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 & Nonlinear system. The organization has 2717 authors who have published 5585 publications receiving 175925 citations.

Strict upper error bounds on computed outputs of interest in computational structural mechanics

Abstract: This paper introduces new strict error bounds of computed outputs of interest for time-dependent nonlinear problems in quasi-statics as well as in dynamics. All sources of errors, including modeling errors, are taken into account. Therefore, such error bounds are also suitable tools for analyzing various approximations, particularly in dynamics. Small-displacement problems without softening, such as (visco)plasticity problems, are included through the classical thermodynamics framework involving internal state variables; the material models are not necessarily standard.

Process and context in choice models

Abstract: We develop a general framework that extends choice models by including an explicit representation of the process and context of decision making. Process refers to the steps involved in decision making. Context refers to factors affecting the process, focusing in this paper on social networks. The extended choice framework includes more behavioral richness through the explicit representation of the planning process preceding an action and its dynamics and the effects of context (family, friends, and market) on the process leading to a choice, as well as the inclusion of new types of subjective data in choice models. We discuss the key issues involved in applying the extended framework, focusing on richer data requirements, theories, and models, and present three partial demonstrations of the proposed framework. Future research challenges include the development of more comprehensive empirical tests of the extended modeling framework.

Emptiness of Multi-pushdown Automata Is 2ETIME-Complete

Abstract: We consider multi-pushdown automata, a multi-stack extension of pushdown automata that comes with a constraint on stack operations: a pop can only be performed on the first non-empty stack (which implies that we assume a linear ordering on the collection of stacks). We show that the emptiness problem for multi-pushdown automata is 2ETIME-complete wrt. the number of stacks. Containment in 2ETIME is shown by translating an automaton into a grammar for which we can check if the generated language is empty. The lower bound is established by simulating the behavior of an alternating Turing machine working in exponential space. We also compare multi-pushdown automata with the model of bounded-phase multi-stack (visibly) pushdown automata.

Asymptotics for the Low-Lying Eigenstates of the Schrödinger Operator with Magnetic Field near Corners

Abstract: The Neumann realization for the Schrodinger operator with magnetic field is considered in a bounded two-dimensional domain with corners. This operator is associated with a small semi-classical parameter h or, equivalently, with a large magnetic field.We investigate the behavior of its eigenpairs as h tends to zero, like in a semi-classical limit. We prove, in the situation where the domain is a polygon and the magnetic field is constant, that the lowest eigenvalues are exponentially close to those of model problems associated with the corners. We approximate the corresponding eigenvectors by linear combinations of functions concentrated in corners at the scale $$\sqrt h .$$ If the domain has curved sides and the magnetic field is smoothly varying, we exhibit a full asymptotics for eigenpairs in powers of $$\sqrt h .$$ Communicated by Christian Gerard

Markov solutions for the $3D$ stochastic Navier--Stokes equations with state dependent noise

Abstract: We construct a Markov family of solutions for the 3D Navier-Stokes equations perturbed by a non degenerate noise. We improve the result of [3] in two directions. We see that in fact not only a transition semigroup but a Markov family of solutions can be constructed. Moreover, we consider a state dependant noise. Another feature of this work is that we greatly simplify the proofs of [3].