Maximum entropy principle for Kaniadakis statistics and networks

Detalhes bibliográficos
Autor(a) principal: Moreira, Darlan Araújo
Data de Publicação: 2013
Outros Autores: Macedo Filho, Antônio de, Silva Junior, Raimundo, Silva, Luciano Rodrigues da
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFRN
Texto Completo: https://repositorio.ufrn.br/handle/123456789/30641
Resumo: In this Letter we investigate a connection between Kaniadakis power-law statistics and networks. By following the maximum entropy principle, we maximize the Kaniadakis entropy and derive the optimal degree distribution of complex networks. We show that the degree distribution follows P(k) =P0 expκ (−k/ηκ ) with expκ (x) = (√1 + κ2x2 + κx)1/κ , and |κ| < 1. In order to check our approach we study a preferential attachment growth model introduced by Soares et al. [Europhys. Lett. 70 (2005) 70] and a growing random network (GRN) model investigated by Krapivsky et al. [Phys. Rev. Lett. 85 (2000) 4629]. Our results are compared with the ones calculated through the Tsallis statistics
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spelling Moreira, Darlan AraújoMacedo Filho, Antônio deSilva Junior, RaimundoSilva, Luciano Rodrigues da2020-11-23T21:20:26Z2020-11-23T21:20:26Z2013-05-03MACEDO FILHO, A.; MOREIRA, D.A.; SILVA, R.; SILVA, Luciano R. da. Maximum entropy principle for Kaniadakis statistics and networks. Physics Letters A, [S.L.], v. 377, n. 12, p. 842-846, maio 2013. Disponível em: https://www.sciencedirect.com/science/article/pii/S0375960113000984?via%3Dihub. Acesso em: 08 set. 2020. http://dx.doi.org/10.1016/j.physleta.2013.01.032.0375-9601https://repositorio.ufrn.br/handle/123456789/3064110.1016/j.physleta.2013.01.032ElsevierAttribution 3.0 Brazilhttp://creativecommons.org/licenses/by/3.0/br/info:eu-repo/semantics/openAccessGeneralized statisticsDegree distributionNetworksMaximum entropy principle for Kaniadakis statistics and networksinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleIn this Letter we investigate a connection between Kaniadakis power-law statistics and networks. By following the maximum entropy principle, we maximize the Kaniadakis entropy and derive the optimal degree distribution of complex networks. We show that the degree distribution follows P(k) =P0 expκ (−k/ηκ ) with expκ (x) = (√1 + κ2x2 + κx)1/κ , and |κ| < 1. In order to check our approach we study a preferential attachment growth model introduced by Soares et al. [Europhys. Lett. 70 (2005) 70] and a growing random network (GRN) model investigated by Krapivsky et al. [Phys. Rev. Lett. 85 (2000) 4629]. Our results are compared with the ones calculated through the Tsallis statisticsengreponame:Repositório Institucional da UFRNinstname:Universidade Federal do Rio Grande do Norte (UFRN)instacron:UFRNORIGINALMaximumEntropyPrinciple_MOREIRA_2013.pdfMaximumEntropyPrinciple_MOREIRA_2013.pdfapplication/pdf283615https://repositorio.ufrn.br/bitstream/123456789/30641/1/MaximumEntropyPrinciple_MOREIRA_2013.pdf8c6c82a6f73763936c27d2e7412a01abMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8914https://repositorio.ufrn.br/bitstream/123456789/30641/2/license_rdf4d2950bda3d176f570a9f8b328dfbbefMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81484https://repositorio.ufrn.br/bitstream/123456789/30641/3/license.txte9597aa2854d128fd968be5edc8a28d9MD53TEXTMaximumEntropyPrinciple_MOREIRA_2013.pdf.txtMaximumEntropyPrinciple_MOREIRA_2013.pdf.txtExtracted texttext/plain26074https://repositorio.ufrn.br/bitstream/123456789/30641/4/MaximumEntropyPrinciple_MOREIRA_2013.pdf.txt7b75f3528d41864141481ec07348bb4eMD54THUMBNAILMaximumEntropyPrinciple_MOREIRA_2013.pdf.jpgMaximumEntropyPrinciple_MOREIRA_2013.pdf.jpgGenerated Thumbnailimage/jpeg1769https://repositorio.ufrn.br/bitstream/123456789/30641/5/MaximumEntropyPrinciple_MOREIRA_2013.pdf.jpg07d3c36e647c770bd85bb99259899d45MD55123456789/306412020-11-29 04:45:18.271oai:https://repositorio.ufrn.br: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Repositório de PublicaçõesPUBhttp://repositorio.ufrn.br/oai/opendoar:2020-11-29T07:45:18Repositório Institucional da UFRN - Universidade Federal do Rio Grande do Norte (UFRN)false
dc.title.pt_BR.fl_str_mv Maximum entropy principle for Kaniadakis statistics and networks
title Maximum entropy principle for Kaniadakis statistics and networks
spellingShingle Maximum entropy principle for Kaniadakis statistics and networks
Moreira, Darlan Araújo
Generalized statistics
Degree distribution
Networks
title_short Maximum entropy principle for Kaniadakis statistics and networks
title_full Maximum entropy principle for Kaniadakis statistics and networks
title_fullStr Maximum entropy principle for Kaniadakis statistics and networks
title_full_unstemmed Maximum entropy principle for Kaniadakis statistics and networks
title_sort Maximum entropy principle for Kaniadakis statistics and networks
author Moreira, Darlan Araújo
author_facet Moreira, Darlan Araújo
Macedo Filho, Antônio de
Silva Junior, Raimundo
Silva, Luciano Rodrigues da
author_role author
author2 Macedo Filho, Antônio de
Silva Junior, Raimundo
Silva, Luciano Rodrigues da
author2_role author
author
author
dc.contributor.author.fl_str_mv Moreira, Darlan Araújo
Macedo Filho, Antônio de
Silva Junior, Raimundo
Silva, Luciano Rodrigues da
dc.subject.por.fl_str_mv Generalized statistics
Degree distribution
Networks
topic Generalized statistics
Degree distribution
Networks
description In this Letter we investigate a connection between Kaniadakis power-law statistics and networks. By following the maximum entropy principle, we maximize the Kaniadakis entropy and derive the optimal degree distribution of complex networks. We show that the degree distribution follows P(k) =P0 expκ (−k/ηκ ) with expκ (x) = (√1 + κ2x2 + κx)1/κ , and |κ| < 1. In order to check our approach we study a preferential attachment growth model introduced by Soares et al. [Europhys. Lett. 70 (2005) 70] and a growing random network (GRN) model investigated by Krapivsky et al. [Phys. Rev. Lett. 85 (2000) 4629]. Our results are compared with the ones calculated through the Tsallis statistics
publishDate 2013
dc.date.issued.fl_str_mv 2013-05-03
dc.date.accessioned.fl_str_mv 2020-11-23T21:20:26Z
dc.date.available.fl_str_mv 2020-11-23T21:20:26Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.citation.fl_str_mv MACEDO FILHO, A.; MOREIRA, D.A.; SILVA, R.; SILVA, Luciano R. da. Maximum entropy principle for Kaniadakis statistics and networks. Physics Letters A, [S.L.], v. 377, n. 12, p. 842-846, maio 2013. Disponível em: https://www.sciencedirect.com/science/article/pii/S0375960113000984?via%3Dihub. Acesso em: 08 set. 2020. http://dx.doi.org/10.1016/j.physleta.2013.01.032.
dc.identifier.uri.fl_str_mv https://repositorio.ufrn.br/handle/123456789/30641
dc.identifier.issn.none.fl_str_mv 0375-9601
dc.identifier.doi.none.fl_str_mv 10.1016/j.physleta.2013.01.032
identifier_str_mv MACEDO FILHO, A.; MOREIRA, D.A.; SILVA, R.; SILVA, Luciano R. da. Maximum entropy principle for Kaniadakis statistics and networks. Physics Letters A, [S.L.], v. 377, n. 12, p. 842-846, maio 2013. Disponível em: https://www.sciencedirect.com/science/article/pii/S0375960113000984?via%3Dihub. Acesso em: 08 set. 2020. http://dx.doi.org/10.1016/j.physleta.2013.01.032.
0375-9601
10.1016/j.physleta.2013.01.032
url https://repositorio.ufrn.br/handle/123456789/30641
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv Attribution 3.0 Brazil
http://creativecommons.org/licenses/by/3.0/br/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution 3.0 Brazil
http://creativecommons.org/licenses/by/3.0/br/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFRN
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instname_str Universidade Federal do Rio Grande do Norte (UFRN)
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institution UFRN
reponame_str Repositório Institucional da UFRN
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