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On the asymptotic behaviour of the kernel of an adjoint convection-diffusion operator in a long cylinder
No full textInternational audienceThis paper studies the asymptotic behaviour of the principal eigen-function of the adjoint Neumann problem for a convection diffusion operator defined in a long cylinder. The operator coefficients are 1-periodic in the longitudinal variable. Depending on the sign of the so-called longitudinal drift (a weighted average of the coefficients), we prove that this principal eigenfunction is equal to the product of a specified periodic function and of an exponential, up to the addition of fast decaying boundary layer terms
A DDFV method for a Cahn-Hilliard/Stokes phase field model with dynamic boundary conditions
No full textInternational audienceIn this paper we propose a "Discrete Duality Finite Volume" method (DDFV for short) for the diffuse interface modelling of incompressible flows. This numerical method is, conservative, robust and is able to handle general geometries and meshes. The model we study couples the Cahn-Hilliard equation and the unsteady Stokes equation and is endowed with particular nonlinear boundary conditions called dynamic boundary conditions. To implement the scheme for this model we have to define new discrete consistent DDFV operators that allows an energy stable coupling between both discrete equations. We are thus able to obtain the existence of a family of solutions satisfying a suitable energy inequality, even in the case where a first order time-splitting method between the two subsystems is used. We illustrate various properties of such a model with some numerical results
Error estimates for the Euler discretization of an optimal control problem with first-order state constraints
No full textInternational audienceWe study the error introduced in the solution of an optimal control problem with first order state constraints, for which the trajectories are approximated with a classical Euler scheme. We obtain order one approximation results in the L ∞ norm (as opposed to the order 2/3 obtained in the literature). We assume either a strong second order optimality condition, or a weaker one in the case where the state constraint is scalar, satisfies some hypotheses for junction points, and the time step is constant. Our technique is based on some homotopy path of discrete optimal control problems that we study using perturbation analysis of nonlinear programming problems
First time to exit of a continuous Itô process: general moment estimates and L1-convergence rate for discrete time approximations
No full textWe establish general moment estimates for the discrete and continuous exit times of a general Itô process in terms of the distance to the boundary. These estimates serve as intermediate steps to obtain strong convergence results for the approximation of a continuous exit time by a discrete counterpart, computed on a grid. In particular, we prove that the discrete exit time of the Euler scheme of a diffusion converges in the L1 norm with an order 1/2 with respect to the mesh size
Posterior concentration rates for counting processes with Aalen multiplicative intensities
No full textWe provide general conditions to derive posterior concentration rates for Aalen counting processes. The conditions are designed to resemble those proposed in the literature for the problem of density estimation, so that existing results on density estimation can be adapted to the present setting. We apply the general theorem to some prior models including Dirichlet process mixtures of uniform densities to estimate monotone non-increasing intensities and log-splines
An asymptotic plate model for magneto-electro-thermo-elastic sensors and actuators
No full textInternational audienceWe present an asymptotic two-dimensional plate model for linear magneto-electro-thermo-elastic sensors and actuators, under the hypotheses of anisotropy and homogeneity. Four different boundary conditions pertaining to electromagnetic quantities are considered, leading to four different models: the sensor-actuator model, the actuator-sensor model, the actuator model and the sensor model. We validate the obtained two-dimensional models by proving weak convergence results. Each of the four plate problems turns out to be decoupled into a flexural problem, involving the transversal displacement of the plate, and a certain partially or totally coupled membrane problem
Adaptive importance sampling in least-squares Monte Carlo algorithms for backward stochastic differential equations
No full textInternational audienceWe design an importance sampling scheme for backward stochastic differential equations (BSDEs) that minimizes the conditional variance occurring in least-squares Monte Carlo (LSMC) algorithms. The Radon-Nikodym derivative depends on the solution of BSDE, and therefore it is computed adaptively within the LSMC procedure. To allow robust error estimates w.r.t. the unknown change of measure, we properly randomize the initial value of the forward process. We introduce novel methods to analyze the error: firstly, we establish norm stability results due to the random initialization; secondly, we develop refined concentration-of-measure techniques to capture the variance of reduction. Our theoretical results are supported by numerical experiments
Blow-up phenomena for gradient flows of discrete homogeneous functionals
No full textInternational audienceWe investigate gradient flows of some homogeneous functionals in R^N , arising in the Lagrangian approximation of systems of self-interacting and diffusing particles. We focus on the case of negative homogeneity. In the case of strong self-interaction, the functional possesses a cone of negative energy. It is immediate to see that solutions with negative energy at some time become singular in finite time, meaning that a subset of particles concentrate at a single point. Here, we establish that all solutions become singular in finite time for the class of functionals under consideration. The paper is completed with numerical simulations illustrating the striking non linear dynamics when initial data have positive energy
Measurements of the t-tbar production cross section in lepton+jets final states in pp collisions at 8 TeV and ratio of 8 to 7 TeV cross sections
No full textSubmitted to Eur. Phys. J. C ; see paper for full list of authorsInternational audienceA measurement of the top quark pair production (t-tbar) cross section in proton-proton collisions at the centre-of-mass energy of 8 TeV is presented using data collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 19.6 inverse-femtobarns. This analysis is performed in the t-tbar decay channels with one isolated, high transverse momentum electron or muon and at least four jets, at least one of which is required to be identified as originating from hadronization of a b quark. The calibration of the jet energy scale and the efficiency of b jet identification are determined from data. The measured t-tbar cross section is 228.5 +/- 3.8 (stat) +/- 13.7 (syst) +/- 6.0 (lumi) pb. This measurement is compared with an analysis of 7 TeV data, corresponding to an integrated luminosity of 5.0 inverse-femtobarns, to determine the ratio of 8 TeV to 7 TeV cross sections, which is found to be 1.43 +/- 0.04 (stat) +/- 0.07 (syst) +/- 0.05 (lumi). The measurements are in agreement with QCD predictions up to next-to-next-to-leading order
Cryptanalysis of McEliece Cryptosystem Based on Algebraic Geometry Codes and their subcodes
No full textInternational audienceWe give polynomial time attacks on the McEliece public key cryptosystem based either on algebraic geometry (AG) codes or on small codimensional subcodes of AG codes. These attacks consist in the blind reconstruction either of an Error Correcting Pair (ECP), or an Error Correcting Array (ECA) from the single data of an arbitrary generator matrix of a code. Take notice that the choice of computing an ECP or an ECA depends on the number of errors that we need to correct: an ECP provides a decoding algorithm that corrects up to d * −1−g 2 errors, where d * denotes the designed distance and g denotes the genus of the corresponding curve; while with an ECA the decoding algorithm arrives up to d * −1 2 errors. Roughly speaking, for a public code of length n over F q , these attacks run in O(n 4 log(n)) operations in F q for the reconstruction of an ECP and O(n 5) operations for the reconstruction of an ECA. A probabilistic shortcut allows to reduce the complexities respectively to O(n 3+ε log(n)) and O(n 4+ε). Compared to the previous known attack due to Faure and Minder, our attack is efficient on codes from curves of arbitrary genus. Furthermore we investigate how far these methods apply to subcodes of AG codes