{"id":"https://openalex.org/W4381095096","doi":"https://doi.org/10.1007/s41468-023-00126-9","title":"Geometric characterization of the persistence of 1D maps","display_name":"Geometric characterization of the persistence of 1D maps","publication_year":2023,"publication_date":"2023-06-17","ids":{"openalex":"https://openalex.org/W4381095096","doi":"https://doi.org/10.1007/s41468-023-00126-9","pmid":"https://pubmed.ncbi.nlm.nih.gov/39678706"},"language":"en","primary_location":{"id":"doi:10.1007/s41468-023-00126-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41468-023-00126-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41468-023-00126-9.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/s41468-023-00126-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052356139","display_name":"Ranita Biswas","orcid":"https://orcid.org/0000-0002-5372-7890"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Ranita Biswas","raw_affiliation_strings":["IST Austria (Institute of Science and Technology Austria), Klosterneuburg, Austria"],"raw_orcid":"https://orcid.org/0000-0002-5372-7890","affiliations":[{"raw_affiliation_string":"IST Austria (Institute of Science and Technology Austria), Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090549356","display_name":"Sebastiano Cultrera di Montesano","orcid":"https://orcid.org/0000-0001-6249-0832"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Sebastiano Cultrera di Montesano","raw_affiliation_strings":["IST Austria (Institute of Science and Technology Austria), Klosterneuburg, Austria"],"raw_orcid":"https://orcid.org/0000-0001-6249-0832","affiliations":[{"raw_affiliation_string":"IST Austria (Institute of Science and Technology Austria), Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069999967","display_name":"Herbert Edelsbrunner","orcid":"https://orcid.org/0000-0002-9823-6833"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Herbert Edelsbrunner","raw_affiliation_strings":["IST Austria (Institute of Science and Technology Austria), Klosterneuburg, Austria"],"raw_orcid":"https://orcid.org/0000-0002-9823-6833","affiliations":[{"raw_affiliation_string":"IST Austria (Institute of Science and Technology Austria), Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038928621","display_name":"Morteza Saghafian","orcid":"https://orcid.org/0000-0002-4201-5775"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Morteza Saghafian","raw_affiliation_strings":["IST Austria (Institute of Science and Technology Austria), Klosterneuburg, Austria"],"raw_orcid":"https://orcid.org/0000-0002-4201-5775","affiliations":[{"raw_affiliation_string":"IST Austria (Institute of Science and Technology Austria), Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5090549356"],"corresponding_institution_ids":["https://openalex.org/I157556583"],"apc_list":{"value":2490,"currency":"EUR","value_usd":3090},"apc_paid":{"value":2490,"currency":"EUR","value_usd":3090},"fwci":0.1742,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.50566303,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"8","issue":"5","first_page":"1101","last_page":"1119"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9886000156402588,"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/T10540","display_name":"Advanced Fluorescence Microscopy Techniques","score":0.960099995136261,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/persistence","display_name":"Persistence (discontinuity)","score":0.8415069580078125},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.6852251887321472},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3460195064544678},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.3259296417236328},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.1751636564731598},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.08232077956199646},{"id":"https://openalex.org/keywords/geotechnical-engineering","display_name":"Geotechnical engineering","score":0.07017144560813904},{"id":"https://openalex.org/keywords/nanotechnology","display_name":"Nanotechnology","score":0.058728039264678955}],"concepts":[{"id":"https://openalex.org/C2781009140","wikidata":"https://www.wikidata.org/wiki/Q7170389","display_name":"Persistence (discontinuity)","level":2,"score":0.8415069580078125},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.6852251887321472},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3460195064544678},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.3259296417236328},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.1751636564731598},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.08232077956199646},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.07017144560813904},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.058728039264678955}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s41468-023-00126-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41468-023-00126-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41468-023-00126-9.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:39678706","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39678706","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:pubmedcentral.nih.gov:11639680","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11639680","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11639680/pdf/41468_2023_Article_126.pdf","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/s41468-023-00126-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41468-023-00126-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41468-023-00126-9.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":[{"id":"https://metadata.un.org/sdg/5","score":0.699999988079071,"display_name":"Gender equality"}],"awards":[{"id":"https://openalex.org/G2829023891","display_name":"Mathematics, Computer Science","funder_award_id":"Z 342","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3622264694","display_name":"Alpha Shape Theory Extended","funder_award_id":"788183","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6773318802","display_name":null,"funder_award_id":"TRR 109","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6843533210","display_name":null,"funder_award_id":"342-N31","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7139889009","display_name":null,"funder_award_id":"Z 342-N31","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7236747564","display_name":null,"funder_award_id":"I 02979-N35","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7401564395","display_name":null,"funder_award_id":"02979-N35","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7842005466","display_name":null,"funder_award_id":"Horizon 2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8184282109","display_name":null,"funder_award_id":"788183","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4381095096.pdf"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1081919343","https://openalex.org/W2022681869","https://openalex.org/W2031452771","https://openalex.org/W2037613900","https://openalex.org/W2068115726","https://openalex.org/W2161184224","https://openalex.org/W3140579943","https://openalex.org/W3186201766","https://openalex.org/W4390575690"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W1995895161","https://openalex.org/W2007980826","https://openalex.org/W2352063914","https://openalex.org/W3107994849","https://openalex.org/W2047377442","https://openalex.org/W2061531152","https://openalex.org/W3002753104"],"abstract_inverted_index":{"We":[0],"characterize":[1],"critical":[2],"points":[3,37],"of":[4,18,23,29,40,46,59,69,76],"1-dimensional":[5],"maps":[6],"paired":[7],"in":[8,53],"persistent":[9,54],"homology":[10,55],"geometrically":[11],"and":[12,26,38,48],"this":[13],"way":[14],"get":[15],"elementary":[16],"proofs":[17],"theorems":[19],"about":[20],"the":[21,27,43,50,60,67],"symmetry":[22],"persistence":[24,82],"diagrams":[25],"variation":[28],"such":[30],"maps.":[31],"In":[32],"particular,":[33],"we":[34],"identify":[35],"branching":[36],"endpoints":[39],"networks":[41],"as":[42],"sole":[44],"source":[45],"asymmetry":[47],"relate":[49],"cycle":[51],"basis":[52],"with":[56,80],"a":[57,74],"version":[58],"stable":[61],"marriage":[62],"problem.":[63],"Our":[64],"analysis":[65],"provides":[66],"foundations":[68],"fast":[70],"algorithms":[71],"for":[72],"maintaining":[73],"collection":[75],"sorted":[77],"lists":[78],"together":[79],"its":[81],"diagram.":[83]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}