id	sid	tid	token	lemma	pos
ejpam-1354	1	1	compiles/6c5476b1e4d640c77c91f819e8739b8f	compiles/6c5476b1e4d640c77c91f819e8739b8f	PROPN
ejpam-1354	1	2	/	/	SYM
ejpam-1354	1	3	output.dvi	output.dvi	NOUN
ejpam-1354	1	4	european	european	ADJ
ejpam-1354	1	5	journal	journal	NOUN
ejpam-1354	1	6	of	of	ADP
ejpam-1354	1	7	pure	pure	ADJ
ejpam-1354	1	8	and	and	CCONJ
ejpam-1354	1	9	applied	apply	VERB
ejpam-1354	1	10	mathematics	mathematic	NOUN
ejpam-1354	1	11	vol	vol	NOUN
ejpam-1354	1	12	.	.	PROPN
ejpam-1354	2	1	6	6	NUM
ejpam-1354	2	2	,	,	PUNCT
ejpam-1354	2	3	no	no	INTJ
ejpam-1354	2	4	.	.	NOUN
ejpam-1354	2	5	2	2	NUM
ejpam-1354	2	6	,	,	PUNCT
ejpam-1354	2	7	2013	2013	NUM
ejpam-1354	2	8	,	,	PUNCT
ejpam-1354	2	9	172	172	NUM
ejpam-1354	2	10	-	-	SYM
ejpam-1354	2	11	188	188	NUM
ejpam-1354	2	12	issn	issn	PROPN
ejpam-1354	2	13	1307	1307	NUM
ejpam-1354	2	14	-	-	SYM
ejpam-1354	2	15	5543	5543	NUM
ejpam-1354	2	16	–	–	PUNCT
ejpam-1354	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1354	2	18	mathematical	mathematical	ADJ
ejpam-1354	2	19	modeling	modeling	NOUN
ejpam-1354	2	20	of	of	ADP
ejpam-1354	2	21	condensing	condense	VERB
ejpam-1354	2	22	on	on	ADP
ejpam-1354	2	23	metric	metric	ADJ
ejpam-1354	2	24	spaces	space	NOUN
ejpam-1354	2	25	mostafa	mostafa	PROPN
ejpam-1354	2	26	zahri	zahri	PROPN
ejpam-1354	2	27	department	department	PROPN
ejpam-1354	2	28	of	of	ADP
ejpam-1354	2	29	mathematics	mathematics	PROPN
ejpam-1354	2	30	,	,	PUNCT
ejpam-1354	2	31	college	college	NOUN
ejpam-1354	2	32	of	of	ADP
ejpam-1354	2	33	sciences	sciences	PROPN
ejpam-1354	2	34	,	,	PUNCT
ejpam-1354	2	35	taibah	taibah	PROPN
ejpam-1354	2	36	university	university	PROPN
ejpam-1354	2	37	,	,	PUNCT
ejpam-1354	2	38	al	al	PROPN
ejpam-1354	2	39	madinah	madinah	PROPN
ejpam-1354	2	40	,	,	PUNCT
ejpam-1354	2	41	saudi	saudi	PROPN
ejpam-1354	2	42	arabia	arabia	PROPN
ejpam-1354	2	43	abstract	abstract	NOUN
ejpam-1354	2	44	.	.	PUNCT
ejpam-1354	3	1	this	this	DET
ejpam-1354	3	2	work	work	NOUN
ejpam-1354	3	3	aims	aim	VERB
ejpam-1354	3	4	to	to	PART
ejpam-1354	3	5	present	present	VERB
ejpam-1354	3	6	an	an	DET
ejpam-1354	3	7	energy	energy	NOUN
ejpam-1354	3	8	based	base	VERB
ejpam-1354	3	9	model	model	NOUN
ejpam-1354	3	10	of	of	ADP
ejpam-1354	3	11	the	the	DET
ejpam-1354	3	12	collective	collective	ADJ
ejpam-1354	3	13	dynamics	dynamic	NOUN
ejpam-1354	3	14	where	where	SCONJ
ejpam-1354	3	15	local	local	ADJ
ejpam-1354	3	16	interactions	interaction	NOUN
ejpam-1354	3	17	between	between	ADP
ejpam-1354	3	18	particles	particle	NOUN
ejpam-1354	3	19	of	of	ADP
ejpam-1354	3	20	a	a	DET
ejpam-1354	3	21	collection	collection	NOUN
ejpam-1354	3	22	causes	cause	VERB
ejpam-1354	3	23	all	all	DET
ejpam-1354	3	24	particles	particle	NOUN
ejpam-1354	3	25	to	to	PART
ejpam-1354	3	26	reorganize	reorganize	VERB
ejpam-1354	3	27	in	in	ADP
ejpam-1354	3	28	new	new	ADJ
ejpam-1354	3	29	positions	position	NOUN
ejpam-1354	3	30	.	.	PUNCT
ejpam-1354	4	1	the	the	DET
ejpam-1354	4	2	self	self	NOUN
ejpam-1354	4	3	-	-	PUNCT
ejpam-1354	4	4	organizing	organize	VERB
ejpam-1354	4	5	phenomenon	phenomenon	NOUN
ejpam-1354	4	6	involved	involve	VERB
ejpam-1354	4	7	by	by	ADP
ejpam-1354	4	8	singular	singular	ADJ
ejpam-1354	4	9	local	local	ADJ
ejpam-1354	4	10	moves	move	NOUN
ejpam-1354	4	11	of	of	ADP
ejpam-1354	4	12	individual	individual	ADJ
ejpam-1354	4	13	particles	particle	NOUN
ejpam-1354	4	14	leads	lead	VERB
ejpam-1354	4	15	to	to	ADP
ejpam-1354	4	16	condensing	condense	VERB
ejpam-1354	4	17	.	.	PUNCT
ejpam-1354	5	1	this	this	DET
ejpam-1354	5	2	model	model	NOUN
ejpam-1354	5	3	is	be	AUX
ejpam-1354	5	4	analyzed	analyze	VERB
ejpam-1354	5	5	on	on	ADP
ejpam-1354	5	6	metric	metric	ADJ
ejpam-1354	5	7	spaces	space	NOUN
ejpam-1354	5	8	,	,	PUNCT
ejpam-1354	5	9	simulated	simulate	VERB
ejpam-1354	5	10	on	on	ADP
ejpam-1354	5	11	a	a	DET
ejpam-1354	5	12	finite	finite	NOUN
ejpam-1354	5	13	and	and	CCONJ
ejpam-1354	5	14	in	in	ADP
ejpam-1354	5	15	a	a	DET
ejpam-1354	5	16	continuous	continuous	ADJ
ejpam-1354	5	17	euclidean	euclidean	ADJ
ejpam-1354	5	18	subsets	subset	NOUN
ejpam-1354	5	19	.	.	PUNCT
ejpam-1354	6	1	2010	2010	NUM
ejpam-1354	6	2	mathematics	mathematic	NOUN
ejpam-1354	6	3	subject	subject	NOUN
ejpam-1354	6	4	classifications	classification	NOUN
ejpam-1354	6	5	:	:	PUNCT
ejpam-1354	6	6	92d25	92d25	NUM
ejpam-1354	6	7	,	,	PUNCT
ejpam-1354	6	8	70g60	70g60	NUM
ejpam-1354	6	9	key	key	ADJ
ejpam-1354	6	10	words	word	NOUN
ejpam-1354	6	11	and	and	CCONJ
ejpam-1354	6	12	phrases	phrase	NOUN
ejpam-1354	6	13	:	:	PUNCT
ejpam-1354	6	14	self	self	NOUN
ejpam-1354	6	15	-	-	PUNCT
ejpam-1354	6	16	organizing	organize	VERB
ejpam-1354	6	17	groups	group	NOUN
ejpam-1354	6	18	,	,	PUNCT
ejpam-1354	6	19	population	population	NOUN
ejpam-1354	6	20	dynamics	dynamic	NOUN
ejpam-1354	6	21	,	,	PUNCT
ejpam-1354	6	22	collective	collective	ADJ
ejpam-1354	6	23	intelligence	intelligence	NOUN
ejpam-1354	6	24	,	,	PUNCT
ejpam-1354	6	25	condensing	condense	VERB
ejpam-1354	6	26	1	1	NUM
ejpam-1354	6	27	.	.	PUNCT
ejpam-1354	7	1	introduction	introduction	NOUN
ejpam-1354	7	2	in	in	ADP
ejpam-1354	7	3	real	real	ADJ
ejpam-1354	7	4	live	live	ADJ
ejpam-1354	7	5	condensing	condense	VERB
ejpam-1354	7	6	of	of	ADP
ejpam-1354	7	7	populations	population	NOUN
ejpam-1354	7	8	shows	show	VERB
ejpam-1354	7	9	a	a	DET
ejpam-1354	7	10	very	very	ADV
ejpam-1354	7	11	interesting	interesting	ADJ
ejpam-1354	7	12	emergence	emergence	NOUN
ejpam-1354	7	13	phenomena	phenomenon	NOUN
ejpam-1354	7	14	.	.	PUNCT
ejpam-1354	8	1	living	live	VERB
ejpam-1354	8	2	in	in	ADP
ejpam-1354	8	3	a	a	DET
ejpam-1354	8	4	population	population	NOUN
ejpam-1354	8	5	obligate	obligate	NOUN
ejpam-1354	8	6	all	all	DET
ejpam-1354	8	7	members	member	NOUN
ejpam-1354	8	8	to	to	PART
ejpam-1354	8	9	adapt	adapt	VERB
ejpam-1354	8	10	their	their	PRON
ejpam-1354	8	11	moves	move	NOUN
ejpam-1354	8	12	to	to	ADP
ejpam-1354	8	13	the	the	DET
ejpam-1354	8	14	collective	collective	ADJ
ejpam-1354	8	15	dynamics	dynamic	NOUN
ejpam-1354	8	16	of	of	ADP
ejpam-1354	8	17	all	all	DET
ejpam-1354	8	18	individuals	individual	NOUN
ejpam-1354	8	19	[	[	X
ejpam-1354	8	20	1	1	NUM
ejpam-1354	8	21	]	]	PUNCT
ejpam-1354	8	22	.	.	PUNCT
ejpam-1354	9	1	this	this	DET
ejpam-1354	9	2	group	group	NOUN
ejpam-1354	9	3	dynamics	dynamic	NOUN
ejpam-1354	9	4	is	be	AUX
ejpam-1354	9	5	one	one	NUM
ejpam-1354	9	6	of	of	ADP
ejpam-1354	9	7	the	the	DET
ejpam-1354	9	8	challenges	challenge	NOUN
ejpam-1354	9	9	to	to	PART
ejpam-1354	9	10	study	study	VERB
ejpam-1354	9	11	emergence	emergence	NOUN
ejpam-1354	9	12	,	,	PUNCT
ejpam-1354	9	13	for	for	ADP
ejpam-1354	9	14	instance	instance	NOUN
ejpam-1354	9	15	flocking	flocking	NOUN
ejpam-1354	9	16	of	of	ADP
ejpam-1354	9	17	flocks	flock	NOUN
ejpam-1354	9	18	and	and	CCONJ
ejpam-1354	9	19	swarming	swarm	VERB
ejpam-1354	9	20	of	of	ADP
ejpam-1354	9	21	fishes	fish	NOUN
ejpam-1354	9	22	[	[	X
ejpam-1354	9	23	3–5	3–5	NUM
ejpam-1354	9	24	,	,	PUNCT
ejpam-1354	9	25	8	8	NUM
ejpam-1354	9	26	,	,	PUNCT
ejpam-1354	9	27	9	9	NUM
ejpam-1354	9	28	]	]	PUNCT
ejpam-1354	9	29	.	.	PUNCT
ejpam-1354	10	1	another	another	DET
ejpam-1354	10	2	interesting	interesting	ADJ
ejpam-1354	10	3	natural	natural	ADJ
ejpam-1354	10	4	and	and	CCONJ
ejpam-1354	10	5	complex	complex	ADJ
ejpam-1354	10	6	example	example	NOUN
ejpam-1354	10	7	is	be	AUX
ejpam-1354	10	8	the	the	DET
ejpam-1354	10	9	collective	collective	ADJ
ejpam-1354	10	10	motion	motion	NOUN
ejpam-1354	10	11	of	of	ADP
ejpam-1354	10	12	ants	ant	NOUN
ejpam-1354	10	13	.	.	PUNCT
ejpam-1354	11	1	they	they	PRON
ejpam-1354	11	2	live	live	VERB
ejpam-1354	11	3	in	in	ADP
ejpam-1354	11	4	large	large	ADJ
ejpam-1354	11	5	populations	population	NOUN
ejpam-1354	11	6	and	and	CCONJ
ejpam-1354	11	7	show	show	VERB
ejpam-1354	11	8	a	a	DET
ejpam-1354	11	9	complicated	complicated	ADJ
ejpam-1354	11	10	and	and	CCONJ
ejpam-1354	11	11	strict	strict	ADJ
ejpam-1354	11	12	division	division	NOUN
ejpam-1354	11	13	of	of	ADP
ejpam-1354	11	14	labor	labor	NOUN
ejpam-1354	11	15	for	for	ADP
ejpam-1354	11	16	the	the	DET
ejpam-1354	11	17	individual	individual	ADJ
ejpam-1354	11	18	ant	ant	NOUN
ejpam-1354	11	19	,	,	PUNCT
ejpam-1354	11	20	which	which	PRON
ejpam-1354	11	21	on	on	ADP
ejpam-1354	11	22	the	the	DET
ejpam-1354	11	23	one	one	NUM
ejpam-1354	11	24	hand	hand	NOUN
ejpam-1354	11	25	is	be	AUX
ejpam-1354	11	26	not	not	PART
ejpam-1354	11	27	determined	determine	VERB
ejpam-1354	11	28	by	by	ADP
ejpam-1354	11	29	the	the	DET
ejpam-1354	11	30	genetic	genetic	ADJ
ejpam-1354	11	31	structure	structure	NOUN
ejpam-1354	11	32	of	of	ADP
ejpam-1354	11	33	the	the	DET
ejpam-1354	11	34	single	single	ADJ
ejpam-1354	11	35	ant	ant	NOUN
ejpam-1354	11	36	and	and	CCONJ
ejpam-1354	11	37	on	on	ADP
ejpam-1354	11	38	the	the	DET
ejpam-1354	11	39	other	other	ADJ
ejpam-1354	11	40	hand	hand	NOUN
ejpam-1354	11	41	makes	make	VERB
ejpam-1354	11	42	the	the	DET
ejpam-1354	11	43	whole	whole	ADJ
ejpam-1354	11	44	population	population	NOUN
ejpam-1354	11	45	react	react	VERB
ejpam-1354	11	46	effectively	effectively	ADV
ejpam-1354	11	47	to	to	ADP
ejpam-1354	11	48	all	all	DET
ejpam-1354	11	49	kinds	kind	NOUN
ejpam-1354	11	50	of	of	ADP
ejpam-1354	11	51	events	event	NOUN
ejpam-1354	11	52	as	as	SCONJ
ejpam-1354	11	53	if	if	SCONJ
ejpam-1354	11	54	steered	steer	VERB
ejpam-1354	11	55	by	by	ADP
ejpam-1354	11	56	some	some	DET
ejpam-1354	11	57	clever	clever	ADJ
ejpam-1354	11	58	and	and	CCONJ
ejpam-1354	11	59	experienced	experienced	ADJ
ejpam-1354	11	60	brain	brain	NOUN
ejpam-1354	11	61	,	,	PUNCT
ejpam-1354	11	62	which	which	PRON
ejpam-1354	11	63	however	however	ADV
ejpam-1354	11	64	does	do	AUX
ejpam-1354	11	65	not	not	PART
ejpam-1354	11	66	exist	exist	VERB
ejpam-1354	11	67	.	.	PUNCT
ejpam-1354	12	1	the	the	DET
ejpam-1354	12	2	division	division	NOUN
ejpam-1354	12	3	of	of	ADP
ejpam-1354	12	4	labor	labor	NOUN
ejpam-1354	12	5	,	,	PUNCT
ejpam-1354	12	6	which	which	PRON
ejpam-1354	12	7	makes	make	VERB
ejpam-1354	12	8	an	an	DET
ejpam-1354	12	9	ant	ant	NOUN
ejpam-1354	12	10	a	a	DET
ejpam-1354	12	11	forager	forager	NOUN
ejpam-1354	12	12	,	,	PUNCT
ejpam-1354	12	13	and	and	CCONJ
ejpam-1354	12	14	another	another	PRON
ejpam-1354	12	15	might	might	AUX
ejpam-1354	12	16	be	be	AUX
ejpam-1354	12	17	a	a	DET
ejpam-1354	12	18	patroller	patroller	NOUN
ejpam-1354	12	19	is	be	AUX
ejpam-1354	12	20	called	call	VERB
ejpam-1354	12	21	emergent	emergent	ADJ
ejpam-1354	12	22	,	,	PUNCT
ejpam-1354	12	23	see	see	VERB
ejpam-1354	12	24	for	for	ADP
ejpam-1354	12	25	instance	instance	NOUN
ejpam-1354	12	26	[	[	X
ejpam-1354	12	27	2	2	NUM
ejpam-1354	12	28	,	,	PUNCT
ejpam-1354	12	29	10	10	NUM
ejpam-1354	12	30	]	]	PUNCT
ejpam-1354	12	31	.	.	PUNCT
ejpam-1354	13	1	it	it	PRON
ejpam-1354	13	2	is	be	AUX
ejpam-1354	13	3	very	very	ADV
ejpam-1354	13	4	strictly	strictly	ADV
ejpam-1354	13	5	and	and	CCONJ
ejpam-1354	13	6	very	very	ADV
ejpam-1354	13	7	stable	stable	ADJ
ejpam-1354	13	8	,	,	PUNCT
ejpam-1354	13	9	but	but	CCONJ
ejpam-1354	13	10	one	one	NOUN
ejpam-1354	13	11	does	do	AUX
ejpam-1354	13	12	not	not	PART
ejpam-1354	13	13	detect	detect	VERB
ejpam-1354	13	14	it	it	PRON
ejpam-1354	13	15	as	as	ADP
ejpam-1354	13	16	a	a	DET
ejpam-1354	13	17	program	program	NOUN
ejpam-1354	13	18	in	in	ADP
ejpam-1354	13	19	the	the	DET
ejpam-1354	13	20	individual	individual	NOUN
ejpam-1354	13	21	.	.	PUNCT
ejpam-1354	14	1	how	how	SCONJ
ejpam-1354	14	2	is	be	AUX
ejpam-1354	14	3	this	this	PRON
ejpam-1354	14	4	to	to	PART
ejpam-1354	14	5	be	be	AUX
ejpam-1354	14	6	understood	understand	VERB
ejpam-1354	14	7	?	?	PUNCT
ejpam-1354	15	1	this	this	PRON
ejpam-1354	15	2	is	be	AUX
ejpam-1354	15	3	the	the	DET
ejpam-1354	15	4	challenge	challenge	NOUN
ejpam-1354	15	5	of	of	ADP
ejpam-1354	15	6	emergence	emergence	NOUN
ejpam-1354	15	7	as	as	SCONJ
ejpam-1354	15	8	i	i	PRON
ejpam-1354	15	9	see	see	VERB
ejpam-1354	15	10	it	it	PRON
ejpam-1354	15	11	and	and	CCONJ
ejpam-1354	15	12	we	we	PRON
ejpam-1354	15	13	will	will	AUX
ejpam-1354	15	14	briefly	briefly	ADV
ejpam-1354	15	15	discuss	discuss	VERB
ejpam-1354	15	16	in	in	ADP
ejpam-1354	15	17	how	how	SCONJ
ejpam-1354	15	18	far	far	ADV
ejpam-1354	15	19	our	our	PRON
ejpam-1354	15	20	model	model	NOUN
ejpam-1354	15	21	models	model	NOUN
ejpam-1354	15	22	emergence	emergence	VERB
ejpam-1354	15	23	.	.	PUNCT
ejpam-1354	16	1	there	there	PRON
ejpam-1354	16	2	is	be	VERB
ejpam-1354	16	3	an	an	DET
ejpam-1354	16	4	emergent	emergent	ADJ
ejpam-1354	16	5	pattern	pattern	NOUN
ejpam-1354	16	6	:	:	PUNCT
ejpam-1354	16	7	segregation	segregation	NOUN
ejpam-1354	16	8	into	into	ADP
ejpam-1354	16	9	isolated	isolated	ADJ
ejpam-1354	16	10	and	and	CCONJ
ejpam-1354	16	11	ε	ε	PROPN
ejpam-1354	16	12	-	-	PUNCT
ejpam-1354	16	13	distanced	distance	VERB
ejpam-1354	16	14	positions	position	NOUN
ejpam-1354	16	15	.	.	PUNCT
ejpam-1354	17	1	however	however	ADV
ejpam-1354	17	2	,	,	PUNCT
ejpam-1354	17	3	the	the	DET
ejpam-1354	17	4	number	number	NOUN
ejpam-1354	17	5	of	of	ADP
ejpam-1354	17	6	positions	position	NOUN
ejpam-1354	17	7	and	and	CCONJ
ejpam-1354	17	8	the	the	DET
ejpam-1354	17	9	distribution	distribution	NOUN
ejpam-1354	17	10	of	of	ADP
ejpam-1354	17	11	individuals	individual	NOUN
ejpam-1354	17	12	onto	onto	ADP
ejpam-1354	17	13	there	there	PRON
ejpam-1354	17	14	positions	position	NOUN
ejpam-1354	17	15	seem	seem	VERB
ejpam-1354	17	16	to	to	PART
ejpam-1354	17	17	be	be	AUX
ejpam-1354	17	18	random	random	ADJ
ejpam-1354	17	19	.	.	PUNCT
ejpam-1354	18	1	an	an	DET
ejpam-1354	18	2	early	early	ADJ
ejpam-1354	18	3	modeling	modeling	NOUN
ejpam-1354	18	4	of	of	ADP
ejpam-1354	18	5	populations	population	NOUN
ejpam-1354	18	6	are	be	AUX
ejpam-1354	18	7	subject	subject	ADJ
ejpam-1354	18	8	for	for	ADP
ejpam-1354	18	9	example	example	NOUN
ejpam-1354	18	10	of	of	ADP
ejpam-1354	18	11	the	the	DET
ejpam-1354	18	12	the	the	DET
ejpam-1354	18	13	price	price	NOUN
ejpam-1354	18	14	equation	equation	NOUN
ejpam-1354	18	15	[	[	X
ejpam-1354	18	16	13	13	NUM
ejpam-1354	18	17	,	,	PUNCT
ejpam-1354	18	18	14	14	NUM
ejpam-1354	18	19	]	]	PUNCT
ejpam-1354	18	20	.	.	PUNCT
ejpam-1354	19	1	this	this	PRON
ejpam-1354	19	2	describes	describe	VERB
ejpam-1354	19	3	characteristics	characteristic	NOUN
ejpam-1354	19	4	of	of	ADP
ejpam-1354	19	5	a	a	DET
ejpam-1354	19	6	population	population	NOUN
ejpam-1354	19	7	model	model	NOUN
ejpam-1354	19	8	that	that	PRON
ejpam-1354	19	9	clumps	clump	VERB
ejpam-1354	19	10	individuals	individual	NOUN
ejpam-1354	19	11	by	by	ADP
ejpam-1354	19	12	shared	shared	ADJ
ejpam-1354	19	13	email	email	NOUN
ejpam-1354	19	14	address	address	NOUN
ejpam-1354	19	15	:	:	PUNCT
ejpam-1354	19	16	mzahri@taibahu.edu.sa	mzahri@taibahu.edu.sa	PROPN
ejpam-1354	19	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1354	20	1	172	172	NUM
ejpam-1354	21	1	c	c	X
ejpam-1354	21	2	©	©	PROPN
ejpam-1354	21	3	2013	2013	NUM
ejpam-1354	21	4	ejpam	ejpam	NOUN
ejpam-1354	21	5	all	all	DET
ejpam-1354	21	6	rights	right	NOUN
ejpam-1354	21	7	reserved	reserve	VERB
ejpam-1354	21	8	.	.	PUNCT
ejpam-1354	22	1	m.	m.	NOUN
ejpam-1354	22	2	zahri	zahri	PROPN
ejpam-1354	22	3	/	/	SYM
ejpam-1354	22	4	eur	eur	PROPN
ejpam-1354	22	5	.	.	PUNCT
ejpam-1354	23	1	j.	j.	PROPN
ejpam-1354	23	2	pure	pure	PROPN
ejpam-1354	23	3	appl	appl	PROPN
ejpam-1354	23	4	.	.	PROPN
ejpam-1354	23	5	math	math	PROPN
ejpam-1354	23	6	,	,	PUNCT
ejpam-1354	23	7	6	6	NUM
ejpam-1354	23	8	(	(	PUNCT
ejpam-1354	23	9	2013	2013	NUM
ejpam-1354	23	10	)	)	PUNCT
ejpam-1354	23	11	,	,	PUNCT
ejpam-1354	23	12	172	172	NUM
ejpam-1354	23	13	-	-	SYM
ejpam-1354	23	14	188	188	NUM
ejpam-1354	23	15	173	173	NUM
ejpam-1354	23	16	property	property	NOUN
ejpam-1354	23	17	.	.	PUNCT
ejpam-1354	24	1	that	that	PRON
ejpam-1354	24	2	is	be	AUX
ejpam-1354	24	3	,	,	PUNCT
ejpam-1354	24	4	individuals	individual	NOUN
ejpam-1354	24	5	with	with	ADP
ejpam-1354	24	6	the	the	DET
ejpam-1354	24	7	same	same	ADJ
ejpam-1354	24	8	height	height	NOUN
ejpam-1354	24	9	are	be	AUX
ejpam-1354	24	10	modeled	model	VERB
ejpam-1354	24	11	as	as	ADP
ejpam-1354	24	12	having	have	VERB
ejpam-1354	24	13	the	the	DET
ejpam-1354	24	14	same	same	ADJ
ejpam-1354	24	15	fitness	fitness	NOUN
ejpam-1354	24	16	and	and	CCONJ
ejpam-1354	24	17	thus	thus	ADV
ejpam-1354	24	18	each	each	PRON
ejpam-1354	24	19	have	have	VERB
ejpam-1354	24	20	the	the	DET
ejpam-1354	24	21	same	same	ADJ
ejpam-1354	24	22	number	number	NOUN
ejpam-1354	24	23	of	of	ADP
ejpam-1354	24	24	offspring	offspring	NOUN
ejpam-1354	24	25	.	.	PUNCT
ejpam-1354	25	1	so	so	ADV
ejpam-1354	25	2	in	in	ADP
ejpam-1354	25	3	these	these	DET
ejpam-1354	25	4	population	population	NOUN
ejpam-1354	25	5	models	model	NOUN
ejpam-1354	25	6	,	,	PUNCT
ejpam-1354	25	7	once	once	ADV
ejpam-1354	25	8	many	many	ADJ
ejpam-1354	25	9	distinct	distinct	ADJ
ejpam-1354	25	10	groups	group	NOUN
ejpam-1354	25	11	collide	collide	VERB
ejpam-1354	25	12	into	into	ADP
ejpam-1354	25	13	one	one	NUM
ejpam-1354	25	14	similar	similar	ADJ
ejpam-1354	25	15	group	group	NOUN
ejpam-1354	25	16	,	,	PUNCT
ejpam-1354	25	17	they	they	PRON
ejpam-1354	25	18	do	do	AUX
ejpam-1354	25	19	not	not	PART
ejpam-1354	25	20	break	break	VERB
ejpam-1354	25	21	apart	apart	ADV
ejpam-1354	25	22	ever	ever	ADV
ejpam-1354	25	23	again	again	ADV
ejpam-1354	25	24	.	.	PUNCT
ejpam-1354	26	1	thus	thus	ADV
ejpam-1354	26	2	,	,	PUNCT
ejpam-1354	26	3	these	these	DET
ejpam-1354	26	4	population	population	NOUN
ejpam-1354	26	5	models	model	NOUN
ejpam-1354	26	6	share	share	VERB
ejpam-1354	26	7	some	some	DET
ejpam-1354	26	8	characteristics	characteristic	NOUN
ejpam-1354	26	9	with	with	ADP
ejpam-1354	26	10	our	our	PRON
ejpam-1354	26	11	work	work	NOUN
ejpam-1354	26	12	.	.	PUNCT
ejpam-1354	27	1	unfortunately	unfortunately	ADV
ejpam-1354	27	2	,	,	PUNCT
ejpam-1354	27	3	conventional	conventional	ADJ
ejpam-1354	27	4	population	population	NOUN
ejpam-1354	27	5	dynamics	dynamic	NOUN
ejpam-1354	27	6	tend	tend	VERB
ejpam-1354	27	7	to	to	PART
ejpam-1354	27	8	show	show	VERB
ejpam-1354	27	9	consensus	consensus	NOUN
ejpam-1354	27	10	(	(	PUNCT
ejpam-1354	27	11	where	where	SCONJ
ejpam-1354	27	12	the	the	DET
ejpam-1354	27	13	consensus	consensus	NOUN
ejpam-1354	27	14	property	property	NOUN
ejpam-1354	27	15	might	might	AUX
ejpam-1354	27	16	be	be	AUX
ejpam-1354	27	17	a	a	DET
ejpam-1354	27	18	polymorphic	polymorphic	ADJ
ejpam-1354	27	19	mix	mix	NOUN
ejpam-1354	27	20	)	)	PUNCT
ejpam-1354	27	21	or	or	CCONJ
ejpam-1354	27	22	limit	limit	NOUN
ejpam-1354	27	23	-	-	PUNCT
ejpam-1354	27	24	cycle	cycle	NOUN
ejpam-1354	27	25	behavior	behavior	NOUN
ejpam-1354	27	26	.	.	PUNCT
ejpam-1354	28	1	isolated	isolated	ADJ
ejpam-1354	28	2	equilibria	equilibrium	NOUN
ejpam-1354	28	3	are	be	AUX
ejpam-1354	28	4	usually	usually	ADV
ejpam-1354	28	5	not	not	PART
ejpam-1354	28	6	explicit	explicit	ADJ
ejpam-1354	28	7	results	result	NOUN
ejpam-1354	28	8	of	of	ADP
ejpam-1354	28	9	conventional	conventional	ADJ
ejpam-1354	28	10	population	population	NOUN
ejpam-1354	28	11	models	model	NOUN
ejpam-1354	28	12	.	.	PUNCT
ejpam-1354	29	1	where	where	SCONJ
ejpam-1354	29	2	again	again	ADV
ejpam-1354	29	3	,	,	PUNCT
ejpam-1354	29	4	polymorphism	polymorphism	NOUN
ejpam-1354	29	5	is	be	AUX
ejpam-1354	29	6	represented	represent	VERB
ejpam-1354	29	7	in	in	ADP
ejpam-1354	29	8	other	other	ADJ
ejpam-1354	29	9	ways	way	NOUN
ejpam-1354	29	10	in	in	ADP
ejpam-1354	29	11	these	these	DET
ejpam-1354	29	12	cases	case	NOUN
ejpam-1354	29	13	,	,	PUNCT
ejpam-1354	29	14	for	for	SCONJ
ejpam-1354	29	15	more	more	ADJ
ejpam-1354	29	16	details	detail	NOUN
ejpam-1354	29	17	see	see	VERB
ejpam-1354	29	18	for	for	ADP
ejpam-1354	29	19	instance	instance	NOUN
ejpam-1354	29	20	[	[	X
ejpam-1354	29	21	6	6	NUM
ejpam-1354	29	22	,	,	PUNCT
ejpam-1354	29	23	7	7	NUM
ejpam-1354	29	24	]	]	PUNCT
ejpam-1354	29	25	.	.	PUNCT
ejpam-1354	30	1	modeling	modeling	NOUN
ejpam-1354	30	2	of	of	ADP
ejpam-1354	30	3	diffusion	diffusion	NOUN
ejpam-1354	30	4	phenomena	phenomenon	NOUN
ejpam-1354	30	5	are	be	AUX
ejpam-1354	30	6	widely	widely	ADV
ejpam-1354	30	7	studied	study	VERB
ejpam-1354	30	8	and	and	CCONJ
ejpam-1354	30	9	analyzed	analyze	VERB
ejpam-1354	30	10	using	use	VERB
ejpam-1354	30	11	several	several	ADJ
ejpam-1354	30	12	mathematical	mathematical	ADJ
ejpam-1354	30	13	and	and	CCONJ
ejpam-1354	30	14	physical	physical	ADJ
ejpam-1354	30	15	techniques	technique	NOUN
ejpam-1354	30	16	,	,	PUNCT
ejpam-1354	30	17	for	for	ADP
ejpam-1354	30	18	instance	instance	NOUN
ejpam-1354	30	19	using	use	VERB
ejpam-1354	30	20	partial	partial	ADJ
ejpam-1354	30	21	differential	differential	ADJ
ejpam-1354	30	22	equations	equation	NOUN
ejpam-1354	30	23	or	or	CCONJ
ejpam-1354	30	24	particle	particle	NOUN
ejpam-1354	30	25	methods	method	NOUN
ejpam-1354	30	26	.	.	PUNCT
ejpam-1354	31	1	the	the	DET
ejpam-1354	31	2	inverse	inverse	NOUN
ejpam-1354	31	3	problem	problem	NOUN
ejpam-1354	31	4	,	,	PUNCT
ejpam-1354	31	5	which	which	PRON
ejpam-1354	31	6	is	be	AUX
ejpam-1354	31	7	condensing	condense	VERB
ejpam-1354	31	8	,	,	PUNCT
ejpam-1354	31	9	is	be	AUX
ejpam-1354	31	10	till	till	SCONJ
ejpam-1354	31	11	now	now	ADV
ejpam-1354	31	12	an	an	DET
ejpam-1354	31	13	open	open	ADJ
ejpam-1354	31	14	and	and	CCONJ
ejpam-1354	31	15	a	a	DET
ejpam-1354	31	16	very	very	ADV
ejpam-1354	31	17	interesting	interesting	ADJ
ejpam-1354	31	18	case	case	NOUN
ejpam-1354	31	19	.	.	PUNCT
ejpam-1354	32	1	this	this	DET
ejpam-1354	32	2	mixture	mixture	NOUN
ejpam-1354	32	3	with	with	ADP
ejpam-1354	32	4	the	the	DET
ejpam-1354	32	5	collective	collective	ADJ
ejpam-1354	32	6	dynamics	dynamic	NOUN
ejpam-1354	32	7	provide	provide	VERB
ejpam-1354	32	8	many	many	ADJ
ejpam-1354	32	9	mathematical	mathematical	ADJ
ejpam-1354	32	10	open	open	ADJ
ejpam-1354	32	11	questions	question	NOUN
ejpam-1354	32	12	.	.	PUNCT
ejpam-1354	33	1	for	for	ADP
ejpam-1354	33	2	example	example	NOUN
ejpam-1354	33	3	consensus	consensus	NOUN
ejpam-1354	33	4	or	or	CCONJ
ejpam-1354	33	5	total	total	ADJ
ejpam-1354	33	6	condensing	condense	VERB
ejpam-1354	33	7	of	of	ADP
ejpam-1354	33	8	opinions	opinion	NOUN
ejpam-1354	33	9	in	in	ADP
ejpam-1354	33	10	social	social	ADJ
ejpam-1354	33	11	aggregation	aggregation	NOUN
ejpam-1354	33	12	[	[	X
ejpam-1354	33	13	11	11	NUM
ejpam-1354	33	14	,	,	PUNCT
ejpam-1354	33	15	12	12	NUM
ejpam-1354	33	16	]	]	PUNCT
ejpam-1354	33	17	in	in	ADP
ejpam-1354	33	18	the	the	DET
ejpam-1354	33	19	context	context	NOUN
ejpam-1354	33	20	of	of	ADP
ejpam-1354	33	21	the	the	DET
ejpam-1354	33	22	opinion	opinion	NOUN
ejpam-1354	33	23	dynamics	dynamic	NOUN
ejpam-1354	33	24	,	,	PUNCT
ejpam-1354	33	25	is	be	AUX
ejpam-1354	33	26	one	one	NUM
ejpam-1354	33	27	of	of	ADP
ejpam-1354	33	28	these	these	DET
ejpam-1354	33	29	unsolved	unsolved	ADJ
ejpam-1354	33	30	problems	problem	NOUN
ejpam-1354	33	31	.	.	PUNCT
ejpam-1354	34	1	the	the	DET
ejpam-1354	34	2	agents	agent	NOUN
ejpam-1354	34	3	move	move	VERB
ejpam-1354	34	4	simultaneously	simultaneously	ADV
ejpam-1354	34	5	to	to	ADP
ejpam-1354	34	6	the	the	DET
ejpam-1354	34	7	barycenter	barycenter	NOUN
ejpam-1354	34	8	of	of	ADP
ejpam-1354	34	9	all	all	DET
ejpam-1354	34	10	agents	agent	NOUN
ejpam-1354	34	11	in	in	ADP
ejpam-1354	34	12	an	an	DET
ejpam-1354	34	13	ε	ε	PROPN
ejpam-1354	34	14	neighborhood	neighborhood	NOUN
ejpam-1354	34	15	,	,	PUNCT
ejpam-1354	34	16	see	see	VERB
ejpam-1354	34	17	also	also	ADV
ejpam-1354	34	18	[	[	X
ejpam-1354	34	19	5	5	NUM
ejpam-1354	34	20	]	]	PUNCT
ejpam-1354	34	21	.	.	PUNCT
ejpam-1354	35	1	the	the	DET
ejpam-1354	35	2	final	final	ADJ
ejpam-1354	35	3	state	state	NOUN
ejpam-1354	35	4	of	of	ADP
ejpam-1354	35	5	this	this	DET
ejpam-1354	35	6	time	time	NOUN
ejpam-1354	35	7	dependent	dependent	ADJ
ejpam-1354	35	8	model	model	NOUN
ejpam-1354	35	9	may	may	AUX
ejpam-1354	35	10	be	be	AUX
ejpam-1354	35	11	consensus	consensus	NOUN
ejpam-1354	35	12	if	if	SCONJ
ejpam-1354	35	13	all	all	DET
ejpam-1354	35	14	agents	agent	NOUN
ejpam-1354	35	15	meet	meet	VERB
ejpam-1354	35	16	at	at	ADP
ejpam-1354	35	17	the	the	DET
ejpam-1354	35	18	same	same	ADJ
ejpam-1354	35	19	position	position	NOUN
ejpam-1354	35	20	or	or	CCONJ
ejpam-1354	35	21	grouping	group	VERB
ejpam-1354	35	22	in	in	ADP
ejpam-1354	35	23	several	several	ADJ
ejpam-1354	35	24	ε	ε	PROPN
ejpam-1354	35	25	distanced	distance	VERB
ejpam-1354	35	26	classes	class	NOUN
ejpam-1354	35	27	of	of	ADP
ejpam-1354	35	28	agents	agent	NOUN
ejpam-1354	35	29	such	such	ADJ
ejpam-1354	35	30	that	that	SCONJ
ejpam-1354	35	31	all	all	DET
ejpam-1354	35	32	agents	agent	NOUN
ejpam-1354	35	33	in	in	ADP
ejpam-1354	35	34	the	the	DET
ejpam-1354	35	35	same	same	ADJ
ejpam-1354	35	36	class	class	NOUN
ejpam-1354	35	37	maintain	maintain	VERB
ejpam-1354	35	38	the	the	DET
ejpam-1354	35	39	same	same	ADJ
ejpam-1354	35	40	position	position	NOUN
ejpam-1354	35	41	.	.	PUNCT
ejpam-1354	36	1	in	in	ADP
ejpam-1354	36	2	this	this	DET
ejpam-1354	36	3	work	work	NOUN
ejpam-1354	36	4	,	,	PUNCT
ejpam-1354	36	5	we	we	PRON
ejpam-1354	36	6	are	be	AUX
ejpam-1354	36	7	interested	interested	ADJ
ejpam-1354	36	8	to	to	PART
ejpam-1354	36	9	extend	extend	VERB
ejpam-1354	36	10	the	the	DET
ejpam-1354	36	11	barycenter	barycenter	NOUN
ejpam-1354	36	12	dynamics	dynamic	NOUN
ejpam-1354	36	13	presented	present	VERB
ejpam-1354	36	14	for	for	ADP
ejpam-1354	36	15	example	example	NOUN
ejpam-1354	36	16	by	by	ADP
ejpam-1354	36	17	[	[	X
ejpam-1354	36	18	5	5	NUM
ejpam-1354	36	19	,	,	PUNCT
ejpam-1354	36	20	12	12	NUM
ejpam-1354	36	21	]	]	PUNCT
ejpam-1354	36	22	to	to	ADP
ejpam-1354	36	23	an	an	DET
ejpam-1354	36	24	energy	energy	NOUN
ejpam-1354	36	25	-	-	PUNCT
ejpam-1354	36	26	based	base	VERB
ejpam-1354	36	27	model	model	NOUN
ejpam-1354	36	28	.	.	PUNCT
ejpam-1354	37	1	observe	observe	VERB
ejpam-1354	37	2	that	that	SCONJ
ejpam-1354	37	3	the	the	DET
ejpam-1354	37	4	barycenter	barycenter	NOUN
ejpam-1354	37	5	of	of	ADP
ejpam-1354	37	6	a	a	DET
ejpam-1354	37	7	positive	positive	ADJ
ejpam-1354	37	8	measure	measure	NOUN
ejpam-1354	37	9	m	m	INTJ
ejpam-1354	37	10	locally	locally	ADV
ejpam-1354	37	11	minimizes	minimize	VERB
ejpam-1354	37	12	the	the	DET
ejpam-1354	37	13	ε	ε	PROPN
ejpam-1354	37	14	-	-	PUNCT
ejpam-1354	37	15	energy	energy	NOUN
ejpam-1354	37	16	of	of	ADP
ejpam-1354	37	17	a	a	DET
ejpam-1354	37	18	spatial	spatial	ADJ
ejpam-1354	37	19	position	position	NOUN
ejpam-1354	37	20	x	x	NOUN
ejpam-1354	37	21	:	:	PUNCT
ejpam-1354	37	22	eε(x	eε(x	NUM
ejpam-1354	37	23	,	,	PUNCT
ejpam-1354	37	24	m	m	NOUN
ejpam-1354	37	25	)	)	PUNCT
ejpam-1354	38	1	=	=	SYM
ejpam-1354	38	2	∫	∫	PROPN
ejpam-1354	38	3	d(x	d(x	PROPN
ejpam-1354	38	4	,	,	PUNCT
ejpam-1354	38	5	y)≤ε	y)≤ε	NOUN
ejpam-1354	38	6	d2(x	d2(x	NOUN
ejpam-1354	38	7	,	,	PUNCT
ejpam-1354	38	8	y)m(d	y)m(d	PROPN
ejpam-1354	38	9	y	y	PROPN
ejpam-1354	38	10	)	)	PUNCT
ejpam-1354	38	11	,	,	PUNCT
ejpam-1354	38	12	(	(	PUNCT
ejpam-1354	38	13	1	1	X
ejpam-1354	38	14	)	)	PUNCT
ejpam-1354	39	1	where	where	SCONJ
ejpam-1354	39	2	for	for	ADP
ejpam-1354	39	3	the	the	DET
ejpam-1354	39	4	barycenter	barycenter	NOUN
ejpam-1354	39	5	dynamics	dynamic	NOUN
ejpam-1354	39	6	,	,	PUNCT
ejpam-1354	39	7	d	d	X
ejpam-1354	39	8	(	(	PUNCT
ejpam-1354	39	9	·	·	PUNCT
ejpam-1354	39	10	,	,	PUNCT
ejpam-1354	39	11	·	·	PUNCT
ejpam-1354	39	12	)	)	PUNCT
ejpam-1354	39	13	is	be	AUX
ejpam-1354	39	14	an	an	DET
ejpam-1354	39	15	euclidean	euclidean	ADJ
ejpam-1354	39	16	distance	distance	NOUN
ejpam-1354	39	17	.	.	PUNCT
ejpam-1354	40	1	this	this	DET
ejpam-1354	40	2	observation	observation	NOUN
ejpam-1354	40	3	is	be	AUX
ejpam-1354	40	4	the	the	DET
ejpam-1354	40	5	starting	starting	NOUN
ejpam-1354	40	6	point	point	NOUN
ejpam-1354	40	7	for	for	ADP
ejpam-1354	40	8	our	our	PRON
ejpam-1354	40	9	present	present	ADJ
ejpam-1354	40	10	study	study	NOUN
ejpam-1354	40	11	to	to	PART
ejpam-1354	40	12	generalize	generalize	VERB
ejpam-1354	40	13	the	the	DET
ejpam-1354	40	14	barycenter	barycenter	NOUN
ejpam-1354	40	15	dynamics	dynamic	NOUN
ejpam-1354	40	16	.	.	PUNCT
ejpam-1354	41	1	we	we	PRON
ejpam-1354	41	2	replace	replace	VERB
ejpam-1354	41	3	the	the	DET
ejpam-1354	41	4	euclidean	euclidean	ADJ
ejpam-1354	41	5	space	space	NOUN
ejpam-1354	41	6	by	by	ADP
ejpam-1354	41	7	an	an	DET
ejpam-1354	41	8	arbitrary	arbitrary	ADJ
ejpam-1354	41	9	metric	metric	ADJ
ejpam-1354	41	10	space	space	NOUN
ejpam-1354	41	11	,	,	PUNCT
ejpam-1354	41	12	and	and	CCONJ
ejpam-1354	41	13	let	let	VERB
ejpam-1354	41	14	the	the	DET
ejpam-1354	41	15	agents	agent	NOUN
ejpam-1354	41	16	move	move	VERB
ejpam-1354	41	17	to	to	ADP
ejpam-1354	41	18	where	where	SCONJ
ejpam-1354	41	19	the	the	DET
ejpam-1354	41	20	local	local	ADJ
ejpam-1354	41	21	energy	energy	NOUN
ejpam-1354	41	22	is	be	AUX
ejpam-1354	41	23	minimal	minimal	ADJ
ejpam-1354	41	24	within	within	ADP
ejpam-1354	41	25	an	an	DET
ejpam-1354	41	26	ε	ε	PROPN
ejpam-1354	41	27	neighborhood	neighborhood	NOUN
ejpam-1354	41	28	.	.	PUNCT
ejpam-1354	42	1	moreover	moreover	ADV
ejpam-1354	42	2	,	,	PUNCT
ejpam-1354	42	3	note	note	VERB
ejpam-1354	42	4	that	that	SCONJ
ejpam-1354	42	5	the	the	DET
ejpam-1354	42	6	second	second	ADJ
ejpam-1354	42	7	claim	claim	NOUN
ejpam-1354	42	8	does	do	AUX
ejpam-1354	42	9	not	not	PART
ejpam-1354	42	10	provide	provide	VERB
ejpam-1354	42	11	the	the	DET
ejpam-1354	42	12	synchronized	synchronize	VERB
ejpam-1354	42	13	barycenter	barycenter	NOUN
ejpam-1354	42	14	dynamics	dynamic	NOUN
ejpam-1354	42	15	,	,	PUNCT
ejpam-1354	42	16	as	as	SCONJ
ejpam-1354	42	17	it	it	PRON
ejpam-1354	42	18	is	be	AUX
ejpam-1354	42	19	already	already	ADV
ejpam-1354	42	20	demonstrated	demonstrate	VERB
ejpam-1354	42	21	by	by	ADP
ejpam-1354	42	22	two	two	NUM
ejpam-1354	42	23	agents	agent	NOUN
ejpam-1354	42	24	and	and	CCONJ
ejpam-1354	42	25	euclidean	euclidean	ADJ
ejpam-1354	42	26	metric	metric	NOUN
ejpam-1354	42	27	:	:	PUNCT
ejpam-1354	42	28	two	two	NUM
ejpam-1354	42	29	agents	agent	NOUN
ejpam-1354	42	30	may	may	AUX
ejpam-1354	42	31	decrease	decrease	VERB
ejpam-1354	42	32	the	the	DET
ejpam-1354	42	33	energy	energy	NOUN
ejpam-1354	42	34	to	to	ADP
ejpam-1354	42	35	zero	zero	NUM
ejpam-1354	42	36	by	by	ADP
ejpam-1354	42	37	jumping	jump	VERB
ejpam-1354	42	38	either	either	CCONJ
ejpam-1354	42	39	to	to	ADP
ejpam-1354	42	40	the	the	DET
ejpam-1354	42	41	same	same	ADJ
ejpam-1354	42	42	place	place	NOUN
ejpam-1354	42	43	,	,	PUNCT
ejpam-1354	42	44	or	or	CCONJ
ejpam-1354	42	45	to	to	ADP
ejpam-1354	42	46	different	different	ADJ
ejpam-1354	42	47	places	place	NOUN
ejpam-1354	42	48	if	if	SCONJ
ejpam-1354	42	49	the	the	DET
ejpam-1354	42	50	distance	distance	NOUN
ejpam-1354	42	51	exceeds	exceed	VERB
ejpam-1354	42	52	ε	ε	PROPN
ejpam-1354	42	53	.	.	PUNCT
ejpam-1354	43	1	since	since	SCONJ
ejpam-1354	43	2	the	the	DET
ejpam-1354	43	3	energy	energy	NOUN
ejpam-1354	43	4	minimizing	minimize	VERB
ejpam-1354	43	5	points	point	NOUN
ejpam-1354	43	6	are	be	AUX
ejpam-1354	43	7	in	in	ADP
ejpam-1354	43	8	general	general	ADJ
ejpam-1354	43	9	not	not	PART
ejpam-1354	43	10	unique	unique	ADJ
ejpam-1354	43	11	on	on	ADP
ejpam-1354	43	12	metric	metric	ADJ
ejpam-1354	43	13	spaces	space	NOUN
ejpam-1354	43	14	,	,	PUNCT
ejpam-1354	43	15	it	it	PRON
ejpam-1354	43	16	is	be	AUX
ejpam-1354	43	17	important	important	ADJ
ejpam-1354	43	18	to	to	PART
ejpam-1354	43	19	note	note	VERB
ejpam-1354	43	20	that	that	SCONJ
ejpam-1354	43	21	our	our	PRON
ejpam-1354	43	22	dynamics	dynamic	NOUN
ejpam-1354	43	23	,	,	PUNCT
ejpam-1354	43	24	because	because	SCONJ
ejpam-1354	43	25	of	of	ADP
ejpam-1354	43	26	the	the	DET
ejpam-1354	43	27	second	second	ADJ
ejpam-1354	43	28	claim	claim	NOUN
ejpam-1354	43	29	,	,	PUNCT
ejpam-1354	43	30	is	be	AUX
ejpam-1354	43	31	not	not	PART
ejpam-1354	43	32	a	a	DET
ejpam-1354	43	33	deterministic	deterministic	ADJ
ejpam-1354	43	34	one	one	NOUN
ejpam-1354	43	35	.	.	PUNCT
ejpam-1354	44	1	furthermore	furthermore	ADV
ejpam-1354	44	2	,	,	PUNCT
ejpam-1354	44	3	the	the	DET
ejpam-1354	44	4	convergence	convergence	NOUN
ejpam-1354	44	5	of	of	ADP
ejpam-1354	44	6	the	the	DET
ejpam-1354	44	7	process	process	NOUN
ejpam-1354	44	8	of	of	ADP
ejpam-1354	44	9	condensing	condense	VERB
ejpam-1354	44	10	sequences	sequence	NOUN
ejpam-1354	44	11	is	be	AUX
ejpam-1354	44	12	not	not	PART
ejpam-1354	44	13	guaranteed	guarantee	VERB
ejpam-1354	44	14	.	.	PUNCT
ejpam-1354	45	1	this	this	DET
ejpam-1354	45	2	fact	fact	NOUN
ejpam-1354	45	3	can	can	AUX
ejpam-1354	45	4	be	be	AUX
ejpam-1354	45	5	seen	see	VERB
ejpam-1354	45	6	in	in	ADP
ejpam-1354	45	7	the	the	DET
ejpam-1354	45	8	case	case	NOUN
ejpam-1354	45	9	of	of	ADP
ejpam-1354	45	10	two	two	NUM
ejpam-1354	45	11	agents	agent	NOUN
ejpam-1354	45	12	,	,	PUNCT
ejpam-1354	45	13	they	they	PRON
ejpam-1354	45	14	may	may	AUX
ejpam-1354	45	15	exchange	exchange	VERB
ejpam-1354	45	16	their	their	PRON
ejpam-1354	45	17	position	position	NOUN
ejpam-1354	45	18	forever	forever	ADV
ejpam-1354	45	19	,	,	PUNCT
ejpam-1354	45	20	with	with	ADP
ejpam-1354	45	21	periodic	periodic	ADJ
ejpam-1354	45	22	local	local	ADJ
ejpam-1354	45	23	energy	energy	NOUN
ejpam-1354	45	24	.	.	PUNCT
ejpam-1354	46	1	therefore	therefore	ADV
ejpam-1354	46	2	,	,	PUNCT
ejpam-1354	46	3	in	in	ADP
ejpam-1354	46	4	order	order	NOUN
ejpam-1354	46	5	to	to	PART
ejpam-1354	46	6	prove	prove	VERB
ejpam-1354	46	7	the	the	DET
ejpam-1354	46	8	convergence	convergence	NOUN
ejpam-1354	46	9	,	,	PUNCT
ejpam-1354	46	10	let	let	VERB
ejpam-1354	46	11	us	we	PRON
ejpam-1354	46	12	consider	consider	VERB
ejpam-1354	46	13	that	that	SCONJ
ejpam-1354	46	14	the	the	DET
ejpam-1354	46	15	agents	agent	NOUN
ejpam-1354	46	16	do	do	AUX
ejpam-1354	46	17	not	not	PART
ejpam-1354	46	18	move	move	VERB
ejpam-1354	46	19	simultaneously	simultaneously	ADV
ejpam-1354	46	20	but	but	CCONJ
ejpam-1354	46	21	one	one	NUM
ejpam-1354	46	22	at	at	ADP
ejpam-1354	46	23	a	a	DET
ejpam-1354	46	24	time	time	NOUN
ejpam-1354	46	25	in	in	ADP
ejpam-1354	46	26	an	an	DET
ejpam-1354	46	27	arbitrary	arbitrary	ADJ
ejpam-1354	46	28	order	order	NOUN
ejpam-1354	46	29	.	.	PUNCT
ejpam-1354	47	1	by	by	ADP
ejpam-1354	47	2	doing	do	VERB
ejpam-1354	47	3	so	so	ADV
ejpam-1354	47	4	,	,	PUNCT
ejpam-1354	47	5	they	they	PRON
ejpam-1354	47	6	decrease	decrease	VERB
ejpam-1354	47	7	the	the	DET
ejpam-1354	47	8	global	global	ADJ
ejpam-1354	47	9	ε	ε	PROPN
ejpam-1354	47	10	-	-	PUNCT
ejpam-1354	47	11	energy	energy	NOUN
ejpam-1354	47	12	:	:	PUNCT
ejpam-1354	47	13	eε(m	eε(m	NUM
ejpam-1354	47	14	)	)	PUNCT
ejpam-1354	48	1	=	=	SYM
ejpam-1354	48	2	∫	∫	PROPN
ejpam-1354	48	3	x	x	SYM
ejpam-1354	48	4	eε(x	eε(x	NUM
ejpam-1354	48	5	,	,	PUNCT
ejpam-1354	48	6	m)m(d	m)m(d	ADJ
ejpam-1354	48	7	x	x	X
ejpam-1354	48	8	)	)	PUNCT
ejpam-1354	48	9	=	=	SYM
ejpam-1354	49	1	∫	∫	PROPN
ejpam-1354	49	2	x	x	SYM
ejpam-1354	49	3	∫	∫	PROPN
ejpam-1354	49	4	d(x	d(x	PROPN
ejpam-1354	49	5	,	,	PUNCT
ejpam-1354	49	6	y)≤ε	y)≤ε	NOUN
ejpam-1354	49	7	d2(x	d2(x	NOUN
ejpam-1354	49	8	,	,	PUNCT
ejpam-1354	49	9	y)m(d	y)m(d	PROPN
ejpam-1354	49	10	y)m(d	y)m(d	PROPN
ejpam-1354	49	11	x	x	X
ejpam-1354	49	12	)	)	PUNCT
ejpam-1354	49	13	,	,	PUNCT
ejpam-1354	49	14	(	(	PUNCT
ejpam-1354	49	15	2	2	X
ejpam-1354	49	16	)	)	PUNCT
ejpam-1354	49	17	which	which	PRON
ejpam-1354	49	18	guaranties	guarantie	VERB
ejpam-1354	49	19	the	the	DET
ejpam-1354	49	20	convergence	convergence	NOUN
ejpam-1354	49	21	and	and	CCONJ
ejpam-1354	49	22	in	in	ADP
ejpam-1354	49	23	fact	fact	NOUN
ejpam-1354	49	24	zero	zero	NUM
ejpam-1354	49	25	energy	energy	NOUN
ejpam-1354	49	26	after	after	ADP
ejpam-1354	49	27	finitely	finitely	ADV
ejpam-1354	49	28	many	many	ADJ
ejpam-1354	49	29	steps	step	NOUN
ejpam-1354	49	30	.	.	PUNCT
ejpam-1354	50	1	it	it	PRON
ejpam-1354	50	2	is	be	AUX
ejpam-1354	50	3	also	also	ADV
ejpam-1354	50	4	important	important	ADJ
ejpam-1354	50	5	to	to	PART
ejpam-1354	50	6	note	note	VERB
ejpam-1354	50	7	that	that	SCONJ
ejpam-1354	50	8	the	the	DET
ejpam-1354	50	9	arbitrary	arbitrary	ADJ
ejpam-1354	50	10	order	order	NOUN
ejpam-1354	50	11	of	of	ADP
ejpam-1354	50	12	action	action	NOUN
ejpam-1354	50	13	of	of	ADP
ejpam-1354	50	14	different	different	ADJ
ejpam-1354	50	15	agents	agent	NOUN
ejpam-1354	50	16	and	and	CCONJ
ejpam-1354	50	17	the	the	DET
ejpam-1354	50	18	nonuniqueness	nonuniqueness	NOUN
ejpam-1354	50	19	of	of	ADP
ejpam-1354	50	20	the	the	DET
ejpam-1354	50	21	positions	position	NOUN
ejpam-1354	50	22	minimizing	minimize	VERB
ejpam-1354	50	23	the	the	DET
ejpam-1354	50	24	local	local	ADJ
ejpam-1354	50	25	energy	energy	NOUN
ejpam-1354	50	26	introduce	introduce	NOUN
ejpam-1354	50	27	sources	source	NOUN
ejpam-1354	50	28	of	of	ADP
ejpam-1354	50	29	indeterminacy	indeterminacy	NOUN
ejpam-1354	50	30	.	.	PUNCT
ejpam-1354	51	1	m.	m.	NOUN
ejpam-1354	51	2	zahri	zahri	PROPN
ejpam-1354	51	3	/	/	SYM
ejpam-1354	51	4	eur	eur	PROPN
ejpam-1354	51	5	.	.	PUNCT
ejpam-1354	52	1	j.	j.	PROPN
ejpam-1354	52	2	pure	pure	PROPN
ejpam-1354	52	3	appl	appl	PROPN
ejpam-1354	52	4	.	.	PROPN
ejpam-1354	52	5	math	math	PROPN
ejpam-1354	52	6	,	,	PUNCT
ejpam-1354	52	7	6	6	NUM
ejpam-1354	52	8	(	(	PUNCT
ejpam-1354	52	9	2013	2013	NUM
ejpam-1354	52	10	)	)	PUNCT
ejpam-1354	52	11	,	,	PUNCT
ejpam-1354	52	12	172	172	NUM
ejpam-1354	52	13	-	-	SYM
ejpam-1354	52	14	188	188	NUM
ejpam-1354	52	15	174	174	NUM
ejpam-1354	52	16	such	such	ADJ
ejpam-1354	52	17	indeterminacy	indeterminacy	NOUN
ejpam-1354	52	18	gives	give	VERB
ejpam-1354	52	19	the	the	DET
ejpam-1354	52	20	opportunity	opportunity	NOUN
ejpam-1354	52	21	for	for	ADP
ejpam-1354	52	22	stochastic	stochastic	ADJ
ejpam-1354	52	23	investigations	investigation	NOUN
ejpam-1354	52	24	,	,	PUNCT
ejpam-1354	52	25	which	which	PRON
ejpam-1354	52	26	however	however	ADV
ejpam-1354	52	27	are	be	AUX
ejpam-1354	52	28	not	not	PART
ejpam-1354	52	29	part	part	NOUN
ejpam-1354	52	30	of	of	ADP
ejpam-1354	52	31	the	the	DET
ejpam-1354	52	32	present	present	ADJ
ejpam-1354	52	33	study	study	NOUN
ejpam-1354	52	34	.	.	PUNCT
ejpam-1354	53	1	our	our	PRON
ejpam-1354	53	2	concern	concern	NOUN
ejpam-1354	53	3	in	in	ADP
ejpam-1354	53	4	this	this	DET
ejpam-1354	53	5	paper	paper	NOUN
ejpam-1354	53	6	is	be	AUX
ejpam-1354	53	7	the	the	DET
ejpam-1354	53	8	introduction	introduction	NOUN
ejpam-1354	53	9	of	of	ADP
ejpam-1354	53	10	a	a	DET
ejpam-1354	53	11	new	new	ADJ
ejpam-1354	53	12	class	class	NOUN
ejpam-1354	53	13	of	of	ADP
ejpam-1354	53	14	dynamical	dynamical	ADJ
ejpam-1354	53	15	systems	system	NOUN
ejpam-1354	53	16	together	together	ADV
ejpam-1354	53	17	with	with	ADP
ejpam-1354	53	18	some	some	DET
ejpam-1354	53	19	elementary	elementary	ADJ
ejpam-1354	53	20	analysis	analysis	NOUN
ejpam-1354	53	21	and	and	CCONJ
ejpam-1354	53	22	a	a	DET
ejpam-1354	53	23	number	number	NOUN
ejpam-1354	53	24	of	of	ADP
ejpam-1354	53	25	numerical	numerical	ADJ
ejpam-1354	53	26	simulations	simulation	NOUN
ejpam-1354	53	27	.	.	PUNCT
ejpam-1354	54	1	it	it	PRON
ejpam-1354	54	2	is	be	AUX
ejpam-1354	54	3	important	important	ADJ
ejpam-1354	54	4	to	to	PART
ejpam-1354	54	5	note	note	VERB
ejpam-1354	54	6	that	that	SCONJ
ejpam-1354	54	7	,	,	PUNCT
ejpam-1354	54	8	the	the	DET
ejpam-1354	54	9	arbitrary	arbitrary	ADJ
ejpam-1354	54	10	range	range	NOUN
ejpam-1354	54	11	of	of	ADP
ejpam-1354	54	12	the	the	DET
ejpam-1354	54	13	reactions	reaction	NOUN
ejpam-1354	54	14	of	of	ADP
ejpam-1354	54	15	the	the	DET
ejpam-1354	54	16	particles	particle	NOUN
ejpam-1354	54	17	and	and	CCONJ
ejpam-1354	54	18	the	the	DET
ejpam-1354	54	19	non	non	ADJ
ejpam-1354	54	20	uniqueness	uniqueness	NOUN
ejpam-1354	54	21	of	of	ADP
ejpam-1354	54	22	the	the	DET
ejpam-1354	54	23	positions	position	NOUN
ejpam-1354	54	24	minimizing	minimize	VERB
ejpam-1354	54	25	the	the	DET
ejpam-1354	54	26	local	local	ADJ
ejpam-1354	54	27	energy	energy	NOUN
ejpam-1354	54	28	give	give	VERB
ejpam-1354	54	29	a	a	DET
ejpam-1354	54	30	source	source	NOUN
ejpam-1354	54	31	of	of	ADP
ejpam-1354	54	32	stochastic	stochastic	ADJ
ejpam-1354	54	33	investigations	investigation	NOUN
ejpam-1354	54	34	,	,	PUNCT
ejpam-1354	54	35	which	which	PRON
ejpam-1354	54	36	we	we	PRON
ejpam-1354	54	37	analyze	analyze	VERB
ejpam-1354	54	38	in	in	ADP
ejpam-1354	54	39	a	a	DET
ejpam-1354	54	40	future	future	ADJ
ejpam-1354	54	41	work	work	NOUN
ejpam-1354	54	42	.	.	PUNCT
ejpam-1354	55	1	in	in	ADP
ejpam-1354	55	2	this	this	DET
ejpam-1354	55	3	work	work	NOUN
ejpam-1354	55	4	,	,	PUNCT
ejpam-1354	55	5	we	we	PRON
ejpam-1354	55	6	are	be	AUX
ejpam-1354	55	7	interested	interested	ADJ
ejpam-1354	55	8	to	to	PART
ejpam-1354	55	9	extend	extend	VERB
ejpam-1354	55	10	the	the	DET
ejpam-1354	55	11	barycenter	barycenter	NOUN
ejpam-1354	55	12	model	model	NOUN
ejpam-1354	55	13	to	to	ADP
ejpam-1354	55	14	an	an	DET
ejpam-1354	55	15	energy	energy	NOUN
ejpam-1354	55	16	based	base	VERB
ejpam-1354	55	17	model	model	NOUN
ejpam-1354	55	18	,	,	PUNCT
ejpam-1354	55	19	to	to	PART
ejpam-1354	55	20	perform	perform	VERB
ejpam-1354	55	21	theoretical	theoretical	ADJ
ejpam-1354	55	22	analysis	analysis	NOUN
ejpam-1354	55	23	for	for	ADP
ejpam-1354	55	24	this	this	DET
ejpam-1354	55	25	model	model	NOUN
ejpam-1354	55	26	such	such	ADJ
ejpam-1354	55	27	as	as	ADP
ejpam-1354	55	28	convergence	convergence	NOUN
ejpam-1354	55	29	theorems	theorem	NOUN
ejpam-1354	55	30	and	and	CCONJ
ejpam-1354	55	31	to	to	PART
ejpam-1354	55	32	numerically	numerically	ADV
ejpam-1354	55	33	validate	validate	VERB
ejpam-1354	55	34	our	our	PRON
ejpam-1354	55	35	results	result	NOUN
ejpam-1354	55	36	in	in	ADP
ejpam-1354	55	37	finite	finite	NOUN
ejpam-1354	55	38	and	and	CCONJ
ejpam-1354	55	39	continuous	continuous	ADJ
ejpam-1354	55	40	metric	metric	ADJ
ejpam-1354	55	41	spaces	space	NOUN
ejpam-1354	55	42	.	.	PUNCT
ejpam-1354	56	1	this	this	DET
ejpam-1354	56	2	paper	paper	NOUN
ejpam-1354	56	3	is	be	AUX
ejpam-1354	56	4	structured	structure	VERB
ejpam-1354	56	5	in	in	ADP
ejpam-1354	56	6	two	two	NUM
ejpam-1354	56	7	principal	principal	ADJ
ejpam-1354	56	8	sections	section	NOUN
ejpam-1354	56	9	.	.	PUNCT
ejpam-1354	57	1	the	the	DET
ejpam-1354	57	2	first	first	ADJ
ejpam-1354	57	3	one	one	NOUN
ejpam-1354	57	4	proposes	propose	VERB
ejpam-1354	57	5	the	the	DET
ejpam-1354	57	6	construction	construction	NOUN
ejpam-1354	57	7	of	of	ADP
ejpam-1354	57	8	condensing	condense	VERB
ejpam-1354	57	9	sequences	sequence	NOUN
ejpam-1354	57	10	.	.	PUNCT
ejpam-1354	58	1	the	the	DET
ejpam-1354	58	2	second	second	ADJ
ejpam-1354	58	3	section	section	NOUN
ejpam-1354	58	4	proposes	propose	VERB
ejpam-1354	58	5	a	a	DET
ejpam-1354	58	6	numerical	numerical	ADJ
ejpam-1354	58	7	simulation	simulation	NOUN
ejpam-1354	58	8	of	of	ADP
ejpam-1354	58	9	such	such	DET
ejpam-1354	58	10	a	a	DET
ejpam-1354	58	11	phenomena	phenomenon	NOUN
ejpam-1354	58	12	.	.	PUNCT
ejpam-1354	59	1	some	some	DET
ejpam-1354	59	2	general	general	ADJ
ejpam-1354	59	3	remarks	remark	NOUN
ejpam-1354	59	4	are	be	AUX
ejpam-1354	59	5	then	then	ADV
ejpam-1354	59	6	listed	list	VERB
ejpam-1354	59	7	.	.	PUNCT
ejpam-1354	60	1	2	2	X
ejpam-1354	60	2	.	.	X
ejpam-1354	60	3	discrete	discrete	ADJ
ejpam-1354	60	4	energy	energy	NOUN
ejpam-1354	60	5	function	function	NOUN
ejpam-1354	60	6	let	let	VERB
ejpam-1354	60	7	x	x	PRON
ejpam-1354	60	8	be	be	AUX
ejpam-1354	60	9	a	a	DET
ejpam-1354	60	10	finite	finite	ADJ
ejpam-1354	60	11	set	set	NOUN
ejpam-1354	60	12	of	of	ADP
ejpam-1354	60	13	rn	rn	PROPN
ejpam-1354	60	14	.	.	PUNCT
ejpam-1354	61	1	a	a	DET
ejpam-1354	61	2	non	non	ADJ
ejpam-1354	61	3	-	-	ADJ
ejpam-1354	61	4	negative	negative	ADJ
ejpam-1354	61	5	measure	measure	NOUN
ejpam-1354	61	6	m	m	VERB
ejpam-1354	61	7	on	on	ADP
ejpam-1354	61	8	x	x	VERB
ejpam-1354	61	9	is	be	AUX
ejpam-1354	61	10	represented	represent	VERB
ejpam-1354	61	11	by	by	ADP
ejpam-1354	61	12	a	a	DET
ejpam-1354	61	13	function	function	NOUN
ejpam-1354	61	14	m	m	NOUN
ejpam-1354	61	15	:	:	PUNCT
ejpam-1354	62	1	x	x	X
ejpam-1354	62	2	7→	7→	NUM
ejpam-1354	63	1	[	[	X
ejpam-1354	63	2	0,∞	0,∞	NUM
ejpam-1354	63	3	)	)	PUNCT
ejpam-1354	64	1	and	and	CCONJ
ejpam-1354	64	2	we	we	PRON
ejpam-1354	64	3	denote	denote	VERB
ejpam-1354	64	4	by	by	ADP
ejpam-1354	64	5	m+(x	m+(x	PROPN
ejpam-1354	64	6	)	)	PUNCT
ejpam-1354	64	7	the	the	DET
ejpam-1354	64	8	set	set	NOUN
ejpam-1354	64	9	of	of	ADP
ejpam-1354	64	10	all	all	DET
ejpam-1354	64	11	positive	positive	ADJ
ejpam-1354	64	12	measures	measure	NOUN
ejpam-1354	64	13	on	on	ADP
ejpam-1354	64	14	x	x	PUNCT
ejpam-1354	64	15	with	with	ADP
ejpam-1354	64	16	discrete	discrete	ADJ
ejpam-1354	64	17	support	support	NOUN
ejpam-1354	64	18	.	.	PUNCT
ejpam-1354	65	1	a	a	DET
ejpam-1354	65	2	measure	measure	NOUN
ejpam-1354	65	3	m	m	NOUN
ejpam-1354	65	4	∈	∈	NOUN
ejpam-1354	65	5	m+(x	m+(x	PRON
ejpam-1354	65	6	)	)	PUNCT
ejpam-1354	65	7	is	be	AUX
ejpam-1354	65	8	given	give	VERB
ejpam-1354	65	9	as	as	ADP
ejpam-1354	65	10	m=	m=	VERB
ejpam-1354	65	11	∑	∑	PROPN
ejpam-1354	65	12	x∈x	x∈x	NOUN
ejpam-1354	65	13	m(x)δx	m(x)δx	PROPN
ejpam-1354	66	1	=	=	SYM
ejpam-1354	66	2	∑	∑	PUNCT
ejpam-1354	66	3	x∈s(m	x∈s(m	PROPN
ejpam-1354	66	4	)	)	PUNCT
ejpam-1354	66	5	m(x)δx	m(x)δx	PROPN
ejpam-1354	66	6	(	(	PUNCT
ejpam-1354	66	7	3	3	NUM
ejpam-1354	66	8	)	)	PUNCT
ejpam-1354	66	9	where	where	SCONJ
ejpam-1354	66	10	δx	δx	PROPN
ejpam-1354	66	11	denotes	denote	VERB
ejpam-1354	66	12	the	the	DET
ejpam-1354	66	13	kronecker	kronecker	NOUN
ejpam-1354	66	14	symbol	symbol	NOUN
ejpam-1354	66	15	and	and	CCONJ
ejpam-1354	66	16	by	by	ADP
ejpam-1354	66	17	s(m	s(m	PROPN
ejpam-1354	66	18	)	)	PUNCT
ejpam-1354	66	19	we	we	PRON
ejpam-1354	66	20	denote	denote	VERB
ejpam-1354	66	21	the	the	DET
ejpam-1354	66	22	support	support	NOUN
ejpam-1354	66	23	of	of	ADP
ejpam-1354	66	24	m	m	AUX
ejpam-1354	66	25	given	give	VERB
ejpam-1354	66	26	as	as	ADP
ejpam-1354	66	27	s(m	s(m	PROPN
ejpam-1354	66	28	)	)	PUNCT
ejpam-1354	66	29	:	:	PUNCT
ejpam-1354	66	30	=	=	PUNCT
ejpam-1354	66	31	�	�	PROPN
ejpam-1354	66	32	y	y	PROPN
ejpam-1354	66	33	∈	∈	PROPN
ejpam-1354	66	34	x	x	PUNCT
ejpam-1354	66	35	|m(y	|m(y	PROPN
ejpam-1354	66	36	)	)	PUNCT
ejpam-1354	66	37	>	>	X
ejpam-1354	66	38	0	0	PUNCT
ejpam-1354	66	39	.	.	PUNCT
ejpam-1354	67	1	definition	definition	NOUN
ejpam-1354	67	2	1	1	NUM
ejpam-1354	67	3	.	.	PUNCT
ejpam-1354	68	1	let	let	VERB
ejpam-1354	68	2	a	a	DET
ejpam-1354	68	3	pair	pair	NOUN
ejpam-1354	68	4	(	(	PUNCT
ejpam-1354	68	5	a	a	PRON
ejpam-1354	68	6	,	,	PUNCT
ejpam-1354	68	7	a∗	a∗	ADJ
ejpam-1354	68	8	)	)	PUNCT
ejpam-1354	68	9	∈	∈	PROPN
ejpam-1354	68	10	x	x	SYM
ejpam-1354	68	11	×	×	NOUN
ejpam-1354	68	12	x	x	PUNCT
ejpam-1354	68	13	operates	operate	VERB
ejpam-1354	68	14	on	on	ADP
ejpam-1354	68	15	the	the	DET
ejpam-1354	68	16	set	set	NOUN
ejpam-1354	68	17	m+(x	m+(x	PROPN
ejpam-1354	68	18	)	)	PUNCT
ejpam-1354	68	19	as	as	ADP
ejpam-1354	68	20	following	follow	VERB
ejpam-1354	68	21	m	m	PROPN
ejpam-1354	68	22	7→m∗	7→m∗	NUM
ejpam-1354	68	23	=	=	SYM
ejpam-1354	68	24	(	(	PUNCT
ejpam-1354	68	25	a	a	PRON
ejpam-1354	68	26	,	,	PUNCT
ejpam-1354	68	27	a∗	a∗	NOUN
ejpam-1354	68	28	,	,	PUNCT
ejpam-1354	68	29	m	m	PROPN
ejpam-1354	68	30	)	)	PUNCT
ejpam-1354	68	31	(	(	PUNCT
ejpam-1354	68	32	4	4	X
ejpam-1354	68	33	)	)	PUNCT
ejpam-1354	68	34	m∗(x	m∗(x	NOUN
ejpam-1354	68	35	)	)	PUNCT
ejpam-1354	68	36	:	:	PUNCT
ejpam-1354	69	1	=	=	PUNCT
ejpam-1354	69	2			NOUN
ejpam-1354	69	3			PRON
ejpam-1354	69	4			NOUN
ejpam-1354	69	5	m(x	m(x	PROPN
ejpam-1354	69	6	)	)	PUNCT
ejpam-1354	69	7	;	;	PUNCT
ejpam-1354	69	8	if	if	SCONJ
ejpam-1354	69	9	x	x	X
ejpam-1354	69	10	/∈	/∈	PUNCT
ejpam-1354	69	11	{	{	PUNCT
ejpam-1354	69	12	a	a	PRON
ejpam-1354	69	13	,	,	PUNCT
ejpam-1354	69	14	a∗	a∗	PROPN
ejpam-1354	69	15	}	}	PUNCT
ejpam-1354	69	16	,	,	PUNCT
ejpam-1354	69	17	0	0	NUM
ejpam-1354	69	18	;	;	PUNCT
ejpam-1354	69	19	if	if	SCONJ
ejpam-1354	69	20	x	x	X
ejpam-1354	69	21	=	=	SYM
ejpam-1354	69	22	a	a	PRON
ejpam-1354	69	23	,	,	PUNCT
ejpam-1354	69	24	m(a	m(a	NOUN
ejpam-1354	69	25	)	)	PUNCT
ejpam-1354	69	26	+	+	NOUN
ejpam-1354	69	27	m(a∗	m(a∗	X
ejpam-1354	69	28	)	)	PUNCT
ejpam-1354	69	29	;	;	PUNCT
ejpam-1354	69	30	if	if	SCONJ
ejpam-1354	69	31	x	x	SYM
ejpam-1354	69	32	=	=	NOUN
ejpam-1354	69	33	a∗.	a∗.	NOUN
ejpam-1354	69	34	the	the	DET
ejpam-1354	69	35	mapping	mapping	NOUN
ejpam-1354	69	36	above	above	ADV
ejpam-1354	69	37	is	be	AUX
ejpam-1354	69	38	a	a	DET
ejpam-1354	69	39	mass	mass	ADJ
ejpam-1354	69	40	translating	translating	NOUN
ejpam-1354	69	41	map	map	NOUN
ejpam-1354	69	42	.	.	PUNCT
ejpam-1354	70	1	where	where	SCONJ
ejpam-1354	70	2	,	,	PUNCT
ejpam-1354	70	3	the	the	DET
ejpam-1354	70	4	move	move	NOUN
ejpam-1354	70	5	of	of	ADP
ejpam-1354	70	6	a	a	PRON
ejpam-1354	70	7	to	to	ADP
ejpam-1354	70	8	a∗	a∗	PROPN
ejpam-1354	70	9	means	mean	VERB
ejpam-1354	70	10	that	that	SCONJ
ejpam-1354	70	11	the	the	DET
ejpam-1354	70	12	mass	mass	ADJ
ejpam-1354	70	13	point	point	NOUN
ejpam-1354	70	14	of	of	ADP
ejpam-1354	70	15	a∗	a∗	NOUN
ejpam-1354	70	16	will	will	AUX
ejpam-1354	70	17	be	be	AUX
ejpam-1354	70	18	adjusted	adjust	VERB
ejpam-1354	70	19	by	by	ADP
ejpam-1354	70	20	a	a	DET
ejpam-1354	70	21	new	new	ADJ
ejpam-1354	70	22	mass	mass	NOUN
ejpam-1354	70	23	,	,	PUNCT
ejpam-1354	70	24	namely	namely	ADV
ejpam-1354	70	25	the	the	DET
ejpam-1354	70	26	mass	mass	NOUN
ejpam-1354	70	27	of	of	ADP
ejpam-1354	70	28	a.	a.	NOUN
ejpam-1354	70	29	the	the	DET
ejpam-1354	70	30	fussing	fussing	NOUN
ejpam-1354	70	31	operator	operator	NOUN
ejpam-1354	70	32	(	(	PUNCT
ejpam-1354	70	33	4	4	NUM
ejpam-1354	70	34	)	)	PUNCT
ejpam-1354	70	35	has	have	VERB
ejpam-1354	70	36	different	different	ADJ
ejpam-1354	70	37	interpretations	interpretation	NOUN
ejpam-1354	70	38	,	,	PUNCT
ejpam-1354	70	39	namely	namely	ADV
ejpam-1354	70	40	if	if	SCONJ
ejpam-1354	70	41	the	the	DET
ejpam-1354	70	42	agents	agent	NOUN
ejpam-1354	70	43	a	a	PRON
ejpam-1354	70	44	with	with	ADP
ejpam-1354	70	45	identity	identity	NOUN
ejpam-1354	70	46	like	like	ADP
ejpam-1354	70	47	a	a	DET
ejpam-1354	70	48	bird	bird	NOUN
ejpam-1354	70	49	or	or	CCONJ
ejpam-1354	70	50	a	a	DET
ejpam-1354	70	51	fish	fish	NOUN
ejpam-1354	70	52	,	,	PUNCT
ejpam-1354	70	53	so	so	CCONJ
ejpam-1354	70	54	the	the	DET
ejpam-1354	70	55	moving	move	VERB
ejpam-1354	70	56	action	action	NOUN
ejpam-1354	70	57	represents	represent	VERB
ejpam-1354	70	58	for	for	ADP
ejpam-1354	70	59	example	example	NOUN
ejpam-1354	70	60	the	the	DET
ejpam-1354	70	61	grouping	group	VERB
ejpam-1354	70	62	phenomena	phenomenon	NOUN
ejpam-1354	70	63	either	either	CCONJ
ejpam-1354	70	64	by	by	ADP
ejpam-1354	70	65	forming	form	VERB
ejpam-1354	70	66	a	a	DET
ejpam-1354	70	67	massive	massive	ADJ
ejpam-1354	70	68	group	group	NOUN
ejpam-1354	70	69	or	or	CCONJ
ejpam-1354	70	70	several	several	ADJ
ejpam-1354	70	71	ε	ε	PROPN
ejpam-1354	70	72	distanced	distance	VERB
ejpam-1354	70	73	subgroups	subgroup	NOUN
ejpam-1354	70	74	.	.	PUNCT
ejpam-1354	71	1	but	but	CCONJ
ejpam-1354	71	2	if	if	SCONJ
ejpam-1354	71	3	the	the	DET
ejpam-1354	71	4	considered	consider	VERB
ejpam-1354	71	5	agent	agent	NOUN
ejpam-1354	71	6	is	be	AUX
ejpam-1354	71	7	identicalness	identicalness	NOUN
ejpam-1354	71	8	the	the	DET
ejpam-1354	71	9	fusing	fuse	VERB
ejpam-1354	71	10	characteristic	characteristic	NOUN
ejpam-1354	71	11	explains	explain	VERB
ejpam-1354	71	12	the	the	DET
ejpam-1354	71	13	physical	physical	ADJ
ejpam-1354	71	14	fusion	fusion	NOUN
ejpam-1354	71	15	of	of	ADP
ejpam-1354	71	16	masses	masse	NOUN
ejpam-1354	71	17	.	.	PUNCT
ejpam-1354	72	1	one	one	NUM
ejpam-1354	72	2	of	of	ADP
ejpam-1354	72	3	our	our	PRON
ejpam-1354	72	4	main	main	ADJ
ejpam-1354	72	5	concerns	concern	NOUN
ejpam-1354	72	6	is	be	AUX
ejpam-1354	72	7	to	to	PART
ejpam-1354	72	8	define	define	VERB
ejpam-1354	72	9	and	and	CCONJ
ejpam-1354	72	10	to	to	PART
ejpam-1354	72	11	analyze	analyze	VERB
ejpam-1354	72	12	the	the	DET
ejpam-1354	72	13	local	local	ADJ
ejpam-1354	72	14	and	and	CCONJ
ejpam-1354	72	15	the	the	DET
ejpam-1354	72	16	global	global	ADJ
ejpam-1354	72	17	energies	energy	NOUN
ejpam-1354	72	18	already	already	ADV
ejpam-1354	72	19	mentioned	mention	VERB
ejpam-1354	72	20	by	by	ADP
ejpam-1354	72	21	equations	equation	NOUN
ejpam-1354	72	22	(	(	PUNCT
ejpam-1354	72	23	1	1	NUM
ejpam-1354	72	24	)	)	PUNCT
ejpam-1354	72	25	and	and	CCONJ
ejpam-1354	72	26	(	(	PUNCT
ejpam-1354	72	27	2	2	X
ejpam-1354	72	28	)	)	PUNCT
ejpam-1354	72	29	with	with	ADP
ejpam-1354	72	30	respect	respect	NOUN
ejpam-1354	72	31	to	to	ADP
ejpam-1354	72	32	a	a	DET
ejpam-1354	72	33	positive	positive	ADJ
ejpam-1354	72	34	discrete	discrete	ADJ
ejpam-1354	72	35	measure	measure	NOUN
ejpam-1354	72	36	.	.	PUNCT
ejpam-1354	73	1	definition	definition	NOUN
ejpam-1354	73	2	2	2	NUM
ejpam-1354	73	3	.	.	PUNCT
ejpam-1354	74	1	for	for	ADP
ejpam-1354	74	2	a	a	DET
ejpam-1354	74	3	fixed	fix	VERB
ejpam-1354	74	4	real	real	ADJ
ejpam-1354	74	5	number	number	NOUN
ejpam-1354	74	6	ε	ε	PROPN
ejpam-1354	74	7	>	>	PUNCT
ejpam-1354	74	8	0	0	PROPN
ejpam-1354	74	9	and	and	CCONJ
ejpam-1354	74	10	a	a	DET
ejpam-1354	74	11	given	give	VERB
ejpam-1354	74	12	n	n	NUM
ejpam-1354	74	13	points	point	NOUN
ejpam-1354	74	14	metric	metric	ADJ
ejpam-1354	74	15	metric	metric	ADJ
ejpam-1354	74	16	space	space	NOUN
ejpam-1354	74	17	,	,	PUNCT
ejpam-1354	74	18	the	the	DET
ejpam-1354	74	19	ε	ε	PROPN
ejpam-1354	74	20	-	-	PUNCT
ejpam-1354	74	21	energy	energy	NOUN
ejpam-1354	74	22	of	of	ADP
ejpam-1354	74	23	mass	mass	ADJ
ejpam-1354	74	24	point	point	NOUN
ejpam-1354	74	25	a	a	DET
ejpam-1354	74	26	∈	∈	NOUN
ejpam-1354	74	27	x	x	PUNCT
ejpam-1354	74	28	with	with	ADP
ejpam-1354	74	29	respect	respect	NOUN
ejpam-1354	74	30	to	to	ADP
ejpam-1354	74	31	a	a	DET
ejpam-1354	74	32	positive	positive	ADJ
ejpam-1354	74	33	measure	measure	NOUN
ejpam-1354	74	34	m	m	VERB
ejpam-1354	74	35	is	be	AUX
ejpam-1354	74	36	eε(a	eε(a	VERB
ejpam-1354	74	37	,	,	PUNCT
ejpam-1354	74	38	m	m	NOUN
ejpam-1354	74	39	)	)	PUNCT
ejpam-1354	74	40	=	=	SYM
ejpam-1354	74	41	∑	∑	PUNCT
ejpam-1354	74	42	d(a	d(a	PROPN
ejpam-1354	74	43	,	,	PUNCT
ejpam-1354	74	44	y)≤ε	y)≤ε	NOUN
ejpam-1354	74	45	m(y)d2(a	m(y)d2(a	PROPN
ejpam-1354	74	46	,	,	PUNCT
ejpam-1354	74	47	y	y	PROPN
ejpam-1354	74	48	)	)	PUNCT
ejpam-1354	74	49	,	,	PUNCT
ejpam-1354	74	50	(	(	PUNCT
ejpam-1354	74	51	5	5	X
ejpam-1354	74	52	)	)	PUNCT
ejpam-1354	74	53	m.	m.	NOUN
ejpam-1354	74	54	zahri	zahri	PROPN
ejpam-1354	74	55	/	/	SYM
ejpam-1354	74	56	eur	eur	PROPN
ejpam-1354	74	57	.	.	PUNCT
ejpam-1354	75	1	j.	j.	PROPN
ejpam-1354	75	2	pure	pure	PROPN
ejpam-1354	75	3	appl	appl	PROPN
ejpam-1354	75	4	.	.	PROPN
ejpam-1354	75	5	math	math	PROPN
ejpam-1354	75	6	,	,	PUNCT
ejpam-1354	75	7	6	6	NUM
ejpam-1354	75	8	(	(	PUNCT
ejpam-1354	75	9	2013	2013	NUM
ejpam-1354	75	10	)	)	PUNCT
ejpam-1354	75	11	,	,	PUNCT
ejpam-1354	75	12	172	172	NUM
ejpam-1354	75	13	-	-	SYM
ejpam-1354	75	14	188	188	NUM
ejpam-1354	75	15	175	175	NUM
ejpam-1354	75	16	and	and	CCONJ
ejpam-1354	75	17	the	the	DET
ejpam-1354	75	18	global	global	ADJ
ejpam-1354	75	19	ε	ε	PROPN
ejpam-1354	75	20	-	-	PUNCT
ejpam-1354	75	21	energy	energy	NOUN
ejpam-1354	75	22	of	of	ADP
ejpam-1354	75	23	a	a	DET
ejpam-1354	75	24	positive	positive	ADJ
ejpam-1354	75	25	measure	measure	NOUN
ejpam-1354	75	26	m	m	VERB
ejpam-1354	75	27	in	in	ADP
ejpam-1354	75	28	m+(x	m+(x	PROPN
ejpam-1354	75	29	)	)	PUNCT
ejpam-1354	75	30	is	be	AUX
ejpam-1354	75	31	given	give	VERB
ejpam-1354	75	32	as	as	ADP
ejpam-1354	75	33	:	:	PUNCT
ejpam-1354	75	34	eε(m	eε(m	NUM
ejpam-1354	75	35	)	)	PUNCT
ejpam-1354	75	36	=	=	PUNCT
ejpam-1354	75	37	∑	∑	PUNCT
ejpam-1354	75	38	d(x	d(x	PROPN
ejpam-1354	75	39	,	,	PUNCT
ejpam-1354	75	40	y)≤ε	y)≤ε	NOUN
ejpam-1354	75	41	m(x)m(y)d2(x	m(x)m(y)d2(x	NOUN
ejpam-1354	75	42	,	,	PUNCT
ejpam-1354	75	43	y	y	PROPN
ejpam-1354	75	44	)	)	PUNCT
ejpam-1354	75	45	.	.	PUNCT
ejpam-1354	76	1	(	(	PUNCT
ejpam-1354	76	2	6	6	NUM
ejpam-1354	76	3	)	)	PUNCT
ejpam-1354	76	4	to	to	PART
ejpam-1354	76	5	observe	observe	VERB
ejpam-1354	76	6	the	the	DET
ejpam-1354	76	7	energy	energy	NOUN
ejpam-1354	76	8	evolution	evolution	NOUN
ejpam-1354	76	9	of	of	ADP
ejpam-1354	76	10	both	both	CCONJ
ejpam-1354	76	11	the	the	DET
ejpam-1354	76	12	local	local	ADJ
ejpam-1354	76	13	and	and	CCONJ
ejpam-1354	76	14	the	the	DET
ejpam-1354	76	15	global	global	ADJ
ejpam-1354	76	16	energies	energy	NOUN
ejpam-1354	76	17	according	accord	VERB
ejpam-1354	76	18	to	to	ADP
ejpam-1354	76	19	the	the	DET
ejpam-1354	76	20	moves	move	NOUN
ejpam-1354	76	21	presented	present	VERB
ejpam-1354	76	22	in	in	ADP
ejpam-1354	76	23	definition	definition	NOUN
ejpam-1354	76	24	1	1	NUM
ejpam-1354	76	25	,	,	PUNCT
ejpam-1354	76	26	we	we	PRON
ejpam-1354	76	27	propose	propose	VERB
ejpam-1354	76	28	the	the	DET
ejpam-1354	76	29	following	following	ADJ
ejpam-1354	76	30	example	example	NOUN
ejpam-1354	76	31	:	:	PUNCT
ejpam-1354	76	32	example	example	NOUN
ejpam-1354	77	1	1	1	X
ejpam-1354	77	2	.	.	X
ejpam-1354	78	1	we	we	PRON
ejpam-1354	78	2	consider	consider	VERB
ejpam-1354	78	3	a	a	DET
ejpam-1354	78	4	three	three	NUM
ejpam-1354	78	5	points	point	NOUN
ejpam-1354	78	6	metric	metric	ADJ
ejpam-1354	78	7	space	space	NOUN
ejpam-1354	78	8	as	as	ADP
ejpam-1354	78	9	subset	subset	NOUN
ejpam-1354	78	10	of	of	ADP
ejpam-1354	78	11	the	the	DET
ejpam-1354	78	12	real	real	ADJ
ejpam-1354	78	13	line	line	NOUN
ejpam-1354	78	14	.	.	PUNCT
ejpam-1354	79	1	we	we	PRON
ejpam-1354	79	2	assume	assume	VERB
ejpam-1354	79	3	that	that	SCONJ
ejpam-1354	79	4	two	two	NUM
ejpam-1354	79	5	neighbors	neighbor	NOUN
ejpam-1354	79	6	points	point	VERB
ejpam-1354	79	7	have	have	VERB
ejpam-1354	79	8	a	a	DET
ejpam-1354	79	9	distance	distance	NOUN
ejpam-1354	79	10	of	of	ADP
ejpam-1354	79	11	one	one	NUM
ejpam-1354	79	12	and	and	CCONJ
ejpam-1354	79	13	we	we	PRON
ejpam-1354	79	14	define	define	VERB
ejpam-1354	79	15	a	a	DET
ejpam-1354	79	16	measure	measure	NOUN
ejpam-1354	79	17	m	m	NOUN
ejpam-1354	79	18	by	by	ADP
ejpam-1354	79	19	the	the	DET
ejpam-1354	79	20	masses	masse	NOUN
ejpam-1354	79	21	punted	punt	VERB
ejpam-1354	79	22	in	in	ADP
ejpam-1354	79	23	the	the	DET
ejpam-1354	79	24	three	three	NUM
ejpam-1354	79	25	points	point	NOUN
ejpam-1354	79	26	.	.	PUNCT
ejpam-1354	80	1	we	we	PRON
ejpam-1354	80	2	denote	denote	VERB
ejpam-1354	80	3	the	the	DET
ejpam-1354	80	4	mass	mass	NOUN
ejpam-1354	80	5	of	of	ADP
ejpam-1354	80	6	m	m	PRON
ejpam-1354	80	7	in	in	ADP
ejpam-1354	80	8	each	each	DET
ejpam-1354	80	9	point	point	NOUN
ejpam-1354	80	10	by	by	ADP
ejpam-1354	80	11	the	the	DET
ejpam-1354	80	12	the	the	DET
ejpam-1354	80	13	numbers	number	NOUN
ejpam-1354	80	14	given	give	VERB
ejpam-1354	80	15	on	on	ADP
ejpam-1354	80	16	the	the	DET
ejpam-1354	80	17	figures	figure	NOUN
ejpam-1354	80	18	1	1	NUM
ejpam-1354	80	19	.	.	X
ejpam-1354	81	1	for	for	ADP
ejpam-1354	81	2	ε	ε	PROPN
ejpam-1354	81	3	=	=	SYM
ejpam-1354	81	4	1	1	NUM
ejpam-1354	81	5	let	let	VERB
ejpam-1354	81	6	us	we	PRON
ejpam-1354	81	7	consider	consider	VERB
ejpam-1354	81	8	three	three	NUM
ejpam-1354	81	9	moves	move	NOUN
ejpam-1354	81	10	,	,	PUNCT
ejpam-1354	81	11	namely	namely	ADV
ejpam-1354	81	12	(	(	PUNCT
ejpam-1354	81	13	a	a	X
ejpam-1354	81	14	)	)	PUNCT
ejpam-1354	81	15	,	,	PUNCT
ejpam-1354	81	16	(	(	PUNCT
ejpam-1354	81	17	b	b	X
ejpam-1354	81	18	)	)	PUNCT
ejpam-1354	81	19	and	and	CCONJ
ejpam-1354	81	20	(	(	PUNCT
ejpam-1354	81	21	c	c	NOUN
ejpam-1354	81	22	)	)	PUNCT
ejpam-1354	81	23	.	.	PUNCT
ejpam-1354	82	1	2	2	NUM
ejpam-1354	82	2	1	1	NUM
ejpam-1354	82	3	1	1	NUM
ejpam-1354	82	4	3	3	NUM
ejpam-1354	82	5	1	1	NUM
ejpam-1354	82	6	move	move	NOUN
ejpam-1354	82	7	move	move	NOUN
ejpam-1354	82	8	2	2	NUM
ejpam-1354	82	9	2	2	NUM
ejpam-1354	82	10	2	2	NUM
ejpam-1354	82	11	2	2	NUM
ejpam-1354	82	12	1	1	NUM
ejpam-1354	82	13	11	11	NUM
ejpam-1354	82	14	1	1	NUM
ejpam-1354	82	15	11	11	NUM
ejpam-1354	82	16	2	2	NUM
ejpam-1354	82	17	2	2	NUM
ejpam-1354	82	18	132	132	NUM
ejpam-1354	82	19	move	move	NOUN
ejpam-1354	82	20	(	(	PUNCT
ejpam-1354	82	21	a	a	DET
ejpam-1354	82	22	)	)	PUNCT
ejpam-1354	82	23	move	move	NOUN
ejpam-1354	82	24	(	(	PUNCT
ejpam-1354	82	25	c	c	NOUN
ejpam-1354	82	26	)	)	PUNCT
ejpam-1354	82	27	move	move	NOUN
ejpam-1354	82	28	(	(	PUNCT
ejpam-1354	82	29	d	d	NOUN
ejpam-1354	82	30	)	)	PUNCT
ejpam-1354	82	31	move	move	NOUN
ejpam-1354	82	32	(	(	PUNCT
ejpam-1354	82	33	b	b	NOUN
ejpam-1354	82	34	)	)	PUNCT
ejpam-1354	82	35	movemove	movemove	NOUN
ejpam-1354	82	36	x	x	SYM
ejpam-1354	82	37	1	1	NUM
ejpam-1354	82	38	x	x	SYM
ejpam-1354	82	39	2	2	NUM
ejpam-1354	82	40	x	x	SYM
ejpam-1354	82	41	3	3	NUM
ejpam-1354	82	42	x	x	SYM
ejpam-1354	82	43	1	1	NUM
ejpam-1354	82	44	x	x	SYM
ejpam-1354	82	45	2	2	NUM
ejpam-1354	82	46	x	x	SYM
ejpam-1354	82	47	3	3	NUM
ejpam-1354	82	48	x	x	SYM
ejpam-1354	82	49	3	3	NUM
ejpam-1354	82	50	x	x	SYM
ejpam-1354	82	51	2x	2x	NUM
ejpam-1354	82	52	1	1	NUM
ejpam-1354	82	53	x	x	SYM
ejpam-1354	82	54	1	1	NUM
ejpam-1354	82	55	x	x	SYM
ejpam-1354	82	56	2	2	NUM
ejpam-1354	82	57	x	x	SYM
ejpam-1354	82	58	3	3	NUM
ejpam-1354	82	59	figure	figure	NOUN
ejpam-1354	82	60	1	1	NUM
ejpam-1354	82	61	:	:	PUNCT
ejpam-1354	82	62	examples	example	NOUN
ejpam-1354	82	63	of	of	ADP
ejpam-1354	82	64	moves	move	NOUN
ejpam-1354	82	65	show	show	VERB
ejpam-1354	82	66	that	that	SCONJ
ejpam-1354	82	67	the	the	DET
ejpam-1354	82	68	resulting	result	VERB
ejpam-1354	82	69	masses	masse	NOUN
ejpam-1354	82	70	are	be	AUX
ejpam-1354	82	71	given	give	VERB
ejpam-1354	82	72	as	as	ADP
ejpam-1354	82	73	initial	initial	ADJ
ejpam-1354	82	74	mass	mass	ADJ
ejpam-1354	82	75	distribution	distribution	NOUN
ejpam-1354	82	76	:	:	PUNCT
ejpam-1354	82	77	m=	m=	X
ejpam-1354	82	78	2δ1+δx2	2δ1+δx2	NUM
ejpam-1354	82	79	+	+	ADJ
ejpam-1354	82	80	δx3	δx3	PROPN
ejpam-1354	82	81	move	move	NOUN
ejpam-1354	82	82	(	(	PUNCT
ejpam-1354	82	83	a	a	X
ejpam-1354	82	84	):	):	PUNCT
ejpam-1354	82	85	m−→	m−→	ADJ
ejpam-1354	82	86	m∗a	m∗a	PUNCT
ejpam-1354	82	87	=	=	SYM
ejpam-1354	82	88	3δx2	3δx2	NUM
ejpam-1354	82	89	+	+	NOUN
ejpam-1354	82	90	δx3	δx3	PROPN
ejpam-1354	82	91	.	.	PUNCT
ejpam-1354	83	1	move	move	NOUN
ejpam-1354	83	2	(	(	PUNCT
ejpam-1354	83	3	b	b	NOUN
ejpam-1354	83	4	):	):	PUNCT
ejpam-1354	83	5	m−→	m−→	ADJ
ejpam-1354	83	6	m∗b	m∗b	PRON
ejpam-1354	83	7	=	=	SYM
ejpam-1354	83	8	2δx1	2δx1	NUM
ejpam-1354	83	9	+	+	CCONJ
ejpam-1354	83	10	2δx2	2δx2	NUM
ejpam-1354	83	11	.	.	PUNCT
ejpam-1354	84	1	move	move	NOUN
ejpam-1354	84	2	(	(	PUNCT
ejpam-1354	84	3	c	c	NOUN
ejpam-1354	84	4	):	):	PUNCT
ejpam-1354	84	5	m−→	m−→	NOUN
ejpam-1354	84	6	m∗c	m∗c	NUM
ejpam-1354	84	7	=	=	SYM
ejpam-1354	84	8	2δx1	2δx1	NUM
ejpam-1354	84	9	+	+	NUM
ejpam-1354	84	10	2δx3	2δx3	NUM
ejpam-1354	84	11	.	.	PUNCT
ejpam-1354	85	1	move	move	NOUN
ejpam-1354	85	2	(	(	PUNCT
ejpam-1354	85	3	d	d	NOUN
ejpam-1354	85	4	):	):	PUNCT
ejpam-1354	85	5	m−→	m−→	ADJ
ejpam-1354	85	6	m∗d	m∗d	X
ejpam-1354	85	7	=	=	SYM
ejpam-1354	85	8	3δx1	3δx1	NUM
ejpam-1354	85	9	+	+	NOUN
ejpam-1354	85	10	δx3	δx3	PROPN
ejpam-1354	85	11	.	.	PUNCT
ejpam-1354	86	1	figure	figure	VERB
ejpam-1354	86	2	1	1	NUM
ejpam-1354	86	3	presents	present	NOUN
ejpam-1354	86	4	three	three	NUM
ejpam-1354	86	5	example	example	NOUN
ejpam-1354	86	6	of	of	ADP
ejpam-1354	86	7	moves	move	NOUN
ejpam-1354	86	8	:	:	PUNCT
ejpam-1354	86	9	m.	m.	NOUN
ejpam-1354	86	10	zahri	zahri	PROPN
ejpam-1354	86	11	/	/	SYM
ejpam-1354	86	12	eur	eur	PROPN
ejpam-1354	86	13	.	.	PUNCT
ejpam-1354	87	1	j.	j.	PROPN
ejpam-1354	87	2	pure	pure	PROPN
ejpam-1354	87	3	appl	appl	PROPN
ejpam-1354	87	4	.	.	PROPN
ejpam-1354	87	5	math	math	PROPN
ejpam-1354	87	6	,	,	PUNCT
ejpam-1354	87	7	6	6	NUM
ejpam-1354	87	8	(	(	PUNCT
ejpam-1354	87	9	2013	2013	NUM
ejpam-1354	87	10	)	)	PUNCT
ejpam-1354	87	11	,	,	PUNCT
ejpam-1354	87	12	172	172	NUM
ejpam-1354	87	13	-	-	SYM
ejpam-1354	87	14	188	188	NUM
ejpam-1354	87	15	176	176	NUM
ejpam-1354	87	16	(	(	PUNCT
ejpam-1354	87	17	a	a	NOUN
ejpam-1354	87	18	)	)	PUNCT
ejpam-1354	87	19	the	the	DET
ejpam-1354	87	20	mass	mass	NOUN
ejpam-1354	87	21	2	2	NUM
ejpam-1354	87	22	in	in	ADP
ejpam-1354	87	23	x1	x1	PROPN
ejpam-1354	87	24	moves	move	NOUN
ejpam-1354	87	25	to	to	ADP
ejpam-1354	87	26	the	the	DET
ejpam-1354	87	27	mass	mass	NOUN
ejpam-1354	87	28	1	1	NUM
ejpam-1354	87	29	on	on	ADP
ejpam-1354	87	30	the	the	DET
ejpam-1354	87	31	middle	middle	NOUN
ejpam-1354	87	32	(	(	PUNCT
ejpam-1354	87	33	i.e.	i.e.	X
ejpam-1354	87	34	posted	post	VERB
ejpam-1354	87	35	at	at	ADP
ejpam-1354	87	36	x2	x2	PROPN
ejpam-1354	87	37	)	)	PUNCT
ejpam-1354	87	38	.	.	PUNCT
ejpam-1354	88	1	i.e.	i.e.	X
ejpam-1354	88	2	m→	m→	ADP
ejpam-1354	88	3	m∗a	m∗a	NUM
ejpam-1354	88	4	with	with	ADP
ejpam-1354	88	5	conserving	conserve	VERB
ejpam-1354	88	6	global	global	ADJ
ejpam-1354	88	7	energy	energy	NOUN
ejpam-1354	88	8	e(m	e(m	PROPN
ejpam-1354	88	9	)	)	PUNCT
ejpam-1354	88	10	=	=	SYM
ejpam-1354	88	11	e(m∗a	e(m∗a	NOUN
ejpam-1354	88	12	)	)	PUNCT
ejpam-1354	88	13	=	=	SYM
ejpam-1354	89	1	6	6	X
ejpam-1354	89	2	.	.	PUNCT
ejpam-1354	89	3	consequently	consequently	ADV
ejpam-1354	89	4	,	,	PUNCT
ejpam-1354	89	5	the	the	DET
ejpam-1354	89	6	total	total	ADJ
ejpam-1354	89	7	energy	energy	NOUN
ejpam-1354	89	8	does	do	AUX
ejpam-1354	89	9	not	not	PART
ejpam-1354	89	10	change	change	VERB
ejpam-1354	89	11	e(m	e(m	NOUN
ejpam-1354	89	12	)	)	PUNCT
ejpam-1354	89	13	=	=	SYM
ejpam-1354	89	14	e(m∗a	e(m∗a	NOUN
ejpam-1354	89	15	)	)	PUNCT
ejpam-1354	89	16	=	=	SYM
ejpam-1354	90	1	6	6	NUM
ejpam-1354	90	2	.	.	PUNCT
ejpam-1354	90	3	(	(	PUNCT
ejpam-1354	90	4	b	b	X
ejpam-1354	90	5	)	)	PUNCT
ejpam-1354	90	6	the	the	DET
ejpam-1354	90	7	mass	mass	NOUN
ejpam-1354	90	8	1	1	NUM
ejpam-1354	90	9	(	(	PUNCT
ejpam-1354	90	10	in	in	ADP
ejpam-1354	90	11	x3	x3	ADJ
ejpam-1354	90	12	)	)	PUNCT
ejpam-1354	90	13	on	on	ADP
ejpam-1354	90	14	the	the	DET
ejpam-1354	90	15	left	left	ADJ
ejpam-1354	90	16	moves	move	NOUN
ejpam-1354	90	17	to	to	ADP
ejpam-1354	90	18	the	the	DET
ejpam-1354	90	19	mass	mass	ADJ
ejpam-1354	90	20	one	one	NOUN
ejpam-1354	90	21	on	on	ADP
ejpam-1354	90	22	the	the	DET
ejpam-1354	90	23	middle	middle	NOUN
ejpam-1354	90	24	(	(	PUNCT
ejpam-1354	90	25	i.e.	i.e.	X
ejpam-1354	90	26	x2	x2	ADJ
ejpam-1354	90	27	)	)	PUNCT
ejpam-1354	90	28	,	,	PUNCT
ejpam-1354	90	29	hence	hence	ADV
ejpam-1354	90	30	,	,	PUNCT
ejpam-1354	90	31	m→	m→	NOUN
ejpam-1354	90	32	m∗	m∗	VERB
ejpam-1354	90	33	b	b	NOUN
ejpam-1354	90	34	with	with	ADP
ejpam-1354	90	35	increasing	increase	VERB
ejpam-1354	90	36	global	global	ADJ
ejpam-1354	90	37	energy	energy	NOUN
ejpam-1354	90	38	e(m	e(m	PROPN
ejpam-1354	90	39	)	)	PUNCT
ejpam-1354	90	40	=	=	PUNCT
ejpam-1354	91	1	6	6	NUM
ejpam-1354	91	2	<	<	X
ejpam-1354	91	3	e(m∗	e(m∗	X
ejpam-1354	91	4	b	b	NOUN
ejpam-1354	91	5	)	)	PUNCT
ejpam-1354	92	1	=	=	SYM
ejpam-1354	92	2	8	8	X
ejpam-1354	92	3	.	.	PUNCT
ejpam-1354	93	1	consequently	consequently	ADV
ejpam-1354	93	2	,	,	PUNCT
ejpam-1354	93	3	the	the	DET
ejpam-1354	93	4	total	total	ADJ
ejpam-1354	93	5	energy	energy	NOUN
ejpam-1354	93	6	increases	increase	VERB
ejpam-1354	93	7	e(m∗	e(m∗	ADJ
ejpam-1354	93	8	b	b	NOUN
ejpam-1354	93	9	)	)	PUNCT
ejpam-1354	93	10	=	=	SYM
ejpam-1354	93	11	8	8	NUM
ejpam-1354	93	12	:	:	PUNCT
ejpam-1354	93	13	(	(	PUNCT
ejpam-1354	93	14	c	c	X
ejpam-1354	93	15	)	)	PUNCT
ejpam-1354	93	16	the	the	DET
ejpam-1354	93	17	mass	mass	NOUN
ejpam-1354	93	18	1	1	NUM
ejpam-1354	93	19	in	in	ADP
ejpam-1354	93	20	x2	x2	PROPN
ejpam-1354	93	21	in	in	ADP
ejpam-1354	93	22	the	the	DET
ejpam-1354	93	23	middle	middle	ADJ
ejpam-1354	93	24	moves	move	NOUN
ejpam-1354	93	25	to	to	ADP
ejpam-1354	93	26	the	the	DET
ejpam-1354	93	27	mass	mass	NOUN
ejpam-1354	93	28	1	1	NUM
ejpam-1354	93	29	to	to	ADP
ejpam-1354	93	30	the	the	DET
ejpam-1354	93	31	right	right	ADJ
ejpam-1354	93	32	one	one	NUM
ejpam-1354	93	33	.	.	PUNCT
ejpam-1354	94	1	which	which	PRON
ejpam-1354	94	2	causes	cause	VERB
ejpam-1354	94	3	a	a	DET
ejpam-1354	94	4	vanishing	vanishing	NOUN
ejpam-1354	94	5	of	of	ADP
ejpam-1354	94	6	the	the	DET
ejpam-1354	94	7	total	total	ADJ
ejpam-1354	94	8	energy	energy	NOUN
ejpam-1354	94	9	:	:	PUNCT
ejpam-1354	94	10	m→	m→	NOUN
ejpam-1354	94	11	m∗c	m∗c	NUM
ejpam-1354	94	12	with	with	ADP
ejpam-1354	94	13	decreasing	decrease	VERB
ejpam-1354	94	14	global	global	ADJ
ejpam-1354	94	15	energyve(m	energyve(m	X
ejpam-1354	94	16	)	)	PUNCT
ejpam-1354	94	17	=	=	PUNCT
ejpam-1354	94	18	6	6	NUM
ejpam-1354	94	19	>	>	SYM
ejpam-1354	94	20	e(m∗c	e(m∗c	PROPN
ejpam-1354	94	21	)	)	PUNCT
ejpam-1354	95	1	=	=	SYM
ejpam-1354	95	2	0	0	X
ejpam-1354	95	3	.	.	PUNCT
ejpam-1354	96	1	(	(	PUNCT
ejpam-1354	96	2	d	d	X
ejpam-1354	96	3	)	)	PUNCT
ejpam-1354	96	4	the	the	DET
ejpam-1354	96	5	mass	mass	NOUN
ejpam-1354	96	6	1	1	NUM
ejpam-1354	96	7	in	in	ADP
ejpam-1354	96	8	x2	x2	PROPN
ejpam-1354	96	9	in	in	ADP
ejpam-1354	96	10	the	the	DET
ejpam-1354	96	11	middle	middle	ADJ
ejpam-1354	96	12	moves	move	NOUN
ejpam-1354	96	13	to	to	ADP
ejpam-1354	96	14	the	the	DET
ejpam-1354	96	15	mass	mass	NOUN
ejpam-1354	96	16	1	1	NUM
ejpam-1354	96	17	to	to	ADP
ejpam-1354	96	18	the	the	DET
ejpam-1354	96	19	left	left	ADJ
ejpam-1354	96	20	one	one	NUM
ejpam-1354	96	21	.	.	PUNCT
ejpam-1354	97	1	m→	m→	NOUN
ejpam-1354	97	2	m∗	m∗	VERB
ejpam-1354	97	3	d	d	NOUN
ejpam-1354	97	4	with	with	ADP
ejpam-1354	97	5	decreasing	decrease	VERB
ejpam-1354	97	6	global	global	ADJ
ejpam-1354	97	7	energy	energy	NOUN
ejpam-1354	97	8	e(m	e(m	PROPN
ejpam-1354	97	9	)	)	PUNCT
ejpam-1354	97	10	=	=	PUNCT
ejpam-1354	98	1	6	6	NUM
ejpam-1354	98	2	>	>	PUNCT
ejpam-1354	98	3	e(m∗	e(m∗	NUM
ejpam-1354	98	4	d	d	NOUN
ejpam-1354	98	5	)	)	PUNCT
ejpam-1354	99	1	=	=	SYM
ejpam-1354	99	2	0	0	X
ejpam-1354	99	3	.	.	PUNCT
ejpam-1354	100	1	in	in	ADP
ejpam-1354	100	2	our	our	PRON
ejpam-1354	100	3	model	model	NOUN
ejpam-1354	100	4	we	we	PRON
ejpam-1354	100	5	are	be	AUX
ejpam-1354	100	6	looking	look	VERB
ejpam-1354	100	7	for	for	ADP
ejpam-1354	100	8	a	a	DET
ejpam-1354	100	9	local	local	ADJ
ejpam-1354	100	10	rule	rule	NOUN
ejpam-1354	100	11	for	for	ADP
ejpam-1354	100	12	a	a	DET
ejpam-1354	100	13	move	move	NOUN
ejpam-1354	100	14	of	of	ADP
ejpam-1354	100	15	particles	particle	NOUN
ejpam-1354	100	16	,	,	PUNCT
ejpam-1354	100	17	which	which	PRON
ejpam-1354	100	18	causes	cause	VERB
ejpam-1354	100	19	an	an	DET
ejpam-1354	100	20	decreasing	decreasing	NOUN
ejpam-1354	100	21	of	of	ADP
ejpam-1354	100	22	the	the	DET
ejpam-1354	100	23	global	global	ADJ
ejpam-1354	100	24	energy	energy	NOUN
ejpam-1354	100	25	.	.	PUNCT
ejpam-1354	101	1	definition	definition	NOUN
ejpam-1354	101	2	3	3	NUM
ejpam-1354	101	3	.	.	PUNCT
ejpam-1354	102	1	a	a	DET
ejpam-1354	102	2	pair	pair	NOUN
ejpam-1354	102	3	of	of	ADP
ejpam-1354	102	4	masses	masse	NOUN
ejpam-1354	102	5	(	(	PUNCT
ejpam-1354	102	6	m	m	NOUN
ejpam-1354	102	7	,	,	PUNCT
ejpam-1354	102	8	m∗	m∗	PROPN
ejpam-1354	102	9	)	)	PUNCT
ejpam-1354	102	10	∈	∈	PROPN
ejpam-1354	102	11	m+(x	m+(x	PUNCT
ejpam-1354	102	12	)	)	PUNCT
ejpam-1354	102	13	×m+(x	×m+(x	PROPN
ejpam-1354	102	14	)	)	PUNCT
ejpam-1354	102	15	is	be	AUX
ejpam-1354	102	16	called	call	VERB
ejpam-1354	102	17	an	an	DET
ejpam-1354	102	18	ε	ε	NOUN
ejpam-1354	102	19	-	-	PUNCT
ejpam-1354	102	20	move	move	NOUN
ejpam-1354	102	21	,	,	PUNCT
ejpam-1354	102	22	if	if	SCONJ
ejpam-1354	102	23	there	there	PRON
ejpam-1354	102	24	is	be	VERB
ejpam-1354	102	25	a	a	DET
ejpam-1354	102	26	pair	pair	NOUN
ejpam-1354	102	27	of	of	ADP
ejpam-1354	102	28	mass	mass	ADJ
ejpam-1354	102	29	points	point	NOUN
ejpam-1354	102	30	(	(	PUNCT
ejpam-1354	102	31	a	a	PRON
ejpam-1354	102	32	,	,	PUNCT
ejpam-1354	102	33	a∗	a∗	ADJ
ejpam-1354	102	34	)	)	PUNCT
ejpam-1354	102	35	∈	∈	PROPN
ejpam-1354	102	36	x	x	X
ejpam-1354	102	37	×	×	NOUN
ejpam-1354	102	38	x	x	INTJ
ejpam-1354	102	39	such	such	ADJ
ejpam-1354	102	40	that	that	SCONJ
ejpam-1354	102	41	:	:	PUNCT
ejpam-1354	102	42	(	(	PUNCT
ejpam-1354	102	43	i	i	NOUN
ejpam-1354	102	44	)	)	PUNCT
ejpam-1354	102	45	m∗	m∗	VERB
ejpam-1354	102	46	=	=	SYM
ejpam-1354	102	47	(	(	PUNCT
ejpam-1354	102	48	a	a	PRON
ejpam-1354	102	49	,	,	PUNCT
ejpam-1354	102	50	a∗	a∗	NOUN
ejpam-1354	102	51	,	,	PUNCT
ejpam-1354	102	52	m	m	PROPN
ejpam-1354	102	53	)	)	PUNCT
ejpam-1354	102	54	,	,	PUNCT
ejpam-1354	102	55	(	(	PUNCT
ejpam-1354	102	56	ii	ii	NOUN
ejpam-1354	102	57	)	)	PUNCT
ejpam-1354	102	58	d(a	d(a	PROPN
ejpam-1354	102	59	,	,	PUNCT
ejpam-1354	102	60	a∗)≤	a∗)≤	PROPN
ejpam-1354	102	61	ε	ε	PROPN
ejpam-1354	102	62	,	,	PUNCT
ejpam-1354	102	63	(	(	PUNCT
ejpam-1354	102	64	neighborhood	neighborhood	NOUN
ejpam-1354	102	65	condition	condition	NOUN
ejpam-1354	102	66	)	)	PUNCT
ejpam-1354	102	67	(	(	PUNCT
ejpam-1354	102	68	iii	iii	NOUN
ejpam-1354	102	69	)	)	PUNCT
ejpam-1354	102	70	eε(a	eε(a	VERB
ejpam-1354	102	71	∗	∗	NOUN
ejpam-1354	102	72	,	,	PUNCT
ejpam-1354	102	73	m∗	m∗	NOUN
ejpam-1354	102	74	)	)	PUNCT
ejpam-1354	102	75	<	<	X
ejpam-1354	102	76	eε(a	eε(a	NOUN
ejpam-1354	102	77	,	,	PUNCT
ejpam-1354	102	78	m	m	PROPN
ejpam-1354	102	79	)	)	PUNCT
ejpam-1354	102	80	.	.	PUNCT
ejpam-1354	103	1	(	(	PUNCT
ejpam-1354	103	2	energy	energy	NOUN
ejpam-1354	103	3	-	-	PUNCT
ejpam-1354	103	4	minimizing	minimize	VERB
ejpam-1354	103	5	condition	condition	NOUN
ejpam-1354	103	6	)	)	PUNCT
ejpam-1354	103	7	figure	figure	NOUN
ejpam-1354	103	8	2	2	NUM
ejpam-1354	103	9	presents	present	VERB
ejpam-1354	103	10	an	an	DET
ejpam-1354	103	11	illustration	illustration	NOUN
ejpam-1354	103	12	of	of	ADP
ejpam-1354	103	13	an	an	DET
ejpam-1354	103	14	admissible	admissible	ADJ
ejpam-1354	103	15	move	move	NOUN
ejpam-1354	103	16	based	base	VERB
ejpam-1354	103	17	on	on	ADP
ejpam-1354	103	18	the	the	DET
ejpam-1354	103	19	energy	energy	NOUN
ejpam-1354	103	20	,	,	PUNCT
ejpam-1354	103	21	where	where	SCONJ
ejpam-1354	103	22	the	the	DET
ejpam-1354	103	23	particle	particle	NOUN
ejpam-1354	103	24	moves	move	VERB
ejpam-1354	103	25	to	to	ADP
ejpam-1354	103	26	a	a	DET
ejpam-1354	103	27	new	new	ADJ
ejpam-1354	103	28	position	position	NOUN
ejpam-1354	103	29	with	with	ADP
ejpam-1354	103	30	only	only	ADV
ejpam-1354	103	31	one	one	NUM
ejpam-1354	103	32	neighbors	neighbor	NOUN
ejpam-1354	103	33	:	:	PUNCT
ejpam-1354	103	34	definition	definition	NOUN
ejpam-1354	103	35	4	4	NUM
ejpam-1354	103	36	.	.	PUNCT
ejpam-1354	104	1	if	if	SCONJ
ejpam-1354	104	2	every	every	DET
ejpam-1354	104	3	pair	pair	NOUN
ejpam-1354	104	4	(	(	PUNCT
ejpam-1354	104	5	mi	mi	PROPN
ejpam-1354	104	6	,	,	PUNCT
ejpam-1354	104	7	mi+1	mi+1	NOUN
ejpam-1354	104	8	)	)	PUNCT
ejpam-1354	104	9	of	of	ADP
ejpam-1354	104	10	a	a	DET
ejpam-1354	104	11	nonnegative	nonnegative	ADJ
ejpam-1354	104	12	measures	measure	NOUN
ejpam-1354	104	13	is	be	AUX
ejpam-1354	104	14	an	an	DET
ejpam-1354	104	15	ε	ε	NOUN
ejpam-1354	104	16	-	-	PUNCT
ejpam-1354	104	17	move	move	NOUN
ejpam-1354	104	18	according	accord	VERB
ejpam-1354	104	19	to	to	ADP
ejpam-1354	104	20	definition	definition	NOUN
ejpam-1354	104	21	3	3	NUM
ejpam-1354	104	22	,	,	PUNCT
ejpam-1354	104	23	then	then	ADV
ejpam-1354	104	24	the	the	DET
ejpam-1354	104	25	sequence	sequence	NOUN
ejpam-1354	104	26	(	(	PUNCT
ejpam-1354	104	27	mi)i>0	mi)i>0	PROPN
ejpam-1354	104	28	⊂	⊂	X
ejpam-1354	104	29	m+(x	m+(x	X
ejpam-1354	104	30	)	)	PUNCT
ejpam-1354	104	31	will	will	AUX
ejpam-1354	104	32	be	be	AUX
ejpam-1354	104	33	called	call	VERB
ejpam-1354	104	34	ε	ε	PROPN
ejpam-1354	104	35	-	-	PUNCT
ejpam-1354	104	36	condensing	condensing	NOUN
ejpam-1354	104	37	.	.	PUNCT
ejpam-1354	105	1	clearly	clearly	ADV
ejpam-1354	105	2	for	for	ADP
ejpam-1354	105	3	every	every	DET
ejpam-1354	105	4	a	a	PRON
ejpam-1354	105	5	,	,	PUNCT
ejpam-1354	105	6	a∗	a∗	PROPN
ejpam-1354	105	7	∈	∈	PROPN
ejpam-1354	105	8	s(m	s(m	PROPN
ejpam-1354	105	9	)	)	PUNCT
ejpam-1354	105	10	if	if	SCONJ
ejpam-1354	105	11	d(a	d(a	PROPN
ejpam-1354	105	12	,	,	PUNCT
ejpam-1354	105	13	a∗	a∗	ADJ
ejpam-1354	105	14	)	)	PUNCT
ejpam-1354	105	15	≤	≤	NUM
ejpam-1354	105	16	ε	ε	PROPN
ejpam-1354	105	17	,	,	PUNCT
ejpam-1354	105	18	then	then	ADV
ejpam-1354	105	19	either	either	CCONJ
ejpam-1354	105	20	(	(	PUNCT
ejpam-1354	105	21	a	a	PRON
ejpam-1354	105	22	,	,	PUNCT
ejpam-1354	105	23	a∗	a∗	ADJ
ejpam-1354	105	24	,	,	PUNCT
ejpam-1354	105	25	m	m	PROPN
ejpam-1354	105	26	)	)	PUNCT
ejpam-1354	105	27	or	or	CCONJ
ejpam-1354	105	28	(	(	PUNCT
ejpam-1354	105	29	a∗	a∗	PROPN
ejpam-1354	105	30	,	,	PUNCT
ejpam-1354	105	31	a	a	PRON
ejpam-1354	105	32	,	,	PUNCT
ejpam-1354	105	33	m	m	VERB
ejpam-1354	105	34	)	)	PUNCT
ejpam-1354	105	35	is	be	AUX
ejpam-1354	105	36	an	an	DET
ejpam-1354	105	37	εmove	εmove	NOUN
ejpam-1354	105	38	.	.	PUNCT
ejpam-1354	106	1	therefore	therefore	ADV
ejpam-1354	106	2	,	,	PUNCT
ejpam-1354	106	3	whenever	whenever	SCONJ
ejpam-1354	106	4	eε(m	eε(m	PUNCT
ejpam-1354	106	5	)	)	PUNCT
ejpam-1354	106	6	>	>	X
ejpam-1354	106	7	0	0	PUNCT
ejpam-1354	106	8	there	there	PRON
ejpam-1354	106	9	is	be	VERB
ejpam-1354	106	10	an	an	DET
ejpam-1354	106	11	ε	ε	NOUN
ejpam-1354	106	12	-	-	PUNCT
ejpam-1354	106	13	move	move	NOUN
ejpam-1354	106	14	(	(	PUNCT
ejpam-1354	106	15	m	m	NOUN
ejpam-1354	106	16	,	,	PUNCT
ejpam-1354	106	17	m∗	m∗	PROPN
ejpam-1354	106	18	)	)	PUNCT
ejpam-1354	106	19	.	.	PUNCT
ejpam-1354	107	1	thus	thus	ADV
ejpam-1354	107	2	,	,	PUNCT
ejpam-1354	107	3	for	for	ADP
ejpam-1354	107	4	every	every	DET
ejpam-1354	107	5	finite	finite	NOUN
ejpam-1354	107	6	m	m	VERB
ejpam-1354	107	7	with	with	ADP
ejpam-1354	107	8	nonvanishing	nonvanishe	VERB
ejpam-1354	107	9	energy	energy	NOUN
ejpam-1354	107	10	,	,	PUNCT
ejpam-1354	107	11	there	there	PRON
ejpam-1354	107	12	is	be	VERB
ejpam-1354	107	13	an	an	DET
ejpam-1354	107	14	ε	ε	PROPN
ejpam-1354	107	15	-	-	PUNCT
ejpam-1354	107	16	condensing	condense	VERB
ejpam-1354	107	17	sequence	sequence	NOUN
ejpam-1354	107	18	m1	m1	NOUN
ejpam-1354	107	19	,	,	PUNCT
ejpam-1354	107	20	m2	m2	PROPN
ejpam-1354	107	21	,	,	PUNCT
ejpam-1354	107	22	.	.	PUNCT
ejpam-1354	107	23	.	.	PUNCT
ejpam-1354	108	1	..	..	PUNCT
ejpam-1354	109	1	our	our	PRON
ejpam-1354	109	2	theorem	theorem	NOUN
ejpam-1354	109	3	says	say	VERB
ejpam-1354	109	4	that	that	SCONJ
ejpam-1354	109	5	such	such	DET
ejpam-1354	109	6	a	a	DET
ejpam-1354	109	7	sequence	sequence	NOUN
ejpam-1354	109	8	is	be	AUX
ejpam-1354	109	9	finite	finite	ADJ
ejpam-1354	110	1	.	.	PUNCT
ejpam-1354	110	2	remark	remark	PROPN
ejpam-1354	110	3	1	1	NUM
ejpam-1354	110	4	.	.	PUNCT
ejpam-1354	111	1	note	note	VERB
ejpam-1354	111	2	that	that	SCONJ
ejpam-1354	111	3	the	the	DET
ejpam-1354	111	4	resulting	result	VERB
ejpam-1354	111	5	measure	measure	NOUN
ejpam-1354	111	6	of	of	ADP
ejpam-1354	111	7	a	a	DET
ejpam-1354	111	8	condensing	condense	VERB
ejpam-1354	111	9	sequence	sequence	NOUN
ejpam-1354	111	10	depends	depend	VERB
ejpam-1354	111	11	not	not	PART
ejpam-1354	111	12	only	only	ADV
ejpam-1354	111	13	on	on	ADP
ejpam-1354	111	14	the	the	DET
ejpam-1354	111	15	initial	initial	ADJ
ejpam-1354	111	16	measure	measure	NOUN
ejpam-1354	111	17	,	,	PUNCT
ejpam-1354	111	18	but	but	CCONJ
ejpam-1354	111	19	also	also	ADV
ejpam-1354	111	20	on	on	ADP
ejpam-1354	111	21	the	the	DET
ejpam-1354	111	22	reactions	reaction	NOUN
ejpam-1354	111	23	order	order	NOUN
ejpam-1354	111	24	of	of	ADP
ejpam-1354	111	25	the	the	DET
ejpam-1354	111	26	particles	particle	NOUN
ejpam-1354	111	27	.	.	PUNCT
ejpam-1354	112	1	hence	hence	ADV
ejpam-1354	112	2	,	,	PUNCT
ejpam-1354	112	3	we	we	PRON
ejpam-1354	112	4	introduce	introduce	VERB
ejpam-1354	112	5	a	a	DET
ejpam-1354	112	6	random	random	ADJ
ejpam-1354	112	7	range	range	NOUN
ejpam-1354	112	8	for	for	ADP
ejpam-1354	112	9	ordering	ordering	NOUN
ejpam-1354	112	10	of	of	ADP
ejpam-1354	112	11	particle	particle	NOUN
ejpam-1354	112	12	reactions	reaction	NOUN
ejpam-1354	112	13	.	.	PUNCT
ejpam-1354	113	1	this	this	PRON
ejpam-1354	113	2	gives	give	VERB
ejpam-1354	113	3	an	an	DET
ejpam-1354	113	4	interrelating	interrelating	ADJ
ejpam-1354	113	5	source	source	NOUN
ejpam-1354	113	6	of	of	ADP
ejpam-1354	113	7	stochastic	stochastic	ADJ
ejpam-1354	113	8	investigations	investigation	NOUN
ejpam-1354	113	9	,	,	PUNCT
ejpam-1354	113	10	which	which	PRON
ejpam-1354	113	11	are	be	AUX
ejpam-1354	113	12	not	not	PART
ejpam-1354	113	13	subject	subject	ADJ
ejpam-1354	113	14	of	of	ADP
ejpam-1354	113	15	our	our	PRON
ejpam-1354	113	16	present	present	ADJ
ejpam-1354	113	17	paper	paper	NOUN
ejpam-1354	113	18	.	.	PUNCT
ejpam-1354	114	1	moreover	moreover	ADV
ejpam-1354	114	2	,	,	PUNCT
ejpam-1354	114	3	the	the	DET
ejpam-1354	114	4	simultaneous	simultaneous	ADJ
ejpam-1354	114	5	displacement	displacement	ADJ
ejpam-1354	114	6	sequences	sequence	NOUN
ejpam-1354	114	7	are	be	AUX
ejpam-1354	114	8	studied	study	VERB
ejpam-1354	114	9	in	in	ADP
ejpam-1354	114	10	another	another	DET
ejpam-1354	114	11	context	context	NOUN
ejpam-1354	114	12	in	in	ADP
ejpam-1354	114	13	literature	literature	NOUN
ejpam-1354	114	14	by	by	ADP
ejpam-1354	114	15	using	use	VERB
ejpam-1354	114	16	synchronous	synchronous	ADJ
ejpam-1354	114	17	communication	communication	NOUN
ejpam-1354	114	18	,	,	PUNCT
ejpam-1354	114	19	moves	move	NOUN
ejpam-1354	114	20	and	and	CCONJ
ejpam-1354	114	21	reactions	reaction	NOUN
ejpam-1354	114	22	,	,	PUNCT
ejpam-1354	114	23	for	for	ADP
ejpam-1354	114	24	example	example	NOUN
ejpam-1354	114	25	,	,	PUNCT
ejpam-1354	114	26	we	we	PRON
ejpam-1354	114	27	refer	refer	VERB
ejpam-1354	114	28	to	to	ADP
ejpam-1354	114	29	the	the	DET
ejpam-1354	114	30	models	model	NOUN
ejpam-1354	114	31	studied	study	VERB
ejpam-1354	114	32	in	in	ADP
ejpam-1354	114	33	[	[	X
ejpam-1354	114	34	5	5	NUM
ejpam-1354	114	35	,	,	PUNCT
ejpam-1354	114	36	11	11	NUM
ejpam-1354	114	37	]	]	PUNCT
ejpam-1354	114	38	.	.	PUNCT
ejpam-1354	115	1	m.	m.	PROPN
ejpam-1354	115	2	zahri	zahri	PROPN
ejpam-1354	115	3	/	/	SYM
ejpam-1354	115	4	eur	eur	PROPN
ejpam-1354	115	5	.	.	PUNCT
ejpam-1354	116	1	j.	j.	PROPN
ejpam-1354	116	2	pure	pure	PROPN
ejpam-1354	116	3	appl	appl	PROPN
ejpam-1354	116	4	.	.	PROPN
ejpam-1354	116	5	math	math	PROPN
ejpam-1354	116	6	,	,	PUNCT
ejpam-1354	116	7	6	6	NUM
ejpam-1354	116	8	(	(	PUNCT
ejpam-1354	116	9	2013	2013	NUM
ejpam-1354	116	10	)	)	PUNCT
ejpam-1354	116	11	,	,	PUNCT
ejpam-1354	116	12	172	172	NUM
ejpam-1354	116	13	-	-	SYM
ejpam-1354	116	14	188	188	NUM
ejpam-1354	116	15	177	177	NUM
ejpam-1354	116	16	move	move	NOUN
ejpam-1354	116	17	infinitlty	infinitlty	PROPN
ejpam-1354	116	18	moves	move	NOUN
ejpam-1354	116	19	move	move	VERB
ejpam-1354	116	20	move	move	NOUN
ejpam-1354	116	21	figure	figure	NOUN
ejpam-1354	116	22	2	2	NUM
ejpam-1354	116	23	:	:	PUNCT
ejpam-1354	116	24	example	example	NOUN
ejpam-1354	116	25	of	of	ADP
ejpam-1354	116	26	four	four	NUM
ejpam-1354	116	27	energy	energy	NOUN
ejpam-1354	116	28	based	base	VERB
ejpam-1354	116	29	admissible	admissible	ADJ
ejpam-1354	116	30	moves	move	NOUN
ejpam-1354	116	31	(	(	PUNCT
ejpam-1354	116	32	from	from	ADP
ejpam-1354	116	33	the	the	DET
ejpam-1354	116	34	left	left	NOUN
ejpam-1354	116	35	to	to	ADP
ejpam-1354	116	36	the	the	DET
ejpam-1354	116	37	right	right	NOUN
ejpam-1354	116	38	)	)	PUNCT
ejpam-1354	116	39	(	(	PUNCT
ejpam-1354	116	40	a	a	X
ejpam-1354	116	41	)	)	PUNCT
ejpam-1354	116	42	,	,	PUNCT
ejpam-1354	116	43	(	(	PUNCT
ejpam-1354	116	44	b	b	NOUN
ejpam-1354	116	45	)	)	PUNCT
ejpam-1354	116	46	,	,	PUNCT
ejpam-1354	116	47	(	(	PUNCT
ejpam-1354	116	48	c	c	X
ejpam-1354	116	49	)	)	PUNCT
ejpam-1354	116	50	and	and	CCONJ
ejpam-1354	116	51	(	(	PUNCT
ejpam-1354	116	52	d	d	NOUN
ejpam-1354	116	53	)	)	PUNCT
ejpam-1354	116	54	.	.	PUNCT
ejpam-1354	117	1	the	the	DET
ejpam-1354	117	2	dotted	dotted	ADJ
ejpam-1354	117	3	circles	circle	NOUN
ejpam-1354	117	4	represent	represent	VERB
ejpam-1354	117	5	the	the	DET
ejpam-1354	117	6	destination	destination	NOUN
ejpam-1354	117	7	of	of	ADP
ejpam-1354	117	8	the	the	DET
ejpam-1354	117	9	moving	move	VERB
ejpam-1354	117	10	particle	particle	NOUN
ejpam-1354	117	11	.	.	PUNCT
ejpam-1354	118	1	lemma	lemma	PROPN
ejpam-1354	118	2	1	1	X
ejpam-1354	118	3	.	.	PUNCT
ejpam-1354	119	1	let	let	VERB
ejpam-1354	119	2	m	m	AUX
ejpam-1354	119	3	∈	∈	PROPN
ejpam-1354	119	4	m+(x	m+(x	PROPN
ejpam-1354	119	5	)	)	PUNCT
ejpam-1354	119	6	,	,	PUNCT
ejpam-1354	119	7	a	a	X
ejpam-1354	119	8	,	,	PUNCT
ejpam-1354	119	9	a∗	a∗	PROPN
ejpam-1354	119	10	∈	∈	PROPN
ejpam-1354	119	11	x	x	PUNCT
ejpam-1354	119	12	such	such	ADJ
ejpam-1354	119	13	that	that	SCONJ
ejpam-1354	119	14	d(a	d(a	PROPN
ejpam-1354	119	15	,	,	PUNCT
ejpam-1354	119	16	a∗)≤	a∗)≤	PROPN
ejpam-1354	119	17	ε	ε	PROPN
ejpam-1354	119	18	.	.	PUNCT
ejpam-1354	120	1	then	then	ADV
ejpam-1354	120	2	eε(m)−	eε(m)−	NOUN
ejpam-1354	120	3	eε(m	eε(m	PUNCT
ejpam-1354	120	4	∗	∗	NOUN
ejpam-1354	120	5	)	)	PUNCT
ejpam-1354	120	6	=	=	SYM
ejpam-1354	120	7	2m(a	2m(a	NUM
ejpam-1354	120	8	)	)	PUNCT
ejpam-1354	120	9	�	�	PROPN
ejpam-1354	120	10	eε(a	eε(a	ADP
ejpam-1354	120	11	,	,	PUNCT
ejpam-1354	120	12	m)−	m)−	PROPN
ejpam-1354	120	13	eε(a	eε(a	VERB
ejpam-1354	120	14	∗	∗	NOUN
ejpam-1354	120	15	,	,	PUNCT
ejpam-1354	120	16	m	m	NOUN
ejpam-1354	120	17	)	)	PUNCT
ejpam-1354	121	1	+	+	ADJ
ejpam-1354	121	2	m(a)d2(a	m(a)d2(a	PROPN
ejpam-1354	121	3	,	,	PUNCT
ejpam-1354	121	4	a∗	a∗	ADJ
ejpam-1354	121	5	)	)	PUNCT
ejpam-1354	121	6	�	�	PROPN
ejpam-1354	121	7	,	,	PUNCT
ejpam-1354	121	8	(	(	PUNCT
ejpam-1354	121	9	7	7	X
ejpam-1354	121	10	)	)	PUNCT
ejpam-1354	121	11	proof	proof	NOUN
ejpam-1354	121	12	.	.	PUNCT
ejpam-1354	122	1	to	to	PART
ejpam-1354	122	2	simplify	simplify	VERB
ejpam-1354	122	3	,	,	PUNCT
ejpam-1354	122	4	we	we	PRON
ejpam-1354	122	5	use	use	VERB
ejpam-1354	122	6	the	the	DET
ejpam-1354	122	7	following	follow	VERB
ejpam-1354	122	8	notation	notation	NOUN
ejpam-1354	122	9	i	i	PRON
ejpam-1354	122	10	m	m	VERB
ejpam-1354	122	11	:	:	PUNCT
ejpam-1354	122	12	=	=	SYM
ejpam-1354	122	13	∑	∑	PUNCT
ejpam-1354	122	14	d(x	d(x	PROPN
ejpam-1354	122	15	,	,	PUNCT
ejpam-1354	122	16	y)≤ε;{x	y)≤ε;{x	INTJ
ejpam-1354	122	17	,	,	PUNCT
ejpam-1354	122	18	y}∩{a	y}∩{a	PROPN
ejpam-1354	122	19	,	,	PUNCT
ejpam-1354	122	20	a∗}=	a∗}=	ADJ
ejpam-1354	122	21	;	;	PUNCT
ejpam-1354	122	22	m(x)m(y)d(x	m(x)m(y)d(x	NOUN
ejpam-1354	122	23	,	,	PUNCT
ejpam-1354	122	24	y)2	y)2	NOUN
ejpam-1354	122	25	(	(	PUNCT
ejpam-1354	122	26	8)	8)	NUM
ejpam-1354	122	27	by	by	ADP
ejpam-1354	122	28	computing	compute	VERB
ejpam-1354	122	29	the	the	DET
ejpam-1354	122	30	energy	energy	NOUN
ejpam-1354	122	31	of	of	ADP
ejpam-1354	122	32	m	m	VERB
ejpam-1354	122	33	we	we	PRON
ejpam-1354	122	34	get	get	VERB
ejpam-1354	122	35	eε(m	eε(m	PUNCT
ejpam-1354	122	36	)	)	PUNCT
ejpam-1354	123	1	=	=	PUNCT
ejpam-1354	123	2	∑	∑	PUNCT
ejpam-1354	123	3	d(x	d(x	PROPN
ejpam-1354	123	4	,	,	PUNCT
ejpam-1354	123	5	y)≤ε	y)≤ε	NOUN
ejpam-1354	123	6	m(x)m(y)d2(x	m(x)m(y)d2(x	NOUN
ejpam-1354	123	7	,	,	PUNCT
ejpam-1354	123	8	y	y	NOUN
ejpam-1354	123	9	)	)	PUNCT
ejpam-1354	123	10	=	=	NOUN
ejpam-1354	123	11	im+	im+	ADJ
ejpam-1354	123	12	2m(a	2m(a	NOUN
ejpam-1354	123	13	)	)	PUNCT
ejpam-1354	123	14	∑	∑	PUNCT
ejpam-1354	123	15	d(a	d(a	PROPN
ejpam-1354	123	16	,	,	PUNCT
ejpam-1354	123	17	x)≤ε	x)≤ε	PROPN
ejpam-1354	123	18	m(y)d2(a	m(y)d2(a	PROPN
ejpam-1354	123	19	,	,	PUNCT
ejpam-1354	123	20	y	y	PROPN
ejpam-1354	123	21	)	)	PUNCT
ejpam-1354	124	1	+	+	CCONJ
ejpam-1354	124	2	2m(a∗	2m(a∗	NUM
ejpam-1354	124	3	)	)	PUNCT
ejpam-1354	124	4	∑	∑	PUNCT
ejpam-1354	124	5	d(a∗,y)≤ε	d(a∗,y)≤ε	PROPN
ejpam-1354	124	6	m(y)d2(a∗	m(y)d2(a∗	PROPN
ejpam-1354	124	7	,	,	PUNCT
ejpam-1354	124	8	y	y	PROPN
ejpam-1354	124	9	)	)	PUNCT
ejpam-1354	124	10	−	−	ADP
ejpam-1354	124	11	2m(a)m(a∗)d2(a	2m(a)m(a∗)d2(a	NUM
ejpam-1354	124	12	,	,	PUNCT
ejpam-1354	124	13	a∗	a∗	NOUN
ejpam-1354	124	14	)	)	PUNCT
ejpam-1354	125	1	=	=	SYM
ejpam-1354	125	2	im+	im+	ADJ
ejpam-1354	125	3	2m(a)eε(a	2m(a)eε(a	PROPN
ejpam-1354	125	4	,	,	PUNCT
ejpam-1354	125	5	m	m	VERB
ejpam-1354	125	6	)	)	PUNCT
ejpam-1354	126	1	+	+	CCONJ
ejpam-1354	126	2	2m(a∗)eε(a	2m(a∗)eε(a	NUM
ejpam-1354	126	3	∗	∗	NOUN
ejpam-1354	126	4	,	,	PUNCT
ejpam-1354	126	5	m)−	m)−	PROPN
ejpam-1354	126	6	2m(a)m(a∗)d2(a	2m(a)m(a∗)d2(a	NUM
ejpam-1354	126	7	,	,	PUNCT
ejpam-1354	126	8	a∗	a∗	NOUN
ejpam-1354	126	9	)	)	PUNCT
ejpam-1354	126	10	.	.	PUNCT
ejpam-1354	127	1	(	(	PUNCT
ejpam-1354	127	2	9	9	X
ejpam-1354	127	3	)	)	PUNCT
ejpam-1354	127	4	m.	m.	NOUN
ejpam-1354	127	5	zahri	zahri	PROPN
ejpam-1354	127	6	/	/	SYM
ejpam-1354	127	7	eur	eur	PROPN
ejpam-1354	127	8	.	.	PUNCT
ejpam-1354	128	1	j.	j.	PROPN
ejpam-1354	128	2	pure	pure	PROPN
ejpam-1354	128	3	appl	appl	PROPN
ejpam-1354	128	4	.	.	PROPN
ejpam-1354	128	5	math	math	PROPN
ejpam-1354	128	6	,	,	PUNCT
ejpam-1354	128	7	6	6	NUM
ejpam-1354	128	8	(	(	PUNCT
ejpam-1354	128	9	2013	2013	NUM
ejpam-1354	128	10	)	)	PUNCT
ejpam-1354	128	11	,	,	PUNCT
ejpam-1354	128	12	172	172	NUM
ejpam-1354	128	13	-	-	SYM
ejpam-1354	128	14	188	188	NUM
ejpam-1354	128	15	178	178	NUM
ejpam-1354	128	16	similarly	similarly	ADV
ejpam-1354	128	17	for	for	ADP
ejpam-1354	128	18	m∗	m∗	NOUN
ejpam-1354	128	19	=	=	SYM
ejpam-1354	128	20	(	(	PUNCT
ejpam-1354	128	21	a	a	PRON
ejpam-1354	128	22	,	,	PUNCT
ejpam-1354	128	23	a∗	a∗	NOUN
ejpam-1354	128	24	,	,	PUNCT
ejpam-1354	128	25	m	m	PROPN
ejpam-1354	128	26	)	)	PUNCT
ejpam-1354	128	27	,	,	PUNCT
ejpam-1354	128	28	we	we	PRON
ejpam-1354	128	29	have	have	AUX
ejpam-1354	128	30	eε(m	eε(m	NOUN
ejpam-1354	128	31	∗	∗	NOUN
ejpam-1354	128	32	)	)	PUNCT
ejpam-1354	128	33	=	=	X
ejpam-1354	128	34	im∗	im∗	NOUN
ejpam-1354	128	35	+	+	CCONJ
ejpam-1354	128	36	2m∗(a)eε(a	2m∗(a)eε(a	NUM
ejpam-1354	128	37	,	,	PUNCT
ejpam-1354	128	38	m∗	m∗	NOUN
ejpam-1354	128	39	)	)	PUNCT
ejpam-1354	129	1	+	+	CCONJ
ejpam-1354	129	2	2m∗(a∗)eε(a	2m∗(a∗)eε(a	NUM
ejpam-1354	129	3	∗	∗	NOUN
ejpam-1354	129	4	,	,	PUNCT
ejpam-1354	129	5	m∗)−	m∗)−	NOUN
ejpam-1354	129	6	2m∗(a)m∗(a∗)d2(a	2m∗(a)m∗(a∗)d2(a	NOUN
ejpam-1354	129	7	,	,	PUNCT
ejpam-1354	129	8	a∗	a∗	ADJ
ejpam-1354	129	9	)	)	PUNCT
ejpam-1354	129	10	note	note	NOUN
ejpam-1354	129	11	that	that	SCONJ
ejpam-1354	130	1	i	i	PRON
ejpam-1354	130	2	m	m	VERB
ejpam-1354	130	3	=	=	VERB
ejpam-1354	130	4	im∗	im∗	NOUN
ejpam-1354	130	5	;	;	PUNCT
ejpam-1354	130	6	m∗(a	m∗(a	PROPN
ejpam-1354	130	7	)	)	PUNCT
ejpam-1354	130	8	=	=	SYM
ejpam-1354	130	9	0	0	NUM
ejpam-1354	130	10	;	;	PUNCT
ejpam-1354	130	11	m∗(a∗	m∗(a∗	X
ejpam-1354	130	12	)	)	PUNCT
ejpam-1354	130	13	=	=	SYM
ejpam-1354	130	14	m(a	m(a	PROPN
ejpam-1354	130	15	)	)	PUNCT
ejpam-1354	130	16	+	+	NOUN
ejpam-1354	130	17	m(a∗	m(a∗	X
ejpam-1354	130	18	)	)	PUNCT
ejpam-1354	130	19	and	and	CCONJ
ejpam-1354	130	20	e(a∗	e(a∗	NOUN
ejpam-1354	130	21	,	,	PUNCT
ejpam-1354	130	22	m∗	m∗	PROPN
ejpam-1354	130	23	)	)	PUNCT
ejpam-1354	130	24	=	=	SYM
ejpam-1354	130	25	e(a∗	e(a∗	X
ejpam-1354	130	26	,	,	PUNCT
ejpam-1354	130	27	m)−m(a)d2(a∗	m)−m(a)d2(a∗	NUM
ejpam-1354	130	28	,	,	PUNCT
ejpam-1354	130	29	a	a	PRON
ejpam-1354	130	30	)	)	PUNCT
ejpam-1354	130	31	.	.	PUNCT
ejpam-1354	131	1	(	(	PUNCT
ejpam-1354	131	2	10	10	NUM
ejpam-1354	131	3	)	)	PUNCT
ejpam-1354	131	4	therefore	therefore	ADV
ejpam-1354	131	5	eε(m	eε(m	PUNCT
ejpam-1354	131	6	∗	∗	NOUN
ejpam-1354	131	7	)	)	PUNCT
ejpam-1354	132	1	=	=	SYM
ejpam-1354	132	2	im+	im+	ADJ
ejpam-1354	132	3	2(m(a	2(m(a	NUM
ejpam-1354	132	4	)	)	PUNCT
ejpam-1354	132	5	+	+	PROPN
ejpam-1354	132	6	m(a∗))eε(a	m(a∗))eε(a	NOUN
ejpam-1354	132	7	∗	∗	NOUN
ejpam-1354	132	8	,	,	PUNCT
ejpam-1354	132	9	m∗	m∗	NOUN
ejpam-1354	132	10	)	)	PUNCT
ejpam-1354	132	11	=	=	SYM
ejpam-1354	132	12	im+	im+	ADJ
ejpam-1354	132	13	2	2	NUM
ejpam-1354	132	14	�	�	PROPN
ejpam-1354	132	15	m(a	m(a	PROPN
ejpam-1354	132	16	)	)	PUNCT
ejpam-1354	132	17	+	+	ADJ
ejpam-1354	132	18	m(a∗	m(a∗	X
ejpam-1354	132	19	)	)	PUNCT
ejpam-1354	132	20	�	�	NOUN
ejpam-1354	132	21	�	�	PROPN
ejpam-1354	132	22	eε(a	eε(a	VERB
ejpam-1354	132	23	∗	∗	NOUN
ejpam-1354	132	24	,	,	PUNCT
ejpam-1354	132	25	m)−m(a)d2(a∗	m)−m(a)d2(a∗	NUM
ejpam-1354	132	26	,	,	PUNCT
ejpam-1354	132	27	a	a	PRON
ejpam-1354	132	28	)	)	PUNCT
ejpam-1354	132	29	�	�	PROPN
ejpam-1354	132	30	,	,	PUNCT
ejpam-1354	132	31	(	(	PUNCT
ejpam-1354	132	32	11	11	NUM
ejpam-1354	132	33	)	)	PUNCT
ejpam-1354	132	34	and	and	CCONJ
ejpam-1354	132	35	from	from	ADP
ejpam-1354	132	36	(	(	PUNCT
ejpam-1354	132	37	9	9	NUM
ejpam-1354	132	38	)	)	PUNCT
ejpam-1354	132	39	and	and	CCONJ
ejpam-1354	132	40	(	(	PUNCT
ejpam-1354	132	41	11	11	X
ejpam-1354	132	42	)	)	PUNCT
ejpam-1354	132	43	it	it	PRON
ejpam-1354	132	44	follows	follow	VERB
ejpam-1354	132	45	the	the	DET
ejpam-1354	132	46	result	result	NOUN
ejpam-1354	132	47	of	of	ADP
ejpam-1354	132	48	the	the	DET
ejpam-1354	132	49	lemma	lemma	PROPN
ejpam-1354	132	50	.	.	PUNCT
ejpam-1354	133	1	lemma	lemma	PROPN
ejpam-1354	133	2	2	2	NUM
ejpam-1354	133	3	.	.	PUNCT
ejpam-1354	134	1	for	for	ADP
ejpam-1354	134	2	m	m	PROPN
ejpam-1354	134	3	∈	∈	PROPN
ejpam-1354	134	4	m+(x	m+(x	PRON
ejpam-1354	134	5	)	)	PUNCT
ejpam-1354	134	6	let	let	AUX
ejpam-1354	134	7	n(m	n(m	PRON
ejpam-1354	134	8	)	)	PUNCT
ejpam-1354	134	9	be	be	VERB
ejpam-1354	134	10	the	the	DET
ejpam-1354	134	11	number	number	NOUN
ejpam-1354	134	12	of	of	ADP
ejpam-1354	134	13	elements	element	NOUN
ejpam-1354	134	14	a	a	DET
ejpam-1354	134	15	∈	∈	NOUN
ejpam-1354	134	16	x	x	PUNCT
ejpam-1354	134	17	such	such	ADJ
ejpam-1354	134	18	that	that	SCONJ
ejpam-1354	134	19	m(a	m(a	NOUN
ejpam-1354	134	20	)	)	PUNCT
ejpam-1354	134	21	>	>	X
ejpam-1354	135	1	0	0	X
ejpam-1354	135	2	.	.	PUNCT
ejpam-1354	135	3	(	(	PUNCT
ejpam-1354	135	4	i.e.	i.e.	X
ejpam-1354	135	5	n(m	n(m	NOUN
ejpam-1354	135	6	)	)	PUNCT
ejpam-1354	135	7	=	=	PUNCT
ejpam-1354	136	1	|s(m)|	|s(m)|	PROPN
ejpam-1354	136	2	.	.	PUNCT
ejpam-1354	137	1	if	if	SCONJ
ejpam-1354	137	2	m1	m1	PROPN
ejpam-1354	137	3	,	,	PUNCT
ejpam-1354	137	4	m2	m2	PROPN
ejpam-1354	137	5	,	,	PUNCT
ejpam-1354	137	6	.	.	PUNCT
ejpam-1354	137	7	.	.	PUNCT
ejpam-1354	138	1	.	.	PUNCT
ejpam-1354	139	1	is	be	AUX
ejpam-1354	139	2	a	a	DET
ejpam-1354	139	3	sequence	sequence	NOUN
ejpam-1354	139	4	of	of	ADP
ejpam-1354	139	5	measures	measure	NOUN
ejpam-1354	139	6	on	on	ADP
ejpam-1354	139	7	x	x	PUNCT
ejpam-1354	139	8	which	which	PRON
ejpam-1354	139	9	is	be	AUX
ejpam-1354	139	10	singular	singular	ADJ
ejpam-1354	139	11	and	and	CCONJ
ejpam-1354	139	12	ε−condensing	ε−condensing	NOUN
ejpam-1354	139	13	,	,	PUNCT
ejpam-1354	139	14	then	then	ADV
ejpam-1354	139	15	(	(	PUNCT
ejpam-1354	139	16	i	i	NOUN
ejpam-1354	139	17	)	)	PUNCT
ejpam-1354	139	18	i→	i→	PROPN
ejpam-1354	139	19	eε(m	eε(m	NOUN
ejpam-1354	139	20	i	i	NOUN
ejpam-1354	139	21	)	)	PUNCT
ejpam-1354	139	22	is	be	AUX
ejpam-1354	139	23	strictly	strictly	ADV
ejpam-1354	139	24	decreasing	decrease	VERB
ejpam-1354	139	25	and	and	CCONJ
ejpam-1354	139	26	(	(	PUNCT
ejpam-1354	139	27	ii	ii	NOUN
ejpam-1354	139	28	)	)	PUNCT
ejpam-1354	139	29	i→	i→	PROPN
ejpam-1354	139	30	n(mi	n(mi	PROPN
ejpam-1354	139	31	)	)	PUNCT
ejpam-1354	139	32	is	be	AUX
ejpam-1354	139	33	non	non	ADJ
ejpam-1354	139	34	-	-	ADJ
ejpam-1354	139	35	increasing	increase	VERB
ejpam-1354	139	36	.	.	PUNCT
ejpam-1354	140	1	proof	proof	NOUN
ejpam-1354	140	2	.	.	PUNCT
ejpam-1354	141	1	the	the	DET
ejpam-1354	141	2	first	first	ADJ
ejpam-1354	141	3	claim	claim	NOUN
ejpam-1354	141	4	follows	follow	VERB
ejpam-1354	141	5	from	from	ADP
ejpam-1354	141	6	lemma	lemma	PROPN
ejpam-1354	141	7	1	1	NUM
ejpam-1354	141	8	.	.	PUNCT
ejpam-1354	141	9	to	to	PART
ejpam-1354	141	10	show	show	VERB
ejpam-1354	141	11	the	the	DET
ejpam-1354	141	12	second	second	ADJ
ejpam-1354	141	13	let	let	NOUN
ejpam-1354	141	14	s(m	s(m	PROPN
ejpam-1354	141	15	)	)	PUNCT
ejpam-1354	141	16	be	be	AUX
ejpam-1354	141	17	the	the	DET
ejpam-1354	141	18	support	support	NOUN
ejpam-1354	141	19	of	of	ADP
ejpam-1354	141	20	the	the	DET
ejpam-1354	141	21	measure	measure	NOUN
ejpam-1354	141	22	m.	m.	NOUN
ejpam-1354	141	23	consider	consider	VERB
ejpam-1354	141	24	m∗	m∗	NOUN
ejpam-1354	141	25	=	=	SYM
ejpam-1354	141	26	(	(	PUNCT
ejpam-1354	141	27	a	a	PRON
ejpam-1354	141	28	,	,	PUNCT
ejpam-1354	141	29	a∗	a∗	NOUN
ejpam-1354	141	30	,	,	PUNCT
ejpam-1354	141	31	m	m	PROPN
ejpam-1354	141	32	)	)	PUNCT
ejpam-1354	141	33	.	.	PUNCT
ejpam-1354	142	1	if	if	SCONJ
ejpam-1354	142	2	a	a	DET
ejpam-1354	142	3	/∈	/∈	SYM
ejpam-1354	142	4	s(m	s(m	NOUN
ejpam-1354	142	5	)	)	PUNCT
ejpam-1354	142	6	then	then	ADV
ejpam-1354	142	7	s(m	s(m	PROPN
ejpam-1354	142	8	)	)	PUNCT
ejpam-1354	142	9	=	=	SYM
ejpam-1354	142	10	s(m∗	s(m∗	NUM
ejpam-1354	142	11	)	)	PUNCT
ejpam-1354	142	12	and	and	CCONJ
ejpam-1354	142	13	n(m	n(m	PROPN
ejpam-1354	142	14	)	)	PUNCT
ejpam-1354	142	15	=	=	SYM
ejpam-1354	142	16	n(m∗	n(m∗	X
ejpam-1354	142	17	)	)	PUNCT
ejpam-1354	142	18	.	.	PUNCT
ejpam-1354	143	1	if	if	SCONJ
ejpam-1354	143	2	a	a	DET
ejpam-1354	143	3	∈	∈	PROPN
ejpam-1354	143	4	s(m	s(m	PROPN
ejpam-1354	143	5	)	)	PUNCT
ejpam-1354	143	6	and	and	CCONJ
ejpam-1354	143	7	a∗	a∗	PROPN
ejpam-1354	143	8	∈	∈	PROPN
ejpam-1354	143	9	s(m	s(m	PROPN
ejpam-1354	143	10	)	)	PUNCT
ejpam-1354	143	11	then	then	ADV
ejpam-1354	143	12	s(m∗	s(m∗	NUM
ejpam-1354	143	13	)	)	PUNCT
ejpam-1354	143	14	=	=	PUNCT
ejpam-1354	143	15	s(m)\{a	s(m)\{a	VERB
ejpam-1354	143	16	}	}	PUNCT
ejpam-1354	143	17	and	and	CCONJ
ejpam-1354	143	18	n(m∗	n(m∗	ADV
ejpam-1354	143	19	)	)	PUNCT
ejpam-1354	143	20	<	<	X
ejpam-1354	143	21	n(m	n(m	PROPN
ejpam-1354	143	22	)	)	PUNCT
ejpam-1354	143	23	.	.	PUNCT
ejpam-1354	144	1	if	if	SCONJ
ejpam-1354	144	2	a	a	DET
ejpam-1354	144	3	∈	∈	PROPN
ejpam-1354	144	4	s(m	s(m	PROPN
ejpam-1354	144	5	)	)	PUNCT
ejpam-1354	144	6	,	,	PUNCT
ejpam-1354	144	7	a∗	a∗	PROPN
ejpam-1354	144	8	/∈	/∈	SYM
ejpam-1354	144	9	s(m	s(m	PROPN
ejpam-1354	144	10	)	)	PUNCT
ejpam-1354	144	11	then	then	ADV
ejpam-1354	144	12	s(m∗	s(m∗	NUM
ejpam-1354	144	13	)	)	PUNCT
ejpam-1354	144	14	=	=	SYM
ejpam-1354	144	15	(	(	PUNCT
ejpam-1354	144	16	s(m	s(m	PROPN
ejpam-1354	144	17	)	)	PUNCT
ejpam-1354	144	18	\	\	NOUN
ejpam-1354	144	19	{	{	PUNCT
ejpam-1354	144	20	a})∪	a})∪	PROPN
ejpam-1354	144	21	{	{	PUNCT
ejpam-1354	144	22	a∗	a∗	PROPN
ejpam-1354	144	23	}	}	PUNCT
ejpam-1354	144	24	,	,	PUNCT
ejpam-1354	144	25	and	and	CCONJ
ejpam-1354	144	26	again	again	ADV
ejpam-1354	144	27	n(m	n(m	PROPN
ejpam-1354	144	28	)	)	PUNCT
ejpam-1354	144	29	=	=	SYM
ejpam-1354	144	30	n(m∗	n(m∗	NUM
ejpam-1354	144	31	)	)	PUNCT
ejpam-1354	144	32	.	.	PUNCT
ejpam-1354	145	1	theorem	theorem	NOUN
ejpam-1354	145	2	1	1	X
ejpam-1354	145	3	.	.	PUNCT
ejpam-1354	146	1	let	let	VERB
ejpam-1354	146	2	us	we	PRON
ejpam-1354	146	3	consider	consider	VERB
ejpam-1354	146	4	(	(	PUNCT
ejpam-1354	146	5	x	x	NOUN
ejpam-1354	146	6	,	,	PUNCT
ejpam-1354	146	7	d	d	X
ejpam-1354	146	8	)	)	PUNCT
ejpam-1354	146	9	a	a	DET
ejpam-1354	146	10	finite	finite	ADJ
ejpam-1354	146	11	metric	metric	ADJ
ejpam-1354	146	12	space	space	NOUN
ejpam-1354	146	13	.	.	PUNCT
ejpam-1354	147	1	every	every	DET
ejpam-1354	147	2	singularly	singularly	ADV
ejpam-1354	147	3	ε	ε	NOUN
ejpam-1354	147	4	-	-	PUNCT
ejpam-1354	147	5	condensing	condense	VERB
ejpam-1354	147	6	sequence	sequence	NOUN
ejpam-1354	147	7	of	of	ADP
ejpam-1354	147	8	m+(x	m+(x	PROPN
ejpam-1354	147	9	)	)	PUNCT
ejpam-1354	147	10	is	be	AUX
ejpam-1354	147	11	finite	finite	ADJ
ejpam-1354	147	12	.	.	PUNCT
ejpam-1354	148	1	proof	proof	NOUN
ejpam-1354	148	2	.	.	PUNCT
ejpam-1354	149	1	let	let	VERB
ejpam-1354	149	2	m1	m1	PROPN
ejpam-1354	149	3	,	,	PUNCT
ejpam-1354	149	4	m2	m2	PROPN
ejpam-1354	149	5	,	,	PUNCT
ejpam-1354	149	6	.	.	PUNCT
ejpam-1354	149	7	.	.	PUNCT
ejpam-1354	150	1	.	.	PUNCT
ejpam-1354	151	1	be	be	AUX
ejpam-1354	151	2	an	an	DET
ejpam-1354	151	3	infinite	infinite	ADJ
ejpam-1354	151	4	sequence	sequence	NOUN
ejpam-1354	151	5	of	of	ADP
ejpam-1354	151	6	measures	measure	NOUN
ejpam-1354	151	7	,	,	PUNCT
ejpam-1354	151	8	which	which	PRON
ejpam-1354	151	9	is	be	AUX
ejpam-1354	151	10	ε−condensing	ε−condense	VERB
ejpam-1354	151	11	.	.	PUNCT
ejpam-1354	152	1	because	because	SCONJ
ejpam-1354	152	2	of	of	ADP
ejpam-1354	152	3	the	the	DET
ejpam-1354	152	4	preceding	precede	VERB
ejpam-1354	152	5	lemma	lemma	PROPN
ejpam-1354	152	6	,	,	PUNCT
ejpam-1354	152	7	we	we	PRON
ejpam-1354	152	8	may	may	AUX
ejpam-1354	152	9	assume	assume	VERB
ejpam-1354	152	10	that	that	SCONJ
ejpam-1354	152	11	i	i	PRON
ejpam-1354	152	12	→	→	SYM
ejpam-1354	152	13	n(mi	n(mi	NUM
ejpam-1354	152	14	)	)	PUNCT
ejpam-1354	152	15	is	be	AUX
ejpam-1354	152	16	constant	constant	ADJ
ejpam-1354	152	17	.	.	PUNCT
ejpam-1354	153	1	hence	hence	ADV
ejpam-1354	153	2	,	,	PUNCT
ejpam-1354	153	3	for	for	ADP
ejpam-1354	153	4	every	every	DET
ejpam-1354	153	5	i	i	PRON
ejpam-1354	153	6	the	the	DET
ejpam-1354	153	7	measure	measure	NOUN
ejpam-1354	153	8	mi+1	mi+1	INTJ
ejpam-1354	153	9	is	be	AUX
ejpam-1354	153	10	a	a	DET
ejpam-1354	153	11	permutation	permutation	NOUN
ejpam-1354	153	12	of	of	ADP
ejpam-1354	153	13	mi	mi	PROPN
ejpam-1354	153	14	i.e.	i.e.	X
ejpam-1354	153	15	mi+1	mi+1	X
ejpam-1354	153	16	=	=	SYM
ejpam-1354	153	17	mi	mi	PROPN
ejpam-1354	153	18	◦	◦	PROPN
ejpam-1354	153	19	πi	πi	PROPN
ejpam-1354	153	20	,	,	PUNCT
ejpam-1354	153	21	where	where	SCONJ
ejpam-1354	153	22	πi	πi	ADV
ejpam-1354	153	23	:	:	PUNCT
ejpam-1354	153	24	x	x	X
ejpam-1354	153	25	→	→	PUNCT
ejpam-1354	153	26	x	x	X
ejpam-1354	153	27	is	be	AUX
ejpam-1354	153	28	a	a	DET
ejpam-1354	153	29	permutation	permutation	NOUN
ejpam-1354	153	30	of	of	ADP
ejpam-1354	153	31	x	x	X
ejpam-1354	153	32	.	.	PUNCT
ejpam-1354	154	1	therefore	therefore	ADV
ejpam-1354	154	2	,	,	PUNCT
ejpam-1354	154	3	mi	mi	PROPN
ejpam-1354	154	4	=	=	PROPN
ejpam-1354	154	5	m1	m1	PROPN
ejpam-1354	154	6	◦	◦	NOUN
ejpam-1354	154	7	π1	π1	PROPN
ejpam-1354	154	8	◦	◦	NOUN
ejpam-1354	154	9	.	.	PUNCT
ejpam-1354	154	10	.	.	PUNCT
ejpam-1354	154	11	.	.	PUNCT
ejpam-1354	155	1	◦	◦	NOUN
ejpam-1354	155	2	πi−1	πi−1	PROPN
ejpam-1354	155	3	.	.	PROPN
ejpam-1354	156	1	as	as	SCONJ
ejpam-1354	156	2	the	the	DET
ejpam-1354	156	3	group	group	NOUN
ejpam-1354	156	4	of	of	ADP
ejpam-1354	156	5	permutations	permutation	NOUN
ejpam-1354	156	6	of	of	ADP
ejpam-1354	156	7	x	x	PUNCT
ejpam-1354	156	8	is	be	AUX
ejpam-1354	156	9	finite	finite	ADJ
ejpam-1354	156	10	,	,	PUNCT
ejpam-1354	156	11	there	there	PRON
ejpam-1354	156	12	exist	exist	VERB
ejpam-1354	156	13	a	a	DET
ejpam-1354	156	14	natural	natural	ADJ
ejpam-1354	156	15	numbers	number	NOUN
ejpam-1354	156	16	i	i	PRON
ejpam-1354	156	17	,	,	PUNCT
ejpam-1354	156	18	k	k	PROPN
ejpam-1354	156	19	>	>	X
ejpam-1354	156	20	0	0	NUM
ejpam-1354	156	21	such	such	ADJ
ejpam-1354	156	22	that	that	DET
ejpam-1354	156	23	π1	π1	ADJ
ejpam-1354	156	24	◦	◦	NOUN
ejpam-1354	156	25	.	.	PUNCT
ejpam-1354	156	26	.	.	PUNCT
ejpam-1354	157	1	.πi	.πi	X
ejpam-1354	158	1	=	=	SYM
ejpam-1354	158	2	π1	π1	PROPN
ejpam-1354	158	3	◦	◦	NOUN
ejpam-1354	158	4	.	.	PUNCT
ejpam-1354	158	5	.	.	PUNCT
ejpam-1354	158	6	.	.	PUNCT
ejpam-1354	159	1	◦	◦	NOUN
ejpam-1354	159	2	πi+k	πi+k	PROPN
ejpam-1354	159	3	,	,	PUNCT
ejpam-1354	159	4	and	and	CCONJ
ejpam-1354	159	5	mi+1	mi+1	X
ejpam-1354	159	6	=	=	SYM
ejpam-1354	159	7	mi+k+1	mi+k+1	NOUN
ejpam-1354	159	8	,	,	PUNCT
ejpam-1354	159	9	which	which	PRON
ejpam-1354	159	10	however	however	ADV
ejpam-1354	159	11	is	be	AUX
ejpam-1354	159	12	impossible	impossible	ADJ
ejpam-1354	159	13	in	in	ADP
ejpam-1354	159	14	view	view	NOUN
ejpam-1354	159	15	of	of	ADP
ejpam-1354	159	16	lemma	lemma	PROPN
ejpam-1354	159	17	2	2	NUM
ejpam-1354	159	18	.	.	NOUN
ejpam-1354	159	19	remark	remark	NOUN
ejpam-1354	159	20	2	2	NUM
ejpam-1354	159	21	.	.	X
ejpam-1354	160	1	there	there	PRON
ejpam-1354	160	2	exist	exist	VERB
ejpam-1354	160	3	infinite	infinite	ADJ
ejpam-1354	160	4	non	non	ADJ
ejpam-1354	160	5	-	-	ADJ
ejpam-1354	160	6	converging	converging	ADJ
ejpam-1354	160	7	condensing	condense	VERB
ejpam-1354	160	8	sequences	sequence	NOUN
ejpam-1354	160	9	:	:	PUNCT
ejpam-1354	160	10	consider	consider	VERB
ejpam-1354	160	11	a	a	DET
ejpam-1354	160	12	simultaneously	simultaneously	ADV
ejpam-1354	160	13	condensing	condense	VERB
ejpam-1354	160	14	sequence	sequence	NOUN
ejpam-1354	160	15	with	with	ADP
ejpam-1354	160	16	two	two	NUM
ejpam-1354	160	17	mass	mass	ADJ
ejpam-1354	160	18	points	point	NOUN
ejpam-1354	160	19	mn	mn	PROPN
ejpam-1354	160	20	=	=	SYM
ejpam-1354	160	21	ms	ms	PROPN
ejpam-1354	160	22	,	,	PUNCT
ejpam-1354	160	23	where	where	SCONJ
ejpam-1354	160	24	mn	mn	PROPN
ejpam-1354	160	25	is	be	AUX
ejpam-1354	160	26	the	the	DET
ejpam-1354	160	27	mass	mass	NOUN
ejpam-1354	160	28	of	of	ADP
ejpam-1354	160	29	a	a	DET
ejpam-1354	160	30	point	point	NOUN
ejpam-1354	160	31	in	in	ADP
ejpam-1354	160	32	the	the	DET
ejpam-1354	160	33	north	north	NOUN
ejpam-1354	160	34	pole	pole	NOUN
ejpam-1354	160	35	of	of	ADP
ejpam-1354	160	36	unit	unit	NOUN
ejpam-1354	160	37	circle	circle	NOUN
ejpam-1354	160	38	and	and	CCONJ
ejpam-1354	160	39	ms	ms	NOUN
ejpam-1354	160	40	is	be	AUX
ejpam-1354	160	41	a	a	DET
ejpam-1354	160	42	mass	mass	NOUN
ejpam-1354	160	43	of	of	ADP
ejpam-1354	160	44	a	a	DET
ejpam-1354	160	45	point	point	NOUN
ejpam-1354	160	46	in	in	ADP
ejpam-1354	160	47	the	the	DET
ejpam-1354	160	48	south	south	ADJ
ejpam-1354	160	49	pole	pole	NOUN
ejpam-1354	160	50	.	.	PUNCT
ejpam-1354	161	1	note	note	VERB
ejpam-1354	161	2	that	that	SCONJ
ejpam-1354	161	3	,	,	PUNCT
ejpam-1354	161	4	this	this	DET
ejpam-1354	161	5	metric	metric	ADJ
ejpam-1354	161	6	space	space	NOUN
ejpam-1354	161	7	is	be	AUX
ejpam-1354	161	8	not	not	PART
ejpam-1354	161	9	a	a	DET
ejpam-1354	161	10	finite	finite	ADJ
ejpam-1354	161	11	metric	metric	ADJ
ejpam-1354	161	12	space	space	NOUN
ejpam-1354	161	13	but	but	CCONJ
ejpam-1354	161	14	to	to	PART
ejpam-1354	161	15	explain	explain	VERB
ejpam-1354	161	16	this	this	DET
ejpam-1354	161	17	example	example	NOUN
ejpam-1354	161	18	in	in	ADP
ejpam-1354	161	19	a	a	DET
ejpam-1354	161	20	finite	finite	ADJ
ejpam-1354	161	21	metric	metric	ADJ
ejpam-1354	161	22	space	space	NOUN
ejpam-1354	161	23	,	,	PUNCT
ejpam-1354	161	24	one	one	PRON
ejpam-1354	161	25	can	can	AUX
ejpam-1354	161	26	use	use	VERB
ejpam-1354	161	27	only	only	ADV
ejpam-1354	161	28	m.	m.	NOUN
ejpam-1354	161	29	zahri	zahri	PROPN
ejpam-1354	161	30	/	/	SYM
ejpam-1354	161	31	eur	eur	PROPN
ejpam-1354	161	32	.	.	PUNCT
ejpam-1354	162	1	j.	j.	PROPN
ejpam-1354	162	2	pure	pure	PROPN
ejpam-1354	162	3	appl	appl	PROPN
ejpam-1354	162	4	.	.	PROPN
ejpam-1354	162	5	math	math	PROPN
ejpam-1354	162	6	,	,	PUNCT
ejpam-1354	162	7	6	6	NUM
ejpam-1354	162	8	(	(	PUNCT
ejpam-1354	162	9	2013	2013	NUM
ejpam-1354	162	10	)	)	PUNCT
ejpam-1354	162	11	,	,	PUNCT
ejpam-1354	162	12	172	172	NUM
ejpam-1354	162	13	-	-	SYM
ejpam-1354	162	14	188	188	NUM
ejpam-1354	162	15	179	179	NUM
ejpam-1354	162	16	four	four	NUM
ejpam-1354	162	17	points	point	NOUN
ejpam-1354	162	18	metric	metric	ADJ
ejpam-1354	162	19	spaces	space	NOUN
ejpam-1354	162	20	,	,	PUNCT
ejpam-1354	162	21	namely	namely	ADV
ejpam-1354	162	22	the	the	DET
ejpam-1354	162	23	north	north	NOUN
ejpam-1354	162	24	,	,	PUNCT
ejpam-1354	162	25	the	the	DET
ejpam-1354	162	26	south	south	ADJ
ejpam-1354	162	27	pole	pole	NOUN
ejpam-1354	162	28	and	and	CCONJ
ejpam-1354	162	29	the	the	DET
ejpam-1354	162	30	midpoints	midpoint	NOUN
ejpam-1354	162	31	of	of	ADP
ejpam-1354	162	32	them	they	PRON
ejpam-1354	162	33	on	on	ADP
ejpam-1354	162	34	the	the	DET
ejpam-1354	162	35	unit	unit	NOUN
ejpam-1354	162	36	circle	circle	NOUN
ejpam-1354	162	37	.	.	PUNCT
ejpam-1354	163	1	here	here	ADV
ejpam-1354	163	2	,	,	PUNCT
ejpam-1354	163	3	m	m	VERB
ejpam-1354	163	4	is	be	AUX
ejpam-1354	163	5	given	give	VERB
ejpam-1354	163	6	as	as	ADP
ejpam-1354	163	7	m	m	VERB
ejpam-1354	163	8	:	:	PUNCT
ejpam-1354	163	9	=	=	PUNCT
ejpam-1354	163	10	msδ	msδ	NOUN
ejpam-1354	163	11	3π	3π	NOUN
ejpam-1354	163	12	2	2	NUM
ejpam-1354	164	1	+	+	NOUN
ejpam-1354	164	2	mnδ	mnδ	X
ejpam-1354	164	3	π	π	PROPN
ejpam-1354	164	4	2	2	NUM
ejpam-1354	164	5	.	.	PUNCT
ejpam-1354	165	1	if	if	SCONJ
ejpam-1354	165	2	we	we	PRON
ejpam-1354	165	3	consider	consider	VERB
ejpam-1354	165	4	the	the	DET
ejpam-1354	165	5	rule	rule	NOUN
ejpam-1354	165	6	of	of	ADP
ejpam-1354	165	7	simultaneously	simultaneously	ADV
ejpam-1354	165	8	moves	move	NOUN
ejpam-1354	165	9	(	(	PUNCT
ejpam-1354	165	10	hk	hk	NOUN
ejpam-1354	165	11	-	-	PUNCT
ejpam-1354	165	12	model	model	NOUN
ejpam-1354	165	13	)	)	PUNCT
ejpam-1354	165	14	studied	study	VERB
ejpam-1354	165	15	by	by	ADP
ejpam-1354	165	16	[	[	X
ejpam-1354	165	17	11	11	NUM
ejpam-1354	165	18	,	,	PUNCT
ejpam-1354	165	19	12	12	NUM
ejpam-1354	165	20	]	]	PUNCT
ejpam-1354	165	21	.	.	PUNCT
ejpam-1354	166	1	an	an	DET
ejpam-1354	166	2	admissible	admissible	ADJ
ejpam-1354	166	3	moves	move	NOUN
ejpam-1354	166	4	scenario	scenario	NOUN
ejpam-1354	166	5	is	be	AUX
ejpam-1354	166	6	the	the	DET
ejpam-1354	166	7	periodic	periodic	ADJ
ejpam-1354	166	8	one	one	NUM
ejpam-1354	166	9	,	,	PUNCT
ejpam-1354	166	10	namely	namely	ADV
ejpam-1354	166	11	3π	3π	NUM
ejpam-1354	166	12	2	2	NUM
ejpam-1354	166	13	moves	move	NOUN
ejpam-1354	166	14	to	to	ADP
ejpam-1354	166	15	0	0	NUM
ejpam-1354	166	16	and	and	CCONJ
ejpam-1354	166	17	π	π	PROPN
ejpam-1354	166	18	2	2	NUM
ejpam-1354	166	19	moves	move	NOUN
ejpam-1354	166	20	to	to	ADP
ejpam-1354	166	21	π	π	PROPN
ejpam-1354	166	22	.	.	PUNCT
ejpam-1354	167	1	the	the	DET
ejpam-1354	167	2	condensing	condense	VERB
ejpam-1354	167	3	sequence	sequence	NOUN
ejpam-1354	167	4	constructed	construct	VERB
ejpam-1354	167	5	above	above	ADP
ejpam-1354	167	6	m1	m1	PROPN
ejpam-1354	167	7	,	,	PUNCT
ejpam-1354	167	8	m2	m2	PROPN
ejpam-1354	167	9	,	,	PUNCT
ejpam-1354	167	10	.	.	PUNCT
ejpam-1354	167	11	.	.	PUNCT
ejpam-1354	168	1	.	.	PUNCT
ejpam-1354	169	1	is	be	AUX
ejpam-1354	169	2	simultaneously	simultaneously	ADV
ejpam-1354	169	3	condensing	condense	VERB
ejpam-1354	169	4	and	and	CCONJ
ejpam-1354	169	5	does	do	AUX
ejpam-1354	169	6	not	not	PART
ejpam-1354	169	7	converge	converge	VERB
ejpam-1354	169	8	.	.	PUNCT
ejpam-1354	170	1	we	we	PRON
ejpam-1354	170	2	can	can	AUX
ejpam-1354	170	3	also	also	ADV
ejpam-1354	170	4	construct	construct	VERB
ejpam-1354	170	5	another	another	DET
ejpam-1354	170	6	type	type	NOUN
ejpam-1354	170	7	of	of	ADP
ejpam-1354	170	8	non	non	ADJ
ejpam-1354	170	9	converging	converge	VERB
ejpam-1354	170	10	condensing	condense	VERB
ejpam-1354	170	11	sequences	sequence	NOUN
ejpam-1354	170	12	.	.	PUNCT
ejpam-1354	171	1	we	we	PRON
ejpam-1354	171	2	believe	believe	VERB
ejpam-1354	171	3	that	that	SCONJ
ejpam-1354	171	4	,	,	PUNCT
ejpam-1354	171	5	in	in	ADP
ejpam-1354	171	6	this	this	DET
ejpam-1354	171	7	case	case	NOUN
ejpam-1354	171	8	,	,	PUNCT
ejpam-1354	171	9	non	non	PRON
ejpam-1354	171	10	converging	converge	VERB
ejpam-1354	171	11	sequences	sequence	NOUN
ejpam-1354	171	12	have	have	VERB
ejpam-1354	171	13	a	a	DET
ejpam-1354	171	14	periodic	periodic	ADJ
ejpam-1354	171	15	behavior	behavior	NOUN
ejpam-1354	171	16	.	.	PUNCT
ejpam-1354	172	1	in	in	ADP
ejpam-1354	172	2	the	the	DET
ejpam-1354	172	3	case	case	NOUN
ejpam-1354	172	4	of	of	ADP
ejpam-1354	172	5	the	the	DET
ejpam-1354	172	6	existing	exist	VERB
ejpam-1354	172	7	of	of	ADP
ejpam-1354	172	8	many	many	ADJ
ejpam-1354	172	9	positions	position	NOUN
ejpam-1354	172	10	minimizing	minimize	VERB
ejpam-1354	172	11	the	the	DET
ejpam-1354	172	12	energy	energy	NOUN
ejpam-1354	172	13	,	,	PUNCT
ejpam-1354	172	14	the	the	DET
ejpam-1354	172	15	particle	particle	NOUN
ejpam-1354	172	16	moves	move	VERB
ejpam-1354	172	17	to	to	ADP
ejpam-1354	172	18	one	one	NUM
ejpam-1354	172	19	of	of	ADP
ejpam-1354	172	20	them	they	PRON
ejpam-1354	172	21	.	.	PUNCT
ejpam-1354	173	1	3	3	X
ejpam-1354	173	2	.	.	X
ejpam-1354	173	3	continuous	continuous	ADJ
ejpam-1354	173	4	energy	energy	NOUN
ejpam-1354	173	5	function	function	NOUN
ejpam-1354	173	6	in	in	ADP
ejpam-1354	173	7	this	this	DET
ejpam-1354	173	8	section	section	NOUN
ejpam-1354	173	9	,	,	PUNCT
ejpam-1354	173	10	we	we	PRON
ejpam-1354	173	11	shall	shall	AUX
ejpam-1354	173	12	assume	assume	VERB
ejpam-1354	173	13	that	that	SCONJ
ejpam-1354	173	14	all	all	DET
ejpam-1354	173	15	bounded	bound	VERB
ejpam-1354	173	16	subsets	subset	NOUN
ejpam-1354	173	17	of	of	ADP
ejpam-1354	173	18	the	the	DET
ejpam-1354	173	19	metric	metric	ADJ
ejpam-1354	173	20	space	space	NOUN
ejpam-1354	173	21	(	(	PUNCT
ejpam-1354	173	22	x	x	X
ejpam-1354	173	23	,	,	PUNCT
ejpam-1354	173	24	d	d	X
ejpam-1354	173	25	)	)	PUNCT
ejpam-1354	173	26	are	be	AUX
ejpam-1354	173	27	compact	compact	ADJ
ejpam-1354	173	28	.	.	PUNCT
ejpam-1354	174	1	hence	hence	ADV
ejpam-1354	174	2	,	,	PUNCT
ejpam-1354	174	3	x	x	X
ejpam-1354	174	4	is	be	AUX
ejpam-1354	174	5	locally	locally	ADV
ejpam-1354	174	6	compact	compact	ADJ
ejpam-1354	174	7	and	and	CCONJ
ejpam-1354	174	8	we	we	PRON
ejpam-1354	174	9	may	may	AUX
ejpam-1354	174	10	use	use	VERB
ejpam-1354	174	11	radon	radon	NOUN
ejpam-1354	174	12	measures	measure	NOUN
ejpam-1354	174	13	.	.	PUNCT
ejpam-1354	175	1	let	let	VERB
ejpam-1354	175	2	m+(r	m+(r	PROPN
ejpam-1354	175	3	n	n	CCONJ
ejpam-1354	175	4	)	)	PUNCT
ejpam-1354	175	5	be	be	AUX
ejpam-1354	175	6	the	the	DET
ejpam-1354	175	7	set	set	NOUN
ejpam-1354	175	8	of	of	ADP
ejpam-1354	175	9	nonnegative	nonnegative	ADJ
ejpam-1354	175	10	radon	radon	ADJ
ejpam-1354	175	11	measures	measure	NOUN
ejpam-1354	175	12	on	on	ADP
ejpam-1354	175	13	x	x	X
ejpam-1354	175	14	.	.	PUNCT
ejpam-1354	176	1	we	we	PRON
ejpam-1354	176	2	shall	shall	AUX
ejpam-1354	176	3	however	however	ADV
ejpam-1354	176	4	for	for	ADP
ejpam-1354	176	5	simplicity	simplicity	NOUN
ejpam-1354	176	6	deal	deal	NOUN
ejpam-1354	176	7	with	with	ADP
ejpam-1354	176	8	discrete	discrete	ADJ
ejpam-1354	176	9	measures	measure	NOUN
ejpam-1354	176	10	and	and	CCONJ
ejpam-1354	176	11	discrete	discrete	ADJ
ejpam-1354	176	12	time	time	NOUN
ejpam-1354	176	13	only	only	ADV
ejpam-1354	176	14	.	.	PUNCT
ejpam-1354	177	1	a	a	DET
ejpam-1354	177	2	measure	measure	NOUN
ejpam-1354	177	3	is	be	AUX
ejpam-1354	177	4	given	give	VERB
ejpam-1354	177	5	as	as	ADP
ejpam-1354	177	6	m	m	VERB
ejpam-1354	177	7	:	:	PUNCT
ejpam-1354	177	8	=	=	SYM
ejpam-1354	177	9	∑	∑	PUNCT
ejpam-1354	177	10	x∈s(m	x∈s(m	PROPN
ejpam-1354	177	11	)	)	PUNCT
ejpam-1354	177	12	m(x)δx	m(x)δx	PROPN
ejpam-1354	177	13	,	,	PUNCT
ejpam-1354	177	14	where	where	SCONJ
ejpam-1354	177	15	s(m	s(m	NOUN
ejpam-1354	177	16	)	)	PUNCT
ejpam-1354	177	17	denote	denote	VERB
ejpam-1354	177	18	the	the	DET
ejpam-1354	177	19	support	support	NOUN
ejpam-1354	177	20	of	of	ADP
ejpam-1354	177	21	m	m	PRON
ejpam-1354	177	22	and	and	CCONJ
ejpam-1354	177	23	δx	δx	VERB
ejpam-1354	177	24	the	the	DET
ejpam-1354	177	25	kronecker	kronecker	NOUN
ejpam-1354	177	26	symbol	symbol	NOUN
ejpam-1354	177	27	.	.	PUNCT
ejpam-1354	178	1	note	note	VERB
ejpam-1354	178	2	that	that	SCONJ
ejpam-1354	178	3	s(m	s(m	PROPN
ejpam-1354	178	4	)	)	PUNCT
ejpam-1354	178	5	is	be	AUX
ejpam-1354	178	6	discrete	discrete	ADJ
ejpam-1354	178	7	.	.	PUNCT
ejpam-1354	179	1	for	for	ADP
ejpam-1354	179	2	such	such	DET
ejpam-1354	179	3	a	a	DET
ejpam-1354	179	4	measure	measure	NOUN
ejpam-1354	179	5	,	,	PUNCT
ejpam-1354	179	6	the	the	DET
ejpam-1354	179	7	energy	energy	NOUN
ejpam-1354	179	8	map	map	NOUN
ejpam-1354	179	9	e	e	NOUN
ejpam-1354	179	10	,	,	PUNCT
ejpam-1354	179	11	defined	define	VERB
ejpam-1354	179	12	by	by	ADP
ejpam-1354	179	13	(	(	PUNCT
ejpam-1354	179	14	6	6	NUM
ejpam-1354	179	15	)	)	PUNCT
ejpam-1354	179	16	is	be	AUX
ejpam-1354	179	17	in	in	ADP
ejpam-1354	179	18	general	general	ADJ
ejpam-1354	179	19	a	a	DET
ejpam-1354	179	20	not	not	PART
ejpam-1354	179	21	continuous	continuous	ADJ
ejpam-1354	179	22	function	function	NOUN
ejpam-1354	179	23	of	of	ADP
ejpam-1354	179	24	m.	m.	NOUN
ejpam-1354	179	25	the	the	DET
ejpam-1354	179	26	following	follow	VERB
ejpam-1354	179	27	example	example	NOUN
ejpam-1354	179	28	illustrates	illustrate	VERB
ejpam-1354	179	29	this	this	PRON
ejpam-1354	179	30	:	:	PUNCT
ejpam-1354	179	31	for	for	ADP
ejpam-1354	179	32	x	x	X
ejpam-1354	179	33	=	=	SYM
ejpam-1354	179	34	r	r	NOUN
ejpam-1354	179	35	,	,	PUNCT
ejpam-1354	179	36	s(m	s(m	NOUN
ejpam-1354	179	37	)	)	PUNCT
ejpam-1354	179	38	=	=	PUNCT
ejpam-1354	179	39	{	{	PUNCT
ejpam-1354	179	40	1,2	1,2	NUM
ejpam-1354	179	41	}	}	PUNCT
ejpam-1354	179	42	,	,	PUNCT
ejpam-1354	179	43	ε	ε	PROPN
ejpam-1354	179	44	=	=	SYM
ejpam-1354	179	45	1	1	NUM
ejpam-1354	179	46	and	and	CCONJ
ejpam-1354	179	47	a	a	DET
ejpam-1354	179	48	given	give	VERB
ejpam-1354	179	49	m	m	PRON
ejpam-1354	179	50	with	with	ADP
ejpam-1354	179	51	m=	m=	ADJ
ejpam-1354	179	52	∑	∑	ADV
ejpam-1354	179	53	x∈{1,2	x∈{1,2	ADJ
ejpam-1354	179	54	}	}	PUNCT
ejpam-1354	179	55	m(x)δx	m(x)δx	PROPN
ejpam-1354	180	1	=	=	SYM
ejpam-1354	180	2	δ1+δ2	δ1+δ2	PROPN
ejpam-1354	180	3	,	,	PUNCT
ejpam-1354	180	4	it	it	PRON
ejpam-1354	180	5	follows	follow	VERB
ejpam-1354	180	6	that	that	SCONJ
ejpam-1354	180	7	e(m	e(m	PROPN
ejpam-1354	180	8	)	)	PUNCT
ejpam-1354	180	9	=	=	SYM
ejpam-1354	181	1	2	2	X
ejpam-1354	181	2	.	.	PUNCT
ejpam-1354	181	3	now	now	ADV
ejpam-1354	181	4	let	let	VERB
ejpam-1354	181	5	m	m	PRON
ejpam-1354	181	6	j	j	AUX
ejpam-1354	181	7	be	be	AUX
ejpam-1354	181	8	a	a	DET
ejpam-1354	181	9	sequence	sequence	NOUN
ejpam-1354	181	10	of	of	ADP
ejpam-1354	181	11	positive	positive	ADJ
ejpam-1354	181	12	measures	measure	NOUN
ejpam-1354	181	13	defined	define	VERB
ejpam-1354	181	14	as	as	ADP
ejpam-1354	181	15	m	m	PROPN
ejpam-1354	181	16	j	j	PROPN
ejpam-1354	181	17	=	=	SYM
ejpam-1354	181	18	δ1	δ1	PROPN
ejpam-1354	181	19	+	+	X
ejpam-1354	181	20	δ2	δ2	VERB
ejpam-1354	181	21	+	+	PRON
ejpam-1354	181	22	1	1	NUM
ejpam-1354	181	23	j	j	NOUN
ejpam-1354	181	24	,	,	PUNCT
ejpam-1354	181	25	it	it	PRON
ejpam-1354	181	26	follows	follow	VERB
ejpam-1354	181	27	lim	lim	PROPN
ejpam-1354	181	28	j	j	PROPN
ejpam-1354	181	29	m	m	PROPN
ejpam-1354	181	30	j	j	PROPN
ejpam-1354	181	31	=	=	SYM
ejpam-1354	181	32	m	m	PROPN
ejpam-1354	181	33	,	,	PUNCT
ejpam-1354	181	34	and	and	CCONJ
ejpam-1354	181	35	e(m	e(m	PROPN
ejpam-1354	181	36	j	j	PROPN
ejpam-1354	181	37	)	)	PUNCT
ejpam-1354	181	38	=	=	SYM
ejpam-1354	181	39	0	0	NUM
ejpam-1354	181	40	,	,	PUNCT
ejpam-1354	181	41	and	and	CCONJ
ejpam-1354	181	42	e(lim	e(lim	PROPN
ejpam-1354	181	43	j	j	PROPN
ejpam-1354	181	44	m	m	PROPN
ejpam-1354	181	45	j	j	PROPN
ejpam-1354	181	46	)	)	PUNCT
ejpam-1354	181	47	=	=	SYM
ejpam-1354	181	48	2	2	NUM
ejpam-1354	181	49	6=	6=	NUM
ejpam-1354	181	50	lim	lim	PROPN
ejpam-1354	181	51	j	j	PROPN
ejpam-1354	181	52	e(m	e(m	PROPN
ejpam-1354	181	53	j	j	PROPN
ejpam-1354	181	54	)	)	PUNCT
ejpam-1354	182	1	=	=	SYM
ejpam-1354	182	2	0	0	X
ejpam-1354	182	3	.	.	PUNCT
ejpam-1354	183	1	hence	hence	ADV
ejpam-1354	183	2	,	,	PUNCT
ejpam-1354	183	3	the	the	DET
ejpam-1354	183	4	map	map	NOUN
ejpam-1354	183	5	e	e	NOUN
ejpam-1354	183	6	with	with	ADP
ejpam-1354	183	7	the	the	DET
ejpam-1354	183	8	definition	definition	NOUN
ejpam-1354	183	9	(	(	PUNCT
ejpam-1354	183	10	6	6	NUM
ejpam-1354	183	11	)	)	PUNCT
ejpam-1354	183	12	is	be	AUX
ejpam-1354	183	13	not	not	PART
ejpam-1354	183	14	continuous	continuous	ADJ
ejpam-1354	183	15	in	in	ADP
ejpam-1354	183	16	m.	m.	NOUN
ejpam-1354	183	17	in	in	ADP
ejpam-1354	183	18	order	order	NOUN
ejpam-1354	183	19	to	to	PART
ejpam-1354	183	20	obtain	obtain	VERB
ejpam-1354	183	21	an	an	DET
ejpam-1354	183	22	energy	energy	NOUN
ejpam-1354	183	23	function	function	NOUN
ejpam-1354	183	24	which	which	PRON
ejpam-1354	183	25	depends	depend	VERB
ejpam-1354	183	26	continuously	continuously	ADV
ejpam-1354	183	27	on	on	ADP
ejpam-1354	183	28	m	m	PRON
ejpam-1354	183	29	,	,	PUNCT
ejpam-1354	183	30	we	we	PRON
ejpam-1354	183	31	extend	extend	VERB
ejpam-1354	183	32	the	the	DET
ejpam-1354	183	33	definition	definition	NOUN
ejpam-1354	183	34	(	(	PUNCT
ejpam-1354	183	35	6	6	NUM
ejpam-1354	183	36	)	)	PUNCT
ejpam-1354	183	37	to	to	ADP
ejpam-1354	183	38	the	the	DET
ejpam-1354	183	39	following	following	NOUN
ejpam-1354	183	40	:	:	PUNCT
ejpam-1354	183	41	e(m	e(m	X
ejpam-1354	183	42	)	)	PUNCT
ejpam-1354	183	43	=	=	PUNCT
ejpam-1354	184	1	∑	∑	PUNCT
ejpam-1354	184	2	x	x	SYM
ejpam-1354	184	3	,	,	PUNCT
ejpam-1354	184	4	y	y	PROPN
ejpam-1354	184	5	m(x)m(y)ϕ(x	m(x)m(y)ϕ(x	PROPN
ejpam-1354	184	6	,	,	PUNCT
ejpam-1354	184	7	y)d2(x	y)d2(x	PROPN
ejpam-1354	184	8	,	,	PUNCT
ejpam-1354	184	9	y	y	PROPN
ejpam-1354	184	10	)	)	PUNCT
ejpam-1354	184	11	,	,	PUNCT
ejpam-1354	184	12	(	(	PUNCT
ejpam-1354	184	13	12	12	NUM
ejpam-1354	184	14	)	)	PUNCT
ejpam-1354	184	15	m.	m.	NOUN
ejpam-1354	184	16	zahri	zahri	PROPN
ejpam-1354	184	17	/	/	SYM
ejpam-1354	184	18	eur	eur	PROPN
ejpam-1354	184	19	.	.	PUNCT
ejpam-1354	185	1	j.	j.	PROPN
ejpam-1354	185	2	pure	pure	PROPN
ejpam-1354	185	3	appl	appl	PROPN
ejpam-1354	185	4	.	.	PROPN
ejpam-1354	185	5	math	math	PROPN
ejpam-1354	185	6	,	,	PUNCT
ejpam-1354	185	7	6	6	NUM
ejpam-1354	185	8	(	(	PUNCT
ejpam-1354	185	9	2013	2013	NUM
ejpam-1354	185	10	)	)	PUNCT
ejpam-1354	185	11	,	,	PUNCT
ejpam-1354	185	12	172	172	NUM
ejpam-1354	185	13	-	-	SYM
ejpam-1354	185	14	188	188	NUM
ejpam-1354	185	15	180	180	NUM
ejpam-1354	185	16	where	where	SCONJ
ejpam-1354	185	17	the	the	DET
ejpam-1354	185	18	mapping	mapping	NOUN
ejpam-1354	185	19	ϕ	ϕ	NOUN
ejpam-1354	185	20	given	give	VERB
ejpam-1354	185	21	as	as	ADP
ejpam-1354	185	22	ϕ	ϕ	NOUN
ejpam-1354	185	23	:	:	PUNCT
ejpam-1354	185	24	x	x	SYM
ejpam-1354	185	25	×	×	NOUN
ejpam-1354	185	26	x	x	PUNCT
ejpam-1354	185	27	−→	−→	NOUN
ejpam-1354	185	28	[	[	X
ejpam-1354	185	29	0,1	0,1	NUM
ejpam-1354	185	30	]	]	PUNCT
ejpam-1354	185	31	;	;	PUNCT
ejpam-1354	185	32	ϕ(x	ϕ(x	PROPN
ejpam-1354	185	33	,	,	PUNCT
ejpam-1354	185	34	y	y	PROPN
ejpam-1354	185	35	)	)	PUNCT
ejpam-1354	185	36	:	:	PUNCT
ejpam-1354	186	1	=	=	SYM
ejpam-1354	186	2	(	(	PUNCT
ejpam-1354	186	3	1	1	NUM
ejpam-1354	186	4	,	,	PUNCT
ejpam-1354	186	5	if	if	SCONJ
ejpam-1354	186	6	d(x	d(x	PROPN
ejpam-1354	186	7	,	,	PUNCT
ejpam-1354	186	8	y)≤	y)≤	PROPN
ejpam-1354	186	9	ε	ε	PROPN
ejpam-1354	186	10	,	,	PUNCT
ejpam-1354	186	11	0	0	NUM
ejpam-1354	186	12	,	,	PUNCT
ejpam-1354	186	13	if	if	SCONJ
ejpam-1354	186	14	d(x	d(x	NOUN
ejpam-1354	186	15	,	,	PUNCT
ejpam-1354	186	16	y)≥	y)≥	PROPN
ejpam-1354	186	17	ε+	ε+	X
ejpam-1354	186	18	θ	θ	NOUN
ejpam-1354	186	19	.	.	PUNCT
ejpam-1354	187	1	(	(	PUNCT
ejpam-1354	187	2	13	13	NUM
ejpam-1354	187	3	)	)	PUNCT
ejpam-1354	187	4	is	be	AUX
ejpam-1354	187	5	a	a	DET
ejpam-1354	187	6	continuous	continuous	ADJ
ejpam-1354	187	7	function	function	NOUN
ejpam-1354	187	8	for	for	ADP
ejpam-1354	187	9	ε	ε	PROPN
ejpam-1354	187	10	>	>	X
ejpam-1354	187	11	0	0	PUNCT
ejpam-1354	187	12	and	and	CCONJ
ejpam-1354	187	13	θ	θ	X
ejpam-1354	187	14	>	>	X
ejpam-1354	187	15	0	0	X
ejpam-1354	187	16	.	.	PUNCT
ejpam-1354	188	1	these	these	DET
ejpam-1354	188	2	parameters	parameter	NOUN
ejpam-1354	188	3	will	will	AUX
ejpam-1354	188	4	be	be	AUX
ejpam-1354	188	5	fixed	fix	VERB
ejpam-1354	188	6	throughout	throughout	ADP
ejpam-1354	188	7	this	this	DET
ejpam-1354	188	8	paper	paper	NOUN
ejpam-1354	188	9	.	.	PUNCT
ejpam-1354	189	1	the	the	DET
ejpam-1354	189	2	function	function	NOUN
ejpam-1354	189	3	ϕ	ϕ	NOUN
ejpam-1354	189	4	will	will	AUX
ejpam-1354	189	5	be	be	AUX
ejpam-1354	189	6	called	call	VERB
ejpam-1354	189	7	intensity	intensity	NOUN
ejpam-1354	189	8	function	function	NOUN
ejpam-1354	189	9	.	.	PUNCT
ejpam-1354	190	1	let	let	AUX
ejpam-1354	190	2	me(x	me(x	VERB
ejpam-1354	190	3	)	)	PUNCT
ejpam-1354	190	4	be	be	AUX
ejpam-1354	190	5	the	the	DET
ejpam-1354	190	6	set	set	NOUN
ejpam-1354	190	7	of	of	ADP
ejpam-1354	190	8	discrete	discrete	ADJ
ejpam-1354	190	9	and	and	CCONJ
ejpam-1354	190	10	nonnegative	nonnegative	ADJ
ejpam-1354	190	11	measure	measure	NOUN
ejpam-1354	190	12	with	with	ADP
ejpam-1354	190	13	e(m)<∞.	e(m)<∞.	PROPN
ejpam-1354	190	14	a	a	DET
ejpam-1354	190	15	pair	pair	NOUN
ejpam-1354	190	16	(	(	PUNCT
ejpam-1354	190	17	a	a	PRON
ejpam-1354	190	18	,	,	PUNCT
ejpam-1354	190	19	a∗	a∗	ADJ
ejpam-1354	190	20	)	)	PUNCT
ejpam-1354	190	21	∈	∈	PROPN
ejpam-1354	190	22	x	x	SYM
ejpam-1354	190	23	×	×	NOUN
ejpam-1354	190	24	x	x	PUNCT
ejpam-1354	190	25	operates	operate	VERB
ejpam-1354	190	26	on	on	ADP
ejpam-1354	190	27	me(x	me(x	NUM
ejpam-1354	190	28	)	)	PUNCT
ejpam-1354	190	29	as	as	SCONJ
ejpam-1354	190	30	finite	finite	VERB
ejpam-1354	190	31	the	the	DET
ejpam-1354	190	32	case	case	NOUN
ejpam-1354	190	33	such	such	ADJ
ejpam-1354	190	34	that	that	SCONJ
ejpam-1354	190	35	m	m	PROPN
ejpam-1354	190	36	7→	7→	NUM
ejpam-1354	190	37	m∗(x	m∗(x	NOUN
ejpam-1354	190	38	)	)	PUNCT
ejpam-1354	190	39	=	=	PUNCT
ejpam-1354	190	40	(	(	PUNCT
ejpam-1354	190	41	a	a	PRON
ejpam-1354	190	42	,	,	PUNCT
ejpam-1354	190	43	a∗	a∗	NOUN
ejpam-1354	190	44	,	,	PUNCT
ejpam-1354	190	45	m	m	PROPN
ejpam-1354	190	46	)	)	PUNCT
ejpam-1354	190	47	.	.	PUNCT
ejpam-1354	191	1	note	note	VERB
ejpam-1354	191	2	that	that	SCONJ
ejpam-1354	191	3	if	if	SCONJ
ejpam-1354	191	4	m	m	PROPN
ejpam-1354	191	5	∈	∈	NOUN
ejpam-1354	191	6	me(x	me(x	NOUN
ejpam-1354	191	7	)	)	PUNCT
ejpam-1354	191	8	then	then	ADV
ejpam-1354	191	9	m∗	m∗	VERB
ejpam-1354	191	10	∈	∈	PROPN
ejpam-1354	191	11	me(x	me(x	NUM
ejpam-1354	191	12	)	)	PUNCT
ejpam-1354	191	13	.	.	PUNCT
ejpam-1354	192	1	the	the	DET
ejpam-1354	192	2	energy	energy	NOUN
ejpam-1354	192	3	of	of	ADP
ejpam-1354	192	4	a	a	DET
ejpam-1354	192	5	point	point	NOUN
ejpam-1354	192	6	a	a	DET
ejpam-1354	192	7	∈	∈	NOUN
ejpam-1354	192	8	x	x	PUNCT
ejpam-1354	192	9	with	with	ADP
ejpam-1354	192	10	respect	respect	NOUN
ejpam-1354	192	11	to	to	ADP
ejpam-1354	192	12	m	m	PROPN
ejpam-1354	192	13	∈	∈	NOUN
ejpam-1354	192	14	me(x	me(x	X
ejpam-1354	192	15	)	)	PUNCT
ejpam-1354	192	16	is	be	AUX
ejpam-1354	192	17	a	a	DET
ejpam-1354	192	18	map	map	NOUN
ejpam-1354	192	19	e	e	NOUN
ejpam-1354	192	20	defined	define	VERB
ejpam-1354	192	21	as	as	ADP
ejpam-1354	192	22	e	e	NOUN
ejpam-1354	192	23	:	:	PUNCT
ejpam-1354	192	24	x	x	X
ejpam-1354	192	25	×me(x	×me(x	ADJ
ejpam-1354	192	26	)	)	PUNCT
ejpam-1354	192	27	−→	−→	NOUN
ejpam-1354	192	28	r	r	NOUN
ejpam-1354	192	29	+	+	NOUN
ejpam-1354	192	30	;	;	PUNCT
ejpam-1354	192	31	e(a	e(a	NOUN
ejpam-1354	192	32	,	,	PUNCT
ejpam-1354	192	33	m	m	NOUN
ejpam-1354	192	34	)	)	PUNCT
ejpam-1354	192	35	=	=	PUNCT
ejpam-1354	193	1	∑	∑	PUNCT
ejpam-1354	193	2	y	y	PROPN
ejpam-1354	193	3	m(y)ϕ(a	m(y)ϕ(a	NOUN
ejpam-1354	193	4	,	,	PUNCT
ejpam-1354	193	5	y)n2(a−	y)n2(a−	PROPN
ejpam-1354	193	6	y	y	NOUN
ejpam-1354	193	7	)	)	PUNCT
ejpam-1354	193	8	.	.	PUNCT
ejpam-1354	194	1	(	(	PUNCT
ejpam-1354	194	2	14	14	X
ejpam-1354	194	3	)	)	PUNCT
ejpam-1354	194	4	lemma	lemma	PROPN
ejpam-1354	194	5	3	3	NUM
ejpam-1354	194	6	.	.	PUNCT
ejpam-1354	194	7	for	for	ADP
ejpam-1354	194	8	a	a	DET
ejpam-1354	194	9	,	,	PUNCT
ejpam-1354	194	10	a∗	a∗	PROPN
ejpam-1354	194	11	∈	∈	PROPN
ejpam-1354	194	12	x	x	X
ejpam-1354	194	13	,	,	PUNCT
ejpam-1354	194	14	m	m	PROPN
ejpam-1354	194	15	∈	∈	NOUN
ejpam-1354	194	16	me(x	me(x	NOUN
ejpam-1354	194	17	)	)	PUNCT
ejpam-1354	194	18	and	and	CCONJ
ejpam-1354	194	19	m∗	m∗	VERB
ejpam-1354	194	20	:	:	PUNCT
ejpam-1354	194	21	=	=	SYM
ejpam-1354	194	22	(	(	PUNCT
ejpam-1354	194	23	a	a	PRON
ejpam-1354	194	24	,	,	PUNCT
ejpam-1354	194	25	a∗	a∗	NOUN
ejpam-1354	194	26	,	,	PUNCT
ejpam-1354	194	27	m	m	PROPN
ejpam-1354	194	28	)	)	PUNCT
ejpam-1354	194	29	,	,	PUNCT
ejpam-1354	194	30	we	we	PRON
ejpam-1354	194	31	have	have	VERB
ejpam-1354	194	32	e(m)−	e(m)−	PROPN
ejpam-1354	194	33	e(m∗	e(m∗	NUM
ejpam-1354	194	34	)	)	PUNCT
ejpam-1354	194	35	=	=	SYM
ejpam-1354	194	36	2m(a	2m(a	PROPN
ejpam-1354	194	37	)	)	PUNCT
ejpam-1354	194	38	�	�	PROPN
ejpam-1354	194	39	e(a	e(a	PROPN
ejpam-1354	194	40	,	,	PUNCT
ejpam-1354	194	41	m)−	m)−	PROPN
ejpam-1354	194	42	e(a∗	e(a∗	NOUN
ejpam-1354	194	43	,	,	PUNCT
ejpam-1354	194	44	m∗	m∗	PROPN
ejpam-1354	194	45	)	)	PUNCT
ejpam-1354	194	46	�	�	PROPN
ejpam-1354	194	47	.	.	PUNCT
ejpam-1354	195	1	(	(	PUNCT
ejpam-1354	195	2	15	15	X
ejpam-1354	195	3	)	)	PUNCT
ejpam-1354	195	4	proof	proof	NOUN
ejpam-1354	195	5	.	.	PUNCT
ejpam-1354	196	1	for	for	ADP
ejpam-1354	196	2	simplicity	simplicity	NOUN
ejpam-1354	196	3	,	,	PUNCT
ejpam-1354	196	4	let	let	VERB
ejpam-1354	196	5	us	we	PRON
ejpam-1354	196	6	denote	denote	VERB
ejpam-1354	196	7	by	by	ADP
ejpam-1354	196	8	i	i	PRON
ejpam-1354	196	9	m	m	VERB
ejpam-1354	196	10	the	the	DET
ejpam-1354	196	11	following	follow	VERB
ejpam-1354	196	12	term	term	NOUN
ejpam-1354	196	13	:	:	PUNCT
ejpam-1354	196	14	i	i	PRON
ejpam-1354	196	15	m	m	VERB
ejpam-1354	196	16	:	:	PUNCT
ejpam-1354	196	17	=	=	SYM
ejpam-1354	196	18	∑	∑	PUNCT
ejpam-1354	196	19	{	{	PUNCT
ejpam-1354	196	20	x	x	PROPN
ejpam-1354	196	21	,	,	PUNCT
ejpam-1354	196	22	y}∩{a	y}∩{a	PROPN
ejpam-1354	196	23	,	,	PUNCT
ejpam-1354	196	24	a∗}=	a∗}=	PROPN
ejpam-1354	196	25	;	;	PUNCT
ejpam-1354	196	26	m(x)m(y)ϕ(x	m(x)m(y)ϕ(x	PROPN
ejpam-1354	196	27	,	,	PUNCT
ejpam-1354	196	28	y)d2(x	y)d2(x	PROPN
ejpam-1354	196	29	,	,	PUNCT
ejpam-1354	196	30	y	y	PROPN
ejpam-1354	196	31	)	)	PUNCT
ejpam-1354	196	32	,	,	PUNCT
ejpam-1354	196	33	and	and	CCONJ
ejpam-1354	196	34	easily	easily	ADV
ejpam-1354	196	35	we	we	PRON
ejpam-1354	196	36	see	see	VERB
ejpam-1354	196	37	that	that	SCONJ
ejpam-1354	196	38	the	the	DET
ejpam-1354	196	39	energy	energy	NOUN
ejpam-1354	196	40	of	of	ADP
ejpam-1354	196	41	m	m	PROPN
ejpam-1354	196	42	can	can	AUX
ejpam-1354	196	43	be	be	AUX
ejpam-1354	196	44	written	write	VERB
ejpam-1354	196	45	as	as	ADP
ejpam-1354	196	46	e(m	e(m	NOUN
ejpam-1354	196	47	)	)	PUNCT
ejpam-1354	197	1	=	=	SYM
ejpam-1354	197	2	im+	im+	ADJ
ejpam-1354	197	3	2m(a)e(a	2m(a)e(a	NUM
ejpam-1354	197	4	,	,	PUNCT
ejpam-1354	197	5	m	m	PRON
ejpam-1354	197	6	)	)	PUNCT
ejpam-1354	198	1	+	+	CCONJ
ejpam-1354	198	2	2m(a∗)e(a∗	2m(a∗)e(a∗	NUM
ejpam-1354	198	3	,	,	PUNCT
ejpam-1354	198	4	m	m	NOUN
ejpam-1354	198	5	)	)	PUNCT
ejpam-1354	198	6	−	−	NOUN
ejpam-1354	198	7	2m(a∗)m(a)ϕ(a∗	2m(a∗)m(a)ϕ(a∗	NUM
ejpam-1354	198	8	,	,	PUNCT
ejpam-1354	198	9	a)n2(a∗−	a)n2(a∗−	PROPN
ejpam-1354	198	10	a	a	PRON
ejpam-1354	198	11	)	)	PUNCT
ejpam-1354	198	12	.	.	PUNCT
ejpam-1354	199	1	(	(	PUNCT
ejpam-1354	199	2	16	16	NUM
ejpam-1354	199	3	)	)	PUNCT
ejpam-1354	199	4	similarly	similarly	ADV
ejpam-1354	199	5	for	for	ADP
ejpam-1354	199	6	m∗	m∗	NOUN
ejpam-1354	199	7	(	(	PUNCT
ejpam-1354	199	8	by	by	ADP
ejpam-1354	199	9	replacing	replace	VERB
ejpam-1354	199	10	m	m	PRON
ejpam-1354	199	11	by	by	ADP
ejpam-1354	199	12	m∗	m∗	NOUN
ejpam-1354	199	13	)	)	PUNCT
ejpam-1354	199	14	,	,	PUNCT
ejpam-1354	199	15	we	we	PRON
ejpam-1354	199	16	get	get	VERB
ejpam-1354	199	17	e(m∗	e(m∗	PRON
ejpam-1354	199	18	)	)	PUNCT
ejpam-1354	200	1	=	=	NOUN
ejpam-1354	200	2	im∗	im∗	NOUN
ejpam-1354	200	3	+	+	CCONJ
ejpam-1354	200	4	2m∗(a)e(a	2m∗(a)e(a	ADJ
ejpam-1354	200	5	,	,	PUNCT
ejpam-1354	200	6	m∗	m∗	NOUN
ejpam-1354	200	7	)	)	PUNCT
ejpam-1354	200	8	+	+	CCONJ
ejpam-1354	200	9	2m(a∗)e(a∗	2m(a∗)e(a∗	NUM
ejpam-1354	200	10	,	,	PUNCT
ejpam-1354	200	11	m∗	m∗	NOUN
ejpam-1354	200	12	)	)	PUNCT
ejpam-1354	200	13	−	−	NOUN
ejpam-1354	200	14	2m∗(a∗)m∗(a)ϕ(a∗	2m∗(a∗)m∗(a)ϕ(a∗	NUM
ejpam-1354	200	15	,	,	PUNCT
ejpam-1354	200	16	a)d2(a∗	a)d2(a∗	VERB
ejpam-1354	200	17	,	,	PUNCT
ejpam-1354	200	18	a	a	PRON
ejpam-1354	200	19	)	)	PUNCT
ejpam-1354	200	20	.	.	PUNCT
ejpam-1354	201	1	(	(	PUNCT
ejpam-1354	201	2	17	17	NUM
ejpam-1354	201	3	)	)	PUNCT
ejpam-1354	201	4	note	note	NOUN
ejpam-1354	201	5	that	that	SCONJ
ejpam-1354	201	6	m∗(a	m∗(a	NOUN
ejpam-1354	201	7	)	)	PUNCT
ejpam-1354	201	8	=	=	SYM
ejpam-1354	201	9	0	0	PUNCT
ejpam-1354	202	1	and	and	CCONJ
ejpam-1354	202	2	i	i	PRON
ejpam-1354	202	3	m	m	NOUN
ejpam-1354	202	4	=	=	VERB
ejpam-1354	202	5	im∗	im∗	NOUN
ejpam-1354	202	6	.	.	PUNCT
ejpam-1354	203	1	in	in	ADP
ejpam-1354	203	2	addition	addition	NOUN
ejpam-1354	203	3	we	we	PRON
ejpam-1354	203	4	have	have	VERB
ejpam-1354	203	5	:	:	PUNCT
ejpam-1354	203	6	e(a∗	e(a∗	NUM
ejpam-1354	203	7	,	,	PUNCT
ejpam-1354	203	8	m∗	m∗	PROPN
ejpam-1354	203	9	)	)	PUNCT
ejpam-1354	203	10	=	=	SYM
ejpam-1354	204	1	e(a∗	e(a∗	ADP
ejpam-1354	204	2	,	,	PUNCT
ejpam-1354	204	3	m)−m(a)ϕ(a∗	m)−m(a)ϕ(a∗	PROPN
ejpam-1354	204	4	,	,	PUNCT
ejpam-1354	204	5	a)n2(a∗−	a)n2(a∗−	PROPN
ejpam-1354	204	6	a	a	NOUN
ejpam-1354	204	7	)	)	PUNCT
ejpam-1354	204	8	.	.	PUNCT
ejpam-1354	205	1	(	(	PUNCT
ejpam-1354	205	2	18	18	NUM
ejpam-1354	205	3	)	)	PUNCT
ejpam-1354	205	4	therefore	therefore	ADV
ejpam-1354	205	5	,	,	PUNCT
ejpam-1354	205	6	from	from	ADP
ejpam-1354	205	7	(	(	PUNCT
ejpam-1354	205	8	17)–(18	17)–(18	NUM
ejpam-1354	205	9	)	)	PUNCT
ejpam-1354	205	10	it	it	PRON
ejpam-1354	205	11	follows	follow	VERB
ejpam-1354	205	12	:	:	PUNCT
ejpam-1354	205	13	e(m∗	e(m∗	NUM
ejpam-1354	205	14	)	)	PUNCT
ejpam-1354	205	15	=	=	SYM
ejpam-1354	205	16	im∗	im∗	PROPN
ejpam-1354	205	17	+	+	CCONJ
ejpam-1354	205	18	2m∗(a)e(a	2m∗(a)e(a	ADJ
ejpam-1354	205	19	,	,	PUNCT
ejpam-1354	205	20	m∗	m∗	NOUN
ejpam-1354	205	21	)	)	PUNCT
ejpam-1354	205	22	.	.	PUNCT
ejpam-1354	206	1	from	from	ADP
ejpam-1354	206	2	(	(	PUNCT
ejpam-1354	206	3	16	16	NUM
ejpam-1354	206	4	)	)	PUNCT
ejpam-1354	206	5	and	and	CCONJ
ejpam-1354	206	6	the	the	DET
ejpam-1354	206	7	last	last	ADJ
ejpam-1354	206	8	equality	equality	NOUN
ejpam-1354	206	9	,	,	PUNCT
ejpam-1354	206	10	we	we	PRON
ejpam-1354	206	11	get	get	VERB
ejpam-1354	206	12	(	(	PUNCT
ejpam-1354	206	13	15	15	NUM
ejpam-1354	206	14	)	)	PUNCT
ejpam-1354	206	15	,	,	PUNCT
ejpam-1354	206	16	which	which	PRON
ejpam-1354	206	17	prove	prove	VERB
ejpam-1354	206	18	the	the	DET
ejpam-1354	206	19	result	result	NOUN
ejpam-1354	206	20	of	of	ADP
ejpam-1354	206	21	the	the	DET
ejpam-1354	206	22	lemma	lemma	PROPN
ejpam-1354	206	23	.	.	PUNCT
ejpam-1354	207	1	definition	definition	NOUN
ejpam-1354	207	2	5	5	NUM
ejpam-1354	207	3	(	(	PUNCT
ejpam-1354	207	4	moves	move	NOUN
ejpam-1354	207	5	on	on	ADP
ejpam-1354	207	6	continuous	continuous	ADJ
ejpam-1354	207	7	metric	metric	ADJ
ejpam-1354	207	8	spaces	space	NOUN
ejpam-1354	207	9	)	)	PUNCT
ejpam-1354	207	10	.	.	PUNCT
ejpam-1354	208	1	a	a	DET
ejpam-1354	208	2	pair	pair	NOUN
ejpam-1354	208	3	(	(	PUNCT
ejpam-1354	208	4	m	m	NOUN
ejpam-1354	208	5	,	,	PUNCT
ejpam-1354	208	6	m∗	m∗	PROPN
ejpam-1354	208	7	)	)	PUNCT
ejpam-1354	208	8	is	be	AUX
ejpam-1354	208	9	called	call	VERB
ejpam-1354	208	10	condensing	condense	VERB
ejpam-1354	208	11	,	,	PUNCT
ejpam-1354	208	12	if	if	SCONJ
ejpam-1354	208	13	there	there	PRON
ejpam-1354	208	14	is	be	VERB
ejpam-1354	208	15	(	(	PUNCT
ejpam-1354	208	16	a	a	PRON
ejpam-1354	208	17	,	,	PUNCT
ejpam-1354	208	18	a∗	a∗	ADJ
ejpam-1354	208	19	)	)	PUNCT
ejpam-1354	208	20	∈	∈	PROPN
ejpam-1354	208	21	s(m)×	s(m)×	PROPN
ejpam-1354	208	22	x	x	PUNCT
ejpam-1354	208	23	such	such	ADJ
ejpam-1354	208	24	that	that	SCONJ
ejpam-1354	208	25	(	(	PUNCT
ejpam-1354	208	26	i	i	NOUN
ejpam-1354	208	27	)	)	PUNCT
ejpam-1354	208	28	d(a	d(a	PROPN
ejpam-1354	208	29	,	,	PUNCT
ejpam-1354	208	30	a∗)≤	a∗)≤	PROPN
ejpam-1354	208	31	ε+	ε+	NUM
ejpam-1354	208	32	θ	θ	PROPN
ejpam-1354	208	33	,	,	PUNCT
ejpam-1354	208	34	(	(	PUNCT
ejpam-1354	208	35	ii	ii	NOUN
ejpam-1354	208	36	)	)	PUNCT
ejpam-1354	208	37	m∗	m∗	NOUN
ejpam-1354	209	1	=	=	SYM
ejpam-1354	209	2	(	(	PUNCT
ejpam-1354	209	3	a	a	PRON
ejpam-1354	209	4	,	,	PUNCT
ejpam-1354	209	5	a∗	a∗	NOUN
ejpam-1354	209	6	,	,	PUNCT
ejpam-1354	209	7	m	m	PROPN
ejpam-1354	209	8	)	)	PUNCT
ejpam-1354	209	9	and	and	CCONJ
ejpam-1354	209	10	m.	m.	PROPN
ejpam-1354	209	11	zahri	zahri	PROPN
ejpam-1354	209	12	/	/	SYM
ejpam-1354	209	13	eur	eur	PROPN
ejpam-1354	209	14	.	.	PUNCT
ejpam-1354	210	1	j.	j.	PROPN
ejpam-1354	210	2	pure	pure	PROPN
ejpam-1354	210	3	appl	appl	PROPN
ejpam-1354	210	4	.	.	PROPN
ejpam-1354	210	5	math	math	PROPN
ejpam-1354	210	6	,	,	PUNCT
ejpam-1354	210	7	6	6	NUM
ejpam-1354	210	8	(	(	PUNCT
ejpam-1354	210	9	2013	2013	NUM
ejpam-1354	210	10	)	)	PUNCT
ejpam-1354	210	11	,	,	PUNCT
ejpam-1354	210	12	172	172	NUM
ejpam-1354	210	13	-	-	SYM
ejpam-1354	210	14	188	188	NUM
ejpam-1354	210	15	181	181	NUM
ejpam-1354	210	16	(	(	PUNCT
ejpam-1354	210	17	iii	iii	NOUN
ejpam-1354	210	18	)	)	PUNCT
ejpam-1354	210	19	e(a∗	e(a∗	NOUN
ejpam-1354	210	20	,	,	PUNCT
ejpam-1354	210	21	m∗)ϕ(a	m∗)ϕ(a	NOUN
ejpam-1354	210	22	,	,	PUNCT
ejpam-1354	210	23	a∗	a∗	NOUN
ejpam-1354	210	24	)	)	PUNCT
ejpam-1354	210	25	<	<	X
ejpam-1354	210	26	e(y	e(y	PROPN
ejpam-1354	210	27	,	,	PUNCT
ejpam-1354	210	28	m∗)ϕ(a	m∗)ϕ(a	NOUN
ejpam-1354	210	29	,	,	PUNCT
ejpam-1354	210	30	y	y	NOUN
ejpam-1354	210	31	)	)	PUNCT
ejpam-1354	210	32	,	,	PUNCT
ejpam-1354	210	33	d(a	d(a	PROPN
ejpam-1354	210	34	,	,	PUNCT
ejpam-1354	210	35	y)≤	y)≤	PROPN
ejpam-1354	210	36	ε+	ε+	X
ejpam-1354	210	37	θ	θ	PROPN
ejpam-1354	210	38	,	,	PUNCT
ejpam-1354	210	39	∀y	∀y	NUM
ejpam-1354	210	40	.	.	PUNCT
ejpam-1354	211	1	a	a	DET
ejpam-1354	211	2	sequence	sequence	NOUN
ejpam-1354	211	3	of	of	ADP
ejpam-1354	211	4	nonnegative	nonnegative	ADJ
ejpam-1354	211	5	measures	measure	NOUN
ejpam-1354	211	6	m1	m1	NOUN
ejpam-1354	211	7	,	,	PUNCT
ejpam-1354	211	8	m2	m2	PROPN
ejpam-1354	211	9	,	,	PUNCT
ejpam-1354	211	10	.	.	PUNCT
ejpam-1354	211	11	.	.	PUNCT
ejpam-1354	211	12	.	.	PUNCT
ejpam-1354	212	1	is	be	AUX
ejpam-1354	212	2	called	call	VERB
ejpam-1354	212	3	condensing	condense	VERB
ejpam-1354	212	4	,	,	PUNCT
ejpam-1354	212	5	if	if	SCONJ
ejpam-1354	212	6	for	for	ADP
ejpam-1354	212	7	every	every	DET
ejpam-1354	212	8	i	i	PRON
ejpam-1354	212	9	the	the	DET
ejpam-1354	212	10	pair	pair	NOUN
ejpam-1354	212	11	(	(	PUNCT
ejpam-1354	212	12	mi	mi	PROPN
ejpam-1354	212	13	,	,	PUNCT
ejpam-1354	212	14	mi+1	mi+1	PROPN
ejpam-1354	212	15	)	)	PUNCT
ejpam-1354	212	16	is	be	AUX
ejpam-1354	212	17	condensing	condense	VERB
ejpam-1354	212	18	.	.	PUNCT
ejpam-1354	213	1	it	it	PRON
ejpam-1354	213	2	is	be	AUX
ejpam-1354	213	3	important	important	ADJ
ejpam-1354	213	4	to	to	PART
ejpam-1354	213	5	note	note	VERB
ejpam-1354	213	6	that	that	SCONJ
ejpam-1354	213	7	a	a	DET
ejpam-1354	213	8	singular	singular	ADJ
ejpam-1354	213	9	move	move	NOUN
ejpam-1354	213	10	according	accord	VERB
ejpam-1354	213	11	to	to	ADP
ejpam-1354	213	12	definition	definition	NOUN
ejpam-1354	213	13	5	5	NUM
ejpam-1354	213	14	satisfies	satisfy	VERB
ejpam-1354	213	15	the	the	DET
ejpam-1354	213	16	minimality	minimality	NOUN
ejpam-1354	213	17	condition	condition	NOUN
ejpam-1354	213	18	:	:	PUNCT
ejpam-1354	213	19	if	if	SCONJ
ejpam-1354	213	20	a	a	DET
ejpam-1354	213	21	moves	move	NOUN
ejpam-1354	213	22	to	to	PART
ejpam-1354	213	23	a∗	a∗	VERB
ejpam-1354	213	24	then	then	ADV
ejpam-1354	213	25	e(a	e(a	PROPN
ejpam-1354	213	26	,	,	PUNCT
ejpam-1354	213	27	m	m	PROPN
ejpam-1354	213	28	)	)	PUNCT
ejpam-1354	213	29	>	>	X
ejpam-1354	213	30	e(a∗	e(a∗	SYM
ejpam-1354	213	31	,	,	PUNCT
ejpam-1354	213	32	m∗	m∗	PROPN
ejpam-1354	213	33	)	)	PUNCT
ejpam-1354	213	34	.	.	PUNCT
ejpam-1354	214	1	in	in	ADP
ejpam-1354	214	2	other	other	ADJ
ejpam-1354	214	3	words	word	NOUN
ejpam-1354	214	4	the	the	DET
ejpam-1354	214	5	particle	particle	NOUN
ejpam-1354	214	6	a	a	DET
ejpam-1354	214	7	moves	move	NOUN
ejpam-1354	214	8	where	where	SCONJ
ejpam-1354	214	9	the	the	DET
ejpam-1354	214	10	local	local	ADJ
ejpam-1354	214	11	energy	energy	NOUN
ejpam-1354	214	12	smaller	small	ADJ
ejpam-1354	214	13	,	,	PUNCT
ejpam-1354	214	14	in	in	ADP
ejpam-1354	214	15	this	this	DET
ejpam-1354	214	16	case	case	NOUN
ejpam-1354	214	17	it	it	PRON
ejpam-1354	214	18	moves	move	VERB
ejpam-1354	214	19	where	where	SCONJ
ejpam-1354	214	20	the	the	DET
ejpam-1354	214	21	energy	energy	NOUN
ejpam-1354	214	22	is	be	AUX
ejpam-1354	214	23	minimal	minimal	ADJ
ejpam-1354	214	24	.	.	PUNCT
ejpam-1354	215	1	our	our	PRON
ejpam-1354	215	2	goal	goal	NOUN
ejpam-1354	215	3	is	be	AUX
ejpam-1354	215	4	to	to	PART
ejpam-1354	215	5	construct	construct	VERB
ejpam-1354	215	6	a	a	DET
ejpam-1354	215	7	condensing	condense	VERB
ejpam-1354	215	8	sequence	sequence	NOUN
ejpam-1354	215	9	,	,	PUNCT
ejpam-1354	215	10	with	with	ADP
ejpam-1354	215	11	vanishing	vanish	VERB
ejpam-1354	215	12	energy	energy	NOUN
ejpam-1354	215	13	(	(	PUNCT
ejpam-1354	215	14	stable	stable	ADJ
ejpam-1354	215	15	state	state	NOUN
ejpam-1354	215	16	)	)	PUNCT
ejpam-1354	215	17	at	at	ADP
ejpam-1354	215	18	the	the	DET
ejpam-1354	215	19	limit	limit	NOUN
ejpam-1354	215	20	state	state	NOUN
ejpam-1354	215	21	.	.	PUNCT
ejpam-1354	216	1	the	the	DET
ejpam-1354	216	2	following	follow	VERB
ejpam-1354	216	3	corollary	corollary	NOUN
ejpam-1354	216	4	is	be	AUX
ejpam-1354	216	5	useful	useful	ADJ
ejpam-1354	216	6	:	:	PUNCT
ejpam-1354	216	7	corollary	corollary	ADJ
ejpam-1354	216	8	1	1	NUM
ejpam-1354	216	9	.	.	PUNCT
ejpam-1354	217	1	if	if	SCONJ
ejpam-1354	217	2	(	(	PUNCT
ejpam-1354	217	3	mi)i≥0	mi)i≥0	PROPN
ejpam-1354	217	4	is	be	AUX
ejpam-1354	217	5	a	a	DET
ejpam-1354	217	6	singularly	singularly	ADV
ejpam-1354	217	7	condensing	condense	VERB
ejpam-1354	217	8	sequence	sequence	NOUN
ejpam-1354	217	9	,	,	PUNCT
ejpam-1354	217	10	then	then	ADV
ejpam-1354	217	11	lim	lim	PROPN
ejpam-1354	217	12	i→∞	i→∞	PROPN
ejpam-1354	217	13	e(mi	e(mi	NOUN
ejpam-1354	217	14	)	)	PUNCT
ejpam-1354	217	15	=	=	PUNCT
ejpam-1354	217	16	`	`	PUNCT
ejpam-1354	217	17	≥	≥	NOUN
ejpam-1354	217	18	0	0	NUM
ejpam-1354	217	19	.	.	PUNCT
ejpam-1354	218	1	proof	proof	NOUN
ejpam-1354	218	2	.	.	PUNCT
ejpam-1354	219	1	the	the	DET
ejpam-1354	219	2	proof	proof	NOUN
ejpam-1354	219	3	follows	follow	VERB
ejpam-1354	219	4	immediately	immediately	ADV
ejpam-1354	219	5	from	from	ADP
ejpam-1354	219	6	definition	definition	NOUN
ejpam-1354	219	7	5	5	NUM
ejpam-1354	219	8	and	and	CCONJ
ejpam-1354	219	9	lemma	lemma	PROPN
ejpam-1354	219	10	3	3	X
ejpam-1354	219	11	.	.	PUNCT
ejpam-1354	220	1	our	our	PRON
ejpam-1354	220	2	main	main	ADJ
ejpam-1354	220	3	concern	concern	NOUN
ejpam-1354	220	4	in	in	ADP
ejpam-1354	220	5	the	the	DET
ejpam-1354	220	6	following	following	NOUN
ejpam-1354	220	7	is	be	AUX
ejpam-1354	220	8	to	to	PART
ejpam-1354	220	9	prove	prove	VERB
ejpam-1354	220	10	the	the	DET
ejpam-1354	220	11	existence	existence	NOUN
ejpam-1354	220	12	of	of	ADP
ejpam-1354	220	13	condensing	condense	VERB
ejpam-1354	220	14	sequences	sequence	NOUN
ejpam-1354	220	15	converging	converge	VERB
ejpam-1354	220	16	to	to	ADP
ejpam-1354	220	17	a	a	DET
ejpam-1354	220	18	measure	measure	NOUN
ejpam-1354	220	19	m	m	ADP
ejpam-1354	220	20	,	,	PUNCT
ejpam-1354	220	21	such	such	ADJ
ejpam-1354	220	22	that	that	SCONJ
ejpam-1354	220	23	e(m	e(m	NOUN
ejpam-1354	220	24	)	)	PUNCT
ejpam-1354	220	25	=	=	SYM
ejpam-1354	221	1	0	0	X
ejpam-1354	221	2	.	.	PUNCT
ejpam-1354	221	3	especially	especially	ADV
ejpam-1354	221	4	to	to	PART
ejpam-1354	221	5	define	define	VERB
ejpam-1354	221	6	special	special	ADJ
ejpam-1354	221	7	cases	case	NOUN
ejpam-1354	221	8	of	of	ADP
ejpam-1354	221	9	condensing	condense	VERB
ejpam-1354	221	10	sequences	sequence	NOUN
ejpam-1354	221	11	,	,	PUNCT
ejpam-1354	221	12	which	which	PRON
ejpam-1354	221	13	converges	converge	VERB
ejpam-1354	221	14	in	in	ADP
ejpam-1354	221	15	finite	finite	ADJ
ejpam-1354	221	16	time	time	NOUN
ejpam-1354	221	17	steps	step	NOUN
ejpam-1354	221	18	.	.	PUNCT
ejpam-1354	222	1	therefore	therefore	ADV
ejpam-1354	222	2	,	,	PUNCT
ejpam-1354	222	3	we	we	PRON
ejpam-1354	222	4	define	define	VERB
ejpam-1354	222	5	the	the	DET
ejpam-1354	222	6	effectively	effectively	ADV
ejpam-1354	222	7	condensing	condense	VERB
ejpam-1354	222	8	sequences	sequence	NOUN
ejpam-1354	222	9	:	:	PUNCT
ejpam-1354	222	10	a	a	DET
ejpam-1354	222	11	singularly	singularly	ADV
ejpam-1354	222	12	condensing	condense	VERB
ejpam-1354	222	13	sequence	sequence	NOUN
ejpam-1354	222	14	m1	m1	NOUN
ejpam-1354	222	15	,	,	PUNCT
ejpam-1354	222	16	m2	m2	PROPN
ejpam-1354	222	17	,	,	PUNCT
ejpam-1354	222	18	.	.	PUNCT
ejpam-1354	222	19	.	.	PUNCT
ejpam-1354	222	20	.	.	PUNCT
ejpam-1354	223	1	is	be	AUX
ejpam-1354	223	2	called	call	VERB
ejpam-1354	223	3	effectively	effectively	ADV
ejpam-1354	223	4	condensing	condense	VERB
ejpam-1354	223	5	sequence	sequence	NOUN
ejpam-1354	223	6	,	,	PUNCT
ejpam-1354	223	7	if	if	SCONJ
ejpam-1354	223	8	there	there	PRON
ejpam-1354	223	9	exists	exist	VERB
ejpam-1354	223	10	c	c	NOUN
ejpam-1354	223	11	>	>	X
ejpam-1354	223	12	0	0	NUM
ejpam-1354	223	13	such	such	ADJ
ejpam-1354	223	14	that	that	SCONJ
ejpam-1354	223	15	(	(	PUNCT
ejpam-1354	223	16	i	i	NOUN
ejpam-1354	223	17	)	)	PUNCT
ejpam-1354	223	18	mi+1	mi+1	NOUN
ejpam-1354	223	19	=	=	SYM
ejpam-1354	223	20	(	(	PUNCT
ejpam-1354	223	21	a	a	PRON
ejpam-1354	223	22	,	,	PUNCT
ejpam-1354	223	23	a∗	a∗	PROPN
ejpam-1354	223	24	,	,	PUNCT
ejpam-1354	223	25	mi	mi	PROPN
ejpam-1354	223	26	)	)	PUNCT
ejpam-1354	223	27	and	and	CCONJ
ejpam-1354	223	28	(	(	PUNCT
ejpam-1354	223	29	ii	ii	NOUN
ejpam-1354	223	30	)	)	PUNCT
ejpam-1354	223	31	e(mi)−	e(mi)−	NOUN
ejpam-1354	223	32	e(mi+1)≥	e(mi+1)≥	PROPN
ejpam-1354	223	33	cα(mi	cα(mi	PROPN
ejpam-1354	223	34	)	)	PUNCT
ejpam-1354	223	35	,	,	PUNCT
ejpam-1354	223	36	where	where	SCONJ
ejpam-1354	223	37	α(mi	α(mi	NOUN
ejpam-1354	223	38	)	)	PUNCT
ejpam-1354	223	39	=	=	SYM
ejpam-1354	223	40	max	max	PROPN
ejpam-1354	223	41	y	y	PROPN
ejpam-1354	223	42	�	�	PROPN
ejpam-1354	223	43	ϕ(y	ϕ(y	PROPN
ejpam-1354	223	44	,	,	PUNCT
ejpam-1354	223	45	a)d2(y	a)d2(y	ADV
ejpam-1354	223	46	,	,	PUNCT
ejpam-1354	223	47	a)|y	a)|y	NOUN
ejpam-1354	223	48	∈	∈	PROPN
ejpam-1354	223	49	s(mi	s(mi	PROPN
ejpam-1354	223	50	)	)	PUNCT
ejpam-1354	223	51	.	.	PUNCT
ejpam-1354	224	1	remark	remark	VERB
ejpam-1354	224	2	3	3	NUM
ejpam-1354	224	3	.	.	PUNCT
ejpam-1354	224	4	note	note	VERB
ejpam-1354	224	5	that	that	SCONJ
ejpam-1354	224	6	by	by	ADP
ejpam-1354	224	7	setting	set	VERB
ejpam-1354	224	8	c	c	NOUN
ejpam-1354	224	9	=	=	SYM
ejpam-1354	224	10	2	2	NUM
ejpam-1354	224	11	min	min	NOUN
ejpam-1354	224	12	a	a	DET
ejpam-1354	224	13	�	�	PROPN
ejpam-1354	224	14	m(a)|a	m(a)|a	PROPN
ejpam-1354	224	15	∈	∈	PROPN
ejpam-1354	224	16	s(mi	s(mi	PROPN
ejpam-1354	224	17	)	)	PUNCT
ejpam-1354	224	18	,	,	PUNCT
ejpam-1354	224	19	and	and	CCONJ
ejpam-1354	224	20	using	use	VERB
ejpam-1354	224	21	the	the	DET
ejpam-1354	224	22	results	result	NOUN
ejpam-1354	224	23	above	above	ADV
ejpam-1354	224	24	,	,	PUNCT
ejpam-1354	224	25	it	it	PRON
ejpam-1354	224	26	follows	follow	VERB
ejpam-1354	224	27	the	the	DET
ejpam-1354	224	28	existence	existence	NOUN
ejpam-1354	224	29	of	of	ADP
ejpam-1354	224	30	the	the	DET
ejpam-1354	224	31	effectively	effectively	ADV
ejpam-1354	224	32	condensing	condense	VERB
ejpam-1354	224	33	sequence	sequence	NOUN
ejpam-1354	224	34	.	.	PUNCT
ejpam-1354	225	1	lemma	lemma	PROPN
ejpam-1354	225	2	4	4	X
ejpam-1354	225	3	.	.	PUNCT
ejpam-1354	225	4	suppose	suppose	VERB
ejpam-1354	225	5	that	that	SCONJ
ejpam-1354	225	6	(	(	PUNCT
ejpam-1354	225	7	mi)i≥0	mi)i≥0	PROPN
ejpam-1354	225	8	is	be	AUX
ejpam-1354	225	9	an	an	DET
ejpam-1354	225	10	effectively	effectively	ADV
ejpam-1354	225	11	condensing	condense	VERB
ejpam-1354	225	12	.	.	PUNCT
ejpam-1354	226	1	if	if	SCONJ
ejpam-1354	226	2	lim	lim	PROPN
ejpam-1354	226	3	i→∞	i→∞	NUM
ejpam-1354	226	4	e(mi	e(mi	NOUN
ejpam-1354	226	5	)	)	PUNCT
ejpam-1354	226	6	=	=	SYM
ejpam-1354	226	7	e(m	e(m	PROPN
ejpam-1354	226	8	)	)	PUNCT
ejpam-1354	226	9	,	,	PUNCT
ejpam-1354	226	10	then	then	ADV
ejpam-1354	226	11	α(m	α(m	PROPN
ejpam-1354	226	12	)	)	PUNCT
ejpam-1354	227	1	=	=	SYM
ejpam-1354	227	2	0	0	X
ejpam-1354	227	3	.	.	PUNCT
ejpam-1354	228	1	(	(	PUNCT
ejpam-1354	228	2	19	19	NUM
ejpam-1354	228	3	)	)	PUNCT
ejpam-1354	228	4	proof	proof	NOUN
ejpam-1354	228	5	.	.	PUNCT
ejpam-1354	229	1	consider	consider	VERB
ejpam-1354	229	2	η	η	PROPN
ejpam-1354	229	3	>	>	X
ejpam-1354	229	4	0	0	PROPN
ejpam-1354	229	5	,	,	PUNCT
ejpam-1354	229	6	from	from	ADP
ejpam-1354	229	7	lim	lim	PROPN
ejpam-1354	229	8	i→∞	i→∞	NUM
ejpam-1354	229	9	e(mi	e(mi	NOUN
ejpam-1354	229	10	)	)	PUNCT
ejpam-1354	229	11	=	=	SYM
ejpam-1354	230	1	e(m	e(m	PROPN
ejpam-1354	230	2	)	)	PUNCT
ejpam-1354	230	3	,	,	PUNCT
ejpam-1354	230	4	exists	exist	VERB
ejpam-1354	230	5	i0	i0	PROPN
ejpam-1354	230	6	such	such	ADJ
ejpam-1354	230	7	that	that	SCONJ
ejpam-1354	230	8	for	for	ADP
ejpam-1354	230	9	all	all	PRON
ejpam-1354	230	10	i	i	PRON
ejpam-1354	230	11	>	>	X
ejpam-1354	230	12	i0	i0	PROPN
ejpam-1354	230	13	,	,	PUNCT
ejpam-1354	230	14	it	it	PRON
ejpam-1354	230	15	follows	follow	VERB
ejpam-1354	230	16	2cα(mi)≤	2cα(mi)≤	NUM
ejpam-1354	230	17	e(mi)−	e(mi)−	NOUN
ejpam-1354	230	18	e(m)≤	e(m)≤	PROPN
ejpam-1354	230	19	η	η	PROPN
ejpam-1354	230	20	,	,	PUNCT
ejpam-1354	230	21	(	(	PUNCT
ejpam-1354	230	22	20	20	NUM
ejpam-1354	230	23	)	)	PUNCT
ejpam-1354	230	24	for	for	ADP
ejpam-1354	230	25	large	large	ADJ
ejpam-1354	230	26	i	i	NOUN
ejpam-1354	230	27	,	,	PUNCT
ejpam-1354	230	28	we	we	PRON
ejpam-1354	230	29	get	get	AUX
ejpam-1354	230	30	limi	limi	VERB
ejpam-1354	230	31	α(m	α(m	PROPN
ejpam-1354	230	32	i	i	PROPN
ejpam-1354	230	33	)	)	PUNCT
ejpam-1354	230	34	=	=	SYM
ejpam-1354	230	35	0	0	PUNCT
ejpam-1354	230	36	and	and	CCONJ
ejpam-1354	230	37	still	still	ADV
ejpam-1354	230	38	α(m	α(m	ADJ
ejpam-1354	230	39	)	)	PUNCT
ejpam-1354	231	1	=	=	SYM
ejpam-1354	231	2	0	0	X
ejpam-1354	231	3	.	.	PUNCT
ejpam-1354	231	4	m.	m.	NOUN
ejpam-1354	231	5	zahri	zahri	PROPN
ejpam-1354	231	6	/	/	SYM
ejpam-1354	231	7	eur	eur	PROPN
ejpam-1354	231	8	.	.	PUNCT
ejpam-1354	232	1	j.	j.	PROPN
ejpam-1354	232	2	pure	pure	PROPN
ejpam-1354	232	3	appl	appl	PROPN
ejpam-1354	232	4	.	.	PROPN
ejpam-1354	232	5	math	math	PROPN
ejpam-1354	232	6	,	,	PUNCT
ejpam-1354	232	7	6	6	NUM
ejpam-1354	232	8	(	(	PUNCT
ejpam-1354	232	9	2013	2013	NUM
ejpam-1354	232	10	)	)	PUNCT
ejpam-1354	232	11	,	,	PUNCT
ejpam-1354	232	12	172	172	NUM
ejpam-1354	232	13	-	-	SYM
ejpam-1354	232	14	188	188	NUM
ejpam-1354	232	15	182	182	NUM
ejpam-1354	232	16	theorem	theorem	NOUN
ejpam-1354	232	17	2	2	NUM
ejpam-1354	232	18	.	.	PUNCT
ejpam-1354	233	1	every	every	DET
ejpam-1354	233	2	effectively	effectively	ADV
ejpam-1354	233	3	condensing	condense	VERB
ejpam-1354	233	4	sequence	sequence	NOUN
ejpam-1354	233	5	of	of	ADP
ejpam-1354	233	6	masses	masse	NOUN
ejpam-1354	233	7	converges	converge	VERB
ejpam-1354	233	8	.	.	PUNCT
ejpam-1354	234	1	proof	proof	NOUN
ejpam-1354	234	2	.	.	PUNCT
ejpam-1354	235	1	since	since	SCONJ
ejpam-1354	235	2	x	x	PRON
ejpam-1354	235	3	is	be	AUX
ejpam-1354	235	4	compact	compact	ADJ
ejpam-1354	235	5	,	,	PUNCT
ejpam-1354	235	6	then	then	ADV
ejpam-1354	235	7	∪is(m	∪is(m	PROPN
ejpam-1354	235	8	i	i	PROPN
ejpam-1354	235	9	)	)	PUNCT
ejpam-1354	235	10	is	be	AUX
ejpam-1354	235	11	relative	relative	ADJ
ejpam-1354	235	12	compact	compact	ADJ
ejpam-1354	235	13	and	and	CCONJ
ejpam-1354	235	14	there	there	PRON
ejpam-1354	235	15	exists	exist	VERB
ejpam-1354	235	16	a	a	DET
ejpam-1354	235	17	subsequence	subsequence	NOUN
ejpam-1354	235	18	mi	mi	PROPN
ejpam-1354	235	19	j	j	PROPN
ejpam-1354	235	20	of	of	ADP
ejpam-1354	235	21	mi	mi	PROPN
ejpam-1354	235	22	such	such	ADJ
ejpam-1354	235	23	that	that	SCONJ
ejpam-1354	235	24	lim	lim	PROPN
ejpam-1354	235	25	j	j	PROPN
ejpam-1354	235	26	mi	mi	PROPN
ejpam-1354	235	27	j	j	PROPN
ejpam-1354	235	28	=	=	PROPN
ejpam-1354	235	29	m	m	PROPN
ejpam-1354	235	30	and	and	CCONJ
ejpam-1354	235	31	lim	lim	PROPN
ejpam-1354	235	32	j	j	PROPN
ejpam-1354	235	33	e(mi	e(mi	PROPN
ejpam-1354	235	34	j	j	PROPN
ejpam-1354	235	35	)	)	PUNCT
ejpam-1354	235	36	=	=	PUNCT
ejpam-1354	236	1	e(m	e(m	PROPN
ejpam-1354	236	2	)	)	PUNCT
ejpam-1354	236	3	.	.	PUNCT
ejpam-1354	237	1	from	from	ADP
ejpam-1354	237	2	lemma	lemma	PROPN
ejpam-1354	237	3	4	4	NUM
ejpam-1354	237	4	it	it	PRON
ejpam-1354	237	5	follows	follow	VERB
ejpam-1354	237	6	that	that	SCONJ
ejpam-1354	237	7	lim	lim	PROPN
ejpam-1354	237	8	j	j	PROPN
ejpam-1354	238	1	α(m	α(m	PROPN
ejpam-1354	238	2	i	i	PRON
ejpam-1354	238	3	j	j	PROPN
ejpam-1354	238	4	)	)	PUNCT
ejpam-1354	239	1	=	=	SYM
ejpam-1354	239	2	0	0	NUM
ejpam-1354	239	3	and	and	CCONJ
ejpam-1354	239	4	α(m	α(m	PROPN
ejpam-1354	239	5	)	)	PUNCT
ejpam-1354	240	1	=	=	SYM
ejpam-1354	241	1	0	0	X
ejpam-1354	241	2	.	.	PUNCT
ejpam-1354	242	1	since	since	SCONJ
ejpam-1354	242	2	the	the	DET
ejpam-1354	242	3	sequence	sequence	NOUN
ejpam-1354	242	4	m1	m1	NOUN
ejpam-1354	242	5	,	,	PUNCT
ejpam-1354	242	6	m2	m2	PROPN
ejpam-1354	242	7	,	,	PUNCT
ejpam-1354	242	8	.	.	PUNCT
ejpam-1354	242	9	.	.	PUNCT
ejpam-1354	243	1	.	.	PUNCT
ejpam-1354	244	1	is	be	AUX
ejpam-1354	244	2	effectively	effectively	ADV
ejpam-1354	244	3	condensing	condense	VERB
ejpam-1354	244	4	,	,	PUNCT
ejpam-1354	244	5	and	and	CCONJ
ejpam-1354	244	6	from	from	ADP
ejpam-1354	244	7	definition	definition	NOUN
ejpam-1354	244	8	5	5	NUM
ejpam-1354	244	9	there	there	ADV
ejpam-1354	244	10	exists	exist	VERB
ejpam-1354	244	11	k	k	X
ejpam-1354	244	12	such	such	ADJ
ejpam-1354	244	13	that	that	SCONJ
ejpam-1354	244	14	α(mk	α(mk	NOUN
ejpam-1354	244	15	)	)	PUNCT
ejpam-1354	244	16	=	=	SYM
ejpam-1354	245	1	0	0	X
ejpam-1354	245	2	.	.	PUNCT
ejpam-1354	246	1	therefore	therefore	ADV
ejpam-1354	246	2	,	,	PUNCT
ejpam-1354	246	3	for	for	ADP
ejpam-1354	246	4	all	all	DET
ejpam-1354	246	5	x	x	SYM
ejpam-1354	246	6	,	,	PUNCT
ejpam-1354	246	7	y	y	PROPN
ejpam-1354	246	8	∈	∈	PROPN
ejpam-1354	246	9	s(mk	s(mk	PROPN
ejpam-1354	246	10	)	)	PUNCT
ejpam-1354	246	11	,	,	PUNCT
ejpam-1354	246	12	it	it	PRON
ejpam-1354	246	13	follows	follow	VERB
ejpam-1354	246	14	d(x	d(x	NOUN
ejpam-1354	246	15	,	,	PUNCT
ejpam-1354	246	16	y	y	X
ejpam-1354	246	17	)	)	PUNCT
ejpam-1354	246	18	=	=	SYM
ejpam-1354	246	19	0	0	NUM
ejpam-1354	246	20	or	or	CCONJ
ejpam-1354	246	21	d(x	d(x	NOUN
ejpam-1354	246	22	,	,	PUNCT
ejpam-1354	246	23	y)≥	y)≥	PROPN
ejpam-1354	246	24	ε+	ε+	X
ejpam-1354	246	25	θ	θ	PROPN
ejpam-1354	246	26	(	(	PUNCT
ejpam-1354	246	27	21	21	NUM
ejpam-1354	246	28	)	)	PUNCT
ejpam-1354	246	29	hence	hence	ADV
ejpam-1354	246	30	,	,	PUNCT
ejpam-1354	246	31	e(mk	e(mk	NOUN
ejpam-1354	246	32	)	)	PUNCT
ejpam-1354	246	33	=	=	SYM
ejpam-1354	246	34	0	0	PUNCT
ejpam-1354	247	1	and	and	CCONJ
ejpam-1354	247	2	still	still	ADV
ejpam-1354	247	3	mk	mk	PROPN
ejpam-1354	247	4	is	be	AUX
ejpam-1354	247	5	a	a	DET
ejpam-1354	247	6	collection	collection	NOUN
ejpam-1354	247	7	of	of	ADP
ejpam-1354	247	8	isolated	isolated	ADJ
ejpam-1354	247	9	masses	masse	NOUN
ejpam-1354	247	10	with	with	ADP
ejpam-1354	247	11	propriety	propriety	NOUN
ejpam-1354	247	12	(	(	PUNCT
ejpam-1354	247	13	21	21	NUM
ejpam-1354	247	14	)	)	PUNCT
ejpam-1354	247	15	or	or	CCONJ
ejpam-1354	247	16	a	a	DET
ejpam-1354	247	17	point	point	NOUN
ejpam-1354	247	18	mass	mass	NOUN
ejpam-1354	247	19	m=	m=	X
ejpam-1354	247	20	m(x	m(x	PROPN
ejpam-1354	247	21	)	)	PUNCT
ejpam-1354	247	22	δa	δa	PROPN
ejpam-1354	247	23	for	for	ADP
ejpam-1354	247	24	a	a	DET
ejpam-1354	247	25	∈	∈	PROPN
ejpam-1354	247	26	x	x	X
ejpam-1354	247	27	.	.	PUNCT
ejpam-1354	248	1	remark	remark	PROPN
ejpam-1354	248	2	4	4	NUM
ejpam-1354	248	3	.	.	NOUN
ejpam-1354	249	1	•	•	NOUN
ejpam-1354	249	2	we	we	PRON
ejpam-1354	249	3	have	have	AUX
ejpam-1354	249	4	remarked	remark	VERB
ejpam-1354	249	5	that	that	SCONJ
ejpam-1354	249	6	even	even	ADV
ejpam-1354	249	7	if	if	SCONJ
ejpam-1354	249	8	the	the	DET
ejpam-1354	249	9	energy	energy	NOUN
ejpam-1354	249	10	of	of	ADP
ejpam-1354	249	11	the	the	DET
ejpam-1354	249	12	limit	limit	NOUN
ejpam-1354	249	13	measure	measure	NOUN
ejpam-1354	249	14	vanishes	vanish	VERB
ejpam-1354	249	15	,	,	PUNCT
ejpam-1354	249	16	the	the	DET
ejpam-1354	249	17	results	result	NOUN
ejpam-1354	249	18	are	be	AUX
ejpam-1354	249	19	non	non	PRON
ejpam-1354	249	20	necessary	necessary	ADJ
ejpam-1354	249	21	a	a	DET
ejpam-1354	249	22	singleton	singleton	NOUN
ejpam-1354	249	23	(	(	PUNCT
ejpam-1354	249	24	total	total	ADJ
ejpam-1354	249	25	condensing	condensing	NOUN
ejpam-1354	249	26	)	)	PUNCT
ejpam-1354	249	27	.	.	PUNCT
ejpam-1354	250	1	the	the	DET
ejpam-1354	250	2	limit	limit	NOUN
ejpam-1354	250	3	measure	measure	NOUN
ejpam-1354	250	4	is	be	AUX
ejpam-1354	250	5	a	a	DET
ejpam-1354	250	6	collection	collection	NOUN
ejpam-1354	250	7	of	of	ADP
ejpam-1354	250	8	segregated	segregated	ADJ
ejpam-1354	250	9	(	(	PUNCT
ejpam-1354	250	10	separated	separated	ADJ
ejpam-1354	250	11	)	)	PUNCT
ejpam-1354	250	12	subgroups	subgroup	NOUN
ejpam-1354	250	13	or	or	CCONJ
ejpam-1354	250	14	singleton	singleton	PROPN
ejpam-1354	250	15	mass	mass	NOUN
ejpam-1354	250	16	point	point	NOUN
ejpam-1354	250	17	.	.	PUNCT
ejpam-1354	251	1	this	this	PRON
ejpam-1354	251	2	is	be	AUX
ejpam-1354	251	3	justified	justify	VERB
ejpam-1354	251	4	by	by	ADP
ejpam-1354	251	5	the	the	DET
ejpam-1354	251	6	condition	condition	NOUN
ejpam-1354	251	7	(	(	PUNCT
ejpam-1354	251	8	21	21	NUM
ejpam-1354	251	9	)	)	PUNCT
ejpam-1354	251	10	.	.	PUNCT
ejpam-1354	252	1	total	total	ADJ
ejpam-1354	252	2	condensing	condense	VERB
ejpam-1354	252	3	of	of	ADP
ejpam-1354	252	4	particles	particle	NOUN
ejpam-1354	252	5	as	as	ADP
ejpam-1354	252	6	physical	physical	ADJ
ejpam-1354	252	7	phenomenon	phenomenon	NOUN
ejpam-1354	252	8	is	be	AUX
ejpam-1354	252	9	subject	subject	ADJ
ejpam-1354	252	10	of	of	ADP
ejpam-1354	252	11	several	several	ADJ
ejpam-1354	252	12	studies	study	NOUN
ejpam-1354	252	13	of	of	ADP
ejpam-1354	252	14	many	many	ADJ
ejpam-1354	252	15	scientists	scientist	NOUN
ejpam-1354	252	16	such	such	ADJ
ejpam-1354	252	17	as	as	ADP
ejpam-1354	252	18	consensus	consensus	NOUN
ejpam-1354	252	19	dynamics	dynamic	NOUN
ejpam-1354	252	20	of	of	ADP
ejpam-1354	252	21	opinions	opinion	NOUN
ejpam-1354	252	22	.	.	PUNCT
ejpam-1354	253	1	for	for	ADP
ejpam-1354	253	2	more	more	ADJ
ejpam-1354	253	3	details	detail	NOUN
ejpam-1354	253	4	see	see	VERB
ejpam-1354	253	5	the	the	DET
ejpam-1354	253	6	model	model	NOUN
ejpam-1354	253	7	proposed	propose	VERB
ejpam-1354	253	8	by	by	ADP
ejpam-1354	253	9	hegselmann	hegselmann	PROPN
ejpam-1354	253	10	and	and	CCONJ
ejpam-1354	253	11	krause	krause	NOUN
ejpam-1354	253	12	in	in	ADP
ejpam-1354	253	13	[	[	X
ejpam-1354	253	14	11	11	NUM
ejpam-1354	253	15	]	]	PUNCT
ejpam-1354	253	16	.	.	PUNCT
ejpam-1354	254	1	•	•	INTJ
ejpam-1354	254	2	it	it	PRON
ejpam-1354	254	3	is	be	AUX
ejpam-1354	254	4	important	important	ADJ
ejpam-1354	254	5	to	to	PART
ejpam-1354	254	6	note	note	VERB
ejpam-1354	254	7	that	that	SCONJ
ejpam-1354	254	8	if	if	SCONJ
ejpam-1354	254	9	s(m	s(m	PROPN
ejpam-1354	254	10	)	)	PUNCT
ejpam-1354	254	11	=	=	SYM
ejpam-1354	255	1	q	q	PROPN
ejpam-1354	255	2	∩	∩	NOUN
ejpam-1354	255	3	[	[	X
ejpam-1354	255	4	0,1	0,1	NUM
ejpam-1354	255	5	]	]	PUNCT
ejpam-1354	255	6	(	(	PUNCT
ejpam-1354	255	7	i.e.	i.e.	X
ejpam-1354	255	8	,	,	PUNCT
ejpam-1354	255	9	s(m	s(m	PROPN
ejpam-1354	255	10	)	)	PUNCT
ejpam-1354	255	11	is	be	AUX
ejpam-1354	255	12	the	the	DET
ejpam-1354	255	13	rational	rational	ADJ
ejpam-1354	255	14	numbers	number	NOUN
ejpam-1354	255	15	on	on	ADP
ejpam-1354	255	16	the	the	DET
ejpam-1354	255	17	interval	interval	NOUN
ejpam-1354	255	18	[	[	X
ejpam-1354	255	19	0,1	0,1	NOUN
ejpam-1354	255	20	]	]	PUNCT
ejpam-1354	255	21	)	)	PUNCT
ejpam-1354	255	22	.	.	PUNCT
ejpam-1354	256	1	because	because	SCONJ
ejpam-1354	256	2	of	of	ADP
ejpam-1354	256	3	the	the	DET
ejpam-1354	256	4	assumption	assumption	NOUN
ejpam-1354	256	5	of	of	ADP
ejpam-1354	256	6	one	one	NUM
ejpam-1354	256	7	-	-	PUNCT
ejpam-1354	256	8	by	by	ADP
ejpam-1354	256	9	-	-	PUNCT
ejpam-1354	256	10	one	one	NUM
ejpam-1354	256	11	asynchronous	asynchronous	ADJ
ejpam-1354	256	12	interleaving	interleaving	NOUN
ejpam-1354	256	13	,	,	PUNCT
ejpam-1354	256	14	a	a	DET
ejpam-1354	256	15	single	single	ADJ
ejpam-1354	256	16	iteration	iteration	NOUN
ejpam-1354	256	17	of	of	ADP
ejpam-1354	256	18	the	the	DET
ejpam-1354	256	19	condensing	condense	VERB
ejpam-1354	256	20	algorithm	algorithm	NOUN
ejpam-1354	256	21	will	will	AUX
ejpam-1354	256	22	not	not	PART
ejpam-1354	256	23	finish	finish	VERB
ejpam-1354	256	24	in	in	ADP
ejpam-1354	256	25	finite	finite	ADJ
ejpam-1354	256	26	time	time	NOUN
ejpam-1354	256	27	see	see	VERB
ejpam-1354	256	28	for	for	ADP
ejpam-1354	256	29	instance	instance	NOUN
ejpam-1354	256	30	the	the	DET
ejpam-1354	256	31	second	second	ADJ
ejpam-1354	256	32	illustration	illustration	NOUN
ejpam-1354	256	33	in	in	ADP
ejpam-1354	256	34	figure	figure	NOUN
ejpam-1354	256	35	2	2	NUM
ejpam-1354	256	36	.	.	PUNCT
ejpam-1354	257	1	moreover	moreover	ADV
ejpam-1354	257	2	,	,	PUNCT
ejpam-1354	257	3	finite	finite	ADJ
ejpam-1354	257	4	-	-	PUNCT
ejpam-1354	257	5	time	time	NOUN
ejpam-1354	257	6	convergence	convergence	NOUN
ejpam-1354	257	7	is	be	AUX
ejpam-1354	257	8	impossible	impossible	ADJ
ejpam-1354	257	9	,	,	PUNCT
ejpam-1354	257	10	even	even	ADV
ejpam-1354	257	11	if	if	SCONJ
ejpam-1354	257	12	the	the	DET
ejpam-1354	257	13	energy	energy	NOUN
ejpam-1354	257	14	vanish	vanish	VERB
ejpam-1354	257	15	after	after	ADP
ejpam-1354	257	16	infinite	infinite	ADJ
ejpam-1354	257	17	steps	step	NOUN
ejpam-1354	257	18	so	so	SCONJ
ejpam-1354	257	19	it	it	PRON
ejpam-1354	257	20	seems	seem	VERB
ejpam-1354	257	21	like	like	SCONJ
ejpam-1354	257	22	finite	finite	ADJ
ejpam-1354	257	23	-	-	PUNCT
ejpam-1354	257	24	time	time	NOUN
ejpam-1354	257	25	convergence	convergence	NOUN
ejpam-1354	257	26	is	be	AUX
ejpam-1354	257	27	impossible	impossible	ADJ
ejpam-1354	257	28	while	while	SCONJ
ejpam-1354	257	29	s(m	s(m	PROPN
ejpam-1354	257	30	)	)	PUNCT
ejpam-1354	257	31	is	be	AUX
ejpam-1354	257	32	allowed	allow	VERB
ejpam-1354	257	33	to	to	PART
ejpam-1354	257	34	be	be	AUX
ejpam-1354	257	35	countably	countably	ADV
ejpam-1354	257	36	infinite	infinite	ADJ
ejpam-1354	257	37	.	.	PUNCT
ejpam-1354	258	1	by	by	ADP
ejpam-1354	258	2	considering	consider	VERB
ejpam-1354	258	3	the	the	DET
ejpam-1354	258	4	following	follow	VERB
ejpam-1354	258	5	energy	energy	NOUN
ejpam-1354	258	6	function	function	NOUN
ejpam-1354	258	7	:	:	PUNCT
ejpam-1354	258	8	lim	lim	PROPN
ejpam-1354	258	9	n→∞	n→∞	NUM
ejpam-1354	258	10	e(mn	e(mn	NOUN
ejpam-1354	258	11	)	)	PUNCT
ejpam-1354	258	12	=	=	VERB
ejpam-1354	258	13	lim	lim	PROPN
ejpam-1354	258	14	n→∞	n→∞	NUM
ejpam-1354	258	15	1	1	NUM
ejpam-1354	258	16	n	n	PROPN
ejpam-1354	258	17	=	=	SYM
ejpam-1354	258	18	0	0	NUM
ejpam-1354	258	19	,	,	PUNCT
ejpam-1354	258	20	(	(	PUNCT
ejpam-1354	258	21	22	22	NUM
ejpam-1354	258	22	)	)	PUNCT
ejpam-1354	258	23	there	there	PRON
ejpam-1354	258	24	is	be	VERB
ejpam-1354	258	25	no	no	DET
ejpam-1354	258	26	guarantee	guarantee	NOUN
ejpam-1354	258	27	of	of	ADP
ejpam-1354	258	28	the	the	DET
ejpam-1354	258	29	existence	existence	NOUN
ejpam-1354	258	30	of	of	ADP
ejpam-1354	258	31	the	the	DET
ejpam-1354	258	32	mass	mass	NOUN
ejpam-1354	258	33	convergence	convergence	NOUN
ejpam-1354	258	34	.	.	PUNCT
ejpam-1354	259	1	4	4	X
ejpam-1354	259	2	.	.	X
ejpam-1354	259	3	numerical	numerical	ADJ
ejpam-1354	259	4	simulations	simulation	NOUN
ejpam-1354	259	5	4.1	4.1	NUM
ejpam-1354	259	6	.	.	PUNCT
ejpam-1354	260	1	finite	finite	VERB
ejpam-1354	260	2	metric	metric	ADJ
ejpam-1354	260	3	space	space	NOUN
ejpam-1354	260	4	in	in	ADP
ejpam-1354	260	5	our	our	PRON
ejpam-1354	260	6	simulations	simulation	NOUN
ejpam-1354	260	7	,	,	PUNCT
ejpam-1354	260	8	we	we	PRON
ejpam-1354	260	9	do	do	VERB
ejpam-1354	260	10	three	three	NUM
ejpam-1354	260	11	numerical	numerical	ADJ
ejpam-1354	260	12	experiments	experiment	NOUN
ejpam-1354	260	13	on	on	ADP
ejpam-1354	260	14	finite	finite	ADJ
ejpam-1354	260	15	metric	metric	ADJ
ejpam-1354	260	16	spaces	space	NOUN
ejpam-1354	260	17	(	(	PUNCT
ejpam-1354	260	18	fms	fms	PROPN
ejpam-1354	260	19	)	)	PUNCT
ejpam-1354	260	20	as	as	ADP
ejpam-1354	260	21	a	a	DET
ejpam-1354	260	22	subset	subset	NOUN
ejpam-1354	260	23	of	of	ADP
ejpam-1354	260	24	an	an	DET
ejpam-1354	260	25	euclidean	euclidean	ADJ
ejpam-1354	260	26	space	space	NOUN
ejpam-1354	260	27	,	,	PUNCT
ejpam-1354	260	28	namely	namely	ADV
ejpam-1354	260	29	[	[	X
ejpam-1354	260	30	0,1]2	0,1]2	NUM
ejpam-1354	260	31	.	.	PUNCT
ejpam-1354	261	1	the	the	DET
ejpam-1354	261	2	finite	finite	PROPN
ejpam-1354	261	3	set	set	NOUN
ejpam-1354	261	4	will	will	AUX
ejpam-1354	261	5	be	be	AUX
ejpam-1354	261	6	constructed	construct	VERB
ejpam-1354	261	7	as	as	ADP
ejpam-1354	261	8	121	121	NUM
ejpam-1354	261	9	points	point	NOUN
ejpam-1354	261	10	metric	metric	ADJ
ejpam-1354	261	11	space	space	NOUN
ejpam-1354	261	12	a	a	DET
ejpam-1354	261	13	subset	subset	NOUN
ejpam-1354	261	14	of	of	ADP
ejpam-1354	261	15	a	a	DET
ejpam-1354	261	16	continuous	continuous	ADJ
ejpam-1354	261	17	metric	metric	ADJ
ejpam-1354	261	18	space	space	NOUN
ejpam-1354	261	19	.	.	PUNCT
ejpam-1354	262	1	the	the	DET
ejpam-1354	262	2	numerical	numerical	ADJ
ejpam-1354	262	3	simulations	simulation	NOUN
ejpam-1354	262	4	are	be	AUX
ejpam-1354	262	5	listed	list	VERB
ejpam-1354	262	6	as	as	SCONJ
ejpam-1354	262	7	follows	follow	VERB
ejpam-1354	262	8	:	:	PUNCT
ejpam-1354	262	9	(	(	PUNCT
ejpam-1354	262	10	a	a	X
ejpam-1354	262	11	)	)	PUNCT
ejpam-1354	262	12	and	and	CCONJ
ejpam-1354	262	13	(	(	PUNCT
ejpam-1354	262	14	b	b	NOUN
ejpam-1354	262	15	)	)	PUNCT
ejpam-1354	262	16	uniform	uniform	ADJ
ejpam-1354	262	17	mass	mass	PROPN
ejpam-1354	262	18	distribution,(c	distribution,(c	PROPN
ejpam-1354	262	19	)	)	PUNCT
ejpam-1354	262	20	uniform	uniform	ADJ
ejpam-1354	262	21	random	random	ADJ
ejpam-1354	262	22	mass	mass	NOUN
ejpam-1354	262	23	distribution	distribution	NOUN
ejpam-1354	262	24	in	in	ADP
ejpam-1354	262	25	[	[	X
ejpam-1354	262	26	0,4	0,4	NOUN
ejpam-1354	262	27	]	]	PUNCT
ejpam-1354	262	28	(	(	PUNCT
ejpam-1354	262	29	i.e.	i.e.	X
ejpam-1354	262	30	m(x	m(x	X
ejpam-1354	262	31	)	)	PUNCT
ejpam-1354	262	32	∈	∈	PROPN
ejpam-1354	263	1	[	[	X
ejpam-1354	263	2	0,4	0,4	NOUN
ejpam-1354	263	3	]	]	PUNCT
ejpam-1354	263	4	for	for	ADP
ejpam-1354	263	5	x	x	PUNCT
ejpam-1354	263	6	element	element	NOUN
ejpam-1354	263	7	of	of	ADP
ejpam-1354	263	8	the	the	DET
ejpam-1354	263	9	fms	fms	PROPN
ejpam-1354	263	10	subset	subset	NOUN
ejpam-1354	263	11	of	of	ADP
ejpam-1354	263	12	[	[	X
ejpam-1354	263	13	0,1]2	0,1]2	NUM
ejpam-1354	263	14	)	)	PUNCT
ejpam-1354	263	15	.	.	PUNCT
ejpam-1354	264	1	the	the	DET
ejpam-1354	264	2	metric	metric	NOUN
ejpam-1354	264	3	used	use	VERB
ejpam-1354	264	4	here	here	ADV
ejpam-1354	264	5	is	be	AUX
ejpam-1354	264	6	the	the	DET
ejpam-1354	264	7	euclidean	euclidean	ADJ
ejpam-1354	264	8	one	one	NUM
ejpam-1354	264	9	.	.	PUNCT
ejpam-1354	265	1	for	for	ADP
ejpam-1354	265	2	simplicity	simplicity	NOUN
ejpam-1354	265	3	,	,	PUNCT
ejpam-1354	265	4	the	the	DET
ejpam-1354	265	5	initial	initial	ADJ
ejpam-1354	265	6	measure	measure	NOUN
ejpam-1354	265	7	will	will	AUX
ejpam-1354	265	8	be	be	AUX
ejpam-1354	265	9	defined	define	VERB
ejpam-1354	265	10	as	as	ADP
ejpam-1354	265	11	a	a	DET
ejpam-1354	265	12	positive	positive	ADJ
ejpam-1354	265	13	measure	measure	NOUN
ejpam-1354	265	14	m	m	VERB
ejpam-1354	265	15	:	:	PUNCT
ejpam-1354	265	16	=	=	SYM
ejpam-1354	265	17	∑	∑	PUNCT
ejpam-1354	265	18	x∈x	x∈x	PROPN
ejpam-1354	265	19	m(x)δx	m(x)δx	PROPN
ejpam-1354	265	20	,	,	PUNCT
ejpam-1354	265	21	such	such	ADJ
ejpam-1354	265	22	that	that	DET
ejpam-1354	265	23	s(m	s(m	NOUN
ejpam-1354	265	24	)	)	PUNCT
ejpam-1354	266	1	=	=	SYM
ejpam-1354	266	2	x	x	PROPN
ejpam-1354	266	3	and	and	CCONJ
ejpam-1354	266	4	m(x	m(x	NOUN
ejpam-1354	266	5	)	)	PUNCT
ejpam-1354	266	6	>	>	X
ejpam-1354	267	1	0	0	X
ejpam-1354	267	2	.	.	PUNCT
ejpam-1354	268	1	we	we	PRON
ejpam-1354	268	2	run	run	VERB
ejpam-1354	268	3	our	our	PRON
ejpam-1354	268	4	code	code	NOUN
ejpam-1354	268	5	by	by	ADP
ejpam-1354	268	6	using	use	VERB
ejpam-1354	268	7	an	an	DET
ejpam-1354	268	8	arbitrary	arbitrary	ADJ
ejpam-1354	268	9	m.	m.	NOUN
ejpam-1354	268	10	zahri	zahri	PROPN
ejpam-1354	268	11	/	/	SYM
ejpam-1354	268	12	eur	eur	PROPN
ejpam-1354	268	13	.	.	PUNCT
ejpam-1354	269	1	j.	j.	PROPN
ejpam-1354	269	2	pure	pure	PROPN
ejpam-1354	269	3	appl	appl	PROPN
ejpam-1354	269	4	.	.	PROPN
ejpam-1354	269	5	math	math	PROPN
ejpam-1354	269	6	,	,	PUNCT
ejpam-1354	269	7	6	6	NUM
ejpam-1354	269	8	(	(	PUNCT
ejpam-1354	269	9	2013	2013	NUM
ejpam-1354	269	10	)	)	PUNCT
ejpam-1354	269	11	,	,	PUNCT
ejpam-1354	269	12	172	172	NUM
ejpam-1354	269	13	-	-	SYM
ejpam-1354	269	14	188	188	NUM
ejpam-1354	269	15	183	183	NUM
ejpam-1354	269	16	order	order	NOUN
ejpam-1354	269	17	of	of	ADP
ejpam-1354	269	18	reactions	reaction	NOUN
ejpam-1354	269	19	(	(	PUNCT
ejpam-1354	269	20	the	the	DET
ejpam-1354	269	21	array	array	NOUN
ejpam-1354	269	22	of	of	ADP
ejpam-1354	269	23	121	121	NUM
ejpam-1354	269	24	index	index	NOUN
ejpam-1354	269	25	will	will	AUX
ejpam-1354	269	26	be	be	AUX
ejpam-1354	269	27	permuted	permute	VERB
ejpam-1354	269	28	randomly	randomly	ADV
ejpam-1354	269	29	at	at	ADP
ejpam-1354	269	30	each	each	DET
ejpam-1354	269	31	iteration	iteration	NOUN
ejpam-1354	269	32	step	step	NOUN
ejpam-1354	269	33	)	)	PUNCT
ejpam-1354	269	34	.	.	PUNCT
ejpam-1354	270	1	it	it	PRON
ejpam-1354	270	2	is	be	AUX
ejpam-1354	270	3	important	important	ADJ
ejpam-1354	270	4	to	to	PART
ejpam-1354	270	5	note	note	VERB
ejpam-1354	270	6	that	that	SCONJ
ejpam-1354	270	7	the	the	DET
ejpam-1354	270	8	positions	position	NOUN
ejpam-1354	270	9	,	,	PUNCT
ejpam-1354	270	10	which	which	PRON
ejpam-1354	270	11	minimize	minimize	VERB
ejpam-1354	270	12	the	the	DET
ejpam-1354	270	13	energy	energy	NOUN
ejpam-1354	270	14	are	be	AUX
ejpam-1354	270	15	not	not	PART
ejpam-1354	270	16	unique	unique	ADJ
ejpam-1354	270	17	,	,	PUNCT
ejpam-1354	270	18	therefore	therefore	ADV
ejpam-1354	270	19	,	,	PUNCT
ejpam-1354	270	20	we	we	PRON
ejpam-1354	270	21	choose	choose	VERB
ejpam-1354	270	22	randomly	randomly	ADV
ejpam-1354	270	23	one	one	NUM
ejpam-1354	270	24	of	of	ADP
ejpam-1354	270	25	them	they	PRON
ejpam-1354	270	26	.	.	PUNCT
ejpam-1354	271	1	moreover	moreover	ADV
ejpam-1354	271	2	all	all	DET
ejpam-1354	271	3	points	point	NOUN
ejpam-1354	271	4	of	of	ADP
ejpam-1354	271	5	the	the	DET
ejpam-1354	271	6	metric	metric	ADJ
ejpam-1354	271	7	space	space	NOUN
ejpam-1354	271	8	are	be	AUX
ejpam-1354	271	9	considered	consider	VERB
ejpam-1354	271	10	,	,	PUNCT
ejpam-1354	271	11	namely	namely	ADV
ejpam-1354	271	12	with	with	ADP
ejpam-1354	271	13	positive	positive	ADJ
ejpam-1354	271	14	or	or	CCONJ
ejpam-1354	271	15	zero	zero	NUM
ejpam-1354	271	16	mass	mass	NOUN
ejpam-1354	271	17	.	.	PUNCT
ejpam-1354	272	1	our	our	PRON
ejpam-1354	272	2	main	main	ADJ
ejpam-1354	272	3	concern	concern	NOUN
ejpam-1354	272	4	here	here	ADV
ejpam-1354	272	5	is	be	AUX
ejpam-1354	272	6	to	to	PART
ejpam-1354	272	7	observe	observe	VERB
ejpam-1354	272	8	the	the	DET
ejpam-1354	272	9	condensing	condense	VERB
ejpam-1354	272	10	behavior	behavior	NOUN
ejpam-1354	272	11	of	of	ADP
ejpam-1354	272	12	the	the	DET
ejpam-1354	272	13	limit	limit	NOUN
ejpam-1354	272	14	state	state	NOUN
ejpam-1354	272	15	of	of	ADP
ejpam-1354	272	16	each	each	DET
ejpam-1354	272	17	simulation	simulation	NOUN
ejpam-1354	272	18	.	.	PUNCT
ejpam-1354	273	1	hence	hence	ADV
ejpam-1354	273	2	,	,	PUNCT
ejpam-1354	273	3	if	if	SCONJ
ejpam-1354	273	4	m	m	NOUN
ejpam-1354	273	5	is	be	AUX
ejpam-1354	273	6	a	a	DET
ejpam-1354	273	7	limit	limit	NOUN
ejpam-1354	273	8	measure	measure	NOUN
ejpam-1354	273	9	of	of	ADP
ejpam-1354	273	10	a	a	DET
ejpam-1354	273	11	condensing	condense	VERB
ejpam-1354	273	12	sequence	sequence	NOUN
ejpam-1354	273	13	,	,	PUNCT
ejpam-1354	273	14	then	then	ADV
ejpam-1354	273	15	eε(m	eε(m	PUNCT
ejpam-1354	273	16	)	)	PUNCT
ejpam-1354	273	17	=	=	SYM
ejpam-1354	273	18	0	0	NUM
ejpam-1354	273	19	,	,	PUNCT
ejpam-1354	273	20	is	be	AUX
ejpam-1354	273	21	equivalent	equivalent	ADJ
ejpam-1354	273	22	either	either	ADV
ejpam-1354	273	23	to	to	ADP
ejpam-1354	273	24	m(x	m(x	PROPN
ejpam-1354	273	25	)	)	PUNCT
ejpam-1354	274	1	=	=	PUNCT
ejpam-1354	274	2	m(a	m(a	PROPN
ejpam-1354	274	3	)	)	PUNCT
ejpam-1354	274	4	for	for	ADP
ejpam-1354	274	5	a	a	DET
ejpam-1354	274	6	∈	∈	PROPN
ejpam-1354	274	7	x	x	X
ejpam-1354	274	8	or	or	CCONJ
ejpam-1354	274	9	d(x	d(x	PROPN
ejpam-1354	274	10	,	,	PUNCT
ejpam-1354	274	11	y	y	PROPN
ejpam-1354	274	12	)	)	PUNCT
ejpam-1354	274	13	>	>	X
ejpam-1354	274	14	ε	ε	PROPN
ejpam-1354	274	15	for	for	ADP
ejpam-1354	274	16	all	all	DET
ejpam-1354	274	17	x	x	SYM
ejpam-1354	274	18	,	,	PUNCT
ejpam-1354	274	19	y	y	PROPN
ejpam-1354	274	20	∈	∈	PROPN
ejpam-1354	274	21	s(m	s(m	PROPN
ejpam-1354	274	22	)	)	PUNCT
ejpam-1354	274	23	.	.	PUNCT
ejpam-1354	275	1	note	note	VERB
ejpam-1354	275	2	also	also	ADV
ejpam-1354	275	3	both	both	DET
ejpam-1354	275	4	cases	case	NOUN
ejpam-1354	275	5	despond	despond	VERB
ejpam-1354	275	6	not	not	PART
ejpam-1354	275	7	only	only	ADV
ejpam-1354	275	8	on	on	ADP
ejpam-1354	275	9	the	the	DET
ejpam-1354	275	10	choice	choice	NOUN
ejpam-1354	275	11	of	of	ADP
ejpam-1354	275	12	ε	ε	PROPN
ejpam-1354	275	13	but	but	CCONJ
ejpam-1354	275	14	also	also	ADV
ejpam-1354	275	15	of	of	ADP
ejpam-1354	275	16	the	the	DET
ejpam-1354	275	17	random	random	ADJ
ejpam-1354	275	18	of	of	ADP
ejpam-1354	275	19	the	the	DET
ejpam-1354	275	20	reactions	reaction	NOUN
ejpam-1354	275	21	and	and	CCONJ
ejpam-1354	275	22	the	the	DET
ejpam-1354	275	23	non	non	ADJ
ejpam-1354	275	24	-	-	NOUN
ejpam-1354	275	25	uniqueness	uniqueness	NOUN
ejpam-1354	275	26	of	of	ADP
ejpam-1354	275	27	the	the	DET
ejpam-1354	275	28	points	point	NOUN
ejpam-1354	275	29	minimizing	minimizing	NOUN
ejpam-1354	275	30	of	of	ADP
ejpam-1354	275	31	the	the	DET
ejpam-1354	275	32	energy	energy	NOUN
ejpam-1354	275	33	function	function	NOUN
ejpam-1354	275	34	.	.	PUNCT
ejpam-1354	276	1	it	it	PRON
ejpam-1354	276	2	is	be	AUX
ejpam-1354	276	3	also	also	ADV
ejpam-1354	276	4	important	important	ADJ
ejpam-1354	276	5	to	to	PART
ejpam-1354	276	6	note	note	VERB
ejpam-1354	276	7	that	that	SCONJ
ejpam-1354	276	8	if	if	SCONJ
ejpam-1354	276	9	ε	ε	PROPN
ejpam-1354	276	10	≥	≥	PRON
ejpam-1354	276	11	diam(x	diam(x	PROPN
ejpam-1354	276	12	)	)	PUNCT
ejpam-1354	276	13	,	,	PUNCT
ejpam-1354	276	14	then	then	ADV
ejpam-1354	276	15	limi	limi	PROPN
ejpam-1354	276	16	mi	mi	PROPN
ejpam-1354	276	17	=	=	PROPN
ejpam-1354	276	18	m(x	m(x	PROPN
ejpam-1354	276	19	)	)	PUNCT
ejpam-1354	276	20	δa	δa	PROPN
ejpam-1354	276	21	for	for	ADP
ejpam-1354	276	22	a	a	DET
ejpam-1354	276	23	∈	∈	PROPN
ejpam-1354	276	24	x	x	X
ejpam-1354	276	25	.	.	PUNCT
ejpam-1354	277	1	in	in	ADP
ejpam-1354	277	2	this	this	DET
ejpam-1354	277	3	case	case	NOUN
ejpam-1354	277	4	we	we	PRON
ejpam-1354	277	5	have	have	VERB
ejpam-1354	277	6	a	a	DET
ejpam-1354	277	7	total	total	ADJ
ejpam-1354	277	8	collision	collision	NOUN
ejpam-1354	277	9	of	of	ADP
ejpam-1354	277	10	the	the	DET
ejpam-1354	277	11	particles	particle	NOUN
ejpam-1354	277	12	.	.	PUNCT
ejpam-1354	278	1	these	these	DET
ejpam-1354	278	2	limits	limit	NOUN
ejpam-1354	278	3	are	be	AUX
ejpam-1354	278	4	reached	reach	VERB
ejpam-1354	278	5	by	by	ADP
ejpam-1354	278	6	vanishing	vanish	VERB
ejpam-1354	278	7	global	global	ADJ
ejpam-1354	278	8	energy	energy	NOUN
ejpam-1354	278	9	.	.	PUNCT
ejpam-1354	279	1	figure	figure	NOUN
ejpam-1354	279	2	3	3	NUM
ejpam-1354	279	3	shows	show	VERB
ejpam-1354	279	4	clearly	clearly	ADV
ejpam-1354	279	5	that	that	SCONJ
ejpam-1354	279	6	the	the	DET
ejpam-1354	279	7	time	time	NOUN
ejpam-1354	279	8	despondent	despondent	ADJ
ejpam-1354	279	9	global	global	ADJ
ejpam-1354	279	10	energies	energy	NOUN
ejpam-1354	279	11	converge	converge	VERB
ejpam-1354	279	12	to	to	ADP
ejpam-1354	279	13	zero	zero	NUM
ejpam-1354	279	14	.	.	PUNCT
ejpam-1354	280	1	it	it	PRON
ejpam-1354	280	2	is	be	AUX
ejpam-1354	280	3	important	important	ADJ
ejpam-1354	280	4	to	to	PART
ejpam-1354	280	5	note	note	VERB
ejpam-1354	280	6	,	,	PUNCT
ejpam-1354	280	7	that	that	SCONJ
ejpam-1354	280	8	the	the	DET
ejpam-1354	280	9	limits	limit	NOUN
ejpam-1354	280	10	are	be	AUX
ejpam-1354	280	11	attained	attain	VERB
ejpam-1354	280	12	after	after	ADP
ejpam-1354	280	13	different	different	ADJ
ejpam-1354	280	14	number	number	NOUN
ejpam-1354	280	15	of	of	ADP
ejpam-1354	280	16	iteration	iteration	NOUN
ejpam-1354	280	17	as	as	SCONJ
ejpam-1354	280	18	indicated	indicate	VERB
ejpam-1354	280	19	by	by	ADP
ejpam-1354	280	20	table	table	NOUN
ejpam-1354	280	21	1	1	NUM
ejpam-1354	280	22	,	,	PUNCT
ejpam-1354	280	23	which	which	PRON
ejpam-1354	280	24	summarizes	summarize	VERB
ejpam-1354	280	25	the	the	DET
ejpam-1354	280	26	results	result	NOUN
ejpam-1354	280	27	of	of	ADP
ejpam-1354	280	28	the	the	DET
ejpam-1354	280	29	three	three	NUM
ejpam-1354	280	30	simulations	simulation	NOUN
ejpam-1354	280	31	on	on	ADP
ejpam-1354	280	32	the	the	DET
ejpam-1354	280	33	euclidean	euclidean	ADJ
ejpam-1354	280	34	finite	finite	NOUN
ejpam-1354	280	35	metric	metric	ADJ
ejpam-1354	280	36	space	space	NOUN
ejpam-1354	280	37	:	:	PUNCT
ejpam-1354	280	38	figure	figure	VERB
ejpam-1354	280	39	4	4	NUM
ejpam-1354	280	40	presents	present	VERB
ejpam-1354	280	41	three	three	NUM
ejpam-1354	280	42	condensing	condense	VERB
ejpam-1354	280	43	iterations	iteration	NOUN
ejpam-1354	280	44	in	in	ADP
ejpam-1354	280	45	x	x	PUNCT
ejpam-1354	280	46	of	of	ADP
ejpam-1354	280	47	the	the	DET
ejpam-1354	280	48	three	three	NUM
ejpam-1354	280	49	simulations	simulation	NOUN
ejpam-1354	280	50	(	(	PUNCT
ejpam-1354	280	51	left	leave	VERB
ejpam-1354	280	52	,	,	PUNCT
ejpam-1354	280	53	middle	middle	ADJ
ejpam-1354	280	54	and	and	CCONJ
ejpam-1354	280	55	right	right	ADJ
ejpam-1354	280	56	columns	column	NOUN
ejpam-1354	280	57	)	)	PUNCT
ejpam-1354	280	58	.	.	PUNCT
ejpam-1354	281	1	the	the	DET
ejpam-1354	281	2	small	small	ADJ
ejpam-1354	281	3	dark	dark	ADJ
ejpam-1354	281	4	dots	dot	NOUN
ejpam-1354	281	5	represent	represent	VERB
ejpam-1354	281	6	the	the	DET
ejpam-1354	281	7	metric	metric	ADJ
ejpam-1354	281	8	space	space	NOUN
ejpam-1354	281	9	and	and	CCONJ
ejpam-1354	281	10	the	the	DET
ejpam-1354	281	11	large	large	ADJ
ejpam-1354	281	12	ones	one	NOUN
ejpam-1354	281	13	represent	represent	VERB
ejpam-1354	281	14	the	the	DET
ejpam-1354	281	15	particles	particle	NOUN
ejpam-1354	281	16	.	.	PUNCT
ejpam-1354	282	1	the	the	DET
ejpam-1354	282	2	initial	initial	ADJ
ejpam-1354	282	3	measure	measure	NOUN
ejpam-1354	282	4	is	be	AUX
ejpam-1354	282	5	a	a	DET
ejpam-1354	282	6	collection	collection	NOUN
ejpam-1354	282	7	of	of	ADP
ejpam-1354	282	8	point	point	NOUN
ejpam-1354	282	9	masses	masse	NOUN
ejpam-1354	282	10	such	such	ADJ
ejpam-1354	282	11	that	that	SCONJ
ejpam-1354	282	12	each	each	DET
ejpam-1354	282	13	point	point	NOUN
ejpam-1354	282	14	of	of	ADP
ejpam-1354	282	15	the	the	DET
ejpam-1354	282	16	grid	grid	NOUN
ejpam-1354	282	17	has	have	VERB
ejpam-1354	282	18	a	a	DET
ejpam-1354	282	19	positive	positive	ADJ
ejpam-1354	282	20	mass	mass	NOUN
ejpam-1354	282	21	.	.	PUNCT
ejpam-1354	283	1	a	a	DET
ejpam-1354	283	2	move	move	NOUN
ejpam-1354	283	3	is	be	AUX
ejpam-1354	283	4	only	only	ADV
ejpam-1354	283	5	admissible	admissible	ADJ
ejpam-1354	283	6	on	on	ADP
ejpam-1354	283	7	the	the	DET
ejpam-1354	283	8	small	small	ADJ
ejpam-1354	283	9	points	point	NOUN
ejpam-1354	283	10	(	(	PUNCT
ejpam-1354	283	11	fms	fms	PROPN
ejpam-1354	283	12	)	)	PUNCT
ejpam-1354	283	13	.	.	PUNCT
ejpam-1354	284	1	in	in	ADP
ejpam-1354	284	2	this	this	DET
ejpam-1354	284	3	case	case	NOUN
ejpam-1354	284	4	the	the	DET
ejpam-1354	284	5	limit	limit	NOUN
ejpam-1354	284	6	measure	measure	NOUN
ejpam-1354	284	7	is	be	AUX
ejpam-1354	284	8	a	a	DET
ejpam-1354	284	9	collection	collection	NOUN
ejpam-1354	284	10	of	of	ADP
ejpam-1354	284	11	ε	ε	PROPN
ejpam-1354	284	12	-	-	PUNCT
ejpam-1354	284	13	isolated	isolate	VERB
ejpam-1354	284	14	mass	mass	NOUN
ejpam-1354	284	15	points	point	NOUN
ejpam-1354	284	16	.	.	PUNCT
ejpam-1354	285	1	it	it	PRON
ejpam-1354	285	2	is	be	AUX
ejpam-1354	285	3	also	also	ADV
ejpam-1354	285	4	important	important	ADJ
ejpam-1354	285	5	to	to	PART
ejpam-1354	285	6	note	note	VERB
ejpam-1354	285	7	that	that	SCONJ
ejpam-1354	285	8	this	this	DET
ejpam-1354	285	9	plot	plot	NOUN
ejpam-1354	285	10	shows	show	VERB
ejpam-1354	285	11	in	in	ADP
ejpam-1354	285	12	the	the	DET
ejpam-1354	285	13	first	first	ADJ
ejpam-1354	285	14	four	four	NUM
ejpam-1354	285	15	rows	row	NOUN
ejpam-1354	285	16	,	,	PUNCT
ejpam-1354	285	17	only	only	ADV
ejpam-1354	285	18	the	the	DET
ejpam-1354	285	19	center	center	NOUN
ejpam-1354	285	20	of	of	ADP
ejpam-1354	285	21	mass	mass	NOUN
ejpam-1354	285	22	of	of	ADP
ejpam-1354	285	23	each	each	DET
ejpam-1354	285	24	point	point	NOUN
ejpam-1354	285	25	mass	mass	PROPN
ejpam-1354	285	26	,	,	PUNCT
ejpam-1354	285	27	the	the	DET
ejpam-1354	285	28	weight	weight	NOUN
ejpam-1354	285	29	is	be	AUX
ejpam-1354	285	30	given	give	VERB
ejpam-1354	285	31	as	as	ADP
ejpam-1354	285	32	a	a	DET
ejpam-1354	285	33	density	density	NOUN
ejpam-1354	285	34	in	in	ADP
ejpam-1354	285	35	the	the	DET
ejpam-1354	285	36	last	last	ADJ
ejpam-1354	285	37	plot	plot	NOUN
ejpam-1354	285	38	of	of	ADP
ejpam-1354	285	39	figure	figure	NOUN
ejpam-1354	285	40	4	4	NUM
ejpam-1354	285	41	.	.	PUNCT
ejpam-1354	285	42	table	table	NOUN
ejpam-1354	285	43	1	1	NUM
ejpam-1354	285	44	:	:	PUNCT
ejpam-1354	285	45	results	result	NOUN
ejpam-1354	285	46	of	of	ADP
ejpam-1354	285	47	simulations	simulation	NOUN
ejpam-1354	285	48	(	(	PUNCT
ejpam-1354	285	49	a	a	X
ejpam-1354	285	50	)	)	PUNCT
ejpam-1354	285	51	,	,	PUNCT
ejpam-1354	285	52	(	(	PUNCT
ejpam-1354	285	53	b	b	X
ejpam-1354	285	54	)	)	PUNCT
ejpam-1354	285	55	and	and	CCONJ
ejpam-1354	285	56	(	(	PUNCT
ejpam-1354	285	57	c	c	NOUN
ejpam-1354	285	58	)	)	PUNCT
ejpam-1354	285	59	.	.	PUNCT
ejpam-1354	286	1	parameter	parameter	PROPN
ejpam-1354	286	2	/	/	SYM
ejpam-1354	286	3	sim	sim	NOUN
ejpam-1354	286	4	.	.	PUNCT
ejpam-1354	287	1	(	(	PUNCT
ejpam-1354	287	2	a	a	X
ejpam-1354	287	3	)	)	PUNCT
ejpam-1354	287	4	(	(	PUNCT
ejpam-1354	287	5	b	b	X
ejpam-1354	287	6	)	)	PUNCT
ejpam-1354	287	7	(	(	PUNCT
ejpam-1354	287	8	c	c	X
ejpam-1354	287	9	)	)	PUNCT
ejpam-1354	287	10	np	np	ADP
ejpam-1354	287	11	121	121	NUM
ejpam-1354	287	12	121	121	NUM
ejpam-1354	287	13	121	121	NUM
ejpam-1354	287	14	ε	ε	PROPN
ejpam-1354	287	15	0.19	0.19	NUM
ejpam-1354	287	16	0.19	0.19	NUM
ejpam-1354	287	17	0.19	0.19	NUM
ejpam-1354	287	18	initial	initial	ADJ
ejpam-1354	287	19	state	state	NOUN
ejpam-1354	287	20	121	121	NUM
ejpam-1354	287	21	masses	masse	NOUN
ejpam-1354	287	22	(	(	PUNCT
ejpam-1354	287	23	one	one	NUM
ejpam-1354	287	24	)	)	PUNCT
ejpam-1354	287	25	121	121	NUM
ejpam-1354	287	26	masses	masse	NOUN
ejpam-1354	287	27	(	(	PUNCT
ejpam-1354	287	28	one	one	NUM
ejpam-1354	287	29	)	)	PUNCT
ejpam-1354	287	30	121	121	NUM
ejpam-1354	287	31	masses	masse	NOUN
ejpam-1354	287	32	(	(	PUNCT
ejpam-1354	287	33	in	in	ADP
ejpam-1354	287	34	u(0,4	u(0,4	NOUN
ejpam-1354	287	35	)	)	PUNCT
ejpam-1354	287	36	)	)	PUNCT
ejpam-1354	287	37	final	final	ADJ
ejpam-1354	287	38	state	state	NOUN
ejpam-1354	287	39	21	21	NUM
ejpam-1354	287	40	isolated	isolate	VERB
ejpam-1354	287	41	masses	masse	NOUN
ejpam-1354	287	42	27	27	NUM
ejpam-1354	287	43	iso	iso	NOUN
ejpam-1354	287	44	.	.	PUNCT
ejpam-1354	288	1	masses	mass	VERB
ejpam-1354	288	2	21	21	NUM
ejpam-1354	288	3	iso	iso	NOUN
ejpam-1354	288	4	.	.	PUNCT
ejpam-1354	289	1	masses	masse	NOUN
ejpam-1354	289	2	number	number	NOUN
ejpam-1354	289	3	of	of	ADP
ejpam-1354	289	4	iterations	iteration	NOUN
ejpam-1354	289	5	290	290	NUM
ejpam-1354	289	6	273	273	NUM
ejpam-1354	289	7	215	215	NUM
ejpam-1354	289	8	0	0	NUM
ejpam-1354	289	9	50	50	NUM
ejpam-1354	289	10	100	100	NUM
ejpam-1354	289	11	150	150	NUM
ejpam-1354	289	12	200	200	NUM
ejpam-1354	289	13	250	250	NUM
ejpam-1354	289	14	300	300	NUM
ejpam-1354	289	15	0	0	NUM
ejpam-1354	289	16	10	10	NUM
ejpam-1354	289	17	20	20	NUM
ejpam-1354	289	18	30	30	NUM
ejpam-1354	289	19	40	40	NUM
ejpam-1354	289	20	50	50	NUM
ejpam-1354	289	21	60	60	NUM
ejpam-1354	290	1	i	i	NOUN
ejpam-1354	290	2	e	e	VERB
ejpam-1354	290	3	(	(	PUNCT
ejpam-1354	290	4	m	m	VERB
ejpam-1354	290	5	i	i	NOUN
ejpam-1354	290	6	)	)	PUNCT
ejpam-1354	290	7	(	(	PUNCT
ejpam-1354	290	8	a	a	X
ejpam-1354	290	9	)	)	PUNCT
ejpam-1354	290	10	0	0	NUM
ejpam-1354	290	11	50	50	NUM
ejpam-1354	290	12	100	100	NUM
ejpam-1354	290	13	150	150	NUM
ejpam-1354	290	14	200	200	NUM
ejpam-1354	290	15	250	250	NUM
ejpam-1354	290	16	300	300	NUM
ejpam-1354	290	17	0	0	NUM
ejpam-1354	290	18	10	10	NUM
ejpam-1354	290	19	20	20	NUM
ejpam-1354	290	20	30	30	NUM
ejpam-1354	290	21	40	40	NUM
ejpam-1354	290	22	50	50	NUM
ejpam-1354	290	23	60	60	NUM
ejpam-1354	291	1	i	i	NOUN
ejpam-1354	291	2	e	e	VERB
ejpam-1354	291	3	(	(	PUNCT
ejpam-1354	291	4	m	m	VERB
ejpam-1354	291	5	i	i	NOUN
ejpam-1354	291	6	)	)	PUNCT
ejpam-1354	291	7	(	(	PUNCT
ejpam-1354	291	8	b	b	X
ejpam-1354	291	9	)	)	PUNCT
ejpam-1354	291	10	0	0	NUM
ejpam-1354	291	11	50	50	NUM
ejpam-1354	291	12	100	100	NUM
ejpam-1354	291	13	150	150	NUM
ejpam-1354	291	14	200	200	NUM
ejpam-1354	291	15	250	250	NUM
ejpam-1354	291	16	300	300	NUM
ejpam-1354	291	17	0	0	NUM
ejpam-1354	291	18	10	10	NUM
ejpam-1354	291	19	20	20	NUM
ejpam-1354	291	20	30	30	NUM
ejpam-1354	291	21	40	40	NUM
ejpam-1354	291	22	50	50	NUM
ejpam-1354	291	23	60	60	NUM
ejpam-1354	292	1	i	i	NOUN
ejpam-1354	292	2	e	e	VERB
ejpam-1354	292	3	(	(	PUNCT
ejpam-1354	292	4	m	m	VERB
ejpam-1354	292	5	i	i	NOUN
ejpam-1354	292	6	)	)	PUNCT
ejpam-1354	292	7	(	(	PUNCT
ejpam-1354	292	8	c	c	X
ejpam-1354	292	9	)	)	PUNCT
ejpam-1354	292	10	figure	figure	NOUN
ejpam-1354	292	11	3	3	NUM
ejpam-1354	292	12	:	:	PUNCT
ejpam-1354	292	13	energy	energy	NOUN
ejpam-1354	292	14	functions	function	NOUN
ejpam-1354	292	15	of	of	ADP
ejpam-1354	292	16	simulation	simulation	NOUN
ejpam-1354	292	17	(	(	PUNCT
ejpam-1354	292	18	a	a	NOUN
ejpam-1354	292	19	)	)	PUNCT
ejpam-1354	292	20	,	,	PUNCT
ejpam-1354	292	21	(	(	PUNCT
ejpam-1354	292	22	b	b	NOUN
ejpam-1354	292	23	)	)	PUNCT
ejpam-1354	292	24	,	,	PUNCT
ejpam-1354	292	25	and	and	CCONJ
ejpam-1354	292	26	(	(	PUNCT
ejpam-1354	292	27	c	c	NOUN
ejpam-1354	292	28	)	)	PUNCT
ejpam-1354	292	29	.	.	PUNCT
ejpam-1354	293	1	m.	m.	NOUN
ejpam-1354	293	2	zahri	zahri	PROPN
ejpam-1354	293	3	/	/	SYM
ejpam-1354	293	4	eur	eur	PROPN
ejpam-1354	293	5	.	.	PUNCT
ejpam-1354	294	1	j.	j.	PROPN
ejpam-1354	294	2	pure	pure	PROPN
ejpam-1354	294	3	appl	appl	PROPN
ejpam-1354	294	4	.	.	PROPN
ejpam-1354	294	5	math	math	PROPN
ejpam-1354	294	6	,	,	PUNCT
ejpam-1354	294	7	6	6	NUM
ejpam-1354	294	8	(	(	PUNCT
ejpam-1354	294	9	2013	2013	NUM
ejpam-1354	294	10	)	)	PUNCT
ejpam-1354	294	11	,	,	PUNCT
ejpam-1354	294	12	172	172	NUM
ejpam-1354	294	13	-	-	SYM
ejpam-1354	294	14	188	188	NUM
ejpam-1354	294	15	184	184	NUM
ejpam-1354	294	16	0	0	NUM
ejpam-1354	294	17	0.1	0.1	NUM
ejpam-1354	294	18	0.2	0.2	NUM
ejpam-1354	294	19	0.3	0.3	NUM
ejpam-1354	294	20	0.4	0.4	NUM
ejpam-1354	294	21	0.5	0.5	NUM
ejpam-1354	294	22	0.6	0.6	NUM
ejpam-1354	294	23	0.7	0.7	NUM
ejpam-1354	295	1	0.8	0.8	NUM
ejpam-1354	295	2	0.9	0.9	NUM
ejpam-1354	295	3	1	1	NUM
ejpam-1354	295	4	0	0	NUM
ejpam-1354	295	5	0.1	0.1	NUM
ejpam-1354	295	6	0.2	0.2	NUM
ejpam-1354	295	7	0.3	0.3	NUM
ejpam-1354	295	8	0.4	0.4	NUM
ejpam-1354	295	9	0.5	0.5	NUM
ejpam-1354	295	10	0.6	0.6	NUM
ejpam-1354	295	11	0.7	0.7	NUM
ejpam-1354	295	12	0.8	0.8	NUM
ejpam-1354	295	13	0.9	0.9	NUM
ejpam-1354	295	14	1	1	NUM
ejpam-1354	295	15	(	(	PUNCT
ejpam-1354	295	16	a	a	NOUN
ejpam-1354	295	17	)	)	PUNCT
ejpam-1354	295	18	initial	initial	ADJ
ejpam-1354	295	19	density	density	NOUN
ejpam-1354	295	20	0	0	NUM
ejpam-1354	295	21	0.1	0.1	NUM
ejpam-1354	295	22	0.2	0.2	NUM
ejpam-1354	295	23	0.3	0.3	NUM
ejpam-1354	295	24	0.4	0.4	NUM
ejpam-1354	295	25	0.5	0.5	NUM
ejpam-1354	295	26	0.6	0.6	NUM
ejpam-1354	295	27	0.7	0.7	NUM
ejpam-1354	295	28	0.8	0.8	NUM
ejpam-1354	295	29	0.9	0.9	NUM
ejpam-1354	295	30	1	1	NUM
ejpam-1354	295	31	0	0	NUM
ejpam-1354	295	32	0.1	0.1	NUM
ejpam-1354	295	33	0.2	0.2	NUM
ejpam-1354	295	34	0.3	0.3	NUM
ejpam-1354	295	35	0.4	0.4	NUM
ejpam-1354	295	36	0.5	0.5	NUM
ejpam-1354	295	37	0.6	0.6	NUM
ejpam-1354	295	38	0.7	0.7	NUM
ejpam-1354	295	39	0.8	0.8	NUM
ejpam-1354	295	40	0.9	0.9	NUM
ejpam-1354	295	41	1	1	NUM
ejpam-1354	295	42	(	(	PUNCT
ejpam-1354	295	43	b	b	NOUN
ejpam-1354	295	44	)	)	PUNCT
ejpam-1354	295	45	initial	initial	ADJ
ejpam-1354	295	46	density	density	NOUN
ejpam-1354	295	47	0	0	NUM
ejpam-1354	295	48	0.1	0.1	NUM
ejpam-1354	295	49	0.2	0.2	NUM
ejpam-1354	295	50	0.3	0.3	NUM
ejpam-1354	295	51	0.4	0.4	NUM
ejpam-1354	295	52	0.5	0.5	NUM
ejpam-1354	295	53	0.6	0.6	NUM
ejpam-1354	295	54	0.7	0.7	NUM
ejpam-1354	295	55	0.8	0.8	NUM
ejpam-1354	295	56	0.9	0.9	NUM
ejpam-1354	295	57	1	1	NUM
ejpam-1354	295	58	0	0	NUM
ejpam-1354	295	59	0.1	0.1	NUM
ejpam-1354	295	60	0.2	0.2	NUM
ejpam-1354	295	61	0.3	0.3	NUM
ejpam-1354	295	62	0.4	0.4	NUM
ejpam-1354	295	63	0.5	0.5	NUM
ejpam-1354	295	64	0.6	0.6	NUM
ejpam-1354	295	65	0.7	0.7	NUM
ejpam-1354	295	66	0.8	0.8	NUM
ejpam-1354	295	67	0.9	0.9	NUM
ejpam-1354	295	68	1	1	NUM
ejpam-1354	295	69	(	(	PUNCT
ejpam-1354	295	70	c	c	NOUN
ejpam-1354	295	71	)	)	PUNCT
ejpam-1354	295	72	initial	initial	ADJ
ejpam-1354	295	73	density	density	NOUN
ejpam-1354	295	74	0	0	NUM
ejpam-1354	295	75	0.1	0.1	NUM
ejpam-1354	295	76	0.2	0.2	NUM
ejpam-1354	295	77	0.3	0.3	NUM
ejpam-1354	295	78	0.4	0.4	NUM
ejpam-1354	295	79	0.5	0.5	NUM
ejpam-1354	295	80	0.6	0.6	NUM
ejpam-1354	295	81	0.7	0.7	NUM
ejpam-1354	295	82	0.8	0.8	NUM
ejpam-1354	295	83	0.9	0.9	NUM
ejpam-1354	295	84	1	1	NUM
ejpam-1354	295	85	0	0	NUM
ejpam-1354	295	86	0.1	0.1	NUM
ejpam-1354	295	87	0.2	0.2	NUM
ejpam-1354	295	88	0.3	0.3	NUM
ejpam-1354	295	89	0.4	0.4	NUM
ejpam-1354	295	90	0.5	0.5	NUM
ejpam-1354	295	91	0.6	0.6	NUM
ejpam-1354	295	92	0.7	0.7	NUM
ejpam-1354	295	93	0.8	0.8	NUM
ejpam-1354	295	94	0.9	0.9	NUM
ejpam-1354	295	95	1	1	NUM
ejpam-1354	295	96	(	(	PUNCT
ejpam-1354	295	97	a	a	PRON
ejpam-1354	295	98	)	)	PUNCT
ejpam-1354	295	99	final	final	ADJ
ejpam-1354	295	100	density	density	NOUN
ejpam-1354	295	101	0	0	NUM
ejpam-1354	295	102	0.1	0.1	NUM
ejpam-1354	295	103	0.2	0.2	NUM
ejpam-1354	295	104	0.3	0.3	NUM
ejpam-1354	295	105	0.4	0.4	NUM
ejpam-1354	295	106	0.5	0.5	NUM
ejpam-1354	295	107	0.6	0.6	NUM
ejpam-1354	295	108	0.7	0.7	NUM
ejpam-1354	295	109	0.8	0.8	NUM
ejpam-1354	295	110	0.9	0.9	NUM
ejpam-1354	295	111	1	1	NUM
ejpam-1354	295	112	0	0	NUM
ejpam-1354	295	113	0.1	0.1	NUM
ejpam-1354	295	114	0.2	0.2	NUM
ejpam-1354	295	115	0.3	0.3	NUM
ejpam-1354	295	116	0.4	0.4	NUM
ejpam-1354	295	117	0.5	0.5	NUM
ejpam-1354	295	118	0.6	0.6	NUM
ejpam-1354	295	119	0.7	0.7	NUM
ejpam-1354	295	120	0.8	0.8	NUM
ejpam-1354	295	121	0.9	0.9	NUM
ejpam-1354	295	122	1	1	NUM
ejpam-1354	295	123	(	(	PUNCT
ejpam-1354	295	124	b	b	NOUN
ejpam-1354	295	125	)	)	PUNCT
ejpam-1354	295	126	final	final	ADJ
ejpam-1354	295	127	density	density	NOUN
ejpam-1354	295	128	0	0	NUM
ejpam-1354	295	129	0.1	0.1	NUM
ejpam-1354	295	130	0.2	0.2	NUM
ejpam-1354	295	131	0.3	0.3	NUM
ejpam-1354	295	132	0.4	0.4	NUM
ejpam-1354	295	133	0.5	0.5	NUM
ejpam-1354	295	134	0.6	0.6	NUM
ejpam-1354	295	135	0.7	0.7	NUM
ejpam-1354	295	136	0.8	0.8	NUM
ejpam-1354	295	137	0.9	0.9	NUM
ejpam-1354	295	138	1	1	NUM
ejpam-1354	295	139	0	0	NUM
ejpam-1354	295	140	0.1	0.1	NUM
ejpam-1354	295	141	0.2	0.2	NUM
ejpam-1354	295	142	0.3	0.3	NUM
ejpam-1354	295	143	0.4	0.4	NUM
ejpam-1354	295	144	0.5	0.5	NUM
ejpam-1354	295	145	0.6	0.6	NUM
ejpam-1354	295	146	0.7	0.7	NUM
ejpam-1354	295	147	0.8	0.8	NUM
ejpam-1354	295	148	0.9	0.9	NUM
ejpam-1354	295	149	1	1	NUM
ejpam-1354	295	150	(	(	PUNCT
ejpam-1354	295	151	c	c	NOUN
ejpam-1354	295	152	)	)	PUNCT
ejpam-1354	295	153	final	final	ADJ
ejpam-1354	295	154	density	density	NOUN
ejpam-1354	295	155	figure	figure	NOUN
ejpam-1354	295	156	4	4	NUM
ejpam-1354	295	157	:	:	PUNCT
ejpam-1354	295	158	condensing	condense	VERB
ejpam-1354	295	159	in	in	ADP
ejpam-1354	295	160	an	an	DET
ejpam-1354	295	161	euclidian	euclidian	ADJ
ejpam-1354	295	162	finite	finite	NOUN
ejpam-1354	295	163	metric	metric	ADJ
ejpam-1354	295	164	space	space	NOUN
ejpam-1354	295	165	of	of	ADP
ejpam-1354	295	166	simulations	simulation	NOUN
ejpam-1354	295	167	(	(	PUNCT
ejpam-1354	295	168	a	a	X
ejpam-1354	295	169	)	)	PUNCT
ejpam-1354	295	170	,	,	PUNCT
ejpam-1354	295	171	(	(	PUNCT
ejpam-1354	295	172	b	b	NOUN
ejpam-1354	295	173	)	)	PUNCT
ejpam-1354	295	174	,	,	PUNCT
ejpam-1354	295	175	and	and	CCONJ
ejpam-1354	295	176	(	(	PUNCT
ejpam-1354	295	177	c	c	NOUN
ejpam-1354	295	178	)	)	PUNCT
ejpam-1354	295	179	.	.	PUNCT
ejpam-1354	296	1	4.2	4.2	NUM
ejpam-1354	296	2	.	.	X
ejpam-1354	297	1	condensing	condense	VERB
ejpam-1354	297	2	on	on	ADP
ejpam-1354	297	3	the	the	DET
ejpam-1354	297	4	real	real	ADJ
ejpam-1354	297	5	line	line	NOUN
ejpam-1354	297	6	this	this	DET
ejpam-1354	297	7	section	section	NOUN
ejpam-1354	297	8	presents	present	VERB
ejpam-1354	297	9	simulations	simulation	NOUN
ejpam-1354	297	10	on	on	ADP
ejpam-1354	297	11	the	the	DET
ejpam-1354	297	12	real	real	ADJ
ejpam-1354	297	13	line	line	NOUN
ejpam-1354	297	14	.	.	PUNCT
ejpam-1354	298	1	in	in	ADP
ejpam-1354	298	2	order	order	NOUN
ejpam-1354	298	3	to	to	PART
ejpam-1354	298	4	compute	compute	VERB
ejpam-1354	298	5	the	the	DET
ejpam-1354	298	6	density	density	NOUN
ejpam-1354	298	7	of	of	ADP
ejpam-1354	298	8	the	the	DET
ejpam-1354	298	9	points	point	NOUN
ejpam-1354	298	10	masses	masse	NOUN
ejpam-1354	298	11	of	of	ADP
ejpam-1354	298	12	a	a	DET
ejpam-1354	298	13	measure	measure	NOUN
ejpam-1354	298	14	at	at	ADP
ejpam-1354	298	15	each	each	DET
ejpam-1354	298	16	iteration	iteration	NOUN
ejpam-1354	298	17	,	,	PUNCT
ejpam-1354	298	18	the	the	DET
ejpam-1354	298	19	space	space	NOUN
ejpam-1354	298	20	domain	domain	NOUN
ejpam-1354	298	21	is	be	AUX
ejpam-1354	298	22	the	the	DET
ejpam-1354	298	23	discretized	discretized	ADJ
ejpam-1354	298	24	into	into	ADP
ejpam-1354	298	25	n	n	PROPN
ejpam-1354	298	26	x	x	PROPN
ejpam-1354	298	27	uniform	uniform	ADJ
ejpam-1354	298	28	gridpoints	gridpoint	NOUN
ejpam-1354	298	29	.	.	PUNCT
ejpam-1354	299	1	we	we	PRON
ejpam-1354	299	2	carry	carry	VERB
ejpam-1354	299	3	out	out	ADP
ejpam-1354	299	4	two	two	NUM
ejpam-1354	299	5	tests	test	NOUN
ejpam-1354	299	6	of	of	ADP
ejpam-1354	299	7	condensing	condense	VERB
ejpam-1354	299	8	sequences	sequence	NOUN
ejpam-1354	299	9	of	of	ADP
ejpam-1354	299	10	two	two	NUM
ejpam-1354	299	11	discrete	discrete	ADJ
ejpam-1354	299	12	measures	measure	NOUN
ejpam-1354	299	13	with	with	ADP
ejpam-1354	299	14	support	support	NOUN
ejpam-1354	299	15	s(m	s(m	NOUN
ejpam-1354	299	16	)	)	PUNCT
ejpam-1354	300	1	=	=	PRON
ejpam-1354	300	2	{	{	PUNCT
ejpam-1354	300	3	x1	x1	PROPN
ejpam-1354	300	4	,	,	PUNCT
ejpam-1354	300	5	.	.	PUNCT
ejpam-1354	300	6	.	.	PUNCT
ejpam-1354	301	1	.	.	PUNCT
ejpam-1354	302	1	,	,	PUNCT
ejpam-1354	302	2	x50	x50	VERB
ejpam-1354	302	3	}	}	PUNCT
ejpam-1354	302	4	⊂	⊂	PROPN
ejpam-1354	303	1	[	[	X
ejpam-1354	303	2	0,1	0,1	NUM
ejpam-1354	303	3	]	]	PUNCT
ejpam-1354	303	4	.	.	PUNCT
ejpam-1354	304	1	the	the	DET
ejpam-1354	304	2	emergence	emergence	NOUN
ejpam-1354	304	3	of	of	ADP
ejpam-1354	304	4	s(m	s(m	PROPN
ejpam-1354	304	5	)	)	PUNCT
ejpam-1354	304	6	requires	require	VERB
ejpam-1354	304	7	the	the	DET
ejpam-1354	304	8	extension	extension	NOUN
ejpam-1354	304	9	of	of	ADP
ejpam-1354	304	10	the	the	DET
ejpam-1354	304	11	computation	computation	NOUN
ejpam-1354	304	12	domain	domain	NOUN
ejpam-1354	304	13	,	,	PUNCT
ejpam-1354	304	14	namely	namely	ADV
ejpam-1354	304	15	even	even	ADV
ejpam-1354	304	16	if	if	SCONJ
ejpam-1354	304	17	the	the	DET
ejpam-1354	304	18	initial	initial	ADJ
ejpam-1354	304	19	spatial	spatial	ADJ
ejpam-1354	304	20	positions	position	NOUN
ejpam-1354	304	21	are	be	AUX
ejpam-1354	304	22	chosen	choose	VERB
ejpam-1354	304	23	in	in	ADP
ejpam-1354	304	24	[	[	X
ejpam-1354	304	25	0,1	0,1	NUM
ejpam-1354	304	26	]	]	PUNCT
ejpam-1354	304	27	,	,	PUNCT
ejpam-1354	304	28	the	the	DET
ejpam-1354	304	29	final	final	ADJ
ejpam-1354	304	30	measure	measure	NOUN
ejpam-1354	304	31	has	have	VERB
ejpam-1354	304	32	not	not	PART
ejpam-1354	304	33	necessary	necessary	ADJ
ejpam-1354	304	34	positions	position	NOUN
ejpam-1354	304	35	in	in	ADP
ejpam-1354	304	36	[	[	X
ejpam-1354	304	37	0,1	0,1	NUM
ejpam-1354	304	38	]	]	PUNCT
ejpam-1354	304	39	only	only	ADV
ejpam-1354	304	40	.	.	PUNCT
ejpam-1354	305	1	we	we	PRON
ejpam-1354	305	2	run	run	VERB
ejpam-1354	305	3	our	our	PRON
ejpam-1354	305	4	code	code	NOUN
ejpam-1354	305	5	after	after	ADP
ejpam-1354	305	6	fixing	fix	VERB
ejpam-1354	305	7	the	the	DET
ejpam-1354	305	8	order	order	NOUN
ejpam-1354	305	9	of	of	ADP
ejpam-1354	305	10	reactions	reaction	NOUN
ejpam-1354	305	11	(	(	PUNCT
ejpam-1354	305	12	the	the	DET
ejpam-1354	305	13	array	array	NOUN
ejpam-1354	305	14	of	of	ADP
ejpam-1354	305	15	50	50	NUM
ejpam-1354	305	16	indexes	index	NOUN
ejpam-1354	305	17	will	will	AUX
ejpam-1354	305	18	randomly	randomly	ADV
ejpam-1354	305	19	permuted	permute	VERB
ejpam-1354	305	20	)	)	PUNCT
ejpam-1354	305	21	.	.	PUNCT
ejpam-1354	306	1	the	the	DET
ejpam-1354	306	2	following	follow	VERB
ejpam-1354	306	3	table	table	NOUN
ejpam-1354	306	4	summarizes	summarize	VERB
ejpam-1354	306	5	the	the	DET
ejpam-1354	306	6	results	result	NOUN
ejpam-1354	306	7	of	of	ADP
ejpam-1354	306	8	the	the	DET
ejpam-1354	306	9	simulations	simulation	NOUN
ejpam-1354	306	10	on	on	ADP
ejpam-1354	306	11	the	the	DET
ejpam-1354	306	12	real	real	ADJ
ejpam-1354	306	13	line	line	NOUN
ejpam-1354	306	14	:	:	PUNCT
ejpam-1354	306	15	table	table	NOUN
ejpam-1354	306	16	2	2	NUM
ejpam-1354	306	17	:	:	PUNCT
ejpam-1354	306	18	results	result	NOUN
ejpam-1354	306	19	of	of	ADP
ejpam-1354	306	20	simulations	simulation	NOUN
ejpam-1354	306	21	in	in	ADP
ejpam-1354	306	22	the	the	DET
ejpam-1354	306	23	real	real	ADJ
ejpam-1354	306	24	line	line	NOUN
ejpam-1354	306	25	.	.	PUNCT
ejpam-1354	307	1	parameter	parameter	NOUN
ejpam-1354	307	2	/	/	SYM
ejpam-1354	307	3	sim	sim	NOUN
ejpam-1354	307	4	.	.	PUNCT
ejpam-1354	308	1	(	(	PUNCT
ejpam-1354	308	2	a	a	X
ejpam-1354	308	3	)	)	PUNCT
ejpam-1354	308	4	(	(	PUNCT
ejpam-1354	308	5	b	b	X
ejpam-1354	308	6	)	)	PUNCT
ejpam-1354	308	7	ε	ε	PROPN
ejpam-1354	308	8	0.02	0.02	NUM
ejpam-1354	308	9	0.02	0.02	NUM
ejpam-1354	308	10	θ	θ	NOUN
ejpam-1354	308	11	0.01	0.01	NUM
ejpam-1354	308	12	0.01	0.01	NUM
ejpam-1354	308	13	initial	initial	ADJ
ejpam-1354	308	14	state	state	NOUN
ejpam-1354	308	15	50	50	NUM
ejpam-1354	308	16	masses	masse	NOUN
ejpam-1354	308	17	(	(	PUNCT
ejpam-1354	308	18	one	one	NUM
ejpam-1354	308	19	)	)	PUNCT
ejpam-1354	308	20	50	50	NUM
ejpam-1354	308	21	masses	masse	NOUN
ejpam-1354	308	22	(	(	PUNCT
ejpam-1354	308	23	u(0,4	u(0,4	NOUN
ejpam-1354	308	24	)	)	PUNCT
ejpam-1354	308	25	)	)	PUNCT
ejpam-1354	308	26	final	final	ADJ
ejpam-1354	308	27	state	state	NOUN
ejpam-1354	308	28	4	4	NUM
ejpam-1354	308	29	isolated	isolate	VERB
ejpam-1354	308	30	masses	masse	NOUN
ejpam-1354	308	31	4	4	NUM
ejpam-1354	308	32	isolated	isolated	ADJ
ejpam-1354	308	33	masses	masse	NOUN
ejpam-1354	308	34	number	number	NOUN
ejpam-1354	308	35	of	of	ADP
ejpam-1354	308	36	iterations	iteration	NOUN
ejpam-1354	308	37	176	176	NUM
ejpam-1354	308	38	196	196	NUM
ejpam-1354	308	39	figure	figure	NOUN
ejpam-1354	308	40	5	5	NUM
ejpam-1354	308	41	presents	present	VERB
ejpam-1354	308	42	the	the	DET
ejpam-1354	308	43	density	density	NOUN
ejpam-1354	308	44	of	of	ADP
ejpam-1354	308	45	a	a	DET
ejpam-1354	308	46	measure	measure	NOUN
ejpam-1354	308	47	with	with	ADP
ejpam-1354	308	48	50	50	NUM
ejpam-1354	308	49	point	point	NOUN
ejpam-1354	308	50	masses	masse	NOUN
ejpam-1354	308	51	in	in	ADP
ejpam-1354	308	52	many	many	ADJ
ejpam-1354	308	53	condensing	condense	VERB
ejpam-1354	308	54	iterations	iteration	NOUN
ejpam-1354	308	55	for	for	ADP
ejpam-1354	308	56	ε	ε	PROPN
ejpam-1354	308	57	=	=	SYM
ejpam-1354	308	58	0.02,θ	0.02,θ	PUNCT
ejpam-1354	308	59	=	=	PUNCT
ejpam-1354	309	1	0.01	0.01	NUM
ejpam-1354	309	2	,	,	PUNCT
ejpam-1354	309	3	the	the	DET
ejpam-1354	309	4	initial	initial	NOUN
ejpam-1354	309	5	and	and	CCONJ
ejpam-1354	309	6	the	the	DET
ejpam-1354	309	7	limit	limit	NOUN
ejpam-1354	309	8	measure	measure	NOUN
ejpam-1354	309	9	.	.	PUNCT
ejpam-1354	310	1	the	the	DET
ejpam-1354	310	2	initial	initial	ADJ
ejpam-1354	310	3	state	state	NOUN
ejpam-1354	310	4	is	be	AUX
ejpam-1354	310	5	a	a	DET
ejpam-1354	310	6	deterministic	deterministic	ADJ
ejpam-1354	310	7	distribution	distribution	NOUN
ejpam-1354	310	8	of	of	ADP
ejpam-1354	310	9	masses	masse	NOUN
ejpam-1354	310	10	and	and	CCONJ
ejpam-1354	310	11	the	the	DET
ejpam-1354	310	12	limit	limit	NOUN
ejpam-1354	310	13	measure	measure	NOUN
ejpam-1354	310	14	(	(	PUNCT
ejpam-1354	310	15	175	175	NUM
ejpam-1354	310	16	iterations	iteration	NOUN
ejpam-1354	310	17	)	)	PUNCT
ejpam-1354	310	18	is	be	AUX
ejpam-1354	310	19	constituted	constitute	VERB
ejpam-1354	310	20	only	only	ADV
ejpam-1354	310	21	from	from	ADP
ejpam-1354	310	22	ε	ε	PROPN
ejpam-1354	310	23	+	+	CCONJ
ejpam-1354	310	24	θ	θ	PROPN
ejpam-1354	310	25	isolated	isolate	VERB
ejpam-1354	310	26	masses	masse	NOUN
ejpam-1354	310	27	.	.	PUNCT
ejpam-1354	311	1	also	also	ADV
ejpam-1354	311	2	,	,	PUNCT
ejpam-1354	311	3	figure	figure	VERB
ejpam-1354	311	4	5	5	NUM
ejpam-1354	311	5	presents	present	VERB
ejpam-1354	311	6	the	the	DET
ejpam-1354	311	7	density	density	NOUN
ejpam-1354	311	8	of	of	ADP
ejpam-1354	311	9	measure	measure	NOUN
ejpam-1354	311	10	with	with	ADP
ejpam-1354	311	11	50	50	NUM
ejpam-1354	311	12	point	point	NOUN
ejpam-1354	311	13	masses	masse	NOUN
ejpam-1354	311	14	m.	m.	NOUN
ejpam-1354	311	15	zahri	zahri	PROPN
ejpam-1354	311	16	/	/	SYM
ejpam-1354	311	17	eur	eur	PROPN
ejpam-1354	311	18	.	.	PUNCT
ejpam-1354	312	1	j.	j.	PROPN
ejpam-1354	312	2	pure	pure	PROPN
ejpam-1354	312	3	appl	appl	PROPN
ejpam-1354	312	4	.	.	PROPN
ejpam-1354	312	5	math	math	PROPN
ejpam-1354	312	6	,	,	PUNCT
ejpam-1354	312	7	6	6	NUM
ejpam-1354	312	8	(	(	PUNCT
ejpam-1354	312	9	2013	2013	NUM
ejpam-1354	312	10	)	)	PUNCT
ejpam-1354	312	11	,	,	PUNCT
ejpam-1354	312	12	172	172	NUM
ejpam-1354	312	13	-	-	SYM
ejpam-1354	312	14	188	188	NUM
ejpam-1354	312	15	185	185	NUM
ejpam-1354	312	16	in	in	ADP
ejpam-1354	312	17	several	several	ADJ
ejpam-1354	312	18	condensing	condense	VERB
ejpam-1354	312	19	iterations	iteration	NOUN
ejpam-1354	312	20	on	on	ADP
ejpam-1354	312	21	the	the	DET
ejpam-1354	312	22	real	real	ADJ
ejpam-1354	312	23	line	line	NOUN
ejpam-1354	312	24	,	,	PUNCT
ejpam-1354	312	25	for	for	ADP
ejpam-1354	312	26	ε	ε	PROPN
ejpam-1354	312	27	=	=	SYM
ejpam-1354	312	28	0.02,θ	0.02,θ	PUNCT
ejpam-1354	312	29	=	=	PUNCT
ejpam-1354	313	1	0.01	0.01	NUM
ejpam-1354	313	2	.	.	PUNCT
ejpam-1354	314	1	the	the	DET
ejpam-1354	314	2	first	first	ADJ
ejpam-1354	314	3	and	and	CCONJ
ejpam-1354	314	4	the	the	DET
ejpam-1354	314	5	last	last	ADJ
ejpam-1354	314	6	figures	figure	NOUN
ejpam-1354	314	7	respectively	respectively	ADV
ejpam-1354	314	8	presents	present	VERB
ejpam-1354	314	9	the	the	DET
ejpam-1354	314	10	initial	initial	NOUN
ejpam-1354	314	11	and	and	CCONJ
ejpam-1354	314	12	the	the	DET
ejpam-1354	314	13	limit	limit	NOUN
ejpam-1354	314	14	measures	measure	NOUN
ejpam-1354	314	15	.	.	PUNCT
ejpam-1354	315	1	the	the	DET
ejpam-1354	315	2	initial	initial	ADJ
ejpam-1354	315	3	state	state	NOUN
ejpam-1354	315	4	is	be	AUX
ejpam-1354	315	5	generated	generate	VERB
ejpam-1354	315	6	with	with	ADP
ejpam-1354	315	7	a	a	DET
ejpam-1354	315	8	uniform	uniform	ADJ
ejpam-1354	315	9	random	random	ADJ
ejpam-1354	315	10	distribution	distribution	NOUN
ejpam-1354	315	11	(	(	PUNCT
ejpam-1354	315	12	u(0,4	u(0,4	NOUN
ejpam-1354	315	13	)	)	PUNCT
ejpam-1354	315	14	(	(	PUNCT
ejpam-1354	315	15	on	on	ADP
ejpam-1354	315	16	the	the	DET
ejpam-1354	315	17	figures	figure	NOUN
ejpam-1354	315	18	,	,	PUNCT
ejpam-1354	315	19	the	the	DET
ejpam-1354	315	20	density	density	NOUN
ejpam-1354	315	21	is	be	AUX
ejpam-1354	315	22	normalized	normalize	VERB
ejpam-1354	315	23	)	)	PUNCT
ejpam-1354	315	24	and	and	CCONJ
ejpam-1354	315	25	the	the	DET
ejpam-1354	315	26	final	final	ADJ
ejpam-1354	315	27	state	state	NOUN
ejpam-1354	315	28	(	(	PUNCT
ejpam-1354	315	29	iter	iter	NOUN
ejpam-1354	315	30	.	.	PUNCT
ejpam-1354	315	31	195	195	NUM
ejpam-1354	315	32	)	)	PUNCT
ejpam-1354	315	33	is	be	AUX
ejpam-1354	315	34	constituted	constitute	VERB
ejpam-1354	315	35	only	only	ADV
ejpam-1354	315	36	from	from	ADP
ejpam-1354	315	37	(	(	PUNCT
ejpam-1354	315	38	ε	ε	PROPN
ejpam-1354	315	39	+	+	CCONJ
ejpam-1354	315	40	θ	θ	NOUN
ejpam-1354	315	41	)	)	PUNCT
ejpam-1354	315	42	-isolated	-isolate	VERB
ejpam-1354	315	43	masses	masse	NOUN
ejpam-1354	315	44	.	.	PUNCT
ejpam-1354	316	1	the	the	DET
ejpam-1354	316	2	simulations	simulation	NOUN
ejpam-1354	316	3	in	in	ADP
ejpam-1354	316	4	figure	figure	NOUN
ejpam-1354	316	5	5	5	NUM
ejpam-1354	316	6	have	have	VERB
ejpam-1354	316	7	different	different	ADJ
ejpam-1354	316	8	initial	initial	ADJ
ejpam-1354	316	9	mass	mass	NOUN
ejpam-1354	316	10	but	but	CCONJ
ejpam-1354	316	11	they	they	PRON
ejpam-1354	316	12	have	have	VERB
ejpam-1354	316	13	the	the	DET
ejpam-1354	316	14	same	same	ADJ
ejpam-1354	316	15	condensing	condense	VERB
ejpam-1354	316	16	behavior	behavior	NOUN
ejpam-1354	316	17	.	.	PUNCT
ejpam-1354	317	1	the	the	DET
ejpam-1354	317	2	final	final	ADJ
ejpam-1354	317	3	states	state	NOUN
ejpam-1354	317	4	are	be	AUX
ejpam-1354	317	5	isolated	isolate	VERB
ejpam-1354	317	6	point	point	NOUN
ejpam-1354	317	7	masses	masse	NOUN
ejpam-1354	317	8	with	with	ADP
ejpam-1354	317	9	different	different	ADJ
ejpam-1354	317	10	supports	support	NOUN
ejpam-1354	317	11	and	and	CCONJ
ejpam-1354	317	12	different	different	ADJ
ejpam-1354	317	13	masses	masse	NOUN
ejpam-1354	317	14	.	.	PUNCT
ejpam-1354	318	1	0	0	NUM
ejpam-1354	318	2	0.1	0.1	NUM
ejpam-1354	318	3	0.2	0.2	NUM
ejpam-1354	318	4	0.3	0.3	NUM
ejpam-1354	318	5	0.4	0.4	NUM
ejpam-1354	318	6	0.5	0.5	NUM
ejpam-1354	318	7	0.6	0.6	NUM
ejpam-1354	318	8	0.7	0.7	NUM
ejpam-1354	318	9	0.8	0.8	NUM
ejpam-1354	318	10	0.9	0.9	NUM
ejpam-1354	318	11	1	1	NUM
ejpam-1354	318	12	0	0	NUM
ejpam-1354	318	13	0.1	0.1	NUM
ejpam-1354	318	14	0.2	0.2	NUM
ejpam-1354	318	15	0.3	0.3	NUM
ejpam-1354	318	16	0.4	0.4	NUM
ejpam-1354	318	17	0.5	0.5	NUM
ejpam-1354	318	18	0.6	0.6	NUM
ejpam-1354	318	19	0.7	0.7	NUM
ejpam-1354	318	20	0.8	0.8	NUM
ejpam-1354	318	21	0.9	0.9	NUM
ejpam-1354	318	22	1	1	NUM
ejpam-1354	318	23	(	(	PUNCT
ejpam-1354	318	24	a	a	NOUN
ejpam-1354	318	25	)	)	PUNCT
ejpam-1354	318	26	initial	initial	ADJ
ejpam-1354	318	27	0	0	NUM
ejpam-1354	318	28	0.1	0.1	NUM
ejpam-1354	318	29	0.2	0.2	NUM
ejpam-1354	318	30	0.3	0.3	NUM
ejpam-1354	318	31	0.4	0.4	NUM
ejpam-1354	318	32	0.5	0.5	NUM
ejpam-1354	318	33	0.6	0.6	NUM
ejpam-1354	318	34	0.7	0.7	NUM
ejpam-1354	318	35	0.8	0.8	NUM
ejpam-1354	318	36	0.9	0.9	NUM
ejpam-1354	318	37	1	1	NUM
ejpam-1354	318	38	0	0	NUM
ejpam-1354	318	39	0.1	0.1	NUM
ejpam-1354	318	40	0.2	0.2	NUM
ejpam-1354	318	41	0.3	0.3	NUM
ejpam-1354	318	42	0.4	0.4	NUM
ejpam-1354	318	43	0.5	0.5	NUM
ejpam-1354	318	44	0.6	0.6	NUM
ejpam-1354	318	45	0.7	0.7	NUM
ejpam-1354	318	46	0.8	0.8	NUM
ejpam-1354	318	47	0.9	0.9	NUM
ejpam-1354	318	48	1	1	NUM
ejpam-1354	318	49	(	(	PUNCT
ejpam-1354	318	50	b	b	NOUN
ejpam-1354	318	51	)	)	PUNCT
ejpam-1354	318	52	initial	initial	ADJ
ejpam-1354	318	53	0	0	NUM
ejpam-1354	318	54	0.1	0.1	NUM
ejpam-1354	318	55	0.2	0.2	NUM
ejpam-1354	318	56	0.3	0.3	NUM
ejpam-1354	318	57	0.4	0.4	NUM
ejpam-1354	318	58	0.5	0.5	NUM
ejpam-1354	318	59	0.6	0.6	NUM
ejpam-1354	318	60	0.7	0.7	NUM
ejpam-1354	318	61	0.8	0.8	NUM
ejpam-1354	318	62	0.9	0.9	NUM
ejpam-1354	318	63	1	1	NUM
ejpam-1354	318	64	0	0	NUM
ejpam-1354	318	65	0.1	0.1	NUM
ejpam-1354	318	66	0.2	0.2	NUM
ejpam-1354	318	67	0.3	0.3	NUM
ejpam-1354	318	68	0.4	0.4	NUM
ejpam-1354	318	69	0.5	0.5	NUM
ejpam-1354	318	70	0.6	0.6	NUM
ejpam-1354	318	71	0.7	0.7	NUM
ejpam-1354	318	72	0.8	0.8	NUM
ejpam-1354	318	73	0.9	0.9	NUM
ejpam-1354	318	74	1	1	NUM
ejpam-1354	318	75	(	(	PUNCT
ejpam-1354	318	76	a	a	PRON
ejpam-1354	318	77	)	)	PUNCT
ejpam-1354	318	78	iteration	iteration	NOUN
ejpam-1354	319	1	195	195	NUM
ejpam-1354	319	2	0	0	NUM
ejpam-1354	319	3	0.1	0.1	NUM
ejpam-1354	319	4	0.2	0.2	NUM
ejpam-1354	319	5	0.3	0.3	NUM
ejpam-1354	319	6	0.4	0.4	NUM
ejpam-1354	319	7	0.5	0.5	NUM
ejpam-1354	319	8	0.6	0.6	NUM
ejpam-1354	319	9	0.7	0.7	NUM
ejpam-1354	319	10	0.8	0.8	NUM
ejpam-1354	319	11	0.9	0.9	NUM
ejpam-1354	319	12	1	1	NUM
ejpam-1354	319	13	0	0	NUM
ejpam-1354	319	14	0.1	0.1	NUM
ejpam-1354	319	15	0.2	0.2	NUM
ejpam-1354	319	16	0.3	0.3	NUM
ejpam-1354	319	17	0.4	0.4	NUM
ejpam-1354	319	18	0.5	0.5	NUM
ejpam-1354	319	19	0.6	0.6	NUM
ejpam-1354	319	20	0.7	0.7	NUM
ejpam-1354	319	21	0.8	0.8	NUM
ejpam-1354	319	22	0.9	0.9	NUM
ejpam-1354	319	23	1	1	NUM
ejpam-1354	319	24	(	(	PUNCT
ejpam-1354	319	25	b	b	NOUN
ejpam-1354	319	26	)	)	PUNCT
ejpam-1354	319	27	iteration	iteration	NOUN
ejpam-1354	319	28	175	175	NUM
ejpam-1354	319	29	figure	figure	NOUN
ejpam-1354	319	30	5	5	NUM
ejpam-1354	319	31	:	:	PUNCT
ejpam-1354	319	32	initial	initial	ADJ
ejpam-1354	319	33	and	and	CCONJ
ejpam-1354	319	34	final	final	ADJ
ejpam-1354	319	35	densities	density	NOUN
ejpam-1354	319	36	of	of	ADP
ejpam-1354	319	37	condensing	condense	VERB
ejpam-1354	319	38	measures	measure	NOUN
ejpam-1354	319	39	on	on	ADP
ejpam-1354	319	40	the	the	DET
ejpam-1354	319	41	real	real	ADJ
ejpam-1354	319	42	line	line	NOUN
ejpam-1354	319	43	for	for	ADP
ejpam-1354	319	44	simulations	simulation	NOUN
ejpam-1354	319	45	(	(	PUNCT
ejpam-1354	319	46	a	a	X
ejpam-1354	319	47	)	)	PUNCT
ejpam-1354	319	48	and	and	CCONJ
ejpam-1354	319	49	(	(	PUNCT
ejpam-1354	319	50	b	b	X
ejpam-1354	319	51	)	)	PUNCT
ejpam-1354	319	52	4.3	4.3	NUM
ejpam-1354	319	53	.	.	PUNCT
ejpam-1354	320	1	condensing	condense	VERB
ejpam-1354	320	2	on	on	ADP
ejpam-1354	320	3	the	the	DET
ejpam-1354	320	4	real	real	ADJ
ejpam-1354	320	5	plane	plane	NOUN
ejpam-1354	320	6	this	this	DET
ejpam-1354	320	7	section	section	NOUN
ejpam-1354	320	8	presents	present	VERB
ejpam-1354	320	9	simulations	simulation	NOUN
ejpam-1354	320	10	on	on	ADP
ejpam-1354	320	11	the	the	DET
ejpam-1354	320	12	real	real	ADJ
ejpam-1354	320	13	plane	plane	NOUN
ejpam-1354	320	14	.	.	PUNCT
ejpam-1354	321	1	in	in	ADP
ejpam-1354	321	2	order	order	NOUN
ejpam-1354	321	3	to	to	PART
ejpam-1354	321	4	compute	compute	VERB
ejpam-1354	321	5	the	the	DET
ejpam-1354	321	6	density	density	NOUN
ejpam-1354	321	7	of	of	ADP
ejpam-1354	321	8	the	the	DET
ejpam-1354	321	9	points	point	NOUN
ejpam-1354	321	10	masses	masse	NOUN
ejpam-1354	321	11	of	of	ADP
ejpam-1354	321	12	a	a	DET
ejpam-1354	321	13	measure	measure	NOUN
ejpam-1354	321	14	at	at	ADP
ejpam-1354	321	15	each	each	DET
ejpam-1354	321	16	iteration	iteration	NOUN
ejpam-1354	321	17	,	,	PUNCT
ejpam-1354	321	18	the	the	DET
ejpam-1354	321	19	space	space	NOUN
ejpam-1354	321	20	domain	domain	NOUN
ejpam-1354	321	21	is	be	AUX
ejpam-1354	321	22	the	the	DET
ejpam-1354	321	23	discretized	discretized	ADJ
ejpam-1354	321	24	into	into	ADP
ejpam-1354	321	25	n	n	PROPN
ejpam-1354	321	26	x×n	x×n	NOUN
ejpam-1354	321	27	x	x	SYM
ejpam-1354	321	28	uniform	uniform	ADJ
ejpam-1354	321	29	two	two	NUM
ejpam-1354	321	30	-	-	PUNCT
ejpam-1354	321	31	dimensional	dimensional	ADJ
ejpam-1354	321	32	gridpoints	gridpoint	NOUN
ejpam-1354	321	33	.	.	PUNCT
ejpam-1354	322	1	we	we	PRON
ejpam-1354	322	2	carry	carry	VERB
ejpam-1354	322	3	out	out	ADP
ejpam-1354	322	4	two	two	NUM
ejpam-1354	322	5	tests	test	NOUN
ejpam-1354	322	6	of	of	ADP
ejpam-1354	322	7	condensing	condense	VERB
ejpam-1354	322	8	sequences	sequence	NOUN
ejpam-1354	322	9	of	of	ADP
ejpam-1354	322	10	two	two	NUM
ejpam-1354	322	11	measures	measure	NOUN
ejpam-1354	322	12	m	m	VERB
ejpam-1354	322	13	:	:	PUNCT
ejpam-1354	322	14	=	=	SYM
ejpam-1354	322	15	∑	∑	PUNCT
ejpam-1354	322	16	x∈s(m)⊂[0,1]2	x∈s(m)⊂[0,1]2	PROPN
ejpam-1354	322	17	m(x)δx	m(x)δx	PROPN
ejpam-1354	322	18	.	.	PUNCT
ejpam-1354	323	1	where	where	SCONJ
ejpam-1354	323	2	s(m	s(m	NOUN
ejpam-1354	323	3	)	)	PUNCT
ejpam-1354	323	4	=	=	PRON
ejpam-1354	323	5	{	{	PUNCT
ejpam-1354	323	6	x1	x1	PROPN
ejpam-1354	323	7	,	,	PUNCT
ejpam-1354	323	8	.	.	PUNCT
ejpam-1354	323	9	.	.	PUNCT
ejpam-1354	324	1	.	.	PUNCT
ejpam-1354	325	1	,	,	PUNCT
ejpam-1354	326	1	x441	x441	PROPN
ejpam-1354	326	2	}	}	PUNCT
ejpam-1354	326	3	.	.	PUNCT
ejpam-1354	327	1	we	we	PRON
ejpam-1354	327	2	run	run	VERB
ejpam-1354	327	3	our	our	PRON
ejpam-1354	327	4	code	code	NOUN
ejpam-1354	327	5	after	after	ADP
ejpam-1354	327	6	fixing	fix	VERB
ejpam-1354	327	7	the	the	DET
ejpam-1354	327	8	order	order	NOUN
ejpam-1354	327	9	of	of	ADP
ejpam-1354	327	10	reactions	reaction	NOUN
ejpam-1354	327	11	(	(	PUNCT
ejpam-1354	327	12	the	the	DET
ejpam-1354	327	13	array	array	NOUN
ejpam-1354	327	14	of	of	ADP
ejpam-1354	327	15	441	441	NUM
ejpam-1354	327	16	index	index	NOUN
ejpam-1354	327	17	will	will	AUX
ejpam-1354	327	18	be	be	AUX
ejpam-1354	327	19	randomly	randomly	ADV
ejpam-1354	327	20	permuted	permute	VERB
ejpam-1354	327	21	)	)	PUNCT
ejpam-1354	327	22	.	.	PUNCT
ejpam-1354	328	1	the	the	DET
ejpam-1354	328	2	following	follow	VERB
ejpam-1354	328	3	table	table	NOUN
ejpam-1354	328	4	summarizes	summarize	VERB
ejpam-1354	328	5	the	the	DET
ejpam-1354	328	6	results	result	NOUN
ejpam-1354	328	7	of	of	ADP
ejpam-1354	328	8	the	the	DET
ejpam-1354	328	9	m.	m.	NOUN
ejpam-1354	328	10	zahri	zahri	PROPN
ejpam-1354	328	11	/	/	SYM
ejpam-1354	328	12	eur	eur	PROPN
ejpam-1354	328	13	.	.	PUNCT
ejpam-1354	329	1	j.	j.	PROPN
ejpam-1354	329	2	pure	pure	PROPN
ejpam-1354	329	3	appl	appl	PROPN
ejpam-1354	329	4	.	.	PROPN
ejpam-1354	329	5	math	math	PROPN
ejpam-1354	329	6	,	,	PUNCT
ejpam-1354	329	7	6	6	NUM
ejpam-1354	329	8	(	(	PUNCT
ejpam-1354	329	9	2013	2013	NUM
ejpam-1354	329	10	)	)	PUNCT
ejpam-1354	329	11	,	,	PUNCT
ejpam-1354	329	12	172	172	NUM
ejpam-1354	329	13	-	-	SYM
ejpam-1354	329	14	188	188	NUM
ejpam-1354	329	15	186	186	NUM
ejpam-1354	329	16	simulations	simulation	NOUN
ejpam-1354	329	17	on	on	ADP
ejpam-1354	329	18	the	the	DET
ejpam-1354	329	19	real	real	ADJ
ejpam-1354	329	20	plane	plane	NOUN
ejpam-1354	329	21	(	(	PUNCT
ejpam-1354	329	22	(	(	PUNCT
ejpam-1354	329	23	ε	ε	PROPN
ejpam-1354	329	24	,	,	PUNCT
ejpam-1354	329	25	θ	θ	NOUN
ejpam-1354	329	26	)	)	PUNCT
ejpam-1354	329	27	=	=	SYM
ejpam-1354	329	28	(	(	PUNCT
ejpam-1354	329	29	0.1,0.001	0.1,0.001	NUM
ejpam-1354	329	30	)	)	PUNCT
ejpam-1354	329	31	):	):	PUNCT
ejpam-1354	329	32	table	table	NOUN
ejpam-1354	329	33	3	3	NUM
ejpam-1354	329	34	:	:	PUNCT
ejpam-1354	329	35	results	result	NOUN
ejpam-1354	329	36	of	of	ADP
ejpam-1354	329	37	two	two	NUM
ejpam-1354	329	38	simulations	simulation	NOUN
ejpam-1354	329	39	on	on	ADP
ejpam-1354	329	40	the	the	DET
ejpam-1354	329	41	real	real	ADJ
ejpam-1354	329	42	plane	plane	NOUN
ejpam-1354	329	43	.	.	PUNCT
ejpam-1354	330	1	parameter	parameter	NOUN
ejpam-1354	330	2	/	/	SYM
ejpam-1354	330	3	sim	sim	NOUN
ejpam-1354	330	4	.	.	PUNCT
ejpam-1354	331	1	(	(	PUNCT
ejpam-1354	331	2	a	a	X
ejpam-1354	331	3	)	)	PUNCT
ejpam-1354	331	4	(	(	PUNCT
ejpam-1354	331	5	b	b	X
ejpam-1354	331	6	)	)	PUNCT
ejpam-1354	331	7	ε	ε	PROPN
ejpam-1354	331	8	0.1	0.1	NUM
ejpam-1354	331	9	0.1	0.1	NUM
ejpam-1354	331	10	θ	θ	NOUN
ejpam-1354	331	11	0.001	0.001	NUM
ejpam-1354	331	12	0.001	0.001	NUM
ejpam-1354	331	13	initial	initial	ADJ
ejpam-1354	331	14	state	state	NOUN
ejpam-1354	331	15	441	441	NUM
ejpam-1354	331	16	masses	masse	NOUN
ejpam-1354	331	17	(	(	PUNCT
ejpam-1354	331	18	one	one	NUM
ejpam-1354	331	19	)	)	PUNCT
ejpam-1354	331	20	441	441	NUM
ejpam-1354	331	21	masses	masse	NOUN
ejpam-1354	331	22	(	(	PUNCT
ejpam-1354	331	23	u(0,4	u(0,4	NOUN
ejpam-1354	331	24	)	)	PUNCT
ejpam-1354	331	25	)	)	PUNCT
ejpam-1354	331	26	final	final	ADJ
ejpam-1354	331	27	state	state	NOUN
ejpam-1354	331	28	condensing	condense	VERB
ejpam-1354	331	29	condensing	condense	VERB
ejpam-1354	331	30	number	number	NOUN
ejpam-1354	331	31	of	of	ADP
ejpam-1354	331	32	iterations	iteration	NOUN
ejpam-1354	331	33	more	more	ADJ
ejpam-1354	331	34	than	than	ADP
ejpam-1354	331	35	10000	10000	NUM
ejpam-1354	331	36	more	more	ADJ
ejpam-1354	331	37	than	than	ADP
ejpam-1354	331	38	20000	20000	NUM
ejpam-1354	331	39	figure	figure	NOUN
ejpam-1354	331	40	6	6	NUM
ejpam-1354	331	41	presents	present	VERB
ejpam-1354	331	42	the	the	DET
ejpam-1354	331	43	two	two	NUM
ejpam-1354	331	44	-	-	PUNCT
ejpam-1354	331	45	dimensional	dimensional	ADJ
ejpam-1354	331	46	density	density	NOUN
ejpam-1354	331	47	of	of	ADP
ejpam-1354	331	48	the	the	DET
ejpam-1354	331	49	measure	measure	NOUN
ejpam-1354	331	50	.	.	PUNCT
ejpam-1354	332	1	this	this	DET
ejpam-1354	332	2	simulation	simulation	NOUN
ejpam-1354	332	3	needs	need	VERB
ejpam-1354	332	4	more	more	ADJ
ejpam-1354	332	5	the	the	DET
ejpam-1354	332	6	10000	10000	NUM
ejpam-1354	332	7	condensing	condense	VERB
ejpam-1354	332	8	iterations	iteration	NOUN
ejpam-1354	332	9	until	until	SCONJ
ejpam-1354	332	10	the	the	DET
ejpam-1354	332	11	last	last	ADJ
ejpam-1354	332	12	iteration	iteration	NOUN
ejpam-1354	332	13	presented	present	VERB
ejpam-1354	332	14	in	in	ADP
ejpam-1354	332	15	the	the	DET
ejpam-1354	332	16	last	last	ADJ
ejpam-1354	332	17	figure	figure	NOUN
ejpam-1354	332	18	.	.	PUNCT
ejpam-1354	333	1	our	our	PRON
ejpam-1354	333	2	code	code	NOUN
ejpam-1354	333	3	breaks	break	VERB
ejpam-1354	333	4	down	down	ADP
ejpam-1354	333	5	,	,	PUNCT
ejpam-1354	333	6	when	when	SCONJ
ejpam-1354	333	7	the	the	DET
ejpam-1354	333	8	total	total	ADJ
ejpam-1354	333	9	energy	energy	NOUN
ejpam-1354	333	10	will	will	AUX
ejpam-1354	333	11	be	be	AUX
ejpam-1354	333	12	negligible	negligible	ADJ
ejpam-1354	333	13	(	(	PUNCT
ejpam-1354	333	14	compared	compare	VERB
ejpam-1354	333	15	with	with	ADP
ejpam-1354	333	16	a	a	DET
ejpam-1354	333	17	fixed	fix	VERB
ejpam-1354	333	18	tolerance	tolerance	NOUN
ejpam-1354	333	19	)	)	PUNCT
ejpam-1354	333	20	.	.	PUNCT
ejpam-1354	334	1	it	it	PRON
ejpam-1354	334	2	is	be	AUX
ejpam-1354	334	3	clearly	clearly	ADV
ejpam-1354	334	4	shown	show	VERB
ejpam-1354	334	5	in	in	ADP
ejpam-1354	334	6	figure	figure	NOUN
ejpam-1354	334	7	6	6	NUM
ejpam-1354	334	8	that	that	SCONJ
ejpam-1354	334	9	the	the	DET
ejpam-1354	334	10	particles	particle	NOUN
ejpam-1354	334	11	build	build	VERB
ejpam-1354	334	12	a	a	DET
ejpam-1354	334	13	mass	mass	NOUN
ejpam-1354	334	14	points	point	NOUN
ejpam-1354	334	15	with	with	ADP
ejpam-1354	334	16	height	height	NOUN
ejpam-1354	334	17	density	density	NOUN
ejpam-1354	334	18	in	in	ADP
ejpam-1354	334	19	the	the	DET
ejpam-1354	334	20	middle	middle	NOUN
ejpam-1354	334	21	of	of	ADP
ejpam-1354	334	22	the	the	DET
ejpam-1354	334	23	computation	computation	NOUN
ejpam-1354	334	24	domain	domain	NOUN
ejpam-1354	334	25	.	.	PUNCT
ejpam-1354	335	1	this	this	DET
ejpam-1354	335	2	result	result	NOUN
ejpam-1354	335	3	will	will	AUX
ejpam-1354	335	4	be	be	AUX
ejpam-1354	335	5	different	different	ADJ
ejpam-1354	335	6	if	if	SCONJ
ejpam-1354	335	7	we	we	PRON
ejpam-1354	335	8	simulate	simulate	VERB
ejpam-1354	335	9	another	another	DET
ejpam-1354	335	10	simulation	simulation	NOUN
ejpam-1354	335	11	,	,	PUNCT
ejpam-1354	335	12	even	even	ADV
ejpam-1354	335	13	if	if	SCONJ
ejpam-1354	335	14	we	we	PRON
ejpam-1354	335	15	use	use	VERB
ejpam-1354	335	16	the	the	DET
ejpam-1354	335	17	same	same	ADJ
ejpam-1354	335	18	data	datum	NOUN
ejpam-1354	335	19	for	for	ADP
ejpam-1354	335	20	the	the	DET
ejpam-1354	335	21	initial	initial	ADJ
ejpam-1354	335	22	measure	measure	NOUN
ejpam-1354	335	23	.	.	PUNCT
ejpam-1354	336	1	0	0	NUM
ejpam-1354	336	2	0.2	0.2	NUM
ejpam-1354	336	3	0.4	0.4	NUM
ejpam-1354	336	4	0.6	0.6	NUM
ejpam-1354	336	5	0.8	0.8	NUM
ejpam-1354	336	6	1	1	NUM
ejpam-1354	336	7	0	0	NUM
ejpam-1354	336	8	0.2	0.2	NUM
ejpam-1354	336	9	0.4	0.4	NUM
ejpam-1354	336	10	0.6	0.6	NUM
ejpam-1354	336	11	0.8	0.8	NUM
ejpam-1354	336	12	1	1	NUM
ejpam-1354	336	13	0	0	NUM
ejpam-1354	336	14	0.1	0.1	NUM
ejpam-1354	336	15	0.2	0.2	NUM
ejpam-1354	336	16	0.3	0.3	NUM
ejpam-1354	336	17	0.4	0.4	NUM
ejpam-1354	336	18	0.5	0.5	NUM
ejpam-1354	336	19	0.6	0.6	NUM
ejpam-1354	336	20	0.7	0.7	NUM
ejpam-1354	336	21	initial	initial	ADJ
ejpam-1354	336	22	0	0	NUM
ejpam-1354	336	23	0.2	0.2	NUM
ejpam-1354	336	24	0.4	0.4	NUM
ejpam-1354	336	25	0.6	0.6	NUM
ejpam-1354	336	26	0.8	0.8	NUM
ejpam-1354	336	27	1	1	NUM
ejpam-1354	336	28	0	0	NUM
ejpam-1354	336	29	0.2	0.2	NUM
ejpam-1354	336	30	0.4	0.4	NUM
ejpam-1354	336	31	0.6	0.6	NUM
ejpam-1354	336	32	0.8	0.8	NUM
ejpam-1354	336	33	1	1	NUM
ejpam-1354	336	34	0	0	NUM
ejpam-1354	336	35	0.1	0.1	NUM
ejpam-1354	336	36	0.2	0.2	NUM
ejpam-1354	336	37	0.3	0.3	NUM
ejpam-1354	336	38	0.4	0.4	NUM
ejpam-1354	336	39	0.5	0.5	NUM
ejpam-1354	336	40	0.6	0.6	NUM
ejpam-1354	336	41	0.7	0.7	NUM
ejpam-1354	336	42	iteration	iteration	NOUN
ejpam-1354	336	43	1	1	NUM
ejpam-1354	336	44	,	,	PUNCT
ejpam-1354	336	45	000	000	NUM
ejpam-1354	336	46	0	0	NUM
ejpam-1354	336	47	0.2	0.2	NUM
ejpam-1354	336	48	0.4	0.4	NUM
ejpam-1354	336	49	0.6	0.6	NUM
ejpam-1354	336	50	0.8	0.8	NUM
ejpam-1354	336	51	1	1	NUM
ejpam-1354	336	52	0	0	NUM
ejpam-1354	336	53	0.2	0.2	NUM
ejpam-1354	336	54	0.4	0.4	NUM
ejpam-1354	336	55	0.6	0.6	NUM
ejpam-1354	336	56	0.8	0.8	NUM
ejpam-1354	336	57	1	1	NUM
ejpam-1354	336	58	0	0	NUM
ejpam-1354	336	59	0.1	0.1	NUM
ejpam-1354	336	60	0.2	0.2	NUM
ejpam-1354	336	61	0.3	0.3	NUM
ejpam-1354	336	62	0.4	0.4	NUM
ejpam-1354	336	63	0.5	0.5	NUM
ejpam-1354	336	64	0.6	0.6	NUM
ejpam-1354	336	65	0.7	0.7	NUM
ejpam-1354	336	66	iteration	iteration	NOUN
ejpam-1354	336	67	5	5	NUM
ejpam-1354	336	68	,	,	PUNCT
ejpam-1354	336	69	000	000	NUM
ejpam-1354	336	70	0	0	NUM
ejpam-1354	336	71	0.2	0.2	NUM
ejpam-1354	336	72	0.4	0.4	NUM
ejpam-1354	336	73	0.6	0.6	NUM
ejpam-1354	336	74	0.8	0.8	NUM
ejpam-1354	336	75	1	1	NUM
ejpam-1354	336	76	0	0	NUM
ejpam-1354	336	77	0.2	0.2	NUM
ejpam-1354	336	78	0.4	0.4	NUM
ejpam-1354	336	79	0.6	0.6	NUM
ejpam-1354	336	80	0.8	0.8	NUM
ejpam-1354	336	81	1	1	NUM
ejpam-1354	336	82	0	0	NUM
ejpam-1354	336	83	0.1	0.1	NUM
ejpam-1354	336	84	0.2	0.2	NUM
ejpam-1354	336	85	0.3	0.3	NUM
ejpam-1354	336	86	0.4	0.4	NUM
ejpam-1354	336	87	0.5	0.5	NUM
ejpam-1354	336	88	0.6	0.6	NUM
ejpam-1354	336	89	0.7	0.7	NUM
ejpam-1354	336	90	iteration	iteration	NOUN
ejpam-1354	336	91	7	7	NUM
ejpam-1354	336	92	,	,	PUNCT
ejpam-1354	336	93	500	500	NUM
ejpam-1354	336	94	0	0	NUM
ejpam-1354	336	95	0.2	0.2	NUM
ejpam-1354	336	96	0.4	0.4	NUM
ejpam-1354	336	97	0.6	0.6	NUM
ejpam-1354	336	98	0.8	0.8	NUM
ejpam-1354	336	99	1	1	NUM
ejpam-1354	336	100	0	0	NUM
ejpam-1354	336	101	0.2	0.2	NUM
ejpam-1354	336	102	0.4	0.4	NUM
ejpam-1354	336	103	0.6	0.6	NUM
ejpam-1354	336	104	0.8	0.8	NUM
ejpam-1354	336	105	1	1	NUM
ejpam-1354	336	106	0	0	NUM
ejpam-1354	336	107	0.1	0.1	NUM
ejpam-1354	336	108	0.2	0.2	NUM
ejpam-1354	336	109	0.3	0.3	NUM
ejpam-1354	336	110	0.4	0.4	NUM
ejpam-1354	336	111	0.5	0.5	NUM
ejpam-1354	336	112	0.6	0.6	NUM
ejpam-1354	336	113	0.7	0.7	NUM
ejpam-1354	336	114	iteration	iteration	NOUN
ejpam-1354	336	115	10	10	NUM
ejpam-1354	336	116	,	,	PUNCT
ejpam-1354	336	117	000	000	NUM
ejpam-1354	336	118	0	0	NUM
ejpam-1354	336	119	0.2	0.2	NUM
ejpam-1354	336	120	0.4	0.4	NUM
ejpam-1354	336	121	0.6	0.6	NUM
ejpam-1354	336	122	0.8	0.8	NUM
ejpam-1354	336	123	1	1	NUM
ejpam-1354	336	124	0	0	NUM
ejpam-1354	336	125	0.2	0.2	NUM
ejpam-1354	336	126	0.4	0.4	NUM
ejpam-1354	336	127	0.6	0.6	NUM
ejpam-1354	336	128	0.8	0.8	NUM
ejpam-1354	336	129	1	1	NUM
ejpam-1354	336	130	0	0	NUM
ejpam-1354	336	131	0.1	0.1	NUM
ejpam-1354	336	132	0.2	0.2	NUM
ejpam-1354	336	133	0.3	0.3	NUM
ejpam-1354	336	134	0.4	0.4	NUM
ejpam-1354	336	135	0.5	0.5	NUM
ejpam-1354	336	136	0.6	0.6	NUM
ejpam-1354	336	137	0.7	0.7	NUM
ejpam-1354	336	138	iteration	iteration	NOUN
ejpam-1354	336	139	20	20	NUM
ejpam-1354	336	140	,	,	PUNCT
ejpam-1354	336	141	000	000	NUM
ejpam-1354	336	142	figure	figure	VERB
ejpam-1354	336	143	6	6	NUM
ejpam-1354	336	144	:	:	PUNCT
ejpam-1354	336	145	densities	density	NOUN
ejpam-1354	336	146	of	of	ADP
ejpam-1354	336	147	condensing	condense	VERB
ejpam-1354	336	148	particles	particle	NOUN
ejpam-1354	336	149	on	on	ADP
ejpam-1354	336	150	real	real	ADJ
ejpam-1354	336	151	plane	plane	NOUN
ejpam-1354	336	152	of	of	ADP
ejpam-1354	336	153	the	the	DET
ejpam-1354	336	154	simulation	simulation	NOUN
ejpam-1354	336	155	(	(	PUNCT
ejpam-1354	336	156	b	b	NOUN
ejpam-1354	336	157	)	)	PUNCT
ejpam-1354	336	158	figure	figure	NOUN
ejpam-1354	336	159	6	6	NUM
ejpam-1354	336	160	presents	present	VERB
ejpam-1354	336	161	the	the	DET
ejpam-1354	336	162	density	density	NOUN
ejpam-1354	336	163	of	of	ADP
ejpam-1354	336	164	six	six	NUM
ejpam-1354	336	165	condensing	condense	VERB
ejpam-1354	336	166	iterations	iteration	NOUN
ejpam-1354	336	167	,	,	PUNCT
ejpam-1354	336	168	we	we	PRON
ejpam-1354	336	169	show	show	VERB
ejpam-1354	336	170	the	the	DET
ejpam-1354	336	171	initial	initial	NOUN
ejpam-1354	336	172	and	and	CCONJ
ejpam-1354	336	173	the	the	DET
ejpam-1354	336	174	final	final	ADJ
ejpam-1354	336	175	mass	mass	NOUN
ejpam-1354	336	176	and	and	CCONJ
ejpam-1354	336	177	some	some	DET
ejpam-1354	336	178	iterations	iteration	NOUN
ejpam-1354	336	179	.	.	PUNCT
ejpam-1354	337	1	the	the	DET
ejpam-1354	337	2	mass	mass	NOUN
ejpam-1354	337	3	is	be	AUX
ejpam-1354	337	4	concentrated	concentrate	VERB
ejpam-1354	337	5	on	on	ADP
ejpam-1354	337	6	one	one	NUM
ejpam-1354	337	7	point	point	NOUN
ejpam-1354	337	8	on	on	ADP
ejpam-1354	337	9	the	the	DET
ejpam-1354	337	10	middle	middle	NOUN
ejpam-1354	337	11	of	of	ADP
ejpam-1354	337	12	the	the	DET
ejpam-1354	337	13	computational	computational	ADJ
ejpam-1354	337	14	domain	domain	NOUN
ejpam-1354	337	15	.	.	PUNCT
ejpam-1354	338	1	5	5	X
ejpam-1354	338	2	.	.	X
ejpam-1354	338	3	concluding	conclude	VERB
ejpam-1354	338	4	remarks	remark	VERB
ejpam-1354	338	5	the	the	DET
ejpam-1354	338	6	present	present	ADJ
ejpam-1354	338	7	work	work	NOUN
ejpam-1354	338	8	proposes	propose	VERB
ejpam-1354	338	9	a	a	DET
ejpam-1354	338	10	new	new	ADJ
ejpam-1354	338	11	model	model	NOUN
ejpam-1354	338	12	for	for	ADP
ejpam-1354	338	13	condensing	condense	VERB
ejpam-1354	338	14	sequences	sequence	NOUN
ejpam-1354	338	15	,	,	PUNCT
ejpam-1354	338	16	with	with	ADP
ejpam-1354	338	17	special	special	ADJ
ejpam-1354	338	18	interest	interest	NOUN
ejpam-1354	338	19	on	on	ADP
ejpam-1354	338	20	the	the	DET
ejpam-1354	338	21	condensing	condense	VERB
ejpam-1354	338	22	process	process	NOUN
ejpam-1354	338	23	of	of	ADP
ejpam-1354	338	24	particles	particle	NOUN
ejpam-1354	338	25	.	.	PUNCT
ejpam-1354	339	1	we	we	PRON
ejpam-1354	339	2	have	have	AUX
ejpam-1354	339	3	observed	observe	VERB
ejpam-1354	339	4	that	that	SCONJ
ejpam-1354	339	5	the	the	DET
ejpam-1354	339	6	limit	limit	NOUN
ejpam-1354	339	7	states	state	NOUN
ejpam-1354	339	8	depends	depend	VERB
ejpam-1354	339	9	not	not	PART
ejpam-1354	339	10	only	only	ADV
ejpam-1354	339	11	references	reference	NOUN
ejpam-1354	339	12	187	187	NUM
ejpam-1354	339	13	from	from	ADP
ejpam-1354	339	14	the	the	DET
ejpam-1354	339	15	initial	initial	ADJ
ejpam-1354	339	16	state	state	NOUN
ejpam-1354	339	17	but	but	CCONJ
ejpam-1354	339	18	also	also	ADV
ejpam-1354	339	19	of	of	ADP
ejpam-1354	339	20	the	the	DET
ejpam-1354	339	21	condensing	condense	VERB
ejpam-1354	339	22	succession	succession	NOUN
ejpam-1354	339	23	or	or	CCONJ
ejpam-1354	339	24	the	the	DET
ejpam-1354	339	25	reaction	reaction	NOUN
ejpam-1354	339	26	order	order	NOUN
ejpam-1354	339	27	,	,	PUNCT
ejpam-1354	339	28	therefore	therefore	ADV
ejpam-1354	339	29	,	,	PUNCT
ejpam-1354	339	30	they	they	PRON
ejpam-1354	339	31	have	have	VERB
ejpam-1354	339	32	non	non	ADJ
ejpam-1354	339	33	uniform	uniform	NOUN
ejpam-1354	339	34	and	and	CCONJ
ejpam-1354	339	35	different	different	ADJ
ejpam-1354	339	36	distribution	distribution	NOUN
ejpam-1354	339	37	of	of	ADP
ejpam-1354	339	38	mass	mass	NOUN
ejpam-1354	339	39	and	and	CCONJ
ejpam-1354	339	40	form	form	NOUN
ejpam-1354	339	41	ε	ε	NOUN
ejpam-1354	339	42	-	-	PUNCT
ejpam-1354	339	43	isolated	isolate	VERB
ejpam-1354	339	44	subgroups	subgroup	NOUN
ejpam-1354	339	45	.	.	PUNCT
ejpam-1354	340	1	in	in	ADP
ejpam-1354	340	2	one	one	NUM
ejpam-1354	340	3	hand	hand	NOUN
ejpam-1354	340	4	,	,	PUNCT
ejpam-1354	340	5	we	we	PRON
ejpam-1354	340	6	have	have	AUX
ejpam-1354	340	7	shown	show	VERB
ejpam-1354	340	8	how	how	SCONJ
ejpam-1354	340	9	a	a	DET
ejpam-1354	340	10	collection	collection	NOUN
ejpam-1354	340	11	of	of	ADP
ejpam-1354	340	12	particles	particle	NOUN
ejpam-1354	340	13	with	with	ADP
ejpam-1354	340	14	a	a	DET
ejpam-1354	340	15	local	local	ADJ
ejpam-1354	340	16	control	control	NOUN
ejpam-1354	340	17	rule	rule	NOUN
ejpam-1354	340	18	,	,	PUNCT
ejpam-1354	340	19	forms	form	VERB
ejpam-1354	340	20	an	an	DET
ejpam-1354	340	21	isolated	isolated	ADJ
ejpam-1354	340	22	distribution	distribution	NOUN
ejpam-1354	340	23	of	of	ADP
ejpam-1354	340	24	masses	masse	NOUN
ejpam-1354	340	25	with	with	ADP
ejpam-1354	340	26	zero	zero	NUM
ejpam-1354	340	27	global	global	ADJ
ejpam-1354	340	28	energy	energy	NOUN
ejpam-1354	340	29	.	.	PUNCT
ejpam-1354	341	1	in	in	ADP
ejpam-1354	341	2	the	the	DET
ejpam-1354	341	3	other	other	ADJ
ejpam-1354	341	4	hand	hand	NOUN
ejpam-1354	341	5	,	,	PUNCT
ejpam-1354	341	6	we	we	PRON
ejpam-1354	341	7	have	have	AUX
ejpam-1354	341	8	seen	see	VERB
ejpam-1354	341	9	that	that	SCONJ
ejpam-1354	341	10	the	the	DET
ejpam-1354	341	11	energy	energy	NOUN
ejpam-1354	341	12	as	as	ADP
ejpam-1354	341	13	local	local	ADJ
ejpam-1354	341	14	rule	rule	NOUN
ejpam-1354	341	15	is	be	AUX
ejpam-1354	341	16	in	in	ADP
ejpam-1354	341	17	reality	reality	NOUN
ejpam-1354	341	18	a	a	DET
ejpam-1354	341	19	global	global	ADJ
ejpam-1354	341	20	criteria	criterion	NOUN
ejpam-1354	341	21	for	for	ADP
ejpam-1354	341	22	forming	form	VERB
ejpam-1354	341	23	subgroups	subgroup	NOUN
ejpam-1354	341	24	.	.	PUNCT
ejpam-1354	342	1	however	however	ADV
ejpam-1354	342	2	,	,	PUNCT
ejpam-1354	342	3	one	one	PRON
ejpam-1354	342	4	can	can	AUX
ejpam-1354	342	5	easily	easily	ADV
ejpam-1354	342	6	show	show	VERB
ejpam-1354	342	7	that	that	SCONJ
ejpam-1354	342	8	the	the	DET
ejpam-1354	342	9	dynamics	dynamic	NOUN
ejpam-1354	342	10	of	of	ADP
ejpam-1354	342	11	the	the	DET
ejpam-1354	342	12	group	group	NOUN
ejpam-1354	342	13	is	be	AUX
ejpam-1354	342	14	a	a	DET
ejpam-1354	342	15	consequence	consequence	NOUN
ejpam-1354	342	16	of	of	ADP
ejpam-1354	342	17	individual	individual	ADJ
ejpam-1354	342	18	moves	move	NOUN
ejpam-1354	342	19	of	of	ADP
ejpam-1354	342	20	agents	agent	NOUN
ejpam-1354	342	21	.	.	PUNCT
ejpam-1354	343	1	moreover	moreover	ADV
ejpam-1354	343	2	,	,	PUNCT
ejpam-1354	343	3	it	it	PRON
ejpam-1354	343	4	should	should	AUX
ejpam-1354	343	5	be	be	AUX
ejpam-1354	343	6	stressed	stress	VERB
ejpam-1354	343	7	that	that	SCONJ
ejpam-1354	343	8	the	the	DET
ejpam-1354	343	9	stochastic	stochastic	ADJ
ejpam-1354	343	10	behavior	behavior	NOUN
ejpam-1354	343	11	of	of	ADP
ejpam-1354	343	12	our	our	PRON
ejpam-1354	343	13	simulations	simulation	NOUN
ejpam-1354	343	14	is	be	AUX
ejpam-1354	343	15	due	due	ADJ
ejpam-1354	343	16	to	to	ADP
ejpam-1354	343	17	random	random	ADJ
ejpam-1354	343	18	choice	choice	NOUN
ejpam-1354	343	19	of	of	ADP
ejpam-1354	343	20	positions	position	NOUN
ejpam-1354	343	21	minimizing	minimize	VERB
ejpam-1354	343	22	the	the	DET
ejpam-1354	343	23	local	local	ADJ
ejpam-1354	343	24	energy	energy	NOUN
ejpam-1354	343	25	and	and	CCONJ
ejpam-1354	343	26	the	the	DET
ejpam-1354	343	27	random	random	ADJ
ejpam-1354	343	28	range	range	NOUN
ejpam-1354	343	29	of	of	ADP
ejpam-1354	343	30	reactions	reaction	NOUN
ejpam-1354	343	31	of	of	ADP
ejpam-1354	343	32	the	the	DET
ejpam-1354	343	33	particles	particle	NOUN
ejpam-1354	343	34	.	.	PUNCT
ejpam-1354	344	1	the	the	DET
ejpam-1354	344	2	present	present	ADJ
ejpam-1354	344	3	study	study	NOUN
ejpam-1354	344	4	could	could	AUX
ejpam-1354	344	5	be	be	AUX
ejpam-1354	344	6	considered	consider	VERB
ejpam-1354	344	7	as	as	ADP
ejpam-1354	344	8	example	example	NOUN
ejpam-1354	344	9	for	for	ADP
ejpam-1354	344	10	explaining	explain	VERB
ejpam-1354	344	11	the	the	DET
ejpam-1354	344	12	concept	concept	NOUN
ejpam-1354	344	13	of	of	ADP
ejpam-1354	344	14	consensus	consensus	NOUN
ejpam-1354	344	15	and	and	CCONJ
ejpam-1354	344	16	emergence	emergence	ADJ
ejpam-1354	344	17	phenomena	phenomenon	NOUN
ejpam-1354	344	18	.	.	PUNCT
ejpam-1354	345	1	references	reference	NOUN
ejpam-1354	345	2	[	[	X
ejpam-1354	345	3	1	1	NUM
ejpam-1354	345	4	]	]	PUNCT
ejpam-1354	345	5	p.	p.	NOUN
ejpam-1354	345	6	babak	babak	PROPN
ejpam-1354	345	7	,	,	PUNCT
ejpam-1354	345	8	g.	g.	PROPN
ejpam-1354	345	9	magnússon	magnússon	PROPN
ejpam-1354	345	10	,	,	PUNCT
ejpam-1354	345	11	,	,	PUNCT
ejpam-1354	345	12	and	and	CCONJ
ejpam-1354	345	13	s.	s.	PROPN
ejpam-1354	345	14	th	th	PROPN
ejpam-1354	345	15	.	.	PUNCT
ejpam-1354	345	16	sigurdsson	sigurdsson	PROPN
ejpam-1354	345	17	.	.	PUNCT
ejpam-1354	346	1	dynamics	dynamic	NOUN
ejpam-1354	346	2	of	of	ADP
ejpam-1354	346	3	group	group	NOUN
ejpam-1354	346	4	formation	formation	NOUN
ejpam-1354	346	5	in	in	ADP
ejpam-1354	346	6	collective	collective	ADJ
ejpam-1354	346	7	motion	motion	NOUN
ejpam-1354	346	8	of	of	ADP
ejpam-1354	346	9	organisms	organism	NOUN
ejpam-1354	346	10	.	.	PUNCT
ejpam-1354	347	1	mathematical	mathematical	ADJ
ejpam-1354	347	2	medicine	medicine	NOUN
ejpam-1354	347	3	and	and	CCONJ
ejpam-1354	347	4	biology	biology	NOUN
ejpam-1354	347	5	,	,	PUNCT
ejpam-1354	347	6	21(4):269–292	21(4):269–292	NUM
ejpam-1354	347	7	,	,	PUNCT
ejpam-1354	347	8	2004	2004	NUM
ejpam-1354	347	9	.	.	PUNCT
ejpam-1354	348	1	[	[	X
ejpam-1354	348	2	2	2	X
ejpam-1354	348	3	]	]	PUNCT
ejpam-1354	348	4	s.	s.	PROPN
ejpam-1354	348	5	n.	n.	PROPN
ejpam-1354	348	6	beshers	besher	NOUN
ejpam-1354	348	7	and	and	CCONJ
ejpam-1354	348	8	j.	j.	PROPN
ejpam-1354	348	9	h.	h.	PROPN
ejpam-1354	348	10	fewell	fewell	PROPN
ejpam-1354	348	11	.	.	PUNCT
ejpam-1354	349	1	models	model	NOUN
ejpam-1354	349	2	of	of	ADP
ejpam-1354	349	3	division	division	NOUN
ejpam-1354	349	4	of	of	ADP
ejpam-1354	349	5	labor	labor	NOUN
ejpam-1354	349	6	in	in	ADP
ejpam-1354	349	7	social	social	ADJ
ejpam-1354	349	8	insects	insect	NOUN
ejpam-1354	349	9	.	.	PUNCT
ejpam-1354	350	1	annual	annual	ADJ
ejpam-1354	350	2	review	review	NOUN
ejpam-1354	350	3	of	of	ADP
ejpam-1354	350	4	entomology	entomology	NOUN
ejpam-1354	350	5	,	,	PUNCT
ejpam-1354	350	6	46(1):413–440	46(1):413–440	PROPN
ejpam-1354	350	7	,	,	PUNCT
ejpam-1354	350	8	2001	2001	NUM
ejpam-1354	350	9	.	.	PUNCT
ejpam-1354	351	1	[	[	X
ejpam-1354	351	2	3	3	X
ejpam-1354	351	3	]	]	X
ejpam-1354	351	4	b.	b.	PROPN
ejpam-1354	351	5	birnir	birnir	PROPN
ejpam-1354	351	6	.	.	PUNCT
ejpam-1354	352	1	an	an	DET
ejpam-1354	352	2	ode	ode	ADJ
ejpam-1354	352	3	model	model	NOUN
ejpam-1354	352	4	of	of	ADP
ejpam-1354	352	5	the	the	DET
ejpam-1354	352	6	motion	motion	NOUN
ejpam-1354	352	7	of	of	ADP
ejpam-1354	352	8	pelagic	pelagic	ADJ
ejpam-1354	352	9	fish	fish	NOUN
ejpam-1354	352	10	.	.	PUNCT
ejpam-1354	353	1	journal	journal	NOUN
ejpam-1354	353	2	of	of	ADP
ejpam-1354	353	3	statistical	statistical	ADJ
ejpam-1354	353	4	physics	physics	NOUN
ejpam-1354	353	5	,	,	PUNCT
ejpam-1354	353	6	128(1–2):535–568	128(1–2):535–568	NUM
ejpam-1354	353	7	,	,	PUNCT
ejpam-1354	353	8	2007	2007	NUM
ejpam-1354	353	9	.	.	PUNCT
ejpam-1354	354	1	[	[	X
ejpam-1354	354	2	4	4	NUM
ejpam-1354	354	3	]	]	X
ejpam-1354	354	4	c.	c.	PROPN
ejpam-1354	354	5	m.	m.	PROPN
ejpam-1354	354	6	breder	breder	PROPN
ejpam-1354	354	7	.	.	PUNCT
ejpam-1354	355	1	equations	equation	NOUN
ejpam-1354	355	2	descriptive	descriptive	VERB
ejpam-1354	355	3	of	of	ADP
ejpam-1354	355	4	fish	fish	NOUN
ejpam-1354	355	5	schools	school	NOUN
ejpam-1354	355	6	and	and	CCONJ
ejpam-1354	355	7	other	other	ADJ
ejpam-1354	355	8	animal	animal	NOUN
ejpam-1354	355	9	aggregations	aggregation	NOUN
ejpam-1354	355	10	.	.	PUNCT
ejpam-1354	356	1	ecology	ecology	NOUN
ejpam-1354	356	2	,	,	PUNCT
ejpam-1354	356	3	35(3):361–370	35(3):361–370	PROPN
ejpam-1354	356	4	,	,	PUNCT
ejpam-1354	356	5	1954	1954	NUM
ejpam-1354	356	6	.	.	PUNCT
ejpam-1354	357	1	[	[	X
ejpam-1354	357	2	5	5	NUM
ejpam-1354	357	3	]	]	PUNCT
ejpam-1354	357	4	f.	f.	PROPN
ejpam-1354	357	5	cucker	cucker	PROPN
ejpam-1354	357	6	and	and	CCONJ
ejpam-1354	357	7	s.	s.	PROPN
ejpam-1354	357	8	smale	smale	PROPN
ejpam-1354	357	9	.	.	PUNCT
ejpam-1354	358	1	emergent	emergent	ADJ
ejpam-1354	358	2	behavior	behavior	NOUN
ejpam-1354	358	3	in	in	ADP
ejpam-1354	358	4	flocks	flock	NOUN
ejpam-1354	358	5	.	.	PUNCT
ejpam-1354	359	1	ieee	ieee	NOUN
ejpam-1354	359	2	transactions	transaction	NOUN
ejpam-1354	359	3	on	on	ADP
ejpam-1354	359	4	automatic	automatic	ADJ
ejpam-1354	359	5	control	control	NOUN
ejpam-1354	359	6	,	,	PUNCT
ejpam-1354	359	7	52(5):852–862	52(5):852–862	PROPN
ejpam-1354	359	8	,	,	PUNCT
ejpam-1354	359	9	2007	2007	NUM
ejpam-1354	359	10	.	.	PUNCT
ejpam-1354	360	1	[	[	X
ejpam-1354	360	2	6	6	NUM
ejpam-1354	360	3	]	]	PUNCT
ejpam-1354	360	4	s.	s.	PROPN
ejpam-1354	360	5	a.	a.	PROPN
ejpam-1354	360	6	frank	frank	PROPN
ejpam-1354	360	7	.	.	PUNCT
ejpam-1354	361	1	george	george	PROPN
ejpam-1354	361	2	price	price	PROPN
ejpam-1354	361	3	’s	’s	PART
ejpam-1354	361	4	contributions	contribution	NOUN
ejpam-1354	361	5	to	to	ADP
ejpam-1354	361	6	evolutionary	evolutionary	ADJ
ejpam-1354	361	7	genetics	genetic	NOUN
ejpam-1354	361	8	.	.	PUNCT
ejpam-1354	362	1	journal	journal	PROPN
ejpam-1354	362	2	of	of	ADP
ejpam-1354	362	3	theoretical	theoretical	ADJ
ejpam-1354	362	4	biology	biology	NOUN
ejpam-1354	362	5	,	,	PUNCT
ejpam-1354	362	6	175(3):373–388	175(3):373–388	NUM
ejpam-1354	362	7	,	,	PUNCT
ejpam-1354	362	8	1995	1995	NUM
ejpam-1354	362	9	.	.	PUNCT
ejpam-1354	363	1	[	[	X
ejpam-1354	363	2	7	7	X
ejpam-1354	363	3	]	]	PUNCT
ejpam-1354	363	4	s.	s.	PROPN
ejpam-1354	363	5	a.	a.	PROPN
ejpam-1354	363	6	frank	frank	PROPN
ejpam-1354	363	7	.	.	PUNCT
ejpam-1354	364	1	the	the	DET
ejpam-1354	364	2	price	price	NOUN
ejpam-1354	364	3	equation	equation	NOUN
ejpam-1354	364	4	,	,	PUNCT
ejpam-1354	364	5	fisher	fisher	PROPN
ejpam-1354	364	6	’s	’s	PART
ejpam-1354	364	7	fundamental	fundamental	ADJ
ejpam-1354	364	8	theorem	theorem	PROPN
ejpam-1354	364	9	,	,	PUNCT
ejpam-1354	364	10	kin	kin	PROPN
ejpam-1354	364	11	selection	selection	PROPN
ejpam-1354	364	12	,	,	PUNCT
ejpam-1354	364	13	and	and	CCONJ
ejpam-1354	364	14	causal	causal	ADJ
ejpam-1354	364	15	analysis	analysis	NOUN
ejpam-1354	364	16	.	.	PUNCT
ejpam-1354	365	1	evolution	evolution	NOUN
ejpam-1354	365	2	,	,	PUNCT
ejpam-1354	365	3	51(6):1712–1729	51(6):1712–1729	NOUN
ejpam-1354	365	4	,	,	PUNCT
ejpam-1354	365	5	1997	1997	NUM
ejpam-1354	365	6	.	.	PUNCT
ejpam-1354	366	1	[	[	X
ejpam-1354	366	2	8	8	NUM
ejpam-1354	366	3	]	]	X
ejpam-1354	366	4	v.	v.	CCONJ
ejpam-1354	366	5	gazi	gazi	PROPN
ejpam-1354	366	6	,	,	PUNCT
ejpam-1354	366	7	y.	y.	PROPN
ejpam-1354	366	8	s.	s.	PROPN
ejpam-1354	366	9	hanay	hanay	PROPN
ejpam-1354	366	10	b.	b.	PROPN
ejpam-1354	366	11	fidan	fidan	PROPN
ejpam-1354	366	12	,	,	PUNCT
ejpam-1354	366	13	and	and	CCONJ
ejpam-1354	366	14	m.	m.	PROPN
ejpam-1354	366	15	i.	i.	PROPN
ejpam-1354	366	16	köksal	köksal	PROPN
ejpam-1354	366	17	.	.	PUNCT
ejpam-1354	367	1	aggregation	aggregation	NOUN
ejpam-1354	367	2	,	,	PUNCT
ejpam-1354	367	3	foraging	foraging	NOUN
ejpam-1354	367	4	,	,	PUNCT
ejpam-1354	367	5	and	and	CCONJ
ejpam-1354	367	6	formation	formation	NOUN
ejpam-1354	367	7	control	control	NOUN
ejpam-1354	367	8	of	of	ADP
ejpam-1354	367	9	swarms	swarm	NOUN
ejpam-1354	367	10	with	with	ADP
ejpam-1354	367	11	non	non	ADJ
ejpam-1354	367	12	-	-	ADJ
ejpam-1354	367	13	holonomic	holonomic	ADJ
ejpam-1354	367	14	agents	agent	NOUN
ejpam-1354	367	15	using	use	VERB
ejpam-1354	367	16	potential	potential	ADJ
ejpam-1354	367	17	functions	function	NOUN
ejpam-1354	367	18	and	and	CCONJ
ejpam-1354	367	19	sliding	slide	VERB
ejpam-1354	367	20	mode	mode	NOUN
ejpam-1354	367	21	techniques	technique	NOUN
ejpam-1354	367	22	.	.	PUNCT
ejpam-1354	368	1	turkish	turkish	ADJ
ejpam-1354	368	2	journal	journal	NOUN
ejpam-1354	368	3	of	of	ADP
ejpam-1354	368	4	electrical	electrical	ADJ
ejpam-1354	368	5	engineering	engineering	NOUN
ejpam-1354	368	6	&	&	CCONJ
ejpam-1354	368	7	computer	computer	PROPN
ejpam-1354	368	8	sciences	sciences	PROPN
ejpam-1354	368	9	,	,	PUNCT
ejpam-1354	368	10	15(2):149–168	15(2):149–168	NUM
ejpam-1354	368	11	,	,	PUNCT
ejpam-1354	368	12	2007	2007	NUM
ejpam-1354	368	13	.	.	PUNCT
ejpam-1354	369	1	[	[	X
ejpam-1354	369	2	9	9	NUM
ejpam-1354	369	3	]	]	PUNCT
ejpam-1354	369	4	m.	m.	NOUN
ejpam-1354	369	5	gordon	gordon	PROPN
ejpam-1354	369	6	.	.	PUNCT
ejpam-1354	370	1	the	the	DET
ejpam-1354	370	2	organization	organization	NOUN
ejpam-1354	370	3	of	of	ADP
ejpam-1354	370	4	work	work	NOUN
ejpam-1354	370	5	in	in	ADP
ejpam-1354	370	6	social	social	ADJ
ejpam-1354	370	7	insect	insect	NOUN
ejpam-1354	370	8	colonies	colony	NOUN
ejpam-1354	370	9	.	.	PUNCT
ejpam-1354	371	1	nature	nature	NOUN
ejpam-1354	371	2	,	,	PUNCT
ejpam-1354	371	3	380(6570):121	380(6570):121	NUM
ejpam-1354	371	4	–	–	PUNCT
ejpam-1354	371	5	124	124	NUM
ejpam-1354	371	6	,	,	PUNCT
ejpam-1354	371	7	1996	1996	NUM
ejpam-1354	371	8	.	.	PUNCT
ejpam-1354	372	1	[	[	X
ejpam-1354	372	2	10	10	NUM
ejpam-1354	372	3	]	]	PUNCT
ejpam-1354	372	4	m.	m.	NOUN
ejpam-1354	372	5	j.	j.	PROPN
ejpam-1354	372	6	greene	greene	PROPN
ejpam-1354	372	7	and	and	CCONJ
ejpam-1354	372	8	d.	d.	PROPN
ejpam-1354	372	9	m.	m.	PROPN
ejpam-1354	372	10	gordon	gordon	PROPN
ejpam-1354	372	11	.	.	PUNCT
ejpam-1354	373	1	how	how	SCONJ
ejpam-1354	373	2	patrollers	patroller	NOUN
ejpam-1354	373	3	set	set	VERB
ejpam-1354	373	4	foraging	forage	VERB
ejpam-1354	373	5	direction	direction	NOUN
ejpam-1354	373	6	in	in	ADP
ejpam-1354	373	7	harvester	harvester	NOUN
ejpam-1354	373	8	ants	ant	NOUN
ejpam-1354	373	9	.	.	PUNCT
ejpam-1354	374	1	the	the	DET
ejpam-1354	374	2	american	american	PROPN
ejpam-1354	374	3	naturalist	naturalist	PROPN
ejpam-1354	374	4	,	,	PUNCT
ejpam-1354	374	5	170(6):943–948	170(6):943–948	NUM
ejpam-1354	374	6	,	,	PUNCT
ejpam-1354	374	7	2007	2007	NUM
ejpam-1354	374	8	.	.	PUNCT
ejpam-1354	374	9	references	reference	NOUN
ejpam-1354	374	10	188	188	NUM
ejpam-1354	374	11	[	[	SYM
ejpam-1354	374	12	11	11	NUM
ejpam-1354	374	13	]	]	X
ejpam-1354	374	14	r.	r.	PROPN
ejpam-1354	374	15	hegselmann	hegselmann	PROPN
ejpam-1354	374	16	and	and	CCONJ
ejpam-1354	374	17	u.	u.	PROPN
ejpam-1354	374	18	krause	krause	PROPN
ejpam-1354	374	19	.	.	PUNCT
ejpam-1354	375	1	opinion	opinion	NOUN
ejpam-1354	375	2	dynamics	dynamic	NOUN
ejpam-1354	375	3	and	and	CCONJ
ejpam-1354	375	4	bounded	bound	VERB
ejpam-1354	375	5	confidence	confidence	NOUN
ejpam-1354	375	6	models	model	NOUN
ejpam-1354	375	7	,	,	PUNCT
ejpam-1354	375	8	analysis	analysis	NOUN
ejpam-1354	375	9	,	,	PUNCT
ejpam-1354	375	10	and	and	CCONJ
ejpam-1354	375	11	simulation	simulation	NOUN
ejpam-1354	375	12	.	.	PUNCT
ejpam-1354	376	1	journal	journal	PROPN
ejpam-1354	376	2	of	of	ADP
ejpam-1354	376	3	artificial	artificial	ADJ
ejpam-1354	376	4	societies	society	NOUN
ejpam-1354	376	5	and	and	CCONJ
ejpam-1354	376	6	social	social	ADJ
ejpam-1354	376	7	simulation	simulation	NOUN
ejpam-1354	376	8	,	,	PUNCT
ejpam-1354	376	9	5(3):1–33	5(3):1–33	NUM
ejpam-1354	376	10	,	,	PUNCT
ejpam-1354	376	11	2002	2002	NUM
ejpam-1354	376	12	.	.	PUNCT
ejpam-1354	377	1	[	[	X
ejpam-1354	377	2	12	12	NUM
ejpam-1354	377	3	]	]	X
ejpam-1354	377	4	r.	r.	PROPN
ejpam-1354	377	5	hegselmann	hegselmann	PROPN
ejpam-1354	377	6	and	and	CCONJ
ejpam-1354	377	7	u.	u.	PROPN
ejpam-1354	377	8	krause	krause	PROPN
ejpam-1354	377	9	.	.	PUNCT
ejpam-1354	378	1	truth	truth	NOUN
ejpam-1354	378	2	and	and	CCONJ
ejpam-1354	378	3	cognitive	cognitive	ADJ
ejpam-1354	378	4	division	division	NOUN
ejpam-1354	378	5	of	of	ADP
ejpam-1354	378	6	labour	labour	NOUN
ejpam-1354	378	7	:	:	PUNCT
ejpam-1354	378	8	first	first	ADJ
ejpam-1354	378	9	steps	step	NOUN
ejpam-1354	378	10	towards	towards	ADP
ejpam-1354	378	11	a	a	DET
ejpam-1354	378	12	computer	computer	NOUN
ejpam-1354	378	13	aided	aid	VERB
ejpam-1354	378	14	social	social	ADJ
ejpam-1354	378	15	epistemology	epistemology	NOUN
ejpam-1354	378	16	.	.	PUNCT
ejpam-1354	379	1	journal	journal	PROPN
ejpam-1354	379	2	of	of	ADP
ejpam-1354	379	3	artificial	artificial	ADJ
ejpam-1354	379	4	societies	society	NOUN
ejpam-1354	379	5	and	and	CCONJ
ejpam-1354	379	6	social	social	ADJ
ejpam-1354	379	7	simulation	simulation	NOUN
ejpam-1354	379	8	,	,	PUNCT
ejpam-1354	379	9	9(3):10	9(3):10	NOUN
ejpam-1354	379	10	,	,	PUNCT
ejpam-1354	379	11	2006	2006	NUM
ejpam-1354	379	12	.	.	PUNCT
ejpam-1354	380	1	[	[	X
ejpam-1354	380	2	13	13	NUM
ejpam-1354	380	3	]	]	X
ejpam-1354	380	4	g.	g.	PROPN
ejpam-1354	380	5	r.	r.	PROPN
ejpam-1354	380	6	price	price	PROPN
ejpam-1354	380	7	.	.	PUNCT
ejpam-1354	381	1	selection	selection	NOUN
ejpam-1354	381	2	and	and	CCONJ
ejpam-1354	381	3	covariance	covariance	NOUN
ejpam-1354	381	4	.	.	PUNCT
ejpam-1354	382	1	nature	nature	NOUN
ejpam-1354	382	2	,	,	PUNCT
ejpam-1354	382	3	227(5257):520–521	227(5257):520–521	NUM
ejpam-1354	382	4	,	,	PUNCT
ejpam-1354	382	5	1970	1970	NUM
ejpam-1354	382	6	.	.	PUNCT
ejpam-1354	383	1	[	[	X
ejpam-1354	383	2	14	14	NUM
ejpam-1354	383	3	]	]	X
ejpam-1354	383	4	g.	g.	PROPN
ejpam-1354	383	5	r.	r.	PROPN
ejpam-1354	383	6	price	price	PROPN
ejpam-1354	383	7	.	.	PUNCT
ejpam-1354	384	1	extension	extension	NOUN
ejpam-1354	384	2	of	of	ADP
ejpam-1354	384	3	covariance	covariance	NOUN
ejpam-1354	384	4	selection	selection	NOUN
ejpam-1354	384	5	mathematics	mathematic	NOUN
ejpam-1354	384	6	.	.	PUNCT
ejpam-1354	385	1	annals	annal	NOUN
ejpam-1354	385	2	of	of	ADP
ejpam-1354	385	3	human	human	ADJ
ejpam-1354	385	4	genetics	genetic	NOUN
ejpam-1354	385	5	,	,	PUNCT
ejpam-1354	385	6	35(4):485–490	35(4):485–490	NUM
ejpam-1354	385	7	,	,	PUNCT
ejpam-1354	385	8	1972	1972	NUM
ejpam-1354	385	9	.	.	PUNCT