id	sid	tid	token	lemma	pos
ejpam-3074	1	1	european	european	PROPN
ejpam-3074	1	2	journal	journal	PROPN
ejpam-3074	1	3	of	of	ADP
ejpam-3074	1	4	pure	pure	ADJ
ejpam-3074	1	5	and	and	CCONJ
ejpam-3074	1	6	applied	apply	VERB
ejpam-3074	1	7	mathematics	mathematic	NOUN
ejpam-3074	1	8	vol	vol	NOUN
ejpam-3074	1	9	.	.	PROPN
ejpam-3074	2	1	10	10	NUM
ejpam-3074	2	2	,	,	PUNCT
ejpam-3074	2	3	no	no	INTJ
ejpam-3074	2	4	.	.	NOUN
ejpam-3074	2	5	4	4	NUM
ejpam-3074	2	6	,	,	PUNCT
ejpam-3074	2	7	2017	2017	NUM
ejpam-3074	2	8	,	,	PUNCT
ejpam-3074	2	9	602	602	NUM
ejpam-3074	2	10	-	-	SYM
ejpam-3074	2	11	613	613	NUM
ejpam-3074	2	12	issn	issn	PROPN
ejpam-3074	2	13	1307	1307	NUM
ejpam-3074	2	14	-	-	SYM
ejpam-3074	2	15	5543	5543	NUM
ejpam-3074	2	16	–	–	PUNCT
ejpam-3074	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3074	2	18	published	publish	VERB
ejpam-3074	2	19	by	by	ADP
ejpam-3074	2	20	new	new	PROPN
ejpam-3074	2	21	york	york	PROPN
ejpam-3074	2	22	business	business	PROPN
ejpam-3074	2	23	global	global	PROPN
ejpam-3074	2	24	honorary	honorary	PROPN
ejpam-3074	2	25	invited	invite	VERB
ejpam-3074	2	26	paper	paper	NOUN
ejpam-3074	2	27	origin	origin	NOUN
ejpam-3074	2	28	of	of	ADP
ejpam-3074	2	29	neural	neural	ADJ
ejpam-3074	2	30	firing	firing	NOUN
ejpam-3074	2	31	and	and	CCONJ
ejpam-3074	2	32	synthesis	synthesis	NOUN
ejpam-3074	2	33	in	in	ADP
ejpam-3074	2	34	making	make	VERB
ejpam-3074	2	35	comparisons	comparison	NOUN
ejpam-3074	2	36	thomas	thomas	PROPN
ejpam-3074	2	37	l.	l.	PROPN
ejpam-3074	2	38	saaty1	saaty1	PROPN
ejpam-3074	2	39	,	,	PUNCT
ejpam-3074	2	40	luis	luis	PROPN
ejpam-3074	2	41	g.	g.	PROPN
ejpam-3074	2	42	vargas1,∗	vargas1,∗	PROPN
ejpam-3074	2	43	1	1	NUM
ejpam-3074	2	44	department	department	PROPN
ejpam-3074	2	45	of	of	ADP
ejpam-3074	2	46	business	business	NOUN
ejpam-3074	2	47	analytics	analytic	NOUN
ejpam-3074	2	48	and	and	CCONJ
ejpam-3074	2	49	operations	operation	NOUN
ejpam-3074	2	50	,	,	PUNCT
ejpam-3074	2	51	joseph	joseph	PROPN
ejpam-3074	2	52	m.	m.	PROPN
ejpam-3074	2	53	katz	katz	PROPN
ejpam-3074	2	54	graduate	graduate	PROPN
ejpam-3074	2	55	school	school	NOUN
ejpam-3074	2	56	of	of	ADP
ejpam-3074	2	57	business	business	NOUN
ejpam-3074	2	58	,	,	PUNCT
ejpam-3074	2	59	university	university	PROPN
ejpam-3074	2	60	of	of	ADP
ejpam-3074	2	61	pittsburgh	pittsburgh	PROPN
ejpam-3074	2	62	,	,	PUNCT
ejpam-3074	2	63	usa	usa	PROPN
ejpam-3074	3	1	we	we	PRON
ejpam-3074	3	2	are	be	AUX
ejpam-3074	3	3	all	all	PRON
ejpam-3074	3	4	agreed	agree	VERB
ejpam-3074	3	5	that	that	SCONJ
ejpam-3074	3	6	your	your	PRON
ejpam-3074	3	7	theory	theory	NOUN
ejpam-3074	3	8	is	be	AUX
ejpam-3074	3	9	crazy	crazy	ADJ
ejpam-3074	3	10	.	.	PUNCT
ejpam-3074	4	1	the	the	DET
ejpam-3074	4	2	question	question	NOUN
ejpam-3074	4	3	that	that	PRON
ejpam-3074	4	4	divides	divide	VERB
ejpam-3074	4	5	us	we	PRON
ejpam-3074	4	6	is	be	AUX
ejpam-3074	4	7	whether	whether	SCONJ
ejpam-3074	4	8	it	it	PRON
ejpam-3074	4	9	is	be	AUX
ejpam-3074	4	10	crazy	crazy	ADJ
ejpam-3074	4	11	enough	enough	ADV
ejpam-3074	4	12	to	to	PART
ejpam-3074	4	13	have	have	VERB
ejpam-3074	4	14	a	a	DET
ejpam-3074	4	15	chance	chance	NOUN
ejpam-3074	4	16	of	of	ADP
ejpam-3074	4	17	being	be	AUX
ejpam-3074	4	18	correct	correct	ADJ
ejpam-3074	4	19	.	.	PUNCT
ejpam-3074	5	1	-niels	-niel	NOUN
ejpam-3074	5	2	bohr	bohr	NOUN
ejpam-3074	5	3	abstract	abstract	NOUN
ejpam-3074	5	4	.	.	PUNCT
ejpam-3074	6	1	the	the	DET
ejpam-3074	6	2	nervous	nervous	ADJ
ejpam-3074	6	3	system	system	NOUN
ejpam-3074	6	4	uses	use	VERB
ejpam-3074	6	5	its	its	PRON
ejpam-3074	6	6	own	own	ADJ
ejpam-3074	6	7	kind	kind	NOUN
ejpam-3074	6	8	of	of	ADP
ejpam-3074	6	9	mathematical	mathematical	ADJ
ejpam-3074	6	10	function	function	NOUN
ejpam-3074	6	11	patterns	pattern	NOUN
ejpam-3074	6	12	for	for	ADP
ejpam-3074	6	13	both	both	CCONJ
ejpam-3074	6	14	external	external	ADJ
ejpam-3074	6	15	and	and	CCONJ
ejpam-3074	6	16	internal	internal	ADJ
ejpam-3074	6	17	realities	reality	NOUN
ejpam-3074	6	18	.	.	PUNCT
ejpam-3074	7	1	the	the	DET
ejpam-3074	7	2	conscious	conscious	ADJ
ejpam-3074	7	3	part	part	NOUN
ejpam-3074	7	4	of	of	ADP
ejpam-3074	7	5	the	the	DET
ejpam-3074	7	6	nervous	nervous	ADJ
ejpam-3074	7	7	system	system	NOUN
ejpam-3074	7	8	is	be	AUX
ejpam-3074	7	9	there	there	ADV
ejpam-3074	7	10	to	to	PART
ejpam-3074	7	11	respond	respond	VERB
ejpam-3074	7	12	to	to	ADP
ejpam-3074	7	13	what	what	PRON
ejpam-3074	7	14	happens	happen	VERB
ejpam-3074	7	15	outside	outside	ADV
ejpam-3074	7	16	by	by	ADP
ejpam-3074	7	17	regulating	regulate	VERB
ejpam-3074	7	18	externally	externally	ADV
ejpam-3074	7	19	received	receive	VERB
ejpam-3074	7	20	information	information	NOUN
ejpam-3074	7	21	signals	signal	NOUN
ejpam-3074	7	22	from	from	ADP
ejpam-3074	7	23	the	the	DET
ejpam-3074	7	24	senses	sense	NOUN
ejpam-3074	7	25	and	and	CCONJ
ejpam-3074	7	26	the	the	DET
ejpam-3074	7	27	skin	skin	NOUN
ejpam-3074	7	28	and	and	CCONJ
ejpam-3074	7	29	muscles	muscle	NOUN
ejpam-3074	7	30	of	of	ADP
ejpam-3074	7	31	the	the	DET
ejpam-3074	7	32	body	body	NOUN
ejpam-3074	7	33	itself	itself	PRON
ejpam-3074	7	34	.	.	PUNCT
ejpam-3074	8	1	to	to	PART
ejpam-3074	8	2	do	do	VERB
ejpam-3074	8	3	that	that	PRON
ejpam-3074	8	4	,	,	PUNCT
ejpam-3074	8	5	it	it	PRON
ejpam-3074	8	6	needs	need	VERB
ejpam-3074	8	7	to	to	PART
ejpam-3074	8	8	communicate	communicate	VERB
ejpam-3074	8	9	with	with	ADP
ejpam-3074	8	10	its	its	PRON
ejpam-3074	8	11	subconscious	subconscious	ADJ
ejpam-3074	8	12	using	use	VERB
ejpam-3074	8	13	the	the	DET
ejpam-3074	8	14	familiar	familiar	ADJ
ejpam-3074	8	15	language	language	NOUN
ejpam-3074	8	16	of	of	ADP
ejpam-3074	8	17	neural	neural	ADJ
ejpam-3074	8	18	firing	firing	NOUN
ejpam-3074	8	19	.	.	PUNCT
ejpam-3074	9	1	in	in	ADP
ejpam-3074	9	2	this	this	DET
ejpam-3074	9	3	paper	paper	NOUN
ejpam-3074	9	4	,	,	PUNCT
ejpam-3074	9	5	we	we	PRON
ejpam-3074	9	6	show	show	VERB
ejpam-3074	9	7	that	that	SCONJ
ejpam-3074	9	8	because	because	SCONJ
ejpam-3074	9	9	reciprocal	reciprocal	ADJ
ejpam-3074	9	10	pairwise	pairwise	NOUN
ejpam-3074	9	11	comparisons	comparison	NOUN
ejpam-3074	9	12	are	be	AUX
ejpam-3074	9	13	performed	perform	VERB
ejpam-3074	9	14	at	at	ADP
ejpam-3074	9	15	the	the	DET
ejpam-3074	9	16	neural	neural	ADJ
ejpam-3074	9	17	level	level	NOUN
ejpam-3074	9	18	,	,	PUNCT
ejpam-3074	9	19	the	the	DET
ejpam-3074	9	20	division	division	NOUN
ejpam-3074	9	21	algebra	algebra	NOUN
ejpam-3074	9	22	of	of	ADP
ejpam-3074	9	23	the	the	DET
ejpam-3074	9	24	octonions	octonion	NOUN
ejpam-3074	9	25	,	,	PUNCT
ejpam-3074	9	26	in	in	ADP
ejpam-3074	9	27	which	which	PRON
ejpam-3074	9	28	commutativity	commutativity	NOUN
ejpam-3074	9	29	and	and	CCONJ
ejpam-3074	9	30	associativity	associativity	NOUN
ejpam-3074	9	31	are	be	AUX
ejpam-3074	9	32	not	not	PART
ejpam-3074	9	33	satisfied	satisfied	ADJ
ejpam-3074	9	34	,	,	PUNCT
ejpam-3074	9	35	provides	provide	VERB
ejpam-3074	9	36	the	the	DET
ejpam-3074	9	37	structure	structure	NOUN
ejpam-3074	9	38	needed	need	VERB
ejpam-3074	9	39	to	to	PART
ejpam-3074	9	40	represent	represent	VERB
ejpam-3074	9	41	mental	mental	ADJ
ejpam-3074	9	42	processes	process	NOUN
ejpam-3074	9	43	and	and	CCONJ
ejpam-3074	9	44	that	that	SCONJ
ejpam-3074	9	45	these	these	DET
ejpam-3074	9	46	processes	process	NOUN
ejpam-3074	9	47	could	could	AUX
ejpam-3074	9	48	be	be	AUX
ejpam-3074	9	49	represented	represent	VERB
ejpam-3074	9	50	in	in	ADP
ejpam-3074	9	51	g2	g2	PROPN
ejpam-3074	9	52	-	-	PUNCT
ejpam-3074	9	53	manifolds	manifolds	PROPN
ejpam-3074	9	54	.	.	PUNCT
ejpam-3074	10	1	2010	2010	NUM
ejpam-3074	10	2	mathematics	mathematic	NOUN
ejpam-3074	10	3	subject	subject	NOUN
ejpam-3074	10	4	classifications	classification	NOUN
ejpam-3074	10	5	:	:	PUNCT
ejpam-3074	10	6	16w20	16w20	NUM
ejpam-3074	10	7	,	,	PUNCT
ejpam-3074	10	8	20g20	20g20	NUM
ejpam-3074	10	9	,	,	PUNCT
ejpam-3074	10	10	90b50	90b50	NOUN
ejpam-3074	10	11	key	key	ADJ
ejpam-3074	10	12	words	word	NOUN
ejpam-3074	10	13	and	and	CCONJ
ejpam-3074	10	14	phrases	phrase	NOUN
ejpam-3074	10	15	:	:	PUNCT
ejpam-3074	10	16	neural	neural	ADJ
ejpam-3074	10	17	firing	firing	NOUN
ejpam-3074	10	18	and	and	CCONJ
ejpam-3074	10	19	synthesis	synthesis	NOUN
ejpam-3074	10	20	,	,	PUNCT
ejpam-3074	10	21	the	the	DET
ejpam-3074	10	22	fundamental	fundamental	ADJ
ejpam-3074	10	23	equation	equation	NOUN
ejpam-3074	10	24	of	of	ADP
ejpam-3074	10	25	pairwise	pairwise	NOUN
ejpam-3074	10	26	comparisons	comparison	NOUN
ejpam-3074	10	27	,	,	PUNCT
ejpam-3074	10	28	the	the	DET
ejpam-3074	10	29	group	group	NOUN
ejpam-3074	10	30	of	of	ADP
ejpam-3074	10	31	the	the	DET
ejpam-3074	10	32	automorphisms	automorphism	NOUN
ejpam-3074	10	33	of	of	ADP
ejpam-3074	10	34	the	the	DET
ejpam-3074	10	35	octonions	octonions	PROPN
ejpam-3074	10	36	1	1	NUM
ejpam-3074	10	37	.	.	PUNCT
ejpam-3074	11	1	introduction	introduction	NOUN
ejpam-3074	11	2	we	we	PRON
ejpam-3074	11	3	use	use	VERB
ejpam-3074	11	4	our	our	PRON
ejpam-3074	11	5	nervous	nervous	ADJ
ejpam-3074	11	6	system	system	NOUN
ejpam-3074	11	7	to	to	PART
ejpam-3074	11	8	understand	understand	VERB
ejpam-3074	11	9	the	the	DET
ejpam-3074	11	10	external	external	ADJ
ejpam-3074	11	11	reality	reality	NOUN
ejpam-3074	11	12	scientifically	scientifically	ADV
ejpam-3074	11	13	studied	study	VERB
ejpam-3074	11	14	in	in	ADP
ejpam-3074	11	15	physics	physics	NOUN
ejpam-3074	11	16	in	in	ADP
ejpam-3074	11	17	sorting	sort	VERB
ejpam-3074	11	18	out	out	ADP
ejpam-3074	11	19	natural	natural	ADJ
ejpam-3074	11	20	law	law	NOUN
ejpam-3074	11	21	.	.	PUNCT
ejpam-3074	12	1	in	in	ADP
ejpam-3074	12	2	the	the	DET
ejpam-3074	12	3	past	past	ADJ
ejpam-3074	12	4	century	century	NOUN
ejpam-3074	12	5	or	or	CCONJ
ejpam-3074	12	6	so	so	ADV
ejpam-3074	12	7	the	the	DET
ejpam-3074	12	8	nervous	nervous	ADJ
ejpam-3074	12	9	system	system	NOUN
ejpam-3074	12	10	has	have	AUX
ejpam-3074	12	11	also	also	ADV
ejpam-3074	12	12	been	be	AUX
ejpam-3074	12	13	used	use	VERB
ejpam-3074	12	14	to	to	PART
ejpam-3074	12	15	study	study	VERB
ejpam-3074	12	16	internal	internal	ADJ
ejpam-3074	12	17	reality	reality	NOUN
ejpam-3074	12	18	through	through	ADP
ejpam-3074	12	19	the	the	DET
ejpam-3074	12	20	workings	working	NOUN
ejpam-3074	12	21	of	of	ADP
ejpam-3074	12	22	the	the	DET
ejpam-3074	12	23	brain	brain	NOUN
ejpam-3074	12	24	itself	itself	PRON
ejpam-3074	12	25	and	and	CCONJ
ejpam-3074	12	26	how	how	SCONJ
ejpam-3074	12	27	it	it	PRON
ejpam-3074	12	28	gives	give	VERB
ejpam-3074	12	29	rise	rise	NOUN
ejpam-3074	12	30	to	to	ADP
ejpam-3074	12	31	thought	thought	NOUN
ejpam-3074	12	32	,	,	PUNCT
ejpam-3074	12	33	feeling	feeling	NOUN
ejpam-3074	12	34	and	and	CCONJ
ejpam-3074	12	35	memory	memory	NOUN
ejpam-3074	12	36	.	.	PUNCT
ejpam-3074	13	1	it	it	PRON
ejpam-3074	13	2	has	have	AUX
ejpam-3074	13	3	been	be	AUX
ejpam-3074	13	4	discovered	discover	VERB
ejpam-3074	13	5	that	that	SCONJ
ejpam-3074	13	6	animals	animal	NOUN
ejpam-3074	13	7	brought	bring	VERB
ejpam-3074	13	8	up	up	ADP
ejpam-3074	13	9	in	in	ADP
ejpam-3074	13	10	a	a	DET
ejpam-3074	13	11	stimulating	stimulate	VERB
ejpam-3074	13	12	environment	environment	NOUN
ejpam-3074	13	13	have	have	VERB
ejpam-3074	13	14	many	many	ADJ
ejpam-3074	13	15	more	more	ADJ
ejpam-3074	13	16	synapses	synapsis	NOUN
ejpam-3074	13	17	and	and	CCONJ
ejpam-3074	13	18	as	as	ADP
ejpam-3074	13	19	a	a	DET
ejpam-3074	13	20	result	result	NOUN
ejpam-3074	13	21	,	,	PUNCT
ejpam-3074	13	22	a	a	DET
ejpam-3074	13	23	heavier	heavy	ADJ
ejpam-3074	13	24	∗corresponding	∗corresponde	VERB
ejpam-3074	13	25	author	author	NOUN
ejpam-3074	13	26	.	.	PUNCT
ejpam-3074	14	1	email	email	NOUN
ejpam-3074	14	2	addresses	address	NOUN
ejpam-3074	14	3	:	:	PUNCT
ejpam-3074	14	4	saaty@katz.pitt.edu	saaty@katz.pitt.edu	NUM
ejpam-3074	14	5	(	(	PUNCT
ejpam-3074	14	6	t.	t.	PROPN
ejpam-3074	14	7	l.	l.	PROPN
ejpam-3074	14	8	saaty	saaty	PROPN
ejpam-3074	14	9	)	)	PUNCT
ejpam-3074	14	10	,	,	PUNCT
ejpam-3074	14	11	lgvargas@pitt.edu	lgvargas@pitt.edu	PROPN
ejpam-3074	15	1	(	(	PUNCT
ejpam-3074	15	2	l.	l.	PROPN
ejpam-3074	15	3	g.	g.	PROPN
ejpam-3074	15	4	vargas	vargas	PROPN
ejpam-3074	15	5	)	)	PUNCT
ejpam-3074	15	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3074	16	1	602	602	NUM
ejpam-3074	17	1	c	c	X
ejpam-3074	17	2	©	©	PROPN
ejpam-3074	17	3	2017	2017	NUM
ejpam-3074	17	4	ejpam	ejpam	NOUN
ejpam-3074	17	5	all	all	DET
ejpam-3074	17	6	rights	right	NOUN
ejpam-3074	17	7	reserved	reserve	VERB
ejpam-3074	17	8	.	.	PUNCT
ejpam-3074	18	1	t.	t.	PROPN
ejpam-3074	18	2	l.	l.	PROPN
ejpam-3074	18	3	saaty	saaty	PROPN
ejpam-3074	18	4	,	,	PUNCT
ejpam-3074	18	5	l.	l.	PROPN
ejpam-3074	18	6	g.	g.	PROPN
ejpam-3074	18	7	vargas	vargas	PROPN
ejpam-3074	18	8	/	/	SYM
ejpam-3074	18	9	eur	eur	PROPN
ejpam-3074	18	10	.	.	PUNCT
ejpam-3074	19	1	j.	j.	PROPN
ejpam-3074	19	2	pure	pure	PROPN
ejpam-3074	19	3	appl	appl	PROPN
ejpam-3074	19	4	.	.	PROPN
ejpam-3074	19	5	math	math	PROPN
ejpam-3074	19	6	,	,	PUNCT
ejpam-3074	19	7	10	10	NUM
ejpam-3074	19	8	(	(	PUNCT
ejpam-3074	19	9	4	4	NUM
ejpam-3074	19	10	)	)	PUNCT
ejpam-3074	19	11	(	(	PUNCT
ejpam-3074	19	12	2017	2017	NUM
ejpam-3074	19	13	)	)	PUNCT
ejpam-3074	19	14	,	,	PUNCT
ejpam-3074	19	15	602	602	NUM
ejpam-3074	19	16	-	-	SYM
ejpam-3074	19	17	613	613	NUM
ejpam-3074	19	18	603	603	NUM
ejpam-3074	19	19	brain	brain	NOUN
ejpam-3074	19	20	than	than	ADP
ejpam-3074	19	21	their	their	PRON
ejpam-3074	19	22	unstimulated	unstimulated	ADJ
ejpam-3074	19	23	counterparts	counterpart	NOUN
ejpam-3074	19	24	.	.	PUNCT
ejpam-3074	20	1	thus	thus	ADV
ejpam-3074	20	2	,	,	PUNCT
ejpam-3074	20	3	the	the	DET
ejpam-3074	20	4	brain	brain	NOUN
ejpam-3074	20	5	itself	itself	PRON
ejpam-3074	20	6	changes	change	VERB
ejpam-3074	20	7	over	over	ADP
ejpam-3074	20	8	time	time	NOUN
ejpam-3074	20	9	that	that	PRON
ejpam-3074	20	10	makes	make	VERB
ejpam-3074	20	11	it	it	PRON
ejpam-3074	20	12	harder	hard	ADJ
ejpam-3074	20	13	to	to	PART
ejpam-3074	20	14	describe	describe	VERB
ejpam-3074	20	15	it	it	PRON
ejpam-3074	20	16	well	well	ADV
ejpam-3074	20	17	as	as	ADP
ejpam-3074	20	18	a	a	DET
ejpam-3074	20	19	closed	closed	ADJ
ejpam-3074	20	20	system	system	NOUN
ejpam-3074	20	21	with	with	ADP
ejpam-3074	20	22	all	all	DET
ejpam-3074	20	23	its	its	PRON
ejpam-3074	20	24	activities	activity	NOUN
ejpam-3074	20	25	.	.	PUNCT
ejpam-3074	21	1	to	to	PART
ejpam-3074	21	2	understand	understand	VERB
ejpam-3074	21	3	change	change	NOUN
ejpam-3074	21	4	we	we	PRON
ejpam-3074	21	5	need	need	VERB
ejpam-3074	21	6	to	to	PART
ejpam-3074	21	7	compare	compare	VERB
ejpam-3074	21	8	different	different	ADJ
ejpam-3074	21	9	states	state	NOUN
ejpam-3074	21	10	of	of	ADP
ejpam-3074	21	11	the	the	DET
ejpam-3074	21	12	brain	brain	NOUN
ejpam-3074	21	13	that	that	PRON
ejpam-3074	21	14	derive	derive	VERB
ejpam-3074	21	15	from	from	ADP
ejpam-3074	21	16	its	its	PRON
ejpam-3074	21	17	workings	working	NOUN
ejpam-3074	21	18	.	.	PUNCT
ejpam-3074	22	1	to	to	PART
ejpam-3074	22	2	appreciate	appreciate	VERB
ejpam-3074	22	3	how	how	SCONJ
ejpam-3074	22	4	basic	basic	ADJ
ejpam-3074	22	5	comparisons	comparison	NOUN
ejpam-3074	22	6	are	be	AUX
ejpam-3074	22	7	,	,	PUNCT
ejpam-3074	22	8	we	we	PRON
ejpam-3074	22	9	refer	refer	VERB
ejpam-3074	22	10	to	to	ADP
ejpam-3074	22	11	what	what	PRON
ejpam-3074	22	12	philosopher	philosopher	NOUN
ejpam-3074	22	13	arthur	arthur	PROPN
ejpam-3074	22	14	schopenhauer	schopenhauer	PROPN
ejpam-3074	22	15	wrote,”every	wrote,”every	PROPN
ejpam-3074	22	16	truth	truth	NOUN
ejpam-3074	22	17	is	be	AUX
ejpam-3074	22	18	the	the	DET
ejpam-3074	22	19	reference	reference	NOUN
ejpam-3074	22	20	of	of	ADP
ejpam-3074	22	21	a	a	DET
ejpam-3074	22	22	judgment	judgment	NOUN
ejpam-3074	22	23	to	to	ADP
ejpam-3074	22	24	something	something	PRON
ejpam-3074	22	25	outside	outside	ADP
ejpam-3074	22	26	it	it	PRON
ejpam-3074	22	27	,	,	PUNCT
ejpam-3074	22	28	and	and	CCONJ
ejpam-3074	22	29	intrinsic	intrinsic	ADJ
ejpam-3074	22	30	truth	truth	NOUN
ejpam-3074	22	31	is	be	AUX
ejpam-3074	22	32	a	a	DET
ejpam-3074	22	33	contradiction	contradiction	NOUN
ejpam-3074	22	34	”	"	PUNCT
ejpam-3074	22	35	.	.	PUNCT
ejpam-3074	23	1	the	the	DET
ejpam-3074	23	2	nervous	nervous	ADJ
ejpam-3074	23	3	system	system	NOUN
ejpam-3074	23	4	is	be	AUX
ejpam-3074	23	5	a	a	DET
ejpam-3074	23	6	response	response	NOUN
ejpam-3074	23	7	mechanism	mechanism	NOUN
ejpam-3074	23	8	that	that	PRON
ejpam-3074	23	9	carries	carry	VERB
ejpam-3074	23	10	out	out	ADP
ejpam-3074	23	11	its	its	PRON
ejpam-3074	23	12	work	work	NOUN
ejpam-3074	23	13	electrochemically	electrochemically	ADV
ejpam-3074	23	14	at	at	ADP
ejpam-3074	23	15	the	the	DET
ejpam-3074	23	16	molecular	molecular	ADJ
ejpam-3074	23	17	level	level	NOUN
ejpam-3074	23	18	.	.	PUNCT
ejpam-3074	24	1	it	it	PRON
ejpam-3074	24	2	does	do	VERB
ejpam-3074	24	3	that	that	PRON
ejpam-3074	24	4	subconsciously	subconsciously	ADV
ejpam-3074	24	5	through	through	ADP
ejpam-3074	24	6	feedback	feedback	NOUN
ejpam-3074	24	7	and	and	CCONJ
ejpam-3074	24	8	is	be	AUX
ejpam-3074	24	9	also	also	ADV
ejpam-3074	24	10	modified	modify	VERB
ejpam-3074	24	11	by	by	ADP
ejpam-3074	24	12	the	the	DET
ejpam-3074	24	13	functions	function	NOUN
ejpam-3074	24	14	of	of	ADP
ejpam-3074	24	15	the	the	DET
ejpam-3074	24	16	body	body	NOUN
ejpam-3074	24	17	where	where	SCONJ
ejpam-3074	24	18	it	it	PRON
ejpam-3074	24	19	resides	reside	VERB
ejpam-3074	24	20	,	,	PUNCT
ejpam-3074	24	21	sustained	sustain	VERB
ejpam-3074	24	22	through	through	ADP
ejpam-3074	24	23	chemicals	chemical	NOUN
ejpam-3074	24	24	that	that	PRON
ejpam-3074	24	25	give	give	VERB
ejpam-3074	24	26	rise	rise	NOUN
ejpam-3074	24	27	to	to	ADP
ejpam-3074	24	28	its	its	PRON
ejpam-3074	24	29	electrical	electrical	ADJ
ejpam-3074	24	30	firing	firing	NOUN
ejpam-3074	24	31	actions	action	NOUN
ejpam-3074	24	32	and	and	CCONJ
ejpam-3074	24	33	reactions	reaction	NOUN
ejpam-3074	24	34	.	.	PUNCT
ejpam-3074	25	1	the	the	DET
ejpam-3074	25	2	nervous	nervous	ADJ
ejpam-3074	25	3	system	system	NOUN
ejpam-3074	25	4	uses	use	VERB
ejpam-3074	25	5	its	its	PRON
ejpam-3074	25	6	own	own	ADJ
ejpam-3074	25	7	kind	kind	NOUN
ejpam-3074	25	8	of	of	ADP
ejpam-3074	25	9	mathematical	mathematical	ADJ
ejpam-3074	25	10	function	function	NOUN
ejpam-3074	25	11	patterns	pattern	NOUN
ejpam-3074	25	12	for	for	ADP
ejpam-3074	25	13	both	both	CCONJ
ejpam-3074	25	14	external	external	ADJ
ejpam-3074	25	15	and	and	CCONJ
ejpam-3074	25	16	internal	internal	ADJ
ejpam-3074	25	17	realities	reality	NOUN
ejpam-3074	25	18	.	.	PUNCT
ejpam-3074	26	1	that	that	PRON
ejpam-3074	26	2	is	be	AUX
ejpam-3074	26	3	the	the	DET
ejpam-3074	26	4	subject	subject	NOUN
ejpam-3074	26	5	of	of	ADP
ejpam-3074	26	6	this	this	DET
ejpam-3074	26	7	paper	paper	NOUN
ejpam-3074	27	1	[	[	X
ejpam-3074	27	2	13	13	NUM
ejpam-3074	27	3	,	,	PUNCT
ejpam-3074	27	4	14	14	NUM
ejpam-3074	27	5	]	]	PUNCT
ejpam-3074	27	6	.	.	PUNCT
ejpam-3074	28	1	we	we	PRON
ejpam-3074	28	2	can	can	AUX
ejpam-3074	28	3	not	not	PART
ejpam-3074	28	4	think	think	VERB
ejpam-3074	28	5	or	or	CCONJ
ejpam-3074	28	6	feel	feel	VERB
ejpam-3074	28	7	or	or	CCONJ
ejpam-3074	28	8	apprehend	apprehend	VERB
ejpam-3074	28	9	something	something	PRON
ejpam-3074	28	10	that	that	PRON
ejpam-3074	28	11	our	our	PRON
ejpam-3074	28	12	brain	brain	NOUN
ejpam-3074	28	13	and	and	CCONJ
ejpam-3074	28	14	nervous	nervous	ADJ
ejpam-3074	28	15	system	system	NOUN
ejpam-3074	28	16	are	be	AUX
ejpam-3074	28	17	incapable	incapable	ADJ
ejpam-3074	28	18	of	of	ADP
ejpam-3074	28	19	grasping	grasp	VERB
ejpam-3074	28	20	.	.	PUNCT
ejpam-3074	29	1	our	our	PRON
ejpam-3074	29	2	neurons	neuron	NOUN
ejpam-3074	29	3	fire	fire	VERB
ejpam-3074	29	4	one	one	NUM
ejpam-3074	29	5	at	at	ADP
ejpam-3074	29	6	a	a	DET
ejpam-3074	29	7	time	time	NOUN
ejpam-3074	29	8	and	and	CCONJ
ejpam-3074	29	9	the	the	DET
ejpam-3074	29	10	simultaneous	simultaneous	ADJ
ejpam-3074	29	11	firings	firing	NOUN
ejpam-3074	29	12	of	of	ADP
ejpam-3074	29	13	many	many	ADJ
ejpam-3074	29	14	neurons	neuron	NOUN
ejpam-3074	29	15	give	give	VERB
ejpam-3074	29	16	rise	rise	NOUN
ejpam-3074	29	17	to	to	ADP
ejpam-3074	29	18	all	all	PRON
ejpam-3074	29	19	that	that	PRON
ejpam-3074	29	20	happens	happen	VERB
ejpam-3074	29	21	to	to	ADP
ejpam-3074	29	22	us	we	PRON
ejpam-3074	29	23	and	and	CCONJ
ejpam-3074	29	24	inside	inside	ADP
ejpam-3074	29	25	us	we	PRON
ejpam-3074	29	26	.	.	PUNCT
ejpam-3074	30	1	the	the	DET
ejpam-3074	30	2	limiting	limit	VERB
ejpam-3074	30	3	factors	factor	NOUN
ejpam-3074	30	4	in	in	ADP
ejpam-3074	30	5	understanding	understanding	NOUN
ejpam-3074	30	6	is	be	AUX
ejpam-3074	30	7	the	the	DET
ejpam-3074	30	8	way	way	NOUN
ejpam-3074	30	9	our	our	PRON
ejpam-3074	30	10	nervous	nervous	ADJ
ejpam-3074	30	11	system	system	NOUN
ejpam-3074	30	12	works	work	VERB
ejpam-3074	30	13	.	.	PUNCT
ejpam-3074	31	1	our	our	PRON
ejpam-3074	31	2	collective	collective	ADJ
ejpam-3074	31	3	responses	response	NOUN
ejpam-3074	31	4	form	form	VERB
ejpam-3074	31	5	a	a	DET
ejpam-3074	31	6	box	box	NOUN
ejpam-3074	31	7	that	that	PRON
ejpam-3074	31	8	we	we	PRON
ejpam-3074	31	9	can	can	AUX
ejpam-3074	31	10	not	not	PART
ejpam-3074	31	11	go	go	VERB
ejpam-3074	31	12	beyond	beyond	ADV
ejpam-3074	31	13	at	at	ADP
ejpam-3074	31	14	will	will	NOUN
ejpam-3074	31	15	by	by	ADP
ejpam-3074	31	16	using	use	VERB
ejpam-3074	31	17	imagination	imagination	NOUN
ejpam-3074	31	18	that	that	PRON
ejpam-3074	31	19	is	be	AUX
ejpam-3074	31	20	a	a	DET
ejpam-3074	31	21	by	by	ADP
ejpam-3074	31	22	-	-	PUNCT
ejpam-3074	31	23	product	product	NOUN
ejpam-3074	31	24	of	of	ADP
ejpam-3074	31	25	that	that	DET
ejpam-3074	31	26	instrument	instrument	NOUN
ejpam-3074	31	27	itself	itself	PRON
ejpam-3074	31	28	.	.	PUNCT
ejpam-3074	32	1	a	a	DET
ejpam-3074	32	2	well	well	ADV
ejpam-3074	32	3	-	-	PUNCT
ejpam-3074	32	4	known	know	VERB
ejpam-3074	32	5	example	example	NOUN
ejpam-3074	32	6	of	of	ADP
ejpam-3074	32	7	thinking	think	VERB
ejpam-3074	32	8	outside	outside	ADP
ejpam-3074	32	9	the	the	DET
ejpam-3074	32	10	box	box	NOUN
ejpam-3074	32	11	,	,	PUNCT
ejpam-3074	32	12	beyond	beyond	ADP
ejpam-3074	32	13	our	our	PRON
ejpam-3074	32	14	present	present	ADJ
ejpam-3074	32	15	state	state	NOUN
ejpam-3074	32	16	of	of	ADP
ejpam-3074	32	17	mind	mind	NOUN
ejpam-3074	32	18	,	,	PUNCT
ejpam-3074	32	19	is	be	AUX
ejpam-3074	32	20	a	a	DET
ejpam-3074	32	21	9	9	NUM
ejpam-3074	32	22	-	-	PUNCT
ejpam-3074	32	23	point	point	NOUN
ejpam-3074	32	24	exercise	exercise	NOUN
ejpam-3074	32	25	.	.	PUNCT
ejpam-3074	33	1	the	the	DET
ejpam-3074	33	2	question	question	NOUN
ejpam-3074	33	3	is	be	AUX
ejpam-3074	33	4	,	,	PUNCT
ejpam-3074	33	5	what	what	PRON
ejpam-3074	33	6	is	be	AUX
ejpam-3074	33	7	it	it	PRON
ejpam-3074	33	8	beyond	beyond	ADP
ejpam-3074	33	9	what	what	PRON
ejpam-3074	33	10	we	we	PRON
ejpam-3074	33	11	know	know	VERB
ejpam-3074	33	12	about	about	ADP
ejpam-3074	33	13	the	the	DET
ejpam-3074	33	14	fundamentals	fundamental	NOUN
ejpam-3074	33	15	of	of	ADP
ejpam-3074	33	16	space	space	NOUN
ejpam-3074	33	17	and	and	CCONJ
ejpam-3074	33	18	time	time	NOUN
ejpam-3074	33	19	and	and	CCONJ
ejpam-3074	33	20	energy	energy	NOUN
ejpam-3074	33	21	,	,	PUNCT
ejpam-3074	33	22	physics	physics	NOUN
ejpam-3074	33	23	,	,	PUNCT
ejpam-3074	33	24	and	and	CCONJ
ejpam-3074	33	25	particularly	particularly	ADV
ejpam-3074	33	26	an	an	DET
ejpam-3074	33	27	objective	objective	ADJ
ejpam-3074	33	28	and	and	CCONJ
ejpam-3074	33	29	subjective	subjective	ADJ
ejpam-3074	33	30	philosophy	philosophy	NOUN
ejpam-3074	33	31	and	and	CCONJ
ejpam-3074	33	32	psychology	psychology	NOUN
ejpam-3074	33	33	lurking	lurk	VERB
ejpam-3074	33	34	behind	behind	ADP
ejpam-3074	33	35	the	the	DET
ejpam-3074	33	36	scene	scene	NOUN
ejpam-3074	33	37	ready	ready	ADJ
ejpam-3074	33	38	to	to	PART
ejpam-3074	33	39	be	be	AUX
ejpam-3074	33	40	discovered	discover	VERB
ejpam-3074	33	41	as	as	ADP
ejpam-3074	33	42	our	our	PRON
ejpam-3074	33	43	existing	exist	VERB
ejpam-3074	33	44	way	way	NOUN
ejpam-3074	33	45	of	of	ADP
ejpam-3074	33	46	knowledge	knowledge	NOUN
ejpam-3074	33	47	evolved	evolve	VERB
ejpam-3074	33	48	through	through	ADP
ejpam-3074	33	49	research	research	NOUN
ejpam-3074	33	50	and	and	CCONJ
ejpam-3074	33	51	exploration	exploration	NOUN
ejpam-3074	33	52	.	.	PUNCT
ejpam-3074	34	1	yet	yet	CCONJ
ejpam-3074	34	2	it	it	PRON
ejpam-3074	34	3	is	be	AUX
ejpam-3074	34	4	all	all	DET
ejpam-3074	34	5	a	a	DET
ejpam-3074	34	6	consequence	consequence	NOUN
ejpam-3074	34	7	of	of	ADP
ejpam-3074	34	8	electrical	electrical	ADJ
ejpam-3074	34	9	firing	firing	NOUN
ejpam-3074	34	10	and	and	CCONJ
ejpam-3074	34	11	neurons	neuron	NOUN
ejpam-3074	34	12	that	that	PRON
ejpam-3074	34	13	together	together	ADV
ejpam-3074	34	14	capture	capture	VERB
ejpam-3074	34	15	what	what	PRON
ejpam-3074	34	16	is	be	AUX
ejpam-3074	34	17	out	out	ADV
ejpam-3074	34	18	there	there	ADV
ejpam-3074	34	19	.	.	PUNCT
ejpam-3074	35	1	we	we	PRON
ejpam-3074	35	2	can	can	AUX
ejpam-3074	35	3	only	only	ADV
ejpam-3074	35	4	know	know	VERB
ejpam-3074	35	5	it	it	PRON
ejpam-3074	35	6	if	if	SCONJ
ejpam-3074	35	7	we	we	PRON
ejpam-3074	35	8	are	be	AUX
ejpam-3074	35	9	able	able	ADJ
ejpam-3074	35	10	to	to	PART
ejpam-3074	35	11	detect	detect	VERB
ejpam-3074	35	12	and	and	CCONJ
ejpam-3074	35	13	synthesize	synthesize	VERB
ejpam-3074	35	14	it	it	PRON
ejpam-3074	35	15	into	into	ADP
ejpam-3074	35	16	a	a	DET
ejpam-3074	35	17	whole	whole	NOUN
ejpam-3074	35	18	.	.	PUNCT
ejpam-3074	36	1	still	still	ADV
ejpam-3074	36	2	we	we	PRON
ejpam-3074	36	3	can	can	AUX
ejpam-3074	36	4	not	not	PART
ejpam-3074	36	5	know	know	VERB
ejpam-3074	36	6	what	what	PRON
ejpam-3074	36	7	we	we	PRON
ejpam-3074	36	8	are	be	AUX
ejpam-3074	36	9	not	not	PART
ejpam-3074	36	10	able	able	ADJ
ejpam-3074	36	11	to	to	PART
ejpam-3074	36	12	know	know	VERB
ejpam-3074	36	13	through	through	ADP
ejpam-3074	36	14	the	the	DET
ejpam-3074	36	15	firing	firing	NOUN
ejpam-3074	36	16	of	of	ADP
ejpam-3074	36	17	neurons	neuron	NOUN
ejpam-3074	36	18	.	.	PUNCT
ejpam-3074	37	1	that	that	PRON
ejpam-3074	37	2	is	be	AUX
ejpam-3074	37	3	the	the	DET
ejpam-3074	37	4	total	total	ADJ
ejpam-3074	37	5	sum	sum	NOUN
ejpam-3074	37	6	of	of	ADP
ejpam-3074	37	7	the	the	DET
ejpam-3074	37	8	reality	reality	NOUN
ejpam-3074	37	9	that	that	PRON
ejpam-3074	37	10	we	we	PRON
ejpam-3074	37	11	know	know	VERB
ejpam-3074	37	12	.	.	PUNCT
ejpam-3074	38	1	the	the	DET
ejpam-3074	38	2	question	question	NOUN
ejpam-3074	38	3	is	be	AUX
ejpam-3074	38	4	whether	whether	SCONJ
ejpam-3074	38	5	there	there	PRON
ejpam-3074	38	6	is	be	VERB
ejpam-3074	38	7	something	something	PRON
ejpam-3074	38	8	out	out	ADV
ejpam-3074	38	9	there	there	ADV
ejpam-3074	38	10	or	or	CCONJ
ejpam-3074	38	11	inside	inside	ADP
ejpam-3074	38	12	us	we	PRON
ejpam-3074	38	13	that	that	SCONJ
ejpam-3074	38	14	we	we	PRON
ejpam-3074	38	15	are	be	AUX
ejpam-3074	38	16	ever	ever	ADV
ejpam-3074	38	17	incapable	incapable	ADJ
ejpam-3074	38	18	of	of	ADP
ejpam-3074	38	19	knowing	know	VERB
ejpam-3074	38	20	.	.	PUNCT
ejpam-3074	39	1	to	to	PART
ejpam-3074	39	2	identify	identify	VERB
ejpam-3074	39	3	such	such	DET
ejpam-3074	39	4	a	a	DET
ejpam-3074	39	5	thing	thing	NOUN
ejpam-3074	39	6	,	,	PUNCT
ejpam-3074	39	7	we	we	PRON
ejpam-3074	39	8	must	must	AUX
ejpam-3074	39	9	be	be	AUX
ejpam-3074	39	10	aware	aware	ADJ
ejpam-3074	39	11	of	of	ADP
ejpam-3074	39	12	it	it	PRON
ejpam-3074	39	13	.	.	PUNCT
ejpam-3074	40	1	to	to	PART
ejpam-3074	40	2	be	be	AUX
ejpam-3074	40	3	aware	aware	ADJ
ejpam-3074	40	4	of	of	ADP
ejpam-3074	40	5	something	something	PRON
ejpam-3074	40	6	we	we	PRON
ejpam-3074	40	7	must	must	AUX
ejpam-3074	40	8	be	be	AUX
ejpam-3074	40	9	able	able	ADJ
ejpam-3074	40	10	to	to	PART
ejpam-3074	40	11	create	create	VERB
ejpam-3074	40	12	it	it	PRON
ejpam-3074	40	13	as	as	ADP
ejpam-3074	40	14	a	a	DET
ejpam-3074	40	15	firing	firing	NOUN
ejpam-3074	40	16	neuron	neuron	NOUN
ejpam-3074	40	17	.	.	PUNCT
ejpam-3074	41	1	but	but	CCONJ
ejpam-3074	41	2	neurons	neuron	NOUN
ejpam-3074	41	3	fire	fire	NOUN
ejpam-3074	41	4	in	in	ADP
ejpam-3074	41	5	special	special	ADJ
ejpam-3074	41	6	ways	way	NOUN
ejpam-3074	41	7	that	that	PRON
ejpam-3074	41	8	satisfy	satisfy	VERB
ejpam-3074	41	9	the	the	DET
ejpam-3074	41	10	requirements	requirement	NOUN
ejpam-3074	41	11	of	of	ADP
ejpam-3074	41	12	arithmetic	arithmetic	ADJ
ejpam-3074	41	13	and	and	CCONJ
ejpam-3074	41	14	that	that	SCONJ
ejpam-3074	41	15	knowledge	knowledge	NOUN
ejpam-3074	41	16	is	be	AUX
ejpam-3074	41	17	tied	tie	VERB
ejpam-3074	41	18	to	to	ADP
ejpam-3074	41	19	the	the	DET
ejpam-3074	41	20	firings	firing	NOUN
ejpam-3074	41	21	and	and	CCONJ
ejpam-3074	41	22	to	to	ADP
ejpam-3074	41	23	combining	combine	VERB
ejpam-3074	41	24	them	they	PRON
ejpam-3074	41	25	arithmetically	arithmetically	ADV
ejpam-3074	41	26	in	in	ADP
ejpam-3074	41	27	particular	particular	ADJ
ejpam-3074	41	28	ways	way	NOUN
ejpam-3074	41	29	.	.	PUNCT
ejpam-3074	42	1	the	the	DET
ejpam-3074	42	2	power	power	NOUN
ejpam-3074	42	3	of	of	ADP
ejpam-3074	42	4	our	our	PRON
ejpam-3074	42	5	brain	brain	NOUN
ejpam-3074	42	6	depends	depend	VERB
ejpam-3074	42	7	on	on	ADP
ejpam-3074	42	8	the	the	DET
ejpam-3074	42	9	firing	firing	NOUN
ejpam-3074	42	10	and	and	CCONJ
ejpam-3074	42	11	complexity	complexity	NOUN
ejpam-3074	42	12	of	of	ADP
ejpam-3074	42	13	connecting	connect	VERB
ejpam-3074	42	14	ten	ten	NUM
ejpam-3074	42	15	to	to	ADP
ejpam-3074	42	16	the	the	DET
ejpam-3074	42	17	eleventh	eleventh	ADJ
ejpam-3074	42	18	power	power	NOUN
ejpam-3074	42	19	of	of	ADP
ejpam-3074	42	20	the	the	DET
ejpam-3074	42	21	number	number	NOUN
ejpam-3074	42	22	of	of	ADP
ejpam-3074	42	23	neurons	neuron	NOUN
ejpam-3074	42	24	which	which	PRON
ejpam-3074	42	25	takes	take	VERB
ejpam-3074	42	26	more	more	ADJ
ejpam-3074	42	27	than	than	ADP
ejpam-3074	42	28	a	a	DET
ejpam-3074	42	29	lifetime	lifetime	NOUN
ejpam-3074	42	30	of	of	ADP
ejpam-3074	42	31	approximately	approximately	ADV
ejpam-3074	42	32	3.5	3.5	NUM
ejpam-3074	42	33	to	to	ADP
ejpam-3074	42	34	the	the	DET
ejpam-3074	42	35	ninth	ninth	ADJ
ejpam-3074	42	36	seconds	second	NOUN
ejpam-3074	42	37	to	to	PART
ejpam-3074	42	38	use	use	VERB
ejpam-3074	42	39	them	they	PRON
ejpam-3074	42	40	.	.	PUNCT
ejpam-3074	43	1	but	but	CCONJ
ejpam-3074	43	2	many	many	ADJ
ejpam-3074	43	3	are	be	AUX
ejpam-3074	43	4	connected	connect	VERB
ejpam-3074	43	5	and	and	CCONJ
ejpam-3074	43	6	fire	fire	NOUN
ejpam-3074	43	7	at	at	ADP
ejpam-3074	43	8	the	the	DET
ejpam-3074	43	9	same	same	ADJ
ejpam-3074	43	10	instant	instant	NOUN
ejpam-3074	43	11	of	of	ADP
ejpam-3074	43	12	time	time	NOUN
ejpam-3074	43	13	.	.	PUNCT
ejpam-3074	44	1	the	the	DET
ejpam-3074	44	2	conscious	conscious	ADJ
ejpam-3074	44	3	part	part	NOUN
ejpam-3074	44	4	of	of	ADP
ejpam-3074	44	5	the	the	DET
ejpam-3074	44	6	nervous	nervous	ADJ
ejpam-3074	44	7	system	system	NOUN
ejpam-3074	44	8	is	be	AUX
ejpam-3074	44	9	there	there	ADV
ejpam-3074	44	10	to	to	PART
ejpam-3074	44	11	respond	respond	VERB
ejpam-3074	44	12	to	to	ADP
ejpam-3074	44	13	what	what	PRON
ejpam-3074	44	14	happens	happen	VERB
ejpam-3074	44	15	outside	outside	ADV
ejpam-3074	44	16	by	by	ADP
ejpam-3074	44	17	regulating	regulate	VERB
ejpam-3074	44	18	externally	externally	ADV
ejpam-3074	44	19	received	receive	VERB
ejpam-3074	44	20	information	information	NOUN
ejpam-3074	44	21	signals	signal	NOUN
ejpam-3074	44	22	from	from	ADP
ejpam-3074	44	23	the	the	DET
ejpam-3074	44	24	senses	sense	NOUN
ejpam-3074	44	25	and	and	CCONJ
ejpam-3074	44	26	the	the	DET
ejpam-3074	44	27	skin	skin	NOUN
ejpam-3074	44	28	and	and	CCONJ
ejpam-3074	44	29	muscles	muscle	NOUN
ejpam-3074	44	30	of	of	ADP
ejpam-3074	44	31	the	the	DET
ejpam-3074	44	32	body	body	NOUN
ejpam-3074	44	33	itself.to	itself.to	X
ejpam-3074	44	34	do	do	VERB
ejpam-3074	44	35	that	that	PRON
ejpam-3074	44	36	,	,	PUNCT
ejpam-3074	44	37	it	it	PRON
ejpam-3074	44	38	needs	need	VERB
ejpam-3074	44	39	to	to	PART
ejpam-3074	44	40	communicate	communicate	VERB
ejpam-3074	44	41	with	with	ADP
ejpam-3074	44	42	its	its	PRON
ejpam-3074	44	43	subconscious	subconscious	ADJ
ejpam-3074	44	44	using	use	VERB
ejpam-3074	44	45	the	the	DET
ejpam-3074	44	46	familiar	familiar	ADJ
ejpam-3074	44	47	language	language	NOUN
ejpam-3074	44	48	of	of	ADP
ejpam-3074	44	49	neural	neural	ADJ
ejpam-3074	44	50	firing	firing	NOUN
ejpam-3074	44	51	.	.	PUNCT
ejpam-3074	45	1	the	the	DET
ejpam-3074	45	2	subconscious	subconscious	ADJ
ejpam-3074	45	3	is	be	AUX
ejpam-3074	45	4	able	able	ADJ
ejpam-3074	45	5	to	to	PART
ejpam-3074	45	6	compare	compare	VERB
ejpam-3074	45	7	the	the	DET
ejpam-3074	45	8	states	state	NOUN
ejpam-3074	45	9	of	of	ADP
ejpam-3074	45	10	the	the	DET
ejpam-3074	45	11	body	body	NOUN
ejpam-3074	45	12	from	from	ADP
ejpam-3074	45	13	instant	instant	NOUN
ejpam-3074	45	14	to	to	ADP
ejpam-3074	45	15	instant	instant	NOUN
ejpam-3074	45	16	.	.	PUNCT
ejpam-3074	46	1	comparisons	comparison	NOUN
ejpam-3074	46	2	of	of	ADP
ejpam-3074	46	3	both	both	DET
ejpam-3074	46	4	variables	variable	NOUN
ejpam-3074	46	5	and	and	CCONJ
ejpam-3074	46	6	of	of	ADP
ejpam-3074	46	7	functions	function	NOUN
ejpam-3074	46	8	are	be	AUX
ejpam-3074	46	9	made	make	VERB
ejpam-3074	46	10	to	to	PART
ejpam-3074	46	11	determine	determine	VERB
ejpam-3074	46	12	the	the	DET
ejpam-3074	46	13	magnitude	magnitude	NOUN
ejpam-3074	46	14	of	of	ADP
ejpam-3074	46	15	influence	influence	NOUN
ejpam-3074	46	16	that	that	PRON
ejpam-3074	46	17	a	a	DET
ejpam-3074	46	18	dominant	dominant	ADJ
ejpam-3074	46	19	element	element	NOUN
ejpam-3074	46	20	has	have	VERB
ejpam-3074	46	21	over	over	ADP
ejpam-3074	46	22	a	a	DET
ejpam-3074	46	23	lesser	less	ADJ
ejpam-3074	46	24	element	element	NOUN
ejpam-3074	46	25	.	.	PUNCT
ejpam-3074	47	1	if	if	SCONJ
ejpam-3074	47	2	the	the	DET
ejpam-3074	47	3	dominant	dominant	ADJ
ejpam-3074	47	4	element	element	NOUN
ejpam-3074	47	5	t.	t.	PROPN
ejpam-3074	47	6	l.	l.	PROPN
ejpam-3074	47	7	saaty	saaty	PROPN
ejpam-3074	47	8	,	,	PUNCT
ejpam-3074	47	9	l.	l.	PROPN
ejpam-3074	47	10	g.	g.	PROPN
ejpam-3074	47	11	vargas	vargas	PROPN
ejpam-3074	47	12	/	/	SYM
ejpam-3074	47	13	eur	eur	PROPN
ejpam-3074	47	14	.	.	PUNCT
ejpam-3074	48	1	j.	j.	PROPN
ejpam-3074	48	2	pure	pure	PROPN
ejpam-3074	48	3	appl	appl	PROPN
ejpam-3074	48	4	.	.	PROPN
ejpam-3074	48	5	math	math	PROPN
ejpam-3074	48	6	,	,	PUNCT
ejpam-3074	48	7	10	10	NUM
ejpam-3074	48	8	(	(	PUNCT
ejpam-3074	48	9	4	4	NUM
ejpam-3074	48	10	)	)	PUNCT
ejpam-3074	48	11	(	(	PUNCT
ejpam-3074	48	12	2017	2017	NUM
ejpam-3074	48	13	)	)	PUNCT
ejpam-3074	48	14	,	,	PUNCT
ejpam-3074	48	15	602	602	NUM
ejpam-3074	48	16	-	-	SYM
ejpam-3074	48	17	613	613	NUM
ejpam-3074	48	18	604	604	NUM
ejpam-3074	48	19	is	be	AUX
ejpam-3074	48	20	x	x	NUM
ejpam-3074	48	21	times	time	NOUN
ejpam-3074	48	22	the	the	DET
ejpam-3074	48	23	dominated	dominate	VERB
ejpam-3074	48	24	element	element	NOUN
ejpam-3074	48	25	,	,	PUNCT
ejpam-3074	48	26	then	then	ADV
ejpam-3074	48	27	the	the	DET
ejpam-3074	48	28	latter	latter	ADJ
ejpam-3074	48	29	is	be	AUX
ejpam-3074	48	30	1	1	NUM
ejpam-3074	48	31	/	/	SYM
ejpam-3074	48	32	x	x	PUNCT
ejpam-3074	48	33	times	time	NOUN
ejpam-3074	48	34	the	the	DET
ejpam-3074	48	35	dominant	dominant	ADJ
ejpam-3074	48	36	one.this	one.this	PRON
ejpam-3074	48	37	reciprocal	reciprocal	ADJ
ejpam-3074	48	38	value	value	NOUN
ejpam-3074	48	39	is	be	AUX
ejpam-3074	48	40	assigned	assign	VERB
ejpam-3074	48	41	automatically	automatically	ADV
ejpam-3074	48	42	in	in	ADP
ejpam-3074	48	43	a	a	DET
ejpam-3074	48	44	group	group	NOUN
ejpam-3074	48	45	of	of	ADP
ejpam-3074	48	46	many	many	ADJ
ejpam-3074	48	47	comparisons	comparison	NOUN
ejpam-3074	48	48	as	as	SCONJ
ejpam-3074	48	49	we	we	PRON
ejpam-3074	48	50	show	show	VERB
ejpam-3074	48	51	below	below	ADV
ejpam-3074	48	52	.	.	PUNCT
ejpam-3074	49	1	because	because	SCONJ
ejpam-3074	49	2	of	of	ADP
ejpam-3074	49	3	this	this	DET
ejpam-3074	49	4	reciprocal	reciprocal	ADJ
ejpam-3074	49	5	relationship	relationship	NOUN
ejpam-3074	49	6	,	,	PUNCT
ejpam-3074	49	7	we	we	PRON
ejpam-3074	49	8	need	need	VERB
ejpam-3074	49	9	to	to	PART
ejpam-3074	49	10	work	work	VERB
ejpam-3074	49	11	with	with	ADP
ejpam-3074	49	12	division	division	NOUN
ejpam-3074	49	13	and	and	CCONJ
ejpam-3074	49	14	more	more	ADV
ejpam-3074	49	15	generally	generally	ADV
ejpam-3074	49	16	with	with	ADP
ejpam-3074	49	17	a	a	DET
ejpam-3074	49	18	division	division	NOUN
ejpam-3074	49	19	algebra	algebra	NOUN
ejpam-3074	49	20	.	.	PUNCT
ejpam-3074	50	1	since	since	SCONJ
ejpam-3074	50	2	we	we	PRON
ejpam-3074	50	3	must	must	AUX
ejpam-3074	50	4	work	work	VERB
ejpam-3074	50	5	in	in	ADP
ejpam-3074	50	6	division	division	NOUN
ejpam-3074	50	7	algebras	algebra	NOUN
ejpam-3074	50	8	we	we	PRON
ejpam-3074	50	9	briefly	briefly	ADV
ejpam-3074	50	10	summarize	summarize	VERB
ejpam-3074	50	11	what	what	PRON
ejpam-3074	50	12	is	be	AUX
ejpam-3074	50	13	known	know	VERB
ejpam-3074	50	14	about	about	ADP
ejpam-3074	50	15	their	their	PRON
ejpam-3074	50	16	origin	origin	NOUN
ejpam-3074	50	17	.	.	PUNCT
ejpam-3074	51	1	it	it	PRON
ejpam-3074	51	2	was	be	AUX
ejpam-3074	51	3	proved	prove	VERB
ejpam-3074	51	4	by	by	ADP
ejpam-3074	51	5	adolf	adolf	PROPN
ejpam-3074	51	6	hurwitz	hurwitz	PROPN
ejpam-3074	52	1	[	[	X
ejpam-3074	52	2	8	8	NUM
ejpam-3074	52	3	]	]	PUNCT
ejpam-3074	52	4	,	,	PUNCT
ejpam-3074	52	5	that	that	SCONJ
ejpam-3074	52	6	there	there	PRON
ejpam-3074	52	7	are	be	VERB
ejpam-3074	52	8	exactly	exactly	ADV
ejpam-3074	52	9	four	four	NUM
ejpam-3074	52	10	normed	normed	ADJ
ejpam-3074	52	11	division	division	NOUN
ejpam-3074	52	12	algebras	algebra	NOUN
ejpam-3074	52	13	:	:	PUNCT
ejpam-3074	52	14	the	the	DET
ejpam-3074	52	15	real	real	ADJ
ejpam-3074	52	16	numbers	number	NOUN
ejpam-3074	52	17	(	(	PUNCT
ejpam-3074	52	18	r	r	NOUN
ejpam-3074	52	19	)	)	PUNCT
ejpam-3074	52	20	,	,	PUNCT
ejpam-3074	52	21	the	the	DET
ejpam-3074	52	22	complex	complex	ADJ
ejpam-3074	52	23	numbers	number	NOUN
ejpam-3074	52	24	(	(	PUNCT
ejpam-3074	52	25	c	c	NOUN
ejpam-3074	52	26	)	)	PUNCT
ejpam-3074	52	27	,	,	PUNCT
ejpam-3074	52	28	the	the	DET
ejpam-3074	52	29	quaternions	quaternion	NOUN
ejpam-3074	52	30	(	(	PUNCT
ejpam-3074	52	31	h	h	NOUN
ejpam-3074	52	32	)	)	PUNCT
ejpam-3074	52	33	,	,	PUNCT
ejpam-3074	52	34	and	and	CCONJ
ejpam-3074	52	35	the	the	DET
ejpam-3074	52	36	octonions	octonion	NOUN
ejpam-3074	52	37	(	(	PUNCT
ejpam-3074	52	38	o	o	NOUN
ejpam-3074	52	39	)	)	PUNCT
ejpam-3074	52	40	.	.	PUNCT
ejpam-3074	53	1	the	the	DET
ejpam-3074	53	2	octonions	octonion	NOUN
ejpam-3074	53	3	were	be	AUX
ejpam-3074	53	4	discovered	discover	VERB
ejpam-3074	53	5	by	by	ADP
ejpam-3074	53	6	john	john	PROPN
ejpam-3074	53	7	t.	t.	PROPN
ejpam-3074	53	8	graves	grave	NOUN
ejpam-3074	53	9	in	in	ADP
ejpam-3074	53	10	1844	1844	NUM
ejpam-3074	53	11	[	[	X
ejpam-3074	53	12	7	7	NUM
ejpam-3074	53	13	]	]	PUNCT
ejpam-3074	53	14	who	who	PRON
ejpam-3074	53	15	called	call	VERB
ejpam-3074	53	16	them	they	PRON
ejpam-3074	53	17	octaves	octave	NOUN
ejpam-3074	53	18	.	.	PUNCT
ejpam-3074	54	1	before	before	SCONJ
ejpam-3074	54	2	john	john	PROPN
ejpam-3074	54	3	graves	graves	PROPN
ejpam-3074	54	4	had	have	VERB
ejpam-3074	54	5	a	a	DET
ejpam-3074	54	6	chance	chance	NOUN
ejpam-3074	54	7	to	to	PART
ejpam-3074	54	8	publish	publish	VERB
ejpam-3074	54	9	his	his	PRON
ejpam-3074	54	10	work	work	NOUN
ejpam-3074	54	11	,	,	PUNCT
ejpam-3074	54	12	arthur	arthur	PROPN
ejpam-3074	54	13	cayley	cayley	PROPN
ejpam-3074	54	14	published	publish	VERB
ejpam-3074	54	15	a	a	DET
ejpam-3074	54	16	paper	paper	NOUN
ejpam-3074	54	17	in	in	ADP
ejpam-3074	54	18	1845	1845	NUM
ejpam-3074	54	19	[	[	X
ejpam-3074	54	20	4	4	NUM
ejpam-3074	54	21	]	]	PUNCT
ejpam-3074	54	22	in	in	ADP
ejpam-3074	54	23	which	which	PRON
ejpam-3074	54	24	the	the	DET
ejpam-3074	54	25	octonions	octonion	NOUN
ejpam-3074	54	26	were	be	AUX
ejpam-3074	54	27	mentioned	mention	VERB
ejpam-3074	54	28	.	.	PUNCT
ejpam-3074	55	1	they	they	PRON
ejpam-3074	55	2	were	be	AUX
ejpam-3074	55	3	later	later	ADV
ejpam-3074	55	4	called	call	VERB
ejpam-3074	55	5	cayley	cayley	ADJ
ejpam-3074	55	6	-	-	PUNCT
ejpam-3074	55	7	numbers	number	NOUN
ejpam-3074	55	8	by	by	ADP
ejpam-3074	55	9	others	other	NOUN
ejpam-3074	55	10	.	.	PUNCT
ejpam-3074	56	1	an	an	DET
ejpam-3074	56	2	excellent	excellent	ADJ
ejpam-3074	56	3	exposition	exposition	NOUN
ejpam-3074	56	4	of	of	ADP
ejpam-3074	56	5	octonions	octonions	PROPN
ejpam-3074	56	6	can	can	AUX
ejpam-3074	56	7	be	be	AUX
ejpam-3074	56	8	found	find	VERB
ejpam-3074	56	9	in	in	ADP
ejpam-3074	56	10	[	[	X
ejpam-3074	56	11	2	2	NUM
ejpam-3074	56	12	]	]	PUNCT
ejpam-3074	56	13	,	,	PUNCT
ejpam-3074	56	14	and	and	CCONJ
ejpam-3074	56	15	of	of	ADP
ejpam-3074	56	16	quaternions	quaternion	NOUN
ejpam-3074	56	17	in	in	ADP
ejpam-3074	56	18	[	[	X
ejpam-3074	56	19	11	11	NUM
ejpam-3074	56	20	]	]	PUNCT
ejpam-3074	56	21	.	.	PUNCT
ejpam-3074	57	1	the	the	DET
ejpam-3074	57	2	book	book	NOUN
ejpam-3074	57	3	by	by	ADP
ejpam-3074	57	4	conway	conway	PROPN
ejpam-3074	57	5	and	and	CCONJ
ejpam-3074	57	6	smith	smith	NOUN
ejpam-3074	58	1	[	[	X
ejpam-3074	58	2	5	5	NUM
ejpam-3074	58	3	]	]	PUNCT
ejpam-3074	58	4	explains	explain	VERB
ejpam-3074	58	5	in	in	ADP
ejpam-3074	58	6	some	some	DET
ejpam-3074	58	7	detail	detail	NOUN
ejpam-3074	58	8	both	both	CCONJ
ejpam-3074	58	9	quaternions	quaternion	NOUN
ejpam-3074	58	10	and	and	CCONJ
ejpam-3074	58	11	octonions	octonion	NOUN
ejpam-3074	58	12	.	.	PUNCT
ejpam-3074	59	1	immediately	immediately	ADV
ejpam-3074	59	2	beyond	beyond	ADP
ejpam-3074	59	3	these	these	DET
ejpam-3074	59	4	four	four	NUM
ejpam-3074	59	5	division	division	NOUN
ejpam-3074	59	6	algebras	algebra	NOUN
ejpam-3074	59	7	are	be	AUX
ejpam-3074	59	8	the16	the16	NOUN
ejpam-3074	59	9	dimensional	dimensional	ADJ
ejpam-3074	59	10	sedenions	sedenion	NOUN
ejpam-3074	59	11	.	.	PUNCT
ejpam-3074	60	1	in	in	ADP
ejpam-3074	60	2	fact	fact	NOUN
ejpam-3074	60	3	,	,	PUNCT
ejpam-3074	60	4	one	one	PRON
ejpam-3074	60	5	can	can	AUX
ejpam-3074	60	6	get	get	VERB
ejpam-3074	60	7	an	an	DET
ejpam-3074	60	8	algebra	algebra	NOUN
ejpam-3074	60	9	of	of	ADP
ejpam-3074	60	10	dimension	dimension	NOUN
ejpam-3074	60	11	2n	2n	NUM
ejpam-3074	60	12	for	for	ADP
ejpam-3074	60	13	any	any	DET
ejpam-3074	60	14	non	non	ADJ
ejpam-3074	60	15	-	-	ADJ
ejpam-3074	60	16	negative	negative	ADJ
ejpam-3074	60	17	n	n	CCONJ
ejpam-3074	60	18	>	>	X
ejpam-3074	60	19	3	3	NUM
ejpam-3074	60	20	,	,	PUNCT
ejpam-3074	60	21	but	but	CCONJ
ejpam-3074	60	22	these	these	DET
ejpam-3074	60	23	algebras	algebra	NOUN
ejpam-3074	60	24	are	be	AUX
ejpam-3074	60	25	perhaps	perhaps	ADV
ejpam-3074	60	26	less	less	ADV
ejpam-3074	60	27	interesting	interesting	ADJ
ejpam-3074	60	28	because	because	SCONJ
ejpam-3074	60	29	they	they	PRON
ejpam-3074	60	30	are	be	AUX
ejpam-3074	60	31	no	no	ADV
ejpam-3074	60	32	longer	long	ADJ
ejpam-3074	60	33	division	division	NOUN
ejpam-3074	60	34	algebras	algebra	NOUN
ejpam-3074	60	35	that	that	PRON
ejpam-3074	60	36	is	be	AUX
ejpam-3074	60	37	ab	ab	PROPN
ejpam-3074	60	38	=	=	NOUN
ejpam-3074	60	39	0	0	NUM
ejpam-3074	60	40	no	no	ADV
ejpam-3074	60	41	longer	long	ADV
ejpam-3074	60	42	implies	imply	VERB
ejpam-3074	60	43	that	that	SCONJ
ejpam-3074	60	44	either	either	CCONJ
ejpam-3074	60	45	a	a	DET
ejpam-3074	60	46	=	=	SYM
ejpam-3074	60	47	0	0	NUM
ejpam-3074	60	48	or	or	CCONJ
ejpam-3074	60	49	b	b	NOUN
ejpam-3074	60	50	=	=	SYM
ejpam-3074	60	51	0	0	PROPN
ejpam-3074	60	52	.	.	PUNCT
ejpam-3074	60	53	brain	brain	NOUN
ejpam-3074	60	54	activity	activity	NOUN
ejpam-3074	60	55	creates	create	VERB
ejpam-3074	60	56	consciousness	consciousness	NOUN
ejpam-3074	60	57	.	.	PUNCT
ejpam-3074	61	1	according	accord	VERB
ejpam-3074	61	2	to	to	ADP
ejpam-3074	61	3	mark	mark	PROPN
ejpam-3074	61	4	robert	robert	PROPN
ejpam-3074	61	5	waldman	waldman	PROPN
ejpam-3074	61	6	consciousness	consciousness	NOUN
ejpam-3074	61	7	exists	exist	VERB
ejpam-3074	61	8	at	at	ADP
ejpam-3074	61	9	eight	eight	NUM
ejpam-3074	61	10	inclusive	inclusive	ADJ
ejpam-3074	61	11	levels	level	NOUN
ejpam-3074	61	12	:	:	PUNCT
ejpam-3074	61	13	reality	reality	NOUN
ejpam-3074	61	14	(	(	PUNCT
ejpam-3074	61	15	which	which	PRON
ejpam-3074	61	16	plato	plato	PROPN
ejpam-3074	61	17	called	call	VERB
ejpam-3074	61	18	phenomena	phenomena	PROPN
ejpam-3074	61	19	)	)	PUNCT
ejpam-3074	61	20	consisting	consist	VERB
ejpam-3074	61	21	of	of	ADP
ejpam-3074	61	22	the	the	DET
ejpam-3074	61	23	three	three	NUM
ejpam-3074	61	24	space	space	NOUN
ejpam-3074	61	25	physical	physical	ADJ
ejpam-3074	61	26	dimensions	dimension	NOUN
ejpam-3074	61	27	and	and	CCONJ
ejpam-3074	61	28	time	time	NOUN
ejpam-3074	61	29	,	,	PUNCT
ejpam-3074	61	30	and	and	CCONJ
ejpam-3074	61	31	seven	seven	NUM
ejpam-3074	61	32	states	state	NOUN
ejpam-3074	61	33	of	of	ADP
ejpam-3074	61	34	consciousness	consciousness	NOUN
ejpam-3074	61	35	(	(	PUNCT
ejpam-3074	61	36	called	call	VERB
ejpam-3074	61	37	by	by	ADP
ejpam-3074	61	38	plato	plato	PROPN
ejpam-3074	61	39	nuomena	nuomena	PROPN
ejpam-3074	61	40	)	)	PUNCT
ejpam-3074	61	41	that	that	PRON
ejpam-3074	61	42	cover	cover	VERB
ejpam-3074	61	43	instinctual	instinctual	ADJ
ejpam-3074	61	44	awareness	awareness	NOUN
ejpam-3074	61	45	(	(	PUNCT
ejpam-3074	61	46	wakefulness	wakefulness	NOUN
ejpam-3074	61	47	)	)	PUNCT
ejpam-3074	61	48	,	,	PUNCT
ejpam-3074	61	49	habitual	habitual	ADJ
ejpam-3074	61	50	responsiveness	responsiveness	NOUN
ejpam-3074	61	51	,	,	PUNCT
ejpam-3074	61	52	intentional	intentional	ADJ
ejpam-3074	61	53	decision	decision	NOUN
ejpam-3074	61	54	-	-	PUNCT
ejpam-3074	61	55	making	making	NOUN
ejpam-3074	61	56	,	,	PUNCT
ejpam-3074	61	57	free	free	ADV
ejpam-3074	61	58	-	-	PUNCT
ejpam-3074	61	59	floating	float	VERB
ejpam-3074	61	60	imagination	imagination	NOUN
ejpam-3074	61	61	,	,	PUNCT
ejpam-3074	61	62	self	self	NOUN
ejpam-3074	61	63	-	-	PUNCT
ejpam-3074	61	64	reflective	reflective	ADJ
ejpam-3074	61	65	awareness	awareness	NOUN
ejpam-3074	61	66	,	,	PUNCT
ejpam-3074	61	67	transformational	transformational	ADJ
ejpam-3074	61	68	awareness	awareness	NOUN
ejpam-3074	61	69	and	and	CCONJ
ejpam-3074	61	70	enlightenment	enlightenment	PROPN
ejpam-3074	61	71	.	.	PUNCT
ejpam-3074	62	1	waldmans	waldmans	PROPN
ejpam-3074	62	2	model	model	PROPN
ejpam-3074	62	3	of	of	ADP
ejpam-3074	62	4	human	human	ADJ
ejpam-3074	62	5	consciousness	consciousness	NOUN
ejpam-3074	62	6	consolidates	consolidate	VERB
ejpam-3074	62	7	more	more	ADJ
ejpam-3074	62	8	than	than	ADP
ejpam-3074	62	9	31,000	31,000	NUM
ejpam-3074	62	10	studies	study	NOUN
ejpam-3074	62	11	contained	contain	VERB
ejpam-3074	62	12	in	in	ADP
ejpam-3074	62	13	the	the	DET
ejpam-3074	62	14	database	database	NOUN
ejpam-3074	62	15	of	of	ADP
ejpam-3074	62	16	the	the	DET
ejpam-3074	62	17	national	national	ADJ
ejpam-3074	62	18	library	library	NOUN
ejpam-3074	62	19	of	of	ADP
ejpam-3074	62	20	medicine	medicine	NOUN
ejpam-3074	62	21	.	.	PUNCT
ejpam-3074	63	1	the	the	DET
ejpam-3074	63	2	first	first	ADJ
ejpam-3074	63	3	four	four	NUM
ejpam-3074	63	4	levels	level	NOUN
ejpam-3074	63	5	seem	seem	VERB
ejpam-3074	63	6	to	to	PART
ejpam-3074	63	7	correspond	correspond	VERB
ejpam-3074	63	8	to	to	ADP
ejpam-3074	63	9	the	the	DET
ejpam-3074	63	10	perceptual	perceptual	ADJ
ejpam-3074	63	11	-	-	PUNCT
ejpam-3074	63	12	cognitive	cognitive	ADJ
ejpam-3074	63	13	-	-	PUNCT
ejpam-3074	63	14	active	active	ADJ
ejpam-3074	63	15	loop	loop	NOUN
ejpam-3074	63	16	mentioned	mention	VERB
ejpam-3074	63	17	by	by	ADP
ejpam-3074	63	18	goertzel	goertzel	ADJ
ejpam-3074	64	1	[	[	X
ejpam-3074	64	2	6	6	NUM
ejpam-3074	64	3	]	]	PUNCT
ejpam-3074	64	4	.	.	PUNCT
ejpam-3074	65	1	”	"	PUNCT
ejpam-3074	65	2	the	the	DET
ejpam-3074	65	3	quaternion	quaternion	NOUN
ejpam-3074	65	4	structure	structure	NOUN
ejpam-3074	65	5	is	be	AUX
ejpam-3074	65	6	interpreted	interpret	VERB
ejpam-3074	65	7	as	as	ADP
ejpam-3074	65	8	a	a	DET
ejpam-3074	65	9	”	"	PUNCT
ejpam-3074	65	10	perceptual	perceptual	NOUN
ejpam-3074	65	11	-	-	PUNCT
ejpam-3074	65	12	cognitive	cognitive	ADJ
ejpam-3074	65	13	-	-	PUNCT
ejpam-3074	65	14	active	active	ADJ
ejpam-3074	65	15	loop	loop	NOUN
ejpam-3074	65	16	,	,	PUNCT
ejpam-3074	65	17	”	"	PUNCT
ejpam-3074	65	18	representing	represent	VERB
ejpam-3074	65	19	the	the	DET
ejpam-3074	65	20	basic	basic	ADJ
ejpam-3074	65	21	structure	structure	NOUN
ejpam-3074	65	22	of	of	ADP
ejpam-3074	65	23	engagement	engagement	NOUN
ejpam-3074	65	24	with	with	ADP
ejpam-3074	65	25	the	the	DET
ejpam-3074	65	26	world	world	NOUN
ejpam-3074	65	27	.	.	PUNCT
ejpam-3074	66	1	this	this	DET
ejpam-3074	66	2	structure	structure	NOUN
ejpam-3074	66	3	is	be	AUX
ejpam-3074	66	4	seen	see	VERB
ejpam-3074	66	5	to	to	PART
ejpam-3074	66	6	lead	lead	VERB
ejpam-3074	66	7	naturally	naturally	ADV
ejpam-3074	66	8	to	to	ADP
ejpam-3074	66	9	a	a	DET
ejpam-3074	66	10	certain	certain	ADJ
ejpam-3074	66	11	type	type	NOUN
ejpam-3074	66	12	of	of	ADP
ejpam-3074	66	13	adaptive	adaptive	ADJ
ejpam-3074	66	14	learning	learning	NOUN
ejpam-3074	66	15	,	,	PUNCT
ejpam-3074	66	16	analogous	analogous	ADJ
ejpam-3074	66	17	to	to	ADP
ejpam-3074	66	18	backtracking	backtrack	VERB
ejpam-3074	66	19	in	in	ADP
ejpam-3074	66	20	artificial	artificial	ADJ
ejpam-3074	66	21	intelligence	intelligence	NOUN
ejpam-3074	66	22	.	.	PUNCT
ejpam-3074	67	1	the	the	DET
ejpam-3074	67	2	remaining	remain	VERB
ejpam-3074	67	3	levels	level	NOUN
ejpam-3074	67	4	appear	appear	VERB
ejpam-3074	67	5	to	to	PART
ejpam-3074	67	6	need	need	VERB
ejpam-3074	67	7	the	the	DET
ejpam-3074	67	8	octonions	octonion	NOUN
ejpam-3074	67	9	as	as	ADP
ejpam-3074	67	10	goertzel	goertzel	ADJ
ejpam-3074	67	11	[	[	X
ejpam-3074	67	12	6	6	NUM
ejpam-3074	67	13	]	]	PUNCT
ejpam-3074	67	14	writes	write	VERB
ejpam-3074	67	15	:	:	PUNCT
ejpam-3074	67	16	the	the	DET
ejpam-3074	67	17	octonion	octonion	NOUN
ejpam-3074	67	18	structure	structure	NOUN
ejpam-3074	67	19	is	be	AUX
ejpam-3074	67	20	seen	see	VERB
ejpam-3074	67	21	to	to	PART
ejpam-3074	67	22	ensue	ensue	VERB
ejpam-3074	67	23	from	from	ADP
ejpam-3074	67	24	adding	add	VERB
ejpam-3074	67	25	to	to	ADP
ejpam-3074	67	26	the	the	DET
ejpam-3074	67	27	quaternions	quaternion	NOUN
ejpam-3074	67	28	an	an	DET
ejpam-3074	67	29	extra	extra	ADJ
ejpam-3074	67	30	mental	mental	ADJ
ejpam-3074	67	31	process	process	NOUN
ejpam-3074	67	32	that	that	PRON
ejpam-3074	67	33	observes	observe	VERB
ejpam-3074	67	34	the	the	DET
ejpam-3074	67	35	others	other	NOUN
ejpam-3074	67	36	.	.	PUNCT
ejpam-3074	68	1	this	this	DET
ejpam-3074	68	2	extra	extra	ADJ
ejpam-3074	68	3	element	element	NOUN
ejpam-3074	68	4	is	be	AUX
ejpam-3074	68	5	called	call	VERB
ejpam-3074	68	6	the	the	DET
ejpam-3074	68	7	”	"	PUNCT
ejpam-3074	68	8	inner	inner	ADJ
ejpam-3074	68	9	eye	eye	NOUN
ejpam-3074	68	10	”	"	PUNCT
ejpam-3074	68	11	and	and	CCONJ
ejpam-3074	68	12	is	be	AUX
ejpam-3074	68	13	hypothesized	hypothesize	VERB
ejpam-3074	68	14	to	to	PART
ejpam-3074	68	15	provide	provide	VERB
ejpam-3074	68	16	for	for	ADP
ejpam-3074	68	17	reflexive	reflexive	ADJ
ejpam-3074	68	18	consciousness	consciousness	NOUN
ejpam-3074	68	19	and	and	CCONJ
ejpam-3074	68	20	higher	high	ADJ
ejpam-3074	68	21	-	-	PUNCT
ejpam-3074	68	22	order	order	NOUN
ejpam-3074	68	23	thought	thought	NOUN
ejpam-3074	68	24	.	.	PUNCT
ejpam-3074	68	25	”	"	PUNCT
ejpam-3074	69	1	we	we	PRON
ejpam-3074	69	2	are	be	AUX
ejpam-3074	69	3	left	leave	VERB
ejpam-3074	69	4	with	with	ADP
ejpam-3074	69	5	the	the	DET
ejpam-3074	69	6	need	need	NOUN
ejpam-3074	69	7	for	for	ADP
ejpam-3074	69	8	the	the	DET
ejpam-3074	69	9	eight	eight	NUM
ejpam-3074	69	10	dimensional	dimensional	ADJ
ejpam-3074	69	11	octonions	octonion	NOUN
ejpam-3074	69	12	that	that	PRON
ejpam-3074	69	13	arise	arise	VERB
ejpam-3074	69	14	from	from	ADP
ejpam-3074	69	15	the	the	DET
ejpam-3074	69	16	different	different	ADJ
ejpam-3074	69	17	physics	physics	NOUN
ejpam-3074	69	18	manifestations	manifestation	NOUN
ejpam-3074	69	19	of	of	ADP
ejpam-3074	69	20	our	our	PRON
ejpam-3074	69	21	world	world	NOUN
ejpam-3074	69	22	,	,	PUNCT
ejpam-3074	69	23	the	the	DET
ejpam-3074	69	24	functions	function	NOUN
ejpam-3074	69	25	of	of	ADP
ejpam-3074	69	26	the	the	DET
ejpam-3074	69	27	nervous	nervous	ADJ
ejpam-3074	69	28	system	system	NOUN
ejpam-3074	69	29	and	and	CCONJ
ejpam-3074	69	30	from	from	ADP
ejpam-3074	69	31	the	the	DET
ejpam-3074	69	32	mathematical	mathematical	ADJ
ejpam-3074	69	33	account	account	NOUN
ejpam-3074	69	34	of	of	ADP
ejpam-3074	69	35	proportionality	proportionality	NOUN
ejpam-3074	69	36	between	between	ADP
ejpam-3074	69	37	perception	perception	NOUN
ejpam-3074	69	38	and	and	CCONJ
ejpam-3074	69	39	physical	physical	ADJ
ejpam-3074	69	40	reality	reality	NOUN
ejpam-3074	69	41	.	.	PUNCT
ejpam-3074	70	1	physically	physically	ADV
ejpam-3074	70	2	,	,	PUNCT
ejpam-3074	70	3	as	as	SCONJ
ejpam-3074	70	4	opposed	oppose	VERB
ejpam-3074	70	5	to	to	ADP
ejpam-3074	70	6	behaviorally	behaviorally	ADV
ejpam-3074	70	7	(	(	PUNCT
ejpam-3074	70	8	which	which	PRON
ejpam-3074	70	9	is	be	AUX
ejpam-3074	70	10	our	our	PRON
ejpam-3074	70	11	concern	concern	NOUN
ejpam-3074	70	12	here	here	ADV
ejpam-3074	70	13	)	)	PUNCT
ejpam-3074	70	14	the	the	DET
ejpam-3074	70	15	multiplication	multiplication	NOUN
ejpam-3074	70	16	of	of	ADP
ejpam-3074	70	17	octonions	octonions	PROPN
ejpam-3074	70	18	is	be	AUX
ejpam-3074	70	19	used	use	VERB
ejpam-3074	70	20	to	to	PART
ejpam-3074	70	21	describe	describe	VERB
ejpam-3074	70	22	rotations	rotation	NOUN
ejpam-3074	70	23	in	in	ADP
ejpam-3074	70	24	7	7	NUM
ejpam-3074	70	25	dimensions	dimension	NOUN
ejpam-3074	70	26	with	with	ADP
ejpam-3074	70	27	stretch	stretch	NOUN
ejpam-3074	70	28	and	and	CCONJ
ejpam-3074	70	29	contraction	contraction	NOUN
ejpam-3074	70	30	as	as	ADP
ejpam-3074	70	31	the	the	DET
ejpam-3074	70	32	t.	t.	PROPN
ejpam-3074	70	33	l.	l.	PROPN
ejpam-3074	70	34	saaty	saaty	PROPN
ejpam-3074	70	35	,	,	PUNCT
ejpam-3074	70	36	l.	l.	PROPN
ejpam-3074	70	37	g.	g.	PROPN
ejpam-3074	70	38	vargas	vargas	PROPN
ejpam-3074	70	39	/	/	SYM
ejpam-3074	70	40	eur	eur	PROPN
ejpam-3074	70	41	.	.	PUNCT
ejpam-3074	71	1	j.	j.	PROPN
ejpam-3074	71	2	pure	pure	PROPN
ejpam-3074	71	3	appl	appl	PROPN
ejpam-3074	71	4	.	.	PROPN
ejpam-3074	71	5	math	math	PROPN
ejpam-3074	71	6	,	,	PUNCT
ejpam-3074	71	7	10	10	NUM
ejpam-3074	71	8	(	(	PUNCT
ejpam-3074	71	9	4	4	NUM
ejpam-3074	71	10	)	)	PUNCT
ejpam-3074	71	11	(	(	PUNCT
ejpam-3074	71	12	2017	2017	NUM
ejpam-3074	71	13	)	)	PUNCT
ejpam-3074	71	14	,	,	PUNCT
ejpam-3074	71	15	602	602	NUM
ejpam-3074	71	16	-	-	SYM
ejpam-3074	71	17	613	613	NUM
ejpam-3074	71	18	605	605	NUM
ejpam-3074	71	19	additional	additional	ADJ
ejpam-3074	71	20	8th	8th	ADJ
ejpam-3074	71	21	dimension	dimension	NOUN
ejpam-3074	71	22	.	.	PUNCT
ejpam-3074	72	1	the	the	DET
ejpam-3074	72	2	role	role	NOUN
ejpam-3074	72	3	of	of	ADP
ejpam-3074	72	4	the	the	DET
ejpam-3074	72	5	octonions	octonion	NOUN
ejpam-3074	72	6	is	be	AUX
ejpam-3074	72	7	more	more	ADJ
ejpam-3074	72	8	than	than	ADP
ejpam-3074	72	9	just	just	ADV
ejpam-3074	72	10	describing	describe	VERB
ejpam-3074	72	11	geometric	geometric	ADJ
ejpam-3074	72	12	properties	property	NOUN
ejpam-3074	72	13	.	.	PUNCT
ejpam-3074	73	1	the	the	DET
ejpam-3074	73	2	octonions	octonion	NOUN
ejpam-3074	73	3	are	be	AUX
ejpam-3074	73	4	the	the	DET
ejpam-3074	73	5	foundation	foundation	NOUN
ejpam-3074	73	6	for	for	ADP
ejpam-3074	73	7	their	their	PRON
ejpam-3074	73	8	group	group	NOUN
ejpam-3074	73	9	of	of	ADP
ejpam-3074	73	10	automorphisms	automorphism	NOUN
ejpam-3074	73	11	known	know	VERB
ejpam-3074	73	12	as	as	ADP
ejpam-3074	73	13	g2	g2	PROPN
ejpam-3074	73	14	on	on	ADP
ejpam-3074	73	15	which	which	PRON
ejpam-3074	73	16	physics	physics	NOUN
ejpam-3074	73	17	models	model	NOUN
ejpam-3074	73	18	of	of	ADP
ejpam-3074	73	19	the	the	DET
ejpam-3074	73	20	universe	universe	NOUN
ejpam-3074	73	21	,	,	PUNCT
ejpam-3074	73	22	superstring	superstre	VERB
ejpam-3074	73	23	theory	theory	NOUN
ejpam-3074	73	24	,	,	PUNCT
ejpam-3074	73	25	are	be	AUX
ejpam-3074	73	26	built	build	VERB
ejpam-3074	73	27	.	.	PUNCT
ejpam-3074	74	1	we	we	PRON
ejpam-3074	74	2	discuss	discuss	VERB
ejpam-3074	74	3	this	this	PRON
ejpam-3074	74	4	later	later	ADV
ejpam-3074	74	5	in	in	ADP
ejpam-3074	74	6	the	the	DET
ejpam-3074	74	7	paper	paper	NOUN
ejpam-3074	74	8	.	.	PUNCT
ejpam-3074	75	1	the	the	DET
ejpam-3074	75	2	following	follow	VERB
ejpam-3074	75	3	question	question	NOUN
ejpam-3074	75	4	is	be	AUX
ejpam-3074	75	5	a	a	DET
ejpam-3074	75	6	bold	bold	ADJ
ejpam-3074	75	7	assertion	assertion	NOUN
ejpam-3074	75	8	just	just	ADV
ejpam-3074	75	9	short	short	ADV
ejpam-3074	75	10	of	of	ADP
ejpam-3074	75	11	sounding	sound	VERB
ejpam-3074	75	12	crazy	crazy	ADJ
ejpam-3074	75	13	.	.	PUNCT
ejpam-3074	76	1	why	why	SCONJ
ejpam-3074	76	2	are	be	AUX
ejpam-3074	76	3	octonions	octonion	NOUN
ejpam-3074	76	4	necessary	necessary	ADJ
ejpam-3074	76	5	and	and	CCONJ
ejpam-3074	76	6	sufficient	sufficient	ADJ
ejpam-3074	76	7	to	to	PART
ejpam-3074	76	8	represent	represent	VERB
ejpam-3074	76	9	all	all	DET
ejpam-3074	76	10	brain	brain	NOUN
ejpam-3074	76	11	activity	activity	NOUN
ejpam-3074	76	12	and	and	CCONJ
ejpam-3074	76	13	the	the	DET
ejpam-3074	76	14	feelings	feeling	NOUN
ejpam-3074	76	15	and	and	CCONJ
ejpam-3074	76	16	knowledge	knowledge	NOUN
ejpam-3074	76	17	we	we	PRON
ejpam-3074	76	18	use	use	VERB
ejpam-3074	76	19	to	to	PART
ejpam-3074	76	20	explain	explain	VERB
ejpam-3074	76	21	all	all	PRON
ejpam-3074	76	22	we	we	PRON
ejpam-3074	76	23	can	can	AUX
ejpam-3074	76	24	ever	ever	ADV
ejpam-3074	76	25	conceptualize	conceptualize	VERB
ejpam-3074	76	26	?	?	PUNCT
ejpam-3074	77	1	the	the	DET
ejpam-3074	77	2	necessity	necessity	NOUN
ejpam-3074	77	3	follows	follow	VERB
ejpam-3074	77	4	from	from	ADP
ejpam-3074	77	5	the	the	DET
ejpam-3074	77	6	fact	fact	NOUN
ejpam-3074	77	7	that	that	SCONJ
ejpam-3074	77	8	if	if	SCONJ
ejpam-3074	77	9	comparisons	comparison	NOUN
ejpam-3074	77	10	are	be	AUX
ejpam-3074	77	11	taken	take	VERB
ejpam-3074	77	12	as	as	ADP
ejpam-3074	77	13	the	the	DET
ejpam-3074	77	14	most	most	ADV
ejpam-3074	77	15	fundamental	fundamental	ADJ
ejpam-3074	77	16	axiom	axiom	NOUN
ejpam-3074	77	17	of	of	ADP
ejpam-3074	77	18	all	all	DET
ejpam-3074	77	19	knowledge	knowledge	NOUN
ejpam-3074	77	20	,	,	PUNCT
ejpam-3074	77	21	decision	decision	NOUN
ejpam-3074	77	22	making	making	NOUN
ejpam-3074	77	23	and	and	CCONJ
ejpam-3074	77	24	action	action	NOUN
ejpam-3074	77	25	,	,	PUNCT
ejpam-3074	77	26	octonions	octonion	NOUN
ejpam-3074	77	27	are	be	AUX
ejpam-3074	77	28	the	the	DET
ejpam-3074	77	29	largest	large	ADJ
ejpam-3074	77	30	division	division	NOUN
ejpam-3074	77	31	algebra	algebra	NOUN
ejpam-3074	77	32	.	.	PUNCT
ejpam-3074	78	1	the	the	DET
ejpam-3074	78	2	other	other	ADJ
ejpam-3074	78	3	three	three	NUM
ejpam-3074	78	4	algebras	algebra	NOUN
ejpam-3074	78	5	are	be	AUX
ejpam-3074	78	6	special	special	ADJ
ejpam-3074	78	7	cases	case	NOUN
ejpam-3074	78	8	of	of	ADP
ejpam-3074	78	9	octonions	octonions	NOUN
ejpam-3074	78	10	.	.	PUNCT
ejpam-3074	79	1	the	the	DET
ejpam-3074	79	2	proof	proof	NOUN
ejpam-3074	79	3	of	of	ADP
ejpam-3074	79	4	sufficiency	sufficiency	NOUN
ejpam-3074	79	5	is	be	AUX
ejpam-3074	79	6	vast	vast	ADJ
ejpam-3074	79	7	and	and	CCONJ
ejpam-3074	79	8	empirical	empirical	ADJ
ejpam-3074	79	9	as	as	SCONJ
ejpam-3074	79	10	we	we	PRON
ejpam-3074	79	11	shall	shall	AUX
ejpam-3074	79	12	see	see	VERB
ejpam-3074	79	13	below	below	ADV
ejpam-3074	79	14	.	.	PUNCT
ejpam-3074	80	1	in	in	ADP
ejpam-3074	80	2	passing	pass	VERB
ejpam-3074	80	3	,	,	PUNCT
ejpam-3074	80	4	we	we	PRON
ejpam-3074	80	5	note	note	VERB
ejpam-3074	80	6	that	that	SCONJ
ejpam-3074	80	7	the	the	DET
ejpam-3074	80	8	fourier	fourier	NOUN
ejpam-3074	80	9	transform	transform	NOUN
ejpam-3074	80	10	is	be	AUX
ejpam-3074	80	11	needed	need	VERB
ejpam-3074	80	12	to	to	PART
ejpam-3074	80	13	transform	transform	VERB
ejpam-3074	80	14	electrochemical	electrochemical	ADJ
ejpam-3074	80	15	vibrations	vibration	NOUN
ejpam-3074	80	16	to	to	ADP
ejpam-3074	80	17	the	the	DET
ejpam-3074	80	18	real	real	ADJ
ejpam-3074	80	19	world	world	NOUN
ejpam-3074	80	20	of	of	ADP
ejpam-3074	80	21	space	space	NOUN
ejpam-3074	80	22	and	and	CCONJ
ejpam-3074	80	23	time	time	NOUN
ejpam-3074	80	24	.	.	PUNCT
ejpam-3074	81	1	such	such	DET
ejpam-3074	81	2	a	a	DET
ejpam-3074	81	3	transformation	transformation	NOUN
ejpam-3074	81	4	is	be	AUX
ejpam-3074	81	5	not	not	PART
ejpam-3074	81	6	needed	need	VERB
ejpam-3074	81	7	to	to	PART
ejpam-3074	81	8	transform	transform	VERB
ejpam-3074	81	9	thoughts	thought	NOUN
ejpam-3074	81	10	themselves	themselves	PRON
ejpam-3074	81	11	and	and	CCONJ
ejpam-3074	81	12	we	we	PRON
ejpam-3074	81	13	need	need	VERB
ejpam-3074	81	14	a	a	DET
ejpam-3074	81	15	different	different	ADJ
ejpam-3074	81	16	way	way	NOUN
ejpam-3074	81	17	to	to	PART
ejpam-3074	81	18	write	write	VERB
ejpam-3074	81	19	about	about	ADP
ejpam-3074	81	20	the	the	DET
ejpam-3074	81	21	synthesis	synthesis	NOUN
ejpam-3074	81	22	of	of	ADP
ejpam-3074	81	23	firings	firing	NOUN
ejpam-3074	81	24	of	of	ADP
ejpam-3074	81	25	neurons	neuron	NOUN
ejpam-3074	81	26	.	.	PUNCT
ejpam-3074	82	1	we	we	PRON
ejpam-3074	82	2	believe	believe	VERB
ejpam-3074	82	3	that	that	SCONJ
ejpam-3074	82	4	the	the	DET
ejpam-3074	82	5	property	property	NOUN
ejpam-3074	82	6	that	that	PRON
ejpam-3074	82	7	makes	make	VERB
ejpam-3074	82	8	the	the	DET
ejpam-3074	82	9	octonions	octonion	NOUN
ejpam-3074	82	10	sufficient	sufficient	ADJ
ejpam-3074	82	11	to	to	PART
ejpam-3074	82	12	represent	represent	VERB
ejpam-3074	82	13	thoughts	thought	NOUN
ejpam-3074	82	14	is	be	AUX
ejpam-3074	82	15	density	density	NOUN
ejpam-3074	82	16	,	,	PUNCT
ejpam-3074	82	17	i.e.	i.e.	X
ejpam-3074	82	18	,	,	PUNCT
ejpam-3074	82	19	all	all	DET
ejpam-3074	82	20	thoughts	thought	NOUN
ejpam-3074	82	21	are	be	AUX
ejpam-3074	82	22	represented	represent	VERB
ejpam-3074	82	23	by	by	ADP
ejpam-3074	82	24	a	a	DET
ejpam-3074	82	25	finite	finite	ADJ
ejpam-3074	82	26	combination	combination	NOUN
ejpam-3074	82	27	of	of	ADP
ejpam-3074	82	28	the	the	DET
ejpam-3074	82	29	solutions	solution	NOUN
ejpam-3074	82	30	of	of	ADP
ejpam-3074	82	31	the	the	DET
ejpam-3074	82	32	fundamental	fundamental	ADJ
ejpam-3074	82	33	equation	equation	NOUN
ejpam-3074	82	34	of	of	ADP
ejpam-3074	82	35	proportionality	proportionality	NOUN
ejpam-3074	82	36	given	give	VERB
ejpam-3074	82	37	below	below	ADV
ejpam-3074	82	38	.	.	PUNCT
ejpam-3074	83	1	the	the	DET
ejpam-3074	83	2	reason	reason	NOUN
ejpam-3074	83	3	why	why	SCONJ
ejpam-3074	83	4	there	there	PRON
ejpam-3074	83	5	is	be	VERB
ejpam-3074	83	6	no	no	DET
ejpam-3074	83	7	need	need	NOUN
ejpam-3074	83	8	for	for	ADP
ejpam-3074	83	9	a	a	DET
ejpam-3074	83	10	transformation	transformation	NOUN
ejpam-3074	83	11	such	such	ADJ
ejpam-3074	83	12	as	as	ADP
ejpam-3074	83	13	the	the	DET
ejpam-3074	83	14	fourier	fourier	NOUN
ejpam-3074	83	15	transform	transform	NOUN
ejpam-3074	83	16	is	be	AUX
ejpam-3074	83	17	that	that	SCONJ
ejpam-3074	83	18	in	in	ADP
ejpam-3074	83	19	the	the	DET
ejpam-3074	83	20	physical	physical	ADJ
ejpam-3074	83	21	domain	domain	NOUN
ejpam-3074	83	22	the	the	DET
ejpam-3074	83	23	solution	solution	NOUN
ejpam-3074	83	24	of	of	ADP
ejpam-3074	83	25	the	the	DET
ejpam-3074	83	26	fundamental	fundamental	ADJ
ejpam-3074	83	27	equation	equation	NOUN
ejpam-3074	83	28	is	be	AUX
ejpam-3074	83	29	not	not	PART
ejpam-3074	83	30	itself	itself	PRON
ejpam-3074	83	31	dense	dense	ADJ
ejpam-3074	83	32	.	.	PUNCT
ejpam-3074	84	1	thus	thus	ADV
ejpam-3074	84	2	,	,	PUNCT
ejpam-3074	84	3	it	it	PRON
ejpam-3074	84	4	needs	need	VERB
ejpam-3074	84	5	the	the	DET
ejpam-3074	84	6	transformation	transformation	NOUN
ejpam-3074	84	7	that	that	PRON
ejpam-3074	84	8	leads	lead	VERB
ejpam-3074	84	9	to	to	ADP
ejpam-3074	84	10	dirac	dirac	NOUN
ejpam-3074	84	11	type	type	NOUN
ejpam-3074	84	12	distributions	distribution	NOUN
ejpam-3074	84	13	that	that	PRON
ejpam-3074	84	14	are	be	AUX
ejpam-3074	84	15	known	know	VERB
ejpam-3074	84	16	to	to	PART
ejpam-3074	84	17	be	be	AUX
ejpam-3074	84	18	dense	dense	ADJ
ejpam-3074	84	19	and	and	CCONJ
ejpam-3074	84	20	sufficient	sufficient	ADJ
ejpam-3074	84	21	to	to	PART
ejpam-3074	84	22	represent	represent	VERB
ejpam-3074	84	23	reality	reality	NOUN
ejpam-3074	84	24	.	.	PUNCT
ejpam-3074	85	1	2	2	X
ejpam-3074	85	2	.	.	X
ejpam-3074	85	3	how	how	SCONJ
ejpam-3074	85	4	reciprocal	reciprocal	ADJ
ejpam-3074	85	5	comparisons	comparison	NOUN
ejpam-3074	85	6	work	work	VERB
ejpam-3074	85	7	a	a	DET
ejpam-3074	85	8	basic	basic	ADJ
ejpam-3074	85	9	concept	concept	NOUN
ejpam-3074	85	10	at	at	ADP
ejpam-3074	85	11	the	the	DET
ejpam-3074	85	12	core	core	NOUN
ejpam-3074	85	13	of	of	ADP
ejpam-3074	85	14	understanding	understanding	NOUN
ejpam-3074	85	15	is	be	AUX
ejpam-3074	85	16	the	the	DET
ejpam-3074	85	17	reciprocal	reciprocal	ADJ
ejpam-3074	85	18	property	property	NOUN
ejpam-3074	85	19	.	.	PUNCT
ejpam-3074	86	1	essentially	essentially	ADV
ejpam-3074	86	2	this	this	DET
ejpam-3074	86	3	property	property	NOUN
ejpam-3074	86	4	asserts	assert	VERB
ejpam-3074	86	5	that	that	SCONJ
ejpam-3074	86	6	,	,	PUNCT
ejpam-3074	86	7	for	for	ADP
ejpam-3074	86	8	example	example	NOUN
ejpam-3074	86	9	,	,	PUNCT
ejpam-3074	86	10	when	when	SCONJ
ejpam-3074	86	11	comparing	compare	VERB
ejpam-3074	86	12	two	two	NUM
ejpam-3074	86	13	stones	stone	NOUN
ejpam-3074	86	14	according	accord	VERB
ejpam-3074	86	15	to	to	ADP
ejpam-3074	86	16	weight	weight	NOUN
ejpam-3074	86	17	with	with	ADP
ejpam-3074	86	18	the	the	DET
ejpam-3074	86	19	aid	aid	NOUN
ejpam-3074	86	20	of	of	ADP
ejpam-3074	86	21	the	the	DET
ejpam-3074	86	22	hands	hand	NOUN
ejpam-3074	86	23	and	and	CCONJ
ejpam-3074	86	24	one	one	NUM
ejpam-3074	86	25	stone	stone	NOUN
ejpam-3074	86	26	is	be	AUX
ejpam-3074	86	27	judged	judge	VERB
ejpam-3074	86	28	to	to	PART
ejpam-3074	86	29	be	be	AUX
ejpam-3074	86	30	five	five	NUM
ejpam-3074	86	31	times	time	NOUN
ejpam-3074	86	32	heavier	heavy	ADJ
ejpam-3074	86	33	than	than	ADP
ejpam-3074	86	34	the	the	DET
ejpam-3074	86	35	other	other	ADJ
ejpam-3074	86	36	,	,	PUNCT
ejpam-3074	86	37	then	then	ADV
ejpam-3074	86	38	the	the	DET
ejpam-3074	86	39	other	other	ADJ
ejpam-3074	86	40	is	be	AUX
ejpam-3074	86	41	automatically	automatically	ADV
ejpam-3074	86	42	one	one	NUM
ejpam-3074	86	43	fifth	fifth	ADJ
ejpam-3074	86	44	the	the	DET
ejpam-3074	86	45	weight	weight	NOUN
ejpam-3074	86	46	of	of	ADP
ejpam-3074	86	47	the	the	DET
ejpam-3074	86	48	first	first	ADJ
ejpam-3074	86	49	.	.	PUNCT
ejpam-3074	87	1	both	both	DET
ejpam-3074	87	2	stones	stone	NOUN
ejpam-3074	87	3	participate	participate	VERB
ejpam-3074	87	4	in	in	ADP
ejpam-3074	87	5	the	the	DET
ejpam-3074	87	6	judgment	judgment	NOUN
ejpam-3074	87	7	,	,	PUNCT
ejpam-3074	87	8	the	the	DET
ejpam-3074	87	9	smaller	small	ADJ
ejpam-3074	87	10	one	one	NOUN
ejpam-3074	87	11	serving	serve	VERB
ejpam-3074	87	12	as	as	ADP
ejpam-3074	87	13	a	a	DET
ejpam-3074	87	14	unit	unit	NOUN
ejpam-3074	87	15	of	of	ADP
ejpam-3074	87	16	reference	reference	NOUN
ejpam-3074	87	17	.	.	PUNCT
ejpam-3074	88	1	all	all	DET
ejpam-3074	88	2	our	our	PRON
ejpam-3074	88	3	senses	sense	NOUN
ejpam-3074	88	4	can	can	AUX
ejpam-3074	88	5	make	make	VERB
ejpam-3074	88	6	such	such	ADJ
ejpam-3074	88	7	comparisons	comparison	NOUN
ejpam-3074	88	8	and	and	CCONJ
ejpam-3074	88	9	so	so	ADV
ejpam-3074	88	10	does	do	VERB
ejpam-3074	88	11	our	our	PRON
ejpam-3074	88	12	mind	mind	NOUN
ejpam-3074	88	13	in	in	ADP
ejpam-3074	88	14	comparing	compare	VERB
ejpam-3074	88	15	abstract	abstract	ADJ
ejpam-3074	88	16	ideas	idea	NOUN
ejpam-3074	88	17	with	with	ADP
ejpam-3074	88	18	respect	respect	NOUN
ejpam-3074	88	19	to	to	ADP
ejpam-3074	88	20	common	common	ADJ
ejpam-3074	88	21	properties	property	NOUN
ejpam-3074	88	22	.	.	PUNCT
ejpam-3074	89	1	this	this	DET
ejpam-3074	89	2	process	process	NOUN
ejpam-3074	89	3	must	must	AUX
ejpam-3074	89	4	also	also	ADV
ejpam-3074	89	5	take	take	VERB
ejpam-3074	89	6	place	place	NOUN
ejpam-3074	89	7	at	at	ADP
ejpam-3074	89	8	the	the	DET
ejpam-3074	89	9	very	very	ADV
ejpam-3074	89	10	elementary	elementary	ADJ
ejpam-3074	89	11	molecular	molecular	ADJ
ejpam-3074	89	12	level	level	NOUN
ejpam-3074	89	13	.	.	PUNCT
ejpam-3074	90	1	from	from	ADP
ejpam-3074	90	2	such	such	ADJ
ejpam-3074	90	3	comparisons	comparison	NOUN
ejpam-3074	90	4	among	among	ADP
ejpam-3074	90	5	objects	object	NOUN
ejpam-3074	90	6	in	in	ADP
ejpam-3074	90	7	pairs	pair	NOUN
ejpam-3074	90	8	,	,	PUNCT
ejpam-3074	90	9	a	a	DET
ejpam-3074	90	10	relative	relative	ADJ
ejpam-3074	90	11	scale	scale	NOUN
ejpam-3074	90	12	of	of	ADP
ejpam-3074	90	13	measurement	measurement	NOUN
ejpam-3074	90	14	is	be	AUX
ejpam-3074	90	15	derived	derive	VERB
ejpam-3074	90	16	among	among	ADP
ejpam-3074	90	17	the	the	DET
ejpam-3074	90	18	objects	object	NOUN
ejpam-3074	90	19	.	.	PUNCT
ejpam-3074	91	1	reciprocal	reciprocal	ADJ
ejpam-3074	91	2	comparison	comparison	NOUN
ejpam-3074	91	3	is	be	AUX
ejpam-3074	91	4	an	an	DET
ejpam-3074	91	5	inherent	inherent	ADJ
ejpam-3074	91	6	conscious	conscious	ADJ
ejpam-3074	91	7	ability	ability	NOUN
ejpam-3074	91	8	of	of	ADP
ejpam-3074	91	9	all	all	DET
ejpam-3074	91	10	human	human	ADJ
ejpam-3074	91	11	beings	being	NOUN
ejpam-3074	91	12	which	which	PRON
ejpam-3074	91	13	enables	enable	VERB
ejpam-3074	91	14	us	we	PRON
ejpam-3074	91	15	to	to	PART
ejpam-3074	91	16	scale	scale	VERB
ejpam-3074	91	17	things	thing	NOUN
ejpam-3074	91	18	encountered	encounter	VERB
ejpam-3074	91	19	in	in	ADP
ejpam-3074	91	20	practice	practice	NOUN
ejpam-3074	91	21	.	.	PUNCT
ejpam-3074	92	1	the	the	DET
ejpam-3074	92	2	logical	logical	ADJ
ejpam-3074	92	3	question	question	NOUN
ejpam-3074	92	4	then	then	ADV
ejpam-3074	92	5	is	be	AUX
ejpam-3074	92	6	:	:	PUNCT
ejpam-3074	92	7	is	be	AUX
ejpam-3074	92	8	our	our	PRON
ejpam-3074	92	9	judgment	judgment	NOUN
ejpam-3074	92	10	sufficiently	sufficiently	ADV
ejpam-3074	92	11	accurate	accurate	ADJ
ejpam-3074	92	12	to	to	PART
ejpam-3074	92	13	ensure	ensure	VERB
ejpam-3074	92	14	that	that	SCONJ
ejpam-3074	92	15	if	if	SCONJ
ejpam-3074	92	16	stone	stone	NOUN
ejpam-3074	92	17	a	a	PRON
ejpam-3074	92	18	is	be	AUX
ejpam-3074	92	19	,	,	PUNCT
ejpam-3074	92	20	for	for	ADP
ejpam-3074	92	21	example	example	NOUN
ejpam-3074	92	22	,	,	PUNCT
ejpam-3074	92	23	five	five	NUM
ejpam-3074	92	24	times	time	NOUN
ejpam-3074	92	25	heavier	heavy	ADJ
ejpam-3074	92	26	than	than	ADP
ejpam-3074	92	27	stone	stone	NOUN
ejpam-3074	92	28	b	b	PROPN
ejpam-3074	92	29	and	and	CCONJ
ejpam-3074	92	30	stone	stone	PROPN
ejpam-3074	92	31	b	b	PROPN
ejpam-3074	92	32	is	be	AUX
ejpam-3074	92	33	three	three	NUM
ejpam-3074	92	34	times	time	NOUN
ejpam-3074	92	35	heavier	heavy	ADJ
ejpam-3074	92	36	than	than	ADP
ejpam-3074	92	37	stone	stone	NOUN
ejpam-3074	92	38	c	c	NOUN
ejpam-3074	92	39	that	that	PRON
ejpam-3074	92	40	we	we	PRON
ejpam-3074	92	41	would	would	AUX
ejpam-3074	92	42	judge	judge	VERB
ejpam-3074	92	43	a	a	PRON
ejpam-3074	92	44	to	to	PART
ejpam-3074	92	45	be	be	AUX
ejpam-3074	92	46	fifteen	fifteen	NUM
ejpam-3074	92	47	times	time	NOUN
ejpam-3074	92	48	heavier	heavy	ADJ
ejpam-3074	92	49	than	than	ADP
ejpam-3074	92	50	c	c	PROPN
ejpam-3074	92	51	?	?	PUNCT
ejpam-3074	93	1	most	most	ADV
ejpam-3074	93	2	likely	likely	ADJ
ejpam-3074	93	3	not	not	PART
ejpam-3074	93	4	.	.	PUNCT
ejpam-3074	94	1	to	to	PART
ejpam-3074	94	2	improve	improve	VERB
ejpam-3074	94	3	the	the	DET
ejpam-3074	94	4	accuracy	accuracy	NOUN
ejpam-3074	94	5	of	of	ADP
ejpam-3074	94	6	the	the	DET
ejpam-3074	94	7	scale	scale	NOUN
ejpam-3074	94	8	derived	derive	VERB
ejpam-3074	94	9	from	from	ADP
ejpam-3074	94	10	the	the	DET
ejpam-3074	94	11	paired	pair	VERB
ejpam-3074	94	12	comparisons	comparison	NOUN
ejpam-3074	94	13	we	we	PRON
ejpam-3074	94	14	should	should	AUX
ejpam-3074	94	15	also	also	ADV
ejpam-3074	94	16	compare	compare	VERB
ejpam-3074	94	17	a	a	PRON
ejpam-3074	94	18	with	with	ADP
ejpam-3074	94	19	c.	c.	NOUN
ejpam-3074	94	20	we	we	PRON
ejpam-3074	94	21	would	would	AUX
ejpam-3074	94	22	then	then	ADV
ejpam-3074	94	23	need	need	VERB
ejpam-3074	94	24	to	to	PART
ejpam-3074	94	25	say	say	VERB
ejpam-3074	94	26	something	something	PRON
ejpam-3074	94	27	about	about	ADP
ejpam-3074	94	28	the	the	DET
ejpam-3074	94	29	inconsistency	inconsistency	NOUN
ejpam-3074	94	30	in	in	ADP
ejpam-3074	94	31	performing	perform	VERB
ejpam-3074	94	32	comparisons	comparison	NOUN
ejpam-3074	94	33	.	.	PUNCT
ejpam-3074	95	1	in	in	ADP
ejpam-3074	95	2	general	general	ADJ
ejpam-3074	95	3	,	,	PUNCT
ejpam-3074	95	4	if	if	SCONJ
ejpam-3074	95	5	indicates	indicate	VERB
ejpam-3074	95	6	the	the	DET
ejpam-3074	95	7	relative	relative	ADJ
ejpam-3074	95	8	dominance	dominance	NOUN
ejpam-3074	95	9	of	of	ADP
ejpam-3074	95	10	object	object	NOUN
ejpam-3074	95	11	i	i	PRON
ejpam-3074	95	12	over	over	ADP
ejpam-3074	95	13	object	object	NOUN
ejpam-3074	95	14	j	j	PROPN
ejpam-3074	95	15	when	when	SCONJ
ejpam-3074	95	16	comparing	compare	VERB
ejpam-3074	95	17	n	n	NOUN
ejpam-3074	95	18	objects	object	NOUN
ejpam-3074	95	19	in	in	ADP
ejpam-3074	95	20	pairs	pair	NOUN
ejpam-3074	95	21	,	,	PUNCT
ejpam-3074	95	22	the	the	DET
ejpam-3074	95	23	comparisons	comparison	NOUN
ejpam-3074	95	24	are	be	AUX
ejpam-3074	95	25	said	say	VERB
ejpam-3074	95	26	to	to	PART
ejpam-3074	95	27	be	be	AUX
ejpam-3074	95	28	consistent	consistent	ADJ
ejpam-3074	95	29	if	if	SCONJ
ejpam-3074	95	30	the	the	DET
ejpam-3074	95	31	relation	relation	NOUN
ejpam-3074	95	32	aij	aij	PROPN
ejpam-3074	95	33	ajk	ajk	PROPN
ejpam-3074	95	34	=	=	PROPN
ejpam-3074	95	35	aik	aik	PROPN
ejpam-3074	95	36	holds	hold	VERB
ejpam-3074	95	37	for	for	ADP
ejpam-3074	95	38	t.	t.	PROPN
ejpam-3074	95	39	l.	l.	PROPN
ejpam-3074	95	40	saaty	saaty	PROPN
ejpam-3074	95	41	,	,	PUNCT
ejpam-3074	95	42	l.	l.	PROPN
ejpam-3074	95	43	g.	g.	PROPN
ejpam-3074	95	44	vargas	vargas	PROPN
ejpam-3074	95	45	/	/	SYM
ejpam-3074	95	46	eur	eur	PROPN
ejpam-3074	95	47	.	.	PUNCT
ejpam-3074	96	1	j.	j.	PROPN
ejpam-3074	96	2	pure	pure	PROPN
ejpam-3074	96	3	appl	appl	PROPN
ejpam-3074	96	4	.	.	PROPN
ejpam-3074	96	5	math	math	PROPN
ejpam-3074	96	6	,	,	PUNCT
ejpam-3074	96	7	10	10	NUM
ejpam-3074	96	8	(	(	PUNCT
ejpam-3074	96	9	4	4	NUM
ejpam-3074	96	10	)	)	PUNCT
ejpam-3074	96	11	(	(	PUNCT
ejpam-3074	96	12	2017	2017	NUM
ejpam-3074	96	13	)	)	PUNCT
ejpam-3074	96	14	,	,	PUNCT
ejpam-3074	96	15	602	602	NUM
ejpam-3074	96	16	-	-	SYM
ejpam-3074	96	17	613	613	NUM
ejpam-3074	96	18	606	606	NUM
ejpam-3074	96	19	all	all	DET
ejpam-3074	96	20	i	i	PROPN
ejpam-3074	96	21	,	,	PUNCT
ejpam-3074	96	22	j	j	PROPN
ejpam-3074	96	23	,	,	PUNCT
ejpam-3074	96	24	k	k	PROPN
ejpam-3074	96	25	=	=	SYM
ejpam-3074	96	26	1	1	NUM
ejpam-3074	96	27	,	,	PUNCT
ejpam-3074	96	28	2	2	NUM
ejpam-3074	96	29	,	,	PUNCT
ejpam-3074	96	30	,	,	PUNCT
ejpam-3074	96	31	n	n	X
ejpam-3074	96	32	.	.	PUNCT
ejpam-3074	97	1	the	the	DET
ejpam-3074	97	2	reciprocal	reciprocal	ADJ
ejpam-3074	97	3	property	property	NOUN
ejpam-3074	97	4	mentioned	mention	VERB
ejpam-3074	97	5	above	above	ADV
ejpam-3074	97	6	is	be	AUX
ejpam-3074	97	7	given	give	VERB
ejpam-3074	97	8	by	by	ADP
ejpam-3074	97	9	aji	aji	PROPN
ejpam-3074	97	10	=	=	SYM
ejpam-3074	97	11	1	1	NUM
ejpam-3074	97	12	/	/	SYM
ejpam-3074	97	13	aij	aij	PROPN
ejpam-3074	97	14	and	and	CCONJ
ejpam-3074	97	15	follows	follow	VERB
ejpam-3074	97	16	from	from	ADP
ejpam-3074	97	17	consistency	consistency	NOUN
ejpam-3074	97	18	but	but	CCONJ
ejpam-3074	97	19	it	it	PRON
ejpam-3074	97	20	does	do	AUX
ejpam-3074	97	21	not	not	PART
ejpam-3074	97	22	imply	imply	VERB
ejpam-3074	97	23	it	it	PRON
ejpam-3074	97	24	and	and	CCONJ
ejpam-3074	97	25	is	be	AUX
ejpam-3074	97	26	thus	thus	ADV
ejpam-3074	97	27	a	a	DET
ejpam-3074	97	28	weaker	weak	ADJ
ejpam-3074	97	29	condition	condition	NOUN
ejpam-3074	97	30	that	that	PRON
ejpam-3074	97	31	can	can	AUX
ejpam-3074	97	32	be	be	AUX
ejpam-3074	97	33	safely	safely	ADV
ejpam-3074	97	34	say	say	VERB
ejpam-3074	97	35	predates	predate	NOUN
ejpam-3074	97	36	consistency	consistency	NOUN
ejpam-3074	97	37	.	.	PUNCT
ejpam-3074	98	1	the	the	DET
ejpam-3074	98	2	usual	usual	ADJ
ejpam-3074	98	3	criterion	criterion	NOUN
ejpam-3074	98	4	of	of	ADP
ejpam-3074	98	5	transitivity	transitivity	NOUN
ejpam-3074	98	6	is	be	AUX
ejpam-3074	98	7	implied	imply	VERB
ejpam-3074	98	8	by	by	ADP
ejpam-3074	98	9	consistency	consistency	NOUN
ejpam-3074	98	10	but	but	CCONJ
ejpam-3074	98	11	not	not	PART
ejpam-3074	98	12	conversely	conversely	ADV
ejpam-3074	98	13	.	.	PUNCT
ejpam-3074	99	1	consider	consider	VERB
ejpam-3074	99	2	n	n	PRON
ejpam-3074	99	3	stocks	stock	NOUN
ejpam-3074	99	4	,	,	PUNCT
ejpam-3074	99	5	a1	a1	NOUN
ejpam-3074	99	6	,	,	PUNCT
ejpam-3074	99	7	...	...	PUNCT
ejpam-3074	99	8	,	,	PUNCT
ejpam-3074	99	9	an	an	PRON
ejpam-3074	99	10	,	,	PUNCT
ejpam-3074	99	11	with	with	ADP
ejpam-3074	99	12	known	known	ADJ
ejpam-3074	99	13	worth	worth	ADJ
ejpam-3074	99	14	w1	w1	NOUN
ejpam-3074	99	15	,	,	PUNCT
ejpam-3074	99	16	...	...	PUNCT
ejpam-3074	99	17	,	,	PUNCT
ejpam-3074	99	18	wn	wn	PROPN
ejpam-3074	99	19	,	,	PUNCT
ejpam-3074	99	20	respectively	respectively	ADV
ejpam-3074	99	21	,	,	PUNCT
ejpam-3074	99	22	and	and	CCONJ
ejpam-3074	99	23	suppose	suppose	VERB
ejpam-3074	99	24	that	that	SCONJ
ejpam-3074	99	25	pairwise	pairwise	NOUN
ejpam-3074	99	26	ratios	ratio	NOUN
ejpam-3074	99	27	are	be	AUX
ejpam-3074	99	28	formed	form	VERB
ejpam-3074	99	29	to	to	PART
ejpam-3074	99	30	show	show	VERB
ejpam-3074	99	31	the	the	DET
ejpam-3074	99	32	worth	worth	NOUN
ejpam-3074	99	33	of	of	ADP
ejpam-3074	99	34	each	each	DET
ejpam-3074	99	35	stock	stock	NOUN
ejpam-3074	99	36	with	with	ADP
ejpam-3074	99	37	respect	respect	NOUN
ejpam-3074	99	38	to	to	ADP
ejpam-3074	99	39	all	all	DET
ejpam-3074	99	40	others	other	NOUN
ejpam-3074	99	41	as	as	ADP
ejpam-3074	99	42	in	in	ADP
ejpam-3074	99	43	table	table	NOUN
ejpam-3074	99	44	1	1	NUM
ejpam-3074	99	45	.	.	PUNCT
ejpam-3074	100	1	we	we	PRON
ejpam-3074	100	2	can	can	AUX
ejpam-3074	100	3	recover	recover	VERB
ejpam-3074	100	4	the	the	DET
ejpam-3074	100	5	scale	scale	NOUN
ejpam-3074	100	6	w	w	NOUN
ejpam-3074	100	7	using	use	VERB
ejpam-3074	100	8	the	the	DET
ejpam-3074	100	9	equation	equation	NOUN
ejpam-3074	100	10	next	next	ADV
ejpam-3074	100	11	to	to	ADP
ejpam-3074	100	12	it	it	PRON
ejpam-3074	100	13	as	as	ADP
ejpam-3074	100	14	in	in	ADP
ejpam-3074	100	15	table	table	NOUN
ejpam-3074	100	16	2	2	NUM
ejpam-3074	100	17	which	which	PRON
ejpam-3074	100	18	briefly	briefly	ADV
ejpam-3074	100	19	says	say	VERB
ejpam-3074	100	20	that	that	SCONJ
ejpam-3074	101	1	aw	aw	INTJ
ejpam-3074	101	2	=	=	SYM
ejpam-3074	101	3	nw	nw	PROPN
ejpam-3074	101	4	.	.	PROPN
ejpam-3074	101	5	table	table	NOUN
ejpam-3074	101	6	1	1	NUM
ejpam-3074	101	7	.	.	X
ejpam-3074	101	8	matrix	matrix	NOUN
ejpam-3074	101	9	of	of	ADP
ejpam-3074	101	10	ratios	ratio	NOUN
ejpam-3074	101	11	table	table	VERB
ejpam-3074	101	12	2	2	NUM
ejpam-3074	101	13	.	.	X
ejpam-3074	101	14	equation	equation	NOUN
ejpam-3074	101	15	to	to	PART
ejpam-3074	101	16	get	get	VERB
ejpam-3074	101	17	back	back	ADV
ejpam-3074	101	18	the	the	DET
ejpam-3074	101	19	scale	scale	NOUN
ejpam-3074	101	20	a1	a1	NOUN
ejpam-3074	101	21	·	·	PUNCT
ejpam-3074	101	22	·	·	PUNCT
ejpam-3074	101	23	·	·	PUNCT
ejpam-3074	102	1	an	an	DET
ejpam-3074	102	2	a	a	DET
ejpam-3074	102	3	=	=	NOUN
ejpam-3074	102	4	a1	a1	NOUN
ejpam-3074	102	5	...	...	PUNCT
ejpam-3074	102	6	an	an	DET
ejpam-3074	102	7			NUM
ejpam-3074	102	8	w1	w1	NOUN
ejpam-3074	102	9	w1	w1	NOUN
ejpam-3074	102	10	·	·	PUNCT
ejpam-3074	102	11	·	·	PUNCT
ejpam-3074	102	12	·	·	PUNCT
ejpam-3074	102	13	w1	w1	NOUN
ejpam-3074	102	14	wn	wn	PROPN
ejpam-3074	102	15	...	...	PUNCT
ejpam-3074	102	16	.	.	PUNCT
ejpam-3074	102	17	.	.	PUNCT
ejpam-3074	102	18	.	.	PUNCT
ejpam-3074	102	19	...	...	PUNCT
ejpam-3074	103	1	wn	wn	PROPN
ejpam-3074	103	2	w1	w1	PROPN
ejpam-3074	103	3	·	·	PUNCT
ejpam-3074	103	4	·	·	PUNCT
ejpam-3074	103	5	·	·	PUNCT
ejpam-3074	104	1	wn	wn	INTJ
ejpam-3074	104	2	wn	wn	PROPN
ejpam-3074	104	3			PROPN
ejpam-3074	104	4			NOUN
ejpam-3074	104	5	w1	w1	NOUN
ejpam-3074	104	6	w1	w1	NOUN
ejpam-3074	104	7	·	·	PUNCT
ejpam-3074	104	8	·	·	PUNCT
ejpam-3074	104	9	·	·	PUNCT
ejpam-3074	104	10	w1	w1	NOUN
ejpam-3074	104	11	wn	wn	PROPN
ejpam-3074	104	12	...	...	PUNCT
ejpam-3074	104	13	.	.	PUNCT
ejpam-3074	104	14	.	.	PUNCT
ejpam-3074	104	15	.	.	PUNCT
ejpam-3074	104	16	...	...	PUNCT
ejpam-3074	105	1	wn	wn	PROPN
ejpam-3074	105	2	w1	w1	PROPN
ejpam-3074	105	3	·	·	PUNCT
ejpam-3074	105	4	·	·	PUNCT
ejpam-3074	105	5	·	·	PUNCT
ejpam-3074	106	1	wn	wn	INTJ
ejpam-3074	106	2	wn	wn	PROPN
ejpam-3074	106	3			PROPN
ejpam-3074	106	4	w1	w1	NOUN
ejpam-3074	106	5	...	...	PUNCT
ejpam-3074	106	6	wn	wn	INTJ
ejpam-3074	106	7			NUM
ejpam-3074	106	8	=	=	SYM
ejpam-3074	106	9	n	n	PROPN
ejpam-3074	106	10	w1	w1	NOUN
ejpam-3074	106	11	...	...	PUNCT
ejpam-3074	107	1	wn	wn	PROPN
ejpam-3074	107	2			PROPN
ejpam-3074	107	3	thus	thus	ADV
ejpam-3074	107	4	,	,	PUNCT
ejpam-3074	107	5	to	to	PART
ejpam-3074	107	6	recover	recover	VERB
ejpam-3074	107	7	the	the	DET
ejpam-3074	107	8	scale	scale	NOUN
ejpam-3074	107	9	w	w	NOUN
ejpam-3074	107	10	from	from	ADP
ejpam-3074	107	11	the	the	DET
ejpam-3074	107	12	matrix	matrix	NOUN
ejpam-3074	107	13	of	of	ADP
ejpam-3074	107	14	ratios	ratio	NOUN
ejpam-3074	107	15	a	a	PRON
ejpam-3074	107	16	,	,	PUNCT
ejpam-3074	107	17	one	one	PRON
ejpam-3074	107	18	must	must	AUX
ejpam-3074	107	19	solve	solve	VERB
ejpam-3074	107	20	the	the	DET
ejpam-3074	107	21	eigenvalue	eigenvalue	PROPN
ejpam-3074	107	22	problem	problem	NOUN
ejpam-3074	108	1	aw	aw	INTJ
ejpam-3074	108	2	=	=	PUNCT
ejpam-3074	108	3	nw	nw	PROPN
ejpam-3074	108	4	or	or	CCONJ
ejpam-3074	108	5	(	(	PUNCT
ejpam-3074	108	6	a	a	DET
ejpam-3074	108	7	−	−	NOUN
ejpam-3074	108	8	ni)w	ni)w	PROPN
ejpam-3074	108	9	=	=	SYM
ejpam-3074	108	10	0	0	X
ejpam-3074	108	11	.	.	PUNCT
ejpam-3074	109	1	this	this	PRON
ejpam-3074	109	2	is	be	AUX
ejpam-3074	109	3	a	a	DET
ejpam-3074	109	4	system	system	NOUN
ejpam-3074	109	5	of	of	ADP
ejpam-3074	109	6	homogeneous	homogeneous	ADJ
ejpam-3074	109	7	linear	linear	PROPN
ejpam-3074	109	8	equations	equation	NOUN
ejpam-3074	109	9	.	.	PUNCT
ejpam-3074	110	1	it	it	PRON
ejpam-3074	110	2	has	have	VERB
ejpam-3074	110	3	a	a	DET
ejpam-3074	110	4	nontrivial	nontrivial	ADJ
ejpam-3074	110	5	solution	solution	NOUN
ejpam-3074	110	6	if	if	SCONJ
ejpam-3074	110	7	and	and	CCONJ
ejpam-3074	110	8	only	only	ADV
ejpam-3074	110	9	if	if	SCONJ
ejpam-3074	110	10	the	the	DET
ejpam-3074	110	11	determinant	determinant	NOUN
ejpam-3074	110	12	of	of	ADP
ejpam-3074	110	13	a−	a−	PROPN
ejpam-3074	110	14	ni	ni	PROPN
ejpam-3074	110	15	vanishes	vanish	VERB
ejpam-3074	110	16	,	,	PUNCT
ejpam-3074	110	17	that	that	ADV
ejpam-3074	110	18	is	is	ADV
ejpam-3074	110	19	,	,	PUNCT
ejpam-3074	110	20	n	n	PRON
ejpam-3074	110	21	is	be	AUX
ejpam-3074	110	22	an	an	DET
ejpam-3074	110	23	eigenvalue	eigenvalue	NOUN
ejpam-3074	110	24	of	of	ADP
ejpam-3074	110	25	a	a	PRON
ejpam-3074	110	26	and	and	CCONJ
ejpam-3074	110	27	w	w	PROPN
ejpam-3074	110	28	is	be	AUX
ejpam-3074	110	29	its	its	PRON
ejpam-3074	110	30	eigenvector	eigenvector	NOUN
ejpam-3074	110	31	.	.	PUNCT
ejpam-3074	111	1	it	it	PRON
ejpam-3074	111	2	turns	turn	VERB
ejpam-3074	111	3	out	out	ADP
ejpam-3074	111	4	that	that	SCONJ
ejpam-3074	111	5	n	n	PROPN
ejpam-3074	111	6	is	be	AUX
ejpam-3074	111	7	the	the	DET
ejpam-3074	111	8	maximum	maximum	PROPN
ejpam-3074	111	9	eigenvalue	eigenvalue	NOUN
ejpam-3074	111	10	and	and	CCONJ
ejpam-3074	111	11	the	the	DET
ejpam-3074	111	12	entries	entry	NOUN
ejpam-3074	111	13	of	of	ADP
ejpam-3074	111	14	w	w	ADP
ejpam-3074	111	15	which	which	PRON
ejpam-3074	111	16	are	be	AUX
ejpam-3074	111	17	the	the	DET
ejpam-3074	111	18	priorities	priority	NOUN
ejpam-3074	111	19	we	we	PRON
ejpam-3074	111	20	want	want	VERB
ejpam-3074	111	21	are	be	AUX
ejpam-3074	111	22	always	always	ADV
ejpam-3074	111	23	positive	positive	ADJ
ejpam-3074	111	24	.	.	PUNCT
ejpam-3074	112	1	in	in	ADP
ejpam-3074	112	2	the	the	DET
ejpam-3074	112	3	general	general	ADJ
ejpam-3074	112	4	case	case	NOUN
ejpam-3074	112	5	when	when	SCONJ
ejpam-3074	112	6	only	only	ADV
ejpam-3074	112	7	judgments	judgment	NOUN
ejpam-3074	112	8	but	but	CCONJ
ejpam-3074	112	9	not	not	PART
ejpam-3074	112	10	the	the	DET
ejpam-3074	112	11	numbers	number	NOUN
ejpam-3074	112	12	themselves	themselves	PRON
ejpam-3074	112	13	are	be	AUX
ejpam-3074	112	14	available	available	ADJ
ejpam-3074	112	15	,	,	PUNCT
ejpam-3074	112	16	the	the	DET
ejpam-3074	112	17	precise	precise	ADJ
ejpam-3074	112	18	value	value	NOUN
ejpam-3074	112	19	of	of	ADP
ejpam-3074	112	20	wi	wi	PROPN
ejpam-3074	112	21	/	/	SYM
ejpam-3074	112	22	wj	wj	PROPN
ejpam-3074	112	23	which	which	PRON
ejpam-3074	112	24	is	be	AUX
ejpam-3074	112	25	a	a	DET
ejpam-3074	112	26	dimensionless	dimensionless	NOUN
ejpam-3074	112	27	number	number	NOUN
ejpam-3074	112	28	and	and	CCONJ
ejpam-3074	112	29	thus	thus	ADV
ejpam-3074	112	30	belongs	belong	VERB
ejpam-3074	112	31	to	to	ADP
ejpam-3074	112	32	an	an	DET
ejpam-3074	112	33	absolute	absolute	ADJ
ejpam-3074	112	34	scale	scale	NOUN
ejpam-3074	112	35	that	that	PRON
ejpam-3074	112	36	is	be	AUX
ejpam-3074	112	37	invariant	invariant	ADJ
ejpam-3074	112	38	under	under	ADP
ejpam-3074	112	39	the	the	DET
ejpam-3074	112	40	identity	identity	NOUN
ejpam-3074	112	41	transformation	transformation	NOUN
ejpam-3074	112	42	,	,	PUNCT
ejpam-3074	112	43	is	be	AUX
ejpam-3074	112	44	not	not	PART
ejpam-3074	112	45	known	know	VERB
ejpam-3074	112	46	,	,	PUNCT
ejpam-3074	112	47	but	but	CCONJ
ejpam-3074	112	48	instead	instead	ADV
ejpam-3074	112	49	only	only	ADV
ejpam-3074	112	50	an	an	DET
ejpam-3074	112	51	estimate	estimate	NOUN
ejpam-3074	112	52	of	of	ADP
ejpam-3074	112	53	it	it	PRON
ejpam-3074	112	54	can	can	AUX
ejpam-3074	112	55	be	be	AUX
ejpam-3074	112	56	given	give	VERB
ejpam-3074	112	57	as	as	ADP
ejpam-3074	112	58	a	a	DET
ejpam-3074	112	59	numerical	numerical	ADJ
ejpam-3074	112	60	judgment	judgment	NOUN
ejpam-3074	112	61	from	from	ADP
ejpam-3074	112	62	the	the	DET
ejpam-3074	112	63	fundamental	fundamental	ADJ
ejpam-3074	112	64	scale	scale	NOUN
ejpam-3074	112	65	.	.	PUNCT
ejpam-3074	113	1	the	the	DET
ejpam-3074	113	2	maximum	maximum	PROPN
ejpam-3074	113	3	eigenvalue	eigenvalue	PROPN
ejpam-3074	113	4	is	be	AUX
ejpam-3074	113	5	no	no	ADV
ejpam-3074	113	6	longer	long	ADV
ejpam-3074	113	7	equal	equal	ADJ
ejpam-3074	113	8	to	to	ADP
ejpam-3074	113	9	n	n	NOUN
ejpam-3074	113	10	but	but	CCONJ
ejpam-3074	113	11	is	be	AUX
ejpam-3074	113	12	replaced	replace	VERB
ejpam-3074	113	13	by	by	ADP
ejpam-3074	113	14	the	the	DET
ejpam-3074	113	15	maximum	maximum	PROPN
ejpam-3074	113	16	eigenvalue	eigenvalue	NOUN
ejpam-3074	113	17	of	of	ADP
ejpam-3074	113	18	the	the	DET
ejpam-3074	113	19	matrix	matrix	NOUN
ejpam-3074	113	20	of	of	ADP
ejpam-3074	113	21	judgments	judgment	NOUN
ejpam-3074	113	22	.	.	PUNCT
ejpam-3074	114	1	tables	table	NOUN
ejpam-3074	114	2	1	1	NUM
ejpam-3074	114	3	and	and	CCONJ
ejpam-3074	114	4	2	2	NUM
ejpam-3074	114	5	become	become	NOUN
ejpam-3074	114	6	tables	table	NOUN
ejpam-3074	114	7	3	3	NUM
ejpam-3074	114	8	and	and	CCONJ
ejpam-3074	114	9	4	4	NUM
ejpam-3074	114	10	,	,	PUNCT
ejpam-3074	114	11	respectively	respectively	ADV
ejpam-3074	114	12	,	,	PUNCT
ejpam-3074	114	13	and	and	CCONJ
ejpam-3074	114	14	the	the	DET
ejpam-3074	114	15	solution	solution	NOUN
ejpam-3074	114	16	is	be	AUX
ejpam-3074	114	17	obtained	obtain	VERB
ejpam-3074	114	18	from	from	ADP
ejpam-3074	114	19	the	the	DET
ejpam-3074	114	20	equation	equation	NOUN
ejpam-3074	114	21	a′w′	a′w′	NUM
ejpam-3074	114	22	=	=	NOUN
ejpam-3074	114	23	λmaxw	λmaxw	NOUN
ejpam-3074	114	24	′.	′.	NOUN
ejpam-3074	114	25	table	table	NOUN
ejpam-3074	114	26	3	3	NUM
ejpam-3074	114	27	.	.	X
ejpam-3074	114	28	matrix	matrix	NOUN
ejpam-3074	114	29	of	of	ADP
ejpam-3074	114	30	ratios	ratio	NOUN
ejpam-3074	114	31	a′	a′	NOUN
ejpam-3074	114	32	=	=	SYM
ejpam-3074	114	33			PROPN
ejpam-3074	114	34	1	1	NUM
ejpam-3074	114	35	a12	a12	NOUN
ejpam-3074	114	36	·	·	PUNCT
ejpam-3074	114	37	·	·	PUNCT
ejpam-3074	114	38	·	·	PUNCT
ejpam-3074	115	1	a1n	a1n	ADP
ejpam-3074	115	2	1	1	NUM
ejpam-3074	115	3	/	/	SYM
ejpam-3074	115	4	a12	a12	NOUN
ejpam-3074	115	5	1	1	NUM
ejpam-3074	115	6	·	·	PUNCT
ejpam-3074	115	7	·	·	PUNCT
ejpam-3074	115	8	·	·	PUNCT
ejpam-3074	115	9	a2n	a2n	PROPN
ejpam-3074	115	10	...	...	PUNCT
ejpam-3074	115	11	...	...	PUNCT
ejpam-3074	115	12	...	...	PUNCT
ejpam-3074	115	13	...	...	PUNCT
ejpam-3074	116	1	1	1	X
ejpam-3074	116	2	/	/	SYM
ejpam-3074	116	3	a1n	a1n	PRON
ejpam-3074	116	4	1	1	NUM
ejpam-3074	116	5	/	/	SYM
ejpam-3074	116	6	a2n	a2n	PRON
ejpam-3074	116	7	·	·	PUNCT
ejpam-3074	116	8	·	·	PUNCT
ejpam-3074	116	9	·	·	PUNCT
ejpam-3074	116	10	1	1	NUM
ejpam-3074	116	11			ADJ
ejpam-3074	116	12	table	table	NOUN
ejpam-3074	116	13	4	4	NUM
ejpam-3074	116	14	.	.	PUNCT
ejpam-3074	116	15	equation	equation	NOUN
ejpam-3074	116	16	to	to	PART
ejpam-3074	116	17	get	get	VERB
ejpam-3074	116	18	back	back	ADV
ejpam-3074	116	19	the	the	DET
ejpam-3074	116	20	scale	scale	NOUN
ejpam-3074	116	21	a′w	a′w	NOUN
ejpam-3074	116	22	=	=	SYM
ejpam-3074	116	23			PROPN
ejpam-3074	116	24	1	1	NUM
ejpam-3074	116	25	a12	a12	NOUN
ejpam-3074	116	26	·	·	PUNCT
ejpam-3074	116	27	·	·	PUNCT
ejpam-3074	116	28	·	·	PUNCT
ejpam-3074	117	1	a1n	a1n	ADP
ejpam-3074	117	2	1	1	NUM
ejpam-3074	117	3	/	/	SYM
ejpam-3074	117	4	a12	a12	NOUN
ejpam-3074	117	5	1	1	NUM
ejpam-3074	117	6	·	·	PUNCT
ejpam-3074	117	7	·	·	PUNCT
ejpam-3074	117	8	·	·	PUNCT
ejpam-3074	117	9	a2n	a2n	PROPN
ejpam-3074	117	10	...	...	PUNCT
ejpam-3074	117	11	...	...	PUNCT
ejpam-3074	117	12	...	...	PUNCT
ejpam-3074	117	13	...	...	PUNCT
ejpam-3074	118	1	1	1	X
ejpam-3074	118	2	/	/	SYM
ejpam-3074	118	3	a1n	a1n	PRON
ejpam-3074	118	4	1	1	NUM
ejpam-3074	118	5	/	/	SYM
ejpam-3074	118	6	a2n	a2n	PRON
ejpam-3074	118	7	·	·	PUNCT
ejpam-3074	118	8	·	·	PUNCT
ejpam-3074	118	9	·	·	PUNCT
ejpam-3074	118	10	1	1	NUM
ejpam-3074	118	11			ADJ
ejpam-3074	118	12			PROPN
ejpam-3074	118	13	w1	w1	NOUN
ejpam-3074	118	14	w2	w2	NOUN
ejpam-3074	118	15	...	...	PUNCT
ejpam-3074	119	1	wn	wn	PROPN
ejpam-3074	119	2			PROPN
ejpam-3074	119	3	=	=	PUNCT
ejpam-3074	119	4	λmax	λmax	NOUN
ejpam-3074	119	5			PROPN
ejpam-3074	119	6	w1	w1	PROPN
ejpam-3074	119	7	w2	w2	PROPN
ejpam-3074	119	8	...	...	PUNCT
ejpam-3074	120	1	wn	wn	PROPN
ejpam-3074	120	2			PROPN
ejpam-3074	120	3	t.	t.	PROPN
ejpam-3074	120	4	l.	l.	PROPN
ejpam-3074	120	5	saaty	saaty	PROPN
ejpam-3074	120	6	,	,	PUNCT
ejpam-3074	120	7	l.	l.	PROPN
ejpam-3074	120	8	g.	g.	PROPN
ejpam-3074	120	9	vargas	vargas	PROPN
ejpam-3074	120	10	/	/	SYM
ejpam-3074	120	11	eur	eur	PROPN
ejpam-3074	120	12	.	.	PUNCT
ejpam-3074	121	1	j.	j.	PROPN
ejpam-3074	121	2	pure	pure	PROPN
ejpam-3074	121	3	appl	appl	PROPN
ejpam-3074	121	4	.	.	PROPN
ejpam-3074	121	5	math	math	PROPN
ejpam-3074	121	6	,	,	PUNCT
ejpam-3074	121	7	10	10	NUM
ejpam-3074	121	8	(	(	PUNCT
ejpam-3074	121	9	4	4	NUM
ejpam-3074	121	10	)	)	PUNCT
ejpam-3074	121	11	(	(	PUNCT
ejpam-3074	121	12	2017	2017	NUM
ejpam-3074	121	13	)	)	PUNCT
ejpam-3074	121	14	,	,	PUNCT
ejpam-3074	121	15	602	602	NUM
ejpam-3074	121	16	-	-	SYM
ejpam-3074	121	17	613	613	NUM
ejpam-3074	121	18	607	607	NUM
ejpam-3074	121	19	3	3	NUM
ejpam-3074	121	20	.	.	PUNCT
ejpam-3074	122	1	generalizing	generalize	VERB
ejpam-3074	122	2	from	from	ADP
ejpam-3074	122	3	discrete	discrete	ADJ
ejpam-3074	122	4	to	to	ADP
ejpam-3074	122	5	continuous	continuous	ADJ
ejpam-3074	122	6	judgments	judgment	NOUN
ejpam-3074	122	7	there	there	PRON
ejpam-3074	122	8	is	be	VERB
ejpam-3074	122	9	a	a	DET
ejpam-3074	122	10	way	way	NOUN
ejpam-3074	122	11	to	to	PART
ejpam-3074	122	12	formulate	formulate	VERB
ejpam-3074	122	13	the	the	DET
ejpam-3074	122	14	problem	problem	NOUN
ejpam-3074	122	15	of	of	ADP
ejpam-3074	122	16	automatic	automatic	ADJ
ejpam-3074	122	17	decisions	decision	NOUN
ejpam-3074	122	18	that	that	PRON
ejpam-3074	122	19	relates	relate	VERB
ejpam-3074	122	20	to	to	ADP
ejpam-3074	122	21	the	the	DET
ejpam-3074	122	22	stimulus	stimulus	ADJ
ejpam-3074	122	23	-	-	PUNCT
ejpam-3074	122	24	response	response	NOUN
ejpam-3074	122	25	equation	equation	NOUN
ejpam-3074	122	26	w(as	w(as	PROPN
ejpam-3074	122	27	)	)	PUNCT
ejpam-3074	122	28	=	=	SYM
ejpam-3074	122	29	bw(s	bw(s	X
ejpam-3074	122	30	)	)	PUNCT
ejpam-3074	122	31	it	it	PRON
ejpam-3074	122	32	involves	involve	VERB
ejpam-3074	122	33	generalizing	generalize	VERB
ejpam-3074	122	34	the	the	DET
ejpam-3074	122	35	discrete	discrete	ADJ
ejpam-3074	122	36	,	,	PUNCT
ejpam-3074	122	37	eigenvalueoriented	eigenvalueoriente	VERB
ejpam-3074	122	38	decision	decision	NOUN
ejpam-3074	122	39	-	-	PUNCT
ejpam-3074	122	40	making	making	NOUN
ejpam-3074	122	41	of	of	ADP
ejpam-3074	122	42	the	the	DET
ejpam-3074	122	43	ahp	ahp	NOUN
ejpam-3074	122	44	to	to	ADP
ejpam-3074	122	45	the	the	DET
ejpam-3074	122	46	continuous	continuous	ADJ
ejpam-3074	122	47	case	case	NOUN
ejpam-3074	122	48	where	where	SCONJ
ejpam-3074	122	49	fredholms	fredholm	NOUN
ejpam-3074	122	50	equation	equation	NOUN
ejpam-3074	122	51	is	be	AUX
ejpam-3074	122	52	the	the	DET
ejpam-3074	122	53	continuous	continuous	ADJ
ejpam-3074	122	54	version	version	NOUN
ejpam-3074	122	55	of	of	ADP
ejpam-3074	122	56	the	the	DET
ejpam-3074	122	57	discrete	discrete	ADJ
ejpam-3074	122	58	eigenvalue	eigenvalue	NOUN
ejpam-3074	122	59	formulation	formulation	NOUN
ejpam-3074	122	60	.	.	PUNCT
ejpam-3074	123	1	in	in	ADP
ejpam-3074	123	2	that	that	DET
ejpam-3074	123	3	generalization	generalization	NOUN
ejpam-3074	123	4	,	,	PUNCT
ejpam-3074	123	5	it	it	PRON
ejpam-3074	123	6	turns	turn	VERB
ejpam-3074	123	7	out	out	ADP
ejpam-3074	123	8	that	that	SCONJ
ejpam-3074	123	9	the	the	DET
ejpam-3074	123	10	functional	functional	ADJ
ejpam-3074	123	11	equation	equation	NOUN
ejpam-3074	123	12	w(as	w(as	PROPN
ejpam-3074	123	13	)	)	PUNCT
ejpam-3074	123	14	=	=	SYM
ejpam-3074	123	15	bw(s	bw(s	X
ejpam-3074	123	16	)	)	PUNCT
ejpam-3074	123	17	is	be	AUX
ejpam-3074	123	18	a	a	DET
ejpam-3074	123	19	necessary	necessary	ADJ
ejpam-3074	123	20	condition	condition	NOUN
ejpam-3074	123	21	for	for	ADP
ejpam-3074	123	22	fredholms	fredholm	NOUN
ejpam-3074	123	23	integral	integral	ADJ
ejpam-3074	123	24	equation	equation	NOUN
ejpam-3074	123	25	of	of	ADP
ejpam-3074	123	26	the	the	DET
ejpam-3074	123	27	second	second	ADJ
ejpam-3074	123	28	kind	kind	NOUN
ejpam-3074	123	29	to	to	PART
ejpam-3074	123	30	be	be	AUX
ejpam-3074	123	31	solvable	solvable	ADJ
ejpam-3074	123	32	.	.	PUNCT
ejpam-3074	124	1	instead	instead	ADV
ejpam-3074	124	2	of	of	ADP
ejpam-3074	124	3	finding	find	VERB
ejpam-3074	124	4	the	the	DET
ejpam-3074	124	5	eigenvector	eigenvector	NOUN
ejpam-3074	124	6	of	of	ADP
ejpam-3074	124	7	a	a	DET
ejpam-3074	124	8	pairwise	pairwise	NOUN
ejpam-3074	124	9	comparison	comparison	NOUN
ejpam-3074	124	10	matrix	matrix	NOUN
ejpam-3074	124	11	one	one	PRON
ejpam-3074	124	12	uses	use	VERB
ejpam-3074	124	13	the	the	DET
ejpam-3074	124	14	kernel	kernel	NOUN
ejpam-3074	124	15	of	of	ADP
ejpam-3074	124	16	an	an	DET
ejpam-3074	124	17	operator	operator	NOUN
ejpam-3074	124	18	.	.	PUNCT
ejpam-3074	125	1	operations	operation	NOUN
ejpam-3074	125	2	on	on	ADP
ejpam-3074	125	3	the	the	DET
ejpam-3074	125	4	matrix	matrix	NOUN
ejpam-3074	125	5	translate	translate	NOUN
ejpam-3074	125	6	to	to	ADP
ejpam-3074	125	7	operations	operation	NOUN
ejpam-3074	125	8	on	on	ADP
ejpam-3074	125	9	the	the	DET
ejpam-3074	125	10	kernel	kernel	NOUN
ejpam-3074	125	11	.	.	PUNCT
ejpam-3074	126	1	from	from	ADP
ejpam-3074	126	2	the	the	DET
ejpam-3074	126	3	matrix	matrix	NOUN
ejpam-3074	126	4	formulation	formulation	NOUN
ejpam-3074	126	5	leading	lead	VERB
ejpam-3074	126	6	to	to	ADP
ejpam-3074	126	7	the	the	DET
ejpam-3074	126	8	solution	solution	NOUN
ejpam-3074	126	9	of	of	ADP
ejpam-3074	126	10	a	a	DET
ejpam-3074	126	11	principal	principal	ADJ
ejpam-3074	126	12	eigenvalue	eigenvalue	NOUN
ejpam-3074	126	13	problem	problem	NOUN
ejpam-3074	126	14	we	we	PRON
ejpam-3074	126	15	have	have	VERB
ejpam-3074	126	16	b∫	b∫	PROPN
ejpam-3074	126	17	a	a	DET
ejpam-3074	126	18	k(s	k(s	PROPN
ejpam-3074	126	19	,	,	PUNCT
ejpam-3074	126	20	t)w(t)dt	t)w(t)dt	PROPN
ejpam-3074	126	21	=	=	SYM
ejpam-3074	126	22	λmaxw(s	λmaxw(s	PROPN
ejpam-3074	126	23	)	)	PUNCT
ejpam-3074	126	24	or	or	CCONJ
ejpam-3074	126	25	λ	λ	ADP
ejpam-3074	126	26	b∫	b∫	PROPN
ejpam-3074	126	27	a	a	DET
ejpam-3074	126	28	k(s	k(s	PROPN
ejpam-3074	126	29	,	,	PUNCT
ejpam-3074	126	30	t)w(t)dt	t)w(t)dt	PROPN
ejpam-3074	126	31	=	=	SYM
ejpam-3074	126	32	w(s	w(s	PROPN
ejpam-3074	126	33	)	)	PUNCT
ejpam-3074	126	34	b∫	b∫	NOUN
ejpam-3074	126	35	a	a	DET
ejpam-3074	126	36	w(s)ds	w(s)ds	NOUN
ejpam-3074	126	37	=	=	SYM
ejpam-3074	126	38	1	1	NUM
ejpam-3074	126	39	where	where	SCONJ
ejpam-3074	126	40	the	the	DET
ejpam-3074	126	41	positive	positive	ADJ
ejpam-3074	126	42	matrix	matrix	NOUN
ejpam-3074	126	43	a	a	PRON
ejpam-3074	126	44	is	be	AUX
ejpam-3074	126	45	replaced	replace	VERB
ejpam-3074	126	46	by	by	ADP
ejpam-3074	126	47	a	a	DET
ejpam-3074	126	48	positive	positive	ADJ
ejpam-3074	126	49	kernel	kernel	NOUN
ejpam-3074	126	50	k(s	k(s	PROPN
ejpam-3074	126	51	,	,	PUNCT
ejpam-3074	126	52	t	t	PROPN
ejpam-3074	126	53	)	)	PUNCT
ejpam-3074	126	54	>	>	X
ejpam-3074	126	55	0	0	NUM
ejpam-3074	126	56	,	,	PUNCT
ejpam-3074	126	57	the	the	DET
ejpam-3074	126	58	continuous	continuous	ADJ
ejpam-3074	126	59	version	version	NOUN
ejpam-3074	126	60	of	of	ADP
ejpam-3074	126	61	pairwise	pairwise	NOUN
ejpam-3074	126	62	comparisons	comparison	NOUN
ejpam-3074	126	63	and	and	CCONJ
ejpam-3074	126	64	the	the	DET
ejpam-3074	126	65	eigenvector	eigenvector	NOUN
ejpam-3074	126	66	w	w	NOUN
ejpam-3074	126	67	by	by	ADP
ejpam-3074	126	68	the	the	DET
ejpam-3074	126	69	eigenfunction	eigenfunction	NOUN
ejpam-3074	126	70	w(s	w(s	PROPN
ejpam-3074	126	71	)	)	PUNCT
ejpam-3074	126	72	.	.	PUNCT
ejpam-3074	127	1	note	note	VERB
ejpam-3074	127	2	that	that	SCONJ
ejpam-3074	127	3	the	the	DET
ejpam-3074	127	4	entries	entry	NOUN
ejpam-3074	127	5	in	in	ADP
ejpam-3074	127	6	a	a	DET
ejpam-3074	127	7	matrix	matrix	NOUN
ejpam-3074	127	8	depend	depend	VERB
ejpam-3074	127	9	on	on	ADP
ejpam-3074	127	10	the	the	DET
ejpam-3074	127	11	two	two	NUM
ejpam-3074	127	12	variables	variable	NOUN
ejpam-3074	127	13	i	i	PRON
ejpam-3074	127	14	and	and	CCONJ
ejpam-3074	127	15	j	j	PROPN
ejpam-3074	127	16	that	that	PRON
ejpam-3074	127	17	assume	assume	VERB
ejpam-3074	127	18	discrete	discrete	ADJ
ejpam-3074	127	19	values	value	NOUN
ejpam-3074	127	20	.	.	PUNCT
ejpam-3074	128	1	thus	thus	ADV
ejpam-3074	128	2	,	,	PUNCT
ejpam-3074	128	3	the	the	DET
ejpam-3074	128	4	matrix	matrix	NOUN
ejpam-3074	128	5	itself	itself	PRON
ejpam-3074	128	6	depends	depend	VERB
ejpam-3074	128	7	on	on	ADP
ejpam-3074	128	8	these	these	DET
ejpam-3074	128	9	discrete	discrete	ADJ
ejpam-3074	128	10	variables	variable	NOUN
ejpam-3074	128	11	and	and	CCONJ
ejpam-3074	128	12	its	its	PRON
ejpam-3074	128	13	generalization	generalization	NOUN
ejpam-3074	128	14	,	,	PUNCT
ejpam-3074	128	15	the	the	DET
ejpam-3074	128	16	kernel	kernel	PROPN
ejpam-3074	128	17	function	function	PROPN
ejpam-3074	128	18	,	,	PUNCT
ejpam-3074	128	19	depends	depend	VERB
ejpam-3074	128	20	on	on	ADP
ejpam-3074	128	21	two	two	NUM
ejpam-3074	128	22	(	(	PUNCT
ejpam-3074	128	23	continuous	continuous	ADJ
ejpam-3074	128	24	)	)	PUNCT
ejpam-3074	128	25	variables	variable	NOUN
ejpam-3074	128	26	.	.	PUNCT
ejpam-3074	129	1	the	the	DET
ejpam-3074	129	2	reason	reason	NOUN
ejpam-3074	129	3	for	for	ADP
ejpam-3074	129	4	calling	call	VERB
ejpam-3074	129	5	it	it	PRON
ejpam-3074	129	6	a	a	DET
ejpam-3074	129	7	kernel	kernel	NOUN
ejpam-3074	129	8	is	be	AUX
ejpam-3074	129	9	the	the	DET
ejpam-3074	129	10	role	role	NOUN
ejpam-3074	129	11	it	it	PRON
ejpam-3074	129	12	plays	play	VERB
ejpam-3074	129	13	in	in	ADP
ejpam-3074	129	14	the	the	DET
ejpam-3074	129	15	integral	integral	ADJ
ejpam-3074	129	16	,	,	PUNCT
ejpam-3074	129	17	where	where	SCONJ
ejpam-3074	129	18	without	without	ADP
ejpam-3074	129	19	knowing	know	VERB
ejpam-3074	129	20	it	it	PRON
ejpam-3074	129	21	,	,	PUNCT
ejpam-3074	129	22	we	we	PRON
ejpam-3074	129	23	can	can	AUX
ejpam-3074	129	24	not	not	PART
ejpam-3074	129	25	determine	determine	VERB
ejpam-3074	129	26	the	the	DET
ejpam-3074	129	27	exact	exact	ADJ
ejpam-3074	129	28	form	form	NOUN
ejpam-3074	129	29	of	of	ADP
ejpam-3074	129	30	the	the	DET
ejpam-3074	129	31	solution	solution	NOUN
ejpam-3074	129	32	.	.	PUNCT
ejpam-3074	130	1	the	the	DET
ejpam-3074	130	2	standard	standard	ADJ
ejpam-3074	130	3	way	way	NOUN
ejpam-3074	130	4	in	in	ADP
ejpam-3074	130	5	which	which	PRON
ejpam-3074	130	6	the	the	DET
ejpam-3074	130	7	first	first	ADJ
ejpam-3074	130	8	equation	equation	NOUN
ejpam-3074	130	9	is	be	AUX
ejpam-3074	130	10	written	write	VERB
ejpam-3074	130	11	is	be	AUX
ejpam-3074	130	12	to	to	PART
ejpam-3074	130	13	move	move	VERB
ejpam-3074	130	14	the	the	DET
ejpam-3074	130	15	eigenvalue	eigenvalue	NOUN
ejpam-3074	130	16	to	to	ADP
ejpam-3074	130	17	the	the	DET
ejpam-3074	130	18	left	left	ADJ
ejpam-3074	130	19	-	-	PUNCT
ejpam-3074	130	20	hand	hand	NOUN
ejpam-3074	130	21	side	side	NOUN
ejpam-3074	130	22	which	which	PRON
ejpam-3074	130	23	gives	give	VERB
ejpam-3074	130	24	it	it	PRON
ejpam-3074	130	25	the	the	DET
ejpam-3074	130	26	reciprocal	reciprocal	ADJ
ejpam-3074	130	27	form	form	NOUN
ejpam-3074	130	28	.	.	PUNCT
ejpam-3074	131	1	in	in	ADP
ejpam-3074	131	2	general	general	ADJ
ejpam-3074	131	3	,	,	PUNCT
ejpam-3074	131	4	by	by	ADP
ejpam-3074	131	5	abuse	abuse	NOUN
ejpam-3074	131	6	of	of	ADP
ejpam-3074	131	7	notation	notation	NOUN
ejpam-3074	131	8	,	,	PUNCT
ejpam-3074	131	9	one	one	PRON
ejpam-3074	131	10	continues	continue	VERB
ejpam-3074	131	11	to	to	PART
ejpam-3074	131	12	use	use	VERB
ejpam-3074	131	13	the	the	DET
ejpam-3074	131	14	symbol	symbol	NOUN
ejpam-3074	131	15	λ	λ	NOUN
ejpam-3074	131	16	to	to	PART
ejpam-3074	131	17	represent	represent	VERB
ejpam-3074	131	18	the	the	DET
ejpam-3074	131	19	reciprocal	reciprocal	ADJ
ejpam-3074	131	20	value	value	NOUN
ejpam-3074	131	21	and	and	CCONJ
ejpam-3074	131	22	with	with	ADP
ejpam-3074	131	23	it	it	PRON
ejpam-3074	131	24	one	one	PRON
ejpam-3074	131	25	includes	include	VERB
ejpam-3074	131	26	the	the	DET
ejpam-3074	131	27	familiar	familiar	ADJ
ejpam-3074	131	28	condition	condition	NOUN
ejpam-3074	131	29	of	of	ADP
ejpam-3074	131	30	normalization	normalization	NOUN
ejpam-3074	131	31	∫	∫	PROPN
ejpam-3074	132	1	b	b	PROPN
ejpam-3074	132	2	a	a	DET
ejpam-3074	132	3	w(s)ds	w(s)ds	NOUN
ejpam-3074	132	4	=	=	SYM
ejpam-3074	132	5	1	1	NUM
ejpam-3074	132	6	.	.	PUNCT
ejpam-3074	133	1	here	here	ADV
ejpam-3074	133	2	also	also	ADV
ejpam-3074	133	3	,	,	PUNCT
ejpam-3074	133	4	the	the	DET
ejpam-3074	133	5	kernel	kernel	PROPN
ejpam-3074	133	6	k(s	k(s	PROPN
ejpam-3074	133	7	,	,	PUNCT
ejpam-3074	133	8	t)is	t)is	PROPN
ejpam-3074	133	9	said	say	VERB
ejpam-3074	133	10	to	to	PART
ejpam-3074	133	11	be	be	AUX
ejpam-3074	133	12	1	1	NUM
ejpam-3074	133	13	)	)	PUNCT
ejpam-3074	133	14	consistent	consistent	ADJ
ejpam-3074	133	15	and	and	CCONJ
ejpam-3074	133	16	therefore	therefore	ADV
ejpam-3074	133	17	also	also	ADV
ejpam-3074	133	18	reciprocal	reciprocal	ADJ
ejpam-3074	133	19	,	,	PUNCT
ejpam-3074	133	20	ifk(s	ifk(s	NOUN
ejpam-3074	133	21	,	,	PUNCT
ejpam-3074	133	22	t)k(t	t)k(t	NOUN
ejpam-3074	133	23	,	,	PUNCT
ejpam-3074	133	24	u	u	NOUN
ejpam-3074	133	25	)	)	PUNCT
ejpam-3074	133	26	=	=	SYM
ejpam-3074	133	27	k(s	k(s	PROPN
ejpam-3074	133	28	,	,	PUNCT
ejpam-3074	133	29	u	u	NOUN
ejpam-3074	133	30	)	)	PUNCT
ejpam-3074	133	31	,	,	PUNCT
ejpam-3074	133	32	for	for	ADP
ejpam-3074	133	33	all	all	DET
ejpam-3074	133	34	s	s	PROPN
ejpam-3074	133	35	,	,	PUNCT
ejpam-3074	133	36	t	t	PROPN
ejpam-3074	133	37	and	and	CCONJ
ejpam-3074	133	38	u	u	NOUN
ejpam-3074	133	39	,	,	PUNCT
ejpam-3074	133	40	or	or	CCONJ
ejpam-3074	133	41	2	2	NUM
ejpam-3074	133	42	)	)	PUNCT
ejpam-3074	133	43	reciprocal	reciprocal	ADJ
ejpam-3074	133	44	,	,	PUNCT
ejpam-3074	133	45	but	but	CCONJ
ejpam-3074	133	46	perhaps	perhaps	ADV
ejpam-3074	133	47	not	not	PART
ejpam-3074	133	48	consistent	consistent	ADJ
ejpam-3074	133	49	,	,	PUNCT
ejpam-3074	133	50	if	if	SCONJ
ejpam-3074	133	51	k(s	k(s	PROPN
ejpam-3074	133	52	,	,	PUNCT
ejpam-3074	133	53	t)k(t	t)k(t	NOUN
ejpam-3074	133	54	,	,	PUNCT
ejpam-3074	133	55	s	s	PART
ejpam-3074	133	56	)	)	PUNCT
ejpam-3074	133	57	=	=	SYM
ejpam-3074	133	58	1	1	NUM
ejpam-3074	133	59	for	for	ADP
ejpam-3074	133	60	all	all	DET
ejpam-3074	133	61	s	s	NOUN
ejpam-3074	133	62	,	,	PUNCT
ejpam-3074	133	63	t.	t.	NOUN
ejpam-3074	133	64	a	a	DET
ejpam-3074	133	65	value	value	NOUN
ejpam-3074	133	66	of	of	ADP
ejpam-3074	133	67	λ	λ	PROPN
ejpam-3074	133	68	for	for	ADP
ejpam-3074	133	69	which	which	PRON
ejpam-3074	133	70	fredholms	fredholm	NOUN
ejpam-3074	133	71	equation	equation	NOUN
ejpam-3074	133	72	has	have	VERB
ejpam-3074	133	73	a	a	DET
ejpam-3074	133	74	nonzero	nonzero	ADJ
ejpam-3074	133	75	solution	solution	NOUN
ejpam-3074	133	76	w(t	w(t	PROPN
ejpam-3074	133	77	)	)	PUNCT
ejpam-3074	133	78	is	be	AUX
ejpam-3074	133	79	called	call	VERB
ejpam-3074	133	80	a	a	DET
ejpam-3074	133	81	characteristic	characteristic	ADJ
ejpam-3074	133	82	value	value	NOUN
ejpam-3074	133	83	(	(	PUNCT
ejpam-3074	133	84	or	or	CCONJ
ejpam-3074	133	85	its	its	PRON
ejpam-3074	133	86	reciprocal	reciprocal	NOUN
ejpam-3074	133	87	is	be	AUX
ejpam-3074	133	88	called	call	VERB
ejpam-3074	133	89	an	an	DET
ejpam-3074	133	90	eigenvalue	eigenvalue	NOUN
ejpam-3074	133	91	)	)	PUNCT
ejpam-3074	133	92	and	and	CCONJ
ejpam-3074	133	93	the	the	DET
ejpam-3074	133	94	corresponding	corresponding	ADJ
ejpam-3074	133	95	solution	solution	NOUN
ejpam-3074	133	96	is	be	AUX
ejpam-3074	133	97	called	call	VERB
ejpam-3074	133	98	an	an	DET
ejpam-3074	133	99	eigenfunction	eigenfunction	NOUN
ejpam-3074	133	100	.	.	PUNCT
ejpam-3074	134	1	an	an	DET
ejpam-3074	134	2	eigenfunction	eigenfunction	NOUN
ejpam-3074	134	3	is	be	AUX
ejpam-3074	134	4	determined	determine	VERB
ejpam-3074	134	5	to	to	ADP
ejpam-3074	134	6	within	within	ADP
ejpam-3074	134	7	a	a	DET
ejpam-3074	134	8	multiplicative	multiplicative	ADJ
ejpam-3074	134	9	constant	constant	NOUN
ejpam-3074	134	10	.	.	PUNCT
ejpam-3074	135	1	if	if	SCONJ
ejpam-3074	135	2	w(t	w(t	PROPN
ejpam-3074	135	3	)	)	PUNCT
ejpam-3074	135	4	is	be	AUX
ejpam-3074	135	5	an	an	DET
ejpam-3074	135	6	eigenfunction	eigenfunction	NOUN
ejpam-3074	135	7	corresponding	correspond	VERB
ejpam-3074	135	8	to	to	ADP
ejpam-3074	135	9	the	the	DET
ejpam-3074	135	10	characteristic	characteristic	ADJ
ejpam-3074	135	11	value	value	NOUN
ejpam-3074	135	12	λ	λ	NOUN
ejpam-3074	135	13	and	and	CCONJ
ejpam-3074	135	14	if	if	SCONJ
ejpam-3074	135	15	c	c	PROPN
ejpam-3074	135	16	is	be	AUX
ejpam-3074	135	17	an	an	DET
ejpam-3074	135	18	arbitrary	arbitrary	ADJ
ejpam-3074	135	19	constant	constant	ADJ
ejpam-3074	135	20	,	,	PUNCT
ejpam-3074	135	21	we	we	PRON
ejpam-3074	135	22	see	see	VERB
ejpam-3074	135	23	by	by	ADP
ejpam-3074	135	24	substituting	substitute	VERB
ejpam-3074	135	25	in	in	ADP
ejpam-3074	135	26	the	the	DET
ejpam-3074	135	27	equation	equation	NOUN
ejpam-3074	135	28	that	that	PRON
ejpam-3074	135	29	cw(t	cw(t	ADV
ejpam-3074	135	30	)	)	PUNCT
ejpam-3074	135	31	is	be	AUX
ejpam-3074	135	32	also	also	ADV
ejpam-3074	135	33	an	an	DET
ejpam-3074	135	34	eigenfunction	eigenfunction	NOUN
ejpam-3074	135	35	corresponding	correspond	VERB
ejpam-3074	135	36	to	to	ADP
ejpam-3074	135	37	the	the	DET
ejpam-3074	135	38	same	same	ADJ
ejpam-3074	135	39	λ	λ	NOUN
ejpam-3074	135	40	.	.	PUNCT
ejpam-3074	136	1	the	the	DET
ejpam-3074	136	2	value	value	NOUN
ejpam-3074	136	3	λ	λ	X
ejpam-3074	136	4	=	=	SYM
ejpam-3074	136	5	0	0	NUM
ejpam-3074	136	6	is	be	AUX
ejpam-3074	136	7	not	not	PART
ejpam-3074	136	8	a	a	DET
ejpam-3074	136	9	characteristic	characteristic	ADJ
ejpam-3074	136	10	value	value	NOUN
ejpam-3074	136	11	because	because	SCONJ
ejpam-3074	136	12	we	we	PRON
ejpam-3074	136	13	have	have	VERB
ejpam-3074	136	14	the	the	DET
ejpam-3074	136	15	corresponding	corresponding	ADJ
ejpam-3074	136	16	solution	solution	NOUN
ejpam-3074	136	17	w(t	w(t	PROPN
ejpam-3074	136	18	)	)	PUNCT
ejpam-3074	137	1	=	=	SYM
ejpam-3074	137	2	0	0	NUM
ejpam-3074	138	1	for	for	ADP
ejpam-3074	138	2	every	every	DET
ejpam-3074	138	3	value	value	NOUN
ejpam-3074	138	4	of	of	ADP
ejpam-3074	138	5	t	t	PROPN
ejpam-3074	138	6	,	,	PUNCT
ejpam-3074	138	7	which	which	PRON
ejpam-3074	138	8	is	be	AUX
ejpam-3074	138	9	the	the	DET
ejpam-3074	138	10	trivial	trivial	ADJ
ejpam-3074	138	11	case	case	NOUN
ejpam-3074	138	12	,	,	PUNCT
ejpam-3074	138	13	excluded	exclude	VERB
ejpam-3074	138	14	in	in	ADP
ejpam-3074	138	15	our	our	PRON
ejpam-3074	138	16	discussion	discussion	NOUN
ejpam-3074	138	17	.	.	PUNCT
ejpam-3074	139	1	3.1	3.1	NUM
ejpam-3074	139	2	.	.	PUNCT
ejpam-3074	140	1	how	how	SCONJ
ejpam-3074	140	2	neurons	neuron	NOUN
ejpam-3074	140	3	compare	compare	VERB
ejpam-3074	140	4	charges	charge	NOUN
ejpam-3074	140	5	turning	turn	VERB
ejpam-3074	140	6	to	to	ADP
ejpam-3074	140	7	neurons	neuron	NOUN
ejpam-3074	140	8	,	,	PUNCT
ejpam-3074	140	9	consider	consider	VERB
ejpam-3074	140	10	a	a	DET
ejpam-3074	140	11	neuron	neuron	NOUN
ejpam-3074	140	12	that	that	PRON
ejpam-3074	140	13	compares	compare	VERB
ejpam-3074	140	14	neurotransmitter	neurotransmitter	NOUN
ejpam-3074	140	15	-	-	PUNCT
ejpam-3074	140	16	generated	generate	VERB
ejpam-3074	140	17	charges	charge	NOUN
ejpam-3074	140	18	in	in	ADP
ejpam-3074	140	19	increments	increment	NOUN
ejpam-3074	140	20	of	of	ADP
ejpam-3074	140	21	time	time	NOUN
ejpam-3074	140	22	.	.	PUNCT
ejpam-3074	141	1	let	let	VERB
ejpam-3074	141	2	[	[	X
ejpam-3074	141	3	0	0	NUM
ejpam-3074	141	4	,	,	PUNCT
ejpam-3074	141	5	t	t	PROPN
ejpam-3074	141	6	]	]	PUNCT
ejpam-3074	141	7	be	be	AUX
ejpam-3074	141	8	a	a	DET
ejpam-3074	141	9	time	time	NOUN
ejpam-3074	141	10	interval	interval	NOUN
ejpam-3074	141	11	,	,	PUNCT
ejpam-3074	141	12	let	let	VERB
ejpam-3074	141	13	0	0	NUM
ejpam-3074	142	1	=	=	SYM
ejpam-3074	142	2	t0	t0	PROPN
ejpam-3074	142	3	<	<	X
ejpam-3074	142	4	t1	t1	NOUN
ejpam-3074	142	5	<	<	X
ejpam-3074	142	6	...	...	PUNCT
ejpam-3074	142	7	tn−1	tn−1	ADJ
ejpam-3074	142	8	be	be	AUX
ejpam-3074	142	9	a	a	DET
ejpam-3074	142	10	partition	partition	NOUN
ejpam-3074	142	11	of	of	ADP
ejpam-3074	142	12	the	the	DET
ejpam-3074	142	13	interval	interval	NOUN
ejpam-3074	142	14	[	[	X
ejpam-3074	142	15	0	0	NUM
ejpam-3074	142	16	,	,	PUNCT
ejpam-3074	142	17	t	t	X
ejpam-3074	142	18	]	]	PUNCT
ejpam-3074	142	19	,	,	PUNCT
ejpam-3074	142	20	and	and	CCONJ
ejpam-3074	142	21	ik(tk−1	ik(tk−1	NUM
ejpam-3074	142	22	,	,	PUNCT
ejpam-3074	142	23	tk	tk	NOUN
ejpam-3074	142	24	]	]	X
ejpam-3074	142	25	,	,	PUNCT
ejpam-3074	142	26	k	k	PROPN
ejpam-3074	142	27	=	=	SYM
ejpam-3074	142	28	1	1	NUM
ejpam-3074	142	29	,	,	PUNCT
ejpam-3074	142	30	2	2	NUM
ejpam-3074	142	31	,	,	PUNCT
ejpam-3074	142	32	,	,	PUNCT
ejpam-3074	142	33	n.	n.	PROPN
ejpam-3074	142	34	let	let	VERB
ejpam-3074	142	35	,	,	PUNCT
ejpam-3074	142	36	w(t	w(t	PROPN
ejpam-3074	142	37	)	)	PUNCT
ejpam-3074	142	38	,	,	PUNCT
ejpam-3074	142	39	t	t	PROPN
ejpam-3074	142	40	∈	∈	PROPN
ejpam-3074	143	1	[	[	X
ejpam-3074	143	2	0	0	NUM
ejpam-3074	143	3	,	,	PUNCT
ejpam-3074	143	4	t	t	PROPN
ejpam-3074	143	5	]	]	PUNCT
ejpam-3074	143	6	be	be	AUX
ejpam-3074	143	7	a	a	DET
ejpam-3074	143	8	single	single	ADJ
ejpam-3074	143	9	t.	t.	PROPN
ejpam-3074	143	10	l.	l.	PROPN
ejpam-3074	143	11	saaty	saaty	PROPN
ejpam-3074	143	12	,	,	PUNCT
ejpam-3074	143	13	l.	l.	PROPN
ejpam-3074	143	14	g.	g.	PROPN
ejpam-3074	143	15	vargas	vargas	PROPN
ejpam-3074	143	16	/	/	SYM
ejpam-3074	143	17	eur	eur	PROPN
ejpam-3074	143	18	.	.	PUNCT
ejpam-3074	144	1	j.	j.	PROPN
ejpam-3074	144	2	pure	pure	PROPN
ejpam-3074	144	3	appl	appl	PROPN
ejpam-3074	144	4	.	.	PROPN
ejpam-3074	144	5	math	math	PROPN
ejpam-3074	144	6	,	,	PUNCT
ejpam-3074	144	7	10	10	NUM
ejpam-3074	144	8	(	(	PUNCT
ejpam-3074	144	9	4	4	NUM
ejpam-3074	144	10	)	)	PUNCT
ejpam-3074	144	11	(	(	PUNCT
ejpam-3074	144	12	2017	2017	NUM
ejpam-3074	144	13	)	)	PUNCT
ejpam-3074	144	14	,	,	PUNCT
ejpam-3074	144	15	602	602	NUM
ejpam-3074	144	16	-	-	SYM
ejpam-3074	144	17	613	613	NUM
ejpam-3074	144	18	608	608	NUM
ejpam-3074	144	19	firing	firing	NOUN
ejpam-3074	144	20	(	(	PUNCT
ejpam-3074	144	21	voltage	voltage	NOUN
ejpam-3074	144	22	discharge	discharge	NOUN
ejpam-3074	144	23	)	)	PUNCT
ejpam-3074	144	24	of	of	ADP
ejpam-3074	144	25	a	a	DET
ejpam-3074	144	26	neuron	neuron	NOUN
ejpam-3074	144	27	in	in	ADP
ejpam-3074	144	28	spontaneous	spontaneous	ADJ
ejpam-3074	144	29	activity	activity	NOUN
ejpam-3074	144	30	.	.	PUNCT
ejpam-3074	145	1	let	let	VERB
ejpam-3074	145	2	g(t	g(t	PROPN
ejpam-3074	145	3	)	)	PUNCT
ejpam-3074	145	4	,	,	PUNCT
ejpam-3074	145	5	t	t	PROPN
ejpam-3074	145	6	∈	∈	PROPN
ejpam-3074	146	1	[	[	X
ejpam-3074	146	2	0	0	NUM
ejpam-3074	146	3	,	,	PUNCT
ejpam-3074	146	4	t	t	PROPN
ejpam-3074	146	5	]	]	PUNCT
ejpam-3074	146	6	be	be	AUX
ejpam-3074	146	7	the	the	DET
ejpam-3074	146	8	cumulative	cumulative	ADJ
ejpam-3074	146	9	response	response	NOUN
ejpam-3074	146	10	of	of	ADP
ejpam-3074	146	11	the	the	DET
ejpam-3074	146	12	neuron	neuron	NOUN
ejpam-3074	146	13	in	in	ADP
ejpam-3074	146	14	spontaneous	spontaneous	ADJ
ejpam-3074	146	15	activity	activity	NOUN
ejpam-3074	146	16	over	over	ADP
ejpam-3074	146	17	time	time	NOUN
ejpam-3074	146	18	.	.	PUNCT
ejpam-3074	147	1	then	then	ADV
ejpam-3074	147	2	,	,	PUNCT
ejpam-3074	147	3	we	we	PRON
ejpam-3074	147	4	have	have	VERB
ejpam-3074	147	5	dg(t)/dt	dg(t)/dt	NOUN
ejpam-3074	147	6	=	=	SYM
ejpam-3074	147	7	w(t	w(t	PROPN
ejpam-3074	147	8	)	)	PUNCT
ejpam-3074	147	9	.	.	PUNCT
ejpam-3074	148	1	note	note	VERB
ejpam-3074	148	2	that	that	SCONJ
ejpam-3074	148	3	g(t	g(t	PROPN
ejpam-3074	148	4	)	)	PUNCT
ejpam-3074	148	5	is	be	AUX
ejpam-3074	148	6	monotonically	monotonically	ADV
ejpam-3074	148	7	increasing	increase	VERB
ejpam-3074	148	8	and	and	CCONJ
ejpam-3074	148	9	hence	hence	ADV
ejpam-3074	148	10	,	,	PUNCT
ejpam-3074	148	11	w(t	w(t	PROPN
ejpam-3074	148	12	)	)	PUNCT
ejpam-3074	148	13	>	>	X
ejpam-3074	148	14	0	0	PUNCT
ejpam-3074	148	15	and	and	CCONJ
ejpam-3074	148	16	w(0	w(0	PROPN
ejpam-3074	148	17	)	)	PUNCT
ejpam-3074	148	18	=	=	NOUN
ejpam-3074	149	1	0	0	X
ejpam-3074	149	2	.	.	PUNCT
ejpam-3074	149	3	let	let	VERB
ejpam-3074	149	4	k	k	PROPN
ejpam-3074	149	5	=	=	SYM
ejpam-3074	149	6	(	(	PUNCT
ejpam-3074	149	7	ii	ii	PROPN
ejpam-3074	149	8	,	,	PUNCT
ejpam-3074	149	9	ij	ij	NOUN
ejpam-3074	149	10	)	)	PUNCT
ejpam-3074	150	1	=	=	SYM
ejpam-3074	150	2	g(ti)−g(ti−1	g(ti)−g(ti−1	PROPN
ejpam-3074	150	3	)	)	PUNCT
ejpam-3074	150	4	g(tj)−g(tj−1	g(tj)−g(tj−1	PROPN
ejpam-3074	150	5	)	)	PUNCT
ejpam-3074	150	6	be	be	AUX
ejpam-3074	150	7	the	the	DET
ejpam-3074	150	8	relative	relative	ADJ
ejpam-3074	150	9	comparison	comparison	NOUN
ejpam-3074	150	10	of	of	ADP
ejpam-3074	150	11	the	the	DET
ejpam-3074	150	12	response	response	NOUN
ejpam-3074	150	13	of	of	ADP
ejpam-3074	150	14	the	the	DET
ejpam-3074	150	15	neuron	neuron	NOUN
ejpam-3074	150	16	during	during	ADP
ejpam-3074	150	17	a	a	DET
ejpam-3074	150	18	time	time	NOUN
ejpam-3074	150	19	interval	interval	NOUN
ejpam-3074	150	20	ii	ii	PROPN
ejpam-3074	150	21	with	with	ADP
ejpam-3074	150	22	another	another	DET
ejpam-3074	150	23	time	time	NOUN
ejpam-3074	150	24	interval	interval	NOUN
ejpam-3074	150	25	ij	ij	NOUN
ejpam-3074	150	26	.	.	PUNCT
ejpam-3074	151	1	we	we	PRON
ejpam-3074	151	2	have	have	VERB
ejpam-3074	151	3	1	1	NUM
ejpam-3074	151	4	n	n	NOUN
ejpam-3074	151	5	n∑	n∑	PROPN
ejpam-3074	151	6	j=1	j=1	PROPN
ejpam-3074	151	7	k(ii	k(ii	PROPN
ejpam-3074	151	8	,	,	PUNCT
ejpam-3074	151	9	ij)[g(tj)−g(tj−1	ij)[g(tj)−g(tj−1	NUM
ejpam-3074	151	10	)	)	PUNCT
ejpam-3074	151	11	]	]	PUNCT
ejpam-3074	152	1	=	=	PUNCT
ejpam-3074	152	2	g(ti)−g(ti−1	g(ti)−g(ti−1	PROPN
ejpam-3074	152	3	)	)	PUNCT
ejpam-3074	152	4	,	,	PUNCT
ejpam-3074	152	5	i	i	PRON
ejpam-3074	152	6	=	=	NOUN
ejpam-3074	152	7	1	1	NUM
ejpam-3074	152	8	,	,	PUNCT
ejpam-3074	152	9	2	2	NUM
ejpam-3074	152	10	,	,	PUNCT
ejpam-3074	152	11	...	...	PUNCT
ejpam-3074	152	12	,	,	PUNCT
ejpam-3074	152	13	n.	n.	NOUN
ejpam-3074	152	14	(	(	PUNCT
ejpam-3074	152	15	1	1	NUM
ejpam-3074	152	16	)	)	PUNCT
ejpam-3074	152	17	if	if	SCONJ
ejpam-3074	152	18	g(t	g(t	PROPN
ejpam-3074	152	19	)	)	PUNCT
ejpam-3074	152	20	is	be	AUX
ejpam-3074	152	21	of	of	ADP
ejpam-3074	152	22	class	class	NOUN
ejpam-3074	152	23	c1(0	c1(0	PROPN
ejpam-3074	152	24	,	,	PUNCT
ejpam-3074	152	25	t	t	X
ejpam-3074	152	26	]	]	PUNCT
ejpam-3074	152	27	,	,	PUNCT
ejpam-3074	152	28	then	then	ADV
ejpam-3074	152	29	as	as	SCONJ
ejpam-3074	152	30	∆tk	∆tk	PROPN
ejpam-3074	152	31	≡	≡	PROPN
ejpam-3074	152	32	tk−	tk−	X
ejpam-3074	152	33	tk−1	tk−1	PROPN
ejpam-3074	152	34	→	→	SYM
ejpam-3074	152	35	0	0	NUM
ejpam-3074	152	36	for	for	ADP
ejpam-3074	152	37	all	all	DET
ejpam-3074	152	38	k	k	PROPN
ejpam-3074	152	39	,	,	PUNCT
ejpam-3074	152	40	k(ii	k(ii	PROPN
ejpam-3074	152	41	,	,	PUNCT
ejpam-3074	152	42	ij)→	ij)→	PROPN
ejpam-3074	152	43	k(s	k(s	PROPN
ejpam-3074	152	44	,	,	PUNCT
ejpam-3074	152	45	t	t	PROPN
ejpam-3074	152	46	)	)	PUNCT
ejpam-3074	152	47	=	=	SYM
ejpam-3074	152	48	w(s	w(s	PROPN
ejpam-3074	152	49	)	)	PUNCT
ejpam-3074	152	50	w(t	w(t	PROPN
ejpam-3074	152	51	)	)	PUNCT
ejpam-3074	152	52	,	,	PUNCT
ejpam-3074	152	53	s	s	X
ejpam-3074	152	54	,	,	PUNCT
ejpam-3074	152	55	t	t	PROPN
ejpam-3074	152	56	∈	∈	PROPN
ejpam-3074	152	57	(	(	PUNCT
ejpam-3074	152	58	0	0	NUM
ejpam-3074	152	59	,	,	PUNCT
ejpam-3074	152	60	t	t	NOUN
ejpam-3074	152	61	]	]	PUNCT
ejpam-3074	152	62	.	.	PUNCT
ejpam-3074	153	1	in	in	ADP
ejpam-3074	153	2	addition	addition	NOUN
ejpam-3074	153	3	,	,	PUNCT
ejpam-3074	153	4	because	because	SCONJ
ejpam-3074	153	5	the	the	DET
ejpam-3074	153	6	left	leave	VERB
ejpam-3074	153	7	-	-	PUNCT
ejpam-3074	153	8	hand	hand	NOUN
ejpam-3074	153	9	side	side	NOUN
ejpam-3074	153	10	of	of	ADP
ejpam-3074	153	11	(	(	PUNCT
ejpam-3074	153	12	1	1	NUM
ejpam-3074	153	13	)	)	PUNCT
ejpam-3074	153	14	is	be	AUX
ejpam-3074	153	15	an	an	DET
ejpam-3074	153	16	average	average	NOUN
ejpam-3074	153	17	,	,	PUNCT
ejpam-3074	153	18	we	we	PRON
ejpam-3074	153	19	obtain	obtain	VERB
ejpam-3074	153	20	as	as	ADP
ejpam-3074	153	21	∆tk	∆tk	PROPN
ejpam-3074	153	22	→	→	SYM
ejpam-3074	153	23	0	0	NUM
ejpam-3074	153	24	for	for	ADP
ejpam-3074	153	25	all	all	DET
ejpam-3074	153	26	k	k	PROPN
ejpam-3074	153	27	and	and	CCONJ
ejpam-3074	153	28	as	as	ADP
ejpam-3074	153	29	n→∞	n→∞	NUM
ejpam-3074	153	30	:	:	PUNCT
ejpam-3074	153	31	1	1	NUM
ejpam-3074	153	32	t	t	X
ejpam-3074	153	33	t∫	t∫	PROPN
ejpam-3074	153	34	0	0	NUM
ejpam-3074	153	35	k(s	k(s	PROPN
ejpam-3074	153	36	,	,	PUNCT
ejpam-3074	153	37	t)w(t)dt	t)w(t)dt	PROPN
ejpam-3074	153	38	=	=	SYM
ejpam-3074	153	39	w(s	w(s	PROPN
ejpam-3074	153	40	)	)	PUNCT
ejpam-3074	153	41	it	it	PRON
ejpam-3074	153	42	can	can	AUX
ejpam-3074	153	43	be	be	AUX
ejpam-3074	153	44	easily	easily	ADV
ejpam-3074	153	45	shown	show	VERB
ejpam-3074	153	46	that	that	SCONJ
ejpam-3074	153	47	t	t	PROPN
ejpam-3074	153	48	is	be	AUX
ejpam-3074	153	49	the	the	DET
ejpam-3074	153	50	principal	principal	ADJ
ejpam-3074	153	51	eigenvalue	eigenvalue	NOUN
ejpam-3074	153	52	of	of	ADP
ejpam-3074	153	53	the	the	DET
ejpam-3074	153	54	consistent	consistent	ADJ
ejpam-3074	153	55	kernel	kernel	PROPN
ejpam-3074	153	56	k(s	k(s	PROPN
ejpam-3074	153	57	,	,	PUNCT
ejpam-3074	153	58	t	t	PROPN
ejpam-3074	153	59	)	)	PUNCT
ejpam-3074	153	60	.	.	PUNCT
ejpam-3074	154	1	in	in	ADP
ejpam-3074	154	2	general	general	ADJ
ejpam-3074	154	3	,	,	PUNCT
ejpam-3074	154	4	if	if	SCONJ
ejpam-3074	154	5	k(s	k(s	PROPN
ejpam-3074	154	6	,	,	PUNCT
ejpam-3074	154	7	t	t	PROPN
ejpam-3074	154	8	)	)	PUNCT
ejpam-3074	154	9	is	be	AUX
ejpam-3074	154	10	reciprocal	reciprocal	ADJ
ejpam-3074	154	11	but	but	CCONJ
ejpam-3074	154	12	not	not	PART
ejpam-3074	154	13	consistent	consistent	ADJ
ejpam-3074	154	14	,	,	PUNCT
ejpam-3074	154	15	the	the	DET
ejpam-3074	154	16	homogeneous	homogeneous	ADJ
ejpam-3074	154	17	equation	equation	NOUN
ejpam-3074	154	18	takes	take	VERB
ejpam-3074	154	19	the	the	DET
ejpam-3074	154	20	form	form	NOUN
ejpam-3074	154	21	given	give	VERB
ejpam-3074	154	22	by	by	ADP
ejpam-3074	154	23	w(s	w(s	PROPN
ejpam-3074	154	24	)	)	PUNCT
ejpam-3074	155	1	=	=	PUNCT
ejpam-3074	155	2	λ0	λ0	NOUN
ejpam-3074	155	3	∫	∫	PROPN
ejpam-3074	155	4	ω	ω	PROPN
ejpam-3074	155	5	k(s	k(s	PROPN
ejpam-3074	155	6	,	,	PUNCT
ejpam-3074	155	7	t)w(t)dt	t)w(t)dt	PROPN
ejpam-3074	155	8	.	.	PUNCT
ejpam-3074	156	1	(	(	PUNCT
ejpam-3074	156	2	2	2	NUM
ejpam-3074	156	3	)	)	PUNCT
ejpam-3074	156	4	because	because	SCONJ
ejpam-3074	156	5	positive	positive	ADJ
ejpam-3074	156	6	reciprocal	reciprocal	ADJ
ejpam-3074	156	7	kernels	kernel	NOUN
ejpam-3074	156	8	are	be	AUX
ejpam-3074	156	9	non	non	ADJ
ejpam-3074	156	10	-	-	ADJ
ejpam-3074	156	11	factorable	factorable	ADJ
ejpam-3074	156	12	(	(	PUNCT
ejpam-3074	156	13	the	the	DET
ejpam-3074	156	14	property	property	NOUN
ejpam-3074	156	15	that	that	PRON
ejpam-3074	156	16	corresponds	correspond	VERB
ejpam-3074	156	17	to	to	ADP
ejpam-3074	156	18	irreducibility	irreducibility	NOUN
ejpam-3074	156	19	for	for	ADP
ejpam-3074	156	20	non	non	ADJ
ejpam-3074	156	21	-	-	ADJ
ejpam-3074	156	22	negative	negative	ADJ
ejpam-3074	156	23	matrices	matrix	NOUN
ejpam-3074	156	24	)	)	PUNCT
ejpam-3074	156	25	,	,	PUNCT
ejpam-3074	156	26	there	there	PRON
ejpam-3074	156	27	exists	exist	VERB
ejpam-3074	156	28	a	a	DET
ejpam-3074	156	29	unique	unique	ADJ
ejpam-3074	156	30	simple	simple	ADJ
ejpam-3074	156	31	eigenvalue	eigenvalue	NOUN
ejpam-3074	156	32	λ−1	λ−1	PROPN
ejpam-3074	156	33	0	0	NUM
ejpam-3074	156	34	whose	whose	DET
ejpam-3074	156	35	modulus	modulus	NOUN
ejpam-3074	156	36	dominates	dominate	VERB
ejpam-3074	156	37	the	the	DET
ejpam-3074	156	38	moduli	modulus	NOUN
ejpam-3074	156	39	of	of	ADP
ejpam-3074	156	40	all	all	DET
ejpam-3074	156	41	other	other	ADJ
ejpam-3074	156	42	eigenvalues.the	eigenvalues.the	DET
ejpam-3074	156	43	corresponding	correspond	VERB
ejpam-3074	156	44	eigenfunction	eigenfunction	NOUN
ejpam-3074	156	45	w(s	w(s	PROPN
ejpam-3074	156	46	)	)	PUNCT
ejpam-3074	156	47	is	be	AUX
ejpam-3074	156	48	the	the	DET
ejpam-3074	156	49	response	response	NOUN
ejpam-3074	156	50	function	function	NOUN
ejpam-3074	156	51	of	of	ADP
ejpam-3074	156	52	the	the	DET
ejpam-3074	156	53	neuron	neuron	NOUN
ejpam-3074	156	54	in	in	ADP
ejpam-3074	156	55	spontaneous	spontaneous	ADJ
ejpam-3074	156	56	activity	activity	NOUN
ejpam-3074	156	57	.	.	PUNCT
ejpam-3074	157	1	if	if	SCONJ
ejpam-3074	157	2	k(s	k(s	PROPN
ejpam-3074	157	3	,	,	PUNCT
ejpam-3074	157	4	t	t	PROPN
ejpam-3074	157	5	)	)	PUNCT
ejpam-3074	157	6	is	be	AUX
ejpam-3074	157	7	consistent	consistent	ADJ
ejpam-3074	157	8	,	,	PUNCT
ejpam-3074	157	9	it	it	PRON
ejpam-3074	157	10	can	can	AUX
ejpam-3074	157	11	be	be	AUX
ejpam-3074	157	12	written	write	VERB
ejpam-3074	157	13	as	as	ADP
ejpam-3074	157	14	a	a	DET
ejpam-3074	157	15	ratio	ratio	NOUN
ejpam-3074	157	16	k(s	k(s	PROPN
ejpam-3074	157	17	,	,	PUNCT
ejpam-3074	157	18	t	t	PROPN
ejpam-3074	157	19	)	)	PUNCT
ejpam-3074	157	20	=	=	SYM
ejpam-3074	157	21	k(s)/k(t	k(s)/k(t	PROPN
ejpam-3074	157	22	)	)	PUNCT
ejpam-3074	157	23	and	and	CCONJ
ejpam-3074	157	24	w(s	w(s	PROPN
ejpam-3074	157	25	)	)	PUNCT
ejpam-3074	157	26	=	=	VERB
ejpam-3074	158	1	k(s)/	k(s)/	AUX
ejpam-3074	158	2	∫	∫	PROPN
ejpam-3074	158	3	ω	ω	NUM
ejpam-3074	158	4	w(s)ds	w(s)ds	PROPN
ejpam-3074	158	5	.	.	PUNCT
ejpam-3074	159	1	saaty	saaty	NOUN
ejpam-3074	159	2	(	(	PUNCT
ejpam-3074	159	3	[	[	X
ejpam-3074	159	4	12	12	NUM
ejpam-3074	159	5	]	]	PUNCT
ejpam-3074	159	6	,	,	PUNCT
ejpam-3074	159	7	p.113	p.113	NOUN
ejpam-3074	159	8	)	)	PUNCT
ejpam-3074	159	9	has	have	AUX
ejpam-3074	159	10	shown	show	VERB
ejpam-3074	159	11	that	that	SCONJ
ejpam-3074	159	12	:	:	PUNCT
ejpam-3074	159	13	a	a	DET
ejpam-3074	159	14	necessary	necessary	ADJ
ejpam-3074	159	15	and	and	CCONJ
ejpam-3074	159	16	sufficient	sufficient	ADJ
ejpam-3074	159	17	condition	condition	NOUN
ejpam-3074	159	18	for	for	ADP
ejpam-3074	159	19	w(s	w(s	PROPN
ejpam-3074	159	20	)	)	PUNCT
ejpam-3074	159	21	to	to	PART
ejpam-3074	159	22	be	be	AUX
ejpam-3074	159	23	an	an	DET
ejpam-3074	159	24	eigenfunction	eigenfunction	NOUN
ejpam-3074	159	25	solution	solution	NOUN
ejpam-3074	159	26	of	of	ADP
ejpam-3074	159	27	fredholm	fredholm	ADJ
ejpam-3074	159	28	equation	equation	NOUN
ejpam-3074	159	29	of	of	ADP
ejpam-3074	159	30	the	the	DET
ejpam-3074	159	31	second	second	ADJ
ejpam-3074	159	32	kind	kind	NOUN
ejpam-3074	159	33	(	(	PUNCT
ejpam-3074	159	34	2	2	NUM
ejpam-3074	159	35	)	)	PUNCT
ejpam-3074	159	36	with	with	ADP
ejpam-3074	159	37	a	a	DET
ejpam-3074	159	38	consistent	consistent	ADJ
ejpam-3074	159	39	kernel	kernel	NOUN
ejpam-3074	159	40	that	that	PRON
ejpam-3074	159	41	is	be	AUX
ejpam-3074	159	42	homogeneous	homogeneous	ADJ
ejpam-3074	159	43	of	of	ADP
ejpam-3074	159	44	order	order	NOUN
ejpam-3074	159	45	one	one	PRON
ejpam-3074	159	46	is	be	AUX
ejpam-3074	159	47	that	that	SCONJ
ejpam-3074	159	48	it	it	PRON
ejpam-3074	159	49	satisfies	satisfy	VERB
ejpam-3074	159	50	the	the	DET
ejpam-3074	159	51	functional	functional	ADJ
ejpam-3074	159	52	equation	equation	NOUN
ejpam-3074	159	53	w(as	w(as	PROPN
ejpam-3074	159	54	)	)	PUNCT
ejpam-3074	159	55	=	=	SYM
ejpam-3074	159	56	bw(s	bw(s	NOUN
ejpam-3074	159	57	)	)	PUNCT
ejpam-3074	159	58	(	(	PUNCT
ejpam-3074	159	59	3	3	X
ejpam-3074	159	60	)	)	PUNCT
ejpam-3074	159	61	t.	t.	PROPN
ejpam-3074	159	62	l.	l.	PROPN
ejpam-3074	159	63	saaty	saaty	PROPN
ejpam-3074	159	64	,	,	PUNCT
ejpam-3074	159	65	l.	l.	PROPN
ejpam-3074	159	66	g.	g.	PROPN
ejpam-3074	159	67	vargas	vargas	PROPN
ejpam-3074	159	68	/	/	SYM
ejpam-3074	159	69	eur	eur	PROPN
ejpam-3074	159	70	.	.	PUNCT
ejpam-3074	160	1	j.	j.	PROPN
ejpam-3074	160	2	pure	pure	PROPN
ejpam-3074	160	3	appl	appl	PROPN
ejpam-3074	160	4	.	.	PROPN
ejpam-3074	160	5	math	math	PROPN
ejpam-3074	160	6	,	,	PUNCT
ejpam-3074	160	7	10	10	NUM
ejpam-3074	160	8	(	(	PUNCT
ejpam-3074	160	9	4	4	NUM
ejpam-3074	160	10	)	)	PUNCT
ejpam-3074	160	11	(	(	PUNCT
ejpam-3074	160	12	2017	2017	NUM
ejpam-3074	160	13	)	)	PUNCT
ejpam-3074	160	14	,	,	PUNCT
ejpam-3074	160	15	602	602	NUM
ejpam-3074	160	16	-	-	SYM
ejpam-3074	160	17	613	613	NUM
ejpam-3074	160	18	609	609	NUM
ejpam-3074	160	19	4	4	NUM
ejpam-3074	160	20	.	.	PUNCT
ejpam-3074	161	1	the	the	DET
ejpam-3074	161	2	solution	solution	NOUN
ejpam-3074	161	3	of	of	ADP
ejpam-3074	161	4	the	the	DET
ejpam-3074	161	5	functional	functional	ADJ
ejpam-3074	161	6	equation	equation	NOUN
ejpam-3074	161	7	w(as	w(as	PROPN
ejpam-3074	161	8	)	)	PUNCT
ejpam-3074	161	9	=	=	SYM
ejpam-3074	161	10	bw(s	bw(s	NOUN
ejpam-3074	161	11	)	)	PUNCT
ejpam-3074	161	12	in	in	ADP
ejpam-3074	161	13	saaty	saaty	NOUN
ejpam-3074	161	14	(	(	PUNCT
ejpam-3074	161	15	[	[	X
ejpam-3074	161	16	12	12	NUM
ejpam-3074	161	17	]	]	PUNCT
ejpam-3074	161	18	,	,	PUNCT
ejpam-3074	161	19	pp	pp	ADJ
ejpam-3074	161	20	.	.	PUNCT
ejpam-3074	162	1	113	113	NUM
ejpam-3074	162	2	-	-	SYM
ejpam-3074	162	3	121	121	NUM
ejpam-3074	162	4	)	)	PUNCT
ejpam-3074	162	5	,	,	PUNCT
ejpam-3074	162	6	the	the	DET
ejpam-3074	162	7	solutions	solution	NOUN
ejpam-3074	162	8	of	of	ADP
ejpam-3074	162	9	(	(	PUNCT
ejpam-3074	162	10	3	3	X
ejpam-3074	162	11	)	)	PUNCT
ejpam-3074	162	12	are	be	AUX
ejpam-3074	162	13	given	give	VERB
ejpam-3074	162	14	in	in	ADP
ejpam-3074	162	15	the	the	DET
ejpam-3074	162	16	real	real	ADJ
ejpam-3074	162	17	(	(	PUNCT
ejpam-3074	162	18	r	r	NOUN
ejpam-3074	162	19	)	)	PUNCT
ejpam-3074	162	20	,	,	PUNCT
ejpam-3074	162	21	the	the	DET
ejpam-3074	162	22	complex	complex	ADJ
ejpam-3074	162	23	(	(	PUNCT
ejpam-3074	162	24	c	c	NOUN
ejpam-3074	162	25	)	)	PUNCT
ejpam-3074	162	26	,	,	PUNCT
ejpam-3074	162	27	the	the	DET
ejpam-3074	162	28	quaternionsl	quaternionsl	PROPN
ejpam-3074	162	29	(	(	PUNCT
ejpam-3074	162	30	h	h	NOUN
ejpam-3074	162	31	)	)	PUNCT
ejpam-3074	162	32	,	,	PUNCT
ejpam-3074	162	33	and	and	CCONJ
ejpam-3074	162	34	the	the	DET
ejpam-3074	162	35	octonions	octonion	NOUN
ejpam-3074	162	36	(	(	PUNCT
ejpam-3074	162	37	o	o	NOUN
ejpam-3074	162	38	)	)	PUNCT
ejpam-3074	162	39	spaces	space	NOUN
ejpam-3074	162	40	.	.	PUNCT
ejpam-3074	163	1	these	these	PRON
ejpam-3074	163	2	are	be	AUX
ejpam-3074	163	3	the	the	DET
ejpam-3074	163	4	only	only	ADJ
ejpam-3074	163	5	normed	normed	ADJ
ejpam-3074	163	6	division	division	NOUN
ejpam-3074	163	7	(	(	PUNCT
ejpam-3074	163	8	or	or	CCONJ
ejpam-3074	163	9	composition	composition	NOUN
ejpam-3074	163	10	)	)	PUNCT
ejpam-3074	163	11	algebras	algebras	PROPN
ejpam-3074	163	12	.	.	PUNCT
ejpam-3074	164	1	a	a	DET
ejpam-3074	164	2	composition	composition	NOUN
ejpam-3074	164	3	algebra	algebra	NOUN
ejpam-3074	164	4	a	a	PRON
ejpam-3074	164	5	is	be	AUX
ejpam-3074	164	6	an	an	DET
ejpam-3074	164	7	algebra	algebra	NOUN
ejpam-3074	164	8	whose	whose	DET
ejpam-3074	164	9	norm	norm	NOUN
ejpam-3074	164	10	is	be	AUX
ejpam-3074	164	11	multiplicative	multiplicative	ADJ
ejpam-3074	164	12	.	.	PUNCT
ejpam-3074	165	1	let	let	VERB
ejpam-3074	165	2	h	h	PRON
ejpam-3074	165	3	be	be	AUX
ejpam-3074	165	4	a	a	DET
ejpam-3074	165	5	composition	composition	NOUN
ejpam-3074	165	6	subalgebra	subalgebra	NOUN
ejpam-3074	165	7	of	of	ADP
ejpam-3074	165	8	a	a	PRON
ejpam-3074	165	9	and	and	CCONJ
ejpam-3074	165	10	x	x	SYM
ejpam-3074	165	11	∈	∈	PROPN
ejpam-3074	165	12	a	a	PRON
ejpam-3074	165	13	with	with	NOUN
ejpam-3074	165	14	x	x	PART
ejpam-3074	165	15	orthogonal	orthogonal	ADJ
ejpam-3074	165	16	to	to	ADP
ejpam-3074	165	17	h.	h.	PROPN
ejpam-3074	165	18	if	if	SCONJ
ejpam-3074	165	19	h	h	NOUN
ejpam-3074	165	20	is	be	AUX
ejpam-3074	165	21	associative	associative	ADJ
ejpam-3074	165	22	then	then	ADV
ejpam-3074	165	23	h	h	PROPN
ejpam-3074	165	24	⊕	⊕	PROPN
ejpam-3074	165	25	xh	xh	PROPN
ejpam-3074	165	26	is	be	AUX
ejpam-3074	165	27	a	a	DET
ejpam-3074	165	28	composition	composition	NOUN
ejpam-3074	165	29	algebra	algebra	NOUN
ejpam-3074	165	30	.	.	PUNCT
ejpam-3074	166	1	hurwitz	hurwitz	PROPN
ejpam-3074	167	1	[	[	X
ejpam-3074	167	2	8	8	NUM
ejpam-3074	167	3	]	]	PUNCT
ejpam-3074	167	4	proved	prove	VERB
ejpam-3074	167	5	that	that	SCONJ
ejpam-3074	167	6	the	the	DET
ejpam-3074	167	7	only	only	ADJ
ejpam-3074	167	8	composition	composition	NOUN
ejpam-3074	167	9	algebras	algebra	NOUN
ejpam-3074	167	10	are	be	AUX
ejpam-3074	167	11	r	r	NOUN
ejpam-3074	167	12	,	,	PUNCT
ejpam-3074	167	13	c	c	NOUN
ejpam-3074	167	14	,	,	PUNCT
ejpam-3074	167	15	h	h	NOUN
ejpam-3074	167	16	and	and	CCONJ
ejpam-3074	167	17	o	o	X
ejpam-3074	167	18	.the	.the	PRON
ejpam-3074	168	1	smallest	small	ADJ
ejpam-3074	168	2	composition	composition	NOUN
ejpam-3074	168	3	algebra	algebra	NOUN
ejpam-3074	168	4	is	be	AUX
ejpam-3074	168	5	r.	r.	NOUN
ejpam-3074	168	6	since	since	SCONJ
ejpam-3074	168	7	r	r	NOUN
ejpam-3074	168	8	is	be	AUX
ejpam-3074	168	9	associative	associative	ADJ
ejpam-3074	169	1	and	and	CCONJ
ejpam-3074	169	2	i	i	PRON
ejpam-3074	169	3	is	be	AUX
ejpam-3074	169	4	orthogonal	orthogonal	ADJ
ejpam-3074	169	5	to	to	ADP
ejpam-3074	169	6	r	r	NOUN
ejpam-3074	169	7	,	,	PUNCT
ejpam-3074	169	8	c	c	NOUN
ejpam-3074	169	9	=	=	SYM
ejpam-3074	169	10	r	r	NOUN
ejpam-3074	169	11	⊕	⊕	PROPN
ejpam-3074	169	12	ir	ir	PROPN
ejpam-3074	169	13	is	be	AUX
ejpam-3074	169	14	a	a	DET
ejpam-3074	169	15	composition	composition	NOUN
ejpam-3074	169	16	algebra	algebra	NOUN
ejpam-3074	169	17	.	.	PUNCT
ejpam-3074	170	1	now	now	ADV
ejpam-3074	170	2	as	as	SCONJ
ejpam-3074	170	3	c	c	PROPN
ejpam-3074	170	4	is	be	AUX
ejpam-3074	170	5	associative	associative	ADJ
ejpam-3074	170	6	and	and	CCONJ
ejpam-3074	170	7	j	j	PROPN
ejpam-3074	170	8	is	be	AUX
ejpam-3074	170	9	orthogonal	orthogonal	ADJ
ejpam-3074	170	10	to	to	ADP
ejpam-3074	170	11	{	{	PUNCT
ejpam-3074	170	12	1	1	NUM
ejpam-3074	170	13	,	,	PUNCT
ejpam-3074	170	14	i	i	PRON
ejpam-3074	170	15	}	}	PUNCT
ejpam-3074	170	16	,	,	PUNCT
ejpam-3074	170	17	hence	hence	ADV
ejpam-3074	170	18	to	to	ADP
ejpam-3074	170	19	c	c	PROPN
ejpam-3074	170	20	,	,	PUNCT
ejpam-3074	170	21	thus	thus	ADV
ejpam-3074	170	22	h	h	NOUN
ejpam-3074	170	23	=	=	SYM
ejpam-3074	170	24	c	c	PROPN
ejpam-3074	170	25	⊕	⊕	PROPN
ejpam-3074	170	26	jc	jc	PROPN
ejpam-3074	170	27	is	be	AUX
ejpam-3074	170	28	a	a	DET
ejpam-3074	170	29	composition	composition	NOUN
ejpam-3074	170	30	algebra	algebra	NOUN
ejpam-3074	170	31	.	.	PUNCT
ejpam-3074	171	1	finally	finally	ADV
ejpam-3074	171	2	,	,	PUNCT
ejpam-3074	171	3	since	since	SCONJ
ejpam-3074	171	4	h	h	NOUN
ejpam-3074	171	5	is	be	AUX
ejpam-3074	171	6	associative	associative	ADJ
ejpam-3074	171	7	and	and	CCONJ
ejpam-3074	171	8	l	l	NOUN
ejpam-3074	171	9	is	be	AUX
ejpam-3074	171	10	orthogonal	orthogonal	ADJ
ejpam-3074	171	11	to	to	ADP
ejpam-3074	171	12	{	{	PUNCT
ejpam-3074	171	13	1	1	NUM
ejpam-3074	171	14	,	,	PUNCT
ejpam-3074	171	15	i	i	PRON
ejpam-3074	171	16	,	,	PUNCT
ejpam-3074	171	17	j	j	PROPN
ejpam-3074	171	18	,	,	PUNCT
ejpam-3074	171	19	k	k	NOUN
ejpam-3074	171	20	}	}	PUNCT
ejpam-3074	171	21	,	,	PUNCT
ejpam-3074	171	22	hence	hence	ADV
ejpam-3074	171	23	to	to	ADP
ejpam-3074	171	24	h	h	NOUN
ejpam-3074	171	25	,	,	PUNCT
ejpam-3074	171	26	o	o	NOUN
ejpam-3074	171	27	=	=	PUNCT
ejpam-3074	171	28	h	h	PROPN
ejpam-3074	171	29	⊕	⊕	PROPN
ejpam-3074	171	30	lh	lh	PROPN
ejpam-3074	171	31	is	be	AUX
ejpam-3074	171	32	a	a	DET
ejpam-3074	171	33	composition	composition	NOUN
ejpam-3074	171	34	algebra	algebra	NOUN
ejpam-3074	171	35	.	.	PUNCT
ejpam-3074	172	1	the	the	DET
ejpam-3074	172	2	process	process	NOUN
ejpam-3074	172	3	of	of	ADP
ejpam-3074	172	4	doubling	double	VERB
ejpam-3074	172	5	the	the	DET
ejpam-3074	172	6	composition	composition	NOUN
ejpam-3074	172	7	algebra	algebra	NOUN
ejpam-3074	172	8	to	to	PART
ejpam-3074	172	9	obtain	obtain	VERB
ejpam-3074	172	10	another	another	DET
ejpam-3074	172	11	composition	composition	NOUN
ejpam-3074	172	12	algebra	algebra	NOUN
ejpam-3074	172	13	ends	end	VERB
ejpam-3074	172	14	with	with	ADP
ejpam-3074	172	15	the	the	DET
ejpam-3074	172	16	octonions	octonion	NOUN
ejpam-3074	172	17	because	because	SCONJ
ejpam-3074	172	18	o	o	NOUN
ejpam-3074	172	19	is	be	AUX
ejpam-3074	172	20	not	not	PART
ejpam-3074	172	21	associative	associative	ADJ
ejpam-3074	172	22	.	.	PUNCT
ejpam-3074	173	1	since	since	SCONJ
ejpam-3074	173	2	the	the	DET
ejpam-3074	173	3	dimension	dimension	NOUN
ejpam-3074	173	4	of	of	ADP
ejpam-3074	173	5	a	a	DET
ejpam-3074	173	6	composition	composition	NOUN
ejpam-3074	173	7	algebra	algebra	NOUN
ejpam-3074	173	8	is	be	AUX
ejpam-3074	173	9	a	a	DET
ejpam-3074	173	10	power	power	NOUN
ejpam-3074	173	11	of	of	ADP
ejpam-3074	173	12	two	two	NUM
ejpam-3074	173	13	,	,	PUNCT
ejpam-3074	173	14	these	these	PRON
ejpam-3074	173	15	are	be	AUX
ejpam-3074	173	16	the	the	DET
ejpam-3074	173	17	only	only	ADJ
ejpam-3074	173	18	composition	composition	NOUN
ejpam-3074	173	19	algebras	algebra	NOUN
ejpam-3074	173	20	.	.	PUNCT
ejpam-3074	174	1	the	the	DET
ejpam-3074	174	2	solution	solution	NOUN
ejpam-3074	174	3	of	of	ADP
ejpam-3074	174	4	the	the	DET
ejpam-3074	174	5	equation	equation	NOUN
ejpam-3074	174	6	w(as	w(as	PROPN
ejpam-3074	174	7	)	)	PUNCT
ejpam-3074	174	8	=	=	SYM
ejpam-3074	174	9	bw(s	bw(s	NOUN
ejpam-3074	174	10	)	)	PUNCT
ejpam-3074	174	11	in	in	ADP
ejpam-3074	174	12	octonions	octonions	PROPN
ejpam-3074	174	13	,	,	PUNCT
ejpam-3074	174	14	of	of	ADP
ejpam-3074	174	15	which	which	PRON
ejpam-3074	174	16	solutions	solution	NOUN
ejpam-3074	174	17	in	in	ADP
ejpam-3074	174	18	the	the	DET
ejpam-3074	174	19	other	other	ADJ
ejpam-3074	174	20	three	three	NUM
ejpam-3074	174	21	spaces	space	NOUN
ejpam-3074	174	22	are	be	AUX
ejpam-3074	174	23	special	special	ADJ
ejpam-3074	174	24	cases	case	NOUN
ejpam-3074	174	25	,	,	PUNCT
ejpam-3074	174	26	is	be	AUX
ejpam-3074	174	27	given	give	VERB
ejpam-3074	174	28	by	by	ADP
ejpam-3074	174	29	w(r	w(r	PROPN
ejpam-3074	174	30	)	)	PUNCT
ejpam-3074	175	1	=	=	SYM
ejpam-3074	175	2	r	r	X
ejpam-3074	175	3	(	(	PUNCT
ejpam-3074	175	4	ln	ln	NOUN
ejpam-3074	175	5	b	b	PROPN
ejpam-3074	175	6	ln	ln	X
ejpam-3074	175	7	a)p	a)p	X
ejpam-3074	175	8	(	(	PUNCT
ejpam-3074	175	9	ln	ln	NOUN
ejpam-3074	175	10	r	r	NOUN
ejpam-3074	175	11	ln	ln	NOUN
ejpam-3074	175	12	a	a	PRON
ejpam-3074	175	13	)	)	PUNCT
ejpam-3074	175	14	⊕	⊕	PROPN
ejpam-3074	175	15	p	p	NOUN
ejpam-3074	175	16	(	(	PUNCT
ejpam-3074	175	17	ln	ln	NOUN
ejpam-3074	175	18	r	r	NOUN
ejpam-3074	175	19	ln	ln	NOUN
ejpam-3074	175	20	a	a	NOUN
ejpam-3074	175	21	)	)	PUNCT
ejpam-3074	175	22	r	r	NOUN
ejpam-3074	175	23	(	(	PUNCT
ejpam-3074	175	24	ln	ln	NOUN
ejpam-3074	175	25	b	b	PROPN
ejpam-3074	175	26	ln	ln	NOUN
ejpam-3074	175	27	a	a	NOUN
ejpam-3074	175	28	)	)	PUNCT
ejpam-3074	175	29	=	=	SYM
ejpam-3074	175	30	wg(r)⊕	wg(r)⊕	NUM
ejpam-3074	175	31	wd(r	wd(r	NOUN
ejpam-3074	175	32	)	)	PUNCT
ejpam-3074	175	33	(	(	PUNCT
ejpam-3074	175	34	4	4	X
ejpam-3074	175	35	)	)	PUNCT
ejpam-3074	175	36	where	where	SCONJ
ejpam-3074	175	37	a	a	PRON
ejpam-3074	175	38	and	and	CCONJ
ejpam-3074	175	39	b	b	NOUN
ejpam-3074	175	40	are	be	AUX
ejpam-3074	175	41	constants	constant	NOUN
ejpam-3074	175	42	in	in	ADP
ejpam-3074	175	43	,	,	PUNCT
ejpam-3074	175	44	c	c	AUX
ejpam-3074	175	45	,	,	PUNCT
ejpam-3074	175	46	rε	rε	DET
ejpam-3074	175	47	o	o	PROPN
ejpam-3074	175	48	and	and	CCONJ
ejpam-3074	175	49	p	p	X
ejpam-3074	175	50	(	(	PUNCT
ejpam-3074	175	51	ln	ln	NOUN
ejpam-3074	175	52	r	r	NOUN
ejpam-3074	175	53	ln	ln	NOUN
ejpam-3074	175	54	a	a	NOUN
ejpam-3074	175	55	)	)	PUNCT
ejpam-3074	175	56	is	be	AUX
ejpam-3074	175	57	a	a	DET
ejpam-3074	175	58	periodic	periodic	ADJ
ejpam-3074	175	59	function	function	NOUN
ejpam-3074	175	60	of	of	ADP
ejpam-3074	175	61	period	period	NOUN
ejpam-3074	175	62	1	1	NUM
ejpam-3074	175	63	,	,	PUNCT
ejpam-3074	175	64	e.g.	e.g.	ADV
ejpam-3074	175	65	,	,	PUNCT
ejpam-3074	175	66	cos(2πu	cos(2πu	PROPN
ejpam-3074	175	67	)	)	PUNCT
ejpam-3074	175	68	.	.	PUNCT
ejpam-3074	176	1	a	a	DET
ejpam-3074	176	2	constant	constant	ADJ
ejpam-3074	176	3	in	in	ADP
ejpam-3074	176	4	o	o	PROPN
ejpam-3074	176	5	is	be	AUX
ejpam-3074	176	6	of	of	ADP
ejpam-3074	176	7	the	the	DET
ejpam-3074	176	8	form	form	NOUN
ejpam-3074	176	9	a	a	DET
ejpam-3074	176	10	=	=	SYM
ejpam-3074	176	11	a0	a0	NOUN
ejpam-3074	176	12	+	+	CCONJ
ejpam-3074	176	13	0e1	0e1	NUM
ejpam-3074	177	1	+	+	CCONJ
ejpam-3074	177	2	0e2	0e2	NOUN
ejpam-3074	178	1	+	+	CCONJ
ejpam-3074	178	2	0e3	0e3	NUM
ejpam-3074	179	1	+	+	NUM
ejpam-3074	179	2	0e4	0e4	NUM
ejpam-3074	180	1	+	+	CCONJ
ejpam-3074	180	2	0e5	0e5	NUM
ejpam-3074	181	1	+	+	CCONJ
ejpam-3074	181	2	0e6	0e6	X
ejpam-3074	182	1	+	+	CCONJ
ejpam-3074	182	2	0e7	0e7	NUM
ejpam-3074	182	3	,	,	PUNCT
ejpam-3074	182	4	a0εr	a0εr	PUNCT
ejpam-3074	182	5	.	.	PUNCT
ejpam-3074	182	6	using	use	VERB
ejpam-3074	182	7	the	the	DET
ejpam-3074	182	8	transformation	transformation	NOUN
ejpam-3074	182	9	ln	ln	PROPN
ejpam-3074	182	10	b	b	PROPN
ejpam-3074	182	11	ln	ln	NOUN
ejpam-3074	182	12	a	a	DET
ejpam-3074	182	13	=	=	NOUN
ejpam-3074	182	14	r	r	NOUN
ejpam-3074	182	15	or	or	CCONJ
ejpam-3074	182	16	r	r	NOUN
ejpam-3074	182	17	=	=	PUNCT
ejpam-3074	182	18	au	au	X
ejpam-3074	182	19	we	we	PRON
ejpam-3074	182	20	have	have	VERB
ejpam-3074	182	21	w̃(u)a	w̃(u)a	PROPN
ejpam-3074	182	22	(	(	PUNCT
ejpam-3074	182	23	ln	ln	ADJ
ejpam-3074	182	24	bln	bln	PROPN
ejpam-3074	183	1	a)up	a)up	PROPN
ejpam-3074	183	2	(	(	PUNCT
ejpam-3074	183	3	u)⊕	u)⊕	NOUN
ejpam-3074	183	4	a	a	DET
ejpam-3074	183	5	(	(	PUNCT
ejpam-3074	183	6	ln	ln	ADJ
ejpam-3074	183	7	bln	bln	X
ejpam-3074	183	8	a)u	a)u	NOUN
ejpam-3074	183	9	=	=	SYM
ejpam-3074	183	10	w̃g(u)⊕	w̃g(u)⊕	PROPN
ejpam-3074	183	11	w̃d(u	w̃d(u	PROPN
ejpam-3074	183	12	)	)	PUNCT
ejpam-3074	183	13	(	(	PUNCT
ejpam-3074	183	14	5	5	X
ejpam-3074	183	15	)	)	PUNCT
ejpam-3074	183	16	the	the	DET
ejpam-3074	183	17	direct	direct	ADJ
ejpam-3074	183	18	sum	sum	NOUN
ejpam-3074	183	19	of	of	ADP
ejpam-3074	183	20	functions	function	NOUN
ejpam-3074	183	21	is	be	AUX
ejpam-3074	183	22	a	a	DET
ejpam-3074	183	23	formal	formal	ADJ
ejpam-3074	183	24	representation	representation	NOUN
ejpam-3074	183	25	,	,	PUNCT
ejpam-3074	183	26	not	not	PART
ejpam-3074	183	27	exactly	exactly	ADV
ejpam-3074	183	28	a	a	DET
ejpam-3074	183	29	sum	sum	NOUN
ejpam-3074	183	30	of	of	ADP
ejpam-3074	183	31	functions	function	NOUN
ejpam-3074	183	32	.	.	PUNCT
ejpam-3074	184	1	let	let	VERB
ejpam-3074	184	2	u	u	PRON
ejpam-3074	184	3	be	be	AUX
ejpam-3074	184	4	the	the	DET
ejpam-3074	184	5	domain	domain	NOUN
ejpam-3074	184	6	of	of	ADP
ejpam-3074	184	7	definition	definition	NOUN
ejpam-3074	184	8	of	of	ADP
ejpam-3074	184	9	the	the	DET
ejpam-3074	184	10	functions	function	NOUN
ejpam-3074	184	11	given	give	VERB
ejpam-3074	184	12	by	by	ADP
ejpam-3074	184	13	(	(	PUNCT
ejpam-3074	184	14	5	5	NUM
ejpam-3074	184	15	)	)	PUNCT
ejpam-3074	184	16	and	and	CCONJ
ejpam-3074	184	17	let	let	VERB
ejpam-3074	184	18	ug	ug	INTJ
ejpam-3074	185	1	and	and	CCONJ
ejpam-3074	185	2	ud	ud	AUX
ejpam-3074	185	3	be	be	AUX
ejpam-3074	185	4	the	the	DET
ejpam-3074	185	5	domains	domain	NOUN
ejpam-3074	185	6	of	of	ADP
ejpam-3074	185	7	definition	definition	NOUN
ejpam-3074	185	8	of	of	ADP
ejpam-3074	185	9	the	the	DET
ejpam-3074	185	10	functions	function	NOUN
ejpam-3074	185	11	ŵg(u	ŵg(u	PROPN
ejpam-3074	185	12	)	)	PUNCT
ejpam-3074	185	13	and	and	CCONJ
ejpam-3074	185	14	w̃d(u	w̃d(u	PROPN
ejpam-3074	185	15	)	)	PUNCT
ejpam-3074	185	16	,	,	PUNCT
ejpam-3074	185	17	respectively	respectively	ADV
ejpam-3074	185	18	.	.	PUNCT
ejpam-3074	186	1	if	if	SCONJ
ejpam-3074	186	2	ug	ug	ADP
ejpam-3074	186	3	∩	∩	NOUN
ejpam-3074	186	4	ud	ud	ADP
ejpam-3074	186	5	6=	6=	NOUN
ejpam-3074	186	6	∅	∅	NOUN
ejpam-3074	186	7	,	,	PUNCT
ejpam-3074	186	8	w̃g(u	w̃g(u	X
ejpam-3074	186	9	)	)	PUNCT
ejpam-3074	186	10	=	=	PUNCT
ejpam-3074	186	11	w̃d(u	w̃d(u	PROPN
ejpam-3074	186	12	)	)	PUNCT
ejpam-3074	186	13	=	=	SYM
ejpam-3074	186	14	0	0	NUM
ejpam-3074	186	15	for	for	ADP
ejpam-3074	186	16	all	all	DET
ejpam-3074	186	17	uεug	uεug	PROPN
ejpam-3074	186	18	∩	∩	NOUN
ejpam-3074	186	19	ud	ud	ADP
ejpam-3074	186	20	.	.	PUNCT
ejpam-3074	187	1	if	if	SCONJ
ejpam-3074	187	2	the	the	DET
ejpam-3074	187	3	solution	solution	NOUN
ejpam-3074	187	4	to	to	ADP
ejpam-3074	187	5	the	the	DET
ejpam-3074	187	6	equation	equation	NOUN
ejpam-3074	187	7	w(as	w(as	PROPN
ejpam-3074	187	8	)	)	PUNCT
ejpam-3074	187	9	=	=	SYM
ejpam-3074	187	10	bw(s	bw(s	X
ejpam-3074	187	11	)	)	PUNCT
ejpam-3074	187	12	satisfies	satisfy	VERB
ejpam-3074	187	13	w̃(uv	w̃(uv	NOUN
ejpam-3074	187	14	)	)	PUNCT
ejpam-3074	187	15	=	=	SYM
ejpam-3074	187	16	w̃(u)w̃(v	w̃(u)w̃(v	NOUN
ejpam-3074	187	17	)	)	PUNCT
ejpam-3074	187	18	,	,	PUNCT
ejpam-3074	187	19	then	then	ADV
ejpam-3074	187	20	it	it	PRON
ejpam-3074	187	21	would	would	AUX
ejpam-3074	187	22	belong	belong	VERB
ejpam-3074	187	23	to	to	ADP
ejpam-3074	187	24	the	the	DET
ejpam-3074	187	25	group	group	NOUN
ejpam-3074	187	26	of	of	ADP
ejpam-3074	187	27	automorphisms	automorphism	NOUN
ejpam-3074	187	28	of	of	ADP
ejpam-3074	187	29	the	the	DET
ejpam-3074	187	30	octonions	octonions	PROPN
ejpam-3074	187	31	g2	g2	PROPN
ejpam-3074	187	32	.	.	PUNCT
ejpam-3074	188	1	if	if	SCONJ
ejpam-3074	188	2	these	these	DET
ejpam-3074	188	3	functions	function	NOUN
ejpam-3074	188	4	were	be	AUX
ejpam-3074	188	5	dense	dense	ADJ
ejpam-3074	188	6	in	in	ADP
ejpam-3074	188	7	the	the	DET
ejpam-3074	188	8	space	space	NOUN
ejpam-3074	188	9	of	of	ADP
ejpam-3074	188	10	continuous	continuous	ADJ
ejpam-3074	188	11	functions	function	NOUN
ejpam-3074	188	12	defined	define	VERB
ejpam-3074	188	13	on	on	ADP
ejpam-3074	188	14	the	the	DET
ejpam-3074	188	15	octonions	octonion	NOUN
ejpam-3074	188	16	,	,	PUNCT
ejpam-3074	188	17	then	then	ADV
ejpam-3074	188	18	all	all	DET
ejpam-3074	188	19	the	the	DET
ejpam-3074	188	20	functions	function	NOUN
ejpam-3074	188	21	could	could	AUX
ejpam-3074	188	22	be	be	AUX
ejpam-3074	188	23	expressed	express	VERB
ejpam-3074	188	24	as	as	ADP
ejpam-3074	188	25	linear	linear	ADJ
ejpam-3074	188	26	combinations	combination	NOUN
ejpam-3074	188	27	of	of	ADP
ejpam-3074	188	28	the	the	DET
ejpam-3074	188	29	solution	solution	NOUN
ejpam-3074	188	30	of	of	ADP
ejpam-3074	188	31	the	the	DET
ejpam-3074	188	32	equation	equation	NOUN
ejpam-3074	188	33	and	and	CCONJ
ejpam-3074	188	34	they	they	PRON
ejpam-3074	188	35	could	could	AUX
ejpam-3074	188	36	generate	generate	VERB
ejpam-3074	188	37	the	the	DET
ejpam-3074	188	38	group	group	NOUN
ejpam-3074	188	39	of	of	ADP
ejpam-3074	188	40	automorphisms	automorphisms	PROPN
ejpam-3074	188	41	.	.	PUNCT
ejpam-3074	189	1	then	then	ADV
ejpam-3074	189	2	,	,	PUNCT
ejpam-3074	189	3	any	any	DET
ejpam-3074	189	4	representation	representation	NOUN
ejpam-3074	189	5	of	of	ADP
ejpam-3074	189	6	brain	brain	NOUN
ejpam-3074	189	7	activity	activity	NOUN
ejpam-3074	189	8	with	with	ADP
ejpam-3074	189	9	octonions	octonion	NOUN
ejpam-3074	189	10	can	can	AUX
ejpam-3074	189	11	be	be	AUX
ejpam-3074	189	12	expressed	express	VERB
ejpam-3074	189	13	with	with	ADP
ejpam-3074	189	14	the	the	DET
ejpam-3074	189	15	solution	solution	NOUN
ejpam-3074	189	16	of	of	ADP
ejpam-3074	189	17	the	the	DET
ejpam-3074	189	18	equation	equation	NOUN
ejpam-3074	189	19	w(as	w(as	PROPN
ejpam-3074	189	20	)	)	PUNCT
ejpam-3074	189	21	=	=	SYM
ejpam-3074	189	22	bw(s	bw(s	NUM
ejpam-3074	189	23	)	)	PUNCT
ejpam-3074	189	24	.	.	PUNCT
ejpam-3074	190	1	thus	thus	ADV
ejpam-3074	190	2	,	,	PUNCT
ejpam-3074	190	3	the	the	DET
ejpam-3074	190	4	question	question	NOUN
ejpam-3074	190	5	is	be	AUX
ejpam-3074	190	6	:	:	PUNCT
ejpam-3074	190	7	when	when	SCONJ
ejpam-3074	190	8	does	do	VERB
ejpam-3074	190	9	w̃(uv	w̃(uv	NOUN
ejpam-3074	190	10	)	)	PUNCT
ejpam-3074	190	11	=	=	SYM
ejpam-3074	191	1	w̃(u)w̃(v	w̃(u)w̃(v	NOUN
ejpam-3074	191	2	)	)	PUNCT
ejpam-3074	191	3	hold	hold	VERB
ejpam-3074	191	4	for	for	ADP
ejpam-3074	191	5	the	the	DET
ejpam-3074	191	6	solution	solution	NOUN
ejpam-3074	191	7	of	of	ADP
ejpam-3074	191	8	w(as	w(as	PROPN
ejpam-3074	191	9	)	)	PUNCT
ejpam-3074	191	10	=	=	SYM
ejpam-3074	191	11	bw(s	bw(s	PROPN
ejpam-3074	191	12	)	)	PUNCT
ejpam-3074	191	13	?	?	PUNCT
ejpam-3074	192	1	theorem	theorem	NOUN
ejpam-3074	192	2	1	1	NUM
ejpam-3074	192	3	.	.	PUNCT
ejpam-3074	193	1	if	if	SCONJ
ejpam-3074	193	2	the	the	DET
ejpam-3074	193	3	periodic	periodic	ADJ
ejpam-3074	193	4	function	function	NOUN
ejpam-3074	193	5	of	of	ADP
ejpam-3074	193	6	period	period	NOUN
ejpam-3074	193	7	1	1	NUM
ejpam-3074	193	8	,	,	PUNCT
ejpam-3074	193	9	p	p	X
ejpam-3074	193	10	(	(	PUNCT
ejpam-3074	193	11	u	u	NOUN
ejpam-3074	193	12	)	)	PUNCT
ejpam-3074	193	13	satisfies	satisfy	VERB
ejpam-3074	193	14	the	the	DET
ejpam-3074	193	15	semigroup	semigroup	PROPN
ejpam-3074	193	16	condition	condition	NOUN
ejpam-3074	193	17	,	,	PUNCT
ejpam-3074	193	18	p	p	X
ejpam-3074	193	19	(	(	PUNCT
ejpam-3074	193	20	u+	u+	NOUN
ejpam-3074	193	21	v	v	NOUN
ejpam-3074	193	22	)	)	PUNCT
ejpam-3074	194	1	=	=	SYM
ejpam-3074	194	2	p	p	X
ejpam-3074	194	3	(	(	PUNCT
ejpam-3074	194	4	u)p	u)p	ADJ
ejpam-3074	194	5	(	(	PUNCT
ejpam-3074	194	6	v	v	NOUN
ejpam-3074	194	7	)	)	PUNCT
ejpam-3074	194	8	then	then	ADV
ejpam-3074	194	9	w̃(uv	w̃(uv	NOUN
ejpam-3074	194	10	)	)	PUNCT
ejpam-3074	194	11	=	=	SYM
ejpam-3074	194	12	w̃(u)w̃(v	w̃(u)w̃(v	NOUN
ejpam-3074	194	13	)	)	PUNCT
ejpam-3074	194	14	.	.	PUNCT
ejpam-3074	195	1	proof	proof	NOUN
ejpam-3074	195	2	.	.	PUNCT
ejpam-3074	196	1	let	let	VERB
ejpam-3074	196	2	w(r	w(r	NUM
ejpam-3074	196	3	)	)	PUNCT
ejpam-3074	197	1	=	=	SYM
ejpam-3074	197	2	r	r	X
ejpam-3074	197	3	(	(	PUNCT
ejpam-3074	197	4	ln	ln	NOUN
ejpam-3074	197	5	b	b	PROPN
ejpam-3074	197	6	ln	ln	X
ejpam-3074	197	7	a)p	a)p	X
ejpam-3074	197	8	(	(	PUNCT
ejpam-3074	197	9	ln	ln	NOUN
ejpam-3074	197	10	r	r	NOUN
ejpam-3074	197	11	ln	ln	NOUN
ejpam-3074	197	12	a	a	NOUN
ejpam-3074	197	13	)	)	PUNCT
ejpam-3074	197	14	rεo	rεo	NOUN
ejpam-3074	197	15	.	.	PUNCT
ejpam-3074	198	1	we	we	PRON
ejpam-3074	198	2	have	have	VERB
ejpam-3074	198	3	t.	t.	PROPN
ejpam-3074	198	4	l.	l.	PROPN
ejpam-3074	198	5	saaty	saaty	PROPN
ejpam-3074	198	6	,	,	PUNCT
ejpam-3074	198	7	l.	l.	PROPN
ejpam-3074	198	8	g.	g.	PROPN
ejpam-3074	198	9	vargas	vargas	PROPN
ejpam-3074	198	10	/	/	SYM
ejpam-3074	198	11	eur	eur	PROPN
ejpam-3074	198	12	.	.	PUNCT
ejpam-3074	199	1	j.	j.	PROPN
ejpam-3074	199	2	pure	pure	PROPN
ejpam-3074	199	3	appl	appl	PROPN
ejpam-3074	199	4	.	.	PROPN
ejpam-3074	199	5	math	math	PROPN
ejpam-3074	199	6	,	,	PUNCT
ejpam-3074	199	7	10	10	NUM
ejpam-3074	199	8	(	(	PUNCT
ejpam-3074	199	9	4	4	NUM
ejpam-3074	199	10	)	)	PUNCT
ejpam-3074	199	11	(	(	PUNCT
ejpam-3074	199	12	2017	2017	NUM
ejpam-3074	199	13	)	)	PUNCT
ejpam-3074	199	14	,	,	PUNCT
ejpam-3074	199	15	602	602	NUM
ejpam-3074	199	16	-	-	SYM
ejpam-3074	199	17	613	613	NUM
ejpam-3074	199	18	610	610	NUM
ejpam-3074	199	19	w(st	w(st	NOUN
ejpam-3074	199	20	)	)	PUNCT
ejpam-3074	199	21	=	=	SYM
ejpam-3074	200	1	st	st	PROPN
ejpam-3074	200	2	(	(	PUNCT
ejpam-3074	200	3	ln	ln	PROPN
ejpam-3074	200	4	b	b	PROPN
ejpam-3074	200	5	ln	ln	X
ejpam-3074	200	6	a)p	a)p	X
ejpam-3074	200	7	(	(	PUNCT
ejpam-3074	200	8	ln	ln	X
ejpam-3074	200	9	(	(	PUNCT
ejpam-3074	200	10	st	st	PROPN
ejpam-3074	200	11	)	)	PUNCT
ejpam-3074	200	12	ln	ln	NOUN
ejpam-3074	200	13	a	a	NOUN
ejpam-3074	200	14	)	)	PUNCT
ejpam-3074	200	15	=	=	SYM
ejpam-3074	201	1	s	s	X
ejpam-3074	201	2	(	(	PUNCT
ejpam-3074	201	3	ln	ln	NOUN
ejpam-3074	201	4	b	b	PROPN
ejpam-3074	201	5	ln	ln	X
ejpam-3074	201	6	a)t	a)t	ADV
ejpam-3074	201	7	(	(	PUNCT
ejpam-3074	201	8	ln	ln	PROPN
ejpam-3074	201	9	b	b	PROPN
ejpam-3074	201	10	ln	ln	X
ejpam-3074	201	11	a)p	a)p	X
ejpam-3074	201	12	(	(	PUNCT
ejpam-3074	201	13	ln	ln	NOUN
ejpam-3074	201	14	s	s	VERB
ejpam-3074	201	15	ln	ln	NOUN
ejpam-3074	201	16	a	a	PRON
ejpam-3074	201	17	+	+	X
ejpam-3074	201	18	ln	ln	ADJ
ejpam-3074	201	19	t	t	NOUN
ejpam-3074	201	20	ln	ln	NOUN
ejpam-3074	201	21	a	a	NOUN
ejpam-3074	201	22	)	)	PUNCT
ejpam-3074	201	23	substituting	substitute	VERB
ejpam-3074	201	24	s	s	X
ejpam-3074	201	25	=	=	X
ejpam-3074	201	26	au	au	X
ejpam-3074	201	27	and	and	CCONJ
ejpam-3074	201	28	t	t	X
ejpam-3074	202	1	=	=	SYM
ejpam-3074	202	2	av	av	PROPN
ejpam-3074	202	3	we	we	PRON
ejpam-3074	202	4	have	have	VERB
ejpam-3074	202	5	w̃(uv	w̃(uv	NOUN
ejpam-3074	202	6	)	)	PUNCT
ejpam-3074	202	7	=	=	SYM
ejpam-3074	203	1	a	a	PRON
ejpam-3074	203	2	(	(	PUNCT
ejpam-3074	203	3	ln	ln	ADJ
ejpam-3074	203	4	bln	bln	PROPN
ejpam-3074	203	5	a)ua	a)ua	PROPN
ejpam-3074	203	6	(	(	PUNCT
ejpam-3074	203	7	ln	ln	ADJ
ejpam-3074	203	8	bln	bln	PROPN
ejpam-3074	203	9	a)vp	a)vp	PROPN
ejpam-3074	203	10	(	(	PUNCT
ejpam-3074	203	11	u	u	NOUN
ejpam-3074	203	12	+	+	PROPN
ejpam-3074	203	13	v	v	NOUN
ejpam-3074	203	14	)	)	PUNCT
ejpam-3074	203	15	and	and	CCONJ
ejpam-3074	203	16	w̃(uv	w̃(uv	NOUN
ejpam-3074	203	17	)	)	PUNCT
ejpam-3074	203	18	=	=	SYM
ejpam-3074	203	19	w̃(u)w̃(v	w̃(u)w̃(v	NOUN
ejpam-3074	203	20	)	)	PUNCT
ejpam-3074	203	21	obtains	obtain	VERB
ejpam-3074	203	22	if	if	SCONJ
ejpam-3074	203	23	p	p	NOUN
ejpam-3074	203	24	(	(	PUNCT
ejpam-3074	203	25	u+	u+	NOUN
ejpam-3074	203	26	v	v	NOUN
ejpam-3074	203	27	)	)	PUNCT
ejpam-3074	203	28	=	=	SYM
ejpam-3074	204	1	p	p	X
ejpam-3074	204	2	(	(	PUNCT
ejpam-3074	204	3	u)p	u)p	ADJ
ejpam-3074	204	4	(	(	PUNCT
ejpam-3074	204	5	v	v	NOUN
ejpam-3074	204	6	)	)	PUNCT
ejpam-3074	204	7	.	.	PUNCT
ejpam-3074	205	1	q.e.d	q.e.d	PROPN
ejpam-3074	205	2	this	this	DET
ejpam-3074	205	3	theorem	theorem	NOUN
ejpam-3074	205	4	implies	imply	VERB
ejpam-3074	205	5	that	that	SCONJ
ejpam-3074	205	6	the	the	DET
ejpam-3074	205	7	solution	solution	NOUN
ejpam-3074	205	8	of	of	ADP
ejpam-3074	205	9	the	the	DET
ejpam-3074	205	10	functional	functional	ADJ
ejpam-3074	205	11	equation	equation	NOUN
ejpam-3074	205	12	(	(	PUNCT
ejpam-3074	205	13	3	3	X
ejpam-3074	205	14	)	)	PUNCT
ejpam-3074	205	15	belongs	belong	VERB
ejpam-3074	205	16	to	to	ADP
ejpam-3074	205	17	the	the	DET
ejpam-3074	205	18	group	group	NOUN
ejpam-3074	205	19	of	of	ADP
ejpam-3074	205	20	automorphism	automorphism	NOUN
ejpam-3074	205	21	g2	g2	PROPN
ejpam-3074	205	22	.	.	PUNCT
ejpam-3074	206	1	the	the	DET
ejpam-3074	206	2	solution	solution	NOUN
ejpam-3074	206	3	of	of	ADP
ejpam-3074	206	4	the	the	DET
ejpam-3074	206	5	equation	equation	NOUN
ejpam-3074	206	6	w(as	w(as	PROPN
ejpam-3074	206	7	)	)	PUNCT
ejpam-3074	206	8	=	=	SYM
ejpam-3074	206	9	bw(s	bw(s	X
ejpam-3074	206	10	)	)	PUNCT
ejpam-3074	206	11	in	in	ADP
ejpam-3074	206	12	the	the	DET
ejpam-3074	206	13	group	group	NOUN
ejpam-3074	206	14	of	of	ADP
ejpam-3074	206	15	automorphisms	automorphism	NOUN
ejpam-3074	206	16	of	of	ADP
ejpam-3074	206	17	the	the	DET
ejpam-3074	206	18	octonions	octonions	PROPN
ejpam-3074	206	19	g2	g2	PROPN
ejpam-3074	206	20	is	be	AUX
ejpam-3074	206	21	given	give	VERB
ejpam-3074	206	22	by	by	ADP
ejpam-3074	206	23	the	the	DET
ejpam-3074	206	24	damped	damped	ADJ
ejpam-3074	206	25	exponential	exponential	ADJ
ejpam-3074	206	26	function	function	NOUN
ejpam-3074	206	27	w̃(u	w̃(u	NOUN
ejpam-3074	206	28	)	)	PUNCT
ejpam-3074	207	1	=	=	SYM
ejpam-3074	207	2	bue2nπu	bue2nπu	NOUN
ejpam-3074	207	3	(	(	PUNCT
ejpam-3074	207	4	6	6	NUM
ejpam-3074	207	5	)	)	PUNCT
ejpam-3074	207	6	proof	proof	NOUN
ejpam-3074	207	7	.	.	PUNCT
ejpam-3074	208	1	the	the	DET
ejpam-3074	208	2	solution	solution	NOUN
ejpam-3074	208	3	of	of	ADP
ejpam-3074	208	4	the	the	DET
ejpam-3074	208	5	functional	functional	ADJ
ejpam-3074	208	6	equation	equation	NOUN
ejpam-3074	208	7	p	p	NOUN
ejpam-3074	208	8	(	(	PUNCT
ejpam-3074	208	9	u	u	NOUN
ejpam-3074	208	10	+	+	NOUN
ejpam-3074	208	11	v	v	NOUN
ejpam-3074	208	12	)	)	PUNCT
ejpam-3074	209	1	=	=	SYM
ejpam-3074	209	2	p	p	X
ejpam-3074	209	3	(	(	PUNCT
ejpam-3074	209	4	u)p	u)p	ADJ
ejpam-3074	209	5	(	(	PUNCT
ejpam-3074	209	6	v	v	NOUN
ejpam-3074	209	7	)	)	PUNCT
ejpam-3074	209	8	is	be	AUX
ejpam-3074	209	9	given	give	VERB
ejpam-3074	209	10	by	by	ADP
ejpam-3074	209	11	p	p	PROPN
ejpam-3074	209	12	(	(	PUNCT
ejpam-3074	209	13	u	u	NOUN
ejpam-3074	209	14	)	)	PUNCT
ejpam-3074	209	15	=	=	SYM
ejpam-3074	209	16	eu	eu	PROPN
ejpam-3074	209	17	.	.	PROPN
ejpam-3074	210	1	since	since	SCONJ
ejpam-3074	210	2	p	p	PROPN
ejpam-3074	210	3	(	(	PUNCT
ejpam-3074	210	4	.	.	PUNCT
ejpam-3074	210	5	)	)	PUNCT
ejpam-3074	210	6	must	must	AUX
ejpam-3074	210	7	be	be	AUX
ejpam-3074	210	8	a	a	DET
ejpam-3074	210	9	periodic	periodic	ADJ
ejpam-3074	210	10	function	function	NOUN
ejpam-3074	210	11	of	of	ADP
ejpam-3074	210	12	period	period	NOUN
ejpam-3074	210	13	1	1	NUM
ejpam-3074	210	14	,	,	PUNCT
ejpam-3074	210	15	then	then	ADV
ejpam-3074	210	16	p	p	X
ejpam-3074	210	17	(	(	PUNCT
ejpam-3074	210	18	u	u	NOUN
ejpam-3074	210	19	)	)	PUNCT
ejpam-3074	210	20	=	=	SYM
ejpam-3074	210	21	e2nπu	e2nπu	NOUN
ejpam-3074	210	22	is	be	AUX
ejpam-3074	210	23	a	a	DET
ejpam-3074	210	24	possible	possible	ADJ
ejpam-3074	210	25	solution	solution	NOUN
ejpam-3074	210	26	in	in	ADP
ejpam-3074	210	27	the	the	DET
ejpam-3074	210	28	space	space	NOUN
ejpam-3074	210	29	of	of	ADP
ejpam-3074	210	30	the	the	DET
ejpam-3074	210	31	octonions	octonion	NOUN
ejpam-3074	210	32	if	if	SCONJ
ejpam-3074	210	33	the	the	DET
ejpam-3074	210	34	period	period	NOUN
ejpam-3074	210	35	is	be	AUX
ejpam-3074	210	36	the	the	DET
ejpam-3074	210	37	unit	unit	NOUN
ejpam-3074	210	38	octonion	octonion	NOUN
ejpam-3074	210	39	,	,	PUNCT
ejpam-3074	210	40	i.e.	i.e.	X
ejpam-3074	210	41	,	,	PUNCT
ejpam-3074	210	42	1u	1u	NUM
ejpam-3074	210	43	=	=	SYM
ejpam-3074	210	44	e1	e1	PROPN
ejpam-3074	210	45	+	+	CCONJ
ejpam-3074	210	46	e2	e2	NOUN
ejpam-3074	210	47	+	+	CCONJ
ejpam-3074	210	48	e3	e3	NOUN
ejpam-3074	210	49	+	+	CCONJ
ejpam-3074	210	50	e4	e4	PROPN
ejpam-3074	210	51	+	+	CCONJ
ejpam-3074	210	52	e5	e5	PROPN
ejpam-3074	210	53	+	+	CCONJ
ejpam-3074	210	54	e6	e6	PROPN
ejpam-3074	210	55	+	+	CCONJ
ejpam-3074	210	56	e7	e7	PROPN
ejpam-3074	210	57	and	and	CCONJ
ejpam-3074	210	58	p	p	NOUN
ejpam-3074	210	59	(	(	PUNCT
ejpam-3074	210	60	u	u	NOUN
ejpam-3074	210	61	+	+	NOUN
ejpam-3074	210	62	1u	1u	NUM
ejpam-3074	210	63	)	)	PUNCT
ejpam-3074	210	64	=	=	SYM
ejpam-3074	210	65	e2nπ(u+1u	e2nπ(u+1u	NOUN
ejpam-3074	210	66	)	)	PUNCT
ejpam-3074	210	67	=	=	PUNCT
ejpam-3074	211	1	e2nπu+2nπ1u	e2nπu+2nπ1u	PROPN
ejpam-3074	211	2	=	=	SYM
ejpam-3074	211	3	e2nπu	e2nπu	NOUN
ejpam-3074	211	4	since	since	SCONJ
ejpam-3074	211	5	e2nπ1u	e2nπ1u	PART
ejpam-3074	211	6	=	=	SYM
ejpam-3074	211	7	e2nπ(e1+e2+e3+e4+e5+e6+e7	e2nπ(e1+e2+e3+e4+e5+e6+e7	ADJ
ejpam-3074	211	8	)	)	PUNCT
ejpam-3074	211	9	=	=	SYM
ejpam-3074	212	1	1	1	X
ejpam-3074	212	2	.	.	PUNCT
ejpam-3074	212	3	thus	thus	ADV
ejpam-3074	212	4	,	,	PUNCT
ejpam-3074	212	5	the	the	DET
ejpam-3074	212	6	solution	solution	NOUN
ejpam-3074	212	7	of	of	ADP
ejpam-3074	212	8	the	the	DET
ejpam-3074	212	9	equation	equation	NOUN
ejpam-3074	212	10	w(as	w(as	PROPN
ejpam-3074	212	11	)	)	PUNCT
ejpam-3074	212	12	=	=	SYM
ejpam-3074	212	13	bw(s	bw(s	X
ejpam-3074	212	14	)	)	PUNCT
ejpam-3074	212	15	in	in	ADP
ejpam-3074	212	16	the	the	DET
ejpam-3074	212	17	group	group	NOUN
ejpam-3074	212	18	of	of	ADP
ejpam-3074	212	19	automorphisms	automorphism	NOUN
ejpam-3074	212	20	of	of	ADP
ejpam-3074	212	21	the	the	DET
ejpam-3074	212	22	octonions	octonions	PROPN
ejpam-3074	212	23	g2	g2	PROPN
ejpam-3074	212	24	can	can	AUX
ejpam-3074	212	25	be	be	AUX
ejpam-3074	212	26	written	write	VERB
ejpam-3074	212	27	as	as	ADP
ejpam-3074	212	28	w̃(u	w̃(u	PROPN
ejpam-3074	212	29	)	)	PUNCT
ejpam-3074	212	30	=	=	SYM
ejpam-3074	213	1	a	a	PROPN
ejpam-3074	213	2	(	(	PUNCT
ejpam-3074	213	3	ln	ln	ADJ
ejpam-3074	213	4	bln	bln	PROPN
ejpam-3074	213	5	a)ue2nπu⊕e2nπua	a)ue2nπu⊕e2nπua	PROPN
ejpam-3074	213	6	(	(	PUNCT
ejpam-3074	213	7	ln	ln	PROPN
ejpam-3074	213	8	bln	bln	PROPN
ejpam-3074	213	9	a)v	a)v	X
ejpam-3074	213	10	.	.	PUNCT
ejpam-3074	214	1	however	however	ADV
ejpam-3074	214	2	,	,	PUNCT
ejpam-3074	214	3	because	because	SCONJ
ejpam-3074	214	4	a	a	DET
ejpam-3074	214	5	(	(	PUNCT
ejpam-3074	214	6	ln	ln	ADJ
ejpam-3074	214	7	bln	bln	NUM
ejpam-3074	214	8	a)ue2nπu	a)ue2nπu	NOUN
ejpam-3074	214	9	=	=	SYM
ejpam-3074	214	10	bue2nπu	bue2nπu	NOUN
ejpam-3074	215	1	=	=	PUNCT
ejpam-3074	215	2	e(2nπ+lnb)u	e(2nπ+lnb)u	NOUN
ejpam-3074	215	3	there	there	PRON
ejpam-3074	215	4	is	be	VERB
ejpam-3074	215	5	no	no	DET
ejpam-3074	215	6	need	need	NOUN
ejpam-3074	215	7	to	to	PART
ejpam-3074	215	8	use	use	VERB
ejpam-3074	215	9	the	the	DET
ejpam-3074	215	10	direct	direct	ADJ
ejpam-3074	215	11	sum	sum	NOUN
ejpam-3074	215	12	and	and	CCONJ
ejpam-3074	215	13	we	we	PRON
ejpam-3074	215	14	have	have	AUX
ejpam-3074	215	15	w̃(u	w̃(u	PROPN
ejpam-3074	215	16	)	)	PUNCT
ejpam-3074	215	17	=	=	SYM
ejpam-3074	215	18	bue2nπu	bue2nπu	NOUN
ejpam-3074	215	19	.	.	PUNCT
ejpam-3074	216	1	manogue	manogue	NOUN
ejpam-3074	216	2	and	and	CCONJ
ejpam-3074	216	3	schray	schray	VERB
ejpam-3074	216	4	[	[	X
ejpam-3074	216	5	9	9	NUM
ejpam-3074	216	6	]	]	PUNCT
ejpam-3074	216	7	showed	show	VERB
ejpam-3074	216	8	that	that	SCONJ
ejpam-3074	216	9	the	the	DET
ejpam-3074	216	10	automorphisms	automorphism	NOUN
ejpam-3074	216	11	of	of	ADP
ejpam-3074	216	12	o	o	PROPN
ejpam-3074	216	13	can	can	AUX
ejpam-3074	216	14	be	be	AUX
ejpam-3074	216	15	generated	generate	VERB
ejpam-3074	216	16	by	by	ADP
ejpam-3074	216	17	octonions	octonion	NOUN
ejpam-3074	216	18	of	of	ADP
ejpam-3074	216	19	the	the	DET
ejpam-3074	216	20	form	form	NOUN
ejpam-3074	216	21	eûθ+cos(θ)+	eûθ+cos(θ)+	NOUN
ejpam-3074	216	22	ûsin(θ	ûsin(θ	NOUN
ejpam-3074	216	23	)	)	PUNCT
ejpam-3074	216	24	with	with	ADP
ejpam-3074	216	25	û	û	PRON
ejpam-3074	216	26	a	a	DET
ejpam-3074	216	27	pure	pure	ADJ
ejpam-3074	216	28	imaginary	imaginary	ADJ
ejpam-3074	216	29	,	,	PUNCT
ejpam-3074	216	30	unit	unit	NOUN
ejpam-3074	216	31	octonion	octonion	NOUN
ejpam-3074	216	32	,	,	PUNCT
ejpam-3074	216	33	but	but	CCONJ
ejpam-3074	216	34	where	where	SCONJ
ejpam-3074	216	35	θ	θ	PROPN
ejpam-3074	216	36	must	must	AUX
ejpam-3074	216	37	be	be	AUX
ejpam-3074	216	38	restricted	restrict	VERB
ejpam-3074	216	39	to	to	PART
ejpam-3074	216	40	be	be	AUX
ejpam-3074	216	41	a	a	DET
ejpam-3074	216	42	multiple	multiple	NOUN
ejpam-3074	216	43	of	of	ADP
ejpam-3074	216	44	π/3	π/3	PROPN
ejpam-3074	216	45	,	,	PUNCT
ejpam-3074	216	46	corresponding	correspond	VERB
ejpam-3074	216	47	to	to	ADP
ejpam-3074	216	48	the	the	DET
ejpam-3074	216	49	sixth	sixth	ADJ
ejpam-3074	216	50	roots	root	NOUN
ejpam-3074	216	51	of	of	ADP
ejpam-3074	216	52	unity	unity	NOUN
ejpam-3074	216	53	,	,	PUNCT
ejpam-3074	216	54	i.e.	i.e.	X
ejpam-3074	216	55	,	,	PUNCT
ejpam-3074	216	56	ek	ek	X
ejpam-3074	216	57	(	(	PUNCT
ejpam-3074	216	58	π	π	PROPN
ejpam-3074	216	59	3	3	NUM
ejpam-3074	216	60	)	)	PUNCT
ejpam-3074	216	61	û	û	PROPN
ejpam-3074	216	62	,	,	PUNCT
ejpam-3074	216	63	k	k	NOUN
ejpam-3074	216	64	=	=	SYM
ejpam-3074	216	65	0	0	NUM
ejpam-3074	216	66	,	,	PUNCT
ejpam-3074	216	67	...	...	PUNCT
ejpam-3074	216	68	,	,	PUNCT
ejpam-3074	216	69	5	5	X
ejpam-3074	216	70	.	.	PUNCT
ejpam-3074	217	1	thus	thus	ADV
ejpam-3074	217	2	,	,	PUNCT
ejpam-3074	217	3	if	if	SCONJ
ejpam-3074	217	4	2nπ	2nπ	NOUN
ejpam-3074	217	5	+	+	CCONJ
ejpam-3074	217	6	lnb	lnb	PROPN
ejpam-3074	217	7	=	=	SYM
ejpam-3074	217	8	k	k	PROPN
ejpam-3074	217	9	(	(	PUNCT
ejpam-3074	217	10	π	π	NOUN
ejpam-3074	217	11	3	3	NUM
ejpam-3074	217	12	)	)	PUNCT
ejpam-3074	217	13	or	or	CCONJ
ejpam-3074	217	14	b	b	X
ejpam-3074	218	1	=	=	NOUN
ejpam-3074	218	2	e(k−6n)π	e(k−6n)π	NOUN
ejpam-3074	218	3	3	3	NUM
ejpam-3074	218	4	the	the	DET
ejpam-3074	218	5	solution	solution	NOUN
ejpam-3074	218	6	of	of	ADP
ejpam-3074	218	7	the	the	DET
ejpam-3074	218	8	functional	functional	ADJ
ejpam-3074	218	9	equation	equation	NOUN
ejpam-3074	218	10	(	(	PUNCT
ejpam-3074	218	11	3	3	X
ejpam-3074	218	12	)	)	PUNCT
ejpam-3074	218	13	can	can	AUX
ejpam-3074	218	14	generate	generate	VERB
ejpam-3074	218	15	the	the	DET
ejpam-3074	218	16	group	group	NOUN
ejpam-3074	218	17	of	of	ADP
ejpam-3074	218	18	automorphism	automorphism	NOUN
ejpam-3074	218	19	g2	g2	PROPN
ejpam-3074	218	20	.	.	PUNCT
ejpam-3074	219	1	5	5	NUM
ejpam-3074	219	2	.	.	X
ejpam-3074	219	3	synthesis	synthesis	NOUN
ejpam-3074	219	4	of	of	ADP
ejpam-3074	219	5	neural	neural	ADJ
ejpam-3074	219	6	responses	response	NOUN
ejpam-3074	219	7	let	let	VERB
ejpam-3074	219	8	us	we	PRON
ejpam-3074	219	9	assume	assume	VERB
ejpam-3074	219	10	that	that	SCONJ
ejpam-3074	219	11	the	the	DET
ejpam-3074	219	12	response	response	NOUN
ejpam-3074	219	13	of	of	ADP
ejpam-3074	219	14	the	the	DET
ejpam-3074	219	15	brain	brain	NOUN
ejpam-3074	219	16	to	to	ADP
ejpam-3074	219	17	each	each	DET
ejpam-3074	219	18	distinct	distinct	ADJ
ejpam-3074	219	19	type	type	NOUN
ejpam-3074	219	20	of	of	ADP
ejpam-3074	219	21	information	information	NOUN
ejpam-3074	219	22	obtained	obtain	VERB
ejpam-3074	219	23	from	from	ADP
ejpam-3074	219	24	senses	sense	NOUN
ejpam-3074	219	25	or	or	CCONJ
ejpam-3074	219	26	generated	generate	VERB
ejpam-3074	219	27	form	form	NOUN
ejpam-3074	219	28	within	within	ADP
ejpam-3074	219	29	the	the	DET
ejpam-3074	219	30	brain	brain	NOUN
ejpam-3074	219	31	satisfies	satisfy	VERB
ejpam-3074	219	32	the	the	DET
ejpam-3074	219	33	equation	equation	NOUN
ejpam-3074	219	34	w(as	w(as	PROPN
ejpam-3074	219	35	)	)	PUNCT
ejpam-3074	219	36	=	=	SYM
ejpam-3074	219	37	bw(s	bw(s	NOUN
ejpam-3074	219	38	)	)	PUNCT
ejpam-3074	219	39	,	,	PUNCT
ejpam-3074	219	40	and	and	CCONJ
ejpam-3074	219	41	hence	hence	ADV
ejpam-3074	219	42	,	,	PUNCT
ejpam-3074	219	43	the	the	DET
ejpam-3074	219	44	response	response	NOUN
ejpam-3074	219	45	can	can	AUX
ejpam-3074	219	46	be	be	AUX
ejpam-3074	219	47	modeled	model	VERB
ejpam-3074	219	48	by	by	ADP
ejpam-3074	219	49	the	the	DET
ejpam-3074	219	50	function	function	NOUN
ejpam-3074	219	51	w̃(u	w̃(u	PROPN
ejpam-3074	219	52	)	)	PUNCT
ejpam-3074	220	1	=	=	SYM
ejpam-3074	220	2	bue2nπu	bue2nπu	NOUN
ejpam-3074	220	3	.	.	PUNCT
ejpam-3074	221	1	now	now	ADV
ejpam-3074	221	2	all	all	DET
ejpam-3074	221	3	the	the	DET
ejpam-3074	221	4	different	different	ADJ
ejpam-3074	221	5	types	type	NOUN
ejpam-3074	221	6	of	of	ADP
ejpam-3074	221	7	responses	response	NOUN
ejpam-3074	221	8	need	need	VERB
ejpam-3074	221	9	to	to	PART
ejpam-3074	221	10	be	be	AUX
ejpam-3074	221	11	synthesized	synthesize	VERB
ejpam-3074	221	12	to	to	PART
ejpam-3074	221	13	create	create	VERB
ejpam-3074	221	14	a	a	DET
ejpam-3074	221	15	consistent	consistent	ADJ
ejpam-3074	221	16	picture	picture	NOUN
ejpam-3074	221	17	of	of	ADP
ejpam-3074	221	18	the	the	DET
ejpam-3074	221	19	functioning	functioning	NOUN
ejpam-3074	221	20	of	of	ADP
ejpam-3074	221	21	the	the	DET
ejpam-3074	221	22	brain	brain	NOUN
ejpam-3074	221	23	at	at	ADP
ejpam-3074	221	24	any	any	DET
ejpam-3074	221	25	point	point	NOUN
ejpam-3074	221	26	in	in	ADP
ejpam-3074	221	27	time	time	NOUN
ejpam-3074	221	28	.	.	PUNCT
ejpam-3074	222	1	the	the	DET
ejpam-3074	222	2	synthesizing	synthesize	VERB
ejpam-3074	222	3	principle	principle	NOUN
ejpam-3074	222	4	is	be	AUX
ejpam-3074	222	5	a	a	DET
ejpam-3074	222	6	solution	solution	NOUN
ejpam-3074	222	7	of	of	ADP
ejpam-3074	222	8	the	the	DET
ejpam-3074	222	9	functional	functional	ADJ
ejpam-3074	222	10	equation	equation	NOUN
ejpam-3074	222	11	w(as	w(as	PROPN
ejpam-3074	222	12	)	)	PUNCT
ejpam-3074	222	13	=	=	SYM
ejpam-3074	222	14	bw(s	bw(s	X
ejpam-3074	222	15	)	)	PUNCT
ejpam-3074	222	16	in	in	ADP
ejpam-3074	222	17	operator	operator	NOUN
ejpam-3074	222	18	form	form	NOUN
ejpam-3074	222	19	given	give	VERB
ejpam-3074	222	20	by	by	ADP
ejpam-3074	222	21	brillouet	brillouet	NOUN
ejpam-3074	222	22	-	-	PUNCT
ejpam-3074	222	23	bellout	bellout	NOUN
ejpam-3074	222	24	[	[	X
ejpam-3074	222	25	3	3	NUM
ejpam-3074	222	26	]	]	PUNCT
ejpam-3074	222	27	w(αx	w(αx	PROPN
ejpam-3074	222	28	)	)	PUNCT
ejpam-3074	222	29	=	=	SYM
ejpam-3074	222	30	βw(x	βw(x	NUM
ejpam-3074	222	31	)	)	PUNCT
ejpam-3074	222	32	.	.	PUNCT
ejpam-3074	223	1	(	(	PUNCT
ejpam-3074	223	2	7	7	X
ejpam-3074	223	3	)	)	PUNCT
ejpam-3074	223	4	the	the	DET
ejpam-3074	223	5	operator	operator	NOUN
ejpam-3074	223	6	w	w	PROPN
ejpam-3074	223	7	,	,	PUNCT
ejpam-3074	223	8	defined	define	VERB
ejpam-3074	223	9	from	from	ADP
ejpam-3074	223	10	a	a	DET
ejpam-3074	223	11	normed	normed	ADJ
ejpam-3074	223	12	linear	linear	ADJ
ejpam-3074	223	13	space	space	NOUN
ejpam-3074	223	14	e	e	NOUN
ejpam-3074	223	15	to	to	ADP
ejpam-3074	223	16	another	another	DET
ejpam-3074	223	17	normed	norme	VERB
ejpam-3074	223	18	linear	linear	ADJ
ejpam-3074	223	19	space	space	NOUN
ejpam-3074	223	20	g	g	NOUN
ejpam-3074	223	21	,	,	PUNCT
ejpam-3074	223	22	w	w	NOUN
ejpam-3074	223	23	:	:	PUNCT
ejpam-3074	223	24	e	e	X
ejpam-3074	223	25	→	→	SYM
ejpam-3074	223	26	g	g	PROPN
ejpam-3074	223	27	,	,	PUNCT
ejpam-3074	223	28	is	be	AUX
ejpam-3074	223	29	a	a	DET
ejpam-3074	223	30	way	way	NOUN
ejpam-3074	223	31	of	of	ADP
ejpam-3074	223	32	thinking	think	VERB
ejpam-3074	223	33	about	about	ADP
ejpam-3074	223	34	synthesis	synthesis	NOUN
ejpam-3074	223	35	of	of	ADP
ejpam-3074	223	36	neural	neural	ADJ
ejpam-3074	223	37	responses	response	NOUN
ejpam-3074	223	38	.	.	PUNCT
ejpam-3074	224	1	for	for	ADP
ejpam-3074	224	2	example	example	NOUN
ejpam-3074	224	3	,	,	PUNCT
ejpam-3074	224	4	if	if	SCONJ
ejpam-3074	224	5	t.	t.	PROPN
ejpam-3074	224	6	l.	l.	PROPN
ejpam-3074	224	7	saaty	saaty	PROPN
ejpam-3074	224	8	,	,	PUNCT
ejpam-3074	224	9	l.	l.	PROPN
ejpam-3074	224	10	g.	g.	PROPN
ejpam-3074	224	11	vargas	vargas	PROPN
ejpam-3074	224	12	/	/	SYM
ejpam-3074	224	13	eur	eur	PROPN
ejpam-3074	224	14	.	.	PUNCT
ejpam-3074	225	1	j.	j.	PROPN
ejpam-3074	225	2	pure	pure	PROPN
ejpam-3074	225	3	appl	appl	PROPN
ejpam-3074	225	4	.	.	PROPN
ejpam-3074	225	5	math	math	PROPN
ejpam-3074	225	6	,	,	PUNCT
ejpam-3074	225	7	10	10	NUM
ejpam-3074	225	8	(	(	PUNCT
ejpam-3074	225	9	4	4	NUM
ejpam-3074	225	10	)	)	PUNCT
ejpam-3074	225	11	(	(	PUNCT
ejpam-3074	225	12	2017	2017	NUM
ejpam-3074	225	13	)	)	PUNCT
ejpam-3074	225	14	,	,	PUNCT
ejpam-3074	225	15	602	602	NUM
ejpam-3074	225	16	-	-	SYM
ejpam-3074	225	17	613	613	NUM
ejpam-3074	225	18	611	611	NUM
ejpam-3074	225	19	α	α	NOUN
ejpam-3074	225	20	is	be	AUX
ejpam-3074	225	21	a	a	DET
ejpam-3074	225	22	root	root	NOUN
ejpam-3074	225	23	of	of	ADP
ejpam-3074	225	24	1	1	NUM
ejpam-3074	225	25	of	of	ADP
ejpam-3074	225	26	order	order	NOUN
ejpam-3074	225	27	n	n	CCONJ
ejpam-3074	225	28	,	,	PUNCT
ejpam-3074	225	29	and	and	CCONJ
ejpam-3074	225	30	βn	βn	NOUN
ejpam-3074	225	31	=	=	SYM
ejpam-3074	225	32	1	1	NUM
ejpam-3074	225	33	there	there	PRON
ejpam-3074	225	34	exists	exist	VERB
ejpam-3074	225	35	a	a	DET
ejpam-3074	225	36	unique	unique	ADJ
ejpam-3074	225	37	p	p	NOUN
ejpam-3074	225	38	in	in	ADP
ejpam-3074	225	39	{	{	PUNCT
ejpam-3074	225	40	0.1	0.1	NUM
ejpam-3074	225	41	,	,	PUNCT
ejpam-3074	225	42	...	...	PUNCT
ejpam-3074	225	43	,	,	PUNCT
ejpam-3074	225	44	n−	n−	NOUN
ejpam-3074	225	45	1	1	NUM
ejpam-3074	225	46	}	}	PUNCT
ejpam-3074	225	47	such	such	ADJ
ejpam-3074	225	48	that	that	SCONJ
ejpam-3074	225	49	β	β	NOUN
ejpam-3074	225	50	=	=	PUNCT
ejpam-3074	225	51	αp	αp	NOUN
ejpam-3074	225	52	and	and	CCONJ
ejpam-3074	225	53	the	the	DET
ejpam-3074	225	54	solution	solution	NOUN
ejpam-3074	225	55	of	of	ADP
ejpam-3074	225	56	the	the	DET
ejpam-3074	225	57	functional	functional	ADJ
ejpam-3074	225	58	equation	equation	NOUN
ejpam-3074	225	59	in	in	ADP
ejpam-3074	225	60	operator	operator	NOUN
ejpam-3074	225	61	form	form	NOUN
ejpam-3074	225	62	(	(	PUNCT
ejpam-3074	225	63	7	7	X
ejpam-3074	225	64	)	)	PUNCT
ejpam-3074	225	65	is	be	AUX
ejpam-3074	225	66	given	give	VERB
ejpam-3074	225	67	by	by	ADP
ejpam-3074	225	68	w(x1	w(x1	NOUN
ejpam-3074	225	69	,	,	PUNCT
ejpam-3074	225	70	...	...	PUNCT
ejpam-3074	225	71	,	,	PUNCT
ejpam-3074	225	72	xq	xq	PROPN
ejpam-3074	225	73	)	)	PUNCT
ejpam-3074	226	1	=	=	SYM
ejpam-3074	226	2	∑	∑	PROPN
ejpam-3074	226	3	(	(	PUNCT
ejpam-3074	226	4	n1,	n1,	ADJ
ejpam-3074	226	5	...	...	NOUN
ejpam-3074	226	6	,nq)εj	,nq)εj	PUNCT
ejpam-3074	226	7	an1,	an1,	NOUN
ejpam-3074	226	8	...	...	PUNCT
ejpam-3074	226	9	,nqx	,nqx	PUNCT
ejpam-3074	226	10	n1	n1	PROPN
ejpam-3074	226	11	1	1	NUM
ejpam-3074	226	12	xn2	xn2	NOUN
ejpam-3074	226	13	2	2	NUM
ejpam-3074	226	14	...	...	PUNCT
ejpam-3074	226	15	x	x	X
ejpam-3074	226	16	nq	nq	PROPN
ejpam-3074	226	17	q	q	X
ejpam-3074	226	18	(	(	PUNCT
ejpam-3074	226	19	8)	8)	NUM
ejpam-3074	226	20	where	where	SCONJ
ejpam-3074	226	21	j	j	PROPN
ejpam-3074	226	22	=	=	PRON
ejpam-3074	226	23	{	{	PUNCT
ejpam-3074	226	24	(	(	PUNCT
ejpam-3074	226	25	n1	n1	NOUN
ejpam-3074	226	26	,	,	PUNCT
ejpam-3074	226	27	...	...	PUNCT
ejpam-3074	226	28	,	,	PUNCT
ejpam-3074	226	29	nq	nq	X
ejpam-3074	226	30	)	)	PUNCT
ejpam-3074	226	31	∈	∈	PROPN
ejpam-3074	226	32	nq|n1	nq|n1	VERB
ejpam-3074	226	33	+	+	X
ejpam-3074	226	34	...	...	PUNCT
ejpam-3074	226	35	+	+	CCONJ
ejpam-3074	226	36	nq	nq	PROPN
ejpam-3074	226	37	=	=	PROPN
ejpam-3074	226	38	p+	p+	PROPN
ejpam-3074	226	39	jn	jn	PROPN
ejpam-3074	226	40	,	,	PUNCT
ejpam-3074	226	41	for	for	ADP
ejpam-3074	226	42	some	some	DET
ejpam-3074	226	43	j	j	PROPN
ejpam-3074	226	44	∈	∈	PROPN
ejpam-3074	226	45	n	n	ADV
ejpam-3074	226	46	and	and	CCONJ
ejpam-3074	226	47	an1,	an1,	ADJ
ejpam-3074	226	48	...	...	PUNCT
ejpam-3074	226	49	,nq	,nq	PUNCT
ejpam-3074	226	50	∈	∈	PROPN
ejpam-3074	226	51	g	g	ADP
ejpam-3074	226	52	the	the	DET
ejpam-3074	226	53	solution	solution	NOUN
ejpam-3074	226	54	(	(	PUNCT
ejpam-3074	226	55	8)	8)	NUM
ejpam-3074	226	56	will	will	AUX
ejpam-3074	226	57	allow	allow	VERB
ejpam-3074	226	58	us	we	PRON
ejpam-3074	226	59	to	to	PART
ejpam-3074	226	60	synthesize	synthesize	VERB
ejpam-3074	226	61	the	the	DET
ejpam-3074	226	62	functions	function	NOUN
ejpam-3074	226	63	given	give	VERB
ejpam-3074	226	64	by	by	ADP
ejpam-3074	226	65	(	(	PUNCT
ejpam-3074	226	66	6	6	NUM
ejpam-3074	226	67	)	)	PUNCT
ejpam-3074	226	68	.	.	PUNCT
ejpam-3074	227	1	each	each	PRON
ejpam-3074	227	2	of	of	ADP
ejpam-3074	227	3	the	the	DET
ejpam-3074	227	4	components	component	NOUN
ejpam-3074	227	5	of	of	ADP
ejpam-3074	227	6	(	(	PUNCT
ejpam-3074	227	7	8)	8)	NUM
ejpam-3074	227	8	could	could	AUX
ejpam-3074	227	9	be	be	AUX
ejpam-3074	227	10	the	the	DET
ejpam-3074	227	11	functions	function	NOUN
ejpam-3074	227	12	given	give	VERB
ejpam-3074	227	13	by	by	ADP
ejpam-3074	227	14	(	(	PUNCT
ejpam-3074	227	15	6	6	NUM
ejpam-3074	227	16	)	)	PUNCT
ejpam-3074	227	17	.	.	PUNCT
ejpam-3074	228	1	hence	hence	ADV
ejpam-3074	228	2	,	,	PUNCT
ejpam-3074	228	3	for	for	SCONJ
ejpam-3074	228	4	the	the	DET
ejpam-3074	228	5	group	group	NOUN
ejpam-3074	228	6	of	of	ADP
ejpam-3074	228	7	automorphisms	automorphism	NOUN
ejpam-3074	228	8	of	of	ADP
ejpam-3074	228	9	the	the	DET
ejpam-3074	228	10	octonions	octonions	PROPN
ejpam-3074	228	11	g2	g2	PROPN
ejpam-3074	228	12	,	,	PUNCT
ejpam-3074	228	13	synthesis	synthesis	NOUN
ejpam-3074	228	14	of	of	ADP
ejpam-3074	228	15	the	the	DET
ejpam-3074	228	16	firing	firing	NOUN
ejpam-3074	228	17	of	of	ADP
ejpam-3074	228	18	neurons	neuron	NOUN
ejpam-3074	228	19	under	under	ADP
ejpam-3074	228	20	the	the	DET
ejpam-3074	228	21	conditions	condition	NOUN
ejpam-3074	228	22	of	of	ADP
ejpam-3074	228	23	equation	equation	NOUN
ejpam-3074	228	24	(	(	PUNCT
ejpam-3074	228	25	8)	8)	NUM
ejpam-3074	228	26	is	be	AUX
ejpam-3074	228	27	given	give	VERB
ejpam-3074	228	28	by	by	ADP
ejpam-3074	228	29	w(x1	w(x1	NOUN
ejpam-3074	228	30	,	,	PUNCT
ejpam-3074	228	31	...	...	PUNCT
ejpam-3074	228	32	,	,	PUNCT
ejpam-3074	228	33	xq	xq	PROPN
ejpam-3074	228	34	)	)	PUNCT
ejpam-3074	228	35	=	=	SYM
ejpam-3074	228	36	∑	∑	PROPN
ejpam-3074	228	37	(	(	PUNCT
ejpam-3074	228	38	n1,	n1,	ADJ
ejpam-3074	228	39	...	...	NOUN
ejpam-3074	228	40	,nq)εj	,nq)εj	PUNCT
ejpam-3074	228	41	an1,	an1,	NOUN
ejpam-3074	228	42	...	...	PUNCT
ejpam-3074	228	43	,nqx	,nqx	PUNCT
ejpam-3074	228	44	n1	n1	PROPN
ejpam-3074	228	45	1	1	NUM
ejpam-3074	228	46	...	...	PUNCT
ejpam-3074	228	47	x	x	X
ejpam-3074	228	48	nq	nq	PROPN
ejpam-3074	228	49	q	q	PROPN
ejpam-3074	228	50	.	.	PUNCT
ejpam-3074	229	1	thus	thus	ADV
ejpam-3074	229	2	for	for	ADP
ejpam-3074	229	3	w̃i(u)εxi	w̃i(u)εxi	NUM
ejpam-3074	229	4	,	,	PUNCT
ejpam-3074	229	5	i	i	NOUN
ejpam-3074	229	6	=	=	NOUN
ejpam-3074	229	7	1	1	NUM
ejpam-3074	229	8	,	,	PUNCT
ejpam-3074	229	9	2	2	NUM
ejpam-3074	229	10	,	,	PUNCT
ejpam-3074	229	11	...	...	PUNCT
ejpam-3074	229	12	,	,	PUNCT
ejpam-3074	229	13	q	q	PUNCT
ejpam-3074	229	14	we	we	PRON
ejpam-3074	229	15	have	have	VERB
ejpam-3074	229	16	w	w	PROPN
ejpam-3074	229	17	(	(	PUNCT
ejpam-3074	229	18	w̃1	w̃1	PROPN
ejpam-3074	229	19	,	,	PUNCT
ejpam-3074	229	20	...	...	PUNCT
ejpam-3074	229	21	,	,	PUNCT
ejpam-3074	229	22	w̃q	w̃q	X
ejpam-3074	229	23	)	)	PUNCT
ejpam-3074	229	24	=	=	SYM
ejpam-3074	229	25	∑	∑	PROPN
ejpam-3074	229	26	(	(	PUNCT
ejpam-3074	229	27	n1,	n1,	ADJ
ejpam-3074	229	28	...	...	NOUN
ejpam-3074	229	29	,nq)εj	,nq)εj	PUNCT
ejpam-3074	229	30	an1,	an1,	NOUN
ejpam-3074	229	31	...	...	PUNCT
ejpam-3074	229	32	,nq	,nq	PUNCT
ejpam-3074	229	33	w̃1(u1)n1w̃q(uq	w̃1(u1)n1w̃q(uq	PROPN
ejpam-3074	229	34	)	)	PUNCT
ejpam-3074	229	35	nq	nq	PROPN
ejpam-3074	229	36	=	=	PUNCT
ejpam-3074	229	37	∑	∑	PROPN
ejpam-3074	229	38	(	(	PUNCT
ejpam-3074	229	39	n1,	n1,	ADJ
ejpam-3074	229	40	...	...	NOUN
ejpam-3074	229	41	,nq)εj	,nq)εj	PUNCT
ejpam-3074	229	42	an1,	an1,	NOUN
ejpam-3074	229	43	...	...	PUNCT
ejpam-3074	229	44	,nq	,nq	PUNCT
ejpam-3074	229	45	[	[	PUNCT
ejpam-3074	229	46	b1	b1	NOUN
ejpam-3074	229	47	u1e2nπu1	u1e2nπu1	ADP
ejpam-3074	229	48	]	]	X
ejpam-3074	229	49	n1	n1	NOUN
ejpam-3074	229	50	...	...	PUNCT
ejpam-3074	229	51	[	[	PUNCT
ejpam-3074	229	52	bq	bq	INTJ
ejpam-3074	229	53	uqe2nπuq	uqe2nπuq	PROPN
ejpam-3074	229	54	]	]	SYM
ejpam-3074	229	55	nq	nq	X
ejpam-3074	229	56	(	(	PUNCT
ejpam-3074	229	57	9	9	NUM
ejpam-3074	229	58	)	)	PUNCT
ejpam-3074	229	59	=	=	SYM
ejpam-3074	229	60	∑	∑	PROPN
ejpam-3074	229	61	(	(	PUNCT
ejpam-3074	229	62	n1,	n1,	ADJ
ejpam-3074	229	63	...	...	NOUN
ejpam-3074	229	64	,nq)εj	,nq)εj	PUNCT
ejpam-3074	229	65	an1,	an1,	NOUN
ejpam-3074	229	66	...	...	PUNCT
ejpam-3074	229	67	,nq	,nq	PUNCT
ejpam-3074	230	1	q∏	q∏	PROPN
ejpam-3074	230	2	i=1	i=1	PROPN
ejpam-3074	230	3	eni(2nπ+lnbi)ui	eni(2nπ+lnbi)ui	PROPN
ejpam-3074	230	4	,	,	PUNCT
ejpam-3074	230	5	uiεo	uiεo	SCONJ
ejpam-3074	230	6	note	note	VERB
ejpam-3074	230	7	the	the	DET
ejpam-3074	230	8	similarity	similarity	NOUN
ejpam-3074	230	9	of	of	ADP
ejpam-3074	230	10	expression	expression	NOUN
ejpam-3074	230	11	(	(	PUNCT
ejpam-3074	230	12	9	9	NUM
ejpam-3074	230	13	)	)	PUNCT
ejpam-3074	230	14	with	with	ADP
ejpam-3074	230	15	the	the	DET
ejpam-3074	230	16	fourier	fourier	PROPN
ejpam-3074	230	17	series	series	NOUN
ejpam-3074	230	18	approximation	approximation	NOUN
ejpam-3074	230	19	of	of	ADP
ejpam-3074	230	20	a	a	DET
ejpam-3074	230	21	real	real	ADJ
ejpam-3074	230	22	periodic	periodic	ADJ
ejpam-3074	230	23	function	function	NOUN
ejpam-3074	230	24	of	of	ADP
ejpam-3074	230	25	period	period	NOUN
ejpam-3074	230	26	l	l	NOUN
ejpam-3074	230	27	in	in	ADP
ejpam-3074	230	28	o	o	PROPN
ejpam-3074	230	29	(	(	PUNCT
ejpam-3074	230	30	martinez	martinez	PROPN
ejpam-3074	230	31	et	et	PROPN
ejpam-3074	230	32	al	al	PROPN
ejpam-3074	230	33	.	.	PUNCT
ejpam-3074	231	1	[	[	X
ejpam-3074	231	2	10	10	NUM
ejpam-3074	231	3	]	]	PUNCT
ejpam-3074	231	4	.	.	PUNCT
ejpam-3074	232	1	for	for	ADP
ejpam-3074	232	2	l	l	NOUN
ejpam-3074	232	3	=	=	SYM
ejpam-3074	232	4	1	1	NUM
ejpam-3074	232	5	the	the	DET
ejpam-3074	232	6	fourier	fourier	NOUN
ejpam-3074	232	7	series	series	NOUN
ejpam-3074	232	8	approximation	approximation	NOUN
ejpam-3074	232	9	of	of	ADP
ejpam-3074	232	10	the	the	DET
ejpam-3074	232	11	function	function	NOUN
ejpam-3074	232	12	p	p	NOUN
ejpam-3074	232	13	(	(	PUNCT
ejpam-3074	232	14	u	u	NOUN
ejpam-3074	232	15	)	)	PUNCT
ejpam-3074	232	16	,	,	PUNCT
ejpam-3074	232	17	for	for	ADP
ejpam-3074	232	18	p	p	PROPN
ejpam-3074	232	19	(	(	PUNCT
ejpam-3074	232	20	u	u	NOUN
ejpam-3074	232	21	)	)	PUNCT
ejpam-3074	232	22	,	,	PUNCT
ejpam-3074	232	23	real	real	ADJ
ejpam-3074	232	24	,	,	PUNCT
ejpam-3074	232	25	is	be	AUX
ejpam-3074	232	26	given	give	VERB
ejpam-3074	232	27	by	by	ADP
ejpam-3074	232	28	p̃	p̃	PROPN
ejpam-3074	232	29	(	(	PUNCT
ejpam-3074	232	30	u	u	NOUN
ejpam-3074	232	31	)	)	PUNCT
ejpam-3074	232	32	=	=	SYM
ejpam-3074	232	33	c0	c0	NOUN
ejpam-3074	232	34	+	+	CCONJ
ejpam-3074	232	35	1	1	NUM
ejpam-3074	232	36	7	7	NUM
ejpam-3074	232	37	∞∑	∞∑	NUM
ejpam-3074	232	38	n=−∞	n=−∞	NUM
ejpam-3074	232	39	n6=0	n6=0	PROPN
ejpam-3074	232	40	7∑	7∑	NOUN
ejpam-3074	232	41	k=1	k=1	PART
ejpam-3074	232	42	ckne	ckne	VERB
ejpam-3074	232	43	ek2nπu	ek2nπu	PROPN
ejpam-3074	232	44	where	where	SCONJ
ejpam-3074	232	45	ckn	ckn	NOUN
ejpam-3074	232	46	=	=	NOUN
ejpam-3074	232	47	1	1	NUM
ejpam-3074	232	48	2	2	NUM
ejpam-3074	232	49	+1/2∫	+1/2∫	NUM
ejpam-3074	232	50	−1/2	−1/2	ADJ
ejpam-3074	232	51	e−ek2nπxdx	e−ek2nπxdx	NOUN
ejpam-3074	232	52	.	.	PUNCT
ejpam-3074	233	1	our	our	PRON
ejpam-3074	233	2	periodic	periodic	ADJ
ejpam-3074	233	3	function	function	NOUN
ejpam-3074	233	4	of	of	ADP
ejpam-3074	233	5	period	period	NOUN
ejpam-3074	233	6	1	1	NUM
ejpam-3074	233	7	defined	define	VERB
ejpam-3074	233	8	in	in	ADP
ejpam-3074	233	9	o	o	PROPN
ejpam-3074	233	10	already	already	ADV
ejpam-3074	233	11	has	have	VERB
ejpam-3074	233	12	that	that	DET
ejpam-3074	233	13	form	form	NOUN
ejpam-3074	233	14	i.e.	i.e.	X
ejpam-3074	233	15	,	,	PUNCT
ejpam-3074	233	16	p	p	X
ejpam-3074	233	17	(	(	PUNCT
ejpam-3074	233	18	u	u	NOUN
ejpam-3074	233	19	)	)	PUNCT
ejpam-3074	233	20	=	=	SYM
ejpam-3074	233	21	e2nπu	e2nπu	NOUN
ejpam-3074	233	22	,	,	PUNCT
ejpam-3074	233	23	uεo	uεo	PROPN
ejpam-3074	233	24	.	.	PUNCT
ejpam-3074	234	1	thus	thus	ADV
ejpam-3074	234	2	,	,	PUNCT
ejpam-3074	234	3	the	the	DET
ejpam-3074	234	4	following	following	ADJ
ejpam-3074	234	5	result	result	NOUN
ejpam-3074	234	6	is	be	AUX
ejpam-3074	234	7	intuitive	intuitive	ADJ
ejpam-3074	234	8	.	.	PUNCT
ejpam-3074	235	1	theorem	theorem	NOUN
ejpam-3074	235	2	2	2	NUM
ejpam-3074	235	3	.	.	PUNCT
ejpam-3074	236	1	the	the	DET
ejpam-3074	236	2	functions	function	NOUN
ejpam-3074	236	3	given	give	VERB
ejpam-3074	236	4	by	by	ADP
ejpam-3074	236	5	w̃(u	w̃(u	PROPN
ejpam-3074	236	6	)	)	PUNCT
ejpam-3074	236	7	=	=	SYM
ejpam-3074	236	8	bue2nπu	bue2nπu	NOUN
ejpam-3074	236	9	,	,	PUNCT
ejpam-3074	236	10	uεo	uεo	NOUN
ejpam-3074	236	11	are	be	AUX
ejpam-3074	236	12	dense	dense	ADJ
ejpam-3074	236	13	in	in	ADP
ejpam-3074	236	14	the	the	DET
ejpam-3074	236	15	space	space	NOUN
ejpam-3074	236	16	of	of	ADP
ejpam-3074	236	17	continuous	continuous	ADJ
ejpam-3074	236	18	functions	function	NOUN
ejpam-3074	236	19	in	in	ADP
ejpam-3074	236	20	o.	o.	PROPN
ejpam-3074	236	21	the	the	DET
ejpam-3074	236	22	density	density	NOUN
ejpam-3074	236	23	of	of	ADP
ejpam-3074	236	24	w̃(u	w̃(u	PROPN
ejpam-3074	236	25	)	)	PUNCT
ejpam-3074	236	26	=	=	SYM
ejpam-3074	236	27	bue2nπu	bue2nπu	NOUN
ejpam-3074	236	28	,	,	PUNCT
ejpam-3074	236	29	u	u	PROPN
ejpam-3074	236	30	∈	∈	NOUN
ejpam-3074	236	31	o	o	NOUN
ejpam-3074	236	32	allows	allow	VERB
ejpam-3074	236	33	to	to	PART
ejpam-3074	236	34	say	say	VERB
ejpam-3074	236	35	that	that	SCONJ
ejpam-3074	236	36	all	all	DET
ejpam-3074	236	37	brain	brain	NOUN
ejpam-3074	236	38	activity	activity	NOUN
ejpam-3074	236	39	can	can	AUX
ejpam-3074	236	40	be	be	AUX
ejpam-3074	236	41	represented	represent	VERB
ejpam-3074	236	42	by	by	ADP
ejpam-3074	236	43	these	these	DET
ejpam-3074	236	44	functions	function	NOUN
ejpam-3074	236	45	and	and	CCONJ
ejpam-3074	236	46	that	that	SCONJ
ejpam-3074	236	47	the	the	DET
ejpam-3074	236	48	density	density	NOUN
ejpam-3074	236	49	extends	extend	VERB
ejpam-3074	236	50	beyond	beyond	ADP
ejpam-3074	236	51	the	the	DET
ejpam-3074	236	52	firing	firing	NOUN
ejpam-3074	236	53	of	of	ADP
ejpam-3074	236	54	a	a	DET
ejpam-3074	236	55	neuron	neuron	NOUN
ejpam-3074	236	56	.	.	PUNCT
ejpam-3074	237	1	that	that	PRON
ejpam-3074	237	2	is	is	ADV
ejpam-3074	237	3	,	,	PUNCT
ejpam-3074	237	4	one	one	PRON
ejpam-3074	237	5	would	would	AUX
ejpam-3074	237	6	expect	expect	VERB
ejpam-3074	237	7	that	that	SCONJ
ejpam-3074	237	8	the	the	DET
ejpam-3074	237	9	synthesis	synthesis	NOUN
ejpam-3074	237	10	of	of	ADP
ejpam-3074	237	11	these	these	DET
ejpam-3074	237	12	functions	function	NOUN
ejpam-3074	237	13	is	be	AUX
ejpam-3074	237	14	also	also	ADV
ejpam-3074	237	15	dense	dense	ADJ
ejpam-3074	237	16	in	in	ADP
ejpam-3074	237	17	the	the	DET
ejpam-3074	237	18	space	space	NOUN
ejpam-3074	237	19	of	of	ADP
ejpam-3074	237	20	continuous	continuous	ADJ
ejpam-3074	237	21	functions	function	NOUN
ejpam-3074	237	22	defined	define	VERB
ejpam-3074	237	23	in	in	ADP
ejpam-3074	237	24	o.	o.	NOUN
ejpam-3074	237	25	theorem	theorem	NOUN
ejpam-3074	237	26	3	3	NUM
ejpam-3074	237	27	.	.	PUNCT
ejpam-3074	238	1	the	the	DET
ejpam-3074	238	2	synthesis	synthesis	NOUN
ejpam-3074	238	3	of	of	ADP
ejpam-3074	238	4	neural	neural	ADJ
ejpam-3074	238	5	activity	activity	NOUN
ejpam-3074	238	6	given	give	VERB
ejpam-3074	238	7	by	by	ADP
ejpam-3074	238	8	(	(	PUNCT
ejpam-3074	238	9	w̃1	w̃1	PROPN
ejpam-3074	238	10	,	,	PUNCT
ejpam-3074	238	11	...	...	PUNCT
ejpam-3074	238	12	,	,	PUNCT
ejpam-3074	238	13	w̃q)(u	w̃q)(u	ADJ
ejpam-3074	238	14	)	)	PUNCT
ejpam-3074	238	15	=	=	SYM
ejpam-3074	238	16	∑	∑	PROPN
ejpam-3074	238	17	(	(	PUNCT
ejpam-3074	238	18	n1,	n1,	ADJ
ejpam-3074	238	19	...	...	NOUN
ejpam-3074	238	20	,nq)εj	,nq)εj	PUNCT
ejpam-3074	238	21	an1,	an1,	NOUN
ejpam-3074	238	22	...	...	PUNCT
ejpam-3074	238	23	,nq	,nq	PUNCT
ejpam-3074	238	24	q∏	q∏	PROPN
ejpam-3074	238	25	i=1	i=1	PROPN
ejpam-3074	238	26	eni(2nπ+lnbi)ui	eni(2nπ+lnbi)ui	PROPN
ejpam-3074	238	27	,	,	PUNCT
ejpam-3074	238	28	ui	ui	PROPN
ejpam-3074	238	29	∈	∈	PROPN
ejpam-3074	238	30	o	o	NOUN
ejpam-3074	238	31	is	be	AUX
ejpam-3074	238	32	dense	dense	ADJ
ejpam-3074	238	33	in	in	ADP
ejpam-3074	238	34	the	the	DET
ejpam-3074	238	35	space	space	NOUN
ejpam-3074	238	36	of	of	ADP
ejpam-3074	238	37	continuous	continuous	ADJ
ejpam-3074	238	38	functions	function	NOUN
ejpam-3074	238	39	in	in	ADP
ejpam-3074	238	40	o.	o.	PROPN
ejpam-3074	238	41	t.	t.	PROPN
ejpam-3074	238	42	l.	l.	PROPN
ejpam-3074	238	43	saaty	saaty	PROPN
ejpam-3074	238	44	,	,	PUNCT
ejpam-3074	238	45	l.	l.	PROPN
ejpam-3074	238	46	g.	g.	PROPN
ejpam-3074	238	47	vargas	vargas	PROPN
ejpam-3074	238	48	/	/	SYM
ejpam-3074	238	49	eur	eur	PROPN
ejpam-3074	238	50	.	.	PUNCT
ejpam-3074	239	1	j.	j.	PROPN
ejpam-3074	239	2	pure	pure	PROPN
ejpam-3074	239	3	appl	appl	PROPN
ejpam-3074	239	4	.	.	PROPN
ejpam-3074	239	5	math	math	PROPN
ejpam-3074	239	6	,	,	PUNCT
ejpam-3074	239	7	10	10	NUM
ejpam-3074	239	8	(	(	PUNCT
ejpam-3074	239	9	4	4	NUM
ejpam-3074	239	10	)	)	PUNCT
ejpam-3074	239	11	(	(	PUNCT
ejpam-3074	239	12	2017	2017	NUM
ejpam-3074	239	13	)	)	PUNCT
ejpam-3074	239	14	,	,	PUNCT
ejpam-3074	239	15	602	602	NUM
ejpam-3074	239	16	-	-	SYM
ejpam-3074	239	17	613	613	NUM
ejpam-3074	239	18	612	612	NUM
ejpam-3074	239	19	6	6	NUM
ejpam-3074	239	20	.	.	PUNCT
ejpam-3074	240	1	the	the	DET
ejpam-3074	240	2	discrete	discrete	ADJ
ejpam-3074	240	3	nature	nature	NOUN
ejpam-3074	240	4	of	of	ADP
ejpam-3074	240	5	the	the	DET
ejpam-3074	240	6	brain	brain	NOUN
ejpam-3074	240	7	and	and	CCONJ
ejpam-3074	240	8	the	the	DET
ejpam-3074	240	9	creation	creation	NOUN
ejpam-3074	240	10	of	of	ADP
ejpam-3074	240	11	consciousness	consciousness	NOUN
ejpam-3074	240	12	:	:	PUNCT
ejpam-3074	240	13	why	why	SCONJ
ejpam-3074	240	14	do	do	AUX
ejpam-3074	240	15	we	we	PRON
ejpam-3074	240	16	need	need	VERB
ejpam-3074	240	17	octonions	octonion	NOUN
ejpam-3074	240	18	to	to	PART
ejpam-3074	240	19	represent	represent	VERB
ejpam-3074	240	20	neural	neural	ADJ
ejpam-3074	240	21	activity	activity	NOUN
ejpam-3074	240	22	?	?	PUNCT
ejpam-3074	241	1	physicists	physicist	NOUN
ejpam-3074	241	2	have	have	AUX
ejpam-3074	241	3	been	be	AUX
ejpam-3074	241	4	trying	try	VERB
ejpam-3074	241	5	to	to	PART
ejpam-3074	241	6	find	find	VERB
ejpam-3074	241	7	the	the	DET
ejpam-3074	241	8	smallest	small	ADJ
ejpam-3074	241	9	particle	particle	NOUN
ejpam-3074	241	10	in	in	ADP
ejpam-3074	241	11	the	the	DET
ejpam-3074	241	12	universe	universe	NOUN
ejpam-3074	241	13	and	and	CCONJ
ejpam-3074	241	14	the	the	DET
ejpam-3074	241	15	forces	force	NOUN
ejpam-3074	241	16	that	that	PRON
ejpam-3074	241	17	keep	keep	VERB
ejpam-3074	241	18	them	they	PRON
ejpam-3074	241	19	together	together	ADV
ejpam-3074	241	20	for	for	ADP
ejpam-3074	241	21	a	a	DET
ejpam-3074	241	22	long	long	ADJ
ejpam-3074	241	23	time	time	NOUN
ejpam-3074	241	24	.	.	PUNCT
ejpam-3074	242	1	although	although	SCONJ
ejpam-3074	242	2	the	the	DET
ejpam-3074	242	3	theories	theory	NOUN
ejpam-3074	242	4	that	that	PRON
ejpam-3074	242	5	try	try	VERB
ejpam-3074	242	6	to	to	PART
ejpam-3074	242	7	explain	explain	VERB
ejpam-3074	242	8	how	how	SCONJ
ejpam-3074	242	9	these	these	DET
ejpam-3074	242	10	particles	particle	NOUN
ejpam-3074	242	11	manage	manage	VERB
ejpam-3074	242	12	to	to	PART
ejpam-3074	242	13	stay	stay	VERB
ejpam-3074	242	14	together	together	ADV
ejpam-3074	242	15	to	to	PART
ejpam-3074	242	16	create	create	VERB
ejpam-3074	242	17	life	life	NOUN
ejpam-3074	242	18	are	be	AUX
ejpam-3074	242	19	mathematically	mathematically	ADV
ejpam-3074	242	20	represented	represent	VERB
ejpam-3074	242	21	under	under	ADP
ejpam-3074	242	22	the	the	DET
ejpam-3074	242	23	assumption	assumption	NOUN
ejpam-3074	242	24	of	of	ADP
ejpam-3074	242	25	continuity	continuity	NOUN
ejpam-3074	242	26	,	,	PUNCT
ejpam-3074	242	27	matter	matter	NOUN
ejpam-3074	242	28	is	be	AUX
ejpam-3074	242	29	not	not	PART
ejpam-3074	242	30	continuous	continuous	ADJ
ejpam-3074	242	31	,	,	PUNCT
ejpam-3074	242	32	but	but	CCONJ
ejpam-3074	242	33	brain	brain	NOUN
ejpam-3074	242	34	activity	activity	NOUN
ejpam-3074	242	35	is	be	AUX
ejpam-3074	242	36	continuous	continuous	ADJ
ejpam-3074	242	37	,	,	PUNCT
ejpam-3074	242	38	if	if	SCONJ
ejpam-3074	242	39	life	life	NOUN
ejpam-3074	242	40	,	,	PUNCT
ejpam-3074	242	41	as	as	SCONJ
ejpam-3074	242	42	we	we	PRON
ejpam-3074	242	43	understand	understand	VERB
ejpam-3074	242	44	it	it	PRON
ejpam-3074	242	45	,	,	PUNCT
ejpam-3074	242	46	exists	exist	VERB
ejpam-3074	242	47	in	in	ADP
ejpam-3074	242	48	the	the	DET
ejpam-3074	242	49	system	system	NOUN
ejpam-3074	242	50	studied	study	VERB
ejpam-3074	242	51	.	.	PUNCT
ejpam-3074	243	1	according	accord	VERB
ejpam-3074	243	2	to	to	ADP
ejpam-3074	243	3	b.	b.	PROPN
ejpam-3074	243	4	s.	s.	PROPN
ejpam-3074	243	5	acharya	acharya	PROPN
ejpam-3074	243	6	[	[	X
ejpam-3074	243	7	1	1	X
ejpam-3074	243	8	]	]	PUNCT
ejpam-3074	243	9	the	the	DET
ejpam-3074	243	10	known	know	VERB
ejpam-3074	243	11	physics	physics	NOUN
ejpam-3074	243	12	in	in	ADP
ejpam-3074	243	13	our	our	PRON
ejpam-3074	243	14	universe	universe	NOUN
ejpam-3074	243	15	is	be	AUX
ejpam-3074	243	16	well	well	ADV
ejpam-3074	243	17	modeled	model	VERB
ejpam-3074	243	18	by	by	ADP
ejpam-3074	243	19	the	the	DET
ejpam-3074	243	20	standard	standard	ADJ
ejpam-3074	243	21	model	model	NOUN
ejpam-3074	243	22	of	of	ADP
ejpam-3074	243	23	particle	particle	NOUN
ejpam-3074	243	24	physics	physics	NOUN
ejpam-3074	243	25	along	along	ADP
ejpam-3074	243	26	with	with	ADP
ejpam-3074	243	27	general	general	ADJ
ejpam-3074	243	28	relativity	relativity	NOUN
ejpam-3074	243	29	.	.	PUNCT
ejpam-3074	244	1	this	this	DET
ejpam-3074	244	2	mathematical	mathematical	ADJ
ejpam-3074	244	3	model	model	NOUN
ejpam-3074	244	4	is	be	AUX
ejpam-3074	244	5	based	base	VERB
ejpam-3074	244	6	on	on	ADP
ejpam-3074	244	7	(	(	PUNCT
ejpam-3074	244	8	1	1	X
ejpam-3074	244	9	)	)	PUNCT
ejpam-3074	244	10	maxwell	maxwell	PROPN
ejpam-3074	244	11	equations	equation	NOUN
ejpam-3074	244	12	,	,	PUNCT
ejpam-3074	244	13	(	(	PUNCT
ejpam-3074	244	14	2	2	X
ejpam-3074	244	15	)	)	PUNCT
ejpam-3074	244	16	yang	yang	PROPN
ejpam-3074	244	17	-	-	PUNCT
ejpam-3074	244	18	mills	mill	NOUN
ejpam-3074	244	19	equations	equation	NOUN
ejpam-3074	244	20	,	,	PUNCT
ejpam-3074	244	21	(	(	PUNCT
ejpam-3074	244	22	3	3	X
ejpam-3074	244	23	)	)	PUNCT
ejpam-3074	244	24	dirac	dirac	NOUN
ejpam-3074	244	25	equation	equation	NOUN
ejpam-3074	244	26	,	,	PUNCT
ejpam-3074	244	27	(	(	PUNCT
ejpam-3074	244	28	4	4	X
ejpam-3074	244	29	)	)	PUNCT
ejpam-3074	244	30	higgs	higgs	NOUN
ejpam-3074	244	31	equation	equation	NOUN
ejpam-3074	244	32	and	and	CCONJ
ejpam-3074	244	33	(	(	PUNCT
ejpam-3074	244	34	5	5	NUM
ejpam-3074	244	35	)	)	PUNCT
ejpam-3074	244	36	einstein	einstein	NOUN
ejpam-3074	244	37	equations	equations	PROPN
ejpam-3074	244	38	.	.	PUNCT
ejpam-3074	245	1	string	string	NOUN
ejpam-3074	245	2	theory	theory	NOUN
ejpam-3074	245	3	is	be	AUX
ejpam-3074	245	4	based	base	VERB
ejpam-3074	245	5	on	on	ADP
ejpam-3074	245	6	equations	equation	NOUN
ejpam-3074	245	7	that	that	PRON
ejpam-3074	245	8	describe	describe	VERB
ejpam-3074	245	9	2	2	NUM
ejpam-3074	245	10	-	-	PUNCT
ejpam-3074	245	11	dimensional	dimensional	ADJ
ejpam-3074	245	12	surfaces	surface	NOUN
ejpam-3074	245	13	embedded	embed	VERB
ejpam-3074	245	14	in	in	ADP
ejpam-3074	245	15	space	space	NOUN
ejpam-3074	245	16	-	-	PUNCT
ejpam-3074	245	17	time	time	NOUN
ejpam-3074	245	18	.	.	PUNCT
ejpam-3074	246	1	the	the	DET
ejpam-3074	246	2	equations	equation	NOUN
ejpam-3074	246	3	that	that	PRON
ejpam-3074	246	4	describe	describe	VERB
ejpam-3074	246	5	low	low	ADJ
ejpam-3074	246	6	energy	energy	NOUN
ejpam-3074	246	7	harmonics	harmonic	NOUN
ejpam-3074	246	8	of	of	ADP
ejpam-3074	246	9	such	such	ADJ
ejpam-3074	246	10	strings	string	NOUN
ejpam-3074	246	11	include	include	VERB
ejpam-3074	246	12	the	the	DET
ejpam-3074	246	13	five	five	NUM
ejpam-3074	246	14	set	set	NOUN
ejpam-3074	246	15	of	of	ADP
ejpam-3074	246	16	equations	equation	NOUN
ejpam-3074	246	17	just	just	ADV
ejpam-3074	246	18	mentioned	mention	VERB
ejpam-3074	246	19	.	.	PUNCT
ejpam-3074	247	1	incorporating	incorporate	VERB
ejpam-3074	247	2	the	the	DET
ejpam-3074	247	3	property	property	NOUN
ejpam-3074	247	4	of	of	ADP
ejpam-3074	247	5	supersymmetry	supersymmetry	NOUN
ejpam-3074	247	6	creates	create	VERB
ejpam-3074	247	7	superstring	superstring	ADJ
ejpam-3074	247	8	theory	theory	NOUN
ejpam-3074	247	9	that	that	PRON
ejpam-3074	247	10	solves	solve	VERB
ejpam-3074	247	11	some	some	DET
ejpam-3074	247	12	fundamental	fundamental	ADJ
ejpam-3074	247	13	problems	problem	NOUN
ejpam-3074	247	14	of	of	ADP
ejpam-3074	247	15	string	string	NOUN
ejpam-3074	247	16	theory	theory	NOUN
ejpam-3074	247	17	and	and	CCONJ
ejpam-3074	247	18	creates	create	VERB
ejpam-3074	247	19	a	a	DET
ejpam-3074	247	20	symmetry	symmetry	NOUN
ejpam-3074	247	21	between	between	ADP
ejpam-3074	247	22	fermions	fermion	NOUN
ejpam-3074	247	23	and	and	CCONJ
ejpam-3074	247	24	bosons.there	bosons.there	PROPN
ejpam-3074	247	25	are	be	AUX
ejpam-3074	247	26	five	five	NUM
ejpam-3074	247	27	superstring	superstring	ADJ
ejpam-3074	247	28	theories	theory	NOUN
ejpam-3074	247	29	and	and	CCONJ
ejpam-3074	247	30	they	they	PRON
ejpam-3074	247	31	are	be	AUX
ejpam-3074	247	32	defined	define	VERB
ejpam-3074	247	33	in	in	ADP
ejpam-3074	247	34	ten	ten	NUM
ejpam-3074	247	35	dimensions	dimension	NOUN
ejpam-3074	247	36	,	,	PUNCT
ejpam-3074	247	37	but	but	CCONJ
ejpam-3074	247	38	only	only	ADV
ejpam-3074	247	39	time	time	NOUN
ejpam-3074	247	40	and	and	CCONJ
ejpam-3074	247	41	three	three	NUM
ejpam-3074	247	42	-	-	PUNCT
ejpam-3074	247	43	dimensional	dimensional	ADJ
ejpam-3074	247	44	space	space	NOUN
ejpam-3074	247	45	have	have	AUX
ejpam-3074	247	46	been	be	AUX
ejpam-3074	247	47	observed	observe	VERB
ejpam-3074	247	48	,	,	PUNCT
ejpam-3074	247	49	and	and	CCONJ
ejpam-3074	247	50	thus	thus	ADV
ejpam-3074	247	51	,	,	PUNCT
ejpam-3074	247	52	the	the	DET
ejpam-3074	247	53	extra	extra	ADJ
ejpam-3074	247	54	six	six	NUM
ejpam-3074	247	55	dimensions	dimension	NOUN
ejpam-3074	247	56	are	be	AUX
ejpam-3074	247	57	hidden	hide	VERB
ejpam-3074	247	58	.	.	PUNCT
ejpam-3074	248	1	since	since	SCONJ
ejpam-3074	248	2	these	these	DET
ejpam-3074	248	3	superstring	superstring	NOUN
ejpam-3074	248	4	theories	theory	NOUN
ejpam-3074	248	5	are	be	AUX
ejpam-3074	248	6	interrelated	interrelate	VERB
ejpam-3074	248	7	,	,	PUNCT
ejpam-3074	248	8	a	a	DET
ejpam-3074	248	9	new	new	ADJ
ejpam-3074	248	10	theory	theory	NOUN
ejpam-3074	248	11	emerged	emerge	VERB
ejpam-3074	248	12	known	know	VERB
ejpam-3074	248	13	as	as	ADP
ejpam-3074	248	14	m	m	NOUN
ejpam-3074	248	15	theory	theory	NOUN
ejpam-3074	248	16	that	that	PRON
ejpam-3074	248	17	resides	reside	VERB
ejpam-3074	248	18	in	in	ADP
ejpam-3074	248	19	eleven	eleven	NUM
ejpam-3074	248	20	dimensions	dimension	NOUN
ejpam-3074	248	21	.	.	PUNCT
ejpam-3074	249	1	representations	representation	NOUN
ejpam-3074	249	2	in	in	ADP
ejpam-3074	249	3	m	m	NOUN
ejpam-3074	249	4	theory	theory	NOUN
ejpam-3074	249	5	use	use	NOUN
ejpam-3074	249	6	g2	g2	PROPN
ejpam-3074	249	7	manifolds	manifolds	PROPN
ejpam-3074	249	8	.	.	PUNCT
ejpam-3074	250	1	g2	g2	PROPN
ejpam-3074	250	2	-manifolds	-manifolds	PROPN
ejpam-3074	250	3	are	be	AUX
ejpam-3074	250	4	models	model	NOUN
ejpam-3074	250	5	of	of	ADP
ejpam-3074	250	6	the	the	DET
ejpam-3074	250	7	extra	extra	ADJ
ejpam-3074	250	8	dimensions	dimension	NOUN
ejpam-3074	250	9	in	in	ADP
ejpam-3074	250	10	the	the	DET
ejpam-3074	250	11	m	m	PROPN
ejpam-3074	250	12	theory	theory	NOUN
ejpam-3074	250	13	.	.	PUNCT
ejpam-3074	251	1	smooth	smooth	ADJ
ejpam-3074	251	2	g2	g2	PROPN
ejpam-3074	251	3	-manifolds	-manifold	NOUN
ejpam-3074	251	4	are	be	AUX
ejpam-3074	251	5	not	not	PART
ejpam-3074	251	6	that	that	ADV
ejpam-3074	251	7	relevant	relevant	ADJ
ejpam-3074	251	8	in	in	ADP
ejpam-3074	251	9	particle	particle	NOUN
ejpam-3074	251	10	physics	physics	NOUN
ejpam-3074	251	11	,	,	PUNCT
ejpam-3074	251	12	but	but	CCONJ
ejpam-3074	251	13	they	they	PRON
ejpam-3074	251	14	are	be	AUX
ejpam-3074	251	15	important	important	ADJ
ejpam-3074	251	16	in	in	ADP
ejpam-3074	251	17	superstring	superstre	VERB
ejpam-3074	251	18	theory	theory	NOUN
ejpam-3074	251	19	.	.	PUNCT
ejpam-3074	252	1	in	in	ADP
ejpam-3074	252	2	differential	differential	ADJ
ejpam-3074	252	3	geometry	geometry	NOUN
ejpam-3074	252	4	,	,	PUNCT
ejpam-3074	252	5	a	a	DET
ejpam-3074	252	6	g2	g2	PROPN
ejpam-3074	252	7	-manifold	-manifold	PROPN
ejpam-3074	252	8	is	be	AUX
ejpam-3074	252	9	a	a	DET
ejpam-3074	252	10	seven	seven	NUM
ejpam-3074	252	11	-	-	PUNCT
ejpam-3074	252	12	dimensional	dimensional	ADJ
ejpam-3074	252	13	riemannian	riemannian	ADJ
ejpam-3074	252	14	manifold	manifold	NOUN
ejpam-3074	252	15	(	(	PUNCT
ejpam-3074	252	16	a	a	DET
ejpam-3074	252	17	manifold	manifold	NOUN
ejpam-3074	252	18	with	with	ADP
ejpam-3074	252	19	an	an	DET
ejpam-3074	252	20	inner	inner	ADJ
ejpam-3074	252	21	product	product	NOUN
ejpam-3074	252	22	defined	define	VERB
ejpam-3074	252	23	on	on	ADP
ejpam-3074	252	24	the	the	DET
ejpam-3074	252	25	tangent	tangent	ADJ
ejpam-3074	252	26	space	space	NOUN
ejpam-3074	252	27	at	at	ADP
ejpam-3074	252	28	each	each	DET
ejpam-3074	252	29	point	point	NOUN
ejpam-3074	252	30	)	)	PUNCT
ejpam-3074	252	31	with	with	ADP
ejpam-3074	252	32	holonomy	holonomy	PROPN
ejpam-3074	252	33	group	group	NOUN
ejpam-3074	252	34	contained	contain	VERB
ejpam-3074	252	35	in	in	ADP
ejpam-3074	252	36	g2	g2	PROPN
ejpam-3074	252	37	one	one	NUM
ejpam-3074	252	38	of	of	ADP
ejpam-3074	252	39	the	the	DET
ejpam-3074	252	40	five	five	NUM
ejpam-3074	252	41	exceptional	exceptional	ADJ
ejpam-3074	252	42	lie	lie	NOUN
ejpam-3074	252	43	groups	group	NOUN
ejpam-3074	252	44	that	that	PRON
ejpam-3074	252	45	can	can	AUX
ejpam-3074	252	46	be	be	AUX
ejpam-3074	252	47	described	describe	VERB
ejpam-3074	252	48	as	as	ADP
ejpam-3074	252	49	the	the	DET
ejpam-3074	252	50	automorphism	automorphism	NOUN
ejpam-3074	252	51	group	group	NOUN
ejpam-3074	252	52	of	of	ADP
ejpam-3074	252	53	the	the	DET
ejpam-3074	252	54	octonions.in	octonions.in	X
ejpam-3074	252	55	differential	differential	ADJ
ejpam-3074	252	56	geometry	geometry	NOUN
ejpam-3074	252	57	,	,	PUNCT
ejpam-3074	252	58	the	the	DET
ejpam-3074	252	59	holonomy	holonomy	NOUN
ejpam-3074	252	60	of	of	ADP
ejpam-3074	252	61	a	a	DET
ejpam-3074	252	62	connection	connection	NOUN
ejpam-3074	252	63	on	on	ADP
ejpam-3074	252	64	a	a	DET
ejpam-3074	252	65	smooth	smooth	ADJ
ejpam-3074	252	66	manifold	manifold	NOUN
ejpam-3074	252	67	relates	relate	VERB
ejpam-3074	252	68	to	to	ADP
ejpam-3074	252	69	the	the	DET
ejpam-3074	252	70	curvature	curvature	NOUN
ejpam-3074	252	71	of	of	ADP
ejpam-3074	252	72	the	the	DET
ejpam-3074	252	73	connection	connection	NOUN
ejpam-3074	252	74	and	and	CCONJ
ejpam-3074	252	75	measures	measure	NOUN
ejpam-3074	252	76	the	the	DET
ejpam-3074	252	77	extent	extent	NOUN
ejpam-3074	252	78	to	to	PART
ejpam-3074	252	79	which	which	PRON
ejpam-3074	252	80	parallel	parallel	ADJ
ejpam-3074	252	81	transport	transport	NOUN
ejpam-3074	252	82	around	around	ADP
ejpam-3074	252	83	closed	closed	ADJ
ejpam-3074	252	84	loops	loop	NOUN
ejpam-3074	252	85	fails	fail	VERB
ejpam-3074	252	86	to	to	PART
ejpam-3074	252	87	preserve	preserve	VERB
ejpam-3074	252	88	the	the	DET
ejpam-3074	252	89	geometrical	geometrical	ADJ
ejpam-3074	252	90	data	datum	NOUN
ejpam-3074	252	91	being	be	AUX
ejpam-3074	252	92	transported	transport	VERB
ejpam-3074	252	93	.	.	PUNCT
ejpam-3074	253	1	thus	thus	ADV
ejpam-3074	253	2	,	,	PUNCT
ejpam-3074	253	3	we	we	PRON
ejpam-3074	253	4	think	think	VERB
ejpam-3074	253	5	that	that	SCONJ
ejpam-3074	253	6	this	this	PRON
ejpam-3074	253	7	is	be	AUX
ejpam-3074	253	8	the	the	DET
ejpam-3074	253	9	connection	connection	NOUN
ejpam-3074	253	10	between	between	ADP
ejpam-3074	253	11	the	the	DET
ejpam-3074	253	12	solution	solution	NOUN
ejpam-3074	253	13	of	of	ADP
ejpam-3074	253	14	the	the	DET
ejpam-3074	253	15	functional	functional	ADJ
ejpam-3074	253	16	equation	equation	NOUN
ejpam-3074	253	17	w(as	w(as	PROPN
ejpam-3074	253	18	)	)	PUNCT
ejpam-3074	253	19	=	=	SYM
ejpam-3074	253	20	bw(s	bw(s	NOUN
ejpam-3074	253	21	)	)	PUNCT
ejpam-3074	253	22	and	and	CCONJ
ejpam-3074	253	23	superstring	superstre	VERB
ejpam-3074	253	24	theory	theory	NOUN
ejpam-3074	253	25	.	.	PUNCT
ejpam-3074	254	1	the	the	DET
ejpam-3074	254	2	firing	firing	NOUN
ejpam-3074	254	3	of	of	ADP
ejpam-3074	254	4	the	the	DET
ejpam-3074	254	5	neurons	neuron	NOUN
ejpam-3074	254	6	through	through	ADP
ejpam-3074	254	7	the	the	DET
ejpam-3074	254	8	continuous	continuous	ADJ
ejpam-3074	254	9	paired	pair	VERB
ejpam-3074	254	10	comparison	comparison	NOUN
ejpam-3074	254	11	process	process	NOUN
ejpam-3074	254	12	generate	generate	VERB
ejpam-3074	254	13	a	a	DET
ejpam-3074	254	14	smooth	smooth	ADJ
ejpam-3074	254	15	g2	g2	NOUN
ejpam-3074	254	16	-manifold	-manifold	PROPN
ejpam-3074	254	17	in	in	ADP
ejpam-3074	254	18	which	which	PRON
ejpam-3074	254	19	cognition	cognition	NOUN
ejpam-3074	254	20	must	must	AUX
ejpam-3074	254	21	take	take	VERB
ejpam-3074	254	22	place	place	NOUN
ejpam-3074	254	23	,	,	PUNCT
ejpam-3074	254	24	and	and	CCONJ
ejpam-3074	254	25	hence	hence	ADV
ejpam-3074	254	26	,	,	PUNCT
ejpam-3074	254	27	the	the	DET
ejpam-3074	254	28	representations	representation	NOUN
ejpam-3074	254	29	of	of	ADP
ejpam-3074	254	30	our	our	PRON
ejpam-3074	254	31	thoughts	thought	NOUN
ejpam-3074	254	32	must	must	AUX
ejpam-3074	254	33	take	take	VERB
ejpam-3074	254	34	place	place	NOUN
ejpam-3074	254	35	in	in	ADP
ejpam-3074	254	36	smooth	smooth	ADJ
ejpam-3074	254	37	g2	g2	PROPN
ejpam-3074	254	38	-manifolds	-manifold	NOUN
ejpam-3074	254	39	.	.	PUNCT
ejpam-3074	255	1	references	reference	NOUN
ejpam-3074	255	2	613	613	NUM
ejpam-3074	255	3	references	reference	NOUN
ejpam-3074	255	4	[	[	X
ejpam-3074	255	5	1	1	NUM
ejpam-3074	255	6	]	]	X
ejpam-3074	255	7	b.s	b.s	PROPN
ejpam-3074	255	8	.	.	PROPN
ejpam-3074	255	9	acharya	acharya	PROPN
ejpam-3074	255	10	(	(	PUNCT
ejpam-3074	255	11	2014	2014	NUM
ejpam-3074	255	12	)	)	PUNCT
ejpam-3074	255	13	.	.	PUNCT
ejpam-3074	256	1	physics	physics	PROPN
ejpam-3074	256	2	and	and	CCONJ
ejpam-3074	256	3	g2	g2	PROPN
ejpam-3074	256	4	-manifolds	-manifolds	PROPN
ejpam-3074	256	5	,	,	PUNCT
ejpam-3074	256	6	talk	talk	NOUN
ejpam-3074	256	7	delivered	deliver	VERB
ejpam-3074	256	8	october	october	PROPN
ejpam-3074	256	9	7	7	NUM
ejpam-3074	256	10	,	,	PUNCT
ejpam-3074	256	11	2014	2014	NUM
ejpam-3074	256	12	at	at	ADP
ejpam-3074	256	13	kings	king	NOUN
ejpam-3074	256	14	college	college	PROPN
ejpam-3074	256	15	,	,	PUNCT
ejpam-3074	256	16	london	london	PROPN
ejpam-3074	256	17	.	.	PUNCT
ejpam-3074	257	1	[	[	X
ejpam-3074	257	2	2	2	NUM
ejpam-3074	257	3	]	]	PUNCT
ejpam-3074	257	4	baez	baez	NOUN
ejpam-3074	257	5	,	,	PUNCT
ejpam-3074	257	6	j.c	j.c	PROPN
ejpam-3074	257	7	.	.	PROPN
ejpam-3074	257	8	(	(	PUNCT
ejpam-3074	257	9	2001	2001	NUM
ejpam-3074	257	10	)	)	PUNCT
ejpam-3074	257	11	.	.	PUNCT
ejpam-3074	258	1	the	the	DET
ejpam-3074	258	2	octonions	octonion	NOUN
ejpam-3074	258	3	,	,	PUNCT
ejpam-3074	258	4	bulletin	bulletin	NOUN
ejpam-3074	258	5	of	of	ADP
ejpam-3074	258	6	the	the	DET
ejpam-3074	258	7	american	american	PROPN
ejpam-3074	258	8	mathematical	mathematical	PROPN
ejpam-3074	258	9	society	society	NOUN
ejpam-3074	258	10	,	,	PUNCT
ejpam-3074	258	11	39	39	NUM
ejpam-3074	258	12	,	,	PUNCT
ejpam-3074	258	13	2,145	2,145	NUM
ejpam-3074	258	14	-	-	SYM
ejpam-3074	258	15	205	205	NUM
ejpam-3074	258	16	.	.	PUNCT
ejpam-3074	259	1	[	[	X
ejpam-3074	259	2	3	3	NUM
ejpam-3074	259	3	]	]	SYM
ejpam-3074	259	4	brillouet	brillouet	NOUN
ejpam-3074	259	5	-	-	PUNCT
ejpam-3074	259	6	bellout	bellout	NOUN
ejpam-3074	259	7	,	,	PUNCT
ejpam-3074	259	8	n.	n.	NOUN
ejpam-3074	259	9	(	(	PUNCT
ejpam-3074	259	10	1999	1999	NUM
ejpam-3074	259	11	)	)	PUNCT
ejpam-3074	259	12	.	.	PUNCT
ejpam-3074	260	1	on	on	ADP
ejpam-3074	260	2	a	a	DET
ejpam-3074	260	3	simple	simple	ADJ
ejpam-3074	260	4	linear	linear	ADJ
ejpam-3074	260	5	functional	functional	ADJ
ejpam-3074	260	6	equation	equation	NOUN
ejpam-3074	260	7	on	on	ADP
ejpam-3074	260	8	normed	normed	ADJ
ejpam-3074	260	9	linear	linear	PROPN
ejpam-3074	260	10	spaces	space	NOUN
ejpam-3074	260	11	,	,	PUNCT
ejpam-3074	260	12	ecole	ecole	X
ejpam-3074	260	13	centrale	centrale	X
ejpam-3074	260	14	de	de	X
ejpam-3074	260	15	nantes	nante	NOUN
ejpam-3074	260	16	.	.	PUNCT
ejpam-3074	261	1	f-44072	f-44072	NOUN
ejpam-3074	261	2	nantes	nante	NOUN
ejpam-3074	261	3	cedex	cedex	NOUN
ejpam-3074	261	4	03	03	NUM
ejpam-3074	261	5	,	,	PUNCT
ejpam-3074	261	6	france	france	PROPN
ejpam-3074	261	7	,	,	PUNCT
ejpam-3074	261	8	october	october	PROPN
ejpam-3074	261	9	.	.	PUNCT
ejpam-3074	262	1	[	[	X
ejpam-3074	262	2	4	4	NUM
ejpam-3074	262	3	]	]	X
ejpam-3074	262	4	cayley	cayley	NOUN
ejpam-3074	262	5	,	,	PUNCT
ejpam-3074	262	6	a.	a.	NOUN
ejpam-3074	262	7	(	(	PUNCT
ejpam-3074	262	8	1963	1963	NUM
ejpam-3074	262	9	)	)	PUNCT
ejpam-3074	262	10	.	.	PUNCT
ejpam-3074	263	1	on	on	ADP
ejpam-3074	263	2	jacobi	jacobi	PROPN
ejpam-3074	263	3	’s	’s	PART
ejpam-3074	263	4	elliptic	elliptic	ADJ
ejpam-3074	263	5	functions	function	NOUN
ejpam-3074	263	6	,	,	PUNCT
ejpam-3074	263	7	in	in	ADP
ejpam-3074	263	8	reply	reply	NOUN
ejpam-3074	263	9	to	to	ADP
ejpam-3074	263	10	the	the	DET
ejpam-3074	263	11	rev	rev	PROPN
ejpam-3074	263	12	.	.	PROPN
ejpam-3074	263	13	b.	b.	PROPN
ejpam-3074	263	14	bronwin	bronwin	PROPN
ejpam-3074	263	15	;	;	PUNCT
ejpam-3074	263	16	and	and	CCONJ
ejpam-3074	263	17	on	on	ADP
ejpam-3074	263	18	quaternions(appendix	quaternions(appendix	PROPN
ejpam-3074	263	19	only	only	ADV
ejpam-3074	263	20	)	)	PUNCT
ejpam-3074	263	21	,	,	PUNCT
ejpam-3074	263	22	in	in	ADP
ejpam-3074	263	23	the	the	DET
ejpam-3074	263	24	collected	collect	VERB
ejpam-3074	263	25	mathematical	mathematical	ADJ
ejpam-3074	263	26	papers	paper	NOUN
ejpam-3074	263	27	,	,	PUNCT
ejpam-3074	263	28	johnson	johnson	PROPN
ejpam-3074	263	29	reprint	reprint	PROPN
ejpam-3074	263	30	co.	co.	PROPN
ejpam-3074	263	31	,	,	PUNCT
ejpam-3074	263	32	newyork	newyork	PROPN
ejpam-3074	263	33	,	,	PUNCT
ejpam-3074	263	34	p.	p.	NOUN
ejpam-3074	263	35	127	127	NUM
ejpam-3074	263	36	.	.	PUNCT
ejpam-3074	264	1	[	[	X
ejpam-3074	264	2	5	5	NUM
ejpam-3074	264	3	]	]	PUNCT
ejpam-3074	264	4	conway	conway	PROPN
ejpam-3074	264	5	j.h	j.h	PROPN
ejpam-3074	264	6	.	.	PROPN
ejpam-3074	264	7	and	and	CCONJ
ejpam-3074	264	8	d.a	d.a	PROPN
ejpam-3074	264	9	.	.	PROPN
ejpam-3074	264	10	smith	smith	PROPN
ejpam-3074	264	11	(	(	PUNCT
ejpam-3074	264	12	2003	2003	NUM
ejpam-3074	264	13	)	)	PUNCT
ejpam-3074	264	14	.	.	PUNCT
ejpam-3074	265	1	on	on	ADP
ejpam-3074	265	2	quaternions	quaternion	NOUN
ejpam-3074	265	3	and	and	CCONJ
ejpam-3074	265	4	octonions	octonion	NOUN
ejpam-3074	265	5	,	,	PUNCT
ejpam-3074	265	6	a.k	a.k	PROPN
ejpam-3074	265	7	.	.	PROPN
ejpam-3074	265	8	peters	peters	PROPN
ejpam-3074	265	9	,	,	PUNCT
ejpam-3074	265	10	natick	natick	PROPN
ejpam-3074	265	11	,	,	PUNCT
ejpam-3074	265	12	ma	ma	PROPN
ejpam-3074	265	13	.	.	PUNCT
ejpam-3074	266	1	[	[	X
ejpam-3074	266	2	6	6	NUM
ejpam-3074	266	3	]	]	X
ejpam-3074	266	4	goertzel	goertzel	PROPN
ejpam-3074	266	5	,	,	PUNCT
ejpam-3074	266	6	b.	b.	PROPN
ejpam-3074	266	7	(	(	PUNCT
ejpam-3074	266	8	1996	1996	NUM
ejpam-3074	266	9	)	)	PUNCT
ejpam-3074	266	10	.	.	PUNCT
ejpam-3074	267	1	on	on	ADP
ejpam-3074	267	2	the	the	DET
ejpam-3074	267	3	algebraic	algebraic	ADJ
ejpam-3074	267	4	structure	structure	NOUN
ejpam-3074	267	5	of	of	ADP
ejpam-3074	267	6	consciousness	consciousness	NOUN
ejpam-3074	267	7	,	,	PUNCT
ejpam-3074	267	8	dynamical	dynamical	ADJ
ejpam-3074	267	9	psychology	psychology	NOUN
ejpam-3074	267	10	:	:	PUNCT
ejpam-3074	267	11	an	an	DET
ejpam-3074	267	12	international	international	ADJ
ejpam-3074	267	13	,	,	PUNCT
ejpam-3074	267	14	interdisciplinary	interdisciplinary	ADJ
ejpam-3074	267	15	journal	journal	NOUN
ejpam-3074	267	16	of	of	ADP
ejpam-3074	267	17	complex	complex	ADJ
ejpam-3074	267	18	mental	mental	ADJ
ejpam-3074	267	19	processes	process	NOUN
ejpam-3074	267	20	[	[	X
ejpam-3074	267	21	7	7	NUM
ejpam-3074	267	22	]	]	X
ejpam-3074	267	23	hamilton	hamilton	PROPN
ejpam-3074	267	24	,	,	PUNCT
ejpam-3074	267	25	w.r	w.r	PROPN
ejpam-3074	267	26	.	.	PROPN
ejpam-3074	267	27	(	(	PUNCT
ejpam-3074	267	28	1967	1967	NUM
ejpam-3074	267	29	)	)	PUNCT
ejpam-3074	267	30	.	.	PUNCT
ejpam-3074	268	1	four	four	NUM
ejpam-3074	268	2	and	and	CCONJ
ejpam-3074	268	3	eight	eight	NUM
ejpam-3074	268	4	square	square	ADJ
ejpam-3074	268	5	theorems	theorem	NOUN
ejpam-3074	268	6	,	,	PUNCT
ejpam-3074	268	7	in	in	ADP
ejpam-3074	268	8	appendix	appendix	NOUN
ejpam-3074	268	9	3	3	NUM
ejpam-3074	268	10	of	of	ADP
ejpam-3074	268	11	the	the	DET
ejpam-3074	268	12	mathematical	mathematical	ADJ
ejpam-3074	268	13	papers	paper	NOUN
ejpam-3074	268	14	of	of	ADP
ejpam-3074	268	15	william	william	PROPN
ejpam-3074	268	16	rowan	rowan	PROPN
ejpam-3074	268	17	hamilton	hamilton	PROPN
ejpam-3074	268	18	,	,	PUNCT
ejpam-3074	268	19	vol	vol	NOUN
ejpam-3074	268	20	.	.	PROPN
ejpam-3074	269	1	3	3	NUM
ejpam-3074	269	2	,	,	PUNCT
ejpam-3074	269	3	eds	ed	NOUN
ejpam-3074	269	4	.	.	PUNCT
ejpam-3074	270	1	h.	h.	PROPN
ejpam-3074	270	2	halberstam	halberstam	PROPN
ejpam-3074	270	3	and	and	CCONJ
ejpam-3074	270	4	r.	r.	PROPN
ejpam-3074	270	5	e.	e.	PROPN
ejpam-3074	270	6	ingram	ingram	PROPN
ejpam-3074	270	7	,	,	PUNCT
ejpam-3074	270	8	cambridge	cambridge	PROPN
ejpam-3074	270	9	university	university	PROPN
ejpam-3074	270	10	press	press	PROPN
ejpam-3074	270	11	,	,	PUNCT
ejpam-3074	270	12	cambridge	cambridge	PROPN
ejpam-3074	270	13	,	,	PUNCT
ejpam-3074	270	14	pp	pp	PROPN
ejpam-3074	270	15	.	.	PUNCT
ejpam-3074	270	16	648	648	NUM
ejpam-3074	270	17	-	-	SYM
ejpam-3074	270	18	656	656	NUM
ejpam-3074	270	19	.	.	PUNCT
ejpam-3074	271	1	[	[	X
ejpam-3074	271	2	8	8	NUM
ejpam-3074	271	3	]	]	X
ejpam-3074	271	4	hurwitz	hurwitz	PROPN
ejpam-3074	271	5	,	,	PUNCT
ejpam-3074	271	6	a.	a.	PROPN
ejpam-3074	271	7	(	(	PUNCT
ejpam-3074	271	8	1898	1898	NUM
ejpam-3074	271	9	)	)	PUNCT
ejpam-3074	271	10	.	.	PUNCT
ejpam-3074	272	1	uber	uber	ADJ
ejpam-3074	272	2	die	die	VERB
ejpam-3074	272	3	composition	composition	NOUN
ejpam-3074	272	4	der	der	NOUN
ejpam-3074	272	5	quadratischen	quadratischen	PROPN
ejpam-3074	272	6	formen	formen	PROPN
ejpam-3074	272	7	von	von	PROPN
ejpam-3074	272	8	beliebig	beliebig	PROPN
ejpam-3074	272	9	vielen	vielen	VERB
ejpam-3074	272	10	variabeln	variabeln	ADJ
ejpam-3074	272	11	,	,	PUNCT
ejpam-3074	272	12	nachr	nachr	PROPN
ejpam-3074	272	13	.	.	PUNCT
ejpam-3074	273	1	ges	ges	PROPN
ejpam-3074	273	2	.	.	PROPN
ejpam-3074	273	3	wiss	wiss	PROPN
ejpam-3074	273	4	.	.	PUNCT
ejpam-3074	274	1	göttingen	göttingen	NOUN
ejpam-3074	274	2	309	309	NUM
ejpam-3074	274	3	-	-	SYM
ejpam-3074	274	4	316	316	NUM
ejpam-3074	274	5	.	.	PUNCT
ejpam-3074	275	1	[	[	X
ejpam-3074	275	2	9	9	NUM
ejpam-3074	275	3	]	]	X
ejpam-3074	275	4	manogue	manogue	PROPN
ejpam-3074	275	5	c.a	c.a	PROPN
ejpam-3074	275	6	.	.	PROPN
ejpam-3074	275	7	and	and	CCONJ
ejpam-3074	275	8	j.	j.	PROPN
ejpam-3074	275	9	schray	schray	PROPN
ejpam-3074	275	10	(	(	PUNCT
ejpam-3074	275	11	1993	1993	NUM
ejpam-3074	275	12	)	)	PUNCT
ejpam-3074	275	13	.	.	PUNCT
ejpam-3074	276	1	finite	finite	PROPN
ejpam-3074	276	2	lorentz	lorentz	PROPN
ejpam-3074	276	3	transformations	transformation	NOUN
ejpam-3074	276	4	,	,	PUNCT
ejpam-3074	276	5	automorphisms	automorphism	NOUN
ejpam-3074	276	6	,	,	PUNCT
ejpam-3074	276	7	and	and	CCONJ
ejpam-3074	276	8	division	division	NOUN
ejpam-3074	276	9	algebras	algebras	PROPN
ejpam-3074	276	10	,	,	PUNCT
ejpam-3074	276	11	j.	j.	PROPN
ejpam-3074	276	12	math	math	PROPN
ejpam-3074	276	13	.	.	PUNCT
ejpam-3074	277	1	phys.34	phys.34	NOUN
ejpam-3074	277	2	,	,	PUNCT
ejpam-3074	277	3	3746	3746	NUM
ejpam-3074	277	4	-	-	SYM
ejpam-3074	277	5	3767	3767	NUM
ejpam-3074	277	6	.	.	PUNCT
ejpam-3074	278	1	[	[	X
ejpam-3074	278	2	10	10	NUM
ejpam-3074	278	3	]	]	X
ejpam-3074	278	4	martinez	martinez	PROPN
ejpam-3074	278	5	,	,	PUNCT
ejpam-3074	278	6	c.a.p	c.a.p	PROPN
ejpam-3074	278	7	.	.	PROPN
ejpam-3074	278	8	,	,	PUNCT
ejpam-3074	278	9	a.l.m	a.l.m	PROPN
ejpam-3074	278	10	.	.	PUNCT
ejpam-3074	279	1	martinez	martinez	PROPN
ejpam-3074	279	2	,	,	PUNCT
ejpam-3074	279	3	m.f	m.f	PROPN
ejpam-3074	279	4	.	.	PROPN
ejpam-3074	279	5	borges	borges	PROPN
ejpam-3074	279	6	and	and	CCONJ
ejpam-3074	279	7	e.v	e.v	PROPN
ejpam-3074	279	8	.	.	PROPN
ejpam-3074	279	9	castelani	castelani	PROPN
ejpam-3074	279	10	(	(	PUNCT
ejpam-3074	279	11	2013	2013	NUM
ejpam-3074	279	12	)	)	PUNCT
ejpam-3074	279	13	.	.	PUNCT
ejpam-3074	280	1	square	square	NOUN
ejpam-3074	280	2	of	of	ADP
ejpam-3074	280	3	the	the	DET
ejpam-3074	280	4	error	error	NOUN
ejpam-3074	280	5	octonionic	octonionic	NOUN
ejpam-3074	280	6	theorem	theorem	NOUN
ejpam-3074	280	7	and	and	CCONJ
ejpam-3074	280	8	hypercomplex	hypercomplex	ADJ
ejpam-3074	280	9	fourier	fourier	NOUN
ejpam-3074	280	10	series	series	PROPN
ejpam-3074	280	11	,	,	PUNCT
ejpam-3074	280	12	tendencias	tendencias	PROPN
ejpam-3074	280	13	em	em	PROPN
ejpam-3074	280	14	matematica	matematica	PROPN
ejpam-3074	280	15	aplicada	aplicada	PROPN
ejpam-3074	280	16	e	e	PROPN
ejpam-3074	280	17	computacional	computacional	PROPN
ejpam-3074	280	18	14	14	NUM
ejpam-3074	280	19	,	,	PUNCT
ejpam-3074	280	20	3	3	NUM
ejpam-3074	280	21	,	,	PUNCT
ejpam-3074	280	22	483	483	NUM
ejpam-3074	280	23	-	-	SYM
ejpam-3074	280	24	495	495	NUM
ejpam-3074	280	25	.	.	PUNCT
ejpam-3074	281	1	[	[	X
ejpam-3074	281	2	11	11	NUM
ejpam-3074	281	3	]	]	SYM
ejpam-3074	281	4	morais	morais	PROPN
ejpam-3074	281	5	,	,	PUNCT
ejpam-3074	281	6	j.p	j.p	PROPN
ejpam-3074	281	7	.	.	PROPN
ejpam-3074	281	8	,	,	PUNCT
ejpam-3074	281	9	s.	s.	PROPN
ejpam-3074	281	10	georgiev	georgiev	PROPN
ejpam-3074	281	11	and	and	CCONJ
ejpam-3074	281	12	w.	w.	PROPN
ejpam-3074	281	13	spröβig	spröβig	PROPN
ejpam-3074	281	14	(	(	PUNCT
ejpam-3074	281	15	2014	2014	NUM
ejpam-3074	281	16	)	)	PUNCT
ejpam-3074	281	17	.	.	PUNCT
ejpam-3074	281	18	real	real	ADJ
ejpam-3074	281	19	quaternionic	quaternionic	ADJ
ejpam-3074	281	20	calculus	calculus	NOUN
ejpam-3074	281	21	handbook	handbook	NOUN
ejpam-3074	281	22	,	,	PUNCT
ejpam-3074	281	23	birkhuser	birkhuser	NOUN
ejpam-3074	281	24	.	.	PUNCT
ejpam-3074	282	1	springer	springer	PROPN
ejpam-3074	282	2	,	,	PUNCT
ejpam-3074	282	3	basel	basel	PROPN
ejpam-3074	282	4	.	.	PUNCT
ejpam-3074	283	1	[	[	X
ejpam-3074	283	2	12	12	NUM
ejpam-3074	283	3	]	]	PUNCT
ejpam-3074	283	4	saaty	saaty	NOUN
ejpam-3074	283	5	,	,	PUNCT
ejpam-3074	283	6	t.l	t.l	PROPN
ejpam-3074	283	7	.	.	PUNCT
ejpam-3074	283	8	(	(	PUNCT
ejpam-3074	283	9	2015	2015	NUM
ejpam-3074	283	10	)	)	PUNCT
ejpam-3074	283	11	.	.	PUNCT
ejpam-3074	284	1	the	the	DET
ejpam-3074	284	2	neural	neural	ADJ
ejpam-3074	284	3	network	network	NOUN
ejpam-3074	284	4	process	process	NOUN
ejpam-3074	284	5	(	(	PUNCT
ejpam-3074	284	6	nnp	nnp	NOUN
ejpam-3074	284	7	):	):	PUNCT
ejpam-3074	284	8	generalization	generalization	NOUN
ejpam-3074	284	9	of	of	ADP
ejpam-3074	284	10	the	the	DET
ejpam-3074	284	11	ahp	ahp	PROPN
ejpam-3074	284	12	and	and	CCONJ
ejpam-3074	284	13	anp	anp	PROPN
ejpam-3074	284	14	to	to	ADP
ejpam-3074	284	15	the	the	DET
ejpam-3074	284	16	continuous	continuous	ADJ
ejpam-3074	284	17	case	case	NOUN
ejpam-3074	284	18	of	of	ADP
ejpam-3074	284	19	neural	neural	ADJ
ejpam-3074	284	20	firing	firing	NOUN
ejpam-3074	284	21	,	,	PUNCT
ejpam-3074	284	22	rws	rws	VERB
ejpam-3074	284	23	publications	publication	NOUN
ejpam-3074	284	24	(	(	PUNCT
ejpam-3074	284	25	www.rwspublications.com	www.rwspublications.com	X
ejpam-3074	284	26	)	)	PUNCT
ejpam-3074	285	1	[	[	X
ejpam-3074	285	2	13	13	NUM
ejpam-3074	285	3	]	]	SYM
ejpam-3074	285	4	saaty	saaty	NOUN
ejpam-3074	285	5	,	,	PUNCT
ejpam-3074	285	6	t.l	t.l	PROPN
ejpam-3074	285	7	.	.	PUNCT
ejpam-3074	285	8	(	(	PUNCT
ejpam-3074	285	9	2017a	2017a	NUM
ejpam-3074	285	10	)	)	PUNCT
ejpam-3074	285	11	.	.	PUNCT
ejpam-3074	286	1	neurons	neuron	NOUN
ejpam-3074	286	2	the	the	DET
ejpam-3074	286	3	decision	decision	NOUN
ejpam-3074	286	4	makers	maker	NOUN
ejpam-3074	286	5	,	,	PUNCT
ejpam-3074	286	6	part	part	NOUN
ejpam-3074	286	7	i	i	PRON
ejpam-3074	286	8	:	:	PUNCT
ejpam-3074	286	9	the	the	DET
ejpam-3074	286	10	firing	firing	NOUN
ejpam-3074	286	11	function	function	NOUN
ejpam-3074	286	12	of	of	ADP
ejpam-3074	286	13	a	a	DET
ejpam-3074	286	14	single	single	ADJ
ejpam-3074	286	15	neuron	neuron	NOUN
ejpam-3074	286	16	,	,	PUNCT
ejpam-3074	286	17	neural	neural	ADJ
ejpam-3074	286	18	networks	network	NOUN
ejpam-3074	286	19	86	86	NUM
ejpam-3074	286	20	,	,	PUNCT
ejpam-3074	286	21	102	102	NUM
ejpam-3074	286	22	-	-	SYM
ejpam-3074	286	23	114	114	NUM
ejpam-3074	286	24	.	.	PUNCT
ejpam-3074	287	1	[	[	X
ejpam-3074	287	2	14	14	NUM
ejpam-3074	287	3	]	]	PUNCT
ejpam-3074	287	4	saaty	saaty	NOUN
ejpam-3074	287	5	,	,	PUNCT
ejpam-3074	287	6	t.l	t.l	PROPN
ejpam-3074	287	7	.	.	PUNCT
ejpam-3074	287	8	(	(	PUNCT
ejpam-3074	287	9	2017b	2017b	NUM
ejpam-3074	287	10	)	)	PUNCT
ejpam-3074	287	11	.	.	PUNCT
ejpam-3074	288	1	neurons	neuron	NOUN
ejpam-3074	288	2	the	the	DET
ejpam-3074	288	3	decision	decision	NOUN
ejpam-3074	288	4	makers	maker	NOUN
ejpam-3074	288	5	,	,	PUNCT
ejpam-3074	288	6	part	part	PROPN
ejpam-3074	288	7	ii	ii	PROPN
ejpam-3074	288	8	:	:	PUNCT
ejpam-3074	288	9	part	part	NOUN
ejpam-3074	288	10	2the	2the	NUM
ejpam-3074	288	11	firings	firing	NOUN
ejpam-3074	288	12	of	of	ADP
ejpam-3074	288	13	many	many	ADJ
ejpam-3074	288	14	neurons	neuron	NOUN
ejpam-3074	288	15	and	and	CCONJ
ejpam-3074	288	16	their	their	PRON
ejpam-3074	288	17	density	density	NOUN
ejpam-3074	288	18	;	;	PUNCT
ejpam-3074	288	19	the	the	DET
ejpam-3074	288	20	neural	neural	ADJ
ejpam-3074	288	21	network	network	NOUN
ejpam-3074	288	22	its	its	PRON
ejpam-3074	288	23	connections	connection	NOUN
ejpam-3074	288	24	and	and	CCONJ
ejpam-3074	288	25	field	field	NOUN
ejpam-3074	288	26	of	of	ADP
ejpam-3074	288	27	firings	firing	NOUN
ejpam-3074	288	28	,	,	PUNCT
ejpam-3074	288	29	neural	neural	ADJ
ejpam-3074	288	30	networks	network	NOUN
ejpam-3074	288	31	86	86	NUM
ejpam-3074	288	32	,	,	PUNCT
ejpam-3074	288	33	115	115	NUM
ejpam-3074	288	34	-	-	SYM
ejpam-3074	288	35	122	122	NUM
ejpam-3074	288	36	.	.	PUNCT
ejpam-3074	289	1	[	[	X
ejpam-3074	289	2	15	15	NUM
ejpam-3074	289	3	]	]	X
ejpam-3074	289	4	waldman	waldman	PROPN
ejpam-3074	289	5	,	,	PUNCT
ejpam-3074	289	6	m.r	m.r	PROPN
ejpam-3074	289	7	.	.	PROPN
ejpam-3074	289	8	(	(	PUNCT
ejpam-3074	289	9	2014	2014	NUM
ejpam-3074	289	10	)	)	PUNCT
ejpam-3074	289	11	.	.	PUNCT
ejpam-3074	290	1	neurowisdom	neurowisdom	NOUN
ejpam-3074	290	2	101	101	NUM
ejpam-3074	290	3	.	.	PUNCT
ejpam-3074	291	1	e	e	X
ejpam-3074	291	2	-	-	NOUN
ejpam-3074	291	3	book	book	NOUN
ejpam-3074	291	4	.	.	PUNCT
ejpam-3074	292	1	c	c	X
ejpam-3074	292	2	©	©	PROPN
ejpam-3074	292	3	mark	mark	PROPN
ejpam-3074	292	4	robert	robert	PROPN
ejpam-3074	292	5	waldman	waldman	PROPN
ejpam-3074	292	6	.	.	PUNCT