用等间距分格子法计算互信息函数确定延迟时间

以等间距划分空间格子的方法,计算了互信息函数,进而给出了延迟时间。以强迫布鲁塞尔振子为例,给出了重构运动状态。     

基于符号分析的极大联合熵延迟时间求取方法

本文通过符号分析法求取联合熵的极大值点, 进而得到相空间重构的最佳延迟时间, 通过对几个典型的混沌系统进行数值仿真试验, 结果表明, 该方法简化了计算, 提高了效率, 能够准确快速地获得最佳延迟时间, 从而有效地重构原系统的相空间, 为混沌信号识别提供一种快速有效的途径. 关键词： 相空间重构 延迟时间 联合熵 符号分析     

确定延迟时间互信息法的一种算法

介绍了相空间重构中确定重构延迟时间的互信息法理论及其具体的计算方法.针对互信息法应用中计算复杂、程序难以编写问题,提出了一种基于网格层数的简便实用程序算法.对网格层数参数进行了结果分析,表明在利用互信息法确定重构延迟时间时,只需要计算到某一个网格层数即可,不需要计算出精确的互信息值,简化了计算的复杂程度.最后通过对Lorenz和Rossler两个吸引子的Lyapunov指数计算,证实了该算法的合理性.     

确定等价电子杨盘基的等概率比对方法

给出了等价电子正则杨盘T^［λ］_ig的基本对称算子、完全对称算子概念,同时给出了这些对称算子作用于任一Slater函数_i所产生的根态、生成态概念.由正交归一化杨盘T^［λ］_ie的纵置换算子A^［λ］_ie的构造规则,给出了A^［λ］_ie中存在的对称算子和确定T^［λ］_ie的等概率比对方法,从而基本避免了牵涉到许多算子的极其复杂的代数,给出了求解N值较大的电子系统杨盘基问题的新方法. 关键词： 正则杨盘 对称算子 根态 等概率比对方法     

混沌时序相空间重构参数确定的信息论方法

根据信息论基本原理，研究了混沌时间序列相空间重构参数延迟时间和嵌入维数的选取.提出了用符号分析的方法计算互信息函数，确定出延迟时间，在此基础上，提出了一种估计嵌入维数的信息论方法，即根据重构向量条件熵随向量维数的变化关系来确定嵌入维数，通过对几种典型混沌动力学系统的数值验证，结果表明该方法能够确定出合适的相空间重构嵌入维数. 关键词： 混沌 相空间重构 互信息 条件熵 符号分析     

确定SHPB实验中延迟时间的曲线拟合法

 利用已知的试件密度，用预估的透射波与实测的透射波进行早期形状比较，确定试件弹性波速度，进而确定了SHPB试验数据处理时的延迟时间。     

等概率符号化样本熵应用于脑电分析

样本熵(或近似熵)以信息增长率刻画时间序列的复杂性,能应用于短时序列,因而在生理信号分析中被广泛采用.然而,一方面由于传统样本熵采用与标准差线性相关的容限,使得熵值易受非平稳突变干扰的影响,另一方面传统样本熵还受序列概率分布的影响,从而导致其并非单纯反映序列的信息增长率.针对上述两个问题,将符号动力学与样本熵结合,提出等概率符号化样本熵方法,并对其物理意义、数学推导及参数选取都做了详细阐述.通过对噪声数据的仿真计算,验证了该方法的正确性及其区分不同强度时间相关的有效性.此方法应用于脑电信号分析的结果表明,在不对信号做人工伪迹去除的前提下,只需要1.25 s的脑电信号即可有效地区分出注意力集中和注意力发散两种状态.这进一步证明了该方法可很好地抵御非平稳突变干扰,能快速获得短时序列的潜在动力学特性,对脑电生物反馈技术具有很大的应用价值.     

开关触发延迟时间和抖动测量的不确定度分析

为明确脉冲功率装置开关触发延迟时间和抖动测量的可信度,进行了不确定度评定。使用拟合的线性关系式结合示波器水平分辨力导致的不确定度建立开关延迟时间不确定度的数学模型;根据抖动的定义建立抖动的测量不确定度数学模型。两者均按B类不确定度评定。以相关实验数据为基础计算了各个不确定度分量、合成标准不确定度以及扩展不确定度。按工程测量要求置信概率为95％,取包含因子为2,可得初级实验平台（PTS）单路样机激光触发开关触发延迟时间测量的扩展不确定度为0.38 ns;抖动测量的扩展不确定度为0.13 ns。延迟时间和抖动测量结果的不确定度满足实验分析的要求。     

开关触发延迟时间和抖动测量的不确定度分析

为明确脉冲功率装置开关触发延迟时间和抖动测量的可信度,进行了不确定度评定。使用拟合的线性关系式结合示波器水平分辨力导致的不确定度建立开关延迟时间不确定度的数学模型;根据抖动的定义建立抖动的测量不确定度数学模型。两者均按B类不确定度评定。以相关实验数据为基础计算了各个不确定度分量、合成标准不确定度以及扩展不确定度。按工程测量要求置信概率为95%,取包含因子为2,可得初级实验平台(PTS)单路样机激光触发开关触发延迟时间测量的扩展不确定度为0.38 ns;抖动测量的扩展不确定度为0.13 ns。延迟时间和抖动测量结果的不确定度满足实验分析的要求。     

基于互信息改进型脉冲耦合神经网络多值图像分割

为了自动地进行图像的多值分割,从原始图像与分割图像之间的相互关系出发,以最大互信息为优化分割目标,以互信息熵差作为一种新的分类类数判据,在对传统脉冲耦合神经网络模型改进的基础上,提出了一种基于最大互信息改进型脉冲耦合神经网络图像多值分割算法.理论分析和实验结果表明,该方法能够自动确定最佳分割迭代次数及最佳分割灰度类数,对分割图像具有良好的特征划分能力,且在分割类数较少的情况下,能较好地保持图像细节、纹理及边缘等信息,对不同图像分割准确度高,具有较强的适用性.     

Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics

The modeling and prediction of chaotic time series require proper reconstruction of the state space from the available data in order to successfully estimate invariant properties of the embedded attractor. Thus, one must choose appropriate time delay τ∗ and embedding dimension p for phase space reconstruction. The value of τ∗ can be estimated from the Mutual Information, but this method is rather cumbersome computationally. Additionally, some researchers have recommended that τ∗ should be chosen to be dependent on the embedding dimension p by means of an appropriate value for the time delay τw=(p−1)τ∗, which is the optimal time delay for independence of the time series. The C-C method, based on Correlation Integral, is a method simpler than Mutual Information and has been proposed to select optimally τw and τ∗. In this paper, we suggest a simple method for estimating τ∗ and τw based on symbolic analysis and symbolic entropy. As in the C-C method, τ∗ is estimated as the first local optimal time delay and τw as the time delay for independence of the time series. The method is applied to several chaotic time series that are the base of comparison for several techniques. The numerical simulations for these systems verify that the proposed symbolic-based method is useful for practitioners and, according to the studied models, has a better performance than the C-C method for the choice of the time delay and embedding dimension. In addition, the method is applied to EEG data in order to study and compare some dynamic characteristics of brain activity under epileptic episodes     

Information Bottleneck Analysis by a Conditional Mutual Information Bound

Task-nuisance decomposition describes why the information bottleneck loss I(z;x)−βI(z;y) is a suitable objective for supervised learning. The true category y is predicted for input x using latent variables z. When n is a nuisance independent from y, I(z;n) can be decreased by reducing I(z;x) since the latter upper bounds the former. We extend this framework by demonstrating that conditional mutual information I(z;x|y) provides an alternative upper bound for I(z;n). This bound is applicable even if z is not a sufficient representation of x, that is, I(z;y)≠I(x;y). We used mutual information neural estimation (MINE) to estimate I(z;x|y). Experiments demonstrated that I(z;x|y) is smaller than I(z;x) for layers closer to the input, matching the claim that the former is a tighter bound than the latter. Because of this difference, the information plane differs when I(z;x|y) is used instead of I(z;x).     

Adaptation of Partial Mutual Information from Mixed Embedding to Discrete-Valued Time Series

A causality analysis aims at estimating the interactions of the observed variables and subsequently the connectivity structure of the observed dynamical system or stochastic process. The partial mutual information from mixed embedding (PMIME) is found appropriate for the causality analysis of continuous-valued time series, even of high dimension, as it applies a dimension reduction by selecting the most relevant lag variables of all the observed variables to the response, using conditional mutual information (CMI). The presence of lag components of the driving variable in this vector implies a direct causal (driving-response) effect. In this study, the PMIME is appropriately adapted to discrete-valued multivariate time series, called the discrete PMIME (DPMIME). An appropriate estimation of the discrete probability distributions and CMI for discrete variables is implemented in the DPMIME. Further, the asymptotic distribution of the estimated CMI is derived, allowing for a parametric significance test for the CMI in the DPMIME, whereas for the PMIME, there is no parametric test for the CMI and the test is performed using resampling. Monte Carlo simulations are performed using different generating systems of discrete-valued time series. The simulation suggests that the parametric significance test for the CMI in the progressive algorithm of the DPMIME is compared favorably to the corresponding resampling significance test, and the accuracy of the DPMIME in the estimation of direct causality converges with the time-series length to the accuracy of the PMIME. Further, the DPMIME is used to investigate whether the global financial crisis has an effect on the causality network of the financial world market.     

Characterization of Pathogen Airborne Inoculum Density by Information Theoretic Analysis of Spore Trap Time Series Data

In a previous study, air sampling using vortex air samplers combined with species-specific amplification of pathogen DNA was carried out over two years in four or five locations in the Salinas Valley of California. The resulting time series data for the abundance of pathogen DNA trapped per day displayed complex dynamics with features of both deterministic (chaotic) and stochastic uncertainty. Methods of nonlinear time series analysis developed for the reconstruction of low dimensional attractors provided new insights into the complexity of pathogen abundance data. In particular, the analyses suggested that the length of time series data that it is practical or cost-effective to collect may limit the ability to definitively classify the uncertainty in the data. Over the two years of the study, five location/year combinations were classified as having stochastic linear dynamics and four were not. Calculation of entropy values for either the number of pathogen DNA copies or for a binary string indicating whether the pathogen abundance data were increasing revealed (1) some robust differences in the dynamics between seasons that were not obvious in the time series data themselves and (2) that the series were almost all at their theoretical maximum entropy value when considered from the simple perspective of whether instantaneous change along the sequence was positive.     

Influence of Dark Energy on Gravitational Time Delay

We investigate the gravitational time delay of light in the Schwarzschild black hole space-time surrounded by quintessence. With the analysis and numerical methods, we find that the gravitational time delay of light in the Schwarzschild black hole space-time surrounded by quintessence increases when the normalization factor c increases, and that the gravitational time delay also decreases when the quintessential state parameter ωq increases.     

Influence of Dark Energy on Gravitational Time Delay

We investigate the gravitational time delay of light in the Schwarzschild black hole space-time surrounded by quintessence. With the analysis and numerical methods, we find that the gravitational time delay of light in the Schwarzschild black hole space-time surrounded by quintessence increases when the normalization factor c increases, and that the gravitational time delay also decreases when the quintessential state parameter ω_q increases.     

Volatility Dynamics of Non-Linear Volatile Time Series and Analysis of Information Flow: Evidence from Cryptocurrency Data

This paper aims to empirically examine long memory and bi-directional information flow between estimated volatilities of highly volatile time series datasets of five cryptocurrencies. We propose the employment of Garman and Klass (GK), Parkinson’s, Rogers and Satchell (RS), and Garman and Klass-Yang and Zhang (GK-YZ), and Open-High-Low-Close (OHLC) volatility estimators to estimate cryptocurrencies’ volatilities. The study applies methods such as mutual information, transfer entropy (TE), effective transfer entropy (ETE), and Rényi transfer entropy (RTE) to quantify the information flow between estimated volatilities. Additionally, Hurst exponent computations examine the existence of long memory in log returns and OHLC volatilities based on simple R/S, corrected R/S, empirical, corrected empirical, and theoretical methods. Our results confirm the long-run dependence and non-linear behavior of all cryptocurrency’s log returns and volatilities. In our analysis, TE and ETE estimates are statistically significant for all OHLC estimates. We report the highest information flow from BTC to LTC volatility (RS). Similarly, BNB and XRP share the most prominent information flow between volatilities estimated by GK, Parkinson’s, and GK-YZ. The study presents the practicable addition of OHLC volatility estimators for quantifying the information flow and provides an additional choice to compare with other volatility estimators, such as stochastic volatility models.     

Whitening as a Tool for Estimating Mutual Information in Spatiotemporal Data Sets

We address the issue of inferring the connectivity structure of spatially extended dynamical systems by estimation of mutual information between pairs of sites. The well-known problems resulting from correlations within and between the time series are addressed by explicit temporal and spatial modelling steps which aim at approximately removing all spatial and temporal correlations, i.e. at whitening the data, such that it is replaced by spatiotemporal innovations; this approach provides a link to the maximum-likelihood method and, for appropriately chosen models, removes the problem of estimating probability distributions of unknown, possibly complicated shape. A parsimonious multivariate autoregressive model based on nearest-neighbour interactions is employed. Mutual information can be reinterpreted in the framework of dynamical model comparison (i.e. likelihood ratio testing), since it is shown to be equivalent to the difference of the log-likelihoods of coupled and uncoupled models for a pair of sites, and a parametric estimator of mutual information can be derived. We also discuss, within the framework of model comparison, the relationship between the coefficient of linear correlation and mutual information. The practical application of this methodology is demonstrated for simulated multivariate time series generated by a stochastic coupled-map lattice. The parsimonious modelling approach is compared to general multivariate autoregressive modelling and to Independent Component Analysis (ICA).