Many neuro-degenerative diseases are difficult to diagnose in their early stages. For example, early diagnosis of Mild Cognitive Impairment (MCI) requires a wide variety of tests to distinguish MCI symptoms and normal consequences of aging. In this article, we use the wavelet–skeleton approach to find some characteristic patterns in the electroencephalograms (EEGs) of healthy adult patients and patients with cognitive dysfunctions. We analyze the EEG activity recorded during natural sleep of 11 elderly patients aged between 60 and 75, six of whom have mild cognitive impairment, and apply a nonlinear analysis method based on continuous wavelet transformskeletons. Our studies show that a comprehensive analysis of EEG signals of the entire sleep state allows us to identify a significant decrease in the average duration of oscillatory patterns in the frequency band [12; 14] Hz in the presence of mild cognitive impairment. Thus, the changes in this frequency range can be interpreted as related to the activity in the motor cortex, as a candidate for developing the criteria for early objective MCI.

In this paper, we show the possibility of creating and identifying the features of an artificial neural network (ANN), which consists of mathematical models of biological neurons. The FitzHugh–Nagumo (FHN) system is used as a paradigmatic model demonstrating basic neuron activities. First, in order to reveal how biological neurons can be embedded within an ANN, we train the ANN with nonlinear neurons to solve a basic image recognition problem with an MNIST database; next, we describe how FHN systems can be introduced into this trained ANN. After all, we show that an ANN with FHN systems inside can be successfully trained with improved accuracy comparing with first trained ANN and then with inserted FHN systems. This approach opens up great opportunities in terms of the direction of analog neural networks, in which artificial neurons can be replaced by more appropriate biological ones.

Stationary Modes and Localized Metastable States in a Triangular Lattice of Active Particles, Sergeev K. S., Dmitriev S. V., Korznikova E. A., Chetverikov A. P.