	13	56	1	1	NUM
ejpam-3712	13	57	,	,	PUNCT
ejpam-3712	13	58	2	2	NUM
ejpam-3712	13	59	)	)	PUNCT
ejpam-3712	13	60	if	if	SCONJ
ejpam-3712	13	61	i	i	PRON
ejpam-3712	13	62	=	=	SYM
ejpam-3712	13	63	2	2	NUM
ejpam-3712	13	64	and	and	CCONJ
ejpam-3712	13	65	j	j	PROPN
ejpam-3712	13	66	∈	∈	PROPN
ejpam-3712	13	67	(	(	PUNCT
ejpam-3712	13	68	1	1	NUM
ejpam-3712	13	69	,	,	PUNCT
ejpam-3712	13	70	2	2	NUM
ejpam-3712	13	71	,	,	PUNCT
ejpam-3712	13	72	...	...	PUNCT
ejpam-3712	13	73	5	5	X
ejpam-3712	13	74	)	)	PUNCT
ejpam-3712	13	75	(	(	PUNCT
ejpam-3712	13	76	1	1	NUM
ejpam-3712	13	77	2	2	NUM
ejpam-3712	13	78	,	,	PUNCT
ejpam-3712	13	79	1	1	NUM
ejpam-3712	13	80	,	,	PUNCT
ejpam-3712	13	81	2	2	NUM
ejpam-3712	13	82	)	)	PUNCT
ejpam-3712	14	1	otherwise	otherwise	ADV
ejpam-3712	14	2	and	and	CCONJ
ejpam-3712	14	3	i	i	PRON
ejpam-3712	14	4	∈	∈	PROPN
ejpam-3712	14	5	(	(	PUNCT
ejpam-3712	14	6	1	1	NUM
ejpam-3712	14	7	,	,	PUNCT
ejpam-3712	14	8	2	2	NUM
ejpam-3712	14	9	)	)	PUNCT
ejpam-3712	14	10	(	(	PUNCT
ejpam-3712	14	11	12	12	NUM
ejpam-3712	14	12	,	,	PUNCT
ejpam-3712	14	13	2	2	NUM
ejpam-3712	14	14	)	)	PUNCT
ejpam-3712	14	15	if	if	SCONJ
ejpam-3712	14	16	i	i	PRON
ejpam-3712	14	17	=	=	NOUN
ejpam-3712	14	18	3	3	NUM
ejpam-3712	14	19	ϕ1,a(x	ϕ1,a(x	NOUN
ejpam-3712	14	20	)	)	PUNCT
ejpam-3712	14	21	=	=	PUNCT
ejpam-3712	15	1	loga(x)(a	loga(x)(a	NOUN
ejpam-3712	15	2	>	>	X
ejpam-3712	15	3	0	0	NUM
ejpam-3712	15	4	)	)	PUNCT
ejpam-3712	15	5	;	;	PUNCT
ejpam-3712	15	6	ϕ2,a(x	ϕ2,a(x	X
ejpam-3712	15	7	)	)	PUNCT
ejpam-3712	15	8	=	=	PUNCT
ejpam-3712	15	9	xa(a	xa(a	PUNCT
ejpam-3712	15	10	∈	∈	PROPN
ejpam-3712	15	11	r	r	NOUN
ejpam-3712	15	12	\	\	PROPN
ejpam-3712	15	13	0	0	NUM
ejpam-3712	15	14	)	)	PUNCT
ejpam-3712	15	15	;	;	PUNCT
ejpam-3712	15	16	ϕ3,a(x	ϕ3,a(x	X
ejpam-3712	15	17	)	)	PUNCT
ejpam-3712	15	18	=	=	NOUN
ejpam-3712	15	19	ax(a	ax(a	X
ejpam-3712	15	20	>	>	X
ejpam-3712	15	21	0	0	NUM
ejpam-3712	15	22	)	)	PUNCT
ejpam-3712	15	23	;	;	PUNCT
ejpam-3712	15	24	now	now	ADV
ejpam-3712	15	25	,	,	PUNCT
ejpam-3712	15	26	the	the	DET
ejpam-3712	15	27	naming	name	VERB
ejpam-3712	15	28	convention	convention	NOUN
ejpam-3712	15	29	for	for	ADP
ejpam-3712	15	30	the	the	DET
ejpam-3712	15	31	discrete	discrete	ADJ
ejpam-3712	15	32	adriatic	adriatic	ADJ
ejpam-3712	15	33	indices	index	NOUN
ejpam-3712	15	34	is	be	AUX
ejpam-3712	15	35	as	as	SCONJ
ejpam-3712	15	36	follows	follow	VERB
ejpam-3712	15	37	:	:	PUNCT
ejpam-3712	15	38	1	1	X
ejpam-3712	15	39	.	.	X
ejpam-3712	15	40	γ1	γ1	NOUN
ejpam-3712	15	41	corresponds	correspond	VERB
ejpam-3712	15	42	to	to	ADP
ejpam-3712	15	43	randi	randi	PROPN
ejpam-3712	15	44	type	type	PROPN
ejpam-3712	15	45	;	;	PUNCT
ejpam-3712	15	46	γ1(x	γ1(x	PROPN
ejpam-3712	15	47	,	,	PUNCT
ejpam-3712	15	48	y	y	NOUN
ejpam-3712	15	49	)	)	PUNCT
ejpam-3712	16	1	=	=	SYM
ejpam-3712	16	2	x.y	x.y	PROPN
ejpam-3712	16	3	•	•	PROPN
ejpam-3712	16	4	randi	randi	PROPN
ejpam-3712	16	5	type	type	PROPN
ejpam-3712	16	6	lodeg	lodeg	ADJ
ejpam-3712	16	7	index	index	NOUN
ejpam-3712	16	8	:	:	PUNCT
ejpam-3712	16	9	adr(g	adr(g	PROPN
ejpam-3712	16	10	)	)	PUNCT
ejpam-3712	16	11	=	=	SYM
ejpam-3712	16	12	∑	∑	PUNCT
ejpam-3712	16	13	uv∈e(g	uv∈e(g	NUM
ejpam-3712	16	14	)	)	PUNCT
ejpam-3712	16	15	γ1(ϕ1,1(du	γ1(ϕ1,1(du	NUM
ejpam-3712	16	16	)	)	PUNCT
ejpam-3712	16	17	,	,	PUNCT
ejpam-3712	16	18	ϕ1,1(dv	ϕ1,1(dv	NUM
ejpam-3712	16	19	)	)	PUNCT
ejpam-3712	16	20	)	)	PUNCT
ejpam-3712	17	1	•	•	NUM
ejpam-3712	17	2	randi	randi	PROPN
ejpam-3712	17	3	type	type	PROPN
ejpam-3712	17	4	sdi	sdi	PROPN
ejpam-3712	17	5	index	index	NOUN
ejpam-3712	17	6	:	:	PUNCT
ejpam-3712	17	7	adr(g	adr(g	PROPN
ejpam-3712	17	8	)	)	PUNCT
ejpam-3712	17	9	=	=	SYM
ejpam-3712	17	10	∑	∑	PUNCT
ejpam-3712	17	11	uv∈e(g	uv∈e(g	NUM
ejpam-3712	17	12	)	)	PUNCT
ejpam-3712	17	13	γ1(ϕ2,2(du	γ1(ϕ2,2(du	NOUN
ejpam-3712	17	14	)	)	PUNCT
ejpam-3712	17	15	,	,	PUNCT
ejpam-3712	17	16	ϕ2,2(dv	ϕ2,2(dv	NUM
ejpam-3712	17	17	)	)	PUNCT
ejpam-3712	17	18	)	)	PUNCT
ejpam-3712	18	1	•	•	NUM
ejpam-3712	18	2	randi	randi	PROPN
ejpam-3712	18	3	type	type	PROPN
ejpam-3712	18	4	hadi	hadi	PROPN
ejpam-3712	18	5	index	index	PROPN
ejpam-3712	18	6	:	:	PUNCT
ejpam-3712	18	7	adr(g	adr(g	PROPN
ejpam-3712	18	8	)	)	PUNCT
ejpam-3712	18	9	=	=	SYM
ejpam-3712	18	10	∑	∑	PUNCT
ejpam-3712	18	11	uv∈e(g	uv∈e(g	NUM
ejpam-3712	18	12	)	)	PUNCT
ejpam-3712	18	13	γ1(ϕ3,1/2(du	γ1(ϕ3,1/2(du	PROPN
ejpam-3712	18	14	)	)	PUNCT
ejpam-3712	18	15	,	,	PUNCT
ejpam-3712	18	16	ϕ3,1/2(dv	ϕ3,1/2(dv	PROPN
ejpam-3712	18	17	)	)	PUNCT
ejpam-3712	18	18	)	)	PUNCT
ejpam-3712	19	1	2	2	X
ejpam-3712	19	2	.	.	X
ejpam-3712	19	3	γ2	γ2	NOUN
ejpam-3712	19	4	corresponds	correspond	NOUN
ejpam-3712	19	5	to	to	ADP
ejpam-3712	19	6	sum	sum	NOUN
ejpam-3712	19	7	;	;	PUNCT
ejpam-3712	19	8	γ2(x	γ2(x	NUM
ejpam-3712	19	9	,	,	PUNCT
ejpam-3712	19	10	y	y	NOUN
ejpam-3712	19	11	)	)	PUNCT
ejpam-3712	19	12	=	=	SYM
ejpam-3712	20	1	x+	x+	PUNCT
ejpam-3712	20	2	y	y	PROPN
ejpam-3712	20	3	•	•	ADJ
ejpam-3712	20	4	sum	sum	NOUN
ejpam-3712	20	5	lordeg	lordeg	PROPN
ejpam-3712	20	6	index	index	NOUN
ejpam-3712	20	7	:	:	PUNCT
ejpam-3712	20	8	adr(g	adr(g	PROPN
ejpam-3712	20	9	)	)	PUNCT
ejpam-3712	20	10	=	=	SYM
ejpam-3712	20	11	∑	∑	PUNCT
ejpam-3712	20	12	uv∈e(g	uv∈e(g	NUM
ejpam-3712	20	13	)	)	PUNCT
ejpam-3712	20	14	γ2(ϕ1,1/2(du	γ2(ϕ1,1/2(du	PROPN
ejpam-3712	20	15	)	)	PUNCT
ejpam-3712	20	16	,	,	PUNCT
ejpam-3712	20	17	ϕ1,1/2(dv	ϕ1,1/2(dv	NUM
ejpam-3712	20	18	)	)	PUNCT
ejpam-3712	20	19	)	)	PUNCT
ejpam-3712	21	1	3	3	X
ejpam-3712	21	2	.	.	X
ejpam-3712	21	3	γ3	γ3	NOUN
ejpam-3712	21	4	corresponds	correspond	VERB
ejpam-3712	21	5	to	to	ADP
ejpam-3712	21	6	inverse	inverse	NOUN
ejpam-3712	21	7	sum	sum	NOUN
ejpam-3712	21	8	;	;	PUNCT
ejpam-3712	21	9	γ3(x	γ3(x	PROPN
ejpam-3712	21	10	,	,	PUNCT
ejpam-3712	21	11	y	y	PROPN
ejpam-3712	21	12	)	)	PUNCT
ejpam-3712	21	13	=	=	PUNCT
ejpam-3712	22	1			PUNCT
ejpam-3712	22	2	1	1	NUM
ejpam-3712	22	3	x+	x+	ADJ
ejpam-3712	22	4	y	y	PROPN
ejpam-3712	22	5	,	,	PUNCT
ejpam-3712	22	6	if	if	SCONJ
ejpam-3712	22	7	x+	x+	X
ejpam-3712	22	8	y	y	PROPN
ejpam-3712	22	9	6=	6=	ADP
ejpam-3712	22	10	0	0	NUM
ejpam-3712	22	11	0	0	NUM
ejpam-3712	22	12	,	,	PUNCT
ejpam-3712	22	13	otherwise	otherwise	ADV
ejpam-3712	22	14	.	.	PUNCT
ejpam-3712	23	1	•	•	ADJ
ejpam-3712	23	2	inverse	inverse	NOUN
ejpam-3712	23	3	sum	sum	NOUN
ejpam-3712	23	4	lordeg	lordeg	PROPN
ejpam-3712	23	5	index	index	NOUN
ejpam-3712	23	6	:	:	PUNCT
ejpam-3712	23	7	adr(g	adr(g	PROPN
ejpam-3712	23	8	)	)	PUNCT
ejpam-3712	23	9	=	=	SYM
ejpam-3712	23	10	∑	∑	PUNCT
ejpam-3712	23	11	uv∈e(g	uv∈e(g	NUM
ejpam-3712	23	12	)	)	PUNCT
ejpam-3712	23	13	γ3(ϕ1,1/2(du	γ3(ϕ1,1/2(du	PROPN
ejpam-3712	23	14	)	)	PUNCT
ejpam-3712	23	15	,	,	PUNCT
ejpam-3712	23	16	ϕ1,1/2(dv	ϕ1,1/2(dv	NUM
ejpam-3712	23	17	)	)	PUNCT
ejpam-3712	23	18	)	)	PUNCT
ejpam-3712	24	1	•	•	NUM
ejpam-3712	24	2	inverse	inverse	NOUN
ejpam-3712	24	3	sum	sum	NOUN
ejpam-3712	24	4	indeg	indeg	PROPN
ejpam-3712	24	5	index	index	NOUN
ejpam-3712	24	6	:	:	PUNCT
ejpam-3712	24	7	adr(g	adr(g	PROPN
ejpam-3712	24	8	)	)	PUNCT
ejpam-3712	24	9	=	=	SYM
ejpam-3712	24	10	∑	∑	PUNCT
ejpam-3712	24	11	uv∈e(g	uv∈e(g	NUM
ejpam-3712	24	12	)	)	PUNCT
ejpam-3712	24	13	γ3(ϕ2,−1(du	γ3(ϕ2,−1(du	NOUN
ejpam-3712	24	14	)	)	PUNCT
ejpam-3712	24	15	,	,	PUNCT
ejpam-3712	24	16	ϕ2,−1(dv	ϕ2,−1(dv	NOUN
ejpam-3712	24	17	)	)	PUNCT
ejpam-3712	24	18	)	)	PUNCT
ejpam-3712	25	1	4	4	X
ejpam-3712	25	2	.	.	X
ejpam-3712	25	3	γ4	γ4	NOUN
ejpam-3712	25	4	corresponds	correspond	NOUN
ejpam-3712	25	5	to	to	ADP
ejpam-3712	25	6	misbalance	misbalance	NOUN
ejpam-3712	25	7	;	;	PUNCT
ejpam-3712	25	8	γ4(x	γ4(x	NUM
ejpam-3712	25	9	,	,	PUNCT
ejpam-3712	25	10	y	y	NOUN
ejpam-3712	25	11	)	)	PUNCT
ejpam-3712	25	12	=|	=|	NOUN
ejpam-3712	26	1	x−	x−	PROPN
ejpam-3712	26	2	y	y	PROPN
ejpam-3712	26	3	|	|	ADV
ejpam-3712	26	4	•	•	NUM
ejpam-3712	26	5	misbalance	misbalance	NOUN
ejpam-3712	26	6	lodeg	lodeg	ADJ
ejpam-3712	26	7	index	index	NOUN
ejpam-3712	26	8	:	:	PUNCT
ejpam-3712	26	9	adr(g	adr(g	PROPN
ejpam-3712	26	10	)	)	PUNCT
ejpam-3712	26	11	=	=	SYM
ejpam-3712	26	12	∑	∑	PUNCT
ejpam-3712	26	13	uv∈e(g	uv∈e(g	NUM
ejpam-3712	26	14	)	)	PUNCT
ejpam-3712	26	15	γ4(ϕ1,1(du	γ4(ϕ1,1(du	NOUN
ejpam-3712	26	16	)	)	PUNCT
ejpam-3712	26	17	,	,	PUNCT
ejpam-3712	26	18	ϕ1,1(dv	ϕ1,1(dv	NUM
ejpam-3712	26	19	)	)	PUNCT
ejpam-3712	26	20	)	)	PUNCT
ejpam-3712	27	1	t.	t.	PROPN
ejpam-3712	27	2	deepika	deepika	PROPN
ejpam-3712	27	3	,	,	PUNCT
ejpam-3712	27	4	v.	v.	ADP
ejpam-3712	27	5	lokesha	lokesha	PROPN
ejpam-3712	27	6	/	/	SYM
ejpam-3712	27	7	eur	eur	PROPN
ejpam-3712	27	8	.	.	PUNCT
ejpam-3712	28	1	j.	j.	PROPN
ejpam-3712	28	2	pure	pure	PROPN
ejpam-3712	28	3	appl	appl	PROPN
ejpam-3712	28	4	.	.	PROPN
ejpam-3712	28	5	math	math	PROPN
ejpam-3712	28	6	,	,	PUNCT
ejpam-3712	28	7	13	13	NUM
ejpam-3712	28	8	(	(	PUNCT
ejpam-3712	28	9	5	5	NUM
ejpam-3712	28	10	)	)	PUNCT
ejpam-3712	28	11	(	(	PUNCT
ejpam-3712	28	12	2020	2020	NUM
ejpam-3712	28	13	)	)	PUNCT
ejpam-3712	28	14	,	,	PUNCT
ejpam-3712	28	15	1149	1149	NUM
ejpam-3712	28	16	-	-	SYM
ejpam-3712	28	17	1161	1161	NUM
ejpam-3712	28	18	1151	1151	NUM
ejpam-3712	28	19	•	•	NOUN
ejpam-3712	28	20	misbalance	misbalance	PROPN
ejpam-3712	28	21	losdeg	losdeg	PROPN
ejpam-3712	28	22	index	index	NOUN
ejpam-3712	28	23	:	:	PUNCT
ejpam-3712	28	24	adr(g	adr(g	PROPN
ejpam-3712	28	25	)	)	PUNCT
ejpam-3712	28	26	=	=	SYM
ejpam-3712	28	27	∑	∑	PUNCT
ejpam-3712	28	28	uv∈e(g	uv∈e(g	NUM
ejpam-3712	28	29	)	)	PUNCT
ejpam-3712	28	30	γ4(ϕ1,2(du	γ4(ϕ1,2(du	PROPN
ejpam-3712	28	31	)	)	PUNCT
ejpam-3712	28	32	,	,	PUNCT
ejpam-3712	28	33	ϕ1,2(dv	ϕ1,2(dv	NUM
ejpam-3712	28	34	)	)	PUNCT
ejpam-3712	28	35	)	)	PUNCT
ejpam-3712	28	36	•	•	NUM
ejpam-3712	28	37	misbalance	misbalance	NOUN
ejpam-3712	28	38	rodeg	rodeg	ADJ
ejpam-3712	28	39	index	index	NOUN
ejpam-3712	28	40	:	:	PUNCT
ejpam-3712	28	41	adr(g	adr(g	PROPN
ejpam-3712	28	42	)	)	PUNCT
ejpam-3712	28	43	=	=	SYM
ejpam-3712	28	44	∑	∑	PUNCT
ejpam-3712	28	45	uv∈e(g	uv∈e(g	NUM
ejpam-3712	28	46	)	)	PUNCT
ejpam-3712	28	47	γ4(ϕ2,1/2(du	γ4(ϕ2,1/2(du	PROPN
ejpam-3712	28	48	)	)	PUNCT
ejpam-3712	28	49	,	,	PUNCT
ejpam-3712	28	50	ϕ2,1/2(dv	ϕ2,1/2(dv	PROPN
ejpam-3712	28	51	)	)	PUNCT
ejpam-3712	28	52	)	)	PUNCT
ejpam-3712	29	1	•	•	NUM
ejpam-3712	29	2	misbalance	misbalance	PROPN
ejpam-3712	29	3	deg	deg	PROPN
ejpam-3712	29	4	index	index	PROPN
ejpam-3712	29	5	:	:	PUNCT
ejpam-3712	29	6	adr(g	adr(g	PROPN
ejpam-3712	29	7	)	)	PUNCT
ejpam-3712	29	8	=	=	SYM
ejpam-3712	29	9	∑	∑	PUNCT
ejpam-3712	29	10	uv∈e(g	uv∈e(g	NUM
ejpam-3712	29	11	)	)	PUNCT
ejpam-3712	29	12	γ4(ϕ2,1(du	γ4(ϕ2,1(du	PROPN
ejpam-3712	29	13	)	)	PUNCT
ejpam-3712	29	14	,	,	PUNCT
ejpam-3712	29	15	ϕ2,1(dv	ϕ2,1(dv	NUM
ejpam-3712	29	16	)	)	PUNCT
ejpam-3712	29	17	)	)	PUNCT
ejpam-3712	29	18	•	•	NUM
ejpam-3712	29	19	misbalance	misbalance	PROPN
ejpam-3712	29	20	hadeg	hadeg	NOUN
ejpam-3712	29	21	index	index	NOUN
ejpam-3712	29	22	:	:	PUNCT
ejpam-3712	29	23	adr(g	adr(g	PROPN
ejpam-3712	29	24	)	)	PUNCT
ejpam-3712	29	25	=	=	SYM
ejpam-3712	29	26	∑	∑	PUNCT
ejpam-3712	29	27	uv∈e(g	uv∈e(g	NUM
ejpam-3712	29	28	)	)	PUNCT
ejpam-3712	29	29	γ4(ϕ3,1/2(du	γ4(ϕ3,1/2(du	NUM
ejpam-3712	29	30	)	)	PUNCT
ejpam-3712	29	31	,	,	PUNCT
ejpam-3712	29	32	ϕ3,1/2(dv	ϕ3,1/2(dv	PROPN
ejpam-3712	29	33	)	)	PUNCT
ejpam-3712	29	34	)	)	PUNCT
ejpam-3712	30	1	5	5	X
ejpam-3712	30	2	.	.	PUNCT
ejpam-3712	31	1	γ5	γ5	NOUN
ejpam-3712	31	2	corresponds	correspond	VERB
ejpam-3712	31	3	to	to	ADP
ejpam-3712	31	4	inverse	inverse	NOUN
ejpam-3712	31	5	misbalance	misbalance	NOUN
ejpam-3712	31	6	;	;	PUNCT
ejpam-3712	31	7	γ5(x	γ5(x	PROPN
ejpam-3712	31	8	,	,	PUNCT
ejpam-3712	31	9	y	y	NOUN
ejpam-3712	31	10	)	)	PUNCT
ejpam-3712	31	11	=	=	PUNCT
ejpam-3712	32	1			PUNCT
ejpam-3712	32	2	1	1	NUM
ejpam-3712	32	3	|	|	ADV
ejpam-3712	33	1	x−	x−	PROPN
ejpam-3712	33	2	y	y	PROPN
ejpam-3712	33	3	|	|	ADV
ejpam-3712	33	4	,	,	PUNCT
ejpam-3712	33	5	if	if	SCONJ
ejpam-3712	33	6	x	x	PROPN
ejpam-3712	33	7	6=	6=	NUM
ejpam-3712	33	8	y	y	PROPN
ejpam-3712	33	9	0	0	NUM
ejpam-3712	33	10	,	,	PUNCT
ejpam-3712	33	11	if	if	SCONJ
ejpam-3712	33	12	x	x	ADP
ejpam-3712	33	13	=	=	SYM
ejpam-3712	33	14	y	y	PROPN
ejpam-3712	33	15	•	•	NUM
ejpam-3712	33	16	misbalance	misbalance	PROPN
ejpam-3712	33	17	indeg	indeg	ADJ
ejpam-3712	33	18	index	index	NOUN
ejpam-3712	33	19	:	:	PUNCT
ejpam-3712	33	20	adr(g	adr(g	PROPN
ejpam-3712	33	21	)	)	PUNCT
ejpam-3712	33	22	=	=	SYM
ejpam-3712	33	23	∑	∑	PUNCT
ejpam-3712	33	24	uv∈e(g	uv∈e(g	NUM
ejpam-3712	33	25	)	)	PUNCT
ejpam-3712	33	26	γ5(ϕ2,−1(du	γ5(ϕ2,−1(du	NOUN
ejpam-3712	33	27	)	)	PUNCT
ejpam-3712	33	28	,	,	PUNCT
ejpam-3712	33	29	ϕ2,−1(dv	ϕ2,−1(dv	NOUN
ejpam-3712	33	30	)	)	PUNCT
ejpam-3712	33	31	)	)	PUNCT
ejpam-3712	33	32	•	•	NUM
ejpam-3712	33	33	misbalance	misbalance	PROPN
ejpam-3712	33	34	irdeg	irdeg	NOUN
ejpam-3712	33	35	index	index	NOUN
ejpam-3712	33	36	:	:	PUNCT
ejpam-3712	33	37	adr(g	adr(g	PROPN
ejpam-3712	33	38	)	)	PUNCT
ejpam-3712	33	39	=	=	SYM
ejpam-3712	33	40	∑	∑	PUNCT
ejpam-3712	33	41	uv∈e(g	uv∈e(g	NUM
ejpam-3712	33	42	)	)	PUNCT
ejpam-3712	33	43	γ5(ϕ2,−1/2(du	γ5(ϕ2,−1/2(du	NOUN
ejpam-3712	33	44	)	)	PUNCT
ejpam-3712	33	45	,	,	PUNCT
ejpam-3712	33	46	ϕ2,−1/2(dv	ϕ2,−1/2(dv	PROPN
ejpam-3712	33	47	)	)	PUNCT
ejpam-3712	33	48	)	)	PUNCT
ejpam-3712	34	1	•	•	NUM
ejpam-3712	34	2	misbalance	misbalance	PROPN
ejpam-3712	34	3	indi	indi	PROPN
ejpam-3712	34	4	index	index	NOUN
ejpam-3712	34	5	:	:	PUNCT
ejpam-3712	34	6	adr(g	adr(g	PROPN
ejpam-3712	34	7	)	)	PUNCT
ejpam-3712	34	8	=	=	SYM
ejpam-3712	34	9	∑	∑	PUNCT
ejpam-3712	34	10	uv∈e(g	uv∈e(g	NUM
ejpam-3712	34	11	)	)	PUNCT
ejpam-3712	34	12	γ5(ϕ2,−1(du	γ5(ϕ2,−1(du	NOUN
ejpam-3712	34	13	)	)	PUNCT
ejpam-3712	34	14	,	,	PUNCT
ejpam-3712	34	15	ϕ2,−1(dv	ϕ2,−1(dv	NOUN
ejpam-3712	34	16	)	)	PUNCT
ejpam-3712	34	17	)	)	PUNCT
ejpam-3712	35	1	6	6	X
ejpam-3712	35	2	.	.	X
ejpam-3712	36	1	γ6	γ6	PROPN
ejpam-3712	36	2	corresponds	correspond	VERB
ejpam-3712	36	3	to	to	ADP
ejpam-3712	36	4	min	min	NOUN
ejpam-3712	36	5	-	-	PUNCT
ejpam-3712	36	6	max	max	NOUN
ejpam-3712	36	7	;	;	PUNCT
ejpam-3712	36	8	γ6(x	γ6(x	PROPN
ejpam-3712	36	9	,	,	PUNCT
ejpam-3712	36	10	y	y	NOUN
ejpam-3712	36	11	)	)	PUNCT
ejpam-3712	36	12	=	=	PUNCT
ejpam-3712	37	1			PUNCT
ejpam-3712	37	2	min{x	min{x	PROPN
ejpam-3712	37	3	,	,	PUNCT
ejpam-3712	37	4	y	y	NOUN
ejpam-3712	37	5	}	}	PUNCT
ejpam-3712	37	6	max{x	max{x	PROPN
ejpam-3712	37	7	,	,	PUNCT
ejpam-3712	37	8	y	y	NOUN
ejpam-3712	37	9	}	}	PUNCT
ejpam-3712	37	10	,	,	PUNCT
ejpam-3712	37	11	if	if	SCONJ
ejpam-3712	37	12	max{x	max{x	PROPN
ejpam-3712	37	13	,	,	PUNCT
ejpam-3712	37	14	y	y	NOUN
ejpam-3712	37	15	}	}	PUNCT
ejpam-3712	37	16	6=	6=	ADP
ejpam-3712	37	17	0	0	NUM
ejpam-3712	37	18	0	0	NUM
ejpam-3712	37	19	,	,	PUNCT
ejpam-3712	37	20	if	if	SCONJ
ejpam-3712	37	21	max{x	max{x	PROPN
ejpam-3712	37	22	,	,	PUNCT
ejpam-3712	37	23	y	y	NOUN
ejpam-3712	37	24	}	}	PUNCT
ejpam-3712	37	25	=	=	SYM
ejpam-3712	37	26	0	0	NUM
ejpam-3712	37	27	•	•	NUM
ejpam-3712	37	28	min	min	NOUN
ejpam-3712	37	29	-	-	ADJ
ejpam-3712	37	30	max	max	PROPN
ejpam-3712	37	31	rodeg	rodeg	PROPN
ejpam-3712	37	32	index	index	NOUN
ejpam-3712	37	33	:	:	PUNCT
ejpam-3712	37	34	adr(g	adr(g	PROPN
ejpam-3712	37	35	)	)	PUNCT
ejpam-3712	37	36	=	=	SYM
ejpam-3712	37	37	∑	∑	PUNCT
ejpam-3712	37	38	uv∈e(g	uv∈e(g	NUM
ejpam-3712	37	39	)	)	PUNCT
ejpam-3712	37	40	γ6(ϕ2,1/2(du	γ6(ϕ2,1/2(du	NOUN
ejpam-3712	37	41	)	)	PUNCT
ejpam-3712	37	42	,	,	PUNCT
ejpam-3712	37	43	ϕ2,1/2(dv	ϕ2,1/2(dv	PROPN
ejpam-3712	37	44	)	)	PUNCT
ejpam-3712	37	45	)	)	PUNCT
ejpam-3712	38	1	•	•	ADP
ejpam-3712	38	2	min	min	NOUN
ejpam-3712	38	3	-	-	ADJ
ejpam-3712	38	4	max	max	PROPN
ejpam-3712	38	5	sdi	sdi	PROPN
ejpam-3712	38	6	index	index	NOUN
ejpam-3712	38	7	:	:	PUNCT
ejpam-3712	38	8	adr(g	adr(g	PROPN
ejpam-3712	38	9	)	)	PUNCT
ejpam-3712	38	10	=	=	SYM
ejpam-3712	38	11	∑	∑	PUNCT
ejpam-3712	38	12	uv∈e(g	uv∈e(g	NOUN
ejpam-3712	38	13	)	)	PUNCT
ejpam-3712	38	14	γ6(ϕ2,2(du	γ6(ϕ2,2(du	PROPN
ejpam-3712	38	15	)	)	PUNCT
ejpam-3712	38	16	,	,	PUNCT
ejpam-3712	38	17	ϕ2,2(dv	ϕ2,2(dv	NUM
ejpam-3712	38	18	)	)	PUNCT
ejpam-3712	38	19	)	)	PUNCT
ejpam-3712	39	1	7	7	X
ejpam-3712	39	2	.	.	X
ejpam-3712	39	3	γ7	γ7	PROPN
ejpam-3712	39	4	corresponds	correspond	NOUN
ejpam-3712	39	5	to	to	ADP
ejpam-3712	39	6	max	max	PROPN
ejpam-3712	39	7	-	-	PUNCT
ejpam-3712	39	8	min	min	PROPN
ejpam-3712	39	9	;	;	PUNCT
ejpam-3712	39	10	γ7(x	γ7(x	NUM
ejpam-3712	39	11	,	,	PUNCT
ejpam-3712	39	12	y	y	NOUN
ejpam-3712	39	13	)	)	PUNCT
ejpam-3712	39	14	=	=	PUNCT
ejpam-3712	39	15			PUNCT
ejpam-3712	39	16	max{x	max{x	PROPN
ejpam-3712	39	17	,	,	PUNCT
ejpam-3712	39	18	y	y	NOUN
ejpam-3712	39	19	}	}	PUNCT
ejpam-3712	39	20	min{x	min{x	PROPN
ejpam-3712	39	21	,	,	PUNCT
ejpam-3712	39	22	y	y	NOUN
ejpam-3712	39	23	}	}	PUNCT
ejpam-3712	39	24	,	,	PUNCT
ejpam-3712	39	25	if	if	SCONJ
ejpam-3712	39	26	min{x	min{x	PROPN
ejpam-3712	39	27	,	,	PUNCT
ejpam-3712	39	28	y	y	NOUN
ejpam-3712	39	29	}	}	PUNCT
ejpam-3712	39	30	6=	6=	ADP
ejpam-3712	39	31	0	0	NUM
ejpam-3712	39	32	0	0	NUM
ejpam-3712	39	33	,	,	PUNCT
ejpam-3712	39	34	if	if	SCONJ
ejpam-3712	39	35	min{x	min{x	PROPN
ejpam-3712	39	36	,	,	PUNCT
ejpam-3712	39	37	y	y	NOUN
ejpam-3712	39	38	}	}	PUNCT
ejpam-3712	39	39	=	=	SYM
ejpam-3712	39	40	0	0	NUM
ejpam-3712	39	41	•	•	NUM
ejpam-3712	39	42	max	max	PROPN
ejpam-3712	39	43	-	-	PUNCT
ejpam-3712	39	44	min	min	PROPN
ejpam-3712	39	45	rodeg	rodeg	PROPN
ejpam-3712	39	46	index	index	NOUN
ejpam-3712	39	47	:	:	PUNCT
ejpam-3712	39	48	adr(g	adr(g	PROPN
ejpam-3712	39	49	)	)	PUNCT
ejpam-3712	39	50	=	=	SYM
ejpam-3712	39	51	∑	∑	PUNCT
ejpam-3712	39	52	uv∈e(g	uv∈e(g	NUM
ejpam-3712	39	53	)	)	PUNCT
ejpam-3712	39	54	γ7(ϕ2,1/2(du	γ7(ϕ2,1/2(du	PROPN
ejpam-3712	39	55	)	)	PUNCT
ejpam-3712	39	56	,	,	PUNCT
ejpam-3712	39	57	ϕ2,1/2(dv	ϕ2,1/2(dv	PROPN
ejpam-3712	39	58	)	)	PUNCT
ejpam-3712	39	59	)	)	PUNCT
ejpam-3712	40	1	t.	t.	PROPN
ejpam-3712	40	2	deepika	deepika	PROPN
ejpam-3712	40	3	,	,	PUNCT
ejpam-3712	40	4	v.	v.	ADP
ejpam-3712	40	5	lokesha	lokesha	PROPN
ejpam-3712	40	6	/	/	SYM
ejpam-3712	40	7	eur	eur	PROPN
ejpam-3712	40	8	.	.	PUNCT
ejpam-3712	41	1	j.	j.	PROPN
ejpam-3712	41	2	pure	pure	PROPN
ejpam-3712	41	3	appl	appl	PROPN
ejpam-3712	41	4	.	.	PROPN
ejpam-3712	41	5	math	math	PROPN
ejpam-3712	41	6	,	,	PUNCT
ejpam-3712	41	7	13	13	NUM
ejpam-3712	41	8	(	(	PUNCT
ejpam-3712	41	9	5	5	NUM
ejpam-3712	41	10	)	)	PUNCT
ejpam-3712	41	11	(	(	PUNCT
ejpam-3712	41	12	2020	2020	NUM
ejpam-3712	41	13	)	)	PUNCT
ejpam-3712	41	14	,	,	PUNCT
ejpam-3712	41	15	1149	1149	NUM
ejpam-3712	41	16	-	-	SYM
ejpam-3712	41	17	1161	1161	NUM
ejpam-3712	41	18	1152	1152	NUM
ejpam-3712	41	19	•	•	NUM
ejpam-3712	41	20	max	max	PROPN
ejpam-3712	41	21	-	-	PUNCT
ejpam-3712	41	22	min	min	PROPN
ejpam-3712	41	23	deg	deg	PROPN
ejpam-3712	41	24	index	index	PROPN
ejpam-3712	41	25	:	:	PUNCT
ejpam-3712	41	26	adr(g	adr(g	PROPN
ejpam-3712	41	27	)	)	PUNCT
ejpam-3712	41	28	=	=	SYM
ejpam-3712	41	29	∑	∑	PUNCT
ejpam-3712	41	30	uv∈e(g	uv∈e(g	NUM
ejpam-3712	41	31	)	)	PUNCT
ejpam-3712	41	32	γ7(ϕ2,1(du	γ7(ϕ2,1(du	NUM
ejpam-3712	41	33	)	)	PUNCT
ejpam-3712	41	34	,	,	PUNCT
ejpam-3712	41	35	ϕ2,1(dv	ϕ2,1(dv	NUM
ejpam-3712	41	36	)	)	PUNCT
ejpam-3712	41	37	)	)	PUNCT
ejpam-3712	42	1	•	•	NUM
ejpam-3712	42	2	max	max	PROPN
ejpam-3712	42	3	-	-	PUNCT
ejpam-3712	42	4	min	min	PROPN
ejpam-3712	42	5	sdeg	sdeg	ADJ
ejpam-3712	42	6	index	index	NOUN
ejpam-3712	42	7	:	:	PUNCT
ejpam-3712	42	8	adr(g	adr(g	PROPN
ejpam-3712	42	9	)	)	PUNCT
ejpam-3712	42	10	=	=	SYM
ejpam-3712	42	11	∑	∑	PUNCT
ejpam-3712	42	12	uv∈e(g	uv∈e(g	NUM
ejpam-3712	42	13	)	)	PUNCT
ejpam-3712	42	14	γ7(ϕ2,2(du	γ7(ϕ2,2(du	PROPN
ejpam-3712	42	15	)	)	PUNCT
ejpam-3712	42	16	,	,	PUNCT
ejpam-3712	42	17	ϕ2,2(dv	ϕ2,2(dv	NUM
ejpam-3712	42	18	)	)	PUNCT
ejpam-3712	42	19	)	)	PUNCT
ejpam-3712	43	1	8	8	NUM
ejpam-3712	43	2	.	.	PUNCT
ejpam-3712	44	1	γ8	γ8	NOUN
ejpam-3712	44	2	corresponds	correspond	NOUN
ejpam-3712	44	3	to	to	ADP
ejpam-3712	44	4	symmetric	symmetric	ADJ
ejpam-3712	44	5	division	division	NOUN
ejpam-3712	44	6	;	;	PUNCT
ejpam-3712	44	7	γ8(x	γ8(x	PROPN
ejpam-3712	44	8	,	,	PUNCT
ejpam-3712	44	9	y	y	NOUN
ejpam-3712	44	10	)	)	PUNCT
ejpam-3712	44	11	=	=	PUNCT
ejpam-3712	45	1			PUNCT
ejpam-3712	45	2	x	x	PUNCT
ejpam-3712	45	3	y	y	PROPN
ejpam-3712	45	4	+	+	NOUN
ejpam-3712	45	5	y	y	PROPN
ejpam-3712	45	6	x	x	INTJ
ejpam-3712	45	7	,	,	PUNCT
ejpam-3712	45	8	if	if	SCONJ
ejpam-3712	45	9	x	x	X
ejpam-3712	45	10	,	,	PUNCT
ejpam-3712	45	11	y	y	PROPN
ejpam-3712	45	12	6=	6=	ADP
ejpam-3712	45	13	0	0	NUM
ejpam-3712	45	14	0	0	NUM
ejpam-3712	45	15	,	,	PUNCT
ejpam-3712	45	16	otherwise	otherwise	ADV
ejpam-3712	45	17	•	•	NUM
ejpam-3712	45	18	symmetric	symmetric	ADJ
ejpam-3712	45	19	division	division	NOUN
ejpam-3712	45	20	deg	deg	PROPN
ejpam-3712	45	21	index	index	PROPN
ejpam-3712	45	22	:	:	PUNCT
ejpam-3712	45	23	adr(g	adr(g	PROPN
ejpam-3712	45	24	)	)	PUNCT
ejpam-3712	45	25	=	=	SYM
ejpam-3712	45	26	∑	∑	PUNCT
ejpam-3712	45	27	uv∈e(g	uv∈e(g	NUM
ejpam-3712	45	28	)	)	PUNCT
ejpam-3712	45	29	γ8(ϕ2,1(du	γ8(ϕ2,1(du	PROPN
ejpam-3712	45	30	)	)	PUNCT
ejpam-3712	45	31	,	,	PUNCT
ejpam-3712	45	32	ϕ2,1(dv	ϕ2,1(dv	NUM
ejpam-3712	45	33	)	)	PUNCT
ejpam-3712	45	34	)	)	PUNCT
ejpam-3712	46	1	the	the	DET
ejpam-3712	46	2	probabilistic	probabilistic	ADJ
ejpam-3712	46	3	neural	neural	ADJ
ejpam-3712	46	4	network	network	NOUN
ejpam-3712	46	5	(	(	PUNCT
ejpam-3712	46	6	pnn	pnn	PROPN
ejpam-3712	46	7	)	)	PUNCT
ejpam-3712	46	8	gives	give	VERB
ejpam-3712	46	9	new	new	ADJ
ejpam-3712	46	10	directions	direction	NOUN
ejpam-3712	46	11	in	in	ADP
ejpam-3712	46	12	the	the	DET
ejpam-3712	46	13	quantitative	quantitative	ADJ
ejpam-3712	46	14	structure	structure	NOUN
ejpam-3712	46	15	-	-	PUNCT
ejpam-3712	46	16	activity	activity	NOUN
ejpam-3712	46	17	relationship	relationship	NOUN
ejpam-3712	46	18	(	(	PUNCT
ejpam-3712	46	19	qsar)/quantitative	qsar)/quantitative	ADJ
ejpam-3712	46	20	structure	structure	NOUN
ejpam-3712	46	21	-	-	PUNCT
ejpam-3712	46	22	property	property	NOUN
ejpam-3712	46	23	relationship	relationship	NOUN
ejpam-3712	46	24	(	(	PUNCT
ejpam-3712	46	25	qspr	qspr	NOUN
ejpam-3712	46	26	)	)	PUNCT
ejpam-3712	46	27	studies	study	NOUN
ejpam-3712	46	28	[	[	X
ejpam-3712	46	29	3	3	NUM
ejpam-3712	46	30	]	]	PUNCT
ejpam-3712	46	31	.	.	PUNCT
ejpam-3712	47	1	the	the	DET
ejpam-3712	47	2	pnn	pnn	PROPN
ejpam-3712	47	3	methodology	methodology	NOUN
ejpam-3712	47	4	is	be	AUX
ejpam-3712	47	5	applicable	applicable	ADJ
ejpam-3712	47	6	to	to	ADP
ejpam-3712	47	7	classification	classification	NOUN
ejpam-3712	47	8	problems	problem	NOUN
ejpam-3712	47	9	and	and	CCONJ
ejpam-3712	47	10	the	the	DET
ejpam-3712	47	11	basic	basic	ADJ
ejpam-3712	47	12	underlying	underlying	ADJ
ejpam-3712	47	13	theory	theory	NOUN
ejpam-3712	47	14	behind	behind	ADP
ejpam-3712	47	15	these	these	DET
ejpam-3712	47	16	probability	probability	NOUN
ejpam-3712	47	17	-	-	PUNCT
ejpam-3712	47	18	based	base	VERB
ejpam-3712	47	19	methods	method	NOUN
ejpam-3712	47	20	is	be	AUX
ejpam-3712	47	21	presented	present	VERB
ejpam-3712	47	22	along	along	ADP
ejpam-3712	47	23	with	with	ADP
ejpam-3712	47	24	applications	application	NOUN
ejpam-3712	47	25	of	of	ADP
ejpam-3712	47	26	the	the	DET
ejpam-3712	47	27	pnn	pnn	PROPN
ejpam-3712	47	28	methodology	methodology	NOUN
ejpam-3712	47	29	.	.	PUNCT
ejpam-3712	48	1	the	the	DET
ejpam-3712	48	2	pnn	pnn	PROPN
ejpam-3712	48	3	model	model	NOUN
ejpam-3712	48	4	presented	present	VERB
ejpam-3712	48	5	identifies	identify	VERB
ejpam-3712	48	6	molecules	molecule	NOUN
ejpam-3712	48	7	as	as	ADP
ejpam-3712	48	8	potential	potential	ADJ
ejpam-3712	48	9	soluble	soluble	ADJ
ejpam-3712	48	10	epoxide	epoxide	NOUN
ejpam-3712	48	11	hydrolase	hydrolase	NOUN
ejpam-3712	48	12	inhibitors	inhibitor	NOUN
ejpam-3712	48	13	using	use	VERB
ejpam-3712	48	14	a	a	DET
ejpam-3712	48	15	binary	binary	ADJ
ejpam-3712	48	16	classification	classification	NOUN
ejpam-3712	48	17	scheme	scheme	NOUN
ejpam-3712	48	18	.	.	PUNCT
ejpam-3712	49	1	this	this	DET
ejpam-3712	49	2	network	network	NOUN
ejpam-3712	49	3	inputs	input	NOUN
ejpam-3712	49	4	consist	consist	VERB
ejpam-3712	49	5	of	of	ADP
ejpam-3712	49	6	a	a	DET
ejpam-3712	49	7	small	small	ADJ
ejpam-3712	49	8	set	set	NOUN
ejpam-3712	49	9	of	of	ADP
ejpam-3712	49	10	descriptors	descriptor	NOUN
ejpam-3712	49	11	that	that	PRON
ejpam-3712	49	12	encode	encode	VERB
ejpam-3712	49	13	structural	structural	ADJ
ejpam-3712	49	14	features	feature	NOUN
ejpam-3712	49	15	at	at	ADP
ejpam-3712	49	16	the	the	DET
ejpam-3712	49	17	molecular	molecular	ADJ
ejpam-3712	49	18	level	level	NOUN
ejpam-3712	49	19	(	(	PUNCT
ejpam-3712	49	20	refer	refer	VERB
ejpam-3712	49	21	[	[	X
ejpam-3712	49	22	4	4	NUM
ejpam-3712	49	23	,	,	PUNCT
ejpam-3712	49	24	14	14	NUM
ejpam-3712	49	25	]	]	PUNCT
ejpam-3712	49	26	)	)	PUNCT
ejpam-3712	49	27	.	.	PUNCT
ejpam-3712	50	1	the	the	DET
ejpam-3712	50	2	topological	topological	ADJ
ejpam-3712	50	3	indices	index	NOUN
ejpam-3712	50	4	are	be	AUX
ejpam-3712	50	5	exploited	exploit	VERB
ejpam-3712	50	6	to	to	ADP
ejpam-3712	50	7	hypothesis	hypothesis	NOUN
ejpam-3712	50	8	the	the	DET
ejpam-3712	50	9	physical	physical	ADJ
ejpam-3712	50	10	features	feature	NOUN
ejpam-3712	50	11	related	relate	VERB
ejpam-3712	50	12	to	to	ADP
ejpam-3712	50	13	the	the	DET
ejpam-3712	50	14	bio	bio	NOUN
ejpam-3712	50	15	-	-	NOUN
ejpam-3712	50	16	activities	activity	NOUN
ejpam-3712	50	17	,	,	PUNCT
ejpam-3712	50	18	chemical	chemical	NOUN
ejpam-3712	50	19	reactivities	reactivity	NOUN
ejpam-3712	50	20	in	in	ADP
ejpam-3712	50	21	certain	certain	ADJ
ejpam-3712	50	22	networks	network	NOUN
ejpam-3712	50	23	.	.	PUNCT
ejpam-3712	51	1	in	in	ADP
ejpam-3712	51	2	this	this	DET
ejpam-3712	51	3	article	article	NOUN
ejpam-3712	51	4	,	,	PUNCT
ejpam-3712	51	5	we	we	PRON
ejpam-3712	51	6	established	establish	VERB
ejpam-3712	51	7	the	the	DET
ejpam-3712	51	8	degree	degree	NOUN
ejpam-3712	51	9	-	-	PUNCT
ejpam-3712	51	10	based	base	VERB
ejpam-3712	51	11	discrete	discrete	ADJ
ejpam-3712	51	12	adriatic	adriatic	ADJ
ejpam-3712	51	13	indices	index	NOUN
ejpam-3712	51	14	of	of	ADP
ejpam-3712	51	15	the	the	DET
ejpam-3712	51	16	probabilistic	probabilistic	ADJ
ejpam-3712	51	17	neural	neural	ADJ
ejpam-3712	51	18	network	network	NOUN
ejpam-3712	51	19	.	.	PUNCT
ejpam-3712	52	1	recently	recently	ADV
ejpam-3712	52	2	,	,	PUNCT
ejpam-3712	52	3	[	[	X
ejpam-3712	52	4	1	1	NUM
ejpam-3712	52	5	,	,	PUNCT
ejpam-3712	52	6	12	12	NUM
ejpam-3712	52	7	]	]	PUNCT
ejpam-3712	52	8	exposed	expose	VERB
ejpam-3712	52	9	the	the	DET
ejpam-3712	52	10	148	148	NUM
ejpam-3712	52	11	adriatic	adriatic	ADJ
ejpam-3712	52	12	indices	index	NOUN
ejpam-3712	52	13	among	among	ADP
ejpam-3712	52	14	which	which	PRON
ejpam-3712	52	15	symmetric	symmetric	ADJ
ejpam-3712	52	16	division	division	NOUN
ejpam-3712	52	17	deg	deg	X
ejpam-3712	52	18	(	(	PUNCT
ejpam-3712	52	19	sdd	sdd	NOUN
ejpam-3712	52	20	)	)	PUNCT
ejpam-3712	52	21	index	index	NOUN
ejpam-3712	52	22	is	be	AUX
ejpam-3712	52	23	one	one	NUM
ejpam-3712	52	24	of	of	ADP
ejpam-3712	52	25	the	the	DET
ejpam-3712	52	26	discrete	discrete	ADJ
ejpam-3712	52	27	adriatic	adriatic	ADJ
ejpam-3712	52	28	indices	index	NOUN
ejpam-3712	52	29	,	,	PUNCT
ejpam-3712	52	30	and	and	CCONJ
ejpam-3712	52	31	it	it	PRON
ejpam-3712	52	32	has	have	AUX
ejpam-3712	52	33	been	be	AUX
ejpam-3712	52	34	proved	prove	VERB
ejpam-3712	52	35	as	as	ADP
ejpam-3712	52	36	a	a	DET
ejpam-3712	52	37	good	good	ADJ
ejpam-3712	52	38	predictor	predictor	NOUN
ejpam-3712	52	39	for	for	ADP
ejpam-3712	52	40	total	total	ADJ
ejpam-3712	52	41	surface	surface	NOUN
ejpam-3712	52	42	area	area	NOUN
ejpam-3712	52	43	for	for	ADP
ejpam-3712	52	44	polychlorobiphenyls	polychlorobiphenyls	ADJ
ejpam-3712	52	45	.	.	PUNCT
ejpam-3712	53	1	newly	newly	ADV
ejpam-3712	53	2	,	,	PUNCT
ejpam-3712	53	3	lokesha	lokesha	PROPN
ejpam-3712	53	4	et	et	PROPN
ejpam-3712	53	5	.	.	PUNCT
ejpam-3712	54	1	al	al	PROPN
ejpam-3712	54	2	.	.	PROPN
ejpam-3712	54	3	,	,	PUNCT
ejpam-3712	55	1	[	[	X
ejpam-3712	55	2	5	5	NUM
ejpam-3712	55	3	,	,	PUNCT
ejpam-3712	55	4	6	6	NUM
ejpam-3712	55	5	,	,	PUNCT
ejpam-3712	55	6	8	8	NUM
ejpam-3712	55	7	]	]	PUNCT
ejpam-3712	55	8	worked	work	VERB
ejpam-3712	55	9	out	out	ADP
ejpam-3712	55	10	for	for	ADP
ejpam-3712	55	11	sdd	sdd	ADJ
ejpam-3712	55	12	index	index	NOUN
ejpam-3712	55	13	of	of	ADP
ejpam-3712	55	14	unicyclic	unicyclic	ADJ
ejpam-3712	55	15	and	and	CCONJ
ejpam-3712	55	16	bicyclic	bicyclic	NOUN
ejpam-3712	55	17	later	later	ADV
ejpam-3712	55	18	it	it	PRON
ejpam-3712	55	19	is	be	AUX
ejpam-3712	55	20	also	also	ADV
ejpam-3712	55	21	extended	extend	VERB
ejpam-3712	55	22	to	to	ADP
ejpam-3712	55	23	tricyclic	tricyclic	ADJ
ejpam-3712	55	24	and	and	CCONJ
ejpam-3712	55	25	tetracyclic	tetracyclic	NOUN
ejpam-3712	55	26	,	,	PUNCT
ejpam-3712	55	27	also	also	ADV
ejpam-3712	55	28	they	they	PRON
ejpam-3712	55	29	did	do	VERB
ejpam-3712	55	30	for	for	ADP
ejpam-3712	55	31	graph	graph	NOUN
ejpam-3712	55	32	operations	operation	NOUN
ejpam-3712	55	33	.	.	PUNCT
ejpam-3712	56	1	newly	newly	ADV
ejpam-3712	56	2	,	,	PUNCT
ejpam-3712	56	3	deepika	deepika	PROPN
ejpam-3712	56	4	et	et	PROPN
ejpam-3712	56	5	al	al	PROPN
ejpam-3712	57	1	[	[	X
ejpam-3712	57	2	9	9	NUM
ejpam-3712	57	3	]	]	PUNCT
ejpam-3712	57	4	,	,	PUNCT
ejpam-3712	57	5	computed	compute	VERB
ejpam-3712	57	6	the	the	DET
ejpam-3712	57	7	graph	graph	NOUN
ejpam-3712	57	8	structure	structure	NOUN
ejpam-3712	57	9	of	of	ADP
ejpam-3712	57	10	2d	2d	NOUN
ejpam-3712	57	11	-	-	PUNCT
ejpam-3712	57	12	lattice	lattice	NOUN
ejpam-3712	57	13	,	,	PUNCT
ejpam-3712	57	14	nanotube	nanotube	NOUN
ejpam-3712	57	15	and	and	CCONJ
ejpam-3712	57	16	nanotorus	nanotorus	NOUN
ejpam-3712	57	17	exploiting	exploit	VERB
ejpam-3712	57	18	the	the	DET
ejpam-3712	57	19	definitions	definition	NOUN
ejpam-3712	57	20	of	of	ADP
ejpam-3712	57	21	sdd	sdd	NOUN
ejpam-3712	57	22	and	and	CCONJ
ejpam-3712	57	23	other	other	ADJ
ejpam-3712	57	24	topological	topological	ADJ
ejpam-3712	57	25	indices	index	NOUN
ejpam-3712	57	26	via	via	ADP
ejpam-3712	57	27	certain	certain	ADJ
ejpam-3712	57	28	graph	graph	NOUN
ejpam-3712	57	29	operators	operator	NOUN
ejpam-3712	57	30	which	which	PRON
ejpam-3712	57	31	gives	give	VERB
ejpam-3712	57	32	more	more	ADJ
ejpam-3712	57	33	attraction	attraction	NOUN
ejpam-3712	57	34	towards	towards	ADP
ejpam-3712	57	35	to	to	ADP
ejpam-3712	57	36	this	this	DET
ejpam-3712	57	37	index	index	NOUN
ejpam-3712	57	38	(	(	PUNCT
ejpam-3712	57	39	also	also	ADV
ejpam-3712	57	40	see	see	VERB
ejpam-3712	57	41	[	[	X
ejpam-3712	57	42	2	2	NUM
ejpam-3712	57	43	,	,	PUNCT
ejpam-3712	57	44	10	10	NUM
ejpam-3712	57	45	,	,	PUNCT
ejpam-3712	57	46	13	13	NUM
ejpam-3712	57	47	]	]	PUNCT
ejpam-3712	57	48	)	)	PUNCT
ejpam-3712	57	49	.	.	PUNCT
ejpam-3712	58	1	in	in	ADP
ejpam-3712	58	2	the	the	DET
ejpam-3712	58	3	last	last	ADJ
ejpam-3712	58	4	decade	decade	NOUN
ejpam-3712	58	5	the	the	DET
ejpam-3712	58	6	probabilistic	probabilistic	ADJ
ejpam-3712	58	7	neural	neural	ADJ
ejpam-3712	58	8	networks	network	NOUN
ejpam-3712	58	9	are	be	AUX
ejpam-3712	58	10	widely	widely	ADV
ejpam-3712	58	11	studied	study	VERB
ejpam-3712	58	12	in	in	ADP
ejpam-3712	58	13	different	different	ADJ
ejpam-3712	58	14	classification	classification	NOUN
ejpam-3712	58	15	problems	problem	NOUN
ejpam-3712	58	16	.	.	PUNCT
ejpam-3712	59	1	these	these	PRON
ejpam-3712	59	2	are	be	AUX
ejpam-3712	59	3	applied	apply	VERB
ejpam-3712	59	4	to	to	PART
ejpam-3712	59	5	solve	solve	VERB
ejpam-3712	59	6	the	the	DET
ejpam-3712	59	7	problems	problem	NOUN
ejpam-3712	59	8	related	relate	VERB
ejpam-3712	59	9	to	to	PART
ejpam-3712	59	10	email	email	VERB
ejpam-3712	59	11	security	security	NOUN
ejpam-3712	59	12	enhancement	enhancement	NOUN
ejpam-3712	59	13	and	and	CCONJ
ejpam-3712	59	14	in	in	ADP
ejpam-3712	59	15	the	the	DET
ejpam-3712	59	16	intrusion	intrusion	NOUN
ejpam-3712	59	17	detection	detection	NOUN
ejpam-3712	59	18	systems	system	NOUN
ejpam-3712	59	19	.	.	PUNCT
ejpam-3712	60	1	the	the	DET
ejpam-3712	60	2	probabilistic	probabilistic	ADJ
ejpam-3712	60	3	neural	neural	ADJ
ejpam-3712	60	4	networks	network	NOUN
ejpam-3712	60	5	are	be	AUX
ejpam-3712	60	6	also	also	ADV
ejpam-3712	60	7	applied	apply	VERB
ejpam-3712	60	8	in	in	ADP
ejpam-3712	60	9	medicine	medicine	NOUN
ejpam-3712	60	10	such	such	ADJ
ejpam-3712	60	11	as	as	ADP
ejpam-3712	60	12	for	for	ADP
ejpam-3712	60	13	detecting	detect	VERB
ejpam-3712	60	14	resistivity	resistivity	NOUN
ejpam-3712	60	15	to	to	ADP
ejpam-3712	60	16	antibiotics	antibiotic	NOUN
ejpam-3712	60	17	,	,	PUNCT
ejpam-3712	60	18	for	for	ADP
ejpam-3712	60	19	diagnosing	diagnose	VERB
ejpam-3712	60	20	hepatitis	hepatitis	NOUN
ejpam-3712	60	21	,	,	PUNCT
ejpam-3712	60	22	and	and	CCONJ
ejpam-3712	60	23	for	for	ADP
ejpam-3712	60	24	the	the	DET
ejpam-3712	60	25	quantification	quantification	NOUN
ejpam-3712	60	26	and	and	CCONJ
ejpam-3712	60	27	segmentation	segmentation	NOUN
ejpam-3712	60	28	of	of	ADP
ejpam-3712	60	29	brain	brain	NOUN
ejpam-3712	60	30	tissues	tissue	NOUN
ejpam-3712	60	31	from	from	ADP
ejpam-3712	60	32	mr	mr	PROPN
ejpam-3712	60	33	images	image	NOUN
ejpam-3712	60	34	(	(	PUNCT
ejpam-3712	60	35	also	also	ADV
ejpam-3712	60	36	see	see	VERB
ejpam-3712	60	37	[	[	X
ejpam-3712	60	38	7	7	NUM
ejpam-3712	60	39	,	,	PUNCT
ejpam-3712	60	40	11	11	NUM
ejpam-3712	60	41	]	]	NUM
ejpam-3712	60	42	)	)	PUNCT
ejpam-3712	60	43	.	.	PUNCT
ejpam-3712	61	1	in	in	ADP
ejpam-3712	61	2	the	the	DET
ejpam-3712	61	3	present	present	ADJ
ejpam-3712	61	4	study	study	NOUN
ejpam-3712	61	5	,	,	PUNCT
ejpam-3712	61	6	we	we	PRON
ejpam-3712	61	7	compute	compute	VERB
ejpam-3712	61	8	the	the	DET
ejpam-3712	61	9	topological	topological	ADJ
ejpam-3712	61	10	indices	index	NOUN
ejpam-3712	61	11	such	such	ADJ
ejpam-3712	61	12	as	as	ADP
ejpam-3712	61	13	newly	newly	ADV
ejpam-3712	61	14	defined	define	VERB
ejpam-3712	61	15	adriatic	adriatic	ADJ
ejpam-3712	61	16	indices	index	NOUN
ejpam-3712	61	17	to	to	PART
ejpam-3712	61	18	continue	continue	VERB
ejpam-3712	61	19	the	the	DET
ejpam-3712	61	20	progressive	progressive	ADJ
ejpam-3712	61	21	study	study	NOUN
ejpam-3712	61	22	of	of	ADP
ejpam-3712	61	23	the	the	DET
ejpam-3712	61	24	probabilistic	probabilistic	ADJ
ejpam-3712	61	25	neural	neural	ADJ
ejpam-3712	61	26	networks	network	NOUN
ejpam-3712	61	27	.	.	PUNCT
ejpam-3712	62	1	t.	t.	PROPN
ejpam-3712	62	2	deepika	deepika	PROPN
ejpam-3712	62	3	,	,	PUNCT
ejpam-3712	62	4	v.	v.	ADP
ejpam-3712	62	5	lokesha	lokesha	PROPN
ejpam-3712	62	6	/	/	SYM
ejpam-3712	62	7	eur	eur	PROPN
ejpam-3712	62	8	.	.	PUNCT
ejpam-3712	63	1	j.	j.	PROPN
ejpam-3712	63	2	pure	pure	PROPN
ejpam-3712	63	3	appl	appl	PROPN
ejpam-3712	63	4	.	.	PROPN
ejpam-3712	63	5	math	math	PROPN
ejpam-3712	63	6	,	,	PUNCT
ejpam-3712	63	7	13	13	NUM
ejpam-3712	63	8	(	(	PUNCT
ejpam-3712	63	9	5	5	NUM
ejpam-3712	63	10	)	)	PUNCT
ejpam-3712	63	11	(	(	PUNCT
ejpam-3712	63	12	2020	2020	NUM
ejpam-3712	63	13	)	)	PUNCT
ejpam-3712	63	14	,	,	PUNCT
ejpam-3712	63	15	1149	1149	NUM
ejpam-3712	63	16	-	-	SYM
ejpam-3712	63	17	1161	1161	NUM
ejpam-3712	63	18	1153	1153	NUM
ejpam-3712	63	19	the	the	DET
ejpam-3712	63	20	construction	construction	NOUN
ejpam-3712	63	21	of	of	ADP
ejpam-3712	63	22	the	the	DET
ejpam-3712	63	23	probabilistic	probabilistic	ADJ
ejpam-3712	63	24	neural	neural	ADJ
ejpam-3712	63	25	network	network	NOUN
ejpam-3712	63	26	.	.	PUNCT
ejpam-3712	64	1	we	we	PRON
ejpam-3712	64	2	consider	consider	VERB
ejpam-3712	64	3	the	the	DET
ejpam-3712	64	4	probabilistic	probabilistic	ADJ
ejpam-3712	64	5	neural	neural	ADJ
ejpam-3712	64	6	network	network	NOUN
ejpam-3712	64	7	consisting	consist	VERB
ejpam-3712	64	8	on	on	ADP
ejpam-3712	64	9	three	three	NUM
ejpam-3712	64	10	layers	layer	NOUN
ejpam-3712	64	11	of	of	ADP
ejpam-3712	64	12	nodes	node	NOUN
ejpam-3712	64	13	.	.	PUNCT
ejpam-3712	65	1	•	•	NUM
ejpam-3712	65	2	the	the	DET
ejpam-3712	65	3	first	first	ADJ
ejpam-3712	65	4	layer	layer	NOUN
ejpam-3712	65	5	called	call	VERB
ejpam-3712	65	6	by	by	ADP
ejpam-3712	65	7	input	input	NOUN
ejpam-3712	65	8	layer	layer	NOUN
ejpam-3712	65	9	has	have	VERB
ejpam-3712	65	10	a	a	DET
ejpam-3712	65	11	certain	certain	ADJ
ejpam-3712	65	12	number	number	NOUN
ejpam-3712	65	13	of	of	ADP
ejpam-3712	65	14	nodes	node	NOUN
ejpam-3712	65	15	,	,	PUNCT
ejpam-3712	65	16	the	the	DET
ejpam-3712	65	17	second	second	ADJ
ejpam-3712	65	18	layer	layer	NOUN
ejpam-3712	65	19	called	call	VERB
ejpam-3712	65	20	by	by	ADP
ejpam-3712	65	21	hidden	hidden	ADJ
ejpam-3712	65	22	layer	layer	NOUN
ejpam-3712	65	23	consists	consist	VERB
ejpam-3712	65	24	on	on	ADP
ejpam-3712	65	25	a	a	DET
ejpam-3712	65	26	certain	certain	ADJ
ejpam-3712	65	27	number	number	NOUN
ejpam-3712	65	28	of	of	ADP
ejpam-3712	65	29	classes	class	NOUN
ejpam-3712	65	30	such	such	ADJ
ejpam-3712	65	31	that	that	SCONJ
ejpam-3712	65	32	each	each	DET
ejpam-3712	65	33	class	class	NOUN
ejpam-3712	65	34	contains	contain	VERB
ejpam-3712	65	35	a	a	DET
ejpam-3712	65	36	particular	particular	ADJ
ejpam-3712	65	37	number	number	NOUN
ejpam-3712	65	38	of	of	ADP
ejpam-3712	65	39	nodes	node	NOUN
ejpam-3712	65	40	,	,	PUNCT
ejpam-3712	65	41	and	and	CCONJ
ejpam-3712	65	42	the	the	DET
ejpam-3712	65	43	third	third	ADJ
ejpam-3712	65	44	layer	layer	NOUN
ejpam-3712	65	45	called	call	VERB
ejpam-3712	65	46	by	by	ADP
ejpam-3712	65	47	output	output	NOUN
ejpam-3712	65	48	layer	layer	NOUN
ejpam-3712	65	49	has	have	VERB
ejpam-3712	65	50	a	a	DET
ejpam-3712	65	51	number	number	NOUN
ejpam-3712	65	52	of	of	ADP
ejpam-3712	65	53	nodes	node	NOUN
ejpam-3712	65	54	equal	equal	ADJ
ejpam-3712	65	55	to	to	ADP
ejpam-3712	65	56	the	the	DET
ejpam-3712	65	57	number	number	NOUN
ejpam-3712	65	58	of	of	ADP
ejpam-3712	65	59	classes	class	NOUN
ejpam-3712	65	60	of	of	ADP
ejpam-3712	65	61	the	the	DET
ejpam-3712	65	62	second	second	ADJ
ejpam-3712	65	63	layer	layer	NOUN
ejpam-3712	65	64	.	.	PUNCT
ejpam-3712	66	1	•	•	NUM
ejpam-3712	66	2	the	the	DET
ejpam-3712	66	3	architecture	architecture	NOUN
ejpam-3712	66	4	of	of	ADP
ejpam-3712	66	5	a	a	DET
ejpam-3712	66	6	probabilistic	probabilistic	ADJ
ejpam-3712	66	7	neural	neural	ADJ
ejpam-3712	66	8	network	network	NOUN
ejpam-3712	66	9	,	,	PUNCT
ejpam-3712	66	10	each	each	DET
ejpam-3712	66	11	node	node	NOUN
ejpam-3712	66	12	of	of	ADP
ejpam-3712	66	13	input	input	NOUN
ejpam-3712	66	14	layer	layer	NOUN
ejpam-3712	66	15	is	be	AUX
ejpam-3712	66	16	connected	connect	VERB
ejpam-3712	66	17	to	to	ADP
ejpam-3712	66	18	all	all	DET
ejpam-3712	66	19	the	the	DET
ejpam-3712	66	20	nodes	node	NOUN
ejpam-3712	66	21	of	of	ADP
ejpam-3712	66	22	each	each	DET
ejpam-3712	66	23	class	class	NOUN
ejpam-3712	66	24	of	of	ADP
ejpam-3712	66	25	the	the	DET
ejpam-3712	66	26	hidden	hide	VERB
ejpam-3712	66	27	layer	layer	NOUN
ejpam-3712	66	28	and	and	CCONJ
ejpam-3712	66	29	all	all	DET
ejpam-3712	66	30	the	the	DET
ejpam-3712	66	31	nodes	node	NOUN
ejpam-3712	66	32	of	of	ADP
ejpam-3712	66	33	each	each	DET
ejpam-3712	66	34	class	class	NOUN
ejpam-3712	66	35	of	of	ADP
ejpam-3712	66	36	the	the	DET
ejpam-3712	66	37	hidden	hide	VERB
ejpam-3712	66	38	layer	layer	NOUN
ejpam-3712	66	39	are	be	AUX
ejpam-3712	66	40	connected	connect	VERB
ejpam-3712	66	41	to	to	ADP
ejpam-3712	66	42	a	a	DET
ejpam-3712	66	43	unique	unique	ADJ
ejpam-3712	66	44	node	node	NOUN
ejpam-3712	66	45	of	of	ADP
ejpam-3712	66	46	the	the	DET
ejpam-3712	66	47	output	output	NOUN
ejpam-3712	66	48	layer	layer	NOUN
ejpam-3712	66	49	.	.	PUNCT
ejpam-3712	67	1	•	•	NUM
ejpam-3712	67	2	assume	assume	VERB
ejpam-3712	67	3	the	the	DET
ejpam-3712	67	4	input	input	NOUN
ejpam-3712	67	5	layer	layer	NOUN
ejpam-3712	67	6	has	have	VERB
ejpam-3712	67	7	n	n	NUM
ejpam-3712	67	8	nodes	node	NOUN
ejpam-3712	67	9	,	,	PUNCT
ejpam-3712	67	10	the	the	DET
ejpam-3712	67	11	hidden	hide	VERB
ejpam-3712	67	12	layer	layer	NOUN
ejpam-3712	67	13	consists	consist	VERB
ejpam-3712	67	14	on	on	ADP
ejpam-3712	67	15	k	k	PROPN
ejpam-3712	67	16	classes	class	NOUN
ejpam-3712	67	17	such	such	ADJ
ejpam-3712	67	18	that	that	SCONJ
ejpam-3712	67	19	each	each	DET
ejpam-3712	67	20	class	class	NOUN
ejpam-3712	67	21	has	have	VERB
ejpam-3712	67	22	m	m	NOUN
ejpam-3712	67	23	nodes	node	NOUN
ejpam-3712	67	24	,	,	PUNCT
ejpam-3712	67	25	and	and	CCONJ
ejpam-3712	67	26	the	the	DET
ejpam-3712	67	27	third	third	ADJ
ejpam-3712	67	28	layer	layer	NOUN
ejpam-3712	67	29	called	call	VERB
ejpam-3712	67	30	by	by	ADP
ejpam-3712	67	31	output	output	NOUN
ejpam-3712	67	32	layer	layer	NOUN
ejpam-3712	67	33	has	have	VERB
ejpam-3712	67	34	k	k	PROPN
ejpam-3712	67	35	nodes	node	NOUN
ejpam-3712	67	36	.	.	PUNCT
ejpam-3712	68	1	thus	thus	ADV
ejpam-3712	68	2	,	,	PUNCT
ejpam-3712	68	3	a	a	DET
ejpam-3712	68	4	probabilistic	probabilistic	ADJ
ejpam-3712	68	5	neural	neural	ADJ
ejpam-3712	68	6	network	network	NOUN
ejpam-3712	68	7	denoted	denote	VERB
ejpam-3712	68	8	by	by	ADP
ejpam-3712	68	9	pnn(n	pnn(n	PROPN
ejpam-3712	68	10	,	,	PUNCT
ejpam-3712	68	11	k	k	PROPN
ejpam-3712	68	12	,	,	PUNCT
ejpam-3712	68	13	m	m	NOUN
ejpam-3712	68	14	)	)	PUNCT
ejpam-3712	68	15	is	be	AUX
ejpam-3712	68	16	such	such	ADJ
ejpam-3712	68	17	that	that	SCONJ
ejpam-3712	68	18	|v	|v	PROPN
ejpam-3712	68	19	(	(	PUNCT
ejpam-3712	68	20	pnn(n	pnn(n	PROPN
ejpam-3712	68	21	,	,	PUNCT
ejpam-3712	68	22	k	k	NOUN
ejpam-3712	68	23	,	,	PUNCT
ejpam-3712	68	24	m))|	m))|	PROPN
ejpam-3712	68	25	=	=	SYM
ejpam-3712	68	26	v	v	PROPN
ejpam-3712	68	27	=	=	SYM
ejpam-3712	68	28	n+	n+	X
ejpam-3712	68	29	k(m+	k(m+	NOUN
ejpam-3712	68	30	1	1	NUM
ejpam-3712	68	31	)	)	PUNCT
ejpam-3712	68	32	and	and	CCONJ
ejpam-3712	68	33	|e(pnn(n	|e(pnn(n	NUM
ejpam-3712	68	34	,	,	PUNCT
ejpam-3712	68	35	k	k	NOUN
ejpam-3712	68	36	,	,	PUNCT
ejpam-3712	68	37	m))|	m))|	PROPN
ejpam-3712	68	38	=	=	SYM
ejpam-3712	68	39	e	e	X
ejpam-3712	68	40	=	=	PUNCT
ejpam-3712	68	41	km(n+	km(n+	PROPN
ejpam-3712	68	42	1	1	NUM
ejpam-3712	68	43	)	)	PUNCT
ejpam-3712	68	44	,	,	PUNCT
ejpam-3712	68	45	where	where	SCONJ
ejpam-3712	68	46	(	(	PUNCT
ejpam-3712	68	47	n	n	X
ejpam-3712	68	48	,	,	PUNCT
ejpam-3712	68	49	k	k	PROPN
ejpam-3712	68	50	,	,	PUNCT
ejpam-3712	68	51	m	m	NOUN
ejpam-3712	68	52	)	)	PUNCT
ejpam-3712	68	53	∈	∈	PROPN
ejpam-3712	68	54	n	n	CCONJ
ejpam-3712	68	55	(	(	PUNCT
ejpam-3712	68	56	set	set	NOUN
ejpam-3712	68	57	of	of	ADP
ejpam-3712	68	58	natural	natural	ADJ
ejpam-3712	68	59	numbers	number	NOUN
ejpam-3712	68	60	)	)	PUNCT
ejpam-3712	68	61	.	.	PUNCT
ejpam-3712	69	1	in	in	ADP
ejpam-3712	69	2	fig	fig	NOUN
ejpam-3712	69	3	.	.	PUNCT
ejpam-3712	70	1	1	1	NUM
ejpam-3712	70	2	,	,	PUNCT
ejpam-3712	70	3	the	the	DET
ejpam-3712	70	4	probabilistic	probabilistic	ADJ
ejpam-3712	70	5	neural	neural	ADJ
ejpam-3712	70	6	network	network	NOUN
ejpam-3712	70	7	is	be	AUX
ejpam-3712	70	8	shown	show	VERB
ejpam-3712	70	9	for	for	ADP
ejpam-3712	70	10	n	n	NOUN
ejpam-3712	70	11	=	=	SYM
ejpam-3712	70	12	4	4	NUM
ejpam-3712	70	13	,	,	PUNCT
ejpam-3712	70	14	k	k	NOUN
ejpam-3712	70	15	=	=	SYM
ejpam-3712	70	16	2	2	NUM
ejpam-3712	70	17	and	and	CCONJ
ejpam-3712	70	18	m	m	PROPN
ejpam-3712	70	19	=	=	ADJ
ejpam-3712	70	20	3	3	X
ejpam-3712	70	21	.	.	X
ejpam-3712	70	22	figure	figure	NOUN
ejpam-3712	70	23	1	1	NUM
ejpam-3712	70	24	:	:	PUNCT
ejpam-3712	70	25	the	the	DET
ejpam-3712	70	26	probabilistic	probabilistic	ADJ
ejpam-3712	70	27	neural	neural	ADJ
ejpam-3712	70	28	network	network	NOUN
ejpam-3712	70	29	pnn(4	pnn(4	NOUN
ejpam-3712	70	30	,	,	PUNCT
ejpam-3712	70	31	2	2	NUM
ejpam-3712	70	32	,	,	PUNCT
ejpam-3712	70	33	3	3	X
ejpam-3712	70	34	)	)	PUNCT
ejpam-3712	70	35	we	we	PRON
ejpam-3712	70	36	define	define	VERB
ejpam-3712	70	37	the	the	DET
ejpam-3712	70	38	partitions	partition	NOUN
ejpam-3712	70	39	of	of	ADP
ejpam-3712	70	40	the	the	DET
ejpam-3712	70	41	edge	edge	NOUN
ejpam-3712	70	42	set	set	NOUN
ejpam-3712	70	43	of	of	ADP
ejpam-3712	70	44	pnn(n	pnn(n	PROPN
ejpam-3712	70	45	,	,	PUNCT
ejpam-3712	70	46	k	k	PROPN
ejpam-3712	70	47	,	,	PUNCT
ejpam-3712	70	48	m	m	NOUN
ejpam-3712	70	49	)	)	PUNCT
ejpam-3712	70	50	with	with	ADP
ejpam-3712	70	51	respect	respect	NOUN
ejpam-3712	70	52	to	to	ADP
ejpam-3712	70	53	degree	degree	NOUN
ejpam-3712	70	54	of	of	ADP
ejpam-3712	70	55	vertices	vertex	NOUN
ejpam-3712	70	56	.	.	PUNCT
ejpam-3712	71	1	there	there	PRON
ejpam-3712	71	2	are	be	VERB
ejpam-3712	71	3	two	two	NUM
ejpam-3712	71	4	types	type	NOUN
ejpam-3712	71	5	of	of	ADP
ejpam-3712	71	6	edges	edge	NOUN
ejpam-3712	71	7	with	with	ADP
ejpam-3712	71	8	respect	respect	NOUN
ejpam-3712	71	9	to	to	ADP
ejpam-3712	71	10	degrees	degree	NOUN
ejpam-3712	71	11	of	of	ADP
ejpam-3712	71	12	end	end	NOUN
ejpam-3712	71	13	vertices	vertex	NOUN
ejpam-3712	71	14	in	in	ADP
ejpam-3712	71	15	pnn(n	pnn(n	PROPN
ejpam-3712	71	16	,	,	PUNCT
ejpam-3712	71	17	k	k	NOUN
ejpam-3712	71	18	,	,	PUNCT
ejpam-3712	71	19	m	m	NOUN
ejpam-3712	71	20	)	)	PUNCT
ejpam-3712	71	21	,	,	PUNCT
ejpam-3712	71	22	namely	namely	ADV
ejpam-3712	71	23	with	with	SCONJ
ejpam-3712	71	24	degrees	degree	NOUN
ejpam-3712	71	25	of	of	ADP
ejpam-3712	71	26	end	end	NOUN
ejpam-3712	71	27	vertices	vertice	VERB
ejpam-3712	71	28	km	km	PROPN
ejpam-3712	71	29	,	,	PUNCT
ejpam-3712	71	30	n+	n+	NUM
ejpam-3712	71	31	1	1	NUM
ejpam-3712	71	32	and	and	CCONJ
ejpam-3712	71	33	degrees	degree	NOUN
ejpam-3712	71	34	of	of	ADP
ejpam-3712	71	35	end	end	NOUN
ejpam-3712	71	36	vertices	vertex	NOUN
ejpam-3712	71	37	n+	n+	PUNCT
ejpam-3712	71	38	1,m	1,m	X
ejpam-3712	71	39	.	.	PUNCT
ejpam-3712	72	1	thus	thus	ADV
ejpam-3712	72	2	,	,	PUNCT
ejpam-3712	72	3	we	we	PRON
ejpam-3712	72	4	have	have	AUX
ejpam-3712	72	5	shown	show	VERB
ejpam-3712	72	6	in	in	ADP
ejpam-3712	72	7	the	the	DET
ejpam-3712	72	8	following	follow	VERB
ejpam-3712	72	9	table	table	NOUN
ejpam-3712	72	10	1	1	NUM
ejpam-3712	72	11	.	.	PUNCT
ejpam-3712	72	12	table	table	NOUN
ejpam-3712	72	13	1	1	NUM
ejpam-3712	72	14	:	:	PUNCT
ejpam-3712	72	15	the	the	DET
ejpam-3712	72	16	edge	edge	NOUN
ejpam-3712	72	17	partition	partition	NOUN
ejpam-3712	72	18	of	of	ADP
ejpam-3712	72	19	the	the	DET
ejpam-3712	72	20	edges	edge	NOUN
ejpam-3712	72	21	of	of	ADP
ejpam-3712	72	22	pnn(n	pnn(n	PROPN
ejpam-3712	72	23	,	,	PUNCT
ejpam-3712	72	24	k	k	PROPN
ejpam-3712	72	25	,	,	PUNCT
ejpam-3712	72	26	m	m	NOUN
ejpam-3712	72	27	)	)	PUNCT
ejpam-3712	72	28	based	base	VERB
ejpam-3712	72	29	on	on	ADP
ejpam-3712	72	30	degrees	degree	NOUN
ejpam-3712	72	31	of	of	ADP
ejpam-3712	72	32	end	end	NOUN
ejpam-3712	72	33	vertices	vertex	NOUN
ejpam-3712	72	34	e{d(u),d(v	e{d(u),d(v	ADJ
ejpam-3712	72	35	)	)	PUNCT
ejpam-3712	72	36	}	}	PUNCT
ejpam-3712	72	37	ekm	ekm	NOUN
ejpam-3712	72	38	,	,	PUNCT
ejpam-3712	72	39	n+1	n+1	NUM
ejpam-3712	72	40	en+1,m	en+1,m	NOUN
ejpam-3712	72	41	e{d(u),d(v	e{d(u),d(v	ADJ
ejpam-3712	72	42	)	)	PUNCT
ejpam-3712	72	43	}	}	PUNCT
ejpam-3712	72	44	nkm	nkm	VERB
ejpam-3712	72	45	km	km	NOUN
ejpam-3712	72	46	2	2	NUM
ejpam-3712	72	47	.	.	PUNCT
ejpam-3712	72	48	main	main	ADJ
ejpam-3712	72	49	results	result	NOUN
ejpam-3712	72	50	in	in	ADP
ejpam-3712	72	51	this	this	DET
ejpam-3712	72	52	section	section	NOUN
ejpam-3712	72	53	,	,	PUNCT
ejpam-3712	72	54	we	we	PRON
ejpam-3712	72	55	established	establish	VERB
ejpam-3712	72	56	some	some	DET
ejpam-3712	72	57	results	result	NOUN
ejpam-3712	72	58	for	for	ADP
ejpam-3712	72	59	probabilistic	probabilistic	ADJ
ejpam-3712	72	60	neural	neural	ADJ
ejpam-3712	72	61	networks	network	NOUN
ejpam-3712	72	62	using	use	VERB
ejpam-3712	72	63	different	different	ADJ
ejpam-3712	72	64	adriatic	adriatic	ADJ
ejpam-3712	72	65	indices	index	NOUN
ejpam-3712	72	66	t.	t.	PROPN
ejpam-3712	72	67	deepika	deepika	PROPN
ejpam-3712	72	68	,	,	PUNCT
ejpam-3712	72	69	v.	v.	ADP
ejpam-3712	72	70	lokesha	lokesha	PROPN
ejpam-3712	72	71	/	/	SYM
ejpam-3712	72	72	eur	eur	PROPN
ejpam-3712	72	73	.	.	PUNCT
ejpam-3712	73	1	j.	j.	PROPN
ejpam-3712	73	2	pure	pure	PROPN
ejpam-3712	73	3	appl	appl	PROPN
ejpam-3712	73	4	.	.	PROPN
ejpam-3712	73	5	math	math	PROPN
ejpam-3712	73	6	,	,	PUNCT
ejpam-3712	73	7	13	13	NUM
ejpam-3712	73	8	(	(	PUNCT
ejpam-3712	73	9	5	5	NUM
ejpam-3712	73	10	)	)	PUNCT
ejpam-3712	73	11	(	(	PUNCT
ejpam-3712	73	12	2020	2020	NUM
ejpam-3712	73	13	)	)	PUNCT
ejpam-3712	73	14	,	,	PUNCT
ejpam-3712	73	15	1149	1149	NUM
ejpam-3712	73	16	-	-	SYM
ejpam-3712	73	17	1161	1161	NUM
ejpam-3712	73	18	1154	1154	NUM
ejpam-3712	73	19	theorem	theorem	NOUN
ejpam-3712	73	20	1	1	NUM
ejpam-3712	73	21	.	.	PUNCT
ejpam-3712	74	1	let	let	VERB
ejpam-3712	74	2	g	g	NOUN
ejpam-3712	74	3	be	be	AUX
ejpam-3712	74	4	the	the	DET
ejpam-3712	74	5	probabilistic	probabilistic	ADJ
ejpam-3712	74	6	neural	neural	ADJ
ejpam-3712	74	7	network	network	NOUN
ejpam-3712	74	8	pnn(n	pnn(n	PROPN
ejpam-3712	74	9	,	,	PUNCT
ejpam-3712	74	10	k	k	PROPN
ejpam-3712	74	11	,	,	PUNCT
ejpam-3712	74	12	m	m	PROPN
ejpam-3712	74	13	)	)	PUNCT
ejpam-3712	74	14	then	then	ADV
ejpam-3712	74	15	for	for	ADP
ejpam-3712	74	16	(	(	PUNCT
ejpam-3712	74	17	n	n	CCONJ
ejpam-3712	74	18	,	,	PUNCT
ejpam-3712	74	19	k	k	PROPN
ejpam-3712	74	20	,	,	PUNCT
ejpam-3712	74	21	m	m	PROPN
ejpam-3712	74	22	)	)	PUNCT
ejpam-3712	74	23	≥	≥	NOUN
ejpam-3712	74	24	1	1	NUM
ejpam-3712	74	25	,	,	PUNCT
ejpam-3712	74	26	its	its	PRON
ejpam-3712	74	27	misbalance	misbalance	PROPN
ejpam-3712	74	28	deg	deg	PROPN
ejpam-3712	74	29	index	index	PROPN
ejpam-3712	74	30	,	,	PUNCT
ejpam-3712	74	31	misbalance	misbalance	PROPN
ejpam-3712	74	32	indeg	indeg	ADJ
ejpam-3712	74	33	index	index	PROPN
ejpam-3712	74	34	,	,	PUNCT
ejpam-3712	74	35	misbalance	misbalance	NOUN
ejpam-3712	74	36	rodeg	rodeg	ADJ
ejpam-3712	74	37	index	index	NOUN
ejpam-3712	74	38	and	and	CCONJ
ejpam-3712	74	39	misbalance	misbalance	NOUN
ejpam-3712	74	40	irdeg	irdeg	NOUN
ejpam-3712	74	41	index	index	NOUN
ejpam-3712	74	42	is	be	AUX
ejpam-3712	74	43	given	give	VERB
ejpam-3712	74	44	by	by	ADP
ejpam-3712	74	45	mbiα(g	mbiα(g	PROPN
ejpam-3712	74	46	)	)	PUNCT
ejpam-3712	74	47	=	=	SYM
ejpam-3712	74	48			NUM
ejpam-3712	74	49	nkm|km−	nkm|km−	PROPN
ejpam-3712	74	50	(	(	PUNCT
ejpam-3712	74	51	n+	n+	NUM
ejpam-3712	74	52	1)|+	1)|+	NUM
ejpam-3712	74	53	km|(n+	km|(n+	PROPN
ejpam-3712	74	54	1)−m|	1)−m|	NUM
ejpam-3712	74	55	for	for	ADP
ejpam-3712	74	56	α	α	NOUN
ejpam-3712	74	57	=	=	SYM
ejpam-3712	74	58	1	1	NUM
ejpam-3712	74	59	nkm|	nkm|	SYM
ejpam-3712	74	60	1	1	NUM
ejpam-3712	74	61	km	km	NOUN
ejpam-3712	74	62	−	−	NOUN
ejpam-3712	74	63	1	1	NUM
ejpam-3712	74	64	n+	n+	ADP
ejpam-3712	74	65	1	1	NUM
ejpam-3712	74	66	|+	|+	NOUN
ejpam-3712	74	67	km|	km|	PROPN
ejpam-3712	74	68	1	1	NUM
ejpam-3712	74	69	n+	n+	SYM
ejpam-3712	74	70	1	1	NUM
ejpam-3712	74	71	−	−	NUM
ejpam-3712	74	72	1	1	NUM
ejpam-3712	74	73	m	m	NOUN
ejpam-3712	74	74	|	|	ADJ
ejpam-3712	74	75	for	for	ADP
ejpam-3712	74	76	α	α	NOUN
ejpam-3712	74	77	=	=	SYM
ejpam-3712	74	78	−1	−1	NOUN
ejpam-3712	74	79	nkm|	nkm|	ADJ
ejpam-3712	74	80	√	√	ADJ
ejpam-3712	74	81	km−	km−	PROPN
ejpam-3712	74	82	√	√	NUM
ejpam-3712	74	83	n+	n+	NUM
ejpam-3712	74	84	1|+	1|+	NUM
ejpam-3712	74	85	km|	km|	ADJ
ejpam-3712	74	86	√	√	NUM
ejpam-3712	74	87	n+	n+	NUM
ejpam-3712	74	88	1−	1−	NUM
ejpam-3712	74	89	√	√	PROPN
ejpam-3712	74	90	m|	m|	NOUN
ejpam-3712	74	91	for	for	ADP
ejpam-3712	74	92	α	α	NOUN
ejpam-3712	74	93	=	=	SYM
ejpam-3712	74	94	1	1	NUM
ejpam-3712	74	95	2	2	NUM
ejpam-3712	74	96	nkm|	nkm|	NUM
ejpam-3712	74	97	1√	1√	NUM
ejpam-3712	74	98	km	km	NOUN
ejpam-3712	75	1	−	−	PROPN
ejpam-3712	75	2	1√	1√	NOUN
ejpam-3712	75	3	n+	n+	ADP
ejpam-3712	75	4	1	1	NUM
ejpam-3712	75	5	|+	|+	NOUN
ejpam-3712	75	6	km|	km|	PROPN
ejpam-3712	75	7	1√	1√	PROPN
ejpam-3712	75	8	n+	n+	ADP
ejpam-3712	75	9	1	1	NUM
ejpam-3712	75	10	−	−	PROPN
ejpam-3712	75	11	1√	1√	PROPN
ejpam-3712	75	12	m	m	NOUN
ejpam-3712	75	13	|	|	ADJ
ejpam-3712	75	14	for	for	ADP
ejpam-3712	75	15	α	α	NOUN
ejpam-3712	75	16	=	=	SYM
ejpam-3712	75	17	−1	−1	NOUN
ejpam-3712	75	18	2	2	NUM
ejpam-3712	75	19	proof	proof	NOUN
ejpam-3712	75	20	.	.	PUNCT
ejpam-3712	76	1	let	let	VERB
ejpam-3712	76	2	g	g	NOUN
ejpam-3712	76	3	be	be	AUX
ejpam-3712	76	4	the	the	DET
ejpam-3712	76	5	pnn(n	pnn(n	PROPN
ejpam-3712	76	6	,	,	PUNCT
ejpam-3712	76	7	k	k	PROPN
ejpam-3712	76	8	,	,	PUNCT
ejpam-3712	76	9	m	m	NOUN
ejpam-3712	76	10	)	)	PUNCT
ejpam-3712	76	11	,	,	PUNCT
ejpam-3712	76	12	for	for	ADP
ejpam-3712	76	13	(	(	PUNCT
ejpam-3712	76	14	n	n	CCONJ
ejpam-3712	76	15	,	,	PUNCT
ejpam-3712	76	16	k	k	PROPN
ejpam-3712	76	17	,	,	PUNCT
ejpam-3712	76	18	m	m	PROPN
ejpam-3712	76	19	)	)	PUNCT
ejpam-3712	76	20	≥	≥	NOUN
ejpam-3712	76	21	1	1	NUM
ejpam-3712	76	22	.	.	PUNCT
ejpam-3712	77	1	the	the	DET
ejpam-3712	77	2	number	number	NOUN
ejpam-3712	77	3	of	of	ADP
ejpam-3712	77	4	vertices	vertex	NOUN
ejpam-3712	77	5	and	and	CCONJ
ejpam-3712	77	6	edges	edge	NOUN
ejpam-3712	77	7	in	in	ADP
ejpam-3712	77	8	pnn(n	pnn(n	PROPN
ejpam-3712	77	9	,	,	PUNCT
ejpam-3712	77	10	k	k	PROPN
ejpam-3712	77	11	,	,	PUNCT
ejpam-3712	77	12	m	m	NOUN
ejpam-3712	77	13	)	)	PUNCT
ejpam-3712	77	14	are	be	AUX
ejpam-3712	77	15	n+k(m+1	n+k(m+1	PRON
ejpam-3712	77	16	)	)	PUNCT
ejpam-3712	77	17	and	and	CCONJ
ejpam-3712	77	18	km(n+1	km(n+1	PROPN
ejpam-3712	77	19	)	)	PUNCT
ejpam-3712	77	20	respectively	respectively	ADV
ejpam-3712	77	21	.	.	PUNCT
ejpam-3712	78	1	there	there	PRON
ejpam-3712	78	2	are	be	VERB
ejpam-3712	78	3	two	two	NUM
ejpam-3712	78	4	types	type	NOUN
ejpam-3712	78	5	of	of	ADP
ejpam-3712	78	6	edges	edge	NOUN
ejpam-3712	78	7	in	in	ADP
ejpam-3712	78	8	pnn(n	pnn(n	PROPN
ejpam-3712	78	9	,	,	PUNCT
ejpam-3712	78	10	k	k	PROPN
ejpam-3712	78	11	,	,	PUNCT
ejpam-3712	78	12	m	m	NOUN
ejpam-3712	78	13	)	)	PUNCT
ejpam-3712	78	14	based	base	VERB
ejpam-3712	78	15	on	on	ADP
ejpam-3712	78	16	degrees	degree	NOUN
ejpam-3712	78	17	of	of	ADP
ejpam-3712	78	18	end	end	NOUN
ejpam-3712	78	19	vertices	vertex	NOUN
ejpam-3712	78	20	of	of	ADP
ejpam-3712	78	21	each	each	DET
ejpam-3712	78	22	edge	edge	NOUN
ejpam-3712	78	23	.	.	PUNCT
ejpam-3712	79	1	table	table	NOUN
ejpam-3712	79	2	1	1	NUM
ejpam-3712	79	3	shows	show	VERB
ejpam-3712	79	4	such	such	DET
ejpam-3712	79	5	an	an	DET
ejpam-3712	79	6	edge	edge	NOUN
ejpam-3712	79	7	partition	partition	NOUN
ejpam-3712	79	8	of	of	ADP
ejpam-3712	79	9	pnn(n	pnn(n	PROPN
ejpam-3712	79	10	,	,	PUNCT
ejpam-3712	79	11	k	k	PROPN
ejpam-3712	79	12	,	,	PUNCT
ejpam-3712	79	13	m	m	NOUN
ejpam-3712	79	14	)	)	PUNCT
ejpam-3712	79	15	.	.	PUNCT
ejpam-3712	80	1	now	now	ADV
ejpam-3712	80	2	by	by	ADP
ejpam-3712	80	3	using	use	VERB
ejpam-3712	80	4	the	the	DET
ejpam-3712	80	5	definition	definition	NOUN
ejpam-3712	80	6	of	of	ADP
ejpam-3712	80	7	misbalance	misbalance	NOUN
ejpam-3712	80	8	indices	index	NOUN
ejpam-3712	80	9	and	and	CCONJ
ejpam-3712	80	10	table	table	NOUN
ejpam-3712	80	11	1	1	NUM
ejpam-3712	80	12	we	we	PRON
ejpam-3712	80	13	obtain	obtain	VERB
ejpam-3712	80	14	the	the	DET
ejpam-3712	80	15	required	require	VERB
ejpam-3712	80	16	results	result	NOUN
ejpam-3712	80	17	as	as	SCONJ
ejpam-3712	80	18	follows	follow	VERB
ejpam-3712	80	19	we	we	PRON
ejpam-3712	80	20	consider	consider	VERB
ejpam-3712	80	21	the	the	DET
ejpam-3712	80	22	following	follow	VERB
ejpam-3712	80	23	cases	case	NOUN
ejpam-3712	80	24	for	for	ADP
ejpam-3712	80	25	the	the	DET
ejpam-3712	80	26	possible	possible	ADJ
ejpam-3712	80	27	values	value	NOUN
ejpam-3712	80	28	of	of	ADP
ejpam-3712	80	29	α	α	PRON
ejpam-3712	80	30	case	case	NOUN
ejpam-3712	80	31	1	1	NUM
ejpam-3712	80	32	:	:	PUNCT
ejpam-3712	80	33	α	α	NOUN
ejpam-3712	80	34	=	=	NOUN
ejpam-3712	80	35	1	1	NUM
ejpam-3712	80	36	applying	apply	VERB
ejpam-3712	80	37	the	the	DET
ejpam-3712	80	38	formula	formula	NOUN
ejpam-3712	80	39	of	of	ADP
ejpam-3712	80	40	misbalance	misbalance	NOUN
ejpam-3712	80	41	deg	deg	PROPN
ejpam-3712	80	42	index	index	NOUN
ejpam-3712	80	43	for	for	ADP
ejpam-3712	80	44	α	α	NOUN
ejpam-3712	80	45	=	=	SYM
ejpam-3712	80	46	1	1	NUM
ejpam-3712	80	47	and	and	CCONJ
ejpam-3712	80	48	by	by	ADP
ejpam-3712	80	49	using	use	VERB
ejpam-3712	80	50	edge	edge	NOUN
ejpam-3712	80	51	partition	partition	NOUN
ejpam-3712	80	52	given	give	VERB
ejpam-3712	80	53	in	in	ADP
ejpam-3712	80	54	table	table	NOUN
ejpam-3712	80	55	1	1	NUM
ejpam-3712	80	56	we	we	PRON
ejpam-3712	80	57	get	get	VERB
ejpam-3712	80	58	mbi1	mbi1	PROPN
ejpam-3712	80	59	=	=	SYM
ejpam-3712	80	60	∑	∑	PUNCT
ejpam-3712	80	61	uv∈e(g	uv∈e(g	NOUN
ejpam-3712	80	62	)	)	PUNCT
ejpam-3712	81	1	|	|	ADV
ejpam-3712	81	2	du	du	PROPN
ejpam-3712	82	1	−	−	PROPN
ejpam-3712	82	2	dv	dv	PROPN
ejpam-3712	82	3	|	|	ADV
ejpam-3712	82	4	=	=	PUNCT
ejpam-3712	82	5	∑	∑	PUNCT
ejpam-3712	82	6	uv∈ekm	uv∈ekm	PROPN
ejpam-3712	82	7	,	,	PUNCT
ejpam-3712	82	8	n+1	n+1	PROPN
ejpam-3712	82	9	|	|	PROPN
ejpam-3712	82	10	du	du	PROPN
ejpam-3712	83	1	−	−	PROPN
ejpam-3712	83	2	dv	dv	PROPN
ejpam-3712	84	1	|	|	PROPN
ejpam-3712	85	1	+	+	CCONJ
ejpam-3712	85	2	∑	∑	ADP
ejpam-3712	85	3	uv∈en+1,m	uv∈en+1,m	PROPN
ejpam-3712	85	4	|	|	ADV
ejpam-3712	85	5	du	du	PROPN
ejpam-3712	86	1	−	−	PROPN
ejpam-3712	86	2	dv	dv	PROPN
ejpam-3712	86	3	|	|	ADV
ejpam-3712	86	4	=	=	PRON
ejpam-3712	86	5	nkm	nkm	VERB
ejpam-3712	86	6	|	|	ADV
ejpam-3712	86	7	km−	km−	X
ejpam-3712	86	8	(	(	PUNCT
ejpam-3712	86	9	n+	n+	NOUN
ejpam-3712	86	10	1	1	X
ejpam-3712	86	11	)	)	PUNCT
ejpam-3712	87	1	|	|	ADV
ejpam-3712	87	2	+	+	NUM
ejpam-3712	87	3	km	km	NOUN
ejpam-3712	87	4	|	|	ADV
ejpam-3712	87	5	(	(	PUNCT
ejpam-3712	87	6	n+	n+	NUM
ejpam-3712	87	7	1)−m	1)−m	NUM
ejpam-3712	88	1	|	|	NOUN
ejpam-3712	88	2	=	=	SYM
ejpam-3712	88	3	km	km	PROPN
ejpam-3712	88	4	[	[	PUNCT
ejpam-3712	88	5	n	n	NOUN
ejpam-3712	88	6	|	|	ADV
ejpam-3712	88	7	km−	km−	X
ejpam-3712	88	8	(	(	PUNCT
ejpam-3712	88	9	n+	n+	NOUN
ejpam-3712	88	10	1	1	X
ejpam-3712	88	11	)	)	PUNCT
ejpam-3712	89	1	|	|	ADV
ejpam-3712	90	1	+	+	CCONJ
ejpam-3712	90	2	|	|	ADV
ejpam-3712	90	3	(	(	PUNCT
ejpam-3712	90	4	n+	n+	NUM
ejpam-3712	90	5	1)−m	1)−m	NUM
ejpam-3712	90	6	|	|	NOUN
ejpam-3712	90	7	]	]	PUNCT
ejpam-3712	90	8	case	case	NOUN
ejpam-3712	90	9	2	2	NUM
ejpam-3712	90	10	:	:	PUNCT
ejpam-3712	90	11	α	α	NOUN
ejpam-3712	90	12	=	=	SYM
ejpam-3712	90	13	−1	−1	NOUN
ejpam-3712	90	14	,	,	PUNCT
ejpam-3712	90	15	applying	apply	VERB
ejpam-3712	90	16	the	the	DET
ejpam-3712	90	17	formula	formula	NOUN
ejpam-3712	90	18	of	of	ADP
ejpam-3712	90	19	misbalance	misbalance	NOUN
ejpam-3712	90	20	indeg	indeg	ADJ
ejpam-3712	90	21	index	index	NOUN
ejpam-3712	90	22	for	for	ADP
ejpam-3712	90	23	α	α	NOUN
ejpam-3712	90	24	=	=	PUNCT
ejpam-3712	90	25	−1	−1	NOUN
ejpam-3712	90	26	and	and	CCONJ
ejpam-3712	90	27	by	by	ADP
ejpam-3712	90	28	using	use	VERB
ejpam-3712	90	29	edge	edge	NOUN
ejpam-3712	90	30	partition	partition	NOUN
ejpam-3712	90	31	given	give	VERB
ejpam-3712	90	32	in	in	ADP
ejpam-3712	90	33	table	table	NOUN
ejpam-3712	90	34	1	1	NUM
ejpam-3712	90	35	we	we	PRON
ejpam-3712	90	36	get	get	VERB
ejpam-3712	90	37	mbi−1	mbi−1	PROPN
ejpam-3712	90	38	=	=	SYM
ejpam-3712	90	39	∑	∑	NOUN
ejpam-3712	90	40	uv∈e(g	uv∈e(g	NOUN
ejpam-3712	90	41	)	)	PUNCT
ejpam-3712	90	42	|	|	ADV
ejpam-3712	90	43	1	1	NUM
ejpam-3712	90	44	du	du	NOUN
ejpam-3712	90	45	−	−	PROPN
ejpam-3712	90	46	1	1	NUM
ejpam-3712	90	47	dv	dv	PROPN
ejpam-3712	90	48	|	|	ADV
ejpam-3712	90	49	=	=	PUNCT
ejpam-3712	90	50	∑	∑	PUNCT
ejpam-3712	90	51	uv∈ekm	uv∈ekm	PROPN
ejpam-3712	90	52	,	,	PUNCT
ejpam-3712	90	53	n+1	n+1	PROPN
ejpam-3712	90	54	|	|	ADJ
ejpam-3712	90	55	1	1	NUM
ejpam-3712	90	56	du	du	NOUN
ejpam-3712	90	57	−	−	PROPN
ejpam-3712	90	58	1	1	NUM
ejpam-3712	90	59	dv	dv	PROPN
ejpam-3712	91	1	|	|	NOUN
ejpam-3712	91	2	+	+	CCONJ
ejpam-3712	91	3	∑	∑	ADP
ejpam-3712	91	4	uv∈en+1,m	uv∈en+1,m	NOUN
ejpam-3712	91	5	|	|	ADV
ejpam-3712	91	6	1	1	NUM
ejpam-3712	91	7	du	du	NOUN
ejpam-3712	91	8	−	−	PROPN
ejpam-3712	91	9	1	1	NUM
ejpam-3712	91	10	dv	dv	PROPN
ejpam-3712	91	11	|	|	ADV
ejpam-3712	91	12	=	=	PRON
ejpam-3712	91	13	nkm	nkm	VERB
ejpam-3712	91	14	|	|	ADV
ejpam-3712	91	15	1	1	NUM
ejpam-3712	91	16	km	km	NOUN
ejpam-3712	91	17	−	−	NOUN
ejpam-3712	91	18	1	1	NUM
ejpam-3712	91	19	n+	n+	SYM
ejpam-3712	91	20	1	1	NUM
ejpam-3712	92	1	|	|	ADV
ejpam-3712	92	2	+	+	NOUN
ejpam-3712	92	3	km	km	NOUN
ejpam-3712	92	4	|	|	ADV
ejpam-3712	92	5	1	1	NUM
ejpam-3712	92	6	n+	n+	ADP
ejpam-3712	92	7	1	1	NUM
ejpam-3712	92	8	−	−	NUM
ejpam-3712	92	9	1	1	NUM
ejpam-3712	92	10	m	m	NOUN
ejpam-3712	92	11	|	|	NOUN
ejpam-3712	92	12	=	=	SYM
ejpam-3712	92	13	km	km	PROPN
ejpam-3712	92	14	[	[	PUNCT
ejpam-3712	92	15	n	n	CCONJ
ejpam-3712	92	16	|	|	ADV
ejpam-3712	92	17	1	1	NUM
ejpam-3712	92	18	km	km	NOUN
ejpam-3712	92	19	−	−	NOUN
ejpam-3712	92	20	1	1	NUM
ejpam-3712	92	21	n+	n+	SYM
ejpam-3712	92	22	1	1	NUM
ejpam-3712	93	1	|	|	ADV
ejpam-3712	94	1	+	+	CCONJ
ejpam-3712	94	2	|	|	ADV
ejpam-3712	94	3	1	1	NUM
ejpam-3712	94	4	n+	n+	ADP
ejpam-3712	94	5	1	1	NUM
ejpam-3712	94	6	−	−	NUM
ejpam-3712	94	7	1	1	NUM
ejpam-3712	94	8	m	m	NOUN
ejpam-3712	94	9	|	|	ADV
ejpam-3712	94	10	]	]	PUNCT
ejpam-3712	94	11	t.	t.	PROPN
ejpam-3712	94	12	deepika	deepika	PROPN
ejpam-3712	94	13	,	,	PUNCT
ejpam-3712	94	14	v.	v.	ADP
ejpam-3712	94	15	lokesha	lokesha	PROPN
ejpam-3712	94	16	/	/	SYM
ejpam-3712	94	17	eur	eur	PROPN
ejpam-3712	94	18	.	.	PUNCT
ejpam-3712	95	1	j.	j.	PROPN
ejpam-3712	95	2	pure	pure	PROPN
ejpam-3712	95	3	appl	appl	PROPN
ejpam-3712	95	4	.	.	PROPN
ejpam-3712	95	5	math	math	PROPN
ejpam-3712	95	6	,	,	PUNCT
ejpam-3712	95	7	13	13	NUM
ejpam-3712	95	8	(	(	PUNCT
ejpam-3712	95	9	5	5	NUM
ejpam-3712	95	10	)	)	PUNCT
ejpam-3712	95	11	(	(	PUNCT
ejpam-3712	95	12	2020	2020	NUM
ejpam-3712	95	13	)	)	PUNCT
ejpam-3712	95	14	,	,	PUNCT
ejpam-3712	95	15	1149	1149	NUM
ejpam-3712	95	16	-	-	SYM
ejpam-3712	95	17	1161	1161	NUM
ejpam-3712	95	18	1155	1155	NUM
ejpam-3712	95	19	case	case	NOUN
ejpam-3712	95	20	3	3	NUM
ejpam-3712	95	21	:	:	PUNCT
ejpam-3712	95	22	α	α	NOUN
ejpam-3712	95	23	=	=	SYM
ejpam-3712	95	24	1	1	NUM
ejpam-3712	95	25	2	2	NUM
ejpam-3712	95	26	,	,	PUNCT
ejpam-3712	95	27	edge	edge	VERB
ejpam-3712	95	28	partition	partition	NOUN
ejpam-3712	95	29	for	for	ADP
ejpam-3712	95	30	misbalance	misbalance	NOUN
ejpam-3712	95	31	rodeg	rodeg	ADJ
ejpam-3712	95	32	index	index	NOUN
ejpam-3712	95	33	whenα	whenα	NOUN
ejpam-3712	95	34	=	=	NOUN
ejpam-3712	95	35	1	1	NUM
ejpam-3712	95	36	2	2	NUM
ejpam-3712	95	37	we	we	PRON
ejpam-3712	95	38	get	get	VERB
ejpam-3712	95	39	mbi	mbi	NOUN
ejpam-3712	95	40	1	1	NUM
ejpam-3712	95	41	2	2	NUM
ejpam-3712	95	42	=	=	SYM
ejpam-3712	95	43	∑	∑	NOUN
ejpam-3712	95	44	uv∈e(g	uv∈e(g	NOUN
ejpam-3712	95	45	)	)	PUNCT
ejpam-3712	96	1	|	|	ADV
ejpam-3712	96	2	√	√	ADP
ejpam-3712	96	3	du	du	PROPN
ejpam-3712	96	4	−	−	PROPN
ejpam-3712	97	1	√	√	PROPN
ejpam-3712	97	2	dv	dv	PROPN
ejpam-3712	97	3	|	|	NOUN
ejpam-3712	97	4	=	=	X
ejpam-3712	97	5	∑	∑	PUNCT
ejpam-3712	97	6	uv∈ekm	uv∈ekm	PROPN
ejpam-3712	97	7	,	,	PUNCT
ejpam-3712	97	8	n+1	n+1	PROPN
ejpam-3712	97	9	|	|	ADV
ejpam-3712	97	10	√	√	ADV
ejpam-3712	97	11	du	du	PROPN
ejpam-3712	97	12	−	−	PROPN
ejpam-3712	97	13	√	√	PROPN
ejpam-3712	98	1	dv	dv	PROPN
ejpam-3712	98	2	|	|	INTJ
ejpam-3712	98	3	+	+	CCONJ
ejpam-3712	98	4	∑	∑	ADP
ejpam-3712	98	5	uv∈en+1,m	uv∈en+1,m	PROPN
ejpam-3712	98	6	|	|	ADV
ejpam-3712	98	7	√	√	PROPN
ejpam-3712	98	8	du	du	PROPN
ejpam-3712	98	9	−	−	PROPN
ejpam-3712	99	1	√	√	PROPN
ejpam-3712	100	1	dv	dv	PROPN
ejpam-3712	101	1	|	|	NOUN
ejpam-3712	101	2	=	=	PRON
ejpam-3712	101	3	nkm	nkm	VERB
ejpam-3712	101	4	|	|	ADV
ejpam-3712	101	5	√	√	CCONJ
ejpam-3712	101	6	km−	km−	PROPN
ejpam-3712	101	7	√	√	NUM
ejpam-3712	101	8	n+	n+	NUM
ejpam-3712	101	9	1	1	NUM
ejpam-3712	102	1	|	|	ADV
ejpam-3712	102	2	+	+	NOUN
ejpam-3712	102	3	km	km	NOUN
ejpam-3712	102	4	|	|	ADV
ejpam-3712	102	5	√	√	PUNCT
ejpam-3712	102	6	n+	n+	PUNCT
ejpam-3712	102	7	1−	1−	NUM
ejpam-3712	103	1	√	√	INTJ
ejpam-3712	103	2	m	m	VERB
ejpam-3712	103	3	|	|	NOUN
ejpam-3712	104	1	=	=	PRON
ejpam-3712	104	2	[	[	PUNCT
ejpam-3712	104	3	|	|	ADV
ejpam-3712	104	4	√	√	CCONJ
ejpam-3712	104	5	km−	km−	PROPN
ejpam-3712	104	6	√	√	NUM
ejpam-3712	104	7	n+	n+	ADP
ejpam-3712	104	8	1	1	NUM
ejpam-3712	105	1	|	|	ADV
ejpam-3712	106	1	+	+	CCONJ
ejpam-3712	106	2	|	|	ADV
ejpam-3712	106	3	√	√	ADJ
ejpam-3712	106	4	n+	n+	NUM
ejpam-3712	106	5	1−	1−	NUM
ejpam-3712	106	6	√	√	INTJ
ejpam-3712	107	1	m	m	VERB
ejpam-3712	107	2	|	|	ADV
ejpam-3712	107	3	]	]	PUNCT
ejpam-3712	107	4	case	case	NOUN
ejpam-3712	107	5	4	4	NUM
ejpam-3712	107	6	:	:	PUNCT
ejpam-3712	108	1	α	α	NOUN
ejpam-3712	108	2	=	=	SYM
ejpam-3712	108	3	−1	−1	NOUN
ejpam-3712	108	4	2	2	NUM
ejpam-3712	108	5	,	,	PUNCT
ejpam-3712	108	6	for	for	ADP
ejpam-3712	108	7	misbalance	misbalance	NOUN
ejpam-3712	108	8	irdeg	irdeg	NOUN
ejpam-3712	108	9	index	index	NOUN
ejpam-3712	108	10	when	when	SCONJ
ejpam-3712	108	11	α	α	PROPN
ejpam-3712	108	12	=	=	VERB
ejpam-3712	108	13	−1	−1	NOUN
ejpam-3712	108	14	2	2	NUM
ejpam-3712	108	15	using	use	VERB
ejpam-3712	108	16	edge	edge	NOUN
ejpam-3712	108	17	partition	partition	NOUN
ejpam-3712	108	18	given	give	VERB
ejpam-3712	108	19	in	in	ADP
ejpam-3712	108	20	table	table	NOUN
ejpam-3712	108	21	1	1	NUM
ejpam-3712	108	22	we	we	PRON
ejpam-3712	108	23	get	get	VERB
ejpam-3712	108	24	mbi−	mbi−	PROPN
ejpam-3712	108	25	1	1	NUM
ejpam-3712	108	26	2	2	NUM
ejpam-3712	108	27	=	=	SYM
ejpam-3712	108	28	∑	∑	NOUN
ejpam-3712	108	29	uv∈e(g	uv∈e(g	NOUN
ejpam-3712	108	30	)	)	PUNCT
ejpam-3712	108	31	|	|	ADV
ejpam-3712	108	32	1√	1√	PROPN
ejpam-3712	108	33	du	du	PROPN
ejpam-3712	108	34	−	−	PROPN
ejpam-3712	108	35	1√	1√	PROPN
ejpam-3712	108	36	dv	dv	PROPN
ejpam-3712	109	1	|	|	NOUN
ejpam-3712	109	2	=	=	X
ejpam-3712	109	3	∑	∑	PUNCT
ejpam-3712	109	4	uv∈ekm	uv∈ekm	PROPN
ejpam-3712	109	5	,	,	PUNCT
ejpam-3712	109	6	n+1	n+1	PROPN
ejpam-3712	109	7	|	|	PROPN
ejpam-3712	109	8	1√	1√	PROPN
ejpam-3712	109	9	du	du	PROPN
ejpam-3712	109	10	−	−	PROPN
ejpam-3712	109	11	1√	1√	PROPN
ejpam-3712	109	12	dv	dv	PROPN
ejpam-3712	110	1	|	|	PROPN
ejpam-3712	111	1	+	+	CCONJ
ejpam-3712	111	2	∑	∑	ADP
ejpam-3712	111	3	uv∈en+1,m	uv∈en+1,m	ADJ
ejpam-3712	111	4	|	|	PROPN
ejpam-3712	111	5	1√	1√	PROPN
ejpam-3712	111	6	du	du	PROPN
ejpam-3712	111	7	−	−	PROPN
ejpam-3712	111	8	1√	1√	PROPN
ejpam-3712	111	9	dv	dv	PROPN
ejpam-3712	112	1	|	|	NOUN
ejpam-3712	112	2	=	=	PRON
ejpam-3712	112	3	nkm	nkm	VERB
ejpam-3712	112	4	|	|	ADV
ejpam-3712	112	5	1√	1√	NUM
ejpam-3712	112	6	km	km	NOUN
ejpam-3712	112	7	−	−	PROPN
ejpam-3712	112	8	1√	1√	NOUN
ejpam-3712	112	9	n+	n+	ADP
ejpam-3712	112	10	1	1	NUM
ejpam-3712	113	1	|	|	ADV
ejpam-3712	113	2	+	+	NOUN
ejpam-3712	113	3	km	km	NOUN
ejpam-3712	113	4	|	|	ADV
ejpam-3712	113	5	1√	1√	ADJ
ejpam-3712	113	6	n+	n+	ADP
ejpam-3712	113	7	1	1	NUM
ejpam-3712	113	8	−	−	PROPN
ejpam-3712	113	9	1√	1√	PROPN
ejpam-3712	113	10	m	m	NOUN
ejpam-3712	113	11	|	|	NOUN
ejpam-3712	113	12	=	=	SYM
ejpam-3712	113	13	km	km	PROPN
ejpam-3712	113	14	[	[	PUNCT
ejpam-3712	113	15	n	n	CCONJ
ejpam-3712	113	16	|	|	ADV
ejpam-3712	113	17	1√	1√	NUM
ejpam-3712	113	18	km	km	NOUN
ejpam-3712	113	19	−	−	PROPN
ejpam-3712	113	20	1√	1√	NOUN
ejpam-3712	113	21	n+	n+	ADP
ejpam-3712	113	22	1	1	NUM
ejpam-3712	114	1	|	|	ADV
ejpam-3712	115	1	+	+	CCONJ
ejpam-3712	115	2	|	|	ADV
ejpam-3712	115	3	1√	1√	ADJ
ejpam-3712	115	4	n+	n+	ADP
ejpam-3712	115	5	1	1	NUM
ejpam-3712	115	6	−	−	PROPN
ejpam-3712	115	7	1√	1√	PROPN
ejpam-3712	115	8	m	m	NOUN
ejpam-3712	115	9	|	|	ADV
ejpam-3712	115	10	]	]	PUNCT
ejpam-3712	115	11	theorem	theorem	NOUN
ejpam-3712	115	12	2	2	X
ejpam-3712	115	13	.	.	PUNCT
ejpam-3712	116	1	let	let	VERB
ejpam-3712	116	2	g	g	NOUN
ejpam-3712	116	3	be	be	AUX
ejpam-3712	116	4	the	the	DET
ejpam-3712	116	5	probabilistic	probabilistic	ADJ
ejpam-3712	116	6	neural	neural	ADJ
ejpam-3712	116	7	network	network	NOUN
ejpam-3712	116	8	pnn(n	pnn(n	PROPN
ejpam-3712	116	9	,	,	PUNCT
ejpam-3712	116	10	k	k	PROPN
ejpam-3712	116	11	,	,	PUNCT
ejpam-3712	116	12	m	m	PROPN
ejpam-3712	116	13	)	)	PUNCT
ejpam-3712	116	14	then	then	ADV
ejpam-3712	116	15	for	for	ADP
ejpam-3712	116	16	(	(	PUNCT
ejpam-3712	116	17	n	n	CCONJ
ejpam-3712	116	18	,	,	PUNCT
ejpam-3712	116	19	k	k	PROPN
ejpam-3712	116	20	,	,	PUNCT
ejpam-3712	116	21	m	m	PROPN
ejpam-3712	116	22	)	)	PUNCT
ejpam-3712	116	23	≥	≥	NOUN
ejpam-3712	116	24	1	1	NUM
ejpam-3712	116	25	,	,	PUNCT
ejpam-3712	116	26	its	its	PRON
ejpam-3712	116	27	max	max	PROPN
ejpam-3712	116	28	-	-	PUNCT
ejpam-3712	116	29	min	min	PROPN
ejpam-3712	116	30	deg	deg	PROPN
ejpam-3712	116	31	index	index	PROPN
ejpam-3712	116	32	,	,	PUNCT
ejpam-3712	116	33	max	max	PROPN
ejpam-3712	116	34	-	-	PUNCT
ejpam-3712	116	35	min	min	PROPN
ejpam-3712	116	36	sdeg	sdeg	ADJ
ejpam-3712	116	37	index	index	NOUN
ejpam-3712	116	38	and	and	CCONJ
ejpam-3712	116	39	max	max	PROPN
ejpam-3712	116	40	rodeg	rodeg	PROPN
ejpam-3712	116	41	index	index	NOUN
ejpam-3712	116	42	is	be	AUX
ejpam-3712	116	43	given	give	VERB
ejpam-3712	116	44	by	by	ADP
ejpam-3712	116	45	max	max	PROPN
ejpam-3712	116	46	-	-	PUNCT
ejpam-3712	116	47	min	min	PROPN
ejpam-3712	116	48	deg	deg	PROPN
ejpam-3712	116	49	index	index	NOUN
ejpam-3712	116	50	=	=	PROPN
ejpam-3712	116	51	k	k	PROPN
ejpam-3712	117	1	n+	n+	ADP
ejpam-3712	117	2	1	1	NUM
ejpam-3712	117	3	(	(	PUNCT
ejpam-3712	117	4	m2nk	m2nk	NOUN
ejpam-3712	117	5	+	+	CCONJ
ejpam-3712	117	6	(	(	PUNCT
ejpam-3712	117	7	n+	n+	X
ejpam-3712	117	8	1)2	1)2	NUM
ejpam-3712	117	9	)	)	PUNCT
ejpam-3712	117	10	max	max	PROPN
ejpam-3712	117	11	-	-	PUNCT
ejpam-3712	117	12	min	min	PROPN
ejpam-3712	117	13	sdeg	sdeg	ADJ
ejpam-3712	117	14	index	index	NOUN
ejpam-3712	117	15	=	=	SYM
ejpam-3712	117	16	k	k	PROPN
ejpam-3712	117	17	[	[	PUNCT
ejpam-3712	117	18	k2m4n+	k2m4n+	PROPN
ejpam-3712	117	19	(	(	PUNCT
ejpam-3712	117	20	n+	n+	NUM
ejpam-3712	117	21	1)4	1)4	NUM
ejpam-3712	117	22	(	(	PUNCT
ejpam-3712	117	23	n+	n+	NUM
ejpam-3712	117	24	1)2	1)2	NUM
ejpam-3712	117	25	m	m	NOUN
ejpam-3712	117	26	]	]	X
ejpam-3712	117	27	max	max	ADJ
ejpam-3712	117	28	-	-	PUNCT
ejpam-3712	117	29	rodeg	rodeg	ADJ
ejpam-3712	117	30	index	index	NOUN
ejpam-3712	117	31	=	=	SYM
ejpam-3712	117	32	km	km	NOUN
ejpam-3712	117	33	[	[	PUNCT
ejpam-3712	117	34	n	n	CCONJ
ejpam-3712	117	35	√	√	NUM
ejpam-3712	117	36	km	km	NOUN
ejpam-3712	117	37	n+	n+	ADP
ejpam-3712	117	38	1	1	NUM
ejpam-3712	117	39	+	+	CCONJ
ejpam-3712	117	40	√	√	NUM
ejpam-3712	117	41	n+	n+	PUNCT
ejpam-3712	117	42	1	1	NUM
ejpam-3712	117	43	m	m	NOUN
ejpam-3712	117	44	]	]	PUNCT
ejpam-3712	117	45	proof	proof	NOUN
ejpam-3712	117	46	.	.	PUNCT
ejpam-3712	118	1	let	let	VERB
ejpam-3712	118	2	g	g	NOUN
ejpam-3712	118	3	be	be	AUX
ejpam-3712	118	4	the	the	DET
ejpam-3712	118	5	pnn(n	pnn(n	PROPN
ejpam-3712	118	6	,	,	PUNCT
ejpam-3712	118	7	k	k	PROPN
ejpam-3712	118	8	,	,	PUNCT
ejpam-3712	118	9	m	m	NOUN
ejpam-3712	118	10	)	)	PUNCT
ejpam-3712	118	11	,	,	PUNCT
ejpam-3712	118	12	for	for	ADP
ejpam-3712	118	13	(	(	PUNCT
ejpam-3712	118	14	n	n	CCONJ
ejpam-3712	118	15	,	,	PUNCT
ejpam-3712	118	16	k	k	PROPN
ejpam-3712	118	17	,	,	PUNCT
ejpam-3712	118	18	m	m	PROPN
ejpam-3712	118	19	)	)	PUNCT
ejpam-3712	118	20	≥	≥	NOUN
ejpam-3712	118	21	1	1	NUM
ejpam-3712	118	22	.	.	PUNCT
ejpam-3712	119	1	the	the	DET
ejpam-3712	119	2	number	number	NOUN
ejpam-3712	119	3	of	of	ADP
ejpam-3712	119	4	vertices	vertex	NOUN
ejpam-3712	119	5	and	and	CCONJ
ejpam-3712	119	6	edges	edge	NOUN
ejpam-3712	119	7	in	in	ADP
ejpam-3712	119	8	pnn(n	pnn(n	PROPN
ejpam-3712	119	9	,	,	PUNCT
ejpam-3712	119	10	k	k	PROPN
ejpam-3712	119	11	,	,	PUNCT
ejpam-3712	119	12	m	m	NOUN
ejpam-3712	119	13	)	)	PUNCT
ejpam-3712	119	14	are	be	AUX
ejpam-3712	119	15	n+k(m+1	n+k(m+1	PRON
ejpam-3712	119	16	)	)	PUNCT
ejpam-3712	119	17	and	and	CCONJ
ejpam-3712	119	18	km(n+1	km(n+1	PROPN
ejpam-3712	119	19	)	)	PUNCT
ejpam-3712	119	20	respectively	respectively	ADV
ejpam-3712	119	21	.	.	PUNCT
ejpam-3712	120	1	there	there	PRON
ejpam-3712	120	2	are	be	VERB
ejpam-3712	120	3	two	two	NUM
ejpam-3712	120	4	types	type	NOUN
ejpam-3712	120	5	of	of	ADP
ejpam-3712	120	6	edges	edge	NOUN
ejpam-3712	120	7	in	in	ADP
ejpam-3712	120	8	pnn(n	pnn(n	PROPN
ejpam-3712	120	9	,	,	PUNCT
ejpam-3712	120	10	k	k	PROPN
ejpam-3712	120	11	,	,	PUNCT
ejpam-3712	120	12	m	m	NOUN
ejpam-3712	120	13	)	)	PUNCT
ejpam-3712	120	14	based	base	VERB
ejpam-3712	120	15	on	on	ADP
ejpam-3712	120	16	degrees	degree	NOUN
ejpam-3712	120	17	of	of	ADP
ejpam-3712	120	18	end	end	NOUN
ejpam-3712	120	19	vertices	vertex	NOUN
ejpam-3712	120	20	of	of	ADP
ejpam-3712	120	21	each	each	DET
ejpam-3712	120	22	edge	edge	NOUN
ejpam-3712	120	23	.	.	PUNCT
ejpam-3712	121	1	table	table	NOUN
ejpam-3712	121	2	1	1	NUM
ejpam-3712	121	3	shows	show	VERB
ejpam-3712	121	4	such	such	DET
ejpam-3712	121	5	an	an	DET
ejpam-3712	121	6	edge	edge	NOUN
ejpam-3712	121	7	partition	partition	NOUN
ejpam-3712	121	8	of	of	ADP
ejpam-3712	121	9	pnn(n	pnn(n	PROPN
ejpam-3712	121	10	,	,	PUNCT
ejpam-3712	121	11	k	k	PROPN
ejpam-3712	121	12	,	,	PUNCT
ejpam-3712	121	13	m	m	NOUN
ejpam-3712	121	14	)	)	PUNCT
ejpam-3712	121	15	.	.	PUNCT
ejpam-3712	122	1	now	now	ADV
ejpam-3712	122	2	by	by	ADP
ejpam-3712	122	3	using	use	VERB
ejpam-3712	122	4	the	the	DET
ejpam-3712	122	5	formulas	formula	NOUN
ejpam-3712	122	6	of	of	ADP
ejpam-3712	122	7	max	max	PROPN
ejpam-3712	122	8	-	-	PUNCT
ejpam-3712	122	9	min	min	PROPN
ejpam-3712	122	10	deg	deg	PROPN
ejpam-3712	122	11	index	index	PROPN
ejpam-3712	122	12	,	,	PUNCT
ejpam-3712	122	13	max	max	PROPN
ejpam-3712	122	14	-	-	PUNCT
ejpam-3712	122	15	min	min	PROPN
ejpam-3712	122	16	sdeg	sdeg	ADJ
ejpam-3712	122	17	index	index	NOUN
ejpam-3712	122	18	,	,	PUNCT
ejpam-3712	122	19	max	max	PROPN
ejpam-3712	122	20	rodeg	rodeg	PROPN
ejpam-3712	122	21	index	index	NOUN
ejpam-3712	122	22	and	and	CCONJ
ejpam-3712	122	23	table	table	NOUN
ejpam-3712	122	24	1	1	NUM
ejpam-3712	122	25	we	we	PRON
ejpam-3712	122	26	obtain	obtain	VERB
ejpam-3712	122	27	the	the	DET
ejpam-3712	122	28	required	require	VERB
ejpam-3712	122	29	results	result	NOUN
ejpam-3712	122	30	as	as	SCONJ
ejpam-3712	122	31	follows	follow	VERB
ejpam-3712	122	32	max	max	PROPN
ejpam-3712	122	33	-	-	PUNCT
ejpam-3712	122	34	min	min	PROPN
ejpam-3712	122	35	deg	deg	PROPN
ejpam-3712	122	36	index	index	NOUN
ejpam-3712	122	37	=	=	SYM
ejpam-3712	122	38	∑	∑	NOUN
ejpam-3712	122	39	uv∈e(g	uv∈e(g	NOUN
ejpam-3712	122	40	)	)	PUNCT
ejpam-3712	122	41	max(du	max(du	NOUN
ejpam-3712	122	42	,	,	PUNCT
ejpam-3712	122	43	dv	dv	PROPN
ejpam-3712	122	44	)	)	PUNCT
ejpam-3712	122	45	min(du	min(du	PROPN
ejpam-3712	122	46	,	,	PUNCT
ejpam-3712	122	47	dv	dv	PROPN
ejpam-3712	122	48	)	)	PUNCT
ejpam-3712	122	49	t.	t.	PROPN
ejpam-3712	122	50	deepika	deepika	PROPN
ejpam-3712	122	51	,	,	PUNCT
ejpam-3712	122	52	v.	v.	ADP
ejpam-3712	122	53	lokesha	lokesha	PROPN
ejpam-3712	122	54	/	/	SYM
ejpam-3712	122	55	eur	eur	PROPN
ejpam-3712	122	56	.	.	PUNCT
ejpam-3712	123	1	j.	j.	PROPN
ejpam-3712	123	2	pure	pure	PROPN
ejpam-3712	123	3	appl	appl	PROPN
ejpam-3712	123	4	.	.	PROPN
ejpam-3712	123	5	math	math	PROPN
ejpam-3712	123	6	,	,	PUNCT
ejpam-3712	123	7	13	13	NUM
ejpam-3712	123	8	(	(	PUNCT
ejpam-3712	123	9	5	5	NUM
ejpam-3712	123	10	)	)	PUNCT
ejpam-3712	123	11	(	(	PUNCT
ejpam-3712	123	12	2020	2020	NUM
ejpam-3712	123	13	)	)	PUNCT
ejpam-3712	123	14	,	,	PUNCT
ejpam-3712	123	15	1149	1149	NUM
ejpam-3712	123	16	-	-	SYM
ejpam-3712	123	17	1161	1161	NUM
ejpam-3712	123	18	1156	1156	NUM
ejpam-3712	123	19	=	=	PUNCT
ejpam-3712	123	20	∑	∑	PUNCT
ejpam-3712	123	21	uv∈ekm	uv∈ekm	PROPN
ejpam-3712	123	22	,	,	PUNCT
ejpam-3712	123	23	n+1	n+1	NUM
ejpam-3712	123	24	max(du	max(du	NOUN
ejpam-3712	123	25	,	,	PUNCT
ejpam-3712	123	26	dv	dv	PROPN
ejpam-3712	123	27	)	)	PUNCT
ejpam-3712	123	28	min(du	min(du	PROPN
ejpam-3712	123	29	,	,	PUNCT
ejpam-3712	123	30	dv	dv	PROPN
ejpam-3712	123	31	)	)	PUNCT
ejpam-3712	124	1	+	+	CCONJ
ejpam-3712	124	2	∑	∑	PROPN
ejpam-3712	124	3	uv∈en+1,m	uv∈en+1,m	NOUN
ejpam-3712	124	4	max(du	max(du	NOUN
ejpam-3712	124	5	,	,	PUNCT
ejpam-3712	124	6	dv	dv	PROPN
ejpam-3712	124	7	)	)	PUNCT
ejpam-3712	124	8	min(du	min(du	PROPN
ejpam-3712	124	9	,	,	PUNCT
ejpam-3712	124	10	dv	dv	PROPN
ejpam-3712	124	11	)	)	PUNCT
ejpam-3712	124	12	=	=	SYM
ejpam-3712	124	13	nkm	nkm	X
ejpam-3712	124	14	(	(	PUNCT
ejpam-3712	124	15	km	km	NOUN
ejpam-3712	124	16	n+	n+	ADP
ejpam-3712	124	17	1	1	NUM
ejpam-3712	124	18	)	)	PUNCT
ejpam-3712	125	1	+	+	NUM
ejpam-3712	125	2	km	km	NOUN
ejpam-3712	125	3	(	(	PUNCT
ejpam-3712	125	4	n+	n+	NOUN
ejpam-3712	125	5	1	1	NUM
ejpam-3712	125	6	m	m	NOUN
ejpam-3712	125	7	)	)	PUNCT
ejpam-3712	126	1	=	=	SYM
ejpam-3712	126	2	k	k	PROPN
ejpam-3712	126	3	n+	n+	PUNCT
ejpam-3712	126	4	1	1	NUM
ejpam-3712	126	5	(	(	PUNCT
ejpam-3712	126	6	m2nk	m2nk	NOUN
ejpam-3712	126	7	+	+	CCONJ
ejpam-3712	126	8	(	(	PUNCT
ejpam-3712	126	9	n+	n+	X
ejpam-3712	126	10	1)2	1)2	NUM
ejpam-3712	126	11	)	)	PUNCT
ejpam-3712	126	12	max	max	PROPN
ejpam-3712	126	13	-	-	PUNCT
ejpam-3712	126	14	min	min	PROPN
ejpam-3712	126	15	sdeg	sdeg	ADJ
ejpam-3712	126	16	index	index	NOUN
ejpam-3712	126	17	=	=	SYM
ejpam-3712	126	18	∑	∑	PUNCT
ejpam-3712	126	19	uv∈e(g	uv∈e(g	NUM
ejpam-3712	126	20	)	)	PUNCT
ejpam-3712	126	21	(	(	PUNCT
ejpam-3712	126	22	max(du	max(du	PROPN
ejpam-3712	126	23	,	,	PUNCT
ejpam-3712	126	24	dv	dv	PROPN
ejpam-3712	126	25	)	)	PUNCT
ejpam-3712	126	26	min(du	min(du	PROPN
ejpam-3712	126	27	,	,	PUNCT
ejpam-3712	126	28	dv	dv	PROPN
ejpam-3712	126	29	)	)	PUNCT
ejpam-3712	126	30	)	)	PUNCT
ejpam-3712	126	31	2	2	NUM
ejpam-3712	126	32	=	=	SYM
ejpam-3712	126	33	∑	∑	PUNCT
ejpam-3712	126	34	uv∈ekm	uv∈ekm	PROPN
ejpam-3712	126	35	,	,	PUNCT
ejpam-3712	126	36	n+1	n+1	PROPN
ejpam-3712	126	37	(	(	PUNCT
ejpam-3712	126	38	max(du	max(du	PROPN
ejpam-3712	126	39	,	,	PUNCT
ejpam-3712	126	40	dv	dv	PROPN
ejpam-3712	126	41	)	)	PUNCT
ejpam-3712	126	42	min(du	min(du	PROPN
ejpam-3712	126	43	,	,	PUNCT
ejpam-3712	126	44	dv	dv	PROPN
ejpam-3712	126	45	)	)	PUNCT
ejpam-3712	126	46	)	)	PUNCT
ejpam-3712	126	47	2	2	NUM
ejpam-3712	127	1	+	+	CCONJ
ejpam-3712	127	2	∑	∑	ADV
ejpam-3712	127	3	uv∈en+1,m	uv∈en+1,m	NOUN
ejpam-3712	127	4	(	(	PUNCT
ejpam-3712	127	5	max(du	max(du	PROPN
ejpam-3712	127	6	,	,	PUNCT
ejpam-3712	127	7	dv	dv	PROPN
ejpam-3712	127	8	)	)	PUNCT
ejpam-3712	127	9	min(du	min(du	PROPN
ejpam-3712	127	10	,	,	PUNCT
ejpam-3712	127	11	dv	dv	PROPN
ejpam-3712	127	12	)	)	PUNCT
ejpam-3712	127	13	)	)	PUNCT
ejpam-3712	127	14	2	2	NUM
ejpam-3712	127	15	=	=	SYM
ejpam-3712	127	16	nkm	nkm	X
ejpam-3712	127	17	(	(	PUNCT
ejpam-3712	127	18	km	km	NOUN
ejpam-3712	127	19	n+	n+	ADP
ejpam-3712	127	20	1	1	NUM
ejpam-3712	127	21	)	)	SYM
ejpam-3712	127	22	2	2	NUM
ejpam-3712	127	23	+	+	NUM
ejpam-3712	127	24	km	km	PROPN
ejpam-3712	127	25	(	(	PUNCT
ejpam-3712	127	26	n+	n+	NUM
ejpam-3712	127	27	1	1	NUM
ejpam-3712	127	28	m	m	NOUN
ejpam-3712	127	29	)	)	PUNCT
ejpam-3712	127	30	2	2	NUM
ejpam-3712	127	31	=	=	SYM
ejpam-3712	127	32	k	k	X
ejpam-3712	127	33	[	[	PUNCT
ejpam-3712	127	34	k2m4n+	k2m4n+	PROPN
ejpam-3712	127	35	(	(	PUNCT
ejpam-3712	127	36	n+	n+	NUM
ejpam-3712	127	37	1)4	1)4	NUM
ejpam-3712	127	38	(	(	PUNCT
ejpam-3712	127	39	n+	n+	NUM
ejpam-3712	127	40	1)2	1)2	NUM
ejpam-3712	127	41	m	m	NOUN
ejpam-3712	127	42	]	]	X
ejpam-3712	127	43	max	max	PROPN
ejpam-3712	127	44	rodeg	rodeg	PROPN
ejpam-3712	127	45	index	index	NOUN
ejpam-3712	127	46	=	=	SYM
ejpam-3712	127	47	∑	∑	PUNCT
ejpam-3712	127	48	uv∈e(g	uv∈e(g	NUM
ejpam-3712	127	49	)	)	PUNCT
ejpam-3712	127	50	√	√	NOUN
ejpam-3712	127	51	max(du	max(du	NOUN
ejpam-3712	127	52	,	,	PUNCT
ejpam-3712	127	53	dv	dv	PROPN
ejpam-3712	127	54	)	)	PUNCT
ejpam-3712	127	55	min(du	min(du	PROPN
ejpam-3712	127	56	,	,	PUNCT
ejpam-3712	127	57	dv	dv	PROPN
ejpam-3712	127	58	)	)	PUNCT
ejpam-3712	127	59	=	=	SYM
ejpam-3712	127	60	∑	∑	PUNCT
ejpam-3712	127	61	uv∈ekm	uv∈ekm	PROPN
ejpam-3712	127	62	,	,	PUNCT
ejpam-3712	127	63	n+1	n+1	PROPN
ejpam-3712	127	64	√	√	PROPN
ejpam-3712	127	65	max(du	max(du	NOUN
ejpam-3712	127	66	,	,	PUNCT
ejpam-3712	127	67	dv	dv	PROPN
ejpam-3712	127	68	)	)	PUNCT
ejpam-3712	127	69	min(du	min(du	PROPN
ejpam-3712	127	70	,	,	PUNCT
ejpam-3712	127	71	dv	dv	PROPN
ejpam-3712	127	72	)	)	PUNCT
ejpam-3712	127	73	+	+	CCONJ
ejpam-3712	127	74	∑	∑	ADP
ejpam-3712	127	75	uv∈en+1,m	uv∈en+1,m	ADJ
ejpam-3712	127	76	√	√	NUM
ejpam-3712	127	77	max(du	max(du	NOUN
ejpam-3712	127	78	,	,	PUNCT
ejpam-3712	127	79	dv	dv	PROPN
ejpam-3712	127	80	)	)	PUNCT
ejpam-3712	127	81	min(du	min(du	PROPN
ejpam-3712	127	82	,	,	PUNCT
ejpam-3712	127	83	dv	dv	PROPN
ejpam-3712	127	84	)	)	PUNCT
ejpam-3712	127	85	=	=	PRON
ejpam-3712	127	86	nkm	nkm	VERB
ejpam-3712	127	87	√	√	NUM
ejpam-3712	127	88	km	km	NOUN
ejpam-3712	127	89	n+	n+	ADP
ejpam-3712	127	90	1	1	NUM
ejpam-3712	127	91	+	+	NUM
ejpam-3712	127	92	km	km	NOUN
ejpam-3712	127	93	√	√	NUM
ejpam-3712	127	94	n+	n+	PUNCT
ejpam-3712	127	95	1	1	NUM
ejpam-3712	127	96	m	m	NOUN
ejpam-3712	127	97	=	=	VERB
ejpam-3712	127	98	km	km	PROPN
ejpam-3712	127	99	[	[	PUNCT
ejpam-3712	127	100	n	n	CCONJ
ejpam-3712	127	101	√	√	NUM
ejpam-3712	127	102	km	km	NOUN
ejpam-3712	127	103	n+	n+	ADP
ejpam-3712	127	104	1	1	NUM
ejpam-3712	127	105	+	+	CCONJ
ejpam-3712	127	106	√	√	NUM
ejpam-3712	127	107	n+	n+	PUNCT
ejpam-3712	127	108	1	1	NUM
ejpam-3712	127	109	m	m	NOUN
ejpam-3712	127	110	]	]	PUNCT
ejpam-3712	127	111	theorem	theorem	ADJ
ejpam-3712	127	112	3	3	X
ejpam-3712	127	113	.	.	PUNCT
ejpam-3712	128	1	let	let	VERB
ejpam-3712	128	2	g	g	NOUN
ejpam-3712	128	3	be	be	AUX
ejpam-3712	128	4	the	the	DET
ejpam-3712	128	5	probabilistic	probabilistic	ADJ
ejpam-3712	128	6	neural	neural	ADJ
ejpam-3712	128	7	network	network	NOUN
ejpam-3712	128	8	pnn(n	pnn(n	PROPN
ejpam-3712	128	9	,	,	PUNCT
ejpam-3712	128	10	k	k	PROPN
ejpam-3712	128	11	,	,	PUNCT
ejpam-3712	128	12	m	m	PROPN
ejpam-3712	128	13	)	)	PUNCT
ejpam-3712	128	14	then	then	ADV
ejpam-3712	128	15	for	for	ADP
ejpam-3712	128	16	(	(	PUNCT
ejpam-3712	128	17	n	n	CCONJ
ejpam-3712	128	18	,	,	PUNCT
ejpam-3712	128	19	k	k	PROPN
ejpam-3712	128	20	,	,	PUNCT
ejpam-3712	128	21	m	m	PROPN
ejpam-3712	128	22	)	)	PUNCT
ejpam-3712	128	23	≥	≥	NOUN
ejpam-3712	128	24	1	1	NUM
ejpam-3712	128	25	,	,	PUNCT
ejpam-3712	128	26	its	its	PRON
ejpam-3712	128	27	min	min	ADJ
ejpam-3712	128	28	-	-	ADJ
ejpam-3712	128	29	max	max	ADJ
ejpam-3712	128	30	rodeg	rodeg	ADJ
ejpam-3712	128	31	index	index	NOUN
ejpam-3712	128	32	and	and	CCONJ
ejpam-3712	128	33	min	min	NOUN
ejpam-3712	128	34	-	-	ADJ
ejpam-3712	128	35	max	max	PROPN
ejpam-3712	128	36	sdi	sdi	PROPN
ejpam-3712	128	37	index	index	NOUN
ejpam-3712	128	38	is	be	AUX
ejpam-3712	128	39	given	give	VERB
ejpam-3712	128	40	by	by	ADP
ejpam-3712	128	41	min	min	ADJ
ejpam-3712	128	42	-	-	ADJ
ejpam-3712	128	43	max	max	ADJ
ejpam-3712	128	44	rodeg	rodeg	NOUN
ejpam-3712	128	45	index	index	NOUN
ejpam-3712	128	46	=	=	SYM
ejpam-3712	128	47	km	km	NOUN
ejpam-3712	128	48	[	[	PUNCT
ejpam-3712	128	49	n	n	CCONJ
ejpam-3712	128	50	√	√	NUM
ejpam-3712	128	51	n+	n+	NUM
ejpam-3712	128	52	1	1	NUM
ejpam-3712	128	53	km	km	NOUN
ejpam-3712	128	54	+	+	CCONJ
ejpam-3712	128	55	√	√	PROPN
ejpam-3712	128	56	m	m	VERB
ejpam-3712	128	57	n+	n+	ADP
ejpam-3712	128	58	1	1	NUM
ejpam-3712	128	59	]	]	SYM
ejpam-3712	128	60	min	min	ADJ
ejpam-3712	128	61	-	-	ADJ
ejpam-3712	128	62	max	max	ADJ
ejpam-3712	128	63	sdi	sdi	PROPN
ejpam-3712	128	64	index	index	NOUN
ejpam-3712	128	65	=	=	PUNCT
ejpam-3712	128	66	n(n+	n(n+	X
ejpam-3712	129	1	1)4	1)4	PROPN
ejpam-3712	129	2	+	+	NUM
ejpam-3712	129	3	k2m4	k2m4	X
ejpam-3712	129	4	km(n+	km(n+	PROPN
ejpam-3712	129	5	1)2	1)2	NUM
ejpam-3712	129	6	proof	proof	NOUN
ejpam-3712	129	7	.	.	PUNCT
ejpam-3712	130	1	let	let	VERB
ejpam-3712	130	2	g	g	NOUN
ejpam-3712	130	3	be	be	AUX
ejpam-3712	130	4	the	the	DET
ejpam-3712	130	5	pnn(n	pnn(n	PROPN
ejpam-3712	130	6	,	,	PUNCT
ejpam-3712	130	7	k	k	PROPN
ejpam-3712	130	8	,	,	PUNCT
ejpam-3712	130	9	m	m	NOUN
ejpam-3712	130	10	)	)	PUNCT
ejpam-3712	130	11	,	,	PUNCT
ejpam-3712	130	12	for	for	ADP
ejpam-3712	130	13	(	(	PUNCT
ejpam-3712	130	14	n	n	CCONJ
ejpam-3712	130	15	,	,	PUNCT
ejpam-3712	130	16	k	k	PROPN
ejpam-3712	130	17	,	,	PUNCT
ejpam-3712	130	18	m	m	PROPN
ejpam-3712	130	19	)	)	PUNCT
ejpam-3712	130	20	≥	≥	NOUN
ejpam-3712	130	21	1	1	NUM
ejpam-3712	130	22	.	.	PUNCT
ejpam-3712	131	1	the	the	DET
ejpam-3712	131	2	number	number	NOUN
ejpam-3712	131	3	of	of	ADP
ejpam-3712	131	4	vertices	vertex	NOUN
ejpam-3712	131	5	and	and	CCONJ
ejpam-3712	131	6	edges	edge	NOUN
ejpam-3712	131	7	in	in	ADP
ejpam-3712	131	8	pnn(n	pnn(n	PROPN
ejpam-3712	131	9	,	,	PUNCT
ejpam-3712	131	10	k	k	PROPN
ejpam-3712	131	11	,	,	PUNCT
ejpam-3712	131	12	m	m	NOUN
ejpam-3712	131	13	)	)	PUNCT
ejpam-3712	131	14	are	be	AUX
ejpam-3712	131	15	n+	n+	ADP
ejpam-3712	131	16	k(m+	k(m+	NOUN
ejpam-3712	131	17	1	1	NUM
ejpam-3712	131	18	)	)	PUNCT
ejpam-3712	131	19	and	and	CCONJ
ejpam-3712	131	20	km(n+	km(n+	PROPN
ejpam-3712	131	21	1	1	NUM
ejpam-3712	131	22	)	)	PUNCT
ejpam-3712	131	23	respectively	respectively	ADV
ejpam-3712	131	24	.	.	PUNCT
ejpam-3712	132	1	there	there	PRON
ejpam-3712	132	2	are	be	VERB
ejpam-3712	132	3	two	two	NUM
ejpam-3712	132	4	types	type	NOUN
ejpam-3712	132	5	of	of	ADP
ejpam-3712	132	6	edges	edge	NOUN
ejpam-3712	132	7	in	in	ADP
ejpam-3712	132	8	pnn(n	pnn(n	PROPN
ejpam-3712	132	9	,	,	PUNCT
ejpam-3712	132	10	k	k	PROPN
ejpam-3712	132	11	,	,	PUNCT
ejpam-3712	132	12	m	m	NOUN
ejpam-3712	132	13	)	)	PUNCT
ejpam-3712	132	14	based	base	VERB
ejpam-3712	132	15	on	on	ADP
ejpam-3712	132	16	degrees	degree	NOUN
ejpam-3712	132	17	of	of	ADP
ejpam-3712	132	18	end	end	NOUN
ejpam-3712	132	19	vertices	vertex	NOUN
ejpam-3712	132	20	of	of	ADP
ejpam-3712	132	21	each	each	DET
ejpam-3712	132	22	edge	edge	NOUN
ejpam-3712	132	23	.	.	PUNCT
ejpam-3712	133	1	table	table	NOUN
ejpam-3712	133	2	1	1	NUM
ejpam-3712	133	3	shows	show	VERB
ejpam-3712	133	4	t.	t.	PROPN
ejpam-3712	133	5	deepika	deepika	PROPN
ejpam-3712	133	6	,	,	PUNCT
ejpam-3712	133	7	v.	v.	ADP
ejpam-3712	133	8	lokesha	lokesha	PROPN
ejpam-3712	133	9	/	/	SYM
ejpam-3712	133	10	eur	eur	PROPN
ejpam-3712	133	11	.	.	PUNCT
ejpam-3712	134	1	j.	j.	PROPN
ejpam-3712	134	2	pure	pure	PROPN
ejpam-3712	134	3	appl	appl	PROPN
ejpam-3712	134	4	.	.	PROPN
ejpam-3712	134	5	math	math	PROPN
ejpam-3712	134	6	,	,	PUNCT
ejpam-3712	134	7	13	13	NUM
ejpam-3712	134	8	(	(	PUNCT
ejpam-3712	134	9	5	5	NUM
ejpam-3712	134	10	)	)	PUNCT
ejpam-3712	134	11	(	(	PUNCT
ejpam-3712	134	12	2020	2020	NUM
ejpam-3712	134	13	)	)	PUNCT
ejpam-3712	134	14	,	,	PUNCT
ejpam-3712	134	15	1149	1149	NUM
ejpam-3712	134	16	-	-	SYM
ejpam-3712	134	17	1161	1161	NUM
ejpam-3712	134	18	1157	1157	NUM
ejpam-3712	134	19	such	such	DET
ejpam-3712	134	20	an	an	DET
ejpam-3712	134	21	edge	edge	NOUN
ejpam-3712	134	22	partition	partition	NOUN
ejpam-3712	134	23	of	of	ADP
ejpam-3712	134	24	pnn(n	pnn(n	PROPN
ejpam-3712	134	25	,	,	PUNCT
ejpam-3712	134	26	k	k	PROPN
ejpam-3712	134	27	,	,	PUNCT
ejpam-3712	134	28	m	m	NOUN
ejpam-3712	134	29	)	)	PUNCT
ejpam-3712	134	30	.	.	PUNCT
ejpam-3712	135	1	now	now	ADV
ejpam-3712	135	2	by	by	ADP
ejpam-3712	135	3	using	use	VERB
ejpam-3712	135	4	the	the	DET
ejpam-3712	135	5	formulas	formula	NOUN
ejpam-3712	135	6	of	of	ADP
ejpam-3712	135	7	min	min	ADJ
ejpam-3712	135	8	-	-	ADJ
ejpam-3712	135	9	max	max	PROPN
ejpam-3712	135	10	rodeg	rodeg	PROPN
ejpam-3712	135	11	index	index	NOUN
ejpam-3712	135	12	,	,	PUNCT
ejpam-3712	135	13	min	min	PROPN
ejpam-3712	135	14	-	-	ADJ
ejpam-3712	135	15	max	max	ADJ
ejpam-3712	135	16	sdi	sdi	PROPN
ejpam-3712	135	17	index	index	NOUN
ejpam-3712	135	18	and	and	CCONJ
ejpam-3712	135	19	table	table	NOUN
ejpam-3712	135	20	1	1	NUM
ejpam-3712	135	21	we	we	PRON
ejpam-3712	135	22	obtain	obtain	VERB
ejpam-3712	135	23	the	the	DET
ejpam-3712	135	24	required	require	VERB
ejpam-3712	135	25	results	result	NOUN
ejpam-3712	135	26	as	as	SCONJ
ejpam-3712	135	27	follows	follow	VERB
ejpam-3712	135	28	min	min	PROPN
ejpam-3712	135	29	-	-	ADJ
ejpam-3712	135	30	max	max	ADJ
ejpam-3712	135	31	rodeg	rodeg	NOUN
ejpam-3712	135	32	index	index	NOUN
ejpam-3712	135	33	=	=	SYM
ejpam-3712	135	34	∑	∑	PUNCT
ejpam-3712	135	35	uv∈e(g	uv∈e(g	NUM
ejpam-3712	135	36	)	)	PUNCT
ejpam-3712	135	37	√	√	NUM
ejpam-3712	135	38	min(du	min(du	NOUN
ejpam-3712	135	39	,	,	PUNCT
ejpam-3712	135	40	dv	dv	PROPN
ejpam-3712	135	41	)	)	PUNCT
ejpam-3712	135	42	max(du	max(du	PROPN
ejpam-3712	135	43	,	,	PUNCT
ejpam-3712	135	44	dv	dv	PROPN
ejpam-3712	135	45	)	)	PUNCT
ejpam-3712	135	46	=	=	SYM
ejpam-3712	135	47	∑	∑	PUNCT
ejpam-3712	135	48	uv∈ekm	uv∈ekm	PROPN
ejpam-3712	135	49	,	,	PUNCT
ejpam-3712	135	50	n+1	n+1	PROPN
ejpam-3712	135	51	√	√	PUNCT
ejpam-3712	135	52	min(du	min(du	NOUN
ejpam-3712	135	53	,	,	PUNCT
ejpam-3712	135	54	dv	dv	PROPN
ejpam-3712	135	55	)	)	PUNCT
ejpam-3712	135	56	max(du	max(du	PROPN
ejpam-3712	135	57	,	,	PUNCT
ejpam-3712	135	58	dv	dv	PROPN
ejpam-3712	135	59	)	)	PUNCT
ejpam-3712	136	1	+	+	CCONJ
ejpam-3712	136	2	∑	∑	ADP
ejpam-3712	136	3	uv∈en+1,m	uv∈en+1,m	ADJ
ejpam-3712	136	4	√	√	NUM
ejpam-3712	136	5	min(du	min(du	NOUN
ejpam-3712	136	6	,	,	PUNCT
ejpam-3712	136	7	dv	dv	PROPN
ejpam-3712	136	8	)	)	PUNCT
ejpam-3712	136	9	max(du	max(du	PROPN
ejpam-3712	136	10	,	,	PUNCT
ejpam-3712	136	11	dv	dv	PROPN
ejpam-3712	136	12	)	)	PUNCT
ejpam-3712	136	13	=	=	PRON
ejpam-3712	136	14	nkm	nkm	VERB
ejpam-3712	136	15	√	√	NUM
ejpam-3712	136	16	n+	n+	NUM
ejpam-3712	136	17	1	1	NUM
ejpam-3712	136	18	km	km	NOUN
ejpam-3712	136	19	+	+	CCONJ
ejpam-3712	136	20	km	km	NOUN
ejpam-3712	136	21	√	√	VERB
ejpam-3712	136	22	m	m	VERB
ejpam-3712	136	23	n+	n+	ADP
ejpam-3712	136	24	1	1	NUM
ejpam-3712	136	25	=	=	SYM
ejpam-3712	136	26	km	km	NOUN
ejpam-3712	136	27	[	[	PUNCT
ejpam-3712	136	28	n	n	CCONJ
ejpam-3712	136	29	√	√	NUM
ejpam-3712	136	30	n+	n+	NUM
ejpam-3712	136	31	1	1	NUM
ejpam-3712	136	32	km	km	NOUN
ejpam-3712	136	33	+	+	CCONJ
ejpam-3712	136	34	√	√	PROPN
ejpam-3712	136	35	m	m	VERB
ejpam-3712	136	36	n+	n+	ADP
ejpam-3712	136	37	1	1	NUM
ejpam-3712	136	38	]	]	SYM
ejpam-3712	136	39	min	min	ADJ
ejpam-3712	136	40	-	-	ADJ
ejpam-3712	136	41	max	max	ADJ
ejpam-3712	136	42	sdi	sdi	PROPN
ejpam-3712	136	43	index	index	NOUN
ejpam-3712	136	44	=	=	SYM
ejpam-3712	136	45	∑	∑	PUNCT
ejpam-3712	136	46	uv∈e(g	uv∈e(g	NUM
ejpam-3712	136	47	)	)	PUNCT
ejpam-3712	136	48	(	(	PUNCT
ejpam-3712	136	49	min(du	min(du	X
ejpam-3712	136	50	,	,	PUNCT
ejpam-3712	136	51	dv	dv	PROPN
ejpam-3712	136	52	)	)	PUNCT
ejpam-3712	136	53	max(du	max(du	PROPN
ejpam-3712	136	54	,	,	PUNCT
ejpam-3712	136	55	dv	dv	PROPN
ejpam-3712	136	56	)	)	PUNCT
ejpam-3712	136	57	)	)	PUNCT
ejpam-3712	136	58	2	2	NUM
ejpam-3712	136	59	=	=	SYM
ejpam-3712	136	60	∑	∑	PUNCT
ejpam-3712	136	61	uv∈ekm	uv∈ekm	PROPN
ejpam-3712	136	62	,	,	PUNCT
ejpam-3712	136	63	n+1	n+1	PROPN
ejpam-3712	136	64	(	(	PUNCT
ejpam-3712	136	65	min(du	min(du	X
ejpam-3712	136	66	,	,	PUNCT
ejpam-3712	136	67	dv	dv	PROPN
ejpam-3712	136	68	)	)	PUNCT
ejpam-3712	136	69	max(du	max(du	PROPN
ejpam-3712	136	70	,	,	PUNCT
ejpam-3712	136	71	dv	dv	PROPN
ejpam-3712	136	72	)	)	PUNCT
ejpam-3712	136	73	)	)	PUNCT
ejpam-3712	136	74	2	2	NUM
ejpam-3712	137	1	+	+	CCONJ
ejpam-3712	137	2	∑	∑	ADV
ejpam-3712	137	3	uv∈en+1,m	uv∈en+1,m	NOUN
ejpam-3712	137	4	(	(	PUNCT
ejpam-3712	137	5	min(du	min(du	X
ejpam-3712	137	6	,	,	PUNCT
ejpam-3712	137	7	dv	dv	PROPN
ejpam-3712	137	8	)	)	PUNCT
ejpam-3712	137	9	max(du	max(du	PROPN
ejpam-3712	137	10	,	,	PUNCT
ejpam-3712	137	11	dv	dv	PROPN
ejpam-3712	137	12	)	)	PUNCT
ejpam-3712	137	13	)	)	PUNCT
ejpam-3712	137	14	2	2	NUM
ejpam-3712	137	15	=	=	SYM
ejpam-3712	137	16	nkm	nkm	X
ejpam-3712	137	17	(	(	PUNCT
ejpam-3712	137	18	n+	n+	NUM
ejpam-3712	137	19	1	1	NUM
ejpam-3712	137	20	km	km	NOUN
ejpam-3712	137	21	)	)	PUNCT
ejpam-3712	137	22	2	2	NUM
ejpam-3712	137	23	+	+	NUM
ejpam-3712	137	24	km	km	PROPN
ejpam-3712	137	25	(	(	PUNCT
ejpam-3712	137	26	m	m	NOUN
ejpam-3712	137	27	n+	n+	ADP
ejpam-3712	137	28	1	1	NUM
ejpam-3712	137	29	)	)	SYM
ejpam-3712	137	30	2	2	NUM
ejpam-3712	137	31	=	=	SYM
ejpam-3712	137	32	n(n+	n(n+	X
ejpam-3712	137	33	1)4	1)4	PROPN
ejpam-3712	137	34	+	+	NUM
ejpam-3712	137	35	k2m4	k2m4	X
ejpam-3712	137	36	km(n+	km(n+	PROPN
ejpam-3712	137	37	1)2	1)2	NUM
ejpam-3712	137	38	theorem	theorem	NOUN
ejpam-3712	137	39	4	4	NUM
ejpam-3712	137	40	.	.	PUNCT
ejpam-3712	138	1	let	let	VERB
ejpam-3712	138	2	g	g	NOUN
ejpam-3712	138	3	be	be	AUX
ejpam-3712	138	4	the	the	DET
ejpam-3712	138	5	probabilistic	probabilistic	ADJ
ejpam-3712	138	6	neural	neural	ADJ
ejpam-3712	138	7	network	network	NOUN
ejpam-3712	138	8	pnn(n	pnn(n	PROPN
ejpam-3712	138	9	,	,	PUNCT
ejpam-3712	138	10	k	k	PROPN
ejpam-3712	138	11	,	,	PUNCT
ejpam-3712	138	12	m	m	PROPN
ejpam-3712	138	13	)	)	PUNCT
ejpam-3712	138	14	then	then	ADV
ejpam-3712	138	15	for	for	ADP
ejpam-3712	138	16	(	(	PUNCT
ejpam-3712	138	17	n	n	CCONJ
ejpam-3712	138	18	,	,	PUNCT
ejpam-3712	138	19	k	k	PROPN
ejpam-3712	138	20	,	,	PUNCT
ejpam-3712	138	21	m	m	PROPN
ejpam-3712	138	22	)	)	PUNCT
ejpam-3712	138	23	≥	≥	NOUN
ejpam-3712	138	24	1	1	NUM
ejpam-3712	138	25	,	,	PUNCT
ejpam-3712	138	26	its	its	PRON
ejpam-3712	138	27	inverse	inverse	NOUN
ejpam-3712	138	28	sum	sum	NOUN
ejpam-3712	138	29	indeg	indeg	NOUN
ejpam-3712	138	30	index	index	NOUN
ejpam-3712	138	31	and	and	CCONJ
ejpam-3712	138	32	symmetric	symmetric	ADJ
ejpam-3712	138	33	division	division	NOUN
ejpam-3712	138	34	deg	deg	PROPN
ejpam-3712	138	35	index	index	NOUN
ejpam-3712	138	36	is	be	AUX
ejpam-3712	138	37	given	give	VERB
ejpam-3712	138	38	by	by	ADP
ejpam-3712	138	39	isi(g	isi(g	NOUN
ejpam-3712	138	40	)	)	PUNCT
ejpam-3712	139	1	=	=	SYM
ejpam-3712	139	2	km2	km2	X
ejpam-3712	139	3	[	[	PUNCT
ejpam-3712	139	4	k(m+	k(m+	X
ejpam-3712	139	5	n)(2n+	n)(2n+	PROPN
ejpam-3712	139	6	1	1	NUM
ejpam-3712	139	7	)	)	PUNCT
ejpam-3712	139	8	+	+	CCONJ
ejpam-3712	139	9	(	(	PUNCT
ejpam-3712	139	10	n+	n+	NUM
ejpam-3712	139	11	1)2	1)2	NUM
ejpam-3712	139	12	(	(	PUNCT
ejpam-3712	139	13	m+	m+	NUM
ejpam-3712	139	14	n+	n+	SYM
ejpam-3712	139	15	1)(km+	1)(km+	NUM
ejpam-3712	139	16	n+	n+	NUM
ejpam-3712	139	17	1	1	NUM
ejpam-3712	139	18	)	)	PUNCT
ejpam-3712	139	19	]	]	PUNCT
ejpam-3712	140	1	sdd(g	sdd(g	VERB
ejpam-3712	140	2	)	)	PUNCT
ejpam-3712	140	3	=	=	SYM
ejpam-3712	140	4	1	1	NUM
ejpam-3712	140	5	n+	n+	SYM
ejpam-3712	140	6	1	1	NUM
ejpam-3712	140	7	[	[	PUNCT
ejpam-3712	140	8	n(n+	n(n+	X
ejpam-3712	140	9	1)2	1)2	NUM
ejpam-3712	140	10	+	+	CCONJ
ejpam-3712	140	11	k(m2(1	k(m2(1	NOUN
ejpam-3712	140	12	+	+	CCONJ
ejpam-3712	140	13	kn	kn	PROPN
ejpam-3712	140	14	)	)	PUNCT
ejpam-3712	141	1	+	+	CCONJ
ejpam-3712	141	2	n2	n2	ADJ
ejpam-3712	141	3	+	+	CCONJ
ejpam-3712	141	4	3	3	NUM
ejpam-3712	141	5	)	)	PUNCT
ejpam-3712	141	6	]	]	PUNCT
ejpam-3712	141	7	proof	proof	NOUN
ejpam-3712	141	8	.	.	PUNCT
ejpam-3712	142	1	let	let	VERB
ejpam-3712	142	2	g	g	NOUN
ejpam-3712	142	3	be	be	AUX
ejpam-3712	142	4	the	the	DET
ejpam-3712	142	5	pnn(n	pnn(n	PROPN
ejpam-3712	142	6	,	,	PUNCT
ejpam-3712	142	7	k	k	PROPN
ejpam-3712	142	8	,	,	PUNCT
ejpam-3712	142	9	m	m	NOUN
ejpam-3712	142	10	)	)	PUNCT
ejpam-3712	142	11	,	,	PUNCT
ejpam-3712	142	12	for	for	ADP
ejpam-3712	142	13	(	(	PUNCT
ejpam-3712	142	14	n	n	CCONJ
ejpam-3712	142	15	,	,	PUNCT
ejpam-3712	142	16	k	k	PROPN
ejpam-3712	142	17	,	,	PUNCT
ejpam-3712	142	18	m	m	PROPN
ejpam-3712	142	19	)	)	PUNCT
ejpam-3712	142	20	≥	≥	NOUN
ejpam-3712	142	21	1	1	NUM
ejpam-3712	142	22	.	.	PUNCT
ejpam-3712	143	1	the	the	DET
ejpam-3712	143	2	number	number	NOUN
ejpam-3712	143	3	of	of	ADP
ejpam-3712	143	4	vertices	vertex	NOUN
ejpam-3712	143	5	and	and	CCONJ
ejpam-3712	143	6	edges	edge	NOUN
ejpam-3712	143	7	in	in	ADP
ejpam-3712	143	8	pnn(n	pnn(n	PROPN
ejpam-3712	143	9	,	,	PUNCT
ejpam-3712	143	10	k	k	PROPN
ejpam-3712	143	11	,	,	PUNCT
ejpam-3712	143	12	m	m	NOUN
ejpam-3712	143	13	)	)	PUNCT
ejpam-3712	143	14	are	be	AUX
ejpam-3712	143	15	n+	n+	ADP
ejpam-3712	143	16	k(m+	k(m+	NOUN
ejpam-3712	143	17	1	1	NUM
ejpam-3712	143	18	)	)	PUNCT
ejpam-3712	143	19	and	and	CCONJ
ejpam-3712	143	20	km(n+	km(n+	PROPN
ejpam-3712	143	21	1	1	NUM
ejpam-3712	143	22	)	)	PUNCT
ejpam-3712	143	23	respectively	respectively	ADV
ejpam-3712	143	24	.	.	PUNCT
ejpam-3712	144	1	there	there	PRON
ejpam-3712	144	2	are	be	VERB
ejpam-3712	144	3	two	two	NUM
ejpam-3712	144	4	types	type	NOUN
ejpam-3712	144	5	of	of	ADP
ejpam-3712	144	6	edges	edge	NOUN
ejpam-3712	144	7	in	in	ADP
ejpam-3712	144	8	pnn(n	pnn(n	PROPN
ejpam-3712	144	9	,	,	PUNCT
ejpam-3712	144	10	k	k	PROPN
ejpam-3712	144	11	,	,	PUNCT
ejpam-3712	144	12	m	m	NOUN
ejpam-3712	144	13	)	)	PUNCT
ejpam-3712	144	14	based	base	VERB
ejpam-3712	144	15	on	on	ADP
ejpam-3712	144	16	degrees	degree	NOUN
ejpam-3712	144	17	of	of	ADP
ejpam-3712	144	18	end	end	NOUN
ejpam-3712	144	19	vertices	vertex	NOUN
ejpam-3712	144	20	of	of	ADP
ejpam-3712	144	21	each	each	DET
ejpam-3712	144	22	edge	edge	NOUN
ejpam-3712	144	23	.	.	PUNCT
ejpam-3712	145	1	table	table	NOUN
ejpam-3712	145	2	1	1	NUM
ejpam-3712	145	3	shows	show	VERB
ejpam-3712	145	4	such	such	DET
ejpam-3712	145	5	an	an	DET
ejpam-3712	145	6	edge	edge	NOUN
ejpam-3712	145	7	partition	partition	NOUN
ejpam-3712	145	8	of	of	ADP
ejpam-3712	145	9	pnn(n	pnn(n	PROPN
ejpam-3712	145	10	,	,	PUNCT
ejpam-3712	145	11	k	k	PROPN
ejpam-3712	145	12	,	,	PUNCT
ejpam-3712	145	13	m	m	NOUN
ejpam-3712	145	14	)	)	PUNCT
ejpam-3712	145	15	.	.	PUNCT
ejpam-3712	146	1	now	now	ADV
ejpam-3712	146	2	by	by	ADP
ejpam-3712	146	3	using	use	VERB
ejpam-3712	146	4	the	the	DET
ejpam-3712	146	5	formulas	formula	NOUN
ejpam-3712	146	6	of	of	ADP
ejpam-3712	146	7	isi	isi	PROPN
ejpam-3712	146	8	,	,	PUNCT
ejpam-3712	146	9	sdd	sdd	NOUN
ejpam-3712	146	10	and	and	CCONJ
ejpam-3712	146	11	table	table	NOUN
ejpam-3712	146	12	1	1	NUM
ejpam-3712	146	13	we	we	PRON
ejpam-3712	146	14	obtain	obtain	VERB
ejpam-3712	146	15	the	the	DET
ejpam-3712	146	16	required	require	VERB
ejpam-3712	146	17	results	result	NOUN
ejpam-3712	146	18	as	as	SCONJ
ejpam-3712	146	19	follows	follow	VERB
ejpam-3712	146	20	isi(g	isi(g	NOUN
ejpam-3712	146	21	)	)	PUNCT
ejpam-3712	146	22	=	=	SYM
ejpam-3712	146	23	∑	∑	PUNCT
ejpam-3712	146	24	uv∈e(g	uv∈e(g	NOUN
ejpam-3712	146	25	)	)	PUNCT
ejpam-3712	147	1	dudv	dudv	ADP
ejpam-3712	147	2	du	du	PROPN
ejpam-3712	148	1	+	+	CCONJ
ejpam-3712	148	2	dv	dv	PROPN
ejpam-3712	148	3	t.	t.	PROPN
ejpam-3712	148	4	deepika	deepika	PROPN
ejpam-3712	148	5	,	,	PUNCT
ejpam-3712	148	6	v.	v.	ADP
ejpam-3712	148	7	lokesha	lokesha	PROPN
ejpam-3712	148	8	/	/	SYM
ejpam-3712	148	9	eur	eur	PROPN
ejpam-3712	148	10	.	.	PUNCT
ejpam-3712	149	1	j.	j.	PROPN
ejpam-3712	149	2	pure	pure	PROPN
ejpam-3712	149	3	appl	appl	PROPN
ejpam-3712	149	4	.	.	PROPN
ejpam-3712	149	5	math	math	PROPN
ejpam-3712	149	6	,	,	PUNCT
ejpam-3712	149	7	13	13	NUM
ejpam-3712	149	8	(	(	PUNCT
ejpam-3712	149	9	5	5	NUM
ejpam-3712	149	10	)	)	PUNCT
ejpam-3712	149	11	(	(	PUNCT
ejpam-3712	149	12	2020	2020	NUM
ejpam-3712	149	13	)	)	PUNCT
ejpam-3712	149	14	,	,	PUNCT
ejpam-3712	149	15	1149	1149	NUM
ejpam-3712	149	16	-	-	SYM
ejpam-3712	149	17	1161	1161	NUM
ejpam-3712	149	18	1158	1158	NUM
ejpam-3712	149	19	=	=	PUNCT
ejpam-3712	149	20	∑	∑	PUNCT
ejpam-3712	149	21	uv∈ekm	uv∈ekm	PROPN
ejpam-3712	149	22	,	,	PUNCT
ejpam-3712	149	23	n+1	n+1	PROPN
ejpam-3712	149	24	dudv	dudv	NOUN
ejpam-3712	149	25	du	du	NOUN
ejpam-3712	150	1	+	+	CCONJ
ejpam-3712	151	1	dv	dv	PROPN
ejpam-3712	152	1	+	+	CCONJ
ejpam-3712	152	2	∑	∑	PROPN
ejpam-3712	152	3	uv∈en+1,m	uv∈en+1,m	PROPN
ejpam-3712	152	4	dudv	dudv	NOUN
ejpam-3712	152	5	du	du	PROPN
ejpam-3712	152	6	+	+	CCONJ
ejpam-3712	152	7	dv	dv	PROPN
ejpam-3712	152	8	=	=	PROPN
ejpam-3712	152	9	nkm	nkm	PROPN
ejpam-3712	152	10	[	[	PUNCT
ejpam-3712	152	11	(	(	PUNCT
ejpam-3712	152	12	km)(n+	km)(n+	PROPN
ejpam-3712	152	13	1	1	NUM
ejpam-3712	152	14	)	)	PUNCT
ejpam-3712	152	15	km+	km+	NOUN
ejpam-3712	152	16	(	(	PUNCT
ejpam-3712	152	17	n+	n+	NOUN
ejpam-3712	152	18	1	1	NUM
ejpam-3712	152	19	)	)	PUNCT
ejpam-3712	152	20	]	]	PUNCT
ejpam-3712	153	1	+	+	CCONJ
ejpam-3712	153	2	km	km	NOUN
ejpam-3712	153	3	[	[	PUNCT
ejpam-3712	153	4	(	(	PUNCT
ejpam-3712	153	5	n+	n+	NOUN
ejpam-3712	153	6	1)(m	1)(m	NUM
ejpam-3712	153	7	)	)	PUNCT
ejpam-3712	153	8	(	(	PUNCT
ejpam-3712	153	9	n+	n+	X
ejpam-3712	153	10	1	1	X
ejpam-3712	153	11	)	)	PUNCT
ejpam-3712	153	12	+	+	NOUN
ejpam-3712	153	13	m	m	NOUN
ejpam-3712	153	14	=	=	ADJ
ejpam-3712	153	15	km	km	PROPN
ejpam-3712	153	16	[	[	PUNCT
ejpam-3712	153	17	n	n	CCONJ
ejpam-3712	153	18	(	(	PUNCT
ejpam-3712	153	19	km	km	NOUN
ejpam-3712	153	20	km+	km+	NOUN
ejpam-3712	153	21	1	1	NUM
ejpam-3712	153	22	)	)	PUNCT
ejpam-3712	153	23	+	+	CCONJ
ejpam-3712	153	24	(	(	PUNCT
ejpam-3712	153	25	m	m	VERB
ejpam-3712	153	26	1	1	NUM
ejpam-3712	153	27	+	+	NOUN
ejpam-3712	153	28	m	m	VERB
ejpam-3712	153	29	)	)	PUNCT
ejpam-3712	153	30	]	]	PUNCT
ejpam-3712	154	1	=	=	PUNCT
ejpam-3712	154	2	km2	km2	X
ejpam-3712	154	3	[	[	PUNCT
ejpam-3712	154	4	k(m+	k(m+	X
ejpam-3712	154	5	n)(2n+	n)(2n+	PROPN
ejpam-3712	154	6	1	1	NUM
ejpam-3712	154	7	)	)	PUNCT
ejpam-3712	154	8	+	+	CCONJ
ejpam-3712	154	9	(	(	PUNCT
ejpam-3712	154	10	n+	n+	NUM
ejpam-3712	154	11	1)2	1)2	NUM
ejpam-3712	154	12	(	(	PUNCT
ejpam-3712	154	13	m+	m+	NUM
ejpam-3712	154	14	n+	n+	SYM
ejpam-3712	154	15	1)(km+	1)(km+	NUM
ejpam-3712	154	16	n+	n+	NUM
ejpam-3712	154	17	1	1	NUM
ejpam-3712	154	18	)	)	PUNCT
ejpam-3712	154	19	]	]	PUNCT
ejpam-3712	155	1	min−maxsdiindex	min−maxsdiindex	PUNCT
ejpam-3712	155	2	=	=	PUNCT
ejpam-3712	155	3	∑	∑	PUNCT
ejpam-3712	155	4	uv∈e(g	uv∈e(g	NUM
ejpam-3712	155	5	)	)	PUNCT
ejpam-3712	155	6	(	(	PUNCT
ejpam-3712	155	7	min(du	min(du	X
ejpam-3712	155	8	,	,	PUNCT
ejpam-3712	155	9	dv	dv	PROPN
ejpam-3712	155	10	)	)	PUNCT
ejpam-3712	155	11	max(du	max(du	PROPN
ejpam-3712	155	12	,	,	PUNCT
ejpam-3712	155	13	dv	dv	PROPN
ejpam-3712	155	14	)	)	PUNCT
ejpam-3712	155	15	)	)	PUNCT
ejpam-3712	155	16	2	2	NUM
ejpam-3712	155	17	=	=	SYM
ejpam-3712	155	18	∑	∑	PUNCT
ejpam-3712	155	19	uv∈ekm	uv∈ekm	PROPN
ejpam-3712	155	20	,	,	PUNCT
ejpam-3712	155	21	n+1	n+1	PROPN
ejpam-3712	155	22	(	(	PUNCT
ejpam-3712	155	23	min(du	min(du	X
ejpam-3712	155	24	,	,	PUNCT
ejpam-3712	155	25	dv	dv	PROPN
ejpam-3712	155	26	)	)	PUNCT
ejpam-3712	155	27	max(du	max(du	PROPN
ejpam-3712	155	28	,	,	PUNCT
ejpam-3712	155	29	dv	dv	PROPN
ejpam-3712	155	30	)	)	PUNCT
ejpam-3712	155	31	)	)	PUNCT
ejpam-3712	155	32	2	2	NUM
ejpam-3712	156	1	+	+	CCONJ
ejpam-3712	156	2	∑	∑	ADV
ejpam-3712	156	3	uv∈en+1,m	uv∈en+1,m	NOUN
ejpam-3712	156	4	(	(	PUNCT
ejpam-3712	156	5	min(du	min(du	X
ejpam-3712	156	6	,	,	PUNCT
ejpam-3712	156	7	dv	dv	PROPN
ejpam-3712	156	8	)	)	PUNCT
ejpam-3712	156	9	max(du	max(du	PROPN
ejpam-3712	156	10	,	,	PUNCT
ejpam-3712	156	11	dv	dv	PROPN
ejpam-3712	156	12	)	)	PUNCT
ejpam-3712	156	13	)	)	PUNCT
ejpam-3712	156	14	2	2	NUM
ejpam-3712	156	15	=	=	SYM
ejpam-3712	156	16	nkm	nkm	X
ejpam-3712	156	17	(	(	PUNCT
ejpam-3712	156	18	n+	n+	NUM
ejpam-3712	156	19	1	1	NUM
ejpam-3712	156	20	km	km	NOUN
ejpam-3712	156	21	)	)	PUNCT
ejpam-3712	156	22	2	2	NUM
ejpam-3712	156	23	+	+	NUM
ejpam-3712	156	24	km	km	PROPN
ejpam-3712	156	25	(	(	PUNCT
ejpam-3712	156	26	m	m	NOUN
ejpam-3712	156	27	n+	n+	ADP
ejpam-3712	156	28	1	1	NUM
ejpam-3712	156	29	)	)	SYM
ejpam-3712	156	30	2	2	NUM
ejpam-3712	156	31	=	=	SYM
ejpam-3712	156	32	n(n+	n(n+	X
ejpam-3712	156	33	1)4	1)4	PROPN
ejpam-3712	156	34	+	+	NUM
ejpam-3712	156	35	k2m4	k2m4	X
ejpam-3712	156	36	km(n+	km(n+	PROPN
ejpam-3712	156	37	1)2	1)2	NUM
ejpam-3712	156	38	let	let	VERB
ejpam-3712	156	39	g	g	NOUN
ejpam-3712	156	40	be	be	AUX
ejpam-3712	156	41	the	the	DET
ejpam-3712	156	42	probabilistic	probabilistic	ADJ
ejpam-3712	156	43	neural	neural	ADJ
ejpam-3712	156	44	network	network	NOUN
ejpam-3712	156	45	pnn(n	pnn(n	PROPN
ejpam-3712	156	46	,	,	PUNCT
ejpam-3712	156	47	k	k	PROPN
ejpam-3712	156	48	,	,	PUNCT
ejpam-3712	156	49	m	m	PROPN
ejpam-3712	156	50	)	)	PUNCT
ejpam-3712	156	51	then	then	ADV
ejpam-3712	156	52	for	for	ADP
ejpam-3712	156	53	(	(	PUNCT
ejpam-3712	156	54	n	n	CCONJ
ejpam-3712	156	55	,	,	PUNCT
ejpam-3712	156	56	k	k	PROPN
ejpam-3712	156	57	,	,	PUNCT
ejpam-3712	156	58	m	m	PROPN
ejpam-3712	156	59	)	)	PUNCT
ejpam-3712	156	60	≥	≥	NOUN
ejpam-3712	156	61	1	1	NUM
ejpam-3712	156	62	,	,	PUNCT
ejpam-3712	156	63	its	its	PRON
ejpam-3712	156	64	adriatic	adriatic	ADJ
ejpam-3712	156	65	indices	index	NOUN
ejpam-3712	156	66	of	of	ADP
ejpam-3712	156	67	pnn	pnn	PROPN
ejpam-3712	156	68	of	of	ADP
ejpam-3712	156	69	γj(x	γj(x	PROPN
ejpam-3712	156	70	,	,	PUNCT
ejpam-3712	156	71	y	y	PROPN
ejpam-3712	156	72	)	)	PUNCT
ejpam-3712	156	73	(	(	PUNCT
ejpam-3712	156	74	j	j	NOUN
ejpam-3712	156	75	=	=	SYM
ejpam-3712	156	76	1	1	NUM
ejpam-3712	156	77	,	,	PUNCT
ejpam-3712	156	78	2	2	NUM
ejpam-3712	156	79	,	,	PUNCT
ejpam-3712	156	80	...	...	PUNCT
ejpam-3712	156	81	8)	8)	NUM
ejpam-3712	156	82	index	index	NOUN
ejpam-3712	156	83	is	be	AUX
ejpam-3712	156	84	given	give	VERB
ejpam-3712	156	85	by	by	ADP
ejpam-3712	156	86	•	•	NUM
ejpam-3712	156	87	adr(pnn)γ1(x	adr(pnn)γ1(x	NOUN
ejpam-3712	156	88	,	,	PUNCT
ejpam-3712	156	89	y	y	NOUN
ejpam-3712	156	90	)	)	PUNCT
ejpam-3712	156	91	=	=	SYM
ejpam-3712	157	1			PRON
ejpam-3712	157	2	km.log(n+	km.log(n+	PROPN
ejpam-3712	157	3	1).log(knmn+1	1).log(knmn+1	PROPN
ejpam-3712	157	4	)	)	PUNCT
ejpam-3712	157	5	,	,	PUNCT
ejpam-3712	157	6	if	if	SCONJ
ejpam-3712	157	7	ϕi	ϕi	ADP
ejpam-3712	157	8	,	,	PUNCT
ejpam-3712	157	9	a	a	DET
ejpam-3712	157	10	=	=	SYM
ejpam-3712	157	11	ϕ1,1	ϕ1,1	NOUN
ejpam-3712	157	12	2n4	2n4	NUM
ejpam-3712	158	1	+	+	CCONJ
ejpam-3712	159	1	58k4	58k4	NUM
ejpam-3712	159	2	+	+	CCONJ
ejpam-3712	159	3	6m4	6m4	NUM
ejpam-3712	159	4	+	+	SYM
ejpam-3712	159	5	60	60	NUM
ejpam-3712	159	6	,	,	PUNCT
ejpam-3712	159	7	if	if	SCONJ
ejpam-3712	159	8	ϕ2,2	ϕ2,2	DET
ejpam-3712	159	9	2	2	NUM
ejpam-3712	159	10	22n	22n	NOUN
ejpam-3712	159	11	+	+	CCONJ
ejpam-3712	159	12	58	58	NUM
ejpam-3712	159	13	22k	22k	NOUN
ejpam-3712	159	14	+	+	CCONJ
ejpam-3712	159	15	6	6	NUM
ejpam-3712	159	16	22	22	NUM
ejpam-3712	159	17	m	m	NOUN
ejpam-3712	159	18	+	+	NOUN
ejpam-3712	159	19	15	15	NUM
ejpam-3712	159	20	,	,	PUNCT
ejpam-3712	159	21	if	if	SCONJ
ejpam-3712	159	22	ϕ3,1/2	ϕ3,1/2	ADJ
ejpam-3712	159	23	.	.	PUNCT
ejpam-3712	160	1	•	•	ADP
ejpam-3712	160	2	adr(pnn)γ2(x	adr(pnn)γ2(x	NUM
ejpam-3712	160	3	,	,	PUNCT
ejpam-3712	160	4	y	y	PROPN
ejpam-3712	160	5	)	)	PUNCT
ejpam-3712	160	6	=	=	PUNCT
ejpam-3712	160	7	km(n+	km(n+	PROPN
ejpam-3712	160	8	1	1	NUM
ejpam-3712	160	9	)	)	PUNCT
ejpam-3712	160	10	√	√	ADV
ejpam-3712	160	11	log(n+	log(n+	NOUN
ejpam-3712	160	12	1	1	NUM
ejpam-3712	160	13	)	)	PUNCT
ejpam-3712	160	14	+	+	CCONJ
ejpam-3712	160	15	√	√	PROPN
ejpam-3712	160	16	log(km	log(km	NOUN
ejpam-3712	160	17	)	)	PUNCT
ejpam-3712	161	1	+	+	CCONJ
ejpam-3712	161	2	√	√	NUM
ejpam-3712	161	3	log(m	log(m	NUM
ejpam-3712	161	4	)	)	PUNCT
ejpam-3712	161	5	,	,	PUNCT
ejpam-3712	161	6	if	if	SCONJ
ejpam-3712	161	7	ϕi	ϕi	ADP
ejpam-3712	161	8	,	,	PUNCT
ejpam-3712	161	9	a	a	PRON
ejpam-3712	161	10	=	=	X
ejpam-3712	161	11	ϕ1,1/2	ϕ1,1/2	NOUN
ejpam-3712	161	12	•	•	NOUN
ejpam-3712	161	13	adr(pnn)γ3(x	adr(pnn)γ3(x	NOUN
ejpam-3712	161	14	,	,	PUNCT
ejpam-3712	161	15	y	y	NOUN
ejpam-3712	161	16	)	)	PUNCT
ejpam-3712	161	17	=	=	PUNCT
ejpam-3712	162	1			NOUN
ejpam-3712	162	2	1	1	NUM
ejpam-3712	162	3	km(n+	km(n+	PROPN
ejpam-3712	162	4	1	1	NUM
ejpam-3712	162	5	)	)	PUNCT
ejpam-3712	162	6	√	√	ADV
ejpam-3712	162	7	log(n+	log(n+	NOUN
ejpam-3712	162	8	1	1	NUM
ejpam-3712	162	9	)	)	PUNCT
ejpam-3712	162	10	+	+	CCONJ
ejpam-3712	162	11	√	√	PROPN
ejpam-3712	162	12	log(km	log(km	NOUN
ejpam-3712	162	13	)	)	PUNCT
ejpam-3712	163	1	+	+	CCONJ
ejpam-3712	163	2	√	√	NUM
ejpam-3712	163	3	log(m	log(m	NUM
ejpam-3712	163	4	)	)	PUNCT
ejpam-3712	163	5	,	,	PUNCT
ejpam-3712	163	6	if	if	SCONJ
ejpam-3712	163	7	ϕi	ϕi	ADP
ejpam-3712	163	8	,	,	PUNCT
ejpam-3712	163	9	a	a	PRON
ejpam-3712	163	10	=	=	X
ejpam-3712	163	11	ϕ1,1/2	ϕ1,1/2	NOUN
ejpam-3712	163	12	km2	km2	NOUN
ejpam-3712	163	13	[	[	PUNCT
ejpam-3712	163	14	nk(n+	nk(n+	NOUN
ejpam-3712	163	15	1	1	NUM
ejpam-3712	163	16	)	)	PUNCT
ejpam-3712	163	17	km+	km+	NOUN
ejpam-3712	163	18	n+	n+	PUNCT
ejpam-3712	163	19	1	1	NUM
ejpam-3712	163	20	+	+	CCONJ
ejpam-3712	163	21	n+	n+	NUM
ejpam-3712	163	22	1	1	NUM
ejpam-3712	163	23	m+	m+	NUM
ejpam-3712	163	24	n+	n+	ADP
ejpam-3712	163	25	1	1	NUM
ejpam-3712	163	26	]	]	PUNCT
ejpam-3712	163	27	,	,	PUNCT
ejpam-3712	163	28	if	if	SCONJ
ejpam-3712	163	29	ϕ2,−1	ϕ2,−1	PROPN
ejpam-3712	163	30	•	•	ADP
ejpam-3712	163	31	adr(pnn)γ4(x	adr(pnn)γ4(x	NOUN
ejpam-3712	163	32	,	,	PUNCT
ejpam-3712	163	33	y	y	NOUN
ejpam-3712	163	34	)	)	PUNCT
ejpam-3712	163	35	=	=	PUNCT
ejpam-3712	164	1			PROPN
ejpam-3712	164	2	km[log(knmn−1)−	km[log(knmn−1)−	PROPN
ejpam-3712	164	3	(	(	PUNCT
ejpam-3712	164	4	n−	n−	NOUN
ejpam-3712	164	5	1)log(n+	1)log(n+	NOUN
ejpam-3712	164	6	1	1	NUM
ejpam-3712	164	7	)	)	PUNCT
ejpam-3712	164	8	]	]	X
ejpam-3712	164	9	,	,	PUNCT
ejpam-3712	164	10	if	if	SCONJ
ejpam-3712	164	11	ϕi	ϕi	ADP
ejpam-3712	164	12	,	,	PUNCT
ejpam-3712	164	13	a	a	DET
ejpam-3712	164	14	=	=	SYM
ejpam-3712	164	15	ϕ1,1	ϕ1,1	PROPN
ejpam-3712	164	16	2km[log(knmn−1)−	2km[log(knmn−1)−	PROPN
ejpam-3712	164	17	(	(	PUNCT
ejpam-3712	164	18	n−	n−	NOUN
ejpam-3712	164	19	1)log(n+	1)log(n+	NOUN
ejpam-3712	164	20	1	1	NUM
ejpam-3712	164	21	)	)	PUNCT
ejpam-3712	164	22	]	]	X
ejpam-3712	164	23	,	,	PUNCT
ejpam-3712	164	24	if	if	SCONJ
ejpam-3712	164	25	ϕ1,2	ϕ1,2	ADJ
ejpam-3712	164	26	nkm	nkm	VERB
ejpam-3712	164	27	|	|	ADV
ejpam-3712	164	28	√	√	ADP
ejpam-3712	164	29	km−	km−	PROPN
ejpam-3712	164	30	√	√	NUM
ejpam-3712	164	31	n+	n+	NUM
ejpam-3712	164	32	1	1	NUM
ejpam-3712	165	1	|	|	ADV
ejpam-3712	165	2	+	+	NOUN
ejpam-3712	165	3	km	km	NOUN
ejpam-3712	165	4	|	|	ADV
ejpam-3712	165	5	√	√	PUNCT
ejpam-3712	165	6	n+	n+	NUM
ejpam-3712	165	7	1−	1−	NUM
ejpam-3712	166	1	√	√	INTJ
ejpam-3712	166	2	m	m	VERB
ejpam-3712	166	3	|	|	ADV
ejpam-3712	166	4	,	,	PUNCT
ejpam-3712	166	5	if	if	SCONJ
ejpam-3712	166	6	ϕ2,1/2	ϕ2,1/2	PRON
ejpam-3712	166	7	nkm	nkm	VERB
ejpam-3712	166	8	|	|	ADV
ejpam-3712	166	9	km−	km−	X
ejpam-3712	166	10	(	(	PUNCT
ejpam-3712	166	11	n+	n+	NOUN
ejpam-3712	166	12	1	1	X
ejpam-3712	166	13	)	)	PUNCT
ejpam-3712	167	1	|	|	ADV
ejpam-3712	167	2	+	+	NUM
ejpam-3712	167	3	km	km	NOUN
ejpam-3712	167	4	|	|	ADV
ejpam-3712	167	5	(	(	PUNCT
ejpam-3712	167	6	n+	n+	NUM
ejpam-3712	167	7	1)−m	1)−m	NUM
ejpam-3712	167	8	|	|	ADV
ejpam-3712	167	9	,	,	PUNCT
ejpam-3712	167	10	if	if	SCONJ
ejpam-3712	167	11	ϕ2,1	ϕ2,1	PROPN
ejpam-3712	167	12	km[n2−km	km[n2−km	VERB
ejpam-3712	167	13	+	+	CCONJ
ejpam-3712	167	14	2n+1	2n+1	PROPN
ejpam-3712	167	15	−	−	PROPN
ejpam-3712	167	16	n2−(n+1	n2−(n+1	NOUN
ejpam-3712	167	17	)	)	PUNCT
ejpam-3712	167	18	−	−	ADP
ejpam-3712	168	1	2−m	2−m	NUM
ejpam-3712	168	2	]	]	PUNCT
ejpam-3712	168	3	,	,	PUNCT
ejpam-3712	168	4	if	if	SCONJ
ejpam-3712	168	5	ϕ3,1/2	ϕ3,1/2	PROPN
ejpam-3712	168	6	t.	t.	PROPN
ejpam-3712	168	7	deepika	deepika	PROPN
ejpam-3712	168	8	,	,	PUNCT
ejpam-3712	168	9	v.	v.	ADP
ejpam-3712	168	10	lokesha	lokesha	PROPN
ejpam-3712	168	11	/	/	SYM
ejpam-3712	168	12	eur	eur	PROPN
ejpam-3712	168	13	.	.	PUNCT
ejpam-3712	169	1	j.	j.	PROPN
ejpam-3712	169	2	pure	pure	PROPN
ejpam-3712	169	3	appl	appl	PROPN
ejpam-3712	169	4	.	.	PROPN
ejpam-3712	169	5	math	math	PROPN
ejpam-3712	169	6	,	,	PUNCT
ejpam-3712	169	7	13	13	NUM
ejpam-3712	169	8	(	(	PUNCT
ejpam-3712	169	9	5	5	NUM
ejpam-3712	169	10	)	)	PUNCT
ejpam-3712	169	11	(	(	PUNCT
ejpam-3712	169	12	2020	2020	NUM
ejpam-3712	169	13	)	)	PUNCT
ejpam-3712	169	14	,	,	PUNCT
ejpam-3712	169	15	1149	1149	NUM
ejpam-3712	169	16	-	-	SYM
ejpam-3712	169	17	1161	1161	NUM
ejpam-3712	169	18	1159	1159	NUM
ejpam-3712	169	19	•	•	NOUN
ejpam-3712	169	20	adr(pnn)γ5(x	adr(pnn)γ5(x	NOUN
ejpam-3712	169	21	,	,	PUNCT
ejpam-3712	169	22	y	y	NOUN
ejpam-3712	169	23	)	)	PUNCT
ejpam-3712	169	24	=	=	SYM
ejpam-3712	170	1			PRON
ejpam-3712	170	2	nkm	nkm	VERB
ejpam-3712	170	3	|	|	ADV
ejpam-3712	170	4	1	1	NUM
ejpam-3712	170	5	km	km	NOUN
ejpam-3712	170	6	−	−	NOUN
ejpam-3712	170	7	1	1	NUM
ejpam-3712	170	8	n+1	n+1	PROPN
ejpam-3712	171	1	|	|	ADV
ejpam-3712	171	2	+	+	NOUN
ejpam-3712	171	3	km	km	NOUN
ejpam-3712	171	4	|	|	ADV
ejpam-3712	171	5	1	1	NUM
ejpam-3712	171	6	n+1	n+1	NUM
ejpam-3712	171	7	−	−	NUM
ejpam-3712	171	8	1	1	NUM
ejpam-3712	171	9	m	m	NOUN
ejpam-3712	171	10	|	|	ADJ
ejpam-3712	171	11	,	,	PUNCT
ejpam-3712	171	12	if	if	SCONJ
ejpam-3712	171	13	ϕi	ϕi	ADP
ejpam-3712	171	14	,	,	PUNCT
ejpam-3712	171	15	a	a	DET
ejpam-3712	171	16	=	=	X
ejpam-3712	171	17	ϕ2,−1	ϕ2,−1	PROPN
ejpam-3712	171	18	nkm	nkm	VERB
ejpam-3712	171	19	|	|	ADV
ejpam-3712	171	20	1√	1√	NUM
ejpam-3712	171	21	km	km	NOUN
ejpam-3712	171	22	−	−	PROPN
ejpam-3712	171	23	1√	1√	NOUN
ejpam-3712	171	24	n+1	n+1	PROPN
ejpam-3712	172	1	|	|	ADV
ejpam-3712	172	2	+	+	NOUN
ejpam-3712	172	3	km	km	NOUN
ejpam-3712	172	4	|	|	ADV
ejpam-3712	172	5	1√	1√	PROPN
ejpam-3712	172	6	n+1	n+1	PROPN
ejpam-3712	172	7	−	−	PROPN
ejpam-3712	172	8	1√	1√	PROPN
ejpam-3712	172	9	m	m	NOUN
ejpam-3712	172	10	|	|	ADJ
ejpam-3712	172	11	,	,	PUNCT
ejpam-3712	172	12	if	if	SCONJ
ejpam-3712	172	13	ϕ2,−1/2	ϕ2,−1/2	ADV
ejpam-3712	172	14	0	0	NUM
ejpam-3712	172	15	,	,	PUNCT
ejpam-3712	172	16	if	if	SCONJ
ejpam-3712	172	17	ϕ2,−1	ϕ2,−1	PROPN
ejpam-3712	172	18	•	•	NUM
ejpam-3712	172	19	adr(pnn)γ6(x	adr(pnn)γ6(x	PROPN
ejpam-3712	172	20	,	,	PUNCT
ejpam-3712	172	21	y	y	NOUN
ejpam-3712	172	22	)	)	PUNCT
ejpam-3712	172	23	=	=	SYM
ejpam-3712	172	24	km	km	NOUN
ejpam-3712	172	25	[	[	PUNCT
ejpam-3712	172	26	n	n	CCONJ
ejpam-3712	172	27	√	√	NOUN
ejpam-3712	172	28	n+1	n+1	NUM
ejpam-3712	172	29	km	km	NOUN
ejpam-3712	172	30	+	+	CCONJ
ejpam-3712	172	31	√	√	PROPN
ejpam-3712	172	32	m	m	VERB
ejpam-3712	172	33	n+1	n+1	NUM
ejpam-3712	172	34	]	]	PUNCT
ejpam-3712	172	35	,	,	PUNCT
ejpam-3712	172	36	if	if	SCONJ
ejpam-3712	172	37	ϕi	ϕi	ADP
ejpam-3712	172	38	,	,	PUNCT
ejpam-3712	172	39	a	a	DET
ejpam-3712	172	40	=	=	PUNCT
ejpam-3712	172	41	ϕ2,1/2	ϕ2,1/2	NOUN
ejpam-3712	172	42	14(n+	14(n+	NOUN
ejpam-3712	172	43	k	k	PROPN
ejpam-3712	173	1	+	+	PROPN
ejpam-3712	173	2	m	m	NOUN
ejpam-3712	173	3	)	)	PUNCT
ejpam-3712	173	4	,	,	PUNCT
ejpam-3712	173	5	if	if	SCONJ
ejpam-3712	173	6	ϕ2,2	ϕ2,2	NUM
ejpam-3712	173	7	•	•	NOUN
ejpam-3712	173	8	adr(pnn)γ7(x	adr(pnn)γ7(x	NOUN
ejpam-3712	173	9	,	,	PUNCT
ejpam-3712	173	10	y	y	NOUN
ejpam-3712	173	11	)	)	PUNCT
ejpam-3712	173	12	=	=	SYM
ejpam-3712	173	13			NUM
ejpam-3712	173	14	km	km	NOUN
ejpam-3712	173	15	[	[	PUNCT
ejpam-3712	173	16	n	n	CCONJ
ejpam-3712	173	17	√	√	NUM
ejpam-3712	173	18	km	km	NOUN
ejpam-3712	173	19	n+1	n+1	PROPN
ejpam-3712	174	1	+	+	CCONJ
ejpam-3712	175	1	√	√	NOUN
ejpam-3712	175	2	n+1	n+1	NUM
ejpam-3712	175	3	m	m	PRON
ejpam-3712	175	4	]	]	PUNCT
ejpam-3712	175	5	,	,	PUNCT
ejpam-3712	175	6	if	if	SCONJ
ejpam-3712	175	7	ϕi	ϕi	ADP
ejpam-3712	175	8	,	,	PUNCT
ejpam-3712	175	9	a	a	PRON
ejpam-3712	175	10	=	=	X
ejpam-3712	176	1	ϕ2,1/2	ϕ2,1/2	NOUN
ejpam-3712	176	2	k	k	PROPN
ejpam-3712	176	3	n+1(m2nk	n+1(m2nk	PROPN
ejpam-3712	177	1	+	+	CCONJ
ejpam-3712	177	2	(	(	PUNCT
ejpam-3712	177	3	n+	n+	X
ejpam-3712	177	4	1)2	1)2	NUM
ejpam-3712	177	5	)	)	PUNCT
ejpam-3712	177	6	,	,	PUNCT
ejpam-3712	178	1	if	if	SCONJ
ejpam-3712	178	2	ϕ2,1	ϕ2,1	ADP
ejpam-3712	178	3	k	k	PROPN
ejpam-3712	179	1	[	[	PUNCT
ejpam-3712	179	2	k2m4n+(n+1)4	k2m4n+(n+1)4	PROPN
ejpam-3712	179	3	(	(	PUNCT
ejpam-3712	179	4	n+1)2	n+1)2	PROPN
ejpam-3712	179	5	m	m	NOUN
ejpam-3712	179	6	]	]	PUNCT
ejpam-3712	179	7	,	,	PUNCT
ejpam-3712	179	8	if	if	SCONJ
ejpam-3712	179	9	ϕ2,2	ϕ2,2	NUM
ejpam-3712	179	10	•	•	NOUN
ejpam-3712	179	11	adr(pnn)γ8(x	adr(pnn)γ8(x	NOUN
ejpam-3712	179	12	,	,	PUNCT
ejpam-3712	179	13	y	y	NOUN
ejpam-3712	179	14	)	)	PUNCT
ejpam-3712	179	15	=	=	SYM
ejpam-3712	179	16	1	1	NUM
ejpam-3712	179	17	n+1	n+1	PROPN
ejpam-3712	179	18	[	[	PUNCT
ejpam-3712	179	19	n(n+	n(n+	X
ejpam-3712	179	20	1)2	1)2	NUM
ejpam-3712	179	21	+	+	CCONJ
ejpam-3712	179	22	k(m2(1	k(m2(1	NOUN
ejpam-3712	179	23	+	+	CCONJ
ejpam-3712	179	24	kn	kn	PROPN
ejpam-3712	179	25	)	)	PUNCT
ejpam-3712	179	26	+	+	CCONJ
ejpam-3712	179	27	n2	n2	ADJ
ejpam-3712	179	28	+	+	CCONJ
ejpam-3712	179	29	3	3	NUM
ejpam-3712	179	30	)	)	PUNCT
ejpam-3712	179	31	]	]	PUNCT
ejpam-3712	179	32	,	,	PUNCT
ejpam-3712	179	33	if	if	SCONJ
ejpam-3712	179	34	ϕi	ϕi	ADP
ejpam-3712	179	35	,	,	PUNCT
ejpam-3712	179	36	a	a	DET
ejpam-3712	179	37	=	=	X
ejpam-3712	179	38	ϕ2,1	ϕ2,1	PART
ejpam-3712	179	39	figure	figure	NOUN
ejpam-3712	179	40	2	2	NUM
ejpam-3712	179	41	:	:	PUNCT
ejpam-3712	179	42	the	the	DET
ejpam-3712	179	43	probabilistic	probabilistic	ADJ
ejpam-3712	179	44	neural	neural	ADJ
ejpam-3712	179	45	network	network	NOUN
ejpam-3712	179	46	pnn(n	pnn(n	PROPN
ejpam-3712	179	47	,	,	PUNCT
ejpam-3712	179	48	n	n	CCONJ
ejpam-3712	179	49	,	,	PUNCT
ejpam-3712	179	50	1	1	NUM
ejpam-3712	179	51	)	)	PUNCT
ejpam-3712	179	52	3	3	NUM
ejpam-3712	179	53	.	.	X
ejpam-3712	179	54	conclusion	conclusion	NOUN
ejpam-3712	179	55	we	we	PRON
ejpam-3712	179	56	compare	compare	VERB
ejpam-3712	179	57	the	the	DET
ejpam-3712	179	58	results	result	NOUN
ejpam-3712	179	59	of	of	ADP
ejpam-3712	179	60	the	the	DET
ejpam-3712	179	61	computed	computed	ADJ
ejpam-3712	179	62	adriatic	adriatic	ADJ
ejpam-3712	179	63	indices	index	NOUN
ejpam-3712	179	64	for	for	ADP
ejpam-3712	179	65	the	the	DET
ejpam-3712	179	66	probabilistic	probabilistic	ADJ
ejpam-3712	179	67	neural	neural	ADJ
ejpam-3712	179	68	network	network	NOUN
ejpam-3712	179	69	pnn(n	pnn(n	PROPN
ejpam-3712	179	70	,	,	PUNCT
ejpam-3712	179	71	k	k	PROPN
ejpam-3712	179	72	,	,	PUNCT
ejpam-3712	179	73	m	m	NOUN
ejpam-3712	179	74	)	)	PUNCT
ejpam-3712	179	75	with	with	ADP
ejpam-3712	179	76	the	the	DET
ejpam-3712	179	77	help	help	NOUN
ejpam-3712	179	78	of	of	ADP
ejpam-3712	179	79	software	software	NOUN
ejpam-3712	179	80	package	package	NOUN
ejpam-3712	179	81	.	.	PUNCT
ejpam-3712	180	1	in	in	ADP
ejpam-3712	180	2	the	the	DET
ejpam-3712	180	3	main	main	ADJ
ejpam-3712	180	4	results	result	NOUN
ejpam-3712	180	5	the	the	DET
ejpam-3712	180	6	formulae	formulae	NOUN
ejpam-3712	180	7	of	of	ADP
ejpam-3712	180	8	all	all	DET
ejpam-3712	180	9	the	the	DET
ejpam-3712	180	10	indices	index	NOUN
ejpam-3712	180	11	are	be	AUX
ejpam-3712	180	12	computed	compute	VERB
ejpam-3712	180	13	in	in	ADP
ejpam-3712	180	14	term	term	NOUN
ejpam-3712	180	15	of	of	ADP
ejpam-3712	180	16	n	n	CCONJ
ejpam-3712	180	17	,	,	PUNCT
ejpam-3712	180	18	k	k	NOUN
ejpam-3712	180	19	,	,	PUNCT
ejpam-3712	180	20	and	and	CCONJ
ejpam-3712	180	21	m	m	PROPN
ejpam-3712	180	22	,	,	PUNCT
ejpam-3712	180	23	where	where	SCONJ
ejpam-3712	180	24	n	n	PRON
ejpam-3712	180	25	is	be	AUX
ejpam-3712	180	26	number	number	NOUN
ejpam-3712	180	27	of	of	ADP
ejpam-3712	180	28	nodes	node	NOUN
ejpam-3712	180	29	in	in	ADP
ejpam-3712	180	30	first	first	ADJ
ejpam-3712	180	31	layer	layer	NOUN
ejpam-3712	180	32	,	,	PUNCT
ejpam-3712	180	33	the	the	DET
ejpam-3712	180	34	second	second	ADJ
ejpam-3712	180	35	layer	layer	NOUN
ejpam-3712	180	36	is	be	AUX
ejpam-3712	180	37	consisting	consist	VERB
ejpam-3712	180	38	on	on	ADP
ejpam-3712	180	39	k	k	PROPN
ejpam-3712	180	40	classes	class	NOUN
ejpam-3712	180	41	such	such	ADJ
ejpam-3712	180	42	that	that	SCONJ
ejpam-3712	180	43	each	each	DET
ejpam-3712	180	44	class	class	NOUN
ejpam-3712	180	45	has	have	VERB
ejpam-3712	180	46	m	m	PROPN
ejpam-3712	180	47	nodes	node	NOUN
ejpam-3712	180	48	and	and	CCONJ
ejpam-3712	180	49	the	the	DET
ejpam-3712	180	50	third	third	ADJ
ejpam-3712	180	51	layer	layer	NOUN
ejpam-3712	180	52	contains	contain	VERB
ejpam-3712	180	53	k	k	PROPN
ejpam-3712	180	54	nodes	node	NOUN
ejpam-3712	180	55	.	.	PUNCT
ejpam-3712	181	1	moreover	moreover	ADV
ejpam-3712	181	2	,	,	PUNCT
ejpam-3712	181	3	the	the	DET
ejpam-3712	181	4	total	total	ADJ
ejpam-3712	181	5	number	number	NOUN
ejpam-3712	181	6	of	of	ADP
ejpam-3712	181	7	vertices	vertex	NOUN
ejpam-3712	181	8	in	in	ADP
ejpam-3712	181	9	the	the	DET
ejpam-3712	181	10	probabilistic	probabilistic	ADJ
ejpam-3712	181	11	neural	neural	ADJ
ejpam-3712	181	12	network	network	NOUN
ejpam-3712	181	13	pnn(n	pnn(n	PROPN
ejpam-3712	181	14	,	,	PUNCT
ejpam-3712	181	15	k	k	PROPN
ejpam-3712	181	16	,	,	PUNCT
ejpam-3712	181	17	m	m	NOUN
ejpam-3712	181	18	)	)	PUNCT
ejpam-3712	181	19	(	(	PUNCT
ejpam-3712	181	20	order	order	NOUN
ejpam-3712	181	21	of	of	ADP
ejpam-3712	181	22	pnn(n	pnn(n	PROPN
ejpam-3712	181	23	,	,	PUNCT
ejpam-3712	181	24	k	k	PROPN
ejpam-3712	181	25	,	,	PUNCT
ejpam-3712	181	26	m	m	NOUN
ejpam-3712	181	27	)	)	PUNCT
ejpam-3712	181	28	)	)	PUNCT
ejpam-3712	181	29	is	be	AUX
ejpam-3712	181	30	|v	|v	X
ejpam-3712	181	31	(	(	PUNCT
ejpam-3712	181	32	pnn(n	pnn(n	PROPN
ejpam-3712	181	33	,	,	PUNCT
ejpam-3712	181	34	k	k	NOUN
ejpam-3712	181	35	,	,	PUNCT
ejpam-3712	181	36	m))|	m))|	PROPN
ejpam-3712	181	37	=	=	SYM
ejpam-3712	181	38	v	v	NOUN
ejpam-3712	181	39	=	=	SYM
ejpam-3712	181	40	n	n	PROPN
ejpam-3712	181	41	+	+	NUM
ejpam-3712	181	42	k(m	k(m	PROPN
ejpam-3712	182	1	+	+	CCONJ
ejpam-3712	182	2	1	1	NUM
ejpam-3712	182	3	)	)	PUNCT
ejpam-3712	182	4	.	.	PUNCT
ejpam-3712	183	1	if	if	SCONJ
ejpam-3712	183	2	we	we	PRON
ejpam-3712	183	3	assume	assume	VERB
ejpam-3712	183	4	k	k	X
ejpam-3712	183	5	=	=	PUNCT
ejpam-3712	183	6	n	n	PROPN
ejpam-3712	183	7	and	and	CCONJ
ejpam-3712	183	8	m	m	PROPN
ejpam-3712	183	9	=	=	ADJ
ejpam-3712	183	10	1	1	NUM
ejpam-3712	183	11	,	,	PUNCT
ejpam-3712	183	12	then	then	ADV
ejpam-3712	183	13	the	the	DET
ejpam-3712	183	14	probabilistic	probabilistic	ADJ
ejpam-3712	183	15	neural	neural	ADJ
ejpam-3712	183	16	network	network	NOUN
ejpam-3712	183	17	becomes	become	VERB
ejpam-3712	183	18	pnn(n	pnn(n	PROPN
ejpam-3712	183	19	,	,	PUNCT
ejpam-3712	183	20	n	n	CCONJ
ejpam-3712	183	21	,	,	PUNCT
ejpam-3712	183	22	1	1	NUM
ejpam-3712	183	23	)	)	PUNCT
ejpam-3712	183	24	with	with	ADP
ejpam-3712	183	25	order	order	NOUN
ejpam-3712	183	26	v	v	ADP
ejpam-3712	183	27	=	=	SYM
ejpam-3712	183	28	3n	3n	NOUN
ejpam-3712	183	29	,	,	PUNCT
ejpam-3712	183	30	where	where	SCONJ
ejpam-3712	183	31	n	n	PRON
ejpam-3712	183	32	is	be	AUX
ejpam-3712	183	33	a	a	DET
ejpam-3712	183	34	natural	natural	ADJ
ejpam-3712	183	35	number	number	NOUN
ejpam-3712	183	36	.	.	PUNCT
ejpam-3712	184	1	in	in	ADP
ejpam-3712	184	2	fig	fig	NOUN
ejpam-3712	184	3	.	.	PUNCT
ejpam-3712	185	1	2	2	NUM
ejpam-3712	185	2	,	,	PUNCT
ejpam-3712	185	3	along	along	ADP
ejpam-3712	185	4	the	the	DET
ejpam-3712	185	5	horizontal	horizontal	ADJ
ejpam-3712	185	6	line	line	NOUN
ejpam-3712	185	7	the	the	DET
ejpam-3712	185	8	values	value	NOUN
ejpam-3712	185	9	of	of	ADP
ejpam-3712	185	10	v	v	NOUN
ejpam-3712	185	11	for	for	ADP
ejpam-3712	185	12	the	the	DET
ejpam-3712	185	13	probabilistic	probabilistic	ADJ
ejpam-3712	185	14	neural	neural	ADJ
ejpam-3712	185	15	network	network	NOUN
ejpam-3712	185	16	references	reference	NOUN
ejpam-3712	185	17	1160	1160	NUM
ejpam-3712	185	18	pnn(n	pnn(n	PROPN
ejpam-3712	185	19	,	,	PUNCT
ejpam-3712	185	20	n	n	CCONJ
ejpam-3712	185	21	,	,	PUNCT
ejpam-3712	185	22	1	1	NUM
ejpam-3712	185	23	)	)	PUNCT
ejpam-3712	185	24	are	be	AUX
ejpam-3712	185	25	taken	take	VERB
ejpam-3712	185	26	and	and	CCONJ
ejpam-3712	185	27	along	along	ADP
ejpam-3712	185	28	the	the	DET
ejpam-3712	185	29	vertical	vertical	ADJ
ejpam-3712	185	30	line	line	NOUN
ejpam-3712	185	31	the	the	DET
ejpam-3712	185	32	computed	computed	ADJ
ejpam-3712	185	33	values	value	NOUN
ejpam-3712	185	34	of	of	ADP
ejpam-3712	185	35	the	the	DET
ejpam-3712	185	36	indices	index	NOUN
ejpam-3712	185	37	are	be	AUX
ejpam-3712	185	38	shown	show	VERB
ejpam-3712	185	39	.	.	PUNCT
ejpam-3712	186	1	among	among	ADP
ejpam-3712	186	2	them	they	PRON
ejpam-3712	186	3	the	the	DET
ejpam-3712	186	4	randic	randic	ADJ
ejpam-3712	186	5	type	type	NOUN
ejpam-3712	186	6	index	index	NOUN
ejpam-3712	186	7	is	be	AUX
ejpam-3712	186	8	dominant	dominant	ADJ
ejpam-3712	186	9	.	.	PUNCT
ejpam-3712	187	1	moreover	moreover	ADV
ejpam-3712	187	2	,	,	PUNCT
ejpam-3712	187	3	all	all	DET
ejpam-3712	187	4	the	the	DET
ejpam-3712	187	5	adriatic	adriatic	ADJ
ejpam-3712	187	6	indices	index	NOUN
ejpam-3712	187	7	remain	remain	VERB
ejpam-3712	187	8	constant	constant	ADJ
ejpam-3712	187	9	approximately	approximately	ADV
ejpam-3712	187	10	with	with	ADP
ejpam-3712	187	11	increasing	increase	VERB
ejpam-3712	187	12	values	value	NOUN
ejpam-3712	187	13	of	of	ADP
ejpam-3712	187	14	v.	v.	ADP
ejpam-3712	187	15	in	in	ADP
ejpam-3712	187	16	this	this	DET
ejpam-3712	187	17	paper	paper	NOUN
ejpam-3712	187	18	,	,	PUNCT
ejpam-3712	187	19	the	the	DET
ejpam-3712	187	20	adriatic	adriatic	ADJ
ejpam-3712	187	21	indices	index	NOUN
ejpam-3712	187	22	of	of	ADP
ejpam-3712	187	23	the	the	DET
ejpam-3712	187	24	probabilistic	probabilistic	ADJ
ejpam-3712	187	25	neural	neural	ADJ
ejpam-3712	187	26	network	network	NOUN
ejpam-3712	187	27	are	be	AUX
ejpam-3712	187	28	studied	study	VERB
ejpam-3712	187	29	and	and	CCONJ
ejpam-3712	187	30	the	the	DET
ejpam-3712	187	31	analytical	analytical	ADJ
ejpam-3712	187	32	closed	close	VERB
ejpam-3712	187	33	formulas	formula	NOUN
ejpam-3712	187	34	are	be	AUX
ejpam-3712	187	35	determined	determined	ADJ
ejpam-3712	187	36	that	that	PRON
ejpam-3712	187	37	will	will	AUX
ejpam-3712	187	38	help	help	VERB
ejpam-3712	187	39	to	to	PART
ejpam-3712	187	40	understand	understand	VERB
ejpam-3712	187	41	the	the	DET
ejpam-3712	187	42	underlying	underlie	VERB
ejpam-3712	187	43	topologies	topology	NOUN
ejpam-3712	187	44	related	relate	VERB
ejpam-3712	187	45	to	to	ADP
ejpam-3712	187	46	the	the	DET
ejpam-3712	187	47	physical	physical	ADJ
ejpam-3712	187	48	features	feature	NOUN
ejpam-3712	187	49	of	of	ADP
ejpam-3712	187	50	this	this	DET
ejpam-3712	187	51	network	network	NOUN
ejpam-3712	187	52	.	.	PUNCT
ejpam-3712	188	1	acknowledgements	acknowledgement	VERB
ejpam-3712	188	2	the	the	DET
ejpam-3712	188	3	authors	author	NOUN
ejpam-3712	188	4	thank	thank	VERB
ejpam-3712	188	5	the	the	DET
ejpam-3712	188	6	referees	referee	NOUN
ejpam-3712	188	7	for	for	ADP
ejpam-3712	188	8	their	their	PRON
ejpam-3712	188	9	useful	useful	ADJ
ejpam-3712	188	10	comments	comment	NOUN
ejpam-3712	188	11	that	that	PRON
ejpam-3712	188	12	helped	help	VERB
ejpam-3712	188	13	to	to	PART
ejpam-3712	188	14	improve	improve	VERB
ejpam-3712	188	15	this	this	DET
ejpam-3712	188	16	paper	paper	NOUN
ejpam-3712	188	17	.	.	PUNCT
ejpam-3712	189	1	references	reference	NOUN
ejpam-3712	189	2	[	[	X
ejpam-3712	189	3	1	1	X
ejpam-3712	189	4	]	]	X
ejpam-3712	189	5	v.	v.	PROPN
ejpam-3712	189	6	alexander	alexander	PROPN
ejpam-3712	189	7	.	.	PUNCT
ejpam-3712	190	1	upper	upper	ADJ
ejpam-3712	190	2	and	and	CCONJ
ejpam-3712	190	3	lower	low	ADJ
ejpam-3712	190	4	bounds	bound	NOUN
ejpam-3712	190	5	of	of	ADP
ejpam-3712	190	6	symmetric	symmetric	ADJ
ejpam-3712	190	7	division	division	NOUN
ejpam-3712	190	8	deg	deg	PROPN
ejpam-3712	190	9	index	index	PROPN
ejpam-3712	190	10	.	.	PUNCT
ejpam-3712	191	1	iranian	iranian	PROPN
ejpam-3712	191	2	journal	journal	PROPN
ejpam-3712	191	3	of	of	ADP
ejpam-3712	191	4	mathematical	mathematical	ADJ
ejpam-3712	191	5	chemistry	chemistry	NOUN
ejpam-3712	191	6	,	,	PUNCT
ejpam-3712	191	7	5(2):91–98	5(2):91–98	NUM
ejpam-3712	191	8	,	,	PUNCT
ejpam-3712	191	9	2014	2014	NUM
ejpam-3712	191	10	.	.	PUNCT
ejpam-3712	192	1	[	[	X
ejpam-3712	192	2	2	2	NUM
ejpam-3712	192	3	]	]	X
ejpam-3712	192	4	n.	n.	PROPN
ejpam-3712	192	5	ananda	ananda	PROPN
ejpam-3712	192	6	,	,	PUNCT
ejpam-3712	192	7	p.s	p.s	PROPN
ejpam-3712	192	8	.	.	PROPN
ejpam-3712	192	9	ranjini	ranjini	PROPN
ejpam-3712	192	10	,	,	PUNCT
ejpam-3712	192	11	v.	v.	ADP
ejpam-3712	192	12	lokesha	lokesha	PROPN
ejpam-3712	192	13	,	,	PUNCT
ejpam-3712	192	14	and	and	CCONJ
ejpam-3712	192	15	s.a	s.a	PROPN
ejpam-3712	192	16	.	.	PROPN
ejpam-3712	192	17	wazzan	wazzan	PROPN
ejpam-3712	192	18	.	.	PUNCT
ejpam-3712	193	1	subdivision	subdivision	NOUN
ejpam-3712	193	2	and	and	CCONJ
ejpam-3712	193	3	semitotal	semitotal	ADJ
ejpam-3712	193	4	point	point	NOUN
ejpam-3712	193	5	graphs	graph	NOUN
ejpam-3712	193	6	of	of	ADP
ejpam-3712	193	7	archimedean	archimedean	ADJ
ejpam-3712	193	8	lattices	lattice	NOUN
ejpam-3712	193	9	on	on	ADP
ejpam-3712	193	10	some	some	DET
ejpam-3712	193	11	toplogical	toplogical	ADJ
ejpam-3712	193	12	indices	index	NOUN
ejpam-3712	193	13	.	.	PUNCT
ejpam-3712	194	1	volume	volume	NOUN
ejpam-3712	194	2	22	22	NUM
ejpam-3712	194	3	,	,	PUNCT
ejpam-3712	194	4	pages	page	VERB
ejpam-3712	194	5	830–837	830–837	NUM
ejpam-3712	194	6	.	.	PUNCT
ejpam-3712	195	1	proceedings	proceeding	NOUN
ejpam-3712	195	2	of	of	ADP
ejpam-3712	195	3	the	the	DET
ejpam-3712	195	4	jangieon	jangieon	PROPN
ejpam-3712	195	5	mathematical	mathematical	PROPN
ejpam-3712	195	6	society	society	NOUN
ejpam-3712	195	7	,	,	PUNCT
ejpam-3712	195	8	2019	2019	NUM
ejpam-3712	195	9	.	.	PUNCT
ejpam-3712	196	1	[	[	X
ejpam-3712	196	2	3	3	X
ejpam-3712	196	3	]	]	X
ejpam-3712	196	4	j.	j.	PROPN
ejpam-3712	196	5	devillers	devillers	PROPN
ejpam-3712	196	6	and	and	CCONJ
ejpam-3712	196	7	a.	a.	NOUN
ejpam-3712	196	8	t.	t.	PROPN
ejpam-3712	196	9	balaban	balaban	PROPN
ejpam-3712	196	10	(	(	PUNCT
ejpam-3712	196	11	eds	ed	NOUN
ejpam-3712	196	12	.	.	PUNCT
ejpam-3712	196	13	)	)	PUNCT
ejpam-3712	196	14	.	.	PUNCT
ejpam-3712	197	1	gordon	gordon	PROPN
ejpam-3712	197	2	and	and	CCONJ
ejpam-3712	197	3	breach	breach	PROPN
ejpam-3712	197	4	,	,	PUNCT
ejpam-3712	197	5	amsterdam	amsterdam	PROPN
ejpam-3712	197	6	,	,	PUNCT
ejpam-3712	197	7	1999	1999	NUM
ejpam-3712	197	8	.	.	PUNCT
ejpam-3712	198	1	[	[	X
ejpam-3712	198	2	4	4	NUM
ejpam-3712	198	3	]	]	X
ejpam-3712	198	4	budak	budak	PROPN
ejpam-3712	198	5	f.u	f.u	PROPN
ejpam-3712	198	6	and	and	CCONJ
ejpam-3712	198	7	beyli	beyli	PROPN
ejpam-3712	198	8	e.d	e.d	PROPN
ejpam-3712	198	9	.	.	PROPN
ejpam-3712	198	10	detection	detection	NOUN
ejpam-3712	198	11	of	of	ADP
ejpam-3712	198	12	resistivity	resistivity	NOUN
ejpam-3712	198	13	for	for	ADP
ejpam-3712	198	14	antibiotics	antibiotic	NOUN
ejpam-3712	198	15	by	by	ADP
ejpam-3712	198	16	probabilistic	probabilistic	ADJ
ejpam-3712	198	17	neural	neural	ADJ
ejpam-3712	198	18	networks	network	NOUN
ejpam-3712	198	19	.	.	PUNCT
ejpam-3712	199	1	journal	journal	PROPN
ejpam-3712	199	2	of	of	ADP
ejpam-3712	199	3	medical	medical	ADJ
ejpam-3712	199	4	systems	system	NOUN
ejpam-3712	199	5	,	,	PUNCT
ejpam-3712	199	6	35:87–91	35:87–91	NUM
ejpam-3712	199	7	,	,	PUNCT
ejpam-3712	199	8	2011	2011	NUM
ejpam-3712	199	9	.	.	PUNCT
ejpam-3712	200	1	[	[	X
ejpam-3712	200	2	5	5	NUM
ejpam-3712	200	3	]	]	PUNCT
ejpam-3712	200	4	c.	c.	PROPN
ejpam-3712	200	5	k.	k.	PROPN
ejpam-3712	200	6	gupta	gupta	PROPN
ejpam-3712	200	7	,	,	PUNCT
ejpam-3712	200	8	v.	v.	ADP
ejpam-3712	200	9	lokesha	lokesha	PROPN
ejpam-3712	200	10	,	,	PUNCT
ejpam-3712	200	11	and	and	CCONJ
ejpam-3712	200	12	s.	s.	PROPN
ejpam-3712	200	13	b.	b.	PROPN
ejpam-3712	200	14	shetty	shetty	PROPN
ejpam-3712	200	15	.	.	PUNCT
ejpam-3712	201	1	on	on	ADP
ejpam-3712	201	2	the	the	DET
ejpam-3712	201	3	symmetric	symmetric	ADJ
ejpam-3712	201	4	division	division	NOUN
ejpam-3712	201	5	deg	deg	PROPN
ejpam-3712	201	6	index	index	NOUN
ejpam-3712	201	7	of	of	ADP
ejpam-3712	201	8	graph	graph	NOUN
ejpam-3712	201	9	.	.	PUNCT
ejpam-3712	202	1	41(1):59–80	41(1):59–80	NUM
ejpam-3712	202	2	,	,	PUNCT
ejpam-3712	202	3	2016	2016	NUM
ejpam-3712	202	4	.	.	PUNCT
ejpam-3712	203	1	[	[	X
ejpam-3712	203	2	6	6	NUM
ejpam-3712	203	3	]	]	PUNCT
ejpam-3712	203	4	c.	c.	PROPN
ejpam-3712	203	5	k.	k.	PROPN
ejpam-3712	203	6	gupta	gupta	PROPN
ejpam-3712	203	7	,	,	PUNCT
ejpam-3712	203	8	v.	v.	ADP
ejpam-3712	203	9	lokesha	lokesha	PROPN
ejpam-3712	203	10	,	,	PUNCT
ejpam-3712	203	11	s.	s.	PROPN
ejpam-3712	203	12	b.	b.	PROPN
ejpam-3712	203	13	shetty	shetty	PROPN
ejpam-3712	203	14	,	,	PUNCT
ejpam-3712	203	15	and	and	CCONJ
ejpam-3712	203	16	p.	p.	PROPN
ejpam-3712	203	17	s.	s.	PROPN
ejpam-3712	203	18	ranjini	ranjini	PROPN
ejpam-3712	203	19	.	.	PUNCT
ejpam-3712	204	1	graph	graph	NOUN
ejpam-3712	204	2	operations	operation	NOUN
ejpam-3712	204	3	on	on	ADP
ejpam-3712	204	4	symmetric	symmetric	ADJ
ejpam-3712	204	5	division	division	NOUN
ejpam-3712	204	6	deg	deg	PROPN
ejpam-3712	204	7	index	index	NOUN
ejpam-3712	204	8	of	of	ADP
ejpam-3712	204	9	graphs	graph	NOUN
ejpam-3712	204	10	.	.	PUNCT
ejpam-3712	205	1	6(1):280286	6(1):280286	NUM
ejpam-3712	205	2	,	,	PUNCT
ejpam-3712	205	3	2017	2017	NUM
ejpam-3712	205	4	.	.	PUNCT
ejpam-3712	206	1	[	[	X
ejpam-3712	206	2	7	7	X
ejpam-3712	206	3	]	]	X
ejpam-3712	206	4	m.	m.	NOUN
ejpam-3712	206	5	javaid	javaid	PROPN
ejpam-3712	206	6	and	and	CCONJ
ejpam-3712	206	7	jinde	jinde	VERB
ejpam-3712	206	8	cao	cao	PROPN
ejpam-3712	206	9	.	.	PUNCT
ejpam-3712	207	1	computing	compute	VERB
ejpam-3712	207	2	topological	topological	ADJ
ejpam-3712	207	3	indices	index	NOUN
ejpam-3712	207	4	of	of	ADP
ejpam-3712	207	5	probabilistic	probabilistic	ADJ
ejpam-3712	207	6	neural	neural	ADJ
ejpam-3712	207	7	network	network	NOUN
ejpam-3712	207	8	.	.	PUNCT
ejpam-3712	208	1	30:38693876	30:38693876	NUM
ejpam-3712	208	2	,	,	PUNCT
ejpam-3712	208	3	2018	2018	NUM
ejpam-3712	208	4	.	.	PUNCT
ejpam-3712	209	1	[	[	X
ejpam-3712	209	2	8	8	NUM
ejpam-3712	209	3	]	]	X
ejpam-3712	209	4	v.	v.	ADP
ejpam-3712	209	5	lokesha	lokesha	PROPN
ejpam-3712	209	6	and	and	CCONJ
ejpam-3712	209	7	t.	t.	PROPN
ejpam-3712	209	8	deepika	deepika	PROPN
ejpam-3712	209	9	.	.	PUNCT
ejpam-3712	210	1	symmetric	symmetric	ADJ
ejpam-3712	210	2	division	division	PROPN
ejpam-3712	210	3	deg	deg	PROPN
ejpam-3712	210	4	index	index	NOUN
ejpam-3712	210	5	of	of	ADP
ejpam-3712	210	6	tricyclic	tricyclic	ADJ
ejpam-3712	210	7	and	and	CCONJ
ejpam-3712	210	8	tetracyclic	tetracyclic	NOUN
ejpam-3712	210	9	graphs	graph	NOUN
ejpam-3712	210	10	.	.	PUNCT
ejpam-3712	211	1	volume	volume	NOUN
ejpam-3712	211	2	7	7	NUM
ejpam-3712	211	3	,	,	PUNCT
ejpam-3712	211	4	pages	page	NOUN
ejpam-3712	211	5	53–55	53–55	NUM
ejpam-3712	211	6	.	.	PUNCT
ejpam-3712	212	1	international	international	ADJ
ejpam-3712	212	2	journal	journal	NOUN
ejpam-3712	212	3	of	of	ADP
ejpam-3712	212	4	scientific	scientific	ADJ
ejpam-3712	212	5	and	and	CCONJ
ejpam-3712	212	6	engineering	engineering	NOUN
ejpam-3712	212	7	research	research	NOUN
ejpam-3712	212	8	,	,	PUNCT
ejpam-3712	212	9	2016	2016	NUM
ejpam-3712	212	10	.	.	PUNCT
ejpam-3712	213	1	[	[	X
ejpam-3712	213	2	9	9	NUM
ejpam-3712	213	3	]	]	PUNCT
ejpam-3712	213	4	v.	v.	ADP
ejpam-3712	213	5	lokesha	lokesha	PROPN
ejpam-3712	213	6	,	,	PUNCT
ejpam-3712	213	7	t.	t.	PROPN
ejpam-3712	213	8	deepika	deepika	PROPN
ejpam-3712	213	9	,	,	PUNCT
ejpam-3712	213	10	p.	p.	PROPN
ejpam-3712	213	11	s.	s.	PROPN
ejpam-3712	213	12	ranjini	ranjini	PROPN
ejpam-3712	213	13	,	,	PUNCT
ejpam-3712	213	14	and	and	CCONJ
ejpam-3712	213	15	cangul	cangul	NOUN
ejpam-3712	213	16	.	.	PUNCT
ejpam-3712	213	17	i.	i.	PROPN
ejpam-3712	213	18	n.	n.	PROPN
ejpam-3712	213	19	,	,	PUNCT
ejpam-3712	213	20	operations	operation	NOUN
ejpam-3712	213	21	of	of	ADP
ejpam-3712	213	22	nanostructures	nanostructure	NOUN
ejpam-3712	213	23	via	via	ADP
ejpam-3712	213	24	sdd	sdd	PROPN
ejpam-3712	213	25	,	,	PUNCT
ejpam-3712	213	26	abc4	abc4	PROPN
ejpam-3712	213	27	,	,	PUNCT
ejpam-3712	213	28	ga5	ga5	PROPN
ejpam-3712	213	29	indices	index	NOUN
ejpam-3712	213	30	.	.	PUNCT
ejpam-3712	214	1	2(1):173–180	2(1):173–180	NUM
ejpam-3712	214	2	,	,	PUNCT
ejpam-3712	214	3	2017	2017	NUM
ejpam-3712	214	4	.	.	PUNCT
ejpam-3712	215	1	[	[	X
ejpam-3712	215	2	10	10	NUM
ejpam-3712	215	3	]	]	X
ejpam-3712	215	4	v.	v.	ADP
ejpam-3712	215	5	lokesha	lokesha	PROPN
ejpam-3712	215	6	,	,	PUNCT
ejpam-3712	215	7	m.	m.	NOUN
ejpam-3712	215	8	manjunath	manjunath	PROPN
ejpam-3712	215	9	,	,	PUNCT
ejpam-3712	215	10	and	and	CCONJ
ejpam-3712	215	11	k.m	k.m	PROPN
ejpam-3712	215	12	.	.	PROPN
ejpam-3712	215	13	devendraiah	devendraiah	PROPN
ejpam-3712	215	14	.	.	PUNCT
ejpam-3712	216	1	adriatic	adriatic	ADJ
ejpam-3712	216	2	indices	index	NOUN
ejpam-3712	216	3	and	and	CCONJ
ejpam-3712	216	4	sanskruti	sanskruti	NOUN
ejpam-3712	216	5	index	index	NOUN
ejpam-3712	216	6	envisage	envisage	NOUN
ejpam-3712	216	7	of	of	ADP
ejpam-3712	216	8	carbon	carbon	NOUN
ejpam-3712	216	9	nanocone	nanocone	NOUN
ejpam-3712	216	10	.	.	PUNCT
ejpam-3712	217	1	9(4):280286	9(4):280286	NUM
ejpam-3712	217	2	,	,	PUNCT
ejpam-3712	217	3	2019	2019	NUM
ejpam-3712	217	4	.	.	PUNCT
ejpam-3712	218	1	[	[	X
ejpam-3712	218	2	11	11	NUM
ejpam-3712	218	3	]	]	X
ejpam-3712	218	4	bascil	bascil	PROPN
ejpam-3712	218	5	ms	ms	NOUN
ejpam-3712	218	6	and	and	CCONJ
ejpam-3712	218	7	oztekin	oztekin	PROPN
ejpam-3712	218	8	h.	h.	PROPN
ejpam-3712	218	9	a	a	DET
ejpam-3712	218	10	study	study	NOUN
ejpam-3712	218	11	on	on	ADP
ejpam-3712	218	12	hepatitis	hepatitis	NOUN
ejpam-3712	218	13	disease	disease	NOUN
ejpam-3712	218	14	diagnosis	diagnosis	NOUN
ejpam-3712	218	15	using	use	VERB
ejpam-3712	218	16	probabilistic	probabilistic	ADJ
ejpam-3712	218	17	neural	neural	ADJ
ejpam-3712	218	18	network	network	NOUN
ejpam-3712	218	19	.	.	PUNCT
ejpam-3712	219	1	36:1603–1606	36:1603–1606	NUM
ejpam-3712	219	2	,	,	PUNCT
ejpam-3712	219	3	2012	2012	NUM
ejpam-3712	219	4	.	.	PUNCT
ejpam-3712	220	1	references	reference	NOUN
ejpam-3712	220	2	1161	1161	NUM
ejpam-3712	220	3	[	[	X
ejpam-3712	220	4	12	12	NUM
ejpam-3712	220	5	]	]	X
ejpam-3712	220	6	damir	damir	PROPN
ejpam-3712	220	7	vukicevic	vukicevic	PROPN
ejpam-3712	220	8	and	and	CCONJ
ejpam-3712	220	9	marija	marija	PROPN
ejpam-3712	220	10	gasperov	gasperov	PROPN
ejpam-3712	220	11	.	.	PUNCT
ejpam-3712	221	1	bond	bond	NOUN
ejpam-3712	221	2	additive	additive	VERB
ejpam-3712	221	3	modeling	model	VERB
ejpam-3712	221	4	1	1	NUM
ejpam-3712	221	5	.	.	PUNCT
ejpam-3712	222	1	adriatic	adriatic	ADJ
ejpam-3712	222	2	indices	index	NOUN
ejpam-3712	222	3	.	.	PUNCT
ejpam-3712	223	1	83(3	83(3	VERB
ejpam-3712	223	2	)	)	PUNCT
ejpam-3712	223	3	,	,	PUNCT
ejpam-3712	223	4	2010	2010	NUM
ejpam-3712	223	5	.	.	PUNCT
ejpam-3712	224	1	[	[	X
ejpam-3712	224	2	13	13	NUM
ejpam-3712	224	3	]	]	PUNCT
ejpam-3712	224	4	zeba	zeba	PROPN
ejpam-3712	224	5	y	y	PROPN
ejpam-3712	224	6	,	,	PUNCT
ejpam-3712	224	7	b.	b.	PROPN
ejpam-3712	224	8	chaluvaraja	chaluvaraja	PROPN
ejpam-3712	224	9	,	,	PUNCT
ejpam-3712	224	10	v.	v.	ADP
ejpam-3712	224	11	lokesha	lokesha	PROPN
ejpam-3712	224	12	,	,	PUNCT
ejpam-3712	224	13	and	and	CCONJ
ejpam-3712	224	14	deepika	deepika	PROPN
ejpam-3712	224	15	t.	t.	PROPN
ejpam-3712	224	16	computation	computation	NOUN
ejpam-3712	224	17	of	of	ADP
ejpam-3712	224	18	misbalanced	misbalanced	ADJ
ejpam-3712	224	19	type	type	NOUN
ejpam-3712	224	20	degree	degree	NOUN
ejpam-3712	224	21	indices	index	NOUN
ejpam-3712	224	22	of	of	ADP
ejpam-3712	224	23	certain	certain	ADJ
ejpam-3712	224	24	classes	class	NOUN
ejpam-3712	224	25	of	of	ADP
ejpam-3712	224	26	derived	derive	VERB
ejpam-3712	224	27	regular	regular	ADJ
ejpam-3712	224	28	graph	graph	NOUN
ejpam-3712	224	29	.	.	PUNCT
ejpam-3712	225	1	3:6169	3:6169	NUM
ejpam-3712	225	2	,	,	PUNCT
ejpam-3712	225	3	2019	2019	NUM
ejpam-3712	225	4	.	.	PUNCT
ejpam-3712	226	1	[	[	X
ejpam-3712	226	2	14	14	NUM
ejpam-3712	226	3	]	]	X
ejpam-3712	226	4	zeba	zeba	PROPN
ejpam-3712	226	5	y	y	PROPN
ejpam-3712	226	6	,	,	PUNCT
ejpam-3712	226	7	v.	v.	ADP
ejpam-3712	226	8	lokesha	lokesha	PROPN
ejpam-3712	226	9	,	,	PUNCT
ejpam-3712	226	10	and	and	CCONJ
ejpam-3712	226	11	deepika	deepika	PROPN
ejpam-3712	226	12	.	.	PUNCT
ejpam-3712	227	1	t.	t.	NOUN
ejpam-3712	227	2	graph	graph	NOUN
ejpam-3712	227	3	operations	operation	NOUN
ejpam-3712	227	4	on	on	ADP
ejpam-3712	227	5	symmetric	symmetric	ADJ
ejpam-3712	227	6	division	division	NOUN
ejpam-3712	227	7	deg	deg	PROPN
ejpam-3712	227	8	index	index	NOUN
ejpam-3712	227	9	of	of	ADP
ejpam-3712	227	10	graphs	graph	NOUN
ejpam-3712	227	11	.	.	PUNCT
ejpam-3712	228	1	28(1):69–76	28(1):69–76	NUM
ejpam-3712	228	2	,	,	PUNCT
ejpam-3712	228	3	2019	2019	NUM
ejpam-3712	228	4	.	.	PUNCT