三峡兴隆洞出土12~15万年前的古人类化石和象牙刻划

在重庆市奉节县兴隆洞发掘出土早期智人牙齿、石器、有人工刻划痕迹的象牙和丰富的哺乳动物化石. 这些材料的种类、特点和埋藏状况说明该洞穴是一处远古人类的居住遗址. 通过出土动物群推断和铀系年代测定, 古人类在该洞穴的生存行为发生在中更新世晚期, 距今12~15万年前. 这是在三峡地区首次发现的早期智人化石. 出现在剑齿象门齿上的刻划纹成组分布, 组成简单而抽象的图案, 是目前所知最早的人类有意识的刻划作品, 对原始艺术的起源和东亚地区现代人类的起源、演化和行为方式的研究具有重要的学术意义.     

Multiple Correspondence Analysis via Polynomial Transformations of Ordered Categorical Variables

We present an alternative approach to Multiple Correspondence Analysis (MCA) that is appropriate when the data consist of ordered categorical variables. MCA displays objects (individuals, units) and variables as individual points and sets of category points in a low-dimensional space. We propose a hybrid decomposition on the basis of the classical indicator super-matrix, using the singular value decomposition, and the bivariate moment decomposition by orthogonal polynomials. When compared to standard MCA, the hybrid decomposition will give the same representation of the categories of the variables, but additionally, we obtain a clear association interpretation among the categories in terms of linear, quadratic and higher order components. Moreover, the graphical display of the individual units will show an automatic clustering.     

The runt test for multimodality

Single linkage clusters on a set of points are the maximal connected sets in a graph constructed by connecting all points closer than a given threshold distance. The complete set of single linkage clusters is obtained from all the graphs constructed using different threshold distances. The set of clusters forms a hierarchical tree, in which each non-singleton cluster divides into two or more subclusters; the runt size for each single linkage cluster is the number of points in its smallest subcluster. The maximum runt size over all single linkage clusters is our proposed test statistic for assessing multimodality. We give significance levels of the test for two null hypotheses, and consider its power against some bimodal alternatives. Research partially supported by NSF Grant No. DMS-8617919.     

Resistant orthogonal procrustes analysis

In this paper two alternative loss criteria for the least squares Procrustes problem are studied. These alternative criteria are based on the Huber function and on the more radical biweight function, which are designed to be resistant to outliers. Using iterative majorization it is shown how a convergent reweighted least squares algorithm can be developed. In asimulation study it turns out that the proposed methods perform well over a specific range of contamination. When a uniform dilation factor is included, mixed results are obtained. The methods also yield a set of weights that can be used for diagnostic purposes.     

Clustering the rows and columns of a contingency table

A number of ways of investigating heterogeneity in a two-way contingency table are reviewed. In particular, we consider chi-square decompositions of the Pearson chi-square statistic with respect to the nodes of a hierarchical clustering of the rows and/or the columns of the table. A cut-off point which indicates significant clustering may be defined on the binary trees associated with the respective row and column cluster analyses. This approach provides a simple graphical procedure which is useful in interpreting a significant chi-square statistic of a contingency table.The author gratefully acknowledges the constructive comments of the referees and the editor.     

Comments on “aggregation of equivalence relations” by P. C. Fishburn and A. Rubinstein

The theorem of the paper Aggregation of Equivalence Relations, by Fishburn and Rubinstein, states a result already known. This theorem improves a result from Mirkin (1975) and appears as a corollary occurring in Leclerc (1984).

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Resume L'unique théorème de l'article Aggregation of Equivalence Relations de Fishburn et Rubinstein est déja connu. Il améliore, en fait, un résultat de Mirkin (1975) et apparait en tant que corollaire dans Leclerc (1984).