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

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.

Quantifying Chaos by Various Computational Methods. Part 1: Simple Systems.

The aim of the paper was to analyze the given nonlinear problem by different methods of computation of the Lyapunov exponents (Wolf method, Rosenstein method, Kantz method, the method based on the modification of a neural network, and the synchronization method) for the classical problems governed by difference and differential equations (Hénon map, hyperchaotic Hénon map, logistic map, Rössler attractor, Lorenz attractor) and with the use of both Fourier spectra and Gauss wavelets. It has been shown that a modification of the neural network method makes it possible to compute a spectrum of Lyapunov exponents, and then to detect a transition of the system regular dynamics into chaos, hyperchaos, and others. The aim of the comparison was to evaluate the considered algorithms, study their convergence, and also identify the most suitable algorithms for specific system types and objectives.

Quantifying Chaos by Various Computational Methods. Part 2: Vibrations of the Bernoulli-Euler Beam Subjected to Periodic and Colored Noise.

In this part of the paper, the theory of nonlinear dynamics of flexible Euler-Bernoulli beams (the kinematic model of the first-order approximation) under transverse harmonic load and colored noise has been proposed. It has been shown that the introduced concept of phase transition allows for further generalization of the problem. The concept has been extended to a so-called noise-induced transition, which is a novel transition type exhibited by nonequilibrium systems embedded in a stochastic fluctuated medium, the properties of which depend on time and are influenced by external noise.

A new look at the essence of the imaging photoplethysmography.

Photoplethysmography (PPG) is a noninvasive optical method accepted in the clinical use for measurements of arterial oxygen saturation. It is widely believed that the light intensity after interaction with the biological tissue in vivo is modulated at the heartbeat frequency mainly due to pulsatile variations of the light absorption caused by arterial blood-volume pulsations. Here we report experimental observations, which are not consistent with this model and demonstrate the importance of elastic deformations of the capillary bed in the formation of the PPG waveform.