{"id":"https://openalex.org/W186822082","doi":null,"title":"Analyzing stratified spaces using persistent versions of intersection and local homology","display_name":"Analyzing stratified spaces using persistent versions of intersection and local homology","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W186822082","mag":"186822082"},"language":"en","primary_location":{"id":"pmh:oai:dukespace.lib.duke.edu:10161/680","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/10161/680","pdf_url":null,"source":{"id":"https://openalex.org/S4306400687","display_name":"DukeSpace (Duke University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I170897317","host_organization_name":"Duke University","host_organization_lineage":["https://openalex.org/I170897317"],"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":"","raw_type":"Dissertation"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10161/680","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046061686","display_name":"John Harer","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Harer","raw_affiliation_strings":["Duke University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Duke University","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007045835","display_name":"Paul L Bendich","orcid":"https://orcid.org/0000-0002-4862-0730","observed_orcids":["https://orcid.org/0000-0002-4862-0730"]},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul Bendich","raw_affiliation_strings":["Duke University"],"raw_orcid":"https://orcid.org/0000-0002-4862-0730","affiliations":[{"raw_affiliation_string":"Duke University","institution_ids":["https://openalex.org/I170897317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I170897317"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9984999895095825,"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":0.9984999895095825,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.00019999999494757503,"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/persistent-homology","display_name":"persistent homology","score":0.8880000114440918},{"id":"https://openalex.org/keywords/intersection-homology","display_name":"intersection homology","score":0.9710000157356262},{"id":"https://openalex.org/keywords/local-homology","display_name":"local homology","score":0.9990000128746033},{"id":"https://openalex.org/keywords/stratified-spaces","display_name":"stratified spaces","score":0.9599999785423279},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"simplicial complexes","score":0.8370000123977661},{"id":"https://openalex.org/keywords/local-maxima","display_name":"local maxima","score":0.6710000038146973},{"id":"https://openalex.org/keywords/dense-sampling","display_name":"dense sampling","score":0.6499999761581421},{"id":"https://openalex.org/keywords/high-dimensional-data","display_name":"high-dimensional data","score":0.6309999823570251},{"id":"https://openalex.org/keywords/noisy-data","display_name":"noisy data","score":0.7080000042915344}],"concepts":[{"id":"https://openalex.org/C63549537","wikidata":"https://www.wikidata.org/wiki/Q6056721","display_name":"Intersection homology","level":3,"score":0.7968616485595703},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7570810317993164},{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.7088961601257324},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.6993139982223511},{"id":"https://openalex.org/C201595698","wikidata":"https://www.wikidata.org/wiki/Q2421905","display_name":"Mayer\u2013Vietoris sequence","level":5,"score":0.6203528046607971},{"id":"https://openalex.org/C135783237","wikidata":"https://www.wikidata.org/wiki/Q3139850","display_name":"Morse homology","level":4,"score":0.6106852293014526},{"id":"https://openalex.org/C139962677","wikidata":"https://www.wikidata.org/wiki/Q1095056","display_name":"Singular homology","level":3,"score":0.5576055645942688},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.49413707852363586},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4663134515285492},{"id":"https://openalex.org/C79536532","wikidata":"https://www.wikidata.org/wiki/Q1959911","display_name":"Relative homology","level":3,"score":0.4506995975971222},{"id":"https://openalex.org/C55537702","wikidata":"https://www.wikidata.org/wiki/Q3139849","display_name":"Cellular homology","level":3,"score":0.24319490790367126},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.18825283646583557},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14209559559822083},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.12721365690231323},{"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/C72738302","wikidata":"https://www.wikidata.org/wiki/Q5384738","display_name":"Equivariant cohomology","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:dukespace.lib.duke.edu:10161/680","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/10161/680","pdf_url":null,"source":{"id":"https://openalex.org/S4306400687","display_name":"DukeSpace (Duke University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I170897317","host_organization_name":"Duke University","host_organization_lineage":["https://openalex.org/I170897317"],"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":"","raw_type":"Dissertation"},{"id":"mag:186822082","doi":null,"is_oa":false,"landing_page_url":"https://dukespace.lib.duke.edu/dspace/bitstream/10161/680/1/D_Bendich_Paul_a_200808.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:dukespace.lib.duke.edu:10161/680","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/10161/680","pdf_url":null,"source":{"id":"https://openalex.org/S4306400687","display_name":"DukeSpace (Duke University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I170897317","host_organization_name":"Duke University","host_organization_lineage":["https://openalex.org/I170897317"],"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":"","raw_type":"Dissertation"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W204424931","https://openalex.org/W1496383623","https://openalex.org/W1515675992","https://openalex.org/W1516289958","https://openalex.org/W1572740858","https://openalex.org/W1989871800","https://openalex.org/W1990536341","https://openalex.org/W2001141328","https://openalex.org/W2003267593","https://openalex.org/W2009940349","https://openalex.org/W2015714288","https://openalex.org/W2020428772","https://openalex.org/W2050439505","https://openalex.org/W2061634390","https://openalex.org/W2071014748","https://openalex.org/W2072204993","https://openalex.org/W2078028084","https://openalex.org/W2090807899","https://openalex.org/W2097308346","https://openalex.org/W2104339857","https://openalex.org/W2107605271","https://openalex.org/W2110541499","https://openalex.org/W2153986241","https://openalex.org/W3013843370"],"related_works":["https://openalex.org/W7099419824","https://openalex.org/W2038900692","https://openalex.org/W2115896258","https://openalex.org/W7096042789","https://openalex.org/W7096223466","https://openalex.org/W7098922420","https://openalex.org/W1515675992","https://openalex.org/W4238153223","https://openalex.org/W1989871800","https://openalex.org/W1658297171"],"abstract_inverted_index":{"This":[0,162],"dissertation":[1],"places":[2],"intersection":[3,75],"homology":[4,7,19,76,122,153,171],"and":[5,23,50,82,130],"local":[6,133,152,170],"within":[8,181],"the":[9,39,56,65,88,99,151,164,178,188,191,198],"framework":[10],"of":[11,41,58,60,73,101,119,144,150,155,166,169,185,187,193,200,206],"persistence,":[12],"which":[13,55,105,173],"was":[14],"originally":[15],"developed":[16],"for":[17,38,48,54,77,125,146],"ordinary":[18],"by":[20],"Edelsbrunner,":[21],"Letscher,":[22],"Zomorodian.":[24],"The":[25],"eventual":[26],"goal,":[27],"begun":[28],"but":[29],"not":[30],"completed":[31],"here,":[32],"is":[33],"to":[34,93,176],"provide":[35],"analytical":[36],"tools":[37],"study":[40],"embedded":[42,127],"stratified":[43,80,128,157],"spaces,":[44],"as":[45,47],"well":[46],"high-dimensional":[49],"possibly":[51],"noisy":[52],"datasets":[53],"number":[57],"degrees":[59],"freedom":[61],"may":[62],"vary":[63],"across":[64],"parameter":[66],"space.":[67],"Specifically,":[68],"we":[69,140,196],"create":[70],"a":[71,78,95,102,111,117,142,147,156,160,167,182,204],"theory":[72,143],"persistent":[74],"filtered":[79],"space":[81,129,158],"prove":[83,98,197],"several":[84],"structural":[85],"theorems":[86],"about":[87],"pair":[89,108],"groups":[90,109,154],"asso-":[91],"ciated":[92],"such":[94],"filtration.":[96],"We":[97,114],"correctness":[100,199],"cubic":[103],"algorithm":[104],"computes":[106],"these":[107],"in":[110,135],"simplicial":[112],"setting.":[113],"also":[115],"define":[116],"series":[118,168],"intersec-":[120],"tion":[121],"elevation":[123],"functions":[124],"an":[126],"characterize":[131],"their":[132],"maxima":[134],"dimension":[136],"one.":[137],"In":[138],"addition,":[139],"develop":[141],"persistence":[145],"multi-scale":[148],"analogue":[149],"at":[159,203],"point.":[161,189],"takes":[163],"form":[165],"vineyards":[172],"allow":[174],"one":[175],"assess":[177],"homological":[179],"structure":[180],"one-parameter":[183],"family":[184],"neighborhoods":[186],"Under":[190],"assumption":[192],"dense":[194],"sampling,":[195],"this":[201],"assessment":[202],"variety":[205],"radius":[207],"scales.":[208]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2016-06-24T00:00:00"}
