{"id":"https://openalex.org/W3194475752","doi":"https://doi.org/10.1007/s00454-023-00620-y","title":"The Cone of $$5\\times 5$$ Completely Positive Matrices","display_name":"The Cone of $$5\\times 5$$ Completely Positive Matrices","publication_year":2024,"publication_date":"2024-01-24","ids":{"openalex":"https://openalex.org/W3194475752","doi":"https://doi.org/10.1007/s00454-023-00620-y","mag":"3194475752"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-023-00620-y","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00454-023-00620-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00620-y.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00620-y.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038259635","display_name":"Max J. Pfeffer","orcid":"https://orcid.org/0000-0002-7739-4031"},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Max Pfeffer","raw_affiliation_strings":["Institute of Numerical and Applied Mathematics, University of G\u00f6ttingen, G\u00f6ttingen, Germany"],"raw_orcid":"https://orcid.org/0000-0002-7739-4031","affiliations":[{"raw_affiliation_string":"Institute of Numerical and Applied Mathematics, University of G\u00f6ttingen, G\u00f6ttingen, Germany","institution_ids":["https://openalex.org/I74656192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033018384","display_name":"Jos\u00e9 Alejandro Samper","orcid":null},"institutions":[{"id":"https://openalex.org/I162148367","display_name":"Pontificia Universidad Cat\u00f3lica de Chile","ror":"https://ror.org/04teye511","country_code":"CL","type":"education","lineage":["https://openalex.org/I162148367"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 Alejandro Samper","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Pontificia Universidad Cat\u00f3lica de Chile, Santiago, Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Pontificia Universidad Cat\u00f3lica de Chile, Santiago, Chile","institution_ids":["https://openalex.org/I162148367"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038259635"],"corresponding_institution_ids":["https://openalex.org/I74656192"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00394594,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"71","issue":"2","first_page":"442","last_page":"466"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/boundary","display_name":"Boundary (topology)","score":0.6841450929641724},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.6537121534347534},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5920063257217407},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.5407860279083252},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4944591522216797},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4724726378917694},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.42231523990631104},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3855544924736023},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37084999680519104},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3555331826210022},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21078422665596008}],"concepts":[{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6841450929641724},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6537121534347534},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5920063257217407},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.5407860279083252},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4944591522216797},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4724726378917694},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.42231523990631104},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3855544924736023},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37084999680519104},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3555331826210022},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21078422665596008},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00454-023-00620-y","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00454-023-00620-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00620-y.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:publications.goettingen-research-online.de:2/142130","is_oa":true,"landing_page_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/142130","pdf_url":null,"source":{"id":"https://openalex.org/S4306401634","display_name":"GoeScholar  The Publication Server of the Georg-August-Universit\u00e4t G\u00f6ttingen (Georg-August-Universit\u00e4t G\u00f6ttingen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210122495","host_organization_name":"Asklepios Klinik St. Georg","host_organization_lineage":["https://openalex.org/I4210122495"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00454-023-00620-y","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00454-023-00620-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00620-y.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1671185074","display_name":null,"funder_award_id":"448293816","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G1881010436","display_name":"COMBINATORICS OF CELL COMPLEXES AND POSETS MANIFOLDS POLYTOPES AND MATROIDS.","funder_award_id":"11221076","funder_id":"https://openalex.org/F4320331146","funder_display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321870","display_name":"Georg-August-Universit\u00e4t G\u00f6ttingen","ror":"https://ror.org/01y9bpm73"},{"id":"https://openalex.org/F4320327897","display_name":"Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften","ror":"https://ror.org/00ez2he07"},{"id":"https://openalex.org/F4320331146","display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3194475752.pdf"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W167979754","https://openalex.org/W598314002","https://openalex.org/W1562374723","https://openalex.org/W1729990846","https://openalex.org/W1976335834","https://openalex.org/W2033911254","https://openalex.org/W2040500267","https://openalex.org/W2070643312","https://openalex.org/W2079135578","https://openalex.org/W2083533556","https://openalex.org/W2086720359","https://openalex.org/W2111617833","https://openalex.org/W2167623372","https://openalex.org/W2203301234","https://openalex.org/W2793753754","https://openalex.org/W2806263336","https://openalex.org/W2937842032","https://openalex.org/W2995905072","https://openalex.org/W3029645440","https://openalex.org/W3044264873","https://openalex.org/W3103043995","https://openalex.org/W3104064817","https://openalex.org/W3127047037","https://openalex.org/W4301014524","https://openalex.org/W4302087481","https://openalex.org/W6629309582"],"related_works":["https://openalex.org/W2371409811","https://openalex.org/W2794559785","https://openalex.org/W2956921597","https://openalex.org/W2950281908","https://openalex.org/W1754499339","https://openalex.org/W2013873776","https://openalex.org/W2070412032","https://openalex.org/W2152992791","https://openalex.org/W2583828359","https://openalex.org/W2963117165"],"abstract_inverted_index":{"Abstract":[0],"We":[1,46],"study":[2],"the":[3,11,34,48,57,78,84,105,108],"cone":[4],"of":[5,51,107],"completely":[6],"positive":[7],"(cp)":[8],"matrices":[9,82],"for":[10,32,81],"first":[12],"interesting":[13],"case":[14],"$$n":[15],"=":[16],"5$$":[17],"<mml:math":[18],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[19],"<mml:mrow>":[20],"<mml:mi>n</mml:mi>":[21],"<mml:mo>=</mml:mo>":[22],"<mml:mn>5</mml:mn>":[23],"</mml:mrow>":[24],"</mml:math>":[25],".":[26],"This":[27],"is":[28,69,72],"a":[29],"semialgebraic":[30],"set":[31],"which":[33],"polynomial":[35],"equalities":[36],"and":[37,54,74,96],"inequlities":[38],"that":[39,71,103],"define":[40],"its":[41],"boundary":[42,53],"can":[43,93],"be":[44,94],"derived.":[45],"characterize":[47],"different":[49],"loci":[50],"this":[52],"we":[55],"examine":[56],"two":[58],"open":[59],"sets":[60],"with":[61],"cp-rank":[62],"5":[63],"or":[64],"6.":[65],"A":[66],"numerical":[67,99],"algorithm":[68],"presented":[70],"fast":[73],"able":[75],"to":[76],"compute":[77],"cp-factorization":[79,109],"even":[80],"in":[83],"boundary.":[85],"With":[86],"our":[87],"results,":[88],"many":[89],"new":[90],"example":[91],"cases":[92],"produced":[95],"several":[97],"insightful":[98],"experiments":[100],"are":[101],"performed":[102],"illustrate":[104],"difficulty":[106],"problem.":[110]},"counts_by_year":[],"updated_date":"2025-12-26T23:08:49.675405","created_date":"2025-10-10T00:00:00"}