We consider guarding a city of k vertical buildings, each having a rectangular base, by placing guards only at vertices. The aim is to use the smallest number of guards. The problem is a 2.5D variant of the traditional art gallery problem, and finds applications in urban security. We give upper and lower bounds on the number of guards needed for a few versions of the problem. Specifically, we p...

We consider combinatorial problems motivated by sensor networks for beacon-based point-to-point routing and covering. A beacon b is a point that can be activated to effect a ‘magnetic pull’ toward itself everywhere in a polygonal domain P . The routing problem asks how many beacons are required to route between any pair of points in a polygonal domain P . In simple polygons with n vertices we s...

Among the techniques for capturing nearby groundwater, covered horizontal well (draining gallery) stands out in its different types of water mine, qanat, and cimbre. The collected by these means is used to supply people livestock, irrigation, movement hydraulic devices, etc. Because they are carried surface gravity (without need energy) because only recharging groundwater table that takes place...

For any k we construct a simply connected compact set (art gallery) in IR3 whose every point sees a positive fraction (in fact, more than 59) of the gallery, but the whole gallery cannot be guarded by k guards. This disproves a conjecture of Kavraki, Latombe, Motwani, and Raghavan.

In many face recognition tasks the pose and illumination conditions of the probe and gallery images are di erent. In other cases multiple gallery or probe images may be available, each captured from a di erent pose and under a di erent illumination. We propose a face recognition algorithm which can use any number of gallery images per subject captured at arbitrary poses and under arbitrary illu...

Some researchers argue that gestures serve an interpersonal function, such as making the intended message clear (e.g., Gallagher & Frith, 2003; cf. Kita, 2000). In this study, we tested whether gestures serve an interpersonal function, specifically predicting that the higher participants’ autism spectrum quotient, the less frequently they would gesture. Participants completed the Autism Spectru...

1. INTRODUCTION. The premise of this article—what our friends in theatre would call its " conceit " —is that we are about to visit a gallery devoted to the history of calculus. Admittedly no such institution exists, but it is easily imagined. One need only think of an art museum, albeit one whose masterpieces are not canvases but theorems and whose masters are not Courbet and Cezanne but Leibni...

We exploit duality considerations in the study of singular combinatorial 2-discs (diagrams) and are led to the following innovations concerning the geometry of the word problem for finite presentations of groups. We define a filling function called gallery length that measures the diameter of the 1-skeleton of the dual of diagrams; we show it to be a group invariant and we give upper bounds on ...

The first Micro Gallery opened at the National Gallery in London on July 21st 1991. The first facility of its kind, it provided visitors with a comprehensive multimedia reference to the Gallery's collection. Since then the author and his colleagues have had the privilege of working on two further projects of a similar nature. The Image Gallery at the San Diego Museum of Art opened on October 26...

Let P be an orthogonal polygon with n vertices, and let V ∗ and E∗ be specified sets of vertices and edges of P . We prove that P has a guard set of cardinality at most ⌊(n+ 3|V ∗|+ 2|E∗|) /4⌋ that includes each vertex in V ∗ and at least one point of each edge in E∗. Our bound is sharp and reduces to the orthogonal art gallery theorem of Kahn, Klawe and Kleitman when V ∗ and E∗ are empty.