Growth patterns and scaling laws governing AIDS epidemic in Brazilian cities

Brazil holds approximately 1/3 of population living infected with AIDS (acquired immunodeficiency syndrome) in Central and South Americas, and it was also the first developing country to implement a large-scale control and intervention program against AIDS epidemic. In this scenario, we investigate the temporal evolution and current status of the AIDS epidemic in Brazil. Specifically, we analyze records of annual absolute frequency of cases for more than 5000 cities for the first 33 years of the infection in Brazil. We found that (i) the annual absolute frequencies exhibit a logistic-type growth with an exponential regime in the first few years of the AIDS spreading; (ii) the actual reproduction number decaying as a power law; (iii) the distribution of the annual absolute frequencies among cities decays with a power law behavior; (iv) the annual absolute frequencies and the number of inhabitants have an allometric relationship; (v) the temporal evolution of the annual absolute frequencies have different profile depending on the average annual absolute frequencies in the cities. These findings yield a general quantitative description of the AIDS infection dynamics in Brazil since the beginning. They also provide clues about the effectiveness of treatment and control programs against the infection, that has had a different impact depending on the number of inhabitants of cities. In this framework, our results give insights into the overall dynamics of AIDS epidemic, which may contribute to select empirically accurate models.Comment: 12 pages, 6 figure

Scaling laws and universality in the choice of election candidates

Nowadays there is an increasing interest of physicists in finding regularities related to social phenomena. This interest is clearly motivated by applications that a statistical mechanical description of the human behavior may have in our society. By using this framework, we address this work to cover an open question related to elections: the choice of elections candidates (candidature process). Our analysis reveals that, apart from the social motivations, this system displays features of traditional out-of-equilibrium physical phenomena such as scale-free statistics and universality. Basically, we found a non-linear (power law) mean correspondence between the number of candidates and the size of the electorate (number of voters), and also that this choice has a multiplicative underlying process (lognormal behavior). The universality of our findings is supported by data from 16 elections from 5 countries. In addition, we show that aspects of network scale-free can be connected to this universal behavior.Comment: Accepted for publication in EP

An Improved Description of the Dielectric Breakdown in Oxides Based on a Generalized Weibull distribution

In this work, we address modal parameter fluctuations in statistical distributions describing charge-to-breakdown $(Q_{BD})$ and/or time-to-breakdown $(t_{BD})$ during the dielectric breakdown regime of ultra-thin oxides, which are of high interest for the advancement of electronic technology. We reobtain a generalized Weibull distribution ($q$-Weibull), which properly describes $(t_{BD})$ data when oxide thickness fluctuations are present, in order to improve reliability assessment of ultra-thin oxides by time-to-breakdown $(t_{BD})$ extrapolation and area scaling. The incorporation of fluctuations allows a physical interpretation of the $q$-Weibull distribution in connection with the Tsallis statistics. In support to our results, we analyze $t_{BD}$ data of SiO$_2$-based MOS devices obtained experimentally and theoretically through a percolation model, demonstrating an advantageous description of the dielectric breakdown by the $q$-Weibull distribution.Comment: 5 pages, 3 figure

Statistical Laws Governing Fluctuations in Word Use from Word Birth to Word Death

We analyze the dynamic properties of 10^7 words recorded in English, Spanish and Hebrew over the period 1800--2008 in order to gain insight into the coevolution of language and culture. We report language independent patterns useful as benchmarks for theoretical models of language evolution. A significantly decreasing (increasing) trend in the birth (death) rate of words indicates a recent shift in the selection laws governing word use. For new words, we observe a peak in the growth-rate fluctuations around 40 years after introduction, consistent with the typical entry time into standard dictionaries and the human generational timescale. Pronounced changes in the dynamics of language during periods of war shows that word correlations, occurring across time and between words, are largely influenced by coevolutionary social, technological, and political factors. We quantify cultural memory by analyzing the long-term correlations in the use of individual words using detrended fluctuation analysis.Comment: Version 1: 31 pages, 17 figures, 3 tables. Version 2 is streamlined, eliminates substantial material and incorporates referee comments: 19 pages, 14 figures, 3 table

Evolution of scaling emergence in large-scale spatial epidemic spreading

Background: Zipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings on the dependence between these two scalings, which is still hardly been clarified. Methodology/Principal Findings: In this article, we observe an evolution process of the scalings: the Zipf's law and the Heaps' law are naturally shaped to coexist at the initial time, while the crossover comes with the emergence of their inconsistency at the larger time before reaching a stable state, where the Heaps' law still exists with the disappearance of strict Zipf's law. Such findings are illustrated with a scenario of large-scale spatial epidemic spreading, and the empirical results of pandemic disease support a universal analysis of the relation between the two laws regardless of the biological details of disease. Employing the United States(U.S.) domestic air transportation and demographic data to construct a metapopulation model for simulating the pandemic spread at the U.S. country level, we uncover that the broad heterogeneity of the infrastructure plays a key role in the evolution of scaling emergence. Conclusions/Significance: The analyses of large-scale spatial epidemic spreading help understand the temporal evolution of scalings, indicating the coexistence of the Zipf's law and the Heaps' law depends on the collective dynamics of epidemic processes, and the heterogeneity of epidemic spread indicates the significance of performing targeted containment strategies at the early time of a pandemic disease.Comment: 24pages, 7figures, accepted by PLoS ON

Statistical properties of the circulation of magazines and newspapers

We analyze data sets containing the circulation of magazines and newspapers. We show that the cumulative distribution follows, in the range of large circulation, a power law behavior whose exponent is $\mu\simeq 1.5$; and deviations from the asymptotic power law behavior can be well described by a q-exponential distribution (Zipf-Mandelbrot law) from Tsallis statistics. We also show that, in the range of large circulation, the distribution of logarithmic growth rates is consistent with an exponential; and the standard deviation of the growth rates is practically independent of the circulation (size). Moreover, we employ a model, inspired in one of the simplest model for firm growth, in order to reproduce some of our findings

A non-Gaussian model in polymeric network

We investigate a finite chain approximation, the non-Gaussian Tsallis distribution, to the polymeric network, which gives an improvement to the Gaussian model. This distribution presents some necessary characteristics, like a cutoff to the maximum chain length and a continuous limit to the Gaussian one for a large number of monomers. It also presents a simple quadratic structure that allows to generalize the Gaussian properties such as exact-moments calculation and Wick theorem. We obtain the free-energy density in its full tensorial structure