Complexity-entropy causality plane as a complexity measure for two-dimensional patterns

Autores
Ribeiro, Haroldo V.; Zunino, Luciano José; Lenzi, Ervin K.; Santoro, Perseu A.; Mendes, Renio S.
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index. We build up a numerical procedure that can be easily implemented to evaluate the complexity of two or higher-dimensional patterns. We work out this method in different scenarios where numerical experiments and empirical data were taken into account. Specifically, we have applied the method to i) fractal landscapes generated numerically where we compare our measures with the Hurst exponent; ii) liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; iii) 12 characteristic textures of liquid crystals wher the different values show that the method can distinguish different phases; iv) and Ising surfaces where our method identified the critical temperature and also proved to be stable.
Fil: Ribeiro, Haroldo V.. Universidade Estadual de Maringá; Brasil
Fil: Zunino, Luciano José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Investigaciones Ópticas. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Investigaciones Ópticas. Universidad Nacional de La Plata. Centro de Investigaciones Ópticas; Argentina
Fil: Lenzi, Ervin K.. Universidade Estadual de Maringá; Brasil
Fil: Santoro, Perseu A.. Universidade Estadual de Maringá; Brasil
Fil: Mendes, Renio S.. Universidade Estadual de Maringá; Brasil
Materia
COMPLEXITY
COMPLEXITY-ENTROPY CAUSALITY PLANE
TWO-DIMENSIONAL PATTERNS
HIGHER-DIMENSIONAL PATTERNS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/75348
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Complexity-entropy causality plane as a complexity measure for two-dimensional patternsRibeiro, Haroldo V.Zunino, Luciano JoséLenzi, Ervin K.Santoro, Perseu A.Mendes, Renio S.COMPLEXITYCOMPLEXITY-ENTROPY CAUSALITY PLANETWO-DIMENSIONAL PATTERNSHIGHER-DIMENSIONAL PATTERNShttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index. We build up a numerical procedure that can be easily implemented to evaluate the complexity of two or higher-dimensional patterns. We work out this method in different scenarios where numerical experiments and empirical data were taken into account. Specifically, we have applied the method to i) fractal landscapes generated numerically where we compare our measures with the Hurst exponent; ii) liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; iii) 12 characteristic textures of liquid crystals wher the different values show that the method can distinguish different phases; iv) and Ising surfaces where our method identified the critical temperature and also proved to be stable.Fil: Ribeiro, Haroldo V.. Universidade Estadual de Maringá; BrasilFil: Zunino, Luciano José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Investigaciones Ópticas. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Investigaciones Ópticas. Universidad Nacional de La Plata. Centro de Investigaciones Ópticas; ArgentinaFil: Lenzi, Ervin K.. Universidade Estadual de Maringá; BrasilFil: Santoro, Perseu A.. Universidade Estadual de Maringá; BrasilFil: Mendes, Renio S.. Universidade Estadual de Maringá; BrasilPublic Library of Science2012-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/75348Ribeiro, Haroldo V.; Zunino, Luciano José; Lenzi, Ervin K.; Santoro, Perseu A.; Mendes, Renio S.; Complexity-entropy causality plane as a complexity measure for two-dimensional patterns; Public Library of Science; Plos One; 7; 8; 8-2012; 1-9; e406891932-6203CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1371/journal.pone.0040689info:eu-repo/semantics/altIdentifier/url/https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0040689info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:51:10Zoai:ri.conicet.gov.ar:11336/75348instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:51:10.889CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Complexity-entropy causality plane as a complexity measure for two-dimensional patterns
title Complexity-entropy causality plane as a complexity measure for two-dimensional patterns
spellingShingle Complexity-entropy causality plane as a complexity measure for two-dimensional patterns
Ribeiro, Haroldo V.
COMPLEXITY
COMPLEXITY-ENTROPY CAUSALITY PLANE
TWO-DIMENSIONAL PATTERNS
HIGHER-DIMENSIONAL PATTERNS
title_short Complexity-entropy causality plane as a complexity measure for two-dimensional patterns
title_full Complexity-entropy causality plane as a complexity measure for two-dimensional patterns
title_fullStr Complexity-entropy causality plane as a complexity measure for two-dimensional patterns
title_full_unstemmed Complexity-entropy causality plane as a complexity measure for two-dimensional patterns
title_sort Complexity-entropy causality plane as a complexity measure for two-dimensional patterns
dc.creator.none.fl_str_mv Ribeiro, Haroldo V.
Zunino, Luciano José
Lenzi, Ervin K.
Santoro, Perseu A.
Mendes, Renio S.
author Ribeiro, Haroldo V.
author_facet Ribeiro, Haroldo V.
Zunino, Luciano José
Lenzi, Ervin K.
Santoro, Perseu A.
Mendes, Renio S.
author_role author
author2 Zunino, Luciano José
Lenzi, Ervin K.
Santoro, Perseu A.
Mendes, Renio S.
author2_role author
author
author
author
dc.subject.none.fl_str_mv COMPLEXITY
COMPLEXITY-ENTROPY CAUSALITY PLANE
TWO-DIMENSIONAL PATTERNS
HIGHER-DIMENSIONAL PATTERNS
topic COMPLEXITY
COMPLEXITY-ENTROPY CAUSALITY PLANE
TWO-DIMENSIONAL PATTERNS
HIGHER-DIMENSIONAL PATTERNS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index. We build up a numerical procedure that can be easily implemented to evaluate the complexity of two or higher-dimensional patterns. We work out this method in different scenarios where numerical experiments and empirical data were taken into account. Specifically, we have applied the method to i) fractal landscapes generated numerically where we compare our measures with the Hurst exponent; ii) liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; iii) 12 characteristic textures of liquid crystals wher the different values show that the method can distinguish different phases; iv) and Ising surfaces where our method identified the critical temperature and also proved to be stable.
Fil: Ribeiro, Haroldo V.. Universidade Estadual de Maringá; Brasil
Fil: Zunino, Luciano José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Investigaciones Ópticas. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Investigaciones Ópticas. Universidad Nacional de La Plata. Centro de Investigaciones Ópticas; Argentina
Fil: Lenzi, Ervin K.. Universidade Estadual de Maringá; Brasil
Fil: Santoro, Perseu A.. Universidade Estadual de Maringá; Brasil
Fil: Mendes, Renio S.. Universidade Estadual de Maringá; Brasil
description Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index. We build up a numerical procedure that can be easily implemented to evaluate the complexity of two or higher-dimensional patterns. We work out this method in different scenarios where numerical experiments and empirical data were taken into account. Specifically, we have applied the method to i) fractal landscapes generated numerically where we compare our measures with the Hurst exponent; ii) liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; iii) 12 characteristic textures of liquid crystals wher the different values show that the method can distinguish different phases; iv) and Ising surfaces where our method identified the critical temperature and also proved to be stable.
publishDate 2012
dc.date.none.fl_str_mv 2012-08
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/75348
Ribeiro, Haroldo V.; Zunino, Luciano José; Lenzi, Ervin K.; Santoro, Perseu A.; Mendes, Renio S.; Complexity-entropy causality plane as a complexity measure for two-dimensional patterns; Public Library of Science; Plos One; 7; 8; 8-2012; 1-9; e40689
1932-6203
CONICET Digital
CONICET
url http://hdl.handle.net/11336/75348
identifier_str_mv Ribeiro, Haroldo V.; Zunino, Luciano José; Lenzi, Ervin K.; Santoro, Perseu A.; Mendes, Renio S.; Complexity-entropy causality plane as a complexity measure for two-dimensional patterns; Public Library of Science; Plos One; 7; 8; 8-2012; 1-9; e40689
1932-6203
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1371/journal.pone.0040689
info:eu-repo/semantics/altIdentifier/url/https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0040689
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Public Library of Science
publisher.none.fl_str_mv Public Library of Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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