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.     

Essential Tension: Mathematics - Physics - Philosophy

The author focuses on the tension "realism - idealism" in the philosophy of mathematics, but he does that from the perspective of a theoretical physicist. It is not only that one's standpoint in the philosophy of mathematics determines our understanding of the effectiveness of mathematics in physics, but also the fact that mathematics is so effective in physical sciences tells us something about the nature of mathematics.     

Local and Global Properties of the World

The essence of the method of physics is inseparably connected with the problem of interplay between local and global properties of the universe. In the present paper we discuss this interplay as it is present in three major departments of contemporary physics: general relativity, quantum mechanics and some attempts at quantizing gravity (especially geometrodynamics and its recent successors in the form of various pregeometry conceptions). It turns out that all big interpretative issues involved in this problem point towards the necessity of changing from the standard space-time geometry to some radically new, most probably non-local, generalization. We argue that the recent noncommutative geometry offers attractive possibilities, and gives us a conceptual insight into its algebraic foundations. Noncommutative spaces are, in general, non-local, and their applications to physics, known at present, seem very promising. One would expect that beneath the Planck threshold there reigns a "noncommutative pregeometry", and only when crossing this threshold does the usual space-time geometry emerges.     

Pyramidal classification based on incomplete dissimilarity data

Two algorithms for pyramidal classification — a generalization of hierarchical classification — are presented that can work with incomplete dissimilarity data. These approaches — a modification of the pyramidal ascending classification algorithm and a least squares based penalty method — are described and compared using two different types of complete dissimilarity data in which randomly chosen dissimilarities are assumed missing and the non-missing ones are subjected to random error. We also consider relationships between hierarchical classification and pyramidal classification solutions when both are based on incomplete dissimilarity data.     

Algorithms for ℓ<Subscript>1</Subscript>-Embeddability and Related Problems

Assouad has shown that a real-valued distance d = (d_ij)_{1 ≤ i < j ≤ n} is isometrically embeddable in ℓ₁space if and only if it belongs to the cut cone on n points. Determining if this condition holds is NP-complete. We use Assouad's result in a constructive column generation algorithm for ℓ₁-embeddability. The subproblem is an unconstrained 0-1 quadratic program, solved by Tabu Search and Variable Neighborhood Search heuristics as well as by an exact enumerative algorithm. Computational results are reported. Several ways to approximate a distance which is not ℓ₁-embeddable by another one which is are also studied.     

07式军服标志服饰术语“绶带”应为“穗带”

中国人民解放军07式军服增加了丰富多样的各类标志服饰，并首次向所有军官配发了礼服。其中，礼服上垂挂的金黄色丝带被权威机构和新闻媒体冠以“绶带”之称谓。实际上，“绶带”这一术语的指称对象是错误的，那条金黄色丝带应该叫作“穗带”。     

Embodied Anomaly Resolution in Molecular Genetics: A Case Study of RNAi

Scientific anomalies are observations and facts that contradict current scientific theories and they are instrumental in scientific theory change. Philosophers of science have approached scientific theory change from different perspectives as Darden (Theory change in science: Strategies from Mendelian genetics, 1991) observes: Lakatos (In: Lakatos, Musgrave (eds) Criticism and the growth of knowledge, 1970) approaches it as a progressive “research programmes” consisting of incremental improvements (“monster barring” in Lakatos, Proofs and refutations: The logic of mathematical discovery, 1976), Kuhn (The structure of scientific revolutions, 1996) observes that changes in “paradigms” are instigated by a crisis from some anomaly, and Hanson (In: Feigl, Maxwell (eds) Current issues in the philosophy of science, 1961) proposes that discovery does not begin with hypothesis but with some “problematic phenomena requiring explanation”. Even though anomalies are important in all of these approaches to scientific theory change, there have been only few investigations into the specific role anomalies play in scientific theory change. Furthermore, much of these approaches focus on the theories themselves and not on how the scientists and their experiments bring about scientific change (Gooding, Experiment and the making of meaning: Human agency in scientific observation and experiment, 1990). To address these issues, this paper approaches scientific anomaly resolution from a meaning construction point of view. Conceptual integration theory (Fauconnier and Turner, Cogn Sci 22:133–187, 1996; The way we think: Conceptual blending and mind’s hidden complexities, 2002) from cognitive linguistics describes how one constructs meaning from various stimuli, such as text and diagrams, through conceptual integration or blending. The conceptual integration networks that describe the conceptual integration process characterize cognition that occurs unconsciously during meaning construction. These same networks are used to describe some of the cognition while resolving an anomaly in molecular genetics called RNA interference (RNAi) in a case study. The RNAi case study is a cognitive-historical reconstruction (Nersessian, In: Giere (ed) Cognitive models of science, 1992) that reconstructs how the RNAi anomaly was resolved. This reconstruction traces four relevant molecular genetics publications in describing the cognition necessary in accounting for how RNAi was resolved through strategies (Darden 1991), abductive reasoning (Peirce, In: Hartshorne, Weiss (eds) Collected papers, 1958), and experimental reasoning (Gooding 1990). The results of the case study show that experiments play a crucial role in formulating an explanation of the RNAi anomaly and the integration networks describe the experiments’ role. Furthermore, these results suggest that RNAi anomaly resolution is embodied. It is embodied in a sense that cognition described in the cognitive-historical reconstruction is experientially based.

Seriation in the Presence of Errors: NP-Hardness of <Emphasis Type="Italic">l</Emphasis><Subscript><Emphasis Type="Italic">∞</Emphasis></Subscript> -Fitting Robinson Structures to Dissimilarity Matrices

In this paper, we establish that the following fitting problem is NP-hard: given a finite set X and a dissimilarity measure d on X (d is a symmetric function from X ² to the nonnegative real numbers and vanishing on the diagonal), we wish to find a Robinsonian dissimilarity d _R on X minimizing the l _∞ -error ||d − d _R || _∞ = max_x,y ∈X{|d(x, y) − d _R (x, y)|} between d and d _R . Recall that a dissimilarity d _R on X is called monotone (or Robinsonian) if there exists a total order ≺ on X such that x ≺ z ≺ y implies that d(x, y) ≥ max{d(x, z), d(z, y)}. The Robinsonian dissimilarities appear in seriation and clustering problems, in sparse matrix ordering and DNA sequencing.     

女权主义或女性主义辨析——由feminism的中译引发的思考

针对目前feminism一词存在"女权主义"和"女性主义"两种中文译名的分歧,在回顾西方feminism的发展进程之后,试图从翻译意义论的角度来考察两个译名的形成原因和两者之间存在的差距,从而为feminism找到一个贴切的中文翻译。     

On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions

We discuss the foundations of constructive mathematics, including recursive mathematics and intuitionism, in relation to classical mathematics. There are connections with the foundations of physics, due to the way in which the different branches of mathematics reflect reality. Many different axioms and their interrelationship are discussed. We show that there is a fundamental problem in BISH (Bishop’s school of constructive mathematics) with regard to its current definition of ‘continuous function’. This problem is closely related to the definition in BISH of ‘locally compact’. Possible approaches to this problem are discussed. Topology seems to be a key to understanding many issues. We offer several new simplifying axioms, which can form bridges between the various branches of constructive mathematics and classical mathematics (‘reuniting the antipodes’). We give a simplification of basic intuitionistic theory, especially with regard to so-called ‘bar induction’. We then plead for a limited number of axiomatic systems, which differentiate between the various branches of mathematics. Finally, in the appendix we offer BISH an elegant topological definition of ‘locally compact’, which unlike the current definition is equivalent to the usual classical and/or intuitionistic definition in classical and intuitionistic mathematics, respectively.     

Intelligent Choice of the Number of Clusters in K-Means Clustering: An Experimental Study with Different Cluster Spreads

The issue of determining “the right number of clusters” in K-Means has attracted considerable interest, especially in the recent years. Cluster intermix appears to be a factor most affecting the clustering results. This paper proposes an experimental setting for comparison of different approaches at data generated from Gaussian clusters with the controlled parameters of between- and within-cluster spread to model cluster intermix. The setting allows for evaluating the centroid recovery on par with conventional evaluation of the cluster recovery. The subjects of our interest are two versions of the “intelligent” K-Means method, ik-Means, that find the “right” number of clusters by extracting “anomalous patterns” from the data one-by-one. We compare them with seven other methods, including Hartigan’s rule, averaged Silhouette width and Gap statistic, under different between- and within-cluster spread-shape conditions. There are several consistent patterns in the results of our experiments, such as that the right K is reproduced best by Hartigan’s rule – but not clusters or their centroids. This leads us to propose an adjusted version of iK-Means, which performs well in the current experiment setting.     

论科技伦理评估的理论基础及评估标准

科技评估可分为效果评估和伦理评估,两者是科技评估的事实和价值二维。"显见义务论"可以作为科技伦理评估的理论基础。评估标准是科技伦理评估的核心,应通过科技活动中的法律权利来选定"显见"的科技伦理原则作为科技伦理评估的评估标准。     

Splitting an Ordering into a Partition to Minimize Diameter

k consisting of k clusters, with k > 2. Bottom-up agglomerative approaches are also commonly used to construct partitions, and we discuss these in terms of worst-case performance for metric data sets. Our main contribution derives from a new restricted partition formulation that requires each cluster to be an interval of a given ordering of the objects being clustered. Dynamic programming can optimally split such an ordering into a partition P^k for a large class of objectives that includes min-diameter. We explore a variety of ordering heuristics and show that our algorithm, when combined with an appropriate ordering heuristic, outperforms traditional algorithms on both random and non-random data sets.     

《新法算书》中的月亮模型

在简要介绍月亮视运动各种差的基础上，重建《新法算书》所载哥白尼月亮模型及其确定几何参数方法。叙述第谷月亮理论的发展过程，指出《新法算书》中的第谷新法实质上就是没有考虑二均差修正的第谷最初的月亮模型，最后给出用第谷新法推算月亮加减差的过程。     

Axiomatization and Models of Scientific Theories

In this paper we discuss two approaches to the axiomatization of scientific theories in the context of the so called semantic approach, according to which (roughly) a theory can be seen as a class of models. The two approaches are associated respectively to Suppes’ and to da Costa and Chuaqui’s works. We argue that theories can be developed both in a way more akin to the usual mathematical practice (Suppes), in an informal set theoretical environment, writing the set theoretical predicate in the language of set theory itself or, more rigorously (da Costa and Chuaqui), by employing formal languages that help us in writing the postulates to define a class of structures. Both approaches are called internal, for we work within a mathematical framework, here taken to be first-order ZFC. We contrast these approaches with an external one, here discussed briefly. We argue that each one has its strong and weak points, whose discussion is relevant for the philosophical foundations of science.     

An Algorithm for Computing Cutpoints in Finite Metric Spaces

The theory of the tight span, a cell complex that can be associated to every metric D, offers a unifying view on existing approaches for analyzing distance data, in particular for decomposing a metric D into a sum of simpler metrics as well as for representing it by certain specific edge-weighted graphs, often referred to as realizations of D. Many of these approaches involve the explicit or implicit computation of the so-called cutpoints of (the tight span of) D, such as the algorithm for computing the “building blocks” of optimal realizations of D recently presented by A. Hertz and S. Varone. The main result of this paper is an algorithm for computing the set of these cutpoints for a metric D on a finite set with n elements in O(n3) time. As a direct consequence, this improves the run time of the aforementioned O(n6)-algorithm by Hertz and Varone by “three orders of magnitude”.     

论《译者的任务》中intention的翻译

随着经济全球化和学术思想自由化的发展,越来越多的学术著作被译介到中国,术语汉译如何规范化也理所当然地成为译界关注的焦点。通过对《译者的任务》中intention的研究,发现该术语的翻译存在一词多译或同名异译的现象。基于此,文章试图从深层次挖掘相关概念的区别和联系,希望对intention的翻译做正本清源式的讨论。     

Quantum Nonlocality and the Challenge to Scientific Realism

In this essay I examine various aspects of the nearcentury-long debate concerning the conceptualfoundations of quantum mechanics and the problems ithas posed for physicists and philosophers fromEinstein to the present. Most crucial here is theissue of realism and the question whether quantumtheory is compatible with any kind of realist orcausal-explanatory account which goes beyond theempirical-predictive data. This was Einstein's chiefconcern in the famous series of exchanges with NielsBohr when he refused to accept the truth orcompleteness of a doctrine (orthodox QM) which ruledsuch questions to be strictly inadmissible. I discussthe later history of quantum-theoretical debate withparticular reference to the issue of nonlocality,i.e., the phenomenon of superluminal(faster-than-light) interaction betweenwidely-separated particles. Then I show how thestandard `Copenhagen' interpretation of QM hasinfluenced current anti-realist orontological-relativist approaches to philosophy ofscience. Indeed, there are clear signs that somephilosophers have retreated from a realist positionvery largely in response to just these problems. So itis important to ask exactly why – on what scientificor philosophical grounds – any preferred alternative(causal-realist) construal should have been ruled outas a matter of orthodox QM wisdom. Moreconstructively, my paper presents various arguments infavour of one such alternative, the `hidden-variables'theory developed since the early 1950s by David Bohmand consistently marginalised by proponents of theCopenhagen doctrine.     

中医药术语英译通则在中医病名翻译中的应用

《国际疾病分类》第11版(ICD-11)传统医学部分的发布,将中医药国际化向前推进了一步。因其囊括的中医疾病术语数量有限,中医病名对外翻译尚有很多工作需要开展。文章概述了中医药术语的英译规范原则与方法;讨论了对应性、同一性、系统性、简洁性、回译性、约定俗成、民族性等翻译原则在病名英译中的使用,并从术语部件的规范、双译法的使用、中西医病名关系的处理等方面细化了各原则在翻译中医疾病时的实现方法。音译法适用于跨学科、含义多且难以找到合适译名的中医疾病术语部件,而双译法可以解决中医术语翻译归化与异化的分歧,同时促进学术、文化及医学技术层面的传播,满足中医临床中西医双诊断以及中医进入西方国家医疗保险体系等现实需求。     

Structural Similarity: Spectral Methods for Relaxed Blockmodeling

In this paper we propose the concept of structural similarity as a relaxation of blockmodeling in social network analysis. Most previous approaches attempt to relax the constraints on partitions, for instance, that of being a structural or regular equivalence to being approximately structural or regular, respectively. In contrast, our approach is to relax the partitions themselves: structural similarities yield similarity values instead of equivalence or non-equivalence of actors, while strictly obeying the requirement made for exact regular equivalences. Structural similarities are based on a vector space interpretation and yield efficient spectral methods that, in a more restrictive manner, have been successfully applied to difficult combinatorial problems such as graph coloring. While traditional blockmodeling approaches have to rely on local search heuristics, our framework yields algorithms that are provably optimal for specific data-generation models. Furthermore, the stability of structural similarities can be well characterized making them suitable for the analysis of noisy or dynamically changing network data.