scholarly journals Analysis of EEG Data Using Complex Geometric Structurization

2021 ◽  
pp. 1-28
Author(s):  
E. A. Kwessi ◽  
L. J. Edwards
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Time Series Data ◽  
Health Condition ◽  
Series Data ◽  
Complex Structures ◽  
Embedding Theory ◽  
Novel Approach ◽  
Eeg Data ◽  
Electroencephalogram Eeg

Abstract Electroencephalogram (EEG) is a common tool used to understand brain activities. The data are typically obtained by placing electrodes at the surface of the scalp and recording the oscillations of currents passing through the electrodes. These oscillations can sometimes lead to various interpretations, depending on, for example, the subject's health condition, the experiment carried out, the sensitivity of the tools used, or human manipulations. The data obtained over time can be considered a time series. There is evidence in the literature that epilepsy EEG data may be chaotic. Either way, the Embedding Theory in dynamical systems suggests that time series from a complex system could be used to reconstruct its phase space under proper conditions. In this letter, we propose an analysis of epilepsy EEG time series data based on a novel approach dubbed complex geometric structurization. Complex geometric structurization stems from the construction of strange attractors using Embedding Theory from dynamical systems. The complex geometric structures are themselves obtained using a geometry tool, the α-shapes from shape analysis. Initial analyses show a proof of concept in that these complex structures capture the expected changes brain in lobes under consideration. Further, a deeper analysis suggests that these complex structures can be used as biomarkers for seizure changes.

scholarly journals Uncertainty quantification of the effects of biotic interactions on community dynamics from nonlinear time-series data

2018 ◽  
Vol 15 (147) ◽  
pp. 20180695 ◽  
Author(s):  
Simone Cenci ◽  
Serguei Saavedra
Keyword(s):  
Time Series ◽  
Community Dynamics ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Model Averaging ◽  
Biotic Interactions ◽  
Series Data ◽  
Time Intervals ◽  
Novel Approach ◽  
Data Generating Process

Biotic interactions are expected to play a major role in shaping the dynamics of ecological systems. Yet, quantifying the effects of biotic interactions has been challenging due to a lack of appropriate methods to extract accurate measurements of interaction parameters from experimental data. One of the main limitations of existing methods is that the parameters inferred from noisy, sparsely sampled, nonlinear data are seldom uniquely identifiable. That is, many different parameters can be compatible with the same dataset and can generalize to independent data equally well. Hence, it is difficult to justify conclusive assertions about the effect of biotic interactions without information about their associated uncertainty. Here, we develop an ensemble method based on model averaging to quantify the uncertainty associated with the effect of biotic interactions on community dynamics from non-equilibrium ecological time-series data. Our method is able to detect the most informative time intervals for each biotic interaction within a multivariate time series and can be easily adapted to different regression schemes. Overall, this novel approach can be used to associate a time-dependent uncertainty with the effect of biotic interactions. Moreover, because we quantify uncertainty with minimal assumptions about the data-generating process, our approach can be applied to any data for which interactions among variables strongly affect the overall dynamics of the system.

scholarly journals Extracting Nonlinear Dynamics from Psychological and Behavioral Time Series Through HAVOK Analysis

2020 ◽  
Author(s):  
Robert Glenn Moulder ◽  
Elena Martynova ◽  
Steven M. Boker
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Time Series Data ◽  
Nonlinear Dynamical Systems ◽  
Series Data ◽  
Alternative View ◽  
Unified Framework ◽  
Nonlinear Dynamical ◽  
Depth Analysis ◽  
Analysis Of Time Series

Analytical methods derived from nonlinear dynamical systems, complexity, and chaos theories offer researchers a framework for in-depth analysis of time series data. However, relatively few studies involving time series data obtained from psychological and behavioral research employ such methods. This paucity of application is due to a lack of general analysis frameworks for modeling time series data with strong nonlinear components. In this article, we describe the potential of Hankel alternative view of Koopman (HAVOK) analysis for solving this issue. HAVOK analysis is a unified framework for nonlinear dynamical systems analysis of time series data. By utilizing HAVOK analysis, researchers may model nonlinear time series data in a linear framework while simultaneously reconstructing attractor manifolds and obtaining a secondary time series representing the amount of nonlinear forcing occurring in a system at any given time. We begin by showing the mathematical underpinnings of HAVOK analysis and then show example applications of HAVOK analysis for modeling time series data derived from real psychological and behavioral studies.

scholarly journals Observation error covariance specification in dynamical systems for data assimilation using recurrent neural networks

2021 ◽  
Author(s):  
Sibo Cheng ◽  
Mingming Qiu
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Dynamical Systems ◽  
Data Assimilation ◽  
Recurrent Neural Networks ◽  
Time Series Data ◽  
Series Data ◽  
Observation Data ◽  
Observation Error ◽  
Error Covariance

AbstractData assimilation techniques are widely used to predict complex dynamical systems with uncertainties, based on time-series observation data. Error covariance matrices modeling is an important element in data assimilation algorithms which can considerably impact the forecasting accuracy. The estimation of these covariances, which usually relies on empirical assumptions and physical constraints, is often imprecise and computationally expensive, especially for systems of large dimensions. In this work, we propose a data-driven approach based on long short term memory (LSTM) recurrent neural networks (RNN) to improve both the accuracy and the efficiency of observation covariance specification in data assimilation for dynamical systems. Learning the covariance matrix from observed/simulated time-series data, the proposed approach does not require any knowledge or assumption about prior error distribution, unlike classical posterior tuning methods. We have compared the novel approach with two state-of-the-art covariance tuning algorithms, namely DI01 and D05, first in a Lorenz dynamical system and then in a 2D shallow water twin experiments framework with different covariance parameterization using ensemble assimilation. This novel method shows significant advantages in observation covariance specification, assimilation accuracy, and computational efficiency.

scholarly journals Entropy Analysis of High-Definition Transcranial Electric Stimulation Effects on EEG Dynamics

2019 ◽  
Vol 9 (8) ◽  
pp. 208 ◽  
Author(s):  
Diego C. Nascimento ◽  
Gabriela Depetri ◽  
Luiz H. Stefano ◽  
Osvaldo Anacleto ◽  
Joao P. Leite ◽  
...  
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Statistical Tests ◽  
Series Data ◽  
Entropy Analysis ◽  
Summary Statistic ◽  
High Definition ◽  
Stationary Characteristic ◽  
Linear Dynamical Systems ◽  
Eeg Data

A foundation of medical research is time series analysis—the behavior of variables of interest with respect to time. Time series data are often analyzed using the mean, with statistical tests applied to mean differences, and has the assumption that data are stationary. Although widely practiced, this method has limitations. Here we present an alternative statistical approach with sample analysis that provides a summary statistic accounting for the non-stationary nature of time series data. This work discusses the use of entropy as a measurement of the complexity of time series, in the context of Neuroscience, due to the non-stationary characteristic of the data. To elucidate our argument, we conducted entropy analysis on a sample of electroencephalographic (EEG) data from an interventional study using non-invasive electrical brain stimulation. We demonstrated that entropy analysis could identify intervention-related change in EEG data, supporting that entropy can be a useful “summary” statistic in non-linear dynamical systems.

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