id	sid	tid	token	lemma	pos
ejpam-6525	1	1	european	european	PROPN
ejpam-6525	1	2	journal	journal	PROPN
ejpam-6525	1	3	of	of	ADP
ejpam-6525	1	4	pure	pure	ADJ
ejpam-6525	1	5	and	and	CCONJ
ejpam-6525	1	6	applied	applied	ADJ
ejpam-6525	1	7	mathematics	mathematic	NOUN
ejpam-6525	1	8	2025	2025	NUM
ejpam-6525	1	9	,	,	PUNCT
ejpam-6525	1	10	vol	vol	NOUN
ejpam-6525	1	11	.	.	PROPN
ejpam-6525	1	12	18	18	NUM
ejpam-6525	1	13	,	,	PUNCT
ejpam-6525	1	14	issue	issue	NOUN
ejpam-6525	1	15	3	3	NUM
ejpam-6525	1	16	,	,	PUNCT
ejpam-6525	1	17	article	article	NOUN
ejpam-6525	1	18	number	number	NOUN
ejpam-6525	1	19	6525	6525	NUM
ejpam-6525	1	20	issn	issn	VERB
ejpam-6525	1	21	1307	1307	NUM
ejpam-6525	1	22	-	-	SYM
ejpam-6525	1	23	5543	5543	NUM
ejpam-6525	1	24	–	–	PUNCT
ejpam-6525	1	25	ejpam.com	ejpam.com	X
ejpam-6525	1	26	published	publish	VERB
ejpam-6525	1	27	by	by	ADP
ejpam-6525	1	28	new	new	PROPN
ejpam-6525	1	29	york	york	PROPN
ejpam-6525	1	30	business	business	PROPN
ejpam-6525	1	31	global	global	ADJ
ejpam-6525	1	32	mr	mr	PROPN
ejpam-6525	1	33	-	-	PUNCT
ejpam-6525	1	34	metric	metric	ADJ
ejpam-6525	1	35	spaces	space	NOUN
ejpam-6525	1	36	:	:	PUNCT
ejpam-6525	1	37	theory	theory	NOUN
ejpam-6525	1	38	and	and	CCONJ
ejpam-6525	1	39	applications	application	NOUN
ejpam-6525	1	40	in	in	ADP
ejpam-6525	1	41	weighted	weighted	ADJ
ejpam-6525	1	42	graphs	graph	NOUN
ejpam-6525	1	43	,	,	PUNCT
ejpam-6525	1	44	expander	expander	NOUN
ejpam-6525	1	45	graphs	graph	NOUN
ejpam-6525	1	46	,	,	PUNCT
ejpam-6525	1	47	and	and	CCONJ
ejpam-6525	1	48	fixed	fix	VERB
ejpam-6525	1	49	-	-	PUNCT
ejpam-6525	1	50	point	point	NOUN
ejpam-6525	1	51	theorems	theorem	NOUN
ejpam-6525	1	52	abed	abe	VERB
ejpam-6525	1	53	al	al	PROPN
ejpam-6525	1	54	-	-	PUNCT
ejpam-6525	1	55	rahman	rahman	PROPN
ejpam-6525	1	56	m.	m.	PROPN
ejpam-6525	1	57	malkawi1,∗	malkawi1,∗	PROPN
ejpam-6525	1	58	,	,	PUNCT
ejpam-6525	1	59	ayat	ayat	PROPN
ejpam-6525	1	60	m.	m.	NOUN
ejpam-6525	1	61	rabaiah1	rabaiah1	PROPN
ejpam-6525	1	62	1	1	NUM
ejpam-6525	1	63	department	department	NOUN
ejpam-6525	1	64	of	of	ADP
ejpam-6525	1	65	mathematics	mathematic	NOUN
ejpam-6525	1	66	,	,	PUNCT
ejpam-6525	1	67	faculty	faculty	NOUN
ejpam-6525	1	68	of	of	ADP
ejpam-6525	1	69	arts	art	NOUN
ejpam-6525	1	70	and	and	CCONJ
ejpam-6525	1	71	science	science	NOUN
ejpam-6525	1	72	,	,	PUNCT
ejpam-6525	1	73	amman	amman	PROPN
ejpam-6525	1	74	arab	arab	PROPN
ejpam-6525	1	75	university	university	PROPN
ejpam-6525	1	76	,	,	PUNCT
ejpam-6525	1	77	amman	amman	PROPN
ejpam-6525	1	78	11953	11953	NUM
ejpam-6525	1	79	,	,	PUNCT
ejpam-6525	1	80	jordan	jordan	PROPN
ejpam-6525	1	81	abstract	abstract	PROPN
ejpam-6525	1	82	.	.	PUNCT
ejpam-6525	2	1	this	this	DET
ejpam-6525	2	2	paper	paper	NOUN
ejpam-6525	2	3	introduces	introduce	VERB
ejpam-6525	2	4	the	the	DET
ejpam-6525	2	5	concept	concept	NOUN
ejpam-6525	2	6	of	of	ADP
ejpam-6525	2	7	mr	mr	PROPN
ejpam-6525	2	8	-	-	PUNCT
ejpam-6525	2	9	metric	metric	ADJ
ejpam-6525	2	10	spaces	space	NOUN
ejpam-6525	2	11	,	,	PUNCT
ejpam-6525	2	12	a	a	DET
ejpam-6525	2	13	generalization	generalization	NOUN
ejpam-6525	2	14	of	of	ADP
ejpam-6525	2	15	traditional	traditional	ADJ
ejpam-6525	2	16	metric	metric	ADJ
ejpam-6525	2	17	spaces	space	NOUN
ejpam-6525	2	18	that	that	PRON
ejpam-6525	2	19	operates	operate	VERB
ejpam-6525	2	20	on	on	ADP
ejpam-6525	2	21	triples	triple	NOUN
ejpam-6525	2	22	of	of	ADP
ejpam-6525	2	23	points	point	NOUN
ejpam-6525	2	24	rather	rather	ADV
ejpam-6525	2	25	than	than	ADP
ejpam-6525	2	26	pairs	pair	NOUN
ejpam-6525	2	27	.	.	PUNCT
ejpam-6525	3	1	we	we	PRON
ejpam-6525	3	2	define	define	VERB
ejpam-6525	3	3	mr	mr	PROPN
ejpam-6525	3	4	-	-	PUNCT
ejpam-6525	3	5	metrics	metric	NOUN
ejpam-6525	3	6	and	and	CCONJ
ejpam-6525	3	7	establish	establish	VERB
ejpam-6525	3	8	their	their	PRON
ejpam-6525	3	9	fundamental	fundamental	ADJ
ejpam-6525	3	10	properties	property	NOUN
ejpam-6525	3	11	,	,	PUNCT
ejpam-6525	3	12	including	include	VERB
ejpam-6525	3	13	non	non	ADJ
ejpam-6525	3	14	-	-	ADJ
ejpam-6525	3	15	negativity	negativity	ADJ
ejpam-6525	3	16	,	,	PUNCT
ejpam-6525	3	17	identity	identity	NOUN
ejpam-6525	3	18	,	,	PUNCT
ejpam-6525	3	19	symmetry	symmetry	NOUN
ejpam-6525	3	20	,	,	PUNCT
ejpam-6525	3	21	and	and	CCONJ
ejpam-6525	3	22	a	a	DET
ejpam-6525	3	23	generalized	generalized	ADJ
ejpam-6525	3	24	triangle	triangle	NOUN
ejpam-6525	3	25	inequality	inequality	NOUN
ejpam-6525	3	26	with	with	ADP
ejpam-6525	3	27	a	a	DET
ejpam-6525	3	28	constant	constant	ADJ
ejpam-6525	3	29	r	r	NOUN
ejpam-6525	3	30	>	>	X
ejpam-6525	3	31	1	1	NUM
ejpam-6525	3	32	.	.	PUNCT
ejpam-6525	3	33	three	three	NUM
ejpam-6525	3	34	main	main	ADJ
ejpam-6525	3	35	theorems	theorem	NOUN
ejpam-6525	3	36	are	be	AUX
ejpam-6525	3	37	presented	present	VERB
ejpam-6525	3	38	:	:	PUNCT
ejpam-6525	3	39	(	(	PUNCT
ejpam-6525	3	40	1	1	X
ejpam-6525	3	41	)	)	PUNCT
ejpam-6525	3	42	a	a	DET
ejpam-6525	3	43	construction	construction	NOUN
ejpam-6525	3	44	of	of	ADP
ejpam-6525	3	45	mr	mr	NOUN
ejpam-6525	3	46	-	-	PUNCT
ejpam-6525	3	47	metrics	metric	NOUN
ejpam-6525	3	48	on	on	ADP
ejpam-6525	3	49	weighted	weighted	ADJ
ejpam-6525	3	50	graphs	graph	NOUN
ejpam-6525	3	51	via	via	ADP
ejpam-6525	3	52	minimal	minimal	ADJ
ejpam-6525	3	53	spanning	span	VERB
ejpam-6525	3	54	subtrees	subtree	NOUN
ejpam-6525	3	55	,	,	PUNCT
ejpam-6525	3	56	with	with	ADP
ejpam-6525	3	57	applications	application	NOUN
ejpam-6525	3	58	in	in	ADP
ejpam-6525	3	59	network	network	NOUN
ejpam-6525	3	60	design	design	PROPN
ejpam-6525	3	61	and	and	CCONJ
ejpam-6525	3	62	vlsi	vlsi	PROPN
ejpam-6525	3	63	circuit	circuit	PROPN
ejpam-6525	3	64	optimization	optimization	NOUN
ejpam-6525	3	65	;	;	PUNCT
ejpam-6525	3	66	(	(	PUNCT
ejpam-6525	3	67	2	2	X
ejpam-6525	3	68	)	)	PUNCT
ejpam-6525	3	69	a	a	DET
ejpam-6525	3	70	set	set	NOUN
ejpam-6525	3	71	-	-	PUNCT
ejpam-6525	3	72	valued	value	VERB
ejpam-6525	3	73	fixed	fix	VERB
ejpam-6525	3	74	-	-	PUNCT
ejpam-6525	3	75	point	point	NOUN
ejpam-6525	3	76	theorem	theorem	NOUN
ejpam-6525	3	77	for	for	ADP
ejpam-6525	3	78	contractions	contraction	NOUN
ejpam-6525	3	79	in	in	ADP
ejpam-6525	3	80	mrmetric	mrmetric	ADJ
ejpam-6525	3	81	spaces	space	NOUN
ejpam-6525	3	82	,	,	PUNCT
ejpam-6525	3	83	applied	apply	VERB
ejpam-6525	3	84	to	to	ADP
ejpam-6525	3	85	distributed	distribute	VERB
ejpam-6525	3	86	consensus	consensus	NOUN
ejpam-6525	3	87	and	and	CCONJ
ejpam-6525	3	88	fault	fault	NOUN
ejpam-6525	3	89	-	-	PUNCT
ejpam-6525	3	90	tolerant	tolerant	ADJ
ejpam-6525	3	91	systems	system	NOUN
ejpam-6525	3	92	;	;	PUNCT
ejpam-6525	3	93	and	and	CCONJ
ejpam-6525	3	94	(	(	PUNCT
ejpam-6525	3	95	3	3	X
ejpam-6525	3	96	)	)	PUNCT
ejpam-6525	3	97	an	an	DET
ejpam-6525	3	98	mr	mr	PROPN
ejpam-6525	3	99	-	-	PUNCT
ejpam-6525	3	100	metric	metric	NOUN
ejpam-6525	3	101	based	base	VERB
ejpam-6525	3	102	on	on	ADP
ejpam-6525	3	103	coupling	couple	VERB
ejpam-6525	3	104	times	time	NOUN
ejpam-6525	3	105	in	in	ADP
ejpam-6525	3	106	expander	expander	NOUN
ejpam-6525	3	107	graphs	graph	NOUN
ejpam-6525	3	108	,	,	PUNCT
ejpam-6525	3	109	with	with	ADP
ejpam-6525	3	110	implications	implication	NOUN
ejpam-6525	3	111	for	for	ADP
ejpam-6525	3	112	distributed	distribute	VERB
ejpam-6525	3	113	storage	storage	NOUN
ejpam-6525	3	114	and	and	CCONJ
ejpam-6525	3	115	decentralized	decentralized	ADJ
ejpam-6525	3	116	machine	machine	NOUN
ejpam-6525	3	117	learning	learning	NOUN
ejpam-6525	3	118	.	.	PUNCT
ejpam-6525	4	1	the	the	DET
ejpam-6525	4	2	results	result	NOUN
ejpam-6525	4	3	are	be	AUX
ejpam-6525	4	4	supported	support	VERB
ejpam-6525	4	5	by	by	ADP
ejpam-6525	4	6	rigorous	rigorous	ADJ
ejpam-6525	4	7	proofs	proof	NOUN
ejpam-6525	4	8	,	,	PUNCT
ejpam-6525	4	9	illustrative	illustrative	ADJ
ejpam-6525	4	10	examples	example	NOUN
ejpam-6525	4	11	,	,	PUNCT
ejpam-6525	4	12	and	and	CCONJ
ejpam-6525	4	13	performance	performance	NOUN
ejpam-6525	4	14	analyses	analysis	NOUN
ejpam-6525	4	15	demonstrating	demonstrate	VERB
ejpam-6525	4	16	practical	practical	ADJ
ejpam-6525	4	17	advantages	advantage	NOUN
ejpam-6525	4	18	over	over	ADP
ejpam-6525	4	19	traditional	traditional	ADJ
ejpam-6525	4	20	methods	method	NOUN
ejpam-6525	4	21	.	.	PUNCT
ejpam-6525	5	1	2020	2020	NUM
ejpam-6525	5	2	mathematics	mathematic	NOUN
ejpam-6525	5	3	subject	subject	NOUN
ejpam-6525	5	4	classifications	classification	NOUN
ejpam-6525	5	5	:	:	PUNCT
ejpam-6525	5	6	54e35	54e35	NUM
ejpam-6525	5	7	,	,	PUNCT
ejpam-6525	5	8	05c12	05c12	NOUN
ejpam-6525	5	9	,	,	PUNCT
ejpam-6525	5	10	47h10	47h10	NUM
ejpam-6525	5	11	,	,	PUNCT
ejpam-6525	5	12	68r10	68r10	NUM
ejpam-6525	5	13	,	,	PUNCT
ejpam-6525	5	14	60j10	60j10	NOUN
ejpam-6525	5	15	.	.	PUNCT
ejpam-6525	6	1	key	key	ADJ
ejpam-6525	6	2	words	word	NOUN
ejpam-6525	6	3	and	and	CCONJ
ejpam-6525	6	4	phrases	phrase	NOUN
ejpam-6525	6	5	:	:	PUNCT
ejpam-6525	6	6	mr	mr	ADJ
ejpam-6525	6	7	-	-	PUNCT
ejpam-6525	6	8	metric	metric	ADJ
ejpam-6525	6	9	spaces	space	NOUN
ejpam-6525	6	10	,	,	PUNCT
ejpam-6525	6	11	weighted	weight	VERB
ejpam-6525	6	12	graphs	graph	NOUN
ejpam-6525	6	13	,	,	PUNCT
ejpam-6525	6	14	expander	expander	NOUN
ejpam-6525	6	15	graphs	graph	NOUN
ejpam-6525	6	16	,	,	PUNCT
ejpam-6525	6	17	fixed	fix	VERB
ejpam-6525	6	18	-	-	PUNCT
ejpam-6525	6	19	point	point	NOUN
ejpam-6525	6	20	theorems	theorem	NOUN
ejpam-6525	6	21	,	,	PUNCT
ejpam-6525	6	22	network	network	NOUN
ejpam-6525	6	23	design	design	NOUN
ejpam-6525	6	24	,	,	PUNCT
ejpam-6525	6	25	distributed	distribute	VERB
ejpam-6525	6	26	consensus	consensus	NOUN
ejpam-6525	6	27	,	,	PUNCT
ejpam-6525	6	28	coupling	couple	VERB
ejpam-6525	6	29	times	time	NOUN
ejpam-6525	6	30	.	.	PUNCT
ejpam-6525	7	1	1	1	X
ejpam-6525	7	2	.	.	X
ejpam-6525	7	3	introduction	introduction	NOUN
ejpam-6525	7	4	metric	metric	ADJ
ejpam-6525	7	5	space	space	NOUN
ejpam-6525	7	6	theory	theory	NOUN
ejpam-6525	7	7	has	have	AUX
ejpam-6525	7	8	undergone	undergo	VERB
ejpam-6525	7	9	significant	significant	ADJ
ejpam-6525	7	10	generalizations	generalization	NOUN
ejpam-6525	7	11	since	since	SCONJ
ejpam-6525	7	12	its	its	PRON
ejpam-6525	7	13	inception	inception	NOUN
ejpam-6525	7	14	,	,	PUNCT
ejpam-6525	7	15	with	with	ADP
ejpam-6525	7	16	various	various	ADJ
ejpam-6525	7	17	extended	extended	ADJ
ejpam-6525	7	18	metric	metric	ADJ
ejpam-6525	7	19	structures	structure	NOUN
ejpam-6525	7	20	being	be	AUX
ejpam-6525	7	21	developed	develop	VERB
ejpam-6525	7	22	to	to	PART
ejpam-6525	7	23	address	address	VERB
ejpam-6525	7	24	limitations	limitation	NOUN
ejpam-6525	7	25	in	in	ADP
ejpam-6525	7	26	classical	classical	ADJ
ejpam-6525	7	27	settings	setting	NOUN
ejpam-6525	7	28	.	.	PUNCT
ejpam-6525	8	1	the	the	DET
ejpam-6525	8	2	concept	concept	NOUN
ejpam-6525	8	3	of	of	ADP
ejpam-6525	8	4	mr	mr	PROPN
ejpam-6525	8	5	-	-	PUNCT
ejpam-6525	8	6	metric	metric	ADJ
ejpam-6525	8	7	spaces	space	NOUN
ejpam-6525	8	8	,	,	PUNCT
ejpam-6525	8	9	introduced	introduce	VERB
ejpam-6525	8	10	by	by	ADP
ejpam-6525	8	11	[	[	X
ejpam-6525	8	12	1	1	NUM
ejpam-6525	8	13	]	]	PUNCT
ejpam-6525	8	14	,	,	PUNCT
ejpam-6525	8	15	represents	represent	VERB
ejpam-6525	8	16	a	a	DET
ejpam-6525	8	17	fundamental	fundamental	ADJ
ejpam-6525	8	18	advancement	advancement	NOUN
ejpam-6525	8	19	by	by	ADP
ejpam-6525	8	20	considering	consider	VERB
ejpam-6525	8	21	distance	distance	NOUN
ejpam-6525	8	22	functions	function	NOUN
ejpam-6525	8	23	defined	define	VERB
ejpam-6525	8	24	on	on	ADP
ejpam-6525	8	25	triples	triple	NOUN
ejpam-6525	8	26	of	of	ADP
ejpam-6525	8	27	points	point	NOUN
ejpam-6525	8	28	rather	rather	ADV
ejpam-6525	8	29	than	than	ADP
ejpam-6525	8	30	traditional	traditional	ADJ
ejpam-6525	8	31	pairwise	pairwise	NOUN
ejpam-6525	8	32	metrics	metric	NOUN
ejpam-6525	8	33	.	.	PUNCT
ejpam-6525	9	1	this	this	DET
ejpam-6525	9	2	innovative	innovative	ADJ
ejpam-6525	9	3	approach	approach	NOUN
ejpam-6525	9	4	builds	build	VERB
ejpam-6525	9	5	upon	upon	SCONJ
ejpam-6525	9	6	earlier	early	ADJ
ejpam-6525	9	7	work	work	NOUN
ejpam-6525	9	8	in	in	ADP
ejpam-6525	9	9	generalized	generalized	ADJ
ejpam-6525	9	10	metric	metric	ADJ
ejpam-6525	9	11	spaces	space	NOUN
ejpam-6525	9	12	[	[	X
ejpam-6525	9	13	2	2	NUM
ejpam-6525	9	14	,	,	PUNCT
ejpam-6525	9	15	3	3	NUM
ejpam-6525	9	16	]	]	PUNCT
ejpam-6525	9	17	while	while	SCONJ
ejpam-6525	9	18	introducing	introduce	VERB
ejpam-6525	9	19	novel	novel	ADJ
ejpam-6525	9	20	topological	topological	ADJ
ejpam-6525	9	21	and	and	CCONJ
ejpam-6525	9	22	analytical	analytical	ADJ
ejpam-6525	9	23	properties	property	NOUN
ejpam-6525	9	24	.	.	PUNCT
ejpam-6525	10	1	the	the	DET
ejpam-6525	10	2	mr	mr	PROPN
ejpam-6525	10	3	-	-	PUNCT
ejpam-6525	10	4	metric	metric	ADJ
ejpam-6525	10	5	framework	framework	NOUN
ejpam-6525	10	6	extends	extend	VERB
ejpam-6525	10	7	the	the	DET
ejpam-6525	10	8	axioms	axiom	NOUN
ejpam-6525	10	9	of	of	ADP
ejpam-6525	10	10	traditional	traditional	ADJ
ejpam-6525	10	11	metrics	metric	NOUN
ejpam-6525	10	12	through	through	ADP
ejpam-6525	10	13	a	a	DET
ejpam-6525	10	14	function	function	NOUN
ejpam-6525	10	15	m	m	VERB
ejpam-6525	10	16	:	:	PUNCT
ejpam-6525	11	1	x×	x×	PUNCT
ejpam-6525	11	2	x×	x×	PUNCT
ejpam-6525	11	3	x→	x→	PUNCT
ejpam-6525	12	1	[	[	X
ejpam-6525	12	2	0,∞	0,∞	X
ejpam-6525	12	3	)	)	PUNCT
ejpam-6525	12	4	satisfying	satisfying	NOUN
ejpam-6525	12	5	:	:	PUNCT
ejpam-6525	12	6	∗corresponding	∗corresponde	VERB
ejpam-6525	12	7	author	author	NOUN
ejpam-6525	12	8	.	.	PUNCT
ejpam-6525	13	1	doi	doi	NOUN
ejpam-6525	13	2	:	:	PUNCT
ejpam-6525	13	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6525	https://doi.org/10.29020/nybg.ejpam.v18i3.6525	PROPN
ejpam-6525	13	4	email	email	NOUN
ejpam-6525	13	5	addresses	address	NOUN
ejpam-6525	13	6	:	:	PUNCT
ejpam-6525	13	7	a.malkawi@aau.edu.jo	a.malkawi@aau.edu.jo	PROPN
ejpam-6525	13	8	and	and	CCONJ
ejpam-6525	13	9	math.malkawi@gmail.com	math.malkawi@gmail.com	X
ejpam-6525	13	10	(	(	PUNCT
ejpam-6525	13	11	a.	a.	NOUN
ejpam-6525	13	12	malkawi	malkawi	PROPN
ejpam-6525	13	13	)	)	PUNCT
ejpam-6525	13	14	,	,	PUNCT
ejpam-6525	13	15	a.rabaieha@aau.edu.jo	a.rabaieha@aau.edu.jo	PROPN
ejpam-6525	13	16	(	(	PUNCT
ejpam-6525	13	17	a.	a.	NOUN
ejpam-6525	13	18	m.	m.	PROPN
ejpam-6525	13	19	rabaiah	rabaiah	PROPN
ejpam-6525	13	20	)	)	PUNCT
ejpam-6525	13	21	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6525	14	1	1	1	NUM
ejpam-6525	14	2	copyright	copyright	NOUN
ejpam-6525	14	3	:	:	PUNCT
ejpam-6525	14	4	©	©	PROPN
ejpam-6525	14	5	2025	2025	NUM
ejpam-6525	14	6	the	the	DET
ejpam-6525	14	7	author(s	author(s	NOUN
ejpam-6525	14	8	)	)	PUNCT
ejpam-6525	14	9	.	.	PUNCT
ejpam-6525	15	1	(	(	PUNCT
ejpam-6525	15	2	cc	cc	NOUN
ejpam-6525	15	3	by	by	ADP
ejpam-6525	15	4	-	-	PUNCT
ejpam-6525	15	5	nc	nc	PROPN
ejpam-6525	15	6	4.0	4.0	NUM
ejpam-6525	15	7	)	)	PUNCT
ejpam-6525	15	8	a.	a.	NOUN
ejpam-6525	15	9	malkawi	malkawi	PROPN
ejpam-6525	15	10	,	,	PUNCT
ejpam-6525	15	11	a.	a.	PROPN
ejpam-6525	15	12	m.	m.	NOUN
ejpam-6525	15	13	rabaiah	rabaiah	PROPN
ejpam-6525	15	14	/	/	SYM
ejpam-6525	15	15	eur	eur	PROPN
ejpam-6525	15	16	.	.	PUNCT
ejpam-6525	16	1	j.	j.	PROPN
ejpam-6525	16	2	pure	pure	PROPN
ejpam-6525	16	3	appl	appl	PROPN
ejpam-6525	16	4	.	.	PROPN
ejpam-6525	16	5	math	math	PROPN
ejpam-6525	16	6	,	,	PUNCT
ejpam-6525	16	7	18	18	NUM
ejpam-6525	16	8	(	(	PUNCT
ejpam-6525	16	9	3	3	NUM
ejpam-6525	16	10	)	)	PUNCT
ejpam-6525	16	11	(	(	PUNCT
ejpam-6525	16	12	2025	2025	NUM
ejpam-6525	16	13	)	)	PUNCT
ejpam-6525	16	14	,	,	PUNCT
ejpam-6525	16	15	6525	6525	NUM
ejpam-6525	16	16	2	2	NUM
ejpam-6525	16	17	of	of	ADP
ejpam-6525	16	18	14	14	NUM
ejpam-6525	16	19	•	•	NUM
ejpam-6525	16	20	non	non	ADJ
ejpam-6525	16	21	-	-	ADJ
ejpam-6525	16	22	negativity	negativity	NOUN
ejpam-6525	16	23	and	and	CCONJ
ejpam-6525	16	24	identity	identity	NOUN
ejpam-6525	16	25	:	:	PUNCT
ejpam-6525	16	26	m(v	m(v	NUM
ejpam-6525	16	27	,	,	PUNCT
ejpam-6525	16	28	ξ	ξ	PROPN
ejpam-6525	16	29	,	,	PUNCT
ejpam-6525	16	30	s	s	PART
ejpam-6525	16	31	)	)	PUNCT
ejpam-6525	16	32	≥	≥	NOUN
ejpam-6525	16	33	0	0	NUM
ejpam-6525	16	34	with	with	ADP
ejpam-6525	16	35	equality	equality	NOUN
ejpam-6525	16	36	iff	iff	VERB
ejpam-6525	16	37	v	v	ADP
ejpam-6525	16	38	=	=	SYM
ejpam-6525	16	39	ξ	ξ	PROPN
ejpam-6525	16	40	=	=	SYM
ejpam-6525	16	41	s	s	PART
ejpam-6525	16	42	•	•	NOUN
ejpam-6525	16	43	symmetry	symmetry	NOUN
ejpam-6525	16	44	under	under	ADP
ejpam-6525	16	45	all	all	DET
ejpam-6525	16	46	permutations	permutation	NOUN
ejpam-6525	16	47	of	of	ADP
ejpam-6525	16	48	arguments	argument	NOUN
ejpam-6525	16	49	•	•	ADP
ejpam-6525	16	50	a	a	DET
ejpam-6525	16	51	generalized	generalized	ADJ
ejpam-6525	16	52	triangle	triangle	NOUN
ejpam-6525	16	53	inequality	inequality	NOUN
ejpam-6525	16	54	with	with	ADP
ejpam-6525	16	55	constant	constant	ADJ
ejpam-6525	16	56	r	r	NOUN
ejpam-6525	16	57	>	>	X
ejpam-6525	16	58	1	1	NUM
ejpam-6525	16	59	for	for	ADP
ejpam-6525	16	60	further	further	ADJ
ejpam-6525	16	61	details	detail	NOUN
ejpam-6525	16	62	,	,	PUNCT
ejpam-6525	16	63	we	we	PRON
ejpam-6525	16	64	refer	refer	VERB
ejpam-6525	16	65	readers	reader	NOUN
ejpam-6525	16	66	to	to	ADP
ejpam-6525	16	67	the	the	DET
ejpam-6525	16	68	works	work	NOUN
ejpam-6525	16	69	cited	cite	VERB
ejpam-6525	16	70	in	in	ADP
ejpam-6525	16	71	[	[	X
ejpam-6525	16	72	4–21	4–21	PROPN
ejpam-6525	16	73	]	]	PUNCT
ejpam-6525	16	74	.	.	PUNCT
ejpam-6525	17	1	recent	recent	ADJ
ejpam-6525	17	2	work	work	NOUN
ejpam-6525	17	3	by	by	ADP
ejpam-6525	17	4	[	[	X
ejpam-6525	17	5	22	22	NUM
ejpam-6525	17	6	]	]	PUNCT
ejpam-6525	17	7	has	have	AUX
ejpam-6525	17	8	demonstrated	demonstrate	VERB
ejpam-6525	17	9	that	that	SCONJ
ejpam-6525	17	10	mr	mr	PROPN
ejpam-6525	17	11	-	-	PUNCT
ejpam-6525	17	12	metrics	metric	NOUN
ejpam-6525	17	13	provide	provide	VERB
ejpam-6525	17	14	a	a	DET
ejpam-6525	17	15	natural	natural	ADJ
ejpam-6525	17	16	framework	framework	NOUN
ejpam-6525	17	17	for	for	ADP
ejpam-6525	17	18	analyzing	analyze	VERB
ejpam-6525	17	19	complex	complex	ADJ
ejpam-6525	17	20	network	network	NOUN
ejpam-6525	17	21	structures	structure	NOUN
ejpam-6525	17	22	,	,	PUNCT
ejpam-6525	17	23	particularly	particularly	ADV
ejpam-6525	17	24	in	in	ADP
ejpam-6525	17	25	weighted	weight	VERB
ejpam-6525	17	26	graphs	graph	NOUN
ejpam-6525	17	27	and	and	CCONJ
ejpam-6525	17	28	expander	expander	NOUN
ejpam-6525	17	29	graphs	graph	NOUN
ejpam-6525	17	30	.	.	PUNCT
ejpam-6525	18	1	this	this	PRON
ejpam-6525	18	2	builds	build	VERB
ejpam-6525	18	3	upon	upon	SCONJ
ejpam-6525	18	4	earlier	early	ADJ
ejpam-6525	18	5	results	result	NOUN
ejpam-6525	18	6	in	in	ADP
ejpam-6525	18	7	b	b	NOUN
ejpam-6525	18	8	-	-	ADJ
ejpam-6525	18	9	metric	metric	ADJ
ejpam-6525	18	10	spaces	space	NOUN
ejpam-6525	18	11	[	[	X
ejpam-6525	18	12	3	3	NUM
ejpam-6525	18	13	]	]	PUNCT
ejpam-6525	18	14	and	and	CCONJ
ejpam-6525	18	15	ωb	ωb	NOUN
ejpam-6525	18	16	-	-	PUNCT
ejpam-6525	18	17	distance	distance	NOUN
ejpam-6525	18	18	mappings	mapping	NOUN
ejpam-6525	18	19	[	[	X
ejpam-6525	18	20	23	23	NUM
ejpam-6525	18	21	]	]	PUNCT
ejpam-6525	18	22	.	.	PUNCT
ejpam-6525	19	1	the	the	DET
ejpam-6525	19	2	triple	triple	ADV
ejpam-6525	19	3	-	-	PUNCT
ejpam-6525	19	4	based	base	VERB
ejpam-6525	19	5	distance	distance	NOUN
ejpam-6525	19	6	measure	measure	NOUN
ejpam-6525	19	7	captures	capture	VERB
ejpam-6525	19	8	higher	high	ADJ
ejpam-6525	19	9	-	-	PUNCT
ejpam-6525	19	10	order	order	NOUN
ejpam-6525	19	11	relationships	relationship	NOUN
ejpam-6525	19	12	that	that	PRON
ejpam-6525	19	13	are	be	AUX
ejpam-6525	19	14	essential	essential	ADJ
ejpam-6525	19	15	in	in	ADP
ejpam-6525	19	16	modern	modern	ADJ
ejpam-6525	19	17	applications	application	NOUN
ejpam-6525	19	18	ranging	range	VERB
ejpam-6525	19	19	from	from	ADP
ejpam-6525	19	20	distributed	distribute	VERB
ejpam-6525	19	21	systems	system	NOUN
ejpam-6525	19	22	to	to	ADP
ejpam-6525	19	23	vlsi	vlsi	PROPN
ejpam-6525	19	24	design	design	PROPN
ejpam-6525	19	25	.	.	PUNCT
ejpam-6525	20	1	key	key	ADJ
ejpam-6525	20	2	motivations	motivation	NOUN
ejpam-6525	20	3	for	for	ADP
ejpam-6525	20	4	studying	study	VERB
ejpam-6525	20	5	mr	mr	PROPN
ejpam-6525	20	6	-	-	ADJ
ejpam-6525	20	7	metric	metric	ADJ
ejpam-6525	20	8	spaces	space	NOUN
ejpam-6525	20	9	include	include	VERB
ejpam-6525	20	10	:	:	PUNCT
ejpam-6525	20	11	(	(	PUNCT
ejpam-6525	20	12	i	i	NOUN
ejpam-6525	20	13	)	)	PUNCT
ejpam-6525	20	14	their	their	PRON
ejpam-6525	20	15	ability	ability	NOUN
ejpam-6525	20	16	to	to	PART
ejpam-6525	20	17	model	model	VERB
ejpam-6525	20	18	minimal	minimal	ADJ
ejpam-6525	20	19	connection	connection	NOUN
ejpam-6525	20	20	costs	cost	NOUN
ejpam-6525	20	21	in	in	ADP
ejpam-6525	20	22	network	network	NOUN
ejpam-6525	20	23	design	design	NOUN
ejpam-6525	20	24	problems	problem	NOUN
ejpam-6525	20	25	via	via	ADP
ejpam-6525	20	26	theorem	theorem	ADJ
ejpam-6525	20	27	2.1	2.1	NUM
ejpam-6525	20	28	’s	’s	PART
ejpam-6525	20	29	weighted	weight	VERB
ejpam-6525	20	30	graph	graph	NOUN
ejpam-6525	20	31	embedding	embed	VERB
ejpam-6525	20	32	(	(	PUNCT
ejpam-6525	20	33	ii	ii	NOUN
ejpam-6525	20	34	)	)	PUNCT
ejpam-6525	20	35	the	the	DET
ejpam-6525	20	36	set	set	NOUN
ejpam-6525	20	37	-	-	PUNCT
ejpam-6525	20	38	valued	value	VERB
ejpam-6525	20	39	fixed	fix	VERB
ejpam-6525	20	40	point	point	NOUN
ejpam-6525	20	41	theory	theory	NOUN
ejpam-6525	20	42	developed	develop	VERB
ejpam-6525	20	43	in	in	ADP
ejpam-6525	20	44	theorem	theorem	ADJ
ejpam-6525	20	45	2.2	2.2	NUM
ejpam-6525	20	46	,	,	PUNCT
ejpam-6525	20	47	extending	extend	VERB
ejpam-6525	20	48	classical	classical	ADJ
ejpam-6525	20	49	results	result	NOUN
ejpam-6525	20	50	[	[	X
ejpam-6525	20	51	24	24	NUM
ejpam-6525	20	52	]	]	PUNCT
ejpam-6525	20	53	(	(	PUNCT
ejpam-6525	20	54	iii	iii	NOUN
ejpam-6525	20	55	)	)	PUNCT
ejpam-6525	20	56	applications	application	NOUN
ejpam-6525	20	57	in	in	ADP
ejpam-6525	20	58	expander	expander	NOUN
ejpam-6525	20	59	graph	graph	VERB
ejpam-6525	20	60	analysis	analysis	NOUN
ejpam-6525	20	61	through	through	ADP
ejpam-6525	20	62	coupling	couple	VERB
ejpam-6525	20	63	time	time	NOUN
ejpam-6525	20	64	metrics	metric	NOUN
ejpam-6525	20	65	(	(	PUNCT
ejpam-6525	20	66	theorem	theorem	VERB
ejpam-6525	20	67	2.3	2.3	NUM
ejpam-6525	20	68	)	)	PUNCT
ejpam-6525	20	69	this	this	DET
ejpam-6525	20	70	paper	paper	NOUN
ejpam-6525	20	71	makes	make	VERB
ejpam-6525	20	72	three	three	NUM
ejpam-6525	20	73	principal	principal	ADJ
ejpam-6525	20	74	contributions	contribution	NOUN
ejpam-6525	20	75	:	:	PUNCT
ejpam-6525	20	76	•	•	ADP
ejpam-6525	20	77	a	a	DET
ejpam-6525	20	78	constructive	constructive	ADJ
ejpam-6525	20	79	method	method	NOUN
ejpam-6525	20	80	for	for	ADP
ejpam-6525	20	81	generating	generate	VERB
ejpam-6525	20	82	mr	mr	NOUN
ejpam-6525	20	83	-	-	PUNCT
ejpam-6525	20	84	metrics	metric	NOUN
ejpam-6525	20	85	on	on	ADP
ejpam-6525	20	86	weighted	weighted	ADJ
ejpam-6525	20	87	graphs	graph	NOUN
ejpam-6525	20	88	via	via	ADP
ejpam-6525	20	89	minimal	minimal	ADJ
ejpam-6525	20	90	spanning	span	VERB
ejpam-6525	20	91	subtrees	subtree	NOUN
ejpam-6525	20	92	,	,	PUNCT
ejpam-6525	20	93	with	with	ADP
ejpam-6525	20	94	applications	application	NOUN
ejpam-6525	20	95	in	in	ADP
ejpam-6525	20	96	network	network	NOUN
ejpam-6525	20	97	optimization	optimization	NOUN
ejpam-6525	20	98	(	(	PUNCT
ejpam-6525	20	99	section	section	NOUN
ejpam-6525	20	100	3.1	3.1	NUM
ejpam-6525	20	101	)	)	PUNCT
ejpam-6525	20	102	•	•	ADP
ejpam-6525	20	103	a	a	DET
ejpam-6525	20	104	fixed	fix	VERB
ejpam-6525	20	105	-	-	PUNCT
ejpam-6525	20	106	point	point	NOUN
ejpam-6525	20	107	theory	theory	NOUN
ejpam-6525	20	108	for	for	ADP
ejpam-6525	20	109	set	set	NOUN
ejpam-6525	20	110	-	-	PUNCT
ejpam-6525	20	111	valued	value	VERB
ejpam-6525	20	112	contractions	contraction	NOUN
ejpam-6525	20	113	in	in	ADP
ejpam-6525	20	114	mr	mr	PROPN
ejpam-6525	20	115	-	-	PUNCT
ejpam-6525	20	116	metric	metric	ADJ
ejpam-6525	20	117	spaces	space	NOUN
ejpam-6525	20	118	,	,	PUNCT
ejpam-6525	20	119	generalizing	generalize	VERB
ejpam-6525	20	120	results	result	NOUN
ejpam-6525	20	121	from	from	ADP
ejpam-6525	20	122	[	[	X
ejpam-6525	20	123	25	25	NUM
ejpam-6525	20	124	]	]	SYM
ejpam-6525	20	125	•	•	NUM
ejpam-6525	20	126	new	new	ADJ
ejpam-6525	20	127	bounds	bound	NOUN
ejpam-6525	20	128	on	on	ADP
ejpam-6525	20	129	coupling	couple	VERB
ejpam-6525	20	130	times	time	NOUN
ejpam-6525	20	131	in	in	ADP
ejpam-6525	20	132	expander	expander	NOUN
ejpam-6525	20	133	graphs	graph	NOUN
ejpam-6525	20	134	using	use	VERB
ejpam-6525	20	135	mr	mr	PROPN
ejpam-6525	20	136	-	-	PUNCT
ejpam-6525	20	137	metric	metric	ADJ
ejpam-6525	20	138	analysis	analysis	NOUN
ejpam-6525	20	139	,	,	PUNCT
ejpam-6525	20	140	improving	improve	VERB
ejpam-6525	20	141	upon	upon	SCONJ
ejpam-6525	20	142	previous	previous	ADJ
ejpam-6525	20	143	work	work	NOUN
ejpam-6525	20	144	[	[	X
ejpam-6525	20	145	26	26	NUM
ejpam-6525	20	146	]	]	PUNCT
ejpam-6525	20	147	our	our	PRON
ejpam-6525	20	148	results	result	NOUN
ejpam-6525	20	149	find	find	VERB
ejpam-6525	20	150	immediate	immediate	ADJ
ejpam-6525	20	151	applications	application	NOUN
ejpam-6525	20	152	in	in	ADP
ejpam-6525	20	153	content	content	NOUN
ejpam-6525	20	154	delivery	delivery	NOUN
ejpam-6525	20	155	networks	network	NOUN
ejpam-6525	20	156	(	(	PUNCT
ejpam-6525	20	157	algorithm	algorithm	NOUN
ejpam-6525	20	158	1	1	NUM
ejpam-6525	20	159	)	)	PUNCT
ejpam-6525	20	160	,	,	PUNCT
ejpam-6525	20	161	fault	fault	NOUN
ejpam-6525	20	162	-	-	PUNCT
ejpam-6525	20	163	tolerant	tolerant	ADJ
ejpam-6525	20	164	computing	computing	NOUN
ejpam-6525	20	165	(	(	PUNCT
ejpam-6525	20	166	table	table	NOUN
ejpam-6525	20	167	2	2	NUM
ejpam-6525	20	168	)	)	PUNCT
ejpam-6525	20	169	,	,	PUNCT
ejpam-6525	20	170	and	and	CCONJ
ejpam-6525	20	171	distributed	distribute	VERB
ejpam-6525	20	172	storage	storage	NOUN
ejpam-6525	20	173	systems	system	NOUN
ejpam-6525	20	174	(	(	PUNCT
ejpam-6525	20	175	table	table	NOUN
ejpam-6525	20	176	3	3	NUM
ejpam-6525	20	177	)	)	PUNCT
ejpam-6525	20	178	.	.	PUNCT
ejpam-6525	21	1	the	the	DET
ejpam-6525	21	2	mrmetric	mrmetric	ADJ
ejpam-6525	21	3	framework	framework	NOUN
ejpam-6525	21	4	also	also	ADV
ejpam-6525	21	5	enables	enable	VERB
ejpam-6525	21	6	new	new	ADJ
ejpam-6525	21	7	approaches	approach	NOUN
ejpam-6525	21	8	to	to	ADP
ejpam-6525	21	9	decentralized	decentralized	ADJ
ejpam-6525	21	10	machine	machine	NOUN
ejpam-6525	21	11	learning	learning	NOUN
ejpam-6525	21	12	(	(	PUNCT
ejpam-6525	21	13	example	example	NOUN
ejpam-6525	21	14	3.6	3.6	NUM
ejpam-6525	21	15	)	)	PUNCT
ejpam-6525	21	16	and	and	CCONJ
ejpam-6525	21	17	blockchain	blockchain	PROPN
ejpam-6525	21	18	consensus	consensus	PROPN
ejpam-6525	21	19	protocols	protocol	NOUN
ejpam-6525	21	20	(	(	PUNCT
ejpam-6525	21	21	example	example	NOUN
ejpam-6525	21	22	3.4	3.4	NUM
ejpam-6525	21	23	)	)	PUNCT
ejpam-6525	21	24	,	,	PUNCT
ejpam-6525	21	25	as	as	SCONJ
ejpam-6525	21	26	demonstrated	demonstrate	VERB
ejpam-6525	21	27	in	in	ADP
ejpam-6525	21	28	our	our	PRON
ejpam-6525	21	29	experimental	experimental	ADJ
ejpam-6525	21	30	analyses	analysis	NOUN
ejpam-6525	21	31	.	.	PUNCT
ejpam-6525	22	1	the	the	DET
ejpam-6525	22	2	paper	paper	NOUN
ejpam-6525	22	3	is	be	AUX
ejpam-6525	22	4	organized	organize	VERB
ejpam-6525	22	5	as	as	SCONJ
ejpam-6525	22	6	follows	follow	VERB
ejpam-6525	22	7	:	:	PUNCT
ejpam-6525	22	8	section	section	NOUN
ejpam-6525	22	9	2	2	NUM
ejpam-6525	22	10	presents	present	VERB
ejpam-6525	22	11	the	the	DET
ejpam-6525	22	12	main	main	ADJ
ejpam-6525	22	13	theoretical	theoretical	ADJ
ejpam-6525	22	14	results	result	NOUN
ejpam-6525	22	15	and	and	CCONJ
ejpam-6525	22	16	section	section	NOUN
ejpam-6525	22	17	3	3	NUM
ejpam-6525	22	18	discusses	discuss	VERB
ejpam-6525	22	19	applications	application	NOUN
ejpam-6525	22	20	with	with	ADP
ejpam-6525	22	21	computational	computational	ADJ
ejpam-6525	22	22	examples	example	NOUN
ejpam-6525	22	23	.	.	PUNCT
ejpam-6525	23	1	definition	definition	NOUN
ejpam-6525	23	2	1	1	NUM
ejpam-6525	23	3	.	.	PUNCT
ejpam-6525	24	1	[	[	X
ejpam-6525	24	2	1	1	X
ejpam-6525	24	3	]	]	PUNCT
ejpam-6525	24	4	consider	consider	VERB
ejpam-6525	24	5	a	a	DET
ejpam-6525	24	6	non	non	ADJ
ejpam-6525	24	7	-	-	ADJ
ejpam-6525	24	8	empty	empty	ADJ
ejpam-6525	24	9	set	set	NOUN
ejpam-6525	24	10	x	x	PUNCT
ejpam-6525	24	11	̸=	̸=	PROPN
ejpam-6525	24	12	∅	∅	NOUN
ejpam-6525	24	13	and	and	CCONJ
ejpam-6525	24	14	a	a	DET
ejpam-6525	24	15	real	real	ADJ
ejpam-6525	24	16	number	number	NOUN
ejpam-6525	24	17	r	r	NOUN
ejpam-6525	24	18	>	>	X
ejpam-6525	24	19	1	1	NUM
ejpam-6525	24	20	.	.	PUNCT
ejpam-6525	25	1	a	a	DET
ejpam-6525	25	2	function	function	NOUN
ejpam-6525	25	3	m	m	VERB
ejpam-6525	25	4	:	:	PUNCT
ejpam-6525	26	1	x×	x×	PUNCT
ejpam-6525	26	2	x×	x×	PUNCT
ejpam-6525	26	3	x→	x→	PUNCT
ejpam-6525	27	1	[	[	X
ejpam-6525	27	2	0,∞	0,∞	NOUN
ejpam-6525	27	3	)	)	PUNCT
ejpam-6525	27	4	is	be	AUX
ejpam-6525	27	5	termed	term	VERB
ejpam-6525	27	6	an	an	DET
ejpam-6525	27	7	mr	mr	PROPN
ejpam-6525	27	8	-	-	PUNCT
ejpam-6525	27	9	metric	metric	NOUN
ejpam-6525	27	10	if	if	SCONJ
ejpam-6525	27	11	it	it	PRON
ejpam-6525	27	12	satisfies	satisfy	VERB
ejpam-6525	27	13	the	the	DET
ejpam-6525	27	14	following	follow	VERB
ejpam-6525	27	15	conditions	condition	NOUN
ejpam-6525	27	16	for	for	ADP
ejpam-6525	27	17	all	all	PRON
ejpam-6525	27	18	v	v	NOUN
ejpam-6525	27	19	,	,	PUNCT
ejpam-6525	27	20	ξ	ξ	PROPN
ejpam-6525	27	21	,	,	PUNCT
ejpam-6525	27	22	s	s	PART
ejpam-6525	27	23	,	,	PUNCT
ejpam-6525	27	24	ℓ1	ℓ1	NOUN
ejpam-6525	27	25	∈	∈	NOUN
ejpam-6525	28	1	x	x	X
ejpam-6525	28	2	:	:	PUNCT
ejpam-6525	28	3	•	•	ADP
ejpam-6525	28	4	m(v	m(v	PROPN
ejpam-6525	28	5	,	,	PUNCT
ejpam-6525	28	6	ξ	ξ	PROPN
ejpam-6525	28	7	,	,	PUNCT
ejpam-6525	28	8	s	s	PART
ejpam-6525	28	9	)	)	PUNCT
ejpam-6525	28	10	≥	≥	NOUN
ejpam-6525	28	11	0	0	NUM
ejpam-6525	28	12	.	.	PUNCT
ejpam-6525	28	13	a.	a.	PROPN
ejpam-6525	28	14	malkawi	malkawi	PROPN
ejpam-6525	28	15	,	,	PUNCT
ejpam-6525	28	16	a.	a.	PROPN
ejpam-6525	28	17	m.	m.	NOUN
ejpam-6525	28	18	rabaiah	rabaiah	PROPN
ejpam-6525	28	19	/	/	SYM
ejpam-6525	28	20	eur	eur	PROPN
ejpam-6525	28	21	.	.	PUNCT
ejpam-6525	29	1	j.	j.	PROPN
ejpam-6525	29	2	pure	pure	PROPN
ejpam-6525	29	3	appl	appl	PROPN
ejpam-6525	29	4	.	.	PROPN
ejpam-6525	29	5	math	math	PROPN
ejpam-6525	29	6	,	,	PUNCT
ejpam-6525	29	7	18	18	NUM
ejpam-6525	29	8	(	(	PUNCT
ejpam-6525	29	9	3	3	NUM
ejpam-6525	29	10	)	)	PUNCT
ejpam-6525	29	11	(	(	PUNCT
ejpam-6525	29	12	2025	2025	NUM
ejpam-6525	29	13	)	)	PUNCT
ejpam-6525	29	14	,	,	PUNCT
ejpam-6525	29	15	6525	6525	NUM
ejpam-6525	29	16	3	3	NUM
ejpam-6525	29	17	of	of	ADP
ejpam-6525	29	18	14	14	NUM
ejpam-6525	29	19	•	•	NUM
ejpam-6525	29	20	m(v	m(v	NOUN
ejpam-6525	29	21	,	,	PUNCT
ejpam-6525	29	22	ξ	ξ	PROPN
ejpam-6525	29	23	,	,	PUNCT
ejpam-6525	29	24	s	s	PART
ejpam-6525	29	25	)	)	PUNCT
ejpam-6525	29	26	=	=	SYM
ejpam-6525	29	27	0	0	PUNCT
ejpam-6525	30	1	if	if	SCONJ
ejpam-6525	30	2	and	and	CCONJ
ejpam-6525	30	3	only	only	ADV
ejpam-6525	30	4	if	if	SCONJ
ejpam-6525	30	5	v	v	NOUN
ejpam-6525	30	6	=	=	SYM
ejpam-6525	30	7	ξ	ξ	PROPN
ejpam-6525	30	8	=	=	PUNCT
ejpam-6525	30	9	s.	s.	PROPN
ejpam-6525	30	10	•	•	ADP
ejpam-6525	30	11	m(v	m(v	PROPN
ejpam-6525	30	12	,	,	PUNCT
ejpam-6525	30	13	ξ	ξ	PROPN
ejpam-6525	30	14	,	,	PUNCT
ejpam-6525	30	15	s	s	PART
ejpam-6525	30	16	)	)	PUNCT
ejpam-6525	30	17	remains	remain	VERB
ejpam-6525	30	18	invariant	invariant	ADJ
ejpam-6525	30	19	under	under	ADP
ejpam-6525	30	20	any	any	DET
ejpam-6525	30	21	permutation	permutation	NOUN
ejpam-6525	30	22	p(v	p(v	NOUN
ejpam-6525	30	23	,	,	PUNCT
ejpam-6525	30	24	ξ	ξ	PROPN
ejpam-6525	30	25	,	,	PUNCT
ejpam-6525	30	26	s	s	PART
ejpam-6525	30	27	)	)	PUNCT
ejpam-6525	30	28	,	,	PUNCT
ejpam-6525	30	29	i.e.	i.e.	X
ejpam-6525	30	30	,	,	PUNCT
ejpam-6525	30	31	m(v	m(v	PROPN
ejpam-6525	30	32	,	,	PUNCT
ejpam-6525	30	33	ξ	ξ	PROPN
ejpam-6525	30	34	,	,	PUNCT
ejpam-6525	30	35	s	s	PART
ejpam-6525	30	36	)	)	PUNCT
ejpam-6525	30	37	=	=	SYM
ejpam-6525	30	38	m(p(v	m(p(v	PROPN
ejpam-6525	30	39	,	,	PUNCT
ejpam-6525	30	40	ξ	ξ	PROPN
ejpam-6525	30	41	,	,	PUNCT
ejpam-6525	30	42	s	s	NOUN
ejpam-6525	30	43	)	)	PUNCT
ejpam-6525	30	44	)	)	PUNCT
ejpam-6525	30	45	.	.	PUNCT
ejpam-6525	31	1	•	•	NUM
ejpam-6525	31	2	the	the	DET
ejpam-6525	31	3	following	follow	VERB
ejpam-6525	31	4	inequality	inequality	NOUN
ejpam-6525	31	5	holds	hold	VERB
ejpam-6525	31	6	:	:	PUNCT
ejpam-6525	31	7	m(v	m(v	NUM
ejpam-6525	31	8	,	,	PUNCT
ejpam-6525	31	9	ξ	ξ	PROPN
ejpam-6525	31	10	,	,	PUNCT
ejpam-6525	31	11	s	s	NOUN
ejpam-6525	31	12	)	)	PUNCT
ejpam-6525	31	13	≤	≤	NOUN
ejpam-6525	31	14	r	r	NOUN
ejpam-6525	32	1	[	[	X
ejpam-6525	32	2	m(v	m(v	X
ejpam-6525	32	3	,	,	PUNCT
ejpam-6525	32	4	ξ	ξ	X
ejpam-6525	32	5	,	,	PUNCT
ejpam-6525	32	6	ℓ1	ℓ1	NOUN
ejpam-6525	32	7	)	)	PUNCT
ejpam-6525	33	1	+	+	SYM
ejpam-6525	33	2	m(v	m(v	NOUN
ejpam-6525	33	3	,	,	PUNCT
ejpam-6525	33	4	ℓ1	ℓ1	NOUN
ejpam-6525	33	5	,	,	PUNCT
ejpam-6525	33	6	s	s	X
ejpam-6525	33	7	)	)	PUNCT
ejpam-6525	33	8	+	+	ADJ
ejpam-6525	33	9	m(ℓ1	m(ℓ1	NOUN
ejpam-6525	33	10	,	,	PUNCT
ejpam-6525	33	11	ξ	ξ	PROPN
ejpam-6525	33	12	,	,	PUNCT
ejpam-6525	33	13	s	s	PART
ejpam-6525	33	14	)	)	PUNCT
ejpam-6525	33	15	]	]	PUNCT
ejpam-6525	33	16	.	.	PUNCT
ejpam-6525	34	1	a	a	DET
ejpam-6525	34	2	structure	structure	NOUN
ejpam-6525	34	3	(	(	PUNCT
ejpam-6525	34	4	x	x	X
ejpam-6525	34	5	,	,	PUNCT
ejpam-6525	34	6	m	m	NOUN
ejpam-6525	34	7	)	)	PUNCT
ejpam-6525	34	8	that	that	PRON
ejpam-6525	34	9	adheres	adhere	VERB
ejpam-6525	34	10	to	to	ADP
ejpam-6525	34	11	these	these	DET
ejpam-6525	34	12	properties	property	NOUN
ejpam-6525	34	13	is	be	AUX
ejpam-6525	34	14	defined	define	VERB
ejpam-6525	34	15	as	as	ADP
ejpam-6525	34	16	an	an	DET
ejpam-6525	34	17	mr	mr	PROPN
ejpam-6525	34	18	-	-	PUNCT
ejpam-6525	34	19	metric	metric	ADJ
ejpam-6525	34	20	space	space	NOUN
ejpam-6525	34	21	.	.	PUNCT
ejpam-6525	35	1	2	2	X
ejpam-6525	35	2	.	.	X
ejpam-6525	35	3	main	main	ADJ
ejpam-6525	35	4	results	result	NOUN
ejpam-6525	35	5	theorem	theorem	VERB
ejpam-6525	35	6	1	1	NUM
ejpam-6525	35	7	(	(	PUNCT
ejpam-6525	35	8	weighted	weight	VERB
ejpam-6525	35	9	graph	graph	NOUN
ejpam-6525	35	10	embedding	embed	VERB
ejpam-6525	35	11	)	)	PUNCT
ejpam-6525	35	12	.	.	PUNCT
ejpam-6525	36	1	let	let	VERB
ejpam-6525	36	2	g	g	PROPN
ejpam-6525	36	3	=	=	SYM
ejpam-6525	36	4	(	(	PUNCT
ejpam-6525	36	5	v	v	NOUN
ejpam-6525	36	6	,	,	PUNCT
ejpam-6525	36	7	e	e	NOUN
ejpam-6525	36	8	,	,	PUNCT
ejpam-6525	36	9	w	w	NOUN
ejpam-6525	36	10	)	)	PUNCT
ejpam-6525	36	11	be	be	VERB
ejpam-6525	36	12	a	a	DET
ejpam-6525	36	13	weighted	weighted	ADJ
ejpam-6525	36	14	graph	graph	NOUN
ejpam-6525	36	15	with	with	ADP
ejpam-6525	36	16	w(e	w(e	NOUN
ejpam-6525	36	17	)	)	PUNCT
ejpam-6525	36	18	≥	≥	NOUN
ejpam-6525	36	19	1	1	NUM
ejpam-6525	36	20	.	.	PUNCT
ejpam-6525	37	1	the	the	DET
ejpam-6525	37	2	function	function	NOUN
ejpam-6525	37	3	:	:	PUNCT
ejpam-6525	37	4	m(u	m(u	PROPN
ejpam-6525	37	5	,	,	PUNCT
ejpam-6525	37	6	v	v	NOUN
ejpam-6525	37	7	,	,	PUNCT
ejpam-6525	37	8	w	w	NOUN
ejpam-6525	37	9	)	)	PUNCT
ejpam-6525	37	10	=	=	SYM
ejpam-6525	37	11	min	min	NOUN
ejpam-6525	37	12	t⊆g	t⊆g	PROPN
ejpam-6525	37	13	spanning	span	VERB
ejpam-6525	37	14	u	u	NOUN
ejpam-6525	37	15	,	,	PUNCT
ejpam-6525	37	16	v	v	NOUN
ejpam-6525	37	17	,	,	PUNCT
ejpam-6525	37	18	w	w	PROPN
ejpam-6525	37	19	(	(	PUNCT
ejpam-6525	37	20	∑	∑	PROPN
ejpam-6525	37	21	e∈t	e∈t	PROPN
ejpam-6525	37	22	w(e	w(e	PROPN
ejpam-6525	37	23	)	)	PUNCT
ejpam-6525	37	24	)	)	PUNCT
ejpam-6525	37	25	,	,	PUNCT
ejpam-6525	37	26	defines	define	VERB
ejpam-6525	37	27	an	an	DET
ejpam-6525	37	28	mr	mr	PROPN
ejpam-6525	37	29	-	-	PUNCT
ejpam-6525	37	30	metric	metric	ADJ
ejpam-6525	37	31	space	space	NOUN
ejpam-6525	37	32	with	with	ADP
ejpam-6525	37	33	r	r	NOUN
ejpam-6525	37	34	=	=	SYM
ejpam-6525	37	35	2	2	NUM
ejpam-6525	37	36	.	.	PUNCT
ejpam-6525	37	37	proof	proof	NOUN
ejpam-6525	37	38	.	.	PUNCT
ejpam-6525	38	1	we	we	PRON
ejpam-6525	38	2	need	need	VERB
ejpam-6525	38	3	to	to	PART
ejpam-6525	38	4	verify	verify	VERB
ejpam-6525	38	5	that	that	SCONJ
ejpam-6525	38	6	m	m	VERB
ejpam-6525	38	7	satisfies	satisfy	VERB
ejpam-6525	38	8	all	all	DET
ejpam-6525	38	9	the	the	DET
ejpam-6525	38	10	axioms	axiom	NOUN
ejpam-6525	38	11	of	of	ADP
ejpam-6525	38	12	an	an	DET
ejpam-6525	38	13	mr	mr	PROPN
ejpam-6525	38	14	-	-	PUNCT
ejpam-6525	38	15	metric	metric	ADJ
ejpam-6525	38	16	:	:	PUNCT
ejpam-6525	38	17	1	1	NUM
ejpam-6525	38	18	.	.	X
ejpam-6525	38	19	non	non	ADJ
ejpam-6525	38	20	-	-	ADJ
ejpam-6525	38	21	negativity	negativity	NOUN
ejpam-6525	38	22	and	and	CCONJ
ejpam-6525	38	23	identity	identity	NOUN
ejpam-6525	38	24	:	:	PUNCT
ejpam-6525	38	25	by	by	ADP
ejpam-6525	38	26	definition	definition	NOUN
ejpam-6525	38	27	,	,	PUNCT
ejpam-6525	38	28	m(u	m(u	PROPN
ejpam-6525	38	29	,	,	PUNCT
ejpam-6525	38	30	v	v	NOUN
ejpam-6525	38	31	,	,	PUNCT
ejpam-6525	38	32	w	w	NOUN
ejpam-6525	38	33	)	)	PUNCT
ejpam-6525	38	34	is	be	AUX
ejpam-6525	38	35	the	the	DET
ejpam-6525	38	36	minimum	minimum	ADJ
ejpam-6525	38	37	weight	weight	NOUN
ejpam-6525	38	38	of	of	ADP
ejpam-6525	38	39	a	a	DET
ejpam-6525	38	40	subtree	subtree	ADJ
ejpam-6525	38	41	connecting	connect	VERB
ejpam-6525	38	42	u	u	NOUN
ejpam-6525	38	43	,	,	PUNCT
ejpam-6525	38	44	v	v	PROPN
ejpam-6525	38	45	,	,	PUNCT
ejpam-6525	38	46	w.	w.	NOUN
ejpam-6525	38	47	since	since	SCONJ
ejpam-6525	38	48	edge	edge	NOUN
ejpam-6525	38	49	weights	weight	NOUN
ejpam-6525	38	50	w(e	w(e	NOUN
ejpam-6525	38	51	)	)	PUNCT
ejpam-6525	38	52	≥	≥	NOUN
ejpam-6525	38	53	1,m(u	1,m(u	NUM
ejpam-6525	38	54	,	,	PUNCT
ejpam-6525	38	55	v	v	NOUN
ejpam-6525	38	56	,	,	PUNCT
ejpam-6525	38	57	w	w	NOUN
ejpam-6525	38	58	)	)	PUNCT
ejpam-6525	38	59	≥	≥	NOUN
ejpam-6525	38	60	0	0	NUM
ejpam-6525	38	61	.	.	PUNCT
ejpam-6525	39	1	if	if	SCONJ
ejpam-6525	39	2	u	u	PROPN
ejpam-6525	39	3	=	=	SYM
ejpam-6525	39	4	v	v	PROPN
ejpam-6525	39	5	=	=	SYM
ejpam-6525	39	6	w	w	PROPN
ejpam-6525	39	7	,	,	PUNCT
ejpam-6525	39	8	the	the	DET
ejpam-6525	39	9	minimal	minimal	ADJ
ejpam-6525	39	10	subtree	subtree	NOUN
ejpam-6525	39	11	is	be	AUX
ejpam-6525	39	12	the	the	DET
ejpam-6525	39	13	single	single	ADJ
ejpam-6525	39	14	vertex	vertex	NOUN
ejpam-6525	39	15	{	{	PUNCT
ejpam-6525	39	16	u	u	NOUN
ejpam-6525	39	17	}	}	PUNCT
ejpam-6525	39	18	,	,	PUNCT
ejpam-6525	39	19	so	so	SCONJ
ejpam-6525	39	20	m(u	m(u	PROPN
ejpam-6525	39	21	,	,	PUNCT
ejpam-6525	39	22	u	u	NOUN
ejpam-6525	39	23	,	,	PUNCT
ejpam-6525	39	24	u	u	NOUN
ejpam-6525	39	25	)	)	PUNCT
ejpam-6525	39	26	=	=	SYM
ejpam-6525	39	27	0	0	X
ejpam-6525	39	28	.	.	PUNCT
ejpam-6525	40	1	conversely	conversely	ADV
ejpam-6525	40	2	,	,	PUNCT
ejpam-6525	40	3	if	if	SCONJ
ejpam-6525	40	4	m(u	m(u	PROPN
ejpam-6525	40	5	,	,	PUNCT
ejpam-6525	40	6	v	v	NOUN
ejpam-6525	40	7	,	,	PUNCT
ejpam-6525	40	8	w	w	NOUN
ejpam-6525	40	9	)	)	PUNCT
ejpam-6525	40	10	=	=	SYM
ejpam-6525	40	11	0	0	PUNCT
ejpam-6525	40	12	then	then	ADV
ejpam-6525	40	13	all	all	PRON
ejpam-6525	40	14	edges	edge	NOUN
ejpam-6525	40	15	in	in	ADP
ejpam-6525	40	16	the	the	DET
ejpam-6525	40	17	spanning	span	VERB
ejpam-6525	40	18	subtree	subtree	NOUN
ejpam-6525	40	19	must	must	AUX
ejpam-6525	40	20	have	have	VERB
ejpam-6525	40	21	weight	weight	NOUN
ejpam-6525	40	22	0	0	NUM
ejpam-6525	40	23	,	,	PUNCT
ejpam-6525	40	24	which	which	PRON
ejpam-6525	40	25	is	be	AUX
ejpam-6525	40	26	impossible	impossible	ADJ
ejpam-6525	40	27	since	since	SCONJ
ejpam-6525	40	28	w(e	w(e	NOUN
ejpam-6525	40	29	)	)	PUNCT
ejpam-6525	40	30	≥	≥	NOUN
ejpam-6525	40	31	1	1	NUM
ejpam-6525	40	32	.	.	PUNCT
ejpam-6525	41	1	thus	thus	ADV
ejpam-6525	41	2	,	,	PUNCT
ejpam-6525	41	3	u	u	NOUN
ejpam-6525	41	4	=	=	PROPN
ejpam-6525	41	5	v	v	PROPN
ejpam-6525	41	6	=	=	SYM
ejpam-6525	41	7	w.	w.	PROPN
ejpam-6525	41	8	2	2	PROPN
ejpam-6525	41	9	.	.	X
ejpam-6525	41	10	symmetry	symmetry	NOUN
ejpam-6525	41	11	:	:	PUNCT
ejpam-6525	41	12	the	the	DET
ejpam-6525	41	13	value	value	NOUN
ejpam-6525	41	14	m(u	m(u	PROPN
ejpam-6525	41	15	,	,	PUNCT
ejpam-6525	41	16	v	v	NOUN
ejpam-6525	41	17	,	,	PUNCT
ejpam-6525	41	18	w	w	NOUN
ejpam-6525	41	19	)	)	PUNCT
ejpam-6525	41	20	is	be	AUX
ejpam-6525	41	21	invariant	invariant	ADJ
ejpam-6525	41	22	under	under	ADP
ejpam-6525	41	23	any	any	DET
ejpam-6525	41	24	permutation	permutation	NOUN
ejpam-6525	41	25	of	of	ADP
ejpam-6525	41	26	u	u	NOUN
ejpam-6525	41	27	,	,	PUNCT
ejpam-6525	41	28	v	v	NOUN
ejpam-6525	41	29	,	,	PUNCT
ejpam-6525	41	30	w	w	VERB
ejpam-6525	41	31	because	because	SCONJ
ejpam-6525	41	32	the	the	DET
ejpam-6525	41	33	minimal	minimal	ADJ
ejpam-6525	41	34	spanning	span	VERB
ejpam-6525	41	35	subtree	subtree	NOUN
ejpam-6525	41	36	does	do	AUX
ejpam-6525	41	37	not	not	PART
ejpam-6525	41	38	depend	depend	VERB
ejpam-6525	41	39	on	on	ADP
ejpam-6525	41	40	the	the	DET
ejpam-6525	41	41	order	order	NOUN
ejpam-6525	41	42	of	of	ADP
ejpam-6525	41	43	the	the	DET
ejpam-6525	41	44	vertices	vertex	NOUN
ejpam-6525	41	45	.	.	PUNCT
ejpam-6525	42	1	3	3	X
ejpam-6525	42	2	.	.	NOUN
ejpam-6525	42	3	generalized	generalize	VERB
ejpam-6525	42	4	triangle	triangle	NOUN
ejpam-6525	42	5	inequality	inequality	NOUN
ejpam-6525	42	6	:	:	PUNCT
ejpam-6525	42	7	we	we	PRON
ejpam-6525	42	8	must	must	AUX
ejpam-6525	42	9	show	show	VERB
ejpam-6525	42	10	:	:	PUNCT
ejpam-6525	42	11	m(u	m(u	PROPN
ejpam-6525	42	12	,	,	PUNCT
ejpam-6525	42	13	v	v	NOUN
ejpam-6525	42	14	,	,	PUNCT
ejpam-6525	42	15	w	w	NOUN
ejpam-6525	42	16	)	)	PUNCT
ejpam-6525	42	17	≤	≤	NUM
ejpam-6525	42	18	2	2	NUM
ejpam-6525	42	19	[	[	PUNCT
ejpam-6525	42	20	m(u	m(u	PROPN
ejpam-6525	42	21	,	,	PUNCT
ejpam-6525	42	22	v	v	NOUN
ejpam-6525	42	23	,	,	PUNCT
ejpam-6525	42	24	ℓ	ℓ	NOUN
ejpam-6525	42	25	)	)	PUNCT
ejpam-6525	43	1	+	+	NOUN
ejpam-6525	43	2	m(u	m(u	PROPN
ejpam-6525	43	3	,	,	PUNCT
ejpam-6525	43	4	ℓ	ℓ	NOUN
ejpam-6525	43	5	,	,	PUNCT
ejpam-6525	43	6	w	w	NOUN
ejpam-6525	43	7	)	)	PUNCT
ejpam-6525	44	1	+	+	NOUN
ejpam-6525	44	2	m(ℓ	m(ℓ	NOUN
ejpam-6525	44	3	,	,	PUNCT
ejpam-6525	44	4	v	v	NOUN
ejpam-6525	44	5	,	,	PUNCT
ejpam-6525	44	6	w	w	NOUN
ejpam-6525	44	7	)	)	PUNCT
ejpam-6525	44	8	]	]	PUNCT
ejpam-6525	44	9	.	.	PUNCT
ejpam-6525	45	1	let	let	VERB
ejpam-6525	45	2	t1	t1	NOUN
ejpam-6525	45	3	,	,	PUNCT
ejpam-6525	45	4	t2	t2	NOUN
ejpam-6525	45	5	,	,	PUNCT
ejpam-6525	45	6	t3	t3	PROPN
ejpam-6525	45	7	be	be	AUX
ejpam-6525	45	8	minimal	minimal	ADJ
ejpam-6525	45	9	subtrees	subtree	NOUN
ejpam-6525	45	10	spanning	span	VERB
ejpam-6525	45	11	{	{	PUNCT
ejpam-6525	45	12	u	u	NOUN
ejpam-6525	45	13	,	,	PUNCT
ejpam-6525	45	14	v	v	NOUN
ejpam-6525	45	15	,	,	PUNCT
ejpam-6525	45	16	ℓ	ℓ	NOUN
ejpam-6525	45	17	}	}	PUNCT
ejpam-6525	45	18	,	,	PUNCT
ejpam-6525	45	19	{	{	PUNCT
ejpam-6525	45	20	u	u	NOUN
ejpam-6525	45	21	,	,	PUNCT
ejpam-6525	45	22	ℓ	ℓ	PROPN
ejpam-6525	45	23	,	,	PUNCT
ejpam-6525	45	24	w	w	NOUN
ejpam-6525	45	25	}	}	PUNCT
ejpam-6525	45	26	,	,	PUNCT
ejpam-6525	45	27	and	and	CCONJ
ejpam-6525	45	28	{	{	PUNCT
ejpam-6525	45	29	ℓ	ℓ	NOUN
ejpam-6525	45	30	,	,	PUNCT
ejpam-6525	45	31	v	v	NOUN
ejpam-6525	45	32	,	,	PUNCT
ejpam-6525	45	33	w	w	NOUN
ejpam-6525	45	34	}	}	PUNCT
ejpam-6525	45	35	,	,	PUNCT
ejpam-6525	45	36	respectively	respectively	ADV
ejpam-6525	45	37	.	.	PUNCT
ejpam-6525	46	1	the	the	DET
ejpam-6525	46	2	union	union	NOUN
ejpam-6525	46	3	t1∪t2∪t3	t1∪t2∪t3	PROPN
ejpam-6525	46	4	contains	contain	VERB
ejpam-6525	46	5	paths	path	NOUN
ejpam-6525	46	6	connecting	connect	VERB
ejpam-6525	46	7	u	u	NOUN
ejpam-6525	46	8	,	,	PUNCT
ejpam-6525	46	9	v	v	PROPN
ejpam-6525	46	10	,	,	PUNCT
ejpam-6525	46	11	w.	w.	PROPN
ejpam-6525	46	12	any	any	DET
ejpam-6525	46	13	minimal	minimal	ADJ
ejpam-6525	46	14	subtree	subtree	NOUN
ejpam-6525	46	15	t	t	NOUN
ejpam-6525	46	16	spanning	span	VERB
ejpam-6525	46	17	{	{	PUNCT
ejpam-6525	46	18	u	u	NOUN
ejpam-6525	46	19	,	,	PUNCT
ejpam-6525	46	20	v	v	NOUN
ejpam-6525	46	21	,	,	PUNCT
ejpam-6525	46	22	w	w	NOUN
ejpam-6525	46	23	}	}	PUNCT
ejpam-6525	46	24	can	can	AUX
ejpam-6525	46	25	be	be	AUX
ejpam-6525	46	26	constructed	construct	VERB
ejpam-6525	46	27	by	by	ADP
ejpam-6525	46	28	combining	combine	VERB
ejpam-6525	46	29	parts	part	NOUN
ejpam-6525	46	30	of	of	ADP
ejpam-6525	46	31	t1	t1	NOUN
ejpam-6525	46	32	,	,	PUNCT
ejpam-6525	46	33	t2	t2	NOUN
ejpam-6525	46	34	,	,	PUNCT
ejpam-6525	46	35	t3	t3	PROPN
ejpam-6525	46	36	.	.	PUNCT
ejpam-6525	47	1	due	due	ADP
ejpam-6525	47	2	to	to	ADP
ejpam-6525	47	3	overlapping	overlap	VERB
ejpam-6525	47	4	edges	edge	NOUN
ejpam-6525	47	5	,	,	PUNCT
ejpam-6525	47	6	the	the	DET
ejpam-6525	47	7	total	total	ADJ
ejpam-6525	47	8	weight	weight	NOUN
ejpam-6525	47	9	satisfies	satisfie	NOUN
ejpam-6525	47	10	:	:	PUNCT
ejpam-6525	47	11	∑	∑	PUNCT
ejpam-6525	47	12	e∈t	e∈t	PROPN
ejpam-6525	47	13	w(e	w(e	NOUN
ejpam-6525	47	14	)	)	PUNCT
ejpam-6525	47	15	≤	≤	NUM
ejpam-6525	47	16	2	2	NUM
ejpam-6525	47	17	∑	∑	NOUN
ejpam-6525	47	18	e∈t1	e∈t1	ADJ
ejpam-6525	47	19	w(e	w(e	NOUN
ejpam-6525	47	20	)	)	PUNCT
ejpam-6525	48	1	+	+	CCONJ
ejpam-6525	48	2	∑	∑	ADP
ejpam-6525	48	3	e∈t2	e∈t2	PROPN
ejpam-6525	48	4	w(e	w(e	NOUN
ejpam-6525	48	5	)	)	PUNCT
ejpam-6525	49	1	+	+	CCONJ
ejpam-6525	49	2	∑	∑	PROPN
ejpam-6525	49	3	e∈t3	e∈t3	NOUN
ejpam-6525	49	4	w(e	w(e	NOUN
ejpam-6525	49	5	)	)	PUNCT
ejpam-6525	50	1			PROPN
ejpam-6525	50	2	.	.	PUNCT
ejpam-6525	51	1	taking	take	VERB
ejpam-6525	51	2	minima	minima	NOUN
ejpam-6525	51	3	on	on	ADP
ejpam-6525	51	4	both	both	DET
ejpam-6525	51	5	sides	side	NOUN
ejpam-6525	51	6	yields	yield	VERB
ejpam-6525	51	7	the	the	DET
ejpam-6525	51	8	inequality	inequality	NOUN
ejpam-6525	51	9	with	with	ADP
ejpam-6525	51	10	r	r	NOUN
ejpam-6525	51	11	=	=	SYM
ejpam-6525	51	12	2	2	NUM
ejpam-6525	51	13	.	.	X
ejpam-6525	51	14	conclusion	conclusion	NOUN
ejpam-6525	51	15	:	:	PUNCT
ejpam-6525	51	16	sincem	sincem	NOUN
ejpam-6525	51	17	satisfies	satisfy	VERB
ejpam-6525	51	18	all	all	DET
ejpam-6525	51	19	the	the	DET
ejpam-6525	51	20	axioms	axiom	NOUN
ejpam-6525	51	21	,	,	PUNCT
ejpam-6525	51	22	(	(	PUNCT
ejpam-6525	51	23	v	v	NOUN
ejpam-6525	51	24	,	,	PUNCT
ejpam-6525	51	25	m	m	NOUN
ejpam-6525	51	26	)	)	PUNCT
ejpam-6525	51	27	is	be	AUX
ejpam-6525	51	28	an	an	DET
ejpam-6525	51	29	mr	mr	PROPN
ejpam-6525	51	30	-	-	PUNCT
ejpam-6525	51	31	metric	metric	ADJ
ejpam-6525	51	32	space	space	NOUN
ejpam-6525	51	33	with	with	ADP
ejpam-6525	51	34	r	r	NOUN
ejpam-6525	51	35	=	=	SYM
ejpam-6525	51	36	2	2	NUM
ejpam-6525	51	37	.	.	PUNCT
ejpam-6525	51	38	a.	a.	NOUN
ejpam-6525	51	39	malkawi	malkawi	PROPN
ejpam-6525	51	40	,	,	PUNCT
ejpam-6525	51	41	a.	a.	PROPN
ejpam-6525	51	42	m.	m.	NOUN
ejpam-6525	51	43	rabaiah	rabaiah	PROPN
ejpam-6525	51	44	/	/	SYM
ejpam-6525	51	45	eur	eur	PROPN
ejpam-6525	51	46	.	.	PUNCT
ejpam-6525	52	1	j.	j.	PROPN
ejpam-6525	52	2	pure	pure	PROPN
ejpam-6525	52	3	appl	appl	PROPN
ejpam-6525	52	4	.	.	PROPN
ejpam-6525	52	5	math	math	PROPN
ejpam-6525	52	6	,	,	PUNCT
ejpam-6525	52	7	18	18	NUM
ejpam-6525	52	8	(	(	PUNCT
ejpam-6525	52	9	3	3	NUM
ejpam-6525	52	10	)	)	PUNCT
ejpam-6525	52	11	(	(	PUNCT
ejpam-6525	52	12	2025	2025	NUM
ejpam-6525	52	13	)	)	PUNCT
ejpam-6525	52	14	,	,	PUNCT
ejpam-6525	52	15	6525	6525	NUM
ejpam-6525	52	16	4	4	NUM
ejpam-6525	52	17	of	of	ADP
ejpam-6525	52	18	14	14	NUM
ejpam-6525	52	19	theorem	theorem	ADJ
ejpam-6525	52	20	2	2	NUM
ejpam-6525	52	21	(	(	PUNCT
ejpam-6525	52	22	set	set	NOUN
ejpam-6525	52	23	-	-	PUNCT
ejpam-6525	52	24	valued	value	VERB
ejpam-6525	52	25	fixed	fix	VERB
ejpam-6525	52	26	points	point	NOUN
ejpam-6525	52	27	in	in	ADP
ejpam-6525	52	28	mr	mr	NOUN
ejpam-6525	52	29	-	-	PUNCT
ejpam-6525	52	30	graphs	graph	NOUN
ejpam-6525	52	31	)	)	PUNCT
ejpam-6525	52	32	.	.	PUNCT
ejpam-6525	53	1	let	let	AUX
ejpam-6525	53	2	(	(	PUNCT
ejpam-6525	53	3	v	v	NOUN
ejpam-6525	53	4	,	,	PUNCT
ejpam-6525	53	5	m	m	VERB
ejpam-6525	53	6	)	)	PUNCT
ejpam-6525	53	7	be	be	VERB
ejpam-6525	53	8	an	an	DET
ejpam-6525	53	9	mr	mr	ADJ
ejpam-6525	53	10	-	-	PUNCT
ejpam-6525	53	11	metric	metric	ADJ
ejpam-6525	53	12	graph	graph	NOUN
ejpam-6525	53	13	space	space	NOUN
ejpam-6525	53	14	and	and	CCONJ
ejpam-6525	53	15	t	t	PROPN
ejpam-6525	53	16	:	:	PUNCT
ejpam-6525	53	17	v	v	X
ejpam-6525	53	18	→	→	SYM
ejpam-6525	53	19	2v	2v	PROPN
ejpam-6525	53	20	a	a	DET
ejpam-6525	53	21	set	set	NOUN
ejpam-6525	53	22	-	-	PUNCT
ejpam-6525	53	23	valued	value	VERB
ejpam-6525	53	24	map	map	NOUN
ejpam-6525	53	25	satisfying	satisfying	ADJ
ejpam-6525	53	26	:	:	PUNCT
ejpam-6525	53	27	hm	hm	INTJ
ejpam-6525	53	28	(	(	PUNCT
ejpam-6525	53	29	t	t	PROPN
ejpam-6525	53	30	(	(	PUNCT
ejpam-6525	53	31	u	u	NOUN
ejpam-6525	53	32	)	)	PUNCT
ejpam-6525	53	33	,	,	PUNCT
ejpam-6525	53	34	t	t	PROPN
ejpam-6525	53	35	(	(	PUNCT
ejpam-6525	53	36	v	v	NOUN
ejpam-6525	53	37	)	)	PUNCT
ejpam-6525	53	38	,	,	PUNCT
ejpam-6525	53	39	t	t	PROPN
ejpam-6525	53	40	(	(	PUNCT
ejpam-6525	53	41	w	w	NOUN
ejpam-6525	53	42	)	)	PUNCT
ejpam-6525	53	43	)	)	PUNCT
ejpam-6525	53	44	≤	≤	PUNCT
ejpam-6525	54	1	k	k	X
ejpam-6525	54	2	·	·	PUNCT
ejpam-6525	54	3	m(u	m(u	PROPN
ejpam-6525	54	4	,	,	PUNCT
ejpam-6525	54	5	v	v	NOUN
ejpam-6525	54	6	,	,	PUNCT
ejpam-6525	54	7	w	w	NOUN
ejpam-6525	54	8	)	)	PUNCT
ejpam-6525	54	9	,	,	PUNCT
ejpam-6525	54	10	k	k	PROPN
ejpam-6525	54	11	∈	∈	PROPN
ejpam-6525	55	1	[	[	X
ejpam-6525	55	2	0	0	NUM
ejpam-6525	55	3	,	,	PUNCT
ejpam-6525	55	4	1	1	NUM
ejpam-6525	55	5	/	/	SYM
ejpam-6525	55	6	r	r	NOUN
ejpam-6525	55	7	)	)	PUNCT
ejpam-6525	55	8	.	.	PUNCT
ejpam-6525	56	1	then	then	ADV
ejpam-6525	56	2	,	,	PUNCT
ejpam-6525	56	3	t	t	PROPN
ejpam-6525	56	4	has	have	VERB
ejpam-6525	56	5	a	a	DET
ejpam-6525	56	6	fixed	fix	VERB
ejpam-6525	56	7	point	point	NOUN
ejpam-6525	56	8	v∗	v∗	PROPN
ejpam-6525	56	9	∈	∈	PROPN
ejpam-6525	56	10	t	t	PROPN
ejpam-6525	56	11	(	(	PUNCT
ejpam-6525	56	12	v∗	v∗	PROPN
ejpam-6525	56	13	)	)	PUNCT
ejpam-6525	56	14	.	.	PUNCT
ejpam-6525	57	1	proof	proof	NOUN
ejpam-6525	57	2	.	.	PUNCT
ejpam-6525	58	1	we	we	PRON
ejpam-6525	58	2	prove	prove	VERB
ejpam-6525	58	3	this	this	PRON
ejpam-6525	58	4	via	via	ADP
ejpam-6525	58	5	a	a	DET
ejpam-6525	58	6	generalized	generalized	ADJ
ejpam-6525	58	7	banach	banach	NOUN
ejpam-6525	58	8	fixed	fix	VERB
ejpam-6525	58	9	-	-	PUNCT
ejpam-6525	58	10	point	point	NOUN
ejpam-6525	58	11	argument	argument	NOUN
ejpam-6525	58	12	adapted	adapt	VERB
ejpam-6525	58	13	to	to	ADP
ejpam-6525	58	14	mrmetric	mrmetric	ADJ
ejpam-6525	58	15	spaces	space	NOUN
ejpam-6525	58	16	.	.	PUNCT
ejpam-6525	59	1	the	the	DET
ejpam-6525	59	2	key	key	ADJ
ejpam-6525	59	3	steps	step	NOUN
ejpam-6525	59	4	are	be	AUX
ejpam-6525	59	5	:	:	PUNCT
ejpam-6525	59	6	1	1	X
ejpam-6525	59	7	.	.	X
ejpam-6525	59	8	definition	definition	NOUN
ejpam-6525	59	9	of	of	ADP
ejpam-6525	59	10	hm	hm	INTJ
ejpam-6525	59	11	:	:	PUNCT
ejpam-6525	59	12	for	for	ADP
ejpam-6525	59	13	non	non	ADJ
ejpam-6525	59	14	-	-	ADJ
ejpam-6525	59	15	empty	empty	ADJ
ejpam-6525	59	16	subsets	subset	NOUN
ejpam-6525	59	17	a	a	DET
ejpam-6525	59	18	,	,	PUNCT
ejpam-6525	59	19	b	b	NOUN
ejpam-6525	59	20	,	,	PUNCT
ejpam-6525	59	21	c	c	PROPN
ejpam-6525	59	22	⊆	⊆	NUM
ejpam-6525	59	23	v	v	NOUN
ejpam-6525	59	24	,	,	PUNCT
ejpam-6525	59	25	define	define	NOUN
ejpam-6525	59	26	:	:	PUNCT
ejpam-6525	59	27	hm	hm	INTJ
ejpam-6525	59	28	(	(	PUNCT
ejpam-6525	59	29	a	a	DET
ejpam-6525	59	30	,	,	PUNCT
ejpam-6525	59	31	b	b	NOUN
ejpam-6525	59	32	,	,	PUNCT
ejpam-6525	59	33	c	c	NOUN
ejpam-6525	59	34	)	)	PUNCT
ejpam-6525	60	1	=	=	SYM
ejpam-6525	60	2	max	max	PROPN
ejpam-6525	60	3	{	{	PUNCT
ejpam-6525	60	4	sup	sup	PROPN
ejpam-6525	60	5	a∈a	a∈a	PROPN
ejpam-6525	60	6	inf	inf	PROPN
ejpam-6525	60	7	b∈b	b∈b	NOUN
ejpam-6525	60	8	,	,	PUNCT
ejpam-6525	60	9	c∈c	c∈c	NOUN
ejpam-6525	60	10	m(a	m(a	PROPN
ejpam-6525	60	11	,	,	PUNCT
ejpam-6525	60	12	b	b	NOUN
ejpam-6525	60	13	,	,	PUNCT
ejpam-6525	60	14	c	c	NOUN
ejpam-6525	60	15	)	)	PUNCT
ejpam-6525	60	16	,	,	PUNCT
ejpam-6525	60	17	sup	sup	PROPN
ejpam-6525	60	18	b∈b	b∈b	PROPN
ejpam-6525	60	19	inf	inf	PROPN
ejpam-6525	60	20	a∈a	a∈a	ADJ
ejpam-6525	60	21	,	,	PUNCT
ejpam-6525	60	22	c∈c	c∈c	NOUN
ejpam-6525	60	23	m(a	m(a	PROPN
ejpam-6525	60	24	,	,	PUNCT
ejpam-6525	60	25	b	b	NOUN
ejpam-6525	60	26	,	,	PUNCT
ejpam-6525	60	27	c	c	NOUN
ejpam-6525	60	28	)	)	PUNCT
ejpam-6525	60	29	,	,	PUNCT
ejpam-6525	60	30	sup	sup	NOUN
ejpam-6525	60	31	c∈c	c∈c	PROPN
ejpam-6525	60	32	inf	inf	PROPN
ejpam-6525	60	33	a∈a	a∈a	ADJ
ejpam-6525	60	34	,	,	PUNCT
ejpam-6525	60	35	b∈b	b∈b	PROPN
ejpam-6525	60	36	m(a	m(a	PROPN
ejpam-6525	60	37	,	,	PUNCT
ejpam-6525	60	38	b	b	NOUN
ejpam-6525	60	39	,	,	PUNCT
ejpam-6525	60	40	c	c	NOUN
ejpam-6525	60	41	)	)	PUNCT
ejpam-6525	60	42	}	}	PUNCT
ejpam-6525	60	43	.	.	PUNCT
ejpam-6525	61	1	2	2	X
ejpam-6525	61	2	.	.	X
ejpam-6525	61	3	construction	construction	NOUN
ejpam-6525	61	4	of	of	ADP
ejpam-6525	61	5	iterative	iterative	ADJ
ejpam-6525	61	6	sequence	sequence	NOUN
ejpam-6525	61	7	:	:	PUNCT
ejpam-6525	61	8	fix	fix	VERB
ejpam-6525	61	9	an	an	DET
ejpam-6525	61	10	initial	initial	ADJ
ejpam-6525	61	11	point	point	NOUN
ejpam-6525	61	12	v0	v0	NOUN
ejpam-6525	61	13	∈	∈	PROPN
ejpam-6525	61	14	v	v	NOUN
ejpam-6525	61	15	.	.	PUNCT
ejpam-6525	62	1	for	for	ADP
ejpam-6525	62	2	n	n	PRON
ejpam-6525	62	3	≥	≥	NOUN
ejpam-6525	62	4	0	0	NUM
ejpam-6525	62	5	,	,	PUNCT
ejpam-6525	62	6	choose	choose	VERB
ejpam-6525	62	7	vn+1	vn+1	PROPN
ejpam-6525	62	8	∈	∈	PROPN
ejpam-6525	62	9	t	t	PROPN
ejpam-6525	62	10	(	(	PUNCT
ejpam-6525	62	11	vn	vn	PROPN
ejpam-6525	62	12	)	)	PUNCT
ejpam-6525	62	13	such	such	ADJ
ejpam-6525	62	14	that	that	SCONJ
ejpam-6525	62	15	:	:	PUNCT
ejpam-6525	62	16	m(vn	m(vn	NUM
ejpam-6525	62	17	,	,	PUNCT
ejpam-6525	62	18	vn+1	vn+1	PROPN
ejpam-6525	62	19	,	,	PUNCT
ejpam-6525	62	20	vn+1	vn+1	PROPN
ejpam-6525	62	21	)	)	PUNCT
ejpam-6525	62	22	≤	≤	PUNCT
ejpam-6525	63	1	hm	hm	INTJ
ejpam-6525	63	2	(	(	PUNCT
ejpam-6525	63	3	t	t	PROPN
ejpam-6525	63	4	(	(	PUNCT
ejpam-6525	63	5	vn−1	vn−1	PROPN
ejpam-6525	63	6	)	)	PUNCT
ejpam-6525	63	7	,	,	PUNCT
ejpam-6525	63	8	t	t	PROPN
ejpam-6525	63	9	(	(	PUNCT
ejpam-6525	63	10	vn	vn	PROPN
ejpam-6525	63	11	)	)	PUNCT
ejpam-6525	63	12	,	,	PUNCT
ejpam-6525	63	13	t	t	PROPN
ejpam-6525	63	14	(	(	PUNCT
ejpam-6525	63	15	vn	vn	PROPN
ejpam-6525	63	16	)	)	PUNCT
ejpam-6525	63	17	)	)	PUNCT
ejpam-6525	64	1	+	+	CCONJ
ejpam-6525	64	2	ϵn	ϵn	X
ejpam-6525	64	3	,	,	PUNCT
ejpam-6525	64	4	where	where	SCONJ
ejpam-6525	64	5	ϵn	ϵn	PROPN
ejpam-6525	64	6	is	be	AUX
ejpam-6525	64	7	a	a	DET
ejpam-6525	64	8	summable	summable	ADJ
ejpam-6525	64	9	sequence	sequence	NOUN
ejpam-6525	64	10	ensuring	ensure	VERB
ejpam-6525	64	11	convergence	convergence	NOUN
ejpam-6525	64	12	(	(	PUNCT
ejpam-6525	64	13	e.g.	e.g.	ADV
ejpam-6525	64	14	,	,	PUNCT
ejpam-6525	64	15	ϵn	ϵn	NOUN
ejpam-6525	64	16	=	=	SYM
ejpam-6525	64	17	knϵ0	knϵ0	PROPN
ejpam-6525	64	18	)	)	PUNCT
ejpam-6525	64	19	.	.	PUNCT
ejpam-6525	65	1	3	3	X
ejpam-6525	65	2	.	.	X
ejpam-6525	65	3	contraction	contraction	NOUN
ejpam-6525	65	4	property	property	NOUN
ejpam-6525	65	5	:	:	PUNCT
ejpam-6525	65	6	by	by	ADP
ejpam-6525	65	7	the	the	DET
ejpam-6525	65	8	hypothesis	hypothesis	NOUN
ejpam-6525	65	9	on	on	ADP
ejpam-6525	65	10	t	t	PROPN
ejpam-6525	65	11	,	,	PUNCT
ejpam-6525	65	12	we	we	PRON
ejpam-6525	65	13	have	have	VERB
ejpam-6525	65	14	:	:	PUNCT
ejpam-6525	65	15	m(vn	m(vn	NUM
ejpam-6525	65	16	,	,	PUNCT
ejpam-6525	65	17	vn+1	vn+1	PROPN
ejpam-6525	65	18	,	,	PUNCT
ejpam-6525	65	19	vn+1	vn+1	PROPN
ejpam-6525	65	20	)	)	PUNCT
ejpam-6525	65	21	≤	≤	PUNCT
ejpam-6525	66	1	k	k	X
ejpam-6525	66	2	·	·	PUNCT
ejpam-6525	66	3	m(vn−1	m(vn−1	PROPN
ejpam-6525	66	4	,	,	PUNCT
ejpam-6525	66	5	vn	vn	NOUN
ejpam-6525	66	6	,	,	PUNCT
ejpam-6525	66	7	vn	vn	PROPN
ejpam-6525	66	8	)	)	PUNCT
ejpam-6525	66	9	+	+	CCONJ
ejpam-6525	66	10	ϵn	ϵn	X
ejpam-6525	66	11	.	.	PUNCT
ejpam-6525	67	1	iterating	iterate	VERB
ejpam-6525	67	2	this	this	DET
ejpam-6525	67	3	yields	yield	NOUN
ejpam-6525	67	4	:	:	PUNCT
ejpam-6525	67	5	m(vn	m(vn	NUM
ejpam-6525	67	6	,	,	PUNCT
ejpam-6525	67	7	vn+1	vn+1	PROPN
ejpam-6525	67	8	,	,	PUNCT
ejpam-6525	67	9	vn+1	vn+1	PROPN
ejpam-6525	67	10	)	)	PUNCT
ejpam-6525	67	11	≤	≤	PUNCT
ejpam-6525	67	12	knm(v0	knm(v0	PROPN
ejpam-6525	67	13	,	,	PUNCT
ejpam-6525	67	14	v1	v1	NOUN
ejpam-6525	67	15	,	,	PUNCT
ejpam-6525	67	16	v1	v1	NOUN
ejpam-6525	67	17	)	)	PUNCT
ejpam-6525	68	1	+	+	NUM
ejpam-6525	68	2	n∑	n∑	PROPN
ejpam-6525	68	3	i=1	i=1	PROPN
ejpam-6525	68	4	kn−iϵi	kn−iϵi	PROPN
ejpam-6525	68	5	.	.	PUNCT
ejpam-6525	69	1	4	4	X
ejpam-6525	69	2	.	.	X
ejpam-6525	69	3	cauchy	cauchy	ADJ
ejpam-6525	69	4	sequence	sequence	NOUN
ejpam-6525	69	5	:	:	PUNCT
ejpam-6525	69	6	for	for	ADP
ejpam-6525	69	7	m	m	PROPN
ejpam-6525	69	8	>	>	X
ejpam-6525	69	9	n	n	CCONJ
ejpam-6525	69	10	,	,	PUNCT
ejpam-6525	69	11	the	the	DET
ejpam-6525	69	12	mr	mr	PROPN
ejpam-6525	69	13	-	-	PUNCT
ejpam-6525	69	14	metric	metric	ADJ
ejpam-6525	69	15	inequality	inequality	NOUN
ejpam-6525	69	16	gives	give	VERB
ejpam-6525	69	17	:	:	PUNCT
ejpam-6525	69	18	m(vn	m(vn	NUM
ejpam-6525	69	19	,	,	PUNCT
ejpam-6525	69	20	vm	vm	PROPN
ejpam-6525	69	21	,	,	PUNCT
ejpam-6525	69	22	vm	vm	NOUN
ejpam-6525	69	23	)	)	PUNCT
ejpam-6525	69	24	≤	≤	NOUN
ejpam-6525	70	1	r	r	NOUN
ejpam-6525	70	2	[	[	X
ejpam-6525	70	3	m(vn	m(vn	NUM
ejpam-6525	70	4	,	,	PUNCT
ejpam-6525	70	5	vn+1	vn+1	PROPN
ejpam-6525	70	6	,	,	PUNCT
ejpam-6525	70	7	vn+1	vn+1	PROPN
ejpam-6525	70	8	)	)	PUNCT
ejpam-6525	71	1	+	+	NOUN
ejpam-6525	71	2	m(vn+1	m(vn+1	ADJ
ejpam-6525	71	3	,	,	PUNCT
ejpam-6525	71	4	vm	vm	PROPN
ejpam-6525	71	5	,	,	PUNCT
ejpam-6525	71	6	vm	vm	PROPN
ejpam-6525	71	7	)	)	PUNCT
ejpam-6525	71	8	]	]	PUNCT
ejpam-6525	71	9	.	.	PUNCT
ejpam-6525	72	1	by	by	ADP
ejpam-6525	72	2	induction	induction	NOUN
ejpam-6525	72	3	,	,	PUNCT
ejpam-6525	72	4	the	the	DET
ejpam-6525	72	5	right	right	ADJ
ejpam-6525	72	6	-	-	PUNCT
ejpam-6525	72	7	hand	hand	NOUN
ejpam-6525	72	8	side	side	NOUN
ejpam-6525	72	9	decays	decay	VERB
ejpam-6525	72	10	geometrically	geometrically	ADV
ejpam-6525	72	11	since	since	SCONJ
ejpam-6525	72	12	kr	kr	PROPN
ejpam-6525	72	13	<	<	X
ejpam-6525	72	14	1	1	NUM
ejpam-6525	72	15	.	.	PUNCT
ejpam-6525	73	1	thus	thus	ADV
ejpam-6525	73	2	,	,	PUNCT
ejpam-6525	73	3	{	{	PUNCT
ejpam-6525	73	4	vn	vn	NOUN
ejpam-6525	73	5	}	}	PUNCT
ejpam-6525	73	6	is	be	AUX
ejpam-6525	73	7	cauchy	cauchy	NOUN
ejpam-6525	73	8	.	.	PUNCT
ejpam-6525	74	1	5	5	NUM
ejpam-6525	74	2	.	.	PUNCT
ejpam-6525	74	3	fixed	fix	VERB
ejpam-6525	74	4	point	point	NOUN
ejpam-6525	74	5	:	:	PUNCT
ejpam-6525	74	6	by	by	ADP
ejpam-6525	74	7	completeness	completeness	NOUN
ejpam-6525	74	8	(	(	PUNCT
ejpam-6525	74	9	implied	imply	VERB
ejpam-6525	74	10	by	by	ADP
ejpam-6525	74	11	the	the	DET
ejpam-6525	74	12	graph	graph	NOUN
ejpam-6525	74	13	structure	structure	NOUN
ejpam-6525	74	14	)	)	PUNCT
ejpam-6525	74	15	,	,	PUNCT
ejpam-6525	74	16	vn	vn	PROPN
ejpam-6525	74	17	→	→	SYM
ejpam-6525	74	18	v∗.	v∗.	PROPN
ejpam-6525	74	19	using	use	VERB
ejpam-6525	74	20	the	the	DET
ejpam-6525	74	21	closure	closure	NOUN
ejpam-6525	74	22	of	of	ADP
ejpam-6525	74	23	t	t	NOUN
ejpam-6525	74	24	:	:	PUNCT
ejpam-6525	74	25	hm	hm	INTJ
ejpam-6525	74	26	(	(	PUNCT
ejpam-6525	74	27	t	t	PROPN
ejpam-6525	74	28	(	(	PUNCT
ejpam-6525	74	29	v∗	v∗	PROPN
ejpam-6525	74	30	)	)	PUNCT
ejpam-6525	74	31	,	,	PUNCT
ejpam-6525	74	32	t	t	PROPN
ejpam-6525	74	33	(	(	PUNCT
ejpam-6525	74	34	v∗	v∗	PROPN
ejpam-6525	74	35	)	)	PUNCT
ejpam-6525	74	36	,	,	PUNCT
ejpam-6525	74	37	t	t	PROPN
ejpam-6525	74	38	(	(	PUNCT
ejpam-6525	74	39	v∗	v∗	PROPN
ejpam-6525	74	40	)	)	PUNCT
ejpam-6525	74	41	)	)	PUNCT
ejpam-6525	74	42	≤	≤	PUNCT
ejpam-6525	75	1	k	k	X
ejpam-6525	75	2	·	·	PUNCT
ejpam-6525	75	3	m(v∗	m(v∗	PROPN
ejpam-6525	75	4	,	,	PUNCT
ejpam-6525	75	5	v∗	v∗	ADJ
ejpam-6525	75	6	,	,	PUNCT
ejpam-6525	75	7	v∗	v∗	NOUN
ejpam-6525	75	8	)	)	PUNCT
ejpam-6525	75	9	=	=	SYM
ejpam-6525	75	10	0	0	NUM
ejpam-6525	75	11	,	,	PUNCT
ejpam-6525	75	12	which	which	PRON
ejpam-6525	75	13	implies	imply	VERB
ejpam-6525	75	14	v∗	v∗	PROPN
ejpam-6525	75	15	∈	∈	PROPN
ejpam-6525	75	16	t	t	PROPN
ejpam-6525	75	17	(	(	PUNCT
ejpam-6525	75	18	v∗	v∗	PROPN
ejpam-6525	75	19	)	)	PUNCT
ejpam-6525	75	20	.	.	PUNCT
ejpam-6525	76	1	theorem	theorem	ADJ
ejpam-6525	76	2	3	3	NUM
ejpam-6525	76	3	(	(	PUNCT
ejpam-6525	76	4	mr	mr	NOUN
ejpam-6525	76	5	-	-	PUNCT
ejpam-6525	76	6	metrics	metric	NOUN
ejpam-6525	76	7	on	on	ADP
ejpam-6525	76	8	expander	expander	NOUN
ejpam-6525	76	9	graphs	graph	NOUN
ejpam-6525	76	10	)	)	PUNCT
ejpam-6525	76	11	.	.	PUNCT
ejpam-6525	77	1	let	let	VERB
ejpam-6525	77	2	g	g	PRON
ejpam-6525	77	3	be	be	AUX
ejpam-6525	77	4	a	a	DET
ejpam-6525	77	5	d	d	ADJ
ejpam-6525	77	6	-	-	ADJ
ejpam-6525	77	7	regular	regular	ADJ
ejpam-6525	77	8	expander	expander	NOUN
ejpam-6525	77	9	with	with	ADP
ejpam-6525	77	10	spectral	spectral	ADJ
ejpam-6525	77	11	gap	gap	NOUN
ejpam-6525	77	12	λ	λ	PROPN
ejpam-6525	77	13	.	.	PUNCT
ejpam-6525	78	1	the	the	DET
ejpam-6525	78	2	expected	expect	VERB
ejpam-6525	78	3	coupling	coupling	NOUN
ejpam-6525	78	4	time	time	NOUN
ejpam-6525	78	5	:	:	PUNCT
ejpam-6525	78	6	m(u	m(u	PROPN
ejpam-6525	78	7	,	,	PUNCT
ejpam-6525	78	8	v	v	NOUN
ejpam-6525	78	9	,	,	PUNCT
ejpam-6525	78	10	w	w	NOUN
ejpam-6525	78	11	)	)	PUNCT
ejpam-6525	78	12	=	=	SYM
ejpam-6525	78	13	ex∼u	ex∼u	PROPN
ejpam-6525	78	14	,	,	PUNCT
ejpam-6525	78	15	y∼v	y∼v	PROPN
ejpam-6525	78	16	,	,	PUNCT
ejpam-6525	78	17	z∼w	z∼w	X
ejpam-6525	79	1	[	[	X
ejpam-6525	79	2	τcouple(x	τcouple(x	PROPN
ejpam-6525	79	3	,	,	PUNCT
ejpam-6525	79	4	y	y	PROPN
ejpam-6525	79	5	,	,	PUNCT
ejpam-6525	79	6	z	z	NOUN
ejpam-6525	79	7	)	)	PUNCT
ejpam-6525	79	8	]	]	PUNCT
ejpam-6525	79	9	,	,	PUNCT
ejpam-6525	79	10	defines	define	VERB
ejpam-6525	79	11	an	an	DET
ejpam-6525	79	12	mr	mr	NOUN
ejpam-6525	79	13	-	-	PUNCT
ejpam-6525	79	14	metric	metric	NOUN
ejpam-6525	79	15	with	with	ADP
ejpam-6525	79	16	r	r	NOUN
ejpam-6525	79	17	=	=	SYM
ejpam-6525	79	18	o	o	X
ejpam-6525	79	19	(	(	PUNCT
ejpam-6525	79	20	1	1	NUM
ejpam-6525	79	21	λ	λ	NOUN
ejpam-6525	79	22	)	)	PUNCT
ejpam-6525	79	23	.	.	PUNCT
ejpam-6525	80	1	proof	proof	NOUN
ejpam-6525	80	2	.	.	PUNCT
ejpam-6525	81	1	we	we	PRON
ejpam-6525	81	2	verify	verify	VERB
ejpam-6525	81	3	each	each	DET
ejpam-6525	81	4	axiom	axiom	NOUN
ejpam-6525	81	5	of	of	ADP
ejpam-6525	81	6	the	the	DET
ejpam-6525	81	7	mr	mr	PROPN
ejpam-6525	81	8	-	-	PUNCT
ejpam-6525	81	9	metric	metric	NOUN
ejpam-6525	81	10	and	and	CCONJ
ejpam-6525	81	11	establish	establish	VERB
ejpam-6525	81	12	the	the	DET
ejpam-6525	81	13	constant	constant	ADJ
ejpam-6525	81	14	r	r	NOUN
ejpam-6525	81	15	:	:	PUNCT
ejpam-6525	81	16	a.	a.	NOUN
ejpam-6525	81	17	malkawi	malkawi	PROPN
ejpam-6525	81	18	,	,	PUNCT
ejpam-6525	81	19	a.	a.	PROPN
ejpam-6525	81	20	m.	m.	NOUN
ejpam-6525	81	21	rabaiah	rabaiah	PROPN
ejpam-6525	81	22	/	/	SYM
ejpam-6525	81	23	eur	eur	PROPN
ejpam-6525	81	24	.	.	PUNCT
ejpam-6525	82	1	j.	j.	PROPN
ejpam-6525	82	2	pure	pure	PROPN
ejpam-6525	82	3	appl	appl	PROPN
ejpam-6525	82	4	.	.	PROPN
ejpam-6525	82	5	math	math	PROPN
ejpam-6525	82	6	,	,	PUNCT
ejpam-6525	82	7	18	18	NUM
ejpam-6525	82	8	(	(	PUNCT
ejpam-6525	82	9	3	3	NUM
ejpam-6525	82	10	)	)	PUNCT
ejpam-6525	82	11	(	(	PUNCT
ejpam-6525	82	12	2025	2025	NUM
ejpam-6525	82	13	)	)	PUNCT
ejpam-6525	82	14	,	,	PUNCT
ejpam-6525	82	15	6525	6525	NUM
ejpam-6525	82	16	5	5	NUM
ejpam-6525	82	17	of	of	ADP
ejpam-6525	82	18	14	14	NUM
ejpam-6525	82	19	1	1	NUM
ejpam-6525	82	20	.	.	PUNCT
ejpam-6525	83	1	non	non	ADJ
ejpam-6525	83	2	-	-	ADJ
ejpam-6525	83	3	negativity	negativity	NOUN
ejpam-6525	83	4	and	and	CCONJ
ejpam-6525	83	5	identity	identity	NOUN
ejpam-6525	83	6	by	by	ADP
ejpam-6525	83	7	definition	definition	NOUN
ejpam-6525	83	8	,	,	PUNCT
ejpam-6525	83	9	coupling	couple	VERB
ejpam-6525	83	10	times	times	PROPN
ejpam-6525	83	11	τc(x	τc(x	PROPN
ejpam-6525	83	12	,	,	PUNCT
ejpam-6525	83	13	y	y	PROPN
ejpam-6525	83	14	,	,	PUNCT
ejpam-6525	83	15	z	z	NOUN
ejpam-6525	83	16	)	)	PUNCT
ejpam-6525	83	17	are	be	AUX
ejpam-6525	83	18	non	non	ADJ
ejpam-6525	83	19	-	-	ADJ
ejpam-6525	83	20	negative	negative	ADJ
ejpam-6525	83	21	random	random	ADJ
ejpam-6525	83	22	variables	variable	NOUN
ejpam-6525	83	23	,	,	PUNCT
ejpam-6525	83	24	so	so	SCONJ
ejpam-6525	83	25	their	their	PRON
ejpam-6525	83	26	expectation	expectation	NOUN
ejpam-6525	83	27	m(u	m(u	PROPN
ejpam-6525	83	28	,	,	PUNCT
ejpam-6525	83	29	v	v	NOUN
ejpam-6525	83	30	,	,	PUNCT
ejpam-6525	83	31	w	w	NOUN
ejpam-6525	83	32	)	)	PUNCT
ejpam-6525	83	33	≥	≥	NOUN
ejpam-6525	83	34	0	0	NUM
ejpam-6525	83	35	.	.	PUNCT
ejpam-6525	84	1	for	for	ADP
ejpam-6525	84	2	the	the	DET
ejpam-6525	84	3	identity	identity	NOUN
ejpam-6525	84	4	property	property	NOUN
ejpam-6525	84	5	:	:	PUNCT
ejpam-6525	84	6	•	•	ADP
ejpam-6525	84	7	if	if	SCONJ
ejpam-6525	84	8	u	u	PROPN
ejpam-6525	84	9	=	=	SYM
ejpam-6525	84	10	v	v	PROPN
ejpam-6525	84	11	=	=	SYM
ejpam-6525	84	12	w	w	NOUN
ejpam-6525	84	13	,	,	PUNCT
ejpam-6525	84	14	then	then	ADV
ejpam-6525	84	15	τc(u	τc(u	NUM
ejpam-6525	84	16	,	,	PUNCT
ejpam-6525	84	17	u	u	NOUN
ejpam-6525	84	18	,	,	PUNCT
ejpam-6525	84	19	u	u	NOUN
ejpam-6525	84	20	)	)	PUNCT
ejpam-6525	84	21	=	=	SYM
ejpam-6525	84	22	0	0	NUM
ejpam-6525	84	23	almost	almost	ADV
ejpam-6525	84	24	surely	surely	ADV
ejpam-6525	84	25	,	,	PUNCT
ejpam-6525	84	26	hence	hence	ADV
ejpam-6525	84	27	m(u	m(u	PROPN
ejpam-6525	84	28	,	,	PUNCT
ejpam-6525	84	29	u	u	NOUN
ejpam-6525	84	30	,	,	PUNCT
ejpam-6525	84	31	u	u	NOUN
ejpam-6525	84	32	)	)	PUNCT
ejpam-6525	84	33	=	=	SYM
ejpam-6525	85	1	0	0	NUM
ejpam-6525	85	2	.	.	NOUN
ejpam-6525	85	3	•	•	NOUN
ejpam-6525	85	4	if	if	SCONJ
ejpam-6525	85	5	m(u	m(u	PROPN
ejpam-6525	85	6	,	,	PUNCT
ejpam-6525	85	7	v	v	NOUN
ejpam-6525	85	8	,	,	PUNCT
ejpam-6525	85	9	w	w	NOUN
ejpam-6525	85	10	)	)	PUNCT
ejpam-6525	85	11	=	=	SYM
ejpam-6525	85	12	0	0	NUM
ejpam-6525	85	13	,	,	PUNCT
ejpam-6525	85	14	then	then	ADV
ejpam-6525	85	15	τc(x	τc(x	PUNCT
ejpam-6525	85	16	,	,	PUNCT
ejpam-6525	85	17	y	y	PROPN
ejpam-6525	85	18	,	,	PUNCT
ejpam-6525	85	19	z	z	NOUN
ejpam-6525	85	20	)	)	PUNCT
ejpam-6525	85	21	=	=	SYM
ejpam-6525	85	22	0	0	PUNCT
ejpam-6525	85	23	almost	almost	ADV
ejpam-6525	85	24	surely	surely	ADV
ejpam-6525	85	25	for	for	ADP
ejpam-6525	85	26	random	random	ADJ
ejpam-6525	85	27	walks	walk	NOUN
ejpam-6525	85	28	starting	start	VERB
ejpam-6525	85	29	at	at	ADP
ejpam-6525	85	30	u	u	PROPN
ejpam-6525	85	31	,	,	PUNCT
ejpam-6525	85	32	v	v	PROPN
ejpam-6525	85	33	,	,	PUNCT
ejpam-6525	85	34	w.	w.	NOUN
ejpam-6525	85	35	this	this	PRON
ejpam-6525	85	36	implies	imply	VERB
ejpam-6525	85	37	x	x	PUNCT
ejpam-6525	85	38	=	=	SYM
ejpam-6525	85	39	y	y	PROPN
ejpam-6525	85	40	=	=	PUNCT
ejpam-6525	85	41	z	z	NOUN
ejpam-6525	85	42	at	at	ADP
ejpam-6525	85	43	time	time	NOUN
ejpam-6525	85	44	0	0	NUM
ejpam-6525	85	45	,	,	PUNCT
ejpam-6525	85	46	so	so	SCONJ
ejpam-6525	85	47	u	u	NOUN
ejpam-6525	85	48	=	=	X
ejpam-6525	85	49	v	v	PROPN
ejpam-6525	85	50	=	=	SYM
ejpam-6525	85	51	w.	w.	PROPN
ejpam-6525	85	52	2	2	PROPN
ejpam-6525	85	53	.	.	X
ejpam-6525	85	54	symmetry	symmetry	VERB
ejpam-6525	85	55	the	the	DET
ejpam-6525	85	56	coupling	coupling	NOUN
ejpam-6525	85	57	time	time	NOUN
ejpam-6525	85	58	τc(x	τc(x	PUNCT
ejpam-6525	85	59	,	,	PUNCT
ejpam-6525	85	60	y	y	PROPN
ejpam-6525	85	61	,	,	PUNCT
ejpam-6525	85	62	z	z	NOUN
ejpam-6525	85	63	)	)	PUNCT
ejpam-6525	85	64	is	be	AUX
ejpam-6525	85	65	invariant	invariant	ADJ
ejpam-6525	85	66	under	under	ADP
ejpam-6525	85	67	permutation	permutation	NOUN
ejpam-6525	85	68	of	of	ADP
ejpam-6525	85	69	(	(	PUNCT
ejpam-6525	85	70	x	x	NOUN
ejpam-6525	85	71	,	,	PUNCT
ejpam-6525	85	72	y	y	PROPN
ejpam-6525	85	73	,	,	PUNCT
ejpam-6525	85	74	z	z	NOUN
ejpam-6525	85	75	)	)	PUNCT
ejpam-6525	85	76	by	by	ADP
ejpam-6525	85	77	definition	definition	NOUN
ejpam-6525	85	78	.	.	PUNCT
ejpam-6525	86	1	thus	thus	ADV
ejpam-6525	86	2	:	:	PUNCT
ejpam-6525	86	3	m(u	m(u	PROPN
ejpam-6525	86	4	,	,	PUNCT
ejpam-6525	86	5	v	v	NOUN
ejpam-6525	86	6	,	,	PUNCT
ejpam-6525	86	7	w	w	NOUN
ejpam-6525	86	8	)	)	PUNCT
ejpam-6525	86	9	=	=	NOUN
ejpam-6525	86	10	m(p(u	m(p(u	X
ejpam-6525	86	11	,	,	PUNCT
ejpam-6525	86	12	v	v	NOUN
ejpam-6525	86	13	,	,	PUNCT
ejpam-6525	86	14	w	w	NOUN
ejpam-6525	86	15	)	)	PUNCT
ejpam-6525	86	16	)	)	PUNCT
ejpam-6525	86	17	for	for	ADP
ejpam-6525	86	18	any	any	DET
ejpam-6525	86	19	permutation	permutation	NOUN
ejpam-6525	86	20	p.	p.	NOUN
ejpam-6525	86	21	3	3	NUM
ejpam-6525	86	22	.	.	PUNCT
ejpam-6525	86	23	generalized	generalized	ADJ
ejpam-6525	86	24	triangle	triangle	NOUN
ejpam-6525	86	25	inequality	inequality	NOUN
ejpam-6525	86	26	we	we	PRON
ejpam-6525	86	27	must	must	AUX
ejpam-6525	86	28	prove	prove	VERB
ejpam-6525	86	29	:	:	PUNCT
ejpam-6525	86	30	m(u	m(u	PROPN
ejpam-6525	86	31	,	,	PUNCT
ejpam-6525	86	32	v	v	NOUN
ejpam-6525	86	33	,	,	PUNCT
ejpam-6525	86	34	w	w	NOUN
ejpam-6525	86	35	)	)	PUNCT
ejpam-6525	86	36	≤	≤	NOUN
ejpam-6525	86	37	r	r	NOUN
ejpam-6525	86	38	[	[	X
ejpam-6525	86	39	m(u	m(u	PROPN
ejpam-6525	86	40	,	,	PUNCT
ejpam-6525	86	41	v	v	NOUN
ejpam-6525	86	42	,	,	PUNCT
ejpam-6525	86	43	ℓ	ℓ	NOUN
ejpam-6525	86	44	)	)	PUNCT
ejpam-6525	86	45	+	+	NOUN
ejpam-6525	86	46	m(u	m(u	PROPN
ejpam-6525	86	47	,	,	PUNCT
ejpam-6525	86	48	ℓ	ℓ	NOUN
ejpam-6525	86	49	,	,	PUNCT
ejpam-6525	86	50	w	w	NOUN
ejpam-6525	86	51	)	)	PUNCT
ejpam-6525	87	1	+	+	NOUN
ejpam-6525	87	2	m(ℓ	m(ℓ	NOUN
ejpam-6525	87	3	,	,	PUNCT
ejpam-6525	87	4	v	v	NOUN
ejpam-6525	87	5	,	,	PUNCT
ejpam-6525	87	6	w	w	NOUN
ejpam-6525	87	7	)	)	PUNCT
ejpam-6525	87	8	]	]	PUNCT
ejpam-6525	87	9	.	.	PUNCT
ejpam-6525	88	1	key	key	ADJ
ejpam-6525	88	2	lemma	lemma	PROPN
ejpam-6525	88	3	:	:	PUNCT
ejpam-6525	88	4	coupling	couple	VERB
ejpam-6525	88	5	time	time	NOUN
ejpam-6525	88	6	bound	bind	VERB
ejpam-6525	88	7	for	for	ADP
ejpam-6525	88	8	any	any	DET
ejpam-6525	88	9	vertices	vertex	NOUN
ejpam-6525	88	10	u	u	NOUN
ejpam-6525	88	11	,	,	PUNCT
ejpam-6525	88	12	v	v	NOUN
ejpam-6525	88	13	,	,	PUNCT
ejpam-6525	88	14	w	w	PROPN
ejpam-6525	88	15	,	,	PUNCT
ejpam-6525	88	16	ℓ	ℓ	INTJ
ejpam-6525	88	17	,	,	PUNCT
ejpam-6525	88	18	there	there	PRON
ejpam-6525	88	19	exists	exist	VERB
ejpam-6525	88	20	a	a	DET
ejpam-6525	88	21	coupling	coupling	NOUN
ejpam-6525	88	22	where	where	SCONJ
ejpam-6525	88	23	:	:	PUNCT
ejpam-6525	88	24	e[τc(u	e[τc(u	PROPN
ejpam-6525	88	25	,	,	PUNCT
ejpam-6525	88	26	v	v	NOUN
ejpam-6525	88	27	,	,	PUNCT
ejpam-6525	88	28	w	w	NOUN
ejpam-6525	88	29	)	)	PUNCT
ejpam-6525	88	30	]	]	PUNCT
ejpam-6525	88	31	≤	≤	NUM
ejpam-6525	88	32	c(λ	c(λ	PROPN
ejpam-6525	88	33	)	)	PUNCT
ejpam-6525	88	34	(	(	PUNCT
ejpam-6525	88	35	e[τc(u	e[τc(u	PROPN
ejpam-6525	88	36	,	,	PUNCT
ejpam-6525	88	37	v	v	NOUN
ejpam-6525	88	38	,	,	PUNCT
ejpam-6525	88	39	ℓ	ℓ	NOUN
ejpam-6525	88	40	)	)	PUNCT
ejpam-6525	88	41	]	]	PUNCT
ejpam-6525	89	1	+	+	PUNCT
ejpam-6525	89	2	e[τc(u	e[τc(u	PROPN
ejpam-6525	89	3	,	,	PUNCT
ejpam-6525	89	4	ℓ	ℓ	PROPN
ejpam-6525	89	5	,	,	PUNCT
ejpam-6525	89	6	w	w	NOUN
ejpam-6525	89	7	)	)	PUNCT
ejpam-6525	89	8	]	]	PUNCT
ejpam-6525	89	9	+	+	NUM
ejpam-6525	89	10	e[τc(ℓ	e[τc(ℓ	NOUN
ejpam-6525	89	11	,	,	PUNCT
ejpam-6525	89	12	v	v	NOUN
ejpam-6525	89	13	,	,	PUNCT
ejpam-6525	89	14	w	w	NOUN
ejpam-6525	89	15	)	)	PUNCT
ejpam-6525	89	16	]	]	PUNCT
ejpam-6525	89	17	)	)	PUNCT
ejpam-6525	89	18	with	with	ADP
ejpam-6525	89	19	c(λ	c(λ	PROPN
ejpam-6525	89	20	)	)	PUNCT
ejpam-6525	89	21	=	=	SYM
ejpam-6525	89	22	o(1	o(1	PROPN
ejpam-6525	89	23	/	/	SYM
ejpam-6525	89	24	λ	λ	NOUN
ejpam-6525	89	25	)	)	PUNCT
ejpam-6525	89	26	.	.	PUNCT
ejpam-6525	90	1	proof	proof	NOUN
ejpam-6525	90	2	.	.	PUNCT
ejpam-6525	91	1	[	[	X
ejpam-6525	91	2	proof	proof	NOUN
ejpam-6525	91	3	of	of	ADP
ejpam-6525	91	4	lemma	lemma	PROPN
ejpam-6525	91	5	]	]	PUNCT
ejpam-6525	91	6	using	use	VERB
ejpam-6525	91	7	the	the	DET
ejpam-6525	91	8	expander	expander	NOUN
ejpam-6525	91	9	mixing	mix	VERB
ejpam-6525	91	10	lemma	lemma	PROPN
ejpam-6525	91	11	,	,	PUNCT
ejpam-6525	91	12	the	the	DET
ejpam-6525	91	13	probability	probability	NOUN
ejpam-6525	91	14	that	that	SCONJ
ejpam-6525	91	15	random	random	ADJ
ejpam-6525	91	16	walks	walk	NOUN
ejpam-6525	91	17	have	have	AUX
ejpam-6525	91	18	n’t	not	PART
ejpam-6525	91	19	coupled	couple	VERB
ejpam-6525	91	20	decays	decay	NOUN
ejpam-6525	91	21	exponentially	exponentially	ADV
ejpam-6525	91	22	with	with	ADP
ejpam-6525	91	23	rate	rate	NOUN
ejpam-6525	91	24	λ	λ	PROPN
ejpam-6525	91	25	.	.	PROPN
ejpam-6525	91	26	for	for	ADP
ejpam-6525	91	27	triple	triple	ADJ
ejpam-6525	91	28	coupling	coupling	NOUN
ejpam-6525	91	29	:	:	PUNCT
ejpam-6525	91	30	1	1	X
ejpam-6525	91	31	.	.	X
ejpam-6525	91	32	first	first	ADJ
ejpam-6525	91	33	couple	couple	NOUN
ejpam-6525	91	34	(	(	PUNCT
ejpam-6525	91	35	x	x	NOUN
ejpam-6525	91	36	,	,	PUNCT
ejpam-6525	91	37	y	y	PROPN
ejpam-6525	91	38	)	)	PUNCT
ejpam-6525	91	39	starting	start	VERB
ejpam-6525	91	40	from	from	ADP
ejpam-6525	91	41	(	(	PUNCT
ejpam-6525	91	42	u	u	NOUN
ejpam-6525	91	43	,	,	PUNCT
ejpam-6525	91	44	v	v	NOUN
ejpam-6525	91	45	):	):	PUNCT
ejpam-6525	91	46	expected	expect	VERB
ejpam-6525	91	47	time	time	NOUN
ejpam-6525	91	48	≤	≤	NUM
ejpam-6525	91	49	c1	c1	PROPN
ejpam-6525	91	50	λ	λ	PROPN
ejpam-6525	91	51	.	.	PUNCT
ejpam-6525	92	1	2	2	X
ejpam-6525	92	2	.	.	X
ejpam-6525	92	3	then	then	ADV
ejpam-6525	92	4	couple	couple	VERB
ejpam-6525	92	5	the	the	DET
ejpam-6525	92	6	result	result	NOUN
ejpam-6525	92	7	with	with	ADP
ejpam-6525	92	8	z	z	NOUN
ejpam-6525	92	9	starting	start	VERB
ejpam-6525	92	10	from	from	ADP
ejpam-6525	92	11	w	w	NOUN
ejpam-6525	92	12	:	:	PUNCT
ejpam-6525	92	13	additional	additional	ADJ
ejpam-6525	92	14	time	time	NOUN
ejpam-6525	92	15	≤	≤	ADV
ejpam-6525	92	16	c2	c2	PROPN
ejpam-6525	92	17	λ	λ	PROPN
ejpam-6525	92	18	.	.	PUNCT
ejpam-6525	93	1	the	the	DET
ejpam-6525	93	2	worst	bad	ADJ
ejpam-6525	93	3	-	-	PUNCT
ejpam-6525	93	4	case	case	NOUN
ejpam-6525	93	5	path	path	NOUN
ejpam-6525	93	6	length	length	NOUN
ejpam-6525	93	7	between	between	ADP
ejpam-6525	93	8	any	any	DET
ejpam-6525	93	9	three	three	NUM
ejpam-6525	93	10	points	point	NOUN
ejpam-6525	93	11	is	be	AUX
ejpam-6525	93	12	controlled	control	VERB
ejpam-6525	93	13	by	by	ADP
ejpam-6525	93	14	the	the	DET
ejpam-6525	93	15	spectral	spectral	ADJ
ejpam-6525	93	16	gap	gap	NOUN
ejpam-6525	93	17	,	,	PUNCT
ejpam-6525	93	18	giving	give	VERB
ejpam-6525	93	19	the	the	DET
ejpam-6525	93	20	o(1	o(1	NOUN
ejpam-6525	93	21	/	/	SYM
ejpam-6525	93	22	λ	λ	NOUN
ejpam-6525	93	23	)	)	PUNCT
ejpam-6525	93	24	factor	factor	NOUN
ejpam-6525	93	25	.	.	PUNCT
ejpam-6525	94	1	the	the	DET
ejpam-6525	94	2	detailed	detailed	ADJ
ejpam-6525	94	3	analysis	analysis	NOUN
ejpam-6525	94	4	uses	use	VERB
ejpam-6525	94	5	the	the	DET
ejpam-6525	94	6	markov	markov	NOUN
ejpam-6525	94	7	property	property	NOUN
ejpam-6525	94	8	and	and	CCONJ
ejpam-6525	94	9	the	the	DET
ejpam-6525	94	10	fact	fact	NOUN
ejpam-6525	94	11	that	that	SCONJ
ejpam-6525	94	12	for	for	ADP
ejpam-6525	94	13	expanders	expander	NOUN
ejpam-6525	94	14	,	,	PUNCT
ejpam-6525	94	15	the	the	DET
ejpam-6525	94	16	mixing	mixing	NOUN
ejpam-6525	94	17	time	time	NOUN
ejpam-6525	94	18	is	be	AUX
ejpam-6525	94	19	o	o	NOUN
ejpam-6525	94	20	(	(	PUNCT
ejpam-6525	94	21	lognλ	lognλ	NOUN
ejpam-6525	94	22	)	)	PUNCT
ejpam-6525	94	23	.	.	PUNCT
ejpam-6525	95	1	taking	take	VERB
ejpam-6525	95	2	r	r	NOUN
ejpam-6525	95	3	=	=	SYM
ejpam-6525	95	4	3c(λ	3c(λ	NUM
ejpam-6525	95	5	)	)	PUNCT
ejpam-6525	96	1	=	=	PUNCT
ejpam-6525	96	2	o(1	o(1	PROPN
ejpam-6525	96	3	/	/	SYM
ejpam-6525	96	4	λ	λ	NOUN
ejpam-6525	96	5	)	)	PUNCT
ejpam-6525	96	6	completes	complete	VERB
ejpam-6525	96	7	the	the	DET
ejpam-6525	96	8	proof	proof	NOUN
ejpam-6525	96	9	of	of	ADP
ejpam-6525	96	10	the	the	DET
ejpam-6525	96	11	triangle	triangle	NOUN
ejpam-6525	96	12	inequality	inequality	NOUN
ejpam-6525	96	13	.	.	PUNCT
ejpam-6525	97	1	conclusion	conclusion	NOUN
ejpam-6525	97	2	all	all	DET
ejpam-6525	97	3	mr	mr	PROPN
ejpam-6525	97	4	-	-	PUNCT
ejpam-6525	97	5	metric	metric	ADJ
ejpam-6525	97	6	axioms	axiom	NOUN
ejpam-6525	97	7	are	be	AUX
ejpam-6525	97	8	satisfied	satisfied	ADJ
ejpam-6525	97	9	with	with	ADP
ejpam-6525	97	10	r	r	NOUN
ejpam-6525	97	11	=	=	SYM
ejpam-6525	97	12	o(1	o(1	PROPN
ejpam-6525	97	13	/	/	SYM
ejpam-6525	97	14	λ	λ	NOUN
ejpam-6525	97	15	)	)	PUNCT
ejpam-6525	97	16	,	,	PUNCT
ejpam-6525	97	17	making	make	VERB
ejpam-6525	97	18	(	(	PUNCT
ejpam-6525	97	19	v	v	NOUN
ejpam-6525	97	20	,	,	PUNCT
ejpam-6525	97	21	m	m	NOUN
ejpam-6525	97	22	)	)	PUNCT
ejpam-6525	97	23	an	an	DET
ejpam-6525	97	24	mr	mr	PROPN
ejpam-6525	97	25	-	-	PUNCT
ejpam-6525	97	26	metric	metric	ADJ
ejpam-6525	97	27	space	space	NOUN
ejpam-6525	97	28	.	.	PUNCT
ejpam-6525	98	1	a.	a.	PROPN
ejpam-6525	98	2	malkawi	malkawi	PROPN
ejpam-6525	98	3	,	,	PUNCT
ejpam-6525	98	4	a.	a.	PROPN
ejpam-6525	98	5	m.	m.	NOUN
ejpam-6525	98	6	rabaiah	rabaiah	PROPN
ejpam-6525	98	7	/	/	SYM
ejpam-6525	98	8	eur	eur	PROPN
ejpam-6525	98	9	.	.	PUNCT
ejpam-6525	99	1	j.	j.	PROPN
ejpam-6525	99	2	pure	pure	PROPN
ejpam-6525	99	3	appl	appl	PROPN
ejpam-6525	99	4	.	.	PROPN
ejpam-6525	99	5	math	math	PROPN
ejpam-6525	99	6	,	,	PUNCT
ejpam-6525	99	7	18	18	NUM
ejpam-6525	99	8	(	(	PUNCT
ejpam-6525	99	9	3	3	NUM
ejpam-6525	99	10	)	)	PUNCT
ejpam-6525	99	11	(	(	PUNCT
ejpam-6525	99	12	2025	2025	NUM
ejpam-6525	99	13	)	)	PUNCT
ejpam-6525	99	14	,	,	PUNCT
ejpam-6525	99	15	6525	6525	NUM
ejpam-6525	99	16	6	6	NUM
ejpam-6525	99	17	of	of	ADP
ejpam-6525	99	18	14	14	NUM
ejpam-6525	99	19	3	3	NUM
ejpam-6525	99	20	.	.	PUNCT
ejpam-6525	100	1	examples	example	NOUN
ejpam-6525	100	2	and	and	CCONJ
ejpam-6525	100	3	applications	application	NOUN
ejpam-6525	100	4	3.1	3.1	NUM
ejpam-6525	100	5	.	.	PUNCT
ejpam-6525	100	6	weighted	weight	VERB
ejpam-6525	100	7	graph	graph	NOUN
ejpam-6525	100	8	embedding	embed	VERB
ejpam-6525	100	9	example	example	NOUN
ejpam-6525	100	10	1	1	NUM
ejpam-6525	100	11	(	(	PUNCT
ejpam-6525	100	12	network	network	NOUN
ejpam-6525	100	13	design	design	NOUN
ejpam-6525	100	14	with	with	ADP
ejpam-6525	100	15	latency	latency	NOUN
ejpam-6525	100	16	constraints	constraint	NOUN
ejpam-6525	100	17	)	)	PUNCT
ejpam-6525	100	18	.	.	PUNCT
ejpam-6525	101	1	consider	consider	VERB
ejpam-6525	101	2	a	a	DET
ejpam-6525	101	3	5	5	NUM
ejpam-6525	101	4	g	g	NOUN
ejpam-6525	101	5	cellular	cellular	ADJ
ejpam-6525	101	6	network	network	NOUN
ejpam-6525	101	7	modeled	model	VERB
ejpam-6525	101	8	as	as	ADP
ejpam-6525	101	9	a	a	DET
ejpam-6525	101	10	weighted	weighted	ADJ
ejpam-6525	101	11	graph	graph	NOUN
ejpam-6525	101	12	g	g	PROPN
ejpam-6525	101	13	=	=	SYM
ejpam-6525	101	14	(	(	PUNCT
ejpam-6525	101	15	v	v	NOUN
ejpam-6525	101	16	,	,	PUNCT
ejpam-6525	101	17	e	e	NOUN
ejpam-6525	101	18	,	,	PUNCT
ejpam-6525	101	19	w	w	NOUN
ejpam-6525	101	20	)	)	PUNCT
ejpam-6525	101	21	where	where	SCONJ
ejpam-6525	101	22	:	:	PUNCT
ejpam-6525	101	23	•	•	NUM
ejpam-6525	101	24	vertices	vertex	NOUN
ejpam-6525	101	25	v	v	NOUN
ejpam-6525	101	26	represent	represent	VERB
ejpam-6525	101	27	base	base	NOUN
ejpam-6525	101	28	stations	station	NOUN
ejpam-6525	101	29	•	•	NOUN
ejpam-6525	101	30	edges	edge	NOUN
ejpam-6525	101	31	e	e	AUX
ejpam-6525	101	32	represent	represent	VERB
ejpam-6525	101	33	fiber	fiber	NOUN
ejpam-6525	101	34	links	link	NOUN
ejpam-6525	101	35	•	•	NOUN
ejpam-6525	101	36	weights	weight	NOUN
ejpam-6525	101	37	w(e	w(e	NOUN
ejpam-6525	101	38	)	)	PUNCT
ejpam-6525	101	39	quantify	quantify	VERB
ejpam-6525	101	40	latency	latency	NOUN
ejpam-6525	101	41	in	in	ADP
ejpam-6525	101	42	milliseconds	millisecond	NOUN
ejpam-6525	101	43	a	a	DET
ejpam-6525	101	44	b	b	NOUN
ejpam-6525	101	45	c	c	NOUN
ejpam-6525	101	46	d	d	X
ejpam-6525	101	47	e	e	PROPN
ejpam-6525	101	48	f	f	PROPN
ejpam-6525	101	49	user	user	PROPN
ejpam-6525	101	50	cluster	cluster	PROPN
ejpam-6525	101	51	1	1	NUM
ejpam-6525	101	52	user	user	NOUN
ejpam-6525	101	53	cluster	cluster	NOUN
ejpam-6525	101	54	2	2	NUM
ejpam-6525	101	55	user	user	NOUN
ejpam-6525	101	56	cluster	cluster	NOUN
ejpam-6525	101	57	3	3	NUM
ejpam-6525	101	58	4ms	4ms	NOUN
ejpam-6525	101	59	7	7	NUM
ejpam-6525	101	60	m	m	NOUN
ejpam-6525	101	61	s	s	NOUN
ejpam-6525	101	62	5	5	NUM
ejpam-6525	101	63	m	m	NOUN
ejpam-6525	101	64	s	s	NOUN
ejpam-6525	101	65	3ms	3ms	ADJ
ejpam-6525	101	66	6ms	6ms	ADJ
ejpam-6525	101	67	2	2	NUM
ejpam-6525	101	68	m	m	NOUN
ejpam-6525	101	69	s	s	NOUN
ejpam-6525	101	70	8ms	8ms	ADJ
ejpam-6525	101	71	4	4	NUM
ejpam-6525	101	72	m	m	NOUN
ejpam-6525	101	73	s	s	PART
ejpam-6525	101	74	figure	figure	NOUN
ejpam-6525	101	75	1	1	NUM
ejpam-6525	101	76	:	:	PUNCT
ejpam-6525	101	77	a	a	DET
ejpam-6525	101	78	weighted	weight	VERB
ejpam-6525	101	79	network	network	NOUN
ejpam-6525	101	80	graph	graph	NOUN
ejpam-6525	101	81	showing	show	VERB
ejpam-6525	101	82	base	base	NOUN
ejpam-6525	101	83	stations	station	NOUN
ejpam-6525	101	84	(	(	PUNCT
ejpam-6525	101	85	circles	circle	NOUN
ejpam-6525	101	86	)	)	PUNCT
ejpam-6525	101	87	,	,	PUNCT
ejpam-6525	101	88	user	user	NOUN
ejpam-6525	101	89	clusters	cluster	NOUN
ejpam-6525	101	90	(	(	PUNCT
ejpam-6525	101	91	colored	colored	ADJ
ejpam-6525	101	92	rectangles	rectangle	NOUN
ejpam-6525	101	93	)	)	PUNCT
ejpam-6525	101	94	,	,	PUNCT
ejpam-6525	101	95	and	and	CCONJ
ejpam-6525	101	96	latency	latency	NOUN
ejpam-6525	101	97	values	value	NOUN
ejpam-6525	101	98	.	.	PUNCT
ejpam-6525	102	1	the	the	DET
ejpam-6525	102	2	bold	bold	ADJ
ejpam-6525	102	3	path	path	NOUN
ejpam-6525	102	4	represents	represent	VERB
ejpam-6525	102	5	the	the	DET
ejpam-6525	102	6	minimal	minimal	ADJ
ejpam-6525	102	7	-	-	PUNCT
ejpam-6525	102	8	latency	latency	NOUN
ejpam-6525	102	9	connection	connection	NOUN
ejpam-6525	102	10	between	between	ADP
ejpam-6525	102	11	the	the	DET
ejpam-6525	102	12	three	three	NUM
ejpam-6525	102	13	user	user	NOUN
ejpam-6525	102	14	clusters	cluster	NOUN
ejpam-6525	102	15	with	with	ADP
ejpam-6525	102	16	total	total	ADJ
ejpam-6525	102	17	weight	weight	NOUN
ejpam-6525	102	18	4	4	NUM
ejpam-6525	102	19	+	+	CCONJ
ejpam-6525	102	20	3	3	NUM
ejpam-6525	102	21	+	+	SYM
ejpam-6525	102	22	2	2	NUM
ejpam-6525	102	23	=	=	SYM
ejpam-6525	102	24	9ms	9ms	NOUN
ejpam-6525	102	25	.	.	PUNCT
ejpam-6525	103	1	for	for	ADP
ejpam-6525	103	2	three	three	NUM
ejpam-6525	103	3	user	user	NOUN
ejpam-6525	103	4	clusters	cluster	NOUN
ejpam-6525	103	5	at	at	ADP
ejpam-6525	103	6	nodes	node	NOUN
ejpam-6525	103	7	u	u	PROPN
ejpam-6525	103	8	,	,	PUNCT
ejpam-6525	103	9	v	v	NOUN
ejpam-6525	103	10	,	,	PUNCT
ejpam-6525	103	11	w	w	PROPN
ejpam-6525	103	12	,	,	PUNCT
ejpam-6525	103	13	the	the	DET
ejpam-6525	103	14	mr	mr	PROPN
ejpam-6525	103	15	-	-	PUNCT
ejpam-6525	103	16	metric	metric	NOUN
ejpam-6525	103	17	:	:	PUNCT
ejpam-6525	103	18	m(u	m(u	PROPN
ejpam-6525	103	19	,	,	PUNCT
ejpam-6525	103	20	v	v	NOUN
ejpam-6525	103	21	,	,	PUNCT
ejpam-6525	103	22	w	w	NOUN
ejpam-6525	103	23	)	)	PUNCT
ejpam-6525	103	24	=	=	SYM
ejpam-6525	103	25	min	min	PROPN
ejpam-6525	103	26	t	t	PROPN
ejpam-6525	103	27	(	(	PUNCT
ejpam-6525	103	28	∑	∑	PUNCT
ejpam-6525	103	29	e∈t	e∈t	PROPN
ejpam-6525	103	30	w(e	w(e	PROPN
ejpam-6525	103	31	)	)	PUNCT
ejpam-6525	103	32	)	)	PUNCT
ejpam-6525	103	33	where	where	SCONJ
ejpam-6525	103	34	t	t	PROPN
ejpam-6525	103	35	spans	span	VERB
ejpam-6525	103	36	u	u	PROPN
ejpam-6525	103	37	,	,	PUNCT
ejpam-6525	103	38	v	v	NOUN
ejpam-6525	103	39	,	,	PUNCT
ejpam-6525	103	40	w	w	PROPN
ejpam-6525	103	41	computes	compute	VERB
ejpam-6525	103	42	the	the	DET
ejpam-6525	103	43	minimal	minimal	ADJ
ejpam-6525	103	44	-	-	PUNCT
ejpam-6525	103	45	latency	latency	NOUN
ejpam-6525	103	46	backbone	backbone	NOUN
ejpam-6525	103	47	connecting	connect	VERB
ejpam-6525	103	48	these	these	DET
ejpam-6525	103	49	clusters	cluster	NOUN
ejpam-6525	103	50	.	.	PUNCT
ejpam-6525	104	1	in	in	ADP
ejpam-6525	104	2	figure	figure	NOUN
ejpam-6525	104	3	1	1	NUM
ejpam-6525	104	4	,	,	PUNCT
ejpam-6525	104	5	this	this	PRON
ejpam-6525	104	6	corresponds	correspond	VERB
ejpam-6525	104	7	to	to	ADP
ejpam-6525	104	8	finding	find	VERB
ejpam-6525	104	9	the	the	DET
ejpam-6525	104	10	steiner	steiner	NOUN
ejpam-6525	104	11	tree	tree	NOUN
ejpam-6525	104	12	with	with	ADP
ejpam-6525	104	13	minimal	minimal	ADJ
ejpam-6525	104	14	total	total	ADJ
ejpam-6525	104	15	weight	weight	NOUN
ejpam-6525	104	16	(	(	PUNCT
ejpam-6525	104	17	shown	show	VERB
ejpam-6525	104	18	in	in	ADP
ejpam-6525	104	19	bold	bold	ADJ
ejpam-6525	104	20	)	)	PUNCT
ejpam-6525	104	21	.	.	PUNCT
ejpam-6525	105	1	remark	remark	PROPN
ejpam-6525	105	2	1	1	NUM
ejpam-6525	105	3	.	.	PUNCT
ejpam-6525	106	1	the	the	DET
ejpam-6525	106	2	mr	mr	PROPN
ejpam-6525	106	3	-	-	PUNCT
ejpam-6525	106	4	propertym(u	propertym(u	NOUN
ejpam-6525	106	5	,	,	PUNCT
ejpam-6525	106	6	v	v	NOUN
ejpam-6525	106	7	,	,	PUNCT
ejpam-6525	106	8	w	w	NOUN
ejpam-6525	106	9	)	)	PUNCT
ejpam-6525	106	10	≤	≤	NOUN
ejpam-6525	106	11	2[m(u	2[m(u	NUM
ejpam-6525	106	12	,	,	PUNCT
ejpam-6525	106	13	v	v	NOUN
ejpam-6525	106	14	,	,	PUNCT
ejpam-6525	106	15	x)+m(u	x)+m(u	NOUN
ejpam-6525	106	16	,	,	PUNCT
ejpam-6525	106	17	x	x	NOUN
ejpam-6525	106	18	,	,	PUNCT
ejpam-6525	106	19	w)+m(x	w)+m(x	NOUN
ejpam-6525	106	20	,	,	PUNCT
ejpam-6525	106	21	v	v	NOUN
ejpam-6525	106	22	,	,	PUNCT
ejpam-6525	106	23	w	w	NOUN
ejpam-6525	106	24	)	)	PUNCT
ejpam-6525	106	25	]	]	PUNCT
ejpam-6525	106	26	ensures	ensure	VERB
ejpam-6525	106	27	that	that	SCONJ
ejpam-6525	106	28	adding	add	VERB
ejpam-6525	106	29	a	a	DET
ejpam-6525	106	30	relay	relay	NOUN
ejpam-6525	106	31	node	node	NOUN
ejpam-6525	106	32	x	x	PUNCT
ejpam-6525	106	33	never	never	ADV
ejpam-6525	106	34	worsens	worsen	VERB
ejpam-6525	106	35	the	the	DET
ejpam-6525	106	36	optimal	optimal	ADJ
ejpam-6525	106	37	connection	connection	NOUN
ejpam-6525	106	38	by	by	ADP
ejpam-6525	106	39	more	more	ADJ
ejpam-6525	106	40	than	than	ADP
ejpam-6525	106	41	a	a	DET
ejpam-6525	106	42	factor	factor	NOUN
ejpam-6525	106	43	of	of	ADP
ejpam-6525	106	44	2	2	NUM
ejpam-6525	106	45	.	.	PUNCT
ejpam-6525	106	46	a.	a.	NOUN
ejpam-6525	106	47	malkawi	malkawi	PROPN
ejpam-6525	106	48	,	,	PUNCT
ejpam-6525	106	49	a.	a.	PROPN
ejpam-6525	106	50	m.	m.	NOUN
ejpam-6525	106	51	rabaiah	rabaiah	PROPN
ejpam-6525	106	52	/	/	SYM
ejpam-6525	106	53	eur	eur	PROPN
ejpam-6525	106	54	.	.	PUNCT
ejpam-6525	107	1	j.	j.	PROPN
ejpam-6525	107	2	pure	pure	PROPN
ejpam-6525	107	3	appl	appl	PROPN
ejpam-6525	107	4	.	.	PROPN
ejpam-6525	107	5	math	math	PROPN
ejpam-6525	107	6	,	,	PUNCT
ejpam-6525	107	7	18	18	NUM
ejpam-6525	107	8	(	(	PUNCT
ejpam-6525	107	9	3	3	NUM
ejpam-6525	107	10	)	)	PUNCT
ejpam-6525	107	11	(	(	PUNCT
ejpam-6525	107	12	2025	2025	NUM
ejpam-6525	107	13	)	)	PUNCT
ejpam-6525	107	14	,	,	PUNCT
ejpam-6525	107	15	6525	6525	NUM
ejpam-6525	107	16	7	7	NUM
ejpam-6525	107	17	of	of	ADP
ejpam-6525	107	18	14	14	NUM
ejpam-6525	107	19	algorithm	algorithm	NOUN
ejpam-6525	107	20	1	1	NUM
ejpam-6525	107	21	2	2	NUM
ejpam-6525	107	22	-	-	PUNCT
ejpam-6525	107	23	approximate	approximate	ADJ
ejpam-6525	107	24	server	server	NOUN
ejpam-6525	107	25	placement	placement	NOUN
ejpam-6525	107	26	application	application	NOUN
ejpam-6525	107	27	1	1	NUM
ejpam-6525	107	28	(	(	PUNCT
ejpam-6525	107	29	approximation	approximation	NOUN
ejpam-6525	107	30	algorithm	algorithm	NOUN
ejpam-6525	107	31	for	for	ADP
ejpam-6525	107	32	content	content	NOUN
ejpam-6525	107	33	delivery	delivery	NOUN
ejpam-6525	107	34	networks	network	NOUN
ejpam-6525	107	35	)	)	PUNCT
ejpam-6525	107	36	.	.	PUNCT
ejpam-6525	108	1	require	require	NOUN
ejpam-6525	108	2	:	:	PUNCT
ejpam-6525	108	3	weighted	weight	VERB
ejpam-6525	108	4	graph	graph	NOUN
ejpam-6525	108	5	g	g	PROPN
ejpam-6525	108	6	=	=	SYM
ejpam-6525	108	7	(	(	PUNCT
ejpam-6525	108	8	v	v	NOUN
ejpam-6525	108	9	,	,	PUNCT
ejpam-6525	108	10	e	e	NOUN
ejpam-6525	108	11	,	,	PUNCT
ejpam-6525	108	12	w	w	NOUN
ejpam-6525	108	13	)	)	PUNCT
ejpam-6525	108	14	,	,	PUNCT
ejpam-6525	108	15	demand	demand	NOUN
ejpam-6525	108	16	points	point	VERB
ejpam-6525	108	17	d	d	X
ejpam-6525	108	18	⊂	⊂	PROPN
ejpam-6525	108	19	v	v	PROPN
ejpam-6525	108	20	ensure	ensure	VERB
ejpam-6525	108	21	:	:	PUNCT
ejpam-6525	108	22	server	server	NOUN
ejpam-6525	108	23	locations	location	NOUN
ejpam-6525	108	24	s	s	PART
ejpam-6525	108	25	⊂	⊂	PROPN
ejpam-6525	108	26	v	v	ADP
ejpam-6525	108	27	1	1	NUM
ejpam-6525	108	28	:	:	PUNCT
ejpam-6525	108	29	initialize	initialize	VERB
ejpam-6525	108	30	s	s	PRON
ejpam-6525	108	31	←	←	PROPN
ejpam-6525	108	32	∅	∅	NOUN
ejpam-6525	108	33	2	2	NUM
ejpam-6525	108	34	:	:	PUNCT
ejpam-6525	108	35	while	while	SCONJ
ejpam-6525	108	36	|s|	|s|	PROPN
ejpam-6525	108	37	<	<	X
ejpam-6525	108	38	k	k	X
ejpam-6525	108	39	do	do	AUX
ejpam-6525	108	40	3	3	NUM
ejpam-6525	108	41	:	:	PUNCT
ejpam-6525	108	42	find	find	VERB
ejpam-6525	108	43	(	(	PUNCT
ejpam-6525	108	44	u∗	u∗	ADJ
ejpam-6525	108	45	,	,	PUNCT
ejpam-6525	108	46	v∗	v∗	ADJ
ejpam-6525	108	47	,	,	PUNCT
ejpam-6525	108	48	w∗	w∗	NOUN
ejpam-6525	108	49	)	)	PUNCT
ejpam-6525	108	50	=	=	PUNCT
ejpam-6525	109	1	argmax	argmax	PRON
ejpam-6525	109	2	u	u	NOUN
ejpam-6525	109	3	,	,	PUNCT
ejpam-6525	109	4	v	v	NOUN
ejpam-6525	109	5	,	,	PUNCT
ejpam-6525	109	6	w∈d	w∈d	ADJ
ejpam-6525	109	7	m(u	m(u	PROPN
ejpam-6525	109	8	,	,	PUNCT
ejpam-6525	109	9	v	v	NOUN
ejpam-6525	109	10	,	,	PUNCT
ejpam-6525	109	11	w	w	NOUN
ejpam-6525	109	12	)	)	PUNCT
ejpam-6525	109	13	4	4	NUM
ejpam-6525	109	14	:	:	PUNCT
ejpam-6525	109	15	compute	compute	PROPN
ejpam-6525	109	16	steiner	steiner	PROPN
ejpam-6525	109	17	tree	tree	PROPN
ejpam-6525	109	18	t	t	PROPN
ejpam-6525	109	19	spanning	span	VERB
ejpam-6525	109	20	u∗	u∗	PROPN
ejpam-6525	109	21	,	,	PUNCT
ejpam-6525	109	22	v∗	v∗	PROPN
ejpam-6525	109	23	,	,	PUNCT
ejpam-6525	109	24	w∗	w∗	NOUN
ejpam-6525	109	25	using	use	VERB
ejpam-6525	109	26	:	:	PUNCT
ejpam-6525	109	27	5	5	NUM
ejpam-6525	109	28	:	:	SYM
ejpam-6525	109	29	1	1	NUM
ejpam-6525	109	30	.	.	X
ejpam-6525	109	31	metric	metric	ADJ
ejpam-6525	109	32	closure	closure	NOUN
ejpam-6525	109	33	of	of	ADP
ejpam-6525	109	34	g	g	PROPN
ejpam-6525	109	35	6	6	NUM
ejpam-6525	109	36	:	:	SYM
ejpam-6525	109	37	2	2	NUM
ejpam-6525	109	38	.	.	X
ejpam-6525	109	39	minimum	minimum	ADJ
ejpam-6525	109	40	spanning	span	VERB
ejpam-6525	109	41	tree	tree	NOUN
ejpam-6525	109	42	(	(	PUNCT
ejpam-6525	109	43	mst	mst	PROPN
ejpam-6525	109	44	)	)	PUNCT
ejpam-6525	109	45	approximation	approximation	NOUN
ejpam-6525	109	46	7	7	NUM
ejpam-6525	109	47	:	:	PUNCT
ejpam-6525	109	48	add	add	VERB
ejpam-6525	109	49	to	to	ADP
ejpam-6525	109	50	s	s	PRON
ejpam-6525	109	51	the	the	DET
ejpam-6525	109	52	node	node	NOUN
ejpam-6525	109	53	x	x	SYM
ejpam-6525	109	54	∈	∈	PROPN
ejpam-6525	109	55	t	t	NOUN
ejpam-6525	109	56	minimizing	minimize	VERB
ejpam-6525	109	57	maxu	maxu	NOUN
ejpam-6525	109	58	,	,	PUNCT
ejpam-6525	109	59	v	v	NOUN
ejpam-6525	109	60	,	,	PUNCT
ejpam-6525	109	61	wm(u	wm(u	X
ejpam-6525	109	62	,	,	PUNCT
ejpam-6525	109	63	v	v	NOUN
ejpam-6525	109	64	,	,	PUNCT
ejpam-6525	109	65	w	w	NOUN
ejpam-6525	109	66	)	)	PUNCT
ejpam-6525	109	67	8	8	NUM
ejpam-6525	109	68	:	:	PUNCT
ejpam-6525	109	69	remove	remove	VERB
ejpam-6525	109	70	covered	covered	ADJ
ejpam-6525	109	71	demands	demand	NOUN
ejpam-6525	109	72	:	:	PUNCT
ejpam-6525	109	73	d	d	X
ejpam-6525	109	74	←	←	PROPN
ejpam-6525	109	75	d	d	X
ejpam-6525	109	76	\	\	PROPN
ejpam-6525	109	77	{	{	PUNCT
ejpam-6525	109	78	u∗	u∗	PROPN
ejpam-6525	109	79	,	,	PUNCT
ejpam-6525	109	80	v∗	v∗	ADJ
ejpam-6525	109	81	,	,	PUNCT
ejpam-6525	109	82	w∗	w∗	NOUN
ejpam-6525	109	83	}	}	PUNCT
ejpam-6525	109	84	9	9	NUM
ejpam-6525	109	85	:	:	PUNCT
ejpam-6525	109	86	end	end	NOUN
ejpam-6525	109	87	while	while	SCONJ
ejpam-6525	109	88	10	10	NUM
ejpam-6525	109	89	:	:	PUNCT
ejpam-6525	109	90	return	return	VERB
ejpam-6525	109	91	s	s	PART
ejpam-6525	109	92	performance	performance	NOUN
ejpam-6525	109	93	analysis	analysis	NOUN
ejpam-6525	109	94	:	:	PUNCT
ejpam-6525	109	95	•	•	NUM
ejpam-6525	109	96	approximation	approximation	NOUN
ejpam-6525	109	97	ratio	ratio	NOUN
ejpam-6525	109	98	:	:	PUNCT
ejpam-6525	109	99	guaranteed	guarantee	VERB
ejpam-6525	109	100	2	2	NUM
ejpam-6525	109	101	-	-	PUNCT
ejpam-6525	109	102	approximation	approximation	NOUN
ejpam-6525	109	103	due	due	ADJ
ejpam-6525	109	104	to	to	ADP
ejpam-6525	109	105	:	:	PUNCT
ejpam-6525	109	106	malg(u	malg(u	ADJ
ejpam-6525	109	107	,	,	PUNCT
ejpam-6525	109	108	v	v	NOUN
ejpam-6525	109	109	,	,	PUNCT
ejpam-6525	109	110	w	w	NOUN
ejpam-6525	109	111	)	)	PUNCT
ejpam-6525	109	112	≤	≤	NUM
ejpam-6525	109	113	2	2	NUM
ejpam-6525	109	114	·	·	SYM
ejpam-6525	109	115	mopt(u	mopt(u	PROPN
ejpam-6525	109	116	,	,	PUNCT
ejpam-6525	109	117	v	v	NOUN
ejpam-6525	109	118	,	,	PUNCT
ejpam-6525	109	119	w	w	NOUN
ejpam-6525	109	120	)	)	PUNCT
ejpam-6525	109	121	following	follow	VERB
ejpam-6525	109	122	from	from	ADP
ejpam-6525	109	123	theorem	theorem	ADJ
ejpam-6525	109	124	1	1	NUM
ejpam-6525	109	125	’s	’s	NOUN
ejpam-6525	109	126	r	r	NOUN
ejpam-6525	109	127	=	=	SYM
ejpam-6525	109	128	2	2	NUM
ejpam-6525	109	129	property	property	NOUN
ejpam-6525	109	130	.	.	PUNCT
ejpam-6525	110	1	•	•	NUM
ejpam-6525	110	2	time	time	NOUN
ejpam-6525	110	3	complexity	complexity	NOUN
ejpam-6525	110	4	:	:	PUNCT
ejpam-6525	110	5	o(|d|3	o(|d|3	ADV
ejpam-6525	110	6	·	·	PUNCT
ejpam-6525	110	7	|v	|v	X
ejpam-6525	110	8	|2	|2	NUM
ejpam-6525	110	9	)	)	PUNCT
ejpam-6525	110	10	using	use	VERB
ejpam-6525	110	11	:	:	PUNCT
ejpam-6525	110	12	–	–	PUNCT
ejpam-6525	110	13	all	all	PRON
ejpam-6525	110	14	-	-	PUNCT
ejpam-6525	110	15	pairs	pair	NOUN
ejpam-6525	110	16	shortest	short	ADJ
ejpam-6525	110	17	paths	path	NOUN
ejpam-6525	110	18	:	:	PUNCT
ejpam-6525	110	19	o(|v	o(|v	PROPN
ejpam-6525	110	20	|3	|3	NOUN
ejpam-6525	110	21	)	)	PUNCT
ejpam-6525	110	22	(	(	PUNCT
ejpam-6525	110	23	preprocessing	preprocessing	NOUN
ejpam-6525	110	24	)	)	PUNCT
ejpam-6525	110	25	–	–	PUNCT
ejpam-6525	110	26	mst	mst	PROPN
ejpam-6525	110	27	computation	computation	NOUN
ejpam-6525	110	28	:	:	PUNCT
ejpam-6525	110	29	o(|v	o(|v	X
ejpam-6525	110	30	|2	|2	NUM
ejpam-6525	110	31	)	)	PUNCT
ejpam-6525	110	32	per	per	ADP
ejpam-6525	110	33	triple	triple	ADJ
ejpam-6525	110	34	•	•	CCONJ
ejpam-6525	110	35	practical	practical	ADJ
ejpam-6525	110	36	impact	impact	NOUN
ejpam-6525	110	37	:	:	PUNCT
ejpam-6525	110	38	reduces	reduce	VERB
ejpam-6525	110	39	backbone	backbone	NOUN
ejpam-6525	110	40	latency	latency	NOUN
ejpam-6525	110	41	by	by	ADP
ejpam-6525	110	42	38	38	NUM
ejpam-6525	110	43	%	%	NOUN
ejpam-6525	110	44	compared	compare	VERB
ejpam-6525	110	45	to	to	ADP
ejpam-6525	110	46	k	k	ADJ
ejpam-6525	110	47	-	-	PUNCT
ejpam-6525	110	48	means	mean	VERB
ejpam-6525	110	49	placement	placement	NOUN
ejpam-6525	110	50	in	in	ADP
ejpam-6525	110	51	real	real	ADJ
ejpam-6525	110	52	-	-	PUNCT
ejpam-6525	110	53	world	world	NOUN
ejpam-6525	110	54	tests	test	NOUN
ejpam-6525	110	55	(	(	PUNCT
ejpam-6525	110	56	see	see	VERB
ejpam-6525	110	57	table	table	NOUN
ejpam-6525	110	58	1	1	NUM
ejpam-6525	110	59	)	)	PUNCT
ejpam-6525	110	60	.	.	PUNCT
ejpam-6525	111	1	method	method	PROPN
ejpam-6525	111	2	avg	avg	PROPN
ejpam-6525	111	3	.	.	PROPN
ejpam-6525	111	4	latency	latency	PROPN
ejpam-6525	111	5	(	(	PUNCT
ejpam-6525	111	6	ms	ms	PROPN
ejpam-6525	111	7	)	)	PUNCT
ejpam-6525	111	8	95th	95th	NOUN
ejpam-6525	111	9	percentile	percentile	ADJ
ejpam-6525	111	10	mr	mr	PROPN
ejpam-6525	111	11	-	-	PUNCT
ejpam-6525	111	12	metric	metric	ADJ
ejpam-6525	111	13	12.4	12.4	NUM
ejpam-6525	111	14	18.7	18.7	NUM
ejpam-6525	111	15	k	k	NOUN
ejpam-6525	111	16	-	-	PUNCT
ejpam-6525	111	17	means	mean	VERB
ejpam-6525	111	18	19.8	19.8	NUM
ejpam-6525	111	19	29.3	29.3	NUM
ejpam-6525	111	20	table	table	NOUN
ejpam-6525	111	21	1	1	NUM
ejpam-6525	111	22	:	:	PUNCT
ejpam-6525	111	23	performance	performance	NOUN
ejpam-6525	111	24	comparison	comparison	NOUN
ejpam-6525	111	25	on	on	ADP
ejpam-6525	111	26	eu	eu	ADJ
ejpam-6525	111	27	-	-	ADJ
ejpam-6525	111	28	wide	wide	ADJ
ejpam-6525	111	29	cdn	cdn	NOUN
ejpam-6525	111	30	example	example	NOUN
ejpam-6525	111	31	2	2	NUM
ejpam-6525	111	32	(	(	PUNCT
ejpam-6525	111	33	vlsi	vlsi	PROPN
ejpam-6525	111	34	circuit	circuit	PROPN
ejpam-6525	111	35	design	design	PROPN
ejpam-6525	111	36	)	)	PUNCT
ejpam-6525	111	37	.	.	PUNCT
ejpam-6525	112	1	in	in	ADP
ejpam-6525	112	2	chip	chip	NOUN
ejpam-6525	112	3	layout	layout	NOUN
ejpam-6525	112	4	optimization	optimization	NOUN
ejpam-6525	112	5	:	:	PUNCT
ejpam-6525	112	6	•	•	NUM
ejpam-6525	112	7	vertices	vertex	NOUN
ejpam-6525	112	8	represent	represent	VERB
ejpam-6525	112	9	components	component	NOUN
ejpam-6525	112	10	•	•	PRON
ejpam-6525	112	11	edges	edge	NOUN
ejpam-6525	112	12	represent	represent	VERB
ejpam-6525	112	13	wire	wire	NOUN
ejpam-6525	112	14	connections	connection	NOUN
ejpam-6525	112	15	•	•	ADP
ejpam-6525	112	16	weights	weight	NOUN
ejpam-6525	112	17	model	model	NOUN
ejpam-6525	112	18	signal	signal	PROPN
ejpam-6525	112	19	propagation	propagation	NOUN
ejpam-6525	112	20	delay	delay	NOUN
ejpam-6525	112	21	a.	a.	NOUN
ejpam-6525	112	22	malkawi	malkawi	PROPN
ejpam-6525	112	23	,	,	PUNCT
ejpam-6525	112	24	a.	a.	PROPN
ejpam-6525	112	25	m.	m.	NOUN
ejpam-6525	112	26	rabaiah	rabaiah	PROPN
ejpam-6525	112	27	/	/	SYM
ejpam-6525	112	28	eur	eur	PROPN
ejpam-6525	112	29	.	.	PUNCT
ejpam-6525	113	1	j.	j.	PROPN
ejpam-6525	113	2	pure	pure	PROPN
ejpam-6525	113	3	appl	appl	PROPN
ejpam-6525	113	4	.	.	PROPN
ejpam-6525	113	5	math	math	PROPN
ejpam-6525	113	6	,	,	PUNCT
ejpam-6525	113	7	18	18	NUM
ejpam-6525	113	8	(	(	PUNCT
ejpam-6525	113	9	3	3	NUM
ejpam-6525	113	10	)	)	PUNCT
ejpam-6525	113	11	(	(	PUNCT
ejpam-6525	113	12	2025	2025	NUM
ejpam-6525	113	13	)	)	PUNCT
ejpam-6525	113	14	,	,	PUNCT
ejpam-6525	113	15	6525	6525	NUM
ejpam-6525	113	16	8	8	NUM
ejpam-6525	113	17	of	of	ADP
ejpam-6525	113	18	14	14	NUM
ejpam-6525	113	19	the	the	DET
ejpam-6525	113	20	mr	mr	PROPN
ejpam-6525	113	21	-	-	PUNCT
ejpam-6525	113	22	metric	metric	ADJ
ejpam-6525	113	23	identifies	identify	VERB
ejpam-6525	113	24	critical	critical	ADJ
ejpam-6525	113	25	triplets	triplet	NOUN
ejpam-6525	113	26	of	of	ADP
ejpam-6525	113	27	components	component	NOUN
ejpam-6525	113	28	where	where	SCONJ
ejpam-6525	113	29	:	:	PUNCT
ejpam-6525	113	30	m(cpu	m(cpu	PROPN
ejpam-6525	113	31	,	,	PUNCT
ejpam-6525	113	32	gpu	gpu	NOUN
ejpam-6525	113	33	,	,	PUNCT
ejpam-6525	113	34	memory	memory	NOUN
ejpam-6525	113	35	)	)	PUNCT
ejpam-6525	113	36	>	>	PUNCT
ejpam-6525	113	37	clock	clock	NOUN
ejpam-6525	113	38	cycle	cycle	NOUN
ejpam-6525	113	39	threshold	threshold	NOUN
ejpam-6525	113	40	requiring	require	VERB
ejpam-6525	113	41	placement	placement	NOUN
ejpam-6525	113	42	optimization	optimization	NOUN
ejpam-6525	113	43	.	.	PUNCT
ejpam-6525	114	1	the	the	DET
ejpam-6525	114	2	r	r	NOUN
ejpam-6525	114	3	=	=	SYM
ejpam-6525	114	4	2	2	NUM
ejpam-6525	114	5	property	property	NOUN
ejpam-6525	114	6	bounds	bound	VERB
ejpam-6525	114	7	the	the	DET
ejpam-6525	114	8	error	error	NOUN
ejpam-6525	114	9	when	when	SCONJ
ejpam-6525	114	10	estimating	estimate	VERB
ejpam-6525	114	11	via	via	ADP
ejpam-6525	114	12	intermediate	intermediate	ADJ
ejpam-6525	114	13	nodes	node	NOUN
ejpam-6525	114	14	.	.	PUNCT
ejpam-6525	115	1	3.2	3.2	NUM
ejpam-6525	115	2	.	.	PUNCT
ejpam-6525	115	3	theorem	theorem	ADJ
ejpam-6525	115	4	2	2	NUM
ejpam-6525	115	5	:	:	PUNCT
ejpam-6525	115	6	set	set	NOUN
ejpam-6525	115	7	-	-	PUNCT
ejpam-6525	115	8	valued	value	VERB
ejpam-6525	115	9	fixed	fix	VERB
ejpam-6525	115	10	points	point	NOUN
ejpam-6525	115	11	in	in	ADP
ejpam-6525	115	12	mr	mr	PROPN
ejpam-6525	115	13	-	-	PUNCT
ejpam-6525	115	14	spaces	space	NOUN
ejpam-6525	115	15	example	example	NOUN
ejpam-6525	115	16	3	3	NUM
ejpam-6525	115	17	(	(	PUNCT
ejpam-6525	115	18	distributed	distribute	VERB
ejpam-6525	115	19	consensus	consensus	NOUN
ejpam-6525	115	20	in	in	ADP
ejpam-6525	115	21	multi	multi	ADJ
ejpam-6525	115	22	-	-	ADJ
ejpam-6525	115	23	agent	agent	ADJ
ejpam-6525	115	24	systems	system	NOUN
ejpam-6525	115	25	)	)	PUNCT
ejpam-6525	115	26	.	.	PUNCT
ejpam-6525	116	1	consider	consider	VERB
ejpam-6525	116	2	a	a	DET
ejpam-6525	116	3	network	network	NOUN
ejpam-6525	116	4	of	of	ADP
ejpam-6525	116	5	n	n	NOUN
ejpam-6525	116	6	agents	agent	NOUN
ejpam-6525	116	7	v	v	NOUN
ejpam-6525	116	8	=	=	SYM
ejpam-6525	116	9	{	{	PUNCT
ejpam-6525	116	10	v1	v1	PROPN
ejpam-6525	116	11	,	,	PUNCT
ejpam-6525	116	12	...	...	PUNCT
ejpam-6525	116	13	,	,	PUNCT
ejpam-6525	116	14	vn	vn	INTJ
ejpam-6525	116	15	}	}	PUNCT
ejpam-6525	116	16	with	with	ADP
ejpam-6525	116	17	:	:	PUNCT
ejpam-6525	116	18	•	•	NUM
ejpam-6525	116	19	communication	communication	NOUN
ejpam-6525	116	20	graph	graph	NOUN
ejpam-6525	116	21	g	g	PROPN
ejpam-6525	116	22	=	=	PUNCT
ejpam-6525	116	23	(	(	PUNCT
ejpam-6525	116	24	v	v	NOUN
ejpam-6525	116	25	,	,	PUNCT
ejpam-6525	116	26	e	e	NOUN
ejpam-6525	116	27	)	)	PUNCT
ejpam-6525	116	28	with	with	ADP
ejpam-6525	116	29	neighborhood	neighborhood	NOUN
ejpam-6525	116	30	sets	set	VERB
ejpam-6525	116	31	n(vi	n(vi	NOUN
ejpam-6525	116	32	)	)	PUNCT
ejpam-6525	116	33	•	•	ADP
ejpam-6525	116	34	mr	mr	PROPN
ejpam-6525	116	35	-	-	PUNCT
ejpam-6525	116	36	metric	metric	ADJ
ejpam-6525	116	37	m(u	m(u	PROPN
ejpam-6525	116	38	,	,	PUNCT
ejpam-6525	116	39	v	v	NOUN
ejpam-6525	116	40	,	,	PUNCT
ejpam-6525	116	41	w	w	NOUN
ejpam-6525	116	42	)	)	PUNCT
ejpam-6525	116	43	measuring	measure	VERB
ejpam-6525	116	44	opinion	opinion	NOUN
ejpam-6525	116	45	divergence	divergence	NOUN
ejpam-6525	116	46	define	define	VERB
ejpam-6525	116	47	the	the	DET
ejpam-6525	116	48	opinion	opinion	NOUN
ejpam-6525	116	49	update	update	NOUN
ejpam-6525	116	50	rule	rule	NOUN
ejpam-6525	116	51	as	as	ADP
ejpam-6525	116	52	a	a	DET
ejpam-6525	116	53	set	set	NOUN
ejpam-6525	116	54	-	-	PUNCT
ejpam-6525	116	55	valued	value	VERB
ejpam-6525	116	56	map	map	NOUN
ejpam-6525	116	57	:	:	PUNCT
ejpam-6525	116	58	t	t	PROPN
ejpam-6525	116	59	(	(	PUNCT
ejpam-6525	116	60	vi	vi	NOUN
ejpam-6525	116	61	)	)	PUNCT
ejpam-6525	116	62	=	=	SYM
ejpam-6525	116	63	mode	mode	NOUN
ejpam-6525	116	64	(	(	PUNCT
ejpam-6525	116	65	{	{	PUNCT
ejpam-6525	116	66	xj	xj	PROPN
ejpam-6525	116	67	:	:	PUNCT
ejpam-6525	116	68	vj	vj	PROPN
ejpam-6525	116	69	∈	∈	PROPN
ejpam-6525	116	70	n(vi	n(vi	PROPN
ejpam-6525	116	71	)	)	PUNCT
ejpam-6525	116	72	}	}	PUNCT
ejpam-6525	116	73	∪	∪	X
ejpam-6525	116	74	{	{	PUNCT
ejpam-6525	116	75	xi	xi	NOUN
ejpam-6525	116	76	}	}	PUNCT
ejpam-6525	116	77	)	)	PUNCT
ejpam-6525	116	78	where	where	SCONJ
ejpam-6525	116	79	mode	mode	NOUN
ejpam-6525	116	80	returns	return	VERB
ejpam-6525	116	81	all	all	DET
ejpam-6525	116	82	most	most	ADV
ejpam-6525	116	83	frequent	frequent	ADJ
ejpam-6525	116	84	opinions	opinion	NOUN
ejpam-6525	116	85	in	in	ADP
ejpam-6525	116	86	the	the	DET
ejpam-6525	116	87	neighborhood	neighborhood	NOUN
ejpam-6525	116	88	.	.	PUNCT
ejpam-6525	117	1	[	[	X
ejpam-6525	117	2	consensus	consensus	NOUN
ejpam-6525	117	3	protocol	protocol	NOUN
ejpam-6525	117	4	]	]	PUNCT
ejpam-6525	117	5	at	at	ADP
ejpam-6525	117	6	each	each	DET
ejpam-6525	117	7	iteration	iteration	NOUN
ejpam-6525	117	8	k	k	NOUN
ejpam-6525	117	9	:	:	PUNCT
ejpam-6525	117	10	(	(	PUNCT
ejpam-6525	117	11	i	i	NOUN
ejpam-6525	117	12	)	)	PUNCT
ejpam-6525	117	13	each	each	DET
ejpam-6525	117	14	agent	agent	NOUN
ejpam-6525	117	15	broadcasts	broadcast	VERB
ejpam-6525	117	16	its	its	PRON
ejpam-6525	117	17	current	current	ADJ
ejpam-6525	117	18	opinion	opinion	NOUN
ejpam-6525	117	19	x	x	X
ejpam-6525	117	20	(	(	PUNCT
ejpam-6525	117	21	k	k	NOUN
ejpam-6525	117	22	)	)	PUNCT
ejpam-6525	117	23	i	i	PRON
ejpam-6525	117	24	(	(	PUNCT
ejpam-6525	117	25	ii	ii	NOUN
ejpam-6525	117	26	)	)	PUNCT
ejpam-6525	117	27	receives	receive	VERB
ejpam-6525	117	28	opinions	opinion	NOUN
ejpam-6525	117	29	{	{	PUNCT
ejpam-6525	117	30	x(k)j	x(k)j	PROPN
ejpam-6525	117	31	:	:	PUNCT
ejpam-6525	117	32	vj	vj	PROPN
ejpam-6525	117	33	∈	∈	PROPN
ejpam-6525	117	34	n(vi	n(vi	PROPN
ejpam-6525	117	35	)	)	PUNCT
ejpam-6525	117	36	}	}	PUNCT
ejpam-6525	117	37	(	(	PUNCT
ejpam-6525	117	38	iii	iii	X
ejpam-6525	117	39	)	)	PUNCT
ejpam-6525	117	40	updates	update	VERB
ejpam-6525	117	41	to	to	ADP
ejpam-6525	117	42	x	x	PROPN
ejpam-6525	117	43	(	(	PUNCT
ejpam-6525	117	44	k+1	k+1	X
ejpam-6525	117	45	)	)	PUNCT
ejpam-6525	117	46	i	i	PRON
ejpam-6525	117	47	∈	∈	PROPN
ejpam-6525	117	48	t	t	PROPN
ejpam-6525	117	49	(	(	PUNCT
ejpam-6525	117	50	v(k)i	v(k)i	PROPN
ejpam-6525	117	51	)	)	PUNCT
ejpam-6525	117	52	theorem	theorem	VERB
ejpam-6525	117	53	4	4	NUM
ejpam-6525	117	54	(	(	PUNCT
ejpam-6525	117	55	convergence	convergence	NOUN
ejpam-6525	117	56	guarantee	guarantee	NOUN
ejpam-6525	117	57	)	)	PUNCT
ejpam-6525	117	58	.	.	PUNCT
ejpam-6525	118	1	if	if	SCONJ
ejpam-6525	118	2	the	the	DET
ejpam-6525	118	3	system	system	NOUN
ejpam-6525	118	4	satisfies	satisfy	VERB
ejpam-6525	118	5	:	:	PUNCT
ejpam-6525	118	6	hm	hm	INTJ
ejpam-6525	118	7	(	(	PUNCT
ejpam-6525	118	8	t	t	PROPN
ejpam-6525	118	9	(	(	PUNCT
ejpam-6525	118	10	u	u	NOUN
ejpam-6525	118	11	)	)	PUNCT
ejpam-6525	118	12	,	,	PUNCT
ejpam-6525	118	13	t	t	PROPN
ejpam-6525	118	14	(	(	PUNCT
ejpam-6525	118	15	v	v	NOUN
ejpam-6525	118	16	)	)	PUNCT
ejpam-6525	118	17	,	,	PUNCT
ejpam-6525	118	18	t	t	PROPN
ejpam-6525	118	19	(	(	PUNCT
ejpam-6525	118	20	w	w	NOUN
ejpam-6525	118	21	)	)	PUNCT
ejpam-6525	118	22	)	)	PUNCT
ejpam-6525	118	23	≤	≤	NUM
ejpam-6525	118	24	1	1	NUM
ejpam-6525	118	25	3	3	NUM
ejpam-6525	118	26	m(u	m(u	PROPN
ejpam-6525	118	27	,	,	PUNCT
ejpam-6525	118	28	v	v	NOUN
ejpam-6525	118	29	,	,	PUNCT
ejpam-6525	118	30	w	w	NOUN
ejpam-6525	118	31	)	)	PUNCT
ejpam-6525	118	32	then	then	ADV
ejpam-6525	118	33	:	:	PUNCT
ejpam-6525	118	34	•	•	X
ejpam-6525	118	35	there	there	PRON
ejpam-6525	118	36	exists	exist	VERB
ejpam-6525	118	37	a	a	DET
ejpam-6525	118	38	fixed	fix	VERB
ejpam-6525	118	39	point	point	NOUN
ejpam-6525	118	40	x∗	x∗	PROPN
ejpam-6525	118	41	with	with	ADP
ejpam-6525	118	42	x∗	x∗	PROPN
ejpam-6525	118	43	∈	∈	PROPN
ejpam-6525	118	44	t	t	PROPN
ejpam-6525	118	45	(	(	PUNCT
ejpam-6525	118	46	x∗	x∗	PROPN
ejpam-6525	118	47	)	)	PUNCT
ejpam-6525	118	48	•	•	ADP
ejpam-6525	118	49	the	the	DET
ejpam-6525	118	50	protocol	protocol	NOUN
ejpam-6525	118	51	converges	converge	VERB
ejpam-6525	118	52	to	to	PART
ejpam-6525	118	53	consensus	consensus	VERB
ejpam-6525	118	54	almost	almost	ADV
ejpam-6525	118	55	surely	surely	ADV
ejpam-6525	118	56	•	•	ADJ
ejpam-6525	118	57	convergence	convergence	NOUN
ejpam-6525	118	58	time	time	NOUN
ejpam-6525	118	59	is	be	AUX
ejpam-6525	118	60	o(log	o(log	PROPN
ejpam-6525	118	61	1	1	NUM
ejpam-6525	118	62	ϵ	ϵ	NOUN
ejpam-6525	118	63	)	)	PUNCT
ejpam-6525	118	64	for	for	ADP
ejpam-6525	118	65	ϵ-precision	ϵ-precision	NOUN
ejpam-6525	118	66	proof	proof	NOUN
ejpam-6525	118	67	.	.	PUNCT
ejpam-6525	119	1	the	the	DET
ejpam-6525	119	2	key	key	ADJ
ejpam-6525	119	3	steps	step	NOUN
ejpam-6525	119	4	are	be	AUX
ejpam-6525	119	5	:	:	PUNCT
ejpam-6525	119	6	(	(	PUNCT
ejpam-6525	119	7	i	i	NOUN
ejpam-6525	119	8	)	)	PUNCT
ejpam-6525	119	9	show	show	VERB
ejpam-6525	119	10	t	t	PROPN
ejpam-6525	119	11	is	be	AUX
ejpam-6525	119	12	contraction	contraction	NOUN
ejpam-6525	119	13	in	in	ADP
ejpam-6525	119	14	hausdorff	hausdorff	PROPN
ejpam-6525	119	15	-	-	PUNCT
ejpam-6525	119	16	mr	mr	PROPN
ejpam-6525	119	17	metric	metric	NOUN
ejpam-6525	119	18	:	:	PUNCT
ejpam-6525	119	19	hm	hm	INTJ
ejpam-6525	119	20	(	(	PUNCT
ejpam-6525	119	21	t	t	PROPN
ejpam-6525	119	22	(	(	PUNCT
ejpam-6525	119	23	x	x	NOUN
ejpam-6525	119	24	)	)	PUNCT
ejpam-6525	119	25	,	,	PUNCT
ejpam-6525	119	26	t	t	PROPN
ejpam-6525	119	27	(	(	PUNCT
ejpam-6525	119	28	y	y	PROPN
ejpam-6525	119	29	)	)	PUNCT
ejpam-6525	119	30	,	,	PUNCT
ejpam-6525	119	31	t	t	PROPN
ejpam-6525	119	32	(	(	PUNCT
ejpam-6525	119	33	z	z	NOUN
ejpam-6525	119	34	)	)	PUNCT
ejpam-6525	119	35	)	)	PUNCT
ejpam-6525	119	36	≤	≤	PUNCT
ejpam-6525	120	1	k	k	X
ejpam-6525	120	2	·	·	PUNCT
ejpam-6525	120	3	m(x	m(x	PROPN
ejpam-6525	120	4	,	,	PUNCT
ejpam-6525	120	5	y	y	PROPN
ejpam-6525	120	6	,	,	PUNCT
ejpam-6525	120	7	z	z	NOUN
ejpam-6525	120	8	)	)	PUNCT
ejpam-6525	120	9	with	with	ADP
ejpam-6525	120	10	k	k	PROPN
ejpam-6525	120	11	=	=	SYM
ejpam-6525	120	12	1	1	NUM
ejpam-6525	120	13	3	3	NUM
ejpam-6525	120	14	<	<	SYM
ejpam-6525	120	15	1	1	NUM
ejpam-6525	120	16	r=2	r=2	PROPN
ejpam-6525	120	17	.	.	PUNCT
ejpam-6525	120	18	a.	a.	PROPN
ejpam-6525	120	19	malkawi	malkawi	PROPN
ejpam-6525	120	20	,	,	PUNCT
ejpam-6525	120	21	a.	a.	PROPN
ejpam-6525	120	22	m.	m.	NOUN
ejpam-6525	120	23	rabaiah	rabaiah	PROPN
ejpam-6525	120	24	/	/	SYM
ejpam-6525	120	25	eur	eur	PROPN
ejpam-6525	120	26	.	.	PUNCT
ejpam-6525	121	1	j.	j.	PROPN
ejpam-6525	121	2	pure	pure	PROPN
ejpam-6525	121	3	appl	appl	PROPN
ejpam-6525	121	4	.	.	PROPN
ejpam-6525	121	5	math	math	PROPN
ejpam-6525	121	6	,	,	PUNCT
ejpam-6525	121	7	18	18	NUM
ejpam-6525	121	8	(	(	PUNCT
ejpam-6525	121	9	3	3	NUM
ejpam-6525	121	10	)	)	PUNCT
ejpam-6525	121	11	(	(	PUNCT
ejpam-6525	121	12	2025	2025	NUM
ejpam-6525	121	13	)	)	PUNCT
ejpam-6525	121	14	,	,	PUNCT
ejpam-6525	121	15	6525	6525	NUM
ejpam-6525	121	16	9	9	NUM
ejpam-6525	121	17	of	of	ADP
ejpam-6525	121	18	14	14	NUM
ejpam-6525	121	19	(	(	PUNCT
ejpam-6525	121	20	ii	ii	NOUN
ejpam-6525	121	21	)	)	PUNCT
ejpam-6525	121	22	prove	prove	VERB
ejpam-6525	121	23	the	the	DET
ejpam-6525	121	24	space	space	NOUN
ejpam-6525	121	25	(	(	PUNCT
ejpam-6525	121	26	2v	2v	PROPN
ejpam-6525	121	27	,	,	PUNCT
ejpam-6525	121	28	hm	hm	INTJ
ejpam-6525	121	29	)	)	PUNCT
ejpam-6525	121	30	is	be	AUX
ejpam-6525	121	31	complete	complete	ADJ
ejpam-6525	121	32	.	.	PUNCT
ejpam-6525	122	1	(	(	PUNCT
ejpam-6525	122	2	iii	iii	NOUN
ejpam-6525	122	3	)	)	PUNCT
ejpam-6525	122	4	apply	apply	VERB
ejpam-6525	122	5	banach	banach	ADV
ejpam-6525	122	6	fixed	fix	VERB
ejpam-6525	122	7	-	-	PUNCT
ejpam-6525	122	8	point	point	NOUN
ejpam-6525	122	9	theorem	theorem	NOUN
ejpam-6525	122	10	for	for	ADP
ejpam-6525	122	11	set	set	NOUN
ejpam-6525	122	12	-	-	PUNCT
ejpam-6525	122	13	valued	value	VERB
ejpam-6525	122	14	maps	map	NOUN
ejpam-6525	122	15	.	.	PUNCT
ejpam-6525	123	1	application	application	NOUN
ejpam-6525	123	2	2	2	NUM
ejpam-6525	123	3	(	(	PUNCT
ejpam-6525	123	4	fault	fault	NOUN
ejpam-6525	123	5	-	-	PUNCT
ejpam-6525	123	6	tolerant	tolerant	ADJ
ejpam-6525	123	7	logic	logic	NOUN
ejpam-6525	123	8	circuits	circuit	NOUN
ejpam-6525	123	9	)	)	PUNCT
ejpam-6525	123	10	.	.	PUNCT
ejpam-6525	124	1	circuit	circuit	NOUN
ejpam-6525	124	2	model	model	NOUN
ejpam-6525	124	3	:	:	PUNCT
ejpam-6525	124	4	•	•	NUM
ejpam-6525	124	5	states	state	NOUN
ejpam-6525	124	6	v	v	NOUN
ejpam-6525	124	7	=	=	SYM
ejpam-6525	124	8	{	{	PUNCT
ejpam-6525	124	9	0	0	NUM
ejpam-6525	124	10	,	,	PUNCT
ejpam-6525	124	11	1}n	1}n	NUM
ejpam-6525	124	12	with	with	ADP
ejpam-6525	124	13	hamming	ham	VERB
ejpam-6525	124	14	mr	mr	PROPN
ejpam-6525	124	15	-	-	ADJ
ejpam-6525	124	16	metric	metric	ADJ
ejpam-6525	124	17	:	:	PUNCT
ejpam-6525	124	18	m(x	m(x	PROPN
ejpam-6525	124	19	,	,	PUNCT
ejpam-6525	124	20	y	y	PROPN
ejpam-6525	124	21	,	,	PUNCT
ejpam-6525	124	22	z	z	NOUN
ejpam-6525	124	23	)	)	PUNCT
ejpam-6525	124	24	=	=	SYM
ejpam-6525	124	25	minimal	minimal	ADJ
ejpam-6525	124	26	flips	flip	VERB
ejpam-6525	124	27	to	to	PART
ejpam-6525	124	28	make	make	VERB
ejpam-6525	124	29	x	x	SYM
ejpam-6525	124	30	=	=	PUNCT
ejpam-6525	124	31	y	y	NOUN
ejpam-6525	124	32	=	=	SYM
ejpam-6525	124	33	z	z	NOUN
ejpam-6525	124	34	•	•	NUM
ejpam-6525	124	35	gates	gate	NOUN
ejpam-6525	124	36	as	as	ADP
ejpam-6525	124	37	set	set	NOUN
ejpam-6525	124	38	-	-	PUNCT
ejpam-6525	124	39	valued	value	VERB
ejpam-6525	124	40	maps	map	NOUN
ejpam-6525	124	41	tg	tg	INTJ
ejpam-6525	124	42	:	:	PUNCT
ejpam-6525	124	43	v	v	X
ejpam-6525	124	44	→	→	SYM
ejpam-6525	124	45	2v	2v	PROPN
ejpam-6525	124	46	algorithm	algorithm	PROPN
ejpam-6525	124	47	2	2	NUM
ejpam-6525	124	48	stable	stable	ADJ
ejpam-6525	124	49	circuit	circuit	NOUN
ejpam-6525	124	50	computation	computation	NOUN
ejpam-6525	124	51	require	require	VERB
ejpam-6525	124	52	:	:	PUNCT
ejpam-6525	124	53	initial	initial	ADJ
ejpam-6525	124	54	state	state	NOUN
ejpam-6525	124	55	x(0	x(0	PROPN
ejpam-6525	124	56	)	)	PUNCT
ejpam-6525	124	57	∈	∈	PROPN
ejpam-6525	124	58	{	{	PUNCT
ejpam-6525	124	59	0	0	NUM
ejpam-6525	124	60	,	,	PUNCT
ejpam-6525	124	61	1}n	1}n	NUM
ejpam-6525	124	62	,	,	PUNCT
ejpam-6525	124	63	gates	gate	NOUN
ejpam-6525	124	64	{	{	PUNCT
ejpam-6525	124	65	tg	tg	NOUN
ejpam-6525	124	66	}	}	PUNCT
ejpam-6525	124	67	ensure	ensure	VERB
ejpam-6525	124	68	:	:	PUNCT
ejpam-6525	124	69	stable	stable	ADJ
ejpam-6525	124	70	output	output	NOUN
ejpam-6525	124	71	x∗	x∗	PROPN
ejpam-6525	124	72	1	1	NUM
ejpam-6525	124	73	:	:	PUNCT
ejpam-6525	124	74	for	for	ADP
ejpam-6525	124	75	k	k	PROPN
ejpam-6525	124	76	=	=	SYM
ejpam-6525	124	77	0	0	PROPN
ejpam-6525	124	78	to	to	PART
ejpam-6525	124	79	tmax	tmax	ADV
ejpam-6525	124	80	do	do	VERB
ejpam-6525	124	81	2	2	NUM
ejpam-6525	124	82	:	:	PUNCT
ejpam-6525	124	83	compute	compute	PROPN
ejpam-6525	124	84	t	t	PROPN
ejpam-6525	124	85	(	(	PUNCT
ejpam-6525	124	86	x(k	x(k	PROPN
ejpam-6525	124	87	)	)	PUNCT
ejpam-6525	124	88	)	)	PUNCT
ejpam-6525	125	1	=	=	PUNCT
ejpam-6525	126	1	⋃	⋃	ADP
ejpam-6525	126	2	g∈gates	g∈gate	NOUN
ejpam-6525	126	3	tg(x(k	tg(x(k	NOUN
ejpam-6525	126	4	)	)	PUNCT
ejpam-6525	126	5	)	)	PUNCT
ejpam-6525	126	6	3	3	NUM
ejpam-6525	126	7	:	:	PUNCT
ejpam-6525	126	8	select	select	ADJ
ejpam-6525	126	9	x(k+1	x(k+1	NOUN
ejpam-6525	126	10	)	)	PUNCT
ejpam-6525	126	11	∈	∈	PROPN
ejpam-6525	126	12	t	t	PROPN
ejpam-6525	126	13	(	(	PUNCT
ejpam-6525	126	14	x(k	x(k	PROPN
ejpam-6525	126	15	)	)	PUNCT
ejpam-6525	126	16	)	)	PUNCT
ejpam-6525	126	17	minimizing	minimize	VERB
ejpam-6525	126	18	m(x(k	m(x(k	NOUN
ejpam-6525	126	19	)	)	PUNCT
ejpam-6525	126	20	,	,	PUNCT
ejpam-6525	126	21	x(k+1	x(k+1	NUM
ejpam-6525	126	22	)	)	PUNCT
ejpam-6525	126	23	,	,	PUNCT
ejpam-6525	126	24	x(k+1	x(k+1	NOUN
ejpam-6525	126	25	)	)	PUNCT
ejpam-6525	126	26	)	)	PUNCT
ejpam-6525	127	1	4	4	NUM
ejpam-6525	127	2	:	:	PUNCT
ejpam-6525	127	3	if	if	SCONJ
ejpam-6525	127	4	hm	hm	INTJ
ejpam-6525	127	5	(	(	PUNCT
ejpam-6525	127	6	t	t	PROPN
ejpam-6525	127	7	(	(	PUNCT
ejpam-6525	127	8	x(k	x(k	PROPN
ejpam-6525	127	9	)	)	PUNCT
ejpam-6525	127	10	)	)	PUNCT
ejpam-6525	127	11	,	,	PUNCT
ejpam-6525	127	12	t	t	PROPN
ejpam-6525	127	13	(	(	PUNCT
ejpam-6525	127	14	x(k	x(k	PROPN
ejpam-6525	127	15	)	)	PUNCT
ejpam-6525	127	16	)	)	PUNCT
ejpam-6525	127	17	,	,	PUNCT
ejpam-6525	127	18	t	t	PROPN
ejpam-6525	127	19	(	(	PUNCT
ejpam-6525	127	20	x(k	x(k	PROPN
ejpam-6525	127	21	)	)	PUNCT
ejpam-6525	127	22	)	)	PUNCT
ejpam-6525	127	23	)	)	PUNCT
ejpam-6525	128	1	<	<	X
ejpam-6525	129	1	ϵ	ϵ	X
ejpam-6525	129	2	then	then	ADV
ejpam-6525	129	3	5	5	NUM
ejpam-6525	129	4	:	:	PUNCT
ejpam-6525	129	5	break	break	NOUN
ejpam-6525	129	6	▷	▷	ADV
ejpam-6525	129	7	reached	reach	VERB
ejpam-6525	129	8	fixed	fix	VERB
ejpam-6525	129	9	point	point	NOUN
ejpam-6525	129	10	6	6	NUM
ejpam-6525	129	11	:	:	PUNCT
ejpam-6525	129	12	end	end	VERB
ejpam-6525	129	13	if	if	SCONJ
ejpam-6525	129	14	7	7	NUM
ejpam-6525	129	15	:	:	PUNCT
ejpam-6525	129	16	end	end	VERB
ejpam-6525	129	17	for	for	ADP
ejpam-6525	129	18	8	8	NUM
ejpam-6525	129	19	:	:	PUNCT
ejpam-6525	129	20	return	return	VERB
ejpam-6525	129	21	x(k	x(k	NOUN
ejpam-6525	129	22	)	)	PUNCT
ejpam-6525	129	23	performance	performance	NOUN
ejpam-6525	129	24	analysis	analysis	NOUN
ejpam-6525	129	25	:	:	PUNCT
ejpam-6525	129	26	circuit	circuit	NOUN
ejpam-6525	129	27	type	type	NOUN
ejpam-6525	129	28	convergence	convergence	NOUN
ejpam-6525	129	29	steps	step	VERB
ejpam-6525	129	30	error	error	NOUN
ejpam-6525	129	31	rate	rate	NOUN
ejpam-6525	129	32	speedup	speedup	NOUN
ejpam-6525	129	33	mr	mr	PROPN
ejpam-6525	129	34	-	-	PUNCT
ejpam-6525	129	35	stable	stable	ADJ
ejpam-6525	129	36	o(log	o(log	PROPN
ejpam-6525	129	37	n	n	CCONJ
ejpam-6525	129	38	)	)	PUNCT
ejpam-6525	129	39	10−9	10−9	NUM
ejpam-6525	129	40	3.2x	3.2x	NUM
ejpam-6525	129	41	traditional	traditional	ADJ
ejpam-6525	129	42	o(n	o(n	NUM
ejpam-6525	129	43	)	)	PUNCT
ejpam-6525	130	1	10−6	10−6	NUM
ejpam-6525	130	2	1.0x	1.0x	NUM
ejpam-6525	130	3	table	table	NOUN
ejpam-6525	130	4	2	2	NUM
ejpam-6525	130	5	:	:	PUNCT
ejpam-6525	130	6	comparison	comparison	NOUN
ejpam-6525	130	7	on	on	ADP
ejpam-6525	130	8	16	16	NUM
ejpam-6525	130	9	-	-	PUNCT
ejpam-6525	130	10	bit	bit	NOUN
ejpam-6525	130	11	alu	alu	NOUN
ejpam-6525	130	12	design	design	NOUN
ejpam-6525	130	13	remark	remark	NOUN
ejpam-6525	130	14	2	2	NUM
ejpam-6525	130	15	.	.	PUNCT
ejpam-6525	131	1	the	the	DET
ejpam-6525	131	2	contraction	contraction	NOUN
ejpam-6525	131	3	condition	condition	NOUN
ejpam-6525	131	4	k	k	X
ejpam-6525	131	5	<	<	X
ejpam-6525	131	6	1	1	NUM
ejpam-6525	131	7	2	2	NUM
ejpam-6525	131	8	ensures	ensure	NOUN
ejpam-6525	131	9	:	:	PUNCT
ejpam-6525	131	10	max	max	PROPN
ejpam-6525	131	11	x	x	PROPN
ejpam-6525	131	12	,	,	PUNCT
ejpam-6525	131	13	y	y	PROPN
ejpam-6525	131	14	|t	|t	PROPN
ejpam-6525	131	15	(	(	PUNCT
ejpam-6525	131	16	x)∆t	x)∆t	X
ejpam-6525	131	17	(	(	PUNCT
ejpam-6525	131	18	y)|	y)|	PROPN
ejpam-6525	131	19	m(x	m(x	PROPN
ejpam-6525	131	20	,	,	PUNCT
ejpam-6525	131	21	y	y	PROPN
ejpam-6525	131	22	,	,	PUNCT
ejpam-6525	131	23	y	y	NOUN
ejpam-6525	131	24	)	)	PUNCT
ejpam-6525	131	25	≤	≤	PUNCT
ejpam-6525	132	1	k	k	X
ejpam-6525	132	2	where	where	SCONJ
ejpam-6525	132	3	∆	∆	PROPN
ejpam-6525	132	4	is	be	AUX
ejpam-6525	132	5	set	set	VERB
ejpam-6525	132	6	symmetric	symmetric	ADJ
ejpam-6525	132	7	difference	difference	NOUN
ejpam-6525	132	8	.	.	PUNCT
ejpam-6525	133	1	example	example	NOUN
ejpam-6525	133	2	4	4	NUM
ejpam-6525	133	3	(	(	PUNCT
ejpam-6525	133	4	blockchain	blockchain	NOUN
ejpam-6525	133	5	finality	finality	NOUN
ejpam-6525	133	6	gadgets	gadget	NOUN
ejpam-6525	133	7	)	)	PUNCT
ejpam-6525	133	8	.	.	PUNCT
ejpam-6525	134	1	consider	consider	VERB
ejpam-6525	134	2	a	a	DET
ejpam-6525	134	3	blockchain	blockchain	PROPN
ejpam-6525	134	4	network	network	NOUN
ejpam-6525	134	5	where	where	SCONJ
ejpam-6525	134	6	:	:	PUNCT
ejpam-6525	134	7	•	•	NUM
ejpam-6525	134	8	nodes	node	NOUN
ejpam-6525	134	9	have	have	VERB
ejpam-6525	134	10	partial	partial	ADJ
ejpam-6525	134	11	views	view	NOUN
ejpam-6525	134	12	of	of	ADP
ejpam-6525	134	13	the	the	DET
ejpam-6525	134	14	dag	dag	PROPN
ejpam-6525	134	15	(	(	PUNCT
ejpam-6525	134	16	block	block	NOUN
ejpam-6525	134	17	tree	tree	NOUN
ejpam-6525	134	18	)	)	PUNCT
ejpam-6525	134	19	•	•	ADP
ejpam-6525	134	20	t	t	PROPN
ejpam-6525	134	21	(	(	PUNCT
ejpam-6525	134	22	v	v	NOUN
ejpam-6525	134	23	)	)	PUNCT
ejpam-6525	134	24	outputs	output	NOUN
ejpam-6525	134	25	possible	possible	ADJ
ejpam-6525	134	26	finalized	finalized	ADJ
ejpam-6525	134	27	blocks	block	NOUN
ejpam-6525	134	28	a.	a.	NOUN
ejpam-6525	134	29	malkawi	malkawi	PROPN
ejpam-6525	134	30	,	,	PUNCT
ejpam-6525	134	31	a.	a.	PROPN
ejpam-6525	134	32	m.	m.	NOUN
ejpam-6525	134	33	rabaiah	rabaiah	PROPN
ejpam-6525	134	34	/	/	SYM
ejpam-6525	134	35	eur	eur	PROPN
ejpam-6525	134	36	.	.	PUNCT
ejpam-6525	135	1	j.	j.	PROPN
ejpam-6525	135	2	pure	pure	PROPN
ejpam-6525	135	3	appl	appl	PROPN
ejpam-6525	135	4	.	.	PROPN
ejpam-6525	135	5	math	math	PROPN
ejpam-6525	135	6	,	,	PUNCT
ejpam-6525	135	7	18	18	NUM
ejpam-6525	135	8	(	(	PUNCT
ejpam-6525	135	9	3	3	NUM
ejpam-6525	135	10	)	)	PUNCT
ejpam-6525	135	11	(	(	PUNCT
ejpam-6525	135	12	2025	2025	NUM
ejpam-6525	135	13	)	)	PUNCT
ejpam-6525	135	14	,	,	PUNCT
ejpam-6525	135	15	6525	6525	NUM
ejpam-6525	135	16	10	10	NUM
ejpam-6525	135	17	of	of	ADP
ejpam-6525	135	18	14	14	NUM
ejpam-6525	135	19	•	•	NUM
ejpam-6525	135	20	m(u	m(u	PROPN
ejpam-6525	135	21	,	,	PUNCT
ejpam-6525	135	22	v	v	NOUN
ejpam-6525	135	23	,	,	PUNCT
ejpam-6525	135	24	w	w	NOUN
ejpam-6525	135	25	)	)	PUNCT
ejpam-6525	135	26	measures	measure	VERB
ejpam-6525	135	27	blocktree	blocktree	ADJ
ejpam-6525	135	28	divergence	divergence	NOUN
ejpam-6525	135	29	theorem	theorem	ADJ
ejpam-6525	135	30	2	2	NUM
ejpam-6525	135	31	guarantees	guarantee	VERB
ejpam-6525	135	32	that	that	SCONJ
ejpam-6525	135	33	if	if	SCONJ
ejpam-6525	135	34	validators	validator	NOUN
ejpam-6525	135	35	satisfy	satisfy	VERB
ejpam-6525	135	36	:	:	PUNCT
ejpam-6525	135	37	hm	hm	INTJ
ejpam-6525	135	38	(	(	PUNCT
ejpam-6525	135	39	t	t	PROPN
ejpam-6525	135	40	(	(	PUNCT
ejpam-6525	135	41	u	u	NOUN
ejpam-6525	135	42	)	)	PUNCT
ejpam-6525	135	43	,	,	PUNCT
ejpam-6525	135	44	t	t	PROPN
ejpam-6525	135	45	(	(	PUNCT
ejpam-6525	135	46	v	v	NOUN
ejpam-6525	135	47	)	)	PUNCT
ejpam-6525	135	48	,	,	PUNCT
ejpam-6525	135	49	t	t	PROPN
ejpam-6525	135	50	(	(	PUNCT
ejpam-6525	135	51	w	w	NOUN
ejpam-6525	135	52	)	)	PUNCT
ejpam-6525	135	53	)	)	PUNCT
ejpam-6525	135	54	≤	≤	NUM
ejpam-6525	135	55	1	1	NUM
ejpam-6525	135	56	4	4	NUM
ejpam-6525	135	57	m(u	m(u	PROPN
ejpam-6525	135	58	,	,	PUNCT
ejpam-6525	135	59	v	v	NOUN
ejpam-6525	135	60	,	,	PUNCT
ejpam-6525	135	61	w	w	NOUN
ejpam-6525	135	62	)	)	PUNCT
ejpam-6525	135	63	the	the	DET
ejpam-6525	135	64	network	network	NOUN
ejpam-6525	135	65	achieves	achieve	VERB
ejpam-6525	135	66	deterministic	deterministic	ADJ
ejpam-6525	135	67	finality	finality	NOUN
ejpam-6525	135	68	.	.	PUNCT
ejpam-6525	136	1	3.3	3.3	NUM
ejpam-6525	136	2	.	.	PUNCT
ejpam-6525	136	3	theorem	theorem	VERB
ejpam-6525	136	4	3	3	NUM
ejpam-6525	136	5	:	:	PUNCT
ejpam-6525	136	6	mr	mr	PROPN
ejpam-6525	136	7	-	-	PUNCT
ejpam-6525	136	8	metrics	metric	NOUN
ejpam-6525	136	9	on	on	ADP
ejpam-6525	136	10	expander	expander	NOUN
ejpam-6525	136	11	graphs	graph	NOUN
ejpam-6525	136	12	example	example	NOUN
ejpam-6525	136	13	5	5	NUM
ejpam-6525	136	14	(	(	PUNCT
ejpam-6525	136	15	random	random	ADJ
ejpam-6525	136	16	walk	walk	NOUN
ejpam-6525	136	17	sampling	sample	VERB
ejpam-6525	136	18	in	in	ADP
ejpam-6525	136	19	expander	expander	NOUN
ejpam-6525	136	20	graphs	graph	NOUN
ejpam-6525	136	21	)	)	PUNCT
ejpam-6525	136	22	.	.	PUNCT
ejpam-6525	137	1	consider	consider	VERB
ejpam-6525	137	2	a	a	DET
ejpam-6525	137	3	d	d	ADJ
ejpam-6525	137	4	-	-	ADJ
ejpam-6525	137	5	regular	regular	ADJ
ejpam-6525	137	6	expander	expander	NOUN
ejpam-6525	137	7	graph	graph	NOUN
ejpam-6525	137	8	g	g	PROPN
ejpam-6525	137	9	=	=	SYM
ejpam-6525	137	10	(	(	PUNCT
ejpam-6525	137	11	v	v	NOUN
ejpam-6525	137	12	,	,	PUNCT
ejpam-6525	137	13	e	e	NOUN
ejpam-6525	137	14	)	)	PUNCT
ejpam-6525	137	15	with	with	ADP
ejpam-6525	137	16	:	:	PUNCT
ejpam-6525	137	17	•	•	NOUN
ejpam-6525	137	18	spectral	spectral	ADJ
ejpam-6525	137	19	gap	gap	NOUN
ejpam-6525	137	20	λ	λ	NOUN
ejpam-6525	137	21	=	=	SYM
ejpam-6525	137	22	1−	1−	NUM
ejpam-6525	137	23	µ2	µ2	NOUN
ejpam-6525	137	24	where	where	SCONJ
ejpam-6525	137	25	µ2	µ2	PROPN
ejpam-6525	137	26	is	be	AUX
ejpam-6525	137	27	the	the	DET
ejpam-6525	137	28	second	second	ADV
ejpam-6525	137	29	largest	large	ADJ
ejpam-6525	137	30	eigenvalue	eigenvalue	NOUN
ejpam-6525	137	31	•	•	NUM
ejpam-6525	137	32	normalized	normalize	VERB
ejpam-6525	137	33	laplacian	laplacian	ADJ
ejpam-6525	137	34	l	l	NOUN
ejpam-6525	138	1	=	=	PUNCT
ejpam-6525	138	2	i	i	PRON
ejpam-6525	138	3	−	−	PROPN
ejpam-6525	138	4	1	1	NUM
ejpam-6525	138	5	da	da	PROPN
ejpam-6525	138	6	•	•	NOUN
ejpam-6525	138	7	expansion	expansion	NOUN
ejpam-6525	138	8	parameter	parameter	NOUN
ejpam-6525	138	9	α	α	NOUN
ejpam-6525	138	10	=	=	NOUN
ejpam-6525	138	11	min|s|≤n/2	min|s|≤n/2	ADJ
ejpam-6525	138	12	|∂s|	|∂s|	PROPN
ejpam-6525	138	13	|s|	|s|	PROPN
ejpam-6525	138	14	≥	≥	PROPN
ejpam-6525	138	15	λ	λ	PROPN
ejpam-6525	138	16	2	2	NUM
ejpam-6525	138	17	the	the	DET
ejpam-6525	138	18	triple	triple	ADJ
ejpam-6525	138	19	coupling	coupling	NOUN
ejpam-6525	138	20	time	time	NOUN
ejpam-6525	138	21	mr	mr	PROPN
ejpam-6525	138	22	-	-	ADJ
ejpam-6525	138	23	metric	metric	NOUN
ejpam-6525	138	24	is	be	AUX
ejpam-6525	138	25	defined	define	VERB
ejpam-6525	138	26	as	as	ADP
ejpam-6525	138	27	:	:	PUNCT
ejpam-6525	138	28	m(u	m(u	PROPN
ejpam-6525	138	29	,	,	PUNCT
ejpam-6525	138	30	v	v	NOUN
ejpam-6525	138	31	,	,	PUNCT
ejpam-6525	138	32	w	w	NOUN
ejpam-6525	138	33	)	)	PUNCT
ejpam-6525	138	34	=	=	SYM
ejpam-6525	138	35	e[τcouple(xt	e[τcouple(xt	PROPN
ejpam-6525	138	36	,	,	PUNCT
ejpam-6525	138	37	yt	yt	PROPN
ejpam-6525	138	38	,	,	PUNCT
ejpam-6525	138	39	zt	zt	PROPN
ejpam-6525	138	40	)	)	PUNCT
ejpam-6525	138	41	]	]	PUNCT
ejpam-6525	138	42	where	where	SCONJ
ejpam-6525	138	43	xt	xt	X
ejpam-6525	138	44	,	,	PUNCT
ejpam-6525	138	45	yt	yt	PROPN
ejpam-6525	138	46	,	,	PUNCT
ejpam-6525	138	47	zt	zt	PROPN
ejpam-6525	138	48	are	be	AUX
ejpam-6525	138	49	coupled	couple	VERB
ejpam-6525	138	50	random	random	ADJ
ejpam-6525	138	51	walks	walk	NOUN
ejpam-6525	138	52	starting	start	VERB
ejpam-6525	138	53	at	at	ADP
ejpam-6525	138	54	u	u	PROPN
ejpam-6525	138	55	,	,	PUNCT
ejpam-6525	138	56	v	v	PROPN
ejpam-6525	138	57	,	,	PUNCT
ejpam-6525	138	58	w.	w.	PROPN
ejpam-6525	138	59	theorem	theorem	VERB
ejpam-6525	138	60	5	5	NUM
ejpam-6525	138	61	(	(	PUNCT
ejpam-6525	138	62	mixing	mix	VERB
ejpam-6525	138	63	time	time	NOUN
ejpam-6525	138	64	bound	bind	VERB
ejpam-6525	138	65	)	)	PUNCT
ejpam-6525	138	66	.	.	PUNCT
ejpam-6525	139	1	for	for	ADP
ejpam-6525	139	2	any	any	DET
ejpam-6525	139	3	ϵ	ϵ	PROPN
ejpam-6525	139	4	>	>	X
ejpam-6525	139	5	0	0	PROPN
ejpam-6525	139	6	,	,	PUNCT
ejpam-6525	139	7	the	the	DET
ejpam-6525	139	8	ϵ-mixing	ϵ-mixing	NOUN
ejpam-6525	139	9	time	time	NOUN
ejpam-6525	139	10	satisfies	satisfie	NOUN
ejpam-6525	139	11	:	:	PUNCT
ejpam-6525	139	12	tmix(ϵ	tmix(ϵ	X
ejpam-6525	139	13	)	)	PUNCT
ejpam-6525	139	14	≤	≤	NOUN
ejpam-6525	139	15	1	1	NUM
ejpam-6525	139	16	λ	λ	NOUN
ejpam-6525	139	17	log	log	NOUN
ejpam-6525	139	18	(	(	PUNCT
ejpam-6525	139	19	n	n	NOUN
ejpam-6525	139	20	ϵ	ϵ	NOUN
ejpam-6525	139	21	)	)	PUNCT
ejpam-6525	139	22	with	with	ADP
ejpam-6525	139	23	explicit	explicit	ADJ
ejpam-6525	139	24	constant	constant	ADJ
ejpam-6525	139	25	:	:	PUNCT
ejpam-6525	139	26	m(u	m(u	PROPN
ejpam-6525	139	27	,	,	PUNCT
ejpam-6525	139	28	v	v	NOUN
ejpam-6525	139	29	,	,	PUNCT
ejpam-6525	139	30	w	w	NOUN
ejpam-6525	139	31	)	)	PUNCT
ejpam-6525	139	32	≤	≤	NOUN
ejpam-6525	139	33	3	3	NUM
ejpam-6525	139	34	λ	λ	NOUN
ejpam-6525	139	35	(	(	PUNCT
ejpam-6525	139	36	1	1	NUM
ejpam-6525	139	37	+	+	NUM
ejpam-6525	139	38	log	log	NOUN
ejpam-6525	139	39	(	(	PUNCT
ejpam-6525	139	40	min(πu	min(πu	PROPN
ejpam-6525	139	41	,	,	PUNCT
ejpam-6525	139	42	πv	πv	INTJ
ejpam-6525	139	43	,	,	PUNCT
ejpam-6525	139	44	πw	πw	NOUN
ejpam-6525	139	45	)	)	PUNCT
ejpam-6525	139	46	−1	−1	NOUN
ejpam-6525	139	47	√	√	NOUN
ejpam-6525	139	48	3	3	NUM
ejpam-6525	139	49	)	)	PUNCT
ejpam-6525	139	50	)	)	PUNCT
ejpam-6525	139	51	where	where	SCONJ
ejpam-6525	139	52	πx	πx	ADP
ejpam-6525	139	53	=	=	PUNCT
ejpam-6525	139	54	dx	dx	PROPN
ejpam-6525	139	55	2|e|	2|e|	NUM
ejpam-6525	139	56	is	be	AUX
ejpam-6525	139	57	the	the	DET
ejpam-6525	139	58	stationary	stationary	ADJ
ejpam-6525	139	59	distribution	distribution	NOUN
ejpam-6525	139	60	.	.	PUNCT
ejpam-6525	140	1	proof	proof	NOUN
ejpam-6525	140	2	.	.	PUNCT
ejpam-6525	141	1	the	the	DET
ejpam-6525	141	2	proof	proof	NOUN
ejpam-6525	141	3	involves	involve	VERB
ejpam-6525	141	4	three	three	NUM
ejpam-6525	141	5	key	key	ADJ
ejpam-6525	141	6	steps	step	NOUN
ejpam-6525	141	7	:	:	PUNCT
ejpam-6525	141	8	(	(	PUNCT
ejpam-6525	141	9	i	i	NOUN
ejpam-6525	141	10	)	)	PUNCT
ejpam-6525	141	11	coupling	couple	VERB
ejpam-6525	141	12	argument	argument	NOUN
ejpam-6525	141	13	:	:	PUNCT
ejpam-6525	141	14	construct	construct	VERB
ejpam-6525	141	15	a	a	DET
ejpam-6525	141	16	joint	joint	ADJ
ejpam-6525	141	17	process	process	NOUN
ejpam-6525	141	18	(	(	PUNCT
ejpam-6525	141	19	xt	xt	PROPN
ejpam-6525	141	20	,	,	PUNCT
ejpam-6525	141	21	yt	yt	PROPN
ejpam-6525	141	22	,	,	PUNCT
ejpam-6525	141	23	zt	zt	PROPN
ejpam-6525	141	24	)	)	PUNCT
ejpam-6525	142	1	where	where	SCONJ
ejpam-6525	142	2	:	:	PUNCT
ejpam-6525	142	3	p[xt+1	p[xt+1	PROPN
ejpam-6525	142	4	̸=	̸=	PROPN
ejpam-6525	142	5	yt+1|ft	yt+1|ft	PROPN
ejpam-6525	142	6	]	]	X
ejpam-6525	142	7	≤	≤	NUM
ejpam-6525	142	8	(	(	PUNCT
ejpam-6525	142	9	1−	1−	NUM
ejpam-6525	142	10	λ	λ	SYM
ejpam-6525	142	11	2	2	NUM
ejpam-6525	142	12	)	)	PUNCT
ejpam-6525	142	13	ixt	ixt	ADJ
ejpam-6525	142	14	̸=yt	̸=yt	PROPN
ejpam-6525	142	15	(	(	PUNCT
ejpam-6525	142	16	ii	ii	NOUN
ejpam-6525	142	17	)	)	PUNCT
ejpam-6525	142	18	spectral	spectral	ADJ
ejpam-6525	142	19	analysis	analysis	NOUN
ejpam-6525	142	20	:	:	PUNCT
ejpam-6525	142	21	using	use	VERB
ejpam-6525	142	22	the	the	DET
ejpam-6525	142	23	expander	expander	NOUN
ejpam-6525	142	24	mixing	mix	VERB
ejpam-6525	142	25	lemma	lemma	PROPN
ejpam-6525	142	26	:	:	PUNCT
ejpam-6525	142	27	|p[xt	|p[xt	PROPN
ejpam-6525	142	28	∈	∈	PROPN
ejpam-6525	142	29	s]−	s]−	NOUN
ejpam-6525	142	30	π(s)|	π(s)|	PROPN
ejpam-6525	142	31	≤	≤	PROPN
ejpam-6525	142	32	e−λt	e−λt	NOUN
ejpam-6525	142	33	a.	a.	NOUN
ejpam-6525	142	34	malkawi	malkawi	PROPN
ejpam-6525	142	35	,	,	PUNCT
ejpam-6525	142	36	a.	a.	PROPN
ejpam-6525	142	37	m.	m.	NOUN
ejpam-6525	142	38	rabaiah	rabaiah	PROPN
ejpam-6525	142	39	/	/	SYM
ejpam-6525	142	40	eur	eur	PROPN
ejpam-6525	142	41	.	.	PUNCT
ejpam-6525	143	1	j.	j.	PROPN
ejpam-6525	143	2	pure	pure	PROPN
ejpam-6525	143	3	appl	appl	PROPN
ejpam-6525	143	4	.	.	PROPN
ejpam-6525	143	5	math	math	PROPN
ejpam-6525	143	6	,	,	PUNCT
ejpam-6525	143	7	18	18	NUM
ejpam-6525	143	8	(	(	PUNCT
ejpam-6525	143	9	3	3	NUM
ejpam-6525	143	10	)	)	PUNCT
ejpam-6525	143	11	(	(	PUNCT
ejpam-6525	143	12	2025	2025	NUM
ejpam-6525	143	13	)	)	PUNCT
ejpam-6525	143	14	,	,	PUNCT
ejpam-6525	143	15	6525	6525	NUM
ejpam-6525	143	16	11	11	NUM
ejpam-6525	143	17	of	of	ADP
ejpam-6525	143	18	14	14	NUM
ejpam-6525	143	19	(	(	PUNCT
ejpam-6525	143	20	iii	iii	NOUN
ejpam-6525	143	21	)	)	PUNCT
ejpam-6525	143	22	triangle	triangle	NOUN
ejpam-6525	143	23	inequality	inequality	NOUN
ejpam-6525	143	24	for	for	ADP
ejpam-6525	143	25	coupling	coupling	NOUN
ejpam-6525	143	26	:	:	PUNCT
ejpam-6525	143	27	combine	combine	VERB
ejpam-6525	143	28	pairwise	pairwise	NOUN
ejpam-6525	143	29	couplings	coupling	NOUN
ejpam-6525	143	30	via	via	ADP
ejpam-6525	143	31	:	:	PUNCT
ejpam-6525	143	32	τcouple(x	τcouple(x	PROPN
ejpam-6525	143	33	,	,	PUNCT
ejpam-6525	143	34	y	y	PROPN
ejpam-6525	143	35	,	,	PUNCT
ejpam-6525	143	36	z	z	NOUN
ejpam-6525	143	37	)	)	PUNCT
ejpam-6525	143	38	≤	≤	NUM
ejpam-6525	143	39	max(τcouple(x	max(τcouple(x	NOUN
ejpam-6525	143	40	,	,	PUNCT
ejpam-6525	143	41	y	y	NOUN
ejpam-6525	143	42	)	)	PUNCT
ejpam-6525	143	43	,	,	PUNCT
ejpam-6525	143	44	τcouple(y	τcouple(y	PROPN
ejpam-6525	143	45	,	,	PUNCT
ejpam-6525	143	46	z	z	NOUN
ejpam-6525	143	47	)	)	PUNCT
ejpam-6525	143	48	)	)	PUNCT
ejpam-6525	144	1	+	+	CCONJ
ejpam-6525	144	2	c(λ	c(λ	NOUN
ejpam-6525	144	3	)	)	PUNCT
ejpam-6525	144	4	application	application	NOUN
ejpam-6525	144	5	3	3	NUM
ejpam-6525	144	6	(	(	PUNCT
ejpam-6525	144	7	distributed	distribute	VERB
ejpam-6525	144	8	storage	storage	NOUN
ejpam-6525	144	9	with	with	ADP
ejpam-6525	144	10	expander	expander	NOUN
ejpam-6525	144	11	codes	code	NOUN
ejpam-6525	144	12	)	)	PUNCT
ejpam-6525	144	13	.	.	PUNCT
ejpam-6525	145	1	system	system	NOUN
ejpam-6525	145	2	model	model	NOUN
ejpam-6525	145	3	:	:	PUNCT
ejpam-6525	145	4	•	•	NUM
ejpam-6525	145	5	data	datum	NOUN
ejpam-6525	145	6	blocks	block	NOUN
ejpam-6525	145	7	encoded	encode	VERB
ejpam-6525	145	8	across	across	ADP
ejpam-6525	145	9	n	n	PRON
ejpam-6525	145	10	nodes	node	NOUN
ejpam-6525	145	11	using	use	VERB
ejpam-6525	145	12	[	[	X
ejpam-6525	145	13	n	n	CCONJ
ejpam-6525	145	14	,	,	PUNCT
ejpam-6525	145	15	k	k	NOUN
ejpam-6525	145	16	,	,	PUNCT
ejpam-6525	145	17	d]-expander	d]-expander	NOUN
ejpam-6525	145	18	code	code	PROPN
ejpam-6525	145	19	•	•	ADP
ejpam-6525	146	1	each	each	DET
ejpam-6525	146	2	node	node	NOUN
ejpam-6525	146	3	has	have	VERB
ejpam-6525	146	4	storage	storage	NOUN
ejpam-6525	146	5	capacity	capacity	NOUN
ejpam-6525	146	6	c	c	NOUN
ejpam-6525	146	7	and	and	CCONJ
ejpam-6525	146	8	degree	degree	NOUN
ejpam-6525	147	1	d	d	NOUN
ejpam-6525	147	2	=	=	PUNCT
ejpam-6525	147	3	o(log	o(log	PROPN
ejpam-6525	147	4	n	n	CCONJ
ejpam-6525	147	5	)	)	PUNCT
ejpam-6525	147	6	•	•	PRON
ejpam-6525	147	7	recovery	recovery	NOUN
ejpam-6525	147	8	requires	require	VERB
ejpam-6525	147	9	accessing	access	VERB
ejpam-6525	147	10	any	any	DET
ejpam-6525	147	11	k	k	PROPN
ejpam-6525	147	12	nodes	node	NOUN
ejpam-6525	147	13	algorithm	algorithm	NOUN
ejpam-6525	147	14	3	3	NUM
ejpam-6525	147	15	optimal	optimal	ADJ
ejpam-6525	147	16	data	datum	NOUN
ejpam-6525	147	17	retrieval	retrieval	NOUN
ejpam-6525	147	18	protocol	protocol	NOUN
ejpam-6525	147	19	require	require	NOUN
ejpam-6525	147	20	:	:	PUNCT
ejpam-6525	147	21	failed	fail	VERB
ejpam-6525	147	22	nodes	node	NOUN
ejpam-6525	147	23	f	f	PROPN
ejpam-6525	147	24	⊂	⊂	PROPN
ejpam-6525	147	25	v	v	PROPN
ejpam-6525	147	26	,	,	PUNCT
ejpam-6525	147	27	request	request	NOUN
ejpam-6525	147	28	size	size	NOUN
ejpam-6525	147	29	r	r	NOUN
ejpam-6525	147	30	ensure	ensure	VERB
ejpam-6525	147	31	:	:	PUNCT
ejpam-6525	147	32	recovered	recover	VERB
ejpam-6525	147	33	data	datum	NOUN
ejpam-6525	147	34	d	d	NOUN
ejpam-6525	147	35	1	1	NUM
ejpam-6525	147	36	:	:	PUNCT
ejpam-6525	147	37	identify	identify	VERB
ejpam-6525	147	38	surviving	survive	VERB
ejpam-6525	147	39	nodes	node	NOUN
ejpam-6525	147	40	s	s	PART
ejpam-6525	148	1	=	=	SYM
ejpam-6525	148	2	v	v	ADJ
ejpam-6525	148	3	\	\	PROPN
ejpam-6525	148	4	f	f	PROPN
ejpam-6525	148	5	2	2	NUM
ejpam-6525	148	6	:	:	PUNCT
ejpam-6525	148	7	construct	construct	VERB
ejpam-6525	148	8	routing	routing	NOUN
ejpam-6525	148	9	graph	graph	NOUN
ejpam-6525	148	10	g′	g′	NOUN
ejpam-6525	148	11	=	=	SYM
ejpam-6525	148	12	g[f	g[f	PROPN
ejpam-6525	148	13	∪	∪	ADP
ejpam-6525	148	14	s	s	PART
ejpam-6525	148	15	]	]	X
ejpam-6525	148	16	3	3	NUM
ejpam-6525	148	17	:	:	PUNCT
ejpam-6525	148	18	while	while	SCONJ
ejpam-6525	148	19	|d|	|d|	PROPN
ejpam-6525	148	20	<	<	X
ejpam-6525	148	21	r	r	X
ejpam-6525	148	22	do	do	VERB
ejpam-6525	148	23	4	4	NUM
ejpam-6525	148	24	:	:	PUNCT
ejpam-6525	148	25	select	select	VERB
ejpam-6525	148	26	triple	triple	ADJ
ejpam-6525	148	27	(	(	PUNCT
ejpam-6525	148	28	u	u	NOUN
ejpam-6525	148	29	,	,	PUNCT
ejpam-6525	148	30	v	v	NOUN
ejpam-6525	148	31	,	,	PUNCT
ejpam-6525	148	32	w	w	NOUN
ejpam-6525	148	33	)	)	PUNCT
ejpam-6525	148	34	∈	∈	PROPN
ejpam-6525	148	35	s3	s3	NOUN
ejpam-6525	148	36	minimizing	minimize	VERB
ejpam-6525	148	37	m(u	m(u	PROPN
ejpam-6525	148	38	,	,	PUNCT
ejpam-6525	148	39	v	v	NOUN
ejpam-6525	148	40	,	,	PUNCT
ejpam-6525	148	41	w	w	NOUN
ejpam-6525	148	42	)	)	PUNCT
ejpam-6525	148	43	5	5	NUM
ejpam-6525	148	44	:	:	PUNCT
ejpam-6525	148	45	initiate	initiate	VERB
ejpam-6525	148	46	random	random	ADJ
ejpam-6525	148	47	walks	walk	NOUN
ejpam-6525	148	48	xt	xt	PROPN
ejpam-6525	148	49	,	,	PUNCT
ejpam-6525	148	50	yt	yt	PROPN
ejpam-6525	148	51	,	,	PUNCT
ejpam-6525	148	52	zt	zt	PROPN
ejpam-6525	148	53	from	from	ADP
ejpam-6525	148	54	u	u	PROPN
ejpam-6525	148	55	,	,	PUNCT
ejpam-6525	148	56	v	v	NOUN
ejpam-6525	148	57	,	,	PUNCT
ejpam-6525	148	58	w	w	PROPN
ejpam-6525	148	59	6	6	NUM
ejpam-6525	148	60	:	:	SYM
ejpam-6525	148	61	couple	couple	NOUN
ejpam-6525	148	62	walks	walk	VERB
ejpam-6525	148	63	at	at	ADP
ejpam-6525	148	64	meeting	meeting	NOUN
ejpam-6525	148	65	pointsm	pointsm	NOUN
ejpam-6525	148	66	=	=	PRON
ejpam-6525	148	67	{	{	PUNCT
ejpam-6525	148	68	(	(	PUNCT
ejpam-6525	148	69	x	x	NOUN
ejpam-6525	148	70	,	,	PUNCT
ejpam-6525	148	71	y	y	PROPN
ejpam-6525	148	72	,	,	PUNCT
ejpam-6525	148	73	z	z	NOUN
ejpam-6525	148	74	)	)	PUNCT
ejpam-6525	148	75	:	:	PUNCT
ejpam-6525	149	1	x	x	X
ejpam-6525	149	2	=	=	PUNCT
ejpam-6525	149	3	y	y	PROPN
ejpam-6525	149	4	=	=	PUNCT
ejpam-6525	149	5	z	z	NOUN
ejpam-6525	149	6	}	}	PUNCT
ejpam-6525	149	7	7	7	NUM
ejpam-6525	149	8	:	:	PUNCT
ejpam-6525	149	9	retrieve	retrieve	VERB
ejpam-6525	149	10	symbols	symbol	NOUN
ejpam-6525	149	11	σ(x	σ(x	PROPN
ejpam-6525	149	12	)	)	PUNCT
ejpam-6525	149	13	for	for	ADP
ejpam-6525	149	14	x	x	SYM
ejpam-6525	149	15	∈m	∈m	NOUN
ejpam-6525	149	16	8	8	NUM
ejpam-6525	149	17	:	:	PUNCT
ejpam-6525	149	18	update	update	NOUN
ejpam-6525	150	1	d	d	X
ejpam-6525	150	2	←	←	PROPN
ejpam-6525	150	3	d	d	X
ejpam-6525	150	4	∪	∪	X
ejpam-6525	150	5	{	{	PUNCT
ejpam-6525	150	6	σ(x	σ(x	PROPN
ejpam-6525	150	7	)	)	PUNCT
ejpam-6525	150	8	:	:	PUNCT
ejpam-6525	150	9	x	x	SYM
ejpam-6525	150	10	∈m	∈m	NOUN
ejpam-6525	150	11	}	}	PUNCT
ejpam-6525	150	12	9	9	NUM
ejpam-6525	150	13	:	:	PUNCT
ejpam-6525	150	14	s	s	X
ejpam-6525	150	15	←	←	PROPN
ejpam-6525	150	16	s	s	PROPN
ejpam-6525	150	17	\	\	PROPN
ejpam-6525	150	18	{	{	PUNCT
ejpam-6525	150	19	u	u	NOUN
ejpam-6525	150	20	,	,	PUNCT
ejpam-6525	150	21	v	v	NOUN
ejpam-6525	150	22	,	,	PUNCT
ejpam-6525	150	23	w	w	NOUN
ejpam-6525	150	24	}	}	PUNCT
ejpam-6525	150	25	10	10	NUM
ejpam-6525	150	26	:	:	PUNCT
ejpam-6525	150	27	end	end	VERB
ejpam-6525	150	28	while	while	SCONJ
ejpam-6525	150	29	performance	performance	NOUN
ejpam-6525	150	30	guarantees	guarantee	NOUN
ejpam-6525	150	31	:	:	PUNCT
ejpam-6525	150	32	metric	metric	ADJ
ejpam-6525	150	33	mr	mr	PROPN
ejpam-6525	150	34	-	-	ADJ
ejpam-6525	150	35	metric	metric	ADJ
ejpam-6525	150	36	bound	bind	VERB
ejpam-6525	150	37	traditional	traditional	ADJ
ejpam-6525	150	38	recovery	recovery	NOUN
ejpam-6525	150	39	time	time	NOUN
ejpam-6525	151	1	o	o	PROPN
ejpam-6525	151	2	(	(	PUNCT
ejpam-6525	151	3	1λ	1λ	NUM
ejpam-6525	151	4	log	log	NOUN
ejpam-6525	151	5	r	r	NOUN
ejpam-6525	151	6	)	)	PUNCT
ejpam-6525	151	7	o(r	o(r	PROPN
ejpam-6525	151	8	)	)	PUNCT
ejpam-6525	151	9	bandwidth	bandwidth	ADJ
ejpam-6525	151	10	o	o	NOUN
ejpam-6525	151	11	(	(	PUNCT
ejpam-6525	151	12	dλ	dλ	NOUN
ejpam-6525	151	13	)	)	PUNCT
ejpam-6525	151	14	o(dr	o(dr	PROPN
ejpam-6525	151	15	)	)	PUNCT
ejpam-6525	151	16	reliability	reliability	NOUN
ejpam-6525	151	17	1−	1−	NUM
ejpam-6525	151	18	e−ω(λr	e−ω(λr	PROPN
ejpam-6525	151	19	)	)	PUNCT
ejpam-6525	151	20	1−o(1	1−o(1	NUM
ejpam-6525	151	21	/	/	SYM
ejpam-6525	151	22	r	r	NOUN
ejpam-6525	151	23	)	)	PUNCT
ejpam-6525	151	24	table	table	NOUN
ejpam-6525	151	25	3	3	NUM
ejpam-6525	151	26	:	:	PUNCT
ejpam-6525	151	27	comparison	comparison	NOUN
ejpam-6525	151	28	for	for	ADP
ejpam-6525	151	29	r	r	NOUN
ejpam-6525	151	30	=	=	SYM
ejpam-6525	151	31	1	1	NUM
ejpam-6525	151	32	tb	tb	NOUN
ejpam-6525	151	33	recovery	recovery	NOUN
ejpam-6525	151	34	on	on	ADP
ejpam-6525	151	35	n	n	NOUN
ejpam-6525	151	36	=	=	SYM
ejpam-6525	151	37	1000	1000	NUM
ejpam-6525	151	38	nodes	node	NOUN
ejpam-6525	151	39	remark	remark	VERB
ejpam-6525	151	40	3	3	NUM
ejpam-6525	151	41	.	.	PUNCT
ejpam-6525	152	1	the	the	DET
ejpam-6525	152	2	mr	mr	PROPN
ejpam-6525	152	3	-	-	PUNCT
ejpam-6525	152	4	metric	metric	ADJ
ejpam-6525	152	5	advantage	advantage	NOUN
ejpam-6525	152	6	comes	come	VERB
ejpam-6525	152	7	from	from	ADP
ejpam-6525	152	8	:	:	PUNCT
ejpam-6525	152	9	e[retrieval	e[retrieval	NUM
ejpam-6525	152	10	time	time	NOUN
ejpam-6525	152	11	]	]	PUNCT
ejpam-6525	152	12	≤	≤	NUM
ejpam-6525	152	13	r∑	r∑	NOUN
ejpam-6525	152	14	i=1	i=1	PROPN
ejpam-6525	152	15	m(ui	m(ui	PROPN
ejpam-6525	152	16	,	,	PUNCT
ejpam-6525	152	17	vi	vi	PROPN
ejpam-6525	152	18	,	,	PUNCT
ejpam-6525	152	19	wi	wi	PROPN
ejpam-6525	152	20	)	)	PUNCT
ejpam-6525	153	1	=	=	SYM
ejpam-6525	153	2	o	o	NOUN
ejpam-6525	153	3	(	(	PUNCT
ejpam-6525	153	4	r	r	NOUN
ejpam-6525	153	5	log	log	NOUN
ejpam-6525	153	6	n	n	PRON
ejpam-6525	153	7	λ	λ	NOUN
ejpam-6525	153	8	)	)	PUNCT
ejpam-6525	153	9	versus	versus	ADP
ejpam-6525	153	10	o(rn	o(rn	NOUN
ejpam-6525	153	11	)	)	PUNCT
ejpam-6525	153	12	for	for	ADP
ejpam-6525	153	13	naive	naive	ADJ
ejpam-6525	153	14	protocols	protocol	NOUN
ejpam-6525	153	15	.	.	PUNCT
ejpam-6525	154	1	example	example	NOUN
ejpam-6525	154	2	6	6	NUM
ejpam-6525	154	3	(	(	PUNCT
ejpam-6525	154	4	decentralized	decentralized	ADJ
ejpam-6525	154	5	machine	machine	NOUN
ejpam-6525	154	6	learning	learning	NOUN
ejpam-6525	154	7	)	)	PUNCT
ejpam-6525	154	8	.	.	PUNCT
ejpam-6525	155	1	in	in	ADP
ejpam-6525	155	2	a	a	DET
ejpam-6525	155	3	federated	federated	ADJ
ejpam-6525	155	4	learning	learning	NOUN
ejpam-6525	155	5	setup	setup	NOUN
ejpam-6525	155	6	:	:	PUNCT
ejpam-6525	155	7	•	•	NUM
ejpam-6525	155	8	workers	worker	NOUN
ejpam-6525	155	9	v	v	AUX
ejpam-6525	155	10	form	form	VERB
ejpam-6525	155	11	a	a	DET
ejpam-6525	155	12	λ	λ	NOUN
ejpam-6525	155	13	-	-	NOUN
ejpam-6525	155	14	expander	expander	NOUN
ejpam-6525	155	15	communication	communication	NOUN
ejpam-6525	155	16	graph	graph	NOUN
ejpam-6525	155	17	a.	a.	NOUN
ejpam-6525	155	18	malkawi	malkawi	PROPN
ejpam-6525	155	19	,	,	PUNCT
ejpam-6525	155	20	a.	a.	PROPN
ejpam-6525	155	21	m.	m.	NOUN
ejpam-6525	155	22	rabaiah	rabaiah	PROPN
ejpam-6525	155	23	/	/	SYM
ejpam-6525	155	24	eur	eur	PROPN
ejpam-6525	155	25	.	.	PUNCT
ejpam-6525	156	1	j.	j.	PROPN
ejpam-6525	156	2	pure	pure	PROPN
ejpam-6525	156	3	appl	appl	PROPN
ejpam-6525	156	4	.	.	PROPN
ejpam-6525	156	5	math	math	PROPN
ejpam-6525	156	6	,	,	PUNCT
ejpam-6525	156	7	18	18	NUM
ejpam-6525	156	8	(	(	PUNCT
ejpam-6525	156	9	3	3	NUM
ejpam-6525	156	10	)	)	PUNCT
ejpam-6525	156	11	(	(	PUNCT
ejpam-6525	156	12	2025	2025	NUM
ejpam-6525	156	13	)	)	PUNCT
ejpam-6525	156	14	,	,	PUNCT
ejpam-6525	156	15	6525	6525	NUM
ejpam-6525	156	16	12	12	NUM
ejpam-6525	156	17	of	of	ADP
ejpam-6525	156	18	14	14	NUM
ejpam-6525	156	19	•	•	NOUN
ejpam-6525	156	20	model	model	NOUN
ejpam-6525	156	21	parameters	parameter	NOUN
ejpam-6525	156	22	θ	θ	PROPN
ejpam-6525	156	23	(	(	PUNCT
ejpam-6525	156	24	t	t	NOUN
ejpam-6525	156	25	)	)	PUNCT
ejpam-6525	156	26	u	u	NOUN
ejpam-6525	156	27	at	at	ADP
ejpam-6525	156	28	each	each	DET
ejpam-6525	156	29	node	node	ADJ
ejpam-6525	156	30	•	•	NOUN
ejpam-6525	156	31	update	update	NOUN
ejpam-6525	156	32	rule	rule	NOUN
ejpam-6525	156	33	:	:	PUNCT
ejpam-6525	156	34	θ(t+1	θ(t+1	NUM
ejpam-6525	156	35	)	)	PUNCT
ejpam-6525	156	36	u	u	NOUN
ejpam-6525	157	1	=	=	NOUN
ejpam-6525	157	2	avg	avg	PROPN
ejpam-6525	157	3	(	(	PUNCT
ejpam-6525	157	4	{	{	PUNCT
ejpam-6525	157	5	θ(t)v	θ(t)v	PROPN
ejpam-6525	157	6	:	:	PUNCT
ejpam-6525	157	7	v	v	X
ejpam-6525	157	8	∈	∈	PROPN
ejpam-6525	157	9	n(u	n(u	PROPN
ejpam-6525	157	10	)	)	PUNCT
ejpam-6525	157	11	}	}	PUNCT
ejpam-6525	157	12	∪	∪	VERB
ejpam-6525	157	13	{	{	PUNCT
ejpam-6525	157	14	θ(t)u	θ(t)u	PROPN
ejpam-6525	157	15	}	}	PUNCT
ejpam-6525	157	16	)	)	PUNCT
ejpam-6525	157	17	the	the	DET
ejpam-6525	157	18	convergence	convergence	NOUN
ejpam-6525	157	19	rate	rate	NOUN
ejpam-6525	157	20	depends	depend	VERB
ejpam-6525	157	21	on	on	ADP
ejpam-6525	157	22	the	the	DET
ejpam-6525	157	23	mr	mr	PROPN
ejpam-6525	157	24	-	-	PUNCT
ejpam-6525	157	25	metric	metric	NOUN
ejpam-6525	157	26	:	:	PUNCT
ejpam-6525	157	27	e	e	X
ejpam-6525	157	28	[	[	PUNCT
ejpam-6525	157	29	∥θ(t)u	∥θ(t)u	ADJ
ejpam-6525	157	30	−	−	PROPN
ejpam-6525	157	31	θ̄(t)∥2	θ̄(t)∥2	NOUN
ejpam-6525	157	32	]	]	PUNCT
ejpam-6525	157	33	≤	≤	NUM
ejpam-6525	157	34	e−λtm(θ	e−λtm(θ	NUM
ejpam-6525	157	35	(	(	PUNCT
ejpam-6525	157	36	0	0	NUM
ejpam-6525	157	37	)	)	PUNCT
ejpam-6525	157	38	1	1	NUM
ejpam-6525	157	39	,	,	PUNCT
ejpam-6525	157	40	θ	θ	PROPN
ejpam-6525	157	41	(	(	PUNCT
ejpam-6525	157	42	0	0	NUM
ejpam-6525	157	43	)	)	PUNCT
ejpam-6525	157	44	2	2	NUM
ejpam-6525	157	45	,	,	PUNCT
ejpam-6525	157	46	θ	θ	PROPN
ejpam-6525	157	47	(	(	PUNCT
ejpam-6525	157	48	0	0	NUM
ejpam-6525	157	49	)	)	PUNCT
ejpam-6525	157	50	3	3	NUM
ejpam-6525	157	51	)	)	PUNCT
ejpam-6525	157	52	where	where	SCONJ
ejpam-6525	157	53	θ̄	θ̄	NOUN
ejpam-6525	157	54	is	be	AUX
ejpam-6525	157	55	the	the	DET
ejpam-6525	157	56	global	global	ADJ
ejpam-6525	157	57	average	average	NOUN
ejpam-6525	157	58	.	.	PUNCT
ejpam-6525	158	1	references	reference	NOUN
ejpam-6525	158	2	[	[	X
ejpam-6525	158	3	1	1	NUM
ejpam-6525	158	4	]	]	PUNCT
ejpam-6525	158	5	a.	a.	NOUN
ejpam-6525	158	6	malkawi	malkawi	PROPN
ejpam-6525	158	7	,	,	PUNCT
ejpam-6525	158	8	a.	a.	PROPN
ejpam-6525	158	9	rabaiah	rabaiah	PROPN
ejpam-6525	158	10	,	,	PUNCT
ejpam-6525	158	11	w.	w.	PROPN
ejpam-6525	158	12	shatanawi	shatanawi	PROPN
ejpam-6525	158	13	,	,	PUNCT
ejpam-6525	158	14	and	and	CCONJ
ejpam-6525	158	15	a.	a.	NOUN
ejpam-6525	158	16	talafhah	talafhah	PROPN
ejpam-6525	158	17	.	.	PUNCT
ejpam-6525	159	1	mr	mr	PROPN
ejpam-6525	159	2	-	-	PUNCT
ejpam-6525	159	3	metric	metric	ADJ
ejpam-6525	159	4	spaces	space	NOUN
ejpam-6525	159	5	and	and	CCONJ
ejpam-6525	159	6	an	an	DET
ejpam-6525	159	7	application	application	NOUN
ejpam-6525	159	8	.	.	PUNCT
ejpam-6525	160	1	preprint	preprint	NOUN
ejpam-6525	160	2	,	,	PUNCT
ejpam-6525	160	3	2021	2021	NUM
ejpam-6525	160	4	.	.	PUNCT
ejpam-6525	161	1	[	[	X
ejpam-6525	161	2	2	2	NUM
ejpam-6525	161	3	]	]	PUNCT
ejpam-6525	161	4	a.	a.	NOUN
ejpam-6525	161	5	malkawi	malkawi	PROPN
ejpam-6525	161	6	,	,	PUNCT
ejpam-6525	161	7	a.	a.	NOUN
ejpam-6525	161	8	talafhah	talafhah	PROPN
ejpam-6525	161	9	,	,	PUNCT
ejpam-6525	161	10	and	and	CCONJ
ejpam-6525	161	11	w.	w.	PROPN
ejpam-6525	161	12	shatanawi	shatanawi	PROPN
ejpam-6525	161	13	.	.	PUNCT
ejpam-6525	162	1	coincidence	coincidence	NOUN
ejpam-6525	162	2	and	and	CCONJ
ejpam-6525	162	3	fixed	fix	VERB
ejpam-6525	162	4	point	point	NOUN
ejpam-6525	162	5	results	result	NOUN
ejpam-6525	162	6	for	for	ADP
ejpam-6525	162	7	(	(	PUNCT
ejpam-6525	162	8	ψ	ψ	NOUN
ejpam-6525	162	9	,	,	PUNCT
ejpam-6525	162	10	l)-m	l)-m	ADJ
ejpam-6525	162	11	-	-	PUNCT
ejpam-6525	162	12	weak	weak	ADJ
ejpam-6525	162	13	contraction	contraction	NOUN
ejpam-6525	162	14	mapping	mapping	NOUN
ejpam-6525	162	15	on	on	ADP
ejpam-6525	162	16	mb	mb	ADJ
ejpam-6525	162	17	-	-	ADJ
ejpam-6525	162	18	metric	metric	ADJ
ejpam-6525	162	19	spaces	space	NOUN
ejpam-6525	162	20	.	.	PUNCT
ejpam-6525	163	1	italian	italian	ADJ
ejpam-6525	163	2	journal	journal	NOUN
ejpam-6525	163	3	of	of	ADP
ejpam-6525	163	4	pure	pure	ADJ
ejpam-6525	163	5	and	and	CCONJ
ejpam-6525	163	6	applied	applied	ADJ
ejpam-6525	163	7	mathematics	mathematic	NOUN
ejpam-6525	163	8	,	,	PUNCT
ejpam-6525	163	9	(	(	PUNCT
ejpam-6525	163	10	47):751–768	47):751–768	NOUN
ejpam-6525	163	11	,	,	PUNCT
ejpam-6525	163	12	2022	2022	NUM
ejpam-6525	163	13	.	.	PUNCT
ejpam-6525	164	1	[	[	X
ejpam-6525	164	2	3	3	NUM
ejpam-6525	164	3	]	]	X
ejpam-6525	164	4	a.	a.	NOUN
ejpam-6525	164	5	malkawi	malkawi	PROPN
ejpam-6525	164	6	,	,	PUNCT
ejpam-6525	164	7	a.	a.	NOUN
ejpam-6525	164	8	tallafha	tallafha	NOUN
ejpam-6525	164	9	,	,	PUNCT
ejpam-6525	164	10	and	and	CCONJ
ejpam-6525	164	11	w.	w.	PROPN
ejpam-6525	164	12	shatanawi	shatanawi	PROPN
ejpam-6525	164	13	.	.	PUNCT
ejpam-6525	165	1	coincidence	coincidence	NOUN
ejpam-6525	165	2	and	and	CCONJ
ejpam-6525	165	3	fixed	fix	VERB
ejpam-6525	165	4	point	point	NOUN
ejpam-6525	165	5	results	result	NOUN
ejpam-6525	165	6	for	for	ADP
ejpam-6525	165	7	generalized	generalized	ADJ
ejpam-6525	165	8	weak	weak	ADJ
ejpam-6525	165	9	contraction	contraction	NOUN
ejpam-6525	165	10	mapping	mapping	NOUN
ejpam-6525	165	11	on	on	ADP
ejpam-6525	165	12	b	b	NOUN
ejpam-6525	165	13	-	-	PUNCT
ejpam-6525	165	14	metric	metric	ADJ
ejpam-6525	165	15	spaces	space	NOUN
ejpam-6525	165	16	.	.	PUNCT
ejpam-6525	166	1	nonlinear	nonlinear	ADJ
ejpam-6525	166	2	functional	functional	ADJ
ejpam-6525	166	3	analysis	analysis	NOUN
ejpam-6525	166	4	and	and	CCONJ
ejpam-6525	166	5	applications	application	NOUN
ejpam-6525	166	6	,	,	PUNCT
ejpam-6525	166	7	26(1):177–195	26(1):177–195	NOUN
ejpam-6525	166	8	,	,	PUNCT
ejpam-6525	166	9	2021	2021	NUM
ejpam-6525	166	10	.	.	PUNCT
ejpam-6525	167	1	[	[	X
ejpam-6525	167	2	4	4	X
ejpam-6525	167	3	]	]	PUNCT
ejpam-6525	167	4	t.	t.	NOUN
ejpam-6525	167	5	qawasmeh	qawasmeh	NOUN
ejpam-6525	167	6	.	.	PUNCT
ejpam-6525	168	1	(	(	PUNCT
ejpam-6525	168	2	h	h	NOUN
ejpam-6525	168	3	,	,	PUNCT
ejpam-6525	168	4	ωb)-interpolative	ωb)-interpolative	ADJ
ejpam-6525	168	5	contractions	contraction	NOUN
ejpam-6525	168	6	in	in	ADP
ejpam-6525	168	7	ωb	ωb	NOUN
ejpam-6525	168	8	-	-	PUNCT
ejpam-6525	168	9	distance	distance	NOUN
ejpam-6525	168	10	mappings	mapping	NOUN
ejpam-6525	168	11	with	with	ADP
ejpam-6525	168	12	applications	application	NOUN
ejpam-6525	168	13	.	.	PUNCT
ejpam-6525	169	1	european	european	ADJ
ejpam-6525	169	2	journal	journal	PROPN
ejpam-6525	169	3	of	of	ADP
ejpam-6525	169	4	pure	pure	ADJ
ejpam-6525	169	5	and	and	CCONJ
ejpam-6525	169	6	applied	applied	ADJ
ejpam-6525	169	7	mathematics	mathematic	NOUN
ejpam-6525	169	8	,	,	PUNCT
ejpam-6525	169	9	16(3):1717	16(3):1717	NUM
ejpam-6525	169	10	–	–	PUNCT
ejpam-6525	169	11	1730	1730	NUM
ejpam-6525	169	12	,	,	PUNCT
ejpam-6525	169	13	2023	2023	NUM
ejpam-6525	169	14	.	.	PUNCT
ejpam-6525	170	1	[	[	X
ejpam-6525	170	2	5	5	NUM
ejpam-6525	170	3	]	]	PUNCT
ejpam-6525	170	4	r.	r.	PROPN
ejpam-6525	170	5	al	al	PROPN
ejpam-6525	170	6	-	-	PUNCT
ejpam-6525	170	7	deiakeh	deiakeh	ADJ
ejpam-6525	170	8	,	,	PUNCT
ejpam-6525	170	9	m.	m.	NOUN
ejpam-6525	170	10	alquran	alquran	PROPN
ejpam-6525	170	11	,	,	PUNCT
ejpam-6525	170	12	m.	m.	PROPN
ejpam-6525	170	13	ali	ali	PROPN
ejpam-6525	170	14	,	,	PUNCT
ejpam-6525	170	15	s.	s.	PROPN
ejpam-6525	170	16	qureshi	qureshi	PROPN
ejpam-6525	170	17	,	,	PUNCT
ejpam-6525	170	18	s.	s.	PROPN
ejpam-6525	170	19	momani	momani	PROPN
ejpam-6525	170	20	,	,	PUNCT
ejpam-6525	170	21	and	and	CCONJ
ejpam-6525	170	22	a.	a.	NOUN
ejpam-6525	170	23	a.	a.	PROPN
ejpam-6525	170	24	r.	r.	PROPN
ejpam-6525	170	25	malkawi	malkawi	PROPN
ejpam-6525	170	26	.	.	PROPN
ejpam-6525	170	27	lie	lie	PROPN
ejpam-6525	170	28	symmetry	symmetry	NOUN
ejpam-6525	170	29	,	,	PUNCT
ejpam-6525	170	30	convergence	convergence	NOUN
ejpam-6525	170	31	analysis	analysis	NOUN
ejpam-6525	170	32	,	,	PUNCT
ejpam-6525	170	33	explicit	explicit	ADJ
ejpam-6525	170	34	solutions	solution	NOUN
ejpam-6525	170	35	,	,	PUNCT
ejpam-6525	170	36	and	and	CCONJ
ejpam-6525	170	37	conservation	conservation	NOUN
ejpam-6525	170	38	laws	law	NOUN
ejpam-6525	170	39	for	for	ADP
ejpam-6525	170	40	the	the	DET
ejpam-6525	170	41	time	time	NOUN
ejpam-6525	170	42	-	-	PUNCT
ejpam-6525	170	43	fractional	fractional	ADJ
ejpam-6525	170	44	modified	modify	VERB
ejpam-6525	170	45	benjamin	benjamin	PROPN
ejpam-6525	170	46	-	-	PUNCT
ejpam-6525	170	47	bona	bona	ADJ
ejpam-6525	170	48	-	-	PUNCT
ejpam-6525	170	49	mahony	mahony	NOUN
ejpam-6525	170	50	equation	equation	NOUN
ejpam-6525	170	51	.	.	PUNCT
ejpam-6525	171	1	journal	journal	PROPN
ejpam-6525	171	2	of	of	ADP
ejpam-6525	171	3	applied	apply	VERB
ejpam-6525	171	4	mathematics	mathematic	NOUN
ejpam-6525	171	5	and	and	CCONJ
ejpam-6525	171	6	computational	computational	ADJ
ejpam-6525	171	7	mechanics	mechanic	NOUN
ejpam-6525	171	8	,	,	PUNCT
ejpam-6525	171	9	23(1):19–31	23(1):19–31	NUM
ejpam-6525	171	10	,	,	PUNCT
ejpam-6525	171	11	2024	2024	NUM
ejpam-6525	171	12	.	.	PUNCT
ejpam-6525	172	1	[	[	X
ejpam-6525	172	2	6	6	NUM
ejpam-6525	172	3	]	]	PUNCT
ejpam-6525	172	4	a.	a.	NOUN
ejpam-6525	172	5	bataihah	bataihah	PROPN
ejpam-6525	172	6	and	and	CCONJ
ejpam-6525	172	7	t.	t.	NOUN
ejpam-6525	172	8	qawasmeh	qawasmeh	NOUN
ejpam-6525	172	9	.	.	PUNCT
ejpam-6525	173	1	a	a	DET
ejpam-6525	173	2	new	new	ADJ
ejpam-6525	173	3	type	type	NOUN
ejpam-6525	173	4	of	of	ADP
ejpam-6525	173	5	distance	distance	NOUN
ejpam-6525	173	6	spaces	space	NOUN
ejpam-6525	173	7	and	and	CCONJ
ejpam-6525	173	8	fixed	fix	VERB
ejpam-6525	173	9	point	point	NOUN
ejpam-6525	173	10	results	result	NOUN
ejpam-6525	173	11	.	.	PUNCT
ejpam-6525	174	1	journal	journal	NOUN
ejpam-6525	174	2	of	of	ADP
ejpam-6525	174	3	mathematical	mathematical	ADJ
ejpam-6525	174	4	analysis	analysis	NOUN
ejpam-6525	174	5	,	,	PUNCT
ejpam-6525	174	6	15(4):81–90	15(4):81–90	NUM
ejpam-6525	174	7	,	,	PUNCT
ejpam-6525	174	8	2024	2024	NUM
ejpam-6525	174	9	.	.	PUNCT
ejpam-6525	175	1	[	[	X
ejpam-6525	175	2	7	7	X
ejpam-6525	175	3	]	]	PUNCT
ejpam-6525	175	4	k.	k.	PROPN
ejpam-6525	175	5	abodayeh	abodayeh	PROPN
ejpam-6525	175	6	,	,	PUNCT
ejpam-6525	175	7	w.	w.	PROPN
ejpam-6525	175	8	shatanawi	shatanawi	PROPN
ejpam-6525	175	9	,	,	PUNCT
ejpam-6525	175	10	a.	a.	NOUN
ejpam-6525	175	11	bataihah	bataihah	PROPN
ejpam-6525	175	12	,	,	PUNCT
ejpam-6525	175	13	and	and	CCONJ
ejpam-6525	175	14	a.	a.	PROPN
ejpam-6525	175	15	h.	h.	PROPN
ejpam-6525	175	16	ansari	ansari	PROPN
ejpam-6525	175	17	.	.	PUNCT
ejpam-6525	176	1	some	some	DET
ejpam-6525	176	2	fixed	fix	VERB
ejpam-6525	176	3	point	point	NOUN
ejpam-6525	176	4	and	and	CCONJ
ejpam-6525	176	5	common	common	ADJ
ejpam-6525	176	6	fixed	fix	VERB
ejpam-6525	176	7	point	point	NOUN
ejpam-6525	176	8	results	result	NOUN
ejpam-6525	176	9	through	through	ADP
ejpam-6525	176	10	ω	ω	NOUN
ejpam-6525	176	11	-	-	PUNCT
ejpam-6525	176	12	distance	distance	NOUN
ejpam-6525	176	13	under	under	ADP
ejpam-6525	176	14	nonlinear	nonlinear	ADJ
ejpam-6525	176	15	contractions	contraction	NOUN
ejpam-6525	176	16	.	.	PUNCT
ejpam-6525	177	1	gazi	gazi	PROPN
ejpam-6525	177	2	university	university	PROPN
ejpam-6525	177	3	journal	journal	PROPN
ejpam-6525	177	4	of	of	ADP
ejpam-6525	177	5	science	science	NOUN
ejpam-6525	177	6	,	,	PUNCT
ejpam-6525	177	7	30(1):293–302	30(1):293–302	NOUN
ejpam-6525	177	8	,	,	PUNCT
ejpam-6525	177	9	2017	2017	NUM
ejpam-6525	177	10	.	.	PUNCT
ejpam-6525	178	1	[	[	X
ejpam-6525	178	2	8	8	NUM
ejpam-6525	178	3	]	]	PUNCT
ejpam-6525	178	4	a.	a.	NOUN
ejpam-6525	178	5	bataihah	bataihah	PROPN
ejpam-6525	178	6	,	,	PUNCT
ejpam-6525	178	7	a.	a.	NOUN
ejpam-6525	178	8	tallafha	tallafha	NOUN
ejpam-6525	178	9	,	,	PUNCT
ejpam-6525	178	10	and	and	CCONJ
ejpam-6525	178	11	w.	w.	PROPN
ejpam-6525	178	12	shatanawi	shatanawi	PROPN
ejpam-6525	178	13	.	.	PUNCT
ejpam-6525	179	1	fixed	fix	VERB
ejpam-6525	179	2	point	point	NOUN
ejpam-6525	179	3	results	result	NOUN
ejpam-6525	179	4	with	with	ADP
ejpam-6525	179	5	ωdistance	ωdistance	NOUN
ejpam-6525	179	6	by	by	ADP
ejpam-6525	179	7	utilizing	utilize	VERB
ejpam-6525	179	8	simulation	simulation	NOUN
ejpam-6525	179	9	functions	function	NOUN
ejpam-6525	179	10	.	.	PUNCT
ejpam-6525	180	1	italian	italian	ADJ
ejpam-6525	180	2	journal	journal	NOUN
ejpam-6525	180	3	of	of	ADP
ejpam-6525	180	4	pure	pure	ADJ
ejpam-6525	180	5	and	and	CCONJ
ejpam-6525	180	6	applied	applied	ADJ
ejpam-6525	180	7	mathematics	mathematic	NOUN
ejpam-6525	180	8	,	,	PUNCT
ejpam-6525	180	9	(	(	PUNCT
ejpam-6525	180	10	43):185–196	43):185–196	NOUN
ejpam-6525	180	11	,	,	PUNCT
ejpam-6525	180	12	2017	2017	NUM
ejpam-6525	180	13	.	.	PUNCT
ejpam-6525	181	1	[	[	X
ejpam-6525	181	2	9	9	NUM
ejpam-6525	181	3	]	]	PUNCT
ejpam-6525	181	4	a.	a.	NOUN
ejpam-6525	181	5	rabaiah	rabaiah	PROPN
ejpam-6525	181	6	,	,	PUNCT
ejpam-6525	181	7	a.	a.	NOUN
ejpam-6525	181	8	tallafha	tallafha	NOUN
ejpam-6525	181	9	,	,	PUNCT
ejpam-6525	181	10	and	and	CCONJ
ejpam-6525	181	11	w.	w.	PROPN
ejpam-6525	181	12	shatanawi	shatanawi	PROPN
ejpam-6525	181	13	.	.	PUNCT
ejpam-6525	182	1	common	common	ADJ
ejpam-6525	182	2	fixed	fix	VERB
ejpam-6525	182	3	point	point	NOUN
ejpam-6525	182	4	results	result	NOUN
ejpam-6525	182	5	for	for	ADP
ejpam-6525	182	6	mappings	mapping	NOUN
ejpam-6525	182	7	under	under	ADP
ejpam-6525	182	8	nonlinear	nonlinear	ADJ
ejpam-6525	182	9	contraction	contraction	NOUN
ejpam-6525	182	10	of	of	ADP
ejpam-6525	182	11	cyclic	cyclic	ADJ
ejpam-6525	182	12	form	form	NOUN
ejpam-6525	182	13	in	in	ADP
ejpam-6525	182	14	b	b	NOUN
ejpam-6525	182	15	-	-	ADJ
ejpam-6525	182	16	metric	metric	ADJ
ejpam-6525	182	17	spaces	space	NOUN
ejpam-6525	182	18	.	.	PUNCT
ejpam-6525	183	1	advances	advance	NOUN
ejpam-6525	183	2	in	in	ADP
ejpam-6525	183	3	mathematics	mathematics	NOUN
ejpam-6525	183	4	scientific	scientific	ADJ
ejpam-6525	183	5	journal	journal	NOUN
ejpam-6525	183	6	,	,	PUNCT
ejpam-6525	183	7	26(2):289–301	26(2):289–301	PROPN
ejpam-6525	183	8	,	,	PUNCT
ejpam-6525	183	9	2021	2021	NUM
ejpam-6525	183	10	.	.	PUNCT
ejpam-6525	184	1	[	[	X
ejpam-6525	184	2	10	10	NUM
ejpam-6525	184	3	]	]	PUNCT
ejpam-6525	184	4	k.	k.	PROPN
ejpam-6525	184	5	abodayeh	abodayeh	PROPN
ejpam-6525	184	6	,	,	PUNCT
ejpam-6525	184	7	a.	a.	PROPN
ejpam-6525	184	8	bataihah	bataihah	PROPN
ejpam-6525	184	9	,	,	PUNCT
ejpam-6525	184	10	and	and	CCONJ
ejpam-6525	184	11	w.	w.	PROPN
ejpam-6525	184	12	shatanawi	shatanawi	PROPN
ejpam-6525	184	13	.	.	PUNCT
ejpam-6525	185	1	generalized	generalize	VERB
ejpam-6525	185	2	ω	ω	NUM
ejpam-6525	185	3	-	-	PUNCT
ejpam-6525	185	4	distance	distance	NOUN
ejpam-6525	185	5	mappings	mapping	NOUN
ejpam-6525	185	6	and	and	CCONJ
ejpam-6525	185	7	some	some	DET
ejpam-6525	185	8	fixed	fix	VERB
ejpam-6525	185	9	point	point	NOUN
ejpam-6525	185	10	theorems	theorem	NOUN
ejpam-6525	185	11	.	.	PUNCT
ejpam-6525	186	1	u.p.b	u.p.b	PROPN
ejpam-6525	186	2	.	.	PUNCT
ejpam-6525	187	1	scientific	scientific	ADJ
ejpam-6525	187	2	bulletin	bulletin	NOUN
ejpam-6525	187	3	,	,	PUNCT
ejpam-6525	187	4	series	series	PROPN
ejpam-6525	187	5	a	a	PROPN
ejpam-6525	187	6	,	,	PUNCT
ejpam-6525	187	7	79:223–232	79:223–232	PROPN
ejpam-6525	187	8	,	,	PUNCT
ejpam-6525	187	9	2017	2017	NUM
ejpam-6525	187	10	.	.	PUNCT
ejpam-6525	188	1	a.	a.	NOUN
ejpam-6525	188	2	malkawi	malkawi	PROPN
ejpam-6525	188	3	,	,	PUNCT
ejpam-6525	188	4	a.	a.	PROPN
ejpam-6525	188	5	m.	m.	NOUN
ejpam-6525	188	6	rabaiah	rabaiah	PROPN
ejpam-6525	188	7	/	/	SYM
ejpam-6525	188	8	eur	eur	PROPN
ejpam-6525	188	9	.	.	PUNCT
ejpam-6525	189	1	j.	j.	PROPN
ejpam-6525	189	2	pure	pure	PROPN
ejpam-6525	189	3	appl	appl	PROPN
ejpam-6525	189	4	.	.	PROPN
ejpam-6525	189	5	math	math	PROPN
ejpam-6525	189	6	,	,	PUNCT
ejpam-6525	189	7	18	18	NUM
ejpam-6525	189	8	(	(	PUNCT
ejpam-6525	189	9	3	3	NUM
ejpam-6525	189	10	)	)	PUNCT
ejpam-6525	189	11	(	(	PUNCT
ejpam-6525	189	12	2025	2025	NUM
ejpam-6525	189	13	)	)	PUNCT
ejpam-6525	189	14	,	,	PUNCT
ejpam-6525	189	15	6525	6525	NUM
ejpam-6525	189	16	13	13	NUM
ejpam-6525	189	17	of	of	ADP
ejpam-6525	189	18	14	14	NUM
ejpam-6525	190	1	[	[	X
ejpam-6525	190	2	11	11	NUM
ejpam-6525	190	3	]	]	PUNCT
ejpam-6525	190	4	t.	t.	NOUN
ejpam-6525	190	5	qawasmeh	qawasmeh	NOUN
ejpam-6525	190	6	,	,	PUNCT
ejpam-6525	190	7	w.	w.	PROPN
ejpam-6525	190	8	shatanawi	shatanawi	PROPN
ejpam-6525	190	9	,	,	PUNCT
ejpam-6525	190	10	and	and	CCONJ
ejpam-6525	190	11	a.	a.	NOUN
ejpam-6525	190	12	bataihah	bataihah	PROPN
ejpam-6525	190	13	.	.	PUNCT
ejpam-6525	191	1	common	common	ADJ
ejpam-6525	191	2	fixed	fix	VERB
ejpam-6525	191	3	point	point	NOUN
ejpam-6525	191	4	results	result	NOUN
ejpam-6525	191	5	for	for	ADP
ejpam-6525	191	6	rational	rational	ADJ
ejpam-6525	191	7	(	(	PUNCT
ejpam-6525	191	8	α	α	NOUN
ejpam-6525	191	9	,	,	PUNCT
ejpam-6525	191	10	β)ϕ-mω	β)ϕ-mω	NOUN
ejpam-6525	191	11	contractions	contraction	NOUN
ejpam-6525	191	12	in	in	ADP
ejpam-6525	191	13	complete	complete	ADJ
ejpam-6525	191	14	quasi	quasi	ADJ
ejpam-6525	191	15	metric	metric	ADJ
ejpam-6525	191	16	spaces	space	NOUN
ejpam-6525	191	17	.	.	PUNCT
ejpam-6525	192	1	mathematics	mathematic	NOUN
ejpam-6525	192	2	,	,	PUNCT
ejpam-6525	192	3	7(5):392	7(5):392	NUM
ejpam-6525	192	4	,	,	PUNCT
ejpam-6525	192	5	2017	2017	NUM
ejpam-6525	192	6	.	.	PUNCT
ejpam-6525	193	1	[	[	X
ejpam-6525	193	2	12	12	NUM
ejpam-6525	193	3	]	]	PUNCT
ejpam-6525	193	4	a.	a.	NOUN
ejpam-6525	193	5	a.	a.	PROPN
ejpam-6525	193	6	r.	r.	PROPN
ejpam-6525	193	7	m.	m.	PROPN
ejpam-6525	193	8	malkawi	malkawi	PROPN
ejpam-6525	193	9	.	.	PROPN
ejpam-6525	194	1	convergence	convergence	NOUN
ejpam-6525	194	2	and	and	CCONJ
ejpam-6525	194	3	fixed	fix	VERB
ejpam-6525	194	4	points	point	NOUN
ejpam-6525	194	5	of	of	ADP
ejpam-6525	194	6	self	self	NOUN
ejpam-6525	194	7	-	-	PUNCT
ejpam-6525	194	8	mappings	mapping	NOUN
ejpam-6525	194	9	in	in	ADP
ejpam-6525	194	10	mrmetric	mrmetric	ADJ
ejpam-6525	194	11	spaces	space	NOUN
ejpam-6525	194	12	:	:	PUNCT
ejpam-6525	194	13	theory	theory	NOUN
ejpam-6525	194	14	and	and	CCONJ
ejpam-6525	194	15	applications	application	NOUN
ejpam-6525	194	16	.	.	PUNCT
ejpam-6525	195	1	european	european	ADJ
ejpam-6525	195	2	journal	journal	PROPN
ejpam-6525	195	3	of	of	ADP
ejpam-6525	195	4	pure	pure	ADJ
ejpam-6525	195	5	and	and	CCONJ
ejpam-6525	195	6	applied	applied	ADJ
ejpam-6525	195	7	mathematics	mathematic	NOUN
ejpam-6525	195	8	,	,	PUNCT
ejpam-6525	195	9	18(2):5952	18(2):5952	NUM
ejpam-6525	195	10	,	,	PUNCT
ejpam-6525	195	11	2025	2025	NUM
ejpam-6525	195	12	.	.	PUNCT
ejpam-6525	196	1	[	[	X
ejpam-6525	196	2	13	13	NUM
ejpam-6525	196	3	]	]	PUNCT
ejpam-6525	196	4	a.	a.	NOUN
ejpam-6525	196	5	a.	a.	PROPN
ejpam-6525	196	6	r.	r.	PROPN
ejpam-6525	196	7	m.	m.	PROPN
ejpam-6525	196	8	malkawi	malkawi	PROPN
ejpam-6525	196	9	.	.	PUNCT
ejpam-6525	197	1	fixed	fix	VERB
ejpam-6525	197	2	point	point	NOUN
ejpam-6525	197	3	theorem	theorem	VERB
ejpam-6525	197	4	in	in	ADP
ejpam-6525	197	5	mr	mr	PROPN
ejpam-6525	197	6	-	-	PUNCT
ejpam-6525	197	7	metric	metric	ADJ
ejpam-6525	197	8	spaces	space	NOUN
ejpam-6525	197	9	via	via	ADP
ejpam-6525	197	10	integral	integral	ADJ
ejpam-6525	197	11	type	type	NOUN
ejpam-6525	197	12	contraction	contraction	NOUN
ejpam-6525	197	13	.	.	PUNCT
ejpam-6525	198	1	wseas	wseas	VERB
ejpam-6525	198	2	transactions	transaction	NOUN
ejpam-6525	198	3	on	on	ADP
ejpam-6525	198	4	mathematics	mathematic	NOUN
ejpam-6525	198	5	,	,	PUNCT
ejpam-6525	198	6	24:295–299	24:295–299	PROPN
ejpam-6525	198	7	,	,	PUNCT
ejpam-6525	198	8	2025	2025	NUM
ejpam-6525	198	9	.	.	PUNCT
ejpam-6525	199	1	[	[	X
ejpam-6525	199	2	14	14	NUM
ejpam-6525	199	3	]	]	PUNCT
ejpam-6525	199	4	a.	a.	NOUN
ejpam-6525	199	5	a.	a.	PROPN
ejpam-6525	199	6	r.	r.	PROPN
ejpam-6525	199	7	m.	m.	PROPN
ejpam-6525	199	8	malkawi	malkawi	PROPN
ejpam-6525	199	9	,	,	PUNCT
ejpam-6525	199	10	d.	d.	PROPN
ejpam-6525	199	11	mahmoud	mahmoud	PROPN
ejpam-6525	199	12	,	,	PUNCT
ejpam-6525	199	13	a.	a.	PROPN
ejpam-6525	199	14	m.	m.	PROPN
ejpam-6525	199	15	rabaiah	rabaiah	PROPN
ejpam-6525	199	16	,	,	PUNCT
ejpam-6525	199	17	r.	r.	PROPN
ejpam-6525	199	18	al	al	PROPN
ejpam-6525	199	19	-	-	PUNCT
ejpam-6525	199	20	deiakeh	deiakeh	PROPN
ejpam-6525	199	21	,	,	PUNCT
ejpam-6525	199	22	and	and	CCONJ
ejpam-6525	199	23	w.	w.	PROPN
ejpam-6525	199	24	shatanawi	shatanawi	PROPN
ejpam-6525	199	25	.	.	PUNCT
ejpam-6525	200	1	on	on	ADP
ejpam-6525	200	2	fixed	fix	VERB
ejpam-6525	200	3	point	point	NOUN
ejpam-6525	200	4	theorems	theorem	NOUN
ejpam-6525	200	5	in	in	ADP
ejpam-6525	200	6	mr	mr	PROPN
ejpam-6525	200	7	-	-	PUNCT
ejpam-6525	200	8	metric	metric	ADJ
ejpam-6525	200	9	spaces	space	NOUN
ejpam-6525	200	10	.	.	PUNCT
ejpam-6525	201	1	nonlinear	nonlinear	ADJ
ejpam-6525	201	2	functional	functional	ADJ
ejpam-6525	201	3	analysis	analysis	NOUN
ejpam-6525	201	4	and	and	CCONJ
ejpam-6525	201	5	applications	application	NOUN
ejpam-6525	201	6	,	,	PUNCT
ejpam-6525	201	7	29(4):1125–1136	29(4):1125–1136	NUM
ejpam-6525	201	8	,	,	PUNCT
ejpam-6525	201	9	2024	2024	NUM
ejpam-6525	201	10	.	.	PUNCT
ejpam-6525	202	1	[	[	X
ejpam-6525	202	2	15	15	NUM
ejpam-6525	202	3	]	]	X
ejpam-6525	202	4	g.	g.	PROPN
ejpam-6525	202	5	gharib	gharib	PROPN
ejpam-6525	202	6	,	,	PUNCT
ejpam-6525	202	7	a.	a.	PROPN
ejpam-6525	202	8	malkawi	malkawi	PROPN
ejpam-6525	202	9	,	,	PUNCT
ejpam-6525	202	10	a.	a.	PROPN
ejpam-6525	202	11	rabaiah	rabaiah	PROPN
ejpam-6525	202	12	,	,	PUNCT
ejpam-6525	202	13	w.	w.	PROPN
ejpam-6525	202	14	shatanawi	shatanawi	PROPN
ejpam-6525	202	15	,	,	PUNCT
ejpam-6525	202	16	and	and	CCONJ
ejpam-6525	202	17	m.	m.	NOUN
ejpam-6525	202	18	alsauodi	alsauodi	PROPN
ejpam-6525	202	19	.	.	PUNCT
ejpam-6525	203	1	a	a	DET
ejpam-6525	203	2	common	common	ADJ
ejpam-6525	203	3	fixed	fix	VERB
ejpam-6525	203	4	point	point	NOUN
ejpam-6525	203	5	theorem	theorem	VERB
ejpam-6525	203	6	in	in	ADP
ejpam-6525	203	7	m*-metric	m*-metric	ADV
ejpam-6525	203	8	space	space	NOUN
ejpam-6525	203	9	and	and	CCONJ
ejpam-6525	203	10	an	an	DET
ejpam-6525	203	11	application	application	NOUN
ejpam-6525	203	12	.	.	PUNCT
ejpam-6525	204	1	nonlinear	nonlinear	ADJ
ejpam-6525	204	2	functional	functional	ADJ
ejpam-6525	204	3	analysis	analysis	NOUN
ejpam-6525	204	4	and	and	CCONJ
ejpam-6525	204	5	applications	application	NOUN
ejpam-6525	204	6	,	,	PUNCT
ejpam-6525	204	7	27(2):289–308	27(2):289–308	NUM
ejpam-6525	204	8	,	,	PUNCT
ejpam-6525	204	9	2022	2022	NUM
ejpam-6525	204	10	.	.	PUNCT
ejpam-6525	205	1	[	[	X
ejpam-6525	205	2	16	16	NUM
ejpam-6525	205	3	]	]	PUNCT
ejpam-6525	205	4	s.	s.	PROPN
ejpam-6525	205	5	al	al	PROPN
ejpam-6525	205	6	-	-	PUNCT
ejpam-6525	205	7	sharif	sharif	PROPN
ejpam-6525	205	8	and	and	CCONJ
ejpam-6525	205	9	a.	a.	NOUN
ejpam-6525	205	10	malkawi	malkawi	PROPN
ejpam-6525	205	11	.	.	PUNCT
ejpam-6525	206	1	modification	modification	NOUN
ejpam-6525	206	2	of	of	ADP
ejpam-6525	206	3	conformable	conformable	ADJ
ejpam-6525	206	4	fractional	fractional	ADJ
ejpam-6525	206	5	derivative	derivative	NOUN
ejpam-6525	206	6	with	with	ADP
ejpam-6525	206	7	classical	classical	ADJ
ejpam-6525	206	8	properties	property	NOUN
ejpam-6525	206	9	.	.	PUNCT
ejpam-6525	207	1	italian	italian	ADJ
ejpam-6525	207	2	journal	journal	NOUN
ejpam-6525	207	3	of	of	ADP
ejpam-6525	207	4	pure	pure	ADJ
ejpam-6525	207	5	and	and	CCONJ
ejpam-6525	207	6	applied	applied	ADJ
ejpam-6525	207	7	mathematics	mathematic	NOUN
ejpam-6525	207	8	,	,	PUNCT
ejpam-6525	207	9	44:30–39	44:30–39	PROPN
ejpam-6525	207	10	,	,	PUNCT
ejpam-6525	207	11	2020	2020	NUM
ejpam-6525	207	12	.	.	PUNCT
ejpam-6525	208	1	[	[	X
ejpam-6525	208	2	17	17	NUM
ejpam-6525	208	3	]	]	X
ejpam-6525	208	4	g.	g.	PROPN
ejpam-6525	208	5	m.	m.	PROPN
ejpam-6525	208	6	gharib	gharib	PROPN
ejpam-6525	208	7	,	,	PUNCT
ejpam-6525	208	8	m.	m.	PROPN
ejpam-6525	208	9	s.	s.	PROPN
ejpam-6525	208	10	alsauodi	alsauodi	PROPN
ejpam-6525	208	11	,	,	PUNCT
ejpam-6525	208	12	a.	a.	NOUN
ejpam-6525	208	13	guiatni	guiatni	PROPN
ejpam-6525	208	14	,	,	PUNCT
ejpam-6525	208	15	m.	m.	NOUN
ejpam-6525	208	16	a.	a.	PROPN
ejpam-6525	208	17	al	al	PROPN
ejpam-6525	208	18	-	-	PUNCT
ejpam-6525	208	19	omari	omari	PROPN
ejpam-6525	208	20	,	,	PUNCT
ejpam-6525	208	21	and	and	CCONJ
ejpam-6525	208	22	a.	a.	PROPN
ejpam-6525	208	23	a.r	a.r	PROPN
ejpam-6525	208	24	.	.	PROPN
ejpam-6525	208	25	m.	m.	PROPN
ejpam-6525	208	26	malkawi	malkawi	PROPN
ejpam-6525	208	27	.	.	PUNCT
ejpam-6525	209	1	using	use	VERB
ejpam-6525	209	2	atomic	atomic	ADJ
ejpam-6525	209	3	solution	solution	NOUN
ejpam-6525	209	4	method	method	NOUN
ejpam-6525	209	5	to	to	PART
ejpam-6525	209	6	solve	solve	VERB
ejpam-6525	209	7	the	the	DET
ejpam-6525	209	8	fractional	fractional	ADJ
ejpam-6525	209	9	equations	equation	NOUN
ejpam-6525	209	10	.	.	PUNCT
ejpam-6525	210	1	springer	springer	NOUN
ejpam-6525	210	2	proceedings	proceeding	NOUN
ejpam-6525	210	3	in	in	ADP
ejpam-6525	210	4	mathematics	mathematic	NOUN
ejpam-6525	210	5	and	and	CCONJ
ejpam-6525	210	6	statistics	statistic	NOUN
ejpam-6525	210	7	,	,	PUNCT
ejpam-6525	210	8	418:123–129	418:123–129	NUM
ejpam-6525	210	9	,	,	PUNCT
ejpam-6525	210	10	2023	2023	NUM
ejpam-6525	210	11	.	.	PUNCT
ejpam-6525	211	1	[	[	X
ejpam-6525	211	2	18	18	NUM
ejpam-6525	211	3	]	]	X
ejpam-6525	211	4	i.	i.	PROPN
ejpam-6525	211	5	abu	abu	PROPN
ejpam-6525	211	6	-	-	PUNCT
ejpam-6525	211	7	irwaq	irwaq	PROPN
ejpam-6525	211	8	,	,	PUNCT
ejpam-6525	211	9	w.	w.	PROPN
ejpam-6525	211	10	shatanawi	shatanawi	PROPN
ejpam-6525	211	11	,	,	PUNCT
ejpam-6525	211	12	a.	a.	NOUN
ejpam-6525	211	13	bataihah	bataihah	PROPN
ejpam-6525	211	14	,	,	PUNCT
ejpam-6525	211	15	and	and	CCONJ
ejpam-6525	211	16	nuseir	nuseir	NOUN
ejpam-6525	211	17	.	.	PUNCT
ejpam-6525	211	18	fixed	fix	VERB
ejpam-6525	211	19	point	point	NOUN
ejpam-6525	211	20	results	result	NOUN
ejpam-6525	211	21	for	for	ADP
ejpam-6525	211	22	nonlinear	nonlinear	ADJ
ejpam-6525	211	23	contractions	contraction	NOUN
ejpam-6525	211	24	with	with	ADP
ejpam-6525	211	25	generalized	generalized	ADJ
ejpam-6525	211	26	ω	ω	NUM
ejpam-6525	211	27	-	-	PUNCT
ejpam-6525	211	28	distance	distance	NOUN
ejpam-6525	211	29	mappings	mapping	NOUN
ejpam-6525	211	30	.	.	PUNCT
ejpam-6525	212	1	u.p.b	u.p.b	ADJ
ejpam-6525	212	2	.	.	PUNCT
ejpam-6525	213	1	scientific	scientific	ADJ
ejpam-6525	213	2	bulletin	bulletin	NOUN
ejpam-6525	213	3	,	,	PUNCT
ejpam-6525	213	4	series	series	NOUN
ejpam-6525	213	5	a	a	NOUN
ejpam-6525	213	6	,	,	PUNCT
ejpam-6525	213	7	81(1):57–64	81(1):57–64	NUM
ejpam-6525	213	8	,	,	PUNCT
ejpam-6525	213	9	2019	2019	NUM
ejpam-6525	213	10	.	.	PUNCT
ejpam-6525	214	1	[	[	X
ejpam-6525	214	2	19	19	NUM
ejpam-6525	214	3	]	]	PUNCT
ejpam-6525	214	4	t.	t.	NOUN
ejpam-6525	214	5	qawasmeh	qawasmeh	NOUN
ejpam-6525	214	6	,	,	PUNCT
ejpam-6525	214	7	a.	a.	NOUN
ejpam-6525	214	8	bataihah	bataihah	PROPN
ejpam-6525	214	9	,	,	PUNCT
ejpam-6525	214	10	a.	a.	NOUN
ejpam-6525	214	11	a.	a.	NOUN
ejpam-6525	214	12	hazaymeh	hazaymeh	PROPN
ejpam-6525	214	13	,	,	PUNCT
ejpam-6525	214	14	r.	r.	PROPN
ejpam-6525	214	15	hatamleh	hatamleh	PROPN
ejpam-6525	214	16	,	,	PUNCT
ejpam-6525	214	17	r.	r.	PROPN
ejpam-6525	214	18	abdelrahim	abdelrahim	PROPN
ejpam-6525	214	19	,	,	PUNCT
ejpam-6525	214	20	and	and	CCONJ
ejpam-6525	214	21	a.	a.	NOUN
ejpam-6525	214	22	a.	a.	PROPN
ejpam-6525	214	23	hassan	hassan	PROPN
ejpam-6525	214	24	.	.	PUNCT
ejpam-6525	215	1	new	new	ADJ
ejpam-6525	215	2	fixed	fix	VERB
ejpam-6525	215	3	point	point	NOUN
ejpam-6525	215	4	results	result	NOUN
ejpam-6525	215	5	for	for	ADP
ejpam-6525	215	6	gamma	gamma	NOUN
ejpam-6525	215	7	interpolative	interpolative	ADJ
ejpam-6525	215	8	contractions	contraction	NOUN
ejpam-6525	215	9	through	through	ADP
ejpam-6525	215	10	gamma	gamma	NOUN
ejpam-6525	215	11	distance	distance	NOUN
ejpam-6525	215	12	mappings	mapping	NOUN
ejpam-6525	215	13	.	.	PUNCT
ejpam-6525	216	1	wseas	wseas	NOUN
ejpam-6525	216	2	transactions	transaction	NOUN
ejpam-6525	216	3	on	on	ADP
ejpam-6525	216	4	mathematics	mathematic	NOUN
ejpam-6525	216	5	,	,	PUNCT
ejpam-6525	216	6	24:424–430	24:424–430	PROPN
ejpam-6525	216	7	,	,	PUNCT
ejpam-6525	216	8	2025	2025	NUM
ejpam-6525	216	9	.	.	PUNCT
ejpam-6525	217	1	[	[	X
ejpam-6525	217	2	20	20	NUM
ejpam-6525	217	3	]	]	PUNCT
ejpam-6525	217	4	a.	a.	NOUN
ejpam-6525	217	5	bataihah	bataihah	PROPN
ejpam-6525	217	6	,	,	PUNCT
ejpam-6525	217	7	t.	t.	NOUN
ejpam-6525	217	8	qawasmeh	qawasmeh	NOUN
ejpam-6525	217	9	,	,	PUNCT
ejpam-6525	217	10	i.	i.	PROPN
ejpam-6525	217	11	batiha	batiha	PROPN
ejpam-6525	217	12	,	,	PUNCT
ejpam-6525	217	13	i.	i.	PROPN
ejpam-6525	217	14	m.	m.	PROPN
ejpam-6525	217	15	batiha	batiha	PROPN
ejpam-6525	217	16	,	,	PUNCT
ejpam-6525	217	17	and	and	CCONJ
ejpam-6525	217	18	t.	t.	PROPN
ejpam-6525	217	19	abdeljawad	abdeljawad	NOUN
ejpam-6525	217	20	.	.	PUNCT
ejpam-6525	218	1	gamma	gamma	NOUN
ejpam-6525	218	2	distance	distance	NOUN
ejpam-6525	218	3	mappings	mapping	NOUN
ejpam-6525	218	4	with	with	ADP
ejpam-6525	218	5	application	application	NOUN
ejpam-6525	218	6	to	to	ADP
ejpam-6525	218	7	fractional	fractional	ADJ
ejpam-6525	218	8	boundary	boundary	ADJ
ejpam-6525	218	9	differential	differential	NOUN
ejpam-6525	218	10	equation	equation	NOUN
ejpam-6525	218	11	.	.	PUNCT
ejpam-6525	219	1	journal	journal	PROPN
ejpam-6525	219	2	of	of	ADP
ejpam-6525	219	3	mathematical	mathematical	ADJ
ejpam-6525	219	4	analysis	analysis	NOUN
ejpam-6525	219	5	,	,	PUNCT
ejpam-6525	219	6	15(5):99–106	15(5):99–106	NUM
ejpam-6525	219	7	,	,	PUNCT
ejpam-6525	219	8	2024	2024	NUM
ejpam-6525	219	9	.	.	PUNCT
ejpam-6525	220	1	[	[	X
ejpam-6525	220	2	21	21	NUM
ejpam-6525	220	3	]	]	PUNCT
ejpam-6525	220	4	a.	a.	PROPN
ejpam-6525	220	5	al	al	PROPN
ejpam-6525	220	6	-	-	PUNCT
ejpam-6525	220	7	zghoul	zghoul	PROPN
ejpam-6525	220	8	,	,	PUNCT
ejpam-6525	220	9	t.	t.	NOUN
ejpam-6525	220	10	qawasmeh	qawasmeh	NOUN
ejpam-6525	220	11	,	,	PUNCT
ejpam-6525	220	12	r.	r.	PROPN
ejpam-6525	220	13	hatamleh	hatamleh	PROPN
ejpam-6525	220	14	,	,	PUNCT
ejpam-6525	220	15	and	and	CCONJ
ejpam-6525	220	16	a.	a.	NOUN
ejpam-6525	220	17	alhazimeh	alhazimeh	NOUN
ejpam-6525	220	18	.	.	PUNCT
ejpam-6525	221	1	a	a	DET
ejpam-6525	221	2	new	new	ADJ
ejpam-6525	221	3	contraction	contraction	NOUN
ejpam-6525	221	4	by	by	ADP
ejpam-6525	221	5	utilizing	utilize	VERB
ejpam-6525	221	6	h	h	NOUN
ejpam-6525	221	7	-	-	PUNCT
ejpam-6525	221	8	simulation	simulation	NOUN
ejpam-6525	221	9	functions	function	NOUN
ejpam-6525	221	10	and	and	CCONJ
ejpam-6525	221	11	ω	ω	VERB
ejpam-6525	221	12	-	-	PUNCT
ejpam-6525	221	13	distance	distance	NOUN
ejpam-6525	221	14	mappings	mapping	NOUN
ejpam-6525	221	15	in	in	ADP
ejpam-6525	221	16	the	the	DET
ejpam-6525	221	17	frame	frame	NOUN
ejpam-6525	221	18	of	of	ADP
ejpam-6525	221	19	complete	complete	ADJ
ejpam-6525	221	20	g	g	NOUN
ejpam-6525	221	21	-	-	PUNCT
ejpam-6525	221	22	metric	metric	ADJ
ejpam-6525	221	23	spaces	space	NOUN
ejpam-6525	221	24	.	.	PUNCT
ejpam-6525	222	1	journal	journal	NOUN
ejpam-6525	222	2	of	of	ADP
ejpam-6525	222	3	applied	apply	VERB
ejpam-6525	222	4	mathematics	mathematics	PROPN
ejpam-6525	222	5	&	&	CCONJ
ejpam-6525	222	6	informatics	informatic	NOUN
ejpam-6525	222	7	,	,	PUNCT
ejpam-6525	222	8	42(4):749–759	42(4):749–759	PROPN
ejpam-6525	222	9	,	,	PUNCT
ejpam-6525	222	10	2024	2024	NUM
ejpam-6525	222	11	.	.	PUNCT
ejpam-6525	223	1	[	[	X
ejpam-6525	223	2	22	22	NUM
ejpam-6525	223	3	]	]	PUNCT
ejpam-6525	223	4	a.	a.	NOUN
ejpam-6525	223	5	a.	a.	PROPN
ejpam-6525	223	6	r.	r.	PROPN
ejpam-6525	223	7	m.	m.	PROPN
ejpam-6525	223	8	malkawi	malkawi	PROPN
ejpam-6525	223	9	.	.	PROPN
ejpam-6525	223	10	existence	existence	NOUN
ejpam-6525	223	11	and	and	CCONJ
ejpam-6525	223	12	uniqueness	uniqueness	NOUN
ejpam-6525	223	13	of	of	ADP
ejpam-6525	223	14	fixed	fix	VERB
ejpam-6525	223	15	points	point	NOUN
ejpam-6525	223	16	in	in	ADP
ejpam-6525	223	17	mr	mr	PROPN
ejpam-6525	223	18	-	-	PUNCT
ejpam-6525	223	19	metric	metric	ADJ
ejpam-6525	223	20	spaces	space	NOUN
ejpam-6525	223	21	and	and	CCONJ
ejpam-6525	223	22	their	their	PRON
ejpam-6525	223	23	applications	application	NOUN
ejpam-6525	223	24	.	.	PUNCT
ejpam-6525	224	1	european	european	ADJ
ejpam-6525	224	2	journal	journal	PROPN
ejpam-6525	224	3	of	of	ADP
ejpam-6525	224	4	pure	pure	ADJ
ejpam-6525	224	5	and	and	CCONJ
ejpam-6525	224	6	applied	applied	ADJ
ejpam-6525	224	7	mathematics	mathematic	NOUN
ejpam-6525	224	8	,	,	PUNCT
ejpam-6525	224	9	18(2):6077	18(2):6077	NUM
ejpam-6525	224	10	,	,	PUNCT
ejpam-6525	224	11	2025	2025	NUM
ejpam-6525	224	12	.	.	PUNCT
ejpam-6525	225	1	[	[	X
ejpam-6525	225	2	23	23	NUM
ejpam-6525	225	3	]	]	PUNCT
ejpam-6525	225	4	t.	t.	NOUN
ejpam-6525	225	5	qawasmeh	qawasmeh	NOUN
ejpam-6525	225	6	.	.	PUNCT
ejpam-6525	226	1	h	h	NOUN
ejpam-6525	226	2	-	-	PUNCT
ejpam-6525	226	3	simulation	simulation	NOUN
ejpam-6525	226	4	functions	function	NOUN
ejpam-6525	226	5	and	and	CCONJ
ejpam-6525	226	6	ωb	ωb	NOUN
ejpam-6525	226	7	-	-	PUNCT
ejpam-6525	226	8	distance	distance	NOUN
ejpam-6525	226	9	mappings	mapping	NOUN
ejpam-6525	226	10	in	in	ADP
ejpam-6525	226	11	the	the	DET
ejpam-6525	226	12	setting	setting	NOUN
ejpam-6525	226	13	of	of	ADP
ejpam-6525	226	14	gb	gb	ADV
ejpam-6525	226	15	-	-	PUNCT
ejpam-6525	226	16	metric	metric	ADJ
ejpam-6525	226	17	spaces	space	NOUN
ejpam-6525	226	18	and	and	CCONJ
ejpam-6525	226	19	application	application	NOUN
ejpam-6525	226	20	.	.	PUNCT
ejpam-6525	227	1	nonlinear	nonlinear	ADJ
ejpam-6525	227	2	functional	functional	ADJ
ejpam-6525	227	3	analysis	analysis	NOUN
ejpam-6525	227	4	and	and	CCONJ
ejpam-6525	227	5	applications	application	NOUN
ejpam-6525	227	6	,	,	PUNCT
ejpam-6525	227	7	28(2):557–570	28(2):557–570	NOUN
ejpam-6525	227	8	,	,	PUNCT
ejpam-6525	227	9	2023	2023	NUM
ejpam-6525	227	10	.	.	PUNCT
ejpam-6525	228	1	[	[	X
ejpam-6525	228	2	24	24	NUM
ejpam-6525	228	3	]	]	X
ejpam-6525	228	4	w.	w.	PROPN
ejpam-6525	228	5	shatanawi	shatanawi	PROPN
ejpam-6525	228	6	,	,	PUNCT
ejpam-6525	228	7	t.	t.	NOUN
ejpam-6525	228	8	qawasmeh	qawasmeh	NOUN
ejpam-6525	228	9	,	,	PUNCT
ejpam-6525	228	10	a.	a.	NOUN
ejpam-6525	228	11	bataihah	bataihah	PROPN
ejpam-6525	228	12	,	,	PUNCT
ejpam-6525	228	13	and	and	CCONJ
ejpam-6525	228	14	a.	a.	NOUN
ejpam-6525	228	15	tallafha	tallafha	NOUN
ejpam-6525	228	16	.	.	PUNCT
ejpam-6525	229	1	new	new	ADJ
ejpam-6525	229	2	contractions	contraction	NOUN
ejpam-6525	229	3	and	and	CCONJ
ejpam-6525	229	4	some	some	DET
ejpam-6525	229	5	fixed	fix	VERB
ejpam-6525	229	6	point	point	NOUN
ejpam-6525	229	7	results	result	NOUN
ejpam-6525	229	8	with	with	ADP
ejpam-6525	229	9	application	application	NOUN
ejpam-6525	229	10	based	base	VERB
ejpam-6525	229	11	on	on	ADP
ejpam-6525	229	12	extended	extended	ADJ
ejpam-6525	229	13	quasi	quasi	ADJ
ejpam-6525	229	14	b	b	NOUN
ejpam-6525	229	15	-	-	ADJ
ejpam-6525	229	16	metric	metric	ADJ
ejpam-6525	229	17	spaces	space	NOUN
ejpam-6525	229	18	.	.	PUNCT
ejpam-6525	230	1	u.p.b	u.p.b	ADJ
ejpam-6525	230	2	.	.	PUNCT
ejpam-6525	231	1	scientific	scientific	ADJ
ejpam-6525	231	2	bulletin	bulletin	NOUN
ejpam-6525	231	3	,	,	PUNCT
ejpam-6525	231	4	series	series	PROPN
ejpam-6525	231	5	a	a	PROPN
ejpam-6525	231	6	,	,	PUNCT
ejpam-6525	231	7	83(2):1223–7027	83(2):1223–7027	NUM
ejpam-6525	231	8	,	,	PUNCT
ejpam-6525	231	9	2021	2021	NUM
ejpam-6525	231	10	.	.	PUNCT
ejpam-6525	232	1	a.	a.	PROPN
ejpam-6525	232	2	malkawi	malkawi	PROPN
ejpam-6525	232	3	,	,	PUNCT
ejpam-6525	232	4	a.	a.	PROPN
ejpam-6525	232	5	m.	m.	NOUN
ejpam-6525	232	6	rabaiah	rabaiah	PROPN
ejpam-6525	232	7	/	/	SYM
ejpam-6525	232	8	eur	eur	PROPN
ejpam-6525	232	9	.	.	PUNCT
ejpam-6525	233	1	j.	j.	PROPN
ejpam-6525	233	2	pure	pure	PROPN
ejpam-6525	233	3	appl	appl	PROPN
ejpam-6525	233	4	.	.	PROPN
ejpam-6525	233	5	math	math	PROPN
ejpam-6525	233	6	,	,	PUNCT
ejpam-6525	233	7	18	18	NUM
ejpam-6525	233	8	(	(	PUNCT
ejpam-6525	233	9	3	3	NUM
ejpam-6525	233	10	)	)	PUNCT
ejpam-6525	233	11	(	(	PUNCT
ejpam-6525	233	12	2025	2025	NUM
ejpam-6525	233	13	)	)	PUNCT
ejpam-6525	233	14	,	,	PUNCT
ejpam-6525	233	15	6525	6525	NUM
ejpam-6525	233	16	14	14	NUM
ejpam-6525	233	17	of	of	ADP
ejpam-6525	233	18	14	14	NUM
ejpam-6525	233	19	[	[	X
ejpam-6525	233	20	25	25	NUM
ejpam-6525	233	21	]	]	PUNCT
ejpam-6525	233	22	a.	a.	NOUN
ejpam-6525	233	23	bataihah	bataihah	PROPN
ejpam-6525	233	24	,	,	PUNCT
ejpam-6525	233	25	w.	w.	PROPN
ejpam-6525	233	26	shatanawi	shatanawi	PROPN
ejpam-6525	233	27	,	,	PUNCT
ejpam-6525	233	28	and	and	CCONJ
ejpam-6525	233	29	a.	a.	NOUN
ejpam-6525	233	30	tallafha	tallafha	NOUN
ejpam-6525	233	31	.	.	PUNCT
ejpam-6525	234	1	fixed	fix	VERB
ejpam-6525	234	2	point	point	NOUN
ejpam-6525	234	3	results	result	NOUN
ejpam-6525	234	4	with	with	ADP
ejpam-6525	234	5	simulation	simulation	NOUN
ejpam-6525	234	6	functions	function	NOUN
ejpam-6525	234	7	.	.	PUNCT
ejpam-6525	235	1	nonlinear	nonlinear	ADJ
ejpam-6525	235	2	functional	functional	ADJ
ejpam-6525	235	3	analysis	analysis	NOUN
ejpam-6525	235	4	and	and	CCONJ
ejpam-6525	235	5	applications	application	NOUN
ejpam-6525	235	6	,	,	PUNCT
ejpam-6525	235	7	25(1):13–23	25(1):13–23	NUM
ejpam-6525	235	8	,	,	PUNCT
ejpam-6525	235	9	2020	2020	NUM
ejpam-6525	235	10	.	.	PUNCT
ejpam-6525	236	1	[	[	X
ejpam-6525	236	2	26	26	NUM
ejpam-6525	236	3	]	]	PUNCT
ejpam-6525	236	4	t.	t.	NOUN
ejpam-6525	236	5	qawasmeh	qawasmeh	NOUN
ejpam-6525	236	6	,	,	PUNCT
ejpam-6525	236	7	w.	w.	PROPN
ejpam-6525	236	8	shatanawi	shatanawi	PROPN
ejpam-6525	236	9	,	,	PUNCT
ejpam-6525	236	10	a.	a.	NOUN
ejpam-6525	236	11	bataihah	bataihah	PROPN
ejpam-6525	236	12	,	,	PUNCT
ejpam-6525	236	13	and	and	CCONJ
ejpam-6525	236	14	a.	a.	NOUN
ejpam-6525	236	15	tallafha	tallafha	NOUN
ejpam-6525	236	16	.	.	PUNCT
ejpam-6525	237	1	fixed	fix	VERB
ejpam-6525	237	2	point	point	NOUN
ejpam-6525	237	3	results	result	NOUN
ejpam-6525	237	4	and	and	CCONJ
ejpam-6525	237	5	(	(	PUNCT
ejpam-6525	237	6	α	α	NOUN
ejpam-6525	237	7	,	,	PUNCT
ejpam-6525	237	8	β)-triangular	β)-triangular	ADJ
ejpam-6525	237	9	admissibility	admissibility	NOUN
ejpam-6525	237	10	in	in	ADP
ejpam-6525	237	11	the	the	DET
ejpam-6525	237	12	frame	frame	NOUN
ejpam-6525	237	13	of	of	ADP
ejpam-6525	237	14	complete	complete	ADJ
ejpam-6525	237	15	extended	extended	ADJ
ejpam-6525	237	16	b	b	NOUN
ejpam-6525	237	17	-	-	PUNCT
ejpam-6525	237	18	metric	metric	ADJ
ejpam-6525	237	19	spaces	space	NOUN
ejpam-6525	237	20	and	and	CCONJ
ejpam-6525	237	21	application	application	NOUN
ejpam-6525	237	22	.	.	PUNCT
ejpam-6525	238	1	u.p.b	u.p.b	PROPN
ejpam-6525	238	2	.	.	PUNCT
ejpam-6525	239	1	scientific	scientific	ADJ
ejpam-6525	239	2	bulletin	bulletin	NOUN
ejpam-6525	239	3	,	,	PUNCT
ejpam-6525	239	4	series	series	PROPN
ejpam-6525	239	5	a	a	PROPN
ejpam-6525	239	6	,	,	PUNCT
ejpam-6525	239	7	83(1):113–124	83(1):113–124	PROPN
ejpam-6525	239	8	,	,	PUNCT
ejpam-6525	239	9	2021	2021	NUM
ejpam-6525	239	10	.	.	PUNCT