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Activity Number: 523
Type: Topic Contributed
Date/Time: Wednesday, August 3, 2016 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract #320625 View Presentation
Title: The LCM Filtration for the Cut Distribution of Networks and Its Dual
Author(s): Henry Wynn*
Companies: London School of Economics and Political Science
Keywords: cut ideals, reliability, filtration, persistent homology
Abstract:

Previous work has studied the cut ideal of a network to give exact values and bounds for the reliability under the standard Erdos model of failure. Here the work is extended to the full LCM filtration which describes the number k of minimal failures, with one ideal of the filtration for each k. This description of the failure set can be compared to other descriptions, notably that arising from "signature analysis". The analysis leads to a type of multigraded persistent homomology based on ideals. Moreover there is a dual approach, under Alexander duality, and complete with metric, which leads to a version which is close in spirit to persistent homology based on covers with Euclidian balls. In other words the metric yields a special alpha-complex. The ideal theory points to the use of fast algorithms for the computation of multigraded Betti numbers, required both for the reliability theory and the persistent homology.


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