{"id":"https://openalex.org/W2915591780","doi":"https://doi.org/10.1007/s41468-020-00053-z","title":"Every 1D persistence module is a restriction of some indecomposable 2D persistence module","display_name":"Every 1D persistence module is a restriction of some indecomposable 2D persistence module","publication_year":2020,"publication_date":"2020-05-12","ids":{"openalex":"https://openalex.org/W2915591780","doi":"https://doi.org/10.1007/s41468-020-00053-z","mag":"2915591780"},"language":"en","primary_location":{"id":"doi:10.1007/s41468-020-00053-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41468-020-00053-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41468-020-00053-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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s41468-020-00053-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077056984","display_name":"Micka\u00ebl Buchet","orcid":"https://orcid.org/0000-0002-1372-1531"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Micka\u00ebl Buchet","raw_affiliation_strings":["Institute of Geometry, TU Graz, Graz, Austria","Graz University of Technology,#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Geometry, TU Graz, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]},{"raw_affiliation_string":"Graz University of Technology,#TAB#","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021529936","display_name":"Emerson G. Escolar","orcid":"https://orcid.org/0000-0003-4751-1521"},"institutions":[{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]},{"id":"https://openalex.org/I4210126580","display_name":"RIKEN Center for Advanced Intelligence Project","ror":"https://ror.org/03ckxwf91","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4210126580"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Emerson G. Escolar","raw_affiliation_strings":["Center for Advanced Intelligence Project, RIKEN, Tokyo, Japan","KUIAS, Kyoto University, Kyoto, Japan","Kyoto University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Advanced Intelligence Project, RIKEN, Tokyo, Japan","institution_ids":["https://openalex.org/I4210126580"]},{"raw_affiliation_string":"KUIAS, Kyoto University, Kyoto, Japan","institution_ids":["https://openalex.org/I22299242"]},{"raw_affiliation_string":"Kyoto University","institution_ids":["https://openalex.org/I22299242"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5077056984"],"corresponding_institution_ids":["https://openalex.org/I4092182"],"apc_list":{"value":2490,"currency":"EUR","value_usd":3090},"apc_paid":{"value":2490,"currency":"EUR","value_usd":3090},"fwci":0.1458,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.48585047,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"4","issue":"3","first_page":"387","last_page":"424"},"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9945999979972839,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9621000289916992,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/indecomposable-module","display_name":"Indecomposable module","score":0.9476694464683533},{"id":"https://openalex.org/keywords/persistence","display_name":"Persistence (discontinuity)","score":0.9136583805084229},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5091385245323181},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36039674282073975},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32601404190063477},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.10249137878417969}],"concepts":[{"id":"https://openalex.org/C157480366","wikidata":"https://www.wikidata.org/wiki/Q2499534","display_name":"Indecomposable module","level":2,"score":0.9476694464683533},{"id":"https://openalex.org/C2781009140","wikidata":"https://www.wikidata.org/wiki/Q7170389","display_name":"Persistence (discontinuity)","level":2,"score":0.9136583805084229},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5091385245323181},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36039674282073975},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32601404190063477},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.10249137878417969},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s41468-020-00053-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41468-020-00053-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41468-020-00053-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":"pmh:oai:arXiv.org:1902.07405","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1902.07405","pdf_url":"https://arxiv.org/pdf/1902.07405","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:2915591780","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1902.07405.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.1902.07405","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1902.07405","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":"doi:10.1007/s41468-020-00053-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41468-020-00053-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41468-020-00053-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":[],"funders":[{"id":"https://openalex.org/F4320310430","display_name":"TU Graz, Internationale Beziehungen und Mobilit\u00e4tsprogramme","ror":"https://ror.org/00d7xrm67"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2915591780.pdf","grobid_xml":"https://content.openalex.org/works/W2915591780.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1507692549","https://openalex.org/W1596721197","https://openalex.org/W1964172127","https://openalex.org/W2000793713","https://openalex.org/W2096736341","https://openalex.org/W2110369778","https://openalex.org/W2120713972","https://openalex.org/W2185147444","https://openalex.org/W2511392967","https://openalex.org/W2734095886","https://openalex.org/W2789788391","https://openalex.org/W2903721645","https://openalex.org/W2963700585","https://openalex.org/W2964292054","https://openalex.org/W4238252746","https://openalex.org/W4251980118","https://openalex.org/W4285451384","https://openalex.org/W4300824122","https://openalex.org/W6600109303"],"related_works":["https://openalex.org/W3024294180","https://openalex.org/W3095304567","https://openalex.org/W3037511822","https://openalex.org/W2982539600","https://openalex.org/W2278796013","https://openalex.org/W2059213021","https://openalex.org/W2103738614","https://openalex.org/W3208676376","https://openalex.org/W2031886384","https://openalex.org/W3105146802","https://openalex.org/W2006444452","https://openalex.org/W17249049","https://openalex.org/W2126114988","https://openalex.org/W2092741350","https://openalex.org/W2025556989","https://openalex.org/W1997909760","https://openalex.org/W2010442650","https://openalex.org/W2247145504","https://openalex.org/W2141405193","https://openalex.org/W2061162689"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"recent":[2],"work":[3],"by":[4,15],"Lesnick":[5],"and":[6],"Wright":[7],"proposed":[8],"a":[9,22,30,45,108],"visualisation":[10],"of":[11,24,47,58,110],"2D":[12,50,67,79],"persistence":[13,26,36,51,68,80,85,102,125],"modules":[14,69,86],"using":[16],"their":[17],"restrictions":[18],"onto":[19],"lines,":[20],"giving":[21],"family":[23],"1D":[25,35,84],"modules.":[27],"We":[28],"give":[29],"constructive":[31],"proof":[32],"that":[33,97],"any":[34,98],"module":[37,52,81,103],"with":[38,53,87],"finite":[39,54,88],"support":[40,71,89],"can":[41,104],"be":[42,105],"found":[43,106],"as":[44,74,76,90,107],"restriction":[46,109],"some":[48,111],"indecomposable":[49,66,78,112],"support.":[55],"As":[56],"consequences":[57],"our":[59],"construction,":[60],"we":[61,94],"are":[62],"able":[63],"to":[64],"exhibit":[65],"whose":[70],"has":[72],"holes":[73],"well":[75],"an":[77],"containing":[82],"all":[83],"line":[91],"restrictions.":[92],"Finally,":[93],"also":[95],"show":[96],"finite-rectangle-decomposable":[99],"n":[100],"D":[101,124],"$$(n+1)$$":[113],"<mml:math":[114],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[115],"<mml:mrow>":[116],"<mml:mo>(</mml:mo>":[117],"<mml:mi>n</mml:mi>":[118],"<mml:mo>+</mml:mo>":[119],"<mml:mn>1</mml:mn>":[120],"<mml:mo>)</mml:mo>":[121],"</mml:mrow>":[122],"</mml:math>":[123],"module.":[126]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
