Optimal frame designs for multitasking devices with weight restrictions
Let d=(dj)j∈Im∈Nm be a finite sequence (of dimensions) and α=(αi)i∈In be a sequence of positive numbers (of weights), where Ik={1,…,k} for k∈N. We introduce the (α, d)-designs, i.e., m-tuples Φ=(Fj)j∈Im such that Fj={fij}i∈In is a finite sequence in Cdj, j∈Im, and such that the sequence of non-negat...
| Autores principales: | , , , |
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| Formato: | Articulo Preprint |
| Lenguaje: | Inglés |
| Publicado: |
2020
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/125342 |
| Aporte de: |
| id |
I19-R120-10915-125342 |
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| record_format |
dspace |
| institution |
Universidad Nacional de La Plata |
| institution_str |
I-19 |
| repository_str |
R-120 |
| collection |
SEDICI (UNLP) |
| language |
Inglés |
| topic |
Matemática Frames Frame designs Convex potentials Majorization |
| spellingShingle |
Matemática Frames Frame designs Convex potentials Majorization Benac, María José Massey, Pedro Gustavo Ruiz, Mariano Andrés Stojanoff, Demetrio Optimal frame designs for multitasking devices with weight restrictions |
| topic_facet |
Matemática Frames Frame designs Convex potentials Majorization |
| description |
Let d=(dj)j∈Im∈Nm be a finite sequence (of dimensions) and α=(αi)i∈In be a sequence of positive numbers (of weights), where Ik={1,…,k} for k∈N. We introduce the (α, d)-designs, i.e., m-tuples Φ=(Fj)j∈Im such that Fj={fij}i∈In is a finite sequence in Cdj, j∈Im, and such that the sequence of non-negative numbers (∥fij∥2)j∈Im forms a partition of αi, i∈In. 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 Φop=(Fopj)j∈Im that are universally optimal; that is, for every convex function φ:[0,∞)→[0,∞), then Φop minimizes the joint convex potential induced by φ among (α, d)-designs, namely
$ \sum \limits_{j\in \mathbb I_{m}}\text {P}_{\varphi }(\mathcal F_{j}^{\text {op}})\leq \sum \limits_{j\in \mathbb I_{m}}\text {P}_{\varphi }(\mathcal F_{j}) $
for every (α, d)-design Φ=(Fj)j∈Im, where Pφ(F)=tr(φ(SF)); in particular, Φop minimizes both the joint frame potential and the joint mean square error among (α, d)-designs. We show that in this case, Fopj is a frame for Cdj, for j∈Im. This corresponds to the existence of optimal encoding-decoding schemes for multitasking devices with energy restrictions. |
| format |
Articulo Preprint |
| author |
Benac, María José Massey, Pedro Gustavo Ruiz, Mariano Andrés Stojanoff, Demetrio |
| author_facet |
Benac, María José Massey, Pedro Gustavo Ruiz, Mariano Andrés Stojanoff, Demetrio |
| author_sort |
Benac, María José |
| title |
Optimal frame designs for multitasking devices with weight restrictions |
| 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 |
| publishDate |
2020 |
| url |
http://sedici.unlp.edu.ar/handle/10915/125342 |
| work_keys_str_mv |
AT benacmariajose optimalframedesignsformultitaskingdeviceswithweightrestrictions AT masseypedrogustavo optimalframedesignsformultitaskingdeviceswithweightrestrictions AT ruizmarianoandres optimalframedesignsformultitaskingdeviceswithweightrestrictions AT stojanoffdemetrio optimalframedesignsformultitaskingdeviceswithweightrestrictions |
| bdutipo_str |
Repositorios |
| _version_ |
1764820451535618048 |