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Electromyograms
Published in A. Bakiya, K. Kamalanand, R. L. J. De Britto, Mechano-Electric Correlations in the Human Physiological System, 2021
A. Bakiya, K. Kamalanand, R. L. J. De Britto
Hurst exponent (H) is a quantification of long-term memory of the time sequence in biological signals and is commonly referred as index of dependence. Hurst exponent is a quantification of degree of self-similarity of the time series (Hurst, 1951). If the Hurst exponent value is within the intervals of 0.5 < H < 1, then the time series can be considered as fractals (Positive autocorrelation). If the Hurst exponent value is equal to 0.5, then the time series follows Brownian motion (uncorrelated series). If the Hurst exponent value is within the interval of 0 < H < 0.5, then the time series can be considered as negative autocorrelation (Gospodinov et al., 2019). There are two different groups to estimate the Hurst exponent of biological signals, namely, time-based methods and frequency-based methods. Time-based methods include rescaled adjusted range statistics method (R/S method), index of dispersion for counts, variance-time plot and wavelet-based methods. Periodogram method and Whittle method are the frequency-based methods (Gospodinov et al., 2019).
Methods of Digital Analysis and Interpretation
Published in Victor Raizer, Optical Remote Sensing of Ocean Hydrodynamics, 2019
where =p denotes equality in statistical sense, ξ(r→) is random field, r→={x,y} is coordinate vector, λ>0 is scaling factor, and H is the Hurst exponent or index (Mandelbrot 1983). The Hurst exponent is a statistical measure used to classify time series; it is calculated by rescaled range analysis (R/S) (e.g.,Addison 1997; Weisstein 2003). The Hurst exponent for high-dimensional fractals can be estimated using algorithm (Carbone 2007).
Chapter 11: Miscellaneous Topics Used for Engineering Problems
Published in Abul Hasan Siddiqi, Mohamed Al-Lawati, Messaoud Boulbrachene, Modern Engineering Mathematics, 2017
Abul Hasan Siddiqi, Mohamed Al-Lawati, Messaoud Boulbrachene
The value of Hurst exponent lies between 0 and 1. A value of 0.5 indicates a true random walk (a Brownian motion time series). In a random walk, there is no correlation between any element and future elements. A Hurst exponent value 0.5 < H < 1 indicates persistent behavior (for example a positive auto-correlation). If there is increase of time step there will probably be an increase from ti to ti+1. The same is true of decreases, where a decrease will tend to follow a decrease. A Hurst exponent value 0 < H < 0.5 will exist for a time series with anti-persistent behavior (or negative auto-correlation). Here an increase will tend to be followed by a decrease or a decrease will be followed by an increase. The larger the Hurst exponent, the smaller is the fractal dimension and the smoother is the surface.
Self-organized criticality in manufacturing system unscheduled downtime series and its application to major failure prediction
Published in Quality Engineering, 2023
Bo Li, Hengchang Liu, Feng Yang, Nan Jiang
The Hurst exponent is a fractal statistics parameter, which reflects the system’s long-range "remembering" character or its long-range correlation character. The rescaled-range (R/S) analysis method is commonly adopted to calculate the Hurst value. For an observed time-series data of length T, the length of subsequence was controlled by scale length Range R and standard deviation S are calculated to get the rescaled range value of the subsequence. The detailed process of the calculation can be found in (Price and Newman 2001). Then, by changing the scale length n and repeating the previous steps, a series of scales of length n and their corresponding scale statistical sequence are calculated. Assumed that the sample sequence is divided into subsequences with length the R/S statistics of the th subsequence is:
Dynamics of Premixed Flames Near Lean and Rich Blowout
Published in Combustion Science and Technology, 2022
Somnath De, Sabyasachi Mondal, Arijit Bhattacharya, Sirshendu Mondal, Achintya Mukhopadhyay, Swarnendu Sen
Hurst exponent also measures the long-term memory or correlation of a time series and thus, it can also be referred to as ‘index of long-range dependence’ (Mishura and Zili 2018). H can quantify the tendency of a time series to regress strongly to mean (anti-persistent or mean reversion) or to cluster (persistent or trending pattern) in a specific direction (Kantelhardt et al. 2002). Generally, H < 0.5 signifies the anti-persistent nature of time signal where long-term switching between high and low values in adjacent pairs can be observed. The trending or persistent nature of signal (H > 0.5) indicates the long-term positive auto-correlation where high value can be followed by another high value in the time series. For an uncorrelated time series, H is 0.5.
Temporal detection of sharp landslide deformation with ensemble-based LSTM-RNNs and Hurst exponent
Published in Geomatics, Natural Hazards and Risk, 2021
Huajin Li, Qiang Xu, Yusen He, Xuanmei Fan, He Yang, Songlin Li
The computational results are derived which can be attributed to the following three reasons: First, the dataset utilized in this study are very homogeneous and all case studies are from one macro region which all landslides are induced by water. There exists a strong dependency between the instant displacement and the water-related features according to the previous studies (Li et al. 2020b; Lian et al. 2018; Tao et al. 2020; Wang et al. 2019; Zhu et al. 2020). Hence, for other types of landslides or other time-series dataset, the accuracy and effectiveness still await further validation. Second, the triggering factors as precipitation and water reservoir levels have strong seasonal patterns and are also autoregressive. These temporal patterns are easy to be captured by the EN-LSTM algorithm which is designed to effectively capture the temporal features. For other non-water induced landslide, the triggering factors may not have such explicit temporal pattern which may increase the difficulty for training an accuracy regressors for predicting future landslide displacement. Third, all sharp landslide deformation with large instant displacement values can be perceived as statistical outliers compared with the other displacement patterns. The Hurst exponent is designed to capture such outliers in the temporal domain and has been widely applied in financial engineering sectors such as high-frequency trading systems. For the similar time-series problems, the proposed framework could be a feasible solution as well.