{"id":"https://openalex.org/W2901921701","doi":"https://doi.org/10.1007/s41468-020-00062-y","title":"Another look at recovering local homology from samples of stratified sets","display_name":"Another look at recovering local homology from samples of stratified sets","publication_year":2020,"publication_date":"2020-11-24","ids":{"openalex":"https://openalex.org/W2901921701","doi":"https://doi.org/10.1007/s41468-020-00062-y","mag":"2901921701"},"language":"en","primary_location":{"id":"doi:10.1007/s41468-020-00062-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s41468-020-00062-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210173698","display_name":"Journal of Applied and Computational Topology","issn_l":"2367-1726","issn":["2367-1726","2367-1734"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied and Computational Topology","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1811.09033","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031050042","display_name":"Yuriy Mileyko","orcid":"https://orcid.org/0000-0001-7720-8625"},"institutions":[{"id":"https://openalex.org/I117965899","display_name":"University of Hawai\u02bbi at M\u0101noa","ror":"https://ror.org/01wspgy28","country_code":"US","type":"education","lineage":["https://openalex.org/I117965899"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yuriy Mileyko","raw_affiliation_strings":["Department of Mathematics, University of Hawai\u2018i at M\u0101noa, Honolulu, HI, USA","Department of Mathematics, University of Hawai\u2018i at M\u0101noa, Honolulu, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Hawai\u2018i at M\u0101noa, Honolulu, HI, USA","institution_ids":["https://openalex.org/I117965899"]},{"raw_affiliation_string":"Department of Mathematics, University of Hawai\u2018i at M\u0101noa, Honolulu, USA","institution_ids":["https://openalex.org/I117965899"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5031050042"],"corresponding_institution_ids":["https://openalex.org/I117965899"],"apc_list":{"value":2490,"currency":"EUR","value_usd":3090},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01349824,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"5","issue":"1","first_page":"55","last_page":"97"},"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":0.9187999963760376,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homology","display_name":"Homology (biology)","score":0.7514825463294983},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6609853506088257},{"id":"https://openalex.org/keywords/persistent-homology","display_name":"Persistent homology","score":0.6069797277450562},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5819138884544373},{"id":"https://openalex.org/keywords/mayer\u2013vietoris-sequence","display_name":"Mayer\u2013Vietoris sequence","score":0.5354397892951965},{"id":"https://openalex.org/keywords/singular-homology","display_name":"Singular homology","score":0.5331014394760132},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5123413801193237},{"id":"https://openalex.org/keywords/relative-homology","display_name":"Relative homology","score":0.4417240619659424},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4361984133720398},{"id":"https://openalex.org/keywords/morse-homology","display_name":"Morse homology","score":0.43077677488327026},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41194161772727966},{"id":"https://openalex.org/keywords/cellular-homology","display_name":"Cellular homology","score":0.34913235902786255},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.34805846214294434},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2562083303928375},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.19367939233779907},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16191169619560242},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15103206038475037},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.09560984373092651},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09272736310958862},{"id":"https://openalex.org/keywords/genetics","display_name":"Genetics","score":0.07618328928947449}],"concepts":[{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.7514825463294983},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6609853506088257},{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.6069797277450562},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5819138884544373},{"id":"https://openalex.org/C201595698","wikidata":"https://www.wikidata.org/wiki/Q2421905","display_name":"Mayer\u2013Vietoris sequence","level":5,"score":0.5354397892951965},{"id":"https://openalex.org/C139962677","wikidata":"https://www.wikidata.org/wiki/Q1095056","display_name":"Singular homology","level":3,"score":0.5331014394760132},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5123413801193237},{"id":"https://openalex.org/C79536532","wikidata":"https://www.wikidata.org/wiki/Q1959911","display_name":"Relative homology","level":3,"score":0.4417240619659424},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4361984133720398},{"id":"https://openalex.org/C135783237","wikidata":"https://www.wikidata.org/wiki/Q3139850","display_name":"Morse homology","level":4,"score":0.43077677488327026},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41194161772727966},{"id":"https://openalex.org/C55537702","wikidata":"https://www.wikidata.org/wiki/Q3139849","display_name":"Cellular homology","level":3,"score":0.34913235902786255},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.34805846214294434},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2562083303928375},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.19367939233779907},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16191169619560242},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15103206038475037},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.09560984373092651},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09272736310958862},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.07618328928947449},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C68365058","wikidata":"https://www.wikidata.org/wiki/Q1179446","display_name":"De Rham cohomology","level":4,"score":0.0},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.0},{"id":"https://openalex.org/C72738302","wikidata":"https://www.wikidata.org/wiki/Q5384738","display_name":"Equivariant cohomology","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s41468-020-00062-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s41468-020-00062-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210173698","display_name":"Journal of Applied and Computational Topology","issn_l":"2367-1726","issn":["2367-1726","2367-1734"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied and Computational Topology","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1811.09033","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.09033","pdf_url":"https://arxiv.org/pdf/1811.09033","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"raw_type":"text"},{"id":"mag:2901921701","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1811.09033.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"doi:10.48550/arxiv.1811.09033","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1811.09033","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1811.09033","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.09033","pdf_url":"https://arxiv.org/pdf/1811.09033","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"raw_type":"text"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.75,"id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G5550204662","display_name":null,"funder_award_id":"1622370","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2901921701.pdf","grobid_xml":"https://content.openalex.org/works/W2901921701.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W138198174","https://openalex.org/W204424931","https://openalex.org/W963510603","https://openalex.org/W1500527815","https://openalex.org/W1824091107","https://openalex.org/W2001887552","https://openalex.org/W2005235405","https://openalex.org/W2008318377","https://openalex.org/W2026940923","https://openalex.org/W2037613900","https://openalex.org/W2053964005","https://openalex.org/W2054863674","https://openalex.org/W2071391326","https://openalex.org/W2104339857","https://openalex.org/W2107385756","https://openalex.org/W2107605271","https://openalex.org/W2137630416","https://openalex.org/W2144044408","https://openalex.org/W2153986241","https://openalex.org/W2157878484","https://openalex.org/W2265449668","https://openalex.org/W2730468593","https://openalex.org/W2963490465","https://openalex.org/W2964207424","https://openalex.org/W3013843370","https://openalex.org/W3139497334","https://openalex.org/W3146195181","https://openalex.org/W4214508989","https://openalex.org/W4300596011","https://openalex.org/W6606051743"],"related_works":["https://openalex.org/W2405964180","https://openalex.org/W1597154499","https://openalex.org/W2259415067","https://openalex.org/W2147574294","https://openalex.org/W2940763224","https://openalex.org/W2318791702","https://openalex.org/W2066191910","https://openalex.org/W3100454687","https://openalex.org/W3143351869","https://openalex.org/W2009328525","https://openalex.org/W2963971663","https://openalex.org/W2606944287","https://openalex.org/W2518610711","https://openalex.org/W2015397797","https://openalex.org/W2093904227","https://openalex.org/W2024442599","https://openalex.org/W34517249","https://openalex.org/W124404839","https://openalex.org/W2900953251","https://openalex.org/W1965211543"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}