Partition-extrapolation methods for numerical quadratures

Partition-extrapolation methods for numerical quadratures are based on dividing the range of integration into an infinite number of subdomains, evaluating the subintegrals over a finite number of subdomains numerically, and then estimating the integral by extrapolation of the partial sums. There is considerable flexibility in the choice of subdivisions, method of evaluating the subintegrals and extrapolation procedure.

The treatment is heuristic, it being shown that the present methods compare favorably with previous methods for a variety of examples involving semi-infinite ranges or integrands with singularities.     

Positive quadratures for volterra equations

The present paper deals with discretizations to linear Volterra equations which preserve the possible positivity of the Volterra operator. It is shown that the method must be implicit and e.g. that the repeated trapezoidal rule has this property. It is then shown how this property can be used in studying the asymptotic behaviour of the solutionsx _n of the discretized equations, asn→∞ with a fixed steph.     

On quartic splines with application to quadratures

This paper presents a formulatioin and a study of an interpolatory quartic spline which interpolates the first and second derivatives of a given function. This formulation can be applied, in particular, to quadratures.     

Convergence of quadratures for Cauchy principal value integrals

Quadrature formulas based on the “practical” abscissasx _k=cos(k π/n),k=0(1)n, are obtained for the numerical evaluation of the weighted Cauchy principal value integrals $$\mathop {\rlap{--} \smallint }\limits_{ - 1}^1 (1 - x)^\alpha (1 + x)^\beta (f(x))/(x - a)){\rm E}dx,$$ where α,β>?1 andaε(?1, 1). An interesting problem concerning these quadrature formulas is their convergence for a suitable class of functions. We establish convergence of these quadrature formulas for the class of functions which are Hölder-continuous on [?1, 1].     

Gauss-Legendre and Chebyshev quadratures for singular integrals

Exact expressions are presented for efficient computation of the weights in Gauss-Legendre and Chebyshev quadratures for selected singular integrands. The singularities may be of Cauchy type, logarithmic type or algebraic-logarithmic end-point branching points. We provide Fortran 90 routines for computing the weights for both the Gauss-Legendre and the Chebyshev (Fejér-1) meshes whose size can be set by the user.

New program summary

Program title: SINGQUADCatalogue identifier: AEBR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBR_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 4128No. of bytes in distributed program, including test data, etc.: 25 815Distribution format: tar.gzProgramming language: Fortran 90Computer: Any with a Fortran 90 compilerOperating system: Linux, Windows, MacRAM: Depending on the complexity of the problemClassification: 4.11Nature of problem: Program provides Gauss-Legendre and Chebyshev (Fejér-1) weights for various singular integrands.Solution method: The weights are obtained from the condition that the quadrature of order N must be exact for a polynomial of degree?(N−1). The weights are expressed as moments of the singular kernels associated with Legendre or Chebyshev polynomials. These moments are obtained in analytic form amenable for computation.Additional comments: If the NAGWare f95 compiler is used, the option, “-kind = byte”, must be included in the compile command lines of the Makefile.Running time: The test run supplied with the distribution takes a couple of seconds to execute.     

Optimal quadratures with regard to the efficiency

In this paper first one studies the optimality problem with regard to the efficiency for some classes of numerical quadrature algorithms. Then one investigates the concordance between the «efficiency criteria» and the «?-complexity criteria».     

Numerical quadratures for singular and hypersingular integrals

We present a procedure for the design of high-order quadrature rules for the numerical evaluation of singular and hypersingular integrals; such integrals are frequently encountered in solution of integral equations of potential theory in two dimensions. Unlike integrals of both smooth and weakly singular functions, hypersingular integrals are pseudo-differential operators, being limits of certain integrals; as a result, standard quadrature formulae fail for hypersingular integrals. On the other hand, such expressions are often encountered in mathematical physics (see, for example, [1]), and it is desirable to have simple and efficient “quadrature” formulae for them. The algorithm we present constructs high-order “quadratures” for the evaluation of hypersingular integrals. The additional advantage of the scheme is the fact that each of the quadratures it produces can be used simultaneously for the efficient evaluation of hypersingular integrals, Hilbert transforms, and integrals involving both smooth and logarithmically singular functions; this results in significantly simplified implementations. The performance of the procedure is illustrated with several numerical examples.     

Exact and interpolatory quadratures for curvature tensor estimation

The computation of the curvature of smooth surfaces has a long history in differential geometry and is essential for many geometric modeling applications such as feature detection. We present a novel approach to calculate the mean curvature from arbitrary normal curvatures. Then, we demonstrate how the same method can be used to obtain new formulae to compute the Gaussian curvature and the curvature tensor. The idea is to compute the curvature integrals by a weighted sum by making use of the periodic structure of the normal curvatures to make the quadratures exact. Finally, we derive an approximation formula for the curvature of discrete data like meshes and show its convergence if quadratically converging normals are available.     

数据流上自适应的稀疏Skyline挖掘

Skyline 查询的结果集为数据集中不被其他对象所``支配'的对象的全体. 近年来, 它在在线服务、决策支持和实时监测等领域的良好应用前景, 使其成为数据管理与数据挖掘领域的研究热点. 实际应用中, 用户通常期望快速、渐进地获得 Skyline 计算结果, 而流数据的连续、海量、高维等特性, 使得在确保查询质量损失受控的前提下挖掘稀疏 Skyline 集合成为一个极具价值和挑战性的问题. 本文首先提出一个新颖的概念: 稀疏 Skyline (Sparse-skyline), 它采用一个 Skyline 对象来代表其周围 ε-邻域内的所有 Skyline 对象; 接着, 给出了通过数据维度之间的相关性来自适应调整查询质量的两个在线算法; 最后, 理论分析和实验结果表明, 与现有的 Skyline 挖掘算法相比, 本文提出的方法具有良好的性能和效率, 更适合于数据流应用.     

自适应Smith补偿器在基于IP的网络控制系统中的应用

在基于IP网络的网络控制系统(NCS s)中,网络诱导时延变化显著且往往大于一个采样周期.本文引用数据通信中应用广泛的网络回程时间来估计NCS s中时变的全回路网络诱导时延,并提出了一种新的自适应Sm ith补偿器.仿真结果表明,该补偿器能够有效地消除网络诱导时延变化对控制性能的负面影响;结合该自适应Sm ith补偿器所设计的控制系统能够获得很好的控制性能与较强的鲁棒性.     

面向群业务的移动互联网自适应资源分配机制

现有的移动互联网资源分配机制大多面向单一业务,无法高效支持群业务。针对这一问题,提出一种面向群业务的自适应资源分配机制。综合考虑动态变化的异构网络环境、群业务特征和用户需求,采用吸引子选择模型来计算备选网络的优先级;在此基础上,运用逼近理想接入网络法对备选网络进行多属性判决,为群业务选择适宜的接入网络。仿真结果表明,该机制显著提高了用户体验和网络资源的利用率。     

传感器网络分布式鲁棒自适应估计算法

从被噪声污染的信号测量值中获得对某一参数的估计,从而确定不同物理量间的相互依赖关系是传感器网络的一个重要应用,然而测量环境可能存在冲击噪声或脉冲干扰,导致获得的测量数据中包含了大大偏离实际范围的离群值(outliers),从而无法获得有效的参数估计.为了解决这个问题,论文提出了一种分布式鲁棒自适应估计算法,该算法基于离群值稀疏性的思想,在代价函数中引入?1范数,对可能的离群值进行识别并剔除,同时利用网络各节点的相互协作,进一步提高参数估计的性能.通过计算机仿真实验,验证了该算法具有较好的鲁棒性.     

Adaptive stratified reservoir sampling over heterogeneous data streams

Reservoir sampling is a known technique for maintaining a random sample of a fixed size over a data stream of an unknown size. While reservoir sampling is suitable for applications demanding a sample over the whole data stream, it is not designed for applications in which an input stream is composed of sub-streams with heterogeneous statistical properties. For this class of applications, the conventional reservoir sampling technique can lead to a potential damage in the statistical quality of the sample because it does not guarantee the inclusion of a statistically sufficient number of tuples in the sample from each sub-stream. In this paper, we address this heterogeneity problem by stratifying the reservoir sample among the underlying sub-streams. This stratification poses two challenges. First, a fixed-size reservoir should be allocated to individual sub-streams optimally, specifically to have the stratified reservoir sample used to generate estimates at the level of either the whole data stream or the individual sub-streams. Second, the allocation should be adjusted adaptively if and when new sub-streams appear in or existing sub-streams disappear from the input stream and as their statistical properties change. We propose a novel adaptive stratified reservoir sampling algorithm designed to meet these challenges. An extensive performance study shows the superiority of the achieved sample quality and demonstrates the adaptivity of the proposed sampling algorithm.     

Hermite and gauss type optimal quadratures for analytic functions

For integrals \(\int\limits_{ - 1}^\iota {w(x)f(x)dx} \) with a non-negative weight functionw(x) and analyticf, we develop Hermite and Gauss type optimal quadratures over the Hilbert spaceH ²(C_r) of functions analytic in a circle. Our development of these optimal quadratures in very similar to that of classical Hermite and Gauss quadratures; the role played by fundamental polynomials in the classical theory is replaced here by certain «fundamental rational functions». We then show, by arguments similar to those used in the classical case, that a Gauss type optimal quadrature has positive weights an abscissas lying in (?¹, 1).     

无线Ad hoc网络上的自适应多描述编码*

为了在带宽较小、拓扑实时变化、易受外界影响的无线Ad hoc网络中实行视频的可靠通信,提出了一种自适应多相变换多描述编码策略。通过不同的相位点来产生多种描述,利用OLSR路由协议中的Hop和ETX来动态改变各描述的量化步长,以适应实时变化的Ad hoc网络。仿真实验证明,与传统的单描述编码（如H.264/AVC）相比,自适应多相变换多描述编码在提高信噪比、降低丢包率和平均失真方面比传统方式均有明显改善。仿真实验证明了所提出方案传输视频是优越的、可行的。     

一种自适应概念变化的数据流分类器

多数分类方法基于数据服从静态分布的假设,然而真实世界中数据的采集通常跨越一段时间,如果忽略潜在概念的变化将会严重降低分类模式的预测性能.目前挖掘概念变化的数据流已经成为研究的热点,在入侵检测、系统性能保持等方面有重要应用.提出一种基于SPRINT的在线分类方法SSPRINT,可以动态调整训练窗口的尺寸和分类模型重建期间允许接受的新样本的个数,以自动适应当前概念变化发生的速度;在网络性能数据流上的测试验证了SSPRINT的性能.     

Adaptive end-to-end QoS for multimedia over heterogeneous wireless networks

There has been a surge of interest for multimedia applications over wireless networks in recent years. A colossal number of ways have been proposed to decrease delay, delay jitter and loss in wireless networks and good user-perceived quality in video over internet. This paper studies the multimedia over heterogeneous wireless networks, requirements and problems, and proposes a new scheme to overcome the obstacles. The proposed scheme, takes into account the effects of Application-Level Wireless Multilevel ECN marking (AWMECN), thus helps us overcome the congestion/loss mistake problems. For handoff, handover and lossy link problems, it is considered that a freezing mechanism is in use in application layer and assumed that the upper layers can be aware of disconnection periods to make the rate adaptation decisions. Also a new scheme has been added to receiver to gracefully degrade the quality when no other action is available to combat the long delays without data which is caused by handoffs and wireless temporary disconnections. The transport layer mechanism is chosen to be UDP for avoiding TCP regarding problems. We believe that obtaining a good quality of video depends on good performance of all layers and tried to use the best mechanism in each layer.     

Adaptive scheduling for shared window joins over data streams

Recently a few Continuous Query systems have been developed to cope with applications involving continuous data streams. At the same time, numerous algorithms are proposed for better performance. A recent work on this subject was to define scheduling strategies on shared window joins over data streams from multiple query expressions. In these strategies, a tuple with the highest priority is selected to process from multiple candidates. However, the performance of these static strategies is deeply influenced when data are bursting, because the priority is determined only by static information, such as the query windows, arriving order, etc. In this paper, we propose a novel adaptive strategy where the priority of a tuple is integrated with realtime information. A thorough experimental evaluation has demonstrated that this new strategy can outperform the existing strategies.