Eleven density functionals are compared with regard to their performance for the lattice constants of solids. We consider standard functionals, such as the local-density approximation and the Perdew-Burke-Ernzerhof PBE generalized-gradient approximation GGA , as well as variations of PBE GGA, such as PBEsol and similar functionals, PBE-type functionals employing a tighter Lieb-Oxford bound, and...

We provide a general theoretical framework to derive Bernstein-von Mises theorems for matrix functionals. The conditions on functionals and priors are explicit and easy to check. Results are obtained for various functionals including entries of covariance matrix, entries of precision matrix, quadratic forms, log-determinant, eigenvalues in the Bayesian Gaussian covariance/precision matrix estim...

We investigate the hypothesis that the macroscopic properties of a porous material can be determined from limited morphological information. Specifically, we investigate this hypothesis for the Minkowski functionals of two-phase media in 2-D. We look at two methods for generating samples with desired Minkowski functionals: the Gibbs sampler and the Metropolis-Hastings algorithm. The Metropolis-...

Abstract. Let B(H) be the space of bounded operators on a notnecessarily-separable Hilbert space H . Working within Bishop-style constructive analysis, we prove that certain weak-operator continuous linear functionals on B(H) are finite sums of functionals of the form T 〈Tx, y〉. We also prove that the identification of weakand strong-operator continuous linear functionals on B(H) cannot be esta...

We provide a natural characterization of the type two Mehlhorn-CookUrquhart basic feasible functionals as the provably total type two functionals of our (classical) applicative theory PT introduced in [30], thus providing a proof of a result claimed in the conclusion of [30]. This further characterization of the basic feasible functionals underpins their importance as a key candidate for the no...

For image filtering applications, it has been observed recently that both diffusion filtering and associated regularization models provide similar filtering properties. The comparison has been performed for regularization functionals with convex penalization functional. In this paper we discuss the relation between non-convex regularization functionals and associated time dependent diffusion fi...

We prove that the sequential functionals of some fixed types at type level 2, taking finite sequences of unary functions as arguments, do form a directed complete partial ordering. This gives a full characterisation of for which types the partially ordered set of sequential functionals has this property. As a tool, we prove a normal form theorem for the finite sequential functionals of the type...

Reconstruction of noise-corrupted surfaces may be stated as a (in general nonconvex) functional minimization problem. For functionals with quadratic data term, this paper addresses the criteria for such functionals to be convex, and the variational approach for minimization. I present two automatic and general methods of approximation with convex functionals based on Gaussian convolution. They ...

We study the tail behavior of the distribution of certain subadditive functionals acting on the sample paths of Lévy processes. The functionals we consider have, roughly speaking, the following property: only the points of the process that lie above a certain curve contribute to the value of the functional. Our assumptions will make sure that the process ends up eventually below the curve. Our ...

We prove that the sequential functionals of some fixed types at type level 2, taking finite sequences of unary functions as arguments, form a directed complete partial ordering. This gives a full characterisation of the types for which the partially ordered set of sequential functionals has this property. As a tool, we prove a normal form theorem for the finite sequential functionals of the typ...