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Transportation cost-information and concentration inequalities for bifurcating Markov chains
No full textInternational audienceWe investigate the transportation cost-information inequalities for bifurcating Markov chains which are a class of processes indexed by binary tree. These processes provide models for cell growth when each individual in one generation gives birth to two offsprings in the next one. Transportation cost inequalities provide useful concentra-tion inequalities. We also study deviation inequalities for the empiri-cal means under relaxed assumptions on the Wasserstein contraction of the Markov kernels. Applications to bifurcating non linear autore-gressive processes are considered: deviation inequalities for pointwise estimates of the non linear leading functions
High dimensional matrix estimation with unknown variance of the noise
No full textInternational audienceWe propose a new pivotal method for estimating high-dimensional matrices. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix corrupted by noise. We propose a new method for estimating which does not rely on the knowledge or an estimation of the standard deviation of the noise . Our estimator achieves, up to a logarithmic factor, optimal rates of convergence under the Frobenius risk and, thus, has the same prediction performance as previously proposed estimators which rely on the knowledge of . Our method is based on the solution of a convex optimization problem which makes it computationally attractive
The scaling limit of random simple triangulations and random simple quadrangulations
No full textInternational audienceLet M-n be a simple triangulation of the sphere S-2, drawn uniformly at random from all such triangulations with n vertices. Endow M-n with the uniform probability measure on its vertices. After rescaling graph distance by (3/(4n))(1/4), the resulting random measured metric space converges in distribution, in the Gromov-Hausdorff-Prokhorov sense, to the Brownian map. In proving the preceding fact, we introduce a labelling function for the vertices of M-n. Under this labelling, distances to a distinguished point are essentially given by vertex labels, with an error given by the winding number of an associated closed loop in the map. We establish similar results for simple quadrangulations
Pseudorapidity dependence of long-range two-particle correlations in pPb collisions at sqrt(s[NN])=5.02 TeV
No full textSubmitted to Phys. Rev. C ; see paper for full list of authorsInternational audienceTwo-particle correlations in pPb collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV are studied as a function of the pseudorapidity separation (Delta eta) of the particle pair at small relative azimuthal angle (abs(Delta phi)< pi/3). The correlations are decomposed into a jet component that dominates the short-range correlations (abs(Delta eta) < 1), and a component that persists at large Delta eta and may originate from collective behavior of the produced system. The events are classified in terms of the multiplicity of the produced particles. Finite azimuthal anisotropies are observed in high-multiplicity events. The second and third Fourier components of the particle-pair azimuthal correlations, V[2] and V[3], are extracted after subtraction of the jet component. The single-particle anisotropy parameters v[2] and v[3] are normalized by their lab frame mid-rapidity value and are studied as a function of eta[cm]. The normalized v[2] distribution is found to be asymmetric about eta[cm] = 0, with smaller values observed at forward pseudorapidity, corresponding to the direction of the proton beam, while no significant pseudorapidity dependence is observed for the normalized v[3] distribution within the statistical uncertainties
Spline regression for hazard rate estimation when data are censored and measured with error
No full textInternational audienceIn this paper, we study an estimation problem where the variables of interest are subject to both right censoring and measurement error. In this context, we propose a nonparametric estimation strategy of the hazard rate, based on a regression contrast minimized in a finite dimensional functional space generated by splines bases. We prove a risk bound of the estimator in term of integrated mean square error, discuss the rate of convergence when the dimension of the projection space is adequately chosen. Then, we define a data driven criterion of model selection and prove that the resulting estimator performs an adequate compromise. The method is illustrated via simulation experiments which prove that the strategy is successful
Optimal scaling of the Random Walk Metropolis algorithm under Lp mean differentiability
No full textInternational audienceThis paper considers the optimal scaling problem for high-dimensional random walk Metropolis algorithms for densities which are differentiable in Lp mean but which may be irregular at some points (like the Laplace density for example) and/or are supported on an interval. Our main result is the weak convergence of the Markov chain (appropriately rescaled in time and space) to a Langevin diffusion process as the dimension d goes to infinity. Because the log-density might be non-differentiable, the limiting diffusion could be singular. The scaling limit is established under assumptions which are much weaker than the one used in the original derivation of [6]. This result has important practical implications for the use of random walk Metropolis algorithms in Bayesian frameworks based on sparsity inducing priors
Suboptimal feedback control of PDEs by solving HJB equations on adaptive sparse grids
No full textInternational audienceAn approach to solve finite time horizon suboptimal feedback control problems for partial differential equations is proposed by solving dynamic programming equations on adaptive sparse grids. The approach is illustrated for the wave equation and an extension to equations of Schrödinger type is indicated. A semi-discrete optimal control problem is introduced and the feedback control is derived from the corresponding value function.The value function can be characterized as the solution of an evolutionary Hamilton-Jacobi Bellman (HJB) equation which is defined over a state space whose dimension is equal to the dimension of the underlying semi-discrete system. Besides a low dimensional semi-discretization it is important to solve the HJB equation efficiently to address the curse of dimensionality.We propose to apply a semi-Lagrangian scheme using spatially adaptive sparse grids. Sparse grids allow the discretization of the value functions in (higher) space dimensions since the curse of dimensionality of full grid methods arises to a much smaller extent. For additional efficiency an adaptive grid refinement procedure is explored.We present several numerical examples studying the effect the parameters characterizing the sparse grid have on the accuracy of the value function and the optimal trajectory
The Purcell Three-link swimmer: some geometric and numerical aspects related to periodic optimal controls
No full textInternational audienceThe maximum principle combined with numerical methods is a powerful tool to compute solutions for optimal control problems. This approach turns out to be extremely useful in applications, including solving problems which require establishing periodic trajectories for Hamiltonian systems, optimizing the production of photobioreactors over a one-day period, finding the best periodic controls for locomotion models (e.g. walking, flying and swimming). In this article we investigate some geometric and numerical aspects related to optimal control problems for the so-called Purcell Three-link swimmer [20], in which the cost to minimize represents the energy consumed by the swimmer. More precisely, employing the maximum principle and shooting methods we derive optimal trajectories and controls, which have particular periodic features. Moreover, invoking a linearization procedure of the control system along a reference extremal, we estimate the conjugate points, which play a crucial role for the second order optimality conditions. We also show how, making use of techniques imported by the sub-Riemannian geometry, the nilpotent approximation of the system provides a model which is integrable, obtaining explicit expressions in terms of elliptic functions. This approximation allows to compute optimal periodic controls for small deformations of the body, allowing the swimmer to move minimizing its energy. Numerical simulations are presented using Hampath and Bocop codes
Some results on anisotropic fractional mean curvature flows
No full textInternational audienceWe show the consistency of a threshold dynamics type algorithm for the anisotropic motion by fractional mean curvature, in the presence of a time dependent forcing term. Beside the consistency result, we show that convex sets remain convex during the evolution, and the evolution of a bounded convex set is uniquely defined
Search for anomalous single top quark production in association with a photon in pp collisions at sqrt(s) = 8 TeV
No full textSee paper for full list of authors - Submitted to JHEPInternational audienceThe result of a search for flavor changing neutral currents (FCNC) through single top quark production in association with a photon is presented. The study is based on proton-proton collisions at a center-of-mass energy of 8 TeV using data collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 19.8 inverse femtobarns. The search for t gamma events where t to Wb and W to mu nu is conducted in final states with a muon, a photon, at least one hadronic jet with at most one being consistent with originating from a bottom quark, and missing transverse momentum. No evidence of single top quark production in association with a photon through a FCNC is observed. Upper limits at the 95% confidence level are set on the tu gamma and tc gamma anomalous couplings and translated into upper limits on the branching fraction of the FCNC top quark decays: B(t to u gamma) < 1.3E-4 and B(t to c gamma) < 1.7E-3. Upper limits are also set on the cross section of associated t gamma production in a restricted phase-space region. These are the most stringent limits currently available