id	sid	tid	token	lemma	pos
ap-1859	1	1	acta	acta	PROPN
ap-1859	1	2	polytechnica	polytechnica	PROPN
ap-1859	1	3	doi:10.14311	doi:10.14311	PROPN
ap-1859	1	4	/	/	SYM
ap-1859	1	5	ap.2013.53.0410	ap.2013.53.0410	PROPN
ap-1859	1	6	acta	acta	PROPN
ap-1859	1	7	polytechnica	polytechnica	PROPN
ap-1859	1	8	53(5):410–415	53(5):410–415	PROPN
ap-1859	1	9	,	,	PUNCT
ap-1859	1	10	2013	2013	NUM
ap-1859	1	11	©	©	PROPN
ap-1859	1	12	czech	czech	PROPN
ap-1859	1	13	technical	technical	PROPN
ap-1859	1	14	university	university	PROPN
ap-1859	1	15	in	in	ADP
ap-1859	1	16	prague	prague	PROPN
ap-1859	1	17	,	,	PUNCT
ap-1859	1	18	2013	2013	NUM
ap-1859	1	19	available	available	ADJ
ap-1859	1	20	online	online	ADV
ap-1859	1	21	at	at	ADP
ap-1859	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-1859	1	23	examples	example	NOUN
ap-1859	1	24	of	of	ADP
ap-1859	1	25	quantum	quantum	ADJ
ap-1859	1	26	holonomy	holonomy	NOUN
ap-1859	1	27	with	with	ADP
ap-1859	1	28	topology	topology	NOUN
ap-1859	1	29	changes	change	VERB
ap-1859	1	30	taksu	taksu	PROPN
ap-1859	1	31	cheona	cheona	PROPN
ap-1859	1	32	,	,	PUNCT
ap-1859	1	33	atushi	atushi	PROPN
ap-1859	1	34	tanakab	tanakab	PROPN
ap-1859	1	35	,	,	PUNCT
ap-1859	1	36	ondřej	ondřej	NOUN
ap-1859	1	37	tureka,∗	tureka,∗	ADP
ap-1859	1	38	a	a	DET
ap-1859	1	39	laboratory	laboratory	NOUN
ap-1859	1	40	of	of	ADP
ap-1859	1	41	physics	physics	PROPN
ap-1859	1	42	,	,	PUNCT
ap-1859	1	43	kochi	kochi	PROPN
ap-1859	1	44	university	university	PROPN
ap-1859	1	45	of	of	ADP
ap-1859	1	46	technology	technology	NOUN
ap-1859	1	47	,	,	PUNCT
ap-1859	1	48	tosa	tosa	PROPN
ap-1859	1	49	yamada	yamada	PROPN
ap-1859	1	50	,	,	PUNCT
ap-1859	1	51	782	782	NUM
ap-1859	1	52	-	-	SYM
ap-1859	1	53	8502	8502	NUM
ap-1859	1	54	kochi	kochi	NOUN
ap-1859	1	55	,	,	PUNCT
ap-1859	1	56	japan	japan	PROPN
ap-1859	1	57	b	b	PROPN
ap-1859	1	58	department	department	PROPN
ap-1859	1	59	of	of	ADP
ap-1859	1	60	physics	physics	PROPN
ap-1859	1	61	,	,	PUNCT
ap-1859	1	62	tokyo	tokyo	PROPN
ap-1859	1	63	metropolitan	metropolitan	PROPN
ap-1859	1	64	university	university	PROPN
ap-1859	1	65	,	,	PUNCT
ap-1859	1	66	hachioji	hachioji	NOUN
ap-1859	1	67	,	,	PUNCT
ap-1859	1	68	192	192	NUM
ap-1859	1	69	-	-	SYM
ap-1859	1	70	0397	0397	NUM
ap-1859	1	71	tokyo	tokyo	PROPN
ap-1859	1	72	,	,	PUNCT
ap-1859	1	73	japan	japan	PROPN
ap-1859	1	74	∗	∗	PROPN
ap-1859	1	75	corresponding	correspond	VERB
ap-1859	1	76	author	author	NOUN
ap-1859	1	77	:	:	PUNCT
ap-1859	1	78	ondrej.turek@kochi-tech.ac.jp	ondrej.turek@kochi-tech.ac.jp	PROPN
ap-1859	1	79	abstract	abstract	ADJ
ap-1859	1	80	.	.	PUNCT
ap-1859	2	1	we	we	PRON
ap-1859	2	2	study	study	VERB
ap-1859	2	3	a	a	DET
ap-1859	2	4	family	family	NOUN
ap-1859	2	5	of	of	ADP
ap-1859	2	6	closed	closed	ADJ
ap-1859	2	7	quantum	quantum	NOUN
ap-1859	2	8	graphs	graph	NOUN
ap-1859	2	9	described	describe	VERB
ap-1859	2	10	by	by	ADP
ap-1859	2	11	one	one	NUM
ap-1859	2	12	singular	singular	ADJ
ap-1859	2	13	vertex	vertex	NOUN
ap-1859	2	14	of	of	ADP
ap-1859	2	15	order	order	NOUN
ap-1859	2	16	n	n	NOUN
ap-1859	2	17	=	=	SYM
ap-1859	2	18	4	4	X
ap-1859	2	19	.	.	PUNCT
ap-1859	2	20	by	by	ADP
ap-1859	2	21	suitable	suitable	ADJ
ap-1859	2	22	choice	choice	NOUN
ap-1859	2	23	of	of	ADP
ap-1859	2	24	the	the	DET
ap-1859	2	25	parameters	parameter	NOUN
ap-1859	2	26	specifying	specify	VERB
ap-1859	2	27	the	the	DET
ap-1859	2	28	singular	singular	ADJ
ap-1859	2	29	vertex	vertex	NOUN
ap-1859	2	30	,	,	PUNCT
ap-1859	2	31	we	we	PRON
ap-1859	2	32	can	can	AUX
ap-1859	2	33	construct	construct	VERB
ap-1859	2	34	a	a	DET
ap-1859	2	35	closed	closed	ADJ
ap-1859	2	36	path	path	NOUN
ap-1859	2	37	in	in	ADP
ap-1859	2	38	the	the	DET
ap-1859	2	39	parameter	parameter	NOUN
ap-1859	2	40	space	space	NOUN
ap-1859	2	41	that	that	PRON
ap-1859	2	42	physically	physically	ADV
ap-1859	2	43	corresponds	correspond	VERB
ap-1859	2	44	to	to	ADP
ap-1859	2	45	the	the	DET
ap-1859	2	46	smooth	smooth	ADJ
ap-1859	2	47	interpolation	interpolation	NOUN
ap-1859	2	48	of	of	ADP
ap-1859	2	49	different	different	ADJ
ap-1859	2	50	topologies	topology	NOUN
ap-1859	2	51	a	a	DET
ap-1859	2	52	ring	ring	NOUN
ap-1859	2	53	,	,	PUNCT
ap-1859	2	54	separate	separate	VERB
ap-1859	2	55	two	two	NUM
ap-1859	2	56	lines	line	NOUN
ap-1859	2	57	,	,	PUNCT
ap-1859	2	58	separate	separate	VERB
ap-1859	2	59	two	two	NUM
ap-1859	2	60	rings	ring	NOUN
ap-1859	2	61	,	,	PUNCT
ap-1859	2	62	two	two	NUM
ap-1859	2	63	rings	ring	NOUN
ap-1859	2	64	with	with	ADP
ap-1859	2	65	a	a	DET
ap-1859	2	66	contact	contact	NOUN
ap-1859	2	67	point	point	NOUN
ap-1859	2	68	.	.	PUNCT
ap-1859	3	1	we	we	PRON
ap-1859	3	2	find	find	VERB
ap-1859	3	3	that	that	SCONJ
ap-1859	3	4	the	the	DET
ap-1859	3	5	spectrum	spectrum	NOUN
ap-1859	3	6	of	of	ADP
ap-1859	3	7	a	a	DET
ap-1859	3	8	quantum	quantum	ADJ
ap-1859	3	9	particle	particle	NOUN
ap-1859	3	10	on	on	ADP
ap-1859	3	11	this	this	DET
ap-1859	3	12	family	family	NOUN
ap-1859	3	13	of	of	ADP
ap-1859	3	14	graphs	graph	NOUN
ap-1859	3	15	shows	show	VERB
ap-1859	3	16	quantum	quantum	ADJ
ap-1859	3	17	holonomy	holonomy	NOUN
ap-1859	3	18	.	.	PUNCT
ap-1859	4	1	keywords	keyword	NOUN
ap-1859	4	2	:	:	PUNCT
ap-1859	4	3	quantum	quantum	ADJ
ap-1859	4	4	graph	graph	NOUN
ap-1859	4	5	,	,	PUNCT
ap-1859	4	6	boundary	boundary	ADJ
ap-1859	4	7	condition	condition	NOUN
ap-1859	4	8	,	,	PUNCT
ap-1859	4	9	eigenvalue	eigenvalue	PROPN
ap-1859	4	10	holonomy	holonomy	NOUN
ap-1859	4	11	.	.	PUNCT
ap-1859	5	1	submitted	submit	VERB
ap-1859	5	2	:	:	PUNCT
ap-1859	5	3	15	15	NUM
ap-1859	5	4	february	february	NOUN
ap-1859	5	5	2013	2013	NUM
ap-1859	5	6	.	.	PUNCT
ap-1859	6	1	accepted	accept	VERB
ap-1859	6	2	:	:	PUNCT
ap-1859	6	3	15	15	NUM
ap-1859	6	4	april	april	PROPN
ap-1859	6	5	2013	2013	NUM
ap-1859	6	6	.	.	PUNCT
ap-1859	7	1	1	1	X
ap-1859	7	2	.	.	X
ap-1859	7	3	introduction	introduction	NOUN
ap-1859	7	4	the	the	DET
ap-1859	7	5	idea	idea	NOUN
ap-1859	7	6	of	of	ADP
ap-1859	7	7	quantum	quantum	ADJ
ap-1859	7	8	mechanics	mechanic	NOUN
ap-1859	7	9	on	on	ADP
ap-1859	7	10	graphs	graph	NOUN
ap-1859	7	11	has	have	AUX
ap-1859	7	12	been	be	AUX
ap-1859	7	13	introduced	introduce	VERB
ap-1859	7	14	in	in	ADP
ap-1859	7	15	the	the	DET
ap-1859	7	16	last	last	ADJ
ap-1859	7	17	century	century	NOUN
ap-1859	7	18	.	.	PUNCT
ap-1859	8	1	a	a	DET
ap-1859	8	2	quantum	quantum	NOUN
ap-1859	8	3	graph	graph	NOUN
ap-1859	8	4	is	be	AUX
ap-1859	8	5	a	a	DET
ap-1859	8	6	metric	metric	ADJ
ap-1859	8	7	graph	graph	NOUN
ap-1859	8	8	with	with	ADP
ap-1859	8	9	a	a	DET
ap-1859	8	10	hamiltonian	hamiltonian	ADJ
ap-1859	8	11	acting	act	VERB
ap-1859	8	12	on	on	ADP
ap-1859	8	13	functions	function	NOUN
ap-1859	8	14	on	on	ADP
ap-1859	8	15	its	its	PRON
ap-1859	8	16	edges	edge	NOUN
ap-1859	8	17	.	.	PUNCT
ap-1859	9	1	during	during	ADP
ap-1859	9	2	the	the	DET
ap-1859	9	3	last	last	ADJ
ap-1859	9	4	30	30	NUM
ap-1859	9	5	years	year	NOUN
ap-1859	9	6	,	,	PUNCT
ap-1859	9	7	this	this	DET
ap-1859	9	8	concept	concept	NOUN
ap-1859	9	9	has	have	AUX
ap-1859	9	10	been	be	AUX
ap-1859	9	11	developed	develop	VERB
ap-1859	9	12	into	into	ADP
ap-1859	9	13	a	a	DET
ap-1859	9	14	powerful	powerful	ADJ
ap-1859	9	15	tool	tool	NOUN
ap-1859	9	16	for	for	ADP
ap-1859	9	17	the	the	DET
ap-1859	9	18	study	study	NOUN
ap-1859	9	19	of	of	ADP
ap-1859	9	20	particles	particle	NOUN
ap-1859	9	21	on	on	ADP
ap-1859	9	22	tiny	tiny	ADJ
ap-1859	9	23	graph	graph	NOUN
ap-1859	9	24	-	-	PUNCT
ap-1859	9	25	like	like	ADJ
ap-1859	9	26	structures	structure	NOUN
ap-1859	9	27	[	[	X
ap-1859	9	28	5	5	NUM
ap-1859	9	29	]	]	PUNCT
ap-1859	9	30	.	.	PUNCT
ap-1859	10	1	since	since	SCONJ
ap-1859	10	2	a	a	DET
ap-1859	10	3	graph	graph	NOUN
ap-1859	10	4	is	be	AUX
ap-1859	10	5	a	a	DET
ap-1859	10	6	one	one	NUM
ap-1859	10	7	-	-	PUNCT
ap-1859	10	8	dimensional	dimensional	ADJ
ap-1859	10	9	variety	variety	NOUN
ap-1859	10	10	,	,	PUNCT
ap-1859	10	11	the	the	DET
ap-1859	10	12	analysis	analysis	NOUN
ap-1859	10	13	of	of	ADP
ap-1859	10	14	a	a	DET
ap-1859	10	15	quantal	quantal	ADJ
ap-1859	10	16	particle	particle	NOUN
ap-1859	10	17	on	on	ADP
ap-1859	10	18	a	a	DET
ap-1859	10	19	graph	graph	NOUN
ap-1859	10	20	consists	consist	VERB
ap-1859	10	21	in	in	ADP
ap-1859	10	22	solving	solve	VERB
ap-1859	10	23	a	a	DET
ap-1859	10	24	system	system	NOUN
ap-1859	10	25	of	of	ADP
ap-1859	10	26	ordinary	ordinary	ADJ
ap-1859	10	27	differential	differential	ADJ
ap-1859	10	28	equations	equation	NOUN
ap-1859	10	29	,	,	PUNCT
ap-1859	10	30	which	which	PRON
ap-1859	10	31	makes	make	VERB
ap-1859	10	32	the	the	DET
ap-1859	10	33	graph	graph	NOUN
ap-1859	10	34	models	model	NOUN
ap-1859	10	35	simple	simple	ADJ
ap-1859	10	36	from	from	ADP
ap-1859	10	37	the	the	DET
ap-1859	10	38	mathematical	mathematical	ADJ
ap-1859	10	39	point	point	NOUN
ap-1859	10	40	of	of	ADP
ap-1859	10	41	view	view	NOUN
ap-1859	10	42	.	.	PUNCT
ap-1859	11	1	therefore	therefore	ADV
ap-1859	11	2	,	,	PUNCT
ap-1859	11	3	quantum	quantum	ADJ
ap-1859	11	4	mechanics	mechanic	NOUN
ap-1859	11	5	on	on	ADP
ap-1859	11	6	graphs	graph	NOUN
ap-1859	11	7	can	can	AUX
ap-1859	11	8	also	also	ADV
ap-1859	11	9	serve	serve	VERB
ap-1859	11	10	as	as	ADP
ap-1859	11	11	a	a	DET
ap-1859	11	12	useful	useful	ADJ
ap-1859	11	13	laboratory	laboratory	NOUN
ap-1859	11	14	for	for	ADP
ap-1859	11	15	the	the	DET
ap-1859	11	16	study	study	NOUN
ap-1859	11	17	of	of	ADP
ap-1859	11	18	various	various	ADJ
ap-1859	11	19	complex	complex	ADJ
ap-1859	11	20	quantum	quantum	NOUN
ap-1859	11	21	phenomena	phenomenon	NOUN
ap-1859	11	22	in	in	ADP
ap-1859	11	23	a	a	DET
ap-1859	11	24	simple	simple	ADJ
ap-1859	11	25	setting	setting	NOUN
ap-1859	11	26	.	.	PUNCT
ap-1859	12	1	here	here	ADV
ap-1859	12	2	we	we	PRON
ap-1859	12	3	examine	examine	VERB
ap-1859	12	4	the	the	DET
ap-1859	12	5	influence	influence	NOUN
ap-1859	12	6	of	of	ADP
ap-1859	12	7	the	the	DET
ap-1859	12	8	topology	topology	NOUN
ap-1859	12	9	of	of	ADP
ap-1859	12	10	quantum	quantum	NOUN
ap-1859	12	11	graphs	graph	NOUN
ap-1859	12	12	on	on	ADP
ap-1859	12	13	spectral	spectral	ADJ
ap-1859	12	14	properties	property	NOUN
ap-1859	12	15	,	,	PUNCT
ap-1859	12	16	taking	take	VERB
ap-1859	12	17	inspiration	inspiration	NOUN
ap-1859	12	18	from	from	ADP
ap-1859	12	19	the	the	DET
ap-1859	12	20	works	work	NOUN
ap-1859	12	21	[	[	X
ap-1859	12	22	1	1	NUM
ap-1859	12	23	]	]	PUNCT
ap-1859	12	24	and	and	CCONJ
ap-1859	12	25	[	[	X
ap-1859	12	26	7	7	NUM
ap-1859	12	27	]	]	PUNCT
ap-1859	12	28	.	.	PUNCT
ap-1859	13	1	we	we	PRON
ap-1859	13	2	may	may	AUX
ap-1859	13	3	regard	regard	VERB
ap-1859	13	4	that	that	SCONJ
ap-1859	13	5	the	the	DET
ap-1859	13	6	topology	topology	NOUN
ap-1859	13	7	change	change	NOUN
ap-1859	13	8	mimics	mimic	VERB
ap-1859	13	9	a	a	DET
ap-1859	13	10	macroscopic	macroscopic	ADJ
ap-1859	13	11	or	or	CCONJ
ap-1859	13	12	violent	violent	ADJ
ap-1859	13	13	variation	variation	NOUN
ap-1859	13	14	of	of	ADP
ap-1859	13	15	systems	system	NOUN
ap-1859	13	16	,	,	PUNCT
ap-1859	13	17	e.g.	e.g.	ADV
ap-1859	13	18	,	,	PUNCT
ap-1859	13	19	the	the	DET
ap-1859	13	20	rupture	rupture	NOUN
ap-1859	13	21	and	and	CCONJ
ap-1859	13	22	connection	connection	NOUN
ap-1859	13	23	of	of	ADP
ap-1859	13	24	quantum	quantum	ADJ
ap-1859	13	25	wires	wire	NOUN
ap-1859	13	26	.	.	PUNCT
ap-1859	14	1	we	we	PRON
ap-1859	14	2	will	will	AUX
ap-1859	14	3	show	show	VERB
ap-1859	14	4	that	that	SCONJ
ap-1859	14	5	a	a	DET
ap-1859	14	6	parametric	parametric	ADJ
ap-1859	14	7	evolution	evolution	NOUN
ap-1859	14	8	of	of	ADP
ap-1859	14	9	an	an	DET
ap-1859	14	10	eigenenergy	eigenenergy	NOUN
ap-1859	14	11	may	may	AUX
ap-1859	14	12	form	form	VERB
ap-1859	14	13	an	an	DET
ap-1859	14	14	open	open	ADJ
ap-1859	14	15	trajectory	trajectory	NOUN
ap-1859	14	16	along	along	ADP
ap-1859	14	17	a	a	DET
ap-1859	14	18	cycle	cycle	NOUN
ap-1859	14	19	involving	involve	VERB
ap-1859	14	20	the	the	DET
ap-1859	14	21	topology	topology	NOUN
ap-1859	14	22	changes	change	NOUN
ap-1859	14	23	of	of	ADP
ap-1859	14	24	graphs	graph	NOUN
ap-1859	14	25	.	.	PUNCT
ap-1859	15	1	if	if	SCONJ
ap-1859	15	2	this	this	PRON
ap-1859	15	3	is	be	AUX
ap-1859	15	4	the	the	DET
ap-1859	15	5	case	case	NOUN
ap-1859	15	6	,	,	PUNCT
ap-1859	15	7	the	the	DET
ap-1859	15	8	trajectory	trajectory	NOUN
ap-1859	15	9	of	of	ADP
ap-1859	15	10	the	the	DET
ap-1859	15	11	corresponding	corresponding	ADJ
ap-1859	15	12	eigenspace	eigenspace	NOUN
ap-1859	15	13	is	be	AUX
ap-1859	15	14	also	also	ADV
ap-1859	15	15	open	open	ADJ
ap-1859	15	16	.	.	PUNCT
ap-1859	16	1	such	such	DET
ap-1859	16	2	a	a	DET
ap-1859	16	3	discontinuity	discontinuity	NOUN
ap-1859	16	4	of	of	ADP
ap-1859	16	5	individual	individual	ADJ
ap-1859	16	6	eigenobjects	eigenobject	NOUN
ap-1859	16	7	is	be	AUX
ap-1859	16	8	called	call	VERB
ap-1859	16	9	quantum	quantum	ADJ
ap-1859	16	10	holonomy	holonomy	NOUN
ap-1859	16	11	[	[	X
ap-1859	16	12	2	2	NUM
ap-1859	16	13	,	,	PUNCT
ap-1859	16	14	4	4	NUM
ap-1859	16	15	,	,	PUNCT
ap-1859	16	16	8	8	NUM
ap-1859	16	17	,	,	PUNCT
ap-1859	16	18	10	10	NUM
ap-1859	16	19	]	]	PUNCT
ap-1859	16	20	.	.	PUNCT
ap-1859	17	1	2	2	X
ap-1859	17	2	.	.	X
ap-1859	17	3	the	the	DET
ap-1859	17	4	model	model	NOUN
ap-1859	17	5	let	let	VERB
ap-1859	17	6	us	we	PRON
ap-1859	17	7	consider	consider	VERB
ap-1859	17	8	a	a	DET
ap-1859	17	9	node	node	NOUN
ap-1859	17	10	with	with	ADP
ap-1859	17	11	four	four	NUM
ap-1859	17	12	outgoing	outgoing	ADJ
ap-1859	17	13	onedimensional	onedimensional	ADJ
ap-1859	17	14	lines	line	NOUN
ap-1859	17	15	of	of	ADP
ap-1859	17	16	finite	finite	ADJ
ap-1859	17	17	length	length	NOUN
ap-1859	17	18	.	.	PUNCT
ap-1859	18	1	let	let	VERB
ap-1859	18	2	the	the	DET
ap-1859	18	3	first	first	ADJ
ap-1859	18	4	two	two	NUM
ap-1859	18	5	lines	line	NOUN
ap-1859	18	6	be	be	AUX
ap-1859	18	7	stuck	stick	VERB
ap-1859	18	8	together	together	ADV
ap-1859	18	9	at	at	ADP
ap-1859	18	10	their	their	PRON
ap-1859	18	11	outer	outer	ADJ
ap-1859	18	12	endpoints	endpoint	NOUN
ap-1859	18	13	to	to	PART
ap-1859	18	14	form	form	VERB
ap-1859	18	15	a	a	DET
ap-1859	18	16	ring	ring	NOUN
ap-1859	18	17	of	of	ADP
ap-1859	18	18	length	length	NOUN
ap-1859	18	19	l1	l1	PROPN
ap-1859	18	20	,	,	PUNCT
ap-1859	18	21	and	and	CCONJ
ap-1859	18	22	likewise	likewise	ADV
ap-1859	18	23	,	,	PUNCT
ap-1859	18	24	the	the	DET
ap-1859	18	25	second	second	ADJ
ap-1859	18	26	two	two	NUM
ap-1859	18	27	lines	line	NOUN
ap-1859	18	28	be	be	AUX
ap-1859	18	29	stuck	stick	VERB
ap-1859	18	30	together	together	ADV
ap-1859	18	31	at	at	ADP
ap-1859	18	32	their	their	PRON
ap-1859	18	33	outer	outer	ADJ
ap-1859	18	34	endpoints	endpoint	NOUN
ap-1859	18	35	to	to	PART
ap-1859	18	36	form	form	VERB
ap-1859	18	37	a	a	DET
ap-1859	18	38	ring	ring	NOUN
ap-1859	18	39	of	of	ADP
ap-1859	18	40	length	length	NOUN
ap-1859	18	41	l2	l2	NOUN
ap-1859	18	42	,	,	PUNCT
ap-1859	18	43	giving	give	VERB
ap-1859	18	44	the	the	DET
ap-1859	18	45	whole	whole	ADJ
ap-1859	18	46	object	object	NOUN
ap-1859	18	47	the	the	DET
ap-1859	18	48	shape	shape	NOUN
ap-1859	18	49	of	of	ADP
ap-1859	18	50	the	the	DET
ap-1859	18	51	character	character	NOUN
ap-1859	18	52	“	"	PUNCT
ap-1859	18	53	∞	∞	PROPN
ap-1859	18	54	”	"	PUNCT
ap-1859	18	55	(	(	PUNCT
ap-1859	18	56	fig	fig	NOUN
ap-1859	18	57	.	.	PUNCT
ap-1859	19	1	1	1	NUM
ap-1859	19	2	)	)	PUNCT
ap-1859	19	3	.	.	PUNCT
ap-1859	20	1	we	we	PRON
ap-1859	20	2	assume	assume	VERB
ap-1859	20	3	there	there	PRON
ap-1859	20	4	is	be	VERB
ap-1859	20	5	no	no	DET
ap-1859	20	6	potential	potential	NOUN
ap-1859	20	7	on	on	ADP
ap-1859	20	8	the	the	DET
ap-1859	20	9	lines	line	NOUN
ap-1859	20	10	outside	outside	ADP
ap-1859	20	11	the	the	DET
ap-1859	20	12	central	central	ADJ
ap-1859	20	13	vertex	vertex	NOUN
ap-1859	20	14	.	.	PUNCT
ap-1859	21	1	therefore	therefore	ADV
ap-1859	21	2	,	,	PUNCT
ap-1859	21	3	a	a	DET
ap-1859	21	4	quantum	quantum	NOUN
ap-1859	21	5	particle	particle	NOUN
ap-1859	21	6	confined	confine	VERB
ap-1859	21	7	to	to	ADP
ap-1859	21	8	this	this	DET
ap-1859	21	9	object	object	NOUN
ap-1859	21	10	figure	figure	NOUN
ap-1859	21	11	1	1	NUM
ap-1859	21	12	.	.	PUNCT
ap-1859	22	1	a	a	DET
ap-1859	22	2	closed	closed	ADJ
ap-1859	22	3	quantum	quantum	NOUN
ap-1859	22	4	graph	graph	NOUN
ap-1859	22	5	with	with	ADP
ap-1859	22	6	an	an	DET
ap-1859	22	7	n	n	NOUN
ap-1859	22	8	=	=	SYM
ap-1859	22	9	4	4	NUM
ap-1859	22	10	singular	singular	ADJ
ap-1859	22	11	vertex	vertex	NOUN
ap-1859	22	12	.	.	PUNCT
ap-1859	23	1	moves	move	NOUN
ap-1859	23	2	freely	freely	ADV
ap-1859	23	3	on	on	ADP
ap-1859	23	4	the	the	DET
ap-1859	23	5	lines	line	NOUN
ap-1859	23	6	,	,	PUNCT
ap-1859	23	7	and	and	CCONJ
ap-1859	23	8	the	the	DET
ap-1859	23	9	only	only	ADJ
ap-1859	23	10	non	non	ADJ
ap-1859	23	11	-	-	ADJ
ap-1859	23	12	trivial	trivial	ADJ
ap-1859	23	13	part	part	NOUN
ap-1859	23	14	of	of	ADP
ap-1859	23	15	the	the	DET
ap-1859	23	16	system	system	NOUN
ap-1859	23	17	is	be	AUX
ap-1859	23	18	the	the	DET
ap-1859	23	19	connection	connection	NOUN
ap-1859	23	20	condition	condition	NOUN
ap-1859	23	21	of	of	ADP
ap-1859	23	22	the	the	DET
ap-1859	23	23	wave	wave	NOUN
ap-1859	23	24	function	function	NOUN
ap-1859	23	25	at	at	ADP
ap-1859	23	26	the	the	DET
ap-1859	23	27	node	node	NOUN
ap-1859	23	28	.	.	PUNCT
ap-1859	24	1	we	we	PRON
ap-1859	24	2	assign	assign	VERB
ap-1859	24	3	the	the	DET
ap-1859	24	4	coordinates	coordinate	NOUN
ap-1859	24	5	x1	x1	PROPN
ap-1859	24	6	∈	∈	PROPN
ap-1859	25	1	[	[	X
ap-1859	25	2	0	0	NUM
ap-1859	25	3	,	,	PUNCT
ap-1859	25	4	l1	l1	PROPN
ap-1859	25	5	]	]	PUNCT
ap-1859	25	6	and	and	CCONJ
ap-1859	25	7	x2	x2	PROPN
ap-1859	25	8	∈	∈	PROPN
ap-1859	25	9	[	[	X
ap-1859	25	10	0	0	NUM
ap-1859	25	11	,	,	PUNCT
ap-1859	25	12	l2	l2	NOUN
ap-1859	25	13	]	]	PUNCT
ap-1859	25	14	to	to	ADP
ap-1859	25	15	the	the	DET
ap-1859	25	16	left	left	ADJ
ap-1859	25	17	ring	ring	NOUN
ap-1859	25	18	and	and	CCONJ
ap-1859	25	19	the	the	DET
ap-1859	25	20	right	right	ADJ
ap-1859	25	21	ring	ring	NOUN
ap-1859	25	22	.	.	PUNCT
ap-1859	26	1	the	the	DET
ap-1859	26	2	values	value	NOUN
ap-1859	26	3	x1	x1	NOUN
ap-1859	27	1	=	=	SYM
ap-1859	27	2	0	0	PUNCT
ap-1859	27	3	and	and	CCONJ
ap-1859	27	4	x2	x2	PROPN
ap-1859	27	5	=	=	SYM
ap-1859	27	6	0	0	NUM
ap-1859	27	7	correspond	correspond	VERB
ap-1859	27	8	to	to	ADP
ap-1859	27	9	the	the	DET
ap-1859	27	10	inner	inner	ADJ
ap-1859	27	11	endpoints	endpoint	NOUN
ap-1859	27	12	1	1	NUM
ap-1859	27	13	and	and	CCONJ
ap-1859	27	14	3	3	NUM
ap-1859	27	15	,	,	PUNCT
ap-1859	27	16	respectively	respectively	ADV
ap-1859	27	17	,	,	PUNCT
ap-1859	27	18	whereas	whereas	SCONJ
ap-1859	27	19	the	the	DET
ap-1859	27	20	values	value	NOUN
ap-1859	27	21	l1	l1	PROPN
ap-1859	27	22	and	and	CCONJ
ap-1859	27	23	l2	l2	NOUN
ap-1859	27	24	correspond	correspond	VERB
ap-1859	27	25	to	to	ADP
ap-1859	27	26	the	the	DET
ap-1859	27	27	inner	inner	ADJ
ap-1859	27	28	endpoints	endpoint	NOUN
ap-1859	27	29	2	2	NUM
ap-1859	27	30	and	and	CCONJ
ap-1859	27	31	4	4	NUM
ap-1859	27	32	,	,	PUNCT
ap-1859	27	33	see	see	VERB
ap-1859	27	34	fig	fig	NOUN
ap-1859	27	35	.	.	PUNCT
ap-1859	28	1	1	1	X
ap-1859	28	2	.	.	PUNCT
ap-1859	28	3	the	the	DET
ap-1859	28	4	behavior	behavior	NOUN
ap-1859	28	5	of	of	ADP
ap-1859	28	6	a	a	DET
ap-1859	28	7	particle	particle	NOUN
ap-1859	28	8	in	in	ADP
ap-1859	28	9	the	the	DET
ap-1859	28	10	central	central	ADJ
ap-1859	28	11	vertex	vertex	NOUN
ap-1859	28	12	of	of	ADP
ap-1859	28	13	degree	degree	NOUN
ap-1859	28	14	4	4	NUM
ap-1859	28	15	is	be	AUX
ap-1859	28	16	determined	determine	VERB
ap-1859	28	17	by	by	ADP
ap-1859	28	18	a	a	DET
ap-1859	28	19	boundary	boundary	ADJ
ap-1859	28	20	condition	condition	NOUN
ap-1859	28	21	in	in	ADP
ap-1859	28	22	the	the	DET
ap-1859	28	23	vertex	vertex	NOUN
ap-1859	28	24	.	.	PUNCT
ap-1859	29	1	the	the	DET
ap-1859	29	2	general	general	ADJ
ap-1859	29	3	form	form	NOUN
ap-1859	29	4	of	of	ADP
ap-1859	29	5	a	a	DET
ap-1859	29	6	boundary	boundary	ADJ
ap-1859	29	7	condition	condition	NOUN
ap-1859	29	8	in	in	ADP
ap-1859	29	9	a	a	DET
ap-1859	29	10	vertex	vertex	NOUN
ap-1859	29	11	of	of	ADP
ap-1859	29	12	degree	degree	NOUN
ap-1859	29	13	n	n	PROPN
ap-1859	29	14	follows	follow	VERB
ap-1859	29	15	from	from	ADP
ap-1859	29	16	the	the	DET
ap-1859	29	17	study	study	NOUN
ap-1859	29	18	of	of	ADP
ap-1859	29	19	self	self	NOUN
ap-1859	29	20	-	-	PUNCT
ap-1859	29	21	adjoint	adjoint	NOUN
ap-1859	29	22	extensions	extension	NOUN
ap-1859	29	23	of	of	ADP
ap-1859	29	24	the	the	DET
ap-1859	29	25	laplacian	laplacian	ADJ
ap-1859	29	26	operator	operator	NOUN
ap-1859	29	27	on	on	ADP
ap-1859	29	28	a	a	DET
ap-1859	29	29	graph	graph	NOUN
ap-1859	29	30	.	.	PUNCT
ap-1859	30	1	the	the	DET
ap-1859	30	2	boundary	boundary	ADJ
ap-1859	30	3	condition	condition	NOUN
ap-1859	30	4	consists	consist	VERB
ap-1859	30	5	of	of	ADP
ap-1859	30	6	n	n	PRON
ap-1859	30	7	equations	equation	NOUN
ap-1859	30	8	connecting	connect	VERB
ap-1859	30	9	the	the	DET
ap-1859	30	10	boundary	boundary	ADJ
ap-1859	30	11	values	value	NOUN
ap-1859	30	12	and	and	CCONJ
ap-1859	30	13	derivatives	derivative	NOUN
ap-1859	30	14	that	that	PRON
ap-1859	30	15	can	can	AUX
ap-1859	30	16	be	be	AUX
ap-1859	30	17	written	write	VERB
ap-1859	30	18	in	in	ADP
ap-1859	30	19	the	the	DET
ap-1859	30	20	form	form	NOUN
ap-1859	30	21	[	[	X
ap-1859	30	22	6	6	NUM
ap-1859	30	23	]	]	PUNCT
ap-1859	30	24	aψ	aψ	X
ap-1859	31	1	+	+	NOUN
ap-1859	31	2	bψ′	bψ′	NOUN
ap-1859	31	3	=	=	SYM
ap-1859	31	4	0	0	PROPN
ap-1859	31	5	,	,	PUNCT
ap-1859	31	6	(	(	PUNCT
ap-1859	31	7	1	1	X
ap-1859	31	8	)	)	PUNCT
ap-1859	31	9	ab†	ab†	NOUN
ap-1859	31	10	=	=	SYM
ap-1859	31	11	ba†	ba†	PROPN
ap-1859	31	12	and	and	CCONJ
ap-1859	31	13	rank(a|b	rank(a|b	PROPN
ap-1859	31	14	)	)	PUNCT
ap-1859	31	15	=	=	SYM
ap-1859	32	1	n	n	CCONJ
ap-1859	32	2	(	(	PUNCT
ap-1859	32	3	2	2	NUM
ap-1859	32	4	)	)	PUNCT
ap-1859	32	5	with	with	ADP
ap-1859	32	6	(	(	PUNCT
ap-1859	32	7	a|b	a|b	NOUN
ap-1859	32	8	)	)	PUNCT
ap-1859	32	9	denoting	denote	VERB
ap-1859	32	10	the	the	DET
ap-1859	32	11	n	n	NUM
ap-1859	32	12	×	×	NOUN
ap-1859	32	13	2n	2n	NUM
ap-1859	32	14	matrix	matrix	NOUN
ap-1859	32	15	composed	compose	VERB
ap-1859	32	16	from	from	ADP
ap-1859	32	17	the	the	DET
ap-1859	32	18	columns	column	NOUN
ap-1859	32	19	of	of	ADP
ap-1859	32	20	matrices	matrix	NOUN
ap-1859	32	21	a	a	PRON
ap-1859	32	22	and	and	CCONJ
ap-1859	32	23	b.	b.	NOUN
ap-1859	32	24	for	for	ADP
ap-1859	32	25	the	the	DET
ap-1859	32	26	graph	graph	NOUN
ap-1859	32	27	depicted	depict	VERB
ap-1859	32	28	in	in	ADP
ap-1859	32	29	figure	figure	NOUN
ap-1859	32	30	1	1	NUM
ap-1859	32	31	,	,	PUNCT
ap-1859	32	32	we	we	PRON
ap-1859	32	33	have	have	VERB
ap-1859	32	34	ψ	ψ	X
ap-1859	32	35	=	=	X
ap-1859	32	36			PROPN
ap-1859	32	37	ψ1(0	ψ1(0	PROPN
ap-1859	32	38	)	)	PUNCT
ap-1859	32	39	ψ1(l1	ψ1(l1	NOUN
ap-1859	32	40	)	)	PUNCT
ap-1859	32	41	ψ2(0	ψ2(0	NOUN
ap-1859	32	42	)	)	PUNCT
ap-1859	32	43	ψ2(l2	ψ2(l2	NOUN
ap-1859	32	44	)	)	PUNCT
ap-1859	32	45			NOUN
ap-1859	32	46	,	,	PUNCT
ap-1859	32	47	ψ′	ψ′	PUNCT
ap-1859	32	48	=	=	SYM
ap-1859	32	49			PROPN
ap-1859	32	50	ψ′	ψ′	NUM
ap-1859	32	51	1(0	1(0	NUM
ap-1859	32	52	)	)	PUNCT
ap-1859	32	53	−ψ′	−ψ′	NUM
ap-1859	32	54	1(l1	1(l1	NUM
ap-1859	32	55	)	)	PUNCT
ap-1859	32	56	ψ′	ψ′	NUM
ap-1859	32	57	2(0	2(0	NUM
ap-1859	32	58	)	)	PUNCT
ap-1859	32	59	−ψ′	−ψ′	X
ap-1859	32	60	2(l2	2(l2	NUM
ap-1859	32	61	)	)	PUNCT
ap-1859	32	62			NOUN
ap-1859	32	63	.	.	PUNCT
ap-1859	33	1	(	(	PUNCT
ap-1859	33	2	3	3	X
ap-1859	33	3	)	)	PUNCT
ap-1859	33	4	410	410	NUM
ap-1859	33	5	http://dx.doi.org/10.14311/ap.2013.53.0410	http://dx.doi.org/10.14311/ap.2013.53.0410	ADP
ap-1859	33	6	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-1859	33	7	vol	vol	NOUN
ap-1859	33	8	.	.	PUNCT
ap-1859	34	1	53	53	NUM
ap-1859	34	2	no	no	NOUN
ap-1859	34	3	.	.	PUNCT
ap-1859	35	1	5/2013	5/2013	NUM
ap-1859	35	2	examples	example	NOUN
ap-1859	35	3	of	of	ADP
ap-1859	35	4	quantum	quantum	ADJ
ap-1859	35	5	holonomy	holonomy	NOUN
ap-1859	35	6	with	with	ADP
ap-1859	35	7	topology	topology	NOUN
ap-1859	35	8	changes	change	NOUN
ap-1859	35	9	figure	figure	VERB
ap-1859	35	10	2	2	NUM
ap-1859	35	11	.	.	PUNCT
ap-1859	36	1	graphs	graph	NOUN
ap-1859	36	2	of	of	ADP
ap-1859	36	3	functions	function	NOUN
ap-1859	36	4	defined	define	VERB
ap-1859	36	5	by	by	ADP
ap-1859	36	6	(	(	PUNCT
ap-1859	36	7	7	7	NUM
ap-1859	36	8	)	)	PUNCT
ap-1859	36	9	for	for	ADP
ap-1859	36	10	θ	θ	PROPN
ap-1859	36	11	∈	∈	PROPN
ap-1859	37	1	[	[	X
ap-1859	37	2	0	0	NUM
ap-1859	37	3	,	,	PUNCT
ap-1859	37	4	2π	2π	NOUN
ap-1859	37	5	]	]	PUNCT
ap-1859	37	6	.	.	PUNCT
ap-1859	38	1	in	in	ADP
ap-1859	38	2	our	our	PRON
ap-1859	38	3	model	model	NOUN
ap-1859	38	4	,	,	PUNCT
ap-1859	38	5	we	we	PRON
ap-1859	38	6	focus	focus	VERB
ap-1859	38	7	on	on	ADP
ap-1859	38	8	a	a	DET
ap-1859	38	9	specific	specific	ADJ
ap-1859	38	10	subset	subset	NOUN
ap-1859	38	11	of	of	ADP
ap-1859	38	12	all	all	DET
ap-1859	38	13	possible	possible	ADJ
ap-1859	38	14	connection	connection	NOUN
ap-1859	38	15	conditions	condition	NOUN
ap-1859	38	16	(	(	PUNCT
ap-1859	38	17	1	1	NUM
ap-1859	38	18	)	)	PUNCT
ap-1859	38	19	,	,	PUNCT
ap-1859	38	20	namely	namely	PROPN
ap-1859	38	21	1	1	NUM
ap-1859	38	22	t	t	NOUN
ap-1859	38	23	b(θ	b(θ	ADJ
ap-1859	38	24	)	)	PUNCT
ap-1859	38	25	t	t	PROPN
ap-1859	38	26	a(θ	a(θ	PROPN
ap-1859	38	27	)	)	PUNCT
ap-1859	38	28	s	s	PART
ap-1859	38	29	d(θ	d(θ	PROPN
ap-1859	38	30	)	)	PUNCT
ap-1859	38	31	0	0	PROPN
ap-1859	38	32	1−	1−	NUM
ap-1859	38	33	c(θ	c(θ	PROPN
ap-1859	38	34	)	)	PUNCT
ap-1859	38	35	0	0	NUM
ap-1859	38	36	t	t	PROPN
ap-1859	38	37	a(θ	a(θ	PROPN
ap-1859	38	38	)	)	PUNCT
ap-1859	38	39	0	0	NUM
ap-1859	38	40	0	0	NUM
ap-1859	38	41	c(θ	c(θ	PROPN
ap-1859	38	42	)	)	PUNCT
ap-1859	38	43	t	t	PROPN
ap-1859	38	44	b′(θ	b′(θ	PROPN
ap-1859	38	45	)	)	PUNCT
ap-1859	38	46	0	0	NUM
ap-1859	38	47	0	0	NUM
ap-1859	38	48	0	0	NUM
ap-1859	38	49	0	0	NUM
ap-1859	38	50	ψ′	ψ′	NOUN
ap-1859	38	51	=	=	SYM
ap-1859	38	52			ADJ
ap-1859	38	53	0	0	NUM
ap-1859	38	54	0	0	NUM
ap-1859	38	55	0	0	NUM
ap-1859	38	56	0	0	NUM
ap-1859	38	57	−t	−t	PROPN
ap-1859	38	58	b(θ	b(θ	ADJ
ap-1859	38	59	)	)	PUNCT
ap-1859	38	60	c(θ	c(θ	PROPN
ap-1859	38	61	)	)	PUNCT
ap-1859	38	62	0	0	NUM
ap-1859	38	63	0	0	NUM
ap-1859	38	64	−t	−t	PROPN
ap-1859	38	65	a(θ	a(θ	PROPN
ap-1859	38	66	)	)	PUNCT
ap-1859	38	67	0	0	NUM
ap-1859	38	68	1−	1−	NUM
ap-1859	38	69	c(θ	c(θ	PROPN
ap-1859	38	70	)	)	PUNCT
ap-1859	38	71	0	0	NUM
ap-1859	38	72	−s	−s	PROPN
ap-1859	38	73	d(θ	d(θ	PROPN
ap-1859	38	74	)	)	PUNCT
ap-1859	38	75	−t	−t	NOUN
ap-1859	38	76	a(θ	a(θ	PROPN
ap-1859	38	77	)	)	PUNCT
ap-1859	38	78	−t	−t	NOUN
ap-1859	38	79	b′(θ	b′(θ	PROPN
ap-1859	38	80	)	)	PUNCT
ap-1859	38	81	1	1	NUM
ap-1859	38	82	ψ	ψ	NOUN
ap-1859	38	83	(	(	PUNCT
ap-1859	38	84	4	4	NUM
ap-1859	38	85	)	)	PUNCT
ap-1859	38	86	where	where	SCONJ
ap-1859	38	87	t	t	NOUN
ap-1859	38	88	and	and	CCONJ
ap-1859	38	89	s	s	VERB
ap-1859	38	90	are	be	AUX
ap-1859	38	91	positive	positive	ADJ
ap-1859	38	92	constants	constant	NOUN
ap-1859	38	93	,	,	PUNCT
ap-1859	38	94	and	and	CCONJ
ap-1859	38	95	a(θ	a(θ	NOUN
ap-1859	38	96	)	)	PUNCT
ap-1859	38	97	,	,	PUNCT
ap-1859	38	98	b(θ	b(θ	ADV
ap-1859	38	99	)	)	PUNCT
ap-1859	38	100	,	,	PUNCT
ap-1859	38	101	b′(θ	b′(θ	PROPN
ap-1859	38	102	)	)	PUNCT
ap-1859	38	103	,	,	PUNCT
ap-1859	38	104	c(θ	c(θ	PROPN
ap-1859	38	105	)	)	PUNCT
ap-1859	38	106	and	and	CCONJ
ap-1859	38	107	d(θ	d(θ	PROPN
ap-1859	38	108	)	)	PUNCT
ap-1859	38	109	are	be	AUX
ap-1859	38	110	real	real	ADJ
ap-1859	38	111	periodic	periodic	ADJ
ap-1859	38	112	functions	function	NOUN
ap-1859	38	113	of	of	ADP
ap-1859	38	114	θ	θ	PROPN
ap-1859	38	115	with	with	ADP
ap-1859	38	116	period	period	NOUN
ap-1859	38	117	2π	2π	NOUN
ap-1859	38	118	that	that	PRON
ap-1859	38	119	vary	vary	VERB
ap-1859	38	120	within	within	ADP
ap-1859	38	121	the	the	DET
ap-1859	38	122	range	range	NOUN
ap-1859	38	123	between	between	ADP
ap-1859	38	124	0	0	NUM
ap-1859	38	125	and	and	CCONJ
ap-1859	38	126	1	1	NUM
ap-1859	38	127	.	.	PUNCT
ap-1859	39	1	in	in	ADP
ap-1859	39	2	addition	addition	NOUN
ap-1859	39	3	,	,	PUNCT
ap-1859	39	4	it	it	PRON
ap-1859	39	5	can	can	AUX
ap-1859	39	6	easily	easily	ADV
ap-1859	39	7	be	be	AUX
ap-1859	39	8	shown	show	VERB
ap-1859	39	9	that	that	SCONJ
ap-1859	39	10	the	the	DET
ap-1859	39	11	functions	function	NOUN
ap-1859	39	12	must	must	AUX
ap-1859	39	13	satisfy	satisfy	VERB
ap-1859	39	14	a(θ	a(θ	VERB
ap-1859	39	15	)	)	PUNCT
ap-1859	39	16	6=	6=	SYM
ap-1859	39	17	0	0	PUNCT
ap-1859	40	1	=	=	NOUN
ap-1859	40	2	⇒	⇒	NOUN
ap-1859	40	3	c(θ	c(θ	PROPN
ap-1859	40	4	)	)	PUNCT
ap-1859	41	1	=	=	SYM
ap-1859	41	2	0	0	NUM
ap-1859	41	3	,	,	PUNCT
ap-1859	41	4	(	(	PUNCT
ap-1859	41	5	5	5	NUM
ap-1859	41	6	)	)	PUNCT
ap-1859	41	7	b(θ	b(θ	ADJ
ap-1859	41	8	)	)	PUNCT
ap-1859	41	9	,	,	PUNCT
ap-1859	41	10	b′(θ	b′(θ	PROPN
ap-1859	41	11	)	)	PUNCT
ap-1859	41	12	6=	6=	ADP
ap-1859	41	13	0	0	PUNCT
ap-1859	42	1	=	=	NOUN
ap-1859	42	2	⇒	⇒	NOUN
ap-1859	42	3	c(θ	c(θ	PROPN
ap-1859	42	4	)	)	PUNCT
ap-1859	43	1	=	=	SYM
ap-1859	43	2	1	1	NUM
ap-1859	43	3	(	(	PUNCT
ap-1859	43	4	6	6	NUM
ap-1859	43	5	)	)	PUNCT
ap-1859	43	6	for	for	ADP
ap-1859	43	7	all	all	DET
ap-1859	43	8	θ	θ	NOUN
ap-1859	43	9	∈	∈	PROPN
ap-1859	44	1	[	[	X
ap-1859	44	2	0	0	NUM
ap-1859	44	3	,	,	PUNCT
ap-1859	44	4	2π	2π	NOUN
ap-1859	44	5	]	]	PUNCT
ap-1859	44	6	in	in	ADP
ap-1859	44	7	order	order	NOUN
ap-1859	44	8	that	that	SCONJ
ap-1859	44	9	the	the	DET
ap-1859	44	10	matrices	matrix	NOUN
ap-1859	44	11	a	a	PRON
ap-1859	44	12	,	,	PUNCT
ap-1859	44	13	b	b	PROPN
ap-1859	44	14	involved	involve	VERB
ap-1859	44	15	in	in	ADP
ap-1859	44	16	the	the	DET
ap-1859	44	17	connection	connection	NOUN
ap-1859	44	18	condition	condition	NOUN
ap-1859	44	19	(	(	PUNCT
ap-1859	44	20	4	4	X
ap-1859	44	21	)	)	PUNCT
ap-1859	44	22	obey	obey	NOUN
ap-1859	44	23	(	(	PUNCT
ap-1859	44	24	2	2	NUM
ap-1859	44	25	)	)	PUNCT
ap-1859	44	26	.	.	PUNCT
ap-1859	45	1	it	it	PRON
ap-1859	45	2	can	can	AUX
ap-1859	45	3	be	be	AUX
ap-1859	45	4	shown	show	VERB
ap-1859	45	5	that	that	SCONJ
ap-1859	45	6	the	the	DET
ap-1859	45	7	boundary	boundary	ADJ
ap-1859	45	8	condition	condition	NOUN
ap-1859	45	9	(	(	PUNCT
ap-1859	45	10	4	4	X
ap-1859	45	11	)	)	PUNCT
ap-1859	45	12	never	never	ADV
ap-1859	45	13	requires	require	VERB
ap-1859	45	14	the	the	DET
ap-1859	45	15	wave	wave	NOUN
ap-1859	45	16	function	function	NOUN
ap-1859	45	17	to	to	PART
ap-1859	45	18	obey	obey	VERB
ap-1859	45	19	ψ1(0	ψ1(0	PROPN
ap-1859	45	20	)	)	PUNCT
ap-1859	46	1	=	=	PUNCT
ap-1859	46	2	ψ1(l1	ψ1(l1	NOUN
ap-1859	46	3	)	)	PUNCT
ap-1859	46	4	=	=	SYM
ap-1859	46	5	ψ2(0	ψ2(0	NOUN
ap-1859	46	6	)	)	PUNCT
ap-1859	46	7	=	=	SYM
ap-1859	46	8	ψ2(l2	ψ2(l2	NOUN
ap-1859	46	9	)	)	PUNCT
ap-1859	46	10	.	.	PUNCT
ap-1859	47	1	this	this	PRON
ap-1859	47	2	implies	imply	VERB
ap-1859	47	3	a	a	DET
ap-1859	47	4	generic	generic	ADJ
ap-1859	47	5	discontinuity	discontinuity	NOUN
ap-1859	47	6	of	of	ADP
ap-1859	47	7	the	the	DET
ap-1859	47	8	wave	wave	NOUN
ap-1859	47	9	function	function	NOUN
ap-1859	47	10	in	in	ADP
ap-1859	47	11	the	the	DET
ap-1859	47	12	central	central	ADJ
ap-1859	47	13	vertex	vertex	NOUN
ap-1859	47	14	,	,	PUNCT
ap-1859	47	15	for	for	ADP
ap-1859	47	16	which	which	PRON
ap-1859	47	17	we	we	PRON
ap-1859	47	18	call	call	VERB
ap-1859	47	19	the	the	DET
ap-1859	47	20	vertex	vertex	NOUN
ap-1859	47	21	“	"	PUNCT
ap-1859	47	22	singular	singular	PROPN
ap-1859	47	23	”	"	PUNCT
ap-1859	47	24	.	.	PUNCT
ap-1859	48	1	2.1	2.1	NUM
ap-1859	48	2	.	.	PUNCT
ap-1859	49	1	long	long	ADJ
ap-1859	49	2	cycle	cycle	NOUN
ap-1859	49	3	we	we	PRON
ap-1859	49	4	first	first	ADV
ap-1859	49	5	consider	consider	VERB
ap-1859	49	6	the	the	DET
ap-1859	49	7	boundary	boundary	ADJ
ap-1859	49	8	conditions	condition	NOUN
ap-1859	49	9	(	(	PUNCT
ap-1859	49	10	4	4	NUM
ap-1859	49	11	)	)	PUNCT
ap-1859	49	12	with	with	ADP
ap-1859	49	13	functions	function	NOUN
ap-1859	49	14	a(θ	a(θ	VERB
ap-1859	49	15	)	)	PUNCT
ap-1859	49	16	,	,	PUNCT
ap-1859	49	17	b(θ	b(θ	ADV
ap-1859	49	18	)	)	PUNCT
ap-1859	49	19	,	,	PUNCT
ap-1859	49	20	b′(θ	b′(θ	PROPN
ap-1859	49	21	)	)	PUNCT
ap-1859	49	22	,	,	PUNCT
ap-1859	49	23	c(θ	c(θ	PROPN
ap-1859	49	24	)	)	PUNCT
ap-1859	49	25	and	and	CCONJ
ap-1859	49	26	d(θ	d(θ	PROPN
ap-1859	49	27	)	)	PUNCT
ap-1859	49	28	chosen	choose	VERB
ap-1859	49	29	as	as	ADP
ap-1859	49	30	a(θ	a(θ	PROPN
ap-1859	49	31	)	)	PUNCT
ap-1859	49	32	=	=	PUNCT
ap-1859	50	1	cos	cos	ADP
ap-1859	50	2	θ	θ	PROPN
ap-1859	50	3	−	−	NUM
ap-1859	50	4	1	1	NUM
ap-1859	50	5	2	2	NUM
ap-1859	50	6	+	+	CCONJ
ap-1859	50	7	∣∣∣cos	∣∣∣cos	PROPN
ap-1859	50	8	θ	θ	PROPN
ap-1859	50	9	−	−	NOUN
ap-1859	50	10	1	1	NUM
ap-1859	50	11	2	2	NUM
ap-1859	50	12	∣∣∣	∣∣∣	ADJ
ap-1859	50	13	,	,	PUNCT
ap-1859	50	14	b(θ	b(θ	ADJ
ap-1859	50	15	)	)	PUNCT
ap-1859	50	16	=	=	SYM
ap-1859	51	1	−	−	PROPN
ap-1859	51	2	cos	cos	ADP
ap-1859	51	3	θ	θ	PROPN
ap-1859	51	4	−	−	NUM
ap-1859	51	5	1	1	NUM
ap-1859	51	6	2	2	NUM
ap-1859	51	7	+	+	CCONJ
ap-1859	51	8	∣∣∣cos	∣∣∣cos	PROPN
ap-1859	51	9	θ	θ	PROPN
ap-1859	52	1	+	+	CCONJ
ap-1859	52	2	1	1	NUM
ap-1859	52	3	2	2	NUM
ap-1859	52	4	∣∣∣	∣∣∣	ADJ
ap-1859	52	5	,	,	PUNCT
ap-1859	52	6	b′(θ	b′(θ	NOUN
ap-1859	52	7	)	)	PUNCT
ap-1859	52	8	=	=	SYM
ap-1859	53	1	1	1	NUM
ap-1859	53	2	4−	4−	NUM
ap-1859	53	3	2	2	NUM
ap-1859	53	4	√	√	NUM
ap-1859	53	5	3	3	NUM
ap-1859	53	6	{	{	PUNCT
ap-1859	53	7	sin	sin	NOUN
ap-1859	53	8	θ	θ	PROPN
ap-1859	53	9	−	−	NOUN
ap-1859	53	10	√	√	NOUN
ap-1859	53	11	3	3	NUM
ap-1859	53	12	cos	cos	PROPN
ap-1859	53	13	θ	θ	PROPN
ap-1859	53	14	−	−	NOUN
ap-1859	54	1	√	√	NOUN
ap-1859	54	2	3	3	NUM
ap-1859	54	3	−	−	PROPN
ap-1859	54	4	∣∣sin	∣∣sin	PROPN
ap-1859	54	5	θ	θ	PROPN
ap-1859	54	6	−√3	−√3	NOUN
ap-1859	54	7	cos	cos	PROPN
ap-1859	55	1	θ	θ	PROPN
ap-1859	55	2	−	−	NOUN
ap-1859	55	3	√	√	NOUN
ap-1859	55	4	3	3	NUM
ap-1859	55	5	∣∣	∣∣	NOUN
ap-1859	55	6	}	}	PUNCT
ap-1859	55	7	,	,	PUNCT
ap-1859	55	8	c(θ	c(θ	PROPN
ap-1859	55	9	)	)	PUNCT
ap-1859	56	1	=	=	PUNCT
ap-1859	57	1	1√	1√	NOUN
ap-1859	57	2	3−	3−	NUM
ap-1859	57	3	1	1	NUM
ap-1859	57	4	{	{	PUNCT
ap-1859	57	5	√	√	NOUN
ap-1859	57	6	3	3	NUM
ap-1859	57	7	2	2	NUM
ap-1859	57	8	−	−	NOUN
ap-1859	57	9	1	1	NUM
ap-1859	57	10	2	2	NUM
ap-1859	57	11	+	+	NUM
ap-1859	57	12	∣∣∣∣∣∣∣sin	∣∣∣∣∣∣∣sin	NOUN
ap-1859	57	13	θ2	θ2	PROPN
ap-1859	57	14	∣∣∣−	∣∣∣−	PROPN
ap-1859	57	15	1	1	NUM
ap-1859	57	16	2	2	NUM
ap-1859	57	17	∣∣∣∣	∣∣∣∣	NOUN
ap-1859	57	18	−	−	NOUN
ap-1859	57	19	∣∣∣∣∣∣∣sin	∣∣∣∣∣∣∣sin	NOUN
ap-1859	57	20	θ2	θ2	PROPN
ap-1859	57	21	∣∣∣−	∣∣∣−	ADJ
ap-1859	57	22	√	√	ADP
ap-1859	57	23	3	3	NUM
ap-1859	57	24	2	2	NUM
ap-1859	57	25	∣∣∣∣	∣∣∣∣	NOUN
ap-1859	57	26	}	}	PUNCT
ap-1859	57	27	,	,	PUNCT
ap-1859	57	28	d(θ	d(θ	PROPN
ap-1859	57	29	)	)	PUNCT
ap-1859	57	30	=	=	PUNCT
ap-1859	58	1	1	1	NUM
ap-1859	58	2	2	2	NUM
ap-1859	58	3	√	√	NUM
ap-1859	58	4	3	3	NUM
ap-1859	58	5	{	{	PUNCT
ap-1859	58	6	|	|	ADV
ap-1859	58	7	sin	sin	VERB
ap-1859	58	8	θ|	θ|	PROPN
ap-1859	58	9	−	−	ADP
ap-1859	58	10	sin	sin	NOUN
ap-1859	58	11	θ	θ	PROPN
ap-1859	58	12	+	+	CCONJ
ap-1859	58	13	√	√	NUM
ap-1859	58	14	3	3	NUM
ap-1859	58	15	−	−	NOUN
ap-1859	58	16	∣∣|	∣∣|	PUNCT
ap-1859	58	17	sin	sin	VERB
ap-1859	58	18	θ|	θ|	PROPN
ap-1859	58	19	−	−	ADP
ap-1859	58	20	sin	sin	NOUN
ap-1859	58	21	θ	θ	PROPN
ap-1859	58	22	−	−	NOUN
ap-1859	58	23	√	√	NOUN
ap-1859	58	24	3	3	NUM
ap-1859	58	25	∣∣	∣∣	PUNCT
ap-1859	58	26	}	}	PUNCT
ap-1859	58	27	.	.	PUNCT
ap-1859	59	1	(	(	PUNCT
ap-1859	59	2	7	7	X
ap-1859	59	3	)	)	PUNCT
ap-1859	59	4	the	the	DET
ap-1859	59	5	graphs	graph	NOUN
ap-1859	59	6	of	of	ADP
ap-1859	59	7	these	these	DET
ap-1859	59	8	functions	function	NOUN
ap-1859	59	9	for	for	ADP
ap-1859	59	10	θ	θ	PROPN
ap-1859	59	11	∈	∈	PROPN
ap-1859	60	1	[	[	X
ap-1859	60	2	0	0	NUM
ap-1859	60	3	,	,	PUNCT
ap-1859	60	4	2π	2π	NOUN
ap-1859	60	5	]	]	PUNCT
ap-1859	60	6	are	be	AUX
ap-1859	60	7	plotted	plot	VERB
ap-1859	60	8	in	in	ADP
ap-1859	60	9	fig	fig	NOUN
ap-1859	60	10	.	.	PUNCT
ap-1859	61	1	2	2	X
ap-1859	61	2	.	.	X
ap-1859	61	3	the	the	DET
ap-1859	61	4	interval	interval	NOUN
ap-1859	61	5	[	[	X
ap-1859	61	6	0	0	NUM
ap-1859	61	7	,	,	PUNCT
ap-1859	61	8	2π	2π	NOUN
ap-1859	61	9	]	]	PUNCT
ap-1859	61	10	can	can	AUX
ap-1859	61	11	be	be	AUX
ap-1859	61	12	divided	divide	VERB
ap-1859	61	13	into	into	ADP
ap-1859	61	14	six	six	NUM
ap-1859	61	15	regions	region	NOUN
ap-1859	61	16	,	,	PUNCT
ap-1859	61	17	in	in	ADP
ap-1859	61	18	each	each	PRON
ap-1859	61	19	of	of	ADP
ap-1859	61	20	which	which	PRON
ap-1859	61	21	the	the	DET
ap-1859	61	22	vector	vector	NOUN
ap-1859	61	23	(	(	PUNCT
ap-1859	61	24	a(θ	a(θ	PROPN
ap-1859	61	25	)	)	PUNCT
ap-1859	61	26	,	,	PUNCT
ap-1859	61	27	b(θ	b(θ	ADJ
ap-1859	61	28	)	)	PUNCT
ap-1859	61	29	,	,	PUNCT
ap-1859	61	30	b′(θ	b′(θ	PROPN
ap-1859	61	31	)	)	PUNCT
ap-1859	61	32	,	,	PUNCT
ap-1859	61	33	c(θ	c(θ	PROPN
ap-1859	61	34	)	)	PUNCT
ap-1859	61	35	,	,	PUNCT
ap-1859	61	36	d(θ	d(θ	PROPN
ap-1859	61	37	)	)	PUNCT
ap-1859	61	38	)	)	PUNCT
ap-1859	61	39	has	have	VERB
ap-1859	61	40	a	a	DET
ap-1859	61	41	different	different	ADJ
ap-1859	61	42	structure	structure	NOUN
ap-1859	61	43	of	of	ADP
ap-1859	61	44	zero	zero	NUM
ap-1859	61	45	and	and	CCONJ
ap-1859	61	46	nonzero	nonzero	NOUN
ap-1859	61	47	entries	entry	NOUN
ap-1859	61	48	.	.	PUNCT
ap-1859	62	1	as	as	SCONJ
ap-1859	62	2	we	we	PRON
ap-1859	62	3	show	show	VERB
ap-1859	62	4	below	below	ADV
ap-1859	62	5	,	,	PUNCT
ap-1859	62	6	these	these	DET
ap-1859	62	7	regions	region	NOUN
ap-1859	62	8	correspond	correspond	VERB
ap-1859	62	9	to	to	ADP
ap-1859	62	10	mutually	mutually	ADV
ap-1859	62	11	different	different	ADJ
ap-1859	62	12	topologies	topology	NOUN
ap-1859	62	13	of	of	ADP
ap-1859	62	14	the	the	DET
ap-1859	62	15	system	system	NOUN
ap-1859	62	16	.	.	PUNCT
ap-1859	63	1	this	this	PRON
ap-1859	63	2	extends	extend	VERB
ap-1859	63	3	the	the	DET
ap-1859	63	4	basic	basic	ADJ
ap-1859	63	5	idea	idea	NOUN
ap-1859	63	6	of	of	ADP
ap-1859	63	7	parametric	parametric	ADJ
ap-1859	63	8	systems	system	NOUN
ap-1859	63	9	with	with	ADP
ap-1859	63	10	a	a	DET
ap-1859	63	11	varying	vary	VERB
ap-1859	63	12	topology	topology	NOUN
ap-1859	63	13	introduced	introduce	VERB
ap-1859	63	14	in	in	ADP
ap-1859	63	15	the	the	DET
ap-1859	63	16	works	work	NOUN
ap-1859	63	17	of	of	ADP
ap-1859	63	18	balachandran	balachandran	PROPN
ap-1859	63	19	et	et	PROPN
ap-1859	63	20	.	.	PUNCT
ap-1859	64	1	al	al	PROPN
ap-1859	64	2	.	.	PUNCT
ap-1859	65	1	[	[	X
ap-1859	65	2	1	1	X
ap-1859	65	3	]	]	PUNCT
ap-1859	65	4	and	and	CCONJ
ap-1859	65	5	also	also	ADV
ap-1859	65	6	in	in	ADP
ap-1859	65	7	[	[	X
ap-1859	65	8	7	7	NUM
ap-1859	65	9	]	]	PUNCT
ap-1859	65	10	.	.	PUNCT
ap-1859	66	1	our	our	PRON
ap-1859	66	2	use	use	NOUN
ap-1859	66	3	of	of	ADP
ap-1859	66	4	a	a	DET
ap-1859	66	5	single	single	ADJ
ap-1859	66	6	n	n	NOUN
ap-1859	66	7	=	=	SYM
ap-1859	66	8	4	4	NUM
ap-1859	66	9	singular	singular	ADJ
ap-1859	66	10	vertex	vertex	NOUN
ap-1859	66	11	makes	make	VERB
ap-1859	66	12	the	the	DET
ap-1859	66	13	treatment	treatment	NOUN
ap-1859	66	14	more	more	ADV
ap-1859	66	15	systematic	systematic	ADJ
ap-1859	66	16	and	and	CCONJ
ap-1859	66	17	more	more	ADV
ap-1859	66	18	unified	unified	ADJ
ap-1859	66	19	.	.	PUNCT
ap-1859	67	1	region	region	NOUN
ap-1859	67	2	i.	i.	PROPN
ap-1859	67	3	for	for	ADP
ap-1859	67	4	θ	θ	PROPN
ap-1859	67	5	∈	∈	PROPN
ap-1859	68	1	[	[	X
ap-1859	68	2	0	0	NUM
ap-1859	68	3	,	,	PUNCT
ap-1859	68	4	π	π	PROPN
ap-1859	68	5	3	3	NUM
ap-1859	68	6	]	]	PUNCT
ap-1859	68	7	,	,	PUNCT
ap-1859	68	8	we	we	PRON
ap-1859	68	9	have	have	VERB
ap-1859	68	10	1	1	NUM
ap-1859	68	11	t	t	NOUN
ap-1859	68	12	·	·	PUNCT
ap-1859	68	13	a(θ	a(θ	VERB
ap-1859	68	14	)	)	PUNCT
ap-1859	68	15	1	1	NUM
ap-1859	68	16	t	t	NOUN
ap-1859	68	17	·	·	PUNCT
ap-1859	68	18	a(θ	a(θ	ADJ
ap-1859	68	19	)	)	PUNCT
ap-1859	68	20	ψ′	ψ′	NOUN
ap-1859	68	21	=	=	NOUN
ap-1859	68	22	−t	−t	NOUN
ap-1859	68	23	·	·	PUNCT
ap-1859	68	24	a(θ	a(θ	VERB
ap-1859	68	25	)	)	PUNCT
ap-1859	68	26	1	1	NUM
ap-1859	68	27	−t	−t	NOUN
ap-1859	68	28	·	·	PUNCT
ap-1859	68	29	a(θ	a(θ	VERB
ap-1859	68	30	)	)	PUNCT
ap-1859	68	31	1	1	NUM
ap-1859	68	32	ψ	ψ	NOUN
ap-1859	68	33	,	,	PUNCT
ap-1859	68	34	(	(	PUNCT
ap-1859	68	35	8)	8)	NUM
ap-1859	68	36	where	where	SCONJ
ap-1859	68	37	ta(θ	ta(θ	NUM
ap-1859	68	38	)	)	PUNCT
ap-1859	68	39	takes	take	VERB
ap-1859	68	40	the	the	DET
ap-1859	68	41	value	value	NOUN
ap-1859	68	42	t	t	NOUN
ap-1859	68	43	at	at	ADP
ap-1859	68	44	θ	θ	PROPN
ap-1859	68	45	=	=	SYM
ap-1859	68	46	0	0	PUNCT
ap-1859	68	47	and	and	CCONJ
ap-1859	68	48	it	it	PRON
ap-1859	68	49	continuously	continuously	ADV
ap-1859	68	50	decreases	decrease	VERB
ap-1859	68	51	down	down	ADV
ap-1859	68	52	to	to	ADP
ap-1859	68	53	0	0	NUM
ap-1859	68	54	at	at	ADP
ap-1859	68	55	θ	θ	PROPN
ap-1859	68	56	=	=	SYM
ap-1859	68	57	π	π	NOUN
ap-1859	68	58	3	3	NUM
ap-1859	68	59	.	.	PUNCT
ap-1859	69	1	with	with	ADP
ap-1859	69	2	regard	regard	NOUN
ap-1859	69	3	to	to	ADP
ap-1859	69	4	the	the	DET
ap-1859	69	5	structure	structure	NOUN
ap-1859	69	6	of	of	ADP
ap-1859	69	7	(	(	PUNCT
ap-1859	69	8	8)	8)	NUM
ap-1859	69	9	,	,	PUNCT
ap-1859	69	10	endpoint	endpoint	NOUN
ap-1859	69	11	1	1	NUM
ap-1859	69	12	is	be	AUX
ap-1859	69	13	joined	join	VERB
ap-1859	69	14	to	to	PART
ap-1859	69	15	endpoint	endpoint	VERB
ap-1859	69	16	2	2	NUM
ap-1859	69	17	and	and	CCONJ
ap-1859	69	18	endpoint	endpoint	VERB
ap-1859	69	19	3	3	NUM
ap-1859	69	20	is	be	AUX
ap-1859	69	21	joined	join	VERB
ap-1859	69	22	to	to	PART
ap-1859	69	23	endpoint	endpoint	VERB
ap-1859	69	24	4	4	NUM
ap-1859	69	25	.	.	PUNCT
ap-1859	70	1	on	on	ADP
ap-1859	70	2	the	the	DET
ap-1859	70	3	other	other	ADJ
ap-1859	70	4	hand	hand	NOUN
ap-1859	70	5	,	,	PUNCT
ap-1859	70	6	endpoints	endpoint	NOUN
ap-1859	70	7	1	1	NUM
ap-1859	70	8	and	and	CCONJ
ap-1859	70	9	2	2	NUM
ap-1859	70	10	are	be	AUX
ap-1859	70	11	separated	separate	VERB
ap-1859	70	12	,	,	PUNCT
ap-1859	70	13	so	so	ADV
ap-1859	70	14	are	be	AUX
ap-1859	70	15	3	3	NUM
ap-1859	70	16	and	and	CCONJ
ap-1859	70	17	4	4	NUM
ap-1859	70	18	.	.	PUNCT
ap-1859	71	1	therefore	therefore	ADV
ap-1859	71	2	,	,	PUNCT
ap-1859	71	3	the	the	DET
ap-1859	71	4	system	system	NOUN
ap-1859	71	5	is	be	AUX
ap-1859	71	6	topologically	topologically	ADV
ap-1859	71	7	equivalent	equivalent	ADJ
ap-1859	71	8	to	to	ADP
ap-1859	71	9	a	a	DET
ap-1859	71	10	single	single	ADJ
ap-1859	71	11	ring	ring	NOUN
ap-1859	71	12	,	,	PUNCT
ap-1859	71	13	see	see	VERB
ap-1859	71	14	fig	fig	NOUN
ap-1859	71	15	.	.	PUNCT
ap-1859	72	1	3	3	X
ap-1859	72	2	.	.	X
ap-1859	72	3	region	region	PROPN
ap-1859	72	4	ii	ii	PROPN
ap-1859	72	5	.	.	PUNCT
ap-1859	73	1	for	for	ADP
ap-1859	73	2	θ	θ	PROPN
ap-1859	73	3	∈	∈	PROPN
ap-1859	73	4	[	[	PUNCT
ap-1859	73	5	π	π	NOUN
ap-1859	73	6	3	3	NUM
ap-1859	73	7	,	,	PUNCT
ap-1859	73	8	2π	2π	PROPN
ap-1859	73	9	3	3	NUM
ap-1859	73	10	]	]	PUNCT
ap-1859	73	11	,	,	PUNCT
ap-1859	73	12	we	we	PRON
ap-1859	73	13	have	have	VERB
ap-1859	73	14	1	1	NUM
ap-1859	73	15	1−	1−	NUM
ap-1859	73	16	c(θ	c(θ	PROPN
ap-1859	73	17	)	)	PUNCT
ap-1859	73	18	c(θ	c(θ	PROPN
ap-1859	73	19	)	)	PUNCT
ap-1859	73	20	ψ′	ψ′	NOUN
ap-1859	73	21	=	=	SYM
ap-1859	73	22			PROPN
ap-1859	73	23	c(θ	c(θ	PROPN
ap-1859	73	24	)	)	PUNCT
ap-1859	73	25	1−	1−	NUM
ap-1859	73	26	c(θ	c(θ	PROPN
ap-1859	73	27	)	)	PUNCT
ap-1859	73	28	1	1	NUM
ap-1859	73	29	ψ	ψ	NOUN
ap-1859	73	30	,	,	PUNCT
ap-1859	73	31	(	(	PUNCT
ap-1859	73	32	9	9	NUM
ap-1859	73	33	)	)	PUNCT
ap-1859	73	34	where	where	SCONJ
ap-1859	73	35	we	we	PRON
ap-1859	73	36	start	start	VERB
ap-1859	73	37	with	with	ADP
ap-1859	73	38	the	the	DET
ap-1859	73	39	value	value	NOUN
ap-1859	73	40	c	c	X
ap-1859	73	41	(	(	PUNCT
ap-1859	73	42	π	π	NOUN
ap-1859	73	43	3	3	NUM
ap-1859	73	44	)	)	PUNCT
ap-1859	73	45	=	=	SYM
ap-1859	73	46	0	0	PUNCT
ap-1859	73	47	and	and	CCONJ
ap-1859	73	48	continuously	continuously	ADV
ap-1859	73	49	increase	increase	VERB
ap-1859	73	50	it	it	PRON
ap-1859	73	51	up	up	ADP
ap-1859	73	52	to	to	ADP
ap-1859	73	53	c	c	PROPN
ap-1859	73	54	(	(	PUNCT
ap-1859	73	55	2π	2π	PROPN
ap-1859	73	56	3	3	NUM
ap-1859	73	57	)	)	PUNCT
ap-1859	73	58	=	=	SYM
ap-1859	74	1	1	1	X
ap-1859	74	2	.	.	PUNCT
ap-1859	74	3	since	since	SCONJ
ap-1859	74	4	all	all	DET
ap-1859	74	5	four	four	NUM
ap-1859	74	6	inner	inner	ADJ
ap-1859	74	7	411	411	NUM
ap-1859	74	8	t.	t.	NOUN
ap-1859	74	9	cheon	cheon	PROPN
ap-1859	74	10	,	,	PUNCT
ap-1859	74	11	a.	a.	PROPN
ap-1859	74	12	tanaka	tanaka	PROPN
ap-1859	74	13	,	,	PUNCT
ap-1859	74	14	o.	o.	PROPN
ap-1859	74	15	turek	turek	PROPN
ap-1859	74	16	acta	acta	PROPN
ap-1859	74	17	polytechnica	polytechnica	PROPN
ap-1859	74	18	figure	figure	NOUN
ap-1859	74	19	3	3	NUM
ap-1859	74	20	.	.	NOUN
ap-1859	74	21	cycle	cycle	NOUN
ap-1859	74	22	of	of	ADP
ap-1859	74	23	topological	topological	ADJ
ap-1859	74	24	changes	change	NOUN
ap-1859	74	25	corresponding	correspond	VERB
ap-1859	74	26	to	to	ADP
ap-1859	74	27	functions	function	NOUN
ap-1859	74	28	(	(	PUNCT
ap-1859	74	29	7	7	NUM
ap-1859	74	30	)	)	PUNCT
ap-1859	74	31	.	.	PUNCT
ap-1859	75	1	endpoints	endpoint	NOUN
ap-1859	75	2	are	be	AUX
ap-1859	75	3	separated	separate	VERB
ap-1859	75	4	,	,	PUNCT
ap-1859	75	5	the	the	DET
ap-1859	75	6	system	system	NOUN
ap-1859	75	7	is	be	AUX
ap-1859	75	8	topologically	topologically	ADV
ap-1859	75	9	equivalent	equivalent	ADJ
ap-1859	75	10	to	to	ADP
ap-1859	75	11	two	two	NUM
ap-1859	75	12	separate	separate	ADJ
ap-1859	75	13	lines	line	NOUN
ap-1859	75	14	.	.	PUNCT
ap-1859	76	1	region	region	PROPN
ap-1859	76	2	iii	iii	PROPN
ap-1859	76	3	.	.	PROPN
ap-1859	77	1	for	for	ADP
ap-1859	77	2	θ	θ	PROPN
ap-1859	77	3	∈	∈	PROPN
ap-1859	77	4	[	[	PUNCT
ap-1859	77	5	2π	2π	PROPN
ap-1859	77	6	3	3	NUM
ap-1859	77	7	,	,	PUNCT
ap-1859	77	8	π	π	PROPN
ap-1859	77	9	]	]	X
ap-1859	77	10	,	,	PUNCT
ap-1859	77	11	we	we	PRON
ap-1859	77	12	have	have	VERB
ap-1859	77	13	1	1	NUM
ap-1859	77	14	t	t	NOUN
ap-1859	77	15	·	·	PUNCT
ap-1859	77	16	b(θ	b(θ	ADV
ap-1859	77	17	)	)	PUNCT
ap-1859	77	18	1	1	NUM
ap-1859	77	19	t	t	NOUN
ap-1859	77	20	·	·	PUNCT
ap-1859	77	21	b′(θ	b′(θ	NOUN
ap-1859	77	22	)	)	PUNCT
ap-1859	77	23	ψ′	ψ′	NOUN
ap-1859	77	24	=	=	NOUN
ap-1859	77	25	−t	−t	NOUN
ap-1859	77	26	·	·	PUNCT
ap-1859	77	27	b(θ	b(θ	ADJ
ap-1859	77	28	)	)	PUNCT
ap-1859	77	29	1	1	NUM
ap-1859	77	30	−t	−t	NOUN
ap-1859	77	31	·	·	SYM
ap-1859	77	32	b′(θ	b′(θ	PROPN
ap-1859	77	33	)	)	PUNCT
ap-1859	77	34	1	1	NUM
ap-1859	77	35	ψ	ψ	NOUN
ap-1859	77	36	,	,	PUNCT
ap-1859	77	37	(	(	PUNCT
ap-1859	77	38	10	10	NUM
ap-1859	77	39	)	)	PUNCT
ap-1859	77	40	where	where	SCONJ
ap-1859	77	41	tb(θ	tb(θ	NUM
ap-1859	77	42	)	)	PUNCT
ap-1859	77	43	continuously	continuously	ADV
ap-1859	77	44	increases	increase	VERB
ap-1859	77	45	from	from	ADP
ap-1859	77	46	tb	tb	NOUN
ap-1859	77	47	(	(	PUNCT
ap-1859	77	48	2π	2π	PROPN
ap-1859	77	49	3	3	NUM
ap-1859	77	50	)	)	PUNCT
ap-1859	77	51	=	=	PUNCT
ap-1859	78	1	0	0	NUM
ap-1859	78	2	up	up	ADP
ap-1859	78	3	to	to	ADP
ap-1859	78	4	tb(π	tb(π	NOUN
ap-1859	78	5	)	)	PUNCT
ap-1859	78	6	=	=	SYM
ap-1859	78	7	t	t	PROPN
ap-1859	78	8	,	,	PUNCT
ap-1859	78	9	while	while	SCONJ
ap-1859	78	10	tb′(θ	tb′(θ	PROPN
ap-1859	78	11	)	)	PUNCT
ap-1859	78	12	takes	take	VERB
ap-1859	78	13	the	the	DET
ap-1859	78	14	value	value	NOUN
ap-1859	78	15	tb′(θ	tb′(θ	NOUN
ap-1859	78	16	)	)	PUNCT
ap-1859	79	1	=	=	SYM
ap-1859	79	2	0	0	NUM
ap-1859	80	1	at	at	ADP
ap-1859	80	2	θ	θ	X
ap-1859	80	3	=	=	SYM
ap-1859	80	4	2π	2π	PROPN
ap-1859	80	5	3	3	NUM
ap-1859	80	6	,	,	PUNCT
ap-1859	80	7	continuously	continuously	ADV
ap-1859	80	8	increases	increase	VERB
ap-1859	80	9	up	up	ADP
ap-1859	80	10	to	to	ADP
ap-1859	80	11	t	t	NOUN
ap-1859	80	12	at	at	ADP
ap-1859	80	13	θ	θ	PROPN
ap-1859	80	14	=	=	SYM
ap-1859	80	15	5π	5π	PROPN
ap-1859	80	16	6	6	NUM
ap-1859	80	17	and	and	CCONJ
ap-1859	80	18	comes	come	VERB
ap-1859	80	19	back	back	ADV
ap-1859	80	20	down	down	ADV
ap-1859	80	21	to	to	ADP
ap-1859	80	22	0	0	NUM
ap-1859	80	23	at	at	ADP
ap-1859	80	24	θ	θ	PROPN
ap-1859	80	25	=	=	SYM
ap-1859	80	26	π	π	X
ap-1859	80	27	.	.	PUNCT
ap-1859	81	1	the	the	DET
ap-1859	81	2	connection	connection	NOUN
ap-1859	81	3	condition	condition	NOUN
ap-1859	81	4	(	(	PUNCT
ap-1859	81	5	10	10	NUM
ap-1859	81	6	)	)	PUNCT
ap-1859	81	7	implies	imply	VERB
ap-1859	81	8	separated	separate	VERB
ap-1859	81	9	endpoints	endpoint	NOUN
ap-1859	81	10	1	1	NUM
ap-1859	81	11	and	and	CCONJ
ap-1859	81	12	3	3	NUM
ap-1859	81	13	,	,	PUNCT
ap-1859	81	14	as	as	ADV
ap-1859	81	15	well	well	ADV
ap-1859	81	16	as	as	ADP
ap-1859	81	17	2	2	NUM
ap-1859	81	18	and	and	CCONJ
ap-1859	81	19	4	4	NUM
ap-1859	81	20	,	,	PUNCT
ap-1859	81	21	making	make	VERB
ap-1859	81	22	the	the	DET
ap-1859	81	23	system	system	NOUN
ap-1859	81	24	topologically	topologically	ADV
ap-1859	81	25	equivalent	equivalent	ADJ
ap-1859	81	26	to	to	ADP
ap-1859	81	27	two	two	NUM
ap-1859	81	28	separate	separate	ADJ
ap-1859	81	29	rings	ring	NOUN
ap-1859	81	30	.	.	PUNCT
ap-1859	82	1	region	region	PROPN
ap-1859	82	2	iv	iv	PROPN
ap-1859	82	3	.	.	PUNCT
ap-1859	83	1	for	for	ADP
ap-1859	83	2	θ	θ	PROPN
ap-1859	83	3	∈	∈	PROPN
ap-1859	84	1	[	[	X
ap-1859	84	2	π	π	X
ap-1859	84	3	,	,	PUNCT
ap-1859	84	4	4π	4π	NUM
ap-1859	84	5	3	3	NUM
ap-1859	84	6	]	]	PUNCT
ap-1859	84	7	,	,	PUNCT
ap-1859	84	8	we	we	PRON
ap-1859	84	9	have	have	VERB
ap-1859	84	10	1	1	NUM
ap-1859	84	11	t	t	NOUN
ap-1859	84	12	·	·	PUNCT
ap-1859	84	13	b(θ	b(θ	ADV
ap-1859	84	14	)	)	PUNCT
ap-1859	84	15	s	s	PART
ap-1859	84	16	·	·	PUNCT
ap-1859	84	17	d(θ	d(θ	NOUN
ap-1859	84	18	)	)	PUNCT
ap-1859	84	19	1	1	NUM
ap-1859	84	20	ψ′	ψ′	NOUN
ap-1859	84	21	=	=	NOUN
ap-1859	84	22	−t	−t	NOUN
ap-1859	84	23	·	·	PUNCT
ap-1859	84	24	b(θ	b(θ	ADJ
ap-1859	84	25	)	)	PUNCT
ap-1859	84	26	1	1	NUM
ap-1859	84	27	−s	−s	NOUN
ap-1859	84	28	·	·	SYM
ap-1859	84	29	d(θ	d(θ	NOUN
ap-1859	84	30	)	)	PUNCT
ap-1859	84	31	1	1	NUM
ap-1859	84	32	ψ	ψ	NOUN
ap-1859	84	33	,	,	PUNCT
ap-1859	84	34	(	(	PUNCT
ap-1859	84	35	11	11	NUM
ap-1859	84	36	)	)	PUNCT
ap-1859	84	37	where	where	SCONJ
ap-1859	84	38	tb(θ	tb(θ	NUM
ap-1859	84	39	)	)	PUNCT
ap-1859	84	40	continuously	continuously	ADV
ap-1859	84	41	decreases	decrease	VERB
ap-1859	84	42	from	from	ADP
ap-1859	84	43	tb	tb	NOUN
ap-1859	84	44	(	(	PUNCT
ap-1859	84	45	π	π	PROPN
ap-1859	84	46	2	2	NUM
ap-1859	84	47	)	)	PUNCT
ap-1859	84	48	=	=	SYM
ap-1859	84	49	t	t	PROPN
ap-1859	84	50	to	to	PART
ap-1859	84	51	tb	tb	PROPN
ap-1859	85	1	(	(	PUNCT
ap-1859	85	2	4π	4π	NOUN
ap-1859	85	3	3	3	NUM
ap-1859	85	4	)	)	PUNCT
ap-1859	85	5	=	=	SYM
ap-1859	85	6	0	0	NUM
ap-1859	85	7	,	,	PUNCT
ap-1859	85	8	while	while	SCONJ
ap-1859	85	9	sd(θ	sd(θ	ADV
ap-1859	85	10	)	)	PUNCT
ap-1859	85	11	continuously	continuously	ADV
ap-1859	85	12	increases	increase	VERB
ap-1859	85	13	from	from	ADP
ap-1859	85	14	sd	sd	ADP
ap-1859	85	15	(	(	PUNCT
ap-1859	85	16	π	π	PROPN
ap-1859	85	17	2	2	NUM
ap-1859	85	18	)	)	PUNCT
ap-1859	85	19	=	=	PUNCT
ap-1859	85	20	0	0	NUM
ap-1859	85	21	up	up	ADP
ap-1859	85	22	to	to	ADP
ap-1859	85	23	sd	sd	NOUN
ap-1859	85	24	(	(	PUNCT
ap-1859	85	25	4π	4π	NOUN
ap-1859	85	26	3	3	NUM
ap-1859	85	27	)	)	PUNCT
ap-1859	85	28	=	=	VERB
ap-1859	86	1	s.	s.	PROPN
ap-1859	86	2	the	the	DET
ap-1859	86	3	system	system	NOUN
ap-1859	86	4	is	be	AUX
ap-1859	86	5	topologically	topologically	ADV
ap-1859	86	6	equivalent	equivalent	ADJ
ap-1859	86	7	to	to	ADP
ap-1859	86	8	a	a	DET
ap-1859	86	9	ring	ring	NOUN
ap-1859	86	10	and	and	CCONJ
ap-1859	86	11	a	a	DET
ap-1859	86	12	line	line	NOUN
ap-1859	86	13	connected	connect	VERB
ap-1859	86	14	at	at	ADP
ap-1859	86	15	a	a	DET
ap-1859	86	16	single	single	ADJ
ap-1859	86	17	point	point	NOUN
ap-1859	86	18	since	since	SCONJ
ap-1859	86	19	three	three	NUM
ap-1859	86	20	of	of	ADP
ap-1859	86	21	four	four	NUM
ap-1859	86	22	endpoints	endpoint	NOUN
ap-1859	86	23	,	,	PUNCT
ap-1859	86	24	namely	namely	ADV
ap-1859	86	25	1	1	NUM
ap-1859	86	26	,	,	PUNCT
ap-1859	86	27	2	2	NUM
ap-1859	86	28	and	and	CCONJ
ap-1859	86	29	4	4	NUM
ap-1859	86	30	,	,	PUNCT
ap-1859	86	31	are	be	AUX
ap-1859	86	32	connected	connect	VERB
ap-1859	86	33	in	in	ADP
ap-1859	86	34	the	the	DET
ap-1859	86	35	node	node	NOUN
ap-1859	86	36	.	.	PUNCT
ap-1859	87	1	note	note	VERB
ap-1859	87	2	that	that	SCONJ
ap-1859	87	3	at	at	ADP
ap-1859	87	4	the	the	DET
ap-1859	87	5	juncture	juncture	NOUN
ap-1859	87	6	of	of	ADP
ap-1859	87	7	regions	region	NOUN
ap-1859	87	8	iii	iii	PROPN
ap-1859	87	9	and	and	CCONJ
ap-1859	87	10	iv	iv	NUM
ap-1859	87	11	,	,	PUNCT
ap-1859	87	12	the	the	DET
ap-1859	87	13	system	system	NOUN
ap-1859	87	14	is	be	AUX
ap-1859	87	15	topologically	topologically	ADV
ap-1859	87	16	equivalent	equivalent	ADJ
ap-1859	87	17	to	to	ADP
ap-1859	87	18	a	a	DET
ap-1859	87	19	separated	separate	VERB
ap-1859	87	20	line	line	NOUN
ap-1859	87	21	and	and	CCONJ
ap-1859	87	22	a	a	DET
ap-1859	87	23	ring	ring	NOUN
ap-1859	87	24	.	.	PUNCT
ap-1859	88	1	region	region	NOUN
ap-1859	88	2	v.	v.	ADP
ap-1859	88	3	for	for	ADP
ap-1859	88	4	θ	θ	PROPN
ap-1859	88	5	∈	∈	PROPN
ap-1859	88	6	[	[	PUNCT
ap-1859	88	7	4π	4π	NUM
ap-1859	88	8	3	3	NUM
ap-1859	88	9	,	,	PUNCT
ap-1859	88	10	5π	5π	PROPN
ap-1859	88	11	3	3	NUM
ap-1859	88	12	]	]	PUNCT
ap-1859	88	13	,	,	PUNCT
ap-1859	88	14	we	we	PRON
ap-1859	88	15	have	have	VERB
ap-1859	88	16	1	1	NUM
ap-1859	88	17	s	s	PART
ap-1859	88	18	1−	1−	NUM
ap-1859	88	19	c(θ	c(θ	PROPN
ap-1859	88	20	)	)	PUNCT
ap-1859	88	21	c(θ	c(θ	PROPN
ap-1859	88	22	)	)	PUNCT
ap-1859	88	23	ψ′	ψ′	NOUN
ap-1859	88	24	=	=	SYM
ap-1859	88	25			PROPN
ap-1859	88	26	c(θ	c(θ	PROPN
ap-1859	88	27	)	)	PUNCT
ap-1859	88	28	1−	1−	NUM
ap-1859	88	29	c(θ	c(θ	PROPN
ap-1859	88	30	)	)	PUNCT
ap-1859	88	31	−s	−s	NOUN
ap-1859	88	32	1	1	NUM
ap-1859	88	33	ψ	ψ	NOUN
ap-1859	88	34	,	,	PUNCT
ap-1859	88	35	(	(	PUNCT
ap-1859	88	36	12	12	NUM
ap-1859	88	37	)	)	PUNCT
ap-1859	88	38	where	where	SCONJ
ap-1859	88	39	c	c	NOUN
ap-1859	88	40	continuously	continuously	ADV
ap-1859	88	41	decreases	decrease	VERB
ap-1859	88	42	from	from	ADP
ap-1859	88	43	c	c	PROPN
ap-1859	88	44	(	(	PUNCT
ap-1859	88	45	4π	4π	NUM
ap-1859	88	46	3	3	NUM
ap-1859	88	47	)	)	PUNCT
ap-1859	88	48	=	=	PUNCT
ap-1859	89	1	1	1	NUM
ap-1859	89	2	down	down	ADP
ap-1859	89	3	to	to	ADP
ap-1859	89	4	c	c	PROPN
ap-1859	89	5	(	(	PUNCT
ap-1859	89	6	5π	5π	PROPN
ap-1859	89	7	3	3	NUM
ap-1859	89	8	)	)	PUNCT
ap-1859	89	9	=	=	SYM
ap-1859	90	1	0	0	X
ap-1859	90	2	.	.	PUNCT
ap-1859	91	1	the	the	DET
ap-1859	91	2	system	system	NOUN
ap-1859	91	3	is	be	AUX
ap-1859	91	4	topologically	topologically	ADV
ap-1859	91	5	equivalent	equivalent	ADJ
ap-1859	91	6	to	to	ADP
ap-1859	91	7	a	a	DET
ap-1859	91	8	single	single	ADJ
ap-1859	91	9	line	line	NOUN
ap-1859	91	10	,	,	PUNCT
ap-1859	91	11	since	since	SCONJ
ap-1859	91	12	only	only	ADV
ap-1859	91	13	endpoints	endpoint	NOUN
ap-1859	91	14	1	1	NUM
ap-1859	91	15	and	and	CCONJ
ap-1859	91	16	4	4	NUM
ap-1859	91	17	are	be	AUX
ap-1859	91	18	connected	connect	VERB
ap-1859	91	19	,	,	PUNCT
ap-1859	91	20	whereas	whereas	SCONJ
ap-1859	91	21	2	2	NUM
ap-1859	91	22	and	and	CCONJ
ap-1859	91	23	3	3	NUM
ap-1859	91	24	are	be	AUX
ap-1859	91	25	separated	separate	VERB
ap-1859	91	26	.	.	PUNCT
ap-1859	92	1	region	region	PROPN
ap-1859	92	2	vi	vi	PROPN
ap-1859	92	3	.	.	PROPN
ap-1859	93	1	for	for	ADP
ap-1859	93	2	θ	θ	PROPN
ap-1859	93	3	∈	∈	PROPN
ap-1859	93	4	[	[	PUNCT
ap-1859	93	5	5π	5π	NOUN
ap-1859	93	6	3	3	NUM
ap-1859	93	7	,	,	PUNCT
ap-1859	93	8	2π	2π	NOUN
ap-1859	93	9	]	]	PUNCT
ap-1859	93	10	,	,	PUNCT
ap-1859	93	11	we	we	PRON
ap-1859	93	12	have	have	VERB
ap-1859	93	13	1	1	NUM
ap-1859	93	14	t	t	NOUN
ap-1859	93	15	·	·	PUNCT
ap-1859	93	16	a(θ	a(θ	PROPN
ap-1859	93	17	)	)	PUNCT
ap-1859	93	18	s	s	PART
ap-1859	93	19	·	·	PUNCT
ap-1859	93	20	d(θ	d(θ	PROPN
ap-1859	93	21	)	)	PUNCT
ap-1859	93	22	1	1	NUM
ap-1859	93	23	t	t	NOUN
ap-1859	93	24	·	·	PUNCT
ap-1859	93	25	a(θ	a(θ	ADJ
ap-1859	93	26	)	)	PUNCT
ap-1859	93	27	ψ′	ψ′	NOUN
ap-1859	93	28	=	=	NOUN
ap-1859	93	29	−t	−t	NOUN
ap-1859	93	30	·	·	PUNCT
ap-1859	93	31	a(θ	a(θ	VERB
ap-1859	93	32	)	)	PUNCT
ap-1859	93	33	1	1	NUM
ap-1859	93	34	−s	−s	NOUN
ap-1859	93	35	·	·	SYM
ap-1859	93	36	d(θ	d(θ	PROPN
ap-1859	93	37	)	)	PUNCT
ap-1859	93	38	−t	−t	NOUN
ap-1859	93	39	·	·	PUNCT
ap-1859	93	40	a(θ	a(θ	VERB
ap-1859	93	41	)	)	PUNCT
ap-1859	93	42	1	1	NUM
ap-1859	93	43	ψ	ψ	NOUN
ap-1859	93	44	,	,	PUNCT
ap-1859	93	45	(	(	PUNCT
ap-1859	93	46	13	13	NUM
ap-1859	93	47	)	)	PUNCT
ap-1859	93	48	where	where	SCONJ
ap-1859	93	49	ta(θ	ta(θ	NUM
ap-1859	93	50	)	)	PUNCT
ap-1859	93	51	continuously	continuously	ADV
ap-1859	93	52	increases	increase	VERB
ap-1859	93	53	from	from	ADP
ap-1859	93	54	ta	ta	ADP
ap-1859	93	55	(	(	PUNCT
ap-1859	93	56	5π	5π	PROPN
ap-1859	93	57	3	3	NUM
ap-1859	93	58	)	)	PUNCT
ap-1859	93	59	up	up	ADP
ap-1859	93	60	to	to	ADP
ap-1859	93	61	ta(2π	ta(2π	NUM
ap-1859	93	62	)	)	PUNCT
ap-1859	93	63	=	=	SYM
ap-1859	93	64	t	t	PROPN
ap-1859	93	65	,	,	PUNCT
ap-1859	93	66	while	while	SCONJ
ap-1859	93	67	sd(θ	sd(θ	ADV
ap-1859	93	68	)	)	PUNCT
ap-1859	93	69	continuously	continuously	ADV
ap-1859	93	70	decreases	decrease	VERB
ap-1859	93	71	from	from	ADP
ap-1859	93	72	sd	sd	NOUN
ap-1859	93	73	(	(	PUNCT
ap-1859	93	74	5π	5π	PROPN
ap-1859	93	75	3	3	NUM
ap-1859	93	76	)	)	PUNCT
ap-1859	94	1	=	=	PRON
ap-1859	94	2	s	s	VERB
ap-1859	94	3	down	down	ADP
ap-1859	94	4	to	to	ADP
ap-1859	94	5	sd(2π	sd(2π	NOUN
ap-1859	94	6	)	)	PUNCT
ap-1859	94	7	=	=	SYM
ap-1859	95	1	0	0	X
ap-1859	95	2	.	.	PUNCT
ap-1859	96	1	in	in	ADP
ap-1859	96	2	this	this	DET
ap-1859	96	3	region	region	NOUN
ap-1859	96	4	,	,	PUNCT
ap-1859	96	5	the	the	DET
ap-1859	96	6	system	system	NOUN
ap-1859	96	7	is	be	AUX
ap-1859	96	8	topologically	topologically	ADV
ap-1859	96	9	equivalent	equivalent	ADJ
ap-1859	96	10	to	to	ADP
ap-1859	96	11	two	two	NUM
ap-1859	96	12	rings	ring	NOUN
ap-1859	96	13	connected	connect	VERB
ap-1859	96	14	at	at	ADP
ap-1859	96	15	a	a	DET
ap-1859	96	16	single	single	ADJ
ap-1859	96	17	point	point	NOUN
ap-1859	96	18	since	since	SCONJ
ap-1859	96	19	all	all	DET
ap-1859	96	20	four	four	NUM
ap-1859	96	21	endpoints	endpoint	NOUN
ap-1859	96	22	are	be	AUX
ap-1859	96	23	connected	connect	VERB
ap-1859	96	24	together	together	ADV
ap-1859	96	25	at	at	ADP
ap-1859	96	26	the	the	DET
ap-1859	96	27	central	central	ADJ
ap-1859	96	28	node	node	NOUN
ap-1859	96	29	.	.	PUNCT
ap-1859	97	1	therefore	therefore	ADV
ap-1859	97	2	,	,	PUNCT
ap-1859	97	3	with	with	ADP
ap-1859	97	4	the	the	DET
ap-1859	97	5	parameter	parameter	NOUN
ap-1859	97	6	change	change	VERB
ap-1859	97	7	θ	θ	X
ap-1859	97	8	=	=	SYM
ap-1859	97	9	0→	0→	PROPN
ap-1859	97	10	2π	2π	NOUN
ap-1859	97	11	,	,	PUNCT
ap-1859	97	12	seven	seven	NUM
ap-1859	97	13	distinct	distinct	ADJ
ap-1859	97	14	topologies	topology	NOUN
ap-1859	97	15	are	be	AUX
ap-1859	97	16	traversed	traverse	VERB
ap-1859	97	17	in	in	ADP
ap-1859	97	18	a	a	DET
ap-1859	97	19	continuous	continuous	ADJ
ap-1859	97	20	manner	manner	NOUN
ap-1859	97	21	.	.	PUNCT
ap-1859	98	1	the	the	DET
ap-1859	98	2	situation	situation	NOUN
ap-1859	98	3	is	be	AUX
ap-1859	98	4	illustrated	illustrate	VERB
ap-1859	98	5	in	in	ADP
ap-1859	98	6	fig	fig	NOUN
ap-1859	98	7	.	.	PUNCT
ap-1859	99	1	3	3	X
ap-1859	99	2	.	.	X
ap-1859	99	3	the	the	DET
ap-1859	99	4	system	system	NOUN
ap-1859	99	5	is	be	AUX
ap-1859	99	6	never	never	ADV
ap-1859	99	7	identical	identical	ADJ
ap-1859	99	8	for	for	ADP
ap-1859	99	9	any	any	DET
ap-1859	99	10	two	two	NUM
ap-1859	99	11	different	different	ADJ
ap-1859	99	12	values	value	NOUN
ap-1859	99	13	of	of	ADP
ap-1859	99	14	θ	θ	PROPN
ap-1859	99	15	in	in	ADP
ap-1859	99	16	[	[	X
ap-1859	99	17	0	0	NUM
ap-1859	99	18	,	,	PUNCT
ap-1859	99	19	2π	2π	NOUN
ap-1859	99	20	)	)	PUNCT
ap-1859	99	21	,	,	PUNCT
ap-1859	99	22	because	because	SCONJ
ap-1859	99	23	the	the	DET
ap-1859	99	24	functions	function	NOUN
ap-1859	99	25	a(θ	a(θ	VERB
ap-1859	99	26	)	)	PUNCT
ap-1859	99	27	to	to	ADP
ap-1859	99	28	d(θ	d(θ	PROPN
ap-1859	99	29	)	)	PUNCT
ap-1859	99	30	form	form	VERB
ap-1859	99	31	mutually	mutually	ADV
ap-1859	99	32	different	different	ADJ
ap-1859	99	33	combinations	combination	NOUN
ap-1859	99	34	of	of	ADP
ap-1859	99	35	patterns	pattern	NOUN
ap-1859	99	36	in	in	ADP
ap-1859	99	37	all	all	DET
ap-1859	99	38	six	six	NUM
ap-1859	99	39	regions	region	NOUN
ap-1859	99	40	.	.	PUNCT
ap-1859	100	1	2.2	2.2	NUM
ap-1859	100	2	.	.	PUNCT
ap-1859	100	3	short	short	ADJ
ap-1859	100	4	cycle	cycle	NOUN
ap-1859	100	5	as	as	ADP
ap-1859	100	6	an	an	DET
ap-1859	100	7	additional	additional	ADJ
ap-1859	100	8	model	model	NOUN
ap-1859	100	9	,	,	PUNCT
ap-1859	100	10	we	we	PRON
ap-1859	100	11	consider	consider	VERB
ap-1859	100	12	a	a	DET
ap-1859	100	13	simplified	simplified	ADJ
ap-1859	100	14	parametric	parametric	ADJ
ap-1859	100	15	cycle	cycle	NOUN
ap-1859	100	16	represented	represent	VERB
ap-1859	100	17	by	by	ADP
ap-1859	100	18	the	the	DET
ap-1859	100	19	boundary	boundary	ADJ
ap-1859	100	20	condition	condition	NOUN
ap-1859	100	21	(	(	PUNCT
ap-1859	100	22	4	4	NUM
ap-1859	100	23	)	)	PUNCT
ap-1859	100	24	with	with	ADP
ap-1859	100	25	a(θ	a(θ	NOUN
ap-1859	100	26	)	)	PUNCT
ap-1859	100	27	=	=	SYM
ap-1859	100	28	1	1	NUM
ap-1859	100	29	2	2	NUM
ap-1859	100	30	(	(	PUNCT
ap-1859	100	31	cos	cos	PROPN
ap-1859	100	32	θ	θ	PROPN
ap-1859	100	33	+	+	CCONJ
ap-1859	100	34	|cos	|co	NOUN
ap-1859	100	35	θ|	θ|	PROPN
ap-1859	100	36	)	)	PUNCT
ap-1859	100	37	,	,	PUNCT
ap-1859	100	38	b(θ	b(θ	ADV
ap-1859	100	39	)	)	PUNCT
ap-1859	100	40	=	=	SYM
ap-1859	100	41	b′(θ	b′(θ	PROPN
ap-1859	100	42	)	)	PUNCT
ap-1859	100	43	=	=	SYM
ap-1859	100	44	0	0	NUM
ap-1859	100	45	,	,	PUNCT
ap-1859	100	46	c(θ	c(θ	PROPN
ap-1859	100	47	)	)	PUNCT
ap-1859	100	48	=	=	SYM
ap-1859	100	49	1	1	NUM
ap-1859	100	50	2	2	NUM
ap-1859	100	51	(	(	PUNCT
ap-1859	100	52	−	−	PROPN
ap-1859	100	53	cos	cos	PROPN
ap-1859	100	54	θ	θ	PROPN
ap-1859	100	55	+	+	CCONJ
ap-1859	100	56	|cos	|co	NOUN
ap-1859	100	57	θ|	θ|	PROPN
ap-1859	100	58	)	)	PUNCT
ap-1859	100	59	,	,	PUNCT
ap-1859	100	60	d(θ	d(θ	PROPN
ap-1859	100	61	)	)	PUNCT
ap-1859	100	62	=	=	SYM
ap-1859	100	63	1	1	NUM
ap-1859	100	64	2	2	NUM
ap-1859	100	65	(	(	PUNCT
ap-1859	100	66	−	−	PROPN
ap-1859	100	67	sin	sin	NOUN
ap-1859	100	68	θ	θ	PROPN
ap-1859	100	69	+	+	CCONJ
ap-1859	100	70	|sin	|sin	PROPN
ap-1859	100	71	θ|	θ|	NOUN
ap-1859	100	72	)	)	PUNCT
ap-1859	100	73	.	.	PUNCT
ap-1859	101	1	(	(	PUNCT
ap-1859	101	2	14	14	NUM
ap-1859	101	3	)	)	PUNCT
ap-1859	101	4	the	the	DET
ap-1859	101	5	graphs	graph	NOUN
ap-1859	101	6	of	of	ADP
ap-1859	101	7	these	these	DET
ap-1859	101	8	functions	function	NOUN
ap-1859	101	9	are	be	AUX
ap-1859	101	10	plotted	plot	VERB
ap-1859	101	11	in	in	ADP
ap-1859	101	12	fig	fig	NOUN
ap-1859	101	13	.	.	PUNCT
ap-1859	102	1	4	4	X
ap-1859	102	2	.	.	X
ap-1859	102	3	this	this	DET
ap-1859	102	4	system	system	NOUN
ap-1859	102	5	traverses	traverse	VERB
ap-1859	102	6	four	four	NUM
ap-1859	102	7	distinct	distinct	ADJ
ap-1859	102	8	segments	segment	NOUN
ap-1859	102	9	in	in	ADP
ap-1859	102	10	the	the	DET
ap-1859	102	11	parameter	parameter	NOUN
ap-1859	102	12	space	space	NOUN
ap-1859	102	13	of	of	ADP
ap-1859	102	14	θ	θ	PROPN
ap-1859	102	15	,	,	PUNCT
ap-1859	102	16	as	as	SCONJ
ap-1859	102	17	θ	θ	PROPN
ap-1859	102	18	runs	run	VERB
ap-1859	102	19	from	from	ADP
ap-1859	102	20	0	0	NUM
ap-1859	102	21	to	to	ADP
ap-1859	102	22	2π	2π	NOUN
ap-1859	102	23	.	.	PUNCT
ap-1859	103	1	the	the	DET
ap-1859	103	2	segments	segment	NOUN
ap-1859	103	3	correspond	correspond	VERB
ap-1859	103	4	to	to	ADP
ap-1859	103	5	four	four	NUM
ap-1859	103	6	topologies	topology	NOUN
ap-1859	103	7	,	,	PUNCT
ap-1859	103	8	cf	cf	NOUN
ap-1859	103	9	.	.	PUNCT
ap-1859	103	10	fig	fig	NOUN
ap-1859	103	11	.	.	PUNCT
ap-1859	104	1	5	5	NUM
ap-1859	104	2	.	.	X
ap-1859	104	3	namely	namely	ADV
ap-1859	104	4	,	,	PUNCT
ap-1859	104	5	a	a	DET
ap-1859	104	6	ring	ring	NOUN
ap-1859	104	7	,	,	PUNCT
ap-1859	104	8	two	two	NUM
ap-1859	104	9	disjoint	disjoint	ADJ
ap-1859	104	10	lines	line	NOUN
ap-1859	104	11	,	,	PUNCT
ap-1859	104	12	a	a	DET
ap-1859	104	13	line	line	NOUN
ap-1859	104	14	attached	attach	VERB
ap-1859	104	15	to	to	ADP
ap-1859	104	16	a	a	DET
ap-1859	104	17	ring	ring	NOUN
ap-1859	104	18	,	,	PUNCT
ap-1859	104	19	and	and	CCONJ
ap-1859	104	20	two	two	NUM
ap-1859	104	21	rings	ring	NOUN
ap-1859	104	22	connected	connect	VERB
ap-1859	104	23	at	at	ADP
ap-1859	104	24	a	a	DET
ap-1859	104	25	point	point	NOUN
ap-1859	104	26	.	.	PUNCT
ap-1859	105	1	412	412	NUM
ap-1859	105	2	vol	vol	NOUN
ap-1859	105	3	.	.	PUNCT
ap-1859	106	1	53	53	NUM
ap-1859	106	2	no	no	NOUN
ap-1859	106	3	.	.	PUNCT
ap-1859	107	1	5/2013	5/2013	NUM
ap-1859	107	2	examples	example	NOUN
ap-1859	107	3	of	of	ADP
ap-1859	107	4	quantum	quantum	ADJ
ap-1859	107	5	holonomy	holonomy	NOUN
ap-1859	107	6	with	with	ADP
ap-1859	107	7	topology	topology	NOUN
ap-1859	107	8	changes	change	NOUN
ap-1859	107	9	figure	figure	VERB
ap-1859	107	10	4	4	NUM
ap-1859	107	11	.	.	PUNCT
ap-1859	108	1	graphs	graph	NOUN
ap-1859	108	2	of	of	ADP
ap-1859	108	3	functions	function	NOUN
ap-1859	108	4	defined	define	VERB
ap-1859	108	5	by	by	ADP
ap-1859	108	6	(	(	PUNCT
ap-1859	108	7	14	14	NUM
ap-1859	108	8	)	)	PUNCT
ap-1859	108	9	for	for	ADP
ap-1859	108	10	θ	θ	PROPN
ap-1859	108	11	∈	∈	PROPN
ap-1859	109	1	[	[	X
ap-1859	109	2	0	0	NUM
ap-1859	109	3	,	,	PUNCT
ap-1859	109	4	2π	2π	NOUN
ap-1859	109	5	]	]	PUNCT
ap-1859	109	6	.	.	PUNCT
ap-1859	110	1	3	3	X
ap-1859	110	2	.	.	X
ap-1859	110	3	quantum	quantum	ADJ
ap-1859	110	4	holonomy	holonomy	NOUN
ap-1859	110	5	the	the	DET
ap-1859	110	6	system	system	NOUN
ap-1859	110	7	wave	wave	NOUN
ap-1859	110	8	functions	function	NOUN
ap-1859	110	9	can	can	AUX
ap-1859	110	10	be	be	AUX
ap-1859	110	11	written	write	VERB
ap-1859	110	12	in	in	ADP
ap-1859	110	13	the	the	DET
ap-1859	110	14	form	form	NOUN
ap-1859	110	15	ψ1(x1	ψ1(x1	NUM
ap-1859	110	16	)	)	PUNCT
ap-1859	110	17	=	=	SYM
ap-1859	110	18	α1	α1	PROPN
ap-1859	110	19	sin	sin	NOUN
ap-1859	110	20	kx1	kx1	X
ap-1859	110	21	+	+	CCONJ
ap-1859	110	22	β1	β1	PROPN
ap-1859	110	23	cos	cos	PROPN
ap-1859	110	24	kx1	kx1	PROPN
ap-1859	110	25	,	,	PUNCT
ap-1859	110	26	ψ2(x2	ψ2(x2	NOUN
ap-1859	110	27	)	)	PUNCT
ap-1859	110	28	=	=	VERB
ap-1859	111	1	α2	α2	ADJ
ap-1859	111	2	sin	sin	NOUN
ap-1859	111	3	kx2	kx2	PROPN
ap-1859	111	4	+	+	CCONJ
ap-1859	111	5	β2	β2	PROPN
ap-1859	111	6	cos	cos	PROPN
ap-1859	111	7	kx2	kx2	PROPN
ap-1859	111	8	.	.	PUNCT
ap-1859	112	1	(	(	PUNCT
ap-1859	112	2	15	15	NUM
ap-1859	112	3	)	)	PUNCT
ap-1859	112	4	in	in	ADP
ap-1859	112	5	this	this	DET
ap-1859	112	6	notation	notation	NOUN
ap-1859	112	7	,	,	PUNCT
ap-1859	112	8	we	we	PRON
ap-1859	112	9	have	have	VERB
ap-1859	112	10	ψ	ψ	X
ap-1859	112	11	=	=	PUNCT
ap-1859	112	12	u	u	X
ap-1859	112	13			PROPN
ap-1859	112	14	α1	α1	PROPN
ap-1859	112	15	β1	β1	PROPN
ap-1859	112	16	α2	α2	PROPN
ap-1859	112	17	β2	β2	PROPN
ap-1859	112	18			NOUN
ap-1859	112	19	,	,	PUNCT
ap-1859	112	20	ψ′	ψ′	PROPN
ap-1859	112	21	=	=	SYM
ap-1859	112	22	kv	kv	PROPN
ap-1859	112	23			PROPN
ap-1859	112	24	α1	α1	PROPN
ap-1859	112	25	β1	β1	PROPN
ap-1859	112	26	α2	α2	PROPN
ap-1859	112	27	β2	β2	PROPN
ap-1859	112	28			NOUN
ap-1859	112	29	(	(	PUNCT
ap-1859	112	30	16	16	NUM
ap-1859	112	31	)	)	PUNCT
ap-1859	112	32	with	with	ADP
ap-1859	112	33	u	u	NOUN
ap-1859	112	34	=	=	SYM
ap-1859	112	35			ADJ
ap-1859	112	36	1	1	NUM
ap-1859	112	37	sin	sin	NOUN
ap-1859	112	38	kl1	kl1	PROPN
ap-1859	112	39	cos	cos	PROPN
ap-1859	112	40	kl1	kl1	PROPN
ap-1859	112	41	1	1	NUM
ap-1859	112	42	sin	sin	NOUN
ap-1859	112	43	kl2	kl2	PROPN
ap-1859	112	44	cos	cos	PROPN
ap-1859	112	45	kl2	kl2	PROPN
ap-1859	112	46			PROPN
ap-1859	112	47	,	,	PUNCT
ap-1859	112	48	v	v	NOUN
ap-1859	112	49	=	=	SYM
ap-1859	112	50			ADJ
ap-1859	112	51	1	1	NUM
ap-1859	112	52	−	−	NOUN
ap-1859	112	53	cos	cos	ADP
ap-1859	112	54	kl1	kl1	PROPN
ap-1859	112	55	sin	sin	NOUN
ap-1859	112	56	kl1	kl1	PROPN
ap-1859	112	57	1	1	NUM
ap-1859	112	58	−	−	PROPN
ap-1859	112	59	cos	cos	PROPN
ap-1859	112	60	kl2	kl2	PROPN
ap-1859	112	61	sin	sin	PROPN
ap-1859	112	62	kl2	kl2	PROPN
ap-1859	112	63			PROPN
ap-1859	112	64	.	.	PUNCT
ap-1859	113	1	(	(	PUNCT
ap-1859	113	2	17	17	NUM
ap-1859	113	3	)	)	PUNCT
ap-1859	113	4	the	the	DET
ap-1859	113	5	spectra	spectra	NOUN
ap-1859	113	6	of	of	ADP
ap-1859	113	7	the	the	DET
ap-1859	113	8	system	system	NOUN
ap-1859	113	9	can	can	AUX
ap-1859	113	10	be	be	AUX
ap-1859	113	11	calculated	calculate	VERB
ap-1859	113	12	from	from	ADP
ap-1859	113	13	the	the	DET
ap-1859	113	14	secular	secular	ADJ
ap-1859	113	15	equation	equation	NOUN
ap-1859	113	16	|au	|au	NOUN
ap-1859	113	17	+	+	CCONJ
ap-1859	113	18	kbv	kbv	X
ap-1859	113	19	|	|	ADV
ap-1859	113	20	=	=	NOUN
ap-1859	113	21	0	0	PROPN
ap-1859	113	22	.	.	PUNCT
ap-1859	114	1	(	(	PUNCT
ap-1859	114	2	18	18	NUM
ap-1859	114	3	)	)	PUNCT
ap-1859	114	4	it	it	PRON
ap-1859	114	5	turns	turn	VERB
ap-1859	114	6	out	out	ADP
ap-1859	114	7	that	that	SCONJ
ap-1859	114	8	certain	certain	ADJ
ap-1859	114	9	choices	choice	NOUN
ap-1859	114	10	of	of	ADP
ap-1859	114	11	s	s	PROPN
ap-1859	114	12	,	,	PUNCT
ap-1859	114	13	t	t	PROPN
ap-1859	114	14	and	and	CCONJ
ap-1859	114	15	ratio	ratio	PROPN
ap-1859	114	16	l1	l1	PROPN
ap-1859	114	17	/	/	SYM
ap-1859	114	18	l2	l2	PROPN
ap-1859	114	19	result	result	VERB
ap-1859	114	20	in	in	ADP
ap-1859	114	21	a	a	DET
ap-1859	114	22	quantum	quantum	ADJ
ap-1859	114	23	holonomy	holonomy	NOUN
ap-1859	114	24	.	.	PUNCT
ap-1859	115	1	below	below	ADP
ap-1859	115	2	we	we	PRON
ap-1859	115	3	present	present	VERB
ap-1859	115	4	the	the	DET
ap-1859	115	5	results	result	NOUN
ap-1859	115	6	,	,	PUNCT
ap-1859	115	7	separately	separately	ADV
ap-1859	115	8	for	for	ADP
ap-1859	115	9	the	the	DET
ap-1859	115	10	long	long	ADJ
ap-1859	115	11	cycle	cycle	NOUN
ap-1859	115	12	and	and	CCONJ
ap-1859	115	13	the	the	DET
ap-1859	115	14	short	short	ADJ
ap-1859	115	15	cycle	cycle	NOUN
ap-1859	115	16	.	.	PUNCT
ap-1859	116	1	figure	figure	NOUN
ap-1859	116	2	5	5	NUM
ap-1859	116	3	.	.	PUNCT
ap-1859	117	1	cycle	cycle	NOUN
ap-1859	117	2	of	of	ADP
ap-1859	117	3	topological	topological	ADJ
ap-1859	117	4	changes	change	NOUN
ap-1859	117	5	corresponding	correspond	VERB
ap-1859	117	6	to	to	ADP
ap-1859	117	7	functions	function	NOUN
ap-1859	117	8	(	(	PUNCT
ap-1859	117	9	14	14	NUM
ap-1859	117	10	)	)	PUNCT
ap-1859	117	11	.	.	PUNCT
ap-1859	118	1	3.1	3.1	NUM
ap-1859	118	2	.	.	PUNCT
ap-1859	118	3	long	long	ADJ
ap-1859	118	4	cycle	cycle	NOUN
ap-1859	118	5	we	we	PRON
ap-1859	118	6	first	first	ADV
ap-1859	118	7	consider	consider	VERB
ap-1859	118	8	the	the	DET
ap-1859	118	9	long	long	ADJ
ap-1859	118	10	cycle	cycle	NOUN
ap-1859	118	11	of	of	ADP
ap-1859	118	12	parameter	parameter	NOUN
ap-1859	118	13	change	change	NOUN
ap-1859	118	14	represented	represent	VERB
ap-1859	118	15	by	by	ADP
ap-1859	118	16	(	(	PUNCT
ap-1859	118	17	7	7	NUM
ap-1859	118	18	)	)	PUNCT
ap-1859	118	19	.	.	PUNCT
ap-1859	119	1	we	we	PRON
ap-1859	119	2	performed	perform	VERB
ap-1859	119	3	a	a	DET
ap-1859	119	4	numerical	numerical	ADJ
ap-1859	119	5	calculation	calculation	NOUN
ap-1859	119	6	of	of	ADP
ap-1859	119	7	the	the	DET
ap-1859	119	8	spectral	spectral	ADJ
ap-1859	119	9	sets	set	NOUN
ap-1859	119	10	of	of	ADP
ap-1859	119	11	the	the	DET
ap-1859	119	12	system	system	NOUN
ap-1859	119	13	for	for	ADP
ap-1859	119	14	six	six	NUM
ap-1859	119	15	different	different	ADJ
ap-1859	119	16	settings	setting	NOUN
ap-1859	119	17	of	of	ADP
ap-1859	119	18	the	the	DET
ap-1859	119	19	parameters	parameter	NOUN
ap-1859	119	20	s	s	PROPN
ap-1859	119	21	,	,	PUNCT
ap-1859	119	22	t	t	PROPN
ap-1859	119	23	,	,	PUNCT
ap-1859	119	24	l1	l1	PROPN
ap-1859	119	25	/	/	SYM
ap-1859	119	26	l2	l2	NOUN
ap-1859	119	27	.	.	PUNCT
ap-1859	120	1	we	we	PRON
ap-1859	120	2	studied	study	VERB
ap-1859	120	3	two	two	NUM
ap-1859	120	4	combinations	combination	NOUN
ap-1859	120	5	of	of	ADP
ap-1859	120	6	s	s	PROPN
ap-1859	120	7	,	,	PUNCT
ap-1859	120	8	t	t	PROPN
ap-1859	120	9	,	,	PUNCT
ap-1859	120	10	namely	namely	ADV
ap-1859	120	11	•	•	NUM
ap-1859	120	12	t	t	NOUN
ap-1859	120	13	=	=	SYM
ap-1859	120	14	0.1	0.1	NUM
ap-1859	120	15	,	,	PUNCT
ap-1859	120	16	s	s	PART
ap-1859	120	17	=	=	SYM
ap-1859	120	18	1	1	NUM
ap-1859	120	19	,	,	PUNCT
ap-1859	120	20	•	•	NUM
ap-1859	120	21	t	t	NOUN
ap-1859	120	22	=	=	SYM
ap-1859	120	23	0.5	0.5	NUM
ap-1859	120	24	,	,	PUNCT
ap-1859	120	25	s	s	PART
ap-1859	120	26	=	=	NOUN
ap-1859	120	27	0.5	0.5	NUM
ap-1859	120	28	,	,	PUNCT
ap-1859	120	29	and	and	CCONJ
ap-1859	120	30	for	for	ADP
ap-1859	120	31	each	each	PRON
ap-1859	120	32	of	of	ADP
ap-1859	120	33	them	they	PRON
ap-1859	120	34	,	,	PUNCT
ap-1859	120	35	we	we	PRON
ap-1859	120	36	considered	consider	VERB
ap-1859	120	37	three	three	NUM
ap-1859	120	38	different	different	ADJ
ap-1859	120	39	ratios	ratio	NOUN
ap-1859	120	40	l1	l1	PROPN
ap-1859	120	41	/	/	SYM
ap-1859	120	42	l2	l2	NOUN
ap-1859	120	43	(	(	PUNCT
ap-1859	120	44	with	with	ADP
ap-1859	120	45	l1	l1	PROPN
ap-1859	120	46	+	+	CCONJ
ap-1859	120	47	l2	l2	NOUN
ap-1859	120	48	=	=	SYM
ap-1859	120	49	1	1	NUM
ap-1859	120	50	)	)	PUNCT
ap-1859	120	51	,	,	PUNCT
ap-1859	120	52	namely	namely	ADV
ap-1859	120	53	•	•	VERB
ap-1859	120	54	the	the	DET
ap-1859	120	55	golden	golden	ADJ
ap-1859	120	56	mean	mean	NOUN
ap-1859	120	57	l1	l1	PROPN
ap-1859	120	58	/	/	SYM
ap-1859	120	59	l2	l2	NOUN
ap-1859	120	60	=	=	SYM
ap-1859	120	61	(	(	PUNCT
ap-1859	120	62	1	1	NUM
ap-1859	120	63	+	+	CCONJ
ap-1859	120	64	√	√	NUM
ap-1859	120	65	5)/2	5)/2	NUM
ap-1859	120	66	,	,	PUNCT
ap-1859	120	67	•	•	ADP
ap-1859	120	68	the	the	DET
ap-1859	120	69	silver	silver	NOUN
ap-1859	120	70	mean	mean	NOUN
ap-1859	120	71	l1	l1	PROPN
ap-1859	120	72	/	/	SYM
ap-1859	120	73	l2	l2	NOUN
ap-1859	120	74	=	=	SYM
ap-1859	120	75	1	1	NUM
ap-1859	120	76	+	+	CCONJ
ap-1859	120	77	√	√	NUM
ap-1859	120	78	2	2	NUM
ap-1859	120	79	,	,	PUNCT
ap-1859	120	80	•	•	DET
ap-1859	120	81	the	the	DET
ap-1859	120	82	bronze	bronze	NOUN
ap-1859	120	83	mean	mean	NOUN
ap-1859	120	84	l1	l1	PROPN
ap-1859	120	85	/	/	SYM
ap-1859	120	86	l2	l2	NOUN
ap-1859	120	87	=	=	SYM
ap-1859	120	88	(	(	PUNCT
ap-1859	120	89	3	3	NUM
ap-1859	120	90	+	+	CCONJ
ap-1859	120	91	√	√	NOUN
ap-1859	120	92	13)/2	13)/2	NUM
ap-1859	120	93	.	.	PUNCT
ap-1859	121	1	we	we	PRON
ap-1859	121	2	explain	explain	VERB
ap-1859	121	3	the	the	DET
ap-1859	121	4	numerical	numerical	ADJ
ap-1859	121	5	result	result	NOUN
ap-1859	121	6	shown	show	VERB
ap-1859	121	7	in	in	ADP
ap-1859	121	8	figure	figure	NOUN
ap-1859	121	9	6	6	NUM
ap-1859	121	10	.	.	PUNCT
ap-1859	122	1	the	the	DET
ap-1859	122	2	spectral	spectral	ADJ
ap-1859	122	3	sets	set	NOUN
ap-1859	122	4	have	have	VERB
ap-1859	122	5	period	period	NOUN
ap-1859	122	6	2π	2π	NOUN
ap-1859	122	7	as	as	ADP
ap-1859	122	8	functions	function	NOUN
ap-1859	122	9	of	of	ADP
ap-1859	122	10	θ	θ	PROPN
ap-1859	122	11	.	.	PUNCT
ap-1859	123	1	this	this	PRON
ap-1859	123	2	is	be	AUX
ap-1859	123	3	because	because	SCONJ
ap-1859	123	4	all	all	DET
ap-1859	123	5	the	the	DET
ap-1859	123	6	hamiltonians	hamiltonian	NOUN
ap-1859	123	7	are	be	AUX
ap-1859	123	8	2π	2π	PROPN
ap-1859	123	9	periodic	periodic	ADJ
ap-1859	123	10	by	by	ADP
ap-1859	123	11	construction	construction	NOUN
ap-1859	123	12	.	.	PUNCT
ap-1859	124	1	on	on	ADP
ap-1859	124	2	the	the	DET
ap-1859	124	3	other	other	ADJ
ap-1859	124	4	hand	hand	NOUN
ap-1859	124	5	,	,	PUNCT
ap-1859	124	6	however	however	ADV
ap-1859	124	7	,	,	PUNCT
ap-1859	124	8	some	some	DET
ap-1859	124	9	wavenumber	wavenumber	NOUN
ap-1859	124	10	do	do	AUX
ap-1859	124	11	not	not	PART
ap-1859	124	12	have	have	VERB
ap-1859	124	13	the	the	DET
ap-1859	124	14	2π	2π	NUM
ap-1859	124	15	periodicity	periodicity	NOUN
ap-1859	124	16	.	.	PUNCT
ap-1859	125	1	for	for	ADP
ap-1859	125	2	example	example	NOUN
ap-1859	125	3	,	,	PUNCT
ap-1859	125	4	let	let	VERB
ap-1859	125	5	us	we	PRON
ap-1859	125	6	keep	keep	VERB
ap-1859	125	7	track	track	NOUN
ap-1859	125	8	of	of	ADP
ap-1859	125	9	the	the	DET
ap-1859	125	10	wavenumber	wavenumber	NOUN
ap-1859	125	11	(	(	PUNCT
ap-1859	125	12	say	say	VERB
ap-1859	125	13	k0	k0	PROPN
ap-1859	125	14	)	)	PUNCT
ap-1859	125	15	of	of	ADP
ap-1859	125	16	the	the	DET
ap-1859	125	17	ground	ground	NOUN
ap-1859	125	18	state	state	NOUN
ap-1859	125	19	at	at	ADP
ap-1859	125	20	θ	θ	PROPN
ap-1859	125	21	=	=	SYM
ap-1859	125	22	0	0	NUM
ap-1859	125	23	in	in	ADP
ap-1859	125	24	the	the	DET
ap-1859	125	25	uppermost	uppermost	ADJ
ap-1859	125	26	figure	figure	NOUN
ap-1859	125	27	.	.	PUNCT
ap-1859	126	1	around	around	ADP
ap-1859	126	2	π/3	π/3	X
ap-1859	126	3	<	<	X
ap-1859	126	4	θ	θ	X
ap-1859	126	5	<	<	X
ap-1859	126	6	2π/3	2π/3	PROPN
ap-1859	126	7	,	,	PUNCT
ap-1859	126	8	k0	k0	PROPN
ap-1859	126	9	increase	increase	NOUN
ap-1859	126	10	suddenly	suddenly	ADV
ap-1859	126	11	and	and	CCONJ
ap-1859	126	12	form	form	VERB
ap-1859	126	13	three	three	NUM
ap-1859	126	14	crossings	crossing	NOUN
ap-1859	126	15	with	with	ADP
ap-1859	126	16	other	other	ADJ
ap-1859	126	17	eigenstates	eigenstate	NOUN
ap-1859	126	18	.	.	PUNCT
ap-1859	127	1	because	because	SCONJ
ap-1859	127	2	the	the	DET
ap-1859	127	3	graphs	graph	NOUN
ap-1859	127	4	consist	consist	VERB
ap-1859	127	5	of	of	ADP
ap-1859	127	6	two	two	NUM
ap-1859	127	7	disjoint	disjoint	ADJ
ap-1859	127	8	parts	part	NOUN
ap-1859	127	9	,	,	PUNCT
ap-1859	127	10	these	these	DET
ap-1859	127	11	crossings	crossing	NOUN
ap-1859	127	12	are	be	AUX
ap-1859	127	13	not	not	PART
ap-1859	127	14	avoided	avoid	VERB
ap-1859	127	15	.	.	PUNCT
ap-1859	128	1	the	the	DET
ap-1859	128	2	eigenfunction	eigenfunction	NOUN
ap-1859	128	3	corresponding	correspond	VERB
ap-1859	128	4	to	to	ADP
ap-1859	128	5	k0	k0	PROPN
ap-1859	128	6	is	be	AUX
ap-1859	128	7	localized	localize	VERB
ap-1859	128	8	within	within	ADP
ap-1859	128	9	a	a	DET
ap-1859	128	10	disjoint	disjoint	NOUN
ap-1859	128	11	fragment	fragment	NOUN
ap-1859	128	12	,	,	PUNCT
ap-1859	128	13	and	and	CCONJ
ap-1859	128	14	the	the	DET
ap-1859	128	15	other	other	ADJ
ap-1859	128	16	three	three	NUM
ap-1859	128	17	eigenfunctions	eigenfunction	NOUN
ap-1859	128	18	involving	involve	VERB
ap-1859	128	19	the	the	DET
ap-1859	128	20	crossings	crossing	NOUN
ap-1859	128	21	are	be	AUX
ap-1859	128	22	localized	localize	VERB
ap-1859	128	23	in	in	ADP
ap-1859	128	24	the	the	DET
ap-1859	128	25	other	other	ADJ
ap-1859	128	26	part	part	NOUN
ap-1859	128	27	.	.	PUNCT
ap-1859	129	1	hence	hence	ADV
ap-1859	129	2	,	,	PUNCT
ap-1859	129	3	as	as	ADP
ap-1859	129	4	a	a	DET
ap-1859	129	5	result	result	NOUN
ap-1859	129	6	of	of	ADP
ap-1859	129	7	a	a	DET
ap-1859	129	8	2π	2π	NOUN
ap-1859	129	9	-	-	NOUN
ap-1859	129	10	cycle	cycle	NOUN
ap-1859	129	11	of	of	ADP
ap-1859	129	12	θ	θ	PROPN
ap-1859	129	13	,	,	PUNCT
ap-1859	129	14	k0	k0	PROPN
ap-1859	129	15	becomes	become	VERB
ap-1859	129	16	the	the	DET
ap-1859	129	17	wavenumber	wavenumber	NOUN
ap-1859	129	18	of	of	ADP
ap-1859	129	19	the	the	DET
ap-1859	129	20	third	third	ADJ
ap-1859	129	21	excited	excited	ADJ
ap-1859	129	22	state	state	NOUN
ap-1859	129	23	.	.	PUNCT
ap-1859	130	1	this	this	PRON
ap-1859	130	2	is	be	AUX
ap-1859	130	3	an	an	DET
ap-1859	130	4	example	example	NOUN
ap-1859	130	5	of	of	ADP
ap-1859	130	6	the	the	DET
ap-1859	130	7	holonomy	holonomy	NOUN
ap-1859	130	8	in	in	ADP
ap-1859	130	9	eigenvalue	eigenvalue	PROPN
ap-1859	130	10	and	and	CCONJ
ap-1859	130	11	eigenspace	eigenspace	NOUN
ap-1859	130	12	.	.	PUNCT
ap-1859	131	1	some	some	DET
ap-1859	131	2	other	other	ADJ
ap-1859	131	3	wavenumbers	wavenumber	NOUN
ap-1859	131	4	,	,	PUNCT
ap-1859	131	5	e.g.	e.g.	ADV
ap-1859	131	6	,	,	PUNCT
ap-1859	131	7	4	4	NUM
ap-1859	131	8	-	-	PUNCT
ap-1859	131	9	th	th	X
ap-1859	131	10	excited	excited	ADJ
ap-1859	131	11	state	state	NOUN
ap-1859	131	12	at	at	ADP
ap-1859	131	13	θ	θ	PROPN
ap-1859	131	14	=	=	SYM
ap-1859	131	15	0	0	NUM
ap-1859	131	16	in	in	ADP
ap-1859	131	17	the	the	DET
ap-1859	131	18	leftmost	leftmost	ADJ
ap-1859	131	19	figure	figure	NOUN
ap-1859	131	20	,	,	PUNCT
ap-1859	131	21	are	be	AUX
ap-1859	131	22	not	not	PART
ap-1859	131	23	involved	involve	VERB
ap-1859	131	24	by	by	ADP
ap-1859	131	25	the	the	DET
ap-1859	131	26	holonomy	holonomy	NOUN
ap-1859	131	27	.	.	PUNCT
ap-1859	132	1	by	by	ADP
ap-1859	132	2	changing	change	VERB
ap-1859	132	3	the	the	DET
ap-1859	132	4	ratio	ratio	NOUN
ap-1859	132	5	l1	l1	PROPN
ap-1859	132	6	/	/	SYM
ap-1859	132	7	l2	l2	NOUN
ap-1859	132	8	,	,	PUNCT
ap-1859	132	9	we	we	PRON
ap-1859	132	10	see	see	VERB
ap-1859	132	11	various	various	ADJ
ap-1859	132	12	patterns	pattern	NOUN
ap-1859	132	13	of	of	ADP
ap-1859	132	14	the	the	DET
ap-1859	132	15	quantum	quantum	ADJ
ap-1859	132	16	holonomy	holonomy	NOUN
ap-1859	132	17	.	.	PUNCT
ap-1859	133	1	also	also	ADV
ap-1859	133	2	,	,	PUNCT
ap-1859	133	3	the	the	DET
ap-1859	133	4	holonomies	holonomie	NOUN
ap-1859	133	5	appear	appear	VERB
ap-1859	133	6	in	in	ADP
ap-1859	133	7	various	various	ADJ
ap-1859	133	8	choice	choice	NOUN
ap-1859	133	9	of	of	ADP
ap-1859	133	10	the	the	DET
ap-1859	133	11	parameters	parameter	NOUN
ap-1859	133	12	,	,	PUNCT
ap-1859	133	13	cf	cf	X
ap-1859	133	14	.	.	PUNCT
ap-1859	134	1	figure	figure	NOUN
ap-1859	134	2	7	7	NUM
ap-1859	134	3	.	.	X
ap-1859	134	4	413	413	NUM
ap-1859	134	5	t.	t.	NOUN
ap-1859	134	6	cheon	cheon	PROPN
ap-1859	134	7	,	,	PUNCT
ap-1859	134	8	a.	a.	PROPN
ap-1859	134	9	tanaka	tanaka	PROPN
ap-1859	134	10	,	,	PUNCT
ap-1859	134	11	o.	o.	PROPN
ap-1859	134	12	turek	turek	PROPN
ap-1859	134	13	acta	acta	PROPN
ap-1859	134	14	polytechnica	polytechnica	PROPN
ap-1859	134	15	figure	figure	NOUN
ap-1859	134	16	6	6	NUM
ap-1859	134	17	.	.	PUNCT
ap-1859	134	18	holonomy	holonomy	NOUN
ap-1859	134	19	as	as	ADP
ap-1859	134	20	a	a	DET
ap-1859	134	21	result	result	NOUN
ap-1859	134	22	of	of	ADP
ap-1859	134	23	the	the	DET
ap-1859	134	24	long	long	ADJ
ap-1859	134	25	cycle	cycle	NOUN
ap-1859	134	26	topology	topology	NOUN
ap-1859	134	27	change	change	NOUN
ap-1859	134	28	for	for	ADP
ap-1859	134	29	t	t	NOUN
ap-1859	134	30	=	=	SYM
ap-1859	134	31	0.1	0.1	NUM
ap-1859	134	32	,	,	PUNCT
ap-1859	134	33	s	s	PART
ap-1859	134	34	=	=	NOUN
ap-1859	134	35	1	1	NUM
ap-1859	134	36	.	.	PUNCT
ap-1859	135	1	the	the	DET
ap-1859	135	2	ratio	ratio	NOUN
ap-1859	135	3	l1	l1	PROPN
ap-1859	135	4	/	/	SYM
ap-1859	135	5	l2	l2	NOUN
ap-1859	135	6	is	be	AUX
ap-1859	135	7	chosen	choose	VERB
ap-1859	135	8	as	as	ADP
ap-1859	135	9	the	the	DET
ap-1859	135	10	bronze	bronze	NOUN
ap-1859	135	11	mean	mean	NOUN
ap-1859	135	12	(	(	PUNCT
ap-1859	135	13	top	top	NOUN
ap-1859	135	14	)	)	PUNCT
ap-1859	135	15	,	,	PUNCT
ap-1859	135	16	silver	silver	NOUN
ap-1859	135	17	mean	mean	NOUN
ap-1859	135	18	(	(	PUNCT
ap-1859	135	19	middle	middle	ADJ
ap-1859	135	20	)	)	PUNCT
ap-1859	135	21	and	and	CCONJ
ap-1859	135	22	golden	golden	ADJ
ap-1859	135	23	mean	mean	NOUN
ap-1859	135	24	(	(	PUNCT
ap-1859	135	25	bottom	bottom	NOUN
ap-1859	135	26	)	)	PUNCT
ap-1859	135	27	.	.	PUNCT
ap-1859	136	1	figure	figure	VERB
ap-1859	136	2	7	7	NUM
ap-1859	136	3	.	.	PUNCT
ap-1859	136	4	holonomy	holonomy	NOUN
ap-1859	136	5	as	as	ADP
ap-1859	136	6	a	a	DET
ap-1859	136	7	result	result	NOUN
ap-1859	136	8	of	of	ADP
ap-1859	136	9	the	the	DET
ap-1859	136	10	long	long	ADJ
ap-1859	136	11	cycle	cycle	NOUN
ap-1859	136	12	topology	topology	NOUN
ap-1859	136	13	change	change	NOUN
ap-1859	136	14	for	for	ADP
ap-1859	136	15	t	t	NOUN
ap-1859	136	16	=	=	SYM
ap-1859	136	17	0.5	0.5	NUM
ap-1859	136	18	,	,	PUNCT
ap-1859	136	19	s	s	PART
ap-1859	136	20	=	=	NOUN
ap-1859	136	21	0.5	0.5	NUM
ap-1859	136	22	.	.	PUNCT
ap-1859	137	1	the	the	DET
ap-1859	137	2	ratio	ratio	NOUN
ap-1859	137	3	l1	l1	PROPN
ap-1859	137	4	/	/	SYM
ap-1859	137	5	l2	l2	NOUN
ap-1859	137	6	is	be	AUX
ap-1859	137	7	chosen	choose	VERB
ap-1859	137	8	as	as	ADP
ap-1859	137	9	the	the	DET
ap-1859	137	10	bronze	bronze	NOUN
ap-1859	137	11	mean	mean	NOUN
ap-1859	137	12	(	(	PUNCT
ap-1859	137	13	top	top	NOUN
ap-1859	137	14	)	)	PUNCT
ap-1859	137	15	,	,	PUNCT
ap-1859	137	16	silver	silver	NOUN
ap-1859	137	17	mean	mean	NOUN
ap-1859	137	18	(	(	PUNCT
ap-1859	137	19	middle	middle	ADJ
ap-1859	137	20	)	)	PUNCT
ap-1859	137	21	and	and	CCONJ
ap-1859	137	22	golden	golden	ADJ
ap-1859	137	23	mean	mean	NOUN
ap-1859	137	24	(	(	PUNCT
ap-1859	137	25	bottom	bottom	NOUN
ap-1859	137	26	)	)	PUNCT
ap-1859	137	27	.	.	PUNCT
ap-1859	138	1	figure	figure	VERB
ap-1859	138	2	8	8	NUM
ap-1859	138	3	.	.	PUNCT
ap-1859	139	1	holonomy	holonomy	NOUN
ap-1859	139	2	as	as	ADP
ap-1859	139	3	a	a	DET
ap-1859	139	4	result	result	NOUN
ap-1859	139	5	of	of	ADP
ap-1859	139	6	the	the	DET
ap-1859	139	7	short	short	ADJ
ap-1859	139	8	cycle	cycle	NOUN
ap-1859	139	9	topology	topology	NOUN
ap-1859	139	10	change	change	NOUN
ap-1859	139	11	for	for	ADP
ap-1859	139	12	t	t	NOUN
ap-1859	139	13	=	=	SYM
ap-1859	139	14	0.1	0.1	NUM
ap-1859	139	15	,	,	PUNCT
ap-1859	139	16	s	s	PART
ap-1859	139	17	=	=	NOUN
ap-1859	139	18	1	1	NUM
ap-1859	139	19	.	.	PUNCT
ap-1859	140	1	the	the	DET
ap-1859	140	2	ratio	ratio	NOUN
ap-1859	140	3	l1	l1	PROPN
ap-1859	140	4	/	/	SYM
ap-1859	140	5	l2	l2	NOUN
ap-1859	140	6	is	be	AUX
ap-1859	140	7	chosen	choose	VERB
ap-1859	140	8	as	as	ADP
ap-1859	140	9	the	the	DET
ap-1859	140	10	bronze	bronze	NOUN
ap-1859	140	11	mean	mean	NOUN
ap-1859	140	12	(	(	PUNCT
ap-1859	140	13	top	top	NOUN
ap-1859	140	14	)	)	PUNCT
ap-1859	140	15	,	,	PUNCT
ap-1859	140	16	silver	silver	NOUN
ap-1859	140	17	mean	mean	NOUN
ap-1859	140	18	(	(	PUNCT
ap-1859	140	19	middle	middle	ADJ
ap-1859	140	20	)	)	PUNCT
ap-1859	140	21	and	and	CCONJ
ap-1859	140	22	golden	golden	ADJ
ap-1859	140	23	mean	mean	NOUN
ap-1859	140	24	(	(	PUNCT
ap-1859	140	25	bottom	bottom	NOUN
ap-1859	140	26	)	)	PUNCT
ap-1859	140	27	.	.	PUNCT
ap-1859	141	1	3.2	3.2	NUM
ap-1859	141	2	.	.	PUNCT
ap-1859	142	1	short	short	ADJ
ap-1859	142	2	cycle	cycle	NOUN
ap-1859	142	3	let	let	VERB
ap-1859	142	4	us	we	PRON
ap-1859	142	5	proceed	proceed	VERB
ap-1859	142	6	to	to	ADP
ap-1859	142	7	the	the	DET
ap-1859	142	8	simplified	simplified	ADJ
ap-1859	142	9	cycle	cycle	NOUN
ap-1859	142	10	represented	represent	VERB
ap-1859	142	11	by	by	ADP
ap-1859	142	12	(	(	PUNCT
ap-1859	142	13	14	14	NUM
ap-1859	142	14	)	)	PUNCT
ap-1859	142	15	,	,	PUNCT
ap-1859	142	16	in	in	ADP
ap-1859	142	17	which	which	PRON
ap-1859	142	18	four	four	NUM
ap-1859	142	19	distinct	distinct	ADJ
ap-1859	142	20	topologies	topology	NOUN
ap-1859	142	21	are	be	AUX
ap-1859	142	22	connected	connect	VERB
ap-1859	142	23	in	in	ADP
ap-1859	142	24	a	a	DET
ap-1859	142	25	single	single	ADJ
ap-1859	142	26	sequence	sequence	NOUN
ap-1859	142	27	.	.	PUNCT
ap-1859	143	1	the	the	DET
ap-1859	143	2	spectra	spectra	NOUN
ap-1859	143	3	as	as	ADP
ap-1859	143	4	functions	function	NOUN
ap-1859	143	5	of	of	ADP
ap-1859	143	6	the	the	DET
ap-1859	143	7	angle	angle	NOUN
ap-1859	143	8	parameter	parameter	NOUN
ap-1859	143	9	θ	θ	PROPN
ap-1859	143	10	∈	∈	PROPN
ap-1859	144	1	[	[	X
ap-1859	144	2	0	0	NUM
ap-1859	144	3	,	,	PUNCT
ap-1859	144	4	2π	2π	NOUN
ap-1859	144	5	)	)	PUNCT
ap-1859	144	6	have	have	AUX
ap-1859	144	7	been	be	AUX
ap-1859	144	8	calculated	calculate	VERB
ap-1859	144	9	for	for	ADP
ap-1859	144	10	the	the	DET
ap-1859	144	11	choice	choice	NOUN
ap-1859	144	12	of	of	ADP
ap-1859	144	13	parameters	parameter	NOUN
ap-1859	144	14	t	t	NOUN
ap-1859	144	15	=	=	SYM
ap-1859	144	16	0.1	0.1	NUM
ap-1859	144	17	,	,	PUNCT
ap-1859	144	18	s	s	PART
ap-1859	144	19	=	=	SYM
ap-1859	144	20	1	1	NUM
ap-1859	144	21	and	and	CCONJ
ap-1859	144	22	l1	l1	PROPN
ap-1859	144	23	/	/	SYM
ap-1859	144	24	l2	l2	NOUN
ap-1859	144	25	attaining	attain	VERB
ap-1859	144	26	the	the	DET
ap-1859	144	27	value	value	NOUN
ap-1859	144	28	of	of	ADP
ap-1859	144	29	the	the	DET
ap-1859	144	30	golden	golden	ADJ
ap-1859	144	31	mean	mean	NOUN
ap-1859	144	32	,	,	PUNCT
ap-1859	144	33	the	the	DET
ap-1859	144	34	silver	silver	NOUN
ap-1859	144	35	mean	mean	NOUN
ap-1859	144	36	and	and	CCONJ
ap-1859	144	37	the	the	DET
ap-1859	144	38	bronze	bronze	NOUN
ap-1859	144	39	mean	mean	NOUN
ap-1859	144	40	.	.	PUNCT
ap-1859	145	1	the	the	DET
ap-1859	145	2	results	result	NOUN
ap-1859	145	3	are	be	AUX
ap-1859	145	4	depicted	depict	VERB
ap-1859	145	5	in	in	ADP
ap-1859	145	6	fig	fig	NOUN
ap-1859	145	7	.	.	PUNCT
ap-1859	146	1	8	8	NUM
ap-1859	146	2	.	.	X
ap-1859	147	1	4	4	NUM
ap-1859	147	2	.	.	X
ap-1859	148	1	on	on	ADP
ap-1859	148	2	the	the	DET
ap-1859	148	3	boundary	boundary	ADJ
ap-1859	148	4	condition	condition	NOUN
ap-1859	148	5	the	the	DET
ap-1859	148	6	boundary	boundary	ADJ
ap-1859	148	7	condition	condition	NOUN
ap-1859	148	8	(	(	PUNCT
ap-1859	148	9	1	1	X
ap-1859	148	10	)	)	PUNCT
ap-1859	148	11	represents	represent	VERB
ap-1859	148	12	a	a	DET
ap-1859	148	13	certain	certain	ADJ
ap-1859	148	14	singular	singular	ADJ
ap-1859	148	15	potential	potential	NOUN
ap-1859	148	16	in	in	ADP
ap-1859	148	17	the	the	DET
ap-1859	148	18	vertex	vertex	NOUN
ap-1859	148	19	that	that	PRON
ap-1859	148	20	has	have	VERB
ap-1859	148	21	in	in	ADP
ap-1859	148	22	general	general	ADJ
ap-1859	148	23	a	a	DET
ap-1859	148	24	highly	highly	ADV
ap-1859	148	25	nontrivial	nontrivial	ADJ
ap-1859	148	26	nature	nature	NOUN
ap-1859	148	27	.	.	PUNCT
ap-1859	149	1	as	as	SCONJ
ap-1859	149	2	has	have	AUX
ap-1859	149	3	been	be	AUX
ap-1859	149	4	shown	show	VERB
ap-1859	149	5	in	in	ADP
ap-1859	149	6	[	[	X
ap-1859	149	7	3	3	NUM
ap-1859	149	8	,	,	PUNCT
ap-1859	149	9	9	9	NUM
ap-1859	149	10	]	]	PUNCT
ap-1859	149	11	,	,	PUNCT
ap-1859	149	12	the	the	DET
ap-1859	149	13	physical	physical	ADJ
ap-1859	149	14	content	content	NOUN
ap-1859	149	15	of	of	ADP
ap-1859	149	16	a	a	DET
ap-1859	149	17	generic	generic	ADJ
ap-1859	149	18	boundary	boundary	ADJ
ap-1859	149	19	condition	condition	NOUN
ap-1859	149	20	corresponds	correspond	VERB
ap-1859	149	21	to	to	ADP
ap-1859	149	22	a	a	DET
ap-1859	149	23	set	set	NOUN
ap-1859	149	24	of	of	ADP
ap-1859	149	25	infinitely	infinitely	ADV
ap-1859	149	26	strong	strong	ADJ
ap-1859	149	27	δ	δ	PROPN
ap-1859	149	28	potentials	potential	NOUN
ap-1859	149	29	sited	site	VERB
ap-1859	149	30	in	in	ADP
ap-1859	149	31	points	point	NOUN
ap-1859	149	32	in	in	ADP
ap-1859	149	33	an	an	DET
ap-1859	149	34	infinitely	infinitely	ADV
ap-1859	149	35	small	small	ADJ
ap-1859	149	36	web	web	NOUN
ap-1859	149	37	located	locate	VERB
ap-1859	149	38	in	in	ADP
ap-1859	149	39	the	the	DET
ap-1859	149	40	vertex	vertex	NOUN
ap-1859	149	41	.	.	PUNCT
ap-1859	150	1	we	we	PRON
ap-1859	150	2	sketch	sketch	VERB
ap-1859	150	3	what	what	PRON
ap-1859	150	4	the	the	DET
ap-1859	150	5	webs	webs	NOUN
ap-1859	150	6	look	look	VERB
ap-1859	150	7	like	like	ADP
ap-1859	150	8	for	for	ADP
ap-1859	150	9	the	the	DET
ap-1859	150	10	boundary	boundary	ADJ
ap-1859	150	11	conditions	condition	NOUN
ap-1859	150	12	of	of	ADP
ap-1859	150	13	our	our	PRON
ap-1859	150	14	model	model	NOUN
ap-1859	150	15	in	in	ADP
ap-1859	150	16	figures	figure	NOUN
ap-1859	150	17	9	9	NUM
ap-1859	150	18	,	,	PUNCT
ap-1859	150	19	10	10	NUM
ap-1859	150	20	and	and	CCONJ
ap-1859	150	21	11	11	NUM
ap-1859	150	22	.	.	PUNCT
ap-1859	151	1	in	in	ADP
ap-1859	151	2	all	all	PRON
ap-1859	151	3	of	of	ADP
ap-1859	151	4	the	the	DET
ap-1859	151	5	finite	finite	ADJ
ap-1859	151	6	approximations	approximation	NOUN
ap-1859	151	7	,	,	PUNCT
ap-1859	151	8	the	the	DET
ap-1859	151	9	parameter	parameter	NOUN
ap-1859	151	10	ε	ε	PROPN
ap-1859	151	11	has	have	VERB
ap-1859	151	12	to	to	PART
ap-1859	151	13	be	be	AUX
ap-1859	151	14	chosen	choose	VERB
ap-1859	151	15	small	small	ADJ
ap-1859	151	16	with	with	ADP
ap-1859	151	17	respect	respect	NOUN
ap-1859	151	18	to	to	ADP
ap-1859	151	19	the	the	DET
ap-1859	151	20	wavelength	wavelength	NOUN
ap-1859	151	21	of	of	ADP
ap-1859	151	22	the	the	DET
ap-1859	151	23	particle	particle	NOUN
ap-1859	151	24	.	.	PUNCT
ap-1859	152	1	for	for	ADP
ap-1859	152	2	ε→	ε→	PROPN
ap-1859	152	3	0	0	NUM
ap-1859	152	4	,	,	PUNCT
ap-1859	152	5	the	the	DET
ap-1859	152	6	approximation	approximation	NOUN
ap-1859	152	7	effectively	effectively	ADV
ap-1859	152	8	produces	produce	VERB
ap-1859	152	9	the	the	DET
ap-1859	152	10	boundary	boundary	ADJ
ap-1859	152	11	conditions	condition	NOUN
ap-1859	152	12	(	(	PUNCT
ap-1859	152	13	4	4	NUM
ap-1859	152	14	)	)	PUNCT
ap-1859	152	15	.	.	PUNCT
ap-1859	153	1	the	the	DET
ap-1859	153	2	result	result	NOUN
ap-1859	153	3	has	have	AUX
ap-1859	153	4	been	be	AUX
ap-1859	153	5	obtained	obtain	VERB
ap-1859	153	6	using	use	VERB
ap-1859	153	7	the	the	DET
ap-1859	153	8	formulas	formula	NOUN
ap-1859	153	9	from	from	ADP
ap-1859	153	10	[	[	X
ap-1859	153	11	3	3	NUM
ap-1859	153	12	,	,	PUNCT
ap-1859	153	13	9	9	NUM
ap-1859	153	14	]	]	PUNCT
ap-1859	153	15	.	.	PUNCT
ap-1859	154	1	it	it	PRON
ap-1859	154	2	illustrates	illustrate	VERB
ap-1859	154	3	in	in	ADP
ap-1859	154	4	a	a	DET
ap-1859	154	5	simple	simple	ADJ
ap-1859	154	6	way	way	NOUN
ap-1859	154	7	the	the	DET
ap-1859	154	8	relation	relation	NOUN
ap-1859	154	9	between	between	ADP
ap-1859	154	10	the	the	DET
ap-1859	154	11	global	global	ADJ
ap-1859	154	12	topology	topology	NOUN
ap-1859	154	13	of	of	ADP
ap-1859	154	14	the	the	DET
ap-1859	154	15	system	system	NOUN
ap-1859	154	16	and	and	CCONJ
ap-1859	154	17	the	the	DET
ap-1859	154	18	topology	topology	NOUN
ap-1859	154	19	of	of	ADP
ap-1859	154	20	the	the	DET
ap-1859	154	21	internal	internal	ADJ
ap-1859	154	22	infinitely	infinitely	ADV
ap-1859	154	23	small	small	ADJ
ap-1859	154	24	web	web	NOUN
ap-1859	154	25	.	.	PROPN
ap-1859	154	26	5	5	NUM
ap-1859	154	27	.	.	X
ap-1859	154	28	discussion	discussion	NOUN
ap-1859	154	29	the	the	DET
ap-1859	154	30	creation	creation	NOUN
ap-1859	154	31	of	of	ADP
ap-1859	154	32	the	the	DET
ap-1859	154	33	holonomy	holonomy	NOUN
ap-1859	154	34	in	in	ADP
ap-1859	154	35	our	our	PRON
ap-1859	154	36	model	model	NOUN
ap-1859	154	37	can	can	AUX
ap-1859	154	38	be	be	AUX
ap-1859	154	39	explained	explain	VERB
ap-1859	154	40	in	in	ADP
ap-1859	154	41	the	the	DET
ap-1859	154	42	following	following	ADJ
ap-1859	154	43	way	way	NOUN
ap-1859	154	44	.	.	PUNCT
ap-1859	155	1	in	in	ADP
ap-1859	155	2	regions	region	NOUN
ap-1859	155	3	i	i	PRON
ap-1859	155	4	,	,	PUNCT
ap-1859	155	5	iv	iv	PROPN
ap-1859	155	6	,	,	PUNCT
ap-1859	155	7	v	v	NOUN
ap-1859	155	8	and	and	CCONJ
ap-1859	155	9	vi	vi	NOUN
ap-1859	155	10	,	,	PUNCT
ap-1859	155	11	when	when	SCONJ
ap-1859	155	12	the	the	DET
ap-1859	155	13	graph	graph	NOUN
ap-1859	155	14	consists	consist	VERB
ap-1859	155	15	of	of	ADP
ap-1859	155	16	a	a	DET
ap-1859	155	17	single	single	ADJ
ap-1859	155	18	component	component	NOUN
ap-1859	155	19	,	,	PUNCT
ap-1859	155	20	the	the	DET
ap-1859	155	21	eigenvalues	eigenvalue	NOUN
ap-1859	155	22	as	as	ADP
ap-1859	155	23	functions	function	NOUN
ap-1859	155	24	of	of	ADP
ap-1859	155	25	the	the	DET
ap-1859	155	26	system	system	NOUN
ap-1859	155	27	parameter	parameter	NOUN
ap-1859	155	28	θ	θ	PROPN
ap-1859	155	29	can	can	AUX
ap-1859	155	30	change	change	VERB
ap-1859	155	31	their	their	PRON
ap-1859	155	32	values	value	NOUN
ap-1859	155	33	,	,	PUNCT
ap-1859	155	34	but	but	CCONJ
ap-1859	155	35	they	they	PRON
ap-1859	155	36	never	never	ADV
ap-1859	155	37	cross	cross	VERB
ap-1859	155	38	each	each	DET
ap-1859	155	39	other	other	ADJ
ap-1859	155	40	,	,	PUNCT
ap-1859	155	41	because	because	SCONJ
ap-1859	155	42	crossings	crossing	NOUN
ap-1859	155	43	will	will	AUX
ap-1859	155	44	be	be	AUX
ap-1859	155	45	avoided	avoid	VERB
ap-1859	155	46	generically	generically	ADV
ap-1859	155	47	.	.	PUNCT
ap-1859	156	1	however	however	ADV
ap-1859	156	2	,	,	PUNCT
ap-1859	156	3	in	in	ADP
ap-1859	156	4	regions	region	NOUN
ap-1859	156	5	ii	ii	PROPN
ap-1859	156	6	and	and	CCONJ
ap-1859	156	7	iii	iii	PROPN
ap-1859	156	8	,	,	PUNCT
ap-1859	156	9	the	the	DET
ap-1859	156	10	graph	graph	NOUN
ap-1859	156	11	is	be	AUX
ap-1859	156	12	separated	separate	VERB
ap-1859	156	13	into	into	ADP
ap-1859	156	14	two	two	NUM
ap-1859	156	15	components	component	NOUN
ap-1859	156	16	(	(	PUNCT
ap-1859	156	17	two	two	NUM
ap-1859	156	18	lines	line	NOUN
ap-1859	156	19	or	or	CCONJ
ap-1859	156	20	two	two	NUM
ap-1859	156	21	rings	ring	NOUN
ap-1859	156	22	)	)	PUNCT
ap-1859	156	23	,	,	PUNCT
ap-1859	156	24	i.e.	i.e.	X
ap-1859	156	25	,	,	PUNCT
ap-1859	156	26	the	the	DET
ap-1859	156	27	system	system	NOUN
ap-1859	156	28	is	be	AUX
ap-1859	156	29	in	in	ADP
ap-1859	156	30	fact	fact	NOUN
ap-1859	156	31	made	make	VERB
ap-1859	156	32	up	up	ADP
ap-1859	156	33	of	of	ADP
ap-1859	156	34	two	two	NUM
ap-1859	156	35	independent	independent	ADJ
ap-1859	156	36	entities	entity	NOUN
ap-1859	156	37	,	,	PUNCT
ap-1859	156	38	both	both	PRON
ap-1859	156	39	having	have	VERB
ap-1859	156	40	its	its	PRON
ap-1859	156	41	own	own	ADJ
ap-1859	156	42	energy	energy	NOUN
ap-1859	156	43	levels	level	NOUN
ap-1859	156	44	that	that	PRON
ap-1859	156	45	can	can	AUX
ap-1859	156	46	independently	independently	ADV
ap-1859	156	47	vary	vary	VERB
ap-1859	156	48	with	with	ADP
ap-1859	156	49	change	change	NOUN
ap-1859	156	50	of	of	ADP
ap-1859	156	51	the	the	DET
ap-1859	156	52	system	system	NOUN
ap-1859	156	53	param414	param414	NOUN
ap-1859	156	54	vol	vol	NOUN
ap-1859	156	55	.	.	PUNCT
ap-1859	157	1	53	53	NUM
ap-1859	157	2	no	no	NOUN
ap-1859	157	3	.	.	PUNCT
ap-1859	158	1	5/2013	5/2013	NUM
ap-1859	158	2	examples	example	NOUN
ap-1859	158	3	of	of	ADP
ap-1859	158	4	quantum	quantum	ADJ
ap-1859	158	5	holonomy	holonomy	NOUN
ap-1859	158	6	with	with	ADP
ap-1859	158	7	topology	topology	NOUN
ap-1859	158	8	changes	change	NOUN
ap-1859	158	9	figure	figure	VERB
ap-1859	158	10	9	9	NUM
ap-1859	158	11	.	.	PUNCT
ap-1859	159	1	finite	finite	PROPN
ap-1859	159	2	approximation	approximation	NOUN
ap-1859	159	3	of	of	ADP
ap-1859	159	4	the	the	DET
ap-1859	159	5	physical	physical	ADJ
ap-1859	159	6	meaning	meaning	NOUN
ap-1859	159	7	of	of	ADP
ap-1859	159	8	boundary	boundary	ADJ
ap-1859	159	9	condition	condition	NOUN
ap-1859	159	10	(	(	PUNCT
ap-1859	159	11	4	4	NUM
ap-1859	159	12	)	)	PUNCT
ap-1859	159	13	for	for	ADP
ap-1859	159	14	θ	θ	NOUN
ap-1859	159	15	belonging	belong	VERB
ap-1859	159	16	to	to	ADP
ap-1859	159	17	sectors	sector	NOUN
ap-1859	159	18	i	i	PRON
ap-1859	159	19	and	and	CCONJ
ap-1859	159	20	ii	ii	PROPN
ap-1859	159	21	.	.	PUNCT
ap-1859	160	1	the	the	DET
ap-1859	160	2	strengths	strength	NOUN
ap-1859	160	3	of	of	ADP
ap-1859	160	4	the	the	DET
ap-1859	160	5	δ	δ	PROPN
ap-1859	160	6	potentials	potential	VERB
ap-1859	160	7	in	in	ADP
ap-1859	160	8	vertices	vertex	NOUN
ap-1859	160	9	1	1	NUM
ap-1859	160	10	,	,	PUNCT
ap-1859	160	11	2	2	NUM
ap-1859	160	12	,	,	PUNCT
ap-1859	160	13	3	3	NUM
ap-1859	160	14	,	,	PUNCT
ap-1859	160	15	4	4	NUM
ap-1859	160	16	are	be	AUX
ap-1859	160	17	given	give	VERB
ap-1859	160	18	by	by	ADP
ap-1859	160	19	the	the	DET
ap-1859	160	20	following	follow	VERB
ap-1859	160	21	formulas	formula	NOUN
ap-1859	160	22	.	.	PUNCT
ap-1859	161	1	left	leave	VERB
ap-1859	161	2	:	:	PUNCT
ap-1859	161	3	v1	v1	VERB
ap-1859	161	4	=	=	SYM
ap-1859	161	5	v2	v2	PROPN
ap-1859	161	6	=	=	SYM
ap-1859	161	7	(	(	PUNCT
ap-1859	161	8	ta)2−ta	ta)2−ta	PROPN
ap-1859	161	9	ε	ε	PROPN
ap-1859	161	10	,	,	PUNCT
ap-1859	161	11	v3	v3	PROPN
ap-1859	161	12	=	=	SYM
ap-1859	161	13	v4	v4	PROPN
ap-1859	161	14	=	=	PUNCT
ap-1859	161	15	1−ta	1−ta	PROPN
ap-1859	161	16	ε	ε	PROPN
ap-1859	161	17	.	.	PUNCT
ap-1859	162	1	right	right	ADJ
ap-1859	162	2	:	:	PUNCT
ap-1859	162	3	v1	v1	NOUN
ap-1859	162	4	=	=	SYM
ap-1859	162	5	0	0	NUM
ap-1859	162	6	,	,	PUNCT
ap-1859	162	7	v2	v2	PROPN
ap-1859	162	8	=	=	SYM
ap-1859	162	9	c	c	PROPN
ap-1859	162	10	1−c	1−c	NUM
ap-1859	162	11	,	,	PUNCT
ap-1859	162	12	v3	v3	PROPN
ap-1859	162	13	=	=	PROPN
ap-1859	163	1	1−c	1−c	NUM
ap-1859	163	2	c	c	NOUN
ap-1859	163	3	,	,	PUNCT
ap-1859	163	4	v4	v4	PROPN
ap-1859	163	5	=	=	SYM
ap-1859	163	6	1	1	NUM
ap-1859	163	7	ε	ε	PROPN
ap-1859	163	8	.	.	PUNCT
ap-1859	164	1	figure	figure	NOUN
ap-1859	164	2	10	10	NUM
ap-1859	164	3	.	.	PUNCT
ap-1859	165	1	finite	finite	PROPN
ap-1859	165	2	approximation	approximation	NOUN
ap-1859	165	3	of	of	ADP
ap-1859	165	4	the	the	DET
ap-1859	165	5	physical	physical	ADJ
ap-1859	165	6	meaning	meaning	NOUN
ap-1859	165	7	of	of	ADP
ap-1859	165	8	boundary	boundary	ADJ
ap-1859	165	9	condition	condition	NOUN
ap-1859	165	10	(	(	PUNCT
ap-1859	165	11	4	4	NUM
ap-1859	165	12	)	)	PUNCT
ap-1859	165	13	for	for	ADP
ap-1859	165	14	θ	θ	NOUN
ap-1859	165	15	belonging	belong	VERB
ap-1859	165	16	to	to	ADP
ap-1859	165	17	sectors	sectors	PROPN
ap-1859	165	18	iii	iii	PROPN
ap-1859	165	19	and	and	CCONJ
ap-1859	165	20	iv	iv	NOUN
ap-1859	165	21	.	.	PUNCT
ap-1859	166	1	the	the	DET
ap-1859	166	2	strengths	strength	NOUN
ap-1859	166	3	of	of	ADP
ap-1859	166	4	the	the	DET
ap-1859	166	5	δ	δ	PROPN
ap-1859	166	6	potentials	potential	VERB
ap-1859	166	7	in	in	ADP
ap-1859	166	8	vertices	vertex	NOUN
ap-1859	166	9	1	1	NUM
ap-1859	166	10	,	,	PUNCT
ap-1859	166	11	2	2	NUM
ap-1859	166	12	,	,	PUNCT
ap-1859	166	13	3	3	NUM
ap-1859	166	14	,	,	PUNCT
ap-1859	166	15	4	4	NUM
ap-1859	166	16	are	be	AUX
ap-1859	166	17	given	give	VERB
ap-1859	166	18	by	by	ADP
ap-1859	166	19	the	the	DET
ap-1859	166	20	following	follow	VERB
ap-1859	166	21	formulas	formula	NOUN
ap-1859	166	22	.	.	PUNCT
ap-1859	167	1	left	leave	VERB
ap-1859	167	2	:	:	PUNCT
ap-1859	167	3	v1	v1	PROPN
ap-1859	167	4	=	=	SYM
ap-1859	167	5	(	(	PUNCT
ap-1859	167	6	tb)2−tb	tb)2−tb	PROPN
ap-1859	167	7	ε	ε	PROPN
ap-1859	167	8	,	,	PUNCT
ap-1859	167	9	v2	v2	PROPN
ap-1859	167	10	=	=	SYM
ap-1859	167	11	1−tb	1−tb	PROPN
ap-1859	167	12	ε	ε	PROPN
ap-1859	167	13	,	,	PUNCT
ap-1859	167	14	v3	v3	PROPN
ap-1859	167	15	=	=	PUNCT
ap-1859	167	16	(	(	PUNCT
ap-1859	167	17	tb′)2−tb′	tb′)2−tb′	NUM
ap-1859	167	18	ε	ε	PROPN
ap-1859	167	19	,	,	PUNCT
ap-1859	167	20	v4	v4	PROPN
ap-1859	167	21	=	=	SYM
ap-1859	167	22	1−tb′	1−tb′	PROPN
ap-1859	167	23	ε	ε	PROPN
ap-1859	167	24	.	.	PUNCT
ap-1859	168	1	right	right	ADJ
ap-1859	168	2	:	:	PUNCT
ap-1859	168	3	v1	v1	NOUN
ap-1859	168	4	=	=	SYM
ap-1859	168	5	(	(	PUNCT
ap-1859	168	6	tb1)2+(sd)2−tb1−sd	tb1)2+(sd)2−tb1−sd	NUM
ap-1859	168	7	ε	ε	PROPN
ap-1859	168	8	,	,	PUNCT
ap-1859	168	9	v2	v2	PROPN
ap-1859	168	10	=	=	SYM
ap-1859	168	11	1−tb1	1−tb1	NUM
ap-1859	168	12	ε	ε	PROPN
ap-1859	168	13	,	,	PUNCT
ap-1859	168	14	v3	v3	PROPN
ap-1859	168	15	=	=	PROPN
ap-1859	168	16	1	1	NUM
ap-1859	168	17	ε	ε	PROPN
ap-1859	168	18	,	,	PUNCT
ap-1859	168	19	v4	v4	PROPN
ap-1859	168	20	=	=	PUNCT
ap-1859	168	21	1−sd	1−sd	PROPN
ap-1859	168	22	ε	ε	PROPN
ap-1859	168	23	.	.	PUNCT
ap-1859	169	1	eter	eter	PROPN
ap-1859	169	2	θ	θ	PROPN
ap-1859	169	3	.	.	PUNCT
ap-1859	170	1	therefore	therefore	ADV
ap-1859	170	2	,	,	PUNCT
ap-1859	170	3	if	if	SCONJ
ap-1859	170	4	the	the	DET
ap-1859	170	5	parametrization	parametrization	NOUN
ap-1859	170	6	of	of	ADP
ap-1859	170	7	boundary	boundary	ADJ
ap-1859	170	8	conditions	condition	NOUN
ap-1859	170	9	is	be	AUX
ap-1859	170	10	conveniently	conveniently	ADV
ap-1859	170	11	chosen	choose	VERB
ap-1859	170	12	,	,	PUNCT
ap-1859	170	13	the	the	DET
ap-1859	170	14	eigenvalues	eigenvalue	NOUN
ap-1859	170	15	as	as	ADP
ap-1859	170	16	functions	function	NOUN
ap-1859	170	17	of	of	ADP
ap-1859	170	18	θ	θ	PROPN
ap-1859	170	19	can	can	AUX
ap-1859	170	20	cross	cross	VERB
ap-1859	170	21	each	each	DET
ap-1859	170	22	other	other	ADJ
ap-1859	170	23	,	,	PUNCT
ap-1859	170	24	which	which	PRON
ap-1859	170	25	leads	lead	VERB
ap-1859	170	26	to	to	ADP
ap-1859	170	27	the	the	DET
ap-1859	170	28	holonomy	holonomy	ADJ
ap-1859	170	29	effect	effect	NOUN
ap-1859	170	30	.	.	PUNCT
ap-1859	171	1	acknowledgements	acknowledgement	NOUN
ap-1859	171	2	we	we	PRON
ap-1859	171	3	thank	thank	VERB
ap-1859	171	4	professor	professor	PROPN
ap-1859	171	5	p.	p.	PROPN
ap-1859	171	6	exner	exner	NOUN
ap-1859	171	7	and	and	CCONJ
ap-1859	171	8	professor	professor	PROPN
ap-1859	171	9	i.	i.	PROPN
ap-1859	171	10	tsutsui	tsutsui	PROPN
ap-1859	171	11	for	for	ADP
ap-1859	171	12	stimulating	stimulate	VERB
ap-1859	171	13	discussions	discussion	NOUN
ap-1859	171	14	.	.	PUNCT
ap-1859	172	1	this	this	DET
ap-1859	172	2	research	research	NOUN
ap-1859	172	3	was	be	AUX
ap-1859	172	4	supported	support	VERB
ap-1859	172	5	by	by	ADP
ap-1859	172	6	the	the	DET
ap-1859	172	7	japan	japan	PROPN
ap-1859	172	8	ministry	ministry	PROPN
ap-1859	172	9	of	of	ADP
ap-1859	172	10	education	education	PROPN
ap-1859	172	11	,	,	PUNCT
ap-1859	172	12	culture	culture	NOUN
ap-1859	172	13	,	,	PUNCT
ap-1859	172	14	sports	sport	NOUN
ap-1859	172	15	,	,	PUNCT
ap-1859	172	16	science	science	NOUN
ap-1859	172	17	and	and	CCONJ
ap-1859	172	18	technology	technology	NOUN
ap-1859	172	19	under	under	ADP
ap-1859	172	20	grant	grant	NOUN
ap-1859	172	21	numbers	number	NOUN
ap-1859	172	22	24540412	24540412	NUM
ap-1859	172	23	and	and	CCONJ
ap-1859	172	24	22540396	22540396	NUM
ap-1859	172	25	.	.	PUNCT
ap-1859	173	1	figure	figure	VERB
ap-1859	173	2	11	11	NUM
ap-1859	173	3	.	.	PUNCT
ap-1859	174	1	finite	finite	PROPN
ap-1859	174	2	approximation	approximation	NOUN
ap-1859	174	3	of	of	ADP
ap-1859	174	4	the	the	DET
ap-1859	174	5	physical	physical	ADJ
ap-1859	174	6	meaning	meaning	NOUN
ap-1859	174	7	of	of	ADP
ap-1859	174	8	the	the	DET
ap-1859	174	9	boundary	boundary	ADJ
ap-1859	174	10	condition	condition	NOUN
ap-1859	174	11	(	(	PUNCT
ap-1859	174	12	4	4	NUM
ap-1859	174	13	)	)	PUNCT
ap-1859	174	14	for	for	ADP
ap-1859	174	15	θ	θ	PROPN
ap-1859	174	16	belonging	belong	VERB
ap-1859	174	17	to	to	ADP
ap-1859	174	18	the	the	DET
ap-1859	174	19	sectors	sector	NOUN
ap-1859	174	20	v	v	ADP
ap-1859	174	21	and	and	CCONJ
ap-1859	174	22	vi	vi	NOUN
ap-1859	174	23	.	.	PUNCT
ap-1859	175	1	the	the	DET
ap-1859	175	2	strengths	strength	NOUN
ap-1859	175	3	of	of	ADP
ap-1859	175	4	the	the	DET
ap-1859	175	5	δ	δ	PROPN
ap-1859	175	6	potentials	potential	VERB
ap-1859	175	7	in	in	ADP
ap-1859	175	8	the	the	DET
ap-1859	175	9	vertices	vertex	NOUN
ap-1859	175	10	1,2,3,4	1,2,3,4	NUM
ap-1859	175	11	are	be	AUX
ap-1859	175	12	given	give	VERB
ap-1859	175	13	by	by	ADP
ap-1859	175	14	the	the	DET
ap-1859	175	15	following	follow	VERB
ap-1859	175	16	formulas	formula	NOUN
ap-1859	175	17	.	.	PUNCT
ap-1859	176	1	left	leave	VERB
ap-1859	176	2	:	:	PUNCT
ap-1859	176	3	v1	v1	NOUN
ap-1859	176	4	=	=	SYM
ap-1859	176	5	s2−s	s2−s	PROPN
ap-1859	176	6	ε	ε	PROPN
ap-1859	176	7	,	,	PUNCT
ap-1859	176	8	v2	v2	PROPN
ap-1859	176	9	=	=	SYM
ap-1859	176	10	c	c	PROPN
ap-1859	176	11	1−c	1−c	NUM
ap-1859	176	12	,	,	PUNCT
ap-1859	176	13	v3	v3	PROPN
ap-1859	176	14	=	=	PROPN
ap-1859	177	1	1−c	1−c	NUM
ap-1859	177	2	c	c	NOUN
ap-1859	177	3	,	,	PUNCT
ap-1859	177	4	v4	v4	PROPN
ap-1859	177	5	=	=	SYM
ap-1859	177	6	1−s	1−s	PROPN
ap-1859	177	7	ε	ε	PROPN
ap-1859	177	8	.	.	PUNCT
ap-1859	178	1	right	right	ADJ
ap-1859	178	2	:	:	PUNCT
ap-1859	178	3	v1	v1	NOUN
ap-1859	178	4	=	=	SYM
ap-1859	178	5	(	(	PUNCT
ap-1859	178	6	ta)2+(sd)2−ta−sd−3tsad	ta)2+(sd)2−ta−sd−3tsad	ADJ
ap-1859	178	7	ε	ε	PROPN
ap-1859	178	8	,	,	PUNCT
ap-1859	178	9	v2	v2	PROPN
ap-1859	178	10	=	=	SYM
ap-1859	178	11	(	(	PUNCT
ap-1859	178	12	ta)2−ta−3tsad	ta)2−ta−3tsad	X
ap-1859	178	13	ε	ε	PROPN
ap-1859	178	14	,	,	PUNCT
ap-1859	178	15	v3	v3	PROPN
ap-1859	178	16	=	=	PUNCT
ap-1859	178	17	1−ta	1−ta	PROPN
ap-1859	178	18	ε	ε	PROPN
ap-1859	178	19	,	,	PUNCT
ap-1859	178	20	v4	v4	PROPN
ap-1859	178	21	=	=	PUNCT
ap-1859	178	22	1−ta−sd	1−ta−sd	NUM
ap-1859	178	23	ε	ε	X
ap-1859	178	24	.	.	PUNCT
ap-1859	179	1	references	reference	NOUN
ap-1859	179	2	[	[	X
ap-1859	179	3	1	1	NUM
ap-1859	179	4	]	]	PUNCT
ap-1859	179	5	a.	a.	NOUN
ap-1859	179	6	p.	p.	PROPN
ap-1859	179	7	balachandran	balachandran	PROPN
ap-1859	179	8	,	,	PUNCT
ap-1859	179	9	g.	g.	PROPN
ap-1859	179	10	bimonteb	bimonteb	PROPN
ap-1859	179	11	,	,	PUNCT
ap-1859	179	12	g.	g.	PROPN
ap-1859	179	13	marmoc	marmoc	PROPN
ap-1859	179	14	,	,	PUNCT
ap-1859	179	15	and	and	CCONJ
ap-1859	179	16	a.	a.	NOUN
ap-1859	179	17	simoni	simoni	PROPN
ap-1859	179	18	.	.	PUNCT
ap-1859	180	1	topology	topology	NOUN
ap-1859	180	2	change	change	NOUN
ap-1859	180	3	and	and	CCONJ
ap-1859	180	4	quantum	quantum	NOUN
ap-1859	180	5	physics	physics	NOUN
ap-1859	180	6	.	.	PUNCT
ap-1859	180	7	nucl	nucl	PROPN
ap-1859	180	8	.	.	PUNCT
ap-1859	181	1	phys	phy	NOUN
ap-1859	181	2	.	.	PUNCT
ap-1859	182	1	b	b	X
ap-1859	182	2	446:299–314	446:299–314	NUM
ap-1859	182	3	,	,	PUNCT
ap-1859	182	4	1995	1995	NUM
ap-1859	182	5	.	.	PUNCT
ap-1859	183	1	[	[	X
ap-1859	183	2	2	2	NUM
ap-1859	183	3	]	]	PUNCT
ap-1859	183	4	m.	m.	NOUN
ap-1859	183	5	v.	v.	ADP
ap-1859	183	6	berry	berry	PROPN
ap-1859	183	7	.	.	PUNCT
ap-1859	184	1	quantal	quantal	ADJ
ap-1859	184	2	phase	phase	NOUN
ap-1859	184	3	factors	factor	NOUN
ap-1859	184	4	accompanying	accompany	VERB
ap-1859	184	5	adiabatic	adiabatic	ADJ
ap-1859	184	6	changes	change	NOUN
ap-1859	184	7	.	.	PUNCT
ap-1859	185	1	proc	proc	NOUN
ap-1859	185	2	.	.	PUNCT
ap-1859	186	1	r.	r.	PROPN
ap-1859	186	2	soc	soc	PROPN
ap-1859	186	3	.	.	PUNCT
ap-1859	187	1	london	london	PROPN
ap-1859	187	2	a	a	DET
ap-1859	187	3	392:45–57	392:45–57	NUM
ap-1859	187	4	(	(	PUNCT
ap-1859	187	5	1984	1984	NUM
ap-1859	187	6	)	)	PUNCT
ap-1859	187	7	.	.	PUNCT
ap-1859	188	1	[	[	X
ap-1859	188	2	3	3	X
ap-1859	188	3	]	]	PUNCT
ap-1859	188	4	t.	t.	PROPN
ap-1859	188	5	cheon	cheon	PROPN
ap-1859	188	6	,	,	PUNCT
ap-1859	188	7	p.	p.	NOUN
ap-1859	188	8	exner	exner	NOUN
ap-1859	188	9	and	and	CCONJ
ap-1859	188	10	o.	o.	NOUN
ap-1859	188	11	turek	turek	PROPN
ap-1859	188	12	.	.	PUNCT
ap-1859	189	1	approximation	approximation	NOUN
ap-1859	189	2	of	of	ADP
ap-1859	189	3	a	a	DET
ap-1859	189	4	general	general	ADJ
ap-1859	189	5	singular	singular	ADJ
ap-1859	189	6	vertex	vertex	NOUN
ap-1859	189	7	coupling	coupling	NOUN
ap-1859	189	8	in	in	ADP
ap-1859	189	9	quantum	quantum	NOUN
ap-1859	189	10	graphs	graph	NOUN
ap-1859	189	11	.	.	PUNCT
ap-1859	190	1	ann	ann	PROPN
ap-1859	190	2	.	.	PUNCT
ap-1859	191	1	phys	phys	PROPN
ap-1859	191	2	.	.	PUNCT
ap-1859	192	1	(	(	PUNCT
ap-1859	192	2	ny	ny	NOUN
ap-1859	192	3	)	)	PUNCT
ap-1859	192	4	325:548–578	325:548–578	NUM
ap-1859	192	5	,	,	PUNCT
ap-1859	192	6	2010	2010	NUM
ap-1859	192	7	.	.	PUNCT
ap-1859	193	1	[	[	X
ap-1859	193	2	4	4	X
ap-1859	193	3	]	]	PUNCT
ap-1859	193	4	t.	t.	PROPN
ap-1859	193	5	cheon	cheon	PROPN
ap-1859	193	6	and	and	CCONJ
ap-1859	193	7	a.	a.	PROPN
ap-1859	193	8	tanaka	tanaka	PROPN
ap-1859	193	9	.	.	PUNCT
ap-1859	194	1	new	new	ADJ
ap-1859	194	2	anatomy	anatomy	NOUN
ap-1859	194	3	of	of	ADP
ap-1859	194	4	quantum	quantum	NOUN
ap-1859	194	5	holonomy	holonomy	NOUN
ap-1859	194	6	.	.	PUNCT
ap-1859	195	1	europhys	europhys	PROPN
ap-1859	195	2	.	.	PUNCT
ap-1859	196	1	lett	lett	PROPN
ap-1859	196	2	.	.	PUNCT
ap-1859	196	3	85:20001(5p	85:20001(5p	PROPN
ap-1859	196	4	)	)	PUNCT
ap-1859	196	5	,	,	PUNCT
ap-1859	196	6	2009	2009	NUM
ap-1859	196	7	.	.	PUNCT
ap-1859	197	1	[	[	X
ap-1859	197	2	5	5	NUM
ap-1859	197	3	]	]	PUNCT
ap-1859	197	4	p.	p.	NOUN
ap-1859	197	5	exner	exner	PROPN
ap-1859	197	6	,	,	PUNCT
ap-1859	197	7	j.p	j.p	PROPN
ap-1859	197	8	.	.	PROPN
ap-1859	197	9	keating	keating	PROPN
ap-1859	197	10	,	,	PUNCT
ap-1859	197	11	p.	p.	PROPN
ap-1859	197	12	kuchment	kuchment	NOUN
ap-1859	197	13	,	,	PUNCT
ap-1859	197	14	t.	t.	PROPN
ap-1859	197	15	sunada	sunada	PROPN
ap-1859	197	16	,	,	PUNCT
ap-1859	197	17	a.	a.	PROPN
ap-1859	197	18	teplyaev	teplyaev	PROPN
ap-1859	197	19	,	,	PUNCT
ap-1859	197	20	eds	ed	NOUN
ap-1859	197	21	.	.	PUNCT
ap-1859	197	22	analysis	analysis	NOUN
ap-1859	197	23	on	on	ADP
ap-1859	197	24	graphs	graph	NOUN
ap-1859	197	25	and	and	CCONJ
ap-1859	197	26	applications	application	NOUN
ap-1859	197	27	.	.	PUNCT
ap-1859	198	1	ams	am	NOUN
ap-1859	198	2	proc	proc	PROPN
ap-1859	198	3	.	.	PUNCT
ap-1859	199	1	of	of	ADP
ap-1859	199	2	symposia	symposia	NOUN
ap-1859	199	3	in	in	ADP
ap-1859	199	4	pure	pure	ADJ
ap-1859	199	5	math	math	NOUN
ap-1859	199	6	.	.	PUNCT
ap-1859	200	1	ser	ser	PROPN
ap-1859	200	2	.	.	PROPN
ap-1859	200	3	,	,	PUNCT
ap-1859	200	4	vol	vol	NOUN
ap-1859	200	5	.	.	PROPN
ap-1859	201	1	77	77	NUM
ap-1859	201	2	,	,	PUNCT
ap-1859	201	3	providence	providence	NOUN
ap-1859	201	4	,	,	PUNCT
ap-1859	201	5	r.i	r.i	PROPN
ap-1859	201	6	.	.	PROPN
ap-1859	201	7	,	,	PUNCT
ap-1859	201	8	2008	2008	NUM
ap-1859	201	9	,	,	PUNCT
ap-1859	201	10	and	and	CCONJ
ap-1859	201	11	references	reference	NOUN
ap-1859	201	12	therein	therein	ADV
ap-1859	201	13	.	.	PUNCT
ap-1859	202	1	[	[	X
ap-1859	202	2	6	6	NUM
ap-1859	202	3	]	]	PUNCT
ap-1859	202	4	v.	v.	PROPN
ap-1859	202	5	kostrykin	kostrykin	PROPN
ap-1859	202	6	,	,	PUNCT
ap-1859	202	7	r.	r.	PROPN
ap-1859	202	8	schrader	schrader	PROPN
ap-1859	202	9	.	.	PUNCT
ap-1859	203	1	kirchhoff	kirchhoff	PROPN
ap-1859	203	2	’s	’s	PART
ap-1859	203	3	rule	rule	NOUN
ap-1859	203	4	for	for	ADP
ap-1859	203	5	quantum	quantum	ADJ
ap-1859	203	6	wires	wire	NOUN
ap-1859	203	7	.	.	PUNCT
ap-1859	204	1	j.	j.	PROPN
ap-1859	204	2	phys	phys	PROPN
ap-1859	204	3	.	.	PUNCT
ap-1859	205	1	a	a	DET
ap-1859	205	2	:	:	PUNCT
ap-1859	205	3	math	math	NOUN
ap-1859	205	4	.	.	PUNCT
ap-1859	206	1	gen	gen	PROPN
ap-1859	206	2	.	.	PUNCT
ap-1859	206	3	32:595–630	32:595–630	NUM
ap-1859	206	4	,	,	PUNCT
ap-1859	206	5	1999	1999	NUM
ap-1859	206	6	.	.	PUNCT
ap-1859	207	1	[	[	X
ap-1859	207	2	7	7	NUM
ap-1859	207	3	]	]	PUNCT
ap-1859	207	4	a.	a.	NOUN
ap-1859	207	5	d.	d.	PROPN
ap-1859	207	6	shapere	shapere	PROPN
ap-1859	207	7	,	,	PUNCT
ap-1859	207	8	f.	f.	PROPN
ap-1859	207	9	wilczek	wilczek	PROPN
ap-1859	207	10	,	,	PUNCT
ap-1859	207	11	z.	z.	PROPN
ap-1859	207	12	xiong	xiong	PROPN
ap-1859	207	13	.	.	PUNCT
ap-1859	207	14	models	model	NOUN
ap-1859	207	15	of	of	ADP
ap-1859	207	16	topology	topology	NOUN
ap-1859	207	17	change	change	NOUN
ap-1859	207	18	.	.	PUNCT
ap-1859	208	1	arxiv:1210.3545	arxiv:1210.3545	PROPN
ap-1859	208	2	.	.	PUNCT
ap-1859	209	1	[	[	X
ap-1859	209	2	8	8	NUM
ap-1859	209	3	]	]	PUNCT
ap-1859	209	4	b.	b.	PROPN
ap-1859	209	5	simon	simon	PROPN
ap-1859	209	6	.	.	PUNCT
ap-1859	210	1	holonomy	holonomy	PROPN
ap-1859	210	2	,	,	PUNCT
ap-1859	210	3	the	the	DET
ap-1859	210	4	quantum	quantum	ADJ
ap-1859	210	5	adiabatic	adiabatic	NOUN
ap-1859	210	6	theorem	theorem	NOUN
ap-1859	210	7	,	,	PUNCT
ap-1859	210	8	and	and	CCONJ
ap-1859	210	9	berry	berry	VERB
ap-1859	210	10	’s	’s	PART
ap-1859	210	11	phase	phase	NOUN
ap-1859	210	12	.	.	PUNCT
ap-1859	211	1	phys	phy	NOUN
ap-1859	211	2	.	.	PUNCT
ap-1859	212	1	rev	rev	PROPN
ap-1859	212	2	.	.	PROPN
ap-1859	212	3	lett	lett	PROPN
ap-1859	212	4	.	.	PUNCT
ap-1859	213	1	51:2167–2170	51:2167–2170	NUM
ap-1859	213	2	,	,	PUNCT
ap-1859	213	3	1983	1983	NUM
ap-1859	213	4	.	.	PUNCT
ap-1859	214	1	[	[	X
ap-1859	214	2	9	9	NUM
ap-1859	214	3	]	]	PUNCT
ap-1859	214	4	o.	o.	NOUN
ap-1859	214	5	turek	turek	PROPN
ap-1859	214	6	,	,	PUNCT
ap-1859	214	7	t.	t.	PROPN
ap-1859	214	8	cheon	cheon	PROPN
ap-1859	214	9	.	.	PUNCT
ap-1859	215	1	potential	potential	ADJ
ap-1859	215	2	-	-	PUNCT
ap-1859	215	3	controlled	control	VERB
ap-1859	215	4	filtering	filtering	NOUN
ap-1859	215	5	in	in	ADP
ap-1859	215	6	quantum	quantum	ADJ
ap-1859	215	7	star	star	NOUN
ap-1859	215	8	graphs	graph	NOUN
ap-1859	215	9	,	,	PUNCT
ap-1859	215	10	.	.	PUNCT
ap-1859	216	1	ann	ann	PROPN
ap-1859	216	2	.	.	PUNCT
ap-1859	217	1	phys	phys	PROPN
ap-1859	217	2	.	.	PUNCT
ap-1859	218	1	(	(	PUNCT
ap-1859	218	2	ny	ny	NOUN
ap-1859	218	3	)	)	PUNCT
ap-1859	218	4	330:104–141	330:104–141	NUM
ap-1859	218	5	,	,	PUNCT
ap-1859	218	6	2013	2013	NUM
ap-1859	218	7	.	.	PUNCT
ap-1859	219	1	[	[	X
ap-1859	219	2	10	10	NUM
ap-1859	219	3	]	]	X
ap-1859	219	4	f.	f.	PROPN
ap-1859	219	5	wilczek	wilczek	PROPN
ap-1859	219	6	and	and	CCONJ
ap-1859	219	7	a.	a.	NOUN
ap-1859	219	8	zee	zee	PROPN
ap-1859	219	9	.	.	PUNCT
ap-1859	220	1	appearance	appearance	NOUN
ap-1859	220	2	of	of	ADP
ap-1859	220	3	gauge	gauge	ADJ
ap-1859	220	4	structure	structure	NOUN
ap-1859	220	5	in	in	ADP
ap-1859	220	6	simple	simple	ADJ
ap-1859	220	7	dynamical	dynamical	ADJ
ap-1859	220	8	systems	system	NOUN
ap-1859	220	9	.	.	PUNCT
ap-1859	221	1	phys	phy	NOUN
ap-1859	221	2	.	.	PUNCT
ap-1859	222	1	rev	rev	PROPN
ap-1859	222	2	.	.	PROPN
ap-1859	222	3	lett	lett	PROPN
ap-1859	222	4	.	.	PUNCT
ap-1859	223	1	52:2111–2114	52:2111–2114	NUM
ap-1859	223	2	,	,	PUNCT
ap-1859	223	3	1984	1984	NUM
ap-1859	223	4	.	.	PUNCT
ap-1859	224	1	415	415	NUM
ap-1859	224	2	acta	acta	PROPN
ap-1859	224	3	polytechnica	polytechnica	PROPN
ap-1859	224	4	53(5):410–415	53(5):410–415	PROPN
ap-1859	224	5	,	,	PUNCT
ap-1859	224	6	2013	2013	NUM
ap-1859	224	7	1	1	NUM
ap-1859	224	8	introduction	introduction	NOUN
ap-1859	224	9	2	2	NUM
ap-1859	224	10	the	the	DET
ap-1859	224	11	model	model	NOUN
ap-1859	224	12	2.1	2.1	NUM
ap-1859	224	13	long	long	ADJ
ap-1859	224	14	cycle	cycle	NOUN
ap-1859	224	15	2.2	2.2	NUM
ap-1859	224	16	short	short	ADJ
ap-1859	224	17	cycle	cycle	NOUN
ap-1859	224	18	3	3	NUM
ap-1859	224	19	quantum	quantum	NOUN
ap-1859	224	20	holonomy	holonomy	NOUN
ap-1859	224	21	3.1	3.1	NUM
ap-1859	224	22	long	long	ADJ
ap-1859	224	23	cycle	cycle	NOUN
ap-1859	224	24	3.2	3.2	NUM
ap-1859	224	25	short	short	ADJ
ap-1859	224	26	cycle	cycle	NOUN
ap-1859	224	27	4	4	NUM
ap-1859	224	28	on	on	ADP
ap-1859	224	29	the	the	DET
ap-1859	224	30	boundary	boundary	ADJ
ap-1859	224	31	condition	condition	NOUN
ap-1859	224	32	5	5	NUM
ap-1859	224	33	discussion	discussion	NOUN
ap-1859	224	34	acknowledgements	acknowledgement	NOUN
ap-1859	224	35	references	reference	NOUN