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    Theory of Network Dynamics

    Difficulty level

    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?
    • Calculus (integration and differentiation), basic linear algebra (matrices, determinants)
    • Some basic transform theory, such as knowing what Fourier transforms do, what a convolution is