关于半群作用的混沌及拓扑熵研究

<正>本文讨论了半群作用的拓扑动力系统及混沌的基本概念和性质,在Devaney混沌的基础上给出了半群作用在紧致度量空间上的混沌定义,并证明了拓扑强混合蕴含Devaney混沌。对已有的半群作用的拓扑熵概念进行了分析和总结,提出对各种不同半群作用的拓扑熵的定义之间的关系、熵值的计算和估计、正熵系统的性质以及正熵与混沌之间的关系是未来半群作用的拓扑熵研究的趋势。     

资本市场复杂性理论研究现状及应用分析

本文分析了以EMH为基础的经典资本市场理论的不足，揭示了资本市场的复杂性本质。以复杂性科学方法来研究资本市场的运作规律，分析了耗散、混沌、分形、协同、突变和标度理论对资本市场的研究领域和侧重点以及彼此间的相互联系，对各理论所取得的成果及存在问题进行了论述，并对复杂性科学在资本市场的发展方向进行了展望。     

基于Simulink的Lorenz混沌系统的可视化仿真研究

以Lorenz混沌系统为例,运用仿真软件Simulink建立了Lorenz混沌系统可视化模型,从中分析了Lorenz系统的混沌特性,最后提出了一种延时反馈控制方法,对Lorcnz混沌系统进行稳定控制,该方法的优．最是全程可视化,不需要采用传统的程序代码和算法进行编程,是研究混沌系统的一种简便、有效的新方法。     

基等价与拓扑等价的关系探讨

文章从拓扑空间基的概念出发,讨论基与拓扑的关系,指出了现行教材中的一道习题的不妥之处,给出了判断两个基为等价基的充分必要条件.作为应用,讨论了度量空间及一些拓扑空间的拓扑等价问题.     

基于Lyapunov方法Lorenz混沌系统自适应同步方法

对于具有不确定参数的Lorenz混沌系统，通过参数调节和自适应技术讨论了两个同结构Lorenz混沌系统的同步问题。自适应控制器和参数调节律均由Lyapunov稳定行理论来确定。数字仿真表明了该方法的有效性和实用性。     

基于MATLAB的各类混沌系统的计算机仿真模拟研究

本文利用数学软件MATLAB对Lorenz混沌系统、Rossler混沌系统进行数值计算和模拟一些混沌现象,同时模拟出各类混沌系统的独特性质,如混沌吸引子、倍周期、初值敏感性、相图、分岔图等。通过观察和分析上述特性,加深了我们对混沌现象的理解。     

创新系统软动力学研究纲要

本文根据系统论和全息理论作出适当假设后，简要给出知识信息系统简化的软动力学模型，根据此模型及一些核概念，作者深入研究了创新系统的复杂性，混沌、演化，形成机制和涵义等，并揭示了创新行为与知识信息系统之间的内在关联。     

CHEN混沌系统的同步控制

混沌系统的研究在国内外正在广泛的开展,如何使得对混沌系统的控制达到良好的控制效果构成了问题的关键。由于Chen混沌系统具有的参数不确定性,以至于常规的控制方法很难实现对Chert混沌系统的控制,讨论了一种参数可调节的自适应同步设计方法。设计出了可以使两个同结构的Chen系统状态渐近同步的自适应控制器,其参数调节律Lya2punov稳定性理论来确定。最后进行数字仿真,仿真结果表明了这种方法的有效性和实用性。     

软件系统结构的复杂性度量研究

软件规模及其复杂性的不断增大,致使传统的度量方法不能满足开发人员对软件质量的控制;为了解决这个问题,开发人员需要有新的方法来测量软件的复杂度,从而控制软件质量,优化软件结构。复杂网络的研究为软件开发人员在系统层面上度量软件的复杂性提供了新的认识和理论支持;讨论了基于复杂网络的软件静态结构和动态结构的复杂性度量方法及其对当今大规模软件开发的指导意义;给出了一个软件结构复杂性度量的研究工具。     

重大工程复杂性马尔科夫链—熵度量模型构建

本文利用马尔科夫链来理解重大工程的不确定性和动态演化特征,利用熵理论来量化重大工程的复杂性水平,建立了重大工程复杂性的马尔科夫链-熵度量模型。结果表明,重大工程的复杂性包括技术、环境、组织、目标、信息和任务六个维度,并具有结构性、不确定性和动态性特征。马尔科夫链可以用来描述过程,熵可以用来量化复杂性。该研究可以揭示重大工程的宏观状态与微观状态之间的关系,测度重大工程的复杂性水平,分析可持续发展趋势并进行预测决策和控制。     

4D spinless topological insulator in a periodic electric circuit

According to the mathematical classification of topological band structures, there exist a number of fascinating topological states in dimensions larger than three with exotic boundary phenomena and interesting topological responses. While these topological states are not accessible in condensed matter systems, recent works have shown that synthetic systems, such as photonic crystals or electric circuits, can realize higher-dimensional band structures. Here, we argue that, because of its symmetry properties, the 4D spinless topological insulator is particularly well suited for implementation in these synthetic systems. We explicitly construct a 2D electric circuit lattice, whose resonance frequency spectrum simulates the 4D spinless topological insulator. We perform detailed numerical calculations of the circuit lattice and show that the resonance frequency spectrum exhibits pairs of 3D Weyl boundary states, a hallmark of the nontrivial topology. These pairs of 3D Weyl states with the same chirality are protected by classical time-reversal symmetry that squares to +1, which is inherent in the proposed circuit lattice. We also discuss how the simulated 4D topological band structure can be observed in experiments.     

Parameters Analysis of Sample Entropy,Permutation Entropy and Permutation Ratio Entropy for RR Interval Time Series

Proper parameters can improve performance of entropy methods for discerning electrocardiogram (ECG) signals. So, we tried to determine proper parameters of three entropy methods i.e., a novel permutation ratio entropy (PRE), sample entropy (SmpE) and permutation entropy (PE) for discerning several typical ECG RR interval recordings i.e., normal sinus rhythm (NSR), congestive heart failure (CHF) and NSR and arrhythmia RR (ARR) interval recordings. The three entropy methods were first calculated for a logistic sequence to evaluate their sensitivity to dynamic property changes within a time series. Their capabilities of distinguishing complexity between NSR and CHF, NSR and ARR, and CHF and ARR RR interval recordings were compared. Statistical differences between the three entropy values for normal (i.e., NSR) and abnormal RR interval recordings (i.e., CHF and ARR) were analysed respectively. Performance of the entropy methods in simultaneously discerning the three groups (i.e., NSR, CHF and ARR groups) were also compared. PRE more accurately reflected logistic sequence changes from period doublings to chaos than SmpE or PE did. In experiments with real data, PRE correctly yielded higher values on NSR RR recordings than on CHF and ARR recordings and exhibited significant differences (p < 0.01) on more parameter pairs than SmpE and PE did.     

DECISION TREE COMPLEXITY OF GRAPH PROPERTIES

１　Ｉｎｔｒｏｄｕｃｔｉｏｎ　　ＡｇｒａｐｈＧｉｓａｎｏｒｄｅｒｅｄｐａｉｒｏｆｄｉｓｊｏｉｎｔｓｅｔｓ（Ｖ,Ｅ）ｓｕｃｈｔｈａｔＥｉｓａｓｕｂｓｅｔｏｆｔｈｅｓｅｔｏｆｕｎｏｒｄｅｒｅｄｐａｉｒｓｏｆＶ,ｗｈｅｒｅｔｈｅｓｅｔｓＶａｎｄＥａｒｅｆｉｎｉｔｅ．ＴｈｅｓｅｔＶｉｓｃａｌｌｅｄｔｈｅｓｅｔｏｆｖｅｒｔｉｃｅｓａｎｄＥｉｓｃａｌｌｅｄｔｈｅｓｅｔｏｆｅｄｇｅｓ．ＴｈｅｙａｒｅｕｓｕａｌｌｙｄｅｎｏｔｅｄｂｙＶ（Ｇ）ａｎｄＥ（Ｇ）,ｒｅｓｐｅｃｔｉｖｅｌｙ．Ａｎｅｄｇｅ｛ｘ,ｙ｝ｉｓｓａ…     

组织混沌与组织文化变革及创新关系的研究

本文通过对企业文化研究背景和经济组织混沌特征的分析,指出组织混沌与企业组织文化发展具有协同性。在分析和形成企业组织文化变革动因的过程中诱导混沌,在企业组织文化的变革和创新中利用和控制混沌。借鉴人工神经元网络及其拓扑结构,刻画企业组织不断变革的企业组织文化背景与管理行为动态交互的演进关系,提出了企业组织文化变革与创新的混沌分析框架,进而为组织变革创造组织背景。本文在对某企业组织文化变革的实证研究中印证和应用了上述主要观点。     

Is small actually big? The chaos of technological change

In this paper, we develop themes from complexity and chaos theory that help to explain the technological change process. We apply two quantifiers, correlation dimensions and Lyapunov exponents, to examine the signs and degrees of chaotic technological dynamics. To illustrate our ideas, we study the development of electronic displays from 1976 to 2010, using patent data. The results of the chaos model are matched against the profiles of patent citations. Our analysis contributes to the development of a chaotic model of technological change.     

基于协调论的矿区可持续发展研究

将矿区视为由资源、环境、安全、经济与社会所构成的复杂非线性系统,讨论其特征,以协调论为基础,建立矿区协调熵度量模型,以某典型矿区为例进行实证分析,进一步提出矿区的可持续发展对策。     

概率关系代数研究

基于概率关系的可能世界概念的基本性质,为了能够有效对概率关系查询进行评估,本文对概率关系的元组进行了分类,分为相互不相容的元组和相互独立的元组,提出了概率关系合并操作和四种概率关系代数运算。     

黄土高原生态环境演化复杂性分析

在简要综述复杂性、熵、耗散结构、系统观等相关理论及其应用的基础上，得到该区生态环境演化的一些重要启示：由五大圈层组成的地球生态环境系统，是地球演化到一定阶段而产生的一个开放复杂巨系统；必须使生态环境系统维持在高组织、低熵的状态；重视植被建设；在该区可持续发展中重视子系统自身的智能吸收和再生能力，引导整体向最优方向发展等等。     

Syntactic complexity of Web search queries through the lenses of language models,networks and users

Across the world, millions of users interact with search engines every day to satisfy their information needs. As the Web grows bigger over time, such information needs, manifested through user search queries, also become more complex. However, there has been no systematic study that quantifies the structural complexity of Web search queries. In this research, we make an attempt towards understanding and characterizing the syntactic complexity of search queries using a multi-pronged approach. We use traditional statistical language modeling techniques to quantify and compare the perplexity of queries with natural language (NL). We then use complex network analysis for a comparative analysis of the topological properties of queries issued by real Web users and those generated by statistical models. Finally, we conduct experiments to study whether search engine users are able to identify real queries, when presented along with model-generated ones. The three complementary studies show that the syntactic structure of Web queries is more complex than what n-grams can capture, but simpler than NL. Queries, thus, seem to represent an intermediate stage between syntactic and non-syntactic communication.     

高度敏感生态脆弱区景观可持续性评价

运用熵变分析方法从景观的视角阐明生态脆弱区景观可持续动态演变规律具有重要的理论意义和实践价值。本文基于耗散结构理论和景观复合生态系统理论,以高度敏感生态脆弱区陕西省米脂县高渠乡为例,构建景观可持续评价指标体系,运用信息熵构建研究区景观可持续评价模型,通过计算熵流、熵产生和总熵变,分析研究区2009—2014年间的系统承载力、活力和有序度,探讨研究区的可持续性。研究表明：①建立的景观可持续评价指标体系能够有效地反映景观复合生态系统的功能和演化机制,研究方法可以有效地进行生态脆弱区景观可持续性评价研究;②在2009—2014年间,高渠乡熵流呈减少趋势,熵产生总体上升,总熵变除2012年外,其余年份逐年下降,景观复合生态系统内部朝着健康有序方向发展;③高渠乡可持续总得分呈上升趋势,景观可持续性总体上升。