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    Dynamics of Rate-Based and Spiking Balanced Random Networks

    Difficulty level

    This lesson gives an in-depth look into various types of neuronal networks, as well properties, parameters, and phenomena which characterize them. 

    Topics covered in this lesson
    • What do single neurons compute?
    • What computational properties do they confer on network function?
    • Microcircuits.
    • Main focus: understanding cortex.
    • Collective properties of groups of neurons = neuronal populations.
    • Tuning curves.
    • Cortical columns and layers, a natural substrate for neuronal populations.
    • Rate-based dynamics. Converting a spike train into a continuous function. 
    • Feedforward networks with input- and output layers.
    • Dale's law.
    • Recurrent linear networks.
    • Selective amplification.
    • Steady state dynamics and nullclines.
    • Stable and unstable fixpoints, transitions/bifurcations,
    • Hopf bifurcation, phase planes.
    • Dynamics of single neurons.
    • Population activity, how to predict it, how it responds to novel input.
    • Stationary activity of networks.
    • Hebbian assemblies.
    • Homogeneous networks.
    • Integrate-and-fire neurons.
    • Large populations: going from discrete notation (sums) to continuous (integral).
    • Finite size effects.
    • Types of connectivity: random, distance dependent.
    • Mean-field approach.
    • Fixed point of population activity, finding it from the single neuron F-I curve. 
    • Linear algebra - vectors and matrices, eigenvalues, eigenvectors
    • Calculus - equations with integrals