This is a six-lecture component on Neuroscience for the course MA256 with the lectures for academic year 2015/2016 on:
Tuesdays 3-4pm in B3.03
Thursdays 2-3pm in MS.03
Fridays 3-4pm in B3.03
The first lecture for the neuroscience component is Tuesday 8th February and the last is Friday 19th February. Lecture notes and question sheets will be posted as the course progresses.
Exam time and place: Not yet known
Lecture 1 - The leaky-integrator neuron I.
Overview of the neurobiology (slides). Neuronal capacitance. Effects of leak channels and ionic concentrations.
Lecture 2 - The leaky-integrator neuron II.
Exponential response in time. Low-pass filter response to oscillating current at different frequencies.
Lecture 3 - Voltage-gated currents I.
The effects of voltage-gated currents: positive and negative feedback. Phase-plane analysis and nullclines. Bistability and damped oscillations.
Lecture 4 - Voltage-gated currents II.
Stability analysis at the fixed points. Eigenvalue analysis and the characteristic equation. Derivation of the phase diagram for the two-variable neuronal model. Regions of damped oscillations. Instabilities.
Lecture 5 - The leaky integrate-and-fire neuron.
Threshold and reset added to the leak-integrator neuron. Derivation of the firing rate for the leaky integrate-and-fire model. Examination of the low and high firing-rate limits. Effect of the refractory period. Behaviour of two-variable integrate and fire models.
Lecture 6 - Non-linear integrate-and-fire neurons.
The quadratic integrate-and-fire model featuring an explicit spike mechanism. Firing rate of the model. The exponential integrate-and-fire model as midway between the leaky and quadratic models.