University of Marne-la-Vallée

About: University of Marne-la-Vallée is a based out in . It is known for research contribution in the topics: Estimator & Context (language use). The organization has 831 authors who have published 1855 publications receiving 55316 citations.

Estimating the entropy of a signal with applications

Abstract: We present an estimator of the entropy of a signal. The basic idea is to adopt a model of the probability law, in the form of an AR spectrum. Then, the law parameters can be estimated from the data. We examine the statistical behavior of our estimates of laws and entropy. Finally, we give several examples of applications: an adaptive version of our entropy estimator is applied to detection of law changes, blind deconvolution and sources separation.

On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles

Abstract: In this paper we revisit the Bialynicki-Birula and Mycielski uncertainty principle and its cases of equality. This Shannon entropic version of the well-known Heisenberg uncertainty principle can be used when dealing with variables that admit no variance. In this paper, we extend this uncertainty principle to Renyi entropies. We recall that in both Shannon and Renyi cases, and for a given dimension n , the only case of equality occurs for Gaussian random vectors. We show that as n grows, however, the bound is also asymptotically attained in the cases of n -dimensional Student- t and Student- r distributions. A complete analytical study is performed in a special case of a Student- t distribution. We also show numerically that this effect exists for the particular case of a n -dimensional Cauchy variable, whatever the Renyi entropy considered, extending the results of Abe and illustrating the analytical asymptotic study of the Student- t case. In the Student- r case, we show numerically that the same behavior occurs for uniformly distributed vectors. These particular cases and other ones investigated in this paper are interesting since they show that this asymptotic behavior cannot be considered as a “Gaussianization” of the vector when the dimension increases.

Dynamics of yielding observed in a three-dimensional aqueous dry foam.

Abstract: We study the onset of yielding in stable three-dimensional dry foams following the start up of steady shear flow. By means of a charge-coupled device camera equipped with a small depth-of-field objective, we visualize the Plateau border network in the bulk of the foam. The onset of yielding is identified with the deformation ${\ensuremath{\gamma}}_{c}$ for which shear induced rearrangements start occurring. We show that ${\ensuremath{\gamma}}_{c}$ is independent of shear rate $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}$ in a quasistatic regime whereas at high strain rates, a rapid increase of ${\ensuremath{\gamma}}_{c}$ with $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}$ is observed, in qualitative agreement with theoretical models. Moreover, spatiotemporal image analyses are used to determine the velocity profile in the gap. We find that this profile remains linear up to strains far beyond ${\ensuremath{\gamma}}_{c}.$ Moreover, we have studied the strain history dependence of ${\ensuremath{\gamma}}_{c}.$