We introduce a new update scheme to systematically improve the efficiency of parallel tempering simulations. We show that by adapting the number of sweeps between replica exchanges to the canonical autocorrelation time, the average round-trip time of
a replica in temperature space can be significantly decreased. The temperatures are not dynamically adjusted as in previous attempts but chosen to yield a 50% exchange rate of adjacent replicas. We illustrate the new algorithm with results for the Ising model in two and the Edwards-Anderson Ising spin glass in three dimensions
Analyzing football score data with statistical techniques, we investigate how the highly co-operative nature of the game is reflected in averaged properties such as the distributions of scored goals for the home and away teams. It turns out that in p
articular the tails of the distributions are not well described by independent Bernoulli trials, but rather well modeled by negative binomial or generalized extreme value distributions. To understand this behavior from first principles, we suggest to modify the Bernoulli random process to include a simple component of self-affirmation which seems to describe the data surprisingly well and allows to interpret the observed deviation from Gaussian statistics. The phenomenological distributions used before can be understood as special cases within this framework. We analyzed historical football score data from many leagues in Europe as well as from international tournaments and found the proposed models to be applicable rather universally. In particular, here we compare mens and womens leagues and the separate German leagues during the cold war times and find some remarkable differences.
