Paris Dauphine University

About: Paris Dauphine University is a education organization based out in Paris, France. It is known for research contribution in the topics: Context (language use) & Population. The organization has 1766 authors who have published 6909 publications receiving 162747 citations. The organization is also known as: Paris Dauphine & Dauphine.

A Numerical Method to Solve Multi-Marginal Optimal Transport Problems with Coulomb Cost

Abstract: In this chapter, we present a numerical method, based on iterative Bregman projections, to solve the optimal transport problem with Coulomb cost. This problem is related to the strong interaction limit of Density Functional Theory. The first idea is to introduce an entropic regularization of the Kantorovich formulation of the Optimal Transport problem. The regularized problem then corresponds to the projection of a vector on the intersection of the constraints with respect to the Kullback-Leibler distance. Iterative Bregman projections on each marginal constraint are explicit which enables us to approximate the optimal transport plan. We validate the numerical method against analytical test cases.

From Concordance / Discordance to the Modelling of Positive and Negative Reasons in Decision Aiding

Abstract: The principle of concordance/discordance was introduced by B. Roy in his very early work on Multiple Criteria Decision Analysis. Although such a principle is grounded by strong evidence from real life decision situations, the way in which it has been implemented in existing MCDA methods allows only for its partial and limited use. Indeed, the principle lacks a theoretical frame enabling a more general use in decision analysis. The paper presents a possible generalisation of this principle under the concepts of positive and negative reasons. For this purpose, a new formalism, (a four valued logic) is suggested. Under such a formalism the concordance test is seen as the evaluation of the existence of positive reasons supporting the sentence “x is at least as good as y”, while the discordance test can be viewed as the evaluation of the existence of negative reasons against the same sentence. A number of results obtained in preference modelling and aggregation shows the potentiality of this approach.

On the Korteweg–de Vries Long-Wave Approximation of the Gross–Pitaevskii Equation II

Abstract: In this paper, we proceed along our analysis of the Korteweg-de Vries approximation of the Gross-Pitaevskii equation initiated in a previous paper. At the long-wave limit, we establish that solutions of small amplitude to the one-dimensional Gross-Pitaevskii equation split into two waves with opposite constant speeds $\pm \sqrt{2}$, each of which are solutions to a Korteweg-de Vries equation. We also compute an estimate of the error term which is somewhat optimal as long as travelling waves are considered. At the cost of higher regularity of the initial data, this improves our previous estimate.

Recursive Petri nets: Theory and application to discrete event systems

Abstract: In order to design and analyse complex systems, modelers need formal models with two contradictory requirements: a high expressivity and the decidability of behavioural property checking. Here we present and develop the theory of such a model, the recursive Petri nets. First, we show that the mechanisms supported by recursive Petri nets enable to model patterns of discrete event systems related to the dynamic structure of processes. Furthermore, we prove that these patterns cannot be modelled by ordinary Petri nets. Then we study the decidability of some problems: reachability, finiteness and bisimulation. At last, we develop the concept of linear invariants for this kind of nets and we design efficient computations specifically tailored to take advantage of their structure.