The Medusa of Spatial Sorting: Topological Construction
  We consider the simultaneous movement of finitely many colored points in space, calling it a spatial sorting process. The name suggests a purpose that drives the collection to a configuration of increased or decreased order. Mapping such a process to a subset of space-time, we use persistent homology measurements of the time function to characterize the process topologically. 
Herbert Edelsbrunner and Carl-Philipp Heisenberg and Michael Kerber   and Gabriel Krens
cs.CG math.AT q-bio.CB q-bio.QM