Peter Bubenik
Simplicial models for concurrency.
Wed, 12/01/2010 - 16:01 — SomNambulAuthors: Peter Bubenik
Subjects: and Cluster Computing, Distributed, Parallel
AbstractWe model both concurrent programs and the possible executions from one state
to another in a concurrent program using simplices. The latter are calculated
using necklaces of simplices in the former. For these models, the appropriate
setting is the not the traditional approach to simplicial sets, but a more
recent one due to Joyal.Statistical topology via Morse theory, persistence and nonparametric estimation.
Wed, 08/26/2009 - 14:58 — SomNambulAuthors: Peter Bubenik, Gunnar Carlsson, Peter T. Kim, Zhiming Luo
Subjects: gr. Statistics
AbstractIn this paper we examine the use of topological methods for multivariate
statistics. Using persistent homology from computational algebraic topology, a
random sample is used to construct estimators of persistent homology. This
estimation procedure can then be evaluated using the bottleneck distance
between the estimated persistent homology and the true persistent homology. The
connection to statistics comes from the fact that when viewed as a
nonparametric regression problem, the bottleneck distance is bounded by the
sup-norm loss.
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