Novel Approach for Time-Varying Bispectral Analysis of Non-Stationary EEG Signals

novel parametric method, based on the non-Gaussian AR model, is proposed for the partition of on-stationary EEG data into a finite set of third-order stationary segments. With the assumption of piecewise third-order stationarity of the signal, a series of parametric bispectral estimations of the non-stationary EEG data can be performed so as to describe the time-varying non-Gaussian nonlinear characteristics of the observed EEG signals. A practical method based on the fitness of third-order statistics of the signal by using the non-Gaussian AR model, together with an algorithm with CMI is presented. The experimental results with several simulations and clinical EEG signals have also been investigated and discussed. The results show successful performance of the proposed method in estimating the time-varying bispectral structures of the EEG signals.published_or_final_versio

Reconstructing time-dependent dynamics

The usefulness of the information extracted from biomedical data relies heavily on the underlying theory of the methods used in its extraction. The assumptions of stationarity and autonomicity traditionally applied to dynamical systems break down when considering living systems, due to their inherent time-variability. Living systems are thermodynamically open, and thus constantly interacting with their environment. This results in highly nonlinear, time-dependent dynamics. The aim of signal analysis is to gain insight into the behaviour of the system from which the signal originated. Here, various analysis methods for the characterization of signals and their underlying non-autonomous dynamics are presented, incorporating time-frequency analysis, time-domain decomposition of nonlinear modes, and methods to study mutual interactions and couplings using dynamical Bayesian inference, wavelet-bispectral and time-localised coherence, and entropy and information-based analysis. The recent introduction of chronotaxic systems provides a theoretical framework in which dynamical systems can have amplitudes and frequencies which are time-varying, yet stable, matching well the characteristics of living systems. We demonstrate that considering this theory of chronotaxic systems whilst applying the presented methods results in an approach for the reconstruction of the dynamics of living systems across many scales

Wavelet analysis on transient behaviour of tidal amplitude fluctuations observed by meteor radar in the lower thermosphere above Bulgaria

International audienceOn the basis of bispectral analysis applied to the hourly data set of neutral wind measured by meteor radar in the MLT region above Bulgaria it was demonstrated that nonlinear processes are frequently and regularly acting in the mesopause region. They contribute significantly to the short-term tidal variability and are apparently responsible for the observed complicated behavior of the tidal characteristics. A Morlet wavelet transform is proposed as a technique for studying nonstationary signals. By simulated data it was revealed that the Morlet wavelet transform is especially convenient for analyzing signals with: (1) a wide range of dominant frequencies which are localized in different time intervals; (2) amplitude and frequency modulated spectral components, and (3) singular, wave-like events, observed in the neutral wind of the MLT region and connected mainly with large-scale disturbances propagated from below. By applying a Morlet wavelet transform to the hourly values of the amplitudes of diurnal and semidiurnal tides the basic oscillations with periods of planetary waves (1.5-20 days), as well as their development in time, are obtained. A cross-wavelet analysis is used to clarify the relation between the tidal and mean neutral wind variability. The results of bispectral analysis indicate which planetary waves participated in the nonlinear coupling with the atmospheric tides, while the results of cross-wavelet analysis outline their time intervals if these interactions are local

Nonlinear System Identification of Neural Systems from Neurophysiological Signals

The human nervous system is one of the most complicated systems in nature. Complex nonlinear behaviours have been shown from the single neuron level to the system level. For decades, linear connectivity analysis methods, such as correlation, coherence and Granger causality, have been extensively used to assess the neural connectivities and input-output interconnections in neural systems. Recent studies indicate that these linear methods can only capture a small amount of neural activities and functional relationships, and therefore cannot describe neural behaviours in a precise or complete way. In this review, we highlight recent advances in nonlinear system identification of neural systems, corresponding time and frequency domain analysis, and novel neural connectivity measures based on nonlinear system identification techniques. We argue that nonlinear modelling and analysis are necessary to study neuronal processing and signal transfer in neural systems quantitatively. These approaches can hopefully provide new insights to advance our understanding of neurophysiological mechanisms underlying neural functions. These nonlinear approaches also have the potential to produce sensitive biomarkers to facilitate the development of precision diagnostic tools for evaluating neurological disorders and the effects of targeted intervention