A family of functional inequalities

For displacement convex functionals in the probability space equipped with the Monge-Kantorovich metric we prove the equivalence between the gradient and functional type Lojasiewicz inequalities. In a second part, we specialise these inequalities to some classical geodesically convex functionals. For the Boltzmann entropy, we obtain the equivalence between logarithmic Sobolev and Talagrand's inequalities. On the other hand, the non-linear entropy and the Gagliardo-Nirenberg inequality provide a Talagrand inequality which seems to be a new equivalence. Our method allows also to recover some results on the asymptotic behaviour of the associated gradient flows

A family of functional inequalities

For displacement convex functionals in the probability space equipped with the Monge-Kantorovich metric we prove the equivalence between the gradient and functional type Lojasiewicz inequalities. In a second part, we specialise these inequalities to some classical geodesically convex functionals. For the Boltzmann entropy, we obtain the equivalence between logarithmic Sobolev and Talagrand's inequalities. On the other hand, the non-linear entropy and the Gagliardo-Nirenberg inequality provide a Talagrand inequality which seems to be a new equivalence. Our method allows also to recover some results on the asymptotic behaviour of the associated gradient flows

A family of functional inequalities

For displacement convex functionals in the probability space equipped with the Monge-Kantorovich metric we prove the equivalence between the gradient and functional type Lojasiewicz inequalities. In a second part, we specialise these inequalities to some classical geodesically convex functionals. For the Boltzmann entropy, we obtain the equivalence between logarithmic Sobolev and Talagrand's inequalities. On the other hand, the non-linear entropy and the Gagliardo-Nirenberg inequality provide a Talagrand inequality which seems to be a new equivalence. Our method allows also to recover some results on the asymptotic behaviour of the associated gradient flows

Saline: Improving Best-Effort Job Management in Grids

Although virtualization technologies have recently gained a lot of interest in Grid computing as they allow flexible resource management, the most common way to exploit grids still relies on dedicated services like resource management systems (RMSs) to get resources at a particular time. To improve resource usage, most of these systems provide a best-effort mode where lowest priority jobs can be executed when resources are idle. This particular mode does not provide any guarantee of service and jobs may be killed at any time by the RMS when the nodes they use are subject to higher priority reservations. This behaviour potentially leads to a huge waste of computation time or at least requires users to deal with checkpoints of their best-effort jobs. In this paper, we present Saline, a generic and non-intrusive framework to manage best-effort jobs at grid level through virtual machines (VMs) usage. We discuss the main challenges concerning the design of such a grid system, focusing on VM snapshot management and network configuration. Results of preliminary experiments show the interest of our proposal to ensure an efficient execution of best-effort jobs through the whole grid

Optimal Complexity and Certification of Bregman First-Order Methods

We provide a lower bound showing that the $O(1/k)$ convergence rate of the NoLips method (a.k.a. Bregman Gradient) is optimal for the class of functions satisfying the $h$-smoothness assumption. This assumption, also known as relative smoothness, appeared in the recent developments around the Bregman Gradient method, where acceleration remained an open issue. On the way, we show how to constructively obtain the corresponding worst-case functions by extending the computer-assisted performance estimation framework of Drori and Teboulle (Mathematical Programming, 2014) to Bregman first-order methods, and to handle the classes of differentiable and strictly convex functions.Comment: To appear in Mathematical Programmin

Towards practical large-eddy simulations of complex turbulent flows

International audienceA Shear-Improved Smagorinsky model (SISM) allowing to address non-homogeneous and unsteady flow configurations in a physically-sound manner, without adding significant complication and computation compared to the standard Smagorinsky model, is studied and implemented. Interestingly, the SISM does not call for any adjustable parameter nor ad-hoc damping function. It makes use here of an exponential smoothing algorithm to estimate the ensemble-average of the strain from the temporal evolution of the flow. Application on a flow past a circular cylinder is used as a test of the method