Cutting dense point sets in half

Motion Tracking of Dense Feature Point Sets

Dense point sets have sparse Delaunay triangulations

The spread of a finite set of points is the ratio between the longest and shortest pairwise distances. We prove that the Delaunay triangulation of any set of n points in R3 with spread ∆ has complexity O(∆3). This bound is tight in the worst case for all ∆ = O( √ n). In particular, the Delaunay triangulation of any dense point set has linear complexity. We also generalize this upper bound to re...

Dense point sets with many halving lines

We construct a dense point set of n points in the plane with ne( √ logn) halving lines. This improves the bound O(n log n) of Edelsbrunner, Valtr and Welzl from 1997. We also observe that the upper bound on the maximum number of halving lines of dense point set can be improved to O(n). Our construction can be generalized to higher dimensions, for any d we construct a dense point set of n points...

Computing Half-plane and Strip Discrepancy of Planar Point Sets

Proof: We discuss the structure for nding the maximum value of any of the functions (` + r ()), r 2 S, at a query value of. Finding the minimum value, and nding the maximum and minimum for the functions (` + r ()), can be done in a similar way. So we are interested in the function () := max r2S (` + r ()). The function () is called the upper envelope of the functions (` + r ()). It is known tha...

DNA Intercalators: Cutting plasmids in half

We have designed and synthesized novel intercalating compounds that efficiently hydrolyze supercoiled plasmid DNA lacking depurine/depyrimidine sites. These intercalators consist of conjugates of diamine and thia-heterocyclic naphthalimide. Surprisingly, the initial hydrolyzed products comprised fragments with half the length of the original plasmid. We suggest a mechanochemical mechanism that ...