The visual quality evaluation is one of the fundamental challenging problems in image processing. It plays a central role in the shaping, implementation, optimization, and testing of many methods. The existing image quality assessment methods centered mainly on images altered by common distortions while paying little attention to the distortion introduced by color quantization.

We show that the emerging field of discrete differential geometry can be usefully brought to bear on crystallization problems. In particular, we give a simplified proof of the Heitmann-Radin crystallization theorem (Heitmann and Radin in J Stat Phys 22(3):281-287, 1980), which concerns a system of N identical atoms in two dimensions interacting via the idealized pair potential if , if , 0 if .

Due to the limited field of view of the microscopes, acquisitions of macroscopic specimens require many parallel image stacks to cover the whole volume of interest. Overlapping regions are introduced among stacks in order to make it possible automatic alignment by means of a 3D stitching tool. Since state-of-the-art microscopes coupled with chemical clearing procedures can generate 3D images whose size exceeds the Terabyte, parallelization is required to keep stitching time within acceptable limits.

Defining accurate and flexible models for real-world networks of human beings is instrumental to understand the observed properties of phenomena taking place across those networks and to support computer simulations of dynamic processes of interest for several areas of research - including computational epidemiology, which is recently high on the agenda. In this paper we present a flexible model to generate age-stratified and geo-referenced synthetic social networks on the basis of widely available aggregated demographic data and, possibly, of estimated age-based social mixing patterns.

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.

Methylage is an epigenetic marker of biological age that exploits the correlation between the methylation state of specific CG dinucleotides (CpGs) and chronological age (in years), gestational age (in weeks), cellular age (in cell cycles or as telomere length, in kilobases). Using DNA methylation data, methylage is measurable via the so called epigenetic clocks.

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.

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.

We numerically study the dynamic behavior under a symmetric shear flow of selected examples of concentrated phase emulsions with multicore morphology confined within a microfluidic channel. A variety of nonequilibrium steady states is reported. Under low shear rates, the emulsion is found to exhibit a solidlike behavior, in which cores display a periodic planetarylike motion with approximately equal angular velocity.