Control synthesis for a class of nonlinear systems based on partition of unity

A partition-of-unity-based approach is proposed to derive an approximate model for a class of nonlinear systems. The precision of the approximate model is analyzed by using the modulus of continuity of continuous functions. The system stability of the approximate model is analyzed by using Lyapunov stability theory. A design algorithm for constructing tracking controllers with tracking performance related to tracking error is given based on the approximate model and the partition of unity method.     

Control synthesis for a class of nonlinear systems based on partition of unity

A partition-of-unity-based approach is proposed to derive an approximate model for a class of nonlinear systems. The precision of the approximate model is analyzed by using the modulus of continuity of continuous functions. The system stability of the approximate model is analyzed by using Lyapunov stability theory. A design algorithm for constructing tracking controllers with tracking performance related to tracking error is given based on the approximate model and the partition of unity method.     

Radial basis function partition of unity method for modelling water flow in porous media

Water flow in variably-saturated porous media is modelled by using the highly nonlinear parabolic Richards’ equation. The nonlinearity is due to the hydraulic conductivity and moisture content variables. The latter were estimated by using experimental models, including Gardner, Burdine, Mualem and van Genuchten models. The aim of this work is to develop a new technique based on the radial basis function partition of unity method (RBFPUM) and Gardner model in order to solve Richards’ equation in one and two dimensions. We have used Gardner model to handle the nonlinearity issue and the RBFPUM is used to approximate the solution of the linearized Richards’ equation. Our proposed algorithm is based on testing many configurations of the partitions number and selecting the optimal shape parameter for each case. Then we pick up the optimal configuration (partitions number-shape parameter) that yields the best solution in terms of error and conditioning number. By following this procedure, an optimal solution is ensured for our given problem. As numerical tests, we consider the vertical infiltration of water in soils in order to validate our proposed method.     

基于规则的专家系统中不确定性推理的研究

提出了权值法和修正权值法两种不确定性推理算法,与常用的几种方法相比,权值法根据各证据重要程度的不同,区别对待证据的可信度信息,同时充分利用每一条信息;修正权值法除了具有权值法的优点外,又区分了可信度分布的差异。运用修正权值法已成功建造了多个实用专家系统。     

基于势函数的标签传播社区发现算法

针对标签传播算法(LPA)存在大量随机性、算法稳定性差的问题,提出了基于数据场势函数的标签传播算法(LPAP)。该算法计算所有节点的势值,搜索势值极值点。初始化时仅赋予势值极值点以标签,迭代过程中根据邻接节点中相同标签节点势值之和更新标签,所有节点标签不再改变时迭代结束。实验结果表明：该算法得到的社区划分方式平均是LPA的4.0%,是平衡传播算法(BPA)的12.9%;信息变化参数平均是LPA的45.1%,是BPA的73.3%。具有更好的稳定性,适用于大型网络的社区发现。     

Representing and processing lineages over uncertain data based on the Bayesian network

Processing lineages (also called provenances) over uncertain data consists in tracing the origin of uncertainty based on the process of data production and evolution. In this paper, we focus on the representation and processing of lineages over uncertain data, where we adopt Bayesian network (BN), one of the popular and important probabilistic graphical models (PGMs), as the framework of uncertainty representation and inferences. Starting from the lineage expressed as Boolean formulae for SPJ (Selection–Projection–Join) queries over uncertain data, we propose a method to transform the lineage expression into directed acyclic graphs (DAGs) equivalently. Specifically, we discuss the corresponding probabilistic semantics and properties to guarantee that the graphical model can support effective probabilistic inferences in lineage processing theoretically. Then, we propose the function-based method to compute the conditional probability table (CPT) for each node in the DAG. The BN for representing lineage expressions over uncertain data, called lineage BN and abbreviated as LBN, can be constructed while generally suitable for both safe and unsafe query plans. Therefore, we give the variable-elimination-based algorithm for LBN's exact inferences to obtain the probabilities of query results, called LBN-based query processing. Then, we focus on obtaining the probabilities of inputs or intermediate tuples conditioned on query results, called LBN-based inference query processing, and give the Gibbs-sampling-based algorithm for LBN's approximate inferences. Experimental results show the efficiency and effectiveness of our methods.     

Parallel exact inference on the Cell Broadband Engine processor

We present the design and implementation of a parallel exact inference algorithm on the Cell Broadband Engine (Cell BE) processor, a heterogeneous multicore architecture. Exact inference is a key problem in exploring probabilistic graphical models, where the computation complexity increases dramatically with the network structure and clique size. In this paper, we exploit parallelism in exact inference at multiple levels. We propose a rerooting method to minimize the critical path for exact inference, and an efficient scheduler to dynamically allocate SPEs. In addition, we explore potential table representation and layout to optimize DMA transfer between local store and main memory. We implemented the proposed method and conducted experiments on the Cell BE processor in the IBM QS20 Blade. We achieved speedup up to 10 × on the Cell, compared to state-of-the-art processors. The methodology proposed in this paper can be used for online scheduling of directed acyclic graph (DAG) structured computations.     

New analytical lower bounds on the clique number of a graph

This paper proposes three new analytical lower bounds on the clique number of a graph and compares these bounds with those previously established in the literature. Two proposed bounds are derived from the well-known Motzkin–Straus quadratic programming formulation for the maximum clique problem. Theoretical results on the comparison of various bounds are established. Computational experiments are performed on random graph models such as the Erdös-Rényi model for uniform graphs and the generalized random graph model for power-law graphs that simulate graphs with different densities and assortativity coefficients. Computational results suggest that the proposed new analytical bounds improve the existing ones on many graph instances.     

基于朗斯基函数的混合高斯模型运动目标检测*

针对传统的混合高斯模型在进行运动目标检测时存在拖影和性能差的缺点,本文提出了一种融合朗斯基函数和帧间差分法的混合高斯背景建模算法。该改进算法通过朗斯基矩阵行列式判断相邻像素间空间域相关性,以此增加模型参数更新条件,改进模型参数更新机制;并利用帧间差分法检测运动目标轮廓的灵敏性,将两种检测结果布尔或运算,完善目标轮廓。实验结果表明,该改进算法对拖影现象达到很好的抑制作用,并使算法检测性能得到提高。     

基于广义变分模型的自适应图像去噪算法

通过分析全变分(TV)去噪模型的优缺点,提出了一种新的改进算法。该算法根据最大后验概率(MAP)和马尔可夫随机场(MRF)的理论,推导出一个广义变分的图像去噪模型,并对平衡正则化项和数据保真项的Lagrange乘子λ进行了自适应改进,最后采用了一种鲁棒性好和边缘保持能力强的势函数,结合梯度加权最速下降法和半点格式的数值迭代算法对自适应的广义变分去噪模型寻优求解。实验结果表明,新模型能很好地应用于图像去噪,与现有的算法相比,在峰值信噪比有所提高的同时,图像的主观视觉效果也更好。