{"id":"https://openalex.org/W4404568665","doi":"https://doi.org/10.1090/mcom/4047","title":"Conditional Euclidean distance optimization via relative tangency","display_name":"Conditional Euclidean distance optimization via relative tangency","publication_year":2024,"publication_date":"2024-11-20","ids":{"openalex":"https://openalex.org/W4404568665","doi":"https://doi.org/10.1090/mcom/4047"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/4047","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4047","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"preprint","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/A5007502309","display_name":"Sandra Di Rocco","orcid":"https://orcid.org/0000-0002-7186-1524"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sandra Di Rocco","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037504956","display_name":"Lukas Gustafsson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lukas Gustafsson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5034482984","display_name":"Luca Sodomaco","orcid":"https://orcid.org/0000-0002-0472-6357"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luca Sodomaco","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":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"95","issue":"357","first_page":"477","last_page":"524"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9549000263214111,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9549000263214111,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/euclidean-distance","display_name":"Euclidean distance","score":0.5471006631851196},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.507777988910675},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48613330721855164},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.4667292833328247},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36685219407081604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34811365604400635},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3340412378311157},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1400204598903656}],"concepts":[{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.5471006631851196},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.507777988910675},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48613330721855164},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.4667292833328247},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36685219407081604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34811365604400635},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3340412378311157},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1400204598903656}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/4047","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4047","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5200688502","display_name":null,"funder_award_id":"[NT:2022-03303]","funder_id":"https://openalex.org/F4320320936","funder_display_name":"Royal Swedish Academy of Sciences"}],"funders":[{"id":"https://openalex.org/F4320320936","display_name":"Royal Swedish Academy of Sciences","ror":"https://ror.org/00j62qv07"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W195458456","https://openalex.org/W207855810","https://openalex.org/W1496428155","https://openalex.org/W1534976569","https://openalex.org/W1977415556","https://openalex.org/W2001588532","https://openalex.org/W2015508922","https://openalex.org/W2032925102","https://openalex.org/W2040714878","https://openalex.org/W2063201514","https://openalex.org/W2102892751","https://openalex.org/W2124706092","https://openalex.org/W2125880378","https://openalex.org/W2154187696","https://openalex.org/W2962883824","https://openalex.org/W3013935617","https://openalex.org/W3041792862","https://openalex.org/W3042126099","https://openalex.org/W3094491077","https://openalex.org/W3109299000","https://openalex.org/W3139373549","https://openalex.org/W3200096258","https://openalex.org/W4200142664","https://openalex.org/W4231216667","https://openalex.org/W4244593923","https://openalex.org/W4248269519","https://openalex.org/W4404975392"],"related_works":["https://openalex.org/W2090152127","https://openalex.org/W1965169884","https://openalex.org/W3125580510","https://openalex.org/W2008939113","https://openalex.org/W2151810901","https://openalex.org/W2078582254","https://openalex.org/W2033213447","https://openalex.org/W14679004","https://openalex.org/W1566651525","https://openalex.org/W2977652649"],"abstract_inverted_index":{"We":[0,45,61,147],"introduce":[1,47],"a":[2,19,25,39,91],"theory":[3],"of":[4,18,32,41,50,53,65,67,84,108,121,131,140,151,164],"relative":[5,23,56,71,165],"tangency":[6],"for":[7],"projective":[8],"algebraic":[9],"varieties.":[10],"The":[11,103,128],"dual":[12],"variety":[13,20],"X":[14,21,22,36,37,54,55,95,96,122,123,141,142],"Z":[15,27,28,42,43,58,59,100,101,125,126,144,145],"\u2228":[16],"X_Z^\\vee":[17],"to":[24,35,57,72,94],"subvariety":[26],"is":[29,113,115],"the":[30,48,63,81,85,106,117,136,149],"set":[31],"hyperplanes":[33],"tangent":[34],"at":[38],"point":[40,93],".":[44,60,102,127,146],"also":[46],"concept":[49],"polar":[51],"classes":[52],"explore":[62],"duality":[64],"varieties":[66],"low":[68],"rank":[69],"matrices":[70],"special":[73],"linear":[74],"sections.":[75],"In":[76],"this":[77],"framework,":[78],"we":[79,156],"study":[80],"critical":[82,111,133],"points":[83,112,134],"Euclidean":[86],"Distance":[87],"(ED)":[88],"function":[89],"from":[90],"data":[92,119,153],",":[97],"lying":[98],"on":[99],"locus":[104,120],"where":[105],"number":[107,130],"such":[109,132],"conditional":[110,137],"positive":[114],"called":[116],"ED":[118,138,152],"given":[124,143],"generic":[129],"defines":[135],"degree":[139],"show":[148],"irreducibility":[150],"loci,":[154],"and":[155,160],"compute":[157],"their":[158],"dimensions":[159],"degrees":[161],"in":[162],"terms":[163],"characteristic":[166],"classes.":[167]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}