{"id":"https://openalex.org/W3209339723","doi":"https://doi.org/10.1007/s41468-024-00165-w","title":"Algorithmic reconstruction of the fiber of persistent homology on cell complexes","display_name":"Algorithmic reconstruction of the fiber of persistent homology on cell complexes","publication_year":2024,"publication_date":"2024-04-18","ids":{"openalex":"https://openalex.org/W3209339723","doi":"https://doi.org/10.1007/s41468-024-00165-w","mag":"3209339723"},"language":"en","primary_location":{"id":"doi:10.1007/s41468-024-00165-w","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s41468-024-00165-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41468-024-00165-w.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied and Computational Topology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s41468-024-00165-w.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044189934","display_name":"Jacob Leygonie","orcid":"https://orcid.org/0000-0001-6151-1953"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jacob Leygonie","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027854626","display_name":"Gregory Henselman\u2010Petrusek","orcid":"https://orcid.org/0000-0002-1889-8272"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Gregory Henselman-Petrusek","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK"],"raw_orcid":"https://orcid.org/0000-0002-1889-8272","affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027854626"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":{"value":2490,"currency":"EUR","value_usd":3090},"apc_paid":{"value":2490,"currency":"EUR","value_usd":3090},"fwci":0.319,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54191149,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"8","issue":"7","first_page":"2015","last_page":"2049"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":1.0,"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":1.0,"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/T12859","display_name":"Cell Image Analysis Techniques","score":0.9843999743461609,"subfield":{"id":"https://openalex.org/subfields/1304","display_name":"Biophysics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9840999841690063,"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":0.5933676958084106},{"id":"https://openalex.org/keywords/homology","display_name":"Homology (biology)","score":0.4841357171535492},{"id":"https://openalex.org/keywords/computational-biology","display_name":"Computational biology","score":0.38372159004211426},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3573366701602936},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34852540493011475},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.27388477325439453},{"id":"https://openalex.org/keywords/genetics","display_name":"Genetics","score":0.2274046540260315},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22446408867835999},{"id":"https://openalex.org/keywords/gene","display_name":"Gene","score":0.0943337082862854}],"concepts":[{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.5933676958084106},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.4841357171535492},{"id":"https://openalex.org/C70721500","wikidata":"https://www.wikidata.org/wiki/Q177005","display_name":"Computational biology","level":1,"score":0.38372159004211426},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3573366701602936},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34852540493011475},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.27388477325439453},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.2274046540260315},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22446408867835999},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0943337082862854}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s41468-024-00165-w","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s41468-024-00165-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41468-024-00165-w.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied and Computational Topology","raw_type":"journal-article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:b6544854-fe6b-4b19-877c-04d79a85925b","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Jisc Publications Router","raw_type":"Journal article"}],"best_oa_location":{"id":"doi:10.1007/s41468-024-00165-w","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s41468-024-00165-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41468-024-00165-w.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied and Computational Topology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1132496359","display_name":"Application driven Topological Data Analysis","funder_award_id":"EP/R018472/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6066696820","display_name":null,"funder_award_id":"EP/R018472/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8807841571","display_name":null,"funder_award_id":"DMS-1854748","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3209339723.pdf"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1753705553","https://openalex.org/W2009940349","https://openalex.org/W2010203208","https://openalex.org/W2037613900","https://openalex.org/W2102368730","https://openalex.org/W2102692026","https://openalex.org/W2144044408","https://openalex.org/W2149185044","https://openalex.org/W2326008957","https://openalex.org/W2424211690","https://openalex.org/W2804660809","https://openalex.org/W2912694889","https://openalex.org/W2963221754","https://openalex.org/W2963992494","https://openalex.org/W2964209273","https://openalex.org/W2964237352","https://openalex.org/W2976531748","https://openalex.org/W2997919967","https://openalex.org/W3082163510","https://openalex.org/W3102337400","https://openalex.org/W3140579943","https://openalex.org/W3140959666","https://openalex.org/W3163552377","https://openalex.org/W3195931371","https://openalex.org/W4233690291","https://openalex.org/W6605165097"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2958601279","https://openalex.org/W2102692026","https://openalex.org/W4360887047","https://openalex.org/W3162517897","https://openalex.org/W2770791287","https://openalex.org/W3143913977","https://openalex.org/W4206186921","https://openalex.org/W4386755584","https://openalex.org/W4289362969"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"K":[2,116],"be":[3],"a":[4,21,112,118,136,170,177],"finite":[5],"simplicial,":[6],"cubical,":[7],"delta":[8],"or":[9],"CW":[10,189],"complex.":[11],"The":[12],"persistence":[13],"map":[14],"$$\\textrm{PH}$$":[15],"<mml:math":[16,26,67,93,147],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[17,27,68,94,148],"<mml:mtext>PH</mml:mtext>":[18,71,97,151],"</mml:math>":[19,35,83,109,163],"takes":[20],"filter":[22],"$$f:K\\rightarrow":[23],"\\mathbb":[24],"{R}$$":[25],"<mml:mrow>":[28,69,72,77,95,98,103,149,152,157],"<mml:mi>f</mml:mi>":[29],"<mml:mo>:</mml:mo>":[30],"<mml:mi>K</mml:mi>":[31],"<mml:mo>\u2192</mml:mo>":[32],"<mml:mi>R</mml:mi>":[33],"</mml:mrow>":[34,75,81,82,101,107,108,155,161,162],"as":[36,111],"input":[37],"and":[38,121,134],"returns":[39],"the":[40,43,55,64,89,141,144,181],"barcodes":[41,60],"of":[42,48,172,184],"sublevel":[44],"set":[45],"persistent":[46],"homology":[47],"f":[49],"in":[50],"each":[51],"dimension.":[52],"We":[53,131],"address":[54],"inverse":[56],"problem:":[57],"given":[58],"target":[59],"D":[61],",":[62],"computing":[63],"fiber":[65,145],"$$\\textrm{PH}^{-1}(D)$$":[66,92,146],"<mml:msup>":[70,96,150],"<mml:mo>-</mml:mo>":[73,99,153],"<mml:mn>1</mml:mn>":[74,100,154],"</mml:msup>":[76,102,156],"<mml:mo>(</mml:mo>":[78,104,158],"<mml:mi>D</mml:mi>":[79,105,159],"<mml:mo>)</mml:mo>":[80,106,160],".":[84,164],"For":[85],"this,":[86],"we":[87,122,168],"use":[88],"fact":[90],"that":[91,139],"decomposes":[110],"polyhedral":[113],"complex":[114],"when":[115],"is":[117],"simplicial":[119],"complex,":[120],"generalise":[123],"this":[124],"result":[125],"to":[126],"arbitrary":[127],"based":[128],"chain":[129],"complexes.":[130,190],"then":[132],"design":[133],"implement":[135],"depth-first":[137],"search":[138],"recovers":[140],"polytopes":[142],"forming":[143],"As":[165],"an":[166],"application,":[167],"solve":[169],"corpus":[171],"120":[173],"sample":[174],"problems,":[175],"providing":[176],"first":[178],"insight":[179],"into":[180],"statistical":[182],"structure":[183],"these":[185],"fibers,":[186],"for":[187],"general":[188]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}