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。     

Performance variability is related to change in cognition: Evidence from the Victoria Longitudinal Study.

Performance variability across repeated task administrations may be an important indicator of age-related cognitive functioning. In the present investigation, the authors examined whether age differences and change in inconsistency were related to 6-year (3 occasion) cognitive change. Inconsistency scores were computed from 4 reaction time tasks performed by 446 older adults (54-89 years). Replicating previous cross-sectional results, greater inconsistency was observed for older participants even after controlling for differences in response speed. New longitudinal results demonstrated (a) associations between inconsistency at baseline measurement and 6-year change in cognitive performance; (b) longitudinal change in inconsistency; and (c) intraindividual covariation between 6-year change in inconsistency and 6-year change in level of cognitive function. These findings support the view that performance variability serves as a marker of cognitive aging. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

多污染源随机排污的水质影响分析方法及其应用

针对污水排放特征,将污染源分为连续排放型污染源和间隙排放型污染源。对连续排放型污染源,采用确定性方法定义污染源强;而对于间隙排放型污染源,运用不确定性理论,根据其排放污染源的随机统计特征,对污染源进行随机概化。将不确定性理论应用于多污染源随机排污对环境水体的水质影响分析,给出了基于不确定性理论的水质影响预测方法,建立了二维随机水质数学模型。并将该方法应用于某市水源地水质影响的随机分析,得到了在多污染源随机排放协同影响下水质浓度随机变化的统计特征。     

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.     

电化学腐蚀法制备微细群圆柱

提出了微细群圆柱结构电化学腐蚀加工法及其形状和尺寸控制方式。根据电化学腐蚀基本原理,通过有限元分析计算群圆柱电化学腐蚀加工过程中的电场分布,优化设计阴极形状。开展了电化学腐蚀法制备微细群圆柱结构的工艺试验,获得了良好的试验结果。     

高灵敏度的多波长多光束干涉仪

作者用多纵模He-Ne激光照明多光束Fabry-Perot或Fizeau干涉仪,在一个自由光谱范围内,形成与不同波长对应的子条纹,相邻条纹间的间隔代表的波长数依赖于He-Ne激光腔的光学长度npL与F-P腔长nd之比r=nd/npL.当r是整数时,不同波长对应的相邻干涉级次相互重叠,条纹间隔为λ/2且强度最大;当r是分数时,r=N/M,N,M为互质的整数,相邻条纹之间间隔为λ/2M.不难做到M=10,条纹间隔为K/20.由于多光束干涉条纹细而锐,有利于读数精度提高,可以测量λ/500的程差变化,不需内插就可以给出空间分布的足够信息.这对光学元件的高精度面形检验及低密度流场显示有实际的应用前景.给出了应用的若干例子.     

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.     

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.