{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T07:40:05Z","timestamp":1751528405839,"version":"3.41.0"},"reference-count":68,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["1210426"],"award-info":[{"award-number":["1210426"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100012950","name":"Institut national de recherche en informatique et en automatique","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100012950","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Scientific Council of Universite Paris-Dauphine"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2025,8,31]]},"DOI":"10.1137\/24m1650193","type":"journal-article","created":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T07:02:58Z","timestamp":1751526178000},"page":"3649-3694","source":"Crossref","is-referenced-by-count":0,"title":["Optimal Quantization with Branched Optimal Transport Distances"],"prefix":"10.1137","volume":"57","author":[{"given":"Paul","family":"Pegon","sequence":"first","affiliation":[{"name":"CEREMADE, Universit\u00e9 Paris\u2013Dauphine, Universit\u00e9 PSL, CNRS & MOKAPLAN, Inria Paris, 75016 Paris, France."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2181-169X","authenticated-orcid":true,"given":"Mircea","family":"Petrache","sequence":"additional","affiliation":[{"name":"Facultad de Matem\u00e1ticas and Instituto de Ingener\u00eda Matem\u00e1tica y Computacional, Avda. Vicu\u00f1a Mackenna, 4860 Macul, Santiago, 6904441, Chile."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"351","published-online":{"date-parts":[[2025,7,3]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198502456.001.0001"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/PL00009187"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.5565\/PUBLMAT_49205_09"},{"key":"ref4","series-title":"Lecture Notes in Math. 1955","volume-title":"Optimal Transportation Networks: Models and Theory","author":"Bernot M.","year":"2009"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s00222-019-00911-3"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0531(72)90147-0"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1137\/17M1159452"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1515\/acv-2019-0031"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.4171\/ifb\/436"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-84808-2"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/S1631-073X(02)02575-X"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2010.10.009"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechrescom.2022.104023"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-014-1965-5"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:2008034"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.4171\/ifb\/254"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2016.03.008"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1137\/21M1440281"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-019-1666-1"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202518500604"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1982.1056486"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-85799-0"},{"key":"ref24","first-page":"239","volume":"12","author":"Buttazzo G.","year":"2013","journal-title":"Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-023-02569-5"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2019.01.020"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.21919"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2021167"},{"key":"ref29","doi-asserted-by":"crossref","first-page":"317","DOI":"10.5802\/jep.72","volume":"5","author":"Conti S.","year":"2018","journal-title":"J. \u00c9c. polytech. Math."},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-002-0177-6"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1515\/ans-2018-2035"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144599352836"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.73.016116"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1007\/BF02024494"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1966-0185084-5"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1979.1056067"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-3626-0"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1967.tb04250.x"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0103945"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2003.07.017"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1007\/s11118-020-09875-z"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1007\/s11511-008-0023-6"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.3390\/a14070189"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.4171\/emss\/13"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.5802\/ambp.149"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-022-09927-3"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2022.05.021"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.4171\/ifb\/85"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1515\/acv-2014-0022"},{"key":"ref50","doi-asserted-by":"crossref","unstructured":"Q. M\u00e9rigot, A multiscale approach to optimal transport, Computer Graphics Forum, 30 (2011), pp. 1583\u20131592, https:\/\/doi.org\/10.1111\/j.1467-8659.2011.02032.x.","DOI":"10.1111\/j.1467-8659.2011.02032.x"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1016\/bs.hna.2020.10.001"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2015049"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2006.05.009"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1002\/9780470317013"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-011-0402-6"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(97)00190-8"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.4171\/ifb\/149"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1515\/9783110430417-012"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2018.06.007"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-017-9395-1"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.4171\/zaa\/1620"},{"key":"ref64","volume-title":"Fractal River Basins: Chance and Self-Organization","author":"Rodr\u00edguez-Iturbe I.","year":"2001"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.4171\/ifb\/160"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-20828-2"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2017.06.053"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392829"},{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.1142\/S021919970300094X"},{"key":"ref71","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-003-0237-6"},{"key":"ref72","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1982.1056490"}],"container-title":["SIAM Journal on Mathematical Analysis"],"original-title":[],"language":"en","deposited":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T07:03:01Z","timestamp":1751526181000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M1650193"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,3]]},"references-count":68,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,8,31]]}},"alternative-id":["10.1137\/24M1650193"],"URL":"https:\/\/doi.org\/10.1137\/24m1650193","relation":{},"ISSN":["0036-1410","1095-7154"],"issn-type":[{"value":"0036-1410","type":"print"},{"value":"1095-7154","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,3]]}}}