LPNN-based approach for LASSO problem via a sequence of regularized minimizations

In compressive sampling theory, the least absolute shrinkage and selection operator (LASSO) is a representative problem. Nevertheless, the non-differentiable constraint impedes the use of Lagrange programming neural networks (LPNNs). We present in this article the -LPNN model, a novel algorithm that tackles the LASSO minimization together with the underlying theory support. First, we design a sequence of smooth constrained optimization problems, by introducing a convenient differentiable approximation to the non-differentiable -norm constraint. Next, we prove that the optimal solutions of the regularized intermediate problems converge to the optimal sparse signal for the LASSO. Then, for every regularized problem from the sequence, the -LPNN dynamic model is derived, and the asymptotic stability of its equilibrium state is established as well. Finally, numerical simulations are carried out to compare the performance of the proposed -LPNN algorithm with both the LASSO-LPNN model and a standard digital method.     

Fixed point theorems on fuzzy normed linear spaces

In this paper, definitions of strongly fuzzy convergent sequence, l-fuzzy weakly convergent sequence and l-fuzzy weakly compact set are given in a fuzzy normed linear space. The concepts of fuzzy normal structure, fuzzy non-expansive mapping, uniformly convex fuzzy normed linear space are introduced and fixed point theorems for fuzzy non-expansive mappings are proved.     

A Survey on the Numerics and Computations for the Landau-Lifshitz Equation of Micromagnetism

The Landau-Lifshitz (LL)equation of micromagnetism governs rich variety of the evolution of magnetization patterns in ferromagnetic media. This is due to the complexity of physical quantities appearing in the LL equation. This complexity causes also an interesting mathematical properties of the LL equation: nonlocal character for some quantities,nonconvex side-constraints, strongly nonlinear terms. These effects influence also the numerical approximations. In this work, recent developments on the approximation of weak solutions, together with the overview of well-known methods for strong solutions,are addressed. Author is supported by the Fund for Scientific Research - Flanders FWO (Belgium).     

网络融合边界的电信DoS攻击检测*

为了检测网络融合边界的电信拒绝服务攻击,首先针对攻击的类型分别提出了基于呼叫统计或流量信号分析的检测方法,并采用分步骤的策略设计了检测系统,将两种检测算法分别应用于粗检测步骤,再通过精检测步骤确认攻击并找出攻击源.模拟实验结果表明,该方案能够有效地检测出典型的攻击,并能够实时在线检测,具有良好的实用价值,为应对网络融合所带来的新安全问题提供了一种解决方案.     

Dual–primal proximal point algorithms for extended convex programming

This paper presents a class of dual–primal proximal point algorithms (PPAs) for extended convex programming with linear constraints. By choosing appropriate proximal regularization matrices, the application of the general PPA to the equivalent variational inequality of the extended convex programming with linear constraints can result in easy proximal subproblems. In theory, the sequence generated by the general PPA may fail to converge since the proximal regularization matrix is asymmetric sometimes. So we construct descent directions derived from the solution obtained by the general PPA. Different step lengths and descent directions are chosen with the negligible additional computational load. The global convergence of the new algorithms is proved easily based on the fact that the sequences generated are Fejér monotone. Furthermore, we provide a simple proof for the O(1/t) convergence rate of these algorithms.     

A method for numerical solution of a multidimensional convection-diffusion problem

We propose a modification of the additive splitting algorithm to solve the convection-diffusion problem using an efficient finite-difference scheme. The modification decreases the number of data exchanges and their amount during the numerical solution of a system of multidimensional equations. Approximation, stability, and convergence are considered. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 100–107, January–February 2009.     

计算机辅助外科手术空间配准技术的研究

医学图像和实际手术空间的配准问题是计算机辅助外科手术技术的一个重要的研究热点,它能够帮助医生选择最佳手术路径和减小手术损伤,实现手术的方便快捷和微创,提高手术成功率。主要研究了一种基于ICP算法的计算机辅助外科手术中空间配准技术,通过获取实验模型的空间坐标信息,进行点集配准,找到最优旋转矩阵和最优平移向量。并通过仿真实验给出了模拟的配准结果,仿真试验结果表明,ICP算法配准精度高,适用于计算机辅助外科手术。     

A general formulation of monotonically convergent algorithms in the control of quantum dynamics beyond the linear dipole interaction

This paper presents a general method to formulate monotonically convergent algorithms for identifying optimal control fields to manipulate quantum dynamics phenomena beyond the linear dipole interaction. The method, facilitated by a field-dependent dipole moment operator, is based on an integral equation of the first kind arising from the Heisenberg equation of motion for tracking a time-dependent, dynamical invariant observable associated with a reference control field.     

Existence of optimal controls for systems driven by FBSDEs

We prove the existence of optimal relaxed controls as well as strict optimal controls for systems governed by non linear forward-backward stochastic differential equations (FBSDEs). Our approach is based on weak convergence techniques for the associated FBSDEs in the Jakubowski S-topology and a suitable Skorokhod representation theorem.     

A Jacobi-type method for computing balanced realizations

A new numerical scheme for computing balancing coordinate transformations in linear systems theory is presented. The method is closely related to the Jacobi method for diagonalizing symmetric matrices. Here the minimization of the sum of traces of the Gramians by orthogonal and nonorthogonal Jacobi-type rotations is considered. The algorithm is shown to be globally convergent to a balancing transformation that arranges the Hankel singular values in a prescribed ordering. Local quadratic convergence of the algorithm is shown.