An Algorithm in Computational Geometry and an Exploration in Computational Topology

Tuesday, February 25, 2014 - 1:30pm - 2:30pm
Lind 409
Lori Neuberg (Ziegelmeier) (Macalester College)
In this talk, a novel algorithm related to a fundamental problem in
computational geometry as well as a new exploration in computational
topology will be presented. The convex hull of a set of points, C, appears
as a useful construct in a variety of contexts. For many problems,
particularly in the presence of noise, the true vertex set (and facets) may
be difficult to determine and one should expand the list of high interest
candidates to points lying near the boundary of the convex hull. In the
first part of this talk, a quadratic program for the purpose of stratifying
points in a data cloud based on proximity to the boundary of the convex
hull is discussed. In the second part of this talk, a new exploration of
applying topological data analysis techniques to biological aggregations,
or swarming data, will be discussed. Standard metrics used in the swarming
community require a priori knowledge to reveal structure from such data.
However, an analysis of simulation data indicates that persistent homology
barcodes may naturally reveal this structure.