几类循环图的分数染色数

通过构造几类图的最大独立集,给出了它们的分数染色数的下界;再通过构造具有该下界值的分数染色,给出了这几类循环图的分数染色数的上界,于是就确定了它们的分数染色数.     

Any complete preference structure without circuit admits an interval representation

This article proves that all complete preference structures where the strict preference relation (P) has no circuit admit a representation by intervals of the real line; the rule for deciding whether an interval is indifferent or preferred to another is less straightforward than for interval orders: strict preference is indeed compatible with a certain degree of overlapping of intervals, the allowed degree being specified by means of a so-called tolerance function.     

On the enumeration of rectangular (0, 1)-matrices

The construction and enumeration of (0, 1)-matrices with given line-sums is described for the rectangular cases often encountered in applications. Improved approximations are provided for the number of such matrices. Some new enumeration results for semi-regular bipartite graphs are included, and the related category of the quasi-semiregular bipartite graphs is recognized. The range of certain elements of products of a (0, I)-matrix is considered as a function of the line-sums. This, in turn, is related to the range in the numbers of interchanges available. Improvements in statistical practice that come from these constructions and enumerations are described.     

Estimating school effectiveness with student growth percentile and gain score models

Measuring school effectiveness using student test scores is controversial and some methods used for this can be inaccurate in some situations. The validity of two statistical models – the Student Growth Percentile (SGP) model and a multilevel gain score model – are evaluated. The SGP model conditions on previous test scores thereby unblocking a backdoor path between true school/teacher effectiveness and student test scores. When the product of the coefficients that make up this unblocked backdoor path is positive, the SGP estimates can be inaccurate. The accuracy of the multilevel gain score model was not associated with the product of this backdoor path. The gain score model appears promising in these situations where the SGP and other covariate adjusted models perform poorly.     

Quantile dispersion graphs to compare the efficiencies of cluster randomized designs

The purpose of this article is to compare efficiencies of several cluster randomized designs using the method of quantile dispersion graphs (QDGs). A cluster randomized design is considered whenever subjects are randomized at a group level but analyzed at the individual level. A prior knowledge of the correlation existing between subjects within the same cluster is necessary to design these cluster randomized trials. Using the QDG approach, we are able to compare several cluster randomized designs without requiring any information on the intracluster correlation. For a given design, several quantiles of the power function, which are directly related to the effect size, are obtained for several effect sizes. The quantiles depend on the intracluster correlation present in the model. The dispersion of these quantiles over the space of the unknown intracluster correlation is determined, and then depicted by the QDGs. Two applications of the proposed methodology are presented.     

SEMIPARAMETRIC REGRESSION AND GRAPHICAL MODELS

Semiparametric regression models that use spline basis functions with penalization have graphical model representations. This link is more powerful than previously established mixed model representations of semiparametric regression, as a larger class of models can be accommodated. Complications such as missingness and measurement error are more naturally handled within the graphical model architecture. Directed acyclic graphs, also known as Bayesian networks, play a prominent role. Graphical model-based Bayesian 'inference engines', such as bugs and vibes , facilitate fitting and inference. Underlying these are Markov chain Monte Carlo schemes and recent developments in variational approximation theory and methodology.     

A Discrete Variable Chain Graph for Applicants for Credit

A bank offering unsecured personal loans may be interested in several related outcome variables, including defaulting on the repayments, early repayment or failing to take up an offered loan. Current predictive models used by banks typically consider such variables individually. However, the fact that they are related to each other, and to many interrelated potential predictor variables, suggests that graphical models may provide an attractive alternative solution. We developed such a model for a data set of 15 variables measured on a set of 14 000 applications for unsecured personal loans. The resulting global model of behaviour enabled us to identify several previously unsuspected relationships of considerable interest to the bank. For example, we discovered important but obscure relationships between taking out insurance, prior delinquency with a credit card and delinquency with the loan.     

关于完全二部图的P2k＋1——因子分解

本文给出了完全二部图Ｋｍ，ｎ的Ｐ２ｋ＋１－因子分解存在的必要条件，同时论证了充分条件的二种特殊情况。     

两种m重-四角链图的优美性

刘春峰等证明了A型m重—四角链图、B型m重—四角链图的k—优美性及序列性。文章给出了另一种优美标号(也是k—优美标号),且在此标号下证得了这两种m重—四角链图是交错图,且具有奇优美性及平衡性。     

Mathematical morphology: A useful set of tools for image analysis

In this paper we give an overview of both classical and more modern morphological techniques. We will demonstrate their utility through a range of practical examples. After discussing the fundamental morphological ideas, we show how the classic morphological opening and closing filters lead to measures of size via granulometries, and we will discuss briefly their implementation. We also present an overview of morphological segmentation techniques, and the use of connected openings and thinnings will be demonstrated. This then leads us into the more recent set-theoretic notions of graph based approaches to image analysis.