{"id":"https://openalex.org/W179043391","doi":"https://doi.org/10.1007/978-3-642-39053-1_34","title":"Closed Choice for Finite and for Convex Sets","display_name":"Closed Choice for Finite and for Convex Sets","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W179043391","doi":"https://doi.org/10.1007/978-3-642-39053-1_34","mag":"179043391"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-39053-1_34","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-39053-1_34","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5104581658","display_name":"St\u00e9phane Le Roux","orcid":null},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"St\u00e9phane Le Roux","raw_affiliation_strings":["Department of Mathematics, Technische Universit\u00e4t Darmstadt, Germany","Technische Universit\u00e4t Darmstadt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technische Universit\u00e4t Darmstadt, Germany","institution_ids":["https://openalex.org/I31512782"]},{"raw_affiliation_string":"Technische Universit\u00e4t Darmstadt","institution_ids":["https://openalex.org/I31512782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091475454","display_name":"Arno Pauly","orcid":"https://orcid.org/0000-0002-0173-3295"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Arno Pauly","raw_affiliation_strings":["Clare College, University of Cambridge, United Kingdom","University of Cambridge,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Clare College, University of Cambridge, United Kingdom","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"University of Cambridge,","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":3.268,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.91804897,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"294","last_page":"305"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI 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/T12002","display_name":"Computability, Logic, AI 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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11567","display_name":"semigroups and automata theory","score":0.9872999787330627,"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/cardinality","display_name":"Cardinality (data modeling)","score":0.6668949723243713},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6258535385131836},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6201571226119995},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.6117127537727356},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6065000295639038},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.5763708353042603},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.5253647565841675},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.5025887489318848},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.4998927116394043},{"id":"https://openalex.org/keywords/proper-convex-function","display_name":"Proper convex function","score":0.49591264128685},{"id":"https://openalex.org/keywords/absolutely-convex-set","display_name":"Absolutely convex set","score":0.48322758078575134},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4768594205379486},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4615395665168762},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.46074309945106506},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.45769578218460083},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3874220848083496},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.25709694623947144},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2217245101928711},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10534676909446716},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07005849480628967}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6668949723243713},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6258535385131836},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6201571226119995},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.6117127537727356},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6065000295639038},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.5763708353042603},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.5253647565841675},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.5025887489318848},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4998927116394043},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.49591264128685},{"id":"https://openalex.org/C6018138","wikidata":"https://www.wikidata.org/wiki/Q332715","display_name":"Absolutely convex set","level":5,"score":0.48322758078575134},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4768594205379486},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4615395665168762},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.46074309945106506},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.45769578218460083},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3874220848083496},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.25709694623947144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2217245101928711},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10534676909446716},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07005849480628967},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-642-39053-1_34","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-39053-1_34","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:cronfa.swan.ac.uk:cronfa37382","is_oa":false,"landing_page_url":"https://cronfa.swan.ac.uk/Record/cronfa37382","pdf_url":null,"source":{"id":"https://openalex.org/S4306401612","display_name":"Cronfa (Swansea University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39586589","host_organization_name":"Swansea University","host_organization_lineage":["https://openalex.org/I39586589"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W32678173","https://openalex.org/W63299231","https://openalex.org/W594315820","https://openalex.org/W1517066694","https://openalex.org/W1559786600","https://openalex.org/W1582285885","https://openalex.org/W1585444766","https://openalex.org/W1621754453","https://openalex.org/W1987187730","https://openalex.org/W1991124928","https://openalex.org/W2005926498","https://openalex.org/W2018837422","https://openalex.org/W2044009111","https://openalex.org/W2046783159","https://openalex.org/W2137505175","https://openalex.org/W2137629068","https://openalex.org/W2154952077","https://openalex.org/W2182274314","https://openalex.org/W2611511037","https://openalex.org/W2806893125","https://openalex.org/W2885774045","https://openalex.org/W2896051258","https://openalex.org/W2963097465","https://openalex.org/W3099840387","https://openalex.org/W3103464449","https://openalex.org/W3105905549","https://openalex.org/W3106040729","https://openalex.org/W3123032599","https://openalex.org/W4243563333","https://openalex.org/W4245716479","https://openalex.org/W4292003697"],"related_works":["https://openalex.org/W2026600343","https://openalex.org/W2391247224","https://openalex.org/W4382519084","https://openalex.org/W2478309485","https://openalex.org/W3092518081","https://openalex.org/W2002037426","https://openalex.org/W1978014154","https://openalex.org/W4361807553","https://openalex.org/W2040676043","https://openalex.org/W2356261519"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2026-06-13T07:54:00.901334","created_date":"2025-10-10T00:00:00"}