Strong tractability of integration using scrambled Niederreiter points

We study the randomized worst-case error and the randomized error of scrambled quasi-Monte Carlo (QMC) quadrature as proposed by Owen. The function spaces considered in this article are the weighted Hilbert spaces generated by Haar-like wavelets and the weighted Sobolev-Hilbert spaces. Conditions are found under which multivariate integration is strongly tractable in the randomized worst-case setting and the randomized setting, respectively. The -exponents of strong tractability are found for the scrambled Niederreiter nets and sequences. The sufficient conditions for strong tractability for Sobolev spaces are more lenient for scrambled QMC quadratures than those for deterministic QMC net quadratures.

     

Associated primes of local cohomology modules

Let be an ideal of a commutative Noetherian ring and a finitely generated -module. Let be a natural integer. It is shown that there is a finite subset of , such that is contained in union with the union of the sets , where and . As an immediate consequence, we deduce that the first non- -cofinite local cohomology module of with respect to has only finitely many associated prime ideals.

     

The Fibonacci sequence modulo π, chaos and some rational recursive equations

In this paper, we provide the closed form solution to the inter-related equations

     

Berezinians,Exterior Powers and Recurrent Sequences

We study power expansions of the characteristic function of a linear operator A in a p|q-dimensional superspace V. We show that traces of exterior powers of A satisfy universal recurrence relations of period q. ‘Underlying’ recurrence relations hold in the Grothendieck ring of representations of GL(V). They are expressed by vanishing of certain Hankel determinants of order q+1 in this ring, which generalizes the vanishing of sufficiently high exterior powers of an ordinary vector space. In particular, this allows to express the Berezinian of an operator as a ratio of two polynomial invariants. We analyze the Cayley–Hamilton identity in a superspace. Using the geometric meaning of the Berezinian we also give a simple formulation of the analog of Cramer’s rule Mathematics Subject Classification (2000): 15A15, 58A50, 81R99 To the memory of Felix Alexandrovich Berezin     

Dynamic ℤ d -Random Walks in a Random Scenery: A Strong Law of Large Numbers

In this paper, we study a _d -random walk on nearest neighbours with transition probabilities generated by a dynamical system . We prove, at first, that under some hypotheses, verifies a local limit theorem. Then, we study these walks in a random scenery , a sequence of independent, identically distributed and centred random variables and show that for certain dynamic random walks, satisfies a strong law of large numbers.     

Statistical Dynamics of Clustering in the Genome Structure

Clustering and long-range correlations in the nucleotide sequences of different categories of organisms are discussed. Clustering, mostly observed in higher eucaryotes, can be found at different length scales in DNA and Central Limit Theorems are used as links between these length scales. Several dynamical, statistical, mean-field models are proposed based on biologically motivated dynamical mechanisms and they successfully reproduce both the short range behavior observed in coding DNA and the long range, out-of-equilibrium features of non-coding DNA. Such dynamical mechanisms include aggregation of oligonucleotides, influx and DNA length reduction schemes, transpositions, and fusions of large DNA macromolecules. Fractality can be inferred from the short and long range correlations observed in the sequence structure of higher eucaryotes, where the non-coding part is relatively extended. In these organisms the DNA coding/non-coding alternation has the characteristics of finite size, fractal, random sets.     

Fast convergence of quasi-Monte Carlo for a class of isotropic integrals

We consider the approximation of -dimensional weighted integrals of certain isotropic functions. We are mainly interested in cases where is large. We show that the convergence rate of quasi-Monte Carlo for the approximation of these integrals is . Since this is a worst case result, compared to the expected convergence rate of Monte Carlo, it shows the superiority of quasi-Monte Carlo for this type of integral. This is much faster than the worst case convergence, , of quasi-Monte Carlo.

     

基于极坐标的相向运动图像模糊的递归模型

成像过程中,被摄像目标和摄像机之间的相向运动会造成图像的辐射状模糊,辐射状模糊将减小有效视场,影响成像质量.本文在扇形网格采样的基础上,利用状态空间模型模拟了退化过程,用递归方法解决了空变问题,并利用对状态空间系统求逆的方法对退化图像进行了复原.计算机模拟显示,算法简单,复原图像清晰,取得了较满意的结果.     

Meeting the Welch and Karystinos-Pados Bounds on DS-CDMA Binary Signature Sets

The Welch lower bound on the total-squared-correlation (TSC) of binary signature sets is loose for binary signature sets whose length L is not a multiple of 4. Recently Karystinos and Pados [6,7] developed new bounds that are better than the Welch bound in those cases, and showed how to achieve the bounds with modified Hadamard matrices except in a couple of cases. In this paper, we study the open cases.