École normale supérieure de Cachan

About: École normale supérieure de Cachan is a education organization based out in Cachan, Île-de-France, France. It is known for research contribution in the topics: Decidability & Finite element method. The organization has 2717 authors who have published 5585 publications receiving 175925 citations.

Vortices for a variational problem related to superconductivity

Abstract: We study minimizers of Ginzburg-Landau functional, which depend on a parameter ϵ. These functional appear in superconductivity and two dimensional abelian Higgs models. We study the asymptotic limit, as ϵ → 0, of minimizers and show that the limiting configuration has vortices, which have topological degree one.

Views and queries: Determinacy and rewriting

Abstract: We investigate the question of whether a query Q can be answered using a set V of views. We first define the problem in information-theoretic terms: we say that V determines Q if V provides enough information to uniquely determine the answer to Q. Next, we look at the problem of rewriting Q in terms of V using a specific language. Given a view language V and query language Q, we say that a rewriting language R is complete for V-to-Q rewritings if every Q ∈ Q can be rewritten in terms of V ∈ V using a query in R, whenever V determines Q. While query rewriting using views has been extensively investigated for some specific languages, the connection to the information-theoretic notion of determinacy, and the question of completeness of a rewriting language have received little attention. In this article we investigate systematically the notion of determinacy and its connection to rewriting. The results concern decidability of determinacy for various view and query languages, as well as the power required of complete rewriting languages. We consider languages ranging from first-order to conjunctive queries.

Controllability and observability of linear delay systems: an algebraic approach

Abstract: Interpretations of most existing controllability and observability notions for linear delay systems are given. Module theoretic characterizations are presented. This setting enables a clear and precise comparison of the various examined notions. A new notion of controllability is introduced, which is called pi-freeness.

Parallel Gaussian Process Optimization with Upper Confidence Bound and Pure Exploration

Abstract: In this paper, we consider the challenge of maximizing an unknown function f for which evaluations are noisy and are acquired with high cost. An iterative procedure uses the previous measures to actively select the next estimation of f which is predicted to be the most useful. We focus on the case where the function can be evaluated in parallel with batches of fixed size and analyze the benefit compared to the purely sequential procedure in terms of cumulative regret. We introduce the Gaussian Process Upper Confidence Bound and Pure Exploration algorithm (GP-UCB-PE) which combines the UCB strategy and Pure Exploration in the same batch of evaluations along the parallel iterations. We prove theoretical upper bounds on the regret with batches of size K for this procedure which show the improvement of the order of $\sqrt{K}$ for fixed iteration cost over purely sequential versions. Moreover, the multiplicative constants involved have the property of being dimension-free. We also confirm empirically the efficiency of GP-UCB-PE on real and synthetic problems compared to state-of-the-art competitors.