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

Contents
Prologue
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