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.     

一种引入通信的多移动机器人编队方法*

提出以视觉跟踪为基础并引入通信进行多机器人的编队控制方法,根据需要编写了一种新的通信协议,采用闭环l-Φ实现编队算法.这种多机器人编队控制避免了视觉系统的局限,能够更好地在复杂未知环境中协作完成任务,解决了编队控制的无反馈和实时性不高的问题,使得机器人能够准确迅速地进行跟踪和通信编队,一起顺利达到目标点.试验结果证明了该方法的有效性.     

Quantification of secondary structure prediction improvement using multiple alignments

The use of multiple sequence alignments for secondary structurepredictions is analysed. Seven different protein families, containingonly sequences of known structure, were considered to providea range of alignment and prediction conditions. Using alignmentsobtained by spatial superposition of main chain atoms in knowntertiary protein structures allowed a mean of 8% in secondarystructure prediction accuracy, when compared to those obtainedfrom the individual sequences. Substitution of these alignmentsby those determined directly from an automated sequence alignmentalgorithm showed variations in the prediction accuracy whichcorrelated with the quality of the multiple alignments and distanceof the primary sequence. Secondary structure predictions canbe reliably improved using alignments from an automatic alignmentprocedure with a mean increase of 6.87percnt;, giving an overallprediction accuracy of 68.5%, if there is a minimum of 25% sequenceidentity between all sequences in a family.     

Mechanical behaviour of a combined joint composed of mechanical fastening and adhesive bonding

A study has been made of ‘combined’ joints consisting of mechanical fastening and adhesive bonding between rigid adherends. The mechanical characteristics of such ‘hybrid’ butt and lap shear joints have been derived by theoretical analysis. Results from experimental tests in combined joints giver reasonable agreement with the theoretical equations relating joint load to deformation.     

半刚性钢-混凝土组合节点受弯承载力的计算

在半刚性钢 -混凝土组合框架中 ,混凝土板中的纵向钢筋增加了节点的强度和刚度 ,但是 ,传统的设计方法往往忽略纵向钢筋的作用而采用简化的计算模型。因此 ,出于经济效益考虑 ,应该根据半刚性组合节点的实际受力性能建立更加准确的计算方法。这里详细介绍了考虑混凝土板纵向钢筋作用的半刚性组合节点受弯承载力的计算方法 ,计算结果表明 ,建议的公式与试验结果吻合良好 ,可供规范制定和工程应用参考。     

Failure load prediction of structural adhesive joints : Part 2: Experimental study

The objective of this study was to determine how the fracture of adhesive joints depends on elastic beam parameters describing the adherends and the applied loads. The basic specimen geometry was the cracked lap shear joint constructed of aluminium alloy with various adherend and bondline thicknesses. Loads were applied in different combinations of bending, tension and shear to generate a failure envelope for each adhesive and specimen geometry. It was found that crack propagation for precracked specimens occured at a critical strain energy release rate but was also a function of the G_I/G_II ratio and the bondline thickness. The experiments also showed that the loads required to propagate a crack in a precracked specimen were always lower than the loads required to break the fillet. Hence, by treating uncracked joints as being cracked, where the fictitious crack tip is assumed to coincide with the location of the fillet, a conservative estimate of the failure load is obtained.     

一种融合多帧ICP和图优化的算法研究

当前基于迭代最近点拼接的同时定位与建图算法,存在误差积累、无法满足大范围定位精度的缺陷。为此,提出一种融合多帧迭代最近点和图优化的算法。在时域上处理点云拼接问题,将单帧迭代最近点算法推广到多帧进行最近点迭代,提取同一地点在不同时刻的数据特征,形成多个封闭循环,再运用基于最小二乘的图优化方法对点云拼接后的全网数据进行全局优化,消除累计误差,提升整体的定位精度。采用鲁巷和密歇根的数据进行测试,结果表明,该方法在一定程度上减少了匹配误差,平均误差为1.0m,最小误差为0.2m,可以满足大范围同步定位与建图的精度需求。     

两种基于个体偏好集结的多属性群决策共识方法

针对多属性群决策中的共识问题, 提出两种使群体达成共识的方法. 假设群体决策的结果以从个体偏好通过集结得到的群体偏好为基础, 在使用算术加权集结算子和几何加权集结算子的条件下, 分别设计相应的共识达成算法, 并对算法的收敛性进行分析. 与已有方法相比, 所提出算法能够体现决策个体的差异和决策个体对群体的影响. 通过某市政图书馆空调系统安装方案的选择表明了所提出方法的合理性和可行性.

     

文本分类中训练集相关数量指标的影响研究

针对训练集对分类性能的影响,从训练集的文本数、类别数以及特征项数这三项数量指标出发进行研究。使用多因素方差分析方法及多种语料库定量探讨该三项数量指标对分类性能的影响规律。结果发现特征项数对分类性能的影响在不同的文本数和类别数时是不同的,分类性能受训练集的这三项指标的交互影响,通过对训练集的这三项指标进行优化,提出了从分类算法、特征项选择法以外提高分类性能的途径。在真实数据上的实验结果表明,该方法可有效提高分类性能。     

一类多时变时滞T-S模糊广义系统的容许控制

研究了一类具有多时变时滞的T-S模糊广义系统的容许控制问题。首先,给出了多时变时滞的T-S模糊广义系统数学模型,并且利用Lyapunov稳定性分析方法,得到了多时变时滞的T-S模糊广义系统的容许的一个充分条件,所得的结果对时变时滞的变化率没有限制。该充分条件可以通过严格线性矩阵不等式来求解。然后基于所给出的容许性定理,提出了状态反馈控制器的设计方法.最后,使用算例说明了所给方法的可行性和有效性。