id	sid	tid	token	lemma	pos
ap-4481	1	1	acta	acta	PROPN
ap-4481	1	2	polytechnica	polytechnica	PROPN
ap-4481	1	3	doi:10.14311	doi:10.14311	PROPN
ap-4481	1	4	/	/	SYM
ap-4481	1	5	ap.2017.57.0418	ap.2017.57.0418	PROPN
ap-4481	1	6	acta	acta	PROPN
ap-4481	1	7	polytechnica	polytechnica	PROPN
ap-4481	1	8	57(6):418–423	57(6):418–423	PROPN
ap-4481	1	9	,	,	PUNCT
ap-4481	1	10	2017	2017	NUM
ap-4481	1	11	©	©	PROPN
ap-4481	1	12	czech	czech	PROPN
ap-4481	1	13	technical	technical	PROPN
ap-4481	1	14	university	university	PROPN
ap-4481	1	15	in	in	ADP
ap-4481	1	16	prague	prague	PROPN
ap-4481	1	17	,	,	PUNCT
ap-4481	1	18	2017	2017	NUM
ap-4481	1	19	available	available	ADJ
ap-4481	1	20	online	online	ADV
ap-4481	1	21	at	at	ADP
ap-4481	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-4481	1	23	new	new	ADJ
ap-4481	1	24	spectral	spectral	ADJ
ap-4481	1	25	statistics	statistic	NOUN
ap-4481	1	26	for	for	ADP
ap-4481	1	27	ensembles	ensemble	NOUN
ap-4481	1	28	of	of	ADP
ap-4481	1	29	2×	2×	NUM
ap-4481	1	30	2	2	NUM
ap-4481	1	31	real	real	ADV
ap-4481	1	32	symmetric	symmetric	ADJ
ap-4481	1	33	random	random	ADJ
ap-4481	1	34	matrices	matrix	NOUN
ap-4481	1	35	sachin	sachin	PROPN
ap-4481	1	36	kumara,∗	kumara,∗	PROPN
ap-4481	1	37	,	,	PUNCT
ap-4481	1	38	zafar	zafar	PROPN
ap-4481	1	39	ahmedb	ahmedb	VERB
ap-4481	1	40	a	a	DET
ap-4481	1	41	theoretical	theoretical	ADJ
ap-4481	1	42	physics	physics	NOUN
ap-4481	1	43	section	section	NOUN
ap-4481	1	44	,	,	PUNCT
ap-4481	1	45	bhabha	bhabha	NOUN
ap-4481	1	46	atomic	atomic	PROPN
ap-4481	1	47	research	research	PROPN
ap-4481	1	48	centre	centre	PROPN
ap-4481	1	49	,	,	PUNCT
ap-4481	1	50	mumbai	mumbai	PROPN
ap-4481	1	51	400	400	NUM
ap-4481	1	52	085	085	NUM
ap-4481	1	53	,	,	PUNCT
ap-4481	1	54	india	india	PROPN
ap-4481	1	55	b	b	PROPN
ap-4481	1	56	nuclear	nuclear	PROPN
ap-4481	1	57	physics	physics	NOUN
ap-4481	1	58	division	division	NOUN
ap-4481	1	59	,	,	PUNCT
ap-4481	1	60	bhabha	bhabha	PROPN
ap-4481	1	61	atomic	atomic	PROPN
ap-4481	1	62	research	research	PROPN
ap-4481	1	63	centre	centre	PROPN
ap-4481	1	64	,	,	PUNCT
ap-4481	1	65	mumbai	mumbai	PROPN
ap-4481	1	66	400	400	NUM
ap-4481	1	67	085	085	NUM
ap-4481	1	68	,	,	PUNCT
ap-4481	1	69	india	india	PROPN
ap-4481	1	70	∗	∗	NOUN
ap-4481	1	71	corresponding	correspond	VERB
ap-4481	1	72	author	author	NOUN
ap-4481	1	73	:	:	PUNCT
ap-4481	1	74	sachinv@barc.gov.in	sachinv@barc.gov.in	PROPN
ap-4481	1	75	abstract	abstract	ADJ
ap-4481	1	76	.	.	PUNCT
ap-4481	2	1	we	we	PRON
ap-4481	2	2	investigate	investigate	VERB
ap-4481	2	3	spacing	space	VERB
ap-4481	2	4	statistics	statistic	NOUN
ap-4481	2	5	for	for	ADP
ap-4481	2	6	ensembles	ensemble	NOUN
ap-4481	2	7	of	of	ADP
ap-4481	2	8	various	various	ADJ
ap-4481	2	9	real	real	ADJ
ap-4481	2	10	random	random	ADJ
ap-4481	2	11	matrices	matrix	NOUN
ap-4481	2	12	where	where	SCONJ
ap-4481	2	13	the	the	DET
ap-4481	2	14	matrix	matrix	NOUN
ap-4481	2	15	-	-	PUNCT
ap-4481	2	16	elements	element	NOUN
ap-4481	2	17	have	have	VERB
ap-4481	2	18	various	various	ADJ
ap-4481	2	19	probability	probability	NOUN
ap-4481	2	20	distribution	distribution	NOUN
ap-4481	2	21	functions	function	NOUN
ap-4481	2	22	(	(	PUNCT
ap-4481	2	23	pdfs	pdfs	NOUN
ap-4481	2	24	:	:	PUNCT
ap-4481	2	25	f(x	f(x	PROPN
ap-4481	2	26	)	)	PUNCT
ap-4481	2	27	)	)	PUNCT
ap-4481	2	28	including	include	VERB
ap-4481	2	29	gaussian	gaussian	NOUN
ap-4481	2	30	.	.	PUNCT
ap-4481	3	1	for	for	ADP
ap-4481	3	2	two	two	NUM
ap-4481	3	3	modifications	modification	NOUN
ap-4481	3	4	of	of	ADP
ap-4481	3	5	2×	2×	NUM
ap-4481	3	6	2	2	NUM
ap-4481	3	7	matrices	matrix	NOUN
ap-4481	3	8	with	with	ADP
ap-4481	3	9	various	various	ADJ
ap-4481	3	10	pdfs	pdfs	NOUN
ap-4481	3	11	,	,	PUNCT
ap-4481	3	12	we	we	PRON
ap-4481	3	13	derive	derive	VERB
ap-4481	3	14	the	the	DET
ap-4481	3	15	spacing	space	VERB
ap-4481	3	16	distributions	distribution	NOUN
ap-4481	3	17	p(s	p(s	NOUN
ap-4481	3	18	)	)	PUNCT
ap-4481	3	19	of	of	ADP
ap-4481	3	20	adjacent	adjacent	ADJ
ap-4481	3	21	energy	energy	NOUN
ap-4481	3	22	eigenvalues	eigenvalue	NOUN
ap-4481	3	23	.	.	PUNCT
ap-4481	4	1	nevertheless	nevertheless	ADV
ap-4481	4	2	,	,	PUNCT
ap-4481	4	3	they	they	PRON
ap-4481	4	4	show	show	VERB
ap-4481	4	5	the	the	DET
ap-4481	4	6	linear	linear	ADJ
ap-4481	4	7	level	level	NOUN
ap-4481	4	8	repulsion	repulsion	NOUN
ap-4481	4	9	near	near	ADP
ap-4481	4	10	s	s	NOUN
ap-4481	4	11	=	=	NOUN
ap-4481	4	12	0	0	PUNCT
ap-4481	5	1	as	as	ADP
ap-4481	5	2	αs	αs	INTJ
ap-4481	5	3	where	where	SCONJ
ap-4481	5	4	α	α	NOUN
ap-4481	5	5	depends	depend	VERB
ap-4481	5	6	on	on	ADP
ap-4481	5	7	the	the	DET
ap-4481	5	8	choice	choice	NOUN
ap-4481	5	9	of	of	ADP
ap-4481	5	10	the	the	DET
ap-4481	5	11	pdf	pdf	NOUN
ap-4481	5	12	.	.	PUNCT
ap-4481	6	1	more	more	ADV
ap-4481	6	2	interestingly	interestingly	ADV
ap-4481	6	3	when	when	SCONJ
ap-4481	6	4	f(x	f(x	PROPN
ap-4481	6	5	)	)	PUNCT
ap-4481	7	1	=	=	PUNCT
ap-4481	7	2	xe−x	xe−x	NOUN
ap-4481	7	3	2(f(0	2(f(0	NUM
ap-4481	7	4	)	)	PUNCT
ap-4481	7	5	=	=	SYM
ap-4481	8	1	0	0	NUM
ap-4481	8	2	)	)	PUNCT
ap-4481	8	3	,	,	PUNCT
ap-4481	8	4	we	we	PRON
ap-4481	8	5	get	get	VERB
ap-4481	8	6	cubic	cubic	ADJ
ap-4481	8	7	level	level	NOUN
ap-4481	8	8	repulsion	repulsion	NOUN
ap-4481	8	9	near	near	ADP
ap-4481	8	10	s	s	NOUN
ap-4481	8	11	=	=	NOUN
ap-4481	8	12	0	0	NUM
ap-4481	8	13	:	:	PUNCT
ap-4481	8	14	p(s	p(s	NUM
ap-4481	8	15	)	)	PUNCT
ap-4481	8	16	∼	∼	NOUN
ap-4481	8	17	s3e−s	s3e−s	NOUN
ap-4481	8	18	2	2	NUM
ap-4481	8	19	.	.	PUNCT
ap-4481	9	1	we	we	PRON
ap-4481	9	2	also	also	ADV
ap-4481	9	3	derive	derive	VERB
ap-4481	9	4	the	the	DET
ap-4481	9	5	distribution	distribution	NOUN
ap-4481	9	6	of	of	ADP
ap-4481	9	7	eigenvalues	eigenvalue	NOUN
ap-4481	9	8	d(ε	d(ε	PROPN
ap-4481	9	9	)	)	PUNCT
ap-4481	9	10	for	for	ADP
ap-4481	9	11	these	these	DET
ap-4481	9	12	matrices	matrix	NOUN
ap-4481	9	13	.	.	PUNCT
ap-4481	10	1	keywords	keyword	NOUN
ap-4481	10	2	:	:	PUNCT
ap-4481	10	3	real	real	ADJ
ap-4481	10	4	symmetric	symmetric	ADJ
ap-4481	10	5	matrices	matrix	NOUN
ap-4481	10	6	;	;	PUNCT
ap-4481	10	7	wigner	wigner	NOUN
ap-4481	10	8	surmise	surmise	NOUN
ap-4481	10	9	.	.	PUNCT
ap-4481	11	1	1	1	X
ap-4481	11	2	.	.	X
ap-4481	11	3	introduction	introduction	NOUN
ap-4481	11	4	due	due	ADP
ap-4481	11	5	to	to	ADP
ap-4481	11	6	matrix	matrix	VERB
ap-4481	11	7	mechanics	mechanic	NOUN
ap-4481	11	8	of	of	ADP
ap-4481	11	9	heisenberg	heisenberg	PROPN
ap-4481	11	10	and	and	CCONJ
ap-4481	11	11	method	method	NOUN
ap-4481	11	12	of	of	ADP
ap-4481	11	13	linear	linear	ADJ
ap-4481	11	14	combination	combination	NOUN
ap-4481	11	15	of	of	ADP
ap-4481	11	16	atomic	atomic	ADJ
ap-4481	11	17	orbitals	orbital	NOUN
ap-4481	11	18	(	(	PUNCT
ap-4481	11	19	lcao	lcao	NOUN
ap-4481	11	20	)	)	PUNCT
ap-4481	11	21	one	one	NOUN
ap-4481	11	22	can	can	AUX
ap-4481	11	23	easily	easily	ADV
ap-4481	11	24	visualize	visualize	VERB
ap-4481	11	25	the	the	DET
ap-4481	11	26	eigenspectrum	eigenspectrum	NOUN
ap-4481	11	27	of	of	ADP
ap-4481	11	28	various	various	ADJ
ap-4481	11	29	systems	system	NOUN
ap-4481	11	30	with	with	ADP
ap-4481	11	31	time	time	NOUN
ap-4481	11	32	-	-	PUNCT
ap-4481	11	33	reversal	reversal	NOUN
ap-4481	11	34	symmetry	symmetry	NOUN
ap-4481	11	35	as	as	ADP
ap-4481	11	36	result	result	NOUN
ap-4481	11	37	of	of	ADP
ap-4481	11	38	diagonalization	diagonalization	NOUN
ap-4481	11	39	of	of	ADP
ap-4481	11	40	a	a	DET
ap-4481	11	41	real	real	ADJ
ap-4481	11	42	symmetric	symmetric	ADJ
ap-4481	11	43	matrix	matrix	NOUN
ap-4481	11	44	where	where	SCONJ
ap-4481	11	45	the	the	DET
ap-4481	11	46	matrix	matrix	NOUN
ap-4481	11	47	element	element	NOUN
ap-4481	11	48	are	be	AUX
ap-4481	11	49	calculated	calculate	VERB
ap-4481	11	50	using	use	VERB
ap-4481	11	51	the	the	DET
ap-4481	11	52	inter	inter	ADJ
ap-4481	11	53	-	-	ADJ
ap-4481	11	54	particle	particle	NOUN
ap-4481	11	55	interaction	interaction	NOUN
ap-4481	11	56	.	.	PUNCT
ap-4481	12	1	most	most	ADJ
ap-4481	12	2	of	of	ADP
ap-4481	12	3	the	the	DET
ap-4481	12	4	times	time	NOUN
ap-4481	12	5	this	this	DET
ap-4481	12	6	interaction	interaction	NOUN
ap-4481	12	7	is	be	AUX
ap-4481	12	8	not	not	PART
ap-4481	12	9	known	know	VERB
ap-4481	12	10	.	.	PUNCT
ap-4481	13	1	for	for	ADP
ap-4481	13	2	example	example	NOUN
ap-4481	13	3	,	,	PUNCT
ap-4481	13	4	energy	energy	NOUN
ap-4481	13	5	levels	level	NOUN
ap-4481	13	6	of	of	ADP
ap-4481	13	7	various	various	ADJ
ap-4481	13	8	nuclei	nucleus	NOUN
ap-4481	13	9	are	be	AUX
ap-4481	13	10	known	know	VERB
ap-4481	13	11	experimentally	experimentally	ADV
ap-4481	13	12	but	but	CCONJ
ap-4481	13	13	the	the	DET
ap-4481	13	14	nuclear	nuclear	ADJ
ap-4481	13	15	interaction	interaction	NOUN
ap-4481	13	16	is	be	AUX
ap-4481	13	17	not	not	PART
ap-4481	13	18	really	really	ADV
ap-4481	13	19	known	know	VERB
ap-4481	13	20	.	.	PUNCT
ap-4481	14	1	random	random	ADJ
ap-4481	14	2	matrix	matrix	NOUN
ap-4481	14	3	theory	theory	NOUN
ap-4481	14	4	[	[	X
ap-4481	14	5	1–5	1–5	X
ap-4481	14	6	]	]	PUNCT
ap-4481	14	7	originated	originate	VERB
ap-4481	14	8	by	by	ADP
ap-4481	14	9	considering	consider	VERB
ap-4481	14	10	the	the	DET
ap-4481	14	11	level	level	NOUN
ap-4481	14	12	spacing	space	VERB
ap-4481	14	13	statistics	statistic	NOUN
ap-4481	14	14	p	p	X
ap-4481	14	15	(	(	PUNCT
ap-4481	14	16	s	s	NOUN
ap-4481	14	17	)	)	PUNCT
ap-4481	14	18	between	between	ADP
ap-4481	14	19	eigenvalues	eigenvalue	NOUN
ap-4481	14	20	of	of	ADP
ap-4481	14	21	real	real	ADJ
ap-4481	14	22	symmetric	symmetric	ADJ
ap-4481	14	23	matrices	matrix	NOUN
ap-4481	14	24	r1	r1	NOUN
ap-4481	14	25	=	=	PUNCT
ap-4481	14	26	(	(	PUNCT
ap-4481	14	27	a	a	DET
ap-4481	14	28	b	b	PROPN
ap-4481	14	29	b	b	PROPN
ap-4481	14	30	c	c	PROPN
ap-4481	14	31	)	)	PUNCT
ap-4481	14	32	,	,	PUNCT
ap-4481	14	33	r2	r2	NOUN
ap-4481	14	34	=	=	PUNCT
ap-4481	14	35	(	(	PUNCT
ap-4481	14	36	a+	a+	X
ap-4481	14	37	b	b	X
ap-4481	14	38	c	c	NOUN
ap-4481	14	39	c	c	PROPN
ap-4481	14	40	a−	a−	PROPN
ap-4481	14	41	b	b	PROPN
ap-4481	14	42	)	)	PUNCT
ap-4481	14	43	(	(	PUNCT
ap-4481	14	44	1	1	X
ap-4481	14	45	)	)	PUNCT
ap-4481	14	46	when	when	SCONJ
ap-4481	14	47	matrix	matrix	NOUN
ap-4481	14	48	elements	element	NOUN
ap-4481	14	49	a	a	DET
ap-4481	14	50	,	,	PUNCT
ap-4481	14	51	b	b	NOUN
ap-4481	14	52	,	,	PUNCT
ap-4481	14	53	c	c	PROPN
ap-4481	14	54	are	be	AUX
ap-4481	14	55	random	random	ADJ
ap-4481	14	56	numbers	number	NOUN
ap-4481	14	57	with	with	ADP
ap-4481	14	58	the	the	DET
ap-4481	14	59	probability	probability	NOUN
ap-4481	14	60	distribution	distribution	NOUN
ap-4481	14	61	function	function	NOUN
ap-4481	14	62	(	(	PUNCT
ap-4481	14	63	pdf	pdf	NOUN
ap-4481	14	64	)	)	PUNCT
ap-4481	14	65	as	as	ADP
ap-4481	14	66	gaussian	gaussian	ADJ
ap-4481	14	67	:	:	PUNCT
ap-4481	14	68	f(x	f(x	PROPN
ap-4481	14	69	)	)	PUNCT
ap-4481	15	1	=	=	PUNCT
ap-4481	16	1	1√	1√	NUM
ap-4481	16	2	2π	2π	NOUN
ap-4481	16	3	e	e	X
ap-4481	16	4	−x2	−x2	PROPN
ap-4481	16	5	.	.	PUNCT
ap-4481	17	1	the	the	DET
ap-4481	17	2	spacing	spacing	NOUN
ap-4481	17	3	of	of	ADP
ap-4481	17	4	eigenvalues	eigenvalue	NOUN
ap-4481	17	5	are	be	AUX
ap-4481	17	6	given	give	VERB
ap-4481	17	7	as	as	ADP
ap-4481	17	8	s1	s1	NOUN
ap-4481	17	9	∼	∼	NOUN
ap-4481	17	10	√	√	VERB
ap-4481	17	11	4b2	4b2	NUM
ap-4481	17	12	+	+	CCONJ
ap-4481	17	13	(	(	PUNCT
ap-4481	17	14	a−	a−	PROPN
ap-4481	17	15	c)2	c)2	NOUN
ap-4481	17	16	and	and	CCONJ
ap-4481	17	17	s2	s2	VERB
ap-4481	17	18	∼	∼	NOUN
ap-4481	17	19	√	√	ADP
ap-4481	17	20	b2	b2	NOUN
ap-4481	17	21	+	+	CCONJ
ap-4481	17	22	c2	c2	PROPN
ap-4481	17	23	,	,	PUNCT
ap-4481	17	24	respectively	respectively	ADV
ap-4481	17	25	.	.	PUNCT
ap-4481	18	1	notice	notice	VERB
ap-4481	18	2	that	that	SCONJ
ap-4481	18	3	the	the	DET
ap-4481	18	4	s1	s1	NOUN
ap-4481	18	5	,	,	PUNCT
ap-4481	18	6	is	be	AUX
ap-4481	18	7	function	function	NOUN
ap-4481	18	8	of	of	ADP
ap-4481	18	9	three	three	NUM
ap-4481	18	10	parameters	parameter	NOUN
ap-4481	18	11	(	(	PUNCT
ap-4481	18	12	a	a	PRON
ap-4481	18	13	,	,	PUNCT
ap-4481	18	14	b	b	NOUN
ap-4481	18	15	,	,	PUNCT
ap-4481	18	16	c	c	NOUN
ap-4481	18	17	)	)	PUNCT
ap-4481	18	18	,	,	PUNCT
ap-4481	18	19	whereas	whereas	SCONJ
ap-4481	18	20	s2	s2	NOUN
ap-4481	18	21	function	function	NOUN
ap-4481	18	22	of	of	ADP
ap-4481	18	23	just	just	ADV
ap-4481	18	24	two	two	NUM
ap-4481	18	25	(	(	PUNCT
ap-4481	18	26	b	b	NOUN
ap-4481	18	27	,	,	PUNCT
ap-4481	18	28	c	c	NOUN
ap-4481	18	29	)	)	PUNCT
ap-4481	18	30	.	.	PUNCT
ap-4481	19	1	notwithstanding	notwithstanding	ADP
ap-4481	19	2	this	this	DET
ap-4481	19	3	disparity	disparity	NOUN
ap-4481	19	4	and	and	CCONJ
ap-4481	19	5	the	the	DET
ap-4481	19	6	complexity	complexity	NOUN
ap-4481	19	7	of	of	ADP
ap-4481	19	8	the	the	DET
ap-4481	19	9	multiple	multiple	ADJ
ap-4481	19	10	integral	integral	ADJ
ap-4481	19	11	p	p	X
ap-4481	19	12	(	(	PUNCT
ap-4481	19	13	s	s	NOUN
ap-4481	19	14	)	)	PUNCT
ap-4481	19	15	=	=	PUNCT
ap-4481	19	16	a	a	DET
ap-4481	19	17	∫	∫	PROPN
ap-4481	19	18	∞	∞	PROPN
ap-4481	19	19	−∞	−∞	X
ap-4481	19	20	∫	∫	PROPN
ap-4481	19	21	∞	∞	PROPN
ap-4481	19	22	−∞	−∞	ADP
ap-4481	19	23	∫	∫	PROPN
ap-4481	19	24	∞	∞	PROPN
ap-4481	19	25	−∞	−∞	PROPN
ap-4481	19	26	f(a	f(a	PROPN
ap-4481	19	27	,	,	PUNCT
ap-4481	19	28	b	b	NOUN
ap-4481	19	29	,	,	PUNCT
ap-4481	19	30	c)δ[s	c)δ[s	PROPN
ap-4481	19	31	−	−	PROPN
ap-4481	19	32	s(a	s(a	PROPN
ap-4481	19	33	,	,	PUNCT
ap-4481	19	34	b	b	NOUN
ap-4481	19	35	,	,	PUNCT
ap-4481	19	36	c	c	NOUN
ap-4481	19	37	)	)	PUNCT
ap-4481	19	38	]	]	PUNCT
ap-4481	20	1	da	da	PROPN
ap-4481	20	2	db	db	PROPN
ap-4481	20	3	dc	dc	PROPN
ap-4481	20	4	(	(	PUNCT
ap-4481	20	5	2	2	X
ap-4481	20	6	)	)	PUNCT
ap-4481	20	7	the	the	DET
ap-4481	20	8	spacing	space	VERB
ap-4481	20	9	distributions	distribution	NOUN
ap-4481	20	10	in	in	ADP
ap-4481	20	11	the	the	DET
ap-4481	20	12	two	two	NUM
ap-4481	20	13	cases	case	NOUN
ap-4481	20	14	(	(	PUNCT
ap-4481	20	15	r1	r1	NOUN
ap-4481	20	16	,	,	PUNCT
ap-4481	20	17	r2	r2	PROPN
ap-4481	20	18	)	)	PUNCT
ap-4481	20	19	turned	turn	VERB
ap-4481	20	20	out	out	ADP
ap-4481	20	21	to	to	PART
ap-4481	20	22	be	be	AUX
ap-4481	20	23	the	the	DET
ap-4481	20	24	same	same	ADJ
ap-4481	20	25	:	:	PUNCT
ap-4481	20	26	p	p	X
ap-4481	20	27	(	(	PUNCT
ap-4481	20	28	s	s	NOUN
ap-4481	20	29	)	)	PUNCT
ap-4481	20	30	=	=	SYM
ap-4481	20	31	se−s	se−s	NOUN
ap-4481	20	32	2	2	NUM
ap-4481	20	33	.	.	PUNCT
ap-4481	21	1	when	when	SCONJ
ap-4481	21	2	arranged	arrange	VERB
ap-4481	21	3	to	to	PART
ap-4481	21	4	yield	yield	VERB
ap-4481	21	5	the	the	DET
ap-4481	21	6	average	average	ADJ
ap-4481	21	7	spacing	spacing	NOUN
ap-4481	21	8	as	as	ADP
ap-4481	21	9	1	1	NUM
ap-4481	21	10	,	,	PUNCT
ap-4481	21	11	the	the	DET
ap-4481	21	12	normalized	normalize	VERB
ap-4481	21	13	spacing	spacing	NOUN
ap-4481	21	14	distributions	distribution	NOUN
ap-4481	21	15	is	be	AUX
ap-4481	21	16	written	write	VERB
ap-4481	21	17	as	as	ADP
ap-4481	21	18	pw	pw	PROPN
ap-4481	21	19	(	(	PUNCT
ap-4481	21	20	s	s	X
ap-4481	21	21	)	)	PUNCT
ap-4481	21	22	=	=	SYM
ap-4481	21	23	πs	πs	ADJ
ap-4481	21	24	2	2	NUM
ap-4481	21	25	e−πs	e−πs	NOUN
ap-4481	21	26	2/4	2/4	NUM
ap-4481	21	27	,	,	PUNCT
ap-4481	21	28	(	(	PUNCT
ap-4481	21	29	3	3	X
ap-4481	21	30	)	)	PUNCT
ap-4481	21	31	this	this	PRON
ap-4481	21	32	is	be	AUX
ap-4481	21	33	called	call	VERB
ap-4481	21	34	the	the	DET
ap-4481	21	35	spacing	space	VERB
ap-4481	21	36	distribution	distribution	NOUN
ap-4481	21	37	of	of	ADP
ap-4481	21	38	gaussian	gaussian	ADJ
ap-4481	21	39	orthogonal	orthogonal	NOUN
ap-4481	21	40	ensemble	ensemble	ADJ
ap-4481	21	41	(	(	PUNCT
ap-4481	21	42	goe	goe	NOUN
ap-4481	21	43	)	)	PUNCT
ap-4481	21	44	due	due	ADP
ap-4481	21	45	to	to	ADP
ap-4481	21	46	the	the	DET
ap-4481	21	47	orthogonal	orthogonal	ADJ
ap-4481	21	48	symmetry	symmetry	NOUN
ap-4481	21	49	of	of	ADP
ap-4481	21	50	real	real	ADJ
ap-4481	21	51	symmetric	symmetric	ADJ
ap-4481	21	52	matrices	matrix	NOUN
ap-4481	21	53	.	.	PUNCT
ap-4481	22	1	moreover	moreover	ADV
ap-4481	22	2	pw	pw	PROPN
ap-4481	22	3	is	be	AUX
ap-4481	22	4	well	well	ADV
ap-4481	22	5	known	know	VERB
ap-4481	22	6	as	as	ADP
ap-4481	22	7	wigner	wigner	ADJ
ap-4481	22	8	distribution	distribution	NOUN
ap-4481	22	9	function	function	NOUN
ap-4481	22	10	.	.	PUNCT
ap-4481	23	1	wigner	wigner	NOUN
ap-4481	23	2	surmised	surmise	VERB
ap-4481	23	3	[	[	X
ap-4481	23	4	1–5	1–5	X
ap-4481	23	5	]	]	PUNCT
ap-4481	23	6	that	that	SCONJ
ap-4481	23	7	the	the	DET
ap-4481	23	8	spacing	space	VERB
ap-4481	23	9	distribution	distribution	NOUN
ap-4481	23	10	of	of	ADP
ap-4481	23	11	adjacent	adjacent	ADJ
ap-4481	23	12	eigenvalues	eigenvalue	NOUN
ap-4481	23	13	of	of	ADP
ap-4481	23	14	n	n	DET
ap-4481	23	15	number	number	NOUN
ap-4481	23	16	of	of	ADP
ap-4481	23	17	n×	n×	PROPN
ap-4481	23	18	n	n	PRON
ap-4481	23	19	gaussian	gaussian	ADJ
ap-4481	23	20	random	random	ADJ
ap-4481	23	21	real	real	ADJ
ap-4481	23	22	symmetric	symmetric	ADJ
ap-4481	23	23	matrices	matrix	NOUN
ap-4481	23	24	will	will	AUX
ap-4481	23	25	again	again	ADV
ap-4481	23	26	be	be	AUX
ap-4481	23	27	given	give	VERB
ap-4481	23	28	by	by	ADP
ap-4481	23	29	(	(	PUNCT
ap-4481	23	30	3	3	NUM
ap-4481	23	31	)	)	PUNCT
ap-4481	23	32	.	.	PUNCT
ap-4481	24	1	next	next	ADV
ap-4481	24	2	,	,	PUNCT
ap-4481	24	3	wigner	wigner	NOUN
ap-4481	24	4	predicted	predict	VERB
ap-4481	24	5	that	that	SCONJ
ap-4481	24	6	(	(	PUNCT
ap-4481	24	7	3	3	X
ap-4481	24	8	)	)	PUNCT
ap-4481	24	9	would	would	AUX
ap-4481	24	10	eventually	eventually	ADV
ap-4481	24	11	represent	represent	VERB
ap-4481	24	12	the	the	DET
ap-4481	24	13	spacing	space	VERB
ap-4481	24	14	statistics	statistic	NOUN
ap-4481	24	15	of	of	ADP
ap-4481	24	16	neutron	neutron	NOUN
ap-4481	24	17	-	-	PUNCT
ap-4481	24	18	nucleus	nucleus	NOUN
ap-4481	24	19	scattering	scatter	VERB
ap-4481	24	20	resonances	resonance	NOUN
ap-4481	24	21	and	and	CCONJ
ap-4481	24	22	nuclear	nuclear	ADJ
ap-4481	24	23	levels	level	NOUN
ap-4481	24	24	.	.	PUNCT
ap-4481	25	1	notice	notice	VERB
ap-4481	25	2	that	that	SCONJ
ap-4481	25	3	near	near	ADP
ap-4481	25	4	zero	zero	NUM
ap-4481	25	5	pw	pw	X
ap-4481	25	6	(	(	PUNCT
ap-4481	25	7	s	s	X
ap-4481	25	8	)	)	PUNCT
ap-4481	25	9	is	be	AUX
ap-4481	25	10	linear	linear	ADJ
ap-4481	25	11	as	as	ADP
ap-4481	25	12	πs/4	πs/4	NOUN
ap-4481	25	13	,	,	PUNCT
ap-4481	25	14	this	this	PRON
ap-4481	25	15	is	be	AUX
ap-4481	25	16	called	call	VERB
ap-4481	25	17	the	the	DET
ap-4481	25	18	linear	linear	ADJ
ap-4481	25	19	level	level	NOUN
ap-4481	25	20	repulsion	repulsion	NOUN
ap-4481	25	21	of	of	ADP
ap-4481	25	22	adjacent	adjacent	ADJ
ap-4481	25	23	eigenvalues	eigenvalue	NOUN
ap-4481	25	24	.	.	PUNCT
ap-4481	26	1	the	the	DET
ap-4481	26	2	rotational	rotational	ADJ
ap-4481	26	3	invariance	invariance	NOUN
ap-4481	26	4	and	and	CCONJ
ap-4481	26	5	invariance	invariance	NOUN
ap-4481	26	6	under	under	ADP
ap-4481	26	7	time	time	NOUN
ap-4481	26	8	-	-	PUNCT
ap-4481	26	9	reversal	reversal	NOUN
ap-4481	26	10	of	of	ADP
ap-4481	26	11	a	a	DET
ap-4481	26	12	symmetric	symmetric	ADJ
ap-4481	26	13	matrix	matrix	NOUN
ap-4481	26	14	lie	lie	NOUN
ap-4481	26	15	behind	behind	ADP
ap-4481	26	16	the	the	DET
ap-4481	26	17	linear	linear	ADJ
ap-4481	26	18	level	level	NOUN
ap-4481	26	19	repulsion	repulsion	NOUN
ap-4481	26	20	.	.	PUNCT
ap-4481	27	1	consequently	consequently	ADV
ap-4481	27	2	,	,	PUNCT
ap-4481	27	3	the	the	DET
ap-4481	27	4	spacing	spacing	NOUN
ap-4481	27	5	of	of	ADP
ap-4481	27	6	nuclear	nuclear	ADJ
ap-4481	27	7	levels	level	NOUN
ap-4481	27	8	of	of	ADP
ap-4481	27	9	same	same	ADJ
ap-4481	27	10	angular	angular	ADJ
ap-4481	27	11	momentum	momentum	NOUN
ap-4481	27	12	j	j	PROPN
ap-4481	27	13	and	and	CCONJ
ap-4481	27	14	parity	parity	NOUN
ap-4481	27	15	π	π	AUX
ap-4481	27	16	indeed	indeed	ADV
ap-4481	27	17	display	display	VERB
ap-4481	27	18	[	[	X
ap-4481	27	19	1–5	1–5	X
ap-4481	27	20	]	]	X
ap-4481	27	21	p(s	p(s	NOUN
ap-4481	27	22	)	)	PUNCT
ap-4481	27	23	in	in	ADP
ap-4481	27	24	(	(	PUNCT
ap-4481	27	25	3	3	NUM
ap-4481	27	26	)	)	PUNCT
ap-4481	27	27	.	.	PUNCT
ap-4481	28	1	wigner	wigner	NOUN
ap-4481	28	2	’s	’s	PART
ap-4481	28	3	surmise	surmise	NOUN
ap-4481	28	4	is	be	AUX
ap-4481	28	5	strange	strange	ADJ
ap-4481	28	6	but	but	CCONJ
ap-4481	28	7	true	true	ADJ
ap-4481	28	8	,	,	PUNCT
ap-4481	28	9	each	each	DET
ap-4481	28	10	nucleus	nucleus	NOUN
ap-4481	28	11	behaves	behave	VERB
ap-4481	28	12	like	like	ADP
ap-4481	28	13	a	a	DET
ap-4481	28	14	matrix	matrix	NOUN
ap-4481	28	15	of	of	ADP
ap-4481	28	16	large	large	ADJ
ap-4481	28	17	order	order	NOUN
ap-4481	28	18	.	.	PUNCT
ap-4481	29	1	even	even	ADV
ap-4481	29	2	much	much	ADV
ap-4481	29	3	later	later	ADV
ap-4481	29	4	,	,	PUNCT
ap-4481	29	5	in	in	ADP
ap-4481	29	6	the	the	DET
ap-4481	29	7	recent	recent	ADJ
ap-4481	29	8	years	year	NOUN
ap-4481	29	9	investigations	investigation	NOUN
ap-4481	29	10	on	on	ADP
ap-4481	29	11	spacing	space	VERB
ap-4481	29	12	distributions	distribution	NOUN
ap-4481	29	13	of	of	ADP
ap-4481	29	14	ensembles	ensemble	NOUN
ap-4481	29	15	random	random	ADJ
ap-4481	29	16	matrices	matrix	NOUN
ap-4481	29	17	using	use	VERB
ap-4481	29	18	2×	2×	NUM
ap-4481	29	19	2	2	NUM
ap-4481	29	20	continue	continue	VERB
ap-4481	29	21	to	to	PART
ap-4481	29	22	be	be	AUX
ap-4481	29	23	an	an	DET
ap-4481	29	24	attractive	attractive	ADJ
ap-4481	29	25	proposition	proposition	NOUN
ap-4481	29	26	for	for	ADP
ap-4481	29	27	both	both	CCONJ
ap-4481	29	28	symmetric	symmetric	ADJ
ap-4481	29	29	/	/	SYM
ap-4481	29	30	hermitian	hermitian	NOUN
ap-4481	29	31	[	[	X
ap-4481	29	32	7	7	NUM
ap-4481	29	33	,	,	PUNCT
ap-4481	29	34	8	8	NUM
ap-4481	29	35	]	]	PUNCT
ap-4481	29	36	and	and	CCONJ
ap-4481	29	37	non	non	ADJ
ap-4481	29	38	-	-	ADJ
ap-4481	29	39	hermitian	hermitian	ADJ
ap-4481	29	40	matrices	matrix	NOUN
ap-4481	29	41	[	[	X
ap-4481	29	42	9–14	9–14	X
ap-4481	29	43	]	]	X
ap-4481	29	44	.	.	PUNCT
ap-4481	30	1	in	in	ADP
ap-4481	30	2	these	these	DET
ap-4481	30	3	works	work	NOUN
ap-4481	30	4	[	[	X
ap-4481	30	5	7	7	NUM
ap-4481	30	6	,	,	PUNCT
ap-4481	30	7	8	8	NUM
ap-4481	30	8	]	]	PUNCT
ap-4481	30	9	one	one	PRON
ap-4481	30	10	has	have	AUX
ap-4481	30	11	taken	take	VERB
ap-4481	30	12	gaussian	gaussian	ADJ
ap-4481	30	13	distribution	distribution	NOUN
ap-4481	30	14	with	with	ADP
ap-4481	30	15	zero	zero	NUM
ap-4481	30	16	mean	mean	NOUN
ap-4481	30	17	and	and	CCONJ
ap-4481	30	18	different	different	ADJ
ap-4481	30	19	variances	variance	NOUN
ap-4481	30	20	for	for	ADP
ap-4481	30	21	various	various	ADJ
ap-4481	30	22	entries	entry	NOUN
ap-4481	30	23	of	of	ADP
ap-4481	30	24	the	the	DET
ap-4481	30	25	matrices	matrix	NOUN
ap-4481	30	26	and	and	CCONJ
ap-4481	30	27	derived	derive	VERB
ap-4481	30	28	a	a	DET
ap-4481	30	29	variety	variety	NOUN
ap-4481	30	30	of	of	ADP
ap-4481	30	31	spacing	space	VERB
ap-4481	30	32	distributions	distribution	NOUN
ap-4481	30	33	.	.	PUNCT
ap-4481	31	1	similarly	similarly	ADV
ap-4481	31	2	,	,	PUNCT
ap-4481	31	3	under	under	ADP
ap-4481	31	4	gaussian	gaussian	NOUN
ap-4481	31	5	418	418	NUM
ap-4481	31	6	http://dx.doi.org/10.14311/ap.2017.57.0418	http://dx.doi.org/10.14311/ap.2017.57.0418	NOUN
ap-4481	31	7	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	NOUN
ap-4481	31	8	vol	vol	NOUN
ap-4481	31	9	.	.	PUNCT
ap-4481	31	10	57	57	NUM
ap-4481	31	11	no	no	NOUN
ap-4481	31	12	.	.	PUNCT
ap-4481	32	1	6/2017	6/2017	X
ap-4481	32	2	new	new	ADJ
ap-4481	32	3	spectral	spectral	ADJ
ap-4481	32	4	statistics	statistic	NOUN
ap-4481	32	5	2	2	NUM
ap-4481	32	6	x	x	SYM
ap-4481	32	7	2	2	NUM
ap-4481	32	8	n=105	n=105	PROPN
ap-4481	32	9	semi	semi	ADJ
ap-4481	32	10	-	-	ADJ
ap-4481	32	11	analytic	analytic	ADJ
ap-4481	32	12	wigner	wigner	NOUN
ap-4481	32	13	surmise	surmise	NOUN
ap-4481	32	14	0	0	NUM
ap-4481	32	15	0.4	0.4	NUM
ap-4481	32	16	0.8	0.8	NUM
ap-4481	32	17	1.2	1.2	NUM
ap-4481	32	18	1.6	1.6	NUM
ap-4481	32	19	2	2	NUM
ap-4481	32	20	.	.	PUNCT
ap-4481	33	1	2.4	2.4	NUM
ap-4481	33	2	s	s	NOUN
ap-4481	33	3	0.4	0.4	NUM
ap-4481	33	4	0.8	0.8	NUM
ap-4481	33	5	phsl	phsl	NOUN
ap-4481	33	6	hal	hal	NOUN
ap-4481	33	7	2	2	NUM
ap-4481	33	8	x	x	SYM
ap-4481	33	9	2	2	NUM
ap-4481	33	10	n=105	n=105	PROPN
ap-4481	33	11	semi	semi	ADJ
ap-4481	33	12	-	-	ADJ
ap-4481	33	13	analytic	analytic	ADJ
ap-4481	33	14	wigner	wigner	NOUN
ap-4481	33	15	surmise	surmise	NOUN
ap-4481	33	16	0	0	NUM
ap-4481	33	17	0.4	0.4	NUM
ap-4481	33	18	0.8	0.8	NUM
ap-4481	33	19	1.2	1.2	NUM
ap-4481	33	20	1.6	1.6	NUM
ap-4481	33	21	2	2	NUM
ap-4481	33	22	.	.	PUNCT
ap-4481	33	23	s	s	VERB
ap-4481	33	24	0.3	0.3	NUM
ap-4481	33	25	0.6	0.6	NUM
ap-4481	33	26	0.9	0.9	NUM
ap-4481	33	27	1.2	1.2	NUM
ap-4481	33	28	phsl	phsl	NOUN
ap-4481	33	29	hbl	hbl	NOUN
ap-4481	33	30	figure	figure	NOUN
ap-4481	33	31	1	1	NUM
ap-4481	33	32	.	.	PUNCT
ap-4481	33	33	p(s	p(s	NOUN
ap-4481	33	34	)	)	PUNCT
ap-4481	33	35	for	for	ADP
ap-4481	33	36	(	(	PUNCT
ap-4481	33	37	a	a	X
ap-4481	33	38	):	):	PUNCT
ap-4481	33	39	r1	r1	PROPN
ap-4481	33	40	and	and	CCONJ
ap-4481	33	41	(	(	PUNCT
ap-4481	33	42	b	b	NOUN
ap-4481	33	43	):	):	PUNCT
ap-4481	33	44	r2	r2	NOUN
ap-4481	33	45	matrices	matrix	NOUN
ap-4481	33	46	due	due	ADJ
ap-4481	33	47	to	to	ADP
ap-4481	33	48	the	the	DET
ap-4481	33	49	uniform	uniform	ADJ
ap-4481	33	50	distribution	distribution	NOUN
ap-4481	33	51	of	of	ADP
ap-4481	33	52	elements	element	NOUN
ap-4481	33	53	.	.	PUNCT
ap-4481	34	1	the	the	DET
ap-4481	34	2	solid	solid	ADJ
ap-4481	34	3	lines	line	NOUN
ap-4481	34	4	are	be	AUX
ap-4481	34	5	due	due	ADJ
ap-4481	34	6	to	to	PART
ap-4481	34	7	(	(	PUNCT
ap-4481	34	8	7	7	NUM
ap-4481	34	9	)	)	PUNCT
ap-4481	34	10	and	and	CCONJ
ap-4481	34	11	(	(	PUNCT
ap-4481	34	12	10	10	NUM
ap-4481	34	13	)	)	PUNCT
ap-4481	34	14	,	,	PUNCT
ap-4481	34	15	dashed	dash	VERB
ap-4481	34	16	lines	line	NOUN
ap-4481	34	17	represent	represent	VERB
ap-4481	34	18	the	the	DET
ap-4481	34	19	wigner	wigner	ADJ
ap-4481	34	20	distribution	distribution	NOUN
ap-4481	34	21	(	(	PUNCT
ap-4481	34	22	3	3	NUM
ap-4481	34	23	)	)	PUNCT
ap-4481	34	24	.	.	PUNCT
ap-4481	35	1	these	these	DET
ap-4481	35	2	two	two	NUM
ap-4481	35	3	p(s	p(s	NOUN
ap-4481	35	4	)	)	PUNCT
ap-4481	35	5	are	be	AUX
ap-4481	35	6	distinctly	distinctly	ADV
ap-4481	35	7	different	different	ADJ
ap-4481	35	8	but	but	CCONJ
ap-4481	35	9	near	near	ADP
ap-4481	35	10	s	s	NOUN
ap-4481	35	11	=	=	SYM
ap-4481	35	12	0	0	NUM
ap-4481	35	13	they	they	PRON
ap-4481	35	14	are	be	AUX
ap-4481	35	15	linear	linear	ADJ
ap-4481	35	16	(	(	PUNCT
ap-4481	35	17	αs	αs	ADJ
ap-4481	35	18	)	)	PUNCT
ap-4481	35	19	,	,	PUNCT
ap-4481	35	20	with	with	ADP
ap-4481	35	21	α	α	PRON
ap-4481	35	22	as	as	ADP
ap-4481	35	23	1.23	1.23	NUM
ap-4481	35	24	and	and	CCONJ
ap-4481	35	25	1.01	1.01	NUM
ap-4481	35	26	,	,	PUNCT
ap-4481	35	27	respectively	respectively	ADV
ap-4481	35	28	pdf	pdf	NOUN
ap-4481	35	29	,	,	PUNCT
ap-4481	35	30	for	for	ADP
ap-4481	35	31	ensembles	ensemble	NOUN
ap-4481	35	32	of	of	ADP
ap-4481	35	33	several	several	ADJ
ap-4481	35	34	2×	2×	NUM
ap-4481	35	35	2	2	NUM
ap-4481	35	36	pseudo	pseudo	NOUN
ap-4481	35	37	-	-	ADJ
ap-4481	35	38	symmetric	symmetric	ADJ
ap-4481	35	39	and	and	CCONJ
ap-4481	35	40	pseudo	pseudo	NOUN
ap-4481	35	41	-	-	NOUN
ap-4481	35	42	hermitian	hermitian	ADJ
ap-4481	35	43	representing	represent	VERB
ap-4481	35	44	parity	parity	NOUN
ap-4481	35	45	-	-	PUNCT
ap-4481	35	46	time	time	NOUN
ap-4481	35	47	-	-	PUNCT
ap-4481	35	48	reversal	reversal	NOUN
ap-4481	35	49	symmetric	symmetric	ADJ
ap-4481	35	50	systems	system	NOUN
ap-4481	35	51	the	the	DET
ap-4481	35	52	novel	novel	ADJ
ap-4481	35	53	expressions	expression	NOUN
ap-4481	35	54	of	of	ADP
ap-4481	35	55	p(s	p(s	NOUN
ap-4481	35	56	)	)	PUNCT
ap-4481	35	57	have	have	AUX
ap-4481	35	58	been	be	AUX
ap-4481	35	59	derived	derive	VERB
ap-4481	35	60	[	[	X
ap-4481	35	61	9–14	9–14	X
ap-4481	35	62	]	]	X
ap-4481	35	63	.	.	PUNCT
ap-4481	36	1	here	here	ADV
ap-4481	36	2	,	,	PUNCT
ap-4481	36	3	we	we	PRON
ap-4481	36	4	show	show	VERB
ap-4481	36	5	that	that	SCONJ
ap-4481	36	6	even	even	ADV
ap-4481	36	7	two	two	NUM
ap-4481	36	8	modifications	modification	NOUN
ap-4481	36	9	of	of	ADP
ap-4481	36	10	real	real	ADJ
ap-4481	36	11	symmetric	symmetric	ADJ
ap-4481	36	12	2×	2×	NUM
ap-4481	36	13	2	2	NUM
ap-4481	36	14	random	random	ADJ
ap-4481	36	15	matrices	matrix	NOUN
ap-4481	36	16	yield	yield	VERB
ap-4481	36	17	different	different	ADJ
ap-4481	36	18	p(s	p(s	NOUN
ap-4481	36	19	)	)	PUNCT
ap-4481	36	20	under	under	ADP
ap-4481	36	21	the	the	DET
ap-4481	36	22	same	same	ADJ
ap-4481	36	23	probability	probability	NOUN
ap-4481	36	24	distribution	distribution	NOUN
ap-4481	36	25	function	function	NOUN
ap-4481	36	26	(	(	PUNCT
ap-4481	36	27	pdf	pdf	NOUN
ap-4481	36	28	)	)	PUNCT
ap-4481	36	29	f(x	f(x	PROPN
ap-4481	36	30	)	)	PUNCT
ap-4481	36	31	.	.	PUNCT
ap-4481	37	1	similarly	similarly	ADV
ap-4481	37	2	,	,	PUNCT
ap-4481	37	3	one	one	NUM
ap-4481	37	4	type	type	NOUN
ap-4481	37	5	of	of	ADP
ap-4481	37	6	matrix	matrix	NOUN
ap-4481	37	7	under	under	ADP
ap-4481	37	8	several	several	ADJ
ap-4481	37	9	non	non	ADJ
ap-4481	37	10	-	-	ADJ
ap-4481	37	11	gaussian	gaussian	ADJ
ap-4481	37	12	pdfs	pdfs	NOUN
ap-4481	37	13	yield	yield	VERB
ap-4481	37	14	distinct	distinct	ADJ
ap-4481	37	15	expressions	expression	NOUN
ap-4481	37	16	for	for	ADP
ap-4481	37	17	p(s	p(s	NUM
ap-4481	37	18	)	)	PUNCT
ap-4481	37	19	.	.	PUNCT
ap-4481	38	1	however	however	ADV
ap-4481	38	2	,	,	PUNCT
ap-4481	38	3	all	all	DET
ap-4481	38	4	the	the	DET
ap-4481	38	5	spacing	space	VERB
ap-4481	38	6	distributions	distribution	NOUN
ap-4481	38	7	display	display	VERB
ap-4481	38	8	the	the	DET
ap-4481	38	9	linear	linear	NOUN
ap-4481	38	10	(	(	PUNCT
ap-4481	38	11	αs	αs	ADJ
ap-4481	38	12	)	)	PUNCT
ap-4481	38	13	level	level	NOUN
ap-4481	38	14	repulsion	repulsion	NOUN
ap-4481	38	15	near	near	ADP
ap-4481	38	16	s	s	NOUN
ap-4481	38	17	=	=	SYM
ap-4481	38	18	0	0	NUM
ap-4481	38	19	wherein	wherein	ADJ
ap-4481	38	20	α	α	PROPN
ap-4481	38	21	depends	depend	VERB
ap-4481	38	22	on	on	ADP
ap-4481	38	23	the	the	DET
ap-4481	38	24	type	type	NOUN
ap-4481	38	25	of	of	ADP
ap-4481	38	26	pdf	pdf	NOUN
ap-4481	38	27	and	and	CCONJ
ap-4481	38	28	the	the	DET
ap-4481	38	29	type	type	NOUN
ap-4481	38	30	of	of	ADP
ap-4481	38	31	matrix	matrix	NOUN
ap-4481	38	32	(	(	PUNCT
ap-4481	38	33	1	1	X
ap-4481	38	34	)	)	PUNCT
ap-4481	38	35	being	be	AUX
ap-4481	38	36	used	use	VERB
ap-4481	38	37	.	.	PUNCT
ap-4481	39	1	the	the	DET
ap-4481	39	2	question	question	NOUN
ap-4481	39	3	of	of	ADP
ap-4481	39	4	using	use	VERB
ap-4481	39	5	a	a	DET
ap-4481	39	6	non	non	ADJ
ap-4481	39	7	-	-	ADJ
ap-4481	39	8	gaussian	gaussian	ADJ
ap-4481	39	9	probability	probability	NOUN
ap-4481	39	10	distribution	distribution	NOUN
ap-4481	39	11	to	to	PART
ap-4481	39	12	test	test	VERB
ap-4481	39	13	wigner	wigner	NOUN
ap-4481	39	14	’s	’s	PART
ap-4481	39	15	second	second	ADJ
ap-4481	39	16	conjecture	conjecture	NOUN
ap-4481	39	17	does	do	AUX
ap-4481	39	18	not	not	PART
ap-4481	39	19	appear	appear	VERB
ap-4481	39	20	to	to	PART
ap-4481	39	21	have	have	AUX
ap-4481	39	22	attracted	attract	VERB
ap-4481	39	23	much	much	ADJ
ap-4481	39	24	attention	attention	NOUN
ap-4481	39	25	after	after	ADP
ap-4481	39	26	[	[	X
ap-4481	39	27	6	6	NUM
ap-4481	39	28	]	]	PUNCT
ap-4481	39	29	.	.	PUNCT
ap-4481	40	1	however	however	ADV
ap-4481	40	2	,	,	PUNCT
ap-4481	40	3	it	it	PRON
ap-4481	40	4	is	be	AUX
ap-4481	40	5	generally	generally	ADV
ap-4481	40	6	believed	believe	VERB
ap-4481	40	7	that	that	SCONJ
ap-4481	40	8	spectral	spectral	ADJ
ap-4481	40	9	distributions	distribution	NOUN
ap-4481	40	10	are	be	AUX
ap-4481	40	11	insensitive	insensitive	ADJ
ap-4481	40	12	to	to	ADP
ap-4481	40	13	pdfs	pdfs	PROPN
ap-4481	40	14	.	.	PUNCT
ap-4481	41	1	use	use	NOUN
ap-4481	41	2	of	of	ADP
ap-4481	41	3	many	many	ADJ
ap-4481	41	4	non	non	ADJ
ap-4481	41	5	-	-	ADJ
ap-4481	41	6	gaussian	gaussian	ADJ
ap-4481	41	7	distributions	distribution	NOUN
ap-4481	41	8	for	for	ADP
ap-4481	41	9	finding	find	VERB
ap-4481	41	10	the	the	DET
ap-4481	41	11	probability	probability	NOUN
ap-4481	41	12	[	[	X
ap-4481	41	13	15	15	NUM
ap-4481	41	14	]	]	PUNCT
ap-4481	41	15	of	of	ADP
ap-4481	41	16	occurrence	occurrence	NOUN
ap-4481	41	17	of	of	ADP
ap-4481	41	18	real	real	ADJ
ap-4481	41	19	eigenvalues	eigenvalue	NOUN
ap-4481	41	20	for	for	ADP
ap-4481	41	21	the	the	DET
ap-4481	41	22	product	product	NOUN
ap-4481	41	23	of	of	ADP
ap-4481	41	24	n	n	PRON
ap-4481	41	25	number	number	NOUN
ap-4481	41	26	of	of	ADP
ap-4481	41	27	2×	2×	NUM
ap-4481	41	28	2	2	NUM
ap-4481	41	29	real	real	ADV
ap-4481	41	30	random	random	ADJ
ap-4481	41	31	matrices	matrix	NOUN
ap-4481	41	32	is	be	AUX
ap-4481	41	33	worth	worth	ADJ
ap-4481	41	34	mentioning	mention	VERB
ap-4481	41	35	.	.	PUNCT
ap-4481	42	1	the	the	DET
ap-4481	42	2	other	other	ADJ
ap-4481	42	3	interesting	interesting	ADJ
ap-4481	42	4	spectral	spectral	ADJ
ap-4481	42	5	statistics	statistic	NOUN
ap-4481	42	6	denoted	denote	VERB
ap-4481	42	7	as	as	ADP
ap-4481	42	8	d(ε	d(ε	PROPN
ap-4481	42	9	)	)	PUNCT
ap-4481	42	10	is	be	AUX
ap-4481	42	11	called	call	VERB
ap-4481	42	12	distribution	distribution	NOUN
ap-4481	42	13	of	of	ADP
ap-4481	42	14	eigenvalues	eigenvalue	NOUN
ap-4481	42	15	of	of	ADP
ap-4481	42	16	n×	n×	PROPN
ap-4481	42	17	n	n	CCONJ
ap-4481	42	18	real	real	ADJ
ap-4481	42	19	symmetric	symmetric	ADJ
ap-4481	42	20	matrices	matrix	NOUN
ap-4481	42	21	when	when	SCONJ
ap-4481	42	22	n	n	PRON
ap-4481	42	23	is	be	AUX
ap-4481	42	24	large	large	ADJ
ap-4481	42	25	.	.	PUNCT
ap-4481	43	1	wigner	wigner	NOUN
ap-4481	43	2	proposed	propose	VERB
ap-4481	43	3	it	it	PRON
ap-4481	43	4	to	to	PART
ap-4481	43	5	be	be	AUX
ap-4481	43	6	[	[	X
ap-4481	43	7	1–5	1–5	X
ap-4481	43	8	]	]	X
ap-4481	43	9	d(ε	d(ε	NOUN
ap-4481	43	10	)	)	PUNCT
ap-4481	43	11	=	=	SYM
ap-4481	44	1	2	2	NUM
ap-4481	44	2	π	π	NOUN
ap-4481	44	3	√	√	PROPN
ap-4481	44	4	1−	1−	NUM
ap-4481	44	5	ε2	ε2	PROPN
ap-4481	44	6	,	,	PUNCT
ap-4481	44	7	ε	ε	PROPN
ap-4481	44	8	=	=	SYM
ap-4481	44	9	e	e	PROPN
ap-4481	44	10	/	/	SYM
ap-4481	44	11	e∗	e∗	NOUN
ap-4481	44	12	(	(	PUNCT
ap-4481	44	13	4	4	NUM
ap-4481	44	14	)	)	PUNCT
ap-4481	44	15	which	which	PRON
ap-4481	44	16	is	be	AUX
ap-4481	44	17	well	well	ADV
ap-4481	44	18	known	know	VERB
ap-4481	44	19	as	as	ADP
ap-4481	44	20	wigner	wigner	NOUN
ap-4481	44	21	’s	’s	PART
ap-4481	44	22	semicircle	semicircle	NOUN
ap-4481	44	23	law	law	NOUN
ap-4481	44	24	.	.	PUNCT
ap-4481	45	1	in	in	ADP
ap-4481	45	2	case	case	NOUN
ap-4481	45	3	of	of	ADP
ap-4481	45	4	large	large	ADJ
ap-4481	45	5	values	value	NOUN
ap-4481	45	6	of	of	ADP
ap-4481	45	7	n	n	NUM
ap-4481	45	8	,	,	PUNCT
ap-4481	45	9	e∗	e∗	PROPN
ap-4481	45	10	is	be	AUX
ap-4481	45	11	the	the	DET
ap-4481	45	12	maximum	maximum	PROPN
ap-4481	45	13	eigenvalue	eigenvalue	NOUN
ap-4481	45	14	of	of	ADP
ap-4481	45	15	the	the	DET
ap-4481	45	16	matrix	matrix	NOUN
ap-4481	45	17	.	.	PUNCT
ap-4481	46	1	due	due	ADP
ap-4481	46	2	to	to	ADP
ap-4481	46	3	the	the	DET
ap-4481	46	4	historic	historic	ADJ
ap-4481	46	5	connection	connection	NOUN
ap-4481	46	6	of	of	ADP
ap-4481	46	7	2×2	2×2	NUM
ap-4481	46	8	matrices	matrix	NOUN
ap-4481	46	9	in	in	ADP
ap-4481	46	10	rmt	rmt	NOUN
ap-4481	46	11	and	and	CCONJ
ap-4481	46	12	specially	specially	ADV
ap-4481	46	13	due	due	ADJ
ap-4481	46	14	to	to	ADP
ap-4481	46	15	the	the	DET
ap-4481	46	16	astonishing	astonishing	ADJ
ap-4481	46	17	sameness	sameness	NOUN
ap-4481	46	18	of	of	ADP
ap-4481	46	19	p(s	p(s	NOUN
ap-4481	46	20	)	)	PUNCT
ap-4481	46	21	in	in	ADP
ap-4481	46	22	case	case	NOUN
ap-4481	46	23	of	of	ADP
ap-4481	46	24	goe	goe	NOUN
ap-4481	46	25	for	for	ADP
ap-4481	46	26	n	n	NOUN
ap-4481	46	27	=	=	SYM
ap-4481	46	28	2	2	NUM
ap-4481	46	29	and	and	CCONJ
ap-4481	46	30	n	n	NOUN
ap-4481	46	31	>	>	X
ap-4481	46	32	>	>	X
ap-4481	46	33	2	2	NUM
ap-4481	46	34	,	,	PUNCT
ap-4481	46	35	the	the	DET
ap-4481	46	36	question	question	NOUN
ap-4481	46	37	arising	arise	VERB
ap-4481	46	38	here	here	ADV
ap-4481	46	39	is	be	AUX
ap-4481	46	40	as	as	ADP
ap-4481	46	41	to	to	ADP
ap-4481	46	42	what	what	PRON
ap-4481	46	43	is	be	AUX
ap-4481	46	44	the	the	DET
ap-4481	46	45	analytic	analytic	ADJ
ap-4481	46	46	form	form	NOUN
ap-4481	46	47	of	of	ADP
ap-4481	46	48	d(ε	d(ε	NOUN
ap-4481	46	49	)	)	PUNCT
ap-4481	46	50	in	in	ADP
ap-4481	46	51	case	case	NOUN
ap-4481	46	52	of	of	ADP
ap-4481	46	53	n	n	NOUN
ap-4481	46	54	=	=	SYM
ap-4481	46	55	2	2	NUM
ap-4481	46	56	.	.	PUNCT
ap-4481	46	57	due	due	ADP
ap-4481	46	58	to	to	ADP
ap-4481	46	59	the	the	DET
ap-4481	46	60	numerical	numerical	ADJ
ap-4481	46	61	calculations	calculation	NOUN
ap-4481	46	62	of	of	ADP
ap-4481	46	63	porter	porter	NOUN
ap-4481	46	64	we	we	PRON
ap-4481	46	65	know	know	VERB
ap-4481	46	66	that	that	SCONJ
ap-4481	46	67	qualitatively	qualitatively	ADV
ap-4481	46	68	d(ε	d(ε	NOUN
ap-4481	46	69	)	)	PUNCT
ap-4481	46	70	makes	make	VERB
ap-4481	46	71	an	an	DET
ap-4481	46	72	interesting	interesting	ADJ
ap-4481	46	73	transition	transition	NOUN
ap-4481	46	74	from	from	ADP
ap-4481	46	75	a	a	DET
ap-4481	46	76	bell	bell	NOUN
ap-4481	46	77	shape	shape	NOUN
ap-4481	46	78	to	to	ADP
ap-4481	46	79	the	the	DET
ap-4481	46	80	semi	semi	NOUN
ap-4481	46	81	-	-	NOUN
ap-4481	46	82	circle	circle	NOUN
ap-4481	46	83	as	as	ADP
ap-4481	46	84	the	the	DET
ap-4481	46	85	n	n	NOUN
ap-4481	46	86	increases	increase	NOUN
ap-4481	46	87	.	.	PUNCT
ap-4481	47	1	in	in	ADP
ap-4481	47	2	case	case	NOUN
ap-4481	47	3	of	of	ADP
ap-4481	47	4	n	n	NOUN
ap-4481	47	5	=	=	SYM
ap-4481	47	6	2	2	NUM
ap-4481	47	7	,	,	PUNCT
ap-4481	47	8	we	we	PRON
ap-4481	47	9	collect	collect	VERB
ap-4481	47	10	a	a	DET
ap-4481	47	11	large	large	ADJ
ap-4481	47	12	number	number	NOUN
ap-4481	47	13	(	(	PUNCT
ap-4481	47	14	n	n	CCONJ
ap-4481	47	15	)	)	PUNCT
ap-4481	47	16	of	of	ADP
ap-4481	47	17	matrices	matrix	NOUN
ap-4481	47	18	and	and	CCONJ
ap-4481	47	19	find	find	VERB
ap-4481	47	20	the	the	DET
ap-4481	47	21	mean	mean	NOUN
ap-4481	47	22	of	of	ADP
ap-4481	47	23	positive	positive	ADJ
ap-4481	47	24	eigenvalues	eigenvalue	NOUN
ap-4481	47	25	to	to	PART
ap-4481	47	26	fix	fix	VERB
ap-4481	47	27	e∗	e∗	NOUN
ap-4481	47	28	=	=	SYM
ap-4481	47	29	ē	ē	ADV
ap-4481	47	30	to	to	PART
ap-4481	47	31	obtain	obtain	VERB
ap-4481	47	32	d(ε	d(ε	NOUN
ap-4481	47	33	)	)	PUNCT
ap-4481	47	34	both	both	CCONJ
ap-4481	47	35	analytically	analytically	ADV
ap-4481	47	36	and	and	CCONJ
ap-4481	47	37	by	by	ADP
ap-4481	47	38	finding	find	VERB
ap-4481	47	39	their	their	PRON
ap-4481	47	40	histograms	histogram	NOUN
ap-4481	47	41	numerically	numerically	ADV
ap-4481	47	42	.	.	PUNCT
ap-4481	48	1	the	the	DET
ap-4481	48	2	obtained	obtain	VERB
ap-4481	48	3	d(ε	d(ε	PROPN
ap-4481	48	4	)	)	PUNCT
ap-4481	48	5	once	once	ADV
ap-4481	48	6	again	again	ADV
ap-4481	48	7	are	be	AUX
ap-4481	48	8	unlike	unlike	ADP
ap-4481	48	9	the	the	DET
ap-4481	48	10	wigner	wigner	NOUN
ap-4481	48	11	’s	’s	PART
ap-4481	48	12	semi	semi	ADJ
ap-4481	48	13	-	-	ADJ
ap-4481	48	14	circle	circle	ADJ
ap-4481	48	15	law	law	NOUN
ap-4481	48	16	(	(	PUNCT
ap-4481	48	17	4	4	NUM
ap-4481	48	18	)	)	PUNCT
ap-4481	48	19	(	(	PUNCT
ap-4481	48	20	for	for	ADP
ap-4481	48	21	n	n	NOUN
ap-4481	48	22	=	=	SYM
ap-4481	48	23	2	2	NUM
ap-4481	48	24	)	)	PUNCT
ap-4481	48	25	and	and	CCONJ
ap-4481	48	26	our	our	PRON
ap-4481	48	27	analytic	analytic	ADJ
ap-4481	48	28	/	/	SYM
ap-4481	48	29	semi	semi	ADJ
ap-4481	48	30	-	-	ADJ
ap-4481	48	31	analytic	analytic	ADJ
ap-4481	48	32	results	result	NOUN
ap-4481	48	33	agree	agree	VERB
ap-4481	48	34	excellently	excellently	ADV
ap-4481	48	35	with	with	ADP
ap-4481	48	36	the	the	DET
ap-4481	48	37	numerically	numerically	ADV
ap-4481	48	38	computed	compute	VERB
ap-4481	48	39	histograms	histogram	NOUN
ap-4481	48	40	.	.	PUNCT
ap-4481	49	1	in	in	ADP
ap-4481	49	2	§	§	PROPN
ap-4481	49	3	2	2	NUM
ap-4481	49	4	,	,	PUNCT
ap-4481	49	5	we	we	PRON
ap-4481	49	6	wish	wish	VERB
ap-4481	49	7	to	to	PART
ap-4481	49	8	present	present	VERB
ap-4481	49	9	analytic	analytic	ADJ
ap-4481	49	10	or	or	CCONJ
ap-4481	49	11	semi	semi	ADJ
ap-4481	49	12	-	-	ADJ
ap-4481	49	13	analytic	analytic	ADJ
ap-4481	49	14	p(s	p(s	NOUN
ap-4481	49	15	)	)	PUNCT
ap-4481	49	16	for	for	ADP
ap-4481	49	17	four	four	NUM
ap-4481	49	18	non	non	ADJ
ap-4481	49	19	-	-	ADJ
ap-4481	49	20	gaussian	gaussian	ADJ
ap-4481	49	21	pdfs	pdfs	NOUN
ap-4481	49	22	of	of	ADP
ap-4481	49	23	elements	element	NOUN
ap-4481	49	24	of	of	ADP
ap-4481	49	25	matrices	matrix	NOUN
ap-4481	49	26	for	for	ADP
ap-4481	49	27	two	two	NUM
ap-4481	49	28	types	type	NOUN
ap-4481	49	29	of	of	ADP
ap-4481	49	30	2×	2×	NUM
ap-4481	49	31	2	2	NUM
ap-4481	49	32	.	.	PUNCT
ap-4481	50	1	these	these	DET
ap-4481	50	2	non	non	ADJ
ap-4481	50	3	-	-	ADJ
ap-4481	50	4	gaussian	gaussian	ADJ
ap-4481	50	5	pdfs	pdfs	NOUN
ap-4481	50	6	are	be	AUX
ap-4481	50	7	:	:	PUNCT
ap-4481	50	8	uniform	uniform	ADJ
ap-4481	50	9	(	(	PUNCT
ap-4481	50	10	u	u	NOUN
ap-4481	50	11	)	)	PUNCT
ap-4481	50	12	,	,	PUNCT
ap-4481	50	13	exponential	exponential	NOUN
ap-4481	50	14	(	(	PUNCT
ap-4481	50	15	e	e	NOUN
ap-4481	50	16	:	:	PUNCT
ap-4481	50	17	f(x	f(x	PROPN
ap-4481	50	18	)	)	PUNCT
ap-4481	50	19	=	=	PUNCT
ap-4481	51	1	e−|x|	e−|x|	NOUN
ap-4481	51	2	,	,	PUNCT
ap-4481	51	3	super	super	ADJ
ap-4481	51	4	-	-	ADJ
ap-4481	51	5	gaussian	gaussian	ADJ
ap-4481	51	6	(	(	PUNCT
ap-4481	51	7	sg	sg	PROPN
ap-4481	51	8	:	:	PUNCT
ap-4481	51	9	f(x	f(x	PROPN
ap-4481	51	10	)	)	PUNCT
ap-4481	52	1	=	=	PUNCT
ap-4481	52	2	e−x	e−x	NOUN
ap-4481	52	3	4	4	NUM
ap-4481	52	4	)	)	PUNCT
ap-4481	52	5	and	and	CCONJ
ap-4481	52	6	maxwellian	maxwellian	NOUN
ap-4481	52	7	(	(	PUNCT
ap-4481	52	8	m	m	NOUN
ap-4481	52	9	:	:	PUNCT
ap-4481	52	10	f(x	f(x	PROPN
ap-4481	52	11	)	)	PUNCT
ap-4481	53	1	=	=	PUNCT
ap-4481	53	2	xe−x	xe−x	NOUN
ap-4481	53	3	2	2	NUM
ap-4481	53	4	)	)	PUNCT
ap-4481	53	5	.	.	PUNCT
ap-4481	54	1	in	in	ADP
ap-4481	54	2	§	§	PROPN
ap-4481	54	3	3	3	NUM
ap-4481	54	4	,	,	PUNCT
ap-4481	54	5	we	we	PRON
ap-4481	54	6	derive	derive	VERB
ap-4481	54	7	d(ε	d(ε	PROPN
ap-4481	54	8	)	)	PUNCT
ap-4481	54	9	for	for	ADP
ap-4481	54	10	r1	r1	NOUN
ap-4481	54	11	and	and	CCONJ
ap-4481	54	12	r2	r2	PROPN
ap-4481	54	13	and	and	CCONJ
ap-4481	54	14	plot	plot	VERB
ap-4481	54	15	them	they	PRON
ap-4481	54	16	in	in	ADP
ap-4481	54	17	figure	figure	NOUN
ap-4481	54	18	4	4	NUM
ap-4481	54	19	with	with	ADP
ap-4481	54	20	their	their	PRON
ap-4481	54	21	numerically	numerically	ADV
ap-4481	54	22	computed	compute	VERB
ap-4481	54	23	histograms	histogram	NOUN
ap-4481	54	24	.	.	PUNCT
ap-4481	55	1	2	2	X
ap-4481	55	2	.	.	NUM
ap-4481	55	3	ensembles	ensemble	NOUN
ap-4481	55	4	of	of	ADP
ap-4481	55	5	2×	2×	NUM
ap-4481	55	6	2	2	NUM
ap-4481	55	7	real	real	ADJ
ap-4481	55	8	-	-	PUNCT
ap-4481	55	9	symmetric	symmetric	ADJ
ap-4481	55	10	random	random	ADJ
ap-4481	55	11	matrices	matrix	NOUN
ap-4481	55	12	and	and	CCONJ
ap-4481	55	13	their	their	PRON
ap-4481	55	14	spacing	space	VERB
ap-4481	55	15	distributions	distribution	NOUN
ap-4481	55	16	in	in	ADP
ap-4481	55	17	this	this	DET
ap-4481	55	18	section	section	NOUN
ap-4481	55	19	we	we	PRON
ap-4481	55	20	find	find	VERB
ap-4481	55	21	p	p	PROPN
ap-4481	55	22	(	(	PUNCT
ap-4481	55	23	s	s	NOUN
ap-4481	55	24	)	)	PUNCT
ap-4481	55	25	(	(	PUNCT
ap-4481	55	26	2	2	X
ap-4481	55	27	)	)	PUNCT
ap-4481	55	28	for	for	ADP
ap-4481	55	29	two	two	NUM
ap-4481	55	30	real	real	ADJ
ap-4481	55	31	symmetric	symmetric	ADJ
ap-4481	55	32	matrices	matrix	NOUN
ap-4481	55	33	r1	r1	NOUN
ap-4481	55	34	and	and	CCONJ
ap-4481	55	35	r2	r2	NOUN
ap-4481	55	36	for	for	ADP
ap-4481	55	37	four	four	NUM
ap-4481	55	38	pdfs	pdfs	NOUN
ap-4481	55	39	(	(	PUNCT
ap-4481	55	40	u	u	NOUN
ap-4481	55	41	,	,	PUNCT
ap-4481	55	42	e	e	PROPN
ap-4481	55	43	,	,	PUNCT
ap-4481	55	44	sg	sg	PROPN
ap-4481	55	45	,	,	PUNCT
ap-4481	55	46	m	m	PROPN
ap-4481	55	47	)	)	PUNCT
ap-4481	55	48	.	.	PUNCT
ap-4481	56	1	by	by	ADP
ap-4481	56	2	finding	find	VERB
ap-4481	56	3	the	the	DET
ap-4481	56	4	average	average	ADJ
ap-4481	56	5	spacing	spacing	NOUN
ap-4481	56	6	as	as	ADP
ap-4481	56	7	s̄	s̄	NOUN
ap-4481	56	8	=	=	SYM
ap-4481	56	9	∫∞	∫∞	NOUN
ap-4481	56	10	0	0	NUM
ap-4481	56	11	sp	sp	ADP
ap-4481	56	12	(	(	PUNCT
ap-4481	56	13	s	s	NOUN
ap-4481	56	14	)	)	PUNCT
ap-4481	56	15	ds/	ds/	NOUN
ap-4481	56	16	∫∞	∫∞	NOUN
ap-4481	56	17	0	0	PUNCT
ap-4481	57	1	p	p	X
ap-4481	57	2	(	(	PUNCT
ap-4481	57	3	s)s	s)s	X
ap-4481	57	4	,	,	PUNCT
ap-4481	57	5	we	we	PRON
ap-4481	57	6	then	then	ADV
ap-4481	57	7	find	find	VERB
ap-4481	57	8	the	the	DET
ap-4481	57	9	normalized	normalized	ADJ
ap-4481	57	10	spacing	space	VERB
ap-4481	57	11	distribution	distribution	NOUN
ap-4481	57	12	p(s	p(s	NOUN
ap-4481	57	13	=	=	SYM
ap-4481	57	14	s	s	NOUN
ap-4481	57	15	/	/	SYM
ap-4481	57	16	s̄	s̄	NOUN
ap-4481	57	17	)	)	PUNCT
ap-4481	57	18	.	.	PUNCT
ap-4481	58	1	we	we	PRON
ap-4481	58	2	thus	thus	ADV
ap-4481	58	3	conform	conform	VERB
ap-4481	58	4	to	to	ADP
ap-4481	58	5	the	the	DET
ap-4481	58	6	invariance	invariance	NOUN
ap-4481	58	7	of	of	ADP
ap-4481	58	8	distributions	distribution	NOUN
ap-4481	58	9	in	in	ADP
ap-4481	58	10	two	two	NUM
ap-4481	58	11	s	s	NOUN
ap-4481	58	12	and	and	CCONJ
ap-4481	58	13	s	s	PRON
ap-4481	58	14	as	as	ADP
ap-4481	58	15	p(s)ds	p(s)ds	NOUN
ap-4481	58	16	=	=	SYM
ap-4481	58	17	p	p	X
ap-4481	58	18	(	(	PUNCT
ap-4481	58	19	s)ds	s)ds	PROPN
ap-4481	58	20	.	.	PROPN
ap-4481	58	21	2.1	2.1	NUM
ap-4481	58	22	.	.	PUNCT
ap-4481	58	23	uniform	uniform	ADJ
ap-4481	58	24	distribution	distribution	NOUN
ap-4481	58	25	:	:	PUNCT
ap-4481	58	26	f(x	f(x	PROPN
ap-4481	58	27	)	)	PUNCT
ap-4481	58	28	=	=	PUNCT
ap-4481	59	1	1	1	NUM
ap-4481	59	2	,	,	PUNCT
ap-4481	59	3	0	0	NUM
ap-4481	59	4	≤	≤	NUM
ap-4481	59	5	|x|	|x|	PROPN
ap-4481	59	6	≤	≤	PROPN
ap-4481	59	7	λ	λ	PROPN
ap-4481	59	8	,	,	PUNCT
ap-4481	59	9	f(x	f(x	PROPN
ap-4481	59	10	)	)	PUNCT
ap-4481	59	11	=	=	SYM
ap-4481	60	1	0	0	NUM
ap-4481	60	2	,	,	PUNCT
ap-4481	60	3	|x|	|x|	PROPN
ap-4481	60	4	>	>	X
ap-4481	60	5	λ	λ	PROPN
ap-4481	60	6	for	for	ADP
ap-4481	60	7	the	the	DET
ap-4481	60	8	matrix	matrix	NOUN
ap-4481	60	9	r1	r1	NOUN
ap-4481	60	10	,	,	PUNCT
ap-4481	60	11	we	we	PRON
ap-4481	60	12	have	have	VERB
ap-4481	60	13	to	to	PART
ap-4481	60	14	evaluate	evaluate	VERB
ap-4481	60	15	p	p	PROPN
ap-4481	60	16	(	(	PUNCT
ap-4481	60	17	s	s	X
ap-4481	60	18	)	)	PUNCT
ap-4481	60	19	=	=	PUNCT
ap-4481	60	20	a	a	DET
ap-4481	60	21	∫	∫	PROPN
ap-4481	60	22	λ	λ	PROPN
ap-4481	60	23	−λ	−λ	PROPN
ap-4481	60	24	∫	∫	PROPN
ap-4481	60	25	λ	λ	PROPN
ap-4481	61	1	−λ	−λ	PROPN
ap-4481	61	2	∫	∫	PROPN
ap-4481	61	3	λ	λ	PROPN
ap-4481	61	4	−λ	−λ	PROPN
ap-4481	61	5	δ	δ	PROPN
ap-4481	61	6	[	[	PUNCT
ap-4481	61	7	s	s	NOUN
ap-4481	61	8	−	−	NOUN
ap-4481	61	9	√	√	PROPN
ap-4481	61	10	4b2	4b2	NUM
ap-4481	61	11	+	+	CCONJ
ap-4481	61	12	(	(	PUNCT
ap-4481	61	13	a−	a−	PROPN
ap-4481	61	14	c)2	c)2	PROPN
ap-4481	61	15	]	]	PUNCT
ap-4481	61	16	da	da	X
ap-4481	61	17	dbdc	dbdc	NOUN
ap-4481	61	18	,	,	PUNCT
ap-4481	61	19	(	(	PUNCT
ap-4481	61	20	5	5	X
ap-4481	61	21	)	)	PUNCT
ap-4481	61	22	419	419	NUM
ap-4481	61	23	sachin	sachin	PROPN
ap-4481	61	24	kumar	kumar	PROPN
ap-4481	61	25	,	,	PUNCT
ap-4481	61	26	zafar	zafar	PROPN
ap-4481	61	27	ahmed	ahmed	PROPN
ap-4481	61	28	acta	acta	PROPN
ap-4481	61	29	polytechnica	polytechnica	PROPN
ap-4481	61	30	2	2	NUM
ap-4481	61	31	x	x	SYM
ap-4481	61	32	2	2	NUM
ap-4481	61	33	n=105	n=105	PROPN
ap-4481	61	34	semi	semi	ADJ
ap-4481	61	35	-	-	ADJ
ap-4481	61	36	analytic	analytic	ADJ
ap-4481	61	37	wigner	wigner	NOUN
ap-4481	61	38	surmise	surmise	NOUN
ap-4481	61	39	0	0	NUM
ap-4481	61	40	0.5	0.5	NUM
ap-4481	61	41	1	1	NUM
ap-4481	61	42	.	.	NOUN
ap-4481	61	43	1.5	1.5	NUM
ap-4481	61	44	2	2	NUM
ap-4481	61	45	.	.	X
ap-4481	61	46	2.5	2.5	NUM
ap-4481	61	47	3	3	NUM
ap-4481	61	48	.	.	PUNCT
ap-4481	61	49	3.5	3.5	NUM
ap-4481	61	50	s	s	NOUN
ap-4481	61	51	0.4	0.4	NUM
ap-4481	61	52	0.8	0.8	NUM
ap-4481	61	53	phsl	phsl	NOUN
ap-4481	61	54	hal	hal	NOUN
ap-4481	61	55	2	2	NUM
ap-4481	61	56	x	x	SYM
ap-4481	61	57	2	2	NUM
ap-4481	61	58	n=105	n=105	PROPN
ap-4481	61	59	semi	semi	ADJ
ap-4481	61	60	-	-	ADJ
ap-4481	61	61	analytic	analytic	ADJ
ap-4481	61	62	wigner	wigner	NOUN
ap-4481	61	63	surmise	surmise	NOUN
ap-4481	61	64	0	0	NUM
ap-4481	61	65	0.4	0.4	NUM
ap-4481	61	66	0.8	0.8	NUM
ap-4481	61	67	1.2	1.2	NUM
ap-4481	61	68	1.6	1.6	NUM
ap-4481	61	69	2	2	NUM
ap-4481	61	70	.	.	PUNCT
ap-4481	61	71	2.4	2.4	NUM
ap-4481	61	72	2.8	2.8	NUM
ap-4481	61	73	3.2	3.2	NUM
ap-4481	61	74	3.6	3.6	NUM
ap-4481	61	75	s	s	NOUN
ap-4481	61	76	0.2	0.2	NUM
ap-4481	61	77	0.4	0.4	NUM
ap-4481	61	78	0.6	0.6	NUM
ap-4481	61	79	0.8	0.8	NUM
ap-4481	61	80	phsl	phsl	NOUN
ap-4481	61	81	hbl	hbl	NOUN
ap-4481	61	82	figure	figure	NOUN
ap-4481	61	83	2	2	NUM
ap-4481	61	84	.	.	PUNCT
ap-4481	61	85	the	the	DET
ap-4481	61	86	same	same	ADJ
ap-4481	61	87	as	as	ADP
ap-4481	61	88	in	in	ADP
ap-4481	61	89	figure	figure	NOUN
ap-4481	61	90	1	1	NUM
ap-4481	61	91	,	,	PUNCT
ap-4481	61	92	for	for	ADP
ap-4481	61	93	exponential	exponential	ADJ
ap-4481	61	94	pdf	pdf	NOUN
ap-4481	61	95	(	(	PUNCT
ap-4481	61	96	e	e	NOUN
ap-4481	61	97	:	:	PUNCT
ap-4481	61	98	e−|x|	e−|x|	X
ap-4481	61	99	)	)	PUNCT
ap-4481	61	100	arising	arise	VERB
ap-4481	61	101	from	from	ADP
ap-4481	61	102	semi	semi	ADJ
ap-4481	61	103	-	-	ADJ
ap-4481	61	104	analytic	analytic	ADJ
ap-4481	61	105	expression	expression	NOUN
ap-4481	61	106	(	(	PUNCT
ap-4481	61	107	13	13	NUM
ap-4481	61	108	)	)	PUNCT
ap-4481	61	109	and	and	CCONJ
ap-4481	61	110	semi	semi	ADJ
ap-4481	61	111	-	-	ADJ
ap-4481	61	112	analytic	analytic	ADJ
ap-4481	61	113	form	form	NOUN
ap-4481	61	114	(	(	PUNCT
ap-4481	61	115	15	15	NUM
ap-4481	61	116	)	)	PUNCT
ap-4481	61	117	.	.	PUNCT
ap-4481	62	1	here	here	ADV
ap-4481	62	2	α	α	PROPN
ap-4481	62	3	values	value	NOUN
ap-4481	62	4	are	be	AUX
ap-4481	62	5	4.05	4.05	NUM
ap-4481	62	6	and	and	CCONJ
ap-4481	62	7	2.91	2.91	NUM
ap-4481	62	8	,	,	PUNCT
ap-4481	62	9	respectively	respectively	ADV
ap-4481	62	10	.	.	PUNCT
ap-4481	63	1	without	without	ADP
ap-4481	63	2	a	a	DET
ap-4481	63	3	loss	loss	NOUN
ap-4481	63	4	of	of	ADP
ap-4481	63	5	generality	generality	NOUN
ap-4481	63	6	we	we	PRON
ap-4481	63	7	may	may	AUX
ap-4481	63	8	choose	choose	VERB
ap-4481	63	9	λ	λ	NOUN
ap-4481	63	10	=	=	SYM
ap-4481	63	11	1	1	X
ap-4481	63	12	.	.	PUNCT
ap-4481	63	13	let	let	VERB
ap-4481	63	14	us	we	PRON
ap-4481	63	15	introduce	introduce	VERB
ap-4481	63	16	the	the	DET
ap-4481	63	17	transformation	transformation	NOUN
ap-4481	63	18	from	from	ADP
ap-4481	63	19	(	(	PUNCT
ap-4481	63	20	a	a	PRON
ap-4481	63	21	,	,	PUNCT
ap-4481	63	22	b	b	NOUN
ap-4481	63	23	,	,	PUNCT
ap-4481	63	24	c	c	NOUN
ap-4481	63	25	)	)	PUNCT
ap-4481	63	26	to	to	ADP
ap-4481	63	27	(	(	PUNCT
ap-4481	63	28	u	u	NOUN
ap-4481	63	29	,	,	PUNCT
ap-4481	63	30	v	v	NOUN
ap-4481	63	31	,	,	PUNCT
ap-4481	63	32	w	w	NOUN
ap-4481	63	33	)	)	PUNCT
ap-4481	63	34	as	as	ADP
ap-4481	63	35	u	u	NOUN
ap-4481	63	36	=	=	SYM
ap-4481	63	37	a−	a−	PROPN
ap-4481	63	38	c	c	PROPN
ap-4481	63	39	,	,	PUNCT
ap-4481	63	40	v	v	NOUN
ap-4481	63	41	=	=	SYM
ap-4481	63	42	a+	a+	PUNCT
ap-4481	63	43	c	c	NOUN
ap-4481	63	44	,	,	PUNCT
ap-4481	63	45	w	w	PROPN
ap-4481	63	46	=	=	SYM
ap-4481	63	47	2b	2b	NOUN
ap-4481	63	48	,	,	PUNCT
ap-4481	63	49	(	(	PUNCT
ap-4481	63	50	5	5	X
ap-4481	63	51	)	)	PUNCT
ap-4481	63	52	becomes	become	VERB
ap-4481	63	53	p	p	NOUN
ap-4481	63	54	(	(	PUNCT
ap-4481	63	55	s	s	NOUN
ap-4481	63	56	)	)	PUNCT
ap-4481	63	57	=	=	SYM
ap-4481	63	58			X
ap-4481	63	59	a	a	DET
ap-4481	63	60	∫	∫	PROPN
ap-4481	63	61	s	s	PART
ap-4481	63	62	0	0	NUM
ap-4481	63	63	du	du	PROPN
ap-4481	63	64	∫	∫	PROPN
ap-4481	63	65	2	2	NUM
ap-4481	63	66	0	0	NUM
ap-4481	63	67	dw	dw	PROPN
ap-4481	63	68	∫	∫	PROPN
ap-4481	63	69	2−u	2−u	NUM
ap-4481	64	1	u−2	u−2	ADJ
ap-4481	64	2	δ(s	δ(s	PROPN
ap-4481	64	3	−	−	NOUN
ap-4481	64	4	√	√	PROPN
ap-4481	64	5	w2	w2	NOUN
ap-4481	64	6	+	+	CCONJ
ap-4481	64	7	u2	u2	PROPN
ap-4481	64	8	)	)	PUNCT
ap-4481	64	9	dv	dv	PROPN
ap-4481	64	10	,	,	PUNCT
ap-4481	64	11	0	0	NUM
ap-4481	64	12	≤	≤	NUM
ap-4481	64	13	s	s	PART
ap-4481	64	14	≤	≤	NUM
ap-4481	64	15	2	2	NUM
ap-4481	64	16	a	a	DET
ap-4481	64	17	∫	∫	PROPN
ap-4481	64	18	2√	2√	PROPN
ap-4481	64	19	s2−4	s2−4	PROPN
ap-4481	64	20	du	du	PROPN
ap-4481	64	21	∫	∫	PROPN
ap-4481	64	22	2	2	NUM
ap-4481	64	23	0	0	NUM
ap-4481	64	24	dw	dw	PROPN
ap-4481	64	25	∫	∫	PROPN
ap-4481	64	26	2−u	2−u	NUM
ap-4481	65	1	u−2	u−2	ADJ
ap-4481	65	2	δ(s	δ(s	PROPN
ap-4481	65	3	−	−	NOUN
ap-4481	65	4	√	√	PROPN
ap-4481	65	5	w2	w2	NOUN
ap-4481	65	6	+	+	CCONJ
ap-4481	65	7	u2	u2	PROPN
ap-4481	65	8	)	)	PUNCT
ap-4481	65	9	dv	dv	PROPN
ap-4481	65	10	,	,	PUNCT
ap-4481	65	11	2	2	NUM
ap-4481	65	12	<	<	X
ap-4481	65	13	s	s	X
ap-4481	65	14	<	<	X
ap-4481	65	15	2	2	NUM
ap-4481	65	16	√	√	NUM
ap-4481	65	17	2	2	NUM
ap-4481	65	18	0	0	NUM
ap-4481	65	19	,	,	PUNCT
ap-4481	65	20	s	s	VERB
ap-4481	65	21	≥	≥	NOUN
ap-4481	65	22	2	2	NUM
ap-4481	65	23	√	√	NUM
ap-4481	65	24	2	2	NUM
ap-4481	65	25	.	.	PUNCT
ap-4481	66	1	(	(	PUNCT
ap-4481	66	2	6	6	X
ap-4481	66	3	)	)	PUNCT
ap-4481	66	4	we	we	PRON
ap-4481	66	5	find	find	VERB
ap-4481	66	6	that	that	SCONJ
ap-4481	66	7	integrals	integral	NOUN
ap-4481	66	8	in	in	ADP
ap-4481	66	9	(	(	PUNCT
ap-4481	66	10	6	6	NUM
ap-4481	66	11	)	)	PUNCT
ap-4481	66	12	can	can	AUX
ap-4481	66	13	be	be	AUX
ap-4481	66	14	done	do	VERB
ap-4481	66	15	and	and	CCONJ
ap-4481	66	16	p	p	X
ap-4481	66	17	(	(	PUNCT
ap-4481	66	18	s	s	NOUN
ap-4481	66	19	)	)	PUNCT
ap-4481	66	20	turns	turn	VERB
ap-4481	66	21	out	out	ADP
ap-4481	66	22	to	to	PART
ap-4481	66	23	be	be	AUX
ap-4481	66	24	a	a	DET
ap-4481	66	25	piecewise	piecewise	NOUN
ap-4481	66	26	continuous	continuous	ADJ
ap-4481	66	27	function	function	NOUN
ap-4481	66	28	given	give	VERB
ap-4481	66	29	as	as	ADP
ap-4481	66	30	p	p	NOUN
ap-4481	66	31	(	(	PUNCT
ap-4481	66	32	s	s	NOUN
ap-4481	66	33	)	)	PUNCT
ap-4481	66	34	=	=	SYM
ap-4481	66	35			PRON
ap-4481	66	36	a′s(π	a′s(π	VERB
ap-4481	66	37	−	−	PROPN
ap-4481	66	38	s)/4	s)/4	PROPN
ap-4481	66	39	,	,	PUNCT
ap-4481	66	40	0	0	NUM
ap-4481	66	41	≤	≤	NUM
ap-4481	66	42	s	s	PART
ap-4481	66	43	≤	≤	NOUN
ap-4481	66	44	2	2	NUM
ap-4481	66	45	,	,	PUNCT
ap-4481	66	46	a′	a′	PROPN
ap-4481	66	47	s2	s2	PROPN
ap-4481	66	48	[	[	X
ap-4481	66	49	sin−1(2	sin−1(2	PROPN
ap-4481	66	50	/	/	SYM
ap-4481	66	51	s)−	s)−	PROPN
ap-4481	67	1	sin−1	sin−1	PROPN
ap-4481	67	2	(	(	PUNCT
ap-4481	67	3	√	√	PROPN
ap-4481	67	4	s2	s2	NOUN
ap-4481	67	5	−	−	NOUN
ap-4481	67	6	4	4	NUM
ap-4481	67	7	/	/	SYM
ap-4481	67	8	s	s	NOUN
ap-4481	67	9	)	)	PUNCT
ap-4481	67	10	]	]	PUNCT
ap-4481	68	1	+	+	CCONJ
ap-4481	68	2	s	s	X
ap-4481	68	3	4	4	NUM
ap-4481	68	4	[	[	PUNCT
ap-4481	68	5	√	√	NUM
ap-4481	68	6	s2	s2	NOUN
ap-4481	68	7	−	−	PROPN
ap-4481	68	8	4−	4−	NOUN
ap-4481	68	9	2	2	NUM
ap-4481	68	10	]	]	PUNCT
ap-4481	68	11	,	,	PUNCT
ap-4481	68	12	2	2	NUM
ap-4481	68	13	<	<	X
ap-4481	68	14	s	s	X
ap-4481	68	15	<	<	X
ap-4481	68	16	2	2	NUM
ap-4481	68	17	√	√	NUM
ap-4481	68	18	2	2	NUM
ap-4481	68	19	,	,	PUNCT
ap-4481	68	20	0	0	NUM
ap-4481	68	21	,	,	PUNCT
ap-4481	68	22	s	s	VERB
ap-4481	68	23	≥	≥	NOUN
ap-4481	68	24	2	2	NUM
ap-4481	68	25	√	√	NUM
ap-4481	68	26	2	2	NUM
ap-4481	68	27	.	.	PUNCT
ap-4481	68	28	(	(	PUNCT
ap-4481	68	29	7	7	NUM
ap-4481	68	30	)	)	PUNCT
ap-4481	68	31	for	for	ADP
ap-4481	68	32	the	the	DET
ap-4481	68	33	matrix	matrix	NOUN
ap-4481	68	34	r2	r2	NOUN
ap-4481	68	35	(	(	PUNCT
ap-4481	68	36	1	1	NUM
ap-4481	68	37	)	)	PUNCT
ap-4481	68	38	,	,	PUNCT
ap-4481	68	39	p	p	X
ap-4481	68	40	(	(	PUNCT
ap-4481	68	41	s	s	X
ap-4481	68	42	)	)	PUNCT
ap-4481	68	43	=	=	PUNCT
ap-4481	68	44	a	a	DET
ap-4481	68	45	∫	∫	PROPN
ap-4481	68	46	λ	λ	PROPN
ap-4481	68	47	−λ	−λ	PROPN
ap-4481	68	48	∫	∫	PROPN
ap-4481	68	49	λ	λ	PROPN
ap-4481	68	50	−λ	−λ	PROPN
ap-4481	68	51	∫	∫	PROPN
ap-4481	68	52	λ	λ	PROPN
ap-4481	68	53	−λ	−λ	PROPN
ap-4481	68	54	δ[s	δ[s	PROPN
ap-4481	68	55	−	−	PROPN
ap-4481	68	56	√	√	NUM
ap-4481	68	57	b2	b2	NOUN
ap-4481	68	58	+	+	CCONJ
ap-4481	68	59	c2	c2	PROPN
ap-4481	68	60	]	]	PUNCT
ap-4481	68	61	dadbdc	dadbdc	NOUN
ap-4481	68	62	.	.	PUNCT
ap-4481	69	1	(	(	PUNCT
ap-4481	69	2	8)	8)	NUM
ap-4481	69	3	the	the	DET
ap-4481	69	4	a	a	ADV
ap-4481	69	5	-	-	PUNCT
ap-4481	69	6	integral	integral	ADJ
ap-4481	69	7	is	be	AUX
ap-4481	69	8	separable	separable	ADJ
ap-4481	69	9	and	and	CCONJ
ap-4481	69	10	it	it	PRON
ap-4481	69	11	will	will	AUX
ap-4481	69	12	yield	yield	VERB
ap-4481	69	13	a	a	DET
ap-4481	69	14	multiplicative	multiplicative	ADJ
ap-4481	69	15	constant	constant	NOUN
ap-4481	69	16	.	.	PUNCT
ap-4481	70	1	we	we	PRON
ap-4481	70	2	convert	convert	VERB
ap-4481	70	3	the	the	DET
ap-4481	70	4	double	double	ADJ
ap-4481	70	5	integral	integral	NOUN
ap-4481	70	6	in	in	ADP
ap-4481	70	7	b	b	PROPN
ap-4481	70	8	and	and	CCONJ
ap-4481	70	9	c	c	NOUN
ap-4481	70	10	in	in	ADV
ap-4481	70	11	to	to	ADP
ap-4481	70	12	polar	polar	ADJ
ap-4481	70	13	form	form	NOUN
ap-4481	70	14	as	as	ADP
ap-4481	70	15	b	b	NOUN
ap-4481	70	16	=	=	SYM
ap-4481	70	17	r	r	NOUN
ap-4481	70	18	cos	cos	PROPN
ap-4481	70	19	θ	θ	PROPN
ap-4481	70	20	,	,	PUNCT
ap-4481	70	21	c	c	NOUN
ap-4481	70	22	=	=	SYM
ap-4481	70	23	r	r	NOUN
ap-4481	70	24	sin	sin	NOUN
ap-4481	70	25	θ	θ	NOUN
ap-4481	70	26	p	p	X
ap-4481	70	27	(	(	PUNCT
ap-4481	70	28	s	s	NOUN
ap-4481	70	29	)	)	PUNCT
ap-4481	70	30	=	=	PUNCT
ap-4481	70	31			PROPN
ap-4481	70	32	a′	a′	NOUN
ap-4481	70	33	∫	∫	PROPN
ap-4481	70	34	1	1	NUM
ap-4481	70	35	0	0	NUM
ap-4481	70	36	∫	∫	PROPN
ap-4481	70	37	π/4	π/4	PROPN
ap-4481	70	38	0	0	NUM
ap-4481	71	1	r	r	NOUN
ap-4481	71	2	drδ(s	drδ(s	PUNCT
ap-4481	71	3	−	−	NOUN
ap-4481	71	4	r	r	NOUN
ap-4481	71	5	)	)	PUNCT
ap-4481	71	6	dθ	dθ	NOUN
ap-4481	71	7	,	,	PUNCT
ap-4481	71	8	0	0	NUM
ap-4481	71	9	≤	≤	NUM
ap-4481	71	10	s	s	PART
ap-4481	71	11	≤	≤	NUM
ap-4481	71	12	1	1	NUM
ap-4481	71	13	a′	a′	NOUN
ap-4481	71	14	∫√2	∫√2	PROPN
ap-4481	71	15	1	1	NUM
ap-4481	71	16	∫	∫	NOUN
ap-4481	71	17	π/4	π/4	PROPN
ap-4481	71	18	cos−1(1	cos−1(1	NUM
ap-4481	71	19	/	/	SYM
ap-4481	71	20	r	r	NOUN
ap-4481	71	21	)	)	PUNCT
ap-4481	71	22	r	r	NOUN
ap-4481	71	23	drδ(s	drδ(s	PUNCT
ap-4481	71	24	−	−	NOUN
ap-4481	71	25	r	r	NOUN
ap-4481	71	26	)	)	PUNCT
ap-4481	71	27	dθ	dθ	NOUN
ap-4481	71	28	,	,	PUNCT
ap-4481	71	29	1	1	NUM
ap-4481	71	30	<	<	X
ap-4481	71	31	s	s	X
ap-4481	71	32	<	<	X
ap-4481	71	33	√	√	PROPN
ap-4481	71	34	2	2	NUM
ap-4481	71	35	,	,	PUNCT
ap-4481	71	36	0	0	NUM
ap-4481	71	37	,	,	PUNCT
ap-4481	71	38	s	s	VERB
ap-4481	71	39	≥	≥	NOUN
ap-4481	71	40	√	√	NUM
ap-4481	71	41	2	2	NUM
ap-4481	71	42	.	.	PUNCT
ap-4481	72	1	(	(	PUNCT
ap-4481	72	2	9	9	NUM
ap-4481	72	3	)	)	PUNCT
ap-4481	72	4	finally	finally	ADV
ap-4481	72	5	for	for	ADP
ap-4481	72	6	real	real	ADJ
ap-4481	72	7	symmetric	symmetric	ADJ
ap-4481	72	8	matrix	matrix	NOUN
ap-4481	72	9	r2	r2	NOUN
ap-4481	72	10	(	(	PUNCT
ap-4481	72	11	1	1	NUM
ap-4481	72	12	)	)	PUNCT
ap-4481	72	13	when	when	SCONJ
ap-4481	72	14	the	the	DET
ap-4481	72	15	elements	element	NOUN
ap-4481	72	16	are	be	AUX
ap-4481	72	17	distributed	distribute	VERB
ap-4481	72	18	uniformly	uniformly	ADV
ap-4481	72	19	over	over	ADP
ap-4481	72	20	[	[	X
ap-4481	72	21	-1,1	-1,1	NOUN
ap-4481	72	22	]	]	X
ap-4481	72	23	,	,	PUNCT
ap-4481	72	24	from	from	ADP
ap-4481	72	25	(	(	PUNCT
ap-4481	72	26	9	9	X
ap-4481	72	27	)	)	PUNCT
ap-4481	72	28	we	we	PRON
ap-4481	72	29	get	get	VERB
ap-4481	72	30	the	the	DET
ap-4481	72	31	continuous	continuous	ADJ
ap-4481	72	32	three	three	NUM
ap-4481	72	33	piece	piece	NOUN
ap-4481	72	34	spacing	space	VERB
ap-4481	72	35	distribution	distribution	NOUN
ap-4481	72	36	function	function	NOUN
ap-4481	72	37	for	for	ADP
ap-4481	72	38	s	s	PROPN
ap-4481	72	39	∈	∈	PROPN
ap-4481	72	40	(	(	PUNCT
ap-4481	72	41	0,∞	0,∞	NUM
ap-4481	72	42	)	)	PUNCT
ap-4481	72	43	(	(	PUNCT
ap-4481	72	44	λ	λ	X
ap-4481	72	45	=	=	NOUN
ap-4481	72	46	1	1	NUM
ap-4481	72	47	)	)	PUNCT
ap-4481	72	48	as	as	ADP
ap-4481	72	49	p	p	X
ap-4481	72	50	(	(	PUNCT
ap-4481	72	51	s	s	NOUN
ap-4481	72	52	)	)	PUNCT
ap-4481	72	53	=	=	SYM
ap-4481	73	1			PROPN
ap-4481	73	2	a′	a′	PROPN
ap-4481	73	3	πs/2	πs/2	PROPN
ap-4481	73	4	,	,	PUNCT
ap-4481	73	5	0	0	NUM
ap-4481	73	6	≤	≤	NUM
ap-4481	73	7	s	s	PART
ap-4481	73	8	≤	≤	NUM
ap-4481	73	9	1	1	NUM
ap-4481	73	10	,	,	PUNCT
ap-4481	73	11	2a′s[π/4−	2a′s[π/4−	NUM
ap-4481	73	12	cos−1(1	cos−1(1	NUM
ap-4481	73	13	/	/	SYM
ap-4481	73	14	s	s	NOUN
ap-4481	73	15	)	)	PUNCT
ap-4481	73	16	]	]	PUNCT
ap-4481	73	17	,	,	PUNCT
ap-4481	73	18	1	1	NUM
ap-4481	73	19	<	<	X
ap-4481	73	20	s	s	X
ap-4481	73	21	<	<	X
ap-4481	73	22	√	√	PROPN
ap-4481	73	23	2	2	NUM
ap-4481	73	24	,	,	PUNCT
ap-4481	73	25	0	0	NUM
ap-4481	73	26	,	,	PUNCT
ap-4481	73	27	s	s	VERB
ap-4481	73	28	≥	≥	NOUN
ap-4481	73	29	√	√	NUM
ap-4481	73	30	2	2	NUM
ap-4481	73	31	.	.	PUNCT
ap-4481	74	1	(	(	PUNCT
ap-4481	74	2	10	10	NUM
ap-4481	74	3	)	)	PUNCT
ap-4481	74	4	in	in	ADP
ap-4481	74	5	figure	figure	NOUN
ap-4481	74	6	1	1	NUM
ap-4481	74	7	,	,	PUNCT
ap-4481	74	8	we	we	PRON
ap-4481	74	9	plot	plot	VERB
ap-4481	74	10	p(s	p(s	NOUN
ap-4481	74	11	)	)	PUNCT
ap-4481	74	12	arising	arise	VERB
ap-4481	74	13	from	from	ADP
ap-4481	74	14	analytic	analytic	ADJ
ap-4481	74	15	results	result	NOUN
ap-4481	74	16	(	(	PUNCT
ap-4481	74	17	7,10	7,10	NUM
ap-4481	74	18	)	)	PUNCT
ap-4481	74	19	along	along	ADP
ap-4481	74	20	with	with	ADP
ap-4481	74	21	the	the	DET
ap-4481	74	22	histograms	histogram	NOUN
ap-4481	74	23	generated	generate	VERB
ap-4481	74	24	from	from	ADP
ap-4481	74	25	100000	100000	NUM
ap-4481	74	26	(=	(=	NOUN
ap-4481	74	27	n	n	CCONJ
ap-4481	74	28	)	)	PUNCT
ap-4481	74	29	,	,	PUNCT
ap-4481	74	30	2×	2×	NUM
ap-4481	74	31	2	2	NUM
ap-4481	74	32	real	real	ADJ
ap-4481	74	33	symmetric	symmetric	ADJ
ap-4481	74	34	matrices	matrix	NOUN
ap-4481	74	35	of	of	ADP
ap-4481	74	36	the	the	DET
ap-4481	74	37	types	type	NOUN
ap-4481	74	38	(	(	PUNCT
ap-4481	74	39	a	a	X
ap-4481	74	40	):	):	PUNCT
ap-4481	74	41	r1	r1	PROPN
ap-4481	74	42	and	and	CCONJ
ap-4481	74	43	(	(	PUNCT
ap-4481	74	44	b	b	NOUN
ap-4481	74	45	):	):	PUNCT
ap-4481	74	46	r2	r2	PROPN
ap-4481	74	47	.	.	PUNCT
ap-4481	75	1	near	near	ADP
ap-4481	75	2	s	s	PART
ap-4481	75	3	=	=	SYM
ap-4481	75	4	0	0	NUM
ap-4481	75	5	,	,	PUNCT
ap-4481	75	6	they	they	PRON
ap-4481	75	7	show	show	VERB
ap-4481	75	8	linear	linear	ADJ
ap-4481	75	9	repulsion	repulsion	NOUN
ap-4481	75	10	,	,	PUNCT
ap-4481	75	11	where	where	SCONJ
ap-4481	75	12	α	α	X
ap-4481	75	13	(	(	PUNCT
ap-4481	75	14	the	the	DET
ap-4481	75	15	coefficient	coefficient	NOUN
ap-4481	75	16	of	of	ADP
ap-4481	75	17	linearity	linearity	NOUN
ap-4481	75	18	)	)	PUNCT
ap-4481	75	19	is	be	AUX
ap-4481	75	20	1.23	1.23	NUM
ap-4481	75	21	and	and	CCONJ
ap-4481	75	22	1.09	1.09	NUM
ap-4481	75	23	,	,	PUNCT
ap-4481	75	24	respectively	respectively	ADV
ap-4481	75	25	.	.	PUNCT
ap-4481	76	1	notice	notice	VERB
ap-4481	76	2	the	the	DET
ap-4481	76	3	excellent	excellent	ADJ
ap-4481	76	4	agreement	agreement	NOUN
ap-4481	76	5	of	of	ADP
ap-4481	76	6	solid	solid	ADJ
ap-4481	76	7	lines	line	NOUN
ap-4481	76	8	with	with	ADP
ap-4481	76	9	histograms	histogram	NOUN
ap-4481	76	10	,	,	PUNCT
ap-4481	76	11	the	the	DET
ap-4481	76	12	dashed	dash	VERB
ap-4481	76	13	lines	line	NOUN
ap-4481	76	14	represent	represent	VERB
ap-4481	76	15	wigner	wigner	NOUN
ap-4481	76	16	’s	’s	PART
ap-4481	76	17	distribution	distribution	NOUN
ap-4481	76	18	(	(	PUNCT
ap-4481	76	19	3	3	NUM
ap-4481	76	20	)	)	PUNCT
ap-4481	76	21	.	.	PUNCT
ap-4481	77	1	2.2	2.2	NUM
ap-4481	77	2	.	.	PUNCT
ap-4481	77	3	exponential	exponential	ADJ
ap-4481	77	4	distribution	distribution	NOUN
ap-4481	77	5	:	:	PUNCT
ap-4481	77	6	f(x	f(x	PROPN
ap-4481	77	7	)	)	PUNCT
ap-4481	77	8	=	=	SYM
ap-4481	78	1	e−|x|	e−|x|	X
ap-4481	78	2	multiple	multiple	ADJ
ap-4481	78	3	integrals	integral	NOUN
ap-4481	78	4	in	in	ADP
ap-4481	78	5	p	p	PROPN
ap-4481	78	6	(	(	PUNCT
ap-4481	78	7	s	s	NOUN
ap-4481	78	8	)	)	PUNCT
ap-4481	78	9	for	for	ADP
ap-4481	78	10	r1	r1	PROPN
ap-4481	78	11	under	under	ADP
ap-4481	78	12	exponential	exponential	ADJ
ap-4481	78	13	pdf	pdf	NOUN
ap-4481	78	14	can	can	AUX
ap-4481	78	15	be	be	AUX
ap-4481	78	16	written	write	VERB
ap-4481	78	17	as	as	ADP
ap-4481	78	18	p	p	PROPN
ap-4481	78	19	(	(	PUNCT
ap-4481	78	20	s	s	NOUN
ap-4481	78	21	)	)	PUNCT
ap-4481	78	22	=	=	PUNCT
ap-4481	78	23	a	a	DET
ap-4481	78	24	∫	∫	PROPN
ap-4481	78	25	∞	∞	PROPN
ap-4481	78	26	−∞	−∞	X
ap-4481	78	27	∫	∫	PROPN
ap-4481	78	28	∞	∞	PROPN
ap-4481	78	29	∞	∞	NUM
ap-4481	78	30	∫	∫	PROPN
ap-4481	78	31	∞	∞	PROPN
ap-4481	79	1	−∞	−∞	PUNCT
ap-4481	79	2	e−(|a|+|b|+|c|)δ	e−(|a|+|b|+|c|)δ	ADP
ap-4481	79	3	[	[	PUNCT
ap-4481	79	4	s	s	NOUN
ap-4481	79	5	−	−	NOUN
ap-4481	79	6	√	√	PROPN
ap-4481	79	7	4b2	4b2	NUM
ap-4481	79	8	+	+	CCONJ
ap-4481	79	9	(	(	PUNCT
ap-4481	79	10	a−	a−	PROPN
ap-4481	79	11	c)2	c)2	PROPN
ap-4481	79	12	]	]	PUNCT
ap-4481	79	13	da	da	X
ap-4481	79	14	dbdc	dbdc	NOUN
ap-4481	79	15	.	.	PUNCT
ap-4481	80	1	(	(	PUNCT
ap-4481	80	2	11	11	NUM
ap-4481	80	3	)	)	SYM
ap-4481	80	4	420	420	NUM
ap-4481	80	5	vol	vol	NOUN
ap-4481	80	6	.	.	PUNCT
ap-4481	81	1	57	57	NUM
ap-4481	81	2	no	no	NOUN
ap-4481	81	3	.	.	PUNCT
ap-4481	82	1	6/2017	6/2017	X
ap-4481	82	2	new	new	ADJ
ap-4481	82	3	spectral	spectral	ADJ
ap-4481	82	4	statistics	statistic	NOUN
ap-4481	82	5	2	2	NUM
ap-4481	82	6	x	x	SYM
ap-4481	82	7	2	2	NUM
ap-4481	82	8	n=105	n=105	PROPN
ap-4481	82	9	semi	semi	ADJ
ap-4481	82	10	-	-	ADJ
ap-4481	82	11	analytic	analytic	ADJ
ap-4481	82	12	wigner	wigner	NOUN
ap-4481	82	13	surmise	surmise	NOUN
ap-4481	82	14	0	0	NUM
ap-4481	82	15	0.4	0.4	NUM
ap-4481	82	16	0.8	0.8	NUM
ap-4481	82	17	1.2	1.2	NUM
ap-4481	82	18	1.6	1.6	NUM
ap-4481	82	19	2	2	NUM
ap-4481	82	20	.	.	PUNCT
ap-4481	82	21	2.4	2.4	NUM
ap-4481	82	22	2.8	2.8	NUM
ap-4481	82	23	s	s	NOUN
ap-4481	82	24	0.2	0.2	NUM
ap-4481	82	25	0.4	0.4	NUM
ap-4481	82	26	0.6	0.6	NUM
ap-4481	82	27	0.8	0.8	NUM
ap-4481	82	28	phsl	phsl	NOUN
ap-4481	82	29	hal	hal	NOUN
ap-4481	82	30	2	2	NUM
ap-4481	82	31	x	x	SYM
ap-4481	82	32	2	2	NUM
ap-4481	82	33	n=105	n=105	PROPN
ap-4481	82	34	analytic	analytic	ADJ
ap-4481	82	35	wigner	wigner	NOUN
ap-4481	82	36	surmise	surmise	NOUN
ap-4481	82	37	0	0	NUM
ap-4481	82	38	0.4	0.4	NUM
ap-4481	82	39	0.8	0.8	NUM
ap-4481	82	40	1.2	1.2	NUM
ap-4481	82	41	1.6	1.6	NUM
ap-4481	82	42	2	2	NUM
ap-4481	82	43	.	.	PUNCT
ap-4481	82	44	2.4	2.4	NUM
ap-4481	82	45	2.8	2.8	NUM
ap-4481	82	46	s	s	NOUN
ap-4481	82	47	0.3	0.3	NUM
ap-4481	82	48	0.6	0.6	NUM
ap-4481	82	49	0.9	0.9	NUM
ap-4481	82	50	phsl	phsl	NOUN
ap-4481	82	51	hbl	hbl	NOUN
ap-4481	82	52	figure	figure	NOUN
ap-4481	82	53	3	3	NUM
ap-4481	82	54	.	.	PUNCT
ap-4481	83	1	the	the	DET
ap-4481	83	2	same	same	ADJ
ap-4481	83	3	as	as	ADP
ap-4481	83	4	in	in	ADP
ap-4481	83	5	figures	figure	NOUN
ap-4481	83	6	1	1	NUM
ap-4481	83	7	and	and	CCONJ
ap-4481	83	8	2	2	NUM
ap-4481	83	9	,	,	PUNCT
ap-4481	83	10	for	for	ADP
ap-4481	83	11	super	super	ADJ
ap-4481	83	12	-	-	ADJ
ap-4481	83	13	gaussian	gaussian	ADJ
ap-4481	83	14	pdf	pdf	NOUN
ap-4481	83	15	(	(	PUNCT
ap-4481	83	16	sg	sg	ADJ
ap-4481	83	17	:	:	PUNCT
ap-4481	83	18	e−x4	e−x4	X
ap-4481	83	19	)	)	PUNCT
ap-4481	83	20	arising	arise	VERB
ap-4481	83	21	from	from	ADP
ap-4481	83	22	the	the	DET
ap-4481	83	23	semi	semi	ADJ
ap-4481	83	24	-	-	ADJ
ap-4481	83	25	analytic	analytic	ADJ
ap-4481	83	26	expression	expression	NOUN
ap-4481	83	27	(	(	PUNCT
ap-4481	83	28	18	18	NUM
ap-4481	83	29	)	)	PUNCT
ap-4481	83	30	and	and	CCONJ
ap-4481	83	31	the	the	DET
ap-4481	83	32	analytic	analytic	ADJ
ap-4481	83	33	one	one	NUM
ap-4481	83	34	(	(	PUNCT
ap-4481	83	35	19	19	NUM
ap-4481	83	36	)	)	PUNCT
ap-4481	83	37	.	.	PUNCT
ap-4481	84	1	here	here	ADV
ap-4481	84	2	α	α	PROPN
ap-4481	84	3	values	value	NOUN
ap-4481	84	4	are	be	AUX
ap-4481	84	5	1.30	1.30	NUM
ap-4481	84	6	and	and	CCONJ
ap-4481	84	7	0.91	0.91	NUM
ap-4481	84	8	,	,	PUNCT
ap-4481	84	9	respectively	respectively	ADV
ap-4481	84	10	.	.	PUNCT
ap-4481	85	1	we	we	PRON
ap-4481	85	2	transform	transform	VERB
ap-4481	85	3	p	p	NOUN
ap-4481	85	4	(	(	PUNCT
ap-4481	85	5	s	s	NOUN
ap-4481	85	6	)	)	PUNCT
ap-4481	85	7	into	into	ADP
ap-4481	85	8	the	the	DET
ap-4481	85	9	three	three	NUM
ap-4481	85	10	dimensional	dimensional	ADJ
ap-4481	85	11	spherical	spherical	ADJ
ap-4481	85	12	polar	polar	ADJ
ap-4481	85	13	co	co	NOUN
ap-4481	85	14	-	-	NOUN
ap-4481	85	15	ordinates	ordinate	NOUN
ap-4481	85	16	using	use	VERB
ap-4481	85	17	2b	2b	NOUN
ap-4481	85	18	=	=	SYM
ap-4481	85	19	r	r	NOUN
ap-4481	85	20	cos	cos	PROPN
ap-4481	85	21	θ	θ	PROPN
ap-4481	85	22	,	,	PUNCT
ap-4481	85	23	a	a	DET
ap-4481	85	24	=	=	NOUN
ap-4481	85	25	r	r	NOUN
ap-4481	85	26	sin	sin	NOUN
ap-4481	85	27	θ	θ	NOUN
ap-4481	85	28	cosφ	cosφ	NOUN
ap-4481	85	29	,	,	PUNCT
ap-4481	85	30	c	c	NOUN
ap-4481	85	31	=	=	SYM
ap-4481	85	32	r	r	NOUN
ap-4481	85	33	sin	sin	NOUN
ap-4481	85	34	θ	θ	NOUN
ap-4481	85	35	sinφ	sinφ	NOUN
ap-4481	85	36	as	as	ADP
ap-4481	85	37	p	p	PROPN
ap-4481	85	38	(	(	PUNCT
ap-4481	85	39	s	s	NOUN
ap-4481	85	40	)	)	PUNCT
ap-4481	85	41	=	=	PUNCT
ap-4481	85	42	a	a	DET
ap-4481	85	43	∫	∫	PROPN
ap-4481	85	44	∞	∞	NUM
ap-4481	85	45	0	0	NUM
ap-4481	86	1	∫	∫	PROPN
ap-4481	86	2	π	π	NOUN
ap-4481	86	3	0	0	NUM
ap-4481	86	4	∫	∫	PROPN
ap-4481	86	5	2π	2π	PROPN
ap-4481	86	6	0	0	NUM
ap-4481	87	1	e−r(|cos	e−r(|cos	PROPN
ap-4481	87	2	θ|/2+sin	θ|/2+sin	NOUN
ap-4481	87	3	θ(|cosφ|+|sinφ|))δ[s	θ(|cosφ|+|sinφ|))δ[s	PROPN
ap-4481	87	4	−	−	PROPN
ap-4481	87	5	rg(θ	rg(θ	PROPN
ap-4481	87	6	,	,	PUNCT
ap-4481	87	7	φ)]r2	φ)]r2	PROPN
ap-4481	87	8	dr	dr	PROPN
ap-4481	87	9	sin	sin	PROPN
ap-4481	87	10	θ	θ	PROPN
ap-4481	87	11	dθ	dθ	NOUN
ap-4481	87	12	dφ	dφ	INTJ
ap-4481	87	13	.	.	PUNCT
ap-4481	88	1	(	(	PUNCT
ap-4481	88	2	12	12	NUM
ap-4481	88	3	)	)	PUNCT
ap-4481	88	4	crashing	crash	VERB
ap-4481	88	5	the	the	DET
ap-4481	88	6	delta	delta	NOUN
ap-4481	88	7	function	function	NOUN
ap-4481	88	8	in	in	ADP
ap-4481	88	9	above	above	ADV
ap-4481	88	10	,	,	PUNCT
ap-4481	88	11	we	we	PRON
ap-4481	88	12	get	get	VERB
ap-4481	88	13	a	a	DET
ap-4481	88	14	θ	θ	PROPN
ap-4481	88	15	,	,	PUNCT
ap-4481	88	16	φ	φ	X
ap-4481	88	17	integral	integral	ADJ
ap-4481	88	18	p	p	X
ap-4481	88	19	(	(	PUNCT
ap-4481	88	20	s	s	NOUN
ap-4481	88	21	)	)	PUNCT
ap-4481	88	22	=	=	SYM
ap-4481	88	23	a′	a′	PROPN
ap-4481	88	24	∫	∫	PROPN
ap-4481	88	25	π/2	π/2	PROPN
ap-4481	88	26	0	0	NUM
ap-4481	89	1	∫	∫	PROPN
ap-4481	89	2	π	π	NOUN
ap-4481	89	3	0	0	X
ap-4481	90	1	e−s(|cos	e−s(|cos	PROPN
ap-4481	90	2	θ|/2+sin	θ|/2+sin	ADP
ap-4481	90	3	θ(|cosφ|+|sinφ|))/g(θ	θ(|cosφ|+|sinφ|))/g(θ	NOUN
ap-4481	90	4	,	,	PUNCT
ap-4481	90	5	φ	φ	NOUN
ap-4481	90	6	)	)	PUNCT
ap-4481	90	7	s2	s2	NOUN
ap-4481	90	8	|g[θ	|g[θ	NUM
ap-4481	90	9	,	,	PUNCT
ap-4481	90	10	φ)|3	φ)|3	NOUN
ap-4481	90	11	sin	sin	NOUN
ap-4481	90	12	θ	θ	PROPN
ap-4481	90	13	dθ	dθ	VERB
ap-4481	90	14	dφ	dφ	ADP
ap-4481	90	15	,	,	PUNCT
ap-4481	90	16	g(θ	g(θ	PROPN
ap-4481	90	17	,	,	PUNCT
ap-4481	90	18	φ	φ	NOUN
ap-4481	90	19	)	)	PUNCT
ap-4481	90	20	=	=	SYM
ap-4481	91	1	√	√	NUM
ap-4481	91	2	1−	1−	NUM
ap-4481	91	3	sin2	sin2	NOUN
ap-4481	91	4	θ	θ	PROPN
ap-4481	91	5	sin	sin	VERB
ap-4481	91	6	2φ	2φ	NUM
ap-4481	91	7	,	,	PUNCT
ap-4481	91	8	(	(	PUNCT
ap-4481	91	9	13	13	NUM
ap-4481	91	10	)	)	PUNCT
ap-4481	91	11	due	due	ADP
ap-4481	91	12	to	to	ADP
ap-4481	91	13	the	the	DET
ap-4481	91	14	symmetry	symmetry	NOUN
ap-4481	91	15	of	of	ADP
ap-4481	91	16	integrand	integrand	NOUN
ap-4481	91	17	the	the	DET
ap-4481	91	18	domains	domain	NOUN
ap-4481	91	19	of	of	ADP
ap-4481	91	20	integrations	integration	NOUN
ap-4481	91	21	in	in	ADP
ap-4481	91	22	(	(	PUNCT
ap-4481	91	23	13	13	NUM
ap-4481	91	24	)	)	PUNCT
ap-4481	91	25	have	have	AUX
ap-4481	91	26	been	be	AUX
ap-4481	91	27	reduced	reduce	VERB
ap-4481	91	28	.	.	PUNCT
ap-4481	92	1	the	the	DET
ap-4481	92	2	p	p	X
ap-4481	92	3	(	(	PUNCT
ap-4481	92	4	s	s	NOUN
ap-4481	92	5	)	)	PUNCT
ap-4481	92	6	of	of	ADP
ap-4481	92	7	r2	r2	PROPN
ap-4481	92	8	for	for	ADP
ap-4481	92	9	exponential	exponential	ADJ
ap-4481	92	10	distribution	distribution	NOUN
ap-4481	92	11	can	can	AUX
ap-4481	92	12	be	be	AUX
ap-4481	92	13	written	write	VERB
ap-4481	92	14	as	as	ADP
ap-4481	92	15	p	p	PROPN
ap-4481	92	16	(	(	PUNCT
ap-4481	92	17	s	s	NOUN
ap-4481	92	18	)	)	PUNCT
ap-4481	92	19	=	=	PUNCT
ap-4481	92	20	a	a	DET
ap-4481	92	21	∫	∫	PROPN
ap-4481	92	22	∞	∞	PROPN
ap-4481	92	23	−∞	−∞	X
ap-4481	92	24	∫	∫	PROPN
ap-4481	92	25	∞	∞	PROPN
ap-4481	92	26	−∞	−∞	ADP
ap-4481	92	27	∫	∫	PROPN
ap-4481	92	28	∞	∞	PROPN
ap-4481	92	29	−∞	−∞	ADP
ap-4481	92	30	e−(|a|+|b|+|c|)δ[s	e−(|a|+|b|+|c|)δ[	NOUN
ap-4481	92	31	−	−	PROPN
ap-4481	92	32	√	√	NUM
ap-4481	92	33	b2	b2	PROPN
ap-4481	92	34	+	+	CCONJ
ap-4481	92	35	c2	c2	PROPN
ap-4481	92	36	]	]	PUNCT
ap-4481	92	37	dadbdc	dadbdc	NOUN
ap-4481	92	38	.	.	PUNCT
ap-4481	93	1	(	(	PUNCT
ap-4481	93	2	14	14	NUM
ap-4481	93	3	)	)	PUNCT
ap-4481	93	4	here	here	ADV
ap-4481	93	5	the	the	DET
ap-4481	93	6	a	a	ADV
ap-4481	93	7	-	-	PUNCT
ap-4481	93	8	integral	integral	ADJ
ap-4481	93	9	is	be	AUX
ap-4481	93	10	separable	separable	ADJ
ap-4481	93	11	and	and	CCONJ
ap-4481	93	12	gives	give	VERB
ap-4481	93	13	1	1	NUM
ap-4481	93	14	.	.	PUNCT
ap-4481	94	1	the	the	DET
ap-4481	94	2	remaining	remain	VERB
ap-4481	94	3	double	double	ADJ
ap-4481	94	4	integral	integral	ADJ
ap-4481	94	5	can	can	AUX
ap-4481	94	6	be	be	AUX
ap-4481	94	7	converted	convert	VERB
ap-4481	94	8	to	to	ADP
ap-4481	94	9	polar	polar	ADJ
ap-4481	94	10	form	form	NOUN
ap-4481	94	11	as	as	ADP
ap-4481	94	12	p	p	PROPN
ap-4481	94	13	(	(	PUNCT
ap-4481	94	14	s	s	NOUN
ap-4481	94	15	)	)	PUNCT
ap-4481	94	16	=	=	PUNCT
ap-4481	95	1	a′s	a′s	ADJ
ap-4481	95	2	∫	∫	PROPN
ap-4481	95	3	π/2	π/2	PROPN
ap-4481	95	4	0	0	NUM
ap-4481	95	5	e−s(sin	e−s(sin	PROPN
ap-4481	95	6	θ+cos	θ+cos	PUNCT
ap-4481	95	7	θ	θ	PROPN
ap-4481	95	8	)	)	PUNCT
ap-4481	95	9	dθ	dθ	PROPN
ap-4481	95	10	.	.	PUNCT
ap-4481	96	1	(	(	PUNCT
ap-4481	96	2	15	15	NUM
ap-4481	96	3	)	)	PUNCT
ap-4481	96	4	the	the	DET
ap-4481	96	5	integrals	integral	NOUN
ap-4481	96	6	(	(	PUNCT
ap-4481	96	7	13	13	NUM
ap-4481	96	8	)	)	PUNCT
ap-4481	96	9	,	,	PUNCT
ap-4481	96	10	(	(	PUNCT
ap-4481	96	11	15	15	X
ap-4481	96	12	)	)	PUNCT
ap-4481	96	13	are	be	AUX
ap-4481	96	14	further	far	ADV
ap-4481	96	15	inexpressible	inexpressible	ADJ
ap-4481	96	16	in	in	ADP
ap-4481	96	17	terms	term	NOUN
ap-4481	96	18	of	of	ADP
ap-4481	96	19	known	know	VERB
ap-4481	96	20	functions	function	NOUN
ap-4481	96	21	.	.	PUNCT
ap-4481	97	1	p(s	p(s	NOUN
ap-4481	97	2	)	)	PUNCT
ap-4481	97	3	for	for	ADP
ap-4481	97	4	these	these	DET
ap-4481	97	5	two	two	NUM
ap-4481	97	6	cases	case	NOUN
ap-4481	97	7	are	be	AUX
ap-4481	97	8	plotted	plot	VERB
ap-4481	97	9	in	in	ADP
ap-4481	97	10	figure	figure	NOUN
ap-4481	97	11	2	2	NUM
ap-4481	97	12	,	,	PUNCT
ap-4481	97	13	they	they	PRON
ap-4481	97	14	look	look	VERB
ap-4481	97	15	similar	similar	ADJ
ap-4481	97	16	though	though	SCONJ
ap-4481	97	17	distinct	distinct	ADJ
ap-4481	97	18	,	,	PUNCT
ap-4481	97	19	notice	notice	VERB
ap-4481	97	20	their	their	PRON
ap-4481	97	21	linear	linear	ADJ
ap-4481	97	22	behaviour	behaviour	NOUN
ap-4481	97	23	near	near	ADP
ap-4481	97	24	s	s	PROPN
ap-4481	97	25	=	=	SYM
ap-4481	97	26	0	0	NUM
ap-4481	97	27	like	like	ADP
ap-4481	97	28	wigner	wigner	NOUN
ap-4481	97	29	’s	’s	PART
ap-4481	97	30	distribution	distribution	NOUN
ap-4481	97	31	(	(	PUNCT
ap-4481	97	32	dashed	dash	VERB
ap-4481	97	33	line	line	NOUN
ap-4481	97	34	)	)	PUNCT
ap-4481	97	35	.	.	PUNCT
ap-4481	98	1	2.3	2.3	NUM
ap-4481	98	2	.	.	PUNCT
ap-4481	99	1	super	super	ADJ
ap-4481	99	2	-	-	ADJ
ap-4481	99	3	gaussian	gaussian	ADJ
ap-4481	99	4	distribution	distribution	NOUN
ap-4481	99	5	:	:	PUNCT
ap-4481	99	6	f(x	f(x	NOUN
ap-4481	99	7	)	)	PUNCT
ap-4481	100	1	=	=	PRON
ap-4481	100	2	e−x4	e−x4	NOUN
ap-4481	100	3	for	for	ADP
ap-4481	100	4	r1	r1	PROPN
ap-4481	100	5	(	(	PUNCT
ap-4481	100	6	1	1	NUM
ap-4481	100	7	)	)	PUNCT
ap-4481	100	8	,	,	PUNCT
ap-4481	100	9	the	the	DET
ap-4481	100	10	p	p	X
ap-4481	100	11	(	(	PUNCT
ap-4481	100	12	s	s	NOUN
ap-4481	100	13	)	)	PUNCT
ap-4481	100	14	integral	integral	ADJ
ap-4481	100	15	(	(	PUNCT
ap-4481	100	16	2	2	NUM
ap-4481	100	17	)	)	PUNCT
ap-4481	100	18	becomes	become	VERB
ap-4481	100	19	p	p	NOUN
ap-4481	100	20	(	(	PUNCT
ap-4481	100	21	s	s	X
ap-4481	100	22	)	)	PUNCT
ap-4481	100	23	=	=	PUNCT
ap-4481	100	24	a	a	DET
ap-4481	100	25	∫	∫	PROPN
ap-4481	100	26	∞	∞	PROPN
ap-4481	100	27	−∞	−∞	X
ap-4481	100	28	∫	∫	PROPN
ap-4481	100	29	∞	∞	PROPN
ap-4481	100	30	−∞	−∞	ADP
ap-4481	100	31	∫	∫	PROPN
ap-4481	100	32	∞	∞	PROPN
ap-4481	100	33	−∞	−∞	ADP
ap-4481	100	34	e−(a4+b4+c4)δ[s	e−(a4+b4+c4)δ[	NOUN
ap-4481	100	35	−	−	NOUN
ap-4481	100	36	√	√	PROPN
ap-4481	100	37	4b2	4b2	NUM
ap-4481	100	38	+	+	CCONJ
ap-4481	100	39	(	(	PUNCT
ap-4481	100	40	a−	a−	PROPN
ap-4481	100	41	c)2	c)2	PROPN
ap-4481	100	42	]	]	PUNCT
ap-4481	100	43	dadbdc	dadbdc	NOUN
ap-4481	100	44	.	.	PUNCT
ap-4481	101	1	(	(	PUNCT
ap-4481	101	2	16	16	NUM
ap-4481	101	3	)	)	PUNCT
ap-4481	101	4	we	we	PRON
ap-4481	101	5	transform	transform	VERB
ap-4481	101	6	p	p	NOUN
ap-4481	101	7	(	(	PUNCT
ap-4481	101	8	s	s	NOUN
ap-4481	101	9	)	)	PUNCT
ap-4481	101	10	into	into	ADP
ap-4481	101	11	the	the	DET
ap-4481	101	12	three	three	NUM
ap-4481	101	13	dimensional	dimensional	ADJ
ap-4481	101	14	spherical	spherical	ADJ
ap-4481	101	15	polar	polar	ADJ
ap-4481	101	16	co	co	NOUN
ap-4481	101	17	-	-	NOUN
ap-4481	101	18	ordinates	ordinate	NOUN
ap-4481	101	19	using	use	VERB
ap-4481	101	20	2b	2b	NOUN
ap-4481	101	21	=	=	SYM
ap-4481	101	22	r	r	NOUN
ap-4481	101	23	cos	cos	PROPN
ap-4481	101	24	θ	θ	PROPN
ap-4481	101	25	,	,	PUNCT
ap-4481	101	26	a	a	DET
ap-4481	101	27	=	=	NOUN
ap-4481	101	28	r	r	NOUN
ap-4481	101	29	sin	sin	NOUN
ap-4481	101	30	θ	θ	NOUN
ap-4481	101	31	cosφ	cosφ	NOUN
ap-4481	101	32	,	,	PUNCT
ap-4481	101	33	c	c	NOUN
ap-4481	101	34	=	=	SYM
ap-4481	101	35	r	r	NOUN
ap-4481	101	36	sin	sin	NOUN
ap-4481	101	37	θ	θ	NOUN
ap-4481	101	38	sinφ	sinφ	NOUN
ap-4481	101	39	as	as	ADP
ap-4481	101	40	p	p	PROPN
ap-4481	101	41	(	(	PUNCT
ap-4481	101	42	s	s	NOUN
ap-4481	101	43	)	)	PUNCT
ap-4481	101	44	=	=	PUNCT
ap-4481	101	45	a	a	DET
ap-4481	101	46	∫	∫	PROPN
ap-4481	101	47	∞	∞	NUM
ap-4481	101	48	0	0	NUM
ap-4481	102	1	∫	∫	PROPN
ap-4481	102	2	π	π	NOUN
ap-4481	102	3	0	0	NUM
ap-4481	102	4	∫	∫	PROPN
ap-4481	102	5	2π	2π	NOUN
ap-4481	102	6	0	0	NUM
ap-4481	103	1	e−r	e−r	NOUN
ap-4481	103	2	4(cos4θ/16+sin4	4(cos4θ/16+sin4	NOUN
ap-4481	103	3	θ(cos4	θ(cos4	NOUN
ap-4481	103	4	φ+sin4	φ+sin4	SYM
ap-4481	103	5	φ))δ[s	φ))δ[s	NOUN
ap-4481	103	6	−	−	PROPN
ap-4481	103	7	rg(θ	rg(θ	NOUN
ap-4481	103	8	,	,	PUNCT
ap-4481	103	9	φ)]r2	φ)]r2	PROPN
ap-4481	103	10	dr	dr	PROPN
ap-4481	103	11	sin	sin	PROPN
ap-4481	103	12	θ	θ	PROPN
ap-4481	103	13	dθ	dθ	NOUN
ap-4481	103	14	dφ	dφ	INTJ
ap-4481	103	15	.	.	PUNCT
ap-4481	104	1	(	(	PUNCT
ap-4481	104	2	17	17	NUM
ap-4481	104	3	)	)	PUNCT
ap-4481	104	4	crashing	crash	VERB
ap-4481	104	5	the	the	DET
ap-4481	104	6	delta	delta	NOUN
ap-4481	104	7	function	function	NOUN
ap-4481	104	8	in	in	ADP
ap-4481	104	9	above	above	ADV
ap-4481	104	10	,	,	PUNCT
ap-4481	104	11	we	we	PRON
ap-4481	104	12	get	get	VERB
ap-4481	104	13	a	a	DET
ap-4481	104	14	θ	θ	PROPN
ap-4481	104	15	,	,	PUNCT
ap-4481	104	16	φ	φ	X
ap-4481	104	17	integral	integral	ADJ
ap-4481	104	18	p	p	X
ap-4481	104	19	(	(	PUNCT
ap-4481	104	20	s	s	NOUN
ap-4481	104	21	)	)	PUNCT
ap-4481	104	22	=	=	SYM
ap-4481	104	23	a′	a′	PROPN
ap-4481	104	24	∫	∫	PROPN
ap-4481	104	25	π/2	π/2	PROPN
ap-4481	104	26	0	0	NUM
ap-4481	105	1	∫	∫	PROPN
ap-4481	105	2	π	π	X
ap-4481	105	3	0	0	NUM
ap-4481	105	4	e−s	e−s	PROPN
ap-4481	105	5	4(cos4	4(cos4	NOUN
ap-4481	105	6	θ/16+sin4	θ/16+sin4	NOUN
ap-4481	105	7	θ(cos4	θ(cos4	NOUN
ap-4481	105	8	φ+sin4	φ+sin4	ADJ
ap-4481	105	9	φ))/g4(θ	φ))/g4(θ	PROPN
ap-4481	105	10	,	,	PUNCT
ap-4481	105	11	φ	φ	NOUN
ap-4481	105	12	)	)	PUNCT
ap-4481	105	13	s2	s2	PROPN
ap-4481	105	14	|g(θ	|g(θ	PROPN
ap-4481	105	15	,	,	PUNCT
ap-4481	105	16	φ)|3	φ)|3	NOUN
ap-4481	105	17	sin	sin	NOUN
ap-4481	105	18	θ	θ	PROPN
ap-4481	105	19	dθ	dθ	VERB
ap-4481	105	20	dφ	dφ	ADP
ap-4481	105	21	,	,	PUNCT
ap-4481	105	22	g(θ	g(θ	PROPN
ap-4481	105	23	,	,	PUNCT
ap-4481	105	24	φ	φ	NOUN
ap-4481	105	25	)	)	PUNCT
ap-4481	105	26	=	=	SYM
ap-4481	105	27	√	√	NUM
ap-4481	105	28	1−	1−	NUM
ap-4481	105	29	sin2	sin2	NOUN
ap-4481	105	30	θ	θ	PROPN
ap-4481	105	31	sin	sin	NOUN
ap-4481	105	32	2φ	2φ	NUM
ap-4481	105	33	.	.	PUNCT
ap-4481	106	1	(	(	PUNCT
ap-4481	106	2	18	18	NUM
ap-4481	106	3	)	)	PUNCT
ap-4481	106	4	421	421	NUM
ap-4481	106	5	sachin	sachin	PROPN
ap-4481	106	6	kumar	kumar	PROPN
ap-4481	106	7	,	,	PUNCT
ap-4481	106	8	zafar	zafar	PROPN
ap-4481	106	9	ahmed	ahmed	PROPN
ap-4481	106	10	acta	acta	PROPN
ap-4481	106	11	polytechnica	polytechnica	PROPN
ap-4481	106	12	for	for	ADP
ap-4481	106	13	the	the	DET
ap-4481	106	14	matrix	matrix	NOUN
ap-4481	106	15	r2	r2	NOUN
ap-4481	106	16	,	,	PUNCT
ap-4481	106	17	the	the	DET
ap-4481	106	18	a	a	ADV
ap-4481	106	19	-	-	PUNCT
ap-4481	106	20	integral	integral	ADJ
ap-4481	106	21	in	in	ADP
ap-4481	106	22	p	p	PROPN
ap-4481	106	23	(	(	PUNCT
ap-4481	106	24	s	s	X
ap-4481	106	25	)	)	PUNCT
ap-4481	106	26	is	be	AUX
ap-4481	106	27	separable	separable	NOUN
ap-4481	106	28	gives	give	VERB
ap-4481	106	29	a	a	DET
ap-4481	106	30	multiplying	multiply	VERB
ap-4481	106	31	constant	constant	ADJ
ap-4481	106	32	.	.	PUNCT
ap-4481	107	1	then	then	ADV
ap-4481	107	2	the	the	DET
ap-4481	107	3	double	double	ADJ
ap-4481	107	4	integral	integral	NOUN
ap-4481	107	5	in	in	ADP
ap-4481	107	6	b	b	PROPN
ap-4481	107	7	,	,	PUNCT
ap-4481	107	8	c	c	PROPN
ap-4481	107	9	is	be	AUX
ap-4481	107	10	changed	change	VERB
ap-4481	107	11	to	to	ADP
ap-4481	107	12	polar	polar	ADJ
ap-4481	107	13	form	form	NOUN
ap-4481	107	14	where	where	SCONJ
ap-4481	107	15	by	by	ADP
ap-4481	107	16	crashing	crash	VERB
ap-4481	107	17	the	the	DET
ap-4481	107	18	delta	delta	NOUN
ap-4481	107	19	function	function	NOUN
ap-4481	107	20	we	we	PRON
ap-4481	107	21	get	get	VERB
ap-4481	107	22	an	an	DET
ap-4481	107	23	integral	integral	ADJ
ap-4481	107	24	p	p	X
ap-4481	107	25	(	(	PUNCT
ap-4481	107	26	s	s	NOUN
ap-4481	107	27	)	)	PUNCT
ap-4481	107	28	=	=	PUNCT
ap-4481	108	1	a′s	a′s	ADJ
ap-4481	108	2	∫	∫	PROPN
ap-4481	108	3	π/2	π/2	NUM
ap-4481	108	4	0	0	NUM
ap-4481	109	1	e−s(cos4	e−s(cos4	ADV
ap-4481	109	2	θ+sin4	θ+sin4	VERB
ap-4481	109	3	θ	θ	NOUN
ap-4481	109	4	)	)	PUNCT
ap-4481	109	5	dθ	dθ	PROPN
ap-4481	109	6	=	=	PROPN
ap-4481	109	7	a′se−3s4/4	a′se−3s4/4	PROPN
ap-4481	109	8	∫	∫	PROPN
ap-4481	109	9	2π	2π	PROPN
ap-4481	109	10	0	0	NUM
ap-4481	109	11	e−(s4	e−(s4	PROPN
ap-4481	109	12	cos	cos	PROPN
ap-4481	109	13	t)/4	t)/4	PROPN
ap-4481	109	14	dt	dt	PROPN
ap-4481	110	1	=	=	PUNCT
ap-4481	110	2	a′πs	a′πs	ADJ
ap-4481	110	3	2	2	NUM
ap-4481	110	4	e−3s4/4i0(s4/4	e−3s4/4i0(s4/4	NOUN
ap-4481	110	5	)	)	PUNCT
ap-4481	110	6	,	,	PUNCT
ap-4481	110	7	(	(	PUNCT
ap-4481	110	8	19	19	NUM
ap-4481	110	9	)	)	PUNCT
ap-4481	110	10	p(s	p(s	NOUN
ap-4481	110	11	)	)	PUNCT
ap-4481	110	12	corresponding	correspond	VERB
ap-4481	110	13	to	to	ADP
ap-4481	110	14	(	(	PUNCT
ap-4481	110	15	18	18	NUM
ap-4481	110	16	)	)	PUNCT
ap-4481	110	17	and	and	CCONJ
ap-4481	110	18	(	(	PUNCT
ap-4481	110	19	19	19	NUM
ap-4481	110	20	)	)	PUNCT
ap-4481	110	21	are	be	AUX
ap-4481	110	22	plotted	plot	VERB
ap-4481	110	23	in	in	ADP
ap-4481	110	24	figure	figure	NOUN
ap-4481	110	25	3	3	NUM
ap-4481	110	26	showing	show	VERB
ap-4481	110	27	linear	linear	ADJ
ap-4481	110	28	level	level	NOUN
ap-4481	110	29	repulsion	repulsion	NOUN
ap-4481	110	30	near	near	ADP
ap-4481	110	31	s	s	NOUN
ap-4481	110	32	=	=	NOUN
ap-4481	110	33	0	0	NUM
ap-4481	110	34	.	.	PROPN
ap-4481	110	35	2.4	2.4	NUM
ap-4481	110	36	.	.	PUNCT
ap-4481	111	1	maxwellian	maxwellian	ADJ
ap-4481	111	2	distribution	distribution	NOUN
ap-4481	111	3	:	:	PUNCT
ap-4481	111	4	f(x	f(x	PROPN
ap-4481	111	5	)	)	PUNCT
ap-4481	112	1	=	=	PUNCT
ap-4481	112	2	xe−x2	xe−x2	PROPN
ap-4481	112	3	,	,	PUNCT
ap-4481	112	4	x	x	X
ap-4481	112	5	>	>	X
ap-4481	112	6	0	0	PUNCT
ap-4481	112	7	for	for	ADP
ap-4481	112	8	r1	r1	NOUN
ap-4481	112	9	type	type	NOUN
ap-4481	112	10	of	of	ADP
ap-4481	112	11	real	real	ADJ
ap-4481	112	12	symmetric	symmetric	ADJ
ap-4481	112	13	matrix	matrix	NOUN
ap-4481	112	14	p	p	NOUN
ap-4481	112	15	(	(	PUNCT
ap-4481	112	16	s	s	X
ap-4481	112	17	)	)	PUNCT
ap-4481	112	18	is	be	AUX
ap-4481	112	19	not	not	PART
ap-4481	112	20	simple	simple	ADJ
ap-4481	112	21	,	,	PUNCT
ap-4481	112	22	however	however	ADV
ap-4481	112	23	here	here	ADV
ap-4481	112	24	we	we	PRON
ap-4481	112	25	would	would	AUX
ap-4481	112	26	like	like	VERB
ap-4481	112	27	to	to	PART
ap-4481	112	28	show	show	VERB
ap-4481	112	29	that	that	SCONJ
ap-4481	112	30	when	when	SCONJ
ap-4481	112	31	the	the	DET
ap-4481	112	32	pdf	pdf	NOUN
ap-4481	112	33	does	do	AUX
ap-4481	112	34	not	not	PART
ap-4481	112	35	peak	peak	VERB
ap-4481	112	36	at	at	ADP
ap-4481	112	37	x	x	X
ap-4481	112	38	=	=	SYM
ap-4481	112	39	0	0	NUM
ap-4481	112	40	,	,	PUNCT
ap-4481	112	41	we	we	PRON
ap-4481	112	42	get	get	VERB
ap-4481	112	43	highly	highly	ADV
ap-4481	112	44	non	non	ADJ
ap-4481	112	45	-	-	ADJ
ap-4481	112	46	linear	linear	ADJ
ap-4481	112	47	behaviour	behaviour	NOUN
ap-4481	112	48	of	of	ADP
ap-4481	112	49	p	p	PROPN
ap-4481	112	50	(	(	PUNCT
ap-4481	112	51	s	s	NOUN
ap-4481	112	52	)	)	PUNCT
ap-4481	112	53	near	near	ADP
ap-4481	112	54	s	s	NOUN
ap-4481	112	55	=	=	NOUN
ap-4481	112	56	0	0	NUM
ap-4481	112	57	for	for	ADP
ap-4481	112	58	r2	r2	PROPN
ap-4481	112	59	,	,	PUNCT
ap-4481	112	60	to	to	ADP
ap-4481	112	61	this	this	DET
ap-4481	112	62	end	end	NOUN
ap-4481	112	63	we	we	PRON
ap-4481	112	64	convert	convert	VERB
ap-4481	112	65	the	the	DET
ap-4481	112	66	integral	integral	ADJ
ap-4481	112	67	(	(	PUNCT
ap-4481	112	68	2	2	NUM
ap-4481	112	69	)	)	PUNCT
ap-4481	112	70	to	to	ADP
ap-4481	112	71	polar	polar	ADJ
ap-4481	112	72	form	form	NOUN
ap-4481	112	73	and	and	CCONJ
ap-4481	112	74	get	get	VERB
ap-4481	112	75	p	p	NOUN
ap-4481	112	76	(	(	PUNCT
ap-4481	112	77	s	s	NOUN
ap-4481	112	78	)	)	PUNCT
ap-4481	112	79	=	=	SYM
ap-4481	112	80	a′s3e−s	a′s3e−s	PROPN
ap-4481	112	81	2	2	NUM
ap-4481	112	82	,	,	PUNCT
ap-4481	112	83	(	(	PUNCT
ap-4481	112	84	20	20	X
ap-4481	112	85	)	)	PUNCT
ap-4481	112	86	displaying	display	VERB
ap-4481	112	87	nonlinear	nonlinear	ADJ
ap-4481	112	88	cubic	cubic	ADJ
ap-4481	112	89	behaviour	behaviour	NOUN
ap-4481	112	90	∼	∼	NOUN
ap-4481	112	91	s3	s3	PROPN
ap-4481	112	92	behaviour	behaviour	NOUN
ap-4481	112	93	near	near	ADP
ap-4481	112	94	s	s	PROPN
ap-4481	112	95	=	=	NOUN
ap-4481	112	96	0	0	PROPN
ap-4481	112	97	.	.	PUNCT
ap-4481	113	1	in	in	ADP
ap-4481	113	2	rmt	rmt	NOUN
ap-4481	113	3	,	,	PUNCT
ap-4481	113	4	the	the	DET
ap-4481	113	5	pdf	pdf	NOUN
ap-4481	113	6	of	of	ADP
ap-4481	113	7	matrix	matrix	NOUN
ap-4481	113	8	elements	element	NOUN
ap-4481	113	9	is	be	AUX
ap-4481	113	10	usually	usually	ADV
ap-4481	113	11	taken	take	VERB
ap-4481	113	12	as	as	ADP
ap-4481	113	13	symmetric	symmetric	ADJ
ap-4481	113	14	and	and	CCONJ
ap-4481	113	15	peaking	peak	VERB
ap-4481	113	16	at	at	ADP
ap-4481	113	17	x	x	X
ap-4481	113	18	=	=	SYM
ap-4481	113	19	0	0	NUM
ap-4481	113	20	and	and	CCONJ
ap-4481	113	21	one	one	NUM
ap-4481	113	22	gets	get	VERB
ap-4481	113	23	linear	linear	ADJ
ap-4481	113	24	level	level	NOUN
ap-4481	113	25	repulsion	repulsion	NOUN
ap-4481	113	26	near	near	ADP
ap-4481	113	27	s	s	NOUN
ap-4481	113	28	=	=	NOUN
ap-4481	113	29	0	0	PROPN
ap-4481	113	30	.	.	PUNCT
ap-4481	114	1	but	but	CCONJ
ap-4481	114	2	when	when	SCONJ
ap-4481	114	3	we	we	PRON
ap-4481	114	4	take	take	VERB
ap-4481	114	5	the	the	DET
ap-4481	114	6	non	non	ADJ
ap-4481	114	7	-	-	ADJ
ap-4481	114	8	symmetric	symmetric	ADJ
ap-4481	114	9	maxwellian	maxwellian	ADJ
ap-4481	114	10	distribution	distribution	NOUN
ap-4481	114	11	(	(	PUNCT
ap-4481	114	12	f(0	f(0	NOUN
ap-4481	114	13	)	)	PUNCT
ap-4481	114	14	=	=	NOUN
ap-4481	114	15	0	0	NUM
ap-4481	114	16	)	)	PUNCT
ap-4481	114	17	,	,	PUNCT
ap-4481	114	18	we	we	PRON
ap-4481	114	19	get	get	VERB
ap-4481	114	20	cubic	cubic	ADJ
ap-4481	114	21	level	level	NOUN
ap-4481	114	22	repulsion	repulsion	NOUN
ap-4481	114	23	near	near	ADP
ap-4481	114	24	s	s	NOUN
ap-4481	114	25	=	=	NOUN
ap-4481	114	26	0	0	PROPN
ap-4481	114	27	.	.	PUNCT
ap-4481	115	1	therefore	therefore	ADV
ap-4481	115	2	,	,	PUNCT
ap-4481	115	3	it	it	PRON
ap-4481	115	4	would	would	AUX
ap-4481	115	5	be	be	AUX
ap-4481	115	6	interesting	interesting	ADJ
ap-4481	115	7	to	to	PART
ap-4481	115	8	see	see	VERB
ap-4481	115	9	whether	whether	SCONJ
ap-4481	115	10	for	for	ADP
ap-4481	115	11	n×	n×	PRON
ap-4481	115	12	n	n	CCONJ
ap-4481	115	13	(	(	PUNCT
ap-4481	115	14	n	n	CCONJ
ap-4481	115	15	large	large	ADJ
ap-4481	115	16	)	)	PUNCT
ap-4481	115	17	the	the	DET
ap-4481	115	18	cubic	cubic	ADJ
ap-4481	115	19	level	level	NOUN
ap-4481	115	20	repulsion	repulsion	NOUN
ap-4481	115	21	persists	persist	VERB
ap-4481	115	22	.	.	PUNCT
ap-4481	116	1	3	3	X
ap-4481	116	2	.	.	X
ap-4481	116	3	distribution	distribution	NOUN
ap-4481	116	4	of	of	ADP
ap-4481	116	5	eigenvalues	eigenvalue	NOUN
ap-4481	116	6	d(ε	d(ε	PROPN
ap-4481	116	7	)	)	PUNCT
ap-4481	116	8	of	of	ADP
ap-4481	116	9	2×	2×	NUM
ap-4481	116	10	2	2	NUM
ap-4481	116	11	gaussian	gaussian	ADJ
ap-4481	116	12	random	random	ADJ
ap-4481	116	13	matrices	matrix	NOUN
ap-4481	116	14	we	we	PRON
ap-4481	116	15	collect	collect	VERB
ap-4481	116	16	2n	2n	NUM
ap-4481	116	17	eigenvalues	eigenvalue	NOUN
ap-4481	116	18	of	of	ADP
ap-4481	116	19	n	n	PRON
ap-4481	116	20	2	2	NUM
ap-4481	116	21	×	×	NOUN
ap-4481	116	22	2	2	NUM
ap-4481	116	23	matrices	matrix	NOUN
ap-4481	116	24	to	to	PART
ap-4481	116	25	find	find	VERB
ap-4481	116	26	the	the	DET
ap-4481	116	27	mean	mean	NOUN
ap-4481	116	28	of	of	ADP
ap-4481	116	29	positive	positive	ADJ
ap-4481	116	30	eigenvalue	eigenvalue	NOUN
ap-4481	116	31	(	(	PUNCT
ap-4481	116	32	ē	ē	NOUN
ap-4481	116	33	)	)	PUNCT
ap-4481	116	34	and	and	CCONJ
ap-4481	116	35	divide	divide	VERB
ap-4481	116	36	all	all	DET
ap-4481	116	37	eigenvalues	eigenvalue	NOUN
ap-4481	116	38	by	by	ADP
ap-4481	116	39	ē	ē	ADV
ap-4481	116	40	and	and	CCONJ
ap-4481	116	41	find	find	VERB
ap-4481	116	42	histograms	histogram	NOUN
ap-4481	116	43	d(ε	d(ε	PROPN
ap-4481	116	44	)	)	PUNCT
ap-4481	116	45	.	.	PUNCT
ap-4481	117	1	for	for	ADP
ap-4481	117	2	a	a	DET
ap-4481	117	3	large	large	ADJ
ap-4481	117	4	real	real	ADJ
ap-4481	117	5	symmetric	symmetric	ADJ
ap-4481	117	6	matrix	matrix	NOUN
ap-4481	117	7	this	this	DET
ap-4481	117	8	distribution	distribution	NOUN
ap-4481	117	9	is	be	AUX
ap-4481	117	10	well	well	ADV
ap-4481	117	11	known	know	VERB
ap-4481	117	12	as	as	ADP
ap-4481	117	13	semi	semi	ADJ
ap-4481	117	14	-	-	ADJ
ap-4481	117	15	circle	circle	ADJ
ap-4481	117	16	law	law	NOUN
ap-4481	117	17	(	(	PUNCT
ap-4481	117	18	4	4	NUM
ap-4481	117	19	)	)	PUNCT
ap-4481	117	20	.	.	PUNCT
ap-4481	118	1	the	the	DET
ap-4481	118	2	distribution	distribution	NOUN
ap-4481	118	3	of	of	ADP
ap-4481	118	4	eigenvalues	eigenvalue	NOUN
ap-4481	118	5	e1(a	e1(a	ADP
ap-4481	118	6	,	,	PUNCT
ap-4481	118	7	b	b	NOUN
ap-4481	118	8	,	,	PUNCT
ap-4481	118	9	c	c	NOUN
ap-4481	118	10	)	)	PUNCT
ap-4481	118	11	and	and	CCONJ
ap-4481	118	12	e2(a	e2(a	NOUN
ap-4481	118	13	,	,	PUNCT
ap-4481	118	14	b	b	NOUN
ap-4481	118	15	,	,	PUNCT
ap-4481	118	16	c	c	NOUN
ap-4481	118	17	)	)	PUNCT
ap-4481	118	18	can	can	AUX
ap-4481	118	19	be	be	AUX
ap-4481	118	20	obtained	obtain	VERB
ap-4481	118	21	analytically	analytically	ADV
ap-4481	118	22	as	as	ADP
ap-4481	118	23	g(e	g(e	PROPN
ap-4481	118	24	)	)	PUNCT
ap-4481	119	1	=	=	PUNCT
ap-4481	119	2	a	a	DET
ap-4481	119	3	∫	∫	PROPN
ap-4481	119	4	∞	∞	PROPN
ap-4481	119	5	−∞	−∞	X
ap-4481	119	6	∫	∫	PROPN
ap-4481	119	7	∞	∞	PROPN
ap-4481	119	8	−∞	−∞	ADP
ap-4481	119	9	∫	∫	PROPN
ap-4481	119	10	∞	∞	PROPN
ap-4481	119	11	−∞	−∞	PROPN
ap-4481	119	12	f(a	f(a	PROPN
ap-4481	119	13	,	,	PUNCT
ap-4481	119	14	b	b	NOUN
ap-4481	119	15	,	,	PUNCT
ap-4481	119	16	c)[δ(e	c)[δ(e	PUNCT
ap-4481	119	17	−	−	PROPN
ap-4481	119	18	e1	e1	PROPN
ap-4481	119	19	]	]	PUNCT
ap-4481	120	1	+	+	CCONJ
ap-4481	120	2	δ(e	δ(e	PROPN
ap-4481	120	3	−	−	PROPN
ap-4481	120	4	e2	e2	PROPN
ap-4481	120	5	)	)	PUNCT
ap-4481	120	6	]	]	PUNCT
ap-4481	120	7	dadbdc	dadbdc	NOUN
ap-4481	120	8	,	,	PUNCT
ap-4481	120	9	ē	ē	ADV
ap-4481	120	10	=	=	SYM
ap-4481	120	11	∫∞	∫∞	NOUN
ap-4481	120	12	0	0	NUM
ap-4481	121	1	g(e	g(e	PROPN
ap-4481	121	2	)	)	PUNCT
ap-4481	122	1	de∫∞	de∫∞	PROPN
ap-4481	122	2	0	0	NUM
ap-4481	122	3	g(e	g(e	PROPN
ap-4481	122	4	)	)	PUNCT
ap-4481	123	1	de	de	X
ap-4481	123	2	,	,	PUNCT
ap-4481	123	3	ε	ε	PROPN
ap-4481	123	4	=	=	SYM
ap-4481	123	5	e	e	PROPN
ap-4481	123	6	ē	ē	ADV
ap-4481	123	7	,	,	PUNCT
ap-4481	123	8	d(ε	d(ε	NOUN
ap-4481	123	9	)	)	PUNCT
ap-4481	123	10	=	=	PUNCT
ap-4481	123	11	g(εē)∫∞	g(εē)∫∞	VERB
ap-4481	123	12	−∞	−∞	ADP
ap-4481	123	13	g(εē)dε	g(εē)dε	PROPN
ap-4481	123	14	.	.	PUNCT
ap-4481	124	1	(	(	PUNCT
ap-4481	124	2	21	21	NUM
ap-4481	124	3	)	)	PUNCT
ap-4481	124	4	once	once	ADV
ap-4481	124	5	again	again	ADV
ap-4481	124	6	f(x	f(x	PROPN
ap-4481	124	7	)	)	PUNCT
ap-4481	124	8	is	be	AUX
ap-4481	124	9	the	the	DET
ap-4481	124	10	pdf	pdf	NOUN
ap-4481	124	11	of	of	ADP
ap-4481	124	12	matrix	matrix	NOUN
ap-4481	124	13	elements	element	NOUN
ap-4481	124	14	.	.	PUNCT
ap-4481	125	1	here	here	ADV
ap-4481	125	2	,	,	PUNCT
ap-4481	125	3	e1,2	e1,2	ADJ
ap-4481	125	4	=	=	SYM
ap-4481	125	5	1	1	NUM
ap-4481	125	6	2	2	NUM
ap-4481	125	7	(	(	PUNCT
ap-4481	125	8	a	a	PRON
ap-4481	125	9	+	+	NOUN
ap-4481	125	10	c	c	NOUN
ap-4481	125	11	±	±	NUM
ap-4481	125	12	√	√	PROPN
ap-4481	125	13	(	(	PUNCT
ap-4481	125	14	a−	a−	PROPN
ap-4481	125	15	c)2	c)2	PROPN
ap-4481	125	16	+	+	CCONJ
ap-4481	125	17	4b2	4b2	NOUN
ap-4481	125	18	)	)	PUNCT
ap-4481	125	19	for	for	ADP
ap-4481	125	20	r1	r1	NOUN
ap-4481	125	21	and	and	CCONJ
ap-4481	125	22	e1,2	e1,2	NOUN
ap-4481	125	23	=	=	DET
ap-4481	125	24	a	a	DET
ap-4481	125	25	±	±	NOUN
ap-4481	125	26	√	√	NOUN
ap-4481	125	27	b2	b2	NOUN
ap-4481	125	28	+	+	CCONJ
ap-4481	125	29	c2	c2	PROPN
ap-4481	125	30	for	for	ADP
ap-4481	125	31	r2	r2	PROPN
ap-4481	125	32	.	.	PUNCT
ap-4481	126	1	for	for	SCONJ
ap-4481	126	2	r1	r1	PROPN
ap-4481	126	3	,	,	PUNCT
ap-4481	126	4	g(e	g(e	PROPN
ap-4481	126	5	)	)	PUNCT
ap-4481	126	6	can	can	AUX
ap-4481	126	7	be	be	AUX
ap-4481	126	8	obtained	obtain	VERB
ap-4481	126	9	from	from	ADP
ap-4481	126	10	(	(	PUNCT
ap-4481	126	11	21	21	NUM
ap-4481	126	12	)	)	PUNCT
ap-4481	126	13	,	,	PUNCT
ap-4481	126	14	by	by	ADP
ap-4481	126	15	using	use	VERB
ap-4481	126	16	gaussian	gaussian	ADJ
ap-4481	126	17	pdf	pdf	NOUN
ap-4481	126	18	,	,	PUNCT
ap-4481	126	19	defining	define	VERB
ap-4481	126	20	a+	a+	PUNCT
ap-4481	126	21	c	c	NOUN
ap-4481	126	22	=	=	SYM
ap-4481	126	23	u	u	PROPN
ap-4481	126	24	,	,	PUNCT
ap-4481	126	25	a−	a−	PROPN
ap-4481	126	26	c	c	NOUN
ap-4481	126	27	=	=	SYM
ap-4481	126	28	v	v	PROPN
ap-4481	126	29	and	and	CCONJ
ap-4481	126	30	crashing	crash	VERB
ap-4481	126	31	the	the	DET
ap-4481	126	32	delta	delta	NOUN
ap-4481	126	33	function	function	NOUN
ap-4481	126	34	w.r.t	w.r.t	VERB
ap-4481	126	35	.	.	PUNCT
ap-4481	127	1	u.	u.	PROPN
ap-4481	127	2	next	next	ADV
ap-4481	127	3	,	,	PUNCT
ap-4481	127	4	we	we	PRON
ap-4481	127	5	use	use	VERB
ap-4481	127	6	polar	polar	ADJ
ap-4481	127	7	co	co	NOUN
ap-4481	127	8	-	-	NOUN
ap-4481	127	9	ordinates	ordinate	NOUN
ap-4481	127	10	v	v	ADP
ap-4481	127	11	=	=	SYM
ap-4481	127	12	r	r	NOUN
ap-4481	127	13	cos	cos	PROPN
ap-4481	127	14	θ	θ	PROPN
ap-4481	127	15	and	and	CCONJ
ap-4481	127	16	b	b	X
ap-4481	127	17	=	=	SYM
ap-4481	127	18	r	r	NOUN
ap-4481	127	19	2	2	NUM
ap-4481	127	20	sin	sin	NOUN
ap-4481	127	21	θ	θ	NOUN
ap-4481	127	22	to	to	PART
ap-4481	127	23	get	get	VERB
ap-4481	127	24	g(e	g(e	PROPN
ap-4481	127	25	)	)	PUNCT
ap-4481	128	1	=	=	PUNCT
ap-4481	128	2	a′e−2e2	a′e−2e2	NOUN
ap-4481	128	3	∫	∫	PROPN
ap-4481	129	1	∞	∞	PROPN
ap-4481	129	2	0	0	NUM
ap-4481	130	1	∫	∫	PROPN
ap-4481	130	2	2π	2π	PROPN
ap-4481	130	3	0	0	NUM
ap-4481	130	4	cosh(2er)e−r	cosh(2er)e−r	NUM
ap-4481	130	5	2	2	NUM
ap-4481	130	6	(	(	PUNCT
ap-4481	130	7	7	7	NUM
ap-4481	130	8	8	8	NUM
ap-4481	130	9	+	+	CCONJ
ap-4481	130	10	cos	cos	ADJ
ap-4481	130	11	2θ	2θ	NUM
ap-4481	130	12	8	8	NUM
ap-4481	130	13	)	)	PUNCT
ap-4481	130	14	r	r	NOUN
ap-4481	130	15	dr	dr	PROPN
ap-4481	130	16	dθ	dθ	PROPN
ap-4481	130	17	(	(	PUNCT
ap-4481	130	18	22	22	NUM
ap-4481	130	19	)	)	PUNCT
ap-4481	130	20	which	which	PRON
ap-4481	130	21	reduces	reduce	VERB
ap-4481	130	22	to	to	ADP
ap-4481	130	23	a	a	DET
ap-4481	130	24	one	one	NUM
ap-4481	130	25	-	-	PUNCT
ap-4481	130	26	dimensional	dimensional	ADJ
ap-4481	130	27	integral	integral	ADJ
ap-4481	130	28	g(e	g(e	NOUN
ap-4481	130	29	)	)	PUNCT
ap-4481	131	1	=	=	SYM
ap-4481	131	2	a′′e−2e2	a′′e−2e2	PROPN
ap-4481	131	3	∫	∫	PROPN
ap-4481	131	4	∞	∞	NOUN
ap-4481	131	5	0	0	PUNCT
ap-4481	132	1	r	r	NOUN
ap-4481	132	2	cosh(2er)e−7r2/8i0(r2/8	cosh(2er)e−7r2/8i0(r2/8	NOUN
ap-4481	132	3	)	)	PUNCT
ap-4481	132	4	dr	dr	PROPN
ap-4481	132	5	.	.	PROPN
ap-4481	132	6	(	(	PUNCT
ap-4481	132	7	23	23	NUM
ap-4481	132	8	)	)	PUNCT
ap-4481	132	9	for	for	ADP
ap-4481	132	10	r2	r2	PROPN
ap-4481	132	11	with	with	ADP
ap-4481	132	12	gaussian	gaussian	ADJ
ap-4481	132	13	pdf	pdf	NOUN
ap-4481	132	14	,	,	PUNCT
ap-4481	132	15	we	we	PRON
ap-4481	132	16	crash	crash	VERB
ap-4481	132	17	the	the	DET
ap-4481	132	18	delta	delta	NOUN
ap-4481	132	19	function	function	NOUN
ap-4481	132	20	w.r.t	w.r.t	VERB
ap-4481	132	21	.	.	PUNCT
ap-4481	133	1	the	the	DET
ap-4481	133	2	variable	variable	ADJ
ap-4481	133	3	a	a	PRON
ap-4481	133	4	and	and	CCONJ
ap-4481	133	5	use	use	VERB
ap-4481	133	6	polar	polar	ADJ
ap-4481	133	7	co	co	NOUN
ap-4481	133	8	-	-	NOUN
ap-4481	133	9	ordinates	ordinate	NOUN
ap-4481	133	10	b	b	NOUN
ap-4481	133	11	=	=	SYM
ap-4481	133	12	r	r	NOUN
ap-4481	133	13	cos	cos	PROPN
ap-4481	133	14	θ	θ	PROPN
ap-4481	133	15	,	,	PUNCT
ap-4481	133	16	c	c	NOUN
ap-4481	133	17	=	=	SYM
ap-4481	133	18	r	r	NOUN
ap-4481	133	19	sin	sin	NOUN
ap-4481	133	20	θ	θ	PROPN
ap-4481	133	21	and	and	CCONJ
ap-4481	133	22	we	we	PRON
ap-4481	133	23	get	get	VERB
ap-4481	133	24	a	a	DET
ap-4481	133	25	simple	simple	ADJ
ap-4481	133	26	form	form	NOUN
ap-4481	133	27	g(e	g(e	PROPN
ap-4481	133	28	)	)	PUNCT
ap-4481	134	1	=	=	SYM
ap-4481	134	2	e−e	e−e	X
ap-4481	134	3	2	2	NUM
ap-4481	134	4	[	[	SYM
ap-4481	134	5	2	2	NUM
ap-4481	134	6	+	+	CCONJ
ap-4481	134	7	√	√	PROPN
ap-4481	134	8	2πe	2πe	ADJ
ap-4481	134	9	erf(e/	erf(e/	PUNCT
ap-4481	134	10	√	√	NUM
ap-4481	134	11	2)ee	2)ee	PROPN
ap-4481	134	12	2/2]/(4√π	2/2]/(4√π	NUM
ap-4481	134	13	)	)	PUNCT
ap-4481	134	14	.	.	PUNCT
ap-4481	135	1	(	(	PUNCT
ap-4481	135	2	24	24	NUM
ap-4481	135	3	)	)	PUNCT
ap-4481	135	4	this	this	DET
ap-4481	135	5	function	function	NOUN
ap-4481	135	6	is	be	AUX
ap-4481	135	7	normalized	normalize	VERB
ap-4481	135	8	to	to	ADP
ap-4481	135	9	1	1	NUM
ap-4481	135	10	in	in	ADP
ap-4481	135	11	for	for	ADP
ap-4481	135	12	e	e	PROPN
ap-4481	135	13	∈	∈	PROPN
ap-4481	135	14	(	(	PUNCT
ap-4481	135	15	−∞,∞	−∞,∞	NOUN
ap-4481	135	16	)	)	PUNCT
ap-4481	135	17	,	,	PUNCT
ap-4481	135	18	ē	ē	ADV
ap-4481	135	19	calculated	calculate	VERB
ap-4481	135	20	in	in	ADP
ap-4481	135	21	e	e	PROPN
ap-4481	135	22	∈	∈	PROPN
ap-4481	135	23	(	(	PUNCT
ap-4481	135	24	0,∞	0,∞	NOUN
ap-4481	135	25	)	)	PUNCT
ap-4481	135	26	is	be	AUX
ap-4481	135	27	4+π	4+π	NUM
ap-4481	135	28	4	4	NUM
ap-4481	135	29	√	√	PROPN
ap-4481	135	30	π	π	NOUN
ap-4481	135	31	=	=	SYM
ap-4481	135	32	1.0073	1.0073	NUM
ap-4481	135	33	,	,	PUNCT
ap-4481	135	34	consequently	consequently	ADV
ap-4481	135	35	,	,	PUNCT
ap-4481	135	36	d(ε	d(ε	NOUN
ap-4481	135	37	)	)	PUNCT
ap-4481	135	38	=	=	SYM
ap-4481	135	39	g(ε	g(ε	PROPN
ap-4481	135	40	)	)	PUNCT
ap-4481	135	41	.	.	PUNCT
ap-4481	136	1	see	see	VERB
ap-4481	136	2	the	the	DET
ap-4481	136	3	d(ε	d(ε	PROPN
ap-4481	136	4	)	)	PUNCT
ap-4481	136	5	histograms	histogram	NOUN
ap-4481	136	6	in	in	ADP
ap-4481	136	7	figure	figure	NOUN
ap-4481	136	8	4	4	NUM
ap-4481	136	9	for	for	ADP
ap-4481	136	10	eigenvalues	eigenvalue	NOUN
ap-4481	136	11	of	of	ADP
ap-4481	136	12	n	n	NOUN
ap-4481	136	13	=	=	PUNCT
ap-4481	137	1	8×	8×	ADP
ap-4481	137	2	104	104	NUM
ap-4481	137	3	matrices:(a	matrices:(a	NOUN
ap-4481	137	4	)	)	PUNCT
ap-4481	137	5	r1	r1	NOUN
ap-4481	138	1	and	and	CCONJ
ap-4481	138	2	(	(	PUNCT
ap-4481	138	3	b	b	NOUN
ap-4481	138	4	)	)	PUNCT
ap-4481	138	5	r2	r2	NOUN
ap-4481	138	6	where	where	SCONJ
ap-4481	138	7	the	the	DET
ap-4481	138	8	matrix	matrix	NOUN
ap-4481	138	9	elements	element	NOUN
ap-4481	138	10	are	be	AUX
ap-4481	138	11	gaussian	gaussian	ADJ
ap-4481	138	12	random	random	ADJ
ap-4481	138	13	numbers	number	NOUN
ap-4481	138	14	with	with	ADP
ap-4481	138	15	mean	mean	PROPN
ap-4481	138	16	0	0	NUM
ap-4481	138	17	and	and	CCONJ
ap-4481	138	18	variance	variance	NOUN
ap-4481	138	19	1	1	NUM
ap-4481	138	20	.	.	PUNCT
ap-4481	139	1	in	in	ADP
ap-4481	139	2	figure	figure	NOUN
ap-4481	139	3	4	4	NUM
ap-4481	139	4	,	,	PUNCT
ap-4481	139	5	d(ε	d(ε	PROPN
ap-4481	139	6	)	)	PUNCT
ap-4481	139	7	(	(	PUNCT
ap-4481	139	8	(	(	PUNCT
ap-4481	139	9	23	23	NUM
ap-4481	139	10	)	)	PUNCT
ap-4481	139	11	and	and	CCONJ
ap-4481	139	12	(	(	PUNCT
ap-4481	139	13	24	24	NUM
ap-4481	139	14	)	)	PUNCT
ap-4481	139	15	)	)	PUNCT
ap-4481	139	16	matches	match	VERB
ap-4481	139	17	well	well	ADV
ap-4481	139	18	with	with	ADP
ap-4481	139	19	the	the	DET
ap-4481	139	20	histograms	histogram	NOUN
ap-4481	139	21	.	.	PUNCT
ap-4481	140	1	usually	usually	ADV
ap-4481	140	2	,	,	PUNCT
ap-4481	140	3	d(ε	d(ε	PROPN
ap-4481	140	4	)	)	PUNCT
ap-4481	140	5	is	be	AUX
ap-4481	140	6	plotted	plot	VERB
ap-4481	140	7	by	by	ADP
ap-4481	140	8	taking	take	VERB
ap-4481	140	9	ε	ε	PROPN
ap-4481	140	10	=	=	SYM
ap-4481	140	11	e	e	X
ap-4481	140	12	/	/	SYM
ap-4481	140	13	em	em	NOUN
ap-4481	140	14	,	,	PUNCT
ap-4481	140	15	where	where	SCONJ
ap-4481	140	16	em	em	PRON
ap-4481	140	17	is	be	AUX
ap-4481	140	18	the	the	DET
ap-4481	140	19	maximum	maximum	NOUN
ap-4481	140	20	of	of	ADP
ap-4481	140	21	the	the	DET
ap-4481	140	22	eigenvalues	eigenvalue	NOUN
ap-4481	140	23	and	and	CCONJ
ap-4481	140	24	d(ε	d(ε	PROPN
ap-4481	140	25	)	)	PUNCT
ap-4481	140	26	is	be	AUX
ap-4481	140	27	studied	study	VERB
ap-4481	140	28	for	for	ADP
ap-4481	140	29	−1	−1	NOUN
ap-4481	140	30	≤	≤	NUM
ap-4481	140	31	ε	ε	PROPN
ap-4481	140	32	≤	≤	ADJ
ap-4481	140	33	1	1	NUM
ap-4481	140	34	.	.	PUNCT
ap-4481	141	1	with	with	ADP
ap-4481	141	2	regard	regard	NOUN
ap-4481	141	3	to	to	ADP
ap-4481	141	4	this	this	PRON
ap-4481	141	5	the	the	DET
ap-4481	141	6	x	x	NOUN
ap-4481	141	7	-	-	NOUN
ap-4481	141	8	axis	axis	NOUN
ap-4481	141	9	could	could	AUX
ap-4481	141	10	be	be	AUX
ap-4481	141	11	scaled	scale	VERB
ap-4481	141	12	down	down	ADP
ap-4481	141	13	to	to	ADP
ap-4481	141	14	the	the	DET
ap-4481	141	15	domain	domain	NOUN
ap-4481	141	16	[	[	X
ap-4481	141	17	−1	−1	NOUN
ap-4481	141	18	,	,	PUNCT
ap-4481	141	19	1	1	NUM
ap-4481	141	20	]	]	PUNCT
ap-4481	141	21	to	to	PART
ap-4481	141	22	see	see	VERB
ap-4481	141	23	that	that	SCONJ
ap-4481	141	24	the	the	DET
ap-4481	141	25	ensembles	ensemble	NOUN
ap-4481	141	26	of	of	ADP
ap-4481	141	27	2×	2×	NUM
ap-4481	141	28	2	2	NUM
ap-4481	141	29	real	real	ADJ
ap-4481	141	30	matrices	matrix	NOUN
ap-4481	141	31	defy	defy	VERB
ap-4481	141	32	the	the	DET
ap-4481	141	33	semi	semi	ADJ
ap-4481	141	34	-	-	ADJ
ap-4481	141	35	circle	circle	ADJ
ap-4481	141	36	law	law	NOUN
ap-4481	141	37	which	which	PRON
ap-4481	141	38	is	be	AUX
ap-4481	141	39	observed	observe	VERB
ap-4481	141	40	for	for	ADP
ap-4481	141	41	real	real	ADJ
ap-4481	141	42	symmetric	symmetric	ADJ
ap-4481	141	43	matrices	matrix	NOUN
ap-4481	141	44	of	of	ADP
ap-4481	141	45	large	large	ADJ
ap-4481	141	46	order	order	NOUN
ap-4481	141	47	.	.	PUNCT
ap-4481	142	1	we	we	PRON
ap-4481	142	2	also	also	ADV
ap-4481	142	3	find	find	VERB
ap-4481	142	4	that	that	SCONJ
ap-4481	142	5	d(ε	d(ε	NOUN
ap-4481	142	6	)	)	PUNCT
ap-4481	142	7	for	for	ADP
ap-4481	142	8	both	both	CCONJ
ap-4481	142	9	r1	r1	PROPN
ap-4481	142	10	and	and	CCONJ
ap-4481	142	11	r2	r2	PROPN
ap-4481	142	12	are	be	AUX
ap-4481	142	13	sensitive	sensitive	ADJ
ap-4481	142	14	to	to	ADP
ap-4481	142	15	the	the	DET
ap-4481	142	16	pdf	pdf	NOUN
ap-4481	142	17	of	of	ADP
ap-4481	142	18	matrix	matrix	NOUN
ap-4481	142	19	elements	element	NOUN
ap-4481	142	20	.	.	PUNCT
ap-4481	143	1	422	422	NUM
ap-4481	143	2	vol	vol	NOUN
ap-4481	143	3	.	.	PUNCT
ap-4481	143	4	57	57	NUM
ap-4481	143	5	no	no	NOUN
ap-4481	143	6	.	.	PUNCT
ap-4481	144	1	6/2017	6/2017	X
ap-4481	144	2	new	new	ADJ
ap-4481	144	3	spectral	spectral	ADJ
ap-4481	144	4	statistics	statistic	NOUN
ap-4481	144	5	-3	-3	PUNCT
ap-4481	144	6	0	0	NUM
ap-4481	144	7	3	3	NUM
ap-4481	144	8	ε	ε	PROPN
ap-4481	144	9	0.15	0.15	NUM
ap-4481	144	10	0.3	0.3	NUM
ap-4481	144	11	dhεl	dhεl	NOUN
ap-4481	144	12	hal	hal	PROPN
ap-4481	144	13	-3	-3	PROPN
ap-4481	144	14	0	0	NUM
ap-4481	144	15	3	3	NUM
ap-4481	144	16	ε	ε	PROPN
ap-4481	144	17	0.15	0.15	NUM
ap-4481	144	18	0.3	0.3	NUM
ap-4481	144	19	dhεl	dhεl	VERB
ap-4481	144	20	hbl	hbl	NOUN
ap-4481	144	21	figure	figure	NOUN
ap-4481	144	22	4	4	NUM
ap-4481	144	23	.	.	PUNCT
ap-4481	145	1	distribution	distribution	NOUN
ap-4481	145	2	of	of	ADP
ap-4481	145	3	eigenvalues	eigenvalue	NOUN
ap-4481	145	4	d(ε	d(ε	PROPN
ap-4481	145	5	)	)	PUNCT
ap-4481	145	6	for	for	ADP
ap-4481	145	7	r1	r1	PROPN
ap-4481	145	8	(	(	PUNCT
ap-4481	145	9	a	a	NOUN
ap-4481	145	10	)	)	PUNCT
ap-4481	145	11	and	and	CCONJ
ap-4481	145	12	r2	r2	PROPN
ap-4481	145	13	(	(	PUNCT
ap-4481	145	14	b	b	NOUN
ap-4481	145	15	)	)	PUNCT
ap-4481	145	16	in	in	ADP
ap-4481	145	17	(	(	PUNCT
ap-4481	145	18	1	1	NUM
ap-4481	145	19	)	)	PUNCT
ap-4481	145	20	under	under	ADP
ap-4481	145	21	gaussian	gaussian	ADJ
ap-4481	145	22	pdf	pdf	NOUN
ap-4481	145	23	of	of	ADP
ap-4481	145	24	matrix	matrix	NOUN
ap-4481	145	25	elements	element	NOUN
ap-4481	145	26	.	.	PUNCT
ap-4481	146	1	the	the	DET
ap-4481	146	2	solid	solid	ADJ
ap-4481	146	3	line	line	NOUN
ap-4481	146	4	(	(	PUNCT
ap-4481	146	5	blue	blue	ADJ
ap-4481	146	6	)	)	PUNCT
ap-4481	146	7	is	be	AUX
ap-4481	146	8	due	due	ADJ
ap-4481	146	9	to	to	PART
ap-4481	146	10	(	(	PUNCT
ap-4481	146	11	23	23	NUM
ap-4481	146	12	)	)	PUNCT
ap-4481	146	13	and	and	CCONJ
ap-4481	146	14	(	(	PUNCT
ap-4481	146	15	24	24	NUM
ap-4481	146	16	)	)	PUNCT
ap-4481	146	17	.	.	PUNCT
ap-4481	147	1	the	the	DET
ap-4481	147	2	histograms	histogram	NOUN
ap-4481	147	3	are	be	AUX
ap-4481	147	4	due	due	ADJ
ap-4481	147	5	to	to	ADP
ap-4481	147	6	an	an	DET
ap-4481	147	7	ensemble	ensemble	NOUN
ap-4481	147	8	of	of	ADP
ap-4481	147	9	n	n	NOUN
ap-4481	147	10	=	=	SYM
ap-4481	147	11	8	8	NUM
ap-4481	147	12	×	×	NOUN
ap-4481	147	13	104	104	NUM
ap-4481	147	14	matrices	matrix	NOUN
ap-4481	147	15	.	.	PUNCT
ap-4481	148	1	4	4	X
ap-4481	148	2	.	.	X
ap-4481	148	3	conclusions	conclusion	NOUN
ap-4481	148	4	our	our	PRON
ap-4481	148	5	analytic	analytic	ADJ
ap-4481	148	6	and	and	CCONJ
ap-4481	148	7	semi	semi	ADJ
ap-4481	148	8	-	-	ADJ
ap-4481	148	9	analytic	analytic	ADJ
ap-4481	148	10	results	result	NOUN
ap-4481	148	11	on	on	ADP
ap-4481	148	12	p	p	PROPN
ap-4481	148	13	(	(	PUNCT
ap-4481	148	14	s	s	NOUN
ap-4481	148	15	)	)	PUNCT
ap-4481	148	16	for	for	ADP
ap-4481	148	17	two	two	NUM
ap-4481	148	18	modifications	modification	NOUN
ap-4481	148	19	of	of	ADP
ap-4481	148	20	2×2	2×2	NUM
ap-4481	148	21	real	real	ADJ
ap-4481	148	22	symmetric	symmetric	ADJ
ap-4481	148	23	matrices	matrix	NOUN
ap-4481	148	24	in	in	ADP
ap-4481	148	25	(	(	PUNCT
ap-4481	148	26	7	7	NUM
ap-4481	148	27	)	)	PUNCT
ap-4481	148	28	,	,	PUNCT
ap-4481	148	29	(	(	PUNCT
ap-4481	148	30	10	10	NUM
ap-4481	148	31	)	)	PUNCT
ap-4481	148	32	,	,	PUNCT
ap-4481	148	33	(	(	PUNCT
ap-4481	148	34	13	13	NUM
ap-4481	148	35	)	)	PUNCT
ap-4481	148	36	,	,	PUNCT
ap-4481	148	37	(	(	PUNCT
ap-4481	148	38	15	15	NUM
ap-4481	148	39	)	)	PUNCT
ap-4481	148	40	,	,	PUNCT
ap-4481	148	41	(	(	PUNCT
ap-4481	148	42	18	18	NUM
ap-4481	148	43	)	)	PUNCT
ap-4481	148	44	and	and	CCONJ
ap-4481	148	45	(	(	PUNCT
ap-4481	148	46	19	19	NUM
ap-4481	148	47	)	)	PUNCT
ap-4481	148	48	under	under	ADP
ap-4481	148	49	various	various	ADJ
ap-4481	148	50	probability	probability	NOUN
ap-4481	148	51	distribution	distribution	NOUN
ap-4481	148	52	functions	function	NOUN
ap-4481	148	53	and	and	CCONJ
ap-4481	148	54	the	the	DET
ap-4481	148	55	plotted	plot	VERB
ap-4481	148	56	p(s	p(s	NOUN
ap-4481	148	57	)	)	PUNCT
ap-4481	148	58	in	in	ADP
ap-4481	148	59	figures	figure	NOUN
ap-4481	148	60	1–3	1–3	PROPN
ap-4481	148	61	are	be	AUX
ap-4481	148	62	new	new	ADJ
ap-4481	148	63	and	and	CCONJ
ap-4481	148	64	instructive	instructive	ADJ
ap-4481	148	65	.	.	PUNCT
ap-4481	149	1	they	they	PRON
ap-4481	149	2	all	all	PRON
ap-4481	149	3	give	give	VERB
ap-4481	149	4	the	the	DET
ap-4481	149	5	linear	linear	ADJ
ap-4481	149	6	level	level	NOUN
ap-4481	149	7	repulsion	repulsion	NOUN
ap-4481	149	8	as	as	ADP
ap-4481	149	9	αs	αs	PRON
ap-4481	149	10	near	near	ADP
ap-4481	149	11	s	s	NOUN
ap-4481	149	12	=	=	NOUN
ap-4481	149	13	0	0	PROPN
ap-4481	149	14	but	but	CCONJ
ap-4481	149	15	notably	notably	ADV
ap-4481	149	16	α	α	PRON
ap-4481	149	17	is	be	AUX
ap-4481	149	18	not	not	PART
ap-4481	149	19	fixed	fix	VERB
ap-4481	149	20	.	.	PUNCT
ap-4481	150	1	the	the	DET
ap-4481	150	2	maxwellian	maxwellian	PROPN
ap-4481	150	3	pdf	pdf	PROPN
ap-4481	150	4	(	(	PUNCT
ap-4481	150	5	f(0	f(0	NOUN
ap-4481	150	6	)	)	PUNCT
ap-4481	150	7	=	=	SYM
ap-4481	150	8	0	0	NUM
ap-4481	150	9	)	)	PUNCT
ap-4481	150	10	of	of	ADP
ap-4481	150	11	matrix	matrix	NOUN
ap-4481	150	12	elements	element	NOUN
ap-4481	150	13	presents	present	VERB
ap-4481	150	14	a	a	DET
ap-4481	150	15	striking	striking	ADJ
ap-4481	150	16	result	result	NOUN
ap-4481	150	17	wherein	wherein	SCONJ
ap-4481	150	18	the	the	DET
ap-4481	150	19	level	level	NOUN
ap-4481	150	20	repulsion	repulsion	NOUN
ap-4481	150	21	near	near	ADP
ap-4481	150	22	s	s	NOUN
ap-4481	150	23	=	=	SYM
ap-4481	150	24	0	0	NUM
ap-4481	150	25	is	be	AUX
ap-4481	150	26	cubic	cubic	ADJ
ap-4481	150	27	.	.	PUNCT
ap-4481	151	1	it	it	PRON
ap-4481	151	2	will	will	AUX
ap-4481	151	3	be	be	AUX
ap-4481	151	4	further	far	ADV
ap-4481	151	5	interesting	interesting	ADJ
ap-4481	151	6	to	to	PART
ap-4481	151	7	investigate	investigate	VERB
ap-4481	151	8	spectral	spectral	ADJ
ap-4481	151	9	distributions	distribution	NOUN
ap-4481	151	10	for	for	ADP
ap-4481	151	11	n×	n×	PRON
ap-4481	151	12	n	n	PRON
ap-4481	151	13	matrices	matrix	NOUN
ap-4481	151	14	with	with	ADP
ap-4481	151	15	pdfs	pdfs	PROPN
ap-4481	151	16	which	which	PRON
ap-4481	151	17	are	be	AUX
ap-4481	151	18	non	non	ADJ
ap-4481	151	19	-	-	ADJ
ap-4481	151	20	symmetric	symmetric	ADJ
ap-4481	151	21	and	and	CCONJ
ap-4481	151	22	vanish	vanish	VERB
ap-4481	151	23	at	at	ADP
ap-4481	151	24	x	x	X
ap-4481	151	25	=	=	NOUN
ap-4481	151	26	0	0	NUM
ap-4481	151	27	.	.	PUNCT
ap-4481	152	1	the	the	DET
ap-4481	152	2	distribution	distribution	NOUN
ap-4481	152	3	of	of	ADP
ap-4481	152	4	eigenvalues	eigenvalue	NOUN
ap-4481	152	5	for	for	ADP
ap-4481	152	6	two	two	NUM
ap-4481	152	7	real	real	ADJ
ap-4481	152	8	matrices	matrix	NOUN
ap-4481	152	9	under	under	ADP
ap-4481	152	10	gaussian	gaussian	ADJ
ap-4481	152	11	pdf	pdf	NOUN
ap-4481	152	12	obtained	obtain	VERB
ap-4481	152	13	in	in	ADP
ap-4481	152	14	(	(	PUNCT
ap-4481	152	15	23	23	NUM
ap-4481	152	16	)	)	PUNCT
ap-4481	152	17	and	and	CCONJ
ap-4481	152	18	(	(	PUNCT
ap-4481	152	19	24	24	NUM
ap-4481	152	20	)	)	PUNCT
ap-4481	152	21	are	be	AUX
ap-4481	152	22	also	also	ADV
ap-4481	152	23	new	new	ADJ
ap-4481	152	24	and	and	CCONJ
ap-4481	152	25	instructive	instructive	ADJ
ap-4481	152	26	.	.	PUNCT
ap-4481	153	1	acknowledgements	acknowledgement	NOUN
ap-4481	153	2	s.	s.	PROPN
ap-4481	153	3	k.	k.	PROPN
ap-4481	153	4	wishes	wish	VERB
ap-4481	153	5	to	to	PART
ap-4481	153	6	thank	thank	VERB
ap-4481	153	7	dr	dr	PROPN
ap-4481	153	8	.	.	PROPN
ap-4481	153	9	shashi	shashi	PROPN
ap-4481	153	10	c.	c.	PROPN
ap-4481	153	11	l.	l.	PROPN
ap-4481	153	12	srivastava	srivastava	PROPN
ap-4481	153	13	,	,	PUNCT
ap-4481	153	14	vecc	vecc	PROPN
ap-4481	153	15	,	,	PUNCT
ap-4481	153	16	kolkata	kolkata	PROPN
ap-4481	153	17	,	,	PUNCT
ap-4481	153	18	for	for	ADP
ap-4481	153	19	some	some	DET
ap-4481	153	20	clarifications	clarification	NOUN
ap-4481	153	21	on	on	ADP
ap-4481	153	22	rmt	rmt	NOUN
ap-4481	153	23	.	.	PUNCT
ap-4481	154	1	references	reference	NOUN
ap-4481	154	2	[	[	X
ap-4481	154	3	1	1	NUM
ap-4481	154	4	]	]	PUNCT
ap-4481	154	5	c.	c.	PROPN
ap-4481	154	6	e.	e.	PROPN
ap-4481	154	7	porter	porter	PROPN
ap-4481	154	8	,	,	PUNCT
ap-4481	154	9	statistical	statistical	ADJ
ap-4481	154	10	theories	theory	NOUN
ap-4481	154	11	of	of	ADP
ap-4481	154	12	spectra	spectra	NOUN
ap-4481	154	13	:	:	PUNCT
ap-4481	154	14	fluctuations	fluctuation	NOUN
ap-4481	154	15	(	(	PUNCT
ap-4481	154	16	academic	academic	ADJ
ap-4481	154	17	,	,	PUNCT
ap-4481	154	18	new	new	PROPN
ap-4481	154	19	york	york	PROPN
ap-4481	154	20	,	,	PUNCT
ap-4481	154	21	1965	1965	NUM
ap-4481	154	22	)	)	PUNCT
ap-4481	154	23	.	.	PUNCT
ap-4481	155	1	[	[	X
ap-4481	155	2	2	2	NUM
ap-4481	155	3	]	]	PUNCT
ap-4481	155	4	m.	m.	NOUN
ap-4481	155	5	l.	l.	PROPN
ap-4481	155	6	mehta	mehta	PROPN
ap-4481	155	7	,	,	PUNCT
ap-4481	155	8	random	random	ADJ
ap-4481	155	9	matrices	matrix	NOUN
ap-4481	155	10	3rd	3rd	PROPN
ap-4481	155	11	ed	ed	NOUN
ap-4481	155	12	.	.	PUNCT
ap-4481	156	1	(	(	PUNCT
ap-4481	156	2	amesterdam	amesterdam	PROPN
ap-4481	156	3	,	,	PUNCT
ap-4481	156	4	elsevier	elsevier	NOUN
ap-4481	156	5	,	,	PUNCT
ap-4481	156	6	2004	2004	NUM
ap-4481	156	7	)	)	PUNCT
ap-4481	156	8	.	.	PUNCT
ap-4481	157	1	[	[	X
ap-4481	157	2	3	3	NUM
ap-4481	157	3	]	]	PUNCT
ap-4481	157	4	a.	a.	NOUN
ap-4481	157	5	bohr	bohr	PROPN
ap-4481	157	6	and	and	CCONJ
ap-4481	157	7	mottelson	mottelson	PROPN
ap-4481	157	8	,	,	PUNCT
ap-4481	157	9	nuclear	nuclear	ADJ
ap-4481	157	10	structure	structure	NOUN
ap-4481	157	11	vol	vol	NOUN
ap-4481	157	12	.	.	PUNCT
ap-4481	158	1	i	i	PRON
ap-4481	158	2	(	(	PUNCT
ap-4481	158	3	benjamin	benjamin	PROPN
ap-4481	158	4	,	,	PUNCT
ap-4481	158	5	reading	reading	NOUN
ap-4481	158	6	,	,	PUNCT
ap-4481	158	7	ma	ma	PROPN
ap-4481	158	8	,	,	PUNCT
ap-4481	158	9	1975	1975	NUM
ap-4481	158	10	)	)	PUNCT
ap-4481	158	11	.	.	PUNCT
ap-4481	159	1	[	[	X
ap-4481	159	2	4	4	X
ap-4481	159	3	]	]	PUNCT
ap-4481	159	4	f.	f.	PROPN
ap-4481	159	5	hake	hake	PROPN
ap-4481	159	6	,	,	PUNCT
ap-4481	159	7	quantum	quantum	ADJ
ap-4481	159	8	signatures	signature	NOUN
ap-4481	159	9	of	of	ADP
ap-4481	159	10	chaos	chaos	NOUN
ap-4481	159	11	(	(	PUNCT
ap-4481	159	12	new	new	PROPN
ap-4481	159	13	york	york	PROPN
ap-4481	159	14	springer	springer	NOUN
ap-4481	159	15	,	,	PUNCT
ap-4481	159	16	1992	1992	NUM
ap-4481	159	17	)	)	PUNCT
ap-4481	159	18	.	.	PUNCT
ap-4481	160	1	[	[	X
ap-4481	160	2	5	5	NUM
ap-4481	160	3	]	]	SYM
ap-4481	160	4	e.p	e.p	PROPN
ap-4481	160	5	.	.	PROPN
ap-4481	160	6	wigner	wigner	NOUN
ap-4481	160	7	,	,	PUNCT
ap-4481	160	8	ann	ann	PROPN
ap-4481	160	9	.	.	PROPN
ap-4481	160	10	math	math	PROPN
ap-4481	160	11	.	.	PUNCT
ap-4481	161	1	67	67	NUM
ap-4481	161	2	1958	1958	NUM
ap-4481	161	3	.	.	PUNCT
ap-4481	162	1	[	[	X
ap-4481	162	2	6	6	NUM
ap-4481	162	3	]	]	X
ap-4481	162	4	n.	n.	NOUN
ap-4481	162	5	rosenzweig	rosenzweig	PROPN
ap-4481	162	6	,	,	PUNCT
ap-4481	162	7	phys	phy	NOUN
ap-4481	162	8	.	.	PUNCT
ap-4481	162	9	rev	rev	PROPN
ap-4481	162	10	.	.	PROPN
ap-4481	162	11	lett	lett	PROPN
ap-4481	162	12	.	.	PROPN
ap-4481	163	1	1	1	NUM
ap-4481	163	2	24	24	NUM
ap-4481	163	3	(	(	PUNCT
ap-4481	163	4	1958	1958	NUM
ap-4481	163	5	)	)	PUNCT
ap-4481	163	6	.	.	PUNCT
ap-4481	164	1	[	[	X
ap-4481	164	2	7	7	X
ap-4481	164	3	]	]	X
ap-4481	164	4	p.c	p.c	PROPN
ap-4481	164	5	.	.	PROPN
ap-4481	164	6	huu	huu	PROPN
ap-4481	164	7	-	-	PUNCT
ap-4481	164	8	tai	tai	PROPN
ap-4481	164	9	,	,	PUNCT
ap-4481	164	10	n.	n.	PROPN
ap-4481	164	11	a.	a.	PROPN
ap-4481	164	12	smirnova	smirnova	PROPN
ap-4481	164	13	,	,	PUNCT
ap-4481	164	14	p.	p.	PROPN
ap-4481	164	15	van	van	PROPN
ap-4481	164	16	isacker	isacker	PROPN
ap-4481	164	17	,	,	PUNCT
ap-4481	164	18	j.	j.	PROPN
ap-4481	164	19	phys	phys	PROPN
ap-4481	164	20	.	.	PUNCT
ap-4481	165	1	a	a	DET
ap-4481	165	2	:	:	PUNCT
ap-4481	165	3	math	math	NOUN
ap-4481	165	4	.	.	PUNCT
ap-4481	166	1	gen	gen	PROPN
ap-4481	166	2	.	.	PROPN
ap-4481	166	3	35	35	NUM
ap-4481	166	4	l199	l199	NUM
ap-4481	166	5	(	(	PUNCT
ap-4481	166	6	2002	2002	NUM
ap-4481	166	7	)	)	PUNCT
ap-4481	166	8	.	.	PUNCT
ap-4481	167	1	[	[	X
ap-4481	167	2	8	8	NUM
ap-4481	167	3	]	]	X
ap-4481	167	4	m.v	m.v	PROPN
ap-4481	167	5	.	.	PROPN
ap-4481	167	6	berry	berry	PROPN
ap-4481	167	7	and	and	CCONJ
ap-4481	167	8	p.	p.	NOUN
ap-4481	167	9	shukla	shukla	NOUN
ap-4481	167	10	,	,	PUNCT
ap-4481	167	11	j.	j.	PROPN
ap-4481	167	12	phys	phys	PROPN
ap-4481	167	13	.	.	PUNCT
ap-4481	168	1	a	a	PRON
ap-4481	168	2	:	:	PUNCT
ap-4481	168	3	theor	theor	PROPN
ap-4481	168	4	.	.	PUNCT
ap-4481	169	1	42	42	NUM
ap-4481	169	2	485102	485102	NUM
ap-4481	169	3	(	(	PUNCT
ap-4481	169	4	2009	2009	NUM
ap-4481	169	5	)	)	PUNCT
ap-4481	169	6	.	.	PUNCT
ap-4481	170	1	[	[	X
ap-4481	170	2	9	9	NUM
ap-4481	170	3	]	]	PUNCT
ap-4481	170	4	s.	s.	PROPN
ap-4481	170	5	grossman	grossman	PROPN
ap-4481	170	6	and	and	CCONJ
ap-4481	170	7	m.	m.	PROPN
ap-4481	170	8	robnik	robnik	PROPN
ap-4481	170	9	,	,	PUNCT
ap-4481	170	10	j.	j.	PROPN
ap-4481	170	11	phys	phys	PROPN
ap-4481	170	12	.	.	PUNCT
ap-4481	171	1	a	a	DET
ap-4481	171	2	:	:	PUNCT
ap-4481	171	3	math	math	NOUN
ap-4481	171	4	.	.	PUNCT
ap-4481	172	1	theor	theor	PROPN
ap-4481	172	2	.	.	PUNCT
ap-4481	173	1	40	40	NUM
ap-4481	173	2	409	409	NUM
ap-4481	173	3	(	(	PUNCT
ap-4481	173	4	2007	2007	NUM
ap-4481	173	5	)	)	PUNCT
ap-4481	173	6	.	.	PUNCT
ap-4481	174	1	[	[	X
ap-4481	174	2	10	10	NUM
ap-4481	174	3	]	]	PUNCT
ap-4481	174	4	z.	z.	PROPN
ap-4481	174	5	ahmed	ahmed	PROPN
ap-4481	174	6	,	,	PUNCT
ap-4481	174	7	phys	phy	NOUN
ap-4481	174	8	.	.	PUNCT
ap-4481	175	1	lett	lett	PROPN
ap-4481	175	2	.	.	PUNCT
ap-4481	176	1	a	a	DET
ap-4481	176	2	308	308	NUM
ap-4481	176	3	140	140	NUM
ap-4481	176	4	(	(	PUNCT
ap-4481	176	5	2003	2003	NUM
ap-4481	176	6	)	)	PUNCT
ap-4481	176	7	.	.	PUNCT
ap-4481	177	1	[	[	X
ap-4481	177	2	11	11	NUM
ap-4481	177	3	]	]	PUNCT
ap-4481	177	4	z.	z.	PROPN
ap-4481	177	5	ahmed	ahmed	PROPN
ap-4481	177	6	and	and	CCONJ
ap-4481	177	7	s.r	s.r	PROPN
ap-4481	177	8	jain	jain	PROPN
ap-4481	177	9	,	,	PUNCT
ap-4481	177	10	j.	j.	PROPN
ap-4481	177	11	phys	phys	PROPN
ap-4481	177	12	.	.	PUNCT
ap-4481	178	1	a	a	DET
ap-4481	178	2	:	:	PUNCT
ap-4481	178	3	math	math	NOUN
ap-4481	178	4	.	.	PUNCT
ap-4481	179	1	gen	gen	PROPN
ap-4481	179	2	.	.	PROPN
ap-4481	179	3	36	36	NUM
ap-4481	179	4	3349	3349	NUM
ap-4481	179	5	(	(	PUNCT
ap-4481	179	6	2003	2003	NUM
ap-4481	179	7	)	)	PUNCT
ap-4481	179	8	.	.	PUNCT
ap-4481	180	1	[	[	X
ap-4481	180	2	12	12	NUM
ap-4481	180	3	]	]	PUNCT
ap-4481	180	4	z.	z.	PROPN
ap-4481	180	5	ahmed	ahmed	PROPN
ap-4481	180	6	and	and	CCONJ
ap-4481	180	7	s.r	s.r	PROPN
ap-4481	180	8	.	.	PROPN
ap-4481	180	9	jain	jain	PROPN
ap-4481	180	10	,	,	PUNCT
ap-4481	180	11	phys	phys	PROPN
ap-4481	180	12	.	.	PUNCT
ap-4481	180	13	rev	rev	PROPN
ap-4481	180	14	.	.	PUNCT
ap-4481	181	1	e	e	PROPN
ap-4481	181	2	67	67	NUM
ap-4481	181	3	045106	045106	NUM
ap-4481	181	4	(	(	PUNCT
ap-4481	181	5	r	r	NOUN
ap-4481	181	6	)	)	PUNCT
ap-4481	181	7	(	(	PUNCT
ap-4481	181	8	2003	2003	NUM
ap-4481	181	9	)	)	PUNCT
ap-4481	181	10	.	.	PUNCT
ap-4481	182	1	[	[	X
ap-4481	182	2	13	13	NUM
ap-4481	182	3	]	]	X
ap-4481	182	4	e.m	e.m	PROPN
ap-4481	182	5	.	.	PROPN
ap-4481	182	6	graefe	graefe	PROPN
ap-4481	182	7	,	,	PUNCT
ap-4481	182	8	s.	s.	PROPN
ap-4481	182	9	mudute	mudute	PROPN
ap-4481	182	10	-	-	PUNCT
ap-4481	182	11	ndumbe	ndumbe	NOUN
ap-4481	182	12	and	and	CCONJ
ap-4481	182	13	m.	m.	PROPN
ap-4481	182	14	taylor	taylor	PROPN
ap-4481	182	15	,	,	PUNCT
ap-4481	182	16	j.	j.	PROPN
ap-4481	182	17	phys	phys	PROPN
ap-4481	182	18	.	.	PUNCT
ap-4481	183	1	theor	theor	PROPN
ap-4481	183	2	.	.	PUNCT
ap-4481	184	1	48	48	NUM
ap-4481	184	2	38ft02	38ft02	NUM
ap-4481	184	3	(	(	PUNCT
ap-4481	184	4	2015	2015	NUM
ap-4481	184	5	)	)	PUNCT
ap-4481	184	6	.	.	PUNCT
ap-4481	185	1	[	[	X
ap-4481	185	2	14	14	NUM
ap-4481	185	3	]	]	PUNCT
ap-4481	185	4	j.	j.	PROPN
ap-4481	185	5	gong	gong	PROPN
ap-4481	185	6	and	and	CCONJ
ap-4481	185	7	q.	q.	PROPN
ap-4481	185	8	wang	wang	PROPN
ap-4481	185	9	,	,	PUNCT
ap-4481	185	10	j.	j.	PROPN
ap-4481	185	11	phys	phys	PROPN
ap-4481	185	12	.	.	PUNCT
ap-4481	186	1	45	45	NUM
ap-4481	186	2	444014	444014	NUM
ap-4481	186	3	,	,	PUNCT
ap-4481	186	4	(	(	PUNCT
ap-4481	186	5	2012	2012	NUM
ap-4481	186	6	)	)	PUNCT
ap-4481	186	7	.	.	PUNCT
ap-4481	187	1	[	[	X
ap-4481	187	2	15	15	NUM
ap-4481	187	3	]	]	X
ap-4481	187	4	s.	s.	PROPN
ap-4481	187	5	hameed	hameed	PROPN
ap-4481	187	6	.	.	PUNCT
ap-4481	188	1	k.	k.	PROPN
ap-4481	188	2	jain	jain	PROPN
ap-4481	188	3	and	and	CCONJ
ap-4481	188	4	a.	a.	PROPN
ap-4481	188	5	laxminaraynan	laxminaraynan	PROPN
ap-4481	188	6	,	,	PUNCT
ap-4481	188	7	j.	j.	PROPN
ap-4481	188	8	phys	phys	PROPN
ap-4481	188	9	.	.	PUNCT
ap-4481	189	1	a	a	DET
ap-4481	189	2	:	:	PUNCT
ap-4481	189	3	math	math	NOUN
ap-4481	189	4	.	.	PUNCT
ap-4481	190	1	theor	theor	PROPN
ap-4481	190	2	48	48	NUM
ap-4481	190	3	385204	385204	NUM
ap-4481	190	4	(	(	PUNCT
ap-4481	190	5	2015	2015	NUM
ap-4481	190	6	)	)	PUNCT
ap-4481	190	7	.	.	PUNCT
ap-4481	191	1	423	423	NUM
ap-4481	191	2	acta	acta	PROPN
ap-4481	191	3	polytechnica	polytechnica	PROPN
ap-4481	191	4	57(6):418–423	57(6):418–423	PROPN
ap-4481	191	5	,	,	PUNCT
ap-4481	191	6	2017	2017	NUM
ap-4481	191	7	1	1	NUM
ap-4481	191	8	introduction	introduction	NOUN
ap-4481	191	9	2	2	NUM
ap-4481	191	10	ensembles	ensemble	NOUN
ap-4481	191	11	of	of	ADP
ap-4481	191	12	2x2	2x2	NUM
ap-4481	191	13	real	real	ADJ
ap-4481	191	14	-	-	PUNCT
ap-4481	191	15	symmetric	symmetric	ADJ
ap-4481	191	16	random	random	ADJ
ap-4481	191	17	matrices	matrix	NOUN
ap-4481	191	18	and	and	CCONJ
ap-4481	191	19	their	their	PRON
ap-4481	191	20	spacing	space	VERB
ap-4481	191	21	distributions	distribution	NOUN
ap-4481	191	22	2.1	2.1	NUM
ap-4481	191	23	uniform	uniform	ADJ
ap-4481	191	24	distribution	distribution	NOUN
ap-4481	191	25	2.2	2.2	NUM
ap-4481	191	26	exponential	exponential	ADJ
ap-4481	191	27	distribution	distribution	NOUN
ap-4481	191	28	2.3	2.3	NUM
ap-4481	191	29	super	super	ADJ
ap-4481	191	30	-	-	ADJ
ap-4481	191	31	gaussian	gaussian	ADJ
ap-4481	191	32	distribution	distribution	NOUN
ap-4481	191	33	2.4	2.4	NUM
ap-4481	191	34	maxwellian	maxwellian	ADJ
ap-4481	191	35	distribution	distribution	NOUN
ap-4481	191	36	3	3	NUM
ap-4481	191	37	distribution	distribution	NOUN
ap-4481	191	38	of	of	ADP
ap-4481	191	39	eigenvalues	eigenvalue	NOUN
ap-4481	191	40	d(epsilon	d(epsilon	NOUN
ap-4481	191	41	)	)	PUNCT
ap-4481	191	42	of	of	ADP
ap-4481	191	43	2x2	2x2	NUM
ap-4481	191	44	gaussian	gaussian	ADJ
ap-4481	191	45	random	random	ADJ
ap-4481	191	46	matrices	matrix	NOUN
ap-4481	191	47	4	4	NUM
ap-4481	191	48	conclusions	conclusion	NOUN
ap-4481	191	49	acknowledgements	acknowledgement	NOUN
ap-4481	191	50	references	reference	NOUN