Neuronal Dynamics

Teaching material, python exercises and slides

Lecture Series: Neuronal Dynamics
From single neurons to networks and models of cognition

Wulfram Gerstner, Werner M. Kistler, Richard Naud and Liam Paninski

About the lecture series

The teaching material is organized here over 15 weeks.

Some weeks cover 2 chapters - this is recognizable by the name of the file. Moreover, the more mathematical chapters 13-15 are discussed in the final weeks, after the lectures on dynamics of cognition. Depending on the audience, thse lectures can be dropped.

The material can also be organized in a different order according to the preferences of the teacher and expectations of the students.

Parts I and II are also covered in the video lectures.

Disclaimer

The teaching material provided on this page has been compiled and tested in classes by Wulfram Gerstner. If you use some of the material for teaching, please reference the original sources.

Python exercises

Python exercises accompanying the book are available under neuronaldynamics-exercises.readthedocs.io.

For each of the weeks below, we additionally provide links to the relevant exercises.

I Foundations of Neuronal Dynamics

Ch 1 Introduction

Elements of Neurons and Synapses - Neuronal Dynamics and Passive Membrane - Integrate-And-Fire Model - Generalized Integrate-and-Fire Model - Quality of Integrate-And-Fire Models pptx file - python exercise

Ch 2 The Hodgkin-Huxley Model

Biophysics of neurons - Equilibrium potential/Reversal potential - - Hodgkin-Huxley Model - Threshold effects - - the Zoo of Ion Channels/Detailed biophysical models pptx file - python exercise

Ch 3 Dendrites and Synapses

Synapses - Spatial Structure: The Dendritic Tree - - Compartmental Models - Axons - Synaptic short-term plasticity pptx file - python exercise

Ch 4 Dimensionality Reduction and Phase Plane Analysis (part 1)

Threshold effects/overview - Reduction to two dimensions - Phase plane analysis - nullclines - Analysis of a 2D model pptx file - python exercise

Ch 4 Type I and and Type II neuron models (part 2)

bifurcations - Threshold and excitability - Separation of time scales and reduction to one dimension - pptx file - python exercise

II Generalized Integrate-and-Fire Neurons

Ch 5 Nonlinear Integrate-and-Fire Models

Thresholds in a nonlinear integrate-and-fire model - Exponential Integrate-and-Fire Model - Quadratic Integrate and Fire - Extracting Nonlinear IF from Data - Extracting Nonlinear IF from detailed models pptx file - python exercise

Ch 6 Adaptation and Firing Patterns

Firing Patterns - Adaptive Exponential Integrate-and-Fire - Spike response model (SRM) pptx file - python exercise

Ch 7 Variability of Spike Trains and Neural Codes

Spike train variability - Sources of variability - Poisson Model - Mean Firing Rate - Interval distribution and coefficient of variation - Autocorrelation function and noise spectrum - Renewal statistics - The Problem of Neural Coding pptx file

Ch 8 Noisy Input Models: Barrage of Spike Arrivals

Noise input - Stochastic spike arrival - Subthreshold vs. Superthreshold regime pptx file

Ch 9 Noisy Output: Escape Rate and Soft Threshold

Escape noise - Likelihood of a spike train - Renewal theory - From noisy inputs to escape noise pptx file

Ch 10 Estimating Models

Review: EIF, AdEx SRM, GLM - Parameter Optimization in Linear and Nonlinear Models - Statistical Formulation of Encoding Models - Modeling in vitro data pptx file

Ch 11 Encoding and Decoding with Stochastic Neuron models

Encoding Models for Intracellular Recordings - Encoding Models in Systems Neuroscience -Decoding pptx file

III Networks of Neurons and Population Activity

Ch 12 Neuronal Populations

Columnar organization and Receptive fields - Identical Neurons: A Mathematical Abstraction - Cortical Connectivity - Connectivity Schemes - From Microscopic to Macroscopic: Mean-field argument - Random Networks and Balanced state pptx file

Ch 13 Continuity Equation and the Fokker-Planck Approach

Review: Integrate-and-Fire - Membrane potential density - Continuity equation - Stochastic spike arrival - Flux - Fokker-Planck equation- Networks of leaky integrate-and-fire neurons: Threshold and Reset pptx file - python exercise - python exercise

Ch 14 The Integral-equation Approach

Population activity equations - Recurrent Networks and Interacting Populations - Adaptation in Population Equations pptx file

Ch 15 Fast Transients and Rate Models

How fast are population responses? - Fast transients vs. slow transients in models - Rate models pptx file

IV Dynamics of Cognition

Ch 16 Competing Populations and Decision Making

Review:population dynamics - Perceptual Decision Making - Competition through shared inhibition - Effective 2-dim model - Dynamics of decision making - Alternative Decision Models - Decisions, actions and volition pptx file - python exercise

Ch 17 Memory and Attractor Dynamics

Associations and memory - detour: magnetism - Hopfield Model - storage capacity - - Memory networks with spiking neurons pptx file - python exercise

Ch 18 Cortical Field Models for Perception

Transients - Spatial continuum model - Input-driven regime and sensory cortex models - Bump attractors and spontaneous pattern formation - perception - head direction cells pptx file - python exercise

Ch 19 Synaptic Plasticity and Learning

Hebb rule and experiments - Models of Hebbian learning - Unsupervised learning - Reward-based learning pptx file - python exercise

Ch 20 Outlook: Dynamics in Plastic Networks

Reservoir computing - random networks - stability-optimized circuits - Synaptic Plasticity - Hebbian Plasticity - Reward-modulated plasticity - Oscillations: good or bad? - Helping Patients pptx file

 

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