Skin lesion segmentation is one of the crucial steps for an efficient non-invasive computer-aided early diagnosis of melanoma. This paper investigates how to use colour information, besides saliency, for determining the pigmented lesion region automatically.

In this paper we analyse temporal variations of the phase of a very low frequency (VLF) signal, used for the lower ionosphere monitoring, in periods around four earthquakes (EQs) with magnitude greater than 4. We provide two analyses in time and frequency domains. First, we analyse time evolution of the phase noise. And second, we examine variations of the frequency spectrum using Fast Fourier Transform (FFT) in order to detect hydrodynamic wave excitations and attenuations.

We consider a variational model for two interacting species (or phases), subject to cross and self attractive forces. We show existence and several qualitative properties of minimizers. Depending on the strengths of the forces, different behaviors are possible: phase mixing or phase separation with nested or disjoint phases. In the case of Coulomb interaction forces, we characterize the ground state configurations.

We consider a core-radius approach to nonlocal perimeters governed by isotropic kernels having critical and supercritical exponents, extending the nowadays classical notion of s-fractional perimeter, defined for 0<s<1, to the case s>=1. We show that, as the core-radius vanishes, such core-radius regularized s-fractional perimeters, suitably scaled, ?-converge to the standard Euclidean perimeter.

The diffusive behaviour of simple random-walk proposals of many Markov Chain Monte Carlo (MCMC) algorithms results in slow exploration of the state space making inefficient the convergence to a target distribution. Hamiltonian/Hybrid Monte Carlo (HMC), by introducing fictious momentum variables, adopts Hamiltonian dynamics, rather than a probability distribution, to propose future states in the Markov chain. Splitting schemes are numerical integrators for Hamiltonian problems that may advantageously replace the St¨ormer-Verlet method within HMC methodology.

X-ray Small and Wide Scattering scanning microscopies have been adopted to inspect morphological and structural properties of collagen-based tissues at the atomic and nano scale 1 .

We consider low-energy configurations for the Heitmann-Radin sticky discs functional, in the limit of diverging number of discs. More precisely, we renormalize the Heitmann-Radin potential by subtracting the minimal energy per particle, i.e. the so-called kissing number.