Universally optimal approximation of functionals

Approximation of Non-convex Functionals in Gbv Approximation of Non-convex Functionals in Gbv

Universally Optimal Distribution of Points on Spheres

We study configurations of points on the unit sphere that minimize potential energy for a broad class of potential functions (viewed as functions of the squared Euclidean distance between points). Call a configuration sharp if there are m distances between distinct points in it and it is a spherical (2m− 1)-design. We prove that every sharp configuration minimizes potential energy for all compl...

Essentially Optimal Universally Composable Oblivious Transfer

Oblivious transfer is one of the most important cryptographic primitives, both for theoretical and practical reasons and several protocols were proposed during the years. We provide the first oblivious transfer protocol which is simultaneously optimal on the following list of parameters: Security: it has universal composition. Trust in setup assumptions: only one of the parties needs to trust t...

Variational Approximation of Functionals withCurvatures and Related

We consider the problem of approximating via ?-convergence a class of functionals depending on curvatures of smooth compact boundaries. We investigate the connections between the approximation problem and the lower semicontinuous envelope of the original functional. We provide some examples of lower semicontinuous functionals and their variational approximation.

Thorup-Zwick Emulators are Universally Optimal Hopsets

A (β, )-hopset is, informally, a weighted edge set that, when added to a graph, allows one to get from point a to point b using a path with at most β edges (“hops”) and length (1 + ) dist(a, b). In this paper we observe that Thorup and Zwick’s sublinear additive emulators are also actually (O(k/ ), )hopsets for every > 0, and that with a small change to the Thorup-Zwick construction, the size o...