{"id":"https://openalex.org/W7160868526","doi":"https://doi.org/10.48550/arxiv.2605.07513","title":"Tessellations of Semi-Discrete Flow Matching","display_name":"Tessellations of Semi-Discrete Flow Matching","publication_year":2026,"publication_date":"2026-05-08","ids":{"openalex":"https://openalex.org/W7160868526","doi":"https://doi.org/10.48550/arxiv.2605.07513"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.07513","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.07513","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.07513","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135847330","display_name":"Emile Pierret","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pierret, Emile","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007073244","display_name":"Johannes Hertrich","orcid":"https://orcid.org/0000-0003-4433-8604"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hertrich, Johannes","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135900873","display_name":"Samuel Hurault","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hurault, Samuel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5019518434","display_name":"Julie Delon","orcid":"https://orcid.org/0000-0002-7182-7537"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Delon, Julie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.38350000977516174,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.38350000977516174,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.11680000275373459,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.08190000057220459,"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/flow","display_name":"Flow (mathematics)","score":0.6621999740600586},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.6470000147819519},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4595000147819519},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4523000121116638},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4226999878883362},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.4147999882698059},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.40149998664855957},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.3808000087738037}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6693999767303467},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.6621999740600586},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.6470000147819519},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4595000147819519},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4523000121116638},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4226999878883362},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.4147999882698059},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.40149998664855957},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.398499995470047},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.38199999928474426},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.3808000087738037},{"id":"https://openalex.org/C2779664074","wikidata":"https://www.wikidata.org/wiki/Q3518405","display_name":"Terminal (telecommunication)","level":2,"score":0.36160001158714294},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3465000092983246},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33500000834465027},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.33169999718666077},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3246000111103058},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.2775999903678894},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.2646999955177307},{"id":"https://openalex.org/C40375134","wikidata":"https://www.wikidata.org/wiki/Q1303846","display_name":"Eikonal equation","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.2524999976158142}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.07513","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.07513","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.07513","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.07513","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,84,101],"study":[1],"Flow":[2,34,55,168],"Matching":[3,35,56,169],"in":[4,61,139],"a":[5,9,15,46,124],"semi-discrete":[6,24,51,140,167],"setting":[7,29],"where":[8,39],"Gaussian":[10],"source":[11],"is":[12,26,43,59],"transported":[13],"toward":[14],"discrete":[16],"target":[17,41,95],"supported":[18],"on":[19],"finitely":[20],"many":[21],"points.":[22],"This":[23],"regime":[25],"the":[27,31,40,53,70,74,86,91,94,98,117,121,160,165,175],"theoretical":[28],"behind":[30],"use":[32],"of":[33,79,93],"for":[36],"generative":[37],"modeling,":[38],"distribution":[42],"represented":[44],"by":[45,73,164],"finite":[47],"dataset.":[48],"In":[49],"this":[50],"regime,":[52],"exact":[54,166],"velocity":[57],"field":[58],"available":[60],"closed":[62],"form,":[63],"which":[64],"makes":[65],"it":[66],"possible":[67],"to":[68,116],"analyze":[69],"geometry":[71,161],"induced":[72,163],"terminal":[75,87,99],"flow":[76],"map":[77],"independently":[78],"optimization":[80],"and":[81,150,154],"approximation":[82,173],"effects.":[83],"investigate":[85],"assignment":[88],"regions,":[89],"namely":[90],"preimages":[92],"atoms":[96],"under":[97,111],"flow.":[100],"show":[102],"that":[103,129],"these":[104,130],"regions":[105],"are":[106],"open,":[107],"simply":[108],"connected":[109],"and,":[110],"an":[112],"additional":[113],"assumption,":[114],"homeomorphic":[115],"unit":[118],"ball.":[119],"At":[120],"same":[122],"time,":[123],"planar":[125],"four-point":[126],"example":[127],"shows":[128],"cells":[131,137],"can":[132],"differ":[133],"sharply":[134],"from":[135],"Laguerre":[136],"arising":[138],"optimal":[141],"transport:":[142],"they":[143],"may":[144],"be":[145],"non-convex,":[146],"have":[147],"curved":[148],"boundaries,":[149],"exhibit":[151],"different":[152],"boundedness":[153],"adjacency":[155],"patterns.":[156],"These":[157],"results":[158],"clarify":[159],"intrinsically":[162],"objective":[170],"before":[171],"neural":[172],"enters":[174],"picture.":[176]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-12T00:00:00"}