From the 8th to the 14th of July, I’ll be attending SIAM18 conference, in Portland (Oregon, USA). My flash talk, entitled A New Dimension-reduction Method for Complex Dynamical Networks will take place on July 12 at 16h50. This work is co-signed by myself and Nicolas Doyon, Louis J. Dubé, and Patrick Desrosiers.
We introduce a new dimension-reduction method to describe the large scale behaviour of dynamical processes running on networks, primarily based on the spectral properties of the weighted adjacency matrices that characterize the interactions on the networks. The structural complexity of the networks is used to naturally set the adequate dimensionality of the reduced system. We present and compare three variants of our method. We show that our approximation scheme, even when forced to produce one-dimensional reduced systems, always gives a better description of the dynamics than the one proposed by Gao et al. (Nature, 2016).
Using our combined method of dimension reduction, we are able to predict critical edges by solving two uncoupled equations, instead of 40 coupled equations.