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In this paper, the problem of power efficiency evaluation for n -ports physical systems is investigated. The efficiency analysis that we perform highlights the necessary and sufficient conditions for the system to be passive, and outlines the guidelines for the efficiency maps computation. After addressing the problem from a formal point of view, the analysis is deepened for the case of two-ports linear and nonlinear physical systems, and for the cases of three and four-ports linear systems. The efficiency analysis and the computation of the efficiency maps are addressed as a function of the power variables characterizing all the energetic ports of the considered systems. Furthermore, the salient properties of the efficiency are highlighted and discussed. The theoretical analysis which is developed is then applied to some physical systems of interest for industries and engineers working in the electromechanical, hydraulic and automotive fields: a DC electric motor driving an hydraulic pump for the two-ports systems class, a single-stage planetary gear set for the three-ports systems class, and a Ravigneaux planetary gear set for the four-ports systems class. • Power efficiency modeling and efficiency maps computation for physical systems. • Interchangeable efficiency maps computed on the different systems energetic ports. • Highlighting of intrinsic properties and of a design parameter for two-ports systems. • Efficiency maps computation and intrinsic characteristics of planetary gear sets. [ABSTRACT FROM AUTHOR]

In this paper we build a network-based model to evaluate and compare vaccination plans in order to find the optimal strategies. The age-structured model is designed to take into account the comorbidity status and vaccination hesitancy of the population. The network-based model is calibrated to reported infected cases and deaths in the USA in order to obtain an approximated realistic scenario to test the vaccination strategies. We adapt an algorithm that is based on Bayesian optimization over permutation spaces with heuristics in order to deal with the discrete space of the vaccination strategies. We also developed an ad-hoc randomized algorithm which has a higher computational cost. Both algorithms provide similar patterns of the best found vaccination strategies. We find that these best vaccination plans prioritize the age-groups 40–59 and 60–69 years old, both with comorbidities. This result shows the highly nonlinear complexity related to the problem and its dependence on social contacts and case fatality rates. The developed network-based model adapts well to the uncertainty and heterogeneity of the real world situation and allows us to assess the efficacy of many vaccination strategies. The stochastic nature of the simulations enables us to explore additional potential scenarios and the findings offer useful information for developing vaccination plans for other future potential pandemics. [ABSTRACT FROM AUTHOR]