A generalization of Artin-Mazur completion and rigid completion functors in homotopy theory

Localization and Completion in Homotopy Theory

The Proalgebraic Completion of Rigid Groups

A finitely generated group G is called representation rigid (briefly, rigid) if for every n, G has only finitely many classes of simple C representations in dimension n. Examples include higher rank S-arithmetic groups. By Margulis super rigidity, the latter have a stronger property: they are representation super rigid; i.e., their proalgebraic completion is finite dimensional. We construct exa...

Coherent Functors in Stable Homotopy Theory

such that C and D are compact objects in S (an object X in S is compact if the representable functor Hom(X,−) preserves arbitrary coproducts). The concept of a coherent functor has been introduced explicitly for abelian categories by Auslander [1], but it is also implicit in the work of Freyd on stable homotopy [9]. In this paper we characterize coherent functors in a number of ways and use the...

Graph Matrix Completion in Presence of Outliers

Matrix completion problem has gathered a lot of attention in recent years. In the matrix completion problem, the goal is to recover a low-rank matrix from a subset of its entries. The graph matrix completion was introduced based on the fact that the relation between rows (or columns) of a matrix can be modeled as a graph structure. The graph matrix completion problem is formulated by adding the...

Information Theory of Matrix Completion

Matrix completion is a fundamental problem that comes up in a variety of applications like the Netflix problem, collaborative filtering, computer vision, and crowdsourcing. The goal of the problem is to recover a k-by-n unknown matrix from a subset of its noiseless (or noisy) entries. We define an informationtheoretic notion of completion capacity C that quantifies the maximum number of entries...