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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(More)
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(More)
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 conÿrmation that, for any(More)
The time evolution of the Partridge-Barton model in the presence of the pleiotropic constraint and deleterious somatic mutations is exactly solved for arbitrary fecundity in the context of a matricial formalism. Analytical expressions for the time dependence of the mean survival probabilities are derived. Using the fact that the asymptotic behavior for(More)
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(More)
We introduce an age-structured asexual population model containing all the relevant features of evolutionary aging theories. Beneficial as well as deleterious mutations, heredity, and arbitrary fecundity are present and managed by natural selection. An exact solution without aging is found. We show that fertility is associated with generalized forms of the(More)
We study the optimized version of the multiple invasion percolation model. Some topo-logical aspects as the behavior of the acceptance profile, coordination number and vertex type abundance were investigated and compared to those of the ordinary invasion. Our results indicate that the clusters show a very high degree of connectivity, spoiling the usual(More)