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Lecture Notes in Physics

Statistical Field Theory for Neural Networks

Authors: Helias, Moritz, Dahmen, David

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  • Provides the first self-contained introduction to field theory for neuronal networks
  • Presents the main concepts from field theory that are relevant for network dynamics, including diagrammatic techniques and systematic perturbative and fluctuation expansions
  • Introduces advanced concepts, like the effective action formalism, in mathematical minimal setting
  • Includes in-depth derivations of classical seminal works and recent developments, such as the dynamical mean-field theory and chaos
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eBook 50,28 €
price for France (gross)
  • ISBN 978-3-030-46444-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 63,29 €
price for France (gross)
About this book

This book presents a self-contained introduction to techniques from field theory applied to stochastic and collective dynamics in neuronal networks. These powerful analytical techniques, which are well established in other fields of physics, are the basis of current developments and offer solutions to pressing open problems in theoretical neuroscience and also machine learning. They enable a systematic and quantitative understanding of the dynamics in recurrent and stochastic neuronal networks.

This book is intended for physicists, mathematicians, and computer scientists and it is designed for self-study by researchers who want to enter the field or as the main text for a one semester course at advanced undergraduate or graduate level. The theoretical concepts presented in this book are systematically developed from the very beginning, which only requires basic knowledge of analysis and linear algebra.

About the authors

Moritz Helias is group leader at the Jülich Research Centre and assistant professor in the department of physics of the RWTH Aachen University, Germany. He obtained his diploma in theoretical solid state physics at the University of Hamburg and his PhD in computational neuroscience at the University of Freiburg, Germany. Post-doctoral positions in RIKEN Wako-Shi, Japan and Jülich Research Center followed. His main research interests are neuronal network dynamics and function, and their quantitative analysis with tools from statistical physics and field theory.

David Dahmen is a post-doctoral researcher in the Institute of Neuroscience and Medicine at the Jülich Research Centre, Germany. He obtained his Master's degree in physics from RWTH Aachen University, Germany, working on effective field theory approaches to particle physics. Afterwards he moved to the field of computational neuroscience, where he received his PhD in 2017. His research comprises modeling, analysis and simulation of recurrent neuronal networks with special focus on development and knowledge transfer of mathematical tools and simulation concepts. His main interests are field-theoretic methods for random neural networks, correlations in recurrent networks, and modeling of the local field potential.

Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook 50,28 €
price for France (gross)
  • ISBN 978-3-030-46444-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 63,29 €
price for France (gross)
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Bibliographic Information

Bibliographic Information
Book Title
Statistical Field Theory for Neural Networks
Authors
Series Title
Lecture Notes in Physics
Series Volume
970
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-46444-8
DOI
10.1007/978-3-030-46444-8
Softcover ISBN
978-3-030-46443-1
Series ISSN
0075-8450
Edition Number
1
Number of Pages
XVII, 203
Number of Illustrations
122 b/w illustrations, 5 illustrations in colour
Topics