An improvement on measure methods of the complexity theory and its applications

A new method is proposed to transform the time series gained from a dynamic system to a symbolic series which extracts both overall and local information of the time series. Based on the transformation, two measures are defined to characterize the complexity of the symbolic series. The measures reflect the sensitive dependence of chaotic systems on initial conditions and the randomness of a time series, and thus can distinguish periodic or completely random series from chaotic time series even though the lengths of the time series are not long. Finally, the logistic map and the two-parameter Henón map are studied and the results are satisfactory.     

基于符号动力学的认知事件相关电位的复杂度分析

引入了符号动力学方法分析认知事件相关电位(ERP)的复杂度.以混合模型生成的随机时间序列为例,对近似熵和符号熵作了比较.应用符号熵分析了Oddball范式中不同任务条件(靶刺激和非靶刺激)下的ERP的复杂度.研究发现,额区、中央区和顶区的ERP复杂度在刺激呈现后的任务加工时间段内显著减小(非靶刺激和靶刺激分别在刺激呈现后200—300和400—500ms),而且靶刺激ERP复杂度大约在P300成分的峰值时刻达到最小值,在响应之后逐渐回升.这表明基于符号动力学的复杂度分析能够反映认知任务加工的时间过程,并且 关键词： 事件相关电位 符号动力学 熵     

A measure of statistical complexity based on predictive information with application to finite spin systems

We propose the binding information as an information theoretic measure of complexity between multiple random variables, such as those found in the Ising or Potts models of interacting spins, and compare it with several previously proposed measures of statistical complexity, including excess entropy, Bialek et al.?s predictive information, and the multi-information. We discuss and prove some of the properties of binding information, particularly in relation to multi-information and entropy, and show that, in the case of binary random variables, the processes which maximise binding information are the ‘parity’ processes. The computation of binding information is demonstrated on Ising models of finite spin systems, showing that various upper and lower bounds are respected and also that there is a strong relationship between the introduction of high-order interactions and an increase of binding-information. Finally we discuss some of the implications this has for the use of the binding information as a measure of complexity.     

混沌伪随机序列复杂度分析的符号动力学方法

通过将混沌伪随机序列看成一个符号序列，提出了用符号动力学的 方法来分析混沌伪随机序列的复杂度.以Logistic映射和耦合映射格子系统产生的混沌伪随 机序列为例，说明了该方法的应用，并将计算结果与近似熵ApEn法的计算结果作了比较.结 果表明，该方法可以有效地判断出不同的混沌伪随机序列的复杂程度，而且比近似熵法更为 优越. 关键词： 混沌 伪随机序列 符号动力学 熵     

非线性时间序列互信息与Lempel-Ziv复杂度的相关性研究

为探究非线性动力学系统的互信息和复杂度的相关性，用Logistic映射、Lorenz模型和心电RR间期的非线性时间序列作为实验数据，计算多分段延时互信息和多分段Lempel-Ziv复杂度以及它们之间的相关系数.结果表明这些序列的互信息和复杂度呈强负相关，对Logistic方程生成的201个序列的不同段互信息和不同段复杂度之间的相关系数绝对值都大于0.9162，最大达0.9923；对94个心电RR间期序列都大于0.8555，最大达0.9860.研究还发现互信息比复杂度能更敏感地表现出非线性动力系统的特征. 关键词： 相关系数 互信息 Lempel-Ziv 复杂度 心电RR间期     

钾蒸气中的偶极禁戒双光子共振四波混频和混合激发能量转移受激辐射

本文首次报道了由钾分子-原子系统的混合激发和碰撞能量转移过程产生4F→3D受激辐射以及由钾原子的4S→4F偶极禁戒双光子共振产生4F→3D受激辐射和四波混频的研究结果。     

Subshifts on Infinite Alphabets and Their Entropy

We analyze symbolic dynamics to infinite alphabets by endowing the alphabet with the cofinite topology. The topological entropy is shown to be equal to the supremum of the growth rate of the complexity function with respect to finite subalphabets. For the case of topological Markov chains induced by countably infinite graphs, our approach yields the same entropy as the approach of Gurevich We give formulae for the entropy of countable topological Markov chains in terms of the spectral radius in l2.     

基于复合符号混沌的伪随机数生成器及加密技术

提出了复合符号混沌序列的概念;并以符号动力学的揉序列为基础,将已知的伪随机数与揉序列规则下的短序列复合后得到新的符号混沌序列,再转换成二进制序列,从而得到长度随迭代次数成几何级数增加的伪随机序列(PRN).理论与实证分析都表明这是一个有效的伪随机生成器.为应用到图像的加解密技术中,建立了一个新型元胞自动机.该元胞自动机能有效地避免数据膨胀,加密效率高,并能产生显著的"雪崩效应",提高了加密技术的安全性. 关键词： 复合符号混沌序列 符号动力学 伪随机序列 元胞自动机     

A method of estimating initial conditions of coupled maplattices based on time-varying symbolic dynamics

A novel computationally efficient algorithm in terms of the time-varying symbolic dynamic method is proposed to estimate the unknown initial conditions of coupled map lattices (CMLs). The presented method combines symbolic dynamics with time-varying control parameters to develop a time-varying scheme for estimating the initial condition of multi-dimensional spatiotemporal chaotic signals. The performances of the presented time-varying estimator in both noiseless and noisy environments are analysed and compared with the common time-invariant estimator. Simulations are carried out and the obtained results show that the proposed method provides an efficient estimation of the initial condition of each lattice in the coupled system. The algorithm cannot yield an asymptotically unbiased estimation due to the effect of the coupling term, but the estimation with the time-varying algorithm is closer to the Cramer--Rao lower bound (CRLB) than that with the time-invariant estimation method, especially at high signal-to-noise ratios (SNRs).     

The effects of degree correlations on network topologies and robustness

Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial to an understanding of the function, performance and evolution of complex systems. In the last few years, many network metrics and models have been proposed to investigate the network topology, dynamics and evolution. Since these network metrics and models are derived from a wide range of studies, a systematic study is required to investigate the correlations among them. The present paper explores the effect of degree correlation on the other network metrics through studying an ensemble of graphs where the degree sequence (set of degrees) is fixed. We show that to some extent, the characteristic path length, clustering coefficient, modular extent and robustness of networks are directly influenced by the degree correlation.     

A six-dimensional gauge-Higgs unification model based on E6 gauge symmetry

We construct a six-dimensional gauge-Higgs unification model with the enlarged gauge group of E₆ on S²/Z₂$S^2/Z_2$ orbifold compactification. The standard model particle contents and gauge symmetry are obtained by utilizing a monopole background field and imposing appropriate parity conditions on the orbifold. In particular, a realistic Higgs potential suitable for breaking the electroweak gauge symmetry is obtained without introducing extra matter or assuming an additional symmetry relation between the SU(2) isometry transformation on the S²$S^2$ and the gauge symmetry. The Higgs boson is a KK mode associated with the extra-dimensional components of gauge field. We also compute the KK masses of all fields at tree level.     

基于二次相关的语音信号时延估计改进算法

目前语音信号的时延估计研究,大部分采用的是广义互相关算法。然而,广义互相关时延估计算法易受噪声和混响环境影响。为此,本文提出了一种基于二次相关的语音信号时延估计改进算法,该算法对语音信号进行二次互相关运算,并结合Hilbert变换,对二次互相关峰值进行进一步的锐化处理,使得反映时延的峰值点检测更为准确。实验结果表明,改进的时延估计方法在非平稳的语音信号中能够有效地抑制噪声干扰,且在不同混响条件下时延估计具有更好的性能。     

基于复杂度分析logistic映射和Lorenz模型的研究

采用三次粗粒化方法得到了logistic映射和Lorenz模型的符号序列，运用动态非线性时间序 列分析方法——Lemper-Ziv复杂度，分别对两组符号序列进行了对比分析.对于logistic映 射，其复杂度反映了时间序列的演化；Lorenz模型三个分量的复杂度序列都具有混沌性质， 即由许多振幅非常接近而长度完全不同的循环所组成，反映了Lorenz模型内在的准周期特性 .进一步研究发现，当取不同的窗口长度时，复杂度序列的特征基本相同，并且复杂度反映 了时间序列的时空特性.因此，可以借助复杂度的计算来反演观测资料的动力学结构. 关键词： 三次粗粒化 Lemper-Ziv复杂度 logistic映射 Lorenz模型     

Test of the Duh-Haymet-Henderson theory for mixtures: cavity correlation functions and excess volumes

The accuracy of the Duh-Haymet-Henderson (DHH) integral equation theory for predicting the cavity correlation functions of mixtures has been tested by comparison with molecular simulations. We have compared the cavity correlation functions, internal energies, and pressures computed for Lennard-Jones model mixtures of Ar/Kr, Ar/Ne, and Ar/Xe with these same quantities computed from the DHH theory and also, for reference, the Percus-Yevick (PY) integral equation theory. We found that DHH gave much better accuracy than PY at high densities. At low densities DHH and PY give essentially identical predictions. We have computed excess volumes for Ar/Kr mixtures at two pressures (10 and 20?MPa) at 132.32?K, for which experimentally derived data are available. The DHH theory predicts the correct trends and is quantitatively more accurate than the PY theory for predicting the excess volumes. We have tested the local optimality of the DHH theory for pure fluids by adding two adjustable parameters to the DHH bridge function expression to see if it is possible to improve the DHH predictions of the cavity correlation function empirically, holding the form of the bridge function constant. We found that no single set of adjustable parameter values could improve the accuracy of DHH over multiple different isotherms. Furthermore, perturbing DHH leads to a decrease in accuracy of the predictions of both the pressure and energy, although small improvements in the cavity correlation functions were achieved. Thus, the DHH theory is locally optimal, given the form of the bridge function.     

基于复杂度分析冰芯和石笋代用资料时间序列的研究

运用动态非线性时间序列分析方法——Lemper-Ziv复杂度，分别计算了古里雅冰芯资料和北 京石花洞石笋资料的复杂度，探讨了复杂度的物理内涵及其在气候变化研究中的意义；小波 多尺度分解分析表明，复杂度序列具有明显的特征周期，存在780年、380年、160年和105年 的准周期.进一步研究发现，当取不同的窗口长度时，复杂度序列的特征基本相同；并且复 杂度序列的突变和气候突变在时间尺度上有着较好的对应关系.揭示了近千年来，在380年时 间尺度上的准周期振荡，其振幅一直是在减弱的，而且其固有周期频率逐渐减小.1900年复 杂度开始持续下降，1920年之后变化很小，类似于中国6世纪中期及12世纪中期的变暖期， 因此造成20世纪气候变暖的原因还有待于深入研究. 关键词： Lemper-Ziv复杂度 小波变换 气候 自然变率     

A new method for generating and analysing digital speckle shearing correlation fringe patterns

A method for generating a high visibility digital speckle shearing fringe pattern is proposed. A three-step phase shifting technique which involves the introduction of arbitrary phases is utilized. The phase shifting technique is carried out using a rotating mirror and a theoretical model which involves a linear correlation algorithm is discussed. Experimental results showing correlation fringe patterns and a deformation phase map are presented.     

分数阶混沌系统的Adomian分解法求解及其复杂性分析

根据分数阶微分定义,采用Adomian分解算法,研究了分数阶简化Lorenz系统的数值解.研究发现,该算法与预估-校正算法相比,求解结果更准确,所耗计算资源和内存资源更少,求解整数阶系统时较Runge-Kutta算法更准确;利用Adomian算法得到的分数阶简化Lorenz系统出现混沌的最小阶数为1.35,比利用预估-校正算法得到的最小阶2.79更小.采用相图、分岔图分析了该系统的动力学特性,基于谱熵算法(SE)和C0算法分析了该系统的复杂度.结果表明,复杂度结果和分岔图一致,说明系统的复杂度同样能反映出系统动力学特性;复杂度随阶数q的增加呈总体减小的趋势,而混沌态时系统参数c变化对系统复杂度影响不大.为分数阶混沌系统应用于信息加密、保密通信领域提供了理论与实验依据.     

A method of recovering the initial vectors of globally coupled map lattices based on symbolic dynamics

Based on symbolic dynamics, a novel computationally efficient algorithm is proposed to estimate the unknown initial vectors of globally coupled map lattices (CMLs). It is proved that not all inverse chaotic mapping functions are satisfied for contraction mapping. It is found that the values in phase space do not always converge on their initial values with respect to sufficient backward iteration of the symbolic vectors in terms of global convergence or divergence (CD). Both CD property and the coupling strength are directly related to the mapping function of the existing CML. Furthermore, the CD properties of Logistic, Bernoulli, and Tent chaotic mapping functions are investigated and compared. Various simulation results and the performances of the initial vector estimation with different signal-to-noise ratios (SNRs) are also provided to confirm the proposed algorithm. Finally, based on the spatiotemporal chaotic characteristics of the CML, the conditions of estimating the initial vectors using symbolic dynamics are discussed. The presented method provides both theoretical and experimental results for better understanding and characterizing the behaviours of spatiotemporal chaotic systems.     

基于滑动峭度相关性准则的局部特征尺度分解分量筛选方法

轴承故障振动信号具有非平稳、非线性特征,且可视为多个调幅-调频分量的叠加,单分量的包络蕴含了轴承的故障特征。局部特征尺度分解可将振动信号准确分解为多个内禀尺度分量之和,某些分量能清晰反映轴承的运行状态,根据包络谱可进行故障诊断。为了准确筛选有用分量,提出了基于滑动峭度相关性准则的分量筛选方法。首先,对信号进行局部特征尺度分解,得到若干个内禀尺度分量;然后,对分量和原始信号分别计算滑动峭度,生成时间序列;最后,依据分量滑动峭度序列与原始信号滑动峭度序列的互相关系数筛选有用分量。通过轴承内圈故障数据分析发现：有用分量与非有用分量之间的滑动峭度互相关系数比互相关系数差异明显,区分度更大,有益于分量的分类、筛选。