Electrical source imaging (ESI) aims at reconstructing the electrical brain activity from measurements of the electric field on the scalp. ESI is a key element in the analysis of EEG data, in both research and clinical settings. In the last twenty years several algorithms have been applied for solving the ill- posed EEG inverse problem.

In this paper we establish the higher differentiability of solutions to the Dirichlet problem {div(A(x,Du))+b(x)u(x)=fin?u=0on??under a Sobolev assumption on the partial map x-> A(x, ?). The novelty here is that we take advantage from the regularizing effect of the lower order term to deal with bounded solutions.

The present study assesses the viability of including water vapor data from Interferometry Synthetic Aperture Radar (InSAR) in the initialization of numerical weather prediction (NWP) models, using already available Sentinel-1 A and B products. Despite the limitations resulting from the 6-day return period of images produced by the 2-satellite system, it is found that for a sufficiently large domain designed to contain a set of images every 12 h (at varying locations), the impact on model performance is beneficial or at least neutral.

The paper concerns the weighted uniform approximation of a real function on the d-cube [-1, 1]^d, with d > 1, by means of some multivariate filtered polynomials. These polynomials have been deduced, via tensor product, from certain de la Vallée Poussin type means on [-1, 1], which generalize classical delayed arithmetic means of Fourier partial sums. They are based on arbitrary sequences of filter coefficients, not necessarily connected with a smooth filter function.

In this paper, we use the Z-control approach to get further insight on the role of awareness in the management of epidemics that, just like Covid-19, display a high rate of overexposure because of the large number of asymptomatic people. We focus on a SEIR model including a overexposure mechanism and consider awareness as a time-dependent variable whose dynamics is not assigned a priori.

In a computer-aided system for skin cancer diagnosis, hair removal is one of the main challenges to face before applying a process of automatic skin lesion segmentation and classification. In this paper, we propose a straightforward method to detect and remove hair from dermoscopic images. Preliminarily, the regions to consider as candidate hair regions and the border/corner components located on the image frame are automatically detected. Then, the hair regions are determined using information regarding the saliency, shape and image colors.

We present mesoscale numerical simulations of Rayleigh-Bénard (RB) convection in a two-dimensional model emulsion. The systems under study are constituted of finite-size droplets, whose concentration is systematically varied from small (Newtonian emulsions) to large values (non-Newtonian emulsions). We focus on the characterisation of the heat transfer properties close to the transition from conductive to convective states, where it is well known that a homogeneous Newtonian system exhibits a steady flow and a time-independent heat flux.

We propose and analyze a generalized two dimensional XY model, whose interaction potential has n weighted wells, describing corresponding symmetries of the system. As the lattice spacing vanishes, we derive by -convergence the discrete-to-continuum limit of this model. In the energy regime we deal with, the asymptotic ground states exhibit fractional vortices, connected by string defects. The -limit takes into account both contributions, through a renormalized energy, depending on the configuration of fractional vortices, and a surface energy, proportional to the length of the strings.

In this paper we establish the boundedness and the higher differentiability of solutions to the {div(A(x,Du))+b(x)|u(x)|u(x)=fin ?u=0on ?? under a Sobolev assumption on the partial map x->A(x,?). The novelty here is that we deal with degenerate elliptic operator A(x,?) with p-growth, p>=2, with respect to the gradient variable, in presence of lower order terms. The interplay between b(x) and f(x), introduced in ([1]), gives a regularizing effect also in the degenerate elliptic setting.