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Homological Methods for Quantifying Coverage in Dynamic Sensor Networks

Thursday, March 6, 2014 - 11:30am - 12:20pm
Keller 3-180
Jennifer Gamble (North Carolina State University)
A dynamic sensor network may be represented as a sequence of simplicial complexes, and analyzed using zigzag persistent homology, with the resulting barcode containing birth-death intervals for homological features of the sequence. In this talk I will first describe the relationship between these intervals and the time-varying coverage holes in the network, as well as the scenarios in which the zigzag persistence barcode works well as a coverage descriptor. Further, I will propose a method for making a geometrically-relevant choice of representative cycle for each feature at its birth and/or death time, and propagating that information over the entire interval. This can allow “tracking” of the coverage holes in the network. Additionally, these representative cycles are used in conjunction with a hop-distance filtration to determine size estimates for the holes over time. This estimated size information is then used to enhance the regular barcode, giving a visual and quantitative descriptor of the time-varying network coverage.
MSC Code: 
46M18