NSCI 850: Computational Approaches to Neuroscience

Syllabus (2016-2017)


Classroom: Botterell Hall B129
Day, time: Winter term, Tue 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


(Intro)
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
Examples
Hebbian learning
Associative memory
Synaptic plasticity
Mathematical formulation of Hebbian learning

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


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)
Unsupervised learning
k-means

Slides  |   Matlab code   |   Training set


Introduction
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
Discussion


Slides   |   Matlab code   |   Data set


Arm movement behaviour
Optimal feedback control (OFC)
Approach
Control
Estimation
Principles of OFC
Examples
Role of biomechanics


Slides   |   Matlab code


Introduction
The reinforcement learning problem
Agent-environment interactions
Markov properties
Value functions
Solutions
TD(0)
On-policy TD control (Sarsa)
Off-policy Q-learning
Actor-Critic methods

Slides    |    Data set    |    Matlab code


Why modelling?
Model classifications
10 easy steps to model
        framing the question
        implementing the model
        model testing
        publishing
Lumping and abstraction
Interaction between theory, models and data


Slides





12:30-1pm: Amir
1-1:30pm: Siavash
1:30-2pm: Tal
2-2:30pm: Brandon
2:30-3pm: Laura
3-3:30pm: Ben
3:30-4pm: Lauren

12:30-1pm: Spencer
1-1:30pm: Amory
1:30-2pm: Nelly
2-2:30pm: Cindy
2:30-3pm: Jonny
3-3:30pm: Jae
3:30-4pm: Jerry





Further readings:

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