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Degree assortativity refers to the increased or decreased probability of connecting two neurons based on their in- or out-degrees, relative to what would be expected by chance. We investigate the effects of such assortativity in a network of theta neurons. The Ott/Antonsen ansatz is used to derive equations for the expected state of each neuron, and these equations are then coarse-grained in degree space. We generate families of effective connectivity matrices parametrised by assortativity coefficient and use SVD decompositions of these to efficiently perform numerical bifurcation analysis of the coarse-grained equations. We find that of the four possible types of degree assortativity, two have no effect on the networks dynamics, while the other two can have a significant effect.
We consider the effects of correlations between the in- and out-degrees of individual neurons on the dynamics of a network of neurons. By using theta neurons, we can derive a set of coupled differential equations for the expected dynamics of neurons
We train spiking deep networks using leaky integrate-and-fire (LIF) neurons, and achieve state-of-the-art results for spiking networks on the CIFAR-10 and MNIST datasets. This demonstrates that biologically-plausible spiking LIF neurons can be integr
We consider the deterministic evolution of a time-discretized spiking network of neurons with connection weights having delays, modeled as a discretized neural network of the generalized integrate and fire (gIF) type. The purpose is to study a class
We show that the degree distributions of graphs do not suffice to characterize the synchronization of systems evolving on them. We prove that, for any given degree sequence satisfying certain conditions, there exists a connected graph having that deg
By constructing a multicanonical Monte Carlo simulation, we obtain the full probability distribution $rho_N(r)$ of the degree assortativity coefficient $r$ on configuration networks of size $N$ by using the multiple histogram reweighting method. We s