Methods and Models in Neurophysics (eBook)

Lecture Notes of the Les Houches Summer School 2003

Carson Chow, Jean Dalibard, Boris Gutkin, David Hansel, Claude Meunier (Herausgeber)

eBook Download: PDF

2004 | 1. Auflage
862 Seiten
Elsevier Science (Verlag)
978-0-08-053638-5 (ISBN)

Infos

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.

Inhalt

Front Cover 1
Methods and Models in Neurophysics 4
Copyright Page 5
Contents 20
Course 1. Experimenting with theory 34
1. Overcoming communication barriers 39
2. Modeling with biological neurons-the dynamic clamp 41
3. The traps inherent in building conductance-based models 42
4. Theory can drive new experiments 45
5. Conclusions 46
References 47
Course 2. Understanding neuronal dynamics by geometrical dissection of minimal models 50
1. Introduction 54
2. Revisiting the Hodgkin–Huxley equations 58
3. Morris-Lecar model 71
4. Bursting, cellular level 84
5. Bursting, network generated. Episodic rhythms in the developing spinal cord 91
6. Chapter summary 98
References 102
Course 3. Geometric singular perturbation analysis of neuronal dynamics 106
1. Introduction 110
2. Introduction to dynamical systems 111
3. Properties of a single neuron 123
4. Two mutually coupled cells 130
5. Excitatory-inhibitory networks 141
6. Activity patterns in the basal ganglia 148
References 154
Course 4. Theory of neural synchrony 156
1. Introduction 160
2. Weakly coupled oscillators 161
3. Strongly coupled oscillators: mechanisms of synchrony 186
4. Conclusion 202
Appendix A. Hodgkin–Huxley and Wang-Buszaki models 205
Appendix B. Measure of synchrony and variability in numerical simulations 207
Appendix C. Reduction of a conductance-based model to the QIF model 208
References 210
Course 5. Some useful numerical techniques for simulating integrate-and-fire networks 212
1.Introduction 216
2. The conductance-based I& F model
3. Modified time-stepping schemes 218
4. Synaptic interactions 223
5. Simulating a V1 model 225
References 228
Course 6. Propagation of pulses in cortical networks: the single-spike approximation 230
1. Introduction 235
2. Propagating pulses in networks of excitatory neurons 236
3. Propagating pulses in networks of excitatory and inhibitory neurons 250
4. Discussion 270
Appendix A. Stability of the lower branch 274
References 276
Course 7. Activity-dependent transmission in neocortical synapses 278
1. Introduction 282
2. Phenomenological model of synaptic depression and facilitation 283
3. Dynamic synaptic transmission on the population level 286
4. Recurrent networks with synaptic depression 289
5. Conclusion 296
References 297
Course 8. Theory of large recurrent networks: from spikes to behavior 300
1. Introduction 304
2. From spikes to rates I: rates in asynchronous states 305
3. From spikes to rates II: dynamics and conductances 317
4. Persistent activity and neural integration in the brain 328
5. Feature selectivity in recurrent networks—the ring model 345
6. Models of associative memory 357
7. Concluding remarks 371
References 372
Course 9. Irregular activity in large networks of neurons 374
1. Introduction 378
2. A simple binary model 380
3. A memory model 399
4. A model of visual cortex hypercolumn 405
5. Adding realism: integrate-and-fire network 417
6. Discussion 433
References 435
Course 10. Network models of memory 440
1. Introduction 444
2. Persistent neuronal activity during delayed response experiments 445
3. Scenarios for multistability in neural systems 454
4. Networks of binary neurons with discrete attractors 456
5. Learning 472
6. Networks of spiking neurons with discrete attractors 478
7. Plasticity of persistent activity 492
8. Models with continuous attractors 498
9. Conclusions 501
References 503
Course 11. Pattern formation in visual cortex 510
1. Introduction 514
2. The functional architecture of V 1 518
3. Large-scale models of V1 526
4. Pattern formation in a single hypercolumn 544
5. Pattern formation in a coupled hypercolumn model of V1 561
6. Pattem formation in a planar model of V 1 580
7. Pattem formation in a model of cortical development 594
8. Future directions 601
References 603
Course 12. Symmetry breaking and pattern selection in visual cortical development 608
1. Introduction 612
2. The pattern of orientation preference columns 615
3. Symmetries in the development of orientation columns 616
4. From learning to dynamics 620
5. Generation and motion of pinwheels 621
6. The problem of pinwheel stability 630
7. Weakly nonlinear analysis of pattern selection 631
8. A Swift-Hohenberg model with stable pinwheel patterns 647
9. Discussion 668
References 671
Course 13. Of the evolution of the brain 674
1. Introduction and summary 678
2. The phase transition that made us mammals 678
3. Maps and patterns of threshold-linear units 683
4. Validation of the lamination hypothesis 692
5. What do we need DG and CA1 for? 696
6. Infinite recursion and the origin of cognition 701
7. Reducing local networks to Potts units 707
References 718
Course 14. Theory of point processes for neural systems 724
1. Neural spike trains as point processes 727
2. Integrate and fire models and interspike interval distributions 728
3. The conditional intensity function and interevent time probability density 734
4. Joint probability density of a point process 737
5. Special point process models 741
6. The time-rescaling theorem 748
7. Simulation of point processes 753
8. Poisson limit theorems 757
9. Problems 758
References 759
Course 15. Technique(s) for spike-sorting 762
1. Introduction 766
2. The problem to solve 767
3. Two features of single neuron data we would like to include in the spike-sorting procedure 768
4. Noise properties 771
5. Probabilistic data generation model 774
6. Markov chains 782
7. The Metropolis–Hastings algorithm and its relatives 790
8. Priors choice 795
9. The good use of the ergodic theorem. A warning 797
10. Slow relaxation and the replica exchange method 798
11. An Example from a simulated data set 801
12. Conclusions 811
13. Exercises solutions 813
References 816
Course 16. The emergence of relevant data representations: an information theoretic approach 820
1. Part I: the fundamental dilemma 825
2. Part II: Shannon's information theory—a new perspective 828
3. Part III: relevant data representation 837
4. Part IV: applications and extensions 845
References 860

Produkt-Details

• Erscheint lt. Verlag: 1.12.2005
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber
• Themenwelt: Geisteswissenschaften ► Sprach- / Literaturwissenschaft ► Sprachwissenschaft
• Themenwelt: Naturwissenschaften ► Biologie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Angewandte Physik
• Themenwelt: Technik
• ISBN-10: 0-08-053638-7 / 0080536387
• ISBN-13: 978-0-08-053638-5 / 9780080536385