Cycles,scaling and crossover phenomenon in length of the day (LOD) time series

The dynamics of the temporal fluctuations of the length of the day (LOD) time series from January 1, 1962 to November 2, 2006 were investigated. The power spectrum of the whole time series has revealed annual, semi-annual, decadal and daily oscillatory behaviors, correlated with oceanic–atmospheric processes and interactions. The scaling behavior was analyzed by using the detrended fluctuation analysis (DFA), which has revealed two different scaling regimes, separated by a crossover timescale at approximately 23 days. Flicker-noise process can describe the dynamics of the LOD time regime involving intermediate and long timescales, while Brownian dynamics characterizes the LOD time series for small timescales.     

Multifractal analysis of streamflow records of the East River basin (Pearl River), China

Scaling behaviors of the long daily streamflow series of four hydrological stations (Longchuan (1952-2002), Heyuan (1951-2002), Lingxia (1953-2002) and Boluo (1953-2002)) in the mainstream East River, one of the tributaries of the Pearl River (Zhujiang River) basin, were analyzed using multifractal detrended fluctuation analysis (MF-DFA). The research results indicated that streamflow series of the East River basin are characterized by anti-persistence. MF-DFA technique showed similar scaling properties in the streamflow series of the East River basin on shorter time scales, indicating universal scaling properties over the East River basin. Different intercept values of the fitted lines of log-log curve of F_q(s) versus s implied hydrological regulation of water reservoirs. Based on the numerical results, we suggested that regulation activities by water reservoirs could not impact the scaling properties of the streamflow series. The regulation activities by water reservoir only influenced the fluctuation magnitude. Therefore, we concluded that the streamflow variations were mainly the results of climate changes, and precipitation variations in particular. Strong dependence of generalized Hurst exponent h(q) on q demonstrated multifractal behavior of streamflow series of the East River basin, showing ‘universal’ multifractal behavior of river runoffs. The results of this study may provide valuable information for prediction and assessment of water resources under impacts of climatic changes and human activities in the East River basin.     

Scaling of atmosphere and ocean temperature correlations in observations and climate models

Power-law scaling of near surface air temperature fluctuations and its geographical distribution is analyzed in 100-yr observations and in a 1000-yr simulation of the present-day climate with a complex atmosphere-ocean model. In observations and simulation detrended fluctuation analysis leads to the scaling exponent alpha approximately 1 over the oceans, alpha approximately 0.5 over the inner continents, and alpha approximately 0.65 in transition regions [spectrum S(f) approximately f(-beta),beta=2alpha-1]. Scaling up to decades is demonstrated in observations and coupled atmosphere-ocean models with complex and mixed-layer oceans. Only with the complex ocean model the simulated power laws extend up to centuries.     

Forecasting volatility in Shanghai and Shenzhen markets based on multifractal analysis

This paper analyzes the multifractality in Shanghai and Shenzhen stock markets using multifractal spectrum analysis and multifractal detrended fluctuation analysis. We find that the main source of multifractality is long-range correlations of large and small fluctuations. Then, we introduce a multifractal volatility measure (MV) and find that by taking MV as daily conditional volatility, the simulated series displayed similar “stylized facts” to the original daily return series. By capturing the dynamics of MV using the ARFIMA model, we find that the out-of-sample forecasting performance of the ARFIMA-MV model is better than some GARCH-class models and the ARFIMA-RV model under some criteria of loss function.     

Detrended fluctuation analysis on spot and futures markets of West Texas Intermediate crude oil

In this paper, we study the auto-correlations and cross-correlations of West Texas Intermediate (WTI) crude oil spot and futures return series employing detrended fluctuation analysis (DFA) and detrended cross-correlation analysis (DCCA). Scaling analysis shows that, for time scales smaller than a month, the auto-correlations and cross-correlations are persistent. For time scales larger than a month but smaller than a year, the correlations are anti-persistent, while, for time scales larger than a year, the series are neither auto-correlated nor cross-correlated, indicating the efficient operation of the crude oil markets. Moreover, for small time scales, the degree of short-term cross-correlations is higher than that of auto-correlations. Using the multifractal extension of DFA and DCCA, we find that, for small time scales, the correlations are strongly multifractal, while, for large time scales, the correlations are nearly monofractal. Analyzing the multifractality of shuffled and surrogated series, we find that both long-range correlations and fat-tail distributions make important contributions to the multifractality. Our results have important implications for market efficiency and asset pricing models.     

电子商务中人类活动的标度行为实证研究

应用去趋势波动分析法,对电子商务中人类网上购物行为进行研究,首次探讨了人类浏览及购买行为时间序列(数量波动)标度律.首先,研究发现人类网上购物行为呈现出明显的周期性,其时间序列的概率密度函数具有显著的双模态特征.其次,利用傅里叶变换方法分析浏览以及购买行为时间序列的功率谱,发现其演化过程不同于无关联的泊松过程.最后,基于功率谱过滤周期性趋势的影响,对去除周期趋势后的浏览和购买行为时间序列进行去趋势波动分析,发现其标度行为表明其具有较强的长程关联特性,且平均标度值近似为1,表明其具有自组织临界性.实证研究结果与其他领域如因特网交通流和金融市场价格波动的标度行为相似,有助于理解人类活动如何影响电子商务系统演化和提高在线商务活动效率,对分析电子商务中人类行为活动的机制和预测其波动趋势具有重要的启示作用.     

The effect of respiratory oscillations in heart rate on detrended fluctuation analysis

Characterization of heart rate using detrended fluctuation analysis (DFA) is impeded by respiratory oscillations. In particular, the short-term exponent measured from 15 to 30 beats is compromised in the DFA. We reconstruct respiratory signal from electrocardiograms and attenuate the respiratory oscillation in the heart rate using a frequency-dependent subtraction approach. We validate this method by applying it to an electrocardiogram signal simulated using a coupled differential equation with the respiratory oscillation modelled using a sine function. The exponent estimated using the proposed approach agreed with the exponent incorporated in the model within a narrow range. In contrast, the exponent obtained from the raw data deviated from the expected value. Furthermore, the exponents obtained for the raw heart rate are smaller than the exponents obtained for the respiration oscillation attenuated heart rate. We apply this approach to heart rate measured from 12 preterm infants that were being treated for prematurity related complications. As observed in the simulated data, we show that compared to the raw heart rate, the respiratory oscillation attenuated heart rate shows higher short-term exponent (p < 0.001).     

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.     

Dependence of output power in modulated optical fiber ring resonator on nonlinear refractive index

Nonlinear dynamics in optical fiber ring resonators (OFRRs) can be applied to the estimation of the nonlinear refractive index of optical fibers. The output power of the OFRR becomes convergent, periodic, and chaotic with an increase in the input power. In this study, the dependence of the output power on the nonlinear refractive index is analyzed numerically. The critical input power at which the convergent state changes to the periodic state decreases smaller as the nonlinear refractive index increases. In addition, the maximum oscillation width of the output power decreases monotonically with the nonlinear refractive index. These dependences are sensitive to the parameters of the OFRR. The estimation of the nonlinear refractive index can be realized effectively using the maximum or minimum critical input power, and the maximum oscillation width of the output power even under a subtle fluctuation in the optical fiber ring length.     

Quantum oscillations in a novel organic quasi-two-dimensional (BEDO-TTF)5[RbHg(SCN)4]2 metal

Quantum magnetization and magnetoresistance oscillations are detected in the quasi-two-dimensional organic metal (BEDO-TTF)₅[RbHg(SCN)₄]₂ for the first time. The magnetization oscillation spectrum corresponds to a calculated Fermi surface provided that a magnetic breakdown is realized. The magnetoresistance oscillation spectrum contains additional frequencies, one of which can unambiguously be related to quantum interference. An analysis of the angular dependence of the magnetoresistance oscillation amplitude indicates that the many-body interactions in this metal are weak.     

From 1/f noise to multifractal cascades in heartbeat dynamics

We explore the degree to which concepts developed in statistical physics can be usefully applied to physiological signals. We illustrate the problems related to physiologic signal analysis with representative examples of human heartbeat dynamics under healthy and pathologic conditions. We first review recent progress based on two analysis methods, power spectrum and detrended fluctuation analysis, used to quantify long-range power-law correlations in noisy heartbeat fluctuations. The finding of power-law correlations indicates presence of scale-invariant, fractal structures in the human heartbeat. These fractal structures are represented by self-affine cascades of beat-to-beat fluctuations revealed by wavelet decomposition at different time scales. We then describe very recent work that quantifies multifractal features in these cascades, and the discovery that the multifractal structure of healthy dynamics is lost with congestive heart failure. The analytic tools we discuss may be used on a wide range of physiologic signals. (c) 2001 American Institute of Physics.     

Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant

The intertrade duration of equities is an important financial measure, characterizing trading activities; it is defined as the waiting time between successive trades of an equity. Using the ultrahigh-frequency data of a liquid Chinese stock and its associated warrant, we perform a comparative investigation of the statistical properties of their intertrade duration time series. The distributions of the two equities can be better described by the shifted power-law form than the Weibull form, and their scaled distributions do not collapse onto a single curve. Although the intertrade durations of the two equities have very different magnitude, their intraday patterns exhibit very similar shapes. Both detrended fluctuation analysis (DFA) and detrending moving average analysis (DMA) show that the 1 min intertrade duration time series of the two equities are strongly correlated. In addition, both multifractal detrended fluctuation analysis (MFDFA) and multifractal detrending moving average analysis (MFDMA) unveil that the 1 min intertrade durations possess multifractal nature. However, the difference between the two singularity spectra of the two equities obtained from the MFDMA is much smaller than that from the MFDFA.     

Non-uniform scaling behavior in ultra-low-frequency (ULF) earthquake-related geomagnetic signals

Investigating highly non-stationary time series, which typically exhibit long-range correlations, is a classic problem in physics. Here, we analyze the scaling properties of the dynamics of ultra-low-frequency (ULF) geomagnetic data (in the frequency range between 1 mHz and 10 Hz) observed at Izu Peninsula in Japan. On the basis of the detrended fluctuation analysis (DFA), deviations from uniform power-law scaling were quantified. Our findings point out to a significant non-uniform scaling behavior in ULF geomagnetic data in relationship with the occurrence of intense seismic clusters.     

Detrended fluctuation analysis and Kolmogorov–Sinai entropy of electroencephalogram signals

We measured the electroencephalogram (EEG) of young students in the relaxed state and in the state of the mathematical activities. We applied the detrended fluctuation analysis and Kolmogorov–Sinai entropy (KSE) in the EEG signals. We found that the detrended fluctuation functions follow a power law with Hurst exponents larger than 1/2. The Hurst exponents enhanced at all EEG channels in the state of mathematical activities. The KSE in the relaxed state is larger than those in the state of the mathematical activities. These indicate that the entropy is enhanced in the disorder state of the brain.     

From Shorter to Longer Timescales: Converging Integrated Information Theory (IIT) with the Temporo-Spatial Theory of Consciousness (TTC)

Time is a key element of consciousness as it includes multiple timescales from shorter to longer ones. This is reflected in our experience of various short-term phenomenal contents at discrete points in time as part of an ongoing, more continuous, and long-term ‘stream of consciousness’. Can Integrated Information Theory (IIT) account for this multitude of timescales of consciousness? According to the theory, the relevant spatiotemporal scale for consciousness is the one in which the system reaches the maximum cause-effect power; IIT currently predicts that experience occurs on the order of short timescales, namely, between 100 and 300 ms (theta and alpha frequency range). This can well account for the integration of single inputs into a particular phenomenal content. However, such short timescales leave open the temporal relation of specific phenomenal contents to others during the course of the ongoing time, that is, the stream of consciousness. For that purpose, we converge the IIT with the Temporo-spatial Theory of Consciousness (TTC), which, assuming a multitude of different timescales, can take into view the temporal integration of specific phenomenal contents with other phenomenal contents over time. On the neuronal side, this is detailed by considering those neuronal mechanisms driving the non-additive interaction of pre-stimulus activity with the input resulting in stimulus-related activity. Due to their non-additive interaction, the single input is not only integrated with others in the short-term timescales of 100–300 ms (alpha and theta frequencies) (as predicted by IIT) but, at the same time, also virtually expanded in its temporal (and spatial) features; this is related to the longer timescales (delta and slower frequencies) that are carried over from pre-stimulus to stimulus-related activity. Such a non-additive pre-stimulus-input interaction amounts to temporo-spatial expansion as a key mechanism of TTC for the constitution of phenomenal contents including their embedding or nesting within the ongoing temporal dynamic, i.e., the stream of consciousness. In conclusion, we propose converging the short-term integration of inputs postulated in IIT (100–300 ms as in the alpha and theta frequency range) with the longer timescales (in delta and slower frequencies) of temporo-spatial expansion in TTC.     

De Haas-van Alphen oscillations in the quasi-two-dimensional organic metal (BEDO-TTF)5[CsHg(SCN)4]2

The magnetization oscillations in the quasi-two-dimensional organic metal (BEDO-TTF)₅[CsHg(SCN)₄]₂ are thoroughly investigated over a wide range of magnetic field directions at different temperatures down to 0.4 K. The results obtained are in good agreement with the shape and sizes of the Fermi surface calculated from the x-ray diffraction data. Apart from the fundamental frequencies, the combination frequencies are found in the magnetization oscillation spectrum. It is demonstrated that these combination frequencies are governed by the motion of charge carriers along the real closed orbits inside the network of magnetic breakdown orbits formed under the action of the magnetic field. It is uniquely established that the combination frequencies previously revealed in the magnetoresistance oscillation spectrum of the same metal are associated with the quantum interference effect. The angular dependences of the oscillation amplitude exhibit minima, which are explained by the spin splitting of the Landau levels.     

Electron temperature fluctuation in the HT-7 Tokamak plasma observed by electron cyclotron emission imaging

The fluctuation of the electron temperature has been measured by using the electron cyclotron emission imaging in the Hefei Tokamak-7 (HT-7) plasma. The electron temperature fluctuation with a broadband spectrum shows that it propagates in the electron diamagnetic drift direction, and the mean poloidal wave-number $\bar{k}_{\theta}$is calculated to be about 1.58 cm^-1, or \bar{k}_θ ρ_s≈ 0.34. It indicates that the fluctuation should come from the electron drift wave turbulence. The linear global scaling of the electron temperature fluctuation with the gradient of electron temperature is consistent with the mixing length scale qualitatively. Evolution of spectrum of the fluctuation during the sawtooth oscillation phases is investigated, and the fluctuation is found to increase with the gradient of electron temperature increasing during most phases of the sawtooth oscillation. The results indicate that the electron temperature gradient is probably the driver of the fluctuation enhancement. The steady heat flux driven by electron temperature fluctuation is estimated and compared with the results from power balance estimation.     

基于双树复小波变换的非平稳时间序列去趋势波动分析方法

多重分形去趋势波动分析是研究非平稳时间序列非均匀性和奇异性的有效工具, 针对该方法中趋势项难以确定的问题, 提出一种基于双树复小波变换的方法, 实现了非平稳信号的多重分形自适应去趋势波动分析. 利用双树复小波变换提取信号的多尺度趋势和波动信息, 通过小波系数的希尔伯特变换确定每个时间尺度不重叠子区间的长度, 使多重分形分析具有信号自适应性及较高的计算效率. 以具有解析形式分形特征的倍增级联信号和分数布朗运动时间序列为例验证本文方法的有效性, 所得结果与解析解相吻合. 与传统的多项式去趋势多重分形方法相比, 本文方法根据信号自身特点自适应地确定信号的趋势和不重叠等长度子区间长度, 所得结果更加精确. 对倍增级联信号时间序列取不同的长度, 验证了算法的稳定性. 分别与基于极大重叠离散小波变换和离散小波变换多重分形方法进行比较, 表明本文方法具有更精确的结果和更快的运算速度.     

On the relation between thermostatted ring-polymer molecular dynamics and exact quantum dynamics

Here we obtain the explicit difference in the propagator between thermostatted ring-polymer molecular dynamics (TRPMD) and Matsubara dynamics, a recently derived form of linearisation which conserves the quantum Boltzmann distribution. Examination of this approximation leads to the new results that the TRPMD force on the centroid is identical to the Matsubara force on the centroid, and that (in a harmonic potential) the friction matrix can be chosen to produce either the correct oscillation frequency of the higher ring-polymer normal modes or the correct maximum in their position spectrum. This is illustrated with the position-squared autocorrelation function where TRPMD improves upon other similar methods. However, no physical choice of friction resolves qualitatively incorrect fluctuation dynamics at barriers. These results are broadly consistent with previous numerical studies and advise the use of TRPMD for spectra.