On characteristic sets and degrees of finite automata

The characteristic sets and degrees of finite automata are notions used by Biermann for his finite automaton learner. Some fundamental properties and relations of these notions are considered. A necessary and sufficient condition under which his learner converges to an expected automaton is given.     

Dominating sets in directed graphs

We consider the problem of incrementally computing a minimal dominating set of a directed graph after the insertion or deletion of a set of arcs. Earlier results have either focused on the study of the properties that minimum (not minimal) dominating sets preserved or lacked to investigate which update affects a minimal dominating set and in what ways. In this paper, we first show how to incrementally compute a minimal dominating set on arc insertions. We then reduce the case of computing a minimal dominating set on arc deletions to the case of insertions. Some properties on minimal dominating sets are provided to support the incremental strategy. Lastly, we give a new bound on the size of minimum dominating sets based on those results.     

An optimal test on finite unavoidable sets of words

We give an optimal bound on the maximal length of a word that avoids a finite unavoidable set of words.     

对模糊集、粗糙集和Vague集的比较研究

模糊集、粗糙集和Vague集三种理论都是对经典集合理论的扩展,使得集合论的应用扩展到了含糊的、不确定性的问题领域。介绍了三种集合的基本思想,重点分析三种理论的区别和内在联系,同时对三种理论的发展及应用作了一些探讨性研究。     

Actions,finite state sets and applications to trees

Let M be a monoid acting on a set X; for any x?X and A?X we put x ^?1 A = {m?M/xm?A}. Call A?X finite state if card {x ^?1 A/x?X} <∞.

The finite state subsets of T _Σvia the action T _Σ × P _Σ→T _Σare the recognizable forests (P _Σis the monoid of all Σ-trees with just one leaf labeled by a variable x).

Next we prove that the recognizability of forests is equivalent to the finiteness of a certain “syntactic” monoid A Mezei's-like theorem for trees is established: the finite state subsets of T _Σ × T_г are exactly the finite unions of sets of sets of the form B × C B?Rec(T _Σ) and C?Rec(T _г) Another characterization of such relations is given using bimorphisms.     

Surface processing methods for point sets using finite elements

We present a framework for processing point-based surfaces via partial differential equations (PDEs). Our framework efficiently and effectively brings well-known PDE-based processing techniques to the field of point-based surfaces. At the core of our method is a finite element discretization of PDEs on point surfaces. This discretization is based on the local assembly of PDE-specific mass and stiffness matrices, using a local point coupling computation. Point couplings are computed using a local tangent plane construction and a local Delaunay triangulation of point neighborhoods. The definition of tangent planes relies on moment-based computation with proven scaling and stability properties. Once local stiffness matrices are obtained, we are able to easily assemble global matrices and efficiently solve the corresponding linear systems by standard iterative solvers. We demonstrate our framework by several types of PDE-based surface processing applications, such as segmentation, texture synthesis, bump mapping, and geometric fairing.     

Soft rough fuzzy sets and soft fuzzy rough sets

Fuzzy set theory, soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. Feng et al. introduced the notions of rough soft set, soft rough set and soft rough fuzzy set by combining fuzzy set, rough set and soft set all together. This paper is devoted to the further discussion of the combinations of fuzzy set, rough set and soft set. A new soft rough set model is proposed and its properties are derived. Furthermore, fuzzy soft set is employed to granulate the universe of discourse and a more general model called soft fuzzy rough set is established. The lower and upper approximation operators are presented and their related properties are surveyed.     

基于标签随机有限集的多量测多目标跟踪算法

针对一个扫描周期内单个目标可能产生多个量测的问题, 提出一种基于标签随机有限集的扩展算法. 结合脉冲扩展标签多伯努利(-GLMB) 滤波器和多量测模型, 推导出新的更新方程; 采用假设分解策略对关联过程进行降维, 避免了量测分组过程. 实验分析表明: 所提出算法能对目标数进行无偏估计, 在低探测概率条件下跟踪性能明显优于多量测概率假设密度(MD-PHD) 算法; 计算开销在量测较少时高于MD-PHD, 量测个数增加时增幅低于MD-PHD.

     

基于本体的可拓知识链获取

相对于静态的知识，定义了基于可拓变换的可拓知识，可拓知识是变化的知识．在可拓知识定理（从知识中获取可拓知识）和可拓推理公式的基础上，证明了基于集合的可拓知识定理和基于本体的可拓知识链定理．通过实例，在多维层次数据中，获取问题产生原因的可拓知识链．     

Construction of checking sequences based on characterization sets

A general model for constructing checking sequences employing a characterization set for a given finite state machine is proposed. Some existing methods are shown to be special cases of the proposed model and are proven to construct checking sequences. Examples are provided as applications of the general model and its special cases.     

On partitions of functions on finite sets

Let D and R be finite sets with cardinality n and m respectivelyR ^D be the set of all functions from D into R, and G and H be permutation groups acting on D and R respectively. Two functions f and g in R ^D are said to be related if there exists a σ in G and a τ in H with f(σd) = τg(d) for every d in D. Since the relation is an equivalence relation, R ^D is partitioned into disjoint classes. Roughly, by using the cycle indices of G and H, de Bruijn's theorem determines the number of equivalence classes, and Pólya's theorem, with H being the identity group, gives the function counting series, Pólya-de Bruijn's theorem has many applications (for instance, see Pólya and Read [6]). The theorem and its applications, basically, centered around the partitions of functions. Here, we present an algorithm to determine which functions in R ^D belong to the same equivalent class. Our algorithm does not use the cycle indices of G and H (to compute the cycle index of a given group, in general, is difficult), but it uses the generators of G and H, and the m-nary numbers to code the functions in R ^D . Our algorithm also gives the function counting series and the number of equivalence classes. An important application is that for each positive integer n, we use our algorithm and the symmetric group S _n to determine all isomorphic and nonisomorphic graphs and directed graphs with n vertices.     

三维有限元数据场体绘制算法的研究

三维有限元数据场包含了庞大的信息量,不易于人们深刻理解和分析。可视化技术将数据场以图形、图像的形式显示出来,揭示出三维有限元数据场中蕴藏的丰富内涵。讨论了三维数据场可视化体绘制中射线跟踪法和直接投影法的优点及不足,提出了将射线跟踪法及直接投影法各自优点结合起来的新算法,应用于三维有限元数据场的体绘制。新算法一方面充分利用场在投影区域上的二维连贯性,每次推进的是一个面片而不是一个孤立的像素点,另一方面针对每个视线段子段,充分利用场在深度方向的连贯性,用分析积分法完成累积光强和透明度计算。算法效率高,统一性强。     

模糊识别器与有穷自动机的等价性

针对模糊识别器与有穷自动机的关系,证明了当输入字母表相同时,任给一个模糊识别器,必然存在一个有穷自动机,使得模糊识别器的行为与有穷自动机所接受的语言相同;反之,任给一个有穷自动机,必然存在一个模糊识别器,使得有穷自动机所接受的语言与模糊识别器的行为相同,从而得出它们之间的等价性。     

软模糊粗糙集

软集理论是1999年Molodtsov为了克服传统数学在处理不确定性问题时所遇到的困难而提出的一种新的数学工具。将软集理论与Z.Pawlak粗糙集结合起来,提出了软模糊粗糙集和软模糊粗糙群及它们的同态的概念,讨论了它们相关的性质。     

Sensor control for multi-object state-space estimation using random finite sets

The problem addressed in this paper is information theoretic sensor control for recursive Bayesian multi-object state-space estimation using random finite sets. The proposed algorithm is formulated in the framework of partially observed Markov decision processes where the reward function associated with different sensor actions is computed via the Rényi or alpha divergence between the multi-object prior and the multi-object posterior densities. The proposed algorithm in implemented via the sequential Monte Carlo method. The paper then presents a case study where the problem is to localise an unknown number of sources using a controllable moving sensor which provides range-only detections. Four sensor control reward functions are compared in the study and the proposed scheme is found to perform the best.     

Computer construction and enumeration of all topologies and all hyperconnected topologies on finite sets

In [1] the present authors described an algorithm to construct and enumerate specific topologies on a finite set X _n of n points that is the strictly weaker topologies on X _n than a given topology each of which is not contained in any excluding point topology on X _n . In this paper we describe an algorithm to construct and enumerate all topologies and all hyperconnected topologies on X _n . The topologies on X _n which are weaker than a given topology on X _n will be constructed and enumerated. The algorithm is written in Fortran 77 and implemented on an Pentium 400 system.     

Sine-square embedded fuzzy sets versus type-2 fuzzy sets

The uncertainty is an inherent part of real-world applications. Type-2 fuzzy sets minimize the effects of uncertainties that cannot be modeled using type-1 fuzzy sets. However, the computational complexity of the type-2 fuzzy sets is very high and it is more difficult than type-1 fuzzy sets to use and understand. This paper proposes sine-square embedded fuzzy sets and gives a comparison with type-2 and nonstationary fuzzy sets. The sine-square embedded fuzzy sets consist of type-1 fuzzy sets and the sine function. The footprint of uncertainty in the type-2 fuzzy sets is provided with amplitude and frequency of sine-square function in the proposed algorithm. The proposed sine-square embedded fuzzy sets are much simpler than the type-2 fuzzy sets and the nonstationary fuzzy sets. Two control applications that are chosen as position control of a dc motor and simulation of human lifting motion using five-segment human model are carried out to demonstrate the effectiveness of the proposed approach.     

Constructive Sets in Computable Sets

The original interpretation of the constructive set theory CZF in Martin-Loef‘s type theory uses the‘extensional identity types’.It is generally believed that these‘types’do not belong to type theory.In this paper it will be shown that the interpretation goes through without identity types.This paper will also show that the interpretation can be given in an intensional type theory.This reflects the computational nature of the interpretation.This computational aspect is reinforced by an ω-Set moel of CZF.     

Flou值模糊集的表现定理

为了弥补区间值模糊集和三参数模糊集在模糊信息表达方面的不足,在Flou集的基础上,提出了一种新的L模糊集,Flou值模糊集,并用投票模型对其作出解释。引入Flou嵌套集的概念,结合Flou值模糊集截集的定义及分解定理,建立了Flou值模糊集的表现定理,并用一个实际算例验证了表现定理的有效性。它揭示了Flou集和Flou值模糊集的联系,提供了一种利用Flou嵌套集拼成Flou值模糊集的方法。为处理模糊信息提供了一种新的工具,并为Flou值模糊集的研究和应用奠定了初步的理论基础。     

Vague集上一个新的贴近度公式

基于已有文献给出的一般性Vague集上贴近度的表达式,结合已提出的几个贴近度公式,研究了一个新的贴近度公式具有的性质,揭示了几个贴近度表达式之间的关系。