Optimal frame designs for multitasking devices with weight restrictions

Autores
Benac, Maria Jose; Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let d=(d_j)_j∈I_m ∈ N^m be a finite sequence (of dimensions) and α=(α_i)_i∈ I_n be a sequence of positive numbers (of weights), where I_k={1,...,k} for k ∈ N. We introduce the (α , d)-designs i.e., m-tuples Φ=( F_j)_j ∈ I_m such that F_j={ f_ij}_i∈ I_n is a finite sequence in C^{d_j}, j ∈ I_m, and such that the sequence of non-negative numbers (||f_ij||^2)_j ∈ I_m forms a partition of α_i, i ∈ I_n. We characterize the existence of (α , d)-designs with prescribed properties in terms of majorization relations. We show, by means of a finite-step algorithm, that there exist (α , d)-designs Φ^ op =(F_j^op)_j∈I_m that are universally optimal; that is, for every convex function φ:[0,∞)→ [0,∞) then Φ^ op minimizes the joint convex potential induced by φ among (α , d)-designs, namely Σ_{j ∈ I_m} P_φ( F_j^op) ≤ Σ_{j ∈ I_m} P_φ( F_j) for every (α , d)$-design Φ=( F_j)_{j∈ I_m}, where P_φ(F)=tr(φ(S_F)); in particular, Φ^ op minimizes both the joint frame potential and the joint mean square error among (α , d)-designs. We show that in this case F_j^op is a frame for C^{d_j}, for j ∈ I_m. This corresponds to the existence of optimal encoding-decoding schemes for multitasking devices with energy restrictions.
Fil: Benac, Maria Jose. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Santiago del Estero. Facultad de Ciencias Exactas y Tecnologías. Departamento de Matemática; Argentina
Fil: Massey, Pedro Gustavo. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Ruiz, Mariano Andres. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Stojanoff, Demetrio. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
FRAMES
FRAME DESIGNS
CONVEX POTENTIALS
MAJORIZATION
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:11336/106957
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/106957
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Optimal frame designs for multitasking devices with weight restrictionsBenac, Maria JoseMassey, Pedro GustavoRuiz, Mariano AndresStojanoff, DemetrioFRAMESFRAME DESIGNSCONVEX POTENTIALSMAJORIZATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let d=(d_j)_j∈I_m ∈ N^m be a finite sequence (of dimensions) and α=(α_i)_i∈ I_n be a sequence of positive numbers (of weights), where I_k={1,...,k} for k ∈ N. We introduce the (α , d)-designs i.e., m-tuples Φ=( F_j)_j ∈ I_m such that F_j={ f_ij}_i∈ I_n is a finite sequence in C^{d_j}, j ∈ I_m, and such that the sequence of non-negative numbers (||f_ij||^2)_j ∈ I_m forms a partition of α_i, i ∈ I_n. We characterize the existence of (α , d)-designs with prescribed properties in terms of majorization relations. We show, by means of a finite-step algorithm, that there exist (α , d)-designs Φ^ op =(F_j^op)_j∈I_m that are universally optimal; that is, for every convex function φ:[0,∞)→ [0,∞) then Φ^ op minimizes the joint convex potential induced by φ among (α , d)-designs, namely Σ_{j ∈ I_m} P_φ( F_j^op) ≤ Σ_{j ∈ I_m} P_φ( F_j) for every (α , d)$-design Φ=( F_j)_{j∈ I_m}, where P_φ(F)=tr(φ(S_F)); in particular, Φ^ op minimizes both the joint frame potential and the joint mean square error among (α , d)-designs. We show that in this case F_j^op is a frame for C^{d_j}, for j ∈ I_m. This corresponds to the existence of optimal encoding-decoding schemes for multitasking devices with energy restrictions.Fil: Benac, Maria Jose. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Santiago del Estero. Facultad de Ciencias Exactas y Tecnologías. Departamento de Matemática; ArgentinaFil: Massey, Pedro Gustavo. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Ruiz, Mariano Andres. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Stojanoff, Demetrio. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaSpringer2020-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/106957Benac, Maria Jose; Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; Optimal frame designs for multitasking devices with weight restrictions; Springer; Advances In Computational Mathematics; 46; 2; 4-2020; 1-191019-71681572-9044CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s10444-020-09762-6info:eu-repo/semantics/altIdentifier/doi/10.1007/s10444-020-09762-6info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:01:23Zoai:ri.conicet.gov.ar:11336/106957instacron: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 11:01:24.188CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Optimal frame designs for multitasking devices with weight restrictions
title Optimal frame designs for multitasking devices with weight restrictions
spellingShingle Optimal frame designs for multitasking devices with weight restrictions
Benac, Maria Jose
FRAMES
FRAME DESIGNS
CONVEX POTENTIALS
MAJORIZATION
title_short Optimal frame designs for multitasking devices with weight restrictions
title_full Optimal frame designs for multitasking devices with weight restrictions
title_fullStr Optimal frame designs for multitasking devices with weight restrictions
title_full_unstemmed Optimal frame designs for multitasking devices with weight restrictions
title_sort Optimal frame designs for multitasking devices with weight restrictions
dc.creator.none.fl_str_mv Benac, Maria Jose
Massey, Pedro Gustavo
Ruiz, Mariano Andres
Stojanoff, Demetrio
author Benac, Maria Jose
author_facet Benac, Maria Jose
Massey, Pedro Gustavo
Ruiz, Mariano Andres
Stojanoff, Demetrio
author_role author
author2 Massey, Pedro Gustavo
Ruiz, Mariano Andres
Stojanoff, Demetrio
author2_role author
author
author
dc.subject.none.fl_str_mv FRAMES
FRAME DESIGNS
CONVEX POTENTIALS
MAJORIZATION
topic FRAMES
FRAME DESIGNS
CONVEX POTENTIALS
MAJORIZATION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let d=(d_j)_j∈I_m ∈ N^m be a finite sequence (of dimensions) and α=(α_i)_i∈ I_n be a sequence of positive numbers (of weights), where I_k={1,...,k} for k ∈ N. We introduce the (α , d)-designs i.e., m-tuples Φ=( F_j)_j ∈ I_m such that F_j={ f_ij}_i∈ I_n is a finite sequence in C^{d_j}, j ∈ I_m, and such that the sequence of non-negative numbers (||f_ij||^2)_j ∈ I_m forms a partition of α_i, i ∈ I_n. We characterize the existence of (α , d)-designs with prescribed properties in terms of majorization relations. We show, by means of a finite-step algorithm, that there exist (α , d)-designs Φ^ op =(F_j^op)_j∈I_m that are universally optimal; that is, for every convex function φ:[0,∞)→ [0,∞) then Φ^ op minimizes the joint convex potential induced by φ among (α , d)-designs, namely Σ_{j ∈ I_m} P_φ( F_j^op) ≤ Σ_{j ∈ I_m} P_φ( F_j) for every (α , d)$-design Φ=( F_j)_{j∈ I_m}, where P_φ(F)=tr(φ(S_F)); in particular, Φ^ op minimizes both the joint frame potential and the joint mean square error among (α , d)-designs. We show that in this case F_j^op is a frame for C^{d_j}, for j ∈ I_m. This corresponds to the existence of optimal encoding-decoding schemes for multitasking devices with energy restrictions.
Fil: Benac, Maria Jose. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Santiago del Estero. Facultad de Ciencias Exactas y Tecnologías. Departamento de Matemática; Argentina
Fil: Massey, Pedro Gustavo. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Ruiz, Mariano Andres. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Stojanoff, Demetrio. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description Let d=(d_j)_j∈I_m ∈ N^m be a finite sequence (of dimensions) and α=(α_i)_i∈ I_n be a sequence of positive numbers (of weights), where I_k={1,...,k} for k ∈ N. We introduce the (α , d)-designs i.e., m-tuples Φ=( F_j)_j ∈ I_m such that F_j={ f_ij}_i∈ I_n is a finite sequence in C^{d_j}, j ∈ I_m, and such that the sequence of non-negative numbers (||f_ij||^2)_j ∈ I_m forms a partition of α_i, i ∈ I_n. We characterize the existence of (α , d)-designs with prescribed properties in terms of majorization relations. We show, by means of a finite-step algorithm, that there exist (α , d)-designs Φ^ op =(F_j^op)_j∈I_m that are universally optimal; that is, for every convex function φ:[0,∞)→ [0,∞) then Φ^ op minimizes the joint convex potential induced by φ among (α , d)-designs, namely Σ_{j ∈ I_m} P_φ( F_j^op) ≤ Σ_{j ∈ I_m} P_φ( F_j) for every (α , d)$-design Φ=( F_j)_{j∈ I_m}, where P_φ(F)=tr(φ(S_F)); in particular, Φ^ op minimizes both the joint frame potential and the joint mean square error among (α , d)-designs. We show that in this case F_j^op is a frame for C^{d_j}, for j ∈ I_m. This corresponds to the existence of optimal encoding-decoding schemes for multitasking devices with energy restrictions.
publishDate 2020
dc.date.none.fl_str_mv 2020-04
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/11336/106957
Benac, Maria Jose; Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; Optimal frame designs for multitasking devices with weight restrictions; Springer; Advances In Computational Mathematics; 46; 2; 4-2020; 1-19
1019-7168
1572-9044
CONICET Digital
CONICET
url http://hdl.handle.net/11336/106957
identifier_str_mv Benac, Maria Jose; Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; Optimal frame designs for multitasking devices with weight restrictions; Springer; Advances In Computational Mathematics; 46; 2; 4-2020; 1-19
1019-7168
1572-9044
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://link.springer.com/10.1007/s10444-020-09762-6
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10444-020-09762-6
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 Springer
publisher.none.fl_str_mv Springer
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 12.982451

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