Spiking Neuron Models: Single Neurons, Populations, Plasticity,9780521813846

Spiking Neuron Models: Single Neurons, Populations, Plasticity

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ISBN13: 9780521813846
ISBN10: 0521813840
Format: Hardcover
Pub. Date: 2002-08-26
Publisher(s): Cambridge University Press
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Summary

This introduction to spiking neurons can be used in advanced-level courses in computational neuroscience, theoretical biology, neural modeling, biophysics, or neural networks. It focuses on phenomenological approaches rather than detailed models in order to provide the reader with a conceptual framework. The authors formulate the theoretical concepts clearly without many mathematical details. While the book contains standard material for courses in computational neuroscience, neural modeling, or neural networks, it also provides an entry to current research. No prior knowledge beyond undergraduate mathematics is required.

Table of Contents

Preface xi
Acknowledgments xiv
Introduction
1(28)
Elements of neuronal systems
1(3)
The ideal spiking neuron
2(1)
Spike trains
3(1)
Synapses
4(1)
Elements of neuronal dynamics
4(3)
Postsynaptic potentials
6(1)
Firing threshold and action potential
6(1)
A phenomenological neuron model
7(6)
Definition of the model SRM0
7(2)
Limitations of the model
9(4)
The problem of neuronal coding
13(2)
Rate codes
15(5)
Rate as a spike count (average over time)
15(2)
Rate as a spike density (average over several runs)
17(1)
Rate as a population activity (average over several neurons)
18(2)
Spike codes
20(5)
Time-to-first-spike
20(1)
Phase
21(1)
Correlations and synchrony
22(1)
Stimulus reconstruction and reverse correlation
23(2)
Discussion: spikes or rates?
25(2)
Summary
27(2)
Part one: Single neuron models 29(172)
Detailed neuron models
31(38)
Equilibrium potential
31(3)
Nernst potential
31(2)
Reversal potential
33(1)
Hodgkin--Huxley model
34(7)
Definition of the model
34(3)
Dynamics
37(4)
The zoo of ion channels
41(10)
Sodium channels
41(2)
Potassium channels
43(2)
Low-threshold calcium current
45(2)
High-threshold calcium current and calcium-activated potassium channels
47(3)
Calcium dynamics
50(1)
Synapses
51(2)
Inhibitory synapses
51(1)
Excitatory synapses
52(1)
Spatial structure: the dendritic tree
53(8)
Derivation of the cable equation
54(3)
Green's function (*)
57(3)
Nonlinear extensions to the cable equation
60(1)
Compartmental models
61(5)
Summary
66(3)
Two-dimensional neuron models
69(24)
Reduction to two dimensions
69(5)
General approach
70(2)
Mathematical steps (*)
72(2)
Phase plane analysis
74(8)
Nullclines
74(1)
Stability of fixed points
75(2)
Limit cycles
77(3)
Type I and type II models
80(2)
Threshold and excitability
82(8)
Type I models
84(1)
Type II models
85(1)
Separation of time scales
86(4)
Summary
90(3)
Formal spiking neuron models
93(54)
Integrate-and-fire model
93(9)
Leaky integrate-and-fire model
94(3)
Nonlinear integrate-and-fire model
97(3)
Stimulation by synaptic currents
100(2)
Spike Response Model (SRM)
102(14)
Definition of the SRM
102(6)
Mapping the integrate-and-fire model to the SRM
108(3)
Simplified model SRMo
111(5)
From detailed models to formal spiking neurons
116(17)
Reduction of the Hodgkin--Huxley model
117(6)
Reduction of a cortical neuron model
123(8)
Limitations
131(2)
Multicompartment integrate-and-fire model
133(6)
Definition of the model
133(2)
Relation to the model SRMo
135(2)
Relation to the full Spike Response Model (*)
137(2)
Application: coding by spikes
139(6)
Summary
145(2)
Noise in spiking neuron models
147(54)
Spike train variability
148(2)
Are neurons noisy?
148(1)
Noise sources
149(1)
Statistics of spike trains
150(13)
Input-dependent renewal systems
151(1)
Interval distribution
152(1)
Survivor function and hazard
153(5)
Stationary renewal theory and experiments
158(2)
Autocorrelation of a stationary renewal process
160(3)
Escape noise
163(9)
Escape rate and hazard function
164(4)
Interval distribution and mean firing rate
168(4)
Slow noise in the parameters
172(2)
Diffusive noise
174(10)
Stochastic spike arrival
174(4)
Diffusion limit (*)
178(4)
Interval distribution
182(2)
The subthreshold regime
184(4)
Sub- and superthreshold stimulation
185(2)
Coefficient of variation Cv
187(1)
From diffusive noise to escape noise
188(3)
Stochastic resonance
191(3)
Stochastic firing and rate models
194(4)
Analog neurons
194(2)
Stochastic rate model
196(1)
Population rate model
197(1)
Summary
198(3)
Part two: Population models 201(254)
Population equations
203(46)
Fully connected homogeneous network
204(3)
Density equations
207(15)
Integrate-and-fire neurons with stochastic spike arrival
207(7)
Spike Response Model neurons with escape noise
214(4)
Relation between the approaches
218(4)
Integral equations for the population activity
222(9)
Assumptions
223(1)
Integral equation for the dynamics
223(8)
Asynchronous firing
231(9)
Stationary activity and mean firing rate
231(2)
Gain function and fixed points of the activity
233(2)
Low-connectivity networks
235(5)
Interacting populations and continuum models
240(5)
Several populations
240(2)
Spatial continuum limit
242(3)
Limitations
245(1)
Summary
246(3)
Signal transmission and neuronal coding
249(36)
Linearized population equation
250(11)
Noise-free population dynamics (*)
252(4)
Escape noise (*)
256(4)
Noisy reset (*)
260(1)
Transients
261(7)
Transients in a noise-free network
262(2)
Transients with noise
264(4)
Transfer function
268(5)
Signal term
268(5)
Signal-to-noise ratio
273(1)
The significance of a single spike
273(9)
The effect of an input spike
274(4)
Reverse correlation -- the significance of an output spike
278(4)
Summary
282(3)
Oscillations and synchrony
285(30)
Instability of the asynchronous state
286(6)
Synchronized oscillations and locking
292(10)
Locking in noise-free populations
292(6)
Locking in SRMo neurons with noisy reset (*)
298(2)
Cluster states
300(2)
Oscillations in reverberating loops
302(11)
From oscillations with spiking neurons to binary neurons
305(1)
Mean field dynamics
306(3)
Microscopic dynamics
309(4)
Summary
313(2)
Spatially structured networks
315(36)
Stationary patterns of neuronal activity
316(13)
Homogeneous solutions
318(1)
Stability of homogeneous states
319(5)
``Blobs'' of activity: inhomogeneous states
324(5)
Dynamic patterns of neuronal activity
329(5)
Oscillations
330(2)
Traveling waves
332(2)
Patterns of spike activity
334(7)
Traveling fronts and waves (*)
337(1)
Stability (*)
338(3)
Robust transmission of temporal information
341(7)
Summary
348(3)
Part three: Models of synaptic plasticity
349(2)
Hebbian models
351(36)
Synaptic plasticity
351(5)
Long-term potentiation
352(2)
Temporal aspects
354(2)
Rate-based Hebbian learning
356(6)
A mathematical formulation of Hebb's rule
356(6)
Spike-time-dependent plasticity
362(8)
Phenomenological model
362(3)
Consolidation of synaptic efficacies
365(2)
General framework (*)
367(3)
Detailed models of synaptic plasticity
370(13)
A simple mechanistic model
371(3)
A kinetic model based on NMDA receptors
374(3)
A calcium-based model
377(6)
Summary
383(4)
Learning equations
387(34)
Learning in rate models
387(16)
Correlation matrix and principal components
387(2)
Evolution of synaptic weights
389(5)
Weight normalization
394(4)
Receptive field development
398(5)
Learning in spiking models
403(15)
Learning equation
404(2)
Spike-spike correlations
406(3)
Relation of spike-based to rate-based learning
409(2)
Static-pattern scenario
411(4)
Distribution of synaptic weights
415(3)
Summary
418(3)
Plasticity and coding
421(34)
Learning to be fast
421(4)
Learning to be precise
425(7)
The model
425(2)
Firing time distribution
427(1)
Stationary synaptic weights
428(2)
The role of the firing threshold
430(2)
Sequence learning
432(5)
Subtraction of expectations
437(4)
Electro-sensory system of Mormoryd electric fish
437(2)
Sensory image cancellation
439(2)
Transmission of temporal codes
441(11)
Auditory pathway and sound source localization
442(2)
Phase locking and coincidence detection
444(3)
Tuning of delay lines
447(5)
Summary
452(3)
References 455(22)
Index 477

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