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: Population & Approximation algorithm. The organization has 1766 authors who have published 6909 publications receiving 162747 citations. The organization is also known as: Paris Dauphine & Dauphine.

Paradigms and Challenges

Abstract: The purpose of this introductory part is to present an overall view of what MCDA is today. In Section 1, I will attempt to bring answers to questions such as: what is it reasonable to expect from MCDA? Why decision aiding is more often multicriteria than monocriterion? What are the main limitations to objectivity? Section 2 will be devoted to a presentation of the conceptual architecture that constitutes the main keys for analyzing and structuring problem situations. Decision aiding cannot and must not be envisaged jointly with a hypothesis of perfect knowledge. Different ways for apprehending the various sources of imperfect knowledge will be introduced in Section 3. A robustness analysis is necessary in most cases. The crucial question of how can we take into account all criteria comprehensively in order to compare potential actions to one another will be tackled in Section 4. In this introductory part, I will only present a general framework for positioning the main operational approaches that exist today. In Section 5, I will discuss some more philosophical aspects of MCDA. For providing some aid in a decision context, we have to choose among different paths which one seems to be the most appropriate, or how to combine some of them: the path of realism which leads to the quest for a discussion for discovering, the axiomatic path which is often associated with the quest of norms for prescribing, or the path of constructivism which goes hand in hand with the quest of working hypothesis for recommending.

The European school of MCDA: Emergence, basic features and current works

Abstract: Multiple-criteria decision analysis has evolved considerably since its birth during the 1960s. As part of this evolution, several schools of thought have developed emphasizing different techniques and, more generally, different attitudes as to the way of supporting or aiding decision making. One of these schools is now commonly referred to as the ‘European School’, its members being part of a European Working Group entitled ‘Multicriteria Aid for Decisions’. In the first part of this paper (Section 1) we follow a historical perspective in order to trace the emergence of the European School. Its distinctive features and main ideas are then outlined in Section 2. Finally we provide a general review of the current major research topics developed within this framework (Section 3).

Exact Support Recovery for Sparse Spikes Deconvolution

Abstract: This paper studies sparse spikes deconvolution over the space of measures We focus on the recovery properties of the support of the measure (ie, the location of the Dirac masses) using total variation of measures (TV) regularization This regularization is the natural extension of the $$\ell ^1$$l1 norm of vectors to the setting of measures We show that support identification is governed by a specific solution of the dual problem (a so-called dual certificate) having minimum $$L^2$$L2 norm Our main result shows that if this certificate is non-degenerate (see the definition below), when the signal-to-noise ratio is large enough TV regularization recovers the exact same number of Diracs We show that both the locations and the amplitudes of these Diracs converge toward those of the input measure when the noise drops to zero Moreover, the non-degeneracy of this certificate can be checked by computing a so-called vanishing derivative pre-certificate This proxy can be computed in closed form by solving a linear system Lastly, we draw connections between the support of the recovered measure on a continuous domain and on a discretized grid We show that when the signal-to-noise level is large enough, and provided the aforementioned dual certificate is non-degenerate, the solution of the discretized problem is supported on pairs of Diracs which are neighbors of the Diracs of the input measure This gives a precise description of the convergence of the solution of the discretized problem toward the solution of the continuous grid-free problem, as the grid size tends to zero

A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid

Abstract: We address the numerical simulation of fluid-structure systems involving an incompressible viscous fluid. This issue is particularly difficult to face when the fluid added-mass acting on the structure is strong, as it happens in hemodynamics for example. Indeed, several works have shown that, in such situations, implicit coupling seems to be necessary in order to avoid numerical instabilities. Although significant improvements have been achieved during the last years, solving implicit coupling often exhibits a prohibitive computational cost. In this work, we introduce a semi-implicit coupling scheme which remains stable for a reasonable range of the discretization parameters. The first idea consists in treating implicitly the added-mass effect, whereas the other contributions (geometrical non-linearities, viscous and convective effects) are treated explicitly. The second idea, relies on the fact that this kind of explicit-implicit splitting can be naturally performed using a Chorin-Temam projection scheme in the fluid. We prove (conditional) stability of the scheme for a fully discrete formulation. Several numerical experiments point out the efficiency of the present scheme compared to several implicit approaches.

Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces

Abstract: We establish quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particle simulations in a model mean field problem. The tools include coupling arguments, as well as regularity and moment estimates for solutions of certain diffusive partial differential equations.