id	sid	tid	token	lemma	pos
ap-1364	1	1	wykresx.eps	wykresx.eps	X
ap-1364	1	2	acta	acta	PROPN
ap-1364	1	3	polytechnica	polytechnica	PROPN
ap-1364	1	4	vol	vol	NOUN
ap-1364	1	5	.	.	PUNCT
ap-1364	2	1	51	51	NUM
ap-1364	2	2	no	no	INTJ
ap-1364	2	3	.	.	PUNCT
ap-1364	3	1	1/2011	1/2011	NUM
ap-1364	4	1	the	the	DET
ap-1364	4	2	problem	problem	NOUN
ap-1364	4	3	of	of	ADP
ap-1364	4	4	predecessors	predecessor	NOUN
ap-1364	4	5	on	on	ADP
ap-1364	4	6	spanning	span	VERB
ap-1364	4	7	trees	tree	NOUN
ap-1364	4	8	v.	v.	ADP
ap-1364	4	9	s.	s.	PROPN
ap-1364	4	10	poghosyan	poghosyan	PROPN
ap-1364	4	11	,	,	PUNCT
ap-1364	5	1	v.	v.	PROPN
ap-1364	5	2	b.	b.	PROPN
ap-1364	5	3	priezzhev	priezzhev	PROPN
ap-1364	5	4	abstract	abstract	NOUN
ap-1364	5	5	we	we	PRON
ap-1364	5	6	consider	consider	VERB
ap-1364	5	7	the	the	DET
ap-1364	5	8	equiprobable	equiprobable	ADJ
ap-1364	5	9	distribution	distribution	NOUN
ap-1364	5	10	of	of	ADP
ap-1364	5	11	spanning	span	VERB
ap-1364	5	12	trees	tree	NOUN
ap-1364	5	13	on	on	ADP
ap-1364	5	14	the	the	DET
ap-1364	5	15	square	square	ADJ
ap-1364	5	16	lattice	lattice	NOUN
ap-1364	5	17	.	.	PUNCT
ap-1364	6	1	all	all	DET
ap-1364	6	2	bonds	bond	NOUN
ap-1364	6	3	of	of	ADP
ap-1364	6	4	each	each	DET
ap-1364	6	5	tree	tree	NOUN
ap-1364	6	6	can	can	AUX
ap-1364	6	7	be	be	AUX
ap-1364	6	8	oriented	orient	VERB
ap-1364	6	9	uniquely	uniquely	ADV
ap-1364	6	10	with	with	ADP
ap-1364	6	11	respect	respect	NOUN
ap-1364	6	12	to	to	ADP
ap-1364	6	13	an	an	DET
ap-1364	6	14	arbitrary	arbitrary	ADJ
ap-1364	6	15	chosen	choose	VERB
ap-1364	6	16	site	site	NOUN
ap-1364	6	17	called	call	VERB
ap-1364	6	18	the	the	DET
ap-1364	6	19	root	root	NOUN
ap-1364	6	20	.	.	PUNCT
ap-1364	7	1	the	the	DET
ap-1364	7	2	problem	problem	NOUN
ap-1364	7	3	of	of	ADP
ap-1364	7	4	predecessors	predecessor	NOUN
ap-1364	7	5	is	be	AUX
ap-1364	7	6	to	to	PART
ap-1364	7	7	find	find	VERB
ap-1364	7	8	the	the	DET
ap-1364	7	9	probability	probability	NOUN
ap-1364	7	10	that	that	SCONJ
ap-1364	7	11	a	a	DET
ap-1364	7	12	path	path	NOUN
ap-1364	7	13	along	along	ADP
ap-1364	7	14	the	the	DET
ap-1364	7	15	oriented	orient	VERB
ap-1364	7	16	bonds	bond	NOUN
ap-1364	7	17	passes	pass	VERB
ap-1364	7	18	sequentially	sequentially	ADV
ap-1364	7	19	fixed	fix	VERB
ap-1364	7	20	sites	site	NOUN
ap-1364	7	21	i	i	PRON
ap-1364	7	22	and	and	CCONJ
ap-1364	7	23	j.	j.	PROPN
ap-1364	7	24	the	the	DET
ap-1364	7	25	conformal	conformal	ADJ
ap-1364	7	26	field	field	NOUN
ap-1364	7	27	theory	theory	NOUN
ap-1364	7	28	for	for	ADP
ap-1364	7	29	the	the	DET
ap-1364	7	30	potts	potts	PROPN
ap-1364	7	31	model	model	PROPN
ap-1364	7	32	predicts	predict	VERB
ap-1364	7	33	the	the	DET
ap-1364	7	34	fractal	fractal	ADJ
ap-1364	7	35	dimension	dimension	NOUN
ap-1364	7	36	of	of	ADP
ap-1364	7	37	the	the	DET
ap-1364	7	38	path	path	NOUN
ap-1364	7	39	to	to	PART
ap-1364	7	40	be	be	AUX
ap-1364	7	41	5/4	5/4	NUM
ap-1364	7	42	.	.	PUNCT
ap-1364	8	1	using	use	VERB
ap-1364	8	2	this	this	DET
ap-1364	8	3	result	result	NOUN
ap-1364	8	4	,	,	PUNCT
ap-1364	8	5	we	we	PRON
ap-1364	8	6	show	show	VERB
ap-1364	8	7	that	that	SCONJ
ap-1364	8	8	the	the	DET
ap-1364	8	9	probability	probability	NOUN
ap-1364	8	10	in	in	ADP
ap-1364	8	11	the	the	DET
ap-1364	8	12	predecessors	predecessor	NOUN
ap-1364	8	13	problem	problem	NOUN
ap-1364	8	14	for	for	ADP
ap-1364	8	15	two	two	NUM
ap-1364	8	16	sites	site	NOUN
ap-1364	8	17	separated	separate	VERB
ap-1364	8	18	by	by	ADP
ap-1364	8	19	large	large	ADJ
ap-1364	8	20	distance	distance	NOUN
ap-1364	8	21	r	r	NOUN
ap-1364	8	22	decreases	decrease	NOUN
ap-1364	8	23	as	as	ADP
ap-1364	8	24	p	p	NOUN
ap-1364	8	25	(	(	PUNCT
ap-1364	8	26	r	r	NOUN
ap-1364	8	27	)	)	PUNCT
ap-1364	8	28	∼	∼	NOUN
ap-1364	8	29	r−3/4	r−3/4	NOUN
ap-1364	8	30	.	.	PUNCT
ap-1364	9	1	if	if	SCONJ
ap-1364	9	2	sites	site	NOUN
ap-1364	9	3	i	i	PRON
ap-1364	9	4	and	and	CCONJ
ap-1364	9	5	j	j	PROPN
ap-1364	9	6	are	be	AUX
ap-1364	9	7	nearest	near	ADJ
ap-1364	9	8	neighbors	neighbor	NOUN
ap-1364	9	9	on	on	ADP
ap-1364	9	10	the	the	DET
ap-1364	9	11	square	square	PROPN
ap-1364	9	12	lattice	lattice	NOUN
ap-1364	9	13	,	,	PUNCT
ap-1364	9	14	the	the	DET
ap-1364	9	15	probability	probability	NOUN
ap-1364	9	16	p	p	X
ap-1364	9	17	(	(	PUNCT
ap-1364	9	18	1	1	NUM
ap-1364	9	19	)	)	PUNCT
ap-1364	10	1	=	=	NOUN
ap-1364	10	2	5/16	5/16	NUM
ap-1364	10	3	can	can	AUX
ap-1364	10	4	be	be	AUX
ap-1364	10	5	found	find	VERB
ap-1364	10	6	from	from	ADP
ap-1364	10	7	the	the	DET
ap-1364	10	8	analytical	analytical	ADJ
ap-1364	10	9	theory	theory	NOUN
ap-1364	10	10	developed	develop	VERB
ap-1364	10	11	for	for	ADP
ap-1364	10	12	the	the	DET
ap-1364	10	13	sandpile	sandpile	NOUN
ap-1364	10	14	model	model	NOUN
ap-1364	10	15	.	.	PUNCT
ap-1364	11	1	the	the	DET
ap-1364	11	2	known	know	VERB
ap-1364	11	3	equivalence	equivalence	NOUN
ap-1364	11	4	between	between	ADP
ap-1364	11	5	the	the	DET
ap-1364	11	6	loop	loop	NOUN
ap-1364	11	7	erased	erase	VERB
ap-1364	11	8	random	random	ADJ
ap-1364	11	9	walk	walk	NOUN
ap-1364	11	10	(	(	PUNCT
ap-1364	11	11	lerw	lerw	NOUN
ap-1364	11	12	)	)	PUNCT
ap-1364	11	13	and	and	CCONJ
ap-1364	11	14	the	the	DET
ap-1364	11	15	directed	direct	VERB
ap-1364	11	16	path	path	NOUN
ap-1364	11	17	on	on	ADP
ap-1364	11	18	the	the	DET
ap-1364	11	19	spanning	span	VERB
ap-1364	11	20	tree	tree	NOUN
ap-1364	11	21	states	state	VERB
ap-1364	11	22	that	that	SCONJ
ap-1364	11	23	p	p	X
ap-1364	11	24	(	(	PUNCT
ap-1364	11	25	1	1	NUM
ap-1364	11	26	)	)	PUNCT
ap-1364	11	27	is	be	AUX
ap-1364	11	28	the	the	DET
ap-1364	11	29	probability	probability	NOUN
ap-1364	11	30	for	for	SCONJ
ap-1364	11	31	the	the	DET
ap-1364	11	32	lerw	lerw	NOUN
ap-1364	11	33	started	start	VERB
ap-1364	11	34	at	at	ADP
ap-1364	11	35	i	i	PRON
ap-1364	11	36	to	to	PART
ap-1364	11	37	reach	reach	VERB
ap-1364	11	38	the	the	DET
ap-1364	11	39	neighboring	neighboring	NOUN
ap-1364	11	40	site	site	NOUN
ap-1364	11	41	j.	j.	PROPN
ap-1364	11	42	by	by	ADP
ap-1364	11	43	analogy	analogy	NOUN
ap-1364	11	44	with	with	ADP
ap-1364	11	45	the	the	DET
ap-1364	11	46	self	self	NOUN
ap-1364	11	47	-	-	PUNCT
ap-1364	11	48	avoiding	avoid	VERB
ap-1364	11	49	walk	walk	NOUN
ap-1364	11	50	,	,	PUNCT
ap-1364	11	51	p	p	X
ap-1364	11	52	(	(	PUNCT
ap-1364	11	53	1	1	NUM
ap-1364	11	54	)	)	PUNCT
ap-1364	11	55	can	can	AUX
ap-1364	11	56	be	be	AUX
ap-1364	11	57	called	call	VERB
ap-1364	11	58	the	the	DET
ap-1364	11	59	return	return	NOUN
ap-1364	11	60	probability	probability	NOUN
ap-1364	11	61	.	.	PUNCT
ap-1364	12	1	extensive	extensive	ADJ
ap-1364	12	2	monte	monte	PROPN
ap-1364	12	3	-	-	PUNCT
ap-1364	12	4	carlo	carlo	PROPN
ap-1364	12	5	simulations	simulation	NOUN
ap-1364	12	6	confirm	confirm	VERB
ap-1364	12	7	the	the	DET
ap-1364	12	8	theoretical	theoretical	ADJ
ap-1364	12	9	predictions	prediction	NOUN
ap-1364	12	10	.	.	PUNCT
ap-1364	13	1	keywords	keyword	NOUN
ap-1364	13	2	:	:	PUNCT
ap-1364	13	3	loop	loop	NOUN
ap-1364	13	4	erased	erase	VERB
ap-1364	13	5	random	random	ADJ
ap-1364	13	6	walk	walk	NOUN
ap-1364	13	7	,	,	PUNCT
ap-1364	13	8	spanning	span	VERB
ap-1364	13	9	trees	tree	NOUN
ap-1364	13	10	,	,	PUNCT
ap-1364	13	11	kirchhoff	kirchhoff	NOUN
ap-1364	13	12	theorem	theorem	PROPN
ap-1364	13	13	,	,	PUNCT
ap-1364	13	14	abelian	abelian	PROPN
ap-1364	13	15	sandpile	sandpile	NOUN
ap-1364	13	16	model	model	PROPN
ap-1364	13	17	.	.	PUNCT
ap-1364	14	1	1	1	NUM
ap-1364	14	2	introduction	introduction	NOUN
ap-1364	14	3	and	and	CCONJ
ap-1364	14	4	main	main	ADJ
ap-1364	14	5	results	result	NOUN
ap-1364	14	6	in	in	ADP
ap-1364	14	7	graph	graph	NOUN
ap-1364	14	8	theory	theory	NOUN
ap-1364	14	9	,	,	PUNCT
ap-1364	14	10	the	the	DET
ap-1364	14	11	spanning	span	VERB
ap-1364	14	12	tree	tree	NOUN
ap-1364	14	13	of	of	ADP
ap-1364	14	14	connected	connected	ADJ
ap-1364	14	15	graph	graph	NOUN
ap-1364	14	16	g	g	PROPN
ap-1364	14	17	is	be	AUX
ap-1364	14	18	a	a	DET
ap-1364	14	19	connected	connected	ADJ
ap-1364	14	20	subgraph	subgraph	NOUN
ap-1364	14	21	ofg	ofg	NOUN
ap-1364	14	22	containing	contain	VERB
ap-1364	14	23	all	all	DET
ap-1364	14	24	vertices	vertex	NOUN
ap-1364	14	25	of	of	ADP
ap-1364	14	26	g	g	NOUN
ap-1364	14	27	and	and	CCONJ
ap-1364	14	28	having	have	VERB
ap-1364	14	29	no	no	DET
ap-1364	14	30	cycles	cycle	NOUN
ap-1364	14	31	.	.	PUNCT
ap-1364	15	1	numerous	numerous	ADJ
ap-1364	15	2	applications	application	NOUN
ap-1364	15	3	of	of	ADP
ap-1364	15	4	spanning	span	VERB
ap-1364	15	5	trees	tree	NOUN
ap-1364	15	6	began	begin	VERB
ap-1364	15	7	with	with	ADP
ap-1364	15	8	kirchhoff	kirchhoff	NOUN
ap-1364	15	9	’s	’s	PART
ap-1364	15	10	seminal	seminal	ADJ
ap-1364	15	11	problem	problem	NOUN
ap-1364	15	12	solved	solve	VERB
ap-1364	15	13	in	in	ADP
ap-1364	15	14	1847	1847	NUM
ap-1364	15	15	,	,	PUNCT
ap-1364	15	16	and	and	CCONJ
ap-1364	15	17	then	then	ADV
ap-1364	15	18	spread	spread	VERB
ap-1364	15	19	out	out	ADP
ap-1364	15	20	many	many	ADJ
ap-1364	15	21	branches	branch	NOUN
ap-1364	15	22	of	of	ADP
ap-1364	15	23	mathematics	mathematic	NOUN
ap-1364	15	24	and	and	CCONJ
ap-1364	15	25	theoretical	theoretical	ADJ
ap-1364	15	26	physics	physics	NOUN
ap-1364	15	27	.	.	PUNCT
ap-1364	16	1	in	in	ADP
ap-1364	16	2	statistical	statistical	ADJ
ap-1364	16	3	mechanics	mechanic	NOUN
ap-1364	16	4	,	,	PUNCT
ap-1364	16	5	spanning	span	VERB
ap-1364	16	6	trees	tree	NOUN
ap-1364	16	7	are	be	AUX
ap-1364	16	8	related	relate	VERB
ap-1364	16	9	to	to	ADP
ap-1364	16	10	the	the	DET
ap-1364	16	11	potts	potts	PROPN
ap-1364	16	12	model	model	NOUN
ap-1364	17	1	[	[	X
ap-1364	17	2	1	1	NUM
ap-1364	17	3	]	]	PUNCT
ap-1364	17	4	,	,	PUNCT
ap-1364	17	5	the	the	DET
ap-1364	17	6	dimer	dimer	NOUN
ap-1364	17	7	model	model	NOUN
ap-1364	17	8	[	[	X
ap-1364	17	9	2	2	NUM
ap-1364	17	10	]	]	PUNCT
ap-1364	17	11	,	,	PUNCT
ap-1364	17	12	the	the	DET
ap-1364	17	13	sandpile	sandpile	NOUN
ap-1364	17	14	model	model	NOUN
ap-1364	17	15	[	[	X
ap-1364	17	16	3	3	NUM
ap-1364	17	17	]	]	PUNCT
ap-1364	17	18	and	and	CCONJ
ap-1364	17	19	many	many	ADJ
ap-1364	17	20	others	other	NOUN
ap-1364	17	21	.	.	PUNCT
ap-1364	18	1	a	a	DET
ap-1364	18	2	relation	relation	NOUN
ap-1364	18	3	between	between	ADP
ap-1364	18	4	lattice	lattice	NOUN
ap-1364	18	5	models	model	NOUN
ap-1364	18	6	of	of	ADP
ap-1364	18	7	statistical	statistical	ADJ
ap-1364	18	8	mechanics	mechanic	NOUN
ap-1364	18	9	and	and	CCONJ
ap-1364	18	10	spanning	span	VERB
ap-1364	18	11	trees	tree	NOUN
ap-1364	18	12	via	via	ADP
ap-1364	18	13	the	the	DET
ap-1364	18	14	tutte	tutte	PROPN
ap-1364	18	15	polynomial	polynomial	NOUN
ap-1364	18	16	has	have	AUX
ap-1364	18	17	been	be	AUX
ap-1364	18	18	established	establish	VERB
ap-1364	18	19	by	by	ADP
ap-1364	18	20	fortuin	fortuin	NOUN
ap-1364	18	21	and	and	CCONJ
ap-1364	18	22	kasteleyn	kasteleyn	NOUN
ap-1364	18	23	[	[	X
ap-1364	18	24	4	4	NUM
ap-1364	18	25	]	]	PUNCT
ap-1364	18	26	.	.	PUNCT
ap-1364	19	1	the	the	DET
ap-1364	19	2	kirchhoff	kirchhoff	PROPN
ap-1364	19	3	theorem	theorem	VERB
ap-1364	19	4	claims	claim	NOUN
ap-1364	19	5	that	that	SCONJ
ap-1364	19	6	the	the	DET
ap-1364	19	7	number	number	NOUN
ap-1364	19	8	of	of	ADP
ap-1364	19	9	spanning	span	VERB
ap-1364	19	10	trees	tree	NOUN
ap-1364	19	11	of	of	ADP
ap-1364	19	12	connected	connected	ADJ
ap-1364	19	13	graph	graph	NOUN
ap-1364	19	14	g	g	PROPN
ap-1364	19	15	is	be	AUX
ap-1364	19	16	a	a	DET
ap-1364	19	17	cofactor	cofactor	NOUN
ap-1364	19	18	of	of	ADP
ap-1364	19	19	the	the	DET
ap-1364	19	20	laplacian	laplacian	ADJ
ap-1364	19	21	matrix	matrix	NOUN
ap-1364	19	22	δ	δ	PROPN
ap-1364	19	23	of	of	ADP
ap-1364	19	24	graph	graph	NOUN
ap-1364	19	25	g.	g.	PROPN
ap-1364	19	26	if	if	SCONJ
ap-1364	19	27	one	one	PRON
ap-1364	19	28	deletes	delete	VERB
ap-1364	19	29	any	any	DET
ap-1364	19	30	row	row	NOUN
ap-1364	19	31	and	and	CCONJ
ap-1364	19	32	any	any	DET
ap-1364	19	33	column	column	NOUN
ap-1364	19	34	from	from	ADP
ap-1364	19	35	δ	δ	PROPN
ap-1364	19	36	,	,	PUNCT
ap-1364	19	37	one	one	PRON
ap-1364	19	38	obtains	obtain	VERB
ap-1364	19	39	a	a	DET
ap-1364	19	40	matrix	matrix	NOUN
ap-1364	19	41	δ∗	δ∗	NOUN
ap-1364	19	42	which	which	PRON
ap-1364	19	43	gives	give	VERB
ap-1364	19	44	the	the	DET
ap-1364	19	45	number	number	NOUN
ap-1364	19	46	of	of	ADP
ap-1364	19	47	spanning	span	VERB
ap-1364	19	48	trees	tree	NOUN
ap-1364	19	49	as	as	SCONJ
ap-1364	19	50	detδ∗.	detδ∗.	PROPN
ap-1364	19	51	the	the	DET
ap-1364	19	52	determinantal	determinantal	ADJ
ap-1364	19	53	structure	structure	NOUN
ap-1364	19	54	allows	allow	VERB
ap-1364	19	55	easy	easy	ADJ
ap-1364	19	56	calculation	calculation	NOUN
ap-1364	19	57	of	of	ADP
ap-1364	19	58	local	local	ADJ
ap-1364	19	59	characteristics	characteristic	NOUN
ap-1364	19	60	of	of	ADP
ap-1364	19	61	the	the	DET
ap-1364	19	62	spanning	span	VERB
ap-1364	19	63	trees	tree	NOUN
ap-1364	19	64	,	,	PUNCT
ap-1364	19	65	for	for	ADP
ap-1364	19	66	instance	instance	NOUN
ap-1364	19	67	,	,	PUNCT
ap-1364	19	68	the	the	DET
ap-1364	19	69	average	average	ADJ
ap-1364	19	70	number	number	NOUN
ap-1364	19	71	of	of	ADP
ap-1364	19	72	vertices	vertex	NOUN
ap-1364	19	73	with	with	ADP
ap-1364	19	74	a	a	DET
ap-1364	19	75	given	give	VERB
ap-1364	19	76	number	number	NOUN
ap-1364	19	77	of	of	ADP
ap-1364	19	78	adjacent	adjacent	ADJ
ap-1364	19	79	bonds	bond	NOUN
ap-1364	19	80	.	.	PUNCT
ap-1364	20	1	a	a	DET
ap-1364	20	2	characterization	characterization	NOUN
ap-1364	20	3	of	of	ADP
ap-1364	20	4	non	non	ADJ
ap-1364	20	5	-	-	ADJ
ap-1364	20	6	local	local	ADJ
ap-1364	20	7	objects	object	NOUN
ap-1364	20	8	in	in	ADP
ap-1364	20	9	the	the	DET
ap-1364	20	10	spanning	span	VERB
ap-1364	20	11	tree	tree	NOUN
ap-1364	20	12	is	be	AUX
ap-1364	20	13	not	not	PART
ap-1364	20	14	so	so	ADV
ap-1364	20	15	simple	simple	ADJ
ap-1364	20	16	.	.	PUNCT
ap-1364	21	1	one	one	NUM
ap-1364	21	2	such	such	ADJ
ap-1364	21	3	object	object	NOUN
ap-1364	21	4	is	be	AUX
ap-1364	21	5	the	the	DET
ap-1364	21	6	chemical	chemical	ADJ
ap-1364	21	7	path	path	NOUN
ap-1364	21	8	defined	define	VERB
ap-1364	21	9	as	as	ADP
ap-1364	21	10	a	a	DET
ap-1364	21	11	path	path	NOUN
ap-1364	21	12	along	along	ADP
ap-1364	21	13	two	two	NUM
ap-1364	21	14	or	or	CCONJ
ap-1364	21	15	more	more	ADJ
ap-1364	21	16	bonds	bond	NOUN
ap-1364	21	17	of	of	ADP
ap-1364	21	18	the	the	DET
ap-1364	21	19	tree	tree	NOUN
ap-1364	21	20	.	.	PUNCT
ap-1364	22	1	the	the	DET
ap-1364	22	2	fractal	fractal	ADJ
ap-1364	22	3	dimension	dimension	NOUN
ap-1364	22	4	of	of	ADP
ap-1364	22	5	a	a	DET
ap-1364	22	6	long	long	ADJ
ap-1364	22	7	chemical	chemical	ADJ
ap-1364	22	8	path	path	NOUN
ap-1364	22	9	on	on	ADP
ap-1364	22	10	the	the	DET
ap-1364	22	11	twodimensional	twodimensional	ADJ
ap-1364	22	12	lattice	lattice	NOUN
ap-1364	22	13	has	have	AUX
ap-1364	22	14	been	be	AUX
ap-1364	22	15	calculated	calculate	VERB
ap-1364	22	16	by	by	ADP
ap-1364	22	17	means	mean	NOUN
ap-1364	22	18	of	of	ADP
ap-1364	22	19	a	a	DET
ap-1364	22	20	mapping	mapping	NOUN
ap-1364	22	21	of	of	ADP
ap-1364	22	22	the	the	DET
ap-1364	22	23	spanning	span	VERB
ap-1364	22	24	tree	tree	NOUN
ap-1364	22	25	configurations	configuration	NOUN
ap-1364	22	26	onto	onto	ADP
ap-1364	22	27	the	the	DET
ap-1364	22	28	coulomb	coulomb	NOUN
ap-1364	22	29	gas	gas	NOUN
ap-1364	22	30	model	model	NOUN
ap-1364	22	31	.	.	PUNCT
ap-1364	23	1	a	a	DET
ap-1364	23	2	closely	closely	ADV
ap-1364	23	3	related	relate	VERB
ap-1364	23	4	object	object	NOUN
ap-1364	23	5	is	be	AUX
ap-1364	23	6	the	the	DET
ap-1364	23	7	loop	loop	NOUN
ap-1364	23	8	erased	erase	VERB
ap-1364	23	9	random	random	ADJ
ap-1364	23	10	walk	walk	NOUN
ap-1364	23	11	(	(	PUNCT
ap-1364	23	12	lerw	lerw	NOUN
ap-1364	23	13	)	)	PUNCT
ap-1364	23	14	on	on	ADP
ap-1364	23	15	the	the	DET
ap-1364	23	16	two	two	NUM
ap-1364	23	17	-	-	PUNCT
ap-1364	23	18	dimensional	dimensional	ADJ
ap-1364	23	19	lattice	lattice	NOUN
ap-1364	23	20	[	[	X
ap-1364	23	21	11	11	NUM
ap-1364	23	22	]	]	PUNCT
ap-1364	23	23	,	,	PUNCT
ap-1364	23	24	which	which	PRON
ap-1364	23	25	was	be	AUX
ap-1364	23	26	proven	prove	VERB
ap-1364	23	27	to	to	PART
ap-1364	23	28	be	be	AUX
ap-1364	23	29	equivalent	equivalent	ADJ
ap-1364	23	30	to	to	ADP
ap-1364	23	31	the	the	DET
ap-1364	23	32	directed	direct	VERB
ap-1364	23	33	chemical	chemical	NOUN
ap-1364	23	34	path	path	NOUN
ap-1364	23	35	of	of	ADP
ap-1364	23	36	the	the	DET
ap-1364	23	37	spanning	span	VERB
ap-1364	23	38	tree	tree	NOUN
ap-1364	23	39	of	of	ADP
ap-1364	23	40	the	the	DET
ap-1364	23	41	same	same	ADJ
ap-1364	23	42	lattice	lattice	NOUN
ap-1364	24	1	[	[	X
ap-1364	24	2	7	7	NUM
ap-1364	24	3	,	,	PUNCT
ap-1364	24	4	12	12	NUM
ap-1364	24	5	]	]	PUNCT
ap-1364	24	6	.	.	PUNCT
ap-1364	25	1	in	in	ADP
ap-1364	25	2	this	this	DET
ap-1364	25	3	paper	paper	NOUN
ap-1364	25	4	,	,	PUNCT
ap-1364	25	5	we	we	PRON
ap-1364	25	6	consider	consider	VERB
ap-1364	25	7	a	a	DET
ap-1364	25	8	problem	problem	NOUN
ap-1364	25	9	arising	arise	VERB
ap-1364	25	10	in	in	ADP
ap-1364	25	11	the	the	DET
ap-1364	25	12	theory	theory	NOUN
ap-1364	25	13	of	of	ADP
ap-1364	25	14	lerw	lerw	NOUN
ap-1364	25	15	and	and	CCONJ
ap-1364	25	16	equally	equally	ADV
ap-1364	25	17	distributed	distribute	VERB
ap-1364	25	18	spanning	span	VERB
ap-1364	25	19	trees	tree	NOUN
ap-1364	25	20	:	:	PUNCT
ap-1364	25	21	given	give	VERB
ap-1364	25	22	two	two	NUM
ap-1364	25	23	lattice	lattice	NOUN
ap-1364	25	24	sites	site	NOUN
ap-1364	25	25	i	i	PRON
ap-1364	25	26	and	and	CCONJ
ap-1364	25	27	j	j	PROPN
ap-1364	25	28	,	,	PUNCT
ap-1364	25	29	what	what	PRON
ap-1364	25	30	is	be	AUX
ap-1364	25	31	the	the	DET
ap-1364	25	32	probability	probability	NOUN
ap-1364	25	33	that	that	SCONJ
ap-1364	25	34	the	the	DET
ap-1364	25	35	lerw	lerw	NOUN
ap-1364	25	36	or	or	CCONJ
ap-1364	25	37	the	the	DET
ap-1364	25	38	directed	direct	VERB
ap-1364	25	39	chemical	chemical	NOUN
ap-1364	25	40	path	path	NOUN
ap-1364	25	41	passes	pass	VERB
ap-1364	25	42	i	i	PRON
ap-1364	25	43	and	and	CCONJ
ap-1364	25	44	j	j	NOUN
ap-1364	25	45	?	?	PUNCT
ap-1364	26	1	if	if	SCONJ
ap-1364	26	2	site	site	NOUN
ap-1364	26	3	i	i	PRON
ap-1364	26	4	is	be	AUX
ap-1364	26	5	passed	pass	VERB
ap-1364	26	6	first	first	ADV
ap-1364	26	7	,	,	PUNCT
ap-1364	26	8	we	we	PRON
ap-1364	26	9	say	say	VERB
ap-1364	26	10	that	that	SCONJ
ap-1364	26	11	i	i	PRON
ap-1364	26	12	is	be	AUX
ap-1364	26	13	the	the	DET
ap-1364	26	14	predecessor	predecessor	NOUN
ap-1364	26	15	of	of	ADP
ap-1364	26	16	j	j	PROPN
ap-1364	26	17	and	and	CCONJ
ap-1364	26	18	we	we	PRON
ap-1364	26	19	refer	refer	VERB
ap-1364	26	20	to	to	ADP
ap-1364	26	21	this	this	DET
ap-1364	26	22	problem	problem	NOUN
ap-1364	26	23	as	as	ADP
ap-1364	26	24	the	the	DET
ap-1364	26	25	predecessor	predecessor	NOUN
ap-1364	26	26	problem	problem	NOUN
ap-1364	26	27	.	.	PUNCT
ap-1364	27	1	surprisingly	surprisingly	ADV
ap-1364	27	2	,	,	PUNCT
ap-1364	27	3	the	the	DET
ap-1364	27	4	problem	problem	NOUN
ap-1364	27	5	has	have	VERB
ap-1364	27	6	no	no	DET
ap-1364	27	7	exact	exact	ADJ
ap-1364	27	8	solution	solution	NOUN
ap-1364	27	9	in	in	ADP
ap-1364	27	10	the	the	DET
ap-1364	27	11	general	general	ADJ
ap-1364	27	12	case	case	NOUN
ap-1364	27	13	.	.	PUNCT
ap-1364	28	1	only	only	ADV
ap-1364	28	2	two	two	NUM
ap-1364	28	3	limiting	limit	VERB
ap-1364	28	4	cases	case	NOUN
ap-1364	28	5	are	be	AUX
ap-1364	28	6	available	available	ADJ
ap-1364	28	7	:	:	PUNCT
ap-1364	28	8	(	(	PUNCT
ap-1364	28	9	a	a	X
ap-1364	28	10	)	)	PUNCT
ap-1364	28	11	if	if	SCONJ
ap-1364	28	12	sites	site	NOUN
ap-1364	28	13	i	i	PRON
ap-1364	28	14	and	and	CCONJ
ap-1364	28	15	j	j	PROPN
ap-1364	28	16	are	be	AUX
ap-1364	28	17	separated	separate	VERB
ap-1364	28	18	by	by	ADP
ap-1364	28	19	large	large	ADJ
ap-1364	28	20	distance	distance	NOUN
ap-1364	28	21	r	r	NOUN
ap-1364	28	22	,	,	PUNCT
ap-1364	28	23	the	the	DET
ap-1364	28	24	asymptotics	asymptotic	NOUN
ap-1364	28	25	of	of	ADP
ap-1364	28	26	p	p	X
ap-1364	28	27	(	(	PUNCT
ap-1364	28	28	r	r	NOUN
ap-1364	28	29	)	)	PUNCT
ap-1364	28	30	can	can	AUX
ap-1364	28	31	be	be	AUX
ap-1364	28	32	found	find	VERB
ap-1364	28	33	from	from	ADP
ap-1364	28	34	known	know	VERB
ap-1364	28	35	results	result	NOUN
ap-1364	28	36	on	on	ADP
ap-1364	28	37	the	the	DET
ap-1364	28	38	fractal	fractal	ADJ
ap-1364	28	39	dimension	dimension	NOUN
ap-1364	28	40	of	of	ADP
ap-1364	28	41	the	the	DET
ap-1364	28	42	chemical	chemical	NOUN
ap-1364	28	43	path	path	NOUN
ap-1364	28	44	;	;	PUNCT
ap-1364	28	45	(	(	PUNCT
ap-1364	28	46	b	b	X
ap-1364	28	47	)	)	PUNCT
ap-1364	28	48	if	if	SCONJ
ap-1364	28	49	points	point	VERB
ap-1364	28	50	i	i	PRON
ap-1364	28	51	and	and	CCONJ
ap-1364	28	52	j	j	PROPN
ap-1364	28	53	are	be	AUX
ap-1364	28	54	nearest	near	ADJ
ap-1364	28	55	neighbors	neighbor	NOUN
ap-1364	28	56	of	of	ADP
ap-1364	28	57	the	the	DET
ap-1364	28	58	square	square	PROPN
ap-1364	28	59	lattice	lattice	NOUN
ap-1364	28	60	,	,	PUNCT
ap-1364	28	61	the	the	DET
ap-1364	28	62	seeking	seek	VERB
ap-1364	28	63	probability	probability	NOUN
ap-1364	28	64	can	can	AUX
ap-1364	28	65	be	be	AUX
ap-1364	28	66	found	find	VERB
ap-1364	28	67	from	from	ADP
ap-1364	28	68	the	the	DET
ap-1364	28	69	theory	theory	NOUN
ap-1364	28	70	of	of	ADP
ap-1364	28	71	sandpiles	sandpile	NOUN
ap-1364	29	1	[	[	X
ap-1364	29	2	9	9	NUM
ap-1364	29	3	]	]	PUNCT
ap-1364	29	4	(	(	PUNCT
ap-1364	29	5	see	see	VERB
ap-1364	29	6	also	also	ADV
ap-1364	29	7	[	[	X
ap-1364	29	8	16	16	NUM
ap-1364	29	9	]	]	SYM
ap-1364	29	10	)	)	PUNCT
ap-1364	29	11	.	.	PUNCT
ap-1364	30	1	the	the	DET
ap-1364	30	2	asymptotic	asymptotic	ADJ
ap-1364	30	3	behavior	behavior	NOUN
ap-1364	30	4	of	of	ADP
ap-1364	30	5	p	p	NOUN
ap-1364	30	6	(	(	PUNCT
ap-1364	30	7	r	r	NOUN
ap-1364	30	8	)	)	PUNCT
ap-1364	30	9	for	for	ADP
ap-1364	30	10	large	large	ADJ
ap-1364	30	11	distance	distance	NOUN
ap-1364	30	12	r	r	NOUN
ap-1364	30	13	follows	follow	VERB
ap-1364	30	14	directly	directly	ADV
ap-1364	30	15	from	from	ADP
ap-1364	30	16	the	the	DET
ap-1364	30	17	definition	definition	NOUN
ap-1364	30	18	of	of	ADP
ap-1364	30	19	the	the	DET
ap-1364	30	20	fractal	fractal	ADJ
ap-1364	30	21	dimension	dimension	NOUN
ap-1364	30	22	.	.	PUNCT
ap-1364	31	1	indeed	indeed	ADV
ap-1364	31	2	,	,	PUNCT
ap-1364	31	3	consider	consider	VERB
ap-1364	31	4	a	a	DET
ap-1364	31	5	large	large	ADJ
ap-1364	31	6	square	square	ADJ
ap-1364	31	7	lattice	lattice	PROPN
ap-1364	31	8	l	l	PROPN
ap-1364	31	9	and	and	CCONJ
ap-1364	31	10	the	the	DET
ap-1364	31	11	set	set	NOUN
ap-1364	31	12	of	of	ADP
ap-1364	31	13	uniformly	uniformly	ADV
ap-1364	31	14	distributed	distribute	VERB
ap-1364	31	15	spanning	span	VERB
ap-1364	31	16	trees	tree	NOUN
ap-1364	31	17	on	on	ADP
ap-1364	31	18	l.	l.	NOUN
ap-1364	31	19	we	we	PRON
ap-1364	31	20	assume	assume	VERB
ap-1364	31	21	that	that	SCONJ
ap-1364	31	22	the	the	DET
ap-1364	31	23	root	root	NOUN
ap-1364	31	24	is	be	AUX
ap-1364	31	25	situated	situate	VERB
ap-1364	31	26	at	at	ADP
ap-1364	31	27	the	the	DET
ap-1364	31	28	boundary	boundary	NOUN
ap-1364	31	29	of	of	ADP
ap-1364	31	30	l.	l.	PROPN
ap-1364	31	31	consider	consider	VERB
ap-1364	31	32	site	site	NOUN
ap-1364	31	33	i	i	PRON
ap-1364	31	34	in	in	ADP
ap-1364	31	35	the	the	DET
ap-1364	31	36	bulk	bulk	NOUN
ap-1364	31	37	of	of	ADP
ap-1364	31	38	the	the	DET
ap-1364	31	39	lattice	lattice	NOUN
ap-1364	31	40	and	and	CCONJ
ap-1364	31	41	some	some	DET
ap-1364	31	42	circle	circle	NOUN
ap-1364	31	43	contour	contour	NOUN
ap-1364	31	44	c	c	NOUN
ap-1364	31	45	of	of	ADP
ap-1364	31	46	radius	radius	NOUN
ap-1364	31	47	r	r	NOUN
ap-1364	31	48	with	with	ADP
ap-1364	31	49	the	the	DET
ap-1364	31	50	center	center	NOUN
ap-1364	31	51	in	in	ADP
ap-1364	31	52	i.	i.	PROPN
ap-1364	31	53	let	let	VERB
ap-1364	31	54	π	π	NOUN
ap-1364	31	55	be	be	AUX
ap-1364	31	56	a	a	DET
ap-1364	31	57	directed	direct	VERB
ap-1364	31	58	chemical	chemical	NOUN
ap-1364	31	59	path	path	NOUN
ap-1364	31	60	from	from	ADP
ap-1364	31	61	i	i	PRON
ap-1364	31	62	to	to	ADP
ap-1364	31	63	the	the	DET
ap-1364	31	64	root	root	NOUN
ap-1364	31	65	along	along	ADP
ap-1364	31	66	the	the	DET
ap-1364	31	67	oriented	orient	VERB
ap-1364	31	68	bonds	bond	NOUN
ap-1364	31	69	of	of	ADP
ap-1364	31	70	a	a	DET
ap-1364	31	71	tree	tree	NOUN
ap-1364	31	72	.	.	PUNCT
ap-1364	32	1	all	all	DET
ap-1364	32	2	points	point	NOUN
ap-1364	32	3	of	of	ADP
ap-1364	32	4	the	the	DET
ap-1364	32	5	subset	subset	NOUN
ap-1364	32	6	of	of	ADP
ap-1364	32	7	π	π	PROPN
ap-1364	32	8	inside	inside	ADP
ap-1364	32	9	c	c	PROPN
ap-1364	32	10	are	be	AUX
ap-1364	32	11	descendants	descendant	NOUN
ap-1364	32	12	of	of	ADP
ap-1364	32	13	i.	i.	NOUN
ap-1364	32	14	in	in	ADP
ap-1364	32	15	accordance	accordance	NOUN
ap-1364	32	16	with	with	ADP
ap-1364	32	17	the	the	DET
ap-1364	32	18	definition	definition	NOUN
ap-1364	32	19	of	of	ADP
ap-1364	32	20	the	the	DET
ap-1364	32	21	fractal	fractal	ADJ
ap-1364	32	22	dimension	dimension	NOUN
ap-1364	32	23	of	of	ADP
ap-1364	32	24	the	the	DET
ap-1364	32	25	directed	direct	VERB
ap-1364	32	26	path	path	NOUN
ap-1364	32	27	on	on	ADP
ap-1364	32	28	the	the	DET
ap-1364	32	29	spanning	span	VERB
ap-1364	32	30	tree	tree	NOUN
ap-1364	32	31	,	,	PUNCT
ap-1364	32	32	the	the	DET
ap-1364	32	33	number	number	NOUN
ap-1364	32	34	of	of	ADP
ap-1364	32	35	descendants	descendant	NOUN
ap-1364	32	36	inside	inside	ADP
ap-1364	32	37	c	c	PROPN
ap-1364	32	38	is	be	AUX
ap-1364	32	39	proportional	proportional	ADJ
ap-1364	32	40	to	to	ADP
ap-1364	32	41	r5/4	r5/4	PROPN
ap-1364	32	42	(	(	PUNCT
ap-1364	32	43	see	see	VERB
ap-1364	32	44	majumdar	majumdar	PROPN
ap-1364	32	45	[	[	X
ap-1364	32	46	7	7	NUM
ap-1364	32	47	]	]	NUM
ap-1364	32	48	)	)	PUNCT
ap-1364	32	49	.	.	PUNCT
ap-1364	33	1	the	the	DET
ap-1364	33	2	probability	probability	NOUN
ap-1364	33	3	that	that	DET
ap-1364	33	4	point	point	NOUN
ap-1364	33	5	i	i	PRON
ap-1364	33	6	is	be	AUX
ap-1364	33	7	the	the	DET
ap-1364	33	8	predecessor	predecessor	NOUN
ap-1364	33	9	of	of	ADP
ap-1364	33	10	point	point	NOUN
ap-1364	33	11	j	j	PROPN
ap-1364	33	12	lying	lie	VERB
ap-1364	33	13	at	at	ADP
ap-1364	33	14	distance	distance	NOUN
ap-1364	33	15	r	r	NOUN
ap-1364	33	16	from	from	ADP
ap-1364	33	17	i	i	PRON
ap-1364	33	18	is	be	AUX
ap-1364	33	19	the	the	DET
ap-1364	33	20	density	density	NOUN
ap-1364	33	21	of	of	ADP
ap-1364	33	22	descendants	descendant	NOUN
ap-1364	33	23	ρ(r	ρ(r	PROPN
ap-1364	33	24	)	)	PUNCT
ap-1364	33	25	.	.	PUNCT
ap-1364	34	1	thus	thus	ADV
ap-1364	34	2	,	,	PUNCT
ap-1364	34	3	we	we	PRON
ap-1364	34	4	have	have	VERB
ap-1364	34	5	59	59	NUM
ap-1364	34	6	acta	acta	PROPN
ap-1364	34	7	polytechnica	polytechnica	PROPN
ap-1364	34	8	vol	vol	NOUN
ap-1364	34	9	.	.	PUNCT
ap-1364	35	1	51	51	NUM
ap-1364	35	2	no	no	INTJ
ap-1364	35	3	.	.	PUNCT
ap-1364	36	1	1/2011	1/2011	NUM
ap-1364	36	2	∫	∫	NOUN
ap-1364	36	3	r	r	NOUN
ap-1364	36	4	1	1	NUM
ap-1364	36	5	ρ(r)r	ρ(r)r	PROPN
ap-1364	36	6	dr	dr	PROPN
ap-1364	36	7	∼	∼	NOUN
ap-1364	36	8	r5/4	r5/4	PROPN
ap-1364	36	9	(	(	PUNCT
ap-1364	36	10	1.1	1.1	NUM
ap-1364	36	11	)	)	PUNCT
ap-1364	36	12	from	from	ADP
ap-1364	36	13	where	where	SCONJ
ap-1364	36	14	we	we	PRON
ap-1364	36	15	conclude	conclude	VERB
ap-1364	36	16	that	that	SCONJ
ap-1364	36	17	ρ(r	ρ(r	PROPN
ap-1364	36	18	)	)	PUNCT
ap-1364	36	19	∼	∼	NOUN
ap-1364	36	20	r−3/4	r−3/4	NOUN
ap-1364	36	21	.	.	PUNCT
ap-1364	37	1	as	as	SCONJ
ap-1364	37	2	was	be	AUX
ap-1364	37	3	mentioned	mention	VERB
ap-1364	37	4	above	above	ADV
ap-1364	37	5	,	,	PUNCT
ap-1364	37	6	the	the	DET
ap-1364	37	7	problem	problem	NOUN
ap-1364	37	8	of	of	ADP
ap-1364	37	9	predecessors	predecessor	NOUN
ap-1364	37	10	for	for	ADP
ap-1364	37	11	an	an	DET
ap-1364	37	12	arbitrary	arbitrary	ADJ
ap-1364	37	13	disposition	disposition	NOUN
ap-1364	37	14	of	of	ADP
ap-1364	37	15	two	two	NUM
ap-1364	37	16	lattice	lattice	NOUN
ap-1364	37	17	points	point	NOUN
ap-1364	37	18	is	be	AUX
ap-1364	37	19	not	not	PART
ap-1364	37	20	solved	solve	VERB
ap-1364	37	21	.	.	PUNCT
ap-1364	38	1	in	in	ADP
ap-1364	38	2	section	section	NOUN
ap-1364	38	3	2	2	NUM
ap-1364	38	4	we	we	PRON
ap-1364	38	5	concentrate	concentrate	VERB
ap-1364	38	6	on	on	ADP
ap-1364	38	7	a	a	DET
ap-1364	38	8	particular	particular	ADJ
ap-1364	38	9	problem	problem	NOUN
ap-1364	38	10	of	of	ADP
ap-1364	38	11	probability	probability	NOUN
ap-1364	38	12	p	p	X
ap-1364	38	13	(	(	PUNCT
ap-1364	38	14	1	1	NUM
ap-1364	38	15	)	)	PUNCT
ap-1364	38	16	when	when	SCONJ
ap-1364	38	17	points	point	NOUN
ap-1364	38	18	i	i	PRON
ap-1364	38	19	and	and	CCONJ
ap-1364	38	20	j	j	PROPN
ap-1364	38	21	are	be	AUX
ap-1364	38	22	nearest	near	ADJ
ap-1364	38	23	neighbors	neighbor	NOUN
ap-1364	38	24	of	of	ADP
ap-1364	38	25	the	the	DET
ap-1364	38	26	square	square	ADJ
ap-1364	38	27	lattice	lattice	PROPN
ap-1364	38	28	.	.	PUNCT
ap-1364	39	1	an	an	DET
ap-1364	39	2	essential	essential	ADJ
ap-1364	39	3	element	element	NOUN
ap-1364	39	4	of	of	ADP
ap-1364	39	5	the	the	DET
ap-1364	39	6	theory	theory	NOUN
ap-1364	39	7	of	of	ADP
ap-1364	39	8	sandpiles	sandpile	NOUN
ap-1364	39	9	is	be	AUX
ap-1364	39	10	the	the	DET
ap-1364	39	11	probability	probability	NOUN
ap-1364	39	12	distribution	distribution	NOUN
ap-1364	39	13	of	of	ADP
ap-1364	39	14	sites	site	NOUN
ap-1364	39	15	having	have	VERB
ap-1364	39	16	0	0	NUM
ap-1364	39	17	,	,	PUNCT
ap-1364	39	18	1	1	NUM
ap-1364	39	19	,	,	PUNCT
ap-1364	39	20	2	2	NUM
ap-1364	39	21	and	and	CCONJ
ap-1364	39	22	3	3	NUM
ap-1364	39	23	predecessors	predecessor	NOUN
ap-1364	39	24	among	among	ADP
ap-1364	39	25	the	the	DET
ap-1364	39	26	nearest	near	ADJ
ap-1364	39	27	neighbors	neighbor	NOUN
ap-1364	39	28	.	.	PUNCT
ap-1364	40	1	the	the	DET
ap-1364	40	2	corresponding	corresponding	ADJ
ap-1364	40	3	probabilities	probability	NOUN
ap-1364	40	4	are	be	AUX
ap-1364	40	5	denoted	denote	VERB
ap-1364	40	6	by	by	ADP
ap-1364	40	7	x0	x0	PROPN
ap-1364	40	8	,	,	PUNCT
ap-1364	40	9	x1	x1	PROPN
ap-1364	40	10	,	,	PUNCT
ap-1364	40	11	x2	x2	PROPN
ap-1364	40	12	and	and	CCONJ
ap-1364	40	13	x3	x3	ADJ
ap-1364	40	14	.	.	PUNCT
ap-1364	41	1	having	have	VERB
ap-1364	41	2	explicit	explicit	ADJ
ap-1364	41	3	expressions	expression	NOUN
ap-1364	41	4	for	for	ADP
ap-1364	41	5	these	these	DET
ap-1364	41	6	values	value	NOUN
ap-1364	41	7	,	,	PUNCT
ap-1364	41	8	we	we	PRON
ap-1364	41	9	obtain	obtain	VERB
ap-1364	41	10	p	p	NOUN
ap-1364	41	11	(	(	PUNCT
ap-1364	41	12	1	1	NUM
ap-1364	41	13	)	)	PUNCT
ap-1364	41	14	as	as	ADP
ap-1364	41	15	their	their	PRON
ap-1364	41	16	combination	combination	NOUN
ap-1364	41	17	and	and	CCONJ
ap-1364	41	18	get	get	VERB
ap-1364	41	19	an	an	DET
ap-1364	41	20	unexpectedly	unexpectedly	ADV
ap-1364	41	21	simple	simple	ADJ
ap-1364	41	22	result	result	NOUN
ap-1364	42	1	p	p	X
ap-1364	42	2	(	(	PUNCT
ap-1364	42	3	1	1	NUM
ap-1364	42	4	)	)	PUNCT
ap-1364	42	5	=	=	SYM
ap-1364	42	6	5/16	5/16	NUM
ap-1364	42	7	.	.	PUNCT
ap-1364	43	1	in	in	ADP
ap-1364	43	2	section	section	NOUN
ap-1364	43	3	3	3	NUM
ap-1364	43	4	,	,	PUNCT
ap-1364	43	5	we	we	PRON
ap-1364	43	6	relate	relate	VERB
ap-1364	43	7	this	this	DET
ap-1364	43	8	result	result	NOUN
ap-1364	43	9	to	to	ADP
ap-1364	43	10	the	the	DET
ap-1364	43	11	return	return	NOUN
ap-1364	43	12	probability	probability	NOUN
ap-1364	43	13	of	of	ADP
ap-1364	43	14	the	the	DET
ap-1364	43	15	lerw	lerw	NOUN
ap-1364	43	16	.	.	PUNCT
ap-1364	44	1	section	section	NOUN
ap-1364	44	2	4	4	NUM
ap-1364	44	3	contains	contain	VERB
ap-1364	44	4	the	the	DET
ap-1364	44	5	results	result	NOUN
ap-1364	44	6	of	of	ADP
ap-1364	44	7	monte	monte	PROPN
ap-1364	44	8	-	-	PUNCT
ap-1364	44	9	carlo	carlo	NOUN
ap-1364	44	10	verifications	verification	NOUN
ap-1364	44	11	.	.	PUNCT
ap-1364	45	1	2	2	NUM
ap-1364	45	2	the	the	DET
ap-1364	45	3	problem	problem	NOUN
ap-1364	45	4	of	of	ADP
ap-1364	45	5	predecessors	predecessor	NOUN
ap-1364	45	6	for	for	ADP
ap-1364	45	7	nearest	near	ADJ
ap-1364	45	8	neighbors	neighbor	NOUN
ap-1364	45	9	the	the	DET
ap-1364	45	10	spanning	span	VERB
ap-1364	45	11	tree	tree	NOUN
ap-1364	45	12	enumeration	enumeration	NOUN
ap-1364	45	13	method	method	NOUN
ap-1364	45	14	,	,	PUNCT
ap-1364	45	15	namely	namely	ADV
ap-1364	45	16	the	the	DET
ap-1364	45	17	kirchhoff	kirchhoff	NOUN
ap-1364	45	18	theorem	theorem	NOUN
ap-1364	45	19	is	be	AUX
ap-1364	45	20	proved	prove	VERB
ap-1364	45	21	to	to	PART
ap-1364	45	22	be	be	AUX
ap-1364	45	23	a	a	DET
ap-1364	45	24	powerful	powerful	ADJ
ap-1364	45	25	mathematical	mathematical	ADJ
ap-1364	45	26	instrument	instrument	NOUN
ap-1364	45	27	for	for	ADP
ap-1364	45	28	the	the	DET
ap-1364	45	29	investigation	investigation	NOUN
ap-1364	45	30	of	of	ADP
ap-1364	45	31	various	various	ADJ
ap-1364	45	32	combinatorial	combinatorial	ADJ
ap-1364	45	33	problems	problem	NOUN
ap-1364	45	34	in	in	ADP
ap-1364	45	35	theoretical	theoretical	ADJ
ap-1364	45	36	physics	physics	NOUN
ap-1364	45	37	.	.	PUNCT
ap-1364	46	1	in	in	ADP
ap-1364	46	2	the	the	DET
ap-1364	46	3	last	last	ADJ
ap-1364	46	4	decade	decade	NOUN
ap-1364	46	5	,	,	PUNCT
ap-1364	46	6	it	it	PRON
ap-1364	46	7	has	have	AUX
ap-1364	46	8	been	be	AUX
ap-1364	46	9	developed	develop	VERB
ap-1364	46	10	and	and	CCONJ
ap-1364	46	11	adapted	adapt	VERB
ap-1364	46	12	for	for	ADP
ap-1364	46	13	calculating	calculate	VERB
ap-1364	46	14	the	the	DET
ap-1364	46	15	height	height	NOUN
ap-1364	46	16	probabilities	probability	NOUN
ap-1364	46	17	of	of	ADP
ap-1364	46	18	the	the	DET
ap-1364	46	19	abelian	abelian	ADJ
ap-1364	46	20	sandpile	sandpile	NOUN
ap-1364	46	21	model	model	NOUN
ap-1364	46	22	[	[	X
ap-1364	46	23	5	5	NUM
ap-1364	46	24	,	,	PUNCT
ap-1364	46	25	9	9	NUM
ap-1364	46	26	,	,	PUNCT
ap-1364	46	27	16	16	NUM
ap-1364	46	28	]	]	PUNCT
ap-1364	46	29	.	.	PUNCT
ap-1364	47	1	the	the	DET
ap-1364	47	2	abelian	abelian	PROPN
ap-1364	47	3	sandpile	sandpile	NOUN
ap-1364	47	4	model	model	NOUN
ap-1364	47	5	is	be	AUX
ap-1364	47	6	a	a	DET
ap-1364	47	7	stochastic	stochastic	ADJ
ap-1364	47	8	dynamical	dynamical	ADJ
ap-1364	47	9	system	system	NOUN
ap-1364	47	10	,	,	PUNCT
ap-1364	47	11	which	which	PRON
ap-1364	47	12	describes	describe	VERB
ap-1364	47	13	the	the	DET
ap-1364	47	14	phenomenon	phenomenon	NOUN
ap-1364	47	15	of	of	ADP
ap-1364	47	16	self	self	NOUN
ap-1364	47	17	-	-	PUNCT
ap-1364	47	18	organized	organize	VERB
ap-1364	47	19	criticality	criticality	NOUN
ap-1364	47	20	.	.	PUNCT
ap-1364	48	1	during	during	ADP
ap-1364	48	2	the	the	DET
ap-1364	48	3	evolution	evolution	NOUN
ap-1364	48	4	the	the	DET
ap-1364	48	5	system	system	NOUN
ap-1364	48	6	falls	fall	VERB
ap-1364	48	7	into	into	ADP
ap-1364	48	8	a	a	DET
ap-1364	48	9	subset	subset	NOUN
ap-1364	48	10	of	of	ADP
ap-1364	48	11	all	all	DET
ap-1364	48	12	possible	possible	ADJ
ap-1364	48	13	states	state	NOUN
ap-1364	48	14	,	,	PUNCT
ap-1364	48	15	called	call	VERB
ap-1364	48	16	the	the	DET
ap-1364	48	17	subset	subset	NOUN
ap-1364	48	18	of	of	ADP
ap-1364	48	19	recurrent	recurrent	ADJ
ap-1364	48	20	states	state	NOUN
ap-1364	48	21	.	.	PUNCT
ap-1364	49	1	the	the	DET
ap-1364	49	2	problem	problem	NOUN
ap-1364	49	3	is	be	AUX
ap-1364	49	4	to	to	PART
ap-1364	49	5	calculate	calculate	VERB
ap-1364	49	6	analytically	analytically	ADV
ap-1364	49	7	various	various	ADJ
ap-1364	49	8	observable	observable	ADJ
ap-1364	49	9	values	value	NOUN
ap-1364	49	10	in	in	ADP
ap-1364	49	11	the	the	DET
ap-1364	49	12	recurrent	recurrent	ADJ
ap-1364	49	13	state	state	NOUN
ap-1364	49	14	,	,	PUNCT
ap-1364	49	15	such	such	ADJ
ap-1364	49	16	as	as	ADP
ap-1364	49	17	height	height	NOUN
ap-1364	49	18	probabilities	probability	NOUN
ap-1364	49	19	pi	pi	NOUN
ap-1364	49	20	,	,	PUNCT
ap-1364	49	21	i	i	PRON
ap-1364	49	22	=	=	NOUN
ap-1364	49	23	1	1	NUM
ap-1364	49	24	,	,	PUNCT
ap-1364	49	25	2	2	NUM
ap-1364	49	26	,	,	PUNCT
ap-1364	49	27	3	3	NUM
ap-1364	49	28	,	,	PUNCT
ap-1364	49	29	4	4	NUM
ap-1364	49	30	at	at	ADP
ap-1364	49	31	a	a	DET
ap-1364	49	32	fixed	fix	VERB
ap-1364	49	33	site	site	NOUN
ap-1364	49	34	and	and	CCONJ
ap-1364	49	35	height	height	NOUN
ap-1364	49	36	correlations	correlation	NOUN
ap-1364	49	37	between	between	ADP
ap-1364	49	38	distinct	distinct	ADJ
ap-1364	49	39	fixed	fix	VERB
ap-1364	49	40	sites	site	NOUN
ap-1364	49	41	[	[	X
ap-1364	49	42	18	18	NUM
ap-1364	49	43	]	]	PUNCT
ap-1364	49	44	.	.	PUNCT
ap-1364	50	1	it	it	PRON
ap-1364	50	2	was	be	AUX
ap-1364	50	3	shown	show	VERB
ap-1364	50	4	that	that	SCONJ
ap-1364	50	5	the	the	DET
ap-1364	50	6	calculation	calculation	NOUN
ap-1364	50	7	of	of	ADP
ap-1364	50	8	height	height	NOUN
ap-1364	50	9	probabilities	probability	NOUN
ap-1364	50	10	in	in	ADP
ap-1364	50	11	the	the	DET
ap-1364	50	12	abelian	abelian	ADJ
ap-1364	50	13	sandpile	sandpile	NOUN
ap-1364	50	14	can	can	AUX
ap-1364	50	15	be	be	AUX
ap-1364	50	16	reduced	reduce	VERB
ap-1364	50	17	to	to	ADP
ap-1364	50	18	the	the	DET
ap-1364	50	19	calculation	calculation	NOUN
ap-1364	50	20	of	of	ADP
ap-1364	50	21	x0	x0	PROPN
ap-1364	50	22	,	,	PUNCT
ap-1364	50	23	x1	x1	PROPN
ap-1364	50	24	,	,	PUNCT
ap-1364	50	25	x2	x2	PROPN
ap-1364	50	26	and	and	CCONJ
ap-1364	50	27	x3	x3	VERB
ap-1364	50	28	in	in	ADP
ap-1364	50	29	the	the	DET
ap-1364	50	30	spanning	span	VERB
ap-1364	50	31	tree	tree	NOUN
ap-1364	50	32	model	model	NOUN
ap-1364	50	33	.	.	PUNCT
ap-1364	51	1	the	the	DET
ap-1364	51	2	exact	exact	ADJ
ap-1364	51	3	relation	relation	NOUN
ap-1364	51	4	between	between	ADP
ap-1364	51	5	these	these	DET
ap-1364	51	6	quantities	quantity	NOUN
ap-1364	51	7	is	be	AUX
ap-1364	51	8	given	give	VERB
ap-1364	51	9	by	by	ADP
ap-1364	51	10	p1	p1	PROPN
ap-1364	51	11	=	=	PUNCT
ap-1364	52	1	x0	x0	PROPN
ap-1364	52	2	4	4	NUM
ap-1364	52	3	;	;	PUNCT
ap-1364	52	4	p2	p2	PROPN
ap-1364	52	5	=	=	SYM
ap-1364	52	6	p1	p1	PROPN
ap-1364	52	7	+	+	CCONJ
ap-1364	52	8	x1	x1	PROPN
ap-1364	52	9	3	3	NUM
ap-1364	52	10	;	;	PUNCT
ap-1364	52	11	p3	p3	PROPN
ap-1364	52	12	=	=	PUNCT
ap-1364	52	13	p2	p2	PROPN
ap-1364	53	1	+	+	CCONJ
ap-1364	53	2	x2	x2	PROPN
ap-1364	53	3	2	2	NUM
ap-1364	53	4	;	;	PUNCT
ap-1364	53	5	p4	p4	ADJ
ap-1364	53	6	=	=	SYM
ap-1364	53	7	p3	p3	PROPN
ap-1364	53	8	+	+	NOUN
ap-1364	53	9	x3	x3	ADJ
ap-1364	53	10	.	.	PUNCT
ap-1364	54	1	(	(	PUNCT
ap-1364	54	2	2.2	2.2	NUM
ap-1364	54	3	)	)	PUNCT
ap-1364	54	4	majumdar	majumdar	PROPN
ap-1364	54	5	and	and	CCONJ
ap-1364	54	6	dhar	dhar	PROPN
ap-1364	55	1	[	[	X
ap-1364	55	2	5	5	NUM
ap-1364	55	3	]	]	PUNCT
ap-1364	55	4	found	find	VERB
ap-1364	55	5	in	in	ADP
ap-1364	55	6	1991	1991	NUM
ap-1364	55	7	the	the	DET
ap-1364	55	8	probability	probability	NOUN
ap-1364	55	9	of	of	ADP
ap-1364	55	10	height	height	NOUN
ap-1364	55	11	1	1	NUM
ap-1364	55	12	,	,	PUNCT
ap-1364	55	13	constructing	construct	VERB
ap-1364	55	14	the	the	DET
ap-1364	55	15	corresponding	corresponding	ADJ
ap-1364	55	16	defect	defect	NOUN
ap-1364	55	17	lattice	lattice	NOUN
ap-1364	55	18	for	for	ADP
ap-1364	55	19	the	the	DET
ap-1364	55	20	situation	situation	NOUN
ap-1364	55	21	when	when	SCONJ
ap-1364	55	22	a	a	DET
ap-1364	55	23	site	site	NOUN
ap-1364	55	24	i0	i0	PROPN
ap-1364	55	25	has	have	VERB
ap-1364	55	26	no	no	DET
ap-1364	55	27	predecessors	predecessor	NOUN
ap-1364	55	28	and	and	CCONJ
ap-1364	55	29	calculating	calculate	VERB
ap-1364	55	30	the	the	DET
ap-1364	55	31	determinant	determinant	NOUN
ap-1364	55	32	of	of	ADP
ap-1364	55	33	the	the	DET
ap-1364	55	34	defect	defect	NOUN
ap-1364	55	35	matrix	matrix	NOUN
ap-1364	55	36	δ∗.	δ∗.	ADP
ap-1364	55	37	a	a	DET
ap-1364	55	38	technique	technique	NOUN
ap-1364	55	39	for	for	ADP
ap-1364	55	40	computing	compute	VERB
ap-1364	55	41	the	the	DET
ap-1364	55	42	numbers	number	NOUN
ap-1364	55	43	x1	x1	PROPN
ap-1364	55	44	,	,	PUNCT
ap-1364	55	45	x2	x2	PROPN
ap-1364	55	46	,	,	PUNCT
ap-1364	55	47	x3	x3	PROPN
ap-1364	55	48	was	be	AUX
ap-1364	55	49	devised	devise	VERB
ap-1364	55	50	in	in	ADP
ap-1364	55	51	[	[	X
ap-1364	55	52	9	9	NUM
ap-1364	55	53	]	]	PUNCT
ap-1364	55	54	.	.	PUNCT
ap-1364	56	1	the	the	DET
ap-1364	56	2	results	result	NOUN
ap-1364	56	3	are	be	AUX
ap-1364	56	4	(	(	PUNCT
ap-1364	56	5	see	see	VERB
ap-1364	56	6	also	also	ADV
ap-1364	56	7	[	[	X
ap-1364	56	8	16	16	NUM
ap-1364	56	9	]	]	PUNCT
ap-1364	56	10	for	for	ADP
ap-1364	56	11	details	detail	NOUN
ap-1364	56	12	)	)	PUNCT
ap-1364	56	13	x0	x0	PROPN
ap-1364	57	1	=	=	PUNCT
ap-1364	58	1	8(π	8(π	NUM
ap-1364	58	2	−	−	NOUN
ap-1364	58	3	2	2	X
ap-1364	58	4	)	)	PUNCT
ap-1364	58	5	π3	π3	NOUN
ap-1364	58	6	;	;	PUNCT
ap-1364	59	1	x1	x1	PROPN
ap-1364	59	2	=	=	NOUN
ap-1364	59	3	3	3	NUM
ap-1364	59	4	4	4	NUM
ap-1364	59	5	+	+	SYM
ap-1364	59	6	48	48	NUM
ap-1364	59	7	π3	π3	NOUN
ap-1364	59	8	−	−	NOUN
ap-1364	59	9	15	15	NUM
ap-1364	59	10	π2	π2	ADV
ap-1364	59	11	−	−	PROPN
ap-1364	59	12	3	3	NUM
ap-1364	59	13	2π	2π	NOUN
ap-1364	59	14	;	;	PUNCT
ap-1364	60	1	x2	x2	NOUN
ap-1364	60	2	=	=	NOUN
ap-1364	60	3	1	1	NUM
ap-1364	60	4	4	4	NUM
ap-1364	60	5	−	−	NUM
ap-1364	60	6	48	48	NUM
ap-1364	60	7	π3	π3	NOUN
ap-1364	60	8	+	+	CCONJ
ap-1364	60	9	6	6	NUM
ap-1364	60	10	π2	π2	NOUN
ap-1364	60	11	+	+	CCONJ
ap-1364	60	12	3	3	NUM
ap-1364	60	13	π	π	NOUN
ap-1364	60	14	;	;	PUNCT
ap-1364	60	15	(	(	PUNCT
ap-1364	60	16	2.3	2.3	NUM
ap-1364	60	17	)	)	PUNCT
ap-1364	60	18	x3	x3	NOUN
ap-1364	60	19	=	=	SYM
ap-1364	61	1	16	16	NUM
ap-1364	61	2	π3	π3	NOUN
ap-1364	61	3	+	+	CCONJ
ap-1364	61	4	1	1	NUM
ap-1364	61	5	π2	π2	ADJ
ap-1364	61	6	−	−	PROPN
ap-1364	61	7	3	3	NUM
ap-1364	61	8	2π	2π	NOUN
ap-1364	61	9	,	,	PUNCT
ap-1364	61	10	which	which	PRON
ap-1364	61	11	give	give	VERB
ap-1364	61	12	p1	p1	PROPN
ap-1364	61	13	=	=	PROPN
ap-1364	62	1	2(π	2(π	NUM
ap-1364	63	1	−	−	NOUN
ap-1364	63	2	2	2	NUM
ap-1364	63	3	)	)	PUNCT
ap-1364	63	4	π3	π3	NOUN
ap-1364	63	5	;	;	PUNCT
ap-1364	64	1	p2	p2	PROPN
ap-1364	64	2	=	=	SYM
ap-1364	64	3	1	1	NUM
ap-1364	64	4	4	4	NUM
ap-1364	64	5	+	+	CCONJ
ap-1364	64	6	12	12	NUM
ap-1364	64	7	π3	π3	NOUN
ap-1364	64	8	−	−	NOUN
ap-1364	64	9	3	3	NUM
ap-1364	64	10	π2	π2	ADV
ap-1364	64	11	−	−	PROPN
ap-1364	64	12	1	1	NUM
ap-1364	64	13	2π	2π	NOUN
ap-1364	64	14	;	;	PUNCT
ap-1364	64	15	p3	p3	PROPN
ap-1364	64	16	=	=	SYM
ap-1364	64	17	3	3	NUM
ap-1364	64	18	8	8	NUM
ap-1364	64	19	−	−	NUM
ap-1364	64	20	12	12	NUM
ap-1364	64	21	π3	π3	NOUN
ap-1364	65	1	+	+	CCONJ
ap-1364	65	2	1	1	NUM
ap-1364	65	3	π	π	NOUN
ap-1364	65	4	;	;	PUNCT
ap-1364	65	5	(	(	PUNCT
ap-1364	65	6	2.4	2.4	NUM
ap-1364	65	7	)	)	PUNCT
ap-1364	65	8	p4	p4	NOUN
ap-1364	65	9	=	=	NOUN
ap-1364	65	10	3	3	NUM
ap-1364	65	11	8	8	NUM
ap-1364	65	12	+	+	CCONJ
ap-1364	65	13	4	4	NUM
ap-1364	65	14	π3	π3	NOUN
ap-1364	65	15	+	+	CCONJ
ap-1364	65	16	1	1	NUM
ap-1364	65	17	π2	π2	ADJ
ap-1364	65	18	−	−	PROPN
ap-1364	65	19	1	1	NUM
ap-1364	65	20	2π	2π	NOUN
ap-1364	65	21	.	.	PUNCT
ap-1364	66	1	fig	fig	NOUN
ap-1364	66	2	.	.	PUNCT
ap-1364	67	1	1	1	NUM
ap-1364	67	2	:	:	PUNCT
ap-1364	67	3	all	all	DET
ap-1364	67	4	possible	possible	ADJ
ap-1364	67	5	situations	situation	NOUN
ap-1364	67	6	with	with	ADP
ap-1364	67	7	a	a	DET
ap-1364	67	8	fixed	fix	VERB
ap-1364	67	9	vertex	vertex	NOUN
ap-1364	67	10	i0	i0	PROPN
ap-1364	67	11	(	(	PUNCT
ap-1364	67	12	the	the	DET
ap-1364	67	13	central	central	ADJ
ap-1364	67	14	vertex	vertex	NOUN
ap-1364	67	15	in	in	ADP
ap-1364	67	16	the	the	DET
ap-1364	67	17	diagrams	diagram	NOUN
ap-1364	67	18	)	)	PUNCT
ap-1364	67	19	to	to	PART
ap-1364	67	20	have	have	VERB
ap-1364	67	21	various	various	ADJ
ap-1364	67	22	nearest	near	ADJ
ap-1364	67	23	neighbouring	neighbouring	NOUN
ap-1364	67	24	predecessors	predecessor	NOUN
ap-1364	67	25	on	on	ADP
ap-1364	67	26	the	the	DET
ap-1364	67	27	square	square	ADJ
ap-1364	67	28	lattice	lattice	NOUN
ap-1364	67	29	.	.	PUNCT
ap-1364	68	1	by	by	ADP
ap-1364	68	2	black	black	ADJ
ap-1364	68	3	color	color	NOUN
ap-1364	68	4	we	we	PRON
ap-1364	68	5	denote	denote	VERB
ap-1364	68	6	vertices	vertex	NOUN
ap-1364	68	7	,	,	PUNCT
ap-1364	68	8	which	which	PRON
ap-1364	68	9	are	be	AUX
ap-1364	68	10	predecessors	predecessor	NOUN
ap-1364	68	11	of	of	ADP
ap-1364	68	12	i0	i0	PROPN
ap-1364	68	13	.	.	PUNCT
ap-1364	69	1	white	white	PROPN
ap-1364	69	2	means	mean	VERB
ap-1364	69	3	that	that	SCONJ
ap-1364	69	4	the	the	DET
ap-1364	69	5	corresponding	corresponding	ADJ
ap-1364	69	6	vertex	vertex	NOUN
ap-1364	69	7	is	be	AUX
ap-1364	69	8	not	not	PART
ap-1364	69	9	a	a	DET
ap-1364	69	10	predecessor	predecessor	NOUN
ap-1364	69	11	of	of	ADP
ap-1364	69	12	i0	i0	PROPN
ap-1364	69	13	.	.	PUNCT
ap-1364	70	1	on	on	ADP
ap-1364	70	2	the	the	DET
ap-1364	70	3	k+1st	k+1st	PROPN
ap-1364	70	4	row	row	NOUN
ap-1364	70	5	(	(	PUNCT
ap-1364	70	6	k	k	NOUN
ap-1364	70	7	=	=	SYM
ap-1364	70	8	0	0	NUM
ap-1364	70	9	,	,	PUNCT
ap-1364	70	10	1	1	NUM
ap-1364	70	11	,	,	PUNCT
ap-1364	70	12	2	2	NUM
ap-1364	70	13	,	,	PUNCT
ap-1364	70	14	3	3	X
ap-1364	70	15	)	)	PUNCT
ap-1364	70	16	situations	situation	NOUN
ap-1364	70	17	with	with	ADP
ap-1364	70	18	k	k	PROPN
ap-1364	70	19	predecessors	predecessor	NOUN
ap-1364	70	20	are	be	AUX
ap-1364	70	21	presented	present	VERB
ap-1364	70	22	.	.	PUNCT
ap-1364	71	1	the	the	DET
ap-1364	71	2	configurations	configuration	NOUN
ap-1364	71	3	for	for	ADP
ap-1364	71	4	which	which	PRON
ap-1364	71	5	the	the	DET
ap-1364	71	6	right	right	ADJ
ap-1364	71	7	neighboring	neighboring	NOUN
ap-1364	71	8	vertex	vertex	NOUN
ap-1364	71	9	is	be	AUX
ap-1364	71	10	a	a	DET
ap-1364	71	11	predecessor	predecessor	NOUN
ap-1364	71	12	of	of	ADP
ap-1364	71	13	i0	i0	PROPN
ap-1364	71	14	are	be	AUX
ap-1364	71	15	circled	circle	VERB
ap-1364	71	16	by	by	ADP
ap-1364	71	17	a	a	DET
ap-1364	71	18	dashed	dash	VERB
ap-1364	71	19	line	line	NOUN
ap-1364	71	20	now	now	ADV
ap-1364	71	21	consider	consider	VERB
ap-1364	71	22	the	the	DET
ap-1364	71	23	problem	problem	NOUN
ap-1364	71	24	of	of	ADP
ap-1364	71	25	predecessors	predecessor	NOUN
ap-1364	71	26	for	for	ADP
ap-1364	71	27	nearest	near	ADJ
ap-1364	71	28	neighboring	neighboring	NOUN
ap-1364	71	29	sites	site	NOUN
ap-1364	71	30	.	.	PUNCT
ap-1364	72	1	first	first	ADV
ap-1364	72	2	we	we	PRON
ap-1364	72	3	fix	fix	VERB
ap-1364	72	4	a	a	DET
ap-1364	72	5	site	site	NOUN
ap-1364	72	6	i0	i0	PROPN
ap-1364	72	7	in	in	ADP
ap-1364	72	8	the	the	DET
ap-1364	72	9	bulk	bulk	NOUN
ap-1364	72	10	of	of	ADP
ap-1364	72	11	the	the	DET
ap-1364	72	12	square	square	ADJ
ap-1364	72	13	lattice	lattice	PROPN
ap-1364	72	14	.	.	PUNCT
ap-1364	73	1	denote	denote	VERB
ap-1364	73	2	its	its	PRON
ap-1364	73	3	right	right	NOUN
ap-1364	73	4	nearest	near	ADJ
ap-1364	73	5	neighboring	neighboring	NOUN
ap-1364	73	6	site	site	NOUN
ap-1364	73	7	by	by	ADP
ap-1364	73	8	j0	j0	PROPN
ap-1364	73	9	.	.	PUNCT
ap-1364	74	1	next	next	ADV
ap-1364	74	2	consider	consider	VERB
ap-1364	74	3	four	four	NUM
ap-1364	74	4	various	various	ADJ
ap-1364	74	5	cases	case	NOUN
ap-1364	74	6	,	,	PUNCT
ap-1364	74	7	when	when	SCONJ
ap-1364	74	8	i0	i0	PROPN
ap-1364	74	9	has	have	VERB
ap-1364	74	10	exactly	exactly	ADV
ap-1364	74	11	k	k	X
ap-1364	74	12	nearest	near	ADJ
ap-1364	74	13	neighboring	neighboring	NOUN
ap-1364	74	14	predecessors	predecessor	NOUN
ap-1364	74	15	(	(	PUNCT
ap-1364	74	16	k	k	NOUN
ap-1364	74	17	=	=	SYM
ap-1364	74	18	0	0	NUM
ap-1364	74	19	,	,	PUNCT
ap-1364	74	20	1	1	NUM
ap-1364	74	21	,	,	PUNCT
ap-1364	74	22	2	2	NUM
ap-1364	74	23	,	,	PUNCT
ap-1364	74	24	3	3	NUM
ap-1364	74	25	)	)	PUNCT
ap-1364	74	26	(	(	PUNCT
ap-1364	74	27	see	see	VERB
ap-1364	74	28	fig	fig	NOUN
ap-1364	74	29	.	.	PUNCT
ap-1364	75	1	1	1	NUM
ap-1364	75	2	)	)	PUNCT
ap-1364	75	3	.	.	PUNCT
ap-1364	76	1	for	for	ADP
ap-1364	76	2	k	k	PROPN
ap-1364	76	3	=	=	SYM
ap-1364	76	4	0	0	PROPN
ap-1364	76	5	the	the	DET
ap-1364	76	6	site	site	NOUN
ap-1364	76	7	j0	j0	PROPN
ap-1364	76	8	trivially	trivially	ADV
ap-1364	76	9	is	be	AUX
ap-1364	76	10	not	not	PART
ap-1364	76	11	a	a	DET
ap-1364	76	12	predecessor	predecessor	NOUN
ap-1364	76	13	of	of	ADP
ap-1364	76	14	i0	i0	PROPN
ap-1364	76	15	.	.	PUNCT
ap-1364	77	1	for	for	ADP
ap-1364	77	2	k	k	PROPN
ap-1364	77	3	=	=	SYM
ap-1364	77	4	1	1	NUM
ap-1364	77	5	,	,	PUNCT
ap-1364	77	6	we	we	PRON
ap-1364	77	7	have	have	VERB
ap-1364	77	8	1	1	NUM
ap-1364	77	9	of	of	ADP
ap-1364	77	10	4	4	NUM
ap-1364	77	11	equivalent	equivalent	ADJ
ap-1364	77	12	situations	situation	NOUN
ap-1364	77	13	when	when	SCONJ
ap-1364	77	14	j0	j0	PROPN
ap-1364	77	15	is	be	AUX
ap-1364	77	16	the	the	DET
ap-1364	77	17	predecessor	predecessor	NOUN
ap-1364	77	18	of	of	ADP
ap-1364	77	19	i0	i0	PROPN
ap-1364	77	20	.	.	PUNCT
ap-1364	78	1	for	for	ADP
ap-1364	78	2	k	k	PROPN
ap-1364	78	3	=	=	SYM
ap-1364	78	4	3	3	NUM
ap-1364	78	5	,	,	PUNCT
ap-1364	78	6	we	we	PRON
ap-1364	78	7	have	have	VERB
ap-1364	78	8	3	3	NUM
ap-1364	78	9	of	of	ADP
ap-1364	78	10	4	4	NUM
ap-1364	78	11	equivalent	equivalent	ADJ
ap-1364	78	12	situations	situation	NOUN
ap-1364	78	13	when	when	SCONJ
ap-1364	78	14	j0	j0	PROPN
ap-1364	78	15	is	be	AUX
ap-1364	78	16	the	the	DET
ap-1364	78	17	predecessor	predecessor	NOUN
ap-1364	78	18	.	.	PUNCT
ap-1364	79	1	the	the	DET
ap-1364	79	2	crucial	crucial	ADJ
ap-1364	79	3	case	case	NOUN
ap-1364	79	4	is	be	AUX
ap-1364	79	5	k	k	NOUN
ap-1364	79	6	=	=	SYM
ap-1364	79	7	2	2	X
ap-1364	79	8	.	.	PUNCT
ap-1364	80	1	here	here	ADV
ap-1364	80	2	we	we	PRON
ap-1364	80	3	have	have	VERB
ap-1364	80	4	6	6	NUM
ap-1364	80	5	situations	situation	NOUN
ap-1364	80	6	,	,	PUNCT
ap-1364	80	7	but	but	CCONJ
ap-1364	80	8	not	not	PART
ap-1364	80	9	all	all	PRON
ap-1364	80	10	of	of	ADP
ap-1364	80	11	them	they	PRON
ap-1364	80	12	are	be	AUX
ap-1364	80	13	equivalent	equivalent	ADJ
ap-1364	80	14	.	.	PUNCT
ap-1364	81	1	on	on	ADP
ap-1364	81	2	the	the	DET
ap-1364	81	3	other	other	ADJ
ap-1364	81	4	hand	hand	NOUN
ap-1364	81	5	,	,	PUNCT
ap-1364	81	6	we	we	PRON
ap-1364	81	7	can	can	AUX
ap-1364	81	8	select	select	VERB
ap-1364	81	9	two	two	NUM
ap-1364	81	10	groups	group	NOUN
ap-1364	81	11	of	of	ADP
ap-1364	81	12	4	4	NUM
ap-1364	81	13	and	and	CCONJ
ap-1364	81	14	2	2	NUM
ap-1364	81	15	elements	element	NOUN
ap-1364	81	16	(	(	PUNCT
ap-1364	81	17	the	the	DET
ap-1364	81	18	first	first	ADJ
ap-1364	81	19	four	four	NUM
ap-1364	81	20	and	and	CCONJ
ap-1364	81	21	the	the	DET
ap-1364	81	22	last	last	ADJ
ap-1364	81	23	two	two	NUM
ap-1364	81	24	in	in	ADP
ap-1364	81	25	the	the	DET
ap-1364	81	26	third	third	ADJ
ap-1364	81	27	line	line	NOUN
ap-1364	81	28	of	of	ADP
ap-1364	81	29	fig	fig	NOUN
ap-1364	81	30	.	.	PUNCT
ap-1364	82	1	1	1	NUM
ap-1364	82	2	)	)	PUNCT
ap-1364	83	1	so	so	SCONJ
ap-1364	83	2	that	that	SCONJ
ap-1364	83	3	60	60	NUM
ap-1364	83	4	acta	acta	PROPN
ap-1364	83	5	polytechnica	polytechnica	PROPN
ap-1364	83	6	vol	vol	NOUN
ap-1364	83	7	.	.	PUNCT
ap-1364	84	1	51	51	NUM
ap-1364	84	2	no	no	INTJ
ap-1364	84	3	.	.	PUNCT
ap-1364	85	1	1/2011	1/2011	NUM
ap-1364	85	2	the	the	DET
ap-1364	85	3	elements	element	NOUN
ap-1364	85	4	in	in	ADP
ap-1364	85	5	each	each	DET
ap-1364	85	6	group	group	NOUN
ap-1364	85	7	are	be	AUX
ap-1364	85	8	equivalent	equivalent	ADJ
ap-1364	85	9	.	.	PUNCT
ap-1364	86	1	we	we	PRON
ap-1364	86	2	are	be	AUX
ap-1364	86	3	looking	look	VERB
ap-1364	86	4	for	for	ADP
ap-1364	86	5	situations	situation	NOUN
ap-1364	86	6	where	where	SCONJ
ap-1364	86	7	j0	j0	PROPN
ap-1364	86	8	is	be	AUX
ap-1364	86	9	a	a	DET
ap-1364	86	10	predecessor	predecessor	NOUN
ap-1364	86	11	of	of	ADP
ap-1364	86	12	i0	i0	PROPN
ap-1364	86	13	.	.	PUNCT
ap-1364	87	1	there	there	PRON
ap-1364	87	2	are	be	VERB
ap-1364	87	3	2	2	NUM
ap-1364	87	4	encircled	encircled	ADJ
ap-1364	87	5	elements	element	NOUN
ap-1364	87	6	from	from	ADP
ap-1364	87	7	the	the	DET
ap-1364	87	8	first	first	ADJ
ap-1364	87	9	group	group	NOUN
ap-1364	87	10	and	and	CCONJ
ap-1364	87	11	one	one	NUM
ap-1364	87	12	from	from	ADP
ap-1364	87	13	the	the	DET
ap-1364	87	14	second	second	ADJ
ap-1364	87	15	group	group	NOUN
ap-1364	87	16	,	,	PUNCT
ap-1364	87	17	which	which	PRON
ap-1364	87	18	correspond	correspond	VERB
ap-1364	87	19	to	to	ADP
ap-1364	87	20	the	the	DET
ap-1364	87	21	desired	desire	VERB
ap-1364	87	22	situations	situation	NOUN
ap-1364	87	23	.	.	PUNCT
ap-1364	88	1	thus	thus	ADV
ap-1364	88	2	,	,	PUNCT
ap-1364	88	3	if	if	SCONJ
ap-1364	88	4	we	we	PRON
ap-1364	88	5	take	take	VERB
ap-1364	88	6	the	the	DET
ap-1364	88	7	linear	linear	ADJ
ap-1364	88	8	combination	combination	NOUN
ap-1364	88	9	of	of	ADP
ap-1364	88	10	x1	x1	PROPN
ap-1364	88	11	,	,	PUNCT
ap-1364	88	12	x2	x2	PROPN
ap-1364	88	13	and	and	CCONJ
ap-1364	88	14	x3	x3	ADJ
ap-1364	88	15	with	with	ADP
ap-1364	88	16	coefficients	coefficient	NOUN
ap-1364	88	17	1/4	1/4	NUM
ap-1364	88	18	,	,	PUNCT
ap-1364	88	19	1/2	1/2	NUM
ap-1364	88	20	and	and	CCONJ
ap-1364	88	21	3/4	3/4	NUM
ap-1364	88	22	correspondingly	correspondingly	ADV
ap-1364	88	23	,	,	PUNCT
ap-1364	88	24	we	we	PRON
ap-1364	88	25	get	get	VERB
ap-1364	88	26	the	the	DET
ap-1364	88	27	desired	desire	VERB
ap-1364	88	28	probability	probability	NOUN
ap-1364	88	29	p	p	X
ap-1364	88	30	(	(	PUNCT
ap-1364	88	31	1	1	NUM
ap-1364	88	32	)	)	PUNCT
ap-1364	88	33	that	that	SCONJ
ap-1364	88	34	j0	j0	PROPN
ap-1364	88	35	is	be	AUX
ap-1364	88	36	the	the	DET
ap-1364	88	37	predecessor	predecessor	NOUN
ap-1364	88	38	of	of	ADP
ap-1364	88	39	i0	i0	PROPN
ap-1364	88	40	:	:	PUNCT
ap-1364	88	41	p	p	X
ap-1364	88	42	(	(	PUNCT
ap-1364	88	43	1	1	NUM
ap-1364	88	44	)	)	PUNCT
ap-1364	88	45	=	=	SYM
ap-1364	88	46	1	1	NUM
ap-1364	88	47	4	4	NUM
ap-1364	88	48	x1	x1	NOUN
ap-1364	89	1	+	+	CCONJ
ap-1364	89	2	1	1	NUM
ap-1364	89	3	2	2	NUM
ap-1364	89	4	x2	x2	NOUN
ap-1364	89	5	+	+	CCONJ
ap-1364	89	6	3	3	NUM
ap-1364	89	7	4	4	NUM
ap-1364	89	8	x3	x3	NOUN
ap-1364	89	9	=	=	SYM
ap-1364	89	10	5	5	NUM
ap-1364	89	11	16	16	NUM
ap-1364	89	12	.	.	PUNCT
ap-1364	90	1	(	(	PUNCT
ap-1364	90	2	2.5	2.5	NUM
ap-1364	90	3	)	)	PUNCT
ap-1364	90	4	3	3	NUM
ap-1364	90	5	return	return	VERB
ap-1364	90	6	probability	probability	NOUN
ap-1364	90	7	for	for	ADP
ap-1364	90	8	the	the	DET
ap-1364	90	9	loop	loop	NOUN
ap-1364	90	10	erased	erase	VERB
ap-1364	90	11	random	random	ADJ
ap-1364	90	12	walk	walk	NOUN
ap-1364	90	13	consider	consider	VERB
ap-1364	90	14	a	a	DET
ap-1364	90	15	finite	finite	ADJ
ap-1364	90	16	square	square	PROPN
ap-1364	90	17	lattice	lattice	PROPN
ap-1364	90	18	l	l	PROPN
ap-1364	90	19	with	with	ADP
ap-1364	90	20	vertex	vertex	NOUN
ap-1364	90	21	set	set	VERB
ap-1364	90	22	v	v	NOUN
ap-1364	90	23	and	and	CCONJ
ap-1364	90	24	edge	edge	NOUN
ap-1364	90	25	set	set	VERB
ap-1364	90	26	e.	e.	PROPN
ap-1364	90	27	given	give	VERB
ap-1364	90	28	p	p	PROPN
ap-1364	90	29	=	=	PUNCT
ap-1364	91	1	[	[	X
ap-1364	91	2	u0	u0	ADJ
ap-1364	91	3	,	,	PUNCT
ap-1364	91	4	u1	u1	NOUN
ap-1364	91	5	,	,	PUNCT
ap-1364	91	6	u2	u2	NOUN
ap-1364	91	7	,	,	PUNCT
ap-1364	91	8	.	.	PUNCT
ap-1364	91	9	.	.	PUNCT
ap-1364	91	10	.	.	PUNCT
ap-1364	92	1	,	,	PUNCT
ap-1364	92	2	un	un	PROPN
ap-1364	92	3	]	]	X
ap-1364	92	4	a	a	DET
ap-1364	92	5	path	path	NOUN
ap-1364	92	6	in	in	ADP
ap-1364	92	7	l	l	NOUN
ap-1364	92	8	,	,	PUNCT
ap-1364	92	9	its	its	PRON
ap-1364	92	10	loop	loop	NOUN
ap-1364	92	11	-	-	PUNCT
ap-1364	92	12	erasure	erasure	NOUN
ap-1364	92	13	le(p	le(p	NOUN
ap-1364	92	14	)	)	PUNCT
ap-1364	92	15	=	=	PUNCT
ap-1364	93	1	[	[	X
ap-1364	93	2	γ0	γ0	NOUN
ap-1364	93	3	,	,	PUNCT
ap-1364	93	4	γ1	γ1	NOUN
ap-1364	93	5	,	,	PUNCT
ap-1364	93	6	γ2	γ2	PROPN
ap-1364	93	7	,	,	PUNCT
ap-1364	93	8	.	.	PUNCT
ap-1364	93	9	.	.	PUNCT
ap-1364	94	1	.	.	PUNCT
ap-1364	95	1	,	,	PUNCT
ap-1364	95	2	γm	γm	X
ap-1364	95	3	]	]	PUNCT
ap-1364	95	4	is	be	AUX
ap-1364	95	5	defined	define	VERB
ap-1364	95	6	by	by	ADP
ap-1364	95	7	chronologically	chronologically	ADV
ap-1364	95	8	removing	remove	VERB
ap-1364	95	9	loops	loop	NOUN
ap-1364	95	10	from	from	ADP
ap-1364	95	11	p	p	PROPN
ap-1364	95	12	.	.	PUNCT
ap-1364	96	1	formally	formally	ADV
ap-1364	96	2	,	,	PUNCT
ap-1364	96	3	this	this	DET
ap-1364	96	4	definition	definition	NOUN
ap-1364	96	5	is	be	AUX
ap-1364	96	6	as	as	SCONJ
ap-1364	96	7	follows	follow	VERB
ap-1364	96	8	.	.	PUNCT
ap-1364	97	1	we	we	PRON
ap-1364	97	2	first	first	ADV
ap-1364	97	3	set	set	VERB
ap-1364	97	4	γ0	γ0	NOUN
ap-1364	97	5	=	=	SYM
ap-1364	97	6	u0	u0	ADJ
ap-1364	97	7	.	.	PUNCT
ap-1364	98	1	assuming	assume	VERB
ap-1364	98	2	γ0	γ0	NOUN
ap-1364	98	3	,	,	PUNCT
ap-1364	98	4	.	.	PUNCT
ap-1364	98	5	.	.	PUNCT
ap-1364	99	1	.	.	PUNCT
ap-1364	100	1	,	,	PUNCT
ap-1364	100	2	γk	γk	PROPN
ap-1364	100	3	have	have	AUX
ap-1364	100	4	been	be	AUX
ap-1364	100	5	defined	define	VERB
ap-1364	100	6	,	,	PUNCT
ap-1364	100	7	we	we	PRON
ap-1364	100	8	let	let	VERB
ap-1364	100	9	sk	sk	VERB
ap-1364	100	10	=	=	SYM
ap-1364	100	11	1+max{j	1+max{j	NUM
ap-1364	100	12	:	:	PUNCT
ap-1364	100	13	uj	uj	PROPN
ap-1364	100	14	=	=	SYM
ap-1364	100	15	γk	γk	PROPN
ap-1364	100	16	}	}	PUNCT
ap-1364	100	17	.	.	PUNCT
ap-1364	101	1	if	if	SCONJ
ap-1364	101	2	sk	sk	VERB
ap-1364	101	3	=	=	SYM
ap-1364	101	4	n+1	n+1	PROPN
ap-1364	101	5	,	,	PUNCT
ap-1364	101	6	we	we	PRON
ap-1364	101	7	stop	stop	VERB
ap-1364	101	8	and	and	CCONJ
ap-1364	101	9	le(p	le(p	NOUN
ap-1364	101	10	)	)	PUNCT
ap-1364	101	11	=	=	PUNCT
ap-1364	102	1	[	[	X
ap-1364	102	2	γ0	γ0	NOUN
ap-1364	102	3	,	,	PUNCT
ap-1364	102	4	γ1	γ1	NOUN
ap-1364	102	5	,	,	PUNCT
ap-1364	102	6	γ2	γ2	PROPN
ap-1364	102	7	,	,	PUNCT
ap-1364	102	8	.	.	PUNCT
ap-1364	102	9	.	.	PUNCT
ap-1364	103	1	.	.	PUNCT
ap-1364	104	1	,	,	PUNCT
ap-1364	104	2	γm	γm	X
ap-1364	104	3	]	]	X
ap-1364	104	4	with	with	ADP
ap-1364	104	5	m	m	PROPN
ap-1364	104	6	=	=	SYM
ap-1364	104	7	k.	k.	PROPN
ap-1364	104	8	otherwise	otherwise	ADV
ap-1364	104	9	,	,	PUNCT
ap-1364	104	10	we	we	PRON
ap-1364	104	11	let	let	VERB
ap-1364	104	12	γk+1	γk+1	X
ap-1364	104	13	=	=	SYM
ap-1364	104	14	usk	usk	PROPN
ap-1364	104	15	.	.	PUNCT
ap-1364	105	1	note	note	VERB
ap-1364	105	2	that	that	SCONJ
ap-1364	105	3	the	the	DET
ap-1364	105	4	order	order	NOUN
ap-1364	105	5	in	in	ADP
ap-1364	105	6	which	which	PRON
ap-1364	105	7	we	we	PRON
ap-1364	105	8	remove	remove	VERB
ap-1364	105	9	loops	loop	NOUN
ap-1364	105	10	does	do	AUX
ap-1364	105	11	matter	matter	NOUN
ap-1364	105	12	,	,	PUNCT
ap-1364	105	13	and	and	CCONJ
ap-1364	105	14	it	it	PRON
ap-1364	105	15	follows	follow	VERB
ap-1364	105	16	from	from	ADP
ap-1364	105	17	the	the	DET
ap-1364	105	18	definition	definition	NOUN
ap-1364	105	19	that	that	PRON
ap-1364	105	20	we	we	PRON
ap-1364	105	21	remove	remove	VERB
ap-1364	105	22	loops	loop	NOUN
ap-1364	105	23	as	as	SCONJ
ap-1364	105	24	they	they	PRON
ap-1364	105	25	are	be	AUX
ap-1364	105	26	created	create	VERB
ap-1364	105	27	,	,	PUNCT
ap-1364	105	28	following	follow	VERB
ap-1364	105	29	the	the	DET
ap-1364	105	30	path	path	NOUN
ap-1364	105	31	.	.	PUNCT
ap-1364	106	1	a	a	DET
ap-1364	106	2	walk	walk	NOUN
ap-1364	106	3	obtained	obtain	VERB
ap-1364	106	4	after	after	ADP
ap-1364	106	5	applying	apply	VERB
ap-1364	106	6	the	the	DET
ap-1364	106	7	loop	loop	NOUN
ap-1364	106	8	-	-	PUNCT
ap-1364	106	9	erasure	erasure	NOUN
ap-1364	106	10	to	to	ADP
ap-1364	106	11	a	a	DET
ap-1364	106	12	simple	simple	ADJ
ap-1364	106	13	random	random	ADJ
ap-1364	106	14	walk	walk	NOUN
ap-1364	106	15	path	path	NOUN
ap-1364	106	16	is	be	AUX
ap-1364	106	17	called	call	VERB
ap-1364	106	18	a	a	DET
ap-1364	106	19	loop	loop	NOUN
ap-1364	106	20	-	-	PUNCT
ap-1364	106	21	erased	erase	VERB
ap-1364	106	22	random	random	ADJ
ap-1364	106	23	walk	walk	NOUN
ap-1364	106	24	(	(	PUNCT
ap-1364	106	25	lerw	lerw	NOUN
ap-1364	106	26	)	)	PUNCT
ap-1364	106	27	.	.	PUNCT
ap-1364	107	1	since	since	SCONJ
ap-1364	107	2	the	the	DET
ap-1364	107	3	infinite	infinite	ADJ
ap-1364	107	4	simple	simple	ADJ
ap-1364	107	5	random	random	ADJ
ap-1364	107	6	walk	walk	NOUN
ap-1364	107	7	on	on	ADP
ap-1364	107	8	finite	finite	ADJ
ap-1364	107	9	connected	connect	VERB
ap-1364	107	10	undirected	undirected	ADJ
ap-1364	107	11	graphs	graph	NOUN
ap-1364	107	12	is	be	AUX
ap-1364	107	13	recurrent	recurrent	ADJ
ap-1364	107	14	,	,	PUNCT
ap-1364	107	15	the	the	DET
ap-1364	107	16	infinite	infinite	ADJ
ap-1364	107	17	lerw	lerw	NOUN
ap-1364	107	18	is	be	AUX
ap-1364	107	19	not	not	PART
ap-1364	107	20	defined	define	VERB
ap-1364	107	21	.	.	PUNCT
ap-1364	108	1	on	on	ADP
ap-1364	108	2	the	the	DET
ap-1364	108	3	other	other	ADJ
ap-1364	108	4	hand	hand	NOUN
ap-1364	108	5	,	,	PUNCT
ap-1364	108	6	we	we	PRON
ap-1364	108	7	can	can	AUX
ap-1364	108	8	fix	fix	VERB
ap-1364	108	9	a	a	DET
ap-1364	108	10	subset	subset	NOUN
ap-1364	108	11	w	w	ADP
ap-1364	108	12	⊂	⊂	PROPN
ap-1364	108	13	v	v	ADP
ap-1364	108	14	of	of	ADP
ap-1364	108	15	vertices	vertex	NOUN
ap-1364	108	16	and	and	CCONJ
ap-1364	108	17	define	define	VERB
ap-1364	108	18	lerw	lerw	NOUN
ap-1364	108	19	from	from	ADP
ap-1364	108	20	a	a	DET
ap-1364	108	21	fixed	fix	VERB
ap-1364	108	22	vertex	vertex	NOUN
ap-1364	108	23	u0	u0	NOUN
ap-1364	108	24	to	to	ADP
ap-1364	108	25	w	w	PROPN
ap-1364	108	26	.	.	PUNCT
ap-1364	109	1	to	to	PART
ap-1364	109	2	do	do	VERB
ap-1364	109	3	this	this	PRON
ap-1364	109	4	,	,	PUNCT
ap-1364	109	5	we	we	PRON
ap-1364	109	6	take	take	VERB
ap-1364	109	7	the	the	DET
ap-1364	109	8	path	path	NOUN
ap-1364	109	9	of	of	ADP
ap-1364	109	10	a	a	DET
ap-1364	109	11	simple	simple	ADJ
ap-1364	109	12	random	random	ADJ
ap-1364	109	13	walk	walk	NOUN
ap-1364	109	14	started	start	VERB
ap-1364	109	15	at	at	ADP
ap-1364	109	16	u0	u0	ADJ
ap-1364	109	17	and	and	CCONJ
ap-1364	109	18	stopped	stop	VERB
ap-1364	109	19	upon	upon	SCONJ
ap-1364	109	20	hitting	hit	VERB
ap-1364	109	21	w	w	ADP
ap-1364	109	22	,	,	PUNCT
ap-1364	109	23	after	after	ADP
ap-1364	109	24	which	which	PRON
ap-1364	109	25	we	we	PRON
ap-1364	109	26	apply	apply	VERB
ap-1364	109	27	the	the	DET
ap-1364	109	28	loop	loop	NOUN
ap-1364	109	29	-	-	PUNCT
ap-1364	109	30	erasure	erasure	NOUN
ap-1364	109	31	.	.	PUNCT
ap-1364	110	1	wilson	wilson	PROPN
ap-1364	110	2	established	establish	VERB
ap-1364	110	3	an	an	DET
ap-1364	110	4	algorithm	algorithm	NOUN
ap-1364	110	5	to	to	PART
ap-1364	110	6	generate	generate	VERB
ap-1364	110	7	uniform	uniform	ADJ
ap-1364	110	8	spanning	span	VERB
ap-1364	110	9	trees	tree	NOUN
ap-1364	110	10	,	,	PUNCT
ap-1364	110	11	which	which	PRON
ap-1364	110	12	uses	use	VERB
ap-1364	110	13	lerw	lerw	NOUN
ap-1364	110	14	[	[	X
ap-1364	110	15	13	13	NUM
ap-1364	110	16	]	]	PUNCT
ap-1364	110	17	.	.	PUNCT
ap-1364	111	1	it	it	PRON
ap-1364	111	2	turns	turn	VERB
ap-1364	111	3	out	out	ADP
ap-1364	111	4	to	to	PART
ap-1364	111	5	be	be	AUX
ap-1364	111	6	extremely	extremely	ADV
ap-1364	111	7	useful	useful	ADJ
ap-1364	111	8	not	not	PART
ap-1364	111	9	only	only	ADV
ap-1364	111	10	as	as	ADP
ap-1364	111	11	a	a	DET
ap-1364	111	12	simulation	simulation	NOUN
ap-1364	111	13	tool	tool	NOUN
ap-1364	111	14	,	,	PUNCT
ap-1364	111	15	but	but	CCONJ
ap-1364	111	16	also	also	ADV
ap-1364	111	17	for	for	ADP
ap-1364	111	18	theoretical	theoretical	ADJ
ap-1364	111	19	analysis	analysis	NOUN
ap-1364	111	20	.	.	PUNCT
ap-1364	112	1	it	it	PRON
ap-1364	112	2	runs	run	VERB
ap-1364	112	3	as	as	SCONJ
ap-1364	112	4	follows	follow	VERB
ap-1364	112	5	.	.	PUNCT
ap-1364	113	1	pick	pick	VERB
ap-1364	113	2	an	an	DET
ap-1364	113	3	arbitrary	arbitrary	ADJ
ap-1364	113	4	ordering	ordering	NOUN
ap-1364	113	5	v	v	NOUN
ap-1364	113	6	=	=	SYM
ap-1364	113	7	{	{	PUNCT
ap-1364	113	8	v0	v0	NOUN
ap-1364	113	9	,	,	PUNCT
ap-1364	113	10	v1	v1	NOUN
ap-1364	113	11	,	,	PUNCT
ap-1364	113	12	.	.	PUNCT
ap-1364	113	13	.	.	PUNCT
ap-1364	114	1	.	.	PUNCT
ap-1364	115	1	,	,	PUNCT
ap-1364	115	2	vn	vn	VERB
ap-1364	115	3	}	}	PUNCT
ap-1364	115	4	for	for	ADP
ap-1364	115	5	the	the	DET
ap-1364	115	6	vertices	vertex	NOUN
ap-1364	115	7	in	in	ADP
ap-1364	115	8	l.	l.	PROPN
ap-1364	115	9	let	let	VERB
ap-1364	116	1	s0	s0	PROPN
ap-1364	116	2	=	=	PUNCT
ap-1364	116	3	v0	v0	PROPN
ap-1364	116	4	.	.	PUNCT
ap-1364	117	1	inductively	inductively	ADV
ap-1364	117	2	,	,	PUNCT
ap-1364	117	3	for	for	ADP
ap-1364	117	4	i	i	PROPN
ap-1364	117	5	=	=	SYM
ap-1364	117	6	1	1	NUM
ap-1364	117	7	,	,	PUNCT
ap-1364	117	8	2	2	NUM
ap-1364	117	9	,	,	PUNCT
ap-1364	117	10	.	.	PUNCT
ap-1364	117	11	.	.	PUNCT
ap-1364	117	12	.	.	PUNCT
ap-1364	118	1	,	,	PUNCT
ap-1364	118	2	n	n	PRON
ap-1364	118	3	define	define	VERB
ap-1364	118	4	a	a	DET
ap-1364	118	5	graph	graph	NOUN
ap-1364	118	6	si	si	X
ap-1364	118	7	to	to	PART
ap-1364	118	8	be	be	AUX
ap-1364	118	9	the	the	DET
ap-1364	118	10	union	union	NOUN
ap-1364	118	11	of	of	ADP
ap-1364	118	12	si−1	si−1	PROPN
ap-1364	118	13	and	and	CCONJ
ap-1364	118	14	a	a	DET
ap-1364	118	15	(	(	PUNCT
ap-1364	118	16	conditionally	conditionally	ADV
ap-1364	118	17	independent	independent	ADJ
ap-1364	118	18	)	)	PUNCT
ap-1364	118	19	lerw	lerw	ADJ
ap-1364	118	20	path	path	NOUN
ap-1364	118	21	from	from	ADP
ap-1364	118	22	vi	vi	PROPN
ap-1364	118	23	to	to	ADP
ap-1364	118	24	si−1	si−1	PROPN
ap-1364	118	25	.	.	PUNCT
ap-1364	119	1	note	note	VERB
ap-1364	119	2	,	,	PUNCT
ap-1364	119	3	if	if	SCONJ
ap-1364	119	4	vi	vi	PROPN
ap-1364	119	5	∈	∈	PROPN
ap-1364	119	6	si−1	si−1	PROPN
ap-1364	119	7	,	,	PUNCT
ap-1364	119	8	then	then	ADV
ap-1364	119	9	si	si	PROPN
ap-1364	119	10	=	=	PROPN
ap-1364	119	11	si−1	si−1	PROPN
ap-1364	119	12	.	.	PUNCT
ap-1364	120	1	then	then	ADV
ap-1364	120	2	,	,	PUNCT
ap-1364	120	3	regardless	regardless	ADV
ap-1364	120	4	of	of	ADP
ap-1364	120	5	the	the	DET
ap-1364	120	6	chosen	choose	VERB
ap-1364	120	7	order	order	NOUN
ap-1364	120	8	of	of	ADP
ap-1364	120	9	the	the	DET
ap-1364	120	10	vertices	vertex	NOUN
ap-1364	120	11	,	,	PUNCT
ap-1364	120	12	sn	sn	PROPN
ap-1364	120	13	is	be	AUX
ap-1364	120	14	a	a	DET
ap-1364	120	15	ust	ust	PROPN
ap-1364	120	16	on	on	ADP
ap-1364	120	17	l	l	NOUN
ap-1364	120	18	with	with	ADP
ap-1364	120	19	root	root	NOUN
ap-1364	120	20	v0	v0	NOUN
ap-1364	120	21	.	.	PUNCT
ap-1364	121	1	if	if	SCONJ
ap-1364	121	2	we	we	PRON
ap-1364	121	3	take	take	VERB
ap-1364	121	4	as	as	ADP
ap-1364	121	5	an	an	DET
ap-1364	121	6	initial	initial	ADJ
ap-1364	121	7	condition	condition	NOUN
ap-1364	121	8	s0	s0	NOUN
ap-1364	121	9	=	=	PUNCT
ap-1364	121	10	w	w	PROPN
ap-1364	121	11	,	,	PUNCT
ap-1364	121	12	with	with	ADP
ap-1364	121	13	some	some	DET
ap-1364	121	14	w	w	PROPN
ap-1364	121	15	⊂	⊂	PROPN
ap-1364	121	16	v	v	PROPN
ap-1364	121	17	,	,	PUNCT
ap-1364	121	18	then	then	ADV
ap-1364	121	19	the	the	DET
ap-1364	121	20	generated	generate	VERB
ap-1364	121	21	structures	structure	NOUN
ap-1364	121	22	will	will	AUX
ap-1364	121	23	be	be	AUX
ap-1364	121	24	spanning	span	VERB
ap-1364	121	25	forests	forest	NOUN
ap-1364	121	26	with	with	ADP
ap-1364	121	27	a	a	DET
ap-1364	121	28	set	set	NOUN
ap-1364	121	29	of	of	ADP
ap-1364	121	30	roots	root	NOUN
ap-1364	121	31	w	w	PROPN
ap-1364	121	32	.	.	PUNCT
ap-1364	122	1	the	the	DET
ap-1364	122	2	spanning	span	VERB
ap-1364	122	3	forest	forest	NOUN
ap-1364	122	4	with	with	ADP
ap-1364	122	5	a	a	DET
ap-1364	122	6	fixed	fix	VERB
ap-1364	122	7	set	set	NOUN
ap-1364	122	8	of	of	ADP
ap-1364	122	9	roots	root	NOUN
ap-1364	122	10	can	can	AUX
ap-1364	122	11	be	be	AUX
ap-1364	122	12	considered	consider	VERB
ap-1364	122	13	as	as	ADP
ap-1364	122	14	a	a	DET
ap-1364	122	15	spanning	span	VERB
ap-1364	122	16	tree	tree	NOUN
ap-1364	122	17	,	,	PUNCT
ap-1364	122	18	if	if	SCONJ
ap-1364	122	19	we	we	PRON
ap-1364	122	20	add	add	VERB
ap-1364	122	21	an	an	DET
ap-1364	122	22	auxiliary	auxiliary	ADJ
ap-1364	122	23	vertex	vertex	NOUN
ap-1364	122	24	and	and	CCONJ
ap-1364	122	25	join	join	VERB
ap-1364	122	26	it	it	PRON
ap-1364	122	27	to	to	ADP
ap-1364	122	28	all	all	DET
ap-1364	122	29	the	the	DET
ap-1364	122	30	roots	root	NOUN
ap-1364	122	31	.	.	PUNCT
ap-1364	123	1	now	now	ADV
ap-1364	123	2	consider	consider	VERB
ap-1364	123	3	the	the	DET
ap-1364	123	4	wilson	wilson	PROPN
ap-1364	123	5	algorithm	algorithm	NOUN
ap-1364	123	6	on	on	ADP
ap-1364	123	7	l	l	PROPN
ap-1364	123	8	with	with	SCONJ
ap-1364	123	9	the	the	DET
ap-1364	123	10	set	set	NOUN
ap-1364	123	11	of	of	ADP
ap-1364	123	12	boundary	boundary	ADJ
ap-1364	123	13	vertices	vertex	NOUN
ap-1364	123	14	∂l	∂l	VERB
ap-1364	123	15	and	and	CCONJ
ap-1364	123	16	take	take	VERB
ap-1364	123	17	s0	s0	PROPN
ap-1364	123	18	=	=	SYM
ap-1364	123	19	∂l	∂l	PROPN
ap-1364	123	20	.	.	PUNCT
ap-1364	124	1	when	when	SCONJ
ap-1364	124	2	the	the	DET
ap-1364	124	3	size	size	NOUN
ap-1364	124	4	of	of	ADP
ap-1364	124	5	the	the	DET
ap-1364	124	6	lattice	lattice	NOUN
ap-1364	124	7	tends	tend	VERB
ap-1364	124	8	to	to	PART
ap-1364	124	9	infinity	infinity	VERB
ap-1364	124	10	,	,	PUNCT
ap-1364	124	11	the	the	DET
ap-1364	124	12	boundary	boundary	ADJ
ap-1364	124	13	effects	effect	NOUN
ap-1364	124	14	will	will	AUX
ap-1364	124	15	vanish	vanish	VERB
ap-1364	124	16	,	,	PUNCT
ap-1364	124	17	so	so	SCONJ
ap-1364	124	18	we	we	PRON
ap-1364	124	19	can	can	AUX
ap-1364	124	20	neglect	neglect	VERB
ap-1364	124	21	the	the	DET
ap-1364	124	22	details	detail	NOUN
ap-1364	124	23	of	of	ADP
ap-1364	124	24	the	the	DET
ap-1364	124	25	boundary	boundary	NOUN
ap-1364	124	26	.	.	PUNCT
ap-1364	125	1	so	so	ADV
ap-1364	125	2	we	we	PRON
ap-1364	125	3	will	will	AUX
ap-1364	125	4	not	not	PART
ap-1364	125	5	distinguish	distinguish	VERB
ap-1364	125	6	between	between	ADP
ap-1364	125	7	spanning	span	VERB
ap-1364	125	8	forests	forest	NOUN
ap-1364	125	9	and	and	CCONJ
ap-1364	125	10	spanning	span	VERB
ap-1364	125	11	trees	tree	NOUN
ap-1364	125	12	.	.	PUNCT
ap-1364	126	1	it	it	PRON
ap-1364	126	2	follows	follow	VERB
ap-1364	126	3	from	from	ADP
ap-1364	126	4	the	the	DET
ap-1364	126	5	wilson	wilson	PROPN
ap-1364	126	6	algorithm	algorithm	NOUN
ap-1364	126	7	for	for	ADP
ap-1364	126	8	a	a	DET
ap-1364	126	9	fixed	fix	VERB
ap-1364	126	10	site	site	NOUN
ap-1364	126	11	i0	i0	PROPN
ap-1364	126	12	,	,	PUNCT
ap-1364	126	13	that	that	SCONJ
ap-1364	126	14	if	if	SCONJ
ap-1364	126	15	we	we	PRON
ap-1364	126	16	start	start	VERB
ap-1364	126	17	a	a	DET
ap-1364	126	18	lerw	lerw	NOUN
ap-1364	126	19	from	from	ADP
ap-1364	126	20	i0	i0	PROPN
ap-1364	126	21	upon	upon	SCONJ
ap-1364	126	22	hitting	hit	VERB
ap-1364	126	23	the	the	DET
ap-1364	126	24	boundary	boundary	ADJ
ap-1364	126	25	∂l	∂l	PROPN
ap-1364	126	26	,	,	PUNCT
ap-1364	126	27	we	we	PRON
ap-1364	126	28	will	will	AUX
ap-1364	126	29	generate	generate	VERB
ap-1364	126	30	a	a	DET
ap-1364	126	31	path	path	NOUN
ap-1364	126	32	�	�	PROPN
ap-1364	126	33	of	of	ADP
ap-1364	126	34	a	a	DET
ap-1364	126	35	spanning	span	VERB
ap-1364	126	36	tree	tree	NOUN
ap-1364	126	37	from	from	ADP
ap-1364	126	38	i0	i0	PROPN
ap-1364	126	39	to	to	ADP
ap-1364	126	40	the	the	DET
ap-1364	126	41	boundary	boundary	NOUN
ap-1364	126	42	(	(	PUNCT
ap-1364	126	43	see	see	VERB
ap-1364	126	44	also	also	ADV
ap-1364	126	45	[	[	X
ap-1364	126	46	7	7	NUM
ap-1364	126	47	,	,	PUNCT
ap-1364	126	48	8	8	NUM
ap-1364	126	49	]	]	NUM
ap-1364	126	50	)	)	PUNCT
ap-1364	126	51	.	.	PUNCT
ap-1364	127	1	all	all	DET
ap-1364	127	2	vertices	vertice	VERB
ap-1364	127	3	on	on	ADP
ap-1364	127	4	the	the	DET
ap-1364	127	5	path	path	NOUN
ap-1364	127	6	�	�	PROPN
ap-1364	127	7	form	form	VERB
ap-1364	127	8	the	the	DET
ap-1364	127	9	set	set	NOUN
ap-1364	127	10	of	of	ADP
ap-1364	127	11	descendants	descendant	NOUN
ap-1364	127	12	of	of	ADP
ap-1364	127	13	i0	i0	PROPN
ap-1364	127	14	.	.	PUNCT
ap-1364	128	1	so	so	ADV
ap-1364	128	2	,	,	PUNCT
ap-1364	128	3	if	if	SCONJ
ap-1364	128	4	a	a	DET
ap-1364	128	5	fixed	fix	VERB
ap-1364	128	6	vertex	vertex	NOUN
ap-1364	128	7	j0	j0	PROPN
ap-1364	128	8	belongs	belong	VERB
ap-1364	128	9	to	to	ADP
ap-1364	128	10	�	�	PROPN
ap-1364	128	11	,	,	PUNCT
ap-1364	128	12	i0	i0	PROPN
ap-1364	128	13	is	be	AUX
ap-1364	128	14	a	a	DET
ap-1364	128	15	predecessor	predecessor	NOUN
ap-1364	128	16	of	of	ADP
ap-1364	128	17	j0	j0	PROPN
ap-1364	128	18	.	.	PUNCT
ap-1364	129	1	consequently	consequently	ADV
ap-1364	129	2	,	,	PUNCT
ap-1364	129	3	the	the	DET
ap-1364	129	4	probability	probability	NOUN
ap-1364	129	5	p	p	X
ap-1364	129	6	(	(	PUNCT
ap-1364	129	7	j0−	j0−	PROPN
ap-1364	129	8	i0	i0	PROPN
ap-1364	129	9	)	)	PUNCT
ap-1364	129	10	that	that	SCONJ
ap-1364	129	11	i0	i0	PROPN
ap-1364	129	12	is	be	AUX
ap-1364	129	13	a	a	DET
ap-1364	129	14	predecessor	predecessor	NOUN
ap-1364	129	15	of	of	ADP
ap-1364	129	16	j0	j0	PROPN
ap-1364	129	17	in	in	ADP
ap-1364	129	18	a	a	DET
ap-1364	129	19	randomly	randomly	ADV
ap-1364	129	20	taken	take	VERB
ap-1364	129	21	(	(	PUNCT
ap-1364	129	22	from	from	ADP
ap-1364	129	23	the	the	DET
ap-1364	129	24	uniform	uniform	ADJ
ap-1364	129	25	distribution	distribution	NOUN
ap-1364	129	26	)	)	PUNCT
ap-1364	129	27	spanning	span	VERB
ap-1364	129	28	tree	tree	NOUN
ap-1364	129	29	on	on	ADP
ap-1364	129	30	the	the	DET
ap-1364	129	31	large	large	ADJ
ap-1364	129	32	square	square	ADJ
ap-1364	129	33	lattice	lattice	NOUN
ap-1364	129	34	is	be	AUX
ap-1364	129	35	equal	equal	ADJ
ap-1364	129	36	to	to	ADP
ap-1364	129	37	the	the	DET
ap-1364	129	38	probability	probability	NOUN
ap-1364	129	39	that	that	SCONJ
ap-1364	129	40	the	the	DET
ap-1364	129	41	lerw	lerw	NOUN
ap-1364	129	42	started	start	VERB
ap-1364	129	43	from	from	ADP
ap-1364	129	44	i0	i0	PROPN
ap-1364	129	45	passes	pass	VERB
ap-1364	129	46	j0	j0	PROPN
ap-1364	129	47	.	.	PUNCT
ap-1364	130	1	in	in	ADP
ap-1364	130	2	the	the	DET
ap-1364	130	3	particular	particular	ADJ
ap-1364	130	4	case	case	NOUN
ap-1364	130	5	|j0	|j0	ADP
ap-1364	130	6	−	−	PROPN
ap-1364	130	7	i0|	i0|	SYM
ap-1364	131	1	=	=	NOUN
ap-1364	131	2	1	1	NUM
ap-1364	131	3	,	,	PUNCT
ap-1364	131	4	the	the	DET
ap-1364	131	5	probability	probability	NOUN
ap-1364	132	1	p	p	X
ap-1364	132	2	(	(	PUNCT
ap-1364	132	3	1	1	NUM
ap-1364	132	4	)	)	PUNCT
ap-1364	132	5	=	=	NOUN
ap-1364	132	6	5/16	5/16	NUM
ap-1364	132	7	calculated	calculate	VERB
ap-1364	132	8	in	in	ADP
ap-1364	132	9	the	the	DET
ap-1364	132	10	previous	previous	ADJ
ap-1364	132	11	section	section	NOUN
ap-1364	132	12	is	be	AUX
ap-1364	132	13	the	the	DET
ap-1364	132	14	return	return	NOUN
ap-1364	132	15	probability	probability	NOUN
ap-1364	132	16	for	for	ADP
ap-1364	132	17	the	the	DET
ap-1364	132	18	lerw	lerw	NOUN
ap-1364	132	19	.	.	PUNCT
ap-1364	133	1	4	4	NUM
ap-1364	133	2	monte	monte	PROPN
ap-1364	133	3	-	-	PUNCT
ap-1364	133	4	carlo	carlo	PROPN
ap-1364	133	5	simulations	simulation	NOUN
ap-1364	133	6	consider	consider	VERB
ap-1364	133	7	the	the	DET
ap-1364	133	8	finite	finite	NOUN
ap-1364	133	9	2n	2n	NUM
ap-1364	133	10	+	+	CCONJ
ap-1364	133	11	1	1	NUM
ap-1364	133	12	×	×	NOUN
ap-1364	133	13	2n	2n	NUM
ap-1364	133	14	+	+	CCONJ
ap-1364	133	15	1	1	NUM
ap-1364	133	16	square	square	ADJ
ap-1364	133	17	lattice	lattice	NOUN
ap-1364	133	18	ln	ln	ADV
ap-1364	133	19	.	.	PUNCT
ap-1364	134	1	denote	denote	VERB
ap-1364	134	2	its	its	PRON
ap-1364	134	3	central	central	ADJ
ap-1364	134	4	vertex	vertex	NOUN
ap-1364	134	5	by	by	ADP
ap-1364	134	6	i0	i0	PROPN
ap-1364	134	7	and	and	CCONJ
ap-1364	134	8	assume	assume	VERB
ap-1364	134	9	that	that	SCONJ
ap-1364	134	10	it	it	PRON
ap-1364	134	11	is	be	AUX
ap-1364	134	12	an	an	DET
ap-1364	134	13	origin	origin	NOUN
ap-1364	134	14	of	of	ADP
ap-1364	134	15	the	the	DET
ap-1364	134	16	coordinate	coordinate	NOUN
ap-1364	134	17	system	system	NOUN
ap-1364	134	18	.	.	PUNCT
ap-1364	135	1	we	we	PRON
ap-1364	135	2	deliberately	deliberately	ADV
ap-1364	135	3	took	take	VERB
ap-1364	135	4	an	an	DET
ap-1364	135	5	odd	odd	ADJ
ap-1364	135	6	-	-	PUNCT
ap-1364	135	7	odd	odd	ADJ
ap-1364	135	8	lattice	lattice	NOUN
ap-1364	135	9	to	to	PART
ap-1364	135	10	provide	provide	VERB
ap-1364	135	11	the	the	DET
ap-1364	135	12	symmetry	symmetry	NOUN
ap-1364	135	13	which	which	PRON
ap-1364	135	14	guarantees	guarantee	VERB
ap-1364	135	15	the	the	DET
ap-1364	135	16	most	most	ADV
ap-1364	135	17	efficient	efficient	ADJ
ap-1364	135	18	vanishing	vanishing	NOUN
ap-1364	135	19	of	of	ADP
ap-1364	135	20	the	the	DET
ap-1364	135	21	boundary	boundary	ADJ
ap-1364	135	22	effects	effect	NOUN
ap-1364	135	23	for	for	ADP
ap-1364	135	24	large	large	ADJ
ap-1364	135	25	lattices	lattice	NOUN
ap-1364	135	26	.	.	PUNCT
ap-1364	136	1	after	after	ADP
ap-1364	136	2	generating	generate	VERB
ap-1364	136	3	a	a	DET
ap-1364	136	4	large	large	ADJ
ap-1364	136	5	number	number	NOUN
ap-1364	136	6	of	of	ADP
ap-1364	136	7	lerws	lerws	NOUN
ap-1364	136	8	starting	start	VERB
ap-1364	136	9	from	from	ADP
ap-1364	136	10	i0	i0	PROPN
ap-1364	136	11	,	,	PUNCT
ap-1364	136	12	we	we	PRON
ap-1364	136	13	get	get	VERB
ap-1364	136	14	an	an	DET
ap-1364	136	15	approximation	approximation	NOUN
ap-1364	136	16	of	of	ADP
ap-1364	136	17	the	the	DET
ap-1364	136	18	function	function	NOUN
ap-1364	136	19	pn	pn	PROPN
ap-1364	136	20	(	(	PUNCT
ap-1364	136	21	j0−	j0−	PROPN
ap-1364	136	22	i0	i0	PROPN
ap-1364	136	23	)	)	PUNCT
ap-1364	136	24	≡	≡	PROPN
ap-1364	136	25	pn	pn	PROPN
ap-1364	136	26	(	(	PUNCT
ap-1364	136	27	j0	j0	PROPN
ap-1364	136	28	)	)	PUNCT
ap-1364	136	29	.	.	PUNCT
ap-1364	137	1	given	give	VERB
ap-1364	137	2	fixed	fix	VERB
ap-1364	137	3	j0	j0	PROPN
ap-1364	137	4	,	,	PUNCT
ap-1364	137	5	we	we	PRON
ap-1364	137	6	can	can	AUX
ap-1364	137	7	extrapolate	extrapolate	VERB
ap-1364	137	8	pn	pn	PROPN
ap-1364	137	9	(	(	PUNCT
ap-1364	137	10	j0	j0	PROPN
ap-1364	137	11	)	)	PUNCT
ap-1364	137	12	,	,	PUNCT
ap-1364	137	13	tending	tend	VERB
ap-1364	137	14	n	n	ADV
ap-1364	137	15	to	to	PART
ap-1364	137	16	infinity	infinity	VERB
ap-1364	137	17	and	and	CCONJ
ap-1364	137	18	get	get	VERB
ap-1364	137	19	asymptotical	asymptotical	ADJ
ap-1364	137	20	function	function	NOUN
ap-1364	137	21	p	p	PROPN
ap-1364	137	22	(	(	PUNCT
ap-1364	137	23	j0	j0	PROPN
ap-1364	137	24	)	)	PUNCT
ap-1364	137	25	.	.	PUNCT
ap-1364	138	1	assume	assume	VERB
ap-1364	138	2	that	that	SCONJ
ap-1364	138	3	the	the	DET
ap-1364	138	4	euclidean	euclidean	ADJ
ap-1364	138	5	distance	distance	NOUN
ap-1364	138	6	between	between	ADP
ap-1364	138	7	the	the	DET
ap-1364	138	8	origin	origin	NOUN
ap-1364	138	9	i0	i0	PROPN
ap-1364	138	10	and	and	CCONJ
ap-1364	138	11	j0	j0	PROPN
ap-1364	138	12	is	be	AUX
ap-1364	138	13	r	r	NOUN
ap-1364	138	14	and	and	CCONJ
ap-1364	138	15	the	the	DET
ap-1364	138	16	coordinates	coordinate	NOUN
ap-1364	138	17	of	of	ADP
ap-1364	138	18	j0	j0	PROPN
ap-1364	138	19	are	be	AUX
ap-1364	138	20	(	(	PUNCT
ap-1364	138	21	r	r	NOUN
ap-1364	138	22	cosϕ	cosϕ	NOUN
ap-1364	138	23	,	,	PUNCT
ap-1364	138	24	r	r	NOUN
ap-1364	138	25	sinϕ	sinϕ	NOUN
ap-1364	138	26	)	)	PUNCT
ap-1364	138	27	.	.	PUNCT
ap-1364	139	1	the	the	DET
ap-1364	139	2	monte	monte	PROPN
ap-1364	139	3	-	-	PUNCT
ap-1364	139	4	carlo	carlo	PROPN
ap-1364	139	5	simulations	simulation	NOUN
ap-1364	139	6	and	and	CCONJ
ap-1364	139	7	coulomb	coulomb	NOUN
ap-1364	139	8	gas	gas	NOUN
ap-1364	139	9	arguments	argument	NOUN
ap-1364	139	10	show	show	VERB
ap-1364	139	11	that	that	SCONJ
ap-1364	139	12	the	the	DET
ap-1364	139	13	asymptotical	asymptotical	ADJ
ap-1364	139	14	behaviour	behaviour	NOUN
ap-1364	139	15	of	of	ADP
ap-1364	139	16	the	the	DET
ap-1364	139	17	function	function	NOUN
ap-1364	139	18	p	p	PROPN
ap-1364	139	19	(	(	PUNCT
ap-1364	139	20	j0	j0	PROPN
ap-1364	139	21	)	)	PUNCT
ap-1364	139	22	for	for	ADP
ap-1364	139	23	large	large	ADJ
ap-1364	139	24	r	r	NOUN
ap-1364	139	25	(	(	PUNCT
ap-1364	139	26	r	r	NOUN
ap-1364	139	27	�	�	PROPN
ap-1364	139	28	1	1	NUM
ap-1364	139	29	)	)	PUNCT
ap-1364	139	30	does	do	AUX
ap-1364	139	31	not	not	PART
ap-1364	139	32	depend	depend	VERB
ap-1364	139	33	on	on	ADP
ap-1364	139	34	ϕ.	ϕ.	PROPN
ap-1364	139	35	so	so	ADV
ap-1364	139	36	,	,	PUNCT
ap-1364	139	37	for	for	ADP
ap-1364	139	38	r	r	PROPN
ap-1364	139	39	�	�	PROPN
ap-1364	139	40	1	1	NUM
ap-1364	139	41	we	we	PRON
ap-1364	139	42	have	have	VERB
ap-1364	139	43	p	p	PROPN
ap-1364	139	44	(	(	PUNCT
ap-1364	139	45	j0	j0	PROPN
ap-1364	139	46	)	)	PUNCT
ap-1364	139	47	�	�	PROPN
ap-1364	139	48	p	p	NOUN
ap-1364	139	49	(	(	PUNCT
ap-1364	139	50	r	r	NOUN
ap-1364	139	51	)	)	PUNCT
ap-1364	139	52	.	.	PUNCT
ap-1364	140	1	fig	fig	NOUN
ap-1364	140	2	.	.	PUNCT
ap-1364	141	1	2	2	NUM
ap-1364	141	2	shows	show	VERB
ap-1364	141	3	the	the	DET
ap-1364	141	4	behaviour	behaviour	NOUN
ap-1364	141	5	of	of	ADP
ap-1364	141	6	p	p	X
ap-1364	141	7	(	(	PUNCT
ap-1364	141	8	r	r	NOUN
ap-1364	141	9	)	)	PUNCT
ap-1364	141	10	for	for	ADP
ap-1364	141	11	various	various	ADJ
ap-1364	141	12	j0	j0	PROPN
ap-1364	141	13	on	on	ADP
ap-1364	141	14	the	the	DET
ap-1364	141	15	log	log	NOUN
ap-1364	141	16	-	-	PUNCT
ap-1364	141	17	log	log	NOUN
ap-1364	141	18	scale	scale	NOUN
ap-1364	141	19	,	,	PUNCT
ap-1364	141	20	obtained	obtain	VERB
ap-1364	141	21	from	from	ADP
ap-1364	141	22	monte	monte	PROPN
ap-1364	141	23	-	-	PUNCT
ap-1364	141	24	carlo	carlo	NOUN
ap-1364	141	25	simulations	simulation	NOUN
ap-1364	141	26	.	.	PUNCT
ap-1364	142	1	from	from	ADP
ap-1364	142	2	this	this	DET
ap-1364	142	3	result	result	NOUN
ap-1364	142	4	we	we	PRON
ap-1364	142	5	conclude	conclude	VERB
ap-1364	142	6	that	that	SCONJ
ap-1364	142	7	p	p	X
ap-1364	142	8	(	(	PUNCT
ap-1364	142	9	r	r	NOUN
ap-1364	142	10	)	)	PUNCT
ap-1364	142	11	decreases	decrease	NOUN
ap-1364	142	12	as	as	ADP
ap-1364	142	13	a	a	DET
ap-1364	142	14	power	power	NOUN
ap-1364	142	15	function	function	NOUN
ap-1364	142	16	:	:	PUNCT
ap-1364	142	17	p	p	X
ap-1364	142	18	(	(	PUNCT
ap-1364	142	19	r	r	NOUN
ap-1364	142	20	)	)	PUNCT
ap-1364	142	21	�	�	PROPN
ap-1364	143	1	c	c	PROPN
ap-1364	143	2	rα	rα	INTJ
ap-1364	143	3	,	,	PUNCT
ap-1364	143	4	(	(	PUNCT
ap-1364	143	5	4.6	4.6	NUM
ap-1364	143	6	)	)	PUNCT
ap-1364	143	7	fig	fig	NOUN
ap-1364	143	8	.	.	PUNCT
ap-1364	144	1	2	2	NUM
ap-1364	144	2	:	:	PUNCT
ap-1364	144	3	the	the	DET
ap-1364	144	4	results	result	NOUN
ap-1364	144	5	of	of	ADP
ap-1364	144	6	monte	monte	PROPN
ap-1364	144	7	-	-	PUNCT
ap-1364	144	8	carlo	carlo	NOUN
ap-1364	144	9	simulations	simulation	NOUN
ap-1364	144	10	for	for	ADP
ap-1364	144	11	the	the	DET
ap-1364	144	12	probability	probability	NOUN
ap-1364	144	13	p	p	X
ap-1364	144	14	(	(	PUNCT
ap-1364	144	15	r	r	NOUN
ap-1364	144	16	)	)	PUNCT
ap-1364	144	17	61	61	NUM
ap-1364	144	18	acta	acta	PROPN
ap-1364	144	19	polytechnica	polytechnica	PROPN
ap-1364	144	20	vol	vol	NOUN
ap-1364	144	21	.	.	PUNCT
ap-1364	145	1	51	51	NUM
ap-1364	145	2	no	no	NOUN
ap-1364	145	3	.	.	PUNCT
ap-1364	146	1	1/2011	1/2011	NUM
ap-1364	146	2	with	with	ADP
ap-1364	146	3	α	α	NOUN
ap-1364	146	4	≈	≈	PROPN
ap-1364	146	5	0.751	0.751	NUM
ap-1364	146	6	and	and	CCONJ
ap-1364	146	7	c	c	PROPN
ap-1364	146	8	≈	≈	PROPN
ap-1364	146	9	0.305	0.305	NUM
ap-1364	146	10	.	.	PUNCT
ap-1364	147	1	during	during	ADP
ap-1364	147	2	the	the	DET
ap-1364	147	3	simulations	simulation	NOUN
ap-1364	147	4	,	,	PUNCT
ap-1364	147	5	we	we	PRON
ap-1364	147	6	took	take	VERB
ap-1364	147	7	sizes	size	NOUN
ap-1364	147	8	up	up	ADP
ap-1364	147	9	to	to	ADP
ap-1364	147	10	n	n	NOUN
ap-1364	147	11	=	=	SYM
ap-1364	147	12	100	100	NUM
ap-1364	147	13	and	and	CCONJ
ap-1364	147	14	number	number	NOUN
ap-1364	147	15	of	of	ADP
ap-1364	147	16	simulations	simulation	NOUN
ap-1364	147	17	108	108	NUM
ap-1364	147	18	.	.	PUNCT
ap-1364	148	1	the	the	DET
ap-1364	148	2	obtained	obtain	VERB
ap-1364	148	3	results	result	NOUN
ap-1364	148	4	are	be	AUX
ap-1364	148	5	in	in	ADP
ap-1364	148	6	agreement	agreement	NOUN
ap-1364	148	7	with	with	ADP
ap-1364	148	8	α	α	PROPN
ap-1364	148	9	=	=	SYM
ap-1364	148	10	3/4	3/4	NUM
ap-1364	148	11	,	,	PUNCT
ap-1364	148	12	which	which	PRON
ap-1364	148	13	follows	follow	VERB
ap-1364	148	14	from	from	ADP
ap-1364	148	15	the	the	DET
ap-1364	148	16	coulomb	coulomb	NOUN
ap-1364	148	17	gas	gas	NOUN
ap-1364	148	18	arguments	argument	NOUN
ap-1364	148	19	mentioned	mention	VERB
ap-1364	148	20	above	above	ADV
ap-1364	148	21	.	.	PUNCT
ap-1364	149	1	the	the	DET
ap-1364	149	2	effective	effective	ADJ
ap-1364	149	3	monte	monte	PROPN
ap-1364	149	4	-	-	PUNCT
ap-1364	149	5	carlo	carlo	NOUN
ap-1364	149	6	algorithm	algorithm	NOUN
ap-1364	149	7	allows	allow	VERB
ap-1364	149	8	the	the	DET
ap-1364	149	9	evaluation	evaluation	NOUN
ap-1364	149	10	of	of	ADP
ap-1364	149	11	probabilities	probability	NOUN
ap-1364	149	12	p	p	X
ap-1364	149	13	(	(	PUNCT
ap-1364	149	14	j0	j0	PROPN
ap-1364	149	15	−	−	PROPN
ap-1364	149	16	i0	i0	PROPN
ap-1364	149	17	)	)	PUNCT
ap-1364	149	18	for	for	ADP
ap-1364	149	19	arbitrary	arbitrary	ADJ
ap-1364	149	20	finite	finite	PROPN
ap-1364	149	21	j0	j0	PROPN
ap-1364	149	22	,	,	PUNCT
ap-1364	149	23	i0	i0	PROPN
ap-1364	149	24	.	.	PUNCT
ap-1364	150	1	at	at	ADP
ap-1364	150	2	the	the	DET
ap-1364	150	3	same	same	ADJ
ap-1364	150	4	time	time	NOUN
ap-1364	150	5	,	,	PUNCT
ap-1364	150	6	the	the	DET
ap-1364	150	7	analytical	analytical	ADJ
ap-1364	150	8	calculation	calculation	NOUN
ap-1364	150	9	of	of	ADP
ap-1364	150	10	p	p	NOUN
ap-1364	150	11	(	(	PUNCT
ap-1364	150	12	r	r	NOUN
ap-1364	150	13	)	)	PUNCT
ap-1364	150	14	for	for	ADP
ap-1364	150	15	r	r	NOUN
ap-1364	150	16	>	>	SYM
ap-1364	150	17	1	1	NUM
ap-1364	150	18	remains	remain	VERB
ap-1364	150	19	a	a	DET
ap-1364	150	20	difficult	difficult	ADJ
ap-1364	150	21	unsolved	unsolved	ADJ
ap-1364	150	22	problem	problem	NOUN
ap-1364	150	23	.	.	PUNCT
ap-1364	151	1	acknowledgement	acknowledgement	NOUN
ap-1364	151	2	this	this	DET
ap-1364	151	3	work	work	NOUN
ap-1364	151	4	was	be	AUX
ap-1364	151	5	supported	support	VERB
ap-1364	151	6	by	by	ADP
ap-1364	151	7	russian	russian	ADJ
ap-1364	151	8	rfbr	rfbr	PROPN
ap-1364	151	9	grant	grant	VERB
ap-1364	151	10	no	no	INTJ
ap-1364	151	11	.	.	NOUN
ap-1364	151	12	09	09	NUM
ap-1364	151	13	-	-	PUNCT
ap-1364	151	14	01	01	NUM
ap-1364	151	15	-	-	PUNCT
ap-1364	151	16	00271a	00271a	NUM
ap-1364	151	17	,	,	PUNCT
ap-1364	151	18	and	and	CCONJ
ap-1364	151	19	by	by	ADP
ap-1364	151	20	the	the	DET
ap-1364	151	21	belgian	belgian	ADJ
ap-1364	151	22	interuniversity	interuniversity	NOUN
ap-1364	151	23	attraction	attraction	NOUN
ap-1364	151	24	poles	pole	NOUN
ap-1364	151	25	program	program	NOUN
ap-1364	151	26	p6/02	p6/02	NOUN
ap-1364	151	27	,	,	PUNCT
ap-1364	151	28	through	through	ADP
ap-1364	151	29	the	the	DET
ap-1364	151	30	nosy	nosy	ADJ
ap-1364	151	31	(	(	PUNCT
ap-1364	151	32	nonlinear	nonlinear	ADJ
ap-1364	151	33	systems	system	NOUN
ap-1364	151	34	,	,	PUNCT
ap-1364	151	35	stochastic	stochastic	NOUN
ap-1364	151	36	processes	process	NOUN
ap-1364	151	37	and	and	CCONJ
ap-1364	151	38	statistical	statistical	ADJ
ap-1364	151	39	mechanics	mechanic	NOUN
ap-1364	151	40	)	)	PUNCT
ap-1364	151	41	network	network	NOUN
ap-1364	151	42	.	.	PUNCT
ap-1364	152	1	we	we	PRON
ap-1364	152	2	would	would	AUX
ap-1364	152	3	like	like	VERB
ap-1364	152	4	to	to	PART
ap-1364	152	5	thank	thank	VERB
ap-1364	152	6	p.	p.	NOUN
ap-1364	152	7	ruelle	ruelle	NOUN
ap-1364	152	8	for	for	ADP
ap-1364	152	9	helpful	helpful	ADJ
ap-1364	152	10	discussions	discussion	NOUN
ap-1364	152	11	.	.	PUNCT
ap-1364	153	1	the	the	DET
ap-1364	153	2	montecarlo	montecarlo	PROPN
ap-1364	153	3	simulations	simulation	NOUN
ap-1364	153	4	were	be	AUX
ap-1364	153	5	performed	perform	VERB
ap-1364	153	6	on	on	ADP
ap-1364	153	7	armenian	armenian	ADJ
ap-1364	153	8	cluster	cluster	NOUN
ap-1364	153	9	for	for	ADP
ap-1364	153	10	high	high	ADJ
ap-1364	153	11	performance	performance	NOUN
ap-1364	153	12	computation	computation	NOUN
ap-1364	153	13	(	(	PUNCT
ap-1364	153	14	armcluster	armcluster	NOUN
ap-1364	153	15	,	,	PUNCT
ap-1364	153	16	http://www.cluster.am	http://www.cluster.am	PROPN
ap-1364	153	17	)	)	PUNCT
ap-1364	153	18	.	.	PUNCT
ap-1364	154	1	references	reference	NOUN
ap-1364	154	2	[	[	X
ap-1364	154	3	1	1	NUM
ap-1364	154	4	]	]	SYM
ap-1364	154	5	wu	wu	PROPN
ap-1364	154	6	,	,	PUNCT
ap-1364	154	7	f.	f.	PROPN
ap-1364	154	8	y.	y.	PROPN
ap-1364	154	9	:	:	PUNCT
ap-1364	154	10	rev	rev	PROPN
ap-1364	154	11	.	.	PROPN
ap-1364	155	1	mod	mod	PROPN
ap-1364	155	2	.	.	PUNCT
ap-1364	156	1	phys	phy	NOUN
ap-1364	156	2	.	.	PUNCT
ap-1364	157	1	54	54	NUM
ap-1364	157	2	(	(	PUNCT
ap-1364	157	3	1982	1982	NUM
ap-1364	157	4	)	)	PUNCT
ap-1364	157	5	,	,	PUNCT
ap-1364	157	6	235–268	235–268	NUM
ap-1364	157	7	.	.	PUNCT
ap-1364	158	1	[	[	X
ap-1364	158	2	2	2	NUM
ap-1364	158	3	]	]	X
ap-1364	158	4	fisher	fisher	PROPN
ap-1364	158	5	,	,	PUNCT
ap-1364	158	6	m.	m.	PROPN
ap-1364	158	7	e.	e.	PROPN
ap-1364	158	8	,	,	PUNCT
ap-1364	158	9	stephenson	stephenson	PROPN
ap-1364	158	10	,	,	PUNCT
ap-1364	158	11	j.	j.	PROPN
ap-1364	158	12	:	:	PUNCT
ap-1364	158	13	phys	phy	NOUN
ap-1364	158	14	.	.	PUNCT
ap-1364	158	15	rev	rev	PROPN
ap-1364	158	16	.	.	PROPN
ap-1364	158	17	132	132	NUM
ap-1364	158	18	(	(	PUNCT
ap-1364	158	19	1963	1963	NUM
ap-1364	158	20	)	)	PUNCT
ap-1364	158	21	,	,	PUNCT
ap-1364	158	22	1	1	NUM
ap-1364	158	23	411–1431	411–1431	NUM
ap-1364	158	24	.	.	PUNCT
ap-1364	159	1	[	[	X
ap-1364	159	2	3	3	X
ap-1364	159	3	]	]	X
ap-1364	159	4	bak	bak	NOUN
ap-1364	159	5	,	,	PUNCT
ap-1364	159	6	p.	p.	PROPN
ap-1364	159	7	,	,	PUNCT
ap-1364	159	8	tang	tang	PROPN
ap-1364	159	9	,	,	PUNCT
ap-1364	159	10	c.	c.	PROPN
ap-1364	159	11	,	,	PUNCT
ap-1364	159	12	wiesenfeld	wiesenfeld	VERB
ap-1364	159	13	,	,	PUNCT
ap-1364	159	14	k.	k.	PROPN
ap-1364	159	15	:	:	PUNCT
ap-1364	160	1	phys	phy	NOUN
ap-1364	160	2	.	.	PUNCT
ap-1364	161	1	rev	rev	PROPN
ap-1364	161	2	.	.	PROPN
ap-1364	161	3	lett	lett	PROPN
ap-1364	161	4	.	.	PUNCT
ap-1364	162	1	59	59	NUM
ap-1364	162	2	(	(	PUNCT
ap-1364	162	3	1987	1987	NUM
ap-1364	162	4	)	)	PUNCT
ap-1364	162	5	,	,	PUNCT
ap-1364	162	6	381	381	NUM
ap-1364	162	7	;	;	PUNCT
ap-1364	162	8	dhar	dhar	PROPN
ap-1364	162	9	,	,	PUNCT
ap-1364	162	10	d.	d.	PROPN
ap-1364	162	11	:	:	PUNCT
ap-1364	162	12	phys	phy	NOUN
ap-1364	162	13	.	.	PUNCT
ap-1364	163	1	rev	rev	PROPN
ap-1364	163	2	.	.	PROPN
ap-1364	163	3	lett	lett	PROPN
ap-1364	163	4	.	.	PUNCT
ap-1364	164	1	64	64	NUM
ap-1364	164	2	(	(	PUNCT
ap-1364	164	3	1990	1990	NUM
ap-1364	164	4	)	)	PUNCT
ap-1364	164	5	,	,	PUNCT
ap-1364	164	6	1	1	NUM
ap-1364	164	7	613	613	NUM
ap-1364	164	8	;	;	PUNCT
ap-1364	164	9	priezzhev	priezzhev	NOUN
ap-1364	164	10	,	,	PUNCT
ap-1364	164	11	v.	v.	PROPN
ap-1364	164	12	b.	b.	PROPN
ap-1364	164	13	,	,	PUNCT
ap-1364	164	14	ktitarev	ktitarev	PROPN
ap-1364	164	15	,	,	PUNCT
ap-1364	164	16	d.	d.	PROPN
ap-1364	164	17	v.	v.	PROPN
ap-1364	164	18	,	,	PUNCT
ap-1364	164	19	ivashkevich	ivashkevich	PROPN
ap-1364	164	20	,	,	PUNCT
ap-1364	164	21	e.	e.	PROPN
ap-1364	164	22	v.	v.	PROPN
ap-1364	164	23	:	:	PUNCT
ap-1364	164	24	phys	phy	NOUN
ap-1364	164	25	.	.	PUNCT
ap-1364	165	1	rev	rev	PROPN
ap-1364	165	2	.	.	PROPN
ap-1364	165	3	lett	lett	PROPN
ap-1364	165	4	.	.	PUNCT
ap-1364	166	1	76	76	NUM
ap-1364	166	2	(	(	PUNCT
ap-1364	166	3	1996	1996	NUM
ap-1364	166	4	)	)	PUNCT
ap-1364	166	5	,	,	PUNCT
ap-1364	166	6	2	2	NUM
ap-1364	166	7	093	093	NUM
ap-1364	166	8	;	;	PUNCT
ap-1364	166	9	ivashkevich	ivashkevich	NOUN
ap-1364	166	10	,	,	PUNCT
ap-1364	166	11	e.	e.	PROPN
ap-1364	166	12	v.	v.	PROPN
ap-1364	166	13	:	:	PUNCT
ap-1364	166	14	phys	phy	NOUN
ap-1364	166	15	.	.	PUNCT
ap-1364	167	1	rev	rev	PROPN
ap-1364	167	2	.	.	PROPN
ap-1364	167	3	lett	lett	PROPN
ap-1364	167	4	.	.	PUNCT
ap-1364	168	1	76	76	NUM
ap-1364	168	2	(	(	PUNCT
ap-1364	168	3	1996	1996	NUM
ap-1364	168	4	)	)	PUNCT
ap-1364	168	5	,	,	PUNCT
ap-1364	168	6	3	3	NUM
ap-1364	168	7	368	368	NUM
ap-1364	168	8	;	;	PUNCT
ap-1364	168	9	hu	hu	PROPN
ap-1364	168	10	,	,	PUNCT
ap-1364	168	11	c.-k	c.-k	PROPN
ap-1364	168	12	.	.	PUNCT
ap-1364	168	13	,	,	PUNCT
ap-1364	168	14	et	et	PROPN
ap-1364	168	15	al	al	PROPN
ap-1364	168	16	.	.	PUNCT
ap-1364	168	17	:	:	PUNCT
ap-1364	169	1	phys	phy	NOUN
ap-1364	169	2	.	.	PUNCT
ap-1364	170	1	rev	rev	PROPN
ap-1364	170	2	.	.	PROPN
ap-1364	170	3	lett	lett	PROPN
ap-1364	170	4	.	.	PROPN
ap-1364	170	5	85	85	NUM
ap-1364	170	6	(	(	PUNCT
ap-1364	170	7	2000	2000	NUM
ap-1364	170	8	)	)	PUNCT
ap-1364	170	9	,	,	PUNCT
ap-1364	170	10	4	4	NUM
ap-1364	170	11	048	048	NUM
ap-1364	170	12	.	.	PUNCT
ap-1364	171	1	[	[	X
ap-1364	171	2	4	4	NUM
ap-1364	171	3	]	]	X
ap-1364	171	4	fortuin	fortuin	ADJ
ap-1364	171	5	,	,	PUNCT
ap-1364	171	6	c.	c.	PROPN
ap-1364	171	7	m.	m.	NOUN
ap-1364	171	8	,	,	PUNCT
ap-1364	171	9	kasteleyn	kasteleyn	PROPN
ap-1364	171	10	,	,	PUNCT
ap-1364	171	11	p.	p.	PROPN
ap-1364	171	12	w.	w.	PROPN
ap-1364	171	13	:	:	PUNCT
ap-1364	172	1	physica	physica	NOUN
ap-1364	172	2	,	,	PUNCT
ap-1364	172	3	57	57	NUM
ap-1364	172	4	,	,	PUNCT
ap-1364	172	5	4	4	NUM
ap-1364	172	6	(	(	PUNCT
ap-1364	172	7	1972	1972	NUM
ap-1364	172	8	)	)	PUNCT
ap-1364	172	9	,	,	PUNCT
ap-1364	172	10	536–564	536–564	NUM
ap-1364	172	11	.	.	PUNCT
ap-1364	173	1	[	[	X
ap-1364	173	2	5	5	NUM
ap-1364	173	3	]	]	X
ap-1364	173	4	majumdar	majumdar	PROPN
ap-1364	173	5	,	,	PUNCT
ap-1364	173	6	s.	s.	PROPN
ap-1364	173	7	n.	n.	PROPN
ap-1364	173	8	,	,	PUNCT
ap-1364	173	9	dhar	dhar	PROPN
ap-1364	173	10	,	,	PUNCT
ap-1364	173	11	d.	d.	PROPN
ap-1364	173	12	:	:	PUNCT
ap-1364	173	13	j.	j.	PROPN
ap-1364	173	14	phys	phys	PROPN
ap-1364	173	15	.	.	PUNCT
ap-1364	174	1	a	a	DET
ap-1364	174	2	:	:	PUNCT
ap-1364	174	3	math	math	NOUN
ap-1364	174	4	.	.	PUNCT
ap-1364	175	1	gen	gen	PROPN
ap-1364	175	2	.	.	PROPN
ap-1364	175	3	24	24	NUM
ap-1364	175	4	(	(	PUNCT
ap-1364	175	5	1991	1991	NUM
ap-1364	175	6	)	)	PUNCT
ap-1364	175	7	,	,	PUNCT
ap-1364	175	8	l357	l357	PROPN
ap-1364	175	9	.	.	PUNCT
ap-1364	176	1	[	[	X
ap-1364	176	2	6	6	NUM
ap-1364	176	3	]	]	X
ap-1364	176	4	majumdar	majumdar	PROPN
ap-1364	176	5	,	,	PUNCT
ap-1364	176	6	s.	s.	PROPN
ap-1364	176	7	n.	n.	PROPN
ap-1364	176	8	,	,	PUNCT
ap-1364	176	9	dhar	dhar	PROPN
ap-1364	176	10	,	,	PUNCT
ap-1364	176	11	d.	d.	PROPN
ap-1364	176	12	:	:	PUNCT
ap-1364	176	13	physica	physica	VERB
ap-1364	176	14	a	a	DET
ap-1364	176	15	185	185	NUM
ap-1364	176	16	(	(	PUNCT
ap-1364	176	17	1992	1992	NUM
ap-1364	176	18	)	)	PUNCT
ap-1364	176	19	,	,	PUNCT
ap-1364	176	20	129	129	NUM
ap-1364	176	21	.	.	PUNCT
ap-1364	177	1	[	[	X
ap-1364	177	2	7	7	NUM
ap-1364	177	3	]	]	X
ap-1364	177	4	majumdar	majumdar	PROPN
ap-1364	177	5	,	,	PUNCT
ap-1364	177	6	s.	s.	PROPN
ap-1364	177	7	n.	n.	PROPN
ap-1364	177	8	:	:	PUNCT
ap-1364	177	9	phys	phy	NOUN
ap-1364	177	10	.	.	PUNCT
ap-1364	177	11	rev	rev	PROPN
ap-1364	177	12	.	.	PROPN
ap-1364	177	13	lett	lett	PROPN
ap-1364	177	14	.	.	PUNCT
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ap-1364	178	2	(	(	PUNCT
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ap-1364	178	4	)	)	PUNCT
ap-1364	178	5	,	,	PUNCT
ap-1364	178	6	2	2	NUM
ap-1364	178	7	329–2	329–2	NUM
ap-1364	178	8	331	331	NUM
ap-1364	178	9	.	.	PUNCT
ap-1364	179	1	[	[	X
ap-1364	179	2	8	8	NUM
ap-1364	179	3	]	]	X
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ap-1364	179	5	,	,	PUNCT
ap-1364	179	6	g.	g.	PROPN
ap-1364	179	7	f.	f.	PROPN
ap-1364	179	8	,	,	PUNCT
ap-1364	179	9	schramm	schramm	PROPN
ap-1364	179	10	,	,	PUNCT
ap-1364	179	11	o.	o.	PROPN
ap-1364	179	12	,	,	PUNCT
ap-1364	179	13	werner	werner	PROPN
ap-1364	179	14	,	,	PUNCT
ap-1364	179	15	w.	w.	PROPN
ap-1364	179	16	:	:	PUNCT
ap-1364	179	17	annals	annal	NOUN
ap-1364	179	18	of	of	ADP
ap-1364	179	19	prob	prob	NOUN
ap-1364	179	20	.	.	PROPN
ap-1364	179	21	32	32	NUM
ap-1364	179	22	,	,	PUNCT
ap-1364	179	23	1b	1b	NUM
ap-1364	179	24	(	(	PUNCT
ap-1364	179	25	2004	2004	NUM
ap-1364	179	26	)	)	PUNCT
ap-1364	179	27	,	,	PUNCT
ap-1364	179	28	939–995	939–995	NUM
ap-1364	179	29	.	.	PUNCT
ap-1364	180	1	[	[	X
ap-1364	180	2	9	9	NUM
ap-1364	180	3	]	]	SYM
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ap-1364	180	5	,	,	PUNCT
ap-1364	180	6	v.	v.	PROPN
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ap-1364	180	8	:	:	PUNCT
ap-1364	180	9	j.	j.	PROPN
ap-1364	180	10	stat	stat	PROPN
ap-1364	180	11	.	.	PUNCT
ap-1364	181	1	phys	phy	NOUN
ap-1364	181	2	.	.	PUNCT
ap-1364	182	1	74	74	NUM
ap-1364	182	2	(	(	PUNCT
ap-1364	182	3	1994	1994	NUM
ap-1364	182	4	)	)	PUNCT
ap-1364	182	5	,	,	PUNCT
ap-1364	182	6	955	955	NUM
ap-1364	182	7	.	.	PUNCT
ap-1364	183	1	[	[	X
ap-1364	183	2	10	10	NUM
ap-1364	183	3	]	]	X
ap-1364	183	4	mahieu	mahieu	PROPN
ap-1364	183	5	,	,	PUNCT
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ap-1364	183	7	,	,	PUNCT
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ap-1364	183	9	,	,	PUNCT
ap-1364	183	10	p.	p.	NOUN
ap-1364	183	11	:	:	PUNCT
ap-1364	184	1	phys	phy	NOUN
ap-1364	184	2	.	.	PUNCT
ap-1364	185	1	rev	rev	PROPN
ap-1364	185	2	.	.	PUNCT
ap-1364	186	1	e	e	PROPN
ap-1364	186	2	64	64	NUM
ap-1364	186	3	(	(	PUNCT
ap-1364	186	4	2001	2001	NUM
ap-1364	186	5	)	)	PUNCT
ap-1364	186	6	,	,	PUNCT
ap-1364	186	7	066130	066130	NUM
ap-1364	186	8	;	;	PUNCT
ap-1364	186	9	ruelle	ruelle	NOUN
ap-1364	186	10	,	,	PUNCT
ap-1364	186	11	p.	p.	NOUN
ap-1364	186	12	:	:	PUNCT
ap-1364	187	1	phys	phy	NOUN
ap-1364	187	2	.	.	PUNCT
ap-1364	188	1	lett	lett	PROPN
ap-1364	188	2	.	.	PUNCT
ap-1364	189	1	b	b	ADP
ap-1364	189	2	539	539	NUM
ap-1364	189	3	(	(	PUNCT
ap-1364	189	4	2002	2002	NUM
ap-1364	189	5	)	)	PUNCT
ap-1364	189	6	,	,	PUNCT
ap-1364	189	7	172	172	NUM
ap-1364	189	8	;	;	PUNCT
ap-1364	189	9	jeng	jeng	PROPN
ap-1364	189	10	,	,	PUNCT
ap-1364	189	11	m.	m.	NOUN
ap-1364	189	12	:	:	PUNCT
ap-1364	189	13	phys	phy	NOUN
ap-1364	189	14	.	.	PUNCT
ap-1364	190	1	rev	rev	PROPN
ap-1364	190	2	.	.	PUNCT
ap-1364	191	1	e	e	PROPN
ap-1364	191	2	69	69	NUM
ap-1364	191	3	(	(	PUNCT
ap-1364	191	4	2004	2004	NUM
ap-1364	191	5	)	)	PUNCT
ap-1364	191	6	,	,	PUNCT
ap-1364	191	7	051302	051302	NUM
ap-1364	191	8	;	;	PUNCT
ap-1364	191	9	jeng	jeng	PROPN
ap-1364	191	10	,	,	PUNCT
ap-1364	191	11	m.	m.	NOUN
ap-1364	191	12	:	:	PUNCT
ap-1364	191	13	phys	phy	NOUN
ap-1364	191	14	.	.	PUNCT
ap-1364	191	15	rev	rev	PROPN
ap-1364	191	16	.	.	PUNCT
ap-1364	192	1	e	e	PROPN
ap-1364	192	2	71	71	NUM
ap-1364	192	3	(	(	PUNCT
ap-1364	192	4	2005	2005	NUM
ap-1364	192	5	)	)	PUNCT
ap-1364	192	6	,	,	PUNCT
ap-1364	192	7	036153	036153	NUM
ap-1364	192	8	;	;	PUNCT
ap-1364	192	9	jeng	jeng	PROPN
ap-1364	192	10	,	,	PUNCT
ap-1364	192	11	m.	m.	NOUN
ap-1364	192	12	:	:	PUNCT
ap-1364	192	13	phys	phy	NOUN
ap-1364	192	14	.	.	PUNCT
ap-1364	192	15	rev	rev	PROPN
ap-1364	192	16	.	.	PUNCT
ap-1364	193	1	e	e	PROPN
ap-1364	193	2	71	71	NUM
ap-1364	193	3	(	(	PUNCT
ap-1364	193	4	2005	2005	NUM
ap-1364	193	5	)	)	PUNCT
ap-1364	193	6	,	,	PUNCT
ap-1364	193	7	016140	016140	NUM
ap-1364	193	8	;	;	PUNCT
ap-1364	193	9	moghimi	moghimi	PROPN
ap-1364	193	10	-	-	PUNCT
ap-1364	193	11	araghi	araghi	PROPN
ap-1364	193	12	,	,	PUNCT
ap-1364	193	13	s.	s.	PROPN
ap-1364	193	14	,	,	PUNCT
ap-1364	193	15	rajabpour	rajabpour	PROPN
ap-1364	193	16	,	,	PUNCT
ap-1364	193	17	m.	m.	NOUN
ap-1364	193	18	a.	a.	PROPN
ap-1364	193	19	,	,	PUNCT
ap-1364	193	20	rouhani	rouhani	PROPN
ap-1364	193	21	,	,	PUNCT
ap-1364	193	22	s.	s.	PROPN
ap-1364	193	23	:	:	PUNCT
ap-1364	193	24	nucl	nucl	PROPN
ap-1364	193	25	.	.	PUNCT
ap-1364	194	1	phys	phy	NOUN
ap-1364	194	2	.	.	PUNCT
ap-1364	195	1	b	b	X
ap-1364	195	2	718	718	NUM
ap-1364	195	3	(	(	PUNCT
ap-1364	195	4	2005	2005	NUM
ap-1364	195	5	)	)	PUNCT
ap-1364	195	6	,	,	PUNCT
ap-1364	195	7	362	362	NUM
ap-1364	195	8	;	;	PUNCT
ap-1364	195	9	ruelle	ruelle	NOUN
ap-1364	195	10	,	,	PUNCT
ap-1364	195	11	p.	p.	NOUN
ap-1364	195	12	:	:	PUNCT
ap-1364	195	13	j.	j.	PROPN
ap-1364	195	14	stat	stat	PROPN
ap-1364	195	15	.	.	PUNCT
ap-1364	196	1	mech	mech	PROPN
ap-1364	196	2	.	.	PUNCT
ap-1364	197	1	(	(	PUNCT
ap-1364	197	2	2007	2007	NUM
ap-1364	197	3	)	)	PUNCT
ap-1364	197	4	,	,	PUNCT
ap-1364	197	5	p09013	p09013	NOUN
ap-1364	197	6	.	.	PUNCT
ap-1364	198	1	[	[	X
ap-1364	198	2	11	11	NUM
ap-1364	198	3	]	]	X
ap-1364	198	4	lawler	lawler	PROPN
ap-1364	198	5	,	,	PUNCT
ap-1364	198	6	g.	g.	PROPN
ap-1364	198	7	f.	f.	PROPN
ap-1364	198	8	:	:	PUNCT
ap-1364	198	9	duke	duke	PROPN
ap-1364	198	10	math	math	PROPN
ap-1364	198	11	.	.	PUNCT
ap-1364	199	1	j.	j.	PROPN
ap-1364	199	2	47	47	PROPN
ap-1364	199	3	,	,	PUNCT
ap-1364	199	4	3	3	NUM
ap-1364	199	5	(	(	PUNCT
ap-1364	199	6	1980	1980	NUM
ap-1364	199	7	)	)	PUNCT
ap-1364	199	8	,	,	PUNCT
ap-1364	199	9	655–693	655–693	NUM
ap-1364	199	10	.	.	PUNCT
ap-1364	200	1	[	[	X
ap-1364	200	2	12	12	NUM
ap-1364	200	3	]	]	X
ap-1364	200	4	kenyon	kenyon	PROPN
ap-1364	200	5	,	,	PUNCT
ap-1364	200	6	r.	r.	PROPN
ap-1364	200	7	:	:	PUNCT
ap-1364	200	8	acta	acta	PROPN
ap-1364	200	9	math	math	PROPN
ap-1364	200	10	.	.	PUNCT
ap-1364	201	1	185	185	NUM
ap-1364	201	2	,	,	PUNCT
ap-1364	201	3	2	2	NUM
ap-1364	201	4	(	(	PUNCT
ap-1364	201	5	2000	2000	NUM
ap-1364	201	6	)	)	PUNCT
ap-1364	201	7	,	,	PUNCT
ap-1364	201	8	239–286	239–286	NUM
ap-1364	201	9	.	.	PUNCT
ap-1364	202	1	[	[	X
ap-1364	202	2	13	13	NUM
ap-1364	202	3	]	]	SYM
ap-1364	202	4	wilson	wilson	PROPN
ap-1364	202	5	,	,	PUNCT
ap-1364	202	6	d.	d.	PROPN
ap-1364	202	7	:	:	PUNCT
ap-1364	202	8	proceedings	proceeding	NOUN
ap-1364	202	9	of	of	ADP
ap-1364	202	10	the	the	DET
ap-1364	202	11	twenty	twenty	NUM
ap-1364	202	12	-	-	PUNCT
ap-1364	202	13	eighth	eighth	ADJ
ap-1364	202	14	annual	annual	ADJ
ap-1364	202	15	acm	acm	NOUN
ap-1364	202	16	symposium	symposium	NOUN
ap-1364	202	17	on	on	ADP
ap-1364	202	18	the	the	DET
ap-1364	202	19	theory	theory	NOUN
ap-1364	202	20	of	of	ADP
ap-1364	202	21	computing	computing	NOUN
ap-1364	202	22	,	,	PUNCT
ap-1364	202	23	acm	acm	PROPN
ap-1364	202	24	(	(	PUNCT
ap-1364	202	25	1996	1996	NUM
ap-1364	202	26	)	)	PUNCT
ap-1364	202	27	,	,	PUNCT
ap-1364	202	28	296–303	296–303	NUM
ap-1364	202	29	.	.	PUNCT
ap-1364	203	1	[	[	X
ap-1364	203	2	14	14	NUM
ap-1364	203	3	]	]	PUNCT
ap-1364	203	4	piroux	piroux	NOUN
ap-1364	203	5	,	,	PUNCT
ap-1364	203	6	g.	g.	PROPN
ap-1364	203	7	,	,	PUNCT
ap-1364	203	8	ruelle	ruelle	NOUN
ap-1364	203	9	,	,	PUNCT
ap-1364	203	10	p.	p.	NOUN
ap-1364	203	11	:	:	PUNCT
ap-1364	204	1	j.	j.	PROPN
ap-1364	204	2	stat	stat	PROPN
ap-1364	204	3	mech	mech	PROPN
ap-1364	204	4	.	.	PUNCT
ap-1364	205	1	(	(	PUNCT
ap-1364	205	2	2004	2004	NUM
ap-1364	205	3	)	)	PUNCT
ap-1364	205	4	,	,	PUNCT
ap-1364	205	5	p10005	p10005	NOUN
ap-1364	205	6	.	.	PUNCT
ap-1364	206	1	[	[	X
ap-1364	206	2	15	15	NUM
ap-1364	206	3	]	]	X
ap-1364	206	4	piroux	piroux	NOUN
ap-1364	206	5	,	,	PUNCT
ap-1364	206	6	g.	g.	PROPN
ap-1364	206	7	,	,	PUNCT
ap-1364	206	8	ruelle	ruelle	NOUN
ap-1364	206	9	,	,	PUNCT
ap-1364	206	10	p.	p.	NOUN
ap-1364	206	11	:	:	PUNCT
ap-1364	207	1	j.	j.	PROPN
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ap-1364	207	3	.	.	PUNCT
ap-1364	208	1	a	a	DET
ap-1364	208	2	:	:	PUNCT
ap-1364	208	3	math	math	NOUN
ap-1364	208	4	.	.	PUNCT
ap-1364	209	1	gen	gen	PROPN
ap-1364	209	2	.	.	PROPN
ap-1364	209	3	38	38	NUM
ap-1364	209	4	(	(	PUNCT
ap-1364	209	5	2005	2005	NUM
ap-1364	209	6	)	)	PUNCT
ap-1364	209	7	,	,	PUNCT
ap-1364	209	8	1	1	NUM
ap-1364	209	9	451	451	NUM
ap-1364	209	10	.	.	PUNCT
ap-1364	210	1	[	[	X
ap-1364	210	2	16	16	NUM
ap-1364	210	3	]	]	PUNCT
ap-1364	210	4	piroux	piroux	NOUN
ap-1364	210	5	,	,	PUNCT
ap-1364	210	6	g.	g.	PROPN
ap-1364	210	7	,	,	PUNCT
ap-1364	210	8	ruelle	ruelle	NOUN
ap-1364	210	9	,	,	PUNCT
ap-1364	210	10	p.	p.	NOUN
ap-1364	210	11	:	:	PUNCT
ap-1364	211	1	phys	phy	NOUN
ap-1364	211	2	.	.	PUNCT
ap-1364	212	1	lett	lett	PROPN
ap-1364	212	2	.	.	PUNCT
ap-1364	213	1	b	b	X
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ap-1364	213	3	(	(	PUNCT
ap-1364	213	4	2005	2005	NUM
ap-1364	213	5	)	)	PUNCT
ap-1364	213	6	,	,	PUNCT
ap-1364	213	7	188	188	NUM
ap-1364	213	8	;	;	PUNCT
ap-1364	213	9	jeng	jeng	PROPN
ap-1364	213	10	,	,	PUNCT
ap-1364	213	11	m.	m.	NOUN
ap-1364	213	12	,	,	PUNCT
ap-1364	213	13	piroux	piroux	NOUN
ap-1364	213	14	,	,	PUNCT
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ap-1364	213	16	,	,	PUNCT
ap-1364	213	17	ruelle	ruelle	NOUN
ap-1364	213	18	,	,	PUNCT
ap-1364	213	19	p.	p.	NOUN
ap-1364	213	20	:	:	PUNCT
ap-1364	213	21	j.	j.	PROPN
ap-1364	213	22	stat	stat	PROPN
ap-1364	213	23	.	.	PUNCT
ap-1364	214	1	mech	mech	PROPN
ap-1364	214	2	.	.	PUNCT
ap-1364	215	1	(	(	PUNCT
ap-1364	215	2	2006	2006	NUM
ap-1364	215	3	)	)	PUNCT
ap-1364	215	4	,	,	PUNCT
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ap-1364	216	1	[	[	X
ap-1364	216	2	17	17	NUM
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ap-1364	216	5	,	,	PUNCT
ap-1364	216	6	n.	n.	PROPN
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ap-1364	216	8	.	.	PROPN
ap-1364	216	9	,	,	PUNCT
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ap-1364	216	11	,	,	PUNCT
ap-1364	216	12	v.	v.	PROPN
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ap-1364	216	14	,	,	PUNCT
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ap-1364	216	16	,	,	PUNCT
ap-1364	216	17	p.	p.	PROPN
ap-1364	216	18	,	,	PUNCT
ap-1364	216	19	hu	hu	PROPN
ap-1364	216	20	,	,	PUNCT
ap-1364	216	21	c.-k	c.-k	PROPN
ap-1364	216	22	.	.	PUNCT
ap-1364	216	23	:	:	PUNCT
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ap-1364	217	2	.	.	PUNCT
ap-1364	218	1	rev	rev	PROPN
ap-1364	218	2	.	.	PROPN
ap-1364	218	3	lett	lett	PROPN
ap-1364	218	4	.	.	PUNCT
ap-1364	219	1	95	95	NUM
ap-1364	219	2	(	(	PUNCT
ap-1364	219	3	2005	2005	NUM
ap-1364	219	4	)	)	PUNCT
ap-1364	219	5	,	,	PUNCT
ap-1364	219	6	260602	260602	NUM
ap-1364	219	7	;	;	PUNCT
ap-1364	219	8	izmailian	izmailian	PROPN
ap-1364	219	9	,	,	PUNCT
ap-1364	219	10	n.	n.	PROPN
ap-1364	219	11	sh	sh	PROPN
ap-1364	219	12	.	.	PROPN
ap-1364	219	13	,	,	PUNCT
ap-1364	219	14	priezzhev	priezzhev	PROPN
ap-1364	219	15	,	,	PUNCT
ap-1364	219	16	v.	v.	PROPN
ap-1364	219	17	b.	b.	PROPN
ap-1364	219	18	,	,	PUNCT
ap-1364	219	19	ruelle	ruelle	PROPN
ap-1364	219	20	,	,	PUNCT
ap-1364	219	21	p.	p.	NOUN
ap-1364	219	22	:	:	PUNCT
ap-1364	220	1	symmetry	symmetry	PROPN
ap-1364	220	2	,	,	PUNCT
ap-1364	220	3	integr	integr	PROPN
ap-1364	220	4	.	.	PUNCT
ap-1364	221	1	geom	geom	PROPN
ap-1364	221	2	.	.	PUNCT
ap-1364	221	3	:	:	PUNCT
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ap-1364	222	5	(	(	PUNCT
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ap-1364	222	7	)	)	PUNCT
ap-1364	222	8	,	,	PUNCT
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ap-1364	222	10	.	.	PUNCT
ap-1364	223	1	[	[	X
ap-1364	223	2	18	18	NUM
ap-1364	223	3	]	]	PUNCT
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ap-1364	223	5	,	,	PUNCT
ap-1364	223	6	v.	v.	PROPN
ap-1364	223	7	s.	s.	PROPN
ap-1364	223	8	,	,	PUNCT
ap-1364	223	9	grigorev	grigorev	PROPN
ap-1364	223	10	,	,	PUNCT
ap-1364	223	11	s.	s.	PROPN
ap-1364	223	12	y.	y.	PROPN
ap-1364	223	13	,	,	PUNCT
ap-1364	223	14	priezzhev	priezzhev	NOUN
ap-1364	223	15	,	,	PUNCT
ap-1364	223	16	v.	v.	PROPN
ap-1364	223	17	b.	b.	PROPN
ap-1364	223	18	,	,	PUNCT
ap-1364	223	19	ruelle	ruelle	PROPN
ap-1364	223	20	,	,	PUNCT
ap-1364	223	21	p.	p.	NOUN
ap-1364	223	22	:	:	PUNCT
ap-1364	224	1	phys	phy	NOUN
ap-1364	224	2	.	.	PUNCT
ap-1364	225	1	lett	lett	PROPN
ap-1364	225	2	.	.	PUNCT
ap-1364	226	1	b	b	X
ap-1364	226	2	659	659	NUM
ap-1364	226	3	(	(	PUNCT
ap-1364	226	4	2008	2008	NUM
ap-1364	226	5	)	)	PUNCT
ap-1364	226	6	,	,	PUNCT
ap-1364	226	7	768	768	NUM
ap-1364	226	8	;	;	PUNCT
ap-1364	226	9	j.	j.	PROPN
ap-1364	226	10	stat	stat	PROPN
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ap-1364	226	13	.	.	PUNCT
ap-1364	227	1	(	(	PUNCT
ap-1364	227	2	2010	2010	NUM
ap-1364	227	3	)	)	PUNCT
ap-1364	227	4	,	,	PUNCT
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ap-1364	227	6	.	.	PUNCT
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ap-1364	228	3	]	]	X
ap-1364	228	4	azimi	azimi	NOUN
ap-1364	228	5	-	-	PUNCT
ap-1364	228	6	tafreshi	tafreshi	PROPN
ap-1364	228	7	,	,	PUNCT
ap-1364	228	8	n.	n.	NOUN
ap-1364	228	9	,	,	PUNCT
ap-1364	228	10	dashti	dashti	NOUN
ap-1364	228	11	-	-	PUNCT
ap-1364	228	12	naserabadi	naserabadi	NOUN
ap-1364	228	13	,	,	PUNCT
ap-1364	228	14	h.	h.	PROPN
ap-1364	228	15	,	,	PUNCT
ap-1364	228	16	moghimi	moghimi	PROPN
ap-1364	228	17	-	-	PUNCT
ap-1364	228	18	araghi	araghi	PROPN
ap-1364	228	19	,	,	PUNCT
ap-1364	228	20	s.	s.	PROPN
ap-1364	228	21	,	,	PUNCT
ap-1364	228	22	ruelle	ruelle	NOUN
ap-1364	228	23	,	,	PUNCT
ap-1364	228	24	p.	p.	NOUN
ap-1364	228	25	:	:	PUNCT
ap-1364	228	26	j.	j.	PROPN
ap-1364	228	27	stat	stat	PROPN
ap-1364	228	28	.	.	PUNCT
ap-1364	228	29	mech	mech	PROPN
ap-1364	228	30	.	.	PUNCT
ap-1364	229	1	(	(	PUNCT
ap-1364	229	2	2010	2010	NUM
ap-1364	229	3	)	)	PUNCT
ap-1364	229	4	,	,	PUNCT
ap-1364	229	5	p02004	p02004	PROPN
ap-1364	229	6	.	.	PUNCT
ap-1364	230	1	[	[	X
ap-1364	230	2	20	20	NUM
ap-1364	230	3	]	]	X
ap-1364	230	4	grigorev	grigorev	NOUN
ap-1364	230	5	,	,	PUNCT
ap-1364	230	6	s.	s.	PROPN
ap-1364	230	7	y.	y.	PROPN
ap-1364	230	8	,	,	PUNCT
ap-1364	230	9	poghosyan	poghosyan	PROPN
ap-1364	230	10	,	,	PUNCT
ap-1364	230	11	v.	v.	PROPN
ap-1364	230	12	s.	s.	PROPN
ap-1364	230	13	,	,	PUNCT
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ap-1364	230	15	,	,	PUNCT
ap-1364	230	16	v.	v.	PROPN
ap-1364	230	17	b.	b.	PROPN
ap-1364	230	18	:	:	PUNCT
ap-1364	230	19	j.	j.	PROPN
ap-1364	230	20	stat	stat	PROPN
ap-1364	230	21	.	.	PUNCT
ap-1364	230	22	mech	mech	PROPN
ap-1364	230	23	.	.	PUNCT
ap-1364	231	1	(	(	PUNCT
ap-1364	231	2	2009	2009	NUM
ap-1364	231	3	)	)	PUNCT
ap-1364	231	4	,	,	PUNCT
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ap-1364	231	6	.	.	PUNCT
ap-1364	232	1	v.	v.	ADP
ap-1364	232	2	s.	s.	PROPN
ap-1364	232	3	poghosyan	poghosyan	PROPN
ap-1364	232	4	e	e	NOUN
ap-1364	232	5	-	-	NOUN
ap-1364	232	6	mail	mail	NOUN
ap-1364	232	7	:	:	PUNCT
ap-1364	232	8	vahagn.poghosyan@uclouvain.be	vahagn.poghosyan@uclouvain.be	PROPN
ap-1364	232	9	institute	institute	PROPN
ap-1364	232	10	for	for	ADP
ap-1364	232	11	theoretical	theoretical	ADJ
ap-1364	232	12	physics	physics	NOUN
ap-1364	232	13	the	the	DET
ap-1364	232	14	catholic	catholic	PROPN
ap-1364	232	15	university	university	PROPN
ap-1364	232	16	of	of	ADP
ap-1364	232	17	louvain	louvain	NOUN
ap-1364	232	18	b-1348	b-1348	PROPN
ap-1364	232	19	louvain	louvain	NOUN
ap-1364	232	20	-	-	PUNCT
ap-1364	232	21	la	la	NOUN
ap-1364	232	22	-	-	PUNCT
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ap-1364	232	24	,	,	PUNCT
ap-1364	232	25	belgium	belgium	PROPN
ap-1364	232	26	v.	v.	PROPN
ap-1364	232	27	b.	b.	PROPN
ap-1364	232	28	priezzhev	priezzhev	PROPN
ap-1364	233	1	e	e	NOUN
ap-1364	233	2	-	-	NOUN
ap-1364	233	3	mail	mail	NOUN
ap-1364	233	4	:	:	PUNCT
ap-1364	234	1	priezzvb@theor.jinr.ru	priezzvb@theor.jinr.ru	DET
ap-1364	234	2	bogoliubov	bogoliubov	X
ap-1364	234	3	laboratory	laboratory	NOUN
ap-1364	234	4	of	of	ADP
ap-1364	234	5	theoretical	theoretical	ADJ
ap-1364	234	6	physics	physics	PROPN
ap-1364	234	7	joint	joint	PROPN
ap-1364	234	8	institute	institute	PROPN
ap-1364	234	9	for	for	ADP
ap-1364	234	10	nuclear	nuclear	ADJ
ap-1364	234	11	research	research	NOUN
ap-1364	234	12	141980	141980	NUM
ap-1364	234	13	dubna	dubna	NOUN
ap-1364	234	14	,	,	PUNCT
ap-1364	234	15	russia	russia	PROPN
ap-1364	234	16	62	62	NUM