The domination properties of elliptic invariant diierential operators on symmetric spaces of noncompact type are investigated. Using the relation between parametrices and fundamental solutions on symmetric space we will show that the invariant diierential operator applied to a function can be uniformly estimated by function and an elliptic operator of higher order applied to the function in L p...

The energy model is a simple, biologically inspired approach to extracting relationships between images in tasks like stereopsis and motion analysis. We discuss how adding an extra pooling layer to the energy model makes it possible to learn encodings of transformations that are mostly invariant with respect to image content, and to learn encodings of images that are mostly invariant with respe...

The Novikov-Shubin invariants for a non-compact Riemannian manifold M can be defined in terms of the large time decay of the heat operator of the Laplacian on L p-forms, △p, on M . For the (2n + 1)-dimensional Heisenberg group H2n+1, the Laplacian △p can be decomposed into operators△p,n(k) in unitary representations β̄k which, when restricted to the centre of H, are characters (mapping ω to exp(...

We study the relative impact of small-scale random inhomogeneities and singular perturbations in nonlinear elasticity. More precisely, we analyse the asymptotic behaviour of the energy functionals Fε(ω)(u) = ∫ A ( f ( ω, x ε ,Du ) + ε|∆u| ) dx, where ω is a random parameter and ε > 0 denotes a typical length-scale associated with the variations in the elastic properties of the body. For f stati...

We study the relative impact of small-scale random inhomogeneities and singular perturbations in nonlinear elasticity. More precisely, we analyse the asymptotic behaviour of the energy functionals Fε(ω)(u) = ∫ A ( f ( ω, x ε ,Du ) + ε|∆u| ) dx, where ω is a random parameter and ε > 0 denotes a typical length-scale associated with the variations in the elastic properties of the body. For f stati...