Wavelets in Neuroscience

This book examines theoretical and applied aspects of wavelet analysis in neurophysics, describing in detail different practical applications of the wavelet theory in the areas of neurodynamics and neurophysiology and providing a review of fundamental work that has been carried out in these fields over the last decade.

Chapters 1 and 2 introduce and review the relevant foundations of neurophysics and wavelet theory, respectively, pointing on one hand to the various current challenges in neuroscience and introducing on the other the mathematical techniques of the wavelet transform in its two variants (discrete and continuous) as a powerful and versatile tool for investigating the relevant neuronal dynamics.

Chapter 3 then analyzes results from examining individual neuron dynamics and intracellular processes. The principles for recognizing neuronal spikes from extracellular recordings and the advantages of using wavelets to address these issues are described and combined with approaches based on wavelet neural networks (chapter 4). The features of time-frequency organization of EEG signals are then extensively discussed, from theory to practical applications (chapters 5 and 6). Lastly, the technical details of automatic diagnostics and processing of EEG signals using wavelets are examined (chapter 7).

The book will be a useful resource for neurophysiologists and physicists familiar with nonlinear dynamical systems and data processing, as well as for graduat

• Data Analysis in Neurophysics
• Dynamical Systems in Neuroscience
• Neurodynamics and Neurophysiology
• Neuronal Networks
• Neuronal Spikes and Activity
• Wavelet Theory and Analysis
• Systems Biology

“This book is an excellent description of single neuron and populational neural recordings. … This is a very good book for physiologists, mathematicians, neurologists, anesthetists, neurosurgeons, and students with a specialized interest of neural recordings and functioning. … This book is current and cutting edge as far as neurophysiology is concerned. Many ideas can be acquired for the experimentalists through the studying of this work.” (Joseph J. Grenier, Amazon.com, July, 2015)

“This book gives an introduction to wavelets and then proceeds to demonstrate their use in a neural context. … should be of interest to anyone involved in analysing real neural recordings.” (Carlo Laing, zbMATH 1317.92003, 2015)

• Research and Education Center, Department of Nonlinear Processes, ‘Nonlinear Dynamics of Complex Systems’, Saratov State Technical University, Saratov State University, Saratov, Russia

  Alexander E. Hramov

• Research and Education Center, Department of Nonlinear Processes, ‘Nonlinear Dynamics of Complex Systems', Saratov State Technical University, Saratov State University, Saratov, Russia

  Alexey A. Koronovskii

• Department of Applied Mathematics, Complutense University, Madrid, Spain

  Valeri A. Makarov

• Physics Department, Research and Education Center, ‘Nonlinear Dynamics of Complex Systems', Saratov State University, Saratov State Technical University, Saratov, Russia

  Alexey N. Pavlov

• Institute for Higher Nervous Activity and Neurophysiology, Russian Academy of Sciences, Moscow, Russia

  Evgenia Sitnikova

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