Derivative Free Inclusion Methods for Polynomial Zeros

Two iterative methods for the simultaneous inclusion of complex zeros of a polynomial are presented. Both methods are realized in circular interval arithmetic and do not use polynomial derivatives. The first method of the fourth order is composed as a combination of interval methods with the order of convergence two and three. The second method is constructed using double application of the inclusion method of Weierstrass’ type in serial mode. It is shown that its R-order of convergence is bounded below by the spectral radius of the corresponding matrix. Numerical examples illustrate the convergence rate of the presented methods     

Exact Computation of Polynomial Zeros Expressible by Square Roots

In this paper we give an efficient algorithm to find symbolically correct zeros of a polynomial f ∈ R[X] which can be represented by square roots. R can be any domain if a factorization algorithm over R[X] is given, including finite rings or fields, integers, rational numbers, and finite algebraic or transcendental extensions of those. Asymptotically, the algorithm needs O(T_f(d²)) operations in R, where T_f(d) are the operations for the factorization algorithm over R[X] for a polynomial of degree d. Thus, the algorithm has polynomial running time for instance for polynomials over finite fields or the rationals. We also present a quick test for deciding whether a given polynomial has zeros expressible by square roots and describe some additional methods for special cases.     

Weierstrass-like Methods with Corrections for the Inclusion of Polynomial Zeros

In this paper, we present iterative methods of Weierstress’ type for the simultaneous inclusion of all simple zeros of a polynomial. The main advantage of the proposed methods is the increase of the convergence rate attained by applying suitable correction terms. Using the concept of the R-order of convergence of mutually dependent sequences, we present the convergence analysis for the total-step and the single-step methods. Numerical examples are given.     

Halley-Like Method with Corrections for the Inclusion of Polynomial Zeros

In this paper we present iteration methods of Halley's type for the simultaneous inclusion of all zeros of a polynomial. Using the concept of the R-order of convergence of mutually dependent sequences, we present the convergence analysis for the total-step and the single-step methods with Newton's corrections. The suggested algorithms possess a great computational efficiency since the increase of the convergence rate is attained without additional calculations. A numerical example is given. Received: June 23, 1998     

Ostrowski-Like Method with Corrections for the Inclusion of Polynomial Zeros

In this paper we construct iterative methods of Ostrowski's type for the simultaneous inclusion of all zeros of a polynomial. Using the concept of the R-order of convergence of mutually dependent sequences, we present the convergence analysis of the total-step and the single-step methods with Newton and Halley's corrections. The case of multiple zeros is also considered. The suggested algorithms possess a great computational efficiency since the increase of the convergence rate is attained without additional calculations. Numerical examples and an analysis of computational efficiency are given.     

On The Convergence Of Some Interval Methods For Simultaneous Computation Of Polynomial Zeros

In this paper we consider the convergence of a certain interval method for simultaneous computation of polynomial zeros. Under the legitimacy of suitable isolation of the roots in a restrictive respective circular disks it is established in a limiting sense a finite positive constant in existence for which convergence is certain. This positive constant which is the limiting convergence factor is dependent on the minimum distance between the zeros of the polynomial. This provides a qualitative information that may be found useful on the occasion the roots are clustered. The climax however, is an introduction of a new interval method and an improved modification of an existing one considered.     

基于补零的Zadoff-Chu序列检测算法

介绍单载波频域均衡系统的随机接入方案,提出一种基于补零扩展的Zadoff-Chu序列的前导检测算法。使用素数Zadoff-Chu序列作为用户签名,接收端采用基于时域补零扩展的频域检测方法进行前导检测。仿真结果表明,与传统时域检测算法相比,该算法能在保证检测效果的同时,降低90%计算复杂度。     

多项式循环程序的秩函数探测

秩函数法是循环程序终止性分析的主流方法.针对一类多分支多项式循环程序,这类程序的秩函数计算问题被证明可归结为单形上正定多项式的探测问题,从而便于利用线性规划工具Simplex去计算这类程序的秩函数.不同于现有基于柱形代数分解的量词消去算法,该方法能够在可接受的时间内计算更为复杂的多项式秩函数.     

采用正交多项式曲面拟合法的边缘检测

本文介绍了一种应用局部曲面拟合技术检测图象边缘的方法.其拟合函数是由两个一维三阶正交多项式的张量积构成,图象中的边缘点定义为梯度方向上二阶导数的过零点.文中证明了:采用正交函数进行曲面拟合后的图象及其各阶偏导数均可用卷积完成,而它又可分解为两次一维卷积,从而使计算量大大下降.实验表明,同传统的边缘检测技术相比,该方法具有良好的噪音抑制特性,边缘点的位置确定也很令人满意.     

边缘识别的二维正交多项式拟合及结构变形检测

数字图像中边缘附近的灰度是沿边缘方向和跨边缘方向二维变化的,以前边缘识别的多项式拟合大多采用跨边缘方向的一维拟合。介绍一种采用二维正交多项式进行边缘识别的新方法,由于二维拟合更符合边缘附近小区域内像素灰度二维变化的实际,因此拟合结果优于一维拟合。在进行拟合时,利用正交多项式的正交性将优化方程对角化,避免求逆或解方程,没有多项式拟合优化方程的病态问题,采用高阶多项式拟合可以提高拟合精度。对生成图像的边缘识别结果表明,二维正交多项式拟合识别边缘的精度和稳定性较好。简支梁模型试验表明,采用正交多项式边缘拟合方法检测梁的静变形,图像变形检测精度在0.1像素之内,适当选择图像采集设备和采集范围,点检测精度与传统检测方法的精度相当,边缘检测属线状高密度检测,检测范围远大于传统方法。     

基于统计信息的聚类边界模式检测算法

为有效地检测聚类的边界点,提出基于统计信息的边界模式检测算法。根据数据对象的k距离统计信息设定邻域半径,再利用对象邻域范围内邻居的k距离统计信息寻找边界点。实验结果表明,该算法可以有效地检测出任意形状、不同大小和不同密度聚类的边界点,并可以消除噪声。     

一种复杂背景中的人脸检测与验证方法

设计了一种复杂背景中的人脸检测与验证方法。在预处理部分该方法使用了线性光照拟合的预处理方法以减轻光照的影响。在检测过程中该方法引入了一种 3× 3的划分方式 ,该划分方式下根据人脸器官的灰度分布特性设计了相应的检测规则 ,并结合改进后的 4× 4划分方式下的人脸检测规则构成了最终的人脸检测规则。经过人脸检测过程后 ,对所得的结果使用具有良好抗噪声性能的最小同值分割吸收核区 (Smallest univalue seg-mentassimilating nucleus,SUSAN)方法进行检测结果验证 ,进一步增强了系统的整体性能。最后通过复杂背景下的人脸图片以及叠加噪声后的人脸图片的检测结果说明该方法具有较高的检测率及良好的抗噪声性能。     

Zeros of sampled systems

The zeros of the discrete-time system obtained when sampling a continuous time system are explored. Theorems for the limiting zeros for large and small sampling periods are given. Conditions which guarantee that the sampled system has stable zeros are also presented.     

集群上软件事务内存的层次化冲突检测

大多数事务内存研究都在多核处理器上进行,只有少数研究针对集群计算环境。现有的集群事务内存性能较差,因为事务内存的运行需要进行大量的远程内存访问,而集群的内存分布性使得远程内存访问的性能较差。事务内存运行中的冲突检测是进行远程内存访问最多的操作。我们提出了一种层次化的冲突检测方法,将其分为两个步骤进行,这种层次化的策略可以使集群上的软件事务内存获得高性能。     

Equivalence of Polynomial Identity Testing and Polynomial Factorization

In this paper, we show that the problem of deterministically factoring multivariate polynomials reduces to the problem of deterministic polynomial identity testing. Specifically, we show that given an arithmetic circuit (either explicitly or via black-box access) that computes a multivariate polynomial f, the task of computing arithmetic circuits for the factors of f can be solved deterministically, given a deterministic algorithm for the polynomial identity testing problem (we require either a white-box or a black-box algorithm, depending on the representation of f).Together with the easy observation that deterministic factoring implies a deterministic algorithm for polynomial identity testing, this establishes an equivalence between these two central derandomization problems of arithmetic complexity.Previously, such an equivalence was known only for multilinear circuits (Shpilka & Volkovich, 2010).     

Zeros of the system matrix

This note provides an easy characterization of the zeros of the system matrix in terms of a strong version of system reachability and observabillty. Interpreted in abstract terms, it yields Wonham and Morse's characterization of zero. The results hold for systems defined over an arbitrary field.     

结合深度学习与特征多尺度融合的微钙化簇检测

为了准确识别X线图像中的微钙化簇以进行乳腺癌的辅助诊断与早期预防,结合细粒度级联增强网络(FCE-Net)与多尺度特征融合算法(MFF),提出微钙化簇目标检测方法.首先构建FCE-Net累加卷积模块层级权重,并增强多分支结构,得到细粒度卷积特征图.然后构建MFF候选检测网络,通过二倍上采样融合多尺度特征,得到目标置信度和区域坐标.最后在感兴趣区域池化层分类目标并调整边界框.在MIAS数据集上实验表明,结合FCE-Net与MFF可以提升微小目标的深层特征提取能力,同时增强目标分类与定位的准确度.     

Evolving Clusters for Network Intrusion Detection System Using Genetic-X-Means Algorithm

ABSTRACT

With the rapid growth of Internet communication and the availability of tools to intrude the network, an intrusion detection system (IDS) has become indispensable. Clustering algorithm utilize a distance metric in order to partition data points such that patterns within a single group have the same characteristics from those in a different group. The proposed system builds a clustering engine using genetic-X-means that can assign each new event to a cluster to determine its type. This is in contrast to approaches used by existing clustering-based IDSs, which require the number of attack types in advance. Genetic-X-means handle recently evolving attacks by clustering them into respective classes, and if the attack pattern deviates largely from the existing cluster it is grouped into a new class. Genetic paradigm employs a weighted sum fitness function to choose the predominant features, which reveals the occurrence of intrusions. The weighted sum fitness function used here is dependent on problem instance and not just on the problem class. As the data patterns include categorical attributes, an influence calculation formula which converts categorical attribute to numerical attribute is proposed. The experimental results obtained in this work show that the system attains improvement in terms of detection rate when compared to a conventional IDS. Experiments show that this system can be deployed in a real network or database environment for effective detection of both existing and new attacks.     

Zeros and Local Extrema of Trigonometric Sums

Theorems on the number of zeros and number of local extrema of trigonometric sums, in particular, Gauss and Weyl sums, are proved.     

基于MATLAB的抗差多项式拟合方法在GNSS周跳探测中的应用研究

为了提高GNSS载波相位的定位精度,本文采用历元间求差与抗差估计相结合的方法对过去常常使用的多项式进行改良,最终提出用抗差多项式拟合来探测并修复周跳。本文基于Matlab软件编制程序,并对GNSS载波相位周跳进行了试算。实验结果表明:此方法可以做到对GNSS周跳探测与修复功能,具有文件读写、卫星观测值提取、周跳探测与修复、绘制拟合的误差结果图形等功能。通过这种方法可以探测并修复1周以上的周跳。得出结论:通过抗差多项式拟合方法可以探测并修复GNSS周跳。