In this paper, we study the stability and generalization properties of penalized empirical-risk minimization algorithms. We propose a set of properties of the penalty term that is sufficient to ensure uniform β-stability: we show that if the penalty function satisfies a suitable convexity property, then the induced regularization algorithm is uniformly β-stable. In particular, our results imply...

We construct a new Fortin operator for the lowest order Taylor–Hood element, which is uniformly stable both in L and H. The construction, which is restricted to two space dimensions, is based on a tight connection between a subspace of the Taylor– Hood velocity space and the lowest order Nedelec edge element. General shape regular triangulations are allowed for the H–stability, while some mesh ...

We are interested in inhomogeneous diffusions in which the own law intervenes in the drift. This kind of diffusions corresponds to the hydrodynamical limit of some particle system. One also talks about propagation of chaos. It is well-known, for McKean-Vlasov diffusions, that such a propagation of chaos holds on finite interval. However, it has been proved that the lack of convexity of the exte...

Having a prior assumption about where light originates can disambiguate perceptual scenarios. Previous studies have reported that adult observers use a "light-from-above" prior as well as a convexity prior to constrain perception of shape from shading. Such priors may reflect information acquired about the visual world, where objects tend to be convex and light tends to come from above. In the ...

On arbitrary spacetimes, we study the characteristic Cauchy problem for Dirac fields on a light-cone. We prove the existence and uniqueness of solutions in the future of the light-cone inside a geodesically convex neighbourhood of the vertex. This is done for data in L 2 and we give an explicit definition of the space of data on the light-cone producing a solution in H 1. The method is based on...

The present experiment was designed to examine the roles of painted linear perspective cues, and the convexity bias that are known to influence human observers' perception of three-dimensional (3D) objects and scenes. Reverse-perspective stimuli were used to elicit a depth-inversion illusion, in which far points on the stimulus appear to be closer than near points and vice versa, with a 2 (Type...

Our visual system faces the challenging task to construct integrated visual representations from the visual input projected on our retinae. Previous research has provided mixed evidence as to whether visual awareness of the stimulus parts is required for such integration to occur. Here, we address this issue by taking a novel approach in which we combine a monocular rivalry stimulus (i.e., a bi...

Two-level overlapping Schwarz methods are considered for nite element problems of 3D Maxwell's equations. N ed elec elements built on tetrahedra and hexahedra are considered. Once the relative overlap is xed, the condition number of the additive Schwarz method is bounded, independently of the diameter of the triangulation and the number of subregions. A similar result is obtained for a multipli...

We propose and analyze a new parallel coordinate descent method—‘NSync— in which at each iteration a random subset of coordinates is updated, in parallel, allowing for the subsets to be chosen non-uniformly. We derive convergence rates under a strong convexity assumption, and comment on how to assign probabilities to the sets to optimize the bound. The complexity and practical performance of th...