Elementary Statistics

Fractional two-level factorial designs are often used in the early stages of an investigation to screen for important factors. Traditionally, 2 ^n-k fractional factorial designs of resolution III, IV, or V have been used for this purpose. When the investigator is able to specify the set of nonnegligible factorial effects, it is sometimes possible to obtain an orthogonal design with fewer runs than a standard textbook design by searching within a wider class of designs called parallel-flats designs. The run sizes in this class of designs do not necessarily need to be powers of 2. We discuss an algorithm for constructing orthogonal parallel-flats designs to meet user specifications. Several examples illustrate the use of the algorithm.     

Graph-balancing algorithms for average consensus over directed networks

Consensus strategies find extensive applications in coordination of robot groups and decision-making of agents. Since balanced graph plays an important role in the average consensus problem and many other coordination problems for directed communication networks, this work explores the conditions and algorithms for the digraph balancing problem. Based on the analysis of graph cycles, we prove that a digraph can be balanced if and only if the null space of its incidence matrix contains positive vectors. Then, based on this result and the corresponding analysis, two weight balance algorithms have been proposed, and the conditions for obtaining a unique balanced solution and a set of analytical results on weight balance problems have been introduced. Then, we point out the relationship between the weight balance problem and the features of the corresponding underlying Markov chain. Finally, two numerical examples are presented to verify the proposed algorithms.     

Another look at the phenomenon of phase transition

This study is motivated by the question whether there exists a characteristic feature common to the phenomenon of phase transition of properties taking place in the course of evolution of various sets of objects of different nature. A novel measure model of phase transition is presented, providing an insight into the process underlying different phase transitions. First, it is shown to conform to several famous and extensively investigated cases of phase transition. Then a few close consequences of applying the measure model are presented. It has been proved that monotone properties undergo a sharp phase transition. The measure model provides a sufficient condition of a sharp phase transition common to monotone and non-monotone properties as well. The measure model reveals that if a property Q undergoes a phase transition in the course of evolution of objects of a certain type, then there exist other secondary properties related to the measure of Q that also undergo a phase transition during the evolution.     

Stochastic graph as a model for social networks

Social networks are usually modeled and represented as deterministic graphs with a set of nodes as users and edges as connection between users of networks. Due to the uncertain and dynamic nature of user behavior and human activities in social networks, their structural and behavioral parameters are time varying parameters and for this reason using deterministic graphs for modeling and analysis of behavior of users may not be appropriate. In this paper, we propose that stochastic graphs, in which weights associated with edges are random variables, may be a better candidate as a graph model for social network analysis. Thus, we first propose generalization of some network measures for stochastic graphs and then propose six learning automata based algorithms for calculating these measures under the situation that the probability distribution functions of the edge weights of the graph are unknown. Simulations on different synthetic stochastic graphs for calculating the network measures using the proposed algorithms show that in order to obtain good estimates for the network measures, the required number of samples taken from edges of the graph is significantly lower than that of standard sampling method aims to analysis of human behavior in online social networks.     

Conditional matching preclusion for the alternating group graphs and split-stars

The matching preclusion number of a graph is the minimum number of edges the deletion of which results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. Recently, the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those induced by a single vertex. It is defined to be the minimum number of edges the deletion of which results in a graph with no isolated vertices that has neither perfect matchings nor almost-perfect matchings. In this article, we find this number and classify all optimal sets for the alternating group graphs, one of the most popular interconnection networks, and their companion graphs, the split-stars. Moreover, some general results on the conditional matching preclusion problems are also presented.     

一个特殊图形的边色数

从Petersen图出发,找到一个图形并证明其边色数为7.从说明D.R.Fulkerson在1971年提出的一个猜想是不成立的.在此基础上,还进一步证明了该猜想成立的一些充分条件.     

分子骨架在族性结构处理中的应用研究

利用计算机表示、存储和匹配族性结构面临的一个难题是如何将族性结构展开到一个合适的程度,既能避免过度枚举又包含族性结构应有的信息,本文根据族性结构特点,设计了一个程序用来提取族性结构中的环和环之间的连接片段,然后生成族性结构的分子骨架及相应的还原图,利用SMILES线性编码存储族性结构主要信息,避免了大部分的枚举。     

告警关联方法研究

告警关联是网络故障诊断中的核心任务。现在有许多告警关联方法被应用到网络管理系统中。讨论告警关联的概念,对几种告警关联方法进行研究并分析其优点和不足,同时介绍一些基于不同技术的告警关联产品。最后给出一个网络故障诊断的原型系统。     

清窑机器人机液系统动力学混合建模及其仿真

清窑机器人动态特性包含组成机器人的液压驱动系统和机械本体系统的动态特性.根据功率键合图的建模方法,按照清窑机器人液压系统的组成和工作原理以及机械系统的结构设计进行混合建模,并得到了机器人系统的功率键合图以及9阶非线性动力学方程组.在建立计算机仿真模型的基础上,通过分析与求解以及Simulink的计算机仿真,得出了机器人系统随负载、关节空间位置变化的加速度、速度和位移仿真曲线,并分析了液压驱动系统和机械系统动态特性对机器人系统动态特性的影响.