11/05/2017 - Laplacian matrices over weighted graphs: Genericity properties and applications to the Synchronization of Networks - Palestrante: Camille Poignard (ICMC-USP)
Seminário de Probabilidade e Sistemas Complexos, ICMC-USP & UFSCar
Palestrante: Camille Poignard (ICMC-USP)
Local: Sala 3-012 do ICMC.
Data e horário: Quinta feira, dia 11 de maio de 2017 às 14h.
Título: Laplacian matrices over weighted graphs: Genericity properties and applications to the Synchronization of Networks
Abstract: This work deals with the spectrum of Laplacian matrices over weighted graphs, for which Fiedler [70's] showed their topological descriptions rely on two objects of fundamental importance: the second eigenvalue of the spectrum ("spectral gap") and one of its associated
eigenvectors, the so called "Fiedler eigenvector". Since the seminal work of Fiedler, the use of Spectral graph theory in the study of
dynamical networks has been really successful. First, I will show that given a Laplacian matrix, it is possible to perturb slightly the weights
of its existing links so that its spectrum be composed of only simple eigenvalues, and its Fiedler eigenvector be composed of only non zero
entries. These genericity properties with the constraint of not adding links in the underlying network are stronger than the classical ones,
for which any "topological" perturbation is allowed. Then, I will show how this result can be useful for the synchronization of diffusively
coupled networks, more precisely for the problem of identifying the links for which the perturbations of the weights modify this dynamics,
i.e decreases or enhances the synchronization. The talk does not require any background on graphs theory or on dynamical systems.