A set S that has a non-empty intersection with every set in a collection of sets C is called a hitting set of C. If no element can be removed from S without violating the hitting set property, S is considered to be minimal. Several interesting problems can be partly formulated as ones that a minimal hitting set or more ones have to be found. Many of these problems are required for proper soluti...

2 Hitting times 3 2.1 Typical hitting times are large . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Exponential mixing on spatial graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Expected hitting times degenerate to the stationary distribution . . . . . . . . . . . . . . . . 6 2.4 The case of one dimension . . . . . . . . . . . . . . . ....

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...

The first passage time problem for Brownian motions hitting a barrier has been extensively studied in the literature. In particular, many incarnations of integral equations which link the density of the hitting time to the equation for the barrier itself have appeared. Most interestingly, Peskir (2002b) demonstrates that a master integral equation can be used to generate a countable number of n...

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 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...