Theoretical Neuroscience : Computational and Mathematical Modeling of Neural Systems

by Peter Dayan and L. F. Abbott

• ISBN13: 9780262041997
• ISBN10: 0262041995
• Format: Hardcover
• Copyright: 2001-11-01
• Publisher: Mit Pr

Summary

Theoretical neuroscience provides a quantitative basis for describing what nervous systems do, determining how they function, and uncovering the general principles by which they operate. This text introduces the basic mathematical and computational methods of theoretical neuroscience and presents applications in a variety of areas including vision, sensory-motor integration, development, learning, and memory. The book is divided into three parts. Part I discusses the relationship between sensory stimuli and neural responses, focusing on the representation of information by the spiking activity of neurons. Part II discusses the modeling of neurons and neural circuits on the basis of cellular and synaptic biophysics. Part III analyzes the role of plasticity in development and learning. An appendix covers the mathematical methods used, and exercises are available on the book's Web site.

Author Biography

Peter Dayan is on the faculty of the Gatsby Computational Neuroscience Unit at University College London.

Table of Contents

Preface	p. xiii
Neural Encoding and Decoding	p. 1
Neural Encoding I: Firing Rates and Spike Statistics	p. 3
Introduction	p. 3
Spike Trains and Firing Rates	p. 8
What Makes a Neuron Fire?	p. 17
Spike-Train Statistics	p. 24
The Neural Code	p. 34
Chapter Summary	p. 39
Appendices	p. 40
Annotated Bibliography	p. 43
Neural Encoding II: Reverse Correlation and Visual Receptive Fields	p. 45
Introduction	p. 45
Estimating Firing Rates	p. 45
Introduction to the Early Visual System	p. 51
Reverse-Correlation Methods: Simple Cells	p. 60
Static Nonlinearities: Complex Cells	p. 74
Receptive Fields in the Retina and LGN	p. 77
Constructing V1 Receptive Fields	p. 79
Chapter Summary	p. 81
Appendices	p. 81
Annotated Bibliography	p. 84
Neural Decoding	p. 87
Encoding and Decoding	p. 87
Discrimination	p. 89
Population Decoding	p. 97
Spike-Train Decoding	p. 113
Chapter Summary	p. 118
Appendices	p. 119
Annotated Bibliography	p. 122
Information Theory	p. 123
Entropy and Mutual Information	p. 123
Information and Entropy Maximization	p. 130
Entropy and Information for Spike Trains	p. 145
Chapter Summary	p. 149
Appendix	p. 150
Annotated Bibliography	p. 150
Neurons and Neural Circuits	p. 151
Model Neurons I: Neuroelectronics	p. 153
Introduction	p. 153
Electrical Properties of Neurons	p. 153
Single-Compartment Models	p. 161
Integrate-and-Fire Models	p. 162
Voltage-Dependent Conductances	p. 166
The Hodgkin-Huxley Model	p. 173
Modeling Channels	p. 175
Synaptic Conductances	p. 178
Synapses on Integrate-and-Fire Neurons	p. 188
Chapter Summary	p. 191
Appendices	p. 191
Annotated Bibliography	p. 193
Model Neurons II: Conductances and Morphology	p. 195
Levels of Neuron Modeling	p. 195
Conductance-Based Models	p. 195
The Cable Equation	p. 203
Multi-compartment Models	p. 217
Chapter Summary	p. 224
Appendices	p. 224
Annotated Bibliography	p. 228
Network Models	p. 229
Introduction	p. 229
Firing-Rate Models	p. 231
Feedforward Networks	p. 241
Recurrent Networks	p. 244
Excitatory-Inhibitory Networks	p. 265
Stochastic Networks	p. 273
Chapter Summary	p. 276
Appendix	p. 276
Annotated Bibliography	p. 277
Adaptation and Learning	p. 279
Plasticity and Learning	p. 281
Introduction	p. 281
Synaptic Plasticity Rules	p. 284
Unsupervised Learning	p. 293
Supervised Learning	p. 313
Chapter Summary	p. 326
Appendix	p. 327
Annotated Bibliography	p. 328
Classical Conditioning and Reinforcement Learning	p. 331
Introduction	p. 331
Classical Conditioning	p. 332
Static Action Choice	p. 340
Sequential Action Choice	p. 346
Chapter Summary	p. 354
Appendix	p. 355
Annotated Bibliography	p. 357
Representational Learning	p. 359
Introduction	p. 359
Density Estimation	p. 368
Causal Models for Density Estimation	p. 373
Discussion	p. 389
Chapter Summary	p. 394
Appendix	p. 395
Annotated Bibliography	p. 396
Mathematical Appendix	p. 399
Linear Algebra	p. 399
Finding Extrema and Lagrange Multipliers	p. 408
Differential Equations	p. 410
Electrical Circuits	p. 413
Probability Theory	p. 415
Annotated Bibliography	p. 418
References	p. 419
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