The Cortex and the Critical Point: Understanding the Power of Emergence

Contents
Acknowledgments
Introduction
	The Critical Point in Context
	The Goals and Structure of This Book
I. Background
	1. The Main Idea
		A Simple Model
		Optimal Information Processing
		The Appearance of Emergent Phenomena
		Power Laws
		Avalanches
		A Phase Transition
		From a Model to Data
		The Criticality Hypothesis
		Objections and Responses to the Criticality Hypothesis
		Chapter Summary
	2. Emergent Phenomena
		Methodological Reductionism
		The Wave as an Emergent Phenomenon
		Emergent Phenomena in the Brain
		A Simple Model of Emergent Phenomena in the Brain
		Complex Emergent Phenomena Occur at a Phase Transition
		More Complex Emergent Phenomena?
		How to Study Emergent Phenomena
		Chapter Summary
II. The Critical Point and Its Consequences
	3. The Critical Point
		The Branching Model: A Branching Ratio Near 1
		The Branching Model: A Phase Transition with Control and Order Parameters
		The Branching Model: An Exponent Relation between Multiple Power Laws
		The Branching Model: Fractal Copies of Avalanches
		Signatures of Being near the Critical Point
		Signatures of the Critical Point from the Data
		In Vitro Experiments
		Data: A Branching Ratio near 1
		Data: A Phase Transition with Control and Order Parameters
		Data: An Exponent Relation between Multiple Power Laws
		Data: Fractal Copies of Avalanches
		Objections to These Signatures of Criticality
		Chapter Summary
	4. Optimality
		The Branching Model: Information Transmission
		The Branching Model: Dynamic Range
		The Branching Model: Susceptibility
		Data: Dynamic Range
		Data: Information Transmission
		Data: Susceptibility
		Other Predictions Yet to Be Tested
		Chapter Summary
	5. Universality
		Universality in Physical Systems
		Universality in the Cortex: Indicators
		Indicators Seen across Species
		Indicators Seen across Scales
		Described by a Simple Model
		Chapter Summary
III. Future Directions
	6. Homeostasis and Health
		Homeostasis toward the Critical Point after a Major Perturbation
		Sleep and Homeostasis toward the Critical Point
		Sensory Adaptation toward the Critical Point
		Development toward the Critical Point
		Themes from Homeostasis Results
		Health
		Chapter Summary
	7. Quasicriticality
		Universality: Unfinished Issues
		A Possible Solution: Quasicriticality
		Another View: Slightly Subcritical
		Another View: Subsampling
		Another View: Griffiths Phase
		Chapter Summary
	8. Cortex
		The Expansion of Cortical Area
		Associations of Associations
		The Special Role of Layers 2 and 3
		Multifunctionality and the Critical Point
		Nearly Critical in Layers 2 and 3, but Not in Layer 5
		Staying Nearly Critical While Learning
		Timescales throughout the Hierarchy
		Chapter Summary
	9. Epilogue
		What We Know
		What We Don’t Know
		Frontier Issues
		What I Did Not Cover
Appendix
	Relation between Power-Law Exponent and Slope (Chapters 1 and 6)
	When the Average Value of a Power Law Diverges and When It Does Not (Chapters 1 and 6)
	Long-Range Temporal Correlations (Chapters 1, 6, and 8)
	Informal Derivation of the Exponent Relation (Chapters 3, 5, 6, 7, and 8)
	Avalanche Shape Collapse (Chapters 3, 5, 6, and 8)
	How to Quantify Network Dynamics (Chapters 4 and 8)
	Software and Data for Exercises and Analyses
Notes
	Chapter 1
	Chapter 2
	Chapter 3
	Chapter 4
	Chapter 5
	Chapter 6
	Chapter 7
	Chapter 8
References
Index