Approximations for the von Neumann and Rényi entropies of graphs with circulant type Laplacians

Detalhes bibliográficos
Autor(a) principal: Bebiano, Natália
Data de Publicação: 2022
Outros Autores: Providência, João da, Xu, Wei-Ru
Tipo de documento: Artigo
Idioma: por
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10316/100571
https://doi.org/10.3934/era.2022094
Resumo: In this note, we approximate the von Neumann and R´enyi entropies of high-dimensional graphs using the Euler-Maclaurin summation formula. The obtained estimations have a considerable degree of accuracy. The performed experiments suggest some entropy problems concerning graphs whose Laplacians are g-circulant matrices, i.e., circulant matrices with g-periodic diagonals, or quasi- Toeplitz matrices. Quasi means that in a Toeplitz matrix the first two elements in the main diagonal, and the last two, di er from the remaining diagonal entries by a perturbation.
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spelling Approximations for the von Neumann and Rényi entropies of graphs with circulant type LaplaciansentropygraphsLaplacian matrixEuler-Maclaurin summation formulaIn this note, we approximate the von Neumann and R´enyi entropies of high-dimensional graphs using the Euler-Maclaurin summation formula. The obtained estimations have a considerable degree of accuracy. The performed experiments suggest some entropy problems concerning graphs whose Laplacians are g-circulant matrices, i.e., circulant matrices with g-periodic diagonals, or quasi- Toeplitz matrices. Quasi means that in a Toeplitz matrix the first two elements in the main diagonal, and the last two, di er from the remaining diagonal entries by a perturbation.2022info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/100571http://hdl.handle.net/10316/100571https://doi.org/10.3934/era.2022094por2688-1594Bebiano, NatáliaProvidência, João daXu, Wei-Ruinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2022-07-01T20:31:09Zoai:estudogeral.uc.pt:10316/100571Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:17:55.912592Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Approximations for the von Neumann and Rényi entropies of graphs with circulant type Laplacians
title Approximations for the von Neumann and Rényi entropies of graphs with circulant type Laplacians
spellingShingle Approximations for the von Neumann and Rényi entropies of graphs with circulant type Laplacians
Bebiano, Natália
entropy
graphs
Laplacian matrix
Euler-Maclaurin summation formula
title_short Approximations for the von Neumann and Rényi entropies of graphs with circulant type Laplacians
title_full Approximations for the von Neumann and Rényi entropies of graphs with circulant type Laplacians
title_fullStr Approximations for the von Neumann and Rényi entropies of graphs with circulant type Laplacians
title_full_unstemmed Approximations for the von Neumann and Rényi entropies of graphs with circulant type Laplacians
title_sort Approximations for the von Neumann and Rényi entropies of graphs with circulant type Laplacians
author Bebiano, Natália
author_facet Bebiano, Natália
Providência, João da
Xu, Wei-Ru
author_role author
author2 Providência, João da
Xu, Wei-Ru
author2_role author
author
dc.contributor.author.fl_str_mv Bebiano, Natália
Providência, João da
Xu, Wei-Ru
dc.subject.por.fl_str_mv entropy
graphs
Laplacian matrix
Euler-Maclaurin summation formula
topic entropy
graphs
Laplacian matrix
Euler-Maclaurin summation formula
description In this note, we approximate the von Neumann and R´enyi entropies of high-dimensional graphs using the Euler-Maclaurin summation formula. The obtained estimations have a considerable degree of accuracy. The performed experiments suggest some entropy problems concerning graphs whose Laplacians are g-circulant matrices, i.e., circulant matrices with g-periodic diagonals, or quasi- Toeplitz matrices. Quasi means that in a Toeplitz matrix the first two elements in the main diagonal, and the last two, di er from the remaining diagonal entries by a perturbation.
publishDate 2022
dc.date.none.fl_str_mv 2022
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.uri.fl_str_mv http://hdl.handle.net/10316/100571
http://hdl.handle.net/10316/100571
https://doi.org/10.3934/era.2022094
url http://hdl.handle.net/10316/100571
https://doi.org/10.3934/era.2022094
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv 2688-1594
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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