{"id":"https://openalex.org/W4392650278","doi":"https://doi.org/10.1137/23m1554898","title":"Partial Degeneration of Tensors","display_name":"Partial Degeneration of Tensors","publication_year":2024,"publication_date":"2024-03-11","ids":{"openalex":"https://openalex.org/W4392650278","doi":"https://doi.org/10.1137/23m1554898"},"language":"en","primary_location":{"id":"doi:10.1137/23m1554898","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1554898","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-04957955v1/file/CGLS_PartialDeg.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006329724","display_name":"Matthias Christandl","orcid":"https://orcid.org/0000-0003-2281-3355"},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Matthias Christandl","raw_affiliation_strings":["QMATH, Department of Mathematical Sciences, University of Copenhagen, 2100 Copenhagen, Denmark"],"raw_orcid":"https://orcid.org/0000-0003-2281-3355","affiliations":[{"raw_affiliation_string":"QMATH, Department of Mathematical Sciences, University of Copenhagen, 2100 Copenhagen, Denmark","institution_ids":["https://openalex.org/I124055696"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036385723","display_name":"Fulvio Gesmundo","orcid":"https://orcid.org/0000-0001-6402-021X"},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I4210098964","display_name":"Toulouse Mathematics Institute","ror":null,"country_code":"FR","type":null,"lineage":["https://openalex.org/I4210098964"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fulvio Gesmundo","raw_affiliation_strings":["Institut de Math\u00e9matiques de Toulouse, Universit\u00e9 Paul Sabatier, Toulouse, France"],"raw_orcid":"https://orcid.org/0000-0001-6402-021X","affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Toulouse, Universit\u00e9 Paul Sabatier, Toulouse, France","institution_ids":["https://openalex.org/I134560555","https://openalex.org/I4210098964"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080005389","display_name":"Vladimir Lysikov","orcid":"https://orcid.org/0000-0002-7816-6524"},"institutions":[{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Vladimir Lysikov","raw_affiliation_strings":["Faculty of Computer Science, Ruhr University Bochum, 44801, Bochum, Germany"],"raw_orcid":"https://orcid.org/0000-0002-7816-6524","affiliations":[{"raw_affiliation_string":"Faculty of Computer Science, Ruhr University Bochum, 44801, Bochum, Germany","institution_ids":["https://openalex.org/I904495901"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032649728","display_name":"Vincent Steffan","orcid":"https://orcid.org/0000-0003-4913-6833"},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Vincent Steffan","raw_affiliation_strings":["QMATH, Department of Mathematical Sciences, University of Copenhagen, 2100 Copenhagen, Denmark"],"raw_orcid":"https://orcid.org/0000-0003-4913-6833","affiliations":[{"raw_affiliation_string":"QMATH, Department of Mathematical Sciences, University of Copenhagen, 2100 Copenhagen, Denmark","institution_ids":["https://openalex.org/I124055696"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02373887,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"45","issue":"1","first_page":"771","last_page":"800"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational 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/T12303","display_name":"Tensor decomposition and applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational 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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9970999956130981,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9966999888420105,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7671960592269897},{"id":"https://openalex.org/keywords/degeneration","display_name":"Degeneration (medical)","score":0.5369188189506531},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.46368589997291565},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39959609508514404},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3398926854133606},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3366698622703552},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3246181607246399},{"id":"https://openalex.org/keywords/orthodontics","display_name":"Orthodontics","score":0.14025592803955078},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.09825661778450012}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7671960592269897},{"id":"https://openalex.org/C2779354088","wikidata":"https://www.wikidata.org/wiki/Q15467261","display_name":"Degeneration (medical)","level":2,"score":0.5369188189506531},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.46368589997291565},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39959609508514404},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3398926854133606},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3366698622703552},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3246181607246399},{"id":"https://openalex.org/C29694066","wikidata":"https://www.wikidata.org/wiki/Q118301","display_name":"Orthodontics","level":1,"score":0.14025592803955078},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.09825661778450012},{"id":"https://openalex.org/C142724271","wikidata":"https://www.wikidata.org/wiki/Q7208","display_name":"Pathology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/23m1554898","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1554898","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04957955v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04957955","pdf_url":"https://hal.science/hal-04957955v1/file/CGLS_PartialDeg.pdf","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":"SIAM Journal on Matrix Analysis and Applications, 2024, 45 (1), pp.771-800. ⟨10.1137/23M1554898⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/2d030e7e-223c-4f67-9101-0f1858f5b547","is_oa":true,"landing_page_url":"https://researchprofiles.ku.dk/da/publications/2d030e7e-223c-4f67-9101-0f1858f5b547","pdf_url":"https://curis.ku.dk/ws/files/385690114/PARTIAL_DEGENERATION_OF_TENSORS.pdf","source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Christandl , M , Gesmundo , F , Lysikov , V & Steffan , V 2024 , ' Partial Degeneration of Tensors ' , SIAM Journal on Matrix Analysis and Applications , vol. 45 , no. 1 , pp. 771-800 . https://doi.org/10.1137/23M1554898","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-04957955v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04957955","pdf_url":"https://hal.science/hal-04957955v1/file/CGLS_PartialDeg.pdf","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":"SIAM Journal on Matrix Analysis and Applications, 2024, 45 (1), pp.771-800. ⟨10.1137/23M1554898⟩","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3031957684","display_name":null,"funder_award_id":"81876","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G4105022999","display_name":null,"funder_award_id":"NNF20OC0059939","funder_id":"https://openalex.org/F4320325957","funder_display_name":"Novo Nordisk Fonden"},{"id":"https://openalex.org/G7238040094","display_name":null,"funder_award_id":"663281","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"},{"id":"https://openalex.org/G7352392636","display_name":null,"funder_award_id":"10059","funder_id":"https://openalex.org/F4320310490","funder_display_name":"Villum Fonden"},{"id":"https://openalex.org/G7633023549","display_name":null,"funder_award_id":"NNF20OC005993","funder_id":"https://openalex.org/F4320322436","funder_display_name":"Novo Nordisk"}],"funders":[{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320310490","display_name":"Villum Fonden","ror":"https://ror.org/007ww2d15"},{"id":"https://openalex.org/F4320322436","display_name":"Novo Nordisk","ror":"https://ror.org/0435rc536"},{"id":"https://openalex.org/F4320323873","display_name":"Uniwersytet Warszawski","ror":"https://ror.org/039bjqg32"},{"id":"https://openalex.org/F4320325957","display_name":"Novo Nordisk Fonden","ror":"https://ror.org/04txyc737"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4392650278.pdf","grobid_xml":"https://content.openalex.org/works/W4392650278.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W113644180","https://openalex.org/W1482975181","https://openalex.org/W1561337879","https://openalex.org/W1965965675","https://openalex.org/W1974928788","https://openalex.org/W1985031765","https://openalex.org/W1996440503","https://openalex.org/W2002048434","https://openalex.org/W2029100014","https://openalex.org/W2489016459","https://openalex.org/W2591902642","https://openalex.org/W2619660439","https://openalex.org/W2763778230","https://openalex.org/W2890496316","https://openalex.org/W2937406174","https://openalex.org/W2941570035","https://openalex.org/W2963631653","https://openalex.org/W3038950000","https://openalex.org/W3100298903","https://openalex.org/W3120126550","https://openalex.org/W4200136360","https://openalex.org/W4200400528","https://openalex.org/W4244593923","https://openalex.org/W4280633903"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2397018870","https://openalex.org/W2433928466","https://openalex.org/W2443747300","https://openalex.org/W2427664272","https://openalex.org/W2589587510","https://openalex.org/W2151758487","https://openalex.org/W2980963558","https://openalex.org/W2326549855","https://openalex.org/W4408168216"],"abstract_inverted_index":{"Abstract.":[0],"Tensors":[1],"are":[2],"often":[3],"studied":[4],"by":[5,20,85,104,123],"introducing":[6],"preorders":[7],"such":[8],"as":[9,48],"restriction":[10],"and":[11,42,59,90,101,126,183],"degeneration.":[12],"The":[13,149],"former":[14],"describes":[15,30],"transformations":[16,31],"of":[17,66,70,111,119,140,146,151,162,198],"the":[18,28,33,43,71,78,109,117,130,138,159,181,184,196],"tensors":[19,100],"local":[21,34,72],"linear":[22,35,73],"maps":[23,36,74],"on":[24,97,158,180,190],"its":[25],"tensor":[26,45,91,113,147],"factors;":[27],"latter":[29],"where":[32,68,187],"may":[37],"vary":[38,80],"along":[39,51,81],"a":[40,49,63,82,106,143,163],"curve,":[41],"resulting":[44],"is":[46,75],"expressed":[47],"limit":[50],"this":[52,55,120,134],"curve.":[53,83],"In":[54,173],"work,":[56],"we":[57,93,136,175],"introduce":[58],"study":[60,137],"partial":[61,152,200],"degeneration,":[62],"special":[64],"version":[65],"degeneration":[67],"one":[69,167],"constant":[76],"while":[77],"others":[79],"Motivated":[84],"algebraic":[86],"complexity,":[87],"quantum":[88],"entanglement,":[89],"networks,":[92],"present":[94,176],"constructions":[95],"based":[96,179],"matrix":[98],"multiplication":[99],"find":[102],"examples":[103],"making":[105],"connection":[107],"to":[108,168,195],"theory":[110],"prehomogeneous":[112],"spaces.":[114],"We":[115],"highlight":[116],"subtleties":[118],"new":[121],"notion":[122,139],"showing":[124],"obstruction":[125],"classification":[127],"results":[128],"for":[129],"unit":[131],"tensor.":[132],"To":[133],"end,":[135],"aided":[141,160,191],"rank,":[142],"natural":[144],"generalization":[145],"rank.":[148],"existence":[150,197],"degenerations":[153,170],"gives":[154],"strong":[155],"upper":[156],"bounds":[157,189],"rank":[161,192],"tensor,":[164],"which":[165],"allows":[166],"turn":[169],"into":[171],"restrictions.":[172],"particular,":[174],"several":[177],"examples,":[178],"W-tensor":[182],"Coppersmith\u2013Winograd":[185],"tensors,":[186],"lower":[188],"provide":[193],"obstructions":[194],"certain":[199],"degenerations.":[201]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}