Nonlinear data analysis of experimental (EEG) data and comparison with theoretical (ANN) data

Das, Alaka; Das, Pritha; Roy, Aidan

doi:10.1002/cplx.10024

Cited by 10 publications

(6 citation statements)

References 34 publications

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“…Discussion on D and the program used to calculate it have been discussed in our earlier works. 13 In this paper, we have 15 Ds 9one from each run) for each file and we present the minimum (Min D) and maximum (Max D) of them for each sample in Table 1 and values of parameters used in the calculation are given in Table 2. …”

Section: Fractal Dimension (D)mentioning

confidence: 99%

Fractal Analysis of Different Eastern and Western Musical Instruments

Das¹,

Das

2006

Fractals

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In this paper, we attempt musical analysis by measuring fractal dimension (D) of musical pieces played by several musical instruments. We collected solo performances of popular instruments of Western and Eastern origin as samples. We attempted usual spectral analysis of the selected clips to observe peaks of fundamental and harmonics in frequency regime. After appropriate processing, we converted them into time series data sets and computed their fractal dimension. Based on our results, we conclude that instrumental musical sounds may have higher Ds than those computed from vocal performances of different types of Indian songs.

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Section: Fractal Dimension (D)mentioning

confidence: 99%

Fractal Analysis of Different Eastern and Western Musical Instruments

Das¹,

Das

2006

Fractals

Self Cite

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“…e CML optimization method based on the calculation of local and global Lyapunov exponents calculated by the Sano-Sawada method is presented. Based on the results of studying of chaotic EEG signals using the first Lyapunov exponent, the authors of [23,24] came to the conclusion that the Lyapunov exponent is a reliable chaos measure for low-dimensional or deterministic data (Lorentz system), but when studying data with a high dimension or stochastic nature (EEG signals), it does not give reliable results. In [25], a system for predicting epileptic seizures based on the extraction of correlation dimension, correlation entropy, noise level, Lempel-Ziv complexity, and the highest Lyapunov exponent STLmax for ten patients with focal hippocampal epilepsy was presented.…”

Section: Introductionmentioning

confidence: 99%

EEG Analysis in Structural Focal Epilepsy Using the Methods of Nonlinear Dynamics (Lyapunov Exponents, Lempel–Ziv Complexity, and Multiscale Entropy)

Yakovleva

Кутепов

Karas

et al. 2020

The Scientific World Journal

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This paper analyzes a case with the patient having focal structural epilepsy by processing electroencephalogram (EEG) fragments containing the “sharp wave” pattern of brain activity. EEG signals were recorded using 21 channels. Based on the fact that EEG signals are time series, an approach has been developed for their analysis using nonlinear dynamics tools: calculating the Lyapunov exponent’s spectrum, multiscale entropy, and Lempel–Ziv complexity. The calculation of the first Lyapunov exponent is carried out by three methods: Wolf, Rosenstein, and Sano–Sawada, to obtain reliable results. The seven Lyapunov exponent spectra are calculated by the Sano–Sawada method. For the observed patient, studies showed that with medical treatment, his condition did not improve, and as a result, it was recommended to switch from conservative treatment to surgical. The obtained results of the patient’s EEG study using the indicated nonlinear dynamics methods are in good agreement with the medical report and MRI data. The approach developed for the analysis of EEG signals by nonlinear dynamics methods can be applied for early detection of structural changes.

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“…In , two chaotic indicators namely the correlation dimension and the Lyapunov exponent methods have been applied for the daily river flow of Kizilirmak River. Nonlinear data analysis of experimental EEG signals has been performed in and comparison with theoretical neural networks has been presented.…”

Section: Introductionmentioning

confidence: 99%

Chaos and complexity in mine grade distribution series detected by nonlinear approaches

Aghababa

Sharif

2016

Complexity

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In this article, the underlying dynamics of treating grade distribution is interpreted as a chaotic system instead of a stochastic system for a better understanding. Here, we study the behavior of grade distribution spatial series acquired at the Chadormalu mine in Bafgh city of Iran to distinguish the possible existence of low‐dimensional deterministic chaos. This work applies a variety of nonlinear techniques for detecting the chaotic nature of the grade distribution spatial series and adopts a nonlinear prediction method for predicting the future of the grade distributions. First, the delay time dimension is computed using auto mutual information function to reconstruct the strange attractors. Then, the dimensionality of the trajectories is obtained using Cao's method and, correspondingly, the correlation dimension method is adopted to quantify the embedding dimension. The low embedding dimensions achieved from these methods show the existence of low dimensional chaos in the mining data. Next, the high sensitivity to initial conditions is evaluated using the maximal Lyapunov exponent criterion. Positive Lyapunov exponents obtained demonstrate the exponential divergence of the trajectories and hence the unpredictability of the data. Afterward, the nonlinear surrogate data test is done to further verify the nonlinear structure of the grade distribution series. This analysis provides considerable evidence for the being of low‐dimensional chaotic dynamics underlying the mining spatial series. Lastly, a nonlinear prediction scheme is carried out to predict the grade distribution series. Some computer simulations are presented to illustrate the efficiency of the applied nonlinear tools. © 2016 Wiley Periodicals, Inc. Complexity 21: 355–369, 2016

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Nonlinear data analysis of experimental (EEG) data and comparison with theoretical (ANN) data

Abstract: In this article, nonlinear dynamical tools such as largest Lyapunov exponents (LE),

Cited by 10 publications

References 34 publications

Fractal Analysis of Different Eastern and Western Musical Instruments

Fractal Analysis of Different Eastern and Western Musical Instruments

EEG Analysis in Structural Focal Epilepsy Using the Methods of Nonlinear Dynamics (Lyapunov Exponents, Lempel–Ziv Complexity, and Multiscale Entropy)

Chaos and complexity in mine grade distribution series detected by nonlinear approaches

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