Scaling characteristics of ocean wave height time series

Fluctuations in the significant wave height can be quantified by using scaling statistics. In this paper, the scaling properties of the significant wave height were explored by using a large data set of hourly series from 25 monitoring stations located off the west coast of the US. Detrended fluctuation analysis (DFA) was used to investigate the scaling properties of the series. DFA is a robust technique that can be used to detect long-range correlations in nonstationary time series. The significant wave height data was analyzed by using scales from hourly to monthly. It was found that a common scaling behavior can be observed for all stations. A breakpoint in the scaling region around 4-5 days was apparent. Spectral analysis confirms this result. This breakpoint divided the scaling region into two distinct parts. The first part was for finer scales (up to 4 days) which exhibited Brown noise characteristics, while the second one showed 1/f noise behavior at coarser scales (5 days to 1 month). The first order and the second order DFA (DFA1 and DFA2) were used to check the effect of seasonality. It was found that there were no differences between DFA1 and DFA2 results, indicating that there is no effect of trends in the wave height time series. The resulting scaling coefficients range from 0.696 to 0.890 indicating that the wave height exhibits long-term persistence. There were no coherent spatial variations in the scaling coefficients.     

Comparison of detrending methods for fluctuation analysis

We examine several recently suggested methods for the detection of long-range correlations in data series based on similar ideas as the well-established Detrended Fluctuation Analysis (DFA). In particular, we present a detailed comparison between the regular DFA and two recently suggested methods: the Centered Moving Average (CMA) Method and a Modified Detrended Fluctuation Analysis (MDFA). We find that CMA performs the same as DFA in long data with weak trends and is slightly superior to DFA in short data with weak trends. When comparing standard DFA to MDFA we observe that DFA performs slightly better in almost all examples we studied. We also discuss how several types of trends affect different types of DFA. For weak trends in the data, the new methods are comparable with DFA in these respects. However, if the functional form of the trend in data is not a-priori known, DFA remains the method of choice. Only a comparison of DFA results, using different detrending polynomials, yields full recognition of the trends. A comparison with independent methods is recommended for proving long-range correlations.     

Detrended Fluctuation Analysis of Traffic Data

Different routing strategies may result in different behaviour of traffic on internet. We analyse the correlation of traffic data for three typical routing strategies by the detrended fluctuation analysis （DFA） and lind that the aregree of correlation of the data can be divided into three regions, i.e. weak, medium, and strong correlation. The DFA scalings are constants in both the regions of weak and strong correlations but monotonically increase in the region of medium correlation. We suggest that it is better to consider the traffic on complex network as three phases, i.e. the free, buffer, and congestion phase, than just as two phases believed before, i.e. the free and congestion phase.     

Interpretation of heart rate variability via detrended fluctuation analysis and alphabeta filter

Detrended fluctuation analysis (DFA), suitable for the analysis of nonstationary time series, has confirmed the existence of persistent long-range correlations in healthy heart rate variability data. In this paper, we present the incorporation of the alphabeta filter to DFA to determine patterns in the power-law behavior that can be found in these correlations. Well-known simulated scenarios and real data involving normal and pathological circumstances were used to evaluate this process. The results presented here suggest the existence of evolving patterns, not always following a uniform power-law behavior, that cannot be described by scaling exponents estimated using a linear procedure over two predefined ranges. Instead, the power law is observed to have a continuous variation with segment length. We also show that the study of these patterns, avoiding initial assumptions about the nature of the data, may confer advantages to DFA by revealing more clearly abnormal physiological conditions detected in congestive heart failure patients related to the existence of dominant characteristic scales.     

Effects of quantization on detrended fluctuation analysis

Detrended fluctuation analysis(DFA) is a method foro estimating the long-range power-law correlation exponent in noisy signals.It has been used successfully in many different fields,especially in the research of physiological signals.As an inherent part of these studies,quantization of continuous signals is inevitable.In addition,coarse-graining,to transfer original signals into symbol series in symbolic dynamic analysis,can also be considered as a quantization-like operation.Therefore,it is worth considering whether the quantization of signal has any effect on the result of DFA and if so,how large the effect will be.In this paper we study how the quantized degrees for three types of noise series(anti-correlated,uncorrelated and long-range power-law correlated signals) affect the results of DFA and find that their effects are completely different.The conclusion has an essential value in choosing the resolution of data acquisition instrument and in the processing of coarse-graining of signals.     

Effect of coarse-graining on detrended fluctuation analysis

Several studies have investigated the scaling behavior in naturally occurring biological and physical processes using techniques such as detrended fluctuation analysis (DFA). Data acquisition is an inherent part of these studies and maps the continuous process into digital data. The resulting digital data is discretized in amplitude and time, and shall be referred to as coarse-grained realization in the present study. Since coarse-graining precedes scaling exponent analysis, it is important to understand its effects on scaling exponent estimators such as DFA. In this brief communication, k-means clustering is used to generate coarse-grained realizations of data sets with different correlation properties, namely: anti-correlated noise, long-range correlated noise and uncorrelated noise. It is shown that the coarse-graining can significantly affect the scaling exponent estimates. It is also shown that scaling exponent can be reliably estimated even at low levels of coarse-graining and the number of the clusters required varies across the data sets with different correlation properties.     

第五讲生物医学信息处理--DNA微阵列数据在医学中的应用

飞速发展的生物信息技术为现代医学提供了更为有效的工具．特别是随着人类基因组计划的基本完成和逐步细化，人们已经试图从基因水平上来认识生命现象，特别是一些重要疾病的机理．由于生物特性一般都涉及到多个基因的共同表达，这便出现了同时衡量成千上万个基因的表现水平的所谓DNA微阵列技术与数据．DNA微阵列数据也被称为大规模基因表达谱．根据这些微阵列数据，人们不仅能够对一些疾病进行分析，并且还能够发现一些新的生物特性与规律．另外，利用微阵列数据能够选取出疾病的相关基因并进行疾病的分类与诊断．这项研究无疑将推动医学的发展．最近，人们还进一步通过基因表达水平值来发现基因之间的调控方式，这将为疾病病理的研究与治疗提供更科学的依据．     

Qualitative assessment of gene expression in affymetrix genechip arrays

Affymetrix Genechip microarrays are used widely to determine the simultaneous expression of genes in a given biological paradigm. Probes on the Genechip array are atomic entities which by definition are randomly distributed across the array and in turn govern the gene expression. In the present study, we make several interesting observations. We show that there is considerable correlation between the probe intensities across the array which defy the independence assumption. While the mechanism behind such correlations is unclear, we show that scaling behavior and the profiles of perfect match (PM) as well as mismatch (MM) probes are similar and immune-to-background subtraction. We believe that the observed correlations are possibly an outcome of inherent non-stationarities or patchiness in the array devoid of biological significance. This is demonstrated by inspecting their scaling behavior and profiles of the PM and MM probe intensities obtained from publicly available Genechip arrays from three eukaryotic genomes, namely: Drosophila melanogaster (fruit fly), Homo sapiens (humans) and Mus musculus (house mouse) across distinct biological paradigms and across laboratories, with and without background subtraction. The fluctuation functions were estimated using detrended fluctuation analysis (DFA) with fourth-order polynomial detrending. The results presented in this study provide new insights into correlation signatures of PM and MM probe intensities and suggests the choice of DFA as a tool for qualitative assessment of Affymetrix Genechip microarrays prior to their analysis. A more detailed investigation is necessary in order to understand the source of these correlations.     

Detrended fluctuation analysis of heart intrabeat dynamics

We investigate scaling properties of electrocardiogram (ECG) recordings of healthy subjects and heart failure patients based on detrended fluctuation analysis (DFA). While the vast majority of scaling analysis has focused on the characterization of the long-range correlations of interbeat (i.e., beat-to-beat) dynamics, in this work we consider instead the characterization of intrabeat dynamics. That is, here we use DFA to study correlations for time scales smaller than one heart beat period (about 0.75 s). Our results show that intrabeat dynamics of healthy subject are less correlated than for heart failure dynamics. As in the case of interbeat dynamics, the DFA scaling exponents can be used to discriminate healthy and pathological data. It is shown that 0.5 h recordings suffices to characterize the ECG correlation properties.     

Volatilities, traded volumes, and the hypothesis of price increments in derivative securities

A detrended fluctuation analysis (DFA) is applied to the statistics of Korean treasury bond (KTB) futures from which the logarithmic increments, volatilities, and traded volumes are estimated over a specific time lag. In this study, the logarithmic increment of futures prices has no long-memory property, while the volatility and the traded volume exhibit the existence of the long-memory property. To analyze and calculate whether the volatility clustering is due to a inherent higher-order correlation not detected by with the direct application of the DFA to logarithmic increments of KTB futures, it is of importance to shuffle the original tick data of future prices and to generate a geometric Brownian random walk with the same mean and standard deviation. It was found from a comparison of the three tick data that the higher-order correlation inherent in logarithmic increments leads to volatility clustering. Particularly, the result of the DFA on volatilities and traded volumes can be supported by the hypothesis of price changes.     

Detrending fluctuation analysis based on high-pass filtering

Detrended fluctuation analysis (DFA) is a scaling method commonly used for detecting long-range correlations in non-stationary time series. The DFA method uses a trend based on polynomial fitting to extract and quantify fluctuations at different time scales. Basically, such procedure acts as a (non-dynamical) high-pass filter that removes time series components below a given time scale. As an alternative to the polynomial fitting approach, this paper proposes a DFA method based on well-known high-pass filters (e.g., Butterworth, elliptic, etc.). Numerical results show that the proposed DFA approach yields results similar to traditional DFA method. Maybe, the main advantage of the proposed DFA method is that efficient implementations of high-pass filters are available commercially.     

Memory effect and multifractality of cross-correlations in financial markets

We introduce an instantaneous and an average instantaneous cross-correlation function to detect the temporal cross-correlations between individual stocks based on the daily data of the United States and the Chinese stock markets. The memory effect of the instantaneous cross-correlations is investigated by applying the detrended fluctuation analysis (DFA), where the DFA exponents can be partly explained by the correlation function from the common sense. Long-range memory is observed for the average instantaneous cross-correlations, and persists up to a month magnitude of timescale for the United States stock market and half a month magnitude of timescale for the Chinese stock market. In addition, multifractal nature is investigated by a multifractal detrended fluctuation analysis.     

Effect of significant data loss on identifying electric signals that precede rupture estimated by detrended fluctuation analysis in natural time

Electric field variations that appear before rupture have been recently studied by employing the detrended fluctuation analysis (DFA) to quantify their long-range temporal correlations. These studies revealed that seismic electric signal (SES) activities exhibit a scale invariant feature with an exponent αDFA≈1 over all scales investigated (around five orders of magnitude). Here, we study what happens upon significant data loss, which is a question of primary practical importance, and show that the DFA applied to the natural time representation of the remaining data still reveals for SES activities an exponent close to 1.0, which markedly exceeds the exponent found in artificial (man-made) noises. This enables the identification of a SES activity with probability of 75% even after a significant (70%) data loss. The probability increases to 90% or larger for 50% data loss.     

Noise Analysis of Duplicated Data on Microarrays Using Mixture Distribution Modeling

We propose a technique for estimating gene expression values for duplicated data on cDNA microarrays. In the scatter plots, the distribution is constructed from a mixture of normal two-dimensional distributions, which represent fluctuations in gene expression values due to noise. An expectation-maximization (EM) algorithm is used for estimating the modeling parameters. The probability that duplicated data is shifted by noise is calculated using Bayesian estimation. Six data sets of rice cDNA microarray assays were used to test the proposed technique. Genes in the data sets were subjected to clustering based on probability of true value. Clustering successfully identified candidate genes regulated by circadian rhythms in rice.     

Language time series analysis

We use the detrended fluctuation analysis (DFA) and the Grassberger–Proccacia analysis (GP) methods in order to study language characteristics. Despite that we construct our signals using only word lengths or word frequencies, excluding in this way huge amount of information from language, the application of GP analysis indicates that linguistic signals may be considered as the manifestation of a complex system of high dimensionality, different from random signals or systems of low dimensionality such as the Earth climate. The DFA method is additionally able to distinguish a natural language signal from a computer code signal. This last result may be useful in the field of cryptography.     

去趋势波动分析方法中不重叠等长度子区间长度的确定

针对去趋势波动分析方法中参数不重叠等长度子区间长度s的选取,基于信息论的基本原理,提出使用符号分析方法对原始数据进行符号编码,并使用不同的方式对符号序列进行分段、计算互信息函数.细致描述了不同分段方式对原始混沌序列的信息编码能力,以此判断所采用的分段方式能否真实有效地还原原始序列所包含的全部信息.给出了确定最优分段个数或各分段长度的具体方式,确定了不重叠等长度子区间长度s的选取算法,以及判断所研究序列是否适用于去趋势波动分析方法,避免了以往参数s选取中随机性和主观性给计算结果带来的错误信息.进一步将该方法应用于实际温度资料,计算并分析中国1961—2000年逐日平均温度的去趋势波动分析指数分布状况.     

微阵列芯片的荧光光漂白特性

微阵列技术为大量基因表达水平的同时监控提供了一种高效的手段。随着微阵列芯片朝着小型化、高通量和弱信号方向发展,荧光检测技术以其易寻址和高灵敏度等优势越来越受到世人关注。在微阵列技术中,人们通过检测微阵列芯片上不同位置斑点的荧光信号强度,可以得知微阵列芯片不同位置固定的已知序列探针与荧光染料标记的cDNA样品的杂交情况。对一张微阵列芯片多次扫描后,荧光染料发生光漂白,荧光强度发生衰减变化,它将为微阵列的数据分析带来误差。使用荧光浓度梯度微阵列芯片研究了芯片经多次扫描后荧光斑点强度的衰减情况,通过拟合相同荧光斑点经多次重复扫描后得到的信号强度,得到了荧光斑点强度按指数形式衰减的规律,并在此基础上研究了荧光斑点强度衰减指数模型中的参数与荧光斑点初始浓度的关系,为进行微阵列芯片数据光漂白误差修正提供了实验依据。     

Correlation between detrended fluctuation analysis and the Lempel–Ziv complexity in nonlinear time series analysis

We focus on the study of the correlation between the detrended fluctuation analysis (DFA) and the Lempel-Ziv complexity (LZC) in nonlinear time series analysis in this paper. Typical dynamical systems including logistic map and Duffing model are investigated. Moreover, the influences of the Gaussian random noise on both DFA and LZC are analyzed. The results show a high correlation between DFA and LZC, which can quantify the non-stationarity and the nonlinearity of the time series, respectively. With the enhancement of the random component, the exponent α and the normalized complexity index C show increasing trends. In addition, C is found to be more sensitive to the fluctuation in the nonlinear time series than α. Finally, the correlation between DFA and LZC is applied to the feature extraction of vibration signals for a reciprocating compressor gas valve, and an effective fault diagnosis result is obtained.     

Long range correlation and possible electron conduction through DNA sequences

Long range correlation analysis and charge conductivity investigation are applied to sequences in 16 chromosomes in the Saccharomyces cerevisiae genome. DNA sequence data are analyzed via Hurst’s analysis and Detrended Fluctuation Analysis (DFA) analysis. Super diffusive nature of mapping sequences are evident with the measured Hurst exponent H to be around the value of 0.60 for all sequences in the 16 chromosomes. The DFA result is consistent with the result from the Hurst analysis. Tight binding models are applied for the investigation of charge conduction through DNA sequences. The overall averaged transmission coefficients, 〈T_N〉_av, calculated from sixteen chromosomes are shown to be significantly different from values calculated from random as well as periodic sequences. Sequences from the S. cerevisiae genome promise better charge conduction ability than random sequences. Finally, delocalized electronic wave function patterns are also shown through calculations using the tight binging model. Slightly delocalized electronic wavefunctions are seen on sequences in sixteen chromosomes, as compared with those obtained from random sequences on the same eigenenergies.