Speeding up the FMMR perfect sampling algorithm: A case study revisited

In a previous paper by the second author, two Markov chain Monte Carlo perfect sampling algorithms—one called coupling from the past (CFTP) and the other (FMMR) based on rejection sampling—are compared using as a case study the move‐to‐front (MTF) self‐organizing list chain. Here we revisit that case study and, in particular, exploit the dependence of FMMR on the user‐chosen initial state. We give a stochastic monotonicity result for the running time of FMMR applied to MTF and thus identify the initial state that gives the stochastically smallest running time; by contrast, the initial state used in the previous study gives the stochastically largest running time. By changing from worst choice to best choice of initial state we achieve remarkable speedup of FMMR for MTF; for example, we reduce the running time (as measured in Markov chain steps) from exponential in the length n of the list nearly down to n when the items in the list are requested according to a geometric distribution. For this same example, the running time for CFTP grows exponentially in n. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2003     

p阶平均曲率算子Dirichlet问题的无穷多个解

§ 1　 IntroductionSince the Mountain Pass Theorem came out,the existence of nontrivial solutions,pos-sibly multiple,ofnonlinear elliptic equations has been extensively studied.In this paper,weconsider the following Dirichlet problem for p-(generalized) mean curvature operator:-div((1 +| u|2 ) p- 22 u) =f(x,u) ,　 x∈Ω,u∈ W1 ,p0 (Ω ) , (1 .1 )whereΩ is a bounded domain in Rn(n>p>1 ) with smooth boundary Ω.First let us recall the following Dirichletproblem for p-Laplacian:-Δpu≡ -div…     

Strong tractability of multivariate integration using quasi-Monte Carlo algorithms

We study quasi-Monte Carlo algorithms based on low discrepancy sequences for multivariate integration. We consider the problem of how the minimal number of function evaluations needed to reduce the worst-case error from its initial error by a factor of depends on and the dimension . Strong tractability means that it does not depend on and is bounded by a polynomial in . The least possible value of the power of is called the -exponent of strong tractability. Sloan and Wozniakowski established a necessary and sufficient condition of strong tractability in weighted Sobolev spaces, and showed that the -exponent of strong tractability is between 1 and 2. However, their proof is not constructive.

In this paper we prove in a constructive way that multivariate integration in some weighted Sobolev spaces is strongly tractable with -exponent equal to 1, which is the best possible value under a stronger assumption than Sloan and Wozniakowski's assumption. We show that quasi-Monte Carlo algorithms using Niederreiter's -sequences and Sobol sequences achieve the optimal convergence order for any 0$"> independent of the dimension with a worst case deterministic guarantee (where is the number of function evaluations). This implies that strong tractability with the best -exponent can be achieved in appropriate weighted Sobolev spaces by using Niederreiter's -sequences and Sobol sequences.

     

B(A)CKLUND TRANSFORMATION ON SURFACES WITH CONSTANT MEAN CURVATURE IN R2'1

In this paper,the authors obtain the Backlund transformation on time-like surfaces with constant mean curvature in R2,1.Using this transformation,families of surfaces with constant mean curvature from known ones can be constructed.     

Halin-图的邻强边染色

图G(V,E)的正常κ-边染色f叫做图G(V,E)的κ-邻强边染色当且仅当任意uv∈E(G)满足f[u]≠f[v],其中,f[u]={f(uw)|uw∈E(G)},称f是G的κ-临强边染色,简记为κ-ASEC.并且x′_as(G)=min{k|κ-ASEC of G}叫做G(V,E)的邻强边色数.本文研究了△(G)≥5的Halin-图的邻强边色数.     

随机变量的截尾与一类强偏差定理

通过极限相对对数似然比，利用随机变量截尾的方法并结合鞅这一工具研究相依连续型和离散型随机变量序列的性质，得到一类用不等式表示的强偏差定理．     

Single-server queues with spatially distributed arrivals

Consider a queueing system where customers arrive at a circle according to a homogeneous Poisson process. After choosing their positions on the circle, according to a uniform distribution, they wait for a single server who travels on the circle. The server's movement is modelled by a Brownian motion with drift. Whenever the server encounters a customer, he stops and serves this customer. The service times are independent, but arbitrarily distributed. The model generalizes the continuous cyclic polling system (the diffusion coefficient of the Brownian motion is zero in this case) and can be interpreted as a continuous version of a Markov polling system. Using Tweedie's lemma for positive recurrence of Markov chains with general state space, we show that the system is stable if and only if the traffic intensity is less than one. Moreover, we derive a stochastic decomposition result which leads to equilibrium equations for the stationary configuration of customers on the circle. Steady-state performance characteristics are determined, in particular the expected number of customers in the system as seen by a travelling server and at an arbitrary point in time.     

Overall values of conventional discrepancy indices for related and unrelated models of a non-centrosymmetric crystal with a centrosymmetric group

Theoretical expressions for the overall values of the conventional discrepancy indicesR(F) andR(I) are derived for a non-centrosymmetric crystal with a centrosymmetric group by taking the centrosymmetric group and a part of the other atoms in the unit cell as the trial structure. These results are used to obtain tables of values of these indices in terms of the parameter σ _1c ² and σ ₁ ² which define the fractional contribution to the local mean intensity from the centrosymmetric group and all the known atoms respectively. Contribution No. 561     

STRONG DERIVATIVE AND ITS CONSEQUENCES

We introduce strong derivative, the corresponding Z-integrable and other related concepts. Also, we give an improved version of the fundamental theorem of calculus.     

关于3维Minkowski空间中类空曲面的若干结果

在本文，我们证明２维黎曼流形能实现为Ｌ３中的类空极大曲面的充要条件是相应的Ｒｉｃｃｉ条件成立，此外还确定了Ｌ３中其平均曲率向量ｈ满足条件△ｈ＝λｈ（λ∈Ｒ）的类空曲面