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In this work, we study the impact of considering agents with distinct norm heterogeneity tolerance levels, and with distinct initial levels of thinking, in the evolution of social norms and levels of thinking in an artificial society. To this end, we generalize an agent-based model first proposed by Joshua M. Epstein to consider agents with distinct tolerance levels to norm heterogeneity in their neighborhoods. In this model, agents that are located in a cyclic network can choose between two norms, want to conform to their neighborhoods, and decide how much to think—i.e., how many neighbors to consult in deciding which norm to follow—analyzing the norm heterogeneity in their surroundings. Through computer simulations of the model, we obtain the following results: (i) when agents have distinct levels of tolerance, the society converges, for a wide range of initial levels of thinking, to a steady state showing higher global diversity (measured by the number of stable local groups formed at the steady state, where contiguous agents within each group conform to the same norm) associated with higher levels of thinking than in scenarios where all agents have the same tolerance level; (ii) for lower initial levels of thinking, more initial thinking implies in faster convergence to the steady state in the cases of heterogeneous tolerance levels, and when agents present homogeneous maximum intolerance levels; (iii) in all scenarios, more thinking is required in the process of reaching the steady state (the equilibrium of the model), than to maintain this equilibrium afterward; (iv) our model was able to generate distinct average levels of thinking across groups; and (v), higher levels of initial thinking imply in a society with less global diversity at the steady state, with this inverse relationship following a broken power law. Finally, we show that some of our results are similar to results presented in the literature.

This paper presents a new frequency estimator algorithm for electric power systems that uses the Mathematical Morphology operators of dilation and erosion to predict the Clarke Components from voltage signals of three phases of the system. The frequency is obtained as a function of phase shift between the predicted complex signal and the received complex signal given by the αβ-Transformation. The proposed method presented great accuracy and fast convergence for a wide range of different operational conditions involving transitory events of frequency deviation, amplitude variations, signal phase shifts and stable power swings. In addition, signals distorted by noises, harmonics and inter-harmonics were also tested. In order to demonstrate the quality of the new frequency estimator in each analyzed case, its estimation was compared with the responses obtained by four other methods, in terms of performance indices based on the estimation of transitory error and response convergence time. For all analyzed cases, the proposed methodology presented better results, showing great robustness and high accuracy for its task.