A modified CANDECOMP method for fitting the extended INDSCAL model

A modified CANDECOMP algorithm is presented for fitting the metric version of the Extended INDSCAL model to three-way proximity data. The Extended INDSCAL model assumes, in addition to the common dimensions, a unique dimension for each object. The modified CANDECOMP algorithm fits the Extended INDSCAL model in a dimension-wise fashion and ensures that the subject weights for the common and the unique dimensions are nonnegative. A Monte Carlo study is reported to illustrate that the method is fairly insensitive to the choice of the initial parameter estimates. A second Monte Carlo study shows that the method is able to recover an underlying Extended INDSCAL structure if present in the data. Finally, the method is applied for illustrative purposes to some empirical data on pain relievers. In the final section, some other possible uses of the new method are discussed. Geert De Soete is supported as “Bevoegdverklaard Navorser” of the Belgian “Nationaal Fonds voor Wetenschappelijik Onderzoek”.     

A generalization of GIPSCAL for the analysis of nonsymmetric data

Graphical representation of nonsymmetric relationships data has usually proceeded via separate displays for the symmetric and the skew-symmetric parts of a data matrix. DEDICOM avoids splitting the data into symmetric and skewsymmetric parts, but lacks a graphical representation of the results. Chino's GIPSCAL combines features of both models, but may have a poor goodness-of-fit compared to DEDICOM. We simplify and generalize Chino's method in such a way that it fits the data better. We develop an alternating least squares algorithm for the resulting method, called Generalized GIPSCAL, and adjust it to handle GIPSCAL as well. In addition, we show that Generalized GIPSCAL is a constrained variant of DEDICOM and derive necessary and sufficient conditions for equivalence of the two models. Because these conditions are rather mild, we expect that in many practical cases DEDICOM and Generalized GIPSCAL are (nearly) equivalent, and hence that the graphical representation from Generalized GIPSCAL can be used to display the DEDICOM results graphically. Such a representation is given for an illustration. Finally, we show Generalized GIPSCAL to be a generalization of another method for joint representation of the symmetric and skew-symmetric parts of a data matrix.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the first author, and by research grant number A6394 to the second author, from the Natural Sciences and Engineering Research Council of Canada. The authors are obliged to Jos ten Berge and Naohito Chino for stimulating comments.     

GENFOLD2: A set of models and algorithms for the general UnFOLDing analysis of preference/dominance data

A general set of multidimensional unfolding models and algorithms is presented to analyze preference or dominance data. This class of models termed GENFOLD2 (GENeral UnFOLDing Analysis-Version 2) allows one to perform internal or external analysis, constrained or unconstrained analysis, conditional or unconditional analysis, metric or nonmetric analysis, while providing the flexibility of specifying and/or testing a variety of different types of unfolding-type preference models mentioned in the literature including Caroll's (1972, 1980) simple, weighted, and general unfolding analysis. An alternating weighted least-squares algorithm is utilized and discussed in terms of preventing degenerate solutions in the estimation of the specified parameters. Finally, two applications of this new method are discussed concerning preference data for ten brands of pain relievers and twelve models of residential communication devices.     

Convergence of the majorization method for multidimensional scaling

In this paper we study the convergence properties of an important class of multidimensional scaling algorithms. We unify and extend earlier qualitative results on convergence, which tell us when the algorithms are convergent. In order to prove global convergence results we use the majorization method. We also derive, for the first time, some quantitative convergence theorems, which give information about the speed of convergence. It turns out that in almost all cases convergence is linear, with a convergence rate close to unity. This has the practical consequence that convergence will usually be very slow, and this makes techniques to speed up convergence very important. It is pointed out that step-size techniques will generally not succeed in producing marked improvements in this respect.     

Multidimensional scaling in the city-block metric: A combinatorial approach

We present an approach, independent of the common gradient-based necessary conditions for obtaining a (locally) optimal solution, to multidimensional scaling using the city-block distance function, and implementable in either a metric or nonmetric context. The difficulties encountered in relying on a gradient-based strategy are first reviewed: the general weakness in indicating a good solution that is implied by the satisfaction of the necessary condition of a zero gradient, and the possibility of actual nonconvergence of the associated optimization strategy. To avoid the dependence on gradients for guiding the optimization technique, an alternative iterative procedure is proposed that incorporates (a) combinatorial optimization to construct good object orders along the chosen number of dimensions and (b) nonnegative least-squares to re-estimate the coordinates for the objects based on the object orders. The re-estimated coordinates are used to improve upon the given object orders, which may in turn lead to better coordinates, and so on until convergence of the entire process occurs to a (locally) optimal solution. The approach is illustrated through several data sets on the perception of similarity of rectangles and compared to the results obtained with a gradient-based method.     

An evaluation of five algorithms for generating an initial configuration for SINDSCAL

Five different methods for obtaining a rational initial estimate of the stimulus space in the INDSCAL model were compared using the SINDSCAL program for fitting INDSCAL. The effect of the number of stimuli, the number of subjects, the dimensionality, and the amount of error on the quality and efficiency of the final SINDSCAL solution were investigated in a Monte Carlo study. We found that the quality of the final solution was not affected by the choice of the initialization method, suggesting that SINDSCAL finds a global optimum regardless of the initialization method used. The most efficient procedures were the methods proposed by by de Leeuw and Pruzansky (1978) and by Flury and Gautschi (1986) for the simultaneous diagonalization of several positive definite symmetric matrices, and a method based on linearly constraining the stimulus space using the CANDELINC approach developed by Carroll, Pruzansky, and Kruskal (1980).Geert De Soete is supported as Bevoegdverklaard Navorser of the Belgian Nationaal Fonds voor Wetenschappelijk Onderzoek. The authors gratefully acknowledge the helpful comments and suggestions of the reviewers.     

A latent class procedure for the structural analysis of two-way compositional data

This paper develops a new procedure for simultaneously performing multidimensional scaling and cluster analysis on two-way compositional data of proportions. The objective of the proposed procedure is to delineate patterns of variability in compositions across subjects by simultaneously clustering subjects into latent classes or groups and estimating a joint space of stimulus coordinates and class-specific vectors in a multidimensional space. We use a conditional mixture, maximum likelihood framework with an E-M algorithm for parameter estimation. The proposed procedure is illustrated using a compositional data set reflecting proportions of viewing time across television networks for an area sample of households.     

The representation of three-way proximity data by single and multiple tree structure models

Models for the representation of proximity data (similarities/dissimilarities) can be categorized into one of three groups of models: continuous spatial models, discrete nonspatial models, and hybrid models (which combine aspects of both spatial and discrete models). Multidimensional scaling models and associated methods, used for thespatial representation of such proximity data, have been devised to accommodate two, three, and higher-way arrays. At least one model/method for overlapping (but generally non-hierarchical) clustering called INDCLUS (Carroll and Arabie 1983) has been devised for the case of three-way arrays of proximity data. Tree-fitting methods, used for thediscrete network representation of such proximity data, have only thus far been devised to handle two-way arrays. This paper develops a new methodology called INDTREES (for INdividual Differences in TREE Structures) for fitting various(discrete) tree structures to three-way proximity data. This individual differences generalization is one in which different individuals, for example, are assumed to base their judgments on the same family of trees, but are allowed to have different node heights and/or branch lengths.We initially present an introductory overview focussing on existing two-way models. The INDTREES model and algorithm are then described in detail. Monte Carlo results for the INDTREES fitting of four different three-way data sets are presented. In the application, a single ultrametric tree is fitted to three-way proximity data derived from intention-to-buy-data for various brands of over-the-counter pain relievers for relieving three common types of maladies. Finally, we briefly describe how the INDTREES procedure can be extended to accommodate hybrid modelling, as well as to handle other types of applications.     

Clustering and isolation in the consensus problem for partitions

We examine the problem of aggregating several partitions of a finite set into a single consensus partition We note that the dual concepts of clustering and isolation are especially significant in this connection. The hypothesis that a consensus partition should respect unanimity with respect to either concept leads us to stress a consensus interval rather than a single partition. The extremes of this interval are characterized axiomatically. If a sufficient totality of traits has been measured, and if measurement errors are independent, then a true classifying partition can be expected to lie in the consensus interval. The structure of the partitions in the interval lends itself to partial solutions of the consensus problem Conditional entropy may be used to quantify the uncertainty inherent in the interval as a whole     

Ordination in the presence of group structure,for general multivariate data

A low-dimensional representation of multivariate data is often sought when the individuals belong to a set ofa-priori groups and the objective is to highlight between-group variation relative to that within groups. If all the data are continuous then this objective can be achieved by means of canonical variate analysis, but no corresponding technique exists when the data are categorical or mixed continuous and categorical. On the other hand, if there is noa-priori grouping of the individuals, then ordination of any form of data can be achieved by use of metric scaling (principal coordinate analysis). In this paper we consider a simple extension of the latter approach to incorporate grouped data, and discuss to what extent this method can be viewed as a generalization of canonical variate analysis. Some illustrative examples are also provided.     

snoSeeker:扫描人类基因组中向导和孤儿snoRNA的计算机程序包

核仁小分子RNA(small nucleolar RNA,snoR-NA)是真核生物细胞核内的一大类非编码RNA。按其结构和功能特点,除了MRP RNA,目前已知的sn-oRNA可分为两大类:box C/D和box H/ACA。除了少数snoRNA在rRNA前体的剪切加工和转录后修饰过程中起到重要的作用,大部分snoRNA都是通过反义互补行使功能。box C/D snoRNA指导rRNA或snRNA特定位点的2’-O-甲基化修饰,而box H/ACAsnoRNA指导rRNA或snRNA上的假尿嘧啶化修饰。根据snoRNA是否与rRNAs或snRNAs反义互补,也可将它们分为向导snoRNAs(guide snoRNA)和孤儿snoRNAs(orph…     

The Young-Householder algorithm and the least squares multidimensional scaling of squared distances

It is shown that replacement of the zero diagonal elements of the symmetric data matrix of approximate squared distances by certain other quantities in the Young-Householder algorithm will yield a least squares fit to squared distances instead of to scalar products. Iterative algorithms for obtaining these replacement diagonal elements are described and relationships with the ELEGANT algorithm (de Leeuw 1975; Takane 1977) are discussed. In large residual situations a penalty function approach, motivated by the ELEGANT algorithm, is adopted. Empirical comparisons of the algorithms are given.An early version of this paper was presented at the Multidimensional Data Analysis Workshop, Pembroke College, Cambridge, July 1985. I want to thank Jan de Leeuw and Yoshio Takane for bringing the ELEGANT algorithm to my attention and for clarifying its rationale and notation. My thanks go also to Stephen du Toit for help with the ALSCAL computations reported in Section 7.     

李约瑟《中国科学技术史》与中国自然科学史研究室的成立

李约瑟的《中国科学技术史》第一卷（1954年）出版之后，中国科学院做出了积极的回应。副院长竺可桢邀请并组织叶企孙、陈桢、谭其骧等学者对它进行了评介，科学院对李约瑟还进行了资助。中国学者对此卷既有高度的评价，也有具体的批评。中国科学院派遣代表团参加第八届国际科学史大会又与李约瑟直接相关。李约瑟的中国科学技术史研究对中国科学院成立中国自然科学史研究室起到了促进作用。科学史学科在新中国诞生后迅速走上建制化之路，主要是在20世纪50年代初中国共产党和人民政府特别提倡爱国主义的时代背景下，由于竺可桢等科学院领导的倡导和支持、李约瑟与苏联的积极影响等多种因素综合作用的结果。     

《授时历》的白赤道坐标变换法

计算月亮的白道经度，是中国古代数理天文学之月亮运动理论的核心内容之一。在《授时历》(1280年)之前，人们以九道术算法，通过对黄白道差的计算，推求月亮的白道经度。但是，结果很不理想。在《授时历》中，郭守敬与王恂创设“白道交周”算法，改而考虑白赤道坐标的变换，并由此推求任意给定时刻月亮的赤纬，及其白道经度。通过对原始文献的解读分析，搞清楚了《授时历》白赤道坐标变换的算法模型，并运用现代天文学知识的检验，认定这个算法模型的建立是合理的、成功的。     

三国叙事中的领地行为与资源占有

传统三国研究多在政治、军事、文学等方面。从科学视角研究三国争霸的工作鲜有尝试。将领地、领地行为、资源占有潜力(RHP)等概念予以扩展并用于分析三国争霸叙事,观察到地理空间是人和动物均有的领地,人口是人类独有的领地资源,险要地形、城防工事、口头协议均可用来标记领地,包括对有形领地和精神领地进行控制的权力覆盖是无形的领地资源。皇权让渡、册封、皇族血统是皇权标记行为,民族身份、宗教认同是文化标记行为。资源占有潜力是对有形领地和无形领地控制力的集合,增加资源占有潜力总量是领地争夺防卫中的关键因素。     

对我国科学技术史研究生课程正规化建设的思考

本文客观地阐述了国内科学技术史专业研究生课程设置的概况、优势、特色及其与发达国家的差距,提出了加强我国科学技术史研究生课程正规化、品牌化建设的构想。     

论清代前中期古代数学兴盛的原因及其社会影响

清初中国古代数学重新兴盛起来。它是清代皇帝推动,数学考据法的出现和西方数学引入的刺激等综合作用的结果。通过剖析梅文鼎与焦循两个个案,可以较为深入地理解影响那时数学发展的社会因素。受之影响,数学教育在社会普及,部分与数学相关的自然科学发展起来,中国社会出现了某些思想启蒙,国人的理性精神亦得以孕育。     

民国时期人物研究类期刊的嚆矢——《罗素月刊》刊创、内容及其影响

罗素来华是20世纪年代民国社会的盛事,为文化初新的民国学界注入"引导中国向何处去"的兴奋剂,对民国社会文化产生了广泛而深远的影响。为传播罗素思想,作为罗素来华重要推动者的讲学社创办了《罗素月刊》。《罗素月刊》以人名而名,开创了民国时期人物研究类期刊的先河。本文以《罗素月刊》刊载文章为重点,以历史资料为依托,详细梳理其刊创渊源、刊载宗旨、作者群体、发行情况、学术影响等诸多方面的内容,力求复原其作为民国时期人物研究类期刊的嚆矢之貌。     

创新与内功--对理科研究生"自然辩证法"课程教学的几点体会

自然辩证法教学对理科研究生创新精神的培养是至关重要的.创新是自然辩证法的题中之义、精神实质和目标追求,以创新精神为核心的素质教育功能和以创新机理为核心的方法论功能是自然辩证法的两个基本功能,因此突出自然辩证法的创新精神是搞好其教学的首要前提,展示自然辩证法以创新精神为核心的素质教育功能和以创新机理为核心的方法论功能是搞好其教学的重要途径.同时,施教者"大练内功"是搞好自然辩证法教学的关键之所在.