Multiparameter estimation using only a chaotic time series and its applications

An important extension to the techniques of synchronization-based parameter estimation is presented. Based on adaptive chaos synchronization, several methods are proposed to dynamically estimate multiple parameters using only a scalar chaotic time series. In comparison with previous schemes, the presented methods decrease the cost of parameter estimation and are more applicable in practice. Numerical examples are used to demonstrate the effectiveness and robustness of the presented methods. As an example application, an implementation of multichannel digital communication is proposed, where multiparameter modulation is used to simultaneously transmit more than one digital message. From a theoretical perspective, such an encoding increases the difficulty to directly read out the message from the transmitted signal and decreases the implementation cost.     

Performance of blind source separation algorithms for fMRI analysis using a group ICA method

Independent component analysis (ICA) is a popular blind source separation technique that has proven to be promising for the analysis of functional magnetic resonance imaging (fMRI) data. A number of ICA approaches have been used for fMRI data analysis, and even more ICA algorithms exist; however, the impact of using different algorithms on the results is largely unexplored. In this paper, we study the performance of four major classes of algorithms for spatial ICA, namely, information maximization, maximization of non-Gaussianity, joint diagonalization of cross-cumulant matrices and second-order correlation-based methods, when they are applied to fMRI data from subjects performing a visuo-motor task. We use a group ICA method to study variability among different ICA algorithms, and we propose several analysis techniques to evaluate their performance. We compare how different ICA algorithms estimate activations in expected neuronal areas. The results demonstrate that the ICA algorithms using higher-order statistical information prove to be quite consistent for fMRI data analysis. Infomax, FastICA and joint approximate diagonalization of eigenmatrices (JADE) all yield reliable results, with each having its strengths in specific areas. Eigenvalue decomposition (EVD), an algorithm using second-order statistics, does not perform reliably for fMRI data. Additionally, for iterative ICA algorithms, it is important to investigate the variability of estimates from different runs. We test the consistency of the iterative algorithms Infomax and FastICA by running the algorithm a number of times with different initializations, and we note that they yield consistent results over these multiple runs. Our results greatly improve our confidence in the consistency of ICA for fMRI data analysis.     

Neuronal event detection in fMRI time series using iterative deconvolution techniques

An iterative estimation algorithm for deconvolution of neuronal activity from Blood Oxygen Level Dependent (BOLD) time series data is presented. The algorithm requires knowledge of the hemodynamic impulse response function but does not require knowledge of the stimulation function. The method uses majorization-minimization of a cost function to find an optimal solution to the inverse problem. The cost function includes penalties for the l₁ norm, total variation and negativity. The algorithm is able to identify the occurrence of neuronal activity bursts from BOLD time series accurately. The accuracy of the algorithm was tested in simulations and experimental fMRI data using blocked and event-related designs. The simulations revealed that the algorithm is most sensitive to contrast-to-noise ratio levels and to errors in the assumed hemodynamic model and least sensitive to autocorrelation in the noise. Within normal fMRI conditions, the method is effective for event detection.     

The cross-correlation integral: Its features and application to nonstationarity detection in time series

A generalization of the correlation integral, called the cross-correlation integral, is suggested. Features of the cross-correlation integral are studied, and a new attribute of a time series is defined. It is viewed as some kind of dimension and is associated with the fill rate of the attractor. It is demonstrated that the cross-correlation integral is calculated in much the same way as the wavelet transform of the density of points in the attractor. The cross-correlation integral is applied to detection of nonstationarity in time series. A comparison with statistical methods is made.     

Conditional independence graph for nonlinear time series and its application to international financial markets

Conditional independence graphs are proposed for describing the dependence structure of multivariate nonlinear time series, which extend the graphical modeling approach based on partial correlation. The vertexes represent the components of a multivariate time series and edges denote direct dependence between corresponding series. The conditional independence relations between component series are tested efficiently and consistently using conditional mutual information statistics and a bootstrap procedure. Furthermore, a method combining information theory with surrogate data is applied to test the linearity of the conditional dependence. The efficiency of the methods is approved through simulation time series with different linear and nonlinear dependence relations. Finally, we show how the method can be applied to international financial markets to investigate the nonlinear independence structure.     

Speckle reduction of SAR images using ICA basis enhancement and separation

An approach for synthetic aperture radax (SAR) image de-noising based on independent component analysis (ICA) basis images is proposed. Firstly, the basis images and the code matrix of the original image are obtained using ICA algorithm. Then, pointwise H(o)lder exponent of each basis is computed as a cost criterion for basis enhancement, and then the enhanced basis images are classified into two sets according to a separation rule which separates the clean basis from the original basis. After these key procedures for speckle reduction, the clean image is finally obtained by reconstruction on the clean basis and original code matrix. The reconstructed image shows better visual perception and image quality compared with those obtained by other traditional techniques.     

磁性核壳纳米粒子的制备及其在分离和光谱检测中的应用

磁性及其核壳复合纳米粒子由于在不同领域中具有广泛应用而受到研究者的极大关注,总结了磁性及磁性核壳纳米粒子常见的制备方法及各自的特点,并重点讨论了其在磁分离及光谱检测方面的应用,也介绍了本课题组在纳米粒子合成及应用方面所做的一部分工作。最后对磁性纳米粒子中存在的问题进行了探讨,并对其应用前景进行了展望。     

Normalized linear variance decay dimension density and its application of dynamical complexity detection in physiological (fMRI) time series

The upper and lower bounds of the linear variance decay (LVD) dimension density are analytically deduced using multivariate series with uncorrelated and perfectly correlated component series. Then, the normalized LVD dimension density (δnormLVD) is introduced. In order to measure the complexity of a scalar series with δnormLVD, a pseudo-multivariate series was constructed from the scalar time series using time-delay embedding. Thus, δnormLVD is used to characterize the complexity of the pseudo-multivariate series. The results from the model systems and fMRI data of anxiety subjects reveal that this method can be used to analyze short and noisy time series.     

具有选择与遗忘机制的极端学习机在时间序列预测中的应用

针对训练样本贯序输入时的极端学习机 (ELM)训练问题,提出一种具有选择与遗忘机制的极端学习机 (SF-ELM),并研究了其在混沌时间序列预测中的应用. SF-ELM以逐次增加新训练样本的方式实现在线训练,通过引入遗忘因子以减弱旧训练样本的影响,同时以泛化能力为判断依据,对其输出权值进行选择性递推更新. 混沌时间序列在线预测实例表明,SF-ELM是一种有效的ELM在线训练模式. 相比于在线贯序极端学习机,SF-ELM具有更快的在线训练速度和更高的在线预测精度,因此更适于混沌时间序列在线预测. 关键词： 混沌时间序列 时间序列预测 神经网络 极端学习机     

Nonunitary spin-charge separation in a one-dimensional fermion gas

In this Letter we report exact results on the infrared asymptotics of the one-particle dynamical correlation function of the gas of impenetrable spin 1/2 fermions at infinitesimal temperature. The correlation function shows signs of spin-charge separation with scaling behavior in the charge part and exponential decay as a function of the space coordinate in the spin part. Surprisingly, the anomalous dimensions in the charge part do not correspond to any unitary conformal field theory. We find that the fermion spectral weight has a power law divergency at low energy with the anomalous exponent -1/2.     

Synthesis of time series for the clearness index using a reordering algorithm

Summary Two insolation series, 4 and 8 years long, collected in different sites of the country, are used to contrast the behaviour of a statistical model for the clearness index, developed by the authors. This model is based on the independence between the stationary and the sequential statistic of clearness index series. A set of prospective clearness index coefficients is reordered until acquiring the sequential behaviour. A computer code has been developed to this end.     

Criterion for phase separation in one-dimensional driven systems

A general criterion for the existence of phase separation in driven density-conserving one-dimensional systems is proposed. It is suggested that phase separation is related to the size dependence of the steady-state currents of domains in the system. A quantitative criterion for the existence of phase separation is conjectured using a correspondence made between driven diffusive models and zero-range processes. The criterion is verified in all cases where analytical results are available, and predictions for other models are provided.     

归一化KLD系数及多维序列相关和同步的检测

提出了KLD系数和归一化KLD系数来刻画多维序列的相关结构, 以解决KLD维密度固有的局限性. 利用完全相关和完全不相关的多维序列, 导出KLD维密度的上界和下界函数, 进而导出KLD系数的上界和下界, 在此基础上提出归一化KLD系数. 解析分析和数值仿真都证明, 多维序列相关结构的变化会引起归一化KLD系数线性的变化. 数值仿真还证明, 即使多维序列中仅有其中的两个时间序列的相关结构发生改变, 归一化KLD系数仍能灵敏地检测到. 不仅如此, 归一化KLD系数还可用于非平稳时间序列的分析. 耦合映象格子的数值仿真结果表明, 归一化KLD系数还能够分析非线性系统的相关结构.     

Bio-organism detection in one-dimensional photonic crystals using electromagnetically induced transparency

We propose an optical sensor that allows site-selective detection of a refractive index change occurring due to any infiltration such as a bio-organism in a porous one-dimensional photonic crystal (PC). We use the electromagnetically induced transparency (EIT) to detect and locate the infiltration. With a localized change in the refractive index, the maximum of the peak EIT transmission shifts, which is determined by tuning the control field frequency. The strong dispersion and the narrowing of the absorption free response associated with EIT within the PC form the basis of such enhanced sensitivity.     

Improvement of frequency sensitivity of series photodetector frequency circuit system and its application for Cy5 fluorescence detection

This study elucidated the frequency characteristics of series photodetector frequency circuit system for detection of DNA probe ET996 marked with fluorescence dye Cy5. We developed 48 MHz series photodetector frequency circuit system with good sensitivity for fluorescence detection. In accordance with the theory of series photodetector frequency circuit system, the frequency sensitivity can be improved by adjusting circuit parameters such as A (tan θ), C_q, C₀, and C_p. In this research of A adjustment, the capacitance parameter C_m of 48 MHz series photodetector frequency circuit system was adjusted to improve the frequency sensitivity for detection of fluorescence dye concentration; moreover, the bias of photodetector was also adjusted to improve the frequency sensitivity. In the optimal conditions of capacitance match and photodetector bias, the detection limit of ET996-Cy5 fluorescence dye concentration 2 pmol/L can be measured by 48 MHz sensor system. The results of fluorescence experiment also demonstrated that the frequency shift of 48 MHz sensor system was linearly related to the logarithm of fluorescence dye concentration from 200 nmol/L to 2 pmol/L. The frequency method can be applied simply and the detection limit of ET996-Cy5 fluorescence dye concentration was lower than the conventional fluorescence technique by 2 orders.     

Causality detection based on information-theoretic approaches in time series analysis

Synchronization, a basic nonlinear phenomenon, is widely observed in diverse complex systems studied in physical, biological and other natural sciences, as well as in social sciences, economy and finance. While studying such complex systems, it is important not only to detect synchronized states, but also to identify causal relationships (i.e. who drives whom) between concerned (sub) systems. The knowledge of information-theoretic measures (i.e. mutual information, conditional entropy) is essential for the analysis of information flow between two systems or between constituent subsystems of a complex system. However, the estimation of these measures from a set of finite samples is not trivial. The current extensive literatures on entropy and mutual information estimation provides a wide variety of approaches, from approximation-statistical, studying rate of convergence or consistency of an estimator for a general distribution, over learning algorithms operating on partitioned data space to heuristical approaches. The aim of this paper is to provide a detailed overview of information theoretic approaches for measuring causal influence in multivariate time series and to focus on diverse approaches to the entropy and mutual information estimation.     

Measuring persistence in a stationary time series using the complex network theory

A growing interest exists currently in the analysis of time series by the complex network theory. Here we present a simple and quick way for mapping time series to complex networks. Using a simple rule allows us to transform time series into a textual sequence then we divide it into words with fixed size. Distinct words are nodes of the network, and we have complete control on the network scale by adjusting the word size. Two nodes are linked if their associated words co-occur in sequence. We show that the network topological measures quantify the persistence and the long range correlations in fractional Brownian processes. For a particular word size we assume some relations between the topological measures and the Hurst exponent which characterised the persistence in fractional Brownian processes.     

Inverse problem for multivariate time series using dynamical latent variables

Factor analysis is a well known statistical method to describe the variability among observed variables in terms of a smaller number of unobserved latent variables called factors. While dealing with multivariate time series, the temporal correlation structure of data may be modeled by including correlations in latent factors, but a crucial choice is the covariance function to be implemented. We show that analyzing multivariate time series in terms of latent Gaussian processes, which are mutually independent but with each of them being characterized by exponentially decaying temporal correlations, leads to an efficient implementation of the expectation–maximization algorithm for the maximum likelihood estimation of parameters, due to the properties of block-tridiagonal matrices. The proposed approach solves an ambiguity known as the identifiability problem, which renders the solution of factor analysis determined only up to an orthogonal transformation. Samples with just two temporal points are sufficient for the parameter estimation: hence the proposed approach may be applied even in the absence of prior information about the correlation structure of latent variables by fitting the model to pairs of points with varying time delay. Our modeling allows one to make predictions of the future values of time series and we illustrate our method by applying it to an analysis of published gene expression data from cell culture HeLa.