Abstract. In view of solving theoretically constrained minimization problems, we investigate the properties of the gradient flows with respect to Hessian Riemannian metrics induced by Legendre functions. The first result characterizes Hessian Riemannian structures on convex sets as metrics that have a specific integration property with respect to variational inequalities, giving a new motivation for the introduction of Bregman-type distances. Then, the general evolution problem is introduced, and global convergence is established under quasi-convexity conditions, with interesting refinements in the case of convex minimization. Some explicit examples of these gradient flows are discussed. Dual trajectories are identified, and sufficient conditions for dual convergence are examined for a convex program with positivity and equality constraints. Some convergence rate results are established. In the case of a linear objective function, several optimality characterizations of the orbits are given: optimal path of viscosity methods, continuous-time model of Bregman-type proximal algorithms, geodesics for some adequate metrics, and projections ofq-trajectories of some Lagrange equations and completely integrable Hamiltonian systems.

Abstract. We show that Poisson fibrations integrate to a special kind of symplectic fibrations, called fibered symplectic groupoids.

We provide a framework for extensions of Lie algebroids, including non-abelian extensions and Lie algebroids over different bases. Our approach involves Ehresmann connections, which allows straight generalizations of classical constructions. We exhibit a filtration in cohomology and explain the associated spectral sequence. We also give a description of the groupoid integrating an extension in case a complete connection exists. The integrability is also studied.Partially supported by the Fundação para a Ciência e a Tecnologia through the Program POCI 2010/FEDER and by the Projects POCI/MAT/57888/2004 and POCI/MAT/55958/2004.

A degree 1 non-negative graded super manifold equipped with a degree 1 vector field Q satisfying [Q, Q] = 1, namely a so-called NQ-1 manifold is, in plain differential geometry language, a Lie algebroid. We introduce a notion of fibration for such super manifols, that essentially involves a complete Ehresmann connection. As it is the case for Lie algebras, such fibrations turn out not to be just locally trivial products. We also define homotopy groups and prove the expected long exact sequence associated to a fibration. In particular, Crainic and Fernandes's obstruction to the integrability of Lie algebroids is interpreted as the image of a transgression map in this long exact sequence.

On Friday November 13th at 9:20 pm, three kamikaze bombs went off around the Stade de France a stadium in Saint-Denis just outside Paris, 4 different shootings took place and bombings in Paris and hundreds of people were held hostage in a theater.This multi-site terrorist attack was the first of this magnitude in France. Drawing the lessons of these attacks and those which occurred in other countries from a health perspective is essential to continuously adapt and improve the French response to possible future attacks.Several issues would need to be further explored:Management of uncertainties: When to trigger the plans: after the 1st attack, the 2nd? When do attacks end and when to release mobilized resources?Management of victims: How to ensure that all victims are secured or taken care of? How to provide assistance when attacks are ongoing?Management of teams: Proper follow-up of persons involved in the response: health professionals, police and firemen, emergency call centers but also civil servants within administration that contributed to the response.Communication: Reactivity of all is a key element to secure appropriate resource is mobilized for the response. All actors have to be able to communicate quickly in a secured way.