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     

格子复杂性和符号序列的细粒化

提出一种新的有限长一维符号序列的复杂性度量——格子复杂性，建立在Lempel Ziv复杂性和一维迭代映射系统的符号动力学基础上.同时提出了符号序列的细粒化方法，可与格子复杂性以及Lempel Ziv复杂性结合.新度量在细粒化指数较小时与Lempel Ziv复杂性基本一致，在细粒化指数增大时显示出截然不同的特性.以Logistic映射为对象的计算实验表明，格子复杂性对混沌区的边缘最敏感.最后还讨论了上述复杂性度量的其他一些重要性质. 关键词： 混沌 复杂性度量 格子复杂性 细粒化     

Generation of hierarchically correlated multivariate symbolic sequences

We introduce a method to generate multivariate series of symbols from a finite alphabet with a given hierarchical structure of similarities based on the Hamming distance. The target hierarchical structure of similarities is arbitrary, for instance the one obtained by some hierarchical clustering method applied to an empirical matrix of similarities. The method that we present here is based on a generating mechanism that does not make use of mutation rate, which is widely used in phylogenetic analysis. Here we use the proposed simulation method to investigate the relationship between the bootstrap value associated with a node of a phylogeny and the probability of finding that node in the true phylogeny. The results of this analysis are compared with those obtained in the literature according to an evolutionary model with a per-symbol constant mutation rate. We observe that the relationship between the bootstrap value of a node and the probability of the corresponding clade being correct is sensitive to both the length of data series and the length of the branch connecting the node to its closest ancestor in the phylogenetic tree, whereas such a relationship is only slightly affected by the topology of the true phylogeny and by the absolute value of similarity.     

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     

Physical complexity and Zipf's law

This article deals with a measure of the complexity of a physical system recently proposed by Schapiro and puts it into the context of other recently discussed measures of complexity. We discuss this new measure in terms of a simple Markovian evolution model, extending and specifying the model given by Schapiro, which has the advantage of being analyically tractable. We find that the proposed complexity measure leads to interesting results: there exists a kind of phase transition in this system with a vanishing value of the probabilityc of generating a new species. This phase transition is related to a specific complexity of about 3 bits. By investigating decreasingc (c N ^–q,N the total number of individuals), we find that the complexity per species grows monotonically withq, diverging logarithmically withN as q goes to infinity.     

Mirror objectives with variable focal length

We consider some issues involved in constructing a mirror system with a discrete variable focal length. We propose a procedure for designing two-mirror pancratic (zoom) systems with fixed image plane. In constructing the optimal layouts, we studied a basic two-mirror system to achieve minimum spherical aberration. We present the calculated design characteristics of an objective consisting of two spherical mirrors and providing a three-fold variation in focal length. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 3, pp. 453–459, May–June, 2009.     

Size dependent complexity of sequences in protein families

The size dependent complexity of protein sequences in various families in the FSSP database is characterized by sequence entropy, sequence similarity and sequence identity. As the average length L_f of sequences in the family increases, an increasing trend of the sequence entropy and a decreasing trend of the sequence similarity and sequence identity are found. As L_f increases beyond 250, a saturation of the sequence entropy, the sequence similarity and the sequence identity is observed. Such a saturated behavior of complexity is attributed to the saturation of the probability P_g of global (long-range) interactions in protein structures when L_f >250. It is also found that the alphabet size of residue types describing the sequence diversity depends on the value of L_f, and becomes saturated at 12.     

TD-ERCS离散混沌伪随机序列的复杂性分析

采用相空间直接观察法和行为复杂性算法,系统地分析了新型TD-ERCS离散混沌系统产生的伪随机序列的复杂性,得出了其复杂性变化规律.在Kolmogorov复杂性基础上,应用经典的Limpel-Ziv算法,ApEn算法和PE算法,从一维时间序列到多维相空间重构两方面计算了TD-ERCS离散混沌伪随机序列的复杂度大小.计算结果表明,TD-ERCS系统的行为复杂性高,而且该系统的复杂性大小随系统参数改变的变化范围小,是一个复杂性非常稳定的全域性离散混沌系统,其产生的混沌伪随机序列适合于信息加密或扩频通信. 关键词： 混沌 混沌伪随机序列 TD-ERCS系统 复杂度     

Resonances in a discrete system of variable length

Resonance properties of a finite discrete chain with a periodically varying length are investigated. The evolution equation describing a wave profile in continual approximation is derived. Splitting of the resonance peak is revealed. Wave profiles near the resonances are considered. It is shown that wave profiles formed near different resonances differ from each other in spectral composition. This result is theoretically substantiated.     

On variable length induced vibrations of a vertical string

The purpose of this paper is to study the free lateral responses of vertically translating media with variable length, velocity and tension, subject to general initial conditions. The translating media are modeled as taut strings with fixed boundaries. The problem can be used as a simple model to describe the lateral vibrations of an elevator cable, for which the length changes linearly in time, or for which the length changes harmonically about a constant mean length. In this paper an initial-boundary value problem for a linear, axially moving string equation is formulated. In the given model a rigid body is attached to the lower end of the string, and the suspension of this rigid body against the guide rails is assumed to be rigid. For linearly length variations it is assumed that the axial velocity of the string is small compared to nominal wave velocity and the string mass is small compared to car mass, and for the harmonically length variations small oscillation amplitudes are assumed and it is also assumed that the string mass is small compared to the total mass of the string and the car. A multiple-timescales perturbation method is used to construct formal asymptotic approximations of the solutions to show the complicated dynamical behavior of the string. For the linearly varying length analytic approximations of the exact solution are compared with numerical solution. For the harmonically varying length it will be shown that Galerkin?s truncation method cannot be applied in all cases to obtain approximations valid on long timescales.     

一种确定混沌伪随机序列复杂度的模糊关系熵测度

将模糊关系的概念引入混沌伪随机序列复杂度的测度方法之中,提出了一种新的混沌伪随机序列复杂度测度方法——模糊关系熵(fuzzy relationship entropy,简记为F-REn)测度方法,并推导了F-REn的两个基本性质.仿真结果表明,该测度方法能够有效测度混沌伪随机序列的复杂度,与近似熵(ApEn)测度方法和符号熵测度方法相比,F-REn测度具有更加好的对序列符号空间的适用性、更加小的对测量维度的敏感性和更加强的对分辨率参数的鲁棒性. 关键词： 混沌伪随机序列 模糊理论 复杂度     

Method of the maximum length sequences in a diffraction experiment

A method of the experimental study of the diffraction of acoustic waves with the use of the maximum length sequences is described. This method allows one to measure the pulse response of a system, which makes it a suitable instrument for a diffraction experiment. As an example, the results of an observation of the edge waves appearing at the base of a cylinder at the normal incidence of the acoustic waves were presented. The results of the measurements are compared with the results of the numerical simulation.     

大变焦范围电调谐液晶变焦透镜的研究

基于向列相液晶指向矢随施加电场作用发生变化的特性, 结合几何光学和液晶理论提出了一种液晶透镜结构模型, 研究了电极大小、隔垫物厚度等液晶透镜参数对液晶透镜焦距的影响. 通过优化参数, 得到结构简单、变焦范围较大的新型液晶透镜样品, 在驱动电压0 V_RMS–250 V_RMS下可调的焦距范围为75–230 mm, 达到155 mm.     

Factorial moments analyses show a characteristic length scale in DNA sequences

A unique feature of most of the DNA sequences, found through the factorial moments analysis, is the existence of a characteristic length scale around which the density distribution is nearly Poissonian. Above this point, the DNA sequences, irrespective of their intron contents, show long range correlations with a significant deviation from the Gaussian statistics, while, below this point, the DNA statistics are essentially Gaussian. The famous DNA walk representation is also shown to be a special case of the present analysis.     

Join- and-cut algorithm for self-avoiding walks with variable length and free endpoints

We introduce a new Monte Carlo algorithm for generating self-avoiding walks of variable length and free endpoints. The algorithm works in the unorthodox ensemble consisting of all pairs of SAWs such that the total number of stepsN _tot in the two walks is fixed. The elementary moves of the algorithm are fixed-N (e.g., pivot) moves on the individual walks, and a novel join- and-cut move that concatenates the two walks and then cuts them at a random location. We analyze the dynamic critical behavior of the new algorithm, using a combination of rigorous, heuristic, and numerical methods. In two dimensions the autocorrelation time in CPU units grows as N^1.5, and the behavior improves in higher dimensions. This algorithm allows high-precision estimation of the critical exponent.     

焦线可调光楔列阵系统的研制

针对原形光楔列阵均匀线聚焦光学系统线长不可调的缺点，研制了可连续改变焦线宽纵比的光楔列阵系统，详细分析了它的工作原理，并作了实验验证，得到二者相一致的结果。     

Mixing Bandt-Pompe and Lempel-Ziv approaches: another way to analyze the complexity of continuous-state sequences

In this paper, we propose to mix the approach underlying Bandt-Pompe permutation entropy with Lempel-Ziv complexity, to design what we call Lempel-Ziv permutation complexity. The principle consists of two steps: (i) transformation of a continuous-state series that is intrinsically multivariate or arises from embedding into a sequence of permutation vectors, where the components are the positions of the components of the initial vector when re-arranged; (ii) performing the Lempel-Ziv complexity for this series of ‘symbols’, as part of a discrete finite-size alphabet. On the one hand, the permutation entropy of Bandt-Pompe aims at the study of the entropy of such a sequence; i.e., the entropy of patterns in a sequence (e.g., local increases or decreases). On the other hand, the Lempel-Ziv complexity of a discrete-state sequence aims at the study of the temporal organization of the symbols (i.e., the rate of compressibility of the sequence). Thus, the Lempel-Ziv permutation complexity aims to take advantage of both of these methods. The potential from such a combined approach – of a permutation procedure and a complexity analysis – is evaluated through the illustration of some simulated data and some real data. In both cases, we compare the individual approaches and the combined approach.