{"id":"https://openalex.org/W2964154246","doi":"https://doi.org/10.4310/hha.2014.v16.n2.a18","title":"Distance functions, critical points, and the topology of random \u010cech complexes","display_name":"Distance functions, critical points, and the topology of random \u010cech complexes","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2964154246","doi":"https://doi.org/10.4310/hha.2014.v16.n2.a18","mag":"2964154246"},"language":"en","primary_location":{"id":"doi:10.4310/hha.2014.v16.n2.a18","doi":"https://doi.org/10.4310/hha.2014.v16.n2.a18","is_oa":true,"landing_page_url":"https://doi.org/10.4310/hha.2014.v16.n2.a18","pdf_url":"https://www.intlpress.com/site/pub/files/_fulltext/journals/hha/2014/0016/0002/HHA-2014-0016-0002-a018.pdf","source":{"id":"https://openalex.org/S59725656","display_name":"Homology Homotopy and Applications","issn_l":"1532-0073","issn":["1532-0073","1532-0081"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-3"],"host_organization":"https://openalex.org/P4310316281","host_organization_name":"Lehigh University","host_organization_lineage":["https://openalex.org/P4310316281"],"host_organization_lineage_names":["Lehigh University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Homology, Homotopy and Applications","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.intlpress.com/site/pub/files/_fulltext/journals/hha/2014/0016/0002/HHA-2014-0016-0002-a018.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070671339","display_name":"Omer Bobrowski","orcid":"https://orcid.org/0000-0002-0860-7099","observed_orcids":["https://orcid.org/0000-0002-0860-7099"]},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Omer Bobrowski","raw_affiliation_strings":["Department of Mathematics, Duke University, Durham, North Carolina, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Duke University, Durham, North Carolina, U.S.A","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029952351","display_name":"Robert J. Adler","orcid":"https://orcid.org/0000-0002-8170-0396","observed_orcids":["https://orcid.org/0000-0002-8170-0396"]},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Robert J. Adler","raw_affiliation_strings":["Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.888,"has_fulltext":true,"cited_by_count":50,"citation_normalized_percentile":{"value":0.9565073,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":99},"biblio":{"volume":"16","issue":"2","first_page":"311","last_page":"344"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9580000042915344,"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":0.9580000042915344,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.03350000083446503,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.0012000000569969416,"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/distance-metrics","display_name":"distance measures","score":0.7649999856948853},{"id":"https://openalex.org/keywords/critical-points","display_name":"critical points","score":0.9539999961853027},{"id":"https://openalex.org/keywords/morse-index","display_name":"Morse index","score":0.871999979019165},{"id":"https://openalex.org/keywords/poisson-process","display_name":"Poisson process","score":0.7590000033378601},{"id":"https://openalex.org/keywords/betti-numbers","display_name":"Betti numbers","score":0.859000027179718},{"id":"https://openalex.org/keywords/random-simplicial-complexes","display_name":"random simplicial complexes","score":0.7360000014305115},{"id":"https://openalex.org/keywords/limit-theorems","display_name":"limit theorems","score":0.7490000128746033},{"id":"https://openalex.org/keywords/topological-statistics","display_name":"topological statistics","score":0.42899999022483826},{"id":"https://openalex.org/keywords/point-processes","display_name":"point processes","score":0.3070000112056732}],"concepts":[{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.693134069442749},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39937326312065125},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28438812494277954}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.4310/hha.2014.v16.n2.a18","doi":"https://doi.org/10.4310/hha.2014.v16.n2.a18","is_oa":true,"landing_page_url":"https://doi.org/10.4310/hha.2014.v16.n2.a18","pdf_url":"https://www.intlpress.com/site/pub/files/_fulltext/journals/hha/2014/0016/0002/HHA-2014-0016-0002-a018.pdf","source":{"id":"https://openalex.org/S59725656","display_name":"Homology Homotopy and Applications","issn_l":"1532-0073","issn":["1532-0073","1532-0081"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-3"],"host_organization":"https://openalex.org/P4310316281","host_organization_name":"Lehigh University","host_organization_lineage":["https://openalex.org/P4310316281"],"host_organization_lineage_names":["Lehigh University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Homology, Homotopy and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1107.4775","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1107.4775","pdf_url":"https://arxiv.org/pdf/1107.4775","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,"listed_in":[],"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:1964699373","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1107.4775.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,"listed_in":[],"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.1107.4775","doi":"https://doi.org/10.48550/arxiv.1107.4775","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1107.4775","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,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.4310/hha.2014.v16.n2.a18","doi":"https://doi.org/10.4310/hha.2014.v16.n2.a18","is_oa":true,"landing_page_url":"https://doi.org/10.4310/hha.2014.v16.n2.a18","pdf_url":"https://www.intlpress.com/site/pub/files/_fulltext/journals/hha/2014/0016/0002/HHA-2014-0016-0002-a018.pdf","source":{"id":"https://openalex.org/S59725656","display_name":"Homology Homotopy and Applications","issn_l":"1532-0073","issn":["1532-0073","1532-0081"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-3"],"host_organization":"https://openalex.org/P4310316281","host_organization_name":"Lehigh University","host_organization_lineage":["https://openalex.org/P4310316281"],"host_organization_lineage_names":["Lehigh University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Homology, Homotopy and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G503376696","display_name":null,"funder_award_id":"FA8655-11-1-3039","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320322248","display_name":"Israel Academy of Sciences and Humanities","ror":"https://ror.org/03c6c9520"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"},{"id":"https://openalex.org/F4320338370","display_name":"FP7 Information and Communication Technologies","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2964154246.pdf","grobid_xml":"https://content.openalex.org/works/W2964154246.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W137677586","https://openalex.org/W749223900","https://openalex.org/W1539795534","https://openalex.org/W1859601646","https://openalex.org/W1965334706","https://openalex.org/W1987982457","https://openalex.org/W2008318377","https://openalex.org/W2016966047","https://openalex.org/W2065890194","https://openalex.org/W2071391326","https://openalex.org/W2073443682","https://openalex.org/W2090464710","https://openalex.org/W2091574535","https://openalex.org/W2097532582","https://openalex.org/W2120672285","https://openalex.org/W2136164961","https://openalex.org/W2157071288","https://openalex.org/W2161491327","https://openalex.org/W2797024182","https://openalex.org/W2962885031","https://openalex.org/W3040586665","https://openalex.org/W3083418760","https://openalex.org/W4233604521","https://openalex.org/W4237809015","https://openalex.org/W4298909978","https://openalex.org/W6609374951","https://openalex.org/W6632600758"],"related_works":["https://openalex.org/W1964699373","https://openalex.org/W1542336663","https://openalex.org/W2890130723","https://openalex.org/W3022728133","https://openalex.org/W2950381279","https://openalex.org/W6963820441","https://openalex.org/W2120672285","https://openalex.org/W4408621294","https://openalex.org/W3137268199","https://openalex.org/W7100624677"],"abstract_inverted_index":{"For":[0],"a":[1,41],"finite":[2],"set":[3,26],"of":[4,32,35,50,55,58,67,80,104],"points":[5,34,57,68],"P":[6,14,37,39,60,111],"in":[7,97,99],"R":[8,16,19],"d":[9,13,17,36,59],",":[10,84],"the":[11,25,30,47,65,74,81,101,105],"function":[12],":":[15],"\u2192":[18],"+":[20],"measures":[21],"Euclidean":[22],"distance":[23],"to":[24,94],"P.":[27],"We":[28],"study":[29,46],"number":[31,54],"critical":[33,56],"when":[38],"is":[40],"Poisson":[42],"process.In":[43],"particular,":[44],"we":[45],"limit":[48,89],"behavior":[49],"N":[51,82],"k":[52,83],"-the":[53],"with":[61],"Morse":[62],"index":[63],"k-as":[64],"density":[66],"grows.We":[69],"present":[70],"explicit":[71],"computations":[72],"for":[73],"normalized":[75],"limiting":[76],"expectations":[77],"and":[78],"variances":[79],"as":[85,87],"well":[86],"distributional":[88],"theorems.We":[90],"link":[91],"these":[92],"results":[93,96],"recent":[95],"[16,17]":[98],"which":[100],"Betti":[102],"numbers":[103],"random":[106],"\u010cech":[107],"complex":[108],"based":[109],"on":[110],"were":[112],"studied.":[113]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2019-07-30T00:00:00"}