Emergence of Slow-Switching Assemblies in Structured Neuronal Networks
Fig 1
Network dynamics and eigenvalue spectra of two LIF networks.
One network with uniform synaptic connections (left), and one with 20 groups of clustered excitatory connections (right). To create the clustered network, excitatory neurons were partitioned into groups (with in-group connection probability and out-group connection probability ) while keeping the average connectivity constant (see Materials and Methods and Ref. [22]). The ratio controls the strength of the excitatory clustering. A Visualization of the network topologies (top) and exemplars of raster plots (bottom). The dynamics of the clustered network exhibit the banded structure associated with slow-switching group activity. The magnitude of this switching can be characterized statistically a posteriori from the data through the spike-rate variability metric , defined in Materials and Methods Eq (18), as discussed in the text. In this case, the unclustered network has while the clustered network has a much larger value . B Eigenvalue spectra of the network weight matrices W. The weighted connectivity matrix of the clustered network exhibits a clear eigengap Δλ separating the 19 eigenvalues with largest real parts from the cloud of eigenvalues in the bulk. There is no such eigengap for the unclustered network. As indicated by the two arrows, both matrices have a pair of complex conjugate eigenvalues associated with the (damped) global activation modes of the networks characteristic of balanced networks (see text and Ref. [29]).