We consider various hitting and piercing problems for the family of axis-parallel rectangles induced by a point set. Selection Lemmas on induced objects are classical results in discrete geometry that have been well studied and have applications in many geometric problems like weak epsilon nets and slimming Delaunay triangulations. Selection Lemma type results typically bound the maximum number...

Random walk is a powerful tool, not only for modeling, but also for practical use such as the Internet crawlers. Standard random walks on graphs have been well studied; It is well-known that both hitting time and cover time of a standard random walk are bounded by O(n) for any graph with n vertices, besides the bound is tight for some graphs. Ikeda et al. (2003) provided “β-random walk,” which ...

Abstract In this paper, we revisit energy-based concepts of controllability and reformulate them for control-affine nonlinear systems perturbed by white noise. Specifically, discuss the relation between deterministic corresponding stochastic control in limit small noise case which target state is a measurable subset space. We derive computable expression hitting probabilities mean first times t...

A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. Hitting times for discrete quantum walks on graphs give an average time before the walk reaches an ending condition. We derive an expression for hitting time using superoperators, and numerically evaluate it for the walk on the hypercube for various ...

We are going to analyze simple search tree algorithms for Weighted d-Hitting Set. Although the algorithms are simple, their analysis is technically rather involved. However, this approach allows us to even improve on elsewhere previously published running time estimates for the more restricted case of (unweighted) d-Hitting Set. 1

We are going to analyze simple search tree algorithms for Weighted d-Hitting Set. Although the algorithms are simple, their analysis is technically rather involved. However, this approach allows us to even improve on elsewhere previously published running time estimates for the more restricted case of (unweighted) d-Hitting Set. 1

A sample of i.i.d. continuous time Markov chains being defined, the sum over each component of a real function of the state is considered. For this functional, a central limit theorem for the first hitting time of a prescribed level is proved. The result extends the classical central limit theorem for order statistics. Various reliability models are presented as examples of applications. Mathem...

An 'oscillating' version of Brownian motion is defined and studied. 'Ordinary' Brownian motion and 'reflecting' Brownian motion are shown to arise as special cases. Transition densities, first-passage time distributions, and occupation time distributions for the process are obtained explicitly. Convergence of a simple oscillating random walk to an oscillating Brownian motion process is establis...

We consider the following basic task in the testing of concurrent systems. The input to the task is a partial order of events, which models actions performed on or by the system and specifies ordering constraints between them. The task is to determine if some scheduling of these events can result in a bug. The number of schedules to be explored can, in general, be exponential. Empirically, many...

The following letter describes two pilot studies testing the feasibility of immersive virtual reality therapy on pediatric patients with unilateral lower limb complex regional pain syndrome (CRPS). In these studies, patients completed target-hitting tasks in virtual reality using novel avatar bodies. Patients completed all sessions without adverse effects and both patients and parents were enth...