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Mardi 25 Novembre
| Heure: |
14:00 - 17:00 |
| Lieu: |
Salle B107, bâtiment B, Université de Villetaneuse |
| Résumé: |
Le diamètre asymptotique des associaèdres généralisés |
| Description: |
Lionel Pournin Les associaèdres généralisés ont été introduits par SergeyFomin et Andrei Zelevinsky dans le cadre de la théorie des algèbresamassées, et réalisés géométriquement par Chapoton, Fomin etZelevinsky. Ils sont associés à n'importe quel groupe de Coxeter fini.Parmi eux figurent trois familles infinies de polytopes : lesassociaèdres de type A (associaèdres usuels), de type B ou C(cycloèdres), et de type D.Le diamètre asymptotique des associaèdres de types A, B (ou C), et Dest maintenant connu et cet exposé passera en revue les cas des typesB (ou C), et D. Les preuves ne seront pas données entièrement, maisseulement esquissées. Quelques questions associées seront finalementdiscutées. |
Jeudi 27 Novembre
| Heure: |
16:00 - 17:00 |
| Lieu: |
Salle B107, bâtiment B, Université de Villetaneuse |
| Résumé: |
Precise Robustness Analysis of Real-Time Systems |
| Description: |
Étienne André Quantifying the robustness of a real-time system consists in
measuring the maximum extension of the timing delays such that the
system still satisfies its specification.
In this work, we introduce a more precise notion of robustness,
measuring the allowed variability of the timing delays in their
neighbourhood.
We consider here the formalism of time Petri nets extended with
inhibitor arcs.
We use the inverse method, initially defined for timed automata.
Its output, in the form of a parametric linear constraint relating
all timing delays, allows the designer to characterise the system local
robustness, and hence to identify the delays allowing the least variability.
We also exhibit a condition and a construction for rendering robust
a non-robust system.
This work is a joint work with Laure Petrucci. |
Vendredi 28 Novembre
| Heure: |
11:00 - 12:30 |
| Lieu: |
Salle B107, bâtiment B, Université de Villetaneuse |
| Résumé: |
New applications of moment-SOS hierarchies |
| Description: |
Victor Magron Semidefinite programming is relevant to a wide range of mathematic fields, including combinatorial optimization, control theory, matrix completion. In 2001, Lasserre introduced a hierarchy of semidefinite relaxations for particular polynomial instances of the Generalized Moment Problem (GMP). My talk emphasizes new applications of this moment-SOS hierarchy, investigated during my PhD and Postdoc research.
In the context of formal proofs for nonlinear optimization, one can combine the moment-SOS hierarchy with maxplus approximation of semiconvex functions. Such a framework is mandatory for formal certification of nonlinear inequalities, occurring by thousands in the proof of Kepler Conjecture by Hales.
I also present how to approximate, as closely as desired, the Pareto curve associated with bicriteria polynomial optimization problems or the projections of semialgebraic sets. For each problem, one builds a hierarchy of semidefinite programs, so that the sequence of bounds converges in L1 norm.
Finally, this hierarchy allows to analyze programs containing loop invariants with polynomial assignments. |
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