3-连通无爪图中的最长圈

证明了3-连通无爪图G中的最长圈C满足:|V(C)|≥min{3δ(G)+6,5δ(G)-5,4δ(G),|V(G)|}.     

Maximum cyclic 4-cycle packings of the complete multipartite graph

A graph G is said to be m-sufficient if m is not exceeding the order of G, each vertex of G is of even degree, and the number of edges in G is a multiple of m. A complete multipartite graph is balanced if each of its partite sets has the same size. In this paper it is proved that the complete multipartite graph G can be decomposed into 4-cycles cyclically if and only if G is balanced and 4-sufficient. Moreover, the problem of finding a maximum cyclic packing of the complete multipartite graph with 4-cycles are also presented. Dedicated to Professor Frank K. Hwang on the occasion of his 65th birthday.     

Characterizing the reconstruction and enumerating the patterns of DNA sequences with repeats

A repeat in a DNA sequence is a substring that appears more than once. In DNA sequencing, the occurrence of repeats may hinder the unique reconstruction. In addition, the number of possible reconstructions depends on the pattern of repeats in a DNA sequence. Arratia et al. studied the patterns of DNA sequences with twofold repeats that result in k-way reconstructions. In this paper, multiple-fold repeats, including twofold repeats, are considered. For each pattern of DNA repeats, the possible reconstructions of the DNA sequence are enumerated by its reduced digraph. Then the reconstructions of DNA sequences with repeats are characterized using the pattern graphs. Finally, for DNA sequences with n repeats, the patterns of DNA repeats resulting in k-way reconstruction are enumerated. Dedicated to Professor Frank K. Hwang on the occasion of his 65th birthday.     

具有多阶段任务需求的温备份系统可靠性分析

实际工程中很多系统的任务都具有多个阶段,且不同阶段的外界环境及系统需求均可能发生变化,而工作元件可在任意阶段发生失效,为系统的可靠性分析与建模带来了挑战。为增加系统的可靠性,一种常用的设计方法是配置备份元件。针对多阶段任务下基于需求的温备份系统可靠性建模问题,首先提出了一种基于多值决策图的方法,其次给出了处于不同状态的元件可靠性计算公式,最后通过算例表明该模型适用于具有多阶段任务需求的温备份系统可靠性分析。     

论逻辑图表与逻辑教育

逻辑教育已成为一项至关重要的公民素质教育,但当前的逻辑教育效果并不如人意。本文指出,逻辑图表能帮助人们较轻松和直观地理解和应用逻辑推理,而存在图作为一种图表化理论,对逻辑教育有着突出的合目的性和效用性。     

对称矩阵结合方案中关系图的连通性

设IFq是q个元的域,q是2的幂,S(n,q)是IFq上n×n对称矩阵所成的集合.本文给出了以X=S(n,q)为有限集的两种对称矩阵结合方案,分别讨论了这两种结合方案中结合关系R1和R1的关系图Γ(1)和Γ(1)的连通性.     

基于知识图谱与扎根分析的中国管理理论构建范式研究述评

基于知识图谱理论和扎根理论的方法指导,以中文社会科学引文检索数据库收录的1998~2019年期间,与中国管理研究以及理论构建相关的561篇施引文献和7108篇被引文献作为研究对象。通过运用Citespace V可视化软件,进行中国管理研究与理论构建的知识基础、研究热点和主题演进脉络等的可视化分析与研究;并进一步精选了116篇科技文献为样本数据进行三级扎根编码,构建中国管理理论的研究框架模型。研究表明:中国管理研究目前聚焦于理论构建范式的研究主题,构建中国管理理论要直面实践导向,扎根传统文化,实现实践与文化的融合,要采用多元科学方法论与方法,辩证地使用实证研究方法。     

Parameter estimation procedures for exponential-family random graph models on count-valued networks: A comparative simulation study

The exponential-family random graph models (ERGMs) have emerged as an important framework for modeling social networks for a wide variety of relational types. ERGMs for valued networks are less well-developed than their unvalued counterparts, and pose particular computational challenges. Network data with edge values on the non-negative integers (count-valued networks) is an important such case, with examples ranging from the magnitude of migration and trade flows between places to the frequency of interactions and encounters between individuals. Here, we propose an efficient parallelizable subsampled maximum pseudo-likelihood estimation (MPLE) scheme for count-valued ERGMs, and compare its performance with existing Contrastive Divergence (CD) and Monte Carlo Maximum Likelihood Estimation (MCMLE) approaches via a simulation study based on migration flow networks in two U.S. states. Our results suggest that edge value variance is a key factor in method performance, while network size mainly influences their relative merits in computational time. For small-variance networks, all methods perform well in point estimations while CD greatly overestimates uncertainties, and MPLE underestimates them for dependence terms; all methods have fast estimation for small networks, but CD and subsampled multi-core MPLE provides speed advantages as network size increases. For large-variance networks, both MPLE and MCMLE offer high-quality estimates of coefficients and their uncertainty, but MPLE is significantly faster than MCMLE; MPLE is also a better seeding method for MCMLE than CD, as the latter makes MCMLE more prone to convergence failure. The study suggests that MCMLE and MPLE should be the default approach to estimate ERGMs for small-variance and large-variance valued networks, respectively. We also offer further suggestions regarding choice of computational method for valued ERGMs based on data structure, available computational resources and analytical goals.     

Longitudinal network models and permutation-uniform Markov chains

Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the same parameter, improving data reduction. Further we show that the permutation-uniform subclass of these chains permit interpretation as an independent, identically distributed sequence on the same state space. We then apply these ideas to temporal exponential random graph models, for which permutation uniformity is well suited, and discuss mean-parameter convergence, dyadic independence, and exchangeability. Our framework facilitates our introducing a new network model; simplifies analysis of some network and autoregressive models from the literature, including by permitting closed-form expressions for maximum likelihood estimates for some models; and facilitates applying standard tools to longitudinal-network Markov chains from either asymptotics or single-observation exponential random graph models.     

A Structural Model of Dense Network Formation

This paper proposes an empirical model of network formation, combining strategic and random networks features. Payoffs depend on direct links, but also link externalities. Players meet sequentially at random, myopically updating their links. Under mild assumptions, the network formation process is a potential game and converges to an exponential random graph model (ERGM), generating directed dense networks. I provide new identification results for ERGMs in large networks: if link externalities are nonnegative, the ERGM is asymptotically indistinguishable from an Erdős–Rényi model with independent links. We can identify the parameters only when at least one of the externalities is negative and sufficiently large. However, the standard estimation methods for ERGMs can have exponentially slow convergence, even when the model has asymptotically independent links. I thus estimate parameters using a Bayesian MCMC method. When the parameters are identifiable, I show evidence that the estimation algorithm converges in almost quadratic time.