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I. Foundations of Neuronal Dynamics

• Lecture 1. A first simple neuron model (83 min)
  Part 1 - Neurons and Synapses : Overview (10 min)
  Part 2 - The Passive Membrane (21 min)
  Math detour - Linear differential equation (22 min)
  Part 3 - Leaky Integrate-and-Fire Model (8 min)
  Part 4 - Generalized Integrate and Fire Models (17 min)
  Part 5 - Quality of Integrate-and-Fire Models (5 min)
  

• Lecture 2. The Hodgkin-Huxley model and detailed ion-current based neuron models (77 min)
  Part 1 - Biophysics of neurons (5 min)
  Part 2 - Reversal potential and Nernst equation (11 min)
  Part 3 - Hodgkin-Huxley Model (23 min)
  Part 4 - Threshold in the Hodgkin Huxley Model (26 min)
  Part 5 - Detailed Biophysical Models (12 min)
  

• Lecture 3. Synapses, dendrites and the cable equation (69 min)
  Part 1 - Synapses (15 min)
  Part 2 - Synaptic short term plasticity (9 min)
  Part 3a - Dendrite as a Cable (11 min)
  Part 3b - Derivation of the Cable Equation (10 min)
  Part 4 - Cable equation (10 min)
  Part 5 - Compartmental Models (14 min)
  

• Lecture 4: Two-dimensional models and phase plane analysis (165 min)
  Part 1 - From Hodgkin Huxley to 2D (18 min)
  Math detour 1 - Separation of time scales (11 min)
  Math detour 2 - Exploiting similarities (16 min)
  Part 2 - Phase Plane Analysis (17 min)
  Part 3a - Analysis of a 2D neuron model - pulse input (12 min)
  Part 3b - Analysis of a 2D neuron model - constant input (9 min)
  Math detour 3 - Stability of fixed points (19 min)
  Part 4a - Type I and Type II Neuron Models (16 min)
  Part 4b - Firing threshold in 2D models (21 min)
  Part 5 - Nonlinear Integrate-and-Fire Model (16 min)
  

II. Generalized Integrate-and-Fire Neurons

• Lecture 5. Variability of spike trains (96 min)
  Part 1 - Variability of spike trains (6 min)
  Part 2 - Sources of Variability? (10 min)
  Part 3a - Three definitions of rate code (12 min)
  Part 3b - Poisson Model, survivor function, and interval distribution (15 min)
  Math detour - Poisson Process - A modern approach (20 min)
  Part 4a - Stochastic spike arrival (15 min)
  Part 4b - Membrane potential fluctuations (13 min)
  Part 5 - Stochastic spike firing in integrate and fire models (5 min)
  

• Lecture 6: Noise models (84 min)
  Part 1 - Escape noise (15 min)
  Part 2 - lnterspike intervals & renewal processes (29 min)
  Part 3 - Likelihood of a spike train (18 min)
  Part 4a - Comparison of noise models (19 min)
  Part 4b - From diffuse noise to escape noise (7 min)
  Part 5 - Rate Codes versus Temporal Codes (6 min)
  

• Lecture 7: Modern phenomenological neuron models (94 min)
  Part 1 - Models and data (11 min)
  Part 2a - AdEx : Adaptive exponential integrate-and-fire (11 min)
  Part 2b - Firing patterns and phase plane analysis (10 min)
  Part 3 - Spike Response Model (SRM) (15 min)
  Part 4 - Generalized Linear Model (GLM) (7 min)
  Part 5a - Parameter estimation (14 min)
  Part 5b - Parameter estimation for spike times (7 min)
  Part 6 - Modeling in vitro data (8 min)
  Part 7 - Helping Humans (11 min)
  

III. Networks of Neurons and Population Activity

• Lecture 8. Neuronal Populations (85 min)
  Part 1 - Population activity (9 min)
  Part 2 - Cortical populations: Columns and receptive fields (7 min)
  Part 3 - Connectivity - in cortex and in models(11 min)
  Part 4a - Asynchronous state (13 min)
  Part 4b - Mean-field argument (10 min)
  Part 5 - Stationary mean-field and asynchronous state (16 min)
  Part 6 - Random Networks and balanced state (21 min)
  

• Lecture 9. Fokker-Planck equation for stochastic integrate-and-fire neurons (77 min)
  Part 1 - Integrate-and-fire neurons driven by stochastic spike arrival (6 min)
  Part 2 - Continuity equation/transport equation (15 min)
  Part 3 - The flux of membrane potential trajectories (7 min)
  Part 4 - Derivation of the Fokker-Planck equation (16 min)
  Part 5 - Fokker-Planck equation with threshold (15 min)
  Part 5B - Quiz to Fokker-Planck equation (6 min)
  Part 6 - Random network of integrate-and-fire neurons (12 min)
  

IV. Dynamics of Cognition

• Lecture 10. Associative Memory in a Network of Neurons (57 min)
  Part 1 - Introduction: human memory and networks of neurons (4 min)
  Part 2 - Classification by similarity (5 min)
  Part 3 - Detour: Magnetic Materials (9 min)
  Part 4 - Hopfield Model (15 min)
  Part 5 - Learning of Associations (9 min)
  Part 6 - Storage Capacity (15 min)
  

• Lecture 11. Attractor Networks and Generalizations of the Hopfield model (62 min)
  Part 1 - Attractor Networks (8 min)
  Part 2 - Stochastic Hopfield model(18 min)
  Part 3 - Energy Landscape (14 min)
  Part 4 - Toward biology 1: Low-activity patterns (6 min)
  Part 5 - Toward biology 2: Spiking neurons (16 min)
  

• Lecture 12. Continuum models: Cortical Fields and Perception (62 min)
  Part 1 - Aims and challenges for this chapter (7 min)
  Part 2 - Transients (16 min)
  Part 3 - Spatial Continuum (Cortex) (3 min)
  Part 4 - Spatial continuum (model) (18 min)
  Part 5 - Solution types (8 min)
  Part 6 - Perception(10 min)
  

• Lecture 13. Decision models: Competitive Dynamics (66 min)
  Part 1 - Introduction: Aims and challenges of Decision Models (18 min)
  Part 2 - Perceptual Decision Making (15 min)
  Part 3 - Theory of Decision Dynamics (Cortex) (11 min)
  Part 4 - Solutions of Decision Dynamics: symmetric case and biased case (8 min)
  Part 5 - Simulations and Experiments on Decision Dyanmics(8 min)
  Part 6 - Decisions, actions, volition (6 min)
  

• Lecture 14. Synaptic plasticity and learning (85 min)
  Part 1 - Synaptic plasticity: motivation and aims (6 min)
  Part 2 - Classification of plasticity (17 min)
  Part 3 - Model of Short-Term Plasticity (1 min).
  Part 3B Pointer to the earlier MOOC - video on Synaptic short term plasticity (9 min)
  Part 4 - Models of Long-Term Plasticity: Hebbian learning and Bienenstock-Cooper-Munro rule (17 min)
  Part 5 - STDP: Spike-Timining Dependent Models of Plasticity (11 min)
  Part 6 - From Spiking Plasticity Models to Rate Models: intuitive relation (9 min)
  Part 6b - Pointer to the Math Detour: From Spiking Plasticity Models to Rate Models (math detour, 27 min)
  Part 7 - Triplet STDP Model (11 min)
  Part 8 - Online Learning of Memories (15 min)
  

• Lecture 15 Neural Manifolds and Low-Dimensional Dynamics (39 min)
  Part 1 - What are Neural Manifolds? (9 min)
  Part 2 - Detour/Review: Two views of Neural Activity in the Brain (15 min)
  Part 3 - Low-Rank Recurrent Neural Networks (15 min)
  

• NEURONAL DYNAMICS - From single neurons to networks and models of Cognition; by W. Gerstner, W. Kistler, R. Naud, L. Paninski (Cambridge University Press, July 2014.