Guarding Life

Guarding Art Galleries by Guarding Witnesses

Let P be a simple polygon. We define a witness set W to be a set of points such that if any (prospective) guard set G guards W , then it is guaranteed that G guards P . We show that not all polygons admit a finite witness set. If a finite minimal witness set exists, then it cannot contain any witness in the interior of P ; all witnesses must lie on the boundary of P , and there can be at most o...

Triangle Guarding

We consider the problem of triangle guarding (4-guarding) a simple, 2D polygon Q. A polygon Q is 4-guarded if every point q of Q is contained in the convex hull of some three guards that can all see q. This rather odd condition approximates a desire, for example, to see all sides of q or to locate (via triangulation) q from at least two angularly well-separated views. If we restrict the guards ...

Altitude Terrain Guarding and Guarding Uni-Monotone Polygons

We show that the problem of guarding an x-monotone terrain from an altitude line and the problem of guarding a uni-monotone polygon are equivalent. We present a polynomial time algorithm for both problems, and show that the cardinality of a minimum guard set and the cardinality of a maximum witness set coincide. Thus, uni-monotone polygons are perfect; this result also extends to monotone mount...

Guarding the Body

Guarding the Gate

BACKGROUND Failed treatment trials are common in major depressive disorder and treatment-resistant depression, and remotely performed multifaceted, centralized structured interviews can potentially enhance signal detection by ensuring that enrolled patients meet eligibility criteria. METHODS We assessed the use of a specific remote structured interview that validated the diagnosis, level of t...