Applications of Computational Algebraic Topology

In this note a course given at the "UN Encuentro de Matemáticas 2016" held in Bogotá (Colombia) is described. The course was divided into four parts, devoted, respectively, to basic denitions in Algebraic Topology, to the algorithmic aspects of Topology, to the Kenzo computer system and, f...

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Autores:
Rubio, Julio
Tipo de recurso:
Article of journal
Fecha de publicación:
2016
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/61877
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/61877
http://bdigital.unal.edu.co/60689/
Palabra clave:
51 Matemáticas / Mathematics
Topology
Algorithmic
Programs
Applications
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Rubio, Julio1201a12b-3b4b-4738-bcf3-302ce95823303002019-07-02T20:46:49Z2019-07-02T20:46:49Z2016-07-01ISSN: 2357-6529https://repositorio.unal.edu.co/handle/unal/61877http://bdigital.unal.edu.co/60689/In this note a course given at the "UN Encuentro de Matemáticas 2016" held in Bogotá (Colombia) is described. The course was divided into four parts, devoted, respectively, to basic denitions in Algebraic Topology, to the algorithmic aspects of Topology, to the Kenzo computer system and, finally, to the applications of Computational Algebraic Topology. In the first talk the basic concepts of Algebraic Topology were presented, stressing the importance of replacing the topological space notion by other combinatorial analogues, easing the introduction of homological techniques. In the second talk, we reviewed several algorithms devised to compute homological objects. In the third talk, we described the Kenzo program, using its new version accessible via Internet. In the last talk, persistent homology was introduced and an actual application of topology to image processing was presented, in the frame of a project related to the fight against neurodegenerative diseases, as Alzheimer.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticashttps://revistas.unal.edu.co/index.php/bolma/article/view/62221Universidad Nacional de Colombia Revistas electrónicas UN Boletín de MatemáticasBoletín de MatemáticasRubio, Julio (2016) Applications of Computational Algebraic Topology. Boletín de Matemáticas, 23 (2). pp. 137-142. ISSN 2357-652951 Matemáticas / MathematicsTopologyAlgorithmicProgramsApplicationsApplications of Computational Algebraic TopologyArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL62221-358832-1-PB.pdfapplication/pdf265361https://repositorio.unal.edu.co/bitstream/unal/61877/1/62221-358832-1-PB.pdf42a69b20378e816fc3e9316a22c8d867MD51THUMBNAIL62221-358832-1-PB.pdf.jpg62221-358832-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg5343https://repositorio.unal.edu.co/bitstream/unal/61877/2/62221-358832-1-PB.pdf.jpge714df162382f5d8291728b5e7296d48MD52unal/61877oai:repositorio.unal.edu.co:unal/618772024-04-20 23:26:15.156Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Applications of Computational Algebraic Topology
title Applications of Computational Algebraic Topology
spellingShingle Applications of Computational Algebraic Topology
51 Matemáticas / Mathematics
Topology
Algorithmic
Programs
Applications
title_short Applications of Computational Algebraic Topology
title_full Applications of Computational Algebraic Topology
title_fullStr Applications of Computational Algebraic Topology
title_full_unstemmed Applications of Computational Algebraic Topology
title_sort Applications of Computational Algebraic Topology
dc.creator.fl_str_mv Rubio, Julio
dc.contributor.author.spa.fl_str_mv Rubio, Julio
dc.subject.ddc.spa.fl_str_mv 51 Matemáticas / Mathematics
topic 51 Matemáticas / Mathematics
Topology
Algorithmic
Programs
Applications
dc.subject.proposal.spa.fl_str_mv Topology
Algorithmic
Programs
Applications
description In this note a course given at the "UN Encuentro de Matemáticas 2016" held in Bogotá (Colombia) is described. The course was divided into four parts, devoted, respectively, to basic denitions in Algebraic Topology, to the algorithmic aspects of Topology, to the Kenzo computer system and, finally, to the applications of Computational Algebraic Topology. In the first talk the basic concepts of Algebraic Topology were presented, stressing the importance of replacing the topological space notion by other combinatorial analogues, easing the introduction of homological techniques. In the second talk, we reviewed several algorithms devised to compute homological objects. In the third talk, we described the Kenzo program, using its new version accessible via Internet. In the last talk, persistent homology was introduced and an actual application of topology to image processing was presented, in the frame of a project related to the fight against neurodegenerative diseases, as Alzheimer.
publishDate 2016
dc.date.issued.spa.fl_str_mv 2016-07-01
dc.date.accessioned.spa.fl_str_mv 2019-07-02T20:46:49Z
dc.date.available.spa.fl_str_mv 2019-07-02T20:46:49Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.issn.spa.fl_str_mv ISSN: 2357-6529
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dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/60689/
identifier_str_mv ISSN: 2357-6529
url https://repositorio.unal.edu.co/handle/unal/61877
http://bdigital.unal.edu.co/60689/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv https://revistas.unal.edu.co/index.php/bolma/article/view/62221
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Boletín de Matemáticas
Boletín de Matemáticas
dc.relation.references.spa.fl_str_mv Rubio, Julio (2016) Applications of Computational Algebraic Topology. Boletín de Matemáticas, 23 (2). pp. 137-142. ISSN 2357-6529
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
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dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
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rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas
institution Universidad Nacional de Colombia
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