{"id":"https://openalex.org/W2252892898","doi":"https://doi.org/10.1090/mcom/3137","title":"On \ud835\udf16 approximations of persistence diagrams","display_name":"On \ud835\udf16 approximations of persistence diagrams","publication_year":2015,"publication_date":"2015-12-29","ids":{"openalex":"https://openalex.org/W2252892898","doi":"https://doi.org/10.1090/mcom/3137","mag":"2252892898"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3137","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3137","pdf_url":"https://www.ams.org/mcom/2017-86-306/S0025-5718-2016-03137-3/S0025-5718-2016-03137-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2017-86-306/S0025-5718-2016-03137-3/S0025-5718-2016-03137-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007834707","display_name":"Jonathan Jaquette","orcid":"https://orcid.org/0000-0001-8380-3148"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jonathan Jaquette","raw_affiliation_strings":["Department of Mathematics, Hill Center-Busch Campus, Rutgers University, 110 Frelinghusen Road, Piscataway, New Jersey 08854-8019"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hill Center-Busch Campus, Rutgers University, 110 Frelinghusen Road, Piscataway, New Jersey 08854-8019","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087376780","display_name":"Miroslav Kram\u00e1r","orcid":"https://orcid.org/0000-0001-7773-6516"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]},{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP","US"],"is_corresponding":false,"raw_author_name":"Miroslav Kram\u00e1r","raw_affiliation_strings":["Advanced Institute for Material Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577 Japan","Department of Mathematics, Hill Center-Busch Campus, Rutgers University, 110 Frelinghusen Road, Piscataway, New Jersey 08854-8019"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Advanced Institute for Material Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577 Japan","institution_ids":["https://openalex.org/I201537933"]},{"raw_affiliation_string":"Department of Mathematics, Hill Center-Busch Campus, Rutgers University, 110 Frelinghusen Road, Piscataway, New Jersey 08854-8019","institution_ids":["https://openalex.org/I102322142"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11405264,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"86","issue":"306","first_page":"1887","last_page":"1912"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9997000098228455,"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":0.9997000098228455,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/persistent-homology","display_name":"Persistent homology","score":0.8887057304382324},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7625631093978882},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6909092664718628},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6070472598075867},{"id":"https://openalex.org/keywords/approximations-of-\u03c0","display_name":"Approximations of \u03c0","score":0.5039135813713074},{"id":"https://openalex.org/keywords/persistence","display_name":"Persistence (discontinuity)","score":0.4871542155742645},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4758067727088928},{"id":"https://openalex.org/keywords/homology","display_name":"Homology (biology)","score":0.4571433365345001},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36245933175086975},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35924649238586426},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3205152750015259},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.29570120573043823},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10775798559188843}],"concepts":[{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.8887057304382324},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7625631093978882},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6909092664718628},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6070472598075867},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.5039135813713074},{"id":"https://openalex.org/C2781009140","wikidata":"https://www.wikidata.org/wiki/Q7170389","display_name":"Persistence (discontinuity)","level":2,"score":0.4871542155742645},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4758067727088928},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.4571433365345001},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36245933175086975},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35924649238586426},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3205152750015259},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.29570120573043823},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10775798559188843},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/mcom/3137","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3137","pdf_url":"https://www.ams.org/mcom/2017-86-306/S0025-5718-2016-03137-3/S0025-5718-2016-03137-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1412.1805","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1412.1805","pdf_url":"https://arxiv.org/pdf/1412.1805","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:2252892898","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1412.1805.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.1412.1805","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1412.1805","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.1090/mcom/3137","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3137","pdf_url":"https://www.ams.org/mcom/2017-86-306/S0025-5718-2016-03137-3/S0025-5718-2016-03137-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1389074705","display_name":null,"funder_award_id":"DMS-0915019","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1955125318","display_name":"CDI-Type II: Collaborative Research: Computational Homology, Jamming, and Force Chains in Dense Granular Flows","funder_award_id":"0835621","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3442010469","display_name":null,"funder_award_id":"NSF Grant DMS-1125174","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3811135561","display_name":"Collaborative proposal: Computing Dynamics of Multiparameter Systems","funder_award_id":"0915019","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3999492190","display_name":null,"funder_award_id":"FA9550-09-1-0148","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4868937273","display_name":null,"funder_award_id":"NSF Grant DMS-0835621","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5222733069","display_name":null,"funder_award_id":"FA9550-09-1-0148","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5775421459","display_name":"CDI-TYPE II--COLLABORATIVE RESEARCH:  Using Algebraic Topology to Connect Models with Measurements in Complex Nonequilibrium Systems","funder_award_id":"1125174","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/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2252892898.pdf","grobid_xml":"https://content.openalex.org/works/W2252892898.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W6604841123"],"related_works":["https://openalex.org/W2972803697","https://openalex.org/W3111372129","https://openalex.org/W2100117429","https://openalex.org/W3094622830","https://openalex.org/W1741815943","https://openalex.org/W2396800056","https://openalex.org/W2949804505","https://openalex.org/W1579663377","https://openalex.org/W2963111692","https://openalex.org/W2932952004","https://openalex.org/W2767089775","https://openalex.org/W1885116259","https://openalex.org/W2891557314","https://openalex.org/W2811416829","https://openalex.org/W3091936154","https://openalex.org/W1674667795","https://openalex.org/W3150782421","https://openalex.org/W3205540451","https://openalex.org/W3098725392","https://openalex.org/W3161313012"],"abstract_inverted_index":{"Biological":[0],"and":[1,206],"physical":[2],"systems":[3],"often":[4],"exhibit":[5],"distinct":[6],"structures":[7,27],"at":[8],"different":[9],"spatial/temporal":[10],"scales.":[11],"Persistent":[12],"homology":[13,50],"is":[14,51,118],"an":[15,43],"algebraic":[16],"tool":[17],"that":[18],"provides":[19],"a":[20,35,62,119],"mathematical":[21],"framework":[22,37],"for":[23,38],"analyzing":[24],"the":[25,39,48,55,122,198,211],"multi-scale":[26],"frequently":[28],"observed":[29],"in":[30],"nature.":[31],"In":[32,121],"this":[33],"paper":[34],"theoretical":[36],"algorithmic":[40],"computation":[41],"of":[42,47,61,197,210],"arbitrarily":[44],"good":[45],"approximation":[46,212],"persistent":[49],"developed.":[52],"We":[53,201],"study":[54],"filtrations":[56],"generated":[57],"by":[58,215],"sub-level":[59],"sets":[60],"function":[63],"<inline-formula":[64,105,125,163],"content-type=\"math/mathml\">":[65,106,126,164],"<mml:math":[66,107,127,165],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[67,108,128,166],"alttext=\"f":[68],"colon":[69],"upper":[70,74,138,171],"X":[71,96,130],"right-arrow":[72],"double-struck":[73,170],"R\">":[75],"<mml:semantics>":[76,111,140,173],"<mml:mrow>":[77,141,174],"<mml:mi>f</mml:mi>":[78],"<mml:mo>":[79,176],":":[80],"</mml:mo>":[81,86,178],"<mml:mi>X</mml:mi>":[82,112,142],"<mml:mo":[83,144,150],"stretchy=\"false\">":[84],"\u2192":[85],"<mml:mrow":[87,179],"class=\"MJX-TeXAtom-ORD\">":[88,180],"<mml:mi":[89,181],"mathvariant=\"double-struck\">R</mml:mi>":[90],"</mml:mrow>":[91,92,154,183,184],"<mml:annotation":[93,113,155,185],"encoding=\"application/x-tex\">f":[94],"\\colon":[95],"\\to":[97],"\\mathbb":[98,188],"{R}</mml:annotation>":[99],"</mml:semantics>":[100,115,159,190],"</mml:math>":[101,116,160,191],"</inline-formula>":[102,117,161,192],",":[103,162,193],"where":[104],"alttext=\"upper":[109,129,167],"X\">":[110],"encoding=\"application/x-tex\">X</mml:annotation>":[114],"CW-complex.":[120],"special":[123],"case":[124],"equals":[131],"left-bracket":[132],"0":[133],"comma":[134],"1":[135],"right-bracket":[136],"Superscript":[137],"N\">":[139,172],"<mml:mo>=</mml:mo>":[143],"stretchy=\"false\">[</mml:mo>":[145],"<mml:mn>0</mml:mn>":[146],"<mml:mo>,</mml:mo>":[147],"<mml:mn>1</mml:mn>":[148],"<mml:msup>":[149],"stretchy=\"false\">]</mml:mo>":[151],"<mml:mi>N</mml:mi>":[152,175],"</mml:msup>":[153],"encoding=\"application/x-tex\">X":[156],"=":[157],"[0,1]^N</mml:annotation>":[158],"N":[168],"element-of":[169],"\u2208":[177],"mathvariant=\"double-struck\">N</mml:mi>":[182],"encoding=\"application/x-tex\">N":[186],"\\in":[187],"{N}</mml:annotation>":[189],"we":[194],"discuss":[195],"implementation":[196],"proposed":[199],"algorithms.":[200],"also":[202],"investigate":[203],"<italic>a":[204,207],"priori</italic>":[205],"posteriori</italic>":[208],"bounds":[209],"error":[213],"introduced":[214],"our":[216],"method.":[217]},"counts_by_year":[],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}
