A Characterization of Deterministic Sampling Patterns for Low-Rank Matrix Completion

Low-rank matrix completion (LRMC) problems arise in a wide variety of applications. Previous theory mainly provides conditions for completion under missing-at-random samplings. This paper studies deterministic conditions for completion. An incomplete $d \times N$ matrix is finitely rank-$r$ completable if there are at most finitely many rank-$r$ matrices that agree with all its observed entries. Finite completability is the tipping point in LRMC, as a few additional samples of a finitely completable matrix guarantee its unique completability. The main contribution of this paper is a deterministic sampling condition for finite completability. We use this to also derive deterministic sampling conditions for unique completability that can be efficiently verified. We also show that under uniform random sampling schemes, these conditions are satisfied with high probability if $O(\max\{r,\log d\})$ entries per column are observed. These findings have several implications on LRMC regarding lower bounds, sample and computational complexity, the role of coherence, adaptive settings and the validation of any completion algorithm. We complement our theoretical results with experiments that support our findings and motivate future analysis of uncharted sampling regimes.Comment: This update corrects an error in version 2 of this paper, where we erroneously assumed that columns with more than r+1 observed entries would yield multiple independent constraint

Marriage and care of a spouse with dementia: a cross-cultural study Brazil-Portugal

This study aimed to analyze the meaning of marriage and care of the spouse from the perspective of Brazilian and Portuguese caregivers of elderly people with Alzheimer Disease (AD). Twelve women participated in the study, being the sample obtained by convenience using the snowball technique. We used a questionnaire and a semi-structured interview, data were analyzed by the Bardin content analysis technique. The results pointed out that although the cultural differences between Brazil and Portugal, some meanings related to marriage and care of the spouse in the context of AD were similar for Brazilian and Portuguese wives. Despite marital changes related to dementia, most wives felt well performing their role of caregiver, perhaps because among other variables, this is a task traditionally and culturally expected to be performed by women of both countries.info:eu-repo/semantics/publishedVersio

Oxalatos totais em Setaria anceps cv. kazungula.

bitstream/item/138494/1/COT-12.pdfCNPGC

Hamilton-Jacobi formalism for Linearized Gravity

In this work we study the theory of linearized gravity via the Hamilton-Jacobi formalism. We make a brief review of this theory and its Lagrangian description, as well as a review of the Hamilton-Jacobi approach for singular systems. Then we apply this formalism to analyze the constraint structure of the linearized gravity in instant and front-form dynamics.Comment: To be published in Classical and Quantum Gravit

Deterministic Conditions for Subspace Identifiability from Incomplete Sampling

Consider a generic $r$-dimensional subspace of $\mathbb{R}^d$, $r<d$, and suppose that we are only given projections of this subspace onto small subsets of the canonical coordinates. The paper establishes necessary and sufficient deterministic conditions on the subsets for subspace identifiability.Comment: To appear in Proc. of IEEE ISIT, 201

Comments on regularization ambiguities and local gauge symmetries

We study the regularization ambiguities in an exact renormalized (1+1)-dimensional field theory. We show a relation between the regularization ambiguities and the coupling parameters of the theory as well as their role in the implementation of a local gauge symmetry at quantum level.Comment: Latex 2e, 4 pages. To appear in Modern Physics Letters