多元统计分析中一类矩阵迹函数最小化问题的有效算法

研究来源于多元统计分析中的一类矩阵迹函数最小化问题$\min c+ tr(AX)+\sum\limits_{j=1}^{m}tr(B_j X C_jX^{T}),\ \ {\rm s. t.} \ X^TX=I_p,$其中$c$为常数, $A\in R^{p\times n}\ (n\geq p)$, $B_j\in R^{n\times n}, C_j\in R^{p\times p}$为给定系数矩阵. 数值实验表明已有的Majorization算法虽可行, 但收敛速度缓慢且精度不高. 本文从黎曼流形的角度重新研究该问题, 基于Stiefel流形的几何性质, 构造一类黎曼非单调共轭梯度迭代求解算法, 并给出算法收敛性分析.数值实验和数值比较验证所提出的算法对于问题模型是高效可行的.     

界约束下算子方程最小二乘问题的条件梯度法

研究如下界约束下算子方程最小二乘问题:min x∈Ω‖L(X:A_1,…,At;B_1,…,B_t)-T‖~2,其中‖.‖为Frobenius范数,L(X:A_1…A_t;B_1,…,B_t)为关于X的线性矩阵算子(或齐次线性变换),Ai∈R~(p×m),B_j∈R~(n×q)i,j=1,…,n为算子L的系数矩阵,丁为右端矩阵,ΩR~(m×n)为界约束凸集合.提出了求解问题的条件梯度迭代算法及其简要收敛性分析,并给出条件梯度算法的几类加速形式.随机数据和图像恢复模型数据的实验结果表明说明算法是可行高效的.     

Local Functional Limit Theorems of Increments for Brownian Motion

In this paper, we present a local Csrg–Révész type functional limit theorem for increments of Brownian motion and give its convergence rate. The results also extend the functional forms of Lévy's modulus of continuity for Brownian motion.     

Brown运动增量拟必然局部Strassen重对数律

该文建立了Brown运动增量的拟必然局部Strassen重对数律.利用这一结果,得到了Brown运动拟必然泛函连续模.     

A modified quasi‐Newton diagonal update algorithm for total variation denoising problems and nonlinear monotone equations with applications in compressive sensing

In this paper, we present a new algorithm to accelerate the Chambolle gradient projection method for total variation image restoration. The new proposed method considers an approximation of the Hessian based on the secant equation. Combined with the quasi‐Cauchy equations and diagonal updating, we can obtain a positive definite diagonal matrix. In the proposed minimization method model, we use the positive definite diagonal matrix instead of the constant time stepsize in Chambolle's method. The global convergence of the proposed scheme is proved. Some numerical results illustrate the efficiency of this method. Moreover, we also extend the quasi‐Newton diagonal updating method to solve nonlinear systems of monotone equations. Performance comparisons show that the proposed method is efficient. A practical application of the monotone equations is shown and tested on sparse signal reconstruction in compressed sensing. Copyright © 2015 John Wiley & Sons, Ltd.     

A decoupling two-grid method for the time-dependent Poisson-Nernst-Planck equations

Numerical Algorithms - We study a two-grid strategy for decoupling the time-dependent Poisson-Nernst-Planck equations describing the mass concentration of ions and the electrostatic potential. The...     

Local dynamics and viscoelastic properties of cell biological systems

How the cytoskeleton, a heterogeneous network of dynamic filamentous proteins, provides the cell with structural support is not well understood. Particle-tracking methods, which probe local mechanical properties, are well suited to test existing hypotheses derived from in vitro models of reconstituted cytoskeleton networks. This paper reviews recent applications of single- and multiple-particle tracking microrheology, with an emphasis on the semiflexible polymer F-actin and the flexible polymer keratin, two ubiquitous proteins of the cytoskeleton. Extensive knowledge of the properties of these polymers allows a rigorous comparison between theory and experiments to a level rarely matched by synthetic polymers.     

ANISOTROPIC (p,q)-EQUATIONS WITH COMPETITION PHENOMENA

We consider a nonlinear Robin problem driven by the anisotropic(p,q)-Laplacian and with a reaction exhibiting the competing effects of a parametric sublinear(concave) term and of a superlinear(convex) term.We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies.We also prove the existence of a minimal positive solution and determine the monotonicity and continuity properties of the minimal solution map.