Corpus ID: 236318286

From Trees to Barcodes and Back Again II: Combinatorial and Probabilistic Aspects of a Topological Inverse Problem

  title={From Trees to Barcodes and Back Again II: Combinatorial and Probabilistic Aspects of a Topological Inverse Problem},
  author={Justin Curry and Jordan DeSha and Ad'elie Garin and Kathryn Hess and Lida Kanari and Brendan Mallery},
In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered connection between the symmetric group and barcodes in general position, based on the simple observation that death order is a permutation of birth order. The first important outcome of our study is a clear combinatorial distinction between the space of phylogenetic trees (as defined by Billera, Holmes and Vogtmann) and… Expand


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The fiber of the persistence map for functions on the interval
  • J. Curry
  • Mathematics, Computer Science
  • J. Appl. Comput. Topol.
  • 2018
Enumeration of merge trees and chiral merge trees with the same persistence makes essential use of the Elder Rule, which is given its first detailed proof in this paper. Expand
From Geometry to Topology: Inverse Theorems for Distributed Persistence
The theoretical results are complemented by two synthetic experiments demonstrating the use of distributed persistence in practice, and the inverse results do not actually require considering all subsets of a fixed size, but a relatively small collection satisfying certain covering properties that arise when randomly sampling subsets. Expand