Sarah Tymochko
PhD Student, Dept. of Computational Mathematics, Science, and Engineering


Publications & Preprints


Using Persistent Homology to Quantify a Diurnal Cycle in Hurricane Felix

By: Sarah Tymochko, Elizabeth Munch, Jason Dunion, Kristen Corbosiero, and Ryan Torn

arXiv:1902.06202, 2019

The diurnal cycle of tropical cyclones (TCs) is a daily cycle in clouds that appears in satellite images and may have implications for TC structure and intensity. The diurnal pattern can be seen in infrared (IR) satellite imagery as cyclical pulses in the cloud field that propagate radially outward from the center of nearly all Atlantic-basin TCs. These diurnal pulses, a distinguishing characteristic of the TC diurnal cycle, begin forming in the storm's inner core near sunset each day and appear as a region of cooling cloud-top temperatures. The area of cooling takes on a ring-like appearance as cloud-top warming occurs on its inside edge and the cooling moves away from the storm overnight, reaching several hundred kilometers from the circulation center by the following afternoon. The state-of-the-art TC diurnal cycle measurement has a limited ability to analyze the behavior beyond qualitative observations. We present a method for quantifying the TC diurnal cycle using one-dimensional persistent homology, a tool from Topological Data Analysis, by tracking maximum persistence and quantifying the cycle using the discrete Fourier transform. Using Geostationary Operational Environmental Satellite IR imagery data from Hurricane Felix (2007), our method is able to detect an approximate daily cycle.


Fairest Edge Usage and Minimum Expected Overlap for Random Spanning Trees

By: Nathan Albin, Jason Clemens, Derek Hoare, Pietro Poggi-Corradini, Brandon Sit, and Sarah Tymochko

arXiv:1805.10112, 2018

Random spanning trees of a graph G are governed by a corresponding probability mass distribution (or "law"), μ, defined on the set of all spanning trees of G. This paper addresses the problem of choosing μ in order to utilize the edges as "fairly" as possible. This turns out to be equivalent to minimizing, with respect to μ, the expected overlap of two independent random spanning trees sampled with law μ. In the process, we introduce the notion of homogeneous graphs. These are graphs for which it is possible to choose a random spanning tree so that all edges have equal usage probability. The main result is a deflation process that identifies a hierarchical structure of arbitrary graphs in terms of homogeneous subgraphs, which we call homogeneous cores. A key tool in the analysis is the spanning tree modulus, for which there exists an algorithm based on minimum spanning tree algorithms, such as Kruskal's or Prim's.

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Last Updated: July 2019