Graphical models for skew-normal variates

This paper explores the usefulness of the multivariate skew-normal distribution in the context of graphical models. A slight extension of the family recently discussed by Azzalini & Dalla Valle (1996 ) and Azzalini & Capitanio (1999 ) is described, the main motivation being the additional property of closure under conditioning. After considerations of the main probabilistic features, the focus of the paper is on the construction of conditional independence graphs for skew-normal variables. Necessary and sufficient conditions for conditional independence are stated, and the admissible structures of a graph under restriction on univariate marginal distribution are studied. Finally, parameter estimation is considered. It is shown how the factorization of the likelihood function according to a graph can be rearranged in order to obtain a parameter based factorization.     

Bayesian phylogenetic inference from animal mitochondrial genome arrangements

Summary. The determination of evolutionary relationships is a fundamental problem in evolutionary biology. Genome arrangement data are potentially more informative than deoxyribonucleic acid sequence data for inferring evolutionary relationships between distantly related taxa. We describe a Bayesian framework for phylogenetic inference from mitochondrial genome arrangement data using Markov chain Monte Carlo methods. We apply the method to assess evolutionary relationships between eight animal phyla.     

Maximum Likelihood Estimation in Gaussian Chain Graph Models under the Alternative Markov Property

Abstract.  The Andersson–Madigan–Perlman (AMP) Markov property is a recently proposed alternative Markov property (AMP) for chain graphs. In the case of continuous variables with a joint multivariate Gaussian distribution, it is the AMP rather than the earlier introduced Lauritzen–Wermuth–Frydenberg Markov property that is coherent with data-generation by natural block-recursive regressions. In this paper, we show that maximum likelihood estimates in Gaussian AMP chain graph models can be obtained by combining generalized least squares and iterative proportional fitting to an iterative algorithm. In an appendix, we give useful convergence results for iterative partial maximization algorithms that apply in particular to the described algorithm.     

CAD在位置量规设计中的应用

本文介绍了位置量规设计原理及计算公式，陈述了位置量计算机辅助设计系统的总体设计及软、硬件构成，同时介绍了为加快绘图速度对图形输入板菜单进行重新编制的方法。     

Two Variations of the Minimum Steiner Problem

Given a set S of starting vertices and a set T of terminating vertices in a graph G = (V,E) with non-negative weights on edges, the minimum Steiner network problem is to find a subgraph of G with the minimum total edge weight. In such a subgraph, we require that for each vertex s S and t T, there is a path from s to a terminating vertex as well as a path from a starting vertex to t. This problem can easily be proven NP-hard. For solving the minimum Steiner network problem, we first present an algorithm that runs in time and space that both are polynomial in n with constant degrees, but exponential in |S|+|T|, where n is the number of vertices in G. Then we present an algorithm that uses space that is quadratic in n and runs in time that is polynomial in n with a degree O(max {max {|S|,|T|}–2,min {|S|,|T|}–1}). In spite of this degree, we prove that the number of Steiner vertices in our solution can be as large as |S|+|T|–2. Our algorithm can enumerate all possible optimal solutions. The input graph G can either be undirected or directed acyclic. We also give a linear time algorithm for the special case when min {|S|,|T|} = 1 and max {|S|,|T|} = 2.The minimum union paths problem is similar to the minimum Steiner network problem except that we are given a set H of hitting vertices in G in addition to the sets of starting and terminating vertices. We want to find a subgraph of G with the minimum total edge weight such that the conditions required by the minimum Steiner network problem are satisfied as well as the condition that every hitting vertex is on a path from a starting vertex to a terminating vertex. Furthermore, G must be directed acyclic. For solving the minimum union paths problem, we also present algorithms that have a time and space tradeoff similar to algorithms for the minimum Steiner network problem. We also give a linear time algorithm for the special case when |S| = 1, |T| = 1 and |H| = 2.An extended abstract of part of this paper appears in Hsu et al. (1996).Supported in part by the National Science Foundation under Grants CCR-9309743 and INT-9207212, and by the Office of Naval Research under Grant No. N00014-93-1-0272.Supported in part by the National Science Council, Taiwan, ROC, under Grant No. NSC-83-0408-E-001-021.     

数字集成电路测试生成的一种专家系统方法

介绍了两种基于压缩二分决策图(BDD:Binary Dccision Diagram)并由压缩的BDD来进行测试生成的启发性方法,即临界二分树(CBT:Critical Binary Tree)和节点分决函数(ndf:node psrtition function)方法,它们虽然并不一定是最小化BDD,但它们减小了BDD,从而在专家系统环境下得以对大型数字系统进行测试。     

关于图P_1(∨P_4)T_n的优美性

本文研究了一类图P1∨P4T n的优美性.利用构造函数标号的方法,证明了下面结论:对于任意正整数n,T n是n个顶点的优美树,则当n≥2时,P1∨P4T n是优美图.其中,P1是1个顶点的平凡图,P4是4个顶点的路,图P1∨P4T n是把P1之中的顶点与T n之中的每一个顶点之间都通过一个P4连接起来所得到的.     

基于Granger因果图方法的物价水平国际间传递分析

目前,对Granger因果关系的研究大多数采用两变量Granger因果检验法,由于忽视其它重要变量的影响,常会导致虚假因果关系的出现。鉴此,采用Granger因果图模型方法分析中国及其主要贸易伙伴国(地区)间的物价传递,研究结果表明:美国在物价传递中发挥着主导作用,物价国际间传递存在一定的区域效应;除和中国香港地区存在即期因果关系外,中国对主要贸易伙伴国(地区)的物价水平基本无显著影响,中国既无输出通货膨胀也无输出通货紧缩。同时,样本期内中国物价水平呈现明显的外部"输入性"特征。因此,中国政府应采取措施应对国际的物价冲击,同时防范物价输入性引发的风险,以实现中国物价的稳定。     

Multiple partitioning of multiplex signed networks: Application to European parliament votes

For more than a decade, graphs have been used to model the voting behavior taking place in parliaments. However, the methods described in the literature suffer from several limitations. The two main ones are that 1) they rely on some temporal integration of the raw data, which causes some information loss; and/or 2) they identify groups of antagonistic voters, but not the context associated with their occurrence. In this article, we propose a novel method taking advantage of multiplex signed graphs to solve both these issues. It consists in first partitioning separately each layer, before grouping these partitions by similarity. We show the interest of our approach by applying it to a European Parliament dataset.