Scaling laws in the dynamics of crime growth rate

The increasing number of crimes in areas with large concentrations of people have made cities one of the main sources of violence. Understanding characteristics of how crime rate expands and its relations with the cities size goes beyond an academic question, being a central issue for contemporary society. Here, 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.Comment: Accepted for publication in Physica

Spreading Patterns of the Influenza A (H1N1) Pandemic

We investigate the dynamics of the 2009 influenza A (H1N1/S-OIV) pandemic by analyzing data obtained from World Health Organization containing the total number of laboratory-confirmed cases of infections - by country - in a period of 69 days, from 26 April to 3 July, 2009. Specifically, we find evidence of exponential growth in the total number of confirmed cases and linear growth in the number of countries with confirmed cases. We also find that, i) at early stages, the cumulative distribution of cases among countries exhibits linear behavior on log-log scale, being well approximated by a power law decay; ii) for larger times, the cumulative distribution presents a systematic curvature on log-log scale, indicating a gradual change to lognormal behavior. Finally, we compare these empirical findings with the predictions of a simple stochastic model. Our results could help to select more realistic models of the dynamics of influenza-type pandemics

Studies in quantum electrodynamics in 2 +1 dimensions

Nesta tese estudamos algumas propriedades da eletrodinamica em 2+1 dimensoes. Perturbativamente, esta teoria e inconsistente, devido a ocorrencia de fortes divergencias infravermelhas. E mostrado que tal problemas pode ser sanado quando efeitos nao perturbativos de polarizacao do vacuo sao incorporados, promovendo a melhoria do comportamento infravermelho da teoria. Isto e decorrente da geracao de um termo de chern-simons. Analisamos, tambem, a existencia de estados ligados fermion-fermion, a qual pode ser relevante no contexto da supercondutividade a altas temperaturas. Alem disso, obtemos a contribuicao para o momento magnetico anomalo do fermio vinda da correcao de vertice. Uma motivacao para este trabalho advem de estudos feitos originalmente para o modelo de thirring em 2+1 dimensoes, os quais sao apresentados na parte inicial desta tese.In this thesis we study some properties of electrodynamics in 2+ 1 dimensions. Perturbatively, inconsistencies appear, due to strong infrared divergencies. It is shown that this problem can be overcome when vacuum polarization effects are nonperturbatively incorporated, leading to a better infrared behavior of the theory. This is a consequence of the generation of a Chern-Simons term. Also, we analyse the existence of fermion-fermion bound states, which may be relevant for high-Tc superconductivity. Furthermore, from the vertex corrections we determine the contribution for the fermion anomalous magnetic moment. A motivation for this work comes from earlier studies in the context of the 2+ 1 dimentional Thirring model. Those studies are presented in the initial part of this thesis

Some aspects of 1/n expansion in quantum mechanics and field theory

Alguns aspectos da expansão 1/n em mecânica quântica e teoria de camposSome aspects of 1/n expansion in quantum mechanics and field theor

Studies in quantum electrodynamics in 2 +1 dimensions

Nesta tese estudamos algumas propriedades da eletrodinamica em 2+1 dimensoes. Perturbativamente, esta teoria e inconsistente, devido a ocorrencia de fortes divergencias infravermelhas. E mostrado que tal problemas pode ser sanado quando efeitos nao perturbativos de polarizacao do vacuo sao incorporados, promovendo a melhoria do comportamento infravermelho da teoria. Isto e decorrente da geracao de um termo de chern-simons. Analisamos, tambem, a existencia de estados ligados fermion-fermion, a qual pode ser relevante no contexto da supercondutividade a altas temperaturas. Alem disso, obtemos a contribuicao para o momento magnetico anomalo do fermio vinda da correcao de vertice. Uma motivacao para este trabalho advem de estudos feitos originalmente para o modelo de thirring em 2+1 dimensoes, os quais sao apresentados na parte inicial desta tese.In this thesis we study some properties of electrodynamics in 2+ 1 dimensions. Perturbatively, inconsistencies appear, due to strong infrared divergencies. It is shown that this problem can be overcome when vacuum polarization effects are nonperturbatively incorporated, leading to a better infrared behavior of the theory. This is a consequence of the generation of a Chern-Simons term. Also, we analyse the existence of fermion-fermion bound states, which may be relevant for high-Tc superconductivity. Furthermore, from the vertex corrections we determine the contribution for the fermion anomalous magnetic moment. A motivation for this work comes from earlier studies in the context of the 2+ 1 dimentional Thirring model. Those studies are presented in the initial part of this thesis

Random Walks Associated with Nonlinear Fokker–Planck Equations

A nonlinear random walk related to the porous medium equation (nonlinear Fokker–Planck equation) is investigated. This random walk is such that when the number of steps is sufficiently large, the probability of finding the walker in a certain position after taking a determined number of steps approximates to a q-Gaussian distribution ( G q , β ( x ) ∝ [ 1 − ( 1 − q ) β x 2 ] 1 / ( 1 − q ) ), which is a solution of the porous medium equation. This can be seen as a verification of a generalized central limit theorem where the attractor is a q-Gaussian distribution, reducing to the Gaussian one when the linearity is recovered ( q → 1 ). In addition, motivated by this random walk, a nonlinear Markov chain is suggested

<b>Continuous Time Random Walk and different diffusive regimes</b> - doi: 10.4025/actascitechnol.v34i2.11521

<p class="aresumo">We investigate how it is possible to obtain different diffusive regimes from the Continuous Time Random Walk (CTRW) approach performing suitable changes for the waiting time and jumping distributions in order to get two or more regimes for the same diffusive process. We also obtain diffusion-like equations related to these processes and investigate the connection of the results with anomalous diffusion.</p><p class="apalavrachave"> </p

Solutions of Some Nonlinear Diffusion Equations and Generalized Entropy Framework

We investigate solutions of a generalized diffusion equation that contains nonlinear terms in the presence of external forces and reaction terms. The solutions found here can have a compact or long tail behavior and can be expressed in terms of the q-exponential functions present in the Tsallis framework. In the case of the long-tailed behavior, in the asymptotic limit, these solutions can also be connected with the L´evy distributions. In addition, from the results presented here, a rich class of diffusive processes, including normal and anomalous ones, can be obtained