{"id":"https://openalex.org/W4414034348","doi":"https://doi.org/10.1007/s41468-025-00213-z","title":"The fiber of persistent homology for trees","display_name":"The fiber of persistent homology for trees","publication_year":2025,"publication_date":"2025-09-01","ids":{"openalex":"https://openalex.org/W4414034348","doi":"https://doi.org/10.1007/s41468-025-00213-z","pmid":"https://pubmed.ncbi.nlm.nih.gov/40922982"},"language":"en","primary_location":{"id":"doi:10.1007/s41468-025-00213-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41468-025-00213-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41468-025-00213-z.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","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s41468-025-00213-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048445973","display_name":"David R. Beers","orcid":"https://orcid.org/0000-0002-8757-3500"},"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":"David Beers","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG UK","Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","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, Woodstock Road, Oxford, OX2 6GG UK","Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Woodstock Road, 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/A5048445973"],"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":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23186707,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"9","issue":"3","first_page":"22","last_page":"22"},"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":0.9629999995231628,"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":0.5910171270370483},{"id":"https://openalex.org/keywords/homology","display_name":"Homology (biology)","score":0.4306986629962921},{"id":"https://openalex.org/keywords/computational-biology","display_name":"Computational biology","score":0.39885637164115906},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.35694801807403564},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35662585496902466},{"id":"https://openalex.org/keywords/genetics","display_name":"Genetics","score":0.20805418491363525},{"id":"https://openalex.org/keywords/gene","display_name":"Gene","score":0.08423906564712524},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07911095023155212}],"concepts":[{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.5910171270370483},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.4306986629962921},{"id":"https://openalex.org/C70721500","wikidata":"https://www.wikidata.org/wiki/Q177005","display_name":"Computational biology","level":1,"score":0.39885637164115906},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.35694801807403564},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35662585496902466},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.20805418491363525},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.08423906564712524},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07911095023155212}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s41468-025-00213-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41468-025-00213-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41468-025-00213-z.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":"pmid:40922982","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40922982","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of applied and computational topology","raw_type":null},{"id":"pmh:oai:europepmc.org:11223987","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/12414068","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC12414068/pdf/41468_2025_Article_213.pdf","source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:12414068","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC12414068/","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"J Appl Comput Topol","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s41468-025-00213-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41468-025-00213-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41468-025-00213-z.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/G3949642850","display_name":null,"funder_award_id":"ECF-2022-10","funder_id":"https://openalex.org/F4320320184","funder_display_name":"London Mathematical Society"}],"funders":[{"id":"https://openalex.org/F4320320184","display_name":"London Mathematical Society","ror":"https://ror.org/01r1e1h27"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320337296","display_name":"Mathematical Institute, University of Oxford","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414034348.pdf","grobid_xml":"https://content.openalex.org/works/W4414034348.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1753705553","https://openalex.org/W2010203208","https://openalex.org/W2037613900","https://openalex.org/W2424211690","https://openalex.org/W2573261522","https://openalex.org/W2761733590","https://openalex.org/W2789787607","https://openalex.org/W2911934184","https://openalex.org/W2912694889","https://openalex.org/W2964292054","https://openalex.org/W2966665390","https://openalex.org/W2976531748","https://openalex.org/W3082163510","https://openalex.org/W3082201620","https://openalex.org/W3102337400","https://openalex.org/W3112139959","https://openalex.org/W3140959666","https://openalex.org/W3163552377","https://openalex.org/W3195931371"],"related_works":["https://openalex.org/W4293332653","https://openalex.org/W2958601279","https://openalex.org/W2102692026","https://openalex.org/W4360887047","https://openalex.org/W2578816615","https://openalex.org/W3162517897","https://openalex.org/W1517114513","https://openalex.org/W2770791287","https://openalex.org/W3143913977","https://openalex.org/W4300829093"],"abstract_inverted_index":{"Abstract":[0],"Consider":[1],"the":[2,67,86],"space":[3,37,59,91],"of":[4,89,92],"continuous":[5],"functions":[6],"on":[7,60],"a":[8,18,57],"geometric":[9],"tree":[10],"X":[11,61],"whose":[12,43],"persistent":[13],"homology":[14],"gives":[15],"rise":[16],"to":[17,56,84],"finite":[19],"generic":[20],"barcode":[21,44],"D":[22,46,72],".":[23,47],"We":[24,48],"show":[25],"that":[26,50],"there":[27,39],"are":[28,40],"exactly":[29],"as":[30,38],"many":[31],"path":[32],"connected":[33],"components":[34],"in":[35],"this":[36,90],"merge":[41,68],"trees":[42],"is":[45,53],"find":[49],"each":[51],"component":[52],"homotopy":[54,87],"equivalent":[55],"configuration":[58],"with":[62,73],"specialised":[63],"constraints":[64],"encoded":[65],"by":[66],"tree.":[69],"For":[70],"barcodes":[71],"either":[74],"one":[75],"or":[76],"two":[77],"intervals,":[78],"our":[79],"method":[80],"also":[81],"allows":[82],"us":[83],"compute":[85],"type":[88],"functions.":[93]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}