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Creators/Authors contains: "Micka, Samuel"

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  1. ; ; ; ; (, Canadian Conference on Computational Geometry (CCCG))
    Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in R d , the (augmented) persistent homology transform ((A)PHT) is a family of persistence diagrams, parameterized by directions in the ambient space. A recent advance in understanding the PHT used the framework of reconstruction in order to find finite a set of directions to faithfully represent the shape, a result that is of both theoretical and practical interest. In this paper, we improve upon this result and present an improved algorithm for graph— and, more generally one-skeleton—reconstruction. The improvement comes in reconstructing the edges, where we use a radial binary (multi-)search. The binary search employed takes advantage of the fact that the edges can be ordered radially with respect to a reference plane, a feature unique to graphs. 
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    Accepted Manuscript Full Text Available
  2. ; ; ; ; ; (, iTiCSE 2020)
    Exposure to science, technology, engineering, and mathematics (STEM) at a young age is key to inspiring students to pursue careers in these fields. Thus, many institutions of higher education offer events to engage youth in STEM activities. These events are most effective when they are adapted to the specific audience. In Montana, a large percentage of the K-12 student population is from rural communities, where the ability to participate in such events is limited due to travel logistics and a shortage of relatable materials. We have developed a computer science outreach module that targets these populations through the use of storytelling and the Alice programming environment, thus drawing a parallel between storytelling and building algorithms. We describe the module's implementation, report and analyze feedback, and provide lessons learned from the module's implementation at outreach events. 
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    Full Text Available 
  3. ; ; ; ; ; ; ; ; (, Computational Geometry)
    Full Text Available 
  4. ; ; ; ; ; ; ; ; (, Canadian Conference on Computational Geometry)
    Topological Data Analysis (TDA) studies the “shape” of data. A common topological descriptor is the persistence diagram, which encodes topological features in a topological space at different scales. Turner, Mukherjee, and Boyer showed that one can reconstruct a simplicial complex embedded in R^3 using persistence diagrams generated from all possible height filtrations (an uncountably infinite number of directions). In this paper, we present an algorithm for reconstructing plane graphs K = (V, E) in R^2, i.e., a planar graph with vertices in general position and a straight-line embedding, from a quadratic number height filtrations and their respective persistence diagrams. 
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    Accepted Manuscript Full Text Available