Population Monte Carlo algorithms

We give a cross-disciplinary survey on ``population'' Monte Carlo algorithms. In these algorithms, a set of ``walkers'' or ``particles'' is used as a representation of a high-dimensional vector. The computation is carried out by a random walk and split/deletion of these objects. The algorithms are developed in various fields in physics and statistical sciences and called by lots of different terms -- ``quantum Monte Carlo'', ``transfer-matrix Monte Carlo'', ``Monte Carlo filter (particle filter)'',``sequential Monte Carlo'' and ``PERM'' etc. Here we discuss them in a coherent framework. We also touch on related algorithms -- genetic algorithms and annealed importance sampling.Comment: Title is changed (Population-based Monte Carlo -> Population Monte Carlo). A number of small but important corrections and additions. References are also added. Original Version is read at 2000 Workshop on Information-Based Induction Sciences (July 17-18, 2000, Syuzenji, Shizuoka, Japan). No figure

An Effective-Medium Tight-Binding Model for Silicon

A new method for calculating the total energy of Si systems is presented. The method is based on the effective-medium theory concept of a reference system. Instead of calculating the energy of an atom in the system of interest a reference system is introduced where the local surroundings are similar. The energy of the reference system can be calculated selfconsistently once and for all while the energy difference to the reference system can be obtained approximately. We propose to calculate it using the tight-binding LMTO scheme with the Atomic-Sphere Approximation(ASA) for the potential, and by using the ASA with charge-conserving spheres we are able to treat open system without introducing empty spheres. All steps in the calculational method is {\em ab initio} in the sense that all quantities entering are calculated from first principles without any fitting to experiment. A complete and detailed description of the method is given together with test calculations of the energies of phonons, elastic constants, different structures, surfaces and surface reconstructions. We compare the results to calculations using an empirical tight-binding scheme.Comment: 26 pages (11 uuencoded Postscript figures appended), LaTeX, CAMP-090594-