We describe the emergence of topological singularities in periodic media within the Ginzburg-Landau model and the core-radius approach. The energy functionals of both models are denoted by E, where ? represent the coherence length (in the Ginzburg-Landau model) or the core-radius size (in the core-radius approach) and ? denotes the periodicity scale. We carry out the ? -convergence analysis of E as ?-> 0 and ?= ?-> 0 in the | log ?| scaling regime, showing that the ? -limit consists in the energy cost of finitely many vortex-like point singularities of integer degree.

Wireless sensor networks involve a large area of real-world contexts, such as national security, military and environmental control applications, traffic monitoring, among others. These applications generally consider the use of a large number of low-cost sensing devices to monitor the activities occurring in a certain set of target locations. One of the most important issue that is considered in this context is maximizing network lifetime, that is the amount of time in which this monitoring activity can be performed by opportunely switching the sensors from active to sleep mode.

In the colourful travelling salesman problem (CTSP), given a graph G with a (not necessarily distinct) label (colour) assigned to each edge, a Hamiltonian tour with the minimum number of different labels is sought. The problem is a variant of the well-known Hamiltonian cycle problem and has potential applications in telecommunication networks, optical networks, and multimodal transportation networks, in which one aims to ensure connectivity or other properties by means of a limited number of connection types.

Poisson shot noise processes are natural generalizations of compound Poisson processes that have been widely applied in insurance, neuroscience, seismology, computer science and epidemiology. In this paper we study sharp deviations, fluctuations and the stable probability approximation of Poisson shot noise processes. Our achievements extend, improve and complement existing results in the literature. We apply the theoretical results to Poisson cluster point processes, including generalized linear Hawkes processes, and risk processes with delayed claims. Many examples are discussed in detail.

We prove that positive solutions of the fractional Lane-Emden equation with homogeneous Dirichlet boundary conditions satisfy pointwise estimates in terms of the best constant in Poincaré's inequality on all open sets, and are isolated in $L^1$ on smooth bounded ones, whence we deduce the isolation of the first non-local semilinear eigenvalue .

Age of infection epidemic models [1, 3], based on non-linear integro-dierential equations, naturally describe the evolution of diseases whose infectivity depends on the time since becoming infected. Here we consider a multi-group age of infection model [2] and we extend the investigations in [4], [5] and [6] to provide numerical solutions that retain the main properties of the continuous system. In particular, we use Direct Quadrature methods and prove that the numerical solution is positive and bounded.

Image resizing is a basic tool in image processing, and in literature, we have many methods based on different approaches, which are often specialized in only upscaling or downscaling. In this paper, independently of the (reduced or enlarged) size we aim to get, we approach the problem at a continuous scale where the underlying function representing the image is globally approximated by its Lagrange-Chebyshev I kind interpolation polynomial corresponding to suitable (tensor product) grids of first kind Chebyshev zeros.

This paper provides a unified point of view on fractional perimeters and Riesz potentials. Denoting byH? - for ? 2 .0; 1/ - the ?-fractional perimeter and by J ? - for ? 2 .(d; 0)- the ?-Riesz energies acting on characteristic functions, we prove that both functionals can be seen as limits of renormalized self-attractive energies as well as limits of repulsive interactions between a set and its complement. We also show that the functionals H? and J ? , up to a suitable additive renormalization diverging when ? ? 0, belong to a continuous one-parameter family of functionals, which for ?

In this paper we take into account three different spanning tree problems with degree-dependent objective functions. The main application of these problems is in the field of optical network design. In particular, we propose the classical Minimum Leaves Spanning Tree problem as a relevant problem in this field and show its relations with the Minimum Branch Vertices and the Minimum Degree Sum Problems. We present a unified memetic algorithm for the three problems and show its effectiveness on a wide range of test instances. © 2013 Elsevier B.V. All rights reserved.

Given a graph G with a label (color) assigned to each edge (not necessarily properly) we look for an hamiltonian cycle of G with the minimum number of different colors. The problem has several applications in telecommunication networks, electric networks, multimodal transportation networks, among others, where one aims to ensure connectivity or other properties by means of limited number of different connections. We analyze the complexity of the problem on special graph classes and propose, for the general case, heuristic resolution algorithms.