In this paper we investigate the Erd¨os/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We pr...
Consider a k-element subset P of the plane. It is known that the maximum number of sets similar to P that can be found among n points in the plane is (n2 ) if and only if the cros...
We study the smallest possible number of points in a topological space having k open sets. Equivalently, this is the smallest possible number of elements in a poset having k order ...
Abstract. We start by studying the relationship between two invariants isolated by Shelah, the sets of good and approachable points. As part of our study of these invariants, we pr...
We present a novel framework to exert topology control over a level set evolution. Level set methods offer several advantages over parametric active contours, in particular automat...