Approximations for the von Neumann and Rényi entropies of graphs with circulant type Laplacians
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , |
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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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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799134074907918336 |