Dynamics of rate-based and spiking balanced random networks

# Dynamics of rate-based and spiking balanced random networks

Methods for dimensionality reduction of data, with focus on factor analysis.

##### 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.

External Links

Prerequisites

Linear algebra - vectors and matrices, eigenvalues, eigenvectors. Calculus - equations with integrals.

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