{"id":"https://openalex.org/W4400135982","doi":"https://doi.org/10.1007/s41468-024-00180-x","title":"Bigraded Betti numbers and generalized persistence diagrams","display_name":"Bigraded Betti numbers and generalized persistence diagrams","publication_year":2024,"publication_date":"2024-06-28","ids":{"openalex":"https://openalex.org/W4400135982","doi":"https://doi.org/10.1007/s41468-024-00180-x"},"language":"en","primary_location":{"id":"doi:10.1007/s41468-024-00180-x","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s41468-024-00180-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41468-024-00180-x.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/s41468-024-00180-x.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100386550","display_name":"Woojin Kim","orcid":"https://orcid.org/0000-0001-8081-5872"},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]},{"id":"https://openalex.org/I4210158432","display_name":"National Institute for Mathematical Sciences","ror":"https://ror.org/04n7py080","country_code":"KR","type":"education","lineage":["https://openalex.org/I4210158432"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Woojin Kim","raw_affiliation_strings":["Department of Mathematical Sciences, KAIST, Daejeon, South Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, KAIST, Daejeon, South Korea","institution_ids":["https://openalex.org/I4210158432","https://openalex.org/I157485424"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065785946","display_name":"Samantha Moore","orcid":"https://orcid.org/0000-0003-3016-3188"},"institutions":[{"id":"https://openalex.org/I4210152011","display_name":"North Carolina School of Science and Mathematics","ror":"https://ror.org/03zbydc22","country_code":"US","type":"education","lineage":["https://openalex.org/I4210152011"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Samantha Moore","raw_affiliation_strings":["Department of Mathematics, North Carolina School of Science and Mathematics- Morganton, Morganton, NC, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, North Carolina School of Science and Mathematics- Morganton, Morganton, NC, USA","institution_ids":["https://openalex.org/I4210152011"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100386550"],"corresponding_institution_ids":["https://openalex.org/I157485424","https://openalex.org/I4210158432"],"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":0.11910848,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":"3","first_page":"727","last_page":"760"},"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":0.9952999949455261,"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":0.9909999966621399,"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/persistence","display_name":"Persistence (discontinuity)","score":0.9006955623626709},{"id":"https://openalex.org/keywords/betti-number","display_name":"Betti number","score":0.822469174861908},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49134722352027893},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.4284685552120209},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28015053272247314},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.24140694737434387},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.07472112774848938}],"concepts":[{"id":"https://openalex.org/C2781009140","wikidata":"https://www.wikidata.org/wiki/Q7170389","display_name":"Persistence (discontinuity)","level":2,"score":0.9006955623626709},{"id":"https://openalex.org/C129621563","wikidata":"https://www.wikidata.org/wiki/Q429593","display_name":"Betti number","level":2,"score":0.822469174861908},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49134722352027893},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.4284685552120209},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28015053272247314},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.24140694737434387},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.07472112774848938},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s41468-024-00180-x","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s41468-024-00180-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41468-024-00180-x.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"}],"best_oa_location":{"id":"doi:10.1007/s41468-024-00180-x","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s41468-024-00180-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41468-024-00180-x.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/G4842692603","display_name":null,"funder_award_id":"GRFP-1650116","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4901045547","display_name":null,"funder_award_id":"1650116","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6894402473","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","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/F4320324161","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400135982.pdf","grobid_xml":"https://content.openalex.org/works/W4400135982.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W1516374480","https://openalex.org/W1550890970","https://openalex.org/W1964172127","https://openalex.org/W1991566301","https://openalex.org/W2037613900","https://openalex.org/W2040661328","https://openalex.org/W2043888222","https://openalex.org/W2069314032","https://openalex.org/W2087841994","https://openalex.org/W2098825762","https://openalex.org/W2112471150","https://openalex.org/W2158407067","https://openalex.org/W2335810221","https://openalex.org/W2424211690","https://openalex.org/W2574983198","https://openalex.org/W2588688245","https://openalex.org/W2806874312","https://openalex.org/W2903721645","https://openalex.org/W2912734548","https://openalex.org/W2913946465","https://openalex.org/W2936375853","https://openalex.org/W2942078528","https://openalex.org/W2962690095","https://openalex.org/W2963003109","https://openalex.org/W2963097828","https://openalex.org/W2964292054","https://openalex.org/W2972005378","https://openalex.org/W2982539600","https://openalex.org/W2995087345","https://openalex.org/W3011959994","https://openalex.org/W3037433535","https://openalex.org/W3092727470","https://openalex.org/W3098443453","https://openalex.org/W3100733043","https://openalex.org/W3103850685","https://openalex.org/W3104309020","https://openalex.org/W3106270234","https://openalex.org/W3140292214","https://openalex.org/W3141985190","https://openalex.org/W3190973455","https://openalex.org/W4226031082","https://openalex.org/W4226052765","https://openalex.org/W4251980118","https://openalex.org/W4255383393","https://openalex.org/W4255730106","https://openalex.org/W6600024159","https://openalex.org/W6600721425","https://openalex.org/W6633778719"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2095493290","https://openalex.org/W2971813531","https://openalex.org/W4226419853","https://openalex.org/W2963974879","https://openalex.org/W2588877683","https://openalex.org/W2035886694","https://openalex.org/W2087869914","https://openalex.org/W3104056274","https://openalex.org/W2588688245"],"abstract_inverted_index":{"Abstract":[0],"Commutative":[1],"diagrams":[2,34,49],"of":[3,23,33,51,57,64,70,88,93,100,129,132,155,162,172,185],"vector":[4],"spaces":[5],"and":[6,82],"linear":[7],"maps":[8],"over":[9,136],"$$\\mathbb":[10,137],"{Z}^2$$":[11,105],"<mml:math":[12,106,139,235],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[13,107,140,236],"<mml:msup>":[14,111],"<mml:mrow>":[15,108,112,237],"<mml:mi>Z</mml:mi>":[16,113],"</mml:mrow>":[17,114,117,241],"<mml:mn>2</mml:mn>":[18,115],"</mml:msup>":[19,116],"</mml:math>":[20,118,142,242],"are":[21,35,50,165,216],"objects":[22],"interest":[24],"in":[25,67,205,218],"topological":[26],"data":[27],"analysis":[28],"(TDA)":[29],"where":[30],"this":[31,146],"type":[32],"called":[36,189],"2-parameter":[37,59,186],"persistence":[38,60,130,134,187,229],"modules.":[39],"Given":[40],"that":[41,47,150,182,212,221],"quiver":[42],"representation":[43],"theory":[44],"tells":[45],"us":[46],"such":[48,71],"wild":[52],"type,":[53],"studying":[54],"informative":[55],"invariants":[56,72],"a":[58,98,133,158,206],"module":[61,135],"M":[62,94,156,163],"is":[63,73],"central":[65],"importance":[66],"TDA.":[68,144],"One":[69],"the":[74,85,89,125,151,169,178,190,201,213,219],"generalized":[75,90],"rank":[76,91],"invariant,":[77],"recently":[78],"introduced":[79],"by":[80,167,195],"Kim":[81],"M\u00e9moli.":[83],"Via":[84],"M\u00f6bius":[86],"inversion":[87],"invariant":[92,161,184],",":[95,157,164],"we":[96,148,180],"obtain":[97],"collection":[99,123],"connected":[101],"subsets":[102,174],"$$I\\subset":[103],"\\mathbb":[104],"<mml:mi>I</mml:mi>":[109],"<mml:mo>\u2282</mml:mo>":[110],"with":[119],"signed":[120],"multiplicities.":[121],"This":[122],"generalizes":[124],"well":[126],"known":[127],"notion":[128],"barcode":[131],"{R}$$":[138],"<mml:mi>R</mml:mi>":[141],"from":[143],"In":[145],"paper":[147],"show":[149,211],"bigraded":[152,202],"Betti":[153,203],"numbers":[154,204],"classical":[159],"algebraic":[160],"obtained":[166],"counting":[168],"corner":[170],"points":[171],"these":[173],"I":[175],"s.":[176],"Along":[177],"way,":[179],"verify":[181],"an":[183],"modules":[188,230],"interval":[191],"decomposable":[192],"approximation":[193],"(introduced":[194],"Asashiba":[196],"et":[197],"al.)":[198],"also":[199,210],"encodes":[200],"similar":[207],"fashion.":[208],"We":[209],"aforementioned":[214],"results":[215],"optimal":[217],"sense":[220],"they":[222],"cannot":[223],"be":[224],"extended":[225],"to":[226],"d":[227],"-parameter":[228],"for":[231],"$$d":[232],"\\ge":[233],"3$$":[234],"<mml:mi>d</mml:mi>":[238],"<mml:mo>\u2265</mml:mo>":[239],"<mml:mn>3</mml:mn>":[240],".":[243]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
