ﻻ يوجد ملخص باللغة العربية
We propose a novel algorithm that outputs the final standings of a soccer league, based on a simple dynamics that mimics a soccer tournament. In our model, a team is created with a defined potential(ability) which is updated during the tournament according to the results of previous games. The updated potential modifies a teams future winning/losing probabilities. We show that this evolutionary game is able to reproduce the statistical properties of final standings of actual editions of the Brazilian tournament (Brasileir~{a}o). However, other leagues such as the Italian and the Spanish tournaments have notoriously non-Gaussian traces and cannot be straightforwardly reproduced by this evolutionary non-Markovian model. A complete understanding of these phenomena deserves much more attention, but we suggest a simple explanation based on data collected in Brazil: Here several teams were crowned champion in previous editions corroborating that the champion typically emerges from random fluctuations that partly preserves the gaussian traces during the tournament. On the other hand, in the Italian and Spanish leagues only a few teams in recent history have won their league tournaments. These leagues are based on more robust and hierarchical structures established even before the beginning of the tournament. For the sake of completeness, we also elaborate a totally Gaussian model (which equalizes the winning, drawing, and losing probabilities) and we show that the scores of the Brasileir~{a}o cannot be reproduced. Such aspects stress that evolutionary aspects are not superfluous in our modeling. Finally, we analyse the distortions of our model in situations where a large number of teams is considered, showing the existence of a transition from a single to a double peaked histogram of the final classification scores. An interesting scaling is presented for different sized tournaments.
Recent studies show that in interdependent networks a very small failure in one network may lead to catastrophic consequences. Above a critical fraction of interdependent nodes, even a single node failure can invoke cascading failures that may abrupt
We study the avalanche statistics observed in a minimal random growth model. The growth is governed by a reproduction rate obeying a probability distribution with finite mean a and variance va. These two control parameters determine if the avalanche
For any branching process, we demonstrate that the typical total number $r_{rm mp}( u tau)$ of events triggered over all generations within any sufficiently large time window $tau$ exhibits, at criticality, a super-linear dependence $r_{rm mp}( u tau
An efficient technique is introduced for model inference of complex nonlinear dynamical systems driven by noise. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is robust in a b
We have studied the distribution of traffic flow $q$ for the Nagel-Schreckenberg model by computer simulations. We applied a large-deviation approach, which allowed us to obtain the distribution $P(q)$ over more than one hundred decades in probabilit