Atividade psicomotora, epidemias e lideranças como sistemas complexos

Abstract

In this thesis, we analyzed complex systems using statistical physics tools applied in empirical data. This work is divided into three chapters. Each chapter is dedicated to a type of complex system. In the first one, we analyzed the reaction times needed by individual during the performance of a psychomotor activity that comprised a large number of tasks performed without interruption, this being a cognitive system. We investigated learning in terms of the mean values and their variability. In a broader scenario, we have shown that learning can be associated with a scale factor acting on the reaction times. In addition to these universal patterns, we have verified that performance not displays persistence, but their differences in the absolute values and signs presented. In the second chapter, in a biological context, we reported a statistical analysis of dengue cases numbers in all Brazilian cities over a period of 12 years. We presented the distributions in the cities and their relationship with the population, and its dependence on longitude and latitude. We have characterized the spatial correlation of the number of dengue cases between pairs of cities and have modeled our results based on the Edwards-Wilkinson equation with a fractional spatial derivative. In the third chapter, we performed a study among countries on the times series composed of the term period of successive political and religious leaders, as an example of social system. We have analyzed the characteristic average time in office, how it varied on the time series and the differences amount the types of leaders and their variabilities. We also studied the distributions of time series comparing to with a power law and a Weibull distribution. And finally, the DFA method was applied and we observed long-range correlations on many cases studied.