Zonotopes, Dicings, and Voronoi’s Conjecture on Parallelohedra

AbstractIn 1909, Voronoi conjectured that if some selection of translates of a polytope forms a facet-to-facet tiling of euclidean space, then the polytope is affinely equivalent to the Voronoi polytope for a lattice. He referred to polytopes with this tiling property as parallelohedra, but they are now frequently called parallelotopes. I show that Voronoi’s conjecture holds for the special case where the parallelotope is a zonotope. I also show that the Voronoi polytope for a lattice is a zonotope if and only if the Delaunay tiling for the lattice is a dicing (defined at the beginning of Section 3)

Survival Analysis, Recidivism, and Booking Data from the Stearns County Jail

This Master’s thesis examines booking data from the Stearns County Jail covering the period of January 1, 2003, to January 31, 2015. The examination of the data will make use of Microsoft Excel, JMP, and SAS. The analysis will focus on recidivism, where recidivism is defined as being re-booked into the Stearns County Jail. The analysis will show a lognormal distribution best approximates the process at work behind the recidivism of those individuals going through multiple bookings in the Stearns County Jail. Differing recidivism for males and females are also revealed by the application of survival analysis, and gender is used as an explanatory variable in the lognormal distribution used as a model