# Theory of Network Dynamics

Difficulty level
Beginner
Speaker
Type
Duration
1:24:22

In this lesson, you will learn about spiking neuron networks and linear response models.

Topics covered in this lesson
• Reasons to choose computational neuroscience.
• Linear response dynamics = boiling down complex computations down into to a simpler, mathematically tractable form.
• Linear response functions are known since 1887, formalized by Volterra and Wiener but then mainly for engineering purposes.
• Main idea: perturbing a system in steady state - a small enough perturbation gives a response proportional to the perturbation.
• Transforming stimuli, frequency domain and time domain.
• Green's function = response to a delta perturbation, equivalent to linear response function.
• How measure the linear response function in our system of interest?
• Spike-triggered averages, and how they relate to the Fourier domain.
• Dependence on background noise frequency and the firing rate of the neuron - the more neurons spike, the higher frequencies they can encode.
• Why background noise matters to encoding capability.
• Synchrony and pairwise correlations.
• Correlated input. Where can we use linear response?
• Pairwise spike correlation between neurons increases with firing rate.
• Phase transitions between irregular and periodic activity.
• When does the response start to be oscillatory?
Prerequisites
• Calculus (integration and differentiation), basic linear algebra (matrices, determinants)
• Some basic transform theory, such as knowing what Fourier transforms do, what a convolution is
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