Sharp constants are exhibited in exponential inequalities corresponding to the limiting case of the Sobolev inequalities in Lorentz-Sobolev spaces of arbitrary order.

Cloud detection from geostationary satellite multispectral images through statistical methodologies is investigated. Discriminant analysis methods are considered to this purpose, endowed with a nonparametric density estimation and a linear transform into principal and independent components. The whole methodology is applied to the MSG-SEVIRI sensor through a set of test images covering the central and southern part of Europe.

This paper is devoted to a numerical simulation of the classical WKB system arising in geometric optics expansions. It contains the nonlinear eikonal equation and a linear conservation law whose coefficient can be discontinuous. We address the problem of treating it in such a way superimposed signals can be reproduced by means of the kinetic formulation of ``multibranch solutions'' originally due to Brenier and Corrias. Some existence and uniqueness results are given together with computational test-cases of increasing difficulty displaying up to five multivaluations.

We propose here a well-balanced numerical scheme for the one-dimensional Goldstein-Taylor system which is endowed with all the stability properties inherent to the continuous problem and works in both rarefied and diffusive regimes.

The problem of the interplay between normal and anomalous scaling in turbulent systems stirred by a random forcing with a power-law spectrum is addressed. We consider both linear and nonlinear systems. As for the linear case, we study passive scalars advected by a 2d velocity field in the inverse cascade regime. For the nonlinear case, we review a recent investigation of 3d Navier–Stokes turbulence, and we present new quantitative results for shell models of turbulence.

We report recent results from a high-resolution numerical study of fluid particles transported by a fully developed turbulent flow. Single-particle trajectories were followed for a time range spanning more than three decades, from less than a tenth of the Kolmogorov timescale up to one large-eddy turnover time. We present some results concerning acceleration statistics and the statistics of trapping by vortex filaments.

Knowledge of the exact spatial distribution of brain tissues in images acquired by magnetic resonance imaging (MRI) is necessary to measure and compare the performance of segmentation algorithms. Currently available physical phantoms do not satisfy this requirement. State-of-the-art digital brain phantoms also fall short because they do not handle separately anatomical structures (e.g. basal ganglia) and provide relatively rough simulations of tissue fine structure and inhomogeneity. We present a software procedure for the construction of a realistic MRI digital brain phantom.

The objective of the present paper is to develop a truly functional Bayesian method specifically designed for time series microarray data. The method allows one to identify differentially expressed genes in a time-course microarray experiment, to rank them and to estimate their expression profiles. Each gene expression profile is modeled as an expansion over some orthonormal basis, where the coefficients and the number of basis functions are estimated from the data.