Padrões estatísticos e dinâmicos em homicídios e métricas urbanas

Abstract

Statistical physics has proven to be fruitful to describe phenomena very far from their traditional domain. Here, we consider this framework in an attempt to understand the dynamics and statistical patterns of crime and urban metrics. In chapter 1, we characterize and analyze quantitative aspects of murders in the period from 1980 to 2009 in Brazilian cities. We find that the distribution of the annual, biannual and triannual logarithmic homicide growth rates exhibit the same functional form for distinct scales, that is, a scale invariant behavior. We also identify asymptotic power-law decay relations between the standard deviations of these three growth rates and the initial size. Further, we discuss similarities with complex organizations. In chapter 2, we report on a quantitative analysis of relationships between the number of homicides, population size and other ten urban metrics. By using data from Brazilian cities, we show that well defined average scaling laws with the population size emerge when investigating the relations between population and number of homicides as well as population and urban metrics. We also show that the fluctuations around the scaling laws are log-normally distributed, which enabled us to model these scaling laws by a stochastic-like equation driven by a multiplicative and log-normally distributed noise. Because of the scaling laws, we argue that it is better to employ logarithms in order to describe the number of homicides in function of the urban metrics via regression analysis. In addition to the regression analysis, we propose an approach to correlate crime and urban metrics via the evaluation of the distance between the actual value of the number of homicides (as well as the value of the urban metrics) and the value that is expected by the scaling law with the population size. In chapter 3, we report on the existing connection between power-law distributions and allometries. We present an extensive characterization of this connection when considering all possible pairs of relationships from twelve urban indicators of Brazilian cities. Our analyzes reveal that all twelve urban indicators are asymptotically distributed as power-laws and that, when a pair of indicators present a statistically significant allometry, the allometric exponent becomes completely defined in terms of the exponents of the power-law distributions. In addition, we have also found that the residuals fluctuations surrounding all possible allometries present an almost constant variance and log-normal distributions.