48 research outputs found
Universal Finite-Size-Scaling Functions
The idea of universal finite-size-scaling functions of the Ising model is
tested by Monte Carlo simulations for various lattices. Not only regular
lattices such as the square lattice but quasiperiodic lattices such as the
Penrose lattice are treated. We show that the finite-size-scaling functions of
the order parameter for various lattices are collapsed on a single curve by
choosing two nonuniversal scaling metric factors. We extend the idea of the
universal finite-size-scaling functions to the order-parameter distribution
function. We pay attention to the effects of boundary conditions.
Keywords: Universal Finite-Size-Scaling Function; Ising Model;
Order-Parameter Probability Distribution Function.Comment: 8 pages, Figures are available at
http://glimmung.phys.sci.osaka-u.ac.jp/kikuchi/preprints.html or they will be
sent upon request by e-mai
How to estimate the number of self-avoiding walks over 10^100? Use random walks
Counting the number of N-step self-avoiding walks (SAWs) on a lattice is one
of the most difficult problems of enumerative combinatorics. Once we give up
calculating the exact number of them, however, we have a chance to apply
powerful computational methods of statistical mechanics to this problem. In
this paper, we develop a statistical enumeration method for SAWs using the
multicanonical Monte Carlo method. A key part of this method is to expand the
configuration space of SAWs to random walks, the exact number of which is
known. Using this method, we estimate a number of N-step SAWs on a square
lattice, c_N, up to N=256. The value of c_256 is 5.6(1)*10^108 (the number in
the parentheses is the statistical error of the last digit) and this is larger
than one googol (10^100).Comment: 5 pages, 3 figures, 1 table, to appear in proceedings of YSMSPIP in
Senda
Evolution enhances mutational robustness and suppresses the emergence of a new phenotype: A new computational approach for studying evolution
The aim of this paper is two-fold. First, we propose a new computational method to investigate the particularities of evolution. Second, we apply this method to a model of gene regulatory networks (GRNs) and explore the evolution of mutational robustness and bistability. Living systems have developed their functions through evolutionary processes. To understand the particularities of this process theoretically, evolutionary simulation (ES) alone is insufficient because the outcomes of ES depend on evolutionary pathways. We need a reference system for comparison. An appropriate reference system for this purpose is an ensemble of the randomly sampled genotypes. However, generating high-fitness genotypes by simple random sampling is difficult because such genotypes are rare. In this study, we used the multicanonical Monte Carlo method developed in statistical physics to construct a reference ensemble of GRNs and compared it with the outcomes of ES. We obtained the following results. First, mutational robustness was significantly higher in ES than in the reference ensemble at the same fitness level. Second, the emergence of a new phenotype, bistability, was delayed in evolution. Third, the bistable group of GRNs contains many mutationally fragile GRNs compared with those in the non-bistable group. This suggests that the delayed emergence of bistability is a consequence of the mutation-selection mechanism.Kaneko T., Kikuchi M.. (2022) Evolution enhances mutational robustness and suppresses the emergence of a new phenotype: A new computational approach for studying evolution. PLoS Computational Biology 18(1): e1009796. doi: 10.1371/journal.pcbi.1009796