Universality of Level Spacing Distributions in Classical Chaos

We suggest that random matrix theory applied to a classical action matrix can be used in classical physics to distinguish chaotic from non-chaotic behavior. We consider the 2-D stadium billiard system as well as the 2-D anharmonic and harmonic oscillator. By unfolding of the spectrum of such matrix we compute the level spacing distribution, the spectral auto-correlation and spectral rigidity. We observe Poissonian behavior in the integrable case and Wignerian behavior in the chaotic case. We present numerical evidence that the action matrix of the stadium billiard displays GOE behavior and give an explanation for it. The findings present evidence for universality of level fluctuations - known from quantum chaos - also to hold in classical physics

A Study on the Evolution of Bayesian Network Graph Structures

Abstract. Bayesian Networks (BN) are often sought as useful descriptive and predictive models for theavaHable data. Learning algorithms trying to ascertain automatically the best BN model (graph structure) for some input data are of the greatest interest for practical reasons. In this paper we examine a number of evolutionary programming algorithms for this network induction problem. Our algorithms build on recent advances in the field and are based on selection and various kinds of mutation operators (working at both the directed acyclic and essential graph level). A review of related evolutionary work is also provided. We analyze and discuss the merit and computational toll of these EP algorithms in a couple of benchmark tasks. Some general conclusions'about the most efficient algorithms, and the most appropriate search landscapes are presented.

Modeling of the atomic ordering processes in Fe3Al intermetallics by the monte carlo simulation method combined with electronic theory of alloys

The evolution of atomic ordering processes in Fe3Al has been modeled by the Monte Carlo (MC) simulation method combined with the electronic theory of alloys in pseudopotential approximation. The magnitude of atomic ordering energies of atomic pairs in the Fe3Al system has been calculated by means of electronic theory in pseudopotential approximation up to sixth coordination spheres and subsequently used as input data for MC simulation for more detailed analysis for the first time. The Bragg–Williams long-range order (LRO) and Cowley–Warren short-range order (SRO) parameters have been calculated from the equilibrium configurations attained at the end of MC simulation for each predefined temperature and Al concentration levels, which reveal the evolution of the system from DO3 → B2 → disordered state as temperature increases. The variation of ordering parameters with temperature has identified the transition temperature from DO3 → B2 type superlattice, and from B2 → disordered (a) solid solution at about 540 °C and .900 °C, respectively, showing good qualitative agreement with experimental results. The results of the present study imply that combination of electronic theory of alloys in pseudopotential approximation with MC simulation can be successfully applied for qualitative or semiquantitative analysis of energetical and structural characteristics of atomic ordering processes in Fe3Al intermetallics