Mixing time and simulated annealing for the stochastic cellular automata

Finding a ground state of a given Hamiltonian on a graph $G=(V,E)$ is an important but hard problem. One of the potential approaches is to use a Markov chain Monte Carlo to sample the Gibbs distribution whose highest peaks correspond to the ground states. In this paper, we investigate a particular kind of stochastic cellular automata, in which all spins are updated independently and simultaneously. We prove that (i) if the temperature is fixed sufficiently high, then the mixing time is at most of order $\log|V|$, and that (ii) if the temperature drops in time $n$ as $1/\log n$, then the limiting measure is uniformly distributed over the ground states.Comment: 16 pages, 8 figure

Urinary excretion of 3-phenoxybenzoic acid in middle-aged and elderly general population of Japan

Nagoya University, Department of Medical Technology金沢大学附属病院薬剤部Limited data are available on the background levels of exposure to synthetic pyrethroid (PYR) in Japan, despite their frequent application for agriculture and indoor extermination and possible effects of chronic and/or low-dose PYR exposure on human health. This study was conducted to describe the level and distribution of one of the major PYR metabolites, 3-phenoxybenzoic acid (3-PBA), in urine samples collected from a general population in Japan. The subjects were 535 individuals (184 men and 351 women; 61.5±9.8 years of age, mean±S.D.) residing in a town in Hokkaido, a dairy and agricultural area. Urinary 3-PBA was found detectable in 98% of samples above the limit of detection of 0.02 μg/l. The geometric mean values of urinary 3-PBA in occupationally exposed farmers (n=87) and the remaining general group without occupational exposure (n=448) were 0.38 and 0.29 μg/l, respectively, ranging from <LOD to 17.09 μg/l. No significant differences in urinary 3-PBA concentrations were shown between these two groups. Moreover, 3-PBA concentrations were found comparable to those reported in some countries. The present study is, to our knowledge, the first report of a biological monitoring study of urinary 3-PBA, which elucidated the background environmental exposure level of PYR in the Japanese general population without occupational exposure. Further nationwide studies covering different seasons and age distribution are needed to monitor the urinary 3-PBA levels in Japan

Mean-field behavior of nearest-neighbor oriented percolation on the BCC lattice above 8+18+1 dimensions

In this paper, we consider nearest-neighbor oriented percolation with independent Bernoulli bond-occupation probability on the $d$-dimensional body-centered cubic (BCC) lattice $\mathbb{L}^d$ and the set of non-negative integers $\mathbb{Z}_+$. Thanks to the orderly structure of the BCC lattice, we prove that the infrared bound holds on $\mathbb{L}^d\times\mathbb{Z}_+$ in all dimensions $d\geq 9$. As opposed to ordinary percolation, we have to deal with complex numbers due to asymmetry induced by time-orientation, which makes it hard to bound the bootstrap functions in the lace-expansion analysis. By investigating the Fourier-Laplace transform of the random-walk Green function and the two-point function, we derive the key properties to obtain the upper bounds and resolve a problematic issue in Nguyen and Yang's bound. The issue is caused by the fact that the Fourier transform of the random-walk transition probability can take the value $-1$.Comment: 41 pages, a lot of figures with Tik

Stochastic Optimization : Glauber Dynamics Versus Stochastic Cellular Automata

The topic we address in this paper concerns the minimization of a Hamiltonian function for an Ising model through the application of simulated annealing algorithms based on (single-site) Glauber dynamics and stochastic cellular automata (SCA). Some rigorous results are presented in order to justify the application of simulated annealing for a particular kind of SCA. After that, we compare the SCA algorithm and its variation, namely the ε-SCA algorithm, studied in this paper with the Glauber dynamics by analyzing their accuracy in obtaining optimal solutions for the max-cut problem on Erdös-Rényi random graphs, the traveling salesman problem (TSP), and the minimization of Gaussian and Bernoulli spin glass Hamiltonians. We observed that the SCA performed better than the Glauber dynamics in some special cases, while the ε-SCA showed the highest performance in all scenarios

Stochastic Optimization : Glauber Dynamics Versus Stochastic Cellular Automata

The topic we address in this paper concerns the minimization of a Hamiltonian function for an Ising model through the application of simulated annealing algorithms based on (single-site) Glauber dynamics and stochastic cellular automata (SCA). Some rigorous results are presented in order to justify the application of simulated annealing for a particular kind of SCA. After that, we compare the SCA algorithm and its variation, namely the ε-SCA algorithm, studied in this paper with the Glauber dynamics by analyzing their accuracy in obtaining optimal solutions for the max-cut problem on Erdös-Rényi random graphs, the traveling salesman problem (TSP), and the minimization of Gaussian and Bernoulli spin glass Hamiltonians. We observed that the SCA performed better than the Glauber dynamics in some special cases, while the ε-SCA showed the highest performance in all scenarios