可拓数据挖掘研究进展

可拓学研究用形式化模型解决矛盾问题的理论与方法,可拓数据挖掘是可拓学和数据挖掘结合的产物,它探讨利用可拓学方法和数据挖掘技术,去挖掘数据库中与可拓变换有关的知识,包括可拓分类知识、传导知识等可拓知识.随着经济全球化的推进,环境的多变促使了信息和知识的更新周期缩短,创新和解决矛盾问题越来越成为各行各业的重要工作.因此,如何挖掘可拓知识就成为数据挖掘研究的重要任务.研究表明,可拓数据挖掘将具有广阔的应用前景.将介绍可拓数据挖掘的集合论基础、基本知识和目前研究的主要内容,并提出今后需要进一步探讨的问题及其发展前景.     

物元可拓集集合性质研究

在可拓集合概念基础上,提出了向量可拓集和区间可拓集概念,研究了物元可拓集合的交、并、求补等集合运算及其性质.     

可拓集合及其应用研究

介绍了扩展的可拓集合概念 ,提出了可拓集合论需要进一步研究的内容 ,并综述了可拓集合在人工智能、市场、资源、检测和控制等领域的应用 .     

解决矛盾问题的可拓模型与可拓知识的研究

可拓学是解决矛盾问题的学科,在可拓学的可拓模型原型的基础上,明确了计算机解决矛盾问题的可拓模型,它包括三部分:关联函数、可拓知识和推理算法,其中关联函数和可拓知识对不同的问题需要利用不同的原理,且它们是逐步变化的.在可拓知识中,关联函数的可拓变换需要通过计算证明其值是逐步增加的.这样,矛盾问题在计算机中才能得到解决.本文通过多个实例来说明解决矛盾问题的可拓模型及可拓知识的建立和实现.     

基于可拓集的可拓分类知识获取研究

以可拓集理论为依据,给出基于可拓变换的可拓分类知识的定义,并在信息元集和评价信息元集的基础上,探讨可拓分类知识的获取方法,包括质变域知识的获取、量变域知识的获取和有关拓界的知识的获取.这是可拓数据挖掘的主要内容之一,为从数据库中获取变化的分类知识提供了新的思路.     

可拓目标规划方法及其应用

本文基于可拓数学和物元分析理论，介绍了可拓集合、关联函数和可拓满意点等概念，提出了可拓优化的概念，建立了可拓目标规划模型，给出了可拓目标规划方法的算法．实例表明，可拓目标规划方法有一定的实用性．     

可拓学的应用研究、普及与推广(综述)

可拓学研究的核心是如何通过变换处理矛盾问题.介绍了近年在计算机、设计、管理、控制、检测和中医药等领域利用可拓论和可拓方法的应用研究情况,提出今后可拓学普及与推广的方向.     

管理可拓工程研究

管理可拓工程是可拓工程的一个分支.它把可拓学与管理科学相结合,研究管理过程中矛盾问题的处理.介绍管理可拓工程的研究背景、前期研究工作概况及研究意义,并提出亟待研究的课题,指出目前研究中需要注意的问题.     

可拓营销理论研究

利用物元理论、事元理论和可拓集合理论 ,对需要、产品、市场、资源、企业等进行可拓分析 ,提出可拓营销的基本理论——产品开拓规律、可拓市场、可拓资源、健全企业等     

关于可拓集合的运算

根据蔡文提出的可拓集合的新定义,给出了可拓集合的包含、并、交、非运算的新定义,并讨论了有关运算性质,进而获得可拓域与稳定域的几个交并运算结果.     

Recall in extensive form games

This paper considers characterizations of perfect recall in extensive form games. It is shown that perfect recall can be expressed in terms of choices without any reference to infomation sets. When information sets are taken into account, it is decomposable into an ordering of information sets and that players do not forget what they knew nor what they did. Thus, if information sets are partially ordered, then perfect recall is implied by the player's inability to refine her information from the memory. Received: August 1997/final version: September 1998     

The simple geometry of perfect information games

Perfect information games have a particularly simple structure of equilibria in the associated normal form. For generic such games each of the finitely many connected components of Nash equilibria is contractible. For every perfect information game there is a unique connected and contractible component of subgame perfect equilibria. Finally, the graph of the subgame perfect equilibrium correspondence, after a very mild deformation, looks like the space of perfect information extensive form games.     

Decidable (= separable) objects and morphisms in lextensive categories

After investigating all conceivable properties of decidable objects and maps in left exact categories with well-behaved finite sums (‘lextensive categories’), we give a characterization in such categories of decidable morphisms which are (finite) coverings (in an appropriate sense). Finally, we give two applications of this result, to separable algebras and to local homeomorphisms. In both cases it explains categorically the advantage of two well-known notions — strongly separable algebras and local homeomorphisms with path lifting property, respectively.     

Information patterns and Nash equilibria in extensive games: 1

In this paper we explore the relation between information patterns and Nash Equilibria in extensive games. By information we mean what players know about moves made by others, as well as by chance. For the most part we confine ourselves to pure strategies. But in Section 2 behavioral strategies are also examined. It turns out that they can be modeled as pure strategies of an appropriately enlarged game. Our results, applied to the enlarged game, can then be reinterpreted in terms of the behavioral strategies of the original game.     

A branch and cut algorithm for the hierarchical network design problem

The Hierarchical Network Design Problem consists of locating a minimum cost bi-level network on a graph. The higher level sub-network is a path visiting two or more nodes. The lower level sub-network is a forest connecting the remaining nodes to the path. We optimally solve the problem using an ad hoc branch and cut procedure. Relaxed versions of a base model are solved using an optimization package and, if binary variables have fractional values or if some of the relaxed constraints are violated in the solution, cutting planes are added. Once no more cuts can be added, branch and bound is used. The method for finding valid cutting planes is presented. Finally, we use different available test instances to compare the procedure with the best known published optimal procedure, with good results. In none of the instances we needed to apply branch and bound, but only the cutting planes.     

On the Monoid of All Partial Order-Preserving Extensive Transformations

A partial transformation α on an n-element chain X _n is called order-preserving if x ≤ y implies xα ≤yα for all x, y in the domain of α and it is called extensive if x ≤ xα for all x in the domain of α. The set of all partial order-preserving extensive transformations on X _n forms a semiband POE _n . We determine the maximal subsemigroups as well as the maximal subsemibands of POE _n .     

THE OPTIMAL STOPPING PROBLEM OF A CONTINUOUS PARAMETER PROCESS

Suppose X = (Xr, Fr, t ∈ R+) be an optional reward process with ( Fr) satisfying usual conditions. In this paper, we correct the proof of existence about Snell envelope in [4] and the proof of an important lemma (Lemma 4. 6) in [5], and give a proof of existence about Snell envelope under certain conditions, i. e. EZx- < ∞ and Z is upper-semi-continuous on the right (USCR) or there is a stopping rule (SR)τ ≤σ such that EZx-∞ for any stopping rule σ . At the same time, we prove a four-repeated limit theorem when Z is continuous on the right. The character and the uniqueness of the optimal stopping time (OST) or optimal stopping rule (OSR) are discussed.     

The De Giorgi measure and an obstacle problem related to minimal surfaces in metric spaces

We study the existence of a set with minimal perimeter that separates two disjoint sets in a metric measure space equipped with a doubling measure and supporting a Poincaré inequality. A measure constructed by De Giorgi is used to state a relaxed problem, whose solution coincides with the solution to the original problem for measure theoretically thick sets. Moreover, we study properties of the De Giorgi measure on metric measure spaces and show that it is comparable to the Hausdorff measure of codimension one. We also explore the relationship between the De Giorgi measure and the variational capacity of order one. The theory of functions of bounded variation on metric spaces is used extensively in the arguments.     

Statistical properties of topological Collet-Eckmann maps

We study geometric and statistical properties of complex rational maps satisfying a non-uniform hyperbolicity condition called “Topological Collet-Eckmann”. This condition is weaker than the “Collet-Eckmann” condition. We show that every such map possesses a unique conformal probability measure of minimal exponent, and that this measure is non-atomic, ergodic, and that its Hausdorff dimension is equal to the Hausdorff dimension of the Julia set. Furthermore, we show that there is a unique invariant probability measure that is absolutely continuous with respect to this conformal measure, and that this invariant measure is exponentially mixing (it has exponential decay of correlations) and satisfies the Central Limit Theorem.We also show that for a complex rational map the existence of such invariant measure characterizes the Topological Collet-Eckmann condition: a rational map satisfies the Topological Collet-Eckmann condition if, and only if, it possesses an exponentially mixing invariant measure that is absolutely continuous with respect to some conformal measure, and whose topological support contains at least 2 points.     

Noninjectivity of the Predual Bimodule of the Measure Algebra for Infinite Discrete Groups

In this paper, it is proved that the predual bimodule of the measure algebra of an infinite discrete group is not injective despite the fact that the measure algebra of an amenable group is amenable in the sense of Connes. Thus the well-known result of Khelemskii (claiming that, for a von Neumann algebra, Connes-amenability is equivalent to the condition that the predual bimodule is injective) cannot be extended to measure algebras. Moreover, for a discrete amenable group, we give a simple formula for a normal virtual diagonal of the measure algebra. It is shown that a certain canonical bimodule over the measure algebra is not normal.