{"id":"https:\/\/openalex.org\/W1972374969","doi":"https:\/\/doi.org\/10.1137\/070687293","title":"Target Enumeration via Euler Characteristic Integrals","display_name":"Target Enumeration via Euler Characteristic Integrals","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https:\/\/openalex.org\/W1972374969","doi":"https:\/\/doi.org\/10.1137\/070687293","mag":"1972374969"},"language":"en","primary_location":{"id":"doi:10.1137\/070687293","is_oa":false,"landing_page_url":"https:\/\/doi.org\/10.1137\/070687293","pdf_url":null,"source":{"id":"https:\/\/openalex.org\/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https:\/\/openalex.org\/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https:\/\/openalex.org\/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https:\/\/repository.upenn.edu\/bitstreams\/f8961244-b955-42d0-b0ea-7e4fc226ea54\/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https:\/\/openalex.org\/A5040905411","display_name":"Yuliy Baryshnikov","orcid":"https:\/\/orcid.org\/0000-0003-4801-173X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuliy Baryshnikov","raw_affiliation_strings":["Division of Applied Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https:\/\/openalex.org\/A5111742669","display_name":"Robert Ghrist","orcid":null},"institutions":[{"id":"https:\/\/openalex.org\/I36788626","display_name":"California University of Pennsylvania","ror":"https:\/\/ror.org\/01spssf70","country_code":"US","type":"education","lineage":["https:\/\/openalex.org\/I36788626"]},{"id":"https:\/\/openalex.org\/I79576946","display_name":"University of Pennsylvania","ror":"https:\/\/ror.org\/00b30xv10","country_code":"US","type":"education","lineage":["https:\/\/openalex.org\/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert Ghrist","raw_affiliation_strings":["#N#               * University of Pennsylvania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"#N#               * University of Pennsylvania","institution_ids":["https:\/\/openalex.org\/I36788626","https:\/\/openalex.org\/I79576946"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.4941,"has_fulltext":true,"cited_by_count":87,"citation_normalized_percentile":{"value":0.96539393,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"70","issue":"3","first_page":"825","last_page":"844"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https:\/\/openalex.org\/T11106","display_name":"Data Management and Algorithms","score":0.9980999827384949,"subfield":{"id":"https:\/\/openalex.org\/subfields\/1711","display_name":"Signal Processing"},"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\/T11106","display_name":"Data Management and Algorithms","score":0.9980999827384949,"subfield":{"id":"https:\/\/openalex.org\/subfields\/1711","display_name":"Signal Processing"},"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\/T10757","display_name":"Geographic Information Systems Studies","score":0.989300012588501,"subfield":{"id":"https:\/\/openalex.org\/subfields\/3305","display_name":"Geography, Planning and Development"},"field":{"id":"https:\/\/openalex.org\/fields\/33","display_name":"Social Sciences"},"domain":{"id":"https:\/\/openalex.org\/domains\/2","display_name":"Social Sciences"}},{"id":"https:\/\/openalex.org\/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9753999710083008,"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\/mathematics","display_name":"Mathematics","score":0.6902341246604919},{"id":"https:\/\/openalex.org\/keywords\/enumeration","display_name":"Enumeration","score":0.6613351106643677},{"id":"https:\/\/openalex.org\/keywords\/eulers-formula","display_name":"Euler's formula","score":0.6537879705429077},{"id":"https:\/\/openalex.org\/keywords\/observable","display_name":"Observable","score":0.5519227981567383},{"id":"https:\/\/openalex.org\/keywords\/euler-characteristic","display_name":"Euler characteristic","score":0.4775037169456482},{"id":"https:\/\/openalex.org\/keywords\/sheaf","display_name":"Sheaf","score":0.44645559787750244},{"id":"https:\/\/openalex.org\/keywords\/topology","display_name":"Topology (electrical circuits)","score":0.43642571568489075},{"id":"https:\/\/openalex.org\/keywords\/applied-mathematics","display_name":"Applied mathematics","score":0.43637973070144653},{"id":"https:\/\/openalex.org\/keywords\/mathematical-optimization","display_name":"Mathematical optimization","score":0.33234429359436035},{"id":"https:\/\/openalex.org\/keywords\/computer-science","display_name":"Computer science","score":0.3245922029018402},{"id":"https:\/\/openalex.org\/keywords\/mathematical-analysis","display_name":"Mathematical analysis","score":0.3004376292228699},{"id":"https:\/\/openalex.org\/keywords\/pure-mathematics","display_name":"Pure mathematics","score":0.2510262727737427},{"id":"https:\/\/openalex.org\/keywords\/discrete-mathematics","display_name":"Discrete mathematics","score":0.24340438842773438},{"id":"https:\/\/openalex.org\/keywords\/combinatorics","display_name":"Combinatorics","score":0.1468905508518219}],"concepts":[{"id":"https:\/\/openalex.org\/C33923547","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q395","display_name":"Mathematics","level":0,"score":0.6902341246604919},{"id":"https:\/\/openalex.org\/C156340839","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q2704791","display_name":"Enumeration","level":2,"score":0.6613351106643677},{"id":"https:\/\/openalex.org\/C62884695","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q184871","display_name":"Euler's formula","level":2,"score":0.6537879705429077},{"id":"https:\/\/openalex.org\/C32848918","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q845789","display_name":"Observable","level":2,"score":0.5519227981567383},{"id":"https:\/\/openalex.org\/C196433757","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q852973","display_name":"Euler characteristic","level":2,"score":0.4775037169456482},{"id":"https:\/\/openalex.org\/C4017995","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q595298","display_name":"Sheaf","level":2,"score":0.44645559787750244},{"id":"https:\/\/openalex.org\/C184720557","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.43642571568489075},{"id":"https:\/\/openalex.org\/C28826006","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q33521","display_name":"Applied mathematics","level":1,"score":0.43637973070144653},{"id":"https:\/\/openalex.org\/C126255220","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33234429359436035},{"id":"https:\/\/openalex.org\/C41008148","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q21198","display_name":"Computer science","level":0,"score":0.3245922029018402},{"id":"https:\/\/openalex.org\/C134306372","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3004376292228699},{"id":"https:\/\/openalex.org\/C202444582","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q837863","display_name":"Pure mathematics","level":1,"score":0.2510262727737427},{"id":"https:\/\/openalex.org\/C118615104","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q121416","display_name":"Discrete mathematics","level":1,"score":0.24340438842773438},{"id":"https:\/\/openalex.org\/C114614502","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q76592","display_name":"Combinatorics","level":1,"score":0.1468905508518219},{"id":"https:\/\/openalex.org\/C62520636","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q944","display_name":"Quantum mechanics","level":1,"score":0},{"id":"https:\/\/openalex.org\/C121332964","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q413","display_name":"Physics","level":0,"score":0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137\/070687293","is_oa":false,"landing_page_url":"https:\/\/doi.org\/10.1137\/070687293","pdf_url":null,"source":{"id":"https:\/\/openalex.org\/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https:\/\/openalex.org\/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https:\/\/openalex.org\/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:repository.upenn.edu:grasp_papers-1002","is_oa":true,"landing_page_url":"https:\/\/repository.upenn.edu\/grasp_papers\/2","pdf_url":"https:\/\/repository.upenn.edu\/bitstreams\/f8961244-b955-42d0-b0ea-7e4fc226ea54\/download","source":{"id":"https:\/\/openalex.org\/S4377196331","display_name":"Scholarly Commons (University of Pennsylvania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https:\/\/openalex.org\/I79576946","host_organization_name":"University of Pennsylvania","host_organization_lineage":["https:\/\/openalex.org\/I79576946"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Lab Papers (GRASP)","raw_type":"text"},{"id":"pmh:oai:repository.upenn.edu:20.500.14332\/34769","is_oa":false,"landing_page_url":"https:\/\/repository.upenn.edu\/handle\/20.500.14332\/34769","pdf_url":null,"source":{"id":"https:\/\/openalex.org\/S4306402083","display_name":"ScholarlyCommons (University of Pennsylvania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https:\/\/openalex.org\/I79576946","host_organization_name":"University of Pennsylvania","host_organization_lineage":["https:\/\/openalex.org\/I79576946"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"published","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:repository.upenn.edu:grasp_papers-1002","is_oa":true,"landing_page_url":"https:\/\/repository.upenn.edu\/grasp_papers\/2","pdf_url":"https:\/\/repository.upenn.edu\/bitstreams\/f8961244-b955-42d0-b0ea-7e4fc226ea54\/download","source":{"id":"https:\/\/openalex.org\/S4377196331","display_name":"Scholarly Commons (University of Pennsylvania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https:\/\/openalex.org\/I79576946","host_organization_name":"University of Pennsylvania","host_organization_lineage":["https:\/\/openalex.org\/I79576946"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Lab Papers (GRASP)","raw_type":"text"},"sustainable_development_goals":[{"score":0.550000011920929,"id":"https:\/\/metadata.un.org\/sdg\/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https:\/\/content.openalex.org\/works\/W1972374969.pdf","grobid_xml":"https:\/\/content.openalex.org\/works\/W1972374969.grobid-xml"},"referenced_works_count":35,"referenced_works":["https:\/\/openalex.org\/W40684321","https:\/\/openalex.org\/W938873559","https:\/\/openalex.org\/W1509397417","https:\/\/openalex.org\/W1568989156","https:\/\/openalex.org\/W1597704077","https:\/\/openalex.org\/W1979472779","https:\/\/openalex.org\/W2034944977","https:\/\/openalex.org\/W2034996971","https:\/\/openalex.org\/W2044240207","https:\/\/openalex.org\/W2046748166","https:\/\/openalex.org\/W2048209332","https:\/\/openalex.org\/W2050596175","https:\/\/openalex.org\/W2053761604","https:\/\/openalex.org\/W2055555888","https:\/\/openalex.org\/W2090728922","https:\/\/openalex.org\/W2097380742","https:\/\/openalex.org\/W2107482124","https:\/\/openalex.org\/W2115780336","https:\/\/openalex.org\/W2130561842","https:\/\/openalex.org\/W2133926362","https:\/\/openalex.org\/W2141699373","https:\/\/openalex.org\/W2143383769","https:\/\/openalex.org\/W2144740142","https:\/\/openalex.org\/W2159134310","https:\/\/openalex.org\/W2162052349","https:\/\/openalex.org\/W2162608260","https:\/\/openalex.org\/W2325410206","https:\/\/openalex.org\/W2407868799","https:\/\/openalex.org\/W2500739438","https:\/\/openalex.org\/W2504281202","https:\/\/openalex.org\/W2528287075","https:\/\/openalex.org\/W2983836991","https:\/\/openalex.org\/W3040586665","https:\/\/openalex.org\/W3147444766","https:\/\/openalex.org\/W4238054270"],"related_works":["https:\/\/openalex.org\/W3192281373","https:\/\/openalex.org\/W2020015225","https:\/\/openalex.org\/W2766785516","https:\/\/openalex.org\/W4297714858","https:\/\/openalex.org\/W4302415146","https:\/\/openalex.org\/W2952814730","https:\/\/openalex.org\/W2963185310","https:\/\/openalex.org\/W4319599637","https:\/\/openalex.org\/W1678047659","https:\/\/openalex.org\/W4299701491"],"abstract_inverted_index":{"We":[0,45],"solve":[1,48],"the":[2,6,32,54,61,70],"problem":[3],"of":[4,9,26,29,34,56,60,66,72],"counting":[5],"total":[7],"number":[8,33],"observable":[10],"targets":[11,35],"(e.g.,":[12],"persons,":[13],"vehicles,":[14],"landmarks)":[15],"in":[16],"a":[17,24,73],"region":[18],"using":[19],"local":[20],"counts":[21],"performed":[22],"by":[23],"network":[25],"sensors,":[27],"each":[28],"which":[30],"measures":[31],"nearby":[36],"but":[37],"neither":[38],"their":[39],"identities":[40],"nor":[41],"any":[42],"positional":[43],"information.":[44],"formulate":[46],"and":[47,58],"several":[49],"such":[50],"problems":[51],"based":[52],"on":[53],"types":[55],"sensors":[57],"mobility":[59],"targets.":[62],"The":[63],"main":[64],"contribution":[65],"this":[67],"paper":[68],"is":[69],"adaptation":[71],"topological":[74],"sheaf":[75],"integration":[76],"theory\u2014integration":[77],"with":[78],"respect":[79],"to":[80,86],"Euler":[81],"characteristic\u2014to":[82],"yield":[83],"complete":[84],"solutions":[85],"these":[87],"problems.":[88]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":17},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":8}],"updated_date":"2026-08-24T07:32:12.397491","created_date":"2025-10-10T00:00:00"}