Stabilization of planar collective motion with limited communication

This paper proposes a design methodology to stabilize relative equilibria in a model of identical, steered particles moving in the plane at unit speed. Relative equilibria either correspond to parallel motion of all particles with fixed relative spacing or to circular motion of all particles around the same circle. Particles exchange relative information according to a communication graph that can be undirected or directed and time-invariant or time-varying. The emphasis of this paper is to show how previous results assuming all-to-all communication can be extended to a general communication framework. © 2008 IEEE.

Collective motion of self-propelled particles: Stabilizing symmetric formations on closed curves

We provide feedback control laws to stabilize formations of multiple, unit speed particles on smooth, convex, and closed curves with definite curvature. As in previous work we exploit an analogy with coupled phase oscillators to provide controls which isolate symmetric particle formations that are invariant to rigid translation of all the particles. In this work, we do not require all particles to be able to communicate; rather we assume that inter-particle communication is limited and can be modeled by a fixed, connected, and undirected graph. Because of their unique spectral properties, the Laplacian matrices of circulant graphs play a key role. The methodology is demonstrated using a superellipse, which is a type of curve that includes circles, ellipses, and rounded rectangles. These results can be used in applications involving multiple autonomous vehicles that travel at constant speed around fixed beacons. ©2006 IEEE.

What is the weakest topology in which feedback stability is robust?

Mathematical theorems in control theory are only of interest in so far as their assumptions relate to practical situations. The space of systems with transfer functions in ℋ∞, for example, has many advantages mathematically, but includes large classes of non-physical systems, and one must be careful in drawing inferences from results in that setting. Similarly, the graph topology has long been known to be the weakest, or coarsest, topology in which (1) feedback stability is a robust property (i.e. preserved in small neighbourhoods) and (2) the map from open-to-closed-loop transfer functions is continuous. However, it is not known whether continuity is a necessary part of this statement, or only required for the existing proofs. It is entirely possible that the answer depends on the underlying classes of systems used. The class of systems we concern ourselves with here is the set of systems that can be approximated, in the graph topology, by real rational transfer function matrices. That is, lumped parameter models, or those distributed systems for which it makes sense to use finite element methods. This is precisely the set of systems that have continuous frequency responses in the extended complex plane. For this class, we show that there is indeed a weaker topology; in which feedback stability is robust but for which the maps from open-to-closed-loop transfer functions are not necessarily continuous. © 2013 Copyright Taylor and Francis Group, LLC.

A reversible infinite HMM using normalised random measures

Copyright 2014 by the author(s). We present a nonparametric prior over reversible Markov chains. We use completely random measures, specifically gamma processes, to construct a countably infinite graph with weighted edges. By enforcing symmetry to make the edges undirected we define a prior over random walks on graphs that results in a reversible Markov chain. The resulting prior over infinite transition matrices is closely related to the hierarchical Dirichlet process but enforces reversibility. A reinforcement scheme has recently been proposed with similar properties, but the de Finetti measure is not well characterised. We take the alternative approach of explicitly constructing the mixing measure, which allows more straightforward and efficient inference at the cost of no longer having a closed form predictive distribution. We use our process to construct a reversible infinite HMM which we apply to two real datasets, one from epigenomics and one ion channel recording.

Dense active appearance models using a bounded diameter minimum spanning tree

We present a method for producing dense Active Appearance Models (AAMs), suitable for video-realistic synthesis. To this end we estimate a joint alignment of all training images using a set of pairwise registrations and ensure that these pairwise registrations are only calculated between similar images. This is achieved by defining a graph on the image set whose edge weights correspond to registration errors and computing a bounded diameter minimum spanning tree (BDMST). Dense optical flow is used to compute pairwise registration and we introduce a flow refinement method to align small scale texture. Once registration between training images has been established we propose a method to add vertices to the AAM in a way that minimises error between the observed flow fields and a flow field interpolated between the AAM mesh points. We demonstrate a significant improvement in model compactness using the proposed method and show it dealing with cases that are problematic for current state-of-the-art approaches.

Classification using log Gaussian Cox processes

McCullagh and Yang (2006) suggest a family of classification algorithms based on Cox processes. We further investigate the log Gaussian variant which has a number of appealing properties. Conditioned on the covariates, the distribution over labels is given by a type of conditional Markov random field. In the supervised case, computation of the predictive probability of a single test point scales linearly with the number of training points and the multiclass generalization is straightforward. We show new links between the supervised method and classical nonparametric methods. We give a detailed analysis of the pairwise graph representable Markov random field, which we use to extend the model to semi-supervised learning problems, and propose an inference method based on graph min-cuts. We give the first experimental analysis on supervised and semi-supervised datasets and show good empirical performance.

Viruses' complete genomes classification based on geometrical learning

In this paper, we proposed a method of classification for viruses' complete genomes based on graph geometrical theory in order to viruses classification. Firstly, a model of triangular geometrical graph was put forward, and then constructed feature-space-samples-graphs for classes of viruses' complete genomes in feature space after feature extraction and normalization. Finally, we studied an algorithm for classification of viruses' complete genomes based on feature-space-samples-graphs. Compared with the BLAST algorithm, experiments prove its efficiency.

Research on multi-degree-of-freedom neurons with weighted graphs

In this paper, we redefine the sample points set in the feature space from the point of view of weighted graph and propose a new covering model - Multi-Degree-of-Freedorn Neurons (MDFN). Base on this model, we describe a geometric learning algorithm with 3-degree-of-freedom neurons. It identifies the sample points secs topological character in the feature space, which is different from the traditional "separation" method. Experiment results demonstrates the general superiority of this algorithm over the traditional PCA+NN algorithm in terms of efficiency and accuracy.

Study of GaN thin films grown on vicinal SiC (0001) substrates by molecular beam epitaxy

A detailed study of the characteristics of undoped GaN films, grown on either vicinal or nominal flat SiC (0001) substrates by molecular beam epitaxy, has been carried out using photoluminescence and Raman scattering techniques. The I I K photoluminescence spectra of the GaN film grown on the vicinal SiC (0001) substrate show a strong and sharp near-bandgap peak (full width at half maximum (FWHM) similar to 16 meV). This feature contrasts with that of the GaN film grown on the nominal flat SiC (0001) substrate where the I I K photoluminescence spectra exhibit the near-bandgap peak (FWHM similar to 25 meV) and the intensity is approximately seven times weaker than that of the vicinal film sample. The redshift of the near-bandgap peak associated with excitons bound to shallow donors is related to the stress caused by both the lattice mismatch and the thermal expansion coefficient difference between GaN and SiC substrates. The measured thermal activation energy of the shallow donor of 33.4 meV is determined by using an Arrhenius plot of the near-bandgap luminescence versus I IT from the slope of the graph at high temperature. The temperature dependence of the FWHM of the near-bandgap luminescence has also been studied. The Raman scattering measurements from the vicinal film reveal that the E-2 phonon peak is strengthened and the A(1)(LO) phonon peak is shifted towards the low-frequency side with enhanced intensity, in comparison to that from the nominal flat film, suggesting a reduction in the density of defects and a lower free carrier concentration in the vicinal GaN film.

Analog computation using quantum-dot cell network

A novel analog-computation system using a quantum-dot cell network is proposed to solve complex problems. Analog computation is a promising method for solving a mathematical problem by using a physical system analogous to the problem. We designed a novel quantum-dot cell consisting of three-stacked. quantum dots and constructed a cell network utilizing the nearest-neighbor interactions between the cells. We then mapped a graph 3-colorability problem onto the network so that the single-electron configuration of the network in the ground state corresponded to one of the solutions. We calculated the ground state of the cell network and found solutions to the problems. The results demonstrate that analog computation is a promising approach for solving complex problems.

Research on multi-degree-of-freedom neurons with weighted graphs

In this paper, we redefine the sample points set in the feature space from the point of view of weighted graph and propose a new covering model - Multi-Degree-of-Freedorn Neurons (MDFN). Base on this model, we describe a geometric learning algorithm with 3-degree-of-freedom neurons. It identifies the sample points secs topological character in the feature space, which is different from the traditional "separation" method. Experiment results demonstrates the general superiority of this algorithm over the traditional PCA+NN algorithm in terms of efficiency and accuracy.

Complex networks constructed from irrational number sequences

In this paper, we construct (d, r) networks from sequences of different irrational numbers. In detail, segment an irrational number sequence of length M into groups of d digits which represent the nodes while two consecutive groups overlap by r digits (r = 0,1,...,d-1), and the undirected edges indicate the adjacency between two consecutive groups. (3, r) and (4, r) networks are respectively constructed from 14 different irrational numbers and their topological properties are examined. By observation, we find that network topologies change with different values of d, r and even sequence length M instead of the types of irrational numbers, although they share some similar features with traditional random graphs. We make a further investigation to explain these interesting phenomena and propose the identical-degree random graph model. The results presented in this paper provide some insight into distributions of irrational number digits that may help better understanding of the nature of irrational numbers.

一种基于亮度分析的图像分割方法

图像分割是数字图像处理领域的重要研究内容。随着数字图像处理技术的发展和相关学科的进步，图像分割在图像编辑、计算机视觉、医疗影像、遥感图像等方面都取得了良好的应用，而且具有巨大的应用潜力。 图像分割是一个既很基础又很复杂的问题。经过多年的发展，研究者提出了很多优秀的算法，取得了令人鼓舞的成就。但由于图像分割本身的不确定性和复杂性，还没有一种算法能够解决好所有的分割问题。为了使图像分割的结果更加符合用户需求，交互式的分割方法逐渐成为了图像分割算法的主流。交互方式的简化也就成为了研究者努力的目标。 另一方面，图切分技术(Graph-Cut)是应用于图像分割算法的一种重要工具。Lazy Snapping方法利用人工交互操作来提取图像信息，然后使用图切分来分割图像，取得了较好的分割效果。而且该方法的交互界面简单易用，对模糊边界有较快的响应速度，引起了研究者的重视，是一种结合人工交互与图切分技术的重要分割方法。 鉴于Lazy Snapping方法在处理色彩丰富、对比强烈的图像时出现的交互操作过多、分割容易出错的问题，本文提出了一种基于亮度分析的图像分割方法。该方法在HSV空间下，以亮度为依据来提取前景和背景的特征，取代或简化了Lazy Snapping中的人工操作步骤，然后用图切分技术来进行分割。这种方法能够提取到较准确的图像特征，有效地减轻了用户操作量，明显地改善了分割结果。

基于PAR的高可信装备保障算法推演

算法被誉为计算的“灵魂”（spirit of computing），算法程序的可靠性和正确性对软件系统的可信度起着至关重要的作用。动态规划、贪心、分支限界等传统的算法设计策略缺乏有效的选择标准，一些算法形式化开发方法和工具的应用水平和范围也很有限，因此算法的可靠性已成为高可信软件系统的一个主要瓶颈。 作为军事运筹学的一个重要分支，装备保障计算主要研究军事活动中装备领域的决策优化问题，保障计算软件特别是算法的可靠性在很大程度上决定了装备保障的效率乃至军事行动的成败。利用形式化软件工程的研究成果、特别是引入算法程序的形式化开发方法，对我军通用装备保障领域中的大量算法类问题进行有效求解，有利于优化保障结构、统筹保障资源、整合保障力量、提高保障时效，促进装备整体战斗力水平的提升。 本文以高可信软件开发方法PAR为基础，面向装备保障计算的领域需求，提出了一类离散最优化问题（discrete optimization problem, DOP）的结构模型和算法推演技术，并成功推演了一系列典型的装备保障算法。本论文的主要创新性贡献如下： （1）定义了DOP的结构模型，提出了基于单点结构（Singleton）的问题分划递推策略，进而通过PAR算法推演生成问题的高效求解算法，涵盖了多种传统算法设计策略，显著提高了算法程序设计的机械化水平。 （2）提出了描述DOP分划递推过程的问题简约图（problem reduction graph, PRG）模型，并针对典型DOP结构推演得到了一组PRG构造算法模式，其中每个算法模式都涵盖了满足特定代数结构性质的一大类具体问题。 （3）阐述了PAR算法推演的范畴模型，为算法设计和重用提供了抽象而有效的方法指导。 （4）对我军通用装备保障领域具有代表性的48个问题进行了形式化的算法推演，构建了领域算法库。 （5）在PAR平台的基础上设计了装备保障算法开发平台的原型COPALM，支持DOP算法推演和重用，进而提高了相关应用软件的开发效率。

automated test case generation for the stress testing of multimedia systems

With the advancement in network bandwidth and computing power, multimedia systems have become a popular means for information delivery. However, general principles of system testing cannot be directly applied to testing of multimedia systems on account of their stringent temporal and synchronization requirements. In particular, few studies have been made on the stress testing of multimedia systems with respect to their temporal requirements under resource saturation. Stress testing is important because erroneous behavior is most likely to occur under resource saturation. This paper presents an automatable method of test case generation for the stress testing of multimedia systems. It adapts constraint solving techniques to generate test cases that lead to potential resource saturation in a multimedia system. Coverage of the test cases is defined upon the reachability graph of a multimedia system. The proposed stress testing technique is supported by tools and has been successfully applied to a real-life commercial multimedia system. Although our technique focuses on the stress testing of multimedia systems, the underlying issues and concepts are applicable to other types of real-time systems.