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.