Front Cover -- Methods and Models in Neurophysics -- Copyright Page -- Contents -- Course 1. Experimenting with theory -- 1. Overcoming communication barriers -- 2. Modeling with biological neurons-the dynamic clamp -- 3. The traps inherent in building conductance-based models -- 4. Theory can drive new experiments -- 5. Conclusions -- References -- Course 2. Understanding neuronal dynamics by geometrical dissection of minimal models -- 1. Introduction -- 2. Revisiting the Hodgkin-Huxley equations -- 3. Morris-Lecar model -- 4. Bursting, cellular level -- 5. Bursting, network generated. Episodic rhythms in the developing spinal cord -- 6. Chapter summary -- References -- Course 3. Geometric singular perturbation analysis of neuronal dynamics -- 1. Introduction -- 2. Introduction to dynamical systems -- 3. Properties of a single neuron -- 4. Two mutually coupled cells -- 5. Excitatory-inhibitory networks -- 6. Activity patterns in the basal ganglia -- References -- Course 4. Theory of neural synchrony -- 1. Introduction -- 2. Weakly coupled oscillators -- 3. Strongly coupled oscillators: mechanisms of synchrony -- 4. Conclusion -- Appendix A. Hodgkin-Huxley and Wang-Buszaki models -- Appendix B. Measure of synchrony and variability in numerical simulations -- Appendix C. Reduction of a conductance-based model to the QIF model -- References -- Course 5. Some useful numerical techniques for simulating integrate-and-fire networks -- 1.Introduction -- 2. The conductance-based I&F model -- 3. Modified time-stepping schemes -- 4. Synaptic interactions -- 5. Simulating a V1 model -- References -- Course 6. Propagation of pulses in cortical networks: the single-spike approximation -- 1. Introduction -- 2. Propagating pulses in networks of excitatory neurons -- 3. Propagating pulses in networks of excitatory and inhibitory neurons -- 4. Discussion.

Appendix A. Stability of the lower branch -- References -- Course 7. Activity-dependent transmission in neocortical synapses -- 1. Introduction -- 2. Phenomenological model of synaptic depression and facilitation -- 3. Dynamic synaptic transmission on the population level -- 4. Recurrent networks with synaptic depression -- 5. Conclusion -- References -- Course 8. Theory of large recurrent networks: from spikes to behavior -- 1. Introduction -- 2. From spikes to rates I: rates in asynchronous states -- 3. From spikes to rates II: dynamics and conductances -- 4. Persistent activity and neural integration in the brain -- 5. Feature selectivity in recurrent networks-the ring model -- 6. Models of associative memory -- 7. Concluding remarks -- References -- Course 9. Irregular activity in large networks of neurons -- 1. Introduction -- 2. A simple binary model -- 3. A memory model -- 4. A model of visual cortex hypercolumn -- 5. Adding realism: integrate-and-fire network -- 6. Discussion -- References -- Course 10. Network models of memory -- 1. Introduction -- 2. Persistent neuronal activity during delayed response experiments -- 3. Scenarios for multistability in neural systems -- 4. Networks of binary neurons with discrete attractors -- 5. Learning -- 6. Networks of spiking neurons with discrete attractors -- 7. Plasticity of persistent activity -- 8. Models with continuous attractors -- 9. Conclusions -- References -- Course 11. Pattern formation in visual cortex -- 1. Introduction -- 2. The functional architecture of V 1 -- 3. Large-scale models of V1 -- 4. Pattern formation in a single hypercolumn -- 5. Pattern formation in a coupled hypercolumn model of V1 -- 6. Pattem formation in a planar model of V 1 -- 7. Pattem formation in a model of cortical development -- 8. Future directions -- References.

Course 12. Symmetry breaking and pattern selection in visual cortical development -- 1. Introduction -- 2. The pattern of orientation preference columns -- 3. Symmetries in the development of orientation columns -- 4. From learning to dynamics -- 5. Generation and motion of pinwheels -- 6. The problem of pinwheel stability -- 7. Weakly nonlinear analysis of pattern selection -- 8. A Swift-Hohenberg model with stable pinwheel patterns -- 9. Discussion -- References -- Course 13. Of the evolution of the brain -- 1. Introduction and summary -- 2. The phase transition that made us mammals -- 3. Maps and patterns of threshold-linear units -- 4. Validation of the lamination hypothesis -- 5. What do we need DG and CA1 for? -- 6. Infinite recursion and the origin of cognition -- 7. Reducing local networks to Potts units -- References -- Course 14. Theory of point processes for neural systems -- 1. Neural spike trains as point processes -- 2. Integrate and fire models and interspike interval distributions -- 3. The conditional intensity function and interevent time probability density -- 4. Joint probability density of a point process -- 5. Special point process models -- 6. The time-rescaling theorem -- 7. Simulation of point processes -- 8. Poisson limit theorems -- 9. Problems -- References -- Course 15. Technique(s) for spike-sorting -- 1. Introduction -- 2. The problem to solve -- 3. Two features of single neuron data we would like to include in the spike-sorting procedure -- 4. Noise properties -- 5. Probabilistic data generation model -- 6. Markov chains -- 7. The Metropolis-Hastings algorithm and its relatives -- 8. Priors choice -- 9. The good use of the ergodic theorem. A warning -- 10. Slow relaxation and the replica exchange method -- 11. An Example from a simulated data set -- 12. Conclusions -- 13. Exercises solutions -- References.

Course 16. The emergence of relevant data representations: an information theoretic approach -- 1. Part I: the fundamental dilemma -- 2. Part II: Shannon's information theory-a new perspective -- 3. Part III: relevant data representation -- 4. Part IV: applications and extensions -- References.

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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.