Biomedical subjects
Publications and source records attributed to Heiko Bauke.
Energy spectra of disordered systems share a common feature: If the entropy of the quenched disorder is larger than the entropy of the dynamical variables, the spectrum is locally that of a random energy model and the correlation between energy and configuration is lost. We demonstrate this effect for the Edwards-Anderson model, but we also discuss its universality.
Since the work of Phys. Rev. Lett. 69, 3382 (1992)]] some pseudo-random-number generators are known to yield wrong results in cluster Monte Carlo simulations. In this contribution the fundamental mechanism behind this failure is discussed. Almost all random-number generators calculate a new pseudo-random-number x(i) from preceding values, x(i) =f( x(i-1), x(i-2), ..., x(i-q) ). Failure of these generators in cluster Monte Carlo simulations and related experiments can be attributed to the low entropy of the production rule f() conditioned on the statistics of the input values x(i-1), ..., x(i-q). Being a measure only of the arithmetic operations in the generator rule, the conditional entropy is independent of the lag in the recurrence or the period of the sequence. In that sense it measures a more profound quality of a random-number generator than empirical tests with their limited horizon.
An "easy-hard" phase transition is shown to characterize the multiprocessor scheduling problem in which one has to distribute the workload on a parallel computer such as to minimize the overall run time. The transition can be analyzed in detail by mapping it on a mean-field antiferromagnetic Potts model. The static phase transition, characterized by a vanishing ground state entropy, corresponds to a transition in the performance of practical scheduling algorithms.