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.

Wasserstein regularization of imaging problem

Abstract: This paper introduces a novel and generic framework embedding statistical constraints for variational problems. We resort to the theory of Monge-Kantorovich optimal mass transport to define penalty terms depending on statistics from images. To cope with the computation time issue of the corresponding Wasserstein distances involved in this approach, we propose an approximate variational formulation for statistics represented as point clouds. We illustrate this framework on the problem of regularized color specification. This is achieved by combining the proposed approximate Wasserstein constraint on color statistics with a generic geometric-based regularization term in a unified variational minimization problem. We believe that this methodology may lead to some other interesting applications in image processing, such as medical imaging modification, texture synthesis, etc.

Properties of optimizers of the principal eigenvalue with indefinite weight and Robin conditions

Abstract: In this paper, we are interested in the analysis of a well-known free boundary/shape optimization problem motivated by some issues arising in population dynamics. The question is to determine optimal spatial arrangements of favorable and unfavorable regions for a species to survive. The mathematical formulation of the model leads to an indefinite weight linear eigenvalue problem in a fixed box $\Omega$ and we consider the general case of Robin boundary conditions on $\partial\Omega$. It is well known that it suffices to consider {\it bang-bang} weights taking two values of different signs, that can be parametrized by the characteristic function of the subset $E$ of $\Omega$ on which resources are located. Therefore, the optimal spatial arrangement is obtained by minimizing the positive principal eigenvalue with respect to $E$, under a volume constraint. By using symmetrization techniques, as well as necessary optimality conditions, we prove new qualitative results on the solutions. Namely, we completely solve the problem in dimension 1, we prove the counter-intuitive result that the ball is almost never a solution in dimension 2 or higher, despite what suggest the numerical simulations. We also introduce a new rearrangement in the ball allowing to get a better candidate than the ball for optimality when Neumann boundary conditions are imposed. We also provide numerical illustrations of our results and of the optimal configurations.

Ergodic problem for the Hamilton-Jacobi-Bellman equation. I. Existence of the ergodic attractor

Abstract: The problem of the convergence of the terms λuλ(x), ≠ u(x,T) in the Hamilton-Jacobi-Bellman equations (HJBs) as λ tends to +0, T goes to +∞, to the unique number is called the ergodic problem of the HJBs. We show in this paper what kind of qualitative properties exist behind this kind of convergence. The existence of the ergodic attractor is shown in Theorems 1 and 2. Our solutions of HJBs satisfy the equations in the viscosity solutions sense.

Recherche en marketing: un état des controverses

Abstract: Cet article presente un etat des principales controverses philosophiques et methodologiques existant en marketing. Une analyse de contenu des differents debats ayant oppose les chercheurs fait apparaitre une confusion qui risque de s'eterniser. En effet, les polemiques sont souvent de niveau et de nature differents. L'article propose de retrouver des definitions operationnelles qui integrent les diverses polemiques. Les differents choix auxquels le praticien de la recherche academique doit faire face, et ayant conscience des heuristiques qu'ils impliquent, sont presentes dans un schema integrateur. L'article se conclut par des propositions de triangulation permettant la construction de la connaissance.