Spiking Neuron Models: Single Neurons, Populations, Plasticity

Front Cover
Cambridge University Press, Aug 15, 2002 - Computers - 480 pages
0 Reviews
This is an introduction to spiking neurons for advanced undergraduate or graduate students. It can be used with 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. No prior knowledge beyond undergraduate mathematics is necessary to follow the book. Thus it should appeal to students or researchers in physics, mathematics, or computer science interested in biology; moreover it will also be useful for biologists working in mathematical modeling.
  

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Preface
xi
Acknowledgments
xiv
Introduction
1
1 1 1 The ideal spiking neuron
2
1 12 Spike trains
3
113 Synapses
4
121 Postsynaptic potentials
6
13 A phenomenological neuron model
7
Population equations
203
61 Fully connected homogeneous network
204
62 Density equations
207
622 Spike Response Model neurons with escape noise
214
623 Relation between the approaches
218
63 Integral equations for the population activity
222
631 Assumptions
223
64 Asynchronous firing
231

132 Limitations of the model
9
14 The problem of neuronal coding
13
15 Rate codes
15
152 Rate as a spike density average over several runs
17
153 Rate as a population activity average over several neurons
18
16 Spike codes
20
162 Phase
21
163 Correlations and synchrony
22
164 Stimulus reconstruction and reverse correlation
23
spikes or rates?
25
18 Summary
27
Single neuron models
29
2 Detailed neuron models
31
212 Reversal potential
33
22 HodgkinHuxley model
34
222 Dynamics
37
23 The zoo of ion channels
41
232 Potassium channels
43
233 Lowthreshold calcium current
45
234 Highthreshold calcium current and calciumactivated potassium
47
235 Calcium dynamics
50
24 Synapses
51
242 Excitatory synapses
52
the dendritic tree
53
251 Derivation of the cable equation
54
252 Greens function
57
253 Nonlinear extensions to the cable equation
60
26 Compartmental models
61
27 Summary
66
Twodimensional neuron models
69
311 General approach
70
312 Mathematical steps
72
32 Phase plane analysis
74
322 Stability of fixed points
75
323 Limit cycles
77
324 Type I and type II models
80
33 Threshold and excitability
82
331 Type I models
84
332 Type II models
85
333 Separation of time scales
86
34 Summary
90
Formal spiking neuron models
93
411 Leaky integrateandfire model
94
412 Nonlinear integrateandfire model
97
413 Stimulation by synaptic currents
100
42 Spike Response Model SRM
102
422 Mapping the integrateandfire model to the SRM
108
423 Simplified model SRMₒ
111
43 From detailed models to formal spiking neurons
116
431 Reduction of the HodgkinHuxley model
117
432 Reduction of a cortical neuron model
123
433 Limitations
131
44 Multicompartment integrateandfire model
133
442 Relation to the model SRMₒ
135
443 Relation to the full Spike Response Model
137
coding by spikes
139
46 Summary
145
Noise in spiking neuron models
147
51 Spike train variability
148
572 Noise sources
149
52 Statistics of spike trains
150
52 Inputdependent renewal systems
151
522 Interval distribution
152
523 Survivor function and hazard
153
524 Stationary renewal theory and experiments
158
525 Autocorrelation of a stationary renewal process
160
53 Escape noise
163
531 Escape rate and hazard function
164
532 Interval distribution and mean firing rate
168
54 Slow noise in the parameters
172
55 Diffusive noise
174
552 Diffusion limit
178
553 Interval distribution
182
56 The subthreshold regime
184
561 Sub and superthreshold stimulation
185
562 Coefficient of variation C𝘷
187
57 From diffusive noise to escape noise
188
58 Stochastic resonance
191
59 Stochastic firing and rate models
194
592 Stochastic rate model
196
593 Population rate model
197
510 Summary
198
Population models
201
642 Gain function and fixed points of the activity
233
643 Lowconnectivity networks
235
65 Interacting populations and continuum models
240
652 Spatial continuum limit
242
66 Limitations
245
67 Summary
246
7 Signal transmission and neuronal coding
249
71 Linearized population equation
250
777 Noisefree population dynamics
252
712 Escape noise
256
713 Noisy reset
260
72 Transients
261
721 Transients in a noisefree network
262
722 Transients with noise
264
73 Transfer function
268
732 Signaltonoise ratio
273
741 The effect of an input spike
274
742 Reverse correlation the significance of an output spike
278
75 Summary
282
Oscillations and synchrony
285
81 Instability of the asynchronous state
286
82 Synchronized oscillations and locking
292
822 Locking in SRMₒ neurons with noisy reset
298
823 Cluster states
300
83 Oscillations in reverberating loops
302
831 From oscillations with spiking neurons to binary neurons
305
832 Mean field dynamics
306
833 Microscopic dynamics
309
84 Summary
313
Spatially structured networks
315
91 Stationary patterns of neuronal activity
316
911 Homogeneous solutions
318
912 Stability of homogeneous states
319
inhomogeneous states
324
92 Dynamic patterns of neuronal activity
329
921 Oscillations
330
922 Traveling waves
332
93 Patterns of spike activity
334
931 Traveling fronts and waves
337
932 Stability
338
94 Robust transmission of temporal information
341
95 Summary
348
Models of synaptic plasticity
349
Hebbian models
351
1011 Longterm potentiation
352
1012 Temporal aspects
354
102 Ratebased Hebbian learning
356
103 Spiketimedependent plasticity
362
1032 Consolidation of synaptic efficacies
365
1033 General framework
367
104 Detailed models of synaptic plasticity
370
1041 A simple mechanistic model
371
1042 A kinetic model based on NMDA receptors
374
1043 A calciumbased model
377
105 Summary
383
Learning equations
387
1112 Evolution of synaptic weights
389
1113 Weight normalization
394
1114 Receptive field development
398
112 Learning in spiking models
403
1121 Learning equation
404
1122 Spikespike correlations
406
1123 Relation of spikebased to ratebased learning
409
1124 Staticpattern scenario
411
1125 Distribution of synaptic weights
415
113 Summary
418
Plasticity and coding
421
122 Learning to be precise
425
1222 Firing time distribution
427
1223 Stationary synoptic weights
428
1224 The role of the firing threshold
430
123 Sequence learning
432
124 Subtraction of expectations
437
1242 Sensory image cancellation
439
125 Transmission of temporal codes
441
1251 Auditory pathway and sound source localization
442
1252 Phase locking and coincidence detection
444
7253 Tuning of delay lines
447
126 Summary
452
References
455
Index
477
Copyright

Common terms and phrases

Popular passages

Page 458 - McLennan, H. (1983) Excitatory amino acids in synaptic transmission in the Schaffer collateral-commissural pathway of the rat hippocampus.
Page 456 - N. (1997) Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex, Cerebral Cortex...
Page 455 - E. and Vaadia, E. (1993). Spatiotemporal firing patterns in the frontal cortex of behaving monkeys.
Page 473 - Swindale, NV 1980. A model for the formation of ocular dominance stripes. Proc.
Page 473 - Niebur E. (2000) Attention modulates synchronized neuronal firing in primate somatosensory cortex. Nature 404: 187-190.

References to this book

All Book Search results »

About the author (2002)

Wulfram Gerstner is Director of the Laboratory of Computational Neuroscience and a Professor of Life Sciences and Computer Science at the Ecole Polytechnique Federale de Lausanne (EPFL) in Switzerland. He studied physics in Tubingen and Munich and holds a PhD from the Technical University of Munich. His research in computational neuroscience concentrates on models of spiking neurons and synaptic plasticity. He teaches computational neuroscience to physicists, computer scientists, mathematicians, and life scientists. He is a co-author of Spiking Neuron Models (Cambridge University Press, 2002).

Bibliographic information