Scientists Explain How To Understand The Complex Behavior Of Neural Networks

A team of scientists reviewed in the monograph the application of wavelet analysis to the study of various

neurophysiological data - from recordingsthe dynamics of individual neurons to the collective activity of the entire neural network of the brain. Wavelet analysis is an alternative to classical spectral analysis, but wavelets allow you to generalize spectral analysis data and consider the behavior of a neural network simultaneously on different time scales, highlighting what is most important and eliminating unnecessary rhythms and noise. Thus, the researchers showed how it is possible to take a fresh look at the complex behavior of neural systems at various levels: from the microscopic dynamics of individual nerve cells, that is, analysis of recordings of the activity of individual neurons, to the macroscopic dynamics of global neural networks of the brain - analysis of electroencephalogram and magnetoencephalography data.

The creation of wavelet theory was one ofthe most important events in mathematics over the past few decades. This is probably the only concept that has been used in almost all areas of fundamental science from the theory of elementary particles to biophysics and geophysics. Wavelets are widely used for image recognition and compression, complex signal analysis and synthesis, studying turbulent flows, extracting features from biological and medical data, etc.

Alexander Khramov, Head of the Laboratory of Neuroscience and Cognitive Technologies at Innopolis University

The book includes the latest topics that are relevantfor a wide audience working in experimental and computational neuroscience. The monograph contains 9 chapters, which provide a mathematical introduction to wavelet analysis and an overview of research in this new topic in the field of neuroscience: microdynamics using the example of analyzing the activity of individual neurons using wavelets, hybrid approaches based on wavelets and machine learning, neuronal activity and brain microdynamics with epileptic activity and more.

Scientists wrote a book based on the resultsown research in this area. In 2015, the first edition of the monograph was published; in the second edition, the authors updated the information, revised the existing chapters and wrote new ones, including based on the research they conducted at Innopolis University.

“The monograph can be used as a textbook fornon-specialists, graduate students and undergraduates. The book is an important resource for neurophysiologists, biophysicists and mathematicians familiar with nonlinear dynamical systems and data processing, as well as for graduate students specializing in these and related fields, ”added Alexander Khramov.

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