A cutting-plane method based on redundant rows for improving fractional distance

Decoding performance of linear programming (LP) decoding is closely related to geometrical properties of a fundamental polytope: fractional distance, pseudo codeword, etc. In this paper, an idea of the cutting-plane method is employed to improve the fractional distance of a given binary parity-check matrix. The fractional distance is the minimum weight (with respect to l₁-distance) of nonzero vertices of the fundamental polytope. The cutting polytope is defined based on redundant rows of the parity-check matrix. The redundant rows are codewords of the dual code not yet appearing as rows in the paritycheck matrix. The cutting polytope plays a key role to eliminate unnecessary fractional vertices in the fundamental polytope. We propose a greedy algorithm and its efficient implementation based on the cutting-plane method. It has been confirmed that the fractional distance of some parity-check matrices are actually improved by using the algorithm.     

Vertex adjustment method using geometric constraint forpolygon-based shape coding

A new vertex selection scheme for polygon-based contour coding is proposed. The proposed method consists of `two-step procedure'. Initial vertices are selected by using the conventional iterated refinement method (IRM) or progressive vertex selection (PVS) method. A vertex adjustment process then follows where the initial vertices are updated to produce an optimal polygon in the sense of `error area'. In this step, the gometrical information of the partial contour and its polygon segment is used to reduce the search region for the admissible vertex position. Experimental results are presented to compare the approximation performances and the required computational burdens of the proposed and conventional methods     

QR-factorization method for computing the greatest common divisorof polynomials with inexact coefficients

This paper presents a novel means of computing the greatest common divisor (GCD) of two polynomials with real-valued coefficients that have been perturbed by noise. The method involves the QR-factorization of a near-to-Toeplitz matrix derived from the Sylvester matrix of the two polynomials. It turns out that the GCD to within a constant factor is contained in the last nonzero row of the upper triangular matrix R in the QR-factorization of the near-to-Toeplitz matrix. The QR-factorization is efficiently performed by an algorithm due to Chun et al. (1987). A condition number estimator due to Bischof (1990) and an algorithm for rank estimation due to Zarowski (1998) are employed to account for the effects of noise     

多胞型二维多项式的Schur稳定性

本文提出多胞型二维多项式的Schur稳定的充分必要条件。我们揭示多胞型二维多项式的系数具有线性仿射特性。基于这一仿射特性,将多胞型二维多项式视为具有复变系数的多胞型一维多项式,我们证明多胞型二维多项式的稳定性可由其有限的棱边多项式的稳定性保证。我们提供了一种棱边多项式的稳定性检验算法。     

Complex Gaussian noise moments

The problem of the computation of moments of nonzero mean circularly complex Gaussian noise is treated. The noise need not be symmetric about the carrier frequency. In particular, the second-order moments are computed, and expansions are given. The necessary univariate and bivariate complex Hermite polynomials are discussed. The means of some rational functions useful in FM theory are given. This paper extends work of Rice, Middleton, and Zadeh to complex Gaussian noise with nonzero mean and nonsymmetrical power spectrum.     

Dynamic programming approach to optimal vertex selection for polygon-based shape approximation

A new vertex selection scheme for polygon-based contour coders is presented. In the proposed method, final vertex points are determined by a 'two-step procedure'. In the first step, the initial vertices are simply selected from the contour, thereby constituting a subset of the original contour, using conventional methods such as the iterated refinement method (IRM) or progressive vertex selection (PVS) method. In the second step, a vertex adjustment process is incorporated to generate final vertices that are no longer confined to the contour and are optimal in view of the given distortion measure. For the optimality of the final vertices, a dynamic programming (DP)-based solution for the adjustment of the vertices is proposed. Consequently, the authors offer two main contributions. First, it is shown that DP can be successfully applied to vertex adjustment. Secondly, the use of DP enables global optimality to be achieved in vertex selection without any iterative processes. Experimental results are presented to demonstrate the superiority of the proposed method over traditional methods     

Robust Stability of Multivariate Polynomials, Part 2: Polytopic Coefficient Variations

This paper deals with robustness of stability propety of a class of multivariate polynomials, recently introduced in kharjt. The aim is to show the use of this class when analyzing stability of mutivariate polynomial families with polytopic coefficient variations. This study is developed on the basis of some known stability results for polytopic families of scattering Hurwitz stable (SHS) as well as strict sense stable (SSS) multivariate polynomials.     

Extracting the overlapped sub-regions in wireless sensor networks

In wireless sensor networks, the overlapped sub-regions (faces) are generated due to the intersections among the sensing ranges of nodes. The faces play a significant role in solving the three problems k-coverage (i.e., all the points in the interested field should be covered by at least k active nodes while maintaining connectivity between all active nodes), coverage scheduling and cover sets. To find the faces and discover their coverage degrees, this article presents a distributed algorithm that runs in three steps. First, a colored graph called Intersection Points Colored Graph (IPCG) is proposed, in which the vertices are defined by the range-intersections of nodes-devices and are colored according to the position of these intersections in relation to the ranges of the nodes. The vertex that located on perimeter of the node’s range is colored by red, while the green vertex is an intersection of two ranges inside the range of a third node. The edge that joins two red vertices is colored by red and the edge that joins two green vertices is colored by green while the edge that joins two distinct colored vertices is colored by blue. Second, based on their properties and distinct features, the faces in IPCG are classified into five classes (simple, negative, red, green and positive). Third, based on faces classification, the Three Colored Trees algorithm is proposed to extract the faces in linear time in terms of the number of vertices and edges in IPCG.

     

On a new class of codes for identifying vertices in graphs

We investigate a new class of codes for the optimal covering of vertices in an undirected graph G such that any vertex in G can be uniquely identified by examining the vertices that cover it. We define a ball of radius t centered on a vertex υ to be the set of vertices in G that are at distance at most t from υ. The vertex υ is then said to cover itself and every other vertex in the ball with center υ. Our formal problem statement is as follows: given an undirected graph G and an integer t⩾1, find a (minimal) set C of vertices such that every vertex in G belongs to a unique set of balls of radius t centered at the vertices in C. The set of vertices thus obtained constitutes a code for vertex identification. We first develop topology-independent bounds on the size of C. We then develop methods for constructing C for several specific topologies such as binary cubes, nonbinary cubes, and trees. We also describe the identification of sets of vertices using covering codes that uniquely identify single vertices. We develop methods for constructing optimal topologies that yield identifying codes with a minimum number of codewords. Finally, we describe an application of the theory developed in this paper to fault diagnosis of multiprocessor systems     

Addressing, distances and routing in triangular systems with applications in cellular networks

Triangular systems are the subgraphs of the regular triangular grid which are formed by a simple circuit of the grid and the region bounded by this circuit. They are used to model cellular networks where nodes are base stations. In this paper, we propose an addressing scheme for triangular systems by employing their isometric embeddings into the Cartesian product of three trees. This embedding provides a simple representation of any triangular system with only three small integers per vertex, and allows to employ the compact labeling schemes for trees for distance queries and routing. We show that each such system with n vertices admits a labeling that assigns O(log ² n) bit labels to vertices of the system such that the distance between any two vertices u and v can be determined in constant time by merely inspecting the labels of u and v, without using any other information about the system. Furthermore, there is a labeling, assigning labels of size O(log n) bits to vertices, which allows, given the label of a source vertex and the label of a destination, to compute in constant time the port number of the edge from the source that heads in the direction of the destination. These results are used in solving some problems in cellular networks. Our addressing and distance labeling schemes allow efficient implementation of distance and movement based tracking protocols in cellular networks, by providing information, generally not available to the user, and means for accurate cell distance determination. Our routing and distance labeling schemes provide elegant and efficient routing and connection rerouting protocols for cellular networks. Victor Chepoi received the M.S. degree in Applied Mathematics and Computer Science from Moldova State University, in 1983, and the PhD degree in Theoretical Computer Science from the Belorussian Academy of Sciences, in 1987. He was an Assistant and then an Associate Professor at the Mathematics and Computer Science Department of Moldova State University from 1987 to 1994. He was awarded the Alexander von Humboldt Shtiftung Fellowship from 1994 to 1995 at the University of Hamburg, Germany. During 1995 to 1997, he was a Visiting Professor at the Laboratoire de Biomathematiques, Universite de la Mediterranee, France. During 1998, he was a Fellow at SFB343 “Diskrete Strukturen in der Mathematik”, University of Bielefeld, Germany. Since September 1998 he has been a Professor of Computer Science at Faculte des Sciences de Luminy, Universite de la Maditerranee, France. His research interests include graph theory and combinatorics, design and analysis of network and graph algorithms, geometry and algorithmics of metric spaces, computational geometry, and approximation algorithms. Feodor F. Dragan received the M.S. degree in Applied Mathematics and Computer Science from Moldova State University, in 1985, and the PhD degree in Theoretical Computer Science from the Belorussian Academy of Sciences, in 1990. He was an Assistant and then an Associate Professor at the Mathematics and Computer Science Department of Moldova State University from 1988 to 1999. From 1994 to 1999, he was on leave of absence and worked in Germany as a Research Associate on a Volkswagen Foundation (VW) project and on a German Research Community (DFG) project. He was also awarded a DAAD Research Fellowship (Germany) from 1994 to 1995. During 1999 to 2000, he was a Research Associate at the Computer Science Department of University of California, Los Angeles. Since August 2000 he has been with Kent State University and he is currently an Associate Professor of Computer Science. He has authored more than 70 refereed scientific publications. His research interests include design and analysis of network algorithms, algorithmic graph and hypergraph theory, computational geometry, VLSI CAD, and combinatorial optimization. Yann Vaxes received the PhD degree in Computer Science from the Universite de la Mediterranee, in 1998. Then, he joined the Computer Science Department of this university as an Assistant Professor. His research interests include design and analysis of network algorithms, algorithmic graph theory and combinatorial optimization.     

Enclosure of the Zero Set of Polynomials in Several Complex Variables

The zero set of one general multivariate polynomial is enclosed by unions and intersections of simple unbounded sets. Sets in which multivariate real polynomials exhibit constant sign or stay positive are found. Families of stable and unstable polynomials are explicitly given. Stability means here zero-free in the closed unit n-disk or the n-disk complement. The results achieved are discussed and illustrated by examples.     

Robust Schur Stability of Polynomials with Polynomial Parameter Dependency

The paper considers the robust Schur stability verification of polynomials with coefficients depending polynomially on parameters varying in given intervals. A new algorithm is presented which relies on the expansion of a multivariate polynomial into Bernstein polynomials and is based on the decomposition of the family of polynomials into its symmetric and antisymmetric parts. It is shown how the inspection of both polynomial families on the upper half of the unit circle can be reduced to the analysis of two related polynomial families on the real interval [–1,1]. Then the Bernstein expansion can be applied in order to check whether both polynomial families have a zero in this interval in common.     

Efficient and Exact Reliability Evaluation for Networks With Imperfect Vertices

The factoring theorem, and BDD-based algorithms have been shown to be efficient reliability evaluation methods for networks with perfectly reliable vertices. However, the vertices, and the links of a network may fail in the real world. Imperfect vertices can be factored like links, but the complexity increases exponentially with their number. Exact algorithms based on the factoring theorem can therefore induce great overhead if vertex failures are taken into account. To solve the problem, a set of exact algorithms is presented to deal with vertex failures with little additional overhead. The algorithms can be used to solve terminal-pair, k-terminal, and all-terminal reliability problems in directed, and undirected networks. The essential variable is defined to be a vertex or a link of a network whose failure has the dominating effect on network reliability. The algorithms are so efficient that it takes less than 1.2 seconds on a 1.67 GHz personal computer to identify the essential variable of a network having 2⁹⁹ paths. When vertex failures in a 3 times 10 mesh network are taken into account, the proposed algorithms can induce as little as about 0.3% of runtime overhead, while the best result from factoring algorithms incurs about 300% overhead     

On the identifiability of finite mixtures of distributions (Corresp.)

Finite mixtures of the following ten families of univariate distributions are shown to be identifiable: logarithmic series, discrete rectangular, rectangular, first law of Laplace, noncentralX^{2}, logistic, generalized logistic, generalized hyperbolic-secant, inverse Gaussian, and random walk. A generalized version of a theorem given by Teicher is used to show that the finite mixtures of the following multivariate distributions are also identifiable: negative binomial, logarithmic series, Poisson, normal, inverse Gaussian, and random walk.     

Three-band biorthogonal interpolating complex wavelets with stopband suppression via lifting scheme

Wavelet research has primarily focused on real-valued wavelet bases. However, the complex filterbanks provide much convenience for complex signal processing. For example, in radar and sonar signal processing, the complex signals from the I/Q receiver can be efficiently processed with complex filterbanks rather than real filterbanks. Specifically, the positive and negative Doppler frequencies imply different physical content in the moving target detector (MTD) and moving target identification (MTI); therefore, it is significant to design complex multiband filterbanks that can partition positive and negative frequencies into different subbands. We design two novel families of three-band biorthogonal interpolating complex filterbanks and wavelets by using the three-band lifting scheme. Unlike the traditional three-band filterbanks, the novel complex filterbank is composed of three channels, including the lowpass channel, the positive highpass channel whose passband distributes in the positive frequency region, and the negative highpass channel in the negative frequency region. Such a filterbank/wavelet naturally provides the ability to extract positive frequency components and negative frequency components from complex signals. Moreover, a novel set of design constraints are introduced to manipulate the stopband characteristic of highpass filters and are referred to as stopband suppression, which strengthens the traditional constraints of vanishing moments. Finally, a numerical method is given to further lower stopband sidelobes.     

Trigonometric Polynomials Positive on Frequency Domains and Applications to 2-D FIR Filter Design

We propose a characterization of multivariate trigonometric polynomials that are positive on a given frequency domain. The positive polynomials are parameterized as a linear function of sum-of-squares polynomials and so semidefinite programming (SDP) is applicable. The frequency domain is expressed via the positivity of some trigonometric polynomials. We also give a bounded real lemma (BRL) in which a bounding condition on the magnitude of the frequency response of a multidimensional finite-impulse-response (FIR) filter is expressed as a linear matrix inequality (LMI). This BRL avoids the problem of a lack of spectral factorization in the multidimensional case. All the proposed theoretical contributions can be implemented only as sufficient conditions, due to degree limitations on the sum-of-square polynomials. However, the two-dimensional (2-D) FIR filter designs we study numerically suggest that these limitations have negligible impact on the optimality.     

k阶拟Bent函数在密码设计和通信中的应用

王育民、何大可提出了布尔函数关于线性函数的r阶相关度E(r)的概念来刻划布尔函数抵抗相关攻击的能力，本文以极小化所有非零相关度E(r)为主要目的，利用k阶拟Bent函数的特殊性质，给出了一类基于k阶拟Bent函数的“最佳”非线性组合设计的实现，构造了一类平衡的，具有高阶相关免疫性，而且非零相关度一致地小的非退化的布尔函数，并比较了它与基于部分Bent函数的“最佳”非线性组合设计的优劣。最后我们又利用k阶拟Bent函数构造了一类Bent互补函数族和Bent侣，Bent互补函数族和Bent侣在最佳信号设计方面意义重大，这也表明k阶拟Bent函数在密码设计和通信领域都有比较广的应用前景。     

Grid Colorings in Steganography

A proper vertex coloring of a graph is called rainbow if, for each vertex v, all neighbors of v receive distinct colors. A k-regular graph G is called rainbow (or domatically full) if it admits a rainbow (k+1)-coloring. The d-dimensional grid graph G_d is the graph whose vertices are the points of Zopf^d and two vertices are adjacent if and only if their l₁-distance is 1. We use a simple construction to prove that G_d is rainbow for all d ges 1. We discuss an important application of this result in steganography     

Conventional and reciprocal approaches to the inverse dipole localization problem of electroencephalography

Forward transfer matrices relating dipole source to surface potentials can be determined via conventional or reciprocal approaches. In numerical simulations with a triangulated boundary-element three-concentric-spheres head model, we compare four inverse electroencephalogram (EEG) solutions: those obtained utilizing conventional or reciprocal forward transfer matrices, relating in each case source dipole components to potentials at either triangle centroids or triangle vertices. Single-dipole inverse solutions were obtained using simplex optimization with an additional position constraint limiting solution dipoles to within the brain region. Dipole localization errors are presented in all four cases, for varying dipole eccentricity and two different values of skull conductivity. Both conventional and reciprocal forward transfer matrices yielded inverse dipole solutions of comparable accuracy. Localization errors were low even for highly eccentric source dipoles on account of the nonlinear nature of the single-dipole solution and the position constraint. In the presence of Gaussian noise, both conventional and reciprocal approaches were also found to be equally robust to skull conductivity errors.     

三角形网格的分块DCT压缩

在现有的代表性三角形网格压缩方法中,先采用一定的网格遍历方法来压缩连接信息,同时用遍历路径上的相邻顶点来对每个顶点的几何坐标进行预测,以压缩几何信息.其主要缺点是只利用了遍历路径上的相邻顶点来进行预测,并没有充分去掉顶点间的相关性.其实在空间中一定局部范围内,所有顶点的坐标间都存在着一定的相关性,这些顶点虽然在空间上相邻,但并不一定在遍历路径上相邻.和图像压缩标准JPEG的思路类似,本文提出一种新的基于分块DCT的网格几何信息压缩方法.先将网格划分成很多基本同样大小的块,利用每个块内的所有顶点按遍历次序排列成一维序列后,坐标呈周期性分布的事实,采用一维DCT变换来去除块内顶点间的相关性.实验表明,分块DCT方法取得了较好的几何信息压缩性能.