NSCI 850: Computational Approaches to Neuroscience

Syllabus (2018-2019)

Classroom: Botterell Hall B129
Day, time: Winter term, Mon & Wed 10:30am-1:30pm

What is computational neuroscience
Why model brain function
Introduction to the computational anatomy of the brain

Math tutorial
Ordinary differential equations (ODEs)


Modelling membrane potentials
Ion channels
Hodgkin & Huxley
Modelling synapses
Other considerations
Leaky integrate and fire
The Izhiekevich neuron
Compartmental models

Slides   |   Matlab code

Neuronal firing variability
Spike time variability
Efficient coding hypothesis
Spiking networks
Phase oscillations and synaptic coupling
Synchronization and phase locking
Hebbian learning
Associative memory
Synaptic plasticity
Mathematical formulation of Hebbian learning

Slides   |   Matlab code 1 (Izhiekevich)    |    Matlab code 2 (single Deneve neuron)    |    Matlab code 3 (multiple Deneve neurons)

From spikes to firing rates
Neural transfer functions
Feed-forward networks
Radial-basis function networks
Training algorithms
Gradient descent (back-propagation or Widrow-Hoff)
Unsupervised learning

Slides  |   Matlab code 1    |    Matlab code 2 & Training set

From feed-forward to recurrent networks
Competitive networks
Self-organizing maps (Kohonen maps)
Neural field theory
Path integration
Network stability and chaos

Slides   |   Matlab code 1    |   Matlab code 2    |    Matlab code 3

Linear systems theory
Superposition principle
Impulse response
Laplace transform
The role of feedback
Stability, zeros & poles
Modelling saccades
More on linear systems...

Slides   |   Matlab code

Introduction to Bayesian problems
Bayes’ theorem
Probabilities primer
Conditional probabilities
Population codes
Coding and decoding
Representing uncertainty with population codes
Bayesian integration
Cue combination
Estimation of priors
Causality and inference

Slides   |   Matlab code   |   Data set

Arm movement behaviour
Optimal feedback control (OFC)
Principles of OFC
Role of biomechanics

Slides   |   Matlab code

The reinforcement learning problem
Agent-environment interactions
Markov properties
Value functions
On-policy TD control (Sarsa)
Off-policy Q-learning
Actor-Critic methods

Slides    |    Data set    |    Matlab code

How-to-model guide

10:30 - 11:15:
11:15 - 12:00:
12:00 - 12:45:
12:45 - 1:30:

10:30 - 11:15:
11:15 - 12:00:
12:00 - 12:45:
12:45 - 1:30:

Further readings:

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