Sequential Sampling with Bias and Re-Sampling: Reaction-Diffusion Systems, Sequence Alignment, and Lattice Animals

Peter Grassberger

NIC, Forschungszentrum Jülich, 52425 Juelich, Germany

After giving a short review of the general concept of sequential sampling ("go with the winners", "Russian roulette & splitting", "PERM", ...), I shall discuss three applications which show the wide range of applications of this method. In the first I will treat the long-time properties of the reaction A+B -> B, with particles A diffusing and with B either diffusing or stationary. The second application will deal with estimating the singificance of sequence alignments by generating (biased) random alignments. The final problem will be that of counting the number of n-site clusters on a lattice ("lattice animals") and studying various phase transitions when the mere counting is replaced by weighted counting with the weights given by Boltzmann factors corresponding to non-zero contact energies. In all these cases the method will be more efficient than alternative sampling methods based on the Markov chain Monte Carlo concept.