{"id":"https://openalex.org/W2949981745","doi":"https://doi.org/10.1109/cdc.2013.6760486","title":"Matrix-valued Monge-Kantorovich optimal mass transport","display_name":"Matrix-valued Monge-Kantorovich optimal mass transport","publication_year":2013,"publication_date":"2013-12-01","ids":{"openalex":"https://openalex.org/W2949981745","doi":"https://doi.org/10.1109/cdc.2013.6760486","mag":"2949981745"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2013.6760486","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6760486","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004577779","display_name":"Lipeng Ning","orcid":"https://orcid.org/0000-0003-4992-459X"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lipeng Ning","raw_affiliation_strings":["Department of Electrical & Computer Engineering, University of Minnesota, Minneapolis, MN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical & Computer Engineering, University of Minnesota, Minneapolis, MN","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035194316","display_name":"Tryphon T. Georgiou","orcid":"https://orcid.org/0000-0003-0012-5447"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tryphon T. Georgiou","raw_affiliation_strings":["Department of Electrical & Computer Engineering, University of Minnesota, Minneapolis, MN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical & Computer Engineering, University of Minnesota, Minneapolis, MN","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012935165","display_name":"Allen Tannenbaum","orcid":"https://orcid.org/0000-0002-0567-5256"},"institutions":[{"id":"https://openalex.org/I32389192","display_name":"University of Alabama at Birmingham","ror":"https://ror.org/008s83205","country_code":"US","type":"education","lineage":["https://openalex.org/I32389192"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Allen Tannenbaum","raw_affiliation_strings":["the Department of Electrical & Computer Engineering, University of Alabama, Birmingham, AL"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"the Department of Electrical & Computer Engineering, University of Alabama, Birmingham, AL","institution_ids":["https://openalex.org/I32389192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"4","issue":null,"first_page":"3906","last_page":"3911"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9997000098228455,"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":0.9997000098228455,"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/T12351","display_name":"Geometry and complex manifolds","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9803000092506409,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/transportation-theory","display_name":"Transportation theory","score":0.6272919178009033},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6238856315612793},{"id":"https://openalex.org/keywords/mass-transportation","display_name":"Mass transportation","score":0.5757802128791809},{"id":"https://openalex.org/keywords/multivariable-calculus","display_name":"Multivariable calculus","score":0.5638231635093689},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5521383285522461},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4917187988758087},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4748956263065338},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46467098593711853},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4569428861141205},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.4188345670700073},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3629066050052643},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32207542657852173},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2895045280456543},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2562541365623474},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.13203203678131104},{"id":"https://openalex.org/keywords/public-transport","display_name":"Public transport","score":0.126466304063797}],"concepts":[{"id":"https://openalex.org/C31829261","wikidata":"https://www.wikidata.org/wiki/Q1929885","display_name":"Transportation theory","level":2,"score":0.6272919178009033},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6238856315612793},{"id":"https://openalex.org/C2993719964","wikidata":"https://www.wikidata.org/wiki/Q178512","display_name":"Mass transportation","level":3,"score":0.5757802128791809},{"id":"https://openalex.org/C117312493","wikidata":"https://www.wikidata.org/wiki/Q2035437","display_name":"Multivariable calculus","level":2,"score":0.5638231635093689},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5521383285522461},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4917187988758087},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4748956263065338},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46467098593711853},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4569428861141205},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.4188345670700073},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3629066050052643},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32207542657852173},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2895045280456543},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2562541365623474},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.13203203678131104},{"id":"https://openalex.org/C539828613","wikidata":"https://www.wikidata.org/wiki/Q178512","display_name":"Public transport","level":2,"score":0.126466304063797},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C22212356","wikidata":"https://www.wikidata.org/wiki/Q775325","display_name":"Transport engineering","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2013.6760486","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6760486","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1585160083","https://openalex.org/W1700130116","https://openalex.org/W1985506636","https://openalex.org/W2041887789","https://openalex.org/W2055565049","https://openalex.org/W2071048859","https://openalex.org/W2110102169","https://openalex.org/W2126250321","https://openalex.org/W2150749374","https://openalex.org/W2172071111","https://openalex.org/W2473797792","https://openalex.org/W3104827932","https://openalex.org/W4313905125","https://openalex.org/W6635108014","https://openalex.org/W6685369011","https://openalex.org/W6720823052"],"related_works":["https://openalex.org/W4289541530","https://openalex.org/W2080883268","https://openalex.org/W2890443840","https://openalex.org/W73652264","https://openalex.org/W2041357275","https://openalex.org/W3048498233","https://openalex.org/W1259568217","https://openalex.org/W1841528438","https://openalex.org/W235235066","https://openalex.org/W1876480187"],"abstract_inverted_index":{"We":[0,46],"formulate":[1],"an":[2],"optimal":[3],"transport":[4],"problem":[5],"for":[6,64],"matrix-valued":[7,67],"density":[8],"functions.":[9],"This":[10],"is":[11,41,50,79],"pertinent":[12],"in":[13,28,57],"the":[14,54,58,62,65,72,76],"spectral":[15],"analysis":[16],"of":[17,39,61],"multivariable":[18],"time-series.":[19],"The":[20],"\u201cmass\u201d":[21],"represents":[22],"energy":[23],"at":[24],"various":[25],"frequencies":[26],"whereas,":[27],"addition":[29],"to":[30,52,71],"a":[31,37,84],"usual":[32],"transportation":[33,55,77],"cost":[34,38],"across":[35],"frequencies,":[36],"rotation":[40],"also":[42],"taken":[43],"into":[44],"account.":[45],"show":[47],"that":[48],"it":[49],"natural":[51],"seek":[53],"plan":[56,78],"tensor":[59],"product":[60],"spaces":[63],"two":[66],"marginals.":[68],"In":[69],"contrast":[70],"classical":[73],"Monge-Kantorovich":[74],"setting,":[75],"no":[80],"longer":[81],"supported":[82],"on":[83],"thin":[85],"zero-measure":[86],"set.":[87]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}