Theoretical Neuroscience Computational and Mathematical Modeling of Neural Systems

by Dayan, Peter; Abbott, Laurence F.

• ISBN13: 9780262541855
• ISBN10: 0262541858
• Format: Paperback
• Copyright: 2005-08-12
• Publisher: The MIT Press

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 Professor of Computational Neuroscience at the Gatsby Computational Neuroscience Unit at University College London

Table of Contents

Preface	xiii
I Neural Encoding and Decoding	1	(150)
Neural Encoding I: Firing Rates and Spike Statistics	3	(42)
Introduction	3	(5)
Spike Trains and Firing Rates	8	(9)
What Makes a Neuron Fire?	17	(7)
Spike-Train Statistics	24	(10)
The Neural Code	34	(5)
Chapter Summary	39	(1)
Appendices	40	(3)
Annotated Bibliography	43	(2)
Neural Encoding II: Reverse Correlation and Visual Receptive Fields	45	(42)
Introduction	45	(1)
Estimating Firing Rates	45	(6)
Introduction to the Early Visual System	51	(9)
Reverse-Correlation Methods: Simple Cells	60	(14)
Static Nonlinearities: Complex Cells	74	(3)
Receptive Fields in the Retina and LGN	77	(2)
Constructing V1 Receptive Fields	79	(2)
Chapter Summary	81	(1)
Appendices	81	(3)
Annotated Bibliography	84	(3)
Neural Decoding	87	(36)
Encoding and Decoding	87	(2)
Discrimination	89	(8)
Population Decoding	97	(16)
Spike-Train Decoding	113	(5)
Chapter Summary	118	(1)
Appendices	119	(3)
Annotated Bibliography	122	(1)
Information Theory	123	(28)
Entropy and Mutual Information	123	(7)
Information and Entropy Maximization	130	(15)
Entropy and Information for Spike Trains	145	(4)
Chapter Summary	149	(1)
Appendix	150	(1)
Annotated Bibliography	150	(1)
II Neurons and Neural Circuits	151	(128)
Model Neurons I: Neuroelectronics	153	(42)
Introduction	153	(1)
Electrical Properties of Neurons	153	(8)
Single-Compartment Models	161	(1)
Integrate-and-Fire Models	162	(4)
Voltage-Dependent Conductances	166	(7)
The Hodgkin-Huxley Model	173	(2)
Modeling Channels	175	(3)
Synaptic Conductances	178	(10)
Synapses on Integrate-and-Fire Neurons	188	(3)
Chapter Summary	191	(1)
Appendices	191	(2)
Annotated Bibliography	193	(2)
Model Neurons II: Conductances and Morphology	195	(34)
Levels of Neuron Modeling	195	(1)
Conductance-Based Models	195	(8)
The Cable Equation	203	(14)
Multi-compartment Models	217	(7)
Chapter Summary	224	(1)
Appendices	224	(4)
Annotated Bibliography	228	(1)
Network Models	229	(50)
Introduction	229	(2)
Firing-Rate Models	231	(10)
Feedforward Networks	241	(3)
Recurrent Networks	244	(21)
Excitatory-Inhibitory Networks	265	(8)
Stochastic Networks	273	(3)
Chapter Summary	276	(1)
Appendix	276	(1)
Annotated Bibliography	277	(2)
III Adaptation and Learning	279	(120)
Plasticity and Learning	281	(50)
Introduction	281	(3)
Synaptic Plasticity Rules	284	(9)
Unsupervised Learning	293	(20)
Supervised Learning	313	(13)
Chapter Summary	326	(1)
Appendix	327	(1)
Annotated Bibliography	328	(3)
Classical Conditioning and Reinforcement Learning	331	(28)
Introduction	331	(1)
Classical Conditioning	332	(8)
Static Action Choice	340	(6)
Sequential Action Choice	346	(8)
Chapter Summary	354	(1)
Appendix	355	(2)
Annotated Bibliography	357	(2)
Representational Learning	359	(40)
Introduction	359	(9)
Density Estimation	368	(5)
Causal Models for Density Estimation	373	(16)
Discussion	389	(5)
Chapter Summary	394	(1)
Appendix	395	(1)
Annotated Bibliography	396	(3)
Mathematical Appendix	399	(20)
Linear Algebra	399	(9)
Finding Extrema and Lagrange Multipliers	408	(2)
Differential Equations	410	(3)
Electrical Circuits	413	(2)
Probability Theory	415	(3)
Annotated Bibliography	418	(1)
References	419	(20)
Index	439