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Simulation for chaos game representation of genomes by recurrent iterated function systems 被引量:1
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作者 Zu-Guo Yu Long Shi +1 位作者 Qian-Jun Xiao Vo Anh 《Journal of Biomedical Science and Engineering》 2008年第1期44-51,共8页
Chaos game representation (CGR) of DNA sequences and linked protein sequences from genomes was proposed by Jeffrey (1990) and Yu et al. (2004), respectively. In this paper, we consider the CGR of three kinds of sequen... Chaos game representation (CGR) of DNA sequences and linked protein sequences from genomes was proposed by Jeffrey (1990) and Yu et al. (2004), respectively. In this paper, we consider the CGR of three kinds of sequences from complete genomes: whole genome DNA sequences, linked coding DNA sequences and linked protein sequences. Some fractal patterns are found in these CGRs. A recurrent iterated function systems (RIFS) model is proposed to simulate the CGRs of these sequences from genomes and their induced measures. Numerical results on 50 genomes show that the RIFS model can simulate very well the CGRs and their induced measures. The parameters estimated in the RIFS model reflect information on species classification. 展开更多
关键词 GENOMES CHAOS GAME REPRESENTATION RECURRENT iterated function systems.
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ERGODIC THEOREM FOR INFINITE ITERATED FUNCTION SYSTEMS
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作者 吴享哲 卢英花 吉元君 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第4期465-469,共5页
A set of contraction maps of a metric space is called an iterated function systems. Iterated function systems with condensation, can be considered infinite iterated function systems. Infinite iterated function systems... A set of contraction maps of a metric space is called an iterated function systems. Iterated function systems with condensation, can be considered infinite iterated function systems. Infinite iterated function systems on compact metric spaces were studied. Using the properties of Banach limit and uniform contractiveness, it was proved that the random iterating algorithms for infinite iterated function systems on compact metric spaces-satisfy ergodicity. So the random iterating algorithms for iterated function systems with condensation satisfy ergodicity, too. 展开更多
关键词 iterated function system invariant measure ergodic theorem random iterating algorithm
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AFFINE TRANSFORMATION IN RANDOM ITERATED FUNCTION SYSTEMS
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作者 XIONG Yong(熊勇) +1 位作者 SHI Ding-hua(史定华) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第7期820-826,共7页
Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, th... Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach. 展开更多
关键词 FRACTAL random iterated function system affine transformation
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ITERATED FUNCTION SYSTEM AND GALTON-WATSON TREE
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作者 余旌胡 谢南瑞 《Acta Mathematica Scientia》 SCIE CSCD 2007年第3期456-464,共9页
Given a system {S1,…, SN} of N contractive similarities satisfying some strong separation condition, it has an invariant Set K for the system. In this article, the authors construct some random measure μω supported... Given a system {S1,…, SN} of N contractive similarities satisfying some strong separation condition, it has an invariant Set K for the system. In this article, the authors construct some random measure μω supported on random subset Kω of K, μω having some "non-standard" multifractal structure, which contrasts the well-knoWn multifractal formalism for the invariant measure of system {S1,.., SN} may possess. The main tool is the multifractal structures of a Galton-Watson tree, which are obtained by Liu [9], Shieh-Taylor [14], and MSrters-Shieh [12]. 展开更多
关键词 Multifractal structure iterated function stysem Galton-Watson tree
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SOME NEW ITERATED FUNCTION SYSTEMS CONSISTING OF GENERALIZED CONTRACTIVE MAPPINGS
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作者 Shaoyuan Xu Wangbin Xu Dingxing Zhong 《Analysis in Theory and Applications》 2012年第3期269-277,共9页
Iterated function systems (IFS) were introduced by Hutchinson in 1981 as a natural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahu and A. Chakraborty introduced K-Iterated Function... Iterated function systems (IFS) were introduced by Hutchinson in 1981 as a natural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahu and A. Chakraborty introduced K-Iterated Function System using Kannan mapping which would cover a larger range of mappings. In this paper, following Hutchinson, D. R. Sahu and A. Chakraborty, we present some new iterated function systems by using the so-called generalized contractive mappings, which will also cover a large range of mappings. Our purpose is to prove the existence and uniqueness of attractors for such class of iterated function systems by virtue of a Banach-like fixed point theorem concerning generalized contractive mappings. 展开更多
关键词 iterated function system ATTRACTOR generalized contractive mapping completemetric space fixed point
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Fixed Point Theorems of the Iterated Function Systems
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作者 Ji You-qing Liu Zhi Ri Song-il 《Communications in Mathematical Research》 CSCD 2016年第2期142-150,共9页
In this paper, we present some fixed point theorems of iterated function systems consisting of α-ψ-contractive type mappings in Fractal space constituted by the compact subset of metric space and iterated function s... In this paper, we present some fixed point theorems of iterated function systems consisting of α-ψ-contractive type mappings in Fractal space constituted by the compact subset of metric space and iterated function systems consisting of Banach contractive mappings in Fractal space constituted by the compact subset of generalized metric space, which is Mso extensively applied in topological dynamic system. 展开更多
关键词 fixed point α-ψ-contractive mapping iterated function system gener-alized metric space
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Cantor Type Fixed Sets of Iterated Multifunction Systems Corresponding to Self-Similar Networks
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作者 Levente Simon Anna Soós 《Applied Mathematics》 2016年第4期365-374,共10页
We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph model... We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph models introduced by Barabási, Ravasz and Vicsek ([1] [2]). We generalize the graph models using stars and cliques: both algorithm construct graph sequences such that the next iteration is always based on n replicas of the current iteration, where n is the size of the initial graph structure, being a star or a clique. We analyze these self-similar graph sequences using IMSs in function of the size of the initial star and clique, respectively. Our research uses the Cantor set for the description of the fixed set of these IMSs, which we interpret as the limit object of the analyzed self-similar networks. 展开更多
关键词 Cantor Set Fixed Set iterated function systems iterated Multifunction systems Self-Similar Graphs
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Iterated Function System-Based Crossover Operation for Real-Coded Genetic Algorithm
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作者 S. H. Ling 《Journal of Intelligent Learning Systems and Applications》 2015年第2期37-41,共5页
An iterated function system crossover (IFSX) operation for real-coded genetic algorithms (RCGAs) is presented in this paper. Iterated?function system (IFS) is one type of fractals that maintains a similarity character... An iterated function system crossover (IFSX) operation for real-coded genetic algorithms (RCGAs) is presented in this paper. Iterated?function system (IFS) is one type of fractals that maintains a similarity characteristic. By introducing the IFS into the crossover operation, the RCGA performs better searching solution with a faster convergence in a set of benchmark test functions. 展开更多
关键词 GENETIC ALGORITHM iterated function system CROSSOVER Operation
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Particle filter based on iterated importance density function and parallel resampling 被引量:1
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作者 武勇 王俊 曹运合 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第9期3427-3439,共13页
The design, analysis and parallel implementation of particle filter(PF) were investigated. Firstly, to tackle the particle degeneracy problem in the PF, an iterated importance density function(IIDF) was proposed, wher... The design, analysis and parallel implementation of particle filter(PF) were investigated. Firstly, to tackle the particle degeneracy problem in the PF, an iterated importance density function(IIDF) was proposed, where a new term associating with the current measurement information(CMI) was introduced into the expression of the sampled particles. Through the repeated use of the least squares estimate, the CMI can be integrated into the sampling stage in an iterative manner, conducing to the greatly improved sampling quality. By running the IIDF, an iterated PF(IPF) can be obtained. Subsequently, a parallel resampling(PR) was proposed for the purpose of parallel implementation of IPF, whose main idea was the same as systematic resampling(SR) but performed differently. The PR directly used the integral part of the product of the particle weight and particle number as the number of times that a particle was replicated, and it simultaneously eliminated the particles with the smallest weights, which are the two key differences from the SR. The detailed implementation procedures on the graphics processing unit of IPF based on the PR were presented at last. The performance of the IPF, PR and their parallel implementations are illustrated via one-dimensional numerical simulation and practical application of passive radar target tracking. 展开更多
关键词 particle filter iterated importance density function least squares estimate parallel resampling graphics processing unit
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AN APPLICATION OF HARDY-BOEDEWADT'S THEOREM TO ITERATED FUNCTIONAL EQUATIONS
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作者 张伟年 《Acta Mathematica Scientia》 SCIE CSCD 1995年第3期356-360,共5页
In this paper an iterated functional equation of polynomial type which does not possess the firt order iterative term g(x) is to be discussed. The difficulties resulted from loss of the first order term are overcome b... In this paper an iterated functional equation of polynomial type which does not possess the firt order iterative term g(x) is to be discussed. The difficulties resulted from loss of the first order term are overcome by utilization of Hardy-Boedewadt's theorem. 展开更多
关键词 iterated functional equation iterative root structural operator
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Existence and Uniqueness of Analytic Solutions of Systems of Iterative Functional Equations
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作者 刘新和 《Northeastern Mathematical Journal》 CSCD 2000年第4期428-438,共11页
Let r be a given positive number. Denote by D=D r the closed disc in the complex plane C whose center is the origin and radius is r. Write A(D,D)={f: f is a continuous map from D into itself, and ... Let r be a given positive number. Denote by D=D r the closed disc in the complex plane C whose center is the origin and radius is r. Write A(D,D)={f: f is a continuous map from D into itself, and f|D ° is analytic}. Suppose G,H: D 2n+1 →C are continuous maps (n≥2), and G|(D 2n+1 ) °, H|(D 2n+1 ) ° are analytic. In this paper, we study the system of iterative functional equationsG(z,f(z),…,f n(z), g(z),…,g n(z))=0, H(z,f(z),…,f n(z), g(z),…,g n(z))=0, for any z∈D,and give some conditions for the system of equations to have a solution or a unique solution in A(D,D) ×A(D,D). 展开更多
关键词 iterative functional equation analytic solution difference quotient functional space compact convex set fixed point
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A LAW OF THE ITERATED LOGARITHM FOR NEAREST NEIGHBOR ESTIMATION OF MULTIVARIATE DENSITY FUNCTION
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作者 洪圣岩 陈规景 +1 位作者 孔繁超 高集体 《Acta Mathematica Scientia》 SCIE CSCD 1992年第4期472-478,共7页
Let X be a d-dimensional random vector with unknown density function f(z) = f (z1, ..., z(d)), and let f(n) be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we est... Let X be a d-dimensional random vector with unknown density function f(z) = f (z1, ..., z(d)), and let f(n) be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we established the law of the iterated logarithm of f(n) for general case of d greater-than-or-equal-to 1, which gives the exact pointwise strong convergence rate of f(n). 展开更多
关键词 A LAW OF THE iterated LOGARITHM FOR NEAREST NEIGHBOR ESTIMATION OF MULTIVARIATE DENSITY function exp
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Generalized Product of Iteration Function System
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作者 ZHAO Ting-ting WEI Xiao-peng XIA Jun-tian SANG Lin 《Computer Aided Drafting,Design and Manufacturing》 2005年第2期44-49,共6页
The definition of generalized product of fractal is first put forward for the research on the relations between original fractal and its product of fractal when the transformations of iteration function system (IFS)... The definition of generalized product of fractal is first put forward for the research on the relations between original fractal and its product of fractal when the transformations of iteration function system (IFS) are incomplete. Then the representations of generalized product of IFS are discussed based on the theory of the product of fractal. Furthermore, the dimensional relations between the product of fractal and its semi-product are obtained. The dimensional relations of self-similar set are discussed. Finally, the examples for rendering fractal graphs are given. These results posses potentials in image compression and pattern recognition. 展开更多
关键词 FRACTAL iteration function system product of fractal semi-product of fractal generalized product of fractal
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Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function
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作者 Junrui Yue Yun Zhang Qingyue Bai 《Open Journal of Applied Sciences》 2024年第1期63-69,共7页
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a... This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique. 展开更多
关键词 Fourth-Order Three-Point Boundary Value Problem Sign-Changing Green’s function Fixed Point Index Iterative Technique Monotone Positive Solution EXISTENCE
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Mean Dimension for Non-autonomous Iterated Function Systems
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作者 Meng Deyu Zhao Cao 《数学理论与应用》 2024年第3期119-129,共11页
In this paper we introduce the notions of mean dimension and metric mean dimension for non-autonomous iterated function systems(NAIFSs for short)on countably infinite alphabets which can be regarded as generalizations... In this paper we introduce the notions of mean dimension and metric mean dimension for non-autonomous iterated function systems(NAIFSs for short)on countably infinite alphabets which can be regarded as generalizations of the mean dimension and the Lindenstrauss metric mean dimension for non-autonomous iterated function systems.We also show the relationship between the mean topological dimension and the metric mean dimension. 展开更多
关键词 Non-autonomous iterated function system Mean dimension Metric mean dimension
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迭代函数系IFS吸引子的参数控制与树木的模拟 被引量:10
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作者 刘向东 廖欣 +1 位作者 于海 朱伟国 《计算机工程与应用》 CSCD 北大核心 2000年第5期28-29,共2页
文章讨论了迭代函数系IFS吸引子的参数控制,讨论了IFS参数控制实现模拟树木的方法。
关键词 迭代函数系统 参数控制 ifs吸引子 树木
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基于迭代函数系统IFS的动态树木模拟 被引量:9
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作者 邹运兰 杨志红 王仁芳 《计算机应用与软件》 CSCD 北大核心 2012年第3期118-121,共4页
植物作为自然景物中最常见的现象之一,模拟的方法是应用数学和图形学领域的一个重要课题。迭代函数系统IFS是分形理论的重要分支,由于植物结构的自相似性,利用IFS(Iterated Function System)可以逼真地模拟各植物形态,简述几种模拟植物... 植物作为自然景物中最常见的现象之一,模拟的方法是应用数学和图形学领域的一个重要课题。迭代函数系统IFS是分形理论的重要分支,由于植物结构的自相似性,利用IFS(Iterated Function System)可以逼真地模拟各植物形态,简述几种模拟植物的方法,主要研究迭代函数系统IFS模型,并在VC++6.0环境下基于IFS模型构造出静态蕨叶和树木,详细讨论利用带参量的IFS随机系统实现动画的过程,并利用双缓冲技术,形象逼真地模拟随风摇摆的蕨叶和生长树木的动画效果。实验结果表明,带参数的IFS可使图像发生预期的变化,如果让参数在适当的范围保持连续变化,则动画效果良好。 展开更多
关键词 迭代函数系统 ifs 树木模拟
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基于IFS块的快速图象编码算法 被引量:6
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作者 劳志强 潘云鹤 《计算机研究与发展》 EI CSCD 北大核心 1998年第3期270-273,共4页
文中首先叙述了目前分形块编码研究领域的大致情况,然后,提出了一种新的快速编码算法.用L1距离替换了以往算法所用的L2距离,把匹配过程转换成类似于矢量量化的搜索过程,因而采纳了许多矢量量化的加速算法.还讨论了对平坦区的... 文中首先叙述了目前分形块编码研究领域的大致情况,然后,提出了一种新的快速编码算法.用L1距离替换了以往算法所用的L2距离,把匹配过程转换成类似于矢量量化的搜索过程,因而采纳了许多矢量量化的加速算法.还讨论了对平坦区的处理并提出了新的剖分方法,取得了较好的效果.同其它的分形块编码方法相比,该算法大大缩短了编码时间,改善了压缩图象的质量,特别是它能较大程度地消除块效应,压缩比也有了进一步的提高. 展开更多
关键词 分形块编码 ifs 图象压缩 图象编码 算法
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迭代函数系统IFS吸引子图像局部控制方法的研究 被引量:8
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作者 马石安 陈传波 《小型微型计算机系统》 CSCD 北大核心 2003年第9期1726-1728,共3页
针对目前的 IFS吸引子随机迭代算法在 IFS吸引子图像控制中存在的不足 ,本文给出了两种 IFS吸引子随机迭代算法的改进方法 ,其方法可以对 IFS吸引子图像实现其局部细节与色彩的控制 。
关键词 迭代函数系统 ifs参数控制 动态模拟
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基于IFS随机迭代算法的印花图案设计 被引量:9
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作者 张聿 李玲 付岳莹 《纺织学报》 EI CAS CSCD 北大核心 2008年第2期106-109,113,共5页
根据纺织面料印花图案的特点,利用IFS随机迭代算法的便捷性,运用可视化方法,在基于随机迭代算法讨论IFS图形生成原理的同时,研究了通过参数变化使IFS图形发生变化的基本方法;在此基础上,运用计算机图形技术,对应用IFS图形设计纺织面料... 根据纺织面料印花图案的特点,利用IFS随机迭代算法的便捷性,运用可视化方法,在基于随机迭代算法讨论IFS图形生成原理的同时,研究了通过参数变化使IFS图形发生变化的基本方法;在此基础上,运用计算机图形技术,对应用IFS图形设计纺织面料印花图案的方法作了初步的尝试,并借助电子(喷)印花手段进行印花试验,对纺织面料运用IFS图形资源开发印花产品的途径进行了初步的探讨。 展开更多
关键词 ifs 随机迭代算法 计算机图形方法 图案设计 印花试验
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