An offset spline approximation for plane cubic splines

A plane cubic spline segment is given. We want to approximate its offset line by another cubic spline segment. Therefore we take the known curvatures and tangents at the end-points of the offset line and calculate the corresponding spline. Finally examples are given.     

Practical box splines for reconstruction on the body centered cubic lattice

We introduce a family of box splines for efficient, accurate and smooth reconstruction of volumetric data sampled on the Body Centered Cubic (BCC) lattice, which is the favorable volumetric sampling pattern due to its optimal spectral sphere packing property. First, we construct a box spline based on the four principal directions of the BCC lattice that allows for a linear C(0) reconstruction. Then, the design is extended for higher degrees of continuity. We derive the explicit piecewise polynomial representation of the C(0) and C(2) box splines that are useful for practical reconstruction applications. We further demonstrate that approximation in the shift-invariant space---generated by BCC-lattice shifts of these box splines---is {twice} as efficient as using the tensor-product B-spline solutions on the Cartesian lattice (with comparable smoothness and approximation order, and with the same sampling density). Practical evidence is provided demonstrating that not only the BCC lattice is generally a more accurate sampling pattern, but also allows for extremely efficient reconstructions that outperform tensor-product Cartesian reconstructions.     

Box spline reconstruction on the face-centered cubic lattice

We introduce and analyze an efficient reconstruction algorithm for FCC-sampled data. The reconstruction is based on the 6-direction box spline that is naturally associated with the FCC lattice and shares the continuity and approximation order of the triquadratic B-spline. We observe less aliasing for generic level sets and derive special techniques to attain the higher evaluation efficiency promised by the lower degree and smaller stencil-size of the C1 6-direction box spline over the triquadratic B-spline.     

A simple approximation for the Erlang loss function

In this paper we present a simple non-iterative computational procedure for approximating the Erlang loss function B(N, ). It is applicable to the practical range 10⁻⁵<B(N, )<10⁻¹ and gives results that are within 10% of the exact values. The formula can be computed on a pocket calculator in constant time and could be used to approximately compute B(N, ) for systems of practically any size.     

A simple approximation algorithm for the weighted matching problem

We present a linear time approximation algorithm with a performance ratio of 1/2 for finding a maximum weight matching in an arbitrary graph. Such a result is already known and is due to Preis [STACS'99, Lecture Notes in Comput. Sci., Vol. 1563, 1999, pp. 259-269]. Our algorithm uses a new approach which is much simpler than the one given by Preis and needs no amortized analysis for its running time.     

A simple specification of the parametric cubic segment

A parametric cubic segment may be specified in many ways but most specifications require quantities peculiar to the parametric representation rather than the geometric properties of the curve segment. This paper shows that a three-dimensional cubic segment is specified completely by its end points, end slopes and one intermediate point.     

Operational method for solving fractional differential equations using cubic B-spline approximation

In the present paper we construct the cubic B-spline operational matrix of fractional derivative in the Caputo sense, and use it to solve fractional differential equation. The main characteristic of the approach is that it overcomes the computational difficulty induced by the memory effect. There is no need to save and call all historic information, which can save memory space and reduce computational complexity. Numerical results demonstrate the validity and applicability of the method to solve fractional differential equation. The results from this method are good in terms of accuracy.     

浓缩数据立方中约束立方梯度的挖掘

约束立方梯度挖掘是一项重要的挖掘任务,其主要目的是从数据立方中挖掘出满足梯度约束的梯度-探测元组对.然而,现有的研究都是基于一般数据立方的.研究了浓缩数据立方中约束数据立方梯度的挖掘问题.通过扩展LiveSet驱动算法,提出了一个eLiveSet算法.测试表明,该算法在立方梯度挖掘效率上比现有算法要高.     

A variable-mesh approximation method for singularly perturbed boundary-value problems using cubic spline in tension

A non-uniform mesh difference scheme using cubic spline in tension is presented to solve a class of non-turning point singularly perturbed two point boundary-value problems for second-order ordinary differential equations with a small parameter multiplying the highest derivative subject to Dirichlet-type boundary conditions. To demonstrate the applicability of the proposed method, two numerical examples have been solved and the results are presented along with their comparison with those obtained with and without variable mesh. This paper is a continuation of the previous work [Aziz, T. and Khan, A. (2002). A spline method for second order singularly-perturbed boundary-value problems. J. Comput. Appl. Math., 147(2), 445–452.] given for uniform mesh case.     

Alternating cluster estimation: a new tool for clustering andfunction approximation

Many clustering models define good clusters as extrema of objective functions. Optimization of these models is often done using an alternating optimization (AO) algorithm driven by necessary conditions for local extrema. We abandon the objective function model in favor of a generalized model called alternating cluster estimation (ACE). ACE uses an alternating iteration architecture, but membership and prototype functions are selected directly by the user. Virtually every clustering model can be realized as an instance of ACE. Out of a large variety of possible instances of non-AO models, we present two examples: 1) an algorithm with a dynamically changing prototype function that extracts representative data and 2) a computationally efficient algorithm with hyperconic membership functions that allows easy extraction of membership functions. We illustrate these non-AO instances on three problems: a) simple clustering of plane data where we show that creating an unmatched ACE algorithm overcomes some problems of fuzzy c-means (FCM-AO) and possibilistic c-means (PCM-AO); b) functional approximation by clustering on a simple artificial data set; and c) functional approximation on a 12 input 1 output real world data set. ACE models work pretty well in all three cases     

A simple factor-3 approximation for labeling points with circles

In this paper we present a simple factor-(3+ε), 0<ε<1, approximation algorithm, which runs in O(nlogn+n(1/ε)^O(1/ε2)log(D₃/εD₂)) time, for the problem of labeling a set P of n distinct points with uniform circles. (D₂ is the closest pair of P and D₃ is the minimum diameter of all subsets of P with size three.) This problem is known to be NP-hard. Our bound improves the previous factor of 3.6+ε.     

A simple approximation to rigid body dynamics for computer animation

Recently, the dynamics of linked articulated rigid bodies has become a valuable tool for making realistic three-dimensional computer animations. An exact treatment of rigid body dynamics, however, is based on rather non-intuitive results from classical mechanics (e.g. the Euler equations for rotating bodies) and it relies heavily on sophisticated numerical schemes to solve (large) sets of coupled non-linear algebraic and differential equations. As a result, articulated rigid bodies are not yet supported by most real-time animation systems. This paper discusses an approach to rigid body dynamics which is based on (both conceptually and algorithmically much simpler) point mechanics; this gives rise to an asymptotically exact numerical scheme (NSI) which is useful in the context of real-time animation, provided that the number of degrees of freedom of the simulated system is not too large. Based on NSI, a second scheme (NS2) is derived which is useful for approximating the motions of linked articulated rigid bodies; NS2 turns out to be sufficiently fast to give at least qualitative results in real-time simulation. In general, the algorithm NS2 is not necessarily (asymptotically) exact, but a quantitative analysis shows that in the absence of reaction forces it conserves angular momentum.     

General finite difference approximation for the wave equation with variable coefficients using a cubic spline technique

General implicit finite difference approximations for the wave equation with variable coefficients in one and two space variables are derived by using a cubic spline function and continuous parameter approach. An optimal scheme of the family and high accuracy schemes due to McKee are obtained for special cases of the parameters. The stability of the schemes are discussed and one test example is solved to illustrate the theory.     

An improved approximation algorithm for the metric maximum clustering problem with given cluster sizes

The input to the metric maximum clustering problem with given cluster sizes consists of a complete graph G=(V,E) with edge weights satisfying the triangle inequality, and integers c₁,…,cp. The goal is to find a partition of V into disjoint clusters of sizes c₁,…,cp, maximizing the sum of weights of edges whose two ends belong to the same cluster. We describe an approximation algorithms for this problem with performance guarantee that approaches 0.5 when the cluster sizes are large.     

Synchrony in a self-repair network with a simple lattice

We investigate a synchrony in a self-repairing network of autonomous agents capable of repairing mutually. In this paper, we define two models: a synchronous model and asynchronous one. They differ in the timing when the agents change their state. Computer simulations revealed that the synchronous model has a critical point, while the asynchronous one does not. We also studied a repair scheme in asynchronous model where the repaired agents in turn repair neighbor agents successively in a chain-reactive fashion. Performance of the scheme has been examined by computer simulations. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

On the single processor performance of simple lattice Boltzmann kernels

This report presents a comprehensive survey of the effect of different data layouts on the single processor performance characteristics for the lattice Boltzmann method both for commodity “off-the-shelf” (COTS) architectures and tailored HPC systems, such as vector computers. We cover modern 64-bit processors ranging from IA32 compatible (Intel Xeon/Nocona, AMD Opteron), superscalar RISC (IBM Power4), IA64 (Intel Itanium 2) to classical vector (NEC SX6+) and novel vector (Cray X1) architectures. Combining different data layouts with architecture dependent optimization strategies we demonstrate that the optimal implementation strongly depends on the architecture used. In particular, the correct choice of the data layout could supersede complex cache-blocking techniques in our kernels. Furthermore our results demonstrate that vector systems can outperform COTS architectures by one order of magnitude.     

Benchmarking GPU and CPU codes for Heisenberg spin glass over-relaxation

We present a set of possible implementations for Graphics Processing Units (GPU) of the Over-relaxation technique applied to the 3D Heisenberg spin glass model. The results show that a carefully tuned code can achieve more than 100 GFlops/s of sustained performance and update a single spin in about 0.6 nanoseconds. A multi-hit technique that exploits the GPU shared memory further reduces this time. Such results are compared with those obtained by means of a highly-tuned vector-parallel code on latest generation multi-core CPUs.     

数据仓库中CUBE大小估计算法

文章叙述了数据仓库中Cube估计的三个相关算法,提出了一种优化的估计方法。这种新的优化方法在一定程度上弥补了常用估计方法的缺陷,大大提高了估计值的准确性。Cube的大小估计对于数据仓库进行多维分析是非常重要的。原因是为了提高多维分析的查询速度,要进行一定程度的预计算,这种计算是相当复杂的,而且会占用大量数据库的存储空间,因此预先估计出所需空间大小是非常必要的。     

A simple algorithm for detection of significant vertices for polygonal approximation of chain-coded curves

A simple but efficient method is proposed for detection of significant points of chain-coded curves. The polygonal approximation is achieved by joining successive significant vertices. The algorithm is based on manipulation with chain codes only.