Incrementing Bipartite Digraph Edge-Connectivity

This paper solves the problem of increasing the edge-connectivity of a bipartite digraph by adding the smallest number of new edges that preserve bipartiteness. A natural application arises when we wish to reinforce a 2-dimensional square grid framework with cables. We actually solve the more general problem of covering a crossing family of sets with the smallest number of directed edges, where each new edge must join the blocks of a given bipartition of the elements. The smallest number of new edges is given by a min-max formula that has six infinite families of exceptional cases. We discuss a problem on network flows whose solution has a similar formula with three infinite families of exceptional cases. We also discuss a problem on arborescences whose solution has five infinite families of exceptions. We give an algorithm that increases the edge-connectivity of a bipartite digraph in the same time as the best-known algorithm for the problem without the bipartite constraint: O(km log n) for unweighted digraphs and O(nm log (n ²/m)) for weighted digraphs, where n, m and k are the number of vertices and edges of the given graph and the target connectivity, respectively.     

关于二部图K（m,n）—A（｜A｜=2）的色唯一性的一个注记

设K（m,n)-A表示从完全二部图K（m,n）中删去子边集A所得之图,K（m,n)[A]表示由A导出的K（m,n)的子图,（M,N）表示K（m,n)的二部分,其中|M|=m,|N|=n。文章证明了：当m≥3,|A|=2时,K（m,n)－A（其中K（3,3）[A]≠K（1,2）,K(m,m 1)-A和K（m,m 2）－A（其中K（3,5）[A]≌K（1,2)和|V(K3,5)[A])∩M|=2不同时成立）均是色唯一图。     

一类Halin-图的均匀色数

对Δ(G) =4的Halin -图证明了 |V(G) | 0 (mod3)时 ,对任意整数的k≥「Δ(G) / 2 +1,G是可均匀k -可着色的。从而证明了这类Halin -图的均匀染色数的下界是「Δ(G) / 2 +1。     

Networks and geography: Modelling community network structures as the outcome of both spatial and network processes

This paper focuses on how to extend the exponential random graph models to take into account the geographical embeddedness of individuals in modelling social networks. We develop a hierarchical set of nested models for spatially embedded social networks, in which, following Butts (2002), an interaction function between tie probability and Euclidean distance between nodes is introduced. The models are illustrated by an empirical example from a study of the role of social networks in understanding spatial clustering in unemployment in Australia. The analysis suggests that a spatial effect cannot solely explain the emergence of organised network structure and it is necessary to include both spatial and endogenous network effects in the model.     

“Trust Me”: Differences in expressed and perceived trust relations in an organization

The possibility of resolving the tension between trust as a psychological condition and trust as a general organizing principle depends on assumptions about the convergence of expressed and perceived trust relations. In empirical organizational research these assumptions are frequently left implicit and only rarely modeled directly. Using data that we have collected on trust relations within the top management team of a multiunit industrial group we specify and estimate multivariate exponential random graph models (ERGMs) that reveal important differences in the structural logics underlying networks of expressed and perceived trust relations. Results confirm that trust induces awareness and produces expectations of reciprocity – features that are consistent with the view of trust as a general organizing principle. Results also show that networks of perceived trust relations are characterized by tendencies toward reciprocity and generalized giving of trust. When multivariate network effects are introduced, however, expressed trust relations no longer show a significant tendency toward reciprocation. Interpreted together these results suggest that: (i) the distribution of expressed and perceived trust relations differs; (ii) expressed trust relations in organizations are more hierarchical than are perceived trust relations, and (iii) expressed and perceived trust relations need to be modeled jointly. These findings suggest caution in the adoption and interpretation of trust only as a general organizing principle, and suggest that psychological mechanisms also play an important role in the making and breaking of trust relations within organizations.     

基于Radix结构的软件水印保护技术

动态图软件水印在抗攻击性方面较通常的静态水印有明显的优势。由于这类水印本身可能与宿主程序的功能性之间并无太大关联,使得攻击者可通过透彻分析而对该类水印进行恶意破坏,从而使水印提取过程失败。为此,本文提出了一种利用多常量编码伪水印来对动态图水印进行保护的方法,并设计了针对Rad ix结构动态图水印的保护算法。该算法通过创建多个Rad ix结构的伪水印对宿主程序功能性的依赖关系,对真实水印起到了防篡改的作用,增加了攻击者的攻击难度,从而可对该类水印进行有效的保护。     

我国教师非正式学习研究知识图谱与展望——基于CNKI文献的可视化分析

随着对教师专业发展的深入研究，教师学习问题逐渐引起了学界的关注，同时受非正式学习理论的影响，教师非正式学习已成为一个独特的研究领域，目前形成了一系列的研究成果。为了全方位把握该研究的进展与趋势，运用CiteSpace可视化分析和BICOMB软件，系统梳理学界关于我国教师非正式学习的研究进展状况以及分析未来发展趋势，为后续的研究与实践提供指导和借鉴。     

Stable exponential random graph models with non-parametric components for large dense networks

Exponential random graph models (ERGM) behave peculiar in large networks with thousand(s) of actors (nodes). Standard models containing 2-star or triangle counts as statistics are often unstable leading to completely full or empty networks. Moreover, numerical methods break down which makes it complicated to apply ERGMs to large networks. In this paper we propose two strategies to circumvent these obstacles. First, we use a subsampling scheme to obtain (conditionally) independent observations for model fitting and secondly, we show how linear statistics (like 2-stars etc.) can be replaced by smooth functional components. These two steps in combination allow to fit stable models to large network data, which is illustrated by a data example including a residual analysis.     

Partitioning large-scale artificial society on distributed cluster with statistical movement graph

Distributed agent-based simulation is a popular method to realize computational experiment on large-scale artificial society. Meanwhile, the partitioning strategy of the artificial society models among hosts is playing an essential role for simulation engine to offer high execution efficiency as it has great impact on the communication overheads and computational load-balancing during simulation. Aiming at the problem, we firstly analyze the execution and scheduling process of agents during simulation and model it as wide-sense cyclostationary random process. Then, a static statistical partitioning model is proposed to obtain the optimal partitioning strategy with minimum average communication cost and load imbalance factor. To solve the static statistical partitioning model, this paper turns it into a graph-partitioning problem. A statistical movement graph-based partitioning algorithm is then devised which generates task graph model by mining the statistical movement information from initialization data of simulation model. In the experiments, two other popular partitioning methods are used to evaluate the performance of proposed graph-partitioning algorithm. Furthermore, this paper compares the graph-partitioning performance under different task graph model. The results indicate that our proposed statistical movement graph-based static partitioning method outperforms all other methods in reducing the communication overhead while satisfying the load balance constraint.     

Joint estimation of multiple high‐dimensional Gaussian copula graphical models

A joint estimation approach for multiple high‐dimensional Gaussian copula graphical models is proposed, which achieves estimation robustness by exploiting non‐parametric rank‐based correlation coefficient estimators. Although we focus on continuous data in this paper, the proposed method can be extended to deal with binary or mixed data. Based on a weighted minimisation problem, the estimators can be obtained by implementing second‐order cone programming. Theoretical properties of the procedure are investigated. We show that the proposed joint estimation procedure leads to a faster convergence rate than estimating the graphs individually. It is also shown that the proposed procedure achieves an exact graph structure recovery with probability tending to 1 under certain regularity conditions. Besides theoretical analysis, we conduct numerical simulations to compare the estimation performance and graph recovery performance of some state‐of‐the‐art methods including both joint estimation methods and estimation methods for individuals. The proposed method is then applied to a gene expression data set, which illustrates its practical usefulness.