S. Picoli

q-exponential, Weibull, and q-Weibull distributions: an empirical analysis

In a comparative study, the q-exponential and Weibull distributions are employed to investigate frequency distributions of basketball baskets, cyclone victims, brand-name drugs by retail sales, and highway length. In order to analyze the intermediate cases, a distribution, the q-Weibull one, which interpolates the q-exponential and Weibull ones, is introduced. It is verified that the basketball baskets distribution is well described by a q-exponential, whereas the cyclone victims and brand-name drugs by retail sales ones are better adjusted by a Weibull distribution. On the other hand, for highway length the q-exponential and Weibull distributions do not give satisfactory adjustment, being necessary to employ the q-Weibull distribution. Furthermore, the introduction of this interpolating distribution gives an illumination from the point of view of the stretched exponential against inverse power law (q-exponential with q>1) controversy.

q-distributions in complex systems: a brief review

The nonextensive statistical mechanics proposed by Tsallis is today an intense and growing research field. Probability distributions which emerges from the nonextensive formalism(q-distributions) have been applied to an impressive variety of problems. In particular, the role of q-distributions in the interdisciplinary field of complex systems has been expanding. Here, we make a brief review of q-exponential, q-Gaussian and q-Weibull distributions focusing some of their basic properties and recent applications. The richness of systems analyzed may indicate future directions in this field.

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 (QBD) and/or time-to-breakdown (tBD) 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 (tBD) data when oxide thickness fluctuations are present, in order to improve reliability assessment of ultra-thin oxides by time-to-breakdown (tBD) 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 tBD data of SiO2-based MOS devices obtained experimentally and theoretically through a percolation model, demonstrating an advantageous description of the dielectric breakdown by the q-Weibull distribution.

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 scale-free network can be connected to this universal behavior.

Analogies Between the Cracking Noise of Ethanol-Dampened Charcoal and Earthquakes

We report on an extensive characterization of the cracking noise produced by charcoal samples when dampened with ethanol. We argue that the evaporation of ethanol causes transient and irregularly distributed internal stresses that promote the fragmentation of the samples and mimic some situations found in mining processes. The results show that, in general, the most fundamental seismic laws ruling earthquakes (the Gutenberg-Richter law, the unified scaling law for the recurrence times, Omoris law, the productivity law, and Båths law) hold under the conditions of the experiment. Some discrepancies were also identified (a smaller exponent in the Gutenberg-Richter law, a stationary behavior in the aftershock rates for long times, and a double power-law relationship in the productivity law) and are related to the different loading conditions. Our results thus corroborate and elucidate the parallel between the seismic laws and fracture experiments caused by a more complex loading condition that also occurs in natural and induced seismicity (such as long-term fluid injection and gas-rock outbursts in mining processes).

Dynamics of tournaments: the soccer case

A random walk-like model is considered to discuss statistical aspects of tournaments. The model is applied to soccer leagues with emphasis on the scores. This competitive system was computationally simulated and the results are compared with empirical data from the English, the German and the Spanish leagues and showed a good agreement with them. The present approach enabled us to characterize a diffusion where the scores are not normally distributed, having a short and asymmetric tail extending towards more positive values. We argue that this non-Gaussian behavior is related with the difference between the teams and with the asymmetry of the scores system. In addition, we compared two tournament systems: the all-play-all and the elimination tournaments.

Similarities between the dynamics of geomagnetic signal and of heartbeat intervals

We analyze the dynamics of a widely used measure of geomagnetic activity —the Dst index— and compare our findings with those found in healthy human heartbeat dynamics. We show that the Dst index belongs to a special class of complex signals, exhibiting long-range temporal correlations, multifractality and scale-invariant distribution. Specifically, we find that i) Dst series and magnitude series of Dst increments are long-range correlated while the sign series of Dst increments is anti-correlated; ii) the scaling exponents that govern these temporal correlations increase with geomagnetic activity; iii) Dst series exhibit multifractal behavior; iv) the multifractal spectra that characterize Dst series are practically independent of the geomagnetic activity; and v) the distribution of Dst increments exhibits scale invariance at a wide range of time scales. These results are in surprising agreement with those found in the study of heartbeat intervals. Our findings are consistent with the concept of universality in complex systems and may contribute to a better understanding of the mechanisms that govern geomagnetic activity.

Universal bursty behaviour in human violent conflicts

Understanding the mechanisms and processes underlying the dynamics of collective violence is of considerable current interest. Recent studies indicated the presence of robust patterns characterizing the size and timing of violent events in human conflicts. Since the size and timing of violent events arises as the result of a dynamical process, we explore the possibility of unifying these observations. By analyzing available catalogs on violent events in Iraq (2003–2005), Afghanistan (2008–2010) and Northern Ireland (1969–2001), we show that the inter-event time distributions (calculated for a range of minimum sizes) obeys approximately a simple scaling law which holds for more than three orders of magnitude. This robust pattern suggests a hierarchical organization in size and time providing a unified picture of the dynamics of violent conflicts.

Engagement in the electoral processes: scaling laws and the role of political positions.

We report on a statistical analysis of the engagement in the electoral processes of all Brazilian cities by considering the number of party memberships and the number of candidates for mayor and councillor. By investigating the relationships between the number of party members and the population of voters, we have found that the functional forms of these relationships are well described by sublinear power laws (allometric scaling) surrounded by a multiplicative log-normal noise. We have observed that this pattern is quite similar to those we previously reported for the relationships between the number of candidates (mayor and councillor) and population of voters [Europhys. Lett. 96, 48001 (2011)], suggesting that similar universal laws may be ruling the engagement in the electoral processes. We also note that the power-law exponents display a clear hierarchy, where the more influential is the political position the smaller is the value of the exponent. We have also investigated the probability distributions of the number of candidates (mayor and councillor), party memberships, and voters. The results indicate that the most influential positions are characterized by distributions with very short tails, while less influential positions display an intermediate power-law decay before showing an exponential-like cutoff. We discuss the possibility that, in addition to the political power of the position, limitations in the number of available seats can also be connected with this changing of behavior. We further believe that our empirical findings point out to an under-representation effect, where the larger the city is, the larger are the obstacles for more individuals to become directly engaged in the electoral process.

Earthquake-like patterns of acoustic emission in crumpled plastic sheets

We report remarkable similarities in the output signal of two distinct out-of-equilibrium physical systems —earthquakes and the intermittent acoustic noise emitted by crumpled plastic sheets, i.e. Biaxially Oriented Polypropylene (BOPP) films. We show that both signals share several statistical properties including the distribution of energy, distribution of energy increments for distinct time scales, distribution of return intervals and correlations in the magnitude and sign of energy increments. This analogy is consistent with the concept of universality in complex systems and could provide some insight on the mechanisms behind the complex behavior of earthquakes.