[ABE-L] Seminário PSC quinta feira dia 11 às 14h no ICMC: Camille Poignard (ICMC-USP)

[Sandro Gallo]

Bom dia a todos,

este email é para divulgar o seminário de Probabilidade e Sistemas complexos
 desta semana.

 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.

Estão todos convidados!
Abraço,

Sandro
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