Three-dimensional shapelets and an automated classification scheme for
  dark matter haloes
  We extend the two-dimensional Cartesian shapelet formalism to d-dimensions.
Concentrating on the three-dimensional case, we derive shapelet-based equations
for the mass, centroid, root-mean-square radius, and components of the
quadrupole moment and moment of inertia tensors. Using cosmological N-body
simulations as an application domain, we show that three-dimensional shapelets
can be used to replicate the complex sub-structure of dark matter halos and
demonstrate the basis of an automated classification scheme for halo shapes. We
investigate the shapelet decomposition process from an algorithmic viewpoint,
and consider opportunities for accelerating the computation of shapelet-based
representations using graphics processing units (GPUs).
