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.

We aim to maximize the operational time of a network of sensors, which are used to monitor a predefined set of target locations. The classical approach proposed in the literature consists in individuating subsets of sensors (covers) that can individually monitor the targets, and in assigning appropriate activation times to each cover. Indeed, since sensors may belong to multiple covers, it is important to make sure that their overall battery capacities are not violated.

A product quadrature rule, based on the filtered de la Vallée Poussin polynomial approximation, is proposed for evaluating the finite weighted Hilbert transform in [-1,1]. Convergence results are stated in weighted uniform norm for functions belonging to suitable Besov type subspaces. Several numerical tests are provided, also comparing the rule with other formulas known in literature.

In this work we introduce and study the strong generalized minimum label spanning tree (GMLST), a novel optimization problem defined on edge-labeled graphs. Given a label set associated to each edge of the input graph, the aim is to look for the spanning tree using the minimum number of labels. Differently from the previously introduced GMLST problem, including a given edge in the solution means that all its labels are used. We present a mathematical formulation, as well as three heuristic approaches to solve the problem.

In this work, we consider a scenario in which we have to monitor some locations of interest in a geographical area by means of a wireless sensor network. Our aim is to keep the network operational for as long as possible, while preventing certain sensors from being active simultaneously, since they would interfere with one another causing data loss, need for retransmissions and overall affecting the throughput and efficiency of the network. We propose an exact approach based on column generation, as well as a heuristic algorithm to solve its separation problem.

The dynamic behavior of a self-propelled semiflexible filament of length L is con- sidered under the action of a linear shear flow. The system is studied by using Brownian multi-particle collision dynamics. The system can be characterized in terms of the persistence length Lp of the chain, of the Peclet number, and of the Weissenberg number. The quantity Lp/L measures the bending rigidity of the polymer, the Peclet number Pe is the ratio of active force times L to thermal energy, and the Weissenberg number Wi characterizes the flow strength over thermal effects.

The dynamic behavior of a self-propelled semiflexible filament of length L is considered under the action of an external unbounded shear flow. The system is studied by using Brownian multi-particle collision dynamics. The system can be characterized in terms of the persistence length Lp of the chain, of the Peclet number, and of the Weissenberg number.

We study numerically the role of hydrodynamics in the liquid-hexatic transition of active colloids at intermediate activity, where motility induced phase separation (MIPS) does not occur. We show that in the case of active Brownian particles (ABP), the critical density of the transition decreases upon increasing the particle's mass, enhancing ordering, while self-propulsion has the opposite effect in the activity regime considered.