二分(0,mf-m+1)-图的正交(0,f)-因子分解

设G=(X,Y,E(G))是一个二分图,分别用V(G)=XUY和E(G)表示G的顶点集和边集.设f是定义在V(G)上的整数值函数且对(A)x∈V(G)有f(x)≥k.设H_1,H_2,…,H_k是G的k个顶点不相交的子图,且|E(H_i)|=m,1≤i≤k.本文证明了每个二分(0,mf-m+1)-图G有一个(0,f)-因子分解正交于Hi(i=1,2,…,k).     

Lower bounds in communication complexity based on factorization norms

We introduce a new method to derive lower bounds on randomized and quantum communication complexity. Our method is based on factorization norms, a notion from Banach Space theory. This approach gives us access to several powerful tools from this area such as normed spaces duality and Grothendiek's inequality. This extends the arsenal of methods for deriving lower bounds in communication complexity. As we show, our method subsumes most of the previously known general approaches to lower bounds on communication complexity. Moreover, we extend all (but one) of these lower bounds to the realm of quantum communication complexity with entanglement. Our results also shed some light on the question how much communication can be saved by using entanglement. It is known that entanglement can save one of every two qubits, and examples for which this is tight are also known. It follows from our results that this bound on the saving in communication is tight almost always. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009     

时变系统的稳定化

This paper deals with the stabilization problem for linear time-varying systems within the framework of nest algebras. We give a necessary and sufficient condition for a class of plants to be stabilizable, and we also study the simultaneous and strong stabilization problems.     

Study of Convection in a Liquid with a Free Surface Using Exponential Fitting Discretization

The two-dimensional flow of viscous incompressible liquid in a square cavity with a Tree boundary and differentially heated vertical sides is considered in the present work. The influence of gravitational and thermocapillary convection on temperature and velocity fields is studied in a large range of dimensionless parameters and similarity criteria using method of exponential fitting discretization. Limiting cases of dimensionless parameters are analyzed numerically.     

An alternating direction algorithm for matrix completion with nonnegative factors

This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative low-rank matrices X and Y so that the product XY approximates a nonnegative data matrix M whose elements are partially known (to a certain accuracy). This problem aggregates two existing problems: (i) nonnegative matrix factorization where all entries of M are given, and (ii) low-rank matrix completion where nonnegativity is not required. By taking the advantages of both nonnegativity and low-rankness, one can generally obtain superior results than those of just using one of the two properties. We propose to solve the non-convex constrained least-squares problem using an algorithm based on the classical alternating direction augmented Lagrangian method. Preliminary convergence properties of the algorithm and numerical simulation results are presented. Compared to a recent algorithm for nonnegative matrix factorization, the proposed algorithm produces factorizations of similar quality using only about half of the matrix entries. On tasks of recovering incomplete grayscale and hyperspectral images, the proposed algorithm yields overall better qualities than those produced by two recent matrix-completion algorithms that do not exploit nonnegativity.     

基于改进梯度投影NMF和复Contourlet变换的遥感图像融合

为了尽可能地保留全色图像的空间信息和多光谱图像的光谱信息,提出了一种基于改进梯度投影非负矩阵分解和复Contourlet变换的遥感图像融合方法.首先,以多光谱图像的强度分量图像为标准,对全色图像做直方图匹配,得到新的全色图像;然后,利用复Contourlet变换分别分解多光谱图像的强度分量图像和新的全色图像,得到各自对应的低频分量和高频分量;接着,对两幅低频分量图像采用改进梯度投影的非负矩阵分解作为融合规则获取新的低频分量,并对两幅高频分量图像使用系数绝对值较大法获取新的高频分量;最后,通过逆复Contourlet变换和逆色调-饱和度-强度变换获得融合后的图像.大量实验结果表明,与HSI方法、NMF与无下采样Contourlet变换结合的方法以及提升小波变换与HSI结合的方法相比,本文方法获得的融合图像具有更高的空间分辨率和更多的光谱信息.     

关于酉对称矩阵的QR分解及其算法

为了简化大型行(列)酉对称矩阵的QR分解,研究了行(列)酉对称矩阵的性质,获得了一些新的结果,给出了行(列)酉对称矩阵的QR分解的公式和快速算法,它们可极大地减少行(列)酉对称矩阵的QR分解的计算量与存储量,并且不会丧失数值精度.同时推广和丰富了邹红星等(2002)的研究内容,拓宽了实际应用领域的范围.     

Computing eigenvectors of block tridiagonal matrices based on twisted block factorizations

New methods for computing eigenvectors of symmetric block tridiagonal matrices based on twisted block factorizations are explored. The relation of the block where two twisted factorizations meet to an eigenvector of the block tridiagonal matrix is reviewed. Based on this, several new algorithmic strategies for computing the eigenvector efficiently are motivated and designed. The underlying idea is to determine a good starting vector for an inverse iteration process from the twisted block factorizations such that a good eigenvector approximation can be computed with a single step of inverse iteration.     

(0, mf-k+1)-图中具有正交(0,f)-因子分解的子图

设G是一个简单图, f是定义在V(G)上的整数值函数,且m是大于等于2的整数. 讨论(0, mf-k+1)-图G的正交因子分解, 并且证明了对任意的1≤k≤m, (0, mf-k+1)-图G中存在着一个子图R, 使得R有一个(0,f)-因子分解正交于图G中的任意一个k-子图H.     

Generating Uniformly Distributed Random 2‐Designs with Block Size 3

Jacobson and Matthews introduced the most hopeful method known for efficiently generating uniformly distributed random Latin squares. Cameron conjectures that the same Markov chain will also generate all of the other generalized 2‐designs with block size 3 uniformly at random. For a generalization of Latin squares, we give an affirmative result for any admissible parameter values. We also give the first insight and analysis into a generalization of the 1‐factorization of the complete graph by giving an affirmative result for some admissible parameter values. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 368–380, 2012