Parametrizing and graphing nonsingular cubic curves

Elliptic functions are used to parametrize and graph nonsingular cubic curves. First, a sequence of transformations is derived that reduces a third degree equation to a standard equation. A parametrization in terms of elliptic functions is given for the graph of the standard equation. The transformations convert this parametrization to a parametrization of the graph of the given equation. The details of using this parametrization for computer graphing are presented.     

A parallel graph partitioning algorithm for a message-passing multiprocessor

We develop a parallel algorithm for partitioning the vertices of a graph intop2 sets in such a way that few edges connect vertices in different sets. The algorithm is intended for a message-passing multiprocessor system, such as the hypercube, and is based on the Kernighan-Lin algorithm for finding small edge separators on a single processor.⁽¹⁾ We use this parallel partitioning algorithm to find orderings for factoring large sparse symmetric positive definite matrices. These orderings not only reduce fill, but also result in good processor utilization and low communication overhead during the factorization. We provide a complexity analysis of the algorithm, as well as some numerical results from an Intel hypercube and a hypercube simulator.Publication of this report was partially supported by the National Science Foundation under Grant DCR-8451385 and by AT&T Bell Laboratories through their Ph.D scholarship program.     

基于网络划分和并行运算的P/G布线网络快速分析算法

提出了一个基于网络划分和分布式并行运算的P/G网快速验证方法.对于各子网运算,采用带加速子网运算策略的Cholesky分解法;并根据各个子网运算相互独立的特点,采用基于MPI(Message Passing Interface)的并行结构对子网络运算进行分布式并行运算.实验证明,该快速验证方法在运算时间和内存占用上效果十分良好.     

Quantum Universality from Magic States Distillation Applied to CSS Codes

Given Clifford group operations and the ability to repeatedly prepare a single-qubit mixed state ρ, can one do universal quantum computation? We show a sharp threshold in the Hadamard “magic” direction of the Bloch sphere between those ρ allowing universal quantum computation, and those for which any calculation can be efficiently classically simulated. As a corollary, the ability to repeatedly prepare any pure state which is not a stabilizer state (e.g., any single-qubit pure state which is not a Pauli eigenstate), together with Clifford group operations, gives quantum universality. As motivation for this question, “magic state” distillation procedures can reduce the general fault-tolerance problem to that of performing fault-tolerant Clifford group circuits.     

基于半定规划的量子状态最优无错区分

对于一般的量子状态最优无错区分问题.很难得到最优量子测量的解析形式.因此,有必要寻求有效实用的数值方法.基于半定规划理论,证明了无错状态区分的最优量子测肇的设计问题可以转化为标准的半定规划问题,以及能直接应用半定规划的最优性条件,从而更简明地推导了.一组无错状态区分的最优性条件;通过求解标准的半定规划问题.可在多项式时间内直接得到最优量子测量的数值解以及成功区分状态的最大概率值.实例仿真表明,方法易于计算机实现,能有效地设计出无错状态区分的最优量子测量算子.     

基于Bell态的量子资源访问控制协议

在资源访问无处不在的互联网时代,如何做好对资源的访问控制具有重要的意义.本文利用二粒子纠缠态Bell态的纠缠特性,提出了基于Bell态的资源访问控制协议.该协议基于量子密钥分发（Quantum Key Distribution-QKD）,设计了一种利用不对等密钥（不经意密钥）实现的量子资源访问控制协议,同时实现了对资源请求方的身份认证.本文分析了该协议的安全性,证明了协议可以实现资源不被非法授权用户访问,以及特定授权用户只能访问特定资源.     

Information Free Quantum Bus for Generating Stabiliser States

Efficient generation of spatially delocalised entangledstates is at the heart of quantum information science. Generally,flying qubits are proposed for long range entangling interactions,however here we introduce a bus-mediated alternative for this task.Our scheme permits efficient and flexible generation ofdeterministic two-qubit operator measurements and has links to theimportant concepts of mode-entanglement and repeat-until-successprotocols. Importantly, unlike flying qubit protocols, our busparticle never contains information about the individual quantumstates of the particles, hence is information-free.      

基于量子高维Bell态纠缠交换的分发式投票方案

利用了高维Bell态,设计一种新的量子投票方案.方案分为4个阶段:首先,高维Bell纠缠态粒子被作为投票信息载体被分发给投票者;然后投票者利用最小复杂度搜索寻找竞选者,并用相移操作投出选票;接着代理人收到选票后,运用纠缠交换过程来检测窃听,通过检查粒子的测量结果来发现是否非法攻击;最后代理人利用计票算子统计票数并公布.所有人都只知道总的投票结果,单个投票者的投票信息是保密的.协议分析了各种攻击下的抵抗,证明了这是一个合理,安全,高效的量子投票方素.     

用于快速P/G网分析的Cholesky分解法图模型

通过对Cholesky分解法求解线性方程组的分析,建立Cholesky分解法三角化对称正定阵的图模型,并基于该模型及Mesh结构P／G网络的自身特点,提出一个P／G网快速分析算法．实验证明,该算法能大大降低Mesh结构P／G网络的分析运算时间和内存占用．     

Interpolation type problems in the class of positive trigonometric polynomials of fixed order

This paper is devoted to a family of interpolation type problems for positive trigonometric polynomials of a given ordern. Via the Riesz-Fejér factorization theorem, they can be viewed as natural generalizations of the partial autocorrelation problem for discrete time signals of lengthn+1. The relevant variables for a specific problem are well-defined linear combinations of the coefficients of the underlying trigonometric polynomial. An efficient method is obtained to characterize the feasibility region of the problem, defined as the set of points having these variables as coordinates. It allows us to determine the boundary of that region by computing the extreme eigen values and the corresponding eigenvectors of certain well-defined Hermitian Toeplitz matrices of ordern+1. The method is an extension of one proposed by Steinhardt to solve the coefficient problem for positive cosine polynomials (which belongs to the family). Other interesting applications are the Nevanlinna-Pick interpolation problem for polynomial functions, and the simple interpolation problem for positive trigonometric polynomials. The close connection between the generalized Steinhardt method and classical techniques based on the polarity theorem for convex cones and on the Hahn-Banach extension theorem are established.     

Column and diagonal‐reduction of polynomial matrices by orthogonal transformation

Many of the applications of polynomial matrices in real world systems require column‐ or diagonally‐reduced polynomial matrices. If a given polynomial matrix is not column‐ or diagonally‐reduced, Callier or Wolowich algorithms, which use unimodular transformations, can be applied for column‐ or diagonal‐reduction, respectively, as a pre‐processing step in the applications. However, Callier and Wolowich algorithms may be unstable, from a numerical viewpoint, because they use elementary column and row operations. The purpose of this paper is to present sufficient conditions for existence of a constant orthogonal transformation of the given polynomial matrix so that it becomes column‐ or diagonally‐reduced. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

BH2+与H2S反应机理的量子化学及电子密度拓扑研究

采用密度泛函方法B3LYP和耦合簇方法CCSD在6-311 G(d,p)条件中,研究BH_2~ 与H_2S的气相离子-分子反应的微观反应机理。优化反应势能面上各驻点的几何构型,通过振动分析和IRC计算证实中间体和过渡态的真实性和相互连接关系。采用电子密度拓扑分析反应(1)进程中的若干关键点,讨论反应进程中化学键的断裂、生成和变化规律,找到了该反应的结构过渡区(结构过渡态)和能量过渡态。     

Minimal representations of continuous-time processes having spectral density with zeros in the extended imaginary axis

Given a process y with stationary increments and rational incremental spectral density Φ(s), we parametrize minimal state-space representations of dy. We consider the case when Φ(s) may have zeros on the imaginary axis including infinity and we analyze the zero structure of each state-space representation.     

从运动中恢复目标结构的改进因子分解法

因子分解法是从图像序列中恢复刚体目标几何结构的重要方法。针对传统因子分解法基本过程中存在的不足,及其容易失效的缺点,提出一种改进的因子分解法。该方法避开传统方法中求解修正矩阵的复杂过程,利用旋转矩阵的特性,直接修正由传统方法奇异值分解(SVD)得到的每帧图像的旋转矩阵,然后根据观测矩阵和得到的旋转矩阵,直接利用线性最小二乘法求解目标的结构矩阵。仿真和实测数据的实验结果表明,本文方法能够有效地从序列图像中恢复目标的几何结构,相比传统因子分解法,在稳定性上有较大的提升。     

On States,Channels, and Purification

In this note we introduce purification for a pair (, ), where is a quantum state and is a channel, which allows in particular a natural extension of the properties of related information quantities (mutual and coherent informations) to the channels with arbitrary input and output spaces. PACS: 03.67.Hk     

电子通路与公司绩效关联性之研究

The stimulus of advances in Information Technology (IT), particularly the Internet, has forced firms to explore new organizational forms and deliver service innovation. Emerging Internet-based electronic distribution channels, i.e., Internet channels, might be another forms of services innovation for firms to face the market dynamics. However, empirical studies fail to provide direct evidence of whether Internet channels enhance business performance[1]. In order to fill in the literature gap, this empirical study attempts to investigate performance implications of Internet channels in Taiwan by means of applying data envelopment analysis (DEA). Results show that operating efficiency of financial services firms following the Internet channels announcement is increased. This work therefore concludes that Internet channels have positive influence on business performance.     

Maximum-likelihood detection based on branch and bound algorithm for MIMO systems

Maximum likelihood detection for MIMO systems can be formulated as an integer quadratic programming problem. In this paper, we introduce depth-first branch and bound algorithm with variable dichotomy into MIMO detection. More nodes may be pruned with this structure. At each stage of the branch and bound algorithm, active set algorithm is adopted to solve the dual subproblem. In order to reduce the complexity further, the Cholesky factorization update is presented to solve the linear system at each iteration of active set algorithm efficiently. By relaxing the pruning conditions, we also present the quasi branch and bound algorithm which implements a good tradeoff between performance and complexity. Numerical results show that the complexity of MIMO detection based on branch and bound algorithm is very low, especially in low SNR and large constellations.     

全变分极端通道先验的盲图像去噪去模糊

图像先验是图像复原中求解不适定问题的关键。针对在图像具有显著噪声时,极端通道先验去模糊算法容易产生振铃伪影和无法抑制噪声的缺点,利用全变分模型可以同时抑制噪声和保护边缘的优势,提出一种有效的全变分极端通道先验的盲图像去噪和去模糊模型。首先,将全变分模型分别引入暗通道和亮通道中,用于保护图像的边缘及消除噪声或振铃伪影;其次,利用半二次分裂技术解决模型的非凸问题和估计潜在的清晰图像;最后,用迭代多尺度盲反褶积估计图像的模糊核。实验结果表明,该算法能够在抑制噪声的同时很好地保护图像的边缘细节和消除振铃伪影。相比近几年具有代表性的其他方法,该模型的鲁棒性、主观视觉效果和客观评价指标均有明显提高。