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Abstract:
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Data exhibiting complicated spatial structures are common in many areas of science, but can be difficult to analyze. Persistent homology is a popular approach within the area of Topological Data Analysis (TDA) that offers a new way to represent, visualize, and interpret complex data by extracting topological features, which can be used to infer properties of the underlying structures. In particular, TDA may be useful for analyzing the large-scale structure (LSS) of the Universe, which is an intricate and spatially complex web of matter. TDA produces topological summaries that are interesting and informative descriptors on their own, but hypothesis tests using these summaries would provide a way to make more rigorous comparisons of LSS under different theoretical models. For example, the received cosmological model has cold dark matter (CDM); however, there are some observational inconsistencies with this theory. Another possibility is warm dark matter (WDM). It is of interest to see if a CDM and WDM Universe produce LSS that is topologically distinct. We propose several test statistics for two-sample hypothesis tests using TDA in order to infer these differences.
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