By a Euclidean logic, we understand a formal language whose variables range over subsets of Euclidean space, of some fixed dimension, and whose non-logical primitives have fixed me...
We present some sufficient conditions ensuring the upper semicontinuity and the continuity of the Bregman projection operator Π g C and the relative projection operator P g C in...
In this paper, we focus on the use of random projections as a dimensionality reduction tool for sampled manifolds in highdimensional Euclidean spaces. We show that geodesic paths ...
We study the boundary measures of compact subsets of the d-dimensional Euclidean space, which are closely related to Federer’s curvature measures. We show that they can be comput...
We present a randomised polynomial time algorithm for approximating the volume of a convex body K in n-dimensional Euclidean space. The proof of correctness of the algorithm relie...