Background. Electrocorticography (ECoG) measures the distribution of electrical potentials by means of electrodes grids implanted close to the cortical surface. A full interpretation of ECoG data requires solving the ill-posed inverse problem of reconstructing the spatio-temporal distribution of neural currents responsible for the recorded signals. Only in the last few years some methods have been proposed to solve this inverse problem [1]. Methods. This study [2] addresses the ECoG source modelling using a beamformer method.

Time-scale transforms play a fundamental role in the compact representation of signals and images [1]. Non linear time representation provided a significant contribution to the definition of more flexible and adaptive transforms. However, in many applications signals are better characterized in the frequency domain. In particular, frequency distribution in the frequency axis is strictly dependent on the signal under study. On the contrary, frequency axis partition provided by conventional transforms obeys more rigid rules.

The large amount of work on community detection and its applications leaves unaddressed one important question: the statistical validation of the results. We present a methodology able to clearly detect the truly significance of the communities identified by some technique, permitting us to discard those that could be merely the consequence of edge positions in the network. Given a community detection method and a network of interest, our procedure examines the stability of the partition recovered against random perturbations of the original graph structure.

Gene expression data from high-throughput assays, such as microarray, are often used to predict cancer survival. However, available datasets consist of a small number of samples (n patients) and a large number of gene expression data (p predictors). Therefore, the main challenge is to cope with the high-dimensionality. Moreover, genes are co-regulated and their expression levels are expected to be highly correlated. In order to face these two issues, network based approaches have been proposed.

Unlike for systems in equilibrium, a straightforward definition of a metastable set in the non-stationary, non-equilibrium case may only be given case-by-case-and therefore it is not directly useful any more, in particular in cases where the slowest relaxation time scales are comparable to the time scales at which the external field driving the system varies. We generalize the concept of metastability by relying on the theory of coherent sets.

The problem is addressed of the maximal integrability of the gradient of solutions to quasilinear elliptic equations, with merely measurable coefficients, in two variables. Optimal results are obtained in the framework of Orlicz spaces, and in the more general setting of all rearrangement-invariant spaces. Applications to special instances are exhibited, which provide new gradient bounds, or improve certain results available in the literature. (C) 2016 Elsevier Ltd. All rights reserved.

We establish the statistical mechanics framework for a bundle of N-f living and uncrosslinked actin filaments in a supercritical solution of free monomers pressing against a mobile wall. The filaments are anchored normally to a fixed planar surface at one of their ends and, because of their limited flexibility, they grow almost parallel to each other. Their growing ends hit a moving obstacle, depicted as a second planar wall, parallel to the previous one and subjected to a harmonic compressive force.

Additive partial linear models with nonparametric additive components of heterogeneous smoothness are studied. To achieve optimal rates in large sample situations we use block wavelet penalisation techniques combined with adaptive (group) LASSO procedures for selecting the variables in the linear part and the the additive components in the nonparametric part of the models. Numerical implementations of our procedures for proximal like algorithms are discussed.

We consider the problem of determining quantitative information about corrosion occurring on an inaccesible part of a specimen. The data for the problem consist of prescribed current flux and voltage measurements on an accessible part of the specimen boundary. The problem is modelled by Laplace's equation with an unknown term in the boundary conditions. Our goal is recovering from the data. We prove uniqueness under certain regularity assumptions and construct a regularized numerical method for obtaining approximate solutions to the problem.