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Preface

Acknowledgements

Notation

Chapter 1 Topological Properties

1.1. The Approach to Neural Masses

1.1.1. Direct and Indirect Observations

1.1.2. The Use of Models in a Hierarchy

1.1.3. Macroscopic Forms of Cooperative Neural Activity

1.2. Single Neurons

1.2.1. The Structures of Neurons

1.2.2. The Operations of Neurons

1.2.3. The State Variables of Neurons

1.2.4. Specification of the Active States and Operations

1.2.5. Input-Output Relations of Single Neurons

1.2.6. Multiple Stable States of Neurons

1.2.7. Basic Topologies of Networks of Neurons

1.3. Neural Masses

1.3.1. A Topological Hierarchy of Interactive Sets

1.3.2. The State Variables of KO and KI Sets

1.3.3. The Operations of Neural Sets

1.3.4. Feedback Gain as a Parameter for Interaction

1.3.5. Multiple Stable States and the Levels of Interaction

1.3.6. The Relation of Multiple Stabilities to Neural Signals

1.3.7. The Conditions for Realizability

1.3.8. The Use of Differential Equations

Chapter 2 Time-Dependent Properties

2.1. Measurement of Neural Events

2.1.1. Representation of Events by Functions

2.1.2. Input-Output Functions

2.1.3. Linear Input-Output Functions

2.1.4. The Impulse and the Impulse Response

2.2. Linear Models for Neural Membrane

2.2.1. The Topology of the Membrane

2.2.2. Differential Equations

2.2.3. The Laplace Transform

2.2.4. Application of the Laplace Transform to the Membrane

2.3. Linear Models for Parts of Neurons

2.3.1. Convolution

2.3.2. The Convolution Theorem

2.3.3. Transfer Functions for Pulse Transmission

2.3.4. The Core Conductor Model

2.3.5. Synaptic Delay

2.4. Linear Models for Neurons

2.4.1. Formulation of the Topology

2.4.2. Input-Output Pairs and the Differential Equation

2.4.3. Interpretation of the Parameters

2.4.4. Linear Function for Wave to Pulse Conversion

2.5. Linear Models for Neural Masses

2.5.1. Use of Nonlinear Regression

2.5.2. The KO Neural Set

2.5.3. Oscillatory Responses from a KII Set

Chapter 3 Amplitude-Dependent Properties

3.1. Nonlinear Models for Neural Membranes

3.1.1. The Ionic Hypothesis

3.1.2. Metabolic Forces

3.1.3. The Concept of Equilibrium Potential

3.1.4. The Sodium Permeability Model

3.2. Nonlinear Models for Neurons and Parts of Neurons

3.2.1. Action Potentials in Axons

3.2.2. Threshold Uncertainty in Axons

3.2.3. Postsynaptic Potentials in Dendrites

3.2.4. Amplitude-Dependent Input-Output Relations

3.3. Nonlinear Models for Neural Masses

3.3.1. Background Activity in the Wave Mode

3.3.2. Background Activity in the Pulse Mode

3.3.3. Relations of Waves and Pulses

3.3.4. Wave to Pulse Conversion in the KI Set

3.3.5. Pulse to Wave Conversion in the KI Set

3.3.6. The Forward Gain of the KI Set

Chapter 4 Space-Dependent Properties

4.1. Potential Fields of Single Neurons

4.1.1. Basis Functions for Measurement of Potential in Space

4.1.2. Basis Functions for Potential in Current Fields

4.1.3. Potential Functions for the Core Conductor

4.1.4. Potential Fields of Axons

4.1.5. Nodes and Branched Fibers

4.2. Potential Fields of Neural Masses

4.2.1. Measurement of Observed Fields

4.2.2. Basis Functions for Potential Fields of Neural Masses

4.2.3. Compound Potential Fields: Modular Analysis

4.3. Potential Fields in the Olfactory Bulb

4.3.1. Bulbar Geometry and Topology

4.3.2. Analysis of the Spatial Function of Potential

4.3.3. Time-Dependent Activity

4.4. Potential Fields in the Prepyriform Cortex

4.4.1. Cortical Geometry and Topology

4.4.2. Observed Fields of Cortical Potential

4.4.3. Relation of Potential Fields to Active States

4.5. Divergence and Convergence in Neural Masses

4.5.1. The Operation of Divergence

4.5.2. Evaluation of Spatial Distributions of Active States

4.5.3. Evaluation of Synaptic Divergence

4.5.4. Evaluation of Tractile Divergence

Chapter 5 Interaction: Single Feedback Loops with Fixed Gain

5.1. General Properties of Single Feedback Loops

5.1.1. Types of Neural Feedback

5.1.2. Derivation of the Lumped Piecewise Linear Approximation

5.1.3. Root Locus as a Function of Feedback Gain

5.1.4. Amplitude-Dependent Gain and Stability

5.2. Reduction from the KI Level

5.2.1. Topological Analysis of the Glomerular Layer

5.2.2. Differential Equations for the KIe Set

5.2.3. Self-Stabilization of the KIe Set

5.3. Reduction from the KII Level

5.3.1. Topological Analysis of the Olfactory Bulb

5.3.2. Differential Equations for the Open Loop Cases

5.3.3. Differential Equations for the Closed Loop Cases

5.4. Reduction from the Kill Level

5.4.1. Topological Analysis of the Prepyriform Cortex

5.4.2. Differential Equations for the Cortex

5.4.3. Transfer Function of the LOT Input Channel

5.4.4. Pulse-Wave Relations in Cortex and Bulb

5.4.5. Channels for Centrifugal Input

Chapter 6 Multiple Feedback Loops with Variable Gain

6.1. Equilibrium States: Characteristic Frequency

6.1.1. Definition of the Three Types of Feedback Gain

6.1.2. Solution of the Differential Equations

6.1.3. Experimental and Theoretical Root Loci

6.1.4. Bias Control of Characteristic Frequency

6.1.5. Root Loci Dependent on EEG Amplitudes

6.2. Limit Cycle States: Mechanisms of the EEG

6.2.1. Stability Properties of KII Sets

6.2.2. Limit Cycle States in the First Mode

6.2.3. Limit Cycle States in the Second Mode

6.2.4. Sources of Error and Limitation

6.2.5. Comparisons with Related Mathematical Models

Chapter 7 Signal Processing by Neural Mass Actions

7.1. Behavioral Correlates of Wave Activity in KII Sets

7.1.1. The Operational Basis for Correlation

7.1.2. Factor Analysis of AEPs

7.1.3 Patterns of Change in AEPS with Attention

7.1.4. A Proposed Cortical Mechanism of Attention

7.2. Transformations of Neural Signals by KII Sets

7.2.1. Neural Coding in the Olfactory Bulb

7.2.2. Bulbar Mechanisms for Phase Modulation

7.2.3. Attention and the Cortical Expectation Function

7.2.4. Possible Mechanisms of Cortical Output

7.3. Comments concerning Neocortical Mass Actions

7.3.1. Rhythmic Potentials and Rhythmic Stimulation

7.3.2. DC Polarization and Steady Potentials

7.3.3. Unit Activity Correlated with Sensory and Motor Events

References

Author Index

Subject Index

- 1st Edition - December 2, 2012
- Author: Bozzano G Luisa
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 4 1 2 0 4 7 - 1
- eBook ISBN:9 7 8 - 0 - 3 2 3 - 1 4 0 2 0 - 1

Mass Action in the Nervous System: Examination of the Neurophysiological Basis of Adaptive Behavior through the EEG focuses on the neural mechanisms and the behavioral significance… Read more

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Mass Action in the Nervous System: Examination of the Neurophysiological Basis of Adaptive Behavior through the EEG focuses on the neural mechanisms and the behavioral significance of the electroencephalogram, with emphasis on observations made on the mammalian olfactory system. Organized into seven chapters, this book begins with a brief nonmathematical review of the concept of the neuron and the interrelations among neurons that lead to the formation of interactive masses. Some chapters follow on the linear properties of neurons and their parts; the ionic hypothesis; the nonlinear input-output relations of neurons in masses expressed in terms of amplitude-dependent coefficients in linear differential equations; and the relations between the states of activity of neurons. Subsequent chapters describe the properties resulting from feedback within neural masses; the effects of the nonlinearities in the input-output relations of neurons on the behavior of masses; and some inferences concerning the mechanisms of neural signal processing at the level of neural masses. The book is a model for an advanced text in neurophysiology, and some understanding is assumed of the elements of the fields of linear analysis, probability, statistics, theory of potential, neuroanatomy, electrophysiology, neuropharmacology, and experimental psychology.

Preface

Acknowledgements

Notation

Chapter 1 Topological Properties

1.1. The Approach to Neural Masses

1.1.1. Direct and Indirect Observations

1.1.2. The Use of Models in a Hierarchy

1.1.3. Macroscopic Forms of Cooperative Neural Activity

1.2. Single Neurons

1.2.1. The Structures of Neurons

1.2.2. The Operations of Neurons

1.2.3. The State Variables of Neurons

1.2.4. Specification of the Active States and Operations

1.2.5. Input-Output Relations of Single Neurons

1.2.6. Multiple Stable States of Neurons

1.2.7. Basic Topologies of Networks of Neurons

1.3. Neural Masses

1.3.1. A Topological Hierarchy of Interactive Sets

1.3.2. The State Variables of KO and KI Sets

1.3.3. The Operations of Neural Sets

1.3.4. Feedback Gain as a Parameter for Interaction

1.3.5. Multiple Stable States and the Levels of Interaction

1.3.6. The Relation of Multiple Stabilities to Neural Signals

1.3.7. The Conditions for Realizability

1.3.8. The Use of Differential Equations

Chapter 2 Time-Dependent Properties

2.1. Measurement of Neural Events

2.1.1. Representation of Events by Functions

2.1.2. Input-Output Functions

2.1.3. Linear Input-Output Functions

2.1.4. The Impulse and the Impulse Response

2.2. Linear Models for Neural Membrane

2.2.1. The Topology of the Membrane

2.2.2. Differential Equations

2.2.3. The Laplace Transform

2.2.4. Application of the Laplace Transform to the Membrane

2.3. Linear Models for Parts of Neurons

2.3.1. Convolution

2.3.2. The Convolution Theorem

2.3.3. Transfer Functions for Pulse Transmission

2.3.4. The Core Conductor Model

2.3.5. Synaptic Delay

2.4. Linear Models for Neurons

2.4.1. Formulation of the Topology

2.4.2. Input-Output Pairs and the Differential Equation

2.4.3. Interpretation of the Parameters

2.4.4. Linear Function for Wave to Pulse Conversion

2.5. Linear Models for Neural Masses

2.5.1. Use of Nonlinear Regression

2.5.2. The KO Neural Set

2.5.3. Oscillatory Responses from a KII Set

Chapter 3 Amplitude-Dependent Properties

3.1. Nonlinear Models for Neural Membranes

3.1.1. The Ionic Hypothesis

3.1.2. Metabolic Forces

3.1.3. The Concept of Equilibrium Potential

3.1.4. The Sodium Permeability Model

3.2. Nonlinear Models for Neurons and Parts of Neurons

3.2.1. Action Potentials in Axons

3.2.2. Threshold Uncertainty in Axons

3.2.3. Postsynaptic Potentials in Dendrites

3.2.4. Amplitude-Dependent Input-Output Relations

3.3. Nonlinear Models for Neural Masses

3.3.1. Background Activity in the Wave Mode

3.3.2. Background Activity in the Pulse Mode

3.3.3. Relations of Waves and Pulses

3.3.4. Wave to Pulse Conversion in the KI Set

3.3.5. Pulse to Wave Conversion in the KI Set

3.3.6. The Forward Gain of the KI Set

Chapter 4 Space-Dependent Properties

4.1. Potential Fields of Single Neurons

4.1.1. Basis Functions for Measurement of Potential in Space

4.1.2. Basis Functions for Potential in Current Fields

4.1.3. Potential Functions for the Core Conductor

4.1.4. Potential Fields of Axons

4.1.5. Nodes and Branched Fibers

4.2. Potential Fields of Neural Masses

4.2.1. Measurement of Observed Fields

4.2.2. Basis Functions for Potential Fields of Neural Masses

4.2.3. Compound Potential Fields: Modular Analysis

4.3. Potential Fields in the Olfactory Bulb

4.3.1. Bulbar Geometry and Topology

4.3.2. Analysis of the Spatial Function of Potential

4.3.3. Time-Dependent Activity

4.4. Potential Fields in the Prepyriform Cortex

4.4.1. Cortical Geometry and Topology

4.4.2. Observed Fields of Cortical Potential

4.4.3. Relation of Potential Fields to Active States

4.5. Divergence and Convergence in Neural Masses

4.5.1. The Operation of Divergence

4.5.2. Evaluation of Spatial Distributions of Active States

4.5.3. Evaluation of Synaptic Divergence

4.5.4. Evaluation of Tractile Divergence

Chapter 5 Interaction: Single Feedback Loops with Fixed Gain

5.1. General Properties of Single Feedback Loops

5.1.1. Types of Neural Feedback

5.1.2. Derivation of the Lumped Piecewise Linear Approximation

5.1.3. Root Locus as a Function of Feedback Gain

5.1.4. Amplitude-Dependent Gain and Stability

5.2. Reduction from the KI Level

5.2.1. Topological Analysis of the Glomerular Layer

5.2.2. Differential Equations for the KIe Set

5.2.3. Self-Stabilization of the KIe Set

5.3. Reduction from the KII Level

5.3.1. Topological Analysis of the Olfactory Bulb

5.3.2. Differential Equations for the Open Loop Cases

5.3.3. Differential Equations for the Closed Loop Cases

5.4. Reduction from the Kill Level

5.4.1. Topological Analysis of the Prepyriform Cortex

5.4.2. Differential Equations for the Cortex

5.4.3. Transfer Function of the LOT Input Channel

5.4.4. Pulse-Wave Relations in Cortex and Bulb

5.4.5. Channels for Centrifugal Input

Chapter 6 Multiple Feedback Loops with Variable Gain

6.1. Equilibrium States: Characteristic Frequency

6.1.1. Definition of the Three Types of Feedback Gain

6.1.2. Solution of the Differential Equations

6.1.3. Experimental and Theoretical Root Loci

6.1.4. Bias Control of Characteristic Frequency

6.1.5. Root Loci Dependent on EEG Amplitudes

6.2. Limit Cycle States: Mechanisms of the EEG

6.2.1. Stability Properties of KII Sets

6.2.2. Limit Cycle States in the First Mode

6.2.3. Limit Cycle States in the Second Mode

6.2.4. Sources of Error and Limitation

6.2.5. Comparisons with Related Mathematical Models

Chapter 7 Signal Processing by Neural Mass Actions

7.1. Behavioral Correlates of Wave Activity in KII Sets

7.1.1. The Operational Basis for Correlation

7.1.2. Factor Analysis of AEPs

7.1.3 Patterns of Change in AEPS with Attention

7.1.4. A Proposed Cortical Mechanism of Attention

7.2. Transformations of Neural Signals by KII Sets

7.2.1. Neural Coding in the Olfactory Bulb

7.2.2. Bulbar Mechanisms for Phase Modulation

7.2.3. Attention and the Cortical Expectation Function

7.2.4. Possible Mechanisms of Cortical Output

7.3. Comments concerning Neocortical Mass Actions

7.3.1. Rhythmic Potentials and Rhythmic Stimulation

7.3.2. DC Polarization and Steady Potentials

7.3.3. Unit Activity Correlated with Sensory and Motor Events

References

Author Index

Subject Index

- No. of pages: 496
- Language: English
- Edition: 1
- Published: December 2, 2012
- Imprint: Academic Press
- Paperback ISBN: 9780124120471
- eBook ISBN: 9780323140201

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