An improved series expansion method on the multi-frequency analysis of acoustic boundary element

For the multi-frequency acoustic analysis, a series expansion method has been introduced to reduce the computation time of the frequency-independent parts, but the Runge phenomenon will arise when this method is employed in high frequency band. Therefore, this method is improved by analyzing the application condition and proposing the selection principle of the series truncation number. The argument interval can be adjusted with the wavenumber factor. Therefore, the problem of unstable numeration and poor precision can be solved, and the application scope of this method is expanded. The numerical example of acoustic radiation shows that the improved method is correct for acoustic analysis in wider frequency band with less series truncation number and computation amount.     

改进型声学边界元级数多频算法

对于声学多频分析问题,研究者提出了一种声学边界元级数多频算法节省了重复计算频率无关项的时间,但这种原始算法受到多项式拟合的Runge现象限制,计算频段较窄。进一步改进此原始方法,提出了级数截断项数的选取原则,加入波数因子调整自变量区间避免Runge现象,消除了原始算法的不稳定性,拓展了级数多频算法的适用范围。声辐射计算实例证明了改进的级数多频算法的正确性,所需级数截断项数更少,降低了计算量,能够应用于更高频段的声学分析。      

Iterated function system models in data analysis: detection and separation

We investigate the use of iterated function system (IFS) models for data analysis. An IFS is a discrete-time dynamical system in which each time step corresponds to the application of one of the finite collection of maps. The maps, which represent distinct dynamical regimes, may be selected deterministically or stochastically. Given a time series from an IFS, our algorithm detects the sequence of regime switches under the assumption that each map is continuous. This method is tested on a simple example and an experimental computer performance data set. This methodology has a wide range of potential uses: from change-point detection in time-series data to the field of digital communications.     

Implications of using approximate Bloch-McConnell equations in NMR analyses of chemically exchanging systems: application to the electron self-exchange of plastocyanin

The validity of a series of approximate solutions of the Bloch-McConnell equations normally applied in the analyses of chemically exchanging systems is evaluated, using the electron self-exchange (ESE) in the blue copper protein plastocyanin from Anabaena variabilis as an example. The evaluation is based on a comparison with the results of a complete analysis of the NMR signals of chemically exchanging nuclei that allows an independent and accurate determination of all the involved parameters. The complete analysis is based on the general solution of the Bloch-McConnell equations. It includes a simultaneous analysis of the chemical shift, and the transverse and longitudinal relaxation rates of the observed nuclei as well as the variation of these parameters with the molar fractions of the exchanging species and the rate of the chemical exchange process. The linear prediction model method was used in the data analysis to achieve the highest possible precision. Surprisingly, it is found that the fast exchange condition may not be fulfilled even in cases where a single exchange-averaged NMR signal is observed, and the Larmor frequency and relaxation rates depend linearly on the molar fractions of the exchanging species. In such cases the use of approximate solutions in the analysis of the transverse relaxation rates and the pseudo-contact shifts can lead to erroneous results. In limiting cases close to the fast exchange and slow exchange regimes correct values of some of the parameters can be obtained using the second order approximate solution of the Bloch-McConnell equations. In contrast, the complete analysis of the NMR signals results in an accurate determination of the exchange rates and the NMR parameters of the exchanging sites. This, in turn, can provide information about the structure and function of a protein undergoing chemically exchange. For the investigated plastocyanin the complete analysis results in an accurate determination of the paramagnetic enhancement of the nuclear relaxation rates, the paramagnetic chemical shift, the electron relaxation rate, the electron self-exchange rate, and the distances between the nuclei and the paramagnetic metal ion, viz. the Cu2+ ion.     

A recursive approach to prony parameter estimation

The Prony series method of fitting a series of complex exponentials to a time series can be applied to many acoustic and vibration signals. For example, in the analysis of a structure's response to transient excitation the Prony series method can be used to find the natural frequencies, damping ratios, amplitudes and relative phases of the modes of the structure. One of the main problems with this method is the need to calculate and invert matrices. In this paper an algorithm that combines the Prony series method with the recursive least squares algorithm is described. This eliminates the need to invert any matrices and also requires only part of the data to be available at one particular time. The method is applied to analyze a simulated structure's response and also to analyze the response of a beam to transient excitation.     

A Langevin equation for the rates of currency exchange based on the Markov analysis

We propose a method for analyzing the data for the rates of exchange of various currencies versus the U.S. dollar. The method analyzes the return time series of the data as a Markov process, and develops an effective equation which reconstructs it. We find that the Markov time scale, i.e., the time scale over which the data are Markov-correlated, is one day for the majority of the daily exchange rates that we analyze. We derive an effective Langevin equation to describe the fluctuations in the rates. The equation contains two quantities, D⁽¹⁾ and D⁽²⁾, representing the drift and diffusion coefficients, respectively. We demonstrate how the two coefficients are estimated directly from the data, without using any assumptions or models for the underlying stochastic time series that represent the daily rates of exchange of various currencies versus the U.S. dollar.     

Empirical behavior of a world stock index from intra-day to monthly time scales

Most of the papers that study the distributional and fractal properties of financial instruments focus on stock prices or foreign exchange rates. This typically leads to mixed results concerning the distributions of log-returns and some multi-fractal properties of exchange rates, stock prices, and regional indices. This paper uses a well diversified world stock index as the central object of analysis. Such index approximates the growth optimal portfolio, which is demonstrated under the benchmark approach, it is the ideal reference unit for studying basic securities. When denominating this world index in units of a given currency, one measures the movements of the currency against the entire market. This provides a least disturbed observation of the currency dynamics. In this manner, one can expect to disentangle, e.g., the superposition of the two currencies involved in an exchange rate. This benchmark approach to the empirical analysis of financial data allows us to establish remarkable stylized facts. Most important is the observation that the repeatedly documented multi-fractal appearance of financial time series is very weak and much less pronounced than the deviation of the mono-scaling properties from Brownian-motion type scaling. The generalized Hurst exponent H(2) assumes typical values between 0.55 and 0.6. Accordingly, autocorrelations of log-returns decay according to a power law, and the quadratic variation vanishes when going to vanishing observation time step size. Furthermore, one can identify the Student t distribution as the log-return distribution of a well-diversified world stock index for long time horizons when a long enough data series is used for estimation. The study of dependence properties, finally, reveals that jumps at daily horizon originate primarily in the stock market while at 5min horizon they originate in the foreign exchange market. The principal message of the empirical analysis is that there is evidence that a diffusion model without multi-scaling could reasonably well model the dynamics of a broadly diversified world stock index.     

The Lévy sections theorem: An application to econophysics

We employ the Lévy sections theorem in the analysis of selected dollar exchange rate time series. The theorem is an extension of the classical central limit theorem and offers an alternative to the most usual analysis of the sum variable. We find that the presence of fat tails can be related to the local volatility pattern of the series.     

Determination of association constants at moderately fast chemical exchange: complexation of camphor enantiomers by alpha-cyclodextrin

Association constants in weak molecular complexes can be determined by analysis of chemical shifts variations resulting from changes of guest to host concentration ratio. In the regime of very fast exchange, i.e., when exchange rate is several orders of magnitude larger than the Larmor angular frequency difference of the observed resonance in free and complexed molecule, the apparent position of averaged resonance is a population-weighted mean of resonances of particular forms involved in the equilibrium. The assumption of very fast exchange is often, however, tacitly admitted in literature even in cases where the process of interest is much slower than required. We show that such an unjustified simplification may, under certain circumstances, lead to significant underestimation of association constant and, in consequence, to non-negligible errors in Gibbs free energy under determination. We present a general method, based on iterative numerical NMR line shape analysis, which allows one for the compensation of chemical exchange effects, and delivers both the correct association constants and the exchange rates. The latter are not delivered by the other mentioned method. Practical application of our algorithm is illustrated by the case of camphor-alpha-cyclodextrin complexes.     

Cross-sample entropy of foreign exchange time series

The correlation of foreign exchange rates in currency markets is investigated based on the empirical data of DKK/USD, NOK/USD, CAD/USD, JPY/USD, KRW/USD, SGD/USD, THB/USD and TWD/USD for a period from 1995 to 2002. Cross-SampEn (cross-sample entropy) method is used to compare the returns of every two exchange rate time series to assess their degree of asynchrony. The calculation method of confidence interval of SampEn is extended and applied to cross-SampEn. The cross-SampEn and its confidence interval for every two of the exchange rate time series in periods 1995-1998 (before the Asian currency crisis) and 1999-2002 (after the Asian currency crisis) are calculated. The results show that the cross-SampEn of every two of these exchange rates becomes higher after the Asian currency crisis, indicating a higher asynchrony between the exchange rates. Especially for Singapore, Thailand and Taiwan, the cross-SampEn values after the Asian currency crisis are significantly higher than those before the Asian currency crisis. Comparison with the correlation coefficient shows that cross-SampEn is superior to describe the correlation between time series.     

Statistical properties of the yuan exchange rate index

We choice the yuan exchange rate index based on a basket of currencies as the effective exchange rate of the yuan and investigate the statistical properties of the yuan exchange rate index after China’s exchange rate system reform on the 21st July 2005. After dividing the time series into two parts according to the change in the yuan exchange rate regime in July 2008, we compare the statistical properties of the yuan exchange rate index during these two periods. We find that the distribution of the two return series has the exponential form. We also perform the detrending moving average analysis (DMA) and the multifractal detrending moving average analysis (MFDMA). The two periods possess different degrees of long-range correlations, and the multifractal nature is also unveiled in these two time series. Significant difference is found in the scaling exponents τ(q)$\tau \left(q\right)$ and singularity spectra f(α)$f\left(\alpha \right)$ of the two periods obtained from the MFDMA analysis. Besides, in order to detect the sources of multifractality, shuffling and phase randomization procedures are applied to destroy the long-range temporal correlation and fat-tailed distribution of the yuan exchange rate index respectively. We find that the fat-tailedness plays a critical role in the sources of multifractality in the first period, while the long memory is the major cause in the second period. The results suggest that the change in China’s exchange rate regime in July 2008 gives rise to the different multifractal properties of the yuan exchange rate index in these two periods, and thus has an effect on the effective exchange rate of the yuan after the exchange rate reform on the 21st July 2005.     

Parameter motivated mutual correlation analysis: Application to the study of currency exchange rates based on intermittency parameter and Hurst exponent

We present a novel method for the parameter oriented analysis of mutual correlation between independent time series or between equivalent structures such as ordered data sets. The proposed method is based on the sliding window technique, defines a new type of correlation measure and can be applied to time series from all domains of science and technology, experimental or simulated. A specific parameter that can characterize the time series is computed for each window and a cross correlation analysis is carried out on the set of values obtained for the time series under investigation. We apply this method to the study of some currency daily exchange rates from the point of view of the Hurst exponent and the intermittency parameter. Interesting correlation relationships are revealed and a tentative crisis prediction is presented.     

Visibility graph approach to exchange rate series

By means of a visibility graph, we investigate six important exchange rate series. It is found that the series convert into scale-free and hierarchically structured networks. The relationship between the scaling exponents of the degree distributions and the Hurst exponents obeys the analytical prediction for fractal Brownian motions. The visibility graph can be used to obtain reliable values of Hurst exponents of the series. The characteristics are explained by using the multifractal structures of the series. The exchange rate of EURO to Japanese Yen is widely used to evaluate risk and to estimate trends in speculative investments. Interestingly, the hierarchies of the visibility graphs for the exchange rate series of these two currencies are significantly weak compared with that of the other series.     

Volatility dynamics of wavelet-filtered stock prices

Nontrivial mixture of long-range correlations and noise is one of the characteristic features of the dynamics of complex systems. Filtering of noise in such systems presents a difficult challenge. In the present paper this problem is studied by the example of volatility dynamics of wavelet-filtered stock price time series. Using the universal thresholding method of wavelet filtering and a principle of minimal linear autocorrelation of noise component we find that the quantitative characteristics of long-range memory in the volatility dynamics of denoised series are noticeably different from those of the raw data and the noise.     

结合可视图的多状态交通流时间序列特性分析

交通流时间序列的研究主要采用数据挖掘和机器学习的方法,这些"黑箱"挖掘方法很难直观反映序列特性.为增强交通流时间序列及其特征分析的可视化性,结合可视图理论来构建交通流时间序列的关联网络,从复杂网络角度实现交通流时间序列的特性分析.在网络构建的过程中,考虑到不同交通状态下交通流表征具有的差异性,首先利用交通流参量的相关性对交通流状态进行分类,然后构建不同交通状态下的时间序列复杂网络,并对这些网络的特征属性给出统计分析,如度分布、聚类系数、网络直径、模块化等.研究表明,可视图法可为交通流时间序列映射到网络提供有效途径,并且不同状态下交通流时间序列构建的复杂网络的模块化、聚类系数和度分布等统计特征呈现一定的变化规律,为交通流运行态势的研究提供了可视化的分析角度.     

时间序列三维荧光光谱的异常值检测

异常值的存在往往干扰着时间序列三维荧光光谱的定性和定量分析。充分利用时间维和光谱维的内在特性, 提出了一种有效的异常值检测方法。在时间维结合方差提取异常值可能性最大的波长点;通过对异常值存在方式的分析,在任意两个三维荧光光谱的相似度基础上给出了光谱维上的累积相似度;最后利用时间维的校正矩阵对所有三维荧光光谱的每个波长点荧光强度进行修正并计算对应的累积相似度,从而根据累积相似度对异常值进行判断。时间维校正矩阵的采用不仅提高了算法的有效性而且其特征区域的选择大大减少了光谱维相似度的计算量。相关的数值试验表明光谱维选取50%的波长点仍然能有效对异常值进行检测。     

利用慢特征分析法提取层次结构系统中的外强迫

在大量真实的动力系统中,外部驱动力总是随时间发生变化,正是这种变化导致了非平稳行为的产生.因此,从此类系统的观测数据中提取和分析外强迫(也称驱动力)信号引起了人们越来越多的关注.慢特征分析法(slow feature analysis,SFA)是从非平稳时间序列中提取外强迫信息的一种有效算法.在其基础上利用变参数的Logistic映射产生的非平稳时间序列,通过数值试验进一步讨论了该方法的应用前景,并发展了一些相应的分析技术.试验结果表明,对于模型中包含两个时变驱动力参数的系统,经过一次SFA处理之后,可以进一步利用子波分析技术检索出外强迫信号中的两个参数;对于模型中有两个叠加驱动力层次的三层动力系统,可先通过一次SFA处理,提取出次慢层外强迫信号,对该信号进行二次SFA处理,可提取出最慢层外强迫信号.     

Data assimilation using a GPU accelerated path integral Monte Carlo approach

The answers to data assimilation questions can be expressed as path integrals over all possible state and parameter histories. We show how these path integrals can be evaluated numerically using a Markov Chain Monte Carlo method designed to run in parallel on a graphics processing unit (GPU). We demonstrate the application of the method to an example with a transmembrane voltage time series of a simulated neuron as an input, and using a Hodgkin–Huxley neuron model. By taking advantage of GPU computing, we gain a parallel speedup factor of up to about 300, compared to an equivalent serial computation on a CPU, with performance increasing as the length of the observation time used for data assimilation increases.     

Singular spectrum analysis and Fisher–Shannon analysis of spring flow time series: An application to Anjar Spring,Lebanon

In this study, the time dynamics of water flow from Anjar Spring was investigated, which is one of the major issuing springs in the central part of Lebanon. Likewise, many water sources in Lebanon, this spring has no continuous records for the discharge, and this would prevent the application of standard time series analysis tools. Furthermore, the highly nonstationary character of the series implies that suited methodologies can be employed to get insight into its dynamical features. Therefore, the Singular Spectrum Analysis (SSA) and Fisher–Shannon (FS) method, which are useful methods to disclose dynamical features in noisy nonstationary time series with gaps, are jointly applied to analyze the Anjar Spring water flow series. The SSA revealed that the series can be considered as the superposition of meteo-climatic periodic components, low-frequency trend and noise-like high-frequency fluctuations. The FS method allowed to extract and to identify among all the SSA reconstructed components the long-term trend of the series. The long-term trend is characterized by higher Fisher Information Measure (FIM) and lower Shannon entropy, and thus, represents the main informative component of the whole series. Generally water discharge time series presents very complex time structure, therefore the joint application of the SSA and the FS method would be very useful in disclosing the main informative part of such kind of data series in the view of existing climatic variability and/or anthropogenic challenges.     

胶束型磁共振成像分子探针的设计与应用

飞速发展的分子影像学在肿瘤的早期诊断及检测中发挥着越来越重要的作用.磁共振成像(MRI)是分子影像学的重要分支，具有其他成像技术不可比拟的优越性和广阔的发展前景.它不需要放射性示踪剂，没有电离辐射，具有高的空间、时间分辨率和组织对比度.近年来，新型磁共振分子探针及成像序列取得了一系列进展，包括环境响应型分子探针、¹⁹F成像、¹²⁹Xe超极化成像以及化学交换饱和转移成像等，进一步拓展了MRI的应用范围.研究和开发靶向性好、弛豫效率高且安全性好的新型多模态MRI造影剂，进一步提高灵敏度是MRI领域的一项重要课题，例如将胶束的特性与一些MRI新方法结合，寻找合适的胶束体系，以提高MRI分子探针的灵敏度；或者引入多模态分子探针，弥补磁共振方法的不足.本文综述了胶束型MRI分子探针核心技术的研究进展与应用，并指出分子影像技术在生物医学工程研究和临床诊断中的重要性.