Optimal reconstruction systems for erasures and for the q-potential

Autores
Massey, Pedro Gustavo
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we introduce the q-potential as an extension of the Benedetto–Fickus frame potential, defined on general reconstruction systems and show that protocols are the minimizers of this potential under certain restrictions.We extend recent results of B.G. Bodmannon the structure of optimal protocols with respect to 1 and 2 lost packets where the worst (normalized) reconstruction error is computedwith respect to a compatible unitarily invariant norm.We finally describe necessary and sufficient (spectral) conditions, that we call q-fundamental inequalities, for the existence of protocols with prescribed properties by relating this problem to Klyachko´s and Fulton´s theory on sums of hermitian operators.
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina
Materia
Reconstruction Systems
Q-Potential
Erasures
Compatible Unitarily Invariant Norm
Q-Fundamental Inequality
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:11336/19481
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/19481
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Optimal reconstruction systems for erasures and for the q-potentialMassey, Pedro GustavoReconstruction SystemsQ-PotentialErasuresCompatible Unitarily Invariant NormQ-Fundamental Inequalityhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we introduce the q-potential as an extension of the Benedetto–Fickus frame potential, defined on general reconstruction systems and show that protocols are the minimizers of this potential under certain restrictions.We extend recent results of B.G. Bodmannon the structure of optimal protocols with respect to 1 and 2 lost packets where the worst (normalized) reconstruction error is computedwith respect to a compatible unitarily invariant norm.We finally describe necessary and sufficient (spectral) conditions, that we call q-fundamental inequalities, for the existence of protocols with prescribed properties by relating this problem to Klyachko´s and Fulton´s theory on sums of hermitian operators.Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; ArgentinaElsevier Science Inc2009-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19481Massey, Pedro Gustavo; Optimal reconstruction systems for erasures and for the q-potential; Elsevier Science Inc; Linear Algebra and its Applications; 431; 8; 6-2009; 1302-13160024-3795CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0024379509002493info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2009.05.001info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:42:26Zoai:ri.conicet.gov.ar:11336/19481instacron: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:34982025-10-22 11:42:26.883CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Optimal reconstruction systems for erasures and for the q-potential
title Optimal reconstruction systems for erasures and for the q-potential
spellingShingle Optimal reconstruction systems for erasures and for the q-potential
Massey, Pedro Gustavo
Reconstruction Systems
Q-Potential
Erasures
Compatible Unitarily Invariant Norm
Q-Fundamental Inequality
title_short Optimal reconstruction systems for erasures and for the q-potential
title_full Optimal reconstruction systems for erasures and for the q-potential
title_fullStr Optimal reconstruction systems for erasures and for the q-potential
title_full_unstemmed Optimal reconstruction systems for erasures and for the q-potential
title_sort Optimal reconstruction systems for erasures and for the q-potential
dc.creator.none.fl_str_mv Massey, Pedro Gustavo
author Massey, Pedro Gustavo
author_facet Massey, Pedro Gustavo
author_role author
dc.subject.none.fl_str_mv Reconstruction Systems
Q-Potential
Erasures
Compatible Unitarily Invariant Norm
Q-Fundamental Inequality
topic Reconstruction Systems
Q-Potential
Erasures
Compatible Unitarily Invariant Norm
Q-Fundamental Inequality
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we introduce the q-potential as an extension of the Benedetto–Fickus frame potential, defined on general reconstruction systems and show that protocols are the minimizers of this potential under certain restrictions.We extend recent results of B.G. Bodmannon the structure of optimal protocols with respect to 1 and 2 lost packets where the worst (normalized) reconstruction error is computedwith respect to a compatible unitarily invariant norm.We finally describe necessary and sufficient (spectral) conditions, that we call q-fundamental inequalities, for the existence of protocols with prescribed properties by relating this problem to Klyachko´s and Fulton´s theory on sums of hermitian operators.
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina
description In this paper we introduce the q-potential as an extension of the Benedetto–Fickus frame potential, defined on general reconstruction systems and show that protocols are the minimizers of this potential under certain restrictions.We extend recent results of B.G. Bodmannon the structure of optimal protocols with respect to 1 and 2 lost packets where the worst (normalized) reconstruction error is computedwith respect to a compatible unitarily invariant norm.We finally describe necessary and sufficient (spectral) conditions, that we call q-fundamental inequalities, for the existence of protocols with prescribed properties by relating this problem to Klyachko´s and Fulton´s theory on sums of hermitian operators.
publishDate 2009
dc.date.none.fl_str_mv 2009-06
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/11336/19481
Massey, Pedro Gustavo; Optimal reconstruction systems for erasures and for the q-potential; Elsevier Science Inc; Linear Algebra and its Applications; 431; 8; 6-2009; 1302-1316
0024-3795
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19481
identifier_str_mv Massey, Pedro Gustavo; Optimal reconstruction systems for erasures and for the q-potential; Elsevier Science Inc; Linear Algebra and its Applications; 431; 8; 6-2009; 1302-1316
0024-3795
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0024379509002493
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2009.05.001
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
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science Inc
publisher.none.fl_str_mv Elsevier Science Inc
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
_version_ 1846782111608995840
score 12.982451

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