Teste de validade de métodos de maximização de entropia para construção de modelos com correlação par-a-par

Abstract

In the 21st century humanity has produced more new data (information) than in all its history. Understanding the nature of the various systems that generate this abundance of data has became the great challenge of this century. One way to formally analyze these large databases is to use the information theory developed by Claude Shannon. This theory allows us, using the principle of maximum entropy, to find the distributions of probabilities that best describes the collective behavior of these systems. In this dissertation we discuss the possibility of using Ising models to describe observation of real systems. Due to its limitations, employing the Ising model implies that the elements that constitute the real system can only be in two states, for example active or inactive. In addition, the Ising model counts only interactions between pairs of elements and disregards the possibility of interactions between larger groups of elements. As we will discuss, even with these limitations such a model can well describe results observed in some natural systems, such as networks of neurons. Specifically, we discuss results from earlier work that show that using only the activity averages of each neuron and the correlation between them, using Shannon’s theory, we observe that the states visited by the network follow the Ising distribution. In order to test the applicability of this method in several systems we generate synthetic data, obtained from Ising model in three systems: ferromagnetic, antiferromagnetic and spin glass. We call the system that generate the synthetic data as underlying system. We use methods of maximization of entropy to try to construct model systems that can reproduce the mean and correlations observed in the synthetic data. We thus verify in which situations our methods can actually generate a model system that reproduces the underlying system that generated the data. These results may establish a limit of applicability for the technique discussed.