{"id":"https://openalex.org/W4391447373","doi":"https://doi.org/10.1137/22m1526113","title":"Gaussian Likelihood Geometry of Projective Varieties","display_name":"Gaussian Likelihood Geometry of Projective Varieties","publication_year":2024,"publication_date":"2024-02-01","ids":{"openalex":"https://openalex.org/W4391447373","doi":"https://doi.org/10.1137/22m1526113"},"language":"en","primary_location":{"id":"doi:10.1137/22m1526113","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1526113","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"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 Applied Algebra and Geometry","raw_type":"journal-article"},"type":"article","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":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Sandra Di Rocco","raw_affiliation_strings":["Department of Mathematics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037504956","display_name":"Lukas Gustafsson","orcid":null},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Lukas Gustafsson","raw_affiliation_strings":["Department of Mathematics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038600042","display_name":"Luca Schaffler","orcid":"https://orcid.org/0000-0002-1496-7795"},"institutions":[{"id":"https://openalex.org/I119003972","display_name":"Roma Tre University","ror":"https://ror.org/05vf0dg29","country_code":"IT","type":"education","lineage":["https://openalex.org/I119003972"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Luca Schaffler","raw_affiliation_strings":["Dipartimento di Matematica e Fisica, Universit\u00e0 degli Studi Roma Tre, 00146, Rome, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Fisica, Universit\u00e0 degli Studi Roma Tre, 00146, Rome, Italy","institution_ids":["https://openalex.org/I119003972"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5038600042"],"corresponding_institution_ids":["https://openalex.org/I119003972"],"apc_list":null,"apc_paid":null,"fwci":2.0675,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.81979992,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"8","issue":"1","first_page":"89","last_page":"113"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9912999868392944,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9912999868392944,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9884999990463257,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9761000275611877,"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":0.5763403177261353},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5582166910171509},{"id":"https://openalex.org/keywords/projective-test","display_name":"Projective test","score":0.505460262298584},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.4635903239250183},{"id":"https://openalex.org/keywords/projective-geometry","display_name":"Projective geometry","score":0.4494568407535553},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3601199984550476},{"id":"https://openalex.org/keywords/algebraic-geometry","display_name":"Algebraic geometry","score":0.3368370234966278},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3309807777404785},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32239264249801636},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2213132381439209},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2075670063495636}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5763403177261353},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5582166910171509},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.505460262298584},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4635903239250183},{"id":"https://openalex.org/C185362025","wikidata":"https://www.wikidata.org/wiki/Q177409","display_name":"Projective geometry","level":3,"score":0.4494568407535553},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3601199984550476},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.3368370234966278},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3309807777404785},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32239264249801636},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2213132381439209},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2075670063495636},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/22m1526113","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1526113","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"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 Applied Algebra and Geometry","raw_type":"journal-article"},{"id":"pmh:oai:iris.uniroma3.it:11590/467349","is_oa":false,"landing_page_url":"https://hdl.handle.net/11590/467349","pdf_url":null,"source":{"id":"https://openalex.org/S4377196120","display_name":"Iris (Roma Tre University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119003972","host_organization_name":"Roma Tre University","host_organization_lineage":["https://openalex.org/I119003972"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G3766892416","display_name":null,"funder_award_id":"NT:2018-03688","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"}],"funders":[{"id":"https://openalex.org/F4320322509","display_name":"Kungliga Tekniska H\u00f6gskolan","ror":"https://ror.org/026vcq606"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W644598453","https://openalex.org/W1541268885","https://openalex.org/W1977415556","https://openalex.org/W1992680657","https://openalex.org/W1999278737","https://openalex.org/W2000871144","https://openalex.org/W2001588532","https://openalex.org/W2015508922","https://openalex.org/W2031657232","https://openalex.org/W2040714878","https://openalex.org/W2108917139","https://openalex.org/W2148954977","https://openalex.org/W2983462479","https://openalex.org/W2999824720","https://openalex.org/W3038124051","https://openalex.org/W3094491077","https://openalex.org/W3098373840","https://openalex.org/W3102636382","https://openalex.org/W3105569470","https://openalex.org/W3131349225","https://openalex.org/W4248269519"],"related_works":["https://openalex.org/W1987739464","https://openalex.org/W2887166225","https://openalex.org/W1986892955","https://openalex.org/W1971486231","https://openalex.org/W2061153603","https://openalex.org/W3102050581","https://openalex.org/W4211222346","https://openalex.org/W2077027009","https://openalex.org/W2073400439","https://openalex.org/W17630967"],"abstract_inverted_index":{"We":[0,26],"explore":[1],"the":[2,19,33],"maximum":[3,23],"likelihood":[4,24],"degree":[5],"of":[6,21,35,38,49],"a":[7,12,39],"homogeneous":[8],"polynomial":[9],"$F$":[10],"on":[11,42],"projective":[13],"variety":[14],"$X$,":[15,43],"$\\\\mathrm{MLD}_F(X)$,":[16],"which":[17],"generalizes":[18],"concept":[20],"Gaussian":[22],"degree.":[25],"show":[27],"that":[28],"$\\\\mathrm{MLD}_F(X)$":[29],"is":[30],"equal":[31],"to":[32],"count":[34],"critical":[36],"points":[37],"rational":[40],"function":[41],"and":[44,57],"give":[45],"different":[46],"geometric":[47],"characterizations":[48],"it":[50],"via":[51],"topological":[52],"Euler":[53],"characteristic,":[54],"dual":[55],"varieties,":[56],"Chern":[58],"classes.":[59]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}