Syllabus
Classroom:
TBA
Day, time: Winter
term,
TBA
What is computational neuroscience
Why model brain function
Introduction to the computational anatomy of the brain
- Jan 21: Spiking single
neurons
Preamble
A biological neuron
Electricity primer
A neuron as resistor and capacitor in parallel
Equilibrium potentials
The Hodgkin-Huxley model
The leaky integrate-and-fire model
Modelling synapses
The Izhikevich neuron
Summary and discussion
- Jan 28: Spiking neural networks
Neuronal firing varibility
Synaptic computations
Spiking networks
Phase oscillations and synaptic coupling
Synchronization and phase locking
Examples
Hebbian learning
Associative memory
Synaptic plasticity
Mathematical formulation of Hebbian learning
Discussion
- Feb 4: Rate-based feed-forward artificial neural networks
Introduction
From spikes to firing rates
Neural transfer functions
Feed-forward networks
Perceptron
Radial-basis function networks
Training algorithms
Gradient descent (back-propagation or
Widrow-Hoff)
Genetic algorithms
Unsupervised learning
k-means
Discussion
- Feb 11: Rate-based recurrent artificial neural networks
Introduction
From feed-forward to recurrent networks
Competitive networks
Self-organizing maps (Kohonen maps)
Neural field theory
Path integration
Associative networks
Auto-associative networks
Attractor points
Noise
Network stability and chaos
Discussion
- Feb 18: Modelling at the systems level
From networks to state variables
State space representations
Linear systems
State variables
Control theory (controllability, observability)
Laplace formalism
Transfer functions
State-flow models
Feedback controller
Forward and inverse models
Example: eye movements
Discussion
- Feb 25: Reading week (no classes)
- Mar 4: Bayesian statistics
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
Discussion
- Mar 11: Optimal control theory
Limb biomechanics
Traditional servo control
PID
Physiology & behaviour
Feed-forward control
Internal models
Physiology & behaviour
Optimal Feedback control
LQR
Noise
Physiology & behaviour
Neural network implementations
- Mar 18: Data analysis methods
Data selection
Bootstrapping
Monte-Carlo
Signals
A/D conversion
D/A conversion
Frequency domain transforms
Signal processing techniques
Differentiation
Threshold detection
EMG and kinematics data
Filters
ROC analysis
Cross-correlation
Discussion
- Apr 1: Specific models 1 (final
assignments)
1-2pm: Christopher Kidd
2-3pm: Jason Rajsic
3-4pm: Nathan Chalmers
- Apr 8: Specific models 2 (final
assignments)
1-2pm: Meghan Watson
2-3pm: Andrew Mouck
3-4pm: Graham Raynor
Further
readings:
Please read this
about
academic integrity!
