How Computational Models Predict the Behavior of Complex Systems

In this paper, we argue for the centrality of prediction in the use of computational models in science. We focus on the consequences of the irreversibility of computational models and on the conditional or ceteris paribus, nature of the kinds of their predictions. By irreversibility, we mean the fact that computational models can generally arrive at the same state via many possible sequences of previous states. Thus, while in the natural world, it is generally assumed that physical states have a unique history, representations of those states in a computational model will usually be compatible with more than one possible history in the model. We describe some of the challenges involved in prediction and retrodiction in computational models while arguing that prediction is an essential feature of non-arbitrary decision making. Furthermore, we contend that the non-predictive virtues of computational models are dependent to a significant degree on the predictive success of the models in question.     

Connecting Internal and External Representations: Spatial Transformations of Scientific Visualizations

Many scientific discoveries have depended on external diagrams or visualizations. Many scientists also report to use an internal mental representation or mental imagery to help them solve problems and reason. How do scientists connect these internal and external representations? We examined working scientists as they worked on external scientific visualizations. We coded the number and type of spatial transformations (mental operations that scientists used on internal or external representations or images) and found that there were a very large number of comparisons, either between different visualizations or between a visualization and the scientists’ internal mental representation. We found that when scientists compared visualization to visualization, the comparisons were based primarily on features. However, when scientists compared a visualization to their mental representation, they were attempting to align the two representations. We suggest that this alignment process is how scientists connect internal and external representations.     

基于"术语在线"的科技术语多义表征研究——以航空和航海术语为例

文章以“术语在线”为主要验证平台,以全国科学技术名词审定委员会发布的权威词库为基准语料,对航空与航海相关领域的若干典型交叉词条的义项进行了对比分析,并就其语义框架与阐释空间进行研究。研究发现:首先,在航空与航海领域存在大量的同形同义、同形异义和同义异形现象。其次,此类术语的语义表征依赖于特定的联立关系,受到相应概念元素的规约。一方面,在其依存的具体语义框架内,其语义表征符合单义性原则;另一方面,在学科交叉背景下,该类术语具备明显的学科间性特征,其语义表征具有多义阐释空间。     

A New Representation of Interval Symbolic Data and Its Application in Dynamic Clustering

In this study, we consider the type of interval data summarizing the original samples (individuals) with classical point data. This type of interval data are termed interval symbolic data in a new research domain called, symbolic data analysis. Most of the existing research, such as the (centre, radius) and [lower boundary, upper boundary] representations, represent an interval using only the boundaries of the interval. However, these representations hold true only under the assumption that the individuals contained in the interval follow a uniform distribution. In practice, such representations may result in not only inconsistency with the facts, since the individuals are usually not uniformly distributed in many application aspects, but also information loss for not considering the point data within the intervals during the calculation. In this study, we propose a new representation of the interval symbolic data considering the point data contained in the intervals. Then we apply the city-block distance metric to the new representation and propose a dynamic clustering approach for interval symbolic data. A simulation experiment is conducted to evaluate the performance of our method. The results show that, when the individuals contained in the interval do not follow a uniform distribution, the proposed method significantly outperforms the Hausdorff and city-block distance based on traditional representation in the context of dynamic clustering. Finally, we give an application example on the automobile data set.     

What is Applied Mathematics?

A number of issues connected with the nature of applied mathematics are discussed. Among the claims are these: mathematics "hooks onto" the world by providing models or representations, not by describing the world; classic platonism is to be preferred to structuralism; and several issues in the philosophy of science (reality of spacetime, the quantum state) are intimately connected to the nature of applied mathematics.     

论因果传递性原则

因果关系通常被视为一种传递关系。近年来,哲学家们提出了两类典型的反例来挑战因果传递性原则。当前有代表性的三种解决方案,即相称性方案、面向性方案、对比主义方案,均能够恰当应对第一类反例,但却难以应对第二类反例。通过区分事件系统演化的缺省状态与偏离状态,可以构造一种新的解决方案。在此方案下,因果陈述中所隐含的对系统演化状态的索引化指称得以明晰化,从而可以看到,在两类反例中要么事实上存在因果传递性,要么表面的传递性失败其实源于对案例的不恰当表征。继而因果传递性原则得以捍卫。     

A Combinatorial Approach to Assess the Separability of Clusters

Separability of clusters is an issue that arises in many different areas, and is often used in a rather vague and subjective manner. We introduce a combinatorial notion of interiority to derive a global view on separability of a set of entities. We develop this approach further to evaluate the overall separability of a partition in the context of cluster analysis. Our approach captures combinatorial and geometrical aspects of data and provides, in addition to numerical evaluations, graphical representations particularly useful when data are not easily visualized. We illustrate the methodology on some real and simulated datasets.     

Degenerating Families of Dendrograms

Dendrograms used in data analysis are ultrametric spaces, hence objects of nonarchimedean geometry. It is known that there exist p-adic representations of dendrograms. Completed by a point at infinity, they can be viewed as subtrees of the Bruhat-Tits tree associated to the p-adic projective line. The implications are that certain moduli spaces known in algebraic geometry are in fact p-adic parameter spaces of dendrograms, and stochastic classification can also be handled within this framework. At the end, we calculate the topology of the hidden part of a dendrogram.     

The generation of random,binary unordered trees

Several techniques are given for the uniform generation of trees for use in Monte Carlo studies of clustering and tree representations. First, general strategies are reviewed for random selection from a set of combinatorial objects with special emphasis on two that use random mapping operations. Theorems are given on how the number of such objects in the set (e.g., whether the number is prime) affects which strategies can be used. Based on these results, methods are presented for the random generation of six types of binary unordered trees. Three types of labeling and both rooted and unrooted forms are considered. Presentation of each method includes the theory of the method, the generation algorithm, an analysis of its computational complexity and comments on the distribution of trees over which it samples. Formal proofs and detailed algorithms are in appendices.     

The analysis of free-sorting data: Beyond pairwise cooccurrences

Free-sorting data are obtained when subjects are given a set of objects and are asked to divide them into subsets. Such data are usually reduced by counting for each pair of objects, how many subjects placed both of them into the same subset. The present study examines the utility of a group of additional statistics. the cooccurrences of sets of three objects. Because there are dependencies among the pair and triple cooccurrences, adjusted triple similarity statistics are developed. Multidimensional scaling and cluster analysis — which usually use pair similarities as their input data — can be modified to operate on three-way similarities to create representations of the set of objects. Such methods are applied to a set of empirical sorting data: Rosenberg and Kim's (1975) fifteen kinship terms.The author thanks Phipps Arabie, Lawrence Hubert, Lawrence Jones, Ed Shoben, and Stanley Wasserman for their considerable contributions to this paper.     

Classification of Asymmetric Proximity Data

When clustering asymmetric proximity data, only the average amounts are often considered by assuming that the asymmetry is due to noise. But when the asymmetry is structural, as typically may happen for exchange flows, migration data or confusion data, this may strongly affect the search for the groups because the directions of the exchanges are ignored and not integrated in the clustering process. The clustering model proposed here relies on the decomposition of the asymmetric dissimilarity matrix into symmetric and skew-symmetric effects both decomposed in within and between cluster effects. The classification structures used here are generally based on two different partitions of the objects fitted to the symmetric and the skew-symmetric part of the data, respectively; the restricted case is also presented where the partition fits jointly both of them allowing for clusters of objects similar with respect to the average amounts and directions of the data. Parsimonious models are presented which allow for effective and simple graphical representations of the results.     

Dimensionality Reduction on the Cartesian Product of Embeddings of Multiple Dissimilarity Matrices

We consider the problem of combining multiple dissimilarity representations via the Cartesian product of their embeddings. For concreteness, we choose the inferential task at hand to be classification. The high dimensionality of this Cartesian product space implies the necessity of dimensionality reduction before training a classifier. We propose a supervised dimensionality reduction method, which utilizes the class label information, to help achieve a favorable combination. The simulation and real data results show that our approach can improve classification accuracy compared to the alternatives of principal components analysis and no dimensionality reduction at all.     

论科学技术的经济功能

经济功能日益成为科技社会功能的核心,从系统与环境相互作用的关系视角来看,科学技术的经济功能主要表现为:科学技术对经济运行环境的改善作用;对经济系统要素及其结构的优化作用;对经济运行机制的协同作用.解决目前我国经济体制、经济结构和经济增长方式等问题,必须依靠深化改革、依靠科技进步.     

A graph-theoretic method for organizing overlapping clusters into trees,multiple trees,or extended trees

A clustering that consists of a nested set of clusters may be represented graphically by a tree. In contrast, a clustering that includes non-nested overlapping clusters (sometimes termed a “nonhierarchical” clustering) cannot be represented by a tree. Graphical representations of such non-nested overlapping clusterings are usually complex and difficult to interpret. Carroll and Pruzansky (1975, 1980) suggested representing non-nested clusterings with multiple ultrametric or additive trees. Corter and Tversky (1986) introduced the extended tree (EXTREE) model, which represents a non-nested structure as a tree plus overlapping clusters that are represented by marked segments in the tree. We show here that the problem of finding a nested (i.e., tree-structured) set of clusters in an overlapping clustering can be reformulated as the problem of finding a clique in a graph. Thus, clique-finding algorithms can be used to identify sets of clusters in the solution that can be represented by trees. This formulation provides a means of automatically constructing a multiple tree or extended tree representation of any non-nested clustering. The method, called “clustrees”, is applied to several non-nested overlapping clusterings derived using the MAPCLUS program (Arabie and Carroll 1980).     

科学创造可能性的哲学解读

广义的科学创造实践活动主要以科学发现与技术发明的方式展开.追究发现与发明之可能性的本体因由,则在于其对象的有结构存在.结构性亦即有序性.有序性的表征形式是由序律制约的序元所构成的序链.不同的序链受制于不同的序律,内涵着不同的功能.思维创造是以未知序链的理想功能为诉求,以已知序律为条件,以对认知对象形成的表象、意念及认知组块等序元为质料,以"If……then"产生式匹配构建新序链以实现其新功能,设想新序律以解释新序链.科学创造活动是对其对象无限可能序的试错性解译与重构.     

Perceiving the Infinite and the Infinitesimal World: Unveiling and Optical Diagrams in Mathematics

Many important concepts of the calculus are difficult to grasp, and they may appear epistemologically unjustified. For example, how does a real function appear in “small” neighborhoods of its points? How does it appear at infinity? Diagrams allow us to overcome the difficulty in constructing representations of mathematical critical situations and objects. For example, they actually reveal the behavior of a real function not “close to” a point (as in the standard limit theory) but “in” the point. We are interested in our research in the diagrams which play an optical role –microscopes and “microscopes within microscopes”, telescopes, windows, a mirror role (to externalize rough mental models), and an unveiling role (to help create new and interesting mathematical concepts, theories, and structures). In this paper we describe some examples of optical diagrams as a particular kind of epistemic mediator able to perform the explanatory abductive task of providing a better understanding of the calculus, through a non-standard model of analysis. We also maintain they can be used in many other different epistemological and cognitive situations.     

On The Impossibility Of Empirical Controls Of Scientific Theories – From The Point Of View Of A Psychologist

Standard considerations of philosophy of science are reformulated in psychological terms and arguments, suggesting a fundamental change in life perspective: subjective experiences or introspective data are subject to motivational biases and therefore not admitted as objective empirical facts in science, However, we never experience objects or events of the external world, i.e., so called objective facts, but exclusively subjective percepts or mental events. They are merely assumed to, but may or may not be accurate or distorted mental representations of objects or events of an external world. Accordingly, the latter are theoretical constructs, i.e., constructs of the fictitious but most successful predictive (implicit) theory, called external world, which seems to be constructed from regularities observed in mental events and serves as a reference fiction for, erroneously called empirical, tests of predictions of scientific theories.Relevant Publication: Micko, H.C.: 2001, Psychologie: Von der Geistes – zur Naturwissenschaft – und weiter wohin? Erkenntnistheoretische Erwägungen vor und nach dem Aufkommen des philosophischen Konstruktivismus. Ztschr. f. Psychologie, 209: 54–68.     

TreeOfTrees Method to Evaluate the Congruence Between Gene Trees

A new method, TreeOfTrees, is proposed to compare X-tree structures obtained from several sets of aligned gene sequences of the same taxa. Its aim is to detect genes or sets of genes having different evolutionary histories. The comparison between sets of trees is based on several tree metrics, leading to a unique tree labelled by the gene trees. The robustness values of its edges are estimated by bootstrapping and consensus procedures that allow detecting subsets of genes having differently evolved. Simulations are performed under various evolutionary conditions to test the efficiency of the method and an application on real data is described. Tests of arboricity and various consensus algorithms are also discussed. A corresponding software package is available.     

A mathematical programming approach to fitting general graphs

We present an algorithm for fitting general graphs to proximity data. The algorithm utilizes a mathematical programming procedure based on a penalty function approach to impose additivity constraints upon parameters. For a user-specified number of links, the algorithm seeks to provide the connected network that gives the least-squares approximation to the proximity data with the specified number of links, allowing for linear transformations of the data. The network distance is the minimum-path-length metric for connected graphs. As a limiting case, the algorithm provides a tree where each node corresponds to an object, if the number of links is set equal to the number of objects minus one. A Monte Carlo investigation indicates that the resulting networks tend to fall within one percentage point of the least-squares solution in terms of the variance accounted for, but do not always attain this global optimum. The network model is discussed in relation to ordinal network representations (Klauer 1989) and NETSCAL (Hutchinson 1989), and applied to several well-known data sets.