Hit-and-Run is known to be one of the best random sampling algorithms, its mixing time is polynomial in dimension. Nevertheless, in practice the number of steps required to achieve uniformly distributed samples is rather high. We propose new random walk algorithm based on billiard trajectories. Numerical experiments demonstrate much faster convergence to uniform distribution.

In this paper, we investigate the relationship between weak min-max property and diameter uniformity of domains in Banach spaces with dimension at least 2. As an application, show that uniform are invariant under relatively quasimöbius mappings.

We consider a system of uniform recurrence equations of dimension one. We show how the computation can be carried using minimal memory size with several synchronous processors. This result has applications in register minimization for digital circuitry and parallel simulation of timed event graphs.

We derive high-probability finite-sample uniform rates of consistency for k-NN regression that are optimal up to logarithmic factors under mild assumptions. We moreover show that kNN regression adapts to an unknown lower intrinsic dimension automatically. We then apply the k-NN regression rates to establish new results about estimating the level sets and global maxima of a function from noisy o...

Let Z be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform BriançonSkoda theorem for the local ring OZ ; a result which is previously proved by Huneke by algebraic methods. For ideals with few generators we also get some sharper results.

Abstract. We prove approximate Lipschitz stability for non-overdetermined inverse scattering at fixed energy with incomplete data in dimension d ≥ 2. Our estimates are given in uniform norm for coefficient difference and related stability precision efficiently increases with increasing energy and coefficient difference regularity. In addition, our estimates are rather optimal even in the Born a...

A corollary of a celebrated theorem of Minty is that the subdifferential graph of a closed convex function on Rn has uniform local dimension n. In contrast, there exist nonconvex closed functions whose subdifferentials have large graphs. We consider how far Minty’s corollary extends to functions that are nonconvex but semi-algebraic. © 2011 Elsevier Ltd. All rights reserved.

For a simple symmetric random walk in dimension d ≥ 3, a uniform strong law of large numbers is proved for the number of sites with given local time up to time n. AMS 2000 Subject Classification: Primary 60G50; Secondary 60F15, 60J55.

We consider a system of uniform recurrence equations (URE) of dimension one. We show how its computation can be carried out using minimal memory size with several synchronous processors. This result is then applied to register minimization for digital circuits and parallel computation of task graphs.