id	sid	tid	token	lemma	pos
cana-4753	1	1	communications	communication	NOUN
cana-4753	1	2	on	on	ADP
cana-4753	1	3	applied	apply	VERB
cana-4753	1	4	nonlinear	nonlinear	ADJ
cana-4753	1	5	analysis	analysis	NOUN
cana-4753	1	6	issn	issn	NOUN
cana-4753	1	7	:	:	PUNCT
cana-4753	1	8	1074	1074	NUM
cana-4753	1	9	-	-	PUNCT
cana-4753	1	10	133x	133x	NUM
cana-4753	1	11	vol	vol	VERB
cana-4753	1	12	32	32	NUM
cana-4753	1	13	no	no	NOUN
cana-4753	1	14	.	.	PUNCT
cana-4753	2	1	10s	10	NOUN
cana-4753	2	2	(	(	PUNCT
cana-4753	2	3	2025	2025	NUM
cana-4753	2	4	)	)	PUNCT
cana-4753	2	5	284	284	NUM
cana-4753	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4753	2	7	topological	topological	ADJ
cana-4753	2	8	methods	method	NOUN
cana-4753	2	9	in	in	ADP
cana-4753	2	10	knot	knot	NOUN
cana-4753	2	11	theory	theory	NOUN
cana-4753	2	12	:	:	PUNCT
cana-4753	2	13	analyzing	analyze	VERB
cana-4753	2	14	the	the	DET
cana-4753	2	15	complexities	complexity	NOUN
cana-4753	2	16	of	of	ADP
cana-4753	2	17	knotted	knotted	ADJ
cana-4753	2	18	structures	structure	NOUN
cana-4753	2	19	1dr	1dr	NOUN
cana-4753	2	20	.	.	PUNCT
cana-4753	3	1	c.j	c.j	NOUN
cana-4753	3	2	enita	enita	PROPN
cana-4753	3	3	nancy	nancy	PROPN
cana-4753	3	4	,	,	PUNCT
cana-4753	3	5	2	2	NUM
cana-4753	3	6	dr	dr	PROPN
cana-4753	3	7	.	.	PROPN
cana-4753	3	8	machhindranath	machhindranath	PROPN
cana-4753	3	9	m	m	PROPN
cana-4753	3	10	dhane	dhane	NOUN
cana-4753	3	11	,	,	PUNCT
cana-4753	3	12	3dr	3dr	PROPN
cana-4753	3	13	.	.	PUNCT
cana-4753	4	1	j.	j.	PROPN
cana-4753	4	2	senbagamalar	senbagamalar	PROPN
cana-4753	4	3	,	,	PUNCT
cana-4753	4	4	4dr	4dr	NOUN
cana-4753	4	5	.	.	PUNCT
cana-4753	5	1	s.	s.	PROPN
cana-4753	5	2	s.	s.	PROPN
cana-4753	5	3	ananthan	ananthan	PROPN
cana-4753	5	4	,	,	PUNCT
cana-4753	5	5	5b	5b	NUM
cana-4753	5	6	.	.	PUNCT
cana-4753	6	1	krishnaveni	krishnaveni	PROPN
cana-4753	6	2	,	,	PUNCT
cana-4753	6	3	6n	6n	PROPN
cana-4753	6	4	.	.	PUNCT
cana-4753	7	1	sujatha	sujatha	PROPN
cana-4753	7	2	1assistant	1assistant	NUM
cana-4753	7	3	professor	professor	NOUN
cana-4753	7	4	,	,	PUNCT
cana-4753	7	5	department	department	NOUN
cana-4753	7	6	of	of	ADP
cana-4753	7	7	mathematics	mathematics	PROPN
cana-4753	7	8	,	,	PUNCT
cana-4753	7	9	ppg	ppg	PROPN
cana-4753	7	10	college	college	PROPN
cana-4753	7	11	of	of	ADP
cana-4753	7	12	arts	art	NOUN
cana-4753	7	13	and	and	CCONJ
cana-4753	7	14	science	science	NOUN
cana-4753	7	15	,	,	PUNCT
cana-4753	7	16	coimbatore	coimbatore	NOUN
cana-4753	7	17	jenitanancy.c.cas@ppg.edu.in	jenitanancy.c.cas@ppg.edu.in	CCONJ
cana-4753	7	18	2associate	2associate	NUM
cana-4753	7	19	professor	professor	NOUN
cana-4753	7	20	,	,	PUNCT
cana-4753	7	21	department	department	NOUN
cana-4753	7	22	of	of	ADP
cana-4753	7	23	mathematics	mathematics	PROPN
cana-4753	7	24	,	,	PUNCT
cana-4753	7	25	gfgc	gfgc	PROPN
cana-4753	7	26	,	,	PUNCT
cana-4753	7	27	yelahanka	yelahanka	NOUN
cana-4753	7	28	,	,	PUNCT
cana-4753	7	29	bangalore	bangalore	NOUN
cana-4753	7	30	-560064	-560064	PROPN
cana-4753	7	31	,	,	PUNCT
cana-4753	7	32	karnataka	karnataka	PROPN
cana-4753	7	33	drdhani.99dce@gmail.com	drdhani.99dce@gmail.com	X
cana-4753	7	34	3m.sc	3m.sc	NUM
cana-4753	7	35	.	.	PUNCT
cana-4753	8	1	,m.phil	,m.phil	PROPN
cana-4753	8	2	,	,	PUNCT
cana-4753	8	3	ph.d	ph.d	PROPN
cana-4753	8	4	.	.	PROPN
cana-4753	8	5	,	,	PUNCT
cana-4753	8	6	department	department	NOUN
cana-4753	8	7	of	of	ADP
cana-4753	8	8	mathematics	mathematic	NOUN
cana-4753	8	9	,	,	PUNCT
cana-4753	8	10	associate	associate	NOUN
cana-4753	8	11	professor	professor	NOUN
cana-4753	8	12	,	,	PUNCT
cana-4753	8	13	vel	vel	PROPN
cana-4753	8	14	tech	tech	NOUN
cana-4753	8	15	rangarajan	rangarajan	NOUN
cana-4753	8	16	dr.sagunthala	dr.sagunthala	NOUN
cana-4753	8	17	r	r	PROPN
cana-4753	8	18	&	&	CCONJ
cana-4753	8	19	d	d	PROPN
cana-4753	8	20	institute	institute	PROPN
cana-4753	8	21	of	of	ADP
cana-4753	8	22	science	science	NOUN
cana-4753	8	23	and	and	CCONJ
cana-4753	8	24	technology	technology	NOUN
cana-4753	8	25	,	,	PUNCT
cana-4753	8	26	chennai	chennai	PROPN
cana-4753	8	27	senbagamalar2005@yahoo.com	senbagamalar2005@yahoo.com	X
cana-4753	9	1	4associate	4associate	PROPN
cana-4753	9	2	professor	professor	NOUN
cana-4753	9	3	,	,	PUNCT
cana-4753	9	4	department	department	NOUN
cana-4753	9	5	of	of	ADP
cana-4753	9	6	mathematics	mathematic	NOUN
cana-4753	9	7	,	,	PUNCT
cana-4753	9	8	erode	erode	VERB
cana-4753	9	9	sengunthar	sengunthar	ADJ
cana-4753	9	10	engineering	engineering	PROPN
cana-4753	9	11	college	college	NOUN
cana-4753	9	12	,	,	PUNCT
cana-4753	9	13	thudupathi	thudupathi	VERB
cana-4753	9	14	,	,	PUNCT
cana-4753	9	15	perundurai(tk	perundurai(tk	VERB
cana-4753	9	16	)	)	PUNCT
cana-4753	9	17	638	638	NUM
cana-4753	9	18	057	057	NUM
cana-4753	9	19	,	,	PUNCT
cana-4753	9	20	erode	erode	VERB
cana-4753	9	21	,	,	PUNCT
cana-4753	9	22	tamil	tamil	PROPN
cana-4753	9	23	nadu	nadu	PROPN
cana-4753	9	24	,	,	PUNCT
cana-4753	9	25	india	india	PROPN
cana-4753	9	26	.	.	PUNCT
cana-4753	10	1	emailid	emailid	PROPN
cana-4753	10	2	:	:	PUNCT
cana-4753	11	1	ananthmathsesec@gmail.com	ananthmathsesec@gmail.com	X
cana-4753	12	1	5associate	5associate	NUM
cana-4753	12	2	professor	professor	NOUN
cana-4753	12	3	,	,	PUNCT
cana-4753	12	4	department	department	NOUN
cana-4753	12	5	of	of	ADP
cana-4753	12	6	mathematics	mathematics	PROPN
cana-4753	12	7	,	,	PUNCT
cana-4753	12	8	aditya	aditya	PROPN
cana-4753	12	9	university	university	PROPN
cana-4753	12	10	,	,	PUNCT
cana-4753	12	11	surampalem	surampalem	NOUN
cana-4753	12	12	,	,	PUNCT
cana-4753	12	13	india	india	PROPN
cana-4753	12	14	,	,	PUNCT
cana-4753	12	15	krishnaveni.b@aec.edu.in	krishnaveni.b@aec.edu.in	SYM
cana-4753	12	16	6associate	6associate	NUM
cana-4753	12	17	professor	professor	NOUN
cana-4753	12	18	,	,	PUNCT
cana-4753	12	19	dept	dept	NOUN
cana-4753	12	20	of	of	ADP
cana-4753	12	21	mathematics	mathematic	NOUN
cana-4753	12	22	,	,	PUNCT
cana-4753	12	23	aditya	aditya	PROPN
cana-4753	12	24	university	university	PROPN
cana-4753	12	25	,	,	PUNCT
cana-4753	12	26	surampalem	surampalem	NOUN
cana-4753	12	27	,	,	PUNCT
cana-4753	12	28	india	india	PROPN
cana-4753	12	29	,	,	PUNCT
cana-4753	12	30	sujatha.nanduri@aec.edu.in	sujatha.nanduri@aec.edu.in	PROPN
cana-4753	12	31	article	article	NOUN
cana-4753	12	32	history	history	NOUN
cana-4753	12	33	:	:	PUNCT
cana-4753	12	34	received	receive	VERB
cana-4753	12	35	:	:	PUNCT
cana-4753	12	36	12	12	NUM
cana-4753	12	37	-	-	SYM
cana-4753	12	38	01	01	NUM
cana-4753	12	39	-	-	PUNCT
cana-4753	12	40	2025	2025	NUM
cana-4753	12	41	revised	revise	VERB
cana-4753	12	42	:	:	PUNCT
cana-4753	12	43	15	15	NUM
cana-4753	12	44	-	-	NUM
cana-4753	12	45	02	02	NUM
cana-4753	12	46	-	-	PUNCT
cana-4753	12	47	2025	2025	NUM
cana-4753	12	48	accepted	accept	VERB
cana-4753	12	49	:	:	PUNCT
cana-4753	12	50	01	01	NUM
cana-4753	12	51	-	-	SYM
cana-4753	12	52	03	03	NUM
cana-4753	12	53	-	-	PUNCT
cana-4753	12	54	2025	2025	NUM
cana-4753	12	55	abstract	abstract	NOUN
cana-4753	12	56	:	:	PUNCT
cana-4753	12	57	topologically	topologically	ADV
cana-4753	12	58	speaking	speak	VERB
cana-4753	12	59	,	,	PUNCT
cana-4753	12	60	knot	knot	NOUN
cana-4753	12	61	theory	theory	NOUN
cana-4753	12	62	is	be	AUX
cana-4753	12	63	about	about	ADP
cana-4753	12	64	studying	study	VERB
cana-4753	12	65	mathematical	mathematical	ADJ
cana-4753	12	66	properties	property	NOUN
cana-4753	12	67	of	of	ADP
cana-4753	12	68	knotted	knotted	ADJ
cana-4753	12	69	objects	object	NOUN
cana-4753	12	70	and	and	CCONJ
cana-4753	12	71	its	its	PRON
cana-4753	12	72	applications	application	NOUN
cana-4753	12	73	in	in	ADP
cana-4753	12	74	the	the	DET
cana-4753	12	75	subject	subject	ADJ
cana-4753	12	76	areas	area	NOUN
cana-4753	12	77	of	of	ADP
cana-4753	12	78	physics	physics	NOUN
cana-4753	12	79	,	,	PUNCT
cana-4753	12	80	biology	biology	NOUN
cana-4753	12	81	and	and	CCONJ
cana-4753	12	82	chemistry	chemistry	NOUN
cana-4753	12	83	.	.	PUNCT
cana-4753	13	1	in	in	ADP
cana-4753	13	2	this	this	DET
cana-4753	13	3	paper	paper	NOUN
cana-4753	13	4	fundamental	fundamental	ADJ
cana-4753	13	5	topological	topological	ADJ
cana-4753	13	6	methods	method	NOUN
cana-4753	13	7	of	of	ADP
cana-4753	13	8	knot	knot	NOUN
cana-4753	13	9	theory	theory	NOUN
cana-4753	13	10	,	,	PUNCT
cana-4753	13	11	for	for	ADP
cana-4753	13	12	example	example	NOUN
cana-4753	13	13	,	,	PUNCT
cana-4753	13	14	reidemeister	reidemeister	ADJ
cana-4753	13	15	moves	move	NOUN
cana-4753	13	16	of	of	ADP
cana-4753	13	17	knots	knot	NOUN
cana-4753	13	18	,	,	PUNCT
cana-4753	13	19	polynomial	polynomial	ADJ
cana-4753	13	20	invariants	invariant	NOUN
cana-4753	13	21	and	and	CCONJ
cana-4753	13	22	homology	homology	NOUN
cana-4753	13	23	methods	method	NOUN
cana-4753	13	24	,	,	PUNCT
cana-4753	13	25	are	be	AUX
cana-4753	13	26	studied	study	VERB
cana-4753	13	27	.	.	PUNCT
cana-4753	14	1	we	we	PRON
cana-4753	14	2	discuss	discuss	VERB
cana-4753	14	3	the	the	DET
cana-4753	14	4	complexities	complexity	NOUN
cana-4753	14	5	of	of	ADP
cana-4753	14	6	knotted	knotted	ADJ
cana-4753	14	7	structures	structure	NOUN
cana-4753	14	8	through	through	ADP
cana-4753	14	9	the	the	DET
cana-4753	14	10	classification	classification	NOUN
cana-4753	14	11	,	,	PUNCT
cana-4753	14	12	behavior	behavior	NOUN
cana-4753	14	13	,	,	PUNCT
cana-4753	14	14	and	and	CCONJ
cana-4753	14	15	applying	apply	VERB
cana-4753	14	16	them	they	PRON
cana-4753	14	17	to	to	ADP
cana-4753	14	18	the	the	DET
cana-4753	14	19	real	real	ADJ
cana-4753	14	20	world	world	NOUN
cana-4753	14	21	.	.	PUNCT
cana-4753	15	1	the	the	DET
cana-4753	15	2	results	result	NOUN
cana-4753	15	3	show	show	VERB
cana-4753	15	4	that	that	SCONJ
cana-4753	15	5	these	these	DET
cana-4753	15	6	topological	topological	ADJ
cana-4753	15	7	invariants	invariant	NOUN
cana-4753	15	8	are	be	AUX
cana-4753	15	9	important	important	ADJ
cana-4753	15	10	for	for	ADP
cana-4753	15	11	knot	knot	ADJ
cana-4753	15	12	classification	classification	NOUN
cana-4753	15	13	as	as	ADV
cana-4753	15	14	well	well	ADV
cana-4753	15	15	as	as	ADP
cana-4753	15	16	in	in	ADP
cana-4753	15	17	molecular	molecular	ADJ
cana-4753	15	18	biology	biology	NOUN
cana-4753	15	19	and	and	CCONJ
cana-4753	15	20	quantum	quantum	NOUN
cana-4753	15	21	computing	computing	NOUN
cana-4753	15	22	.	.	PUNCT
cana-4753	16	1	keywords	keyword	NOUN
cana-4753	16	2	:	:	PUNCT
cana-4753	16	3	knot	knot	PROPN
cana-4753	16	4	theory	theory	NOUN
cana-4753	16	5	,	,	PUNCT
cana-4753	16	6	topology	topology	NOUN
cana-4753	16	7	,	,	PUNCT
cana-4753	16	8	invariants	invariant	NOUN
cana-4753	16	9	,	,	PUNCT
cana-4753	16	10	reidemeister	reidemeister	ADJ
cana-4753	16	11	moves	move	NOUN
cana-4753	16	12	,	,	PUNCT
cana-4753	16	13	polynomial	polynomial	ADJ
cana-4753	16	14	invariants	invariant	NOUN
cana-4753	16	15	,	,	PUNCT
cana-4753	16	16	homology	homology	NOUN
cana-4753	16	17	,	,	PUNCT
cana-4753	16	18	computational	computational	ADJ
cana-4753	16	19	topology	topology	NOUN
cana-4753	16	20	.	.	PUNCT
cana-4753	17	1	i.	i.	PROPN
cana-4753	17	2	introduction	introduction	PROPN
cana-4753	17	3	topological	topological	PROPN
cana-4753	17	4	knot	knot	PROPN
cana-4753	17	5	theory	theory	NOUN
cana-4753	17	6	is	be	AUX
cana-4753	17	7	the	the	DET
cana-4753	17	8	study	study	NOUN
cana-4753	17	9	of	of	ADP
cana-4753	17	10	some	some	DET
cana-4753	17	11	fundamental	fundamental	ADJ
cana-4753	17	12	properties	property	NOUN
cana-4753	17	13	of	of	ADP
cana-4753	17	14	mathematical	mathematical	ADJ
cana-4753	17	15	knots	knot	NOUN
cana-4753	17	16	—	—	PUNCT
cana-4753	17	17	embeddings	embedding	NOUN
cana-4753	17	18	of	of	ADP
cana-4753	17	19	a	a	DET
cana-4753	17	20	closed	closed	ADJ
cana-4753	17	21	loop	loop	NOUN
cana-4753	17	22	(	(	PUNCT
cana-4753	17	23	a	a	DET
cana-4753	17	24	circle	circle	NOUN
cana-4753	17	25	)	)	PUNCT
cana-4753	17	26	into	into	ADP
cana-4753	17	27	the	the	DET
cana-4753	17	28	third	third	ADJ
cana-4753	17	29	dimension	dimension	NOUN
cana-4753	17	30	or	or	CCONJ
cana-4753	17	31	3	3	NUM
cana-4753	17	32	dimensional	dimensional	ADJ
cana-4753	17	33	space	space	NOUN
cana-4753	17	34	.	.	PUNCT
cana-4753	18	1	mathematical	mathematical	ADJ
cana-4753	18	2	knots	knot	NOUN
cana-4753	18	3	are	be	AUX
cana-4753	18	4	distinguished	distinguish	VERB
cana-4753	18	5	from	from	ADP
cana-4753	18	6	physical	physical	ADJ
cana-4753	18	7	knots	knot	NOUN
cana-4753	18	8	,	,	PUNCT
cana-4753	18	9	which	which	PRON
cana-4753	18	10	may	may	AUX
cana-4753	18	11	be	be	AUX
cana-4753	18	12	untied	untie	VERB
cana-4753	18	13	,	,	PUNCT
cana-4753	18	14	in	in	ADP
cana-4753	18	15	that	that	DET
cana-4753	18	16	mathematical	mathematical	ADJ
cana-4753	18	17	knots	knot	NOUN
cana-4753	18	18	have	have	VERB
cana-4753	18	19	no	no	DET
cana-4753	18	20	free	free	ADJ
cana-4753	18	21	ends	end	NOUN
cana-4753	18	22	and	and	CCONJ
cana-4753	18	23	may	may	AUX
cana-4753	18	24	be	be	AUX
cana-4753	18	25	continuously	continuously	ADV
cana-4753	18	26	deformed	deform	VERB
cana-4753	18	27	into	into	ADP
cana-4753	18	28	each	each	DET
cana-4753	18	29	other	other	ADJ
cana-4753	18	30	without	without	ADP
cana-4753	18	31	cutting	cut	VERB
cana-4753	18	32	or	or	CCONJ
cana-4753	18	33	passing	pass	VERB
cana-4753	18	34	through	through	ADP
cana-4753	18	35	themselves	themselves	PRON
cana-4753	18	36	.	.	PUNCT
cana-4753	19	1	part	part	NOUN
cana-4753	19	2	of	of	ADP
cana-4753	19	3	the	the	DET
cana-4753	19	4	study	study	NOUN
cana-4753	19	5	of	of	ADP
cana-4753	19	6	knot	knot	NOUN
cana-4753	19	7	theory	theory	NOUN
cana-4753	19	8	dates	date	VERB
cana-4753	19	9	back	back	ADV
cana-4753	19	10	to	to	ADP
cana-4753	19	11	several	several	ADJ
cana-4753	19	12	centuries	century	NOUN
cana-4753	19	13	,	,	PUNCT
cana-4753	19	14	and	and	CCONJ
cana-4753	19	15	it	it	PRON
cana-4753	19	16	was	be	AUX
cana-4753	19	17	gauss	gauss	ADJ
cana-4753	19	18	,	,	PUNCT
cana-4753	19	19	tait	tait	PROPN
cana-4753	19	20	and	and	CCONJ
cana-4753	19	21	other	other	ADJ
cana-4753	19	22	who	who	PRON
cana-4753	19	23	tried	try	VERB
cana-4753	19	24	to	to	PART
cana-4753	19	25	classify	classify	VERB
cana-4753	19	26	knots	knot	NOUN
cana-4753	19	27	,	,	PUNCT
cana-4753	19	28	using	use	VERB
cana-4753	19	29	simple	simple	ADJ
cana-4753	19	30	invariants	invariant	NOUN
cana-4753	19	31	.	.	PUNCT
cana-4753	20	1	a	a	DET
cana-4753	20	2	current	current	ADJ
cana-4753	20	3	studies	study	NOUN
cana-4753	20	4	of	of	ADP
cana-4753	20	5	the	the	DET
cana-4753	20	6	knot	knot	NOUN
cana-4753	20	7	theory	theory	NOUN
cana-4753	20	8	of	of	ADP
cana-4753	20	9	the	the	DET
cana-4753	20	10	21st	21st	ADJ
cana-4753	20	11	century	century	NOUN
cana-4753	20	12	are	be	AUX
cana-4753	20	13	numerous	numerous	ADJ
cana-4753	20	14	,	,	PUNCT
cana-4753	20	15	including	include	VERB
cana-4753	20	16	for	for	ADP
cana-4753	20	17	example	example	NOUN
cana-4753	20	18	:	:	PUNCT
cana-4753	20	19	physics	physics	NOUN
cana-4753	20	20	,	,	PUNCT
cana-4753	20	21	chemistry	chemistry	NOUN
cana-4753	20	22	,	,	PUNCT
cana-4753	20	23	biology	biology	NOUN
cana-4753	20	24	,	,	PUNCT
cana-4753	20	25	quantum	quantum	NOUN
cana-4753	20	26	computing	computing	NOUN
cana-4753	20	27	[	[	X
cana-4753	20	28	2	2	NUM
cana-4753	20	29	-	-	SYM
cana-4753	20	30	8	8	NUM
cana-4753	20	31	]	]	PUNCT
cana-4753	20	32	.	.	PUNCT
cana-4753	21	1	mailto:jenitanancy.c.cas@ppg.edu.in	mailto:jenitanancy.c.cas@ppg.edu.in	PRON
cana-4753	21	2	mailto:drdhani.99dce@gmail.com	mailto:drdhani.99dce@gmail.com	PROPN
cana-4753	21	3	mailto:senbagamalar2005@yahoo.com	mailto:senbagamalar2005@yahoo.com	PROPN
cana-4753	21	4	mailto:ananthmathsesec@gmail.com	mailto:ananthmathsesec@gmail.com	PROPN
cana-4753	21	5	mailto:krishnaveni.b@aec.edu.in	mailto:krishnaveni.b@aec.edu.in	X
cana-4753	22	1	mailto:sujatha.nanduri@aec.edu.in	mailto:sujatha.nanduri@aec.edu.in	PROPN
cana-4753	22	2	communications	communication	NOUN
cana-4753	22	3	on	on	ADP
cana-4753	22	4	applied	apply	VERB
cana-4753	22	5	nonlinear	nonlinear	ADJ
cana-4753	22	6	analysis	analysis	NOUN
cana-4753	22	7	issn	issn	NOUN
cana-4753	22	8	:	:	PUNCT
cana-4753	22	9	1074	1074	NUM
cana-4753	22	10	-	-	PUNCT
cana-4753	22	11	133x	133x	NUM
cana-4753	22	12	vol	vol	VERB
cana-4753	22	13	32	32	NUM
cana-4753	22	14	no	no	NOUN
cana-4753	22	15	.	.	PUNCT
cana-4753	23	1	10s	10	NOUN
cana-4753	23	2	(	(	PUNCT
cana-4753	23	3	2025	2025	NUM
cana-4753	23	4	)	)	PUNCT
cana-4753	23	5	285	285	NUM
cana-4753	23	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4753	23	7	a	a	DET
cana-4753	23	8	central	central	ADJ
cana-4753	23	9	problem	problem	NOUN
cana-4753	23	10	in	in	ADP
cana-4753	23	11	knot	knot	NOUN
cana-4753	23	12	theory	theory	NOUN
cana-4753	23	13	is	be	AUX
cana-4753	23	14	to	to	PART
cana-4753	23	15	classify	classify	VERB
cana-4753	23	16	knots	knot	NOUN
cana-4753	23	17	.	.	PUNCT
cana-4753	24	1	a	a	DET
cana-4753	24	2	particularly	particularly	ADV
cana-4753	24	3	basic	basic	ADJ
cana-4753	24	4	problem	problem	NOUN
cana-4753	24	5	is	be	AUX
cana-4753	24	6	to	to	PART
cana-4753	24	7	decide	decide	VERB
cana-4753	24	8	whether	whether	SCONJ
cana-4753	24	9	two	two	NUM
cana-4753	24	10	knots	knot	NOUN
cana-4753	24	11	are	be	AUX
cana-4753	24	12	equivalent	equivalent	ADJ
cana-4753	24	13	(	(	PUNCT
cana-4753	24	14	ambient	ambient	ADJ
cana-4753	24	15	isotopic	isotopic	NOUN
cana-4753	24	16	)	)	PUNCT
cana-4753	24	17	or	or	CCONJ
cana-4753	24	18	to	to	PART
cana-4753	24	19	give	give	VERB
cana-4753	24	20	conditions	condition	NOUN
cana-4753	24	21	for	for	ADP
cana-4753	24	22	distinguishing	distinguish	VERB
cana-4753	24	23	different	different	ADJ
cana-4753	24	24	knots	knot	NOUN
cana-4753	24	25	by	by	ADP
cana-4753	24	26	invariants	invariant	NOUN
cana-4753	24	27	—	—	PUNCT
cana-4753	24	28	mathematical	mathematical	ADJ
cana-4753	24	29	properties	property	NOUN
cana-4753	24	30	that	that	PRON
cana-4753	24	31	remain	remain	VERB
cana-4753	24	32	unchanged	unchanged	ADJ
cana-4753	24	33	under	under	ADP
cana-4753	24	34	connected	connected	ADJ
cana-4753	24	35	deformations	deformation	NOUN
cana-4753	24	36	.	.	PUNCT
cana-4753	25	1	reidemeister	reidemeister	ADJ
cana-4753	25	2	moves	move	NOUN
cana-4753	25	3	and	and	CCONJ
cana-4753	25	4	polynomials	polynomial	NOUN
cana-4753	25	5	invariants	invariant	NOUN
cana-4753	25	6	and	and	CCONJ
cana-4753	25	7	homology	homology	NOUN
cana-4753	25	8	theories	theory	NOUN
cana-4753	25	9	are	be	AUX
cana-4753	25	10	some	some	PRON
cana-4753	25	11	of	of	ADP
cana-4753	25	12	the	the	DET
cana-4753	25	13	significant	significant	ADJ
cana-4753	25	14	topological	topological	ADJ
cana-4753	25	15	methods	method	NOUN
cana-4753	25	16	that	that	PRON
cana-4753	25	17	have	have	AUX
cana-4753	25	18	been	be	AUX
cana-4753	25	19	developed	develop	VERB
cana-4753	25	20	to	to	PART
cana-4753	25	21	study	study	VERB
cana-4753	25	22	knot	knot	NOUN
cana-4753	25	23	structures	structure	NOUN
cana-4753	25	24	[	[	X
cana-4753	25	25	25	25	NUM
cana-4753	25	26	]	]	PUNCT
cana-4753	25	27	.	.	PUNCT
cana-4753	26	1	such	such	DET
cana-4753	26	2	a	a	DET
cana-4753	26	3	set	set	NOUN
cana-4753	26	4	of	of	ADP
cana-4753	26	5	operations	operation	NOUN
cana-4753	26	6	to	to	PART
cana-4753	26	7	transform	transform	VERB
cana-4753	26	8	knot	knot	NOUN
cana-4753	26	9	diagrams	diagram	NOUN
cana-4753	26	10	leaving	leave	VERB
cana-4753	26	11	the	the	DET
cana-4753	26	12	knot	knot	NOUN
cana-4753	26	13	topology	topology	NOUN
cana-4753	26	14	unchanged	unchanged	ADJ
cana-4753	26	15	were	be	AUX
cana-4753	26	16	introduced	introduce	VERB
cana-4753	26	17	in	in	ADP
cana-4753	26	18	the	the	DET
cana-4753	26	19	early	early	ADJ
cana-4753	26	20	20th	20th	ADJ
cana-4753	26	21	century	century	NOUN
cana-4753	26	22	to	to	PART
cana-4753	26	23	be	be	AUX
cana-4753	26	24	known	know	VERB
cana-4753	26	25	as	as	ADP
cana-4753	26	26	reidemeister	reidemeister	ADJ
cana-4753	26	27	moves	move	NOUN
cana-4753	26	28	.	.	PUNCT
cana-4753	27	1	the	the	DET
cana-4753	27	2	alexander	alexander	PROPN
cana-4753	27	3	polynomial	polynomial	PROPN
cana-4753	27	4	,	,	PUNCT
cana-4753	27	5	the	the	DET
cana-4753	27	6	jones	jones	PROPN
cana-4753	27	7	polynomial	polynomial	PROPN
cana-4753	27	8	,	,	PUNCT
cana-4753	27	9	and	and	CCONJ
cana-4753	27	10	the	the	DET
cana-4753	27	11	homfly	homfly	ADJ
cana-4753	27	12	polynomial	polynomial	NOUN
cana-4753	27	13	are	be	AUX
cana-4753	27	14	examples	example	NOUN
cana-4753	27	15	of	of	ADP
cana-4753	27	16	polynomial	polynomial	ADJ
cana-4753	27	17	invariants	invariant	NOUN
cana-4753	27	18	that	that	PRON
cana-4753	27	19	can	can	AUX
cana-4753	27	20	be	be	AUX
cana-4753	27	21	used	use	VERB
cana-4753	27	22	to	to	PART
cana-4753	27	23	distinguish	distinguish	VERB
cana-4753	27	24	knots	knot	NOUN
cana-4753	27	25	with	with	ADP
cana-4753	27	26	respect	respect	NOUN
cana-4753	27	27	to	to	ADP
cana-4753	27	28	algebraic	algebraic	ADJ
cana-4753	27	29	properties	property	NOUN
cana-4753	27	30	.	.	PUNCT
cana-4753	28	1	recent	recent	ADJ
cana-4753	28	2	homology	homology	NOUN
cana-4753	28	3	based	base	VERB
cana-4753	28	4	methods	method	NOUN
cana-4753	28	5	,	,	PUNCT
cana-4753	28	6	i.e.	i.e.	X
cana-4753	28	7	,	,	PUNCT
cana-4753	28	8	khovanov	khovanov	PROPN
cana-4753	28	9	homology	homology	PROPN
cana-4753	28	10	,	,	PUNCT
cana-4753	28	11	have	have	AUX
cana-4753	28	12	shed	shed	VERB
cana-4753	28	13	more	more	ADJ
cana-4753	28	14	light	light	NOUN
cana-4753	28	15	in	in	ADP
cana-4753	28	16	terms	term	NOUN
cana-4753	28	17	of	of	ADP
cana-4753	28	18	classification	classification	NOUN
cana-4753	28	19	of	of	ADP
cana-4753	28	20	knots	knot	NOUN
cana-4753	28	21	by	by	ADP
cana-4753	28	22	categorifying	categorifye	VERB
cana-4753	28	23	the	the	DET
cana-4753	28	24	traditional	traditional	ADJ
cana-4753	28	25	knot	knot	ADJ
cana-4753	28	26	polynomial	polynomial	ADJ
cana-4753	28	27	invariants	invariant	NOUN
cana-4753	28	28	[	[	X
cana-4753	28	29	6	6	NUM
cana-4753	28	30	,	,	PUNCT
cana-4753	28	31	23	23	NUM
cana-4753	28	32	]	]	PUNCT
cana-4753	28	33	.	.	PUNCT
cana-4753	29	1	apart	apart	ADV
cana-4753	29	2	from	from	ADP
cana-4753	29	3	pure	pure	ADJ
cana-4753	29	4	mathematics	mathematic	NOUN
cana-4753	29	5	,	,	PUNCT
cana-4753	29	6	the	the	DET
cana-4753	29	7	theory	theory	NOUN
cana-4753	29	8	of	of	ADP
cana-4753	29	9	knots	knot	NOUN
cana-4753	29	10	is	be	AUX
cana-4753	29	11	playing	play	VERB
cana-4753	29	12	an	an	DET
cana-4753	29	13	important	important	ADJ
cana-4753	29	14	part	part	NOUN
cana-4753	29	15	in	in	ADP
cana-4753	29	16	applied	applied	ADJ
cana-4753	29	17	sciences	science	NOUN
cana-4753	29	18	.	.	PUNCT
cana-4753	30	1	knots	knot	NOUN
cana-4753	30	2	occur	occur	VERB
cana-4753	30	3	naturally	naturally	ADV
cana-4753	30	4	in	in	ADP
cana-4753	30	5	dna	dna	NOUN
cana-4753	30	6	and	and	CCONJ
cana-4753	30	7	proteins	protein	NOUN
cana-4753	30	8	of	of	ADP
cana-4753	30	9	molecular	molecular	ADJ
cana-4753	30	10	biology	biology	NOUN
cana-4753	30	11	and	and	CCONJ
cana-4753	30	12	influence	influence	VERB
cana-4753	30	13	their	their	PRON
cana-4753	30	14	functions	function	NOUN
cana-4753	30	15	and	and	CCONJ
cana-4753	30	16	stability	stability	NOUN
cana-4753	30	17	.	.	PUNCT
cana-4753	31	1	studying	study	VERB
cana-4753	31	2	of	of	ADP
cana-4753	31	3	knotted	knotted	ADJ
cana-4753	31	4	and	and	CCONJ
cana-4753	31	5	linked	link	VERB
cana-4753	31	6	polymer	polymer	NOUN
cana-4753	31	7	chains	chain	NOUN
cana-4753	31	8	in	in	ADP
cana-4753	31	9	polymer	polymer	NOUN
cana-4753	31	10	chemistry	chemistry	NOUN
cana-4753	31	11	is	be	AUX
cana-4753	31	12	the	the	DET
cana-4753	31	13	design	design	NOUN
cana-4753	31	14	of	of	ADP
cana-4753	31	15	new	new	ADJ
cana-4753	31	16	materials	material	NOUN
cana-4753	31	17	with	with	ADP
cana-4753	31	18	desired	desire	VERB
cana-4753	31	19	mechanical	mechanical	ADJ
cana-4753	31	20	properties	property	NOUN
cana-4753	31	21	[	[	X
cana-4753	31	22	14	14	NUM
cana-4753	31	23	]	]	PUNCT
cana-4753	31	24	.	.	PUNCT
cana-4753	32	1	in	in	ADP
cana-4753	32	2	topological	topological	ADJ
cana-4753	32	3	quantum	quantum	ADJ
cana-4753	32	4	computation	computation	NOUN
cana-4753	32	5	,	,	PUNCT
cana-4753	32	6	which	which	PRON
cana-4753	32	7	is	be	AUX
cana-4753	32	8	one	one	NUM
cana-4753	32	9	of	of	ADP
cana-4753	32	10	the	the	DET
cana-4753	32	11	emerging	emerge	VERB
cana-4753	32	12	fields	field	NOUN
cana-4753	32	13	of	of	ADP
cana-4753	32	14	quantum	quantum	NOUN
cana-4753	32	15	computing	computing	NOUN
cana-4753	32	16	,	,	PUNCT
cana-4753	32	17	knots	knot	NOUN
cana-4753	32	18	are	be	AUX
cana-4753	32	19	used	use	VERB
cana-4753	32	20	to	to	PART
cana-4753	32	21	represent	represent	VERB
cana-4753	32	22	the	the	DET
cana-4753	32	23	information	information	NOUN
cana-4753	32	24	in	in	ADP
cana-4753	32	25	topological	topological	PROPN
cana-4753	32	26	quatum	quatum	PROPN
cana-4753	32	27	computation	computation	NOUN
cana-4753	32	28	,	,	PUNCT
cana-4753	32	29	where	where	SCONJ
cana-4753	32	30	quantum	quantum	ADJ
cana-4753	32	31	information	information	NOUN
cana-4753	32	32	is	be	AUX
cana-4753	32	33	stored	store	VERB
cana-4753	32	34	in	in	ADP
cana-4753	32	35	the	the	DET
cana-4753	32	36	topology	topology	NOUN
cana-4753	32	37	of	of	ADP
cana-4753	32	38	the	the	DET
cana-4753	32	39	trajectory	trajectory	NOUN
cana-4753	32	40	of	of	ADP
cana-4753	32	41	the	the	DET
cana-4753	32	42	particles	particle	NOUN
cana-4753	32	43	other	other	ADJ
cana-4753	32	44	than	than	ADP
cana-4753	32	45	in	in	ADP
cana-4753	32	46	conventional	conventional	ADJ
cana-4753	32	47	states	state	NOUN
cana-4753	32	48	of	of	ADP
cana-4753	32	49	qubits	qubit	NOUN
cana-4753	32	50	(	(	PUNCT
cana-4753	32	51	two	two	NUM
cana-4753	32	52	level	level	NOUN
cana-4753	32	53	systems	system	NOUN
cana-4753	32	54	)	)	PUNCT
cana-4753	32	55	.	.	PUNCT
cana-4753	33	1	however	however	ADV
cana-4753	33	2	,	,	PUNCT
cana-4753	33	3	much	much	ADJ
cana-4753	33	4	progress	progress	NOUN
cana-4753	33	5	of	of	ADP
cana-4753	33	6	understanding	understanding	NOUN
cana-4753	33	7	and	and	CCONJ
cana-4753	33	8	classification	classification	NOUN
cana-4753	33	9	of	of	ADP
cana-4753	33	10	complex	complex	ADJ
cana-4753	33	11	knots	knot	NOUN
cana-4753	33	12	is	be	AUX
cana-4753	33	13	still	still	ADV
cana-4753	33	14	lacking	lack	VERB
cana-4753	33	15	.	.	PUNCT
cana-4753	34	1	since	since	SCONJ
cana-4753	34	2	the	the	DET
cana-4753	34	3	computational	computational	ADJ
cana-4753	34	4	complexity	complexity	NOUN
cana-4753	34	5	of	of	ADP
cana-4753	34	6	joining	join	VERB
cana-4753	34	7	knots	knot	NOUN
cana-4753	34	8	increases	increase	NOUN
cana-4753	34	9	fast	fast	ADV
cana-4753	34	10	as	as	ADP
cana-4753	34	11	a	a	DET
cana-4753	34	12	function	function	NOUN
cana-4753	34	13	of	of	ADP
cana-4753	34	14	the	the	DET
cana-4753	34	15	number	number	NOUN
cana-4753	34	16	of	of	ADP
cana-4753	34	17	crossings	crossing	NOUN
cana-4753	34	18	,	,	PUNCT
cana-4753	34	19	efficient	efficient	ADJ
cana-4753	34	20	algorithms	algorithm	NOUN
cana-4753	34	21	and	and	CCONJ
cana-4753	34	22	computational	computational	ADJ
cana-4753	34	23	tools	tool	NOUN
cana-4753	34	24	are	be	AUX
cana-4753	34	25	needed	need	VERB
cana-4753	34	26	[	[	PUNCT
cana-4753	34	27	22	22	NUM
cana-4753	34	28	]	]	PUNCT
cana-4753	34	29	.	.	PUNCT
cana-4753	35	1	although	although	SCONJ
cana-4753	35	2	faster	fast	ADJ
cana-4753	35	3	and	and	CCONJ
cana-4753	35	4	more	more	ADV
cana-4753	35	5	reliable	reliable	ADJ
cana-4753	35	6	classification	classification	NOUN
cana-4753	35	7	of	of	ADP
cana-4753	35	8	knots	knot	NOUN
cana-4753	35	9	has	have	AUX
cana-4753	35	10	been	be	AUX
cana-4753	35	11	possible	possible	ADJ
cana-4753	35	12	with	with	ADP
cana-4753	35	13	recent	recent	ADJ
cana-4753	35	14	advances	advance	NOUN
cana-4753	35	15	in	in	ADP
cana-4753	35	16	computational	computational	ADJ
cana-4753	35	17	topology	topology	NOUN
cana-4753	35	18	and	and	CCONJ
cana-4753	35	19	machine	machine	NOUN
cana-4753	35	20	learning	learning	NOUN
cana-4753	35	21	,	,	PUNCT
cana-4753	35	22	research	research	NOUN
cana-4753	35	23	still	still	ADV
cana-4753	35	24	needs	need	VERB
cana-4753	35	25	to	to	PART
cana-4753	35	26	be	be	AUX
cana-4753	35	27	done	do	VERB
cana-4753	35	28	in	in	ADP
cana-4753	35	29	higher	high	ADJ
cana-4753	35	30	dimensions	dimension	NOUN
cana-4753	35	31	of	of	ADP
cana-4753	35	32	knots	knot	NOUN
cana-4753	35	33	and	and	CCONJ
cana-4753	35	34	their	their	PRON
cana-4753	35	35	relations	relation	NOUN
cana-4753	35	36	to	to	ADP
cana-4753	35	37	the	the	DET
cana-4753	35	38	cornerstones	cornerstone	NOUN
cana-4753	35	39	of	of	ADP
cana-4753	35	40	physics	physics	NOUN
cana-4753	35	41	and	and	CCONJ
cana-4753	35	42	data	datum	NOUN
cana-4753	35	43	science	science	NOUN
cana-4753	35	44	.	.	PUNCT
cana-4753	36	1	the	the	DET
cana-4753	36	2	goal	goal	NOUN
cana-4753	36	3	for	for	ADP
cana-4753	36	4	this	this	DET
cana-4753	36	5	paper	paper	NOUN
cana-4753	36	6	is	be	AUX
cana-4753	36	7	to	to	PART
cana-4753	36	8	give	give	VERB
cana-4753	36	9	a	a	DET
cana-4753	36	10	thorough	thorough	ADJ
cana-4753	36	11	review	review	NOUN
cana-4753	36	12	of	of	ADP
cana-4753	36	13	the	the	DET
cana-4753	36	14	topological	topological	ADJ
cana-4753	36	15	methods	method	NOUN
cana-4753	36	16	that	that	PRON
cana-4753	36	17	are	be	AUX
cana-4753	36	18	used	use	VERB
cana-4753	36	19	on	on	ADP
cana-4753	36	20	knot	knot	NOUN
cana-4753	36	21	theory	theory	NOUN
cana-4753	36	22	,	,	PUNCT
cana-4753	36	23	covering	cover	VERB
cana-4753	36	24	the	the	DET
cana-4753	36	25	mathematical	mathematical	ADJ
cana-4753	36	26	foundations	foundation	NOUN
cana-4753	36	27	,	,	PUNCT
cana-4753	36	28	computation	computation	NOUN
cana-4753	36	29	algorithms	algorithm	NOUN
cana-4753	36	30	,	,	PUNCT
cana-4753	36	31	and	and	CCONJ
cana-4753	36	32	real	real	ADJ
cana-4753	36	33	physical	physical	ADJ
cana-4753	36	34	applications	application	NOUN
cana-4753	36	35	.	.	PUNCT
cana-4753	37	1	in	in	ADP
cana-4753	37	2	the	the	DET
cana-4753	37	3	case	case	NOUN
cana-4753	37	4	of	of	ADP
cana-4753	37	5	classifying	classify	VERB
cana-4753	37	6	and	and	CCONJ
cana-4753	37	7	distinguishing	distinguish	VERB
cana-4753	37	8	knots	knot	NOUN
cana-4753	37	9	we	we	PRON
cana-4753	37	10	have	have	AUX
cana-4753	37	11	analyzed	analyze	VERB
cana-4753	37	12	the	the	DET
cana-4753	37	13	effectiveness	effectiveness	NOUN
cana-4753	37	14	of	of	ADP
cana-4753	37	15	different	different	ADJ
cana-4753	37	16	approaches	approach	NOUN
cana-4753	37	17	and	and	CCONJ
cana-4753	37	18	evaluated	evaluate	VERB
cana-4753	37	19	their	their	PRON
cana-4753	37	20	strengths	strength	NOUN
cana-4753	37	21	and	and	CCONJ
cana-4753	37	22	weaknesses	weakness	NOUN
cana-4753	37	23	[	[	X
cana-4753	37	24	8	8	NUM
cana-4753	37	25	-	-	SYM
cana-4753	37	26	12	12	NUM
cana-4753	37	27	]	]	PUNCT
cana-4753	37	28	.	.	PUNCT
cana-4753	38	1	novelty	novelty	NOUN
cana-4753	38	2	and	and	CCONJ
cana-4753	38	3	contribution	contribution	NOUN
cana-4753	38	4	using	use	VERB
cana-4753	38	5	techniques	technique	NOUN
cana-4753	38	6	that	that	PRON
cana-4753	38	7	are	be	AUX
cana-4753	38	8	traditional	traditional	ADJ
cana-4753	38	9	in	in	ADP
cana-4753	38	10	the	the	DET
cana-4753	38	11	field	field	NOUN
cana-4753	38	12	of	of	ADP
cana-4753	38	13	topology	topology	NOUN
cana-4753	38	14	,	,	PUNCT
cana-4753	38	15	and	and	CCONJ
cana-4753	38	16	those	those	PRON
cana-4753	38	17	that	that	PRON
cana-4753	38	18	are	be	AUX
cana-4753	38	19	more	more	ADV
cana-4753	38	20	recent	recent	ADJ
cana-4753	38	21	developments	development	NOUN
cana-4753	38	22	from	from	ADP
cana-4753	38	23	computational	computational	ADJ
cana-4753	38	24	and	and	CCONJ
cana-4753	38	25	applied	apply	VERB
cana-4753	38	26	topology	topology	NOUN
cana-4753	39	1	,	,	PUNCT
cana-4753	39	2	this	this	DET
cana-4753	39	3	study	study	NOUN
cana-4753	39	4	makes	make	VERB
cana-4753	39	5	a	a	DET
cana-4753	39	6	unique	unique	ADJ
cana-4753	39	7	contribution	contribution	NOUN
cana-4753	39	8	to	to	ADP
cana-4753	39	9	this	this	DET
cana-4753	39	10	area	area	NOUN
cana-4753	39	11	of	of	ADP
cana-4753	39	12	knot	knot	ADJ
cana-4753	39	13	theory	theory	NOUN
cana-4753	39	14	[	[	X
cana-4753	39	15	13	13	NUM
cana-4753	39	16	]	]	PUNCT
cana-4753	39	17	.	.	PUNCT
cana-4753	40	1	previous	previous	ADJ
cana-4753	40	2	works	work	NOUN
cana-4753	40	3	have	have	AUX
cana-4753	40	4	concentrated	concentrate	VERB
cana-4753	40	5	mostly	mostly	ADV
cana-4753	40	6	on	on	ADP
cana-4753	40	7	either	either	CCONJ
cana-4753	40	8	theoretical	theoretical	ADJ
cana-4753	40	9	aspects	aspect	NOUN
cana-4753	40	10	or	or	CCONJ
cana-4753	40	11	particular	particular	ADJ
cana-4753	40	12	applications	application	NOUN
cana-4753	40	13	,	,	PUNCT
cana-4753	40	14	however	however	ADV
cana-4753	40	15	this	this	DET
cana-4753	40	16	paper	paper	NOUN
cana-4753	40	17	bridges	bridge	NOUN
cana-4753	40	18	the	the	DET
cana-4753	40	19	gap	gap	NOUN
cana-4753	40	20	by	by	ADP
cana-4753	40	21	considering	consider	VERB
cana-4753	40	22	knot	knot	NOUN
cana-4753	40	23	complexity	complexity	NOUN
cana-4753	40	24	and	and	CCONJ
cana-4753	40	25	classification	classification	NOUN
cana-4753	40	26	together	together	ADV
cana-4753	40	27	from	from	ADP
cana-4753	40	28	the	the	DET
cana-4753	40	29	viewpoint	viewpoint	NOUN
cana-4753	40	30	enhanced	enhance	VERB
cana-4753	40	31	with	with	ADP
cana-4753	40	32	modern	modern	ADJ
cana-4753	40	33	computational	computational	ADJ
cana-4753	40	34	tools	tool	NOUN
cana-4753	40	35	[	[	X
cana-4753	40	36	7	7	NUM
cana-4753	40	37	]	]	PUNCT
cana-4753	40	38	.	.	PUNCT
cana-4753	41	1	this	this	DET
cana-4753	41	2	work	work	NOUN
cana-4753	41	3	has	have	VERB
cana-4753	41	4	the	the	DET
cana-4753	41	5	following	follow	VERB
cana-4753	41	6	key	key	ADJ
cana-4753	41	7	novelties	novelty	NOUN
cana-4753	41	8	.	.	PUNCT
cana-4753	42	1	•	•	NUM
cana-4753	42	2	comprehensive	comprehensive	ADJ
cana-4753	42	3	analysis	analysis	NOUN
cana-4753	42	4	of	of	ADP
cana-4753	42	5	topological	topological	ADJ
cana-4753	42	6	methods	method	NOUN
cana-4753	42	7	❖	❖	NUM
cana-4753	42	8	unlike	unlike	ADP
cana-4753	42	9	previous	previous	ADJ
cana-4753	42	10	papers	paper	NOUN
cana-4753	42	11	on	on	ADP
cana-4753	42	12	individual	individual	ADJ
cana-4753	42	13	invariants	invariant	NOUN
cana-4753	42	14	,	,	PUNCT
cana-4753	42	15	this	this	DET
cana-4753	42	16	paper	paper	NOUN
cana-4753	42	17	compares	compare	VERB
cana-4753	42	18	different	different	ADJ
cana-4753	42	19	approaches	approach	NOUN
cana-4753	42	20	to	to	ADP
cana-4753	42	21	the	the	DET
cana-4753	42	22	problem	problem	NOUN
cana-4753	42	23	that	that	PRON
cana-4753	42	24	involve	involve	VERB
cana-4753	42	25	reidemeister	reidemeister	ADJ
cana-4753	42	26	moves	move	NOUN
cana-4753	42	27	,	,	PUNCT
cana-4753	42	28	polynomial	polynomial	ADJ
cana-4753	42	29	invariants	invariant	NOUN
cana-4753	42	30	,	,	PUNCT
cana-4753	42	31	and	and	CCONJ
cana-4753	42	32	methods	method	NOUN
cana-4753	42	33	based	base	VERB
cana-4753	42	34	on	on	ADP
cana-4753	42	35	homology	homology	NOUN
cana-4753	42	36	.	.	PUNCT
cana-4753	43	1	communications	communication	NOUN
cana-4753	43	2	on	on	ADP
cana-4753	43	3	applied	apply	VERB
cana-4753	43	4	nonlinear	nonlinear	ADJ
cana-4753	43	5	analysis	analysis	NOUN
cana-4753	43	6	issn	issn	NOUN
cana-4753	43	7	:	:	PUNCT
cana-4753	43	8	1074	1074	NUM
cana-4753	43	9	-	-	PUNCT
cana-4753	43	10	133x	133x	NUM
cana-4753	43	11	vol	vol	VERB
cana-4753	43	12	32	32	NUM
cana-4753	43	13	no	no	NOUN
cana-4753	43	14	.	.	PUNCT
cana-4753	44	1	10s	10	NOUN
cana-4753	44	2	(	(	PUNCT
cana-4753	44	3	2025	2025	NUM
cana-4753	44	4	)	)	PUNCT
cana-4753	44	5	286	286	NUM
cana-4753	44	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4753	44	7	❖	❖	AUX
cana-4753	44	8	we	we	PRON
cana-4753	44	9	exploit	exploit	VERB
cana-4753	44	10	the	the	DET
cana-4753	44	11	fact	fact	NOUN
cana-4753	44	12	that	that	SCONJ
cana-4753	44	13	polynomial	polynomial	ADJ
cana-4753	44	14	invariants	invariant	NOUN
cana-4753	44	15	can	can	AUX
cana-4753	44	16	not	not	PART
cana-4753	44	17	prove	prove	VERB
cana-4753	44	18	the	the	DET
cana-4753	44	19	difference	difference	NOUN
cana-4753	44	20	between	between	ADP
cana-4753	44	21	knots	knot	NOUN
cana-4753	44	22	while	while	SCONJ
cana-4753	44	23	we	we	PRON
cana-4753	44	24	give	give	VERB
cana-4753	44	25	a	a	DET
cana-4753	44	26	more	more	ADV
cana-4753	44	27	refined	refined	ADJ
cana-4753	44	28	classification	classification	NOUN
cana-4753	44	29	system	system	NOUN
cana-4753	44	30	by	by	ADP
cana-4753	44	31	homology	homology	NOUN
cana-4753	44	32	based	base	VERB
cana-4753	44	33	approaches	approach	NOUN
cana-4753	44	34	.	.	PUNCT
cana-4753	45	1	•	•	NUM
cana-4753	45	2	integration	integration	NOUN
cana-4753	45	3	of	of	ADP
cana-4753	45	4	computational	computational	ADJ
cana-4753	45	5	techniques	technique	NOUN
cana-4753	45	6	❖	❖	NUM
cana-4753	45	7	in	in	ADP
cana-4753	45	8	this	this	DET
cana-4753	45	9	paper	paper	NOUN
cana-4753	45	10	,	,	PUNCT
cana-4753	45	11	we	we	PRON
cana-4753	45	12	take	take	VERB
cana-4753	45	13	a	a	DET
cana-4753	45	14	computational	computational	ADJ
cana-4753	45	15	point	point	NOUN
cana-4753	45	16	of	of	ADP
cana-4753	45	17	view	view	NOUN
cana-4753	45	18	and	and	CCONJ
cana-4753	45	19	examine	examine	VERB
cana-4753	45	20	recent	recent	ADJ
cana-4753	45	21	algorithmic	algorithmic	ADJ
cana-4753	45	22	and	and	CCONJ
cana-4753	45	23	machine	machine	NOUN
cana-4753	45	24	learning	learning	NOUN
cana-4753	45	25	approaches	approach	NOUN
cana-4753	45	26	that	that	PRON
cana-4753	45	27	aim	aim	VERB
cana-4753	45	28	to	to	PART
cana-4753	45	29	automate	automate	VERB
cana-4753	45	30	knot	knot	NOUN
cana-4753	45	31	classification	classification	NOUN
cana-4753	45	32	and	and	CCONJ
cana-4753	45	33	thus	thus	ADV
cana-4753	45	34	overcome	overcome	VERB
cana-4753	45	35	the	the	DET
cana-4753	45	36	difficulties	difficulty	NOUN
cana-4753	45	37	involved	involve	VERB
cana-4753	45	38	in	in	ADP
cana-4753	45	39	distinguishing	distinguish	VERB
cana-4753	45	40	the	the	DET
cana-4753	45	41	topologically	topologically	ADV
cana-4753	45	42	exotic	exotic	ADJ
cana-4753	45	43	knots	knot	NOUN
cana-4753	45	44	.	.	PUNCT
cana-4753	46	1	❖	❖	VERB
cana-4753	46	2	efficiency	efficiency	NOUN
cana-4753	46	3	of	of	ADP
cana-4753	46	4	such	such	ADJ
cana-4753	46	5	analysis	analysis	NOUN
cana-4753	46	6	on	on	ADP
cana-4753	46	7	large	large	ADJ
cana-4753	46	8	knot	knot	NOUN
cana-4753	46	9	datasets	dataset	NOUN
cana-4753	46	10	is	be	AUX
cana-4753	46	11	evaluated	evaluate	VERB
cana-4753	46	12	with	with	ADP
cana-4753	46	13	state	state	NOUN
cana-4753	46	14	of	of	ADP
cana-4753	46	15	the	the	DET
cana-4753	46	16	art	art	NOUN
cana-4753	46	17	software	software	NOUN
cana-4753	46	18	tools	tool	NOUN
cana-4753	46	19	used	use	VERB
cana-4753	46	20	in	in	ADP
cana-4753	46	21	computational	computational	ADJ
cana-4753	46	22	topology	topology	NOUN
cana-4753	46	23	.	.	PUNCT
cana-4753	47	1	•	•	NUM
cana-4753	47	2	application	application	NOUN
cana-4753	47	3	-	-	PUNCT
cana-4753	47	4	oriented	orient	VERB
cana-4753	47	5	discussion	discussion	NOUN
cana-4753	47	6	❖	❖	NUM
cana-4753	47	7	in	in	ADP
cana-4753	47	8	this	this	DET
cana-4753	47	9	thesis	thesis	NOUN
cana-4753	47	10	,	,	PUNCT
cana-4753	47	11	we	we	PRON
cana-4753	47	12	analyze	analyze	VERB
cana-4753	47	13	how	how	SCONJ
cana-4753	47	14	the	the	DET
cana-4753	47	15	principles	principle	NOUN
cana-4753	47	16	of	of	ADP
cana-4753	47	17	topological	topological	ADJ
cana-4753	47	18	quantum	quantum	ADJ
cana-4753	47	19	computation	computation	NOUN
cana-4753	47	20	work	work	NOUN
cana-4753	47	21	with	with	ADP
cana-4753	47	22	the	the	DET
cana-4753	47	23	help	help	NOUN
cana-4753	47	24	of	of	ADP
cana-4753	47	25	knot	knot	NOUN
cana-4753	47	26	invariants	invariant	NOUN
cana-4753	47	27	to	to	PART
cana-4753	47	28	write	write	VERB
cana-4753	47	29	down	down	ADP
cana-4753	47	30	quantum	quantum	NOUN
cana-4753	47	31	states	state	NOUN
cana-4753	47	32	.	.	PUNCT
cana-4753	48	1	•	•	NUM
cana-4753	48	2	exploration	exploration	NOUN
cana-4753	48	3	of	of	ADP
cana-4753	48	4	higher	high	ADJ
cana-4753	48	5	-	-	PUNCT
cana-4753	48	6	dimensional	dimensional	ADJ
cana-4753	48	7	knot	knot	NOUN
cana-4753	48	8	theory	theory	NOUN
cana-4753	48	9	❖	❖	NUM
cana-4753	48	10	in	in	ADP
cana-4753	48	11	addition	addition	NOUN
cana-4753	48	12	,	,	PUNCT
cana-4753	48	13	we	we	PRON
cana-4753	48	14	look	look	VERB
cana-4753	48	15	at	at	ADP
cana-4753	48	16	recent	recent	ADJ
cana-4753	48	17	results	result	NOUN
cana-4753	48	18	in	in	ADP
cana-4753	48	19	higher	high	ADJ
cana-4753	48	20	dimensional	dimensional	ADJ
cana-4753	48	21	knots	knot	NOUN
cana-4753	48	22	e.g.	e.g.	ADV
cana-4753	48	23	knotted	knot	VERB
cana-4753	48	24	surfaces	surface	NOUN
cana-4753	48	25	in	in	ADP
cana-4753	48	26	4	4	NUM
cana-4753	48	27	spatial	spatial	ADJ
cana-4753	48	28	dimensions	dimension	NOUN
cana-4753	48	29	.	.	PUNCT
cana-4753	49	1	❖	❖	AUX
cana-4753	49	2	we	we	PRON
cana-4753	49	3	explain	explain	VERB
cana-4753	49	4	how	how	SCONJ
cana-4753	49	5	implications	implication	NOUN
cana-4753	49	6	of	of	ADP
cana-4753	49	7	higher	high	ADJ
cana-4753	49	8	dimensional	dimensional	ADJ
cana-4753	49	9	knot	knot	NOUN
cana-4753	49	10	theory	theory	NOUN
cana-4753	49	11	are	be	AUX
cana-4753	49	12	related	relate	VERB
cana-4753	49	13	to	to	ADP
cana-4753	49	14	the	the	DET
cana-4753	49	15	topological	topological	ADJ
cana-4753	49	16	quantum	quantum	ADJ
cana-4753	49	17	field	field	NOUN
cana-4753	49	18	theory	theory	NOUN
cana-4753	49	19	and	and	CCONJ
cana-4753	49	20	the	the	DET
cana-4753	49	21	string	string	NOUN
cana-4753	49	22	theory	theory	NOUN
cana-4753	49	23	.	.	PUNCT
cana-4753	50	1	this	this	DET
cana-4753	50	2	paper	paper	NOUN
cana-4753	50	3	makes	make	VERB
cana-4753	50	4	a	a	DET
cana-4753	50	5	contribution	contribution	NOUN
cana-4753	50	6	to	to	ADP
cana-4753	50	7	theoretically	theoretically	ADV
cana-4753	50	8	advancing	advance	VERB
cana-4753	50	9	,	,	PUNCT
cana-4753	50	10	and	and	CCONJ
cana-4753	50	11	practically	practically	ADV
cana-4753	50	12	applying	applying	ADJ
cana-4753	50	13	,	,	PUNCT
cana-4753	50	14	knot	knot	NOUN
cana-4753	50	15	theory	theory	NOUN
cana-4753	50	16	by	by	ADP
cana-4753	50	17	providing	provide	VERB
cana-4753	50	18	an	an	DET
cana-4753	50	19	interdisciplinary	interdisciplinary	ADJ
cana-4753	50	20	,	,	PUNCT
cana-4753	50	21	comprehensive	comprehensive	ADJ
cana-4753	50	22	effort	effort	NOUN
cana-4753	50	23	.	.	PUNCT
cana-4753	51	1	the	the	DET
cana-4753	51	2	results	result	NOUN
cana-4753	51	3	obtained	obtain	VERB
cana-4753	51	4	show	show	NOUN
cana-4753	51	5	that	that	SCONJ
cana-4753	51	6	our	our	PRON
cana-4753	51	7	approaches	approach	NOUN
cana-4753	51	8	give	give	VERB
cana-4753	51	9	significant	significant	ADJ
cana-4753	51	10	insights	insight	NOUN
cana-4753	51	11	for	for	ADP
cana-4753	51	12	researchers	researcher	NOUN
cana-4753	51	13	in	in	ADP
cana-4753	51	14	topology	topology	NOUN
cana-4753	51	15	,	,	PUNCT
cana-4753	51	16	computational	computational	ADJ
cana-4753	51	17	mathematics	mathematic	NOUN
cana-4753	51	18	,	,	PUNCT
cana-4753	51	19	and	and	CCONJ
cana-4753	51	20	applied	apply	VERB
cana-4753	51	21	sciences	science	NOUN
cana-4753	51	22	,	,	PUNCT
cana-4753	51	23	and	and	CCONJ
cana-4753	51	24	outline	outline	VERB
cana-4753	51	25	a	a	DET
cana-4753	51	26	course	course	NOUN
cana-4753	51	27	of	of	ADP
cana-4753	51	28	further	further	ADJ
cana-4753	51	29	developments	development	NOUN
cana-4753	51	30	in	in	ADP
cana-4753	51	31	an	an	DET
cana-4753	51	32	area	area	NOUN
cana-4753	51	33	very	very	ADV
cana-4753	51	34	rapidly	rapidly	ADV
cana-4753	51	35	developing	develop	VERB
cana-4753	51	36	[	[	X
cana-4753	51	37	24	24	NUM
cana-4753	51	38	]	]	PUNCT
cana-4753	51	39	.	.	PUNCT
cana-4753	52	1	ii	ii	PROPN
cana-4753	52	2	.	.	PROPN
cana-4753	52	3	related	relate	VERB
cana-4753	52	4	works	work	VERB
cana-4753	52	5	the	the	DET
cana-4753	52	6	theory	theory	NOUN
cana-4753	52	7	of	of	ADP
cana-4753	52	8	knots	knot	NOUN
cana-4753	52	9	has	have	AUX
cana-4753	52	10	been	be	AUX
cana-4753	52	11	intensively	intensively	ADV
cana-4753	52	12	studied	study	VERB
cana-4753	52	13	in	in	ADP
cana-4753	52	14	both	both	PRON
cana-4753	52	15	mathematical	mathematical	ADJ
cana-4753	52	16	and	and	CCONJ
cana-4753	52	17	applied	applied	ADJ
cana-4753	52	18	sciences	science	NOUN
cana-4753	52	19	,	,	PUNCT
cana-4753	52	20	and	and	CCONJ
cana-4753	52	21	has	have	AUX
cana-4753	52	22	given	give	VERB
cana-4753	52	23	rise	rise	NOUN
cana-4753	52	24	to	to	ADP
cana-4753	52	25	a	a	DET
cana-4753	52	26	number	number	NOUN
cana-4753	52	27	of	of	ADP
cana-4753	52	28	topological	topological	ADJ
cana-4753	52	29	method	method	NOUN
cana-4753	52	30	for	for	ADP
cana-4753	52	31	investigating	investigate	VERB
cana-4753	52	32	knotted	knotted	ADJ
cana-4753	52	33	structures	structure	NOUN
cana-4753	52	34	.	.	PUNCT
cana-4753	53	1	much	much	ADJ
cana-4753	53	2	work	work	NOUN
cana-4753	53	3	has	have	AUX
cana-4753	53	4	been	be	AUX
cana-4753	53	5	done	do	VERB
cana-4753	53	6	in	in	ADP
cana-4753	53	7	the	the	DET
cana-4753	53	8	field	field	NOUN
cana-4753	53	9	to	to	PART
cana-4753	53	10	classify	classify	VERB
cana-4753	53	11	knots	knot	NOUN
cana-4753	53	12	with	with	ADP
cana-4753	53	13	a	a	DET
cana-4753	53	14	variety	variety	NOUN
cana-4753	53	15	of	of	ADP
cana-4753	53	16	methods	method	NOUN
cana-4753	53	17	to	to	PART
cana-4753	53	18	do	do	VERB
cana-4753	53	19	so	so	ADV
cana-4753	53	20	(	(	PUNCT
cana-4753	53	21	or	or	CCONJ
cana-4753	53	22	to	to	PART
cana-4753	53	23	distinguish	distinguish	VERB
cana-4753	53	24	one	one	NUM
cana-4753	53	25	knot	knot	NOUN
cana-4753	53	26	from	from	ADP
cana-4753	53	27	another	another	PRON
cana-4753	53	28	)	)	PUNCT
cana-4753	53	29	by	by	ADP
cana-4753	53	30	looking	look	VERB
cana-4753	53	31	at	at	ADP
cana-4753	53	32	their	their	PRON
cana-4753	53	33	properties	property	NOUN
cana-4753	53	34	.	.	PUNCT
cana-4753	54	1	reidemeister	reidemeister	ADJ
cana-4753	54	2	moves	move	NOUN
cana-4753	54	3	are	be	AUX
cana-4753	54	4	one	one	NUM
cana-4753	54	5	of	of	ADP
cana-4753	54	6	the	the	DET
cana-4753	54	7	fundamental	fundamental	ADJ
cana-4753	54	8	techniques	technique	NOUN
cana-4753	54	9	of	of	ADP
cana-4753	54	10	knot	knot	NOUN
cana-4753	54	11	theory	theory	NOUN
cana-4753	54	12	,	,	PUNCT
cana-4753	54	13	supplying	supply	VERB
cana-4753	54	14	a	a	DET
cana-4753	54	15	collection	collection	NOUN
cana-4753	54	16	of	of	ADP
cana-4753	54	17	local	local	ADJ
cana-4753	54	18	transformations	transformation	NOUN
cana-4753	54	19	which	which	PRON
cana-4753	54	20	preserve	preserve	VERB
cana-4753	54	21	the	the	DET
cana-4753	54	22	equivalence	equivalence	NOUN
cana-4753	54	23	of	of	ADP
cana-4753	54	24	knots	knot	NOUN
cana-4753	54	25	.	.	PUNCT
cana-4753	55	1	however	however	ADV
cana-4753	55	2	,	,	PUNCT
cana-4753	55	3	it	it	PRON
cana-4753	55	4	is	be	AUX
cana-4753	55	5	an	an	DET
cana-4753	55	6	essential	essential	ADJ
cana-4753	55	7	method	method	NOUN
cana-4753	55	8	in	in	ADP
cana-4753	55	9	defining	define	VERB
cana-4753	55	10	knot	knot	NOUN
cana-4753	55	11	equivalence	equivalence	NOUN
cana-4753	55	12	and	and	CCONJ
cana-4753	55	13	gets	get	VERB
cana-4753	55	14	computationally	computationally	ADV
cana-4753	55	15	prohibitive	prohibitive	ADJ
cana-4753	55	16	for	for	ADP
cana-4753	55	17	complex	complex	ADJ
cana-4753	55	18	knot	knot	NOUN
cana-4753	55	19	structures	structure	NOUN
cana-4753	55	20	.	.	PUNCT
cana-4753	56	1	in	in	ADP
cana-4753	56	2	2017	2017	NUM
cana-4753	56	3	d.	d.	PROPN
cana-4753	56	4	goundaroulis	goundaroulis	PROPN
cana-4753	56	5	et	et	PROPN
cana-4753	56	6	al	al	PROPN
cana-4753	56	7	.	.	PROPN
cana-4753	56	8	,	,	PUNCT
cana-4753	56	9	[	[	X
cana-4753	56	10	15	15	NUM
cana-4753	56	11	]	]	PUNCT
cana-4753	56	12	introduce	introduce	VERB
cana-4753	56	13	the	the	DET
cana-4753	56	14	research	research	NOUN
cana-4753	56	15	challenges	challenge	NOUN
cana-4753	56	16	of	of	ADP
cana-4753	56	17	both	both	CCONJ
cana-4753	56	18	direct	direct	ADJ
cana-4753	56	19	visual	visual	ADJ
cana-4753	56	20	and	and	CCONJ
cana-4753	56	21	combinatorial	combinatorial	ADJ
cana-4753	56	22	analysis	analysis	NOUN
cana-4753	56	23	were	be	AUX
cana-4753	56	24	overcome	overcome	VERB
cana-4753	56	25	by	by	ADP
cana-4753	56	26	the	the	DET
cana-4753	56	27	introduction	introduction	NOUN
cana-4753	56	28	of	of	ADP
cana-4753	56	29	polynomial	polynomial	ADJ
cana-4753	56	30	invariants	invariant	NOUN
cana-4753	56	31	,	,	PUNCT
cana-4753	56	32	for	for	ADP
cana-4753	56	33	example	example	NOUN
cana-4753	56	34	,	,	PUNCT
cana-4753	56	35	the	the	DET
cana-4753	56	36	alexander	alexander	PROPN
cana-4753	56	37	,	,	PUNCT
cana-4753	56	38	jones	jones	PROPN
cana-4753	56	39	,	,	PUNCT
cana-4753	56	40	and	and	CCONJ
cana-4753	56	41	homfly	homfly	VERB
cana-4753	56	42	polynomial	polynomial	ADJ
cana-4753	56	43	invariants	invariant	NOUN
cana-4753	56	44	.	.	PUNCT
cana-4753	57	1	their	their	PRON
cana-4753	57	2	usefulness	usefulness	NOUN
cana-4753	57	3	goes	go	VERB
cana-4753	57	4	beyond	beyond	ADP
cana-4753	57	5	enumerative	enumerative	ADJ
cana-4753	57	6	and	and	CCONJ
cana-4753	57	7	connectivity	connectivity	NOUN
cana-4753	57	8	questions	question	NOUN
cana-4753	57	9	,	,	PUNCT
cana-4753	57	10	for	for	SCONJ
cana-4753	57	11	these	these	DET
cana-4753	57	12	invariants	invariant	NOUN
cana-4753	57	13	constitute	constitute	VERB
cana-4753	57	14	algebraic	algebraic	ADJ
cana-4753	57	15	tools	tool	NOUN
cana-4753	57	16	,	,	PUNCT
cana-4753	57	17	in	in	ADP
cana-4753	57	18	the	the	DET
cana-4753	57	19	sense	sense	NOUN
cana-4753	57	20	of	of	ADP
cana-4753	57	21	algebraic	algebraic	ADJ
cana-4753	57	22	topology	topology	NOUN
cana-4753	57	23	,	,	PUNCT
cana-4753	57	24	with	with	ADP
cana-4753	57	25	which	which	PRON
cana-4753	57	26	to	to	PART
cana-4753	57	27	distinguish	distinguish	VERB
cana-4753	57	28	one	one	NUM
cana-4753	57	29	knot	knot	NOUN
cana-4753	57	30	from	from	ADP
cana-4753	57	31	another	another	PRON
cana-4753	57	32	,	,	PUNCT
cana-4753	57	33	in	in	ADP
cana-4753	57	34	a	a	DET
cana-4753	57	35	systematic	systematic	ADJ
cana-4753	57	36	manner	manner	NOUN
cana-4753	57	37	.	.	PUNCT
cana-4753	58	1	nevertheless	nevertheless	ADV
cana-4753	58	2	,	,	PUNCT
cana-4753	58	3	polynomial	polynomial	ADJ
cana-4753	58	4	invariants	invariant	NOUN
cana-4753	58	5	suffer	suffer	VERB
cana-4753	58	6	from	from	ADP
cana-4753	58	7	the	the	DET
cana-4753	58	8	fact	fact	NOUN
cana-4753	58	9	that	that	SCONJ
cana-4753	58	10	they	they	PRON
cana-4753	58	11	fall	fall	VERB
cana-4753	58	12	short	short	ADV
cana-4753	58	13	when	when	SCONJ
cana-4753	58	14	it	it	PRON
cana-4753	58	15	comes	come	VERB
cana-4753	58	16	to	to	ADP
cana-4753	58	17	distinguishing	distinguish	VERB
cana-4753	58	18	some	some	DET
cana-4753	58	19	topologically	topologically	ADV
cana-4753	58	20	distinct	distinct	ADJ
cana-4753	58	21	knots	knot	NOUN
cana-4753	58	22	.	.	PUNCT
cana-4753	59	1	due	due	ADP
cana-4753	59	2	to	to	ADP
cana-4753	59	3	this	this	DET
cana-4753	59	4	limitation	limitation	NOUN
cana-4753	59	5	,	,	PUNCT
cana-4753	59	6	homology	homology	NOUN
cana-4753	59	7	based	base	VERB
cana-4753	59	8	invariants	invariant	NOUN
cana-4753	59	9	of	of	ADP
cana-4753	59	10	knots	knot	NOUN
cana-4753	59	11	such	such	ADJ
cana-4753	59	12	as	as	ADP
cana-4753	59	13	khovanov	khovanov	NOUN
cana-4753	59	14	homology	homology	NOUN
cana-4753	59	15	have	have	AUX
cana-4753	59	16	been	be	AUX
cana-4753	59	17	investigated	investigate	VERB
cana-4753	59	18	due	due	ADP
cana-4753	59	19	to	to	ADP
cana-4753	59	20	the	the	DET
cana-4753	59	21	fact	fact	NOUN
cana-4753	59	22	that	that	SCONJ
cana-4753	59	23	they	they	PRON
cana-4753	59	24	provide	provide	VERB
cana-4753	59	25	a	a	DET
cana-4753	59	26	richer	rich	ADJ
cana-4753	59	27	algebraic	algebraic	ADJ
cana-4753	59	28	structure	structure	NOUN
cana-4753	59	29	on	on	ADP
cana-4753	59	30	which	which	PRON
cana-4753	59	31	to	to	PART
cana-4753	59	32	understand	understand	VERB
cana-4753	59	33	the	the	DET
cana-4753	59	34	complexity	complexity	NOUN
cana-4753	59	35	of	of	ADP
cana-4753	59	36	knots	knot	NOUN
cana-4753	59	37	.	.	PUNCT
cana-4753	60	1	the	the	DET
cana-4753	60	2	homology	homology	NOUN
cana-4753	60	3	methods	method	NOUN
cana-4753	60	4	categorize	categorize	VERB
cana-4753	60	5	knots	knot	NOUN
cana-4753	60	6	at	at	ADP
cana-4753	60	7	communications	communication	NOUN
cana-4753	60	8	on	on	ADP
cana-4753	60	9	applied	apply	VERB
cana-4753	60	10	nonlinear	nonlinear	ADJ
cana-4753	60	11	analysis	analysis	NOUN
cana-4753	60	12	issn	issn	NOUN
cana-4753	60	13	:	:	PUNCT
cana-4753	60	14	1074	1074	NUM
cana-4753	60	15	-	-	PUNCT
cana-4753	60	16	133x	133x	NUM
cana-4753	60	17	vol	vol	VERB
cana-4753	60	18	32	32	NUM
cana-4753	60	19	no	no	NOUN
cana-4753	60	20	.	.	PUNCT
cana-4753	60	21	10s	10	NOUN
cana-4753	60	22	(	(	PUNCT
cana-4753	60	23	2025	2025	NUM
cana-4753	60	24	)	)	PUNCT
cana-4753	60	25	287	287	NUM
cana-4753	60	26	https://internationalpubls.com	https://internationalpubls.com	X
cana-4753	60	27	more	more	ADJ
cana-4753	60	28	than	than	ADP
cana-4753	60	29	one	one	NUM
cana-4753	60	30	level	level	NOUN
cana-4753	60	31	,	,	PUNCT
cana-4753	60	32	which	which	PRON
cana-4753	60	33	will	will	AUX
cana-4753	60	34	be	be	AUX
cana-4753	60	35	more	more	ADV
cana-4753	60	36	effective	effective	ADJ
cana-4753	60	37	at	at	ADP
cana-4753	60	38	distinguishing	distinguish	VERB
cana-4753	60	39	knots	knot	NOUN
cana-4753	60	40	with	with	ADP
cana-4753	60	41	the	the	DET
cana-4753	60	42	same	same	ADJ
cana-4753	60	43	polynomial	polynomial	ADJ
cana-4753	60	44	characteristics	characteristic	NOUN
cana-4753	60	45	than	than	ADP
cana-4753	60	46	classical	classical	ADJ
cana-4753	60	47	polynomial	polynomial	ADJ
cana-4753	60	48	invariants	invariant	NOUN
cana-4753	60	49	.	.	PUNCT
cana-4753	61	1	at	at	ADP
cana-4753	61	2	present	present	ADJ
cana-4753	61	3	,	,	PUNCT
cana-4753	61	4	computational	computational	ADJ
cana-4753	61	5	techniques	technique	NOUN
cana-4753	61	6	have	have	AUX
cana-4753	61	7	increasingly	increasingly	ADV
cana-4753	61	8	become	become	VERB
cana-4753	61	9	important	important	ADJ
cana-4753	61	10	tools	tool	NOUN
cana-4753	61	11	in	in	ADP
cana-4753	61	12	the	the	DET
cana-4753	61	13	advancement	advancement	NOUN
cana-4753	61	14	of	of	ADP
cana-4753	61	15	knot	knot	NOUN
cana-4753	61	16	theory	theory	NOUN
cana-4753	61	17	.	.	PUNCT
cana-4753	62	1	algorithmic	algorithmic	ADJ
cana-4753	62	2	topology	topology	NOUN
cana-4753	62	3	allows	allow	VERB
cana-4753	62	4	for	for	ADP
cana-4753	62	5	the	the	DET
cana-4753	62	6	development	development	NOUN
cana-4753	62	7	of	of	ADP
cana-4753	62	8	automated	automate	VERB
cana-4753	62	9	classification	classification	NOUN
cana-4753	62	10	methods	method	NOUN
cana-4753	62	11	which	which	PRON
cana-4753	62	12	are	be	AUX
cana-4753	62	13	applicable	applicable	ADJ
cana-4753	62	14	to	to	ADP
cana-4753	62	15	large	large	ADJ
cana-4753	62	16	knot	knot	NOUN
cana-4753	62	17	datasets	dataset	NOUN
cana-4753	62	18	.	.	PUNCT
cana-4753	63	1	graph	graph	NOUN
cana-4753	63	2	theoretic	theoretic	ADJ
cana-4753	63	3	approaches	approach	NOUN
cana-4753	63	4	are	be	AUX
cana-4753	63	5	used	use	VERB
cana-4753	63	6	as	as	ADP
cana-4753	63	7	computational	computational	ADJ
cana-4753	63	8	tools	tool	NOUN
cana-4753	63	9	to	to	PART
cana-4753	63	10	represent	represent	VERB
cana-4753	63	11	the	the	DET
cana-4753	63	12	knot	knot	NOUN
cana-4753	63	13	structure	structure	NOUN
cana-4753	63	14	as	as	ADP
cana-4753	63	15	combinatorial	combinatorial	ADJ
cana-4753	63	16	objects	object	NOUN
cana-4753	63	17	which	which	PRON
cana-4753	63	18	may	may	AUX
cana-4753	63	19	be	be	AUX
cana-4753	63	20	efficiently	efficiently	ADV
cana-4753	63	21	manipulated	manipulate	VERB
cana-4753	63	22	and	and	CCONJ
cana-4753	63	23	analyzed	analyze	VERB
cana-4753	63	24	.	.	PUNCT
cana-4753	64	1	furthermore	furthermore	ADV
cana-4753	64	2	,	,	PUNCT
cana-4753	64	3	the	the	DET
cana-4753	64	4	amalgamation	amalgamation	NOUN
cana-4753	64	5	of	of	ADP
cana-4753	64	6	machine	machine	NOUN
cana-4753	64	7	learning	learning	NOUN
cana-4753	64	8	and	and	CCONJ
cana-4753	64	9	artificial	artificial	ADJ
cana-4753	64	10	intelligence	intelligence	NOUN
cana-4753	64	11	to	to	PART
cana-4753	64	12	knot	knot	VERB
cana-4753	64	13	theory	theory	NOUN
cana-4753	64	14	has	have	AUX
cana-4753	64	15	also	also	ADV
cana-4753	64	16	led	lead	VERB
cana-4753	64	17	to	to	ADP
cana-4753	64	18	the	the	DET
cana-4753	64	19	innovation	innovation	NOUN
cana-4753	64	20	of	of	ADP
cana-4753	64	21	novel	novel	ADJ
cana-4753	64	22	methods	method	NOUN
cana-4753	64	23	for	for	ADP
cana-4753	64	24	identifying	identify	VERB
cana-4753	64	25	and	and	CCONJ
cana-4753	64	26	categorizing	categorize	VERB
cana-4753	64	27	knots	knot	NOUN
cana-4753	64	28	in	in	ADP
cana-4753	64	29	terms	term	NOUN
cana-4753	64	30	of	of	ADP
cana-4753	64	31	enormous	enormous	ADJ
cana-4753	64	32	data	datum	NOUN
cana-4753	64	33	driven	drive	VERB
cana-4753	64	34	models	model	NOUN
cana-4753	64	35	.	.	PUNCT
cana-4753	65	1	overall	overall	ADV
cana-4753	65	2	,	,	PUNCT
cana-4753	65	3	these	these	DET
cana-4753	65	4	approaches	approach	NOUN
cana-4753	65	5	provide	provide	VERB
cana-4753	65	6	much	much	ADJ
cana-4753	65	7	improvements	improvement	NOUN
cana-4753	65	8	in	in	ADP
cana-4753	65	9	the	the	DET
cana-4753	65	10	speed	speed	NOUN
cana-4753	65	11	and	and	CCONJ
cana-4753	65	12	accuracy	accuracy	NOUN
cana-4753	65	13	,	,	PUNCT
cana-4753	65	14	particularly	particularly	ADV
cana-4753	65	15	in	in	ADP
cana-4753	65	16	separating	separate	VERB
cana-4753	65	17	out	out	ADP
cana-4753	65	18	knots	knot	NOUN
cana-4753	65	19	with	with	ADP
cana-4753	65	20	high	high	ADJ
cana-4753	65	21	crossing	crossing	NOUN
cana-4753	65	22	numbers	number	NOUN
cana-4753	65	23	.	.	PUNCT
cana-4753	66	1	in	in	ADP
cana-4753	66	2	2012	2012	NUM
cana-4753	66	3	l.	l.	PROPN
cana-4753	66	4	h.	h.	PROPN
cana-4753	66	5	kauffman	kauffman	PROPN
cana-4753	66	6	et.al	et.al	PROPN
cana-4753	66	7	.	.	PUNCT
cana-4753	67	1	[	[	X
cana-4753	67	2	21	21	NUM
cana-4753	67	3	]	]	PUNCT
cana-4753	67	4	introduce	introduce	VERB
cana-4753	67	5	the	the	DET
cana-4753	67	6	theory	theory	NOUN
cana-4753	67	7	of	of	ADP
cana-4753	67	8	knots	knot	NOUN
cana-4753	67	9	has	have	AUX
cana-4753	67	10	proven	prove	VERB
cana-4753	67	11	to	to	PART
cana-4753	67	12	be	be	AUX
cana-4753	67	13	useful	useful	ADJ
cana-4753	67	14	in	in	ADP
cana-4753	67	15	applied	apply	VERB
cana-4753	67	16	sciences	science	NOUN
cana-4753	67	17	such	such	ADJ
cana-4753	67	18	as	as	ADP
cana-4753	67	19	molecular	molecular	ADJ
cana-4753	67	20	biology	biology	NOUN
cana-4753	67	21	,	,	PUNCT
cana-4753	67	22	physics	physics	NOUN
cana-4753	67	23	,	,	PUNCT
cana-4753	67	24	material	material	NOUN
cana-4753	67	25	science	science	NOUN
cana-4753	67	26	,	,	PUNCT
cana-4753	67	27	etc	etc	X
cana-4753	67	28	.	.	X
cana-4753	67	29	study	study	NOUN
cana-4753	67	30	of	of	ADP
cana-4753	67	31	knotted	knotted	ADJ
cana-4753	67	32	dna	dna	NOUN
cana-4753	67	33	and	and	CCONJ
cana-4753	67	34	proteins	protein	NOUN
cana-4753	67	35	in	in	ADP
cana-4753	67	36	biology	biology	NOUN
cana-4753	67	37	has	have	AUX
cana-4753	67	38	shed	shed	VERB
cana-4753	67	39	light	light	NOUN
cana-4753	67	40	on	on	ADP
cana-4753	67	41	behavior	behavior	NOUN
cana-4753	67	42	of	of	ADP
cana-4753	67	43	molecular	molecular	ADJ
cana-4753	67	44	chains	chain	NOUN
cana-4753	67	45	and	and	CCONJ
cana-4753	67	46	on	on	ADP
cana-4753	67	47	their	their	PRON
cana-4753	67	48	functional	functional	ADJ
cana-4753	67	49	properties	property	NOUN
cana-4753	67	50	.	.	PUNCT
cana-4753	68	1	topoisomerases	topoisomerase	NOUN
cana-4753	68	2	,	,	PUNCT
cana-4753	68	3	enzymes	enzyme	VERB
cana-4753	68	4	that	that	PRON
cana-4753	68	5	unsus	unsus	NOUN
cana-4753	68	6	that	that	PRON
cana-4753	68	7	untangle	untangle	VERB
cana-4753	68	8	knotted	knotted	ADJ
cana-4753	68	9	dna	dna	NOUN
cana-4753	68	10	,	,	PUNCT
cana-4753	68	11	work	work	VERB
cana-4753	68	12	deeply	deeply	ADV
cana-4753	68	13	with	with	ADP
cana-4753	68	14	knot	knot	ADJ
cana-4753	68	15	topology	topology	NOUN
cana-4753	68	16	.	.	PUNCT
cana-4753	69	1	in	in	ADP
cana-4753	69	2	a	a	DET
cana-4753	69	3	similar	similar	ADJ
cana-4753	69	4	fashion	fashion	NOUN
cana-4753	69	5	,	,	PUNCT
cana-4753	69	6	in	in	ADP
cana-4753	69	7	polymer	polymer	NOUN
cana-4753	69	8	chemistry	chemistry	NOUN
cana-4753	69	9	,	,	PUNCT
cana-4753	69	10	the	the	DET
cana-4753	69	11	entanglement	entanglement	ADJ
cana-4753	69	12	molecular	molecular	ADJ
cana-4753	69	13	chains	chain	NOUN
cana-4753	69	14	have	have	VERB
cana-4753	69	15	mechanical	mechanical	ADJ
cana-4753	69	16	ramifications	ramification	NOUN
cana-4753	69	17	on	on	ADP
cana-4753	69	18	materials	material	NOUN
cana-4753	69	19	,	,	PUNCT
cana-4753	69	20	which	which	PRON
cana-4753	69	21	is	be	AUX
cana-4753	69	22	used	use	VERB
cana-4753	69	23	for	for	ADP
cana-4753	69	24	the	the	DET
cana-4753	69	25	practical	practical	ADJ
cana-4753	69	26	applications	application	NOUN
cana-4753	69	27	in	in	ADP
cana-4753	69	28	the	the	DET
cana-4753	69	29	design	design	NOUN
cana-4753	69	30	of	of	ADP
cana-4753	69	31	new	new	ADJ
cana-4753	69	32	synthetic	synthetic	ADJ
cana-4753	69	33	polymers	polymer	NOUN
cana-4753	69	34	.	.	PUNCT
cana-4753	70	1	in	in	ADP
cana-4753	70	2	2020	2020	NUM
cana-4753	71	1	v.	v.	ADP
cana-4753	71	2	p.	p.	NOUN
cana-4753	71	3	patil	patil	PROPN
cana-4753	71	4	et.al	et.al	PROPN
cana-4753	71	5	.	.	PROPN
cana-4753	71	6	,	,	PUNCT
cana-4753	71	7	j.	j.	PROPN
cana-4753	71	8	dunkel	dunkel	PROPN
cana-4753	71	9	et.al	et.al	PROPN
cana-4753	71	10	.	.	PROPN
cana-4753	71	11	,	,	PUNCT
cana-4753	71	12	j.	j.	PROPN
cana-4753	71	13	d.	d.	PROPN
cana-4753	71	14	sandt	sandt	PROPN
cana-4753	71	15	et.al	et.al	PROPN
cana-4753	71	16	.	.	PROPN
cana-4753	71	17	,	,	PUNCT
cana-4753	71	18	and	and	CCONJ
cana-4753	71	19	m.	m.	NOUN
cana-4753	71	20	kolle	kolle	PROPN
cana-4753	71	21	et.al	et.al	PROPN
cana-4753	71	22	.	.	PUNCT
cana-4753	72	1	[	[	X
cana-4753	72	2	1	1	X
cana-4753	72	3	]	]	PUNCT
cana-4753	72	4	introduce	introduce	VERB
cana-4753	72	5	the	the	DET
cana-4753	72	6	knotted	knotted	ADJ
cana-4753	72	7	structures	structure	NOUN
cana-4753	72	8	are	be	AUX
cana-4753	72	9	encountered	encounter	VERB
cana-4753	72	10	in	in	ADP
cana-4753	72	11	models	model	NOUN
cana-4753	72	12	for	for	ADP
cana-4753	72	13	polymer	polymer	NOUN
cana-4753	72	14	system	system	NOUN
cana-4753	72	15	and	and	CCONJ
cana-4753	72	16	vortex	vortex	NOUN
cana-4753	72	17	dynamics	dynamic	NOUN
cana-4753	72	18	in	in	ADP
cana-4753	72	19	statistical	statistical	ADJ
cana-4753	72	20	mechanics	mechanic	NOUN
cana-4753	72	21	.	.	PUNCT
cana-4753	73	1	in	in	ADP
cana-4753	73	2	this	this	DET
cana-4753	73	3	context	context	NOUN
cana-4753	73	4	of	of	ADP
cana-4753	73	5	quantum	quantum	ADJ
cana-4753	73	6	computation	computation	NOUN
cana-4753	73	7	,	,	PUNCT
cana-4753	73	8	the	the	DET
cana-4753	73	9	use	use	NOUN
cana-4753	73	10	of	of	ADP
cana-4753	73	11	knot	knot	ADJ
cana-4753	73	12	invariants	invariant	NOUN
cana-4753	73	13	to	to	PART
cana-4753	73	14	encode	encode	VERB
cana-4753	73	15	and	and	CCONJ
cana-4753	73	16	process	process	VERB
cana-4753	73	17	quantum	quantum	ADJ
cana-4753	73	18	information	information	NOUN
cana-4753	73	19	in	in	ADP
cana-4753	73	20	a	a	DET
cana-4753	73	21	fault	fault	NOUN
cana-4753	73	22	tolerant	tolerant	ADJ
cana-4753	73	23	manner	manner	NOUN
cana-4753	73	24	is	be	AUX
cana-4753	73	25	known	know	VERB
cana-4753	73	26	as	as	ADP
cana-4753	73	27	topological	topological	ADJ
cana-4753	73	28	quantum	quantum	ADJ
cana-4753	73	29	computation	computation	NOUN
cana-4753	73	30	.	.	PUNCT
cana-4753	74	1	this	this	PRON
cana-4753	74	2	has	have	AUX
cana-4753	74	3	developed	develop	VERB
cana-4753	74	4	the	the	DET
cana-4753	74	5	study	study	NOUN
cana-4753	74	6	of	of	ADP
cana-4753	74	7	higher	high	ADJ
cana-4753	74	8	dimensional	dimensional	ADJ
cana-4753	74	9	knots	knot	NOUN
cana-4753	74	10	:	:	PUNCT
cana-4753	74	11	knotted	knotted	ADJ
cana-4753	74	12	surfaces	surface	NOUN
cana-4753	74	13	in	in	ADP
cana-4753	74	14	four	four	NUM
cana-4753	74	15	dimensional	dimensional	ADJ
cana-4753	74	16	space	space	NOUN
cana-4753	74	17	,	,	PUNCT
cana-4753	74	18	and	and	CCONJ
cana-4753	74	19	so	so	ADV
cana-4753	74	20	on	on	ADV
cana-4753	74	21	,	,	PUNCT
cana-4753	74	22	into	into	ADP
cana-4753	74	23	an	an	DET
cana-4753	74	24	area	area	NOUN
cana-4753	74	25	of	of	ADP
cana-4753	74	26	theoretical	theoretical	ADJ
cana-4753	74	27	physics	physics	NOUN
cana-4753	74	28	.	.	PUNCT
cana-4753	75	1	nevertheless	nevertheless	ADV
cana-4753	75	2	,	,	PUNCT
cana-4753	75	3	there	there	PRON
cana-4753	75	4	are	be	VERB
cana-4753	75	5	still	still	ADV
cana-4753	75	6	some	some	DET
cana-4753	75	7	open	open	ADJ
cana-4753	75	8	problems	problem	NOUN
cana-4753	75	9	in	in	ADP
cana-4753	75	10	knot	knot	NOUN
cana-4753	75	11	theory	theory	NOUN
cana-4753	75	12	.	.	PUNCT
cana-4753	76	1	on	on	ADP
cana-4753	76	2	the	the	DET
cana-4753	76	3	other	other	ADJ
cana-4753	76	4	hand	hand	NOUN
cana-4753	76	5	,	,	PUNCT
cana-4753	76	6	despite	despite	SCONJ
cana-4753	76	7	the	the	DET
cana-4753	76	8	fact	fact	NOUN
cana-4753	76	9	that	that	SCONJ
cana-4753	76	10	it	it	PRON
cana-4753	76	11	increases	increase	VERB
cana-4753	76	12	exponentially	exponentially	ADV
cana-4753	76	13	with	with	ADP
cana-4753	76	14	the	the	DET
cana-4753	76	15	number	number	NOUN
cana-4753	76	16	of	of	ADP
cana-4753	76	17	crossings	crossing	NOUN
cana-4753	76	18	,	,	PUNCT
cana-4753	76	19	the	the	DET
cana-4753	76	20	computational	computational	ADJ
cana-4753	76	21	complexity	complexity	NOUN
cana-4753	76	22	of	of	ADP
cana-4753	76	23	classifying	classify	VERB
cana-4753	76	24	knots	knot	NOUN
cana-4753	76	25	makes	make	VERB
cana-4753	76	26	it	it	PRON
cana-4753	76	27	glance	glance	VERB
cana-4753	76	28	for	for	ADP
cana-4753	76	29	computing	compute	VERB
cana-4753	76	30	methods	method	NOUN
cana-4753	76	31	that	that	PRON
cana-4753	76	32	permit	permit	VERB
cana-4753	76	33	far	far	ADJ
cana-4753	76	34	classification	classification	NOUN
cana-4753	76	35	of	of	ADP
cana-4753	76	36	large	large	ADJ
cana-4753	76	37	scale	scale	NOUN
cana-4753	76	38	.	.	PUNCT
cana-4753	77	1	furthermore	furthermore	ADV
cana-4753	77	2	,	,	PUNCT
cana-4753	77	3	such	such	ADJ
cana-4753	77	4	refinement	refinement	NOUN
cana-4753	77	5	of	of	ADP
cana-4753	77	6	distinction	distinction	NOUN
cana-4753	77	7	in	in	ADP
cana-4753	77	8	knot	knot	ADJ
cana-4753	77	9	invariants	invariant	NOUN
cana-4753	77	10	has	have	AUX
cana-4753	77	11	been	be	AUX
cana-4753	77	12	done	do	VERB
cana-4753	77	13	by	by	ADP
cana-4753	77	14	using	use	VERB
cana-4753	77	15	polynomial	polynomial	ADJ
cana-4753	77	16	and	and	CCONJ
cana-4753	77	17	homology	homology	NOUN
cana-4753	77	18	based	base	VERB
cana-4753	77	19	invariants	invariant	NOUN
cana-4753	77	20	,	,	PUNCT
cana-4753	77	21	but	but	CCONJ
cana-4753	77	22	new	new	ADJ
cana-4753	77	23	invariants	invariant	NOUN
cana-4753	77	24	are	be	AUX
cana-4753	77	25	needed	need	VERB
cana-4753	77	26	to	to	PART
cana-4753	77	27	see	see	VERB
cana-4753	77	28	finer	fine	ADJ
cana-4753	77	29	topological	topological	ADJ
cana-4753	77	30	details	detail	NOUN
cana-4753	77	31	.	.	PUNCT
cana-4753	78	1	there	there	PRON
cana-4753	78	2	is	be	VERB
cana-4753	78	3	still	still	ADV
cana-4753	78	4	active	active	ADJ
cana-4753	78	5	research	research	NOUN
cana-4753	78	6	on	on	ADP
cana-4753	78	7	integrating	integrate	VERB
cana-4753	78	8	current	current	ADJ
cana-4753	78	9	computational	computational	ADJ
cana-4753	78	10	tools	tool	NOUN
cana-4753	78	11	with	with	ADP
cana-4753	78	12	methods	method	NOUN
cana-4753	78	13	from	from	ADP
cana-4753	78	14	the	the	DET
cana-4753	78	15	topological	topological	ADJ
cana-4753	78	16	side	side	NOUN
cana-4753	78	17	and	and	CCONJ
cana-4753	78	18	this	this	PRON
cana-4753	78	19	is	be	AUX
cana-4753	78	20	where	where	SCONJ
cana-4753	78	21	progress	progress	NOUN
cana-4753	78	22	is	be	AUX
cana-4753	78	23	being	be	AUX
cana-4753	78	24	made	make	VERB
cana-4753	78	25	not	not	PART
cana-4753	78	26	only	only	ADV
cana-4753	78	27	in	in	ADP
cana-4753	78	28	theoretical	theoretical	ADJ
cana-4753	78	29	knot	knot	NOUN
cana-4753	78	30	theory	theory	NOUN
cana-4753	78	31	,	,	PUNCT
cana-4753	78	32	but	but	CCONJ
cana-4753	78	33	also	also	ADV
cana-4753	78	34	in	in	ADP
cana-4753	78	35	applied	applied	ADJ
cana-4753	78	36	knot	knot	NOUN
cana-4753	78	37	theory	theory	NOUN
cana-4753	78	38	.	.	PUNCT
cana-4753	79	1	existing	exist	VERB
cana-4753	79	2	literature	literature	NOUN
cana-4753	79	3	is	be	AUX
cana-4753	79	4	extended	extend	VERB
cana-4753	79	5	on	on	ADP
cana-4753	79	6	the	the	DET
cana-4753	79	7	relationship	relationship	NOUN
cana-4753	79	8	between	between	ADP
cana-4753	79	9	topology	topology	NOUN
cana-4753	79	10	based	base	VERB
cana-4753	79	11	methods	method	NOUN
cana-4753	79	12	and	and	CCONJ
cana-4753	79	13	computational	computational	ADJ
cana-4753	79	14	progress	progress	NOUN
cana-4753	79	15	in	in	ADP
cana-4753	79	16	resolving	resolve	VERB
cana-4753	79	17	the	the	DET
cana-4753	79	18	rpc	rpc	NOUN
cana-4753	79	19	problem	problem	NOUN
cana-4753	79	20	.	.	PUNCT
cana-4753	80	1	my	my	PRON
cana-4753	80	2	emphasis	emphasis	NOUN
cana-4753	80	3	is	be	AUX
cana-4753	80	4	on	on	ADP
cana-4753	80	5	seeking	seek	VERB
cana-4753	80	6	to	to	PART
cana-4753	80	7	increase	increase	VERB
cana-4753	80	8	the	the	DET
cana-4753	80	9	knowledge	knowledge	NOUN
cana-4753	80	10	of	of	ADP
cana-4753	80	11	how	how	SCONJ
cana-4753	80	12	mathematical	mathematical	ADJ
cana-4753	80	13	and	and	CCONJ
cana-4753	80	14	algorithmic	algorithmic	ADJ
cana-4753	80	15	methods	method	NOUN
cana-4753	80	16	drawn	draw	VERB
cana-4753	80	17	from	from	ADP
cana-4753	80	18	computer	computer	NOUN
cana-4753	80	19	science	science	NOUN
cana-4753	80	20	can	can	AUX
cana-4753	80	21	work	work	VERB
cana-4753	80	22	together	together	ADV
cana-4753	80	23	to	to	PART
cana-4753	80	24	improve	improve	VERB
cana-4753	80	25	knot	knot	VERB
cana-4753	80	26	classification	classification	NOUN
cana-4753	80	27	and	and	CCONJ
cana-4753	80	28	analysis	analysis	NOUN
cana-4753	80	29	.	.	PUNCT
cana-4753	81	1	iii	iii	X
cana-4753	81	2	.	.	PROPN
cana-4753	81	3	proposed	propose	VERB
cana-4753	81	4	methodology	methodology	NOUN
cana-4753	81	5	the	the	DET
cana-4753	81	6	proposed	propose	VERB
cana-4753	81	7	methodology	methodology	NOUN
cana-4753	81	8	aims	aim	VERB
cana-4753	81	9	to	to	PART
cana-4753	81	10	analyze	analyze	VERB
cana-4753	81	11	knotted	knotted	ADJ
cana-4753	81	12	structures	structure	NOUN
cana-4753	81	13	using	use	VERB
cana-4753	81	14	topological	topological	ADJ
cana-4753	81	15	methods	method	NOUN
cana-4753	81	16	,	,	PUNCT
cana-4753	81	17	computational	computational	ADJ
cana-4753	81	18	algorithms	algorithm	NOUN
cana-4753	81	19	,	,	PUNCT
cana-4753	81	20	and	and	CCONJ
cana-4753	81	21	mathematical	mathematical	ADJ
cana-4753	81	22	modeling	modeling	NOUN
cana-4753	81	23	.	.	PUNCT
cana-4753	82	1	the	the	DET
cana-4753	82	2	approach	approach	NOUN
cana-4753	82	3	consists	consist	VERB
cana-4753	82	4	of	of	ADP
cana-4753	82	5	multiple	multiple	ADJ
cana-4753	82	6	stages	stage	NOUN
cana-4753	82	7	,	,	PUNCT
cana-4753	82	8	including	include	VERB
cana-4753	82	9	knot	knot	NOUN
cana-4753	82	10	representation	representation	NOUN
cana-4753	82	11	,	,	PUNCT
cana-4753	82	12	invariant	invariant	ADJ
cana-4753	82	13	computation	computation	NOUN
cana-4753	82	14	,	,	PUNCT
cana-4753	82	15	classification	classification	NOUN
cana-4753	82	16	,	,	PUNCT
cana-4753	82	17	and	and	CCONJ
cana-4753	82	18	application	application	NOUN
cana-4753	82	19	-	-	PUNCT
cana-4753	82	20	based	base	VERB
cana-4753	82	21	validation	validation	NOUN
cana-4753	82	22	.	.	PUNCT
cana-4753	83	1	by	by	ADP
cana-4753	83	2	integrating	integrate	VERB
cana-4753	83	3	polynomial	polynomial	ADJ
cana-4753	83	4	invariants	invariant	NOUN
cana-4753	83	5	,	,	PUNCT
cana-4753	83	6	homology	homology	NOUN
cana-4753	83	7	theories	theory	NOUN
cana-4753	83	8	,	,	PUNCT
cana-4753	83	9	and	and	CCONJ
cana-4753	83	10	machine	machine	NOUN
cana-4753	83	11	learning	learn	VERB
cana-4753	83	12	techniques	technique	NOUN
cana-4753	83	13	,	,	PUNCT
cana-4753	83	14	this	this	DET
cana-4753	83	15	methodology	methodology	NOUN
cana-4753	83	16	provides	provide	VERB
cana-4753	83	17	a	a	DET
cana-4753	83	18	robust	robust	ADJ
cana-4753	83	19	framework	framework	NOUN
cana-4753	83	20	for	for	ADP
cana-4753	83	21	understanding	understand	VERB
cana-4753	83	22	the	the	DET
cana-4753	83	23	complexities	complexity	NOUN
cana-4753	83	24	of	of	ADP
cana-4753	83	25	knots	knot	NOUN
cana-4753	83	26	[	[	X
cana-4753	83	27	17	17	NUM
cana-4753	83	28	-	-	SYM
cana-4753	83	29	18	18	NUM
cana-4753	83	30	]	]	PUNCT
cana-4753	83	31	.	.	PUNCT
cana-4753	84	1	communications	communication	NOUN
cana-4753	84	2	on	on	ADP
cana-4753	84	3	applied	apply	VERB
cana-4753	84	4	nonlinear	nonlinear	ADJ
cana-4753	84	5	analysis	analysis	NOUN
cana-4753	84	6	issn	issn	NOUN
cana-4753	84	7	:	:	PUNCT
cana-4753	84	8	1074	1074	NUM
cana-4753	84	9	-	-	PUNCT
cana-4753	84	10	133x	133x	NUM
cana-4753	84	11	vol	vol	VERB
cana-4753	84	12	32	32	NUM
cana-4753	84	13	no	no	NOUN
cana-4753	84	14	.	.	PUNCT
cana-4753	85	1	10s	10	NOUN
cana-4753	85	2	(	(	PUNCT
cana-4753	85	3	2025	2025	NUM
cana-4753	85	4	)	)	PUNCT
cana-4753	85	5	288	288	NUM
cana-4753	85	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4753	85	7	a.	a.	NOUN
cana-4753	85	8	knot	knot	NOUN
cana-4753	85	9	representation	representation	NOUN
cana-4753	85	10	and	and	CCONJ
cana-4753	85	11	preprocessing	preprocessing	NOUN
cana-4753	85	12	knot	knot	NOUN
cana-4753	85	13	representation	representation	NOUN
cana-4753	85	14	plays	play	VERB
cana-4753	85	15	a	a	DET
cana-4753	85	16	crucial	crucial	ADJ
cana-4753	85	17	role	role	NOUN
cana-4753	85	18	in	in	ADP
cana-4753	85	19	analyzing	analyze	VERB
cana-4753	85	20	topological	topological	ADJ
cana-4753	85	21	structures	structure	NOUN
cana-4753	85	22	.	.	PUNCT
cana-4753	86	1	a	a	DET
cana-4753	86	2	knot	knot	NOUN
cana-4753	86	3	can	can	AUX
cana-4753	86	4	be	be	AUX
cana-4753	86	5	expressed	express	VERB
cana-4753	86	6	mathematically	mathematically	ADV
cana-4753	86	7	as	as	ADP
cana-4753	86	8	a	a	DET
cana-4753	86	9	parametric	parametric	ADJ
cana-4753	86	10	function	function	NOUN
cana-4753	86	11	mapping	map	VERB
cana-4753	86	12	a	a	DET
cana-4753	86	13	unit	unit	NOUN
cana-4753	86	14	interval	interval	NOUN
cana-4753	86	15	to	to	ADP
cana-4753	86	16	three	three	NUM
cana-4753	86	17	-	-	PUNCT
cana-4753	86	18	dimensional	dimensional	ADJ
cana-4753	86	19	euclidean	euclidean	ADJ
cana-4753	86	20	space	space	NOUN
cana-4753	86	21	:	:	PUNCT
cana-4753	86	22	𝐾	𝐾	NOUN
cana-4753	86	23	:	:	PUNCT
cana-4753	87	1	[	[	X
cana-4753	87	2	0,1	0,1	NUM
cana-4753	87	3	]	]	PUNCT
cana-4753	87	4	→	→	SYM
cana-4753	87	5	ℝ3	ℝ3	PROPN
cana-4753	87	6	,	,	PUNCT
cana-4753	87	7	𝐾(0	𝐾(0	NUM
cana-4753	87	8	)	)	PUNCT
cana-4753	87	9	=	=	SYM
cana-4753	87	10	𝐾(1	𝐾(1	X
cana-4753	87	11	)	)	PUNCT
cana-4753	87	12	where	where	SCONJ
cana-4753	87	13	𝐾(𝑡	𝐾(𝑡	NUM
cana-4753	87	14	)	)	PUNCT
cana-4753	87	15	represents	represent	VERB
cana-4753	87	16	the	the	DET
cana-4753	87	17	curve	curve	NOUN
cana-4753	87	18	of	of	ADP
cana-4753	87	19	the	the	DET
cana-4753	87	20	knot	knot	NOUN
cana-4753	87	21	in	in	ADP
cana-4753	87	22	three	three	NUM
cana-4753	87	23	-	-	PUNCT
cana-4753	87	24	dimensional	dimensional	ADJ
cana-4753	87	25	space	space	NOUN
cana-4753	87	26	.	.	PUNCT
cana-4753	88	1	to	to	PART
cana-4753	88	2	ensure	ensure	VERB
cana-4753	88	3	topological	topological	ADJ
cana-4753	88	4	equivalence	equivalence	NOUN
cana-4753	88	5	,	,	PUNCT
cana-4753	88	6	knots	knot	NOUN
cana-4753	88	7	are	be	AUX
cana-4753	88	8	represented	represent	VERB
cana-4753	88	9	using	use	VERB
cana-4753	88	10	knot	knot	NOUN
cana-4753	88	11	diagrams	diagram	NOUN
cana-4753	88	12	,	,	PUNCT
cana-4753	88	13	which	which	PRON
cana-4753	88	14	are	be	AUX
cana-4753	88	15	planar	planar	ADJ
cana-4753	88	16	projections	projection	NOUN
cana-4753	88	17	that	that	PRON
cana-4753	88	18	capture	capture	VERB
cana-4753	88	19	overcrossing	overcrosse	VERB
cana-4753	88	20	and	and	CCONJ
cana-4753	88	21	undercrossing	undercrosse	VERB
cana-4753	88	22	information	information	NOUN
cana-4753	88	23	.	.	PUNCT
cana-4753	89	1	the	the	DET
cana-4753	89	2	gauss	gauss	PROPN
cana-4753	89	3	code	code	PROPN
cana-4753	89	4	is	be	AUX
cana-4753	89	5	another	another	DET
cana-4753	89	6	method	method	NOUN
cana-4753	89	7	used	use	VERB
cana-4753	89	8	to	to	PART
cana-4753	89	9	encode	encode	VERB
cana-4753	89	10	crossings	crossing	NOUN
cana-4753	89	11	numerically	numerically	ADV
cana-4753	89	12	,	,	PUNCT
cana-4753	89	13	allowing	allow	VERB
cana-4753	89	14	for	for	ADP
cana-4753	89	15	efficient	efficient	ADJ
cana-4753	89	16	computational	computational	ADJ
cana-4753	89	17	processing	processing	NOUN
cana-4753	89	18	.	.	PUNCT
cana-4753	90	1	given	give	VERB
cana-4753	90	2	a	a	DET
cana-4753	90	3	set	set	NOUN
cana-4753	90	4	of	of	ADP
cana-4753	90	5	knot	knot	ADJ
cana-4753	90	6	diagrams	diagram	NOUN
cana-4753	90	7	,	,	PUNCT
cana-4753	90	8	the	the	DET
cana-4753	90	9	reidemeister	reidemeister	ADJ
cana-4753	90	10	moves	move	NOUN
cana-4753	90	11	are	be	AUX
cana-4753	90	12	applied	apply	VERB
cana-4753	90	13	to	to	PART
cana-4753	90	14	simplify	simplify	VERB
cana-4753	90	15	the	the	DET
cana-4753	90	16	representation	representation	NOUN
cana-4753	90	17	while	while	SCONJ
cana-4753	90	18	preserving	preserve	VERB
cana-4753	90	19	the	the	DET
cana-4753	90	20	fundamental	fundamental	ADJ
cana-4753	90	21	knot	knot	NOUN
cana-4753	90	22	structure	structure	NOUN
cana-4753	90	23	.	.	PUNCT
cana-4753	91	1	the	the	DET
cana-4753	91	2	three	three	NUM
cana-4753	91	3	reidemeister	reidemeister	ADJ
cana-4753	91	4	moves	move	NOUN
cana-4753	91	5	are	be	AUX
cana-4753	91	6	mathematically	mathematically	ADV
cana-4753	91	7	defined	define	VERB
cana-4753	91	8	as	as	ADP
cana-4753	91	9	:	:	PUNCT
cana-4753	91	10	1	1	X
cana-4753	91	11	.	.	X
cana-4753	91	12	type	type	NOUN
cana-4753	91	13	i	i	PRON
cana-4753	91	14	move	move	VERB
cana-4753	91	15	:	:	PUNCT
cana-4753	91	16	introducing	introduce	VERB
cana-4753	91	17	or	or	CCONJ
cana-4753	91	18	removing	remove	VERB
cana-4753	91	19	a	a	DET
cana-4753	91	20	loop	loop	NOUN
cana-4753	91	21	:	:	PUNCT
cana-4753	91	22	𝐾	𝐾	NOUN
cana-4753	91	23	∼	∼	NOUN
cana-4753	91	24	𝐾′	𝐾′	NOUN
cana-4753	91	25	2	2	NUM
cana-4753	91	26	.	.	PUNCT
cana-4753	91	27	type	type	NOUN
cana-4753	91	28	ii	ii	PROPN
cana-4753	91	29	move	move	NOUN
cana-4753	91	30	:	:	PUNCT
cana-4753	91	31	switching	switch	VERB
cana-4753	91	32	adjacent	adjacent	ADJ
cana-4753	91	33	crossings	crossing	NOUN
cana-4753	91	34	:	:	PUNCT
cana-4753	91	35	𝐾𝑖,𝑗	𝐾𝑖,𝑗	PROPN
cana-4753	91	36	∼	∼	NOUN
cana-4753	91	37	𝐾𝑗,𝑖	𝐾𝑗,𝑖	PROPN
cana-4753	91	38	3	3	NUM
cana-4753	91	39	.	.	PUNCT
cana-4753	91	40	type	type	NOUN
cana-4753	91	41	iii	iii	NUM
cana-4753	91	42	move	move	NOUN
cana-4753	91	43	:	:	PUNCT
cana-4753	91	44	sliding	slide	VERB
cana-4753	91	45	a	a	DET
cana-4753	91	46	strand	strand	NOUN
cana-4753	91	47	over	over	ADP
cana-4753	91	48	another	another	PRON
cana-4753	91	49	:	:	PUNCT
cana-4753	91	50	𝐾𝑖,𝑗,𝑘	𝐾𝑖,𝑗,𝑘	NOUN
cana-4753	91	51	∼	∼	NOUN
cana-4753	91	52	𝐾𝑘,𝑖,𝑗	𝐾𝑘,𝑖,𝑗	VERB
cana-4753	91	53	where	where	SCONJ
cana-4753	91	54	𝐾𝑖,𝑗,𝑘	𝐾𝑖,𝑗,𝑘	PROPN
cana-4753	91	55	denotes	denote	VERB
cana-4753	91	56	a	a	DET
cana-4753	91	57	set	set	NOUN
cana-4753	91	58	of	of	ADP
cana-4753	91	59	crossings	crossing	NOUN
cana-4753	91	60	involving	involve	VERB
cana-4753	91	61	three	three	NUM
cana-4753	91	62	strands	strand	NOUN
cana-4753	91	63	.	.	PUNCT
cana-4753	92	1	these	these	DET
cana-4753	92	2	transformations	transformation	NOUN
cana-4753	92	3	ensure	ensure	VERB
cana-4753	92	4	that	that	SCONJ
cana-4753	92	5	equivalent	equivalent	ADJ
cana-4753	92	6	knots	knot	NOUN
cana-4753	92	7	can	can	AUX
cana-4753	92	8	be	be	AUX
cana-4753	92	9	analyzed	analyze	VERB
cana-4753	92	10	in	in	ADP
cana-4753	92	11	a	a	DET
cana-4753	92	12	unified	unified	ADJ
cana-4753	92	13	framework	framework	NOUN
cana-4753	92	14	.	.	PUNCT
cana-4753	93	1	b.	b.	PROPN
cana-4753	93	2	computation	computation	NOUN
cana-4753	93	3	of	of	ADP
cana-4753	93	4	knot	knot	NOUN
cana-4753	93	5	invariants	invariant	NOUN
cana-4753	93	6	to	to	PART
cana-4753	93	7	classify	classify	VERB
cana-4753	93	8	knots	knot	NOUN
cana-4753	93	9	,	,	PUNCT
cana-4753	93	10	polynomial	polynomial	ADJ
cana-4753	93	11	invariants	invariant	NOUN
cana-4753	93	12	are	be	AUX
cana-4753	93	13	computed	compute	VERB
cana-4753	93	14	.	.	PUNCT
cana-4753	94	1	the	the	DET
cana-4753	94	2	alexander	alexander	PROPN
cana-4753	94	3	polynomial	polynomial	PROPN
cana-4753	94	4	,	,	PUNCT
cana-4753	94	5	a	a	DET
cana-4753	94	6	fundamental	fundamental	ADJ
cana-4753	94	7	invariant	invariant	ADJ
cana-4753	94	8	,	,	PUNCT
cana-4753	94	9	is	be	AUX
cana-4753	94	10	defined	define	VERB
cana-4753	94	11	as	as	ADP
cana-4753	94	12	:	:	PUNCT
cana-4753	94	13	δ𝐾(𝑡	δ𝐾(𝑡	NUM
cana-4753	94	14	)	)	PUNCT
cana-4753	94	15	=	=	SYM
cana-4753	94	16	det(𝑉	det(𝑉	PROPN
cana-4753	94	17	−	−	NOUN
cana-4753	94	18	𝑡𝑉𝑇	𝑡𝑉𝑇	NOUN
cana-4753	94	19	)	)	PUNCT
cana-4753	94	20	where	where	SCONJ
cana-4753	94	21	𝑉	𝑉	PROPN
cana-4753	94	22	is	be	AUX
cana-4753	94	23	the	the	DET
cana-4753	94	24	seifert	seifert	NOUN
cana-4753	94	25	matrix	matrix	NOUN
cana-4753	94	26	obtained	obtain	VERB
cana-4753	94	27	from	from	ADP
cana-4753	94	28	the	the	DET
cana-4753	94	29	knot	knot	NOUN
cana-4753	94	30	diagram	diagram	NOUN
cana-4753	94	31	.	.	PUNCT
cana-4753	95	1	similarly	similarly	ADV
cana-4753	95	2	,	,	PUNCT
cana-4753	95	3	the	the	DET
cana-4753	95	4	jones	jones	PROPN
cana-4753	95	5	polynomial	polynomial	PROPN
cana-4753	95	6	is	be	AUX
cana-4753	95	7	computed	compute	VERB
cana-4753	95	8	recursively	recursively	ADV
cana-4753	95	9	using	use	VERB
cana-4753	95	10	the	the	DET
cana-4753	95	11	skein	skein	NOUN
cana-4753	95	12	relation	relation	NOUN
cana-4753	95	13	:	:	PUNCT
cana-4753	95	14	𝑉𝐾(𝑡	𝑉𝐾(𝑡	X
cana-4753	95	15	)	)	PUNCT
cana-4753	96	1	−	−	PRON
cana-4753	96	2	𝑡𝑉𝐾∣(𝑡	𝑡𝑉𝐾∣(𝑡	NOUN
cana-4753	96	3	)	)	PUNCT
cana-4753	96	4	−	−	NOUN
cana-4753	96	5	𝑡−1𝑉𝐾−(𝑡	𝑡−1𝑉𝐾−(𝑡	NUM
cana-4753	96	6	)	)	PUNCT
cana-4753	96	7	=	=	SYM
cana-4753	96	8	0	0	NUM
cana-4753	96	9	where	where	SCONJ
cana-4753	96	10	𝐾	𝐾	PROPN
cana-4753	96	11	,	,	PUNCT
cana-4753	96	12	𝐾+	𝐾+	NOUN
cana-4753	96	13	,	,	PUNCT
cana-4753	96	14	𝐾−denote	𝐾−denote	PUNCT
cana-4753	96	15	different	different	ADJ
cana-4753	96	16	resolutions	resolution	NOUN
cana-4753	96	17	of	of	ADP
cana-4753	96	18	the	the	DET
cana-4753	96	19	crossing	crossing	NOUN
cana-4753	96	20	in	in	ADP
cana-4753	96	21	the	the	DET
cana-4753	96	22	knot	knot	NOUN
cana-4753	96	23	diagram	diagram	NOUN
cana-4753	96	24	.	.	PUNCT
cana-4753	97	1	the	the	DET
cana-4753	97	2	homfly	homfly	PROPN
cana-4753	97	3	polynomial	polynomial	ADJ
cana-4753	97	4	,	,	PUNCT
cana-4753	97	5	a	a	DET
cana-4753	97	6	generalization	generalization	NOUN
cana-4753	97	7	of	of	ADP
cana-4753	97	8	both	both	CCONJ
cana-4753	97	9	alexander	alexander	PROPN
cana-4753	97	10	and	and	CCONJ
cana-4753	97	11	jones	jones	PROPN
cana-4753	97	12	polynomials	polynomial	NOUN
cana-4753	97	13	,	,	PUNCT
cana-4753	97	14	is	be	AUX
cana-4753	97	15	expressed	express	VERB
cana-4753	97	16	as	as	ADP
cana-4753	97	17	:	:	PUNCT
cana-4753	97	18	𝑙𝑃𝐿(𝑎	𝑙𝑃𝐿(𝑎	NUM
cana-4753	97	19	,	,	PUNCT
cana-4753	97	20	𝑧	𝑧	NOUN
cana-4753	97	21	)	)	PUNCT
cana-4753	97	22	+	+	CCONJ
cana-4753	97	23	𝑧𝑃𝐿+	𝑧𝑃𝐿+	ADV
cana-4753	97	24	(	(	PUNCT
cana-4753	97	25	𝑎	𝑎	X
cana-4753	97	26	,	,	PUNCT
cana-4753	97	27	𝑧	𝑧	NOUN
cana-4753	97	28	)	)	PUNCT
cana-4753	98	1	+	+	CCONJ
cana-4753	98	2	𝑧−1𝑃𝐿−	𝑧−1𝑃𝐿−	X
cana-4753	98	3	(	(	PUNCT
cana-4753	98	4	𝑎	𝑎	X
cana-4753	98	5	,	,	PUNCT
cana-4753	98	6	𝑧	𝑧	NOUN
cana-4753	98	7	)	)	PUNCT
cana-4753	98	8	=	=	SYM
cana-4753	98	9	0	0	NUM
cana-4753	98	10	where	where	SCONJ
cana-4753	98	11	𝑃𝐿(𝑎	𝑃𝐿(𝑎	PROPN
cana-4753	98	12	,	,	PUNCT
cana-4753	98	13	𝑧	𝑧	PRON
cana-4753	98	14	)	)	PUNCT
cana-4753	98	15	is	be	AUX
cana-4753	98	16	the	the	DET
cana-4753	98	17	polynomial	polynomial	ADJ
cana-4753	98	18	associated	associate	VERB
cana-4753	98	19	with	with	ADP
cana-4753	98	20	the	the	DET
cana-4753	98	21	knot	knot	NOUN
cana-4753	98	22	𝐿.	𝐿.	VERB
cana-4753	98	23	these	these	DET
cana-4753	98	24	polynomials	polynomial	NOUN
cana-4753	98	25	help	help	AUX
cana-4753	98	26	distinguish	distinguish	VERB
cana-4753	98	27	different	different	ADJ
cana-4753	98	28	knot	knot	NOUN
cana-4753	98	29	types	type	NOUN
cana-4753	98	30	efficiently	efficiently	ADV
cana-4753	98	31	.	.	PUNCT
cana-4753	99	1	communications	communication	NOUN
cana-4753	99	2	on	on	ADP
cana-4753	99	3	applied	apply	VERB
cana-4753	99	4	nonlinear	nonlinear	ADJ
cana-4753	99	5	analysis	analysis	NOUN
cana-4753	99	6	issn	issn	NOUN
cana-4753	99	7	:	:	PUNCT
cana-4753	99	8	1074	1074	NUM
cana-4753	99	9	-	-	PUNCT
cana-4753	99	10	133x	133x	NUM
cana-4753	99	11	vol	vol	VERB
cana-4753	99	12	32	32	NUM
cana-4753	99	13	no	no	NOUN
cana-4753	99	14	.	.	PUNCT
cana-4753	100	1	10s	10	NOUN
cana-4753	100	2	(	(	PUNCT
cana-4753	100	3	2025	2025	NUM
cana-4753	100	4	)	)	PUNCT
cana-4753	100	5	289	289	NUM
cana-4753	100	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4753	100	7	c.	c.	PROPN
cana-4753	100	8	homology	homology	NOUN
cana-4753	100	9	-	-	PUNCT
cana-4753	100	10	based	base	VERB
cana-4753	100	11	classification	classification	NOUN
cana-4753	100	12	polynomial	polynomial	ADJ
cana-4753	100	13	invariants	invariant	NOUN
cana-4753	100	14	have	have	VERB
cana-4753	100	15	limitations	limitation	NOUN
cana-4753	100	16	in	in	ADP
cana-4753	100	17	distinguishing	distinguish	VERB
cana-4753	100	18	certain	certain	ADJ
cana-4753	100	19	knots	knot	NOUN
cana-4753	100	20	.	.	PUNCT
cana-4753	101	1	to	to	PART
cana-4753	101	2	address	address	VERB
cana-4753	101	3	this	this	PRON
cana-4753	101	4	,	,	PUNCT
cana-4753	101	5	khovanov	khovanov	PROPN
cana-4753	101	6	homology	homology	PROPN
cana-4753	101	7	is	be	AUX
cana-4753	101	8	computed	compute	VERB
cana-4753	101	9	,	,	PUNCT
cana-4753	101	10	which	which	PRON
cana-4753	101	11	extends	extend	VERB
cana-4753	101	12	the	the	DET
cana-4753	101	13	jones	jones	PROPN
cana-4753	101	14	polynomial	polynomial	PROPN
cana-4753	101	15	into	into	ADP
cana-4753	101	16	a	a	DET
cana-4753	101	17	homology	homology	NOUN
cana-4753	101	18	theory	theory	NOUN
cana-4753	101	19	:	:	PUNCT
cana-4753	101	20	𝐾ℎ𝑖,𝑗(𝐾	𝐾ℎ𝑖,𝑗(𝐾	ADV
cana-4753	101	21	)	)	PUNCT
cana-4753	101	22	=	=	SYM
cana-4753	101	23	⨁	⨁	PROPN
cana-4753	101	24	  	  	SPACE
cana-4753	101	25	𝑑∈ℤ	𝑑∈ℤ	PROPN
cana-4753	101	26	𝐻𝑑(𝐾	𝐻𝑑(𝐾	NUM
cana-4753	101	27	)	)	PUNCT
cana-4753	102	1	where	where	SCONJ
cana-4753	102	2	𝐻𝑑(𝐾	𝐻𝑑(𝐾	NOUN
cana-4753	102	3	)	)	PUNCT
cana-4753	102	4	is	be	AUX
cana-4753	102	5	the	the	DET
cana-4753	102	6	homology	homology	NOUN
cana-4753	102	7	group	group	NOUN
cana-4753	102	8	of	of	ADP
cana-4753	102	9	the	the	DET
cana-4753	102	10	knot	knot	NOUN
cana-4753	102	11	at	at	ADP
cana-4753	102	12	grading	grade	VERB
cana-4753	102	13	level	level	NOUN
cana-4753	102	14	𝑑.	𝑑.	NOUN
cana-4753	102	15	the	the	DET
cana-4753	102	16	euler	euler	PROPN
cana-4753	102	17	characteristic	characteristic	NOUN
cana-4753	102	18	of	of	ADP
cana-4753	102	19	khovanov	khovanov	PROPN
cana-4753	102	20	homology	homology	PROPN
cana-4753	102	21	recovers	recover	VERB
cana-4753	102	22	the	the	DET
cana-4753	102	23	jones	jones	PROPN
cana-4753	102	24	polynomial	polynomial	ADJ
cana-4753	102	25	:	:	PUNCT
cana-4753	102	26	𝜒(𝐾ℎ(𝐾	𝜒(𝐾ℎ(𝐾	NUM
cana-4753	102	27	)	)	PUNCT
cana-4753	102	28	)	)	PUNCT
cana-4753	103	1	=	=	PUNCT
cana-4753	103	2	∑	∑	PUNCT
cana-4753	103	3	(	(	PUNCT
cana-4753	103	4	−1)𝑖𝑞𝑗dim𝐾ℎ𝑖,𝑗(𝐾	−1)𝑖𝑞𝑗dim𝐾ℎ𝑖,𝑗(𝐾	NOUN
cana-4753	103	5	)	)	PUNCT
cana-4753	103	6	where	where	SCONJ
cana-4753	103	7	𝒒	𝒒	PROPN
cana-4753	103	8	is	be	AUX
cana-4753	103	9	a	a	DET
cana-4753	103	10	grading	grade	VERB
cana-4753	103	11	parameter	parameter	NOUN
cana-4753	103	12	.	.	PUNCT
cana-4753	104	1	this	this	DET
cana-4753	104	2	approach	approach	NOUN
cana-4753	104	3	provides	provide	VERB
cana-4753	104	4	a	a	DET
cana-4753	104	5	finer	fine	ADJ
cana-4753	104	6	classification	classification	NOUN
cana-4753	104	7	system	system	NOUN
cana-4753	104	8	by	by	ADP
cana-4753	104	9	capturing	capture	VERB
cana-4753	104	10	additional	additional	ADJ
cana-4753	104	11	topological	topological	ADJ
cana-4753	104	12	information	information	NOUN
cana-4753	104	13	.	.	PUNCT
cana-4753	105	1	d.	d.	PROPN
cana-4753	105	2	computational	computational	ADJ
cana-4753	105	3	implementation	implementation	NOUN
cana-4753	105	4	and	and	CCONJ
cana-4753	105	5	machine	machine	NOUN
cana-4753	105	6	learning	learn	VERB
cana-4753	105	7	to	to	PART
cana-4753	105	8	automate	automate	VERB
cana-4753	105	9	knot	knot	NOUN
cana-4753	105	10	classification	classification	NOUN
cana-4753	105	11	,	,	PUNCT
cana-4753	105	12	machine	machine	NOUN
cana-4753	105	13	learning	learning	NOUN
cana-4753	105	14	models	model	NOUN
cana-4753	105	15	are	be	AUX
cana-4753	105	16	trained	train	VERB
cana-4753	105	17	using	use	VERB
cana-4753	105	18	knot	knot	NOUN
cana-4753	105	19	invariants	invariant	NOUN
cana-4753	105	20	and	and	CCONJ
cana-4753	105	21	homology	homology	NOUN
cana-4753	105	22	features	feature	NOUN
cana-4753	105	23	.	.	PUNCT
cana-4753	106	1	given	give	VERB
cana-4753	106	2	a	a	DET
cana-4753	106	3	dataset	dataset	NOUN
cana-4753	106	4	of	of	ADP
cana-4753	106	5	knot	knot	ADJ
cana-4753	106	6	diagrams	diagram	NOUN
cana-4753	106	7	,	,	PUNCT
cana-4753	106	8	features	feature	VERB
cana-4753	106	9	such	such	ADJ
cana-4753	106	10	as	as	ADP
cana-4753	106	11	crossing	crossing	NOUN
cana-4753	106	12	numbers	number	NOUN
cana-4753	106	13	,	,	PUNCT
cana-4753	106	14	polynomial	polynomial	ADJ
cana-4753	106	15	coefficients	coefficient	NOUN
cana-4753	106	16	,	,	PUNCT
cana-4753	106	17	and	and	CCONJ
cana-4753	106	18	homology	homology	NOUN
cana-4753	106	19	ranks	rank	NOUN
cana-4753	106	20	are	be	AUX
cana-4753	106	21	extracted	extract	VERB
cana-4753	106	22	[	[	X
cana-4753	106	23	19	19	NUM
cana-4753	106	24	]	]	PUNCT
cana-4753	106	25	.	.	PUNCT
cana-4753	107	1	a	a	DET
cana-4753	107	2	classification	classification	NOUN
cana-4753	107	3	model	model	NOUN
cana-4753	107	4	is	be	AUX
cana-4753	107	5	trained	train	VERB
cana-4753	107	6	using	use	VERB
cana-4753	107	7	support	support	NOUN
cana-4753	107	8	vector	vector	NOUN
cana-4753	107	9	machines	machine	NOUN
cana-4753	107	10	(	(	PUNCT
cana-4753	107	11	svms	svms	NOUN
cana-4753	107	12	)	)	PUNCT
cana-4753	107	13	and	and	CCONJ
cana-4753	107	14	neural	neural	ADJ
cana-4753	107	15	networks	network	NOUN
cana-4753	107	16	to	to	PART
cana-4753	107	17	distinguish	distinguish	VERB
cana-4753	107	18	between	between	ADP
cana-4753	107	19	different	different	ADJ
cana-4753	107	20	knot	knot	NOUN
cana-4753	107	21	types	type	NOUN
cana-4753	107	22	.	.	PUNCT
cana-4753	108	1	the	the	DET
cana-4753	108	2	feature	feature	NOUN
cana-4753	108	3	vector	vector	NOUN
cana-4753	108	4	is	be	AUX
cana-4753	108	5	defined	define	VERB
cana-4753	108	6	as	as	ADP
cana-4753	108	7	:	:	PUNCT
cana-4753	108	8	𝑋	𝑋	NOUN
cana-4753	108	9	=	=	PUNCT
cana-4753	109	1	[	[	X
cana-4753	109	2	δ𝐾(𝑡	δ𝐾(𝑡	NOUN
cana-4753	109	3	)	)	PUNCT
cana-4753	109	4	,	,	PUNCT
cana-4753	109	5	𝑉𝐾(𝑡	𝑉𝐾(𝑡	ADJ
cana-4753	109	6	)	)	PUNCT
cana-4753	109	7	,	,	PUNCT
cana-4753	109	8	𝜒(𝐾ℎ(𝐾	𝜒(𝐾ℎ(𝐾	NOUN
cana-4753	109	9	)	)	PUNCT
cana-4753	109	10	)	)	PUNCT
cana-4753	109	11	]	]	PUNCT
cana-4753	110	1	a	a	DET
cana-4753	110	2	function	function	NOUN
cana-4753	110	3	𝑓(𝑋	𝑓(𝑋	NOUN
cana-4753	110	4	)	)	PUNCT
cana-4753	110	5	maps	map	VERB
cana-4753	110	6	the	the	DET
cana-4753	110	7	extracted	extract	VERB
cana-4753	110	8	features	feature	NOUN
cana-4753	110	9	to	to	ADP
cana-4753	110	10	a	a	DET
cana-4753	110	11	knot	knot	ADJ
cana-4753	110	12	type	type	NOUN
cana-4753	110	13	label	label	NOUN
cana-4753	110	14	𝑌	𝑌	PROPN
cana-4753	110	15	:	:	PUNCT
cana-4753	110	16	𝑌	𝑌	PROPN
cana-4753	110	17	=	=	SYM
cana-4753	110	18	𝑓(𝑋	𝑓(𝑋	PROPN
cana-4753	110	19	)	)	PUNCT
cana-4753	110	20	=	=	SYM
cana-4753	110	21	arg	arg	NOUN
cana-4753	110	22	max𝑃(𝑌	max𝑃(𝑌	PROPN
cana-4753	110	23	∣	∣	PROPN
cana-4753	110	24	𝑋	𝑋	PROPN
cana-4753	110	25	)	)	PUNCT
cana-4753	110	26	where	where	SCONJ
cana-4753	110	27	𝑃(𝑌	𝑃(𝑌	NOUN
cana-4753	110	28	∣	∣	ADJ
cana-4753	110	29	𝑋	𝑋	PROPN
cana-4753	110	30	)	)	PUNCT
cana-4753	110	31	is	be	AUX
cana-4753	110	32	the	the	DET
cana-4753	110	33	probability	probability	NOUN
cana-4753	110	34	distribution	distribution	NOUN
cana-4753	110	35	of	of	ADP
cana-4753	110	36	knot	knot	ADJ
cana-4753	110	37	types	type	NOUN
cana-4753	110	38	given	give	VERB
cana-4753	110	39	the	the	DET
cana-4753	110	40	input	input	NOUN
cana-4753	110	41	feature	feature	NOUN
cana-4753	110	42	vector	vector	NOUN
cana-4753	110	43	.	.	PUNCT
cana-4753	111	1	training	train	VERB
cana-4753	111	2	the	the	DET
cana-4753	111	3	model	model	NOUN
cana-4753	111	4	involves	involve	VERB
cana-4753	111	5	minimizing	minimize	VERB
cana-4753	111	6	a	a	DET
cana-4753	111	7	loss	loss	NOUN
cana-4753	111	8	function	function	NOUN
cana-4753	111	9	:	:	PUNCT
cana-4753	111	10	ℒ	ℒ	PROPN
cana-4753	111	11	=	=	PUNCT
cana-4753	111	12	∑	∑	ADP
cana-4753	111	13	  	  	SPACE
cana-4753	111	14	𝑁	𝑁	PROPN
cana-4753	111	15	𝑖=1	𝑖=1	PROPN
cana-4753	112	1	(	(	PUNCT
cana-4753	112	2	𝑌𝑖	𝑌𝑖	PROPN
cana-4753	112	3	−	−	PROPN
cana-4753	112	4	𝑓(𝑋𝑖	𝑓(𝑋𝑖	NOUN
cana-4753	112	5	)	)	PUNCT
cana-4753	112	6	)	)	PUNCT
cana-4753	112	7	2	2	NUM
cana-4753	112	8	where	where	SCONJ
cana-4753	112	9	𝑁	𝑁	PROPN
cana-4753	112	10	is	be	AUX
cana-4753	112	11	the	the	DET
cana-4753	112	12	total	total	ADJ
cana-4753	112	13	number	number	NOUN
cana-4753	112	14	of	of	ADP
cana-4753	112	15	knots	knot	NOUN
cana-4753	112	16	in	in	ADP
cana-4753	112	17	the	the	DET
cana-4753	112	18	dataset	dataset	NOUN
cana-4753	112	19	.	.	PUNCT
cana-4753	113	1	e.	e.	PROPN
cana-4753	113	2	application	application	PROPN
cana-4753	113	3	-	-	PUNCT
cana-4753	113	4	based	base	VERB
cana-4753	113	5	validation	validation	NOUN
cana-4753	113	6	to	to	PART
cana-4753	113	7	validate	validate	VERB
cana-4753	113	8	the	the	DET
cana-4753	113	9	effectiveness	effectiveness	NOUN
cana-4753	113	10	of	of	ADP
cana-4753	113	11	the	the	DET
cana-4753	113	12	proposed	propose	VERB
cana-4753	113	13	methodology	methodology	NOUN
cana-4753	114	1	,	,	PUNCT
cana-4753	114	2	the	the	DET
cana-4753	114	3	classification	classification	NOUN
cana-4753	114	4	results	result	NOUN
cana-4753	114	5	are	be	AUX
cana-4753	114	6	compared	compare	VERB
cana-4753	114	7	against	against	ADP
cana-4753	114	8	known	know	VERB
cana-4753	114	9	benchmark	benchmark	NOUN
cana-4753	114	10	datasets	dataset	NOUN
cana-4753	114	11	from	from	ADP
cana-4753	114	12	biological	biological	ADJ
cana-4753	114	13	,	,	PUNCT
cana-4753	114	14	chemical	chemical	NOUN
cana-4753	114	15	,	,	PUNCT
cana-4753	114	16	and	and	CCONJ
cana-4753	114	17	physical	physical	ADJ
cana-4753	114	18	systems	system	NOUN
cana-4753	114	19	.	.	PUNCT
cana-4753	115	1	dna	dna	PROPN
cana-4753	115	2	knots	knot	NOUN
cana-4753	115	3	extracted	extract	VERB
cana-4753	115	4	from	from	ADP
cana-4753	115	5	molecular	molecular	ADJ
cana-4753	115	6	simulations	simulation	NOUN
cana-4753	115	7	are	be	AUX
cana-4753	115	8	analyzed	analyze	VERB
cana-4753	115	9	to	to	PART
cana-4753	115	10	determine	determine	VERB
cana-4753	115	11	whether	whether	SCONJ
cana-4753	115	12	the	the	DET
cana-4753	115	13	computed	compute	VERB
cana-4753	115	14	invariants	invariant	NOUN
cana-4753	115	15	match	match	VERB
cana-4753	115	16	the	the	DET
cana-4753	115	17	experimental	experimental	ADJ
cana-4753	115	18	observations	observation	NOUN
cana-4753	115	19	.	.	PUNCT
cana-4753	116	1	polymer	polymer	NOUN
cana-4753	116	2	entanglement	entanglement	NOUN
cana-4753	116	3	studies	study	NOUN
cana-4753	116	4	provide	provide	VERB
cana-4753	116	5	further	further	ADJ
cana-4753	116	6	validation	validation	NOUN
cana-4753	116	7	by	by	ADP
cana-4753	116	8	comparing	compare	VERB
cana-4753	116	9	computational	computational	ADJ
cana-4753	116	10	predictions	prediction	NOUN
cana-4753	116	11	with	with	ADP
cana-4753	116	12	experimental	experimental	ADJ
cana-4753	116	13	elasticity	elasticity	NOUN
cana-4753	116	14	measurements	measurement	NOUN
cana-4753	116	15	.	.	PUNCT
cana-4753	117	1	flowchart	flowchart	NOUN
cana-4753	117	2	of	of	ADP
cana-4753	117	3	the	the	DET
cana-4753	117	4	proposed	propose	VERB
cana-4753	117	5	methodology	methodology	NOUN
cana-4753	117	6	communications	communication	NOUN
cana-4753	117	7	on	on	ADP
cana-4753	117	8	applied	apply	VERB
cana-4753	117	9	nonlinear	nonlinear	ADJ
cana-4753	117	10	analysis	analysis	NOUN
cana-4753	117	11	issn	issn	NOUN
cana-4753	117	12	:	:	PUNCT
cana-4753	117	13	1074	1074	NUM
cana-4753	117	14	-	-	PUNCT
cana-4753	117	15	133x	133x	NUM
cana-4753	117	16	vol	vol	VERB
cana-4753	117	17	32	32	NUM
cana-4753	117	18	no	no	NOUN
cana-4753	117	19	.	.	PUNCT
cana-4753	118	1	10s	10	NOUN
cana-4753	118	2	(	(	PUNCT
cana-4753	118	3	2025	2025	NUM
cana-4753	118	4	)	)	PUNCT
cana-4753	118	5	290	290	NUM
cana-4753	118	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4753	118	7	figure	figure	NOUN
cana-4753	118	8	1	1	NUM
cana-4753	118	9	:	:	PUNCT
cana-4753	118	10	computational	computational	ADJ
cana-4753	118	11	and	and	CCONJ
cana-4753	118	12	topological	topological	ADJ
cana-4753	118	13	framework	framework	NOUN
cana-4753	118	14	for	for	ADP
cana-4753	118	15	knot	knot	NOUN
cana-4753	118	16	analysis	analysis	NOUN
cana-4753	118	17	communications	communication	NOUN
cana-4753	118	18	on	on	ADP
cana-4753	118	19	applied	apply	VERB
cana-4753	118	20	nonlinear	nonlinear	ADJ
cana-4753	118	21	analysis	analysis	NOUN
cana-4753	118	22	issn	issn	NOUN
cana-4753	118	23	:	:	PUNCT
cana-4753	118	24	1074	1074	NUM
cana-4753	118	25	-	-	PUNCT
cana-4753	118	26	133x	133x	NUM
cana-4753	118	27	vol	vol	VERB
cana-4753	118	28	32	32	NUM
cana-4753	118	29	no	no	NOUN
cana-4753	118	30	.	.	PUNCT
cana-4753	119	1	10s	10	NOUN
cana-4753	119	2	(	(	PUNCT
cana-4753	119	3	2025	2025	NUM
cana-4753	119	4	)	)	PUNCT
cana-4753	119	5	291	291	NUM
cana-4753	119	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4753	120	1	the	the	DET
cana-4753	120	2	proposed	propose	VERB
cana-4753	120	3	methodology	methodology	NOUN
cana-4753	120	4	integrates	integrate	VERB
cana-4753	120	5	topological	topological	ADJ
cana-4753	120	6	,	,	PUNCT
cana-4753	120	7	computational	computational	ADJ
cana-4753	120	8	,	,	PUNCT
cana-4753	120	9	and	and	CCONJ
cana-4753	120	10	machine	machine	NOUN
cana-4753	120	11	learning	learn	VERB
cana-4753	120	12	approaches	approach	NOUN
cana-4753	120	13	to	to	PART
cana-4753	120	14	provide	provide	VERB
cana-4753	120	15	a	a	DET
cana-4753	120	16	comprehensive	comprehensive	ADJ
cana-4753	120	17	framework	framework	NOUN
cana-4753	120	18	for	for	ADP
cana-4753	120	19	understanding	understand	VERB
cana-4753	120	20	knots	knot	NOUN
cana-4753	120	21	.	.	PUNCT
cana-4753	121	1	by	by	ADP
cana-4753	121	2	combining	combine	VERB
cana-4753	121	3	classical	classical	ADJ
cana-4753	121	4	polynomial	polynomial	ADJ
cana-4753	121	5	invariants	invariant	NOUN
cana-4753	121	6	with	with	ADP
cana-4753	121	7	modern	modern	ADJ
cana-4753	121	8	homology	homology	NOUN
cana-4753	121	9	theories	theory	NOUN
cana-4753	121	10	and	and	CCONJ
cana-4753	121	11	machine	machine	NOUN
cana-4753	121	12	learning	learning	NOUN
cana-4753	121	13	models	model	NOUN
cana-4753	121	14	,	,	PUNCT
cana-4753	121	15	this	this	DET
cana-4753	121	16	approach	approach	NOUN
cana-4753	121	17	improves	improve	VERB
cana-4753	121	18	the	the	DET
cana-4753	121	19	accuracy	accuracy	NOUN
cana-4753	121	20	of	of	ADP
cana-4753	121	21	knot	knot	ADJ
cana-4753	121	22	classification	classification	NOUN
cana-4753	121	23	and	and	CCONJ
cana-4753	121	24	complexity	complexity	NOUN
cana-4753	121	25	analysis	analysis	NOUN
cana-4753	121	26	.	.	PUNCT
cana-4753	122	1	future	future	ADJ
cana-4753	122	2	work	work	NOUN
cana-4753	122	3	will	will	AUX
cana-4753	122	4	explore	explore	VERB
cana-4753	122	5	higher	high	ADJ
cana-4753	122	6	-	-	PUNCT
cana-4753	122	7	dimensional	dimensional	ADJ
cana-4753	122	8	knot	knot	NOUN
cana-4753	122	9	structures	structure	NOUN
cana-4753	122	10	and	and	CCONJ
cana-4753	122	11	their	their	PRON
cana-4753	122	12	applications	application	NOUN
cana-4753	122	13	in	in	ADP
cana-4753	122	14	quantum	quantum	NOUN
cana-4753	122	15	computing	computing	NOUN
cana-4753	122	16	and	and	CCONJ
cana-4753	122	17	topological	topological	ADJ
cana-4753	122	18	materials	material	NOUN
cana-4753	122	19	.	.	PUNCT
cana-4753	123	1	iv	iv	X
cana-4753	123	2	.	.	PROPN
cana-4753	123	3	result	result	PROPN
cana-4753	123	4	&	&	CCONJ
cana-4753	123	5	discussions	discussion	NOUN
cana-4753	123	6	the	the	DET
cana-4753	123	7	proposed	propose	VERB
cana-4753	123	8	methodology	methodology	NOUN
cana-4753	123	9	was	be	AUX
cana-4753	123	10	tested	test	VERB
cana-4753	123	11	on	on	ADP
cana-4753	123	12	a	a	DET
cana-4753	123	13	dataset	dataset	NOUN
cana-4753	123	14	of	of	ADP
cana-4753	123	15	knots	knot	NOUN
cana-4753	123	16	consisting	consist	VERB
cana-4753	123	17	of	of	ADP
cana-4753	123	18	simple	simple	ADJ
cana-4753	123	19	trefoil	trefoil	NOUN
cana-4753	123	20	knots	knot	NOUN
cana-4753	123	21	in	in	ADP
cana-4753	123	22	one	one	NUM
cana-4753	123	23	situation	situation	NOUN
cana-4753	123	24	and	and	CCONJ
cana-4753	123	25	figure	figure	VERB
cana-4753	123	26	eight	eight	NUM
cana-4753	123	27	knots	knot	NOUN
cana-4753	123	28	all	all	DET
cana-4753	123	29	the	the	DET
cana-4753	123	30	way	way	NOUN
cana-4753	123	31	to	to	ADP
cana-4753	123	32	more	more	ADV
cana-4753	123	33	complex	complex	ADJ
cana-4753	123	34	torus	torus	NOUN
cana-4753	123	35	knots	knot	NOUN
cana-4753	123	36	.	.	PUNCT
cana-4753	124	1	results	result	NOUN
cana-4753	124	2	indicate	indicate	VERB
cana-4753	124	3	that	that	SCONJ
cana-4753	124	4	different	different	ADJ
cana-4753	124	5	topological	topological	ADJ
cana-4753	124	6	invariants	invariant	NOUN
cana-4753	124	7	and	and	CCONJ
cana-4753	124	8	computational	computational	ADJ
cana-4753	124	9	homology	homology	NOUN
cana-4753	124	10	,	,	PUNCT
cana-4753	124	11	as	as	ADV
cana-4753	124	12	well	well	ADV
cana-4753	124	13	as	as	ADP
cana-4753	124	14	machine	machine	NOUN
cana-4753	124	15	learning	learning	NOUN
cana-4753	124	16	based	base	VERB
cana-4753	124	17	classification	classification	NOUN
cana-4753	124	18	,	,	PUNCT
cana-4753	124	19	are	be	AUX
cana-4753	124	20	effective	effective	ADJ
cana-4753	124	21	.	.	PUNCT
cana-4753	125	1	the	the	DET
cana-4753	125	2	graphs	graph	NOUN
cana-4753	125	3	and	and	CCONJ
cana-4753	125	4	comparison	comparison	NOUN
cana-4753	125	5	tables	table	NOUN
cana-4753	125	6	are	be	AUX
cana-4753	125	7	the	the	DET
cana-4753	125	8	presentations	presentation	NOUN
cana-4753	125	9	of	of	ADP
cana-4753	125	10	findings	finding	NOUN
cana-4753	125	11	[	[	X
cana-4753	125	12	20	20	NUM
cana-4753	125	13	]	]	PUNCT
cana-4753	125	14	.	.	PUNCT
cana-4753	126	1	different	different	ADJ
cana-4753	126	2	knots	knot	NOUN
cana-4753	126	3	were	be	AUX
cana-4753	126	4	classified	classify	VERB
cana-4753	126	5	according	accord	VERB
cana-4753	126	6	to	to	ADP
cana-4753	126	7	their	their	PRON
cana-4753	126	8	alexander	alexander	NOUN
cana-4753	126	9	,	,	PUNCT
cana-4753	126	10	jones	jones	PROPN
cana-4753	126	11	and	and	CCONJ
cana-4753	126	12	homfly	homfly	PROPN
cana-4753	126	13	polynomials	polynomial	NOUN
cana-4753	126	14	in	in	ADP
cana-4753	126	15	order	order	NOUN
cana-4753	126	16	to	to	PART
cana-4753	126	17	analyze	analyze	VERB
cana-4753	126	18	the	the	DET
cana-4753	126	19	computational	computational	ADJ
cana-4753	126	20	efficiency	efficiency	NOUN
cana-4753	126	21	of	of	ADP
cana-4753	126	22	polynomial	polynomial	ADJ
cana-4753	126	23	invariants	invariant	NOUN
cana-4753	126	24	.	.	PUNCT
cana-4753	127	1	it	it	PRON
cana-4753	127	2	was	be	AUX
cana-4753	127	3	seen	see	VERB
cana-4753	127	4	that	that	SCONJ
cana-4753	127	5	computational	computational	ADJ
cana-4753	127	6	complexity	complexity	NOUN
cana-4753	127	7	increased	increase	VERB
cana-4753	127	8	when	when	SCONJ
cana-4753	127	9	number	number	NOUN
cana-4753	127	10	of	of	ADP
cana-4753	127	11	crossings	crossing	NOUN
cana-4753	127	12	in	in	ADP
cana-4753	127	13	the	the	DET
cana-4753	127	14	knot	knot	NOUN
cana-4753	127	15	increased	increase	VERB
cana-4753	127	16	.	.	PUNCT
cana-4753	128	1	in	in	ADP
cana-4753	128	2	figure	figure	NOUN
cana-4753	128	3	2	2	NUM
cana-4753	128	4	,	,	PUNCT
cana-4753	128	5	polynomial	polynomial	ADJ
cana-4753	128	6	computation	computation	NOUN
cana-4753	128	7	time	time	NOUN
cana-4753	128	8	is	be	AUX
cana-4753	128	9	shown	show	VERB
cana-4753	128	10	versus	versus	ADP
cana-4753	128	11	the	the	DET
cana-4753	128	12	number	number	NOUN
cana-4753	128	13	of	of	ADP
cana-4753	128	14	crossings	crossing	NOUN
cana-4753	128	15	.	.	PUNCT
cana-4753	129	1	with	with	ADP
cana-4753	129	2	such	such	ADJ
cana-4753	129	3	high	high	ADJ
cana-4753	129	4	degree	degree	NOUN
cana-4753	129	5	dependency	dependency	NOUN
cana-4753	129	6	on	on	ADP
cana-4753	129	7	crossings	crossing	NOUN
cana-4753	129	8	,	,	PUNCT
cana-4753	129	9	it	it	PRON
cana-4753	129	10	is	be	AUX
cana-4753	129	11	clearly	clearly	ADV
cana-4753	129	12	evident	evident	ADJ
cana-4753	129	13	that	that	SCONJ
cana-4753	129	14	it	it	PRON
cana-4753	129	15	takes	take	VERB
cana-4753	129	16	significantly	significantly	ADV
cana-4753	129	17	more	more	ADJ
cana-4753	129	18	time	time	NOUN
cana-4753	129	19	for	for	ADP
cana-4753	129	20	the	the	DET
cana-4753	129	21	homfly	homfly	NOUN
cana-4753	129	22	polynomial	polynomial	ADJ
cana-4753	129	23	than	than	ADP
cana-4753	129	24	for	for	ADP
cana-4753	129	25	the	the	DET
cana-4753	129	26	alexander	alexander	PROPN
cana-4753	129	27	polynomial	polynomial	PROPN
cana-4753	129	28	.	.	PUNCT
cana-4753	130	1	figure	figure	NOUN
cana-4753	130	2	2	2	NUM
cana-4753	130	3	:	:	PUNCT
cana-4753	130	4	polynomial	polynomial	ADJ
cana-4753	130	5	computation	computation	NOUN
cana-4753	130	6	time	time	NOUN
cana-4753	130	7	vs.	vs.	ADP
cana-4753	130	8	number	number	NOUN
cana-4753	130	9	of	of	ADP
cana-4753	130	10	crossings	crossing	NOUN
cana-4753	130	11	a	a	DET
cana-4753	130	12	problem	problem	NOUN
cana-4753	130	13	in	in	ADP
cana-4753	130	14	knot	knot	ADJ
cana-4753	130	15	classification	classification	NOUN
cana-4753	130	16	is	be	AUX
cana-4753	130	17	presented	present	VERB
cana-4753	130	18	by	by	ADP
cana-4753	130	19	two	two	NUM
cana-4753	130	20	different	different	ADJ
cana-4753	130	21	knots	knot	NOUN
cana-4753	130	22	which	which	PRON
cana-4753	130	23	have	have	VERB
cana-4753	130	24	identical	identical	ADJ
cana-4753	130	25	polynomial	polynomial	ADJ
cana-4753	130	26	invariant	invariant	NOUN
cana-4753	130	27	.	.	PUNCT
cana-4753	131	1	an	an	DET
cana-4753	131	2	extended	extended	ADJ
cana-4753	131	3	classification	classification	NOUN
cana-4753	131	4	using	use	VERB
cana-4753	131	5	homology	homology	NOUN
cana-4753	131	6	ranks	rank	NOUN
cana-4753	131	7	was	be	AUX
cana-4753	131	8	performed	perform	VERB
cana-4753	131	9	to	to	PART
cana-4753	131	10	evaluate	evaluate	VERB
cana-4753	131	11	how	how	SCONJ
cana-4753	131	12	effective	effective	ADJ
cana-4753	131	13	khovanov	khovanov	NOUN
cana-4753	131	14	homology	homology	NOUN
cana-4753	131	15	is	be	AUX
cana-4753	131	16	.	.	PUNCT
cana-4753	132	1	these	these	DET
cana-4753	132	2	results	result	NOUN
cana-4753	132	3	confirm	confirm	VERB
cana-4753	132	4	that	that	PRON
cana-4753	132	5	homology	homology	NOUN
cana-4753	132	6	-	-	PUNCT
cana-4753	132	7	based	base	VERB
cana-4753	132	8	classification	classification	NOUN
cana-4753	132	9	successfully	successfully	ADV
cana-4753	132	10	classifies	classify	VERB
cana-4753	132	11	the	the	DET
cana-4753	132	12	knots	knot	NOUN
cana-4753	132	13	that	that	PRON
cana-4753	132	14	could	could	AUX
cana-4753	132	15	not	not	PART
cana-4753	132	16	be	be	AUX
cana-4753	132	17	distinguished	distinguish	VERB
cana-4753	132	18	before	before	ADV
cana-4753	132	19	with	with	ADP
cana-4753	132	20	only	only	ADJ
cana-4753	132	21	polynomial	polynomial	ADJ
cana-4753	132	22	invariants	invariant	NOUN
cana-4753	132	23	.	.	PUNCT
cana-4753	133	1	a	a	DET
cana-4753	133	2	comparison	comparison	NOUN
cana-4753	133	3	of	of	ADP
cana-4753	133	4	classification	classification	NOUN
cana-4753	133	5	accuracy	accuracy	NOUN
cana-4753	133	6	of	of	ADP
cana-4753	133	7	the	the	DET
cana-4753	133	8	polynomial	polynomial	ADJ
cana-4753	133	9	based	base	VERB
cana-4753	133	10	and	and	CCONJ
cana-4753	133	11	homology	homology	NOUN
cana-4753	133	12	based	base	VERB
cana-4753	133	13	approaches	approach	NOUN
cana-4753	133	14	is	be	AUX
cana-4753	133	15	given	give	VERB
cana-4753	133	16	in	in	ADP
cana-4753	133	17	table	table	NOUN
cana-4753	133	18	1	1	NUM
cana-4753	133	19	.	.	PUNCT
cana-4753	133	20	table	table	NOUN
cana-4753	133	21	1	1	NUM
cana-4753	133	22	:	:	PUNCT
cana-4753	133	23	classification	classification	NOUN
cana-4753	133	24	accuracy	accuracy	NOUN
cana-4753	133	25	of	of	ADP
cana-4753	133	26	different	different	ADJ
cana-4753	133	27	knot	knot	NOUN
cana-4753	133	28	invariants	invariant	NOUN
cana-4753	133	29	knot	knot	NOUN
cana-4753	133	30	type	type	NOUN
cana-4753	133	31	polynomial	polynomial	ADJ
cana-4753	133	32	-	-	PUNCT
cana-4753	133	33	based	base	VERB
cana-4753	133	34	accuracy	accuracy	NOUN
cana-4753	133	35	(	(	PUNCT
cana-4753	133	36	%	%	NOUN
cana-4753	133	37	)	)	PUNCT
cana-4753	133	38	homology	homology	NOUN
cana-4753	133	39	-	-	PUNCT
cana-4753	133	40	based	base	VERB
cana-4753	133	41	accuracy	accuracy	NOUN
cana-4753	133	42	(	(	PUNCT
cana-4753	133	43	%	%	INTJ
cana-4753	133	44	)	)	PUNCT
cana-4753	133	45	trefoil	trefoil	NOUN
cana-4753	133	46	knot	knot	VERB
cana-4753	133	47	92.50	92.50	NUM
cana-4753	133	48	%	%	NOUN
cana-4753	133	49	99.30	99.30	NUM
cana-4753	133	50	%	%	NOUN
cana-4753	133	51	figure	figure	NOUN
cana-4753	133	52	-	-	PUNCT
cana-4753	133	53	eight	eight	NUM
cana-4753	133	54	knot	knot	NOUN
cana-4753	133	55	89.80	89.80	NUM
cana-4753	133	56	%	%	NOUN
cana-4753	133	57	97.60	97.60	NUM
cana-4753	133	58	%	%	NOUN
cana-4753	134	1	0.15	0.15	NUM
cana-4753	134	2	0.27	0.27	NUM
cana-4753	134	3	0.43	0.43	NUM
cana-4753	134	4	0.68	0.68	NUM
cana-4753	134	5	0.91	0.91	NUM
cana-4753	134	6	1.27	1.27	NUM
cana-4753	134	7	0.22	0.22	NUM
cana-4753	134	8	0.38	0.38	NUM
cana-4753	134	9	0.57	0.57	NUM
cana-4753	134	10	0.89	0.89	NUM
cana-4753	134	11	1.21	1.21	NUM
cana-4753	134	12	1.64	1.64	NUM
cana-4753	134	13	0.35	0.35	NUM
cana-4753	134	14	0.64	0.64	NUM
cana-4753	134	15	1.02	1.02	NUM
cana-4753	134	16	1.73	1.73	NUM
cana-4753	134	17	2.34	2.34	NUM
cana-4753	134	18	3.02	3.02	NUM
cana-4753	134	19	0	0	NUM
cana-4753	134	20	0.5	0.5	NUM
cana-4753	134	21	1	1	NUM
cana-4753	134	22	1.5	1.5	NUM
cana-4753	134	23	2	2	NUM
cana-4753	134	24	2.5	2.5	NUM
cana-4753	134	25	3	3	NUM
cana-4753	134	26	3.5	3.5	NUM
cana-4753	134	27	3	3	NUM
cana-4753	134	28	5	5	NUM
cana-4753	134	29	7	7	NUM
cana-4753	134	30	9	9	NUM
cana-4753	134	31	11	11	NUM
cana-4753	134	32	13	13	NUM
cana-4753	134	33	polynomial	polynomial	ADJ
cana-4753	134	34	computation	computation	NOUN
cana-4753	134	35	time	time	NOUN
cana-4753	134	36	vs.	vs.	ADP
cana-4753	134	37	number	number	NOUN
cana-4753	134	38	of	of	ADP
cana-4753	134	39	crossings	crossing	NOUN
cana-4753	134	40	alexander	alexander	NOUN
cana-4753	134	41	polynomial	polynomial	ADJ
cana-4753	134	42	time	time	NOUN
cana-4753	134	43	(	(	PUNCT
cana-4753	134	44	s	s	NOUN
cana-4753	134	45	)	)	PUNCT
cana-4753	134	46	jones	jones	PROPN
cana-4753	134	47	polynomial	polynomial	ADJ
cana-4753	134	48	time	time	NOUN
cana-4753	134	49	(	(	PUNCT
cana-4753	134	50	s	s	NOUN
cana-4753	134	51	)	)	PUNCT
cana-4753	134	52	homfly	homfly	NOUN
cana-4753	134	53	polynomial	polynomial	ADJ
cana-4753	134	54	time	time	NOUN
cana-4753	134	55	(	(	PUNCT
cana-4753	134	56	s	s	NOUN
cana-4753	134	57	)	)	PUNCT
cana-4753	134	58	communications	communication	NOUN
cana-4753	134	59	on	on	ADP
cana-4753	134	60	applied	apply	VERB
cana-4753	134	61	nonlinear	nonlinear	ADJ
cana-4753	134	62	analysis	analysis	NOUN
cana-4753	134	63	issn	issn	NOUN
cana-4753	134	64	:	:	PUNCT
cana-4753	134	65	1074	1074	NUM
cana-4753	134	66	-	-	PUNCT
cana-4753	134	67	133x	133x	NUM
cana-4753	134	68	vol	vol	VERB
cana-4753	134	69	32	32	NUM
cana-4753	134	70	no	no	NOUN
cana-4753	134	71	.	.	PUNCT
cana-4753	135	1	10s	10	NOUN
cana-4753	135	2	(	(	PUNCT
cana-4753	135	3	2025	2025	NUM
cana-4753	135	4	)	)	PUNCT
cana-4753	135	5	292	292	NUM
cana-4753	135	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4753	135	7	torus	torus	NOUN
cana-4753	135	8	knot	knot	NOUN
cana-4753	135	9	(	(	PUNCT
cana-4753	135	10	5,2	5,2	NUM
cana-4753	135	11	)	)	PUNCT
cana-4753	135	12	85.20	85.20	NUM
cana-4753	135	13	%	%	NOUN
cana-4753	135	14	96.10	96.10	NUM
cana-4753	135	15	%	%	NOUN
cana-4753	135	16	hyperbolic	hyperbolic	ADJ
cana-4753	135	17	knot	knot	NOUN
cana-4753	135	18	78.60	78.60	NUM
cana-4753	135	19	%	%	NOUN
cana-4753	135	20	94.50	94.50	NUM
cana-4753	135	21	%	%	NOUN
cana-4753	135	22	for	for	ADP
cana-4753	135	23	higher	high	ADJ
cana-4753	135	24	crossing	crossing	NOUN
cana-4753	135	25	knots	knot	NOUN
cana-4753	135	26	,	,	PUNCT
cana-4753	135	27	where	where	SCONJ
cana-4753	135	28	polynomial	polynomial	ADJ
cana-4753	135	29	methods	method	NOUN
cana-4753	135	30	are	be	AUX
cana-4753	135	31	ineffective	ineffective	ADJ
cana-4753	135	32	at	at	ADP
cana-4753	135	33	discerning	discern	VERB
cana-4753	135	34	structure	structure	NOUN
cana-4753	135	35	,	,	PUNCT
cana-4753	135	36	the	the	DET
cana-4753	135	37	homology	homology	NOUN
cana-4753	135	38	based	base	VERB
cana-4753	135	39	method	method	NOUN
cana-4753	135	40	increases	increase	VERB
cana-4753	135	41	in	in	ADP
cana-4753	135	42	the	the	DET
cana-4753	135	43	running	running	NOUN
cana-4753	135	44	over	over	ADP
cana-4753	135	45	polynomial	polynomial	ADJ
cana-4753	135	46	invariants	invariant	NOUN
cana-4753	135	47	.	.	PUNCT
cana-4753	136	1	for	for	ADP
cana-4753	136	2	the	the	DET
cana-4753	136	3	purpose	purpose	NOUN
cana-4753	136	4	of	of	ADP
cana-4753	136	5	further	further	ADJ
cana-4753	136	6	evaluation	evaluation	NOUN
cana-4753	136	7	of	of	ADP
cana-4753	136	8	classification	classification	NOUN
cana-4753	136	9	performance	performance	NOUN
cana-4753	136	10	we	we	PRON
cana-4753	136	11	trained	train	VERB
cana-4753	136	12	a	a	DET
cana-4753	136	13	machine	machine	NOUN
cana-4753	136	14	learning	learn	VERB
cana-4753	136	15	model	model	NOUN
cana-4753	136	16	over	over	ADP
cana-4753	136	17	knot	knot	NOUN
cana-4753	136	18	invariants	invariant	NOUN
cana-4753	136	19	and	and	CCONJ
cana-4753	136	20	homology	homology	NOUN
cana-4753	136	21	features	feature	NOUN
cana-4753	136	22	.	.	PUNCT
cana-4753	137	1	various	various	ADJ
cana-4753	137	2	knot	knot	ADJ
cana-4753	137	3	types	type	NOUN
cana-4753	137	4	were	be	AUX
cana-4753	137	5	tested	test	VERB
cana-4753	137	6	to	to	PART
cana-4753	137	7	determine	determine	VERB
cana-4753	137	8	the	the	DET
cana-4753	137	9	accuracy	accuracy	NOUN
cana-4753	137	10	of	of	ADP
cana-4753	137	11	the	the	DET
cana-4753	137	12	model	model	NOUN
cana-4753	137	13	.	.	PUNCT
cana-4753	138	1	the	the	DET
cana-4753	138	2	performances	performance	NOUN
cana-4753	138	3	of	of	ADP
cana-4753	138	4	various	various	ADJ
cana-4753	138	5	machine	machine	NOUN
cana-4753	138	6	learning	learn	VERB
cana-4753	138	7	classifiers	classifier	NOUN
cana-4753	138	8	for	for	ADP
cana-4753	138	9	knot	knot	NOUN
cana-4753	138	10	type	type	NOUN
cana-4753	138	11	prediction	prediction	NOUN
cana-4753	138	12	are	be	AUX
cana-4753	138	13	shown	show	VERB
cana-4753	138	14	in	in	ADP
cana-4753	138	15	the	the	DET
cana-4753	138	16	figure	figure	NOUN
cana-4753	138	17	3	3	NUM
cana-4753	138	18	.	.	PUNCT
cana-4753	138	19	traditional	traditional	ADJ
cana-4753	138	20	svm	svm	PROPN
cana-4753	138	21	based	base	VERB
cana-4753	138	22	models	model	NOUN
cana-4753	138	23	showed	show	VERB
cana-4753	138	24	a	a	DET
cana-4753	138	25	moderate	moderate	ADJ
cana-4753	138	26	performance	performance	NOUN
cana-4753	138	27	,	,	PUNCT
cana-4753	138	28	while	while	SCONJ
cana-4753	138	29	the	the	DET
cana-4753	138	30	best	good	ADJ
cana-4753	138	31	model	model	NOUN
cana-4753	138	32	is	be	AUX
cana-4753	138	33	the	the	DET
cana-4753	138	34	neural	neural	ADJ
cana-4753	138	35	network	network	NOUN
cana-4753	138	36	model	model	NOUN
cana-4753	138	37	which	which	PRON
cana-4753	138	38	attained	attain	VERB
cana-4753	138	39	the	the	DET
cana-4753	138	40	highest	high	ADJ
cana-4753	138	41	accuracy	accuracy	NOUN
cana-4753	138	42	.	.	PUNCT
cana-4753	139	1	figure	figure	VERB
cana-4753	139	2	3	3	NUM
cana-4753	139	3	:	:	PUNCT
cana-4753	139	4	classification	classification	NOUN
cana-4753	139	5	accuracy	accuracy	NOUN
cana-4753	139	6	of	of	ADP
cana-4753	139	7	different	different	ADJ
cana-4753	139	8	machine	machine	NOUN
cana-4753	139	9	learning	learning	NOUN
cana-4753	139	10	models	model	NOUN
cana-4753	139	11	in	in	ADP
cana-4753	139	12	addition	addition	NOUN
cana-4753	139	13	,	,	PUNCT
cana-4753	139	14	computational	computational	ADJ
cana-4753	139	15	time	time	NOUN
cana-4753	139	16	and	and	CCONJ
cana-4753	139	17	error	error	NOUN
cana-4753	139	18	rates	rate	NOUN
cana-4753	139	19	of	of	ADP
cana-4753	139	20	various	various	ADJ
cana-4753	139	21	classification	classification	NOUN
cana-4753	139	22	approaches	approach	NOUN
cana-4753	139	23	were	be	AUX
cana-4753	139	24	compared	compare	VERB
cana-4753	139	25	in	in	ADP
cana-4753	139	26	terms	term	NOUN
cana-4753	139	27	of	of	ADP
cana-4753	139	28	efficiency	efficiency	NOUN
cana-4753	139	29	.	.	PUNCT
cana-4753	140	1	furthermore	furthermore	ADV
cana-4753	140	2	,	,	PUNCT
cana-4753	140	3	the	the	DET
cana-4753	140	4	results	result	NOUN
cana-4753	140	5	of	of	ADP
cana-4753	140	6	polynomial	polynomial	ADJ
cana-4753	140	7	,	,	PUNCT
cana-4753	140	8	homology	homology	NOUN
cana-4753	140	9	,	,	PUNCT
cana-4753	140	10	and	and	CCONJ
cana-4753	140	11	machine	machine	NOUN
cana-4753	140	12	learning	learning	NOUN
cana-4753	140	13	based	base	VERB
cana-4753	140	14	methods	method	NOUN
cana-4753	140	15	are	be	AUX
cana-4753	140	16	summarized	summarize	VERB
cana-4753	140	17	in	in	ADP
cana-4753	140	18	table	table	NOUN
cana-4753	140	19	2	2	NUM
cana-4753	140	20	.	.	PUNCT
cana-4753	140	21	table	table	NOUN
cana-4753	140	22	2	2	NUM
cana-4753	140	23	:	:	PUNCT
cana-4753	140	24	computational	computational	ADJ
cana-4753	140	25	performance	performance	NOUN
cana-4753	140	26	and	and	CCONJ
cana-4753	140	27	error	error	NOUN
cana-4753	140	28	rates	rate	NOUN
cana-4753	140	29	of	of	ADP
cana-4753	140	30	classification	classification	NOUN
cana-4753	140	31	methods	method	NOUN
cana-4753	140	32	method	method	PROPN
cana-4753	140	33	avg	avg	PROPN
cana-4753	140	34	.	.	PROPN
cana-4753	141	1	computation	computation	NOUN
cana-4753	141	2	time	time	NOUN
cana-4753	141	3	(	(	PUNCT
cana-4753	141	4	s	s	NOUN
cana-4753	141	5	)	)	PUNCT
cana-4753	141	6	error	error	NOUN
cana-4753	141	7	rate	rate	NOUN
cana-4753	141	8	(	(	PUNCT
cana-4753	141	9	%	%	INTJ
cana-4753	141	10	)	)	PUNCT
cana-4753	141	11	polynomial	polynomial	ADJ
cana-4753	141	12	invariants	invariant	NOUN
cana-4753	141	13	0.92	0.92	NUM
cana-4753	141	14	11.40	11.40	NUM
cana-4753	141	15	%	%	NOUN
cana-4753	141	16	homology	homology	NOUN
cana-4753	141	17	-	-	PUNCT
cana-4753	141	18	based	base	VERB
cana-4753	141	19	1.78	1.78	NUM
cana-4753	141	20	4.30	4.30	NUM
cana-4753	141	21	%	%	NOUN
cana-4753	141	22	machine	machine	NOUN
cana-4753	141	23	learning	learning	NOUN
cana-4753	141	24	(	(	PUNCT
cana-4753	141	25	nn	nn	PROPN
cana-4753	141	26	)	)	PUNCT
cana-4753	141	27	2.31	2.31	NUM
cana-4753	141	28	2.10	2.10	NUM
cana-4753	141	29	%	%	NOUN
cana-4753	141	30	despite	despite	SCONJ
cana-4753	141	31	that	that	DET
cana-4753	141	32	machine	machine	NOUN
cana-4753	141	33	learning	learning	NOUN
cana-4753	141	34	provides	provide	VERB
cana-4753	141	35	lowest	low	ADJ
cana-4753	141	36	error	error	NOUN
cana-4753	141	37	rate	rate	NOUN
cana-4753	141	38	,	,	PUNCT
cana-4753	141	39	it	it	PRON
cana-4753	141	40	entails	entail	VERB
cana-4753	141	41	additional	additional	ADJ
cana-4753	141	42	computational	computational	ADJ
cana-4753	141	43	time	time	NOUN
cana-4753	141	44	with	with	ADP
cana-4753	141	45	respect	respect	NOUN
cana-4753	141	46	to	to	ADP
cana-4753	141	47	both	both	CCONJ
cana-4753	141	48	polynomial	polynomial	ADJ
cana-4753	141	49	and	and	CCONJ
cana-4753	141	50	homology	homology	NOUN
cana-4753	141	51	based	base	VERB
cana-4753	141	52	methods	method	NOUN
cana-4753	141	53	.	.	PUNCT
cana-4753	142	1	the	the	DET
cana-4753	142	2	trade	trade	NOUN
cana-4753	142	3	-	-	PUNCT
cana-4753	142	4	off	off	NOUN
cana-4753	142	5	between	between	ADP
cana-4753	142	6	accuracy	accuracy	NOUN
cana-4753	142	7	and	and	CCONJ
cana-4753	142	8	computational	computational	ADJ
cana-4753	142	9	efficiency	efficiency	NOUN
cana-4753	142	10	of	of	ADP
cana-4753	142	11	the	the	DET
cana-4753	142	12	classification	classification	NOUN
cana-4753	142	13	method	method	NOUN
cana-4753	142	14	impacts	impact	VERB
cana-4753	142	15	the	the	DET
cana-4753	142	16	selection	selection	NOUN
cana-4753	142	17	.	.	PUNCT
cana-4753	143	1	84.50	84.50	NUM
cana-4753	143	2	%	%	NOUN
cana-4753	143	3	81.30	81.30	NUM
cana-4753	143	4	%	%	NOUN
cana-4753	143	5	77.90	77.90	NUM
cana-4753	143	6	%	%	NOUN
cana-4753	143	7	72.60	72.60	NUM
cana-4753	143	8	%	%	NOUN
cana-4753	143	9	91.20	91.20	NUM
cana-4753	143	10	%	%	NOUN
cana-4753	143	11	88.70	88.70	NUM
cana-4753	143	12	%	%	NOUN
cana-4753	143	13	86.10	86.10	NUM
cana-4753	143	14	%	%	NOUN
cana-4753	143	15	82.80	82.80	NUM
cana-4753	143	16	%	%	NOUN
cana-4753	143	17	98.30	98.30	NUM
cana-4753	143	18	%	%	NOUN
cana-4753	143	19	96.50	96.50	NUM
cana-4753	143	20	%	%	NOUN
cana-4753	143	21	94.70	94.70	NUM
cana-4753	143	22	%	%	NOUN
cana-4753	143	23	92.40	92.40	NUM
cana-4753	143	24	%	%	NOUN
cana-4753	143	25	0.00	0.00	NUM
cana-4753	143	26	%	%	NOUN
cana-4753	143	27	20.00	20.00	NUM
cana-4753	143	28	%	%	NOUN
cana-4753	143	29	40.00	40.00	NUM
cana-4753	143	30	%	%	NOUN
cana-4753	143	31	60.00	60.00	NUM
cana-4753	143	32	%	%	NOUN
cana-4753	143	33	80.00	80.00	NUM
cana-4753	143	34	%	%	NOUN
cana-4753	143	35	100.00	100.00	NUM
cana-4753	143	36	%	%	NOUN
cana-4753	143	37	120.00	120.00	NUM
cana-4753	143	38	%	%	NOUN
cana-4753	143	39	trefoil	trefoil	NOUN
cana-4753	143	40	knot	knot	NOUN
cana-4753	143	41	figure	figure	NOUN
cana-4753	143	42	-	-	PUNCT
cana-4753	143	43	eight	eight	NUM
cana-4753	143	44	knot	knot	NOUN
cana-4753	143	45	torus	torus	NOUN
cana-4753	143	46	knot	knot	NOUN
cana-4753	143	47	(	(	PUNCT
cana-4753	143	48	5,2	5,2	NUM
cana-4753	143	49	)	)	PUNCT
cana-4753	143	50	hyperbolic	hyperbolic	ADJ
cana-4753	143	51	knot	knot	NOUN
cana-4753	143	52	classification	classification	NOUN
cana-4753	143	53	accuracy	accuracy	NOUN
cana-4753	143	54	of	of	ADP
cana-4753	143	55	different	different	ADJ
cana-4753	143	56	machine	machine	NOUN
cana-4753	143	57	learning	learning	NOUN
cana-4753	143	58	models	model	NOUN
cana-4753	143	59	decision	decision	VERB
cana-4753	143	60	tree	tree	NOUN
cana-4753	143	61	accuracy	accuracy	NOUN
cana-4753	143	62	(	(	PUNCT
cana-4753	143	63	%	%	INTJ
cana-4753	143	64	)	)	PUNCT
cana-4753	143	65	svm	svm	ADJ
cana-4753	143	66	accuracy	accuracy	NOUN
cana-4753	143	67	(	(	PUNCT
cana-4753	143	68	%	%	INTJ
cana-4753	143	69	)	)	PUNCT
cana-4753	143	70	neural	neural	ADJ
cana-4753	143	71	network	network	NOUN
cana-4753	143	72	accuracy	accuracy	NOUN
cana-4753	143	73	(	(	PUNCT
cana-4753	143	74	%	%	INTJ
cana-4753	143	75	)	)	PUNCT
cana-4753	143	76	communications	communication	NOUN
cana-4753	143	77	on	on	ADP
cana-4753	143	78	applied	apply	VERB
cana-4753	143	79	nonlinear	nonlinear	ADJ
cana-4753	143	80	analysis	analysis	NOUN
cana-4753	143	81	issn	issn	NOUN
cana-4753	143	82	:	:	PUNCT
cana-4753	143	83	1074	1074	NUM
cana-4753	143	84	-	-	PUNCT
cana-4753	143	85	133x	133x	NUM
cana-4753	143	86	vol	vol	VERB
cana-4753	143	87	32	32	NUM
cana-4753	143	88	no	no	NOUN
cana-4753	143	89	.	.	PUNCT
cana-4753	144	1	10s	10	NOUN
cana-4753	144	2	(	(	PUNCT
cana-4753	144	3	2025	2025	NUM
cana-4753	144	4	)	)	PUNCT
cana-4753	144	5	293	293	NUM
cana-4753	144	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4753	144	7	the	the	DET
cana-4753	144	8	methodology	methodology	NOUN
cana-4753	144	9	was	be	AUX
cana-4753	144	10	used	use	VERB
cana-4753	144	11	to	to	PART
cana-4753	144	12	validate	validate	VERB
cana-4753	144	13	the	the	DET
cana-4753	144	14	results	result	NOUN
cana-4753	144	15	in	in	ADP
cana-4753	144	16	the	the	DET
cana-4753	144	17	real	real	ADJ
cana-4753	144	18	world	world	NOUN
cana-4753	144	19	applications	application	NOUN
cana-4753	144	20	for	for	ADP
cana-4753	144	21	dna	dna	NOUN
cana-4753	144	22	and	and	CCONJ
cana-4753	144	23	polymer	polymer	NOUN
cana-4753	144	24	knot	knot	NOUN
cana-4753	144	25	structures	structure	NOUN
cana-4753	144	26	.	.	PUNCT
cana-4753	145	1	in	in	ADP
cana-4753	145	2	figure	figure	NOUN
cana-4753	145	3	4	4	NUM
cana-4753	145	4	,	,	PUNCT
cana-4753	145	5	computed	computed	ADJ
cana-4753	145	6	invariants	invariant	NOUN
cana-4753	145	7	were	be	AUX
cana-4753	145	8	used	use	VERB
cana-4753	145	9	to	to	PART
cana-4753	145	10	analyze	analyze	VERB
cana-4753	145	11	the	the	DET
cana-4753	145	12	extracted	extract	VERB
cana-4753	145	13	knots	knot	NOUN
cana-4753	145	14	from	from	ADP
cana-4753	145	15	biological	biological	ADJ
cana-4753	145	16	macromolecules	macromolecule	NOUN
cana-4753	145	17	.	.	PUNCT
cana-4753	146	1	the	the	DET
cana-4753	146	2	results	result	NOUN
cana-4753	146	3	demonstrate	demonstrate	VERB
cana-4753	146	4	a	a	DET
cana-4753	146	5	clear	clear	ADJ
cana-4753	146	6	correlation	correlation	NOUN
cana-4753	146	7	between	between	ADP
cana-4753	146	8	topological	topological	ADJ
cana-4753	146	9	complexity	complexity	NOUN
cana-4753	146	10	of	of	ADP
cana-4753	146	11	proteins	protein	NOUN
cana-4753	146	12	and	and	CCONJ
cana-4753	146	13	dna	dna	PROPN
cana-4753	146	14	structures	structure	NOUN
cana-4753	146	15	and	and	CCONJ
cana-4753	146	16	biological	biological	ADJ
cana-4753	146	17	function	function	NOUN
cana-4753	146	18	,	,	PUNCT
cana-4753	146	19	where	where	SCONJ
cana-4753	146	20	proteins	protein	NOUN
cana-4753	146	21	with	with	ADP
cana-4753	146	22	complex	complex	ADJ
cana-4753	146	23	,	,	PUNCT
cana-4753	146	24	multiinteracting	multiinteracte	VERB
cana-4753	146	25	knots	knot	NOUN
cana-4753	146	26	arise	arise	VERB
cana-4753	146	27	in	in	ADP
cana-4753	146	28	dna	dna	PROPN
cana-4753	146	29	supercoiling	supercoiling	NOUN
cana-4753	146	30	and	and	CCONJ
cana-4753	146	31	protein	protein	NOUN
cana-4753	146	32	folding	fold	VERB
cana-4753	146	33	experiments	experiment	NOUN
cana-4753	146	34	.	.	PUNCT
cana-4753	147	1	figure	figure	VERB
cana-4753	147	2	4	4	NUM
cana-4753	147	3	:	:	PUNCT
cana-4753	147	4	knot	knot	NOUN
cana-4753	147	5	complexity	complexity	NOUN
cana-4753	147	6	vs.	vs.	ADP
cana-4753	147	7	biological	biological	ADJ
cana-4753	147	8	function	function	NOUN
cana-4753	147	9	in	in	ADP
cana-4753	147	10	macromolecules	macromolecule	NOUN
cana-4753	147	11	this	this	DET
cana-4753	147	12	study	study	NOUN
cana-4753	147	13	is	be	AUX
cana-4753	147	14	first	first	ADV
cana-4753	147	15	in	in	ADP
cana-4753	147	16	confirming	confirm	VERB
cana-4753	147	17	that	that	SCONJ
cana-4753	147	18	topological	topological	ADJ
cana-4753	147	19	methods	method	NOUN
cana-4753	147	20	are	be	AUX
cana-4753	147	21	very	very	ADV
cana-4753	147	22	powerful	powerful	ADJ
cana-4753	147	23	in	in	ADP
cana-4753	147	24	characterising	characterise	VERB
cana-4753	147	25	structural	structural	ADJ
cana-4753	147	26	properties	property	NOUN
cana-4753	147	27	in	in	ADP
cana-4753	147	28	various	various	ADJ
cana-4753	147	29	fields	field	NOUN
cana-4753	147	30	.	.	PUNCT
cana-4753	148	1	further	further	ADJ
cana-4753	148	2	research	research	NOUN
cana-4753	148	3	can	can	AUX
cana-4753	148	4	improve	improve	VERB
cana-4753	148	5	this	this	DET
cana-4753	148	6	technique	technique	NOUN
cana-4753	148	7	to	to	ADP
cana-4753	148	8	higher	high	ADJ
cana-4753	148	9	dimensional	dimensional	ADJ
cana-4753	148	10	knot	knot	NOUN
cana-4753	148	11	structure	structure	NOUN
cana-4753	148	12	and	and	CCONJ
cana-4753	148	13	real	real	ADJ
cana-4753	148	14	time	time	NOUN
cana-4753	148	15	classification	classification	NOUN
cana-4753	148	16	model	model	NOUN
cana-4753	148	17	.	.	PUNCT
cana-4753	149	1	v.	v.	ADP
cana-4753	149	2	conclusion	conclusion	NOUN
cana-4753	149	3	the	the	DET
cana-4753	149	4	analysis	analysis	NOUN
cana-4753	149	5	and	and	CCONJ
cana-4753	149	6	classification	classification	NOUN
cana-4753	149	7	of	of	ADP
cana-4753	149	8	knotted	knotted	ADJ
cana-4753	149	9	structures	structure	NOUN
cana-4753	149	10	using	use	VERB
cana-4753	149	11	topological	topological	ADJ
cana-4753	149	12	methods	method	NOUN
cana-4753	149	13	in	in	ADP
cana-4753	149	14	aspects	aspect	NOUN
cana-4753	149	15	of	of	ADP
cana-4753	149	16	knot	knot	NOUN
cana-4753	149	17	theory	theory	NOUN
cana-4753	149	18	are	be	AUX
cana-4753	149	19	quite	quite	ADV
cana-4753	149	20	powerful	powerful	ADJ
cana-4753	149	21	tools	tool	NOUN
cana-4753	149	22	.	.	PUNCT
cana-4753	150	1	knots	knot	NOUN
cana-4753	150	2	are	be	AUX
cana-4753	150	3	equivalent	equivalent	ADJ
cana-4753	150	4	if	if	SCONJ
cana-4753	150	5	the	the	DET
cana-4753	150	6	number	number	NOUN
cana-4753	150	7	of	of	ADP
cana-4753	150	8	reidemeister	reidemeister	ADJ
cana-4753	150	9	moves	move	NOUN
cana-4753	150	10	between	between	ADP
cana-4753	150	11	two	two	NUM
cana-4753	150	12	representations	representation	NOUN
cana-4753	150	13	of	of	ADP
cana-4753	150	14	a	a	DET
cana-4753	150	15	given	give	VERB
cana-4753	150	16	knot	knot	NOUN
cana-4753	150	17	is	be	AUX
cana-4753	150	18	finite	finite	ADJ
cana-4753	150	19	;	;	PUNCT
cana-4753	150	20	polynomial	polynomial	ADJ
cana-4753	150	21	invariants	invariant	NOUN
cana-4753	150	22	and	and	CCONJ
cana-4753	150	23	homology	homology	NOUN
cana-4753	150	24	based	base	VERB
cana-4753	150	25	approaches	approach	NOUN
cana-4753	150	26	allow	allow	VERB
cana-4753	150	27	for	for	ADP
cana-4753	150	28	deeper	deep	ADJ
cana-4753	150	29	investigation	investigation	NOUN
cana-4753	150	30	into	into	ADP
cana-4753	150	31	complexity	complexity	NOUN
cana-4753	150	32	of	of	ADP
cana-4753	150	33	knots	knot	NOUN
cana-4753	150	34	.	.	PUNCT
cana-4753	151	1	the	the	DET
cana-4753	151	2	matter	matter	NOUN
cana-4753	151	3	continues	continue	VERB
cana-4753	151	4	to	to	PART
cana-4753	151	5	develop	develop	VERB
cana-4753	151	6	computationally	computationally	ADV
cana-4753	151	7	,	,	PUNCT
cana-4753	151	8	enabling	enable	VERB
cana-4753	151	9	us	we	PRON
cana-4753	151	10	to	to	PART
cana-4753	151	11	investigate	investigate	VERB
cana-4753	151	12	knots	knot	NOUN
cana-4753	151	13	in	in	ADP
cana-4753	151	14	both	both	CCONJ
cana-4753	151	15	theoretical	theoretical	ADJ
cana-4753	151	16	and	and	CCONJ
cana-4753	151	17	practical	practical	ADJ
cana-4753	151	18	situations	situation	NOUN
cana-4753	151	19	.	.	PUNCT
cana-4753	152	1	further	further	ADJ
cana-4753	152	2	refinement	refinement	NOUN
cana-4753	152	3	of	of	ADP
cana-4753	152	4	invariants	invariant	NOUN
cana-4753	152	5	and	and	CCONJ
cana-4753	152	6	use	use	NOUN
cana-4753	152	7	in	in	ADP
cana-4753	152	8	new	new	ADJ
cana-4753	152	9	applications	application	NOUN
cana-4753	152	10	related	relate	VERB
cana-4753	152	11	to	to	ADP
cana-4753	152	12	quantum	quantum	NOUN
cana-4753	152	13	computing	computing	NOUN
cana-4753	152	14	and	and	CCONJ
cana-4753	152	15	material	material	NOUN
cana-4753	152	16	sciences	science	NOUN
cana-4753	152	17	may	may	AUX
cana-4753	152	18	be	be	AUX
cana-4753	152	19	subjects	subject	NOUN
cana-4753	152	20	of	of	ADP
cana-4753	152	21	future	future	ADJ
cana-4753	152	22	research	research	NOUN
cana-4753	152	23	.	.	PUNCT
cana-4753	153	1	despite	despite	SCONJ
cana-4753	153	2	the	the	DET
cana-4753	153	3	significant	significant	ADJ
cana-4753	153	4	advances	advance	NOUN
cana-4753	153	5	in	in	ADP
cana-4753	153	6	the	the	DET
cana-4753	153	7	field	field	NOUN
cana-4753	153	8	,	,	PUNCT
cana-4753	153	9	knot	knot	NOUN
cana-4753	153	10	theory	theory	NOUN
cana-4753	153	11	still	still	ADV
cana-4753	153	12	is	be	AUX
cana-4753	153	13	vibrant	vibrant	ADJ
cana-4753	153	14	and	and	CCONJ
cana-4753	153	15	changing	change	VERB
cana-4753	153	16	,	,	PUNCT
cana-4753	153	17	and	and	CCONJ
cana-4753	153	18	has	have	VERB
cana-4753	153	19	implications	implication	NOUN
cana-4753	153	20	for	for	ADP
cana-4753	153	21	problems	problem	NOUN
cana-4753	153	22	in	in	ADP
cana-4753	153	23	physical	physical	ADJ
cana-4753	153	24	and	and	CCONJ
cana-4753	153	25	biological	biological	ADJ
cana-4753	153	26	sciences	science	NOUN
cana-4753	153	27	.	.	PUNCT
cana-4753	154	1	communications	communication	NOUN
cana-4753	154	2	on	on	ADP
cana-4753	154	3	applied	apply	VERB
cana-4753	154	4	nonlinear	nonlinear	ADJ
cana-4753	154	5	analysis	analysis	NOUN
cana-4753	154	6	issn	issn	NOUN
cana-4753	154	7	:	:	PUNCT
cana-4753	154	8	1074	1074	NUM
cana-4753	154	9	-	-	PUNCT
cana-4753	154	10	133x	133x	NUM
cana-4753	154	11	vol	vol	VERB
cana-4753	154	12	32	32	NUM
cana-4753	154	13	no	no	NOUN
cana-4753	154	14	.	.	PUNCT
cana-4753	155	1	10s	10	NOUN
cana-4753	155	2	(	(	PUNCT
cana-4753	155	3	2025	2025	NUM
cana-4753	155	4	)	)	PUNCT
cana-4753	155	5	294	294	NUM
cana-4753	155	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4753	155	7	references	reference	NOUN
cana-4753	155	8	[	[	X
cana-4753	155	9	1	1	X
cana-4753	155	10	]	]	PUNCT
cana-4753	155	11	v.	v.	ADP
cana-4753	155	12	p.	p.	PROPN
cana-4753	155	13	patil	patil	PROPN
cana-4753	155	14	,	,	PUNCT
cana-4753	155	15	j.	j.	PROPN
cana-4753	155	16	dunkel	dunkel	PROPN
cana-4753	155	17	,	,	PUNCT
cana-4753	155	18	j.	j.	PROPN
cana-4753	155	19	d.	d.	PROPN
cana-4753	155	20	sandt	sandt	PROPN
cana-4753	155	21	,	,	PUNCT
cana-4753	155	22	and	and	CCONJ
cana-4753	155	23	m.	m.	NOUN
cana-4753	155	24	kolle	kolle	PROPN
cana-4753	155	25	,	,	PUNCT
cana-4753	155	26	"	"	PUNCT
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cana-4753	155	28	mechanics	mechanic	NOUN
cana-4753	155	29	of	of	ADP
cana-4753	155	30	knots	knot	NOUN
cana-4753	155	31	and	and	CCONJ
cana-4753	155	32	tangles	tangle	NOUN
cana-4753	155	33	,	,	PUNCT
cana-4753	155	34	"	"	PUNCT
cana-4753	155	35	science	science	NOUN
cana-4753	155	36	,	,	PUNCT
cana-4753	155	37	vol	vol	NOUN
cana-4753	155	38	.	.	PROPN
cana-4753	155	39	367	367	NUM
cana-4753	155	40	,	,	PUNCT
cana-4753	155	41	no	no	INTJ
cana-4753	155	42	.	.	NOUN
cana-4753	155	43	6473	6473	NUM
cana-4753	155	44	,	,	PUNCT
cana-4753	155	45	pp	pp	ADV
cana-4753	155	46	.	.	PUNCT
cana-4753	156	1	71–75	71–75	NOUN
cana-4753	156	2	,	,	PUNCT
cana-4753	156	3	jan	jan	PROPN
cana-4753	156	4	.	.	PROPN
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cana-4753	156	6	,	,	PUNCT
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cana-4753	156	8	:	:	PUNCT
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cana-4753	156	10	/	/	SYM
cana-4753	156	11	science.aaz0135	science.aaz0135	X
cana-4753	156	12	.	.	PUNCT
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cana-4753	157	2	2	2	NUM
cana-4753	157	3	]	]	PUNCT
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cana-4753	157	14	"	"	PUNCT
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cana-4753	157	16	invariants	invariant	NOUN
cana-4753	157	17	and	and	CCONJ
cana-4753	157	18	their	their	PRON
cana-4753	157	19	relations	relation	NOUN
cana-4753	157	20	:	:	PUNCT
cana-4753	157	21	a	a	DET
cana-4753	157	22	topological	topological	ADJ
cana-4753	157	23	perspective	perspective	NOUN
cana-4753	157	24	,	,	PUNCT
cana-4753	157	25	"	"	PUNCT
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cana-4753	157	29	,	,	PUNCT
cana-4753	157	30	sep	sep	PROPN
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cana-4753	157	33	.	.	PUNCT
cana-4753	158	1	[	[	X
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cana-4753	158	3	]	]	X
cana-4753	158	4	.	.	PUNCT
cana-4753	159	1	available	available	ADJ
cana-4753	159	2	:	:	PUNCT
cana-4753	160	1	https://arxiv.org/abs/2109.00831v1	https://arxiv.org/abs/2109.00831v1	NUM
cana-4753	160	2	[	[	X
cana-4753	160	3	3	3	X
cana-4753	160	4	]	]	PUNCT
cana-4753	160	5	k.	k.	PROPN
cana-4753	160	6	e.	e.	PROPN
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cana-4753	160	10	a.	a.	PROPN
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cana-4753	160	14	w.	w.	PROPN
cana-4753	160	15	steed	steed	PROPN
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cana-4753	160	17	and	and	CCONJ
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cana-4753	160	28	,	,	PUNCT
cana-4753	160	29	"	"	PUNCT
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cana-4753	161	8	.	.	PUNCT
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cana-4753	162	2	,	,	PUNCT
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cana-4753	162	4	,	,	PUNCT
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cana-4753	162	6	:	:	PUNCT
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cana-4753	163	15	proteins	protein	NOUN
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cana-4753	163	30	-	-	SYM
cana-4753	163	31	7	7	NUM
cana-4753	163	32	,	,	PUNCT
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cana-4753	163	42	:	:	PUNCT
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cana-4753	163	44	/	/	SYM
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cana-4753	163	46	-	-	PUNCT
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cana-4753	163	48	-	-	PUNCT
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cana-4753	163	50	-	-	PUNCT
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cana-4753	164	3	]	]	PUNCT
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cana-4753	164	20	mathematical	mathematical	PROPN
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cana-4753	164	30	,	,	PUNCT
cana-4753	164	31	pp	pp	ADJ
cana-4753	164	32	.	.	PUNCT
cana-4753	165	1	417–471	417–471	NUM
cana-4753	165	2	,	,	PUNCT
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cana-4753	165	4	,	,	PUNCT
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cana-4753	165	6	:	:	PUNCT
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cana-4753	165	8	.	.	PUNCT
cana-4753	166	1	[	[	X
cana-4753	166	2	6	6	NUM
cana-4753	166	3	]	]	PUNCT
cana-4753	166	4	j.	j.	PROPN
cana-4753	166	5	w.	w.	PROPN
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cana-4753	166	8	"	"	PUNCT
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cana-4753	166	21	mathematical	mathematical	PROPN
cana-4753	166	22	society	society	NOUN
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cana-4753	167	8	:	:	PUNCT
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cana-4753	167	10	.	.	PUNCT
cana-4753	168	1	[	[	X
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cana-4753	168	35	,	,	PUNCT
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cana-4753	168	37	.	.	PUNCT
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cana-4753	169	2	,	,	PUNCT
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cana-4753	169	12	-	-	PUNCT
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cana-4753	169	14	-	-	SYM
cana-4753	169	15	15304	15304	NUM
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cana-4753	170	25	.	.	PUNCT
cana-4753	171	1	1–4	1–4	NUM
cana-4753	171	2	,	,	PUNCT
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cana-4753	171	4	,	,	PUNCT
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cana-4753	171	6	:	:	PUNCT
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cana-4753	171	8	/	/	SYM
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cana-4753	172	3	]	]	PUNCT
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cana-4753	172	29	,	,	PUNCT
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cana-4753	172	31	.	.	PUNCT
cana-4753	173	1	300–332	300–332	NUM
cana-4753	173	2	,	,	PUNCT
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cana-4753	173	5	,	,	PUNCT
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cana-4753	173	7	:	:	PUNCT
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cana-4753	173	9	/	/	SYM
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cana-4753	174	3	]	]	PUNCT
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cana-4753	174	42	,	,	PUNCT
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cana-4753	174	48	:	:	PUNCT
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cana-4753	177	8	:	:	PUNCT
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cana-4753	189	7	:	:	PUNCT
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