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In recent years it has been increasing evidence that lognormal distributions are widespread in physical and biological sciences, as well as in various phenomena of economics and social sciences. In social sciences, the appearance of lognormal distribution has been noticed, among others, when looking at body weight, and at women's age at first marriage. Likewise, in economics, lognormal distribution appears when looking at consumption in a western society, at call-center service times, and others. The common feature of these situations, which describe the distribution of a certain people's hallmark, is the presence of a desired target to be reached by repeated choices. In this paper we discuss a possible explanation of lognormal distribution forming in human activities by resorting to classical methods of statistical mechanics of multi-agent systems. The microscopic variation of the hallmark around its target value, leading to a linear Fokker-Planck type equation with lognormal equilibrium density, is built up introducing as main criterion for decision a suitable value function in the spirit of the prospect theory of Kahneman and Twersky.

Call centers are service networks in which agents provide telephone-based services. An important part of call center operations is represented by service durations. In recent statistical analysis of real data, it has been noticed that the distribution of service times reveals a remarkable fit to the lognormal distribution. In this paper we discuss a possible source of this behavior by resorting to classical methods of statistical mechanics of multi-agent systems. The microscopic service time variation leading to a linear kinetic equation with lognormal equilibrium density is built up introducing as main criterion for decision a suitable value function in the spirit of the prospect theory of Kahneman and Twersky.

We consider two approaches for solving the classical minimum vertex coloring problem, that is the problem of coloring the vertices of a graph so that adjacent vertices have different colors, minimizing the number of used colors, namely Constraint Programming and Column Generation. Constraint Programming is able to solve very efficiently many of the benchmarks, but suffers from the lack of effective bounding methods.On the contrary, Column Generation provides tight lower bounds by solving the fractional vertex coloring problem exploited in a Branch-and-Price algorithm, as already proposed in the literature. The Column Generation approach is here enhanced by using Constraint Programming to solve the pricing subproblem and to compute heuristic solutions. Moreover new techniques are introduced to improve the performance of the Column Generation approach in solving both the linear relaxation and the integer problem. We report extensive computational results applied to the benchmark instances: we are able to prove optimality of 11 new instances, and to improve the best known lower bounds on other 17 instances. Moreover we extend the solution approaches to a generalization of the problem known as Minimum Vertex Graph Multicoloring Problem where a given number of colors has to be assigned to each vertex.

Abstract-A fundamental and computationally challenging optimization task in wireless networks is to maximize the number of simultaneous transmissions, subject to signal-to-noise-andinterference ratio (SINR) requirements at the receivers. The conventional approach guaranteeing global optimality is to solve an integer programming model with explicit SINR constraints. These constraints are however numerically very difficult. We develop a new integer programming algorithm based on a much more effective representation of the SINR constraints. Computational experiments demonstrate that the new approach performs significantly better in proving optimality.

Various phenomena related to socio-economic aspects of our daily life exhibit equilibrium densities characterized by a power law decay. Maybe the most known example of this property is concerned with wealth distribution in a western society. In this case the polynomial decay at infinity is referred to as Pareto tails phenomenon (Pareto, Cours d’économie politique, 1964). In this paper, the authors discuss a possible source of this behavior by resorting to the powerful approach of statistical mechanics, which enlightens the analogies with the classical kinetic theory of rarefied gases. Among other examples, the distribution of populations in towns and cities is illustrated and discussed.

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