Abstract
The environmental concerns are having a significant impact on the operation of power systems. The traditional Unit Commitment problem, which to minimizes the fuel cost is inadequate when environmental emissions are also considered in the operation of power plants. This paper presents a Biased Random Key Genetic Algorithm (BRKGA) approach combined with non-dominated sorting procedure to find solutions for the unit commitment multiobjective optimization problem. In the first stage, the BRKGA solutions are encoded by using random keys, which are represented as vectors of real numbers in the interval [0,1]. In the subsequent stage, a non-dominated sorting procedure similar to NSGA II is employed to approximate the set of Pareto solution through an evolutionary optimization process. The GA proposed is a variant of the random key genetic algorithm, since bias is introduced in the parent selection procedure, as well as, in the crossover strategy. Test results with the existent benchmark systems of 10 units and 24 hours scheduling horizon are presented. The comparison of the obtained results with those of other Unit Commitment (UC) multiobjective optimization methods reveal the effectiveness of the proposed method.

Abstract
The large-scale integration of microgeneration (MG) can bring several technical benefits, such as: improving the voltage profile, reducing power losses and allowing for network capacity investment deferral. Furthermore, it is now widely accepted that introducing new renewable MG, such as wind turbines, photovoltaic panels or biomass can help control carbon emissions, reduce our dependence on oil and contribute to a sustainable energy growth. This paper presents an empirical analysis of the benefits of MG on avoided losses, voltage profiles and branch congestion. The main goal is to clarify whether the current regulatory framework allows for obtaining all the MG potential gains. The main conclusion is that some legal constraints should be removed, or at least relaxed, in order to promote the growth of distributed power generation, particularly, for domestic MG.

Abstract
We introduce the notion of golden tilings, and we prove a one-to-one correspondence between (i) smooth conjugacy classes of Anosov diffeomorphisms, with an invariant measure absolutely continuous with respect to the Lebesgue measure, (ii) affine classes of golden tilings and (iii) solenoid functions. The solenoid functions give a parametrization of the infinite dimensional space consisting of the mathematical objects described in the above equivalences.

Abstract
We use d'Aspremont and Jacquemin's strategic optimal R&D investment in a duopoly Cournot competition model to construct myopic optimal discrete and continuous R&D dynamics. We show that for some high initial production costs, the success or failure of a firm is very sensitive to small variations in its initial R&D investment strategies.

Abstract
Previous epidemiological studies on SIS model have only considered the dynamic evolution of the mean value and the variance of the infected individuals. In this paper, through cumulant neglection, we use the dynamic equations of all the moments of infected individuals to develop a recursive method to compute the equilibria manifold of the moment closure ODE's. Specifically, we use the stable equilibria of the moment closure ODE's to obtain good approximations of the quasi-stationary states of the SIS model. This is a crucial step when the quasi-stationary distribution is highly skewed.

Abstract
We show that for a specific class of random matching Edgeworthian economies, the expectation of the limiting equilibrium price coincides with the equilibrium price of the related Walrasian economies. This result extends to the study of economies in the presence of uncertainty within the multi-period Arrow-Debreu model, allowing to understand the dynamics of how beliefs survive and propagate through the market.