seminar: Heterogeneously Coupled Maps: Rigorous Mean Field Reduction and Dynamics Reconstruction
speaker: Matteo Tanzi (King's College)abstract: A graph with heterogeneous degrees has most of its nodes making a small number of connections, while the remaining nodes, called hubs, have very high degree. This type of graph is ubiquitously found in models of natural and artificial systems made of interacting components such as, among others, neuronal networks, gene-regulatory networks, and power grids. I will report results addressing the ergodic theoretical properties of uniformly expanding maps coupled on such graphs, focusing the attention on the case where the number of nodes in the graph is very large.
The results justify the emergence of macroscopic behaviour such as coherence of dynamics among hubs with the same number of connections. They also suggest an algorithm to reconstruct the network structure and dynamical features from observations of the dynamics at every node. Tested on computer simulations, the algorithm is able to effectively recover the degree distribution of the network, community structures, local dynamics and effective coupling.
timetable:
Thu 27 Jun, 11:00 - 12:00, Aula Russo
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