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13 juin 2018: 1 événement

  • Séminaires SPOC

    Mercredi 13 juin 10:30-11:30 - Nicolas Tremblay - Laboratoire GIPSA, Grenoble

    Filtering and sampling of graph signals, and its application to clustering

    Résumé : Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps : create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix to define a feature vector for each object, and run k-means on these features to separate objects into k classes. Each of these three steps becomes computationally intensive for large N and/or k. We propose to speed up the last two steps based on recent results in the emerging field of graph signal processing : graph filtering of random signals, and random sampling of bandlimited graph signals. In this presentation, we will take time to go over what filtering and sampling mean for a signal defined on a graph, and explain to what extent they can prove useful for spectral clustering.

    En savoir plus : Séminaires SPOC

13 juin 2018: 1 événement

  • Séminaires Math-Physique

    Mercredi 13 juin 16:15-17:15 - Svetlana Roudenko - The George Washington University

    Séminaire Math-Phys : Existence of blow-up solutions in the KdV-type equations

    Résumé : While the KdV equation and its generalizations with higher power nonlinearities (gKdV) have been long studied, a question about existence of blow-up solutions for higher power nonlinearities has posed lots of challenges and far from being answered. One of the main obstacles is that unlike other dispersive models such as the nonlinear Schrodinger or wave equations, the gKdV equation does not have a suitable virial quantity which is the key to prove the finite time blow-up. Only at the dawn of this century the groundbreaking works of Martel and Merle rigorously proved the existence of finite-time blow-up solutions for the quintic (critical) gKdV equation.
    We consider a higher dimensional extension of the gKdV equation, called generalized Zakharov-Kuznetsov (gZK) equation (the gKdV is limited as a spatially one-dimensional model), and ask if blow-up solutions exist in the corresponding critical gZK equation. We positively answer this question for the two dimensional version of (cubic) Zakharov-Kuznetsov equation. The main ingredient of the proof is the Liouville-type theorem, which uses time-decay estimates, a la virial type quantity and spectral properties associated to it. This is a joint work with Luiz Farah, Justin Holmer and Kai Yang.

    Lieu : Salle A318

    En savoir plus : Séminaires Math-Physique