A Simple Non-Markovian Computational Model of the Statistics of Soccer Leagues: Emergence and Scaling effects

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.Comment: 18 pages, 9 figure

Ambiguity and public good provision in large societies

ArticleIn this paper, we consider the effect of ambiguity on the private provision of public goods. Equilibrium is shown to exist and be unique. We examine how provision of the public good changes as the size of the population increases. We show that when there is uncertainty, there may be less free-riding in large societies

The efficiency of individual optimization in the conditions of competitive growth

The paper aims to discuss statistical properties of the multi-agent based model of competitive growth. Each of the agents is described by growth (or decay) rule of its virtual "mass" with the rate affected by the interaction with other agents. The interaction depends on the strategy vector and mutual distance between agents and both are subjected to the agent's individual optimization process. Steady-state simulations yield phase diagrams with the high and low competition phases (HCP and LCP, respectively) separated by critical point. Particular focus has been made on the indicators of the power-law behavior of the mass distributions with respect to the critical regime. In this regime the study has revealed remarkable anomaly in the optimization efficiency

The problem of shot selection in basketball

In basketball, every time the offense produces a shot opportunity the player with the ball must decide whether the shot is worth taking. In this paper, I explore the question of when a team should shoot and when they should pass up the shot by considering a simple theoretical model of the shot selection process, in which the quality of shot opportunities generated by the offense is assumed to fall randomly within a uniform distribution. I derive an answer to the question "how likely must the shot be to go in before the player should take it?", and show that this "lower cutoff" for shot quality $f$ depends crucially on the number $n$ of shot opportunities remaining (say, before the shot clock expires), with larger $n$ demanding that only higher-quality shots should be taken. The function $f(n)$ is also derived in the presence of a finite turnover rate and used to predict the shooting rate of an optimal-shooting team as a function of time. This prediction is compared to observed shooting rates from the National Basketball Association (NBA), and the comparison suggests that NBA players tend to wait too long before shooting and undervalue the probability of committing a turnover.Comment: 7 pages, 2 figures; comparison to NBA data adde

Activity-dependent heteromerization of the hyperpolarization-activated, cyclic-nucleotide gated (HCN) channels: role of N-linked glycosylation.

Formation of heteromeric complexes of ion channels via co-assembly of different subunit isoforms provides an important mechanism for enhanced channel diversity. We have previously demonstrated co-association of the hyperpolarization activated cyclic-nucleotide gated (HCN1/HCN2) channel isoforms that was regulated by network (seizure) activity in developing hippocampus. However, the mechanisms that underlie this augmented expression of heteromeric complexes have remained unknown. Glycosylation of the HCN channels has been implicated in the stabilization and membrane expression of heteromeric HCN1/HCN2 constructs in heterologous systems. Therefore, we used in vivo and in vitro systems to test the hypothesis that activity modifies HCN1/HCN2 heteromerization in neurons by modulating the glycosylation state of the channel molecules. Seizure-like activity (SA) increased HCN1/HCN2 heteromerization in hippocampus in vivo as well as in hippocampal organotypic slice cultures. This activity increased the abundance of glycosylated HCN1 but not HCN2-channel molecules. In addition, glycosylated HCN1 channels were preferentially co-immunoprecipitated with the HCN2 isoforms. Provoking SA in vitro in the presence of the N-linked glycosylation blocker tunicamycin abrogated the activity-dependent increase of HCN1/HCN2 heteromerization. Thus, hippocampal HCN1 molecules have a significantly higher probability of being glycosylated after SA, and this might promote a stable heteromerization with HCN2

Runaway Events Dominate the Heavy Tail of Citation Distributions

Statistical distributions with heavy tails are ubiquitous in natural and social phenomena. Since the entries in heavy tail have disproportional significance, the knowledge of its exact shape is very important. Citations of scientific papers form one of the best-known heavy tail distributions. Even in this case there is a considerable debate whether citation distribution follows the log-normal or power-law fit. The goal of our study is to solve this debate by measuring citation distribution for a very large and homogeneous data. We measured citation distribution for 418,438 Physics papers published in 1980-1989 and cited by 2008. While the log-normal fit deviates too strong from the data, the discrete power-law function with the exponent $\gamma=3.15$ does better and fits 99.955% of the data. However, the extreme tail of the distribution deviates upward even from the power-law fit and exhibits a dramatic "runaway" behavior. The onset of the runaway regime is revealed macroscopically as the paper garners 1000-1500 citations, however the microscopic measurements of autocorrelation in citation rates are able to predict this behavior in advance.Comment: 6 pages, 5 Figure

The immune cell infiltrate populating meningiomas is composed of mature, antigen-experienced T and B cells

BACKGROUND: Meningiomas often harbor an immune cell infiltrate that can include substantial numbers of T and B cells. However, their phenotype and characteristics remain undefined. To gain a deeper understanding of the T and B cell repertoire in this tumor, we characterized the immune infiltrate of 28 resected meningiomas representing all grades. METHODS: Immunohistochemistry was used to grossly characterize and enumerate infiltrating lymphocytes. A molecular analysis of the immunoglobulin variable region of tumor-infiltrating B cells was used to characterize their antigen experience. Flow cytometry of fresh tissue homogenate and paired peripheral blood lymphocytes was used to identify T cell phenotypes and characterize the T cell repertoire. RESULTS: A conspicuous B and T cell infiltrate, primarily clustered in perivascular spaces, was present in the microenvironment of most tumors examined. Characterization of 294 tumor-infiltrating B cells revealed clear evidence of antigen experience, in that the cardinal features of an antigen-driven B cell response were present. Meningiomas harbored populations of antigen-experienced CD4+ and CD8+ memory/effector T cells, regulatory T cells, and T cells expressing the immune checkpoint molecules PD-1 and Tim-3, indicative of exhaustion. All of these phenotypes were considerably enriched relative to their frequency in the circulation. The T cell repertoire in the tumor microenvironment included populations that were not reflected in paired peripheral blood. CONCLUSION: The tumor microenvironment of meningiomas often includes postgerminal center B cell populations. These tumors invariably include a selected, antigen-experienced, effector T cell population enriched by those that express markers of an exhausted phenotype