Randomness in Competitions

We study the effects of randomness on competitions based on an elementary random process in which there is a finite probability that a weaker team upsets a stronger team. We apply this model to sports leagues and sports tournaments, and compare the theoretical results with empirical data. Our model shows that single-elimination tournaments are efficient but unfair: the number of games is proportional to the number of teams N, but the probability that the weakest team wins decays only algebraically with N. In contrast, leagues, where every team plays every other team, are fair but inefficient: the top $\sqrt{N}$ of teams remain in contention for the championship, while the probability that the weakest team becomes champion is exponentially small. We also propose a gradual elimination schedule that consists of a preliminary round and a championship round. Initially, teams play a small number of preliminary games, and subsequently, a few teams qualify for the championship round. This algorithm is fair and efficient: the best team wins with a high probability and the number of games scales as $N^{9/5}$, whereas traditional leagues require N^3 games to fairly determine a champion.Comment: 10 pages, 8 figures, reviews arXiv:physics/0512144, arXiv:physics/0608007, arXiv:cond-mat/0607694, arXiv:physics/061221

Dynamics of Three Agent Games

We study the dynamics and resulting score distribution of three-agent games where after each competition a single agent wins and scores a point. A single competition is described by a triplet of numbers $p$, $t$ and $q$ denoting the probabilities that the team with the highest, middle or lowest accumulated score wins. We study the full family of solutions in the regime, where the number of agents and competitions is large, which can be regarded as a hydrodynamic limit. Depending on the parameter values $(p,q,t)$, we find six qualitatively different asymptotic score distributions and we also provide a qualitative understanding of these results. We checked our analytical results against numerical simulations of the microscopic model and find these to be in excellent agreement. The three agent game can be regarded as a social model where a player can be favored or disfavored for advancement, based on his/her accumulated score. It is also possible to decide the outcome of a three agent game through a mini tournament of two-a gent competitions among the participating players and it turns out that the resulting possible score distributions are a subset of those obtained for the general three agent-games. We discuss how one can add a steady and democratic decline rate to the model and present a simple geometric construction that allows one to write down the corresponding score evolution equations for $n$-agent games

How to Choose a Champion

League competition is investigated using random processes and scaling techniques. In our model, a weak team can upset a strong team with a fixed probability. Teams play an equal number of head-to-head matches and the team with the largest number of wins is declared to be the champion. The total number of games needed for the best team to win the championship with high certainty, T, grows as the cube of the number of teams, N, i.e., T ~ N^3. This number can be substantially reduced using preliminary rounds where teams play a small number of games and subsequently, only the top teams advance to the next round. When there are k rounds, the total number of games needed for the best team to emerge as champion, T_k, scales as follows, T_k ~N^(\gamma_k) with gamma_k=1/[1-(2/3)^(k+1)]. For example, gamma_k=9/5,27/19,81/65 for k=1,2,3. These results suggest an algorithm for how to infer the best team using a schedule that is linear in N. We conclude that league format is an ineffective method of determining the best team, and that sequential elimination from the bottom up is fair and efficient.Comment: 6 pages, 3 figure

Optimal transport on wireless networks

We present a study of the application of a variant of a recently introduced heuristic algorithm for the optimization of transport routes on complex networks to the problem of finding the optimal routes of communication between nodes on wireless networks. Our algorithm iteratively balances network traffic by minimizing the maximum node betweenness on the network. The variant we consider specifically accounts for the broadcast restrictions imposed by wireless communication by using a different betweenness measure. We compare the performance of our algorithm to two other known algorithms and find that our algorithm achieves the highest transport capacity both for minimum node degree geometric networks, which are directed geometric networks that model wireless communication networks, and for configuration model networks that are uncorrelated scale-free networks.Comment: 5 pages, 4 figure

Childhood cancer and nuclear power plants in Switzerland: a census-based cohort study

Background Previous studies on childhood cancer and nuclear power plants (NPPs) produced conflicting results. We used a cohort approach to examine whether residence near NPPs was associated with leukaemia or any childhood cancer in Switzerland. Methods We computed person-years at risk for children aged 0-15 years born in Switzerland from 1985 to 2009, based on the Swiss censuses 1990 and 2000 and identified cancer cases from the Swiss Childhood Cancer Registry. We geo-coded place of residence at birth and calculated incidence rate ratios (IRRs) with 95% confidence intervals (CIs) comparing the risk of cancer in children born 15 km away, using Poisson regression models. Results We included 2925 children diagnosed with cancer during 21 117 524 person-years of follow-up; 953 (32.6%) had leukaemia. Eight and 12 children diagnosed with leukaemia at ages 0-4 and 0-15 years, and 18 and 31 children diagnosed with any cancer were born 15 km away, the IRRs (95% CI) for leukaemia in 0-4 and 0-15 year olds were 1.20 (0.60-2.41) and 1.05 (0.60-1.86), respectively. For any cancer, corresponding IRRs were 0.97 (0.61-1.54) and 0.89 (0.63-1.27). There was no evidence of a dose-response relationship with distance (P > 0.30). Results were similar for residence at diagnosis and at birth, and when adjusted for potential confounders. Results from sensitivity analyses were consistent with main results. Conclusions This nationwide cohort study found little evidence of an association between residence near NPPs and the risk of leukaemia or any childhood cance

Mitochondria as a Target of Environmental Toxicants

Enormous strides have recently been made in our understanding of the biology and pathobiology of mitochondria. Many diseases have been identified as caused by mitochondrial dysfunction, and many pharmaceuticals have been identified as previously unrecognized mitochondrial toxicants. A much smaller but growing literature indicates that mitochondria are also targeted by environmental pollutants. We briefly review the importance of mitochondrial function and maintenance for health based on the genetics of mitochondrial diseases and the toxicities resulting from pharmaceutical exposure. We then discuss how the principles of mitochondrial vulnerability illustrated by those fields might apply to environmental contaminants, with particular attention to factors that may modulate vulnerability including genetic differences, epigenetic interactions, tissue characteristics, and developmental stage. Finally, we review the literature related to environmental mitochondrial toxicants, with a particular focus on those toxicants that target mitochondrial DNA. We conclude that the fields of environmental toxicology and environmental health should focus more strongly on mitochondri

Role of Repetitive Antigen Patterns for Induction of Antibodies Against Antibodies

Antibody responses against antibodies, such as rheumatoid factors, are found in several immunopathological diseases and may play a role in disease pathogenesis. Experience shows that they are usually difficult to induce experimentally. Antibodies specific for immunoglobulin constant regions (anti-allotypic) or for variable regions (anti-idiotypic) have been investigated in animal models; the latter have even been postulated to regulate antibody and T cell responses via network-like interactions. Why and how such anti-antibodies are induced during autoimmune diseases, has remained largely unclear. Because repetitively arranged epitopes in a paracrystalline structure of a viral envelope cross-link B cell receptors efficiently to induce a prompt T-independent IgM response, this study used immune complexes containing viruses or bacteria to evaluate the role of antigen pattern for induction of anti-antibody responses. We present evidence that antibodies bound to strictly ordered, but not to irregularly arranged, antigens dramatically enhance induction of anti-antibodies, already after a single immunization and without using adjuvants. The results indicate a novel link between anti-antibody responses and infectious agents, and suggest a similar role for repetitive self-antigens such as DNA or collagen involved in chronic immunopathological diseases