Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems / Edition 1

by Peter Dayan, Laurence F. Abbott

Overview

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.

Product Details

ISBN-13:	9780262541855
Publisher:	MIT Press
Publication date:	08/12/2005
Series:	Computational Neuroscience Series
Edition description:	New Edition
Pages:	480
Product dimensions:	8.00(w) x 10.00(h) x 0.96(d)
Age Range:	18 Years

About the Author

Peter Dayan is Professor and Director of the Gatsby Computational Neuroscience Unit at University College London.

Larry Abbott is Professor of Neuroscience and Co-Director of the Center for Theoretical Neuroscience at Columbia University.

Table of Contents

	Preface	xiii
I	Neural Encoding and Decoding	1
1	Neural Encoding I: Firing Rates and Spike Statistics	3
1.1	Introduction	3
1.2	Spike Trains and Firing Rates	8
1.3	What Makes a Neuron Fire?	17
1.4	Spike-Train Statistics	24
1.5	The Neural Code	34
1.6	Chapter Summary	39
1.7	Appendices	40
1.8	Annotated Bibliography	43
2	Neural Encoding II: Reverse Correlation and Visual Receptive Fields	45
2.1	Introduction	45
2.2	Estimating Firing Rates	45
2.3	Introduction to the Early Visual System	51
2.4	Reverse-Correlation Methods: Simple Cells	60
2.5	Static Nonlinearities: Complex Cells	74
2.6	Receptive Fields in the Retina and LGN	77
2.7	Constructing V1 Receptive Fields	79
2.8	Chapter Summary	81
2.9	Appendices	81
2.10	Annotated Bibliography	84
3	Neural Decoding	87
3.1	Encoding and Decoding	87
3.2	Discrimination	89
3.3	Population Decoding	97
3.4	Spike-Train Decoding	113
3.5	Chapter Summary	118
3.6	Appendices	119
3.7	Annotated Bibliography	122
4	Information Theory	123
4.1	Entropy and Mutual Information	123
4.2	Information and Entropy Maximization	130
4.3	Entropy and Information for Spike Trains	145
4.4	Chapter Summary	149
4.5	Appendix	150
4.6	Annotated Bibliography	150
II	Neurons and Neural Circuits	151
5	Model Neurons I: Neuroelectronics	153
5.1	Introduction	153
5.2	Electrical Properties of Neurons	153
5.3	Single-Compartment Models	161
5.4	Integrate-and-Fire Models	162
5.5	Voltage-Dependent Conductances	166
5.6	The Hodgkin-Huxley Model	173
5.7	Modeling Channels	175
5.8	Synaptic Conductances	178
5.9	Synapses on Integrate-and-Fire Neurons	188
5.10	Chapter Summary	191
5.11	Appendices	191
5.12	Annotated Bibliography	193
6	Model Neurons II: Conductances and Morphology	195
6.1	Levels of Neuron Modeling	195
6.2	Conductance-Based Models	195
6.3	The Cable Equation	203
6.4	Multi-compartment Models	217
6.5	Chapter Summary	224
6.6	Appendices	224
6.7	Annotated Bibliography	228
7	Network Models	229
7.1	Introduction	229
7.2	Firing-Rate Models	231
7.3	Feedforward Networks	241
7.4	Recurrent Networks	244
7.5	Excitatory-Inhibitory Networks	265
7.6	Stochastic Networks	273
7.7	Chapter Summary	276
7.8	Appendix	276
7.9	Annotated Bibliography	277
III	Adaptation and Learning	279
8	Plasticity and Learning	281
8.1	Introduction	281
8.2	Synaptic Plasticity Rules	284
8.3	Unsupervised Learning	293
8.4	Supervised Learning	313
8.5	Chapter Summary	326
8.6	Appendix	327
8.7	Annotated Bibliography	328
9	Classical Conditioning and Reinforcement Learning	331
9.1	Introduction	331
9.2	Classical Conditioning	332
9.3	Static Action Choice	340
9.4	Sequential Action Choice	346
9.5	Chapter Summary	354
9.6	Appendix	355
9.7	Annotated Bibliography	357
10	Representational Learning	359
10.1	Introduction	359
10.2	Density Estimation	368
10.3	Causal Models for Density Estimation	373
10.4	Discussion	389
10.5	Chapter Summary	394
10.6	Appendix	395
10.7	Annotated Bibliography	396
	Mathematical Appendix	399
A.1	Linear Algebra	399
A.2	Finding Extrema and Lagrange Multipliers	408
A.3	Differential Equations	410
A.4	Electrical Circuits	413
A.5	Probability Theory	415
A.6	Annotated Bibliography	418
	References	419
	Index	439
	Exercises

What People are Saying About This

Christof Koch

The first comprehensive textbook on computational neuroscience. The topics covered span the gamut from biophysical faithful single cell models to neural networks, from the way nervous systems encode information in spike trains to how this information might be decoded, and from synaptic plasticity to supervised and unsupervised learning. And all of this is presented in a sophisticated yet accessible manner. A must buy for anybody who cares about the way brains compute.

Phillip S. Ulinski

Peter Dayan and L.F. Abbott have crafted an excellent introduction to the various methods of modeling nervous system function. The chapters dealing with neural coding and information theory are particularly welcome because these are new areas that are not well represented in existing texts.

John Hertz

Theoretical Neuroscience marks a milestone in the scientific maturation of integrative neuroscience. In the last decade, computational and mathematical modelling have developed into an integral part of the field, and now we finally have a textbook that reflects the changes in the way our science is being done. It will be a standard source of knowledge for the coming generation of students, both theoretical and experimental. I urge anyone who wants to be part of the development of this science in the next decades to get this book. Read it, and let your students read it.

P. Read Montague

Dayan and Abbott inspire us with a work of tremendous breadth, and each chapter is more exciting than the next. Everyone with an interest in neuroscience will want to read this book. A truly remarkable effort by two of the leaders in the field.

Bard Ermentrout

An excellent book. There are a few volumes already available in theoretical neuroscience but none have the scope that this one does.

Endorsement

Theoretical Neuroscience marks a milestone in the scientific maturation of integrative neuroscience. In the last decade, computational and mathematical modelling have developed into an integral part of the field, and now we finally have a textbook that reflects the changes in the way our science is being done. It will be a standard source of knowledge for the coming generation of students, both theoretical and experimental. I urge anyone who wants to be part of the development of this science in the next decades to get this book. Read it, and let your students read it.

—John Hertz, Nordita (Nordic Institute for Theoretical Physics), Denmark

From the Publisher

Peter Dayan and L.F. Abbott have crafted an excellent introduction to the various methods of modeling nervous system function. The chapters dealing with neural coding and information theory are particularly welcome because these are new areas that are not well represented in existing texts.

—Phillip S. Ulinski

Dayan and Abbott inspire us with a work of tremendous breadth, and each chapter is more exciting than the next. Everyone with an interest in neuroscience will want to read this book. A truly remarkable effort by two of the leaders in the field.

—P. Read Montague, Professor, Division of Neuroscience, and Director, Center for Theoretical Neuroscience, Baylor College of Medicine

Terrence J. Sejnowski

Theoretical Neuroscience provides a rigorous introduction to how neurons code, compute, and adapt. It is a remarkable synthesis of advances from many areas of neuroscience into a coherent computational framework. This book sets the standards for a new generation of modelers.

Editorial Reviews

It will not be surprising if this book becomes the standard text for students and researchers entering theoretical neuroscience for years to come.—M. Brandon Westover, Philosophical Psychology—

Not only does the book set a high standard for theoretical neuroscience, it defines the field.

—Dmitri Chklovskii, Neuron—

From the Publisher

Not only does the book set a high standard for theoretical neuroscience, it defines the field.

—Dmitri Chklovskii, Neuron

Reviews

Not only does the book set a high standard for theoretical neuroscience, it defines the field.

Neuron - Dmitri Chklovskii

It will not be surprising if this book becomes the standard text for students and researchers entering theoretical neuroscience for years to come.

Philosophical Psychology - M. Brandon Westover