Conical Partition Algorithm for Maximizing the Sum of dc Ratios

The following problem is considered in this paper: 0, j = 1,\ldots,m,$$" align="middle" border="0"> are d.c. (difference of convex) functions over a convex compact set D in R^n. Specifically, it is reformulated into the problem of maximizing a linear objective function over a feasible region defined by multiple reverse convex functions. Several favorable properties are developed and a branch-and-bound algorithm based on the conical partition and the outer approximation scheme is presented. Preliminary results of numerical experiments are reported on the efficiency of the proposed algorithm.AMS Subject Classifications: 90C32, 90C30, 65K05.The authors were partially supported by a Grant-in-Aid (Yang Dai: C-13650444; Jianming Shi and Shouyang Wang: C-14550405) of the Ministry of Education, Science, Sports and Culture of Japan.     

Maximizing the Sum of Superdiagonal Matrix Elements in Local Variational Problems with a Singular Integrand

We show that the extremum of the local variational problem with a singular nonlinear integrand found by the optimal path continuation procedure is in fact a local extremum. Conditions simplifying the search for a global extremum are identified. Translated from Prikladnaya Matematika i Informatika, No. 3, pp. 11–19, 1999.     

带有尖形式Fourier系数的指数和估计

设λ_f/(n)是全模群Γ上权为k的全纯Hecke特征形f的第n个Fourier系数,Λ(n)是Mangoldt函数.本文得到了如下估计∑_(Xn≤2X)Λ(n)λ_f(n)e(n~(1/2)α)■f,αX~(5/6)(logX)~(13/2),(α0),改进了Zhao的结果。     

Distribution Metrics and Image Segmentation

The purpose of this paper is to describe certain alternative metrics for quantifying distances between distributions, and to explain their use and relevance in visual tracking. Besides the theoretical interest, such metrics may be used to design filters for image segmentation, that is for solving the key visual task of separating an object from the background in an image. The segmenting curve is represented as the zero level set of a signed distance function. Most existing methods in the geometric active contour framework perform segmentation by maximizing the separation of intensity moments between the interior and the exterior of an evolving contour. Here one can use the given distributional metric to determine a flow which minimizes changes in the distribution inside and outside the curve.     

关于线性变换的像空间与核空间的直和

讨论数域P上有限维线性空间V上线性变换A的方幂A~k的像空间ImA~k与核空间KerA~k的直和,并将结论推广到无限维线性空间.证明了:V=ImA~k+KerA~k当且仅当ImA~k=ImA~(k+1),以及ImA~k∩KerA~k=0当且仅当KerA~k=KerA~(k+1).     

一个与Dedekind和相关的新和式及其在特殊点的值

本文利用正整数模q的正则数的定义以及解析方法研究一类与Dedekind和有关的和式的计算问题,并给出这个和式在一些特殊点上有趣的恒等式.     

改进的水平集方法及其在图像分割中的应用

为了稳定水平集函数的演化过程,提出了一种改进的距离规则化水平集方法,新方法与传统的距离规则化方法相比,能更好地维持水平集函数的符号距离函数特性.为了检验新方法的性能,首先将其应用到基于边缘的主动轮廓模型中并用于图像分割,实验结果表明新方法能有效提高分割效率和精度.同时,还将新方法应用到一种改进的基于区域的主动轮廓模型中,实验结果不仅进一步验证了新方法的有效性,还表明新方法能改善初始位置的鲁棒性.     

Asymptotic Evaluation of a Lattice Sum Associated with the Laplacian Matrix

Analysis Mathematica - The Laplacian matrix is of fundamental importance in the study of graphs, networks, random walks on lattices, and arithmetic of curves. In certain cases, the trace of its...     

一个类似广义Dedekind和S_2(h,n,k)的二次均值

本文的主要目的是利用 Dirichlet L -函数的均值研究 n为奇数时 ,类似广义 Dedekind和 S2 ( h,n,k)的二次均值 ,得到了两个有趣的渐近公式 .     

非局部加权模糊C均值聚类图像分割

去除噪声与保持图像细节特征是含噪声图像分割中面临的一对矛盾。为此,提出一种改进的模糊C均值算法,通过引入非局部加权距离以抑制噪声影响。其中,权值通过局部图像块距离的指数形式计算,并利用半局部统计特性自适应调整其光滑参数。实验结果表明,新方法具有较强的抗噪声能力,同时能够保持较多地细节特征。     

基于随机谱聚类的图像分割算法

图像分割就是把感兴趣的区域从背景中分割、提取出来,为了使分割出来的图像特征信息完整,根据图像的灰度值和空间距离构造了一种相似度函数,得到基于图的灰度值的相似度矩阵,将图像分割转化为图论最小割问题,然后运用谱聚类算法进行分割.针对谱聚类算法运行所需的内存空间和运算量大的特点,提出一种考虑概率因素的随机抽样谱聚类算法.在具体实施时,为了减少背景噪声对分割结果的影响,对图像进行了滤波预处理.结果表明,算法稳定性好,相对现有算法,分割效果得到改善.     

Maximizing a congruence with respect to its partition of idempotents

For a congruence σ on a semigroupS a congruence μ(σ) onS, containing σ, is defined such that the semigroupS/σ is fundamental if and only if σ=μ(σ). The congruence μ(σ) is shown to possess maximality properties and for idempotent-surjective semigroups, μ(σ) is the maximum congruence with respect to the partition of the idempotents determined by σ. Thus μ is the maximum idempotent-separating congruence on any idempotent-surjective semigroup. It is shown that μ(μ(σ))=μ(σ). If ρ is another congruence onS, possibly with the same partition of the idempotents as σ, then it is of interest to know when ρ⊆σ (or ρ⊆μ(σ)) implies μ(ρ)⊆μ(σ) or even μ(ρ)=μ(σ). These implications are not true in general but if σ⊆ρ⊆μ(σ) then μ(ρ)⊆μ(σ). IfS is an idempotent-surjective semigroup and ρ and σ have the same partition of the idempotents then μ(ρ)=μ(σ).     

Maximizing the probability of attaining a target prior to extinction

We present a dynamic programming-based solution to the problem of maximizing the probability of attaining a target set before hitting a cemetery set for a discrete-time Markov control process. Under mild hypotheses we establish that there exists a deterministic stationary policy that achieves the maximum value of this probability. We demonstrate how the maximization of this probability can be computed through the maximization of an expected total reward until the first hitting time to either the target or the cemetery set. Martingale characterizations of thrifty, equalizing, and optimal policies in the context of our problem are also established.     

Maximizing the minimum source-sink path subject to a budget constraint

Given a linear cost function for lengthening arcs, a technique is shown for maximizing, within a budget, the shortest source—sink path length in a graph. The computation is equivalent to the parametric solution of a minimum cost flow problem.This work was done while G.C. Harding was at Cornell University.The work of D.R. Fulkerson was supported by the National Science Foundation under Grant MPS74-24026 and by the Office of Naval Research under Grant NR 044-439.     

基于元胞自动机模型的图像分割算法

针对图像处理中的图像分割任务,我们提出了一个基于模糊元胞自动机模型的图像分割算法.将元胞自动机原理中的演化规则换为模糊规则建立模糊元胞自动机模型,使图像中灰度水平介于目标和背景之间的像素得以更好地归类,从而得到较好的图像分割结果.     

On a Variational Model for Selective Image Segmentation of Features with Infinite Perimeter

Variational models provide reliable formulation for segmentation of features and their boundaries in an image, following the seminal work of Mumford-Shah (1989, Commun. Pure Appl. Math.) on dividing a general surface into piecewise smooth sub-surfaces. A central idea of models based on this work is to minimize the length of feature’s boundaries (i.e., H1 Hausdorff measure). However there exist problems with irregular and oscillatory object boundaries, where minimizing such a length is not appropriate, as noted by Barchiesi et al. (2010, SIAM J. Multiscale Model. Simu.) who proposed to miminize L2 Lebesgue measure of the γ-neighborhood of the boundaries. This paper presents a dual level set selective segmentation model based on Barchiesi et al. (2010) to automatically select a local feature instead of all global features. Our model uses two level set functions: a global level set which segments all boundaries, and the local level set which evolves and finds the boundary of the object closest to the geometric constraints. Using real life images with oscillatory boundaries, we show qualitative results demonstrating the effectiveness of the proposed method.     

Renewed Looks at the Distribution of a Sum of Independent or Dependent Discrete Random Variables and Related Problems

Methodology and Computing in Applied Probability - Butler and Stephens (2017) have investigated the exact and approximate distributions of a sum S of independent binomial random variables with...     

Minimizing a Sum of Norms Subject to Linear Equality Constraints

Numerical analysis of a class of nonlinear duality problems is presented. One side of the duality is to minimize a sum of Euclidean norms subject to linear equality constraints (the constrained MSN problem). The other side is to maximize a linear objective function subject to homogeneous linear equality constraints and quadratic inequalities. Large sparse problems of this form result from the discretization of infinite dimensional duality problems in plastic collapse analysis.The solution method is based on the l ₁ penalty function approach to the constrained MSN problem. This can be formulated as an unconstrained MSN problem for which the first author has recently published an efficient Newton barrier method, and for which new methods are still being developed.Numerical results are presented for plastic collapse problems with up to 180000 variables, 90000 terms in the sum of norms and 90000 linear constraints. The obtained accuracy is of order 10^-8 measured in feasibility and duality gap.     

求解分段常数图象分割模型的一个快速算法

针对Xue-ChengTai等提出的分段常数图象分割模型,我们提出了一个新的快速求解算法。通过引进一个函数来选择模型中的正则化参数β的值,并判断在迭代过程中何时求解不含惩罚项的泛函F。此函数的引入有效地加速了算法的收敛速度。结合原始-对偶Newton方法来求解总变差最小化问题。数值试验表明新算法具有很快的收敛速度与良好的分割效果,且算法对初始值的要求不高。