Elsevier S & T

Methods and Models in Neurophysics: Lecture Notes of the Les Houches Summer School 2003

Chow, Carson

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Table of contents
  • Cover
  • Contentsxix
  • Course 1. Experimenting with theory1
  • 1. Overcoming communication barriers6
  • 2. Modeling with biological neurons-the dynamic clamp8
  • 3. The traps inherent in building conductance-based models9
  • 4. Theory can drive new experiments12
  • 5. Conclusions13
  • References14
  • Course 2. Understanding neuronal dynamics by geometrical dissection of minimal models17
  • 1. Introduction21
  • 2. Revisiting the Hodgkin–Huxley equations25
  • 3. Morris-Lecar model38
  • 4. Bursting, cellular level51
  • 5. Bursting, network generated. Episodic rhythms in the developing spinal cord58
  • 6. Chapter summary65
  • References69
  • Course 3. Geometric singular perturbation analysis of neuronal dynamics73
  • 1. Introduction77
  • 2. Introduction to dynamical systems78
  • 3. Properties of a single neuron90
  • 4. Two mutually coupled cells97
  • 5. Excitatory-inhibitory networks108
  • 6. Activity patterns in the basal ganglia115
  • References121
  • Course 4. Theory of neural synchrony123
  • 1. Introduction127
  • 2. Weakly coupled oscillators128
  • 3. Strongly coupled oscillators: mechanisms of synchrony153
  • 4. Conclusion169
  • Appendix A. Hodgkin–Huxley and Wang-Buszaki models172
  • Appendix B. Measure of synchrony and variability in numerical simulations174
  • Appendix C. Reduction of a conductance-based model to the QIF model175
  • References177
  • Course 5. Some useful numerical techniques for simulating integrate-and-fire networks179
  • 1.Introduction183
  • 2. The conductance-based I&F model184
  • 3. Modified time-stepping schemes185
  • 4. Synaptic interactions190
  • 5. Simulating a V1 model192
  • References195
  • Course 6. Propagation of pulses in cortical networks: the single-spike approximation197
  • 1. Introduction202
  • 2. Propagating pulses in networks of excitatory neurons203
  • 3. Propagating pulses in networks of excitatory and inhibitory neurons217
  • 4. Discussion237
  • Appendix A. Stability of the lower branch241
  • References243
  • Course 7. Activity-dependent transmission in neocortical synapses245
  • 1. Introduction249
  • 2. Phenomenological model of synaptic depression and facilitation250
  • 3. Dynamic synaptic transmission on the population level253
  • 4. Recurrent networks with synaptic depression256
  • 5. Conclusion263
  • References264
  • Course 8. Theory of large recurrent networks: from spikes to behavior267
  • 1. Introduction271
  • 2. From spikes to rates I: rates in asynchronous states272
  • 3. From spikes to rates II: dynamics and conductances284
  • 4. Persistent activity and neural integration in the brain295
  • 5. Feature selectivity in recurrent networks„the ring model312
  • 6. Models of associative memory324
  • 7. Concluding remarks338
  • References339
  • Course 9. Irregular activity in large networks of neurons341
  • 1. Introduction345
  • 2. A simple binary model347
  • 3. A memory model366
  • 4. A model of visual cortex hypercolumn372
  • 5. Adding realism: integrate-and-fire network384
  • 6. Discussion400
  • References402
  • Course 10. Network models of memory407
  • 1. Introduction411
  • 2. Persistent neuronal activity during delayed response experiments412
  • 3. Scenarios for multistability in neural systems421
  • 4. Networks of binary neurons with discrete attractors423
  • 5. Learning439
  • 6. Networks of spiking neurons with discrete attractors445
  • 7. Plasticity of persistent activity459
  • 8. Models with continuous attractors465
  • 9. Conclusions468
  • References470
  • Course 11. Pattern formation in visual cortex477
  • 1. Introduction481
  • 2. The functional architecture of V 1485
  • 3. Large-scale models of V1493
  • 4. Pattern formation in a single hypercolumn511
  • 5. Pattern formation in a coupled hypercolumn model of V1528
  • 6. Pattem formation in a planar model of V 1547
  • 7. Pattem formation in a model of cortical development561
  • 8. Future directions568
  • References570
  • Course 12. Symmetry breaking and pattern selection in visual cortical development575
  • 1. Introduction579
  • 2. The pattern of orientation preference columns582
  • 3. Symmetries in the development of orientation columns583
  • 4. From learning to dynamics587
  • 5. Generation and motion of pinwheels588
  • 6. The problem of pinwheel stability597
  • 7. Weakly nonlinear analysis of pattern selection598
  • 8. A Swift-Hohenberg model with stable pinwheel patterns614
  • 9. Discussion635
  • References638
  • Course 13. Of the evolution of the brain641
  • 1. Introduction and summary645
  • 2. The phase transition that made us mammals645
  • 3. Maps and patterns of threshold-linear units650
  • 4. Validation of the lamination hypothesis659
  • 5. What do we need DG and CA1 for?663
  • 6. Infinite recursion and the origin of cognition668
  • 7. Reducing local networks to Potts units674
  • References685
  • Course 14. Theory of point processes for neural systems691
  • 1. Neural spike trains as point processes694
  • 2. Integrate and fire models and interspike interval distributions695
  • 3. The conditional intensity function and interevent time probability density701
  • 4. Joint probability density of a point process704
  • 5. Special point process models708
  • 6. The time-rescaling theorem715
  • 7. Simulation of point processes720
  • 8. Poisson limit theorems724
  • 9. Problems725
  • References726
  • Course 15. Technique(s) for spike-sorting729
  • 1. Introduction733
  • 2. The problem to solve734
  • 3. Two features of single neuron data we would like to include in the spike-sorting procedure735
  • 4. Noise properties738
  • 5. Probabilistic data generation model741
  • 6. Markov chains749
  • 7. The Metropolis–Hastings algorithm and its relatives757
  • 8. Priors choice762
  • 9. The good use of the ergodic theorem. A warning764
  • 10. Slow relaxation and the replica exchange method765
  • 11. An Example from a simulated data set768
  • 12. Conclusions778
  • 13. Exercises solutions780
  • References783
  • Course 16. The emergence of relevant data representations: an information theoretic approach787
  • 1. Part I: the fundamental dilemma792
  • 2. Part II: Shannon's information theory„a new perspective795
  • 3. Part III: relevant data representation804
  • 4. Part IV: applications and extensions812
  • References827
Book details
  • Vendor Elsevier S & T
  • SKU 9780444517920
  • ISBN-13 9780080536385
  • Author Chow, Carson
  • Category Science
  • Subject Biophysics

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Neuroscience is an interdisciplinary field that strives to understand the functioning of neural systems at levels ranging from biomolecules and cells to behaviour and higher brain functions (perception, memory, cognition). Neurophysics has flourished over the past three decades, becoming an indelible part of neuroscience, and has arguably entered its maturity. It encompasses a vast array of approaches stemming from theoretical physics, computer science, and applied mathematics. This book provides a detailed review of this field from basic concepts to its most recent development.