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Spontaneous EEG contains important information about neuronal network properties that is valuable for understanding different neurological and psychiatric conditions. Rett syndrome (RTT) is a rare neurodevelopmental disorder, caused by mutation in the MECP2 gene. RTT is characterized by severe motor impairments that prevent adequate assessment of cognitive functions. Here we probe EEG parameters obtained in no visual input condition from a 28-channels system in 23 patients with Rett Syndrome and 38 their typically developing peers aged 3–17 years old. Confirming previous results, RTT showed a fronto-central theta power (4–6.25 Hz) increase that correlates with a progression of the disease. Alpha power (6.75–11.75 Hz) across multiple regions was, on the contrary, decreased in RTT, also corresponding to general background slowing reported previously. Among novel results we found an increase in gamma power (31–39.5 Hz) across frontal, central and temporal electrodes, suggesting elevated excitation/inhibition ratio. Long-range temporal correlation measured by detrended fluctuation analysis within 6–13 Hz was also increased, pointing to a more predictable oscillation pattern in RTT. Overall measured EEG parameters allow to differentiate groups with high accuracy, ROC AUC value of 0.92 ± 0.08, indicating clinical relevance. [ABSTRACT FROM AUTHOR]

Spontaneous EEG contains important information about neuronal network properties that is valuable for understanding different neurological and psychiatric conditions. Rett syndrome (RTT) is a rare neurodevelopmental disorder, caused by mutation in the MECP2 gene. RTT is characterized by severe motor impairments that prevent adequate assessment of cognitive functions. Here we probe EEG parameters obtained in no visual input condition from a 28-channels system in 23 patients with Rett Syndrome and 38 their typically developing peers aged 3–17 years old. Confirming previous results, RTT showed a fronto-central theta power (4–6.25 Hz) increase that correlates with a progression of the disease. Alpha power (6.75–11.75 Hz) across multiple regions was, on the contrary, decreased in RTT, also corresponding to general background slowing reported previously. Among novel results we found an increase in gamma power (31–39.5 Hz) across frontal, central and temporal electrodes, suggesting elevated excitation/inhibition ratio. Long-range temporal correlation measured by detrended fluctuation analysis within 6–13 Hz was also increased, pointing to a more predictable oscillation pattern in RTT. Overall measured EEG parameters allow to differentiate groups with high accuracy, ROC AUC value of 0.92 ± 0.08, indicating clinical relevance. [ABSTRACT FROM AUTHOR]

Forecasting a system's behavior is an essential task encountering the complex systems theory. Machine learning offers supervised algorithms, e.g., recurrent neural networks and reservoir computers that predict the behavior of model systems whose states consist of multidimensional time series. In real life, we often have limited information about the behavior of complex systems. The brightest example is the brain neural network described by the electroencephalogram. Forecasting the behavior of these systems is a more challenging task but provides a potential for real-life application. Here, we trained reservoir computer to predict the macroscopic signal produced by the network of phase oscillators. The Lyapunov analysis revealed the chaotic nature of the signal and reservoir computer failed to forecast it. Augmenting the feature space using Takkens' theorem improved the quality of forecasting. RC achieved the best prediction score when the number of signals coincided with the embedding dimension estimated via the nearest false neighbors method. We found that short-time prediction required a large number of features, while long-time prediction utilizes a limited number of features. These results refer to the bias-variance trade-off, an important concept in machine learning. [ABSTRACT FROM AUTHOR]

The spectrum of Lyapunov exponents is powerful tool for the analysis of the complex system dynamics. In the general framework of nonlinear dynamics, a number of the numerical techniques have been developed to obtain the spectrum of Lyapunov exponents for the complex temporal behavior of the systems with a few degree of freedom. Unfortunately, these methods cannot be applied directly to analysis of complex spatio-temporal dynamics of plasma devices which are characterized by the infinite phase space, since they are the spatially extended active media. In the present paper, we propose the method for the calculation of the spectrum of the spatial Lyapunov exponents (SLEs) for the spatially extended beam-plasma systems. The calculation technique is applied to the analysis of chaotic spatio-temporal oscillations in three different beam-plasma model: (1) simple plasma Pierce diode, (2) coupled Pierce diodes, and (3) electron-wave system with backward electromagnetic wave. We find an excellent agreement between the system dynamics and the behavior of the spectrum of the spatial Lyapunov exponents. Along with the proposed method, the possible problems of SLEs calculation are also discussed. It is shown that for the wide class of the spatially extended systems, the set of quantities included in the system state for SLEs calculation can be reduced using the appropriate feature of the plasma systems. [ABSTRACT FROM AUTHOR]