A New Formulation of the Nonmetric Strain Problem in Multidimensional Scaling

A natural extension of classical metric multidimensional scaling is proposed. The result is a new formulation of nonmetric multidimensional scaling in which the strain criterion is minimized subject to order constraints on the disparity variables. Innovative features of the new formulation include: the parametrization of the p-dimensional distance matrices by the positive semidefinite matrices of rank ≤p; optimization of the (squared) disparity variables, rather than the configuration coordinate variables; and a new nondegeneracy constraint, which restricts the set of (squared) disparities rather than the set of distances. Solutions are obtained using an easily implemented gradient projection method for numerical optimization. The method is applied to two published data sets.     

数与力:牛顿科学纲领的基本内核探微

牛顿科学劳作背后的形上理念及其方法论架构乃科学史中的元问题之一,也是以往学界乏有论及的盲区。本文注重一种回到事情本身的理路,从牛顿的具体文本出发,撷取出微分定律的工具理性、力之概念的别样意蕴和运动机制的自然本态等三大理论质点,以图彰显牛顿科学纲领的别样意蕴,并澄清以往学界对牛顿的某些误解与误读之处。     

A Fuzzy Clustering Model for Multivariate Spatial Time Series

Clustering of multivariate spatial-time series should consider: 1) the spatial nature of the objects to be clustered; 2) the characteristics of the feature space, namely the space of multivariate time trajectories; 3) the uncertainty associated to the assignment of a spatial unit to a given cluster on the basis of the above complex features. The last aspect is dealt with by using the Fuzzy C-Means objective function, based on appropriate measures of dissimilarity between time trajectories, by distinguishing the cross-sectional and longitudinal aspects of the trajectories. In order to take into account the spatial nature of the statistical units, a spatial penalization term is added to the above function, depending on a suitable spatial proximity/ contiguity matrix. A tuning coefficient takes care of the balance between, on one side, discriminating according to the pattern of the time trajectories and, on the other side, ensuring an approximate spatial homogeneity of the clusters. A technique for determining an optimal value of this coefficient is proposed, based on an appropriate spatial autocorrelation measure. Finally, the proposed models are applied to the classification of the Italian provinces, on the basis of the observed dynamics of some socio-economical indicators.     

Some New Results on Orthogonally Constrained Candecomp

The use of Candecomp to fit scalar products in the context of Indscal is based on the assumption that, due to the symmetry of the data matrices involved, two components matrices will become equal when Candecomp converges. Bennani Dosse and Ten Berge (2008) have shown that, in the single component case, the assumption can only be violated at saddle points in the case of Gramian matrices. This paper again considers Candecomp applied to symmetric matrices, but with an orthonormality constraint on the components. This constrained version of Candecomp, when applied to symmetric matrices, has long been known under the acronym Indort. When the data matrices are positive definite, or have become positive semidefinite due to double centering, and the saliences are nonnegative – by chance or by constraint –, the component matrices resulting from Indort are shown to be equal. Because Indort is also free from so-called degeneracy problems, it is a highly attractive alternative to Candecomp in the present context. We also consider a well-known successive approach to the orthogonally constrained Indscal problem and we compare, from simulated and real data sets, its results with those given by the simultaneous (Indort) approach.     

莱布尼茨自然观的生态意蕴

莱布尼茨虽生活在被机械自然观逐渐"祛魅"的时代,但他超越了时代的局限,认同机械自然观的解释力的同时也认识到这种自然观的不足,并且他指出了目的论用以解释自然的积极价值。他将机械论与目的论在其自然观中调和起来。在这种调和的视角下,莱布尼茨通过一系列的原则:个体性原则、连续性原则、和谐原则、最佳原则建构出一幅有机的自然图景。今天,人们仍然在机械自然图景中继续着祛魅的进程,所造成的结果是人类生态家园惨遭破坏,人类精神无处安放,而机械自然观无法应对当前人类所面临的这种危机。莱布尼茨的有机自然观对自然的返魅以及构建和谐的生态环境具有建设性意义。     

Metric and Euclidean properties of dissimilarity coefficients

We assemble here properties of certain dissimilarity coefficients and are specially concerned with their metric and Euclidean status. No attempt is made to be exhaustive as far as coefficients are concerned, but certain mathematical results that we have found useful are presented and should help establish similar properties for other coefficients. The response to different types of data is investigated, leading to guidance on the choice of an appropriate coefficient.The authors wish to thank the referees, one of whom did a magnificent job in painstakingly checking the detailed algebra and detecting several slips.     

欧洲中世纪技术的形而上学反思

中世纪欧洲传承了古罗马的技术实用精神，创造出可观的技术成就，给黑暗的中世纪以光明。其间渗透着对技术的怀疑；经院哲学唯名论思想中，有对技术的渴望和谨慎的肯定；而基督教和《圣经》中蕴涵的自然观，反映出《圣经》主张人可以支配自然，为技术活动提供了宗教依据；中世纪的中后期则明显地表现出对技术的肯定态度，孕育出一种新的技术乐观主义。但无论怎样，中世纪还是主张把技术置于神性之下。     

巴特利特创建自相关检验理论的历史探缘

从巴特利特的学术背景出发,立足于"为什么数学",挖掘了巴特利特创建自相关检验理论的发展历程及推动缘由.从理论探究和实践数据分析的双重视角,巴特利特剖析了由于观测数据之间存在"依赖性",普通统计意义下的显著性检验在时间序列分析中通常是无效的.为探讨新的统计推断方式,在推证平稳序列自相关误差公式的基础上,巴特利特最终推断了...     

论思维系统的层次结构和复杂性

通过对传统经验论和唯理论之争的考查，依据现代思维科学与人工智能研究的成果，论证了思维系统的层次结构与复杂性；对辩证唯物主义认识论的相关的部分给予了新的表述。     

实践生成论:对技术否定性本质的一种解读

技术本身是实践地生成的,技术与实践的结合即技术化实践和技术应用,既生成着技术的肯定性本质,也生成着技术的否定性本质,赋予技术某种先天本质的观点是错误的.克服技术负效应的根本途径,不是诅咒和弃绝技术,而是反思和检讨人类实践观念的片面性和实践方式的不合理性.     

华蘅芳《积较术》数学方法分析

在《积较术》中,基于独特的差分定义,华蘅芳构造了一个与Ｎｅｗｔｏｎ有限差分公式完全不同的差分体系,针对各种数表的使用,华蘅芳设计了一种”乘表相加“的计算方法。算理分析表明,这一算法与近代矩阵乘法一致。对《积较术》 中的数学思想与数学方法的分析,揭示了清末传统数学研究所的生长点及其在向近代数学转变过程的积极意义。     

A Proposal for a Coherent Ontology of Fundamental Entities

We argue that the distinction between framework and interaction theories should be taken carefully into consideration when dealing with the philosophical implications of fundamental theories in physics. In particular, conclusions concerning the nature of reality can only be consistently derived from assessing the ontological and epistemic purport of both types of theories. We put forward an epistemic form of realism regarding framework theories, such as Quantum Field Theory. The latter, indeed, informs us about the general properties of quantum fields, laying the groundwork for interaction theories. Yet, concerning interaction theories, we recommend a robust form of ontological realism regarding the entities whose existence is assumed by these theories. As an application, we refer to the case of the Standard Model, so long as it has proved to successfully inform us about the nature of various sorts of fundamental particles making up reality. In short, although we acknowledge that both framework and interaction theories partake in shaping our science-based view of reality, and that neither would do by itself the work we expect them to accomplish together, our proposal for a coherent ontology of fundamental entities advances a compromise between two forms of realism about theories in each case.     

Distribution of some similarity coefficients for dyadic binary data in the case of associated attributes

Parameters are derived of distributions of three coefficients of similarity between pairs (dyads) of operational taxonomic units for multivariate binary data (presence/absence of attributes) under statistical independence. These are applied to test independence for dyadic data. Association among attributes within operational taxonomic units is allowed. It is also permissible for the two units in the dyad to be drawn from different populations having different presence probabilities of attributes. The variance of the distribution of the similarity coefficients under statistical independence is shown to be relatively large in many empirical situations. This result implies that the practical interpretation of these coefficients requires much care. An application using the Jaccard index is given for the assessment of consensus between psychotherapists and their clients.

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La distribution des coefficients de similarité pour les données binaires et les attributs associés

Résumé Les paramètres de la distribution de trois coefficients de similarité entre paires d'éléments taxinomiques opérationels de données multivariables binaires (présence/absence) ont été dérivés dans l'hypothèse d'indépendance statistique. Ces paramètres sont utilisés dans un test d'indépendance pour les données dyadiques. L'existence est autorisée, dans la population d'éléments, d'une association entre plusieurs attributs. Il est également permis que les deux éléments de la dyade soient tirés de deux populations différentes, ayant différentes probabilit és quant à la présence des attributs. Dans beaucoup de situations empiriques, la variance des coefficients de similarité peut être relativement élevée dans le cas d'indépendance statistique. Par conséquence, ces coefficients doivent être interprétés avec précaution. Un exemple est donné pour le coefficient de Jaccard, qui a été employé dans une recherche sur la concordance entre des psychothérapeutes et leurs clients.

     

A Simple Identification Proof for a Mixture of Two Univariate Normal Distributions

A simple proof of the identification of a mixture of two univariate normal distributions is given. The proof is based on the equivalence of local identification with positive definiteness of the information matrix and the equivalence of the latter to a condition on the score vector that is easily checked for this model. Two extensions using the same line of proof are also given. We would like to thank Tom Wansbeek, Michel Wedel, Arie Kapteyn, and two anonymous reviewers for helpful comments on earlier versions of this paper.     

人工意识是否可能

电脑是否可能有意识?问及这一问题,其目的不是要作出肯定或否定的回答.事实上,全球的实验室在探寻计算机意识方面都有不同程度的进展.本文只是提供一种分析的视角,试图理解作为意识活动本质的诸种特性,正是后者在主动与被动之间划出一条分明的界线,人和机器的许多差别在这里找到了解释的根据;也正是它们构成了人工意识赖以建立的基础.     

论怀特海有关宗教与科学的观点

怀特海认为，影响人类最大的两种普遍力量是宗教与科学。宗教作为人性内在的形上诉求，赋予外部世界意义，其文化孕育了近代科学的诞生。专注纯粹事实的客观科学只是一种理性抽象，但它有助于人性明晰且净化了宗教观念。科学与宗教的统一不仅诉诸理论上克服抽象误置为具体的谬误，扬弃事实与价值的二元论并建构一种植根于审美价值经验哲学的努力，而且需要我们在实践中对两者之间的关系持有宽容的态度并作出积极的理解。     

“道法自然”的现代诠释

道家"道法自然"观念的核心内容即是通过"法天地"而体悟其中的"自然"之道以为人类所用。其主要目的有二:一是为人类安身立命,二是借以救治失性的病态人类。"道法自然"的理论根据在于道家认为大自然是至善至美的,而且还认为正是体现于天地万物之中的理性的自然精神造就了这种至善至美。"道法自然"并非机械模仿天地万物尤其是动物的某些个别的、具体的行为,而是要学习它们的不同行为中所体现出来的某些共同的理性精神,也就是说,"道法自然"一定要透过现象而抓取其本质。     

重建类本位的环境人类中心主义生态伦理学

环境危机是由人的失范行为导致的。人如果还有不是为了人类社会的正常生存发展而破坏自然的失范行为,那就说明人还没有彻底摆脱动物的本性,人还不是真正的人,距离人的本质的实现还有相当的距离。因此必须从人的本质出发探求解决环境危机的根本途径。自然中心主义生态伦理学过于崇拜自然而失落了人,否定人的本质。“人类中心主义”生态伦理学把传统的人类中心主义的伦理观、价值观扩大到自然,实际上是削弱人的作用、人的特性,也否定了人的本质。只有以类为本位的环境人类中心主义才能真正体现人的本质,从根本上解决环境危机。     

试论新中国“规划科学”模式的延续和发展——以“自然辩证法研究规划草案”为中心的考察

新中国成立后,哲学社会科学走上由国家主导的"规划科学"模式的道路。但受政治运动冲击、制度缺失等因素的影响,制定的各项哲学社会科学规划大都形同虚设,只有1956年制定的《自然辩证法(数学和自然科学中的哲学问题)十二年(1956-1967)研究规划草案》幸运地成为集中体现并延续上述"规划科学"模式的一个成功特例。虽然草案本身还只是一个不完善的学术性工作计划,但它依然充分发挥了"规划科学"模式的积极作用,推动了具有中国特色的自然辩证法事业的发展,在中国自然辩证法发展史上具有极其重要的地位和作用。     

人工自然观对于文化发展的科学价值

以人工自然的观念来考察人类文化的发展，就把文化和人类社会的发展纳入自然发展的整个发展之中，从而深刻揭示出人工自然对于文化发展的基础性和改革作用机制，将文化发展的观念确立在科学认识的基础之上。建设人工自然的现代文明。