This study highlights recent observations in tennis which have revealed that the head position and gaze direction during the hitting process distinguished significantly elite players (with significant results in Grand Slam tournaments) from other top players: Elite players spent more time tracking the ball and fix the contact zone (or hitting zone) throughout the hitting action. These character...

In this paper, we explore analytically and experimentally a quasi-quantum analogue of the hitting time of the continuous-time quantum walk on a graph. For the classical random walk, the hitting time has been shown to be robust to errors in edge weight structure and to lead to spectral clustering algorithms with improved performance. Our analysis shows that the quasi-quantum analogue of the hitt...

Generating minimal hitting sets of a collection of sets is known to be NP-hard, necessitating heuristic approaches to handle large problems. In this paper a low-cost, approximate minimal hitting set (MHS) algorithm, coined STACCATO, is presented. STACCATO uses a heuristic function, borrowed from a lightweight, statistics-based software fault localization approach, to guide the MHS search. Given...

In a problem of target hitting, the capture basin at cost c is the set of states that can reach the target with a cost lower or equal than c, without breaking the viability constraints. The boundary of a c-capture basin is the c-contour of the problem value function. In this paper, we propose a new algorithm that solves target hitting problems, by iteratively approximating capture basins at suc...

Generating minimal hitting sets of a collection of sets is known to be NPhard, necessitating heuristic approaches to handle large problems. In this paper a low-cost, approximate minimal hitting set (MHS) algorithm, coined Staccato, is presented. Staccato uses a heuristic function, borrowed from a lightweight, statistics-based software fault localization approach, to guide the MHS search. Given ...

We give improved hitting-sets for two special cases of Read-once Oblivious Arithmetic Branching Programs (ROABP). First is the case of an ROABP with known variable order. The best previously known hitting-set for this case had size (nw) where n is the number of variables and w is the width of the ROABP. Even for a constant-width ROABP, nothing better than a quasi-polynomial bound was known. We ...

We investigate the use of generating functions in the analysis of discrete Markov chains. Generating functions are introduced as power series whose coefficients are certain hitting probabilities. Being able to compute such functions implies that the calculation of a number of quantities of interest, including absorption probabilities, expected hitting time and number of visits, and variances th...

We give a general framework for the problem of finding all minimal hitting sets of a family of objects in R by another. We apply this framework to the following problems: (i) hitting hyper-rectangles by points in R; (ii) stabbing connected objects by axis-parallel hyperplanes in R; and (iii) hitting half-planes by points. For both the covering and hitting set versions, we obtain incremental pol...

A kernelization algorithm for the 3-Hitting-Set problem is presented along with a general kernelization for d-Hitting-Set problems. For 3-Hitting-Set, a quadratic kernel is obtained by exploring properties of yes instances and employing what is known as crown reduction. Any 3-Hitting-Set instance is reduced into an equivalent instance that contains at most 5k + k elements (or vertices). This ke...