Plasticity

Title:

Plasticity

Publication Information:

River Edge, N.J. : World Scientific, 2004

ISBN:

9789812387462

General Note:

Accompanies text entitled : Theory of cortical plasticity (QP363.3 T53 2004)

Subject Term:

Neuroplasticity

Neuroplasticity -- Mathematical models

Cerebral cortex

Visual cortex -- Physiology

Added Author:

Cooper, Leon N.

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010071437	CP 5409	Computer File Accompanies Open Access Book	Compact Disc Accompanies Open Access Book	Searching... Unknown

In Theory of Cortical Plasticity, Nobel Laureate Leon Cooper and his collaborators present a systematic development of the Bienenstock, Cooper and Munro (BCM) theory of synaptic plasticity, and discuss experiments that test both its assumptions and consequences. This insightful book provides an elegant analysis of theoretical structure in neuroscience research, and elucidates the role BCM theory has played in guiding research leading to our present understanding of the mechanisms underlying cortical plasticity.

Preface	p. vii
Acknowledgements	p. xi
The Software Package, Plasticity	p. xix
Notation	p. xxi
Common Acronyms and Abbreviations	p. xxiii
1. Introduction	p. 1
1.1 Visual Cortex Plasticity	p. 3
1.2 Theoretical background	p. 5
1.3 Comparison of Theory and Experiment	p. 7
1.4 Cellular basis for the postulates of the BCM theory	p. 9
1.5 A model of inputs to visual cortex cells	p. 11
2. Single Cell Theory	p. 17
2.1 Introduction	p. 17
2.2 Definitions and Notation	p. 18
2.3 BCM synaptic modification	p. 21
2.4 One Dimensional Analysis	p. 23
2.4.1 Fixed threshold	p. 23
2.4.2 Instantaneously sliding threshold	p. 23
2.4.3 Instantaneously sliding threshold with a Probabilistic Input	p. 24
2.4.4 Summary of the One Dimensional Case	p. 25
2.5 The Nonlinear Sliding Threshold	p. 25
2.6 Analysis of a two dimensional neuron	p. 27
2.6.1 Two input environment	p. 28
2.6.2 Stability analysis	p. 29
Selective Critical Points	p. 29
Non-selective critical points	p. 30
2.6.3 Single input environment	p. 32
2.6.4 Many input environment	p. 32
2.7 Some Experimental Consequences	p. 33
2.7.1 Normal Rearing	p. 33
2.7.2 Monocular deprivation	p. 34
2A. Stability of BCM with a Weight Decay Term, in a Linearly Independent Environment	p. 45
2A.1 Initial Fixed Points	p. 45
2A.1.1 Consistency	p. 46
2A.2 Stability	p. 46
2A.2.1 Consistency	p. 49
2A.2.2 Consequences	p. 49
3. Objective Function Formulation	p. 51
3.1 Introduction	p. 51
3.2 Formulation of the BCM Theory Using an Objective Function	p. 51
3.2.1 Single Neuron	p. 52
3.2.2 Extension to a Nonlinear Neuron	p. 55
3.2.3 Extension to a Network with Feed-Forward Inhibition	p. 56
3.3 The BCM feature extraction and coding	p. 58
3.3.1 BCM and suspicious coincidence detection	p. 58
3.4 Information Theoretic Considerations	p. 60
3.4.1 Information theory and synaptic modification rules	p. 60
3.4.2 Information theory and early visual processing	p. 62
3.4.3 Information properties of Principal Components	p. 64
3.5 Extraction of Optimal Unsupervised Features	p. 65
3.5.1 Projection Pursuit and Deviation from Gaussian Distributions	p. 66
3.5.2 Skewness	p. 68
(a) Skewness 1	p. 68
(b) Skewness 2	p. 69
3.5.3 Kurtosis	p. 69
(a) Kurtosis 1	p. 69
(b) Kurtosis 2	p. 69
3.5.4 Quadratic BCM	p. 70
3.5.5 Constrained BCM measure	p. 70
3.5.6 Independent Components and Receptive Fields	p. 71
3.5.7 Kurtosis and ICA	p. 73
3.5.8 Friedman's distance from uniform measure	p. 73
3.5.9 Entropy	p. 74
3.5.10 The concept of minimum mutual information between neurons	p. 76
3.5.11 Some Related Statistical and Computational Issues in BCM	p. 77
3.6 Analysis of the Fixed Points of BCM in High Dimensional Space	p. 78
3.6.1 n linearly independent inputs	p. 79
Stability of the solution	p. 80
3.6.2 Noise with no Patterned Input	p. 82
Noise with Zero Mean	p. 83
Noise with Positive Mean	p. 83
3.6.3 Patterned Input with Noise	p. 84
3.7 Application to Various Rearing Conditions	p. 85
3.7.1 Normal Rearing(NR)	p. 85
3.7.2 Monocular Deprivation (MD)	p. 85
3.7.3 Binocular Deprivation (BD)	p. 86
3.7.4 Reverse Suture (RS)	p. 86
3.7.5 Strabismus	p. 87
3.8 Discussion	p. 87
3A. Convergence of the Solution of the Random Differential Equations	p. 89
3A.1 Convergence of the Deterministic Equation	p. 89
3A.2 Convergence of the Random Equation	p. 90
3B. Analysis and Comparison of BCM and Kurtosis in Extended Distributions	p. 93
3B.1 Two Dimensions	p. 95
3B.2 Monocular Deprivation	p. 98
3B.2.1 Kurtosis	p. 99
3B.2.2 BCM	p. 101
3B.3 Binocular Deprivation	p. 102
3B.3.1 Gaussian Noise	p. 102
3B.3.2 Kurtosis	p. 103
3B.3.3 BCM	p. 103
3B.4 Reverse Suture	p. 105
3B.5 Strabismus	p. 106
3B.5.1 Kurtosis	p. 107
3B.5.2 BCM	p. 108
3C. Statistical Theorems	p. 109
4. Cortical Network Theory	p. 111
4.1 Introduction	p. 111
4.2 Mean Field Theory	p. 112
4.2.1 Position and Stability of Fixed Points of LGN-Cortical Synapses in the Mean Field Network	p. 117
4.2.2 Comparison of Linear Feed-Forward with Lateral Inhibition Network: Mean Field Approximation	p. 119
4.3 Matrix-based analysis of networks of interacting and non-linear BCM neurons	p. 121
4.4 Discussion	p. 122
4A. Asymptotic Behavior of Mean Field Equations with Time Dependent Mean Field	p. 125
5. Review and Analysis of Second Order Learning Rules	p. 127
5.1 Introduction	p. 127
5.2 Hebb's rule and its derivatives	p. 128
5.2.1 Stabilized Hebbian rule	p. 131
5.2.2 Finding multiple principal components	p. 133
5.2.3 Fixed points of saturating Hebb rules	p. 134
5.2.4 Why are Principal Components not Local	p. 136
5.2.5 Summary	p. 137
5.3 Orientation Selectivity	p. 137
5.3.1 An exactly soluble 1D Model	p. 138
5.3.2 Radially symmetric models in 2D	p. 142
5.3.3 2D correlational Models	p. 142
5.3.4 Analysis of Linsker's Model	p. 144
5.3.5 Formation of Receptive Fields in a Natural Image Environment	p. 148
(a) The visual environment	p. 148
(b) PCA simulations with natural images	p. 149
(c) Analysis of receptive fields formed in a Radially Symmetric Environment	p. 150
(d) Non symmetric environment	p. 153
5.3.6 Summary	p. 154
5.4 Ocular Dominance	p. 155
5.4.1 Ocular Dominance in Correlational Low-Dimensional Models	p. 155
5.4.2 Misaligned inputs to cell	p. 159
5.5 Combined Orientation Selectivity and Ocular Dominance	p. 160
5.5.1 The two-eye 1D soluble Model	p. 160
5.5.2 A Correlational Model of Ocular Dominance and Orientation Selectivity	p. 161
5.5.3 Four Channel Models	p. 165
5.5.4 Mixing Principal Components	p. 166
5.5.5 Local External Symmetry Breaking	p. 170
5.5.6 A two eye model with Natural Images	p. 171
5.6 Deprivation Experiments	p. 172
5.6.1 A Simple Correlational Model using Exact PCA Dynamics	p. 172
(a) Normal Rearing (NR)	p. 173
(b) Monocular Deprivation (MD)	p. 174
(c) Reverse Suture (RS)	p. 175
(d) Binocular Deprivation (BD)	p. 175
5.6.2 Simulation results with natural images	p. 176
5.7 Discussion	p. 176
5A. Representing the correlation matrix in a Bessel function Base	p. 185
5A.1 The correlation function for the pre-processed images	p. 187
5B. Properties of Correlation Functions And How to Make Good Ones	p. 189
5C. The Parity Transform: Symmetry properties of the eigenstates of the two eye problem	p. 191
6. Receptive field selectivity in a natural image environment	p. 195
6.1 Modeling Orientation Selectivity	p. 195
6.1.1 The input environment	p. 196
6.1.2 Sufficient conditions for obtaining orientation selectivity	p. 196
6.1.3 Dependence on RF size and localization	p. 197
6.1.4 Spatial frequency of receptive fields	p. 197
6.2 Orientation selectivity with statistically defined learning rules	p. 198
6.3 What drives orientation selectivity	p. 200
6.4 ON/OFF inputs	p. 201
6.5 Direction Selectivity	p. 204
6.5.1 Strobe Rearing	p. 206
6.6 Conclusions	p. 207
6A. Technical Remarks Concerning Simulations of Selectivity	p. 221
6A.1 Testing Orientation and Direction	p. 221
6A.1.1 Orientation Selectivity	p. 221
6A.1.2 Direction Selectivity	p. 222
6A.2 Spatial frequency of receptive fields	p. 223
6A.3 Displaying the Weights	p. 224
6A.4 Different Forms of BCM Modification	p. 224
6A.4.1 Evaluation of the Objective Function using Newton's Method	p. 225
7. Ocular dominance in normal and deprived cortex	p. 229
7.1 Development of normal ocular dominance	p. 229
7.2 Deprivation of normal binocular inputs	p. 233
7.2.1 Binocular Deprivation	p. 234
7.2.2 Monocular Deprivation	p. 234
7.2.3 Recovery from Monocular Deprivation	p. 235
7.2.4 Strabismus	p. 236
7.2.5 Robustness to Parameters	p. 237
7.3 Time Course of Deprivation: Simulation Time Versus Real Time	p. 239
7.4 Dependence of deprivation on spontaneous activity or noise	p. 242
7.5 Conclusions	p. 243
8. Networks of interacting BCM Neurons	p. 253
8.1 Simplified Environments	p. 253
8.2 Natural Image Environment	p. 256
8.2.1 Orientation Selectivity	p. 256
8.2.2 Orientation Selectivity and Ocular Dominance	p. 258
8.2.3 Orientation and Direction Selectivity	p. 259
8.3 Structured lateral connectivity	p. 261
8.4 Conclusions	p. 267
9. Experimental evidence for the assumptions and consequences of the BCM theory	p. 271
9.1 Evidence confirming the postulates of the BCM theory	p. 271
9.1.1 The shape of the plasticity curve	p. 272
Rate based induction	p. 272
Pairing based induction	p. 274
Possible physiological bases of synaptic plasticity	p. 275
9.1.2 The sliding modification threshold	p. 276
9.2 Evidence confirming the consequences of the BCM theory	p. 278
9.3 Conclusion	p. 282
Bibliography	p. 291

Available:*

On Order

Summary

Summary

Table of Contents