It is now well-known that one can reconstruct sparse or compressible signals accurately from a very limited number of measurements, possibly contaminated with noise. This technique known as "compressed sensing" or "compressive sampling" relies on properties of the sensing matrix such as the restricted isometry property. In this Note, we establish new results about the accuracy of the reconstruction from undersampled measurements which improve on earlier estimates, and have the advantage of being more elegant.
We present an efficient reduced-basis discretization procedure for partial differential equations with nonaffine parameter dependence. The method replaces nonaffine coefficient functions with a collateral reduced-basis expansion which then permits an (effectively affine) offline-online computational decomposition. The essential components of the approach are (i) a good collateral reduced-basis approximation space, (ii) a stable and inexpensive interpolation procedure. and (iii) an effective a posteriori estimator to quantify the newly introduced errors. Theoretical and numerical results respectively anticipate and confirm the good behavior of the technique. (C) 2004 Academie des sciences. Published by Elsevier SAS. All rights reserved.
Mean field games. I - The stationary case. We introduce here a general approach to model games with a large number of players. More precisely, we consider N players Nash equilibria for long term stochastic problems and establish rigorously the 'mean field' type equations as N goes to infinity. We also prove general uniqueness results and determine the deterministic limit.
We continue in this Note our study of the notion of mean field games that we introduced in a previous Note. We consider here the case of Nash equilibria for stochastic control type problems in finite horizon. We present general existence and uniqueness results for the partial differential equations systems that we introduce. We also give a possible interpretation of these systems in term of optimal control.
We extend the Hybrid High-Order method introduced by the authors for the Poisson problem to problems with heterogeneous/anisotropic diffusion. The cornerstone is a local discrete gradient reconstruction from element- and face-based polynomial degrees of freedom. Optimal error estimates are proved. (C) 2014 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
We show how to combine our earlier results to deduce strong convergence of the interfaces in the planar critical Ising model and its random-cluster representation to Schramm's SLE curves with parameters kappa = 3 and kappa = 16/3, respectively. (C) 2013 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
In this article, we investigate the orbital Hausdorff continuous dependence of the solutions to integer order and fractional nonlinear non-instantaneous differential equations. The concept of orbital Hausdorff continuous dependence is used to characterize the relations of solutions corresponding to the impulsive points and junction points in the sense of the Hausdorff distance. Then, we establish sufficient conditions to guarantee this specific continuous dependence on their respective trajectories. Finally, two examples are given to illustrate our theoretical results. (C) 2018 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
We prove a Bourgain-Brezis-Mironescu-type formula for a class of nonlocal magnetic spaces, which builds a bridge between a fractional magnetic operator recently introduced and the classical theory. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
We present the main result of Richard and Zamojski  concerning, in homogeneous dynamics, the general problem of the dynamics of sequences of translates of a certain measure in a space of S-arithmetic lattices. (C) 2019 Academie des sciences. Publie par Elsevier Masson SAS. Tous droits reserves.
We present some applications of recent results in homogeneous dynamics to an unlikely intersections problem in Shimura varieties (the Andre-Pink-Zannier conjecture) and its refinements. (C) 2019 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
Using the Faber polynomials, we obtain coefficient expansions for analytic bi-close-to-convex functions and determine coefficient estimates for such functions. We also demonstrate the unpredictable behavior of the early coefficients of subclasses of bi-univalent functions. A function is said to be bi-univalent in a domain if both the function and its inverse map are univalent there. (C) 2014 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.