id	sid	tid	token	lemma	pos
ejpam-521	1	1	6_521_qian.dvi	6_521_qian.dvi	NUM
ejpam-521	1	2	european	european	ADJ
ejpam-521	1	3	journal	journal	NOUN
ejpam-521	1	4	of	of	ADP
ejpam-521	1	5	pure	pure	ADJ
ejpam-521	1	6	and	and	CCONJ
ejpam-521	1	7	applied	apply	VERB
ejpam-521	1	8	mathematics	mathematic	NOUN
ejpam-521	1	9	vol	vol	NOUN
ejpam-521	1	10	.	.	PUNCT
ejpam-521	2	1	3	3	NUM
ejpam-521	2	2	,	,	PUNCT
ejpam-521	2	3	no	no	INTJ
ejpam-521	2	4	.	.	NOUN
ejpam-521	2	5	1	1	NUM
ejpam-521	2	6	,	,	PUNCT
ejpam-521	2	7	2010	2010	NUM
ejpam-521	2	8	,	,	PUNCT
ejpam-521	2	9	51	51	NUM
ejpam-521	2	10	-	-	SYM
ejpam-521	2	11	80	80	NUM
ejpam-521	2	12	issn	issn	PROPN
ejpam-521	2	13	1307	1307	NUM
ejpam-521	2	14	-	-	SYM
ejpam-521	2	15	5543	5543	NUM
ejpam-521	2	16	–	–	PUNCT
ejpam-521	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-521	2	18	stochastic	stochastic	ADJ
ejpam-521	2	19	complexity	complexity	NOUN
ejpam-521	2	20	,	,	PUNCT
ejpam-521	2	21	histograms	histogram	NOUN
ejpam-521	2	22	and	and	CCONJ
ejpam-521	2	23	hypothesis	hypothesis	NOUN
ejpam-521	2	24	testing	testing	NOUN
ejpam-521	2	25	of	of	ADP
ejpam-521	2	26	homogeneity	homogeneity	NOUN
ejpam-521	2	27	guoqi	guoqi	PROPN
ejpam-521	2	28	qian	qian	PROPN
ejpam-521	2	29	department	department	PROPN
ejpam-521	2	30	of	of	ADP
ejpam-521	2	31	mathematics	mathematics	PROPN
ejpam-521	2	32	and	and	CCONJ
ejpam-521	2	33	statistics	statistic	NOUN
ejpam-521	2	34	,	,	PUNCT
ejpam-521	2	35	university	university	NOUN
ejpam-521	2	36	of	of	ADP
ejpam-521	2	37	melbourne	melbourne	PROPN
ejpam-521	2	38	,	,	PUNCT
ejpam-521	2	39	vic	vic	PROPN
ejpam-521	2	40	3010	3010	NUM
ejpam-521	2	41	,	,	PUNCT
ejpam-521	2	42	australia	australia	PROPN
ejpam-521	2	43	.	.	PUNCT
ejpam-521	3	1	abstract	abstract	PROPN
ejpam-521	3	2	.	.	PUNCT
ejpam-521	4	1	information	information	NOUN
ejpam-521	4	2	contained	contain	VERB
ejpam-521	4	3	in	in	ADP
ejpam-521	4	4	a	a	DET
ejpam-521	4	5	sample	sample	NOUN
ejpam-521	4	6	of	of	ADP
ejpam-521	4	7	quantitative	quantitative	ADJ
ejpam-521	4	8	data	datum	NOUN
ejpam-521	4	9	may	may	AUX
ejpam-521	4	10	be	be	AUX
ejpam-521	4	11	summarized	summarize	VERB
ejpam-521	4	12	or	or	CCONJ
ejpam-521	4	13	described	describe	VERB
ejpam-521	4	14	by	by	ADP
ejpam-521	4	15	a	a	DET
ejpam-521	4	16	nonparametric	nonparametric	NOUN
ejpam-521	4	17	histogram	histogram	NOUN
ejpam-521	4	18	density	density	NOUN
ejpam-521	4	19	function	function	NOUN
ejpam-521	4	20	.	.	PUNCT
ejpam-521	5	1	an	an	DET
ejpam-521	5	2	interesting	interesting	ADJ
ejpam-521	5	3	question	question	NOUN
ejpam-521	5	4	is	be	AUX
ejpam-521	5	5	how	how	SCONJ
ejpam-521	5	6	to	to	PART
ejpam-521	5	7	construct	construct	VERB
ejpam-521	5	8	such	such	DET
ejpam-521	5	9	a	a	DET
ejpam-521	5	10	histogram	histogram	NOUN
ejpam-521	5	11	density	density	NOUN
ejpam-521	5	12	to	to	PART
ejpam-521	5	13	express	express	VERB
ejpam-521	5	14	the	the	DET
ejpam-521	5	15	data	data	NOUN
ejpam-521	5	16	information	information	NOUN
ejpam-521	5	17	with	with	ADP
ejpam-521	5	18	minimum	minimum	ADJ
ejpam-521	5	19	stochastic	stochastic	ADJ
ejpam-521	5	20	complexity	complexity	NOUN
ejpam-521	5	21	.	.	PUNCT
ejpam-521	6	1	the	the	DET
ejpam-521	6	2	stochastic	stochastic	ADJ
ejpam-521	6	3	complexity	complexity	NOUN
ejpam-521	6	4	is	be	AUX
ejpam-521	6	5	a	a	DET
ejpam-521	6	6	pseudonym	pseudonym	NOUN
ejpam-521	6	7	of	of	ADP
ejpam-521	6	8	rissanen	rissanen	PROPN
ejpam-521	6	9	’s	’s	PART
ejpam-521	6	10	minimum	minimum	ADJ
ejpam-521	6	11	description	description	NOUN
ejpam-521	6	12	length	length	NOUN
ejpam-521	6	13	(	(	PUNCT
ejpam-521	6	14	mdl	mdl	PROPN
ejpam-521	6	15	)	)	PUNCT
ejpam-521	6	16	which	which	PRON
ejpam-521	6	17	gives	give	VERB
ejpam-521	6	18	the	the	DET
ejpam-521	6	19	length	length	NOUN
ejpam-521	6	20	of	of	ADP
ejpam-521	6	21	a	a	DET
ejpam-521	6	22	sequence	sequence	NOUN
ejpam-521	6	23	of	of	ADP
ejpam-521	6	24	decipherable	decipherable	ADJ
ejpam-521	6	25	binary	binary	PROPN
ejpam-521	6	26	code	code	PROPN
ejpam-521	6	27	resulted	result	VERB
ejpam-521	6	28	from	from	ADP
ejpam-521	6	29	optimally	optimally	ADV
ejpam-521	6	30	encoding	encode	VERB
ejpam-521	6	31	the	the	DET
ejpam-521	6	32	data	data	NOUN
ejpam-521	6	33	information	information	NOUN
ejpam-521	6	34	using	use	VERB
ejpam-521	6	35	a	a	DET
ejpam-521	6	36	probability	probability	NOUN
ejpam-521	6	37	distribution	distribution	NOUN
ejpam-521	6	38	based	base	VERB
ejpam-521	6	39	code	code	NOUN
ejpam-521	6	40	-	-	PUNCT
ejpam-521	6	41	book	book	NOUN
ejpam-521	6	42	.	.	PUNCT
ejpam-521	7	1	here	here	ADV
ejpam-521	7	2	we	we	PRON
ejpam-521	7	3	have	have	AUX
ejpam-521	7	4	derived	derive	VERB
ejpam-521	7	5	an	an	DET
ejpam-521	7	6	optimal	optimal	ADJ
ejpam-521	7	7	generalized	generalized	ADJ
ejpam-521	7	8	histogram	histogram	NOUN
ejpam-521	7	9	density	density	NOUN
ejpam-521	7	10	estimator	estimator	NOUN
ejpam-521	7	11	to	to	PART
ejpam-521	7	12	provide	provide	VERB
ejpam-521	7	13	both	both	CCONJ
ejpam-521	7	14	predictive	predictive	ADJ
ejpam-521	7	15	and	and	CCONJ
ejpam-521	7	16	non	non	ADJ
ejpam-521	7	17	-	-	ADJ
ejpam-521	7	18	predictive	predictive	ADJ
ejpam-521	7	19	coding	code	VERB
ejpam-521	7	20	description	description	NOUN
ejpam-521	7	21	of	of	ADP
ejpam-521	7	22	a	a	DET
ejpam-521	7	23	data	data	NOUN
ejpam-521	7	24	sample	sample	NOUN
ejpam-521	7	25	.	.	PUNCT
ejpam-521	8	1	we	we	PRON
ejpam-521	8	2	have	have	AUX
ejpam-521	8	3	also	also	ADV
ejpam-521	8	4	obtained	obtain	VERB
ejpam-521	8	5	uniform	uniform	NOUN
ejpam-521	8	6	and	and	CCONJ
ejpam-521	8	7	almost	almost	ADV
ejpam-521	8	8	sure	sure	ADJ
ejpam-521	8	9	asymptotic	asymptotic	ADJ
ejpam-521	8	10	approximations	approximation	NOUN
ejpam-521	8	11	for	for	ADP
ejpam-521	8	12	the	the	DET
ejpam-521	8	13	lengths	length	NOUN
ejpam-521	8	14	of	of	ADP
ejpam-521	8	15	both	both	DET
ejpam-521	8	16	descriptions	description	NOUN
ejpam-521	8	17	.	.	PUNCT
ejpam-521	9	1	as	as	ADP
ejpam-521	9	2	an	an	DET
ejpam-521	9	3	application	application	NOUN
ejpam-521	9	4	of	of	ADP
ejpam-521	9	5	this	this	DET
ejpam-521	9	6	result	result	NOUN
ejpam-521	9	7	to	to	ADP
ejpam-521	9	8	statistical	statistical	ADJ
ejpam-521	9	9	inference	inference	NOUN
ejpam-521	9	10	a	a	DET
ejpam-521	9	11	new	new	ADJ
ejpam-521	9	12	procedure	procedure	NOUN
ejpam-521	9	13	for	for	ADP
ejpam-521	9	14	hypothesis	hypothesis	NOUN
ejpam-521	9	15	testing	testing	NOUN
ejpam-521	9	16	of	of	ADP
ejpam-521	9	17	distribution	distribution	NOUN
ejpam-521	9	18	homogeneity	homogeneity	NOUN
ejpam-521	9	19	is	be	AUX
ejpam-521	9	20	proposed	propose	VERB
ejpam-521	9	21	and	and	CCONJ
ejpam-521	9	22	is	be	AUX
ejpam-521	9	23	proved	prove	VERB
ejpam-521	9	24	to	to	PART
ejpam-521	9	25	have	have	VERB
ejpam-521	9	26	an	an	DET
ejpam-521	9	27	asymptotic	asymptotic	ADJ
ejpam-521	9	28	power	power	NOUN
ejpam-521	9	29	of	of	ADP
ejpam-521	9	30	1	1	NUM
ejpam-521	9	31	.	.	SYM
ejpam-521	9	32	2000	2000	NUM
ejpam-521	9	33	mathematics	mathematic	NOUN
ejpam-521	9	34	subject	subject	NOUN
ejpam-521	9	35	classifications	classification	NOUN
ejpam-521	9	36	:	:	PUNCT
ejpam-521	9	37	62g07	62g07	NUM
ejpam-521	9	38	,	,	PUNCT
ejpam-521	9	39	62g20	62g20	NOUN
ejpam-521	9	40	,	,	PUNCT
ejpam-521	9	41	60g10	60g10	NUM
ejpam-521	9	42	key	key	ADJ
ejpam-521	9	43	words	word	NOUN
ejpam-521	9	44	and	and	CCONJ
ejpam-521	9	45	phrases	phrase	NOUN
ejpam-521	9	46	:	:	PUNCT
ejpam-521	9	47	histogram	histogram	NOUN
ejpam-521	9	48	density	density	NOUN
ejpam-521	9	49	estimation	estimation	NOUN
ejpam-521	9	50	,	,	PUNCT
ejpam-521	9	51	minimum	minimum	ADJ
ejpam-521	9	52	description	description	NOUN
ejpam-521	9	53	length	length	NOUN
ejpam-521	9	54	,	,	PUNCT
ejpam-521	9	55	model	model	NOUN
ejpam-521	9	56	selection	selection	NOUN
ejpam-521	9	57	,	,	PUNCT
ejpam-521	9	58	quantization	quantization	NOUN
ejpam-521	9	59	,	,	PUNCT
ejpam-521	9	60	stochastic	stochastic	ADJ
ejpam-521	9	61	complexity	complexity	NOUN
ejpam-521	9	62	,	,	PUNCT
ejpam-521	9	63	test	test	NOUN
ejpam-521	9	64	of	of	ADP
ejpam-521	9	65	homogeneity	homogeneity	NOUN
ejpam-521	9	66	1	1	NUM
ejpam-521	9	67	.	.	PUNCT
ejpam-521	10	1	introduction	introduction	NOUN
ejpam-521	10	2	in	in	ADP
ejpam-521	10	3	digital	digital	ADJ
ejpam-521	10	4	data	data	NOUN
ejpam-521	10	5	-	-	PUNCT
ejpam-521	10	6	transmission	transmission	NOUN
ejpam-521	10	7	systems	system	NOUN
ejpam-521	10	8	,	,	PUNCT
ejpam-521	10	9	input	input	NOUN
ejpam-521	10	10	signals	signal	NOUN
ejpam-521	10	11	are	be	AUX
ejpam-521	10	12	first	first	ADV
ejpam-521	10	13	converted	convert	VERB
ejpam-521	10	14	into	into	ADP
ejpam-521	10	15	digital	digital	ADJ
ejpam-521	10	16	form	form	NOUN
ejpam-521	10	17	at	at	ADP
ejpam-521	10	18	the	the	DET
ejpam-521	10	19	transmitter	transmitter	NOUN
ejpam-521	10	20	,	,	PUNCT
ejpam-521	10	21	then	then	ADV
ejpam-521	10	22	transmitted	transmit	VERB
ejpam-521	10	23	through	through	ADP
ejpam-521	10	24	a	a	DET
ejpam-521	10	25	communication	communication	NOUN
ejpam-521	10	26	channel	channel	NOUN
ejpam-521	10	27	and	and	CCONJ
ejpam-521	10	28	finally	finally	ADV
ejpam-521	10	29	reconstructed	reconstruct	VERB
ejpam-521	10	30	into	into	ADP
ejpam-521	10	31	output	output	NOUN
ejpam-521	10	32	signals	signal	NOUN
ejpam-521	10	33	at	at	ADP
ejpam-521	10	34	the	the	DET
ejpam-521	10	35	receiver	receiver	NOUN
ejpam-521	10	36	.	.	PUNCT
ejpam-521	11	1	at	at	ADP
ejpam-521	11	2	the	the	DET
ejpam-521	11	3	transmitter	transmitter	NOUN
ejpam-521	11	4	a	a	DET
ejpam-521	11	5	quantization	quantization	NOUN
ejpam-521	11	6	procedure	procedure	NOUN
ejpam-521	11	7	is	be	AUX
ejpam-521	11	8	often	often	ADV
ejpam-521	11	9	executed	execute	VERB
ejpam-521	11	10	in	in	ADP
ejpam-521	11	11	which	which	PRON
ejpam-521	11	12	the	the	DET
ejpam-521	11	13	whole	whole	ADJ
ejpam-521	11	14	range	range	NOUN
ejpam-521	11	15	of	of	ADP
ejpam-521	11	16	input	input	NOUN
ejpam-521	11	17	amplitudes	amplitude	NOUN
ejpam-521	11	18	is	be	AUX
ejpam-521	11	19	divided	divide	VERB
ejpam-521	11	20	into	into	ADP
ejpam-521	11	21	a	a	DET
ejpam-521	11	22	finite	finite	ADJ
ejpam-521	11	23	number	number	NOUN
ejpam-521	11	24	of	of	ADP
ejpam-521	11	25	amplitude	amplitude	NOUN
ejpam-521	11	26	sub	sub	NOUN
ejpam-521	11	27	-	-	NOUN
ejpam-521	11	28	ranges	range	NOUN
ejpam-521	11	29	and	and	CCONJ
ejpam-521	11	30	the	the	DET
ejpam-521	11	31	input	input	NOUN
ejpam-521	11	32	amplitudes	amplitude	NOUN
ejpam-521	11	33	in	in	ADP
ejpam-521	11	34	each	each	DET
ejpam-521	11	35	sub	sub	NOUN
ejpam-521	11	36	-	-	ADJ
ejpam-521	11	37	range	range	NOUN
ejpam-521	11	38	are	be	AUX
ejpam-521	11	39	converted	convert	VERB
ejpam-521	11	40	into	into	ADP
ejpam-521	11	41	the	the	DET
ejpam-521	11	42	same	same	ADJ
ejpam-521	11	43	digits	digit	NOUN
ejpam-521	11	44	.	.	PUNCT
ejpam-521	12	1	such	such	ADJ
ejpam-521	12	2	input	input	NOUN
ejpam-521	12	3	digits	digit	NOUN
ejpam-521	12	4	are	be	AUX
ejpam-521	12	5	further	far	ADV
ejpam-521	12	6	encoded	encode	VERB
ejpam-521	12	7	into	into	ADP
ejpam-521	12	8	a	a	DET
ejpam-521	12	9	sequence	sequence	NOUN
ejpam-521	12	10	of	of	ADP
ejpam-521	12	11	prefix	prefix	ADJ
ejpam-521	12	12	binary	binary	ADJ
ejpam-521	12	13	digits	digit	NOUN
ejpam-521	12	14	for	for	ADP
ejpam-521	12	15	transmission	transmission	NOUN
ejpam-521	12	16	.	.	PUNCT
ejpam-521	13	1	(	(	PUNCT
ejpam-521	13	2	prefix	prefix	NOUN
ejpam-521	13	3	codes	code	NOUN
ejpam-521	13	4	are	be	AUX
ejpam-521	13	5	spontaneously	spontaneously	ADV
ejpam-521	13	6	and	and	CCONJ
ejpam-521	13	7	uniquely	uniquely	ADV
ejpam-521	13	8	decipherable	decipherable	ADJ
ejpam-521	13	9	to	to	ADP
ejpam-521	13	10	where	where	SCONJ
ejpam-521	13	11	they	they	PRON
ejpam-521	13	12	are	be	AUX
ejpam-521	13	13	processed	process	VERB
ejpam-521	13	14	.	.	PUNCT
ejpam-521	13	15	)	)	PUNCT
ejpam-521	14	1	in	in	ADP
ejpam-521	14	2	order	order	NOUN
ejpam-521	14	3	to	to	PART
ejpam-521	14	4	achieve	achieve	VERB
ejpam-521	14	5	a	a	DET
ejpam-521	14	6	cost	cost	NOUN
ejpam-521	14	7	-	-	PUNCT
ejpam-521	14	8	efficient	efficient	ADJ
ejpam-521	14	9	transmission	transmission	NOUN
ejpam-521	14	10	,	,	PUNCT
ejpam-521	14	11	an	an	DET
ejpam-521	14	12	optimal	optimal	ADJ
ejpam-521	14	13	encoding	encoding	NOUN
ejpam-521	14	14	system	system	NOUN
ejpam-521	14	15	is	be	AUX
ejpam-521	14	16	necessary	necessary	ADJ
ejpam-521	14	17	by	by	ADP
ejpam-521	14	18	which	which	PRON
ejpam-521	14	19	the	the	DET
ejpam-521	14	20	input	input	NOUN
ejpam-521	14	21	binary	binary	ADJ
ejpam-521	14	22	digits	digit	NOUN
ejpam-521	14	23	sequence	sequence	NOUN
ejpam-521	14	24	is	be	AUX
ejpam-521	14	25	as	as	ADV
ejpam-521	14	26	short	short	ADJ
ejpam-521	14	27	as	as	ADP
ejpam-521	14	28	possible	possible	ADJ
ejpam-521	14	29	.	.	PUNCT
ejpam-521	15	1	by	by	ADP
ejpam-521	15	2	rissanen	rissanen	PROPN
ejpam-521	15	3	’s	’s	PART
ejpam-521	15	4	stochastic	stochastic	ADJ
ejpam-521	15	5	complexity	complexity	NOUN
ejpam-521	15	6	theory	theory	NOUN
ejpam-521	15	7	or	or	CCONJ
ejpam-521	15	8	principle	principle	NOUN
ejpam-521	15	9	of	of	ADP
ejpam-521	15	10	minimum	minimum	ADJ
ejpam-521	15	11	description	description	NOUN
ejpam-521	15	12	length	length	NOUN
ejpam-521	15	13	(	(	PUNCT
ejpam-521	15	14	mdl	mdl	PROPN
ejpam-521	15	15	)	)	PUNCT
ejpam-521	16	1	[	[	X
ejpam-521	16	2	18	18	NUM
ejpam-521	16	3	,	,	PUNCT
ejpam-521	16	4	15	15	NUM
ejpam-521	16	5	,	,	PUNCT
ejpam-521	16	6	13	13	NUM
ejpam-521	16	7	,	,	PUNCT
ejpam-521	16	8	12	12	NUM
ejpam-521	16	9	,	,	PUNCT
ejpam-521	16	10	11	11	NUM
ejpam-521	16	11	,	,	PUNCT
ejpam-521	16	12	9	9	NUM
ejpam-521	16	13	]	]	PUNCT
ejpam-521	16	14	,	,	PUNCT
ejpam-521	16	15	finding	find	VERB
ejpam-521	16	16	an	an	DET
ejpam-521	16	17	optimal	optimal	ADJ
ejpam-521	16	18	encoding	encoding	NOUN
ejpam-521	16	19	system	system	NOUN
ejpam-521	16	20	is	be	AUX
ejpam-521	16	21	equivalent	equivalent	ADJ
ejpam-521	16	22	to	to	ADP
ejpam-521	16	23	finding	find	VERB
ejpam-521	16	24	email	email	NOUN
ejpam-521	16	25	address	address	NOUN
ejpam-521	16	26	:	:	PUNCT
ejpam-521	16	27	g.qian�ms.unimelb.edu.au	g.qian�ms.unimelb.edu.au	PROPN
ejpam-521	16	28	.	.	PUNCT
ejpam-521	17	1	(	(	PUNCT
ejpam-521	17	2	g.	g.	PROPN
ejpam-521	17	3	qian	qian	PROPN
ejpam-521	17	4	)	)	PUNCT
ejpam-521	17	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-521	18	1	51	51	NUM
ejpam-521	18	2	c	c	X
ejpam-521	18	3	©	©	PROPN
ejpam-521	18	4	2009	2009	NUM
ejpam-521	18	5	ejpam	ejpam	NOUN
ejpam-521	18	6	all	all	DET
ejpam-521	18	7	rights	right	NOUN
ejpam-521	18	8	reserved	reserve	VERB
ejpam-521	18	9	.	.	PUNCT
ejpam-521	19	1	g.	g.	PROPN
ejpam-521	19	2	qian	qian	PROPN
ejpam-521	19	3	/	/	SYM
ejpam-521	19	4	eur	eur	PROPN
ejpam-521	19	5	.	.	PUNCT
ejpam-521	20	1	j.	j.	PROPN
ejpam-521	20	2	pure	pure	PROPN
ejpam-521	20	3	appl	appl	PROPN
ejpam-521	20	4	.	.	PROPN
ejpam-521	20	5	math	math	PROPN
ejpam-521	20	6	,	,	PUNCT
ejpam-521	20	7	3	3	NUM
ejpam-521	20	8	(	(	PUNCT
ejpam-521	20	9	2010	2010	NUM
ejpam-521	20	10	)	)	PUNCT
ejpam-521	20	11	,	,	PUNCT
ejpam-521	20	12	51	51	NUM
ejpam-521	20	13	-	-	SYM
ejpam-521	20	14	80	80	NUM
ejpam-521	20	15	52	52	NUM
ejpam-521	20	16	the	the	DET
ejpam-521	20	17	probability	probability	NOUN
ejpam-521	20	18	distribution	distribution	NOUN
ejpam-521	20	19	underlying	underlie	VERB
ejpam-521	20	20	the	the	DET
ejpam-521	20	21	input	input	NOUN
ejpam-521	20	22	signals	signal	NOUN
ejpam-521	20	23	.	.	PUNCT
ejpam-521	21	1	[	[	X
ejpam-521	21	2	4	4	NUM
ejpam-521	21	3	,	,	PUNCT
ejpam-521	21	4	3	3	NUM
ejpam-521	21	5	,	,	PUNCT
ejpam-521	21	6	2	2	NUM
ejpam-521	21	7	]	]	PUNCT
ejpam-521	21	8	has	have	AUX
ejpam-521	21	9	developed	develop	VERB
ejpam-521	21	10	an	an	DET
ejpam-521	21	11	alternative	alternative	ADJ
ejpam-521	21	12	theory	theory	NOUN
ejpam-521	21	13	of	of	ADP
ejpam-521	21	14	prequential	prequential	ADJ
ejpam-521	21	15	analysis	analysis	NOUN
ejpam-521	21	16	which	which	PRON
ejpam-521	21	17	implies	imply	VERB
ejpam-521	21	18	the	the	DET
ejpam-521	21	19	same	same	ADJ
ejpam-521	21	20	conclusion	conclusion	NOUN
ejpam-521	21	21	.	.	PUNCT
ejpam-521	22	1	another	another	DET
ejpam-521	22	2	related	relate	VERB
ejpam-521	22	3	is	be	AUX
ejpam-521	22	4	bozdogan	bozdogan	VERB
ejpam-521	22	5	’s	’s	PART
ejpam-521	22	6	information	information	NOUN
ejpam-521	22	7	complexity	complexity	NOUN
ejpam-521	22	8	criterion	criterion	NOUN
ejpam-521	22	9	(	(	PUNCT
ejpam-521	22	10	icomp	icomp	PROPN
ejpam-521	22	11	)	)	PUNCT
ejpam-521	22	12	(	(	PUNCT
ejpam-521	22	13	cf	cf	NOUN
ejpam-521	22	14	.	.	PUNCT
ejpam-521	23	1	[	[	X
ejpam-521	23	2	1	1	NUM
ejpam-521	23	3	]	]	PUNCT
ejpam-521	23	4	)	)	PUNCT
ejpam-521	23	5	.	.	PUNCT
ejpam-521	24	1	however	however	ADV
ejpam-521	24	2	,	,	PUNCT
ejpam-521	24	3	the	the	DET
ejpam-521	24	4	probability	probability	NOUN
ejpam-521	24	5	distribution	distribution	NOUN
ejpam-521	24	6	for	for	ADP
ejpam-521	24	7	the	the	DET
ejpam-521	24	8	input	input	NOUN
ejpam-521	24	9	signals	signal	NOUN
ejpam-521	24	10	is	be	AUX
ejpam-521	24	11	mostly	mostly	ADV
ejpam-521	24	12	unknown	unknown	ADJ
ejpam-521	24	13	and	and	CCONJ
ejpam-521	24	14	has	have	VERB
ejpam-521	24	15	to	to	PART
ejpam-521	24	16	be	be	AUX
ejpam-521	24	17	estimated	estimate	VERB
ejpam-521	24	18	.	.	PUNCT
ejpam-521	25	1	in	in	ADP
ejpam-521	25	2	the	the	DET
ejpam-521	25	3	context	context	NOUN
ejpam-521	25	4	of	of	ADP
ejpam-521	25	5	digital	digital	ADJ
ejpam-521	25	6	data	data	NOUN
ejpam-521	25	7	-	-	PUNCT
ejpam-521	25	8	transmission	transmission	NOUN
ejpam-521	25	9	involving	involve	VERB
ejpam-521	25	10	quantization	quantization	NOUN
ejpam-521	25	11	aforementioned	aforementione	VERB
ejpam-521	25	12	,	,	PUNCT
ejpam-521	25	13	it	it	PRON
ejpam-521	25	14	is	be	AUX
ejpam-521	25	15	sufficient	sufficient	ADJ
ejpam-521	25	16	to	to	PART
ejpam-521	25	17	find	find	VERB
ejpam-521	25	18	a	a	DET
ejpam-521	25	19	histogram	histogram	NOUN
ejpam-521	25	20	density	density	NOUN
ejpam-521	25	21	estimator	estimator	NOUN
ejpam-521	25	22	of	of	ADP
ejpam-521	25	23	the	the	DET
ejpam-521	25	24	probability	probability	NOUN
ejpam-521	25	25	distribution	distribution	NOUN
ejpam-521	25	26	for	for	ADP
ejpam-521	25	27	the	the	DET
ejpam-521	25	28	input	input	NOUN
ejpam-521	25	29	data	datum	NOUN
ejpam-521	25	30	.	.	PUNCT
ejpam-521	26	1	a	a	DET
ejpam-521	26	2	histogram	histogram	NOUN
ejpam-521	26	3	density	density	NOUN
ejpam-521	26	4	estimator	estimator	NOUN
ejpam-521	26	5	is	be	AUX
ejpam-521	26	6	specified	specify	VERB
ejpam-521	26	7	by	by	ADP
ejpam-521	26	8	a	a	DET
ejpam-521	26	9	sequence	sequence	NOUN
ejpam-521	26	10	of	of	ADP
ejpam-521	26	11	subintervals	subinterval	NOUN
ejpam-521	26	12	partitioning	partition	VERB
ejpam-521	26	13	the	the	DET
ejpam-521	26	14	range	range	NOUN
ejpam-521	26	15	of	of	ADP
ejpam-521	26	16	the	the	DET
ejpam-521	26	17	data	datum	NOUN
ejpam-521	26	18	(	(	PUNCT
ejpam-521	26	19	as	as	ADP
ejpam-521	26	20	corresponding	correspond	VERB
ejpam-521	26	21	to	to	ADP
ejpam-521	26	22	the	the	DET
ejpam-521	26	23	input	input	NOUN
ejpam-521	26	24	amplitude	amplitude	NOUN
ejpam-521	26	25	sub	sub	NOUN
ejpam-521	26	26	-	-	NOUN
ejpam-521	26	27	ranges	range	NOUN
ejpam-521	26	28	in	in	ADP
ejpam-521	26	29	quantization	quantization	NOUN
ejpam-521	26	30	)	)	PUNCT
ejpam-521	26	31	,	,	PUNCT
ejpam-521	26	32	and	and	CCONJ
ejpam-521	26	33	the	the	DET
ejpam-521	26	34	probability	probability	NOUN
ejpam-521	26	35	values	value	NOUN
ejpam-521	26	36	over	over	ADP
ejpam-521	26	37	all	all	DET
ejpam-521	26	38	such	such	ADJ
ejpam-521	26	39	subintervals	subinterval	NOUN
ejpam-521	26	40	.	.	PUNCT
ejpam-521	27	1	once	once	ADV
ejpam-521	27	2	a	a	DET
ejpam-521	27	3	histogram	histogram	NOUN
ejpam-521	27	4	density	density	NOUN
ejpam-521	27	5	estimator	estimator	NOUN
ejpam-521	27	6	is	be	AUX
ejpam-521	27	7	properly	properly	ADV
ejpam-521	27	8	obtained	obtain	VERB
ejpam-521	27	9	,	,	PUNCT
ejpam-521	27	10	it	it	PRON
ejpam-521	27	11	determines	determine	VERB
ejpam-521	27	12	the	the	DET
ejpam-521	27	13	quantization	quantization	NOUN
ejpam-521	27	14	of	of	ADP
ejpam-521	27	15	the	the	DET
ejpam-521	27	16	input	input	NOUN
ejpam-521	27	17	data	datum	NOUN
ejpam-521	27	18	and	and	CCONJ
ejpam-521	27	19	further	far	ADV
ejpam-521	27	20	enables	enable	VERB
ejpam-521	27	21	the	the	DET
ejpam-521	27	22	construction	construction	NOUN
ejpam-521	27	23	of	of	ADP
ejpam-521	27	24	an	an	DET
ejpam-521	27	25	encoding	encoding	NOUN
ejpam-521	27	26	system	system	NOUN
ejpam-521	27	27	to	to	PART
ejpam-521	27	28	encode	encode	VERB
ejpam-521	27	29	the	the	DET
ejpam-521	27	30	quantized	quantize	VERB
ejpam-521	27	31	input	input	NOUN
ejpam-521	27	32	data	datum	NOUN
ejpam-521	27	33	.	.	PUNCT
ejpam-521	28	1	the	the	DET
ejpam-521	28	2	length	length	NOUN
ejpam-521	28	3	of	of	ADP
ejpam-521	28	4	the	the	DET
ejpam-521	28	5	input	input	NOUN
ejpam-521	28	6	binary	binary	NOUN
ejpam-521	28	7	codes	code	NOUN
ejpam-521	28	8	obtained	obtain	VERB
ejpam-521	28	9	under	under	ADP
ejpam-521	28	10	this	this	DET
ejpam-521	28	11	encoding	encoding	NOUN
ejpam-521	28	12	system	system	NOUN
ejpam-521	28	13	then	then	ADV
ejpam-521	28	14	measures	measure	VERB
ejpam-521	28	15	the	the	DET
ejpam-521	28	16	amount	amount	NOUN
ejpam-521	28	17	of	of	ADP
ejpam-521	28	18	information	information	NOUN
ejpam-521	28	19	to	to	PART
ejpam-521	28	20	be	be	AUX
ejpam-521	28	21	transmitted	transmit	VERB
ejpam-521	28	22	to	to	ADP
ejpam-521	28	23	the	the	DET
ejpam-521	28	24	receiver	receiver	NOUN
ejpam-521	28	25	,	,	PUNCT
ejpam-521	28	26	and	and	CCONJ
ejpam-521	28	27	we	we	PRON
ejpam-521	28	28	call	call	VERB
ejpam-521	28	29	it	it	PRON
ejpam-521	28	30	a	a	DET
ejpam-521	28	31	summary	summary	NOUN
ejpam-521	28	32	description	description	NOUN
ejpam-521	28	33	of	of	ADP
ejpam-521	28	34	the	the	DET
ejpam-521	28	35	input	input	NOUN
ejpam-521	28	36	data	datum	NOUN
ejpam-521	28	37	.	.	PUNCT
ejpam-521	29	1	the	the	PRON
ejpam-521	29	2	shorter	short	ADJ
ejpam-521	29	3	this	this	DET
ejpam-521	29	4	description	description	NOUN
ejpam-521	29	5	is	be	AUX
ejpam-521	29	6	the	the	DET
ejpam-521	29	7	more	more	ADV
ejpam-521	29	8	costefficient	costefficient	ADJ
ejpam-521	29	9	data	data	NOUN
ejpam-521	29	10	transmission	transmission	NOUN
ejpam-521	29	11	it	it	PRON
ejpam-521	29	12	would	would	AUX
ejpam-521	29	13	imply	imply	VERB
ejpam-521	29	14	.	.	PUNCT
ejpam-521	30	1	clearly	clearly	ADV
ejpam-521	30	2	,	,	PUNCT
ejpam-521	30	3	the	the	DET
ejpam-521	30	4	optimal	optimal	ADJ
ejpam-521	30	5	histogram	histogram	NOUN
ejpam-521	30	6	density	density	NOUN
ejpam-521	30	7	estimator	estimator	NOUN
ejpam-521	30	8	is	be	AUX
ejpam-521	30	9	the	the	DET
ejpam-521	30	10	one	one	NOUN
ejpam-521	30	11	that	that	PRON
ejpam-521	30	12	would	would	AUX
ejpam-521	30	13	result	result	VERB
ejpam-521	30	14	in	in	ADP
ejpam-521	30	15	the	the	DET
ejpam-521	30	16	shortest	short	ADJ
ejpam-521	30	17	description	description	NOUN
ejpam-521	30	18	of	of	ADP
ejpam-521	30	19	the	the	DET
ejpam-521	30	20	input	input	NOUN
ejpam-521	30	21	data	datum	NOUN
ejpam-521	30	22	.	.	PUNCT
ejpam-521	31	1	the	the	DET
ejpam-521	31	2	discussions	discussion	NOUN
ejpam-521	31	3	so	so	ADV
ejpam-521	31	4	far	far	ADV
ejpam-521	31	5	manifest	manifest	VERB
ejpam-521	31	6	the	the	DET
ejpam-521	31	7	core	core	NOUN
ejpam-521	31	8	of	of	ADP
ejpam-521	31	9	stochastic	stochastic	ADJ
ejpam-521	31	10	complexity	complexity	NOUN
ejpam-521	31	11	theory	theory	NOUN
ejpam-521	31	12	—	—	PUNCT
ejpam-521	31	13	the	the	DET
ejpam-521	31	14	principle	principle	NOUN
ejpam-521	31	15	of	of	ADP
ejpam-521	31	16	minimum	minimum	ADJ
ejpam-521	31	17	description	description	NOUN
ejpam-521	31	18	length	length	NOUN
ejpam-521	31	19	—	—	PUNCT
ejpam-521	31	20	in	in	ADP
ejpam-521	31	21	the	the	DET
ejpam-521	31	22	context	context	NOUN
ejpam-521	31	23	of	of	ADP
ejpam-521	31	24	digital	digital	ADJ
ejpam-521	31	25	data	data	NOUN
ejpam-521	31	26	-	-	PUNCT
ejpam-521	31	27	transmission	transmission	NOUN
ejpam-521	31	28	.	.	PUNCT
ejpam-521	32	1	the	the	DET
ejpam-521	32	2	principles	principle	NOUN
ejpam-521	32	3	of	of	ADP
ejpam-521	32	4	mdl	mdl	NOUN
ejpam-521	32	5	and	and	CCONJ
ejpam-521	32	6	maximum	maximum	ADJ
ejpam-521	32	7	likelihood	likelihood	NOUN
ejpam-521	32	8	together	together	ADV
ejpam-521	32	9	provide	provide	VERB
ejpam-521	32	10	a	a	DET
ejpam-521	32	11	way	way	NOUN
ejpam-521	32	12	for	for	ADP
ejpam-521	32	13	finding	find	VERB
ejpam-521	32	14	the	the	DET
ejpam-521	32	15	best	good	ADJ
ejpam-521	32	16	histogram	histogram	NOUN
ejpam-521	32	17	density	density	NOUN
ejpam-521	32	18	estimator	estimator	NOUN
ejpam-521	32	19	.	.	PUNCT
ejpam-521	33	1	suppose	suppose	VERB
ejpam-521	33	2	the	the	DET
ejpam-521	33	3	input	input	NOUN
ejpam-521	33	4	for	for	ADP
ejpam-521	33	5	digital	digital	ADJ
ejpam-521	33	6	transmission	transmission	NOUN
ejpam-521	33	7	is	be	AUX
ejpam-521	33	8	a	a	DET
ejpam-521	33	9	finite	finite	ADJ
ejpam-521	33	10	data	data	NOUN
ejpam-521	33	11	-	-	PUNCT
ejpam-521	33	12	string	string	NOUN
ejpam-521	33	13	x	x	X
ejpam-521	33	14	n	n	NOUN
ejpam-521	33	15	=	=	SYM
ejpam-521	33	16	(	(	PUNCT
ejpam-521	33	17	x1	x1	PROPN
ejpam-521	33	18	,	,	PUNCT
ejpam-521	33	19	·	·	PUNCT
ejpam-521	33	20	·	·	PUNCT
ejpam-521	33	21	·	·	PUNCT
ejpam-521	33	22	,	,	PUNCT
ejpam-521	33	23	xn	xn	PROPN
ejpam-521	33	24	)	)	PUNCT
ejpam-521	33	25	from	from	ADP
ejpam-521	33	26	a	a	DET
ejpam-521	33	27	system	system	NOUN
ejpam-521	33	28	involving	involve	VERB
ejpam-521	33	29	chance	chance	NOUN
ejpam-521	33	30	,	,	PUNCT
ejpam-521	33	31	and	and	CCONJ
ejpam-521	33	32	we	we	PRON
ejpam-521	33	33	wish	wish	VERB
ejpam-521	33	34	to	to	PART
ejpam-521	33	35	estimate	estimate	VERB
ejpam-521	33	36	the	the	DET
ejpam-521	33	37	probability	probability	NOUN
ejpam-521	33	38	distribution	distribution	NOUN
ejpam-521	33	39	of	of	ADP
ejpam-521	33	40	this	this	DET
ejpam-521	33	41	system	system	NOUN
ejpam-521	33	42	by	by	ADP
ejpam-521	33	43	a	a	DET
ejpam-521	33	44	histogram	histogram	NOUN
ejpam-521	33	45	density	density	NOUN
ejpam-521	33	46	for	for	ADP
ejpam-521	33	47	x	x	PROPN
ejpam-521	33	48	n.	n.	PROPN
ejpam-521	33	49	when	when	SCONJ
ejpam-521	33	50	number	number	NOUN
ejpam-521	33	51	and	and	CCONJ
ejpam-521	33	52	locations	location	NOUN
ejpam-521	33	53	of	of	ADP
ejpam-521	33	54	the	the	DET
ejpam-521	33	55	subintervals	subinterval	NOUN
ejpam-521	33	56	to	to	PART
ejpam-521	33	57	be	be	AUX
ejpam-521	33	58	used	use	VERB
ejpam-521	33	59	are	be	AUX
ejpam-521	33	60	specified	specify	VERB
ejpam-521	33	61	for	for	ADP
ejpam-521	33	62	a	a	DET
ejpam-521	33	63	histogram	histogram	NOUN
ejpam-521	33	64	density	density	NOUN
ejpam-521	33	65	estimator	estimator	NOUN
ejpam-521	33	66	,	,	PUNCT
ejpam-521	33	67	the	the	DET
ejpam-521	33	68	optimal	optimal	ADJ
ejpam-521	33	69	probability	probability	NOUN
ejpam-521	33	70	over	over	ADP
ejpam-521	33	71	each	each	DET
ejpam-521	33	72	subinterval	subinterval	NOUN
ejpam-521	33	73	can	can	AUX
ejpam-521	33	74	be	be	AUX
ejpam-521	33	75	determined	determine	VERB
ejpam-521	33	76	by	by	ADP
ejpam-521	33	77	the	the	DET
ejpam-521	33	78	maximum	maximum	ADJ
ejpam-521	33	79	likelihood	likelihood	NOUN
ejpam-521	33	80	principle	principle	NOUN
ejpam-521	33	81	.	.	PUNCT
ejpam-521	34	1	when	when	SCONJ
ejpam-521	34	2	only	only	ADV
ejpam-521	34	3	the	the	DET
ejpam-521	34	4	number	number	NOUN
ejpam-521	34	5	of	of	ADP
ejpam-521	34	6	subintervals	subinterval	NOUN
ejpam-521	34	7	used	use	VERB
ejpam-521	34	8	in	in	ADP
ejpam-521	34	9	a	a	DET
ejpam-521	34	10	histogram	histogram	NOUN
ejpam-521	34	11	density	density	NOUN
ejpam-521	34	12	estimator	estimator	NOUN
ejpam-521	34	13	is	be	AUX
ejpam-521	34	14	specified	specify	VERB
ejpam-521	34	15	,	,	PUNCT
ejpam-521	34	16	the	the	DET
ejpam-521	34	17	optimal	optimal	ADJ
ejpam-521	34	18	locations	location	NOUN
ejpam-521	34	19	of	of	ADP
ejpam-521	34	20	the	the	DET
ejpam-521	34	21	subintervals	subinterval	NOUN
ejpam-521	34	22	can	can	AUX
ejpam-521	34	23	also	also	ADV
ejpam-521	34	24	be	be	AUX
ejpam-521	34	25	determined	determine	VERB
ejpam-521	34	26	by	by	ADP
ejpam-521	34	27	the	the	DET
ejpam-521	34	28	maximum	maximum	ADJ
ejpam-521	34	29	likelihood	likelihood	NOUN
ejpam-521	34	30	principle	principle	NOUN
ejpam-521	34	31	together	together	ADV
ejpam-521	34	32	with	with	ADP
ejpam-521	34	33	a	a	DET
ejpam-521	34	34	recursive	recursive	ADJ
ejpam-521	34	35	method	method	NOUN
ejpam-521	34	36	.	.	PUNCT
ejpam-521	35	1	thus	thus	ADV
ejpam-521	35	2	for	for	ADP
ejpam-521	35	3	each	each	DET
ejpam-521	35	4	specified	specify	VERB
ejpam-521	35	5	number	number	NOUN
ejpam-521	35	6	of	of	ADP
ejpam-521	35	7	the	the	DET
ejpam-521	35	8	subintervals	subinterval	NOUN
ejpam-521	35	9	,	,	PUNCT
ejpam-521	35	10	a	a	DET
ejpam-521	35	11	temporary	temporary	ADJ
ejpam-521	35	12	histogram	histogram	NOUN
ejpam-521	35	13	density	density	NOUN
ejpam-521	35	14	estimator	estimator	NOUN
ejpam-521	35	15	can	can	AUX
ejpam-521	35	16	be	be	AUX
ejpam-521	35	17	constructed	construct	VERB
ejpam-521	35	18	which	which	PRON
ejpam-521	35	19	then	then	ADV
ejpam-521	35	20	provides	provide	VERB
ejpam-521	35	21	a	a	DET
ejpam-521	35	22	description	description	NOUN
ejpam-521	35	23	of	of	ADP
ejpam-521	35	24	x	x	PUNCT
ejpam-521	35	25	n	n	X
ejpam-521	35	26	with	with	ADP
ejpam-521	35	27	an	an	DET
ejpam-521	35	28	appropriate	appropriate	ADJ
ejpam-521	35	29	prefix	prefix	NOUN
ejpam-521	35	30	code	code	NOUN
ejpam-521	35	31	-	-	PUNCT
ejpam-521	35	32	length	length	NOUN
ejpam-521	35	33	.	.	PUNCT
ejpam-521	36	1	the	the	DET
ejpam-521	36	2	optimal	optimal	ADJ
ejpam-521	36	3	number	number	NOUN
ejpam-521	36	4	of	of	ADP
ejpam-521	36	5	subintervals	subinterval	NOUN
ejpam-521	36	6	and	and	CCONJ
ejpam-521	36	7	accordingly	accordingly	ADV
ejpam-521	36	8	the	the	DET
ejpam-521	36	9	best	good	ADJ
ejpam-521	36	10	histogram	histogram	NOUN
ejpam-521	36	11	density	density	NOUN
ejpam-521	36	12	estimator	estimator	NOUN
ejpam-521	36	13	are	be	AUX
ejpam-521	36	14	therefore	therefore	ADV
ejpam-521	36	15	obtained	obtain	VERB
ejpam-521	36	16	from	from	ADP
ejpam-521	36	17	finding	find	VERB
ejpam-521	36	18	the	the	DET
ejpam-521	36	19	shortest	short	ADJ
ejpam-521	36	20	prefix	prefix	NOUN
ejpam-521	36	21	code	code	NOUN
ejpam-521	36	22	-	-	PUNCT
ejpam-521	36	23	length	length	NOUN
ejpam-521	36	24	for	for	ADP
ejpam-521	36	25	data	data	NOUN
ejpam-521	36	26	description	description	NOUN
ejpam-521	36	27	.	.	PUNCT
ejpam-521	37	1	having	having	AUX
ejpam-521	37	2	seen	see	VERB
ejpam-521	37	3	the	the	DET
ejpam-521	37	4	relationship	relationship	NOUN
ejpam-521	37	5	between	between	ADP
ejpam-521	37	6	the	the	DET
ejpam-521	37	7	best	good	ADJ
ejpam-521	37	8	histogram	histogram	NOUN
ejpam-521	37	9	density	density	NOUN
ejpam-521	37	10	estimator	estimator	NOUN
ejpam-521	37	11	and	and	CCONJ
ejpam-521	37	12	the	the	DET
ejpam-521	37	13	shortest	short	ADJ
ejpam-521	37	14	prefix	prefix	NOUN
ejpam-521	37	15	code	code	NOUN
ejpam-521	37	16	-	-	PUNCT
ejpam-521	37	17	length	length	NOUN
ejpam-521	37	18	for	for	ADP
ejpam-521	37	19	data	data	NOUN
ejpam-521	37	20	description	description	NOUN
ejpam-521	37	21	,	,	PUNCT
ejpam-521	37	22	we	we	PRON
ejpam-521	37	23	now	now	ADV
ejpam-521	37	24	focus	focus	VERB
ejpam-521	37	25	on	on	ADP
ejpam-521	37	26	investigating	investigate	VERB
ejpam-521	37	27	the	the	DET
ejpam-521	37	28	shortest	short	ADJ
ejpam-521	37	29	description	description	NOUN
ejpam-521	37	30	length	length	NOUN
ejpam-521	37	31	of	of	ADP
ejpam-521	37	32	x	x	PROPN
ejpam-521	37	33	n.	n.	NOUN
ejpam-521	37	34	note	note	VERB
ejpam-521	37	35	that	that	SCONJ
ejpam-521	37	36	the	the	DET
ejpam-521	37	37	prefix	prefix	NOUN
ejpam-521	37	38	codewords	codeword	NOUN
ejpam-521	37	39	of	of	ADP
ejpam-521	37	40	x	x	PUNCT
ejpam-521	37	41	n	n	PRON
ejpam-521	37	42	can	can	AUX
ejpam-521	37	43	be	be	AUX
ejpam-521	37	44	obtained	obtain	VERB
ejpam-521	37	45	by	by	ADP
ejpam-521	37	46	either	either	CCONJ
ejpam-521	37	47	a	a	DET
ejpam-521	37	48	non	non	ADJ
ejpam-521	37	49	-	-	ADJ
ejpam-521	37	50	predictive	predictive	ADJ
ejpam-521	37	51	two	two	NUM
ejpam-521	37	52	-	-	PUNCT
ejpam-521	37	53	step	step	NOUN
ejpam-521	37	54	or	or	CCONJ
ejpam-521	37	55	a	a	DET
ejpam-521	37	56	predictive	predictive	ADJ
ejpam-521	37	57	manner	manner	NOUN
ejpam-521	37	58	(	(	PUNCT
ejpam-521	37	59	see	see	VERB
ejpam-521	37	60	chapter	chapter	NOUN
ejpam-521	37	61	3	3	NUM
ejpam-521	37	62	of	of	ADP
ejpam-521	37	63	[	[	X
ejpam-521	37	64	13	13	NUM
ejpam-521	37	65	]	]	NUM
ejpam-521	37	66	)	)	PUNCT
ejpam-521	37	67	.	.	PUNCT
ejpam-521	38	1	even	even	ADV
ejpam-521	38	2	though	though	SCONJ
ejpam-521	38	3	the	the	DET
ejpam-521	38	4	predictive	predictive	ADJ
ejpam-521	38	5	coding	coding	NOUN
ejpam-521	38	6	requires	require	VERB
ejpam-521	38	7	longer	long	ADJ
ejpam-521	38	8	codewords	codeword	NOUN
ejpam-521	38	9	for	for	ADP
ejpam-521	38	10	encoding	encode	VERB
ejpam-521	38	11	x	x	X
ejpam-521	38	12	n	n	CCONJ
ejpam-521	38	13	,	,	PUNCT
ejpam-521	38	14	it	it	PRON
ejpam-521	38	15	enables	enable	VERB
ejpam-521	38	16	the	the	DET
ejpam-521	38	17	data	data	NOUN
ejpam-521	38	18	-	-	PUNCT
ejpam-521	38	19	transmission	transmission	NOUN
ejpam-521	38	20	system	system	NOUN
ejpam-521	38	21	for	for	ADP
ejpam-521	38	22	self	self	NOUN
ejpam-521	38	23	-	-	PUNCT
ejpam-521	38	24	adjustment	adjustment	NOUN
ejpam-521	38	25	and	and	CCONJ
ejpam-521	38	26	updating	updating	NOUN
ejpam-521	38	27	by	by	ADP
ejpam-521	38	28	using	use	VERB
ejpam-521	38	29	the	the	DET
ejpam-521	38	30	data	datum	NOUN
ejpam-521	38	31	in	in	ADP
ejpam-521	38	32	a	a	DET
ejpam-521	38	33	progressive	progressive	ADJ
ejpam-521	38	34	way	way	NOUN
ejpam-521	38	35	.	.	PUNCT
ejpam-521	39	1	in	in	ADP
ejpam-521	39	2	section	section	NOUN
ejpam-521	39	3	2	2	NUM
ejpam-521	39	4	below	below	ADP
ejpam-521	39	5	we	we	PRON
ejpam-521	39	6	first	first	ADV
ejpam-521	39	7	discuss	discuss	VERB
ejpam-521	39	8	an	an	DET
ejpam-521	39	9	optimal	optimal	ADJ
ejpam-521	39	10	quantization	quantization	NOUN
ejpam-521	39	11	scheme	scheme	NOUN
ejpam-521	39	12	of	of	ADP
ejpam-521	39	13	the	the	DET
ejpam-521	39	14	data	datum	NOUN
ejpam-521	39	15	for	for	ADP
ejpam-521	39	16	optimal	optimal	ADJ
ejpam-521	39	17	description	description	NOUN
ejpam-521	39	18	.	.	PUNCT
ejpam-521	40	1	the	the	DET
ejpam-521	40	2	scheme	scheme	NOUN
ejpam-521	40	3	provides	provide	VERB
ejpam-521	40	4	a	a	DET
ejpam-521	40	5	system	system	NOUN
ejpam-521	40	6	of	of	ADP
ejpam-521	40	7	recursive	recursive	ADJ
ejpam-521	40	8	equations	equation	NOUN
ejpam-521	40	9	for	for	ADP
ejpam-521	40	10	determining	determine	VERB
ejpam-521	40	11	the	the	DET
ejpam-521	40	12	optimal	optimal	ADJ
ejpam-521	40	13	locations	location	NOUN
ejpam-521	40	14	of	of	ADP
ejpam-521	40	15	the	the	DET
ejpam-521	40	16	subintervals	subinterval	NOUN
ejpam-521	40	17	in	in	ADP
ejpam-521	40	18	the	the	DET
ejpam-521	40	19	histogram	histogram	NOUN
ejpam-521	40	20	estimator	estimator	NOUN
ejpam-521	40	21	.	.	PUNCT
ejpam-521	41	1	then	then	ADV
ejpam-521	41	2	lengths	length	NOUN
ejpam-521	41	3	of	of	ADP
ejpam-521	41	4	both	both	DET
ejpam-521	41	5	two	two	NUM
ejpam-521	41	6	-	-	PUNCT
ejpam-521	41	7	step	step	NOUN
ejpam-521	41	8	and	and	CCONJ
ejpam-521	41	9	predictive	predictive	ADJ
ejpam-521	41	10	codewords	codeword	NOUN
ejpam-521	41	11	for	for	ADP
ejpam-521	41	12	the	the	DET
ejpam-521	41	13	description	description	NOUN
ejpam-521	41	14	of	of	ADP
ejpam-521	41	15	x	x	PUNCT
ejpam-521	41	16	n	n	PRON
ejpam-521	41	17	are	be	AUX
ejpam-521	41	18	given	give	VERB
ejpam-521	41	19	using	use	VERB
ejpam-521	41	20	the	the	DET
ejpam-521	41	21	mdl	mdl	PROPN
ejpam-521	41	22	principle	principle	NOUN
ejpam-521	41	23	.	.	PUNCT
ejpam-521	42	1	finally	finally	ADV
ejpam-521	42	2	,	,	PUNCT
ejpam-521	42	3	uniform	uniform	ADJ
ejpam-521	42	4	almost	almost	ADV
ejpam-521	42	5	sure	sure	ADV
ejpam-521	42	6	asymptotic	asymptotic	ADJ
ejpam-521	42	7	expansion	expansion	NOUN
ejpam-521	42	8	and	and	CCONJ
ejpam-521	42	9	the	the	DET
ejpam-521	42	10	almost	almost	ADV
ejpam-521	42	11	sure	sure	ADJ
ejpam-521	42	12	lower	low	ADJ
ejpam-521	42	13	and	and	CCONJ
ejpam-521	42	14	upper	upper	ADJ
ejpam-521	42	15	bounds	bound	NOUN
ejpam-521	42	16	for	for	ADP
ejpam-521	42	17	both	both	DET
ejpam-521	42	18	code	code	NOUN
ejpam-521	42	19	lengths	length	NOUN
ejpam-521	42	20	are	be	AUX
ejpam-521	42	21	derived	derive	VERB
ejpam-521	42	22	and	and	CCONJ
ejpam-521	42	23	the	the	DET
ejpam-521	42	24	results	result	NOUN
ejpam-521	42	25	are	be	AUX
ejpam-521	42	26	list	list	NOUN
ejpam-521	42	27	in	in	ADP
ejpam-521	42	28	theorem	theorem	NOUN
ejpam-521	42	29	2	2	NUM
ejpam-521	42	30	to	to	PART
ejpam-521	42	31	theorem	theorem	VERB
ejpam-521	42	32	4	4	NUM
ejpam-521	42	33	.	.	PUNCT
ejpam-521	43	1	g.	g.	PROPN
ejpam-521	43	2	qian	qian	PROPN
ejpam-521	43	3	/	/	SYM
ejpam-521	43	4	eur	eur	PROPN
ejpam-521	43	5	.	.	PUNCT
ejpam-521	44	1	j.	j.	PROPN
ejpam-521	44	2	pure	pure	PROPN
ejpam-521	44	3	appl	appl	PROPN
ejpam-521	44	4	.	.	PROPN
ejpam-521	44	5	math	math	PROPN
ejpam-521	44	6	,	,	PUNCT
ejpam-521	44	7	3	3	NUM
ejpam-521	44	8	(	(	PUNCT
ejpam-521	44	9	2010	2010	NUM
ejpam-521	44	10	)	)	PUNCT
ejpam-521	44	11	,	,	PUNCT
ejpam-521	44	12	51	51	NUM
ejpam-521	44	13	-	-	SYM
ejpam-521	44	14	80	80	NUM
ejpam-521	44	15	53	53	NUM
ejpam-521	44	16	in	in	ADP
ejpam-521	44	17	[	[	X
ejpam-521	44	18	7	7	NUM
ejpam-521	44	19	]	]	PUNCT
ejpam-521	44	20	and	and	CCONJ
ejpam-521	44	21	[	[	X
ejpam-521	44	22	20	20	NUM
ejpam-521	44	23	]	]	PUNCT
ejpam-521	44	24	,	,	PUNCT
ejpam-521	44	25	the	the	DET
ejpam-521	44	26	same	same	ADJ
ejpam-521	44	27	type	type	NOUN
ejpam-521	44	28	of	of	ADP
ejpam-521	44	29	stochastic	stochastic	ADJ
ejpam-521	44	30	complexity	complexity	NOUN
ejpam-521	44	31	based	base	VERB
ejpam-521	44	32	histogram	histogram	NOUN
ejpam-521	44	33	estimation	estimation	NOUN
ejpam-521	44	34	is	be	AUX
ejpam-521	44	35	considered	consider	VERB
ejpam-521	44	36	under	under	ADP
ejpam-521	44	37	the	the	DET
ejpam-521	44	38	assumption	assumption	NOUN
ejpam-521	44	39	of	of	ADP
ejpam-521	44	40	equal	equal	ADJ
ejpam-521	44	41	subinterval	subinterval	NOUN
ejpam-521	44	42	widths	width	NOUN
ejpam-521	44	43	.	.	PUNCT
ejpam-521	45	1	our	our	PRON
ejpam-521	45	2	results	result	NOUN
ejpam-521	45	3	agree	agree	VERB
ejpam-521	45	4	with	with	ADP
ejpam-521	45	5	theirs	theirs	PRON
ejpam-521	45	6	when	when	SCONJ
ejpam-521	45	7	this	this	DET
ejpam-521	45	8	assumption	assumption	NOUN
ejpam-521	45	9	applies	apply	VERB
ejpam-521	45	10	.	.	PUNCT
ejpam-521	46	1	as	as	ADP
ejpam-521	46	2	an	an	DET
ejpam-521	46	3	application	application	NOUN
ejpam-521	46	4	of	of	ADP
ejpam-521	46	5	stochastic	stochastic	ADJ
ejpam-521	46	6	complexity	complexity	NOUN
ejpam-521	46	7	for	for	ADP
ejpam-521	46	8	optimal	optimal	ADJ
ejpam-521	46	9	data	datum	NOUN
ejpam-521	46	10	description	description	NOUN
ejpam-521	46	11	,	,	PUNCT
ejpam-521	46	12	in	in	ADP
ejpam-521	46	13	section	section	NOUN
ejpam-521	46	14	3	3	NUM
ejpam-521	46	15	we	we	PRON
ejpam-521	46	16	consider	consider	VERB
ejpam-521	46	17	the	the	DET
ejpam-521	46	18	problem	problem	NOUN
ejpam-521	46	19	of	of	ADP
ejpam-521	46	20	testing	testing	NOUN
ejpam-521	46	21	of	of	ADP
ejpam-521	46	22	homogeneity	homogeneity	NOUN
ejpam-521	46	23	,	,	PUNCT
ejpam-521	46	24	i.e.	i.e.	X
ejpam-521	46	25	the	the	DET
ejpam-521	46	26	testing	testing	NOUN
ejpam-521	46	27	of	of	ADP
ejpam-521	46	28	the	the	DET
ejpam-521	46	29	hypothesis	hypothesis	NOUN
ejpam-521	46	30	that	that	PRON
ejpam-521	46	31	several	several	ADJ
ejpam-521	46	32	independent	independent	ADJ
ejpam-521	46	33	samples	sample	NOUN
ejpam-521	46	34	are	be	AUX
ejpam-521	46	35	generated	generate	VERB
ejpam-521	46	36	from	from	ADP
ejpam-521	46	37	the	the	DET
ejpam-521	46	38	same	same	ADJ
ejpam-521	46	39	population	population	NOUN
ejpam-521	46	40	.	.	PUNCT
ejpam-521	47	1	a	a	DET
ejpam-521	47	2	test	test	NOUN
ejpam-521	47	3	procedure	procedure	NOUN
ejpam-521	47	4	is	be	AUX
ejpam-521	47	5	proposed	propose	VERB
ejpam-521	47	6	in	in	ADP
ejpam-521	47	7	which	which	PRON
ejpam-521	47	8	we	we	PRON
ejpam-521	47	9	use	use	VERB
ejpam-521	47	10	difference	difference	NOUN
ejpam-521	47	11	of	of	ADP
ejpam-521	47	12	the	the	DET
ejpam-521	47	13	shortest	short	ADJ
ejpam-521	47	14	predictive	predictive	ADJ
ejpam-521	47	15	code	code	NOUN
ejpam-521	47	16	lengths	length	NOUN
ejpam-521	47	17	under	under	ADP
ejpam-521	47	18	the	the	DET
ejpam-521	47	19	null	null	NOUN
ejpam-521	47	20	and	and	CCONJ
ejpam-521	47	21	the	the	DET
ejpam-521	47	22	alternative	alternative	ADJ
ejpam-521	47	23	hypotheses	hypothesis	NOUN
ejpam-521	47	24	respectively	respectively	ADV
ejpam-521	47	25	as	as	ADP
ejpam-521	47	26	a	a	DET
ejpam-521	47	27	universal	universal	ADJ
ejpam-521	47	28	test	test	NOUN
ejpam-521	47	29	statistic	statistic	NOUN
ejpam-521	47	30	.	.	PUNCT
ejpam-521	48	1	the	the	DET
ejpam-521	48	2	size	size	NOUN
ejpam-521	48	3	of	of	ADP
ejpam-521	48	4	the	the	DET
ejpam-521	48	5	test	test	NOUN
ejpam-521	48	6	procedure	procedure	NOUN
ejpam-521	48	7	is	be	AUX
ejpam-521	48	8	shown	show	VERB
ejpam-521	48	9	to	to	PART
ejpam-521	48	10	be	be	AUX
ejpam-521	48	11	determined	determine	VERB
ejpam-521	48	12	by	by	ADP
ejpam-521	48	13	the	the	DET
ejpam-521	48	14	part	part	NOUN
ejpam-521	48	15	of	of	ADP
ejpam-521	48	16	the	the	DET
ejpam-521	48	17	code	code	NOUN
ejpam-521	48	18	lengths	length	NOUN
ejpam-521	48	19	which	which	PRON
ejpam-521	48	20	is	be	AUX
ejpam-521	48	21	used	use	VERB
ejpam-521	48	22	to	to	PART
ejpam-521	48	23	describe	describe	VERB
ejpam-521	48	24	the	the	DET
ejpam-521	48	25	parameters	parameter	NOUN
ejpam-521	48	26	in	in	ADP
ejpam-521	48	27	the	the	DET
ejpam-521	48	28	histogram	histogram	NOUN
ejpam-521	48	29	densities	density	NOUN
ejpam-521	48	30	.	.	PUNCT
ejpam-521	49	1	the	the	DET
ejpam-521	49	2	asymptotic	asymptotic	ADJ
ejpam-521	49	3	power	power	NOUN
ejpam-521	49	4	of	of	ADP
ejpam-521	49	5	the	the	DET
ejpam-521	49	6	test	test	NOUN
ejpam-521	49	7	procedure	procedure	NOUN
ejpam-521	49	8	is	be	AUX
ejpam-521	49	9	shown	show	VERB
ejpam-521	49	10	to	to	PART
ejpam-521	49	11	be	be	AUX
ejpam-521	49	12	1	1	NUM
ejpam-521	49	13	.	.	ADP
ejpam-521	49	14	2	2	NUM
ejpam-521	49	15	.	.	NOUN
ejpam-521	49	16	data	datum	NOUN
ejpam-521	49	17	quantization	quantization	NOUN
ejpam-521	49	18	for	for	ADP
ejpam-521	49	19	optimal	optimal	ADJ
ejpam-521	49	20	information	information	NOUN
ejpam-521	49	21	description	description	NOUN
ejpam-521	49	22	suppose	suppose	VERB
ejpam-521	49	23	x	x	X
ejpam-521	49	24	n	n	X
ejpam-521	49	25	=	=	SYM
ejpam-521	49	26	(	(	PUNCT
ejpam-521	49	27	x1	x1	PROPN
ejpam-521	49	28	,	,	PUNCT
ejpam-521	49	29	·	·	PUNCT
ejpam-521	49	30	·	·	PUNCT
ejpam-521	49	31	·	·	PUNCT
ejpam-521	49	32	,	,	PUNCT
ejpam-521	49	33	xn	xn	X
ejpam-521	49	34	)	)	PUNCT
ejpam-521	49	35	is	be	AUX
ejpam-521	49	36	a	a	DET
ejpam-521	49	37	simple	simple	ADJ
ejpam-521	49	38	random	random	ADJ
ejpam-521	49	39	sample	sample	NOUN
ejpam-521	49	40	from	from	ADP
ejpam-521	49	41	an	an	DET
ejpam-521	49	42	unknown	unknown	ADJ
ejpam-521	49	43	density	density	NOUN
ejpam-521	49	44	function	function	NOUN
ejpam-521	49	45	f	f	PROPN
ejpam-521	49	46	on	on	ADP
ejpam-521	49	47	[	[	X
ejpam-521	49	48	s	s	X
ejpam-521	49	49	,	,	PUNCT
ejpam-521	49	50	t	t	PROPN
ejpam-521	49	51	]	]	PUNCT
ejpam-521	49	52	,	,	PUNCT
ejpam-521	49	53	where	where	SCONJ
ejpam-521	49	54	s	s	PRON
ejpam-521	49	55	and	and	CCONJ
ejpam-521	49	56	t	t	PROPN
ejpam-521	49	57	are	be	AUX
ejpam-521	49	58	finite	finite	ADJ
ejpam-521	49	59	real	real	ADJ
ejpam-521	49	60	numbers	number	NOUN
ejpam-521	49	61	.	.	PUNCT
ejpam-521	50	1	if	if	SCONJ
ejpam-521	50	2	f	f	PROPN
ejpam-521	50	3	were	be	AUX
ejpam-521	50	4	known	know	VERB
ejpam-521	50	5	,	,	PUNCT
ejpam-521	50	6	the	the	DET
ejpam-521	50	7	description	description	NOUN
ejpam-521	50	8	of	of	ADP
ejpam-521	50	9	the	the	DET
ejpam-521	50	10	sample	sample	NOUN
ejpam-521	50	11	could	could	AUX
ejpam-521	50	12	be	be	AUX
ejpam-521	50	13	accomplished	accomplish	VERB
ejpam-521	50	14	by	by	ADP
ejpam-521	50	15	constructing	construct	VERB
ejpam-521	50	16	a	a	DET
ejpam-521	50	17	string	string	NOUN
ejpam-521	50	18	of	of	ADP
ejpam-521	50	19	predictive	predictive	ADJ
ejpam-521	50	20	binary	binary	ADJ
ejpam-521	50	21	codes	code	NOUN
ejpam-521	50	22	for	for	ADP
ejpam-521	50	23	x	x	SYM
ejpam-521	50	24	n	n	CCONJ
ejpam-521	50	25	under	under	ADP
ejpam-521	50	26	the	the	DET
ejpam-521	50	27	information	information	NOUN
ejpam-521	50	28	source	source	NOUN
ejpam-521	50	29	determined	determine	VERB
ejpam-521	50	30	by	by	ADP
ejpam-521	50	31	f	f	PROPN
ejpam-521	50	32	where	where	SCONJ
ejpam-521	50	33	the	the	DET
ejpam-521	50	34	description	description	NOUN
ejpam-521	50	35	length	length	NOUN
ejpam-521	50	36	is	be	AUX
ejpam-521	50	37	proportional	proportional	ADJ
ejpam-521	50	38	to	to	ADP
ejpam-521	50	39	−	−	PROPN
ejpam-521	50	40	log	log	NOUN
ejpam-521	50	41	f	f	PROPN
ejpam-521	50	42	(	(	PUNCT
ejpam-521	50	43	x	x	NOUN
ejpam-521	50	44	n	n	CCONJ
ejpam-521	50	45	)	)	PUNCT
ejpam-521	50	46	.	.	PUNCT
ejpam-521	51	1	(	(	PUNCT
ejpam-521	51	2	see	see	VERB
ejpam-521	51	3	[	[	X
ejpam-521	51	4	13	13	NUM
ejpam-521	51	5	]	]	PUNCT
ejpam-521	51	6	;	;	PUNCT
ejpam-521	51	7	also	also	ADV
ejpam-521	51	8	the	the	DET
ejpam-521	51	9	logarithm	logarithm	NOUN
ejpam-521	51	10	is	be	AUX
ejpam-521	51	11	in	in	ADP
ejpam-521	51	12	base	base	NOUN
ejpam-521	51	13	2	2	NUM
ejpam-521	51	14	throughout	throughout	ADP
ejpam-521	51	15	this	this	DET
ejpam-521	51	16	paper	paper	NOUN
ejpam-521	51	17	unless	unless	SCONJ
ejpam-521	51	18	stated	state	VERB
ejpam-521	51	19	otherwise	otherwise	ADV
ejpam-521	51	20	.	.	PUNCT
ejpam-521	51	21	)	)	PUNCT
ejpam-521	52	1	in	in	ADP
ejpam-521	52	2	other	other	ADJ
ejpam-521	52	3	words	word	NOUN
ejpam-521	52	4	,	,	PUNCT
ejpam-521	52	5	describing	describe	VERB
ejpam-521	52	6	the	the	DET
ejpam-521	52	7	sample	sample	NOUN
ejpam-521	52	8	is	be	AUX
ejpam-521	52	9	the	the	DET
ejpam-521	52	10	same	same	ADJ
ejpam-521	52	11	as	as	ADP
ejpam-521	52	12	finding	find	VERB
ejpam-521	52	13	a	a	DET
ejpam-521	52	14	predictive	predictive	ADJ
ejpam-521	52	15	probability	probability	NOUN
ejpam-521	52	16	density	density	NOUN
ejpam-521	52	17	for	for	ADP
ejpam-521	52	18	the	the	DET
ejpam-521	52	19	sample	sample	NOUN
ejpam-521	52	20	.	.	PUNCT
ejpam-521	53	1	to	to	PART
ejpam-521	53	2	estimate	estimate	VERB
ejpam-521	53	3	the	the	DET
ejpam-521	53	4	unknown	unknown	ADJ
ejpam-521	53	5	density	density	NOUN
ejpam-521	53	6	f	f	PROPN
ejpam-521	53	7	a	a	DET
ejpam-521	53	8	frequently	frequently	ADV
ejpam-521	53	9	used	use	VERB
ejpam-521	53	10	method	method	NOUN
ejpam-521	53	11	is	be	AUX
ejpam-521	53	12	based	base	VERB
ejpam-521	53	13	on	on	ADP
ejpam-521	53	14	data	datum	NOUN
ejpam-521	53	15	quantization	quantization	NOUN
ejpam-521	53	16	:	:	PUNCT
ejpam-521	53	17	first	first	ADV
ejpam-521	53	18	quantize	quantize	VERB
ejpam-521	53	19	x	x	PUNCT
ejpam-521	53	20	n	n	CCONJ
ejpam-521	53	21	by	by	ADP
ejpam-521	53	22	partitioning	partition	VERB
ejpam-521	53	23	[	[	X
ejpam-521	53	24	s	s	X
ejpam-521	53	25	,	,	PUNCT
ejpam-521	53	26	t	t	PROPN
ejpam-521	53	27	]	]	PUNCT
ejpam-521	53	28	into	into	ADP
ejpam-521	53	29	a	a	DET
ejpam-521	53	30	sequence	sequence	NOUN
ejpam-521	53	31	of	of	ADP
ejpam-521	53	32	subintervals	subinterval	NOUN
ejpam-521	53	33	and	and	CCONJ
ejpam-521	53	34	then	then	ADV
ejpam-521	53	35	construct	construct	VERB
ejpam-521	53	36	a	a	DET
ejpam-521	53	37	histogram	histogram	NOUN
ejpam-521	53	38	on	on	ADP
ejpam-521	53	39	the	the	DET
ejpam-521	53	40	partition	partition	NOUN
ejpam-521	53	41	.	.	PUNCT
ejpam-521	54	1	the	the	DET
ejpam-521	54	2	choice	choice	NOUN
ejpam-521	54	3	of	of	ADP
ejpam-521	54	4	the	the	DET
ejpam-521	54	5	partition	partition	NOUN
ejpam-521	54	6	and	and	CCONJ
ejpam-521	54	7	the	the	DET
ejpam-521	54	8	estimate	estimate	NOUN
ejpam-521	54	9	of	of	ADP
ejpam-521	54	10	the	the	DET
ejpam-521	54	11	probability	probability	NOUN
ejpam-521	54	12	for	for	ADP
ejpam-521	54	13	each	each	DET
ejpam-521	54	14	subinterval	subinterval	NOUN
ejpam-521	54	15	may	may	AUX
ejpam-521	54	16	be	be	AUX
ejpam-521	54	17	determined	determine	VERB
ejpam-521	54	18	by	by	ADP
ejpam-521	54	19	the	the	DET
ejpam-521	54	20	maximum	maximum	ADJ
ejpam-521	54	21	likelihood	likelihood	NOUN
ejpam-521	54	22	method	method	NOUN
ejpam-521	54	23	if	if	SCONJ
ejpam-521	54	24	the	the	DET
ejpam-521	54	25	number	number	NOUN
ejpam-521	54	26	of	of	ADP
ejpam-521	54	27	subintervals	subinterval	NOUN
ejpam-521	54	28	is	be	AUX
ejpam-521	54	29	fixed	fix	VERB
ejpam-521	54	30	.	.	PUNCT
ejpam-521	55	1	let	let	VERB
ejpam-521	55	2	qm	qm	PROPN
ejpam-521	55	3	=	=	PUNCT
ejpam-521	55	4	(	(	PUNCT
ejpam-521	55	5	q0,m	q0,m	PROPN
ejpam-521	55	6	,	,	PUNCT
ejpam-521	55	7	q1,m	q1,m	PROPN
ejpam-521	55	8	,	,	PUNCT
ejpam-521	55	9	·	·	PUNCT
ejpam-521	55	10	·	·	PUNCT
ejpam-521	55	11	·	·	PUNCT
ejpam-521	55	12	,	,	PUNCT
ejpam-521	55	13	qm	qm	PROPN
ejpam-521	55	14	,	,	PUNCT
ejpam-521	55	15	m	m	VERB
ejpam-521	55	16	)	)	PUNCT
ejpam-521	55	17	be	be	AUX
ejpam-521	55	18	an	an	DET
ejpam-521	55	19	increasing	increase	VERB
ejpam-521	55	20	sequence	sequence	NOUN
ejpam-521	55	21	of	of	ADP
ejpam-521	55	22	numbers	number	NOUN
ejpam-521	55	23	,	,	PUNCT
ejpam-521	55	24	partitioning	partition	VERB
ejpam-521	55	25	the	the	DET
ejpam-521	55	26	interval	interval	NOUN
ejpam-521	56	1	[	[	X
ejpam-521	56	2	s	s	X
ejpam-521	56	3	,	,	PUNCT
ejpam-521	56	4	t	t	PROPN
ejpam-521	56	5	]	]	PUNCT
ejpam-521	56	6	into	into	ADP
ejpam-521	56	7	m	m	PROPN
ejpam-521	56	8	subintervals	subinterval	NOUN
ejpam-521	56	9	[	[	X
ejpam-521	56	10	q0,m	q0,m	PROPN
ejpam-521	56	11	,	,	PUNCT
ejpam-521	56	12	q1,m	q1,m	PROPN
ejpam-521	56	13	]	]	X
ejpam-521	56	14	,	,	PUNCT
ejpam-521	56	15	(	(	PUNCT
ejpam-521	56	16	q1,m	q1,m	PROPN
ejpam-521	56	17	,	,	PUNCT
ejpam-521	56	18	q2,m	q2,m	PROPN
ejpam-521	56	19	]	]	X
ejpam-521	56	20	,	,	PUNCT
ejpam-521	56	21	·	·	PUNCT
ejpam-521	56	22	·	·	PUNCT
ejpam-521	56	23	·	·	PUNCT
ejpam-521	56	24	,	,	PUNCT
ejpam-521	56	25	(	(	PUNCT
ejpam-521	56	26	qm−1,m	qm−1,m	NOUN
ejpam-521	56	27	,	,	PUNCT
ejpam-521	56	28	qm	qm	PROPN
ejpam-521	56	29	,	,	PUNCT
ejpam-521	56	30	m	m	PROPN
ejpam-521	56	31	]	]	X
ejpam-521	56	32	,	,	PUNCT
ejpam-521	56	33	written	write	VERB
ejpam-521	56	34	as	as	ADP
ejpam-521	56	35	q1,m	q1,m	PROPN
ejpam-521	56	36	,	,	PUNCT
ejpam-521	56	37	q2,m	q2,m	PROPN
ejpam-521	56	38	,	,	PUNCT
ejpam-521	56	39	·	·	PUNCT
ejpam-521	56	40	·	·	PUNCT
ejpam-521	56	41	·	·	PUNCT
ejpam-521	56	42	,	,	PUNCT
ejpam-521	56	43	qm	qm	PROPN
ejpam-521	56	44	,	,	PUNCT
ejpam-521	56	45	m	m	PROPN
ejpam-521	56	46	,	,	PUNCT
ejpam-521	56	47	where	where	SCONJ
ejpam-521	56	48	q0,m	q0,m	PROPN
ejpam-521	56	49	=	=	SYM
ejpam-521	56	50	s	s	PROPN
ejpam-521	56	51	,	,	PUNCT
ejpam-521	56	52	qm	qm	PROPN
ejpam-521	56	53	,	,	PUNCT
ejpam-521	56	54	m	m	PROPN
ejpam-521	56	55	=	=	SYM
ejpam-521	56	56	t	t	PROPN
ejpam-521	56	57	and	and	CCONJ
ejpam-521	56	58	m	m	PROPN
ejpam-521	56	59	is	be	AUX
ejpam-521	56	60	a	a	DET
ejpam-521	56	61	fixed	fix	VERB
ejpam-521	56	62	integer	integer	NOUN
ejpam-521	56	63	satisfying	satisfy	VERB
ejpam-521	56	64	m	m	PROPN
ejpam-521	56	65	≤	≤	ADJ
ejpam-521	56	66	n.	n.	PROPN
ejpam-521	56	67	denote	denote	PROPN
ejpam-521	56	68	ri	ri	PROPN
ejpam-521	56	69	,	,	PUNCT
ejpam-521	56	70	m	m	PROPN
ejpam-521	56	71	=	=	SYM
ejpam-521	56	72	qi	qi	PROPN
ejpam-521	56	73	,	,	PUNCT
ejpam-521	56	74	m	m	VERB
ejpam-521	56	75	−	−	NOUN
ejpam-521	56	76	qi−1,m	qi−1,m	NOUN
ejpam-521	56	77	as	as	ADP
ejpam-521	56	78	the	the	DET
ejpam-521	56	79	length	length	NOUN
ejpam-521	56	80	of	of	ADP
ejpam-521	56	81	q	q	PROPN
ejpam-521	56	82	i	i	PROPN
ejpam-521	56	83	,	,	PUNCT
ejpam-521	56	84	m	m	VERB
ejpam-521	56	85	and	and	CCONJ
ejpam-521	56	86	r	r	NOUN
ejpam-521	56	87	=	=	SYM
ejpam-521	56	88	t	t	PROPN
ejpam-521	56	89	−	−	PROPN
ejpam-521	56	90	s	s	PROPN
ejpam-521	56	91	,	,	PUNCT
ejpam-521	56	92	the	the	DET
ejpam-521	56	93	range	range	NOUN
ejpam-521	56	94	of	of	ADP
ejpam-521	56	95	x	x	PUNCT
ejpam-521	56	96	n.	n.	NOUN
ejpam-521	56	97	consider	consider	VERB
ejpam-521	56	98	the	the	DET
ejpam-521	56	99	histogram	histogram	NOUN
ejpam-521	56	100	densities	density	NOUN
ejpam-521	56	101	defined	define	VERB
ejpam-521	56	102	by	by	ADP
ejpam-521	56	103	f	f	PROPN
ejpam-521	56	104	(	(	PUNCT
ejpam-521	56	105	x	x	SYM
ejpam-521	56	106	|pm	|pm	PROPN
ejpam-521	56	107	,	,	PUNCT
ejpam-521	56	108	qm	qm	PROPN
ejpam-521	56	109	,	,	PUNCT
ejpam-521	56	110	s	s	PROPN
ejpam-521	56	111	,	,	PUNCT
ejpam-521	56	112	t	t	PROPN
ejpam-521	56	113	)	)	PUNCT
ejpam-521	56	114	=	=	PUNCT
ejpam-521	57	1	m	m	VERB
ejpam-521	57	2	∑	∑	PUNCT
ejpam-521	57	3	i=1	i=1	PROPN
ejpam-521	57	4	pi	pi	PROPN
ejpam-521	57	5	,	,	PUNCT
ejpam-521	57	6	m	m	PROPN
ejpam-521	57	7	ri	ri	PROPN
ejpam-521	57	8	,	,	PUNCT
ejpam-521	57	9	m	m	PROPN
ejpam-521	57	10	iqi	iqi	PROPN
ejpam-521	57	11	,	,	PUNCT
ejpam-521	57	12	m	m	VERB
ejpam-521	57	13	(	(	PUNCT
ejpam-521	57	14	x	x	X
ejpam-521	57	15	)	)	PUNCT
ejpam-521	57	16	(	(	PUNCT
ejpam-521	57	17	1	1	X
ejpam-521	57	18	)	)	PUNCT
ejpam-521	57	19	where	where	SCONJ
ejpam-521	57	20	pm	pm	NOUN
ejpam-521	57	21	=	=	SYM
ejpam-521	57	22	(	(	PUNCT
ejpam-521	57	23	p1,m	p1,m	PROPN
ejpam-521	57	24	,	,	PUNCT
ejpam-521	57	25	p2,m	p2,m	PROPN
ejpam-521	57	26	,	,	PUNCT
ejpam-521	57	27	·	·	PUNCT
ejpam-521	57	28	·	·	PUNCT
ejpam-521	57	29	·	·	PUNCT
ejpam-521	57	30	,	,	PUNCT
ejpam-521	57	31	pm	pm	PROPN
ejpam-521	57	32	,	,	PUNCT
ejpam-521	57	33	m	m	NOUN
ejpam-521	57	34	)	)	PUNCT
ejpam-521	57	35	denotes	denote	VERB
ejpam-521	57	36	a	a	DET
ejpam-521	57	37	sequence	sequence	NOUN
ejpam-521	57	38	of	of	ADP
ejpam-521	57	39	nonnegative	nonnegative	ADJ
ejpam-521	57	40	parameters	parameter	NOUN
ejpam-521	57	41	with	with	ADP
ejpam-521	57	42	the	the	DET
ejpam-521	57	43	sum	sum	NOUN
ejpam-521	57	44	equal	equal	ADJ
ejpam-521	57	45	1	1	NUM
ejpam-521	57	46	,	,	PUNCT
ejpam-521	57	47	and	and	CCONJ
ejpam-521	57	48	iqi	iqi	PROPN
ejpam-521	57	49	,	,	PUNCT
ejpam-521	57	50	m	m	PROPN
ejpam-521	57	51	(	(	PUNCT
ejpam-521	57	52	·	·	PUNCT
ejpam-521	57	53	)	)	PUNCT
ejpam-521	57	54	is	be	AUX
ejpam-521	57	55	the	the	DET
ejpam-521	57	56	usual	usual	ADJ
ejpam-521	57	57	indicator	indicator	NOUN
ejpam-521	57	58	function	function	NOUN
ejpam-521	57	59	.	.	PUNCT
ejpam-521	58	1	the	the	DET
ejpam-521	58	2	class	class	NOUN
ejpam-521	58	3	of	of	ADP
ejpam-521	58	4	densities	density	NOUN
ejpam-521	58	5	of	of	ADP
ejpam-521	58	6	the	the	DET
ejpam-521	58	7	form	form	NOUN
ejpam-521	58	8	(	(	PUNCT
ejpam-521	58	9	1	1	X
ejpam-521	58	10	)	)	PUNCT
ejpam-521	58	11	is	be	AUX
ejpam-521	58	12	denoted	denote	VERB
ejpam-521	58	13	by	by	ADP
ejpam-521	58	14	hm	hm	INTJ
ejpam-521	58	15	.	.	PUNCT
ejpam-521	58	16	with	with	ADP
ejpam-521	58	17	the	the	DET
ejpam-521	58	18	above	above	ADJ
ejpam-521	58	19	notation	notation	NOUN
ejpam-521	58	20	,	,	PUNCT
ejpam-521	58	21	the	the	DET
ejpam-521	58	22	log	log	NOUN
ejpam-521	58	23	-	-	PUNCT
ejpam-521	58	24	likelihood	likelihood	NOUN
ejpam-521	58	25	function	function	NOUN
ejpam-521	58	26	of	of	ADP
ejpam-521	58	27	the	the	DET
ejpam-521	58	28	sample	sample	NOUN
ejpam-521	59	1	x	x	PUNCT
ejpam-521	59	2	n	n	CCONJ
ejpam-521	59	3	under	under	ADP
ejpam-521	59	4	hm	hm	INTJ
ejpam-521	59	5	is	be	AUX
ejpam-521	59	6	l(x	l(x	PROPN
ejpam-521	59	7	n	n	CCONJ
ejpam-521	59	8	;	;	PUNCT
ejpam-521	59	9	hm	hm	X
ejpam-521	59	10	)	)	PUNCT
ejpam-521	59	11	=	=	SYM
ejpam-521	60	1	n	n	PROPN
ejpam-521	60	2	∑	∑	PROPN
ejpam-521	60	3	j=1	j=1	PROPN
ejpam-521	60	4	log	log	VERB
ejpam-521	60	5	m	m	VERB
ejpam-521	60	6	∑	∑	NOUN
ejpam-521	60	7	i=1	i=1	PROPN
ejpam-521	60	8	pi	pi	PROPN
ejpam-521	60	9	,	,	PUNCT
ejpam-521	60	10	m	m	PROPN
ejpam-521	60	11	ri	ri	PROPN
ejpam-521	60	12	,	,	PUNCT
ejpam-521	60	13	m	m	PROPN
ejpam-521	60	14	iqi	iqi	PROPN
ejpam-521	60	15	,	,	PUNCT
ejpam-521	60	16	m	m	PROPN
ejpam-521	60	17	(	(	PUNCT
ejpam-521	60	18	x	x	PROPN
ejpam-521	60	19	j	j	NOUN
ejpam-521	60	20	)	)	PUNCT
ejpam-521	60	21	!	!	PUNCT
ejpam-521	61	1	=	=	PUNCT
ejpam-521	61	2	m	m	VERB
ejpam-521	61	3	∑	∑	PROPN
ejpam-521	61	4	i=1	i=1	PROPN
ejpam-521	61	5	ni	ni	PROPN
ejpam-521	61	6	,	,	PUNCT
ejpam-521	61	7	m	m	VERB
ejpam-521	61	8	log	log	NOUN
ejpam-521	61	9	pi	pi	NOUN
ejpam-521	61	10	,	,	PUNCT
ejpam-521	61	11	m	m	PROPN
ejpam-521	61	12	ri	ri	PROPN
ejpam-521	61	13	,	,	PUNCT
ejpam-521	61	14	m	m	VERB
ejpam-521	61	15	(	(	PUNCT
ejpam-521	61	16	2	2	NUM
ejpam-521	61	17	)	)	PUNCT
ejpam-521	61	18	g.	g.	PROPN
ejpam-521	61	19	qian	qian	PROPN
ejpam-521	61	20	/	/	SYM
ejpam-521	61	21	eur	eur	PROPN
ejpam-521	61	22	.	.	PUNCT
ejpam-521	62	1	j.	j.	PROPN
ejpam-521	62	2	pure	pure	PROPN
ejpam-521	62	3	appl	appl	PROPN
ejpam-521	62	4	.	.	PROPN
ejpam-521	62	5	math	math	PROPN
ejpam-521	62	6	,	,	PUNCT
ejpam-521	62	7	3	3	NUM
ejpam-521	62	8	(	(	PUNCT
ejpam-521	62	9	2010	2010	NUM
ejpam-521	62	10	)	)	PUNCT
ejpam-521	62	11	,	,	PUNCT
ejpam-521	62	12	51	51	NUM
ejpam-521	62	13	-	-	SYM
ejpam-521	62	14	80	80	NUM
ejpam-521	62	15	54	54	NUM
ejpam-521	62	16	where	where	SCONJ
ejpam-521	62	17	ni	ni	PROPN
ejpam-521	62	18	,	,	PUNCT
ejpam-521	62	19	m	m	VERB
ejpam-521	62	20	=	=	ADJ
ejpam-521	62	21	∑n	∑n	PROPN
ejpam-521	62	22	j=1	j=1	PROPN
ejpam-521	62	23	iqi	iqi	PROPN
ejpam-521	62	24	,	,	PUNCT
ejpam-521	62	25	m	m	PROPN
ejpam-521	62	26	(	(	PUNCT
ejpam-521	62	27	x	x	SYM
ejpam-521	62	28	j	j	NOUN
ejpam-521	62	29	)	)	PUNCT
ejpam-521	62	30	is	be	AUX
ejpam-521	62	31	the	the	DET
ejpam-521	62	32	number	number	NOUN
ejpam-521	62	33	of	of	ADP
ejpam-521	62	34	data	datum	NOUN
ejpam-521	62	35	points	point	NOUN
ejpam-521	62	36	falling	fall	VERB
ejpam-521	62	37	into	into	ADP
ejpam-521	62	38	q	q	PROPN
ejpam-521	62	39	i	i	PROPN
ejpam-521	62	40	,	,	PUNCT
ejpam-521	62	41	m.	m.	NOUN
ejpam-521	62	42	if	if	SCONJ
ejpam-521	62	43	ni	ni	PROPN
ejpam-521	62	44	,	,	PUNCT
ejpam-521	62	45	m	m	VERB
ejpam-521	62	46	equals	equal	VERB
ejpam-521	62	47	zero	zero	NUM
ejpam-521	62	48	,	,	PUNCT
ejpam-521	62	49	the	the	DET
ejpam-521	62	50	corresponding	corresponding	ADJ
ejpam-521	62	51	pi	pi	NOUN
ejpam-521	62	52	,	,	PUNCT
ejpam-521	62	53	m	m	VERB
ejpam-521	62	54	may	may	AUX
ejpam-521	62	55	not	not	PART
ejpam-521	62	56	be	be	AUX
ejpam-521	62	57	uniquely	uniquely	ADV
ejpam-521	62	58	optimized	optimize	VERB
ejpam-521	62	59	through	through	ADP
ejpam-521	62	60	maximization	maximization	NOUN
ejpam-521	62	61	of	of	ADP
ejpam-521	62	62	l(x	l(x	PROPN
ejpam-521	62	63	n	n	CCONJ
ejpam-521	62	64	;	;	PUNCT
ejpam-521	62	65	hm	hm	X
ejpam-521	62	66	)	)	PUNCT
ejpam-521	62	67	.	.	PUNCT
ejpam-521	63	1	this	this	DET
ejpam-521	63	2	difficulty	difficulty	NOUN
ejpam-521	63	3	may	may	AUX
ejpam-521	63	4	be	be	AUX
ejpam-521	63	5	overcome	overcome	VERB
ejpam-521	63	6	by	by	ADP
ejpam-521	63	7	introducing	introduce	VERB
ejpam-521	63	8	m	m	PROPN
ejpam-521	63	9	numbers	number	NOUN
ejpam-521	63	10	y1	y1	PROPN
ejpam-521	63	11	,	,	PUNCT
ejpam-521	63	12	·	·	PUNCT
ejpam-521	63	13	·	·	PUNCT
ejpam-521	63	14	·	·	PUNCT
ejpam-521	63	15	,	,	PUNCT
ejpam-521	63	16	ym	ym	INTJ
ejpam-521	63	17	(	(	PUNCT
ejpam-521	63	18	abbreviated	abbreviate	VERB
ejpam-521	63	19	as	as	ADP
ejpam-521	63	20	ym	ym	PROPN
ejpam-521	63	21	,	,	PUNCT
ejpam-521	63	22	where	where	SCONJ
ejpam-521	63	23	yi	yi	PROPN
ejpam-521	63	24	is	be	AUX
ejpam-521	63	25	regarded	regard	VERB
ejpam-521	63	26	as	as	ADP
ejpam-521	63	27	an	an	DET
ejpam-521	63	28	observation	observation	NOUN
ejpam-521	63	29	from	from	ADP
ejpam-521	63	30	the	the	DET
ejpam-521	63	31	uniform	uniform	ADJ
ejpam-521	63	32	distribution	distribution	NOUN
ejpam-521	63	33	on	on	ADP
ejpam-521	63	34	q	q	PROPN
ejpam-521	63	35	i	i	PROPN
ejpam-521	63	36	,	,	PUNCT
ejpam-521	63	37	m	m	PROPN
ejpam-521	63	38	,	,	PUNCT
ejpam-521	63	39	and	and	CCONJ
ejpam-521	63	40	mixing	mix	VERB
ejpam-521	63	41	them	they	PRON
ejpam-521	63	42	thoroughly	thoroughly	ADV
ejpam-521	63	43	with	with	ADP
ejpam-521	63	44	the	the	DET
ejpam-521	63	45	n	n	PRON
ejpam-521	63	46	observations	observation	NOUN
ejpam-521	63	47	x	x	PUNCT
ejpam-521	63	48	n	n	CCONJ
ejpam-521	63	49	as	as	ADV
ejpam-521	63	50	if	if	SCONJ
ejpam-521	63	51	both	both	DET
ejpam-521	63	52	ym	ym	PROPN
ejpam-521	63	53	and	and	CCONJ
ejpam-521	63	54	x	x	SYM
ejpam-521	63	55	n	n	PRON
ejpam-521	63	56	were	be	AUX
ejpam-521	63	57	generated	generate	VERB
ejpam-521	63	58	from	from	ADP
ejpam-521	63	59	the	the	DET
ejpam-521	63	60	same	same	ADJ
ejpam-521	63	61	distribution	distribution	NOUN
ejpam-521	63	62	.	.	PUNCT
ejpam-521	64	1	then	then	ADV
ejpam-521	64	2	the	the	DET
ejpam-521	64	3	log	log	NOUN
ejpam-521	64	4	-	-	PUNCT
ejpam-521	64	5	likelihood	likelihood	NOUN
ejpam-521	64	6	function	function	NOUN
ejpam-521	64	7	of	of	ADP
ejpam-521	64	8	x	x	PUNCT
ejpam-521	64	9	n	n	PROPN
ejpam-521	64	10	and	and	CCONJ
ejpam-521	64	11	ym	ym	PROPN
ejpam-521	64	12	is	be	AUX
ejpam-521	64	13	l1(x	l1(x	NOUN
ejpam-521	64	14	n	n	CCONJ
ejpam-521	64	15	;	;	PUNCT
ejpam-521	64	16	hm	hm	X
ejpam-521	64	17	)	)	PUNCT
ejpam-521	64	18	=	=	PUNCT
ejpam-521	65	1	m	m	VERB
ejpam-521	65	2	∑	∑	PROPN
ejpam-521	65	3	i=1	i=1	PROPN
ejpam-521	65	4	(	(	PUNCT
ejpam-521	65	5	ni	ni	PROPN
ejpam-521	65	6	,	,	PUNCT
ejpam-521	65	7	m+	m+	NOUN
ejpam-521	65	8	1	1	NUM
ejpam-521	65	9	)	)	PUNCT
ejpam-521	65	10	log	log	NOUN
ejpam-521	65	11	pi	pi	NOUN
ejpam-521	65	12	,	,	PUNCT
ejpam-521	65	13	m	m	PROPN
ejpam-521	65	14	ri	ri	PROPN
ejpam-521	65	15	,	,	PUNCT
ejpam-521	65	16	m	m	VERB
ejpam-521	65	17	(	(	PUNCT
ejpam-521	65	18	3	3	NUM
ejpam-521	65	19	)	)	PUNCT
ejpam-521	65	20	which	which	PRON
ejpam-521	65	21	does	do	AUX
ejpam-521	65	22	not	not	PART
ejpam-521	65	23	depend	depend	VERB
ejpam-521	65	24	on	on	ADP
ejpam-521	65	25	the	the	DET
ejpam-521	65	26	particular	particular	ADJ
ejpam-521	65	27	values	value	NOUN
ejpam-521	65	28	of	of	ADP
ejpam-521	65	29	ym	ym	PROPN
ejpam-521	65	30	,	,	PUNCT
ejpam-521	65	31	and	and	CCONJ
ejpam-521	65	32	can	can	AUX
ejpam-521	65	33	,	,	PUNCT
ejpam-521	65	34	therefore	therefore	ADV
ejpam-521	65	35	,	,	PUNCT
ejpam-521	65	36	be	be	AUX
ejpam-521	65	37	regarded	regard	VERB
ejpam-521	65	38	as	as	ADP
ejpam-521	65	39	the	the	DET
ejpam-521	65	40	log	log	NOUN
ejpam-521	65	41	-	-	PUNCT
ejpam-521	65	42	likelihood	likelihood	NOUN
ejpam-521	65	43	function	function	NOUN
ejpam-521	65	44	of	of	ADP
ejpam-521	65	45	x	x	PROPN
ejpam-521	65	46	n.	n.	NOUN
ejpam-521	65	47	applying	apply	VERB
ejpam-521	65	48	the	the	DET
ejpam-521	65	49	maximum	maximum	ADJ
ejpam-521	65	50	likelihood	likelihood	NOUN
ejpam-521	65	51	principle	principle	NOUN
ejpam-521	65	52	the	the	DET
ejpam-521	65	53	optimal	optimal	ADJ
ejpam-521	65	54	partition	partition	NOUN
ejpam-521	65	55	qm	qm	PROPN
ejpam-521	65	56	and	and	CCONJ
ejpam-521	65	57	probabilities	probability	NOUN
ejpam-521	65	58	pm	pm	VERB
ejpam-521	65	59	for	for	ADP
ejpam-521	65	60	a	a	DET
ejpam-521	65	61	fixed	fix	VERB
ejpam-521	65	62	m	m	NOUN
ejpam-521	65	63	are	be	AUX
ejpam-521	65	64	the	the	DET
ejpam-521	65	65	ones	one	NOUN
ejpam-521	65	66	which	which	PRON
ejpam-521	65	67	maximize	maximize	VERB
ejpam-521	65	68	l1(x	l1(x	PRON
ejpam-521	65	69	n	n	CCONJ
ejpam-521	65	70	,	,	PUNCT
ejpam-521	65	71	hm	hm	INTJ
ejpam-521	65	72	)	)	PUNCT
ejpam-521	65	73	subject	subject	NOUN
ejpam-521	65	74	to	to	ADP
ejpam-521	65	75	the	the	DET
ejpam-521	65	76	conditions	condition	NOUN
ejpam-521	65	77	that	that	PRON
ejpam-521	65	78	∑	∑	ADP
ejpam-521	65	79	pi	pi	PROPN
ejpam-521	65	80	,	,	PUNCT
ejpam-521	65	81	m	m	VERB
ejpam-521	65	82	=	=	NOUN
ejpam-521	65	83	1	1	NUM
ejpam-521	65	84	and	and	CCONJ
ejpam-521	65	85	∑	∑	ADP
ejpam-521	65	86	ri	ri	PROPN
ejpam-521	65	87	,	,	PUNCT
ejpam-521	65	88	m	m	VERB
ejpam-521	65	89	=	=	SYM
ejpam-521	65	90	r.	r.	NOUN
ejpam-521	65	91	denoting	denote	VERB
ejpam-521	65	92	f	f	PROPN
ejpam-521	66	1	=	=	PUNCT
ejpam-521	66	2	m	m	PROPN
ejpam-521	66	3	∑	∑	PROPN
ejpam-521	66	4	i=1	i=1	PROPN
ejpam-521	66	5	(	(	PUNCT
ejpam-521	66	6	ni	ni	PROPN
ejpam-521	66	7	,	,	PUNCT
ejpam-521	66	8	m+	m+	NOUN
ejpam-521	66	9	1	1	NUM
ejpam-521	66	10	)	)	PUNCT
ejpam-521	66	11	log	log	NOUN
ejpam-521	66	12	pi	pi	NOUN
ejpam-521	66	13	,	,	PUNCT
ejpam-521	66	14	m	m	PROPN
ejpam-521	66	15	ri	ri	PROPN
ejpam-521	66	16	,	,	PUNCT
ejpam-521	66	17	m	m	VERB
ejpam-521	66	18	+	+	NOUN
ejpam-521	66	19	λ1	λ1	ADJ
ejpam-521	66	20	(	(	PUNCT
ejpam-521	66	21	m	m	PROPN
ejpam-521	66	22	∑	∑	PROPN
ejpam-521	66	23	i=1	i=1	PROPN
ejpam-521	66	24	pi	pi	PROPN
ejpam-521	66	25	,	,	PUNCT
ejpam-521	66	26	m−	m−	PROPN
ejpam-521	66	27	1)+λ2	1)+λ2	NUM
ejpam-521	66	28	(	(	PUNCT
ejpam-521	66	29	m	m	PROPN
ejpam-521	66	30	∑	∑	PROPN
ejpam-521	66	31	i=1	i=1	PROPN
ejpam-521	66	32	ri	ri	PROPN
ejpam-521	66	33	,	,	PUNCT
ejpam-521	66	34	m−	m−	PROPN
ejpam-521	66	35	r	r	PROPN
ejpam-521	66	36	)	)	PUNCT
ejpam-521	66	37	,	,	PUNCT
ejpam-521	66	38	(	(	PUNCT
ejpam-521	66	39	4	4	X
ejpam-521	66	40	)	)	PUNCT
ejpam-521	66	41	differentiating	differentiate	VERB
ejpam-521	66	42	f	f	NOUN
ejpam-521	66	43	with	with	ADP
ejpam-521	66	44	respect	respect	NOUN
ejpam-521	66	45	to	to	ADP
ejpam-521	66	46	pi	pi	PROPN
ejpam-521	66	47	,	,	PUNCT
ejpam-521	66	48	m	m	VERB
ejpam-521	66	49	’s	’s	NOUN
ejpam-521	66	50	and	and	CCONJ
ejpam-521	66	51	setting	set	VERB
ejpam-521	66	52	the	the	DET
ejpam-521	66	53	derivatives	derivative	NOUN
ejpam-521	66	54	equal	equal	ADJ
ejpam-521	66	55	to	to	ADP
ejpam-521	66	56	zero	zero	NUM
ejpam-521	66	57	we	we	PRON
ejpam-521	66	58	have	have	VERB
ejpam-521	66	59	∂	∂	NUM
ejpam-521	66	60	f	f	PROPN
ejpam-521	66	61	∂	∂	NUM
ejpam-521	66	62	pi	pi	NOUN
ejpam-521	66	63	,	,	PUNCT
ejpam-521	66	64	m	m	PROPN
ejpam-521	66	65	=	=	SYM
ejpam-521	66	66	ni	ni	PROPN
ejpam-521	66	67	,	,	PUNCT
ejpam-521	66	68	m+	m+	NOUN
ejpam-521	66	69	1	1	NUM
ejpam-521	66	70	pi	pi	NOUN
ejpam-521	66	71	,	,	PUNCT
ejpam-521	66	72	m	m	VERB
ejpam-521	66	73	log	log	NOUN
ejpam-521	66	74	e+λ1	e+λ1	PROPN
ejpam-521	66	75	=	=	SYM
ejpam-521	66	76	0	0	NUM
ejpam-521	66	77	,	,	PUNCT
ejpam-521	66	78	i	i	PRON
ejpam-521	66	79	=	=	NOUN
ejpam-521	66	80	1,2	1,2	NUM
ejpam-521	66	81	,	,	PUNCT
ejpam-521	66	82	·	·	PUNCT
ejpam-521	66	83	·	·	PUNCT
ejpam-521	66	84	·	·	PUNCT
ejpam-521	66	85	,	,	PUNCT
ejpam-521	66	86	m	m	VERB
ejpam-521	66	87	(	(	PUNCT
ejpam-521	66	88	5	5	NUM
ejpam-521	66	89	)	)	PUNCT
ejpam-521	66	90	from	from	ADP
ejpam-521	66	91	which	which	PRON
ejpam-521	66	92	pi	pi	NOUN
ejpam-521	66	93	,	,	PUNCT
ejpam-521	66	94	m	m	VERB
ejpam-521	66	95	=	=	SYM
ejpam-521	66	96	(	(	PUNCT
ejpam-521	66	97	ni	ni	PROPN
ejpam-521	66	98	,	,	PUNCT
ejpam-521	66	99	m	m	VERB
ejpam-521	66	100	+	+	NUM
ejpam-521	66	101	1)/(n	1)/(n	NUM
ejpam-521	66	102	+	+	NUM
ejpam-521	66	103	m	m	NOUN
ejpam-521	66	104	)	)	PUNCT
ejpam-521	66	105	.	.	PUNCT
ejpam-521	67	1	differentiating	differentiate	VERB
ejpam-521	67	2	f	f	PROPN
ejpam-521	67	3	with	with	ADP
ejpam-521	67	4	respect	respect	NOUN
ejpam-521	67	5	to	to	ADP
ejpam-521	67	6	pi	pi	PROPN
ejpam-521	67	7	,	,	PUNCT
ejpam-521	67	8	m	m	VERB
ejpam-521	67	9	’s	’s	ADJ
ejpam-521	67	10	twice	twice	ADV
ejpam-521	67	11	,	,	PUNCT
ejpam-521	67	12	the	the	DET
ejpam-521	67	13	resulting	result	VERB
ejpam-521	67	14	second	second	ADJ
ejpam-521	67	15	derivative	derivative	ADJ
ejpam-521	67	16	matrix	matrix	NOUN
ejpam-521	67	17	�	�	PROPN
ejpam-521	67	18	∂	∂	NUM
ejpam-521	67	19	2f	2f	NUM
ejpam-521	67	20	∂	∂	NUM
ejpam-521	67	21	pi	pi	NOUN
ejpam-521	67	22	,	,	PUNCT
ejpam-521	67	23	m∂	m∂	PROPN
ejpam-521	67	24	p	p	PROPN
ejpam-521	67	25	j	j	PROPN
ejpam-521	67	26	,	,	PUNCT
ejpam-521	67	27	m	m	VERB
ejpam-521	67	28	�	�	PROPN
ejpam-521	67	29	=	=	PUNCT
ejpam-521	67	30	(	(	PUNCT
ejpam-521	67	31	log	log	NOUN
ejpam-521	67	32	e)diag	e)diag	PROPN
ejpam-521	67	33	−n1,m+	−n1,m+	VERB
ejpam-521	67	34	1	1	NUM
ejpam-521	67	35	p2	p2	PROPN
ejpam-521	67	36	1,m	1,m	NOUN
ejpam-521	67	37	,	,	PUNCT
ejpam-521	67	38	·	·	PUNCT
ejpam-521	67	39	·	·	PUNCT
ejpam-521	67	40	·	·	PUNCT
ejpam-521	67	41	,	,	PUNCT
ejpam-521	67	42	−nm	−nm	ADP
ejpam-521	67	43	,	,	PUNCT
ejpam-521	67	44	m+	m+	NOUN
ejpam-521	67	45	1	1	NUM
ejpam-521	67	46	p2	p2	PROPN
ejpam-521	67	47	m	m	PROPN
ejpam-521	67	48	,	,	PUNCT
ejpam-521	67	49	m	m	NOUN
ejpam-521	67	50	!	!	PUNCT
ejpam-521	68	1	≤	≤	ADJ
ejpam-521	68	2	0	0	NUM
ejpam-521	68	3	.	.	PUNCT
ejpam-521	69	1	(	(	PUNCT
ejpam-521	69	2	6	6	NUM
ejpam-521	69	3	)	)	PUNCT
ejpam-521	69	4	therefore	therefore	ADV
ejpam-521	69	5	a	a	DET
ejpam-521	69	6	necessary	necessary	ADJ
ejpam-521	69	7	condition	condition	NOUN
ejpam-521	69	8	for	for	ADP
ejpam-521	69	9	the	the	DET
ejpam-521	69	10	maximization	maximization	NOUN
ejpam-521	69	11	of	of	ADP
ejpam-521	69	12	(	(	PUNCT
ejpam-521	69	13	4	4	NUM
ejpam-521	69	14	)	)	PUNCT
ejpam-521	69	15	is	be	AUX
ejpam-521	69	16	that	that	SCONJ
ejpam-521	69	17	the	the	DET
ejpam-521	69	18	probabilities	probability	NOUN
ejpam-521	69	19	pi	pi	NOUN
ejpam-521	69	20	,	,	PUNCT
ejpam-521	69	21	m	m	VERB
ejpam-521	69	22	are	be	AUX
ejpam-521	69	23	equal	equal	ADJ
ejpam-521	69	24	to	to	ADP
ejpam-521	69	25	the	the	DET
ejpam-521	69	26	relative	relative	ADJ
ejpam-521	69	27	frequencies	frequency	NOUN
ejpam-521	69	28	(	(	PUNCT
ejpam-521	69	29	ni	ni	PROPN
ejpam-521	69	30	,	,	PUNCT
ejpam-521	69	31	m+	m+	NOUN
ejpam-521	69	32	1)/(n+m	1)/(n+m	NUM
ejpam-521	69	33	)	)	PUNCT
ejpam-521	69	34	.	.	PUNCT
ejpam-521	70	1	both	both	CCONJ
ejpam-521	70	2	the	the	DET
ejpam-521	70	3	allocation	allocation	NOUN
ejpam-521	70	4	of	of	ADP
ejpam-521	70	5	ni	ni	PROPN
ejpam-521	70	6	,	,	PUNCT
ejpam-521	70	7	m	m	VERB
ejpam-521	70	8	’s	’s	NOUN
ejpam-521	70	9	and	and	CCONJ
ejpam-521	70	10	the	the	DET
ejpam-521	70	11	ranges	range	NOUN
ejpam-521	70	12	ri	ri	PROPN
ejpam-521	70	13	,	,	PUNCT
ejpam-521	70	14	m	m	PROPN
ejpam-521	70	15	’s	’s	NOUN
ejpam-521	70	16	depend	depend	VERB
ejpam-521	70	17	on	on	ADP
ejpam-521	70	18	the	the	DET
ejpam-521	70	19	partition	partition	NOUN
ejpam-521	70	20	qm	qm	PROPN
ejpam-521	70	21	.	.	PUNCT
ejpam-521	71	1	thus	thus	ADV
ejpam-521	71	2	the	the	DET
ejpam-521	71	3	function	function	NOUN
ejpam-521	71	4	f	f	PROPN
ejpam-521	71	5	is	be	AUX
ejpam-521	71	6	not	not	PART
ejpam-521	71	7	continuous	continuous	ADJ
ejpam-521	71	8	with	with	ADP
ejpam-521	71	9	respect	respect	NOUN
ejpam-521	71	10	to	to	ADP
ejpam-521	71	11	ri	ri	PROPN
ejpam-521	71	12	,	,	PUNCT
ejpam-521	71	13	m	m	VERB
ejpam-521	71	14	’s	’s	ADJ
ejpam-521	71	15	unless	unless	SCONJ
ejpam-521	71	16	the	the	DET
ejpam-521	71	17	allocation	allocation	NOUN
ejpam-521	71	18	of	of	ADP
ejpam-521	71	19	ni	ni	PROPN
ejpam-521	71	20	,	,	PUNCT
ejpam-521	71	21	m	m	VERB
ejpam-521	71	22	’s	’s	PART
ejpam-521	71	23	does	do	AUX
ejpam-521	71	24	not	not	PART
ejpam-521	71	25	change	change	VERB
ejpam-521	71	26	.	.	PUNCT
ejpam-521	72	1	under	under	ADP
ejpam-521	72	2	such	such	ADJ
ejpam-521	72	3	allocation	allocation	NOUN
ejpam-521	72	4	the	the	DET
ejpam-521	72	5	local	local	ADJ
ejpam-521	72	6	maximum	maximum	ADJ
ejpam-521	72	7	/	/	SYM
ejpam-521	72	8	minimum	minimum	ADJ
ejpam-521	72	9	value	value	NOUN
ejpam-521	72	10	of	of	ADP
ejpam-521	72	11	l1(x	l1(x	NOUN
ejpam-521	72	12	n	n	CCONJ
ejpam-521	72	13	;	;	PUNCT
ejpam-521	72	14	hm	hm	X
ejpam-521	72	15	)	)	PUNCT
ejpam-521	72	16	is	be	AUX
ejpam-521	72	17	achieved	achieve	VERB
ejpam-521	72	18	or	or	CCONJ
ejpam-521	72	19	converged	converge	VERB
ejpam-521	72	20	to	to	ADP
ejpam-521	72	21	when	when	SCONJ
ejpam-521	72	22	ri	ri	PROPN
ejpam-521	72	23	,	,	PUNCT
ejpam-521	72	24	m	m	PROPN
ejpam-521	72	25	’s	’s	PART
ejpam-521	72	26	approach	approach	NOUN
ejpam-521	72	27	to	to	ADP
ejpam-521	72	28	their	their	PRON
ejpam-521	72	29	boundary	boundary	ADJ
ejpam-521	72	30	values	value	NOUN
ejpam-521	72	31	,	,	PUNCT
ejpam-521	72	32	i.e.	i.e.	X
ejpam-521	72	33	where	where	SCONJ
ejpam-521	72	34	the	the	DET
ejpam-521	72	35	resultant	resultant	NOUN
ejpam-521	72	36	allocation	allocation	NOUN
ejpam-521	72	37	of	of	ADP
ejpam-521	72	38	ni	ni	PROPN
ejpam-521	72	39	,	,	PUNCT
ejpam-521	72	40	m	m	VERB
ejpam-521	72	41	’s	’s	PART
ejpam-521	72	42	would	would	AUX
ejpam-521	72	43	just	just	ADV
ejpam-521	72	44	about	about	VERB
ejpam-521	72	45	to	to	PART
ejpam-521	72	46	change	change	VERB
ejpam-521	72	47	.	.	PUNCT
ejpam-521	73	1	therefore	therefore	ADV
ejpam-521	73	2	,	,	PUNCT
ejpam-521	73	3	the	the	DET
ejpam-521	73	4	global	global	ADJ
ejpam-521	73	5	maximization	maximization	NOUN
ejpam-521	73	6	of	of	ADP
ejpam-521	73	7	f	f	PROPN
ejpam-521	73	8	with	with	ADP
ejpam-521	73	9	respect	respect	NOUN
ejpam-521	73	10	to	to	ADP
ejpam-521	73	11	ri	ri	PROPN
ejpam-521	73	12	,	,	PUNCT
ejpam-521	73	13	m	m	PROPN
ejpam-521	73	14	’s	’s	PART
ejpam-521	73	15	may	may	AUX
ejpam-521	73	16	not	not	PART
ejpam-521	73	17	exist	exist	VERB
ejpam-521	73	18	.	.	PUNCT
ejpam-521	74	1	in	in	ADP
ejpam-521	74	2	the	the	DET
ejpam-521	74	3	light	light	NOUN
ejpam-521	74	4	of	of	ADP
ejpam-521	74	5	the	the	DET
ejpam-521	74	6	above	above	ADJ
ejpam-521	74	7	discussions	discussion	NOUN
ejpam-521	74	8	and	and	CCONJ
ejpam-521	74	9	in	in	ADP
ejpam-521	74	10	order	order	NOUN
ejpam-521	74	11	to	to	PART
ejpam-521	74	12	keep	keep	VERB
ejpam-521	74	13	the	the	DET
ejpam-521	74	14	code	code	NOUN
ejpam-521	74	15	length	length	NOUN
ejpam-521	74	16	needed	need	VERB
ejpam-521	74	17	for	for	ADP
ejpam-521	74	18	model	model	NOUN
ejpam-521	74	19	description	description	NOUN
ejpam-521	74	20	short	short	ADJ
ejpam-521	74	21	,	,	PUNCT
ejpam-521	74	22	we	we	PRON
ejpam-521	74	23	may	may	AUX
ejpam-521	74	24	reasonably	reasonably	ADV
ejpam-521	74	25	impose	impose	VERB
ejpam-521	74	26	the	the	DET
ejpam-521	74	27	restriction	restriction	NOUN
ejpam-521	74	28	that	that	SCONJ
ejpam-521	74	29	the	the	DET
ejpam-521	74	30	end	end	NOUN
ejpam-521	74	31	points	point	NOUN
ejpam-521	74	32	of	of	ADP
ejpam-521	74	33	every	every	DET
ejpam-521	74	34	subinterval	subinterval	NOUN
ejpam-521	74	35	q	q	PROPN
ejpam-521	74	36	i	i	PROPN
ejpam-521	74	37	,	,	PUNCT
ejpam-521	74	38	m	m	PROPN
ejpam-521	74	39	,	,	PUNCT
ejpam-521	74	40	except	except	SCONJ
ejpam-521	74	41	the	the	DET
ejpam-521	74	42	two	two	NUM
ejpam-521	74	43	end	end	NOUN
ejpam-521	74	44	points	point	NOUN
ejpam-521	74	45	s	s	PART
ejpam-521	74	46	and	and	CCONJ
ejpam-521	74	47	t	t	PROPN
ejpam-521	74	48	,	,	PUNCT
ejpam-521	74	49	i.e.	i.e.	X
ejpam-521	74	50	the	the	DET
ejpam-521	74	51	sequence	sequence	NOUN
ejpam-521	74	52	of	of	ADP
ejpam-521	74	53	the	the	DET
ejpam-521	74	54	break	break	NOUN
ejpam-521	74	55	points	point	NOUN
ejpam-521	74	56	qi	qi	PROPN
ejpam-521	74	57	,	,	PUNCT
ejpam-521	74	58	m	m	PROPN
ejpam-521	74	59	,	,	PUNCT
ejpam-521	74	60	·	·	PUNCT
ejpam-521	74	61	·	·	PUNCT
ejpam-521	74	62	·	·	PUNCT
ejpam-521	74	63	,	,	PUNCT
ejpam-521	74	64	qm−1,m	qm−1,m	NOUN
ejpam-521	74	65	,	,	PUNCT
ejpam-521	74	66	should	should	AUX
ejpam-521	74	67	be	be	AUX
ejpam-521	74	68	at	at	ADP
ejpam-521	74	69	least	least	ADJ
ejpam-521	74	70	d	d	NUM
ejpam-521	74	71	units	unit	NOUN
ejpam-521	74	72	away	away	ADV
ejpam-521	74	73	from	from	ADP
ejpam-521	74	74	the	the	DET
ejpam-521	74	75	nearest	near	ADJ
ejpam-521	74	76	observations	observation	NOUN
ejpam-521	74	77	,	,	PUNCT
ejpam-521	74	78	where	where	SCONJ
ejpam-521	74	79	d	d	NOUN
ejpam-521	74	80	>	>	X
ejpam-521	74	81	0	0	NUM
ejpam-521	74	82	is	be	AUX
ejpam-521	74	83	half	half	NOUN
ejpam-521	74	84	of	of	ADP
ejpam-521	74	85	the	the	DET
ejpam-521	74	86	precision	precision	NOUN
ejpam-521	74	87	of	of	ADP
ejpam-521	74	88	x	x	PUNCT
ejpam-521	74	89	n.	n.	NOUN
ejpam-521	74	90	in	in	ADP
ejpam-521	74	91	other	other	ADJ
ejpam-521	74	92	words	word	NOUN
ejpam-521	74	93	,	,	PUNCT
ejpam-521	74	94	if	if	SCONJ
ejpam-521	74	95	the	the	DET
ejpam-521	74	96	locations	location	NOUN
ejpam-521	74	97	of	of	ADP
ejpam-521	74	98	the	the	DET
ejpam-521	74	99	sample	sample	NOUN
ejpam-521	74	100	x	x	PUNCT
ejpam-521	74	101	n	n	PRON
ejpam-521	74	102	are	be	AUX
ejpam-521	74	103	expressed	express	VERB
ejpam-521	74	104	in	in	ADP
ejpam-521	74	105	an	an	DET
ejpam-521	74	106	ascending	ascend	VERB
ejpam-521	74	107	order	order	NOUN
ejpam-521	74	108	zn	zn	X
ejpam-521	74	109	=	=	SYM
ejpam-521	74	110	z1	z1	PROPN
ejpam-521	74	111	<	<	X
ejpam-521	74	112	z2	z2	PROPN
ejpam-521	74	113	<	<	X
ejpam-521	74	114	·	·	PUNCT
ejpam-521	74	115	·	·	PUNCT
ejpam-521	74	116	·	·	PUNCT
ejpam-521	74	117	<	<	X
ejpam-521	74	118	zn	zn	PROPN
ejpam-521	74	119	,	,	PUNCT
ejpam-521	74	120	where	where	SCONJ
ejpam-521	74	121	n	n	PRON
ejpam-521	74	122	≤	≤	X
ejpam-521	74	123	n	n	CCONJ
ejpam-521	74	124	because	because	SCONJ
ejpam-521	74	125	of	of	ADP
ejpam-521	74	126	possible	possible	ADJ
ejpam-521	74	127	ties	tie	NOUN
ejpam-521	74	128	,	,	PUNCT
ejpam-521	74	129	then	then	ADV
ejpam-521	74	130	qm	qm	PROPN
ejpam-521	74	131	is	be	AUX
ejpam-521	74	132	a	a	DET
ejpam-521	74	133	subsequence	subsequence	NOUN
ejpam-521	74	134	of	of	ADP
ejpam-521	74	135	the	the	DET
ejpam-521	74	136	2n	2n	NUM
ejpam-521	74	137	+	+	CCONJ
ejpam-521	74	138	2	2	NUM
ejpam-521	74	139	long	long	ADJ
ejpam-521	74	140	sequence	sequence	NOUN
ejpam-521	74	141	s	s	PART
ejpam-521	74	142	,	,	PUNCT
ejpam-521	74	143	z1	z1	ADJ
ejpam-521	74	144	−	−	PROPN
ejpam-521	74	145	d	d	PROPN
ejpam-521	74	146	,	,	PUNCT
ejpam-521	74	147	z1	z1	PROPN
ejpam-521	75	1	+	+	CCONJ
ejpam-521	75	2	d	d	PROPN
ejpam-521	75	3	,	,	PUNCT
ejpam-521	75	4	z2	z2	PROPN
ejpam-521	75	5	−	−	PROPN
ejpam-521	75	6	d	d	PROPN
ejpam-521	75	7	,	,	PUNCT
ejpam-521	75	8	z2	z2	PROPN
ejpam-521	75	9	+	+	CCONJ
ejpam-521	75	10	d	d	PROPN
ejpam-521	75	11	,	,	PUNCT
ejpam-521	75	12	·	·	PUNCT
ejpam-521	75	13	·	·	PUNCT
ejpam-521	75	14	·	·	PUNCT
ejpam-521	75	15	,	,	PUNCT
ejpam-521	75	16	zn	zn	X
ejpam-521	75	17	−	−	PROPN
ejpam-521	76	1	d	d	PROPN
ejpam-521	76	2	,	,	PUNCT
ejpam-521	76	3	zn	zn	PROPN
ejpam-521	76	4	+	+	CCONJ
ejpam-521	77	1	d	d	PROPN
ejpam-521	77	2	,	,	PUNCT
ejpam-521	77	3	t	t	PROPN
ejpam-521	77	4	,	,	PUNCT
ejpam-521	77	5	(	(	PUNCT
ejpam-521	77	6	7	7	X
ejpam-521	77	7	)	)	PUNCT
ejpam-521	77	8	g.	g.	NOUN
ejpam-521	77	9	qian	qian	PROPN
ejpam-521	77	10	/	/	SYM
ejpam-521	77	11	eur	eur	PROPN
ejpam-521	77	12	.	.	PUNCT
ejpam-521	78	1	j.	j.	PROPN
ejpam-521	78	2	pure	pure	PROPN
ejpam-521	78	3	appl	appl	PROPN
ejpam-521	78	4	.	.	PROPN
ejpam-521	78	5	math	math	PROPN
ejpam-521	78	6	,	,	PUNCT
ejpam-521	78	7	3	3	NUM
ejpam-521	78	8	(	(	PUNCT
ejpam-521	78	9	2010	2010	NUM
ejpam-521	78	10	)	)	PUNCT
ejpam-521	78	11	,	,	PUNCT
ejpam-521	78	12	51	51	NUM
ejpam-521	78	13	-	-	SYM
ejpam-521	78	14	80	80	NUM
ejpam-521	78	15	55	55	NUM
ejpam-521	78	16	denoted	denote	VERB
ejpam-521	78	17	as	as	ADP
ejpam-521	78	18	s(x	s(x	NOUN
ejpam-521	78	19	n	n	CCONJ
ejpam-521	78	20	)	)	PUNCT
ejpam-521	78	21	=	=	SYM
ejpam-521	78	22	s1	s1	PROPN
ejpam-521	78	23	,	,	PUNCT
ejpam-521	78	24	s2	s2	PROPN
ejpam-521	78	25	,	,	PUNCT
ejpam-521	78	26	·	·	PUNCT
ejpam-521	78	27	·	·	PUNCT
ejpam-521	78	28	·	·	PUNCT
ejpam-521	78	29	,	,	PUNCT
ejpam-521	78	30	s2n+2	s2n+2	ADV
ejpam-521	78	31	,	,	PUNCT
ejpam-521	78	32	with	with	ADP
ejpam-521	78	33	q0,m	q0,m	PROPN
ejpam-521	78	34	=	=	SYM
ejpam-521	78	35	s	s	PROPN
ejpam-521	78	36	and	and	CCONJ
ejpam-521	78	37	qm	qm	PROPN
ejpam-521	78	38	,	,	PUNCT
ejpam-521	78	39	m	m	PROPN
ejpam-521	78	40	=	=	SYM
ejpam-521	78	41	t	t	PROPN
ejpam-521	78	42	,	,	PUNCT
ejpam-521	78	43	such	such	ADJ
ejpam-521	78	44	that	that	SCONJ
ejpam-521	78	45	the	the	DET
ejpam-521	78	46	selected	select	VERB
ejpam-521	78	47	qm	qm	PROPN
ejpam-521	78	48	achieves	achieve	VERB
ejpam-521	78	49	the	the	DET
ejpam-521	78	50	largest	large	ADJ
ejpam-521	78	51	likelihood	likelihood	NOUN
ejpam-521	78	52	l1(x	l1(x	NOUN
ejpam-521	78	53	n	n	CCONJ
ejpam-521	78	54	;	;	PUNCT
ejpam-521	78	55	hm	hm	X
ejpam-521	78	56	)	)	PUNCT
ejpam-521	78	57	among	among	ADP
ejpam-521	78	58	all	all	DET
ejpam-521	78	59	the	the	DET
ejpam-521	78	60	selections	selection	NOUN
ejpam-521	78	61	.	.	PUNCT
ejpam-521	79	1	there	there	PRON
ejpam-521	79	2	are	be	VERB
ejpam-521	79	3	�	�	PROPN
ejpam-521	79	4	2n	2n	NUM
ejpam-521	79	5	m−1	m−1	PROPN
ejpam-521	79	6	�	�	PROPN
ejpam-521	79	7	different	different	ADJ
ejpam-521	79	8	selections	selection	NOUN
ejpam-521	79	9	for	for	ADP
ejpam-521	79	10	qm	qm	PROPN
ejpam-521	79	11	within	within	ADP
ejpam-521	79	12	which	which	PRON
ejpam-521	79	13	the	the	DET
ejpam-521	79	14	optimal	optimal	ADJ
ejpam-521	79	15	sequence	sequence	NOUN
ejpam-521	79	16	is	be	AUX
ejpam-521	79	17	to	to	PART
ejpam-521	79	18	be	be	AUX
ejpam-521	79	19	found	find	VERB
ejpam-521	79	20	.	.	PUNCT
ejpam-521	80	1	in	in	ADP
ejpam-521	80	2	the	the	DET
ejpam-521	80	3	following	following	NOUN
ejpam-521	80	4	we	we	PRON
ejpam-521	80	5	provide	provide	VERB
ejpam-521	80	6	a	a	DET
ejpam-521	80	7	recursive	recursive	ADJ
ejpam-521	80	8	method	method	NOUN
ejpam-521	80	9	for	for	ADP
ejpam-521	80	10	finding	find	VERB
ejpam-521	80	11	the	the	DET
ejpam-521	80	12	optimal	optimal	ADJ
ejpam-521	80	13	qm	qm	PROPN
ejpam-521	80	14	as	as	ADV
ejpam-521	80	15	well	well	ADV
ejpam-521	80	16	as	as	ADP
ejpam-521	80	17	the	the	DET
ejpam-521	80	18	associated	associated	ADJ
ejpam-521	80	19	maximum	maximum	ADJ
ejpam-521	80	20	likelihood	likelihood	NOUN
ejpam-521	80	21	value	value	NOUN
ejpam-521	80	22	.	.	PUNCT
ejpam-521	81	1	a	a	DET
ejpam-521	81	2	similar	similar	ADJ
ejpam-521	81	3	technique	technique	NOUN
ejpam-521	81	4	is	be	AUX
ejpam-521	81	5	used	use	VERB
ejpam-521	81	6	in	in	ADP
ejpam-521	81	7	[	[	X
ejpam-521	81	8	14	14	NUM
ejpam-521	81	9	]	]	PUNCT
ejpam-521	81	10	.	.	PUNCT
ejpam-521	82	1	let	let	VERB
ejpam-521	82	2	l∗1(x	l∗1(x	PROPN
ejpam-521	82	3	n	n	CCONJ
ejpam-521	82	4	;	;	PUNCT
ejpam-521	82	5	m	m	X
ejpam-521	82	6	)	)	PUNCT
ejpam-521	83	1	=	=	SYM
ejpam-521	83	2	max	max	PROPN
ejpam-521	83	3	qm⊂s(x	qm⊂s(x	NUM
ejpam-521	83	4	n	n	CCONJ
ejpam-521	83	5	)	)	PUNCT
ejpam-521	83	6	max	max	PROPN
ejpam-521	83	7	pm	pm	PROPN
ejpam-521	83	8	:	:	PUNCT
ejpam-521	83	9	∑	∑	ADV
ejpam-521	83	10	pi	pi	PROPN
ejpam-521	83	11	,	,	PUNCT
ejpam-521	83	12	m=1	m=1	PROPN
ejpam-521	83	13	l1(x	l1(x	NOUN
ejpam-521	83	14	n	n	CCONJ
ejpam-521	83	15	;	;	PUNCT
ejpam-521	83	16	hm	hm	X
ejpam-521	83	17	)	)	PUNCT
ejpam-521	83	18	=	=	SYM
ejpam-521	83	19	max	max	PROPN
ejpam-521	83	20	qm⊂s(x	qm⊂s(x	NUM
ejpam-521	83	21	n	n	CCONJ
ejpam-521	83	22	)	)	PUNCT
ejpam-521	83	23	m	m	VERB
ejpam-521	83	24	∑	∑	PROPN
ejpam-521	83	25	i=1	i=1	PROPN
ejpam-521	83	26	(	(	PUNCT
ejpam-521	83	27	ni	ni	PROPN
ejpam-521	83	28	,	,	PUNCT
ejpam-521	83	29	m+	m+	NOUN
ejpam-521	83	30	1	1	NUM
ejpam-521	83	31	)	)	PUNCT
ejpam-521	83	32	log	log	NOUN
ejpam-521	83	33	ni	ni	PROPN
ejpam-521	83	34	,	,	PUNCT
ejpam-521	83	35	m+	m+	NOUN
ejpam-521	83	36	1	1	NUM
ejpam-521	83	37	(	(	PUNCT
ejpam-521	83	38	n+m)ri	n+m)ri	PROPN
ejpam-521	83	39	,	,	PUNCT
ejpam-521	83	40	m	m	NOUN
ejpam-521	83	41	.	.	PUNCT
ejpam-521	84	1	(	(	PUNCT
ejpam-521	84	2	8)	8)	NUM
ejpam-521	84	3	it	it	PRON
ejpam-521	84	4	is	be	AUX
ejpam-521	84	5	easy	easy	ADJ
ejpam-521	84	6	to	to	PART
ejpam-521	84	7	see	see	VERB
ejpam-521	84	8	that	that	SCONJ
ejpam-521	84	9	l∗1(x	l∗1(x	PROPN
ejpam-521	84	10	n(τ	n(τ	PROPN
ejpam-521	84	11	)	)	PUNCT
ejpam-521	84	12	;	;	PUNCT
ejpam-521	84	13	m)=	m)=	NOUN
ejpam-521	84	14	max	max	PROPN
ejpam-521	84	15	sm−1≤qm−1,m∈s(x	sm−1≤qm−1,m∈s(x	PROPN
ejpam-521	84	16	n(τ	n(τ	PROPN
ejpam-521	84	17	)	)	PUNCT
ejpam-521	84	18	)	)	PUNCT
ejpam-521	85	1	(	(	PUNCT
ejpam-521	85	2	max	max	PROPN
ejpam-521	85	3	{	{	PUNCT
ejpam-521	85	4	q1,m	q1,m	PROPN
ejpam-521	85	5	,	,	PUNCT
ejpam-521	85	6	·	·	PUNCT
ejpam-521	85	7	·	·	PUNCT
ejpam-521	85	8	·	·	PUNCT
ejpam-521	85	9	,	,	PUNCT
ejpam-521	85	10	qm−2,m}∈s(x	qm−2,m}∈s(x	PROPN
ejpam-521	85	11	n(qm−1,m	n(qm−1,m	PROPN
ejpam-521	85	12	)	)	PUNCT
ejpam-521	85	13	)	)	PUNCT
ejpam-521	85	14	l1(x	l1(x	NOUN
ejpam-521	85	15	n(qm−1,m	n(qm−1,m	PROPN
ejpam-521	85	16	)	)	PUNCT
ejpam-521	85	17	;	;	PUNCT
ejpam-521	85	18	hm−1	hm−1	NOUN
ejpam-521	85	19	)	)	PUNCT
ejpam-521	86	1	+	+	PROPN
ejpam-521	86	2	(	(	PUNCT
ejpam-521	86	3	n(τ)−	n(τ)−	PROPN
ejpam-521	86	4	n(qm−1,m	n(qm−1,m	PROPN
ejpam-521	86	5	)	)	PUNCT
ejpam-521	86	6	+	+	NOUN
ejpam-521	86	7	1	1	X
ejpam-521	86	8	)	)	PUNCT
ejpam-521	86	9	log	log	NOUN
ejpam-521	86	10	n(τ)−	n(τ)−	PROPN
ejpam-521	86	11	n(qm−1,m	n(qm−1,m	PROPN
ejpam-521	86	12	)	)	PUNCT
ejpam-521	86	13	+	+	CCONJ
ejpam-521	86	14	1	1	NUM
ejpam-521	86	15	(	(	PUNCT
ejpam-521	86	16	n(τ)+m)rm	n(τ)+m)rm	PROPN
ejpam-521	86	17	,	,	PUNCT
ejpam-521	86	18	m	m	PRON
ejpam-521	86	19	«	«	PUNCT
ejpam-521	86	20	=	=	SYM
ejpam-521	86	21	max	max	PROPN
ejpam-521	87	1	sm−1≤ν∈s(x	sm−1≤ν∈s(x	ADP
ejpam-521	87	2	n(τ	n(τ	PROPN
ejpam-521	87	3	)	)	PUNCT
ejpam-521	87	4	)	)	PUNCT
ejpam-521	87	5	¨	¨	NOUN
ejpam-521	87	6	l∗1(x	l∗1(x	PROPN
ejpam-521	87	7	n(ν	n(ν	PROPN
ejpam-521	87	8	)	)	PUNCT
ejpam-521	87	9	;	;	PUNCT
ejpam-521	87	10	m−	m−	PROPN
ejpam-521	87	11	1	1	NUM
ejpam-521	87	12	)	)	PUNCT
ejpam-521	87	13	+	+	CCONJ
ejpam-521	87	14	(	(	PUNCT
ejpam-521	87	15	n(τ)−	n(τ)−	PROPN
ejpam-521	87	16	n(ν	n(ν	PROPN
ejpam-521	87	17	)	)	PUNCT
ejpam-521	87	18	+	+	NUM
ejpam-521	87	19	1	1	X
ejpam-521	87	20	)	)	PUNCT
ejpam-521	87	21	log	log	NOUN
ejpam-521	87	22	n(τ)−	n(τ)−	PROPN
ejpam-521	87	23	n(ν	n(ν	PROPN
ejpam-521	87	24	)	)	PUNCT
ejpam-521	87	25	+	+	CCONJ
ejpam-521	87	26	1	1	NUM
ejpam-521	87	27	(	(	PUNCT
ejpam-521	87	28	n(τ)+m)rm	n(τ)+m)rm	PROPN
ejpam-521	87	29	,	,	PUNCT
ejpam-521	87	30	m	m	PRON
ejpam-521	87	31	«	«	PUNCT
ejpam-521	87	32	(	(	PUNCT
ejpam-521	87	33	9	9	NUM
ejpam-521	87	34	)	)	PUNCT
ejpam-521	87	35	where	where	SCONJ
ejpam-521	87	36	x	x	SYM
ejpam-521	87	37	n(ν	n(ν	PROPN
ejpam-521	87	38	)	)	PUNCT
ejpam-521	87	39	denotes	denote	VERB
ejpam-521	87	40	the	the	DET
ejpam-521	87	41	sequence	sequence	NOUN
ejpam-521	87	42	of	of	ADP
ejpam-521	87	43	the	the	DET
ejpam-521	87	44	observations	observation	NOUN
ejpam-521	87	45	falling	fall	VERB
ejpam-521	87	46	within	within	ADP
ejpam-521	87	47	[	[	X
ejpam-521	87	48	s	s	X
ejpam-521	87	49	,	,	PUNCT
ejpam-521	87	50	ν	ν	NOUN
ejpam-521	87	51	]	]	PUNCT
ejpam-521	87	52	,	,	PUNCT
ejpam-521	87	53	and	and	CCONJ
ejpam-521	87	54	n(ν	n(ν	NOUN
ejpam-521	87	55	)	)	PUNCT
ejpam-521	87	56	denotes	denote	VERB
ejpam-521	87	57	the	the	DET
ejpam-521	87	58	number	number	NOUN
ejpam-521	87	59	of	of	ADP
ejpam-521	87	60	the	the	DET
ejpam-521	87	61	observations	observation	NOUN
ejpam-521	87	62	in	in	ADP
ejpam-521	87	63	x	x	PROPN
ejpam-521	87	64	n(ν	n(ν	PROPN
ejpam-521	87	65	)	)	PUNCT
ejpam-521	87	66	.	.	PUNCT
ejpam-521	88	1	the	the	DET
ejpam-521	88	2	recursive	recursive	ADJ
ejpam-521	88	3	equation	equation	NOUN
ejpam-521	88	4	(	(	PUNCT
ejpam-521	88	5	9	9	NUM
ejpam-521	88	6	)	)	PUNCT
ejpam-521	88	7	are	be	AUX
ejpam-521	88	8	to	to	PART
ejpam-521	88	9	be	be	AUX
ejpam-521	88	10	solved	solve	VERB
ejpam-521	88	11	for	for	ADP
ejpam-521	88	12	m	m	PROPN
ejpam-521	88	13	≥	≥	NOUN
ejpam-521	88	14	1	1	NUM
ejpam-521	88	15	and	and	CCONJ
ejpam-521	88	16	ν	ν	PROPN
ejpam-521	88	17	∈	∈	PROPN
ejpam-521	88	18	s(x	s(x	PROPN
ejpam-521	88	19	n(τ	n(τ	PROPN
ejpam-521	88	20	)	)	PUNCT
ejpam-521	88	21	)	)	PUNCT
ejpam-521	88	22	with	with	ADP
ejpam-521	88	23	τ	τ	PROPN
ejpam-521	88	24	≤	≤	PROPN
ejpam-521	88	25	t	t	NOUN
ejpam-521	88	26	until	until	SCONJ
ejpam-521	88	27	the	the	DET
ejpam-521	88	28	desired	desire	VERB
ejpam-521	88	29	range	range	NOUN
ejpam-521	88	30	includes	include	VERB
ejpam-521	88	31	all	all	DET
ejpam-521	88	32	the	the	DET
ejpam-521	88	33	observations	observation	NOUN
ejpam-521	88	34	.	.	PUNCT
ejpam-521	89	1	that	that	PRON
ejpam-521	89	2	is	be	AUX
ejpam-521	89	3	,	,	PUNCT
ejpam-521	89	4	the	the	DET
ejpam-521	89	5	following	follow	VERB
ejpam-521	89	6	maximum	maximum	ADJ
ejpam-521	89	7	log	log	NOUN
ejpam-521	89	8	-	-	PUNCT
ejpam-521	89	9	likelihood	likelihood	NOUN
ejpam-521	89	10	functions	function	NOUN
ejpam-521	89	11	need	need	VERB
ejpam-521	89	12	to	to	PART
ejpam-521	89	13	be	be	AUX
ejpam-521	89	14	solved	solve	VERB
ejpam-521	89	15	in	in	ADP
ejpam-521	89	16	sequence	sequence	NOUN
ejpam-521	89	17	l∗1(x	l∗1(x	PROPN
ejpam-521	89	18	n(s2	n(s2	NOUN
ejpam-521	89	19	)	)	PUNCT
ejpam-521	89	20	,	,	PUNCT
ejpam-521	89	21	1	1	NUM
ejpam-521	89	22	)	)	PUNCT
ejpam-521	89	23	,	,	PUNCT
ejpam-521	89	24	l∗1(x	l∗1(x	PROPN
ejpam-521	89	25	n(s3	n(s3	PROPN
ejpam-521	89	26	)	)	PUNCT
ejpam-521	89	27	,	,	PUNCT
ejpam-521	89	28	1	1	NUM
ejpam-521	89	29	)	)	PUNCT
ejpam-521	89	30	,	,	PUNCT
ejpam-521	89	31	·	·	PUNCT
ejpam-521	89	32	·	·	PUNCT
ejpam-521	89	33	·	·	PUNCT
ejpam-521	89	34	,	,	PUNCT
ejpam-521	89	35	l∗1(x	l∗1(x	PROPN
ejpam-521	89	36	n(t	n(t	PROPN
ejpam-521	89	37	)	)	PUNCT
ejpam-521	89	38	,	,	PUNCT
ejpam-521	89	39	1	1	NUM
ejpam-521	89	40	)	)	PUNCT
ejpam-521	89	41	,	,	PUNCT
ejpam-521	89	42	l∗1(x	l∗1(x	PROPN
ejpam-521	89	43	n(s3	n(s3	PROPN
ejpam-521	89	44	)	)	PUNCT
ejpam-521	89	45	,	,	PUNCT
ejpam-521	89	46	2	2	NUM
ejpam-521	89	47	)	)	PUNCT
ejpam-521	89	48	,	,	PUNCT
ejpam-521	89	49	l∗1(x	l∗1(x	PROPN
ejpam-521	89	50	n(s4	n(s4	PROPN
ejpam-521	89	51	)	)	PUNCT
ejpam-521	89	52	,	,	PUNCT
ejpam-521	89	53	2	2	NUM
ejpam-521	89	54	)	)	PUNCT
ejpam-521	89	55	,	,	PUNCT
ejpam-521	89	56	·	·	PUNCT
ejpam-521	89	57	·	·	PUNCT
ejpam-521	89	58	·	·	PUNCT
ejpam-521	89	59	,	,	PUNCT
ejpam-521	89	60	l∗1(x	l∗1(x	PROPN
ejpam-521	89	61	n(t	n(t	PROPN
ejpam-521	89	62	)	)	PUNCT
ejpam-521	89	63	,	,	PUNCT
ejpam-521	89	64	2	2	NUM
ejpam-521	89	65	)	)	PUNCT
ejpam-521	89	66	,	,	PUNCT
ejpam-521	89	67	·	·	PUNCT
ejpam-521	89	68	·	·	PUNCT
ejpam-521	89	69	·	·	PUNCT
ejpam-521	89	70	·	·	PUNCT
ejpam-521	89	71	·	·	PUNCT
ejpam-521	89	72	·	·	PUNCT
ejpam-521	89	73	(	(	PUNCT
ejpam-521	89	74	10	10	NUM
ejpam-521	89	75	)	)	PUNCT
ejpam-521	89	76	l∗1(x	l∗1(x	PROPN
ejpam-521	89	77	n(sm+1	n(sm+1	PROPN
ejpam-521	89	78	)	)	PUNCT
ejpam-521	89	79	,	,	PUNCT
ejpam-521	89	80	m	m	PROPN
ejpam-521	89	81	)	)	PUNCT
ejpam-521	89	82	,	,	PUNCT
ejpam-521	89	83	l∗1(x	l∗1(x	PROPN
ejpam-521	89	84	n(sm+2	n(sm+2	NUM
ejpam-521	89	85	)	)	PUNCT
ejpam-521	89	86	,	,	PUNCT
ejpam-521	89	87	m	m	PROPN
ejpam-521	89	88	)	)	PUNCT
ejpam-521	89	89	,	,	PUNCT
ejpam-521	89	90	·	·	PUNCT
ejpam-521	89	91	·	·	PUNCT
ejpam-521	89	92	·	·	PUNCT
ejpam-521	89	93	,	,	PUNCT
ejpam-521	89	94	l∗1(x	l∗1(x	PROPN
ejpam-521	89	95	n(t	n(t	PROPN
ejpam-521	89	96	)	)	PUNCT
ejpam-521	89	97	,	,	PUNCT
ejpam-521	89	98	m	m	PROPN
ejpam-521	89	99	)	)	PUNCT
ejpam-521	89	100	,	,	PUNCT
ejpam-521	89	101	for	for	ADP
ejpam-521	89	102	m≤	m≤	NOUN
ejpam-521	89	103	n	n	CCONJ
ejpam-521	89	104	,	,	PUNCT
ejpam-521	89	105	where	where	SCONJ
ejpam-521	89	106	l∗1(x	l∗1(x	PROPN
ejpam-521	89	107	n(si	n(si	PROPN
ejpam-521	89	108	)	)	PUNCT
ejpam-521	89	109	,	,	PUNCT
ejpam-521	89	110	1	1	X
ejpam-521	89	111	)	)	PUNCT
ejpam-521	89	112	=	=	SYM
ejpam-521	89	113	(	(	PUNCT
ejpam-521	89	114	n(si	n(si	PROPN
ejpam-521	89	115	)	)	PUNCT
ejpam-521	89	116	+	+	CCONJ
ejpam-521	89	117	1	1	X
ejpam-521	89	118	)	)	PUNCT
ejpam-521	89	119	log	log	VERB
ejpam-521	89	120	1	1	NUM
ejpam-521	89	121	si	si	NOUN
ejpam-521	89	122	−	−	PROPN
ejpam-521	89	123	s	s	PART
ejpam-521	89	124	,	,	PUNCT
ejpam-521	89	125	2≤	2≤	NUM
ejpam-521	89	126	i	i	PRON
ejpam-521	89	127	≤	≤	VERB
ejpam-521	89	128	2n	2n	NUM
ejpam-521	90	1	+	+	CCONJ
ejpam-521	90	2	2	2	NUM
ejpam-521	90	3	(	(	PUNCT
ejpam-521	90	4	11	11	NUM
ejpam-521	90	5	)	)	PUNCT
ejpam-521	90	6	and	and	CCONJ
ejpam-521	90	7	l∗1(x	l∗1(x	PROPN
ejpam-521	90	8	n(sk	n(sk	PROPN
ejpam-521	90	9	)	)	PUNCT
ejpam-521	90	10	,	,	PUNCT
ejpam-521	90	11	k−	k−	PROPN
ejpam-521	90	12	1	1	NUM
ejpam-521	90	13	)	)	PUNCT
ejpam-521	91	1	=	=	SYM
ejpam-521	91	2	k−1	k−1	PROPN
ejpam-521	91	3	∑	∑	PROPN
ejpam-521	91	4	i=1	i=1	PROPN
ejpam-521	91	5	(	(	PUNCT
ejpam-521	91	6	n(si+1)−	n(si+1)−	PROPN
ejpam-521	91	7	n(si	n(si	PROPN
ejpam-521	91	8	)	)	PUNCT
ejpam-521	92	1	+	+	CCONJ
ejpam-521	92	2	1	1	X
ejpam-521	92	3	)	)	PUNCT
ejpam-521	92	4	log	log	NOUN
ejpam-521	92	5	n(si+1)−	n(si+1)−	PROPN
ejpam-521	92	6	n(si	n(si	PROPN
ejpam-521	92	7	)	)	PUNCT
ejpam-521	93	1	+	+	CCONJ
ejpam-521	93	2	1	1	NUM
ejpam-521	93	3	(	(	PUNCT
ejpam-521	93	4	n(sk	n(sk	NUM
ejpam-521	93	5	)	)	PUNCT
ejpam-521	93	6	+	+	NUM
ejpam-521	93	7	k−	k−	NOUN
ejpam-521	93	8	1)(si+1−	1)(si+1−	NUM
ejpam-521	93	9	si	si	NOUN
ejpam-521	93	10	)	)	PUNCT
ejpam-521	93	11	,	,	PUNCT
ejpam-521	93	12	(	(	PUNCT
ejpam-521	93	13	12	12	NUM
ejpam-521	93	14	)	)	PUNCT
ejpam-521	93	15	for	for	ADP
ejpam-521	93	16	2	2	NUM
ejpam-521	93	17	≤	≤	NOUN
ejpam-521	93	18	k	k	NOUN
ejpam-521	93	19	≤	≤	PROPN
ejpam-521	93	20	n	n	PRON
ejpam-521	93	21	+	+	NOUN
ejpam-521	93	22	1	1	X
ejpam-521	93	23	.	.	X
ejpam-521	94	1	for	for	ADP
ejpam-521	94	2	any	any	DET
ejpam-521	94	3	fixed	fix	VERB
ejpam-521	94	4	m	m	PROPN
ejpam-521	94	5	≤	≤	NOUN
ejpam-521	94	6	n	n	CCONJ
ejpam-521	94	7	,	,	PUNCT
ejpam-521	94	8	the	the	DET
ejpam-521	94	9	evaluation	evaluation	NOUN
ejpam-521	94	10	of	of	ADP
ejpam-521	94	11	(	(	PUNCT
ejpam-521	94	12	9	9	NUM
ejpam-521	94	13	)	)	PUNCT
ejpam-521	94	14	gives	give	VERB
ejpam-521	94	15	the	the	DET
ejpam-521	94	16	maximum	maximum	ADJ
ejpam-521	94	17	loglikelihood	loglikelihood	NOUN
ejpam-521	94	18	for	for	ADP
ejpam-521	94	19	x	x	SYM
ejpam-521	94	20	n	n	PRON
ejpam-521	94	21	as	as	ADV
ejpam-521	94	22	well	well	ADV
ejpam-521	94	23	as	as	ADP
ejpam-521	94	24	the	the	DET
ejpam-521	94	25	optimal	optimal	ADJ
ejpam-521	94	26	partition	partition	NOUN
ejpam-521	94	27	{	{	PUNCT
ejpam-521	94	28	q̃	q̃	PROPN
ejpam-521	94	29	i	i	PROPN
ejpam-521	94	30	,	,	PUNCT
ejpam-521	94	31	m	m	VERB
ejpam-521	94	32	}	}	PUNCT
ejpam-521	94	33	with	with	ADP
ejpam-521	94	34	about	about	ADP
ejpam-521	94	35	m(4n	m(4n	ADJ
ejpam-521	94	36	+	+	NUM
ejpam-521	94	37	3	3	NUM
ejpam-521	94	38	−	−	PROPN
ejpam-521	94	39	m)/2	m)/2	PROPN
ejpam-521	94	40	≤	≤	PUNCT
ejpam-521	95	1	2m(n+	2m(n+	NUM
ejpam-521	95	2	2)−	2)−	NUM
ejpam-521	95	3	m2/2	m2/2	PROPN
ejpam-521	95	4	operations	operation	NOUN
ejpam-521	95	5	.	.	PUNCT
ejpam-521	96	1	the	the	DET
ejpam-521	96	2	corresponding	corresponding	ADJ
ejpam-521	96	3	optimal	optimal	ADJ
ejpam-521	96	4	sequence	sequence	NOUN
ejpam-521	96	5	of	of	ADP
ejpam-521	96	6	break	break	NOUN
ejpam-521	96	7	points	point	NOUN
ejpam-521	96	8	will	will	AUX
ejpam-521	96	9	be	be	AUX
ejpam-521	96	10	denoted	denote	VERB
ejpam-521	96	11	by	by	ADP
ejpam-521	96	12	q̃m	q̃m	PRON
ejpam-521	96	13	=	=	PUNCT
ejpam-521	96	14	(	(	PUNCT
ejpam-521	96	15	q̃1,m	q̃1,m	PROPN
ejpam-521	96	16	,	,	PUNCT
ejpam-521	96	17	·	·	PUNCT
ejpam-521	96	18	·	·	PUNCT
ejpam-521	96	19	·	·	PUNCT
ejpam-521	96	20	,	,	PUNCT
ejpam-521	96	21	q̃m	q̃m	PROPN
ejpam-521	96	22	,	,	PUNCT
ejpam-521	96	23	m	m	NOUN
ejpam-521	96	24	)	)	PUNCT
ejpam-521	96	25	,	,	PUNCT
ejpam-521	96	26	and	and	CCONJ
ejpam-521	96	27	the	the	DET
ejpam-521	96	28	width	width	NOUN
ejpam-521	96	29	of	of	ADP
ejpam-521	96	30	the	the	DET
ejpam-521	96	31	subintervals	subinterval	NOUN
ejpam-521	96	32	by	by	ADP
ejpam-521	96	33	r̃1,m	r̃1,m	PROPN
ejpam-521	96	34	,	,	PUNCT
ejpam-521	96	35	·	·	PUNCT
ejpam-521	96	36	·	·	PUNCT
ejpam-521	96	37	·	·	PUNCT
ejpam-521	96	38	,	,	PUNCT
ejpam-521	96	39	r̃m	r̃m	ADJ
ejpam-521	96	40	,	,	PUNCT
ejpam-521	96	41	m.	m.	NOUN
ejpam-521	96	42	in	in	ADP
ejpam-521	96	43	this	this	DET
ejpam-521	96	44	g.	g.	PROPN
ejpam-521	96	45	qian	qian	PROPN
ejpam-521	96	46	/	/	SYM
ejpam-521	96	47	eur	eur	PROPN
ejpam-521	96	48	.	.	PUNCT
ejpam-521	97	1	j.	j.	PROPN
ejpam-521	97	2	pure	pure	PROPN
ejpam-521	97	3	appl	appl	PROPN
ejpam-521	97	4	.	.	PROPN
ejpam-521	97	5	math	math	PROPN
ejpam-521	97	6	,	,	PUNCT
ejpam-521	97	7	3	3	NUM
ejpam-521	97	8	(	(	PUNCT
ejpam-521	97	9	2010	2010	NUM
ejpam-521	97	10	)	)	PUNCT
ejpam-521	97	11	,	,	PUNCT
ejpam-521	97	12	51	51	NUM
ejpam-521	97	13	-	-	SYM
ejpam-521	97	14	80	80	NUM
ejpam-521	97	15	56	56	NUM
ejpam-521	97	16	paper	paper	NOUN
ejpam-521	97	17	data	data	NOUN
ejpam-521	97	18	quantization	quantization	NOUN
ejpam-521	97	19	will	will	AUX
ejpam-521	97	20	always	always	ADV
ejpam-521	97	21	be	be	AUX
ejpam-521	97	22	based	base	VERB
ejpam-521	97	23	on	on	ADP
ejpam-521	97	24	the	the	DET
ejpam-521	97	25	optimal	optimal	ADJ
ejpam-521	97	26	partition	partition	NOUN
ejpam-521	97	27	{	{	PUNCT
ejpam-521	97	28	q̃	q̃	PROPN
ejpam-521	97	29	i	i	PROPN
ejpam-521	97	30	,	,	PUNCT
ejpam-521	97	31	m	m	VERB
ejpam-521	97	32	}	}	PUNCT
ejpam-521	97	33	(	(	PUNCT
ejpam-521	97	34	except	except	SCONJ
ejpam-521	97	35	in	in	ADP
ejpam-521	97	36	the	the	DET
ejpam-521	97	37	case	case	NOUN
ejpam-521	97	38	of	of	ADP
ejpam-521	97	39	equal	equal	ADJ
ejpam-521	97	40	width	width	ADJ
ejpam-521	97	41	quantization	quantization	NOUN
ejpam-521	97	42	)	)	PUNCT
ejpam-521	97	43	.	.	PUNCT
ejpam-521	98	1	for	for	ADP
ejpam-521	98	2	sake	sake	NOUN
ejpam-521	98	3	of	of	ADP
ejpam-521	98	4	simple	simple	ADJ
ejpam-521	98	5	presentation	presentation	NOUN
ejpam-521	98	6	the	the	DET
ejpam-521	98	7	number	number	NOUN
ejpam-521	98	8	of	of	ADP
ejpam-521	98	9	the	the	DET
ejpam-521	98	10	data	data	NOUN
ejpam-521	98	11	points	point	NOUN
ejpam-521	98	12	falling	fall	VERB
ejpam-521	98	13	into	into	ADP
ejpam-521	98	14	{	{	PUNCT
ejpam-521	98	15	q̃	q̃	PROPN
ejpam-521	98	16	i	i	PROPN
ejpam-521	98	17	,	,	PUNCT
ejpam-521	98	18	m	m	VERB
ejpam-521	98	19	}	}	PUNCT
ejpam-521	98	20	will	will	AUX
ejpam-521	98	21	still	still	ADV
ejpam-521	98	22	be	be	AUX
ejpam-521	98	23	denoted	denote	VERB
ejpam-521	98	24	as	as	ADP
ejpam-521	98	25	ni	ni	PROPN
ejpam-521	98	26	,	,	PUNCT
ejpam-521	98	27	m	m	VERB
ejpam-521	98	28	=	=	ADJ
ejpam-521	98	29	∑n	∑n	PROPN
ejpam-521	98	30	j=1	j=1	PROPN
ejpam-521	98	31	iq̃i	iq̃i	PROPN
ejpam-521	98	32	,	,	PUNCT
ejpam-521	98	33	m	m	VERB
ejpam-521	98	34	(	(	PUNCT
ejpam-521	98	35	x	x	PROPN
ejpam-521	98	36	j	j	PROPN
ejpam-521	98	37	)	)	PUNCT
ejpam-521	98	38	.	.	PUNCT
ejpam-521	99	1	with	with	ADP
ejpam-521	99	2	an	an	DET
ejpam-521	99	3	optimal	optimal	ADJ
ejpam-521	99	4	procedure	procedure	NOUN
ejpam-521	99	5	for	for	ADP
ejpam-521	99	6	the	the	DET
ejpam-521	99	7	quantization	quantization	NOUN
ejpam-521	99	8	of	of	ADP
ejpam-521	99	9	the	the	DET
ejpam-521	99	10	data	datum	NOUN
ejpam-521	99	11	,	,	PUNCT
ejpam-521	99	12	we	we	PRON
ejpam-521	99	13	are	be	AUX
ejpam-521	99	14	now	now	ADV
ejpam-521	99	15	in	in	ADP
ejpam-521	99	16	a	a	DET
ejpam-521	99	17	position	position	NOUN
ejpam-521	99	18	to	to	PART
ejpam-521	99	19	find	find	VERB
ejpam-521	99	20	the	the	DET
ejpam-521	99	21	description	description	NOUN
ejpam-521	99	22	of	of	ADP
ejpam-521	99	23	the	the	DET
ejpam-521	99	24	data	datum	NOUN
ejpam-521	99	25	x	x	X
ejpam-521	99	26	n.	n.	NOUN
ejpam-521	99	27	following	follow	VERB
ejpam-521	99	28	[	[	X
ejpam-521	99	29	13	13	NUM
ejpam-521	99	30	]	]	PUNCT
ejpam-521	99	31	,	,	PUNCT
ejpam-521	99	32	the	the	DET
ejpam-521	99	33	description	description	NOUN
ejpam-521	99	34	length	length	NOUN
ejpam-521	99	35	of	of	ADP
ejpam-521	99	36	the	the	DET
ejpam-521	99	37	data	datum	NOUN
ejpam-521	99	38	x	x	PUNCT
ejpam-521	99	39	n	n	CCONJ
ejpam-521	99	40	,	,	PUNCT
ejpam-521	99	41	for	for	ADP
ejpam-521	99	42	fixed	fixed	ADJ
ejpam-521	99	43	m	m	PROPN
ejpam-521	99	44	and	and	CCONJ
ejpam-521	99	45	corresponding	correspond	VERB
ejpam-521	99	46	q̃m	q̃m	PROPN
ejpam-521	99	47	,	,	PUNCT
ejpam-521	99	48	is	be	AUX
ejpam-521	99	49	defined	define	VERB
ejpam-521	99	50	as	as	ADP
ejpam-521	99	51	a	a	DET
ejpam-521	99	52	two	two	NUM
ejpam-521	99	53	-	-	PUNCT
ejpam-521	99	54	part	part	NOUN
ejpam-521	99	55	code	code	NOUN
ejpam-521	99	56	length	length	NOUN
ejpam-521	99	57	−l∗1(x	−l∗1(x	NOUN
ejpam-521	99	58	n	n	CCONJ
ejpam-521	99	59	;	;	PUNCT
ejpam-521	99	60	m	m	X
ejpam-521	99	61	)	)	PUNCT
ejpam-521	100	1	+	+	CCONJ
ejpam-521	100	2	l2(q̃	l2(q̃	PROPN
ejpam-521	100	3	m	m	PROPN
ejpam-521	100	4	,	,	PUNCT
ejpam-521	100	5	m	m	PROPN
ejpam-521	100	6	,	,	PUNCT
ejpam-521	100	7	δ	δ	PROPN
ejpam-521	100	8	)	)	PUNCT
ejpam-521	100	9	(	(	PUNCT
ejpam-521	100	10	13	13	NUM
ejpam-521	100	11	)	)	PUNCT
ejpam-521	100	12	where	where	SCONJ
ejpam-521	100	13	the	the	DET
ejpam-521	100	14	first	first	ADJ
ejpam-521	100	15	part	part	NOUN
ejpam-521	100	16	−l∗1(x	−l∗1(x	NOUN
ejpam-521	100	17	n	n	CCONJ
ejpam-521	100	18	;	;	PUNCT
ejpam-521	100	19	m	m	VERB
ejpam-521	100	20	)	)	PUNCT
ejpam-521	100	21	can	can	AUX
ejpam-521	100	22	be	be	AUX
ejpam-521	100	23	interpreted	interpret	VERB
ejpam-521	100	24	as	as	ADP
ejpam-521	100	25	the	the	DET
ejpam-521	100	26	code	code	NOUN
ejpam-521	100	27	length	length	NOUN
ejpam-521	100	28	needed	need	VERB
ejpam-521	100	29	to	to	PART
ejpam-521	100	30	describe	describe	VERB
ejpam-521	100	31	the	the	DET
ejpam-521	100	32	data	datum	NOUN
ejpam-521	100	33	x	x	PUNCT
ejpam-521	100	34	n	n	CCONJ
ejpam-521	100	35	under	under	ADP
ejpam-521	100	36	the	the	DET
ejpam-521	100	37	given	give	VERB
ejpam-521	100	38	partition	partition	NOUN
ejpam-521	100	39	and	and	CCONJ
ejpam-521	100	40	histogram	histogram	NOUN
ejpam-521	100	41	density	density	NOUN
ejpam-521	100	42	estimator	estimator	NOUN
ejpam-521	100	43	,	,	PUNCT
ejpam-521	100	44	and	and	CCONJ
ejpam-521	100	45	the	the	DET
ejpam-521	100	46	second	second	ADJ
ejpam-521	100	47	part	part	NOUN
ejpam-521	100	48	l2	l2	NOUN
ejpam-521	100	49	is	be	AUX
ejpam-521	100	50	the	the	DET
ejpam-521	100	51	code	code	NOUN
ejpam-521	100	52	length	length	NOUN
ejpam-521	100	53	needed	need	VERB
ejpam-521	100	54	to	to	PART
ejpam-521	100	55	describe	describe	VERB
ejpam-521	100	56	the	the	DET
ejpam-521	100	57	functional	functional	ADJ
ejpam-521	100	58	form	form	NOUN
ejpam-521	100	59	of	of	ADP
ejpam-521	100	60	the	the	DET
ejpam-521	100	61	partition	partition	NOUN
ejpam-521	100	62	and	and	CCONJ
ejpam-521	100	63	histogram	histogram	NOUN
ejpam-521	100	64	model	model	NOUN
ejpam-521	100	65	employed	employ	VERB
ejpam-521	100	66	.	.	PUNCT
ejpam-521	101	1	l2	l2	NOUN
ejpam-521	101	2	can	can	AUX
ejpam-521	101	3	be	be	AUX
ejpam-521	101	4	obtained	obtain	VERB
ejpam-521	101	5	by	by	ADP
ejpam-521	101	6	first	first	ADV
ejpam-521	101	7	truncating	truncate	VERB
ejpam-521	101	8	the	the	DET
ejpam-521	101	9	parameter	parameter	NOUN
ejpam-521	101	10	m	m	PROPN
ejpam-521	101	11	and	and	CCONJ
ejpam-521	101	12	q̃m	q̃m	ADV
ejpam-521	101	13	to	to	ADP
ejpam-521	101	14	a	a	DET
ejpam-521	101	15	prescribed	prescribed	ADJ
ejpam-521	101	16	precision	precision	NOUN
ejpam-521	101	17	δ	δ	PROPN
ejpam-521	101	18	and	and	CCONJ
ejpam-521	101	19	then	then	ADV
ejpam-521	101	20	encoding	encode	VERB
ejpam-521	101	21	the	the	DET
ejpam-521	101	22	resulting	result	VERB
ejpam-521	101	23	integers	integer	NOUN
ejpam-521	101	24	with	with	ADP
ejpam-521	101	25	the	the	DET
ejpam-521	101	26	technique	technique	NOUN
ejpam-521	101	27	introduced	introduce	VERB
ejpam-521	101	28	in	in	ADP
ejpam-521	101	29	[	[	X
ejpam-521	101	30	5	5	NUM
ejpam-521	101	31	]	]	PUNCT
ejpam-521	101	32	and	and	CCONJ
ejpam-521	101	33	[	[	X
ejpam-521	101	34	13	13	NUM
ejpam-521	101	35	]	]	PUNCT
ejpam-521	101	36	.	.	PUNCT
ejpam-521	102	1	denote	denote	VERB
ejpam-521	102	2	ā	ā	NOUN
ejpam-521	103	1	=	=	PUNCT
ejpam-521	104	1	[	[	X
ejpam-521	104	2	a	a	X
ejpam-521	104	3	/	/	SYM
ejpam-521	104	4	δ	δ	NOUN
ejpam-521	104	5	]	]	PUNCT
ejpam-521	104	6	as	as	ADP
ejpam-521	104	7	the	the	DET
ejpam-521	104	8	nearest	near	ADJ
ejpam-521	104	9	integer	integer	NOUN
ejpam-521	104	10	to	to	ADP
ejpam-521	104	11	a	a	DET
ejpam-521	104	12	/	/	SYM
ejpam-521	104	13	δ	δ	PROPN
ejpam-521	104	14	,	,	PUNCT
ejpam-521	104	15	then	then	ADV
ejpam-521	104	16	l2(q̃	l2(q̃	PROPN
ejpam-521	104	17	m	m	PROPN
ejpam-521	104	18	,	,	PUNCT
ejpam-521	104	19	m	m	PROPN
ejpam-521	104	20	,	,	PUNCT
ejpam-521	104	21	δ	δ	PROPN
ejpam-521	104	22	)	)	PUNCT
ejpam-521	104	23	=	=	PUNCT
ejpam-521	104	24	log	log	PROPN
ejpam-521	104	25	�	�	PROPN
ejpam-521	104	26	∑m−1	∑m−1	PROPN
ejpam-521	104	27	i=1	i=1	PROPN
ejpam-521	104	28	�	�	PROPN
ejpam-521	104	29	�	�	PROPN
ejpam-521	104	30	�	�	PROPN
ejpam-521	104	31	r̃i	r̃i	NOUN
ejpam-521	104	32	,	,	PUNCT
ejpam-521	104	33	m−	m−	PROPN
ejpam-521	104	34	r	r	PROPN
ejpam-521	104	35	m	m	PROPN
ejpam-521	104	36	�	�	PROPN
ejpam-521	104	37	�	�	PROPN
ejpam-521	104	38	�	�	PROPN
ejpam-521	104	39	+	+	PROPN
ejpam-521	104	40	m−	m−	PROPN
ejpam-521	104	41	2	2	NUM
ejpam-521	104	42	m−	m−	PROPN
ejpam-521	104	43	2	2	NUM
ejpam-521	104	44	�	�	PROPN
ejpam-521	104	45	+	+	CCONJ
ejpam-521	104	46	log2.865	log2.865	ADJ
ejpam-521	104	47	+	+	CCONJ
ejpam-521	104	48	log∗(m̄+	log∗(m̄+	NOUN
ejpam-521	104	49	|s̄|+	|s̄|+	VERB
ejpam-521	104	50	r̄	r̄	NOUN
ejpam-521	104	51	+	+	CCONJ
ejpam-521	104	52	1	1	NUM
ejpam-521	104	53	)	)	PUNCT
ejpam-521	104	54	+	+	CCONJ
ejpam-521	104	55	log	log	NOUN
ejpam-521	104	56	(	(	PUNCT
ejpam-521	104	57	m̄+	m̄+	NOUN
ejpam-521	104	58	|s̄|+	|s̄|+	ADP
ejpam-521	104	59	r̄	r̄	NOUN
ejpam-521	104	60	+	+	CCONJ
ejpam-521	104	61	3	3	NUM
ejpam-521	104	62	)	)	PUNCT
ejpam-521	104	63	!	!	PUNCT
ejpam-521	105	1	(	(	PUNCT
ejpam-521	105	2	m̄+	m̄+	NOUN
ejpam-521	105	3	|s̄|+	|s̄|+	VERB
ejpam-521	105	4	r̄)!2	r̄)!2	NOUN
ejpam-521	105	5	!	!	PUNCT
ejpam-521	106	1	+	+	CCONJ
ejpam-521	106	2	log	log	NOUN
ejpam-521	106	3	4	4	NUM
ejpam-521	106	4	!	!	PUNCT
ejpam-521	107	1	a+!(3−	a+!(3−	PROPN
ejpam-521	107	2	a+	a+	NOUN
ejpam-521	107	3	)	)	PUNCT
ejpam-521	107	4	!	!	PUNCT
ejpam-521	108	1	+	+	CCONJ
ejpam-521	108	2	|	|	ADV
ejpam-521	108	3	logδ|	logδ|	NOUN
ejpam-521	108	4	.	.	PUNCT
ejpam-521	109	1	(	(	PUNCT
ejpam-521	109	2	14	14	NUM
ejpam-521	109	3	)	)	PUNCT
ejpam-521	109	4	here	here	ADV
ejpam-521	109	5	log∗(a	log∗(a	X
ejpam-521	109	6	)	)	PUNCT
ejpam-521	109	7	=	=	VERB
ejpam-521	109	8	log	log	NOUN
ejpam-521	109	9	a+	a+	PUNCT
ejpam-521	109	10	log	log	NOUN
ejpam-521	109	11	log	log	NOUN
ejpam-521	109	12	a+	a+	PUNCT
ejpam-521	109	13	·	·	PUNCT
ejpam-521	109	14	·	·	PUNCT
ejpam-521	109	15	·	·	PUNCT
ejpam-521	109	16	,	,	PUNCT
ejpam-521	109	17	with	with	ADP
ejpam-521	109	18	the	the	DET
ejpam-521	109	19	sum	sum	NOUN
ejpam-521	109	20	including	include	VERB
ejpam-521	109	21	all	all	DET
ejpam-521	109	22	the	the	DET
ejpam-521	109	23	positive	positive	ADJ
ejpam-521	109	24	iterates	iterate	NOUN
ejpam-521	109	25	,	,	PUNCT
ejpam-521	109	26	and	and	CCONJ
ejpam-521	109	27	a+	a+	PUNCT
ejpam-521	109	28	is	be	AUX
ejpam-521	109	29	the	the	DET
ejpam-521	109	30	number	number	NOUN
ejpam-521	109	31	of	of	ADP
ejpam-521	109	32	nonnegative	nonnegative	ADJ
ejpam-521	109	33	items	item	NOUN
ejpam-521	109	34	in	in	ADP
ejpam-521	109	35	{	{	PUNCT
ejpam-521	109	36	m̄	m̄	NOUN
ejpam-521	109	37	,	,	PUNCT
ejpam-521	109	38	s̄	s̄	NOUN
ejpam-521	109	39	,	,	PUNCT
ejpam-521	109	40	r̄	r̄	NOUN
ejpam-521	109	41	}	}	PUNCT
ejpam-521	109	42	.	.	PUNCT
ejpam-521	110	1	the	the	DET
ejpam-521	110	2	length	length	NOUN
ejpam-521	110	3	function	function	NOUN
ejpam-521	110	4	(	(	PUNCT
ejpam-521	110	5	14	14	NUM
ejpam-521	110	6	)	)	PUNCT
ejpam-521	110	7	consists	consist	VERB
ejpam-521	110	8	of	of	ADP
ejpam-521	110	9	three	three	NUM
ejpam-521	110	10	parts	part	NOUN
ejpam-521	110	11	.	.	PUNCT
ejpam-521	111	1	since	since	SCONJ
ejpam-521	111	2	the	the	DET
ejpam-521	111	3	encoding	encoding	NOUN
ejpam-521	111	4	of	of	ADP
ejpam-521	111	5	q̃m	q̃m	PRON
ejpam-521	111	6	is	be	AUX
ejpam-521	111	7	equivalent	equivalent	ADJ
ejpam-521	111	8	to	to	ADP
ejpam-521	111	9	the	the	DET
ejpam-521	111	10	encoding	encoding	NOUN
ejpam-521	111	11	of	of	ADP
ejpam-521	111	12	r̃1,m	r̃1,m	PROPN
ejpam-521	111	13	−	−	NOUN
ejpam-521	112	1	r	r	NOUN
ejpam-521	112	2	/	/	SYM
ejpam-521	112	3	m	m	PROPN
ejpam-521	112	4	,	,	PUNCT
ejpam-521	112	5	·	·	PUNCT
ejpam-521	112	6	·	·	PUNCT
ejpam-521	112	7	·	·	PUNCT
ejpam-521	112	8	,	,	PUNCT
ejpam-521	112	9	r̃m−1,m	r̃m−1,m	NOUN
ejpam-521	112	10	−	−	PUNCT
ejpam-521	113	1	r	r	X
ejpam-521	113	2	/	/	SYM
ejpam-521	113	3	m	m	PROPN
ejpam-521	113	4	,	,	PUNCT
ejpam-521	113	5	this	this	PRON
ejpam-521	113	6	will	will	AUX
ejpam-521	113	7	be	be	AUX
ejpam-521	113	8	achieved	achieve	VERB
ejpam-521	113	9	by	by	ADP
ejpam-521	113	10	a	a	DET
ejpam-521	113	11	binary	binary	ADJ
ejpam-521	113	12	string	string	NOUN
ejpam-521	113	13	beginning	begin	VERB
ejpam-521	113	14	with	with	ADP
ejpam-521	113	15	r̃1,m−	r̃1,m−	ADJ
ejpam-521	113	16	r	r	NOUN
ejpam-521	113	17	/	/	SYM
ejpam-521	113	18	m	m	NOUN
ejpam-521	113	19	0	0	NUM
ejpam-521	113	20	’s	’s	NOUN
ejpam-521	113	21	and	and	CCONJ
ejpam-521	113	22	a	a	DET
ejpam-521	113	23	1	1	NUM
ejpam-521	113	24	,	,	PUNCT
ejpam-521	113	25	followed	follow	VERB
ejpam-521	113	26	by	by	ADP
ejpam-521	113	27	r̃2,m	r̃2,m	NOUN
ejpam-521	113	28	−	−	NOUN
ejpam-521	113	29	r	r	NOUN
ejpam-521	113	30	/	/	SYM
ejpam-521	113	31	m	m	NOUN
ejpam-521	113	32	0	0	NUM
ejpam-521	113	33	’s	’s	NOUN
ejpam-521	113	34	and	and	CCONJ
ejpam-521	113	35	a	a	DET
ejpam-521	113	36	1	1	NUM
ejpam-521	113	37	,	,	PUNCT
ejpam-521	113	38	and	and	CCONJ
ejpam-521	113	39	so	so	ADV
ejpam-521	113	40	on	on	ADV
ejpam-521	113	41	until	until	ADP
ejpam-521	113	42	r̃m−1,m−	r̃m−1,m−	ADJ
ejpam-521	113	43	r	r	NOUN
ejpam-521	113	44	/	/	SYM
ejpam-521	113	45	m	m	NOUN
ejpam-521	113	46	0	0	NUM
ejpam-521	113	47	’s	’s	PART
ejpam-521	113	48	being	be	AUX
ejpam-521	113	49	added	add	VERB
ejpam-521	113	50	,	,	PUNCT
ejpam-521	113	51	but	but	CCONJ
ejpam-521	113	52	without	without	ADP
ejpam-521	113	53	attaching	attach	VERB
ejpam-521	113	54	a	a	DET
ejpam-521	113	55	1	1	NUM
ejpam-521	113	56	at	at	ADP
ejpam-521	113	57	the	the	DET
ejpam-521	113	58	end	end	NOUN
ejpam-521	113	59	,	,	PUNCT
ejpam-521	113	60	provided	provide	VERB
ejpam-521	113	61	that	that	SCONJ
ejpam-521	113	62	m	m	PROPN
ejpam-521	113	63	,	,	PUNCT
ejpam-521	113	64	s	s	PROPN
ejpam-521	113	65	,	,	PUNCT
ejpam-521	113	66	t	t	PROPN
ejpam-521	113	67	and	and	CCONJ
ejpam-521	113	68	d	d	PROPN
ejpam-521	113	69	are	be	AUX
ejpam-521	113	70	given	give	VERB
ejpam-521	113	71	.	.	PUNCT
ejpam-521	114	1	under	under	ADP
ejpam-521	114	2	this	this	DET
ejpam-521	114	3	non	non	ADJ
ejpam-521	114	4	-	-	ADJ
ejpam-521	114	5	prefix	prefix	ADJ
ejpam-521	114	6	encoding	encoding	NOUN
ejpam-521	114	7	procedure	procedure	NOUN
ejpam-521	114	8	the	the	DET
ejpam-521	114	9	first	first	ADJ
ejpam-521	114	10	term	term	NOUN
ejpam-521	114	11	of	of	ADP
ejpam-521	114	12	(	(	PUNCT
ejpam-521	114	13	14	14	NUM
ejpam-521	114	14	)	)	PUNCT
ejpam-521	114	15	gives	give	VERB
ejpam-521	114	16	the	the	DET
ejpam-521	114	17	code	code	NOUN
ejpam-521	114	18	length	length	NOUN
ejpam-521	114	19	of	of	ADP
ejpam-521	114	20	q̃m	q̃m	PROPN
ejpam-521	114	21	.	.	PUNCT
ejpam-521	115	1	the	the	DET
ejpam-521	115	2	second	second	ADJ
ejpam-521	115	3	to	to	ADP
ejpam-521	115	4	the	the	DET
ejpam-521	115	5	fifth	fifth	ADJ
ejpam-521	115	6	terms	term	NOUN
ejpam-521	115	7	of	of	ADP
ejpam-521	115	8	(	(	PUNCT
ejpam-521	115	9	14	14	NUM
ejpam-521	115	10	)	)	PUNCT
ejpam-521	115	11	are	be	AUX
ejpam-521	115	12	the	the	DET
ejpam-521	115	13	code	code	NOUN
ejpam-521	115	14	length	length	NOUN
ejpam-521	115	15	needed	need	VERB
ejpam-521	115	16	for	for	ADP
ejpam-521	115	17	encoding	encode	VERB
ejpam-521	115	18	m̄	m̄	NOUN
ejpam-521	115	19	,	,	PUNCT
ejpam-521	115	20	s̄	s̄	NOUN
ejpam-521	115	21	and	and	CCONJ
ejpam-521	115	22	t̄	t̄	PROPN
ejpam-521	115	23	(	(	PUNCT
ejpam-521	115	24	equivalent	equivalent	ADJ
ejpam-521	115	25	to	to	PART
ejpam-521	115	26	m̄	m̄	VERB
ejpam-521	115	27	,	,	PUNCT
ejpam-521	115	28	s̄	s̄	NOUN
ejpam-521	115	29	and	and	CCONJ
ejpam-521	115	30	r̄	r̄	NOUN
ejpam-521	115	31	)	)	PUNCT
ejpam-521	115	32	in	in	ADP
ejpam-521	115	33	a	a	DET
ejpam-521	115	34	prefix	prefix	NOUN
ejpam-521	115	35	manner	manner	NOUN
ejpam-521	115	36	.	.	PUNCT
ejpam-521	116	1	in	in	ADP
ejpam-521	116	2	general	general	ADJ
ejpam-521	116	3	we	we	PRON
ejpam-521	116	4	can	can	AUX
ejpam-521	116	5	encode	encode	VERB
ejpam-521	116	6	a	a	DET
ejpam-521	116	7	set	set	NOUN
ejpam-521	116	8	of	of	ADP
ejpam-521	116	9	integers	integer	NOUN
ejpam-521	116	10	{	{	PUNCT
ejpam-521	116	11	θ1	θ1	NOUN
ejpam-521	116	12	,	,	PUNCT
ejpam-521	116	13	·	·	PUNCT
ejpam-521	116	14	·	·	PUNCT
ejpam-521	116	15	·	·	PUNCT
ejpam-521	116	16	,	,	PUNCT
ejpam-521	116	17	θb	θb	ADP
ejpam-521	116	18	}	}	PUNCT
ejpam-521	116	19	in	in	ADP
ejpam-521	116	20	a	a	DET
ejpam-521	116	21	prefix	prefix	NOUN
ejpam-521	116	22	manner	manner	NOUN
ejpam-521	116	23	with	with	ADP
ejpam-521	116	24	about	about	ADP
ejpam-521	116	25	l3(θ1	l3(θ1	PROPN
ejpam-521	116	26	,	,	PUNCT
ejpam-521	116	27	·	·	PUNCT
ejpam-521	116	28	·	·	PUNCT
ejpam-521	116	29	·	·	PUNCT
ejpam-521	116	30	,	,	PUNCT
ejpam-521	116	31	θb	θb	NOUN
ejpam-521	116	32	)	)	PUNCT
ejpam-521	116	33	=	=	PUNCT
ejpam-521	117	1	log2.865	log2.865	X
ejpam-521	117	2	+	+	X
ejpam-521	117	3	log∗(θ	log∗(θ	ADJ
ejpam-521	117	4	+	+	CCONJ
ejpam-521	117	5	1)+	1)+	NUM
ejpam-521	117	6	log	log	NOUN
ejpam-521	117	7	(	(	PUNCT
ejpam-521	117	8	θ	θ	PROPN
ejpam-521	117	9	+	+	PROPN
ejpam-521	117	10	b	b	NOUN
ejpam-521	117	11	)	)	PUNCT
ejpam-521	117	12	!	!	PUNCT
ejpam-521	118	1	θ	θ	PROPN
ejpam-521	118	2	!	!	PUNCT
ejpam-521	119	1	(	(	PUNCT
ejpam-521	119	2	b−	b−	NOUN
ejpam-521	119	3	1	1	NUM
ejpam-521	119	4	)	)	PUNCT
ejpam-521	119	5	!	!	PUNCT
ejpam-521	120	1	+	+	CCONJ
ejpam-521	120	2	log	log	NOUN
ejpam-521	120	3	(	(	PUNCT
ejpam-521	120	4	b+	b+	X
ejpam-521	120	5	1	1	NUM
ejpam-521	120	6	)	)	PUNCT
ejpam-521	120	7	!	!	PUNCT
ejpam-521	121	1	b+!(b−	b+!(b−	NOUN
ejpam-521	121	2	b+	b+	NOUN
ejpam-521	121	3	)	)	PUNCT
ejpam-521	121	4	!	!	PUNCT
ejpam-521	122	1	(	(	PUNCT
ejpam-521	122	2	15	15	NUM
ejpam-521	122	3	)	)	PUNCT
ejpam-521	122	4	bits	bit	NOUN
ejpam-521	122	5	.	.	PUNCT
ejpam-521	123	1	here	here	ADV
ejpam-521	123	2	θ	θ	X
ejpam-521	124	1	=	=	PUNCT
ejpam-521	124	2	∑	∑	PUNCT
ejpam-521	124	3	i	i	PRON
ejpam-521	124	4	|θi|	|θi|	PROPN
ejpam-521	124	5	,	,	PUNCT
ejpam-521	124	6	and	and	CCONJ
ejpam-521	124	7	b+	b+	X
ejpam-521	124	8	is	be	AUX
ejpam-521	124	9	the	the	DET
ejpam-521	124	10	number	number	NOUN
ejpam-521	124	11	of	of	ADP
ejpam-521	124	12	nonnegative	nonnegative	ADJ
ejpam-521	124	13	items	item	NOUN
ejpam-521	124	14	in	in	ADP
ejpam-521	124	15	{	{	PUNCT
ejpam-521	124	16	θ1	θ1	NOUN
ejpam-521	124	17	,	,	PUNCT
ejpam-521	124	18	·	·	PUNCT
ejpam-521	124	19	·	·	PUNCT
ejpam-521	124	20	·	·	PUNCT
ejpam-521	124	21	,	,	PUNCT
ejpam-521	124	22	θb	θb	NOUN
ejpam-521	124	23	}	}	PUNCT
ejpam-521	124	24	.	.	PUNCT
ejpam-521	125	1	the	the	DET
ejpam-521	125	2	last	last	ADJ
ejpam-521	125	3	term	term	NOUN
ejpam-521	125	4	of	of	ADP
ejpam-521	125	5	(	(	PUNCT
ejpam-521	125	6	14	14	NUM
ejpam-521	125	7	)	)	PUNCT
ejpam-521	125	8	gives	give	VERB
ejpam-521	125	9	us	we	PRON
ejpam-521	125	10	the	the	DET
ejpam-521	125	11	code	code	NOUN
ejpam-521	125	12	length	length	NOUN
ejpam-521	125	13	for	for	ADP
ejpam-521	125	14	encoding	encode	VERB
ejpam-521	125	15	the	the	DET
ejpam-521	125	16	truncation	truncation	NOUN
ejpam-521	125	17	precision	precision	NOUN
ejpam-521	125	18	δ	δ	PROPN
ejpam-521	125	19	.	.	PUNCT
ejpam-521	126	1	since	since	SCONJ
ejpam-521	126	2	a+	a+	PRON
ejpam-521	126	3	equals	equal	VERB
ejpam-521	126	4	either	either	PRON
ejpam-521	126	5	2	2	NUM
ejpam-521	126	6	or	or	CCONJ
ejpam-521	126	7	3	3	NUM
ejpam-521	126	8	,	,	PUNCT
ejpam-521	126	9	the	the	DET
ejpam-521	126	10	fifth	fifth	ADJ
ejpam-521	126	11	term	term	NOUN
ejpam-521	126	12	of	of	ADP
ejpam-521	126	13	(	(	PUNCT
ejpam-521	126	14	14	14	NUM
ejpam-521	126	15	)	)	PUNCT
ejpam-521	126	16	can	can	AUX
ejpam-521	126	17	be	be	AUX
ejpam-521	126	18	replaced	replace	VERB
ejpam-521	126	19	by	by	ADP
ejpam-521	126	20	1	1	NUM
ejpam-521	126	21	reflecting	reflect	VERB
ejpam-521	126	22	the	the	DET
ejpam-521	126	23	fact	fact	NOUN
ejpam-521	126	24	that	that	SCONJ
ejpam-521	126	25	one	one	NUM
ejpam-521	126	26	digit	digit	NOUN
ejpam-521	126	27	is	be	AUX
ejpam-521	126	28	needed	need	VERB
ejpam-521	126	29	to	to	PART
ejpam-521	126	30	tell	tell	VERB
ejpam-521	126	31	if	if	SCONJ
ejpam-521	126	32	s̄	s̄	NOUN
ejpam-521	126	33	is	be	AUX
ejpam-521	126	34	negative	negative	ADJ
ejpam-521	126	35	or	or	CCONJ
ejpam-521	126	36	nonnegative	nonnegative	ADJ
ejpam-521	126	37	.	.	PUNCT
ejpam-521	127	1	with	with	ADP
ejpam-521	127	2	the	the	DET
ejpam-521	127	3	description	description	NOUN
ejpam-521	127	4	length	length	NOUN
ejpam-521	127	5	defined	define	VERB
ejpam-521	127	6	by	by	ADP
ejpam-521	127	7	(	(	PUNCT
ejpam-521	127	8	13	13	NUM
ejpam-521	127	9	)	)	PUNCT
ejpam-521	127	10	the	the	DET
ejpam-521	127	11	shortest	short	ADJ
ejpam-521	127	12	code	code	NOUN
ejpam-521	127	13	length	length	NOUN
ejpam-521	127	14	for	for	ADP
ejpam-521	127	15	the	the	DET
ejpam-521	127	16	data	datum	NOUN
ejpam-521	127	17	x	x	PUNCT
ejpam-521	127	18	n	n	CCONJ
ejpam-521	127	19	by	by	ADP
ejpam-521	127	20	the	the	DET
ejpam-521	127	21	above	above	ADJ
ejpam-521	127	22	coding	code	VERB
ejpam-521	127	23	procedure	procedure	NOUN
ejpam-521	127	24	is	be	AUX
ejpam-521	127	25	min	min	NOUN
ejpam-521	127	26	m	m	ADJ
ejpam-521	127	27	{	{	PUNCT
ejpam-521	127	28	−l∗1(x	−l∗1(x	NOUN
ejpam-521	127	29	n	n	CCONJ
ejpam-521	127	30	;	;	PUNCT
ejpam-521	127	31	m	m	X
ejpam-521	127	32	)	)	PUNCT
ejpam-521	128	1	+	+	CCONJ
ejpam-521	128	2	l2(q̃	l2(q̃	PROPN
ejpam-521	128	3	m	m	PROPN
ejpam-521	128	4	,	,	PUNCT
ejpam-521	128	5	m	m	PROPN
ejpam-521	128	6	,	,	PUNCT
ejpam-521	128	7	δ	δ	PROPN
ejpam-521	128	8	)	)	PUNCT
ejpam-521	128	9	}	}	PUNCT
ejpam-521	128	10	g.	g.	PROPN
ejpam-521	128	11	qian	qian	PROPN
ejpam-521	128	12	/	/	SYM
ejpam-521	128	13	eur	eur	PROPN
ejpam-521	128	14	.	.	PUNCT
ejpam-521	129	1	j.	j.	PROPN
ejpam-521	129	2	pure	pure	PROPN
ejpam-521	129	3	appl	appl	PROPN
ejpam-521	129	4	.	.	PROPN
ejpam-521	129	5	math	math	PROPN
ejpam-521	129	6	,	,	PUNCT
ejpam-521	129	7	3	3	NUM
ejpam-521	129	8	(	(	PUNCT
ejpam-521	129	9	2010	2010	NUM
ejpam-521	129	10	)	)	PUNCT
ejpam-521	129	11	,	,	PUNCT
ejpam-521	129	12	51	51	NUM
ejpam-521	129	13	-	-	SYM
ejpam-521	129	14	80	80	NUM
ejpam-521	129	15	57	57	NUM
ejpam-521	129	16	=	=	SYM
ejpam-521	129	17	−	−	NOUN
ejpam-521	129	18	m∗	m∗	VERB
ejpam-521	129	19	∑	∑	PROPN
ejpam-521	129	20	i=1	i=1	PROPN
ejpam-521	129	21	(	(	PUNCT
ejpam-521	129	22	ni	ni	PROPN
ejpam-521	129	23	,	,	PUNCT
ejpam-521	129	24	m∗	m∗	VERB
ejpam-521	129	25	+	+	CCONJ
ejpam-521	129	26	1	1	X
ejpam-521	129	27	)	)	PUNCT
ejpam-521	129	28	log	log	NOUN
ejpam-521	129	29	ni	ni	PROPN
ejpam-521	129	30	,	,	PUNCT
ejpam-521	129	31	m∗	m∗	VERB
ejpam-521	129	32	+	+	X
ejpam-521	129	33	1	1	NUM
ejpam-521	129	34	(	(	PUNCT
ejpam-521	129	35	n+m∗)r̃i	n+m∗)r̃i	ADV
ejpam-521	129	36	,	,	PUNCT
ejpam-521	129	37	m∗	m∗	NOUN
ejpam-521	129	38	+	+	CCONJ
ejpam-521	130	1	l2(q̃	l2(q̃	PROPN
ejpam-521	130	2	m∗	m∗	NOUN
ejpam-521	130	3	,	,	PUNCT
ejpam-521	130	4	m∗,δ	m∗,δ	PROPN
ejpam-521	130	5	)	)	PUNCT
ejpam-521	130	6	(	(	PUNCT
ejpam-521	130	7	16	16	NUM
ejpam-521	130	8	)	)	PUNCT
ejpam-521	130	9	where	where	SCONJ
ejpam-521	130	10	the	the	DET
ejpam-521	130	11	minimization	minimization	NOUN
ejpam-521	130	12	is	be	AUX
ejpam-521	130	13	done	do	VERB
ejpam-521	130	14	by	by	ADP
ejpam-521	130	15	searching	search	VERB
ejpam-521	130	16	for	for	ADP
ejpam-521	130	17	an	an	DET
ejpam-521	130	18	optimal	optimal	ADJ
ejpam-521	130	19	integer	integer	NOUN
ejpam-521	130	20	m∗	m∗	VERB
ejpam-521	130	21	≤	≤	NOUN
ejpam-521	130	22	n	n	PRON
ejpam-521	130	23	and	and	CCONJ
ejpam-521	130	24	δ	δ	PROPN
ejpam-521	130	25	is	be	AUX
ejpam-521	130	26	a	a	DET
ejpam-521	130	27	prescribed	prescribed	ADJ
ejpam-521	130	28	precision	precision	NOUN
ejpam-521	130	29	.	.	PUNCT
ejpam-521	131	1	if	if	SCONJ
ejpam-521	131	2	the	the	DET
ejpam-521	131	3	sequence	sequence	NOUN
ejpam-521	131	4	of	of	ADP
ejpam-521	131	5	break	break	NOUN
ejpam-521	131	6	points	point	NOUN
ejpam-521	131	7	are	be	AUX
ejpam-521	131	8	distributed	distribute	VERB
ejpam-521	131	9	uniformly	uniformly	ADV
ejpam-521	131	10	in	in	ADP
ejpam-521	131	11	the	the	DET
ejpam-521	131	12	interval	interval	NOUN
ejpam-521	131	13	[	[	X
ejpam-521	131	14	s	s	X
ejpam-521	131	15	,	,	PUNCT
ejpam-521	131	16	t	t	PROPN
ejpam-521	131	17	]	]	PUNCT
ejpam-521	131	18	,	,	PUNCT
ejpam-521	131	19	then	then	ADV
ejpam-521	131	20	r̃i	r̃i	NOUN
ejpam-521	131	21	,	,	PUNCT
ejpam-521	131	22	m	m	VERB
ejpam-521	131	23	=	=	SYM
ejpam-521	131	24	r	r	X
ejpam-521	131	25	/	/	SYM
ejpam-521	131	26	m	m	PROPN
ejpam-521	131	27	and	and	CCONJ
ejpam-521	131	28	the	the	DET
ejpam-521	131	29	first	first	ADJ
ejpam-521	131	30	term	term	NOUN
ejpam-521	131	31	of	of	ADP
ejpam-521	131	32	(	(	PUNCT
ejpam-521	131	33	14	14	NUM
ejpam-521	131	34	)	)	PUNCT
ejpam-521	131	35	becomes	become	VERB
ejpam-521	131	36	zero	zero	NUM
ejpam-521	131	37	.	.	PUNCT
ejpam-521	132	1	the	the	DET
ejpam-521	132	2	code	code	NOUN
ejpam-521	132	3	length	length	NOUN
ejpam-521	132	4	(	(	PUNCT
ejpam-521	132	5	16	16	NUM
ejpam-521	132	6	)	)	PUNCT
ejpam-521	132	7	turns	turn	VERB
ejpam-521	132	8	out	out	ADP
ejpam-521	132	9	to	to	PART
ejpam-521	132	10	be	be	AUX
ejpam-521	132	11	min	min	PROPN
ejpam-521	132	12	m	m	PROPN
ejpam-521	132	13	(	(	PUNCT
ejpam-521	132	14	−	−	PROPN
ejpam-521	132	15	m	m	PROPN
ejpam-521	132	16	∑	∑	PROPN
ejpam-521	132	17	i=1	i=1	PROPN
ejpam-521	132	18	(	(	PUNCT
ejpam-521	132	19	ni	ni	PROPN
ejpam-521	132	20	,	,	PUNCT
ejpam-521	132	21	m+	m+	NOUN
ejpam-521	132	22	1	1	NUM
ejpam-521	132	23	)	)	PUNCT
ejpam-521	132	24	log	log	NOUN
ejpam-521	132	25	(	(	PUNCT
ejpam-521	132	26	ni	ni	PROPN
ejpam-521	132	27	,	,	PUNCT
ejpam-521	132	28	m+	m+	NUM
ejpam-521	132	29	1)m	1)m	NUM
ejpam-521	132	30	(	(	PUNCT
ejpam-521	132	31	n+m)r	n+m)r	PROPN
ejpam-521	132	32	+	+	CCONJ
ejpam-521	132	33	l3(m	l3(m	ADJ
ejpam-521	132	34	,	,	PUNCT
ejpam-521	132	35	s̄	s̄	NOUN
ejpam-521	132	36	,	,	PUNCT
ejpam-521	132	37	r̄	r̄	NOUN
ejpam-521	132	38	)	)	PUNCT
ejpam-521	132	39	+	+	CCONJ
ejpam-521	133	1	|	|	ADV
ejpam-521	133	2	logδ|	logδ|	NOUN
ejpam-521	133	3	)	)	PUNCT
ejpam-521	133	4	.	.	PUNCT
ejpam-521	134	1	(	(	PUNCT
ejpam-521	134	2	17	17	NUM
ejpam-521	134	3	)	)	PUNCT
ejpam-521	134	4	an	an	DET
ejpam-521	134	5	alternative	alternative	NOUN
ejpam-521	134	6	to	to	ADP
ejpam-521	134	7	(	(	PUNCT
ejpam-521	134	8	16	16	NUM
ejpam-521	134	9	)	)	PUNCT
ejpam-521	134	10	is	be	AUX
ejpam-521	134	11	to	to	PART
ejpam-521	134	12	use	use	VERB
ejpam-521	134	13	the	the	DET
ejpam-521	134	14	idea	idea	NOUN
ejpam-521	134	15	of	of	ADP
ejpam-521	134	16	the	the	DET
ejpam-521	134	17	shortest	short	ADJ
ejpam-521	134	18	predictive	predictive	ADJ
ejpam-521	134	19	code	code	NOUN
ejpam-521	134	20	length	length	NOUN
ejpam-521	134	21	.	.	PUNCT
ejpam-521	135	1	this	this	DET
ejpam-521	135	2	idea	idea	NOUN
ejpam-521	135	3	involves	involve	VERB
ejpam-521	135	4	the	the	DET
ejpam-521	135	5	ordering	ordering	NOUN
ejpam-521	135	6	of	of	ADP
ejpam-521	135	7	the	the	DET
ejpam-521	135	8	data	datum	NOUN
ejpam-521	135	9	x	x	PUNCT
ejpam-521	135	10	n	n	CCONJ
ejpam-521	135	11	,	,	PUNCT
ejpam-521	135	12	either	either	CCONJ
ejpam-521	135	13	by	by	ADP
ejpam-521	135	14	location	location	NOUN
ejpam-521	135	15	or	or	CCONJ
ejpam-521	135	16	by	by	ADP
ejpam-521	135	17	time	time	NOUN
ejpam-521	135	18	of	of	ADP
ejpam-521	135	19	arrival	arrival	NOUN
ejpam-521	135	20	,	,	PUNCT
ejpam-521	135	21	then	then	ADV
ejpam-521	135	22	finding	find	VERB
ejpam-521	135	23	the	the	DET
ejpam-521	135	24	histogram	histogram	NOUN
ejpam-521	135	25	density	density	NOUN
ejpam-521	135	26	estimate	estimate	NOUN
ejpam-521	135	27	based	base	VERB
ejpam-521	135	28	on	on	ADP
ejpam-521	135	29	the	the	DET
ejpam-521	135	30	past	past	NOUN
ejpam-521	135	31	and	and	CCONJ
ejpam-521	135	32	making	make	VERB
ejpam-521	135	33	appropriate	appropriate	ADJ
ejpam-521	135	34	modifications	modification	NOUN
ejpam-521	135	35	each	each	DET
ejpam-521	135	36	time	time	NOUN
ejpam-521	135	37	a	a	DET
ejpam-521	135	38	new	new	ADJ
ejpam-521	135	39	observation	observation	NOUN
ejpam-521	135	40	comes	come	VERB
ejpam-521	135	41	[	[	X
ejpam-521	135	42	13	13	NUM
ejpam-521	135	43	,	,	PUNCT
ejpam-521	135	44	20	20	NUM
ejpam-521	135	45	]	]	PUNCT
ejpam-521	135	46	.	.	PUNCT
ejpam-521	136	1	in	in	ADP
ejpam-521	136	2	our	our	PRON
ejpam-521	136	3	situation	situation	NOUN
ejpam-521	136	4	the	the	DET
ejpam-521	136	5	data	datum	NOUN
ejpam-521	136	6	x	x	PUNCT
ejpam-521	136	7	n	n	X
ejpam-521	136	8	is	be	AUX
ejpam-521	136	9	ordered	order	VERB
ejpam-521	136	10	by	by	ADP
ejpam-521	136	11	location	location	NOUN
ejpam-521	136	12	,	,	PUNCT
ejpam-521	136	13	as	as	ADP
ejpam-521	136	14	x(1	x(1	PROPN
ejpam-521	136	15	)	)	PUNCT
ejpam-521	136	16	≤	≤	PUNCT
ejpam-521	136	17	x(2	x(2	PROPN
ejpam-521	136	18	)	)	PUNCT
ejpam-521	136	19	≤	≤	NOUN
ejpam-521	136	20	·	·	PUNCT
ejpam-521	136	21	·	·	PUNCT
ejpam-521	136	22	·	·	PUNCT
ejpam-521	137	1	≤	≤	NUM
ejpam-521	137	2	x(n	x(n	NOUN
ejpam-521	137	3	)	)	PUNCT
ejpam-521	137	4	.	.	PUNCT
ejpam-521	138	1	for	for	ADP
ejpam-521	138	2	any	any	DET
ejpam-521	138	3	fixed	fix	VERB
ejpam-521	138	4	m	m	PROPN
ejpam-521	138	5	≤	≤	NOUN
ejpam-521	138	6	n	n	CCONJ
ejpam-521	138	7	,	,	PUNCT
ejpam-521	138	8	an	an	DET
ejpam-521	138	9	optimal	optimal	ADJ
ejpam-521	138	10	sequence	sequence	NOUN
ejpam-521	138	11	of	of	ADP
ejpam-521	138	12	break	break	NOUN
ejpam-521	138	13	points	point	NOUN
ejpam-521	138	14	q̃m	q̃m	PRON
ejpam-521	138	15	is	be	AUX
ejpam-521	138	16	obtained	obtain	VERB
ejpam-521	138	17	by	by	ADP
ejpam-521	138	18	solving	solve	VERB
ejpam-521	138	19	the	the	DET
ejpam-521	138	20	recursive	recursive	ADJ
ejpam-521	138	21	equation	equation	NOUN
ejpam-521	138	22	(	(	PUNCT
ejpam-521	138	23	9	9	NUM
ejpam-521	138	24	)	)	PUNCT
ejpam-521	138	25	.	.	PUNCT
ejpam-521	139	1	let	let	VERB
ejpam-521	139	2	i(x	i(x	PROPN
ejpam-521	139	3	(	(	PUNCT
ejpam-521	139	4	j	j	NOUN
ejpam-521	139	5	)	)	PUNCT
ejpam-521	139	6	)	)	PUNCT
ejpam-521	140	1	be	be	AUX
ejpam-521	140	2	the	the	DET
ejpam-521	140	3	unique	unique	ADJ
ejpam-521	140	4	integer	integer	NOUN
ejpam-521	140	5	i	i	PRON
ejpam-521	140	6	such	such	ADJ
ejpam-521	140	7	that	that	SCONJ
ejpam-521	140	8	x	x	PROPN
ejpam-521	140	9	(	(	PUNCT
ejpam-521	140	10	j	j	NOUN
ejpam-521	140	11	)	)	PUNCT
ejpam-521	140	12	∈	∈	PROPN
ejpam-521	141	1	q̃	q̃	PROPN
ejpam-521	141	2	i	i	PRON
ejpam-521	141	3	,	,	PUNCT
ejpam-521	141	4	m	m	PROPN
ejpam-521	141	5	,	,	PUNCT
ejpam-521	141	6	and	and	CCONJ
ejpam-521	141	7	ni	ni	PROPN
ejpam-521	141	8	,	,	PUNCT
ejpam-521	141	9	m(ν	m(ν	PROPN
ejpam-521	141	10	)	)	PUNCT
ejpam-521	141	11	=	=	PUNCT
ejpam-521	142	1	∑	∑	PUNCT
ejpam-521	142	2	x	x	PUNCT
ejpam-521	142	3	l≤ν	l≤ν	PROPN
ejpam-521	142	4	iq̃i	iq̃i	PROPN
ejpam-521	142	5	,	,	PUNCT
ejpam-521	142	6	m	m	VERB
ejpam-521	142	7	(	(	PUNCT
ejpam-521	142	8	x	x	SYM
ejpam-521	142	9	l	l	NOUN
ejpam-521	142	10	)	)	PUNCT
ejpam-521	142	11	be	be	AUX
ejpam-521	142	12	the	the	DET
ejpam-521	142	13	number	number	NOUN
ejpam-521	142	14	of	of	ADP
ejpam-521	142	15	those	those	PRON
ejpam-521	142	16	x	x	PUNCT
ejpam-521	142	17	l	l	NOUN
ejpam-521	142	18	’s	’s	PART
ejpam-521	142	19	satisfying	satisfy	VERB
ejpam-521	142	20	x	x	X
ejpam-521	142	21	l	l	NOUN
ejpam-521	142	22	≤	≤	ADJ
ejpam-521	142	23	ν	ν	NOUN
ejpam-521	142	24	and	and	CCONJ
ejpam-521	142	25	falling	fall	VERB
ejpam-521	142	26	into	into	ADP
ejpam-521	142	27	the	the	DET
ejpam-521	142	28	i	i	PROPN
ejpam-521	142	29	-	-	PUNCT
ejpam-521	142	30	th	th	VERB
ejpam-521	142	31	subinterval	subinterval	NOUN
ejpam-521	142	32	q̃	q̃	PROPN
ejpam-521	142	33	i	i	PRON
ejpam-521	142	34	,	,	PUNCT
ejpam-521	142	35	m.	m.	VERB
ejpam-521	142	36	the	the	DET
ejpam-521	142	37	histogram	histogram	NOUN
ejpam-521	142	38	density	density	NOUN
ejpam-521	142	39	estimator	estimator	NOUN
ejpam-521	142	40	based	base	VERB
ejpam-521	142	41	on	on	ADP
ejpam-521	142	42	the	the	DET
ejpam-521	142	43	first	first	ADJ
ejpam-521	142	44	j	j	PROPN
ejpam-521	142	45	observations	observation	NOUN
ejpam-521	142	46	x(1	x(1	PROPN
ejpam-521	142	47	)	)	PUNCT
ejpam-521	142	48	,	,	PUNCT
ejpam-521	142	49	·	·	PUNCT
ejpam-521	142	50	·	·	PUNCT
ejpam-521	142	51	·	·	PUNCT
ejpam-521	142	52	,	,	PUNCT
ejpam-521	142	53	x	x	X
ejpam-521	142	54	(	(	PUNCT
ejpam-521	142	55	j	j	NOUN
ejpam-521	142	56	)	)	PUNCT
ejpam-521	142	57	can	can	AUX
ejpam-521	142	58	be	be	AUX
ejpam-521	142	59	written	write	VERB
ejpam-521	142	60	as	as	ADP
ejpam-521	142	61	f̃	f̃	PROPN
ejpam-521	142	62	(	(	PUNCT
ejpam-521	142	63	x	x	NOUN
ejpam-521	142	64	|x(1	|x(1	PROPN
ejpam-521	142	65	)	)	PUNCT
ejpam-521	142	66	,	,	PUNCT
ejpam-521	142	67	·	·	PUNCT
ejpam-521	142	68	·	·	PUNCT
ejpam-521	142	69	·	·	PUNCT
ejpam-521	143	1	,	,	PUNCT
ejpam-521	143	2	x	x	X
ejpam-521	143	3	(	(	PUNCT
ejpam-521	143	4	j	j	PROPN
ejpam-521	143	5	)	)	PUNCT
ejpam-521	143	6	,	,	PUNCT
ejpam-521	143	7	m	m	NOUN
ejpam-521	143	8	)	)	PUNCT
ejpam-521	143	9	=	=	PUNCT
ejpam-521	143	10	m	m	VERB
ejpam-521	143	11	∑	∑	PROPN
ejpam-521	143	12	i=1	i=1	PROPN
ejpam-521	143	13	ni	ni	PROPN
ejpam-521	143	14	,	,	PUNCT
ejpam-521	143	15	m(x	m(x	PROPN
ejpam-521	143	16	(	(	PUNCT
ejpam-521	143	17	j	j	NOUN
ejpam-521	143	18	)	)	PUNCT
ejpam-521	143	19	)	)	PUNCT
ejpam-521	144	1	+	+	CCONJ
ejpam-521	144	2	1	1	NUM
ejpam-521	144	3	(	(	PUNCT
ejpam-521	144	4	j+m)r̃i	j+m)r̃i	X
ejpam-521	144	5	,	,	PUNCT
ejpam-521	144	6	m	m	VERB
ejpam-521	144	7	iq̃i	iq̃i	PROPN
ejpam-521	144	8	,	,	PUNCT
ejpam-521	144	9	m	m	VERB
ejpam-521	144	10	(	(	PUNCT
ejpam-521	144	11	x	x	X
ejpam-521	144	12	)	)	PUNCT
ejpam-521	144	13	(	(	PUNCT
ejpam-521	144	14	18	18	NUM
ejpam-521	144	15	)	)	PUNCT
ejpam-521	144	16	and	and	CCONJ
ejpam-521	144	17	the	the	DET
ejpam-521	144	18	likelihood	likelihood	NOUN
ejpam-521	144	19	of	of	ADP
ejpam-521	144	20	x	x	PUNCT
ejpam-521	144	21	n	n	PRON
ejpam-521	144	22	can	can	AUX
ejpam-521	144	23	be	be	AUX
ejpam-521	144	24	constructed	construct	VERB
ejpam-521	144	25	in	in	ADP
ejpam-521	144	26	a	a	DET
ejpam-521	144	27	predictive	predictive	ADJ
ejpam-521	144	28	manner	manner	NOUN
ejpam-521	144	29	as	as	ADP
ejpam-521	144	30	f̃	f̃	PROPN
ejpam-521	144	31	(	(	PUNCT
ejpam-521	144	32	x	x	NOUN
ejpam-521	144	33	n	n	CCONJ
ejpam-521	144	34	;	;	PUNCT
ejpam-521	144	35	m	m	X
ejpam-521	144	36	)	)	PUNCT
ejpam-521	145	1	=	=	SYM
ejpam-521	145	2	n	n	CCONJ
ejpam-521	145	3	∏	∏	NUM
ejpam-521	145	4	j=1	j=1	PROPN
ejpam-521	145	5	f̃	f̃	PROPN
ejpam-521	145	6	(	(	PUNCT
ejpam-521	145	7	x	x	X
ejpam-521	145	8	(	(	PUNCT
ejpam-521	145	9	j)|x(1	j)|x(1	PROPN
ejpam-521	145	10	)	)	PUNCT
ejpam-521	145	11	,	,	PUNCT
ejpam-521	145	12	·	·	PUNCT
ejpam-521	145	13	·	·	PUNCT
ejpam-521	145	14	·	·	PUNCT
ejpam-521	145	15	,	,	PUNCT
ejpam-521	145	16	x	x	X
ejpam-521	145	17	(	(	PUNCT
ejpam-521	145	18	j−1	j−1	PROPN
ejpam-521	145	19	)	)	PUNCT
ejpam-521	145	20	,	,	PUNCT
ejpam-521	145	21	m	m	NOUN
ejpam-521	145	22	)	)	PUNCT
ejpam-521	145	23	=	=	SYM
ejpam-521	145	24	n	n	CCONJ
ejpam-521	145	25	∏	∏	PROPN
ejpam-521	145	26	j=1	j=1	NOUN
ejpam-521	145	27	ni(x	ni(x	NUM
ejpam-521	145	28	(	(	PUNCT
ejpam-521	145	29	j)),m	j)),m	PROPN
ejpam-521	145	30	(	(	PUNCT
ejpam-521	145	31	x	x	X
ejpam-521	145	32	(	(	PUNCT
ejpam-521	145	33	j−1	j−1	PROPN
ejpam-521	145	34	)	)	PUNCT
ejpam-521	145	35	)	)	PUNCT
ejpam-521	146	1	+	+	CCONJ
ejpam-521	146	2	1	1	NUM
ejpam-521	146	3	(	(	PUNCT
ejpam-521	146	4	j−	j−	PROPN
ejpam-521	146	5	1+m)r̃i(x	1+m)r̃i(x	NUM
ejpam-521	146	6	(	(	PUNCT
ejpam-521	146	7	j)),m	j)),m	PROPN
ejpam-521	146	8	=	=	SYM
ejpam-521	146	9	(	(	PUNCT
ejpam-521	146	10	m−	m−	PROPN
ejpam-521	146	11	1	1	NUM
ejpam-521	146	12	)	)	PUNCT
ejpam-521	146	13	!	!	PUNCT
ejpam-521	147	1	(	(	PUNCT
ejpam-521	147	2	n+m−	n+m−	NOUN
ejpam-521	147	3	1	1	NUM
ejpam-521	147	4	)	)	PUNCT
ejpam-521	147	5	!	!	PUNCT
ejpam-521	148	1	m	m	VERB
ejpam-521	148	2	∏	∏	PROPN
ejpam-521	148	3	i=1	i=1	PROPN
ejpam-521	148	4	ni	ni	PROPN
ejpam-521	148	5	,	,	PUNCT
ejpam-521	148	6	m	m	PROPN
ejpam-521	148	7	!	!	PUNCT
ejpam-521	149	1	r̃	r̃	ADJ
ejpam-521	149	2	ni	ni	PROPN
ejpam-521	149	3	,	,	PUNCT
ejpam-521	149	4	m	m	VERB
ejpam-521	149	5	i	i	PRON
ejpam-521	149	6	,	,	PUNCT
ejpam-521	149	7	m	m	PROPN
ejpam-521	149	8	.	.	PUNCT
ejpam-521	150	1	(	(	PUNCT
ejpam-521	150	2	19	19	NUM
ejpam-521	150	3	)	)	PUNCT
ejpam-521	150	4	in	in	ADP
ejpam-521	150	5	[	[	X
ejpam-521	150	6	14	14	NUM
ejpam-521	150	7	]	]	SYM
ejpam-521	150	8	−	−	NOUN
ejpam-521	150	9	log	log	NOUN
ejpam-521	150	10	f̃	f̃	PROPN
ejpam-521	150	11	(	(	PUNCT
ejpam-521	150	12	x	x	SYM
ejpam-521	150	13	n	n	CCONJ
ejpam-521	150	14	;	;	PUNCT
ejpam-521	150	15	m	m	X
ejpam-521	150	16	)	)	PUNCT
ejpam-521	150	17	is	be	AUX
ejpam-521	150	18	defined	define	VERB
ejpam-521	150	19	as	as	ADP
ejpam-521	150	20	the	the	DET
ejpam-521	150	21	(	(	PUNCT
ejpam-521	150	22	predictive	predictive	ADJ
ejpam-521	150	23	)	)	PUNCT
ejpam-521	150	24	stochastic	stochastic	ADJ
ejpam-521	150	25	complexity	complexity	NOUN
ejpam-521	150	26	of	of	ADP
ejpam-521	150	27	x	x	PROPN
ejpam-521	150	28	n	n	X
ejpam-521	150	29	under	under	ADP
ejpam-521	150	30	the	the	DET
ejpam-521	150	31	given	give	VERB
ejpam-521	150	32	partition	partition	NOUN
ejpam-521	150	33	.	.	PUNCT
ejpam-521	151	1	now	now	ADV
ejpam-521	151	2	the	the	DET
ejpam-521	151	3	shortest	short	ADJ
ejpam-521	151	4	predictive	predictive	ADJ
ejpam-521	151	5	code	code	NOUN
ejpam-521	151	6	length	length	NOUN
ejpam-521	151	7	for	for	ADP
ejpam-521	151	8	the	the	DET
ejpam-521	151	9	data	datum	NOUN
ejpam-521	151	10	x	x	X
ejpam-521	151	11	n	n	X
ejpam-521	151	12	is	be	AUX
ejpam-521	151	13	min	min	PROPN
ejpam-521	151	14	m	m	PROPN
ejpam-521	151	15	¦	¦	NOUN
ejpam-521	151	16	−	−	PUNCT
ejpam-521	151	17	log	log	NOUN
ejpam-521	151	18	f̃	f̃	PROPN
ejpam-521	151	19	(	(	PUNCT
ejpam-521	151	20	x	x	SYM
ejpam-521	151	21	n	n	CCONJ
ejpam-521	151	22	;	;	PUNCT
ejpam-521	151	23	m	m	X
ejpam-521	151	24	)	)	PUNCT
ejpam-521	152	1	+	+	CCONJ
ejpam-521	152	2	l2(q̃	l2(q̃	PROPN
ejpam-521	152	3	m	m	PROPN
ejpam-521	152	4	,	,	PUNCT
ejpam-521	152	5	m	m	PROPN
ejpam-521	152	6	,	,	PUNCT
ejpam-521	152	7	δ	δ	PROPN
ejpam-521	152	8	)	)	PUNCT
ejpam-521	152	9	©	©	PROPN
ejpam-521	152	10	=	=	PUNCT
ejpam-521	152	11	−	−	PROPN
ejpam-521	152	12	m̂	m̂	NOUN
ejpam-521	152	13	∑	∑	PUNCT
ejpam-521	152	14	i=1	i=1	PROPN
ejpam-521	152	15	log	log	PROPN
ejpam-521	152	16	ni	ni	PROPN
ejpam-521	152	17	,	,	PUNCT
ejpam-521	152	18	m̂!+	m̂!+	VERB
ejpam-521	152	19	m̂	m̂	PROPN
ejpam-521	152	20	∑	∑	PROPN
ejpam-521	152	21	i=1	i=1	PROPN
ejpam-521	152	22	ni	ni	PROPN
ejpam-521	152	23	,	,	PUNCT
ejpam-521	152	24	m̂	m̂	PROPN
ejpam-521	152	25	log	log	NOUN
ejpam-521	152	26	r̃i	r̃i	NOUN
ejpam-521	152	27	,	,	PUNCT
ejpam-521	152	28	m̂−	m̂−	PROPN
ejpam-521	152	29	log	log	NOUN
ejpam-521	152	30	(	(	PUNCT
ejpam-521	152	31	m̂−	m̂−	NOUN
ejpam-521	152	32	1	1	NUM
ejpam-521	152	33	)	)	PUNCT
ejpam-521	152	34	!	!	PUNCT
ejpam-521	153	1	(	(	PUNCT
ejpam-521	153	2	n+	n+	NUM
ejpam-521	153	3	m̂−	m̂−	NOUN
ejpam-521	153	4	1	1	NUM
ejpam-521	153	5	)	)	PUNCT
ejpam-521	153	6	!	!	PUNCT
ejpam-521	154	1	+	+	PUNCT
ejpam-521	155	1	l2(q̃	l2(q̃	PROPN
ejpam-521	155	2	m	m	PROPN
ejpam-521	155	3	,	,	PUNCT
ejpam-521	155	4	m	m	PROPN
ejpam-521	155	5	,	,	PUNCT
ejpam-521	155	6	δ	δ	PROPN
ejpam-521	155	7	)	)	PUNCT
ejpam-521	155	8	(	(	PUNCT
ejpam-521	155	9	20	20	NUM
ejpam-521	155	10	)	)	PUNCT
ejpam-521	155	11	g.	g.	PROPN
ejpam-521	155	12	qian	qian	PROPN
ejpam-521	155	13	/	/	SYM
ejpam-521	155	14	eur	eur	PROPN
ejpam-521	155	15	.	.	PUNCT
ejpam-521	156	1	j.	j.	PROPN
ejpam-521	156	2	pure	pure	PROPN
ejpam-521	156	3	appl	appl	PROPN
ejpam-521	156	4	.	.	PROPN
ejpam-521	156	5	math	math	PROPN
ejpam-521	156	6	,	,	PUNCT
ejpam-521	156	7	3	3	NUM
ejpam-521	156	8	(	(	PUNCT
ejpam-521	156	9	2010	2010	NUM
ejpam-521	156	10	)	)	PUNCT
ejpam-521	156	11	,	,	PUNCT
ejpam-521	156	12	51	51	NUM
ejpam-521	156	13	-	-	SYM
ejpam-521	156	14	80	80	NUM
ejpam-521	156	15	58	58	NUM
ejpam-521	156	16	where	where	SCONJ
ejpam-521	156	17	the	the	DET
ejpam-521	156	18	minimization	minimization	NOUN
ejpam-521	156	19	is	be	AUX
ejpam-521	156	20	achieved	achieve	VERB
ejpam-521	156	21	at	at	ADP
ejpam-521	156	22	m̂	m̂	PROPN
ejpam-521	156	23	≤	≤	NUM
ejpam-521	156	24	n	n	PRON
ejpam-521	156	25	and	and	CCONJ
ejpam-521	156	26	δ	δ	PROPN
ejpam-521	156	27	is	be	AUX
ejpam-521	156	28	a	a	DET
ejpam-521	156	29	prescribed	prescribed	ADJ
ejpam-521	156	30	precision	precision	NOUN
ejpam-521	156	31	.	.	PUNCT
ejpam-521	157	1	in	in	ADP
ejpam-521	157	2	particular	particular	ADJ
ejpam-521	157	3	,	,	PUNCT
ejpam-521	157	4	when	when	SCONJ
ejpam-521	157	5	the	the	DET
ejpam-521	157	6	subintervals	subinterval	NOUN
ejpam-521	157	7	are	be	AUX
ejpam-521	157	8	of	of	ADP
ejpam-521	157	9	equal	equal	ADJ
ejpam-521	157	10	length	length	NOUN
ejpam-521	157	11	,	,	PUNCT
ejpam-521	157	12	the	the	DET
ejpam-521	157	13	expression	expression	NOUN
ejpam-521	157	14	(	(	PUNCT
ejpam-521	157	15	20	20	NUM
ejpam-521	157	16	)	)	PUNCT
ejpam-521	157	17	becomes	become	VERB
ejpam-521	157	18	min	min	PROPN
ejpam-521	157	19	m	m	PROPN
ejpam-521	157	20	¨	¨	NOUN
ejpam-521	157	21	n	n	ADV
ejpam-521	157	22	log	log	VERB
ejpam-521	158	1	r	r	NOUN
ejpam-521	158	2	m	m	VERB
ejpam-521	158	3	+	+	CCONJ
ejpam-521	158	4	log	log	VERB
ejpam-521	158	5	�	�	PROPN
ejpam-521	158	6	n	n	CCONJ
ejpam-521	158	7	n1,m	n1,m	PROPN
ejpam-521	158	8	,	,	PUNCT
ejpam-521	158	9	·	·	PUNCT
ejpam-521	158	10	·	·	PUNCT
ejpam-521	158	11	·	·	PUNCT
ejpam-521	158	12	,	,	PUNCT
ejpam-521	158	13	nm	nm	PROPN
ejpam-521	158	14	,	,	PUNCT
ejpam-521	158	15	m	m	VERB
ejpam-521	158	16	�	�	PROPN
ejpam-521	158	17	+	+	CCONJ
ejpam-521	158	18	log	log	PROPN
ejpam-521	158	19	�	�	PROPN
ejpam-521	158	20	n+m−	n+m−	PROPN
ejpam-521	158	21	1	1	NUM
ejpam-521	158	22	n	n	PRON
ejpam-521	158	23	�	�	PROPN
ejpam-521	158	24	+	+	CCONJ
ejpam-521	158	25	l3(m	l3(m	ADJ
ejpam-521	158	26	,	,	PUNCT
ejpam-521	158	27	s̄	s̄	NOUN
ejpam-521	158	28	,	,	PUNCT
ejpam-521	158	29	r̄)+	r̄)+	PUNCT
ejpam-521	159	1	|	|	ADV
ejpam-521	159	2	logδ|	logδ|	NOUN
ejpam-521	159	3	«	«	PUNCT
ejpam-521	159	4	.	.	PUNCT
ejpam-521	160	1	(	(	PUNCT
ejpam-521	160	2	21	21	NUM
ejpam-521	160	3	)	)	PUNCT
ejpam-521	160	4	having	having	AUX
ejpam-521	160	5	obtained	obtain	VERB
ejpam-521	160	6	the	the	DET
ejpam-521	160	7	shortest	short	ADJ
ejpam-521	160	8	code	code	NOUN
ejpam-521	160	9	length	length	NOUN
ejpam-521	160	10	(	(	PUNCT
ejpam-521	160	11	16	16	NUM
ejpam-521	160	12	)	)	PUNCT
ejpam-521	160	13	and	and	CCONJ
ejpam-521	160	14	shortest	short	ADJ
ejpam-521	160	15	predictive	predictive	ADJ
ejpam-521	160	16	code	code	NOUN
ejpam-521	160	17	length	length	NOUN
ejpam-521	160	18	(	(	PUNCT
ejpam-521	160	19	20	20	NUM
ejpam-521	160	20	)	)	PUNCT
ejpam-521	160	21	,	,	PUNCT
ejpam-521	160	22	it	it	PRON
ejpam-521	160	23	is	be	AUX
ejpam-521	160	24	natural	natural	ADJ
ejpam-521	160	25	to	to	PART
ejpam-521	160	26	ask	ask	VERB
ejpam-521	160	27	how	how	SCONJ
ejpam-521	160	28	they	they	PRON
ejpam-521	160	29	differ	differ	VERB
ejpam-521	160	30	in	in	ADP
ejpam-521	160	31	values	value	NOUN
ejpam-521	160	32	.	.	PUNCT
ejpam-521	161	1	an	an	DET
ejpam-521	161	2	asymptotic	asymptotic	ADJ
ejpam-521	161	3	result	result	NOUN
ejpam-521	161	4	is	be	AUX
ejpam-521	161	5	given	give	VERB
ejpam-521	161	6	below	below	ADV
ejpam-521	161	7	with	with	ADP
ejpam-521	161	8	its	its	PRON
ejpam-521	161	9	proof	proof	NOUN
ejpam-521	161	10	to	to	PART
ejpam-521	161	11	be	be	AUX
ejpam-521	161	12	presented	present	VERB
ejpam-521	161	13	in	in	ADP
ejpam-521	161	14	section	section	NOUN
ejpam-521	161	15	4	4	NUM
ejpam-521	161	16	.	.	PUNCT
ejpam-521	162	1	theorem	theorem	NOUN
ejpam-521	162	2	1	1	NUM
ejpam-521	162	3	.	.	PUNCT
ejpam-521	163	1	let	let	VERB
ejpam-521	163	2	x	x	PRON
ejpam-521	163	3	n	n	PRON
ejpam-521	163	4	be	be	AUX
ejpam-521	163	5	a	a	DET
ejpam-521	163	6	simple	simple	ADJ
ejpam-521	163	7	random	random	ADJ
ejpam-521	163	8	sample	sample	NOUN
ejpam-521	163	9	from	from	ADP
ejpam-521	163	10	an	an	DET
ejpam-521	163	11	unknown	unknown	ADJ
ejpam-521	163	12	density	density	NOUN
ejpam-521	163	13	function	function	NOUN
ejpam-521	163	14	f	f	PROPN
ejpam-521	163	15	on	on	ADP
ejpam-521	163	16	[	[	X
ejpam-521	163	17	s	s	X
ejpam-521	163	18	,	,	PUNCT
ejpam-521	163	19	t	t	PROPN
ejpam-521	163	20	]	]	PUNCT
ejpam-521	163	21	.	.	PUNCT
ejpam-521	164	1	suppose	suppose	VERB
ejpam-521	164	2	the	the	DET
ejpam-521	164	3	following	follow	VERB
ejpam-521	164	4	conditions	condition	NOUN
ejpam-521	164	5	are	be	AUX
ejpam-521	164	6	satisfied	satisfied	ADJ
ejpam-521	164	7	:	:	PUNCT
ejpam-521	164	8	(	(	PUNCT
ejpam-521	164	9	i	i	NOUN
ejpam-521	164	10	)	)	PUNCT
ejpam-521	164	11	.	.	PUNCT
ejpam-521	165	1	0	0	PUNCT
ejpam-521	165	2	<	<	X
ejpam-521	165	3	c1	c1	PROPN
ejpam-521	165	4	≤	≤	PROPN
ejpam-521	165	5	f	f	PROPN
ejpam-521	165	6	≤	≤	PROPN
ejpam-521	165	7	c2	c2	PROPN
ejpam-521	165	8	<	<	X
ejpam-521	165	9	∞	∞	PROPN
ejpam-521	165	10	,	,	PUNCT
ejpam-521	165	11	where	where	SCONJ
ejpam-521	165	12	c1	c1	PROPN
ejpam-521	165	13	and	and	CCONJ
ejpam-521	165	14	c2	c2	PROPN
ejpam-521	165	15	are	be	AUX
ejpam-521	165	16	constants	constant	NOUN
ejpam-521	165	17	;	;	PUNCT
ejpam-521	165	18	(	(	PUNCT
ejpam-521	165	19	ii	ii	NOUN
ejpam-521	165	20	)	)	PUNCT
ejpam-521	165	21	.	.	PUNCT
ejpam-521	166	1	the	the	DET
ejpam-521	166	2	number	number	NOUN
ejpam-521	166	3	of	of	ADP
ejpam-521	166	4	subintervals	subinterval	NOUN
ejpam-521	166	5	m	m	VERB
ejpam-521	166	6	in	in	ADP
ejpam-521	166	7	the	the	DET
ejpam-521	166	8	quantization	quantization	NOUN
ejpam-521	166	9	of	of	ADP
ejpam-521	166	10	x	x	PUNCT
ejpam-521	166	11	n	n	PRON
ejpam-521	166	12	satisfies	satisfie	NOUN
ejpam-521	166	13	nγ1	nγ1	VERB
ejpam-521	166	14	≤	≤	NUM
ejpam-521	166	15	m≤	m≤	PROPN
ejpam-521	166	16	nγ2	nγ2	NOUN
ejpam-521	166	17	,	,	PUNCT
ejpam-521	166	18	(	(	PUNCT
ejpam-521	166	19	22	22	NUM
ejpam-521	166	20	)	)	PUNCT
ejpam-521	166	21	where	where	SCONJ
ejpam-521	166	22	γ1	γ1	NOUN
ejpam-521	166	23	and	and	CCONJ
ejpam-521	166	24	γ2	γ2	PROPN
ejpam-521	166	25	are	be	AUX
ejpam-521	166	26	two	two	NUM
ejpam-521	166	27	constants	constant	NOUN
ejpam-521	166	28	satisfying	satisfy	VERB
ejpam-521	166	29	0	0	NUM
ejpam-521	166	30	<	<	X
ejpam-521	166	31	γ1	γ1	NOUN
ejpam-521	166	32	<	<	X
ejpam-521	166	33	γ2	γ2	PROPN
ejpam-521	166	34	<	<	X
ejpam-521	166	35	1	1	NUM
ejpam-521	166	36	;	;	PUNCT
ejpam-521	166	37	(	(	PUNCT
ejpam-521	166	38	iii	iii	NOUN
ejpam-521	166	39	)	)	PUNCT
ejpam-521	166	40	.	.	PUNCT
ejpam-521	167	1	the	the	DET
ejpam-521	167	2	width	width	ADJ
ejpam-521	167	3	r̃i	r̃i	NOUN
ejpam-521	167	4	,	,	PUNCT
ejpam-521	167	5	m	m	PROPN
ejpam-521	167	6	of	of	ADP
ejpam-521	167	7	each	each	DET
ejpam-521	167	8	optimal	optimal	ADJ
ejpam-521	167	9	subinterval	subinterval	NOUN
ejpam-521	167	10	q̃	q̃	PROPN
ejpam-521	167	11	i	i	PRON
ejpam-521	167	12	,	,	PUNCT
ejpam-521	167	13	m	m	VERB
ejpam-521	167	14	satisfies	satisfie	NOUN
ejpam-521	167	15	b1m−α1	b1m−α1	VERB
ejpam-521	167	16	≤	≤	NUM
ejpam-521	167	17	r̃i	r̃i	NOUN
ejpam-521	167	18	,	,	PUNCT
ejpam-521	167	19	m	m	VERB
ejpam-521	167	20	≤	≤	ADJ
ejpam-521	167	21	b2m−α2	b2m−α2	NOUN
ejpam-521	167	22	(	(	PUNCT
ejpam-521	167	23	23	23	NUM
ejpam-521	167	24	)	)	PUNCT
ejpam-521	167	25	uniformly	uniformly	ADV
ejpam-521	167	26	for	for	SCONJ
ejpam-521	167	27	integers	integer	NOUN
ejpam-521	167	28	m	m	VERB
ejpam-521	167	29	in	in	ADP
ejpam-521	167	30	[	[	X
ejpam-521	167	31	nγ1	nγ1	NOUN
ejpam-521	167	32	,	,	PUNCT
ejpam-521	167	33	nγ2	nγ2	CCONJ
ejpam-521	167	34	]	]	X
ejpam-521	167	35	,	,	PUNCT
ejpam-521	167	36	where	where	SCONJ
ejpam-521	167	37	b1	b1	NOUN
ejpam-521	167	38	,	,	PUNCT
ejpam-521	167	39	b2	b2	NOUN
ejpam-521	167	40	,	,	PUNCT
ejpam-521	167	41	α1,α2	α1,α2	PROPN
ejpam-521	167	42	are	be	AUX
ejpam-521	167	43	constants	constant	NOUN
ejpam-521	167	44	satisfying	satisfy	VERB
ejpam-521	167	45	1	1	NUM
ejpam-521	167	46	≤	≤	NUM
ejpam-521	167	47	α1	α1	PROPN
ejpam-521	167	48	<	<	X
ejpam-521	167	49	1	1	NUM
ejpam-521	167	50	2	2	NUM
ejpam-521	167	51	+	+	NUM
ejpam-521	167	52	1	1	NUM
ejpam-521	167	53	2γ2	2γ2	NUM
ejpam-521	167	54	,	,	PUNCT
ejpam-521	167	55	and	and	CCONJ
ejpam-521	167	56	max{0,2α1	max{0,2α1	VERB
ejpam-521	167	57	−	−	PROPN
ejpam-521	167	58	1	1	NUM
ejpam-521	167	59	γ2	γ2	NOUN
ejpam-521	167	60	}	}	PUNCT
ejpam-521	167	61	<	<	X
ejpam-521	167	62	α2	α2	PROPN
ejpam-521	167	63	≤	≤	ADV
ejpam-521	167	64	1	1	NUM
ejpam-521	167	65	.	.	PUNCT
ejpam-521	168	1	then	then	ADV
ejpam-521	168	2	uniformly	uniformly	ADV
ejpam-521	168	3	in	in	ADP
ejpam-521	168	4	m	m	PROPN
ejpam-521	168	5	∈	∈	NOUN
ejpam-521	169	1	[	[	X
ejpam-521	169	2	nγ1	nγ1	NOUN
ejpam-521	169	3	,	,	PUNCT
ejpam-521	169	4	nγ2	nγ2	PROPN
ejpam-521	169	5	]	]	PUNCT
ejpam-521	169	6	,	,	PUNCT
ejpam-521	169	7	the	the	DET
ejpam-521	169	8	difference	difference	NOUN
ejpam-521	169	9	between	between	ADP
ejpam-521	169	10	the	the	DET
ejpam-521	169	11	shortest	short	ADJ
ejpam-521	169	12	code	code	NOUN
ejpam-521	169	13	length	length	NOUN
ejpam-521	169	14	and	and	CCONJ
ejpam-521	169	15	the	the	DET
ejpam-521	169	16	shortest	short	ADJ
ejpam-521	169	17	predictive	predictive	ADJ
ejpam-521	169	18	code	code	NOUN
ejpam-521	169	19	length	length	NOUN
ejpam-521	169	20	of	of	ADP
ejpam-521	169	21	x	x	PUNCT
ejpam-521	169	22	n	n	X
ejpam-521	169	23	is	be	AUX
ejpam-521	169	24	−	−	PROPN
ejpam-521	169	25	log	log	NOUN
ejpam-521	169	26	f̃	f̃	PROPN
ejpam-521	169	27	(	(	PUNCT
ejpam-521	169	28	x	x	SYM
ejpam-521	169	29	n	n	CCONJ
ejpam-521	169	30	;	;	PUNCT
ejpam-521	169	31	m	m	X
ejpam-521	169	32	)	)	PUNCT
ejpam-521	170	1	+	+	CCONJ
ejpam-521	170	2	l∗1(x	l∗1(x	PROPN
ejpam-521	170	3	n	n	CCONJ
ejpam-521	170	4	;	;	PUNCT
ejpam-521	170	5	m	m	X
ejpam-521	170	6	)	)	PUNCT
ejpam-521	170	7	=	=	SYM
ejpam-521	170	8	α′m	α′m	NOUN
ejpam-521	170	9	log	log	VERB
ejpam-521	170	10	m+	m+	NUM
ejpam-521	170	11	1	1	NUM
ejpam-521	170	12	2	2	NUM
ejpam-521	170	13	m	m	NOUN
ejpam-521	170	14	log	log	NOUN
ejpam-521	170	15	n+o(m	n+o(m	NOUN
ejpam-521	170	16	)	)	PUNCT
ejpam-521	170	17	a.s	a.s	PROPN
ejpam-521	170	18	.	.	PROPN
ejpam-521	171	1	(	(	PUNCT
ejpam-521	171	2	24	24	NUM
ejpam-521	171	3	)	)	PUNCT
ejpam-521	171	4	where	where	SCONJ
ejpam-521	171	5	−1	−1	NOUN
ejpam-521	171	6	2	2	NUM
ejpam-521	171	7	α1	α1	PROPN
ejpam-521	171	8	≤	≤	NOUN
ejpam-521	172	1	α′	α′	NUM
ejpam-521	172	2	≤	≤	NUM
ejpam-521	172	3	−3	−3	PROPN
ejpam-521	172	4	2	2	NUM
ejpam-521	172	5	+	+	NOUN
ejpam-521	172	6	α1	α1	PROPN
ejpam-521	172	7	.	.	PUNCT
ejpam-521	173	1	note	note	VERB
ejpam-521	173	2	that	that	SCONJ
ejpam-521	173	3	if	if	SCONJ
ejpam-521	173	4	the	the	DET
ejpam-521	173	5	support	support	NOUN
ejpam-521	173	6	of	of	ADP
ejpam-521	173	7	the	the	DET
ejpam-521	173	8	density	density	NOUN
ejpam-521	173	9	f	f	PROPN
ejpam-521	173	10	is	be	AUX
ejpam-521	173	11	finite	finite	ADJ
ejpam-521	173	12	,	,	PUNCT
ejpam-521	173	13	then	then	ADV
ejpam-521	173	14	α2	α2	ADJ
ejpam-521	173	15	≤	≤	NOUN
ejpam-521	173	16	1	1	NUM
ejpam-521	173	17	≤	≤	NUM
ejpam-521	173	18	α1	α1	PROPN
ejpam-521	173	19	is	be	AUX
ejpam-521	173	20	necessary	necessary	ADJ
ejpam-521	173	21	for	for	SCONJ
ejpam-521	173	22	condition	condition	NOUN
ejpam-521	173	23	(	(	PUNCT
ejpam-521	173	24	iii	iii	NOUN
ejpam-521	173	25	)	)	PUNCT
ejpam-521	173	26	to	to	PART
ejpam-521	173	27	hold	hold	VERB
ejpam-521	173	28	.	.	PUNCT
ejpam-521	174	1	also	also	ADV
ejpam-521	174	2	conditions	condition	NOUN
ejpam-521	174	3	(	(	PUNCT
ejpam-521	174	4	ii	ii	NOUN
ejpam-521	174	5	)	)	PUNCT
ejpam-521	174	6	and	and	CCONJ
ejpam-521	174	7	(	(	PUNCT
ejpam-521	174	8	iii	iii	NOUN
ejpam-521	174	9	)	)	PUNCT
ejpam-521	174	10	imply	imply	VERB
ejpam-521	174	11	that	that	SCONJ
ejpam-521	174	12	α2	α2	ADJ
ejpam-521	174	13	≤	≤	ADV
ejpam-521	174	14	1	1	NUM
ejpam-521	174	15	≤	≤	NUM
ejpam-521	174	16	α1	α1	PROPN
ejpam-521	174	17	<	<	X
ejpam-521	174	18	1	1	NUM
ejpam-521	174	19	γ2	γ2	NOUN
ejpam-521	174	20	<	<	X
ejpam-521	174	21	1	1	NUM
ejpam-521	174	22	γ1	γ1	NOUN
ejpam-521	174	23	.	.	PUNCT
ejpam-521	175	1	further	far	ADV
ejpam-521	175	2	,	,	PUNCT
ejpam-521	175	3	the	the	DET
ejpam-521	175	4	righthand	righthand	NOUN
ejpam-521	175	5	side	side	NOUN
ejpam-521	175	6	of	of	ADP
ejpam-521	175	7	(	(	PUNCT
ejpam-521	175	8	24	24	NUM
ejpam-521	175	9	)	)	PUNCT
ejpam-521	175	10	becomes	become	VERB
ejpam-521	175	11	1	1	NUM
ejpam-521	175	12	2	2	NUM
ejpam-521	175	13	m	m	NOUN
ejpam-521	175	14	log	log	NOUN
ejpam-521	175	15	n	n	ADV
ejpam-521	175	16	m	m	VERB
ejpam-521	175	17	+	+	ADJ
ejpam-521	175	18	o(m	o(m	NOUN
ejpam-521	175	19	)	)	PUNCT
ejpam-521	175	20	a.s	a.s	PROPN
ejpam-521	175	21	.	.	PROPN
ejpam-521	176	1	if	if	SCONJ
ejpam-521	176	2	α1	α1	PROPN
ejpam-521	176	3	=	=	SYM
ejpam-521	176	4	α2	α2	NOUN
ejpam-521	176	5	=	=	SYM
ejpam-521	176	6	1	1	NUM
ejpam-521	176	7	.	.	X
ejpam-521	176	8	from	from	ADP
ejpam-521	176	9	rissanen	rissanen	PROPN
ejpam-521	176	10	(	(	PUNCT
ejpam-521	176	11	2007	2007	NUM
ejpam-521	176	12	)	)	PUNCT
ejpam-521	176	13	we	we	PRON
ejpam-521	176	14	know	know	VERB
ejpam-521	176	15	that	that	SCONJ
ejpam-521	176	16	the	the	DET
ejpam-521	176	17	shannon	shannon	PROPN
ejpam-521	176	18	complexity	complexity	NOUN
ejpam-521	176	19	is	be	AUX
ejpam-521	176	20	−	−	PROPN
ejpam-521	176	21	log	log	NOUN
ejpam-521	176	22	f	f	PROPN
ejpam-521	176	23	n(x	n(x	PROPN
ejpam-521	176	24	n	n	CCONJ
ejpam-521	176	25	)	)	PUNCT
ejpam-521	176	26	=	=	PUNCT
ejpam-521	177	1	−∑n	−∑n	PROPN
ejpam-521	177	2	i=1	i=1	PROPN
ejpam-521	178	1	log	log	PROPN
ejpam-521	178	2	f	f	PROPN
ejpam-521	178	3	(	(	PUNCT
ejpam-521	178	4	x	x	PROPN
ejpam-521	178	5	i	i	NOUN
ejpam-521	178	6	)	)	PUNCT
ejpam-521	178	7	if	if	SCONJ
ejpam-521	178	8	x	x	PRON
ejpam-521	178	9	n	n	PRON
ejpam-521	178	10	is	be	AUX
ejpam-521	178	11	a	a	DET
ejpam-521	178	12	simple	simple	ADJ
ejpam-521	178	13	random	random	ADJ
ejpam-521	178	14	sample	sample	NOUN
ejpam-521	178	15	.	.	PUNCT
ejpam-521	179	1	the	the	DET
ejpam-521	179	2	expectation	expectation	NOUN
ejpam-521	179	3	of	of	ADP
ejpam-521	179	4	shannon	shannon	PROPN
ejpam-521	179	5	complexity	complexity	NOUN
ejpam-521	179	6	represents	represent	VERB
ejpam-521	179	7	the	the	DET
ejpam-521	179	8	shortest	short	ADJ
ejpam-521	179	9	code	code	NOUN
ejpam-521	179	10	length	length	NOUN
ejpam-521	179	11	of	of	ADP
ejpam-521	179	12	x	x	SYM
ejpam-521	179	13	n	n	CCONJ
ejpam-521	179	14	on	on	ADP
ejpam-521	179	15	average	average	ADJ
ejpam-521	179	16	if	if	SCONJ
ejpam-521	179	17	the	the	DET
ejpam-521	179	18	underlying	underlie	VERB
ejpam-521	179	19	density	density	NOUN
ejpam-521	179	20	f	f	PROPN
ejpam-521	179	21	is	be	AUX
ejpam-521	179	22	known	know	VERB
ejpam-521	179	23	.	.	PUNCT
ejpam-521	180	1	the	the	DET
ejpam-521	180	2	following	follow	VERB
ejpam-521	180	3	three	three	NUM
ejpam-521	180	4	theorems	theorem	NOUN
ejpam-521	180	5	show	show	VERB
ejpam-521	180	6	how	how	SCONJ
ejpam-521	180	7	the	the	DET
ejpam-521	180	8	shortest	short	ADJ
ejpam-521	180	9	code	code	NOUN
ejpam-521	180	10	length	length	NOUN
ejpam-521	180	11	(	(	PUNCT
ejpam-521	180	12	16	16	NUM
ejpam-521	180	13	)	)	PUNCT
ejpam-521	180	14	and	and	CCONJ
ejpam-521	180	15	the	the	DET
ejpam-521	180	16	shortest	short	ADJ
ejpam-521	180	17	predictive	predictive	ADJ
ejpam-521	180	18	code	code	NOUN
ejpam-521	180	19	length	length	NOUN
ejpam-521	180	20	(	(	PUNCT
ejpam-521	180	21	20	20	NUM
ejpam-521	180	22	)	)	PUNCT
ejpam-521	180	23	differ	differ	VERB
ejpam-521	180	24	from	from	ADP
ejpam-521	180	25	the	the	DET
ejpam-521	180	26	shannon	shannon	PROPN
ejpam-521	180	27	complexity	complexity	NOUN
ejpam-521	180	28	.	.	PUNCT
ejpam-521	181	1	the	the	DET
ejpam-521	181	2	proof	proof	NOUN
ejpam-521	181	3	of	of	ADP
ejpam-521	181	4	these	these	DET
ejpam-521	181	5	theorems	theorem	NOUN
ejpam-521	181	6	will	will	AUX
ejpam-521	181	7	be	be	AUX
ejpam-521	181	8	presented	present	VERB
ejpam-521	181	9	in	in	ADP
ejpam-521	181	10	section	section	NOUN
ejpam-521	181	11	4	4	NUM
ejpam-521	181	12	.	.	PUNCT
ejpam-521	182	1	theorem	theorem	NOUN
ejpam-521	182	2	2	2	NUM
ejpam-521	182	3	.	.	PUNCT
ejpam-521	183	1	in	in	ADP
ejpam-521	183	2	addition	addition	NOUN
ejpam-521	183	3	to	to	ADP
ejpam-521	183	4	the	the	DET
ejpam-521	183	5	conditions	condition	NOUN
ejpam-521	183	6	(	(	PUNCT
ejpam-521	183	7	i	i	NOUN
ejpam-521	183	8	)	)	PUNCT
ejpam-521	183	9	,	,	PUNCT
ejpam-521	183	10	(	(	PUNCT
ejpam-521	183	11	ii	ii	NOUN
ejpam-521	183	12	)	)	PUNCT
ejpam-521	183	13	and	and	CCONJ
ejpam-521	183	14	(	(	PUNCT
ejpam-521	183	15	iii	iii	NOUN
ejpam-521	183	16	)	)	PUNCT
ejpam-521	183	17	in	in	ADP
ejpam-521	183	18	theorem	theorem	NOUN
ejpam-521	183	19	1	1	NUM
ejpam-521	183	20	,	,	PUNCT
ejpam-521	183	21	suppose	suppose	VERB
ejpam-521	183	22	that	that	SCONJ
ejpam-521	183	23	g.	g.	PROPN
ejpam-521	183	24	qian	qian	PROPN
ejpam-521	183	25	/	/	SYM
ejpam-521	183	26	eur	eur	PROPN
ejpam-521	183	27	.	.	PUNCT
ejpam-521	184	1	j.	j.	PROPN
ejpam-521	184	2	pure	pure	PROPN
ejpam-521	184	3	appl	appl	PROPN
ejpam-521	184	4	.	.	PROPN
ejpam-521	184	5	math	math	PROPN
ejpam-521	184	6	,	,	PUNCT
ejpam-521	184	7	3	3	NUM
ejpam-521	184	8	(	(	PUNCT
ejpam-521	184	9	2010	2010	NUM
ejpam-521	184	10	)	)	PUNCT
ejpam-521	184	11	,	,	PUNCT
ejpam-521	184	12	51	51	NUM
ejpam-521	184	13	-	-	SYM
ejpam-521	184	14	80	80	NUM
ejpam-521	184	15	59	59	NUM
ejpam-521	184	16	(	(	PUNCT
ejpam-521	184	17	iv	iv	NUM
ejpam-521	184	18	)	)	PUNCT
ejpam-521	184	19	.	.	PUNCT
ejpam-521	185	1	f	f	PROPN
ejpam-521	185	2	is	be	AUX
ejpam-521	185	3	absolutely	absolutely	ADV
ejpam-521	185	4	continuous	continuous	ADJ
ejpam-521	185	5	with	with	ADP
ejpam-521	185	6	derivative	derivative	ADJ
ejpam-521	185	7	ḟ	ḟ	NOUN
ejpam-521	185	8	a.e	a.e	PROPN
ejpam-521	185	9	.	.	PROPN
ejpam-521	185	10	such	such	ADJ
ejpam-521	185	11	that	that	SCONJ
ejpam-521	185	12	|	|	ADV
ejpam-521	185	13	ḟ	ḟ	NOUN
ejpam-521	185	14	(	(	PUNCT
ejpam-521	185	15	x)|	x)|	PROPN
ejpam-521	185	16	≤	≤	PROPN
ejpam-521	185	17	c3	c3	PROPN
ejpam-521	185	18	with	with	ADP
ejpam-521	185	19	c3	c3	PROPN
ejpam-521	185	20	a	a	DET
ejpam-521	185	21	constant	constant	ADJ
ejpam-521	185	22	.	.	PUNCT
ejpam-521	186	1	then	then	ADV
ejpam-521	186	2	uniformly	uniformly	ADV
ejpam-521	186	3	in	in	ADP
ejpam-521	186	4	m	m	PROPN
ejpam-521	186	5	∈	∈	NOUN
ejpam-521	187	1	[	[	X
ejpam-521	187	2	nγ1	nγ1	NOUN
ejpam-521	187	3	,	,	PUNCT
ejpam-521	187	4	nγ2	nγ2	CCONJ
ejpam-521	187	5	]	]	X
ejpam-521	187	6	we	we	PRON
ejpam-521	187	7	have	have	VERB
ejpam-521	187	8	(	(	PUNCT
ejpam-521	187	9	1	1	NUM
ejpam-521	187	10	)	)	PUNCT
ejpam-521	187	11	.	.	PUNCT
ejpam-521	188	1	−amα1	−amα1	NOUN
ejpam-521	188	2	+	+	CCONJ
ejpam-521	189	1	(	(	PUNCT
ejpam-521	189	2	α2	α2	ADJ
ejpam-521	189	3	−α1)m	−α1)m	PROPN
ejpam-521	189	4	log	log	PROPN
ejpam-521	189	5	m+	m+	NUM
ejpam-521	190	1	o(nm−2α2	o(nm−2α2	PROPN
ejpam-521	191	1	+	+	NOUN
ejpam-521	191	2	m	m	VERB
ejpam-521	191	3	log	log	NOUN
ejpam-521	191	4	m	m	NOUN
ejpam-521	191	5	)	)	PUNCT
ejpam-521	191	6	≤	≤	NUM
ejpam-521	191	7	−l∗1(x	−l∗1(x	ADP
ejpam-521	191	8	n	n	NUM
ejpam-521	191	9	;	;	PUNCT
ejpam-521	191	10	m	m	X
ejpam-521	191	11	)	)	PUNCT
ejpam-521	192	1	+	+	CCONJ
ejpam-521	192	2	l2(q̃	l2(q̃	PROPN
ejpam-521	192	3	m	m	PROPN
ejpam-521	192	4	,	,	PUNCT
ejpam-521	192	5	m	m	PROPN
ejpam-521	192	6	,	,	PUNCT
ejpam-521	192	7	δ	δ	PROPN
ejpam-521	192	8	)	)	PUNCT
ejpam-521	193	1	+	+	CCONJ
ejpam-521	193	2	log	log	VERB
ejpam-521	193	3	f	f	PROPN
ejpam-521	193	4	n(x	n(x	PROPN
ejpam-521	193	5	n	n	CCONJ
ejpam-521	193	6	)	)	PUNCT
ejpam-521	193	7	≤	≤	NOUN
ejpam-521	193	8	(	(	PUNCT
ejpam-521	193	9	α1	α1	PROPN
ejpam-521	193	10	−	−	PROPN
ejpam-521	193	11	1)m	1)m	NUM
ejpam-521	193	12	log	log	NOUN
ejpam-521	194	1	m+	m+	NUM
ejpam-521	194	2	c	c	NOUN
ejpam-521	194	3	f	f	PROPN
ejpam-521	194	4	nm−2α2	nm−2α2	NOUN
ejpam-521	194	5	+	+	CCONJ
ejpam-521	194	6	o(nm−2α2	o(nm−2α2	PROPN
ejpam-521	195	1	+	+	NOUN
ejpam-521	196	1	m	m	NOUN
ejpam-521	196	2	log	log	NOUN
ejpam-521	196	3	n	n	CCONJ
ejpam-521	196	4	)	)	PUNCT
ejpam-521	196	5	a.s	a.s	PROPN
ejpam-521	196	6	.	.	PROPN
ejpam-521	197	1	(	(	PUNCT
ejpam-521	197	2	25	25	NUM
ejpam-521	197	3	)	)	PUNCT
ejpam-521	197	4	if	if	SCONJ
ejpam-521	197	5	either	either	CCONJ
ejpam-521	197	6	α1	α1	PROPN
ejpam-521	197	7	6=	6=	NUM
ejpam-521	197	8	1	1	NUM
ejpam-521	197	9	or	or	CCONJ
ejpam-521	197	10	α2	α2	ADJ
ejpam-521	197	11	6=	6=	NUM
ejpam-521	197	12	1	1	NUM
ejpam-521	197	13	;	;	PUNCT
ejpam-521	197	14	and	and	CCONJ
ejpam-521	197	15	−l∗1(x	−l∗1(x	NOUN
ejpam-521	197	16	n	n	CCONJ
ejpam-521	197	17	;	;	PUNCT
ejpam-521	197	18	m	m	X
ejpam-521	197	19	)	)	PUNCT
ejpam-521	198	1	+	+	CCONJ
ejpam-521	198	2	l2(q̃	l2(q̃	PROPN
ejpam-521	198	3	m	m	PROPN
ejpam-521	198	4	,	,	PUNCT
ejpam-521	198	5	m	m	PROPN
ejpam-521	198	6	,	,	PUNCT
ejpam-521	198	7	δ	δ	PROPN
ejpam-521	198	8	)	)	PUNCT
ejpam-521	199	1	+	+	CCONJ
ejpam-521	199	2	log	log	VERB
ejpam-521	199	3	f	f	PROPN
ejpam-521	199	4	n(x	n(x	PROPN
ejpam-521	199	5	n	n	CCONJ
ejpam-521	199	6	)	)	PUNCT
ejpam-521	199	7	=	=	SYM
ejpam-521	199	8	o(nm−2+m	o(nm−2+m	NUM
ejpam-521	199	9	log	log	PROPN
ejpam-521	199	10	n	n	CCONJ
ejpam-521	199	11	)	)	PUNCT
ejpam-521	199	12	a.s	a.s	PROPN
ejpam-521	199	13	.	.	PROPN
ejpam-521	200	1	(	(	PUNCT
ejpam-521	200	2	26	26	NUM
ejpam-521	200	3	)	)	PUNCT
ejpam-521	200	4	if	if	SCONJ
ejpam-521	200	5	α1	α1	PROPN
ejpam-521	200	6	=	=	SYM
ejpam-521	200	7	α2	α2	NOUN
ejpam-521	200	8	=	=	SYM
ejpam-521	201	1	1	1	X
ejpam-521	201	2	.	.	PUNCT
ejpam-521	201	3	(	(	PUNCT
ejpam-521	201	4	2	2	NUM
ejpam-521	201	5	)	)	PUNCT
ejpam-521	201	6	.	.	PUNCT
ejpam-521	202	1	−amα1	−amα1	NOUN
ejpam-521	202	2	+	+	SYM
ejpam-521	202	3	1	1	NUM
ejpam-521	202	4	2	2	NUM
ejpam-521	202	5	m	m	NOUN
ejpam-521	202	6	log	log	NOUN
ejpam-521	202	7	n+	n+	PUNCT
ejpam-521	202	8	(	(	PUNCT
ejpam-521	202	9	α2−	α2−	NOUN
ejpam-521	202	10	3	3	NUM
ejpam-521	202	11	2	2	NUM
ejpam-521	202	12	α1)m	α1)m	NOUN
ejpam-521	202	13	log	log	NOUN
ejpam-521	202	14	m+	m+	NUM
ejpam-521	202	15	o(nm−2α2+m	o(nm−2α2+m	PROPN
ejpam-521	202	16	log	log	PROPN
ejpam-521	202	17	m	m	NOUN
ejpam-521	202	18	)	)	PUNCT
ejpam-521	202	19	≤	≤	NOUN
ejpam-521	202	20	−	−	ADP
ejpam-521	202	21	log	log	NOUN
ejpam-521	202	22	f̃	f̃	PROPN
ejpam-521	202	23	(	(	PUNCT
ejpam-521	202	24	x	x	SYM
ejpam-521	202	25	n	n	CCONJ
ejpam-521	202	26	;	;	PUNCT
ejpam-521	202	27	m	m	X
ejpam-521	202	28	)	)	PUNCT
ejpam-521	203	1	+	+	CCONJ
ejpam-521	203	2	l2(q̃	l2(q̃	PROPN
ejpam-521	203	3	m	m	PROPN
ejpam-521	203	4	,	,	PUNCT
ejpam-521	203	5	m	m	PROPN
ejpam-521	203	6	,	,	PUNCT
ejpam-521	203	7	δ	δ	PROPN
ejpam-521	203	8	)	)	PUNCT
ejpam-521	204	1	+	+	CCONJ
ejpam-521	204	2	log	log	VERB
ejpam-521	204	3	f	f	PROPN
ejpam-521	204	4	n(x	n(x	PROPN
ejpam-521	204	5	n	n	CCONJ
ejpam-521	204	6	)	)	PUNCT
ejpam-521	204	7	≤	≤	NUM
ejpam-521	204	8	1	1	NUM
ejpam-521	204	9	2	2	NUM
ejpam-521	204	10	m	m	NOUN
ejpam-521	204	11	log	log	NOUN
ejpam-521	204	12	n+	n+	PUNCT
ejpam-521	204	13	(	(	PUNCT
ejpam-521	204	14	2α1−	2α1−	NUM
ejpam-521	204	15	5	5	NUM
ejpam-521	204	16	2	2	NUM
ejpam-521	204	17	)	)	PUNCT
ejpam-521	204	18	m	m	VERB
ejpam-521	204	19	log	log	VERB
ejpam-521	205	1	m+	m+	NUM
ejpam-521	205	2	c	c	NOUN
ejpam-521	205	3	f	f	PROPN
ejpam-521	205	4	nm−2α2	nm−2α2	NOUN
ejpam-521	205	5	+	+	CCONJ
ejpam-521	205	6	o(nm−2α2+m	o(nm−2α2+m	ADJ
ejpam-521	205	7	log	log	NOUN
ejpam-521	205	8	n	n	CCONJ
ejpam-521	205	9	)	)	PUNCT
ejpam-521	205	10	a.s	a.s	PROPN
ejpam-521	205	11	.	.	PROPN
ejpam-521	205	12	(	(	PUNCT
ejpam-521	205	13	27	27	NUM
ejpam-521	205	14	)	)	PUNCT
ejpam-521	205	15	if	if	SCONJ
ejpam-521	205	16	either	either	CCONJ
ejpam-521	205	17	α1	α1	PROPN
ejpam-521	205	18	6=	6=	NUM
ejpam-521	205	19	1	1	NUM
ejpam-521	205	20	or	or	CCONJ
ejpam-521	205	21	α2	α2	ADJ
ejpam-521	205	22	6=	6=	NUM
ejpam-521	205	23	1	1	NUM
ejpam-521	205	24	;	;	PUNCT
ejpam-521	205	25	and	and	CCONJ
ejpam-521	205	26	−	−	PROPN
ejpam-521	205	27	log	log	NOUN
ejpam-521	205	28	f̃	f̃	PROPN
ejpam-521	205	29	(	(	PUNCT
ejpam-521	205	30	x	x	SYM
ejpam-521	205	31	n	n	CCONJ
ejpam-521	205	32	;	;	PUNCT
ejpam-521	205	33	m	m	X
ejpam-521	205	34	)	)	PUNCT
ejpam-521	206	1	+	+	CCONJ
ejpam-521	206	2	l2(q̃	l2(q̃	PROPN
ejpam-521	206	3	m	m	PROPN
ejpam-521	206	4	,	,	PUNCT
ejpam-521	206	5	m	m	PROPN
ejpam-521	206	6	,	,	PUNCT
ejpam-521	206	7	δ	δ	PROPN
ejpam-521	206	8	)	)	PUNCT
ejpam-521	207	1	+	+	CCONJ
ejpam-521	208	1	log	log	VERB
ejpam-521	208	2	f	f	PROPN
ejpam-521	208	3	n(x	n(x	PROPN
ejpam-521	208	4	n	n	CCONJ
ejpam-521	208	5	)	)	PUNCT
ejpam-521	208	6	=	=	SYM
ejpam-521	208	7	1	1	NUM
ejpam-521	208	8	2	2	NUM
ejpam-521	208	9	m	m	NOUN
ejpam-521	208	10	log	log	NOUN
ejpam-521	208	11	n	n	ADV
ejpam-521	208	12	m	m	VERB
ejpam-521	208	13	+	+	NUM
ejpam-521	208	14	c	c	NOUN
ejpam-521	208	15	′f	′f	NUM
ejpam-521	208	16	nm−2	nm−2	PROPN
ejpam-521	208	17	+	+	X
ejpam-521	208	18	o(nm−2	o(nm−2	NOUN
ejpam-521	208	19	+	+	NOUN
ejpam-521	208	20	m	m	NOUN
ejpam-521	208	21	log	log	NOUN
ejpam-521	208	22	n	n	CCONJ
ejpam-521	208	23	)	)	PUNCT
ejpam-521	208	24	a.s	a.s	PROPN
ejpam-521	208	25	.	.	PROPN
ejpam-521	209	1	(	(	PUNCT
ejpam-521	209	2	28	28	NUM
ejpam-521	209	3	)	)	PUNCT
ejpam-521	209	4	if	if	SCONJ
ejpam-521	209	5	α1	α1	PROPN
ejpam-521	209	6	=	=	SYM
ejpam-521	209	7	α2	α2	NOUN
ejpam-521	209	8	=	=	SYM
ejpam-521	210	1	1	1	X
ejpam-521	210	2	.	.	X
ejpam-521	211	1	here	here	ADV
ejpam-521	211	2	log	log	VERB
ejpam-521	211	3	f	f	PROPN
ejpam-521	211	4	n(x	n(x	PROPN
ejpam-521	211	5	n	n	CCONJ
ejpam-521	211	6	)	)	PUNCT
ejpam-521	211	7	=	=	VERB
ejpam-521	212	1	∏n	∏n	ADJ
ejpam-521	212	2	j=1	j=1	ADJ
ejpam-521	212	3	f	f	X
ejpam-521	212	4	(	(	PUNCT
ejpam-521	212	5	x	x	PROPN
ejpam-521	212	6	j	j	PROPN
ejpam-521	212	7	)	)	PUNCT
ejpam-521	212	8	,	,	PUNCT
ejpam-521	212	9	c	c	PROPN
ejpam-521	213	1	f	f	PROPN
ejpam-521	213	2	=	=	SYM
ejpam-521	213	3	24−1b2	24−1b2	NUM
ejpam-521	213	4	∫	∫	PROPN
ejpam-521	213	5	t	t	PROPN
ejpam-521	213	6	s	s	PROPN
ejpam-521	213	7	ḟ	ḟ	PROPN
ejpam-521	213	8	2	2	NUM
ejpam-521	213	9	f	f	NOUN
ejpam-521	213	10	−1	−1	NOUN
ejpam-521	213	11	,	,	PUNCT
ejpam-521	213	12	a	a	PRON
ejpam-521	213	13	>	>	X
ejpam-521	213	14	0	0	NUM
ejpam-521	213	15	is	be	AUX
ejpam-521	213	16	a	a	DET
ejpam-521	213	17	constant	constant	ADJ
ejpam-521	213	18	and	and	CCONJ
ejpam-521	213	19	c	c	NOUN
ejpam-521	213	20	′	′	NOUN
ejpam-521	214	1	f	f	NOUN
ejpam-521	214	2	is	be	AUX
ejpam-521	214	3	a	a	DET
ejpam-521	214	4	constant	constant	ADJ
ejpam-521	214	5	between	between	ADP
ejpam-521	214	6	c	c	PROPN
ejpam-521	214	7	f	f	PROPN
ejpam-521	214	8	b1	b1	PROPN
ejpam-521	214	9	b−1	b−1	PROPN
ejpam-521	214	10	2	2	NUM
ejpam-521	214	11	and	and	CCONJ
ejpam-521	214	12	c	c	NOUN
ejpam-521	214	13	f	f	PROPN
ejpam-521	214	14	.	.	PUNCT
ejpam-521	215	1	the	the	DET
ejpam-521	215	2	upper	upper	ADJ
ejpam-521	215	3	bounds	bound	NOUN
ejpam-521	215	4	in	in	ADP
ejpam-521	215	5	(	(	PUNCT
ejpam-521	215	6	25	25	NUM
ejpam-521	215	7	)	)	PUNCT
ejpam-521	215	8	and	and	CCONJ
ejpam-521	215	9	(	(	PUNCT
ejpam-521	215	10	27	27	NUM
ejpam-521	215	11	)	)	PUNCT
ejpam-521	215	12	imply	imply	VERB
ejpam-521	215	13	that	that	SCONJ
ejpam-521	215	14	,	,	PUNCT
ejpam-521	215	15	for	for	ADP
ejpam-521	215	16	a	a	DET
ejpam-521	215	17	given	give	VERB
ejpam-521	215	18	number	number	NOUN
ejpam-521	215	19	of	of	ADP
ejpam-521	215	20	subintervals	subinterval	NOUN
ejpam-521	215	21	m	m	PROPN
ejpam-521	215	22	,	,	PUNCT
ejpam-521	215	23	the	the	DET
ejpam-521	215	24	shortest	short	ADJ
ejpam-521	215	25	predictive	predictive	ADJ
ejpam-521	215	26	code	code	NOUN
ejpam-521	215	27	length	length	NOUN
ejpam-521	215	28	(	(	PUNCT
ejpam-521	215	29	20	20	NUM
ejpam-521	215	30	)	)	PUNCT
ejpam-521	215	31	is	be	AUX
ejpam-521	215	32	likely	likely	ADJ
ejpam-521	215	33	to	to	PART
ejpam-521	215	34	involve	involve	VERB
ejpam-521	215	35	more	more	ADJ
ejpam-521	215	36	redundant	redundant	ADJ
ejpam-521	215	37	code	code	NOUN
ejpam-521	215	38	length	length	NOUN
ejpam-521	215	39	in	in	ADP
ejpam-521	215	40	encoding	encode	VERB
ejpam-521	215	41	the	the	DET
ejpam-521	215	42	unknown	unknown	ADJ
ejpam-521	215	43	f	f	NOUN
ejpam-521	215	44	than	than	ADP
ejpam-521	215	45	the	the	DET
ejpam-521	215	46	shortest	short	ADJ
ejpam-521	215	47	code	code	NOUN
ejpam-521	215	48	length	length	NOUN
ejpam-521	215	49	(	(	PUNCT
ejpam-521	215	50	16	16	NUM
ejpam-521	215	51	)	)	PUNCT
ejpam-521	215	52	.	.	PUNCT
ejpam-521	216	1	theorem	theorem	NOUN
ejpam-521	216	2	3	3	NUM
ejpam-521	216	3	.	.	PUNCT
ejpam-521	217	1	under	under	ADP
ejpam-521	217	2	the	the	DET
ejpam-521	217	3	conditions	condition	NOUN
ejpam-521	217	4	of	of	ADP
ejpam-521	217	5	theorem	theorem	ADJ
ejpam-521	217	6	1	1	NUM
ejpam-521	217	7	and	and	CCONJ
ejpam-521	217	8	theorem	theorem	VERB
ejpam-521	217	9	2	2	NUM
ejpam-521	217	10	and	and	CCONJ
ejpam-521	217	11	having	have	VERB
ejpam-521	217	12	either	either	CCONJ
ejpam-521	217	13	α1	α1	PROPN
ejpam-521	217	14	6=	6=	NUM
ejpam-521	217	15	1	1	NUM
ejpam-521	217	16	or	or	CCONJ
ejpam-521	217	17	α2	α2	ADJ
ejpam-521	217	18	6=	6=	NUM
ejpam-521	217	19	1	1	NUM
ejpam-521	217	20	,	,	PUNCT
ejpam-521	217	21	we	we	PRON
ejpam-521	217	22	have	have	VERB
ejpam-521	217	23	−m1(n	−m1(n	NOUN
ejpam-521	217	24	α1γ2	α1γ2	INTJ
ejpam-521	217	25	+	+	NUM
ejpam-521	217	26	nγ2	nγ2	CCONJ
ejpam-521	217	27	log	log	NOUN
ejpam-521	217	28	n	n	CCONJ
ejpam-521	217	29	)	)	PUNCT
ejpam-521	217	30	≤	≤	NOUN
ejpam-521	217	31	minm∈[nγ1	minm∈[nγ1	PROPN
ejpam-521	217	32	,	,	PUNCT
ejpam-521	217	33	nγ2	nγ2	NOUN
ejpam-521	217	34	]	]	X
ejpam-521	217	35	{	{	PUNCT
ejpam-521	217	36	−l∗1(x	−l∗1(x	NOUN
ejpam-521	217	37	n	n	CCONJ
ejpam-521	217	38	;	;	PUNCT
ejpam-521	217	39	m	m	X
ejpam-521	217	40	)	)	PUNCT
ejpam-521	218	1	+	+	CCONJ
ejpam-521	219	1	l2(q̃	l2(q̃	PROPN
ejpam-521	219	2	m	m	PROPN
ejpam-521	219	3	,	,	PUNCT
ejpam-521	219	4	m	m	PROPN
ejpam-521	219	5	,	,	PUNCT
ejpam-521	219	6	δ)}+	δ)}+	ADJ
ejpam-521	219	7	log	log	NOUN
ejpam-521	219	8	f	f	PROPN
ejpam-521	219	9	n(x	n(x	PROPN
ejpam-521	219	10	n	n	CCONJ
ejpam-521	219	11	)	)	PUNCT
ejpam-521	219	12	≤	≤	NUM
ejpam-521	219	13	m2n	m2n	NOUN
ejpam-521	219	14	1	1	NUM
ejpam-521	219	15	1	1	NUM
ejpam-521	219	16	+	+	NUM
ejpam-521	219	17	2α2	2α2	NUM
ejpam-521	219	18	(	(	PUNCT
ejpam-521	219	19	log	log	NOUN
ejpam-521	219	20	n	n	CCONJ
ejpam-521	219	21	)	)	PUNCT
ejpam-521	219	22	2α2	2α2	NUM
ejpam-521	219	23	1	1	NUM
ejpam-521	219	24	+	+	NUM
ejpam-521	219	25	2α2	2α2	NUM
ejpam-521	220	1	a.s	a.s	PROPN
ejpam-521	220	2	.	.	PROPN
ejpam-521	220	3	(	(	PUNCT
ejpam-521	220	4	29	29	NUM
ejpam-521	220	5	)	)	PUNCT
ejpam-521	220	6	and	and	CCONJ
ejpam-521	220	7	−m3(n	−m3(n	NOUN
ejpam-521	220	8	α1γ2	α1γ2	SYM
ejpam-521	220	9	+	+	NUM
ejpam-521	220	10	nγ2	nγ2	NUM
ejpam-521	220	11	log	log	NOUN
ejpam-521	220	12	n	n	CCONJ
ejpam-521	220	13	)	)	PUNCT
ejpam-521	220	14	g.	g.	PROPN
ejpam-521	220	15	qian	qian	PROPN
ejpam-521	220	16	/	/	SYM
ejpam-521	220	17	eur	eur	PROPN
ejpam-521	220	18	.	.	PUNCT
ejpam-521	221	1	j.	j.	PROPN
ejpam-521	221	2	pure	pure	PROPN
ejpam-521	221	3	appl	appl	PROPN
ejpam-521	221	4	.	.	PROPN
ejpam-521	221	5	math	math	PROPN
ejpam-521	221	6	,	,	PUNCT
ejpam-521	221	7	3	3	NUM
ejpam-521	221	8	(	(	PUNCT
ejpam-521	221	9	2010	2010	NUM
ejpam-521	221	10	)	)	PUNCT
ejpam-521	221	11	,	,	PUNCT
ejpam-521	221	12	51	51	NUM
ejpam-521	221	13	-	-	SYM
ejpam-521	221	14	80	80	NUM
ejpam-521	221	15	60	60	NUM
ejpam-521	221	16	≤	≤	NOUN
ejpam-521	221	17	minm∈[nγ1	minm∈[nγ1	PROPN
ejpam-521	221	18	,	,	PUNCT
ejpam-521	221	19	nγ2	nγ2	NOUN
ejpam-521	221	20	]	]	X
ejpam-521	221	21	{	{	PUNCT
ejpam-521	221	22	−	−	NOUN
ejpam-521	221	23	log	log	NOUN
ejpam-521	221	24	f̃	f̃	PROPN
ejpam-521	221	25	(	(	PUNCT
ejpam-521	221	26	x	x	SYM
ejpam-521	221	27	n	n	CCONJ
ejpam-521	221	28	;	;	PUNCT
ejpam-521	221	29	m	m	X
ejpam-521	221	30	)	)	PUNCT
ejpam-521	222	1	+	+	CCONJ
ejpam-521	223	1	l2(q̃	l2(q̃	PROPN
ejpam-521	223	2	m	m	PROPN
ejpam-521	223	3	,	,	PUNCT
ejpam-521	223	4	m	m	PROPN
ejpam-521	223	5	,	,	PUNCT
ejpam-521	223	6	δ)}+	δ)}+	ADJ
ejpam-521	223	7	log	log	NOUN
ejpam-521	223	8	f	f	PROPN
ejpam-521	223	9	n(x	n(x	PROPN
ejpam-521	223	10	n	n	CCONJ
ejpam-521	223	11	)	)	PUNCT
ejpam-521	223	12	≤	≤	NUM
ejpam-521	223	13	m4n	m4n	VERB
ejpam-521	223	14	1	1	NUM
ejpam-521	223	15	1	1	NUM
ejpam-521	223	16	+	+	NOUN
ejpam-521	223	17	2α2	2α2	NUM
ejpam-521	223	18	(	(	PUNCT
ejpam-521	223	19	log	log	NOUN
ejpam-521	223	20	n	n	CCONJ
ejpam-521	223	21	)	)	PUNCT
ejpam-521	223	22	2α2	2α2	NUM
ejpam-521	223	23	1	1	NUM
ejpam-521	224	1	+	+	NUM
ejpam-521	224	2	2α2	2α2	NUM
ejpam-521	224	3	a.s	a.s	PROPN
ejpam-521	224	4	.	.	PROPN
ejpam-521	224	5	(	(	PUNCT
ejpam-521	224	6	30	30	NUM
ejpam-521	224	7	)	)	PUNCT
ejpam-521	224	8	where	where	SCONJ
ejpam-521	224	9	m1	m1	PROPN
ejpam-521	224	10	,	,	PUNCT
ejpam-521	224	11	m2	m2	PROPN
ejpam-521	224	12	,	,	PUNCT
ejpam-521	224	13	m3	m3	PROPN
ejpam-521	224	14	,	,	PUNCT
ejpam-521	224	15	m4	m4	PROPN
ejpam-521	224	16	are	be	AUX
ejpam-521	224	17	positive	positive	ADJ
ejpam-521	224	18	constants	constant	NOUN
ejpam-521	224	19	depending	depend	VERB
ejpam-521	224	20	on	on	ADP
ejpam-521	224	21	f	f	PROPN
ejpam-521	224	22	.	.	PUNCT
ejpam-521	225	1	theorem	theorem	ADJ
ejpam-521	225	2	3	3	NUM
ejpam-521	225	3	implies	imply	VERB
ejpam-521	225	4	that	that	SCONJ
ejpam-521	225	5	,	,	PUNCT
ejpam-521	225	6	even	even	ADV
ejpam-521	225	7	though	though	SCONJ
ejpam-521	225	8	for	for	ADP
ejpam-521	225	9	a	a	DET
ejpam-521	225	10	fixed	fix	VERB
ejpam-521	225	11	m	m	VERB
ejpam-521	225	12	the	the	DET
ejpam-521	225	13	predictive	predictive	ADJ
ejpam-521	225	14	code	code	NOUN
ejpam-521	225	15	length	length	NOUN
ejpam-521	225	16	(	(	PUNCT
ejpam-521	225	17	27	27	NUM
ejpam-521	225	18	)	)	PUNCT
ejpam-521	225	19	may	may	AUX
ejpam-521	225	20	be	be	AUX
ejpam-521	225	21	longer	long	ADJ
ejpam-521	225	22	than	than	ADP
ejpam-521	225	23	the	the	DET
ejpam-521	225	24	code	code	NOUN
ejpam-521	225	25	length	length	NOUN
ejpam-521	225	26	(	(	PUNCT
ejpam-521	225	27	25	25	NUM
ejpam-521	225	28	)	)	PUNCT
ejpam-521	225	29	by	by	ADP
ejpam-521	225	30	an	an	DET
ejpam-521	225	31	infinite	infinite	ADJ
ejpam-521	225	32	number	number	NOUN
ejpam-521	225	33	of	of	ADP
ejpam-521	225	34	digits	digit	NOUN
ejpam-521	225	35	as	as	ADP
ejpam-521	225	36	n→∞	n→∞	NUM
ejpam-521	225	37	,	,	PUNCT
ejpam-521	225	38	both	both	PRON
ejpam-521	225	39	of	of	ADP
ejpam-521	225	40	them	they	PRON
ejpam-521	225	41	have	have	VERB
ejpam-521	225	42	the	the	DET
ejpam-521	225	43	minimax	minimax	NOUN
ejpam-521	225	44	bounds	bound	NOUN
ejpam-521	225	45	of	of	ADP
ejpam-521	225	46	the	the	DET
ejpam-521	225	47	same	same	ADJ
ejpam-521	225	48	order	order	NOUN
ejpam-521	225	49	.	.	PUNCT
ejpam-521	226	1	theorem	theorem	NOUN
ejpam-521	226	2	3	3	NUM
ejpam-521	226	3	can	can	AUX
ejpam-521	226	4	be	be	AUX
ejpam-521	226	5	further	far	ADV
ejpam-521	226	6	refined	refine	VERB
ejpam-521	226	7	when	when	SCONJ
ejpam-521	226	8	α1	α1	PROPN
ejpam-521	226	9	=	=	SYM
ejpam-521	226	10	α2	α2	NOUN
ejpam-521	226	11	=	=	SYM
ejpam-521	226	12	1	1	NUM
ejpam-521	226	13	is	be	AUX
ejpam-521	226	14	assumed	assume	VERB
ejpam-521	226	15	,	,	PUNCT
ejpam-521	226	16	which	which	PRON
ejpam-521	226	17	is	be	AUX
ejpam-521	226	18	given	give	VERB
ejpam-521	226	19	below	below	ADV
ejpam-521	226	20	.	.	PUNCT
ejpam-521	227	1	theorem	theorem	VERB
ejpam-521	227	2	4	4	NUM
ejpam-521	227	3	.	.	PUNCT
ejpam-521	228	1	under	under	ADP
ejpam-521	228	2	the	the	DET
ejpam-521	228	3	conditions	condition	NOUN
ejpam-521	228	4	of	of	ADP
ejpam-521	228	5	theorem	theorem	ADJ
ejpam-521	228	6	1	1	NUM
ejpam-521	228	7	and	and	CCONJ
ejpam-521	228	8	theorem	theorem	VERB
ejpam-521	228	9	2	2	NUM
ejpam-521	228	10	and	and	CCONJ
ejpam-521	228	11	that	that	DET
ejpam-521	228	12	α1	α1	NOUN
ejpam-521	228	13	=	=	SYM
ejpam-521	228	14	α2	α2	NOUN
ejpam-521	228	15	=	=	SYM
ejpam-521	228	16	1	1	NUM
ejpam-521	228	17	,	,	PUNCT
ejpam-521	228	18	the	the	DET
ejpam-521	228	19	following	following	ADJ
ejpam-521	228	20	statements	statement	NOUN
ejpam-521	228	21	hold	hold	VERB
ejpam-521	228	22	.	.	PUNCT
ejpam-521	229	1	(	(	PUNCT
ejpam-521	229	2	a	a	NOUN
ejpam-521	229	3	)	)	PUNCT
ejpam-521	229	4	.	.	PUNCT
ejpam-521	230	1	min	min	PROPN
ejpam-521	230	2	m∈[nγ1	m∈[nγ1	NOUN
ejpam-521	230	3	,	,	PUNCT
ejpam-521	230	4	nγ2	nγ2	NOUN
ejpam-521	230	5	]	]	PUNCT
ejpam-521	230	6	{	{	PUNCT
ejpam-521	230	7	−l∗1(x	−l∗1(x	NOUN
ejpam-521	230	8	n	n	CCONJ
ejpam-521	230	9	;	;	PUNCT
ejpam-521	230	10	m	m	X
ejpam-521	230	11	)	)	PUNCT
ejpam-521	231	1	+	+	CCONJ
ejpam-521	232	1	l2(q̃	l2(q̃	PROPN
ejpam-521	232	2	m	m	PROPN
ejpam-521	232	3	,	,	PUNCT
ejpam-521	232	4	m	m	PROPN
ejpam-521	232	5	,	,	PUNCT
ejpam-521	232	6	δ)}+	δ)}+	ADJ
ejpam-521	232	7	log	log	NOUN
ejpam-521	232	8	f	f	PROPN
ejpam-521	232	9	n(x	n(x	PROPN
ejpam-521	232	10	n	n	CCONJ
ejpam-521	232	11	)	)	PUNCT
ejpam-521	233	1	=	=	SYM
ejpam-521	233	2	o(n	o(n	NOUN
ejpam-521	233	3	1	1	NUM
ejpam-521	233	4	3	3	NUM
ejpam-521	233	5	(	(	PUNCT
ejpam-521	233	6	log	log	NOUN
ejpam-521	233	7	n	n	CCONJ
ejpam-521	233	8	)	)	PUNCT
ejpam-521	233	9	2	2	NUM
ejpam-521	233	10	3	3	NUM
ejpam-521	233	11	)	)	PUNCT
ejpam-521	233	12	a.s	a.s	PROPN
ejpam-521	233	13	.	.	PROPN
ejpam-521	233	14	(	(	PUNCT
ejpam-521	233	15	31	31	NUM
ejpam-521	233	16	)	)	PUNCT
ejpam-521	233	17	(	(	PUNCT
ejpam-521	233	18	b	b	NOUN
ejpam-521	233	19	)	)	PUNCT
ejpam-521	233	20	.	.	PUNCT
ejpam-521	234	1	min	min	PROPN
ejpam-521	234	2	m∈[nγ1	m∈[nγ1	NOUN
ejpam-521	234	3	,	,	PUNCT
ejpam-521	234	4	nγ2	nγ2	NUM
ejpam-521	234	5	]	]	X
ejpam-521	234	6	{	{	PUNCT
ejpam-521	234	7	−	−	NOUN
ejpam-521	234	8	log	log	NOUN
ejpam-521	234	9	f̃	f̃	PROPN
ejpam-521	234	10	(	(	PUNCT
ejpam-521	234	11	x	x	SYM
ejpam-521	234	12	n	n	CCONJ
ejpam-521	234	13	;	;	PUNCT
ejpam-521	234	14	m	m	X
ejpam-521	234	15	)	)	PUNCT
ejpam-521	235	1	+	+	CCONJ
ejpam-521	236	1	l2(q̃	l2(q̃	PROPN
ejpam-521	236	2	m	m	PROPN
ejpam-521	236	3	,	,	PUNCT
ejpam-521	236	4	m	m	PROPN
ejpam-521	236	5	,	,	PUNCT
ejpam-521	236	6	δ)}+	δ)}+	ADJ
ejpam-521	236	7	log	log	NOUN
ejpam-521	236	8	f	f	PROPN
ejpam-521	236	9	n(x	n(x	PROPN
ejpam-521	236	10	n	n	CCONJ
ejpam-521	236	11	)	)	PUNCT
ejpam-521	237	1	=	=	PUNCT
ejpam-521	237	2	m5n	m5n	NOUN
ejpam-521	237	3	1	1	NUM
ejpam-521	237	4	3	3	NUM
ejpam-521	237	5	(	(	PUNCT
ejpam-521	237	6	log	log	NOUN
ejpam-521	237	7	n	n	CCONJ
ejpam-521	237	8	)	)	PUNCT
ejpam-521	237	9	2	2	NUM
ejpam-521	237	10	3	3	NUM
ejpam-521	237	11	(	(	PUNCT
ejpam-521	237	12	1	1	NUM
ejpam-521	237	13	+	+	NUM
ejpam-521	237	14	o(1	o(1	NOUN
ejpam-521	237	15	)	)	PUNCT
ejpam-521	237	16	)	)	PUNCT
ejpam-521	238	1	a.s	a.s	PROPN
ejpam-521	238	2	.	.	PROPN
ejpam-521	238	3	(	(	PUNCT
ejpam-521	238	4	32	32	NUM
ejpam-521	238	5	)	)	PUNCT
ejpam-521	238	6	(	(	PUNCT
ejpam-521	238	7	c	c	NOUN
ejpam-521	238	8	)	)	PUNCT
ejpam-521	238	9	.	.	PUNCT
ejpam-521	239	1	m∗	m∗	PROPN
ejpam-521	239	2	=	=	SYM
ejpam-521	239	3	o((n/	o((n/	PROPN
ejpam-521	239	4	log	log	NOUN
ejpam-521	239	5	n	n	CCONJ
ejpam-521	239	6	)	)	PUNCT
ejpam-521	239	7	1	1	NUM
ejpam-521	239	8	3	3	X
ejpam-521	239	9	)	)	PUNCT
ejpam-521	240	1	a.s	a.s	PROPN
ejpam-521	240	2	.	.	PROPN
ejpam-521	240	3	(	(	PUNCT
ejpam-521	240	4	33	33	NUM
ejpam-521	240	5	)	)	PUNCT
ejpam-521	240	6	(	(	PUNCT
ejpam-521	240	7	d	d	NOUN
ejpam-521	240	8	)	)	PUNCT
ejpam-521	240	9	.	.	PUNCT
ejpam-521	241	1	m̂=	m̂=	PROPN
ejpam-521	241	2	m6(n/	m6(n/	PROPN
ejpam-521	241	3	log	log	VERB
ejpam-521	241	4	n	n	CCONJ
ejpam-521	241	5	)	)	PUNCT
ejpam-521	241	6	1	1	NUM
ejpam-521	241	7	3	3	NUM
ejpam-521	241	8	(	(	PUNCT
ejpam-521	241	9	1	1	NUM
ejpam-521	241	10	+	+	NUM
ejpam-521	241	11	o(1	o(1	NOUN
ejpam-521	241	12	)	)	PUNCT
ejpam-521	241	13	)	)	PUNCT
ejpam-521	242	1	a.s	a.s	PROPN
ejpam-521	242	2	.	.	PROPN
ejpam-521	242	3	(	(	PUNCT
ejpam-521	242	4	34	34	NUM
ejpam-521	242	5	)	)	PUNCT
ejpam-521	242	6	where	where	SCONJ
ejpam-521	242	7	m5	m5	PROPN
ejpam-521	242	8	and	and	CCONJ
ejpam-521	242	9	m6	m6	PROPN
ejpam-521	242	10	are	be	AUX
ejpam-521	242	11	positive	positive	ADJ
ejpam-521	242	12	constants	constant	NOUN
ejpam-521	242	13	depending	depend	VERB
ejpam-521	242	14	on	on	ADP
ejpam-521	242	15	f	f	PROPN
ejpam-521	242	16	.	.	PUNCT
ejpam-521	243	1	note	note	VERB
ejpam-521	243	2	that	that	SCONJ
ejpam-521	243	3	α1	α1	PROPN
ejpam-521	243	4	=	=	SYM
ejpam-521	243	5	α2	α2	NOUN
ejpam-521	243	6	=	=	SYM
ejpam-521	243	7	1	1	NUM
ejpam-521	243	8	implies	imply	VERB
ejpam-521	243	9	the	the	DET
ejpam-521	243	10	width	width	NOUN
ejpam-521	243	11	of	of	ADP
ejpam-521	243	12	each	each	DET
ejpam-521	243	13	subinterval	subinterval	NOUN
ejpam-521	243	14	in	in	ADP
ejpam-521	243	15	the	the	DET
ejpam-521	243	16	histogram	histogram	NOUN
ejpam-521	243	17	,	,	PUNCT
ejpam-521	243	18	although	although	SCONJ
ejpam-521	243	19	still	still	ADV
ejpam-521	243	20	being	be	AUX
ejpam-521	243	21	variable	variable	ADJ
ejpam-521	243	22	,	,	PUNCT
ejpam-521	243	23	is	be	AUX
ejpam-521	243	24	of	of	ADP
ejpam-521	243	25	the	the	DET
ejpam-521	243	26	same	same	ADJ
ejpam-521	243	27	order	order	NOUN
ejpam-521	243	28	as	as	ADP
ejpam-521	243	29	m−1	m−1	PROPN
ejpam-521	243	30	.	.	PUNCT
ejpam-521	244	1	the	the	DET
ejpam-521	244	2	results	result	NOUN
ejpam-521	244	3	(	(	PUNCT
ejpam-521	244	4	32	32	NUM
ejpam-521	244	5	)	)	PUNCT
ejpam-521	244	6	and	and	CCONJ
ejpam-521	244	7	(	(	PUNCT
ejpam-521	244	8	34	34	NUM
ejpam-521	244	9	)	)	PUNCT
ejpam-521	244	10	are	be	AUX
ejpam-521	244	11	the	the	DET
ejpam-521	244	12	same	same	ADJ
ejpam-521	244	13	as	as	ADP
ejpam-521	244	14	(	(	PUNCT
ejpam-521	244	15	ii	ii	NOUN
ejpam-521	244	16	)	)	PUNCT
ejpam-521	244	17	and	and	CCONJ
ejpam-521	244	18	(	(	PUNCT
ejpam-521	244	19	iv	iv	X
ejpam-521	244	20	)	)	PUNCT
ejpam-521	244	21	of	of	ADP
ejpam-521	244	22	theorem	theorem	ADJ
ejpam-521	244	23	2.4	2.4	NUM
ejpam-521	244	24	of	of	ADP
ejpam-521	244	25	[	[	X
ejpam-521	244	26	20	20	NUM
ejpam-521	244	27	]	]	PUNCT
ejpam-521	244	28	where	where	SCONJ
ejpam-521	244	29	they	they	PRON
ejpam-521	244	30	use	use	VERB
ejpam-521	244	31	predictive	predictive	ADJ
ejpam-521	244	32	histogram	histogram	NOUN
ejpam-521	244	33	estimator	estimator	NOUN
ejpam-521	244	34	of	of	ADP
ejpam-521	244	35	equal	equal	ADJ
ejpam-521	244	36	width	width	ADJ
ejpam-521	244	37	subintervals	subinterval	NOUN
ejpam-521	244	38	.	.	PUNCT
ejpam-521	245	1	this	this	PRON
ejpam-521	245	2	shows	show	VERB
ejpam-521	245	3	that	that	SCONJ
ejpam-521	245	4	using	use	VERB
ejpam-521	245	5	a	a	DET
ejpam-521	245	6	variable	variable	ADJ
ejpam-521	245	7	subinterval	subinterval	NOUN
ejpam-521	245	8	-	-	PUNCT
ejpam-521	245	9	width	width	NOUN
ejpam-521	245	10	optimal	optimal	ADJ
ejpam-521	245	11	histogram	histogram	NOUN
ejpam-521	245	12	density	density	NOUN
ejpam-521	245	13	estimator	estimator	NOUN
ejpam-521	245	14	,	,	PUNCT
ejpam-521	245	15	if	if	SCONJ
ejpam-521	245	16	the	the	DET
ejpam-521	245	17	widths	width	NOUN
ejpam-521	245	18	are	be	AUX
ejpam-521	245	19	of	of	ADP
ejpam-521	245	20	the	the	DET
ejpam-521	245	21	same	same	ADJ
ejpam-521	245	22	order	order	NOUN
ejpam-521	245	23	,	,	PUNCT
ejpam-521	245	24	achieves	achieve	VERB
ejpam-521	245	25	the	the	DET
ejpam-521	245	26	same	same	ADJ
ejpam-521	245	27	order	order	NOUN
ejpam-521	245	28	of	of	ADP
ejpam-521	245	29	shortest	short	ADJ
ejpam-521	245	30	code	code	NOUN
ejpam-521	245	31	length	length	NOUN
ejpam-521	245	32	for	for	ADP
ejpam-521	245	33	description	description	NOUN
ejpam-521	245	34	of	of	ADP
ejpam-521	245	35	x	x	PUNCT
ejpam-521	245	36	n	n	CCONJ
ejpam-521	245	37	as	as	ADP
ejpam-521	245	38	using	use	VERB
ejpam-521	245	39	an	an	DET
ejpam-521	245	40	equal	equal	ADJ
ejpam-521	245	41	width	width	ADJ
ejpam-521	245	42	optimal	optimal	ADJ
ejpam-521	245	43	histogram	histogram	NOUN
ejpam-521	245	44	density	density	NOUN
ejpam-521	245	45	estimator	estimator	NOUN
ejpam-521	245	46	.	.	PUNCT
ejpam-521	246	1	from	from	ADP
ejpam-521	246	2	theorem	theorem	NOUN
ejpam-521	246	3	4	4	NUM
ejpam-521	246	4	we	we	PRON
ejpam-521	246	5	also	also	ADV
ejpam-521	246	6	see	see	VERB
ejpam-521	246	7	that	that	SCONJ
ejpam-521	246	8	the	the	DET
ejpam-521	246	9	results	result	NOUN
ejpam-521	246	10	for	for	ADP
ejpam-521	246	11	the	the	DET
ejpam-521	246	12	shortest	short	ADJ
ejpam-521	246	13	predictive	predictive	ADJ
ejpam-521	246	14	code	code	NOUN
ejpam-521	246	15	length	length	NOUN
ejpam-521	246	16	are	be	AUX
ejpam-521	246	17	more	more	ADV
ejpam-521	246	18	definite	definite	ADJ
ejpam-521	246	19	than	than	ADP
ejpam-521	246	20	for	for	ADP
ejpam-521	246	21	the	the	DET
ejpam-521	246	22	shortest	short	ADJ
ejpam-521	246	23	code	code	NOUN
ejpam-521	246	24	length	length	NOUN
ejpam-521	246	25	.	.	PUNCT
ejpam-521	247	1	therefore	therefore	ADV
ejpam-521	247	2	,	,	PUNCT
ejpam-521	247	3	we	we	PRON
ejpam-521	247	4	will	will	AUX
ejpam-521	247	5	focus	focus	VERB
ejpam-521	247	6	our	our	PRON
ejpam-521	247	7	study	study	NOUN
ejpam-521	247	8	on	on	ADP
ejpam-521	247	9	the	the	DET
ejpam-521	247	10	predictive	predictive	ADJ
ejpam-521	247	11	code	code	NOUN
ejpam-521	247	12	length	length	NOUN
ejpam-521	247	13	in	in	ADP
ejpam-521	247	14	the	the	DET
ejpam-521	247	15	next	next	ADJ
ejpam-521	247	16	section	section	NOUN
ejpam-521	247	17	.	.	PUNCT
ejpam-521	248	1	g.	g.	PROPN
ejpam-521	248	2	qian	qian	PROPN
ejpam-521	248	3	/	/	SYM
ejpam-521	248	4	eur	eur	PROPN
ejpam-521	248	5	.	.	PUNCT
ejpam-521	249	1	j.	j.	PROPN
ejpam-521	249	2	pure	pure	PROPN
ejpam-521	249	3	appl	appl	PROPN
ejpam-521	249	4	.	.	PROPN
ejpam-521	249	5	math	math	PROPN
ejpam-521	249	6	,	,	PUNCT
ejpam-521	249	7	3	3	NUM
ejpam-521	249	8	(	(	PUNCT
ejpam-521	249	9	2010	2010	NUM
ejpam-521	249	10	)	)	PUNCT
ejpam-521	249	11	,	,	PUNCT
ejpam-521	249	12	51	51	NUM
ejpam-521	249	13	-	-	SYM
ejpam-521	249	14	80	80	NUM
ejpam-521	249	15	61	61	NUM
ejpam-521	249	16	3	3	NUM
ejpam-521	249	17	.	.	PUNCT
ejpam-521	249	18	hypothesis	hypothesis	NOUN
ejpam-521	249	19	testing	testing	NOUN
ejpam-521	249	20	for	for	ADP
ejpam-521	249	21	homogeneity	homogeneity	NOUN
ejpam-521	249	22	one	one	NUM
ejpam-521	249	23	of	of	ADP
ejpam-521	249	24	the	the	DET
ejpam-521	249	25	basic	basic	ADJ
ejpam-521	249	26	problems	problem	NOUN
ejpam-521	249	27	in	in	ADP
ejpam-521	249	28	statistical	statistical	ADJ
ejpam-521	249	29	inference	inference	NOUN
ejpam-521	249	30	is	be	AUX
ejpam-521	249	31	testing	test	VERB
ejpam-521	249	32	the	the	DET
ejpam-521	249	33	equality	equality	NOUN
ejpam-521	249	34	of	of	ADP
ejpam-521	249	35	two	two	NUM
ejpam-521	249	36	distributions	distribution	NOUN
ejpam-521	249	37	where	where	SCONJ
ejpam-521	249	38	two	two	NUM
ejpam-521	249	39	independent	independent	ADJ
ejpam-521	249	40	samples	sample	NOUN
ejpam-521	249	41	are	be	AUX
ejpam-521	249	42	observed	observe	VERB
ejpam-521	249	43	from	from	ADP
ejpam-521	249	44	;	;	PUNCT
ejpam-521	249	45	and	and	CCONJ
ejpam-521	249	46	more	more	ADV
ejpam-521	249	47	generally	generally	ADV
ejpam-521	249	48	,	,	PUNCT
ejpam-521	249	49	testing	test	VERB
ejpam-521	249	50	the	the	DET
ejpam-521	249	51	homogeneity	homogeneity	NOUN
ejpam-521	249	52	of	of	ADP
ejpam-521	249	53	k	k	PROPN
ejpam-521	249	54	distributions	distribution	NOUN
ejpam-521	249	55	with	with	ADP
ejpam-521	249	56	k	k	PROPN
ejpam-521	249	57	>	>	X
ejpam-521	249	58	2	2	NUM
ejpam-521	249	59	where	where	SCONJ
ejpam-521	249	60	k	k	PROPN
ejpam-521	249	61	independent	independent	ADJ
ejpam-521	249	62	samples	sample	NOUN
ejpam-521	249	63	are	be	AUX
ejpam-521	249	64	observed	observe	VERB
ejpam-521	249	65	from	from	ADP
ejpam-521	249	66	.	.	PUNCT
ejpam-521	250	1	using	use	VERB
ejpam-521	250	2	the	the	DET
ejpam-521	250	3	data	datum	NOUN
ejpam-521	250	4	quantization	quantization	NOUN
ejpam-521	250	5	method	method	NOUN
ejpam-521	250	6	developed	develop	VERB
ejpam-521	250	7	in	in	ADP
ejpam-521	250	8	section	section	NOUN
ejpam-521	250	9	2	2	NUM
ejpam-521	250	10	we	we	PRON
ejpam-521	250	11	propose	propose	VERB
ejpam-521	250	12	a	a	DET
ejpam-521	250	13	stochastic	stochastic	ADJ
ejpam-521	250	14	complexity	complexity	NOUN
ejpam-521	250	15	based	base	VERB
ejpam-521	250	16	procedure	procedure	NOUN
ejpam-521	250	17	for	for	ADP
ejpam-521	250	18	testing	test	VERB
ejpam-521	250	19	the	the	DET
ejpam-521	250	20	homogeneity	homogeneity	NOUN
ejpam-521	250	21	of	of	ADP
ejpam-521	250	22	k	k	PROPN
ejpam-521	250	23	distributions	distribution	NOUN
ejpam-521	250	24	.	.	PUNCT
ejpam-521	251	1	first	first	ADV
ejpam-521	251	2	,	,	PUNCT
ejpam-521	251	3	a	a	DET
ejpam-521	251	4	shortest	short	ADJ
ejpam-521	251	5	predictive	predictive	ADJ
ejpam-521	251	6	code	code	NOUN
ejpam-521	251	7	length	length	NOUN
ejpam-521	251	8	,	,	PUNCT
ejpam-521	251	9	based	base	VERB
ejpam-521	251	10	on	on	ADP
ejpam-521	251	11	a	a	DET
ejpam-521	251	12	class	class	NOUN
ejpam-521	251	13	of	of	ADP
ejpam-521	251	14	histogram	histogram	NOUN
ejpam-521	251	15	density	density	NOUN
ejpam-521	251	16	estimators	estimator	NOUN
ejpam-521	251	17	with	with	ADP
ejpam-521	251	18	variable	variable	ADJ
ejpam-521	251	19	width	width	ADJ
ejpam-521	251	20	subintervals	subinterval	NOUN
ejpam-521	251	21	,	,	PUNCT
ejpam-521	251	22	is	be	AUX
ejpam-521	251	23	computed	compute	VERB
ejpam-521	251	24	for	for	ADP
ejpam-521	251	25	each	each	PRON
ejpam-521	251	26	of	of	ADP
ejpam-521	251	27	the	the	DET
ejpam-521	251	28	k	k	PROPN
ejpam-521	251	29	independent	independent	ADJ
ejpam-521	251	30	samples	sample	NOUN
ejpam-521	251	31	.	.	PUNCT
ejpam-521	252	1	this	this	PRON
ejpam-521	252	2	,	,	PUNCT
ejpam-521	252	3	when	when	SCONJ
ejpam-521	252	4	minimized	minimize	VERB
ejpam-521	252	5	,	,	PUNCT
ejpam-521	252	6	gives	give	VERB
ejpam-521	252	7	the	the	DET
ejpam-521	252	8	optimal	optimal	ADJ
ejpam-521	252	9	number	number	NOUN
ejpam-521	252	10	of	of	ADP
ejpam-521	252	11	subintervals	subinterval	NOUN
ejpam-521	252	12	and	and	CCONJ
ejpam-521	252	13	their	their	PRON
ejpam-521	252	14	locations	location	NOUN
ejpam-521	252	15	,	,	PUNCT
ejpam-521	252	16	the	the	DET
ejpam-521	252	17	associated	associated	ADJ
ejpam-521	252	18	density	density	NOUN
ejpam-521	252	19	estimator	estimator	NOUN
ejpam-521	252	20	and	and	CCONJ
ejpam-521	252	21	the	the	DET
ejpam-521	252	22	proper	proper	ADJ
ejpam-521	252	23	measurement	measurement	NOUN
ejpam-521	252	24	of	of	ADP
ejpam-521	252	25	the	the	DET
ejpam-521	252	26	information	information	NOUN
ejpam-521	252	27	contained	contain	VERB
ejpam-521	252	28	in	in	ADP
ejpam-521	252	29	each	each	DET
ejpam-521	252	30	sample	sample	NOUN
ejpam-521	252	31	.	.	PUNCT
ejpam-521	253	1	second	second	ADJ
ejpam-521	253	2	,	,	PUNCT
ejpam-521	253	3	the	the	DET
ejpam-521	253	4	shortest	short	ADJ
ejpam-521	253	5	predictive	predictive	ADJ
ejpam-521	253	6	code	code	NOUN
ejpam-521	253	7	length	length	NOUN
ejpam-521	253	8	is	be	AUX
ejpam-521	253	9	computed	compute	VERB
ejpam-521	253	10	for	for	ADP
ejpam-521	253	11	the	the	DET
ejpam-521	253	12	pooled	pooled	ADJ
ejpam-521	253	13	sample	sample	NOUN
ejpam-521	253	14	,	,	PUNCT
ejpam-521	253	15	which	which	PRON
ejpam-521	253	16	when	when	SCONJ
ejpam-521	253	17	minimized	minimize	VERB
ejpam-521	253	18	gives	give	VERB
ejpam-521	253	19	the	the	DET
ejpam-521	253	20	histogram	histogram	NOUN
ejpam-521	253	21	estimator	estimator	NOUN
ejpam-521	253	22	of	of	ADP
ejpam-521	253	23	the	the	DET
ejpam-521	253	24	associated	associated	ADJ
ejpam-521	253	25	mixture	mixture	NOUN
ejpam-521	253	26	distribution	distribution	NOUN
ejpam-521	253	27	.	.	PUNCT
ejpam-521	254	1	finally	finally	ADV
ejpam-521	254	2	,	,	PUNCT
ejpam-521	254	3	the	the	DET
ejpam-521	254	4	shortest	short	ADJ
ejpam-521	254	5	predictive	predictive	ADJ
ejpam-521	254	6	code	code	NOUN
ejpam-521	254	7	length	length	NOUN
ejpam-521	254	8	of	of	ADP
ejpam-521	254	9	the	the	DET
ejpam-521	254	10	pooled	pooled	ADJ
ejpam-521	254	11	sample	sample	NOUN
ejpam-521	254	12	is	be	AUX
ejpam-521	254	13	compared	compare	VERB
ejpam-521	254	14	with	with	ADP
ejpam-521	254	15	the	the	DET
ejpam-521	254	16	sum	sum	NOUN
ejpam-521	254	17	of	of	ADP
ejpam-521	254	18	the	the	DET
ejpam-521	254	19	shortest	short	ADJ
ejpam-521	254	20	predictive	predictive	ADJ
ejpam-521	254	21	code	code	NOUN
ejpam-521	254	22	lengths	length	NOUN
ejpam-521	254	23	of	of	ADP
ejpam-521	254	24	all	all	DET
ejpam-521	254	25	the	the	DET
ejpam-521	254	26	k	k	PROPN
ejpam-521	254	27	samples	sample	NOUN
ejpam-521	254	28	.	.	PUNCT
ejpam-521	255	1	if	if	SCONJ
ejpam-521	255	2	the	the	DET
ejpam-521	255	3	former	former	ADJ
ejpam-521	255	4	one	one	NOUN
ejpam-521	255	5	is	be	AUX
ejpam-521	255	6	smaller	small	ADJ
ejpam-521	255	7	,	,	PUNCT
ejpam-521	255	8	then	then	ADV
ejpam-521	255	9	the	the	DET
ejpam-521	255	10	hypothesis	hypothesis	NOUN
ejpam-521	255	11	that	that	PRON
ejpam-521	255	12	the	the	DET
ejpam-521	255	13	k	k	PROPN
ejpam-521	255	14	distributions	distribution	NOUN
ejpam-521	255	15	are	be	AUX
ejpam-521	255	16	the	the	DET
ejpam-521	255	17	same	same	ADJ
ejpam-521	255	18	is	be	AUX
ejpam-521	255	19	not	not	PART
ejpam-521	255	20	rejected	reject	VERB
ejpam-521	255	21	,	,	PUNCT
ejpam-521	255	22	but	but	CCONJ
ejpam-521	255	23	rejected	reject	VERB
ejpam-521	255	24	otherwise	otherwise	ADV
ejpam-521	255	25	.	.	PUNCT
ejpam-521	256	1	let	let	VERB
ejpam-521	256	2	(	(	PUNCT
ejpam-521	256	3	x11	x11	NOUN
ejpam-521	256	4	,	,	PUNCT
ejpam-521	256	5	·	·	PUNCT
ejpam-521	256	6	·	·	PUNCT
ejpam-521	256	7	·	·	PUNCT
ejpam-521	256	8	,	,	PUNCT
ejpam-521	256	9	x1n1	x1n1	X
ejpam-521	256	10	)	)	PUNCT
ejpam-521	256	11	,	,	PUNCT
ejpam-521	256	12	(	(	PUNCT
ejpam-521	256	13	x21	x21	PROPN
ejpam-521	256	14	,	,	PUNCT
ejpam-521	256	15	·	·	PUNCT
ejpam-521	256	16	·	·	PUNCT
ejpam-521	256	17	·	·	PUNCT
ejpam-521	256	18	,	,	PUNCT
ejpam-521	256	19	x2n2	x2n2	PROPN
ejpam-521	256	20	)	)	PUNCT
ejpam-521	256	21	,	,	PUNCT
ejpam-521	256	22	·	·	PUNCT
ejpam-521	256	23	·	·	PUNCT
ejpam-521	256	24	·	·	PUNCT
ejpam-521	256	25	,	,	PUNCT
ejpam-521	256	26	(	(	PUNCT
ejpam-521	256	27	xk1	xk1	PROPN
ejpam-521	256	28	,	,	PUNCT
ejpam-521	256	29	·	·	PUNCT
ejpam-521	256	30	·	·	PUNCT
ejpam-521	256	31	·	·	PUNCT
ejpam-521	256	32	,	,	PUNCT
ejpam-521	256	33	xknk	xknk	NOUN
ejpam-521	256	34	)	)	PUNCT
ejpam-521	256	35	(	(	PUNCT
ejpam-521	256	36	abbreviated	abbreviate	VERB
ejpam-521	256	37	as	as	ADP
ejpam-521	256	38	x	x	PROPN
ejpam-521	256	39	n1	n1	PROPN
ejpam-521	256	40	1	1	NUM
ejpam-521	256	41	,	,	PUNCT
ejpam-521	256	42	x	x	SYM
ejpam-521	256	43	n2	n2	NOUN
ejpam-521	256	44	2	2	NUM
ejpam-521	256	45	,	,	PUNCT
ejpam-521	256	46	·	·	PUNCT
ejpam-521	256	47	·	·	PUNCT
ejpam-521	256	48	·	·	PUNCT
ejpam-521	256	49	,	,	PUNCT
ejpam-521	256	50	x	x	PUNCT
ejpam-521	256	51	nk	nk	PROPN
ejpam-521	256	52	k	k	PROPN
ejpam-521	256	53	)	)	PUNCT
ejpam-521	256	54	be	be	AUX
ejpam-521	256	55	k	k	X
ejpam-521	256	56	independent	independent	ADJ
ejpam-521	256	57	random	random	ADJ
ejpam-521	256	58	samples	sample	NOUN
ejpam-521	256	59	with	with	ADP
ejpam-521	256	60	sizes	size	NOUN
ejpam-521	256	61	n1	n1	NOUN
ejpam-521	256	62	,	,	PUNCT
ejpam-521	256	63	n2	n2	NOUN
ejpam-521	256	64	,	,	PUNCT
ejpam-521	256	65	·	·	PUNCT
ejpam-521	256	66	·	·	PUNCT
ejpam-521	256	67	·	·	PUNCT
ejpam-521	256	68	,	,	PUNCT
ejpam-521	256	69	nk	nk	PROPN
ejpam-521	256	70	and	and	CCONJ
ejpam-521	256	71	∑k	∑k	PROPN
ejpam-521	256	72	i=1	i=1	PROPN
ejpam-521	256	73	ni	ni	PROPN
ejpam-521	256	74	=	=	PROPN
ejpam-521	256	75	n.	n.	PROPN
ejpam-521	256	76	the	the	DET
ejpam-521	256	77	respective	respective	ADJ
ejpam-521	256	78	unknown	unknown	ADJ
ejpam-521	256	79	population	population	NOUN
ejpam-521	256	80	density	density	NOUN
ejpam-521	256	81	functions	function	NOUN
ejpam-521	256	82	are	be	AUX
ejpam-521	256	83	f1(x	f1(x	NUM
ejpam-521	256	84	)	)	PUNCT
ejpam-521	256	85	,	,	PUNCT
ejpam-521	256	86	f2(x	f2(x	PROPN
ejpam-521	256	87	)	)	PUNCT
ejpam-521	256	88	,	,	PUNCT
ejpam-521	256	89	·	·	PUNCT
ejpam-521	256	90	·	·	PUNCT
ejpam-521	256	91	·	·	PUNCT
ejpam-521	256	92	,	,	PUNCT
ejpam-521	256	93	fk(x	fk(x	PROPN
ejpam-521	256	94	)	)	PUNCT
ejpam-521	256	95	,	,	PUNCT
ejpam-521	256	96	all	all	ADV
ejpam-521	256	97	with	with	ADP
ejpam-521	256	98	the	the	DET
ejpam-521	256	99	same	same	ADJ
ejpam-521	256	100	support	support	NOUN
ejpam-521	257	1	[	[	X
ejpam-521	257	2	s	s	X
ejpam-521	257	3	,	,	PUNCT
ejpam-521	257	4	t	t	PROPN
ejpam-521	257	5	]	]	PUNCT
ejpam-521	257	6	.	.	PUNCT
ejpam-521	258	1	the	the	DET
ejpam-521	258	2	underlying	underlying	ADJ
ejpam-521	258	3	problem	problem	NOUN
ejpam-521	258	4	is	be	AUX
ejpam-521	258	5	the	the	DET
ejpam-521	258	6	testing	testing	NOUN
ejpam-521	258	7	of	of	ADP
ejpam-521	258	8	the	the	DET
ejpam-521	258	9	hypothesis	hypothesis	NOUN
ejpam-521	258	10	h0	h0	NOUN
ejpam-521	258	11	:	:	PUNCT
ejpam-521	258	12	f1	f1	NOUN
ejpam-521	258	13	=	=	SYM
ejpam-521	258	14	f2	f2	PROPN
ejpam-521	258	15	=	=	SYM
ejpam-521	258	16	·	·	PUNCT
ejpam-521	258	17	·	·	PUNCT
ejpam-521	258	18	·	·	PUNCT
ejpam-521	259	1	=	=	SYM
ejpam-521	259	2	fk	fk	INTJ
ejpam-521	259	3	versus	versus	ADP
ejpam-521	259	4	ha	ha	INTJ
ejpam-521	259	5	:	:	PUNCT
ejpam-521	259	6	at	at	ADV
ejpam-521	259	7	least	least	ADV
ejpam-521	259	8	two	two	NUM
ejpam-521	259	9	of	of	ADP
ejpam-521	259	10	them	they	PRON
ejpam-521	259	11	are	be	AUX
ejpam-521	259	12	not	not	PART
ejpam-521	259	13	equal	equal	ADJ
ejpam-521	259	14	.	.	PUNCT
ejpam-521	260	1	(	(	PUNCT
ejpam-521	260	2	35	35	NUM
ejpam-521	260	3	)	)	PUNCT
ejpam-521	260	4	under	under	ADP
ejpam-521	260	5	the	the	DET
ejpam-521	260	6	alternative	alternative	ADJ
ejpam-521	260	7	hypothesis	hypothesis	NOUN
ejpam-521	260	8	ha	ha	INTJ
ejpam-521	260	9	,	,	PUNCT
ejpam-521	260	10	we	we	PRON
ejpam-521	260	11	should	should	AUX
ejpam-521	260	12	describe	describe	VERB
ejpam-521	260	13	the	the	DET
ejpam-521	260	14	information	information	NOUN
ejpam-521	260	15	of	of	ADP
ejpam-521	260	16	the	the	DET
ejpam-521	260	17	k	k	PROPN
ejpam-521	260	18	samples	sample	NOUN
ejpam-521	260	19	x	x	SYM
ejpam-521	260	20	n1	n1	NOUN
ejpam-521	260	21	1	1	NUM
ejpam-521	260	22	,	,	PUNCT
ejpam-521	260	23	x	x	SYM
ejpam-521	260	24	n2	n2	NOUN
ejpam-521	260	25	2	2	NUM
ejpam-521	260	26	,	,	PUNCT
ejpam-521	260	27	·	·	PUNCT
ejpam-521	260	28	·	·	PUNCT
ejpam-521	260	29	·	·	PUNCT
ejpam-521	260	30	,	,	PUNCT
ejpam-521	260	31	x	x	X
ejpam-521	260	32	nk	nk	PROPN
ejpam-521	260	33	k	k	PROPN
ejpam-521	260	34	separately	separately	ADV
ejpam-521	260	35	,	,	PUNCT
ejpam-521	260	36	i.e.	i.e.	X
ejpam-521	260	37	we	we	PRON
ejpam-521	260	38	should	should	AUX
ejpam-521	260	39	find	find	VERB
ejpam-521	260	40	the	the	DET
ejpam-521	260	41	shortest	short	ADJ
ejpam-521	260	42	code	code	NOUN
ejpam-521	260	43	length	length	NOUN
ejpam-521	260	44	for	for	ADP
ejpam-521	260	45	each	each	DET
ejpam-521	260	46	sample	sample	NOUN
ejpam-521	260	47	x	x	PUNCT
ejpam-521	260	48	ni	ni	PROPN
ejpam-521	260	49	i	i	PROPN
ejpam-521	260	50	with	with	ADP
ejpam-521	260	51	density	density	NOUN
ejpam-521	260	52	fi	fi	NOUN
ejpam-521	260	53	.	.	PUNCT
ejpam-521	261	1	by	by	ADP
ejpam-521	261	2	(	(	PUNCT
ejpam-521	261	3	20	20	NUM
ejpam-521	261	4	)	)	PUNCT
ejpam-521	261	5	the	the	DET
ejpam-521	261	6	total	total	ADJ
ejpam-521	261	7	predictive	predictive	ADJ
ejpam-521	261	8	code	code	NOUN
ejpam-521	261	9	length	length	NOUN
ejpam-521	261	10	for	for	ADP
ejpam-521	261	11	the	the	DET
ejpam-521	261	12	k	k	PROPN
ejpam-521	261	13	samples	sample	NOUN
ejpam-521	261	14	is	be	AUX
ejpam-521	261	15	min	min	NOUN
ejpam-521	261	16	m1	m1	PROPN
ejpam-521	261	17	,	,	PUNCT
ejpam-521	261	18	·	·	PUNCT
ejpam-521	261	19	·	·	PUNCT
ejpam-521	261	20	·	·	PUNCT
ejpam-521	261	21	,	,	PUNCT
ejpam-521	261	22	mk	mk	PROPN
ejpam-521	261	23	(	(	PUNCT
ejpam-521	261	24	−	−	PROPN
ejpam-521	261	25	k	k	INTJ
ejpam-521	261	26	∑	∑	PUNCT
ejpam-521	261	27	i=1	i=1	PROPN
ejpam-521	261	28	log	log	PROPN
ejpam-521	261	29	f̃i(x	f̃i(x	PROPN
ejpam-521	261	30	ni	ni	PROPN
ejpam-521	261	31	i	i	PROPN
ejpam-521	261	32	;	;	PUNCT
ejpam-521	261	33	mi)+	mi)+	X
ejpam-521	262	1	k	k	X
ejpam-521	262	2	∑	∑	PUNCT
ejpam-521	262	3	i=1	i=1	PROPN
ejpam-521	263	1	l2(q̃	l2(q̃	PROPN
ejpam-521	263	2	mi	mi	PROPN
ejpam-521	264	1	i	i	PROPN
ejpam-521	264	2	,	,	PUNCT
ejpam-521	264	3	mi	mi	PROPN
ejpam-521	264	4	,	,	PUNCT
ejpam-521	264	5	δ	δ	PROPN
ejpam-521	264	6	)	)	PUNCT
ejpam-521	264	7	)	)	PUNCT
ejpam-521	264	8	(	(	PUNCT
ejpam-521	264	9	36	36	NUM
ejpam-521	264	10	)	)	PUNCT
ejpam-521	264	11	provided	provide	VERB
ejpam-521	264	12	that	that	SCONJ
ejpam-521	264	13	the	the	DET
ejpam-521	264	14	parameter	parameter	NOUN
ejpam-521	264	15	truncation	truncation	NOUN
ejpam-521	264	16	is	be	AUX
ejpam-521	264	17	based	base	VERB
ejpam-521	264	18	on	on	ADP
ejpam-521	264	19	the	the	DET
ejpam-521	264	20	same	same	ADJ
ejpam-521	264	21	precision	precision	NOUN
ejpam-521	264	22	δ	δ	PROPN
ejpam-521	264	23	.	.	PUNCT
ejpam-521	265	1	here	here	ADV
ejpam-521	265	2	f̃i(x	f̃i(x	PROPN
ejpam-521	265	3	ni	ni	PROPN
ejpam-521	265	4	i	i	PROPN
ejpam-521	265	5	;	;	PUNCT
ejpam-521	265	6	mi	mi	PROPN
ejpam-521	265	7	)	)	PUNCT
ejpam-521	265	8	is	be	AUX
ejpam-521	265	9	the	the	DET
ejpam-521	265	10	likelihood	likelihood	NOUN
ejpam-521	265	11	function	function	NOUN
ejpam-521	265	12	of	of	ADP
ejpam-521	265	13	the	the	DET
ejpam-521	265	14	i	i	PROPN
ejpam-521	265	15	-	-	PUNCT
ejpam-521	265	16	th	th	X
ejpam-521	265	17	sample	sample	NOUN
ejpam-521	265	18	x	x	PUNCT
ejpam-521	265	19	ni	ni	NOUN
ejpam-521	265	20	i	i	PRON
ejpam-521	265	21	defined	define	VERB
ejpam-521	265	22	as	as	ADP
ejpam-521	265	23	(	(	PUNCT
ejpam-521	265	24	19	19	NUM
ejpam-521	265	25	)	)	PUNCT
ejpam-521	265	26	,	,	PUNCT
ejpam-521	265	27	i.e.	i.e.	X
ejpam-521	265	28	f̃i(x	f̃i(x	PROPN
ejpam-521	265	29	ni	ni	PROPN
ejpam-521	265	30	i	i	PROPN
ejpam-521	265	31	;	;	PUNCT
ejpam-521	265	32	mi	mi	PROPN
ejpam-521	265	33	)	)	PUNCT
ejpam-521	265	34	=	=	PUNCT
ejpam-521	265	35	(	(	PUNCT
ejpam-521	265	36	mi	mi	PROPN
ejpam-521	265	37	−	−	PROPN
ejpam-521	265	38	1	1	NUM
ejpam-521	265	39	)	)	PUNCT
ejpam-521	265	40	!	!	PUNCT
ejpam-521	266	1	(	(	PUNCT
ejpam-521	266	2	ni	ni	PROPN
ejpam-521	266	3	+	+	PROPN
ejpam-521	266	4	mi	mi	PROPN
ejpam-521	266	5	−	−	PROPN
ejpam-521	266	6	1	1	NUM
ejpam-521	266	7	)	)	PUNCT
ejpam-521	266	8	!	!	PUNCT
ejpam-521	267	1	mi	mi	PROPN
ejpam-521	267	2	∏	∏	PROPN
ejpam-521	267	3	j=1	j=1	PROPN
ejpam-521	267	4	ni	ni	PROPN
ejpam-521	267	5	,	,	PUNCT
ejpam-521	267	6	j	j	PROPN
ejpam-521	267	7	,	,	PUNCT
ejpam-521	267	8	mi	mi	PROPN
ejpam-521	267	9	!	!	PUNCT
ejpam-521	268	1	r̃	r̃	PROPN
ejpam-521	268	2	ni	ni	PROPN
ejpam-521	268	3	,	,	PUNCT
ejpam-521	268	4	j	j	PROPN
ejpam-521	268	5	,	,	PUNCT
ejpam-521	268	6	mi	mi	PROPN
ejpam-521	269	1	i	i	PROPN
ejpam-521	269	2	,	,	PUNCT
ejpam-521	269	3	j	j	PROPN
ejpam-521	269	4	,	,	PUNCT
ejpam-521	269	5	mi	mi	PROPN
ejpam-521	269	6	(	(	PUNCT
ejpam-521	269	7	37	37	NUM
ejpam-521	269	8	)	)	PUNCT
ejpam-521	269	9	where	where	SCONJ
ejpam-521	269	10	r̃i	r̃i	NOUN
ejpam-521	269	11	,	,	PUNCT
ejpam-521	269	12	j	j	PROPN
ejpam-521	269	13	,	,	PUNCT
ejpam-521	269	14	mi	mi	PROPN
ejpam-521	269	15	’s	’s	PART
ejpam-521	269	16	are	be	AUX
ejpam-521	269	17	the	the	DET
ejpam-521	269	18	widths	width	NOUN
ejpam-521	269	19	of	of	ADP
ejpam-521	269	20	the	the	DET
ejpam-521	269	21	optimal	optimal	ADJ
ejpam-521	269	22	partition	partition	NOUN
ejpam-521	269	23	{	{	PUNCT
ejpam-521	269	24	q̃	q̃	PROPN
ejpam-521	269	25	i	i	PROPN
ejpam-521	269	26	,	,	PUNCT
ejpam-521	269	27	j	j	PROPN
ejpam-521	269	28	,	,	PUNCT
ejpam-521	269	29	mi	mi	PROPN
ejpam-521	269	30	}	}	PUNCT
ejpam-521	269	31	of	of	ADP
ejpam-521	269	32	the	the	DET
ejpam-521	269	33	i	i	PROPN
ejpam-521	269	34	-	-	PUNCT
ejpam-521	269	35	th	th	VERB
ejpam-521	269	36	sample	sample	NOUN
ejpam-521	269	37	.	.	PUNCT
ejpam-521	270	1	these	these	PRON
ejpam-521	270	2	are	be	AUX
ejpam-521	270	3	obtained	obtain	VERB
ejpam-521	270	4	by	by	ADP
ejpam-521	270	5	applying	apply	VERB
ejpam-521	270	6	the	the	DET
ejpam-521	270	7	maximum	maximum	ADJ
ejpam-521	270	8	likelihood	likelihood	NOUN
ejpam-521	270	9	principle	principle	NOUN
ejpam-521	270	10	(	(	PUNCT
ejpam-521	270	11	4	4	NUM
ejpam-521	270	12	)	)	PUNCT
ejpam-521	270	13	to	to	ADP
ejpam-521	270	14	the	the	DET
ejpam-521	270	15	i	i	PROPN
ejpam-521	270	16	-	-	PUNCT
ejpam-521	270	17	th	th	X
ejpam-521	270	18	sample	sample	NOUN
ejpam-521	270	19	with	with	ADP
ejpam-521	270	20	fixed	fix	VERB
ejpam-521	270	21	number	number	NOUN
ejpam-521	270	22	of	of	ADP
ejpam-521	270	23	subintervals	subinterval	NOUN
ejpam-521	270	24	mi	mi	PROPN
ejpam-521	270	25	.	.	PUNCT
ejpam-521	271	1	then	then	ADV
ejpam-521	271	2	ni	ni	PROPN
ejpam-521	271	3	,	,	PUNCT
ejpam-521	271	4	j	j	PROPN
ejpam-521	271	5	,	,	PUNCT
ejpam-521	271	6	mi	mi	PROPN
ejpam-521	271	7	is	be	AUX
ejpam-521	271	8	the	the	DET
ejpam-521	271	9	number	number	NOUN
ejpam-521	271	10	of	of	ADP
ejpam-521	271	11	data	datum	NOUN
ejpam-521	271	12	points	point	NOUN
ejpam-521	271	13	falling	fall	VERB
ejpam-521	271	14	into	into	ADP
ejpam-521	271	15	the	the	DET
ejpam-521	271	16	j	j	PROPN
ejpam-521	271	17	-	-	PUNCT
ejpam-521	271	18	th	th	VERB
ejpam-521	271	19	subinterval	subinterval	NOUN
ejpam-521	272	1	q̃	q̃	PROPN
ejpam-521	272	2	i	i	PRON
ejpam-521	272	3	,	,	PUNCT
ejpam-521	272	4	j	j	PROPN
ejpam-521	272	5	,	,	PUNCT
ejpam-521	272	6	mi	mi	PROPN
ejpam-521	272	7	.	.	PUNCT
ejpam-521	273	1	g.	g.	PROPN
ejpam-521	273	2	qian	qian	PROPN
ejpam-521	273	3	/	/	SYM
ejpam-521	273	4	eur	eur	PROPN
ejpam-521	273	5	.	.	PUNCT
ejpam-521	274	1	j.	j.	PROPN
ejpam-521	274	2	pure	pure	PROPN
ejpam-521	274	3	appl	appl	PROPN
ejpam-521	274	4	.	.	PROPN
ejpam-521	274	5	math	math	PROPN
ejpam-521	274	6	,	,	PUNCT
ejpam-521	274	7	3	3	NUM
ejpam-521	274	8	(	(	PUNCT
ejpam-521	274	9	2010	2010	NUM
ejpam-521	274	10	)	)	PUNCT
ejpam-521	274	11	,	,	PUNCT
ejpam-521	274	12	51	51	NUM
ejpam-521	274	13	-	-	SYM
ejpam-521	274	14	80	80	NUM
ejpam-521	274	15	62	62	NUM
ejpam-521	274	16	because	because	SCONJ
ejpam-521	274	17	all	all	PRON
ejpam-521	274	18	of	of	ADP
ejpam-521	274	19	the	the	DET
ejpam-521	274	20	k	k	PROPN
ejpam-521	274	21	samples	sample	NOUN
ejpam-521	274	22	are	be	AUX
ejpam-521	274	23	encoded	encode	VERB
ejpam-521	274	24	simultaneously	simultaneously	ADV
ejpam-521	274	25	,	,	PUNCT
ejpam-521	274	26	the	the	DET
ejpam-521	274	27	second	second	ADJ
ejpam-521	274	28	term	term	NOUN
ejpam-521	274	29	of	of	ADP
ejpam-521	274	30	(	(	PUNCT
ejpam-521	274	31	36	36	NUM
ejpam-521	274	32	)	)	PUNCT
ejpam-521	274	33	could	could	AUX
ejpam-521	274	34	be	be	AUX
ejpam-521	274	35	further	far	ADV
ejpam-521	274	36	reduced	reduce	VERB
ejpam-521	274	37	by	by	ADP
ejpam-521	274	38	a	a	DET
ejpam-521	274	39	more	more	ADV
ejpam-521	274	40	efficient	efficient	ADJ
ejpam-521	274	41	encoding	encoding	NOUN
ejpam-521	274	42	process	process	NOUN
ejpam-521	274	43	as	as	SCONJ
ejpam-521	274	44	given	give	VERB
ejpam-521	274	45	by	by	ADP
ejpam-521	274	46	l4(q̃	l4(q̃	PROPN
ejpam-521	274	47	m1	m1	PROPN
ejpam-521	274	48	1	1	NUM
ejpam-521	274	49	,	,	PUNCT
ejpam-521	274	50	·	·	PUNCT
ejpam-521	274	51	·	·	PUNCT
ejpam-521	274	52	·	·	PUNCT
ejpam-521	275	1	,	,	PUNCT
ejpam-521	275	2	q̃mk	q̃mk	ADP
ejpam-521	275	3	k	k	PROPN
ejpam-521	275	4	,	,	PUNCT
ejpam-521	275	5	m1	m1	PROPN
ejpam-521	275	6	,	,	PUNCT
ejpam-521	275	7	·	·	PUNCT
ejpam-521	275	8	·	·	PUNCT
ejpam-521	275	9	·	·	PUNCT
ejpam-521	275	10	,	,	PUNCT
ejpam-521	275	11	mk	mk	PROPN
ejpam-521	275	12	,	,	PUNCT
ejpam-521	275	13	δ	δ	PROPN
ejpam-521	275	14	)	)	PUNCT
ejpam-521	275	15	=	=	SYM
ejpam-521	276	1	k	k	X
ejpam-521	276	2	∑	∑	PUNCT
ejpam-521	276	3	i=1	i=1	PROPN
ejpam-521	276	4	log	log	PROPN
ejpam-521	276	5	�	�	PROPN
ejpam-521	276	6	∑mi−1	∑mi−1	PROPN
ejpam-521	276	7	j=1	j=1	PROPN
ejpam-521	276	8	�	�	PROPN
ejpam-521	276	9	�	�	PROPN
ejpam-521	276	10	�	�	PROPN
ejpam-521	276	11	r̃i	r̃i	PROPN
ejpam-521	276	12	,	,	PUNCT
ejpam-521	276	13	j	j	PROPN
ejpam-521	276	14	,	,	PUNCT
ejpam-521	276	15	mi	mi	PROPN
ejpam-521	276	16	−	−	PROPN
ejpam-521	276	17	r	r	PROPN
ejpam-521	276	18	mi	mi	PROPN
ejpam-521	276	19	�	�	PROPN
ejpam-521	276	20	�	�	PROPN
ejpam-521	276	21	�	�	PROPN
ejpam-521	276	22	+	+	PROPN
ejpam-521	276	23	mi	mi	NOUN
ejpam-521	276	24	−	−	PROPN
ejpam-521	276	25	2	2	NUM
ejpam-521	276	26	mi	mi	NOUN
ejpam-521	276	27	−	−	PROPN
ejpam-521	276	28	2	2	NUM
ejpam-521	276	29	�	�	PROPN
ejpam-521	276	30	+	+	NOUN
ejpam-521	276	31	l3(m1	l3(m1	NOUN
ejpam-521	276	32	,	,	PUNCT
ejpam-521	276	33	·	·	PUNCT
ejpam-521	276	34	·	·	PUNCT
ejpam-521	276	35	·	·	PUNCT
ejpam-521	276	36	,	,	PUNCT
ejpam-521	276	37	mk	mk	PROPN
ejpam-521	276	38	,	,	PUNCT
ejpam-521	276	39	s̄	s̄	NOUN
ejpam-521	276	40	,	,	PUNCT
ejpam-521	276	41	r̄	r̄	NOUN
ejpam-521	276	42	)	)	PUNCT
ejpam-521	276	43	+	+	CCONJ
ejpam-521	277	1	|	|	ADV
ejpam-521	277	2	logδ|	logδ|	PROPN
ejpam-521	277	3	(	(	PUNCT
ejpam-521	277	4	38	38	NUM
ejpam-521	277	5	)	)	PUNCT
ejpam-521	277	6	where	where	SCONJ
ejpam-521	277	7	q̃	q̃	PROPN
ejpam-521	277	8	mi	mi	PROPN
ejpam-521	277	9	i	i	PRON
ejpam-521	277	10	is	be	AUX
ejpam-521	277	11	the	the	DET
ejpam-521	277	12	sequence	sequence	NOUN
ejpam-521	277	13	of	of	ADP
ejpam-521	277	14	break	break	NOUN
ejpam-521	277	15	points	point	NOUN
ejpam-521	277	16	corresponding	correspond	VERB
ejpam-521	277	17	to	to	ADP
ejpam-521	277	18	the	the	DET
ejpam-521	277	19	optimal	optimal	ADJ
ejpam-521	277	20	partition	partition	NOUN
ejpam-521	277	21	{	{	PUNCT
ejpam-521	277	22	q̃	q̃	PROPN
ejpam-521	277	23	i	i	PROPN
ejpam-521	277	24	,	,	PUNCT
ejpam-521	277	25	j	j	PROPN
ejpam-521	277	26	,	,	PUNCT
ejpam-521	277	27	mi	mi	PROPN
ejpam-521	277	28	}	}	PUNCT
ejpam-521	277	29	.	.	PUNCT
ejpam-521	278	1	the	the	DET
ejpam-521	278	2	efficiency	efficiency	NOUN
ejpam-521	278	3	lies	lie	VERB
ejpam-521	278	4	in	in	ADP
ejpam-521	278	5	the	the	DET
ejpam-521	278	6	fact	fact	NOUN
ejpam-521	278	7	that	that	SCONJ
ejpam-521	278	8	the	the	DET
ejpam-521	278	9	set	set	NOUN
ejpam-521	278	10	of	of	ADP
ejpam-521	278	11	integers	integer	NOUN
ejpam-521	278	12	{	{	PUNCT
ejpam-521	278	13	m1	m1	NOUN
ejpam-521	278	14	,	,	PUNCT
ejpam-521	278	15	·	·	PUNCT
ejpam-521	278	16	·	·	PUNCT
ejpam-521	278	17	·	·	PUNCT
ejpam-521	278	18	,	,	PUNCT
ejpam-521	278	19	mk	mk	PROPN
ejpam-521	278	20	,	,	PUNCT
ejpam-521	278	21	s̄	s̄	NOUN
ejpam-521	278	22	,	,	PUNCT
ejpam-521	278	23	r̄	r̄	NOUN
ejpam-521	278	24	}	}	PUNCT
ejpam-521	278	25	is	be	AUX
ejpam-521	278	26	encoded	encode	VERB
ejpam-521	278	27	in	in	ADP
ejpam-521	278	28	a	a	DET
ejpam-521	278	29	prefix	prefix	NOUN
ejpam-521	278	30	manner	manner	NOUN
ejpam-521	278	31	,	,	PUNCT
ejpam-521	278	32	which	which	PRON
ejpam-521	278	33	requires	require	VERB
ejpam-521	278	34	l3(m1	l3(m1	NOUN
ejpam-521	278	35	,	,	PUNCT
ejpam-521	278	36	·	·	PUNCT
ejpam-521	278	37	·	·	PUNCT
ejpam-521	278	38	·	·	PUNCT
ejpam-521	278	39	,	,	PUNCT
ejpam-521	278	40	mk	mk	PROPN
ejpam-521	278	41	,	,	PUNCT
ejpam-521	278	42	s̄	s̄	NOUN
ejpam-521	278	43	,	,	PUNCT
ejpam-521	278	44	r̄	r̄	NOUN
ejpam-521	278	45	)	)	PUNCT
ejpam-521	278	46	bits	bit	NOUN
ejpam-521	278	47	instead	instead	ADV
ejpam-521	278	48	of	of	ADP
ejpam-521	278	49	∑k	∑k	PROPN
ejpam-521	278	50	i=1	i=1	PROPN
ejpam-521	278	51	l3(mi	l3(mi	PROPN
ejpam-521	278	52	,	,	PUNCT
ejpam-521	278	53	s̄	s̄	NOUN
ejpam-521	278	54	,	,	PUNCT
ejpam-521	278	55	r̄	r̄	NOUN
ejpam-521	278	56	)	)	PUNCT
ejpam-521	278	57	bits	bit	NOUN
ejpam-521	278	58	.	.	PUNCT
ejpam-521	279	1	therefore	therefore	ADV
ejpam-521	279	2	under	under	ADP
ejpam-521	279	3	the	the	DET
ejpam-521	279	4	hypothesis	hypothesis	NOUN
ejpam-521	279	5	ha	ha	INTJ
ejpam-521	279	6	the	the	DET
ejpam-521	279	7	total	total	ADJ
ejpam-521	279	8	predictive	predictive	ADJ
ejpam-521	279	9	code	code	NOUN
ejpam-521	279	10	length	length	NOUN
ejpam-521	279	11	(	(	PUNCT
ejpam-521	279	12	36	36	NUM
ejpam-521	279	13	)	)	PUNCT
ejpam-521	279	14	for	for	ADP
ejpam-521	279	15	the	the	DET
ejpam-521	279	16	k	k	PROPN
ejpam-521	279	17	samples	sample	NOUN
ejpam-521	279	18	can	can	AUX
ejpam-521	279	19	be	be	AUX
ejpam-521	279	20	replaced	replace	VERB
ejpam-521	279	21	by	by	ADP
ejpam-521	279	22	a	a	DET
ejpam-521	279	23	shorter	short	ADJ
ejpam-521	279	24	code	code	NOUN
ejpam-521	279	25	length	length	NOUN
ejpam-521	279	26	c(x	c(x	NOUN
ejpam-521	279	27	n1	n1	NOUN
ejpam-521	279	28	1	1	NUM
ejpam-521	279	29	,	,	PUNCT
ejpam-521	279	30	·	·	PUNCT
ejpam-521	279	31	·	·	PUNCT
ejpam-521	279	32	·	·	PUNCT
ejpam-521	279	33	,	,	PUNCT
ejpam-521	279	34	x	x	PUNCT
ejpam-521	279	35	nk	nk	PROPN
ejpam-521	279	36	k	k	PROPN
ejpam-521	279	37	)	)	PUNCT
ejpam-521	280	1	=	=	SYM
ejpam-521	280	2	min	min	NOUN
ejpam-521	280	3	m1	m1	PROPN
ejpam-521	280	4	,	,	PUNCT
ejpam-521	280	5	·	·	PUNCT
ejpam-521	280	6	·	·	PUNCT
ejpam-521	280	7	·	·	PUNCT
ejpam-521	280	8	,	,	PUNCT
ejpam-521	280	9	mk	mk	PROPN
ejpam-521	280	10	{	{	PUNCT
ejpam-521	280	11	−	−	PROPN
ejpam-521	280	12	k	k	INTJ
ejpam-521	280	13	∑	∑	PUNCT
ejpam-521	280	14	i=1	i=1	PROPN
ejpam-521	280	15	log	log	PROPN
ejpam-521	280	16	f̃i(x	f̃i(x	PROPN
ejpam-521	280	17	ni	ni	PROPN
ejpam-521	280	18	i	i	PROPN
ejpam-521	280	19	;	;	PUNCT
ejpam-521	280	20	mi	mi	PROPN
ejpam-521	280	21	)	)	PUNCT
ejpam-521	280	22	+	+	ADJ
ejpam-521	280	23	l4(q̃	l4(q̃	PROPN
ejpam-521	280	24	m1	m1	PROPN
ejpam-521	280	25	1	1	NUM
ejpam-521	280	26	,	,	PUNCT
ejpam-521	280	27	·	·	PUNCT
ejpam-521	280	28	·	·	PUNCT
ejpam-521	280	29	·	·	PUNCT
ejpam-521	280	30	,	,	PUNCT
ejpam-521	280	31	q̃mk	q̃mk	ADP
ejpam-521	280	32	k	k	PROPN
ejpam-521	280	33	,	,	PUNCT
ejpam-521	280	34	m1	m1	PROPN
ejpam-521	280	35	,	,	PUNCT
ejpam-521	280	36	·	·	PUNCT
ejpam-521	280	37	·	·	PUNCT
ejpam-521	280	38	·	·	PUNCT
ejpam-521	280	39	,	,	PUNCT
ejpam-521	280	40	mk	mk	PROPN
ejpam-521	280	41	,	,	PUNCT
ejpam-521	280	42	δ	δ	PROPN
ejpam-521	280	43	)	)	PUNCT
ejpam-521	280	44	}	}	PUNCT
ejpam-521	280	45	(	(	PUNCT
ejpam-521	280	46	39	39	NUM
ejpam-521	280	47	)	)	PUNCT
ejpam-521	280	48	where	where	SCONJ
ejpam-521	280	49	the	the	DET
ejpam-521	280	50	minimum	minimum	NOUN
ejpam-521	280	51	is	be	AUX
ejpam-521	280	52	attained	attain	VERB
ejpam-521	280	53	at	at	ADP
ejpam-521	280	54	m̂1	m̂1	PROPN
ejpam-521	280	55	,	,	PUNCT
ejpam-521	280	56	·	·	PUNCT
ejpam-521	280	57	·	·	PUNCT
ejpam-521	280	58	·	·	PUNCT
ejpam-521	280	59	,	,	PUNCT
ejpam-521	280	60	m̂k	m̂k	PROPN
ejpam-521	280	61	.	.	PUNCT
ejpam-521	281	1	if	if	SCONJ
ejpam-521	281	2	the	the	DET
ejpam-521	281	3	null	null	ADJ
ejpam-521	281	4	hypothesis	hypothesis	NOUN
ejpam-521	281	5	h0	h0	NOUN
ejpam-521	281	6	is	be	AUX
ejpam-521	281	7	true	true	ADJ
ejpam-521	281	8	,	,	PUNCT
ejpam-521	281	9	that	that	PRON
ejpam-521	281	10	is	be	AUX
ejpam-521	281	11	the	the	DET
ejpam-521	281	12	k	k	PROPN
ejpam-521	281	13	samples	sample	NOUN
ejpam-521	281	14	are	be	AUX
ejpam-521	281	15	drawn	draw	VERB
ejpam-521	281	16	from	from	ADP
ejpam-521	281	17	the	the	DET
ejpam-521	281	18	same	same	ADJ
ejpam-521	281	19	unknown	unknown	ADJ
ejpam-521	281	20	distribution	distribution	NOUN
ejpam-521	281	21	,	,	PUNCT
ejpam-521	281	22	we	we	PRON
ejpam-521	281	23	can	can	AUX
ejpam-521	281	24	describe	describe	VERB
ejpam-521	281	25	the	the	DET
ejpam-521	281	26	information	information	NOUN
ejpam-521	281	27	in	in	ADP
ejpam-521	281	28	the	the	DET
ejpam-521	281	29	k	k	PROPN
ejpam-521	281	30	samples	sample	NOUN
ejpam-521	281	31	using	use	VERB
ejpam-521	281	32	only	only	ADV
ejpam-521	281	33	the	the	DET
ejpam-521	281	34	optimal	optimal	ADJ
ejpam-521	281	35	codewords	codeword	NOUN
ejpam-521	281	36	required	require	VERB
ejpam-521	281	37	to	to	PART
ejpam-521	281	38	encode	encode	VERB
ejpam-521	281	39	the	the	DET
ejpam-521	281	40	pooled	pooled	ADJ
ejpam-521	281	41	sample	sample	NOUN
ejpam-521	281	42	x	x	PUNCT
ejpam-521	281	43	n	n	NOUN
ejpam-521	281	44	=	=	SYM
ejpam-521	281	45	(	(	PUNCT
ejpam-521	281	46	x	x	SYM
ejpam-521	281	47	n1	n1	PROPN
ejpam-521	281	48	1	1	NUM
ejpam-521	281	49	,	,	PUNCT
ejpam-521	281	50	·	·	PUNCT
ejpam-521	281	51	·	·	PUNCT
ejpam-521	281	52	·	·	PUNCT
ejpam-521	281	53	,	,	PUNCT
ejpam-521	281	54	x	x	PUNCT
ejpam-521	281	55	nk	nk	PROPN
ejpam-521	281	56	k	k	PROPN
ejpam-521	281	57	)	)	PUNCT
ejpam-521	281	58	.	.	PUNCT
ejpam-521	282	1	by	by	ADP
ejpam-521	282	2	regarding	regard	VERB
ejpam-521	282	3	the	the	DET
ejpam-521	282	4	pooled	pooled	ADJ
ejpam-521	282	5	sample	sample	NOUN
ejpam-521	282	6	x	x	PUNCT
ejpam-521	282	7	n	n	CCONJ
ejpam-521	282	8	as	as	ADP
ejpam-521	282	9	being	be	AUX
ejpam-521	282	10	drawn	draw	VERB
ejpam-521	282	11	from	from	ADP
ejpam-521	282	12	a	a	DET
ejpam-521	282	13	mixed	mixed	ADJ
ejpam-521	282	14	distribution	distribution	NOUN
ejpam-521	282	15	with	with	ADP
ejpam-521	282	16	density	density	NOUN
ejpam-521	282	17	fmix	fmix	NOUN
ejpam-521	282	18	=	=	PROPN
ejpam-521	282	19	∑k	∑k	PROPN
ejpam-521	282	20	i=1	i=1	PROPN
ejpam-521	282	21	ni	ni	PROPN
ejpam-521	282	22	n	n	PROPN
ejpam-521	282	23	fi	fi	NOUN
ejpam-521	282	24	,	,	PUNCT
ejpam-521	282	25	the	the	DET
ejpam-521	282	26	shortest	short	ADJ
ejpam-521	282	27	predictive	predictive	ADJ
ejpam-521	282	28	code	code	NOUN
ejpam-521	282	29	length	length	NOUN
ejpam-521	282	30	for	for	ADP
ejpam-521	282	31	encoding	encode	VERB
ejpam-521	282	32	x	x	X
ejpam-521	282	33	n	n	PRON
ejpam-521	282	34	is	be	AUX
ejpam-521	282	35	the	the	DET
ejpam-521	282	36	one	one	NOUN
ejpam-521	282	37	defined	define	VERB
ejpam-521	282	38	by	by	ADP
ejpam-521	282	39	(	(	PUNCT
ejpam-521	282	40	20	20	NUM
ejpam-521	282	41	):	):	PUNCT
ejpam-521	282	42	c(x	c(x	NOUN
ejpam-521	282	43	n	n	CCONJ
ejpam-521	282	44	)	)	PUNCT
ejpam-521	282	45	=	=	NOUN
ejpam-521	282	46	min	min	NOUN
ejpam-521	282	47	m	m	VERB
ejpam-521	282	48	{	{	PUNCT
ejpam-521	282	49	−	−	PROPN
ejpam-521	282	50	log	log	NOUN
ejpam-521	282	51	f̃mix(x	f̃mix(x	NOUN
ejpam-521	282	52	n	n	CCONJ
ejpam-521	282	53	;	;	PUNCT
ejpam-521	282	54	m	m	X
ejpam-521	282	55	)	)	PUNCT
ejpam-521	283	1	+	+	CCONJ
ejpam-521	283	2	l2(q̃	l2(q̃	PROPN
ejpam-521	283	3	m	m	NUM
ejpam-521	283	4	mix	mix	NOUN
ejpam-521	283	5	,	,	PUNCT
ejpam-521	283	6	m	m	PROPN
ejpam-521	283	7	,	,	PUNCT
ejpam-521	283	8	δ	δ	PROPN
ejpam-521	283	9	)	)	PUNCT
ejpam-521	283	10	}	}	PUNCT
ejpam-521	283	11	=	=	PUNCT
ejpam-521	283	12	−	−	PROPN
ejpam-521	283	13	m̂	m̂	NOUN
ejpam-521	283	14	∑	∑	PUNCT
ejpam-521	283	15	j=1	j=1	PROPN
ejpam-521	283	16	log	log	VERB
ejpam-521	283	17	n	n	PROPN
ejpam-521	283	18	j	j	PROPN
ejpam-521	283	19	,	,	PUNCT
ejpam-521	283	20	m̂!+	m̂!+	VERB
ejpam-521	283	21	m̂	m̂	PROPN
ejpam-521	283	22	∑	∑	PUNCT
ejpam-521	283	23	j=1	j=1	PROPN
ejpam-521	283	24	n	n	PROPN
ejpam-521	283	25	j	j	PROPN
ejpam-521	283	26	,	,	PUNCT
ejpam-521	283	27	m̂	m̂	PROPN
ejpam-521	283	28	log	log	VERB
ejpam-521	283	29	r̃	r̃	PROPN
ejpam-521	283	30	j	j	PROPN
ejpam-521	283	31	,	,	PUNCT
ejpam-521	283	32	m̂−	m̂−	PROPN
ejpam-521	283	33	log	log	VERB
ejpam-521	283	34	(	(	PUNCT
ejpam-521	283	35	m̂−	m̂−	NOUN
ejpam-521	283	36	1	1	NUM
ejpam-521	283	37	)	)	PUNCT
ejpam-521	283	38	!	!	PUNCT
ejpam-521	284	1	(	(	PUNCT
ejpam-521	284	2	n+	n+	NUM
ejpam-521	284	3	m̂−	m̂−	NOUN
ejpam-521	284	4	1	1	NUM
ejpam-521	284	5	)	)	PUNCT
ejpam-521	284	6	!	!	PUNCT
ejpam-521	285	1	+	+	PUNCT
ejpam-521	286	1	l2(q̃	l2(q̃	PROPN
ejpam-521	286	2	m̂	m̂	NOUN
ejpam-521	286	3	mix	mix	NOUN
ejpam-521	286	4	,	,	PUNCT
ejpam-521	286	5	m̂,δ	m̂,δ	PROPN
ejpam-521	286	6	)	)	PUNCT
ejpam-521	286	7	(	(	PUNCT
ejpam-521	286	8	40	40	NUM
ejpam-521	286	9	)	)	PUNCT
ejpam-521	286	10	where	where	SCONJ
ejpam-521	286	11	the	the	DET
ejpam-521	286	12	minimum	minimum	NOUN
ejpam-521	286	13	is	be	AUX
ejpam-521	286	14	attained	attain	VERB
ejpam-521	286	15	at	at	ADP
ejpam-521	286	16	m̂.	m̂.	NOUN
ejpam-521	286	17	according	accord	VERB
ejpam-521	286	18	to	to	ADP
ejpam-521	286	19	the	the	DET
ejpam-521	286	20	theory	theory	NOUN
ejpam-521	286	21	of	of	ADP
ejpam-521	286	22	stochastic	stochastic	ADJ
ejpam-521	286	23	complexity	complexity	NOUN
ejpam-521	286	24	,	,	PUNCT
ejpam-521	286	25	under	under	ADP
ejpam-521	286	26	the	the	DET
ejpam-521	286	27	right	right	ADJ
ejpam-521	286	28	probabilistic	probabilistic	ADJ
ejpam-521	286	29	model	model	NOUN
ejpam-521	286	30	(	(	PUNCT
ejpam-521	286	31	here	here	ADV
ejpam-521	286	32	the	the	DET
ejpam-521	286	33	density	density	NOUN
ejpam-521	286	34	function	function	NOUN
ejpam-521	286	35	)	)	PUNCT
ejpam-521	286	36	,	,	PUNCT
ejpam-521	286	37	or	or	CCONJ
ejpam-521	286	38	the	the	DET
ejpam-521	286	39	right	right	ADJ
ejpam-521	286	40	constraints	constraint	NOUN
ejpam-521	286	41	inside	inside	ADP
ejpam-521	286	42	the	the	DET
ejpam-521	286	43	probabilistic	probabilistic	ADJ
ejpam-521	286	44	pattern	pattern	NOUN
ejpam-521	286	45	of	of	ADP
ejpam-521	286	46	the	the	DET
ejpam-521	286	47	observations	observation	NOUN
ejpam-521	286	48	,	,	PUNCT
ejpam-521	286	49	the	the	DET
ejpam-521	286	50	corresponding	correspond	VERB
ejpam-521	286	51	encoding	encoding	NOUN
ejpam-521	286	52	process	process	NOUN
ejpam-521	286	53	is	be	AUX
ejpam-521	286	54	expected	expect	VERB
ejpam-521	286	55	to	to	PART
ejpam-521	286	56	produce	produce	VERB
ejpam-521	286	57	a	a	DET
ejpam-521	286	58	shorter	short	ADJ
ejpam-521	286	59	code	code	NOUN
ejpam-521	286	60	length	length	NOUN
ejpam-521	286	61	than	than	ADP
ejpam-521	286	62	the	the	DET
ejpam-521	286	63	one	one	NOUN
ejpam-521	286	64	under	under	ADP
ejpam-521	286	65	a	a	DET
ejpam-521	286	66	wrong	wrong	ADJ
ejpam-521	286	67	model	model	NOUN
ejpam-521	286	68	,	,	PUNCT
ejpam-521	286	69	or	or	CCONJ
ejpam-521	286	70	the	the	DET
ejpam-521	286	71	one	one	NOUN
ejpam-521	286	72	that	that	PRON
ejpam-521	286	73	ignores	ignore	VERB
ejpam-521	286	74	the	the	DET
ejpam-521	286	75	right	right	ADJ
ejpam-521	286	76	constraints	constraint	NOUN
ejpam-521	286	77	in	in	ADP
ejpam-521	286	78	the	the	DET
ejpam-521	286	79	underlying	underlie	VERB
ejpam-521	286	80	model	model	NOUN
ejpam-521	286	81	.	.	PUNCT
ejpam-521	287	1	therefore	therefore	ADV
ejpam-521	287	2	,	,	PUNCT
ejpam-521	287	3	in	in	ADP
ejpam-521	287	4	the	the	DET
ejpam-521	287	5	problem	problem	NOUN
ejpam-521	287	6	of	of	ADP
ejpam-521	287	7	testing	test	VERB
ejpam-521	287	8	the	the	DET
ejpam-521	287	9	hypotheses	hypothesis	NOUN
ejpam-521	287	10	(	(	PUNCT
ejpam-521	287	11	35	35	NUM
ejpam-521	287	12	)	)	PUNCT
ejpam-521	287	13	,	,	PUNCT
ejpam-521	287	14	when	when	SCONJ
ejpam-521	287	15	h0	h0	PROPN
ejpam-521	287	16	is	be	AUX
ejpam-521	287	17	true	true	ADJ
ejpam-521	287	18	the	the	DET
ejpam-521	287	19	shortest	short	ADJ
ejpam-521	287	20	predictive	predictive	ADJ
ejpam-521	287	21	code	code	NOUN
ejpam-521	287	22	length	length	NOUN
ejpam-521	287	23	(	(	PUNCT
ejpam-521	287	24	40	40	NUM
ejpam-521	287	25	)	)	PUNCT
ejpam-521	287	26	is	be	AUX
ejpam-521	287	27	not	not	PART
ejpam-521	287	28	expected	expect	VERB
ejpam-521	287	29	to	to	PART
ejpam-521	287	30	be	be	AUX
ejpam-521	287	31	greater	great	ADJ
ejpam-521	287	32	than	than	ADP
ejpam-521	287	33	(	(	PUNCT
ejpam-521	287	34	39	39	NUM
ejpam-521	287	35	)	)	PUNCT
ejpam-521	287	36	,	,	PUNCT
ejpam-521	287	37	the	the	DET
ejpam-521	287	38	shortest	short	ADJ
ejpam-521	287	39	predictive	predictive	ADJ
ejpam-521	287	40	code	code	NOUN
ejpam-521	287	41	length	length	NOUN
ejpam-521	287	42	obtained	obtain	VERB
ejpam-521	287	43	under	under	ADP
ejpam-521	287	44	the	the	DET
ejpam-521	287	45	encoding	encoding	NOUN
ejpam-521	287	46	process	process	NOUN
ejpam-521	287	47	ignoring	ignore	VERB
ejpam-521	287	48	the	the	DET
ejpam-521	287	49	constraint	constraint	NOUN
ejpam-521	287	50	f1	f1	NOUN
ejpam-521	287	51	=	=	SYM
ejpam-521	287	52	f2	f2	PROPN
ejpam-521	287	53	=	=	SYM
ejpam-521	287	54	·	·	PUNCT
ejpam-521	287	55	·	·	PUNCT
ejpam-521	287	56	·	·	PUNCT
ejpam-521	288	1	=	=	SYM
ejpam-521	288	2	fk	fk	INTJ
ejpam-521	288	3	.	.	PUNCT
ejpam-521	288	4	and	and	CCONJ
ejpam-521	288	5	vise	vise	VERB
ejpam-521	288	6	versa	versa	ADV
ejpam-521	288	7	,	,	PUNCT
ejpam-521	288	8	when	when	SCONJ
ejpam-521	288	9	ha	ha	INTJ
ejpam-521	288	10	is	be	AUX
ejpam-521	288	11	true	true	ADJ
ejpam-521	288	12	the	the	DET
ejpam-521	288	13	corresponding	correspond	VERB
ejpam-521	288	14	code	code	NOUN
ejpam-521	288	15	length	length	NOUN
ejpam-521	288	16	(	(	PUNCT
ejpam-521	288	17	39	39	NUM
ejpam-521	288	18	)	)	PUNCT
ejpam-521	288	19	is	be	AUX
ejpam-521	288	20	expected	expect	VERB
ejpam-521	288	21	to	to	PART
ejpam-521	288	22	be	be	AUX
ejpam-521	288	23	less	less	ADJ
ejpam-521	288	24	than	than	ADP
ejpam-521	288	25	the	the	DET
ejpam-521	288	26	code	code	NOUN
ejpam-521	288	27	length	length	NOUN
ejpam-521	288	28	(	(	PUNCT
ejpam-521	288	29	40	40	NUM
ejpam-521	288	30	)	)	PUNCT
ejpam-521	288	31	,	,	PUNCT
ejpam-521	288	32	which	which	PRON
ejpam-521	288	33	is	be	AUX
ejpam-521	288	34	obtained	obtain	VERB
ejpam-521	288	35	by	by	ADP
ejpam-521	288	36	the	the	DET
ejpam-521	288	37	encoding	encoding	NOUN
ejpam-521	288	38	process	process	NOUN
ejpam-521	288	39	ignoring	ignore	VERB
ejpam-521	288	40	the	the	DET
ejpam-521	288	41	difference	difference	NOUN
ejpam-521	288	42	among	among	ADP
ejpam-521	288	43	the	the	DET
ejpam-521	288	44	fi	fi	NOUN
ejpam-521	288	45	’	'	PUNCT
ejpam-521	288	46	s.	s.	PROPN
ejpam-521	288	47	we	we	PRON
ejpam-521	288	48	summarize	summarize	VERB
ejpam-521	288	49	this	this	DET
ejpam-521	288	50	property	property	NOUN
ejpam-521	288	51	in	in	ADP
ejpam-521	288	52	the	the	DET
ejpam-521	288	53	following	follow	VERB
ejpam-521	288	54	theorem	theorem	PROPN
ejpam-521	288	55	.	.	PUNCT
ejpam-521	288	56	theorem	theorem	NOUN
ejpam-521	288	57	5	5	NUM
ejpam-521	288	58	.	.	PUNCT
ejpam-521	289	1	let	let	VERB
ejpam-521	289	2	x	x	SYM
ejpam-521	289	3	n1	n1	PROPN
ejpam-521	289	4	1	1	NUM
ejpam-521	289	5	,	,	PUNCT
ejpam-521	289	6	·	·	PUNCT
ejpam-521	289	7	·	·	PUNCT
ejpam-521	289	8	·	·	PUNCT
ejpam-521	289	9	,	,	PUNCT
ejpam-521	289	10	x	x	X
ejpam-521	289	11	nk	nk	PROPN
ejpam-521	289	12	k	k	PROPN
ejpam-521	289	13	be	be	AUX
ejpam-521	289	14	simple	simple	ADJ
ejpam-521	289	15	random	random	ADJ
ejpam-521	289	16	samples	sample	NOUN
ejpam-521	289	17	,	,	PUNCT
ejpam-521	289	18	respectively	respectively	ADV
ejpam-521	289	19	,	,	PUNCT
ejpam-521	289	20	drawn	draw	VERB
ejpam-521	289	21	from	from	ADP
ejpam-521	289	22	the	the	DET
ejpam-521	289	23	unknown	unknown	ADJ
ejpam-521	289	24	density	density	NOUN
ejpam-521	289	25	functions	function	NOUN
ejpam-521	289	26	f1	f1	NOUN
ejpam-521	289	27	,	,	PUNCT
ejpam-521	289	28	·	·	PUNCT
ejpam-521	289	29	·	·	PUNCT
ejpam-521	289	30	·	·	PUNCT
ejpam-521	289	31	,	,	PUNCT
ejpam-521	289	32	fk	fk	INTJ
ejpam-521	289	33	on	on	ADP
ejpam-521	289	34	[	[	X
ejpam-521	289	35	s	s	X
ejpam-521	289	36	,	,	PUNCT
ejpam-521	289	37	t	t	PROPN
ejpam-521	289	38	]	]	PUNCT
ejpam-521	289	39	,	,	PUNCT
ejpam-521	289	40	and	and	CCONJ
ejpam-521	289	41	x	x	X
ejpam-521	289	42	n	n	NOUN
ejpam-521	289	43	=	=	SYM
ejpam-521	289	44	(	(	PUNCT
ejpam-521	289	45	x	x	SYM
ejpam-521	289	46	n1	n1	PROPN
ejpam-521	289	47	1	1	NUM
ejpam-521	289	48	,	,	PUNCT
ejpam-521	289	49	·	·	PUNCT
ejpam-521	289	50	·	·	PUNCT
ejpam-521	289	51	·	·	PUNCT
ejpam-521	289	52	,	,	PUNCT
ejpam-521	289	53	x	x	PUNCT
ejpam-521	289	54	nk	nk	PROPN
ejpam-521	289	55	k	k	PROPN
ejpam-521	289	56	)	)	PUNCT
ejpam-521	289	57	the	the	DET
ejpam-521	289	58	pooled	pooled	ADJ
ejpam-521	289	59	sample	sample	NOUN
ejpam-521	289	60	.	.	PUNCT
ejpam-521	290	1	suppose	suppose	VERB
ejpam-521	290	2	that	that	SCONJ
ejpam-521	290	3	the	the	DET
ejpam-521	290	4	conditions	condition	NOUN
ejpam-521	290	5	(	(	PUNCT
ejpam-521	290	6	i	i	NOUN
ejpam-521	290	7	)	)	PUNCT
ejpam-521	290	8	to	to	PART
ejpam-521	290	9	(	(	PUNCT
ejpam-521	290	10	iv	iv	X
ejpam-521	290	11	)	)	PUNCT
ejpam-521	290	12	listed	list	VERB
ejpam-521	290	13	in	in	ADP
ejpam-521	290	14	theorem	theorem	ADJ
ejpam-521	290	15	1	1	NUM
ejpam-521	290	16	and	and	CCONJ
ejpam-521	290	17	theorem	theorem	VERB
ejpam-521	290	18	2	2	NUM
ejpam-521	290	19	are	be	AUX
ejpam-521	290	20	satisfied	satisfied	ADJ
ejpam-521	290	21	for	for	ADP
ejpam-521	290	22	each	each	PRON
ejpam-521	290	23	x	x	SYM
ejpam-521	290	24	ni	ni	PROPN
ejpam-521	290	25	i	i	PROPN
ejpam-521	290	26	and	and	CCONJ
ejpam-521	290	27	the	the	DET
ejpam-521	290	28	corresponding	correspond	VERB
ejpam-521	290	29	fi	fi	NOUN
ejpam-521	290	30	.	.	PUNCT
ejpam-521	291	1	then	then	ADV
ejpam-521	291	2	the	the	DET
ejpam-521	291	3	following	follow	VERB
ejpam-521	291	4	statements	statement	NOUN
ejpam-521	291	5	hold	hold	VERB
ejpam-521	291	6	.	.	PUNCT
ejpam-521	292	1	g.	g.	PROPN
ejpam-521	292	2	qian	qian	PROPN
ejpam-521	292	3	/	/	SYM
ejpam-521	292	4	eur	eur	PROPN
ejpam-521	292	5	.	.	PUNCT
ejpam-521	293	1	j.	j.	PROPN
ejpam-521	293	2	pure	pure	PROPN
ejpam-521	293	3	appl	appl	PROPN
ejpam-521	293	4	.	.	PROPN
ejpam-521	293	5	math	math	PROPN
ejpam-521	293	6	,	,	PUNCT
ejpam-521	293	7	3	3	NUM
ejpam-521	293	8	(	(	PUNCT
ejpam-521	293	9	2010	2010	NUM
ejpam-521	293	10	)	)	PUNCT
ejpam-521	293	11	,	,	PUNCT
ejpam-521	293	12	51	51	NUM
ejpam-521	293	13	-	-	SYM
ejpam-521	293	14	80	80	NUM
ejpam-521	293	15	63	63	NUM
ejpam-521	293	16	(	(	PUNCT
ejpam-521	293	17	a	a	NOUN
ejpam-521	293	18	)	)	PUNCT
ejpam-521	293	19	.	.	PUNCT
ejpam-521	294	1	if	if	SCONJ
ejpam-521	294	2	at	at	ADV
ejpam-521	294	3	least	least	ADV
ejpam-521	294	4	two	two	NUM
ejpam-521	294	5	of	of	ADP
ejpam-521	294	6	f1	f1	NOUN
ejpam-521	294	7	,	,	PUNCT
ejpam-521	294	8	·	·	PUNCT
ejpam-521	294	9	·	·	PUNCT
ejpam-521	294	10	·	·	PUNCT
ejpam-521	294	11	,	,	PUNCT
ejpam-521	294	12	fk	fk	INTJ
ejpam-521	294	13	are	be	AUX
ejpam-521	294	14	not	not	PART
ejpam-521	294	15	equal	equal	ADJ
ejpam-521	294	16	,	,	PUNCT
ejpam-521	294	17	there	there	PRON
ejpam-521	294	18	exists	exist	VERB
ejpam-521	294	19	a	a	DET
ejpam-521	294	20	constant	constant	ADJ
ejpam-521	294	21	η	η	NOUN
ejpam-521	294	22	<	<	X
ejpam-521	294	23	0	0	NUM
ejpam-521	294	24	such	such	ADJ
ejpam-521	294	25	that	that	SCONJ
ejpam-521	294	26	1	1	NUM
ejpam-521	294	27	n	n	NUM
ejpam-521	295	1	[	[	X
ejpam-521	295	2	c(x	c(x	NOUN
ejpam-521	295	3	n1	n1	NOUN
ejpam-521	295	4	1	1	NUM
ejpam-521	295	5	,	,	PUNCT
ejpam-521	295	6	·	·	PUNCT
ejpam-521	295	7	·	·	PUNCT
ejpam-521	295	8	·	·	PUNCT
ejpam-521	295	9	,	,	PUNCT
ejpam-521	295	10	x	x	PUNCT
ejpam-521	295	11	nk	nk	PROPN
ejpam-521	295	12	k	k	PROPN
ejpam-521	295	13	)	)	PUNCT
ejpam-521	295	14	−	−	PROPN
ejpam-521	295	15	c(x	c(x	NOUN
ejpam-521	295	16	n	n	CCONJ
ejpam-521	295	17	)	)	PUNCT
ejpam-521	295	18	]	]	PUNCT
ejpam-521	295	19	<	<	X
ejpam-521	295	20	η	η	X
ejpam-521	295	21	a.s	a.s	PROPN
ejpam-521	295	22	.	.	PROPN
ejpam-521	295	23	(	(	PUNCT
ejpam-521	295	24	41	41	NUM
ejpam-521	295	25	)	)	PUNCT
ejpam-521	295	26	as	as	ADP
ejpam-521	295	27	n1→∞	n1→∞	NOUN
ejpam-521	295	28	,	,	PUNCT
ejpam-521	295	29	·	·	PUNCT
ejpam-521	295	30	·	·	PUNCT
ejpam-521	295	31	·	·	PUNCT
ejpam-521	295	32	,	,	PUNCT
ejpam-521	295	33	nk→∞	nk→∞	NUM
ejpam-521	295	34	satisfying	satisfy	VERB
ejpam-521	295	35	lim	lim	NOUN
ejpam-521	295	36	infn1→∞	infn1→∞	ADP
ejpam-521	295	37	n1	n1	PROPN
ejpam-521	295	38	n	n	CCONJ
ejpam-521	295	39	>	>	X
ejpam-521	295	40	0	0	NUM
ejpam-521	295	41	,	,	PUNCT
ejpam-521	295	42	·	·	PUNCT
ejpam-521	295	43	·	·	PUNCT
ejpam-521	295	44	·	·	PUNCT
ejpam-521	295	45	,	,	PUNCT
ejpam-521	295	46	lim	lim	PROPN
ejpam-521	295	47	infnk→∞	infnk→∞	PROPN
ejpam-521	295	48	nk	nk	PROPN
ejpam-521	295	49	n	n	PROPN
ejpam-521	295	50	>	>	PROPN
ejpam-521	295	51	0	0	NUM
ejpam-521	295	52	.	.	PUNCT
ejpam-521	296	1	(	(	PUNCT
ejpam-521	296	2	b	b	NOUN
ejpam-521	296	3	)	)	PUNCT
ejpam-521	296	4	.	.	PUNCT
ejpam-521	297	1	if	if	SCONJ
ejpam-521	297	2	f1	f1	PROPN
ejpam-521	297	3	=	=	SYM
ejpam-521	297	4	f2	f2	PROPN
ejpam-521	297	5	=	=	SYM
ejpam-521	297	6	·	·	PUNCT
ejpam-521	297	7	·	·	PUNCT
ejpam-521	297	8	·	·	PUNCT
ejpam-521	298	1	=	=	SYM
ejpam-521	298	2	fk	fk	INTJ
ejpam-521	298	3	a.s	a.s	PROPN
ejpam-521	298	4	.	.	PROPN
ejpam-521	298	5	,	,	PUNCT
ejpam-521	298	6	then	then	ADV
ejpam-521	298	7	1	1	NUM
ejpam-521	298	8	n	n	NOUN
ejpam-521	298	9	[	[	X
ejpam-521	298	10	c(x	c(x	NOUN
ejpam-521	298	11	n1	n1	NOUN
ejpam-521	298	12	1	1	NUM
ejpam-521	298	13	,	,	PUNCT
ejpam-521	298	14	·	·	PUNCT
ejpam-521	298	15	·	·	PUNCT
ejpam-521	298	16	·	·	PUNCT
ejpam-521	298	17	,	,	PUNCT
ejpam-521	298	18	x	x	PUNCT
ejpam-521	298	19	nk	nk	PROPN
ejpam-521	298	20	k	k	PROPN
ejpam-521	298	21	)	)	PUNCT
ejpam-521	298	22	−	−	PROPN
ejpam-521	299	1	c(x	c(x	NOUN
ejpam-521	299	2	n)]→	n)]→	X
ejpam-521	299	3	0	0	PUNCT
ejpam-521	299	4	a.s	a.s	PROPN
ejpam-521	299	5	.	.	PROPN
ejpam-521	299	6	(	(	PUNCT
ejpam-521	299	7	42	42	NUM
ejpam-521	299	8	)	)	PUNCT
ejpam-521	299	9	as	as	ADP
ejpam-521	299	10	n1→∞	n1→∞	NOUN
ejpam-521	299	11	,	,	PUNCT
ejpam-521	299	12	·	·	PUNCT
ejpam-521	299	13	·	·	PUNCT
ejpam-521	299	14	·	·	PUNCT
ejpam-521	299	15	,	,	PUNCT
ejpam-521	299	16	nk→∞.	nk→∞.	VERB
ejpam-521	299	17	the	the	DET
ejpam-521	299	18	proof	proof	NOUN
ejpam-521	299	19	of	of	ADP
ejpam-521	299	20	theorem	theorem	NOUN
ejpam-521	299	21	5	5	NUM
ejpam-521	299	22	will	will	AUX
ejpam-521	299	23	be	be	AUX
ejpam-521	299	24	given	give	VERB
ejpam-521	299	25	in	in	ADP
ejpam-521	299	26	section	section	NOUN
ejpam-521	299	27	4	4	NUM
ejpam-521	299	28	.	.	PUNCT
ejpam-521	299	29	from	from	ADP
ejpam-521	299	30	part	part	NOUN
ejpam-521	299	31	(	(	PUNCT
ejpam-521	299	32	a	a	NOUN
ejpam-521	299	33	)	)	PUNCT
ejpam-521	299	34	of	of	ADP
ejpam-521	299	35	the	the	DET
ejpam-521	299	36	above	above	ADJ
ejpam-521	299	37	theorem	theorem	NOUN
ejpam-521	299	38	we	we	PRON
ejpam-521	299	39	know	know	VERB
ejpam-521	299	40	that	that	SCONJ
ejpam-521	299	41	when	when	SCONJ
ejpam-521	299	42	using	use	VERB
ejpam-521	299	43	the	the	DET
ejpam-521	299	44	test	test	NOUN
ejpam-521	299	45	procedure	procedure	NOUN
ejpam-521	299	46	stated	state	VERB
ejpam-521	299	47	in	in	ADP
ejpam-521	299	48	the	the	DET
ejpam-521	299	49	beginning	beginning	NOUN
ejpam-521	299	50	of	of	ADP
ejpam-521	299	51	this	this	DET
ejpam-521	299	52	section	section	NOUN
ejpam-521	299	53	,	,	PUNCT
ejpam-521	299	54	the	the	DET
ejpam-521	299	55	asymptotic	asymptotic	ADJ
ejpam-521	299	56	power	power	NOUN
ejpam-521	299	57	is	be	AUX
ejpam-521	299	58	1	1	NUM
ejpam-521	299	59	in	in	ADP
ejpam-521	299	60	the	the	DET
ejpam-521	299	61	limit	limit	NOUN
ejpam-521	299	62	as	as	SCONJ
ejpam-521	299	63	the	the	DET
ejpam-521	299	64	sample	sample	NOUN
ejpam-521	299	65	sizes	size	NOUN
ejpam-521	299	66	tend	tend	VERB
ejpam-521	299	67	to	to	PART
ejpam-521	299	68	infinity	infinity	VERB
ejpam-521	299	69	;	;	PUNCT
ejpam-521	299	70	namely	namely	ADV
ejpam-521	299	71	,	,	PUNCT
ejpam-521	299	72	almost	almost	ADV
ejpam-521	299	73	surely	surely	ADV
ejpam-521	299	74	the	the	DET
ejpam-521	299	75	shortest	short	ADJ
ejpam-521	299	76	predictive	predictive	ADJ
ejpam-521	299	77	code	code	NOUN
ejpam-521	299	78	length	length	NOUN
ejpam-521	299	79	under	under	ADP
ejpam-521	299	80	ha	ha	INTJ
ejpam-521	299	81	is	be	AUX
ejpam-521	299	82	less	less	ADJ
ejpam-521	299	83	than	than	ADP
ejpam-521	299	84	that	that	PRON
ejpam-521	299	85	under	under	ADP
ejpam-521	299	86	h0	h0	NOUN
ejpam-521	299	87	when	when	SCONJ
ejpam-521	299	88	ha	ha	PRON
ejpam-521	299	89	is	be	AUX
ejpam-521	299	90	true	true	ADJ
ejpam-521	299	91	.	.	PUNCT
ejpam-521	300	1	on	on	ADP
ejpam-521	300	2	the	the	DET
ejpam-521	300	3	other	other	ADJ
ejpam-521	300	4	hand	hand	NOUN
ejpam-521	300	5	,	,	PUNCT
ejpam-521	300	6	when	when	SCONJ
ejpam-521	300	7	the	the	DET
ejpam-521	300	8	null	null	ADJ
ejpam-521	300	9	hypothesis	hypothesis	NOUN
ejpam-521	300	10	h0	h0	NOUN
ejpam-521	300	11	is	be	AUX
ejpam-521	300	12	true	true	ADJ
ejpam-521	300	13	,	,	PUNCT
ejpam-521	300	14	the	the	DET
ejpam-521	300	15	difference	difference	NOUN
ejpam-521	300	16	of	of	ADP
ejpam-521	300	17	the	the	DET
ejpam-521	300	18	two	two	NUM
ejpam-521	300	19	shortest	short	ADJ
ejpam-521	300	20	predictive	predictive	ADJ
ejpam-521	300	21	code	code	NOUN
ejpam-521	300	22	lengths	length	NOUN
ejpam-521	300	23	per	per	ADP
ejpam-521	300	24	observation	observation	NOUN
ejpam-521	300	25	converges	converge	NOUN
ejpam-521	300	26	to	to	ADP
ejpam-521	300	27	zero	zero	NUM
ejpam-521	300	28	almost	almost	ADV
ejpam-521	300	29	surely	surely	ADV
ejpam-521	300	30	as	as	SCONJ
ejpam-521	300	31	the	the	DET
ejpam-521	300	32	sample	sample	NOUN
ejpam-521	300	33	sizes	size	NOUN
ejpam-521	300	34	go	go	VERB
ejpam-521	300	35	to	to	ADP
ejpam-521	300	36	infinity	infinity	NOUN
ejpam-521	300	37	.	.	PUNCT
ejpam-521	301	1	when	when	SCONJ
ejpam-521	301	2	the	the	DET
ejpam-521	301	3	sample	sample	NOUN
ejpam-521	301	4	sizes	size	NOUN
ejpam-521	301	5	are	be	AUX
ejpam-521	301	6	finite	finite	ADJ
ejpam-521	301	7	,	,	PUNCT
ejpam-521	301	8	the	the	DET
ejpam-521	301	9	size	size	NOUN
ejpam-521	301	10	of	of	ADP
ejpam-521	301	11	the	the	DET
ejpam-521	301	12	test	test	NOUN
ejpam-521	301	13	is	be	AUX
ejpam-521	301	14	essentially	essentially	ADV
ejpam-521	301	15	determined	determine	VERB
ejpam-521	301	16	by	by	ADP
ejpam-521	301	17	the	the	DET
ejpam-521	301	18	part	part	NOUN
ejpam-521	301	19	of	of	ADP
ejpam-521	301	20	the	the	DET
ejpam-521	301	21	code	code	NOUN
ejpam-521	301	22	lengths	length	NOUN
ejpam-521	301	23	used	use	VERB
ejpam-521	301	24	for	for	ADP
ejpam-521	301	25	encoding	encode	VERB
ejpam-521	301	26	the	the	DET
ejpam-521	301	27	parameters	parameter	NOUN
ejpam-521	301	28	.	.	PUNCT
ejpam-521	302	1	in	in	ADP
ejpam-521	302	2	the	the	DET
ejpam-521	302	3	encoding	encoding	NOUN
ejpam-521	302	4	process	process	NOUN
ejpam-521	302	5	corresponding	correspond	VERB
ejpam-521	302	6	to	to	ADP
ejpam-521	302	7	(	(	PUNCT
ejpam-521	302	8	39	39	NUM
ejpam-521	302	9	)	)	PUNCT
ejpam-521	302	10	there	there	PRON
ejpam-521	302	11	are	be	VERB
ejpam-521	302	12	more	more	ADJ
ejpam-521	302	13	parameters	parameter	NOUN
ejpam-521	302	14	(	(	PUNCT
ejpam-521	302	15	q̃	q̃	PROPN
ejpam-521	302	16	m1	m1	PROPN
ejpam-521	302	17	1	1	NUM
ejpam-521	302	18	,	,	PUNCT
ejpam-521	302	19	·	·	PUNCT
ejpam-521	302	20	·	·	PUNCT
ejpam-521	302	21	·	·	PUNCT
ejpam-521	302	22	,	,	PUNCT
ejpam-521	302	23	q̃mk	q̃mk	ADP
ejpam-521	302	24	k	k	PROPN
ejpam-521	302	25	,	,	PUNCT
ejpam-521	302	26	m1	m1	PROPN
ejpam-521	302	27	,	,	PUNCT
ejpam-521	302	28	·	·	PUNCT
ejpam-521	302	29	·	·	PUNCT
ejpam-521	302	30	·	·	PUNCT
ejpam-521	302	31	,	,	PUNCT
ejpam-521	302	32	mk	mk	PROPN
ejpam-521	302	33	,	,	PUNCT
ejpam-521	302	34	δ	δ	PROPN
ejpam-521	302	35	)	)	PUNCT
ejpam-521	302	36	to	to	PART
ejpam-521	302	37	be	be	AUX
ejpam-521	302	38	encoded	encode	VERB
ejpam-521	302	39	than	than	ADP
ejpam-521	302	40	in	in	ADP
ejpam-521	302	41	the	the	DET
ejpam-521	302	42	encoding	encoding	NOUN
ejpam-521	302	43	process	process	NOUN
ejpam-521	302	44	corresponding	correspond	VERB
ejpam-521	302	45	to	to	ADP
ejpam-521	302	46	(	(	PUNCT
ejpam-521	302	47	40	40	NUM
ejpam-521	302	48	)	)	PUNCT
ejpam-521	302	49	in	in	ADP
ejpam-521	302	50	which	which	PRON
ejpam-521	302	51	only	only	ADV
ejpam-521	302	52	q̃m	q̃m	DET
ejpam-521	302	53	mix	mix	NOUN
ejpam-521	302	54	,	,	PUNCT
ejpam-521	302	55	m	m	PRON
ejpam-521	302	56	and	and	CCONJ
ejpam-521	302	57	δ	δ	PROPN
ejpam-521	302	58	are	be	AUX
ejpam-521	302	59	to	to	PART
ejpam-521	302	60	be	be	AUX
ejpam-521	302	61	encoded	encode	VERB
ejpam-521	302	62	.	.	PUNCT
ejpam-521	303	1	thus	thus	ADV
ejpam-521	303	2	the	the	DET
ejpam-521	303	3	code	code	NOUN
ejpam-521	303	4	length	length	NOUN
ejpam-521	303	5	(	(	PUNCT
ejpam-521	303	6	39	39	NUM
ejpam-521	303	7	)	)	PUNCT
ejpam-521	303	8	has	have	VERB
ejpam-521	303	9	a	a	DET
ejpam-521	303	10	high	high	ADJ
ejpam-521	303	11	probability	probability	NOUN
ejpam-521	303	12	to	to	PART
ejpam-521	303	13	be	be	AUX
ejpam-521	303	14	larger	large	ADJ
ejpam-521	303	15	than	than	ADP
ejpam-521	303	16	(	(	PUNCT
ejpam-521	303	17	40	40	NUM
ejpam-521	303	18	)	)	PUNCT
ejpam-521	303	19	if	if	SCONJ
ejpam-521	303	20	the	the	DET
ejpam-521	303	21	null	null	ADJ
ejpam-521	303	22	hypothesis	hypothesis	NOUN
ejpam-521	303	23	h0	h0	NOUN
ejpam-521	303	24	is	be	AUX
ejpam-521	303	25	true	true	ADJ
ejpam-521	303	26	,	,	PUNCT
ejpam-521	303	27	implying	imply	VERB
ejpam-521	303	28	the	the	DET
ejpam-521	303	29	test	test	NOUN
ejpam-521	303	30	has	have	VERB
ejpam-521	303	31	a	a	DET
ejpam-521	303	32	firm	firm	ADJ
ejpam-521	303	33	control	control	NOUN
ejpam-521	303	34	of	of	ADP
ejpam-521	303	35	type	type	NOUN
ejpam-521	303	36	i	i	PROPN
ejpam-521	303	37	error	error	NOUN
ejpam-521	303	38	.	.	PUNCT
ejpam-521	304	1	simulation	simulation	NOUN
ejpam-521	304	2	study	study	NOUN
ejpam-521	304	3	could	could	AUX
ejpam-521	304	4	be	be	AUX
ejpam-521	304	5	done	do	VERB
ejpam-521	304	6	to	to	PART
ejpam-521	304	7	investigate	investigate	VERB
ejpam-521	304	8	how	how	SCONJ
ejpam-521	304	9	well	well	ADV
ejpam-521	304	10	the	the	DET
ejpam-521	304	11	two	two	NUM
ejpam-521	304	12	types	type	NOUN
ejpam-521	304	13	of	of	ADP
ejpam-521	304	14	errors	error	NOUN
ejpam-521	304	15	are	be	AUX
ejpam-521	304	16	controlled	control	VERB
ejpam-521	304	17	in	in	ADP
ejpam-521	304	18	the	the	DET
ejpam-521	304	19	proposed	propose	VERB
ejpam-521	304	20	test	test	NOUN
ejpam-521	304	21	.	.	PUNCT
ejpam-521	305	1	but	but	CCONJ
ejpam-521	305	2	we	we	PRON
ejpam-521	305	3	will	will	AUX
ejpam-521	305	4	not	not	PART
ejpam-521	305	5	get	get	VERB
ejpam-521	305	6	into	into	ADP
ejpam-521	305	7	the	the	DET
ejpam-521	305	8	details	detail	NOUN
ejpam-521	305	9	in	in	ADP
ejpam-521	305	10	this	this	DET
ejpam-521	305	11	paper	paper	NOUN
ejpam-521	305	12	.	.	PUNCT
ejpam-521	306	1	a	a	DET
ejpam-521	306	2	simulation	simulation	NOUN
ejpam-521	306	3	study	study	NOUN
ejpam-521	306	4	was	be	AUX
ejpam-521	306	5	done	do	VERB
ejpam-521	306	6	in	in	ADP
ejpam-521	306	7	[	[	X
ejpam-521	306	8	10	10	NUM
ejpam-521	306	9	]	]	PUNCT
ejpam-521	306	10	to	to	PART
ejpam-521	306	11	assess	assess	VERB
ejpam-521	306	12	the	the	DET
ejpam-521	306	13	finite	finite	ADJ
ejpam-521	306	14	sample	sample	NOUN
ejpam-521	306	15	performance	performance	NOUN
ejpam-521	306	16	of	of	ADP
ejpam-521	306	17	the	the	DET
ejpam-521	306	18	homogeneity	homogeneity	NOUN
ejpam-521	306	19	test	test	NOUN
ejpam-521	306	20	proposed	propose	VERB
ejpam-521	306	21	in	in	ADP
ejpam-521	306	22	this	this	DET
ejpam-521	306	23	section	section	NOUN
ejpam-521	306	24	in	in	ADP
ejpam-521	306	25	the	the	DET
ejpam-521	306	26	special	special	ADJ
ejpam-521	306	27	case	case	NOUN
ejpam-521	306	28	of	of	ADP
ejpam-521	306	29	using	use	VERB
ejpam-521	306	30	equal	equal	ADJ
ejpam-521	306	31	width	width	ADJ
ejpam-521	306	32	histogram	histogram	NOUN
ejpam-521	306	33	density	density	NOUN
ejpam-521	306	34	estimators	estimator	NOUN
ejpam-521	306	35	.	.	PUNCT
ejpam-521	307	1	the	the	DET
ejpam-521	307	2	results	result	NOUN
ejpam-521	307	3	there	there	ADV
ejpam-521	307	4	show	show	VERB
ejpam-521	307	5	that	that	SCONJ
ejpam-521	307	6	the	the	DET
ejpam-521	307	7	method	method	NOUN
ejpam-521	307	8	is	be	AUX
ejpam-521	307	9	competitive	competitive	ADJ
ejpam-521	307	10	in	in	ADP
ejpam-521	307	11	comparison	comparison	NOUN
ejpam-521	307	12	to	to	ADP
ejpam-521	307	13	the	the	DET
ejpam-521	307	14	existent	existent	ADJ
ejpam-521	307	15	methods	method	NOUN
ejpam-521	307	16	such	such	ADJ
ejpam-521	307	17	as	as	ADP
ejpam-521	307	18	the	the	DET
ejpam-521	307	19	two	two	NUM
ejpam-521	307	20	sample	sample	NOUN
ejpam-521	307	21	t	t	PROPN
ejpam-521	307	22	test	test	NOUN
ejpam-521	307	23	and	and	CCONJ
ejpam-521	307	24	smirnov	smirnov	ADJ
ejpam-521	307	25	test	test	NOUN
ejpam-521	307	26	when	when	SCONJ
ejpam-521	307	27	the	the	DET
ejpam-521	307	28	data	datum	NOUN
ejpam-521	307	29	can	can	AUX
ejpam-521	307	30	be	be	AUX
ejpam-521	307	31	analyzed	analyze	VERB
ejpam-521	307	32	by	by	ADP
ejpam-521	307	33	all	all	DET
ejpam-521	307	34	these	these	DET
ejpam-521	307	35	methods	method	NOUN
ejpam-521	307	36	.	.	PUNCT
ejpam-521	308	1	but	but	CCONJ
ejpam-521	308	2	the	the	DET
ejpam-521	308	3	proposed	propose	VERB
ejpam-521	308	4	method	method	NOUN
ejpam-521	308	5	is	be	AUX
ejpam-521	308	6	more	more	ADV
ejpam-521	308	7	efficient	efficient	ADJ
ejpam-521	308	8	and	and	CCONJ
ejpam-521	308	9	powerful	powerful	ADJ
ejpam-521	308	10	in	in	ADP
ejpam-521	308	11	some	some	DET
ejpam-521	308	12	situations	situation	NOUN
ejpam-521	308	13	such	such	ADJ
ejpam-521	308	14	as	as	ADP
ejpam-521	308	15	that	that	SCONJ
ejpam-521	308	16	the	the	DET
ejpam-521	308	17	data	datum	NOUN
ejpam-521	308	18	come	come	VERB
ejpam-521	308	19	from	from	ADP
ejpam-521	308	20	different	different	ADJ
ejpam-521	308	21	families	family	NOUN
ejpam-521	308	22	of	of	ADP
ejpam-521	308	23	distributions	distribution	NOUN
ejpam-521	308	24	,	,	PUNCT
ejpam-521	308	25	whereas	whereas	SCONJ
ejpam-521	308	26	the	the	DET
ejpam-521	308	27	other	other	ADJ
ejpam-521	308	28	methods	method	NOUN
ejpam-521	308	29	do	do	AUX
ejpam-521	308	30	not	not	PART
ejpam-521	308	31	perform	perform	VERB
ejpam-521	308	32	well	well	ADV
ejpam-521	308	33	.	.	PUNCT
ejpam-521	309	1	4	4	X
ejpam-521	309	2	.	.	X
ejpam-521	309	3	proofs	proof	NOUN
ejpam-521	309	4	of	of	ADP
ejpam-521	309	5	the	the	DET
ejpam-521	309	6	theorems	theorem	NOUN
ejpam-521	309	7	in	in	ADP
ejpam-521	309	8	this	this	DET
ejpam-521	309	9	section	section	NOUN
ejpam-521	309	10	we	we	PRON
ejpam-521	309	11	provide	provide	VERB
ejpam-521	309	12	proofs	proof	NOUN
ejpam-521	309	13	for	for	ADP
ejpam-521	309	14	all	all	DET
ejpam-521	309	15	the	the	DET
ejpam-521	309	16	theorems	theorem	NOUN
ejpam-521	309	17	listed	list	VERB
ejpam-521	309	18	in	in	ADP
ejpam-521	309	19	this	this	DET
ejpam-521	309	20	paper	paper	NOUN
ejpam-521	309	21	.	.	PUNCT
ejpam-521	310	1	for	for	ADP
ejpam-521	310	2	the	the	DET
ejpam-521	310	3	sake	sake	NOUN
ejpam-521	310	4	of	of	ADP
ejpam-521	310	5	simplicity	simplicity	NOUN
ejpam-521	310	6	,	,	PUNCT
ejpam-521	310	7	the	the	DET
ejpam-521	310	8	logarithms	logarithm	NOUN
ejpam-521	310	9	in	in	ADP
ejpam-521	310	10	the	the	DET
ejpam-521	310	11	proofs	proof	NOUN
ejpam-521	310	12	are	be	AUX
ejpam-521	310	13	all	all	PRON
ejpam-521	310	14	natural	natural	ADJ
ejpam-521	310	15	logarithms	logarithm	NOUN
ejpam-521	310	16	.	.	PUNCT
ejpam-521	311	1	from	from	ADP
ejpam-521	311	2	(	(	PUNCT
ejpam-521	311	3	8)	8)	NUM
ejpam-521	311	4	and	and	CCONJ
ejpam-521	311	5	(	(	PUNCT
ejpam-521	311	6	19	19	NUM
ejpam-521	311	7	)	)	PUNCT
ejpam-521	311	8	,	,	PUNCT
ejpam-521	311	9	−	−	PROPN
ejpam-521	311	10	log	log	NOUN
ejpam-521	311	11	f̃	f̃	PROPN
ejpam-521	311	12	(	(	PUNCT
ejpam-521	311	13	x	x	SYM
ejpam-521	311	14	n	n	CCONJ
ejpam-521	311	15	;	;	PUNCT
ejpam-521	311	16	m	m	X
ejpam-521	311	17	)	)	PUNCT
ejpam-521	312	1	+	+	CCONJ
ejpam-521	312	2	l∗1(x	l∗1(x	PROPN
ejpam-521	312	3	n	n	CCONJ
ejpam-521	312	4	;	;	PUNCT
ejpam-521	312	5	m	m	X
ejpam-521	312	6	)	)	PUNCT
ejpam-521	312	7	=	=	SYM
ejpam-521	313	1	−	−	NOUN
ejpam-521	313	2	log	log	VERB
ejpam-521	313	3			NOUN
ejpam-521	313	4			PROPN
ejpam-521	313	5			PROPN
ejpam-521	313	6	(	(	PUNCT
ejpam-521	313	7	m−	m−	PROPN
ejpam-521	313	8	1	1	NUM
ejpam-521	313	9	)	)	PUNCT
ejpam-521	313	10	!	!	PUNCT
ejpam-521	314	1	(	(	PUNCT
ejpam-521	314	2	n+m−	n+m−	NOUN
ejpam-521	314	3	1	1	NUM
ejpam-521	314	4	)	)	PUNCT
ejpam-521	314	5	!	!	PUNCT
ejpam-521	315	1	m	m	VERB
ejpam-521	315	2	∏	∏	PROPN
ejpam-521	315	3	i=1	i=1	PROPN
ejpam-521	315	4	ni	ni	PROPN
ejpam-521	315	5	,	,	PUNCT
ejpam-521	315	6	m	m	PROPN
ejpam-521	315	7	!	!	PUNCT
ejpam-521	316	1	r̃	r̃	ADJ
ejpam-521	316	2	ni	ni	PROPN
ejpam-521	316	3	,	,	PUNCT
ejpam-521	316	4	m	m	VERB
ejpam-521	316	5	i	i	PRON
ejpam-521	316	6	,	,	PUNCT
ejpam-521	316	7	m	m	VERB
ejpam-521	316	8			ADJ
ejpam-521	316	9			PROPN
ejpam-521	316	10			NOUN
ejpam-521	316	11	+	+	CCONJ
ejpam-521	316	12	m	m	VERB
ejpam-521	316	13	∑	∑	ADJ
ejpam-521	316	14	i=1	i=1	PROPN
ejpam-521	316	15	(	(	PUNCT
ejpam-521	316	16	ni	ni	PROPN
ejpam-521	316	17	,	,	PUNCT
ejpam-521	316	18	m+	m+	NOUN
ejpam-521	316	19	1	1	NUM
ejpam-521	316	20	)	)	PUNCT
ejpam-521	316	21	log	log	NOUN
ejpam-521	316	22	ni	ni	PROPN
ejpam-521	316	23	,	,	PUNCT
ejpam-521	316	24	m+	m+	NOUN
ejpam-521	316	25	1	1	NUM
ejpam-521	316	26	(	(	PUNCT
ejpam-521	316	27	n+m)r̃i	n+m)r̃i	NOUN
ejpam-521	316	28	,	,	PUNCT
ejpam-521	316	29	m	m	NOUN
ejpam-521	316	30	.	.	PUNCT
ejpam-521	317	1	(	(	PUNCT
ejpam-521	317	2	43	43	NUM
ejpam-521	317	3	)	)	PUNCT
ejpam-521	317	4	g.	g.	PROPN
ejpam-521	317	5	qian	qian	PROPN
ejpam-521	317	6	/	/	SYM
ejpam-521	317	7	eur	eur	PROPN
ejpam-521	317	8	.	.	PUNCT
ejpam-521	318	1	j.	j.	PROPN
ejpam-521	318	2	pure	pure	PROPN
ejpam-521	318	3	appl	appl	PROPN
ejpam-521	318	4	.	.	PROPN
ejpam-521	318	5	math	math	PROPN
ejpam-521	318	6	,	,	PUNCT
ejpam-521	318	7	3	3	NUM
ejpam-521	318	8	(	(	PUNCT
ejpam-521	318	9	2010	2010	NUM
ejpam-521	318	10	)	)	PUNCT
ejpam-521	318	11	,	,	PUNCT
ejpam-521	318	12	51	51	NUM
ejpam-521	318	13	-	-	SYM
ejpam-521	318	14	80	80	NUM
ejpam-521	318	15	64	64	NUM
ejpam-521	318	16	by	by	ADP
ejpam-521	318	17	stirling	stirling	PROPN
ejpam-521	318	18	’s	’s	PART
ejpam-521	318	19	formula	formula	NOUN
ejpam-521	318	20	n!=	n!=	NUM
ejpam-521	318	21	p	p	PRON
ejpam-521	318	22	2πnnne−neθn	2πnnne−neθn	PROPN
ejpam-521	318	23	(	(	PUNCT
ejpam-521	318	24	0	0	NUM
ejpam-521	318	25	<	<	X
ejpam-521	318	26	θn	θn	X
ejpam-521	318	27	<	<	X
ejpam-521	318	28	(	(	PUNCT
ejpam-521	318	29	12n)−1	12n)−1	NOUN
ejpam-521	318	30	)	)	PUNCT
ejpam-521	318	31	,	,	PUNCT
ejpam-521	318	32	(	(	PUNCT
ejpam-521	318	33	43	43	NUM
ejpam-521	318	34	)	)	PUNCT
ejpam-521	318	35	can	can	AUX
ejpam-521	318	36	be	be	AUX
ejpam-521	318	37	rewritten	rewrite	VERB
ejpam-521	318	38	as	as	ADP
ejpam-521	318	39	−	−	PROPN
ejpam-521	318	40	log	log	NOUN
ejpam-521	318	41	f̃	f̃	PROPN
ejpam-521	318	42	(	(	PUNCT
ejpam-521	318	43	x	x	SYM
ejpam-521	318	44	n	n	CCONJ
ejpam-521	318	45	;	;	PUNCT
ejpam-521	318	46	m	m	X
ejpam-521	318	47	)	)	PUNCT
ejpam-521	319	1	+	+	CCONJ
ejpam-521	319	2	l∗1(x	l∗1(x	PROPN
ejpam-521	319	3	n	n	CCONJ
ejpam-521	319	4	;	;	PUNCT
ejpam-521	319	5	m	m	X
ejpam-521	319	6	)	)	PUNCT
ejpam-521	319	7	=	=	SYM
ejpam-521	320	1	−	−	PROPN
ejpam-521	320	2	m	m	VERB
ejpam-521	320	3	∑	∑	PUNCT
ejpam-521	320	4	i=1	i=1	PROPN
ejpam-521	320	5	log	log	NOUN
ejpam-521	320	6	r̃i	r̃i	NOUN
ejpam-521	320	7	,	,	PUNCT
ejpam-521	320	8	m+	m+	NUM
ejpam-521	320	9	∑	∑	PROPN
ejpam-521	320	10	ni	ni	PROPN
ejpam-521	320	11	,	,	PUNCT
ejpam-521	320	12	m>0	m>0	NOUN
ejpam-521	320	13	log	log	VERB
ejpam-521	320	14	�	�	PROPN
ejpam-521	320	15	1	1	NUM
ejpam-521	320	16	+	+	SYM
ejpam-521	320	17	1	1	NUM
ejpam-521	320	18	ni	ni	PROPN
ejpam-521	320	19	,	,	PUNCT
ejpam-521	320	20	m	m	PROPN
ejpam-521	320	21	�	�	PROPN
ejpam-521	320	22	ni	ni	PROPN
ejpam-521	320	23	,	,	PUNCT
ejpam-521	320	24	m+1	m+1	PROPN
ejpam-521	320	25	+	+	CCONJ
ejpam-521	320	26	1	1	NUM
ejpam-521	320	27	2	2	NUM
ejpam-521	320	28	∑	∑	NOUN
ejpam-521	320	29	ni	ni	PROPN
ejpam-521	320	30	,	,	PUNCT
ejpam-521	320	31	m>0	m>0	NOUN
ejpam-521	320	32	log	log	VERB
ejpam-521	320	33	ni	ni	PROPN
ejpam-521	320	34	,	,	PUNCT
ejpam-521	320	35	m−m	m−m	PROPN
ejpam-521	320	36	log	log	VERB
ejpam-521	320	37	m+o(m	m+o(m	NOUN
ejpam-521	320	38	)	)	PUNCT
ejpam-521	320	39	.	.	PUNCT
ejpam-521	321	1	(	(	PUNCT
ejpam-521	321	2	44	44	NUM
ejpam-521	321	3	)	)	PUNCT
ejpam-521	321	4	we	we	PRON
ejpam-521	321	5	will	will	AUX
ejpam-521	321	6	show	show	VERB
ejpam-521	321	7	that	that	SCONJ
ejpam-521	321	8	the	the	DET
ejpam-521	321	9	first	first	ADJ
ejpam-521	321	10	term	term	NOUN
ejpam-521	321	11	of	of	ADP
ejpam-521	321	12	(	(	PUNCT
ejpam-521	321	13	44	44	NUM
ejpam-521	321	14	)	)	PUNCT
ejpam-521	321	15	is	be	AUX
ejpam-521	321	16	α12	α12	PROPN
ejpam-521	321	17	m	m	NOUN
ejpam-521	321	18	log	log	NOUN
ejpam-521	321	19	m+o(m	m+o(m	NOUN
ejpam-521	321	20	)	)	PUNCT
ejpam-521	321	21	where	where	SCONJ
ejpam-521	321	22	1≤	1≤	PROPN
ejpam-521	321	23	α12	α12	PROPN
ejpam-521	321	24	≤	≤	PROPN
ejpam-521	321	25	α1	α1	PROPN
ejpam-521	321	26	,	,	PUNCT
ejpam-521	321	27	the	the	DET
ejpam-521	321	28	second	second	ADJ
ejpam-521	321	29	term	term	NOUN
ejpam-521	321	30	is	be	AUX
ejpam-521	321	31	o(m	o(m	NUM
ejpam-521	321	32	)	)	PUNCT
ejpam-521	321	33	and	and	CCONJ
ejpam-521	321	34	the	the	DET
ejpam-521	321	35	third	third	ADJ
ejpam-521	321	36	term	term	NOUN
ejpam-521	321	37	is	be	AUX
ejpam-521	321	38	m	m	PROPN
ejpam-521	321	39	2	2	NUM
ejpam-521	321	40	log	log	NOUN
ejpam-521	321	41	n	n	PRON
ejpam-521	321	42	mα22	mα22	PROPN
ejpam-521	321	43	where	where	SCONJ
ejpam-521	321	44	1≤	1≤	PROPN
ejpam-521	321	45	α22	α22	PROPN
ejpam-521	321	46	≤	≤	PROPN
ejpam-521	321	47	α1	α1	PROPN
ejpam-521	321	48	.	.	PUNCT
ejpam-521	322	1	the	the	DET
ejpam-521	322	2	following	follow	VERB
ejpam-521	322	3	lemmas	lemmas	PROPN
ejpam-521	322	4	will	will	AUX
ejpam-521	322	5	be	be	AUX
ejpam-521	322	6	needed	need	VERB
ejpam-521	322	7	.	.	PUNCT
ejpam-521	323	1	lemma	lemma	PROPN
ejpam-521	323	2	1	1	X
ejpam-521	323	3	.	.	PUNCT
ejpam-521	323	4	suppose	suppose	VERB
ejpam-521	323	5	that	that	SCONJ
ejpam-521	323	6	ni	ni	PROPN
ejpam-521	323	7	,	,	PUNCT
ejpam-521	323	8	m	m	PROPN
ejpam-521	323	9	’s	’s	PART
ejpam-521	323	10	have	have	VERB
ejpam-521	323	11	a	a	DET
ejpam-521	323	12	multinomial	multinomial	ADJ
ejpam-521	323	13	distribution	distribution	NOUN
ejpam-521	323	14	with	with	ADP
ejpam-521	323	15	probabilities	probability	NOUN
ejpam-521	323	16	πi	πi	ADP
ejpam-521	323	17	,	,	PUNCT
ejpam-521	323	18	m	m	PROPN
ejpam-521	323	19	’s	’	VERB
ejpam-521	323	20	such	such	ADJ
ejpam-521	323	21	that	that	DET
ejpam-521	323	22	∑m	∑m	PROPN
ejpam-521	323	23	i=1πi	i=1πi	PROPN
ejpam-521	323	24	,	,	PUNCT
ejpam-521	323	25	m	m	VERB
ejpam-521	323	26	=	=	NOUN
ejpam-521	323	27	1	1	NUM
ejpam-521	323	28	,	,	PUNCT
ejpam-521	323	29	πi	πi	ADV
ejpam-521	323	30	,	,	PUNCT
ejpam-521	323	31	m	m	VERB
ejpam-521	323	32	≥	≥	NOUN
ejpam-521	323	33	b1c1m−α1	b1c1m−α1	PROPN
ejpam-521	323	34	and	and	CCONJ
ejpam-521	323	35	∑m	∑m	PROPN
ejpam-521	323	36	i=1	i=1	PROPN
ejpam-521	323	37	ni	ni	PROPN
ejpam-521	323	38	,	,	PUNCT
ejpam-521	323	39	m	m	VERB
ejpam-521	323	40	=	=	ADJ
ejpam-521	323	41	n.	n.	NOUN
ejpam-521	323	42	then	then	ADV
ejpam-521	323	43	for	for	ADP
ejpam-521	323	44	each	each	DET
ejpam-521	323	45	integer	integer	PROPN
ejpam-521	323	46	w	w	PROPN
ejpam-521	323	47	,	,	PUNCT
ejpam-521	323	48	there	there	PRON
ejpam-521	323	49	exists	exist	VERB
ejpam-521	323	50	a	a	DET
ejpam-521	323	51	constant	constant	ADJ
ejpam-521	323	52	aw	aw	INTJ
ejpam-521	323	53	such	such	ADJ
ejpam-521	323	54	that	that	SCONJ
ejpam-521	323	55	e	e	NOUN
ejpam-521	323	56	(	(	PUNCT
ejpam-521	323	57	m	m	VERB
ejpam-521	323	58	∑	∑	PROPN
ejpam-521	323	59	i=1	i=1	PROPN
ejpam-521	323	60	ni	ni	PROPN
ejpam-521	323	61	,	,	PUNCT
ejpam-521	323	62	m−	m−	PROPN
ejpam-521	323	63	nπi	nπi	PROPN
ejpam-521	323	64	,	,	PUNCT
ejpam-521	323	65	m	m	VERB
ejpam-521	323	66	nπi	nπi	ADJ
ejpam-521	323	67	,	,	PUNCT
ejpam-521	323	68	m	m	NOUN
ejpam-521	323	69	)	)	PUNCT
ejpam-521	323	70	2w	2w	PROPN
ejpam-521	323	71	≤	≤	NUM
ejpam-521	323	72	awn	awn	VERB
ejpam-521	323	73	1	1	NUM
ejpam-521	323	74	2	2	NUM
ejpam-521	323	75	−wm2α1w	−wm2α1w	NOUN
ejpam-521	323	76	.	.	PUNCT
ejpam-521	324	1	(	(	PUNCT
ejpam-521	324	2	45	45	NUM
ejpam-521	324	3	)	)	PUNCT
ejpam-521	324	4	proof	proof	NOUN
ejpam-521	324	5	.	.	PUNCT
ejpam-521	325	1	denote	denote	VERB
ejpam-521	325	2	t1	t1	NOUN
ejpam-521	325	3	=	=	PUNCT
ejpam-521	325	4	∑m	∑m	PROPN
ejpam-521	325	5	i=1	i=1	PROPN
ejpam-521	325	6	ni	ni	PROPN
ejpam-521	325	7	,	,	PUNCT
ejpam-521	325	8	m−nπi	m−nπi	NOUN
ejpam-521	325	9	,	,	PUNCT
ejpam-521	325	10	m	m	VERB
ejpam-521	325	11	nπi	nπi	ADJ
ejpam-521	325	12	,	,	PUNCT
ejpam-521	325	13	m	m	PROPN
ejpam-521	325	14	.	.	PUNCT
ejpam-521	326	1	by	by	ADP
ejpam-521	326	2	the	the	DET
ejpam-521	326	3	definition	definition	NOUN
ejpam-521	326	4	of	of	ADP
ejpam-521	326	5	multinomial	multinomial	ADJ
ejpam-521	326	6	distribution	distribution	NOUN
ejpam-521	326	7	and	and	CCONJ
ejpam-521	326	8	from	from	ADP
ejpam-521	326	9	stirling	stirling	PROPN
ejpam-521	326	10	’s	’s	PART
ejpam-521	326	11	formula	formula	NOUN
ejpam-521	326	12	we	we	PRON
ejpam-521	326	13	have	have	VERB
ejpam-521	326	14	e(t	e(t	NOUN
ejpam-521	326	15	2w	2w	NUM
ejpam-521	326	16	1	1	NUM
ejpam-521	326	17	)	)	PUNCT
ejpam-521	326	18	=	=	SYM
ejpam-521	326	19	∑	∑	PUNCT
ejpam-521	326	20	n1,m+···+nm	n1,m+···+nm	PROPN
ejpam-521	326	21	,	,	PUNCT
ejpam-521	326	22	m	m	PROPN
ejpam-521	326	23	=	=	NOUN
ejpam-521	326	24	n	n	SYM
ejpam-521	326	25	t	t	NOUN
ejpam-521	326	26	2w	2w	NUM
ejpam-521	326	27	1	1	NUM
ejpam-521	326	28	n	n	CCONJ
ejpam-521	326	29	!	!	PUNCT
ejpam-521	327	1	∏m	∏m	PROPN
ejpam-521	327	2	i=1	i=1	PROPN
ejpam-521	327	3	ni	ni	PROPN
ejpam-521	327	4	,	,	PUNCT
ejpam-521	327	5	m	m	PROPN
ejpam-521	327	6	!	!	PUNCT
ejpam-521	328	1	m	m	VERB
ejpam-521	328	2	∏	∏	NUM
ejpam-521	328	3	i=1	i=1	PROPN
ejpam-521	328	4	π	π	PROPN
ejpam-521	328	5	ni	ni	PROPN
ejpam-521	328	6	,	,	PUNCT
ejpam-521	328	7	m	m	VERB
ejpam-521	328	8	i	i	PRON
ejpam-521	328	9	,	,	PUNCT
ejpam-521	328	10	m	m	VERB
ejpam-521	328	11	=	=	PUNCT
ejpam-521	328	12	∑	∑	PUNCT
ejpam-521	328	13	n1,m+···+nm	n1,m+···+nm	PROPN
ejpam-521	328	14	,	,	PUNCT
ejpam-521	328	15	m	m	PROPN
ejpam-521	328	16	=	=	NOUN
ejpam-521	328	17	n	n	SYM
ejpam-521	328	18	t	t	NOUN
ejpam-521	328	19	2w	2w	NUM
ejpam-521	328	20	1	1	NUM
ejpam-521	328	21	m	m	PROPN
ejpam-521	328	22	∏	∏	NUM
ejpam-521	328	23	i=1	i=1	PROPN
ejpam-521	328	24	(	(	PUNCT
ejpam-521	328	25	nπi	nπi	PROPN
ejpam-521	328	26	,	,	PUNCT
ejpam-521	328	27	m	m	NOUN
ejpam-521	328	28	)	)	PUNCT
ejpam-521	328	29	ni	ni	PROPN
ejpam-521	328	30	,	,	PUNCT
ejpam-521	328	31	m	m	VERB
ejpam-521	328	32	ni	ni	PROPN
ejpam-521	328	33	,	,	PUNCT
ejpam-521	328	34	m	m	PROPN
ejpam-521	328	35	!	!	PUNCT
ejpam-521	329	1	e−ni	e−ni	PROPN
ejpam-521	329	2	,	,	PUNCT
ejpam-521	329	3	m	m	VERB
ejpam-521	329	4	p	p	X
ejpam-521	329	5	2πnecn	2πnecn	NUM
ejpam-521	329	6	≤	≤	NUM
ejpam-521	329	7	p2πne	p2πne	PROPN
ejpam-521	329	8	∞	∞	NUM
ejpam-521	329	9	∑	∑	PROPN
ejpam-521	329	10	n=0	n=0	PROPN
ejpam-521	329	11	∑	∑	PROPN
ejpam-521	329	12	n1,m+···+nm	n1,m+···+nm	PROPN
ejpam-521	329	13	,	,	PUNCT
ejpam-521	329	14	m	m	PROPN
ejpam-521	329	15	=	=	NOUN
ejpam-521	329	16	n	n	SYM
ejpam-521	329	17	t	t	NOUN
ejpam-521	329	18	2w	2w	NUM
ejpam-521	329	19	1	1	NUM
ejpam-521	329	20	m	m	PROPN
ejpam-521	329	21	∏	∏	NUM
ejpam-521	329	22	i=1	i=1	PROPN
ejpam-521	329	23	(	(	PUNCT
ejpam-521	329	24	nπi	nπi	PROPN
ejpam-521	329	25	,	,	PUNCT
ejpam-521	329	26	m	m	NOUN
ejpam-521	329	27	)	)	PUNCT
ejpam-521	329	28	ni	ni	PROPN
ejpam-521	329	29	,	,	PUNCT
ejpam-521	329	30	m	m	VERB
ejpam-521	329	31	ni	ni	PROPN
ejpam-521	329	32	,	,	PUNCT
ejpam-521	329	33	m	m	PROPN
ejpam-521	329	34	!	!	PUNCT
ejpam-521	330	1	e−ni	e−ni	PROPN
ejpam-521	330	2	,	,	PUNCT
ejpam-521	330	3	m	m	VERB
ejpam-521	330	4	=	=	PUNCT
ejpam-521	331	1	p	p	X
ejpam-521	331	2	2πne	2πne	NUM
ejpam-521	331	3	∞	∞	PROPN
ejpam-521	331	4	∑	∑	PROPN
ejpam-521	331	5	n1,m=0	n1,m=0	PROPN
ejpam-521	331	6	·	·	PUNCT
ejpam-521	331	7	·	·	PUNCT
ejpam-521	331	8	·	·	PUNCT
ejpam-521	332	1	∞	∞	NUM
ejpam-521	332	2	∑	∑	PUNCT
ejpam-521	332	3	nm	nm	PROPN
ejpam-521	332	4	,	,	PUNCT
ejpam-521	332	5	m=0	m=0	PROPN
ejpam-521	332	6	t	t	PROPN
ejpam-521	332	7	2w	2w	NUM
ejpam-521	332	8	1	1	NUM
ejpam-521	332	9	m	m	PROPN
ejpam-521	332	10	∏	∏	NUM
ejpam-521	332	11	i=1	i=1	PROPN
ejpam-521	332	12	(	(	PUNCT
ejpam-521	332	13	nπi	nπi	PROPN
ejpam-521	332	14	,	,	PUNCT
ejpam-521	332	15	m	m	NOUN
ejpam-521	332	16	)	)	PUNCT
ejpam-521	332	17	ni	ni	PROPN
ejpam-521	332	18	,	,	PUNCT
ejpam-521	332	19	m	m	VERB
ejpam-521	332	20	ni	ni	PROPN
ejpam-521	332	21	,	,	PUNCT
ejpam-521	332	22	m	m	PROPN
ejpam-521	332	23	!	!	PUNCT
ejpam-521	333	1	e−ni	e−ni	PROPN
ejpam-521	333	2	,	,	PUNCT
ejpam-521	333	3	m	m	VERB
ejpam-521	333	4	=	=	X
ejpam-521	334	1	p	p	X
ejpam-521	334	2	2πnee′(t	2πnee′(t	VERB
ejpam-521	334	3	2w	2w	NUM
ejpam-521	334	4	1	1	NUM
ejpam-521	334	5	)	)	PUNCT
ejpam-521	334	6	(	(	PUNCT
ejpam-521	334	7	46	46	NUM
ejpam-521	334	8	)	)	PUNCT
ejpam-521	334	9	where	where	SCONJ
ejpam-521	334	10	the	the	DET
ejpam-521	334	11	final	final	ADJ
ejpam-521	334	12	expectation	expectation	NOUN
ejpam-521	334	13	e′(t	e′(t	VERB
ejpam-521	334	14	2w	2w	NUM
ejpam-521	334	15	1	1	NUM
ejpam-521	334	16	)	)	PUNCT
ejpam-521	334	17	is	be	AUX
ejpam-521	334	18	with	with	ADP
ejpam-521	334	19	respect	respect	NOUN
ejpam-521	334	20	to	to	ADP
ejpam-521	334	21	a	a	DET
ejpam-521	334	22	series	series	NOUN
ejpam-521	334	23	of	of	ADP
ejpam-521	334	24	independent	independent	ADJ
ejpam-521	334	25	poisson	poisson	NOUN
ejpam-521	334	26	random	random	ADJ
ejpam-521	334	27	variables	variable	NOUN
ejpam-521	334	28	{	{	PUNCT
ejpam-521	334	29	ni	ni	PROPN
ejpam-521	334	30	,	,	PUNCT
ejpam-521	334	31	m	m	VERB
ejpam-521	334	32	}	}	PUNCT
ejpam-521	334	33	with	with	ADP
ejpam-521	334	34	parameters	parameter	NOUN
ejpam-521	334	35	{	{	PUNCT
ejpam-521	334	36	nπi	nπi	PROPN
ejpam-521	334	37	,	,	PUNCT
ejpam-521	334	38	m	m	NOUN
ejpam-521	334	39	}	}	PUNCT
ejpam-521	334	40	.	.	PUNCT
ejpam-521	335	1	this	this	DET
ejpam-521	335	2	technique	technique	NOUN
ejpam-521	335	3	,	,	PUNCT
ejpam-521	335	4	used	use	VERB
ejpam-521	335	5	by	by	ADP
ejpam-521	335	6	[	[	X
ejpam-521	335	7	16	16	NUM
ejpam-521	335	8	]	]	PUNCT
ejpam-521	335	9	and	and	CCONJ
ejpam-521	335	10	[	[	X
ejpam-521	335	11	19	19	NUM
ejpam-521	335	12	]	]	X
ejpam-521	335	13	,	,	PUNCT
ejpam-521	335	14	of	of	ADP
ejpam-521	335	15	approximating	approximate	VERB
ejpam-521	335	16	the	the	DET
ejpam-521	335	17	multinomial	multinomial	ADJ
ejpam-521	335	18	distribution	distribution	NOUN
ejpam-521	335	19	by	by	ADP
ejpam-521	335	20	poisson	poisson	NOUN
ejpam-521	335	21	distribution	distribution	NOUN
ejpam-521	335	22	is	be	AUX
ejpam-521	335	23	called	call	VERB
ejpam-521	335	24	poissonization	poissonization	NOUN
ejpam-521	335	25	.	.	PUNCT
ejpam-521	336	1	the	the	DET
ejpam-521	336	2	constant	constant	ADJ
ejpam-521	336	3	cn	cn	PROPN
ejpam-521	336	4	=	=	NOUN
ejpam-521	336	5	o((12n)−1	o((12n)−1	PROPN
ejpam-521	336	6	)	)	PUNCT
ejpam-521	336	7	.	.	PUNCT
ejpam-521	337	1	by	by	ADP
ejpam-521	337	2	shiryayev	shiryayev	PROPN
ejpam-521	337	3	’s	’s	PART
ejpam-521	337	4	[	[	X
ejpam-521	337	5	17	17	NUM
ejpam-521	337	6	]	]	PUNCT
ejpam-521	337	7	theorem	theorem	NOUN
ejpam-521	337	8	6	6	NUM
ejpam-521	337	9	of	of	ADP
ejpam-521	337	10	section	section	NOUN
ejpam-521	337	11	2.12	2.12	NUM
ejpam-521	337	12	,	,	PUNCT
ejpam-521	337	13	the	the	DET
ejpam-521	337	14	2w	2w	NUM
ejpam-521	337	15	-	-	PUNCT
ejpam-521	337	16	th	th	VERB
ejpam-521	337	17	moment	moment	NOUN
ejpam-521	337	18	of	of	ADP
ejpam-521	337	19	t1	t1	NOUN
ejpam-521	337	20	can	can	AUX
ejpam-521	337	21	be	be	AUX
ejpam-521	337	22	written	write	VERB
ejpam-521	337	23	as	as	ADP
ejpam-521	337	24	a	a	DET
ejpam-521	337	25	sum	sum	NOUN
ejpam-521	337	26	of	of	ADP
ejpam-521	337	27	its	its	PRON
ejpam-521	337	28	cumulants	cumulant	NOUN
ejpam-521	337	29	:	:	PUNCT
ejpam-521	337	30	e′(t	e′(t	VERB
ejpam-521	338	1	2w	2w	NUM
ejpam-521	338	2	1	1	NUM
ejpam-521	338	3	)	)	PUNCT
ejpam-521	338	4	=	=	PUNCT
ejpam-521	338	5	∑	∑	PUNCT
ejpam-521	338	6	j1+···+	j1+···+	PROPN
ejpam-521	338	7	jl=2w	jl=2w	NOUN
ejpam-521	338	8	ρ	ρ	PROPN
ejpam-521	338	9	(	(	PUNCT
ejpam-521	338	10	j1	j1	PROPN
ejpam-521	338	11	,	,	PUNCT
ejpam-521	338	12	·	·	PUNCT
ejpam-521	338	13	·	·	PUNCT
ejpam-521	338	14	·	·	PUNCT
ejpam-521	338	15	,	,	PUNCT
ejpam-521	338	16	jl	jl	PROPN
ejpam-521	338	17	)	)	PUNCT
ejpam-521	338	18	l	l	NOUN
ejpam-521	338	19	∏	∏	PUNCT
ejpam-521	339	1	k=1	k=1	NOUN
ejpam-521	339	2	κ	κ	PROPN
ejpam-521	339	3	jk(t1	jk(t1	PROPN
ejpam-521	339	4	)	)	PUNCT
ejpam-521	339	5	(	(	PUNCT
ejpam-521	339	6	47	47	NUM
ejpam-521	339	7	)	)	PUNCT
ejpam-521	339	8	g.	g.	PROPN
ejpam-521	339	9	qian	qian	PROPN
ejpam-521	339	10	/	/	SYM
ejpam-521	339	11	eur	eur	PROPN
ejpam-521	339	12	.	.	PUNCT
ejpam-521	340	1	j.	j.	PROPN
ejpam-521	340	2	pure	pure	PROPN
ejpam-521	340	3	appl	appl	PROPN
ejpam-521	340	4	.	.	PROPN
ejpam-521	340	5	math	math	PROPN
ejpam-521	340	6	,	,	PUNCT
ejpam-521	340	7	3	3	NUM
ejpam-521	340	8	(	(	PUNCT
ejpam-521	340	9	2010	2010	NUM
ejpam-521	340	10	)	)	PUNCT
ejpam-521	340	11	,	,	PUNCT
ejpam-521	340	12	51	51	NUM
ejpam-521	340	13	-	-	SYM
ejpam-521	340	14	80	80	NUM
ejpam-521	340	15	65	65	NUM
ejpam-521	340	16	where	where	SCONJ
ejpam-521	340	17	ρ	ρ	PROPN
ejpam-521	340	18	(	(	PUNCT
ejpam-521	340	19	j1	j1	PROPN
ejpam-521	340	20	,	,	PUNCT
ejpam-521	340	21	·	·	PUNCT
ejpam-521	340	22	·	·	PUNCT
ejpam-521	340	23	·	·	PUNCT
ejpam-521	340	24	,	,	PUNCT
ejpam-521	340	25	jl	jl	NOUN
ejpam-521	340	26	)	)	PUNCT
ejpam-521	340	27	=	=	SYM
ejpam-521	340	28	1	1	NUM
ejpam-521	340	29	l	l	NOUN
ejpam-521	340	30	!	!	PUNCT
ejpam-521	341	1	(	(	PUNCT
ejpam-521	341	2	2w	2w	NUM
ejpam-521	341	3	)	)	PUNCT
ejpam-521	341	4	!	!	PUNCT
ejpam-521	342	1	j1	j1	PROPN
ejpam-521	342	2	!	!	PUNCT
ejpam-521	342	3	·	·	PUNCT
ejpam-521	342	4	·	·	PUNCT
ejpam-521	342	5	·	·	PUNCT
ejpam-521	342	6	jl	jl	NOUN
ejpam-521	342	7	!	!	PUNCT
ejpam-521	343	1	and	and	CCONJ
ejpam-521	343	2	jk	jk	PROPN
ejpam-521	343	3	≥	≥	NUM
ejpam-521	343	4	1	1	NUM
ejpam-521	343	5	,	,	PUNCT
ejpam-521	343	6	l	l	PROPN
ejpam-521	343	7	≤	≤	NOUN
ejpam-521	343	8	2w	2w	NUM
ejpam-521	343	9	.	.	PUNCT
ejpam-521	344	1	because	because	SCONJ
ejpam-521	344	2	ni	ni	PROPN
ejpam-521	344	3	,	,	PUNCT
ejpam-521	344	4	m	m	PROPN
ejpam-521	344	5	’s	’s	PART
ejpam-521	344	6	are	be	AUX
ejpam-521	344	7	independent	independent	ADJ
ejpam-521	344	8	poisson	poisson	NOUN
ejpam-521	344	9	random	random	ADJ
ejpam-521	344	10	variables	variable	NOUN
ejpam-521	344	11	,	,	PUNCT
ejpam-521	344	12	it	it	PRON
ejpam-521	344	13	follows	follow	VERB
ejpam-521	344	14	from	from	ADP
ejpam-521	344	15	the	the	DET
ejpam-521	344	16	section	section	NOUN
ejpam-521	344	17	1.5	1.5	NUM
ejpam-521	344	18	of	of	ADP
ejpam-521	344	19	[	[	X
ejpam-521	344	20	8	8	NUM
ejpam-521	344	21	]	]	PUNCT
ejpam-521	344	22	that	that	SCONJ
ejpam-521	344	23	the	the	DET
ejpam-521	344	24	jk	jk	PROPN
ejpam-521	344	25	-	-	PUNCT
ejpam-521	344	26	th	th	X
ejpam-521	344	27	cumulant	cumulant	NOUN
ejpam-521	344	28	of	of	ADP
ejpam-521	344	29	t1	t1	PROPN
ejpam-521	344	30	κ	κ	PROPN
ejpam-521	344	31	jk(t1	jk(t1	PROPN
ejpam-521	344	32	)	)	PUNCT
ejpam-521	344	33	=	=	PUNCT
ejpam-521	345	1	m	m	VERB
ejpam-521	345	2	∑	∑	PUNCT
ejpam-521	345	3	i=1	i=1	PROPN
ejpam-521	345	4	κ	κ	PROPN
ejpam-521	345	5	jk	jk	PROPN
ejpam-521	345	6	�	�	PROPN
ejpam-521	345	7	ni	ni	PROPN
ejpam-521	345	8	,	,	PUNCT
ejpam-521	345	9	m−	m−	PROPN
ejpam-521	345	10	nπi	nπi	PROPN
ejpam-521	345	11	,	,	PUNCT
ejpam-521	345	12	m	m	VERB
ejpam-521	345	13	nπi	nπi	ADJ
ejpam-521	345	14	,	,	PUNCT
ejpam-521	345	15	m	m	VERB
ejpam-521	345	16	�	�	NOUN
ejpam-521	345	17	=	=	PUNCT
ejpam-521	345	18	m	m	VERB
ejpam-521	345	19	∑	∑	PROPN
ejpam-521	345	20	i=1	i=1	PROPN
ejpam-521	345	21	nπi	nπi	PROPN
ejpam-521	345	22	,	,	PUNCT
ejpam-521	345	23	m	m	PROPN
ejpam-521	345	24	(	(	PUNCT
ejpam-521	345	25	nπi	nπi	ADJ
ejpam-521	345	26	,	,	PUNCT
ejpam-521	345	27	m	m	NOUN
ejpam-521	345	28	)	)	PUNCT
ejpam-521	345	29	jk	jk	PROPN
ejpam-521	345	30	≤	≤	PROPN
ejpam-521	345	31	(	(	PUNCT
ejpam-521	345	32	b1c1	b1c1	NOUN
ejpam-521	345	33	)	)	PUNCT
ejpam-521	346	1	−	−	PROPN
ejpam-521	347	1	jk	jk	PROPN
ejpam-521	348	1	n1−	n1−	PRON
ejpam-521	349	1	jk	jk	PROPN
ejpam-521	350	1	mα1	mα1	PROPN
ejpam-521	350	2	jk	jk	PROPN
ejpam-521	350	3	(	(	PUNCT
ejpam-521	350	4	48	48	NUM
ejpam-521	350	5	)	)	PUNCT
ejpam-521	350	6	if	if	SCONJ
ejpam-521	350	7	jk	jk	PROPN
ejpam-521	350	8	>	>	X
ejpam-521	350	9	1	1	NUM
ejpam-521	350	10	and	and	CCONJ
ejpam-521	350	11	κ	κ	X
ejpam-521	350	12	jk(t1	jk(t1	NOUN
ejpam-521	350	13	)	)	PUNCT
ejpam-521	351	1	=	=	SYM
ejpam-521	351	2	0	0	PUNCT
ejpam-521	352	1	if	if	SCONJ
ejpam-521	352	2	jk	jk	PROPN
ejpam-521	352	3	=	=	NOUN
ejpam-521	352	4	1	1	X
ejpam-521	352	5	.	.	PUNCT
ejpam-521	352	6	thus	thus	ADV
ejpam-521	352	7	e′(t	e′(t	VERB
ejpam-521	352	8	2w	2w	NUM
ejpam-521	352	9	1	1	NUM
ejpam-521	352	10	)	)	PUNCT
ejpam-521	352	11	=	=	SYM
ejpam-521	352	12	∗	∗	NOUN
ejpam-521	352	13	∑	∑	PUNCT
ejpam-521	352	14	ρ	ρ	PROPN
ejpam-521	352	15	(	(	PUNCT
ejpam-521	352	16	j1	j1	PROPN
ejpam-521	352	17	,	,	PUNCT
ejpam-521	352	18	·	·	PUNCT
ejpam-521	352	19	·	·	PUNCT
ejpam-521	352	20	·	·	PUNCT
ejpam-521	352	21	,	,	PUNCT
ejpam-521	352	22	jl	jl	PROPN
ejpam-521	352	23	)	)	PUNCT
ejpam-521	352	24	l	l	NOUN
ejpam-521	352	25	∏	∏	PUNCT
ejpam-521	352	26	k=1	k=1	NOUN
ejpam-521	352	27	κ	κ	PROPN
ejpam-521	352	28	jk(t1	jk(t1	PROPN
ejpam-521	352	29	)	)	PUNCT
ejpam-521	352	30	≤	≤	NOUN
ejpam-521	352	31	∗	∗	NOUN
ejpam-521	352	32	∑	∑	PUNCT
ejpam-521	352	33	ρ	ρ	PROPN
ejpam-521	352	34	(	(	PUNCT
ejpam-521	352	35	j1	j1	PROPN
ejpam-521	352	36	,	,	PUNCT
ejpam-521	352	37	·	·	PUNCT
ejpam-521	352	38	·	·	PUNCT
ejpam-521	352	39	·	·	PUNCT
ejpam-521	352	40	,	,	PUNCT
ejpam-521	352	41	jl	jl	PROPN
ejpam-521	352	42	)	)	PUNCT
ejpam-521	352	43	l	l	NOUN
ejpam-521	352	44	∏	∏	X
ejpam-521	352	45	k=1	k=1	X
ejpam-521	352	46	(	(	PUNCT
ejpam-521	352	47	b1c1	b1c1	NOUN
ejpam-521	352	48	)	)	PUNCT
ejpam-521	353	1	−	−	PROPN
ejpam-521	354	1	jk	jk	PROPN
ejpam-521	355	1	n1−	n1−	PRON
ejpam-521	356	1	jk	jk	PROPN
ejpam-521	357	1	mα1	mα1	PROPN
ejpam-521	357	2	jk	jk	PROPN
ejpam-521	357	3	≤	≤	PROPN
ejpam-521	357	4	awn−wm2α1w	awn−wm2α1w	NOUN
ejpam-521	357	5	(	(	PUNCT
ejpam-521	357	6	49	49	NUM
ejpam-521	357	7	)	)	PUNCT
ejpam-521	357	8	where	where	SCONJ
ejpam-521	357	9	the	the	DET
ejpam-521	357	10	summation	summation	NOUN
ejpam-521	357	11	∑∗	∑∗	PUNCT
ejpam-521	357	12	is	be	AUX
ejpam-521	357	13	taken	take	VERB
ejpam-521	357	14	over	over	ADP
ejpam-521	357	15	all	all	DET
ejpam-521	357	16	partitions	partition	NOUN
ejpam-521	357	17	of	of	ADP
ejpam-521	357	18	2w	2w	NUM
ejpam-521	357	19	such	such	ADJ
ejpam-521	357	20	that	that	SCONJ
ejpam-521	357	21	∑l	∑l	PROPN
ejpam-521	357	22	k=1	k=1	PROPN
ejpam-521	357	23	jk	jk	PROPN
ejpam-521	357	24	=	=	SYM
ejpam-521	357	25	2w	2w	PROPN
ejpam-521	357	26	,	,	PUNCT
ejpam-521	357	27	jk	jk	PROPN
ejpam-521	357	28	≥	≥	NUM
ejpam-521	357	29	2	2	NUM
ejpam-521	357	30	and	and	CCONJ
ejpam-521	357	31	l	l	NOUN
ejpam-521	357	32	≤	≤	NOUN
ejpam-521	357	33	w.	w.	NOUN
ejpam-521	357	34	using	use	VERB
ejpam-521	357	35	the	the	DET
ejpam-521	357	36	same	same	ADJ
ejpam-521	357	37	notation	notation	NOUN
ejpam-521	357	38	for	for	ADP
ejpam-521	357	39	possibly	possibly	ADV
ejpam-521	357	40	different	different	ADJ
ejpam-521	357	41	constants	constant	NOUN
ejpam-521	357	42	and	and	CCONJ
ejpam-521	357	43	substituting	substitute	VERB
ejpam-521	357	44	the	the	DET
ejpam-521	357	45	last	last	ADJ
ejpam-521	357	46	bound	bind	VERB
ejpam-521	357	47	into	into	ADP
ejpam-521	357	48	(	(	PUNCT
ejpam-521	357	49	46	46	NUM
ejpam-521	357	50	)	)	PUNCT
ejpam-521	357	51	the	the	DET
ejpam-521	357	52	lemma	lemma	PROPN
ejpam-521	357	53	is	be	AUX
ejpam-521	357	54	proved	prove	VERB
ejpam-521	357	55	.	.	PUNCT
ejpam-521	358	1	⊳	⊳	PROPN
ejpam-521	358	2	lemma	lemma	PROPN
ejpam-521	358	3	2	2	X
ejpam-521	358	4	.	.	PUNCT
ejpam-521	358	5	suppose	suppose	VERB
ejpam-521	358	6	that	that	SCONJ
ejpam-521	358	7	n	n	PRON
ejpam-521	358	8	is	be	AUX
ejpam-521	358	9	a	a	DET
ejpam-521	358	10	binomial	binomial	ADJ
ejpam-521	358	11	random	random	ADJ
ejpam-521	358	12	variable	variable	NOUN
ejpam-521	358	13	with	with	ADP
ejpam-521	358	14	mean	mean	NOUN
ejpam-521	359	1	np	np	INTJ
ejpam-521	359	2	.	.	PUNCT
ejpam-521	360	1	then	then	ADV
ejpam-521	360	2	for	for	ADP
ejpam-521	360	3	any	any	DET
ejpam-521	360	4	integer	integer	NOUN
ejpam-521	360	5	w	w	ADP
ejpam-521	360	6	>	>	X
ejpam-521	360	7	0	0	NUM
ejpam-521	360	8	,	,	PUNCT
ejpam-521	360	9	there	there	PRON
ejpam-521	360	10	is	be	VERB
ejpam-521	360	11	a	a	DET
ejpam-521	360	12	constant	constant	ADJ
ejpam-521	360	13	aw	aw	INTJ
ejpam-521	360	14	>	>	X
ejpam-521	360	15	0	0	NUM
ejpam-521	360	16	such	such	ADJ
ejpam-521	360	17	that	that	SCONJ
ejpam-521	360	18	e(n	e(n	ADJ
ejpam-521	360	19	−	−	PROPN
ejpam-521	360	20	np)2w	np)2w	NOUN
ejpam-521	360	21	≤	≤	NUM
ejpam-521	360	22	awn	awn	VERB
ejpam-521	360	23	1	1	NUM
ejpam-521	360	24	2	2	NUM
ejpam-521	360	25	+	+	NOUN
ejpam-521	360	26	w	w	NOUN
ejpam-521	360	27	pw	pw	X
ejpam-521	360	28	.	.	PUNCT
ejpam-521	361	1	(	(	PUNCT
ejpam-521	361	2	50	50	NUM
ejpam-521	361	3	)	)	PUNCT
ejpam-521	361	4	proof	proof	NOUN
ejpam-521	361	5	.	.	PUNCT
ejpam-521	362	1	by	by	ADP
ejpam-521	362	2	the	the	DET
ejpam-521	362	3	same	same	ADJ
ejpam-521	362	4	technique	technique	NOUN
ejpam-521	362	5	of	of	ADP
ejpam-521	362	6	poissonization	poissonization	NOUN
ejpam-521	362	7	we	we	PRON
ejpam-521	362	8	have	have	VERB
ejpam-521	362	9	e(n	e(n	ADJ
ejpam-521	362	10	−	−	PROPN
ejpam-521	362	11	np)2w	np)2w	NOUN
ejpam-521	362	12	≤	≤	NUM
ejpam-521	362	13	awn	awn	VERB
ejpam-521	362	14	1	1	NUM
ejpam-521	362	15	2	2	NUM
ejpam-521	362	16	e(n1	e(n1	NOUN
ejpam-521	362	17	−	−	NOUN
ejpam-521	362	18	np)2w	np)2w	NOUN
ejpam-521	362	19	(	(	PUNCT
ejpam-521	362	20	51	51	NUM
ejpam-521	362	21	)	)	PUNCT
ejpam-521	362	22	where	where	SCONJ
ejpam-521	362	23	n1	n1	PROPN
ejpam-521	362	24	is	be	AUX
ejpam-521	362	25	a	a	DET
ejpam-521	362	26	poisson	poisson	NOUN
ejpam-521	362	27	random	random	ADJ
ejpam-521	362	28	variable	variable	NOUN
ejpam-521	362	29	with	with	ADP
ejpam-521	362	30	mean	mean	NOUN
ejpam-521	362	31	np	np	INTJ
ejpam-521	362	32	.	.	PUNCT
ejpam-521	362	33	by	by	ADP
ejpam-521	362	34	the	the	DET
ejpam-521	362	35	equation	equation	NOUN
ejpam-521	362	36	(	(	PUNCT
ejpam-521	362	37	47	47	NUM
ejpam-521	362	38	)	)	PUNCT
ejpam-521	362	39	and	and	CCONJ
ejpam-521	362	40	the	the	DET
ejpam-521	362	41	fact	fact	NOUN
ejpam-521	362	42	that	that	SCONJ
ejpam-521	362	43	κk(n1	κk(n1	INTJ
ejpam-521	363	1	−	−	NUM
ejpam-521	363	2	np	np	NOUN
ejpam-521	363	3	)	)	PUNCT
ejpam-521	363	4	=	=	NOUN
ejpam-521	363	5	np	np	INTJ
ejpam-521	364	1	if	if	SCONJ
ejpam-521	364	2	k	k	PROPN
ejpam-521	364	3	>	>	X
ejpam-521	364	4	1	1	NUM
ejpam-521	364	5	and	and	CCONJ
ejpam-521	364	6	κ1(n1	κ1(n1	ADJ
ejpam-521	364	7	−	−	PROPN
ejpam-521	364	8	np	np	INTJ
ejpam-521	364	9	)	)	PUNCT
ejpam-521	364	10	=	=	SYM
ejpam-521	364	11	0	0	NUM
ejpam-521	365	1	it	it	PRON
ejpam-521	365	2	follows	follow	VERB
ejpam-521	365	3	that	that	SCONJ
ejpam-521	365	4	e(n1	e(n1	NOUN
ejpam-521	365	5	−	−	NOUN
ejpam-521	365	6	np)2w	np)2w	NOUN
ejpam-521	365	7	is	be	AUX
ejpam-521	365	8	a	a	DET
ejpam-521	365	9	polynomial	polynomial	NOUN
ejpam-521	365	10	of	of	ADP
ejpam-521	365	11	order	order	NOUN
ejpam-521	365	12	w	w	NOUN
ejpam-521	365	13	,	,	PUNCT
ejpam-521	365	14	and	and	CCONJ
ejpam-521	365	15	therefore	therefore	ADV
ejpam-521	365	16	(	(	PUNCT
ejpam-521	365	17	50	50	NUM
ejpam-521	365	18	)	)	PUNCT
ejpam-521	365	19	must	must	AUX
ejpam-521	365	20	hold	hold	VERB
ejpam-521	365	21	.	.	PUNCT
ejpam-521	366	1	⊳	⊳	VERB
ejpam-521	366	2	lemma	lemma	PROPN
ejpam-521	366	3	3	3	X
ejpam-521	366	4	.	.	PUNCT
ejpam-521	367	1	under	under	ADP
ejpam-521	367	2	the	the	DET
ejpam-521	367	3	conditions	condition	NOUN
ejpam-521	367	4	that	that	SCONJ
ejpam-521	367	5	r̃i	r̃i	NOUN
ejpam-521	367	6	,	,	PUNCT
ejpam-521	367	7	m	m	PROPN
ejpam-521	367	8	≥	≥	NOUN
ejpam-521	367	9	b1m−α1	b1m−α1	NOUN
ejpam-521	367	10	,	,	PUNCT
ejpam-521	367	11	1≤	1≤	NUM
ejpam-521	367	12	α1	α1	PROPN
ejpam-521	367	13	<	<	X
ejpam-521	367	14	1	1	NUM
ejpam-521	367	15	+	+	CCONJ
ejpam-521	367	16	(	(	PUNCT
ejpam-521	367	17	2γ2	2γ2	NUM
ejpam-521	367	18	)	)	PUNCT
ejpam-521	367	19	−1	−1	NOUN
ejpam-521	367	20	and	and	CCONJ
ejpam-521	367	21	f	f	PROPN
ejpam-521	367	22	≥	≥	PROPN
ejpam-521	367	23	c1	c1	PROPN
ejpam-521	367	24	>	>	X
ejpam-521	367	25	0	0	PROPN
ejpam-521	367	26	,	,	PUNCT
ejpam-521	367	27	m	m	VERB
ejpam-521	367	28	∑	∑	PROPN
ejpam-521	367	29	i=1	i=1	PROPN
ejpam-521	367	30	ni	ni	PROPN
ejpam-521	367	31	,	,	PUNCT
ejpam-521	367	32	m−	m−	PROPN
ejpam-521	367	33	nπi	nπi	PROPN
ejpam-521	367	34	,	,	PUNCT
ejpam-521	367	35	m	m	VERB
ejpam-521	367	36	nπi	nπi	ADJ
ejpam-521	367	37	,	,	PUNCT
ejpam-521	367	38	m	m	PROPN
ejpam-521	367	39	=	=	ADJ
ejpam-521	367	40	o(m	o(m	PROPN
ejpam-521	367	41	)	)	PUNCT
ejpam-521	367	42	a.s	a.s	PROPN
ejpam-521	367	43	.	.	PROPN
ejpam-521	367	44	(	(	PUNCT
ejpam-521	367	45	52	52	NUM
ejpam-521	367	46	)	)	PUNCT
ejpam-521	367	47	uniformly	uniformly	ADV
ejpam-521	367	48	in	in	ADP
ejpam-521	367	49	m	m	PROPN
ejpam-521	367	50	∈	∈	NOUN
ejpam-521	368	1	[	[	X
ejpam-521	368	2	1	1	NUM
ejpam-521	368	3	,	,	PUNCT
ejpam-521	368	4	nγ2	nγ2	NUM
ejpam-521	368	5	]	]	PUNCT
ejpam-521	368	6	as	as	ADP
ejpam-521	368	7	n→∞	n→∞	NUM
ejpam-521	368	8	,	,	PUNCT
ejpam-521	368	9	where	where	SCONJ
ejpam-521	368	10	πi	πi	ADV
ejpam-521	368	11	,	,	PUNCT
ejpam-521	368	12	m	m	VERB
ejpam-521	368	13	=	=	SYM
ejpam-521	368	14	∫	∫	PROPN
ejpam-521	368	15	q̃i	q̃i	PROPN
ejpam-521	368	16	,	,	PUNCT
ejpam-521	368	17	m	m	PROPN
ejpam-521	368	18	f	f	NOUN
ejpam-521	368	19	.	.	PUNCT
ejpam-521	369	1	proof	proof	NOUN
ejpam-521	369	2	.	.	PUNCT
ejpam-521	370	1	for	for	ADP
ejpam-521	370	2	any	any	DET
ejpam-521	370	3	ǫ	ǫ	NOUN
ejpam-521	370	4	>	>	X
ejpam-521	370	5	0	0	NUM
ejpam-521	370	6	,	,	PUNCT
ejpam-521	370	7	p	p	NOUN
ejpam-521	370	8	max	max	PROPN
ejpam-521	370	9	m∈[1,nγ2	m∈[1,nγ2	PROPN
ejpam-521	370	10	]	]	PUNCT
ejpam-521	370	11	�	�	PROPN
ejpam-521	370	12	�	�	PROPN
ejpam-521	370	13	�	�	PROPN
ejpam-521	370	14	�	�	PROPN
ejpam-521	370	15	�	�	PROPN
ejpam-521	370	16	m	m	PROPN
ejpam-521	370	17	∑	∑	PROPN
ejpam-521	370	18	i=1	i=1	PROPN
ejpam-521	370	19	ni	ni	PROPN
ejpam-521	370	20	,	,	PUNCT
ejpam-521	370	21	m−	m−	PROPN
ejpam-521	370	22	nπi	nπi	PROPN
ejpam-521	370	23	,	,	PUNCT
ejpam-521	370	24	m	m	VERB
ejpam-521	370	25	nπi	nπi	ADJ
ejpam-521	370	26	,	,	PUNCT
ejpam-521	370	27	m	m	PROPN
ejpam-521	370	28	�	�	PROPN
ejpam-521	370	29	�	�	PROPN
ejpam-521	370	30	�	�	PROPN
ejpam-521	370	31	�	�	PROPN
ejpam-521	370	32	�	�	PROPN
ejpam-521	370	33	≥	≥	NUM
ejpam-521	370	34	ǫm	ǫm	PROPN
ejpam-521	370	35	!	!	PUNCT
ejpam-521	370	36	≤	≤	NOUN
ejpam-521	370	37	∑	∑	PUNCT
ejpam-521	370	38	m∈[1,nγ2	m∈[1,nγ2	PROPN
ejpam-521	370	39	]	]	X
ejpam-521	370	40	p	p	PROPN
ejpam-521	370	41	�	�	PROPN
ejpam-521	370	42	�	�	PROPN
ejpam-521	370	43	�	�	PROPN
ejpam-521	370	44	�	�	PROPN
ejpam-521	370	45	�	�	PROPN
ejpam-521	370	46	m	m	PROPN
ejpam-521	370	47	∑	∑	PROPN
ejpam-521	370	48	i=1	i=1	PROPN
ejpam-521	370	49	ni	ni	PROPN
ejpam-521	370	50	,	,	PUNCT
ejpam-521	370	51	m−	m−	PROPN
ejpam-521	370	52	nπi	nπi	PROPN
ejpam-521	370	53	,	,	PUNCT
ejpam-521	370	54	m	m	VERB
ejpam-521	370	55	nπi	nπi	ADJ
ejpam-521	370	56	,	,	PUNCT
ejpam-521	370	57	m	m	PROPN
ejpam-521	370	58	�	�	PROPN
ejpam-521	370	59	�	�	PROPN
ejpam-521	370	60	�	�	PROPN
ejpam-521	370	61	�	�	PROPN
ejpam-521	370	62	�	�	PROPN
ejpam-521	370	63	≥	≥	NUM
ejpam-521	370	64	ǫm	ǫm	PROPN
ejpam-521	370	65	!	!	PUNCT
ejpam-521	371	1	g.	g.	PROPN
ejpam-521	371	2	qian	qian	PROPN
ejpam-521	371	3	/	/	SYM
ejpam-521	371	4	eur	eur	PROPN
ejpam-521	371	5	.	.	PUNCT
ejpam-521	372	1	j.	j.	PROPN
ejpam-521	372	2	pure	pure	PROPN
ejpam-521	372	3	appl	appl	PROPN
ejpam-521	372	4	.	.	PROPN
ejpam-521	372	5	math	math	PROPN
ejpam-521	372	6	,	,	PUNCT
ejpam-521	372	7	3	3	NUM
ejpam-521	372	8	(	(	PUNCT
ejpam-521	372	9	2010	2010	NUM
ejpam-521	372	10	)	)	PUNCT
ejpam-521	372	11	,	,	PUNCT
ejpam-521	372	12	51	51	NUM
ejpam-521	372	13	-	-	SYM
ejpam-521	372	14	80	80	NUM
ejpam-521	372	15	66	66	NUM
ejpam-521	372	16	≤	≤	NOUN
ejpam-521	372	17	∑	∑	PUNCT
ejpam-521	372	18	m∈[1,nγ2	m∈[1,nγ2	PROPN
ejpam-521	372	19	]	]	X
ejpam-521	372	20	ǫ−2wm−2w	ǫ−2wm−2w	PROPN
ejpam-521	372	21	e	e	PROPN
ejpam-521	372	22	(	(	PUNCT
ejpam-521	372	23	m	m	PROPN
ejpam-521	372	24	∑	∑	PROPN
ejpam-521	372	25	i=1	i=1	PROPN
ejpam-521	372	26	ni	ni	PROPN
ejpam-521	372	27	,	,	PUNCT
ejpam-521	372	28	m−	m−	PROPN
ejpam-521	372	29	nπi	nπi	PROPN
ejpam-521	372	30	,	,	PUNCT
ejpam-521	372	31	m	m	VERB
ejpam-521	372	32	nπi	nπi	ADJ
ejpam-521	372	33	,	,	PUNCT
ejpam-521	372	34	m	m	PROPN
ejpam-521	372	35	)	)	PUNCT
ejpam-521	372	36	2w	2w	NOUN
ejpam-521	372	37	(	(	PUNCT
ejpam-521	372	38	53	53	NUM
ejpam-521	372	39	)	)	PUNCT
ejpam-521	372	40	where	where	SCONJ
ejpam-521	372	41	the	the	DET
ejpam-521	372	42	last	last	ADJ
ejpam-521	372	43	inequality	inequality	NOUN
ejpam-521	372	44	comes	come	VERB
ejpam-521	372	45	by	by	ADP
ejpam-521	372	46	using	use	VERB
ejpam-521	372	47	chebyshev	chebyshev	PROPN
ejpam-521	372	48	’s	’s	PART
ejpam-521	372	49	inequality	inequality	NOUN
ejpam-521	372	50	.	.	PUNCT
ejpam-521	373	1	from	from	ADP
ejpam-521	373	2	lemma	lemma	PROPN
ejpam-521	373	3	1	1	NUM
ejpam-521	373	4	,	,	PUNCT
ejpam-521	373	5	p	p	PRON
ejpam-521	373	6	max	max	PROPN
ejpam-521	373	7	m∈[1,nγ2	m∈[1,nγ2	PROPN
ejpam-521	373	8	]	]	PUNCT
ejpam-521	373	9	�	�	PROPN
ejpam-521	373	10	�	�	PROPN
ejpam-521	373	11	�	�	PROPN
ejpam-521	373	12	�	�	PROPN
ejpam-521	373	13	�	�	PROPN
ejpam-521	373	14	m	m	PROPN
ejpam-521	373	15	∑	∑	PROPN
ejpam-521	373	16	i=1	i=1	PROPN
ejpam-521	373	17	ni	ni	PROPN
ejpam-521	373	18	,	,	PUNCT
ejpam-521	373	19	m−	m−	PROPN
ejpam-521	373	20	nπi	nπi	PROPN
ejpam-521	373	21	,	,	PUNCT
ejpam-521	373	22	m	m	VERB
ejpam-521	373	23	nπi	nπi	ADJ
ejpam-521	373	24	,	,	PUNCT
ejpam-521	373	25	m	m	PROPN
ejpam-521	373	26	�	�	PROPN
ejpam-521	373	27	�	�	PROPN
ejpam-521	373	28	�	�	PROPN
ejpam-521	373	29	�	�	PROPN
ejpam-521	373	30	�	�	PROPN
ejpam-521	373	31	≥	≥	NUM
ejpam-521	373	32	ǫm	ǫm	PROPN
ejpam-521	373	33	!	!	PUNCT
ejpam-521	374	1	≤	≤	NOUN
ejpam-521	374	2	∑	∑	PUNCT
ejpam-521	374	3	m∈[1,nγ2	m∈[1,nγ2	PROPN
ejpam-521	374	4	]	]	X
ejpam-521	374	5	ǫ−2wm−2wawn	ǫ−2wm−2wawn	NOUN
ejpam-521	374	6	1	1	NUM
ejpam-521	374	7	2	2	NUM
ejpam-521	374	8	−wm2α1w	−wm2α1w	PROPN
ejpam-521	374	9	≤	≤	NOUN
ejpam-521	374	10	awǫ	awǫ	PROPN
ejpam-521	374	11	−2wn(2α1γ2−2γ2−1)w+	−2wn(2α1γ2−2γ2−1)w+	NOUN
ejpam-521	374	12	1	1	NUM
ejpam-521	374	13	2	2	NUM
ejpam-521	374	14	+	+	NOUN
ejpam-521	374	15	γ2	γ2	ADJ
ejpam-521	374	16	.	.	PUNCT
ejpam-521	375	1	(	(	PUNCT
ejpam-521	375	2	54	54	NUM
ejpam-521	375	3	)	)	PUNCT
ejpam-521	375	4	by	by	ADP
ejpam-521	375	5	the	the	DET
ejpam-521	375	6	condition	condition	NOUN
ejpam-521	375	7	that	that	SCONJ
ejpam-521	375	8	α1	α1	PROPN
ejpam-521	375	9	<	<	X
ejpam-521	375	10	1+(2γ2	1+(2γ2	PROPN
ejpam-521	375	11	)	)	PUNCT
ejpam-521	375	12	−1	−1	NOUN
ejpam-521	375	13	,	,	PUNCT
ejpam-521	375	14	the	the	DET
ejpam-521	375	15	sum	sum	NOUN
ejpam-521	375	16	of	of	ADP
ejpam-521	375	17	the	the	DET
ejpam-521	375	18	series	series	NOUN
ejpam-521	375	19	defined	define	VERB
ejpam-521	375	20	by	by	ADP
ejpam-521	375	21	the	the	DET
ejpam-521	375	22	terms	term	NOUN
ejpam-521	375	23	of	of	ADP
ejpam-521	375	24	form	form	NOUN
ejpam-521	375	25	(	(	PUNCT
ejpam-521	375	26	54	54	NUM
ejpam-521	375	27	)	)	PUNCT
ejpam-521	375	28	converges	converge	NOUN
ejpam-521	375	29	as	as	ADP
ejpam-521	375	30	n→∞	n→∞	NUM
ejpam-521	375	31	,	,	PUNCT
ejpam-521	375	32	if	if	SCONJ
ejpam-521	375	33	w	w	PROPN
ejpam-521	375	34	>	>	X
ejpam-521	375	35	3	3	NUM
ejpam-521	375	36	+	+	NOUN
ejpam-521	375	37	2γ2	2γ2	NUM
ejpam-521	375	38	2	2	NUM
ejpam-521	375	39	+	+	NOUN
ejpam-521	375	40	4γ2−4α1γ2	4γ2−4α1γ2	NOUN
ejpam-521	375	41	.	.	PUNCT
ejpam-521	376	1	hence	hence	ADV
ejpam-521	376	2	(	(	PUNCT
ejpam-521	376	3	52	52	NUM
ejpam-521	376	4	)	)	PUNCT
ejpam-521	376	5	follows	follow	VERB
ejpam-521	376	6	from	from	ADP
ejpam-521	376	7	applying	apply	VERB
ejpam-521	376	8	the	the	DET
ejpam-521	376	9	borel	borel	NOUN
ejpam-521	376	10	-	-	PUNCT
ejpam-521	376	11	cantelli	cantelli	PROPN
ejpam-521	376	12	lemma	lemma	PROPN
ejpam-521	376	13	.	.	PUNCT
ejpam-521	377	1	⊳	⊳	PROPN
ejpam-521	377	2	lemma	lemma	PROPN
ejpam-521	377	3	4	4	NUM
ejpam-521	377	4	.	.	PUNCT
ejpam-521	378	1	under	under	ADP
ejpam-521	378	2	the	the	DET
ejpam-521	378	3	conditions	condition	NOUN
ejpam-521	378	4	that	that	PRON
ejpam-521	378	5	b1m−α1	b1m−α1	VERB
ejpam-521	378	6	≤	≤	PUNCT
ejpam-521	378	7	r̃i	r̃i	NOUN
ejpam-521	378	8	,	,	PUNCT
ejpam-521	378	9	m	m	VERB
ejpam-521	378	10	≤	≤	ADJ
ejpam-521	378	11	b2m−α2	b2m−α2	NOUN
ejpam-521	378	12	,	,	PUNCT
ejpam-521	379	1	where	where	SCONJ
ejpam-521	379	2	2α1	2α1	NUM
ejpam-521	379	3	−	−	NOUN
ejpam-521	379	4	γ−1	γ−1	ADJ
ejpam-521	379	5	2	2	NUM
ejpam-521	379	6	<	<	X
ejpam-521	379	7	α2	α2	ADJ
ejpam-521	379	8	≤	≤	NOUN
ejpam-521	379	9	1	1	NUM
ejpam-521	379	10	≤	≤	NUM
ejpam-521	379	11	α1	α1	NOUN
ejpam-521	379	12	<	<	X
ejpam-521	379	13	2−1	2−1	NUM
ejpam-521	379	14	+	+	CCONJ
ejpam-521	379	15	(	(	PUNCT
ejpam-521	379	16	2γ2	2γ2	NUM
ejpam-521	379	17	)	)	PUNCT
ejpam-521	379	18	−1	−1	NOUN
ejpam-521	379	19	and	and	CCONJ
ejpam-521	379	20	0	0	NUM
ejpam-521	379	21	<	<	X
ejpam-521	379	22	c1	c1	PROPN
ejpam-521	379	23	≤	≤	PROPN
ejpam-521	379	24	f	f	PROPN
ejpam-521	379	25	≤	≤	PROPN
ejpam-521	379	26	c2	c2	PROPN
ejpam-521	379	27	,	,	PUNCT
ejpam-521	379	28	max	max	PROPN
ejpam-521	379	29	1≤i≤m	1≤i≤m	NUM
ejpam-521	379	30	�	�	PROPN
ejpam-521	379	31	�	�	PROPN
ejpam-521	379	32	�	�	PROPN
ejpam-521	379	33	�	�	PROPN
ejpam-521	379	34	mα1	mα1	PROPN
ejpam-521	379	35	ni	ni	PROPN
ejpam-521	379	36	,	,	PUNCT
ejpam-521	379	37	m	m	VERB
ejpam-521	379	38	n	n	PROPN
ejpam-521	379	39	−mα1πi	−mα1πi	PROPN
ejpam-521	379	40	,	,	PUNCT
ejpam-521	379	41	m	m	PROPN
ejpam-521	379	42	�	�	PROPN
ejpam-521	379	43	�	�	PROPN
ejpam-521	379	44	�	�	PROPN
ejpam-521	379	45	�	�	PROPN
ejpam-521	379	46	=	=	SYM
ejpam-521	379	47	o(1	o(1	PROPN
ejpam-521	379	48	)	)	PUNCT
ejpam-521	380	1	a.s	a.s	PROPN
ejpam-521	380	2	.	.	PROPN
ejpam-521	380	3	(	(	PUNCT
ejpam-521	380	4	55	55	NUM
ejpam-521	380	5	)	)	PUNCT
ejpam-521	380	6	uniformly	uniformly	ADV
ejpam-521	380	7	in	in	ADP
ejpam-521	380	8	m	m	PROPN
ejpam-521	380	9	∈	∈	NOUN
ejpam-521	381	1	[	[	X
ejpam-521	381	2	1	1	NUM
ejpam-521	381	3	,	,	PUNCT
ejpam-521	381	4	nγ2	nγ2	NUM
ejpam-521	381	5	]	]	PUNCT
ejpam-521	381	6	as	as	ADP
ejpam-521	381	7	n→∞.	n→∞.	PROPN
ejpam-521	381	8	proof	proof	NOUN
ejpam-521	381	9	.	.	PUNCT
ejpam-521	382	1	denote	denote	VERB
ejpam-521	382	2	im	im	PROPN
ejpam-521	382	3	,	,	PUNCT
ejpam-521	382	4	n	n	PROPN
ejpam-521	382	5	=	=	SYM
ejpam-521	382	6	max	max	PROPN
ejpam-521	382	7	1≤i≤m	1≤i≤m	NUM
ejpam-521	382	8	�	�	PROPN
ejpam-521	382	9	�	�	PROPN
ejpam-521	382	10	�	�	PROPN
ejpam-521	382	11	�	�	PROPN
ejpam-521	382	12	mα1	mα1	PROPN
ejpam-521	382	13	ni	ni	PROPN
ejpam-521	382	14	,	,	PUNCT
ejpam-521	382	15	m	m	VERB
ejpam-521	382	16	n	n	PROPN
ejpam-521	382	17	−mα1πi	−mα1πi	PROPN
ejpam-521	382	18	,	,	PUNCT
ejpam-521	382	19	m	m	PROPN
ejpam-521	382	20	�	�	PROPN
ejpam-521	382	21	�	�	PROPN
ejpam-521	382	22	�	�	PROPN
ejpam-521	382	23	�	�	PROPN
ejpam-521	382	24	,	,	PUNCT
ejpam-521	382	25	(	(	PUNCT
ejpam-521	382	26	56	56	NUM
ejpam-521	382	27	)	)	PUNCT
ejpam-521	382	28	then	then	ADV
ejpam-521	382	29	for	for	ADP
ejpam-521	382	30	any	any	DET
ejpam-521	382	31	ǫ	ǫ	NOUN
ejpam-521	382	32	>	>	X
ejpam-521	382	33	0	0	NUM
ejpam-521	382	34	,	,	PUNCT
ejpam-521	382	35	p	p	PROPN
ejpam-521	382	36	�	�	PROPN
ejpam-521	382	37	max	max	PROPN
ejpam-521	382	38	m∈[1,nγ2	m∈[1,nγ2	PROPN
ejpam-521	382	39	]	]	X
ejpam-521	382	40	im	im	PROPN
ejpam-521	382	41	,	,	PUNCT
ejpam-521	382	42	n	n	PROPN
ejpam-521	382	43	>	>	X
ejpam-521	382	44	ǫ	ǫ	DET
ejpam-521	382	45	�	�	PROPN
ejpam-521	382	46	≤	≤	NOUN
ejpam-521	382	47	∑	∑	PUNCT
ejpam-521	382	48	m∈[1,nγ2	m∈[1,nγ2	PROPN
ejpam-521	382	49	]	]	PUNCT
ejpam-521	382	50	p(im	p(im	PROPN
ejpam-521	382	51	,	,	PUNCT
ejpam-521	382	52	n	n	CCONJ
ejpam-521	382	53	>	>	X
ejpam-521	382	54	ǫ	ǫ	X
ejpam-521	382	55	)	)	PUNCT
ejpam-521	382	56	≤	≤	NOUN
ejpam-521	382	57	∑	∑	PUNCT
ejpam-521	382	58	m∈[1,nγ2	m∈[1,nγ2	PROPN
ejpam-521	382	59	]	]	PUNCT
ejpam-521	382	60	m	m	VERB
ejpam-521	382	61	∑	∑	PROPN
ejpam-521	382	62	i=1	i=1	PROPN
ejpam-521	382	63	p	p	PROPN
ejpam-521	382	64	�	�	PROPN
ejpam-521	382	65	�	�	PROPN
ejpam-521	382	66	�	�	PROPN
ejpam-521	382	67	�	�	PROPN
ejpam-521	382	68	�	�	PROPN
ejpam-521	382	69	mα1	mα1	PROPN
ejpam-521	382	70	ni	ni	PROPN
ejpam-521	382	71	,	,	PUNCT
ejpam-521	382	72	m	m	VERB
ejpam-521	382	73	n	n	PROPN
ejpam-521	382	74	−mα1πi	−mα1πi	PROPN
ejpam-521	382	75	,	,	PUNCT
ejpam-521	382	76	m	m	PROPN
ejpam-521	382	77	�	�	PROPN
ejpam-521	382	78	�	�	PROPN
ejpam-521	382	79	�	�	PROPN
ejpam-521	382	80	�	�	PROPN
ejpam-521	382	81	�	�	PROPN
ejpam-521	382	82	≤	≤	PROPN
ejpam-521	382	83	∑	∑	PUNCT
ejpam-521	382	84	m∈[1,nγ2	m∈[1,nγ2	PROPN
ejpam-521	382	85	]	]	PUNCT
ejpam-521	382	86	m	m	VERB
ejpam-521	382	87	∑	∑	PUNCT
ejpam-521	382	88	i=1	i=1	PROPN
ejpam-521	382	89	ǫ−2w	ǫ−2w	NOUN
ejpam-521	382	90	e	e	PROPN
ejpam-521	382	91	�	�	PROPN
ejpam-521	382	92	�	�	PROPN
ejpam-521	382	93	�	�	PROPN
ejpam-521	382	94	�	�	PROPN
ejpam-521	382	95	mα1	mα1	PROPN
ejpam-521	382	96	ni	ni	PROPN
ejpam-521	382	97	,	,	PUNCT
ejpam-521	382	98	m	m	VERB
ejpam-521	382	99	n	n	PROPN
ejpam-521	382	100	−mα1πi	−mα1πi	PROPN
ejpam-521	382	101	,	,	PUNCT
ejpam-521	382	102	m	m	PROPN
ejpam-521	382	103	�	�	PROPN
ejpam-521	382	104	�	�	PROPN
ejpam-521	382	105	�	�	PROPN
ejpam-521	382	106	�	�	PROPN
ejpam-521	382	107	2w	2w	PROPN
ejpam-521	382	108	=	=	PUNCT
ejpam-521	382	109	∑	∑	PUNCT
ejpam-521	382	110	m∈[1,nγ2	m∈[1,nγ2	PROPN
ejpam-521	382	111	]	]	PUNCT
ejpam-521	382	112	m	m	VERB
ejpam-521	382	113	∑	∑	PROPN
ejpam-521	382	114	i=1	i=1	PROPN
ejpam-521	382	115	ǫ−2wm2wα1	ǫ−2wm2wα1	PROPN
ejpam-521	382	116	n−2w	n−2w	PROPN
ejpam-521	382	117	e(ni	e(ni	PROPN
ejpam-521	382	118	,	,	PUNCT
ejpam-521	382	119	m−	m−	PROPN
ejpam-521	382	120	nπi	nπi	PROPN
ejpam-521	382	121	,	,	PUNCT
ejpam-521	382	122	m	m	PROPN
ejpam-521	382	123	)	)	PUNCT
ejpam-521	382	124	2w	2w	NUM
ejpam-521	382	125	,	,	PUNCT
ejpam-521	382	126	(	(	PUNCT
ejpam-521	382	127	57	57	NUM
ejpam-521	382	128	)	)	PUNCT
ejpam-521	382	129	where	where	SCONJ
ejpam-521	382	130	the	the	DET
ejpam-521	382	131	last	last	ADJ
ejpam-521	382	132	inequality	inequality	NOUN
ejpam-521	382	133	is	be	AUX
ejpam-521	382	134	obtained	obtain	VERB
ejpam-521	382	135	by	by	ADP
ejpam-521	382	136	applying	apply	VERB
ejpam-521	382	137	chebyshev	chebyshev	NOUN
ejpam-521	382	138	’s	’s	PART
ejpam-521	382	139	inequality	inequality	NOUN
ejpam-521	382	140	.	.	PUNCT
ejpam-521	383	1	from	from	ADP
ejpam-521	383	2	lemma	lemma	PROPN
ejpam-521	383	3	2	2	NUM
ejpam-521	383	4	and	and	CCONJ
ejpam-521	383	5	the	the	DET
ejpam-521	383	6	property	property	NOUN
ejpam-521	383	7	that	that	PRON
ejpam-521	383	8	c1	c1	PROPN
ejpam-521	383	9	b1m−α1	b1m−α1	VERB
ejpam-521	383	10	≤	≤	NUM
ejpam-521	383	11	πi	πi	PROPN
ejpam-521	383	12	,	,	PUNCT
ejpam-521	383	13	m	m	VERB
ejpam-521	383	14	≤	≤	ADJ
ejpam-521	383	15	c2	c2	PROPN
ejpam-521	383	16	b2m−α2	b2m−α2	PROPN
ejpam-521	383	17	,	,	PUNCT
ejpam-521	383	18	p	p	PROPN
ejpam-521	383	19	�	�	PROPN
ejpam-521	383	20	max	max	PROPN
ejpam-521	383	21	m∈[1,nγ2	m∈[1,nγ2	PROPN
ejpam-521	383	22	]	]	X
ejpam-521	383	23	im	im	PROPN
ejpam-521	383	24	,	,	PUNCT
ejpam-521	383	25	n	n	PROPN
ejpam-521	383	26	>	>	X
ejpam-521	383	27	ǫ	ǫ	DET
ejpam-521	383	28	�	�	PROPN
ejpam-521	383	29	≤	≤	X
ejpam-521	383	30	∑	∑	PUNCT
ejpam-521	383	31	m∈[1,nγ2	m∈[1,nγ2	PROPN
ejpam-521	383	32	]	]	PUNCT
ejpam-521	383	33	m	m	VERB
ejpam-521	383	34	∑	∑	PROPN
ejpam-521	383	35	i=1	i=1	PROPN
ejpam-521	383	36	ǫ−2wm2wα1	ǫ−2wm2wα1	PROPN
ejpam-521	383	37	n−2wawn	n−2wawn	NOUN
ejpam-521	383	38	1	1	NUM
ejpam-521	383	39	2	2	NUM
ejpam-521	383	40	+	+	ADJ
ejpam-521	383	41	w(c2	w(c2	ADJ
ejpam-521	383	42	b2m−α2)w	b2m−α2)w	PROPN
ejpam-521	383	43	g.	g.	PROPN
ejpam-521	383	44	qian	qian	PROPN
ejpam-521	383	45	/	/	SYM
ejpam-521	383	46	eur	eur	PROPN
ejpam-521	383	47	.	.	PUNCT
ejpam-521	384	1	j.	j.	PROPN
ejpam-521	384	2	pure	pure	PROPN
ejpam-521	384	3	appl	appl	PROPN
ejpam-521	384	4	.	.	PROPN
ejpam-521	384	5	math	math	PROPN
ejpam-521	384	6	,	,	PUNCT
ejpam-521	384	7	3	3	NUM
ejpam-521	384	8	(	(	PUNCT
ejpam-521	384	9	2010	2010	NUM
ejpam-521	384	10	)	)	PUNCT
ejpam-521	384	11	,	,	PUNCT
ejpam-521	384	12	51	51	NUM
ejpam-521	384	13	-	-	SYM
ejpam-521	384	14	80	80	NUM
ejpam-521	384	15	67	67	NUM
ejpam-521	384	16	≤	≤	NUM
ejpam-521	384	17	awn2γ2	awn2γ2	NOUN
ejpam-521	384	18	+	+	CCONJ
ejpam-521	384	19	1	1	NUM
ejpam-521	384	20	2	2	NUM
ejpam-521	384	21	+	+	NOUN
ejpam-521	384	22	(	(	PUNCT
ejpam-521	384	23	2α1γ2−α2γ2−1)w	2α1γ2−α2γ2−1)w	NUM
ejpam-521	384	24	.	.	PUNCT
ejpam-521	385	1	(	(	PUNCT
ejpam-521	385	2	58	58	NUM
ejpam-521	385	3	)	)	PUNCT
ejpam-521	385	4	from	from	ADP
ejpam-521	385	5	now	now	ADV
ejpam-521	385	6	on	on	ADP
ejpam-521	385	7	the	the	DET
ejpam-521	385	8	same	same	ADJ
ejpam-521	385	9	notation	notation	NOUN
ejpam-521	385	10	will	will	AUX
ejpam-521	385	11	be	be	AUX
ejpam-521	385	12	used	use	VERB
ejpam-521	385	13	for	for	ADP
ejpam-521	385	14	possibly	possibly	ADV
ejpam-521	385	15	different	different	ADJ
ejpam-521	385	16	constants	constant	NOUN
ejpam-521	385	17	.	.	PUNCT
ejpam-521	386	1	by	by	ADP
ejpam-521	386	2	the	the	DET
ejpam-521	386	3	condition	condition	NOUN
ejpam-521	386	4	that	that	PRON
ejpam-521	386	5	α2	α2	PROPN
ejpam-521	386	6	>	>	X
ejpam-521	386	7	2α1	2α1	NUM
ejpam-521	386	8	−	−	NOUN
ejpam-521	386	9	γ−1	γ−1	PROPN
ejpam-521	386	10	2	2	NUM
ejpam-521	386	11	,	,	PUNCT
ejpam-521	386	12	the	the	DET
ejpam-521	386	13	sum	sum	NOUN
ejpam-521	386	14	of	of	ADP
ejpam-521	386	15	the	the	DET
ejpam-521	386	16	series	series	NOUN
ejpam-521	386	17	defined	define	VERB
ejpam-521	386	18	by	by	ADP
ejpam-521	386	19	the	the	DET
ejpam-521	386	20	terms	term	NOUN
ejpam-521	386	21	of	of	ADP
ejpam-521	386	22	form	form	NOUN
ejpam-521	386	23	(	(	PUNCT
ejpam-521	386	24	58	58	NUM
ejpam-521	386	25	)	)	PUNCT
ejpam-521	386	26	converges	converge	VERB
ejpam-521	386	27	as	as	ADP
ejpam-521	386	28	n→∞	n→∞	NUM
ejpam-521	386	29	,	,	PUNCT
ejpam-521	386	30	if	if	SCONJ
ejpam-521	386	31	w	w	PROPN
ejpam-521	386	32	>	>	X
ejpam-521	386	33	3	3	NUM
ejpam-521	386	34	+	+	NOUN
ejpam-521	386	35	4γ2	4γ2	NUM
ejpam-521	386	36	2	2	NUM
ejpam-521	386	37	+	+	NOUN
ejpam-521	386	38	2α2γ2−4α1γ2	2α2γ2−4α1γ2	NUM
ejpam-521	386	39	.	.	PUNCT
ejpam-521	387	1	hence	hence	ADV
ejpam-521	387	2	(	(	PUNCT
ejpam-521	387	3	55	55	NUM
ejpam-521	387	4	)	)	PUNCT
ejpam-521	387	5	follows	follow	VERB
ejpam-521	387	6	from	from	ADP
ejpam-521	387	7	applying	apply	VERB
ejpam-521	387	8	the	the	DET
ejpam-521	387	9	borel	borel	NOUN
ejpam-521	387	10	-	-	PUNCT
ejpam-521	387	11	cantelli	cantelli	PROPN
ejpam-521	387	12	lemma	lemma	PROPN
ejpam-521	387	13	.	.	PUNCT
ejpam-521	388	1	⊳	⊳	PROPN
ejpam-521	388	2	lemma	lemma	PROPN
ejpam-521	388	3	5	5	NUM
ejpam-521	388	4	.	.	PUNCT
ejpam-521	389	1	under	under	ADP
ejpam-521	389	2	the	the	DET
ejpam-521	389	3	conditions	condition	NOUN
ejpam-521	389	4	that	that	SCONJ
ejpam-521	389	5	r̃i	r̃i	NOUN
ejpam-521	389	6	,	,	PUNCT
ejpam-521	389	7	m	m	VERB
ejpam-521	389	8	≤	≤	ADJ
ejpam-521	389	9	b2m−α2	b2m−α2	NOUN
ejpam-521	389	10	and	and	CCONJ
ejpam-521	389	11	f	f	PROPN
ejpam-521	389	12	≤	≤	PROPN
ejpam-521	389	13	c2	c2	PROPN
ejpam-521	389	14	,	,	PUNCT
ejpam-521	389	15	we	we	PRON
ejpam-521	389	16	have	have	VERB
ejpam-521	389	17	m	m	PROPN
ejpam-521	389	18	∑	∑	PROPN
ejpam-521	389	19	i=1	i=1	PROPN
ejpam-521	389	20	(	(	PUNCT
ejpam-521	389	21	ni	ni	PROPN
ejpam-521	389	22	,	,	PUNCT
ejpam-521	389	23	m−	m−	PROPN
ejpam-521	389	24	nπi	nπi	PROPN
ejpam-521	389	25	,	,	PUNCT
ejpam-521	389	26	m	m	PROPN
ejpam-521	389	27	)	)	PUNCT
ejpam-521	389	28	2−	2−	NUM
ejpam-521	389	29	n=	n=	ADJ
ejpam-521	389	30	o(n	o(n	PROPN
ejpam-521	389	31	)	)	PUNCT
ejpam-521	390	1	a.s	a.s	PROPN
ejpam-521	390	2	.	.	PROPN
ejpam-521	390	3	(	(	PUNCT
ejpam-521	390	4	59	59	NUM
ejpam-521	390	5	)	)	PUNCT
ejpam-521	390	6	uniformly	uniformly	ADV
ejpam-521	390	7	in	in	ADP
ejpam-521	390	8	m	m	PROPN
ejpam-521	390	9	∈	∈	NOUN
ejpam-521	391	1	[	[	X
ejpam-521	391	2	nγ1	nγ1	NOUN
ejpam-521	391	3	,	,	PUNCT
ejpam-521	391	4	n	n	CCONJ
ejpam-521	391	5	]	]	PUNCT
ejpam-521	391	6	as	as	ADP
ejpam-521	391	7	n→∞.	n→∞.	PROPN
ejpam-521	391	8	proof	proof	NOUN
ejpam-521	391	9	.	.	PUNCT
ejpam-521	392	1	suppose	suppose	VERB
ejpam-521	392	2	{	{	PUNCT
ejpam-521	392	3	ni	ni	PROPN
ejpam-521	392	4	,	,	PUNCT
ejpam-521	392	5	m	m	VERB
ejpam-521	392	6	}	}	PUNCT
ejpam-521	392	7	are	be	AUX
ejpam-521	392	8	a	a	DET
ejpam-521	392	9	sequence	sequence	NOUN
ejpam-521	392	10	of	of	ADP
ejpam-521	392	11	independent	independent	ADJ
ejpam-521	392	12	poisson	poisson	NOUN
ejpam-521	392	13	random	random	ADJ
ejpam-521	392	14	variables	variable	NOUN
ejpam-521	392	15	with	with	ADP
ejpam-521	392	16	means	mean	NOUN
ejpam-521	392	17	{	{	PUNCT
ejpam-521	392	18	nπi	nπi	ADJ
ejpam-521	392	19	,	,	PUNCT
ejpam-521	392	20	m	m	NOUN
ejpam-521	392	21	}	}	PUNCT
ejpam-521	392	22	,	,	PUNCT
ejpam-521	392	23	and	and	CCONJ
ejpam-521	392	24	denote	denote	VERB
ejpam-521	392	25	t2	t2	PROPN
ejpam-521	392	26	=	=	SYM
ejpam-521	392	27	∑m	∑m	PROPN
ejpam-521	392	28	i=1(ni	i=1(ni	PROPN
ejpam-521	392	29	,	,	PUNCT
ejpam-521	392	30	m	m	VERB
ejpam-521	392	31	−	−	NOUN
ejpam-521	392	32	nπi	nπi	PROPN
ejpam-521	392	33	,	,	PUNCT
ejpam-521	392	34	m	m	NOUN
ejpam-521	392	35	)	)	PUNCT
ejpam-521	392	36	2	2	X
ejpam-521	392	37	.	.	X
ejpam-521	393	1	we	we	PRON
ejpam-521	393	2	first	first	ADV
ejpam-521	393	3	show	show	VERB
ejpam-521	393	4	that	that	SCONJ
ejpam-521	393	5	the	the	DET
ejpam-521	393	6	j	j	PROPN
ejpam-521	393	7	-	-	PUNCT
ejpam-521	393	8	th	th	VERB
ejpam-521	393	9	cumulants	cumulant	NOUN
ejpam-521	393	10	of	of	ADP
ejpam-521	393	11	t2	t2	PROPN
ejpam-521	393	12	satisfies	satisfy	VERB
ejpam-521	393	13	|κ	|κ	PRON
ejpam-521	393	14	j(t2)|	j(t2)|	PROPN
ejpam-521	393	15	≤	≤	PROPN
ejpam-521	393	16	α	α	PROPN
ejpam-521	393	17	jn	jn	PROPN
ejpam-521	393	18	jm−α2	jm−α2	PROPN
ejpam-521	393	19	(	(	PUNCT
ejpam-521	393	20	j−1	j−1	PROPN
ejpam-521	393	21	)	)	PUNCT
ejpam-521	393	22	(	(	PUNCT
ejpam-521	393	23	60	60	NUM
ejpam-521	393	24	)	)	PUNCT
ejpam-521	393	25	where	where	SCONJ
ejpam-521	393	26	a	a	DET
ejpam-521	393	27	j	j	PROPN
ejpam-521	393	28	is	be	AUX
ejpam-521	393	29	a	a	DET
ejpam-521	393	30	constant	constant	ADJ
ejpam-521	393	31	depending	depend	VERB
ejpam-521	393	32	on	on	ADP
ejpam-521	393	33	j.	j.	PROPN
ejpam-521	393	34	because	because	SCONJ
ejpam-521	393	35	{	{	PUNCT
ejpam-521	393	36	ni	ni	PROPN
ejpam-521	393	37	,	,	PUNCT
ejpam-521	393	38	m	m	VERB
ejpam-521	393	39	}	}	PUNCT
ejpam-521	393	40	are	be	AUX
ejpam-521	393	41	independent	independent	ADJ
ejpam-521	393	42	,	,	PUNCT
ejpam-521	393	43	it	it	PRON
ejpam-521	393	44	follows	follow	VERB
ejpam-521	393	45	that	that	SCONJ
ejpam-521	393	46	κ	κ	PROPN
ejpam-521	393	47	j(t2	j(t2	NOUN
ejpam-521	393	48	)	)	PUNCT
ejpam-521	394	1	=	=	PUNCT
ejpam-521	395	1	m	m	VERB
ejpam-521	395	2	∑	∑	PUNCT
ejpam-521	395	3	i=1	i=1	PROPN
ejpam-521	395	4	κ	κ	PROPN
ejpam-521	395	5	j((ni	j((ni	PROPN
ejpam-521	395	6	,	,	PUNCT
ejpam-521	395	7	m−	m−	PROPN
ejpam-521	395	8	nπi	nπi	PROPN
ejpam-521	395	9	,	,	PUNCT
ejpam-521	395	10	m	m	NOUN
ejpam-521	395	11	)	)	PUNCT
ejpam-521	395	12	2	2	NUM
ejpam-521	395	13	)	)	PUNCT
ejpam-521	395	14	.	.	PUNCT
ejpam-521	396	1	(	(	PUNCT
ejpam-521	396	2	61	61	NUM
ejpam-521	396	3	)	)	PUNCT
ejpam-521	396	4	by	by	ADP
ejpam-521	396	5	applying	apply	VERB
ejpam-521	396	6	theorem	theorem	NOUN
ejpam-521	396	7	6	6	NUM
ejpam-521	396	8	of	of	ADP
ejpam-521	396	9	section	section	NOUN
ejpam-521	396	10	2.12	2.12	NUM
ejpam-521	396	11	of	of	ADP
ejpam-521	396	12	shiryayev	shiryayev	PROPN
ejpam-521	396	13	’s	’s	PART
ejpam-521	396	14	[	[	X
ejpam-521	396	15	17	17	NUM
ejpam-521	396	16	]	]	PUNCT
ejpam-521	396	17	again	again	ADV
ejpam-521	396	18	,	,	PUNCT
ejpam-521	396	19	the	the	DET
ejpam-521	396	20	j	j	PROPN
ejpam-521	396	21	-	-	PUNCT
ejpam-521	396	22	th	th	VERB
ejpam-521	396	23	cumulants	cumulant	NOUN
ejpam-521	396	24	of	of	ADP
ejpam-521	396	25	(	(	PUNCT
ejpam-521	396	26	ni	ni	PROPN
ejpam-521	396	27	,	,	PUNCT
ejpam-521	396	28	m−	m−	PROPN
ejpam-521	396	29	nπi	nπi	PROPN
ejpam-521	396	30	,	,	PUNCT
ejpam-521	396	31	m	m	PROPN
ejpam-521	396	32	)	)	PUNCT
ejpam-521	396	33	2	2	NUM
ejpam-521	396	34	can	can	AUX
ejpam-521	396	35	be	be	AUX
ejpam-521	396	36	written	write	VERB
ejpam-521	396	37	as	as	ADP
ejpam-521	396	38	a	a	DET
ejpam-521	396	39	sum	sum	NOUN
ejpam-521	396	40	of	of	ADP
ejpam-521	396	41	its	its	PRON
ejpam-521	396	42	moments	moment	NOUN
ejpam-521	396	43	:	:	PUNCT
ejpam-521	396	44	κ	κ	X
ejpam-521	396	45	j((ni	j((ni	PROPN
ejpam-521	396	46	,	,	PUNCT
ejpam-521	396	47	m−	m−	PROPN
ejpam-521	396	48	nπi	nπi	PROPN
ejpam-521	396	49	,	,	PUNCT
ejpam-521	396	50	m	m	PROPN
ejpam-521	396	51	)	)	PUNCT
ejpam-521	396	52	2	2	NUM
ejpam-521	396	53	)	)	PUNCT
ejpam-521	396	54	=	=	PUNCT
ejpam-521	397	1	∑	∑	PUNCT
ejpam-521	397	2	j1+···+	j1+···+	PROPN
ejpam-521	397	3	jl=	jl=	PROPN
ejpam-521	397	4	j	j	PROPN
ejpam-521	397	5	ζ	ζ	PROPN
ejpam-521	397	6	(	(	PUNCT
ejpam-521	397	7	j1	j1	PROPN
ejpam-521	397	8	,	,	PUNCT
ejpam-521	397	9	·	·	PUNCT
ejpam-521	397	10	·	·	PUNCT
ejpam-521	397	11	·	·	PUNCT
ejpam-521	397	12	,	,	PUNCT
ejpam-521	397	13	jl	jl	PROPN
ejpam-521	397	14	)	)	PUNCT
ejpam-521	397	15	l	l	NOUN
ejpam-521	397	16	∏	∏	PROPN
ejpam-521	397	17	k=1	k=1	X
ejpam-521	397	18	e((ni	e((ni	PROPN
ejpam-521	397	19	,	,	PUNCT
ejpam-521	397	20	m−	m−	PROPN
ejpam-521	397	21	nπi	nπi	PROPN
ejpam-521	397	22	,	,	PUNCT
ejpam-521	397	23	m	m	PROPN
ejpam-521	397	24	)	)	PUNCT
ejpam-521	397	25	2	2	NUM
ejpam-521	397	26	jk	jk	NOUN
ejpam-521	397	27	)	)	PUNCT
ejpam-521	397	28	(	(	PUNCT
ejpam-521	397	29	62	62	NUM
ejpam-521	397	30	)	)	PUNCT
ejpam-521	397	31	where	where	SCONJ
ejpam-521	397	32	ζ	ζ	NOUN
ejpam-521	397	33	(	(	PUNCT
ejpam-521	397	34	j1	j1	PROPN
ejpam-521	397	35	,	,	PUNCT
ejpam-521	397	36	·	·	PUNCT
ejpam-521	397	37	·	·	PUNCT
ejpam-521	397	38	·	·	PUNCT
ejpam-521	397	39	,	,	PUNCT
ejpam-521	397	40	jl	jl	NOUN
ejpam-521	397	41	)	)	PUNCT
ejpam-521	397	42	=	=	PUNCT
ejpam-521	398	1	(	(	PUNCT
ejpam-521	398	2	−1)l−1	−1)l−1	ADP
ejpam-521	398	3	l	l	X
ejpam-521	398	4	j	j	PROPN
ejpam-521	398	5	!	!	PUNCT
ejpam-521	398	6	j1	j1	PROPN
ejpam-521	398	7	!	!	PUNCT
ejpam-521	398	8	·	·	PUNCT
ejpam-521	398	9	·	·	PUNCT
ejpam-521	398	10	·	·	PUNCT
ejpam-521	398	11	jl	jl	NOUN
ejpam-521	398	12	!	!	PUNCT
ejpam-521	399	1	and	and	CCONJ
ejpam-521	399	2	jk	jk	PROPN
ejpam-521	399	3	≥	≥	NUM
ejpam-521	399	4	1	1	NUM
ejpam-521	399	5	,	,	PUNCT
ejpam-521	399	6	l	l	NOUN
ejpam-521	399	7	≤	≤	X
ejpam-521	399	8	j.	j.	PROPN
ejpam-521	399	9	from	from	ADP
ejpam-521	399	10	lemma	lemma	PROPN
ejpam-521	399	11	2	2	NUM
ejpam-521	399	12	we	we	PRON
ejpam-521	399	13	know	know	VERB
ejpam-521	399	14	that	that	SCONJ
ejpam-521	399	15	e((ni	e((ni	PROPN
ejpam-521	399	16	,	,	PUNCT
ejpam-521	399	17	m−	m−	PROPN
ejpam-521	399	18	nπi	nπi	PROPN
ejpam-521	399	19	,	,	PUNCT
ejpam-521	399	20	m	m	PROPN
ejpam-521	399	21	)	)	PUNCT
ejpam-521	399	22	2	2	NUM
ejpam-521	399	23	jk	jk	PROPN
ejpam-521	399	24	)	)	PUNCT
ejpam-521	399	25	is	be	AUX
ejpam-521	399	26	an	an	DET
ejpam-521	399	27	orderjk	orderjk	NOUN
ejpam-521	399	28	polynomial	polynomial	ADJ
ejpam-521	399	29	of	of	ADP
ejpam-521	399	30	nπi	nπi	ADJ
ejpam-521	399	31	,	,	PUNCT
ejpam-521	399	32	m	m	PRON
ejpam-521	399	33	,	,	PUNCT
ejpam-521	399	34	therefore	therefore	ADV
ejpam-521	399	35	|κ	|κ	ADJ
ejpam-521	399	36	j(t2)|	j(t2)|	PROPN
ejpam-521	399	37	≤	≤	PROPN
ejpam-521	399	38	m	m	VERB
ejpam-521	399	39	∑	∑	PROPN
ejpam-521	399	40	i=1	i=1	PROPN
ejpam-521	399	41	α	α	PROPN
ejpam-521	399	42	j(nπi	j(nπi	PROPN
ejpam-521	399	43	,	,	PUNCT
ejpam-521	399	44	m	m	PROPN
ejpam-521	399	45	)	)	PUNCT
ejpam-521	400	1	j	j	PROPN
ejpam-521	400	2	≤	≤	PROPN
ejpam-521	400	3	α	α	NUM
ejpam-521	400	4	jn	jn	PROPN
ejpam-521	400	5	jm−α2	jm−α2	PROPN
ejpam-521	400	6	(	(	PUNCT
ejpam-521	400	7	j−1	j−1	PROPN
ejpam-521	400	8	)	)	PUNCT
ejpam-521	400	9	(	(	PUNCT
ejpam-521	400	10	63	63	NUM
ejpam-521	400	11	)	)	PUNCT
ejpam-521	400	12	for	for	ADP
ejpam-521	400	13	some	some	DET
ejpam-521	400	14	constant	constant	ADJ
ejpam-521	400	15	a	a	DET
ejpam-521	400	16	j	j	NOUN
ejpam-521	400	17	,	,	PUNCT
ejpam-521	400	18	hence	hence	ADV
ejpam-521	400	19	(	(	PUNCT
ejpam-521	400	20	60	60	NUM
ejpam-521	400	21	)	)	PUNCT
ejpam-521	400	22	holds	hold	VERB
ejpam-521	400	23	.	.	PUNCT
ejpam-521	401	1	by	by	ADP
ejpam-521	401	2	(	(	PUNCT
ejpam-521	401	3	47	47	NUM
ejpam-521	401	4	)	)	PUNCT
ejpam-521	401	5	and	and	CCONJ
ejpam-521	401	6	the	the	DET
ejpam-521	401	7	identities	identity	NOUN
ejpam-521	401	8	κ1(t2	κ1(t2	ADJ
ejpam-521	401	9	−	−	PROPN
ejpam-521	401	10	n	n	CCONJ
ejpam-521	401	11	)	)	PUNCT
ejpam-521	401	12	=	=	NOUN
ejpam-521	401	13	e(t2	e(t2	NOUN
ejpam-521	401	14	−	−	PROPN
ejpam-521	401	15	n	n	CCONJ
ejpam-521	401	16	)	)	PUNCT
ejpam-521	401	17	=	=	SYM
ejpam-521	401	18	0	0	NUM
ejpam-521	401	19	and	and	CCONJ
ejpam-521	401	20	κ	κ	X
ejpam-521	401	21	j(t2	j(t2	NOUN
ejpam-521	401	22	−	−	PROPN
ejpam-521	401	23	n	n	CCONJ
ejpam-521	401	24	)	)	PUNCT
ejpam-521	401	25	=	=	NOUN
ejpam-521	401	26	κ	κ	PRON
ejpam-521	401	27	j(t2	j(t2	NOUN
ejpam-521	401	28	)	)	PUNCT
ejpam-521	401	29	for	for	ADP
ejpam-521	401	30	j	j	PROPN
ejpam-521	401	31	≥	≥	PROPN
ejpam-521	401	32	2	2	NUM
ejpam-521	401	33	,	,	PUNCT
ejpam-521	401	34	it	it	PRON
ejpam-521	401	35	can	can	AUX
ejpam-521	401	36	be	be	AUX
ejpam-521	401	37	seen	see	VERB
ejpam-521	401	38	that	that	PRON
ejpam-521	401	39	e(t2	e(t2	NOUN
ejpam-521	401	40	−	−	PROPN
ejpam-521	401	41	n)2w	n)2w	PUNCT
ejpam-521	401	42	=	=	PUNCT
ejpam-521	401	43	∗	∗	PROPN
ejpam-521	401	44	∑	∑	PROPN
ejpam-521	401	45	ρ(l1	ρ(l1	PROPN
ejpam-521	401	46	,	,	PUNCT
ejpam-521	401	47	·	·	PUNCT
ejpam-521	401	48	·	·	PUNCT
ejpam-521	401	49	·	·	PUNCT
ejpam-521	401	50	,	,	PUNCT
ejpam-521	401	51	lk	lk	PROPN
ejpam-521	401	52	)	)	PUNCT
ejpam-521	401	53	k	k	NOUN
ejpam-521	401	54	∏	∏	PROPN
ejpam-521	401	55	j=1	j=1	NOUN
ejpam-521	401	56	κl	κl	PROPN
ejpam-521	401	57	j	j	PROPN
ejpam-521	401	58	(	(	PUNCT
ejpam-521	401	59	t2	t2	PROPN
ejpam-521	401	60	)	)	PUNCT
ejpam-521	401	61	(	(	PUNCT
ejpam-521	401	62	64	64	NUM
ejpam-521	401	63	)	)	PUNCT
ejpam-521	401	64	g.	g.	PROPN
ejpam-521	401	65	qian	qian	PROPN
ejpam-521	401	66	/	/	SYM
ejpam-521	401	67	eur	eur	PROPN
ejpam-521	401	68	.	.	PUNCT
ejpam-521	402	1	j.	j.	PROPN
ejpam-521	402	2	pure	pure	PROPN
ejpam-521	402	3	appl	appl	PROPN
ejpam-521	402	4	.	.	PROPN
ejpam-521	402	5	math	math	PROPN
ejpam-521	402	6	,	,	PUNCT
ejpam-521	402	7	3	3	NUM
ejpam-521	402	8	(	(	PUNCT
ejpam-521	402	9	2010	2010	NUM
ejpam-521	402	10	)	)	PUNCT
ejpam-521	402	11	,	,	PUNCT
ejpam-521	402	12	51	51	NUM
ejpam-521	402	13	-	-	SYM
ejpam-521	402	14	80	80	NUM
ejpam-521	402	15	68	68	NUM
ejpam-521	402	16	where	where	SCONJ
ejpam-521	402	17	the	the	DET
ejpam-521	402	18	summation	summation	NOUN
ejpam-521	402	19	∑∗	∑∗	PUNCT
ejpam-521	402	20	is	be	AUX
ejpam-521	402	21	taken	take	VERB
ejpam-521	402	22	over	over	ADP
ejpam-521	402	23	all	all	DET
ejpam-521	402	24	the	the	DET
ejpam-521	402	25	partitions	partition	NOUN
ejpam-521	402	26	of	of	ADP
ejpam-521	402	27	2w	2w	NUM
ejpam-521	403	1	such	such	ADJ
ejpam-521	403	2	that	that	SCONJ
ejpam-521	403	3	∑k	∑k	PROPN
ejpam-521	404	1	j=1	j=1	PROPN
ejpam-521	404	2	l	l	NOUN
ejpam-521	404	3	j	j	PROPN
ejpam-521	404	4	=	=	SYM
ejpam-521	404	5	2w	2w	NUM
ejpam-521	404	6	,	,	PUNCT
ejpam-521	404	7	l	l	PROPN
ejpam-521	404	8	j	j	PROPN
ejpam-521	404	9	≥	≥	NUM
ejpam-521	404	10	2	2	NUM
ejpam-521	404	11	and	and	CCONJ
ejpam-521	404	12	k	k	PROPN
ejpam-521	404	13	≤	≤	PROPN
ejpam-521	404	14	w.	w.	NOUN
ejpam-521	404	15	by	by	ADP
ejpam-521	404	16	(	(	PUNCT
ejpam-521	404	17	60	60	NUM
ejpam-521	404	18	)	)	PUNCT
ejpam-521	404	19	it	it	PRON
ejpam-521	404	20	follows	follow	VERB
ejpam-521	404	21	that	that	PRON
ejpam-521	404	22	e(t2	e(t2	NOUN
ejpam-521	404	23	−	−	PROPN
ejpam-521	404	24	n)2w	n)2w	ADV
ejpam-521	404	25	≤	≤	NOUN
ejpam-521	404	26	∗	∗	NOUN
ejpam-521	404	27	∑	∑	SYM
ejpam-521	404	28	awn2wm−α2(2w−k	awn2wm−α2(2w−k	PROPN
ejpam-521	404	29	)	)	PUNCT
ejpam-521	404	30	≤	≤	NUM
ejpam-521	404	31	awn2wm−α2w	awn2wm−α2w	PROPN
ejpam-521	404	32	(	(	PUNCT
ejpam-521	404	33	65	65	NUM
ejpam-521	404	34	)	)	PUNCT
ejpam-521	404	35	for	for	ADP
ejpam-521	404	36	some	some	DET
ejpam-521	404	37	constant	constant	ADJ
ejpam-521	404	38	aw	aw	INTJ
ejpam-521	404	39	depending	depend	VERB
ejpam-521	404	40	on	on	ADP
ejpam-521	404	41	w.	w.	PROPN
ejpam-521	404	42	now	now	ADV
ejpam-521	404	43	for	for	ADP
ejpam-521	404	44	any	any	DET
ejpam-521	404	45	ǫ	ǫ	NOUN
ejpam-521	404	46	>	>	X
ejpam-521	404	47	0	0	NUM
ejpam-521	404	48	,	,	PUNCT
ejpam-521	404	49	p	p	NOUN
ejpam-521	404	50	max	max	PROPN
ejpam-521	404	51	m∈[nγ1	m∈[nγ1	NOUN
ejpam-521	404	52	,	,	PUNCT
ejpam-521	404	53	n	n	CCONJ
ejpam-521	404	54	]	]	X
ejpam-521	404	55	�	�	PROPN
ejpam-521	404	56	�	�	PROPN
ejpam-521	404	57	�	�	PROPN
ejpam-521	404	58	�	�	PROPN
ejpam-521	404	59	�	�	PROPN
ejpam-521	404	60	m	m	PROPN
ejpam-521	404	61	∑	∑	PROPN
ejpam-521	404	62	i=1	i=1	PROPN
ejpam-521	404	63	(	(	PUNCT
ejpam-521	404	64	ni	ni	PROPN
ejpam-521	404	65	,	,	PUNCT
ejpam-521	404	66	m−	m−	PROPN
ejpam-521	404	67	nπi	nπi	PROPN
ejpam-521	404	68	,	,	PUNCT
ejpam-521	404	69	m	m	PROPN
ejpam-521	404	70	)	)	PUNCT
ejpam-521	404	71	2	2	NUM
ejpam-521	404	72	−	−	PROPN
ejpam-521	404	73	n	n	CCONJ
ejpam-521	404	74	�	�	PROPN
ejpam-521	404	75	�	�	PROPN
ejpam-521	404	76	�	�	PROPN
ejpam-521	404	77	�	�	PROPN
ejpam-521	404	78	�	�	PROPN
ejpam-521	404	79	>	>	X
ejpam-521	404	80	ǫn	ǫn	PROPN
ejpam-521	404	81	!	!	PUNCT
ejpam-521	405	1	≤	≤	ADJ
ejpam-521	405	2	∑	∑	PUNCT
ejpam-521	405	3	m∈[nγ1	m∈[nγ1	NOUN
ejpam-521	405	4	,	,	PUNCT
ejpam-521	405	5	n	n	CCONJ
ejpam-521	405	6	]	]	X
ejpam-521	405	7	p	p	PROPN
ejpam-521	405	8	�	�	PROPN
ejpam-521	405	9	�	�	PROPN
ejpam-521	405	10	�	�	PROPN
ejpam-521	405	11	�	�	PROPN
ejpam-521	405	12	�	�	PROPN
ejpam-521	405	13	m	m	PROPN
ejpam-521	405	14	∑	∑	PROPN
ejpam-521	405	15	i=1	i=1	PROPN
ejpam-521	405	16	(	(	PUNCT
ejpam-521	405	17	ni	ni	PROPN
ejpam-521	405	18	,	,	PUNCT
ejpam-521	405	19	m−	m−	PROPN
ejpam-521	405	20	nπi	nπi	PROPN
ejpam-521	405	21	,	,	PUNCT
ejpam-521	405	22	m	m	PROPN
ejpam-521	405	23	)	)	PUNCT
ejpam-521	405	24	2	2	NUM
ejpam-521	405	25	−	−	PROPN
ejpam-521	405	26	n	n	CCONJ
ejpam-521	405	27	�	�	PROPN
ejpam-521	405	28	�	�	PROPN
ejpam-521	405	29	�	�	PROPN
ejpam-521	405	30	�	�	PROPN
ejpam-521	405	31	�	�	PROPN
ejpam-521	405	32	>	>	X
ejpam-521	405	33	ǫn	ǫn	PROPN
ejpam-521	405	34	!	!	PUNCT
ejpam-521	406	1	≤	≤	ADJ
ejpam-521	406	2	∑	∑	PUNCT
ejpam-521	406	3	m∈[nγ1	m∈[nγ1	NOUN
ejpam-521	406	4	,	,	PUNCT
ejpam-521	406	5	n	n	CCONJ
ejpam-521	406	6	]	]	X
ejpam-521	406	7	ǫ−2wn−2w	ǫ−2wn−2w	PROPN
ejpam-521	406	8	e	e	PROPN
ejpam-521	406	9	�	�	PROPN
ejpam-521	406	10	�	�	PROPN
ejpam-521	406	11	�	�	PROPN
ejpam-521	406	12	�	�	PROPN
ejpam-521	406	13	�	�	PROPN
ejpam-521	406	14	m	m	PROPN
ejpam-521	406	15	∑	∑	PROPN
ejpam-521	406	16	i=1	i=1	PROPN
ejpam-521	406	17	(	(	PUNCT
ejpam-521	406	18	ni	ni	PROPN
ejpam-521	406	19	,	,	PUNCT
ejpam-521	406	20	m−	m−	PROPN
ejpam-521	406	21	nπi	nπi	PROPN
ejpam-521	406	22	,	,	PUNCT
ejpam-521	406	23	m	m	PROPN
ejpam-521	406	24	)	)	PUNCT
ejpam-521	406	25	2	2	NUM
ejpam-521	406	26	−	−	PROPN
ejpam-521	406	27	n	n	CCONJ
ejpam-521	406	28	�	�	PROPN
ejpam-521	406	29	�	�	PROPN
ejpam-521	406	30	�	�	PROPN
ejpam-521	406	31	�	�	PROPN
ejpam-521	406	32	�	�	PROPN
ejpam-521	407	1	2w	2w	PROPN
ejpam-521	407	2	≤	≤	PROPN
ejpam-521	407	3	∑	∑	PUNCT
ejpam-521	407	4	m∈[nγ1	m∈[nγ1	NOUN
ejpam-521	407	5	,	,	PUNCT
ejpam-521	407	6	n	n	CCONJ
ejpam-521	407	7	]	]	X
ejpam-521	407	8	ǫ−2wn−2w+	ǫ−2wn−2w+	PUNCT
ejpam-521	407	9	1	1	NUM
ejpam-521	407	10	2	2	NUM
ejpam-521	407	11	e	e	NOUN
ejpam-521	407	12	�	�	PROPN
ejpam-521	407	13	�	�	PROPN
ejpam-521	407	14	�	�	PROPN
ejpam-521	407	15	�	�	PROPN
ejpam-521	407	16	�	�	PROPN
ejpam-521	407	17	m	m	PROPN
ejpam-521	407	18	∑	∑	PROPN
ejpam-521	407	19	i=1	i=1	PROPN
ejpam-521	407	20	(	(	PUNCT
ejpam-521	407	21	ni	ni	PROPN
ejpam-521	407	22	,	,	PUNCT
ejpam-521	407	23	m−	m−	PROPN
ejpam-521	407	24	nπi	nπi	PROPN
ejpam-521	407	25	,	,	PUNCT
ejpam-521	407	26	m	m	PROPN
ejpam-521	407	27	)	)	PUNCT
ejpam-521	407	28	2	2	NUM
ejpam-521	407	29	−	−	PROPN
ejpam-521	407	30	n	n	CCONJ
ejpam-521	407	31	�	�	PROPN
ejpam-521	407	32	�	�	PROPN
ejpam-521	407	33	�	�	PROPN
ejpam-521	407	34	�	�	PROPN
ejpam-521	407	35	�	�	PROPN
ejpam-521	407	36	2w	2w	PROPN
ejpam-521	407	37	(	(	PUNCT
ejpam-521	407	38	66	66	NUM
ejpam-521	407	39	)	)	PUNCT
ejpam-521	407	40	by	by	ADP
ejpam-521	407	41	applying	apply	VERB
ejpam-521	407	42	chebyshev	chebyshev	PROPN
ejpam-521	407	43	’s	’s	PART
ejpam-521	407	44	inequality	inequality	NOUN
ejpam-521	407	45	and	and	CCONJ
ejpam-521	407	46	the	the	DET
ejpam-521	407	47	technique	technique	NOUN
ejpam-521	407	48	of	of	ADP
ejpam-521	407	49	poissonization	poissonization	NOUN
ejpam-521	407	50	.	.	PUNCT
ejpam-521	408	1	from	from	ADP
ejpam-521	408	2	(	(	PUNCT
ejpam-521	408	3	65	65	NUM
ejpam-521	408	4	)	)	PUNCT
ejpam-521	408	5	it	it	PRON
ejpam-521	408	6	follows	follow	VERB
ejpam-521	408	7	that	that	SCONJ
ejpam-521	408	8	p	p	PROPN
ejpam-521	408	9	max	max	PROPN
ejpam-521	408	10	m∈[nγ1	m∈[nγ1	NOUN
ejpam-521	408	11	,	,	PUNCT
ejpam-521	408	12	n	n	CCONJ
ejpam-521	408	13	]	]	X
ejpam-521	408	14	�	�	PROPN
ejpam-521	408	15	�	�	PROPN
ejpam-521	408	16	�	�	PROPN
ejpam-521	408	17	�	�	PROPN
ejpam-521	408	18	�	�	PROPN
ejpam-521	408	19	m	m	PROPN
ejpam-521	408	20	∑	∑	PROPN
ejpam-521	408	21	i=1	i=1	PROPN
ejpam-521	408	22	(	(	PUNCT
ejpam-521	408	23	ni	ni	PROPN
ejpam-521	408	24	,	,	PUNCT
ejpam-521	408	25	m−	m−	PROPN
ejpam-521	408	26	nπi	nπi	PROPN
ejpam-521	408	27	,	,	PUNCT
ejpam-521	408	28	m	m	PROPN
ejpam-521	408	29	)	)	PUNCT
ejpam-521	409	1	2	2	NUM
ejpam-521	409	2	−	−	PROPN
ejpam-521	409	3	n	n	CCONJ
ejpam-521	409	4	�	�	PROPN
ejpam-521	409	5	�	�	PROPN
ejpam-521	409	6	�	�	PROPN
ejpam-521	409	7	�	�	PROPN
ejpam-521	409	8	�	�	PROPN
ejpam-521	409	9	>	>	X
ejpam-521	409	10	ǫn	ǫn	PROPN
ejpam-521	409	11	!	!	PUNCT
ejpam-521	410	1	≤	≤	ADJ
ejpam-521	410	2	∑	∑	PUNCT
ejpam-521	410	3	m∈[nγ1	m∈[nγ1	NOUN
ejpam-521	410	4	,	,	PUNCT
ejpam-521	410	5	n	n	CCONJ
ejpam-521	410	6	]	]	X
ejpam-521	410	7	ǫ−2wn−2w+	ǫ−2wn−2w+	PUNCT
ejpam-521	410	8	1	1	NUM
ejpam-521	410	9	2	2	NUM
ejpam-521	410	10	awn2wm−α2w	awn2wm−α2w	PROPN
ejpam-521	410	11	≤	≤	NOUN
ejpam-521	410	12	awn	awn	VERB
ejpam-521	410	13	3	3	NUM
ejpam-521	410	14	2	2	NUM
ejpam-521	410	15	−α2γ1w	−α2γ1w	NOUN
ejpam-521	410	16	.	.	PUNCT
ejpam-521	411	1	(	(	PUNCT
ejpam-521	411	2	67	67	NUM
ejpam-521	411	3	)	)	PUNCT
ejpam-521	411	4	the	the	DET
ejpam-521	411	5	sum	sum	NOUN
ejpam-521	411	6	of	of	ADP
ejpam-521	411	7	the	the	DET
ejpam-521	411	8	series	series	NOUN
ejpam-521	411	9	defined	define	VERB
ejpam-521	411	10	by	by	ADP
ejpam-521	411	11	the	the	DET
ejpam-521	411	12	terms	term	NOUN
ejpam-521	411	13	of	of	ADP
ejpam-521	411	14	form	form	NOUN
ejpam-521	411	15	(	(	PUNCT
ejpam-521	411	16	67	67	NUM
ejpam-521	411	17	)	)	PUNCT
ejpam-521	411	18	converges	converge	NOUN
ejpam-521	411	19	as	as	ADP
ejpam-521	411	20	n	n	PROPN
ejpam-521	411	21	→	→	SYM
ejpam-521	411	22	∞	∞	PROPN
ejpam-521	411	23	if	if	SCONJ
ejpam-521	411	24	w	w	PROPN
ejpam-521	411	25	>	>	X
ejpam-521	411	26	5	5	NUM
ejpam-521	411	27	2α2γ1	2α2γ1	NUM
ejpam-521	411	28	,	,	PUNCT
ejpam-521	411	29	hence	hence	ADV
ejpam-521	411	30	(	(	PUNCT
ejpam-521	411	31	59	59	NUM
ejpam-521	411	32	)	)	PUNCT
ejpam-521	411	33	follows	follow	VERB
ejpam-521	411	34	by	by	ADP
ejpam-521	411	35	applying	apply	VERB
ejpam-521	411	36	the	the	DET
ejpam-521	411	37	borel	borel	NOUN
ejpam-521	411	38	-	-	PUNCT
ejpam-521	411	39	cantelli	cantelli	PROPN
ejpam-521	411	40	lemma	lemma	PROPN
ejpam-521	411	41	.	.	PUNCT
ejpam-521	412	1	⊳	⊳	NOUN
ejpam-521	412	2	corollary	corollary	ADJ
ejpam-521	412	3	1	1	NUM
ejpam-521	412	4	.	.	PUNCT
ejpam-521	413	1	under	under	ADP
ejpam-521	413	2	the	the	DET
ejpam-521	413	3	conditions	condition	NOUN
ejpam-521	413	4	that	that	PRON
ejpam-521	413	5	b1m−α1	b1m−α1	VERB
ejpam-521	413	6	≤	≤	PUNCT
ejpam-521	413	7	r̃i	r̃i	NOUN
ejpam-521	413	8	,	,	PUNCT
ejpam-521	413	9	m	m	VERB
ejpam-521	413	10	≤	≤	ADJ
ejpam-521	413	11	b2m−α2	b2m−α2	NOUN
ejpam-521	413	12	and	and	CCONJ
ejpam-521	413	13	0	0	NUM
ejpam-521	413	14	<	<	X
ejpam-521	413	15	c1	c1	PROPN
ejpam-521	413	16	≤	≤	PROPN
ejpam-521	413	17	f	f	PROPN
ejpam-521	413	18	≤	≤	PROPN
ejpam-521	413	19	c2	c2	PROPN
ejpam-521	413	20	,	,	PUNCT
ejpam-521	413	21	m	m	VERB
ejpam-521	413	22	∑	∑	ADJ
ejpam-521	413	23	i=1	i=1	PROPN
ejpam-521	413	24	(	(	PUNCT
ejpam-521	413	25	ni	ni	PROPN
ejpam-521	413	26	,	,	PUNCT
ejpam-521	413	27	m−	m−	PROPN
ejpam-521	413	28	nπi	nπi	PROPN
ejpam-521	413	29	,	,	PUNCT
ejpam-521	413	30	m	m	PROPN
ejpam-521	413	31	)	)	PUNCT
ejpam-521	413	32	2	2	NUM
ejpam-521	413	33	(	(	PUNCT
ejpam-521	413	34	nπi	nπi	ADJ
ejpam-521	413	35	,	,	PUNCT
ejpam-521	413	36	m	m	NOUN
ejpam-521	413	37	)	)	PUNCT
ejpam-521	413	38	2	2	NUM
ejpam-521	413	39	=	=	SYM
ejpam-521	413	40	o(n−1m2α1	o(n−1m2α1	NOUN
ejpam-521	413	41	)	)	PUNCT
ejpam-521	413	42	a.s	a.s	PROPN
ejpam-521	413	43	.	.	PROPN
ejpam-521	413	44	(	(	PUNCT
ejpam-521	413	45	68	68	NUM
ejpam-521	413	46	)	)	PUNCT
ejpam-521	413	47	uniformly	uniformly	ADV
ejpam-521	413	48	in	in	ADP
ejpam-521	413	49	m	m	PROPN
ejpam-521	413	50	∈	∈	NOUN
ejpam-521	414	1	[	[	X
ejpam-521	414	2	nγ1	nγ1	NOUN
ejpam-521	414	3	,	,	PUNCT
ejpam-521	414	4	n	n	CCONJ
ejpam-521	414	5	]	]	PUNCT
ejpam-521	414	6	as	as	ADP
ejpam-521	414	7	n→∞.	n→∞.	PROPN
ejpam-521	414	8	lemma	lemma	PROPN
ejpam-521	414	9	6	6	NUM
ejpam-521	414	10	.	.	PUNCT
ejpam-521	415	1	under	under	ADP
ejpam-521	415	2	the	the	DET
ejpam-521	415	3	conditions	condition	NOUN
ejpam-521	415	4	of	of	ADP
ejpam-521	415	5	lemma	lemma	PROPN
ejpam-521	415	6	4	4	NUM
ejpam-521	415	7	,	,	PUNCT
ejpam-521	415	8	the	the	DET
ejpam-521	415	9	following	follow	VERB
ejpam-521	415	10	statement	statement	NOUN
ejpam-521	415	11	is	be	AUX
ejpam-521	415	12	true	true	ADJ
ejpam-521	415	13	:	:	PUNCT
ejpam-521	415	14	∑	∑	PROPN
ejpam-521	415	15	ni	ni	PROPN
ejpam-521	415	16	,	,	PUNCT
ejpam-521	415	17	m>0	m>0	NOUN
ejpam-521	415	18	log	log	VERB
ejpam-521	415	19	ni	ni	PROPN
ejpam-521	415	20	,	,	PUNCT
ejpam-521	415	21	m	m	VERB
ejpam-521	415	22	nπi	nπi	ADJ
ejpam-521	415	23	,	,	PUNCT
ejpam-521	415	24	m	m	PROPN
ejpam-521	415	25	=	=	ADJ
ejpam-521	415	26	o(m	o(m	PROPN
ejpam-521	415	27	)	)	PUNCT
ejpam-521	415	28	a.s	a.s	PROPN
ejpam-521	415	29	.	.	PROPN
ejpam-521	416	1	(	(	PUNCT
ejpam-521	416	2	69	69	NUM
ejpam-521	416	3	)	)	PUNCT
ejpam-521	416	4	uniformly	uniformly	ADV
ejpam-521	416	5	in	in	ADP
ejpam-521	416	6	m	m	PROPN
ejpam-521	416	7	∈	∈	NOUN
ejpam-521	417	1	[	[	X
ejpam-521	417	2	nγ1	nγ1	NOUN
ejpam-521	417	3	,	,	PUNCT
ejpam-521	417	4	nγ2	nγ2	X
ejpam-521	417	5	]	]	PUNCT
ejpam-521	417	6	as	as	ADP
ejpam-521	417	7	n→∞.	n→∞.	PROPN
ejpam-521	417	8	g.	g.	PROPN
ejpam-521	417	9	qian	qian	PROPN
ejpam-521	417	10	/	/	SYM
ejpam-521	417	11	eur	eur	PROPN
ejpam-521	417	12	.	.	PUNCT
ejpam-521	418	1	j.	j.	PROPN
ejpam-521	418	2	pure	pure	PROPN
ejpam-521	418	3	appl	appl	PROPN
ejpam-521	418	4	.	.	PROPN
ejpam-521	418	5	math	math	PROPN
ejpam-521	418	6	,	,	PUNCT
ejpam-521	418	7	3	3	NUM
ejpam-521	418	8	(	(	PUNCT
ejpam-521	418	9	2010	2010	NUM
ejpam-521	418	10	)	)	PUNCT
ejpam-521	418	11	,	,	PUNCT
ejpam-521	418	12	51	51	NUM
ejpam-521	418	13	-	-	SYM
ejpam-521	418	14	80	80	NUM
ejpam-521	418	15	69	69	NUM
ejpam-521	418	16	proof	proof	NOUN
ejpam-521	418	17	.	.	PUNCT
ejpam-521	419	1	first	first	ADV
ejpam-521	419	2	note	note	VERB
ejpam-521	419	3	that	that	SCONJ
ejpam-521	419	4	∑	∑	PROPN
ejpam-521	419	5	ni	ni	PROPN
ejpam-521	419	6	,	,	PUNCT
ejpam-521	419	7	m>0	m>0	NOUN
ejpam-521	419	8	log	log	VERB
ejpam-521	419	9	ni	ni	PROPN
ejpam-521	419	10	,	,	PUNCT
ejpam-521	419	11	m	m	VERB
ejpam-521	419	12	nπi	nπi	ADJ
ejpam-521	419	13	,	,	PUNCT
ejpam-521	419	14	m	m	VERB
ejpam-521	419	15	=	=	SYM
ejpam-521	419	16	∑	∑	PUNCT
ejpam-521	419	17	ni	ni	PROPN
ejpam-521	419	18	,	,	PUNCT
ejpam-521	419	19	m>0	m>0	NOUN
ejpam-521	419	20	log	log	VERB
ejpam-521	419	21	�	�	PROPN
ejpam-521	419	22	1	1	NUM
ejpam-521	419	23	+	+	NUM
ejpam-521	419	24	ni	ni	PROPN
ejpam-521	419	25	,	,	PUNCT
ejpam-521	419	26	m−	m−	PROPN
ejpam-521	419	27	nπi	nπi	PROPN
ejpam-521	419	28	,	,	PUNCT
ejpam-521	419	29	m	m	VERB
ejpam-521	419	30	nπi	nπi	ADJ
ejpam-521	419	31	,	,	PUNCT
ejpam-521	419	32	m	m	VERB
ejpam-521	419	33	�	�	PROPN
ejpam-521	419	34	.	.	PUNCT
ejpam-521	420	1	(	(	PUNCT
ejpam-521	420	2	70	70	NUM
ejpam-521	420	3	)	)	PUNCT
ejpam-521	420	4	by	by	ADP
ejpam-521	420	5	taylor	taylor	PROPN
ejpam-521	420	6	expansion	expansion	NOUN
ejpam-521	420	7	,	,	PUNCT
ejpam-521	420	8	∑	∑	PROPN
ejpam-521	420	9	ni	ni	PROPN
ejpam-521	420	10	,	,	PUNCT
ejpam-521	420	11	m>0	m>0	NOUN
ejpam-521	420	12	log	log	VERB
ejpam-521	420	13	ni	ni	PROPN
ejpam-521	420	14	,	,	PUNCT
ejpam-521	420	15	m	m	VERB
ejpam-521	420	16	nπi	nπi	ADJ
ejpam-521	420	17	,	,	PUNCT
ejpam-521	420	18	m	m	VERB
ejpam-521	420	19	=	=	NOUN
ejpam-521	420	20	m	m	VERB
ejpam-521	420	21	∑	∑	PROPN
ejpam-521	420	22	i=1	i=1	PROPN
ejpam-521	420	23	ni	ni	PROPN
ejpam-521	420	24	,	,	PUNCT
ejpam-521	420	25	m−	m−	PROPN
ejpam-521	420	26	nπi	nπi	PROPN
ejpam-521	420	27	,	,	PUNCT
ejpam-521	420	28	m	m	VERB
ejpam-521	420	29	nπi	nπi	ADJ
ejpam-521	420	30	,	,	PUNCT
ejpam-521	420	31	m	m	VERB
ejpam-521	420	32	−	−	NOUN
ejpam-521	420	33	1	1	NUM
ejpam-521	420	34	2	2	NUM
ejpam-521	420	35	∑	∑	PUNCT
ejpam-521	420	36	ni	ni	PROPN
ejpam-521	420	37	,	,	PUNCT
ejpam-521	420	38	m>0	m>0	NOUN
ejpam-521	420	39	(	(	PUNCT
ejpam-521	420	40	1	1	NUM
ejpam-521	420	41	+	+	NUM
ejpam-521	420	42	ξi	ξi	NOUN
ejpam-521	420	43	,	,	PUNCT
ejpam-521	420	44	m	m	NOUN
ejpam-521	420	45	)	)	PUNCT
ejpam-521	420	46	−2	−2	PROPN
ejpam-521	420	47	(	(	PUNCT
ejpam-521	420	48	ni	ni	PROPN
ejpam-521	420	49	,	,	PUNCT
ejpam-521	420	50	m−	m−	PROPN
ejpam-521	420	51	nπi	nπi	PROPN
ejpam-521	420	52	,	,	PUNCT
ejpam-521	420	53	m	m	PROPN
ejpam-521	420	54	)	)	PUNCT
ejpam-521	420	55	2	2	NUM
ejpam-521	420	56	(	(	PUNCT
ejpam-521	420	57	nπi	nπi	ADJ
ejpam-521	420	58	,	,	PUNCT
ejpam-521	420	59	m	m	NOUN
ejpam-521	420	60	)	)	PUNCT
ejpam-521	420	61	2	2	NUM
ejpam-521	421	1	+	+	CCONJ
ejpam-521	421	2	d	d	X
ejpam-521	421	3	(	(	PUNCT
ejpam-521	421	4	71	71	NUM
ejpam-521	421	5	)	)	PUNCT
ejpam-521	421	6	where	where	SCONJ
ejpam-521	421	7	d	d	PROPN
ejpam-521	421	8	=	=	SYM
ejpam-521	421	9	−∑ni	−∑ni	PROPN
ejpam-521	421	10	,	,	PUNCT
ejpam-521	421	11	m=0	m=0	PROPN
ejpam-521	421	12	ni	ni	PROPN
ejpam-521	421	13	,	,	PUNCT
ejpam-521	421	14	m−nπi	m−nπi	NOUN
ejpam-521	421	15	,	,	PUNCT
ejpam-521	421	16	m	m	VERB
ejpam-521	421	17	nπi	nπi	ADJ
ejpam-521	421	18	,	,	PUNCT
ejpam-521	421	19	m	m	VERB
ejpam-521	421	20	<	<	X
ejpam-521	421	21	m	m	X
ejpam-521	421	22	and	and	CCONJ
ejpam-521	421	23	|ξi	|ξi	NUM
ejpam-521	421	24	,	,	PUNCT
ejpam-521	421	25	m|	m|	NOUN
ejpam-521	421	26	≤	≤	PROPN
ejpam-521	421	27	�	�	PROPN
ejpam-521	421	28	�	�	PROPN
ejpam-521	421	29	�	�	PROPN
ejpam-521	421	30	ni	ni	PROPN
ejpam-521	421	31	,	,	PUNCT
ejpam-521	421	32	m−nπi	m−nπi	NOUN
ejpam-521	421	33	,	,	PUNCT
ejpam-521	421	34	m	m	VERB
ejpam-521	421	35	nπi	nπi	ADJ
ejpam-521	421	36	,	,	PUNCT
ejpam-521	421	37	m	m	PROPN
ejpam-521	421	38	�	�	PROPN
ejpam-521	421	39	�	�	PROPN
ejpam-521	421	40	�	�	PROPN
ejpam-521	421	41	.	.	PUNCT
ejpam-521	422	1	thus	thus	ADV
ejpam-521	422	2	max	max	PROPN
ejpam-521	422	3	1≤i≤m	1≤i≤m	NUM
ejpam-521	422	4	|ξi	|ξi	NUM
ejpam-521	422	5	,	,	PUNCT
ejpam-521	422	6	m|	m|	NOUN
ejpam-521	422	7	≤	≤	PROPN
ejpam-521	422	8	max	max	PROPN
ejpam-521	422	9	1≤i≤m	1≤i≤m	NUM
ejpam-521	422	10	�	�	PROPN
ejpam-521	422	11	�	�	PROPN
ejpam-521	422	12	�	�	PROPN
ejpam-521	422	13	�	�	PROPN
ejpam-521	422	14	ni	ni	PROPN
ejpam-521	422	15	,	,	PUNCT
ejpam-521	422	16	m−	m−	PROPN
ejpam-521	422	17	nπi	nπi	PROPN
ejpam-521	422	18	,	,	PUNCT
ejpam-521	422	19	m	m	VERB
ejpam-521	422	20	nπi	nπi	ADJ
ejpam-521	422	21	,	,	PUNCT
ejpam-521	422	22	m	m	PROPN
ejpam-521	422	23	�	�	PROPN
ejpam-521	422	24	�	�	PROPN
ejpam-521	422	25	�	�	PROPN
ejpam-521	422	26	�	�	PROPN
ejpam-521	422	27	≤	≤	PROPN
ejpam-521	422	28	(	(	PUNCT
ejpam-521	422	29	c1	c1	PROPN
ejpam-521	422	30	b1	b1	PROPN
ejpam-521	422	31	)	)	PUNCT
ejpam-521	423	1	−1	−1	NOUN
ejpam-521	424	1	max	max	PROPN
ejpam-521	424	2	1≤i≤m	1≤i≤m	NUM
ejpam-521	424	3	�	�	PROPN
ejpam-521	424	4	�	�	PROPN
ejpam-521	424	5	�	�	PROPN
ejpam-521	424	6	�	�	PROPN
ejpam-521	424	7	mα1	mα1	PROPN
ejpam-521	424	8	ni	ni	PROPN
ejpam-521	424	9	,	,	PUNCT
ejpam-521	424	10	m	m	VERB
ejpam-521	424	11	n	n	PROPN
ejpam-521	424	12	−mα1πi	−mα1πi	PROPN
ejpam-521	424	13	,	,	PUNCT
ejpam-521	424	14	m	m	PROPN
ejpam-521	424	15	�	�	PROPN
ejpam-521	424	16	�	�	PROPN
ejpam-521	424	17	�	�	PROPN
ejpam-521	424	18	�	�	PROPN
ejpam-521	424	19	,	,	PUNCT
ejpam-521	424	20	(	(	PUNCT
ejpam-521	424	21	72	72	NUM
ejpam-521	424	22	)	)	PUNCT
ejpam-521	424	23	and	and	CCONJ
ejpam-521	424	24	by	by	ADP
ejpam-521	424	25	lemma	lemma	PROPN
ejpam-521	424	26	4	4	NUM
ejpam-521	424	27	max	max	PROPN
ejpam-521	424	28	1≤i≤m	1≤i≤m	NUM
ejpam-521	424	29	|ξi	|ξi	PROPN
ejpam-521	424	30	,	,	PUNCT
ejpam-521	424	31	m|=	m|=	NOUN
ejpam-521	424	32	o(1	o(1	NOUN
ejpam-521	424	33	)	)	PUNCT
ejpam-521	424	34	a.s	a.s	PROPN
ejpam-521	424	35	.	.	PROPN
ejpam-521	424	36	(	(	PUNCT
ejpam-521	424	37	73	73	NUM
ejpam-521	424	38	)	)	PUNCT
ejpam-521	424	39	uniformly	uniformly	ADV
ejpam-521	424	40	in	in	ADP
ejpam-521	424	41	m	m	PROPN
ejpam-521	424	42	∈	∈	NOUN
ejpam-521	425	1	[	[	X
ejpam-521	425	2	1	1	NUM
ejpam-521	425	3	,	,	PUNCT
ejpam-521	425	4	nγ2	nγ2	NUM
ejpam-521	425	5	]	]	PUNCT
ejpam-521	425	6	as	as	ADP
ejpam-521	425	7	n→∞.	n→∞.	VERB
ejpam-521	425	8	by	by	ADP
ejpam-521	425	9	(	(	PUNCT
ejpam-521	425	10	73	73	NUM
ejpam-521	425	11	)	)	PUNCT
ejpam-521	425	12	and	and	CCONJ
ejpam-521	425	13	corollary	corollary	ADJ
ejpam-521	425	14	1	1	NUM
ejpam-521	425	15	it	it	PRON
ejpam-521	425	16	follows	follow	VERB
ejpam-521	425	17	that	that	SCONJ
ejpam-521	425	18	the	the	DET
ejpam-521	425	19	second	second	ADJ
ejpam-521	425	20	term	term	NOUN
ejpam-521	425	21	of	of	ADP
ejpam-521	425	22	the	the	DET
ejpam-521	425	23	right	right	ADJ
ejpam-521	425	24	hand	hand	NOUN
ejpam-521	425	25	side	side	NOUN
ejpam-521	425	26	of	of	ADP
ejpam-521	425	27	(	(	PUNCT
ejpam-521	425	28	71	71	NUM
ejpam-521	425	29	)	)	PUNCT
ejpam-521	425	30	is	be	AUX
ejpam-521	425	31	bounded	bound	VERB
ejpam-521	425	32	uniformly	uniformly	ADV
ejpam-521	425	33	in	in	ADP
ejpam-521	425	34	m	m	PROPN
ejpam-521	425	35	∈	∈	NOUN
ejpam-521	426	1	[	[	X
ejpam-521	426	2	nγ1	nγ1	NOUN
ejpam-521	426	3	,	,	PUNCT
ejpam-521	426	4	nγ2	nγ2	X
ejpam-521	426	5	]	]	PUNCT
ejpam-521	426	6	by	by	ADP
ejpam-521	426	7	o(n−1m2α1	o(n−1m2α1	ADJ
ejpam-521	426	8	)	)	PUNCT
ejpam-521	426	9	a.s	a.s	PROPN
ejpam-521	426	10	..	..	PUNCT
ejpam-521	426	11	the	the	DET
ejpam-521	426	12	latter	latter	ADJ
ejpam-521	426	13	is	be	AUX
ejpam-521	426	14	o(m	o(m	PROPN
ejpam-521	426	15	)	)	PUNCT
ejpam-521	426	16	because	because	SCONJ
ejpam-521	426	17	n	n	CCONJ
ejpam-521	426	18	>	>	X
ejpam-521	426	19	m	m	PROPN
ejpam-521	426	20	1	1	NUM
ejpam-521	426	21	γ2	γ2	ADJ
ejpam-521	426	22	and	and	CCONJ
ejpam-521	426	23	α1	α1	PROPN
ejpam-521	426	24	<	<	X
ejpam-521	426	25	1	1	NUM
ejpam-521	426	26	2	2	NUM
ejpam-521	426	27	+	+	NUM
ejpam-521	426	28	1	1	NUM
ejpam-521	426	29	2γ2	2γ2	NUM
ejpam-521	426	30	.	.	PUNCT
ejpam-521	427	1	therefore	therefore	ADV
ejpam-521	427	2	by	by	ADP
ejpam-521	427	3	lemma	lemma	PROPN
ejpam-521	427	4	3	3	NUM
ejpam-521	427	5	∑	∑	PROPN
ejpam-521	427	6	ni	ni	PROPN
ejpam-521	427	7	,	,	PUNCT
ejpam-521	427	8	m>0	m>0	NOUN
ejpam-521	427	9	log	log	VERB
ejpam-521	427	10	ni	ni	PROPN
ejpam-521	427	11	,	,	PUNCT
ejpam-521	427	12	m	m	VERB
ejpam-521	427	13	nπi	nπi	ADJ
ejpam-521	427	14	,	,	PUNCT
ejpam-521	427	15	m	m	PROPN
ejpam-521	427	16	=	=	ADJ
ejpam-521	427	17	o(m	o(m	PROPN
ejpam-521	427	18	)	)	PUNCT
ejpam-521	427	19	a.s	a.s	PROPN
ejpam-521	427	20	.	.	PROPN
ejpam-521	428	1	(	(	PUNCT
ejpam-521	428	2	74	74	NUM
ejpam-521	428	3	)	)	PUNCT
ejpam-521	428	4	uniformly	uniformly	ADV
ejpam-521	428	5	in	in	ADP
ejpam-521	428	6	m	m	PROPN
ejpam-521	428	7	∈	∈	NOUN
ejpam-521	429	1	[	[	X
ejpam-521	429	2	nγ1	nγ1	NOUN
ejpam-521	429	3	,	,	PUNCT
ejpam-521	429	4	nγ2	nγ2	X
ejpam-521	429	5	]	]	PUNCT
ejpam-521	429	6	as	as	ADP
ejpam-521	429	7	n→∞.	n→∞.	NOUN
ejpam-521	429	8	⊳	⊳	NOUN
ejpam-521	429	9	proof	proof	NOUN
ejpam-521	429	10	.	.	PUNCT
ejpam-521	430	1	[	[	X
ejpam-521	430	2	proof	proof	NOUN
ejpam-521	430	3	of	of	ADP
ejpam-521	430	4	theorem	theorem	NOUN
ejpam-521	430	5	1	1	NUM
ejpam-521	430	6	]	]	PUNCT
ejpam-521	430	7	by	by	ADP
ejpam-521	430	8	condition	condition	NOUN
ejpam-521	430	9	(	(	PUNCT
ejpam-521	430	10	i	i	NOUN
ejpam-521	430	11	)	)	PUNCT
ejpam-521	430	12	and	and	CCONJ
ejpam-521	430	13	(	(	PUNCT
ejpam-521	430	14	iii	iii	X
ejpam-521	430	15	)	)	PUNCT
ejpam-521	430	16	we	we	PRON
ejpam-521	430	17	can	can	AUX
ejpam-521	430	18	obtain	obtain	VERB
ejpam-521	430	19	an	an	DET
ejpam-521	430	20	interval	interval	NOUN
ejpam-521	430	21	estimate	estimate	NOUN
ejpam-521	430	22	,	,	PUNCT
ejpam-521	430	23	respectively	respectively	ADV
ejpam-521	430	24	,	,	PUNCT
ejpam-521	430	25	for	for	SCONJ
ejpam-521	430	26	−∑m	−∑m	PROPN
ejpam-521	430	27	i=1	i=1	PROPN
ejpam-521	430	28	r̃i	r̃i	PROPN
ejpam-521	430	29	,	,	PUNCT
ejpam-521	430	30	m	m	PROPN
ejpam-521	430	31	and	and	CCONJ
ejpam-521	430	32	∑m	∑m	PROPN
ejpam-521	430	33	i=1	i=1	PROPN
ejpam-521	430	34	log	log	VERB
ejpam-521	430	35	nπi	nπi	PROPN
ejpam-521	430	36	,	,	PUNCT
ejpam-521	430	37	m	m	VERB
ejpam-521	430	38	as	as	SCONJ
ejpam-521	430	39	follows	follow	VERB
ejpam-521	430	40	m	m	VERB
ejpam-521	430	41	log	log	NOUN
ejpam-521	430	42	m+o(m	m+o(m	NOUN
ejpam-521	430	43	)	)	PUNCT
ejpam-521	430	44	≤	≤	NOUN
ejpam-521	430	45	−	−	NOUN
ejpam-521	430	46	m	m	NOUN
ejpam-521	430	47	∑	∑	PUNCT
ejpam-521	430	48	i=1	i=1	PROPN
ejpam-521	430	49	log	log	NOUN
ejpam-521	430	50	r̃i	r̃i	NOUN
ejpam-521	430	51	,	,	PUNCT
ejpam-521	430	52	m	m	NOUN
ejpam-521	430	53	≤	≤	ADJ
ejpam-521	430	54	α1	α1	PROPN
ejpam-521	430	55	m	m	VERB
ejpam-521	430	56	log	log	NOUN
ejpam-521	430	57	m+o(m	m+o(m	NOUN
ejpam-521	430	58	)	)	PUNCT
ejpam-521	430	59	(	(	PUNCT
ejpam-521	430	60	75	75	NUM
ejpam-521	430	61	)	)	PUNCT
ejpam-521	430	62	m	m	VERB
ejpam-521	430	63	log	log	PROPN
ejpam-521	430	64	n−α1	n−α1	NOUN
ejpam-521	430	65	m	m	VERB
ejpam-521	430	66	log	log	NOUN
ejpam-521	430	67	m+o(m	m+o(m	NOUN
ejpam-521	430	68	)	)	PUNCT
ejpam-521	430	69	≤	≤	NUM
ejpam-521	430	70	m	m	VERB
ejpam-521	430	71	∑	∑	PROPN
ejpam-521	430	72	i=1	i=1	PROPN
ejpam-521	430	73	log	log	PROPN
ejpam-521	430	74	nπi	nπi	PROPN
ejpam-521	430	75	,	,	PUNCT
ejpam-521	430	76	m	m	VERB
ejpam-521	430	77	≤	≤	NOUN
ejpam-521	430	78	m	m	VERB
ejpam-521	430	79	log	log	NOUN
ejpam-521	430	80	n−m	n−m	AUX
ejpam-521	430	81	log	log	VERB
ejpam-521	430	82	m+o(m	m+o(m	NOUN
ejpam-521	430	83	)	)	PUNCT
ejpam-521	430	84	.	.	PUNCT
ejpam-521	431	1	(	(	PUNCT
ejpam-521	431	2	76	76	NUM
ejpam-521	431	3	)	)	PUNCT
ejpam-521	431	4	hence	hence	ADV
ejpam-521	431	5	there	there	PRON
ejpam-521	431	6	exists	exist	VERB
ejpam-521	431	7	an	an	DET
ejpam-521	431	8	α′	α′	NUM
ejpam-521	431	9	satisfying	satisfy	VERB
ejpam-521	431	10	−1	−1	NOUN
ejpam-521	431	11	2	2	NUM
ejpam-521	431	12	α1	α1	PROPN
ejpam-521	431	13	≤	≤	NOUN
ejpam-521	431	14	α′	α′	NUM
ejpam-521	431	15	≤	≤	NUM
ejpam-521	431	16	−3	−3	PROPN
ejpam-521	431	17	2	2	NUM
ejpam-521	431	18	+	+	NOUN
ejpam-521	431	19	α1	α1	NOUN
ejpam-521	431	20	such	such	ADJ
ejpam-521	431	21	that	that	SCONJ
ejpam-521	431	22	−	−	PROPN
ejpam-521	431	23	m	m	VERB
ejpam-521	431	24	∑	∑	PUNCT
ejpam-521	431	25	i=1	i=1	PROPN
ejpam-521	431	26	log	log	NOUN
ejpam-521	431	27	r̃i	r̃i	NOUN
ejpam-521	431	28	,	,	PUNCT
ejpam-521	431	29	m+	m+	NOUN
ejpam-521	431	30	1	1	NUM
ejpam-521	431	31	2	2	NUM
ejpam-521	431	32	m	m	NOUN
ejpam-521	431	33	∑	∑	PROPN
ejpam-521	431	34	i=1	i=1	PROPN
ejpam-521	431	35	log	log	PROPN
ejpam-521	431	36	nπi	nπi	PROPN
ejpam-521	431	37	,	,	PUNCT
ejpam-521	431	38	m−m	m−m	PROPN
ejpam-521	431	39	log	log	VERB
ejpam-521	431	40	m	m	VERB
ejpam-521	431	41	=	=	PUNCT
ejpam-521	431	42	α′m	α′m	NOUN
ejpam-521	431	43	log	log	VERB
ejpam-521	431	44	m+	m+	NUM
ejpam-521	431	45	1	1	NUM
ejpam-521	431	46	2	2	NUM
ejpam-521	431	47	m	m	NOUN
ejpam-521	431	48	log	log	NOUN
ejpam-521	431	49	n+o(m	n+o(m	NOUN
ejpam-521	431	50	)	)	PUNCT
ejpam-521	431	51	.	.	PUNCT
ejpam-521	432	1	(	(	PUNCT
ejpam-521	432	2	77	77	NUM
ejpam-521	432	3	)	)	PUNCT
ejpam-521	432	4	now	now	ADV
ejpam-521	432	5	we	we	PRON
ejpam-521	432	6	turn	turn	VERB
ejpam-521	432	7	to	to	ADP
ejpam-521	432	8	the	the	DET
ejpam-521	432	9	second	second	ADJ
ejpam-521	432	10	term	term	NOUN
ejpam-521	432	11	of	of	ADP
ejpam-521	432	12	(	(	PUNCT
ejpam-521	432	13	44	44	NUM
ejpam-521	432	14	)	)	PUNCT
ejpam-521	432	15	.	.	PUNCT
ejpam-521	433	1	by	by	ADP
ejpam-521	433	2	taylor	taylor	PROPN
ejpam-521	433	3	expansion	expansion	PROPN
ejpam-521	433	4	∑	∑	PUNCT
ejpam-521	433	5	ni	ni	PROPN
ejpam-521	433	6	,	,	PUNCT
ejpam-521	433	7	m>0	m>0	NOUN
ejpam-521	433	8	log	log	VERB
ejpam-521	433	9	�	�	PROPN
ejpam-521	433	10	1	1	NUM
ejpam-521	433	11	+	+	SYM
ejpam-521	433	12	1	1	NUM
ejpam-521	433	13	ni	ni	PROPN
ejpam-521	433	14	,	,	PUNCT
ejpam-521	433	15	m	m	PROPN
ejpam-521	433	16	�	�	PROPN
ejpam-521	433	17	ni	ni	PROPN
ejpam-521	433	18	,	,	PUNCT
ejpam-521	433	19	m+1	m+1	NUM
ejpam-521	433	20	g.	g.	PROPN
ejpam-521	433	21	qian	qian	PROPN
ejpam-521	433	22	/	/	SYM
ejpam-521	433	23	eur	eur	PROPN
ejpam-521	433	24	.	.	PUNCT
ejpam-521	434	1	j.	j.	PROPN
ejpam-521	434	2	pure	pure	PROPN
ejpam-521	434	3	appl	appl	PROPN
ejpam-521	434	4	.	.	PROPN
ejpam-521	434	5	math	math	PROPN
ejpam-521	434	6	,	,	PUNCT
ejpam-521	434	7	3	3	NUM
ejpam-521	434	8	(	(	PUNCT
ejpam-521	434	9	2010	2010	NUM
ejpam-521	434	10	)	)	PUNCT
ejpam-521	434	11	,	,	PUNCT
ejpam-521	434	12	51	51	NUM
ejpam-521	434	13	-	-	SYM
ejpam-521	434	14	80	80	NUM
ejpam-521	434	15	70	70	NUM
ejpam-521	434	16	=	=	SYM
ejpam-521	434	17	∑	∑	PUNCT
ejpam-521	434	18	ni	ni	PROPN
ejpam-521	434	19	,	,	PUNCT
ejpam-521	434	20	m>0	m>0	PROPN
ejpam-521	434	21	(	(	PUNCT
ejpam-521	434	22	ni	ni	PROPN
ejpam-521	434	23	,	,	PUNCT
ejpam-521	434	24	m+	m+	NOUN
ejpam-521	434	25	1	1	NUM
ejpam-521	434	26	)	)	PUNCT
ejpam-521	434	27	1	1	NUM
ejpam-521	434	28	ni	ni	PROPN
ejpam-521	434	29	,	,	PUNCT
ejpam-521	434	30	m	m	VERB
ejpam-521	434	31	−	−	NUM
ejpam-521	434	32	1	1	NUM
ejpam-521	434	33	2	2	NUM
ejpam-521	434	34	(	(	PUNCT
ejpam-521	434	35	1+ηi	1+ηi	NUM
ejpam-521	434	36	,	,	PUNCT
ejpam-521	434	37	m	m	NOUN
ejpam-521	434	38	)	)	PUNCT
ejpam-521	434	39	−2	−2	PROPN
ejpam-521	434	40	1	1	NUM
ejpam-521	434	41	n2	n2	NOUN
ejpam-521	434	42	i	i	PROPN
ejpam-521	434	43	,	,	PUNCT
ejpam-521	434	44	m	m	PROPN
ejpam-521	434	45	!	!	PUNCT
ejpam-521	435	1	=	=	SYM
ejpam-521	435	2	o(m	o(m	PROPN
ejpam-521	435	3	)	)	PUNCT
ejpam-521	435	4	,	,	PUNCT
ejpam-521	435	5	(	(	PUNCT
ejpam-521	435	6	78	78	NUM
ejpam-521	435	7	)	)	PUNCT
ejpam-521	435	8	where	where	SCONJ
ejpam-521	435	9	0≤	0≤	ADJ
ejpam-521	435	10	ηi	ηi	PROPN
ejpam-521	435	11	,	,	PUNCT
ejpam-521	435	12	m	m	VERB
ejpam-521	435	13	≤	≤	NUM
ejpam-521	435	14	n−1	n−1	PROPN
ejpam-521	436	1	i	i	PROPN
ejpam-521	436	2	,	,	PUNCT
ejpam-521	436	3	m	m	PROPN
ejpam-521	436	4	.	.	PUNCT
ejpam-521	437	1	from	from	ADP
ejpam-521	437	2	lemma	lemma	PROPN
ejpam-521	437	3	6	6	NUM
ejpam-521	437	4	,	,	PUNCT
ejpam-521	437	5	(	(	PUNCT
ejpam-521	437	6	77	77	NUM
ejpam-521	437	7	)	)	PUNCT
ejpam-521	437	8	,	,	PUNCT
ejpam-521	437	9	(	(	PUNCT
ejpam-521	437	10	78	78	NUM
ejpam-521	437	11	)	)	PUNCT
ejpam-521	437	12	and	and	CCONJ
ejpam-521	437	13	(	(	PUNCT
ejpam-521	437	14	44	44	NUM
ejpam-521	437	15	)	)	PUNCT
ejpam-521	437	16	,	,	PUNCT
ejpam-521	437	17	it	it	PRON
ejpam-521	437	18	is	be	AUX
ejpam-521	437	19	easy	easy	ADJ
ejpam-521	437	20	to	to	PART
ejpam-521	437	21	see	see	VERB
ejpam-521	437	22	that	that	PRON
ejpam-521	437	23	−	−	PROPN
ejpam-521	437	24	log	log	VERB
ejpam-521	437	25	f̃	f̃	PROPN
ejpam-521	437	26	(	(	PUNCT
ejpam-521	437	27	x	x	SYM
ejpam-521	437	28	n	n	CCONJ
ejpam-521	437	29	;	;	PUNCT
ejpam-521	437	30	m	m	X
ejpam-521	437	31	)	)	PUNCT
ejpam-521	438	1	+	+	CCONJ
ejpam-521	438	2	l∗1(x	l∗1(x	PROPN
ejpam-521	438	3	n	n	CCONJ
ejpam-521	438	4	;	;	PUNCT
ejpam-521	438	5	m	m	X
ejpam-521	438	6	)	)	PUNCT
ejpam-521	438	7	=	=	SYM
ejpam-521	438	8	α′m	α′m	NOUN
ejpam-521	438	9	log	log	VERB
ejpam-521	438	10	m+	m+	NUM
ejpam-521	438	11	1	1	NUM
ejpam-521	438	12	2	2	NUM
ejpam-521	438	13	m	m	NOUN
ejpam-521	438	14	log	log	NOUN
ejpam-521	438	15	n+o(m	n+o(m	NOUN
ejpam-521	438	16	)	)	PUNCT
ejpam-521	438	17	a.s	a.s	PROPN
ejpam-521	438	18	.	.	PROPN
ejpam-521	438	19	(	(	PUNCT
ejpam-521	438	20	79	79	NUM
ejpam-521	438	21	)	)	PUNCT
ejpam-521	438	22	uniformly	uniformly	ADV
ejpam-521	438	23	in	in	ADP
ejpam-521	438	24	m	m	PROPN
ejpam-521	438	25	∈	∈	NOUN
ejpam-521	439	1	[	[	X
ejpam-521	439	2	nγ1	nγ1	NOUN
ejpam-521	439	3	,	,	PUNCT
ejpam-521	439	4	nγ2	nγ2	X
ejpam-521	439	5	]	]	PUNCT
ejpam-521	439	6	as	as	SCONJ
ejpam-521	439	7	n→∞.	n→∞.	PROPN
ejpam-521	439	8	⊳	⊳	PROPN
ejpam-521	439	9	to	to	PART
ejpam-521	439	10	prove	prove	VERB
ejpam-521	439	11	theorem	theorem	VERB
ejpam-521	439	12	2	2	NUM
ejpam-521	439	13	we	we	PRON
ejpam-521	439	14	need	need	VERB
ejpam-521	439	15	the	the	DET
ejpam-521	439	16	following	follow	VERB
ejpam-521	439	17	lemmas	lemmas	NOUN
ejpam-521	439	18	.	.	PUNCT
ejpam-521	440	1	lemma	lemma	PROPN
ejpam-521	440	2	7	7	NUM
ejpam-521	440	3	.	.	PUNCT
ejpam-521	441	1	under	under	ADP
ejpam-521	441	2	the	the	DET
ejpam-521	441	3	condition	condition	NOUN
ejpam-521	441	4	(	(	PUNCT
ejpam-521	441	5	iii	iii	NOUN
ejpam-521	441	6	)	)	PUNCT
ejpam-521	441	7	of	of	ADP
ejpam-521	441	8	theorem	theorem	NOUN
ejpam-521	441	9	1	1	NUM
ejpam-521	441	10	,	,	PUNCT
ejpam-521	441	11	l2(q̃	l2(q̃	PROPN
ejpam-521	441	12	m	m	PROPN
ejpam-521	441	13	,	,	PUNCT
ejpam-521	441	14	m	m	PROPN
ejpam-521	441	15	,	,	PUNCT
ejpam-521	441	16	δ	δ	PROPN
ejpam-521	441	17	)	)	PUNCT
ejpam-521	441	18	=	=	SYM
ejpam-521	441	19	o(m	o(m	PROPN
ejpam-521	441	20	)	)	PUNCT
ejpam-521	441	21	.	.	PUNCT
ejpam-521	442	1	(	(	PUNCT
ejpam-521	442	2	80	80	NUM
ejpam-521	442	3	)	)	PUNCT
ejpam-521	442	4	proof	proof	NOUN
ejpam-521	442	5	.	.	PUNCT
ejpam-521	443	1	from	from	ADP
ejpam-521	443	2	b1m−α1	b1m−α1	ADJ
ejpam-521	443	3	≤	≤	NUM
ejpam-521	443	4	r̃i	r̃i	NOUN
ejpam-521	443	5	,	,	PUNCT
ejpam-521	443	6	m	m	VERB
ejpam-521	443	7	≤	≤	ADJ
ejpam-521	443	8	b2m−α2	b2m−α2	NOUN
ejpam-521	443	9	it	it	PRON
ejpam-521	443	10	follows	follow	VERB
ejpam-521	443	11	that	that	SCONJ
ejpam-521	443	12	�	�	PROPN
ejpam-521	443	13	�	�	PROPN
ejpam-521	443	14	�	�	PROPN
ejpam-521	443	15	r̃i	r̃i	NOUN
ejpam-521	443	16	,	,	PUNCT
ejpam-521	443	17	m−	m−	PROPN
ejpam-521	443	18	r	r	PROPN
ejpam-521	443	19	m	m	PROPN
ejpam-521	443	20	�	�	PROPN
ejpam-521	443	21	�	�	PROPN
ejpam-521	443	22	�	�	PROPN
ejpam-521	443	23	≤max	≤max	PUNCT
ejpam-521	443	24	�	�	PROPN
ejpam-521	443	25	b2	b2	PROPN
ejpam-521	443	26	mα2	mα2	NOUN
ejpam-521	443	27	−	−	PROPN
ejpam-521	443	28	r	r	NOUN
ejpam-521	443	29	m	m	NOUN
ejpam-521	443	30	,	,	PUNCT
ejpam-521	443	31	r	r	NOUN
ejpam-521	443	32	m	m	NOUN
ejpam-521	443	33	−	−	PROPN
ejpam-521	443	34	b1	b1	PROPN
ejpam-521	443	35	mα1	mα1	PROPN
ejpam-521	443	36	�	�	PROPN
ejpam-521	443	37	≤	≤	PROPN
ejpam-521	443	38	b2	b2	NOUN
ejpam-521	444	1	+	+	CCONJ
ejpam-521	444	2	r	r	NOUN
ejpam-521	444	3	mα2	mα2	NOUN
ejpam-521	444	4	.	.	PUNCT
ejpam-521	445	1	(	(	PUNCT
ejpam-521	445	2	81	81	NUM
ejpam-521	445	3	)	)	PUNCT
ejpam-521	445	4	from	from	ADP
ejpam-521	445	5	this	this	PRON
ejpam-521	445	6	(	(	PUNCT
ejpam-521	445	7	80	80	NUM
ejpam-521	445	8	)	)	PUNCT
ejpam-521	445	9	follows	follow	VERB
ejpam-521	445	10	.	.	PUNCT
ejpam-521	446	1	⊳	⊳	NOUN
ejpam-521	446	2	let	let	VERB
ejpam-521	446	3	f	f	PROPN
ejpam-521	446	4	(	(	PUNCT
ejpam-521	446	5	x	x	X
ejpam-521	446	6	|q̃m	|q̃m	X
ejpam-521	446	7	)	)	PUNCT
ejpam-521	446	8	denote	denote	VERB
ejpam-521	446	9	a	a	DET
ejpam-521	446	10	density	density	NOUN
ejpam-521	446	11	in	in	ADP
ejpam-521	446	12	hm	hm	INTJ
ejpam-521	446	13	which	which	PRON
ejpam-521	446	14	assigns	assign	VERB
ejpam-521	446	15	the	the	DET
ejpam-521	446	16	same	same	ADJ
ejpam-521	446	17	probability	probability	NOUN
ejpam-521	446	18	as	as	ADP
ejpam-521	446	19	f	f	PROPN
ejpam-521	446	20	to	to	ADP
ejpam-521	446	21	each	each	DET
ejpam-521	446	22	subinterval	subinterval	NOUN
ejpam-521	446	23	q̃	q̃	PROPN
ejpam-521	446	24	i	i	PRON
ejpam-521	446	25	,	,	PUNCT
ejpam-521	446	26	m	m	PROPN
ejpam-521	446	27	,	,	PUNCT
ejpam-521	446	28	i.e.	i.e.	X
ejpam-521	446	29	for	for	ADP
ejpam-521	446	30	x	x	SYM
ejpam-521	446	31	∈	∈	PROPN
ejpam-521	446	32	[	[	X
ejpam-521	446	33	s	s	X
ejpam-521	446	34	,	,	PUNCT
ejpam-521	446	35	t	t	PROPN
ejpam-521	446	36	]	]	PUNCT
ejpam-521	446	37	let	let	VERB
ejpam-521	446	38	f	f	PROPN
ejpam-521	446	39	(	(	PUNCT
ejpam-521	446	40	x	x	NOUN
ejpam-521	446	41	|q̃m	|q̃m	X
ejpam-521	446	42	)	)	PUNCT
ejpam-521	446	43	=	=	PUNCT
ejpam-521	446	44	m	m	VERB
ejpam-521	446	45	∑	∑	PUNCT
ejpam-521	446	46	i=1	i=1	PROPN
ejpam-521	446	47	πi	πi	PROPN
ejpam-521	446	48	,	,	PUNCT
ejpam-521	446	49	m	m	VERB
ejpam-521	446	50	r̃i	r̃i	NOUN
ejpam-521	446	51	,	,	PUNCT
ejpam-521	446	52	m	m	VERB
ejpam-521	446	53	iq̃i	iq̃i	PROPN
ejpam-521	446	54	,	,	PUNCT
ejpam-521	446	55	m	m	VERB
ejpam-521	446	56	(	(	PUNCT
ejpam-521	446	57	x	x	NOUN
ejpam-521	446	58	)	)	PUNCT
ejpam-521	446	59	.	.	PUNCT
ejpam-521	447	1	(	(	PUNCT
ejpam-521	447	2	82	82	NUM
ejpam-521	447	3	)	)	PUNCT
ejpam-521	447	4	by	by	ADP
ejpam-521	447	5	lemma	lemma	PROPN
ejpam-521	447	6	7	7	NUM
ejpam-521	447	7	we	we	PRON
ejpam-521	447	8	have	have	VERB
ejpam-521	447	9	−l∗1(x	−l∗1(x	NOUN
ejpam-521	447	10	n	n	CCONJ
ejpam-521	447	11	;	;	PUNCT
ejpam-521	447	12	m	m	X
ejpam-521	447	13	)	)	PUNCT
ejpam-521	448	1	+	+	CCONJ
ejpam-521	448	2	l2(q̃	l2(q̃	PROPN
ejpam-521	448	3	m	m	PROPN
ejpam-521	448	4	,	,	PUNCT
ejpam-521	448	5	m	m	PROPN
ejpam-521	448	6	,	,	PUNCT
ejpam-521	448	7	δ	δ	PROPN
ejpam-521	448	8	)	)	PUNCT
ejpam-521	449	1	+	+	CCONJ
ejpam-521	449	2	log	log	VERB
ejpam-521	449	3	f	f	PROPN
ejpam-521	449	4	n(x	n(x	PROPN
ejpam-521	449	5	n	n	CCONJ
ejpam-521	449	6	)	)	PUNCT
ejpam-521	449	7	=	=	SYM
ejpam-521	449	8	−l∗1(x	−l∗1(x	NOUN
ejpam-521	449	9	n	n	CCONJ
ejpam-521	449	10	;	;	PUNCT
ejpam-521	449	11	m	m	X
ejpam-521	449	12	)	)	PUNCT
ejpam-521	450	1	+	+	CCONJ
ejpam-521	450	2	n	n	X
ejpam-521	450	3	∑	∑	ADP
ejpam-521	450	4	j=1	j=1	PROPN
ejpam-521	450	5	log	log	NOUN
ejpam-521	450	6	f	f	PROPN
ejpam-521	450	7	(	(	PUNCT
ejpam-521	450	8	x	x	SYM
ejpam-521	450	9	j|q̃m	j|q̃m	PROPN
ejpam-521	450	10	)	)	PUNCT
ejpam-521	451	1	+	+	CCONJ
ejpam-521	451	2	n	n	X
ejpam-521	451	3	∑	∑	ADP
ejpam-521	451	4	j=1	j=1	PROPN
ejpam-521	451	5	log	log	NOUN
ejpam-521	451	6	f	f	PROPN
ejpam-521	451	7	(	(	PUNCT
ejpam-521	451	8	x	x	PROPN
ejpam-521	451	9	j	j	NOUN
ejpam-521	451	10	)	)	PUNCT
ejpam-521	451	11	log	log	PROPN
ejpam-521	451	12	f	f	PROPN
ejpam-521	451	13	(	(	PUNCT
ejpam-521	451	14	x	x	SYM
ejpam-521	451	15	j|q̃m	j|q̃m	PROPN
ejpam-521	451	16	)	)	PUNCT
ejpam-521	452	1	+	+	CCONJ
ejpam-521	452	2	o(m	o(m	NOUN
ejpam-521	452	3	)	)	PUNCT
ejpam-521	452	4	.	.	PUNCT
ejpam-521	453	1	(	(	PUNCT
ejpam-521	453	2	83	83	NUM
ejpam-521	453	3	)	)	PUNCT
ejpam-521	453	4	lemma	lemma	PROPN
ejpam-521	453	5	8	8	NUM
ejpam-521	453	6	.	.	PUNCT
ejpam-521	454	1	under	under	ADP
ejpam-521	454	2	the	the	DET
ejpam-521	454	3	condition	condition	NOUN
ejpam-521	454	4	of	of	ADP
ejpam-521	454	5	theorem	theorem	NOUN
ejpam-521	454	6	1	1	NUM
ejpam-521	454	7	,	,	PUNCT
ejpam-521	454	8	there	there	PRON
ejpam-521	454	9	exist	exist	VERB
ejpam-521	454	10	two	two	NUM
ejpam-521	454	11	positive	positive	ADJ
ejpam-521	454	12	constants	constant	NOUN
ejpam-521	454	13	a	a	PRON
ejpam-521	454	14	and	and	CCONJ
ejpam-521	454	15	b	b	NOUN
ejpam-521	454	16	such	such	ADJ
ejpam-521	454	17	that	that	DET
ejpam-521	454	18	bmα2	bmα2	PROPN
ejpam-521	454	19	≤	≤	PROPN
ejpam-521	454	20	∑	∑	PUNCT
ejpam-521	454	21	ni	ni	PROPN
ejpam-521	454	22	,	,	PUNCT
ejpam-521	454	23	m>0	m>0	PROPN
ejpam-521	454	24	ni	ni	PROPN
ejpam-521	454	25	,	,	PUNCT
ejpam-521	454	26	m	m	VERB
ejpam-521	454	27	log	log	NOUN
ejpam-521	454	28	ni	ni	PROPN
ejpam-521	454	29	,	,	PUNCT
ejpam-521	454	30	m	m	VERB
ejpam-521	454	31	nπi	nπi	ADJ
ejpam-521	454	32	,	,	PUNCT
ejpam-521	454	33	m	m	VERB
ejpam-521	454	34	≤	≤	ADJ
ejpam-521	454	35	amα1	amα1	PROPN
ejpam-521	454	36	a.s	a.s	PROPN
ejpam-521	454	37	.	.	PROPN
ejpam-521	454	38	(	(	PUNCT
ejpam-521	454	39	84	84	NUM
ejpam-521	454	40	)	)	PUNCT
ejpam-521	454	41	uniformly	uniformly	ADV
ejpam-521	454	42	in	in	ADP
ejpam-521	454	43	m	m	PROPN
ejpam-521	454	44	∈	∈	NOUN
ejpam-521	455	1	[	[	X
ejpam-521	455	2	nγ1	nγ1	NOUN
ejpam-521	455	3	,	,	PUNCT
ejpam-521	455	4	nγ2	nγ2	X
ejpam-521	455	5	]	]	PUNCT
ejpam-521	455	6	as	as	ADP
ejpam-521	455	7	n→∞.	n→∞.	PROPN
ejpam-521	455	8	proof	proof	NOUN
ejpam-521	455	9	.	.	PUNCT
ejpam-521	456	1	by	by	ADP
ejpam-521	456	2	taylor	taylor	PROPN
ejpam-521	456	3	expansion	expansion	NOUN
ejpam-521	456	4	,	,	PUNCT
ejpam-521	456	5	∑	∑	PROPN
ejpam-521	456	6	ni	ni	PROPN
ejpam-521	456	7	,	,	PUNCT
ejpam-521	456	8	m>0	m>0	PROPN
ejpam-521	456	9	ni	ni	PROPN
ejpam-521	456	10	,	,	PUNCT
ejpam-521	456	11	m	m	VERB
ejpam-521	456	12	log	log	NOUN
ejpam-521	456	13	ni	ni	PROPN
ejpam-521	456	14	,	,	PUNCT
ejpam-521	456	15	m	m	VERB
ejpam-521	456	16	nπi	nπi	ADJ
ejpam-521	456	17	,	,	PUNCT
ejpam-521	456	18	m	m	VERB
ejpam-521	456	19	=	=	SYM
ejpam-521	456	20	∑	∑	PUNCT
ejpam-521	456	21	ni	ni	PROPN
ejpam-521	456	22	,	,	PUNCT
ejpam-521	456	23	m>0	m>0	PROPN
ejpam-521	456	24	ni	ni	PROPN
ejpam-521	456	25	,	,	PUNCT
ejpam-521	456	26	m	m	VERB
ejpam-521	456	27	log	log	NOUN
ejpam-521	456	28	�	�	PROPN
ejpam-521	456	29	1	1	NUM
ejpam-521	456	30	+	+	NUM
ejpam-521	456	31	ni	ni	PROPN
ejpam-521	456	32	,	,	PUNCT
ejpam-521	456	33	m−	m−	PROPN
ejpam-521	456	34	nπi	nπi	PROPN
ejpam-521	456	35	,	,	PUNCT
ejpam-521	456	36	m	m	VERB
ejpam-521	456	37	nπi	nπi	ADJ
ejpam-521	456	38	,	,	PUNCT
ejpam-521	456	39	m	m	VERB
ejpam-521	456	40	�	�	PROPN
ejpam-521	456	41	g.	g.	PROPN
ejpam-521	456	42	qian	qian	PROPN
ejpam-521	456	43	/	/	SYM
ejpam-521	456	44	eur	eur	PROPN
ejpam-521	456	45	.	.	PUNCT
ejpam-521	457	1	j.	j.	PROPN
ejpam-521	457	2	pure	pure	PROPN
ejpam-521	457	3	appl	appl	PROPN
ejpam-521	457	4	.	.	PROPN
ejpam-521	457	5	math	math	PROPN
ejpam-521	457	6	,	,	PUNCT
ejpam-521	457	7	3	3	NUM
ejpam-521	457	8	(	(	PUNCT
ejpam-521	457	9	2010	2010	NUM
ejpam-521	457	10	)	)	PUNCT
ejpam-521	457	11	,	,	PUNCT
ejpam-521	457	12	51	51	NUM
ejpam-521	457	13	-	-	SYM
ejpam-521	457	14	80	80	NUM
ejpam-521	457	15	71	71	NUM
ejpam-521	457	16	=	=	NOUN
ejpam-521	457	17	m	m	VERB
ejpam-521	457	18	∑	∑	PROPN
ejpam-521	457	19	i=1	i=1	PROPN
ejpam-521	457	20	ni	ni	PROPN
ejpam-521	457	21	,	,	PUNCT
ejpam-521	457	22	m	m	PROPN
ejpam-521	457	23			PROPN
ejpam-521	457	24			NUM
ejpam-521	457	25	ni	ni	PROPN
ejpam-521	457	26	,	,	PUNCT
ejpam-521	457	27	m−	m−	PROPN
ejpam-521	457	28	nπi	nπi	PROPN
ejpam-521	457	29	,	,	PUNCT
ejpam-521	457	30	m	m	VERB
ejpam-521	457	31	nπi	nπi	ADJ
ejpam-521	457	32	,	,	PUNCT
ejpam-521	457	33	m	m	VERB
ejpam-521	457	34	−	−	NUM
ejpam-521	457	35	1	1	NUM
ejpam-521	457	36	2	2	NUM
ejpam-521	457	37	(	(	PUNCT
ejpam-521	457	38	1	1	NUM
ejpam-521	457	39	+	+	NUM
ejpam-521	457	40	θi	θi	NUM
ejpam-521	457	41	,	,	PUNCT
ejpam-521	457	42	k	k	NOUN
ejpam-521	457	43	)	)	PUNCT
ejpam-521	457	44	−2	−2	PROPN
ejpam-521	457	45	�	�	PROPN
ejpam-521	457	46	ni	ni	PROPN
ejpam-521	457	47	,	,	PUNCT
ejpam-521	457	48	m−	m−	PROPN
ejpam-521	457	49	nπi	nπi	PROPN
ejpam-521	457	50	,	,	PUNCT
ejpam-521	457	51	m	m	VERB
ejpam-521	457	52	nπi	nπi	ADJ
ejpam-521	457	53	,	,	PUNCT
ejpam-521	457	54	m	m	VERB
ejpam-521	457	55	�	�	X
ejpam-521	457	56	2	2	NUM
ejpam-521	457	57			PROPN
ejpam-521	457	58			PROPN
ejpam-521	457	59	=	=	SYM
ejpam-521	457	60	m	m	PROPN
ejpam-521	457	61	∑	∑	PROPN
ejpam-521	457	62	i=1	i=1	PROPN
ejpam-521	457	63	(	(	PUNCT
ejpam-521	457	64	ni	ni	PROPN
ejpam-521	457	65	,	,	PUNCT
ejpam-521	457	66	m−	m−	PROPN
ejpam-521	457	67	nπi	nπi	PROPN
ejpam-521	457	68	,	,	PUNCT
ejpam-521	457	69	m	m	PROPN
ejpam-521	457	70	)	)	PUNCT
ejpam-521	457	71	2	2	NUM
ejpam-521	457	72	nπi	nπi	NOUN
ejpam-521	457	73	,	,	PUNCT
ejpam-521	457	74	m	m	VERB
ejpam-521	457	75	+	+	NOUN
ejpam-521	457	76	m	m	VERB
ejpam-521	457	77	∑	∑	ADJ
ejpam-521	457	78	i=1	i=1	PROPN
ejpam-521	457	79	(	(	PUNCT
ejpam-521	457	80	ni	ni	PROPN
ejpam-521	457	81	,	,	PUNCT
ejpam-521	457	82	m−	m−	PROPN
ejpam-521	457	83	nπi	nπi	PROPN
ejpam-521	457	84	,	,	PUNCT
ejpam-521	457	85	m	m	PROPN
ejpam-521	457	86	)	)	PUNCT
ejpam-521	457	87	−	−	PROPN
ejpam-521	458	1	m	m	VERB
ejpam-521	458	2	∑	∑	PUNCT
ejpam-521	458	3	i=1	i=1	PROPN
ejpam-521	458	4	1	1	NUM
ejpam-521	458	5	2	2	NUM
ejpam-521	458	6	(	(	PUNCT
ejpam-521	458	7	1	1	NUM
ejpam-521	458	8	+	+	NUM
ejpam-521	458	9	θi	θi	NUM
ejpam-521	458	10	,	,	PUNCT
ejpam-521	458	11	k	k	NOUN
ejpam-521	458	12	)	)	PUNCT
ejpam-521	458	13	−2	−2	PROPN
ejpam-521	458	14	�	�	PROPN
ejpam-521	458	15	(	(	PUNCT
ejpam-521	458	16	ni	ni	PROPN
ejpam-521	458	17	,	,	PUNCT
ejpam-521	458	18	m−	m−	PROPN
ejpam-521	458	19	nπi	nπi	PROPN
ejpam-521	458	20	,	,	PUNCT
ejpam-521	458	21	m	m	PROPN
ejpam-521	458	22	)	)	PUNCT
ejpam-521	458	23	3	3	NUM
ejpam-521	458	24	(	(	PUNCT
ejpam-521	458	25	nπi	nπi	PROPN
ejpam-521	458	26	,	,	PUNCT
ejpam-521	458	27	m	m	NOUN
ejpam-521	458	28	)	)	PUNCT
ejpam-521	458	29	2	2	NUM
ejpam-521	459	1	+	+	CCONJ
ejpam-521	459	2	(	(	PUNCT
ejpam-521	459	3	ni	ni	PROPN
ejpam-521	459	4	,	,	PUNCT
ejpam-521	459	5	m−	m−	PROPN
ejpam-521	459	6	nπi	nπi	PROPN
ejpam-521	459	7	,	,	PUNCT
ejpam-521	459	8	m	m	PROPN
ejpam-521	459	9	)	)	PUNCT
ejpam-521	459	10	2	2	NUM
ejpam-521	459	11	nπi	nπi	NOUN
ejpam-521	459	12	,	,	PUNCT
ejpam-521	459	13	m	m	PROPN
ejpam-521	459	14	�	�	PROPN
ejpam-521	459	15	(	(	PUNCT
ejpam-521	459	16	85	85	NUM
ejpam-521	459	17	)	)	PUNCT
ejpam-521	459	18	where	where	SCONJ
ejpam-521	459	19	|θi	|θi	NUM
ejpam-521	459	20	,	,	PUNCT
ejpam-521	459	21	k|	k|	NOUN
ejpam-521	459	22	≤	≤	NUM
ejpam-521	459	23	�	�	PROPN
ejpam-521	459	24	�	�	PROPN
ejpam-521	459	25	�	�	PROPN
ejpam-521	459	26	ni	ni	PROPN
ejpam-521	459	27	,	,	PUNCT
ejpam-521	459	28	m−nπi	m−nπi	NOUN
ejpam-521	459	29	,	,	PUNCT
ejpam-521	459	30	m	m	VERB
ejpam-521	459	31	nπi	nπi	ADJ
ejpam-521	459	32	,	,	PUNCT
ejpam-521	459	33	m	m	PROPN
ejpam-521	459	34	�	�	PROPN
ejpam-521	459	35	�	�	PROPN
ejpam-521	459	36	�	�	PROPN
ejpam-521	459	37	,	,	PUNCT
ejpam-521	459	38	so	so	SCONJ
ejpam-521	459	39	that	that	SCONJ
ejpam-521	459	40	max1≤i≤m	max1≤i≤m	ADJ
ejpam-521	459	41	|θi	|θi	NUM
ejpam-521	459	42	,	,	PUNCT
ejpam-521	459	43	k|	k|	NOUN
ejpam-521	459	44	=	=	SYM
ejpam-521	459	45	o(1	o(1	PROPN
ejpam-521	459	46	)	)	PUNCT
ejpam-521	459	47	a.s	a.s	PROPN
ejpam-521	459	48	.	.	PROPN
ejpam-521	459	49	uniformly	uniformly	PROPN
ejpam-521	459	50	in	in	ADP
ejpam-521	459	51	m	m	PROPN
ejpam-521	459	52	∈	∈	NOUN
ejpam-521	459	53	[	[	X
ejpam-521	459	54	nγ1	nγ1	NOUN
ejpam-521	459	55	,	,	PUNCT
ejpam-521	459	56	nγ2	nγ2	NUM
ejpam-521	459	57	]	]	PUNCT
ejpam-521	459	58	.	.	PUNCT
ejpam-521	460	1	the	the	DET
ejpam-521	460	2	argument	argument	NOUN
ejpam-521	460	3	is	be	AUX
ejpam-521	460	4	similar	similar	ADJ
ejpam-521	460	5	to	to	ADP
ejpam-521	460	6	the	the	DET
ejpam-521	460	7	one	one	NOUN
ejpam-521	460	8	used	use	VERB
ejpam-521	460	9	to	to	PART
ejpam-521	460	10	establish	establish	VERB
ejpam-521	460	11	(	(	PUNCT
ejpam-521	460	12	73	73	NUM
ejpam-521	460	13	)	)	PUNCT
ejpam-521	460	14	.	.	PUNCT
ejpam-521	461	1	by	by	ADP
ejpam-521	461	2	lemma	lemma	PROPN
ejpam-521	461	3	4	4	NUM
ejpam-521	461	4	,	,	PUNCT
ejpam-521	461	5	lemma	lemma	PROPN
ejpam-521	461	6	5	5	NUM
ejpam-521	461	7	,	,	PUNCT
ejpam-521	461	8	the	the	DET
ejpam-521	461	9	property	property	NOUN
ejpam-521	461	10	πi	πi	PROPN
ejpam-521	461	11	,	,	PUNCT
ejpam-521	461	12	m	m	VERB
ejpam-521	461	13	≥	≥	NOUN
ejpam-521	461	14	b1c1m−α1	b1c1m−α1	PROPN
ejpam-521	461	15	and	and	CCONJ
ejpam-521	461	16	the	the	DET
ejpam-521	461	17	following	follow	VERB
ejpam-521	461	18	inequality	inequality	NOUN
ejpam-521	461	19	obtained	obtain	VERB
ejpam-521	461	20	from	from	ADP
ejpam-521	461	21	(	(	PUNCT
ejpam-521	461	22	85	85	NUM
ejpam-521	461	23	)	)	PUNCT
ejpam-521	461	24	�	�	PROPN
ejpam-521	461	25	�	�	PROPN
ejpam-521	461	26	�	�	PROPN
ejpam-521	461	27	�	�	PROPN
ejpam-521	461	28	�	�	PROPN
ejpam-521	461	29	�	�	PROPN
ejpam-521	461	30	∑	∑	PROPN
ejpam-521	461	31	ni	ni	PROPN
ejpam-521	461	32	,	,	PUNCT
ejpam-521	461	33	m>0	m>0	PROPN
ejpam-521	461	34	ni	ni	PROPN
ejpam-521	461	35	,	,	PUNCT
ejpam-521	461	36	m	m	VERB
ejpam-521	461	37	log	log	NOUN
ejpam-521	461	38	ni	ni	PROPN
ejpam-521	461	39	,	,	PUNCT
ejpam-521	461	40	m	m	VERB
ejpam-521	461	41	nπi	nπi	ADJ
ejpam-521	461	42	,	,	PUNCT
ejpam-521	461	43	m	m	PROPN
ejpam-521	461	44	�	�	PROPN
ejpam-521	461	45	�	�	PROPN
ejpam-521	461	46	�	�	PROPN
ejpam-521	461	47	�	�	PROPN
ejpam-521	461	48	�	�	PROPN
ejpam-521	461	49	�	�	PROPN
ejpam-521	461	50	≤	≤	NUM
ejpam-521	461	51	m	m	VERB
ejpam-521	461	52	∑	∑	PROPN
ejpam-521	461	53	i=1	i=1	PROPN
ejpam-521	461	54	(	(	PUNCT
ejpam-521	461	55	ni	ni	PROPN
ejpam-521	461	56	,	,	PUNCT
ejpam-521	461	57	m−	m−	PROPN
ejpam-521	461	58	nπi	nπi	PROPN
ejpam-521	461	59	,	,	PUNCT
ejpam-521	461	60	m	m	PROPN
ejpam-521	461	61	)	)	PUNCT
ejpam-521	461	62	2	2	NUM
ejpam-521	461	63	nπi	nπi	NOUN
ejpam-521	461	64	,	,	PUNCT
ejpam-521	461	65	m	m	VERB
ejpam-521	461	66	�	�	PROPN
ejpam-521	461	67	1	1	NUM
ejpam-521	461	68	+	+	NUM
ejpam-521	461	69	1	1	NUM
ejpam-521	461	70	2	2	NUM
ejpam-521	461	71	(	(	PUNCT
ejpam-521	461	72	1	1	NUM
ejpam-521	461	73	+	+	NUM
ejpam-521	461	74	θi	θi	NUM
ejpam-521	461	75	,	,	PUNCT
ejpam-521	461	76	k	k	NOUN
ejpam-521	461	77	)	)	PUNCT
ejpam-521	461	78	−2	−2	PROPN
ejpam-521	461	79	�	�	PROPN
ejpam-521	461	80	1	1	NUM
ejpam-521	461	81	+	+	NUM
ejpam-521	461	82	max	max	PROPN
ejpam-521	461	83	1≤i≤m	1≤i≤m	NUM
ejpam-521	461	84	�	�	PROPN
ejpam-521	461	85	�	�	PROPN
ejpam-521	461	86	�	�	PROPN
ejpam-521	461	87	�	�	PROPN
ejpam-521	461	88	ni	ni	PROPN
ejpam-521	461	89	,	,	PUNCT
ejpam-521	461	90	m−	m−	PROPN
ejpam-521	461	91	nπi	nπi	PROPN
ejpam-521	461	92	,	,	PUNCT
ejpam-521	461	93	m	m	VERB
ejpam-521	461	94	nπi	nπi	ADJ
ejpam-521	461	95	,	,	PUNCT
ejpam-521	461	96	m	m	PROPN
ejpam-521	461	97	�	�	PROPN
ejpam-521	461	98	�	�	PROPN
ejpam-521	461	99	�	�	PROPN
ejpam-521	461	100	�	�	PROPN
ejpam-521	461	101	�	�	PROPN
ejpam-521	461	102	�	�	PROPN
ejpam-521	461	103	,	,	PUNCT
ejpam-521	461	104	(	(	PUNCT
ejpam-521	461	105	86	86	NUM
ejpam-521	461	106	)	)	PUNCT
ejpam-521	461	107	the	the	DET
ejpam-521	461	108	lemma	lemma	PROPN
ejpam-521	461	109	can	can	AUX
ejpam-521	461	110	easily	easily	ADV
ejpam-521	461	111	be	be	AUX
ejpam-521	461	112	established	establish	VERB
ejpam-521	461	113	.	.	PUNCT
ejpam-521	462	1	⊳	⊳	VERB
ejpam-521	462	2	the	the	DET
ejpam-521	462	3	following	follow	VERB
ejpam-521	462	4	lemma	lemma	PROPN
ejpam-521	462	5	can	can	AUX
ejpam-521	462	6	similarly	similarly	ADV
ejpam-521	462	7	be	be	AUX
ejpam-521	462	8	proved	prove	VERB
ejpam-521	462	9	using	use	VERB
ejpam-521	462	10	taylor	taylor	PROPN
ejpam-521	462	11	expansion	expansion	NOUN
ejpam-521	462	12	,	,	PUNCT
ejpam-521	462	13	lemma	lemma	PROPN
ejpam-521	462	14	3	3	NUM
ejpam-521	462	15	,	,	PUNCT
ejpam-521	462	16	lemma	lemma	X
ejpam-521	462	17	4	4	NUM
ejpam-521	462	18	and	and	CCONJ
ejpam-521	462	19	corollary	corollary	ADJ
ejpam-521	462	20	1	1	NUM
ejpam-521	462	21	.	.	PUNCT
ejpam-521	463	1	lemma	lemma	PROPN
ejpam-521	463	2	9	9	NUM
ejpam-521	463	3	.	.	PUNCT
ejpam-521	464	1	under	under	ADP
ejpam-521	464	2	the	the	DET
ejpam-521	464	3	conditions	condition	NOUN
ejpam-521	464	4	of	of	ADP
ejpam-521	464	5	theorem	theorem	NOUN
ejpam-521	464	6	1	1	NUM
ejpam-521	464	7	,	,	PUNCT
ejpam-521	464	8	∑	∑	PROPN
ejpam-521	464	9	ni	ni	PROPN
ejpam-521	464	10	,	,	PUNCT
ejpam-521	464	11	m>0	m>0	PROPN
ejpam-521	464	12	1	1	NUM
ejpam-521	464	13	ni	ni	PROPN
ejpam-521	464	14	,	,	PUNCT
ejpam-521	464	15	m	m	VERB
ejpam-521	464	16	=	=	ADJ
ejpam-521	464	17	o(m	o(m	PROPN
ejpam-521	464	18	)	)	PUNCT
ejpam-521	464	19	a.s	a.s	PROPN
ejpam-521	464	20	.	.	PROPN
ejpam-521	464	21	and	and	CCONJ
ejpam-521	464	22	(	(	PUNCT
ejpam-521	464	23	87	87	NUM
ejpam-521	464	24	)	)	PUNCT
ejpam-521	464	25	m	m	VERB
ejpam-521	464	26	∑	∑	PROPN
ejpam-521	464	27	i=1	i=1	PROPN
ejpam-521	464	28	log	log	PROPN
ejpam-521	464	29	ni	ni	PROPN
ejpam-521	464	30	,	,	PUNCT
ejpam-521	464	31	m+	m+	NOUN
ejpam-521	464	32	1	1	NUM
ejpam-521	464	33	nπi	nπi	ADJ
ejpam-521	464	34	,	,	PUNCT
ejpam-521	464	35	m+	m+	NOUN
ejpam-521	464	36	1	1	NUM
ejpam-521	464	37	=	=	SYM
ejpam-521	464	38	o(m	o(m	PROPN
ejpam-521	464	39	)	)	PUNCT
ejpam-521	464	40	a.s	a.s	PROPN
ejpam-521	464	41	.	.	PROPN
ejpam-521	464	42	(	(	PUNCT
ejpam-521	464	43	88	88	NUM
ejpam-521	464	44	)	)	PUNCT
ejpam-521	464	45	uniformly	uniformly	ADV
ejpam-521	464	46	in	in	ADP
ejpam-521	464	47	m	m	PROPN
ejpam-521	464	48	∈	∈	NOUN
ejpam-521	464	49	[	[	X
ejpam-521	464	50	nγ1	nγ1	NOUN
ejpam-521	464	51	,	,	PUNCT
ejpam-521	464	52	nγ2	nγ2	X
ejpam-521	464	53	]	]	PUNCT
ejpam-521	464	54	as	as	ADP
ejpam-521	464	55	n→∞.	n→∞.	PROPN
ejpam-521	464	56	lemma	lemma	PROPN
ejpam-521	464	57	10	10	NUM
ejpam-521	464	58	.	.	PUNCT
ejpam-521	465	1	under	under	ADP
ejpam-521	465	2	the	the	DET
ejpam-521	465	3	conditions	condition	NOUN
ejpam-521	465	4	of	of	ADP
ejpam-521	465	5	theorem	theorem	NOUN
ejpam-521	465	6	1	1	NUM
ejpam-521	465	7	,	,	PUNCT
ejpam-521	465	8	there	there	PRON
ejpam-521	465	9	exists	exist	VERB
ejpam-521	465	10	a	a	DET
ejpam-521	465	11	positive	positive	ADJ
ejpam-521	465	12	constant	constant	NOUN
ejpam-521	465	13	a	a	DET
ejpam-521	465	14	such	such	ADJ
ejpam-521	465	15	that	that	PRON
ejpam-521	465	16	−amα1	−amα1	NOUN
ejpam-521	465	17	+	+	CCONJ
ejpam-521	465	18	(	(	PUNCT
ejpam-521	465	19	α2	α2	ADJ
ejpam-521	465	20	−α1)m	−α1)m	PROPN
ejpam-521	465	21	log	log	NOUN
ejpam-521	465	22	m+o(m)≤	m+o(m)≤	PROPN
ejpam-521	465	23	−l∗1(x	−l∗1(x	NOUN
ejpam-521	465	24	n	n	CCONJ
ejpam-521	465	25	;	;	PUNCT
ejpam-521	465	26	m	m	X
ejpam-521	465	27	)	)	PUNCT
ejpam-521	466	1	+	+	CCONJ
ejpam-521	466	2	n	n	X
ejpam-521	466	3	∑	∑	ADP
ejpam-521	466	4	j=1	j=1	PROPN
ejpam-521	466	5	log	log	NOUN
ejpam-521	466	6	f	f	PROPN
ejpam-521	466	7	(	(	PUNCT
ejpam-521	466	8	x	x	SYM
ejpam-521	466	9	j|q̃m	j|q̃m	PROPN
ejpam-521	466	10	)	)	PUNCT
ejpam-521	466	11	≤	≤	NOUN
ejpam-521	466	12	(	(	PUNCT
ejpam-521	466	13	α1	α1	PROPN
ejpam-521	466	14	−	−	PROPN
ejpam-521	466	15	1)m	1)m	NUM
ejpam-521	466	16	log	log	PROPN
ejpam-521	466	17	m+o(m	m+o(m	NOUN
ejpam-521	466	18	)	)	PUNCT
ejpam-521	467	1	a.s	a.s	PROPN
ejpam-521	467	2	.	.	PROPN
ejpam-521	467	3	(	(	PUNCT
ejpam-521	467	4	89	89	NUM
ejpam-521	467	5	)	)	PUNCT
ejpam-521	467	6	uniformly	uniformly	ADV
ejpam-521	467	7	in	in	ADP
ejpam-521	467	8	m	m	PROPN
ejpam-521	467	9	∈	∈	NOUN
ejpam-521	468	1	[	[	X
ejpam-521	468	2	nγ1	nγ1	NOUN
ejpam-521	468	3	,	,	PUNCT
ejpam-521	468	4	nγ2	nγ2	X
ejpam-521	468	5	]	]	PUNCT
ejpam-521	468	6	as	as	ADP
ejpam-521	468	7	n→∞.	n→∞.	PROPN
ejpam-521	468	8	proof	proof	NOUN
ejpam-521	468	9	.	.	PUNCT
ejpam-521	469	1	first	first	ADV
ejpam-521	469	2	note	note	VERB
ejpam-521	469	3	that	that	SCONJ
ejpam-521	469	4	−l∗1(x	−l∗1(x	NOUN
ejpam-521	469	5	n	n	CCONJ
ejpam-521	469	6	;	;	PUNCT
ejpam-521	469	7	m	m	X
ejpam-521	469	8	)	)	PUNCT
ejpam-521	470	1	+	+	CCONJ
ejpam-521	470	2	n	n	X
ejpam-521	470	3	∑	∑	ADP
ejpam-521	470	4	j=1	j=1	PROPN
ejpam-521	470	5	log	log	NOUN
ejpam-521	470	6	f	f	PROPN
ejpam-521	470	7	(	(	PUNCT
ejpam-521	470	8	x	x	SYM
ejpam-521	470	9	j|q̃m	j|q̃m	PROPN
ejpam-521	470	10	)	)	PUNCT
ejpam-521	470	11	=	=	PUNCT
ejpam-521	471	1	m	m	VERB
ejpam-521	471	2	∑	∑	PROPN
ejpam-521	471	3	i=1	i=1	PROPN
ejpam-521	471	4	ni	ni	PROPN
ejpam-521	471	5	,	,	PUNCT
ejpam-521	471	6	m	m	VERB
ejpam-521	471	7	log	log	VERB
ejpam-521	471	8	πi	πi	ADV
ejpam-521	471	9	,	,	PUNCT
ejpam-521	471	10	m	m	VERB
ejpam-521	471	11	r̃i	r̃i	NOUN
ejpam-521	471	12	,	,	PUNCT
ejpam-521	471	13	m	m	VERB
ejpam-521	471	14	−	−	NOUN
ejpam-521	471	15	m	m	VERB
ejpam-521	471	16	∑	∑	PROPN
ejpam-521	471	17	i=1	i=1	PROPN
ejpam-521	471	18	(	(	PUNCT
ejpam-521	471	19	ni	ni	PROPN
ejpam-521	471	20	,	,	PUNCT
ejpam-521	471	21	m+	m+	NOUN
ejpam-521	471	22	1	1	NUM
ejpam-521	471	23	)	)	PUNCT
ejpam-521	471	24	ni	ni	PROPN
ejpam-521	471	25	,	,	PUNCT
ejpam-521	471	26	m+	m+	NOUN
ejpam-521	471	27	1	1	NUM
ejpam-521	471	28	(	(	PUNCT
ejpam-521	471	29	n+m)r̃i	n+m)r̃i	NOUN
ejpam-521	471	30	,	,	PUNCT
ejpam-521	471	31	m	m	NOUN
ejpam-521	471	32	g.	g.	PROPN
ejpam-521	471	33	qian	qian	PROPN
ejpam-521	471	34	/	/	SYM
ejpam-521	471	35	eur	eur	PROPN
ejpam-521	471	36	.	.	PUNCT
ejpam-521	472	1	j.	j.	PROPN
ejpam-521	472	2	pure	pure	PROPN
ejpam-521	472	3	appl	appl	PROPN
ejpam-521	472	4	.	.	PROPN
ejpam-521	472	5	math	math	PROPN
ejpam-521	472	6	,	,	PUNCT
ejpam-521	472	7	3	3	NUM
ejpam-521	472	8	(	(	PUNCT
ejpam-521	472	9	2010	2010	NUM
ejpam-521	472	10	)	)	PUNCT
ejpam-521	472	11	,	,	PUNCT
ejpam-521	472	12	51	51	NUM
ejpam-521	472	13	-	-	SYM
ejpam-521	472	14	80	80	NUM
ejpam-521	472	15	72	72	NUM
ejpam-521	472	16	=	=	NOUN
ejpam-521	472	17	m	m	VERB
ejpam-521	472	18	∑	∑	PUNCT
ejpam-521	472	19	i=1	i=1	PROPN
ejpam-521	472	20	log	log	NOUN
ejpam-521	472	21	r̃i	r̃i	NOUN
ejpam-521	472	22	,	,	PUNCT
ejpam-521	472	23	m+	m+	NUM
ejpam-521	472	24	m	m	PROPN
ejpam-521	472	25	∑	∑	PROPN
ejpam-521	472	26	i=1	i=1	PROPN
ejpam-521	472	27	ni	ni	PROPN
ejpam-521	472	28	,	,	PUNCT
ejpam-521	472	29	m	m	VERB
ejpam-521	472	30	log	log	NOUN
ejpam-521	472	31	(	(	PUNCT
ejpam-521	472	32	n+m)πi	n+m)πi	PROPN
ejpam-521	472	33	,	,	PUNCT
ejpam-521	472	34	m	m	VERB
ejpam-521	472	35	ni	ni	ADJ
ejpam-521	472	36	,	,	PUNCT
ejpam-521	472	37	m+	m+	NOUN
ejpam-521	472	38	1	1	NUM
ejpam-521	472	39	+	+	CCONJ
ejpam-521	472	40	m	m	VERB
ejpam-521	472	41	∑	∑	ADJ
ejpam-521	472	42	i=1	i=1	PROPN
ejpam-521	472	43	log	log	PROPN
ejpam-521	472	44	nπi	nπi	ADJ
ejpam-521	472	45	,	,	PUNCT
ejpam-521	472	46	m+	m+	NUM
ejpam-521	472	47	1	1	NUM
ejpam-521	472	48	ni	ni	PROPN
ejpam-521	472	49	,	,	PUNCT
ejpam-521	472	50	m+	m+	NOUN
ejpam-521	472	51	1	1	NUM
ejpam-521	473	1	+	+	NOUN
ejpam-521	473	2	m	m	VERB
ejpam-521	473	3	log(n+m)−	log(n+m)−	ADJ
ejpam-521	473	4	m	m	VERB
ejpam-521	473	5	∑	∑	PROPN
ejpam-521	473	6	i=1	i=1	PROPN
ejpam-521	473	7	log(nπi	log(nπi	NOUN
ejpam-521	473	8	,	,	PUNCT
ejpam-521	473	9	m+	m+	NOUN
ejpam-521	473	10	1	1	NUM
ejpam-521	473	11	)	)	PUNCT
ejpam-521	473	12	.	.	PUNCT
ejpam-521	474	1	(	(	PUNCT
ejpam-521	474	2	90	90	NUM
ejpam-521	474	3	)	)	PUNCT
ejpam-521	474	4	the	the	DET
ejpam-521	474	5	second	second	ADJ
ejpam-521	474	6	term	term	NOUN
ejpam-521	474	7	of	of	ADP
ejpam-521	474	8	the	the	DET
ejpam-521	474	9	righthand	righthand	NOUN
ejpam-521	474	10	side	side	NOUN
ejpam-521	474	11	of	of	ADP
ejpam-521	474	12	(	(	PUNCT
ejpam-521	474	13	90	90	NUM
ejpam-521	474	14	)	)	PUNCT
ejpam-521	474	15	m	m	VERB
ejpam-521	474	16	∑	∑	PROPN
ejpam-521	474	17	i=1	i=1	PROPN
ejpam-521	474	18	ni	ni	PROPN
ejpam-521	474	19	,	,	PUNCT
ejpam-521	474	20	m	m	VERB
ejpam-521	474	21	log	log	NOUN
ejpam-521	474	22	(	(	PUNCT
ejpam-521	474	23	n+m)πi	n+m)πi	PROPN
ejpam-521	474	24	,	,	PUNCT
ejpam-521	474	25	m	m	VERB
ejpam-521	474	26	ni	ni	ADJ
ejpam-521	474	27	,	,	PUNCT
ejpam-521	474	28	m+	m+	NOUN
ejpam-521	474	29	1	1	NUM
ejpam-521	474	30	=	=	SYM
ejpam-521	474	31	m	m	VERB
ejpam-521	474	32	∑	∑	PROPN
ejpam-521	474	33	i=1	i=1	PROPN
ejpam-521	474	34	ni	ni	PROPN
ejpam-521	474	35	,	,	PUNCT
ejpam-521	474	36	m	m	VERB
ejpam-521	474	37	log	log	PROPN
ejpam-521	474	38	�	�	PROPN
ejpam-521	474	39	(	(	PUNCT
ejpam-521	474	40	n+m)πi	n+m)πi	PROPN
ejpam-521	474	41	,	,	PUNCT
ejpam-521	474	42	m	m	VERB
ejpam-521	474	43	ni	ni	ADJ
ejpam-521	474	44	,	,	PUNCT
ejpam-521	474	45	m+	m+	NUM
ejpam-521	474	46	1	1	NUM
ejpam-521	474	47	·	·	PUNCT
ejpam-521	474	48	ni	ni	PROPN
ejpam-521	474	49	,	,	PUNCT
ejpam-521	474	50	m	m	VERB
ejpam-521	474	51	nπi	nπi	ADJ
ejpam-521	474	52	,	,	PUNCT
ejpam-521	474	53	m	m	PROPN
ejpam-521	474	54	·	·	PUNCT
ejpam-521	474	55	nπi	nπi	ADJ
ejpam-521	474	56	,	,	PUNCT
ejpam-521	474	57	m	m	PROPN
ejpam-521	474	58	ni	ni	ADJ
ejpam-521	474	59	,	,	PUNCT
ejpam-521	474	60	m	m	PROPN
ejpam-521	474	61	�	�	NOUN
ejpam-521	474	62	=	=	SYM
ejpam-521	474	63	n	n	PRON
ejpam-521	474	64	log	log	VERB
ejpam-521	474	65	�	�	PROPN
ejpam-521	474	66	1	1	NUM
ejpam-521	474	67	+	+	NUM
ejpam-521	474	68	m	m	VERB
ejpam-521	474	69	n	n	PRON
ejpam-521	474	70	�	�	PROPN
ejpam-521	474	71	−	−	PROPN
ejpam-521	474	72	∑	∑	PROPN
ejpam-521	474	73	ni	ni	PROPN
ejpam-521	474	74	,	,	PUNCT
ejpam-521	474	75	m>0	m>0	PROPN
ejpam-521	474	76	ni	ni	PROPN
ejpam-521	474	77	,	,	PUNCT
ejpam-521	474	78	m	m	VERB
ejpam-521	474	79	log	log	NOUN
ejpam-521	474	80	�	�	PROPN
ejpam-521	474	81	1	1	NUM
ejpam-521	474	82	+	+	SYM
ejpam-521	474	83	1	1	NUM
ejpam-521	474	84	ni	ni	PROPN
ejpam-521	474	85	,	,	PUNCT
ejpam-521	474	86	m	m	PROPN
ejpam-521	474	87	�	�	PROPN
ejpam-521	474	88	−	−	PROPN
ejpam-521	474	89	∑	∑	PROPN
ejpam-521	474	90	ni	ni	PROPN
ejpam-521	474	91	,	,	PUNCT
ejpam-521	474	92	m>0	m>0	PROPN
ejpam-521	474	93	ni	ni	PROPN
ejpam-521	474	94	,	,	PUNCT
ejpam-521	474	95	m	m	VERB
ejpam-521	474	96	log	log	NOUN
ejpam-521	474	97	ni	ni	PROPN
ejpam-521	474	98	,	,	PUNCT
ejpam-521	474	99	m	m	VERB
ejpam-521	474	100	nπi	nπi	ADJ
ejpam-521	474	101	,	,	PUNCT
ejpam-521	474	102	m	m	PROPN
ejpam-521	474	103	(	(	PUNCT
ejpam-521	474	104	91	91	NUM
ejpam-521	474	105	)	)	PUNCT
ejpam-521	474	106	and	and	CCONJ
ejpam-521	474	107	∑	∑	PUNCT
ejpam-521	474	108	ni	ni	PROPN
ejpam-521	474	109	,	,	PUNCT
ejpam-521	474	110	m>0	m>0	PROPN
ejpam-521	474	111	ni	ni	PROPN
ejpam-521	474	112	,	,	PUNCT
ejpam-521	474	113	m	m	VERB
ejpam-521	474	114	log	log	NOUN
ejpam-521	474	115	�	�	PROPN
ejpam-521	474	116	1	1	NUM
ejpam-521	474	117	+	+	SYM
ejpam-521	474	118	1	1	NUM
ejpam-521	474	119	ni	ni	PROPN
ejpam-521	474	120	,	,	PUNCT
ejpam-521	474	121	m	m	PROPN
ejpam-521	474	122	�	�	NOUN
ejpam-521	474	123	=	=	SYM
ejpam-521	474	124	∑	∑	PUNCT
ejpam-521	474	125	ni	ni	PROPN
ejpam-521	474	126	,	,	PUNCT
ejpam-521	474	127	m>0	m>0	PROPN
ejpam-521	474	128	ni	ni	PROPN
ejpam-521	474	129	,	,	PUNCT
ejpam-521	474	130	m	m	PROPN
ejpam-521	474	131	1	1	NUM
ejpam-521	474	132	ni	ni	PROPN
ejpam-521	474	133	,	,	PUNCT
ejpam-521	474	134	m	m	VERB
ejpam-521	474	135	+	+	ADJ
ejpam-521	474	136	1	1	NUM
ejpam-521	474	137	2	2	NUM
ejpam-521	474	138	(	(	PUNCT
ejpam-521	474	139	1+ηi	1+ηi	NUM
ejpam-521	474	140	,	,	PUNCT
ejpam-521	474	141	m	m	NOUN
ejpam-521	474	142	)	)	PUNCT
ejpam-521	474	143	−2	−2	PROPN
ejpam-521	474	144	1	1	NUM
ejpam-521	474	145	n2	n2	NOUN
ejpam-521	474	146	i	i	PROPN
ejpam-521	474	147	,	,	PUNCT
ejpam-521	474	148	m	m	VERB
ejpam-521	474	149	!	!	PUNCT
ejpam-521	475	1	(	(	PUNCT
ejpam-521	475	2	92	92	NUM
ejpam-521	475	3	)	)	PUNCT
ejpam-521	475	4	where	where	SCONJ
ejpam-521	475	5	0≤	0≤	ADJ
ejpam-521	475	6	ηi	ηi	PROPN
ejpam-521	475	7	,	,	PUNCT
ejpam-521	475	8	m	m	VERB
ejpam-521	475	9	≤	≤	ADJ
ejpam-521	475	10	1	1	NUM
ejpam-521	475	11	.	.	PUNCT
ejpam-521	476	1	by	by	ADP
ejpam-521	476	2	lemma	lemma	PROPN
ejpam-521	476	3	8	8	NUM
ejpam-521	476	4	and	and	CCONJ
ejpam-521	476	5	(	(	PUNCT
ejpam-521	476	6	87	87	NUM
ejpam-521	476	7	)	)	PUNCT
ejpam-521	476	8	of	of	ADP
ejpam-521	476	9	lemma	lemma	PROPN
ejpam-521	476	10	9	9	NUM
ejpam-521	476	11	we	we	PRON
ejpam-521	476	12	have	have	VERB
ejpam-521	476	13	−amα1	−amα1	NOUN
ejpam-521	477	1	+	+	ADJ
ejpam-521	477	2	o(m)≤	o(m)≤	ADJ
ejpam-521	477	3	m	m	VERB
ejpam-521	477	4	∑	∑	PROPN
ejpam-521	477	5	i=1	i=1	PROPN
ejpam-521	477	6	ni	ni	PROPN
ejpam-521	477	7	,	,	PUNCT
ejpam-521	477	8	m	m	VERB
ejpam-521	477	9	log	log	NOUN
ejpam-521	477	10	(	(	PUNCT
ejpam-521	477	11	n+m)πi	n+m)πi	PROPN
ejpam-521	477	12	,	,	PUNCT
ejpam-521	477	13	m	m	VERB
ejpam-521	477	14	ni	ni	ADJ
ejpam-521	477	15	,	,	PUNCT
ejpam-521	477	16	m+	m+	NOUN
ejpam-521	477	17	1	1	NUM
ejpam-521	477	18	≤	≤	NUM
ejpam-521	477	19	o(m	o(m	NOUN
ejpam-521	477	20	)	)	PUNCT
ejpam-521	477	21	a.s	a.s	PROPN
ejpam-521	477	22	.	.	PROPN
ejpam-521	477	23	(	(	PUNCT
ejpam-521	477	24	93	93	NUM
ejpam-521	477	25	)	)	PUNCT
ejpam-521	477	26	uniformly	uniformly	ADV
ejpam-521	477	27	in	in	ADP
ejpam-521	477	28	m	m	PROPN
ejpam-521	477	29	∈	∈	NOUN
ejpam-521	478	1	[	[	X
ejpam-521	478	2	nγ1	nγ1	NOUN
ejpam-521	478	3	,	,	PUNCT
ejpam-521	478	4	nγ2	nγ2	X
ejpam-521	478	5	]	]	PUNCT
ejpam-521	478	6	as	as	ADP
ejpam-521	478	7	n→∞.	n→∞.	NUM
ejpam-521	478	8	it	it	PRON
ejpam-521	478	9	can	can	AUX
ejpam-521	478	10	also	also	ADV
ejpam-521	478	11	be	be	AUX
ejpam-521	478	12	seen	see	VERB
ejpam-521	478	13	that	that	SCONJ
ejpam-521	478	14	α2	α2	PROPN
ejpam-521	478	15	m	m	PROPN
ejpam-521	478	16	log	log	NOUN
ejpam-521	478	17	m+o(m)≤	m+o(m)≤	PROPN
ejpam-521	478	18	−	−	PROPN
ejpam-521	478	19	m	m	VERB
ejpam-521	478	20	∑	∑	PROPN
ejpam-521	478	21	i=1	i=1	PROPN
ejpam-521	478	22	log	log	PROPN
ejpam-521	478	23	�	�	PROPN
ejpam-521	478	24	πi	πi	ADP
ejpam-521	478	25	,	,	PUNCT
ejpam-521	478	26	m+	m+	NOUN
ejpam-521	478	27	1	1	NUM
ejpam-521	478	28	n	n	PRON
ejpam-521	478	29	�	�	PROPN
ejpam-521	478	30	≤	≤	PROPN
ejpam-521	478	31	α1	α1	PROPN
ejpam-521	478	32	m	m	VERB
ejpam-521	478	33	log	log	NOUN
ejpam-521	478	34	m+o(m	m+o(m	NOUN
ejpam-521	478	35	)	)	PUNCT
ejpam-521	478	36	.	.	PUNCT
ejpam-521	479	1	(	(	PUNCT
ejpam-521	479	2	94	94	NUM
ejpam-521	479	3	)	)	PUNCT
ejpam-521	479	4	from	from	ADP
ejpam-521	479	5	(	(	PUNCT
ejpam-521	479	6	75	75	NUM
ejpam-521	479	7	)	)	PUNCT
ejpam-521	479	8	,	,	PUNCT
ejpam-521	479	9	(	(	PUNCT
ejpam-521	479	10	93	93	NUM
ejpam-521	479	11	)	)	PUNCT
ejpam-521	479	12	,	,	PUNCT
ejpam-521	479	13	(	(	PUNCT
ejpam-521	479	14	88	88	NUM
ejpam-521	479	15	)	)	PUNCT
ejpam-521	479	16	of	of	ADP
ejpam-521	479	17	lemma	lemma	PROPN
ejpam-521	479	18	9	9	NUM
ejpam-521	479	19	,	,	PUNCT
ejpam-521	479	20	and	and	CCONJ
ejpam-521	479	21	(	(	PUNCT
ejpam-521	479	22	94	94	X
ejpam-521	479	23	)	)	PUNCT
ejpam-521	479	24	it	it	PRON
ejpam-521	479	25	follows	follow	VERB
ejpam-521	479	26	that	that	SCONJ
ejpam-521	479	27	−amα1	−amα1	ADP
ejpam-521	479	28	+	+	CCONJ
ejpam-521	479	29	(	(	PUNCT
ejpam-521	479	30	α2	α2	ADJ
ejpam-521	479	31	−α1)m	−α1)m	PROPN
ejpam-521	479	32	log	log	NOUN
ejpam-521	479	33	m+o(m)≤	m+o(m)≤	PROPN
ejpam-521	479	34	−l∗1(x	−l∗1(x	NOUN
ejpam-521	479	35	n	n	CCONJ
ejpam-521	479	36	;	;	PUNCT
ejpam-521	479	37	m	m	X
ejpam-521	479	38	)	)	PUNCT
ejpam-521	480	1	+	+	CCONJ
ejpam-521	480	2	n	n	X
ejpam-521	480	3	∑	∑	ADP
ejpam-521	480	4	j=1	j=1	PROPN
ejpam-521	480	5	log	log	NOUN
ejpam-521	480	6	f	f	PROPN
ejpam-521	480	7	(	(	PUNCT
ejpam-521	480	8	x	x	SYM
ejpam-521	480	9	j|q̃m	j|q̃m	PROPN
ejpam-521	480	10	)	)	PUNCT
ejpam-521	480	11	≤	≤	NOUN
ejpam-521	480	12	(	(	PUNCT
ejpam-521	480	13	α1	α1	PROPN
ejpam-521	480	14	−	−	PROPN
ejpam-521	480	15	1)m	1)m	NUM
ejpam-521	480	16	log	log	PROPN
ejpam-521	480	17	m+o(m	m+o(m	NOUN
ejpam-521	480	18	)	)	PUNCT
ejpam-521	481	1	a.s	a.s	PROPN
ejpam-521	481	2	.	.	PROPN
ejpam-521	481	3	(	(	PUNCT
ejpam-521	481	4	95	95	NUM
ejpam-521	481	5	)	)	PUNCT
ejpam-521	481	6	uniformly	uniformly	ADV
ejpam-521	481	7	in	in	ADP
ejpam-521	481	8	m	m	PROPN
ejpam-521	481	9	∈	∈	NOUN
ejpam-521	482	1	[	[	X
ejpam-521	482	2	nγ1	nγ1	NOUN
ejpam-521	482	3	,	,	PUNCT
ejpam-521	482	4	nγ2	nγ2	X
ejpam-521	482	5	]	]	PUNCT
ejpam-521	482	6	as	as	ADP
ejpam-521	482	7	n→∞.	n→∞.	PROPN
ejpam-521	482	8	⊳	⊳	PROPN
ejpam-521	482	9	lemma	lemma	PROPN
ejpam-521	482	10	11	11	NUM
ejpam-521	482	11	.	.	PUNCT
ejpam-521	483	1	under	under	ADP
ejpam-521	483	2	the	the	DET
ejpam-521	483	3	conditions	condition	NOUN
ejpam-521	483	4	(	(	PUNCT
ejpam-521	483	5	i	i	NOUN
ejpam-521	483	6	)	)	PUNCT
ejpam-521	483	7	to	to	ADP
ejpam-521	483	8	(	(	PUNCT
ejpam-521	483	9	iv	iv	X
ejpam-521	483	10	)	)	PUNCT
ejpam-521	483	11	of	of	ADP
ejpam-521	483	12	theorem	theorem	ADJ
ejpam-521	483	13	2	2	NUM
ejpam-521	483	14	and	and	CCONJ
ejpam-521	483	15	f	f	PROPN
ejpam-521	483	16	6=	6=	PROPN
ejpam-521	483	17	1	1	NUM
ejpam-521	483	18	,	,	PUNCT
ejpam-521	483	19	we	we	PRON
ejpam-521	483	20	have	have	VERB
ejpam-521	483	21	as	as	ADP
ejpam-521	483	22	m→∞	m→∞	NUM
ejpam-521	483	23	e	e	NOUN
ejpam-521	483	24	f	f	NOUN
ejpam-521	483	25	log	log	VERB
ejpam-521	483	26	f	f	PROPN
ejpam-521	483	27	f	f	PROPN
ejpam-521	483	28	(	(	PUNCT
ejpam-521	483	29	·	·	PUNCT
ejpam-521	483	30	|q̃m	|q̃m	NUM
ejpam-521	483	31	)	)	PUNCT
ejpam-521	483	32	=	=	PUNCT
ejpam-521	484	1	m	m	VERB
ejpam-521	484	2	∑	∑	PUNCT
ejpam-521	484	3	i=1	i=1	PROPN
ejpam-521	484	4	1	1	NUM
ejpam-521	484	5	24	24	NUM
ejpam-521	484	6	r̃2	r̃2	PROPN
ejpam-521	484	7	i	i	PROPN
ejpam-521	484	8	,	,	PUNCT
ejpam-521	484	9	m	m	VERB
ejpam-521	484	10	∫	∫	PROPN
ejpam-521	484	11	q̃i	q̃i	PROPN
ejpam-521	484	12	,	,	PUNCT
ejpam-521	484	13	m	m	VERB
ejpam-521	484	14	ḟ	ḟ	NOUN
ejpam-521	484	15	2	2	NUM
ejpam-521	484	16	f	f	NOUN
ejpam-521	484	17	+	+	CCONJ
ejpam-521	484	18	o(m−2α2	o(m−2α2	PROPN
ejpam-521	484	19	)	)	PUNCT
ejpam-521	484	20	.	.	PUNCT
ejpam-521	485	1	(	(	PUNCT
ejpam-521	485	2	96	96	NUM
ejpam-521	485	3	)	)	PUNCT
ejpam-521	485	4	g.	g.	PROPN
ejpam-521	485	5	qian	qian	PROPN
ejpam-521	485	6	/	/	SYM
ejpam-521	485	7	eur	eur	PROPN
ejpam-521	485	8	.	.	PUNCT
ejpam-521	486	1	j.	j.	PROPN
ejpam-521	486	2	pure	pure	PROPN
ejpam-521	486	3	appl	appl	PROPN
ejpam-521	486	4	.	.	PROPN
ejpam-521	486	5	math	math	PROPN
ejpam-521	486	6	,	,	PUNCT
ejpam-521	486	7	3	3	NUM
ejpam-521	486	8	(	(	PUNCT
ejpam-521	486	9	2010	2010	NUM
ejpam-521	486	10	)	)	PUNCT
ejpam-521	486	11	,	,	PUNCT
ejpam-521	486	12	51	51	NUM
ejpam-521	486	13	-	-	SYM
ejpam-521	486	14	80	80	NUM
ejpam-521	486	15	73	73	NUM
ejpam-521	486	16	proof	proof	NOUN
ejpam-521	486	17	.	.	PUNCT
ejpam-521	487	1	by	by	ADP
ejpam-521	487	2	the	the	DET
ejpam-521	487	3	definition	definition	NOUN
ejpam-521	487	4	of	of	ADP
ejpam-521	487	5	f	f	PROPN
ejpam-521	487	6	(	(	PUNCT
ejpam-521	487	7	x	x	SYM
ejpam-521	487	8	|q̃m	|q̃m	PROPN
ejpam-521	487	9	)	)	PUNCT
ejpam-521	487	10	lim	lim	PROPN
ejpam-521	487	11	m→∞	m→∞	PROPN
ejpam-521	487	12	(	(	PUNCT
ejpam-521	487	13	f	f	PROPN
ejpam-521	487	14	(	(	PUNCT
ejpam-521	487	15	x)−	x)−	PROPN
ejpam-521	487	16	f	f	PROPN
ejpam-521	487	17	(	(	PUNCT
ejpam-521	487	18	x	x	NOUN
ejpam-521	487	19	|q̃m	|q̃m	NUM
ejpam-521	487	20	)	)	PUNCT
ejpam-521	487	21	)	)	PUNCT
ejpam-521	488	1	=	=	SYM
ejpam-521	488	2	lim	lim	PROPN
ejpam-521	488	3	m→∞	m→∞	NOUN
ejpam-521	488	4	1	1	NUM
ejpam-521	488	5	r̃i	r̃i	NOUN
ejpam-521	488	6	,	,	PUNCT
ejpam-521	488	7	m(x	m(x	PROPN
ejpam-521	488	8	)	)	PUNCT
ejpam-521	488	9	∫	∫	PROPN
ejpam-521	488	10	q̃i	q̃i	PROPN
ejpam-521	488	11	,	,	PUNCT
ejpam-521	488	12	m(x	m(x	PROPN
ejpam-521	488	13	)	)	PUNCT
ejpam-521	488	14	(	(	PUNCT
ejpam-521	488	15	f	f	X
ejpam-521	488	16	(	(	PUNCT
ejpam-521	488	17	x)−	x)−	PROPN
ejpam-521	488	18	f	f	PROPN
ejpam-521	488	19	(	(	PUNCT
ejpam-521	488	20	y))d	y))d	NOUN
ejpam-521	488	21	y	y	PROPN
ejpam-521	488	22	=	=	SYM
ejpam-521	488	23	0	0	PROPN
ejpam-521	489	1	(	(	PUNCT
ejpam-521	489	2	97	97	NUM
ejpam-521	489	3	)	)	PUNCT
ejpam-521	489	4	uniformly	uniformly	ADV
ejpam-521	489	5	in	in	ADP
ejpam-521	489	6	x	x	PUNCT
ejpam-521	489	7	∈	∈	PROPN
ejpam-521	489	8	[	[	X
ejpam-521	489	9	s	s	X
ejpam-521	489	10	,	,	PUNCT
ejpam-521	489	11	t	t	PROPN
ejpam-521	489	12	]	]	PUNCT
ejpam-521	489	13	,	,	PUNCT
ejpam-521	489	14	where	where	SCONJ
ejpam-521	489	15	q̃	q̃	PROPN
ejpam-521	489	16	i	i	PRON
ejpam-521	489	17	,	,	PUNCT
ejpam-521	489	18	m(x	m(x	PROPN
ejpam-521	489	19	)	)	PUNCT
ejpam-521	489	20	is	be	AUX
ejpam-521	489	21	the	the	DET
ejpam-521	489	22	subinterval	subinterval	NOUN
ejpam-521	489	23	containing	contain	VERB
ejpam-521	489	24	x	x	PUNCT
ejpam-521	489	25	,	,	PUNCT
ejpam-521	489	26	and	and	CCONJ
ejpam-521	490	1	r̃i	r̃i	NOUN
ejpam-521	490	2	,	,	PUNCT
ejpam-521	490	3	m(x	m(x	PROPN
ejpam-521	490	4	)	)	PUNCT
ejpam-521	490	5	is	be	AUX
ejpam-521	490	6	the	the	DET
ejpam-521	490	7	corresponding	corresponding	ADJ
ejpam-521	490	8	width	width	NOUN
ejpam-521	490	9	.	.	PUNCT
ejpam-521	491	1	now	now	ADV
ejpam-521	491	2	by	by	ADP
ejpam-521	491	3	taylor	taylor	NOUN
ejpam-521	491	4	expansion	expansion	NOUN
ejpam-521	491	5	e	e	AUX
ejpam-521	491	6	f	f	NOUN
ejpam-521	491	7	log	log	VERB
ejpam-521	491	8	f	f	PROPN
ejpam-521	491	9	f	f	PROPN
ejpam-521	491	10	(	(	PUNCT
ejpam-521	491	11	·	·	PUNCT
ejpam-521	491	12	|q̃m	|q̃m	NUM
ejpam-521	491	13	)	)	PUNCT
ejpam-521	491	14	=	=	PUNCT
ejpam-521	492	1	m	m	VERB
ejpam-521	492	2	∑	∑	PUNCT
ejpam-521	492	3	i=1	i=1	PROPN
ejpam-521	492	4	∫	∫	PROPN
ejpam-521	493	1	q̃i	q̃i	PROPN
ejpam-521	493	2	,	,	PUNCT
ejpam-521	493	3	m	m	PROPN
ejpam-521	493	4	f	f	PROPN
ejpam-521	493	5	log	log	NOUN
ejpam-521	493	6	�	�	PROPN
ejpam-521	493	7	1	1	NUM
ejpam-521	493	8	+	+	NUM
ejpam-521	493	9	f	f	PROPN
ejpam-521	493	10	−	−	PROPN
ejpam-521	493	11	f	f	PROPN
ejpam-521	493	12	(	(	PUNCT
ejpam-521	493	13	·	·	PUNCT
ejpam-521	493	14	|q̃m	|q̃m	NUM
ejpam-521	493	15	)	)	PUNCT
ejpam-521	493	16	f	f	PROPN
ejpam-521	493	17	(	(	PUNCT
ejpam-521	493	18	·	·	PUNCT
ejpam-521	493	19	|q̃m	|q̃m	NUM
ejpam-521	493	20	)	)	PUNCT
ejpam-521	493	21	�	�	PROPN
ejpam-521	493	22	=	=	PUNCT
ejpam-521	493	23	m	m	PROPN
ejpam-521	493	24	∑	∑	PUNCT
ejpam-521	493	25	i=1	i=1	PROPN
ejpam-521	493	26	∫	∫	PROPN
ejpam-521	493	27	q̃i	q̃i	PROPN
ejpam-521	493	28	,	,	PUNCT
ejpam-521	493	29	m	m	PROPN
ejpam-521	493	30	f	f	NOUN
ejpam-521	493	31	f	f	X
ejpam-521	494	1	−	−	PROPN
ejpam-521	494	2	f	f	PROPN
ejpam-521	494	3	(	(	PUNCT
ejpam-521	494	4	·	·	PUNCT
ejpam-521	494	5	|q̃m	|q̃m	NUM
ejpam-521	494	6	)	)	PUNCT
ejpam-521	494	7	f	f	PROPN
ejpam-521	494	8	(	(	PUNCT
ejpam-521	494	9	·	·	PUNCT
ejpam-521	494	10	|q̃m	|q̃m	NUM
ejpam-521	494	11	)	)	PUNCT
ejpam-521	494	12	−	−	NOUN
ejpam-521	494	13	1	1	NUM
ejpam-521	494	14	2	2	NUM
ejpam-521	494	15	m	m	NOUN
ejpam-521	494	16	∑	∑	PROPN
ejpam-521	494	17	i=1	i=1	PROPN
ejpam-521	494	18	∫	∫	PROPN
ejpam-521	494	19	q̃i	q̃i	PROPN
ejpam-521	494	20	,	,	PUNCT
ejpam-521	494	21	m	m	PROPN
ejpam-521	494	22	f	f	X
ejpam-521	494	23	(	(	PUNCT
ejpam-521	494	24	1+ηi	1+ηi	NUM
ejpam-521	494	25	)	)	PUNCT
ejpam-521	494	26	−2	−2	NOUN
ejpam-521	494	27	�	�	PROPN
ejpam-521	495	1	f	f	PROPN
ejpam-521	495	2	−	−	PROPN
ejpam-521	495	3	f	f	PROPN
ejpam-521	495	4	(	(	PUNCT
ejpam-521	495	5	·	·	PUNCT
ejpam-521	495	6	|q̃m	|q̃m	NUM
ejpam-521	495	7	)	)	PUNCT
ejpam-521	495	8	f	f	PROPN
ejpam-521	495	9	(	(	PUNCT
ejpam-521	495	10	·	·	PUNCT
ejpam-521	495	11	|q̃m	|q̃m	NUM
ejpam-521	495	12	)	)	PUNCT
ejpam-521	495	13	�	�	PROPN
ejpam-521	495	14	2	2	NUM
ejpam-521	495	15	(	(	PUNCT
ejpam-521	495	16	98	98	NUM
ejpam-521	495	17	)	)	PUNCT
ejpam-521	495	18	where	where	SCONJ
ejpam-521	495	19	|ηi(x)|	|ηi(x)|	PROPN
ejpam-521	495	20	≤	≤	PROPN
ejpam-521	495	21	�	�	PROPN
ejpam-521	495	22	�	�	PROPN
ejpam-521	495	23	�	�	PROPN
ejpam-521	495	24	f	f	PROPN
ejpam-521	495	25	−	−	PROPN
ejpam-521	495	26	f	f	PROPN
ejpam-521	495	27	(	(	PUNCT
ejpam-521	495	28	·	·	PUNCT
ejpam-521	495	29	|q̃m	|q̃m	NUM
ejpam-521	495	30	)	)	PUNCT
ejpam-521	495	31	f	f	PROPN
ejpam-521	495	32	(	(	PUNCT
ejpam-521	495	33	·	·	PUNCT
ejpam-521	495	34	|q̃m	|q̃m	NUM
ejpam-521	495	35	)	)	PUNCT
ejpam-521	495	36	�	�	PROPN
ejpam-521	495	37	�	�	PROPN
ejpam-521	495	38	�	�	PROPN
ejpam-521	495	39	and	and	CCONJ
ejpam-521	495	40	by	by	ADP
ejpam-521	495	41	(	(	PUNCT
ejpam-521	495	42	97	97	NUM
ejpam-521	495	43	)	)	PUNCT
ejpam-521	495	44	supx	supx	PROPN
ejpam-521	495	45	|ηi(x)|=	|ηi(x)|=	PROPN
ejpam-521	495	46	o(1	o(1	NOUN
ejpam-521	495	47	)	)	PUNCT
ejpam-521	495	48	.	.	PUNCT
ejpam-521	496	1	hence	hence	ADV
ejpam-521	496	2	e	e	PROPN
ejpam-521	496	3	f	f	PROPN
ejpam-521	496	4	log	log	VERB
ejpam-521	496	5	f	f	PROPN
ejpam-521	496	6	f	f	PROPN
ejpam-521	496	7	(	(	PUNCT
ejpam-521	496	8	·	·	PUNCT
ejpam-521	496	9	|q̃m	|q̃m	NUM
ejpam-521	496	10	)	)	PUNCT
ejpam-521	496	11	=	=	PUNCT
ejpam-521	497	1	m	m	VERB
ejpam-521	497	2	∑	∑	PUNCT
ejpam-521	497	3	i=1	i=1	PROPN
ejpam-521	497	4	∫	∫	PROPN
ejpam-521	497	5	q̃i	q̃i	PROPN
ejpam-521	497	6	,	,	PUNCT
ejpam-521	497	7	m	m	PROPN
ejpam-521	497	8	(	(	PUNCT
ejpam-521	497	9	f	f	PROPN
ejpam-521	497	10	−	−	PROPN
ejpam-521	497	11	f	f	PROPN
ejpam-521	497	12	(	(	PUNCT
ejpam-521	497	13	·	·	PUNCT
ejpam-521	497	14	|q̃m))2	|q̃m))2	NUM
ejpam-521	497	15	f	f	X
ejpam-521	497	16	(	(	PUNCT
ejpam-521	497	17	·	·	PUNCT
ejpam-521	497	18	|q̃m	|q̃m	NUM
ejpam-521	497	19	)	)	PUNCT
ejpam-521	497	20	−1	−1	NOUN
ejpam-521	497	21	2	2	NUM
ejpam-521	497	22	(	(	PUNCT
ejpam-521	497	23	1	1	NUM
ejpam-521	497	24	+	+	NUM
ejpam-521	497	25	o(1	o(1	NOUN
ejpam-521	497	26	)	)	PUNCT
ejpam-521	497	27	)	)	PUNCT
ejpam-521	498	1	m	m	VERB
ejpam-521	498	2	∑	∑	VERB
ejpam-521	498	3	i=1	i=1	PROPN
ejpam-521	498	4	∫	∫	PROPN
ejpam-521	498	5	q̃i	q̃i	PROPN
ejpam-521	498	6	,	,	PUNCT
ejpam-521	498	7	m	m	PROPN
ejpam-521	498	8	(	(	PUNCT
ejpam-521	498	9	f	f	PROPN
ejpam-521	498	10	−	−	PROPN
ejpam-521	498	11	f	f	PROPN
ejpam-521	498	12	(	(	PUNCT
ejpam-521	498	13	·	·	PUNCT
ejpam-521	498	14	|q̃m))3	|q̃m))3	X
ejpam-521	498	15	f	f	X
ejpam-521	498	16	(	(	PUNCT
ejpam-521	498	17	·	·	PUNCT
ejpam-521	498	18	|q̃m)2	|q̃m)2	VERB
ejpam-521	498	19	−	−	ADP
ejpam-521	498	20	1	1	NUM
ejpam-521	498	21	2	2	NUM
ejpam-521	498	22	(	(	PUNCT
ejpam-521	498	23	1	1	NUM
ejpam-521	498	24	+	+	NUM
ejpam-521	498	25	o(1	o(1	NOUN
ejpam-521	498	26	)	)	PUNCT
ejpam-521	498	27	)	)	PUNCT
ejpam-521	499	1	m	m	VERB
ejpam-521	499	2	∑	∑	VERB
ejpam-521	499	3	i=1	i=1	PROPN
ejpam-521	499	4	∫	∫	PROPN
ejpam-521	499	5	q̃i	q̃i	PROPN
ejpam-521	499	6	,	,	PUNCT
ejpam-521	499	7	m	m	PROPN
ejpam-521	499	8	(	(	PUNCT
ejpam-521	499	9	f	f	PROPN
ejpam-521	499	10	−	−	PROPN
ejpam-521	499	11	f	f	PROPN
ejpam-521	499	12	(	(	PUNCT
ejpam-521	499	13	·	·	PUNCT
ejpam-521	499	14	|q̃m))2	|q̃m))2	NUM
ejpam-521	499	15	f	f	X
ejpam-521	499	16	(	(	PUNCT
ejpam-521	499	17	·	·	PUNCT
ejpam-521	499	18	|q̃m	|q̃m	NUM
ejpam-521	499	19	)	)	PUNCT
ejpam-521	499	20	=	=	SYM
ejpam-521	499	21	1	1	NUM
ejpam-521	499	22	2	2	NUM
ejpam-521	499	23	(	(	PUNCT
ejpam-521	499	24	1	1	NUM
ejpam-521	499	25	+	+	NUM
ejpam-521	499	26	o(1	o(1	NOUN
ejpam-521	499	27	)	)	PUNCT
ejpam-521	499	28	)	)	PUNCT
ejpam-521	500	1	m	m	VERB
ejpam-521	500	2	∑	∑	VERB
ejpam-521	500	3	i=1	i=1	PROPN
ejpam-521	500	4	∫	∫	PROPN
ejpam-521	500	5	q̃i	q̃i	PROPN
ejpam-521	500	6	,	,	PUNCT
ejpam-521	500	7	m	m	PROPN
ejpam-521	500	8	(	(	PUNCT
ejpam-521	500	9	f	f	PROPN
ejpam-521	500	10	−	−	PROPN
ejpam-521	500	11	f	f	PROPN
ejpam-521	500	12	(	(	PUNCT
ejpam-521	500	13	·	·	PUNCT
ejpam-521	500	14	|q̃m))2	|q̃m))2	NUM
ejpam-521	500	15	f	f	X
ejpam-521	500	16	(	(	PUNCT
ejpam-521	500	17	·	·	PUNCT
ejpam-521	500	18	|q̃m	|q̃m	NUM
ejpam-521	500	19	)	)	PUNCT
ejpam-521	500	20	(	(	PUNCT
ejpam-521	500	21	99	99	NUM
ejpam-521	500	22	)	)	PUNCT
ejpam-521	500	23	now	now	ADV
ejpam-521	500	24	we	we	PRON
ejpam-521	500	25	apply	apply	VERB
ejpam-521	500	26	the	the	DET
ejpam-521	500	27	technique	technique	NOUN
ejpam-521	500	28	used	use	VERB
ejpam-521	500	29	in	in	ADP
ejpam-521	500	30	proposition	proposition	NOUN
ejpam-521	500	31	2.7	2.7	NUM
ejpam-521	500	32	of	of	ADP
ejpam-521	500	33	[	[	X
ejpam-521	500	34	6	6	NUM
ejpam-521	500	35	]	]	PUNCT
ejpam-521	500	36	to	to	PART
ejpam-521	500	37	prove	prove	VERB
ejpam-521	500	38	that	that	SCONJ
ejpam-521	500	39	m	m	VERB
ejpam-521	500	40	∑	∑	DET
ejpam-521	500	41	i=1	i=1	PROPN
ejpam-521	500	42	∫	∫	PROPN
ejpam-521	500	43	q̃i	q̃i	PROPN
ejpam-521	500	44	,	,	PUNCT
ejpam-521	500	45	m	m	PROPN
ejpam-521	500	46	(	(	PUNCT
ejpam-521	500	47	f	f	PROPN
ejpam-521	500	48	−	−	PROPN
ejpam-521	500	49	f	f	PROPN
ejpam-521	500	50	(	(	PUNCT
ejpam-521	500	51	·	·	PUNCT
ejpam-521	500	52	|q̃m))2	|q̃m))2	NUM
ejpam-521	500	53	f	f	X
ejpam-521	500	54	(	(	PUNCT
ejpam-521	500	55	·	·	PUNCT
ejpam-521	500	56	|q̃m	|q̃m	NUM
ejpam-521	500	57	)	)	PUNCT
ejpam-521	500	58	=	=	SYM
ejpam-521	501	1	1	1	NUM
ejpam-521	501	2	12	12	NUM
ejpam-521	501	3	m	m	NOUN
ejpam-521	501	4	∑	∑	PUNCT
ejpam-521	501	5	i=1	i=1	PROPN
ejpam-521	501	6	r̃2	r̃2	PROPN
ejpam-521	501	7	i	i	PROPN
ejpam-521	501	8	,	,	PUNCT
ejpam-521	501	9	m	m	VERB
ejpam-521	501	10	∫	∫	PROPN
ejpam-521	501	11	q̃i	q̃i	PROPN
ejpam-521	501	12	,	,	PUNCT
ejpam-521	501	13	m	m	VERB
ejpam-521	501	14	ḟ	ḟ	NOUN
ejpam-521	501	15	2	2	NUM
ejpam-521	501	16	f	f	NOUN
ejpam-521	501	17	+	+	CCONJ
ejpam-521	501	18	o(m−2α2	o(m−2α2	PROPN
ejpam-521	501	19	)	)	PUNCT
ejpam-521	501	20	.	.	PUNCT
ejpam-521	502	1	(	(	PUNCT
ejpam-521	502	2	100	100	NUM
ejpam-521	502	3	)	)	PUNCT
ejpam-521	502	4	the	the	DET
ejpam-521	502	5	lemma	lemma	PROPN
ejpam-521	502	6	would	would	AUX
ejpam-521	502	7	follow	follow	VERB
ejpam-521	502	8	from	from	ADP
ejpam-521	502	9	(	(	PUNCT
ejpam-521	502	10	100	100	NUM
ejpam-521	502	11	)	)	PUNCT
ejpam-521	502	12	and	and	CCONJ
ejpam-521	502	13	(	(	PUNCT
ejpam-521	502	14	99	99	NUM
ejpam-521	502	15	)	)	PUNCT
ejpam-521	502	16	.	.	PUNCT
ejpam-521	503	1	by	by	ADP
ejpam-521	503	2	denoting	denote	VERB
ejpam-521	503	3	z	z	NOUN
ejpam-521	503	4	=	=	PUNCT
ejpam-521	503	5	x	x	SYM
ejpam-521	503	6	−	−	NOUN
ejpam-521	503	7	f̃i−1,m	f̃i−1,m	NOUN
ejpam-521	503	8	we	we	PRON
ejpam-521	503	9	have	have	VERB
ejpam-521	503	10	∫	∫	PROPN
ejpam-521	503	11	q̃i	q̃i	PROPN
ejpam-521	503	12	,	,	PUNCT
ejpam-521	503	13	m	m	PROPN
ejpam-521	503	14	(	(	PUNCT
ejpam-521	503	15	f	f	X
ejpam-521	503	16	(	(	PUNCT
ejpam-521	503	17	x)−	x)−	PROPN
ejpam-521	503	18	f	f	PROPN
ejpam-521	503	19	(	(	PUNCT
ejpam-521	503	20	x	x	X
ejpam-521	503	21	|q̃m))2	|q̃m))2	NUM
ejpam-521	503	22	f	f	X
ejpam-521	503	23	(	(	PUNCT
ejpam-521	503	24	x	x	NOUN
ejpam-521	503	25	|q̃m	|q̃m	X
ejpam-521	503	26	)	)	PUNCT
ejpam-521	503	27	d	d	NOUN
ejpam-521	503	28	x	x	SYM
ejpam-521	503	29	=	=	SYM
ejpam-521	503	30	r̃i	r̃i	NOUN
ejpam-521	503	31	,	,	PUNCT
ejpam-521	503	32	m	m	VERB
ejpam-521	503	33	πi	πi	PROPN
ejpam-521	503	34	,	,	PUNCT
ejpam-521	503	35	m	m	PROPN
ejpam-521	503	36	∫	∫	PROPN
ejpam-521	503	37	r̃i	r̃i	PROPN
ejpam-521	503	38	,	,	PUNCT
ejpam-521	503	39	m	m	PROPN
ejpam-521	503	40	0	0	NUM
ejpam-521	504	1	[	[	PUNCT
ejpam-521	504	2	f	f	X
ejpam-521	504	3	(	(	PUNCT
ejpam-521	504	4	z	z	NOUN
ejpam-521	504	5	+	+	CCONJ
ejpam-521	504	6	q̃i−1)−	q̃i−1)−	PROPN
ejpam-521	504	7	f	f	X
ejpam-521	504	8	(	(	PUNCT
ejpam-521	504	9	z	z	NOUN
ejpam-521	504	10	+	+	CCONJ
ejpam-521	504	11	q̃i−1|q̃m)]2dz	q̃i−1|q̃m)]2dz	ADJ
ejpam-521	504	12	=	=	NOUN
ejpam-521	504	13	r̃i	r̃i	NOUN
ejpam-521	504	14	,	,	PUNCT
ejpam-521	504	15	m	m	VERB
ejpam-521	504	16	πi	πi	PROPN
ejpam-521	504	17	,	,	PUNCT
ejpam-521	504	18	m	m	PROPN
ejpam-521	504	19	∫	∫	PROPN
ejpam-521	504	20	r̃i	r̃i	PROPN
ejpam-521	504	21	,	,	PUNCT
ejpam-521	504	22	m	m	PROPN
ejpam-521	504	23	0	0	NUM
ejpam-521	504	24			PROPN
ejpam-521	504	25			X
ejpam-521	504	26	∫	∫	PROPN
ejpam-521	504	27	z	z	NOUN
ejpam-521	504	28	0	0	NUM
ejpam-521	504	29	ḟ	ḟ	NOUN
ejpam-521	504	30	(	(	PUNCT
ejpam-521	504	31	y	y	PROPN
ejpam-521	504	32	+	+	PROPN
ejpam-521	505	1	q̃i−1,m)d	q̃i−1,m)d	PROPN
ejpam-521	505	2	y	y	PROPN
ejpam-521	505	3	−	−	PROPN
ejpam-521	505	4	1	1	NUM
ejpam-521	505	5	r̃i	r̃i	NOUN
ejpam-521	505	6	,	,	PUNCT
ejpam-521	505	7	m	m	NOUN
ejpam-521	505	8	∫	∫	PROPN
ejpam-521	505	9	r̃i	r̃i	PROPN
ejpam-521	505	10	,	,	PUNCT
ejpam-521	505	11	m	m	PROPN
ejpam-521	505	12	0	0	NUM
ejpam-521	505	13	(	(	PUNCT
ejpam-521	505	14	r̃i	r̃i	PROPN
ejpam-521	505	15	,	,	PUNCT
ejpam-521	505	16	m−	m−	PROPN
ejpam-521	505	17	y	y	NOUN
ejpam-521	505	18	)	)	PUNCT
ejpam-521	505	19	ḟ	ḟ	NOUN
ejpam-521	505	20	(	(	PUNCT
ejpam-521	505	21	y	y	PROPN
ejpam-521	505	22	+	+	PROPN
ejpam-521	505	23	q̃i−1,m)d	q̃i−1,m)d	PROPN
ejpam-521	505	24	y	y	PROPN
ejpam-521	505	25			PROPN
ejpam-521	505	26			PROPN
ejpam-521	505	27	2	2	NUM
ejpam-521	505	28	dz	dz	NOUN
ejpam-521	505	29	=	=	PUNCT
ejpam-521	505	30	r̃i	r̃i	NOUN
ejpam-521	505	31	,	,	PUNCT
ejpam-521	505	32	m	m	VERB
ejpam-521	505	33	πi	πi	PROPN
ejpam-521	505	34	,	,	PUNCT
ejpam-521	505	35	m	m	PROPN
ejpam-521	505	36	∫	∫	PROPN
ejpam-521	505	37	r̃i	r̃i	PROPN
ejpam-521	505	38	,	,	PUNCT
ejpam-521	505	39	m	m	PROPN
ejpam-521	505	40	0	0	NUM
ejpam-521	505	41	�	�	PROPN
ejpam-521	505	42	∫	∫	PROPN
ejpam-521	506	1	z	z	PROPN
ejpam-521	506	2	0	0	NUM
ejpam-521	506	3	ḟ	ḟ	NOUN
ejpam-521	506	4	(	(	PUNCT
ejpam-521	506	5	y	y	PROPN
ejpam-521	506	6	+	+	PROPN
ejpam-521	506	7	q̃i−1,m)d	q̃i−1,m)d	PROPN
ejpam-521	506	8	y	y	PROPN
ejpam-521	506	9	�	�	PROPN
ejpam-521	506	10	2	2	NUM
ejpam-521	506	11	dz	dz	NOUN
ejpam-521	506	12	−	−	PROPN
ejpam-521	506	13	1	1	NUM
ejpam-521	506	14	πi	πi	PROPN
ejpam-521	506	15	,	,	PUNCT
ejpam-521	506	16	m	m	VERB
ejpam-521	506	17			PROPN
ejpam-521	506	18			NUM
ejpam-521	506	19	∫	∫	PROPN
ejpam-521	507	1	r̃i	r̃i	PROPN
ejpam-521	507	2	,	,	PUNCT
ejpam-521	507	3	m	m	PROPN
ejpam-521	507	4	0	0	NUM
ejpam-521	507	5	(	(	PUNCT
ejpam-521	507	6	r̃i	r̃i	PROPN
ejpam-521	507	7	,	,	PUNCT
ejpam-521	507	8	m−	m−	PROPN
ejpam-521	507	9	y	y	NOUN
ejpam-521	507	10	)	)	PUNCT
ejpam-521	507	11	ḟ	ḟ	NOUN
ejpam-521	507	12	(	(	PUNCT
ejpam-521	507	13	y	y	PROPN
ejpam-521	507	14	+	+	PROPN
ejpam-521	507	15	q̃i−1,m)d	q̃i−1,m)d	PROPN
ejpam-521	507	16	y	y	PROPN
ejpam-521	507	17			PROPN
ejpam-521	507	18			PROPN
ejpam-521	507	19	2	2	NUM
ejpam-521	507	20	=	=	SYM
ejpam-521	507	21	r̃i	r̃i	NOUN
ejpam-521	507	22	,	,	PUNCT
ejpam-521	507	23	m	m	VERB
ejpam-521	507	24	πi	πi	PROPN
ejpam-521	507	25	,	,	PUNCT
ejpam-521	507	26	m	m	PROPN
ejpam-521	507	27	∫	∫	PROPN
ejpam-521	507	28	r̃i	r̃i	PROPN
ejpam-521	507	29	,	,	PUNCT
ejpam-521	507	30	m	m	PROPN
ejpam-521	507	31	0	0	NUM
ejpam-521	507	32	∫	∫	PROPN
ejpam-521	507	33	z	z	PROPN
ejpam-521	507	34	0	0	NUM
ejpam-521	508	1	∫	∫	PROPN
ejpam-521	508	2	z	z	NOUN
ejpam-521	508	3	0	0	NUM
ejpam-521	509	1	ḟ	ḟ	NOUN
ejpam-521	509	2	(	(	PUNCT
ejpam-521	509	3	u+	u+	NUM
ejpam-521	509	4	q̃i−1,m	q̃i−1,m	NUM
ejpam-521	509	5	)	)	PUNCT
ejpam-521	509	6	ḟ	ḟ	NOUN
ejpam-521	509	7	(	(	PUNCT
ejpam-521	509	8	v+	v+	X
ejpam-521	509	9	q̃i−1,m)dudvdz	q̃i−1,m)dudvdz	ADP
ejpam-521	509	10	g.	g.	PROPN
ejpam-521	509	11	qian	qian	PROPN
ejpam-521	509	12	/	/	SYM
ejpam-521	509	13	eur	eur	PROPN
ejpam-521	509	14	.	.	PUNCT
ejpam-521	510	1	j.	j.	PROPN
ejpam-521	510	2	pure	pure	PROPN
ejpam-521	510	3	appl	appl	PROPN
ejpam-521	510	4	.	.	PROPN
ejpam-521	510	5	math	math	PROPN
ejpam-521	510	6	,	,	PUNCT
ejpam-521	510	7	3	3	NUM
ejpam-521	510	8	(	(	PUNCT
ejpam-521	510	9	2010	2010	NUM
ejpam-521	510	10	)	)	PUNCT
ejpam-521	510	11	,	,	PUNCT
ejpam-521	510	12	51	51	NUM
ejpam-521	510	13	-	-	SYM
ejpam-521	510	14	80	80	NUM
ejpam-521	510	15	74	74	NUM
ejpam-521	510	16	−	−	NUM
ejpam-521	510	17	1	1	NUM
ejpam-521	510	18	πi	πi	PROPN
ejpam-521	510	19	,	,	PUNCT
ejpam-521	510	20	m	m	PROPN
ejpam-521	510	21	∫	∫	PROPN
ejpam-521	510	22	r̃i	r̃i	PROPN
ejpam-521	510	23	,	,	PUNCT
ejpam-521	510	24	m	m	PROPN
ejpam-521	510	25	0	0	NUM
ejpam-521	510	26	∫	∫	PROPN
ejpam-521	510	27	r̃i	r̃i	PROPN
ejpam-521	510	28	,	,	PUNCT
ejpam-521	510	29	m	m	PROPN
ejpam-521	510	30	0	0	NUM
ejpam-521	510	31	(	(	PUNCT
ejpam-521	510	32	r̃i	r̃i	NOUN
ejpam-521	510	33	,	,	PUNCT
ejpam-521	510	34	m−	m−	PROPN
ejpam-521	510	35	u)(r̃i	u)(r̃i	PROPN
ejpam-521	510	36	,	,	PUNCT
ejpam-521	510	37	m−	m−	PROPN
ejpam-521	510	38	v	v	NOUN
ejpam-521	510	39	)	)	PUNCT
ejpam-521	510	40	ḟ	ḟ	NOUN
ejpam-521	510	41	(	(	PUNCT
ejpam-521	510	42	u+	u+	NUM
ejpam-521	510	43	q̃i−1,m	q̃i−1,m	NUM
ejpam-521	510	44	)	)	PUNCT
ejpam-521	510	45	ḟ	ḟ	NOUN
ejpam-521	510	46	(	(	PUNCT
ejpam-521	510	47	v+	v+	X
ejpam-521	510	48	q̃i−1,m)dudv	q̃i−1,m)dudv	X
ejpam-521	510	49	=	=	NOUN
ejpam-521	510	50	r̃i	r̃i	NOUN
ejpam-521	510	51	,	,	PUNCT
ejpam-521	510	52	m	m	VERB
ejpam-521	510	53	πi	πi	PROPN
ejpam-521	510	54	,	,	PUNCT
ejpam-521	510	55	m	m	PROPN
ejpam-521	510	56	∫	∫	PROPN
ejpam-521	510	57	r̃i	r̃i	PROPN
ejpam-521	510	58	,	,	PUNCT
ejpam-521	510	59	m	m	PROPN
ejpam-521	510	60	0	0	NUM
ejpam-521	510	61	∫	∫	PROPN
ejpam-521	510	62	r̃i	r̃i	PROPN
ejpam-521	510	63	,	,	PUNCT
ejpam-521	510	64	m	m	PROPN
ejpam-521	510	65	0	0	NUM
ejpam-521	510	66	(	(	PUNCT
ejpam-521	510	67	r̃i	r̃i	NOUN
ejpam-521	510	68	,	,	PUNCT
ejpam-521	510	69	m−	m−	PROPN
ejpam-521	510	70	u∨	u∨	PROPN
ejpam-521	510	71	v	v	NOUN
ejpam-521	510	72	)	)	PUNCT
ejpam-521	510	73	ḟ	ḟ	NOUN
ejpam-521	510	74	(	(	PUNCT
ejpam-521	510	75	u+	u+	NUM
ejpam-521	510	76	q̃i−1,m	q̃i−1,m	NUM
ejpam-521	510	77	)	)	PUNCT
ejpam-521	510	78	ḟ	ḟ	NOUN
ejpam-521	510	79	(	(	PUNCT
ejpam-521	510	80	v+	v+	X
ejpam-521	510	81	q̃i−1,m)dudv	q̃i−1,m)dudv	X
ejpam-521	511	1	−	−	PROPN
ejpam-521	511	2	1	1	NUM
ejpam-521	511	3	πi	πi	PROPN
ejpam-521	511	4	,	,	PUNCT
ejpam-521	511	5	m	m	PROPN
ejpam-521	511	6	∫	∫	PROPN
ejpam-521	511	7	r̃i	r̃i	PROPN
ejpam-521	511	8	,	,	PUNCT
ejpam-521	511	9	m	m	PROPN
ejpam-521	511	10	0	0	NUM
ejpam-521	511	11	∫	∫	PROPN
ejpam-521	511	12	r̃i	r̃i	PROPN
ejpam-521	511	13	,	,	PUNCT
ejpam-521	511	14	m	m	PROPN
ejpam-521	511	15	0	0	NUM
ejpam-521	511	16	(	(	PUNCT
ejpam-521	511	17	r̃i	r̃i	NOUN
ejpam-521	511	18	,	,	PUNCT
ejpam-521	511	19	m−	m−	PROPN
ejpam-521	511	20	u)(r̃i	u)(r̃i	PROPN
ejpam-521	511	21	,	,	PUNCT
ejpam-521	511	22	m−	m−	PROPN
ejpam-521	511	23	v	v	NOUN
ejpam-521	511	24	)	)	PUNCT
ejpam-521	511	25	ḟ	ḟ	NOUN
ejpam-521	511	26	(	(	PUNCT
ejpam-521	511	27	u+	u+	NUM
ejpam-521	511	28	q̃i−1,m	q̃i−1,m	NUM
ejpam-521	511	29	)	)	PUNCT
ejpam-521	511	30	ḟ	ḟ	NOUN
ejpam-521	511	31	(	(	PUNCT
ejpam-521	511	32	v+	v+	X
ejpam-521	511	33	q̃i−1,m)dudv	q̃i−1,m)dudv	X
ejpam-521	511	34	=	=	NOUN
ejpam-521	511	35	r̃i	r̃i	NOUN
ejpam-521	511	36	,	,	PUNCT
ejpam-521	511	37	m	m	VERB
ejpam-521	511	38	πi	πi	PROPN
ejpam-521	511	39	,	,	PUNCT
ejpam-521	511	40	m	m	PROPN
ejpam-521	511	41	∫	∫	PROPN
ejpam-521	511	42	r̃i	r̃i	PROPN
ejpam-521	511	43	,	,	PUNCT
ejpam-521	511	44	m	m	PROPN
ejpam-521	511	45	0	0	NUM
ejpam-521	511	46	∫	∫	PROPN
ejpam-521	511	47	r̃i	r̃i	PROPN
ejpam-521	511	48	,	,	PUNCT
ejpam-521	511	49	m	m	PROPN
ejpam-521	511	50	0	0	NUM
ejpam-521	511	51	(	(	PUNCT
ejpam-521	511	52	u∧	u∧	PROPN
ejpam-521	511	53	v−	v−	NOUN
ejpam-521	511	54	1	1	NUM
ejpam-521	511	55	r̃i	r̃i	NOUN
ejpam-521	511	56	,	,	PUNCT
ejpam-521	511	57	m	m	VERB
ejpam-521	511	58	uv	uv	NOUN
ejpam-521	511	59	)	)	PUNCT
ejpam-521	511	60	ḟ	ḟ	NOUN
ejpam-521	511	61	(	(	PUNCT
ejpam-521	511	62	u+	u+	NUM
ejpam-521	511	63	q̃i−1,m	q̃i−1,m	NUM
ejpam-521	511	64	)	)	PUNCT
ejpam-521	511	65	ḟ	ḟ	NOUN
ejpam-521	511	66	(	(	PUNCT
ejpam-521	511	67	v+	v+	X
ejpam-521	511	68	q̃i−1,m)dudv	q̃i−1,m)dudv	X
ejpam-521	511	69	(	(	PUNCT
ejpam-521	511	70	101	101	NUM
ejpam-521	511	71	)	)	PUNCT
ejpam-521	511	72	where	where	SCONJ
ejpam-521	511	73	u∨	u∨	NOUN
ejpam-521	511	74	v	v	NOUN
ejpam-521	511	75	=	=	SYM
ejpam-521	511	76	max(u	max(u	PROPN
ejpam-521	511	77	,	,	PUNCT
ejpam-521	511	78	v	v	NOUN
ejpam-521	511	79	)	)	PUNCT
ejpam-521	511	80	and	and	CCONJ
ejpam-521	511	81	u∧	u∧	PROPN
ejpam-521	511	82	v	v	X
ejpam-521	511	83	=	=	SYM
ejpam-521	511	84	min(u	min(u	NOUN
ejpam-521	511	85	,	,	PUNCT
ejpam-521	511	86	v	v	NOUN
ejpam-521	511	87	)	)	PUNCT
ejpam-521	511	88	.	.	PUNCT
ejpam-521	512	1	direct	direct	ADJ
ejpam-521	512	2	computation	computation	NOUN
ejpam-521	512	3	shows	show	VERB
ejpam-521	512	4	that	that	SCONJ
ejpam-521	512	5	∫	∫	PROPN
ejpam-521	512	6	r̃i	r̃i	PROPN
ejpam-521	512	7	,	,	PUNCT
ejpam-521	512	8	m	m	PROPN
ejpam-521	512	9	0	0	NUM
ejpam-521	512	10	∫	∫	PROPN
ejpam-521	512	11	r̃i	r̃i	PROPN
ejpam-521	512	12	,	,	PUNCT
ejpam-521	512	13	m	m	PROPN
ejpam-521	512	14	0	0	NUM
ejpam-521	512	15	(	(	PUNCT
ejpam-521	512	16	u∧	u∧	PROPN
ejpam-521	512	17	v	v	ADP
ejpam-521	512	18	−	−	PROPN
ejpam-521	512	19	1	1	NUM
ejpam-521	512	20	r̃i	r̃i	NOUN
ejpam-521	512	21	,	,	PUNCT
ejpam-521	512	22	m	m	NOUN
ejpam-521	512	23	uv)dudv	uv)dudv	ADJ
ejpam-521	512	24	=	=	NOUN
ejpam-521	512	25	1	1	NUM
ejpam-521	512	26	12	12	NUM
ejpam-521	512	27	r̃3	r̃3	PROPN
ejpam-521	512	28	i	i	PRON
ejpam-521	512	29	,	,	PUNCT
ejpam-521	512	30	m.	m.	NOUN
ejpam-521	512	31	(	(	PUNCT
ejpam-521	512	32	102	102	NUM
ejpam-521	512	33	)	)	PUNCT
ejpam-521	512	34	define	define	VERB
ejpam-521	512	35	¯̇	¯̇	PROPN
ejpam-521	512	36	fi	fi	NOUN
ejpam-521	512	37	,	,	PUNCT
ejpam-521	512	38	m	m	NOUN
ejpam-521	512	39	=	=	NOUN
ejpam-521	512	40	1	1	NUM
ejpam-521	512	41	r̃i	r̃i	NOUN
ejpam-521	512	42	,	,	PUNCT
ejpam-521	512	43	m	m	NOUN
ejpam-521	512	44	∫	∫	PROPN
ejpam-521	512	45	r̃i	r̃i	PROPN
ejpam-521	512	46	,	,	PUNCT
ejpam-521	512	47	m	m	PROPN
ejpam-521	512	48	0	0	NUM
ejpam-521	512	49	ḟ	ḟ	NOUN
ejpam-521	512	50	(	(	PUNCT
ejpam-521	512	51	u+	u+	NUM
ejpam-521	512	52	q̃i−1,m)du	q̃i−1,m)du	NOUN
ejpam-521	512	53	.	.	PUNCT
ejpam-521	513	1	by	by	ADP
ejpam-521	513	2	(	(	PUNCT
ejpam-521	513	3	101	101	NUM
ejpam-521	513	4	)	)	PUNCT
ejpam-521	513	5	m	m	VERB
ejpam-521	513	6	∑	∑	PROPN
ejpam-521	513	7	i=1	i=1	PROPN
ejpam-521	513	8	∫	∫	PROPN
ejpam-521	513	9	q̃i	q̃i	PROPN
ejpam-521	513	10	,	,	PUNCT
ejpam-521	513	11	m	m	PROPN
ejpam-521	513	12	(	(	PUNCT
ejpam-521	513	13	f	f	PROPN
ejpam-521	513	14	−	−	PROPN
ejpam-521	513	15	f	f	PROPN
ejpam-521	513	16	(	(	PUNCT
ejpam-521	513	17	·	·	PUNCT
ejpam-521	513	18	|q̃m))2	|q̃m))2	NUM
ejpam-521	513	19	f	f	X
ejpam-521	513	20	(	(	PUNCT
ejpam-521	513	21	·	·	PUNCT
ejpam-521	513	22	|q̃m	|q̃m	NUM
ejpam-521	513	23	)	)	PUNCT
ejpam-521	513	24	=	=	PUNCT
ejpam-521	513	25	m	m	VERB
ejpam-521	513	26	∑	∑	PROPN
ejpam-521	513	27	i=1	i=1	PUNCT
ejpam-521	513	28	r̃i	r̃i	NOUN
ejpam-521	513	29	,	,	PUNCT
ejpam-521	513	30	m	m	VERB
ejpam-521	513	31	πi	πi	PROPN
ejpam-521	513	32	,	,	PUNCT
ejpam-521	513	33	m	m	PROPN
ejpam-521	513	34	∫	∫	PROPN
ejpam-521	513	35	r̃i	r̃i	PROPN
ejpam-521	513	36	,	,	PUNCT
ejpam-521	513	37	m	m	PROPN
ejpam-521	513	38	0	0	NUM
ejpam-521	513	39	∫	∫	PROPN
ejpam-521	513	40	r̃i	r̃i	PROPN
ejpam-521	513	41	,	,	PUNCT
ejpam-521	513	42	m	m	PROPN
ejpam-521	513	43	0	0	NUM
ejpam-521	513	44	(	(	PUNCT
ejpam-521	513	45	u∧	u∧	PROPN
ejpam-521	513	46	v−	v−	NOUN
ejpam-521	513	47	1	1	NUM
ejpam-521	513	48	r̃i	r̃i	NOUN
ejpam-521	513	49	,	,	PUNCT
ejpam-521	513	50	m	m	VERB
ejpam-521	513	51	uv	uv	NOUN
ejpam-521	513	52	)	)	PUNCT
ejpam-521	513	53	[	[	PUNCT
ejpam-521	513	54	ḟ	ḟ	NOUN
ejpam-521	513	55	(	(	PUNCT
ejpam-521	513	56	u+	u+	NUM
ejpam-521	513	57	q̃i−1,m	q̃i−1,m	NUM
ejpam-521	513	58	)	)	PUNCT
ejpam-521	513	59	ḟ	ḟ	NOUN
ejpam-521	513	60	(	(	PUNCT
ejpam-521	513	61	v+	v+	X
ejpam-521	513	62	q̃i−1,m)−	q̃i−1,m)−	PROPN
ejpam-521	513	63	¯̇f	¯̇f	PROPN
ejpam-521	513	64	2	2	NUM
ejpam-521	513	65	i	i	NOUN
ejpam-521	513	66	,	,	PUNCT
ejpam-521	513	67	m]dudv	m]dudv	PROPN
ejpam-521	513	68	+	+	X
ejpam-521	513	69	m	m	VERB
ejpam-521	513	70	∑	∑	ADJ
ejpam-521	513	71	i=1	i=1	PROPN
ejpam-521	513	72	r̃3	r̃3	PROPN
ejpam-521	513	73	i	i	PRON
ejpam-521	513	74	,	,	PUNCT
ejpam-521	513	75	m	m	VERB
ejpam-521	513	76	12πi	12πi	ADJ
ejpam-521	513	77	,	,	PUNCT
ejpam-521	513	78	m	m	NOUN
ejpam-521	513	79	∫	∫	PROPN
ejpam-521	513	80	r̃i	r̃i	PROPN
ejpam-521	513	81	,	,	PUNCT
ejpam-521	513	82	m	m	PROPN
ejpam-521	513	83	0	0	NUM
ejpam-521	513	84	[	[	PUNCT
ejpam-521	513	85	¯̇f	¯̇f	PROPN
ejpam-521	513	86	2	2	NUM
ejpam-521	513	87	i	i	PROPN
ejpam-521	513	88	,	,	PUNCT
ejpam-521	513	89	m−	m−	PROPN
ejpam-521	513	90	ḟ	ḟ	VERB
ejpam-521	513	91	2(u+	2(u+	PROPN
ejpam-521	513	92	q̃i−1,m)]du	q̃i−1,m)]du	VERB
ejpam-521	513	93	+	+	NUM
ejpam-521	513	94	m	m	VERB
ejpam-521	513	95	∑	∑	ADJ
ejpam-521	513	96	i=1	i=1	PROPN
ejpam-521	513	97	r̃2	r̃2	PROPN
ejpam-521	513	98	i	i	PROPN
ejpam-521	513	99	,	,	PUNCT
ejpam-521	513	100	m	m	VERB
ejpam-521	513	101	12	12	NUM
ejpam-521	513	102	∫	∫	NOUN
ejpam-521	513	103	r̃i	r̃i	NOUN
ejpam-521	513	104	,	,	PUNCT
ejpam-521	513	105	m	m	PROPN
ejpam-521	513	106	0	0	NUM
ejpam-521	513	107	r̃i	r̃i	NOUN
ejpam-521	513	108	,	,	PUNCT
ejpam-521	513	109	m	m	VERB
ejpam-521	513	110	ḟ	ḟ	VERB
ejpam-521	513	111	2(u+	2(u+	NUM
ejpam-521	513	112	q̃i−1,m	q̃i−1,m	NUM
ejpam-521	513	113	)	)	PUNCT
ejpam-521	513	114	πi	πi	ADP
ejpam-521	513	115	,	,	PUNCT
ejpam-521	513	116	m	m	VERB
ejpam-521	513	117	−	−	NOUN
ejpam-521	513	118	ḟ	ḟ	NOUN
ejpam-521	513	119	2(u+	2(u+	PROPN
ejpam-521	513	120	q̃i−1,m	q̃i−1,m	NUM
ejpam-521	513	121	)	)	PUNCT
ejpam-521	513	122	f	f	PROPN
ejpam-521	513	123	(	(	PUNCT
ejpam-521	513	124	u+	u+	NUM
ejpam-521	513	125	q̃i−1,m	q̃i−1,m	PROPN
ejpam-521	513	126	)	)	PUNCT
ejpam-521	513	127	!	!	PUNCT
ejpam-521	513	128	du	du	PROPN
ejpam-521	514	1	+	+	CCONJ
ejpam-521	514	2	1	1	NUM
ejpam-521	514	3	12	12	NUM
ejpam-521	514	4	m	m	NOUN
ejpam-521	514	5	∑	∑	PUNCT
ejpam-521	514	6	i=1	i=1	PROPN
ejpam-521	514	7	r̃2	r̃2	PROPN
ejpam-521	514	8	i	i	PROPN
ejpam-521	514	9	,	,	PUNCT
ejpam-521	514	10	m	m	VERB
ejpam-521	514	11	∫	∫	PROPN
ejpam-521	514	12	q̃i	q̃i	PROPN
ejpam-521	514	13	,	,	PUNCT
ejpam-521	514	14	m	m	VERB
ejpam-521	514	15	ḟ	ḟ	NOUN
ejpam-521	514	16	2(x	2(x	NUM
ejpam-521	514	17	)	)	PUNCT
ejpam-521	514	18	f	f	NOUN
ejpam-521	514	19	(	(	PUNCT
ejpam-521	514	20	x	x	X
ejpam-521	514	21	)	)	PUNCT
ejpam-521	514	22	d	d	NOUN
ejpam-521	514	23	x	x	X
ejpam-521	514	24	.	.	PUNCT
ejpam-521	515	1	(	(	PUNCT
ejpam-521	515	2	103	103	NUM
ejpam-521	515	3	)	)	PUNCT
ejpam-521	515	4	note	note	NOUN
ejpam-521	515	5	that	that	SCONJ
ejpam-521	515	6	|u∧	|u∧	ADJ
ejpam-521	515	7	v−	v−	NOUN
ejpam-521	515	8	1	1	NUM
ejpam-521	515	9	r̃i	r̃i	NOUN
ejpam-521	515	10	,	,	PUNCT
ejpam-521	515	11	m	m	VERB
ejpam-521	515	12	uv|	uv|	ADJ
ejpam-521	515	13	≤	≤	NUM
ejpam-521	515	14	r̃i	r̃i	NOUN
ejpam-521	515	15	,	,	PUNCT
ejpam-521	515	16	m	m	PRON
ejpam-521	515	17	and	and	CCONJ
ejpam-521	515	18	|	|	ADV
ejpam-521	515	19	ḟ	ḟ	NOUN
ejpam-521	515	20	(	(	PUNCT
ejpam-521	515	21	u+	u+	NUM
ejpam-521	515	22	q̃i−1,m	q̃i−1,m	NUM
ejpam-521	515	23	)	)	PUNCT
ejpam-521	515	24	ḟ	ḟ	NOUN
ejpam-521	515	25	(	(	PUNCT
ejpam-521	515	26	v	v	NOUN
ejpam-521	515	27	+	+	CCONJ
ejpam-521	515	28	q̃i−1,m)−	q̃i−1,m)−	PROPN
ejpam-521	515	29	¯̇	¯̇	PROPN
ejpam-521	516	1	f	f	PROPN
ejpam-521	516	2	2	2	NUM
ejpam-521	516	3	i	i	NOUN
ejpam-521	516	4	,	,	PUNCT
ejpam-521	516	5	m|	m|	NOUN
ejpam-521	516	6	≤	≤	NOUN
ejpam-521	516	7	|	|	ADV
ejpam-521	516	8	ḟ	ḟ	NOUN
ejpam-521	516	9	(	(	PUNCT
ejpam-521	516	10	u+	u+	NUM
ejpam-521	516	11	q̃i−1,m)−	q̃i−1,m)−	PROPN
ejpam-521	516	12	¯̇	¯̇	PROPN
ejpam-521	516	13	fi	fi	NOUN
ejpam-521	516	14	,	,	PUNCT
ejpam-521	516	15	m||	m||	VERB
ejpam-521	516	16	ḟ	ḟ	NOUN
ejpam-521	516	17	(	(	PUNCT
ejpam-521	516	18	v	v	NOUN
ejpam-521	516	19	+	+	CCONJ
ejpam-521	516	20	q̃i−1,m)|+	q̃i−1,m)|+	NOUN
ejpam-521	516	21	|	|	ADV
ejpam-521	516	22	ḟ	ḟ	NOUN
ejpam-521	516	23	(	(	PUNCT
ejpam-521	516	24	v	v	NOUN
ejpam-521	516	25	+	+	CCONJ
ejpam-521	516	26	q̃i−1,m)−	q̃i−1,m)−	PROPN
ejpam-521	516	27	¯̇	¯̇	PROPN
ejpam-521	516	28	fi	fi	NOUN
ejpam-521	516	29	,	,	PUNCT
ejpam-521	516	30	m||	m||	PROPN
ejpam-521	516	31	¯̇fi	¯̇fi	PROPN
ejpam-521	516	32	,	,	PUNCT
ejpam-521	516	33	m|	m|	PROPN
ejpam-521	516	34	,	,	PUNCT
ejpam-521	516	35	hence	hence	ADV
ejpam-521	516	36	�	�	PROPN
ejpam-521	516	37	�	�	PROPN
ejpam-521	516	38	�	�	PROPN
ejpam-521	516	39	�	�	PROPN
ejpam-521	516	40	�	�	PROPN
ejpam-521	516	41	m	m	PROPN
ejpam-521	516	42	∑	∑	PROPN
ejpam-521	516	43	i=1	i=1	PROPN
ejpam-521	516	44	r̃i	r̃i	NOUN
ejpam-521	516	45	,	,	PUNCT
ejpam-521	516	46	m	m	VERB
ejpam-521	516	47	πi	πi	PROPN
ejpam-521	516	48	,	,	PUNCT
ejpam-521	516	49	m	m	PROPN
ejpam-521	516	50	∫	∫	PROPN
ejpam-521	516	51	r̃i	r̃i	PROPN
ejpam-521	516	52	,	,	PUNCT
ejpam-521	516	53	m	m	PROPN
ejpam-521	516	54	0	0	NUM
ejpam-521	516	55	∫	∫	PROPN
ejpam-521	516	56	r̃i	r̃i	PROPN
ejpam-521	516	57	,	,	PUNCT
ejpam-521	516	58	m	m	PROPN
ejpam-521	516	59	0	0	NUM
ejpam-521	516	60	(	(	PUNCT
ejpam-521	516	61	u∧	u∧	PROPN
ejpam-521	516	62	v	v	ADP
ejpam-521	516	63	−	−	PROPN
ejpam-521	516	64	1	1	NUM
ejpam-521	516	65	r̃i	r̃i	NOUN
ejpam-521	516	66	,	,	PUNCT
ejpam-521	516	67	m	m	VERB
ejpam-521	516	68	uv	uv	NOUN
ejpam-521	516	69	)	)	PUNCT
ejpam-521	516	70	[	[	PUNCT
ejpam-521	516	71	ḟ	ḟ	NOUN
ejpam-521	516	72	(	(	PUNCT
ejpam-521	516	73	u+	u+	NUM
ejpam-521	516	74	q̃i−1,m	q̃i−1,m	NUM
ejpam-521	516	75	)	)	PUNCT
ejpam-521	516	76	ḟ	ḟ	NOUN
ejpam-521	516	77	(	(	PUNCT
ejpam-521	516	78	v	v	NOUN
ejpam-521	516	79	+	+	CCONJ
ejpam-521	516	80	q̃i−1,m)−	q̃i−1,m)−	PROPN
ejpam-521	516	81	¯̇f	¯̇f	PROPN
ejpam-521	516	82	2	2	NUM
ejpam-521	516	83	i	i	NOUN
ejpam-521	516	84	,	,	PUNCT
ejpam-521	516	85	m]dudv	m]dudv	PROPN
ejpam-521	516	86	�	�	PROPN
ejpam-521	516	87	�	�	PROPN
ejpam-521	516	88	�	�	PROPN
ejpam-521	516	89	�	�	PROPN
ejpam-521	516	90	�	�	PROPN
ejpam-521	516	91	≤	≤	PROPN
ejpam-521	516	92	c−1	c−1	PROPN
ejpam-521	516	93	1	1	NUM
ejpam-521	516	94	m	m	NOUN
ejpam-521	516	95	∑	∑	PROPN
ejpam-521	516	96	i=1	i=1	PROPN
ejpam-521	516	97	r̃i	r̃i	NOUN
ejpam-521	516	98	,	,	PUNCT
ejpam-521	516	99	m	m	PROPN
ejpam-521	516	100	∫	∫	PROPN
ejpam-521	516	101	r̃i	r̃i	PROPN
ejpam-521	516	102	,	,	PUNCT
ejpam-521	516	103	m	m	PROPN
ejpam-521	516	104	0	0	NUM
ejpam-521	516	105	|	|	ADV
ejpam-521	516	106	ḟ	ḟ	NOUN
ejpam-521	516	107	(	(	PUNCT
ejpam-521	516	108	u+	u+	NUM
ejpam-521	516	109	q̃i−1,m)−	q̃i−1,m)−	PROPN
ejpam-521	516	110	¯̇	¯̇	PROPN
ejpam-521	516	111	fi	fi	NOUN
ejpam-521	516	112	,	,	PUNCT
ejpam-521	516	113	m|	m|	NOUN
ejpam-521	516	114	∫	∫	PROPN
ejpam-521	516	115	r̃i	r̃i	PROPN
ejpam-521	516	116	,	,	PUNCT
ejpam-521	516	117	m	m	PROPN
ejpam-521	516	118	0	0	NUM
ejpam-521	516	119	|	|	ADV
ejpam-521	516	120	ḟ	ḟ	NOUN
ejpam-521	516	121	(	(	PUNCT
ejpam-521	516	122	v+	v+	X
ejpam-521	516	123	q̃i−1,m)|	q̃i−1,m)|	NOUN
ejpam-521	516	124	g.	g.	PROPN
ejpam-521	516	125	qian	qian	PROPN
ejpam-521	516	126	/	/	SYM
ejpam-521	516	127	eur	eur	PROPN
ejpam-521	516	128	.	.	PUNCT
ejpam-521	517	1	j.	j.	PROPN
ejpam-521	517	2	pure	pure	PROPN
ejpam-521	517	3	appl	appl	PROPN
ejpam-521	517	4	.	.	PROPN
ejpam-521	517	5	math	math	PROPN
ejpam-521	517	6	,	,	PUNCT
ejpam-521	517	7	3	3	NUM
ejpam-521	517	8	(	(	PUNCT
ejpam-521	517	9	2010	2010	NUM
ejpam-521	517	10	)	)	PUNCT
ejpam-521	517	11	,	,	PUNCT
ejpam-521	517	12	51	51	NUM
ejpam-521	517	13	-	-	SYM
ejpam-521	517	14	80	80	NUM
ejpam-521	517	15	75	75	NUM
ejpam-521	518	1	+	+	NOUN
ejpam-521	518	2	c−1	c−1	PROPN
ejpam-521	518	3	1	1	NUM
ejpam-521	518	4	m	m	NOUN
ejpam-521	518	5	∑	∑	PROPN
ejpam-521	518	6	i=1	i=1	PROPN
ejpam-521	518	7	r̃i	r̃i	NOUN
ejpam-521	518	8	,	,	PUNCT
ejpam-521	518	9	m	m	PROPN
ejpam-521	518	10	∫	∫	PROPN
ejpam-521	518	11	r̃i	r̃i	PROPN
ejpam-521	518	12	,	,	PUNCT
ejpam-521	518	13	m	m	PROPN
ejpam-521	518	14	0	0	NUM
ejpam-521	519	1	|	|	ADV
ejpam-521	519	2	ḟ	ḟ	NOUN
ejpam-521	519	3	(	(	PUNCT
ejpam-521	519	4	v	v	NOUN
ejpam-521	519	5	+	+	CCONJ
ejpam-521	519	6	q̃i−1,m)−	q̃i−1,m)−	PROPN
ejpam-521	519	7	¯̇	¯̇	PROPN
ejpam-521	519	8	fi	fi	NOUN
ejpam-521	519	9	,	,	PUNCT
ejpam-521	519	10	m|	m|	NOUN
ejpam-521	519	11	∫	∫	PROPN
ejpam-521	519	12	r̃i	r̃i	PROPN
ejpam-521	519	13	,	,	PUNCT
ejpam-521	519	14	m	m	PROPN
ejpam-521	519	15	0	0	NUM
ejpam-521	519	16	|	|	ADV
ejpam-521	519	17	¯̇fi	¯̇fi	ADP
ejpam-521	519	18	,	,	PUNCT
ejpam-521	519	19	m|	m|	NOUN
ejpam-521	519	20	≤	≤	NOUN
ejpam-521	519	21	2c−1	2c−1	NUM
ejpam-521	519	22	1	1	NUM
ejpam-521	519	23	m	m	NOUN
ejpam-521	519	24	∑	∑	PROPN
ejpam-521	519	25	i=1	i=1	PROPN
ejpam-521	519	26	r̃i	r̃i	NOUN
ejpam-521	519	27	,	,	PUNCT
ejpam-521	519	28	m	m	PROPN
ejpam-521	519	29	∫	∫	PROPN
ejpam-521	519	30	q̃i	q̃i	PROPN
ejpam-521	519	31	,	,	PUNCT
ejpam-521	519	32	m	m	VERB
ejpam-521	519	33	|	|	ADV
ejpam-521	519	34	ḟ	ḟ	ADP
ejpam-521	519	35	−	−	PROPN
ejpam-521	519	36	¯̇	¯̇	PROPN
ejpam-521	519	37	fi	fi	NOUN
ejpam-521	519	38	,	,	PUNCT
ejpam-521	519	39	m|	m|	PROPN
ejpam-521	519	40	∫	∫	PROPN
ejpam-521	519	41	q̃i	q̃i	PROPN
ejpam-521	519	42	,	,	PUNCT
ejpam-521	519	43	m	m	VERB
ejpam-521	519	44	|	|	ADV
ejpam-521	519	45	¯̇f	¯̇f	ADV
ejpam-521	519	46	|	|	ADV
ejpam-521	519	47	.	.	PUNCT
ejpam-521	520	1	(	(	PUNCT
ejpam-521	520	2	104	104	X
ejpam-521	520	3	)	)	PUNCT
ejpam-521	520	4	using	use	VERB
ejpam-521	520	5	the	the	DET
ejpam-521	520	6	cauchy	cauchy	PROPN
ejpam-521	520	7	-	-	PUNCT
ejpam-521	520	8	schwartz	schwartz	PROPN
ejpam-521	520	9	inequality	inequality	PROPN
ejpam-521	520	10	m	m	VERB
ejpam-521	520	11	∑	∑	PROPN
ejpam-521	520	12	i=1	i=1	PROPN
ejpam-521	520	13	r̃i	r̃i	NOUN
ejpam-521	520	14	,	,	PUNCT
ejpam-521	520	15	m	m	PROPN
ejpam-521	520	16	∫	∫	PROPN
ejpam-521	520	17	q̃i	q̃i	PROPN
ejpam-521	520	18	,	,	PUNCT
ejpam-521	520	19	m	m	VERB
ejpam-521	520	20	|	|	ADV
ejpam-521	520	21	ḟ	ḟ	NOUN
ejpam-521	520	22	−	−	PROPN
ejpam-521	520	23	¯̇fi	¯̇fi	NOUN
ejpam-521	520	24	,	,	PUNCT
ejpam-521	520	25	m|	m|	PROPN
ejpam-521	520	26	∫	∫	PROPN
ejpam-521	520	27	q̃i	q̃i	PROPN
ejpam-521	520	28	,	,	PUNCT
ejpam-521	520	29	m	m	VERB
ejpam-521	520	30	|	|	ADV
ejpam-521	520	31	¯̇f	¯̇f	ADV
ejpam-521	520	32	|	|	ADV
ejpam-521	520	33	≤	≤	NUM
ejpam-521	521	1			NOUN
ejpam-521	521	2			NOUN
ejpam-521	521	3			NOUN
ejpam-521	521	4	m	m	VERB
ejpam-521	521	5	∑	∑	PROPN
ejpam-521	521	6	i=1	i=1	PROPN
ejpam-521	521	7	r̃i	r̃i	NOUN
ejpam-521	521	8	,	,	PUNCT
ejpam-521	521	9	m	m	PROPN
ejpam-521	521	10	∫	∫	PROPN
ejpam-521	521	11	q̃i	q̃i	PROPN
ejpam-521	521	12	,	,	PUNCT
ejpam-521	521	13	m	m	VERB
ejpam-521	521	14	|	|	ADV
ejpam-521	521	15	ḟ	ḟ	NOUN
ejpam-521	521	16	−	−	PROPN
ejpam-521	521	17	¯̇fi	¯̇fi	NOUN
ejpam-521	521	18	,	,	PUNCT
ejpam-521	521	19	m|	m|	NOUN
ejpam-521	521	20	!	!	PUNCT
ejpam-521	521	21	2	2	NUM
ejpam-521	521	22			PROPN
ejpam-521	521	23			PROPN
ejpam-521	521	24			PROPN
ejpam-521	521	25	1	1	NUM
ejpam-521	521	26	2	2	NUM
ejpam-521	521	27			NOUN
ejpam-521	521	28			NOUN
ejpam-521	521	29			NOUN
ejpam-521	521	30	m	m	VERB
ejpam-521	521	31	∑	∑	PROPN
ejpam-521	521	32	i=1	i=1	PROPN
ejpam-521	521	33	r̃i	r̃i	NOUN
ejpam-521	521	34	,	,	PUNCT
ejpam-521	521	35	m	m	PROPN
ejpam-521	521	36	∫	∫	PROPN
ejpam-521	521	37	q̃i	q̃i	PROPN
ejpam-521	521	38	,	,	PUNCT
ejpam-521	521	39	m	m	VERB
ejpam-521	521	40	|	|	ADV
ejpam-521	521	41	¯̇f	¯̇f	ADV
ejpam-521	521	42	|	|	ADV
ejpam-521	521	43	!	!	PUNCT
ejpam-521	522	1	2	2	NUM
ejpam-521	522	2			PROPN
ejpam-521	522	3			PROPN
ejpam-521	522	4			PROPN
ejpam-521	522	5	1	1	NUM
ejpam-521	522	6	2	2	NUM
ejpam-521	522	7	≤	≤	NOUN
ejpam-521	522	8			NOUN
ejpam-521	522	9			NOUN
ejpam-521	522	10	m	m	VERB
ejpam-521	522	11	∑	∑	PROPN
ejpam-521	522	12	i=1	i=1	PROPN
ejpam-521	522	13	r̃2	r̃2	PROPN
ejpam-521	522	14	i	i	PROPN
ejpam-521	522	15	,	,	PUNCT
ejpam-521	522	16	m	m	VERB
ejpam-521	522	17	∫	∫	PROPN
ejpam-521	522	18	q̃i	q̃i	PROPN
ejpam-521	522	19	,	,	PUNCT
ejpam-521	522	20	m	m	VERB
ejpam-521	522	21	|	|	ADV
ejpam-521	522	22	ḟ	ḟ	ADP
ejpam-521	522	23	−	−	PROPN
ejpam-521	522	24	¯̇	¯̇	PROPN
ejpam-521	522	25	fi	fi	NOUN
ejpam-521	522	26	,	,	PUNCT
ejpam-521	522	27	m|2	m|2	PROPN
ejpam-521	522	28			PROPN
ejpam-521	522	29			NUM
ejpam-521	522	30	1	1	NUM
ejpam-521	522	31	2	2	NUM
ejpam-521	522	32			NOUN
ejpam-521	522	33			NOUN
ejpam-521	522	34	m	m	VERB
ejpam-521	522	35	∑	∑	PUNCT
ejpam-521	522	36	i=1	i=1	PROPN
ejpam-521	522	37	r̃2	r̃2	PROPN
ejpam-521	522	38	i	i	PROPN
ejpam-521	522	39	,	,	PUNCT
ejpam-521	522	40	m	m	VERB
ejpam-521	522	41	∫	∫	PROPN
ejpam-521	522	42	q̃i	q̃i	PROPN
ejpam-521	522	43	,	,	PUNCT
ejpam-521	522	44	m	m	VERB
ejpam-521	522	45	|	|	ADV
ejpam-521	522	46	¯̇f	¯̇f	NOUN
ejpam-521	522	47	|2	|2	NUM
ejpam-521	522	48			PROPN
ejpam-521	522	49			NUM
ejpam-521	522	50	1	1	NUM
ejpam-521	522	51	2	2	NUM
ejpam-521	522	52	≤	≤	NOUN
ejpam-521	522	53	cm−2α2	cm−2α2	NOUN
ejpam-521	522	54	∫	∫	PROPN
ejpam-521	523	1	[	[	X
ejpam-521	523	2	s	s	X
ejpam-521	523	3	,	,	PUNCT
ejpam-521	523	4	t	t	PROPN
ejpam-521	523	5	]	]	PUNCT
ejpam-521	523	6	(	(	PUNCT
ejpam-521	523	7	ḟ	ḟ	ADP
ejpam-521	523	8	−	−	PROPN
ejpam-521	523	9	¯̇	¯̇	PROPN
ejpam-521	523	10	fi	fi	PROPN
ejpam-521	523	11	,	,	PUNCT
ejpam-521	523	12	m	m	NOUN
ejpam-521	523	13	)	)	PUNCT
ejpam-521	523	14	2	2	NUM
ejpam-521	523	15	!	!	SYM
ejpam-521	523	16	1	1	NUM
ejpam-521	523	17	2	2	NUM
ejpam-521	523	18	where	where	SCONJ
ejpam-521	523	19	c	c	AUX
ejpam-521	523	20	=	=	SYM
ejpam-521	523	21	(	(	PUNCT
ejpam-521	523	22	t	t	PROPN
ejpam-521	523	23	−	−	PROPN
ejpam-521	523	24	s)b2	s)b2	PROPN
ejpam-521	523	25	2c3	2c3	NUM
ejpam-521	523	26	is	be	AUX
ejpam-521	523	27	a	a	DET
ejpam-521	523	28	constant	constant	ADJ
ejpam-521	523	29	.	.	PUNCT
ejpam-521	524	1	by	by	ADP
ejpam-521	524	2	(	(	PUNCT
ejpam-521	524	3	2.5	2.5	NUM
ejpam-521	524	4	)	)	PUNCT
ejpam-521	524	5	of	of	ADP
ejpam-521	524	6	[	[	X
ejpam-521	524	7	6	6	NUM
ejpam-521	524	8	]	]	PUNCT
ejpam-521	524	9	∫	∫	PROPN
ejpam-521	525	1	[	[	X
ejpam-521	525	2	s	s	X
ejpam-521	525	3	,	,	PUNCT
ejpam-521	525	4	t	t	PROPN
ejpam-521	525	5	]	]	PUNCT
ejpam-521	525	6	(	(	PUNCT
ejpam-521	525	7	ḟ	ḟ	VERB
ejpam-521	525	8	−	−	PROPN
ejpam-521	525	9	¯̇fi	¯̇fi	PROPN
ejpam-521	525	10	,	,	PUNCT
ejpam-521	525	11	m	m	PROPN
ejpam-521	525	12	)	)	PUNCT
ejpam-521	525	13	2→	2→	NUM
ejpam-521	525	14	0	0	PUNCT
ejpam-521	525	15	as	as	ADP
ejpam-521	525	16	m→∞.	m→∞.	PROPN
ejpam-521	525	17	(	(	PUNCT
ejpam-521	525	18	105	105	NUM
ejpam-521	525	19	)	)	PUNCT
ejpam-521	525	20	hence	hence	ADV
ejpam-521	525	21	the	the	DET
ejpam-521	525	22	first	first	ADJ
ejpam-521	525	23	term	term	NOUN
ejpam-521	525	24	of	of	ADP
ejpam-521	525	25	the	the	DET
ejpam-521	525	26	righthand	righthand	NOUN
ejpam-521	525	27	side	side	NOUN
ejpam-521	525	28	of	of	ADP
ejpam-521	525	29	(	(	PUNCT
ejpam-521	525	30	103	103	NUM
ejpam-521	525	31	)	)	PUNCT
ejpam-521	525	32	is	be	AUX
ejpam-521	525	33	bounded	bound	VERB
ejpam-521	525	34	by	by	ADP
ejpam-521	525	35	o(m−2α2	o(m−2α2	PROPN
ejpam-521	525	36	)	)	PUNCT
ejpam-521	525	37	.	.	PUNCT
ejpam-521	526	1	using	use	VERB
ejpam-521	526	2	the	the	DET
ejpam-521	526	3	cauchyschwartz	cauchyschwartz	NOUN
ejpam-521	526	4	inequality	inequality	NOUN
ejpam-521	526	5	,	,	PUNCT
ejpam-521	526	6	(	(	PUNCT
ejpam-521	526	7	105	105	NUM
ejpam-521	526	8	)	)	PUNCT
ejpam-521	526	9	and	and	CCONJ
ejpam-521	526	10	the	the	DET
ejpam-521	526	11	following	follow	VERB
ejpam-521	526	12	result	result	VERB
ejpam-521	526	13	similar	similar	ADJ
ejpam-521	526	14	to	to	ADP
ejpam-521	526	15	(	(	PUNCT
ejpam-521	526	16	105	105	NUM
ejpam-521	526	17	)	)	PUNCT
ejpam-521	526	18	∫	∫	PROPN
ejpam-521	527	1	[	[	X
ejpam-521	527	2	s	s	X
ejpam-521	527	3	,	,	PUNCT
ejpam-521	527	4	t	t	PROPN
ejpam-521	527	5	]	]	X
ejpam-521	527	6	�	�	PROPN
ejpam-521	527	7	ḟ	ḟ	VERB
ejpam-521	527	8	−	−	PROPN
ejpam-521	527	9	πi	πi	PROPN
ejpam-521	527	10	,	,	PUNCT
ejpam-521	527	11	m	m	VERB
ejpam-521	527	12	r̃i	r̃i	NOUN
ejpam-521	527	13	,	,	PUNCT
ejpam-521	527	14	m	m	VERB
ejpam-521	527	15	�	�	X
ejpam-521	527	16	2	2	NUM
ejpam-521	527	17	→	→	SYM
ejpam-521	527	18	0	0	NUM
ejpam-521	527	19	as	as	ADP
ejpam-521	527	20	m→∞	m→∞	NUM
ejpam-521	527	21	,	,	PUNCT
ejpam-521	527	22	(	(	PUNCT
ejpam-521	527	23	106	106	NUM
ejpam-521	527	24	)	)	PUNCT
ejpam-521	527	25	one	one	NOUN
ejpam-521	527	26	can	can	AUX
ejpam-521	527	27	similarly	similarly	ADV
ejpam-521	527	28	show	show	VERB
ejpam-521	527	29	that	that	SCONJ
ejpam-521	527	30	the	the	DET
ejpam-521	527	31	second	second	ADJ
ejpam-521	527	32	and	and	CCONJ
ejpam-521	527	33	third	third	ADJ
ejpam-521	527	34	terms	term	NOUN
ejpam-521	527	35	of	of	ADP
ejpam-521	527	36	the	the	DET
ejpam-521	527	37	righthand	righthand	NOUN
ejpam-521	527	38	side	side	NOUN
ejpam-521	527	39	of	of	ADP
ejpam-521	527	40	(	(	PUNCT
ejpam-521	527	41	103	103	NUM
ejpam-521	527	42	)	)	PUNCT
ejpam-521	527	43	are	be	AUX
ejpam-521	527	44	both	both	PRON
ejpam-521	527	45	bounded	bound	VERB
ejpam-521	527	46	by	by	ADP
ejpam-521	527	47	o(m−2α2	o(m−2α2	PROPN
ejpam-521	527	48	)	)	PUNCT
ejpam-521	527	49	.	.	PUNCT
ejpam-521	528	1	hence	hence	ADV
ejpam-521	528	2	(	(	PUNCT
ejpam-521	528	3	100	100	NUM
ejpam-521	528	4	)	)	PUNCT
ejpam-521	528	5	and	and	CCONJ
ejpam-521	528	6	accordingly	accordingly	ADV
ejpam-521	528	7	the	the	DET
ejpam-521	528	8	lemma	lemma	PROPN
ejpam-521	528	9	is	be	AUX
ejpam-521	528	10	true	true	ADJ
ejpam-521	528	11	.	.	PUNCT
ejpam-521	529	1	⊳	⊳	PROPN
ejpam-521	529	2	lemma	lemma	PROPN
ejpam-521	529	3	12	12	NUM
ejpam-521	529	4	.	.	PUNCT
ejpam-521	530	1	under	under	ADP
ejpam-521	530	2	the	the	DET
ejpam-521	530	3	conditions	condition	NOUN
ejpam-521	530	4	(	(	PUNCT
ejpam-521	530	5	i	i	NOUN
ejpam-521	530	6	)	)	PUNCT
ejpam-521	530	7	to	to	ADP
ejpam-521	530	8	(	(	PUNCT
ejpam-521	530	9	iv	iv	X
ejpam-521	530	10	)	)	PUNCT
ejpam-521	530	11	of	of	ADP
ejpam-521	530	12	theorem	theorem	NOUN
ejpam-521	530	13	2	2	NUM
ejpam-521	530	14	we	we	PRON
ejpam-521	530	15	have	have	VERB
ejpam-521	530	16	n	n	NUM
ejpam-521	530	17	∑	∑	PROPN
ejpam-521	530	18	j=1	j=1	PROPN
ejpam-521	530	19	log	log	VERB
ejpam-521	530	20	f	f	PROPN
ejpam-521	530	21	(	(	PUNCT
ejpam-521	530	22	x	x	PROPN
ejpam-521	530	23	j	j	PROPN
ejpam-521	530	24	)	)	PUNCT
ejpam-521	530	25	f	f	PROPN
ejpam-521	530	26	(	(	PUNCT
ejpam-521	530	27	x	x	SYM
ejpam-521	530	28	j|q̃m	j|q̃m	PROPN
ejpam-521	530	29	)	)	PUNCT
ejpam-521	530	30	=	=	PUNCT
ejpam-521	530	31	ne	ne	PROPN
ejpam-521	530	32	f	f	PROPN
ejpam-521	530	33	log	log	PROPN
ejpam-521	530	34	f	f	PROPN
ejpam-521	530	35	f	f	PROPN
ejpam-521	530	36	(	(	PUNCT
ejpam-521	530	37	·	·	PUNCT
ejpam-521	530	38	|q̃m	|q̃m	NUM
ejpam-521	530	39	)	)	PUNCT
ejpam-521	530	40	+	+	CCONJ
ejpam-521	531	1	o(nm−2α+m	o(nm−2α+m	NOUN
ejpam-521	531	2	log	log	NOUN
ejpam-521	531	3	n	n	CCONJ
ejpam-521	531	4	)	)	PUNCT
ejpam-521	531	5	a.s	a.s	PROPN
ejpam-521	531	6	.	.	PROPN
ejpam-521	531	7	(	(	PUNCT
ejpam-521	531	8	107	107	NUM
ejpam-521	531	9	)	)	PUNCT
ejpam-521	531	10	as	as	ADP
ejpam-521	531	11	n→∞	n→∞	PRON
ejpam-521	531	12	uniformly	uniformly	ADV
ejpam-521	531	13	for	for	ADP
ejpam-521	531	14	m	m	PROPN
ejpam-521	531	15	∈	∈	PROPN
ejpam-521	532	1	[	[	X
ejpam-521	532	2	nγ1	nγ1	NOUN
ejpam-521	532	3	,	,	PUNCT
ejpam-521	532	4	nγ2	nγ2	CCONJ
ejpam-521	532	5	]	]	X
ejpam-521	532	6	,	,	PUNCT
ejpam-521	532	7	where	where	SCONJ
ejpam-521	532	8	α	α	NOUN
ejpam-521	532	9	is	be	AUX
ejpam-521	532	10	a	a	DET
ejpam-521	532	11	constant	constant	ADJ
ejpam-521	532	12	satisfying	satisfy	VERB
ejpam-521	532	13	α2	α2	ADJ
ejpam-521	532	14	≤	≤	PUNCT
ejpam-521	533	1	α	α	DET
ejpam-521	533	2	<	<	X
ejpam-521	533	3	α2	α2	PROPN
ejpam-521	533	4	+	+	CCONJ
ejpam-521	533	5	1	1	NUM
ejpam-521	533	6	2	2	NUM
ejpam-521	533	7	.	.	PUNCT
ejpam-521	534	1	proof	proof	NOUN
ejpam-521	534	2	.	.	PUNCT
ejpam-521	535	1	denote	denote	VERB
ejpam-521	535	2	z	z	PROPN
ejpam-521	535	3	j	j	PROPN
ejpam-521	535	4	,	,	PUNCT
ejpam-521	535	5	m	m	VERB
ejpam-521	535	6	=	=	VERB
ejpam-521	536	1	log	log	NOUN
ejpam-521	536	2	f	f	X
ejpam-521	536	3	(	(	PUNCT
ejpam-521	536	4	x	x	PROPN
ejpam-521	536	5	j	j	PROPN
ejpam-521	536	6	)	)	PUNCT
ejpam-521	536	7	f	f	PROPN
ejpam-521	536	8	(	(	PUNCT
ejpam-521	536	9	x	x	X
ejpam-521	536	10	j	j	PROPN
ejpam-521	536	11	|q̃m	|q̃m	PROPN
ejpam-521	536	12	)	)	PUNCT
ejpam-521	536	13	for	for	ADP
ejpam-521	536	14	each	each	DET
ejpam-521	536	15	x	x	PROPN
ejpam-521	536	16	j	j	PROPN
ejpam-521	536	17	,	,	PUNCT
ejpam-521	536	18	then	then	ADV
ejpam-521	536	19	z	z	PROPN
ejpam-521	536	20	j	j	PROPN
ejpam-521	536	21	,	,	PUNCT
ejpam-521	536	22	m	m	PROPN
ejpam-521	536	23	’s	’	NOUN
ejpam-521	536	24	are	be	AUX
ejpam-521	536	25	i.i.d	i.i.d	ADP
ejpam-521	536	26	.	.	PUNCT
ejpam-521	537	1	and	and	CCONJ
ejpam-521	537	2	|z	|z	PROPN
ejpam-521	537	3	j	j	PROPN
ejpam-521	537	4	,	,	PUNCT
ejpam-521	537	5	m|	m|	NOUN
ejpam-521	537	6	≤max	≤max	NOUN
ejpam-521	537	7	x	x	PUNCT
ejpam-521	538	1	|	|	ADV
ejpam-521	538	2	f	f	NOUN
ejpam-521	539	1	−	−	PROPN
ejpam-521	539	2	f	f	PROPN
ejpam-521	539	3	(	(	PUNCT
ejpam-521	539	4	·	·	PUNCT
ejpam-521	539	5	|q̃m)|	|q̃m)|	PROPN
ejpam-521	539	6	f	f	PROPN
ejpam-521	539	7	(	(	PUNCT
ejpam-521	539	8	·	·	PUNCT
ejpam-521	539	9	|q̃m	|q̃m	NUM
ejpam-521	539	10	)	)	PUNCT
ejpam-521	539	11	≤	≤	NOUN
ejpam-521	539	12	c3	c3	PROPN
ejpam-521	539	13	c1	c1	PROPN
ejpam-521	539	14	max	max	PROPN
ejpam-521	539	15	1≤i≤m	1≤i≤m	NUM
ejpam-521	539	16	r̃i	r̃i	NOUN
ejpam-521	539	17	,	,	PUNCT
ejpam-521	539	18	m.	m.	NOUN
ejpam-521	539	19	(	(	PUNCT
ejpam-521	539	20	108	108	NUM
ejpam-521	539	21	)	)	PUNCT
ejpam-521	539	22	g.	g.	PROPN
ejpam-521	539	23	qian	qian	PROPN
ejpam-521	539	24	/	/	SYM
ejpam-521	539	25	eur	eur	PROPN
ejpam-521	539	26	.	.	PUNCT
ejpam-521	540	1	j.	j.	PROPN
ejpam-521	540	2	pure	pure	PROPN
ejpam-521	540	3	appl	appl	PROPN
ejpam-521	540	4	.	.	PROPN
ejpam-521	540	5	math	math	PROPN
ejpam-521	540	6	,	,	PUNCT
ejpam-521	540	7	3	3	NUM
ejpam-521	540	8	(	(	PUNCT
ejpam-521	540	9	2010	2010	NUM
ejpam-521	540	10	)	)	PUNCT
ejpam-521	540	11	,	,	PUNCT
ejpam-521	540	12	51	51	NUM
ejpam-521	540	13	-	-	SYM
ejpam-521	540	14	80	80	NUM
ejpam-521	540	15	76	76	NUM
ejpam-521	540	16	thus	thus	ADV
ejpam-521	540	17	|z	|z	PROPN
ejpam-521	540	18	j	j	PROPN
ejpam-521	540	19	,	,	PUNCT
ejpam-521	540	20	m−	m−	PROPN
ejpam-521	540	21	ez	ez	PROPN
ejpam-521	540	22	j	j	PROPN
ejpam-521	540	23	,	,	PUNCT
ejpam-521	540	24	m|	m|	NOUN
ejpam-521	540	25	≤	≤	PROPN
ejpam-521	540	26	2c3	2c3	NUM
ejpam-521	540	27	c1	c1	PROPN
ejpam-521	540	28	max	max	PROPN
ejpam-521	541	1	1≤i≤m	1≤i≤m	NUM
ejpam-521	541	2	r̃i	r̃i	NOUN
ejpam-521	541	3	,	,	PUNCT
ejpam-521	541	4	m	m	NOUN
ejpam-521	541	5	def	def	ADJ
ejpam-521	541	6	=	=	SYM
ejpam-521	541	7	b	b	PROPN
ejpam-521	541	8	,	,	PUNCT
ejpam-521	541	9	(	(	PUNCT
ejpam-521	541	10	109	109	NUM
ejpam-521	541	11	)	)	PUNCT
ejpam-521	541	12	and	and	CCONJ
ejpam-521	541	13	n	n	CCONJ
ejpam-521	541	14	∑	∑	PROPN
ejpam-521	541	15	j=1	j=1	PROPN
ejpam-521	541	16	var(z	var(z	PROPN
ejpam-521	541	17	j	j	PROPN
ejpam-521	541	18	,	,	PUNCT
ejpam-521	541	19	m)≤	m)≤	NOUN
ejpam-521	541	20	4n	4n	NOUN
ejpam-521	541	21	c2	c2	PROPN
ejpam-521	541	22	3	3	NUM
ejpam-521	541	23	c2	c2	PROPN
ejpam-521	541	24	1	1	NUM
ejpam-521	541	25	max	max	PROPN
ejpam-521	541	26	1≤i≤m	1≤i≤m	NUM
ejpam-521	541	27	r̃2	r̃2	PROPN
ejpam-521	541	28	i	i	PROPN
ejpam-521	541	29	,	,	PUNCT
ejpam-521	541	30	m	m	VERB
ejpam-521	541	31	def	def	ADJ
ejpam-521	541	32	=	=	PUNCT
ejpam-521	541	33	v.	v.	PROPN
ejpam-521	541	34	(	(	PUNCT
ejpam-521	541	35	110	110	NUM
ejpam-521	541	36	)	)	PUNCT
ejpam-521	541	37	by	by	ADP
ejpam-521	541	38	bernstein	bernstein	PROPN
ejpam-521	541	39	’s	’s	PART
ejpam-521	541	40	inequality	inequality	NOUN
ejpam-521	541	41	,	,	PUNCT
ejpam-521	541	42	for	for	ADP
ejpam-521	541	43	arbitrary	arbitrary	ADJ
ejpam-521	541	44	ǫ	ǫ	NOUN
ejpam-521	541	45	>	>	X
ejpam-521	541	46	0	0	PUNCT
ejpam-521	541	47	p	p	NOUN
ejpam-521	541	48			NOUN
ejpam-521	541	49			NOUN
ejpam-521	541	50			PROPN
ejpam-521	541	51	�	�	PROPN
ejpam-521	541	52	�	�	PROPN
ejpam-521	541	53	�	�	PROPN
ejpam-521	541	54	�	�	PROPN
ejpam-521	541	55	�	�	PROPN
ejpam-521	541	56	�	�	PROPN
ejpam-521	541	57	n	n	CCONJ
ejpam-521	541	58	∑	∑	PROPN
ejpam-521	541	59	j=1	j=1	PROPN
ejpam-521	541	60	(	(	PUNCT
ejpam-521	541	61	z	z	NOUN
ejpam-521	541	62	j	j	PROPN
ejpam-521	541	63	,	,	PUNCT
ejpam-521	541	64	m−	m−	PROPN
ejpam-521	541	65	ez	ez	PROPN
ejpam-521	541	66	j	j	PROPN
ejpam-521	541	67	,	,	PUNCT
ejpam-521	541	68	m	m	PROPN
ejpam-521	541	69	)	)	PUNCT
ejpam-521	541	70	�	�	PROPN
ejpam-521	541	71	�	�	PROPN
ejpam-521	541	72	�	�	PROPN
ejpam-521	541	73	�	�	PROPN
ejpam-521	541	74	�	�	PROPN
ejpam-521	541	75	�	�	PROPN
ejpam-521	541	76	>	>	X
ejpam-521	541	77	η	η	PROPN
ejpam-521	541	78			PROPN
ejpam-521	541	79			NOUN
ejpam-521	541	80			PUNCT
ejpam-521	542	1	≤	≤	ADV
ejpam-521	542	2	2	2	NUM
ejpam-521	542	3	exp	exp	NOUN
ejpam-521	542	4	(	(	PUNCT
ejpam-521	542	5	−	−	PROPN
ejpam-521	542	6	η2	η2	ADJ
ejpam-521	542	7	2(v	2(v	NUM
ejpam-521	542	8	+	+	CCONJ
ejpam-521	542	9	1	1	NUM
ejpam-521	542	10	3	3	NUM
ejpam-521	542	11	bη	bη	NOUN
ejpam-521	542	12	)	)	PUNCT
ejpam-521	542	13	)	)	PUNCT
ejpam-521	542	14	,	,	PUNCT
ejpam-521	542	15	(	(	PUNCT
ejpam-521	542	16	111	111	NUM
ejpam-521	542	17	)	)	PUNCT
ejpam-521	542	18	where	where	SCONJ
ejpam-521	542	19	η	η	X
ejpam-521	542	20	=	=	PROPN
ejpam-521	542	21	n(m−2α+mn−1	n(m−2α+mn−1	PROPN
ejpam-521	542	22	log	log	VERB
ejpam-521	542	23	n)ǫ	n)ǫ	ADJ
ejpam-521	542	24	and	and	CCONJ
ejpam-521	542	25	α2	α2	ADJ
ejpam-521	542	26	≤	≤	NOUN
ejpam-521	542	27	α	α	PROPN
ejpam-521	542	28	<	<	X
ejpam-521	542	29	α2	α2	PROPN
ejpam-521	542	30	+	+	CCONJ
ejpam-521	542	31	1	1	NUM
ejpam-521	542	32	2	2	NUM
ejpam-521	542	33	.	.	PUNCT
ejpam-521	543	1	by	by	ADP
ejpam-521	543	2	the	the	DET
ejpam-521	543	3	definition	definition	NOUN
ejpam-521	543	4	of	of	ADP
ejpam-521	543	5	b	b	PROPN
ejpam-521	543	6	and	and	CCONJ
ejpam-521	543	7	v	v	NOUN
ejpam-521	543	8	,	,	PUNCT
ejpam-521	543	9	v	v	X
ejpam-521	543	10	+	+	CCONJ
ejpam-521	543	11	1	1	NUM
ejpam-521	543	12	3	3	NUM
ejpam-521	543	13	bη	bη	NOUN
ejpam-521	543	14	=	=	SYM
ejpam-521	543	15	4n	4n	PROPN
ejpam-521	543	16	c2	c2	PROPN
ejpam-521	543	17	3	3	NUM
ejpam-521	543	18	c2	c2	PROPN
ejpam-521	543	19	1	1	NUM
ejpam-521	543	20	max	max	PROPN
ejpam-521	543	21	1≤i≤m	1≤i≤m	NUM
ejpam-521	543	22	r̃2	r̃2	PROPN
ejpam-521	543	23	i	i	PROPN
ejpam-521	543	24	,	,	PUNCT
ejpam-521	543	25	m+	m+	NUM
ejpam-521	543	26	2c3	2c3	NUM
ejpam-521	543	27	3c1	3c1	NUM
ejpam-521	543	28	max	max	PROPN
ejpam-521	543	29	1≤i≤m	1≤i≤m	NUM
ejpam-521	543	30	r̃i	r̃i	NOUN
ejpam-521	543	31	,	,	PUNCT
ejpam-521	543	32	mn(m−2α	mn(m−2α	PROPN
ejpam-521	543	33	+	+	ADJ
ejpam-521	543	34	mn−1	mn−1	ADJ
ejpam-521	543	35	log	log	NOUN
ejpam-521	543	36	n)ǫ	n)ǫ	X
ejpam-521	543	37	≤	≤	ADJ
ejpam-521	543	38	c′nm−2α2	c′nm−2α2	NOUN
ejpam-521	543	39	+	+	CCONJ
ejpam-521	543	40	c′′m1−α2	c′′m1−α2	PROPN
ejpam-521	543	41	log	log	NOUN
ejpam-521	543	42	n	n	CCONJ
ejpam-521	543	43	where	where	SCONJ
ejpam-521	543	44	c′	c′	NOUN
ejpam-521	543	45	and	and	CCONJ
ejpam-521	543	46	c′′	c′′	NOUN
ejpam-521	543	47	are	be	AUX
ejpam-521	543	48	constants	constant	NOUN
ejpam-521	543	49	not	not	PART
ejpam-521	543	50	depending	depend	VERB
ejpam-521	543	51	on	on	ADP
ejpam-521	543	52	n	n	PRON
ejpam-521	543	53	and	and	CCONJ
ejpam-521	543	54	m.	m.	NOUN
ejpam-521	543	55	therefore	therefore	ADV
ejpam-521	543	56	,	,	PUNCT
ejpam-521	543	57	η2	η2	X
ejpam-521	543	58	v	v	ADP
ejpam-521	543	59	+	+	CCONJ
ejpam-521	543	60	1	1	NUM
ejpam-521	543	61	3	3	NUM
ejpam-521	543	62	bη	bη	ADP
ejpam-521	543	63	≥	≥	NOUN
ejpam-521	543	64	1	1	NUM
ejpam-521	543	65	2	2	X
ejpam-521	544	1	n2(m−2α	n2(m−2α	PROPN
ejpam-521	544	2	+	+	ADJ
ejpam-521	544	3	mn−1	mn−1	PROPN
ejpam-521	544	4	log	log	VERB
ejpam-521	544	5	n)2ǫ2	n)2ǫ2	PROPN
ejpam-521	544	6	max{c′nm−2α2	max{c′nm−2α2	PROPN
ejpam-521	544	7	,	,	PUNCT
ejpam-521	544	8	c′′m1−α2	c′′m1−α2	PROPN
ejpam-521	544	9	log	log	VERB
ejpam-521	544	10	n	n	CCONJ
ejpam-521	544	11	}	}	PUNCT
ejpam-521	544	12	=	=	NOUN
ejpam-521	544	13	min{c′n(m−2α+α2	min{c′n(m−2α+α2	X
ejpam-521	544	14	+	+	ADJ
ejpam-521	544	15	m1+α2	m1+α2	PROPN
ejpam-521	544	16	n−1	n−1	PROPN
ejpam-521	544	17	log	log	NOUN
ejpam-521	544	18	n)2	n)2	NOUN
ejpam-521	544	19	,	,	PUNCT
ejpam-521	544	20	c′′n2(log	c′′n2(log	PROPN
ejpam-521	544	21	n)−1(m−2α−	n)−1(m−2α−	PROPN
ejpam-521	544	22	1	1	NUM
ejpam-521	544	23	2	2	NUM
ejpam-521	544	24	+	+	CCONJ
ejpam-521	544	25	1	1	NUM
ejpam-521	544	26	2	2	NUM
ejpam-521	544	27	α2	α2	ADJ
ejpam-521	544	28	+	+	PROPN
ejpam-521	544	29	m	m	PROPN
ejpam-521	544	30	1	1	NUM
ejpam-521	544	31	2	2	NUM
ejpam-521	544	32	+	+	CCONJ
ejpam-521	544	33	1	1	NUM
ejpam-521	544	34	2	2	NUM
ejpam-521	544	35	α2	α2	ADJ
ejpam-521	544	36	n−1	n−1	PROPN
ejpam-521	544	37	log	log	NOUN
ejpam-521	544	38	n)2	n)2	NOUN
ejpam-521	544	39	}	}	PUNCT
ejpam-521	544	40	for	for	ADP
ejpam-521	544	41	any	any	DET
ejpam-521	544	42	m	m	NOUN
ejpam-521	544	43	∈	∈	NOUN
ejpam-521	545	1	[	[	X
ejpam-521	545	2	nγ1	nγ1	NOUN
ejpam-521	545	3	,	,	PUNCT
ejpam-521	545	4	nγ2	nγ2	CCONJ
ejpam-521	545	5	]	]	PUNCT
ejpam-521	545	6	and	and	CCONJ
ejpam-521	545	7	hence	hence	ADV
ejpam-521	545	8	η2	η2	VERB
ejpam-521	545	9	v	v	ADP
ejpam-521	545	10	+	+	NOUN
ejpam-521	545	11	1	1	NUM
ejpam-521	545	12	3	3	NUM
ejpam-521	545	13	bη	bη	ADP
ejpam-521	545	14	≥	≥	NOUN
ejpam-521	545	15	o	o	NOUN
ejpam-521	545	16	�	�	PROPN
ejpam-521	545	17	n	n	PRON
ejpam-521	545	18	−2α+2α2	−2α+2α2	NOUN
ejpam-521	545	19	+	+	PROPN
ejpam-521	545	20	1	1	NUM
ejpam-521	545	21	2α+1	2α+1	NOUN
ejpam-521	545	22	(	(	PUNCT
ejpam-521	545	23	log	log	NOUN
ejpam-521	545	24	n	n	CCONJ
ejpam-521	545	25	)	)	PUNCT
ejpam-521	545	26	4α−2α2	4α−2α2	NUM
ejpam-521	545	27	2α+1	2α+1	PROPN
ejpam-521	545	28	�	�	PROPN
ejpam-521	545	29	.	.	PUNCT
ejpam-521	546	1	(	(	PUNCT
ejpam-521	546	2	112	112	NUM
ejpam-521	546	3	)	)	PUNCT
ejpam-521	546	4	by	by	ADP
ejpam-521	546	5	(	(	PUNCT
ejpam-521	546	6	112	112	NUM
ejpam-521	546	7	)	)	PUNCT
ejpam-521	546	8	and	and	CCONJ
ejpam-521	546	9	(	(	PUNCT
ejpam-521	546	10	111	111	NUM
ejpam-521	546	11	)	)	PUNCT
ejpam-521	546	12	,	,	PUNCT
ejpam-521	546	13	it	it	PRON
ejpam-521	546	14	follows	follow	VERB
ejpam-521	546	15	that	that	SCONJ
ejpam-521	546	16	∞	∞	PROPN
ejpam-521	546	17	∑	∑	PUNCT
ejpam-521	546	18	n=1	n=1	PROPN
ejpam-521	546	19	∑	∑	ADV
ejpam-521	546	20	m∈[nγ1	m∈[nγ1	NOUN
ejpam-521	546	21	,	,	PUNCT
ejpam-521	546	22	nγ2	nγ2	NUM
ejpam-521	546	23	]	]	X
ejpam-521	546	24	p	p	X
ejpam-521	546	25			PROPN
ejpam-521	546	26			NOUN
ejpam-521	546	27			PROPN
ejpam-521	546	28	�	�	PROPN
ejpam-521	546	29	�	�	PROPN
ejpam-521	546	30	�	�	PROPN
ejpam-521	546	31	�	�	PROPN
ejpam-521	546	32	�	�	PROPN
ejpam-521	546	33	�	�	PROPN
ejpam-521	546	34	n	n	CCONJ
ejpam-521	546	35	∑	∑	PROPN
ejpam-521	546	36	j=1	j=1	PROPN
ejpam-521	546	37	(	(	PUNCT
ejpam-521	546	38	z	z	NOUN
ejpam-521	546	39	j	j	PROPN
ejpam-521	546	40	,	,	PUNCT
ejpam-521	546	41	m−	m−	PROPN
ejpam-521	546	42	ez	ez	PROPN
ejpam-521	546	43	j	j	PROPN
ejpam-521	546	44	,	,	PUNCT
ejpam-521	546	45	m	m	PROPN
ejpam-521	546	46	)	)	PUNCT
ejpam-521	546	47	�	�	PROPN
ejpam-521	546	48	�	�	PROPN
ejpam-521	546	49	�	�	PROPN
ejpam-521	546	50	�	�	PROPN
ejpam-521	546	51	�	�	PROPN
ejpam-521	546	52	�	�	PROPN
ejpam-521	546	53	>	>	X
ejpam-521	546	54	η	η	PROPN
ejpam-521	546	55			PROPN
ejpam-521	546	56			VERB
ejpam-521	546	57			PUNCT
ejpam-521	547	1	≤	≤	ADV
ejpam-521	547	2	2	2	NUM
ejpam-521	547	3	∞	∞	NUM
ejpam-521	547	4	∑	∑	PUNCT
ejpam-521	547	5	n=1	n=1	PROPN
ejpam-521	547	6	∑	∑	ADV
ejpam-521	547	7	m∈[nγ1	m∈[nγ1	NOUN
ejpam-521	547	8	,	,	PUNCT
ejpam-521	547	9	nγ2	nγ2	NUM
ejpam-521	547	10	]	]	X
ejpam-521	547	11	exp	exp	NOUN
ejpam-521	547	12	§	§	PROPN
ejpam-521	547	13	−o	−o	PROPN
ejpam-521	547	14	�	�	PROPN
ejpam-521	547	15	n	n	PRON
ejpam-521	547	16	−2α+2α2	−2α+2α2	NOUN
ejpam-521	547	17	+	+	PROPN
ejpam-521	547	18	1	1	NUM
ejpam-521	547	19	2α+1	2α+1	NOUN
ejpam-521	547	20	(	(	PUNCT
ejpam-521	547	21	log	log	NOUN
ejpam-521	547	22	n	n	CCONJ
ejpam-521	547	23	)	)	PUNCT
ejpam-521	547	24	4α−2α2	4α−2α2	NUM
ejpam-521	547	25	2α+1	2α+1	NUM
ejpam-521	547	26	�	�	VERB
ejpam-521	547	27	ª	ª	X
ejpam-521	547	28	<	<	NOUN
ejpam-521	547	29	∞.	∞.	PROPN
ejpam-521	547	30	from	from	ADP
ejpam-521	547	31	the	the	DET
ejpam-521	547	32	borel	borel	PROPN
ejpam-521	547	33	-	-	PUNCT
ejpam-521	547	34	cantelli	cantelli	PROPN
ejpam-521	547	35	lemma	lemma	PROPN
ejpam-521	547	36	,	,	PUNCT
ejpam-521	547	37	(	(	PUNCT
ejpam-521	547	38	107	107	NUM
ejpam-521	547	39	)	)	PUNCT
ejpam-521	547	40	follows	follow	VERB
ejpam-521	547	41	.	.	PUNCT
ejpam-521	548	1	⊳	⊳	NOUN
ejpam-521	548	2	proof	proof	NOUN
ejpam-521	548	3	.	.	PUNCT
ejpam-521	549	1	[	[	X
ejpam-521	549	2	proof	proof	NOUN
ejpam-521	549	3	of	of	ADP
ejpam-521	549	4	theorem	theorem	NOUN
ejpam-521	549	5	2	2	NUM
ejpam-521	549	6	]	]	X
ejpam-521	549	7	the	the	DET
ejpam-521	549	8	first	first	ADJ
ejpam-521	549	9	part	part	NOUN
ejpam-521	549	10	of	of	ADP
ejpam-521	549	11	the	the	DET
ejpam-521	549	12	theorem	theorem	NOUN
ejpam-521	549	13	,	,	PUNCT
ejpam-521	549	14	i.e.	i.e.	X
ejpam-521	549	15	the	the	DET
ejpam-521	549	16	equation	equation	NOUN
ejpam-521	549	17	(	(	PUNCT
ejpam-521	549	18	25	25	NUM
ejpam-521	549	19	)	)	PUNCT
ejpam-521	549	20	can	can	AUX
ejpam-521	549	21	be	be	AUX
ejpam-521	549	22	obtained	obtain	VERB
ejpam-521	549	23	from	from	ADP
ejpam-521	549	24	(	(	PUNCT
ejpam-521	549	25	83	83	NUM
ejpam-521	549	26	)	)	PUNCT
ejpam-521	549	27	,	,	PUNCT
ejpam-521	549	28	lemma	lemma	PROPN
ejpam-521	549	29	10	10	NUM
ejpam-521	549	30	,	,	PUNCT
ejpam-521	549	31	lemma	lemma	PROPN
ejpam-521	549	32	11	11	NUM
ejpam-521	549	33	and	and	CCONJ
ejpam-521	549	34	lemma	lemma	PROPN
ejpam-521	549	35	12	12	NUM
ejpam-521	549	36	.	.	PUNCT
ejpam-521	550	1	then	then	ADV
ejpam-521	550	2	the	the	DET
ejpam-521	550	3	second	second	ADJ
ejpam-521	550	4	part	part	NOUN
ejpam-521	550	5	is	be	AUX
ejpam-521	550	6	straightforward	straightforward	ADJ
ejpam-521	550	7	from	from	ADP
ejpam-521	550	8	theorem	theorem	ADJ
ejpam-521	550	9	1	1	NUM
ejpam-521	550	10	.	.	PUNCT
ejpam-521	550	11	⊳	⊳	PROPN
ejpam-521	550	12	g.	g.	PROPN
ejpam-521	550	13	qian	qian	PROPN
ejpam-521	550	14	/	/	SYM
ejpam-521	550	15	eur	eur	PROPN
ejpam-521	550	16	.	.	PUNCT
ejpam-521	551	1	j.	j.	PROPN
ejpam-521	551	2	pure	pure	PROPN
ejpam-521	551	3	appl	appl	PROPN
ejpam-521	551	4	.	.	PROPN
ejpam-521	551	5	math	math	PROPN
ejpam-521	551	6	,	,	PUNCT
ejpam-521	551	7	3	3	NUM
ejpam-521	551	8	(	(	PUNCT
ejpam-521	551	9	2010	2010	NUM
ejpam-521	551	10	)	)	PUNCT
ejpam-521	551	11	,	,	PUNCT
ejpam-521	551	12	51	51	NUM
ejpam-521	551	13	-	-	SYM
ejpam-521	551	14	80	80	NUM
ejpam-521	551	15	77	77	NUM
ejpam-521	551	16	proof	proof	NOUN
ejpam-521	551	17	.	.	PUNCT
ejpam-521	552	1	[	[	X
ejpam-521	552	2	proof	proof	NOUN
ejpam-521	552	3	of	of	ADP
ejpam-521	552	4	theorem	theorem	NOUN
ejpam-521	552	5	3	3	NUM
ejpam-521	552	6	]	]	PUNCT
ejpam-521	552	7	noting	note	VERB
ejpam-521	552	8	that	that	SCONJ
ejpam-521	552	9	min	min	PROPN
ejpam-521	552	10	m∈[nγ1	m∈[nγ1	NOUN
ejpam-521	552	11	,	,	PUNCT
ejpam-521	552	12	nγ2	nγ2	CCONJ
ejpam-521	552	13	]	]	X
ejpam-521	552	14	{	{	PUNCT
ejpam-521	552	15	(	(	PUNCT
ejpam-521	552	16	α1	α1	PROPN
ejpam-521	552	17	−	−	PROPN
ejpam-521	552	18	1)m	1)m	NUM
ejpam-521	552	19	log	log	NOUN
ejpam-521	552	20	m+	m+	NUM
ejpam-521	552	21	c	c	NOUN
ejpam-521	552	22	f	f	PROPN
ejpam-521	552	23	nm−2α2	nm−2α2	PROPN
ejpam-521	552	24	}	}	PUNCT
ejpam-521	552	25	=	=	PUNCT
ejpam-521	552	26	m2n	m2n	NOUN
ejpam-521	552	27	1	1	NUM
ejpam-521	552	28	1	1	NUM
ejpam-521	552	29	+	+	NUM
ejpam-521	552	30	2α2	2α2	NUM
ejpam-521	552	31	(	(	PUNCT
ejpam-521	552	32	log	log	NOUN
ejpam-521	552	33	n	n	CCONJ
ejpam-521	552	34	)	)	PUNCT
ejpam-521	552	35	2α2	2α2	NUM
ejpam-521	552	36	1	1	NUM
ejpam-521	552	37	+	+	NOUN
ejpam-521	552	38	2α2	2α2	NUM
ejpam-521	552	39	,	,	PUNCT
ejpam-521	552	40	(	(	PUNCT
ejpam-521	552	41	113	113	NUM
ejpam-521	552	42	)	)	PUNCT
ejpam-521	552	43	min	min	NOUN
ejpam-521	552	44	m∈[nγ1	m∈[nγ1	NOUN
ejpam-521	552	45	,	,	PUNCT
ejpam-521	552	46	nγ2	nγ2	NOUN
ejpam-521	552	47	]	]	X
ejpam-521	552	48	{	{	PUNCT
ejpam-521	552	49	−amα1	−amα1	NOUN
ejpam-521	552	50	+	+	CCONJ
ejpam-521	552	51	(	(	PUNCT
ejpam-521	552	52	α2	α2	ADJ
ejpam-521	552	53	−α1)m	−α1)m	PROPN
ejpam-521	552	54	log	log	PROPN
ejpam-521	552	55	m	m	NOUN
ejpam-521	552	56	}	}	PUNCT
ejpam-521	552	57	=	=	SYM
ejpam-521	552	58	−m1(n	−m1(n	NOUN
ejpam-521	552	59	α1γ2	α1γ2	PUNCT
ejpam-521	552	60	+	+	NUM
ejpam-521	552	61	nγ2	nγ2	NUM
ejpam-521	552	62	log	log	NOUN
ejpam-521	552	63	n	n	CCONJ
ejpam-521	552	64	)	)	PUNCT
ejpam-521	552	65	,	,	PUNCT
ejpam-521	552	66	(	(	PUNCT
ejpam-521	552	67	114	114	NUM
ejpam-521	552	68	)	)	PUNCT
ejpam-521	552	69	the	the	DET
ejpam-521	552	70	first	first	ADJ
ejpam-521	552	71	part	part	NOUN
ejpam-521	552	72	of	of	ADP
ejpam-521	552	73	theorem	theorem	ADJ
ejpam-521	552	74	3	3	NUM
ejpam-521	552	75	is	be	AUX
ejpam-521	552	76	obvious	obvious	ADJ
ejpam-521	552	77	from	from	ADP
ejpam-521	552	78	theorem	theorem	ADJ
ejpam-521	552	79	2	2	NUM
ejpam-521	552	80	.	.	PUNCT
ejpam-521	553	1	the	the	DET
ejpam-521	553	2	second	second	ADJ
ejpam-521	553	3	part	part	NOUN
ejpam-521	553	4	can	can	AUX
ejpam-521	553	5	be	be	AUX
ejpam-521	553	6	proved	prove	VERB
ejpam-521	553	7	similarly	similarly	ADV
ejpam-521	553	8	.	.	PUNCT
ejpam-521	554	1	⊳	⊳	NOUN
ejpam-521	554	2	proof	proof	NOUN
ejpam-521	554	3	.	.	PUNCT
ejpam-521	555	1	[	[	X
ejpam-521	555	2	proof	proof	NOUN
ejpam-521	555	3	of	of	ADP
ejpam-521	555	4	theorem	theorem	NOUN
ejpam-521	555	5	4	4	NUM
ejpam-521	555	6	]	]	PUNCT
ejpam-521	555	7	regarding	regard	VERB
ejpam-521	555	8	m	m	PROPN
ejpam-521	555	9	as	as	ADP
ejpam-521	555	10	a	a	DET
ejpam-521	555	11	real	real	ADJ
ejpam-521	555	12	value	value	NOUN
ejpam-521	555	13	and	and	CCONJ
ejpam-521	555	14	taking	take	VERB
ejpam-521	555	15	the	the	DET
ejpam-521	555	16	derivative	derivative	NOUN
ejpam-521	555	17	of	of	ADP
ejpam-521	555	18	1	1	NUM
ejpam-521	555	19	2	2	NUM
ejpam-521	555	20	n	n	NOUN
ejpam-521	555	21	log	log	VERB
ejpam-521	555	22	n	n	INTJ
ejpam-521	555	23	m	m	VERB
ejpam-521	555	24	+	+	NUM
ejpam-521	555	25	c	c	NOUN
ejpam-521	555	26	′	′	NUM
ejpam-521	555	27	f	f	PROPN
ejpam-521	555	28	nm−2	nm−2	PROPN
ejpam-521	555	29	with	with	ADP
ejpam-521	555	30	respect	respect	NOUN
ejpam-521	555	31	to	to	ADP
ejpam-521	555	32	m	m	PRON
ejpam-521	555	33	,	,	PUNCT
ejpam-521	555	34	we	we	PRON
ejpam-521	555	35	get	get	VERB
ejpam-521	555	36	min	min	NOUN
ejpam-521	555	37	m∈[nγ1	m∈[nγ1	NOUN
ejpam-521	555	38	,	,	PUNCT
ejpam-521	555	39	nγ2	nγ2	NOUN
ejpam-521	555	40	]	]	PUNCT
ejpam-521	555	41	�	�	PROPN
ejpam-521	555	42	1	1	NUM
ejpam-521	555	43	2	2	NUM
ejpam-521	555	44	n	n	NOUN
ejpam-521	555	45	log	log	VERB
ejpam-521	556	1	n	n	INTJ
ejpam-521	556	2	m	m	VERB
ejpam-521	556	3	+	+	NUM
ejpam-521	556	4	c	c	NOUN
ejpam-521	556	5	′f	′f	PROPN
ejpam-521	556	6	nm−2	nm−2	PROPN
ejpam-521	556	7	�	�	PROPN
ejpam-521	556	8	=	=	PUNCT
ejpam-521	556	9	m5n	m5n	NOUN
ejpam-521	556	10	1	1	NUM
ejpam-521	556	11	3	3	NUM
ejpam-521	556	12	(	(	PUNCT
ejpam-521	556	13	log	log	NOUN
ejpam-521	556	14	n	n	CCONJ
ejpam-521	556	15	)	)	PUNCT
ejpam-521	556	16	2	2	NUM
ejpam-521	556	17	3	3	NUM
ejpam-521	556	18	(	(	PUNCT
ejpam-521	556	19	115	115	NUM
ejpam-521	556	20	)	)	PUNCT
ejpam-521	556	21	and	and	CCONJ
ejpam-521	557	1	the	the	DET
ejpam-521	557	2	minimization	minimization	NOUN
ejpam-521	557	3	is	be	AUX
ejpam-521	557	4	achieved	achieve	VERB
ejpam-521	557	5	at	at	ADP
ejpam-521	557	6	m	m	PROPN
ejpam-521	557	7	=	=	NOUN
ejpam-521	557	8	m6(n/	m6(n/	PROPN
ejpam-521	557	9	log	log	NOUN
ejpam-521	557	10	n	n	CCONJ
ejpam-521	557	11	)	)	PUNCT
ejpam-521	557	12	1	1	NUM
ejpam-521	557	13	3	3	NUM
ejpam-521	557	14	.	.	PUNCT
ejpam-521	558	1	by	by	ADP
ejpam-521	558	2	this	this	DET
ejpam-521	558	3	result	result	NOUN
ejpam-521	558	4	and	and	CCONJ
ejpam-521	558	5	theorem	theorem	VERB
ejpam-521	558	6	2	2	NUM
ejpam-521	558	7	,	,	PUNCT
ejpam-521	558	8	(	(	PUNCT
ejpam-521	558	9	a	a	X
ejpam-521	558	10	)	)	PUNCT
ejpam-521	558	11	,	,	PUNCT
ejpam-521	558	12	(	(	PUNCT
ejpam-521	558	13	b	b	NOUN
ejpam-521	558	14	)	)	PUNCT
ejpam-521	558	15	,	,	PUNCT
ejpam-521	558	16	(	(	PUNCT
ejpam-521	558	17	c	c	X
ejpam-521	558	18	)	)	PUNCT
ejpam-521	558	19	and	and	CCONJ
ejpam-521	558	20	(	(	PUNCT
ejpam-521	558	21	d	d	X
ejpam-521	558	22	)	)	PUNCT
ejpam-521	558	23	are	be	AUX
ejpam-521	558	24	readily	readily	ADV
ejpam-521	558	25	obtained	obtain	VERB
ejpam-521	558	26	.	.	PUNCT
ejpam-521	559	1	⊳	⊳	NOUN
ejpam-521	559	2	proof	proof	NOUN
ejpam-521	559	3	.	.	PUNCT
ejpam-521	560	1	[	[	X
ejpam-521	560	2	proof	proof	NOUN
ejpam-521	560	3	of	of	ADP
ejpam-521	560	4	theorem	theorem	NOUN
ejpam-521	560	5	5	5	NUM
ejpam-521	560	6	]	]	PUNCT
ejpam-521	560	7	as	as	ADP
ejpam-521	560	8	in	in	ADP
ejpam-521	560	9	lemma	lemma	PROPN
ejpam-521	560	10	7	7	NUM
ejpam-521	560	11	,	,	PUNCT
ejpam-521	560	12	it	it	PRON
ejpam-521	560	13	can	can	AUX
ejpam-521	560	14	be	be	AUX
ejpam-521	560	15	shown	show	VERB
ejpam-521	560	16	that	that	SCONJ
ejpam-521	560	17	l4(q̃	l4(q̃	PROPN
ejpam-521	560	18	m1	m1	PROPN
ejpam-521	560	19	1	1	NUM
ejpam-521	560	20	,	,	PUNCT
ejpam-521	560	21	·	·	PUNCT
ejpam-521	560	22	·	·	PUNCT
ejpam-521	560	23	·	·	PUNCT
ejpam-521	560	24	,	,	PUNCT
ejpam-521	560	25	q̃mk	q̃mk	ADP
ejpam-521	560	26	k	k	PROPN
ejpam-521	560	27	,	,	PUNCT
ejpam-521	560	28	m1	m1	PROPN
ejpam-521	560	29	,	,	PUNCT
ejpam-521	560	30	·	·	PUNCT
ejpam-521	560	31	·	·	PUNCT
ejpam-521	560	32	·	·	PUNCT
ejpam-521	560	33	,	,	PUNCT
ejpam-521	560	34	mk	mk	PROPN
ejpam-521	560	35	,	,	PUNCT
ejpam-521	560	36	δ	δ	PROPN
ejpam-521	560	37	)	)	PUNCT
ejpam-521	560	38	=	=	PUNCT
ejpam-521	561	1	o	o	NOUN
ejpam-521	561	2	k	k	PUNCT
ejpam-521	561	3	∑	∑	PUNCT
ejpam-521	561	4	i=1	i=1	PROPN
ejpam-521	561	5	mi	mi	PROPN
ejpam-521	561	6	!	!	PUNCT
ejpam-521	561	7	.	.	PUNCT
ejpam-521	562	1	(	(	PUNCT
ejpam-521	562	2	116	116	NUM
ejpam-521	562	3	)	)	PUNCT
ejpam-521	562	4	if	if	SCONJ
ejpam-521	562	5	either	either	CCONJ
ejpam-521	562	6	α1	α1	PROPN
ejpam-521	562	7	6=	6=	NUM
ejpam-521	562	8	1	1	NUM
ejpam-521	562	9	or	or	CCONJ
ejpam-521	562	10	α2	α2	ADJ
ejpam-521	562	11	6=	6=	NUM
ejpam-521	562	12	1	1	NUM
ejpam-521	562	13	,	,	PUNCT
ejpam-521	562	14	then	then	ADV
ejpam-521	562	15	by	by	ADP
ejpam-521	562	16	theorem	theorem	NOUN
ejpam-521	563	1	3	3	NUM
ejpam-521	563	2	−m3	−m3	PROPN
ejpam-521	563	3	k	k	NOUN
ejpam-521	563	4	∑	∑	PUNCT
ejpam-521	563	5	i=1	i=1	PROPN
ejpam-521	563	6	(	(	PUNCT
ejpam-521	563	7	n	n	NOUN
ejpam-521	563	8	α1γ2	α1γ2	X
ejpam-521	564	1	i	i	NOUN
ejpam-521	564	2	+	+	CCONJ
ejpam-521	564	3	n	n	CCONJ
ejpam-521	564	4	γ2	γ2	NOUN
ejpam-521	565	1	i	i	PRON
ejpam-521	565	2	log	log	VERB
ejpam-521	565	3	ni)≤	ni)≤	X
ejpam-521	565	4	c(x	c(x	NOUN
ejpam-521	565	5	n1	n1	NOUN
ejpam-521	565	6	1	1	NUM
ejpam-521	565	7	,	,	PUNCT
ejpam-521	565	8	·	·	PUNCT
ejpam-521	565	9	·	·	PUNCT
ejpam-521	565	10	·	·	PUNCT
ejpam-521	565	11	,	,	PUNCT
ejpam-521	565	12	x	x	PUNCT
ejpam-521	565	13	nk	nk	PROPN
ejpam-521	565	14	k	k	PROPN
ejpam-521	565	15	)	)	PUNCT
ejpam-521	566	1	+	+	CCONJ
ejpam-521	566	2	k	k	X
ejpam-521	566	3	∑	∑	PUNCT
ejpam-521	566	4	i=1	i=1	PROPN
ejpam-521	566	5	log	log	PROPN
ejpam-521	566	6	f	f	PROPN
ejpam-521	566	7	ni	ni	PROPN
ejpam-521	567	1	i	i	PROPN
ejpam-521	567	2	(	(	PUNCT
ejpam-521	567	3	x	x	PROPN
ejpam-521	567	4	ni	ni	PROPN
ejpam-521	567	5	i	i	PROPN
ejpam-521	567	6	)	)	PUNCT
ejpam-521	567	7	≤	≤	PUNCT
ejpam-521	567	8	m4	m4	PROPN
ejpam-521	568	1	k	k	PROPN
ejpam-521	568	2	∑	∑	PUNCT
ejpam-521	568	3	i=1	i=1	PROPN
ejpam-521	568	4	n	n	ADV
ejpam-521	568	5	1	1	NUM
ejpam-521	568	6	1	1	NUM
ejpam-521	568	7	+	+	NUM
ejpam-521	568	8	2α2	2α2	NUM
ejpam-521	569	1	i	i	PRON
ejpam-521	569	2	(	(	PUNCT
ejpam-521	569	3	log	log	PROPN
ejpam-521	569	4	ni	ni	PROPN
ejpam-521	569	5	)	)	PUNCT
ejpam-521	569	6	2α2	2α2	NUM
ejpam-521	569	7	1	1	NUM
ejpam-521	569	8	+	+	NUM
ejpam-521	569	9	2α2	2α2	NUM
ejpam-521	569	10	a.s	a.s	PROPN
ejpam-521	569	11	.	.	PROPN
ejpam-521	569	12	(	(	PUNCT
ejpam-521	569	13	117	117	NUM
ejpam-521	569	14	)	)	PUNCT
ejpam-521	569	15	and	and	CCONJ
ejpam-521	569	16	−m3(n	−m3(n	NOUN
ejpam-521	569	17	α1γ2	α1γ2	SYM
ejpam-521	569	18	+	+	NUM
ejpam-521	569	19	nγ2	nγ2	NOUN
ejpam-521	569	20	log	log	NOUN
ejpam-521	569	21	n)≤	n)≤	PROPN
ejpam-521	569	22	c(x	c(x	PROPN
ejpam-521	569	23	n	n	CCONJ
ejpam-521	569	24	)	)	PUNCT
ejpam-521	569	25	+	+	CCONJ
ejpam-521	569	26	log	log	VERB
ejpam-521	569	27	f	f	PROPN
ejpam-521	569	28	n	n	PRON
ejpam-521	569	29	mix(x	mix(x	NOUN
ejpam-521	569	30	n)≤	n)≤	NOUN
ejpam-521	569	31	m4n	m4n	VERB
ejpam-521	569	32	1	1	NUM
ejpam-521	569	33	1	1	NUM
ejpam-521	569	34	+	+	NOUN
ejpam-521	569	35	2α2	2α2	NUM
ejpam-521	569	36	(	(	PUNCT
ejpam-521	569	37	log	log	NOUN
ejpam-521	569	38	n	n	CCONJ
ejpam-521	569	39	)	)	PUNCT
ejpam-521	569	40	2α2	2α2	NUM
ejpam-521	569	41	1	1	NUM
ejpam-521	569	42	+	+	NUM
ejpam-521	569	43	2α2	2α2	NUM
ejpam-521	569	44	a.s	a.s	PROPN
ejpam-521	569	45	.	.	PROPN
ejpam-521	569	46	(	(	PUNCT
ejpam-521	569	47	118	118	NUM
ejpam-521	569	48	)	)	PUNCT
ejpam-521	569	49	for	for	ADP
ejpam-521	569	50	some	some	DET
ejpam-521	569	51	positive	positive	ADJ
ejpam-521	569	52	constants	constant	NOUN
ejpam-521	569	53	m3	m3	PROPN
ejpam-521	569	54	and	and	CCONJ
ejpam-521	569	55	m4	m4	PROPN
ejpam-521	569	56	depending	depend	VERB
ejpam-521	569	57	on	on	ADP
ejpam-521	569	58	f1	f1	NOUN
ejpam-521	569	59	,	,	PUNCT
ejpam-521	569	60	·	·	PUNCT
ejpam-521	569	61	·	·	PUNCT
ejpam-521	569	62	·	·	PUNCT
ejpam-521	569	63	,	,	PUNCT
ejpam-521	569	64	fk	fk	INTJ
ejpam-521	569	65	.	.	PUNCT
ejpam-521	570	1	if	if	SCONJ
ejpam-521	570	2	α1	α1	PROPN
ejpam-521	570	3	=	=	SYM
ejpam-521	570	4	α2	α2	NOUN
ejpam-521	570	5	=	=	SYM
ejpam-521	570	6	1	1	NUM
ejpam-521	570	7	,	,	PUNCT
ejpam-521	570	8	then	then	ADV
ejpam-521	570	9	by	by	ADP
ejpam-521	570	10	theorem	theorem	NOUN
ejpam-521	570	11	4	4	NUM
ejpam-521	570	12	(	(	PUNCT
ejpam-521	570	13	b	b	NOUN
ejpam-521	570	14	)	)	PUNCT
ejpam-521	570	15	c(x	c(x	NOUN
ejpam-521	570	16	n1	n1	NOUN
ejpam-521	570	17	1	1	NUM
ejpam-521	570	18	,	,	PUNCT
ejpam-521	570	19	·	·	PUNCT
ejpam-521	570	20	·	·	PUNCT
ejpam-521	570	21	·	·	PUNCT
ejpam-521	570	22	,	,	PUNCT
ejpam-521	570	23	x	x	PUNCT
ejpam-521	570	24	nk	nk	PROPN
ejpam-521	570	25	k	k	PROPN
ejpam-521	570	26	)	)	PUNCT
ejpam-521	571	1	+	+	CCONJ
ejpam-521	571	2	k	k	X
ejpam-521	571	3	∑	∑	PUNCT
ejpam-521	571	4	i=1	i=1	PROPN
ejpam-521	571	5	log	log	PROPN
ejpam-521	571	6	f	f	PROPN
ejpam-521	571	7	ni	ni	PROPN
ejpam-521	572	1	i	i	PROPN
ejpam-521	572	2	(	(	PUNCT
ejpam-521	572	3	x	x	PROPN
ejpam-521	572	4	ni	ni	PROPN
ejpam-521	572	5	i	i	PROPN
ejpam-521	572	6	)	)	PUNCT
ejpam-521	573	1	=	=	PUNCT
ejpam-521	574	1	o	o	NOUN
ejpam-521	575	1	k	k	PUNCT
ejpam-521	575	2	∑	∑	PUNCT
ejpam-521	575	3	i=1	i=1	PROPN
ejpam-521	575	4	n	n	ADV
ejpam-521	575	5	1	1	NUM
ejpam-521	575	6	3	3	NUM
ejpam-521	575	7	i	i	NOUN
ejpam-521	575	8	(	(	PUNCT
ejpam-521	575	9	log	log	NOUN
ejpam-521	575	10	n	n	CCONJ
ejpam-521	575	11	)	)	PUNCT
ejpam-521	575	12	2	2	NUM
ejpam-521	575	13	3	3	NUM
ejpam-521	575	14	!	!	PUNCT
ejpam-521	576	1	a.s	a.s	AUX
ejpam-521	576	2	.	.	PROPN
ejpam-521	576	3	(	(	PUNCT
ejpam-521	576	4	119	119	NUM
ejpam-521	576	5	)	)	PUNCT
ejpam-521	576	6	and	and	CCONJ
ejpam-521	576	7	c(x	c(x	NOUN
ejpam-521	576	8	n	n	CCONJ
ejpam-521	576	9	)	)	PUNCT
ejpam-521	576	10	+	+	CCONJ
ejpam-521	576	11	log	log	VERB
ejpam-521	576	12	f	f	PROPN
ejpam-521	576	13	n	n	NUM
ejpam-521	576	14	mix(x	mix(x	NOUN
ejpam-521	576	15	n	n	CCONJ
ejpam-521	576	16	)	)	PUNCT
ejpam-521	576	17	=	=	SYM
ejpam-521	576	18	o	o	X
ejpam-521	576	19	�	�	PROPN
ejpam-521	576	20	n	n	CCONJ
ejpam-521	576	21	1	1	NUM
ejpam-521	576	22	3	3	NUM
ejpam-521	576	23	(	(	PUNCT
ejpam-521	576	24	log	log	NOUN
ejpam-521	576	25	n	n	CCONJ
ejpam-521	576	26	)	)	PUNCT
ejpam-521	576	27	2	2	NUM
ejpam-521	576	28	3	3	NUM
ejpam-521	576	29	�	�	PROPN
ejpam-521	576	30	a.s	a.s	PROPN
ejpam-521	576	31	..	..	PUNCT
ejpam-521	576	32	(	(	PUNCT
ejpam-521	576	33	120	120	NUM
ejpam-521	576	34	)	)	PUNCT
ejpam-521	576	35	it	it	PRON
ejpam-521	576	36	remains	remain	VERB
ejpam-521	576	37	to	to	PART
ejpam-521	576	38	prove	prove	VERB
ejpam-521	576	39	that	that	SCONJ
ejpam-521	576	40	there	there	PRON
ejpam-521	576	41	exists	exist	VERB
ejpam-521	576	42	a	a	DET
ejpam-521	576	43	constant	constant	ADJ
ejpam-521	576	44	η	η	NOUN
ejpam-521	576	45	<	<	X
ejpam-521	576	46	0	0	NUM
ejpam-521	576	47	such	such	ADJ
ejpam-521	576	48	that	that	SCONJ
ejpam-521	576	49	1	1	NUM
ejpam-521	576	50	n	n	NUM
ejpam-521	576	51	log	log	VERB
ejpam-521	576	52	f	f	PROPN
ejpam-521	576	53	n	n	PRON
ejpam-521	576	54	mix(x	mix(x	NOUN
ejpam-521	576	55	n)−	n)−	PROPN
ejpam-521	576	56	k	k	NOUN
ejpam-521	577	1	∑	∑	PUNCT
ejpam-521	577	2	i=1	i=1	PROPN
ejpam-521	577	3	log	log	PROPN
ejpam-521	577	4	f	f	PROPN
ejpam-521	577	5	ni	ni	PROPN
ejpam-521	578	1	i	i	PROPN
ejpam-521	578	2	(	(	PUNCT
ejpam-521	578	3	x	x	PROPN
ejpam-521	578	4	ni	ni	PROPN
ejpam-521	578	5	i	i	PROPN
ejpam-521	578	6	)	)	PUNCT
ejpam-521	578	7	!	!	PUNCT
ejpam-521	579	1	<	<	X
ejpam-521	580	1	η	η	PROPN
ejpam-521	580	2	a.s	a.s	PROPN
ejpam-521	580	3	.	.	PROPN
ejpam-521	580	4	(	(	PUNCT
ejpam-521	580	5	121	121	NUM
ejpam-521	580	6	)	)	PUNCT
ejpam-521	580	7	g.	g.	PROPN
ejpam-521	580	8	qian	qian	PROPN
ejpam-521	580	9	/	/	SYM
ejpam-521	580	10	eur	eur	PROPN
ejpam-521	580	11	.	.	PUNCT
ejpam-521	581	1	j.	j.	PROPN
ejpam-521	581	2	pure	pure	PROPN
ejpam-521	581	3	appl	appl	PROPN
ejpam-521	581	4	.	.	PROPN
ejpam-521	581	5	math	math	PROPN
ejpam-521	581	6	,	,	PUNCT
ejpam-521	581	7	3	3	NUM
ejpam-521	581	8	(	(	PUNCT
ejpam-521	581	9	2010	2010	NUM
ejpam-521	581	10	)	)	PUNCT
ejpam-521	581	11	,	,	PUNCT
ejpam-521	581	12	51	51	NUM
ejpam-521	581	13	-	-	SYM
ejpam-521	581	14	80	80	NUM
ejpam-521	581	15	78	78	NUM
ejpam-521	581	16	as	as	ADP
ejpam-521	581	17	n1	n1	PROPN
ejpam-521	581	18	→∞	→∞	NOUN
ejpam-521	581	19	,	,	PUNCT
ejpam-521	581	20	·	·	PUNCT
ejpam-521	581	21	·	·	PUNCT
ejpam-521	581	22	·	·	PUNCT
ejpam-521	581	23	,	,	PUNCT
ejpam-521	581	24	nk	nk	PROPN
ejpam-521	581	25	→∞	→∞	X
ejpam-521	581	26	satisfying	satisfy	VERB
ejpam-521	581	27	n1	n1	PROPN
ejpam-521	581	28	n	n	NOUN
ejpam-521	581	29	>	>	X
ejpam-521	581	30	ǫ1	ǫ1	PROPN
ejpam-521	581	31	>	>	X
ejpam-521	581	32	0	0	NUM
ejpam-521	581	33	,	,	PUNCT
ejpam-521	581	34	·	·	PUNCT
ejpam-521	581	35	·	·	PUNCT
ejpam-521	581	36	·	·	PUNCT
ejpam-521	581	37	,	,	PUNCT
ejpam-521	581	38	nk	nk	PROPN
ejpam-521	581	39	n	n	PROPN
ejpam-521	581	40	>	>	X
ejpam-521	581	41	ǫk	ǫk	X
ejpam-521	581	42	>	>	X
ejpam-521	581	43	0	0	NUM
ejpam-521	582	1	for	for	ADP
ejpam-521	582	2	any	any	DET
ejpam-521	582	3	prescribed	prescribed	ADJ
ejpam-521	582	4	constants	constant	NOUN
ejpam-521	582	5	ǫ1	ǫ1	NUM
ejpam-521	582	6	,	,	PUNCT
ejpam-521	582	7	·	·	PUNCT
ejpam-521	582	8	·	·	PUNCT
ejpam-521	582	9	·	·	PUNCT
ejpam-521	582	10	,	,	PUNCT
ejpam-521	582	11	ǫk	ǫk	INTJ
ejpam-521	582	12	,	,	PUNCT
ejpam-521	582	13	if	if	SCONJ
ejpam-521	582	14	at	at	ADV
ejpam-521	582	15	least	least	ADV
ejpam-521	582	16	two	two	NUM
ejpam-521	582	17	of	of	ADP
ejpam-521	582	18	f1	f1	NOUN
ejpam-521	582	19	,	,	PUNCT
ejpam-521	582	20	·	·	PUNCT
ejpam-521	582	21	·	·	PUNCT
ejpam-521	582	22	·	·	PUNCT
ejpam-521	582	23	,	,	PUNCT
ejpam-521	582	24	fk	fk	INTJ
ejpam-521	582	25	are	be	AUX
ejpam-521	582	26	not	not	PART
ejpam-521	582	27	equal	equal	ADJ
ejpam-521	582	28	almost	almost	ADV
ejpam-521	582	29	surely	surely	ADV
ejpam-521	582	30	,	,	PUNCT
ejpam-521	582	31	and	and	CCONJ
ejpam-521	582	32	1	1	NUM
ejpam-521	582	33	n	n	NOUN
ejpam-521	582	34	log	log	VERB
ejpam-521	582	35	f	f	PROPN
ejpam-521	582	36	n	n	PRON
ejpam-521	582	37	mix(x	mix(x	NOUN
ejpam-521	583	1	n)−	n)−	PROPN
ejpam-521	583	2	k	k	NOUN
ejpam-521	584	1	∑	∑	PUNCT
ejpam-521	584	2	i=1	i=1	PROPN
ejpam-521	584	3	log	log	PROPN
ejpam-521	584	4	f	f	PROPN
ejpam-521	584	5	ni	ni	PROPN
ejpam-521	585	1	i	i	PROPN
ejpam-521	585	2	(	(	PUNCT
ejpam-521	585	3	x	x	PROPN
ejpam-521	585	4	ni	ni	PROPN
ejpam-521	585	5	i	i	PROPN
ejpam-521	585	6	)	)	PUNCT
ejpam-521	585	7	!	!	PUNCT
ejpam-521	586	1	→	→	SYM
ejpam-521	586	2	0	0	NUM
ejpam-521	586	3	a.s	a.s	PROPN
ejpam-521	586	4	.	.	PROPN
ejpam-521	586	5	(	(	PUNCT
ejpam-521	586	6	122	122	NUM
ejpam-521	586	7	)	)	PUNCT
ejpam-521	586	8	as	as	ADP
ejpam-521	586	9	n1→∞	n1→∞	NOUN
ejpam-521	586	10	,	,	PUNCT
ejpam-521	586	11	·	·	PUNCT
ejpam-521	586	12	·	·	PUNCT
ejpam-521	586	13	·	·	PUNCT
ejpam-521	586	14	,	,	PUNCT
ejpam-521	586	15	nk→∞	nk→∞	NOUN
ejpam-521	586	16	if	if	SCONJ
ejpam-521	586	17	f1	f1	NOUN
ejpam-521	586	18	=	=	SYM
ejpam-521	586	19	f2	f2	PROPN
ejpam-521	586	20	=	=	SYM
ejpam-521	586	21	·	·	PUNCT
ejpam-521	586	22	·	·	PUNCT
ejpam-521	586	23	·	·	PUNCT
ejpam-521	586	24	=	=	SYM
ejpam-521	586	25	fk	fk	INTJ
ejpam-521	586	26	a.s	a.s	PROPN
ejpam-521	586	27	..	..	PROPN
ejpam-521	586	28	because	because	SCONJ
ejpam-521	586	29	k	k	PROPN
ejpam-521	586	30	∑	∑	PROPN
ejpam-521	586	31	i=1	i=1	PROPN
ejpam-521	586	32	log	log	PROPN
ejpam-521	587	1	f	f	PROPN
ejpam-521	587	2	ni	ni	PROPN
ejpam-521	587	3	i	i	PROPN
ejpam-521	587	4	(	(	PUNCT
ejpam-521	587	5	x	x	PROPN
ejpam-521	587	6	ni	ni	PROPN
ejpam-521	587	7	i	i	PROPN
ejpam-521	587	8	)	)	PUNCT
ejpam-521	588	1	=	=	PUNCT
ejpam-521	589	1	k	k	X
ejpam-521	589	2	∑	∑	PUNCT
ejpam-521	589	3	i=1	i=1	PROPN
ejpam-521	589	4	ni	ni	PROPN
ejpam-521	589	5	∑	∑	PROPN
ejpam-521	589	6	j=1	j=1	PROPN
ejpam-521	589	7	log	log	NOUN
ejpam-521	589	8	fi(x	fi(x	NUM
ejpam-521	590	1	i	i	PRON
ejpam-521	590	2	j	j	PROPN
ejpam-521	590	3	)	)	PUNCT
ejpam-521	591	1	,	,	PUNCT
ejpam-521	591	2	log	log	VERB
ejpam-521	591	3	f	f	PROPN
ejpam-521	591	4	n	n	NUM
ejpam-521	591	5	mix(x	mix(x	NOUN
ejpam-521	591	6	n	n	CCONJ
ejpam-521	591	7	)	)	PUNCT
ejpam-521	591	8	=	=	SYM
ejpam-521	592	1	k	k	PROPN
ejpam-521	592	2	∑	∑	PUNCT
ejpam-521	592	3	i=1	i=1	PROPN
ejpam-521	592	4	ni	ni	PROPN
ejpam-521	592	5	∑	∑	PROPN
ejpam-521	592	6	j=1	j=1	PROPN
ejpam-521	592	7	log	log	NOUN
ejpam-521	592	8	k	k	NOUN
ejpam-521	592	9	∑	∑	PUNCT
ejpam-521	593	1	l=1	l=1	PUNCT
ejpam-521	593	2	nl	nl	PROPN
ejpam-521	593	3	n	n	PROPN
ejpam-521	593	4	fl(x	fl(x	PROPN
ejpam-521	593	5	i	i	PRON
ejpam-521	593	6	j	j	NOUN
ejpam-521	593	7	)	)	PUNCT
ejpam-521	593	8	!	!	PUNCT
ejpam-521	594	1	and	and	CCONJ
ejpam-521	594	2	fi	fi	NOUN
ejpam-521	594	3	’s	’	VERB
ejpam-521	594	4	are	be	AUX
ejpam-521	594	5	bounded	bounded	ADJ
ejpam-521	594	6	density	density	NOUN
ejpam-521	594	7	functions	function	NOUN
ejpam-521	594	8	,	,	PUNCT
ejpam-521	594	9	by	by	ADP
ejpam-521	594	10	the	the	DET
ejpam-521	594	11	strong	strong	ADJ
ejpam-521	594	12	law	law	NOUN
ejpam-521	594	13	of	of	ADP
ejpam-521	594	14	large	large	ADJ
ejpam-521	594	15	numbers	number	NOUN
ejpam-521	594	16	for	for	ADP
ejpam-521	594	17	i.i.d	i.i.d	NOUN
ejpam-521	594	18	.	.	PUNCT
ejpam-521	595	1	random	random	ADJ
ejpam-521	595	2	variables	variable	NOUN
ejpam-521	595	3	it	it	PRON
ejpam-521	595	4	follows	follow	VERB
ejpam-521	595	5	that	that	SCONJ
ejpam-521	595	6	1	1	NUM
ejpam-521	595	7	n	n	NOUN
ejpam-521	595	8	k	k	NOUN
ejpam-521	595	9	∑	∑	PUNCT
ejpam-521	595	10	i=1	i=1	PROPN
ejpam-521	596	1	log	log	PROPN
ejpam-521	597	1	f	f	PROPN
ejpam-521	597	2	ni	ni	PROPN
ejpam-521	597	3	i	i	PROPN
ejpam-521	597	4	(	(	PUNCT
ejpam-521	597	5	x	x	PROPN
ejpam-521	597	6	ni	ni	PROPN
ejpam-521	597	7	i	i	PROPN
ejpam-521	597	8	)	)	PUNCT
ejpam-521	597	9	−	−	PROPN
ejpam-521	598	1	k	k	INTJ
ejpam-521	598	2	∑	∑	PROPN
ejpam-521	598	3	i=1	i=1	PROPN
ejpam-521	598	4	ni	ni	PROPN
ejpam-521	598	5	n	n	PROPN
ejpam-521	598	6	∫	∫	PROPN
ejpam-521	598	7	fi	fi	NOUN
ejpam-521	598	8	log	log	NOUN
ejpam-521	598	9	fi	fi	NOUN
ejpam-521	598	10	→	→	SYM
ejpam-521	598	11	0	0	NUM
ejpam-521	598	12	a.s	a.s	PROPN
ejpam-521	598	13	.	.	PROPN
ejpam-521	598	14	(	(	PUNCT
ejpam-521	598	15	123	123	NUM
ejpam-521	598	16	)	)	PUNCT
ejpam-521	598	17	and	and	CCONJ
ejpam-521	598	18	1	1	NUM
ejpam-521	598	19	n	n	NOUN
ejpam-521	598	20	log	log	VERB
ejpam-521	598	21	f	f	PROPN
ejpam-521	598	22	n	n	PRON
ejpam-521	598	23	mix(x	mix(x	NOUN
ejpam-521	598	24	n)−	n)−	PROPN
ejpam-521	598	25	∫	∫	PROPN
ejpam-521	598	26	fmix	fmix	PROPN
ejpam-521	598	27	log	log	VERB
ejpam-521	598	28	fmix→	fmix→	PROPN
ejpam-521	598	29	0	0	PUNCT
ejpam-521	599	1	a.s	a.s	PROPN
ejpam-521	599	2	.	.	PROPN
ejpam-521	600	1	(	(	PUNCT
ejpam-521	600	2	124	124	NUM
ejpam-521	600	3	)	)	PUNCT
ejpam-521	600	4	as	as	ADP
ejpam-521	600	5	n1→∞	n1→∞	NOUN
ejpam-521	600	6	,	,	PUNCT
ejpam-521	600	7	·	·	PUNCT
ejpam-521	600	8	·	·	PUNCT
ejpam-521	600	9	·	·	PUNCT
ejpam-521	600	10	,	,	PUNCT
ejpam-521	600	11	nk→∞.	nk→∞.	NOUN
ejpam-521	600	12	by	by	ADP
ejpam-521	600	13	the	the	DET
ejpam-521	600	14	convexity	convexity	NOUN
ejpam-521	600	15	of	of	ADP
ejpam-521	600	16	x	x	PART
ejpam-521	600	17	log	log	NOUN
ejpam-521	600	18	x	x	X
ejpam-521	600	19	,	,	PUNCT
ejpam-521	600	20	∫	∫	PROPN
ejpam-521	600	21	fmix	fmix	PROPN
ejpam-521	600	22	log	log	NOUN
ejpam-521	600	23	fmix	fmix	NOUN
ejpam-521	600	24	≤	≤	PUNCT
ejpam-521	601	1	k	k	X
ejpam-521	601	2	∑	∑	PROPN
ejpam-521	601	3	i=1	i=1	PROPN
ejpam-521	601	4	ni	ni	PROPN
ejpam-521	601	5	n	n	PROPN
ejpam-521	601	6	∫	∫	PROPN
ejpam-521	601	7	fi	fi	NOUN
ejpam-521	601	8	log	log	PROPN
ejpam-521	601	9	fi	fi	NOUN
ejpam-521	601	10	(	(	PUNCT
ejpam-521	601	11	125	125	NUM
ejpam-521	601	12	)	)	PUNCT
ejpam-521	601	13	for	for	ADP
ejpam-521	601	14	any	any	DET
ejpam-521	601	15	group	group	NOUN
ejpam-521	601	16	of	of	ADP
ejpam-521	601	17	samples	sample	NOUN
ejpam-521	601	18	of	of	ADP
ejpam-521	601	19	sizes	size	NOUN
ejpam-521	601	20	n1	n1	NOUN
ejpam-521	601	21	,	,	PUNCT
ejpam-521	601	22	·	·	PUNCT
ejpam-521	601	23	·	·	PUNCT
ejpam-521	601	24	·	·	PUNCT
ejpam-521	601	25	,	,	PUNCT
ejpam-521	601	26	nk	nk	PROPN
ejpam-521	601	27	satisfying	satisfy	VERB
ejpam-521	601	28	∑k	∑k	PROPN
ejpam-521	601	29	i=1	i=1	PROPN
ejpam-521	601	30	ni	ni	PROPN
ejpam-521	601	31	=	=	PROPN
ejpam-521	601	32	n	n	CCONJ
ejpam-521	601	33	,	,	PUNCT
ejpam-521	601	34	where	where	SCONJ
ejpam-521	601	35	the	the	DET
ejpam-521	601	36	equality	equality	NOUN
ejpam-521	601	37	holds	hold	VERB
ejpam-521	601	38	if	if	SCONJ
ejpam-521	601	39	and	and	CCONJ
ejpam-521	601	40	only	only	ADV
ejpam-521	601	41	if	if	SCONJ
ejpam-521	601	42	all	all	DET
ejpam-521	601	43	the	the	DET
ejpam-521	601	44	densities	density	NOUN
ejpam-521	601	45	f1	f1	NOUN
ejpam-521	601	46	,	,	PUNCT
ejpam-521	601	47	·	·	PUNCT
ejpam-521	601	48	·	·	PUNCT
ejpam-521	601	49	·	·	PUNCT
ejpam-521	601	50	,	,	PUNCT
ejpam-521	601	51	fk	fk	INTJ
ejpam-521	601	52	are	be	AUX
ejpam-521	601	53	equal	equal	ADJ
ejpam-521	601	54	(	(	PUNCT
ejpam-521	601	55	except	except	SCONJ
ejpam-521	601	56	a	a	DET
ejpam-521	601	57	set	set	NOUN
ejpam-521	601	58	with	with	ADP
ejpam-521	601	59	measure	measure	NOUN
ejpam-521	601	60	zero	zero	NUM
ejpam-521	601	61	)	)	PUNCT
ejpam-521	601	62	.	.	PUNCT
ejpam-521	602	1	therefore	therefore	ADV
ejpam-521	602	2	(	(	PUNCT
ejpam-521	602	3	122	122	NUM
ejpam-521	602	4	)	)	PUNCT
ejpam-521	602	5	is	be	AUX
ejpam-521	602	6	established	establish	VERB
ejpam-521	602	7	by	by	ADP
ejpam-521	602	8	using	use	VERB
ejpam-521	602	9	(	(	PUNCT
ejpam-521	602	10	123	123	NUM
ejpam-521	602	11	)	)	PUNCT
ejpam-521	602	12	and	and	CCONJ
ejpam-521	602	13	(	(	PUNCT
ejpam-521	602	14	124	124	NUM
ejpam-521	602	15	)	)	PUNCT
ejpam-521	602	16	.	.	PUNCT
ejpam-521	603	1	also	also	ADV
ejpam-521	603	2	for	for	ADP
ejpam-521	603	3	any	any	DET
ejpam-521	603	4	ǫ1	ǫ1	PROPN
ejpam-521	603	5	>	>	X
ejpam-521	603	6	0	0	NUM
ejpam-521	603	7	,	,	PUNCT
ejpam-521	603	8	·	·	PUNCT
ejpam-521	603	9	·	·	PUNCT
ejpam-521	603	10	·	·	PUNCT
ejpam-521	603	11	,	,	PUNCT
ejpam-521	603	12	ǫk	ǫk	X
ejpam-521	603	13	>	>	X
ejpam-521	603	14	0	0	NUM
ejpam-521	603	15	,	,	PUNCT
ejpam-521	603	16	if	if	SCONJ
ejpam-521	603	17	n1	n1	PROPN
ejpam-521	603	18	n	n	CCONJ
ejpam-521	603	19	>	>	X
ejpam-521	603	20	ǫ1	ǫ1	PROPN
ejpam-521	603	21	,	,	PUNCT
ejpam-521	603	22	·	·	PUNCT
ejpam-521	603	23	·	·	PUNCT
ejpam-521	603	24	·	·	PUNCT
ejpam-521	603	25	,	,	PUNCT
ejpam-521	603	26	nk	nk	PROPN
ejpam-521	603	27	n	n	PROPN
ejpam-521	603	28	>	>	X
ejpam-521	603	29	ǫk	ǫk	X
ejpam-521	603	30	and	and	CCONJ
ejpam-521	603	31	if	if	SCONJ
ejpam-521	603	32	at	at	ADV
ejpam-521	603	33	least	least	ADV
ejpam-521	603	34	two	two	NUM
ejpam-521	603	35	of	of	ADP
ejpam-521	603	36	f1	f1	NOUN
ejpam-521	603	37	,	,	PUNCT
ejpam-521	603	38	·	·	PUNCT
ejpam-521	603	39	·	·	PUNCT
ejpam-521	603	40	·	·	PUNCT
ejpam-521	603	41	,	,	PUNCT
ejpam-521	603	42	fk	fk	INTJ
ejpam-521	603	43	are	be	AUX
ejpam-521	603	44	not	not	PART
ejpam-521	603	45	equal	equal	ADJ
ejpam-521	603	46	almost	almost	ADV
ejpam-521	603	47	surely	surely	ADV
ejpam-521	603	48	,	,	PUNCT
ejpam-521	603	49	there	there	PRON
ejpam-521	603	50	exists	exist	VERB
ejpam-521	603	51	a	a	DET
ejpam-521	603	52	constant	constant	ADJ
ejpam-521	603	53	η	η	NOUN
ejpam-521	603	54	<	<	X
ejpam-521	603	55	0	0	NUM
ejpam-521	603	56	depending	depend	VERB
ejpam-521	603	57	on	on	ADP
ejpam-521	603	58	ǫ1	ǫ1	NUM
ejpam-521	603	59	,	,	PUNCT
ejpam-521	603	60	·	·	PUNCT
ejpam-521	603	61	·	·	PUNCT
ejpam-521	603	62	·	·	PUNCT
ejpam-521	603	63	,	,	PUNCT
ejpam-521	603	64	ǫk	ǫk	INTJ
ejpam-521	603	65	such	such	ADJ
ejpam-521	603	66	that	that	SCONJ
ejpam-521	603	67	∫	∫	PROPN
ejpam-521	603	68	fmix	fmix	PROPN
ejpam-521	603	69	log	log	NOUN
ejpam-521	603	70	fmix−	fmix−	NOUN
ejpam-521	604	1	k	k	PROPN
ejpam-521	604	2	∑	∑	PROPN
ejpam-521	604	3	i=1	i=1	PROPN
ejpam-521	604	4	ni	ni	PROPN
ejpam-521	604	5	n	n	PROPN
ejpam-521	604	6	∫	∫	PROPN
ejpam-521	604	7	fi	fi	NOUN
ejpam-521	604	8	log	log	PROPN
ejpam-521	604	9	fi	fi	NOUN
ejpam-521	604	10	<	<	X
ejpam-521	604	11	η	η	PROPN
ejpam-521	604	12	(	(	PUNCT
ejpam-521	604	13	126	126	NUM
ejpam-521	604	14	)	)	PUNCT
ejpam-521	604	15	for	for	ADP
ejpam-521	604	16	any	any	DET
ejpam-521	604	17	set	set	NOUN
ejpam-521	604	18	of	of	ADP
ejpam-521	604	19	integers	integer	NOUN
ejpam-521	604	20	{	{	PUNCT
ejpam-521	604	21	ni	ni	NOUN
ejpam-521	604	22	}	}	PUNCT
ejpam-521	604	23	satisfying	satisfy	VERB
ejpam-521	604	24	∑k	∑k	PROPN
ejpam-521	604	25	i=1	i=1	PROPN
ejpam-521	604	26	ni	ni	PROPN
ejpam-521	604	27	=	=	PROPN
ejpam-521	604	28	n.	n.	PROPN
ejpam-521	604	29	hence	hence	ADV
ejpam-521	604	30	(	(	PUNCT
ejpam-521	604	31	121	121	NUM
ejpam-521	604	32	)	)	PUNCT
ejpam-521	604	33	follows	follow	VERB
ejpam-521	604	34	from	from	ADP
ejpam-521	604	35	(	(	PUNCT
ejpam-521	604	36	123	123	NUM
ejpam-521	604	37	)	)	PUNCT
ejpam-521	604	38	and	and	CCONJ
ejpam-521	604	39	(	(	PUNCT
ejpam-521	604	40	124	124	NUM
ejpam-521	604	41	)	)	PUNCT
ejpam-521	604	42	.	.	PUNCT
ejpam-521	605	1	notice	notice	VERB
ejpam-521	605	2	that	that	SCONJ
ejpam-521	605	3	α1γ2	α1γ2	PUNCT
ejpam-521	605	4	<	<	X
ejpam-521	605	5	1	1	NUM
ejpam-521	605	6	,	,	PUNCT
ejpam-521	605	7	γ2	γ2	NOUN
ejpam-521	605	8	<	<	X
ejpam-521	605	9	1	1	NUM
ejpam-521	605	10	and	and	CCONJ
ejpam-521	605	11	1	1	NUM
ejpam-521	605	12	1	1	NUM
ejpam-521	605	13	+	+	NOUN
ejpam-521	605	14	2α2	2α2	NUM
ejpam-521	605	15	<	<	X
ejpam-521	605	16	1	1	NUM
ejpam-521	605	17	,	,	PUNCT
ejpam-521	605	18	(	(	PUNCT
ejpam-521	605	19	41	41	NUM
ejpam-521	605	20	)	)	PUNCT
ejpam-521	605	21	and	and	CCONJ
ejpam-521	605	22	(	(	PUNCT
ejpam-521	605	23	42	42	X
ejpam-521	605	24	)	)	PUNCT
ejpam-521	605	25	hold	hold	VERB
ejpam-521	605	26	by	by	ADP
ejpam-521	605	27	(	(	PUNCT
ejpam-521	605	28	116	116	NUM
ejpam-521	605	29	)	)	PUNCT
ejpam-521	605	30	to	to	ADP
ejpam-521	605	31	(	(	PUNCT
ejpam-521	605	32	122	122	NUM
ejpam-521	605	33	)	)	PUNCT
ejpam-521	605	34	.	.	PUNCT
ejpam-521	606	1	⊳	⊳	NOUN
ejpam-521	606	2	references	reference	NOUN
ejpam-521	606	3	79	79	NUM
ejpam-521	606	4	references	reference	NOUN
ejpam-521	606	5	[	[	X
ejpam-521	606	6	1	1	NUM
ejpam-521	606	7	]	]	PUNCT
ejpam-521	606	8	bozdogan	bozdogan	NOUN
ejpam-521	606	9	,	,	PUNCT
ejpam-521	606	10	h.	h.	PROPN
ejpam-521	606	11	(	(	PUNCT
ejpam-521	606	12	2000	2000	NUM
ejpam-521	606	13	)	)	PUNCT
ejpam-521	606	14	.	.	PUNCT
ejpam-521	607	1	akaike	akaike	ADP
ejpam-521	607	2	’s	’s	PART
ejpam-521	607	3	information	information	NOUN
ejpam-521	607	4	criterion	criterion	NOUN
ejpam-521	607	5	and	and	CCONJ
ejpam-521	607	6	recent	recent	ADJ
ejpam-521	607	7	developments	development	NOUN
ejpam-521	607	8	in	in	ADP
ejpam-521	607	9	information	information	NOUN
ejpam-521	607	10	complexity	complexity	NOUN
ejpam-521	607	11	.	.	PUNCT
ejpam-521	608	1	journal	journal	PROPN
ejpam-521	608	2	of	of	ADP
ejpam-521	608	3	mathematical	mathematical	ADJ
ejpam-521	608	4	psychology	psychology	NOUN
ejpam-521	608	5	,	,	PUNCT
ejpam-521	608	6	44	44	NUM
ejpam-521	608	7	,	,	PUNCT
ejpam-521	608	8	62	62	NUM
ejpam-521	608	9	-	-	SYM
ejpam-521	608	10	91	91	NUM
ejpam-521	608	11	.	.	PUNCT
ejpam-521	609	1	[	[	X
ejpam-521	609	2	2	2	NUM
ejpam-521	609	3	]	]	SYM
ejpam-521	609	4	dawid	dawid	PROPN
ejpam-521	609	5	,	,	PUNCT
ejpam-521	609	6	a.p	a.p	PROPN
ejpam-521	609	7	.	.	PROPN
ejpam-521	609	8	(	(	PUNCT
ejpam-521	609	9	1992	1992	NUM
ejpam-521	609	10	)	)	PUNCT
ejpam-521	609	11	.	.	PUNCT
ejpam-521	610	1	prequential	prequential	ADJ
ejpam-521	610	2	analysis	analysis	NOUN
ejpam-521	610	3	,	,	PUNCT
ejpam-521	610	4	stochastic	stochastic	ADJ
ejpam-521	610	5	complexity	complexity	NOUN
ejpam-521	610	6	and	and	CCONJ
ejpam-521	610	7	bayesian	bayesian	NOUN
ejpam-521	610	8	inference	inference	NOUN
ejpam-521	610	9	.	.	PUNCT
ejpam-521	611	1	bayesian	bayesian	NOUN
ejpam-521	611	2	statistics	statistic	NOUN
ejpam-521	611	3	4	4	NUM
ejpam-521	611	4	(	(	PUNCT
ejpam-521	611	5	j.m	j.m	PROPN
ejpam-521	611	6	.	.	PROPN
ejpam-521	611	7	bernardo	bernardo	PROPN
ejpam-521	611	8	,	,	PUNCT
ejpam-521	611	9	j.o	j.o	PROPN
ejpam-521	611	10	.	.	PROPN
ejpam-521	611	11	berger	berger	PROPN
ejpam-521	611	12	,	,	PUNCT
ejpam-521	611	13	a.p	a.p	PROPN
ejpam-521	611	14	.	.	PROPN
ejpam-521	611	15	dawid	dawid	PROPN
ejpam-521	611	16	and	and	CCONJ
ejpam-521	611	17	a.f.m	a.f.m	PROPN
ejpam-521	611	18	.	.	PROPN
ejpam-521	611	19	smith	smith	PROPN
ejpam-521	611	20	eds	eds	PROPN
ejpam-521	611	21	)	)	PUNCT
ejpam-521	611	22	,	,	PUNCT
ejpam-521	611	23	oxford	oxford	PROPN
ejpam-521	611	24	university	university	PROPN
ejpam-521	611	25	press	press	NOUN
ejpam-521	611	26	,	,	PUNCT
ejpam-521	611	27	109	109	NUM
ejpam-521	611	28	-	-	SYM
ejpam-521	611	29	125	125	NUM
ejpam-521	611	30	(	(	PUNCT
ejpam-521	611	31	with	with	ADP
ejpam-521	611	32	discussions	discussion	NOUN
ejpam-521	611	33	)	)	PUNCT
ejpam-521	611	34	.	.	PUNCT
ejpam-521	612	1	[	[	X
ejpam-521	612	2	3	3	NUM
ejpam-521	612	3	]	]	SYM
ejpam-521	612	4	dawid	dawid	PROPN
ejpam-521	612	5	,	,	PUNCT
ejpam-521	612	6	a.p	a.p	PROPN
ejpam-521	612	7	.	.	PROPN
ejpam-521	612	8	(	(	PUNCT
ejpam-521	612	9	1991	1991	NUM
ejpam-521	612	10	)	)	PUNCT
ejpam-521	612	11	.	.	PUNCT
ejpam-521	613	1	fisherian	fisherian	PROPN
ejpam-521	613	2	inference	inference	PROPN
ejpam-521	613	3	in	in	ADP
ejpam-521	613	4	likelihood	likelihood	NOUN
ejpam-521	613	5	and	and	CCONJ
ejpam-521	613	6	prequential	prequential	ADJ
ejpam-521	613	7	frames	frame	NOUN
ejpam-521	613	8	of	of	ADP
ejpam-521	613	9	reference	reference	NOUN
ejpam-521	613	10	.	.	PUNCT
ejpam-521	614	1	j.	j.	PROPN
ejpam-521	614	2	roy	roy	PROPN
ejpam-521	614	3	.	.	PROPN
ejpam-521	614	4	statist	statist	PROPN
ejpam-521	614	5	.	.	PUNCT
ejpam-521	615	1	soc	soc	PROPN
ejpam-521	615	2	.	.	PUNCT
ejpam-521	616	1	b	b	PROPN
ejpam-521	616	2	53	53	NUM
ejpam-521	616	3	,	,	PUNCT
ejpam-521	616	4	79	79	NUM
ejpam-521	616	5	-	-	SYM
ejpam-521	616	6	109	109	NUM
ejpam-521	616	7	(	(	PUNCT
ejpam-521	616	8	with	with	ADP
ejpam-521	616	9	discussions	discussion	NOUN
ejpam-521	616	10	)	)	PUNCT
ejpam-521	616	11	.	.	PUNCT
ejpam-521	617	1	[	[	X
ejpam-521	617	2	4	4	NUM
ejpam-521	617	3	]	]	SYM
ejpam-521	617	4	dawid	dawid	PROPN
ejpam-521	617	5	,	,	PUNCT
ejpam-521	617	6	a.p	a.p	PROPN
ejpam-521	617	7	.	.	PROPN
ejpam-521	617	8	(	(	PUNCT
ejpam-521	617	9	1984	1984	NUM
ejpam-521	617	10	)	)	PUNCT
ejpam-521	617	11	.	.	PUNCT
ejpam-521	618	1	present	present	ADJ
ejpam-521	618	2	position	position	NOUN
ejpam-521	618	3	and	and	CCONJ
ejpam-521	618	4	potential	potential	ADJ
ejpam-521	618	5	developments	development	NOUN
ejpam-521	618	6	:	:	PUNCT
ejpam-521	618	7	some	some	DET
ejpam-521	618	8	personal	personal	ADJ
ejpam-521	618	9	views	view	NOUN
ejpam-521	618	10	,	,	PUNCT
ejpam-521	618	11	statistical	statistical	ADJ
ejpam-521	618	12	theory	theory	NOUN
ejpam-521	618	13	,	,	PUNCT
ejpam-521	618	14	the	the	DET
ejpam-521	618	15	prequential	prequential	ADJ
ejpam-521	618	16	approach	approach	NOUN
ejpam-521	618	17	.	.	PUNCT
ejpam-521	619	1	j.	j.	PROPN
ejpam-521	619	2	roy	roy	PROPN
ejpam-521	619	3	.	.	PROPN
ejpam-521	619	4	statist	statist	PROPN
ejpam-521	619	5	.	.	PUNCT
ejpam-521	620	1	soc	soc	PROPN
ejpam-521	620	2	.	.	PUNCT
ejpam-521	621	1	a	a	DET
ejpam-521	621	2	,	,	PUNCT
ejpam-521	621	3	47	47	NUM
ejpam-521	621	4	,	,	PUNCT
ejpam-521	621	5	278	278	NUM
ejpam-521	621	6	-	-	SYM
ejpam-521	621	7	292	292	NUM
ejpam-521	621	8	(	(	PUNCT
ejpam-521	621	9	with	with	ADP
ejpam-521	621	10	discussions	discussion	NOUN
ejpam-521	621	11	)	)	PUNCT
ejpam-521	621	12	.	.	PUNCT
ejpam-521	622	1	[	[	X
ejpam-521	622	2	5	5	NUM
ejpam-521	622	3	]	]	PUNCT
ejpam-521	622	4	elias	elias	PROPN
ejpam-521	622	5	,	,	PUNCT
ejpam-521	622	6	p.	p.	NOUN
ejpam-521	622	7	(	(	PUNCT
ejpam-521	622	8	1975	1975	NUM
ejpam-521	622	9	)	)	PUNCT
ejpam-521	622	10	.	.	PUNCT
ejpam-521	623	1	universal	universal	ADJ
ejpam-521	623	2	codeword	codeword	NOUN
ejpam-521	623	3	sets	set	NOUN
ejpam-521	623	4	and	and	CCONJ
ejpam-521	623	5	representations	representation	NOUN
ejpam-521	623	6	of	of	ADP
ejpam-521	623	7	the	the	DET
ejpam-521	623	8	integers	integer	NOUN
ejpam-521	623	9	.	.	PUNCT
ejpam-521	624	1	ieee	ieee	PROPN
ejpam-521	624	2	trans	trans	PROPN
ejpam-521	624	3	.	.	PUNCT
ejpam-521	625	1	information	information	NOUN
ejpam-521	625	2	theory	theory	NOUN
ejpam-521	625	3	21	21	NUM
ejpam-521	625	4	,	,	PUNCT
ejpam-521	625	5	194	194	NUM
ejpam-521	625	6	-	-	SYM
ejpam-521	625	7	203	203	NUM
ejpam-521	625	8	.	.	PUNCT
ejpam-521	626	1	[	[	X
ejpam-521	626	2	6	6	NUM
ejpam-521	626	3	]	]	X
ejpam-521	626	4	freedman	freedman	PROPN
ejpam-521	626	5	,	,	PUNCT
ejpam-521	626	6	d.a	d.a	PROPN
ejpam-521	626	7	.	.	PROPN
ejpam-521	626	8	and	and	CCONJ
ejpam-521	626	9	diaconis	diaconis	PROPN
ejpam-521	626	10	,	,	PUNCT
ejpam-521	626	11	p.	p.	NOUN
ejpam-521	626	12	(	(	PUNCT
ejpam-521	626	13	1981	1981	NUM
ejpam-521	626	14	)	)	PUNCT
ejpam-521	626	15	.	.	PUNCT
ejpam-521	627	1	on	on	ADP
ejpam-521	627	2	the	the	DET
ejpam-521	627	3	histogram	histogram	NOUN
ejpam-521	627	4	as	as	ADP
ejpam-521	627	5	a	a	DET
ejpam-521	627	6	density	density	NOUN
ejpam-521	627	7	estimator	estimator	NOUN
ejpam-521	627	8	:	:	PUNCT
ejpam-521	627	9	l2	l2	NOUN
ejpam-521	627	10	theory	theory	NOUN
ejpam-521	627	11	.	.	PUNCT
ejpam-521	628	1	z.	z.	PROPN
ejpam-521	628	2	wahrscheinlichkeitstheor	wahrscheinlichkeitstheor	PROPN
ejpam-521	628	3	.	.	PUNCT
ejpam-521	629	1	verw	verw	PROPN
ejpam-521	629	2	.	.	PUNCT
ejpam-521	630	1	geb	geb	PROPN
ejpam-521	630	2	.	.	PROPN
ejpam-521	631	1	57	57	NUM
ejpam-521	631	2	,	,	PUNCT
ejpam-521	631	3	453	453	NUM
ejpam-521	631	4	-	-	SYM
ejpam-521	631	5	475	475	NUM
ejpam-521	631	6	.	.	PUNCT
ejpam-521	632	1	[	[	X
ejpam-521	632	2	7	7	NUM
ejpam-521	632	3	]	]	X
ejpam-521	632	4	hall	hall	NOUN
ejpam-521	632	5	,	,	PUNCT
ejpam-521	632	6	p.	p.	PROPN
ejpam-521	632	7	and	and	CCONJ
ejpam-521	632	8	hannan	hannan	PROPN
ejpam-521	632	9	,	,	PUNCT
ejpam-521	632	10	e.j	e.j	PROPN
ejpam-521	632	11	.	.	PROPN
ejpam-521	632	12	(	(	PUNCT
ejpam-521	632	13	1988	1988	NUM
ejpam-521	632	14	)	)	PUNCT
ejpam-521	632	15	.	.	PUNCT
ejpam-521	633	1	on	on	ADP
ejpam-521	633	2	stochastic	stochastic	ADJ
ejpam-521	633	3	complexity	complexity	NOUN
ejpam-521	633	4	and	and	CCONJ
ejpam-521	633	5	nonparametric	nonparametric	NOUN
ejpam-521	633	6	density	density	NOUN
ejpam-521	633	7	estimation	estimation	NOUN
ejpam-521	633	8	.	.	PUNCT
ejpam-521	634	1	biometrika	biometrika	NOUN
ejpam-521	634	2	,	,	PUNCT
ejpam-521	634	3	75	75	NUM
ejpam-521	634	4	,	,	PUNCT
ejpam-521	634	5	705	705	NUM
ejpam-521	634	6	-	-	SYM
ejpam-521	634	7	714	714	NUM
ejpam-521	634	8	.	.	PUNCT
ejpam-521	635	1	[	[	X
ejpam-521	635	2	8	8	NUM
ejpam-521	635	3	]	]	X
ejpam-521	635	4	lehmann	lehmann	PROPN
ejpam-521	635	5	,	,	PUNCT
ejpam-521	635	6	e.l	e.l	PROPN
ejpam-521	635	7	.	.	PROPN
ejpam-521	635	8	and	and	CCONJ
ejpam-521	635	9	casella	casella	PROPN
ejpam-521	635	10	,	,	PUNCT
ejpam-521	635	11	g.	g.	PROPN
ejpam-521	635	12	(	(	PUNCT
ejpam-521	635	13	1998	1998	NUM
ejpam-521	635	14	)	)	PUNCT
ejpam-521	635	15	.	.	PUNCT
ejpam-521	635	16	theory	theory	NOUN
ejpam-521	635	17	of	of	ADP
ejpam-521	635	18	point	point	NOUN
ejpam-521	635	19	estimation	estimation	NOUN
ejpam-521	635	20	.	.	PUNCT
ejpam-521	636	1	springer	springer	NOUN
ejpam-521	636	2	-	-	PUNCT
ejpam-521	636	3	verlag	verlag	PROPN
ejpam-521	636	4	,	,	PUNCT
ejpam-521	636	5	new	new	PROPN
ejpam-521	636	6	york	york	PROPN
ejpam-521	636	7	.	.	PUNCT
ejpam-521	637	1	[	[	X
ejpam-521	637	2	9	9	NUM
ejpam-521	637	3	]	]	X
ejpam-521	637	4	qian	qian	PROPN
ejpam-521	637	5	,	,	PUNCT
ejpam-521	637	6	g.	g.	PROPN
ejpam-521	637	7	and	and	CCONJ
ejpam-521	637	8	künsch	künsch	PROPN
ejpam-521	637	9	,	,	PUNCT
ejpam-521	637	10	h.r	h.r	PROPN
ejpam-521	637	11	.	.	PROPN
ejpam-521	637	12	(	(	PUNCT
ejpam-521	637	13	1998	1998	NUM
ejpam-521	637	14	)	)	PUNCT
ejpam-521	637	15	.	.	PUNCT
ejpam-521	638	1	some	some	DET
ejpam-521	638	2	notes	note	NOUN
ejpam-521	638	3	on	on	ADP
ejpam-521	638	4	rissanen	rissanen	PROPN
ejpam-521	638	5	’s	’s	PART
ejpam-521	638	6	stochastic	stochastic	ADJ
ejpam-521	638	7	complexity	complexity	NOUN
ejpam-521	638	8	.	.	PUNCT
ejpam-521	639	1	ieee	ieee	PROPN
ejpam-521	639	2	trans	trans	PROPN
ejpam-521	639	3	information	information	PROPN
ejpam-521	639	4	theory	theory	NOUN
ejpam-521	639	5	44	44	NUM
ejpam-521	639	6	,	,	PUNCT
ejpam-521	639	7	782	782	NUM
ejpam-521	639	8	-	-	SYM
ejpam-521	639	9	786	786	NUM
ejpam-521	639	10	.	.	PUNCT
ejpam-521	640	1	[	[	X
ejpam-521	640	2	10	10	NUM
ejpam-521	640	3	]	]	X
ejpam-521	640	4	qian	qian	PROPN
ejpam-521	640	5	,	,	PUNCT
ejpam-521	640	6	g.	g.	PROPN
ejpam-521	640	7	gabor	gabor	PROPN
ejpam-521	640	8	,	,	PUNCT
ejpam-521	640	9	g.	g.	PROPN
ejpam-521	640	10	and	and	CCONJ
ejpam-521	640	11	gupta	gupta	PROPN
ejpam-521	640	12	,	,	PUNCT
ejpam-521	640	13	r.p	r.p	PROPN
ejpam-521	640	14	.	.	PROPN
ejpam-521	640	15	(	(	PUNCT
ejpam-521	640	16	1996	1996	NUM
ejpam-521	640	17	)	)	PUNCT
ejpam-521	640	18	.	.	PUNCT
ejpam-521	640	19	test	test	NOUN
ejpam-521	640	20	for	for	ADP
ejpam-521	640	21	homogeniety	homogeniety	NOUN
ejpam-521	640	22	of	of	ADP
ejpam-521	640	23	several	several	ADJ
ejpam-521	640	24	populations	population	NOUN
ejpam-521	640	25	by	by	ADP
ejpam-521	640	26	stochastic	stochastic	ADJ
ejpam-521	640	27	complexity	complexity	NOUN
ejpam-521	640	28	.	.	PUNCT
ejpam-521	641	1	journal	journal	NOUN
ejpam-521	641	2	of	of	ADP
ejpam-521	641	3	statistical	statistical	ADJ
ejpam-521	641	4	planning	planning	NOUN
ejpam-521	641	5	and	and	CCONJ
ejpam-521	641	6	inference	inference	NOUN
ejpam-521	641	7	.	.	PUNCT
ejpam-521	642	1	53	53	NUM
ejpam-521	642	2	.	.	X
ejpam-521	643	1	133	133	NUM
ejpam-521	643	2	-	-	SYM
ejpam-521	643	3	151	151	NUM
ejpam-521	643	4	[	[	SYM
ejpam-521	643	5	11	11	NUM
ejpam-521	643	6	]	]	SYM
ejpam-521	643	7	rissanen	rissanen	NOUN
ejpam-521	643	8	,	,	PUNCT
ejpam-521	643	9	j.	j.	PROPN
ejpam-521	643	10	(	(	PUNCT
ejpam-521	643	11	2007	2007	NUM
ejpam-521	643	12	)	)	PUNCT
ejpam-521	643	13	.	.	PUNCT
ejpam-521	644	1	information	information	NOUN
ejpam-521	644	2	and	and	CCONJ
ejpam-521	644	3	complexity	complexity	NOUN
ejpam-521	644	4	in	in	ADP
ejpam-521	644	5	statistical	statistical	ADJ
ejpam-521	644	6	modeling	modeling	NOUN
ejpam-521	644	7	.	.	PUNCT
ejpam-521	645	1	springer	springer	NOUN
ejpam-521	645	2	,	,	PUNCT
ejpam-521	645	3	new	new	PROPN
ejpam-521	645	4	york	york	PROPN
ejpam-521	645	5	.	.	PUNCT
ejpam-521	646	1	[	[	X
ejpam-521	646	2	12	12	NUM
ejpam-521	646	3	]	]	X
ejpam-521	646	4	rissanen	rissanen	NOUN
ejpam-521	646	5	,	,	PUNCT
ejpam-521	646	6	j.	j.	PROPN
ejpam-521	646	7	(	(	PUNCT
ejpam-521	646	8	1996	1996	NUM
ejpam-521	646	9	)	)	PUNCT
ejpam-521	646	10	.	.	PUNCT
ejpam-521	647	1	fisher	fisher	PROPN
ejpam-521	647	2	information	information	NOUN
ejpam-521	647	3	and	and	CCONJ
ejpam-521	647	4	stochastic	stochastic	ADJ
ejpam-521	647	5	complexity	complexity	NOUN
ejpam-521	647	6	.	.	PUNCT
ejpam-521	648	1	ieee	ieee	PROPN
ejpam-521	648	2	trans	trans	PROPN
ejpam-521	648	3	.	.	PUNCT
ejpam-521	649	1	information	information	NOUN
ejpam-521	649	2	theory	theory	NOUN
ejpam-521	649	3	,	,	PUNCT
ejpam-521	649	4	42	42	NUM
ejpam-521	649	5	,	,	PUNCT
ejpam-521	649	6	40	40	NUM
ejpam-521	649	7	-	-	SYM
ejpam-521	649	8	47	47	NUM
ejpam-521	649	9	.	.	PUNCT
ejpam-521	650	1	[	[	X
ejpam-521	650	2	13	13	NUM
ejpam-521	650	3	]	]	SYM
ejpam-521	650	4	rissanen	rissanen	NOUN
ejpam-521	650	5	,	,	PUNCT
ejpam-521	650	6	j.	j.	PROPN
ejpam-521	650	7	(	(	PUNCT
ejpam-521	650	8	1989	1989	NUM
ejpam-521	650	9	)	)	PUNCT
ejpam-521	650	10	.	.	PUNCT
ejpam-521	651	1	stochastic	stochastic	ADJ
ejpam-521	651	2	complexity	complexity	NOUN
ejpam-521	651	3	in	in	ADP
ejpam-521	651	4	statistical	statistical	ADJ
ejpam-521	651	5	inquiry	inquiry	NOUN
ejpam-521	651	6	.	.	PUNCT
ejpam-521	652	1	world	world	NOUN
ejpam-521	652	2	scientific	scientific	ADJ
ejpam-521	652	3	publishing	publishing	NOUN
ejpam-521	652	4	company	company	NOUN
ejpam-521	652	5	,	,	PUNCT
ejpam-521	652	6	teaneck	teaneck	PROPN
ejpam-521	652	7	,	,	PUNCT
ejpam-521	652	8	nj	nj	PROPN
ejpam-521	652	9	.	.	PUNCT
ejpam-521	653	1	[	[	X
ejpam-521	653	2	14	14	NUM
ejpam-521	653	3	]	]	SYM
ejpam-521	653	4	rissanen	rissanen	PROPN
ejpam-521	653	5	,	,	PUNCT
ejpam-521	653	6	j.	j.	PROPN
ejpam-521	653	7	,	,	PUNCT
ejpam-521	653	8	speed	speed	NOUN
ejpam-521	653	9	,	,	PUNCT
ejpam-521	653	10	t.p	t.p	PROPN
ejpam-521	653	11	.	.	PROPN
ejpam-521	653	12	and	and	CCONJ
ejpam-521	653	13	yu	yu	PROPN
ejpam-521	653	14	,	,	PUNCT
ejpam-521	653	15	b.	b.	PROPN
ejpam-521	653	16	(	(	PUNCT
ejpam-521	653	17	1992	1992	NUM
ejpam-521	653	18	)	)	PUNCT
ejpam-521	653	19	.	.	PUNCT
ejpam-521	654	1	density	density	NOUN
ejpam-521	654	2	estimation	estimation	NOUN
ejpam-521	654	3	by	by	ADP
ejpam-521	654	4	stochastic	stochastic	ADJ
ejpam-521	654	5	complexity	complexity	NOUN
ejpam-521	654	6	.	.	PUNCT
ejpam-521	655	1	ieee	ieee	PROPN
ejpam-521	655	2	trans	trans	PROPN
ejpam-521	655	3	.	.	PUNCT
ejpam-521	656	1	information	information	PROPN
ejpam-521	656	2	theory	theory	NOUN
ejpam-521	656	3	38	38	NUM
ejpam-521	656	4	,	,	PUNCT
ejpam-521	656	5	315	315	NUM
ejpam-521	656	6	-	-	SYM
ejpam-521	656	7	323	323	NUM
ejpam-521	656	8	.	.	PUNCT
ejpam-521	657	1	[	[	X
ejpam-521	657	2	15	15	NUM
ejpam-521	657	3	]	]	X
ejpam-521	657	4	rissanen	rissanen	NOUN
ejpam-521	657	5	,	,	PUNCT
ejpam-521	657	6	j.	j.	PROPN
ejpam-521	657	7	(	(	PUNCT
ejpam-521	657	8	1986	1986	NUM
ejpam-521	657	9	)	)	PUNCT
ejpam-521	657	10	.	.	PUNCT
ejpam-521	658	1	stochastic	stochastic	ADJ
ejpam-521	658	2	complexity	complexity	NOUN
ejpam-521	658	3	and	and	CCONJ
ejpam-521	658	4	modeling	modeling	NOUN
ejpam-521	658	5	.	.	PUNCT
ejpam-521	659	1	ann	ann	PROPN
ejpam-521	659	2	.	.	PUNCT
ejpam-521	659	3	statist	statist	PROPN
ejpam-521	659	4	.	.	PUNCT
ejpam-521	659	5	,	,	PUNCT
ejpam-521	659	6	14	14	NUM
ejpam-521	659	7	,	,	PUNCT
ejpam-521	659	8	1080	1080	NUM
ejpam-521	659	9	-	-	SYM
ejpam-521	659	10	1100	1100	NUM
ejpam-521	659	11	.	.	PUNCT
ejpam-521	660	1	references	reference	NOUN
ejpam-521	660	2	80	80	NUM
ejpam-521	660	3	[	[	X
ejpam-521	660	4	16	16	NUM
ejpam-521	660	5	]	]	PUNCT
ejpam-521	660	6	rosenblatt	rosenblatt	NOUN
ejpam-521	660	7	,	,	PUNCT
ejpam-521	660	8	m.	m.	NOUN
ejpam-521	660	9	(	(	PUNCT
ejpam-521	660	10	1975	1975	NUM
ejpam-521	660	11	)	)	PUNCT
ejpam-521	660	12	.	.	PUNCT
ejpam-521	661	1	a	a	DET
ejpam-521	661	2	quadratic	quadratic	ADJ
ejpam-521	661	3	measure	measure	NOUN
ejpam-521	661	4	of	of	ADP
ejpam-521	661	5	deviation	deviation	NOUN
ejpam-521	661	6	of	of	ADP
ejpam-521	661	7	two	two	NUM
ejpam-521	661	8	-	-	PUNCT
ejpam-521	661	9	dimensional	dimensional	ADJ
ejpam-521	661	10	density	density	NOUN
ejpam-521	661	11	estimates	estimate	NOUN
ejpam-521	661	12	and	and	CCONJ
ejpam-521	661	13	a	a	DET
ejpam-521	661	14	test	test	NOUN
ejpam-521	661	15	of	of	ADP
ejpam-521	661	16	independence	independence	NOUN
ejpam-521	661	17	.	.	PUNCT
ejpam-521	662	1	ann	ann	PROPN
ejpam-521	662	2	.	.	PUNCT
ejpam-521	662	3	statist	statist	PROPN
ejpam-521	662	4	.	.	PUNCT
ejpam-521	663	1	3	3	NUM
ejpam-521	663	2	,	,	PUNCT
ejpam-521	663	3	1	1	NUM
ejpam-521	663	4	-	-	SYM
ejpam-521	663	5	14	14	NUM
ejpam-521	663	6	.	.	PUNCT
ejpam-521	664	1	[	[	X
ejpam-521	664	2	17	17	NUM
ejpam-521	664	3	]	]	X
ejpam-521	664	4	shiryayev	shiryayev	PROPN
ejpam-521	664	5	,	,	PUNCT
ejpam-521	664	6	a.n	a.n	PROPN
ejpam-521	664	7	.	.	PROPN
ejpam-521	665	1	(	(	PUNCT
ejpam-521	665	2	1995).probability	1995).probability	NUM
ejpam-521	665	3	(	(	PUNCT
ejpam-521	665	4	2nd	2nd	NOUN
ejpam-521	665	5	edition	edition	NOUN
ejpam-521	665	6	)	)	PUNCT
ejpam-521	665	7	.	.	PUNCT
ejpam-521	666	1	springer	springer	NOUN
ejpam-521	666	2	-	-	PUNCT
ejpam-521	666	3	verlag	verlag	PROPN
ejpam-521	666	4	,	,	PUNCT
ejpam-521	666	5	new	new	PROPN
ejpam-521	666	6	york	york	PROPN
ejpam-521	666	7	.	.	PUNCT
ejpam-521	667	1	[	[	X
ejpam-521	667	2	18	18	NUM
ejpam-521	667	3	]	]	SYM
ejpam-521	667	4	solomonoff	solomonoff	NOUN
ejpam-521	667	5	,	,	PUNCT
ejpam-521	667	6	r.j	r.j	PROPN
ejpam-521	667	7	.	.	PROPN
ejpam-521	667	8	(	(	PUNCT
ejpam-521	667	9	1978	1978	NUM
ejpam-521	667	10	)	)	PUNCT
ejpam-521	667	11	.	.	PUNCT
ejpam-521	668	1	complexity	complexity	NOUN
ejpam-521	668	2	-	-	PUNCT
ejpam-521	668	3	based	base	VERB
ejpam-521	668	4	induction	induction	NOUN
ejpam-521	668	5	system	system	NOUN
ejpam-521	668	6	:	:	PUNCT
ejpam-521	668	7	comparison	comparison	NOUN
ejpam-521	668	8	and	and	CCONJ
ejpam-521	668	9	convergence	convergence	NOUN
ejpam-521	668	10	theorems	theorem	NOUN
ejpam-521	668	11	.	.	PUNCT
ejpam-521	669	1	ieee	ieee	PROPN
ejpam-521	669	2	trans	trans	PROPN
ejpam-521	669	3	.	.	PUNCT
ejpam-521	670	1	information	information	NOUN
ejpam-521	670	2	theory	theory	NOUN
ejpam-521	670	3	24	24	NUM
ejpam-521	670	4	,	,	PUNCT
ejpam-521	670	5	422	422	NUM
ejpam-521	670	6	-	-	SYM
ejpam-521	670	7	432	432	NUM
ejpam-521	670	8	.	.	PUNCT
ejpam-521	671	1	[	[	X
ejpam-521	671	2	19	19	NUM
ejpam-521	671	3	]	]	PUNCT
ejpam-521	671	4	stone	stone	NOUN
ejpam-521	671	5	,	,	PUNCT
ejpam-521	671	6	c.j	c.j	PROPN
ejpam-521	671	7	.	.	PROPN
ejpam-521	671	8	(	(	PUNCT
ejpam-521	671	9	1985	1985	NUM
ejpam-521	671	10	)	)	PUNCT
ejpam-521	671	11	.	.	PUNCT
ejpam-521	672	1	an	an	DET
ejpam-521	672	2	asymptotic	asymptotic	ADJ
ejpam-521	672	3	optimal	optimal	ADJ
ejpam-521	672	4	histogram	histogram	NOUN
ejpam-521	672	5	selection	selection	NOUN
ejpam-521	672	6	rule	rule	NOUN
ejpam-521	672	7	.	.	PUNCT
ejpam-521	673	1	proceedings	proceeding	NOUN
ejpam-521	673	2	of	of	ADP
ejpam-521	673	3	the	the	DET
ejpam-521	673	4	berkeley	berkeley	PROPN
ejpam-521	673	5	conference	conference	NOUN
ejpam-521	673	6	in	in	ADP
ejpam-521	673	7	honor	honor	NOUN
ejpam-521	673	8	of	of	ADP
ejpam-521	673	9	jerzy	jerzy	PROPN
ejpam-521	673	10	neyman	neyman	PROPN
ejpam-521	673	11	and	and	CCONJ
ejpam-521	673	12	jack	jack	PROPN
ejpam-521	673	13	kiefer	kiefer	PROPN
ejpam-521	673	14	(	(	PUNCT
ejpam-521	673	15	ed	ed	NOUN
ejpam-521	673	16	.	.	PUNCT
ejpam-521	674	1	by	by	ADP
ejpam-521	674	2	le	le	X
ejpam-521	674	3	cam	cam	PROPN
ejpam-521	674	4	,	,	PUNCT
ejpam-521	674	5	l.m	l.m	PROPN
ejpam-521	674	6	.	.	PROPN
ejpam-521	674	7	and	and	CCONJ
ejpam-521	674	8	ohshen	ohshen	ADV
ejpam-521	674	9	,	,	PUNCT
ejpam-521	674	10	r.a	r.a	PROPN
ejpam-521	674	11	.	.	PROPN
ejpam-521	674	12	)	)	PUNCT
ejpam-521	674	13	,	,	PUNCT
ejpam-521	674	14	volume	volume	NOUN
ejpam-521	674	15	ii	ii	PROPN
ejpam-521	674	16	,	,	PUNCT
ejpam-521	674	17	513	513	NUM
ejpam-521	674	18	-	-	SYM
ejpam-521	674	19	520	520	NUM
ejpam-521	674	20	.	.	PUNCT
ejpam-521	674	21	wadsworth	wadsworth	PROPN
ejpam-521	674	22	,	,	PUNCT
ejpam-521	674	23	belmont	belmont	PROPN
ejpam-521	674	24	,	,	PUNCT
ejpam-521	674	25	ca	ca	NOUN
ejpam-521	674	26	.	.	PUNCT
ejpam-521	675	1	[	[	X
ejpam-521	675	2	20	20	NUM
ejpam-521	675	3	]	]	SYM
ejpam-521	675	4	yu	yu	PROPN
ejpam-521	675	5	,	,	PUNCT
ejpam-521	675	6	b.	b.	PROPN
ejpam-521	675	7	and	and	CCONJ
ejpam-521	675	8	speed	speed	NOUN
ejpam-521	675	9	,	,	PUNCT
ejpam-521	675	10	t.p	t.p	PROPN
ejpam-521	675	11	.	.	PROPN
ejpam-521	675	12	(	(	PUNCT
ejpam-521	675	13	1992	1992	NUM
ejpam-521	675	14	)	)	PUNCT
ejpam-521	675	15	.	.	PUNCT
ejpam-521	676	1	data	datum	NOUN
ejpam-521	676	2	compression	compression	NOUN
ejpam-521	676	3	and	and	CCONJ
ejpam-521	676	4	histograms	histogram	NOUN
ejpam-521	676	5	.	.	PUNCT
ejpam-521	677	1	probability	probability	NOUN
ejpam-521	677	2	theory	theory	NOUN
ejpam-521	677	3	and	and	CCONJ
ejpam-521	677	4	related	relate	VERB
ejpam-521	677	5	fields	field	NOUN
ejpam-521	677	6	92	92	NUM
ejpam-521	677	7	,	,	PUNCT
ejpam-521	677	8	195	195	NUM
ejpam-521	677	9	-	-	SYM
ejpam-521	677	10	229	229	NUM
ejpam-521	677	11	.	.	PUNCT