On a Dualization of Graphical Gaussian Models: A Correction Note

Abstract.  We correct two proofs concerning Markov properties for graphs representing marginal independence relations.     

多样性·批评性·学术性－评《文艺湘军百家文库·文艺评论方阵》

《文艺湘军百家文库·文艺评论方阵》及先此出版的《当代湖南文艺评论家选集》丛书,集中汇聚了湖南文学批评50年的主要成果,展示了老中青三代批评家的探寻的风姿。其主要特点突出地表现在异彩纷呈的多样性、真诚鲜明的批评性、科学严谨的学术性等方面。     

《竹山词》常用语研究——兼论其艺术风格与师承

在蒋捷词的研究中,其词派归属和艺术风格历来是众说纷纭的焦点.从语言层面对蒋捷词进行深入具体的分析后,不难发现蒋捷坚持的是"本色当行"的词法,抒发的是泛着冷光的寂寞情怀,追求的是幽深婉曲的艺术效果.他与姜夔和吴文英有着较深的艺术渊源关系,所以其词从总体上讲并非所谓"豪放词"之余韵.     

Markov Properties for Acyclic Directed Mixed Graphs

We consider acyclic directed mixed graphs, in which directed edges ( x → y ) and bi-directed edges ( x ↔ y ) may occur. A simple extension of Pearl's d -separation criterion, called m -separation, is applied to these graphs. We introduce a local Markov property which is equivalent to the global property resulting from the m -separation criterion for arbitrary distributions.     

A Unified Approach to the Characterization of Equivalence Classes of DAGs, Chain Graphs with no Flags and Chain Graphs

Abstract.  A Markov property associates a set of conditional independencies to a graph. Two alternative Markov properties are available for chain graphs (CGs), the Lauritzen–Wermuth–Frydenberg (LWF) and the Andersson–Madigan– Perlman (AMP) Markov properties, which are different in general but coincide for the subclass of CGs with no flags . Markov equivalence induces a partition of the class of CGs into equivalence classes and every equivalence class contains a, possibly empty, subclass of CGs with no flags itself containing a, possibly empty, subclass of directed acyclic graphs (DAGs). LWF-Markov equivalence classes of CGs can be naturally characterized by means of the so-called largest CGs , whereas a graphical characterization of equivalence classes of DAGs is provided by the essential graphs . In this paper, we show the existence of largest CGs with no flags that provide a natural characterization of equivalence classes of CGs of this kind, with respect to both the LWF- and the AMP-Markov properties. We propose a procedure for the construction of the largest CGs, the largest CGs with no flags and the essential graphs, thereby providing a unified approach to the problem. As by-products we obtain a characterization of graphs that are largest CGs with no flags and an alternative characterization of graphs which are largest CGs. Furthermore, a known characterization of the essential graphs is shown to be a special case of our more general framework. The three graphical characterizations have a common structure: they use two versions of a locally verifiable graphical rule. Moreover, in case of DAGs, an immediate comparison of three characterizing graphs is possible.     

正则图的剖分图的秩

讨论几类正则图的剖分图的邻接矩阵的秩。主要有:圈,路,完全图,完全二部图和多部图,度为3与4的循环图。     

Estimation of geodesic tortuosity and constrictivity in stationary random closed sets

We investigate the problem of estimating geodesic tortuosity and constrictivity as two structural characteristics of stationary random closed sets. They are of central importance for the analysis of effective transport properties in porous or composite materials. Loosely speaking, geodesic tortuosity measures the windedness of paths, whereas the notion of constrictivity captures the appearance of bottlenecks resulting from narrow passages within a given materials phase. We first provide mathematically precise definitions of these quantities and introduce appropriate estimators. Then, we show strong consistency of these estimators for unboundedly growing sampling windows. In order to apply our estimators to real data sets, the extent of edge effects needs to be controlled. This is illustrated using a model for a multiphase material that is incorporated in solid oxide fuel cells.     

完全强连通方向图的表征

本文引进了完全强连通方向图的概念,利用邻接阵给出了等价表征。     

Heating up the debate? Measuring fragmentation and polarisation in a German climate change hyperlink network

Research into polarisation on the internet has so far primarily focused on contentious issues and yielded contradictory results. Shifting the focus to a non-contentious setting, this article combines community detection with brokerage analysis and exponential random graph models to assess the degree of polarisation at different levels of a German hyperlink network on climate change. Although homophily accounts for a moderate degree of polarisation at the top level of the network, the communities reveal that other factors prove more decisive in shaping its structure and the article thus contributes to a more refined understanding of the nature of online polarisation.     

Collapsibility for Directed Acyclic Graphs

Abstract.  Collapsibility means that the same statistical result of interest can be obtained before and after marginalization over some variables. In this paper, we discuss three kinds of collapsibility for directed acyclic graphs (DAGs): estimate collapsibility, conditional independence collapsibility and model collapsibility. Related to collapsibility, we discuss removability of variables from a DAG. We present conditions for these three different kinds of collapsibility and relationships among them. We give algorithms to find a minimum variable set containing a variable subset of interest onto which a statistical result is collapsible.