Computingmaximum a posteriori (MAP) estimation in graphical models is an important inference problem with many applications. We present message-passing algorithms for quadratic programming (QP) formulations of MAP estimation for pairwise Markov random fields. In particular, we use the concaveconvex procedure (CCCP) to obtain a locally optimal algorithm for the non-convex QP formulation. A simil...

A graph G with convex-QP stability number (or simply a convex-QP graph) is a graph for which the stability number is equal to the optimal value of a convex quadratic program, say P (G). There are polynomial-time procedures to recognize convex-QP graphs, except when the graph G is adverse or contains an adverse subgraph (that is, a non complete graph, without isolated vertices, such that the lea...

Let p be a prime number. Let w2 and w ∗ 2 denote the exponents of approximation defined by Mahler and Koksma, respectively, in their classifications of p-adic numbers. It is well-known that every p-adic number ξ satisfies w∗ 2(ξ) ≤ w2(ξ) ≤ w∗ 2(ξ) + 1, with w∗ 2(ξ) = w2(ξ) = 2 for almost all ξ. By means of Schneider’s continued fractions, we give explicit examples of p-adic numbers ξ for which ...

Quadratic Programming (QP) problems frequently appear as core component when solving constrained optimal control or estimation problems. The focus of this paper is on accelerating an existing Interior Point Method (IPM) for solving QP problems by exploiting the parallel computing characteristics of GPU. We compare the so-called data-parallel and the problem-parallel approaches to achieve speed ...

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1.1. The case ` 6= p. In this case, we are in the setting of the classical Local Langlands Correspondence, which can be stated (roughly) as follows: Let n ≥ 1. We then have an injective map (1)  continuous representations of Gal(Qp/Qp) on n-dimensional Q`-vector spaces, up to isomorphism  ↪−→  irreducible, admissible representations of GLn(Qp) on Q`-vector spaces, up to isomor...