Centre de Mathématiques Appliquées de l'École polytechnique

Subadditivity and optimal matching of unbounded samples

We obtain new bounds for the optimal matching cost for empirical measures with unbounded support. For a large class of radially symmetric and rapidly decaying probability laws, we prove for the first time the asymptotic rate of convergence for the whole range of power exponents p...

On discrete X-ray transform

We consider a discrete version of X-ray transform going back, in particular, to Strichartz (1982). We suggest non-overdetermined reconstruction for this discrete transform. Extensions to weighted (attenuated) analogues are given. Connections to the continuous case are presented.

Polygonal Faber-Krahn inequality: local minimality via validated computing

The main result of the paper shows that the regular [Formula: see text]-gon is a local minimizer for the first Dirichlet-Laplace eigenvalue among [Formula: see text]-gons having fixed area for [Formula: see text]. The eigenvalue is seen as a function of the coordinates of the ver...

Convergence Analysis of a High-Order Multiscale Finite Element Method (MsFEM) for Stokes Flows in Heterogeneous Media

Abstract. An enriched nonconforming Multiscale Finite Element Method (MsFEM) to solve viscous incompressible flow problems in genuine heterogeneous or porous media was proposed in [Q. Feng, G. Allaire, and P. Omnes, Multiscale Model. Simul., 20 (2022), pp. 462–492]. The main feat...

Properties and Proximal Point Type Methods for Strongly Quasiconvex Functions in Hilbert Spaces

We study strongly quasiconvex functions defined on Hilbert spaces and taking extended real values from both theoretical and algorithmic points of view. To this end, we verify the existence of (global) minimizers and the properties of the proximal operator for such functions, prev...

State Spaces of Multifactor Approximations of Nonnegative Volterra Processes

We show that the state spaces of multifactor Markovian processes, coming from approximations of nonnegative Volterra processes, are given by explicit linear transformations of the nonnegative orthant. We demonstrate the usefulness of this result for applications, including simula...

A barycenter-based approach for the multi-model ensembling of subseasonal forecasts

Abstract. Ensemble forecasts and their combination are examined from the perspective of probability spaces. By treating ensemble forecasts as discrete probability distributions, multi-model ensemble (MME) forecasts are reformulated as barycenters of these distributions. We consid...

The algebraic structures of social organizations: the operad of cooperative games

The main goal of this paper is to settle a conceptual framework for cooperative game theory in which the notion of composition/aggregation of games is the defining structure. This is done via the mathematical theory of algebraic operads: we start by endowing the collection of all...

Noise through an Additional Variable for Mean Field Games Master Equation on Finite State Space

Abstract. This paper provides a mathematical study of the well-posedness of a master equation with terms modeling common noise on finite state space. In this setting, the solution of the master equation depends on an additional variable modeling the value of a stochastic process...

Measuring Dissimilarity between Convex Cones by Means of Max-Min Angles

Abstract. This work introduces a novel dissimilarity measure between two convex cones, based on the max-min angle between them. We demonstrate that this measure is closely related to the Pompeiu–Hausdorff distance, a well-established metric for comparing compact sets. Furthermore...