Sampling inequalities give a precise formulation of the fact that a differentiable function cannot attain large values, if its derivatives are bounded and if it is small on a sufficiently denseâ€¦ (More)

We introduce a class of analytic positive definite multivariate kernels which includes infinite dot product kernels as sometimes used in machine learning, certain new nonlinearly factorizable kernelsâ€¦ (More)

We consider a variational model related to the formation of islands in heteroepitaxial growth on unbounded domains. We first derive the scaling regimes of the minimal energy in terms of the volume ofâ€¦ (More)

A variational model for the epitaxial deposition of a film on a rigid substrate in the presence of a crystallographic misfit is studied. The scaling behavior of the minimal energy in terms of theâ€¦ (More)

We consider reproducing kernels K : âŒ¦ â‡¥ âŒ¦ ! R in multiscale series expansion form, i.e., kernels of the form K (x, y) = P ` 2N`P j2I`` ,j (x) `,j (y) with weightsÃ nd structurally simple basisâ€¦ (More)

This paper introduces a new technique for the analysis of ker nel-based regression problems. The basic tools are sampling inequaliti es which apply to all machine learning problems involving penaltyâ€¦ (More)

The formation of microdomains, also called rafts, in biomembranes can be attributed to the surface tension of the membrane. In order to model this phenomenon, a model involving a coupling between theâ€¦ (More)

A variational model introduced by Spencer and Tersoff (Appl. Phys. Lett. 96:073114, 2010) to describe optimal faceted shapes of epitaxially deposited films is studied analytically in the case inâ€¦ (More)

Variational models for image and signal denoising are based on the minimization of energy functionals consisting of a fidelity term together with higher-order regularization. In addition to theâ€¦ (More)