The Adaptive Behavior of a Soccer Team: An Entropy-Based Analysis.

To optimize its performance, a competitive team, such as a soccer team, must maintain a delicate balance between organization and disorganization. On the one hand, the team should maintain organized patterns of behavior to maximize the cooperation between its members. On the other hand, the team's behavior should be disordered enough to mislead its opponent and to maintain enough degrees of freedom. In this paper, we have analyzed this dynamic in the context of soccer games and examined whether it is correlated with the team's performance. We measured the organization associated with the behavior of a soccer team through the Tsallis entropy of ball passes between the players. Analyzing data taken from the English Premier League (2015/2016), we show that the team's position at the end of the season is correlated with the team's entropy as measured with a super-additive entropy index. Moreover, the entropy score of a team significantly contributes to the prediction of the team's position at the end of the season beyond the prediction gained by the team's position at the end of the previous season.

Identifying the location of a concealed object through unintentional eye movements.

In some investigative and interrogative contexts, the investigator is seeking to identify the location of an object (e.g., implanted bomb) which is known to a given subject (e.g., a terrorist). In this paper, we present a non-intrusive methodology for uncovering the loci of a concealed object by analyzing the subject's eye movements. Using a combination of eye tracking, psychological manipulation and a search algorithm, we have performed two experiments. In the first experiment, we have gained 58% hit rate in identifying the location of the concealed object and in the second experiment 56% hit rate. The pros and cons of the methodology for forensic investigation are discussed.

Coarse-graining of cellular automata, emergence, and the predictability of complex systems.

We study the predictability of emergent phenomena in complex systems. Using nearest-neighbor, one-dimensional cellular automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's classification. The resulting coarse-grained CA that we construct are capable of emulating the large-scale behavior of the original systems without accounting for small-scale details. Several CA that can be coarse-grained by this construction are known to be universal Turing machines; they can emulate any CA or other computing devices and are therefore undecidable. We thus show that because in practice one only seeks coarse-grained information, complex physical systems can be predictable and even decidable at some level of description. The renormalization group flows that we construct induce a hierarchy of CA rules. This hierarchy agrees well with apparent rule complexity and is therefore a good candidate for a complexity measure and a classification method. Finally we argue that the large-scale dynamics of CA can be very simple, at least when measured by the Kolmogorov complexity of the large-scale update rule, and moreover exhibits a novel scaling law. We show that because of this large-scale simplicity, the probability of finding a coarse-grained description of CA approaches unity as one goes to increasingly coarser scales. We interpret this large-scale simplicity as a pattern formation mechanism in which large-scale patterns are forced upon the system by the simplicity of the rules that govern the large-scale dynamics.

Computational irreducibility and the predictability of complex physical systems.

Using elementary cellular automata (CA) as an example, we show how to coarse grain CA in all classes of Wolfram's classification. We find that computationally irreducible physical processes can be predictable and even computationally reducible at a coarse-grained level of description. The resulting coarse-grained CA which we construct emulate the large-scale behavior of the original systems without accounting for small-scale details. At least one of the CA that can be coarse grained is irreducible and known to be a universal Turing machine.

Novel continuum modeling of crystal surface evolution.

We propose a novel approach to continuum modeling of the dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual approach where the continuum limit is achieved when typical surface features consist of many steps, our continuum limit is approached when the number of step configurations of the ensemble is very large. The model can handle singular surface structures such as corners and facets. It has a clear computational advantage over discrete models.