Identificação e modelagem de padrões em sistemas complexos - Ribeiro, Haroldo Valentin (2012)
This thesis is focused on the study and modeling of different complex systems. The systems investigated here were analyzed by using the "physics lens" and are all based on observational, experimental or simulated data. In chapter 1, we investigated the sounds cape dynamics of human agglomeration where we showed that these noises have a non trivial dynamics with non-Gaussian, non-exponential, power-law distributions and long-range correlations. We also showed that an autoregressive model can reproduce most of the empirical findings and that is possible to distinguish between pacific and violent sounds capes. In chapter 2, we reported studies on musical sounds where the distribution of the sound amplitudes was fitted by a stretched gaussian and the parameter of the distribution gives information about the quality of the music. We also saw that there is a kind of coupling between the shape of the distribution and the long-range correlations. We analyzed the ordinal patterns in these sounds using the complexity-entropy causality plane and we employed a supported vector machine to identify the music genres of our dataset. We further investigate the evolution of these patterns over the years for a set of popular songs where we suggest that the songs are becoming more statistically poor. In chapter 3, we studied the dynamics of the advantage in chess matches by using a diffusive approach which revealed several anomalous features and a population-level learning of the game. We have also verified that the error distribution of players follows a log-normal distribution and that to note the mistakes is very important for wining the match. In chapter 4, we analyzed the scores of the game of cricket through a diffusive approach. We verified that the process is super-diffusive, long-range correlated and self-similar; all these features were modeled using a generalized Lange in equation. In chapter 5, we investigated the bubble dynamics in boiling water thought an experiment in which laser beam was scattered by bubbles in the boiling fluid. We found that there are long-range correlations in the laser intensity and that the return intervals are exponentially distributed. A simple model suggests that the main ingredients for this non-trivial dynamics are the correlation and power-law distribution related to the time interval in which bubbles passes through the optical path. Finally, in chapter 6, we have proposed an extension of the complexity-entropy causality plane for measuring the complexity of two-dimensional patterns such as images. Our extension was worked out for fractal surfaces, textures of liquid crystals, and Ising surfaces where we proved the usefulness of our extension.