With more satellite and model precipitation data becoming available, new analytical
methods are needed that can take advantage of emerging data patterns to make well …

Ptychography is a popular imaging technique that combines diffractive imaging with
scanning microscopy. The technique consists of a coherent beam that is scanned across an …

We establish the pointwise convergence of the iterative Lloyd I procedure, also known as the
k-means algorithm, as soon as the starting grid (with size N\geq2) induces a lower mean …

Most crowd simulators focus on navigation and agents flow. In this paper, we present
another perspective that concentrates on the overall distribution of virtual agents and uses …

A multilevel optimization approach (termed MG/Opt) is presented for the solution of equality-
constrained optimization problems. The approach assumes that one has a hierarchy of …

Algebraic Multigrid (AMG) methods were developed originally for numerically solving Partial
Differential Equations (PDE), not necessarily on structured grids. In the last two decades …

We present and analyze a fast algorithm for directly computing measures of generalized
Voronoi regions associated with generators of arbitrary codimension. The algorithm consists …

Self-assembly of shapes from spheres to nonsmooth and possibly nonconvex shapes is
pervasive throughout the sciences. These arrangements arise in biology for animal flocking …

In this thesis, three geometric problems are studied that involve Voronoi regions in Rd which
are generated by codimension k sets, k∈{1,..., d}. Hereafter, these sets will be called …

The curse of dimensionality exists in multiple phenomena. For example, spurred by
advances in detector technology and X-ray optics, beamline upgrades for the Advanced …