{"id":"https://openalex.org/W2740468037","doi":"https://doi.org/10.1137/17m1138972","title":"Simplified Energy Landscape for Modularity Using Total Variation","display_name":"Simplified Energy Landscape for Modularity Using Total Variation","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2740468037","doi":"https://doi.org/10.1137/17m1138972","mag":"2740468037"},"language":"en","primary_location":{"id":"doi:10.1137/17m1138972","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1138972","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1707.09285","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103264590","display_name":"Zachary M. Boyd","orcid":"https://orcid.org/0000-0002-3258-9820"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zachary M. Boyd","raw_affiliation_strings":["University of California at Los Angeles"],"raw_orcid":"https://orcid.org/0000-0002-3258-9820","affiliations":[{"raw_affiliation_string":"University of California at Los Angeles","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061969008","display_name":"Egil Bae","orcid":"https://orcid.org/0000-0002-4621-259X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Egil Bae","raw_affiliation_strings":["Norwegian Defense Research Institute"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Norwegian Defense Research Institute","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101951979","display_name":"Xue\u2010Cheng Tai","orcid":"https://orcid.org/0000-0003-3359-9104"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Xue-Cheng Tai","raw_affiliation_strings":["University of Bergen"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Bergen","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090707978","display_name":"Andrea L. Bertozzi","orcid":"https://orcid.org/0000-0003-0396-7391"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrea L. Bertozzi","raw_affiliation_strings":["University of California at Los Angeles"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California at Los Angeles","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0824,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.40839658,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"78","issue":"5","first_page":"2439","last_page":"2464"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10887","display_name":"Bioinformatics and Genomic Networks","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10887","display_name":"Bioinformatics and Genomic Networks","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/modularity","display_name":"Modularity (biology)","score":0.7620744109153748},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5156596899032593},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4844703674316406},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4591154456138611},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4579890966415405},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.415109783411026},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3755543828010559},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3754403293132782},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.366909384727478},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3403993248939514},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12286829948425293}],"concepts":[{"id":"https://openalex.org/C2779478453","wikidata":"https://www.wikidata.org/wiki/Q6889748","display_name":"Modularity (biology)","level":2,"score":0.7620744109153748},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5156596899032593},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4844703674316406},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4591154456138611},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4579890966415405},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.415109783411026},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3755543828010559},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3754403293132782},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.366909384727478},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3403993248939514},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12286829948425293},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/17m1138972","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1138972","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:arXiv.org:1707.09285","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1707.09285","pdf_url":"https://arxiv.org/pdf/1707.09285","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":"","raw_type":"text"},{"id":"pmh:oai:bora.uib.no:1956/19714","is_oa":true,"landing_page_url":"https://hdl.handle.net/1956/19714","pdf_url":"https://bora.uib.no/bora-xmlui/bitstream/1956/19714/3/17m1138972.pdf","source":{"id":"https://openalex.org/S4306400085","display_name":"Bergen Open Research Archive (BORA) (University of Bergen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4432739","host_organization_name":"University of Bergen","host_organization_lineage":["https://openalex.org/I4432739"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"info:eu-repo/semantics/other"},{"id":"pmh:ark:/13030/qt5pn344bj","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},{"id":"pmh:oai:escholarship.org/ark:/13030/qt5pn344bj","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/5pn344bj","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM JOURNAL ON APPLIED MATHEMATICS, vol 78, iss 5","raw_type":"article"},{"id":"pmh:qt5pn344bj","is_oa":false,"landing_page_url":"http://www.escholarship.org/uc/item/5pn344bj","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Boyd, Z; Bae, E; Tai, X-C; &amp; Bertozzi, AL. (2017). Simplified Energy Landscape for Modularity Using Total Variation. UCLA: Retrieved from: http://www.escholarship.org/uc/item/5pn344bj","raw_type":"article"},{"id":"doi:10.48550/arxiv.1707.09285","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1707.09285","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1707.09285","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1707.09285","pdf_url":"https://arxiv.org/pdf/1707.09285","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":"","raw_type":"text"},"sustainable_development_goals":[{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/2","display_name":"Zero hunger"}],"awards":[{"id":"https://openalex.org/G1823592992","display_name":null,"funder_award_id":"DMS-1417674","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G1975816489","display_name":null,"funder_award_id":"2390033/F20","funder_id":"https://openalex.org/F4320323078","funder_display_name":"Universitetet i Bergen"},{"id":"https://openalex.org/G2332793202","display_name":"Algorithms for Threat Detection in Sensor Systems for Analyzing Chemical and Biological Systems Based on Compressive Sensing and L1 Related Optimization","funder_award_id":"1118971","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2846959751","display_name":null,"funder_award_id":"FA8750-18-2-0066","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G3169272610","display_name":null,"funder_award_id":"DMS-1118971","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3506650081","display_name":null,"funder_award_id":"FA8750-18-2-0066","funder_id":"https://openalex.org/F4320306078","funder_display_name":"U.S. Department of Defense"},{"id":"https://openalex.org/G3693623274","display_name":null,"funder_award_id":"DMS-1737770","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G4713059963","display_name":null,"funder_award_id":"FA8750","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G5645840916","display_name":null,"funder_award_id":"FA8750-18-2-0066","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5948696453","display_name":null,"funder_award_id":"DMS-1737770","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6235043008","display_name":null,"funder_award_id":"RG(R)- RC/17-18/02-MATH","funder_id":"https://openalex.org/F4320320955","funder_display_name":"Hong Kong Baptist University"},{"id":"https://openalex.org/G6762995350","display_name":null,"funder_award_id":"FRG2/17-18/033","funder_id":"https://openalex.org/F4320320955","funder_display_name":"Hong Kong Baptist University"},{"id":"https://openalex.org/G7099875087","display_name":null,"funder_award_id":"FRG2/17","funder_id":"https://openalex.org/F4320320955","funder_display_name":"Hong Kong Baptist University"},{"id":"https://openalex.org/G8570927041","display_name":null,"funder_award_id":"DMS-1417674","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8802953049","display_name":"Extreme-scale algorithms for geometric graphical data models in imaging, social and network science","funder_award_id":"1417674","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8998889701","display_name":"ATD: Sparsity Models for Forecasting Spatio-Temporal Human Dynamics","funder_award_id":"1737770","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/F4320306078","display_name":"U.S. Department of Defense","ror":"https://ror.org/0447fe631"},{"id":"https://openalex.org/F4320320955","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131"},{"id":"https://openalex.org/F4320323078","display_name":"Universitetet i Bergen","ror":"https://ror.org/03zga2b32"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320333566","display_name":"National Defense Science and Engineering Graduate","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":70,"referenced_works":["https://openalex.org/W229097380","https://openalex.org/W309670289","https://openalex.org/W1578099820","https://openalex.org/W1596169490","https://openalex.org/W1644749979","https://openalex.org/W1875112053","https://openalex.org/W1902367374","https://openalex.org/W1969755245","https://openalex.org/W1976702945","https://openalex.org/W1977309280","https://openalex.org/W1978333359","https://openalex.org/W1986753844","https://openalex.org/W1998830482","https://openalex.org/W1998920956","https://openalex.org/W2007680066","https://openalex.org/W2015953751","https://openalex.org/W2023655578","https://openalex.org/W2025543856","https://openalex.org/W2033456101","https://openalex.org/W2033507223","https://openalex.org/W2047583926","https://openalex.org/W2047940964","https://openalex.org/W2057504236","https://openalex.org/W2060945009","https://openalex.org/W2061099285","https://openalex.org/W2061979078","https://openalex.org/W2074617510","https://openalex.org/W2087770851","https://openalex.org/W2095189226","https://openalex.org/W2095293504","https://openalex.org/W2097073572","https://openalex.org/W2103559027","https://openalex.org/W2109726592","https://openalex.org/W2111090475","https://openalex.org/W2111642621","https://openalex.org/W2116040950","https://openalex.org/W2125658625","https://openalex.org/W2127048411","https://openalex.org/W2128366083","https://openalex.org/W2130698343","https://openalex.org/W2131681506","https://openalex.org/W2132914434","https://openalex.org/W2142058898","https://openalex.org/W2145096794","https://openalex.org/W2146818756","https://openalex.org/W2151936673","https://openalex.org/W2152322845","https://openalex.org/W2156028561","https://openalex.org/W2161455936","https://openalex.org/W2163973643","https://openalex.org/W2169898291","https://openalex.org/W2172029033","https://openalex.org/W2316369803","https://openalex.org/W2337910323","https://openalex.org/W2342626288","https://openalex.org/W2416738288","https://openalex.org/W2418015316","https://openalex.org/W2491337109","https://openalex.org/W2513567506","https://openalex.org/W2523352299","https://openalex.org/W2570940516","https://openalex.org/W2944437997","https://openalex.org/W2951271819","https://openalex.org/W2963833097","https://openalex.org/W2963861243","https://openalex.org/W3022380717","https://openalex.org/W3101413764","https://openalex.org/W3123255541","https://openalex.org/W3126033509","https://openalex.org/W4244101998"],"related_works":["https://openalex.org/W2678393227","https://openalex.org/W2238542761","https://openalex.org/W2949808546","https://openalex.org/W2950267499","https://openalex.org/W2033795336","https://openalex.org/W2469409447","https://openalex.org/W2149896468","https://openalex.org/W2398649238","https://openalex.org/W2397577094","https://openalex.org/W2950267167","https://openalex.org/W2571358802","https://openalex.org/W2964011274","https://openalex.org/W3169502490","https://openalex.org/W2949350063","https://openalex.org/W2611894792","https://openalex.org/W3013922679","https://openalex.org/W1749371477","https://openalex.org/W1649185057","https://openalex.org/W2488984458","https://openalex.org/W2605569246"],"abstract_inverted_index":{"Networks":[0],"capture":[1],"pairwise":[2],"interactions":[3],"between":[4],"entities":[5],"and":[6,18,36,185],"are":[7],"frequently":[8],"used":[9,52],"in":[10,33,162,181,231],"applications":[11],"such":[12],"as":[13],"social":[14],"networks,":[15,17,21],"food":[16],"protein":[19],"interaction":[20],"to":[22,53,79,114,158,198],"name":[23],"a":[24,81,90,103,116,121,147,152,166,212],"few.":[25],"Communities,":[26],"cohesive":[27],"groups":[28],"of":[29,45,99,127,165,234],"nodes,":[30],"often":[31],"form":[32],"these":[34],"applications,":[35],"identifying":[37],"them":[38],"gives":[39],"insight":[40],"into":[41],"the":[42,46,97,125,159,163,193,199,202,232],"overall":[43],"organization":[44],"network.":[47],"One":[48],"common":[49],"quality":[50],"function":[51],"identify":[54],"community":[55],"structure":[56],"is":[57,77,101,112,129,187,205,222],"modularity.":[58],"In":[59],"Hu":[60,182,235],"et":[61,183,236],"al.":[62,184,237],"[SIAM":[63],"J.":[64],"Appl.":[65],"Math.,":[66],"73":[67],"(2013),":[68],"pp.":[69],"2224--2246],":[70],"it":[71],"was":[72,229],"shown":[73],"that":[74,109,134,175,186,201],"modularity":[75,110,135],"optimization":[76,111],"equivalent":[78,113],"minimizing":[80,115],"particular":[82],"nonconvex":[83,149],"total":[84],"variation":[85],"(TV)":[86],"based":[87],"functional":[88,119],"over":[89,120],"discrete":[91,122],"domain.":[92],"They":[93],"solve":[94],"this":[95],"problem---assuming":[96],"number":[98,126],"communities":[100,128],"known---using":[102],"Merriman--Bence--Osher":[104],"(MBO)":[105],"scheme.":[106],"We":[107,144,169],"show":[108,133],"convex":[117,138],"TV-based":[118],"domain---again,":[123],"assuming":[124],"known.":[130],"Furthermore,":[131],"we":[132],"has":[136,176,218],"no":[137],"relaxation":[139],"satisfying":[140],"certain":[141,167],"natural":[142],"conditions.":[143],"therefore":[145],"find":[146],"manageable":[148],"approximation":[150],"using":[151],"Ginzburg--Landau":[153],"functional,":[154],"which":[155,221],"provably":[156],"converges":[157],"correct":[160],"energy":[161],"limit":[164],"parameter.":[168],"then":[170],"derive":[171],"an":[172],"MBO":[173],"algorithm":[174],"fewer":[177],"hand-tuned":[178],"parameters":[179],"than":[180,227],"seven":[188],"times":[189,225],"faster":[190],"at":[191],"solving":[192],"associated":[194,216],"diffusion":[195],"equation":[196],"due":[197],"fact":[200],"underlying":[203],"discretization":[204],"unconditionally":[206],"stable.":[207],"Our":[208],"numerical":[209],"tests":[210],"include":[211],"hyperspectral":[213],"video":[214],"whose":[215],"graph":[217],"$2.9\\times10^7$":[219],"edges,":[220],"roughly":[223],"37":[224],"larger":[226],"what":[228],"handled":[230],"paper":[233]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
