Have over a hundred years of brain research revealed all its secrets? This book is motivated by a realization that cortical structure and behavior can be explained by a synergy of seemingly different mathematical notions: global attractors, which define non-invertible neural firing rate dynamics, random graphs, which define connectivity of neural circuit, and prime numbers, which define the dimension and category of cortical operation. Quantum computation is shown to ratify the main conclusion of the book: loosely connected small neural circuits facilitate higher information storage and processing capacities than highly connected large circuits. While these essentially separate mathematical notions have not been commonly involved in the evolution of neuroscience, they are shown in this book to be strongly inter-related in the cortical arena. Furthermore, neurophysiological experiments, as well as observations of natural behavior and evidence found in medical testing of neurologically impaired patients, are shown to support, and to be supported by the mathematical findings.
Related Link(s)
Sample Chapter(s)
Chapter 6: Primal-size Neural Circuits in Trees of Meta-periodic Interaction
Chapter 11: Firing-rate Mode Segregation by Neural Circuit Polarization
Chapter 16: Autonomous Gait Entrainment in the Neurologically Impaired
Contents:
- Prologue
- Introduction
- Some Mathematical Preliminaries
- Cortical Graphs and Neural Circuit Primes:
- Polarity Codes and Subcritical Linguistics
- Hebbian Random Graphs and Firing-rate Dynamics
- Synaptic Polarity and Primal-size Categories of Neural Circuit Codes
- Primal-size Neural Circuits in Trees of Meta-periodic Interaction
- Firing-rate Linguistics:
- Firing-rate Dynamics Irreversibility
- Discrete Iteration Maps of Neural Firing in Cortical Development
- Global Attractors of Neural Firing-rate in Early Development
- Global Attractors of Neural Firing-rate in Maturity
- Firing-rate Mode Segregation by Neural Circuit Polarization
- Learning and Memory by Circuit Polarization
- Cortical Quantum Effects:
- Some Quantum Computation Preliminaries
- Associative Memory by Quantum Set Intersection: The Edge of Small Neural Circuits
- Sensorimotor Control:
- Circuit Polarity in Sensorimotor Control
- Autonomous Gait Entrainment in the Neurologically Impaired
- Circuit Polarity and Singularity Segregation in Cortical Recordings
- Epilogue
- References
- Index
Readership: Professors, teachers, theoreticians, experimentalists, practitioners, advanced undergraduate students and graduate students in the following fields: Neuroscience, Medical Neurology, Mathematics, Physics, Biology, Cognition, Psychology, Information theory, Theoretical and practical coding, Computer Science, Computer Engineering, Software engineering, Hardware engineering, Virtual reality design, Machine learning theory and practice, Popular science.
"The Subcritical Brain weaves together theoretical ideas from random graphs, nonlinear dynamics, prime numbers and quantum computation, to address one of the most important questions in science — how brains compute. A must read for anyone interested in theoretical studies of cortical microcircuits."
Dario Ringach
Professor of Neurobiology & Psychology
David Geffen School of Medicine
University of California, Los Angeles
"Baram's main thesis is that weakly connected small neural circuits offer higher information processing capacities than large neural networks. Paraphrasing this message we may emphasize the importance of diversity in both the brain's system of systems and the education of its researchers. Any reader who is fond of applied mathematics will be delighted to witness the author's skillful use of advanced tools in investigating brain mechanisms and addressing issues of movement disorders in neurologically impaired patients."
David Horn
Professor of Physics
Incumbent of the Edouard and Francoise Jaupart Chair of Theoretical Physics of Particles and Fields
Tel Aviv University
"Professor Yoram Baram has dared set one foot in the world of advanced mathematics and the other in the world of medical practice. In The Subcritical Brain, he creates a bridge between these two worlds that a reader can walk with both confidence and amazement. Neural Networks may have never been approached with such insight and lyricism."
Alberto Espay
Professor of Neurology
University of Cincinnati
"All chapters are of high scientific and literal quality. Each chapter begins with a short mention of the behavioral-neuro-physiological process, continues with a presentation of the prevailing mathematical and theoretical approaches to the addressed subject and culminates in a detailed integrative analysis of the author's insights and research results. The book is recommended to all those interested in translational science aiming to model the abilities of the human mind which is suitable to adapt to our ever-changing environment."
Judith Aharon-Peretz
Professor of Neurology
Medical School
Technion — Israel Institute of Technology
"The book provides an interesting demonstration of the intersection of mathematics and medical practice. I recommend it to students and researchers interested in applied mathematics and brain science."
ZBMath Open
Professor Yoram Baram of the Computer Science department at the Technion — Israel Institute of Technology received his BSc degree in Aeronautical Engineering from Technion in 1972, MSc degree in Aeronautics and Astronautics from MIT in 1974, and PhD degree in Electrical Engineering and Computer Science from MIT in 1976. Specializing in control theory, he spent the next 20 years investigating and teaching System Dynamics in Israel and in the US, including two sabbatical terms as a Senior Research Associate of the National Research Council at the NASA Ames Research Center, where he also served as a consultant from 1986–2006. He holds a US patent for a virtual reality apparatus for gait improvement in neurological patients which he developed from 1999–2004. He also received a Research Award for Best Platform Presentation at a conference on multiple sclerosis CMSC in 2005. In 2006, he was appointed the incumbent of the Technion's Roy Mattas/Winnipeg Chair in Biomedical Engineering. Professor Baram has supervised about 30 graduate students. In recent years he has been working on a mathematical theory of dynamics and information coding in neurobiological systems, while serving as head of the Technion Center for Research in Intelligent Systems. Having retired in 2015, he maintains a full research schedule at the Technion publishing his work in leading neuroscience journals and in his recent book The Subcritical Brain.
