{"id":"https://openalex.org/W2784928080","doi":"https://doi.org/10.1137/18m1198946","title":"Persistent Homology of Morse Decompositions in Combinatorial Dynamics","display_name":"Persistent Homology of Morse Decompositions in Combinatorial Dynamics","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2784928080","doi":"https://doi.org/10.1137/18m1198946","mag":"2784928080"},"language":"en","primary_location":{"id":"doi:10.1137/18m1198946","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1198946","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1801.06590","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025354167","display_name":"Tamal K. Dey","orcid":"https://orcid.org/0000-0001-5160-9738"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tamal K. Dey","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079428434","display_name":"Mateusz Juda","orcid":"https://orcid.org/0000-0003-2023-8430"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mateusz Juda","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-2023-8430","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087210938","display_name":"Tomasz Kapela","orcid":"https://orcid.org/0000-0001-5283-3053"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tomasz Kapela","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-5283-3053","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045733612","display_name":"Jacek Kubica","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jacek Kubica","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039286285","display_name":"Micha\u0142 Lipi\u0144ski","orcid":"https://orcid.org/0000-0001-9789-9750"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Micha\u0142 Lipi\u0144ski","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5072482789","display_name":"Marian Mro\u017cek","orcid":"https://orcid.org/0000-0002-0619-6417"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marian Mrozek","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.01452841,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"18","issue":"1","first_page":"510","last_page":"530"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9519000053405762,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11337","display_name":"Tryptophan and brain disorders","score":0.9293000102043152,"subfield":{"id":"https://openalex.org/subfields/2803","display_name":"Biological Psychiatry"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/persistent-homology","display_name":"Persistent homology","score":0.8652637004852295},{"id":"https://openalex.org/keywords/morse-theory","display_name":"Morse theory","score":0.7557700872421265},{"id":"https://openalex.org/keywords/topological-data-analysis","display_name":"Topological data analysis","score":0.7266506552696228},{"id":"https://openalex.org/keywords/discrete-morse-theory","display_name":"Discrete Morse theory","score":0.6940058469772339},{"id":"https://openalex.org/keywords/persistence","display_name":"Persistence (discontinuity)","score":0.5877598524093628},{"id":"https://openalex.org/keywords/morse-code","display_name":"Morse code","score":0.5187992453575134},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5141696929931641},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.49665528535842896},{"id":"https://openalex.org/keywords/homology","display_name":"Homology (biology)","score":0.46943357586860657},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4651881754398346},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42012256383895874},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.38701048493385315},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35829058289527893},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.34493911266326904},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32093292474746704},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24144133925437927},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14175519347190857},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11515006422996521},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.10691985487937927},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08059579133987427}],"concepts":[{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.8652637004852295},{"id":"https://openalex.org/C156730297","wikidata":"https://www.wikidata.org/wiki/Q2296951","display_name":"Morse theory","level":2,"score":0.7557700872421265},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.7266506552696228},{"id":"https://openalex.org/C170315498","wikidata":"https://www.wikidata.org/wiki/Q5282039","display_name":"Discrete Morse theory","level":3,"score":0.6940058469772339},{"id":"https://openalex.org/C2781009140","wikidata":"https://www.wikidata.org/wiki/Q7170389","display_name":"Persistence (discontinuity)","level":2,"score":0.5877598524093628},{"id":"https://openalex.org/C140031139","wikidata":"https://www.wikidata.org/wiki/Q79897","display_name":"Morse code","level":2,"score":0.5187992453575134},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5141696929931641},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.49665528535842896},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.46943357586860657},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4651881754398346},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42012256383895874},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.38701048493385315},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35829058289527893},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.34493911266326904},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32093292474746704},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24144133925437927},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14175519347190857},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11515006422996521},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.10691985487937927},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08059579133987427},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/18m1198946","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1198946","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1801.06590","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.06590","pdf_url":"https://arxiv.org/pdf/1801.06590","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"mag:2784928080","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1801.06590","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:ruj.uj.edu.pl:item/74324","is_oa":true,"landing_page_url":"https://ruj.uj.edu.pl/xmlui/handle/item/74324","pdf_url":null,"source":{"id":"https://openalex.org/S4306400316","display_name":"Homo Politicus (Academy of Humanities and Economics in Lodz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"artyku\u0142 w czasopi\u015bmie"},{"id":"doi:10.48550/arxiv.1801.06590","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1801.06590","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1801.06590","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.06590","pdf_url":"https://arxiv.org/pdf/1801.06590","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G509936060","display_name":null,"funder_award_id":"2014/14/A/ST1/00453","funder_id":"https://openalex.org/F4320322511","funder_display_name":"Narodowe Centrum Nauki"},{"id":"https://openalex.org/G8438770202","display_name":null,"funder_award_id":"1839252","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"},{"id":"https://openalex.org/G8964230779","display_name":null,"funder_award_id":"1740761","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"}],"funders":[{"id":"https://openalex.org/F4320322511","display_name":"Narodowe Centrum Nauki","ror":"https://ror.org/03ha2q922"},{"id":"https://openalex.org/F4320337387","display_name":"Division of Computing and Communication Foundations","ror":"https://ror.org/01mng8331"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W162901799","https://openalex.org/W643853242","https://openalex.org/W1496383623","https://openalex.org/W1540633728","https://openalex.org/W1558680303","https://openalex.org/W1570807537","https://openalex.org/W1596321532","https://openalex.org/W1970454523","https://openalex.org/W1976948755","https://openalex.org/W1978925672","https://openalex.org/W2008578784","https://openalex.org/W2053436201","https://openalex.org/W2064020260","https://openalex.org/W2072154382","https://openalex.org/W2082618972","https://openalex.org/W2083505163","https://openalex.org/W2097894461","https://openalex.org/W2158407067","https://openalex.org/W2267136012","https://openalex.org/W2292272678","https://openalex.org/W2308445341","https://openalex.org/W2517445839","https://openalex.org/W2755090915","https://openalex.org/W2913946465","https://openalex.org/W2963213081","https://openalex.org/W3013843370","https://openalex.org/W3082060182","https://openalex.org/W3128780189"],"related_works":["https://openalex.org/W3177616761","https://openalex.org/W2765858924","https://openalex.org/W2952867171","https://openalex.org/W2515739812","https://openalex.org/W2016710035","https://openalex.org/W3098848338","https://openalex.org/W2604548412","https://openalex.org/W3037459456","https://openalex.org/W2896542238","https://openalex.org/W2105074712","https://openalex.org/W1485238525","https://openalex.org/W3109521495","https://openalex.org/W3081318846","https://openalex.org/W3011170784","https://openalex.org/W2301884577","https://openalex.org/W1501587098","https://openalex.org/W2618790459","https://openalex.org/W2942499889","https://openalex.org/W1958922472"],"abstract_inverted_index":{"We":[0,38,77],"investigate":[1],"combinatorial":[2],"dynamical":[3,75],"systems":[4,14,48],"on":[5,81],"simplicial":[6],"complexes":[7],"considered":[8],"as":[9,49,61],"finite":[10],"topological":[11],"spaces.":[12],"Such":[13],"arise":[15],"in":[16],"a":[17,50,62,74],"natural":[18],"way":[19],"from":[20,35,73],"sampling":[21],"dynamics":[22,33],"and":[23],"may":[24,58],"be":[25,59],"used":[26],"to":[27,70],"reconstruct":[28],"some":[29],"features":[30],"of":[31,43,46],"the":[32,36,40,54,66],"directly":[34],"sample.":[37],"study":[39],"homological":[41],"persistence":[42,68],"Morse":[44],"decompositions":[45],"such":[47],"tool":[51],"for":[52],"validating":[53],"reconstruction.":[55],"Our":[56],"approach":[57],"viewed":[60],"step":[63],"toward":[64],"applying":[65],"classical":[67],"theory":[69],"data":[71],"collected":[72],"system.":[76],"present":[78],"experimental":[79],"results":[80],"two":[82],"numerical":[83],"examples.":[84]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
