The Subcritical Brain: A Synergy of Segregated Neural Circuits in Memory, Cognition and Sensorimotor Control

Length: 300 pages
Edition: 1
Language: English
Publisher: World Scientific Publishing Company
Publication Date: 2021-05-06
ISBN-10: 9811233098
ISBN-13: 9789811233098
Sales Rank: #0 (See Top 100 Books)

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.

Cover
Halftitle
Title
Copyright
Dedication
Prologue
Contents
Chapter 1. Introduction
    1.1 General
    1.2 Historical account
        1.2.1 The nature of cortical information
        1.2.2 Developmental aspects
        1.2.3 Cortical connectivity
        1.2.4 Somatic and synaptic polarization
        1.2.5 Synaptic and somatic elimination
        1.2.6 Cortical plasticity
        1.2.7 Learning and memory
        1.2.8 Cortical function
        1.2.9 Graphs and categories
        1.2.10 Prime numbers
        1.2.11 Quantum computation
        1.2.12 Sensorimotor control
    1.3 Book outline
Chapter 2. Some Mathematical Preliminaries
    2.1 Introduction
    2.2 Random graph criticality and connectivity
    2.3 Primes, primality testing and prime factorization
    2.4 Continuous and discrete-time dynamical systems
    2.5 Elements of non-invertibility
    2.6 Singularities of discrete iteration maps
    2.7 Cobweb diagrams
    2.8 From continuous-time to discrete-time dynamics of neural firing and plasticity
    2.9 Self-regulation and stability in open and closed-loop control systems
    2.10 Discussion
Part I. Cortical Graphs and Neural Circuit Primes
    Chapter 3. Polarity Codes and Subcritical Linguistics
        3.1 Introduction
        3.2 Neuronal polarity codes
        3.3 Subcritical neural circuit segregation
        3.4 Hebbian linguistic impasse of probabilistically supercritical neural polarity
        3.5 Critical Hebbian linguistic limit of neural polarity
        3.6 Discussion
    Chapter 4. Hebbian Random Graphs and Firing-rate Dynamics
        4.1 Introduction
        4.2 Random Hebbian criticality effects on circuit linguistics
        4.3 Firing-mode reproduction by polarity recall
        4.4 Discussion
    Chapter 5. Synaptic Polarity and Primal-size Categories of Neural Circuit Codes
        5.1 Introduction
        5.2 Polarity codes and primal-size categories under axonal discharge self-feedback
        5.3 Polarity codes and primal-size categories under synaptic self-feedback
        5.4 Neural circuit polarity effects on firing dynamics
        5.5 “Working Memory” and “Magical Numbers”
        5.6 Discussion
    Chapter 6. Primal-size Neural Circuits in Trees of Meta-periodic Interaction
        6.1 Introduction
        6.2 Primal-size neural circuits in meta-periodic interaction
        6.3 Primal-size circuit interaction in firing-rate meta-periodicity
        6.4 Cortical information capacities under primal-size neural circuits
        6.5 Primal-size neural circuits in meta-periodic trees
        6.6 Discussion
Part II. Firing-rate Linguistics
    Chapter 7. Firing-rate Dynamics Irreversibility
        7.1 Introduction
        7.2 Discrete iteration map of neural firing and synaptic plasticity
        7.3 Non-invertibility (time-irreversibility) of the map
        7.4 Discussion
    Chapter 8. Discrete Iteration Maps of Neural Firing in Cortical Development
        8.1 Introduction
        8.2 Reduced discrete iteration maps
        8.3 Discrete iteration maps in developmental stages
            8.3.1 Pre-critical period excitability
            8.3.2 Critical period persistent plasticity
            8.3.3 Convergent plasticity and synaptic maturity
            8.3.4 Synaptic rigidity
        8.4 Discussion
    Chapter 9. Global Attractors of Neural Firing-rate in Early Development
        9.1 Introduction
        9.2 Global attractors of neural firing-rate under pre-critical plasticity
        9.3 Global attractors of neural firing-rate under critical plasticity
        9.4 Robustness of firing-rate global attractors with respect to model parameter
        9.5 Discussion
    Chapter 10. Global Attractors of Neural Firing-rate in Maturity
        10.1 Introduction
        10.2 Global attractors of neural firing-rate in maturity
        10.3 Simulation results
        10.4 Discussion
    Chapter 11. Firing-rate Mode Segregation by Neural Circuit Polarization
        11.1 Introduction
        11.2 Dynamics of somatic and synaptic silencing
        11.3 Underlying asynchronous firing-rate and plasticity models
        11.4 Asynchronous synaptic polarity-gated firing mode segregation
        11.5 Firing mode control by synchronous polarity-gated circuit segregation
        11.6 Neural circuit segregation capacity
        11.7 Synaptic and somatic elimination: From pruning to senescence
        11.8 Discussion
    Chapter 12. Learning and Memory by Circuit Polarization
        12.1 Introduction
        12.2 Short and long-term memory in the individual neuron
        12.3 Short and long-term memory in synchronous circuit
        12.4 Memory modification
        12.5 Associative memory by circuit polarization and segregation
        12.6 Discussion
Part III. Cortical Quantum Effects
    Chapter 13. Some Quantum Computation Preliminaries
        13.1 Introduction
        13.2 States and qubits
        13.3 Measurement
        13.4 Operators and oracles
        13.5 Grover’s quantum search algorithm
        13.6 Discussion
    Chapter 14. Associative Memory by Quantum Set Intersection: The Edge of Small Neural Circuits
        14.1 Introduction
        14.2 Quantum set intersection
        14.3 Quantum associative memory
            14.3.1 Pattern completion
            14.3.2 Pattern correction
        14.4 Associative memory capacity results
            14.4.1 Time complexity
            14.4.2 Equilibrium storage capacity
            14.4.3 Completion capacity
        14.5 Numerical examples and simulations
        14.6 Comparison to other works
        14.7 Discussion
Part IV. Sensorimotor Control
    Chapter 15. Circuit Polarity in Sensorimotor Control
        15.1 Introduction
        15.2 Obstacle detection
        15.3 A bird’s eye view on the descent trajectory
        15.4 Discussion
    Chapter 16. Autonomous Gait Entrainment in the Neurologically Impaired
        16.1 Introduction
        16.2 The edge of autonomy in visual feedback
        16.3 The edge of auditory feedback
        16.4 Dopamine reward and reward-seeking: The edge of memory
        16.5 The edge of geometric dimension
        16.6 The edge of polarity
        16.7 Transformative autonomous entrainment of gait across neurological disorders
        16.8 Discussion
    Chapter 17. Circuit Polarity and Singularity Segregation in Cortical Recordings
        17.1 Introduction
        17.2 Recorded cortical sensorimotor-activity
        17.3 Circuit polarization and singularity segregation in cortical recordings
        17.4 Discussion
Epilogue
References
Index