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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/106957
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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 Técnicas2025-09-29T09:33:24Zoai: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:34982025-09-29 09:33:24.385CONICET 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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1844613026023473152 |
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13.070432 |