Multiplicative Operator Splittings in Nonlinear Diffusion: From Spatial Splitting to Multiple Timesteps

Operator splitting is a powerful concept used in many diversed fields of applied mathematics for the design of effective numerical schemes. Following the success of the additive operator splitting (AOS) in performing an efficient nonlinear diffusion filtering on digital images, we analyze the possibility of using multiplicative operator splittings to process images from different perspectives.We start by examining the potential of using fractional step methods to design a multiplicative operator splitting as an alternative to AOS schemes. By means of a Strang splitting, we attempt to use numerical schemes that are known to be more accurate in linear diffusion processes and apply them on images. Initially we implement the Crank-Nicolson and DuFort-Frankel schemes to diffuse noisy signals in one dimension and devise a simple extrapolation that enables the Crank-Nicolson to be used with high accuracy on these signals. We then combine the Crank-Nicolson in 1D with various multiplicative operator splittings to process images. Based on these ideas we obtain some interesting results. However, from the practical standpoint, due to the computational expenses associated with these schemes and the questionable benefits in applying them to perform nonlinear diffusion filtering when using long timesteps, we conclude that AOS schemes are simple and efficient compared to these alternatives.We then examine the potential utility of using multiple timestep methods combined with AOS schemes, as means to expedite the diffusion process. These methods were developed for molecular dynamics applications and are used efficiently in biomolecular simulations. The idea is to split the forces exerted on atoms into different classes according to their behavior in time, and assign longer timesteps to nonlocal, slowly-varying forces such as the Coulomb and van der Waals interactions, whereas the local forces like bond and angle are treated with smaller timesteps. Multiple timestep integrators can be derived from the Trotter factorization, a decomposition that bears a strong resemblance to a Strang splitting. Both formulations decompose the time propagator into trilateral products to construct multiplicative operator splittings which are second order in time, with the possibility of extending the factorization to higher order expansions. While a Strang splitting is a decomposition across spatial dimensions, where each dimension is subsequently treated with a fractional step, the multiple timestep method is a decomposition across scales. Thus, multiple timestep methods are a realization of the multiplicative operator splitting idea. For certain nonlinear diffusion coefficients with favorable properties, we show that a simple multiple timestep method can improve the diffusion process.     

基于LabWindows/CVI的多线程测控软件设计技术

多线程技术是W in32操作系统的一项重要软件技术。CVI 6.0及其以后版本提供了线程池和异步定时器两种多线程运行机制,为测控软件的设计开发带来了一次技术飞跃。文中结合测控软件设计实例,详细介绍了在CVI平台下多线程编程技术的应用方法。     

Determining the characteristics of systems with multiple inputs and multiple outputs

A simple and computationally efficient method of determining the transfer function and other characteristics of systems with multiple inputs and multiple outputs (MIMO systems) described by autoregression equations is proposed. The method is based on the use of the discrete Fourier transformation. The algorithm is highly suitable for computer implementation. The efficiency and simplicity of the method are illustrated using the example of a system with three inputs and three outputs. The proposed concept may be applied to systems described by the autoregression sliding mean.     

具有多重焦点的波带透镜的设计

本文提出了一种新型的具有多重焦点的波带透镜的概念及其设计方法。可提供某些特定的光场分布,而且具有性能稳定、微型化和可实际制作等特点。     

MIMO链路ad hoc网络传输调度算法

针对MIMO链路ad hoc网络中已有传输调度算法未充分利用MIMO空间复用能力的问题,提出了一种新的传输调度算法.该算法通过考虑MIMO的多流接收能力而有效地减小了调度帧长,通过合理安排节点分配顺序使得节点分配的数据流比较平均,同时,该算法通过允许节点发送多个数据流而高效利用了MIMO的空间复用能力.推导分析了传输调度算法的通过量和时延性能,结果表明,与已有算法相比,采用文中算法可以提高网络的通过量,减小网络的平均时延和最大时延.     

EIGENVECTORS-BASED PARALLELISATION OF NESTED LOOPS WITH AFFINE DEPENDENCES

Abstract

This paper presents a method for parallelising nested loops with affine dependences. The data dependences of a program are represented exactly using a dependence matrix rather than an imprecise dependence abstraction. By a careful analysis of the eigenvectors and eigenvalues of the dependence matrix, we detect the parallelism inherent in the program, partition the iteration space of the program into sequential and parallel regions, and generate parallel code to execute these regions. For a class of programs considered in the paper, the proposed method can expose more coarse-grain and fine-grain parallelism than a hyperplane-based loop transformation.     

EFFECTIVE PARALLELIZATION TECHNIQUES FOR LOOP NESTS WITH NON-UNIFORM DEPENDENCES

The parallelism of loop nests with non-uniform dependences is difficult to extract and ineffectively explored by the existing parallelization schemes. In this paper, we propose new efficient techniques in extracting parallelism of loop nests with non-uniform dependences using their irregularity. By this way, current highly parallel multiprocessor systems such as multithreaded and clustering multiprocessor systems can be fully utilized. These four mechanisms are (a) parallelization part splitting, (b) partial parallelization decomposition, (c) irregular loop interchange and (d) growing pattern detection. They explore parallelisms of special parallel patterns for nested loops with non-uniform dependences. The loop transformations used in uniform loops are also applied in non-uniform dependence loops after legality tests. We apply the results of classical convex theory and detect special parallel patterns of dependence vectors. We also proposed an algorithm that combines above mechanisms to enhance parallelism. We demonstrate that our technique gives much better speedup and extracts more parallelism than the existing techniques. Thus, we are encouraged by these apparent enhancements to pursue further development.     

多特征自适应融合的粒子滤波跟踪算法

针对跟踪过程中目标形态不断变化或部分遮挡导致鲁棒性差的问题,提出一种基于多特征自适应融合的粒子滤波跟踪算法.该算法从视觉特征集中选取了描述能力强的2种特征,并将其按照与目标模型的多尺度相似度进行线性融合;为了减小跟踪漂移,通过计算当前目标模型与初始目标模型的多尺度相似度自适应地更新目标模型.大量仿真实验结果表明,文中算法可以鲁棒地跟踪到部分遮挡和形态变化的运动目标.     

异类传感器实时信息融合的STMHM算法

异类传感器实时信息融合由于两类设备的数据率不同和数据误差的限制,一直未得到有效解决,提出一种空时二维多假设模型(STMHM)算法来解决该问题。设计的融合数据模型,将异类传感器的测量数据映射在二维直角坐标系下;按照新的融合数据模型分别构建两类传感器的目标量测空间和融合空间;设计量测空间时间初始化方法和目标实体空间的滤波算法;通过仿真验证表明:该算法能够实现异类传感器的信息融合,初次融合成功的确认时间在3～5个主动传感器扫描周期。     

基于两电极体系的水质检测分析平台设计

为实现对水质的多参数检测,设计了一个基于两电极体系的水质检测分析平台。该检测平台通过最小化极化电流的思想,采用辅助电极面积远大于工作电极的电极参数,设计了基于两电极体系的集成电极和软硬件系统,摈弃了传统三电极体系的参比电极,同时克服了传统三电极体系容易污染样品的缺点,能实现电化学工作站的诸多功能。本研究在该检测平台上开展了水样的电导率(EC)、pH和重金属浓度的检测研究,获得了较好的结果,可用于实验室及工业现场的水质监测。