Sensors and Sampling: A Homological Approach

#"Sensors #and #Sampling: #A #Homological #Approach" #by #Dr. #Don #Sheehy #Assistant #Professor #of #Computer #Science #University #Connecticut #Storrs
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In their seminal work on homological sensor networks, de Silva and Ghrist showed the surprising fact that its possible to certify the coverage of a coordinate free sensor network even with very minimal knowledge of the space to be covered.  We give a new, simpler proof of the de Silva-Ghrist Topological Coverage Criterion that eliminates any assumptions about the smoothness of the boundary of the underlying space, allowing the results to be applied to much more general problems.   The new proof factors the geometric, topological, and combinatorial aspects of this approach.  This factoring reveals an interesting new connection between the topological coverage condition and the notion of weak feature size in geometric sampling theory.  We then apply this connection to the problem of showing that for a given scale, if one knows the number of connected components and the distance to the boundary, one can also infer the higher betti numbers or provide strong evidence that more samples are needed.  This is in contrast to previous work which merely assumed a good sample and gives no guarantees if the sampling condition is not met.


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  • Fairleigh Dickinson University
  • Teaneck, New Jersey
  • United States 07666
  • Building: Auditorium M105, Muscarelle Center
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  • Contact Event Host

  • Hong Zhao (201)-692-2350, zhao@fdu.edu; Howard Leach h.leach@ieee.org

  • Co-sponsored by SP01 and School of Computer Sciences and Engineering, FDU
  • Starts 09 March 2015 07:00 PM UTC
  • Ends 10 April 2015 04:00 PM UTC
  • No Admission Charge




Agenda

Don Sheehy received his B.S.E. from Princeton University and his Ph.D. in Computer Science from Carnegie Mellon University under Gary Miller.   He spent two years as a postdoc with the Geometrica group at Inria Saclay in France.  He is now Assistant Professor of Computer Science at The University of Connecticut.  His research is in algorithms and data structures in computational geometry and topological data analysis.