NSCI 850: Computational Approaches to Neuroscience

Syllabus (2012-2013)


Classroom: Botterell Hall, Rm B129
Day, time: Winter term, Wed 1-4pm

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

Math tutorial
Ordinary differential equations (ODEs)
Linear algebra

Slides


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

Slides   |   Journal Club (Ben)   |   Assignment   |   Matlab code


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

Slides   |   Journal Club (Gaurav)   |   Assignment   |   Matlab code


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

Slides   |   Journal Club (?)  |   Assignment   |   Matlab code   |   Training set


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

Slides   |   Journal Club (Seamas)   |   Assignment   |   Matlab code 1   |   Matlab code 2   |   Matlab code 3


From networks to state variables
State space representations
Linear systems
State variables
Control theory (controllability, observability)
Superposition principle
Laplace formalism
Transfer functions
State-flow models
Feedback controller
Forward and inverse models
Example:  eye movements
Discussion

Slides   |   Journal Club (Stuart)   |   Assignment   |   Matlab code




Limb biomechanics
Traditional servo control
PID
Physiology & behaviour
Feed-forward control
Internal models
Physiology & behaviour
Optimal Feedback control
LQR
Noise
Physiology & behaviour

Slides   |   Journal Club & supplement (Emese)   |   Assignment   |   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
Discussion

Slides   |   Journal Club (Slava)   |   Assignment   |   Matlab code   |   Data set


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

Slides





1-2pm: Stuart
2-3pm: Gaurav
3-4pm: Ben

1-2pm: Emese
2-3pm: Seamas
3-4pm: Slava




Further readings:

Please read this about academic integrity!