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SUMMARY:An approximate nerve theorem
DTSTART:20160223T101500
DTEND:20160223T113000
DTSTAMP:20260501T113651Z
UID:1c0bf86239d7fc42225841f0785a535c1eba802b3d5c98057b3772c6
CATEGORIES:Conferences - Seminars
DESCRIPTION:Primoz Skraba\n(Artificial Intelligence Laboratory\, Jozej Ste
 fan Institute\, Ljubljana)\nThe nerve theorem [Borsuk 48] states that the 
 homotopy type of a sufficiently nice topological space is captured by the 
 nerve of a good cover of that space. In the case of persistence\, we rarel
 y compute the persistence diagram of a filtration exactly\, but rather an 
 approximation of it. In this talk we introduce the notion of an epsilon-go
 od cover and its application to computing persistence. Rather than require
  a good cover\, one where all the elements of the cover and their finite i
 ntersections are contractible\, we define the notion of an epsilon good co
 ver - one where its all elements and finite intersections are homologicall
 y trivial modulo epsilon-persistent classes (i.e. each element can have a 
 small amount of topological noise). We show an approximation result for th
 e persistence diagram of a filtration of the nerve and the underlying spac
 e which depends on epsilon and the maximal dimension of the nerve and show
  that this bound is tight.
LOCATION:CM113
STATUS:CONFIRMED
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