{"id":"https://openalex.org/W2890680031","doi":"https://doi.org/10.1145/3272127.3275064","title":"Dynamical optimal transport on discrete surfaces","display_name":"Dynamical optimal transport on discrete surfaces","publication_year":2018,"publication_date":"2018-11-28","ids":{"openalex":"https://openalex.org/W2890680031","doi":"https://doi.org/10.1145/3272127.3275064","mag":"2890680031"},"language":"en","primary_location":{"id":"doi:10.1145/3272127.3275064","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3272127.3275064","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3272127.3275064","source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3272127.3275064","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Hugo Lavenant","orcid":null},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Hugo Lavenant","raw_affiliation_strings":["Universit\u00e9 Paris-Sud"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris-Sud","institution_ids":["https://openalex.org/I102197404"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Sebastian Claici","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sebastian Claici","raw_affiliation_strings":["Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Edward Chien","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Edward Chien","raw_affiliation_strings":["Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":null,"display_name":"Justin Solomon","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Justin Solomon","raw_affiliation_strings":["Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3695,"has_fulltext":true,"cited_by_count":29,"citation_normalized_percentile":{"value":0.88351927,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"37","issue":"6","first_page":"1","last_page":"16"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.10540000349283218,"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"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.10540000349283218,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.10289999842643738,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.08889999985694885,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.6312999725341797},{"id":"https://openalex.org/keywords/discrete-space","display_name":"Discrete space","score":0.6294999718666077},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.5954999923706055},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5257999897003174},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.49380001425743103},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.4869000017642975},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.46309998631477356},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4422000050544739},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.429500013589859}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.642300009727478},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.6312999725341797},{"id":"https://openalex.org/C153782549","wikidata":"https://www.wikidata.org/wiki/Q175116","display_name":"Discrete space","level":2,"score":0.6294999718666077},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.5954999923706055},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5257999897003174},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.49380001425743103},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.4869000017642975},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.46309998631477356},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4422000050544739},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.429500013589859},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38510000705718994},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38280001282691956},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.3734000027179718},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.3691999912261963},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.36090001463890076},{"id":"https://openalex.org/C81146285","wikidata":"https://www.wikidata.org/wiki/Q5282053","display_name":"Discrete modelling","level":3,"score":0.35089999437332153},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.34310001134872437},{"id":"https://openalex.org/C2777634741","wikidata":"https://www.wikidata.org/wiki/Q768993","display_name":"Wasserstein metric","level":2,"score":0.34060001373291016},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.33880001306533813},{"id":"https://openalex.org/C197096303","wikidata":"https://www.wikidata.org/wiki/Q869887","display_name":"Probability mass function","level":3,"score":0.3212999999523163},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3140999972820282},{"id":"https://openalex.org/C4107886","wikidata":"https://www.wikidata.org/wiki/Q906377","display_name":"Discrete geometry","level":2,"score":0.29679998755455017},{"id":"https://openalex.org/C96314035","wikidata":"https://www.wikidata.org/wiki/Q5282062","display_name":"Discrete system","level":2,"score":0.28949999809265137},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C2778872062","wikidata":"https://www.wikidata.org/wiki/Q5280765","display_name":"Dirichlet form","level":4,"score":0.26989999413490295},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2597000002861023},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C158557763","wikidata":"https://www.wikidata.org/wiki/Q5166603","display_name":"Convolution of probability distributions","level":4,"score":0.25220000743865967}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/3272127.3275064","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3272127.3275064","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3272127.3275064","source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1809.07083","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1809.07083","pdf_url":"https://arxiv.org/pdf/1809.07083","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":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-01875836v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01875836","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"SIGGRAPH Asia 2018, Dec 2018, Tokyo, Japan. &#x27E8;10.1145/3272127.3275064&#x27E9;","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"doi:10.1145/3272127.3275064","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3272127.3275064","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3272127.3275064","source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4777382478","display_name":null,"funder_award_id":"W911NF-12-R-0011","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5674620021","display_name":null,"funder_award_id":"W911NF-12-R-0011","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G8479273144","display_name":null,"funder_award_id":"IIS-1838071","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G995230906","display_name":"BIGDATA:F: Statistical and Computational Optimal Transport for Geometric Data Analysis","funder_award_id":"1838071","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/F4320324442","display_name":"Skolkovo Institute of Science and Technology","ror":"https://ror.org/03f9nc143"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2890680031.pdf","grobid_xml":"https://content.openalex.org/works/W2890680031.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W1549932963","https://openalex.org/W1585160083","https://openalex.org/W1974956622","https://openalex.org/W1977257583","https://openalex.org/W1985506636","https://openalex.org/W1986660281","https://openalex.org/W1997924480","https://openalex.org/W1998824578","https://openalex.org/W2009172320","https://openalex.org/W2021479652","https://openalex.org/W2028852533","https://openalex.org/W2032323564","https://openalex.org/W2036996178","https://openalex.org/W2042174836","https://openalex.org/W2047767520","https://openalex.org/W2049106345","https://openalex.org/W2049153601","https://openalex.org/W2071048859","https://openalex.org/W2072983001","https://openalex.org/W2093222011","https://openalex.org/W2096413780","https://openalex.org/W2127674094","https://openalex.org/W2132883347","https://openalex.org/W2133921496","https://openalex.org/W2143118902","https://openalex.org/W2149342630","https://openalex.org/W2155488148","https://openalex.org/W2164260102","https://openalex.org/W2166541787","https://openalex.org/W2303314472","https://openalex.org/W2744789862","https://openalex.org/W2900798569","https://openalex.org/W2962746791","https://openalex.org/W3139172074","https://openalex.org/W4230927393","https://openalex.org/W4254707034","https://openalex.org/W4288268095","https://openalex.org/W4292363360"],"related_works":[],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,31,55,66,79,85],"technique":[3,83],"for":[4,39],"interpolating":[5],"between":[6,88],"probability":[7,63],"distributions":[8,64,89],"on":[9,13,30,58,65,90],"discrete":[10,49,67,76,91,108],"surfaces,":[11],"based":[12,29],"the":[14,59,71],"theory":[15],"of":[16,34,62,110,125],"optimal":[17,36,111],"transport.":[18],"Unlike":[19],"previous":[20],"attempts":[21],"that":[22],"use":[23],"linear":[24],"programming,":[25],"our":[26,82,107],"method":[27],"is":[28],"dynamical":[32],"formulation":[33],"quadratic":[35],"transport":[37,112],"proposed":[38],"flat":[40],"domains":[41],"by":[42],"Benamou":[43],"and":[44,122],"Brenier":[45],"[2000],":[46],"adapted":[47],"to":[48,75,114],"surfaces.":[50],"Our":[51],"structure-preserving":[52],"construction":[53],"yields":[54],"Riemannian":[56],"metric":[57],"(finite-dimensional)":[60],"space":[61],"surface,":[68],"which":[69],"translates":[70],"so-called":[72],"Otto":[73],"calculus":[74],"language.":[77],"From":[78],"practical":[80],"perspective,":[81],"provides":[84],"smooth":[86],"interpolation":[87],"surfaces":[92],"with":[93],"less":[94],"diffusion":[95],"than":[96],"state-of-the-art":[97],"algorithms":[98],"involving":[99],"entropic":[100],"regularization.":[101],"Beyond":[102],"interpolation,":[103],"we":[104],"show":[105],"how":[106],"notion":[109],"extends":[113],"other":[115],"tasks,":[116],"such":[117],"as":[118],"distribution-valued":[119],"Dirichlet":[120],"problems":[121],"time":[123],"integration":[124],"gradient":[126],"flows.":[127]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2019,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2018-09-27T00:00:00"}
