{"id":"https://openalex.org/W1483028487","doi":"https://doi.org/10.1007/978-3-642-40020-9_82","title":"A Riemannian Geometry in the q-Exponential Banach Manifold Induced by q-Divergences","display_name":"A Riemannian Geometry in the q-Exponential Banach Manifold Induced by q-Divergences","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1483028487","doi":"https://doi.org/10.1007/978-3-642-40020-9_82","mag":"1483028487"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-40020-9_82","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-40020-9_82","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10784/7411","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088631323","display_name":"Gabriel Ignacio Loaiza Ossa","orcid":"https://orcid.org/0000-0003-2413-1139"},"institutions":[{"id":"https://openalex.org/I862322245","display_name":"Universidad EAFIT","ror":"https://ror.org/03y3y9v44","country_code":"CO","type":"education","lineage":["https://openalex.org/I862322245"]}],"countries":["CO"],"is_corresponding":true,"raw_author_name":"G. Loaiza","raw_affiliation_strings":["Escuela de Ciencias y Humanidades, Departamento de Ciencias B\u00e1sicas, Universidad EAFIT, Medell\u00edn, Colombia","Escuela de Ciencias y Humanidades, Departamento de Ciencias b\u00e1sicas, Universidad Eafit,Medell\u00edn,Colombia"],"affiliations":[{"raw_affiliation_string":"Escuela de Ciencias y Humanidades, Departamento de Ciencias B\u00e1sicas, Universidad EAFIT, Medell\u00edn, Colombia","institution_ids":["https://openalex.org/I862322245"]},{"raw_affiliation_string":"Escuela de Ciencias y Humanidades, Departamento de Ciencias b\u00e1sicas, Universidad Eafit,Medell\u00edn,Colombia","institution_ids":["https://openalex.org/I862322245"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023511294","display_name":"H.R. Quiceno","orcid":null},"institutions":[{"id":"https://openalex.org/I862322245","display_name":"Universidad EAFIT","ror":"https://ror.org/03y3y9v44","country_code":"CO","type":"education","lineage":["https://openalex.org/I862322245"]}],"countries":["CO"],"is_corresponding":false,"raw_author_name":"H. R. Quiceno","raw_affiliation_strings":["Escuela de Ciencias y Humanidades, Departamento de Ciencias B\u00e1sicas, Universidad EAFIT, Medell\u00edn, Colombia","Escuela de Ciencias y Humanidades, Departamento de Ciencias b\u00e1sicas, Universidad Eafit,Medell\u00edn,Colombia"],"affiliations":[{"raw_affiliation_string":"Escuela de Ciencias y Humanidades, Departamento de Ciencias B\u00e1sicas, Universidad EAFIT, Medell\u00edn, Colombia","institution_ids":["https://openalex.org/I862322245"]},{"raw_affiliation_string":"Escuela de Ciencias y Humanidades, Departamento de Ciencias b\u00e1sicas, Universidad Eafit,Medell\u00edn,Colombia","institution_ids":["https://openalex.org/I862322245"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5088631323"],"corresponding_institution_ids":["https://openalex.org/I862322245"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.6886,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.75259875,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"737","last_page":"742"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9767000079154968,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T13500","display_name":"Probability and Statistical Research","score":0.9617999792098999,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/statistical-manifold","display_name":"Statistical manifold","score":0.7209365367889404},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.6901174783706665},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5819489359855652},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5785456299781799},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.5665773749351501},{"id":"https://openalex.org/keywords/riemannian-geometry","display_name":"Riemannian geometry","score":0.5347819328308105},{"id":"https://openalex.org/keywords/banach-manifold","display_name":"Banach manifold","score":0.5134159326553345},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.5120349526405334},{"id":"https://openalex.org/keywords/exponential-map","display_name":"Exponential map (Riemannian geometry)","score":0.4896593689918518},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.4801173210144043},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.43311068415641785},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.42674940824508667},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.42491576075553894},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.40134453773498535},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3951243758201599},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35581445693969727},{"id":"https://openalex.org/keywords/lp-space","display_name":"Lp space","score":0.29657188057899475},{"id":"https://openalex.org/keywords/scalar-curvature","display_name":"Scalar curvature","score":0.20582258701324463},{"id":"https://openalex.org/keywords/sectional-curvature","display_name":"Sectional curvature","score":0.20305347442626953}],"concepts":[{"id":"https://openalex.org/C169391604","wikidata":"https://www.wikidata.org/wiki/Q7604402","display_name":"Statistical manifold","level":5,"score":0.7209365367889404},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.6901174783706665},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5819489359855652},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5785456299781799},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.5665773749351501},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.5347819328308105},{"id":"https://openalex.org/C165593952","wikidata":"https://www.wikidata.org/wiki/Q3554819","display_name":"Banach manifold","level":4,"score":0.5134159326553345},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.5120349526405334},{"id":"https://openalex.org/C102224218","wikidata":"https://www.wikidata.org/wiki/Q25344559","display_name":"Exponential map (Riemannian geometry)","level":5,"score":0.4896593689918518},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.4801173210144043},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.43311068415641785},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.42674940824508667},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.42491576075553894},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.40134453773498535},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3951243758201599},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35581445693969727},{"id":"https://openalex.org/C172294467","wikidata":"https://www.wikidata.org/wiki/Q305936","display_name":"Lp space","level":3,"score":0.29657188057899475},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.20582258701324463},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.20305347442626953},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/978-3-642-40020-9_82","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-40020-9_82","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:repository.eafit.edu.co:10784/27665","is_oa":false,"landing_page_url":"https://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=1718","pdf_url":null,"source":{"id":"https://openalex.org/S4306400073","display_name":"El Repositorio Institucional de la Universidad EAFIT (Universidad EAFIT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I862322245","host_organization_name":"Universidad EAFIT","host_organization_lineage":["https://openalex.org/I862322245"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Lecture Notes In Computer Science","raw_type":"info:eu-repo/semantics/conferencePaper"},{"id":"pmh:oai:repository.eafit.edu.co:10784/5244","is_oa":false,"landing_page_url":"http://hdl.handle.net/10784/5244","pdf_url":null,"source":{"id":"https://openalex.org/S4306400073","display_name":"El Repositorio Institucional de la Universidad EAFIT (Universidad EAFIT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I862322245","host_organization_name":"Universidad EAFIT","host_organization_lineage":["https://openalex.org/I862322245"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:oai:repository.eafit.edu.co:10784/7411","is_oa":true,"landing_page_url":"http://hdl.handle.net/10784/7411","pdf_url":null,"source":{"id":"https://openalex.org/S4306400073","display_name":"El Repositorio Institucional de la Universidad EAFIT (Universidad EAFIT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I862322245","host_organization_name":"Universidad EAFIT","host_organization_lineage":["https://openalex.org/I862322245"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferencePaper"}],"best_oa_location":{"id":"pmh:oai:repository.eafit.edu.co:10784/7411","is_oa":true,"landing_page_url":"http://hdl.handle.net/10784/7411","pdf_url":null,"source":{"id":"https://openalex.org/S4306400073","display_name":"El Repositorio Institucional de la Universidad EAFIT (Universidad EAFIT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I862322245","host_organization_name":"Universidad EAFIT","host_organization_lineage":["https://openalex.org/I862322245"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferencePaper"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W205838020","https://openalex.org/W308817292","https://openalex.org/W1520168181","https://openalex.org/W1573082642","https://openalex.org/W1965555277","https://openalex.org/W1983874169","https://openalex.org/W2000507951","https://openalex.org/W2006681603","https://openalex.org/W2020247984","https://openalex.org/W2035632748","https://openalex.org/W2036422857","https://openalex.org/W2059298155","https://openalex.org/W2060649482","https://openalex.org/W2066137238","https://openalex.org/W2076986444","https://openalex.org/W2130613344","https://openalex.org/W2143436207","https://openalex.org/W2903985818","https://openalex.org/W3098977349"],"related_works":["https://openalex.org/W4291625303","https://openalex.org/W2737579912","https://openalex.org/W2164995684","https://openalex.org/W3184943628","https://openalex.org/W2999284236","https://openalex.org/W3183653752","https://openalex.org/W2905037418","https://openalex.org/W2064273189","https://openalex.org/W4385435140","https://openalex.org/W2961080399"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
