On rare occasions in the history of science, remarkable discoveries transform human society and forever alter mankind's view of the world. Examples of such discoveries include the heliocentric theory, Newtonian physics, the germ theory of disease, quantum theory, plate tectonics and the discovery that DNA carries genetic information. The science philosopher Thomas Kuhn famously described scienc...

The optimization of dynamic problems is both widespread and difficult. When conducting dynamic optimization, a balance between reinitialization and computational expense has to be found. There are multiple approaches to this. In parallel genetic algorithms, multiple sub-populations concurrently try to optimize a potentially dynamic problem. But as the number of sub-population increases, their e...

We describe how guards can be used to ensure that formulas in a partial logic are meaningful, and how guards and guarded formulas can be proved using classical logic. In addition to this theoretical utility, guards are useful in practice as a simple means of exposing aws in speci cations. We illustrate this use of guards with several examples in the Z speci cation language, using Z/EVES.

The problem of wireless localization asks to place and orient stations in the plane, each of which broadcasts a unique key within a fixed angular range, so that each point in the plane can determine whether it is inside or outside a given polygonal region. The primary goal is to minimize the number of stations. In this paper we establish a lower bound of ⌊2n/3⌋−1 stations for polygons in genera...

We define and study the following two-player game on a graph G. Let k ∈ N∗. A set of k guards is occupying some vertices of G while one spy is standing at some node. At each turn, first the spy may move along at most s edges, where s ∈ N∗ is his speed. Then, each guard may move along one edge. The spy and the guards may occupy same vertices. The spy has to escape the surveillance of the guards,...

In this paper, we present a new algorithm for vertex guarding of a triangulated surface, which takes into account the heights of the vertices and considers the global visibility of the guards. In this algorithm, the initial surface is reduced to a collection of simple polygons and trivial triangulated surfaces. This is done by assigning guards to some vertices and removing the faces covered by ...

We investigate a variation of the art gallery problem in which a team of mobile guards tries to track an unpredictable intruder in a simply-connected polygonal environment. In this work, we use the deployment strategy for diagonal guards originally proposed in [1]. The guards are confined to move along the diagonals of a polygon and the intruder can move freely within the environment. We define...