Distorted measures have been used in pricing of insurance contracts for a long time. This paper reviews properties of related acceptability functionals in risk management, called distortion functionals. These functionals may be characterized by being mixtures of average values-at-risk. We give a dual representation of these functionals and show how they functionals may be used in portfolio opti...

We develop the first-order gradient correction to the exchange-correlation free energy of the homogeneous electron gas for use in finite-temperature density functional calculations. Based on this, we propose and implement a simple temperature-dependent extension for functionals beyond the local density approximation. These finitetemperature functionals show improvement over zero-temperature fun...

This paper concerns the problem of estimating linear functionals of the mixing distribution from Poisson mixture observations. In particular, linear functionals for which parametric rate of convergence cannot be achieved are studied. It appears that Gaussian functionals are rather easy to estimate. Estimation of the distibution functions is then considered by approximating this functional by Ga...

In the present investigation, the results of extensive benchmarking study of density functional theory (DFT) methods on some catalytically important metal dimers have been reported. The calculations were carried out on Al2, Ti2, V2, Cr2, Mn2, Fe2, Co2, Ni2, Cu2, and Zn2 using DFT functionals such as GGA, meta GGA, hybrid meta GGA along with recently developed Minnesota functionals. The bond len...

In this paper, the regularized estimation of the displacement vector field (DVF) of a dynamic image sequence is considered. A new class of non-quadratic convex regularization functionals is employed to estimate the motion field in the presence of motion discontinuities and occlusions. The derivation of the functionals is based on entropy considerations and do not require parameter tuning as in ...

We show that to every recursive total continuous functional Φ there is a representative Ψ of Φ in the hierearchy of partial continuous functionals such that Ψ is S1 − S9 computable over the hierarchy of partial continuous functionals. Equivalently, the representative Ψ will be PCF -definable over the partial continuous functionals, where PCF is Plotkin’s programming language for computable func...

HADWIGER INTEGRATION OF DEFINABLE FUNCTIONS Matthew L. Wright Robert Ghrist, Advisor This thesis defines and classifies valuations on definable functionals. The intrinsic volumes are valuations on “tame” subsets of R, and by easy extension, valuations on functionals on R with finitely many level sets, each a “tame” subset of R. We extend these valuations, which we call Hadwiger integrals, to de...