可交换随机变量序列重对数律的收敛速度

本文讨论了可交换随机变量序列{Xn:n≥1)重对数律的收敛速度,得到了可交换随机变量序列与独立序列类似的极限性质,同时给出了可交换序列重对数律收敛速度的一种描述.     

Factorization Representations in the Boundary Crossing Problems for Random Walks on a Markov Chain

Let τ be some stopping time for a random walk S _n defined on transitions of a finite Markov chain and let τ(t) be the first passage time across the level t which occurs after τ. We prove a theorem that establishes a connection between the dual Laplace-Stieltjes transforms of the joint distributions of (τ, S _τ) and (τ(t), S _τ(t)). This result applies to the study of the number of crossings of a strip by sample paths of a random walk.Original Russian Text Copyright © 2005 Lotov V. I. and Orlova N. G.The authors were partially supported by the Russian Foundation for Basic Research (Grant 05-01-00810) and the Grant Council of the President of the Russian Federation (Grant NSh-2139.2003.1).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 833–840, July–August, 2005.     

Scale-free random graphs and Potts model

We introduce a simple algorithm that constructs scale-free random graphs efficiently: each vertexi has a prescribed weight P_i ∝ i^-μ (0 < μ< 1) and an edge can connect verticesi andj with rateP _i P _j . Corresponding equilibrium ensemble is identified and the problem is solved by theq → 1 limit of the q-state Potts model with inhomogeneous interactions for all pairs of spins. The number of loops as well as the giant cluster size and the mean cluster size are obtained in the thermodynamic limit as a function of the edge density. Various critical exponents associated with the percolation transition are also obtained together with finite-size scaling forms. The process of forming the giant cluster is qualitatively different between the cases of λ > 3 and 2 < λ < 3, whereλ = 1 +μ ^-1 is the degree distribution exponent. While for the former, the giant cluster forms abruptly at the percolation transition, for the latter, however, the formation of the giant cluster is gradual and the mean cluster size for finiteN shows double peaks.     

Synthesis and characterization of poly(2‐ethylhexyl methacrylate) copolymers containing pendant,self‐complementary multiple‐hydrogen‐bonding sites

The synthesis and characterization of copolymers containing 2‐ethylhexyl methacrylate and a quadruple‐hydrogen‐bonding site, 2‐ureido‐4[1H]‐pyrimidone methacrylate (UPyMA), are described. An analogous dimeric hydrogen‐bond‐containing copolymer based on 2‐ethylhexyl methacrylate and methacrylic acid (PEHMA‐co‐MAA) was also synthesized for comparative purposes. The glass‐transition temperatures of the poly(2‐ethylhexyl methacrylate‐co‐2‐ureido‐4[1H]‐pyrimidone methacrylate) (PEHMA‐co‐UPyMA) series increased linearly with increasing UPyMA content. Creep compliance measurements as a function of temperature indicated a decrease in the creep compliance with increasing UPyMA content over the range of 1–10 mol % UPyMA. Melt rheological analysis also showed an increase and lengthening of the plateau modulus as a function of frequency with increasing UPyMA content, as well as increasing complex viscosity as a function of temperature. The analogous PEHMA‐co‐MAA copolymer, which contained 11 mol % methacrylic acid, showed, in the melt rheological analysis, behavior similar to that of the PEHMA‐co‐UPyMA copolymer containing only 1 mol % UPyMA units. The multiple‐hydrogen‐bond‐containing copolymers were successfully analyzed with time–temperature superposition for the construction of master curves. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4618–4631, 2005     

Obstacle Effects on One-Dimensional Translocation of ATPase

We apply a general random walk model to the study of the ATPase‘s one-dimensional translocation along obstacle biological environment, and show the effects of random obstacles on the ATPase translocation along single stranded DNA. We find that the obstacle environment can reduce the lifetime of ATPase lattice-bound state which results in the inhibition of ATPase activity. We also carry out the ranges of rate constant of ATPase unidirectonal translocation and bidirectional translocation. Our results are consistent with the experiments and relevant theoretical consideration, and can be used to explain some physiological phenomena.     

Art galleries with guards of uniform range of vision

We are given an art gallery represented by a simple polygon with n sides and an angle (0°,360°]. How many guards of range of vision are required to monitor every point of the polygon in the worst case? After recent results on upper bounds of this problem, we prove new lower bounds for all 0°<<180°. Several lower bounds meet the best known upper bounds, and we expect our lower bounds to be best possible.

Surprisingly, it turns out that n/3 180°-guards are always enough to monitor a polygon of n sides, but if we wish to use (180−)°-guards for any >0, then possibly 2n/3−1 guards are necessary.     

Stochastic resonance in a model of opinion formation on small-world networks

We analyze the phenomenon of stochastic resonance in an Ising-like system on a small-world network. The system, which is subject to the combined action of noise and an external modulation, can be interpreted as a stylized model of opinion formation by imitation under the effects of a “fashion wave”. Both the amplitude threshold for the detection of the external modulation and the width of the stochastic-resonance peak show considerable variation as the randomness of the underlying small-world network is changed. Received 19 December 2001     

A Berry--Esseen Type Estimate for a Weakly Associated Vector Random Field

A Berry--Esseen type estimate is established for a weakly associated vector random field when sums are taken over regularly growing sets.     

分位点随机配序抽样

该文针对统计计算中的某些随机模拟问题提出了分位点随机配序抽样法.该方法是由抽样分布的分位点和伪随机序复合构成的,适用于固定区域上多重积分的计算及随机变量的抽样.该文通过几个典型实例说明该方法在具体问题中的应用,并验证了该方法的计算精度.     

Statistical physics, optimization and source coding

The combinatorial problem of satisfying a given set of constraints that depend on N discrete variables is a fundamental one in optimization and coding theory. Even for instances of randomly generated problems, the question “does there exist an assignment to the variables that satisfies all constraints?” may become extraordinarily difficult to solve in some range of parameters where a glass phase sets in. We shall provide a brief review of the recent advances in the statistical mechanics approach to these satisfiability problems and show how the analytic results have helped to design a new class of message-passing algorithms — the survey propagation (SP) algorithms — that can efficiently solve some combinatorial problems considered intractable. As an application, we discuss how the packing properties of clusters of solutions in randomly generated satisfiability problems can be exploited in the design of simple lossy data compression algorithms.