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SUMMARY:Tomoki Uda (Tohoku University)
DTSTART:20211105T050000Z
DTEND:20211105T060000Z
DTSTAMP:20260423T004701Z
UID:APATG/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/APATG/28/">O
 n Interleaving Distance between Reeb Trees as 𝑹-Pospaces</a>\nby Tomoki
  Uda (Tohoku University) as part of Asia Pacific Seminar on Applied Topolo
 gy and Geometry\n\n\nAbstract\nA Reeb graph is one of the mathematical too
 ls to summarize topology of real-valued functions. Silva\, Munch and Patel
  proposed the interleaving distance between two Reeb graphs as 𝑹-spaces
 . Although this metric is useful to show the stability\, the estimation is
  rough in terms of data resolution. In this talk we will introduce an inte
 rleaving distance between tree pospaces\, which can be also used to prove 
 the stability of Reeb trees. A pospace\, a partially ordered space\, is a 
 poset endowed with a compatible topology. By considering the compatibility
  of both topology and order\, we can achieve sharp evaluation by incorpora
 ting data resolutions as discrete order structures\, while maintaining the
  comparison of “soft” topological structures of trees. Furthermore\, t
 he metric can compare discrete and/or continuous structured 𝑹-pospaces\
 , which is expected to be useful for evaluating the convergence.\n
LOCATION:https://researchseminars.org/talk/APATG/28/
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