{"id":"https://openalex.org/W2888536053","doi":"https://doi.org/10.1007/s10957-019-01508-9","title":"Whitney\u2019s Theorem, Triangular Sets, and Probabilistic Descent on Manifolds","display_name":"Whitney\u2019s Theorem, Triangular Sets, and Probabilistic Descent on Manifolds","publication_year":2019,"publication_date":"2019-03-25","ids":{"openalex":"https://openalex.org/W2888536053","doi":"https://doi.org/10.1007/s10957-019-01508-9","mag":"2888536053"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-019-01508-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-019-01508-9","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1808.08548","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004347998","display_name":"David W. Dreisigmeyer","orcid":"https://orcid.org/0000-0002-8441-0669"},"institutions":[{"id":"https://openalex.org/I1333512998","display_name":"United States Census Bureau","ror":"https://ror.org/01qn7cs15","country_code":"US","type":"funder","lineage":["https://openalex.org/I1333512998","https://openalex.org/I1343035065"]},{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David W. Dreisigmeyer","raw_affiliation_strings":["Center for Economic Studies, United States Census Bureau, Suitland, MD, USA","Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO, USA","Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, USA","Center for Economic Studies, United States Census Bureau, Suitland, USA"],"affiliations":[{"raw_affiliation_string":"Center for Economic Studies, United States Census Bureau, Suitland, MD, USA","institution_ids":["https://openalex.org/I1333512998"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO, USA","institution_ids":["https://openalex.org/I92446798"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, USA","institution_ids":["https://openalex.org/I92446798"]},{"raw_affiliation_string":"Center for Economic Studies, United States Census Bureau, Suitland, USA","institution_ids":["https://openalex.org/I1333512998"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5004347998"],"corresponding_institution_ids":["https://openalex.org/I1333512998","https://openalex.org/I92446798"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00329509,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"182","issue":"3","first_page":"935","last_page":"946"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9621000289916992,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11106","display_name":"Data Management and Algorithms","score":0.9621000289916992,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/embedding","display_name":"Embedding","score":0.774379312992096},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.7561429142951965},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7071878910064697},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.6965538859367371},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.6324595212936401},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.62171471118927},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4912955164909363},{"id":"https://openalex.org/keywords/numerical-continuation","display_name":"Numerical continuation","score":0.48434364795684814},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.48417311906814575},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4686281979084015},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13421261310577393},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0556124746799469}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.774379312992096},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.7561429142951965},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7071878910064697},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.6965538859367371},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.6324595212936401},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.62171471118927},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4912955164909363},{"id":"https://openalex.org/C2775978667","wikidata":"https://www.wikidata.org/wiki/Q7069654","display_name":"Numerical continuation","level":4,"score":0.48434364795684814},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48417311906814575},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4686281979084015},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13421261310577393},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0556124746799469},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10957-019-01508-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-019-01508-9","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1808.08548","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.08548","pdf_url":"https://arxiv.org/pdf/1808.08548","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2888536053","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1808.08548.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:RePEc:spr:joptap:v:182:y:2019:i:3:d:10.1007_s10957-019-01508-9","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-019-01508-9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.48550/arxiv.1808.08548","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1808.08548","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1808.08548","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.08548","pdf_url":"https://arxiv.org/pdf/1808.08548","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1975442862","https://openalex.org/W1998855065","https://openalex.org/W2004067662","https://openalex.org/W2004605684","https://openalex.org/W2021153515","https://openalex.org/W2046714497","https://openalex.org/W2053029682","https://openalex.org/W2067965564","https://openalex.org/W2072012018","https://openalex.org/W2098733422","https://openalex.org/W2120467997","https://openalex.org/W2150928761"],"related_works":["https://openalex.org/W2964229907","https://openalex.org/W1987478056","https://openalex.org/W3105578323","https://openalex.org/W1643101618","https://openalex.org/W655466607","https://openalex.org/W858291407","https://openalex.org/W2954760472","https://openalex.org/W2146632936","https://openalex.org/W3117984933","https://openalex.org/W3090462870","https://openalex.org/W2952174167","https://openalex.org/W2249955721","https://openalex.org/W3188114529","https://openalex.org/W2561040189","https://openalex.org/W2769857238","https://openalex.org/W2007283669","https://openalex.org/W2068898441","https://openalex.org/W2952793515","https://openalex.org/W2944561452","https://openalex.org/W2099937932"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}