On Moments of k-Records from Discrete Distributions

In this article, we establish recurrence relations satisfied by first and second moments of k-records arising from discrete distributions. Then we use these relations to obtain means, variances, and correlation coefficients of geometric k-records. We consider all the three known types of k-records: strong, ordinary, and weak.     

Efficiency of a Class of Unbiased Estimators for the Invariant Distribution Function of a Diffusion Process

We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly consistent and efficient in different metrics. Here we study the properties of optimality for another kind of estimator recently proposed. We consider a class of unbiased estimators and we show that they are also efficient in the sense that their asymptotic risk, defined as the integrated mean square error, attains the same asymptotic minimax lower bound of the empirical distribution function.     

Finding longest increasing and common subsequences in streaming data

We present algorithms and lower bounds for the Longest Increasing Subsequence (LIS) and Longest Common Subsequence (LCS) problems in the data-streaming model. To decide if the LIS of a given stream of elements drawn from an alphabet αbet has length at least k, we discuss a one-pass algorithm using O(k log αbetsize) space, with update time either O(log k) or O(log log αbetsize); for αbetsize = O(1), we can achieve O(log k) space and constant-time updates. We also prove a lower bound of Ω(k) on the space requirement for this problem for general alphabets αbet, even when the input stream is a permutation of αbet. For finding the actual LIS, we give a ⌈log (1 + 1/ɛ)-pass algorithm using O(k^1+ɛlog αbetsize) space, for any ɛ > 0. For LCS, there is a trivial Θ(1)-approximate O(log n)-space streaming algorithm when αbetsize = O(1). For general alphabets αbet, the problem is much harder. We prove several lower bounds on the LCS problem, of which the strongest is the following: it is necessary to use Ω(n/ρ²) space to approximate the LCS of two n-element streams to within a factor of ρ, even if the streams are permutations of each other. A preliminary version of this paper appears in the Proceedings of the 11th International Computing and Combinatorics Conference (COCOON'05), August 2005, pp. 263–272.     

实数上限拓扑空间在拓扑教学中的应用

实数上限拓扑空间是一个简单、直观的拓扑空间．在拓扑学教学中，利用该拓扑空间可以淡化一些抽象的、逻辑性强的概念和理论，引导学生严密、深刻地思考问题，从而达到知识的完全理解和掌握．在总结教学经验的基础上，本文讨论实数上限拓扑空间在四个方面的应用．     

Lower bounds of various criteria in experimental designs

Criterion is essential for measuring the goodness of an experimental design. In this paper, lower bounds of various criteria in experimental designs will be reviewed according to methodology of their construction. The criteria include most well-known ones which are frequently used as benchmarks for orthogonal array, uniform design, supersaturated design and other types of designs. To derive the lower bounds of these criteria, five different approaches are explored. Some new results are given. Throughout the paper, some relationships among different types of lower bounds are also discussed.     

期货套期保值理论及模型的研究进展

文章按照基于均值-方差资产定价理论框架下的套期保值理论和基于下侧风险框架的套期保值理论这两个发展阶段,回顾了套期保值理论及模型的发展,并进一步评述了各类模型的理论基础、应用、存在的不足及未来研究方向。     

On E(s)-optimal supersaturated designs

A popular measure to assess 2-level supersaturated designs is the E(s²)$E(s^2)$ criterion. In this paper, improved lower bounds on E(s²)$E(s^2)$ are obtained. The same improvement has recently been established by Ryan and Bulutoglu [2007. E(s²)$E(s^2)$-optimal supersaturated designs with good minimax properties. J. Statist. Plann. Inference 137, 2250–2262]. However, our analysis provides more details on precisely when an improvement is possible, which is lacking in Ryan and Bulutoglu [2007. E(s²)$E(s^2)$-optimal supersaturated designs with good minimax properties. J. Statist. Plann. Inference 137, 2250–2262]. The equivalence of the bounds obtained by Butler et al. [2001. A general method of constructing E(s²)$E(s^2)$-optimal supersaturated designs. J. Roy. Statist. Soc. B 63, 621–632] (in the cases where their result applies) and those obtained by Bulutoglu and Cheng [2004. Construction of E(s²)$E(s^2)$-optimal supersaturated designs. Ann. Statist. 32, 1662–1678] is established. We also give two simple methods of constructing E(s²)$E(s^2)$-optimal designs.     

A new recombination lower bound and the minimum perfect phylogenetic forest problem

Understanding recombination is a central problem in population genetics. In this paper, we address an established computational problem in this area: compute lower bounds on the minimum number of historical recombinations for generating a set of sequences (Hudson and Kaplan in Genetics 111, 147–164, 1985; Myers and Griffiths in Genetics 163, 375–394, 2003; Gusfield et al. in Discrete Appl. Math. 155, 806–830, 2007; Bafna and Bansal in IEEE/ACM Trans. Comput. Biol. Bioinf. 1, 78–90, 2004 and in J. Comput. Biol. 13, 501–521, 2006; Song et al. in Bioinformatics 421, i413–i244, 2005). In particular, we propose a new recombination lower bound: the forest bound. We show that the forest bound can be formulated as the minimum perfect phylogenetic forest problem, a natural extension to the classic binary perfect phylogeny problem, which may be of interests on its own. We then show that the forest bound is provably higher than the optimal haplotype bound (Myers and Griffiths in Genetics 163, 375–394, 2003), a very good lower bound in practice (Song et al. in Bioinformatics 421, i413–i422, 2005). We prove that, like several other lower bounds (Bafna and Bansal in J. Comput. Biol. 13, 501–521, 2006), computing the forest bound is NP-hard. Finally, we describe an integer linear programming (ILP) formulation that computes the forest bound precisely for certain range of data. Simulation results show that the forest bound may be useful in computing lower bounds for low quality data. A preliminary version of this paper appeared in the Proceedings of COCOON 2007, LNCS, vol. 4598, pp. 16–26. The work was performed while Y. Wu was with UC Davis and supported by grants CCF-0515278 and IIS-0513910 from National Science Foundation. D. Gusfield supported by grants CCF-0515278 and IIS-0513910 from National Science Foundation.     

广东南海县虎头岗下石炭统刘家塘组及假乌拉珊瑚动物群的首次发现

本文概述了虎头岗早石炭世地层划分的沿革;描述了地层层序和地质构造;并对主要珊瑚化石作出鉴定和描述。并就华南区域范围内进行了生物地层及岩石地层对比.确定虎头岗灰岩地层属下石炭统刘家塘组,其生物属Pseudouralinia(假乌拉珊瑚)动物群.