A novel approach for highly space-efficient hardware-accelerated collision detection is presented. This paper focuses on the architecture to traverse bounding volume hierarchies in hardware. It is based on a novel algorithm for testing discretely oriented polytopes (DOPs) for overlap, utilizing only fixed-point (i.e., integer) arithmetic. We derive a bound on the deviation from the mathematical...

We consider a one-dimensional translation invariant point process of density one with uniformly bounded variance of the number NI of particles in any interval I . Despite this suppression of fluctuations we obtain a large deviation principle with rate function F(ρ) ' −L log Prob(ρ) for observing a macroscopic density profile ρ(x), x ∈ [0, 1], corresponding to the coarse-grained and rescaled den...

Logistic regression has been widely used in classification tasks for many years. Its optimization in case of linear separable data has received extensive study due to the problem of a monoton likelihood. This paper presents a new approach, called bounded logistic regression (BLR), by solving the logistic regression as a convex optimization problem with constraints. The paper tests the accuracy ...

Geometric embedding of graphs in a point set in the plane is a well known problem. In this paper, the complexity of a variant of this problem, where the point set is bounded by a simple polygon, is considered. Given a point set in the plane bounded by a simple polygon and a free tree, we show that deciding whether there is a planar straight-line embedding of the tree on the point set inside the...

In this paper, we use the framework of functions of bounded variation and the coarea formula to give an explicit computation for the expectation of the perimeter of excursion sets of shot noise random fields in dimension n ≥ 1. This will then allow us to derive the asymptotic behavior of these mean perimeters as the intensity of the underlying homogeneous Poisson point process goes to infinity....

We consider the solution to a stochastic heat equation. This solution is a random function of time and space. For a fixed point in space, the resulting random function of time, F (t), has a nontrivial quartic variation. This process, therefore, has infinite quadratic variation and is not a semimartingale. It follows that the classical Itô calculus does not apply. Motivated by heuristic ideas ab...

Abstract. The dynamical Borel-Cantelli lemma for some interval maps is considered. For expanding maps whose derivative has bounded variation, any sequence of intervals satisfies the dynamical Borel-Cantelli lemma. If a map has an indifferent fixed point, then the dynamical Borel-Cantelli lemma does not hold even in the case that the map has a finite absolutely continuous invariant measure and s...