Roberto N. Onody

Complex network study of Brazilian soccer players

Although being a very popular sport in many countries, soccer has not received much attention from the scientific community. In this paper, we study soccer from a complex network point of view. First, we consider a bipartite network with two kinds of vertices or nodes: the soccer players and the clubs. Real data were gathered from the 32 editions of the Brazilian soccer championship, in a total of 13 411 soccer players and 127 clubs. We find a lot of interesting and perhaps unsuspected results. The probability that a Brazilian soccer player has worked at N clubs or played M games shows an exponential decay while the probability that he has scored G goals is power law. Now, if two soccer players who have worked at the same club at the same time are connected by an edge, then a new type of network arises (composed exclusively by soccer player nodes). Our analysis shows that for this network the degree distribution decays exponentially. We determine the exact values of the clustering coefficient, the assortativity coefficient and the average shortest path length and compare them with those of the Erdös-Rényi and configuration model. The time evolution of these quantities are calculated and the corresponding results discussed.

Experimental studies of the fingering phenomena in two dimensions and simulation using a modified invasion percolation model

Experiments of water infiltration in a vertical plane through layered soils were carried out in the laboratory. We have followed the fingering dynamics by using image techniques. The fractal theory has been applied to describe the fingering phenomena. We also have simulated a modified site gradient invasion percolation model where most of the physical ingredients relevant to the problem have been incorporated. In contrast to what occurs with the standard gradient invasion percolation model, we have found the formation of many fingers. Taking into account the bond number, the number of fingers, and the wetted area of the experiments, we have fitted the parameters of our model. This opens the possibility of a theoretical prediction of the pore size distribution of the soil. The results are then compared with the experimental data.

Heumann-Hötzel model for aging revisited.

Since its proposition in 1995, the Heumann-Hötzel model has remained as an obscure model of biological aging. The main arguments used against it were its apparent inability to describe populations with many age intervals and its failure to prevent a population extinction when only deleterious mutations are present. We find that with a simple and minor change in the model these difficulties can be surmounted. Our numerical simulations show a plethora of interesting features: the catastrophic senescence, the Gompertz law and that postponing the reproduction increases the survival probability, as has already been experimentally confirmed for the drosophila fly.

Series expansion of the directed percolation probability

Using a transfer-matrix technique the authors obtain extended series expansion of the percolation probability for the directed site percolation problem on the square lattice. Their approach reveals a previously unsuspected connection between his problem and the enumeration of the number of ways of dissecting a ball. They show that the method can also be used to determine a series expansion for the mean cluster size. An analysis based on Pade approximants gives estimates of the critical threshold and also of the critical exponent beta .

Nonlinear Barabási–Albert network

In recent years there has been considerable interest in the structure and dynamics of complex networks. One of the most studied networks is the linear Barabasi–Albert model. Here we investigate the nonlinear Barabasi–Albert growing network. In this model, a new node connects to a vertex of degree k with a probability proportional to kα (α real). Each vertex adds m new edges to the network. We derive an analytic expression for the degree distribution P(k) which is valid for all values of m and α⩽1. In the limit α→−∞ the network is homogeneous. If α>1 there is a gel phase with m super-connected nodes. It is proposed a formula for the clustering coefficient which is in good agreement with numerical simulations. The assortativity coefficient r is determined and it is shown that the nonlinear Barabasi–Albert network is assortative (disassortative) if α 1) and no assortative only when α=1. In the limit α→−∞ the assortativity coefficient can be exactly calculated. We find r=713 when m=2. Finally, the minimum average shortest path length lmin is numerically evaluated. Increasing the network size, lmin diverges for α⩽1 and it is equal to 1 when α>1.

Optimization and self-organized criticality in a magnetic system

We propose a kind of Bak–Sneppen dynamics as a general optimization technique to treat magnetic systems. The resulting dynamics shows self-organized criticality with power-law scaling of the spatial and temporal correlations. An alternative method of the extremal optimization (EO) is also analyzed here. We provided a numerical confirmation that, for any possible value of its free parameter τ, the EO dynamics exhibits a non-critical behavior with an infinite spatial range and exponential decay of the avalanches. Using the chiral clock model as our test system, we compare the efficiency of the two dynamics with regard to their abilities to find the systems ground state.

Cluster, backbone, and elastic backbone structures of the multiple invasion percolation

We study the cluster, the backbone, and the elastic backbone structures of the multiple invasion percolation for both the perimeter and the optimized versions. We investigate the behavior of the mass, the number of red sites ~i.e., sites through which all the current passes !, and loops of those structures. Their corresponding scaling exponents are also estimated. By construction, the mass of the optimized model scales exactly with the gyration radius of the cluster—we verify that this also happens to the backbone. Our simulation shows that the red sites almost disappear, indicating that the cluster has achieved a high degree of connectivity. @S1063-651X~97!14908-X#

Directed bond percolation on the honeycomb lattice

Using a transfer matrix method the authors derive a series expansion for the percolation probability on the directed honeycomb lattice. The high-density series is obtained to order q13. A Pade approximant analysis of the series has been used to estimate the percolation threshold qc and the critical exponent beta .

Fluid Flow In A Directed Porous Media

We present a modified site invasion percolation with a biased growth rule to model a fluid flow in porous media with a privileged direction. The effects of the modifications are systematically analyzed in computer simulations and a number of characteristics parameters such as acceptance profiles and linear mass density are obtained. The asymptotic behavior and scaling relations are also discussed and the associated exponents are numerically estimated.

SELF-ORGANIZED CRITICALITY, OPTIMIZATION AND BIODIVERSITY

By driving to extinction species that are less or poorly adapted, the Darwinian evolutionary theory is intrinsically an optimization theory. We investigate two optimization algorithms with such evolutionary characteristics: the Bak–Sneppen and the Extremal Optimization. By comparing their mean fitness in the steady state regime, we conclude that the Bak–Sneppen dynamics is more efficient than the Extremal Optimization if the parameter τ is in the interval [0, 0.86]. The determination of the spatial correlation and the probability distribution of the avalanches show that the Extremal Optimization dynamics does not lead the system into a critical self-organized state. Through a discrete form of the Bak–Sneppen model we argue that biodiversity is an essential prerequisite to preserve the self-organized criticality.We propose a kind of Bak–Sneppen dynamics as a general optimization technique to treat 9 magnetic systems. The resulting dynamics shows self-organized criticality with power-law scaling of the spatial and temporal correlations. An alternative method of the extremal optimization (EO) 11 is also analyzed here. We provided a numerical con3rmation that, for any possible value of its free parameter , the EO dynamics exhibits a non-critical behavior with an in3nite spatial range 13 and exponential decay of the avalanches. Using the chiral clock model as our test system, we compare the e5ciency of the two dynamics with regard to their abilities to 3nd the system’s 15 ground state. c