Cognitive Phase Transitions in the Cerebral Cortex – Enhancing the Neuron Doctrine by Modeling Neural Fields 1st Edition by Robert 331924406X 9783319244068

Cognitive Phase Transitions in the Cerebral Cortex – Enhancing the Neuron Doctrine by Modeling Neural Fields 1st Edition by Robert Kozma – Ebook Instant Download/Delivery ISBN(s): 331924406X,  9783319244068

Product details:

• ISBN 10: 331924406X
• ISBN 13: 9783319244068
• Author: Robert

This intriguing book was born out of the many discussions the authors had in the past 10 years about the role of scale-free structure and dynamics in producing intelligent behavior in brains. The microscopic dynamics of neural networks is well described by the prevailing paradigm based in a narrow interpretation of the neuron doctrine. This book broadens the doctrine by incorporating the dynamics of neural fields, as first revealed by modeling with differential equations (K-sets).  The book broadens that approach by application of random graph theory (neuropercolation). The book concludes with diverse commentaries that exemplify the wide range of mathematical/conceptual approaches to neural fields. This book is intended for researchers, postdocs, and graduate students, who see the limitations of network theory and seek a beachhead from which to embark on mesoscopic and macroscopic neurodynamics.

Table of contents:

Part I Review of Dynamical Brain Theoriesand Experiments

1 Introduction—On the Languages of Brains

1.1 Brains Are Not Computers

1.2 Symbolic Approaches to Brains

1.3 Connectionism

1.4 Brains as Transient Dynamical Systems

1.5 Random Graph Theory (RGT) for Brain Models

1.6 Neuropercolation Modeling Paradigm

References

2 Experimental Investigation of High-Resolution Spatio-Temporal Patterns

2.1 Method

2.1.1 Experiments with Rabbits

2.1.2 Human ECoG Experiments

2.1.3 Scalp EEG Design Considerations

2.2 Temporal Patterns: The Carrier Wave

2.3 Spatial Patterns of Amplitude Modulation (AM) and Phase Modulation (PM)

2.4 Classification of ECoG and EEG AM Patterns

2.5 Characterization of Synchronization-Desynchronization Transitions in the Cortex

2.6 Experimental Observation of Singularity

2.7 Transmission of Macroscopic Output by Microscopic Pulses

References

3 Interpretation of Experimental Results As Cortical Phase Transitions

3.1 Theoretical Approaches to Nonlinear Cortical Dynamics

3.2 Scales of Representation: Micro-, Meso-, and Macroscopic Levels

3.3 Cinematic Theory of Cortical Phase Transitions

3.4 Characterization of Phase Transitions

3.4.1 Critical State

3.4.2 Singular Dynamics

3.4.3 Symmetry Breaking

3.4.4 Transition Energy

3.4.5 Zero Order Parameter

3.4.6 Correlation Length Divergence

References

4 Short and Long Edges in Random Graphs for Neuropil Modeling

4.1 Motivation of Using Random Graph Theory for Modeling Cortical Processes

4.2 Glossary of Random Graph Terminology

4.3 Neuropercolation Basics

4.4 Critical Behavior in Neuropercolation with Mean-Field, Local, and Mixed Models

4.4.1 Mean-Field Approximation

4.4.2 Mixed Short and Long Connections

4.5 Finite Size Scaling Theory of Criticality in Brain Models

References

5 Critical Behavior in Hierarchical Neuropercolation Models of Cognition

5.1 Basic Principles of Hierarchical Brain Models

5.2 Narrow-Band Oscillations in Lattices with Inhibitory Feedback

5.3 Broad-Band Oscillations in Coupled Multiple Excitatory-Inhibitory Layers

5.4 Exponentially Expanding Graph Model

References

6 Modeling Cortical Phase Transitions Using Random Graph Theory

6.1 Describing Brain Networks in Terms of Graph Theory

6.1.1 Synchronization and the ‘Aha’ Moment

6.1.2 Practical Considerations on Synchrony

6.1.3 Results of Synchronization Measurements

6.2 Evolution of Critical Behavior in the Neuropil—a Hypothesis

6.3 Singularity and sudden transitions—Interpretation of Experimental Findings

References

7 Summary of Main Arguments

7.1 Brain Imaging Combining Structural and Functional MRI, EEG, MEG and Unit Recordings

7.2 Significance of RGT for Brain Modeling

7.2.1 Relevance to Brain Diseases

7.2.2 Neuropercolation as a Novel Mathematical Tool

7.3 Neuromorphic Nanoscale Hardware Platforms

References

Part II Supplementary Materials on BrainStructure and Dynamics

8 Supplement I: Mathematical Framework

8.1 ODE Implementation of Freeman K Sets

8.1.1 Foundations of Freeman K Sets

8.1.2 Hierarchy of Freeman K Sets

8.2 Finite-Size Scaling Theory for Random Graphs

References

9 Supplement II: Signal Processing Tools

9.1 Description of ECoG and EEG Signals

9.2 Hilbert Transform and Analytical Signal Concept for Pattern Analysis

9.2.1 Basic Concepts of Analytic Signals

9.2.2 Amplitude Modulation (AM) Patterns

9.2.3 Frequency Modulation (PM): Temporal Resolution of Frequency

References

10 Supplement III: Neuroanatomy Considerations

10.1 Structural Connectivities: Emergence of Neocortex from Allocortex

10.2 Constancy of Properties of Neocortex Across Species

10.3 Discussion of Scale-Free Structural and Functional Networks

References

Part IIICommentaries on NeuroscienceExperiments at Cell and Population Levels

11 Commentary by B. Baars

11.1 Introduction

11.1.1 Does the Cortex “know” or “intend”?

11.1.2 Cortical Intention Processing

11.1.3 Freeman Neurodynamics

11.2 Binocular Rivalry in Primates

11.3 Dynamic Global Workspace Theory

11.3.1 Direct Evidence for Cortical Binding and Broadcasting

11.4 Freeman Neurodynamics

11.5 An Integrative Hypothesis

11.5.1 Reference Notes

References

12 Commentary by Steven L. Bressler

12.1 Introduction

12.2 Neuron–Neuron Interactions

12.3 Population–Population Interactions

12.4 Discussion

References

13 Commentary by Zoltán Somogyvári and Péter Érdi

13.1 Modeling Population of Neurons: The Third Option

13.2 Mesoscopic Neurodynamics

13.2.1 Statistical Neurodynamics: Historical Remarks

13.3 Forward and Inverse Modeling of the Neuro-Electric Phenomena

13.3.1 Micro-Electric Imaging

13.3.2 Source Reconstruction on Single Neurons

13.3.3 Anatomical Area and Layer Determination: Micro-Electroanatomy

13.4 Conclusions

References

14 Commentary by Frank Ohl

14.1 Introduction

14.2 Traditional Conceptualizations of Auditory Cortex

14.3 Learning-Induced Plasticity in Auditory Cortex and Multisensory Processing

14.4 Towards Understanding the Neurodynamics Underlying Perception and Cognition

14.5 Exploiting Category Formation to Study the Neurodyamics Underlying the “Creation of Meaning’

14.6 Coexistence of Point-Like Topographic and Field-Like Holographic Representation of Information

14.7 Conclusion and Outlook

References

Part IV Commentaries on Differential Equationin Cortical Models

15 Commentary by James J. Wright

15.1 Introduction

15.2 Neural Mean-Field Equations

15.3 Stochastic Equations in ODE Form

15.4 Cortical-Subcortical Interactions

15.5 Pulse-Bursting and the Introduction of Stored Information

15.6 Synchrony as the Global Attractor

15.7 Stimulus-Feature-Linking, Phase Cones, Phase-Transitions, and Null-Spikes

15.8 Information Capacity—Synapses and Their Developmental Organization

15.9 Cortical Computation and Synchronous Fields

15.10 Self-Supervision of Learning

15.11 In Conclusion

References

16 Commentary by Hans Liljenström

16.1 Introduction

16.2 Cortical Network Models

16.2.1 Paleocortical Model

16.2.2 Neocortical Model

16.3 Simulation Results

16.3.1 Bottom-Up: Noise-Induced State Transitions

16.3.2 Top-Down: Network Modulation of Neural Activity

16.4 Discussion

References

17 Commentary by Ray Brown and Morris Hirsch

17.1 Introduction

17.2 Stretching and Folding Provide an Alternative Approach to the Laws of Physics for Modeling Dyna

17.3 Infinitesimal Diffeomorphisms First Originated from Integral Equations

17.4 Deriving IDEs for the KIII Model

17.4.1 The Linear ID Provides Fundamental Insights into the Dynamics of Stretching and Folding Syst

17.4.2 The Standard KIII Model Can Be Reformulated as a Set of Infinitesimal Diffeomorphisms (ID)

17.5 The Application of IDs to K-Neurodynamics May Result in Useful Simplifications of the ODEs Use

17.6 The KIII-ID Model Can Provide a Reduction in Computation as Well as Insights into the Neurody

17.7 The Wave Ψ(X) for Any K Model May Arise from Partial Differential Equations that Must Be Der

17.8 Summary

References

18 Commentary by Ray Brown on Real World Applications

18.1 Introduction

18.2 Implementation of the KIII Model

18.3 Selection of Mesoscopic Components

18.4 Example Results

18.5 Summary

References

Part VCommentaries on New Theoriesof Cortical Dynamics and Cognition

19 Commentary by Paul J. Werbos

19.1 Introduction

19.2 Top Down Versus Bottom up and the Neuron Dogma

19.3 An Approach to Explaining the 4–8 Hertz Abrupt Shifts in Cortex

19.4 Could Field Effects Be Important to Brain and Mind?

19.4.1 Associate Memory or Quantum Effects Inside the Neuron

19.4.2 Dendritic Field Processing

19.4.3 Quantum Fields and Quantum Mind

19.5 Summary and Conclusions

References

20 Commentary by Ichiro Tsuda

20.1 Self-organization and Field Theory

20.2 Differentiation by Variational Principle

References

21 Commentary by Kazuyuki Aihara and Timothée Leleu

21.1 Introduction

21.2 Propagation of Patterns in Modular Networks

References

22 Commentary by Giuseppe Vitiello

22.1 The Brain Is Not a Stupid Star

22.2 Far from the Equilibrium Systems

22.3 Conclusion

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